[suitesparse-metis] 05/28: Imported Upstream version 3.1.0
Wolfgang Fütterer
wlfuetter-guest at moszumanska.debian.org
Mon Sep 7 10:18:01 UTC 2015
This is an automated email from the git hooks/post-receive script.
wlfuetter-guest pushed a commit to branch master
in repository suitesparse-metis.
commit e0f3267d70a73c3d21a701e7ca47b5ec4397de27
Author: Wolfgang Fuetterer <debian at wlf-online.de>
Date: Fri Oct 31 19:58:30 2014 +0100
Imported Upstream version 3.1.0
---
AMD/Demo/Makefile | 90 +
AMD/Demo/amd_demo.c | 178 +
AMD/Demo/amd_demo.out | 179 +
AMD/Demo/amd_demo2.c | 209 +
AMD/Demo/amd_demo2.out | 208 +
AMD/Demo/amd_f77cross.f | 51 +
AMD/Demo/amd_f77cross.out | 51 +
AMD/Demo/amd_f77demo.f | 161 +
AMD/Demo/amd_f77demo.out | 318 +
AMD/Demo/amd_f77simple.f | 38 +
AMD/Demo/amd_f77simple.out | 5 +
AMD/Demo/amd_f77wrapper.c | 96 +
AMD/Demo/amd_l_demo.c | 179 +
AMD/Demo/amd_l_demo.out | 179 +
AMD/Demo/amd_simple.c | 23 +
AMD/Demo/amd_simple.out | 5 +
AMD/Doc/AMD_UserGuide.bib | 98 +
AMD/Doc/AMD_UserGuide.pdf | Bin 0 -> 176721 bytes
AMD/Doc/AMD_UserGuide.tex | 1206 +
AMD/Doc/ChangeLog | 129 +
AMD/Doc/License | 39 +
AMD/Doc/Makefile | 33 +
AMD/Doc/lesser.txt | 504 +
AMD/Include/amd.h | 412 +
AMD/Include/amd_internal.h | 350 +
AMD/Lib/GNUmakefile | 78 +
AMD/Lib/Makefile | 69 +
AMD/Lib/libamd.def | 12 +
AMD/MATLAB/Contents.m | 19 +
AMD/MATLAB/Makefile | 34 +
AMD/MATLAB/amd2.m | 76 +
AMD/MATLAB/amd_demo.m | 83 +
AMD/MATLAB/amd_demo.m.out | 125 +
AMD/MATLAB/amd_install.m | 20 +
AMD/MATLAB/amd_make.m | 32 +
AMD/MATLAB/amd_mex.c | 199 +
AMD/MATLAB/can_24 | 160 +
AMD/Makefile | 67 +
AMD/README.txt | 215 +
AMD/Source/amd.f | 1214 +
AMD/Source/amd_1.c | 181 +
AMD/Source/amd_2.c | 1842 +
AMD/Source/amd_aat.c | 185 +
AMD/Source/amd_control.c | 64 +
AMD/Source/amd_defaults.c | 38 +
AMD/Source/amd_dump.c | 180 +
AMD/Source/amd_global.c | 84 +
AMD/Source/amd_info.c | 120 +
AMD/Source/amd_order.c | 200 +
AMD/Source/amd_post_tree.c | 121 +
AMD/Source/amd_postorder.c | 207 +
AMD/Source/amd_preprocess.c | 119 +
AMD/Source/amd_valid.c | 93 +
AMD/Source/amdbar.f | 1206 +
BTF/Doc/ChangeLog | 38 +
BTF/Doc/lesser.txt | 504 +
BTF/Include/btf.h | 263 +
BTF/Include/btf_internal.h | 64 +
BTF/Lib/Makefile | 59 +
BTF/MATLAB/Contents.m | 20 +
BTF/MATLAB/Makefile | 37 +
BTF/MATLAB/Test/btf_test.m | 19 +
BTF/MATLAB/Test/checkbtf.m | 46 +
BTF/MATLAB/Test/test1.m | 141 +
BTF/MATLAB/Test/test2.m | 109 +
BTF/MATLAB/Test/test3.m | 530 +
BTF/MATLAB/Test/test4.m | 86 +
BTF/MATLAB/Test/test5.m | 86 +
BTF/MATLAB/Test/test6.m | 138 +
BTF/MATLAB/btf.c | 144 +
BTF/MATLAB/btf.m | 38 +
BTF/MATLAB/btf_demo.m | 48 +
BTF/MATLAB/btf_install.m | 17 +
BTF/MATLAB/btf_make.m | 37 +
BTF/MATLAB/drawbtf.m | 27 +
BTF/MATLAB/maxtrans.c | 101 +
BTF/MATLAB/maxtrans.m | 30 +
BTF/MATLAB/strongcomp.c | 179 +
BTF/MATLAB/strongcomp.m | 45 +
BTF/Makefile | 18 +
BTF/README.txt | 109 +
BTF/Source/btf_maxtrans.c | 387 +
BTF/Source/btf_order.c | 132 +
BTF/Source/btf_strongcomp.c | 593 +
CAMD/Demo/Makefile | 57 +
CAMD/Demo/camd_demo.c | 173 +
CAMD/Demo/camd_demo.out | 178 +
CAMD/Demo/camd_demo2.c | 217 +
CAMD/Demo/camd_demo2.out | 209 +
CAMD/Demo/camd_l_demo.c | 176 +
CAMD/Demo/camd_l_demo.out | 178 +
CAMD/Demo/camd_simple.c | 24 +
CAMD/Demo/camd_simple.out | 5 +
CAMD/Doc/CAMD_UserGuide.bib | 98 +
CAMD/Doc/CAMD_UserGuide.pdf | Bin 0 -> 168515 bytes
CAMD/Doc/CAMD_UserGuide.tex | 1050 +
CAMD/Doc/ChangeLog | 54 +
CAMD/Doc/License | 40 +
CAMD/Doc/Makefile | 35 +
CAMD/Doc/camd.sed | 2 +
CAMD/Doc/cdiff | 4 +
CAMD/Doc/docdiff | 37 +
CAMD/Doc/lesser.txt | 504 +
CAMD/Include/camd.h | 419 +
CAMD/Include/camd_internal.h | 337 +
CAMD/Lib/GNUmakefile | 60 +
CAMD/Lib/Makefile | 57 +
CAMD/Lib/libcamd.def | 12 +
CAMD/MATLAB/Contents.m | 15 +
CAMD/MATLAB/Makefile | 34 +
CAMD/MATLAB/camd.m | 80 +
CAMD/MATLAB/camd_demo.m | 116 +
CAMD/MATLAB/camd_demo.m.out | 131 +
CAMD/MATLAB/camd_make.m | 32 +
CAMD/MATLAB/camd_mex.c | 220 +
CAMD/MATLAB/can_24 | 160 +
CAMD/Makefile | 57 +
CAMD/README.txt | 204 +
CAMD/Source/camd_1.c | 184 +
CAMD/Source/camd_2.c | 2013 +
CAMD/Source/camd_aat.c | 184 +
CAMD/Source/camd_control.c | 62 +
CAMD/Source/camd_defaults.c | 37 +
CAMD/Source/camd_dump.c | 190 +
CAMD/Source/camd_global.c | 84 +
CAMD/Source/camd_info.c | 119 +
CAMD/Source/camd_order.c | 201 +
CAMD/Source/camd_postorder.c | 51 +
CAMD/Source/camd_preprocess.c | 119 +
CAMD/Source/camd_valid.c | 113 +
CCOLAMD/Demo/Makefile | 43 +
CCOLAMD/Demo/ccolamd_example.c | 185 +
CCOLAMD/Demo/ccolamd_example.out | 50 +
CCOLAMD/Demo/ccolamd_l_example.c | 188 +
CCOLAMD/Demo/ccolamd_l_example.out | 50 +
CCOLAMD/Doc/ChangeLog | 35 +
CCOLAMD/Doc/lesser.txt | 504 +
CCOLAMD/Include/ccolamd.h | 365 +
CCOLAMD/Lib/Makefile | 32 +
CCOLAMD/MATLAB/Contents.m | 20 +
CCOLAMD/MATLAB/Makefile | 35 +
CCOLAMD/MATLAB/ccolamd.m | 48 +
CCOLAMD/MATLAB/ccolamd_demo.m | 209 +
CCOLAMD/MATLAB/ccolamd_install.m | 18 +
CCOLAMD/MATLAB/ccolamd_make.m | 29 +
CCOLAMD/MATLAB/ccolamd_test.m | 485 +
CCOLAMD/MATLAB/ccolamdmex.c | 228 +
CCOLAMD/MATLAB/ccolamdtestmex.c | 533 +
CCOLAMD/MATLAB/ccolamdtestmex.m | 10 +
CCOLAMD/MATLAB/csymamd.m | 48 +
CCOLAMD/MATLAB/csymamdmex.c | 208 +
CCOLAMD/MATLAB/csymamdtestmex.c | 502 +
CCOLAMD/MATLAB/csymamdtestmex.m | 10 +
CCOLAMD/MATLAB/luflops.m | 33 +
CCOLAMD/Makefile | 49 +
CCOLAMD/README.txt | 150 +
CCOLAMD/Source/ccolamd.c | 4620 +
CCOLAMD/Source/ccolamd_global.c | 25 +
CHOLMOD/Check/License.txt | 24 +
CHOLMOD/Check/cholmod_check.c | 2627 +
CHOLMOD/Check/cholmod_read.c | 1320 +
CHOLMOD/Check/cholmod_write.c | 744 +
CHOLMOD/Check/lesser.txt | 504 +
CHOLMOD/Cholesky/License.txt | 24 +
CHOLMOD/Cholesky/cholmod_amd.c | 212 +
CHOLMOD/Cholesky/cholmod_analyze.c | 896 +
CHOLMOD/Cholesky/cholmod_colamd.c | 210 +
CHOLMOD/Cholesky/cholmod_etree.c | 227 +
CHOLMOD/Cholesky/cholmod_factorize.c | 429 +
CHOLMOD/Cholesky/cholmod_postorder.c | 292 +
CHOLMOD/Cholesky/cholmod_rcond.c | 161 +
CHOLMOD/Cholesky/cholmod_resymbol.c | 609 +
CHOLMOD/Cholesky/cholmod_rowcolcounts.c | 537 +
CHOLMOD/Cholesky/cholmod_rowfac.c | 679 +
CHOLMOD/Cholesky/cholmod_solve.c | 1202 +
CHOLMOD/Cholesky/cholmod_spsolve.c | 397 +
CHOLMOD/Cholesky/lesser.txt | 504 +
CHOLMOD/Cholesky/t_cholmod_lsolve.c | 843 +
CHOLMOD/Cholesky/t_cholmod_ltsolve.c | 841 +
CHOLMOD/Cholesky/t_cholmod_rowfac.c | 458 +
CHOLMOD/Cholesky/t_cholmod_solve.c | 164 +
CHOLMOD/Core/License.txt | 25 +
CHOLMOD/Core/cholmod_aat.c | 302 +
CHOLMOD/Core/cholmod_add.c | 282 +
CHOLMOD/Core/cholmod_band.c | 374 +
CHOLMOD/Core/cholmod_change_factor.c | 1227 +
CHOLMOD/Core/cholmod_common.c | 657 +
CHOLMOD/Core/cholmod_complex.c | 547 +
CHOLMOD/Core/cholmod_copy.c | 407 +
CHOLMOD/Core/cholmod_dense.c | 640 +
CHOLMOD/Core/cholmod_error.c | 80 +
CHOLMOD/Core/cholmod_factor.c | 935 +
CHOLMOD/Core/cholmod_memory.c | 563 +
CHOLMOD/Core/cholmod_sparse.c | 652 +
CHOLMOD/Core/cholmod_transpose.c | 1139 +
CHOLMOD/Core/cholmod_triplet.c | 773 +
CHOLMOD/Core/lesser.txt | 504 +
CHOLMOD/Core/t_cholmod_change_factor.c | 661 +
CHOLMOD/Core/t_cholmod_dense.c | 266 +
CHOLMOD/Core/t_cholmod_transpose.c | 318 +
CHOLMOD/Core/t_cholmod_triplet.c | 176 +
CHOLMOD/Demo/License.txt | 24 +
CHOLMOD/Demo/Makefile | 85 +
CHOLMOD/Demo/Matrix/0.tri | 1 +
CHOLMOD/Demo/Matrix/bcsstk01.rsa | 78 +
CHOLMOD/Demo/Matrix/bcsstk01.tri | 227 +
CHOLMOD/Demo/Matrix/bcsstk02.rsa | 701 +
CHOLMOD/Demo/Matrix/bcsstk02.tri | 2214 +
CHOLMOD/Demo/Matrix/c.mtx | 8 +
CHOLMOD/Demo/Matrix/c.tri | 7 +
CHOLMOD/Demo/Matrix/can___24.mtx | 94 +
CHOLMOD/Demo/Matrix/d.tri | 7 +
CHOLMOD/Demo/Matrix/empty.tri | 0
CHOLMOD/Demo/Matrix/lp_afiro.rra | 55 +
CHOLMOD/Demo/Matrix/lp_afiro.tri | 105 +
CHOLMOD/Demo/Matrix/mangle1.mtx | 1 +
CHOLMOD/Demo/Matrix/mangle2.mtx | 1 +
CHOLMOD/Demo/Matrix/mangle3.mtx | 1 +
CHOLMOD/Demo/Matrix/mangle4.mtx | 1 +
CHOLMOD/Demo/Matrix/mangle5.tri | 7 +
CHOLMOD/Demo/Matrix/mangle6.tri | 2 +
CHOLMOD/Demo/Matrix/mangle7.tri | 2 +
CHOLMOD/Demo/Matrix/mangle8.tri | 2 +
CHOLMOD/Demo/Matrix/n5 | 4061 +
CHOLMOD/Demo/Matrix/one.tri | 3 +
CHOLMOD/Demo/Matrix/pts5ldd03.mtx | 755 +
CHOLMOD/Demo/Matrix/up.tri | 7 +
CHOLMOD/Demo/cholmod_demo.c | 400 +
CHOLMOD/Demo/cholmod_demo.h | 25 +
CHOLMOD/Demo/cholmod_l_demo.c | 402 +
CHOLMOD/Demo/cholmod_simple.c | 50 +
CHOLMOD/Demo/gpl.txt | 340 +
CHOLMOD/Demo/make.out | 213 +
CHOLMOD/Demo/reade.f | 182 +
CHOLMOD/Demo/readhb.f | 105 +
CHOLMOD/Demo/readhb2.f | 121 +
CHOLMOD/Doc/ChangeLog | 190 +
CHOLMOD/Doc/Makefile | 225 +
CHOLMOD/Doc/UserGuide.bib | 196 +
CHOLMOD/Doc/UserGuide.pdf | Bin 0 -> 459421 bytes
CHOLMOD/Doc/UserGuide.tex | 3369 +
CHOLMOD/Doc/footer.tex | 6 +
CHOLMOD/Doc/getmproto | 4 +
CHOLMOD/Doc/getproto | 6 +
CHOLMOD/Doc/header.tex | 4 +
CHOLMOD/Doc/mfile.awk | 1 +
CHOLMOD/Doc/mfooter.tex | 4 +
CHOLMOD/Doc/mheader.tex | 5 +
CHOLMOD/Doc/rule.awk | 1 +
CHOLMOD/Include/License.txt | 9 +
CHOLMOD/Include/README.txt | 25 +
CHOLMOD/Include/cholmod.h | 122 +
CHOLMOD/Include/cholmod_blas.h | 451 +
CHOLMOD/Include/cholmod_check.h | 417 +
CHOLMOD/Include/cholmod_cholesky.h | 498 +
CHOLMOD/Include/cholmod_complexity.h | 264 +
CHOLMOD/Include/cholmod_config.h | 83 +
CHOLMOD/Include/cholmod_core.h | 2268 +
CHOLMOD/Include/cholmod_internal.h | 396 +
CHOLMOD/Include/cholmod_io64.h | 46 +
CHOLMOD/Include/cholmod_matrixops.h | 235 +
CHOLMOD/Include/cholmod_modify.h | 304 +
CHOLMOD/Include/cholmod_partition.h | 233 +
CHOLMOD/Include/cholmod_supernodal.h | 147 +
CHOLMOD/Include/cholmod_template.h | 238 +
CHOLMOD/Lib/Makefile | 472 +
CHOLMOD/MATLAB/Contents.m | 37 +
CHOLMOD/MATLAB/License.txt | 26 +
CHOLMOD/MATLAB/Makefile | 700 +
CHOLMOD/MATLAB/README.txt | 67 +
CHOLMOD/MATLAB/Test/Contents.m | 44 +
CHOLMOD/MATLAB/Test/Results.mat | Bin 0 -> 2419 bytes
CHOLMOD/MATLAB/Test/cholmod_test.m | 181 +
.../Test/cholmod_test_11-May-2007_13-29-15.txt | 12324 ++
CHOLMOD/MATLAB/Test/dg.m | 76 +
CHOLMOD/MATLAB/Test/n2.m | 74 +
CHOLMOD/MATLAB/Test/nn.m | 159 +
CHOLMOD/MATLAB/Test/test0.m | 287 +
CHOLMOD/MATLAB/Test/test1.m | 84 +
CHOLMOD/MATLAB/Test/test10.m | 124 +
CHOLMOD/MATLAB/Test/test11.m | 138 +
CHOLMOD/MATLAB/Test/test11results.m | 50 +
CHOLMOD/MATLAB/Test/test12.m | 214 +
CHOLMOD/MATLAB/Test/test13.m | 35 +
CHOLMOD/MATLAB/Test/test14.m | 127 +
CHOLMOD/MATLAB/Test/test15.m | 180 +
CHOLMOD/MATLAB/Test/test16.m | 35 +
CHOLMOD/MATLAB/Test/test17.m | 32 +
CHOLMOD/MATLAB/Test/test18.m | 40 +
CHOLMOD/MATLAB/Test/test19.m | 29 +
CHOLMOD/MATLAB/Test/test2.m | 42 +
CHOLMOD/MATLAB/Test/test20.m | 56 +
CHOLMOD/MATLAB/Test/test21.m | 45 +
CHOLMOD/MATLAB/Test/test22.m | 209 +
CHOLMOD/MATLAB/Test/test23.m | 122 +
CHOLMOD/MATLAB/Test/test24.m | 60 +
CHOLMOD/MATLAB/Test/test25.m | 66 +
CHOLMOD/MATLAB/Test/test26.m | 90 +
CHOLMOD/MATLAB/Test/test27.m | 15 +
CHOLMOD/MATLAB/Test/test28.m | 61 +
CHOLMOD/MATLAB/Test/test3.m | 42 +
CHOLMOD/MATLAB/Test/test4.m | 56 +
CHOLMOD/MATLAB/Test/test5.m | 95 +
CHOLMOD/MATLAB/Test/test6.m | 167 +
CHOLMOD/MATLAB/Test/test7.m | 63 +
CHOLMOD/MATLAB/Test/test8.m | 121 +
CHOLMOD/MATLAB/Test/test9.m | 80 +
CHOLMOD/MATLAB/Test/testmm.m | 549 +
CHOLMOD/MATLAB/Test/testsolve.m | 43 +
CHOLMOD/MATLAB/Windows/README.txt | 1 +
CHOLMOD/MATLAB/Windows/rand48.c | 24 +
CHOLMOD/MATLAB/Windows/strings.h | 8 +
CHOLMOD/MATLAB/analyze.c | 189 +
CHOLMOD/MATLAB/analyze.m | 65 +
CHOLMOD/MATLAB/bisect.c | 168 +
CHOLMOD/MATLAB/bisect.m | 25 +
CHOLMOD/MATLAB/chol2.c | 164 +
CHOLMOD/MATLAB/chol2.m | 21 +
CHOLMOD/MATLAB/cholmod2.c | 273 +
CHOLMOD/MATLAB/cholmod2.m | 42 +
CHOLMOD/MATLAB/cholmod_demo.m | 164 +
CHOLMOD/MATLAB/cholmod_install.m | 70 +
CHOLMOD/MATLAB/cholmod_make.m | 361 +
CHOLMOD/MATLAB/cholmod_matlab.c | 2162 +
CHOLMOD/MATLAB/cholmod_matlab.h | 178 +
CHOLMOD/MATLAB/etree2.c | 178 +
CHOLMOD/MATLAB/etree2.m | 42 +
CHOLMOD/MATLAB/gpl.txt | 340 +
CHOLMOD/MATLAB/graph_demo.m | 105 +
CHOLMOD/MATLAB/lcc_lib/lapacksyms.def | 718 +
CHOLMOD/MATLAB/lcc_lib/libmwlapack.lib | Bin 0 -> 466678 bytes
CHOLMOD/MATLAB/lchol.c | 159 +
CHOLMOD/MATLAB/lchol.m | 18 +
CHOLMOD/MATLAB/ldl_normest.m | 86 +
CHOLMOD/MATLAB/ldlchol.c | 202 +
CHOLMOD/MATLAB/ldlchol.m | 39 +
CHOLMOD/MATLAB/ldlsolve.c | 178 +
CHOLMOD/MATLAB/ldlsolve.m | 21 +
CHOLMOD/MATLAB/ldlsplit.m | 19 +
CHOLMOD/MATLAB/ldlupdate.c | 174 +
CHOLMOD/MATLAB/ldlupdate.m | 55 +
CHOLMOD/MATLAB/metis.c | 166 +
CHOLMOD/MATLAB/metis.m | 23 +
CHOLMOD/MATLAB/mread.c | 219 +
CHOLMOD/MATLAB/mread.m | 24 +
CHOLMOD/MATLAB/mwrite.c | 183 +
CHOLMOD/MATLAB/mwrite.m | 23 +
CHOLMOD/MATLAB/nesdis.c | 213 +
CHOLMOD/MATLAB/nesdis.m | 54 +
CHOLMOD/MATLAB/rename.h | 10 +
CHOLMOD/MATLAB/resymbol.c | 164 +
CHOLMOD/MATLAB/resymbol.m | 19 +
CHOLMOD/MATLAB/sdmult.c | 99 +
CHOLMOD/MATLAB/sdmult.m | 20 +
CHOLMOD/MATLAB/septree.c | 141 +
CHOLMOD/MATLAB/septree.m | 26 +
CHOLMOD/MATLAB/sparse2.c | 18 +
CHOLMOD/MATLAB/sparse2.m | 28 +
CHOLMOD/MATLAB/spsym.c | 102 +
CHOLMOD/MATLAB/spsym.m | 84 +
CHOLMOD/MATLAB/symbfact2.c | 336 +
CHOLMOD/MATLAB/symbfact2.m | 48 +
CHOLMOD/Makefile | 59 +
CHOLMOD/MatrixOps/License.txt | 25 +
CHOLMOD/MatrixOps/cholmod_drop.c | 183 +
CHOLMOD/MatrixOps/cholmod_horzcat.c | 203 +
CHOLMOD/MatrixOps/cholmod_norm.c | 452 +
CHOLMOD/MatrixOps/cholmod_scale.c | 217 +
CHOLMOD/MatrixOps/cholmod_sdmult.c | 149 +
CHOLMOD/MatrixOps/cholmod_ssmult.c | 487 +
CHOLMOD/MatrixOps/cholmod_submatrix.c | 425 +
CHOLMOD/MatrixOps/cholmod_symmetry.c | 482 +
CHOLMOD/MatrixOps/cholmod_vertcat.c | 201 +
CHOLMOD/MatrixOps/gpl.txt | 340 +
CHOLMOD/MatrixOps/t_cholmod_sdmult.c | 726 +
CHOLMOD/Modify/License.txt | 25 +
CHOLMOD/Modify/cholmod_rowadd.c | 678 +
CHOLMOD/Modify/cholmod_rowdel.c | 461 +
CHOLMOD/Modify/cholmod_updown.c | 1570 +
CHOLMOD/Modify/gpl.txt | 340 +
CHOLMOD/Modify/t_cholmod_updown.c | 214 +
CHOLMOD/Modify/t_cholmod_updown_numkr.c | 746 +
CHOLMOD/Partition/License.txt | 25 +
CHOLMOD/Partition/cholmod_camd.c | 227 +
CHOLMOD/Partition/cholmod_ccolamd.c | 205 +
CHOLMOD/Partition/cholmod_csymamd.c | 141 +
CHOLMOD/Partition/cholmod_metis.c | 792 +
CHOLMOD/Partition/cholmod_nesdis.c | 2164 +
CHOLMOD/Partition/lesser.txt | 504 +
CHOLMOD/README.txt | 84 +
CHOLMOD/Supernodal/License.txt | 25 +
CHOLMOD/Supernodal/cholmod_super_numeric.c | 296 +
CHOLMOD/Supernodal/cholmod_super_solve.c | 221 +
CHOLMOD/Supernodal/cholmod_super_symbolic.c | 794 +
CHOLMOD/Supernodal/gpl.txt | 340 +
CHOLMOD/Supernodal/t_cholmod_super_numeric.c | 741 +
CHOLMOD/Supernodal/t_cholmod_super_solve.c | 430 +
CHOLMOD/Tcov/License.txt | 24 +
CHOLMOD/Tcov/Make.inc | 8 +
CHOLMOD/Tcov/Makefile | 1212 +
CHOLMOD/Tcov/Matrix/0 | 1 +
CHOLMOD/Tcov/Matrix/0_1 | 1 +
CHOLMOD/Tcov/Matrix/1_0 | 1 +
CHOLMOD/Tcov/Matrix/1e99 | 4 +
CHOLMOD/Tcov/Matrix/2.tri | 5 +
CHOLMOD/Tcov/Matrix/20lo | 211 +
CHOLMOD/Tcov/Matrix/2_3 | 7 +
CHOLMOD/Tcov/Matrix/2diag.tri | 3 +
CHOLMOD/Tcov/Matrix/2lo.tri | 4 +
CHOLMOD/Tcov/Matrix/2up.tri | 4 +
CHOLMOD/Tcov/Matrix/3_2 | 7 +
CHOLMOD/Tcov/Matrix/3b | 5 +
CHOLMOD/Tcov/Matrix/3by0.mtx | 2 +
CHOLMOD/Tcov/Matrix/3singular | 5 +
CHOLMOD/Tcov/Matrix/4 | 17 +
CHOLMOD/Tcov/Matrix/4lo | 11 +
CHOLMOD/Tcov/Matrix/5 | 16 +
CHOLMOD/Tcov/Matrix/5by50 | 69 +
CHOLMOD/Tcov/Matrix/a1 | 1 +
CHOLMOD/Tcov/Matrix/a2 | 1 +
CHOLMOD/Tcov/Matrix/afiro | 103 +
CHOLMOD/Tcov/Matrix/c10 | 61 +
CHOLMOD/Tcov/Matrix/c30lo | 115 +
CHOLMOD/Tcov/Matrix/c30up | 115 +
CHOLMOD/Tcov/Matrix/c3singular | 5 +
CHOLMOD/Tcov/Matrix/c5lo | 12 +
CHOLMOD/Tcov/Matrix/c5up | 12 +
CHOLMOD/Tcov/Matrix/c5up2 | 12 +
CHOLMOD/Tcov/Matrix/cha | 7 +
CHOLMOD/Tcov/Matrix/cha.mtx | 8 +
CHOLMOD/Tcov/Matrix/cpi | 2 +
CHOLMOD/Tcov/Matrix/crud1 | 1 +
CHOLMOD/Tcov/Matrix/crud2 | 2 +
CHOLMOD/Tcov/Matrix/cs.mtx | 7 +
CHOLMOD/Tcov/Matrix/csa.mtx | 8 +
CHOLMOD/Tcov/Matrix/cza | 7 +
CHOLMOD/Tcov/Matrix/cza.mtx | 5 +
CHOLMOD/Tcov/Matrix/diag | 21 +
CHOLMOD/Tcov/Matrix/ex5lo | 154 +
CHOLMOD/Tcov/Matrix/fullcha.mtx | 8 +
CHOLMOD/Tcov/Matrix/fullcrud.mtx | 6 +
CHOLMOD/Tcov/Matrix/fullcrud1.mtx | 5 +
CHOLMOD/Tcov/Matrix/fullcrud2.mtx | 6 +
CHOLMOD/Tcov/Matrix/fullcsa.mtx | 8 +
CHOLMOD/Tcov/Matrix/fullcza.mtx | 3 +
CHOLMOD/Tcov/Matrix/fullrsa.mtx | 8 +
CHOLMOD/Tcov/Matrix/fullrza.mtx | 3 +
CHOLMOD/Tcov/Matrix/galenet | 23 +
CHOLMOD/Tcov/Matrix/huge.tri | 2 +
CHOLMOD/Tcov/Matrix/ibm32 | 127 +
CHOLMOD/Tcov/Matrix/itest2 | 27 +
CHOLMOD/Tcov/Matrix/itest6 | 30 +
CHOLMOD/Tcov/Matrix/k01up | 225 +
CHOLMOD/Tcov/Matrix/mega.tri | 2 +
CHOLMOD/Tcov/Matrix/one | 2 +
CHOLMOD/Tcov/Matrix/pi | 2 +
CHOLMOD/Tcov/Matrix/plskz362.mtx | 882 +
CHOLMOD/Tcov/Matrix/r5lo | 11 +
CHOLMOD/Tcov/Matrix/r5lo2 | 15 +
CHOLMOD/Tcov/Matrix/r5up | 11 +
CHOLMOD/Tcov/Matrix/r5up2 | 11 +
CHOLMOD/Tcov/Matrix/rename.h | 10 +
CHOLMOD/Tcov/Matrix/rza.mtx | 5 +
CHOLMOD/Tcov/Matrix/tri | 1 +
CHOLMOD/Tcov/Matrix/tribig | 1 +
CHOLMOD/Tcov/Matrix/z10 | 61 +
CHOLMOD/Tcov/Matrix/z30lo | 115 +
CHOLMOD/Tcov/Matrix/z30up | 115 +
CHOLMOD/Tcov/Matrix/z3singular | 5 +
CHOLMOD/Tcov/Matrix/z5lo | 12 +
CHOLMOD/Tcov/Matrix/z5up | 12 +
CHOLMOD/Tcov/Matrix/z5up2 | 12 +
CHOLMOD/Tcov/Matrix/zero | 1 +
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UMFPACK/Tcov/Make.s2 | 18 +
UMFPACK/Tcov/Make.s3 | 18 +
UMFPACK/Tcov/Make.s4 | 18 +
UMFPACK/Tcov/Make.s5 | 18 +
UMFPACK/Tcov/Make_file | 24 +
UMFPACK/Tcov/Makefile | 16 +
UMFPACK/Tcov/README.txt | 76 +
UMFPACK/Tcov/TestMat/S_d2q06c | 3387 +
UMFPACK/Tcov/TestMat/adlittle | 565 +
UMFPACK/Tcov/TestMat/arc130 | 1170 +
UMFPACK/Tcov/TestMat/cage3 | 27 +
UMFPACK/Tcov/TestMat/d_dyn | 320 +
UMFPACK/Tcov/TestMat/galenet | 39 +
UMFPACK/Tcov/TestMat/matrix1 | 43 +
UMFPACK/Tcov/TestMat/matrix10 | 332 +
UMFPACK/Tcov/TestMat/matrix11 | 332 +
UMFPACK/Tcov/TestMat/matrix12 | 13 +
UMFPACK/Tcov/TestMat/matrix13 | 14 +
UMFPACK/Tcov/TestMat/matrix14 | 5 +
UMFPACK/Tcov/TestMat/matrix15 | 5 +
UMFPACK/Tcov/TestMat/matrix16 | 5 +
UMFPACK/Tcov/TestMat/matrix17 | 5 +
UMFPACK/Tcov/TestMat/matrix18 | 5 +
UMFPACK/Tcov/TestMat/matrix19 | 21 +
UMFPACK/Tcov/TestMat/matrix2 | 44 +
UMFPACK/Tcov/TestMat/matrix20 | 14 +
UMFPACK/Tcov/TestMat/matrix21 | 7 +
UMFPACK/Tcov/TestMat/matrix22 | 14 +
UMFPACK/Tcov/TestMat/matrix23 | 172 +
UMFPACK/Tcov/TestMat/matrix24 | 126 +
UMFPACK/Tcov/TestMat/matrix25 | 13 +
UMFPACK/Tcov/TestMat/matrix26 | 12 +
UMFPACK/Tcov/TestMat/matrix27 | 12 +
UMFPACK/Tcov/TestMat/matrix28 | 21 +
UMFPACK/Tcov/TestMat/matrix29 | 7 +
UMFPACK/Tcov/TestMat/matrix3 | 42 +
UMFPACK/Tcov/TestMat/matrix30 | 7 +
UMFPACK/Tcov/TestMat/matrix4 | 113 +
UMFPACK/Tcov/TestMat/matrix5 | 103 +
UMFPACK/Tcov/TestMat/matrix6 | 43 +
UMFPACK/Tcov/TestMat/matrix7 | 43 +
UMFPACK/Tcov/TestMat/matrix8 | 43 +
UMFPACK/Tcov/TestMat/nug07 | 4094 +
UMFPACK/Tcov/TestMat/shl0 | 2353 +
UMFPACK/Tcov/Top_Makefile | 11 +
UMFPACK/Tcov/acov.di | 15 +
UMFPACK/Tcov/acov.dl | 15 +
UMFPACK/Tcov/acov.zi | 15 +
UMFPACK/Tcov/acov.zl | 15 +
UMFPACK/Tcov/badnum.umf | Bin 0 -> 644 bytes
UMFPACK/Tcov/badnum2.umf | 1 +
UMFPACK/Tcov/badsym.umf | Bin 0 -> 356 bytes
UMFPACK/Tcov/badsym2.umf | 1 +
UMFPACK/Tcov/cov | 12 +
UMFPACK/Tcov/covall | 68 +
UMFPACK/Tcov/cover.awk | 5 +
UMFPACK/Tcov/cover.out | 545 +
UMFPACK/Tcov/cover.out_May5 | 536 +
UMFPACK/Tcov/debug.amd | 1 +
UMFPACK/Tcov/debug.umf | 1 +
UMFPACK/Tcov/ss.awk | 3 +
UMFPACK/Tcov/ucov.di | 98 +
UMFPACK/Tcov/ucov.dl | 98 +
UMFPACK/Tcov/ucov.zi | 98 +
UMFPACK/Tcov/ucov.zl | 98 +
UMFPACK/Tcov/ut.c | 7671 +
1896 files changed, 974441 insertions(+)
diff --git a/AMD/Demo/Makefile b/AMD/Demo/Makefile
new file mode 100644
index 0000000..93c9e06
--- /dev/null
+++ b/AMD/Demo/Makefile
@@ -0,0 +1,90 @@
+#-----------------------------------------------------------------------------
+# compile the AMD demo (for both GNU make or original make)
+#-----------------------------------------------------------------------------
+
+default: amd_simple amd_demo amd_demo2 amd_l_demo
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) -I../Include -I../../UFconfig
+
+INC = ../Include/amd.h ../../UFconfig/UFconfig.h
+
+library:
+ ( cd ../Lib ; $(MAKE) )
+
+f77lib:
+ ( cd ../Lib ; $(MAKE) fortran )
+
+#------------------------------------------------------------------------------
+# Create the demo program, run it, and compare the output
+#------------------------------------------------------------------------------
+
+dist:
+
+amd_demo: amd_demo.c library $(INC)
+ $(C) -o amd_demo amd_demo.c ../Lib/libamd.a $(LIB)
+ ./amd_demo > my_amd_demo.out
+ - diff amd_demo.out my_amd_demo.out
+
+amd_l_demo: amd_l_demo.c library $(INC)
+ $(C) -o amd_l_demo amd_l_demo.c ../Lib/libamd.a $(LIB)
+ ./amd_l_demo > my_amd_l_demo.out
+ - diff amd_l_demo.out my_amd_l_demo.out
+
+amd_demo2: amd_demo2.c library $(INC)
+ $(C) -o amd_demo2 amd_demo2.c ../Lib/libamd.a $(LIB)
+ ./amd_demo2 > my_amd_demo2.out
+ - diff amd_demo2.out my_amd_demo2.out
+
+amd_simple: amd_simple.c library $(INC)
+ $(C) -o amd_simple amd_simple.c ../Lib/libamd.a $(LIB)
+ ./amd_simple > my_amd_simple.out
+ - diff amd_simple.out my_amd_simple.out
+
+#------------------------------------------------------------------------------
+# compile the Fortran demo
+#------------------------------------------------------------------------------
+
+fortran: amd_f77demo amd_f77simple
+
+cross: amd_f77cross
+
+amd_f77demo: amd_f77demo.f f77lib
+ $(F77) $(F77FLAGS) -o amd_f77demo amd_f77demo.f ../Lib/libamdf77.a \
+ $(F77LIB)
+ ./amd_f77demo > my_amd_f77demo.out
+ - diff amd_f77demo.out my_amd_f77demo.out
+
+amd_f77simple: amd_f77simple.f f77lib
+ $(F77) $(F77FLAGS) -o amd_f77simple amd_f77simple.f \
+ ../Lib/libamdf77.a $(F77LIB)
+ ./amd_f77simple > my_amd_f77simple.out
+ - diff amd_f77simple.out my_amd_f77simple.out
+
+amd_f77wrapper.o: amd_f77wrapper.c
+ $(C) -DDINT -c amd_f77wrapper.c
+
+amd_f77cross: amd_f77cross.f amd_f77wrapper.o ../Lib/libamd.a
+ $(F77) $(F77FLAGS) -o amd_f77cross amd_f77cross.f amd_f77wrapper.o \
+ ../Lib/libamd.a $(F77LIB)
+ ./amd_f77cross > my_amd_f77cross.out
+ - diff amd_f77cross.out my_amd_f77cross.out
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) amd_demo my_amd_demo.out
+ - $(RM) amd_l_demo my_amd_l_demo.out
+ - $(RM) amd_demo2 my_amd_demo2.out
+ - $(RM) amd_simple my_amd_simple.out
+ - $(RM) amd_f77demo my_amd_f77demo.out
+ - $(RM) amd_f77simple my_amd_f77simple.out
+ - $(RM) amd_f77cross my_amd_f77cross.out
diff --git a/AMD/Demo/amd_demo.c b/AMD/Demo/amd_demo.c
new file mode 100644
index 0000000..1e8c045
--- /dev/null
+++ b/AMD/Demo/amd_demo.c
@@ -0,0 +1,178 @@
+/* ========================================================================= */
+/* === AMD demo main program =============================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Copyright (c) by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* A simple C main program that illustrates the use of the ANSI C interface
+ * to AMD.
+ */
+
+#include "amd.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+int main (void)
+{
+ /* The symmetric can_24 Harwell/Boeing matrix, including upper and lower
+ * triangular parts, and the diagonal entries. Note that this matrix is
+ * 0-based, with row and column indices in the range 0 to n-1. */
+ int n = 24, nz,
+ Ap [ ] = { 0, 9, 15, 21, 27, 33, 39, 48, 57, 61, 70, 76, 82, 88, 94, 100,
+ 106, 110, 119, 128, 137, 143, 152, 156, 160 },
+ Ai [ ] = {
+ /* column 0: */ 0, 5, 6, 12, 13, 17, 18, 19, 21,
+ /* column 1: */ 1, 8, 9, 13, 14, 17,
+ /* column 2: */ 2, 6, 11, 20, 21, 22,
+ /* column 3: */ 3, 7, 10, 15, 18, 19,
+ /* column 4: */ 4, 7, 9, 14, 15, 16,
+ /* column 5: */ 0, 5, 6, 12, 13, 17,
+ /* column 6: */ 0, 2, 5, 6, 11, 12, 19, 21, 23,
+ /* column 7: */ 3, 4, 7, 9, 14, 15, 16, 17, 18,
+ /* column 8: */ 1, 8, 9, 14,
+ /* column 9: */ 1, 4, 7, 8, 9, 13, 14, 17, 18,
+ /* column 10: */ 3, 10, 18, 19, 20, 21,
+ /* column 11: */ 2, 6, 11, 12, 21, 23,
+ /* column 12: */ 0, 5, 6, 11, 12, 23,
+ /* column 13: */ 0, 1, 5, 9, 13, 17,
+ /* column 14: */ 1, 4, 7, 8, 9, 14,
+ /* column 15: */ 3, 4, 7, 15, 16, 18,
+ /* column 16: */ 4, 7, 15, 16,
+ /* column 17: */ 0, 1, 5, 7, 9, 13, 17, 18, 19,
+ /* column 18: */ 0, 3, 7, 9, 10, 15, 17, 18, 19,
+ /* column 19: */ 0, 3, 6, 10, 17, 18, 19, 20, 21,
+ /* column 20: */ 2, 10, 19, 20, 21, 22,
+ /* column 21: */ 0, 2, 6, 10, 11, 19, 20, 21, 22,
+ /* column 22: */ 2, 20, 21, 22,
+ /* column 23: */ 6, 11, 12, 23 } ;
+
+ int P [24], Pinv [24], i, j, k, jnew, p, inew, result ;
+ double Control [AMD_CONTROL], Info [AMD_INFO] ;
+ char A [24][24] ;
+
+ /* here is an example of how to use AMD_VERSION. This code will work in
+ * any version of AMD. */
+#if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE(1,2))
+ printf ("AMD version %d.%d, date: %s\n", AMD_MAIN_VERSION, AMD_SUB_VERSION,
+ AMD_DATE) ;
+#else
+ printf ("AMD version: 1.1 or earlier\n") ;
+#endif
+
+ printf ("AMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:\n") ;
+
+ /* get the default parameters, and print them */
+ amd_defaults (Control) ;
+ amd_control (Control) ;
+
+ /* print the input matrix */
+ nz = Ap [n] ;
+ printf ("\nInput matrix: %d-by-%d, with %d entries.\n"
+ " Note that for a symmetric matrix such as this one, only the\n"
+ " strictly lower or upper triangular parts would need to be\n"
+ " passed to AMD, since AMD computes the ordering of A+A'. The\n"
+ " diagonal entries are also not needed, since AMD ignores them.\n"
+ , n, n, nz) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf ("\nColumn: %d, number of entries: %d, with row indices in"
+ " Ai [%d ... %d]:\n row indices:",
+ j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ printf (" %d", i) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* print a character plot of the input matrix. This is only reasonable
+ * because the matrix is small. */
+ printf ("\nPlot of input matrix pattern:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (i = 0 ; i < n ; i++) A [i][j] = '.' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ A [i][j] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2d: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* order the matrix */
+ result = amd_order (n, Ap, Ai, P, Control, Info) ;
+ printf ("return value from amd_order: %d (should be %d)\n",
+ result, AMD_OK) ;
+
+ /* print the statistics */
+ amd_info (Info) ;
+
+ if (result != AMD_OK)
+ {
+ printf ("AMD failed\n") ;
+ exit (1) ;
+ }
+
+ /* print the permutation vector, P, and compute the inverse permutation */
+ printf ("Permutation vector:\n") ;
+ for (k = 0 ; k < n ; k++)
+ {
+ /* row/column j is the kth row/column in the permuted matrix */
+ j = P [k] ;
+ Pinv [j] = k ;
+ printf (" %2d", j) ;
+ }
+ printf ("\n\n") ;
+
+ printf ("Inverse permutation vector:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ k = Pinv [j] ;
+ printf (" %2d", k) ;
+ }
+ printf ("\n\n") ;
+
+ /* print a character plot of the permuted matrix. */
+ printf ("\nPlot of permuted matrix pattern:\n") ;
+ for (jnew = 0 ; jnew < n ; jnew++)
+ {
+ j = P [jnew] ;
+ for (inew = 0 ; inew < n ; inew++) A [inew][jnew] = '.' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ inew = Pinv [Ai [p]] ;
+ A [inew][jnew] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2d: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ return (0) ;
+}
diff --git a/AMD/Demo/amd_demo.out b/AMD/Demo/amd_demo.out
new file mode 100644
index 0000000..b577e4e
--- /dev/null
+++ b/AMD/Demo/amd_demo.out
@@ -0,0 +1,179 @@
+AMD version 2.2, date: May 31, 2007
+AMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+Input matrix: 24-by-24, with 160 entries.
+ Note that for a symmetric matrix such as this one, only the
+ strictly lower or upper triangular parts would need to be
+ passed to AMD, since AMD computes the ordering of A+A'. The
+ diagonal entries are also not needed, since AMD ignores them.
+
+Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]:
+ row indices: 0 5 6 12 13 17 18 19 21
+
+Column: 1, number of entries: 6, with row indices in Ai [9 ... 14]:
+ row indices: 1 8 9 13 14 17
+
+Column: 2, number of entries: 6, with row indices in Ai [15 ... 20]:
+ row indices: 2 6 11 20 21 22
+
+Column: 3, number of entries: 6, with row indices in Ai [21 ... 26]:
+ row indices: 3 7 10 15 18 19
+
+Column: 4, number of entries: 6, with row indices in Ai [27 ... 32]:
+ row indices: 4 7 9 14 15 16
+
+Column: 5, number of entries: 6, with row indices in Ai [33 ... 38]:
+ row indices: 0 5 6 12 13 17
+
+Column: 6, number of entries: 9, with row indices in Ai [39 ... 47]:
+ row indices: 0 2 5 6 11 12 19 21 23
+
+Column: 7, number of entries: 9, with row indices in Ai [48 ... 56]:
+ row indices: 3 4 7 9 14 15 16 17 18
+
+Column: 8, number of entries: 4, with row indices in Ai [57 ... 60]:
+ row indices: 1 8 9 14
+
+Column: 9, number of entries: 9, with row indices in Ai [61 ... 69]:
+ row indices: 1 4 7 8 9 13 14 17 18
+
+Column: 10, number of entries: 6, with row indices in Ai [70 ... 75]:
+ row indices: 3 10 18 19 20 21
+
+Column: 11, number of entries: 6, with row indices in Ai [76 ... 81]:
+ row indices: 2 6 11 12 21 23
+
+Column: 12, number of entries: 6, with row indices in Ai [82 ... 87]:
+ row indices: 0 5 6 11 12 23
+
+Column: 13, number of entries: 6, with row indices in Ai [88 ... 93]:
+ row indices: 0 1 5 9 13 17
+
+Column: 14, number of entries: 6, with row indices in Ai [94 ... 99]:
+ row indices: 1 4 7 8 9 14
+
+Column: 15, number of entries: 6, with row indices in Ai [100 ... 105]:
+ row indices: 3 4 7 15 16 18
+
+Column: 16, number of entries: 4, with row indices in Ai [106 ... 109]:
+ row indices: 4 7 15 16
+
+Column: 17, number of entries: 9, with row indices in Ai [110 ... 118]:
+ row indices: 0 1 5 7 9 13 17 18 19
+
+Column: 18, number of entries: 9, with row indices in Ai [119 ... 127]:
+ row indices: 0 3 7 9 10 15 17 18 19
+
+Column: 19, number of entries: 9, with row indices in Ai [128 ... 136]:
+ row indices: 0 3 6 10 17 18 19 20 21
+
+Column: 20, number of entries: 6, with row indices in Ai [137 ... 142]:
+ row indices: 2 10 19 20 21 22
+
+Column: 21, number of entries: 9, with row indices in Ai [143 ... 151]:
+ row indices: 0 2 6 10 11 19 20 21 22
+
+Column: 22, number of entries: 4, with row indices in Ai [152 ... 155]:
+ row indices: 2 20 21 22
+
+Column: 23, number of entries: 4, with row indices in Ai [156 ... 159]:
+ row indices: 6 11 12 23
+
+Plot of input matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . X X . . . . . X X . . . X X X . X . .
+ 1: . X . . . . . . X X . . . X X . . X . . . . . .
+ 2: . . X . . . X . . . . X . . . . . . . . X X X .
+ 3: . . . X . . . X . . X . . . . X . . X X . . . .
+ 4: . . . . X . . X . X . . . . X X X . . . . . . .
+ 5: X . . . . X X . . . . . X X . . . X . . . . . .
+ 6: X . X . . X X . . . . X X . . . . . . X . X . X
+ 7: . . . X X . . X . X . . . . X X X X X . . . . .
+ 8: . X . . . . . . X X . . . . X . . . . . . . . .
+ 9: . X . . X . . X X X . . . X X . . X X . . . . .
+10: . . . X . . . . . . X . . . . . . . X X X X . .
+11: . . X . . . X . . . . X X . . . . . . . . X . X
+12: X . . . . X X . . . . X X . . . . . . . . . . X
+13: X X . . . X . . . X . . . X . . . X . . . . . .
+14: . X . . X . . X X X . . . . X . . . . . . . . .
+15: . . . X X . . X . . . . . . . X X . X . . . . .
+16: . . . . X . . X . . . . . . . X X . . . . . . .
+17: X X . . . X . X . X . . . X . . . X X X . . . .
+18: X . . X . . . X . X X . . . . X . X X X . . . .
+19: X . . X . . X . . . X . . . . . . X X X X X . .
+20: . . X . . . . . . . X . . . . . . . . X X X X .
+21: X . X . . . X . . . X X . . . . . . . X X X X .
+22: . . X . . . . . . . . . . . . . . . . . X X X .
+23: . . . . . . X . . . . X X . . . . . . . . . . X
+return value from amd_order: 0 (should be 0)
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 1516
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+Permutation vector:
+ 22 20 10 23 12 5 16 8 14 4 15 7 1 9 13 17 0 2 3 6 11 18 21 19
+
+Inverse permutation vector:
+ 16 12 17 18 9 5 19 11 7 13 2 20 4 14 8 10 6 15 21 23 1 22 0 3
+
+
+Plot of permuted matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X X . . . . . . . . . . . . . . . X . . . . X .
+ 1: X X X . . . . . . . . . . . . . . X . . . . X X
+ 2: . X X . . . . . . . . . . . . . . . X . . X X X
+ 3: . . . X X . . . . . . . . . . . . . . X X . . .
+ 4: . . . X X X . . . . . . . . . . X . . X X . . .
+ 5: . . . . X X . . . . . . . . X X X . . X . . . .
+ 6: . . . . . . X . . X X X . . . . . . . . . . . .
+ 7: . . . . . . . X X . . . X X . . . . . . . . . .
+ 8: . . . . . . . X X X . X X X . . . . . . . . . .
+ 9: . . . . . . X . X X X X . X . . . . . . . . . .
+10: . . . . . . X . . X X X . . . . . . X . . X . .
+11: . . . . . . X . X X X X . X . X . . X . . X . .
+12: . . . . . . . X X . . . X X X X . . . . . . . .
+13: . . . . . . . X X X . X X X X X . . . . . X . .
+14: . . . . . X . . . . . . X X X X X . . . . . . .
+15: . . . . . X . . . . . X X X X X X . . . . X . X
+16: . . . . X X . . . . . . . . X X X . . X . X X X
+17: X X . . . . . . . . . . . . . . . X . X X . X .
+18: . . X . . . . . . . X X . . . . . . X . . X . X
+19: . . . X X X . . . . . . . . . . X X . X X . X X
+20: . . . X X . . . . . . . . . . . . X . X X . X .
+21: . . X . . . . . . . X X . X . X X . X . . X . X
+22: X X X . . . . . . . . . . . . . X X . X X . X X
+23: . X X . . . . . . . . . . . . X X . X X . X X X
diff --git a/AMD/Demo/amd_demo2.c b/AMD/Demo/amd_demo2.c
new file mode 100644
index 0000000..b718580
--- /dev/null
+++ b/AMD/Demo/amd_demo2.c
@@ -0,0 +1,209 @@
+/* ========================================================================= */
+/* === AMD demo main program (jumbled matrix version) ====================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Copyright (c) by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* A simple C main program that illustrates the use of the ANSI C interface
+ * to AMD.
+ *
+ * Identical to amd_demo.c, except that it operates on an input matrix that has
+ * unsorted columns and duplicate entries.
+ */
+
+#include "amd.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+int main (void)
+{
+ /* The symmetric can_24 Harwell/Boeing matrix (jumbled, and not symmetric).
+ * Since AMD operates on A+A', only A(i,j) or A(j,i) need to be specified,
+ * or both. The diagonal entries are optional (some are missing).
+ * There are many duplicate entries, which must be removed. */
+ int n = 24, nz,
+ Ap [ ] = { 0, 9, 14, 20, 28, 33, 37, 44, 53, 58, 63, 63, 66, 69, 72, 75,
+ 78, 82, 86, 91, 97, 101, 112, 112, 116 },
+ Ai [ ] = {
+ /* column 0: */ 0, 17, 18, 21, 5, 12, 5, 0, 13,
+ /* column 1: */ 14, 1, 8, 13, 17,
+ /* column 2: */ 2, 20, 11, 6, 11, 22,
+ /* column 3: */ 3, 3, 10, 7, 18, 18, 15, 19,
+ /* column 4: */ 7, 9, 15, 14, 16,
+ /* column 5: */ 5, 13, 6, 17,
+ /* column 6: */ 5, 0, 11, 6, 12, 6, 23,
+ /* column 7: */ 3, 4, 9, 7, 14, 16, 15, 17, 18,
+ /* column 8: */ 1, 9, 14, 14, 14,
+ /* column 9: */ 7, 13, 8, 1, 17,
+ /* column 10: */
+ /* column 11: */ 2, 12, 23,
+ /* column 12: */ 5, 11, 12,
+ /* column 13: */ 0, 13, 17,
+ /* column 14: */ 1, 9, 14,
+ /* column 15: */ 3, 15, 16,
+ /* column 16: */ 16, 4, 4, 15,
+ /* column 17: */ 13, 17, 19, 17,
+ /* column 18: */ 15, 17, 19, 9, 10,
+ /* column 19: */ 17, 19, 20, 0, 6, 10,
+ /* column 20: */ 22, 10, 20, 21,
+ /* column 21: */ 6, 2, 10, 19, 20, 11, 21, 22, 22, 22, 22,
+ /* column 22: */
+ /* column 23: */ 12, 11, 12, 23 } ;
+
+ int P [24], Pinv [24], i, j, k, jnew, p, inew, result ;
+ double Control [AMD_CONTROL], Info [AMD_INFO] ;
+ char A [24][24] ;
+
+ printf ("AMD demo, with a jumbled version of the 24-by-24\n") ;
+ printf ("Harwell/Boeing matrix, can_24:\n") ;
+
+ /* get the default parameters, and print them */
+ amd_defaults (Control) ;
+ amd_control (Control) ;
+
+ /* print the input matrix */
+ nz = Ap [n] ;
+ printf ("\nJumbled input matrix: %d-by-%d, with %d entries.\n"
+ " Note that for a symmetric matrix such as this one, only the\n"
+ " strictly lower or upper triangular parts would need to be\n"
+ " passed to AMD, since AMD computes the ordering of A+A'. The\n"
+ " diagonal entries are also not needed, since AMD ignores them.\n"
+ " This version of the matrix has jumbled columns and duplicate\n"
+ " row indices.\n", n, n, nz) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf ("\nColumn: %d, number of entries: %d, with row indices in"
+ " Ai [%d ... %d]:\n row indices:",
+ j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ printf (" %d", i) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* print a character plot of the input matrix. This is only reasonable
+ * because the matrix is small. */
+ printf ("\nPlot of (jumbled) input matrix pattern:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (i = 0 ; i < n ; i++) A [i][j] = '.' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ A [i][j] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2d: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* print a character plot of the matrix A+A'. */
+ printf ("\nPlot of symmetric matrix to be ordered by amd_order:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (i = 0 ; i < n ; i++) A [i][j] = '.' ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ A [j][j] = 'X' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ A [i][j] = 'X' ;
+ A [j][i] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2d: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* order the matrix */
+ result = amd_order (n, Ap, Ai, P, Control, Info) ;
+ printf ("return value from amd_order: %d (should be %d)\n",
+ result, AMD_OK_BUT_JUMBLED) ;
+
+ /* print the statistics */
+ amd_info (Info) ;
+
+ if (result != AMD_OK_BUT_JUMBLED)
+ {
+ printf ("AMD failed\n") ;
+ exit (1) ;
+ }
+
+ /* print the permutation vector, P, and compute the inverse permutation */
+ printf ("Permutation vector:\n") ;
+ for (k = 0 ; k < n ; k++)
+ {
+ /* row/column j is the kth row/column in the permuted matrix */
+ j = P [k] ;
+ Pinv [j] = k ;
+ printf (" %2d", j) ;
+ }
+ printf ("\n\n") ;
+
+ printf ("Inverse permutation vector:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ k = Pinv [j] ;
+ printf (" %2d", k) ;
+ }
+ printf ("\n\n") ;
+
+ /* print a character plot of the permuted matrix. */
+ printf ("\nPlot of (symmetrized) permuted matrix pattern:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (i = 0 ; i < n ; i++) A [i][j] = '.' ;
+ }
+ for (jnew = 0 ; jnew < n ; jnew++)
+ {
+ j = P [jnew] ;
+ A [jnew][jnew] = 'X' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ inew = Pinv [Ai [p]] ;
+ A [inew][jnew] = 'X' ;
+ A [jnew][inew] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2d: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ return (0) ;
+}
diff --git a/AMD/Demo/amd_demo2.out b/AMD/Demo/amd_demo2.out
new file mode 100644
index 0000000..a47f078
--- /dev/null
+++ b/AMD/Demo/amd_demo2.out
@@ -0,0 +1,208 @@
+AMD demo, with a jumbled version of the 24-by-24
+Harwell/Boeing matrix, can_24:
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+Jumbled input matrix: 24-by-24, with 116 entries.
+ Note that for a symmetric matrix such as this one, only the
+ strictly lower or upper triangular parts would need to be
+ passed to AMD, since AMD computes the ordering of A+A'. The
+ diagonal entries are also not needed, since AMD ignores them.
+ This version of the matrix has jumbled columns and duplicate
+ row indices.
+
+Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]:
+ row indices: 0 17 18 21 5 12 5 0 13
+
+Column: 1, number of entries: 5, with row indices in Ai [9 ... 13]:
+ row indices: 14 1 8 13 17
+
+Column: 2, number of entries: 6, with row indices in Ai [14 ... 19]:
+ row indices: 2 20 11 6 11 22
+
+Column: 3, number of entries: 8, with row indices in Ai [20 ... 27]:
+ row indices: 3 3 10 7 18 18 15 19
+
+Column: 4, number of entries: 5, with row indices in Ai [28 ... 32]:
+ row indices: 7 9 15 14 16
+
+Column: 5, number of entries: 4, with row indices in Ai [33 ... 36]:
+ row indices: 5 13 6 17
+
+Column: 6, number of entries: 7, with row indices in Ai [37 ... 43]:
+ row indices: 5 0 11 6 12 6 23
+
+Column: 7, number of entries: 9, with row indices in Ai [44 ... 52]:
+ row indices: 3 4 9 7 14 16 15 17 18
+
+Column: 8, number of entries: 5, with row indices in Ai [53 ... 57]:
+ row indices: 1 9 14 14 14
+
+Column: 9, number of entries: 5, with row indices in Ai [58 ... 62]:
+ row indices: 7 13 8 1 17
+
+Column: 10, number of entries: 0, with row indices in Ai [63 ... 62]:
+ row indices:
+
+Column: 11, number of entries: 3, with row indices in Ai [63 ... 65]:
+ row indices: 2 12 23
+
+Column: 12, number of entries: 3, with row indices in Ai [66 ... 68]:
+ row indices: 5 11 12
+
+Column: 13, number of entries: 3, with row indices in Ai [69 ... 71]:
+ row indices: 0 13 17
+
+Column: 14, number of entries: 3, with row indices in Ai [72 ... 74]:
+ row indices: 1 9 14
+
+Column: 15, number of entries: 3, with row indices in Ai [75 ... 77]:
+ row indices: 3 15 16
+
+Column: 16, number of entries: 4, with row indices in Ai [78 ... 81]:
+ row indices: 16 4 4 15
+
+Column: 17, number of entries: 4, with row indices in Ai [82 ... 85]:
+ row indices: 13 17 19 17
+
+Column: 18, number of entries: 5, with row indices in Ai [86 ... 90]:
+ row indices: 15 17 19 9 10
+
+Column: 19, number of entries: 6, with row indices in Ai [91 ... 96]:
+ row indices: 17 19 20 0 6 10
+
+Column: 20, number of entries: 4, with row indices in Ai [97 ... 100]:
+ row indices: 22 10 20 21
+
+Column: 21, number of entries: 11, with row indices in Ai [101 ... 111]:
+ row indices: 6 2 10 19 20 11 21 22 22 22 22
+
+Column: 22, number of entries: 0, with row indices in Ai [112 ... 111]:
+ row indices:
+
+Column: 23, number of entries: 4, with row indices in Ai [112 ... 115]:
+ row indices: 12 11 12 23
+
+Plot of (jumbled) input matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . . X . . . . . . X . . . . . X . . . .
+ 1: . X . . . . . . X X . . . . X . . . . . . . . .
+ 2: . . X . . . . . . . . X . . . . . . . . . X . .
+ 3: . . . X . . . X . . . . . . . X . . . . . . . .
+ 4: . . . . . . . X . . . . . . . . X . . . . . . .
+ 5: X . . . . X X . . . . . X . . . . . . . . . . .
+ 6: . . X . . X X . . . . . . . . . . . . X . X . .
+ 7: . . . X X . . X . X . . . . . . . . . . . . . .
+ 8: . X . . . . . . . X . . . . . . . . . . . . . .
+ 9: . . . . X . . X X . . . . . X . . . X . . . . .
+10: . . . X . . . . . . . . . . . . . . X X X X . .
+11: . . X . . . X . . . . . X . . . . . . . . X . X
+12: X . . . . . X . . . . X X . . . . . . . . . . X
+13: X X . . . X . . . X . . . X . . . X . . . . . .
+14: . X . . X . . X X . . . . . X . . . . . . . . .
+15: . . . X X . . X . . . . . . . X X . X . . . . .
+16: . . . . X . . X . . . . . . . X X . . . . . . .
+17: X X . . . X . X . X . . . X . . . X X X . . . .
+18: X . . X . . . X . . . . . . . . . . . . . . . .
+19: . . . X . . . . . . . . . . . . . X X X . X . .
+20: . . X . . . . . . . . . . . . . . . . X X X . .
+21: X . . . . . . . . . . . . . . . . . . . X X . .
+22: . . X . . . . . . . . . . . . . . . . . X X . .
+23: . . . . . . X . . . . X . . . . . . . . . . . X
+
+Plot of symmetric matrix to be ordered by amd_order:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . X X . . . . . X X . . . X X X . X . .
+ 1: . X . . . . . . X X . . . X X . . X . . . . . .
+ 2: . . X . . . X . . . . X . . . . . . . . X X X .
+ 3: . . . X . . . X . . X . . . . X . . X X . . . .
+ 4: . . . . X . . X . X . . . . X X X . . . . . . .
+ 5: X . . . . X X . . . . . X X . . . X . . . . . .
+ 6: X . X . . X X . . . . X X . . . . . . X . X . X
+ 7: . . . X X . . X . X . . . . X X X X X . . . . .
+ 8: . X . . . . . . X X . . . . X . . . . . . . . .
+ 9: . X . . X . . X X X . . . X X . . X X . . . . .
+10: . . . X . . . . . . X . . . . . . . X X X X . .
+11: . . X . . . X . . . . X X . . . . . . . . X . X
+12: X . . . . X X . . . . X X . . . . . . . . . . X
+13: X X . . . X . . . X . . . X . . . X . . . . . .
+14: . X . . X . . X X X . . . . X . . . . . . . . .
+15: . . . X X . . X . . . . . . . X X . X . . . . .
+16: . . . . X . . X . . . . . . . X X . . . . . . .
+17: X X . . . X . X . X . . . X . . . X X X . . . .
+18: X . . X . . . X . X X . . . . X . X X X . . . .
+19: X . . X . . X . . . X . . . . . . X X X X X . .
+20: . . X . . . . . . . X . . . . . . . . X X X X .
+21: X . X . . . X . . . X X . . . . . . . X X X X .
+22: . . X . . . . . . . . . . . . . . . . . X X X .
+23: . . . . . . X . . . . X X . . . . . . . . . . X
+return value from amd_order: 1 (should be 1)
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 102
+ symmetry of A: 0.4000
+ number of nonzeros on diagonal: 17
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2080
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+Permutation vector:
+ 22 20 10 23 12 5 16 8 14 4 15 7 1 9 13 17 0 2 3 6 11 18 21 19
+
+Inverse permutation vector:
+ 16 12 17 18 9 5 19 11 7 13 2 20 4 14 8 10 6 15 21 23 1 22 0 3
+
+
+Plot of (symmetrized) permuted matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X X . . . . . . . . . . . . . . . X . . . . X .
+ 1: X X X . . . . . . . . . . . . . . X . . . . X X
+ 2: . X X . . . . . . . . . . . . . . . X . . X X X
+ 3: . . . X X . . . . . . . . . . . . . . X X . . .
+ 4: . . . X X X . . . . . . . . . . X . . X X . . .
+ 5: . . . . X X . . . . . . . . X X X . . X . . . .
+ 6: . . . . . . X . . X X X . . . . . . . . . . . .
+ 7: . . . . . . . X X . . . X X . . . . . . . . . .
+ 8: . . . . . . . X X X . X X X . . . . . . . . . .
+ 9: . . . . . . X . X X X X . X . . . . . . . . . .
+10: . . . . . . X . . X X X . . . . . . X . . X . .
+11: . . . . . . X . X X X X . X . X . . X . . X . .
+12: . . . . . . . X X . . . X X X X . . . . . . . .
+13: . . . . . . . X X X . X X X X X . . . . . X . .
+14: . . . . . X . . . . . . X X X X X . . . . . . .
+15: . . . . . X . . . . . X X X X X X . . . . X . X
+16: . . . . X X . . . . . . . . X X X . . X . X X X
+17: X X . . . . . . . . . . . . . . . X . X X . X .
+18: . . X . . . . . . . X X . . . . . . X . . X . X
+19: . . . X X X . . . . . . . . . . X X . X X . X X
+20: . . . X X . . . . . . . . . . . . X . X X . X .
+21: . . X . . . . . . . X X . X . X X . X . . X . X
+22: X X X . . . . . . . . . . . . . X X . X X . X X
+23: . X X . . . . . . . . . . . . X X . X X . X X X
diff --git a/AMD/Demo/amd_f77cross.f b/AMD/Demo/amd_f77cross.f
new file mode 100644
index 0000000..26513e0
--- /dev/null
+++ b/AMD/Demo/amd_f77cross.f
@@ -0,0 +1,51 @@
+C ======================================================================
+C === AMD_cross ========================================================
+C ======================================================================
+
+C ----------------------------------------------------------------------
+C AMD, Copyright (c) by Timothy A. Davis, Patrick R.
+C Amestoy, and Iain S. Duff. See ../README.txt for
+C License. email: davis at cise.ufl.edu CISE Department, Univ. of
+C Florida. web: http://www.cise.ufl.edu/research/sparse/amd
+C ----------------------------------------------------------------------
+
+C This program provides an example of how to call the C version of AMD
+C from a Fortran program. It is HIGHLY non-portable.
+
+C The amd_order routine returns PERM (1) < 0 if an error occurs.
+C (-1: out of memory, -2: invalid matrix)
+
+C Note that the input matrix is 0-based. From Fortran, column j of the
+C matrix is in AI (AP (I)+1 ... AP (I+1)). The row indices in this
+C set are in the range 0 to N-1. To demonstrate this translation,
+C the input matrix is printed in 1-based form. This program uses
+C the same 5-by-5 test matrix as amd_simple.c.
+
+ INTEGER N, NZ, K, P
+ PARAMETER (N = 5, NZ = 14)
+ INTEGER AP (N+1), AI (NZ), PERM (N)
+ DATA AP / 0, 2, 6, 10, 12, 14 /
+ DATA AI / 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 /
+ DOUBLE PRECISION CONTROL (5), INFO (20)
+
+C print the input matrix
+ PRINT 10, N, N, NZ
+10 FORMAT ('Input matrix:', I2, '-by-', I2, ' with',I3,' entries')
+ DO 40 J = 1, N
+ PRINT 20, J, AP (J+1) - AP (J), AP (J)+1, AP (J+1)
+20 FORMAT ( /, 'Column: ', I2, ' number of entries: ', I2,
+ $ ' with row indices in AI (', I3, ' ... ', I3, ')')
+ PRINT 30, ((AI (P) + 1), P = AP (J) + 1, AP (J+1))
+30 FORMAT (' row indices: ', 24I3)
+40 CONTINUE
+
+ CALL AMDDEFAULTS (CONTROL)
+ CALL AMDORDER (N, AP, AI, PERM, CONTROL, INFO)
+ CALL AMDINFO (INFO)
+
+ DO 60 K = 1, N
+ PRINT 50, K, PERM (K) + 1
+50 FORMAT ('PERM (',I2,') = ', I2)
+60 CONTINUE
+ END
+
diff --git a/AMD/Demo/amd_f77cross.out b/AMD/Demo/amd_f77cross.out
new file mode 100644
index 0000000..6d8a670
--- /dev/null
+++ b/AMD/Demo/amd_f77cross.out
@@ -0,0 +1,51 @@
+Input matrix: 5-by- 5 with 14 entries
+
+Column: 1 number of entries: 2 with row indices in AI ( 1 ... 2)
+ row indices: 1 2
+
+Column: 2 number of entries: 4 with row indices in AI ( 3 ... 6)
+ row indices: 1 2 3 5
+
+Column: 3 number of entries: 4 with row indices in AI ( 7 ... 10)
+ row indices: 2 3 4 5
+
+Column: 4 number of entries: 2 with row indices in AI ( 11 ... 12)
+ row indices: 3 4
+
+Column: 5 number of entries: 2 with row indices in AI ( 13 ... 14)
+ row indices: 2 5
+
+amd: approximate minimum degree ordering, results:
+ status: OK
+ n, dimension of A: 5
+ nz, number of nonzeros in A: 14
+ symmetry of A: 0.8889
+ number of nonzeros on diagonal: 5
+ nonzeros in pattern of A+A' (excl. diagonal): 10
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 228
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 5
+ nonzeros in L (including diagonal): 10
+ # divide operations for LDL' or LU: 5
+ # multiply-subtract operations for LDL': 6
+ # multiply-subtract operations for LU: 7
+ max nz. in any column of L (incl. diagonal): 3
+
+ chol flop count for real A, sqrt counted as 1 flop: 22
+ LDL' flop count for real A: 17
+ LDL' flop count for complex A: 93
+ LU flop count for real A (with no pivoting): 19
+ LU flop count for complex A (with no pivoting): 101
+
+PERM ( 1) = 1
+PERM ( 2) = 4
+PERM ( 3) = 3
+PERM ( 4) = 5
+PERM ( 5) = 2
diff --git a/AMD/Demo/amd_f77demo.f b/AMD/Demo/amd_f77demo.f
new file mode 100644
index 0000000..47b69fb
--- /dev/null
+++ b/AMD/Demo/amd_f77demo.f
@@ -0,0 +1,161 @@
+C ======================================================================
+C === Fortran AMD demo main program ====================================
+C ======================================================================
+
+C ----------------------------------------------------------------------
+C AMD, Copyright (c) by Timothy A. Davis, Patrick R.
+C Amestoy, and Iain S. Duff. See ../README.txt for
+C License. email: davis at cise.ufl.edu CISE Department, Univ. of
+C Florida. web: http://www.cise.ufl.edu/research/sparse/amd
+C ----------------------------------------------------------------------
+
+C A simple Fortran 77 main program that illustrates the use of the
+C Fortran version of AMD (both the AMD and AMDBAR routines). Note
+C that aggressive absorption has no effect on this particular matrix.
+
+C AP and AI contain the symmetric can_24 Harwell/Boeing matrix,
+C including upper and lower triangular parts, but excluding the
+C diagonal entries. Note that this matrix is 1-based, with row
+C and column indices in the range 1 to N.
+
+ INTEGER N, NZ, IWLEN, PFREE, I, J, K, JNEW, P, INEW,
+ $ METHOD, NCMPA
+ PARAMETER (N = 24, NZ = 136, IWLEN = 200)
+ INTEGER PE (N), DEGREE (N), NV (N), NEXT (N), PERM (N), W (N),
+ $ HEAD (N), PINV (N), LEN (N), AP (N+1), AI (NZ), IW (IWLEN)
+ CHARACTER A (24,24)
+
+ DATA AP
+ $ / 1, 9, 14, 19, 24, 29, 34, 42, 50, 53, 61, 66, 71,
+ $ 76, 81, 86, 91, 94, 102, 110, 118, 123, 131, 134, 137 /
+ DATA AI /
+ $ 6, 7, 13, 14, 18, 19, 20, 22,
+ $ 9, 10, 14, 15, 18,
+ $ 7, 12, 21, 22, 23,
+ $ 8, 11, 16, 19, 20,
+ $ 8, 10, 15, 16, 17,
+ $ 1, 7, 13, 14, 18,
+ $ 1, 3, 6, 12, 13, 20, 22, 24,
+ $ 4, 5, 10, 15, 16, 17, 18, 19,
+ $ 2, 10, 15,
+ $ 2, 5, 8, 9, 14, 15, 18, 19,
+ $ 4, 19, 20, 21, 22,
+ $ 3, 7, 13, 22, 24,
+ $ 1, 6, 7, 12, 24,
+ $ 1, 2, 6, 10, 18,
+ $ 2, 5, 8, 9, 10,
+ $ 4, 5, 8, 17, 19,
+ $ 5, 8, 16,
+ $ 1, 2, 6, 8, 10, 14, 19, 20,
+ $ 1, 4, 8, 10, 11, 16, 18, 20,
+ $ 1, 4, 7, 11, 18, 19, 21, 22,
+ $ 3, 11, 20, 22, 23,
+ $ 1, 3, 7, 11, 12, 20, 21, 23,
+ $ 3, 21, 22,
+ $ 7, 12, 13 /
+
+C print the input matrix
+ PRINT 11, N, N, NZ
+11 FORMAT ('AMD Fortran 77 demo, with the 24-by-24',
+ $ ' Harwell/Boeing matrix, can_24:'
+ $ /, 'Input matrix: ', I2, '-by-', I2,' with ',I3,' entries',
+ $ /, 'Note that the Fortran version of AMD requires that'
+ $ /, 'no diagonal entries be present.')
+ DO 20 J = 1, N
+ PRINT 21, J, AP (J+1) - AP (J), AP (J), AP (J+1)-1
+21 FORMAT ( /, 'Column: ', I2, ' number of entries: ', I2,
+ $ ' with row indices in AI (', I3, ' ... ', I3, ')')
+ PRINT 10, ((AI (P)), P = AP (J), AP (J+1) - 1)
+10 FORMAT (' row indices: ', 24I3)
+20 CONTINUE
+
+C print a character plot of the input matrix. This is only
+C reasonable because the matrix is small.
+ PRINT 31
+31 FORMAT ('Plot of input matrix pattern:')
+ DO 50 J = 1,N
+ DO 30 I = 1,N
+ A (I, J) = '.'
+30 CONTINUE
+C add the diagonal entry to the plot
+ A (J, J) = 'X'
+ DO 40 P = AP (J), AP (J+1) - 1
+ I = AI (P)
+ A (I, J) = 'X'
+40 CONTINUE
+50 CONTINUE
+ PRINT 60, ((MOD (J, 10)), J = 1,N)
+60 FORMAT (' ', 24I2)
+ DO 80 I = 1,N
+ PRINT 70, I, (A (I, J), J = 1,N)
+70 FORMAT (' ', I2, ': ', 24A2)
+80 CONTINUE
+
+ DO 190 METHOD = 1,2
+
+C load the matrix into AMD's workspace
+ DO 90 J = 1,N
+ PE (J) = AP (J)
+ LEN (J) = AP (J+1) - AP (J)
+90 CONTINUE
+ DO 100 P = 1,NZ
+ IW (P) = AI (P)
+100 CONTINUE
+ PFREE = NZ + 1
+
+C order the matrix using AMD or AMDBAR
+ IF (METHOD .EQ. 1) THEN
+ PRINT 101
+101 FORMAT (/, '------------------------------------------',
+ $ /, 'ordering the matrix with AMD',
+ $ /, '------------------------------------------')
+ CALL AMD (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT,
+ $ PERM, HEAD, PINV, DEGREE, NCMPA, W)
+ ELSE
+ PRINT 102
+102 FORMAT (/, '------------------------------------------',
+ $ /, 'ordering the matrix with AMDBAR',
+ $ /, '------------------------------------------')
+ CALL AMDBAR (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT,
+ $ PERM, HEAD, PINV, DEGREE, NCMPA, W)
+ ENDIF
+
+C print the permutation vector, PERM, and its inverse, PINV.
+C row/column J = PERM (K) is the Kth row/column in the
+C permuted matrix.
+ PRINT 110, (PERM (K), K = 1,N)
+110 FORMAT (/, 'Permutation vector: ', /, 24I3)
+ PRINT 120, (PINV (J), J = 1,N)
+120 FORMAT (/, 'Inverse permutation vector: ', /, 24I3)
+
+C print a character plot of the permuted matrix.
+ PRINT 121
+121 FORMAT ('Plot of permuted matrix pattern:')
+ DO 150 JNEW = 1,N
+ J = PERM (JNEW)
+ DO 130 INEW = 1,N
+ A (INEW, JNEW) = '.'
+130 CONTINUE
+C add the diagonal entry to the plot
+ A (JNEW, JNEW) = 'X'
+ DO 140 P = AP (J), AP (J+1) - 1
+ INEW = PINV (AI (P))
+ A (INEW, JNEW) = 'X'
+140 CONTINUE
+150 CONTINUE
+ PRINT 60, ((MOD (J, 10)), J = 1,N)
+ DO 160 I = 1,N
+ PRINT 70, I, (A (I, J), J = 1,N)
+160 CONTINUE
+
+C print the permuted matrix, PERM*A*PERM'
+ DO 180 JNEW = 1,N
+ J = PERM (JNEW)
+ PRINT 171, JNEW, J, AP (J+1) - AP (J)
+171 FORMAT (/, 'New column: ', I2, ' old column: ', I2,
+ $ ' number of entries: ', I2)
+ PRINT 170, (PINV (AI (P)), P = AP (J), AP (J+1) - 1)
+170 FORMAT (' new row indices: ', 24I3)
+180 CONTINUE
+190 CONTINUE
+ END
diff --git a/AMD/Demo/amd_f77demo.out b/AMD/Demo/amd_f77demo.out
new file mode 100644
index 0000000..10758dd
--- /dev/null
+++ b/AMD/Demo/amd_f77demo.out
@@ -0,0 +1,318 @@
+AMD Fortran 77 demo, with the 24-by-24 Harwell/Boeing matrix, can_24:
+Input matrix: 24-by-24 with 136 entries
+Note that the Fortran version of AMD requires that
+no diagonal entries be present.
+
+Column: 1 number of entries: 8 with row indices in AI ( 1 ... 8)
+ row indices: 6 7 13 14 18 19 20 22
+
+Column: 2 number of entries: 5 with row indices in AI ( 9 ... 13)
+ row indices: 9 10 14 15 18
+
+Column: 3 number of entries: 5 with row indices in AI ( 14 ... 18)
+ row indices: 7 12 21 22 23
+
+Column: 4 number of entries: 5 with row indices in AI ( 19 ... 23)
+ row indices: 8 11 16 19 20
+
+Column: 5 number of entries: 5 with row indices in AI ( 24 ... 28)
+ row indices: 8 10 15 16 17
+
+Column: 6 number of entries: 5 with row indices in AI ( 29 ... 33)
+ row indices: 1 7 13 14 18
+
+Column: 7 number of entries: 8 with row indices in AI ( 34 ... 41)
+ row indices: 1 3 6 12 13 20 22 24
+
+Column: 8 number of entries: 8 with row indices in AI ( 42 ... 49)
+ row indices: 4 5 10 15 16 17 18 19
+
+Column: 9 number of entries: 3 with row indices in AI ( 50 ... 52)
+ row indices: 2 10 15
+
+Column: 10 number of entries: 8 with row indices in AI ( 53 ... 60)
+ row indices: 2 5 8 9 14 15 18 19
+
+Column: 11 number of entries: 5 with row indices in AI ( 61 ... 65)
+ row indices: 4 19 20 21 22
+
+Column: 12 number of entries: 5 with row indices in AI ( 66 ... 70)
+ row indices: 3 7 13 22 24
+
+Column: 13 number of entries: 5 with row indices in AI ( 71 ... 75)
+ row indices: 1 6 7 12 24
+
+Column: 14 number of entries: 5 with row indices in AI ( 76 ... 80)
+ row indices: 1 2 6 10 18
+
+Column: 15 number of entries: 5 with row indices in AI ( 81 ... 85)
+ row indices: 2 5 8 9 10
+
+Column: 16 number of entries: 5 with row indices in AI ( 86 ... 90)
+ row indices: 4 5 8 17 19
+
+Column: 17 number of entries: 3 with row indices in AI ( 91 ... 93)
+ row indices: 5 8 16
+
+Column: 18 number of entries: 8 with row indices in AI ( 94 ... 101)
+ row indices: 1 2 6 8 10 14 19 20
+
+Column: 19 number of entries: 8 with row indices in AI (102 ... 109)
+ row indices: 1 4 8 10 11 16 18 20
+
+Column: 20 number of entries: 8 with row indices in AI (110 ... 117)
+ row indices: 1 4 7 11 18 19 21 22
+
+Column: 21 number of entries: 5 with row indices in AI (118 ... 122)
+ row indices: 3 11 20 22 23
+
+Column: 22 number of entries: 8 with row indices in AI (123 ... 130)
+ row indices: 1 3 7 11 12 20 21 23
+
+Column: 23 number of entries: 3 with row indices in AI (131 ... 133)
+ row indices: 3 21 22
+
+Column: 24 number of entries: 3 with row indices in AI (134 ... 136)
+ row indices: 7 12 13
+Plot of input matrix pattern:
+ 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4
+ 1: X . . . . X X . . . . . X X . . . X X X . X . .
+ 2: . X . . . . . . X X . . . X X . . X . . . . . .
+ 3: . . X . . . X . . . . X . . . . . . . . X X X .
+ 4: . . . X . . . X . . X . . . . X . . X X . . . .
+ 5: . . . . X . . X . X . . . . X X X . . . . . . .
+ 6: X . . . . X X . . . . . X X . . . X . . . . . .
+ 7: X . X . . X X . . . . X X . . . . . . X . X . X
+ 8: . . . X X . . X . X . . . . X X X X X . . . . .
+ 9: . X . . . . . . X X . . . . X . . . . . . . . .
+ 10: . X . . X . . X X X . . . X X . . X X . . . . .
+ 11: . . . X . . . . . . X . . . . . . . X X X X . .
+ 12: . . X . . . X . . . . X X . . . . . . . . X . X
+ 13: X . . . . X X . . . . X X . . . . . . . . . . X
+ 14: X X . . . X . . . X . . . X . . . X . . . . . .
+ 15: . X . . X . . X X X . . . . X . . . . . . . . .
+ 16: . . . X X . . X . . . . . . . X X . X . . . . .
+ 17: . . . . X . . X . . . . . . . X X . . . . . . .
+ 18: X X . . . X . X . X . . . X . . . X X X . . . .
+ 19: X . . X . . . X . X X . . . . X . X X X . . . .
+ 20: X . . X . . X . . . X . . . . . . X X X X X . .
+ 21: . . X . . . . . . . X . . . . . . . . X X X X .
+ 22: X . X . . . X . . . X X . . . . . . . X X X X .
+ 23: . . X . . . . . . . . . . . . . . . . . X X X .
+ 24: . . . . . . X . . . . X X . . . . . . . . . . X
+
+------------------------------------------
+ordering the matrix with AMD
+------------------------------------------
+
+Permutation vector:
+ 24 23 17 9 15 5 21 13 6 11 16 8 2 10 14 18 1 3 4 19 7 12 22 20
+
+Inverse permutation vector:
+ 17 13 18 19 6 9 21 12 4 14 10 22 8 15 5 11 3 16 20 24 7 23 2 1
+Plot of permuted matrix pattern:
+ 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4
+ 1: X . . . . . . X . . . . . . . . . . . . X X . .
+ 2: . X . . . . X . . . . . . . . . . X . . . . X .
+ 3: . . X . . X . . . . X X . . . . . . . . . . . .
+ 4: . . . X X . . . . . . . X X . . . . . . . . . .
+ 5: . . . X X X . . . . . X X X . . . . . . . . . .
+ 6: . . X . X X . . . . X X . X . . . . . . . . . .
+ 7: . X . . . . X . . X . . . . . . . X . . . . X X
+ 8: X . . . . . . X X . . . . . . . X . . . X X . .
+ 9: . . . . . . . X X . . . . . X X X . . . X . . .
+ 10: . . . . . . X . . X . . . . . . . . X X . . X X
+ 11: . . X . . X . . . . X X . . . . . . X X . . . .
+ 12: . . X . X X . . . . X X . X . X . . X X . . . .
+ 13: . . . X X . . . . . . . X X X X . . . . . . . .
+ 14: . . . X X X . . . . . X X X X X . . . X . . . .
+ 15: . . . . . . . . X . . . X X X X X . . . . . . .
+ 16: . . . . . . . . X . . X X X X X X . . X . . . X
+ 17: . . . . . . . X X . . . . . X X X . . X X . X X
+ 18: . X . . . . X . . . . . . . . . . X . . X X X .
+ 19: . . . . . . . . . X X X . . . . . . X X . . . X
+ 20: . . . . . . . . . X X X . X . X X . X X . . . X
+ 21: X . . . . . . X X . . . . . . . X X . . X X X X
+ 22: X . . . . . . X . . . . . . . . . X . . X X X .
+ 23: . X . . . . X . . X . . . . . . X X . . X X X X
+ 24: . . . . . . X . . X . . . . . X X . X X X . X X
+
+New column: 1 old column: 24 number of entries: 3
+ new row indices: 21 22 8
+
+New column: 2 old column: 23 number of entries: 3
+ new row indices: 18 7 23
+
+New column: 3 old column: 17 number of entries: 3
+ new row indices: 6 12 11
+
+New column: 4 old column: 9 number of entries: 3
+ new row indices: 13 14 5
+
+New column: 5 old column: 15 number of entries: 5
+ new row indices: 13 6 12 4 14
+
+New column: 6 old column: 5 number of entries: 5
+ new row indices: 12 14 5 11 3
+
+New column: 7 old column: 21 number of entries: 5
+ new row indices: 18 10 24 23 2
+
+New column: 8 old column: 13 number of entries: 5
+ new row indices: 17 9 21 22 1
+
+New column: 9 old column: 6 number of entries: 5
+ new row indices: 17 21 8 15 16
+
+New column: 10 old column: 11 number of entries: 5
+ new row indices: 19 20 24 7 23
+
+New column: 11 old column: 16 number of entries: 5
+ new row indices: 19 6 12 3 20
+
+New column: 12 old column: 8 number of entries: 8
+ new row indices: 19 6 14 5 11 3 16 20
+
+New column: 13 old column: 2 number of entries: 5
+ new row indices: 4 14 15 5 16
+
+New column: 14 old column: 10 number of entries: 8
+ new row indices: 13 6 12 4 15 5 16 20
+
+New column: 15 old column: 14 number of entries: 5
+ new row indices: 17 13 9 14 16
+
+New column: 16 old column: 18 number of entries: 8
+ new row indices: 17 13 9 12 14 15 20 24
+
+New column: 17 old column: 1 number of entries: 8
+ new row indices: 9 21 8 15 16 20 24 23
+
+New column: 18 old column: 3 number of entries: 5
+ new row indices: 21 22 7 23 2
+
+New column: 19 old column: 4 number of entries: 5
+ new row indices: 12 10 11 20 24
+
+New column: 20 old column: 19 number of entries: 8
+ new row indices: 17 19 12 14 10 11 16 24
+
+New column: 21 old column: 7 number of entries: 8
+ new row indices: 17 18 9 22 8 24 23 1
+
+New column: 22 old column: 12 number of entries: 5
+ new row indices: 18 21 8 23 1
+
+New column: 23 old column: 22 number of entries: 8
+ new row indices: 17 18 21 10 22 24 7 2
+
+New column: 24 old column: 20 number of entries: 8
+ new row indices: 17 19 21 10 16 20 7 23
+
+------------------------------------------
+ordering the matrix with AMDBAR
+------------------------------------------
+
+Permutation vector:
+ 24 23 17 9 15 5 21 13 6 11 16 8 2 10 14 18 1 3 4 19 7 12 22 20
+
+Inverse permutation vector:
+ 17 13 18 19 6 9 21 12 4 14 10 22 8 15 5 11 3 16 20 24 7 23 2 1
+Plot of permuted matrix pattern:
+ 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4
+ 1: X . . . . . . X . . . . . . . . . . . . X X . .
+ 2: . X . . . . X . . . . . . . . . . X . . . . X .
+ 3: . . X . . X . . . . X X . . . . . . . . . . . .
+ 4: . . . X X . . . . . . . X X . . . . . . . . . .
+ 5: . . . X X X . . . . . X X X . . . . . . . . . .
+ 6: . . X . X X . . . . X X . X . . . . . . . . . .
+ 7: . X . . . . X . . X . . . . . . . X . . . . X X
+ 8: X . . . . . . X X . . . . . . . X . . . X X . .
+ 9: . . . . . . . X X . . . . . X X X . . . X . . .
+ 10: . . . . . . X . . X . . . . . . . . X X . . X X
+ 11: . . X . . X . . . . X X . . . . . . X X . . . .
+ 12: . . X . X X . . . . X X . X . X . . X X . . . .
+ 13: . . . X X . . . . . . . X X X X . . . . . . . .
+ 14: . . . X X X . . . . . X X X X X . . . X . . . .
+ 15: . . . . . . . . X . . . X X X X X . . . . . . .
+ 16: . . . . . . . . X . . X X X X X X . . X . . . X
+ 17: . . . . . . . X X . . . . . X X X . . X X . X X
+ 18: . X . . . . X . . . . . . . . . . X . . X X X .
+ 19: . . . . . . . . . X X X . . . . . . X X . . . X
+ 20: . . . . . . . . . X X X . X . X X . X X . . . X
+ 21: X . . . . . . X X . . . . . . . X X . . X X X X
+ 22: X . . . . . . X . . . . . . . . . X . . X X X .
+ 23: . X . . . . X . . X . . . . . . X X . . X X X X
+ 24: . . . . . . X . . X . . . . . X X . X X X . X X
+
+New column: 1 old column: 24 number of entries: 3
+ new row indices: 21 22 8
+
+New column: 2 old column: 23 number of entries: 3
+ new row indices: 18 7 23
+
+New column: 3 old column: 17 number of entries: 3
+ new row indices: 6 12 11
+
+New column: 4 old column: 9 number of entries: 3
+ new row indices: 13 14 5
+
+New column: 5 old column: 15 number of entries: 5
+ new row indices: 13 6 12 4 14
+
+New column: 6 old column: 5 number of entries: 5
+ new row indices: 12 14 5 11 3
+
+New column: 7 old column: 21 number of entries: 5
+ new row indices: 18 10 24 23 2
+
+New column: 8 old column: 13 number of entries: 5
+ new row indices: 17 9 21 22 1
+
+New column: 9 old column: 6 number of entries: 5
+ new row indices: 17 21 8 15 16
+
+New column: 10 old column: 11 number of entries: 5
+ new row indices: 19 20 24 7 23
+
+New column: 11 old column: 16 number of entries: 5
+ new row indices: 19 6 12 3 20
+
+New column: 12 old column: 8 number of entries: 8
+ new row indices: 19 6 14 5 11 3 16 20
+
+New column: 13 old column: 2 number of entries: 5
+ new row indices: 4 14 15 5 16
+
+New column: 14 old column: 10 number of entries: 8
+ new row indices: 13 6 12 4 15 5 16 20
+
+New column: 15 old column: 14 number of entries: 5
+ new row indices: 17 13 9 14 16
+
+New column: 16 old column: 18 number of entries: 8
+ new row indices: 17 13 9 12 14 15 20 24
+
+New column: 17 old column: 1 number of entries: 8
+ new row indices: 9 21 8 15 16 20 24 23
+
+New column: 18 old column: 3 number of entries: 5
+ new row indices: 21 22 7 23 2
+
+New column: 19 old column: 4 number of entries: 5
+ new row indices: 12 10 11 20 24
+
+New column: 20 old column: 19 number of entries: 8
+ new row indices: 17 19 12 14 10 11 16 24
+
+New column: 21 old column: 7 number of entries: 8
+ new row indices: 17 18 9 22 8 24 23 1
+
+New column: 22 old column: 12 number of entries: 5
+ new row indices: 18 21 8 23 1
+
+New column: 23 old column: 22 number of entries: 8
+ new row indices: 17 18 21 10 22 24 7 2
+
+New column: 24 old column: 20 number of entries: 8
+ new row indices: 17 19 21 10 16 20 7 23
diff --git a/AMD/Demo/amd_f77simple.f b/AMD/Demo/amd_f77simple.f
new file mode 100644
index 0000000..398681b
--- /dev/null
+++ b/AMD/Demo/amd_f77simple.f
@@ -0,0 +1,38 @@
+C ----------------------------------------------------------------------
+C AMD, Copyright (c) by Timothy A. Davis, Patrick R.
+C Amestoy, and Iain S. Duff. See ../README.txt for
+C License. email: davis at cise.ufl.edu CISE Department, Univ. of
+C Florida. web: http://www.cise.ufl.edu/research/sparse/amd
+C ----------------------------------------------------------------------
+
+C This program provides an example of how to call the Fortran version
+C of AMD. It uses the same matrix as the amd_simple.c demo (in C).
+C Note that the diagonal entries are not present, and the matrix is
+C symmetric.
+
+ INTEGER N, NZ, J, K, P, IWLEN, PFREE, NCMPA
+ PARAMETER (N = 5, NZ = 10, IWLEN = 17)
+ INTEGER AP (N+1), AI (NZ), LAST (N), PE (N), LEN (N), ELEN (N),
+ $ IW (IWLEN), DEGREE (N), NV (N), NEXT (N), HEAD (N), W (N)
+ DATA AP / 1, 2, 5, 8, 9, 11/
+ DATA AI / 2, 1,3,5, 2,4,5, 3, 2,3 /
+
+C load the matrix into the AMD workspace
+ DO 10 J = 1,N
+ PE (J) = AP (J)
+ LEN (J) = AP (J+1) - AP (J)
+10 CONTINUE
+ DO 20 P = 1,NZ
+ IW (P) = AI (P)
+20 CONTINUE
+ PFREE = NZ + 1
+
+C order the matrix (destroys the copy of A in IW, PE, and LEN)
+ CALL AMD (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, LAST, HEAD,
+ $ ELEN, DEGREE, NCMPA, W)
+
+ DO 60 K = 1, N
+ PRINT 50, K, LAST (K)
+50 FORMAT ('P (',I2,') = ', I2)
+60 CONTINUE
+ END
diff --git a/AMD/Demo/amd_f77simple.out b/AMD/Demo/amd_f77simple.out
new file mode 100644
index 0000000..c7f902e
--- /dev/null
+++ b/AMD/Demo/amd_f77simple.out
@@ -0,0 +1,5 @@
+P ( 1) = 4
+P ( 2) = 1
+P ( 3) = 3
+P ( 4) = 5
+P ( 5) = 2
diff --git a/AMD/Demo/amd_f77wrapper.c b/AMD/Demo/amd_f77wrapper.c
new file mode 100644
index 0000000..eb1cd54
--- /dev/null
+++ b/AMD/Demo/amd_f77wrapper.c
@@ -0,0 +1,96 @@
+/* ========================================================================= */
+/* === amd_f77wrapper ====================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Copyright (c) by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Fortran interface for the C-callable AMD library (int version only). This
+ * is HIGHLY non-portable. You will need to modify this depending on how your
+ * Fortran and C compilers behave. Two examples are provided.
+ *
+ * To avoid using I/O, and to avoid the extra porting step of a Fortran
+ * function, the status code is returned as the first entry in P (P [0] in C
+ * and P (1) in Fortran) if an error occurs. The error codes are negative
+ * (-1: out of memory, -2: invalid matrix).
+ *
+ * For some C and Fortran compilers, the Fortran compiler appends a single "_"
+ * after each routine name. C doesn't do this, so the translation is made
+ * here. Some Fortran compilers don't append an underscore (xlf on IBM AIX,
+ * for * example).
+ *
+ * Tested with the following compilers:
+ * Solaris with cc and f77 from Sun WorkShop 6 update 1.
+ * SGI Irix with MIPSpro cc and f77 compilers version 7.4
+ * Linux with GNU gcc or Intel's icc, and GNU g77 Intel's ifc Fortran compiler.
+ * (any combination). Note that with g77, a call to amd_order in Fortran
+ * gets translated to a call to amd_order__, with two underscores ("_").
+ * Thus, the Fortran names do not include an underscore.
+ */
+
+#include "amd.h"
+#include <stdio.h>
+
+/* ------------------------------------------------------------------------- */
+/* Linux, Solaris, SGI */
+/* ------------------------------------------------------------------------- */
+
+void amdorder_ (int *n, const int *Ap, const int *Ai, int *P,
+ double *Control, double *Info)
+{
+ int result = amd_order (*n, Ap, Ai, P, Control, Info) ;
+ if (result != AMD_OK && P) P [0] = result ;
+}
+
+void amddefaults_ (double *Control)
+{
+ amd_defaults (Control) ;
+}
+
+void amdcontrol_ (double *Control)
+{
+ fflush (stdout) ;
+ amd_control (Control) ;
+ fflush (stdout) ;
+}
+
+void amdinfo_ (double *Info)
+{
+ fflush (stdout) ;
+ amd_info (Info) ;
+ fflush (stdout) ;
+}
+
+/* ------------------------------------------------------------------------- */
+/* IBM AIX. Probably Windows, Compaq Alpha, and HP Unix as well. */
+/* ------------------------------------------------------------------------- */
+
+void amdorder (int *n, const int *Ap, const int *Ai, int *P,
+ double *Control, double *Info)
+{
+ int result = amd_order (*n, Ap, Ai, P, Control, Info) ;
+ if (result != AMD_OK && P) P [0] = result ;
+}
+
+void amddefaults (double *Control)
+{
+ amd_defaults (Control) ;
+}
+
+void amdcontrol (double *Control)
+{
+ fflush (stdout) ;
+ amd_control (Control) ;
+ fflush (stdout) ;
+}
+
+void amdinfo (double *Info)
+{
+ fflush (stdout) ;
+ amd_info (Info) ;
+ fflush (stdout) ;
+}
diff --git a/AMD/Demo/amd_l_demo.c b/AMD/Demo/amd_l_demo.c
new file mode 100644
index 0000000..342f085
--- /dev/null
+++ b/AMD/Demo/amd_l_demo.c
@@ -0,0 +1,179 @@
+/* ========================================================================= */
+/* === AMD demo main program (UF_long integer version) ===================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Copyright (c) by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* A simple C main program that illustrates the use of the ANSI C interface
+ * to AMD.
+ */
+
+#include "amd.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include "UFconfig.h"
+
+int main (void)
+{
+ /* The symmetric can_24 Harwell/Boeing matrix, including upper and lower
+ * triangular parts, and the diagonal entries. Note that this matrix is
+ * 0-based, with row and column indices in the range 0 to n-1. */
+ UF_long n = 24, nz,
+ Ap [ ] = { 0, 9, 15, 21, 27, 33, 39, 48, 57, 61, 70, 76, 82, 88, 94, 100,
+ 106, 110, 119, 128, 137, 143, 152, 156, 160 },
+ Ai [ ] = {
+ /* column 0: */ 0, 5, 6, 12, 13, 17, 18, 19, 21,
+ /* column 1: */ 1, 8, 9, 13, 14, 17,
+ /* column 2: */ 2, 6, 11, 20, 21, 22,
+ /* column 3: */ 3, 7, 10, 15, 18, 19,
+ /* column 4: */ 4, 7, 9, 14, 15, 16,
+ /* column 5: */ 0, 5, 6, 12, 13, 17,
+ /* column 6: */ 0, 2, 5, 6, 11, 12, 19, 21, 23,
+ /* column 7: */ 3, 4, 7, 9, 14, 15, 16, 17, 18,
+ /* column 8: */ 1, 8, 9, 14,
+ /* column 9: */ 1, 4, 7, 8, 9, 13, 14, 17, 18,
+ /* column 10: */ 3, 10, 18, 19, 20, 21,
+ /* column 11: */ 2, 6, 11, 12, 21, 23,
+ /* column 12: */ 0, 5, 6, 11, 12, 23,
+ /* column 13: */ 0, 1, 5, 9, 13, 17,
+ /* column 14: */ 1, 4, 7, 8, 9, 14,
+ /* column 15: */ 3, 4, 7, 15, 16, 18,
+ /* column 16: */ 4, 7, 15, 16,
+ /* column 17: */ 0, 1, 5, 7, 9, 13, 17, 18, 19,
+ /* column 18: */ 0, 3, 7, 9, 10, 15, 17, 18, 19,
+ /* column 19: */ 0, 3, 6, 10, 17, 18, 19, 20, 21,
+ /* column 20: */ 2, 10, 19, 20, 21, 22,
+ /* column 21: */ 0, 2, 6, 10, 11, 19, 20, 21, 22,
+ /* column 22: */ 2, 20, 21, 22,
+ /* column 23: */ 6, 11, 12, 23 } ;
+
+ UF_long P [24], Pinv [24], i, j, k, jnew, p, inew, result ;
+ double Control [AMD_CONTROL], Info [AMD_INFO] ;
+ char A [24][24] ;
+
+ /* here is an example of how to use AMD_VERSION. This code will work in
+ * any version of AMD. */
+#if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE(1,2))
+ printf ("AMD version %d.%d, date: %s\n", AMD_MAIN_VERSION, AMD_SUB_VERSION,
+ AMD_DATE) ;
+#else
+ printf ("AMD version: 1.1 or earlier\n") ;
+#endif
+
+ printf ("AMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:\n") ;
+
+ /* get the default parameters, and print them */
+ amd_l_defaults (Control) ;
+ amd_l_control (Control) ;
+
+ /* print the input matrix */
+ nz = Ap [n] ;
+ printf ("\nInput matrix: %ld-by-%ld, with %ld entries.\n"
+ " Note that for a symmetric matrix such as this one, only the\n"
+ " strictly lower or upper triangular parts would need to be\n"
+ " passed to AMD, since AMD computes the ordering of A+A'. The\n"
+ " diagonal entries are also not needed, since AMD ignores them.\n"
+ , n, n, nz) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf ("\nColumn: %ld, number of entries: %ld, with row indices in"
+ " Ai [%ld ... %ld]:\n row indices:",
+ j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ printf (" %ld", i) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* print a character plot of the input matrix. This is only reasonable
+ * because the matrix is small. */
+ printf ("\nPlot of input matrix pattern:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (i = 0 ; i < n ; i++) A [i][j] = '.' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ A [i][j] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1ld", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2ld: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* order the matrix */
+ result = amd_l_order (n, Ap, Ai, P, Control, Info) ;
+ printf ("return value from amd_l_order: %ld (should be %d)\n",
+ result, AMD_OK) ;
+
+ /* print the statistics */
+ amd_l_info (Info) ;
+
+ if (result != AMD_OK)
+ {
+ printf ("AMD failed\n") ;
+ exit (1) ;
+ }
+
+ /* print the permutation vector, P, and compute the inverse permutation */
+ printf ("Permutation vector:\n") ;
+ for (k = 0 ; k < n ; k++)
+ {
+ /* row/column j is the kth row/column in the permuted matrix */
+ j = P [k] ;
+ Pinv [j] = k ;
+ printf (" %2ld", j) ;
+ }
+ printf ("\n\n") ;
+
+ printf ("Inverse permutation vector:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ k = Pinv [j] ;
+ printf (" %2ld", k) ;
+ }
+ printf ("\n\n") ;
+
+ /* print a character plot of the permuted matrix. */
+ printf ("\nPlot of permuted matrix pattern:\n") ;
+ for (jnew = 0 ; jnew < n ; jnew++)
+ {
+ j = P [jnew] ;
+ for (inew = 0 ; inew < n ; inew++) A [inew][jnew] = '.' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ inew = Pinv [Ai [p]] ;
+ A [inew][jnew] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1ld", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2ld: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ return (0) ;
+}
diff --git a/AMD/Demo/amd_l_demo.out b/AMD/Demo/amd_l_demo.out
new file mode 100644
index 0000000..58f8489
--- /dev/null
+++ b/AMD/Demo/amd_l_demo.out
@@ -0,0 +1,179 @@
+AMD version 2.2, date: May 31, 2007
+AMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+Input matrix: 24-by-24, with 160 entries.
+ Note that for a symmetric matrix such as this one, only the
+ strictly lower or upper triangular parts would need to be
+ passed to AMD, since AMD computes the ordering of A+A'. The
+ diagonal entries are also not needed, since AMD ignores them.
+
+Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]:
+ row indices: 0 5 6 12 13 17 18 19 21
+
+Column: 1, number of entries: 6, with row indices in Ai [9 ... 14]:
+ row indices: 1 8 9 13 14 17
+
+Column: 2, number of entries: 6, with row indices in Ai [15 ... 20]:
+ row indices: 2 6 11 20 21 22
+
+Column: 3, number of entries: 6, with row indices in Ai [21 ... 26]:
+ row indices: 3 7 10 15 18 19
+
+Column: 4, number of entries: 6, with row indices in Ai [27 ... 32]:
+ row indices: 4 7 9 14 15 16
+
+Column: 5, number of entries: 6, with row indices in Ai [33 ... 38]:
+ row indices: 0 5 6 12 13 17
+
+Column: 6, number of entries: 9, with row indices in Ai [39 ... 47]:
+ row indices: 0 2 5 6 11 12 19 21 23
+
+Column: 7, number of entries: 9, with row indices in Ai [48 ... 56]:
+ row indices: 3 4 7 9 14 15 16 17 18
+
+Column: 8, number of entries: 4, with row indices in Ai [57 ... 60]:
+ row indices: 1 8 9 14
+
+Column: 9, number of entries: 9, with row indices in Ai [61 ... 69]:
+ row indices: 1 4 7 8 9 13 14 17 18
+
+Column: 10, number of entries: 6, with row indices in Ai [70 ... 75]:
+ row indices: 3 10 18 19 20 21
+
+Column: 11, number of entries: 6, with row indices in Ai [76 ... 81]:
+ row indices: 2 6 11 12 21 23
+
+Column: 12, number of entries: 6, with row indices in Ai [82 ... 87]:
+ row indices: 0 5 6 11 12 23
+
+Column: 13, number of entries: 6, with row indices in Ai [88 ... 93]:
+ row indices: 0 1 5 9 13 17
+
+Column: 14, number of entries: 6, with row indices in Ai [94 ... 99]:
+ row indices: 1 4 7 8 9 14
+
+Column: 15, number of entries: 6, with row indices in Ai [100 ... 105]:
+ row indices: 3 4 7 15 16 18
+
+Column: 16, number of entries: 4, with row indices in Ai [106 ... 109]:
+ row indices: 4 7 15 16
+
+Column: 17, number of entries: 9, with row indices in Ai [110 ... 118]:
+ row indices: 0 1 5 7 9 13 17 18 19
+
+Column: 18, number of entries: 9, with row indices in Ai [119 ... 127]:
+ row indices: 0 3 7 9 10 15 17 18 19
+
+Column: 19, number of entries: 9, with row indices in Ai [128 ... 136]:
+ row indices: 0 3 6 10 17 18 19 20 21
+
+Column: 20, number of entries: 6, with row indices in Ai [137 ... 142]:
+ row indices: 2 10 19 20 21 22
+
+Column: 21, number of entries: 9, with row indices in Ai [143 ... 151]:
+ row indices: 0 2 6 10 11 19 20 21 22
+
+Column: 22, number of entries: 4, with row indices in Ai [152 ... 155]:
+ row indices: 2 20 21 22
+
+Column: 23, number of entries: 4, with row indices in Ai [156 ... 159]:
+ row indices: 6 11 12 23
+
+Plot of input matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . X X . . . . . X X . . . X X X . X . .
+ 1: . X . . . . . . X X . . . X X . . X . . . . . .
+ 2: . . X . . . X . . . . X . . . . . . . . X X X .
+ 3: . . . X . . . X . . X . . . . X . . X X . . . .
+ 4: . . . . X . . X . X . . . . X X X . . . . . . .
+ 5: X . . . . X X . . . . . X X . . . X . . . . . .
+ 6: X . X . . X X . . . . X X . . . . . . X . X . X
+ 7: . . . X X . . X . X . . . . X X X X X . . . . .
+ 8: . X . . . . . . X X . . . . X . . . . . . . . .
+ 9: . X . . X . . X X X . . . X X . . X X . . . . .
+10: . . . X . . . . . . X . . . . . . . X X X X . .
+11: . . X . . . X . . . . X X . . . . . . . . X . X
+12: X . . . . X X . . . . X X . . . . . . . . . . X
+13: X X . . . X . . . X . . . X . . . X . . . . . .
+14: . X . . X . . X X X . . . . X . . . . . . . . .
+15: . . . X X . . X . . . . . . . X X . X . . . . .
+16: . . . . X . . X . . . . . . . X X . . . . . . .
+17: X X . . . X . X . X . . . X . . . X X X . . . .
+18: X . . X . . . X . X X . . . . X . X X X . . . .
+19: X . . X . . X . . . X . . . . . . X X X X X . .
+20: . . X . . . . . . . X . . . . . . . . X X X X .
+21: X . X . . . X . . . X X . . . . . . . X X X X .
+22: . . X . . . . . . . . . . . . . . . . . X X X .
+23: . . . . . . X . . . . X X . . . . . . . . . . X
+return value from amd_l_order: 0 (should be 0)
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 3032
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+Permutation vector:
+ 22 20 10 23 12 5 16 8 14 4 15 7 1 9 13 17 0 2 3 6 11 18 21 19
+
+Inverse permutation vector:
+ 16 12 17 18 9 5 19 11 7 13 2 20 4 14 8 10 6 15 21 23 1 22 0 3
+
+
+Plot of permuted matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X X . . . . . . . . . . . . . . . X . . . . X .
+ 1: X X X . . . . . . . . . . . . . . X . . . . X X
+ 2: . X X . . . . . . . . . . . . . . . X . . X X X
+ 3: . . . X X . . . . . . . . . . . . . . X X . . .
+ 4: . . . X X X . . . . . . . . . . X . . X X . . .
+ 5: . . . . X X . . . . . . . . X X X . . X . . . .
+ 6: . . . . . . X . . X X X . . . . . . . . . . . .
+ 7: . . . . . . . X X . . . X X . . . . . . . . . .
+ 8: . . . . . . . X X X . X X X . . . . . . . . . .
+ 9: . . . . . . X . X X X X . X . . . . . . . . . .
+10: . . . . . . X . . X X X . . . . . . X . . X . .
+11: . . . . . . X . X X X X . X . X . . X . . X . .
+12: . . . . . . . X X . . . X X X X . . . . . . . .
+13: . . . . . . . X X X . X X X X X . . . . . X . .
+14: . . . . . X . . . . . . X X X X X . . . . . . .
+15: . . . . . X . . . . . X X X X X X . . . . X . X
+16: . . . . X X . . . . . . . . X X X . . X . X X X
+17: X X . . . . . . . . . . . . . . . X . X X . X .
+18: . . X . . . . . . . X X . . . . . . X . . X . X
+19: . . . X X X . . . . . . . . . . X X . X X . X X
+20: . . . X X . . . . . . . . . . . . X . X X . X .
+21: . . X . . . . . . . X X . X . X X . X . . X . X
+22: X X X . . . . . . . . . . . . . X X . X X . X X
+23: . X X . . . . . . . . . . . . X X . X X . X X X
diff --git a/AMD/Demo/amd_simple.c b/AMD/Demo/amd_simple.c
new file mode 100644
index 0000000..2eae945
--- /dev/null
+++ b/AMD/Demo/amd_simple.c
@@ -0,0 +1,23 @@
+/* ------------------------------------------------------------------------- */
+/* AMD Copyright (c) by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+#include <stdio.h>
+#include "amd.h"
+
+int n = 5 ;
+int Ap [ ] = { 0, 2, 6, 10, 12, 14} ;
+int Ai [ ] = { 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 } ;
+int P [5] ;
+
+int main (void)
+{
+ int k ;
+ (void) amd_order (n, Ap, Ai, P, (double *) NULL, (double *) NULL) ;
+ for (k = 0 ; k < n ; k++) printf ("P [%d] = %d\n", k, P [k]) ;
+ return (0) ;
+}
+
diff --git a/AMD/Demo/amd_simple.out b/AMD/Demo/amd_simple.out
new file mode 100644
index 0000000..08a04e0
--- /dev/null
+++ b/AMD/Demo/amd_simple.out
@@ -0,0 +1,5 @@
+P [0] = 0
+P [1] = 3
+P [2] = 2
+P [3] = 4
+P [4] = 1
diff --git a/AMD/Doc/AMD_UserGuide.bib b/AMD/Doc/AMD_UserGuide.bib
new file mode 100644
index 0000000..03fbfa8
--- /dev/null
+++ b/AMD/Doc/AMD_UserGuide.bib
@@ -0,0 +1,98 @@
+ at string{SIREV = "{SIAM} Review"}
+ at string{SIMAX = "{SIAM} J. Matrix Anal. Applic."}
+ at string{SIAMJSC = "{SIAM} J. Sci. Comput."}
+ at string{TOMS = "{ACM} Trans. Math. Softw."}
+
+ at article{schu:01,
+ author = {J. Schulze},
+ title = {Towards a tighter coupling of bottom-up and top-down sparse matrix ordering methods},
+ journal = {BIT},
+ volume = {41},
+ number = {4},
+ pages = "800--841",
+ year = {2001}
+ }
+
+ at article{GeorgeLiu89,
+ author={George, A. and Liu, J. W. H.},
+ year={1989},
+ title={The Evolution of the Minimum Degree Ordering Algorithm},
+ journal=SIREV,
+ volume={31},
+ number={1},
+ pages={1--19}}
+
+ at article{AmestoyDavisDuff96,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={An approximate minimum degree ordering algorithm},
+ journal=SIMAX,
+ year={1996}
+ ,volume={17}
+ ,number={4}
+ ,pages={886-905}
+ }
+
+ at article{AmestoyDavisDuff04,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={Algorithm 837: An approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={381-388}
+ }
+
+ at misc{hsl:2002,
+ author = {HSL},
+ title = "{HSL} 2002: {A} collection of {F}ortran codes for large
+ scale scientific computation",
+ note = {{\tt www.cse.clrc.ac.uk/nag/hsl}},
+ year = 2002}
+
+
+ at article{RothbergEisenstat98,
+ author={Rothberg, E. and Eisenstat, S. C.},
+ title={Node selection strategies for bottom-up sparse matrix orderings},
+ journal=SIMAX,
+ year={1998}
+ ,volume={19}
+ ,number={3}
+ ,pages={682-695}
+ }
+
+ at article{KarypisKumar98e,
+ author={Karypis, G. and Kumar, V.},
+ title={A fast and high quality multilevel scheme for partitioning irregular graphs},
+ journal=SIAMJSC,
+ year={1998}
+ ,volume={20}
+ ,pages={359-392}
+ }
+
+ at article{Chaco,
+ author={B. Hendrickson and E. Rothberg},
+ title={Improving the runtime and quality of nested dissection ordering},
+ journal=SIAMJSC,
+ year={1999}
+ ,volume={20}
+ ,pages={468--489}
+ }
+
+ at article{PellegriniRomanAmestoy00,
+ author={Pellegrini, F. and Roman, J. and Amestoy, P.},
+ title={Hybridizing nested dissection and halo approximate minimum degree for efficient sparse matrix ordering},
+ journal={Concurrency: Practice and Experience},
+ year={2000}
+ ,volume={12}
+ ,pages={68-84}
+ }
+
+ at article{DavisGilbertLarimoreNg04,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={A column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,pages={353-376}
+ }
+
diff --git a/AMD/Doc/AMD_UserGuide.pdf b/AMD/Doc/AMD_UserGuide.pdf
new file mode 100644
index 0000000..c6c29fe
Binary files /dev/null and b/AMD/Doc/AMD_UserGuide.pdf differ
diff --git a/AMD/Doc/AMD_UserGuide.tex b/AMD/Doc/AMD_UserGuide.tex
new file mode 100644
index 0000000..9381142
--- /dev/null
+++ b/AMD/Doc/AMD_UserGuide.tex
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+\documentclass[11pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+%------------------------------------------------------------------------------
+\begin{document}
+%------------------------------------------------------------------------------
+
+\title{AMD Version 2.2 User Guide}
+\author{Patrick R. Amestoy\thanks{ENSEEIHT-IRIT,
+2 rue Camichel 31017 Toulouse, France.
+email: amestoy at enseeiht.fr. http://www.enseeiht.fr/$\sim$amestoy.}
+\and Timothy A. Davis\thanks{
+Dept.~of Computer and Information Science and Engineering,
+Univ.~of Florida, Gainesville, FL, USA.
+email: davis at cise.ufl.edu.
+http://www.cise.ufl.edu/$\sim$davis.
+This work was supported by the National
+Science Foundation, under grants ASC-9111263, DMS-9223088, and CCR-0203270.
+Portions of the work were done while on sabbatical at Stanford University
+and Lawrence Berkeley National Laboratory (with funding from Stanford
+University and the SciDAC program).
+}
+\and Iain S. Duff\thanks{Rutherford Appleton Laboratory, Chilton, Didcot,
+Oxon OX11 0QX, England. email: i.s.duff at rl.ac.uk.
+http://www.numerical.rl.ac.uk/people/isd/isd.html.
+This work was supported by the EPSRC under grant GR/R46441.
+}}
+
+\date{May 31, 2007}
+\maketitle
+
+%------------------------------------------------------------------------------
+\begin{abstract}
+AMD is a set of routines that implements the approximate minimum degree ordering
+algorithm to permute sparse matrices prior to
+numerical factorization.
+There are versions written in both C and Fortran 77.
+A MATLAB interface is included.
+\end{abstract}
+%------------------------------------------------------------------------------
+
+Technical report TR-04-002 (revised), CISE Department, University of Florida,
+Gainesville, FL, 2007.
+
+AMD Version 2.2, Copyright\copyright 2007 by Timothy A.
+Davis, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved.
+AMD is available under alternate licences; contact T. Davis for details.
+
+{\bf AMD License:}
+ Your use or distribution of AMD or any modified version of
+ AMD implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+{\bf Availability:}
+ http://www.cise.ufl.edu/research/sparse/amd
+
+{\bf Acknowledgments:}
+
+ This work was supported by the National Science Foundation, under
+ grants ASC-9111263 and DMS-9223088 and CCR-0203270.
+ The conversion to C, the addition of the elimination tree
+ post-ordering, and the handling of dense rows and columns
+ were done while Davis was on sabbatical at
+ Stanford University and Lawrence Berkeley National Laboratory.
+
+%------------------------------------------------------------------------------
+\newpage
+\section{Overview}
+%------------------------------------------------------------------------------
+
+AMD is a set of routines for preordering a sparse matrix prior to
+numerical factorization. It uses an approximate minimum degree ordering
+algorithm \cite{AmestoyDavisDuff96,AmestoyDavisDuff04}
+to find a permutation matrix $\m{P}$
+so that the Cholesky factorization $\m{PAP}\tr=\m{LL}\tr$ has fewer
+(often much fewer) nonzero entries than the Cholesky factorization of $\m{A}$.
+The algorithm is typically much faster than other ordering methods
+and minimum degree ordering
+algorithms that compute an exact degree \cite{GeorgeLiu89}.
+Some methods, such as approximate deficiency
+\cite{RothbergEisenstat98} and graph-partitioning based methods
+\cite{Chaco,KarypisKumar98e,PellegriniRomanAmestoy00,schu:01}
+can produce better orderings, depending on the matrix.
+
+The algorithm starts with an undirected graph representation of a
+symmetric sparse matrix $\m{A}$. Node $i$ in the graph corresponds to row
+and column $i$ of the matrix, and there is an edge $(i,j)$ in the graph if
+$a_{ij}$ is nonzero.
+The degree of a node is initialized to the number of off-diagonal nonzeros
+in row $i$, which is the size of the set of nodes
+adjacent to $i$ in the graph.
+
+The selection of a pivot $a_{ii}$ from the diagonal of $\m{A}$ and the first
+step of Gaussian elimination corresponds to one step of graph elimination.
+Numerical fill-in causes new nonzero entries in the matrix
+(fill-in refers to
+nonzeros in $\m{L}$ that are not in $\m{A}$).
+Node $i$ is eliminated and edges are added to its neighbors
+so that they form a clique (or {\em element}). To reduce fill-in,
+node $i$ is selected as the node of least degree in the graph.
+This process repeats until the graph is eliminated.
+
+The clique is represented implicitly. Rather than listing all the
+new edges in the graph, a single list of nodes is kept which represents
+the clique. This list corresponds to the nonzero pattern of the first
+column of $\m{L}$. As the elimination proceeds, some of these cliques
+become subsets of subsequent cliques, and are removed. This graph
+can be stored in place, that is
+using the same amount of memory as the original graph.
+
+The most costly part of the minimum degree algorithm is the recomputation
+of the degrees of nodes adjacent to the current pivot element.
+Rather than keep track of the exact degree, the approximate minimum degree
+algorithm finds an upper bound on the degree that is easier to compute.
+For nodes of least degree, this bound tends to be tight. Using the
+approximate degree instead of the exact degree leads to a substantial savings
+in run time, particularly for very irregularly structured matrices.
+It has no effect on the quality of the ordering.
+
+In the C version of AMD, the elimination phase is followed by an
+elimination tree post-ordering. This has no effect on fill-in, but
+reorganizes the ordering so that the subsequent numerical factorization is
+more efficient. It also includes a pre-processing phase in which nodes of
+very high degree are removed (without causing fill-in), and placed last in the
+permutation $\m{P}$. This reduces the run time substantially if the matrix
+has a few rows with many nonzero entries, and has little effect on the quality
+of the ordering.
+The C version operates on the
+symmetric nonzero pattern of $\m{A}+\m{A}\tr$, so it can be given
+an unsymmetric matrix, or either the lower or upper triangular part of
+a symmetric matrix.
+
+The two Fortran versions of AMD are essentially identical to two versions of
+the AMD algorithm discussed in an earlier paper \cite{AmestoyDavisDuff96}
+(approximate minimum external degree, both with and without aggressive
+absorption).
+For a discussion of the long history of the minimum degree algorithm,
+see \cite{GeorgeLiu89}.
+
+%------------------------------------------------------------------------------
+\section{Availability}
+%------------------------------------------------------------------------------
+
+In addition to appearing as a Collected Algorithm of the ACM, \newline
+AMD is available at http://www.cise.ufl.edu/research/sparse.
+The Fortran version is available as the routine {\tt MC47} in HSL
+(formerly the Harwell Subroutine Library) \cite{hsl:2002}.
+
+%------------------------------------------------------------------------------
+\section{Using AMD in MATLAB}
+%------------------------------------------------------------------------------
+
+The MATLAB function {\tt amd} is now a built-in function in MATLAB 7.3
+(R2006b). The built-in {\tt amd} and the {\tt amd2} function provided here
+differ in how the optional parameters are passed
+(the 2nd input parameter).
+
+To use AMD2 in MATLAB, you must first compile the AMD2 mexFunction.
+Just type {\tt make} in the Unix system shell, while in the {\tt AMD/MATLAB}
+directory. You can also type {\tt amd\_make} in MATLAB, while in the
+{\tt AMD/MATLAB} directory. Place the {\tt AMD/MATLAB} directory in your
+MATLAB path. This can be done on any system with MATLAB, including Windows.
+See Section~\ref{Install} for more details on how to install AMD.
+
+The MATLAB statement {\tt p=amd(A)} finds a permutation vector {\tt p} such
+that the Cholesky factorization {\tt chol(A(p,p))} is typically sparser than
+{\tt chol(A)}.
+If {\tt A} is unsymmetric, {\tt amd(A)} is identical to {\tt amd(A+A')}
+(ignoring numerical cancellation).
+If {\tt A} is not symmetric positive definite,
+but has substantial diagonal entries and a mostly symmetric nonzero pattern,
+then this ordering is also suitable for LU factorization. A partial pivoting
+threshold may be required to prevent pivots from being selected off the
+diagonal, such as the statement {\tt [L,U,P] = lu (A (p,p), 0.1)}.
+Type {\tt help lu} for more details.
+The statement {\tt [L,U,P,Q] = lu (A (p,p))} in MATLAB 6.5 is
+not suitable, however, because it uses UMFPACK Version 4.0 and thus
+does not attempt to select pivots from the diagonal.
+UMFPACK Version 4.1 in MATLAB 7.0 and later
+uses several strategies, including a symmetric pivoting strategy, and
+will give you better results if you want to factorize an unsymmetric matrix
+of this type. Refer to the UMFPACK User Guide for more details, at
+http://www.cise.ufl.edu/research/sparse/umfpack.
+
+The AMD mexFunction is much faster than the built-in MATLAB symmetric minimum
+degree ordering methods, SYMAMD and SYMMMD. Its ordering quality is
+comparable to SYMAMD, and better than SYMMMD
+\cite{DavisGilbertLarimoreNg04}.
+
+An optional input argument can be used to modify the control parameters for
+AMD (aggressive absorption, dense row/column handling, and printing of
+statistics). An optional output
+argument provides statistics on the ordering, including an analysis of the
+fill-in and the floating-point operation count for a subsequent factorization.
+For more details (once AMD is installed),
+type {\tt help amd} in the MATLAB command window.
+
+%------------------------------------------------------------------------------
+\section{Using AMD in a C program}
+\label{Cversion}
+%------------------------------------------------------------------------------
+
+The C-callable AMD library consists of seven user-callable routines and one
+include file. There are two versions of each of the routines, with
+{\tt int} and {\tt long} integers.
+The routines with prefix
+{\tt amd\_l\_} use {\tt long} integer arguments; the others use
+{\tt int} integer arguments. If you compile AMD in the standard
+ILP32 mode (32-bit {\tt int}'s, {\tt long}'s, and pointers) then the versions
+are essentially identical. You will be able to solve problems using up to 2GB
+of memory. If you compile AMD in the standard LP64 mode, the size of an
+{\tt int} remains 32-bits, but the size of a {\tt long} and a pointer both get
+promoted to 64-bits.
+
+The following routines are fully described in Section~\ref{Primary}:
+
+\begin{itemize}
+\item {\tt amd\_order}
+({\tt long} version: {\tt amd\_l\_order})
+ {\footnotesize
+ \begin{verbatim}
+ #include "amd.h"
+ int n, Ap [n+1], Ai [nz], P [n] ;
+ double Control [AMD_CONTROL], Info [AMD_INFO] ;
+ int result = amd_order (n, Ap, Ai, P, Control, Info) ;
+ \end{verbatim}
+ }
+ Computes the approximate minimum degree ordering of an $n$-by-$n$ matrix
+ $\m{A}$. Returns a permutation vector {\tt P} of size {\tt n}, where
+ {\tt P[k] = i} if row and column {\tt i} are the {\tt k}th row and
+ column in the permuted matrix.
+ This routine allocates its own memory of size $1.2e+9n$ integers,
+ where $e$ is the number of nonzeros in $\m{A}+\m{A}\tr$.
+ It computes statistics about the matrix $\m{A}$, such as the symmetry of
+ its nonzero pattern, the number of nonzeros in $\m{L}$,
+ and the number of floating-point operations required for Cholesky and LU
+ factorizations (which are returned in the {\tt Info} array).
+ The user's input matrix is not modified.
+ It returns {\tt AMD\_OK} if successful,
+ {\tt AMD\_OK\_BUT\_JUMBLED} if successful (but the matrix had unsorted
+ and/or duplicate row indices),
+ {\tt AMD\_INVALID} if the matrix is invalid,
+ {\tt AMD\_OUT\_OF\_MEMORY} if out of memory.
+
+\item {\tt amd\_defaults}
+({\tt long} version: {\tt amd\_l\_defaults})
+ {\footnotesize
+ \begin{verbatim}
+ #include "amd.h"
+ double Control [AMD_CONTROL] ;
+ amd_defaults (Control) ;
+ \end{verbatim}
+ }
+ Sets the default control parameters in the {\tt Control} array. These can
+ then be modified as desired before passing the array to the other AMD
+ routines.
+
+\item {\tt amd\_control}
+({\tt long} version: {\tt amd\_l\_control})
+ {\footnotesize
+ \begin{verbatim}
+ #include "amd.h"
+ double Control [AMD_CONTROL] ;
+ amd_control (Control) ;
+ \end{verbatim}
+ }
+ Prints a description of the control parameters, and their values.
+
+\item {\tt amd\_info}
+({\tt long} version: {\tt amd\_l\_info})
+ {\footnotesize
+ \begin{verbatim}
+ #include "amd.h"
+ double Info [AMD_INFO] ;
+ amd_info (Info) ;
+ \end{verbatim}
+ }
+ Prints a description of the statistics computed by AMD, and their values.
+
+\item {\tt amd\_valid}
+({\tt long} version: {\tt amd\_valid})
+ {\footnotesize
+ \begin{verbatim}
+ #include "amd.h"
+ int n, Ap [n+1], Ai [nz] ;
+ int result = amd_valid (n, n, Ap, Ai) ;
+ \end{verbatim}
+ }
+ Returns {\tt AMD\_OK} or {\tt AMD\_OK\_BUT\_JUMBLED}
+ if the matrix is valid as input to {\tt amd\_order};
+ the latter is returned if the matrix has unsorted and/or duplicate
+ row indices in one or more columns.
+ Returns {\tt AMD\_INVALID} if the matrix cannot be passed to
+ {\tt amd\_order}.
+ For {\tt amd\_order}, the matrix must
+ also be square. The first two arguments are the number of rows and the
+ number of columns of the matrix. For its use in AMD, these must both
+ equal {\tt n}.
+
+\item {\tt amd\_2}
+({\tt long} version: {\tt amd\_l2})
+ AMD ordering kernel. It is faster than {\tt amd\_order}, and
+ can be called by the user, but it is difficult to use.
+ It does not check its inputs for errors.
+ It does not require the columns of its input matrix to be sorted,
+ but it destroys the matrix on output. Additional workspace must be passed.
+ Refer to the source file {\tt AMD/Source/amd\_2.c} for a description.
+
+\end{itemize}
+
+The nonzero pattern of the matrix $\m{A}$ is represented in compressed column
+form.
+For an $n$-by-$n$ matrix $\m{A}$ with {\tt nz} nonzero entries, the
+representation consists of two arrays: {\tt Ap} of size {\tt n+1} and {\tt Ai}
+of size {\tt nz}. The row indices of entries in column {\tt j} are stored in
+ {\tt Ai[Ap[j]} $\ldots$ {\tt Ap[j+1]-1]}.
+For {\tt amd\_order},
+if duplicate row indices are present, or if the row indices in any given
+column are not sorted in ascending order, then {\tt amd\_order} creates
+an internal copy of the matrix with sorted rows and no duplicate entries,
+and orders the copy. This adds slightly to the time and memory usage of
+{\tt amd\_order}, but is not an error condition.
+
+The matrix is 0-based, and thus
+row indices must be in the range {\tt 0} to {\tt n-1}.
+The first entry {\tt Ap[0]} must be zero.
+The total number of entries in the matrix is thus {\tt nz = Ap[n]}.
+
+The matrix must be square, but it does not need to be symmetric.
+The {\tt amd\_order} routine constructs the nonzero pattern of
+$\m{B} = \m{A}+\m{A}\tr$ (without forming $\m{A}\tr$ explicitly if
+$\m{A}$ has sorted columns and no duplicate entries),
+and then orders the matrix $\m{B}$. Thus, either the
+lower triangular part of $\m{A}$, the upper triangular part,
+or any combination may be passed. The transpose $\m{A}\tr$ may also be
+passed to {\tt amd\_order}.
+The diagonal entries may be present, but are ignored.
+
+%------------------------------------------------------------------------------
+\subsection{Control parameters}
+\label{control_param}
+%------------------------------------------------------------------------------
+
+Control parameters are set in an optional {\tt Control} array.
+It is optional in the sense that if
+a {\tt NULL} pointer is passed for the {\tt Control} input argument,
+then default control parameters are used.
+%
+\begin{itemize}
+\item {\tt Control[AMD\_DENSE]} (or {\tt Control(1)} in MATLAB):
+controls the threshold for ``dense''
+rows/columns. A dense row/column in $\m{A}+\m{A}\tr$
+can cause AMD to spend significant time
+in ordering the matrix. If {\tt Control[AMD\_DENSE]} $\ge 0$,
+rows/columns with
+more than {\tt Control[AMD\_DENSE]} $\sqrt{n}$ entries are ignored during
+the ordering, and placed last in the output order. The default
+value of {\tt Control[AMD\_DENSE]} is 10. If negative, no rows/columns
+are treated as ``dense.'' Rows/columns with 16 or fewer off-diagonal
+entries are never considered ``dense.''
+%
+\item {\tt Control[AMD\_AGGRESSIVE]} (or {\tt Control(2)} in MATLAB):
+controls whether or not to use
+aggressive absorption, in which a prior element is absorbed into the current
+element if it is a subset of the current element, even if it is not
+adjacent to the current pivot element (refer
+to \cite{AmestoyDavisDuff96,AmestoyDavisDuff04}
+for more details). The default value is nonzero,
+which means that aggressive absorption will be performed. This nearly always
+leads to a better ordering (because the approximate degrees are more
+accurate) and a lower execution time. There are cases where it can
+lead to a slightly worse ordering, however. To turn it off, set
+{\tt Control[AMD\_AGGRESSIVE]} to 0.
+%
+\end{itemize}
+
+Statistics are returned in the {\tt Info} array
+(if {\tt Info} is {\tt NULL}, then no statistics are returned).
+Refer to {\tt amd.h} file, for more details
+(14 different statistics are returned, so the list is not included here).
+
+%------------------------------------------------------------------------------
+\subsection{Sample C program}
+%------------------------------------------------------------------------------
+
+The following program, {\tt amd\_demo.c}, illustrates the basic use of AMD.
+See Section~\ref{Synopsis} for a short description
+of each calling sequence.
+
+{\footnotesize
+\begin{verbatim}
+#include <stdio.h>
+#include "amd.h"
+
+int n = 5 ;
+int Ap [ ] = { 0, 2, 6, 10, 12, 14} ;
+int Ai [ ] = { 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 } ;
+int P [5] ;
+
+int main (void)
+{
+ int k ;
+ (void) amd_order (n, Ap, Ai, P, (double *) NULL, (double *) NULL) ;
+ for (k = 0 ; k < n ; k++) printf ("P [%d] = %d\n", k, P [k]) ;
+ return (0) ;
+}
+\end{verbatim}
+}
+
+The {\tt Ap} and {\tt Ai} arrays represent the binary matrix
+\[
+\m{A} = \left[
+\begin{array}{rrrrr}
+ 1 & 1 & 0 & 0 & 0 \\
+ 1 & 1 & 1 & 0 & 1 \\
+ 0 & 1 & 1 & 1 & 0 \\
+ 0 & 0 & 1 & 1 & 0 \\
+ 0 & 1 & 1 & 0 & 1 \\
+\end{array}
+\right].
+\]
+The diagonal entries are ignored.
+%
+AMD constructs the pattern of $\m{A}+\m{A}\tr$,
+and returns a permutation vector of $(0, 3, 1, 4, 2)$.
+%
+Since the matrix is unsymmetric but with a mostly symmetric nonzero
+pattern, this would be a suitable permutation for an LU factorization of a
+matrix with this nonzero pattern and whose diagonal entries are not too small.
+The program uses default control settings and does not return any statistics
+about the ordering, factorization, or solution ({\tt Control} and {\tt Info}
+are both {\tt (double *) NULL}). It also ignores the status value returned by
+{\tt amd\_order}.
+
+More example programs are included with the AMD package.
+The {\tt amd\_demo.c} program provides a more detailed demo of AMD.
+Another example is the AMD mexFunction, {\tt amd\_mex.c}.
+
+%------------------------------------------------------------------------------
+\subsection{A note about zero-sized arrays}
+%------------------------------------------------------------------------------
+
+AMD uses several user-provided arrays of size {\tt n} or {\tt nz}.
+Either {\tt n} or {\tt nz} can be zero.
+If you attempt to {\tt malloc} an array of size zero,
+however, {\tt malloc} will return a null pointer which AMD will report
+as invalid. If you {\tt malloc} an array of
+size {\tt n} or {\tt nz} to pass to AMD, make sure that you handle the
+{\tt n} = 0 and {\tt nz = 0} cases correctly.
+
+%------------------------------------------------------------------------------
+\section{Synopsis of C-callable routines}
+\label{Synopsis}
+%------------------------------------------------------------------------------
+
+The matrix $\m{A}$ is {\tt n}-by-{\tt n} with {\tt nz} entries.
+
+{\footnotesize
+\begin{verbatim}
+#include "amd.h"
+int n, status, Ap [n+1], Ai [nz], P [n] ;
+double Control [AMD_CONTROL], Info [AMD_INFO] ;
+amd_defaults (Control) ;
+status = amd_order (n, Ap, Ai, P, Control, Info) ;
+amd_control (Control) ;
+amd_info (Info) ;
+status = amd_valid (n, n, Ap, Ai) ;
+\end{verbatim}
+}
+
+The {\tt amd\_l\_*} routines are identical, except that all {\tt int}
+arguments become {\tt long}:
+
+{\footnotesize
+\begin{verbatim}
+#include "amd.h"
+long n, status, Ap [n+1], Ai [nz], P [n] ;
+double Control [AMD_CONTROL], Info [AMD_INFO] ;
+amd_l_defaults (Control) ;
+status = amd_l_order (n, Ap, Ai, P, Control, Info) ;
+amd_l_control (Control) ;
+amd_l_info (Info) ;
+status = amd_l_valid (n, n, Ap, Ai) ;
+\end{verbatim}
+}
+
+%------------------------------------------------------------------------------
+\section{Using AMD in a Fortran program}
+%------------------------------------------------------------------------------
+
+Two Fortran versions of AMD are provided. The {\tt AMD} routine computes the
+approximate minimum degree ordering, using aggressive absorption. The
+{\tt AMDBAR} routine is identical, except that it does not perform aggressive
+absorption. The {\tt AMD} routine is essentially identical to the HSL
+routine {\tt MC47B/BD}.
+Note that earlier versions of the Fortran
+{\tt AMD} and {\tt AMDBAR} routines included an {\tt IOVFLO} argument,
+which is no longer present.
+
+In contrast to the C version, the Fortran routines require a symmetric
+nonzero pattern, with no diagonal entries present although the {\tt MC47A/AD}
+wrapper in HSL allows duplicates, ignores out-of-range entries, and only
+uses entries from the upper triangular part of the matrix. Although we
+have an experimental Fortran code for treating ``dense'' rows, the Fortran
+codes in this release do not treat
+``dense'' rows and columns of $\m{A}$ differently, and thus their run time
+can be high if there are a few dense rows and columns in the matrix.
+They do not perform a post-ordering of the elimination tree,
+compute statistics on the ordering, or check the validity of their input
+arguments. These facilities are provided by {\tt MC47A/AD} and other
+subroutines from HSL.
+Only one {\tt integer}
+version of each Fortran routine is provided.
+Both Fortran routines overwrite the user's input
+matrix, in contrast to the C version.
+%
+The C version does not return the elimination or assembly tree.
+The Fortran version returns an assembly tree;
+refer to the User Guide for details.
+The following is the syntax of the {\tt AMD} Fortran routine.
+The {\tt AMDBAR} routine is identical except for the routine name.
+
+{\footnotesize
+\begin{verbatim}
+ INTEGER N, IWLEN, PFREE, NCMPA, IW (IWLEN), PE (N), DEGREE (N), NV (N),
+ $ NEXT (N), LAST (N), HEAD (N), ELEN (N), W (N), LEN (N)
+ CALL AMD (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT,
+ $ LAST, HEAD, ELEN, DEGREE, NCMPA, W)
+ CALL AMDBAR (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT,
+ $ LAST, HEAD, ELEN, DEGREE, NCMPA, W)
+\end{verbatim}
+}
+
+The input matrix is provided to {\tt AMD} and {\tt AMDBAR}
+in three arrays, {\tt PE}, of size {\tt N},
+{\tt LEN}, of size {\tt N}, and {\tt IW}, of size {\tt IWLEN}. The size of
+{\tt IW} must be at least {\tt NZ+N}. The recommended size is
+{\tt 1.2*NZ + N}.
+On input, the indices of nonzero entries in row {\tt I} are stored in {\tt IW}.
+{\tt PE(I)} is the index in {\tt IW} of the start of row {\tt I}.
+{\tt LEN(I)} is the number of entries in row {\tt I}.
+The matrix is 1-based, with row and column indices in the range 1 to {\tt N}.
+Row {\tt I} is contained in
+{\tt IW (PE(I)} $\ldots \:$ {\tt PE(I) + LEN(I) - 1)}.
+The diagonal entries must not be present. The indices within each row must
+not contain any duplicates, but they need not be sorted. The rows
+themselves need not be in any particular order, and there may be empty space
+between the rows. If {\tt LEN(I)} is zero, then there are no off-diagonal
+entries in row {\tt I}, and {\tt PE(I)} is ignored. The integer
+{\tt PFREE} defines what part of {\tt IW} contains the user's input matrix,
+which is held in {\tt IW(1}~$\ldots~\:${\tt PFREE-1)}.
+The contents of {\tt IW} and {\tt LEN} are undefined on output,
+and {\tt PE} is modified to contain information about the ordering.
+
+As the algorithm proceeds, it modifies the {\tt IW} array, placing the
+pattern of the partially eliminated matrix in
+{\tt IW(PFREE} $\ldots \:${\tt IWLEN)}.
+If this space is exhausted, the space is compressed.
+The number of compressions performed on the {\tt IW} array is
+returned in the scalar {\tt NCMPA}. The value of {\tt PFREE} on output is the
+length of {\tt IW} required for no compressions to be needed.
+
+The output permutation is returned in the array {\tt LAST}, of size {\tt N}.
+If {\tt I=LAST(K)}, then {\tt I} is the {\tt K}th row in the permuted
+matrix. The inverse permutation is returned in the array {\tt ELEN}, where
+{\tt K=ELEN(I)} if {\tt I} is the {\tt K}th row in the permuted matrix.
+On output, the {\tt PE} and {\tt NV} arrays hold the assembly tree,
+a supernodal elimination tree that represents the relationship between
+columns of the Cholesky factor $\m{L}$.
+If {\tt NV(I)} $> 0$, then {\tt I} is a node in the assembly
+tree, and the parent of {\tt I} is {\tt -PE(I)}. If {\tt I} is a root of
+the tree, then {\tt PE(I)} is zero. The value of {\tt NV(I)} is the
+number of entries in the corresponding column of $\m{L}$, including the
+diagonal.
+If {\tt NV(I)} is zero, then {\tt I} is a non-principal node that is
+not in the assembly tree. Node {\tt -PE(I)} is the parent of node {\tt I}
+in a subtree, the root of which is a node in the assembly tree. All nodes
+in one subtree belong to the same supernode in the assembly tree.
+The other size {\tt N} arrays
+({\tt DEGREE}, {\tt HEAD}, {\tt NEXT}, and {\tt W}) are used as workspace,
+and are not defined on input or output.
+
+If you want to use a simpler user-interface and compute the elimination
+tree post-ordering, you should be able to call the C routines {\tt amd\_order}
+or {\tt amd\_l\_order} from a Fortran program. Just be sure to take into
+account the 0-based indexing in the {\tt P}, {\tt Ap}, and {\tt Ai} arguments
+to {\tt amd\_order} and {\tt amd\_l\_order}. A sample interface is provided
+in the files {\tt AMD/Demo/amd\_f77cross.f} and
+{\tt AMD/Demo/amd\_f77wrapper.c}. To compile the {\tt amd\_f77cross} program,
+type {\tt make cross} in the {\tt AMD/Demo} directory. The
+Fortran-to-C calling conventions are highly non-portable, so this example
+is not guaranteed to work with your compiler C and Fortran compilers.
+The output of {\tt amd\_f77cross} is in {\tt amd\_f77cross.out}.
+
+%------------------------------------------------------------------------------
+\section{Sample Fortran main program}
+%------------------------------------------------------------------------------
+
+The following program illustrates the basic usage of the Fortran version of AMD.
+The {\tt AP} and {\tt AI} arrays represent the binary matrix
+\[
+\m{A} = \left[
+\begin{array}{rrrrr}
+ 1 & 1 & 0 & 0 & 0 \\
+ 1 & 1 & 1 & 0 & 1 \\
+ 0 & 1 & 1 & 1 & 1 \\
+ 0 & 0 & 1 & 1 & 0 \\
+ 0 & 1 & 1 & 0 & 1 \\
+\end{array}
+\right]
+\]
+in a conventional 1-based column-oriented form,
+except that the diagonal entries are not present.
+The matrix has the same as nonzero pattern of $\m{A}+\m{A}\tr$ in the C
+program, in Section~\ref{Cversion}.
+The output permutation is $(4, 1, 3, 5, 2)$.
+It differs from the permutation returned by the C routine {\tt amd\_order}
+because a post-order of the elimination tree has not yet been performed.
+
+{\footnotesize
+\begin{verbatim}
+ INTEGER N, NZ, J, K, P, IWLEN, PFREE, NCMPA
+ PARAMETER (N = 5, NZ = 10, IWLEN = 17)
+ INTEGER AP (N+1), AI (NZ), LAST (N), PE (N), LEN (N), ELEN (N),
+ $ IW (IWLEN), DEGREE (N), NV (N), NEXT (N), HEAD (N), W (N)
+ DATA AP / 1, 2, 5, 8, 9, 11/
+ DATA AI / 2, 1,3,5, 2,4,5, 3, 2,3 /
+C load the matrix into the AMD workspace
+ DO 10 J = 1,N
+ PE (J) = AP (J)
+ LEN (J) = AP (J+1) - AP (J)
+10 CONTINUE
+ DO 20 P = 1,NZ
+ IW (P) = AI (P)
+20 CONTINUE
+ PFREE = NZ + 1
+C order the matrix (destroys the copy of A in IW, PE, and LEN)
+ CALL AMD (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT, LAST, HEAD,
+ $ ELEN, DEGREE, NCMPA, W)
+ DO 60 K = 1, N
+ PRINT 50, K, LAST (K)
+50 FORMAT ('P (',I2,') = ', I2)
+60 CONTINUE
+ END
+\end{verbatim}
+}
+
+The {\tt Demo} directory contains an example of how the C version
+may be called from a Fortran program, but this is highly non-portable.
+For this reason, it is placed in the {\tt Demo} directory, not in the
+primary {\tt Source} directory.
+
+%------------------------------------------------------------------------------
+\section{Installation}
+\label{Install}
+%------------------------------------------------------------------------------
+
+The following discussion assumes you have the {\tt make} program, either in
+Unix, or in Windows with Cygwin.
+
+System-dependent configurations are in the {\tt ../UFconfig/UFconfig.mk}
+file. You can edit that file to customize the compilation. The default
+settings will work on most systems.
+Sample configuration files are provided
+for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha.
+
+To compile and install the C-callable AMD library,
+go to the {\tt AMD} directory and type {\tt make}.
+The library will be placed in {\tt AMD/Lib/libamd.a}.
+Three demo programs of the AMD ordering routine will be compiled and tested in
+the {\tt AMD/Demo} directory.
+The outputs of these demo programs will then be compared with output
+files in the distribution.
+
+To compile and install the Fortran-callable AMD library,
+go to the {\tt AMD} directory and type {\tt make fortran}.
+The library will be placed in {\tt AMD/Lib/libamdf77.a}.
+A demo program will be compiled and tested in the {\tt AMD/Demo} directory.
+The output will be compared with an output file in the distribution.
+
+Typing {\tt make clean} will remove all but the final compiled libraries
+and demo programs. Typing {\tt make purge} or {\tt make distclean}
+removes all files not in the original distribution.
+If you compile AMD and then later change the {\tt ../UFconfig/UFconfig.mk} file
+then you should type {\tt make purge} and then {\tt make} to recompile.
+
+When you compile your program that uses the C-callable AMD library,
+you need to add the {\tt AMD/Lib/libamd.a} library
+and you need to tell your compiler to look in the
+{\tt AMD/Include} directory for include
+files. To compile a Fortran program that calls the Fortran AMD library,
+you need to add the {\tt AMD/Lib/libamdf77.a} library.
+See {\tt AMD/Demo/Makefile} for an example.
+
+If all you want to use is the AMD2 mexFunction in MATLAB, you can skip
+the use of the {\tt make} command entirely. Simply type
+{\tt amd\_make} in MATLAB while in the {\tt AMD/MATLAB} directory.
+This works on any system with MATLAB, including Windows.
+Alternately, type {\tt make} in the {\tt AMD/MATLAB} directory,
+or just use the built-in {\tt amd} in MATLAB 7.3 or later.
+
+If you have MATLAB 7.2 or earlier, you must first edit UFconfig/UFconfig.h to
+remove the "-largeArrayDims" option from the MEX command, prior to
+{\tt make mex} or {\tt make} in the MATLAB directory
+(or just use {\tt amd\_make.m} inside MATLAB.
+
+If you are including AMD as a subset of a larger library and do not want
+to link the C standard I/O library, or if you simply do not need to use
+them, you can safely remove the {\tt amd\_control.c} and {\tt amd\_info.c}
+files. Similarly, if you use default parameters (or define your
+own {\tt Control} array), then you can exclude the {\tt amd\_defaults.c}
+file.
+Each of these files contains the user-callable routines of the same
+name. None of these auxiliary routines are directly called by
+{\tt amd\_order}.
+The {\tt amd\_dump.c} file contains debugging routines
+that are neither used nor compiled unless debugging is enabled.
+The {\tt amd\_internal.h} file must be edited to enable debugging;
+refer to the instructions in that file.
+The bare minimum files required to use just {\tt amd\_order} are
+{\tt amd.h} and {\tt amd\_internal.h}
+in the {\tt Include} directory,
+and
+{\tt amd\_1.c},
+{\tt amd\_2.c},
+{\tt amd\_aat.c},
+{\tt amd\_global.c},
+{\tt and\_order.c},
+{\tt amd\_postorder.c},
+{\tt amd\_post\_tree.c},
+{\tt amd\_preprocess.c},
+and
+{\tt amd\_valid.c}
+in the {\tt Source} directory.
+
+%------------------------------------------------------------------------------
+\newpage
+\section{The AMD routines}
+\label{Primary}
+%------------------------------------------------------------------------------
+
+The file {\tt AMD/Include/amd.h} listed below
+describes each user-callable routine in the C version of AMD,
+and gives details on their use.
+
+{\footnotesize
+\begin{verbatim}
+
+/* ========================================================================= */
+/* === AMD: approximate minimum degree ordering =========================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* AMD finds a symmetric ordering P of a matrix A so that the Cholesky
+ * factorization of P*A*P' has fewer nonzeros and takes less work than the
+ * Cholesky factorization of A. If A is not symmetric, then it performs its
+ * ordering on the matrix A+A'. Two sets of user-callable routines are
+ * provided, one for int integers and the other for UF_long integers.
+ *
+ * The method is based on the approximate minimum degree algorithm, discussed
+ * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm",
+ * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp.
+ * 886-905, 1996. This package can perform both the AMD ordering (with
+ * aggressive absorption), and the AMDBAR ordering (without aggressive
+ * absorption) discussed in the above paper. This package differs from the
+ * Fortran codes discussed in the paper:
+ *
+ * (1) it can ignore "dense" rows and columns, leading to faster run times
+ * (2) it computes the ordering of A+A' if A is not symmetric
+ * (3) it is followed by a depth-first post-ordering of the assembly tree
+ * (or supernodal elimination tree)
+ *
+ * For historical reasons, the Fortran versions, amd.f and amdbar.f, have
+ * been left (nearly) unchanged. They compute the identical ordering as
+ * described in the above paper.
+ */
+
+#ifndef AMD_H
+#define AMD_H
+
+/* make it easy for C++ programs to include AMD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* get the definition of size_t: */
+#include <stddef.h>
+
+/* define UF_long */
+#include "UFconfig.h"
+
+int amd_order /* returns AMD_OK, AMD_OK_BUT_JUMBLED,
+ * AMD_INVALID, or AMD_OUT_OF_MEMORY */
+(
+ int n, /* A is n-by-n. n must be >= 0. */
+ const int Ap [ ], /* column pointers for A, of size n+1 */
+ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */
+ int P [ ], /* output permutation, of size n */
+ double Control [ ], /* input Control settings, of size AMD_CONTROL */
+ double Info [ ] /* output Info statistics, of size AMD_INFO */
+) ;
+
+UF_long amd_l_order /* see above for description of arguments */
+(
+ UF_long n,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ UF_long P [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+/* Input arguments (not modified):
+ *
+ * n: the matrix A is n-by-n.
+ * Ap: an int/UF_long array of size n+1, containing column pointers of A.
+ * Ai: an int/UF_long array of size nz, containing the row indices of A,
+ * where nz = Ap [n].
+ * Control: a double array of size AMD_CONTROL, containing control
+ * parameters. Defaults are used if Control is NULL.
+ *
+ * Output arguments (not defined on input):
+ *
+ * P: an int/UF_long array of size n, containing the output permutation. If
+ * row i is the kth pivot row, then P [k] = i. In MATLAB notation,
+ * the reordered matrix is A (P,P).
+ * Info: a double array of size AMD_INFO, containing statistical
+ * information. Ignored if Info is NULL.
+ *
+ * On input, the matrix A is stored in column-oriented form. The row indices
+ * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1].
+ *
+ * If the row indices appear in ascending order in each column, and there
+ * are no duplicate entries, then amd_order is slightly more efficient in
+ * terms of time and memory usage. If this condition does not hold, a copy
+ * of the matrix is created (where these conditions do hold), and the copy is
+ * ordered. This feature is new to v2.0 (v1.2 and earlier required this
+ * condition to hold for the input matrix).
+ *
+ * Row indices must be in the range 0 to
+ * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros
+ * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n].
+ * The matrix does not need to be symmetric, and the diagonal does not need to
+ * be present (if diagonal entries are present, they are ignored except for
+ * the output statistic Info [AMD_NZDIAG]). The arrays Ai and Ap are not
+ * modified. This form of the Ap and Ai arrays to represent the nonzero
+ * pattern of the matrix A is the same as that used internally by MATLAB.
+ * If you wish to use a more flexible input structure, please see the
+ * umfpack_*_triplet_to_col routines in the UMFPACK package, at
+ * http://www.cise.ufl.edu/research/sparse/umfpack.
+ *
+ * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the
+ * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0
+ * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these
+ * restrictions are not met, AMD returns AMD_INVALID.
+ *
+ * AMD returns:
+ *
+ * AMD_OK if the matrix is valid and sufficient memory can be allocated to
+ * perform the ordering.
+ *
+ * AMD_OUT_OF_MEMORY if not enough memory can be allocated.
+ *
+ * AMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is
+ * NULL.
+ *
+ * AMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate
+ * entries, but was otherwise valid.
+ *
+ * The AMD routine first forms the pattern of the matrix A+A', and then
+ * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of
+ * the original is the kth pivotal row. In MATLAB notation, the permuted
+ * matrix is A (P,P), except that 0-based indexing is used instead of the
+ * 1-based indexing in MATLAB.
+ *
+ * The Control array is used to set various parameters for AMD. If a NULL
+ * pointer is passed, default values are used. The Control array is not
+ * modified.
+ *
+ * Control [AMD_DENSE]: controls the threshold for "dense" rows/columns.
+ * A dense row/column in A+A' can cause AMD to spend a lot of time in
+ * ordering the matrix. If Control [AMD_DENSE] >= 0, rows/columns
+ * with more than Control [AMD_DENSE] * sqrt (n) entries are ignored
+ * during the ordering, and placed last in the output order. The
+ * default value of Control [AMD_DENSE] is 10. If negative, no
+ * rows/columns are treated as "dense". Rows/columns with 16 or
+ * fewer off-diagonal entries are never considered "dense".
+ *
+ * Control [AMD_AGGRESSIVE]: controls whether or not to use aggressive
+ * absorption, in which a prior element is absorbed into the current
+ * element if is a subset of the current element, even if it is not
+ * adjacent to the current pivot element (refer to Amestoy, Davis,
+ * & Duff, 1996, for more details). The default value is nonzero,
+ * which means to perform aggressive absorption. This nearly always
+ * leads to a better ordering (because the approximate degrees are
+ * more accurate) and a lower execution time. There are cases where
+ * it can lead to a slightly worse ordering, however. To turn it off,
+ * set Control [AMD_AGGRESSIVE] to 0.
+ *
+ * Control [2..4] are not used in the current version, but may be used in
+ * future versions.
+ *
+ * The Info array provides statistics about the ordering on output. If it is
+ * not present, the statistics are not returned. This is not an error
+ * condition.
+ *
+ * Info [AMD_STATUS]: the return value of AMD, either AMD_OK,
+ * AMD_OK_BUT_JUMBLED, AMD_OUT_OF_MEMORY, or AMD_INVALID.
+ *
+ * Info [AMD_N]: n, the size of the input matrix
+ *
+ * Info [AMD_NZ]: the number of nonzeros in A, nz = Ap [n]
+ *
+ * Info [AMD_SYMMETRY]: the symmetry of the matrix A. It is the number
+ * of "matched" off-diagonal entries divided by the total number of
+ * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also
+ * an entry, for any pair (i,j) for which i != j. In MATLAB notation,
+ * S = spones (A) ;
+ * B = tril (S, -1) + triu (S, 1) ;
+ * symmetry = nnz (B & B') / nnz (B) ;
+ *
+ * Info [AMD_NZDIAG]: the number of entries on the diagonal of A.
+ *
+ * Info [AMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the
+ * diagonal. If A is perfectly symmetric (Info [AMD_SYMMETRY] = 1)
+ * with a fully nonzero diagonal, then Info [AMD_NZ_A_PLUS_AT] = nz-n
+ * (the smallest possible value). If A is perfectly unsymmetric
+ * (Info [AMD_SYMMETRY] = 0, for an upper triangular matrix, for
+ * example) with no diagonal, then Info [AMD_NZ_A_PLUS_AT] = 2*nz
+ * (the largest possible value).
+ *
+ * Info [AMD_NDENSE]: the number of "dense" rows/columns of A+A' that were
+ * removed from A prior to ordering. These are placed last in the
+ * output order P.
+ *
+ * Info [AMD_MEMORY]: the amount of memory used by AMD, in bytes. In the
+ * current version, this is 1.2 * Info [AMD_NZ_A_PLUS_AT] + 9*n
+ * times the size of an integer. This is at most 2.4nz + 9n. This
+ * excludes the size of the input arguments Ai, Ap, and P, which have
+ * a total size of nz + 2*n + 1 integers.
+ *
+ * Info [AMD_NCMPA]: the number of garbage collections performed.
+ *
+ * Info [AMD_LNZ]: the number of nonzeros in L (excluding the diagonal).
+ * This is a slight upper bound because mass elimination is combined
+ * with the approximate degree update. It is a rough upper bound if
+ * there are many "dense" rows/columns. The rest of the statistics,
+ * below, are also slight or rough upper bounds, for the same reasons.
+ * The post-ordering of the assembly tree might also not exactly
+ * correspond to a true elimination tree postordering.
+ *
+ * Info [AMD_NDIV]: the number of divide operations for a subsequent LDL'
+ * or LU factorization of the permuted matrix A (P,P).
+ *
+ * Info [AMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a
+ * subsequent LDL' factorization of A (P,P).
+ *
+ * Info [AMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a
+ * subsequent LU factorization of A (P,P), assuming that no numerical
+ * pivoting is required.
+ *
+ * Info [AMD_DMAX]: the maximum number of nonzeros in any column of L,
+ * including the diagonal.
+ *
+ * Info [14..19] are not used in the current version, but may be used in
+ * future versions.
+ */
+
+/* ------------------------------------------------------------------------- */
+/* direct interface to AMD */
+/* ------------------------------------------------------------------------- */
+
+/* amd_2 is the primary AMD ordering routine. It is not meant to be
+ * user-callable because of its restrictive inputs and because it destroys
+ * the user's input matrix. It does not check its inputs for errors, either.
+ * However, if you can work with these restrictions it can be faster than
+ * amd_order and use less memory (assuming that you can create your own copy
+ * of the matrix for AMD to destroy). Refer to AMD/Source/amd_2.c for a
+ * description of each parameter. */
+
+void amd_2
+(
+ int n,
+ int Pe [ ],
+ int Iw [ ],
+ int Len [ ],
+ int iwlen,
+ int pfree,
+ int Nv [ ],
+ int Next [ ],
+ int Last [ ],
+ int Head [ ],
+ int Elen [ ],
+ int Degree [ ],
+ int W [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+void amd_l2
+(
+ UF_long n,
+ UF_long Pe [ ],
+ UF_long Iw [ ],
+ UF_long Len [ ],
+ UF_long iwlen,
+ UF_long pfree,
+ UF_long Nv [ ],
+ UF_long Next [ ],
+ UF_long Last [ ],
+ UF_long Head [ ],
+ UF_long Elen [ ],
+ UF_long Degree [ ],
+ UF_long W [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* amd_valid */
+/* ------------------------------------------------------------------------- */
+
+/* Returns AMD_OK or AMD_OK_BUT_JUMBLED if the matrix is valid as input to
+ * amd_order; the latter is returned if the matrix has unsorted and/or
+ * duplicate row indices in one or more columns. Returns AMD_INVALID if the
+ * matrix cannot be passed to amd_order. For amd_order, the matrix must also
+ * be square. The first two arguments are the number of rows and the number
+ * of columns of the matrix. For its use in AMD, these must both equal n.
+ *
+ * NOTE: this routine returned TRUE/FALSE in v1.2 and earlier.
+ */
+
+int amd_valid
+(
+ int n_row, /* # of rows */
+ int n_col, /* # of columns */
+ const int Ap [ ], /* column pointers, of size n_col+1 */
+ const int Ai [ ] /* row indices, of size Ap [n_col] */
+) ;
+
+UF_long amd_l_valid
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* AMD memory manager and printf routines */
+/* ------------------------------------------------------------------------- */
+
+/* The user can redefine these to change the malloc, free, and printf routines
+ * that AMD uses. */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN void *(*amd_malloc) (size_t) ; /* pointer to malloc */
+EXTERN void (*amd_free) (void *) ; /* pointer to free */
+EXTERN void *(*amd_realloc) (void *, size_t) ; /* pointer to realloc */
+EXTERN void *(*amd_calloc) (size_t, size_t) ; /* pointer to calloc */
+EXTERN int (*amd_printf) (const char *, ...) ; /* pointer to printf */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Control and Info arrays */
+/* ------------------------------------------------------------------------- */
+
+/* amd_defaults: sets the default control settings */
+void amd_defaults (double Control [ ]) ;
+void amd_l_defaults (double Control [ ]) ;
+
+/* amd_control: prints the control settings */
+void amd_control (double Control [ ]) ;
+void amd_l_control (double Control [ ]) ;
+
+/* amd_info: prints the statistics */
+void amd_info (double Info [ ]) ;
+void amd_l_info (double Info [ ]) ;
+
+#define AMD_CONTROL 5 /* size of Control array */
+#define AMD_INFO 20 /* size of Info array */
+
+/* contents of Control */
+#define AMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */
+#define AMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */
+
+/* default Control settings */
+#define AMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */
+#define AMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */
+
+/* contents of Info */
+#define AMD_STATUS 0 /* return value of amd_order and amd_l_order */
+#define AMD_N 1 /* A is n-by-n */
+#define AMD_NZ 2 /* number of nonzeros in A */
+#define AMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */
+#define AMD_NZDIAG 4 /* # of entries on diagonal */
+#define AMD_NZ_A_PLUS_AT 5 /* nz in A+A' */
+#define AMD_NDENSE 6 /* number of "dense" rows/columns in A */
+#define AMD_MEMORY 7 /* amount of memory used by AMD */
+#define AMD_NCMPA 8 /* number of garbage collections in AMD */
+#define AMD_LNZ 9 /* approx. nz in L, excluding the diagonal */
+#define AMD_NDIV 10 /* number of fl. point divides for LU and LDL' */
+#define AMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */
+#define AMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */
+#define AMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */
+
+/* ------------------------------------------------------------------------- */
+/* return values of AMD */
+/* ------------------------------------------------------------------------- */
+
+#define AMD_OK 0 /* success */
+#define AMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */
+#define AMD_INVALID -2 /* input arguments are not valid */
+#define AMD_OK_BUT_JUMBLED 1 /* input matrix is OK for amd_order, but
+ * columns were not sorted, and/or duplicate entries were present. AMD had
+ * to do extra work before ordering the matrix. This is a warning, not an
+ * error. */
+
+/* ========================================================================== */
+/* === AMD version ========================================================== */
+/* ========================================================================== */
+
+/* AMD Version 1.2 and later include the following definitions.
+ * As an example, to test if the version you are using is 1.2 or later:
+ *
+ * #ifdef AMD_VERSION
+ * if (AMD_VERSION >= AMD_VERSION_CODE (1,2)) ...
+ * #endif
+ *
+ * This also works during compile-time:
+ *
+ * #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE (1,2))
+ * printf ("This is version 1.2 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ *
+ * Versions 1.1 and earlier of AMD do not include a #define'd version number.
+ */
+
+#define AMD_DATE "May 31, 2007"
+#define AMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define AMD_MAIN_VERSION 2
+#define AMD_SUB_VERSION 2
+#define AMD_SUBSUB_VERSION 0
+#define AMD_VERSION AMD_VERSION_CODE(AMD_MAIN_VERSION,AMD_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
+#endif
+\end{verbatim}
+}
+
+
+%------------------------------------------------------------------------------
+\newpage
+% References
+%------------------------------------------------------------------------------
+
+\bibliographystyle{plain}
+\bibliography{AMD_UserGuide}
+
+\end{document}
diff --git a/AMD/Doc/ChangeLog b/AMD/Doc/ChangeLog
new file mode 100644
index 0000000..9b98e38
--- /dev/null
+++ b/AMD/Doc/ChangeLog
@@ -0,0 +1,129 @@
+May 31, 2007: version 2.2.0
+
+ * port to 64-bit MATLAB
+
+ * Makefile moved from Source/ to Lib/
+
+ * minor changes to printing routines (amd_control.c, amd_info.c)
+
+Dec 12, 2006, version 2.0.4
+
+ * minor MATLAB code cleanup
+
+Nov 29, 2006, version 2.0.3
+
+ * changed MATLAB function name to amd2, so as not to conflict with
+ the now built-in version of AMD in MATLAB (which is the same thing
+ as the AMD here...).
+
+Sept 28, 2006, version 2.0.2
+
+ * #define SIZE_T_MAX not done if already defined (Mac OSX).
+
+Aug 31, 2006:
+
+ * trivial change to comments in amd.m
+
+Apr 30, 2006: AMD Version 2.0:
+
+ * long integer redefined as UF_long, controlled by UFconfig.h.
+
+ * amd_order no longer requires its input to have sorted columns. It can
+ also tolerate duplicate entries in each column. If these conditions
+ hold, but the matrix is otherwise valid, amd_order returns
+ AMD_OK_BUT_JUMBLED (a warning, not an error).
+
+ * amd_preprocess no longer deemed user-callable, since it is no longer
+ needed (it was used to ensure the input matrix had sorted columns with
+ no duplicate entries). It still exists, with additional parameters,
+ and is called by amd_order if necessary. amd_wpreprocess and
+ amd_preprocess_valid removed. Fortran interface routine amdpreproc
+ removed.
+
+ * Integer overflow computations modified, to extend the size of problem
+ that the "int" version can solve when used in an LP64 compilation.
+
+ * amd_demo2.c simplified (it tests AMD with a jumbled matrix).
+
+ * amd_valid returned TRUE/FALSE in v1.2. It now returns AMD_OK,
+ AMD_OK_BUT_JUMBLED, or AMD_INVALID. Only in the latter case is the
+ matrix unsuitable as input to amd_order.
+
+ * amd_internal.h include file moved from AMD/Source to AMD/Include.
+
+Nov 15, 2005:
+
+ * minor editting of comments; version number (1.2) unchanged.
+
+Aug. 30, 2005: AMD Version 1.2
+
+ * AMD v1.2 is upward compatible with v1.1 and v1.0, except that v1.2 no
+ longer includes the compile-time redefinition of malloc and free.
+
+ * Makefile modified to use UFconfig.mk. "Make" directory removed.
+
+ * License changed to GNU LGPL.
+
+ * Easier inclusion in C++ programs.
+
+ * option to allow compile-time redefinition of malloc and free
+ (added to v1.1) removed for v1.2. Replaced with a run-time
+ redefinition. AMD includes function pointers for malloc, free,
+ calloc, realloc, and printf, so that all those routines can be
+ redefined at compile time. These function pointers are global
+ variables, and so are not technically thread-safe, unless you
+ use defaults and don't need to change them (the common case)
+ or if you change them in one thread before using them in other
+ threads.
+
+ * added #define'd version number
+
+ * minor modification to AMD_2 to ensure all lines can be tested, without
+ conditional compilation.
+
+ * moved the prototype for AMD_2 from amd_internal.h to amd.h
+
+ * moved the prototype for AMD_valid from amd_internal.h to amd.h
+
+ * MATLAB mexFunction uses libamd.a (compiled with cc) instead of compiling
+ each AMD source file with the mex command
+
+ * long demo (amd_l_demo.c) added.
+
+Jan. 21, 2004: AMD Version 1.1
+
+ * No bugs found or fixed - new features added, only
+ * amd_preprocess added, to allow for more general input of the matrix A.
+ * ME=0 added to amd*.f, unused DEXT variable removed from amdbar.f,
+ to avoid spurious compiler warnings (this was not a bug).
+ * amd_demo2.c and amd_demo2.out added, to test/demo amd_preprocess.
+ * option to allow compile-time redefinition of malloc, free, printf added
+ * amd_demo.c shortened slightly (removed printing of PAP')
+ * User Guide modified (more details added)
+ * linewidth reduced from 80 to 79 columns
+
+Oct. 7, 2003: AMD version 1.0.1.
+
+ * MATLAB mexFunction modified, to remove call to mexCallMATLAB function.
+ This function can take a long time to call, particularly if you are
+ ordering many small matrices.
+
+May 6, 2003: AMD Version 1.0 released.
+
+ * converted to C (compare amd.f and amdbar.f with amd_2.c)
+ * dense rows/column removed prior to ordering
+ * elimination tree post-ordering added
+ * demos, user guide written
+ * statistics added (nz in L, flop count, symmetry of A)
+ * computes the pattern of A+A' if A is unsymmetric
+ * user's input matrix no longer overwritten
+ * degree lists initialized differently
+ * IOVFLO argument removed from Fortran versions (amd.f and amdbar.f)
+ * parameters added (dense row/column detection, aggressive absorption)
+ * MATLAB mexFunction added
+
+Jan, 1996:
+
+ * amdbar.f posted at http://www.netlib.org (with a restricted License)
+ * amd.f appears as MC47B/BD in the Harwell Subroutine Library
+ (without the IOVFLO argument)
diff --git a/AMD/Doc/License b/AMD/Doc/License
new file mode 100644
index 0000000..b01008a
--- /dev/null
+++ b/AMD/Doc/License
@@ -0,0 +1,39 @@
+AMD, Copyright (c) by Timothy A. Davis,
+Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved.
+AMD is available under alternate licenses, contact T. Davis for details.
+
+AMD License:
+
+ Your use or distribution of AMD or any modified version of
+ AMD implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/amd
+
+-------------------------------------------------------------------------------
diff --git a/AMD/Doc/Makefile b/AMD/Doc/Makefile
new file mode 100644
index 0000000..8b593fa
--- /dev/null
+++ b/AMD/Doc/Makefile
@@ -0,0 +1,33 @@
+#------------------------------------------------------------------------------
+# AMD Makefile for compiling on Unix systems (for GNU or original make)
+#------------------------------------------------------------------------------
+
+default: dist
+
+include ../../UFconfig/UFconfig.mk
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+
+#------------------------------------------------------------------------------
+# Create the User Guide and Quick Start Guide
+#------------------------------------------------------------------------------
+
+AMD_UserGuide.pdf: AMD_UserGuide.tex AMD_UserGuide.bib
+ pdflatex AMD_UserGuide
+ bibtex AMD_UserGuide
+ pdflatex AMD_UserGuide
+ pdflatex AMD_UserGuide
+
+dist: AMD_UserGuide.pdf
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+
diff --git a/AMD/Doc/lesser.txt b/AMD/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/AMD/Doc/lesser.txt
@@ -0,0 +1,504 @@
+ GNU LESSER GENERAL PUBLIC LICENSE
+ Version 2.1, February 1999
+
+ Copyright (C) 1991, 1999 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+[This is the first released version of the Lesser GPL. It also counts
+ as the successor of the GNU Library Public License, version 2, hence
+ the version number 2.1.]
+
+ Preamble
+
+ The licenses for most software are designed to take away your
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+can use it too, but we suggest you first think carefully about whether
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+ 12. If the distribution and/or use of the Library is restricted in
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+an explicit geographical distribution limitation excluding those countries,
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+excluded. In such case, this License incorporates the limitation as if
+written in the body of this License.
+
+ 13. The Free Software Foundation may publish revised and/or new
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+Each version is given a distinguishing version number. If the Library
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+conditions either of that version or of any later version published by
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+license version number, you may choose any version ever published by
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+ How to Apply These Terms to Your New Libraries
+
+ If you develop a new library, and you want it to be of the greatest
+possible use to the public, we recommend making it free software that
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+ Copyright (C) <year> <name of author>
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+ This library is free software; you can redistribute it and/or
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+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
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+
+That's all there is to it!
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+
diff --git a/AMD/Include/amd.h b/AMD/Include/amd.h
new file mode 100644
index 0000000..e4fd47e
--- /dev/null
+++ b/AMD/Include/amd.h
@@ -0,0 +1,412 @@
+/* ========================================================================= */
+/* === AMD: approximate minimum degree ordering =========================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* AMD finds a symmetric ordering P of a matrix A so that the Cholesky
+ * factorization of P*A*P' has fewer nonzeros and takes less work than the
+ * Cholesky factorization of A. If A is not symmetric, then it performs its
+ * ordering on the matrix A+A'. Two sets of user-callable routines are
+ * provided, one for int integers and the other for UF_long integers.
+ *
+ * The method is based on the approximate minimum degree algorithm, discussed
+ * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm",
+ * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp.
+ * 886-905, 1996. This package can perform both the AMD ordering (with
+ * aggressive absorption), and the AMDBAR ordering (without aggressive
+ * absorption) discussed in the above paper. This package differs from the
+ * Fortran codes discussed in the paper:
+ *
+ * (1) it can ignore "dense" rows and columns, leading to faster run times
+ * (2) it computes the ordering of A+A' if A is not symmetric
+ * (3) it is followed by a depth-first post-ordering of the assembly tree
+ * (or supernodal elimination tree)
+ *
+ * For historical reasons, the Fortran versions, amd.f and amdbar.f, have
+ * been left (nearly) unchanged. They compute the identical ordering as
+ * described in the above paper.
+ */
+
+#ifndef AMD_H
+#define AMD_H
+
+/* make it easy for C++ programs to include AMD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* get the definition of size_t: */
+#include <stddef.h>
+
+/* define UF_long */
+#include "UFconfig.h"
+
+int amd_order /* returns AMD_OK, AMD_OK_BUT_JUMBLED,
+ * AMD_INVALID, or AMD_OUT_OF_MEMORY */
+(
+ int n, /* A is n-by-n. n must be >= 0. */
+ const int Ap [ ], /* column pointers for A, of size n+1 */
+ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */
+ int P [ ], /* output permutation, of size n */
+ double Control [ ], /* input Control settings, of size AMD_CONTROL */
+ double Info [ ] /* output Info statistics, of size AMD_INFO */
+) ;
+
+UF_long amd_l_order /* see above for description of arguments */
+(
+ UF_long n,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ UF_long P [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+/* Input arguments (not modified):
+ *
+ * n: the matrix A is n-by-n.
+ * Ap: an int/UF_long array of size n+1, containing column pointers of A.
+ * Ai: an int/UF_long array of size nz, containing the row indices of A,
+ * where nz = Ap [n].
+ * Control: a double array of size AMD_CONTROL, containing control
+ * parameters. Defaults are used if Control is NULL.
+ *
+ * Output arguments (not defined on input):
+ *
+ * P: an int/UF_long array of size n, containing the output permutation. If
+ * row i is the kth pivot row, then P [k] = i. In MATLAB notation,
+ * the reordered matrix is A (P,P).
+ * Info: a double array of size AMD_INFO, containing statistical
+ * information. Ignored if Info is NULL.
+ *
+ * On input, the matrix A is stored in column-oriented form. The row indices
+ * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1].
+ *
+ * If the row indices appear in ascending order in each column, and there
+ * are no duplicate entries, then amd_order is slightly more efficient in
+ * terms of time and memory usage. If this condition does not hold, a copy
+ * of the matrix is created (where these conditions do hold), and the copy is
+ * ordered. This feature is new to v2.0 (v1.2 and earlier required this
+ * condition to hold for the input matrix).
+ *
+ * Row indices must be in the range 0 to
+ * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros
+ * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n].
+ * The matrix does not need to be symmetric, and the diagonal does not need to
+ * be present (if diagonal entries are present, they are ignored except for
+ * the output statistic Info [AMD_NZDIAG]). The arrays Ai and Ap are not
+ * modified. This form of the Ap and Ai arrays to represent the nonzero
+ * pattern of the matrix A is the same as that used internally by MATLAB.
+ * If you wish to use a more flexible input structure, please see the
+ * umfpack_*_triplet_to_col routines in the UMFPACK package, at
+ * http://www.cise.ufl.edu/research/sparse/umfpack.
+ *
+ * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the
+ * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0
+ * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these
+ * restrictions are not met, AMD returns AMD_INVALID.
+ *
+ * AMD returns:
+ *
+ * AMD_OK if the matrix is valid and sufficient memory can be allocated to
+ * perform the ordering.
+ *
+ * AMD_OUT_OF_MEMORY if not enough memory can be allocated.
+ *
+ * AMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is
+ * NULL.
+ *
+ * AMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate
+ * entries, but was otherwise valid.
+ *
+ * The AMD routine first forms the pattern of the matrix A+A', and then
+ * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of
+ * the original is the kth pivotal row. In MATLAB notation, the permuted
+ * matrix is A (P,P), except that 0-based indexing is used instead of the
+ * 1-based indexing in MATLAB.
+ *
+ * The Control array is used to set various parameters for AMD. If a NULL
+ * pointer is passed, default values are used. The Control array is not
+ * modified.
+ *
+ * Control [AMD_DENSE]: controls the threshold for "dense" rows/columns.
+ * A dense row/column in A+A' can cause AMD to spend a lot of time in
+ * ordering the matrix. If Control [AMD_DENSE] >= 0, rows/columns
+ * with more than Control [AMD_DENSE] * sqrt (n) entries are ignored
+ * during the ordering, and placed last in the output order. The
+ * default value of Control [AMD_DENSE] is 10. If negative, no
+ * rows/columns are treated as "dense". Rows/columns with 16 or
+ * fewer off-diagonal entries are never considered "dense".
+ *
+ * Control [AMD_AGGRESSIVE]: controls whether or not to use aggressive
+ * absorption, in which a prior element is absorbed into the current
+ * element if is a subset of the current element, even if it is not
+ * adjacent to the current pivot element (refer to Amestoy, Davis,
+ * & Duff, 1996, for more details). The default value is nonzero,
+ * which means to perform aggressive absorption. This nearly always
+ * leads to a better ordering (because the approximate degrees are
+ * more accurate) and a lower execution time. There are cases where
+ * it can lead to a slightly worse ordering, however. To turn it off,
+ * set Control [AMD_AGGRESSIVE] to 0.
+ *
+ * Control [2..4] are not used in the current version, but may be used in
+ * future versions.
+ *
+ * The Info array provides statistics about the ordering on output. If it is
+ * not present, the statistics are not returned. This is not an error
+ * condition.
+ *
+ * Info [AMD_STATUS]: the return value of AMD, either AMD_OK,
+ * AMD_OK_BUT_JUMBLED, AMD_OUT_OF_MEMORY, or AMD_INVALID.
+ *
+ * Info [AMD_N]: n, the size of the input matrix
+ *
+ * Info [AMD_NZ]: the number of nonzeros in A, nz = Ap [n]
+ *
+ * Info [AMD_SYMMETRY]: the symmetry of the matrix A. It is the number
+ * of "matched" off-diagonal entries divided by the total number of
+ * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also
+ * an entry, for any pair (i,j) for which i != j. In MATLAB notation,
+ * S = spones (A) ;
+ * B = tril (S, -1) + triu (S, 1) ;
+ * symmetry = nnz (B & B') / nnz (B) ;
+ *
+ * Info [AMD_NZDIAG]: the number of entries on the diagonal of A.
+ *
+ * Info [AMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the
+ * diagonal. If A is perfectly symmetric (Info [AMD_SYMMETRY] = 1)
+ * with a fully nonzero diagonal, then Info [AMD_NZ_A_PLUS_AT] = nz-n
+ * (the smallest possible value). If A is perfectly unsymmetric
+ * (Info [AMD_SYMMETRY] = 0, for an upper triangular matrix, for
+ * example) with no diagonal, then Info [AMD_NZ_A_PLUS_AT] = 2*nz
+ * (the largest possible value).
+ *
+ * Info [AMD_NDENSE]: the number of "dense" rows/columns of A+A' that were
+ * removed from A prior to ordering. These are placed last in the
+ * output order P.
+ *
+ * Info [AMD_MEMORY]: the amount of memory used by AMD, in bytes. In the
+ * current version, this is 1.2 * Info [AMD_NZ_A_PLUS_AT] + 9*n
+ * times the size of an integer. This is at most 2.4nz + 9n. This
+ * excludes the size of the input arguments Ai, Ap, and P, which have
+ * a total size of nz + 2*n + 1 integers.
+ *
+ * Info [AMD_NCMPA]: the number of garbage collections performed.
+ *
+ * Info [AMD_LNZ]: the number of nonzeros in L (excluding the diagonal).
+ * This is a slight upper bound because mass elimination is combined
+ * with the approximate degree update. It is a rough upper bound if
+ * there are many "dense" rows/columns. The rest of the statistics,
+ * below, are also slight or rough upper bounds, for the same reasons.
+ * The post-ordering of the assembly tree might also not exactly
+ * correspond to a true elimination tree postordering.
+ *
+ * Info [AMD_NDIV]: the number of divide operations for a subsequent LDL'
+ * or LU factorization of the permuted matrix A (P,P).
+ *
+ * Info [AMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a
+ * subsequent LDL' factorization of A (P,P).
+ *
+ * Info [AMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a
+ * subsequent LU factorization of A (P,P), assuming that no numerical
+ * pivoting is required.
+ *
+ * Info [AMD_DMAX]: the maximum number of nonzeros in any column of L,
+ * including the diagonal.
+ *
+ * Info [14..19] are not used in the current version, but may be used in
+ * future versions.
+ */
+
+/* ------------------------------------------------------------------------- */
+/* direct interface to AMD */
+/* ------------------------------------------------------------------------- */
+
+/* amd_2 is the primary AMD ordering routine. It is not meant to be
+ * user-callable because of its restrictive inputs and because it destroys
+ * the user's input matrix. It does not check its inputs for errors, either.
+ * However, if you can work with these restrictions it can be faster than
+ * amd_order and use less memory (assuming that you can create your own copy
+ * of the matrix for AMD to destroy). Refer to AMD/Source/amd_2.c for a
+ * description of each parameter. */
+
+void amd_2
+(
+ int n,
+ int Pe [ ],
+ int Iw [ ],
+ int Len [ ],
+ int iwlen,
+ int pfree,
+ int Nv [ ],
+ int Next [ ],
+ int Last [ ],
+ int Head [ ],
+ int Elen [ ],
+ int Degree [ ],
+ int W [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+void amd_l2
+(
+ UF_long n,
+ UF_long Pe [ ],
+ UF_long Iw [ ],
+ UF_long Len [ ],
+ UF_long iwlen,
+ UF_long pfree,
+ UF_long Nv [ ],
+ UF_long Next [ ],
+ UF_long Last [ ],
+ UF_long Head [ ],
+ UF_long Elen [ ],
+ UF_long Degree [ ],
+ UF_long W [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* amd_valid */
+/* ------------------------------------------------------------------------- */
+
+/* Returns AMD_OK or AMD_OK_BUT_JUMBLED if the matrix is valid as input to
+ * amd_order; the latter is returned if the matrix has unsorted and/or
+ * duplicate row indices in one or more columns. Returns AMD_INVALID if the
+ * matrix cannot be passed to amd_order. For amd_order, the matrix must also
+ * be square. The first two arguments are the number of rows and the number
+ * of columns of the matrix. For its use in AMD, these must both equal n.
+ *
+ * NOTE: this routine returned TRUE/FALSE in v1.2 and earlier.
+ */
+
+int amd_valid
+(
+ int n_row, /* # of rows */
+ int n_col, /* # of columns */
+ const int Ap [ ], /* column pointers, of size n_col+1 */
+ const int Ai [ ] /* row indices, of size Ap [n_col] */
+) ;
+
+UF_long amd_l_valid
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* AMD memory manager and printf routines */
+/* ------------------------------------------------------------------------- */
+
+/* The user can redefine these to change the malloc, free, and printf routines
+ * that AMD uses. */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN void *(*amd_malloc) (size_t) ; /* pointer to malloc */
+EXTERN void (*amd_free) (void *) ; /* pointer to free */
+EXTERN void *(*amd_realloc) (void *, size_t) ; /* pointer to realloc */
+EXTERN void *(*amd_calloc) (size_t, size_t) ; /* pointer to calloc */
+EXTERN int (*amd_printf) (const char *, ...) ; /* pointer to printf */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Control and Info arrays */
+/* ------------------------------------------------------------------------- */
+
+/* amd_defaults: sets the default control settings */
+void amd_defaults (double Control [ ]) ;
+void amd_l_defaults (double Control [ ]) ;
+
+/* amd_control: prints the control settings */
+void amd_control (double Control [ ]) ;
+void amd_l_control (double Control [ ]) ;
+
+/* amd_info: prints the statistics */
+void amd_info (double Info [ ]) ;
+void amd_l_info (double Info [ ]) ;
+
+#define AMD_CONTROL 5 /* size of Control array */
+#define AMD_INFO 20 /* size of Info array */
+
+/* contents of Control */
+#define AMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */
+#define AMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */
+
+/* default Control settings */
+#define AMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */
+#define AMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */
+
+/* contents of Info */
+#define AMD_STATUS 0 /* return value of amd_order and amd_l_order */
+#define AMD_N 1 /* A is n-by-n */
+#define AMD_NZ 2 /* number of nonzeros in A */
+#define AMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */
+#define AMD_NZDIAG 4 /* # of entries on diagonal */
+#define AMD_NZ_A_PLUS_AT 5 /* nz in A+A' */
+#define AMD_NDENSE 6 /* number of "dense" rows/columns in A */
+#define AMD_MEMORY 7 /* amount of memory used by AMD */
+#define AMD_NCMPA 8 /* number of garbage collections in AMD */
+#define AMD_LNZ 9 /* approx. nz in L, excluding the diagonal */
+#define AMD_NDIV 10 /* number of fl. point divides for LU and LDL' */
+#define AMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */
+#define AMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */
+#define AMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */
+
+/* ------------------------------------------------------------------------- */
+/* return values of AMD */
+/* ------------------------------------------------------------------------- */
+
+#define AMD_OK 0 /* success */
+#define AMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */
+#define AMD_INVALID -2 /* input arguments are not valid */
+#define AMD_OK_BUT_JUMBLED 1 /* input matrix is OK for amd_order, but
+ * columns were not sorted, and/or duplicate entries were present. AMD had
+ * to do extra work before ordering the matrix. This is a warning, not an
+ * error. */
+
+/* ========================================================================== */
+/* === AMD version ========================================================== */
+/* ========================================================================== */
+
+/* AMD Version 1.2 and later include the following definitions.
+ * As an example, to test if the version you are using is 1.2 or later:
+ *
+ * #ifdef AMD_VERSION
+ * if (AMD_VERSION >= AMD_VERSION_CODE (1,2)) ...
+ * #endif
+ *
+ * This also works during compile-time:
+ *
+ * #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE (1,2))
+ * printf ("This is version 1.2 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ *
+ * Versions 1.1 and earlier of AMD do not include a #define'd version number.
+ */
+
+#define AMD_DATE "May 31, 2007"
+#define AMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define AMD_MAIN_VERSION 2
+#define AMD_SUB_VERSION 2
+#define AMD_SUBSUB_VERSION 0
+#define AMD_VERSION AMD_VERSION_CODE(AMD_MAIN_VERSION,AMD_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/AMD/Include/amd_internal.h b/AMD/Include/amd_internal.h
new file mode 100644
index 0000000..d515b64
--- /dev/null
+++ b/AMD/Include/amd_internal.h
@@ -0,0 +1,350 @@
+/* ========================================================================= */
+/* === amd_internal.h ====================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* This file is for internal use in AMD itself, and does not normally need to
+ * be included in user code (it is included in UMFPACK, however). All others
+ * should use amd.h instead.
+ *
+ * The following compile-time definitions affect how AMD is compiled.
+ *
+ * -DNPRINT
+ *
+ * Disable all printing. stdio.h will not be included. Printing can
+ * be re-enabled at run-time by setting the global pointer amd_printf
+ * to printf (or mexPrintf for a MATLAB mexFunction).
+ *
+ * -DNMALLOC
+ *
+ * No memory manager is defined at compile-time. You MUST define the
+ * function pointers amd_malloc, amd_free, amd_realloc, and
+ * amd_calloc at run-time for AMD to work properly.
+ */
+
+/* ========================================================================= */
+/* === NDEBUG ============================================================== */
+/* ========================================================================= */
+
+/*
+ * Turning on debugging takes some work (see below). If you do not edit this
+ * file, then debugging is always turned off, regardless of whether or not
+ * -DNDEBUG is specified in your compiler options.
+ *
+ * If AMD is being compiled as a mexFunction, then MATLAB_MEX_FILE is defined,
+ * and mxAssert is used instead of assert. If debugging is not enabled, no
+ * MATLAB include files or functions are used. Thus, the AMD library libamd.a
+ * can be safely used in either a stand-alone C program or in another
+ * mexFunction, without any change.
+ */
+
+/*
+ AMD will be exceedingly slow when running in debug mode. The next three
+ lines ensure that debugging is turned off.
+*/
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+
+/*
+ To enable debugging, uncomment the following line:
+#undef NDEBUG
+*/
+
+/* ------------------------------------------------------------------------- */
+/* ANSI include files */
+/* ------------------------------------------------------------------------- */
+
+/* from stdlib.h: size_t, malloc, free, realloc, and calloc */
+#include <stdlib.h>
+
+#if !defined(NPRINT) || !defined(NDEBUG)
+/* from stdio.h: printf. Not included if NPRINT is defined at compile time.
+ * fopen and fscanf are used when debugging. */
+#include <stdio.h>
+#endif
+
+/* from limits.h: INT_MAX and LONG_MAX */
+#include <limits.h>
+
+/* from math.h: sqrt */
+#include <math.h>
+
+/* ------------------------------------------------------------------------- */
+/* MATLAB include files (only if being used in or via MATLAB) */
+/* ------------------------------------------------------------------------- */
+
+#ifdef MATLAB_MEX_FILE
+#include "matrix.h"
+#include "mex.h"
+#endif
+
+/* ------------------------------------------------------------------------- */
+/* basic definitions */
+/* ------------------------------------------------------------------------- */
+
+#ifdef FLIP
+#undef FLIP
+#endif
+
+#ifdef MAX
+#undef MAX
+#endif
+
+#ifdef MIN
+#undef MIN
+#endif
+
+#ifdef EMPTY
+#undef EMPTY
+#endif
+
+#ifdef GLOBAL
+#undef GLOBAL
+#endif
+
+#ifdef PRIVATE
+#undef PRIVATE
+#endif
+
+/* FLIP is a "negation about -1", and is used to mark an integer i that is
+ * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY
+ * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i
+ * for all integers i. UNFLIP (i) is >= EMPTY. */
+#define EMPTY (-1)
+#define FLIP(i) (-(i)-2)
+#define UNFLIP(i) ((i < EMPTY) ? FLIP (i) : (i))
+
+/* for integer MAX/MIN, or for doubles when we don't care how NaN's behave: */
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+/* logical expression of p implies q: */
+#define IMPLIES(p,q) (!(p) || (q))
+
+/* Note that the IBM RS 6000 xlc predefines TRUE and FALSE in <types.h>. */
+/* The Compaq Alpha also predefines TRUE and FALSE. */
+#ifdef TRUE
+#undef TRUE
+#endif
+#ifdef FALSE
+#undef FALSE
+#endif
+
+#define TRUE (1)
+#define FALSE (0)
+#define PRIVATE static
+#define GLOBAL
+#define EMPTY (-1)
+
+/* Note that Linux's gcc 2.96 defines NULL as ((void *) 0), but other */
+/* compilers (even gcc 2.95.2 on Solaris) define NULL as 0 or (0). We */
+/* need to use the ANSI standard value of 0. */
+#ifdef NULL
+#undef NULL
+#endif
+
+#define NULL 0
+
+/* largest value of size_t */
+#ifndef SIZE_T_MAX
+#define SIZE_T_MAX ((size_t) (-1))
+#endif
+
+/* ------------------------------------------------------------------------- */
+/* integer type for AMD: int or UF_long */
+/* ------------------------------------------------------------------------- */
+
+/* define UF_long */
+#include "UFconfig.h"
+
+#if defined (DLONG) || defined (ZLONG)
+
+#define Int UF_long
+#define ID UF_long_id
+#define Int_MAX UF_long_max
+
+#define AMD_order amd_l_order
+#define AMD_defaults amd_l_defaults
+#define AMD_control amd_l_control
+#define AMD_info amd_l_info
+#define AMD_1 amd_l1
+#define AMD_2 amd_l2
+#define AMD_valid amd_l_valid
+#define AMD_aat amd_l_aat
+#define AMD_postorder amd_l_postorder
+#define AMD_post_tree amd_l_post_tree
+#define AMD_dump amd_l_dump
+#define AMD_debug amd_l_debug
+#define AMD_debug_init amd_l_debug_init
+#define AMD_preprocess amd_l_preprocess
+
+#else
+
+#define Int int
+#define ID "%d"
+#define Int_MAX INT_MAX
+
+#define AMD_order amd_order
+#define AMD_defaults amd_defaults
+#define AMD_control amd_control
+#define AMD_info amd_info
+#define AMD_1 amd_1
+#define AMD_2 amd_2
+#define AMD_valid amd_valid
+#define AMD_aat amd_aat
+#define AMD_postorder amd_postorder
+#define AMD_post_tree amd_post_tree
+#define AMD_dump amd_dump
+#define AMD_debug amd_debug
+#define AMD_debug_init amd_debug_init
+#define AMD_preprocess amd_preprocess
+
+#endif
+
+/* ========================================================================= */
+/* === PRINTF macro ======================================================== */
+/* ========================================================================= */
+
+/* All output goes through the PRINTF macro. */
+#define PRINTF(params) { if (amd_printf != NULL) (void) amd_printf params ; }
+
+/* ------------------------------------------------------------------------- */
+/* AMD routine definitions (user-callable) */
+/* ------------------------------------------------------------------------- */
+
+#include "amd.h"
+
+/* ------------------------------------------------------------------------- */
+/* AMD routine definitions (not user-callable) */
+/* ------------------------------------------------------------------------- */
+
+GLOBAL size_t AMD_aat
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int Len [ ],
+ Int Tp [ ],
+ double Info [ ]
+) ;
+
+GLOBAL void AMD_1
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int P [ ],
+ Int Pinv [ ],
+ Int Len [ ],
+ Int slen,
+ Int S [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+GLOBAL void AMD_postorder
+(
+ Int nn,
+ Int Parent [ ],
+ Int Npiv [ ],
+ Int Fsize [ ],
+ Int Order [ ],
+ Int Child [ ],
+ Int Sibling [ ],
+ Int Stack [ ]
+) ;
+
+GLOBAL Int AMD_post_tree
+(
+ Int root,
+ Int k,
+ Int Child [ ],
+ const Int Sibling [ ],
+ Int Order [ ],
+ Int Stack [ ]
+#ifndef NDEBUG
+ , Int nn
+#endif
+) ;
+
+GLOBAL void AMD_preprocess
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int Rp [ ],
+ Int Ri [ ],
+ Int W [ ],
+ Int Flag [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* debugging definitions */
+/* ------------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+
+/* from assert.h: assert macro */
+#include <assert.h>
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN Int AMD_debug ;
+
+GLOBAL void AMD_debug_init ( char *s ) ;
+
+GLOBAL void AMD_dump
+(
+ Int n,
+ Int Pe [ ],
+ Int Iw [ ],
+ Int Len [ ],
+ Int iwlen,
+ Int pfree,
+ Int Nv [ ],
+ Int Next [ ],
+ Int Last [ ],
+ Int Head [ ],
+ Int Elen [ ],
+ Int Degree [ ],
+ Int W [ ],
+ Int nel
+) ;
+
+#ifdef ASSERT
+#undef ASSERT
+#endif
+
+/* Use mxAssert if AMD is compiled into a mexFunction */
+#ifdef MATLAB_MEX_FILE
+#define ASSERT(expression) (mxAssert ((expression), ""))
+#else
+#define ASSERT(expression) (assert (expression))
+#endif
+
+#define AMD_DEBUG0(params) { PRINTF (params) ; }
+#define AMD_DEBUG1(params) { if (AMD_debug >= 1) PRINTF (params) ; }
+#define AMD_DEBUG2(params) { if (AMD_debug >= 2) PRINTF (params) ; }
+#define AMD_DEBUG3(params) { if (AMD_debug >= 3) PRINTF (params) ; }
+#define AMD_DEBUG4(params) { if (AMD_debug >= 4) PRINTF (params) ; }
+
+#else
+
+/* no debugging */
+#define ASSERT(expression)
+#define AMD_DEBUG0(params)
+#define AMD_DEBUG1(params)
+#define AMD_DEBUG2(params)
+#define AMD_DEBUG3(params)
+#define AMD_DEBUG4(params)
+
+#endif
diff --git a/AMD/Lib/GNUmakefile b/AMD/Lib/GNUmakefile
new file mode 100644
index 0000000..f59b1d6
--- /dev/null
+++ b/AMD/Lib/GNUmakefile
@@ -0,0 +1,78 @@
+#-------------------------------------------------------------------------------
+# AMD Makefile for compiling on Unix systems (for GNU make only)
+#-------------------------------------------------------------------------------
+
+default: ../Lib/libamd.a
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig
+
+#-------------------------------------------------------------------------------
+# source files
+#-------------------------------------------------------------------------------
+
+AMD = amd_aat amd_1 amd_2 amd_dump amd_postorder amd_post_tree amd_defaults \
+ amd_order amd_control amd_info amd_valid amd_preprocess
+
+UFCONFIG = ../../UFconfig/UFconfig.h
+
+INC = ../Include/amd.h ../Include/amd_internal.h $(UFCONFIG)
+
+#-------------------------------------------------------------------------------
+# object files for each version
+#-------------------------------------------------------------------------------
+
+AMDI = $(addsuffix .o, $(subst amd_,amd_i_,$(AMD)))
+AMDL = $(addsuffix .o, $(subst amd_,amd_l_,$(AMD)))
+
+#-------------------------------------------------------------------------------
+# compile each int and long routine (with no real/complex version)
+#-------------------------------------------------------------------------------
+
+amd_global.o: ../Source/amd_global.c $(INC)
+ $(C) -c $< -o $@
+
+amd_i_%.o: ../Source/amd_%.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+amd_l_%.o: ../Source/amd_%.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# Create the libamd.a library (C versions only)
+#-------------------------------------------------------------------------------
+
+../Lib/libamd.a: amd_global.o $(AMDI) $(AMDL)
+ $(AR) ../Lib/libamd.a $^
+ - $(RANLIB) ../Lib/libamd.a
+
+#-------------------------------------------------------------------------------
+# compile the Fortran versions and the libamdf77.a library
+#-------------------------------------------------------------------------------
+
+fortran: ../Lib/libamdf77.a
+
+AMDF77 = amd.o amdbar.o
+
+amd.o: ../Source/amd.f
+ $(F77) $(F77FLAGS) -c ../Source/amd.f -o amd.o
+
+amdbar.o: ../Source/amdbar.f
+ $(F77) $(F77FLAGS) -c ../Source/amdbar.f -o amdbar.o
+
+../Lib/libamdf77.a: $(AMDF77)
+ $(AR) ../Lib/libamdf77.a $^
+ - $(RANLIB) ../Lib/libamdf77.a
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) ../Lib/libamd.a ../Lib/libamdf77.a
diff --git a/AMD/Lib/Makefile b/AMD/Lib/Makefile
new file mode 100644
index 0000000..8e0f197
--- /dev/null
+++ b/AMD/Lib/Makefile
@@ -0,0 +1,69 @@
+#-------------------------------------------------------------------------------
+# AMD Makefile for compiling on Unix systems (for original Make ONLY)
+#-------------------------------------------------------------------------------
+
+# This is a very ugly Makefile, and is only provided for those who do not
+# have GNU make. Note that it is not used if you have GNU make. It ignores
+# dependency checking and just compiles everything.
+
+default: everything
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig
+
+everything:
+ $(C) -DDINT -c ../Source/amd_aat.c -o amd_i_aat.o
+ $(C) -DDINT -c ../Source/amd_1.c -o amd_i_1.o
+ $(C) -DDINT -c ../Source/amd_2.c -o amd_i_2.o
+ $(C) -DDINT -c ../Source/amd_dump.c -o amd_i_dump.o
+ $(C) -DDINT -c ../Source/amd_postorder.c -o amd_i_postorder.o
+ $(C) -DDINT -c ../Source/amd_post_tree.c -o amd_i_post_tree.o
+ $(C) -DDINT -c ../Source/amd_defaults.c -o amd_i_defaults.o
+ $(C) -DDINT -c ../Source/amd_order.c -o amd_i_order.o
+ $(C) -DDINT -c ../Source/amd_control.c -o amd_i_control.o
+ $(C) -DDINT -c ../Source/amd_info.c -o amd_i_info.o
+ $(C) -DDINT -c ../Source/amd_valid.c -o amd_i_valid.o
+ $(C) -DDINT -c ../Source/amd_preprocess.c -o amd_i_preprocess.o
+ $(C) -DDLONG -c ../Source/amd_aat.c -o amd_l_aat.o
+ $(C) -DDLONG -c ../Source/amd_1.c -o ../Source/amd_l_1.o
+ $(C) -DDLONG -c ../Source/amd_2.c -o amd_l_2.o
+ $(C) -DDLONG -c ../Source/amd_dump.c -o amd_l_dump.o
+ $(C) -DDLONG -c ../Source/amd_postorder.c -o amd_l_postorder.o
+ $(C) -DDLONG -c ../Source/amd_post_tree.c -o amd_l_post_tree.o
+ $(C) -DDLONG -c ../Source/amd_defaults.c -o amd_l_defaults.o
+ $(C) -DDLONG -c ../Source/amd_order.c -o amd_l_order.o
+ $(C) -DDLONG -c ../Source/amd_control.c -o amd_l_control.o
+ $(C) -DDLONG -c ../Source/amd_info.c -o amd_l_info.o
+ $(C) -DDLONG -c ../Source/amd_valid.c -o amd_l_valid.o
+ $(C) -DDLONG -c ../Source/amd_preprocess.c -o amd_l_preprocess.o
+ $(C) -c ../Source/amd_global.c
+ $(AR) ../Lib/libamd.a amd_i_aat.o amd_i_1.o amd_i_2.o amd_i_dump.o \
+ amd_i_postorder.o amd_i_post_tree.o amd_i_defaults.o amd_i_order.o \
+ amd_i_control.o amd_i_info.o amd_i_valid.o amd_l_aat.o amd_l_1.o \
+ amd_l_2.o amd_l_dump.o amd_l_postorder.o amd_l_post_tree.o \
+ amd_l_defaults.o amd_l_order.o amd_l_control.o amd_l_info.o \
+ amd_l_valid.o amd_i_preprocess.o amd_l_preprocess.o amd_global.o
+ - $(RANLIB) ../Lib/libamd.a
+
+#-------------------------------------------------------------------------------
+# compile the Fortran versions and the libamdf77.a library
+#-------------------------------------------------------------------------------
+
+fortran:
+ $(F77) $(F77FLAGS) -c ../Source/amd.f -o amd.o
+ $(F77) $(F77FLAGS) -c ../Source/amdbar.f -o amdbar.o
+ $(AR) ../Lib/libamdf77.a amd.o amdbar.o
+ - $(RANLIB) ../Lib/libamdf77.a
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) ../Lib/libamd.a ../Lib/libamdf77.a
diff --git a/AMD/Lib/libamd.def b/AMD/Lib/libamd.def
new file mode 100644
index 0000000..8ed43fc
--- /dev/null
+++ b/AMD/Lib/libamd.def
@@ -0,0 +1,12 @@
+LIBRARY libamd.dll
+EXPORTS
+amd_order
+amd_defaults
+amd_control
+amd_info
+amd_2
+amd_l_order
+amd_l_defaults
+amd_l_control
+amd_l_info
+amd_l2
diff --git a/AMD/MATLAB/Contents.m b/AMD/MATLAB/Contents.m
new file mode 100644
index 0000000..8d43c30
--- /dev/null
+++ b/AMD/MATLAB/Contents.m
@@ -0,0 +1,19 @@
+%Contents of the AMD sparse matrix ordering package:
+%
+% amd2 - p = amd2 (A), the approximate minimum degree ordering of A
+% amd_demo - a demo of amd2, using the can_24 matrix
+% amd_make - to compile amd2 for use in MATLAB
+% amd_install - compile and install amd2 for use in MATLAB
+%
+% See also: amd, amd2, colamd, symamd, colmmd, symmmd, umfpack
+%
+% Note that amd2 and the built-in amd function in MATLAB 7.3 and later are one
+% and the same.
+%
+% Example:
+% p = amd2 (A) ;
+
+% Copyright 1994-2007, Tim Davis, University of Florida,
+% Patrick R. Amestoy, and Iain S. Duff.
+
+help Contents
diff --git a/AMD/MATLAB/Makefile b/AMD/MATLAB/Makefile
new file mode 100644
index 0000000..9abad3c
--- /dev/null
+++ b/AMD/MATLAB/Makefile
@@ -0,0 +1,34 @@
+#------------------------------------------------------------------------------
+# Makefile for the AMD MATLAB mexFunction
+#------------------------------------------------------------------------------
+
+default: amd2
+
+include ../../UFconfig/UFconfig.mk
+
+AMD = ../Lib/libamd.a
+
+I = -I../Include -I../../UFconfig
+
+INC = ../Include/amd.h ../Include/amd_internal.h ../../UFconfig/UFconfig.h
+
+SRC = ../Source/amd_1.c ../Source/amd_2.c ../Source/amd_aat.c \
+ ../Source/amd_control.c ../Source/amd_defaults.c ../Source/amd_dump.c \
+ ../Source/amd_global.c ../Source/amd_info.c ../Source/amd_order.c \
+ ../Source/amd_postorder.c ../Source/amd_post_tree.c \
+ ../Source/amd_preprocess.c ../Source/amd_valid.c
+
+amd2: $(SRC) $(INC) amd_mex.c
+ $(MEX) -DDLONG $(I) -output amd2 amd_mex.c $(SRC)
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) amd2.mex*
diff --git a/AMD/MATLAB/amd2.m b/AMD/MATLAB/amd2.m
new file mode 100644
index 0000000..41aa874
--- /dev/null
+++ b/AMD/MATLAB/amd2.m
@@ -0,0 +1,76 @@
+function [p, Info] = amd2 (A, Control) %#ok
+%AMD2 p = amd2 (A), the approximate minimum degree ordering of A
+% P = AMD2 (S) returns the approximate minimum degree permutation vector for
+% the sparse matrix C = S+S'. The Cholesky factorization of C (P,P), or
+% S (P,P), tends to be sparser than that of C or S. AMD tends to be faster
+% than SYMMMD and SYMAMD, and tends to return better orderings than SYMMMD.
+% S must be square. If S is full, amd(S) is equivalent to amd(sparse(S)).
+%
+% Note that the built-in AMD routine in MATLAB is identical to AMD2,
+% except that AMD in MATLAB allows for a struct input to set the parameters.
+%
+% Usage: P = amd2 (S) ; % finds the ordering
+% [P, Info] = amd2 (S, Control) ; % optional parameters & statistics
+% Control = amd2 ; % returns default parameters
+% amd2 ; % prints default parameters.
+%
+% Control (1); If S is n-by-n, then rows/columns with more than
+% max (16, (Control (1))* sqrt(n)) entries in S+S' are considered
+% "dense", and ignored during ordering. They are placed last in the
+% output permutation. The default is 10.0 if Control is not present.
+% Control (2): If nonzero, then aggressive absorption is performed.
+% This is the default if Control is not present.
+% Control (3): If nonzero, print statistics about the ordering.
+%
+% Info (1): status (0: ok, -1: out of memory, -2: matrix invalid)
+% Info (2): n = size (A,1)
+% Info (3): nnz (A)
+% Info (4): the symmetry of the matrix S (0.0 means purely unsymmetric,
+% 1.0 means purely symmetric). Computed as:
+% B = tril (S, -1) + triu (S, 1) ; symmetry = nnz (B & B') / nnz (B);
+% Info (5): nnz (diag (S))
+% Info (6): nnz in S+S', excluding the diagonal (= nnz (B+B'))
+% Info (7): number "dense" rows/columns in S+S'
+% Info (8): the amount of memory used by AMD, in bytes
+% Info (9): the number of memory compactions performed by AMD
+%
+% The following statistics are slight upper bounds because of the
+% approximate degree in AMD. The bounds are looser if "dense" rows/columns
+% are ignored during ordering (Info (7) > 0). The statistics are for a
+% subsequent factorization of the matrix C (P,P). The LU factorization
+% statistics assume no pivoting.
+%
+% Info (10): the number of nonzeros in L, excluding the diagonal
+% Info (11): the number of divide operations for LL', LDL', or LU
+% Info (12): the number of multiply-subtract pairs for LL' or LDL'
+% Info (13): the number of multiply-subtract pairs for LU
+% Info (14): the max # of nonzeros in any column of L (incl. diagonal)
+% Info (15:20): unused, reserved for future use
+%
+% An assembly tree post-ordering is performed, which is typically the same
+% as an elimination tree post-ordering. It is not always identical because
+% of the approximate degree update used, and because "dense" rows/columns
+% do not take part in the post-order. It well-suited for a subsequent
+% "chol", however. If you require a precise elimination tree post-ordering,
+% then see the example below:
+%
+% Example:
+%
+% P = amd2 (S) ;
+% C = spones (S) + spones (S') ; % skip this if S already symmetric
+% [ignore, Q] = etree (C (P,P)) ;
+% P = P (Q) ;
+%
+% See also AMD, COLMMD, COLAMD, COLPERM, SYMAMD, SYMMMD, SYMRCM.
+
+% --------------------------------------------------------------------------
+% Copyright 1994-2007, Tim Davis, University of Florida
+% Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License.
+% email: davis at cise.ufl.edu CISE Department, Univ. of Florida.
+% web: http://www.cise.ufl.edu/research/sparse/amd
+% --------------------------------------------------------------------------
+%
+% Acknowledgements: This work was supported by the National Science
+% Foundation, under grants ASC-9111263, DMS-9223088, and CCR-0203270.
+
+error ('amd2 mexFunction not found') ;
diff --git a/AMD/MATLAB/amd_demo.m b/AMD/MATLAB/amd_demo.m
new file mode 100644
index 0000000..e889e01
--- /dev/null
+++ b/AMD/MATLAB/amd_demo.m
@@ -0,0 +1,83 @@
+function amd_demo
+%AMD_DEMO a demo of amd2, using the can_24 matrix
+%
+% A demo of AMD for MATLAB.
+%
+% Example:
+% amd_demo
+%
+% See also: amd, amd2, amd_make
+
+% Copyright 1994-2007, Tim Davis, University of Florida,
+% Patrick R. Amestoy, and Iain S. Duff.
+
+% This orders the same matrix as the ANSI C demo, amd_demo.c. It includes an
+% additional analysis of the matrix via MATLAB's symbfact routine.
+
+% First, print the help information for AMD
+help amd2
+
+% Get the Harwell/Boeing can_24 matrix.
+
+load can_24
+A = spconvert (can_24) ;
+
+n = size (A,1) ;
+
+figure (1)
+clf
+hold off
+subplot (2,2,1) ;
+spy (A)
+title ('HB/can24 matrix') ;
+
+% order the matrix. Note that the Info argument is optional.
+fprintf ('\nIf the next step fails, then you have\n') ;
+fprintf ('not yet compiled the AMD mexFunction.\n') ;
+[p, Info] = amd2 (A) ; %#ok
+
+% order again, but this time print some statistics
+[p, Info] = amd2 (A, [10 1 1]) ;
+
+fprintf ('Permutation vector:\n') ;
+fprintf (' %2d', p) ;
+fprintf ('\n\n') ;
+
+subplot (2,2,2) ;
+spy (A (p,p)) ;
+title ('Permuted matrix') ;
+
+% The amd_demo.c program stops here.
+
+fprintf ('Analyze A(p,p) with MATLAB''s symbfact routine:\n') ;
+[cn, height, parent, post, R] = symbfact (A (p,p)) ;
+
+subplot (2,2,3) ;
+spy (R') ;
+title ('Cholesky factor, L') ;
+
+subplot (2,2,4) ;
+treeplot (parent) ;
+title ('elimination tree') ;
+
+% results from symbfact
+lnz = sum (cn) ; % number of nonzeros in L, incl. diagonal
+cn = cn - 1 ; % get the count of off-diagonal entries
+fl = n + sum (cn.^2 + 2*cn) ; % flop count for chol (A (p,p)
+fprintf ('number of nonzeros in L (including diagonal): %d\n', lnz) ;
+fprintf ('floating point operation count for chol (A (p,p)): %d\n', fl) ;
+
+% approximations from amd:
+lnz2 = n + Info (10) ;
+fl2 = n + Info (11) + 2 * Info (12) ;
+fprintf ('\nResults from AMD''s approximate analysis:\n') ;
+fprintf ('number of nonzeros in L (including diagonal): %d\n', lnz2) ;
+fprintf ('floating point operation count for chol (A (p,p)): %d\n\n', fl2) ;
+
+if (lnz2 ~= lnz | fl ~= fl2) %#ok
+ fprintf ('Note that the nonzero and flop counts from AMD are slight\n') ;
+ fprintf ('upper bounds. This is due to the approximate minimum degree\n');
+ fprintf ('method used, in conjunction with "mass elimination".\n') ;
+ fprintf ('See the discussion about mass elimination in amd.h and\n') ;
+ fprintf ('amd_2.c for more details.\n') ;
+end
diff --git a/AMD/MATLAB/amd_demo.m.out b/AMD/MATLAB/amd_demo.m.out
new file mode 100644
index 0000000..4e64482
--- /dev/null
+++ b/AMD/MATLAB/amd_demo.m.out
@@ -0,0 +1,125 @@
+amd_demo
+ AMD2 p = amd2 (A), the approximate minimum degree ordering of A
+ P = AMD2 (S) returns the approximate minimum degree permutation vector for
+ the sparse matrix C = S+S'. The Cholesky factorization of C (P,P), or
+ S (P,P), tends to be sparser than that of C or S. AMD tends to be faster
+ than SYMMMD and SYMAMD, and tends to return better orderings than SYMMMD.
+ S must be square. If S is full, amd(S) is equivalent to amd(sparse(S)).
+
+ Note that the built-in AMD routine in MATLAB is identical to AMD2,
+ except that AMD in MATLAB allows for a struct input to set the parameters.
+
+ Usage: P = amd2 (S) ; % finds the ordering
+ [P, Info] = amd2 (S, Control) ; % optional parameters & statistics
+ Control = amd2 ; % returns default parameters
+ amd2 ; % prints default parameters.
+
+ Control (1); If S is n-by-n, then rows/columns with more than
+ max (16, (Control (1))* sqrt(n)) entries in S+S' are considered
+ "dense", and ignored during ordering. They are placed last in the
+ output permutation. The default is 10.0 if Control is not present.
+ Control (2): If nonzero, then aggressive absorption is performed.
+ This is the default if Control is not present.
+ Control (3): If nonzero, print statistics about the ordering.
+
+ Info (1): status (0: ok, -1: out of memory, -2: matrix invalid)
+ Info (2): n = size (A,1)
+ Info (3): nnz (A)
+ Info (4): the symmetry of the matrix S (0.0 means purely unsymmetric,
+ 1.0 means purely symmetric). Computed as:
+ B = tril (S, -1) + triu (S, 1) ; symmetry = nnz (B & B') / nnz (B);
+ Info (5): nnz (diag (S))
+ Info (6): nnz in S+S', excluding the diagonal (= nnz (B+B'))
+ Info (7): number "dense" rows/columns in S+S'
+ Info (8): the amount of memory used by AMD, in bytes
+ Info (9): the number of memory compactions performed by AMD
+
+ The following statistics are slight upper bounds because of the
+ approximate degree in AMD. The bounds are looser if "dense" rows/columns
+ are ignored during ordering (Info (7) > 0). The statistics are for a
+ subsequent factorization of the matrix C (P,P). The LU factorization
+ statistics assume no pivoting.
+
+ Info (10): the number of nonzeros in L, excluding the diagonal
+ Info (11): the number of divide operations for LL', LDL', or LU
+ Info (12): the number of multiply-subtract pairs for LL' or LDL'
+ Info (13): the number of multiply-subtract pairs for LU
+ Info (14): the max # of nonzeros in any column of L (incl. diagonal)
+ Info (15:20): unused, reserved for future use
+
+ An assembly tree post-ordering is performed, which is typically the same
+ as an elimination tree post-ordering. It is not always identical because
+ of the approximate degree update used, and because "dense" rows/columns
+ do not take part in the post-order. It well-suited for a subsequent
+ "chol", however. If you require a precise elimination tree post-ordering,
+ then see the example below:
+
+ Example:
+
+ P = amd2 (S) ;
+ C = spones (S) + spones (S') ; % skip this if S already symmetric
+ [ignore, Q] = etree (C (P,P)) ;
+ P = P (Q) ;
+
+ See also AMD, COLMMD, COLAMD, COLPERM, SYMAMD, SYMMMD, SYMRCM.
+
+
+If the next step fails, then you have
+not yet compiled the AMD mexFunction.
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+ input matrix A is 24-by-24
+ input matrix A has 160 nonzero entries
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 1516
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+Permutation vector:
+ 23 21 11 24 13 6 17 9 15 5 16 8 2 10 14 18 1 3 4 7 12 19 22 20
+
+Analyze A(p,p) with MATLAB's symbfact routine:
+number of nonzeros in L (including diagonal): 120
+floating point operation count for chol (A (p,p)): 656
+
+Results from AMD's approximate analysis:
+number of nonzeros in L (including diagonal): 121
+floating point operation count for chol (A (p,p)): 671
+
+Note that the nonzero and flop counts from AMD are slight
+upper bounds. This is due to the approximate minimum degree
+method used, in conjunction with "mass elimination".
+See the discussion about mass elimination in amd.h and
+amd_2.c for more details.
+diary off
diff --git a/AMD/MATLAB/amd_install.m b/AMD/MATLAB/amd_install.m
new file mode 100644
index 0000000..844fc85
--- /dev/null
+++ b/AMD/MATLAB/amd_install.m
@@ -0,0 +1,20 @@
+function amd_install
+%AMD_INSTALL compile and install amd2 for use in MATLAB
+% Your current directory must be AMD/MATLAB for this function to work.
+%
+% Example:
+% amd_install
+%
+% See also amd, amd2.
+
+% Copyright 1994-2007, Tim Davis, University of Florida,
+% Patrick R. Amestoy, and Iain S. Duff.
+
+% This orders the same matrix as the ANSI C demo, amd_demo.c. It includes an
+
+amd_make
+addpath (pwd)
+fprintf ('\nThe following path has been added. You may wish to add it\n') ;
+fprintf ('permanently, using the MATLAB pathtool command.\n') ;
+fprintf ('%s\n\n', pwd) ;
+amd_demo
diff --git a/AMD/MATLAB/amd_make.m b/AMD/MATLAB/amd_make.m
new file mode 100644
index 0000000..18e5b50
--- /dev/null
+++ b/AMD/MATLAB/amd_make.m
@@ -0,0 +1,32 @@
+function amd_make
+%AMD_MAKE to compile amd2 for use in MATLAB
+%
+% Example:
+% amd_make
+%
+% See also amd, amd2.
+
+% Copyright 1994-2007, Tim Davis, University of Florida,
+% Patrick R. Amestoy, and Iain S. Duff.
+
+details = 0 ; % 1 if details of each command are to be printed
+
+d = '' ;
+if (~isempty (strfind (computer, '64')))
+ d = '-largeArrayDims' ;
+end
+
+i = sprintf ('-I..%sInclude -I..%s..%sUFconfig', filesep, filesep, filesep) ;
+cmd = sprintf ('mex -O %s -DDLONG -output amd2 %s amd_mex.c', d, i) ;
+files = {'amd_order', 'amd_dump', 'amd_postorder', 'amd_post_tree', ...
+ 'amd_aat', 'amd_2', 'amd_1', 'amd_defaults', 'amd_control', ...
+ 'amd_info', 'amd_valid', 'amd_global', 'amd_preprocess' } ;
+for i = 1 : length (files)
+ cmd = sprintf ('%s ..%sSource%s%s.c', cmd, filesep, filesep, files {i}) ;
+end
+if (details)
+ fprintf ('%s\n', cmd) ;
+end
+eval (cmd) ;
+
+fprintf ('AMD successfully compiled.\n') ;
diff --git a/AMD/MATLAB/amd_mex.c b/AMD/MATLAB/amd_mex.c
new file mode 100644
index 0000000..1d36c7b
--- /dev/null
+++ b/AMD/MATLAB/amd_mex.c
@@ -0,0 +1,199 @@
+/* ========================================================================= */
+/* === AMD mexFunction ===================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/*
+ * Usage:
+ * p = amd (A)
+ * p = amd (A, Control)
+ * [p, Info] = amd (A)
+ * [p, Info] = amd (A, Control)
+ * Control = amd ; % return the default Control settings for AMD
+ * amd ; % print the default Control settings for AMD
+ *
+ * Given a square matrix A, compute a permutation P suitable for a Cholesky
+ * factorization of the matrix B (P,P), where B = spones (A) + spones (A').
+ * The method used is the approximate minimum degree ordering method. See
+ * amd.m and amd.h for more information.
+ *
+ * The input matrix need not have sorted columns, and can have duplicate
+ * entries.
+ */
+
+#include "amd.h"
+#include "mex.h"
+#include "matrix.h"
+#include "UFconfig.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ UF_long i, m, n, *Ap, *Ai, *P, nc, result, spumoni, full ;
+ double *Pout, *InfoOut, Control [AMD_CONTROL], Info [AMD_INFO], *ControlIn ;
+ mxArray *A ;
+
+ /* --------------------------------------------------------------------- */
+ /* get control parameters */
+ /* --------------------------------------------------------------------- */
+
+ amd_malloc = mxMalloc ;
+ amd_free = mxFree ;
+ amd_calloc = mxCalloc ;
+ amd_realloc = mxRealloc ;
+ amd_printf = mexPrintf ;
+
+ spumoni = 0 ;
+ if (nargin == 0)
+ {
+ /* get the default control parameters, and return */
+ pargout [0] = mxCreateDoubleMatrix (AMD_CONTROL, 1, mxREAL) ;
+ amd_l_defaults (mxGetPr (pargout [0])) ;
+ if (nargout == 0)
+ {
+ amd_l_control (mxGetPr (pargout [0])) ;
+ }
+ return ;
+ }
+
+ amd_l_defaults (Control) ;
+ if (nargin > 1)
+ {
+ ControlIn = mxGetPr (pargin [1]) ;
+ nc = mxGetM (pargin [1]) * mxGetN (pargin [1]) ;
+ Control [AMD_DENSE]
+ = (nc > 0) ? ControlIn [AMD_DENSE] : AMD_DEFAULT_DENSE ;
+ Control [AMD_AGGRESSIVE]
+ = (nc > 1) ? ControlIn [AMD_AGGRESSIVE] : AMD_DEFAULT_AGGRESSIVE ;
+ spumoni = (nc > 2) ? (ControlIn [2] != 0) : 0 ;
+ }
+
+ if (spumoni > 0)
+ {
+ amd_l_control (Control) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* get inputs */
+ /* --------------------------------------------------------------------- */
+
+ if (nargout > 2 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: p = amd (A)\nor [p, Info] = amd (A, Control)") ;
+ }
+
+ A = (mxArray *) pargin [0] ;
+ n = mxGetN (A) ;
+ m = mxGetM (A) ;
+ if (spumoni > 0)
+ {
+ mexPrintf (" input matrix A is %d-by-%d\n", m, n) ;
+ }
+ if (mxGetNumberOfDimensions (A) != 2)
+ {
+ mexErrMsgTxt ("amd: A must be 2-dimensional") ;
+ }
+ if (m != n)
+ {
+ mexErrMsgTxt ("amd: A must be square") ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* allocate workspace for output permutation */
+ /* --------------------------------------------------------------------- */
+
+ P = mxMalloc ((n+1) * sizeof (UF_long)) ;
+
+ /* --------------------------------------------------------------------- */
+ /* if A is full, convert to a sparse matrix */
+ /* --------------------------------------------------------------------- */
+
+ full = !mxIsSparse (A) ;
+ if (full)
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf (
+ " input matrix A is full (sparse copy of A will be created)\n");
+ }
+ mexCallMATLAB (1, &A, 1, (mxArray **) pargin, "sparse") ;
+ }
+ Ap = (UF_long *) mxGetJc (A) ;
+ Ai = (UF_long *) mxGetIr (A) ;
+ if (spumoni > 0)
+ {
+ mexPrintf (" input matrix A has %d nonzero entries\n", Ap [n]) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* order the matrix */
+ /* --------------------------------------------------------------------- */
+
+ result = amd_l_order (n, Ap, Ai, P, Control, Info) ;
+
+ /* --------------------------------------------------------------------- */
+ /* if A is full, free the sparse copy of A */
+ /* --------------------------------------------------------------------- */
+
+ if (full)
+ {
+ mxDestroyArray (A) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* print results (including return value) */
+ /* --------------------------------------------------------------------- */
+
+ if (spumoni > 0)
+ {
+ amd_l_info (Info) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* check error conditions */
+ /* --------------------------------------------------------------------- */
+
+ if (result == AMD_OUT_OF_MEMORY)
+ {
+ mexErrMsgTxt ("amd: out of memory") ;
+ }
+ else if (result == AMD_INVALID)
+ {
+ mexErrMsgTxt ("amd: input matrix A is corrupted") ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* copy the outputs to MATLAB */
+ /* --------------------------------------------------------------------- */
+
+ /* output permutation, P */
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ Pout = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Pout [i] = P [i] + 1 ; /* change to 1-based indexing for MATLAB */
+ }
+ mxFree (P) ;
+
+ /* Info */
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (AMD_INFO, 1, mxREAL) ;
+ InfoOut = mxGetPr (pargout [1]) ;
+ for (i = 0 ; i < AMD_INFO ; i++)
+ {
+ InfoOut [i] = Info [i] ;
+ }
+ }
+}
diff --git a/AMD/MATLAB/can_24 b/AMD/MATLAB/can_24
new file mode 100644
index 0000000..38158a1
--- /dev/null
+++ b/AMD/MATLAB/can_24
@@ -0,0 +1,160 @@
+ 1 1 1
+ 6 1 1
+ 7 1 1
+13 1 1
+14 1 1
+18 1 1
+19 1 1
+20 1 1
+22 1 1
+ 2 2 1
+ 9 2 1
+10 2 1
+14 2 1
+15 2 1
+18 2 1
+ 3 3 1
+ 7 3 1
+12 3 1
+21 3 1
+22 3 1
+23 3 1
+ 4 4 1
+ 8 4 1
+11 4 1
+16 4 1
+19 4 1
+20 4 1
+ 5 5 1
+ 8 5 1
+10 5 1
+15 5 1
+16 5 1
+17 5 1
+ 1 6 1
+ 6 6 1
+ 7 6 1
+13 6 1
+14 6 1
+18 6 1
+ 1 7 1
+ 3 7 1
+ 6 7 1
+ 7 7 1
+12 7 1
+13 7 1
+20 7 1
+22 7 1
+24 7 1
+ 4 8 1
+ 5 8 1
+ 8 8 1
+10 8 1
+15 8 1
+16 8 1
+17 8 1
+18 8 1
+19 8 1
+ 2 9 1
+ 9 9 1
+10 9 1
+15 9 1
+ 2 10 1
+ 5 10 1
+ 8 10 1
+ 9 10 1
+10 10 1
+14 10 1
+15 10 1
+18 10 1
+19 10 1
+ 4 11 1
+11 11 1
+19 11 1
+20 11 1
+21 11 1
+22 11 1
+ 3 12 1
+ 7 12 1
+12 12 1
+13 12 1
+22 12 1
+24 12 1
+ 1 13 1
+ 6 13 1
+ 7 13 1
+12 13 1
+13 13 1
+24 13 1
+ 1 14 1
+ 2 14 1
+ 6 14 1
+10 14 1
+14 14 1
+18 14 1
+ 2 15 1
+ 5 15 1
+ 8 15 1
+ 9 15 1
+10 15 1
+15 15 1
+ 4 16 1
+ 5 16 1
+ 8 16 1
+16 16 1
+17 16 1
+19 16 1
+ 5 17 1
+ 8 17 1
+16 17 1
+17 17 1
+ 1 18 1
+ 2 18 1
+ 6 18 1
+ 8 18 1
+10 18 1
+14 18 1
+18 18 1
+19 18 1
+20 18 1
+ 1 19 1
+ 4 19 1
+ 8 19 1
+10 19 1
+11 19 1
+16 19 1
+18 19 1
+19 19 1
+20 19 1
+ 1 20 1
+ 4 20 1
+ 7 20 1
+11 20 1
+18 20 1
+19 20 1
+20 20 1
+21 20 1
+22 20 1
+ 3 21 1
+11 21 1
+20 21 1
+21 21 1
+22 21 1
+23 21 1
+ 1 22 1
+ 3 22 1
+ 7 22 1
+11 22 1
+12 22 1
+20 22 1
+21 22 1
+22 22 1
+23 22 1
+ 3 23 1
+21 23 1
+22 23 1
+23 23 1
+ 7 24 1
+12 24 1
+13 24 1
+24 24 1
diff --git a/AMD/Makefile b/AMD/Makefile
new file mode 100644
index 0000000..ce727aa
--- /dev/null
+++ b/AMD/Makefile
@@ -0,0 +1,67 @@
+#------------------------------------------------------------------------------
+# AMD Makefile (for GNU Make or original make)
+#------------------------------------------------------------------------------
+
+default: demo
+
+include ../UFconfig/UFconfig.mk
+
+# Compile all C code, including the C-callable routines.
+# Do not compile the FORTRAN versions, or MATLAB interface.
+demo:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+# Compile all C code, including the C-callable routine and the mexFunctions.
+# Do not compile the FORTRAN versions.
+all:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+ ( cd MATLAB ; $(MAKE) )
+
+# compile just the C-callable libraries (not mexFunctions or Demos)
+library:
+ ( cd Lib ; $(MAKE) )
+
+# compile the FORTRAN libraries and demo programs (not compiled by "make all")
+fortran:
+ ( cd Lib ; $(MAKE) fortran )
+ ( cd Demo ; $(MAKE) fortran )
+
+# compile a FORTRAN demo program that calls the C version of AMD
+# (not compiled by "make all")
+cross:
+ ( cd Demo ; $(MAKE) cross )
+
+# remove object files, but keep the compiled programs and library archives
+clean:
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+ ( cd MATLAB ; $(MAKE) clean )
+ ( cd Doc ; $(MAKE) clean )
+
+# clean, and then remove compiled programs and library archives
+purge:
+ ( cd Lib ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd MATLAB ; $(MAKE) purge )
+ ( cd Doc ; $(MAKE) purge )
+
+distclean: purge
+
+# create PDF documents for the original distribution
+doc:
+ ( cd Doc ; $(MAKE) )
+
+# get ready for distribution
+dist: purge
+ ( cd Demo ; $(MAKE) dist )
+ ( cd Doc ; $(MAKE) )
+
+ccode: library
+
+lib: library
+
+# compile the MATLAB mexFunction
+mex:
+ ( cd MATLAB ; $(MAKE) )
diff --git a/AMD/README.txt b/AMD/README.txt
new file mode 100644
index 0000000..c6fd2e0
--- /dev/null
+++ b/AMD/README.txt
@@ -0,0 +1,215 @@
+AMD Version 2.2, Copyright (c) 2007 by Timothy A.
+Davis, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved.
+AMD is available under alternate licences; contact T. Davis for details.
+
+AMD: a set of routines for permuting sparse matrices prior to
+ factorization. Includes a version in C, a version in Fortran, and a MATLAB
+ mexFunction.
+
+Requires UFconfig, in the ../UFconfig directory relative to this directory.
+
+Quick start (Unix, or Windows with Cygwin):
+
+ To compile, test, and install AMD, you may wish to first configure the
+ installation by editting the ../UFconfig/UFconfig.mk file. Next, cd to this
+ directory (AMD) and type "make" (or "make lib" if you do not have MATLAB).
+ To compile and run a demo program for the Fortran version, type
+ "make fortran". When done, type "make clean" to remove unused *.o files
+ (keeps the compiled libraries and demo programs). See the User Guide
+ (Doc/AMD_UserGuide.pdf), or ../UFconfig/UFconfig.mk for more details.
+
+Quick start (for MATLAB users);
+
+ To compile, test, and install the AMD mexFunction, cd to the
+ AMD/MATLAB directory and type amd_make at the MATLAB prompt.
+
+If you have MATLAB 7.2 or earlier and use "make mex", you must first edit
+UFconfig/UFconfig.h to remove the "-largeArrayDims" option from the MEX command
+(or just use amd_make.m inside MATLAB).
+
+-------------------------------------------------------------------------------
+
+AMD License:
+
+ Your use or distribution of AMD or any modified version of
+ AMD implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/amd
+
+-------------------------------------------------------------------------------
+
+This is the AMD README file. It is a terse overview of AMD.
+Refer to the User Guide (Doc/AMD_UserGuide.pdf) for how to install
+and use AMD.
+
+Description:
+
+ AMD is a set of routines for pre-ordering sparse matrices prior to Cholesky
+ or LU factorization, using the approximate minimum degree ordering
+ algorithm. Written in ANSI/ISO C with a MATLAB interface, and in
+ Fortran 77.
+
+Authors:
+
+ Timothy A. Davis (davis at cise.ufl.edu), University of Florida.
+ Patrick R. Amestory, ENSEEIHT, Toulouse, France.
+ Iain S. Duff, Rutherford Appleton Laboratory, UK.
+
+Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+
+ Portions of this work were done while on sabbatical at Stanford University
+ and Lawrence Berkeley National Laboratory (with funding from the SciDAC
+ program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon
+ for making this sabbatical possible.
+
+-------------------------------------------------------------------------------
+Files and directories in the AMD distribution:
+-------------------------------------------------------------------------------
+
+ ---------------------------------------------------------------------------
+ Subdirectories of the AMD directory:
+ ---------------------------------------------------------------------------
+
+ Doc documentation
+ Source primary source code
+ Include include file for use in your code that calls AMD
+ Demo demo programs. also serves as test of the AMD installation.
+ MATLAB AMD mexFunction for MATLAB, and supporting m-files
+ Lib where the compiled C-callable and Fortran-callable
+ AMD libraries placed.
+
+ ---------------------------------------------------------------------------
+ Files in the AMD directory:
+ ---------------------------------------------------------------------------
+
+ Makefile top-level Makefile for GNU make or original make.
+ Windows users would require Cygwin to use "make"
+
+ README.txt this file
+
+ ---------------------------------------------------------------------------
+ Doc directory: documentation
+ ---------------------------------------------------------------------------
+
+ ChangeLog change log
+ License the AMD License
+ Makefile for creating the documentation
+ AMD_UserGuide.bib AMD User Guide (references)
+ AMD_UserGuide.tex AMD User Guide (LaTeX)
+ AMD_UserGuide.pdf AMD User Guide (PDF)
+ lesser.txt the GNU LGPL license
+
+ ---------------------------------------------------------------------------
+ Source directory:
+ ---------------------------------------------------------------------------
+
+ amd_order.c user-callable, primary AMD ordering routine
+ amd_control.c user-callable, prints the control parameters
+ amd_defaults.c user-callable, sets default control parameters
+ amd_info.c user-callable, prints the statistics from AMD
+
+ amd_1.c non-user-callable, construct A+A'
+ amd_2.c user-callable, primary ordering kernel
+ (a C version of amd.f and amdbar.f, with
+ post-ordering added)
+ amd_aat.c non-user-callable, computes nnz (A+A')
+ amd_dump.c non-user-callable, debugging routines
+ amd_postorder.c non-user-callable, postorder
+ amd_post_tree.c non-user-callable, postorder just one tree
+ amd_valid.c non-user-callable, verifies a matrix
+ amd_preprocess.c non-user-callable, computes A', removes duplic
+
+ amd.f user-callable Fortran 77 version
+ amdbar.f user-callable Fortran 77 version
+
+ ---------------------------------------------------------------------------
+ Include directory:
+ ---------------------------------------------------------------------------
+
+ amd.h include file for C programs that use AMD
+ amd_internal.h non-user-callable, include file for AMD
+
+ ---------------------------------------------------------------------------
+ Demo directory:
+ ---------------------------------------------------------------------------
+
+ Makefile for GNU make or original make
+
+ amd_demo.c C demo program for AMD
+ amd_demo.out output of amd_demo.c
+
+ amd_demo2.c C demo program for AMD, jumbled matrix
+ amd_demo2.out output of amd_demo2.c
+
+ amd_l_demo.c C demo program for AMD (UF_long version)
+ amd_l_demo.out output of amd_l_demo.c
+
+ amd_simple.c simple C demo program for AMD
+ amd_simple.out output of amd_simple.c
+
+ amd_f77demo.f Fortran 77 demo program for AMD
+ amd_f77demo.out output of amd_f77demo.f
+
+ amd_f77simple.c simple Fortran 77 demo program for AMD
+ amd_f77simple.out output of amd_f77simple.f
+
+ amd_f77cross.f Fortran 77 demo, calls the C version of AMD
+ amd_f77cross.out output of amd_f77cross.f
+ amd_f77wrapper.c Fortran-callable wrapper for C version of AMD
+
+ ---------------------------------------------------------------------------
+ MATLAB directory:
+ ---------------------------------------------------------------------------
+
+ GNUmakefile a nice Makefile, for GNU make
+ Makefile an ugly Unix Makefile (for older make's)
+
+ Contents.m for "help amd2" listing of toolbox contents
+
+ amd2.m MATLAB help file for AMD
+ amd_make.m MATLAB m-file for compiling AMD mexFunction
+ amd_install.m compile and install the AMD mexFunction
+
+ amd_mex.c AMD mexFunction for MATLAB
+
+ amd_demo.m MATLAB demo for AMD
+ amd_demo.m.out diary output of amd_demo.m
+ can_24.mat input file for AMD demo
+
+ ---------------------------------------------------------------------------
+ Lib directory: libamd.a and libamdf77.a libraries placed here
+ ---------------------------------------------------------------------------
+
+ GNUmakefile a nice Makefile, for GNU make
+ Makefile an ugly Unix Makefile (for older make's)
+ libamd.def AMD definitions for Windows
diff --git a/AMD/Source/amd.f b/AMD/Source/amd.f
new file mode 100644
index 0000000..ccfe3e8
--- /dev/null
+++ b/AMD/Source/amd.f
@@ -0,0 +1,1214 @@
+C-----------------------------------------------------------------------
+C AMD: approximate minimum degree, with aggressive absorption
+C-----------------------------------------------------------------------
+
+ SUBROUTINE AMD
+ $ (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT,
+ $ LAST, HEAD, ELEN, DEGREE, NCMPA, W)
+
+ INTEGER N, IWLEN, PFREE, NCMPA, IW (IWLEN), PE (N),
+ $ DEGREE (N), NV (N), NEXT (N), LAST (N), HEAD (N),
+ $ ELEN (N), W (N), LEN (N)
+
+C Given a representation of the nonzero pattern of a symmetric matrix,
+C A, (excluding the diagonal) perform an approximate minimum
+C (UMFPACK/MA38-style) degree ordering to compute a pivot order
+C such that the introduction of nonzeros (fill-in) in the Cholesky
+C factors A = LL^T are kept low. At each step, the pivot
+C selected is the one with the minimum UMFPACK/MA38-style
+C upper-bound on the external degree.
+C
+C Aggresive absorption is used to tighten the bound on the degree.
+
+C **********************************************************************
+C ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ******
+C **********************************************************************
+
+C References:
+C
+C [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern
+C multifrontal method for sparse LU factorization", SIAM J.
+C Matrix Analysis and Applications, vol. 18, no. 1, pp.
+C 140-158. Discusses UMFPACK / MA38, which first introduced
+C the approximate minimum degree used by this routine.
+C
+C [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An
+C approximate degree ordering algorithm," SIAM J. Matrix
+C Analysis and Applications, vol. 17, no. 4, pp. 886-905,
+C 1996. Discusses AMD, AMDBAR, and MC47B.
+C
+C [3] Alan George and Joseph Liu, "The evolution of the minimum
+C degree ordering algorithm," SIAM Review, vol. 31, no. 1,
+C pp. 1-19, 1989. We list below the features mentioned in
+C that paper that this code includes:
+C
+C mass elimination:
+C Yes. MA27 relied on supervariable detection for mass
+C elimination.
+C indistinguishable nodes:
+C Yes (we call these "supervariables"). This was also in
+C the MA27 code - although we modified the method of
+C detecting them (the previous hash was the true degree,
+C which we no longer keep track of). A supervariable is
+C a set of rows with identical nonzero pattern. All
+C variables in a supervariable are eliminated together.
+C Each supervariable has as its numerical name that of
+C one of its variables (its principal variable).
+C quotient graph representation:
+C Yes. We use the term "element" for the cliques formed
+C during elimination. This was also in the MA27 code.
+C The algorithm can operate in place, but it will work
+C more efficiently if given some "elbow room."
+C element absorption:
+C Yes. This was also in the MA27 code.
+C external degree:
+C Yes. The MA27 code was based on the true degree.
+C incomplete degree update and multiple elimination:
+C No. This was not in MA27, either. Our method of
+C degree update within MC47B/BD is element-based, not
+C variable-based. It is thus not well-suited for use
+C with incomplete degree update or multiple elimination.
+
+C-----------------------------------------------------------------------
+C Authors, and Copyright (C) 1995 by:
+C Timothy A. Davis, Patrick Amestoy, Iain S. Duff, & John K. Reid.
+C
+C Acknowledgements:
+C This work (and the UMFPACK package) was supported by the
+C National Science Foundation (ASC-9111263 and DMS-9223088).
+C The UMFPACK/MA38 approximate degree update algorithm, the
+C unsymmetric analog which forms the basis of MC47B/BD, was
+C developed while Tim Davis was supported by CERFACS (Toulouse,
+C France) in a post-doctoral position.
+C
+C Date: September, 1995
+C-----------------------------------------------------------------------
+
+C-----------------------------------------------------------------------
+C INPUT ARGUMENTS (unaltered):
+C-----------------------------------------------------------------------
+
+C n: The matrix order.
+C
+C Restriction: 1 .le. n .lt. (iovflo/2)-2, where iovflo is
+C the largest positive integer that your computer can represent.
+
+C iwlen: The length of iw (1..iwlen). On input, the matrix is
+C stored in iw (1..pfree-1). However, iw (1..iwlen) should be
+C slightly larger than what is required to hold the matrix, at
+C least iwlen .ge. pfree + n is recommended. Otherwise,
+C excessive compressions will take place.
+C *** We do not recommend running this algorithm with ***
+C *** iwlen .lt. pfree + n. ***
+C *** Better performance will be obtained if ***
+C *** iwlen .ge. pfree + n ***
+C *** or better yet ***
+C *** iwlen .gt. 1.2 * pfree ***
+C *** (where pfree is its value on input). ***
+C The algorithm will not run at all if iwlen .lt. pfree-1.
+C
+C Restriction: iwlen .ge. pfree-1
+
+C-----------------------------------------------------------------------
+C INPUT/OUPUT ARGUMENTS:
+C-----------------------------------------------------------------------
+
+C pe: On input, pe (i) is the index in iw of the start of row i, or
+C zero if row i has no off-diagonal non-zeros.
+C
+C During execution, it is used for both supervariables and
+C elements:
+C
+C * Principal supervariable i: index into iw of the
+C description of supervariable i. A supervariable
+C represents one or more rows of the matrix
+C with identical nonzero pattern.
+C * Non-principal supervariable i: if i has been absorbed
+C into another supervariable j, then pe (i) = -j.
+C That is, j has the same pattern as i.
+C Note that j might later be absorbed into another
+C supervariable j2, in which case pe (i) is still -j,
+C and pe (j) = -j2.
+C * Unabsorbed element e: the index into iw of the description
+C of element e, if e has not yet been absorbed by a
+C subsequent element. Element e is created when
+C the supervariable of the same name is selected as
+C the pivot.
+C * Absorbed element e: if element e is absorbed into element
+C e2, then pe (e) = -e2. This occurs when the pattern of
+C e (that is, Le) is found to be a subset of the pattern
+C of e2 (that is, Le2). If element e is "null" (it has
+C no nonzeros outside its pivot block), then pe (e) = 0.
+C
+C On output, pe holds the assembly tree/forest, which implicitly
+C represents a pivot order with identical fill-in as the actual
+C order (via a depth-first search of the tree).
+C
+C On output:
+C If nv (i) .gt. 0, then i represents a node in the assembly tree,
+C and the parent of i is -pe (i), or zero if i is a root.
+C If nv (i) = 0, then (i,-pe (i)) represents an edge in a
+C subtree, the root of which is a node in the assembly tree.
+
+C pfree: On input the tail end of the array, iw (pfree..iwlen),
+C is empty, and the matrix is stored in iw (1..pfree-1).
+C During execution, additional data is placed in iw, and pfree
+C is modified so that iw (pfree..iwlen) is always the unused part
+C of iw. On output, pfree is set equal to the size of iw that
+C would have been needed for no compressions to occur. If
+C ncmpa is zero, then pfree (on output) is less than or equal to
+C iwlen, and the space iw (pfree+1 ... iwlen) was not used.
+C Otherwise, pfree (on output) is greater than iwlen, and all the
+C memory in iw was used.
+
+C-----------------------------------------------------------------------
+C INPUT/MODIFIED (undefined on output):
+C-----------------------------------------------------------------------
+
+C len: On input, len (i) holds the number of entries in row i of the
+C matrix, excluding the diagonal. The contents of len (1..n)
+C are undefined on output.
+
+C iw: On input, iw (1..pfree-1) holds the description of each row i
+C in the matrix. The matrix must be symmetric, and both upper
+C and lower triangular parts must be present. The diagonal must
+C not be present. Row i is held as follows:
+C
+C len (i): the length of the row i data structure
+C iw (pe (i) ... pe (i) + len (i) - 1):
+C the list of column indices for nonzeros
+C in row i (simple supervariables), excluding
+C the diagonal. All supervariables start with
+C one row/column each (supervariable i is just
+C row i).
+C if len (i) is zero on input, then pe (i) is ignored
+C on input.
+C
+C Note that the rows need not be in any particular order,
+C and there may be empty space between the rows.
+C
+C During execution, the supervariable i experiences fill-in.
+C This is represented by placing in i a list of the elements
+C that cause fill-in in supervariable i:
+C
+C len (i): the length of supervariable i
+C iw (pe (i) ... pe (i) + elen (i) - 1):
+C the list of elements that contain i. This list
+C is kept short by removing absorbed elements.
+C iw (pe (i) + elen (i) ... pe (i) + len (i) - 1):
+C the list of supervariables in i. This list
+C is kept short by removing nonprincipal
+C variables, and any entry j that is also
+C contained in at least one of the elements
+C (j in Le) in the list for i (e in row i).
+C
+C When supervariable i is selected as pivot, we create an
+C element e of the same name (e=i):
+C
+C len (e): the length of element e
+C iw (pe (e) ... pe (e) + len (e) - 1):
+C the list of supervariables in element e.
+C
+C An element represents the fill-in that occurs when supervariable
+C i is selected as pivot (which represents the selection of row i
+C and all non-principal variables whose principal variable is i).
+C We use the term Le to denote the set of all supervariables
+C in element e. Absorbed supervariables and elements are pruned
+C from these lists when computationally convenient.
+C
+C CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION.
+C The contents of iw are undefined on output.
+
+C-----------------------------------------------------------------------
+C OUTPUT (need not be set on input):
+C-----------------------------------------------------------------------
+
+C nv: During execution, abs (nv (i)) is equal to the number of rows
+C that are represented by the principal supervariable i. If i is
+C a nonprincipal variable, then nv (i) = 0. Initially,
+C nv (i) = 1 for all i. nv (i) .lt. 0 signifies that i is a
+C principal variable in the pattern Lme of the current pivot
+C element me. On output, nv (e) holds the true degree of element
+C e at the time it was created (including the diagonal part).
+
+C ncmpa: The number of times iw was compressed. If this is
+C excessive, then the execution took longer than what could have
+C been. To reduce ncmpa, try increasing iwlen to be 10% or 20%
+C larger than the value of pfree on input (or at least
+C iwlen .ge. pfree + n). The fastest performance will be
+C obtained when ncmpa is returned as zero. If iwlen is set to
+C the value returned by pfree on *output*, then no compressions
+C will occur.
+
+C elen: See the description of iw above. At the start of execution,
+C elen (i) is set to zero. During execution, elen (i) is the
+C number of elements in the list for supervariable i. When e
+C becomes an element, elen (e) = -nel is set, where nel is the
+C current step of factorization. elen (i) = 0 is done when i
+C becomes nonprincipal.
+C
+C For variables, elen (i) .ge. 0 holds until just before the
+C permutation vectors are computed. For elements,
+C elen (e) .lt. 0 holds.
+C
+C On output elen (1..n) holds the inverse permutation (the same
+C as the 'INVP' argument in Sparspak). That is, if k = elen (i),
+C then row i is the kth pivot row. Row i of A appears as the
+C (elen(i))-th row in the permuted matrix, PAP^T.
+
+C last: In a degree list, last (i) is the supervariable preceding i,
+C or zero if i is the head of the list. In a hash bucket,
+C last (i) is the hash key for i. last (head (hash)) is also
+C used as the head of a hash bucket if head (hash) contains a
+C degree list (see head, below).
+C
+C On output, last (1..n) holds the permutation (the same as the
+C 'PERM' argument in Sparspak). That is, if i = last (k), then
+C row i is the kth pivot row. Row last (k) of A is the k-th row
+C in the permuted matrix, PAP^T.
+
+C-----------------------------------------------------------------------
+C LOCAL (not input or output - used only during execution):
+C-----------------------------------------------------------------------
+
+C degree: If i is a supervariable, then degree (i) holds the
+C current approximation of the external degree of row i (an upper
+C bound). The external degree is the number of nonzeros in row i,
+C minus abs (nv (i)) (the diagonal part). The bound is equal to
+C the external degree if elen (i) is less than or equal to two.
+C
+C We also use the term "external degree" for elements e to refer
+C to |Le \ Lme|. If e is an element, then degree (e) holds |Le|,
+C which is the degree of the off-diagonal part of the element e
+C (not including the diagonal part).
+
+C head: head is used for degree lists. head (deg) is the first
+C supervariable in a degree list (all supervariables i in a
+C degree list deg have the same approximate degree, namely,
+C deg = degree (i)). If the list deg is empty then
+C head (deg) = 0.
+C
+C During supervariable detection head (hash) also serves as a
+C pointer to a hash bucket.
+C If head (hash) .gt. 0, there is a degree list of degree hash.
+C The hash bucket head pointer is last (head (hash)).
+C If head (hash) = 0, then the degree list and hash bucket are
+C both empty.
+C If head (hash) .lt. 0, then the degree list is empty, and
+C -head (hash) is the head of the hash bucket.
+C After supervariable detection is complete, all hash buckets
+C are empty, and the (last (head (hash)) = 0) condition is
+C restored for the non-empty degree lists.
+
+C next: next (i) is the supervariable following i in a link list, or
+C zero if i is the last in the list. Used for two kinds of
+C lists: degree lists and hash buckets (a supervariable can be
+C in only one kind of list at a time).
+
+C w: The flag array w determines the status of elements and
+C variables, and the external degree of elements.
+C
+C for elements:
+C if w (e) = 0, then the element e is absorbed
+C if w (e) .ge. wflg, then w (e) - wflg is the size of
+C the set |Le \ Lme|, in terms of nonzeros (the
+C sum of abs (nv (i)) for each principal variable i that
+C is both in the pattern of element e and NOT in the
+C pattern of the current pivot element, me).
+C if wflg .gt. w (e) .gt. 0, then e is not absorbed and has
+C not yet been seen in the scan of the element lists in
+C the computation of |Le\Lme| in loop 150 below.
+C
+C for variables:
+C during supervariable detection, if w (j) .ne. wflg then j is
+C not in the pattern of variable i
+C
+C The w array is initialized by setting w (i) = 1 for all i,
+C and by setting wflg = 2. It is reinitialized if wflg becomes
+C too large (to ensure that wflg+n does not cause integer
+C overflow).
+
+C-----------------------------------------------------------------------
+C LOCAL INTEGERS:
+C-----------------------------------------------------------------------
+
+ INTEGER DEG, DEGME, DEXT, DMAX, E, ELENME, ELN, HASH, HMOD, I,
+ $ ILAST, INEXT, J, JLAST, JNEXT, K, KNT1, KNT2, KNT3,
+ $ LENJ, LN, MAXMEM, ME, MEM, MINDEG, NEL, NEWMEM,
+ $ NLEFT, NVI, NVJ, NVPIV, SLENME, WE, WFLG, WNVI, X
+
+C deg: the degree of a variable or element
+C degme: size, |Lme|, of the current element, me (= degree (me))
+C dext: external degree, |Le \ Lme|, of some element e
+C dmax: largest |Le| seen so far
+C e: an element
+C elenme: the length, elen (me), of element list of pivotal var.
+C eln: the length, elen (...), of an element list
+C hash: the computed value of the hash function
+C hmod: the hash function is computed modulo hmod = max (1,n-1)
+C i: a supervariable
+C ilast: the entry in a link list preceding i
+C inext: the entry in a link list following i
+C j: a supervariable
+C jlast: the entry in a link list preceding j
+C jnext: the entry in a link list, or path, following j
+C k: the pivot order of an element or variable
+C knt1: loop counter used during element construction
+C knt2: loop counter used during element construction
+C knt3: loop counter used during compression
+C lenj: len (j)
+C ln: length of a supervariable list
+C maxmem: amount of memory needed for no compressions
+C me: current supervariable being eliminated, and the
+C current element created by eliminating that
+C supervariable
+C mem: memory in use assuming no compressions have occurred
+C mindeg: current minimum degree
+C nel: number of pivots selected so far
+C newmem: amount of new memory needed for current pivot element
+C nleft: n - nel, the number of nonpivotal rows/columns remaining
+C nvi: the number of variables in a supervariable i (= nv (i))
+C nvj: the number of variables in a supervariable j (= nv (j))
+C nvpiv: number of pivots in current element
+C slenme: number of variables in variable list of pivotal variable
+C we: w (e)
+C wflg: used for flagging the w array. See description of iw.
+C wnvi: wflg - nv (i)
+C x: either a supervariable or an element
+
+C-----------------------------------------------------------------------
+C LOCAL POINTERS:
+C-----------------------------------------------------------------------
+
+ INTEGER P, P1, P2, P3, PDST, PEND, PJ, PME, PME1, PME2, PN, PSRC
+
+C Any parameter (pe (...) or pfree) or local variable
+C starting with "p" (for Pointer) is an index into iw,
+C and all indices into iw use variables starting with
+C "p." The only exception to this rule is the iwlen
+C input argument.
+
+C p: pointer into lots of things
+C p1: pe (i) for some variable i (start of element list)
+C p2: pe (i) + elen (i) - 1 for some var. i (end of el. list)
+C p3: index of first supervariable in clean list
+C pdst: destination pointer, for compression
+C pend: end of memory to compress
+C pj: pointer into an element or variable
+C pme: pointer into the current element (pme1...pme2)
+C pme1: the current element, me, is stored in iw (pme1...pme2)
+C pme2: the end of the current element
+C pn: pointer into a "clean" variable, also used to compress
+C psrc: source pointer, for compression
+
+C-----------------------------------------------------------------------
+C FUNCTIONS CALLED:
+C-----------------------------------------------------------------------
+
+ INTRINSIC MAX, MIN, MOD
+
+C=======================================================================
+C INITIALIZATIONS
+C=======================================================================
+
+ WFLG = 2
+ MINDEG = 1
+ NCMPA = 0
+ NEL = 0
+ HMOD = MAX (1, N-1)
+ DMAX = 0
+ MEM = PFREE - 1
+ MAXMEM = MEM
+ ME = 0
+
+ DO 10 I = 1, N
+ LAST (I) = 0
+ HEAD (I) = 0
+ NV (I) = 1
+ W (I) = 1
+ ELEN (I) = 0
+ DEGREE (I) = LEN (I)
+10 CONTINUE
+
+C ----------------------------------------------------------------
+C initialize degree lists and eliminate rows with no off-diag. nz.
+C ----------------------------------------------------------------
+
+ DO 20 I = 1, N
+
+ DEG = DEGREE (I)
+
+ IF (DEG .GT. 0) THEN
+
+C ----------------------------------------------------------
+C place i in the degree list corresponding to its degree
+C ----------------------------------------------------------
+
+ INEXT = HEAD (DEG)
+ IF (INEXT .NE. 0) LAST (INEXT) = I
+ NEXT (I) = INEXT
+ HEAD (DEG) = I
+
+ ELSE
+
+C ----------------------------------------------------------
+C we have a variable that can be eliminated at once because
+C there is no off-diagonal non-zero in its row.
+C ----------------------------------------------------------
+
+ NEL = NEL + 1
+ ELEN (I) = -NEL
+ PE (I) = 0
+ W (I) = 0
+
+ ENDIF
+
+20 CONTINUE
+
+C=======================================================================
+C WHILE (selecting pivots) DO
+C=======================================================================
+
+30 CONTINUE
+ IF (NEL .LT. N) THEN
+
+C=======================================================================
+C GET PIVOT OF MINIMUM DEGREE
+C=======================================================================
+
+C -------------------------------------------------------------
+C find next supervariable for elimination
+C -------------------------------------------------------------
+
+ DO 40 DEG = MINDEG, N
+ ME = HEAD (DEG)
+ IF (ME .GT. 0) GOTO 50
+40 CONTINUE
+50 CONTINUE
+ MINDEG = DEG
+
+C -------------------------------------------------------------
+C remove chosen variable from link list
+C -------------------------------------------------------------
+
+ INEXT = NEXT (ME)
+ IF (INEXT .NE. 0) LAST (INEXT) = 0
+ HEAD (DEG) = INEXT
+
+C -------------------------------------------------------------
+C me represents the elimination of pivots nel+1 to nel+nv(me).
+C place me itself as the first in this set. It will be moved
+C to the nel+nv(me) position when the permutation vectors are
+C computed.
+C -------------------------------------------------------------
+
+ ELENME = ELEN (ME)
+ ELEN (ME) = - (NEL + 1)
+ NVPIV = NV (ME)
+ NEL = NEL + NVPIV
+
+C=======================================================================
+C CONSTRUCT NEW ELEMENT
+C=======================================================================
+
+C -------------------------------------------------------------
+C At this point, me is the pivotal supervariable. It will be
+C converted into the current element. Scan list of the
+C pivotal supervariable, me, setting tree pointers and
+C constructing new list of supervariables for the new element,
+C me. p is a pointer to the current position in the old list.
+C -------------------------------------------------------------
+
+C flag the variable "me" as being in Lme by negating nv (me)
+ NV (ME) = -NVPIV
+ DEGME = 0
+
+ IF (ELENME .EQ. 0) THEN
+
+C ----------------------------------------------------------
+C construct the new element in place
+C ----------------------------------------------------------
+
+ PME1 = PE (ME)
+ PME2 = PME1 - 1
+
+ DO 60 P = PME1, PME1 + LEN (ME) - 1
+ I = IW (P)
+ NVI = NV (I)
+ IF (NVI .GT. 0) THEN
+
+C ----------------------------------------------------
+C i is a principal variable not yet placed in Lme.
+C store i in new list
+C ----------------------------------------------------
+
+ DEGME = DEGME + NVI
+C flag i as being in Lme by negating nv (i)
+ NV (I) = -NVI
+ PME2 = PME2 + 1
+ IW (PME2) = I
+
+C ----------------------------------------------------
+C remove variable i from degree list.
+C ----------------------------------------------------
+
+ ILAST = LAST (I)
+ INEXT = NEXT (I)
+ IF (INEXT .NE. 0) LAST (INEXT) = ILAST
+ IF (ILAST .NE. 0) THEN
+ NEXT (ILAST) = INEXT
+ ELSE
+C i is at the head of the degree list
+ HEAD (DEGREE (I)) = INEXT
+ ENDIF
+
+ ENDIF
+60 CONTINUE
+C this element takes no new memory in iw:
+ NEWMEM = 0
+
+ ELSE
+
+C ----------------------------------------------------------
+C construct the new element in empty space, iw (pfree ...)
+C ----------------------------------------------------------
+
+ P = PE (ME)
+ PME1 = PFREE
+ SLENME = LEN (ME) - ELENME
+
+ DO 120 KNT1 = 1, ELENME + 1
+
+ IF (KNT1 .GT. ELENME) THEN
+C search the supervariables in me.
+ E = ME
+ PJ = P
+ LN = SLENME
+ ELSE
+C search the elements in me.
+ E = IW (P)
+ P = P + 1
+ PJ = PE (E)
+ LN = LEN (E)
+ ENDIF
+
+C -------------------------------------------------------
+C search for different supervariables and add them to the
+C new list, compressing when necessary. this loop is
+C executed once for each element in the list and once for
+C all the supervariables in the list.
+C -------------------------------------------------------
+
+ DO 110 KNT2 = 1, LN
+ I = IW (PJ)
+ PJ = PJ + 1
+ NVI = NV (I)
+ IF (NVI .GT. 0) THEN
+
+C -------------------------------------------------
+C compress iw, if necessary
+C -------------------------------------------------
+
+ IF (PFREE .GT. IWLEN) THEN
+C prepare for compressing iw by adjusting
+C pointers and lengths so that the lists being
+C searched in the inner and outer loops contain
+C only the remaining entries.
+
+ PE (ME) = P
+ LEN (ME) = LEN (ME) - KNT1
+ IF (LEN (ME) .EQ. 0) THEN
+C nothing left of supervariable me
+ PE (ME) = 0
+ ENDIF
+ PE (E) = PJ
+ LEN (E) = LN - KNT2
+ IF (LEN (E) .EQ. 0) THEN
+C nothing left of element e
+ PE (E) = 0
+ ENDIF
+
+ NCMPA = NCMPA + 1
+C store first item in pe
+C set first entry to -item
+ DO 70 J = 1, N
+ PN = PE (J)
+ IF (PN .GT. 0) THEN
+ PE (J) = IW (PN)
+ IW (PN) = -J
+ ENDIF
+70 CONTINUE
+
+C psrc/pdst point to source/destination
+ PDST = 1
+ PSRC = 1
+ PEND = PME1 - 1
+
+C while loop:
+80 CONTINUE
+ IF (PSRC .LE. PEND) THEN
+C search for next negative entry
+ J = -IW (PSRC)
+ PSRC = PSRC + 1
+ IF (J .GT. 0) THEN
+ IW (PDST) = PE (J)
+ PE (J) = PDST
+ PDST = PDST + 1
+C copy from source to destination
+ LENJ = LEN (J)
+ DO 90 KNT3 = 0, LENJ - 2
+ IW (PDST + KNT3) = IW (PSRC + KNT3)
+90 CONTINUE
+ PDST = PDST + LENJ - 1
+ PSRC = PSRC + LENJ - 1
+ ENDIF
+ GOTO 80
+ ENDIF
+
+C move the new partially-constructed element
+ P1 = PDST
+ DO 100 PSRC = PME1, PFREE - 1
+ IW (PDST) = IW (PSRC)
+ PDST = PDST + 1
+100 CONTINUE
+ PME1 = P1
+ PFREE = PDST
+ PJ = PE (E)
+ P = PE (ME)
+ ENDIF
+
+C -------------------------------------------------
+C i is a principal variable not yet placed in Lme
+C store i in new list
+C -------------------------------------------------
+
+ DEGME = DEGME + NVI
+C flag i as being in Lme by negating nv (i)
+ NV (I) = -NVI
+ IW (PFREE) = I
+ PFREE = PFREE + 1
+
+C -------------------------------------------------
+C remove variable i from degree link list
+C -------------------------------------------------
+
+ ILAST = LAST (I)
+ INEXT = NEXT (I)
+ IF (INEXT .NE. 0) LAST (INEXT) = ILAST
+ IF (ILAST .NE. 0) THEN
+ NEXT (ILAST) = INEXT
+ ELSE
+C i is at the head of the degree list
+ HEAD (DEGREE (I)) = INEXT
+ ENDIF
+
+ ENDIF
+110 CONTINUE
+
+ IF (E .NE. ME) THEN
+C set tree pointer and flag to indicate element e is
+C absorbed into new element me (the parent of e is me)
+ PE (E) = -ME
+ W (E) = 0
+ ENDIF
+120 CONTINUE
+
+ PME2 = PFREE - 1
+C this element takes newmem new memory in iw (possibly zero)
+ NEWMEM = PFREE - PME1
+ MEM = MEM + NEWMEM
+ MAXMEM = MAX (MAXMEM, MEM)
+ ENDIF
+
+C -------------------------------------------------------------
+C me has now been converted into an element in iw (pme1..pme2)
+C -------------------------------------------------------------
+
+C degme holds the external degree of new element
+ DEGREE (ME) = DEGME
+ PE (ME) = PME1
+ LEN (ME) = PME2 - PME1 + 1
+
+C -------------------------------------------------------------
+C make sure that wflg is not too large. With the current
+C value of wflg, wflg+n must not cause integer overflow
+C -------------------------------------------------------------
+
+ IF (WFLG + N .LE. WFLG) THEN
+ DO 130 X = 1, N
+ IF (W (X) .NE. 0) W (X) = 1
+130 CONTINUE
+ WFLG = 2
+ ENDIF
+
+C=======================================================================
+C COMPUTE (w (e) - wflg) = |Le\Lme| FOR ALL ELEMENTS
+C=======================================================================
+
+C -------------------------------------------------------------
+C Scan 1: compute the external degrees of previous elements
+C with respect to the current element. That is:
+C (w (e) - wflg) = |Le \ Lme|
+C for each element e that appears in any supervariable in Lme.
+C The notation Le refers to the pattern (list of
+C supervariables) of a previous element e, where e is not yet
+C absorbed, stored in iw (pe (e) + 1 ... pe (e) + iw (pe (e))).
+C The notation Lme refers to the pattern of the current element
+C (stored in iw (pme1..pme2)). If (w (e) - wflg) becomes
+C zero, then the element e will be absorbed in scan 2.
+C -------------------------------------------------------------
+
+ DO 150 PME = PME1, PME2
+ I = IW (PME)
+ ELN = ELEN (I)
+ IF (ELN .GT. 0) THEN
+C note that nv (i) has been negated to denote i in Lme:
+ NVI = -NV (I)
+ WNVI = WFLG - NVI
+ DO 140 P = PE (I), PE (I) + ELN - 1
+ E = IW (P)
+ WE = W (E)
+ IF (WE .GE. WFLG) THEN
+C unabsorbed element e has been seen in this loop
+ WE = WE - NVI
+ ELSE IF (WE .NE. 0) THEN
+C e is an unabsorbed element
+C this is the first we have seen e in all of Scan 1
+ WE = DEGREE (E) + WNVI
+ ENDIF
+ W (E) = WE
+140 CONTINUE
+ ENDIF
+150 CONTINUE
+
+C=======================================================================
+C DEGREE UPDATE AND ELEMENT ABSORPTION
+C=======================================================================
+
+C -------------------------------------------------------------
+C Scan 2: for each i in Lme, sum up the degree of Lme (which
+C is degme), plus the sum of the external degrees of each Le
+C for the elements e appearing within i, plus the
+C supervariables in i. Place i in hash list.
+C -------------------------------------------------------------
+
+ DO 180 PME = PME1, PME2
+ I = IW (PME)
+ P1 = PE (I)
+ P2 = P1 + ELEN (I) - 1
+ PN = P1
+ HASH = 0
+ DEG = 0
+
+C ----------------------------------------------------------
+C scan the element list associated with supervariable i
+C ----------------------------------------------------------
+
+ DO 160 P = P1, P2
+ E = IW (P)
+C dext = | Le \ Lme |
+ DEXT = W (E) - WFLG
+ IF (DEXT .GT. 0) THEN
+ DEG = DEG + DEXT
+ IW (PN) = E
+ PN = PN + 1
+ HASH = HASH + E
+ ELSE IF (DEXT .EQ. 0) THEN
+C aggressive absorption: e is not adjacent to me, but
+C the |Le \ Lme| is 0, so absorb it into me
+ PE (E) = -ME
+ W (E) = 0
+ ELSE
+C element e has already been absorbed, due to
+C regular absorption, in do loop 120 above. Ignore it.
+ CONTINUE
+ ENDIF
+160 CONTINUE
+
+C count the number of elements in i (including me):
+ ELEN (I) = PN - P1 + 1
+
+C ----------------------------------------------------------
+C scan the supervariables in the list associated with i
+C ----------------------------------------------------------
+
+ P3 = PN
+ DO 170 P = P2 + 1, P1 + LEN (I) - 1
+ J = IW (P)
+ NVJ = NV (J)
+ IF (NVJ .GT. 0) THEN
+C j is unabsorbed, and not in Lme.
+C add to degree and add to new list
+ DEG = DEG + NVJ
+ IW (PN) = J
+ PN = PN + 1
+ HASH = HASH + J
+ ENDIF
+170 CONTINUE
+
+C ----------------------------------------------------------
+C update the degree and check for mass elimination
+C ----------------------------------------------------------
+
+ IF (DEG .EQ. 0) THEN
+
+C -------------------------------------------------------
+C mass elimination
+C -------------------------------------------------------
+
+C There is nothing left of this node except for an
+C edge to the current pivot element. elen (i) is 1,
+C and there are no variables adjacent to node i.
+C Absorb i into the current pivot element, me.
+
+ PE (I) = -ME
+ NVI = -NV (I)
+ DEGME = DEGME - NVI
+ NVPIV = NVPIV + NVI
+ NEL = NEL + NVI
+ NV (I) = 0
+ ELEN (I) = 0
+
+ ELSE
+
+C -------------------------------------------------------
+C update the upper-bound degree of i
+C -------------------------------------------------------
+
+C the following degree does not yet include the size
+C of the current element, which is added later:
+ DEGREE (I) = MIN (DEGREE (I), DEG)
+
+C -------------------------------------------------------
+C add me to the list for i
+C -------------------------------------------------------
+
+C move first supervariable to end of list
+ IW (PN) = IW (P3)
+C move first element to end of element part of list
+ IW (P3) = IW (P1)
+C add new element to front of list.
+ IW (P1) = ME
+C store the new length of the list in len (i)
+ LEN (I) = PN - P1 + 1
+
+C -------------------------------------------------------
+C place in hash bucket. Save hash key of i in last (i).
+C -------------------------------------------------------
+
+ HASH = MOD (HASH, HMOD) + 1
+ J = HEAD (HASH)
+ IF (J .LE. 0) THEN
+C the degree list is empty, hash head is -j
+ NEXT (I) = -J
+ HEAD (HASH) = -I
+ ELSE
+C degree list is not empty
+C use last (head (hash)) as hash head
+ NEXT (I) = LAST (J)
+ LAST (J) = I
+ ENDIF
+ LAST (I) = HASH
+ ENDIF
+180 CONTINUE
+
+ DEGREE (ME) = DEGME
+
+C -------------------------------------------------------------
+C Clear the counter array, w (...), by incrementing wflg.
+C -------------------------------------------------------------
+
+ DMAX = MAX (DMAX, DEGME)
+ WFLG = WFLG + DMAX
+
+C make sure that wflg+n does not cause integer overflow
+ IF (WFLG + N .LE. WFLG) THEN
+ DO 190 X = 1, N
+ IF (W (X) .NE. 0) W (X) = 1
+190 CONTINUE
+ WFLG = 2
+ ENDIF
+C at this point, w (1..n) .lt. wflg holds
+
+C=======================================================================
+C SUPERVARIABLE DETECTION
+C=======================================================================
+
+ DO 250 PME = PME1, PME2
+ I = IW (PME)
+ IF (NV (I) .LT. 0) THEN
+C i is a principal variable in Lme
+
+C -------------------------------------------------------
+C examine all hash buckets with 2 or more variables. We
+C do this by examing all unique hash keys for super-
+C variables in the pattern Lme of the current element, me
+C -------------------------------------------------------
+
+ HASH = LAST (I)
+C let i = head of hash bucket, and empty the hash bucket
+ J = HEAD (HASH)
+ IF (J .EQ. 0) GOTO 250
+ IF (J .LT. 0) THEN
+C degree list is empty
+ I = -J
+ HEAD (HASH) = 0
+ ELSE
+C degree list is not empty, restore last () of head
+ I = LAST (J)
+ LAST (J) = 0
+ ENDIF
+ IF (I .EQ. 0) GOTO 250
+
+C while loop:
+200 CONTINUE
+ IF (NEXT (I) .NE. 0) THEN
+
+C ----------------------------------------------------
+C this bucket has one or more variables following i.
+C scan all of them to see if i can absorb any entries
+C that follow i in hash bucket. Scatter i into w.
+C ----------------------------------------------------
+
+ LN = LEN (I)
+ ELN = ELEN (I)
+C do not flag the first element in the list (me)
+ DO 210 P = PE (I) + 1, PE (I) + LN - 1
+ W (IW (P)) = WFLG
+210 CONTINUE
+
+C ----------------------------------------------------
+C scan every other entry j following i in bucket
+C ----------------------------------------------------
+
+ JLAST = I
+ J = NEXT (I)
+
+C while loop:
+220 CONTINUE
+ IF (J .NE. 0) THEN
+
+C -------------------------------------------------
+C check if j and i have identical nonzero pattern
+C -------------------------------------------------
+
+ IF (LEN (J) .NE. LN) THEN
+C i and j do not have same size data structure
+ GOTO 240
+ ENDIF
+ IF (ELEN (J) .NE. ELN) THEN
+C i and j do not have same number of adjacent el
+ GOTO 240
+ ENDIF
+C do not flag the first element in the list (me)
+ DO 230 P = PE (J) + 1, PE (J) + LN - 1
+ IF (W (IW (P)) .NE. WFLG) THEN
+C an entry (iw(p)) is in j but not in i
+ GOTO 240
+ ENDIF
+230 CONTINUE
+
+C -------------------------------------------------
+C found it! j can be absorbed into i
+C -------------------------------------------------
+
+ PE (J) = -I
+C both nv (i) and nv (j) are negated since they
+C are in Lme, and the absolute values of each
+C are the number of variables in i and j:
+ NV (I) = NV (I) + NV (J)
+ NV (J) = 0
+ ELEN (J) = 0
+C delete j from hash bucket
+ J = NEXT (J)
+ NEXT (JLAST) = J
+ GOTO 220
+
+C -------------------------------------------------
+240 CONTINUE
+C j cannot be absorbed into i
+C -------------------------------------------------
+
+ JLAST = J
+ J = NEXT (J)
+ GOTO 220
+ ENDIF
+
+C ----------------------------------------------------
+C no more variables can be absorbed into i
+C go to next i in bucket and clear flag array
+C ----------------------------------------------------
+
+ WFLG = WFLG + 1
+ I = NEXT (I)
+ IF (I .NE. 0) GOTO 200
+ ENDIF
+ ENDIF
+250 CONTINUE
+
+C=======================================================================
+C RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVAR. FROM ELEMENT
+C=======================================================================
+
+ P = PME1
+ NLEFT = N - NEL
+ DO 260 PME = PME1, PME2
+ I = IW (PME)
+ NVI = -NV (I)
+ IF (NVI .GT. 0) THEN
+C i is a principal variable in Lme
+C restore nv (i) to signify that i is principal
+ NV (I) = NVI
+
+C -------------------------------------------------------
+C compute the external degree (add size of current elem)
+C -------------------------------------------------------
+
+ DEG = MIN (DEGREE (I) + DEGME - NVI, NLEFT - NVI)
+
+C -------------------------------------------------------
+C place the supervariable at the head of the degree list
+C -------------------------------------------------------
+
+ INEXT = HEAD (DEG)
+ IF (INEXT .NE. 0) LAST (INEXT) = I
+ NEXT (I) = INEXT
+ LAST (I) = 0
+ HEAD (DEG) = I
+
+C -------------------------------------------------------
+C save the new degree, and find the minimum degree
+C -------------------------------------------------------
+
+ MINDEG = MIN (MINDEG, DEG)
+ DEGREE (I) = DEG
+
+C -------------------------------------------------------
+C place the supervariable in the element pattern
+C -------------------------------------------------------
+
+ IW (P) = I
+ P = P + 1
+ ENDIF
+260 CONTINUE
+
+C=======================================================================
+C FINALIZE THE NEW ELEMENT
+C=======================================================================
+
+ NV (ME) = NVPIV + DEGME
+C nv (me) is now the degree of pivot (including diagonal part)
+C save the length of the list for the new element me
+ LEN (ME) = P - PME1
+ IF (LEN (ME) .EQ. 0) THEN
+C there is nothing left of the current pivot element
+ PE (ME) = 0
+ W (ME) = 0
+ ENDIF
+ IF (NEWMEM .NE. 0) THEN
+C element was not constructed in place: deallocate part
+C of it (final size is less than or equal to newmem,
+C since newly nonprincipal variables have been removed).
+ PFREE = P
+ MEM = MEM - NEWMEM + LEN (ME)
+ ENDIF
+
+C=======================================================================
+C END WHILE (selecting pivots)
+ GOTO 30
+ ENDIF
+C=======================================================================
+
+C=======================================================================
+C COMPUTE THE PERMUTATION VECTORS
+C=======================================================================
+
+C ----------------------------------------------------------------
+C The time taken by the following code is O(n). At this
+C point, elen (e) = -k has been done for all elements e,
+C and elen (i) = 0 has been done for all nonprincipal
+C variables i. At this point, there are no principal
+C supervariables left, and all elements are absorbed.
+C ----------------------------------------------------------------
+
+C ----------------------------------------------------------------
+C compute the ordering of unordered nonprincipal variables
+C ----------------------------------------------------------------
+
+ DO 290 I = 1, N
+ IF (ELEN (I) .EQ. 0) THEN
+
+C ----------------------------------------------------------
+C i is an un-ordered row. Traverse the tree from i until
+C reaching an element, e. The element, e, was the
+C principal supervariable of i and all nodes in the path
+C from i to when e was selected as pivot.
+C ----------------------------------------------------------
+
+ J = -PE (I)
+C while (j is a variable) do:
+270 CONTINUE
+ IF (ELEN (J) .GE. 0) THEN
+ J = -PE (J)
+ GOTO 270
+ ENDIF
+ E = J
+
+C ----------------------------------------------------------
+C get the current pivot ordering of e
+C ----------------------------------------------------------
+
+ K = -ELEN (E)
+
+C ----------------------------------------------------------
+C traverse the path again from i to e, and compress the
+C path (all nodes point to e). Path compression allows
+C this code to compute in O(n) time. Order the unordered
+C nodes in the path, and place the element e at the end.
+C ----------------------------------------------------------
+
+ J = I
+C while (j is a variable) do:
+280 CONTINUE
+ IF (ELEN (J) .GE. 0) THEN
+ JNEXT = -PE (J)
+ PE (J) = -E
+ IF (ELEN (J) .EQ. 0) THEN
+C j is an unordered row
+ ELEN (J) = K
+ K = K + 1
+ ENDIF
+ J = JNEXT
+ GOTO 280
+ ENDIF
+C leave elen (e) negative, so we know it is an element
+ ELEN (E) = -K
+ ENDIF
+290 CONTINUE
+
+C ----------------------------------------------------------------
+C reset the inverse permutation (elen (1..n)) to be positive,
+C and compute the permutation (last (1..n)).
+C ----------------------------------------------------------------
+
+ DO 300 I = 1, N
+ K = ABS (ELEN (I))
+ LAST (K) = I
+ ELEN (I) = K
+300 CONTINUE
+
+C=======================================================================
+C RETURN THE MEMORY USAGE IN IW
+C=======================================================================
+
+C If maxmem is less than or equal to iwlen, then no compressions
+C occurred, and iw (maxmem+1 ... iwlen) was unused. Otherwise
+C compressions did occur, and iwlen would have had to have been
+C greater than or equal to maxmem for no compressions to occur.
+C Return the value of maxmem in the pfree argument.
+
+ PFREE = MAXMEM
+
+ RETURN
+ END
+
diff --git a/AMD/Source/amd_1.c b/AMD/Source/amd_1.c
new file mode 100644
index 0000000..30cb277
--- /dev/null
+++ b/AMD/Source/amd_1.c
@@ -0,0 +1,181 @@
+/* ========================================================================= */
+/* === AMD_1 =============================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* AMD_1: Construct A+A' for a sparse matrix A and perform the AMD ordering.
+ *
+ * The n-by-n sparse matrix A can be unsymmetric. It is stored in MATLAB-style
+ * compressed-column form, with sorted row indices in each column, and no
+ * duplicate entries. Diagonal entries may be present, but they are ignored.
+ * Row indices of column j of A are stored in Ai [Ap [j] ... Ap [j+1]-1].
+ * Ap [0] must be zero, and nz = Ap [n] is the number of entries in A. The
+ * size of the matrix, n, must be greater than or equal to zero.
+ *
+ * This routine must be preceded by a call to AMD_aat, which computes the
+ * number of entries in each row/column in A+A', excluding the diagonal.
+ * Len [j], on input, is the number of entries in row/column j of A+A'. This
+ * routine constructs the matrix A+A' and then calls AMD_2. No error checking
+ * is performed (this was done in AMD_valid).
+ */
+
+#include "amd_internal.h"
+
+GLOBAL void AMD_1
+(
+ Int n, /* n > 0 */
+ const Int Ap [ ], /* input of size n+1, not modified */
+ const Int Ai [ ], /* input of size nz = Ap [n], not modified */
+ Int P [ ], /* size n output permutation */
+ Int Pinv [ ], /* size n output inverse permutation */
+ Int Len [ ], /* size n input, undefined on output */
+ Int slen, /* slen >= sum (Len [0..n-1]) + 7n,
+ * ideally slen = 1.2 * sum (Len) + 8n */
+ Int S [ ], /* size slen workspace */
+ double Control [ ], /* input array of size AMD_CONTROL */
+ double Info [ ] /* output array of size AMD_INFO */
+)
+{
+ Int i, j, k, p, pfree, iwlen, pj, p1, p2, pj2, *Iw, *Pe, *Nv, *Head,
+ *Elen, *Degree, *s, *W, *Sp, *Tp ;
+
+ /* --------------------------------------------------------------------- */
+ /* construct the matrix for AMD_2 */
+ /* --------------------------------------------------------------------- */
+
+ ASSERT (n > 0) ;
+
+ iwlen = slen - 6*n ;
+ s = S ;
+ Pe = s ; s += n ;
+ Nv = s ; s += n ;
+ Head = s ; s += n ;
+ Elen = s ; s += n ;
+ Degree = s ; s += n ;
+ W = s ; s += n ;
+ Iw = s ; s += iwlen ;
+
+ ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ;
+
+ /* construct the pointers for A+A' */
+ Sp = Nv ; /* use Nv and W as workspace for Sp and Tp [ */
+ Tp = W ;
+ pfree = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Pe [j] = pfree ;
+ Sp [j] = pfree ;
+ pfree += Len [j] ;
+ }
+
+ /* Note that this restriction on iwlen is slightly more restrictive than
+ * what is strictly required in AMD_2. AMD_2 can operate with no elbow
+ * room at all, but it will be very slow. For better performance, at
+ * least size-n elbow room is enforced. */
+ ASSERT (iwlen >= pfree + n) ;
+
+#ifndef NDEBUG
+ for (p = 0 ; p < iwlen ; p++) Iw [p] = EMPTY ;
+#endif
+
+ for (k = 0 ; k < n ; k++)
+ {
+ AMD_DEBUG1 (("Construct row/column k= "ID" of A+A'\n", k)) ;
+ p1 = Ap [k] ;
+ p2 = Ap [k+1] ;
+
+ /* construct A+A' */
+ for (p = p1 ; p < p2 ; )
+ {
+ /* scan the upper triangular part of A */
+ j = Ai [p] ;
+ ASSERT (j >= 0 && j < n) ;
+ if (j < k)
+ {
+ /* entry A (j,k) in the strictly upper triangular part */
+ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
+ ASSERT (Sp [k] < (k == n-1 ? pfree : Pe [k+1])) ;
+ Iw [Sp [j]++] = k ;
+ Iw [Sp [k]++] = j ;
+ p++ ;
+ }
+ else if (j == k)
+ {
+ /* skip the diagonal */
+ p++ ;
+ break ;
+ }
+ else /* j > k */
+ {
+ /* first entry below the diagonal */
+ break ;
+ }
+ /* scan lower triangular part of A, in column j until reaching
+ * row k. Start where last scan left off. */
+ ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ;
+ pj2 = Ap [j+1] ;
+ for (pj = Tp [j] ; pj < pj2 ; )
+ {
+ i = Ai [pj] ;
+ ASSERT (i >= 0 && i < n) ;
+ if (i < k)
+ {
+ /* A (i,j) is only in the lower part, not in upper */
+ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ;
+ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
+ Iw [Sp [i]++] = j ;
+ Iw [Sp [j]++] = i ;
+ pj++ ;
+ }
+ else if (i == k)
+ {
+ /* entry A (k,j) in lower part and A (j,k) in upper */
+ pj++ ;
+ break ;
+ }
+ else /* i > k */
+ {
+ /* consider this entry later, when k advances to i */
+ break ;
+ }
+ }
+ Tp [j] = pj ;
+ }
+ Tp [k] = p ;
+ }
+
+ /* clean up, for remaining mismatched entries */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (pj = Tp [j] ; pj < Ap [j+1] ; pj++)
+ {
+ i = Ai [pj] ;
+ ASSERT (i >= 0 && i < n) ;
+ /* A (i,j) is only in the lower part, not in upper */
+ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ;
+ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
+ Iw [Sp [i]++] = j ;
+ Iw [Sp [j]++] = i ;
+ }
+ }
+
+#ifndef NDEBUG
+ for (j = 0 ; j < n-1 ; j++) ASSERT (Sp [j] == Pe [j+1]) ;
+ ASSERT (Sp [n-1] == pfree) ;
+#endif
+
+ /* Tp and Sp no longer needed ] */
+
+ /* --------------------------------------------------------------------- */
+ /* order the matrix */
+ /* --------------------------------------------------------------------- */
+
+ AMD_2 (n, Pe, Iw, Len, iwlen, pfree,
+ Nv, Pinv, P, Head, Elen, Degree, W, Control, Info) ;
+}
diff --git a/AMD/Source/amd_2.c b/AMD/Source/amd_2.c
new file mode 100644
index 0000000..97b4f7a
--- /dev/null
+++ b/AMD/Source/amd_2.c
@@ -0,0 +1,1842 @@
+/* ========================================================================= */
+/* === AMD_2 =============================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* AMD_2: performs the AMD ordering on a symmetric sparse matrix A, followed
+ * by a postordering (via depth-first search) of the assembly tree using the
+ * AMD_postorder routine.
+ */
+
+#include "amd_internal.h"
+
+/* ========================================================================= */
+/* === clear_flag ========================================================== */
+/* ========================================================================= */
+
+static Int clear_flag (Int wflg, Int wbig, Int W [ ], Int n)
+{
+ Int x ;
+ if (wflg < 2 || wflg >= wbig)
+ {
+ for (x = 0 ; x < n ; x++)
+ {
+ if (W [x] != 0) W [x] = 1 ;
+ }
+ wflg = 2 ;
+ }
+ /* at this point, W [0..n-1] < wflg holds */
+ return (wflg) ;
+}
+
+
+/* ========================================================================= */
+/* === AMD_2 =============================================================== */
+/* ========================================================================= */
+
+GLOBAL void AMD_2
+(
+ Int n, /* A is n-by-n, where n > 0 */
+ Int Pe [ ], /* Pe [0..n-1]: index in Iw of row i on input */
+ Int Iw [ ], /* workspace of size iwlen. Iw [0..pfree-1]
+ * holds the matrix on input */
+ Int Len [ ], /* Len [0..n-1]: length for row/column i on input */
+ Int iwlen, /* length of Iw. iwlen >= pfree + n */
+ Int pfree, /* Iw [pfree ... iwlen-1] is empty on input */
+
+ /* 7 size-n workspaces, not defined on input: */
+ Int Nv [ ], /* the size of each supernode on output */
+ Int Next [ ], /* the output inverse permutation */
+ Int Last [ ], /* the output permutation */
+ Int Head [ ],
+ Int Elen [ ], /* the size columns of L for each supernode */
+ Int Degree [ ],
+ Int W [ ],
+
+ /* control parameters and output statistics */
+ double Control [ ], /* array of size AMD_CONTROL */
+ double Info [ ] /* array of size AMD_INFO */
+)
+{
+
+/*
+ * Given a representation of the nonzero pattern of a symmetric matrix, A,
+ * (excluding the diagonal) perform an approximate minimum (UMFPACK/MA38-style)
+ * degree ordering to compute a pivot order such that the introduction of
+ * nonzeros (fill-in) in the Cholesky factors A = LL' is kept low. At each
+ * step, the pivot selected is the one with the minimum UMFAPACK/MA38-style
+ * upper-bound on the external degree. This routine can optionally perform
+ * aggresive absorption (as done by MC47B in the Harwell Subroutine
+ * Library).
+ *
+ * The approximate degree algorithm implemented here is the symmetric analog of
+ * the degree update algorithm in MA38 and UMFPACK (the Unsymmetric-pattern
+ * MultiFrontal PACKage, both by Davis and Duff). The routine is based on the
+ * MA27 minimum degree ordering algorithm by Iain Duff and John Reid.
+ *
+ * This routine is a translation of the original AMDBAR and MC47B routines,
+ * in Fortran, with the following modifications:
+ *
+ * (1) dense rows/columns are removed prior to ordering the matrix, and placed
+ * last in the output order. The presence of a dense row/column can
+ * increase the ordering time by up to O(n^2), unless they are removed
+ * prior to ordering.
+ *
+ * (2) the minimum degree ordering is followed by a postordering (depth-first
+ * search) of the assembly tree. Note that mass elimination (discussed
+ * below) combined with the approximate degree update can lead to the mass
+ * elimination of nodes with lower exact degree than the current pivot
+ * element. No additional fill-in is caused in the representation of the
+ * Schur complement. The mass-eliminated nodes merge with the current
+ * pivot element. They are ordered prior to the current pivot element.
+ * Because they can have lower exact degree than the current element, the
+ * merger of two or more of these nodes in the current pivot element can
+ * lead to a single element that is not a "fundamental supernode". The
+ * diagonal block can have zeros in it. Thus, the assembly tree used here
+ * is not guaranteed to be the precise supernodal elemination tree (with
+ * "funadmental" supernodes), and the postordering performed by this
+ * routine is not guaranteed to be a precise postordering of the
+ * elimination tree.
+ *
+ * (3) input parameters are added, to control aggressive absorption and the
+ * detection of "dense" rows/columns of A.
+ *
+ * (4) additional statistical information is returned, such as the number of
+ * nonzeros in L, and the flop counts for subsequent LDL' and LU
+ * factorizations. These are slight upper bounds, because of the mass
+ * elimination issue discussed above.
+ *
+ * (5) additional routines are added to interface this routine to MATLAB
+ * to provide a simple C-callable user-interface, to check inputs for
+ * errors, compute the symmetry of the pattern of A and the number of
+ * nonzeros in each row/column of A+A', to compute the pattern of A+A',
+ * to perform the assembly tree postordering, and to provide debugging
+ * ouput. Many of these functions are also provided by the Fortran
+ * Harwell Subroutine Library routine MC47A.
+ *
+ * (6) both int and UF_long versions are provided. In the descriptions below
+ * and integer is and int or UF_long depending on which version is
+ * being used.
+
+ **********************************************************************
+ ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ******
+ **********************************************************************
+ ** If you want error checking, a more versatile input format, and a **
+ ** simpler user interface, use amd_order or amd_l_order instead. **
+ ** This routine is not meant to be user-callable. **
+ **********************************************************************
+
+ * ----------------------------------------------------------------------------
+ * References:
+ * ----------------------------------------------------------------------------
+ *
+ * [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern multifrontal
+ * method for sparse LU factorization", SIAM J. Matrix Analysis and
+ * Applications, vol. 18, no. 1, pp. 140-158. Discusses UMFPACK / MA38,
+ * which first introduced the approximate minimum degree used by this
+ * routine.
+ *
+ * [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An approximate
+ * minimum degree ordering algorithm," SIAM J. Matrix Analysis and
+ * Applications, vol. 17, no. 4, pp. 886-905, 1996. Discusses AMDBAR and
+ * MC47B, which are the Fortran versions of this routine.
+ *
+ * [3] Alan George and Joseph Liu, "The evolution of the minimum degree
+ * ordering algorithm," SIAM Review, vol. 31, no. 1, pp. 1-19, 1989.
+ * We list below the features mentioned in that paper that this code
+ * includes:
+ *
+ * mass elimination:
+ * Yes. MA27 relied on supervariable detection for mass elimination.
+ *
+ * indistinguishable nodes:
+ * Yes (we call these "supervariables"). This was also in the MA27
+ * code - although we modified the method of detecting them (the
+ * previous hash was the true degree, which we no longer keep track
+ * of). A supervariable is a set of rows with identical nonzero
+ * pattern. All variables in a supervariable are eliminated together.
+ * Each supervariable has as its numerical name that of one of its
+ * variables (its principal variable).
+ *
+ * quotient graph representation:
+ * Yes. We use the term "element" for the cliques formed during
+ * elimination. This was also in the MA27 code. The algorithm can
+ * operate in place, but it will work more efficiently if given some
+ * "elbow room."
+ *
+ * element absorption:
+ * Yes. This was also in the MA27 code.
+ *
+ * external degree:
+ * Yes. The MA27 code was based on the true degree.
+ *
+ * incomplete degree update and multiple elimination:
+ * No. This was not in MA27, either. Our method of degree update
+ * within MC47B is element-based, not variable-based. It is thus
+ * not well-suited for use with incomplete degree update or multiple
+ * elimination.
+ *
+ * Authors, and Copyright (C) 2004 by:
+ * Timothy A. Davis, Patrick Amestoy, Iain S. Duff, John K. Reid.
+ *
+ * Acknowledgements: This work (and the UMFPACK package) was supported by the
+ * National Science Foundation (ASC-9111263, DMS-9223088, and CCR-0203270).
+ * The UMFPACK/MA38 approximate degree update algorithm, the unsymmetric analog
+ * which forms the basis of AMD, was developed while Tim Davis was supported by
+ * CERFACS (Toulouse, France) in a post-doctoral position. This C version, and
+ * the etree postorder, were written while Tim Davis was on sabbatical at
+ * Stanford University and Lawrence Berkeley National Laboratory.
+
+ * ----------------------------------------------------------------------------
+ * INPUT ARGUMENTS (unaltered):
+ * ----------------------------------------------------------------------------
+
+ * n: The matrix order. Restriction: n >= 1.
+ *
+ * iwlen: The size of the Iw array. On input, the matrix is stored in
+ * Iw [0..pfree-1]. However, Iw [0..iwlen-1] should be slightly larger
+ * than what is required to hold the matrix, at least iwlen >= pfree + n.
+ * Otherwise, excessive compressions will take place. The recommended
+ * value of iwlen is 1.2 * pfree + n, which is the value used in the
+ * user-callable interface to this routine (amd_order.c). The algorithm
+ * will not run at all if iwlen < pfree. Restriction: iwlen >= pfree + n.
+ * Note that this is slightly more restrictive than the actual minimum
+ * (iwlen >= pfree), but AMD_2 will be very slow with no elbow room.
+ * Thus, this routine enforces a bare minimum elbow room of size n.
+ *
+ * pfree: On input the tail end of the array, Iw [pfree..iwlen-1], is empty,
+ * and the matrix is stored in Iw [0..pfree-1]. During execution,
+ * additional data is placed in Iw, and pfree is modified so that
+ * Iw [pfree..iwlen-1] is always the unused part of Iw.
+ *
+ * Control: A double array of size AMD_CONTROL containing input parameters
+ * that affect how the ordering is computed. If NULL, then default
+ * settings are used.
+ *
+ * Control [AMD_DENSE] is used to determine whether or not a given input
+ * row is "dense". A row is "dense" if the number of entries in the row
+ * exceeds Control [AMD_DENSE] times sqrt (n), except that rows with 16 or
+ * fewer entries are never considered "dense". To turn off the detection
+ * of dense rows, set Control [AMD_DENSE] to a negative number, or to a
+ * number larger than sqrt (n). The default value of Control [AMD_DENSE]
+ * is AMD_DEFAULT_DENSE, which is defined in amd.h as 10.
+ *
+ * Control [AMD_AGGRESSIVE] is used to determine whether or not aggressive
+ * absorption is to be performed. If nonzero, then aggressive absorption
+ * is performed (this is the default).
+
+ * ----------------------------------------------------------------------------
+ * INPUT/OUPUT ARGUMENTS:
+ * ----------------------------------------------------------------------------
+ *
+ * Pe: An integer array of size n. On input, Pe [i] is the index in Iw of
+ * the start of row i. Pe [i] is ignored if row i has no off-diagonal
+ * entries. Thus Pe [i] must be in the range 0 to pfree-1 for non-empty
+ * rows.
+ *
+ * During execution, it is used for both supervariables and elements:
+ *
+ * Principal supervariable i: index into Iw of the description of
+ * supervariable i. A supervariable represents one or more rows of
+ * the matrix with identical nonzero pattern. In this case,
+ * Pe [i] >= 0.
+ *
+ * Non-principal supervariable i: if i has been absorbed into another
+ * supervariable j, then Pe [i] = FLIP (j), where FLIP (j) is defined
+ * as (-(j)-2). Row j has the same pattern as row i. Note that j
+ * might later be absorbed into another supervariable j2, in which
+ * case Pe [i] is still FLIP (j), and Pe [j] = FLIP (j2) which is
+ * < EMPTY, where EMPTY is defined as (-1) in amd_internal.h.
+ *
+ * Unabsorbed element e: the index into Iw of the description of element
+ * e, if e has not yet been absorbed by a subsequent element. Element
+ * e is created when the supervariable of the same name is selected as
+ * the pivot. In this case, Pe [i] >= 0.
+ *
+ * Absorbed element e: if element e is absorbed into element e2, then
+ * Pe [e] = FLIP (e2). This occurs when the pattern of e (which we
+ * refer to as Le) is found to be a subset of the pattern of e2 (that
+ * is, Le2). In this case, Pe [i] < EMPTY. If element e is "null"
+ * (it has no nonzeros outside its pivot block), then Pe [e] = EMPTY,
+ * and e is the root of an assembly subtree (or the whole tree if
+ * there is just one such root).
+ *
+ * Dense variable i: if i is "dense", then Pe [i] = EMPTY.
+ *
+ * On output, Pe holds the assembly tree/forest, which implicitly
+ * represents a pivot order with identical fill-in as the actual order
+ * (via a depth-first search of the tree), as follows. If Nv [i] > 0,
+ * then i represents a node in the assembly tree, and the parent of i is
+ * Pe [i], or EMPTY if i is a root. If Nv [i] = 0, then (i, Pe [i])
+ * represents an edge in a subtree, the root of which is a node in the
+ * assembly tree. Note that i refers to a row/column in the original
+ * matrix, not the permuted matrix.
+ *
+ * Info: A double array of size AMD_INFO. If present, (that is, not NULL),
+ * then statistics about the ordering are returned in the Info array.
+ * See amd.h for a description.
+
+ * ----------------------------------------------------------------------------
+ * INPUT/MODIFIED (undefined on output):
+ * ----------------------------------------------------------------------------
+ *
+ * Len: An integer array of size n. On input, Len [i] holds the number of
+ * entries in row i of the matrix, excluding the diagonal. The contents
+ * of Len are undefined on output.
+ *
+ * Iw: An integer array of size iwlen. On input, Iw [0..pfree-1] holds the
+ * description of each row i in the matrix. The matrix must be symmetric,
+ * and both upper and lower triangular parts must be present. The
+ * diagonal must not be present. Row i is held as follows:
+ *
+ * Len [i]: the length of the row i data structure in the Iw array.
+ * Iw [Pe [i] ... Pe [i] + Len [i] - 1]:
+ * the list of column indices for nonzeros in row i (simple
+ * supervariables), excluding the diagonal. All supervariables
+ * start with one row/column each (supervariable i is just row i).
+ * If Len [i] is zero on input, then Pe [i] is ignored on input.
+ *
+ * Note that the rows need not be in any particular order, and there
+ * may be empty space between the rows.
+ *
+ * During execution, the supervariable i experiences fill-in. This is
+ * represented by placing in i a list of the elements that cause fill-in
+ * in supervariable i:
+ *
+ * Len [i]: the length of supervariable i in the Iw array.
+ * Iw [Pe [i] ... Pe [i] + Elen [i] - 1]:
+ * the list of elements that contain i. This list is kept short
+ * by removing absorbed elements.
+ * Iw [Pe [i] + Elen [i] ... Pe [i] + Len [i] - 1]:
+ * the list of supervariables in i. This list is kept short by
+ * removing nonprincipal variables, and any entry j that is also
+ * contained in at least one of the elements (j in Le) in the list
+ * for i (e in row i).
+ *
+ * When supervariable i is selected as pivot, we create an element e of
+ * the same name (e=i):
+ *
+ * Len [e]: the length of element e in the Iw array.
+ * Iw [Pe [e] ... Pe [e] + Len [e] - 1]:
+ * the list of supervariables in element e.
+ *
+ * An element represents the fill-in that occurs when supervariable i is
+ * selected as pivot (which represents the selection of row i and all
+ * non-principal variables whose principal variable is i). We use the
+ * term Le to denote the set of all supervariables in element e. Absorbed
+ * supervariables and elements are pruned from these lists when
+ * computationally convenient.
+ *
+ * CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION.
+ * The contents of Iw are undefined on output.
+
+ * ----------------------------------------------------------------------------
+ * OUTPUT (need not be set on input):
+ * ----------------------------------------------------------------------------
+ *
+ * Nv: An integer array of size n. During execution, ABS (Nv [i]) is equal to
+ * the number of rows that are represented by the principal supervariable
+ * i. If i is a nonprincipal or dense variable, then Nv [i] = 0.
+ * Initially, Nv [i] = 1 for all i. Nv [i] < 0 signifies that i is a
+ * principal variable in the pattern Lme of the current pivot element me.
+ * After element me is constructed, Nv [i] is set back to a positive
+ * value.
+ *
+ * On output, Nv [i] holds the number of pivots represented by super
+ * row/column i of the original matrix, or Nv [i] = 0 for non-principal
+ * rows/columns. Note that i refers to a row/column in the original
+ * matrix, not the permuted matrix.
+ *
+ * Elen: An integer array of size n. See the description of Iw above. At the
+ * start of execution, Elen [i] is set to zero for all rows i. During
+ * execution, Elen [i] is the number of elements in the list for
+ * supervariable i. When e becomes an element, Elen [e] = FLIP (esize) is
+ * set, where esize is the size of the element (the number of pivots, plus
+ * the number of nonpivotal entries). Thus Elen [e] < EMPTY.
+ * Elen (i) = EMPTY set when variable i becomes nonprincipal.
+ *
+ * For variables, Elen (i) >= EMPTY holds until just before the
+ * postordering and permutation vectors are computed. For elements,
+ * Elen [e] < EMPTY holds.
+ *
+ * On output, Elen [i] is the degree of the row/column in the Cholesky
+ * factorization of the permuted matrix, corresponding to the original row
+ * i, if i is a super row/column. It is equal to EMPTY if i is
+ * non-principal. Note that i refers to a row/column in the original
+ * matrix, not the permuted matrix.
+ *
+ * Note that the contents of Elen on output differ from the Fortran
+ * version (Elen holds the inverse permutation in the Fortran version,
+ * which is instead returned in the Next array in this C version,
+ * described below).
+ *
+ * Last: In a degree list, Last [i] is the supervariable preceding i, or EMPTY
+ * if i is the head of the list. In a hash bucket, Last [i] is the hash
+ * key for i.
+ *
+ * Last [Head [hash]] is also used as the head of a hash bucket if
+ * Head [hash] contains a degree list (see the description of Head,
+ * below).
+ *
+ * On output, Last [0..n-1] holds the permutation. That is, if
+ * i = Last [k], then row i is the kth pivot row (where k ranges from 0 to
+ * n-1). Row Last [k] of A is the kth row in the permuted matrix, PAP'.
+ *
+ * Next: Next [i] is the supervariable following i in a link list, or EMPTY if
+ * i is the last in the list. Used for two kinds of lists: degree lists
+ * and hash buckets (a supervariable can be in only one kind of list at a
+ * time).
+ *
+ * On output Next [0..n-1] holds the inverse permutation. That is, if
+ * k = Next [i], then row i is the kth pivot row. Row i of A appears as
+ * the (Next[i])-th row in the permuted matrix, PAP'.
+ *
+ * Note that the contents of Next on output differ from the Fortran
+ * version (Next is undefined on output in the Fortran version).
+
+ * ----------------------------------------------------------------------------
+ * LOCAL WORKSPACE (not input or output - used only during execution):
+ * ----------------------------------------------------------------------------
+ *
+ * Degree: An integer array of size n. If i is a supervariable, then
+ * Degree [i] holds the current approximation of the external degree of
+ * row i (an upper bound). The external degree is the number of nonzeros
+ * in row i, minus ABS (Nv [i]), the diagonal part. The bound is equal to
+ * the exact external degree if Elen [i] is less than or equal to two.
+ *
+ * We also use the term "external degree" for elements e to refer to
+ * |Le \ Lme|. If e is an element, then Degree [e] is |Le|, which is the
+ * degree of the off-diagonal part of the element e (not including the
+ * diagonal part).
+ *
+ * Head: An integer array of size n. Head is used for degree lists.
+ * Head [deg] is the first supervariable in a degree list. All
+ * supervariables i in a degree list Head [deg] have the same approximate
+ * degree, namely, deg = Degree [i]. If the list Head [deg] is empty then
+ * Head [deg] = EMPTY.
+ *
+ * During supervariable detection Head [hash] also serves as a pointer to
+ * a hash bucket. If Head [hash] >= 0, there is a degree list of degree
+ * hash. The hash bucket head pointer is Last [Head [hash]]. If
+ * Head [hash] = EMPTY, then the degree list and hash bucket are both
+ * empty. If Head [hash] < EMPTY, then the degree list is empty, and
+ * FLIP (Head [hash]) is the head of the hash bucket. After supervariable
+ * detection is complete, all hash buckets are empty, and the
+ * (Last [Head [hash]] = EMPTY) condition is restored for the non-empty
+ * degree lists.
+ *
+ * W: An integer array of size n. The flag array W determines the status of
+ * elements and variables, and the external degree of elements.
+ *
+ * for elements:
+ * if W [e] = 0, then the element e is absorbed.
+ * if W [e] >= wflg, then W [e] - wflg is the size of the set
+ * |Le \ Lme|, in terms of nonzeros (the sum of ABS (Nv [i]) for
+ * each principal variable i that is both in the pattern of
+ * element e and NOT in the pattern of the current pivot element,
+ * me).
+ * if wflg > W [e] > 0, then e is not absorbed and has not yet been
+ * seen in the scan of the element lists in the computation of
+ * |Le\Lme| in Scan 1 below.
+ *
+ * for variables:
+ * during supervariable detection, if W [j] != wflg then j is
+ * not in the pattern of variable i.
+ *
+ * The W array is initialized by setting W [i] = 1 for all i, and by
+ * setting wflg = 2. It is reinitialized if wflg becomes too large (to
+ * ensure that wflg+n does not cause integer overflow).
+
+ * ----------------------------------------------------------------------------
+ * LOCAL INTEGERS:
+ * ----------------------------------------------------------------------------
+ */
+
+ Int deg, degme, dext, lemax, e, elenme, eln, i, ilast, inext, j,
+ jlast, jnext, k, knt1, knt2, knt3, lenj, ln, me, mindeg, nel, nleft,
+ nvi, nvj, nvpiv, slenme, wbig, we, wflg, wnvi, ok, ndense, ncmpa,
+ dense, aggressive ;
+
+ unsigned Int hash ; /* unsigned, so that hash % n is well defined.*/
+
+/*
+ * deg: the degree of a variable or element
+ * degme: size, |Lme|, of the current element, me (= Degree [me])
+ * dext: external degree, |Le \ Lme|, of some element e
+ * lemax: largest |Le| seen so far (called dmax in Fortran version)
+ * e: an element
+ * elenme: the length, Elen [me], of element list of pivotal variable
+ * eln: the length, Elen [...], of an element list
+ * hash: the computed value of the hash function
+ * i: a supervariable
+ * ilast: the entry in a link list preceding i
+ * inext: the entry in a link list following i
+ * j: a supervariable
+ * jlast: the entry in a link list preceding j
+ * jnext: the entry in a link list, or path, following j
+ * k: the pivot order of an element or variable
+ * knt1: loop counter used during element construction
+ * knt2: loop counter used during element construction
+ * knt3: loop counter used during compression
+ * lenj: Len [j]
+ * ln: length of a supervariable list
+ * me: current supervariable being eliminated, and the current
+ * element created by eliminating that supervariable
+ * mindeg: current minimum degree
+ * nel: number of pivots selected so far
+ * nleft: n - nel, the number of nonpivotal rows/columns remaining
+ * nvi: the number of variables in a supervariable i (= Nv [i])
+ * nvj: the number of variables in a supervariable j (= Nv [j])
+ * nvpiv: number of pivots in current element
+ * slenme: number of variables in variable list of pivotal variable
+ * wbig: = INT_MAX - n for the int version, UF_long_max - n for the
+ * UF_long version. wflg is not allowed to be >= wbig.
+ * we: W [e]
+ * wflg: used for flagging the W array. See description of Iw.
+ * wnvi: wflg - Nv [i]
+ * x: either a supervariable or an element
+ *
+ * ok: true if supervariable j can be absorbed into i
+ * ndense: number of "dense" rows/columns
+ * dense: rows/columns with initial degree > dense are considered "dense"
+ * aggressive: true if aggressive absorption is being performed
+ * ncmpa: number of garbage collections
+
+ * ----------------------------------------------------------------------------
+ * LOCAL DOUBLES, used for statistical output only (except for alpha):
+ * ----------------------------------------------------------------------------
+ */
+
+ double f, r, ndiv, s, nms_lu, nms_ldl, dmax, alpha, lnz, lnzme ;
+
+/*
+ * f: nvpiv
+ * r: degme + nvpiv
+ * ndiv: number of divisions for LU or LDL' factorizations
+ * s: number of multiply-subtract pairs for LU factorization, for the
+ * current element me
+ * nms_lu number of multiply-subtract pairs for LU factorization
+ * nms_ldl number of multiply-subtract pairs for LDL' factorization
+ * dmax: the largest number of entries in any column of L, including the
+ * diagonal
+ * alpha: "dense" degree ratio
+ * lnz: the number of nonzeros in L (excluding the diagonal)
+ * lnzme: the number of nonzeros in L (excl. the diagonal) for the
+ * current element me
+
+ * ----------------------------------------------------------------------------
+ * LOCAL "POINTERS" (indices into the Iw array)
+ * ----------------------------------------------------------------------------
+*/
+
+ Int p, p1, p2, p3, p4, pdst, pend, pj, pme, pme1, pme2, pn, psrc ;
+
+/*
+ * Any parameter (Pe [...] or pfree) or local variable starting with "p" (for
+ * Pointer) is an index into Iw, and all indices into Iw use variables starting
+ * with "p." The only exception to this rule is the iwlen input argument.
+ *
+ * p: pointer into lots of things
+ * p1: Pe [i] for some variable i (start of element list)
+ * p2: Pe [i] + Elen [i] - 1 for some variable i
+ * p3: index of first supervariable in clean list
+ * p4:
+ * pdst: destination pointer, for compression
+ * pend: end of memory to compress
+ * pj: pointer into an element or variable
+ * pme: pointer into the current element (pme1...pme2)
+ * pme1: the current element, me, is stored in Iw [pme1...pme2]
+ * pme2: the end of the current element
+ * pn: pointer into a "clean" variable, also used to compress
+ * psrc: source pointer, for compression
+*/
+
+/* ========================================================================= */
+/* INITIALIZATIONS */
+/* ========================================================================= */
+
+ /* Note that this restriction on iwlen is slightly more restrictive than
+ * what is actually required in AMD_2. AMD_2 can operate with no elbow
+ * room at all, but it will be slow. For better performance, at least
+ * size-n elbow room is enforced. */
+ ASSERT (iwlen >= pfree + n) ;
+ ASSERT (n > 0) ;
+
+ /* initialize output statistics */
+ lnz = 0 ;
+ ndiv = 0 ;
+ nms_lu = 0 ;
+ nms_ldl = 0 ;
+ dmax = 1 ;
+ me = EMPTY ;
+
+ mindeg = 0 ;
+ ncmpa = 0 ;
+ nel = 0 ;
+ lemax = 0 ;
+
+ /* get control parameters */
+ if (Control != (double *) NULL)
+ {
+ alpha = Control [AMD_DENSE] ;
+ aggressive = (Control [AMD_AGGRESSIVE] != 0) ;
+ }
+ else
+ {
+ alpha = AMD_DEFAULT_DENSE ;
+ aggressive = AMD_DEFAULT_AGGRESSIVE ;
+ }
+ /* Note: if alpha is NaN, this is undefined: */
+ if (alpha < 0)
+ {
+ /* only remove completely dense rows/columns */
+ dense = n-2 ;
+ }
+ else
+ {
+ dense = alpha * sqrt ((double) n) ;
+ }
+ dense = MAX (16, dense) ;
+ dense = MIN (n, dense) ;
+ AMD_DEBUG1 (("\n\nAMD (debug), alpha %g, aggr. "ID"\n",
+ alpha, aggressive)) ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ Last [i] = EMPTY ;
+ Head [i] = EMPTY ;
+ Next [i] = EMPTY ;
+ /* if separate Hhead array is used for hash buckets: *
+ Hhead [i] = EMPTY ;
+ */
+ Nv [i] = 1 ;
+ W [i] = 1 ;
+ Elen [i] = 0 ;
+ Degree [i] = Len [i] ;
+ }
+
+#ifndef NDEBUG
+ AMD_DEBUG1 (("\n======Nel "ID" initial\n", nel)) ;
+ AMD_dump (n, Pe, Iw, Len, iwlen, pfree, Nv, Next, Last,
+ Head, Elen, Degree, W, -1) ;
+#endif
+
+ /* initialize wflg */
+ wbig = Int_MAX - n ;
+ wflg = clear_flag (0, wbig, W, n) ;
+
+ /* --------------------------------------------------------------------- */
+ /* initialize degree lists and eliminate dense and empty rows */
+ /* --------------------------------------------------------------------- */
+
+ ndense = 0 ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ deg = Degree [i] ;
+ ASSERT (deg >= 0 && deg < n) ;
+ if (deg == 0)
+ {
+
+ /* -------------------------------------------------------------
+ * we have a variable that can be eliminated at once because
+ * there is no off-diagonal non-zero in its row. Note that
+ * Nv [i] = 1 for an empty variable i. It is treated just
+ * the same as an eliminated element i.
+ * ------------------------------------------------------------- */
+
+ Elen [i] = FLIP (1) ;
+ nel++ ;
+ Pe [i] = EMPTY ;
+ W [i] = 0 ;
+
+ }
+ else if (deg > dense)
+ {
+
+ /* -------------------------------------------------------------
+ * Dense variables are not treated as elements, but as unordered,
+ * non-principal variables that have no parent. They do not take
+ * part in the postorder, since Nv [i] = 0. Note that the Fortran
+ * version does not have this option.
+ * ------------------------------------------------------------- */
+
+ AMD_DEBUG1 (("Dense node "ID" degree "ID"\n", i, deg)) ;
+ ndense++ ;
+ Nv [i] = 0 ; /* do not postorder this node */
+ Elen [i] = EMPTY ;
+ nel++ ;
+ Pe [i] = EMPTY ;
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------
+ * place i in the degree list corresponding to its degree
+ * ------------------------------------------------------------- */
+
+ inext = Head [deg] ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = i ;
+ Next [i] = inext ;
+ Head [deg] = i ;
+
+ }
+ }
+
+/* ========================================================================= */
+/* WHILE (selecting pivots) DO */
+/* ========================================================================= */
+
+ while (nel < n)
+ {
+
+#ifndef NDEBUG
+ AMD_DEBUG1 (("\n======Nel "ID"\n", nel)) ;
+ if (AMD_debug >= 2)
+ {
+ AMD_dump (n, Pe, Iw, Len, iwlen, pfree, Nv, Next,
+ Last, Head, Elen, Degree, W, nel) ;
+ }
+#endif
+
+/* ========================================================================= */
+/* GET PIVOT OF MINIMUM DEGREE */
+/* ========================================================================= */
+
+ /* ----------------------------------------------------------------- */
+ /* find next supervariable for elimination */
+ /* ----------------------------------------------------------------- */
+
+ ASSERT (mindeg >= 0 && mindeg < n) ;
+ for (deg = mindeg ; deg < n ; deg++)
+ {
+ me = Head [deg] ;
+ if (me != EMPTY) break ;
+ }
+ mindeg = deg ;
+ ASSERT (me >= 0 && me < n) ;
+ AMD_DEBUG1 (("=================me: "ID"\n", me)) ;
+
+ /* ----------------------------------------------------------------- */
+ /* remove chosen variable from link list */
+ /* ----------------------------------------------------------------- */
+
+ inext = Next [me] ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = EMPTY ;
+ Head [deg] = inext ;
+
+ /* ----------------------------------------------------------------- */
+ /* me represents the elimination of pivots nel to nel+Nv[me]-1. */
+ /* place me itself as the first in this set. */
+ /* ----------------------------------------------------------------- */
+
+ elenme = Elen [me] ;
+ nvpiv = Nv [me] ;
+ ASSERT (nvpiv > 0) ;
+ nel += nvpiv ;
+
+/* ========================================================================= */
+/* CONSTRUCT NEW ELEMENT */
+/* ========================================================================= */
+
+ /* -----------------------------------------------------------------
+ * At this point, me is the pivotal supervariable. It will be
+ * converted into the current element. Scan list of the pivotal
+ * supervariable, me, setting tree pointers and constructing new list
+ * of supervariables for the new element, me. p is a pointer to the
+ * current position in the old list.
+ * ----------------------------------------------------------------- */
+
+ /* flag the variable "me" as being in Lme by negating Nv [me] */
+ Nv [me] = -nvpiv ;
+ degme = 0 ;
+ ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ;
+
+ if (elenme == 0)
+ {
+
+ /* ------------------------------------------------------------- */
+ /* construct the new element in place */
+ /* ------------------------------------------------------------- */
+
+ pme1 = Pe [me] ;
+ pme2 = pme1 - 1 ;
+
+ for (p = pme1 ; p <= pme1 + Len [me] - 1 ; p++)
+ {
+ i = Iw [p] ;
+ ASSERT (i >= 0 && i < n && Nv [i] >= 0) ;
+ nvi = Nv [i] ;
+ if (nvi > 0)
+ {
+
+ /* ----------------------------------------------------- */
+ /* i is a principal variable not yet placed in Lme. */
+ /* store i in new list */
+ /* ----------------------------------------------------- */
+
+ /* flag i as being in Lme by negating Nv [i] */
+ degme += nvi ;
+ Nv [i] = -nvi ;
+ Iw [++pme2] = i ;
+
+ /* ----------------------------------------------------- */
+ /* remove variable i from degree list. */
+ /* ----------------------------------------------------- */
+
+ ilast = Last [i] ;
+ inext = Next [i] ;
+ ASSERT (ilast >= EMPTY && ilast < n) ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = ilast ;
+ if (ilast != EMPTY)
+ {
+ Next [ilast] = inext ;
+ }
+ else
+ {
+ /* i is at the head of the degree list */
+ ASSERT (Degree [i] >= 0 && Degree [i] < n) ;
+ Head [Degree [i]] = inext ;
+ }
+ }
+ }
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------- */
+ /* construct the new element in empty space, Iw [pfree ...] */
+ /* ------------------------------------------------------------- */
+
+ p = Pe [me] ;
+ pme1 = pfree ;
+ slenme = Len [me] - elenme ;
+
+ for (knt1 = 1 ; knt1 <= elenme + 1 ; knt1++)
+ {
+
+ if (knt1 > elenme)
+ {
+ /* search the supervariables in me. */
+ e = me ;
+ pj = p ;
+ ln = slenme ;
+ AMD_DEBUG2 (("Search sv: "ID" "ID" "ID"\n", me,pj,ln)) ;
+ }
+ else
+ {
+ /* search the elements in me. */
+ e = Iw [p++] ;
+ ASSERT (e >= 0 && e < n) ;
+ pj = Pe [e] ;
+ ln = Len [e] ;
+ AMD_DEBUG2 (("Search element e "ID" in me "ID"\n", e,me)) ;
+ ASSERT (Elen [e] < EMPTY && W [e] > 0 && pj >= 0) ;
+ }
+ ASSERT (ln >= 0 && (ln == 0 || (pj >= 0 && pj < iwlen))) ;
+
+ /* ---------------------------------------------------------
+ * search for different supervariables and add them to the
+ * new list, compressing when necessary. this loop is
+ * executed once for each element in the list and once for
+ * all the supervariables in the list.
+ * --------------------------------------------------------- */
+
+ for (knt2 = 1 ; knt2 <= ln ; knt2++)
+ {
+ i = Iw [pj++] ;
+ ASSERT (i >= 0 && i < n && (i == me || Elen [i] >= EMPTY));
+ nvi = Nv [i] ;
+ AMD_DEBUG2 ((": "ID" "ID" "ID" "ID"\n",
+ i, Elen [i], Nv [i], wflg)) ;
+
+ if (nvi > 0)
+ {
+
+ /* ------------------------------------------------- */
+ /* compress Iw, if necessary */
+ /* ------------------------------------------------- */
+
+ if (pfree >= iwlen)
+ {
+
+ AMD_DEBUG1 (("GARBAGE COLLECTION\n")) ;
+
+ /* prepare for compressing Iw by adjusting pointers
+ * and lengths so that the lists being searched in
+ * the inner and outer loops contain only the
+ * remaining entries. */
+
+ Pe [me] = p ;
+ Len [me] -= knt1 ;
+ /* check if nothing left of supervariable me */
+ if (Len [me] == 0) Pe [me] = EMPTY ;
+ Pe [e] = pj ;
+ Len [e] = ln - knt2 ;
+ /* nothing left of element e */
+ if (Len [e] == 0) Pe [e] = EMPTY ;
+
+ ncmpa++ ; /* one more garbage collection */
+
+ /* store first entry of each object in Pe */
+ /* FLIP the first entry in each object */
+ for (j = 0 ; j < n ; j++)
+ {
+ pn = Pe [j] ;
+ if (pn >= 0)
+ {
+ ASSERT (pn >= 0 && pn < iwlen) ;
+ Pe [j] = Iw [pn] ;
+ Iw [pn] = FLIP (j) ;
+ }
+ }
+
+ /* psrc/pdst point to source/destination */
+ psrc = 0 ;
+ pdst = 0 ;
+ pend = pme1 - 1 ;
+
+ while (psrc <= pend)
+ {
+ /* search for next FLIP'd entry */
+ j = FLIP (Iw [psrc++]) ;
+ if (j >= 0)
+ {
+ AMD_DEBUG2 (("Got object j: "ID"\n", j)) ;
+ Iw [pdst] = Pe [j] ;
+ Pe [j] = pdst++ ;
+ lenj = Len [j] ;
+ /* copy from source to destination */
+ for (knt3 = 0 ; knt3 <= lenj - 2 ; knt3++)
+ {
+ Iw [pdst++] = Iw [psrc++] ;
+ }
+ }
+ }
+
+ /* move the new partially-constructed element */
+ p1 = pdst ;
+ for (psrc = pme1 ; psrc <= pfree-1 ; psrc++)
+ {
+ Iw [pdst++] = Iw [psrc] ;
+ }
+ pme1 = p1 ;
+ pfree = pdst ;
+ pj = Pe [e] ;
+ p = Pe [me] ;
+
+ }
+
+ /* ------------------------------------------------- */
+ /* i is a principal variable not yet placed in Lme */
+ /* store i in new list */
+ /* ------------------------------------------------- */
+
+ /* flag i as being in Lme by negating Nv [i] */
+ degme += nvi ;
+ Nv [i] = -nvi ;
+ Iw [pfree++] = i ;
+ AMD_DEBUG2 ((" s: "ID" nv "ID"\n", i, Nv [i]));
+
+ /* ------------------------------------------------- */
+ /* remove variable i from degree link list */
+ /* ------------------------------------------------- */
+
+ ilast = Last [i] ;
+ inext = Next [i] ;
+ ASSERT (ilast >= EMPTY && ilast < n) ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = ilast ;
+ if (ilast != EMPTY)
+ {
+ Next [ilast] = inext ;
+ }
+ else
+ {
+ /* i is at the head of the degree list */
+ ASSERT (Degree [i] >= 0 && Degree [i] < n) ;
+ Head [Degree [i]] = inext ;
+ }
+ }
+ }
+
+ if (e != me)
+ {
+ /* set tree pointer and flag to indicate element e is
+ * absorbed into new element me (the parent of e is me) */
+ AMD_DEBUG1 ((" Element "ID" => "ID"\n", e, me)) ;
+ Pe [e] = FLIP (me) ;
+ W [e] = 0 ;
+ }
+ }
+
+ pme2 = pfree - 1 ;
+ }
+
+ /* ----------------------------------------------------------------- */
+ /* me has now been converted into an element in Iw [pme1..pme2] */
+ /* ----------------------------------------------------------------- */
+
+ /* degme holds the external degree of new element */
+ Degree [me] = degme ;
+ Pe [me] = pme1 ;
+ Len [me] = pme2 - pme1 + 1 ;
+ ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ;
+
+ Elen [me] = FLIP (nvpiv + degme) ;
+ /* FLIP (Elen (me)) is now the degree of pivot (including
+ * diagonal part). */
+
+#ifndef NDEBUG
+ AMD_DEBUG2 (("New element structure: length= "ID"\n", pme2-pme1+1)) ;
+ for (pme = pme1 ; pme <= pme2 ; pme++) AMD_DEBUG3 ((" "ID"", Iw[pme]));
+ AMD_DEBUG3 (("\n")) ;
+#endif
+
+ /* ----------------------------------------------------------------- */
+ /* make sure that wflg is not too large. */
+ /* ----------------------------------------------------------------- */
+
+ /* With the current value of wflg, wflg+n must not cause integer
+ * overflow */
+
+ wflg = clear_flag (wflg, wbig, W, n) ;
+
+/* ========================================================================= */
+/* COMPUTE (W [e] - wflg) = |Le\Lme| FOR ALL ELEMENTS */
+/* ========================================================================= */
+
+ /* -----------------------------------------------------------------
+ * Scan 1: compute the external degrees of previous elements with
+ * respect to the current element. That is:
+ * (W [e] - wflg) = |Le \ Lme|
+ * for each element e that appears in any supervariable in Lme. The
+ * notation Le refers to the pattern (list of supervariables) of a
+ * previous element e, where e is not yet absorbed, stored in
+ * Iw [Pe [e] + 1 ... Pe [e] + Len [e]]. The notation Lme
+ * refers to the pattern of the current element (stored in
+ * Iw [pme1..pme2]). If aggressive absorption is enabled, and
+ * (W [e] - wflg) becomes zero, then the element e will be absorbed
+ * in Scan 2.
+ * ----------------------------------------------------------------- */
+
+ AMD_DEBUG2 (("me: ")) ;
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n) ;
+ eln = Elen [i] ;
+ AMD_DEBUG3 ((""ID" Elen "ID": \n", i, eln)) ;
+ if (eln > 0)
+ {
+ /* note that Nv [i] has been negated to denote i in Lme: */
+ nvi = -Nv [i] ;
+ ASSERT (nvi > 0 && Pe [i] >= 0 && Pe [i] < iwlen) ;
+ wnvi = wflg - nvi ;
+ for (p = Pe [i] ; p <= Pe [i] + eln - 1 ; p++)
+ {
+ e = Iw [p] ;
+ ASSERT (e >= 0 && e < n) ;
+ we = W [e] ;
+ AMD_DEBUG4 ((" e "ID" we "ID" ", e, we)) ;
+ if (we >= wflg)
+ {
+ /* unabsorbed element e has been seen in this loop */
+ AMD_DEBUG4 ((" unabsorbed, first time seen")) ;
+ we -= nvi ;
+ }
+ else if (we != 0)
+ {
+ /* e is an unabsorbed element */
+ /* this is the first we have seen e in all of Scan 1 */
+ AMD_DEBUG4 ((" unabsorbed")) ;
+ we = Degree [e] + wnvi ;
+ }
+ AMD_DEBUG4 (("\n")) ;
+ W [e] = we ;
+ }
+ }
+ }
+ AMD_DEBUG2 (("\n")) ;
+
+/* ========================================================================= */
+/* DEGREE UPDATE AND ELEMENT ABSORPTION */
+/* ========================================================================= */
+
+ /* -----------------------------------------------------------------
+ * Scan 2: for each i in Lme, sum up the degree of Lme (which is
+ * degme), plus the sum of the external degrees of each Le for the
+ * elements e appearing within i, plus the supervariables in i.
+ * Place i in hash list.
+ * ----------------------------------------------------------------- */
+
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n && Nv [i] < 0 && Elen [i] >= 0) ;
+ AMD_DEBUG2 (("Updating: i "ID" "ID" "ID"\n", i, Elen[i], Len [i]));
+ p1 = Pe [i] ;
+ p2 = p1 + Elen [i] - 1 ;
+ pn = p1 ;
+ hash = 0 ;
+ deg = 0 ;
+ ASSERT (p1 >= 0 && p1 < iwlen && p2 >= -1 && p2 < iwlen) ;
+
+ /* ------------------------------------------------------------- */
+ /* scan the element list associated with supervariable i */
+ /* ------------------------------------------------------------- */
+
+ /* UMFPACK/MA38-style approximate degree: */
+ if (aggressive)
+ {
+ for (p = p1 ; p <= p2 ; p++)
+ {
+ e = Iw [p] ;
+ ASSERT (e >= 0 && e < n) ;
+ we = W [e] ;
+ if (we != 0)
+ {
+ /* e is an unabsorbed element */
+ /* dext = | Le \ Lme | */
+ dext = we - wflg ;
+ if (dext > 0)
+ {
+ deg += dext ;
+ Iw [pn++] = e ;
+ hash += e ;
+ AMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ;
+ }
+ else
+ {
+ /* external degree of e is zero, absorb e into me*/
+ AMD_DEBUG1 ((" Element "ID" =>"ID" (aggressive)\n",
+ e, me)) ;
+ ASSERT (dext == 0) ;
+ Pe [e] = FLIP (me) ;
+ W [e] = 0 ;
+ }
+ }
+ }
+ }
+ else
+ {
+ for (p = p1 ; p <= p2 ; p++)
+ {
+ e = Iw [p] ;
+ ASSERT (e >= 0 && e < n) ;
+ we = W [e] ;
+ if (we != 0)
+ {
+ /* e is an unabsorbed element */
+ dext = we - wflg ;
+ ASSERT (dext >= 0) ;
+ deg += dext ;
+ Iw [pn++] = e ;
+ hash += e ;
+ AMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ;
+ }
+ }
+ }
+
+ /* count the number of elements in i (including me): */
+ Elen [i] = pn - p1 + 1 ;
+
+ /* ------------------------------------------------------------- */
+ /* scan the supervariables in the list associated with i */
+ /* ------------------------------------------------------------- */
+
+ /* The bulk of the AMD run time is typically spent in this loop,
+ * particularly if the matrix has many dense rows that are not
+ * removed prior to ordering. */
+ p3 = pn ;
+ p4 = p1 + Len [i] ;
+ for (p = p2 + 1 ; p < p4 ; p++)
+ {
+ j = Iw [p] ;
+ ASSERT (j >= 0 && j < n) ;
+ nvj = Nv [j] ;
+ if (nvj > 0)
+ {
+ /* j is unabsorbed, and not in Lme. */
+ /* add to degree and add to new list */
+ deg += nvj ;
+ Iw [pn++] = j ;
+ hash += j ;
+ AMD_DEBUG4 ((" s: "ID" hash "ID" Nv[j]= "ID"\n",
+ j, hash, nvj)) ;
+ }
+ }
+
+ /* ------------------------------------------------------------- */
+ /* update the degree and check for mass elimination */
+ /* ------------------------------------------------------------- */
+
+ /* with aggressive absorption, deg==0 is identical to the
+ * Elen [i] == 1 && p3 == pn test, below. */
+ ASSERT (IMPLIES (aggressive, (deg==0) == (Elen[i]==1 && p3==pn))) ;
+
+ if (Elen [i] == 1 && p3 == pn)
+ {
+
+ /* --------------------------------------------------------- */
+ /* mass elimination */
+ /* --------------------------------------------------------- */
+
+ /* There is nothing left of this node except for an edge to
+ * the current pivot element. Elen [i] is 1, and there are
+ * no variables adjacent to node i. Absorb i into the
+ * current pivot element, me. Note that if there are two or
+ * more mass eliminations, fillin due to mass elimination is
+ * possible within the nvpiv-by-nvpiv pivot block. It is this
+ * step that causes AMD's analysis to be an upper bound.
+ *
+ * The reason is that the selected pivot has a lower
+ * approximate degree than the true degree of the two mass
+ * eliminated nodes. There is no edge between the two mass
+ * eliminated nodes. They are merged with the current pivot
+ * anyway.
+ *
+ * No fillin occurs in the Schur complement, in any case,
+ * and this effect does not decrease the quality of the
+ * ordering itself, just the quality of the nonzero and
+ * flop count analysis. It also means that the post-ordering
+ * is not an exact elimination tree post-ordering. */
+
+ AMD_DEBUG1 ((" MASS i "ID" => parent e "ID"\n", i, me)) ;
+ Pe [i] = FLIP (me) ;
+ nvi = -Nv [i] ;
+ degme -= nvi ;
+ nvpiv += nvi ;
+ nel += nvi ;
+ Nv [i] = 0 ;
+ Elen [i] = EMPTY ;
+
+ }
+ else
+ {
+
+ /* --------------------------------------------------------- */
+ /* update the upper-bound degree of i */
+ /* --------------------------------------------------------- */
+
+ /* the following degree does not yet include the size
+ * of the current element, which is added later: */
+
+ Degree [i] = MIN (Degree [i], deg) ;
+
+ /* --------------------------------------------------------- */
+ /* add me to the list for i */
+ /* --------------------------------------------------------- */
+
+ /* move first supervariable to end of list */
+ Iw [pn] = Iw [p3] ;
+ /* move first element to end of element part of list */
+ Iw [p3] = Iw [p1] ;
+ /* add new element, me, to front of list. */
+ Iw [p1] = me ;
+ /* store the new length of the list in Len [i] */
+ Len [i] = pn - p1 + 1 ;
+
+ /* --------------------------------------------------------- */
+ /* place in hash bucket. Save hash key of i in Last [i]. */
+ /* --------------------------------------------------------- */
+
+ /* NOTE: this can fail if hash is negative, because the ANSI C
+ * standard does not define a % b when a and/or b are negative.
+ * That's why hash is defined as an unsigned Int, to avoid this
+ * problem. */
+ hash = hash % n ;
+ ASSERT (((Int) hash) >= 0 && ((Int) hash) < n) ;
+
+ /* if the Hhead array is not used: */
+ j = Head [hash] ;
+ if (j <= EMPTY)
+ {
+ /* degree list is empty, hash head is FLIP (j) */
+ Next [i] = FLIP (j) ;
+ Head [hash] = FLIP (i) ;
+ }
+ else
+ {
+ /* degree list is not empty, use Last [Head [hash]] as
+ * hash head. */
+ Next [i] = Last [j] ;
+ Last [j] = i ;
+ }
+
+ /* if a separate Hhead array is used: *
+ Next [i] = Hhead [hash] ;
+ Hhead [hash] = i ;
+ */
+
+ Last [i] = hash ;
+ }
+ }
+
+ Degree [me] = degme ;
+
+ /* ----------------------------------------------------------------- */
+ /* Clear the counter array, W [...], by incrementing wflg. */
+ /* ----------------------------------------------------------------- */
+
+ /* make sure that wflg+n does not cause integer overflow */
+ lemax = MAX (lemax, degme) ;
+ wflg += lemax ;
+ wflg = clear_flag (wflg, wbig, W, n) ;
+ /* at this point, W [0..n-1] < wflg holds */
+
+/* ========================================================================= */
+/* SUPERVARIABLE DETECTION */
+/* ========================================================================= */
+
+ AMD_DEBUG1 (("Detecting supervariables:\n")) ;
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n) ;
+ AMD_DEBUG2 (("Consider i "ID" nv "ID"\n", i, Nv [i])) ;
+ if (Nv [i] < 0)
+ {
+ /* i is a principal variable in Lme */
+
+ /* ---------------------------------------------------------
+ * examine all hash buckets with 2 or more variables. We do
+ * this by examing all unique hash keys for supervariables in
+ * the pattern Lme of the current element, me
+ * --------------------------------------------------------- */
+
+ /* let i = head of hash bucket, and empty the hash bucket */
+ ASSERT (Last [i] >= 0 && Last [i] < n) ;
+ hash = Last [i] ;
+
+ /* if Hhead array is not used: */
+ j = Head [hash] ;
+ if (j == EMPTY)
+ {
+ /* hash bucket and degree list are both empty */
+ i = EMPTY ;
+ }
+ else if (j < EMPTY)
+ {
+ /* degree list is empty */
+ i = FLIP (j) ;
+ Head [hash] = EMPTY ;
+ }
+ else
+ {
+ /* degree list is not empty, restore Last [j] of head j */
+ i = Last [j] ;
+ Last [j] = EMPTY ;
+ }
+
+ /* if separate Hhead array is used: *
+ i = Hhead [hash] ;
+ Hhead [hash] = EMPTY ;
+ */
+
+ ASSERT (i >= EMPTY && i < n) ;
+ AMD_DEBUG2 (("----i "ID" hash "ID"\n", i, hash)) ;
+
+ while (i != EMPTY && Next [i] != EMPTY)
+ {
+
+ /* -----------------------------------------------------
+ * this bucket has one or more variables following i.
+ * scan all of them to see if i can absorb any entries
+ * that follow i in hash bucket. Scatter i into w.
+ * ----------------------------------------------------- */
+
+ ln = Len [i] ;
+ eln = Elen [i] ;
+ ASSERT (ln >= 0 && eln >= 0) ;
+ ASSERT (Pe [i] >= 0 && Pe [i] < iwlen) ;
+ /* do not flag the first element in the list (me) */
+ for (p = Pe [i] + 1 ; p <= Pe [i] + ln - 1 ; p++)
+ {
+ ASSERT (Iw [p] >= 0 && Iw [p] < n) ;
+ W [Iw [p]] = wflg ;
+ }
+
+ /* ----------------------------------------------------- */
+ /* scan every other entry j following i in bucket */
+ /* ----------------------------------------------------- */
+
+ jlast = i ;
+ j = Next [i] ;
+ ASSERT (j >= EMPTY && j < n) ;
+
+ while (j != EMPTY)
+ {
+ /* ------------------------------------------------- */
+ /* check if j and i have identical nonzero pattern */
+ /* ------------------------------------------------- */
+
+ AMD_DEBUG3 (("compare i "ID" and j "ID"\n", i,j)) ;
+
+ /* check if i and j have the same Len and Elen */
+ ASSERT (Len [j] >= 0 && Elen [j] >= 0) ;
+ ASSERT (Pe [j] >= 0 && Pe [j] < iwlen) ;
+ ok = (Len [j] == ln) && (Elen [j] == eln) ;
+ /* skip the first element in the list (me) */
+ for (p = Pe [j] + 1 ; ok && p <= Pe [j] + ln - 1 ; p++)
+ {
+ ASSERT (Iw [p] >= 0 && Iw [p] < n) ;
+ if (W [Iw [p]] != wflg) ok = 0 ;
+ }
+ if (ok)
+ {
+ /* --------------------------------------------- */
+ /* found it! j can be absorbed into i */
+ /* --------------------------------------------- */
+
+ AMD_DEBUG1 (("found it! j "ID" => i "ID"\n", j,i));
+ Pe [j] = FLIP (i) ;
+ /* both Nv [i] and Nv [j] are negated since they */
+ /* are in Lme, and the absolute values of each */
+ /* are the number of variables in i and j: */
+ Nv [i] += Nv [j] ;
+ Nv [j] = 0 ;
+ Elen [j] = EMPTY ;
+ /* delete j from hash bucket */
+ ASSERT (j != Next [j]) ;
+ j = Next [j] ;
+ Next [jlast] = j ;
+
+ }
+ else
+ {
+ /* j cannot be absorbed into i */
+ jlast = j ;
+ ASSERT (j != Next [j]) ;
+ j = Next [j] ;
+ }
+ ASSERT (j >= EMPTY && j < n) ;
+ }
+
+ /* -----------------------------------------------------
+ * no more variables can be absorbed into i
+ * go to next i in bucket and clear flag array
+ * ----------------------------------------------------- */
+
+ wflg++ ;
+ i = Next [i] ;
+ ASSERT (i >= EMPTY && i < n) ;
+
+ }
+ }
+ }
+ AMD_DEBUG2 (("detect done\n")) ;
+
+/* ========================================================================= */
+/* RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVARIABLES FROM ELEMENT */
+/* ========================================================================= */
+
+ p = pme1 ;
+ nleft = n - nel ;
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n) ;
+ nvi = -Nv [i] ;
+ AMD_DEBUG3 (("Restore i "ID" "ID"\n", i, nvi)) ;
+ if (nvi > 0)
+ {
+ /* i is a principal variable in Lme */
+ /* restore Nv [i] to signify that i is principal */
+ Nv [i] = nvi ;
+
+ /* --------------------------------------------------------- */
+ /* compute the external degree (add size of current element) */
+ /* --------------------------------------------------------- */
+
+ deg = Degree [i] + degme - nvi ;
+ deg = MIN (deg, nleft - nvi) ;
+ ASSERT (IMPLIES (aggressive, deg > 0) && deg >= 0 && deg < n) ;
+
+ /* --------------------------------------------------------- */
+ /* place the supervariable at the head of the degree list */
+ /* --------------------------------------------------------- */
+
+ inext = Head [deg] ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = i ;
+ Next [i] = inext ;
+ Last [i] = EMPTY ;
+ Head [deg] = i ;
+
+ /* --------------------------------------------------------- */
+ /* save the new degree, and find the minimum degree */
+ /* --------------------------------------------------------- */
+
+ mindeg = MIN (mindeg, deg) ;
+ Degree [i] = deg ;
+
+ /* --------------------------------------------------------- */
+ /* place the supervariable in the element pattern */
+ /* --------------------------------------------------------- */
+
+ Iw [p++] = i ;
+
+ }
+ }
+ AMD_DEBUG2 (("restore done\n")) ;
+
+/* ========================================================================= */
+/* FINALIZE THE NEW ELEMENT */
+/* ========================================================================= */
+
+ AMD_DEBUG2 (("ME = "ID" DONE\n", me)) ;
+ Nv [me] = nvpiv ;
+ /* save the length of the list for the new element me */
+ Len [me] = p - pme1 ;
+ if (Len [me] == 0)
+ {
+ /* there is nothing left of the current pivot element */
+ /* it is a root of the assembly tree */
+ Pe [me] = EMPTY ;
+ W [me] = 0 ;
+ }
+ if (elenme != 0)
+ {
+ /* element was not constructed in place: deallocate part of */
+ /* it since newly nonprincipal variables may have been removed */
+ pfree = p ;
+ }
+
+ /* The new element has nvpiv pivots and the size of the contribution
+ * block for a multifrontal method is degme-by-degme, not including
+ * the "dense" rows/columns. If the "dense" rows/columns are included,
+ * the frontal matrix is no larger than
+ * (degme+ndense)-by-(degme+ndense).
+ */
+
+ if (Info != (double *) NULL)
+ {
+ f = nvpiv ;
+ r = degme + ndense ;
+ dmax = MAX (dmax, f + r) ;
+
+ /* number of nonzeros in L (excluding the diagonal) */
+ lnzme = f*r + (f-1)*f/2 ;
+ lnz += lnzme ;
+
+ /* number of divide operations for LDL' and for LU */
+ ndiv += lnzme ;
+
+ /* number of multiply-subtract pairs for LU */
+ s = f*r*r + r*(f-1)*f + (f-1)*f*(2*f-1)/6 ;
+ nms_lu += s ;
+
+ /* number of multiply-subtract pairs for LDL' */
+ nms_ldl += (s + lnzme)/2 ;
+ }
+
+#ifndef NDEBUG
+ AMD_DEBUG2 (("finalize done nel "ID" n "ID"\n ::::\n", nel, n)) ;
+ for (pme = Pe [me] ; pme <= Pe [me] + Len [me] - 1 ; pme++)
+ {
+ AMD_DEBUG3 ((" "ID"", Iw [pme])) ;
+ }
+ AMD_DEBUG3 (("\n")) ;
+#endif
+
+ }
+
+/* ========================================================================= */
+/* DONE SELECTING PIVOTS */
+/* ========================================================================= */
+
+ if (Info != (double *) NULL)
+ {
+
+ /* count the work to factorize the ndense-by-ndense submatrix */
+ f = ndense ;
+ dmax = MAX (dmax, (double) ndense) ;
+
+ /* number of nonzeros in L (excluding the diagonal) */
+ lnzme = (f-1)*f/2 ;
+ lnz += lnzme ;
+
+ /* number of divide operations for LDL' and for LU */
+ ndiv += lnzme ;
+
+ /* number of multiply-subtract pairs for LU */
+ s = (f-1)*f*(2*f-1)/6 ;
+ nms_lu += s ;
+
+ /* number of multiply-subtract pairs for LDL' */
+ nms_ldl += (s + lnzme)/2 ;
+
+ /* number of nz's in L (excl. diagonal) */
+ Info [AMD_LNZ] = lnz ;
+
+ /* number of divide ops for LU and LDL' */
+ Info [AMD_NDIV] = ndiv ;
+
+ /* number of multiply-subtract pairs for LDL' */
+ Info [AMD_NMULTSUBS_LDL] = nms_ldl ;
+
+ /* number of multiply-subtract pairs for LU */
+ Info [AMD_NMULTSUBS_LU] = nms_lu ;
+
+ /* number of "dense" rows/columns */
+ Info [AMD_NDENSE] = ndense ;
+
+ /* largest front is dmax-by-dmax */
+ Info [AMD_DMAX] = dmax ;
+
+ /* number of garbage collections in AMD */
+ Info [AMD_NCMPA] = ncmpa ;
+
+ /* successful ordering */
+ Info [AMD_STATUS] = AMD_OK ;
+ }
+
+/* ========================================================================= */
+/* POST-ORDERING */
+/* ========================================================================= */
+
+/* -------------------------------------------------------------------------
+ * Variables at this point:
+ *
+ * Pe: holds the elimination tree. The parent of j is FLIP (Pe [j]),
+ * or EMPTY if j is a root. The tree holds both elements and
+ * non-principal (unordered) variables absorbed into them.
+ * Dense variables are non-principal and unordered.
+ *
+ * Elen: holds the size of each element, including the diagonal part.
+ * FLIP (Elen [e]) > 0 if e is an element. For unordered
+ * variables i, Elen [i] is EMPTY.
+ *
+ * Nv: Nv [e] > 0 is the number of pivots represented by the element e.
+ * For unordered variables i, Nv [i] is zero.
+ *
+ * Contents no longer needed:
+ * W, Iw, Len, Degree, Head, Next, Last.
+ *
+ * The matrix itself has been destroyed.
+ *
+ * n: the size of the matrix.
+ * No other scalars needed (pfree, iwlen, etc.)
+ * ------------------------------------------------------------------------- */
+
+ /* restore Pe */
+ for (i = 0 ; i < n ; i++)
+ {
+ Pe [i] = FLIP (Pe [i]) ;
+ }
+
+ /* restore Elen, for output information, and for postordering */
+ for (i = 0 ; i < n ; i++)
+ {
+ Elen [i] = FLIP (Elen [i]) ;
+ }
+
+/* Now the parent of j is Pe [j], or EMPTY if j is a root. Elen [e] > 0
+ * is the size of element e. Elen [i] is EMPTY for unordered variable i. */
+
+#ifndef NDEBUG
+ AMD_DEBUG2 (("\nTree:\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ AMD_DEBUG2 ((" "ID" parent: "ID" ", i, Pe [i])) ;
+ ASSERT (Pe [i] >= EMPTY && Pe [i] < n) ;
+ if (Nv [i] > 0)
+ {
+ /* this is an element */
+ e = i ;
+ AMD_DEBUG2 ((" element, size is "ID"\n", Elen [i])) ;
+ ASSERT (Elen [e] > 0) ;
+ }
+ AMD_DEBUG2 (("\n")) ;
+ }
+ AMD_DEBUG2 (("\nelements:\n")) ;
+ for (e = 0 ; e < n ; e++)
+ {
+ if (Nv [e] > 0)
+ {
+ AMD_DEBUG3 (("Element e= "ID" size "ID" nv "ID" \n", e,
+ Elen [e], Nv [e])) ;
+ }
+ }
+ AMD_DEBUG2 (("\nvariables:\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Int cnt ;
+ if (Nv [i] == 0)
+ {
+ AMD_DEBUG3 (("i unordered: "ID"\n", i)) ;
+ j = Pe [i] ;
+ cnt = 0 ;
+ AMD_DEBUG3 ((" j: "ID"\n", j)) ;
+ if (j == EMPTY)
+ {
+ AMD_DEBUG3 ((" i is a dense variable\n")) ;
+ }
+ else
+ {
+ ASSERT (j >= 0 && j < n) ;
+ while (Nv [j] == 0)
+ {
+ AMD_DEBUG3 ((" j : "ID"\n", j)) ;
+ j = Pe [j] ;
+ AMD_DEBUG3 ((" j:: "ID"\n", j)) ;
+ cnt++ ;
+ if (cnt > n) break ;
+ }
+ e = j ;
+ AMD_DEBUG3 ((" got to e: "ID"\n", e)) ;
+ }
+ }
+ }
+#endif
+
+/* ========================================================================= */
+/* compress the paths of the variables */
+/* ========================================================================= */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ if (Nv [i] == 0)
+ {
+
+ /* -------------------------------------------------------------
+ * i is an un-ordered row. Traverse the tree from i until
+ * reaching an element, e. The element, e, was the principal
+ * supervariable of i and all nodes in the path from i to when e
+ * was selected as pivot.
+ * ------------------------------------------------------------- */
+
+ AMD_DEBUG1 (("Path compression, i unordered: "ID"\n", i)) ;
+ j = Pe [i] ;
+ ASSERT (j >= EMPTY && j < n) ;
+ AMD_DEBUG3 ((" j: "ID"\n", j)) ;
+ if (j == EMPTY)
+ {
+ /* Skip a dense variable. It has no parent. */
+ AMD_DEBUG3 ((" i is a dense variable\n")) ;
+ continue ;
+ }
+
+ /* while (j is a variable) */
+ while (Nv [j] == 0)
+ {
+ AMD_DEBUG3 ((" j : "ID"\n", j)) ;
+ j = Pe [j] ;
+ AMD_DEBUG3 ((" j:: "ID"\n", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ }
+ /* got to an element e */
+ e = j ;
+ AMD_DEBUG3 (("got to e: "ID"\n", e)) ;
+
+ /* -------------------------------------------------------------
+ * traverse the path again from i to e, and compress the path
+ * (all nodes point to e). Path compression allows this code to
+ * compute in O(n) time.
+ * ------------------------------------------------------------- */
+
+ j = i ;
+ /* while (j is a variable) */
+ while (Nv [j] == 0)
+ {
+ jnext = Pe [j] ;
+ AMD_DEBUG3 (("j "ID" jnext "ID"\n", j, jnext)) ;
+ Pe [j] = e ;
+ j = jnext ;
+ ASSERT (j >= 0 && j < n) ;
+ }
+ }
+ }
+
+/* ========================================================================= */
+/* postorder the assembly tree */
+/* ========================================================================= */
+
+ AMD_postorder (n, Pe, Nv, Elen,
+ W, /* output order */
+ Head, Next, Last) ; /* workspace */
+
+/* ========================================================================= */
+/* compute output permutation and inverse permutation */
+/* ========================================================================= */
+
+ /* W [e] = k means that element e is the kth element in the new
+ * order. e is in the range 0 to n-1, and k is in the range 0 to
+ * the number of elements. Use Head for inverse order. */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Head [k] = EMPTY ;
+ Next [k] = EMPTY ;
+ }
+ for (e = 0 ; e < n ; e++)
+ {
+ k = W [e] ;
+ ASSERT ((k == EMPTY) == (Nv [e] == 0)) ;
+ if (k != EMPTY)
+ {
+ ASSERT (k >= 0 && k < n) ;
+ Head [k] = e ;
+ }
+ }
+
+ /* construct output inverse permutation in Next,
+ * and permutation in Last */
+ nel = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ e = Head [k] ;
+ if (e == EMPTY) break ;
+ ASSERT (e >= 0 && e < n && Nv [e] > 0) ;
+ Next [e] = nel ;
+ nel += Nv [e] ;
+ }
+ ASSERT (nel == n - ndense) ;
+
+ /* order non-principal variables (dense, & those merged into supervar's) */
+ for (i = 0 ; i < n ; i++)
+ {
+ if (Nv [i] == 0)
+ {
+ e = Pe [i] ;
+ ASSERT (e >= EMPTY && e < n) ;
+ if (e != EMPTY)
+ {
+ /* This is an unordered variable that was merged
+ * into element e via supernode detection or mass
+ * elimination of i when e became the pivot element.
+ * Place i in order just before e. */
+ ASSERT (Next [i] == EMPTY && Nv [e] > 0) ;
+ Next [i] = Next [e] ;
+ Next [e]++ ;
+ }
+ else
+ {
+ /* This is a dense unordered variable, with no parent.
+ * Place it last in the output order. */
+ Next [i] = nel++ ;
+ }
+ }
+ }
+ ASSERT (nel == n) ;
+
+ AMD_DEBUG2 (("\n\nPerm:\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ k = Next [i] ;
+ ASSERT (k >= 0 && k < n) ;
+ Last [k] = i ;
+ AMD_DEBUG2 ((" perm ["ID"] = "ID"\n", k, i)) ;
+ }
+}
diff --git a/AMD/Source/amd_aat.c b/AMD/Source/amd_aat.c
new file mode 100644
index 0000000..4f02b75
--- /dev/null
+++ b/AMD/Source/amd_aat.c
@@ -0,0 +1,185 @@
+/* ========================================================================= */
+/* === AMD_aat ============================================================= */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* AMD_aat: compute the symmetry of the pattern of A, and count the number of
+ * nonzeros each column of A+A' (excluding the diagonal). Assumes the input
+ * matrix has no errors, with sorted columns and no duplicates
+ * (AMD_valid (n, n, Ap, Ai) must be AMD_OK, but this condition is not
+ * checked).
+ */
+
+#include "amd_internal.h"
+
+GLOBAL size_t AMD_aat /* returns nz in A+A' */
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int Len [ ], /* Len [j]: length of column j of A+A', excl diagonal*/
+ Int Tp [ ], /* workspace of size n */
+ double Info [ ]
+)
+{
+ Int p1, p2, p, i, j, pj, pj2, k, nzdiag, nzboth, nz ;
+ double sym ;
+ size_t nzaat ;
+
+#ifndef NDEBUG
+ AMD_debug_init ("AMD AAT") ;
+ for (k = 0 ; k < n ; k++) Tp [k] = EMPTY ;
+ ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ;
+#endif
+
+ if (Info != (double *) NULL)
+ {
+ /* clear the Info array, if it exists */
+ for (i = 0 ; i < AMD_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ Info [AMD_STATUS] = AMD_OK ;
+ }
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Len [k] = 0 ;
+ }
+
+ nzdiag = 0 ;
+ nzboth = 0 ;
+ nz = Ap [n] ;
+
+ for (k = 0 ; k < n ; k++)
+ {
+ p1 = Ap [k] ;
+ p2 = Ap [k+1] ;
+ AMD_DEBUG2 (("\nAAT Column: "ID" p1: "ID" p2: "ID"\n", k, p1, p2)) ;
+
+ /* construct A+A' */
+ for (p = p1 ; p < p2 ; )
+ {
+ /* scan the upper triangular part of A */
+ j = Ai [p] ;
+ if (j < k)
+ {
+ /* entry A (j,k) is in the strictly upper triangular part,
+ * add both A (j,k) and A (k,j) to the matrix A+A' */
+ Len [j]++ ;
+ Len [k]++ ;
+ AMD_DEBUG3 ((" upper ("ID","ID") ("ID","ID")\n", j,k, k,j));
+ p++ ;
+ }
+ else if (j == k)
+ {
+ /* skip the diagonal */
+ p++ ;
+ nzdiag++ ;
+ break ;
+ }
+ else /* j > k */
+ {
+ /* first entry below the diagonal */
+ break ;
+ }
+ /* scan lower triangular part of A, in column j until reaching
+ * row k. Start where last scan left off. */
+ ASSERT (Tp [j] != EMPTY) ;
+ ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ;
+ pj2 = Ap [j+1] ;
+ for (pj = Tp [j] ; pj < pj2 ; )
+ {
+ i = Ai [pj] ;
+ if (i < k)
+ {
+ /* A (i,j) is only in the lower part, not in upper.
+ * add both A (i,j) and A (j,i) to the matrix A+A' */
+ Len [i]++ ;
+ Len [j]++ ;
+ AMD_DEBUG3 ((" lower ("ID","ID") ("ID","ID")\n",
+ i,j, j,i)) ;
+ pj++ ;
+ }
+ else if (i == k)
+ {
+ /* entry A (k,j) in lower part and A (j,k) in upper */
+ pj++ ;
+ nzboth++ ;
+ break ;
+ }
+ else /* i > k */
+ {
+ /* consider this entry later, when k advances to i */
+ break ;
+ }
+ }
+ Tp [j] = pj ;
+ }
+ /* Tp [k] points to the entry just below the diagonal in column k */
+ Tp [k] = p ;
+ }
+
+ /* clean up, for remaining mismatched entries */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (pj = Tp [j] ; pj < Ap [j+1] ; pj++)
+ {
+ i = Ai [pj] ;
+ /* A (i,j) is only in the lower part, not in upper.
+ * add both A (i,j) and A (j,i) to the matrix A+A' */
+ Len [i]++ ;
+ Len [j]++ ;
+ AMD_DEBUG3 ((" lower cleanup ("ID","ID") ("ID","ID")\n",
+ i,j, j,i)) ;
+ }
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* compute the symmetry of the nonzero pattern of A */
+ /* --------------------------------------------------------------------- */
+
+ /* Given a matrix A, the symmetry of A is:
+ * B = tril (spones (A), -1) + triu (spones (A), 1) ;
+ * sym = nnz (B & B') / nnz (B) ;
+ * or 1 if nnz (B) is zero.
+ */
+
+ if (nz == nzdiag)
+ {
+ sym = 1 ;
+ }
+ else
+ {
+ sym = (2 * (double) nzboth) / ((double) (nz - nzdiag)) ;
+ }
+
+ nzaat = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ nzaat += Len [k] ;
+ }
+
+ AMD_DEBUG1 (("AMD nz in A+A', excluding diagonal (nzaat) = %g\n",
+ (double) nzaat)) ;
+ AMD_DEBUG1 ((" nzboth: "ID" nz: "ID" nzdiag: "ID" symmetry: %g\n",
+ nzboth, nz, nzdiag, sym)) ;
+
+ if (Info != (double *) NULL)
+ {
+ Info [AMD_STATUS] = AMD_OK ;
+ Info [AMD_N] = n ;
+ Info [AMD_NZ] = nz ;
+ Info [AMD_SYMMETRY] = sym ; /* symmetry of pattern of A */
+ Info [AMD_NZDIAG] = nzdiag ; /* nonzeros on diagonal of A */
+ Info [AMD_NZ_A_PLUS_AT] = nzaat ; /* nonzeros in A+A' */
+ }
+
+ return (nzaat) ;
+}
diff --git a/AMD/Source/amd_control.c b/AMD/Source/amd_control.c
new file mode 100644
index 0000000..c2aec9f
--- /dev/null
+++ b/AMD/Source/amd_control.c
@@ -0,0 +1,64 @@
+/* ========================================================================= */
+/* === AMD_control ========================================================= */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable. Prints the control parameters for AMD. See amd.h
+ * for details. If the Control array is not present, the defaults are
+ * printed instead.
+ */
+
+#include "amd_internal.h"
+
+GLOBAL void AMD_control
+(
+ double Control [ ]
+)
+{
+ double alpha ;
+ Int aggressive ;
+
+ if (Control != (double *) NULL)
+ {
+ alpha = Control [AMD_DENSE] ;
+ aggressive = Control [AMD_AGGRESSIVE] != 0 ;
+ }
+ else
+ {
+ alpha = AMD_DEFAULT_DENSE ;
+ aggressive = AMD_DEFAULT_AGGRESSIVE ;
+ }
+
+ PRINTF (("\nAMD version %d.%d.%d, %s: approximate minimum degree ordering\n"
+ " dense row parameter: %g\n", AMD_MAIN_VERSION, AMD_SUB_VERSION,
+ AMD_SUBSUB_VERSION, AMD_DATE, alpha)) ;
+
+ if (alpha < 0)
+ {
+ PRINTF ((" no rows treated as dense\n")) ;
+ }
+ else
+ {
+ PRINTF ((
+ " (rows with more than max (%g * sqrt (n), 16) entries are\n"
+ " considered \"dense\", and placed last in output permutation)\n",
+ alpha)) ;
+ }
+
+ if (aggressive)
+ {
+ PRINTF ((" aggressive absorption: yes\n")) ;
+ }
+ else
+ {
+ PRINTF ((" aggressive absorption: no\n")) ;
+ }
+
+ PRINTF ((" size of AMD integer: %d\n\n", sizeof (Int))) ;
+}
diff --git a/AMD/Source/amd_defaults.c b/AMD/Source/amd_defaults.c
new file mode 100644
index 0000000..ffe3f4b
--- /dev/null
+++ b/AMD/Source/amd_defaults.c
@@ -0,0 +1,38 @@
+/* ========================================================================= */
+/* === AMD_defaults ======================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable. Sets default control parameters for AMD. See amd.h
+ * for details.
+ */
+
+#include "amd_internal.h"
+
+/* ========================================================================= */
+/* === AMD defaults ======================================================== */
+/* ========================================================================= */
+
+GLOBAL void AMD_defaults
+(
+ double Control [ ]
+)
+{
+ Int i ;
+
+ if (Control != (double *) NULL)
+ {
+ for (i = 0 ; i < AMD_CONTROL ; i++)
+ {
+ Control [i] = 0 ;
+ }
+ Control [AMD_DENSE] = AMD_DEFAULT_DENSE ;
+ Control [AMD_AGGRESSIVE] = AMD_DEFAULT_AGGRESSIVE ;
+ }
+}
diff --git a/AMD/Source/amd_dump.c b/AMD/Source/amd_dump.c
new file mode 100644
index 0000000..89d67b8
--- /dev/null
+++ b/AMD/Source/amd_dump.c
@@ -0,0 +1,180 @@
+/* ========================================================================= */
+/* === AMD_dump ============================================================ */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Debugging routines for AMD. Not used if NDEBUG is not defined at compile-
+ * time (the default). See comments in amd_internal.h on how to enable
+ * debugging. Not user-callable.
+ */
+
+#include "amd_internal.h"
+
+#ifndef NDEBUG
+
+/* This global variable is present only when debugging */
+GLOBAL Int AMD_debug = -999 ; /* default is no debug printing */
+
+/* ========================================================================= */
+/* === AMD_debug_init ====================================================== */
+/* ========================================================================= */
+
+/* Sets the debug print level, by reading the file debug.amd (if it exists) */
+
+GLOBAL void AMD_debug_init ( char *s )
+{
+ FILE *f ;
+ f = fopen ("debug.amd", "r") ;
+ if (f == (FILE *) NULL)
+ {
+ AMD_debug = -999 ;
+ }
+ else
+ {
+ fscanf (f, ID, &AMD_debug) ;
+ fclose (f) ;
+ }
+ if (AMD_debug >= 0)
+ {
+ printf ("%s: AMD_debug_init, D= "ID"\n", s, AMD_debug) ;
+ }
+}
+
+/* ========================================================================= */
+/* === AMD_dump ============================================================ */
+/* ========================================================================= */
+
+/* Dump AMD's data structure, except for the hash buckets. This routine
+ * cannot be called when the hash buckets are non-empty.
+ */
+
+GLOBAL void AMD_dump (
+ Int n, /* A is n-by-n */
+ Int Pe [ ], /* pe [0..n-1]: index in iw of start of row i */
+ Int Iw [ ], /* workspace of size iwlen, iwlen [0..pfree-1]
+ * holds the matrix on input */
+ Int Len [ ], /* len [0..n-1]: length for row i */
+ Int iwlen, /* length of iw */
+ Int pfree, /* iw [pfree ... iwlen-1] is empty on input */
+ Int Nv [ ], /* nv [0..n-1] */
+ Int Next [ ], /* next [0..n-1] */
+ Int Last [ ], /* last [0..n-1] */
+ Int Head [ ], /* head [0..n-1] */
+ Int Elen [ ], /* size n */
+ Int Degree [ ], /* size n */
+ Int W [ ], /* size n */
+ Int nel
+)
+{
+ Int i, pe, elen, nv, len, e, p, k, j, deg, w, cnt, ilast ;
+
+ if (AMD_debug < 0) return ;
+ ASSERT (pfree <= iwlen) ;
+ AMD_DEBUG3 (("\nAMD dump, pfree: "ID"\n", pfree)) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ pe = Pe [i] ;
+ elen = Elen [i] ;
+ nv = Nv [i] ;
+ len = Len [i] ;
+ w = W [i] ;
+
+ if (elen >= EMPTY)
+ {
+ if (nv == 0)
+ {
+ AMD_DEBUG3 (("\nI "ID": nonprincipal: ", i)) ;
+ ASSERT (elen == EMPTY) ;
+ if (pe == EMPTY)
+ {
+ AMD_DEBUG3 ((" dense node\n")) ;
+ ASSERT (w == 1) ;
+ }
+ else
+ {
+ ASSERT (pe < EMPTY) ;
+ AMD_DEBUG3 ((" i "ID" -> parent "ID"\n", i, FLIP (Pe[i])));
+ }
+ }
+ else
+ {
+ AMD_DEBUG3 (("\nI "ID": active principal supervariable:\n",i));
+ AMD_DEBUG3 ((" nv(i): "ID" Flag: %d\n", nv, (nv < 0))) ;
+ ASSERT (elen >= 0) ;
+ ASSERT (nv > 0 && pe >= 0) ;
+ p = pe ;
+ AMD_DEBUG3 ((" e/s: ")) ;
+ if (elen == 0) AMD_DEBUG3 ((" : ")) ;
+ ASSERT (pe + len <= pfree) ;
+ for (k = 0 ; k < len ; k++)
+ {
+ j = Iw [p] ;
+ AMD_DEBUG3 ((" "ID"", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ if (k == elen-1) AMD_DEBUG3 ((" : ")) ;
+ p++ ;
+ }
+ AMD_DEBUG3 (("\n")) ;
+ }
+ }
+ else
+ {
+ e = i ;
+ if (w == 0)
+ {
+ AMD_DEBUG3 (("\nE "ID": absorbed element: w "ID"\n", e, w)) ;
+ ASSERT (nv > 0 && pe < 0) ;
+ AMD_DEBUG3 ((" e "ID" -> parent "ID"\n", e, FLIP (Pe [e]))) ;
+ }
+ else
+ {
+ AMD_DEBUG3 (("\nE "ID": unabsorbed element: w "ID"\n", e, w)) ;
+ ASSERT (nv > 0 && pe >= 0) ;
+ p = pe ;
+ AMD_DEBUG3 ((" : ")) ;
+ ASSERT (pe + len <= pfree) ;
+ for (k = 0 ; k < len ; k++)
+ {
+ j = Iw [p] ;
+ AMD_DEBUG3 ((" "ID"", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ p++ ;
+ }
+ AMD_DEBUG3 (("\n")) ;
+ }
+ }
+ }
+
+ /* this routine cannot be called when the hash buckets are non-empty */
+ AMD_DEBUG3 (("\nDegree lists:\n")) ;
+ if (nel >= 0)
+ {
+ cnt = 0 ;
+ for (deg = 0 ; deg < n ; deg++)
+ {
+ if (Head [deg] == EMPTY) continue ;
+ ilast = EMPTY ;
+ AMD_DEBUG3 ((ID": \n", deg)) ;
+ for (i = Head [deg] ; i != EMPTY ; i = Next [i])
+ {
+ AMD_DEBUG3 ((" "ID" : next "ID" last "ID" deg "ID"\n",
+ i, Next [i], Last [i], Degree [i])) ;
+ ASSERT (i >= 0 && i < n && ilast == Last [i] &&
+ deg == Degree [i]) ;
+ cnt += Nv [i] ;
+ ilast = i ;
+ }
+ AMD_DEBUG3 (("\n")) ;
+ }
+ ASSERT (cnt == n - nel) ;
+ }
+
+}
+
+#endif
diff --git a/AMD/Source/amd_global.c b/AMD/Source/amd_global.c
new file mode 100644
index 0000000..93f2b45
--- /dev/null
+++ b/AMD/Source/amd_global.c
@@ -0,0 +1,84 @@
+/* ========================================================================= */
+/* === amd_global ========================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+#include <stdlib.h>
+
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#include "matrix.h"
+#endif
+
+#ifndef NULL
+#define NULL 0
+#endif
+
+/* ========================================================================= */
+/* === Default AMD memory manager ========================================== */
+/* ========================================================================= */
+
+/* The user can redefine these global pointers at run-time to change the memory
+ * manager used by AMD. AMD only uses malloc and free; realloc and calloc are
+ * include for completeness, in case another package wants to use the same
+ * memory manager as AMD.
+ *
+ * If compiling as a MATLAB mexFunction, the default memory manager is mxMalloc.
+ * You can also compile AMD as a standard ANSI-C library and link a mexFunction
+ * against it, and then redefine these pointers at run-time, in your
+ * mexFunction.
+ *
+ * If -DNMALLOC is defined at compile-time, no memory manager is specified at
+ * compile-time. You must then define these functions at run-time, before
+ * calling AMD, for AMD to work properly.
+ */
+
+#ifndef NMALLOC
+#ifdef MATLAB_MEX_FILE
+/* MATLAB mexFunction: */
+void *(*amd_malloc) (size_t) = mxMalloc ;
+void (*amd_free) (void *) = mxFree ;
+void *(*amd_realloc) (void *, size_t) = mxRealloc ;
+void *(*amd_calloc) (size_t, size_t) = mxCalloc ;
+#else
+/* standard ANSI-C: */
+void *(*amd_malloc) (size_t) = malloc ;
+void (*amd_free) (void *) = free ;
+void *(*amd_realloc) (void *, size_t) = realloc ;
+void *(*amd_calloc) (size_t, size_t) = calloc ;
+#endif
+#else
+/* no memory manager defined at compile-time; you MUST define one at run-time */
+void *(*amd_malloc) (size_t) = NULL ;
+void (*amd_free) (void *) = NULL ;
+void *(*amd_realloc) (void *, size_t) = NULL ;
+void *(*amd_calloc) (size_t, size_t) = NULL ;
+#endif
+
+/* ========================================================================= */
+/* === Default AMD printf routine ========================================== */
+/* ========================================================================= */
+
+/* The user can redefine this global pointer at run-time to change the printf
+ * routine used by AMD. If NULL, no printing occurs.
+ *
+ * If -DNPRINT is defined at compile-time, stdio.h is not included. Printing
+ * can then be enabled at run-time by setting amd_printf to a non-NULL function.
+ */
+
+#ifndef NPRINT
+#ifdef MATLAB_MEX_FILE
+int (*amd_printf) (const char *, ...) = mexPrintf ;
+#else
+#include <stdio.h>
+int (*amd_printf) (const char *, ...) = printf ;
+#endif
+#else
+int (*amd_printf) (const char *, ...) = NULL ;
+#endif
diff --git a/AMD/Source/amd_info.c b/AMD/Source/amd_info.c
new file mode 100644
index 0000000..0a842ad
--- /dev/null
+++ b/AMD/Source/amd_info.c
@@ -0,0 +1,120 @@
+/* ========================================================================= */
+/* === AMD_info ============================================================ */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable. Prints the output statistics for AMD. See amd.h
+ * for details. If the Info array is not present, nothing is printed.
+ */
+
+#include "amd_internal.h"
+
+#define PRI(format,x) { if (x >= 0) { PRINTF ((format, x)) ; }}
+
+GLOBAL void AMD_info
+(
+ double Info [ ]
+)
+{
+ double n, ndiv, nmultsubs_ldl, nmultsubs_lu, lnz, lnzd ;
+
+ PRINTF (("\nAMD version %d.%d.%d, %s, results:\n",
+ AMD_MAIN_VERSION, AMD_SUB_VERSION, AMD_SUBSUB_VERSION, AMD_DATE)) ;
+
+ if (!Info)
+ {
+ return ;
+ }
+
+ n = Info [AMD_N] ;
+ ndiv = Info [AMD_NDIV] ;
+ nmultsubs_ldl = Info [AMD_NMULTSUBS_LDL] ;
+ nmultsubs_lu = Info [AMD_NMULTSUBS_LU] ;
+ lnz = Info [AMD_LNZ] ;
+ lnzd = (n >= 0 && lnz >= 0) ? (n + lnz) : (-1) ;
+
+ /* AMD return status */
+ PRINTF ((" status: ")) ;
+ if (Info [AMD_STATUS] == AMD_OK)
+ {
+ PRINTF (("OK\n")) ;
+ }
+ else if (Info [AMD_STATUS] == AMD_OUT_OF_MEMORY)
+ {
+ PRINTF (("out of memory\n")) ;
+ }
+ else if (Info [AMD_STATUS] == AMD_INVALID)
+ {
+ PRINTF (("invalid matrix\n")) ;
+ }
+ else if (Info [AMD_STATUS] == AMD_OK_BUT_JUMBLED)
+ {
+ PRINTF (("OK, but jumbled\n")) ;
+ }
+ else
+ {
+ PRINTF (("unknown\n")) ;
+ }
+
+ /* statistics about the input matrix */
+ PRI (" n, dimension of A: %.20g\n", n);
+ PRI (" nz, number of nonzeros in A: %.20g\n",
+ Info [AMD_NZ]) ;
+ PRI (" symmetry of A: %.4f\n",
+ Info [AMD_SYMMETRY]) ;
+ PRI (" number of nonzeros on diagonal: %.20g\n",
+ Info [AMD_NZDIAG]) ;
+ PRI (" nonzeros in pattern of A+A' (excl. diagonal): %.20g\n",
+ Info [AMD_NZ_A_PLUS_AT]) ;
+ PRI (" # dense rows/columns of A+A': %.20g\n",
+ Info [AMD_NDENSE]) ;
+
+ /* statistics about AMD's behavior */
+ PRI (" memory used, in bytes: %.20g\n",
+ Info [AMD_MEMORY]) ;
+ PRI (" # of memory compactions: %.20g\n",
+ Info [AMD_NCMPA]) ;
+
+ /* statistics about the ordering quality */
+ PRINTF (("\n"
+ " The following approximate statistics are for a subsequent\n"
+ " factorization of A(P,P) + A(P,P)'. They are slight upper\n"
+ " bounds if there are no dense rows/columns in A+A', and become\n"
+ " looser if dense rows/columns exist.\n\n")) ;
+
+ PRI (" nonzeros in L (excluding diagonal): %.20g\n",
+ lnz) ;
+ PRI (" nonzeros in L (including diagonal): %.20g\n",
+ lnzd) ;
+ PRI (" # divide operations for LDL' or LU: %.20g\n",
+ ndiv) ;
+ PRI (" # multiply-subtract operations for LDL': %.20g\n",
+ nmultsubs_ldl) ;
+ PRI (" # multiply-subtract operations for LU: %.20g\n",
+ nmultsubs_lu) ;
+ PRI (" max nz. in any column of L (incl. diagonal): %.20g\n",
+ Info [AMD_DMAX]) ;
+
+ /* total flop counts for various factorizations */
+
+ if (n >= 0 && ndiv >= 0 && nmultsubs_ldl >= 0 && nmultsubs_lu >= 0)
+ {
+ PRINTF (("\n"
+ " chol flop count for real A, sqrt counted as 1 flop: %.20g\n"
+ " LDL' flop count for real A: %.20g\n"
+ " LDL' flop count for complex A: %.20g\n"
+ " LU flop count for real A (with no pivoting): %.20g\n"
+ " LU flop count for complex A (with no pivoting): %.20g\n\n",
+ n + ndiv + 2*nmultsubs_ldl,
+ ndiv + 2*nmultsubs_ldl,
+ 9*ndiv + 8*nmultsubs_ldl,
+ ndiv + 2*nmultsubs_lu,
+ 9*ndiv + 8*nmultsubs_lu)) ;
+ }
+}
diff --git a/AMD/Source/amd_order.c b/AMD/Source/amd_order.c
new file mode 100644
index 0000000..d3f6853
--- /dev/null
+++ b/AMD/Source/amd_order.c
@@ -0,0 +1,200 @@
+/* ========================================================================= */
+/* === AMD_order =========================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable AMD minimum degree ordering routine. See amd.h for
+ * documentation.
+ */
+
+#include "amd_internal.h"
+
+/* ========================================================================= */
+/* === AMD_order =========================================================== */
+/* ========================================================================= */
+
+GLOBAL Int AMD_order
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int P [ ],
+ double Control [ ],
+ double Info [ ]
+)
+{
+ Int *Len, *S, nz, i, *Pinv, info, status, *Rp, *Ri, *Cp, *Ci, ok ;
+ size_t nzaat, slen ;
+ double mem = 0 ;
+
+#ifndef NDEBUG
+ AMD_debug_init ("amd") ;
+#endif
+
+ /* clear the Info array, if it exists */
+ info = Info != (double *) NULL ;
+ if (info)
+ {
+ for (i = 0 ; i < AMD_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ Info [AMD_N] = n ;
+ Info [AMD_STATUS] = AMD_OK ;
+ }
+
+ /* make sure inputs exist and n is >= 0 */
+ if (Ai == (Int *) NULL || Ap == (Int *) NULL || P == (Int *) NULL || n < 0)
+ {
+ if (info) Info [AMD_STATUS] = AMD_INVALID ;
+ return (AMD_INVALID) ; /* arguments are invalid */
+ }
+
+ if (n == 0)
+ {
+ return (AMD_OK) ; /* n is 0 so there's nothing to do */
+ }
+
+ nz = Ap [n] ;
+ if (info)
+ {
+ Info [AMD_NZ] = nz ;
+ }
+ if (nz < 0)
+ {
+ if (info) Info [AMD_STATUS] = AMD_INVALID ;
+ return (AMD_INVALID) ;
+ }
+
+ /* check if n or nz will cause size_t overflow */
+ if (((size_t) n) >= SIZE_T_MAX / sizeof (Int)
+ || ((size_t) nz) >= SIZE_T_MAX / sizeof (Int))
+ {
+ if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ return (AMD_OUT_OF_MEMORY) ; /* problem too large */
+ }
+
+ /* check the input matrix: AMD_OK, AMD_INVALID, or AMD_OK_BUT_JUMBLED */
+ status = AMD_valid (n, n, Ap, Ai) ;
+
+ if (status == AMD_INVALID)
+ {
+ if (info) Info [AMD_STATUS] = AMD_INVALID ;
+ return (AMD_INVALID) ; /* matrix is invalid */
+ }
+
+ /* allocate two size-n integer workspaces */
+ Len = amd_malloc (n * sizeof (Int)) ;
+ Pinv = amd_malloc (n * sizeof (Int)) ;
+ mem += n ;
+ mem += n ;
+ if (!Len || !Pinv)
+ {
+ /* :: out of memory :: */
+ amd_free (Len) ;
+ amd_free (Pinv) ;
+ if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ return (AMD_OUT_OF_MEMORY) ;
+ }
+
+ if (status == AMD_OK_BUT_JUMBLED)
+ {
+ /* sort the input matrix and remove duplicate entries */
+ AMD_DEBUG1 (("Matrix is jumbled\n")) ;
+ Rp = amd_malloc ((n+1) * sizeof (Int)) ;
+ Ri = amd_malloc (MAX (nz,1) * sizeof (Int)) ;
+ mem += (n+1) ;
+ mem += MAX (nz,1) ;
+ if (!Rp || !Ri)
+ {
+ /* :: out of memory :: */
+ amd_free (Rp) ;
+ amd_free (Ri) ;
+ amd_free (Len) ;
+ amd_free (Pinv) ;
+ if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ return (AMD_OUT_OF_MEMORY) ;
+ }
+ /* use Len and Pinv as workspace to create R = A' */
+ AMD_preprocess (n, Ap, Ai, Rp, Ri, Len, Pinv) ;
+ Cp = Rp ;
+ Ci = Ri ;
+ }
+ else
+ {
+ /* order the input matrix as-is. No need to compute R = A' first */
+ Rp = NULL ;
+ Ri = NULL ;
+ Cp = (Int *) Ap ;
+ Ci = (Int *) Ai ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* determine the symmetry and count off-diagonal nonzeros in A+A' */
+ /* --------------------------------------------------------------------- */
+
+ nzaat = AMD_aat (n, Cp, Ci, Len, P, Info) ;
+ AMD_DEBUG1 (("nzaat: %g\n", (double) nzaat)) ;
+ ASSERT ((MAX (nz-n, 0) <= nzaat) && (nzaat <= 2 * (size_t) nz)) ;
+
+ /* --------------------------------------------------------------------- */
+ /* allocate workspace for matrix, elbow room, and 6 size-n vectors */
+ /* --------------------------------------------------------------------- */
+
+ S = NULL ;
+ slen = nzaat ; /* space for matrix */
+ ok = ((slen + nzaat/5) >= slen) ; /* check for size_t overflow */
+ slen += nzaat/5 ; /* add elbow room */
+ for (i = 0 ; ok && i < 7 ; i++)
+ {
+ ok = ((slen + n) > slen) ; /* check for size_t overflow */
+ slen += n ; /* size-n elbow room, 6 size-n work */
+ }
+ mem += slen ;
+ ok = ok && (slen < SIZE_T_MAX / sizeof (Int)) ; /* check for overflow */
+ ok = ok && (slen < Int_MAX) ; /* S[i] for Int i must be OK */
+ if (ok)
+ {
+ S = amd_malloc (slen * sizeof (Int)) ;
+ }
+ AMD_DEBUG1 (("slen %g\n", (double) slen)) ;
+ if (!S)
+ {
+ /* :: out of memory :: (or problem too large) */
+ amd_free (Rp) ;
+ amd_free (Ri) ;
+ amd_free (Len) ;
+ amd_free (Pinv) ;
+ if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ return (AMD_OUT_OF_MEMORY) ;
+ }
+ if (info)
+ {
+ /* memory usage, in bytes. */
+ Info [AMD_MEMORY] = mem * sizeof (Int) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* order the matrix */
+ /* --------------------------------------------------------------------- */
+
+ AMD_1 (n, Cp, Ci, P, Pinv, Len, slen, S, Control, Info) ;
+
+ /* --------------------------------------------------------------------- */
+ /* free the workspace */
+ /* --------------------------------------------------------------------- */
+
+ amd_free (Rp) ;
+ amd_free (Ri) ;
+ amd_free (Len) ;
+ amd_free (Pinv) ;
+ amd_free (S) ;
+ if (info) Info [AMD_STATUS] = status ;
+ return (status) ; /* successful ordering */
+}
diff --git a/AMD/Source/amd_post_tree.c b/AMD/Source/amd_post_tree.c
new file mode 100644
index 0000000..b4e063d
--- /dev/null
+++ b/AMD/Source/amd_post_tree.c
@@ -0,0 +1,121 @@
+/* ========================================================================= */
+/* === AMD_post_tree ======================================================= */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Post-ordering of a supernodal elimination tree. */
+
+#include "amd_internal.h"
+
+GLOBAL Int AMD_post_tree
+(
+ Int root, /* root of the tree */
+ Int k, /* start numbering at k */
+ Int Child [ ], /* input argument of size nn, undefined on
+ * output. Child [i] is the head of a link
+ * list of all nodes that are children of node
+ * i in the tree. */
+ const Int Sibling [ ], /* input argument of size nn, not modified.
+ * If f is a node in the link list of the
+ * children of node i, then Sibling [f] is the
+ * next child of node i.
+ */
+ Int Order [ ], /* output order, of size nn. Order [i] = k
+ * if node i is the kth node of the reordered
+ * tree. */
+ Int Stack [ ] /* workspace of size nn */
+#ifndef NDEBUG
+ , Int nn /* nodes are in the range 0..nn-1. */
+#endif
+)
+{
+ Int f, head, h, i ;
+
+#if 0
+ /* --------------------------------------------------------------------- */
+ /* recursive version (Stack [ ] is not used): */
+ /* --------------------------------------------------------------------- */
+
+ /* this is simple, but can caouse stack overflow if nn is large */
+ i = root ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ k = AMD_post_tree (f, k, Child, Sibling, Order, Stack, nn) ;
+ }
+ Order [i] = k++ ;
+ return (k) ;
+#endif
+
+ /* --------------------------------------------------------------------- */
+ /* non-recursive version, using an explicit stack */
+ /* --------------------------------------------------------------------- */
+
+ /* push root on the stack */
+ head = 0 ;
+ Stack [0] = root ;
+
+ while (head >= 0)
+ {
+ /* get head of stack */
+ ASSERT (head < nn) ;
+ i = Stack [head] ;
+ AMD_DEBUG1 (("head of stack "ID" \n", i)) ;
+ ASSERT (i >= 0 && i < nn) ;
+
+ if (Child [i] != EMPTY)
+ {
+ /* the children of i are not yet ordered */
+ /* push each child onto the stack in reverse order */
+ /* so that small ones at the head of the list get popped first */
+ /* and the biggest one at the end of the list gets popped last */
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ head++ ;
+ ASSERT (head < nn) ;
+ ASSERT (f >= 0 && f < nn) ;
+ }
+ h = head ;
+ ASSERT (head < nn) ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ ASSERT (h > 0) ;
+ Stack [h--] = f ;
+ AMD_DEBUG1 (("push "ID" on stack\n", f)) ;
+ ASSERT (f >= 0 && f < nn) ;
+ }
+ ASSERT (Stack [h] == i) ;
+
+ /* delete child list so that i gets ordered next time we see it */
+ Child [i] = EMPTY ;
+ }
+ else
+ {
+ /* the children of i (if there were any) are already ordered */
+ /* remove i from the stack and order it. Front i is kth front */
+ head-- ;
+ AMD_DEBUG1 (("pop "ID" order "ID"\n", i, k)) ;
+ Order [i] = k++ ;
+ ASSERT (k <= nn) ;
+ }
+
+#ifndef NDEBUG
+ AMD_DEBUG1 (("\nStack:")) ;
+ for (h = head ; h >= 0 ; h--)
+ {
+ Int j = Stack [h] ;
+ AMD_DEBUG1 ((" "ID, j)) ;
+ ASSERT (j >= 0 && j < nn) ;
+ }
+ AMD_DEBUG1 (("\n\n")) ;
+ ASSERT (head < nn) ;
+#endif
+
+ }
+ return (k) ;
+}
diff --git a/AMD/Source/amd_postorder.c b/AMD/Source/amd_postorder.c
new file mode 100644
index 0000000..4adcea3
--- /dev/null
+++ b/AMD/Source/amd_postorder.c
@@ -0,0 +1,207 @@
+/* ========================================================================= */
+/* === AMD_postorder ======================================================= */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Perform a postordering (via depth-first search) of an assembly tree. */
+
+#include "amd_internal.h"
+
+GLOBAL void AMD_postorder
+(
+ /* inputs, not modified on output: */
+ Int nn, /* nodes are in the range 0..nn-1 */
+ Int Parent [ ], /* Parent [j] is the parent of j, or EMPTY if root */
+ Int Nv [ ], /* Nv [j] > 0 number of pivots represented by node j,
+ * or zero if j is not a node. */
+ Int Fsize [ ], /* Fsize [j]: size of node j */
+
+ /* output, not defined on input: */
+ Int Order [ ], /* output post-order */
+
+ /* workspaces of size nn: */
+ Int Child [ ],
+ Int Sibling [ ],
+ Int Stack [ ]
+)
+{
+ Int i, j, k, parent, frsize, f, fprev, maxfrsize, bigfprev, bigf, fnext ;
+
+ for (j = 0 ; j < nn ; j++)
+ {
+ Child [j] = EMPTY ;
+ Sibling [j] = EMPTY ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* place the children in link lists - bigger elements tend to be last */
+ /* --------------------------------------------------------------------- */
+
+ for (j = nn-1 ; j >= 0 ; j--)
+ {
+ if (Nv [j] > 0)
+ {
+ /* this is an element */
+ parent = Parent [j] ;
+ if (parent != EMPTY)
+ {
+ /* place the element in link list of the children its parent */
+ /* bigger elements will tend to be at the end of the list */
+ Sibling [j] = Child [parent] ;
+ Child [parent] = j ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ {
+ Int nels, ff, nchild ;
+ AMD_DEBUG1 (("\n\n================================ AMD_postorder:\n"));
+ nels = 0 ;
+ for (j = 0 ; j < nn ; j++)
+ {
+ if (Nv [j] > 0)
+ {
+ AMD_DEBUG1 (( ""ID" : nels "ID" npiv "ID" size "ID
+ " parent "ID" maxfr "ID"\n", j, nels,
+ Nv [j], Fsize [j], Parent [j], Fsize [j])) ;
+ /* this is an element */
+ /* dump the link list of children */
+ nchild = 0 ;
+ AMD_DEBUG1 ((" Children: ")) ;
+ for (ff = Child [j] ; ff != EMPTY ; ff = Sibling [ff])
+ {
+ AMD_DEBUG1 ((ID" ", ff)) ;
+ ASSERT (Parent [ff] == j) ;
+ nchild++ ;
+ ASSERT (nchild < nn) ;
+ }
+ AMD_DEBUG1 (("\n")) ;
+ parent = Parent [j] ;
+ if (parent != EMPTY)
+ {
+ ASSERT (Nv [parent] > 0) ;
+ }
+ nels++ ;
+ }
+ }
+ }
+ AMD_DEBUG1 (("\n\nGo through the children of each node, and put\n"
+ "the biggest child last in each list:\n")) ;
+#endif
+
+ /* --------------------------------------------------------------------- */
+ /* place the largest child last in the list of children for each node */
+ /* --------------------------------------------------------------------- */
+
+ for (i = 0 ; i < nn ; i++)
+ {
+ if (Nv [i] > 0 && Child [i] != EMPTY)
+ {
+
+#ifndef NDEBUG
+ Int nchild ;
+ AMD_DEBUG1 (("Before partial sort, element "ID"\n", i)) ;
+ nchild = 0 ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ ASSERT (f >= 0 && f < nn) ;
+ AMD_DEBUG1 ((" f: "ID" size: "ID"\n", f, Fsize [f])) ;
+ nchild++ ;
+ ASSERT (nchild <= nn) ;
+ }
+#endif
+
+ /* find the biggest element in the child list */
+ fprev = EMPTY ;
+ maxfrsize = EMPTY ;
+ bigfprev = EMPTY ;
+ bigf = EMPTY ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ ASSERT (f >= 0 && f < nn) ;
+ frsize = Fsize [f] ;
+ if (frsize >= maxfrsize)
+ {
+ /* this is the biggest seen so far */
+ maxfrsize = frsize ;
+ bigfprev = fprev ;
+ bigf = f ;
+ }
+ fprev = f ;
+ }
+ ASSERT (bigf != EMPTY) ;
+
+ fnext = Sibling [bigf] ;
+
+ AMD_DEBUG1 (("bigf "ID" maxfrsize "ID" bigfprev "ID" fnext "ID
+ " fprev " ID"\n", bigf, maxfrsize, bigfprev, fnext, fprev)) ;
+
+ if (fnext != EMPTY)
+ {
+ /* if fnext is EMPTY then bigf is already at the end of list */
+
+ if (bigfprev == EMPTY)
+ {
+ /* delete bigf from the element of the list */
+ Child [i] = fnext ;
+ }
+ else
+ {
+ /* delete bigf from the middle of the list */
+ Sibling [bigfprev] = fnext ;
+ }
+
+ /* put bigf at the end of the list */
+ Sibling [bigf] = EMPTY ;
+ ASSERT (Child [i] != EMPTY) ;
+ ASSERT (fprev != bigf) ;
+ ASSERT (fprev != EMPTY) ;
+ Sibling [fprev] = bigf ;
+ }
+
+#ifndef NDEBUG
+ AMD_DEBUG1 (("After partial sort, element "ID"\n", i)) ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ ASSERT (f >= 0 && f < nn) ;
+ AMD_DEBUG1 ((" "ID" "ID"\n", f, Fsize [f])) ;
+ ASSERT (Nv [f] > 0) ;
+ nchild-- ;
+ }
+ ASSERT (nchild == 0) ;
+#endif
+
+ }
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* postorder the assembly tree */
+ /* --------------------------------------------------------------------- */
+
+ for (i = 0 ; i < nn ; i++)
+ {
+ Order [i] = EMPTY ;
+ }
+
+ k = 0 ;
+
+ for (i = 0 ; i < nn ; i++)
+ {
+ if (Parent [i] == EMPTY && Nv [i] > 0)
+ {
+ AMD_DEBUG1 (("Root of assembly tree "ID"\n", i)) ;
+ k = AMD_post_tree (i, k, Child, Sibling, Order, Stack
+#ifndef NDEBUG
+ , nn
+#endif
+ ) ;
+ }
+ }
+}
diff --git a/AMD/Source/amd_preprocess.c b/AMD/Source/amd_preprocess.c
new file mode 100644
index 0000000..86ea07f
--- /dev/null
+++ b/AMD/Source/amd_preprocess.c
@@ -0,0 +1,119 @@
+/* ========================================================================= */
+/* === AMD_preprocess ====================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Sorts, removes duplicate entries, and transposes from the nonzero pattern of
+ * a column-form matrix A, to obtain the matrix R. The input matrix can have
+ * duplicate entries and/or unsorted columns (AMD_valid (n,Ap,Ai) must not be
+ * AMD_INVALID).
+ *
+ * This input condition is NOT checked. This routine is not user-callable.
+ */
+
+#include "amd_internal.h"
+
+/* ========================================================================= */
+/* === AMD_preprocess ====================================================== */
+/* ========================================================================= */
+
+/* AMD_preprocess does not check its input for errors or allocate workspace.
+ * On input, the condition (AMD_valid (n,n,Ap,Ai) != AMD_INVALID) must hold.
+ */
+
+GLOBAL void AMD_preprocess
+(
+ Int n, /* input matrix: A is n-by-n */
+ const Int Ap [ ], /* size n+1 */
+ const Int Ai [ ], /* size nz = Ap [n] */
+
+ /* output matrix R: */
+ Int Rp [ ], /* size n+1 */
+ Int Ri [ ], /* size nz (or less, if duplicates present) */
+
+ Int W [ ], /* workspace of size n */
+ Int Flag [ ] /* workspace of size n */
+)
+{
+
+ /* --------------------------------------------------------------------- */
+ /* local variables */
+ /* --------------------------------------------------------------------- */
+
+ Int i, j, p, p2 ;
+
+ ASSERT (AMD_valid (n, n, Ap, Ai) != AMD_INVALID) ;
+
+ /* --------------------------------------------------------------------- */
+ /* count the entries in each row of A (excluding duplicates) */
+ /* --------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = 0 ; /* # of nonzeros in row i (excl duplicates) */
+ Flag [i] = EMPTY ; /* Flag [i] = j if i appears in column j */
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ p2 = Ap [j+1] ;
+ for (p = Ap [j] ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ if (Flag [i] != j)
+ {
+ /* row index i has not yet appeared in column j */
+ W [i]++ ; /* one more entry in row i */
+ Flag [i] = j ; /* flag row index i as appearing in col j*/
+ }
+ }
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* compute the row pointers for R */
+ /* --------------------------------------------------------------------- */
+
+ Rp [0] = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Rp [i+1] = Rp [i] + W [i] ;
+ }
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = Rp [i] ;
+ Flag [i] = EMPTY ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* construct the row form matrix R */
+ /* --------------------------------------------------------------------- */
+
+ /* R = row form of pattern of A */
+ for (j = 0 ; j < n ; j++)
+ {
+ p2 = Ap [j+1] ;
+ for (p = Ap [j] ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ if (Flag [i] != j)
+ {
+ /* row index i has not yet appeared in column j */
+ Ri [W [i]++] = j ; /* put col j in row i */
+ Flag [i] = j ; /* flag row index i as appearing in col j*/
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ ASSERT (AMD_valid (n, n, Rp, Ri) == AMD_OK) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (W [j] == Rp [j+1]) ;
+ }
+#endif
+}
diff --git a/AMD/Source/amd_valid.c b/AMD/Source/amd_valid.c
new file mode 100644
index 0000000..4d05925
--- /dev/null
+++ b/AMD/Source/amd_valid.c
@@ -0,0 +1,93 @@
+/* ========================================================================= */
+/* === AMD_valid =========================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD, Copyright (c) Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/amd */
+/* ------------------------------------------------------------------------- */
+
+/* Check if a column-form matrix is valid or not. The matrix A is
+ * n_row-by-n_col. The row indices of entries in column j are in
+ * Ai [Ap [j] ... Ap [j+1]-1]. Required conditions are:
+ *
+ * n_row >= 0
+ * n_col >= 0
+ * nz = Ap [n_col] >= 0 number of entries in the matrix
+ * Ap [0] == 0
+ * Ap [j] <= Ap [j+1] for all j in the range 0 to n_col.
+ * Ai [0 ... nz-1] must be in the range 0 to n_row-1.
+ *
+ * If any of the above conditions hold, AMD_INVALID is returned. If the
+ * following condition holds, AMD_OK_BUT_JUMBLED is returned (a warning,
+ * not an error):
+ *
+ * row indices in Ai [Ap [j] ... Ap [j+1]-1] are not sorted in ascending
+ * order, and/or duplicate entries exist.
+ *
+ * Otherwise, AMD_OK is returned.
+ *
+ * In v1.2 and earlier, this function returned TRUE if the matrix was valid
+ * (now returns AMD_OK), or FALSE otherwise (now returns AMD_INVALID or
+ * AMD_OK_BUT_JUMBLED).
+ */
+
+#include "amd_internal.h"
+
+GLOBAL Int AMD_valid
+(
+ /* inputs, not modified on output: */
+ Int n_row, /* A is n_row-by-n_col */
+ Int n_col,
+ const Int Ap [ ], /* column pointers of A, of size n_col+1 */
+ const Int Ai [ ] /* row indices of A, of size nz = Ap [n_col] */
+)
+{
+ Int nz, j, p1, p2, ilast, i, p, result = AMD_OK ;
+
+ if (n_row < 0 || n_col < 0 || Ap == NULL || Ai == NULL)
+ {
+ return (AMD_INVALID) ;
+ }
+ nz = Ap [n_col] ;
+ if (Ap [0] != 0 || nz < 0)
+ {
+ /* column pointers must start at Ap [0] = 0, and Ap [n] must be >= 0 */
+ AMD_DEBUG0 (("column 0 pointer bad or nz < 0\n")) ;
+ return (AMD_INVALID) ;
+ }
+ for (j = 0 ; j < n_col ; j++)
+ {
+ p1 = Ap [j] ;
+ p2 = Ap [j+1] ;
+ AMD_DEBUG2 (("\nColumn: "ID" p1: "ID" p2: "ID"\n", j, p1, p2)) ;
+ if (p1 > p2)
+ {
+ /* column pointers must be ascending */
+ AMD_DEBUG0 (("column "ID" pointer bad\n", j)) ;
+ return (AMD_INVALID) ;
+ }
+ ilast = EMPTY ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ AMD_DEBUG3 (("row: "ID"\n", i)) ;
+ if (i < 0 || i >= n_row)
+ {
+ /* row index out of range */
+ AMD_DEBUG0 (("index out of range, col "ID" row "ID"\n", j, i));
+ return (AMD_INVALID) ;
+ }
+ if (i <= ilast)
+ {
+ /* row index unsorted, or duplicate entry present */
+ AMD_DEBUG1 (("index unsorted/dupl col "ID" row "ID"\n", j, i));
+ result = AMD_OK_BUT_JUMBLED ;
+ }
+ ilast = i ;
+ }
+ }
+ return (result) ;
+}
diff --git a/AMD/Source/amdbar.f b/AMD/Source/amdbar.f
new file mode 100644
index 0000000..1384392
--- /dev/null
+++ b/AMD/Source/amdbar.f
@@ -0,0 +1,1206 @@
+C-----------------------------------------------------------------------
+C AMDBAR: approximate minimum degree, without aggressive absorption
+C-----------------------------------------------------------------------
+
+ SUBROUTINE AMDBAR
+ $ (N, PE, IW, LEN, IWLEN, PFREE, NV, NEXT,
+ $ LAST, HEAD, ELEN, DEGREE, NCMPA, W)
+
+ INTEGER N, IWLEN, PFREE, NCMPA, IW (IWLEN), PE (N),
+ $ DEGREE (N), NV (N), NEXT (N), LAST (N), HEAD (N),
+ $ ELEN (N), W (N), LEN (N)
+
+C Given a representation of the nonzero pattern of a symmetric matrix,
+C A, (excluding the diagonal) perform an approximate minimum
+C (UMFPACK/MA38-style) degree ordering to compute a pivot order
+C such that the introduction of nonzeros (fill-in) in the Cholesky
+C factors A = LL^T are kept low. At each step, the pivot
+C selected is the one with the minimum UMFPACK/MA38-style
+C upper-bound on the external degree.
+C
+C This routine does not do aggresive absorption (as done by AMD).
+
+C **********************************************************************
+C ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ******
+C **********************************************************************
+
+C References:
+C
+C [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern
+C multifrontal method for sparse LU factorization", SIAM J.
+C Matrix Analysis and Applications, vol. 18, no. 1, pp.
+C 140-158. Discusses UMFPACK / MA38, which first introduced
+C the approximate minimum degree used by this routine.
+C
+C [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An
+C approximate degree ordering algorithm," SIAM J. Matrix
+C Analysis and Applications, vol. 17, no. 4, pp. 886-905,
+C 1996. Discusses AMD, AMDBAR, and MC47B.
+C
+C [3] Alan George and Joseph Liu, "The evolution of the minimum
+C degree ordering algorithm," SIAM Review, vol. 31, no. 1,
+C pp. 1-19, 1989. We list below the features mentioned in
+C that paper that this code includes:
+C
+C mass elimination:
+C Yes. MA27 relied on supervariable detection for mass
+C elimination.
+C indistinguishable nodes:
+C Yes (we call these "supervariables"). This was also in
+C the MA27 code - although we modified the method of
+C detecting them (the previous hash was the true degree,
+C which we no longer keep track of). A supervariable is
+C a set of rows with identical nonzero pattern. All
+C variables in a supervariable are eliminated together.
+C Each supervariable has as its numerical name that of
+C one of its variables (its principal variable).
+C quotient graph representation:
+C Yes. We use the term "element" for the cliques formed
+C during elimination. This was also in the MA27 code.
+C The algorithm can operate in place, but it will work
+C more efficiently if given some "elbow room."
+C element absorption:
+C Yes. This was also in the MA27 code.
+C external degree:
+C Yes. The MA27 code was based on the true degree.
+C incomplete degree update and multiple elimination:
+C No. This was not in MA27, either. Our method of
+C degree update within MC47B/BD is element-based, not
+C variable-based. It is thus not well-suited for use
+C with incomplete degree update or multiple elimination.
+
+C-----------------------------------------------------------------------
+C Authors, and Copyright (C) 1995 by:
+C Timothy A. Davis, Patrick Amestoy, Iain S. Duff, & John K. Reid.
+C
+C Acknowledgements:
+C This work (and the UMFPACK package) was supported by the
+C National Science Foundation (ASC-9111263 and DMS-9223088).
+C The UMFPACK/MA38 approximate degree update algorithm, the
+C unsymmetric analog which forms the basis of MC47B/BD, was
+C developed while Tim Davis was supported by CERFACS (Toulouse,
+C France) in a post-doctoral position.
+C
+C Date: September, 1995
+C-----------------------------------------------------------------------
+
+C-----------------------------------------------------------------------
+C INPUT ARGUMENTS (unaltered):
+C-----------------------------------------------------------------------
+
+C n: The matrix order.
+C
+C Restriction: 1 .le. n .lt. (iovflo/2)-2, where iovflo is
+C the largest positive integer that your computer can represent.
+
+C iwlen: The length of iw (1..iwlen). On input, the matrix is
+C stored in iw (1..pfree-1). However, iw (1..iwlen) should be
+C slightly larger than what is required to hold the matrix, at
+C least iwlen .ge. pfree + n is recommended. Otherwise,
+C excessive compressions will take place.
+C *** We do not recommend running this algorithm with ***
+C *** iwlen .lt. pfree + n. ***
+C *** Better performance will be obtained if ***
+C *** iwlen .ge. pfree + n ***
+C *** or better yet ***
+C *** iwlen .gt. 1.2 * pfree ***
+C *** (where pfree is its value on input). ***
+C The algorithm will not run at all if iwlen .lt. pfree-1.
+C
+C Restriction: iwlen .ge. pfree-1
+
+C-----------------------------------------------------------------------
+C INPUT/OUPUT ARGUMENTS:
+C-----------------------------------------------------------------------
+
+C pe: On input, pe (i) is the index in iw of the start of row i, or
+C zero if row i has no off-diagonal non-zeros.
+C
+C During execution, it is used for both supervariables and
+C elements:
+C
+C * Principal supervariable i: index into iw of the
+C description of supervariable i. A supervariable
+C represents one or more rows of the matrix
+C with identical nonzero pattern.
+C * Non-principal supervariable i: if i has been absorbed
+C into another supervariable j, then pe (i) = -j.
+C That is, j has the same pattern as i.
+C Note that j might later be absorbed into another
+C supervariable j2, in which case pe (i) is still -j,
+C and pe (j) = -j2.
+C * Unabsorbed element e: the index into iw of the description
+C of element e, if e has not yet been absorbed by a
+C subsequent element. Element e is created when
+C the supervariable of the same name is selected as
+C the pivot.
+C * Absorbed element e: if element e is absorbed into element
+C e2, then pe (e) = -e2. This occurs when the pattern of
+C e (that is, Le) is found to be a subset of the pattern
+C of e2 (that is, Le2). If element e is "null" (it has
+C no nonzeros outside its pivot block), then pe (e) = 0.
+C
+C On output, pe holds the assembly tree/forest, which implicitly
+C represents a pivot order with identical fill-in as the actual
+C order (via a depth-first search of the tree).
+C
+C On output:
+C If nv (i) .gt. 0, then i represents a node in the assembly tree,
+C and the parent of i is -pe (i), or zero if i is a root.
+C If nv (i) = 0, then (i,-pe (i)) represents an edge in a
+C subtree, the root of which is a node in the assembly tree.
+
+C pfree: On input the tail end of the array, iw (pfree..iwlen),
+C is empty, and the matrix is stored in iw (1..pfree-1).
+C During execution, additional data is placed in iw, and pfree
+C is modified so that iw (pfree..iwlen) is always the unused part
+C of iw. On output, pfree is set equal to the size of iw that
+C would have been needed for no compressions to occur. If
+C ncmpa is zero, then pfree (on output) is less than or equal to
+C iwlen, and the space iw (pfree+1 ... iwlen) was not used.
+C Otherwise, pfree (on output) is greater than iwlen, and all the
+C memory in iw was used.
+
+C-----------------------------------------------------------------------
+C INPUT/MODIFIED (undefined on output):
+C-----------------------------------------------------------------------
+
+C len: On input, len (i) holds the number of entries in row i of the
+C matrix, excluding the diagonal. The contents of len (1..n)
+C are undefined on output.
+
+C iw: On input, iw (1..pfree-1) holds the description of each row i
+C in the matrix. The matrix must be symmetric, and both upper
+C and lower triangular parts must be present. The diagonal must
+C not be present. Row i is held as follows:
+C
+C len (i): the length of the row i data structure
+C iw (pe (i) ... pe (i) + len (i) - 1):
+C the list of column indices for nonzeros
+C in row i (simple supervariables), excluding
+C the diagonal. All supervariables start with
+C one row/column each (supervariable i is just
+C row i).
+C if len (i) is zero on input, then pe (i) is ignored
+C on input.
+C
+C Note that the rows need not be in any particular order,
+C and there may be empty space between the rows.
+C
+C During execution, the supervariable i experiences fill-in.
+C This is represented by placing in i a list of the elements
+C that cause fill-in in supervariable i:
+C
+C len (i): the length of supervariable i
+C iw (pe (i) ... pe (i) + elen (i) - 1):
+C the list of elements that contain i. This list
+C is kept short by removing absorbed elements.
+C iw (pe (i) + elen (i) ... pe (i) + len (i) - 1):
+C the list of supervariables in i. This list
+C is kept short by removing nonprincipal
+C variables, and any entry j that is also
+C contained in at least one of the elements
+C (j in Le) in the list for i (e in row i).
+C
+C When supervariable i is selected as pivot, we create an
+C element e of the same name (e=i):
+C
+C len (e): the length of element e
+C iw (pe (e) ... pe (e) + len (e) - 1):
+C the list of supervariables in element e.
+C
+C An element represents the fill-in that occurs when supervariable
+C i is selected as pivot (which represents the selection of row i
+C and all non-principal variables whose principal variable is i).
+C We use the term Le to denote the set of all supervariables
+C in element e. Absorbed supervariables and elements are pruned
+C from these lists when computationally convenient.
+C
+C CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION.
+C The contents of iw are undefined on output.
+
+C-----------------------------------------------------------------------
+C OUTPUT (need not be set on input):
+C-----------------------------------------------------------------------
+
+C nv: During execution, abs (nv (i)) is equal to the number of rows
+C that are represented by the principal supervariable i. If i is
+C a nonprincipal variable, then nv (i) = 0. Initially,
+C nv (i) = 1 for all i. nv (i) .lt. 0 signifies that i is a
+C principal variable in the pattern Lme of the current pivot
+C element me. On output, nv (e) holds the true degree of element
+C e at the time it was created (including the diagonal part).
+
+C ncmpa: The number of times iw was compressed. If this is
+C excessive, then the execution took longer than what could have
+C been. To reduce ncmpa, try increasing iwlen to be 10% or 20%
+C larger than the value of pfree on input (or at least
+C iwlen .ge. pfree + n). The fastest performance will be
+C obtained when ncmpa is returned as zero. If iwlen is set to
+C the value returned by pfree on *output*, then no compressions
+C will occur.
+
+C elen: See the description of iw above. At the start of execution,
+C elen (i) is set to zero. During execution, elen (i) is the
+C number of elements in the list for supervariable i. When e
+C becomes an element, elen (e) = -nel is set, where nel is the
+C current step of factorization. elen (i) = 0 is done when i
+C becomes nonprincipal.
+C
+C For variables, elen (i) .ge. 0 holds until just before the
+C permutation vectors are computed. For elements,
+C elen (e) .lt. 0 holds.
+C
+C On output elen (1..n) holds the inverse permutation (the same
+C as the 'INVP' argument in Sparspak). That is, if k = elen (i),
+C then row i is the kth pivot row. Row i of A appears as the
+C (elen(i))-th row in the permuted matrix, PAP^T.
+
+C last: In a degree list, last (i) is the supervariable preceding i,
+C or zero if i is the head of the list. In a hash bucket,
+C last (i) is the hash key for i. last (head (hash)) is also
+C used as the head of a hash bucket if head (hash) contains a
+C degree list (see head, below).
+C
+C On output, last (1..n) holds the permutation (the same as the
+C 'PERM' argument in Sparspak). That is, if i = last (k), then
+C row i is the kth pivot row. Row last (k) of A is the k-th row
+C in the permuted matrix, PAP^T.
+
+C-----------------------------------------------------------------------
+C LOCAL (not input or output - used only during execution):
+C-----------------------------------------------------------------------
+
+C degree: If i is a supervariable, then degree (i) holds the
+C current approximation of the external degree of row i (an upper
+C bound). The external degree is the number of nonzeros in row i,
+C minus abs (nv (i)) (the diagonal part). The bound is equal to
+C the external degree if elen (i) is less than or equal to two.
+C
+C We also use the term "external degree" for elements e to refer
+C to |Le \ Lme|. If e is an element, then degree (e) holds |Le|,
+C which is the degree of the off-diagonal part of the element e
+C (not including the diagonal part).
+
+C head: head is used for degree lists. head (deg) is the first
+C supervariable in a degree list (all supervariables i in a
+C degree list deg have the same approximate degree, namely,
+C deg = degree (i)). If the list deg is empty then
+C head (deg) = 0.
+C
+C During supervariable detection head (hash) also serves as a
+C pointer to a hash bucket.
+C If head (hash) .gt. 0, there is a degree list of degree hash.
+C The hash bucket head pointer is last (head (hash)).
+C If head (hash) = 0, then the degree list and hash bucket are
+C both empty.
+C If head (hash) .lt. 0, then the degree list is empty, and
+C -head (hash) is the head of the hash bucket.
+C After supervariable detection is complete, all hash buckets
+C are empty, and the (last (head (hash)) = 0) condition is
+C restored for the non-empty degree lists.
+
+C next: next (i) is the supervariable following i in a link list, or
+C zero if i is the last in the list. Used for two kinds of
+C lists: degree lists and hash buckets (a supervariable can be
+C in only one kind of list at a time).
+
+C w: The flag array w determines the status of elements and
+C variables, and the external degree of elements.
+C
+C for elements:
+C if w (e) = 0, then the element e is absorbed
+C if w (e) .ge. wflg, then w (e) - wflg is the size of
+C the set |Le \ Lme|, in terms of nonzeros (the
+C sum of abs (nv (i)) for each principal variable i that
+C is both in the pattern of element e and NOT in the
+C pattern of the current pivot element, me).
+C if wflg .gt. w (e) .gt. 0, then e is not absorbed and has
+C not yet been seen in the scan of the element lists in
+C the computation of |Le\Lme| in loop 150 below.
+C
+C for variables:
+C during supervariable detection, if w (j) .ne. wflg then j is
+C not in the pattern of variable i
+C
+C The w array is initialized by setting w (i) = 1 for all i,
+C and by setting wflg = 2. It is reinitialized if wflg becomes
+C too large (to ensure that wflg+n does not cause integer
+C overflow).
+
+C-----------------------------------------------------------------------
+C LOCAL INTEGERS:
+C-----------------------------------------------------------------------
+
+ INTEGER DEG, DEGME, DMAX, E, ELENME, ELN, HASH, HMOD, I,
+ $ ILAST, INEXT, J, JLAST, JNEXT, K, KNT1, KNT2, KNT3,
+ $ LENJ, LN, MAXMEM, ME, MEM, MINDEG, NEL, NEWMEM,
+ $ NLEFT, NVI, NVJ, NVPIV, SLENME, WE, WFLG, WNVI, X
+
+C deg: the degree of a variable or element
+C degme: size, |Lme|, of the current element, me (= degree (me))
+C dext: external degree, |Le \ Lme|, of some element e
+C dmax: largest |Le| seen so far
+C e: an element
+C elenme: the length, elen (me), of element list of pivotal var.
+C eln: the length, elen (...), of an element list
+C hash: the computed value of the hash function
+C hmod: the hash function is computed modulo hmod = max (1,n-1)
+C i: a supervariable
+C ilast: the entry in a link list preceding i
+C inext: the entry in a link list following i
+C j: a supervariable
+C jlast: the entry in a link list preceding j
+C jnext: the entry in a link list, or path, following j
+C k: the pivot order of an element or variable
+C knt1: loop counter used during element construction
+C knt2: loop counter used during element construction
+C knt3: loop counter used during compression
+C lenj: len (j)
+C ln: length of a supervariable list
+C maxmem: amount of memory needed for no compressions
+C me: current supervariable being eliminated, and the
+C current element created by eliminating that
+C supervariable
+C mem: memory in use assuming no compressions have occurred
+C mindeg: current minimum degree
+C nel: number of pivots selected so far
+C newmem: amount of new memory needed for current pivot element
+C nleft: n - nel, the number of nonpivotal rows/columns remaining
+C nvi: the number of variables in a supervariable i (= nv (i))
+C nvj: the number of variables in a supervariable j (= nv (j))
+C nvpiv: number of pivots in current element
+C slenme: number of variables in variable list of pivotal variable
+C we: w (e)
+C wflg: used for flagging the w array. See description of iw.
+C wnvi: wflg - nv (i)
+C x: either a supervariable or an element
+
+C-----------------------------------------------------------------------
+C LOCAL POINTERS:
+C-----------------------------------------------------------------------
+
+ INTEGER P, P1, P2, P3, PDST, PEND, PJ, PME, PME1, PME2, PN, PSRC
+
+C Any parameter (pe (...) or pfree) or local variable
+C starting with "p" (for Pointer) is an index into iw,
+C and all indices into iw use variables starting with
+C "p." The only exception to this rule is the iwlen
+C input argument.
+
+C p: pointer into lots of things
+C p1: pe (i) for some variable i (start of element list)
+C p2: pe (i) + elen (i) - 1 for some var. i (end of el. list)
+C p3: index of first supervariable in clean list
+C pdst: destination pointer, for compression
+C pend: end of memory to compress
+C pj: pointer into an element or variable
+C pme: pointer into the current element (pme1...pme2)
+C pme1: the current element, me, is stored in iw (pme1...pme2)
+C pme2: the end of the current element
+C pn: pointer into a "clean" variable, also used to compress
+C psrc: source pointer, for compression
+
+C-----------------------------------------------------------------------
+C FUNCTIONS CALLED:
+C-----------------------------------------------------------------------
+
+ INTRINSIC MAX, MIN, MOD
+
+C=======================================================================
+C INITIALIZATIONS
+C=======================================================================
+
+ WFLG = 2
+ MINDEG = 1
+ NCMPA = 0
+ NEL = 0
+ HMOD = MAX (1, N-1)
+ DMAX = 0
+ MEM = PFREE - 1
+ MAXMEM = MEM
+ ME = 0
+
+ DO 10 I = 1, N
+ LAST (I) = 0
+ HEAD (I) = 0
+ NV (I) = 1
+ W (I) = 1
+ ELEN (I) = 0
+ DEGREE (I) = LEN (I)
+10 CONTINUE
+
+C ----------------------------------------------------------------
+C initialize degree lists and eliminate rows with no off-diag. nz.
+C ----------------------------------------------------------------
+
+ DO 20 I = 1, N
+
+ DEG = DEGREE (I)
+
+ IF (DEG .GT. 0) THEN
+
+C ----------------------------------------------------------
+C place i in the degree list corresponding to its degree
+C ----------------------------------------------------------
+
+ INEXT = HEAD (DEG)
+ IF (INEXT .NE. 0) LAST (INEXT) = I
+ NEXT (I) = INEXT
+ HEAD (DEG) = I
+
+ ELSE
+
+C ----------------------------------------------------------
+C we have a variable that can be eliminated at once because
+C there is no off-diagonal non-zero in its row.
+C ----------------------------------------------------------
+
+ NEL = NEL + 1
+ ELEN (I) = -NEL
+ PE (I) = 0
+ W (I) = 0
+
+ ENDIF
+
+20 CONTINUE
+
+C=======================================================================
+C WHILE (selecting pivots) DO
+C=======================================================================
+
+30 CONTINUE
+ IF (NEL .LT. N) THEN
+
+C=======================================================================
+C GET PIVOT OF MINIMUM DEGREE
+C=======================================================================
+
+C -------------------------------------------------------------
+C find next supervariable for elimination
+C -------------------------------------------------------------
+
+ DO 40 DEG = MINDEG, N
+ ME = HEAD (DEG)
+ IF (ME .GT. 0) GOTO 50
+40 CONTINUE
+50 CONTINUE
+ MINDEG = DEG
+
+C -------------------------------------------------------------
+C remove chosen variable from link list
+C -------------------------------------------------------------
+
+ INEXT = NEXT (ME)
+ IF (INEXT .NE. 0) LAST (INEXT) = 0
+ HEAD (DEG) = INEXT
+
+C -------------------------------------------------------------
+C me represents the elimination of pivots nel+1 to nel+nv(me).
+C place me itself as the first in this set. It will be moved
+C to the nel+nv(me) position when the permutation vectors are
+C computed.
+C -------------------------------------------------------------
+
+ ELENME = ELEN (ME)
+ ELEN (ME) = - (NEL + 1)
+ NVPIV = NV (ME)
+ NEL = NEL + NVPIV
+
+C=======================================================================
+C CONSTRUCT NEW ELEMENT
+C=======================================================================
+
+C -------------------------------------------------------------
+C At this point, me is the pivotal supervariable. It will be
+C converted into the current element. Scan list of the
+C pivotal supervariable, me, setting tree pointers and
+C constructing new list of supervariables for the new element,
+C me. p is a pointer to the current position in the old list.
+C -------------------------------------------------------------
+
+C flag the variable "me" as being in Lme by negating nv (me)
+ NV (ME) = -NVPIV
+ DEGME = 0
+
+ IF (ELENME .EQ. 0) THEN
+
+C ----------------------------------------------------------
+C construct the new element in place
+C ----------------------------------------------------------
+
+ PME1 = PE (ME)
+ PME2 = PME1 - 1
+
+ DO 60 P = PME1, PME1 + LEN (ME) - 1
+ I = IW (P)
+ NVI = NV (I)
+ IF (NVI .GT. 0) THEN
+
+C ----------------------------------------------------
+C i is a principal variable not yet placed in Lme.
+C store i in new list
+C ----------------------------------------------------
+
+ DEGME = DEGME + NVI
+C flag i as being in Lme by negating nv (i)
+ NV (I) = -NVI
+ PME2 = PME2 + 1
+ IW (PME2) = I
+
+C ----------------------------------------------------
+C remove variable i from degree list.
+C ----------------------------------------------------
+
+ ILAST = LAST (I)
+ INEXT = NEXT (I)
+ IF (INEXT .NE. 0) LAST (INEXT) = ILAST
+ IF (ILAST .NE. 0) THEN
+ NEXT (ILAST) = INEXT
+ ELSE
+C i is at the head of the degree list
+ HEAD (DEGREE (I)) = INEXT
+ ENDIF
+
+ ENDIF
+60 CONTINUE
+C this element takes no new memory in iw:
+ NEWMEM = 0
+
+ ELSE
+
+C ----------------------------------------------------------
+C construct the new element in empty space, iw (pfree ...)
+C ----------------------------------------------------------
+
+ P = PE (ME)
+ PME1 = PFREE
+ SLENME = LEN (ME) - ELENME
+
+ DO 120 KNT1 = 1, ELENME + 1
+
+ IF (KNT1 .GT. ELENME) THEN
+C search the supervariables in me.
+ E = ME
+ PJ = P
+ LN = SLENME
+ ELSE
+C search the elements in me.
+ E = IW (P)
+ P = P + 1
+ PJ = PE (E)
+ LN = LEN (E)
+ ENDIF
+
+C -------------------------------------------------------
+C search for different supervariables and add them to the
+C new list, compressing when necessary. this loop is
+C executed once for each element in the list and once for
+C all the supervariables in the list.
+C -------------------------------------------------------
+
+ DO 110 KNT2 = 1, LN
+ I = IW (PJ)
+ PJ = PJ + 1
+ NVI = NV (I)
+ IF (NVI .GT. 0) THEN
+
+C -------------------------------------------------
+C compress iw, if necessary
+C -------------------------------------------------
+
+ IF (PFREE .GT. IWLEN) THEN
+C prepare for compressing iw by adjusting
+C pointers and lengths so that the lists being
+C searched in the inner and outer loops contain
+C only the remaining entries.
+
+ PE (ME) = P
+ LEN (ME) = LEN (ME) - KNT1
+ IF (LEN (ME) .EQ. 0) THEN
+C nothing left of supervariable me
+ PE (ME) = 0
+ ENDIF
+ PE (E) = PJ
+ LEN (E) = LN - KNT2
+ IF (LEN (E) .EQ. 0) THEN
+C nothing left of element e
+ PE (E) = 0
+ ENDIF
+
+ NCMPA = NCMPA + 1
+C store first item in pe
+C set first entry to -item
+ DO 70 J = 1, N
+ PN = PE (J)
+ IF (PN .GT. 0) THEN
+ PE (J) = IW (PN)
+ IW (PN) = -J
+ ENDIF
+70 CONTINUE
+
+C psrc/pdst point to source/destination
+ PDST = 1
+ PSRC = 1
+ PEND = PME1 - 1
+
+C while loop:
+80 CONTINUE
+ IF (PSRC .LE. PEND) THEN
+C search for next negative entry
+ J = -IW (PSRC)
+ PSRC = PSRC + 1
+ IF (J .GT. 0) THEN
+ IW (PDST) = PE (J)
+ PE (J) = PDST
+ PDST = PDST + 1
+C copy from source to destination
+ LENJ = LEN (J)
+ DO 90 KNT3 = 0, LENJ - 2
+ IW (PDST + KNT3) = IW (PSRC + KNT3)
+90 CONTINUE
+ PDST = PDST + LENJ - 1
+ PSRC = PSRC + LENJ - 1
+ ENDIF
+ GOTO 80
+ ENDIF
+
+C move the new partially-constructed element
+ P1 = PDST
+ DO 100 PSRC = PME1, PFREE - 1
+ IW (PDST) = IW (PSRC)
+ PDST = PDST + 1
+100 CONTINUE
+ PME1 = P1
+ PFREE = PDST
+ PJ = PE (E)
+ P = PE (ME)
+ ENDIF
+
+C -------------------------------------------------
+C i is a principal variable not yet placed in Lme
+C store i in new list
+C -------------------------------------------------
+
+ DEGME = DEGME + NVI
+C flag i as being in Lme by negating nv (i)
+ NV (I) = -NVI
+ IW (PFREE) = I
+ PFREE = PFREE + 1
+
+C -------------------------------------------------
+C remove variable i from degree link list
+C -------------------------------------------------
+
+ ILAST = LAST (I)
+ INEXT = NEXT (I)
+ IF (INEXT .NE. 0) LAST (INEXT) = ILAST
+ IF (ILAST .NE. 0) THEN
+ NEXT (ILAST) = INEXT
+ ELSE
+C i is at the head of the degree list
+ HEAD (DEGREE (I)) = INEXT
+ ENDIF
+
+ ENDIF
+110 CONTINUE
+
+ IF (E .NE. ME) THEN
+C set tree pointer and flag to indicate element e is
+C absorbed into new element me (the parent of e is me)
+ PE (E) = -ME
+ W (E) = 0
+ ENDIF
+120 CONTINUE
+
+ PME2 = PFREE - 1
+C this element takes newmem new memory in iw (possibly zero)
+ NEWMEM = PFREE - PME1
+ MEM = MEM + NEWMEM
+ MAXMEM = MAX (MAXMEM, MEM)
+ ENDIF
+
+C -------------------------------------------------------------
+C me has now been converted into an element in iw (pme1..pme2)
+C -------------------------------------------------------------
+
+C degme holds the external degree of new element
+ DEGREE (ME) = DEGME
+ PE (ME) = PME1
+ LEN (ME) = PME2 - PME1 + 1
+
+C -------------------------------------------------------------
+C make sure that wflg is not too large. With the current
+C value of wflg, wflg+n must not cause integer overflow
+C -------------------------------------------------------------
+
+ IF (WFLG + N .LE. WFLG) THEN
+ DO 130 X = 1, N
+ IF (W (X) .NE. 0) W (X) = 1
+130 CONTINUE
+ WFLG = 2
+ ENDIF
+
+C=======================================================================
+C COMPUTE (w (e) - wflg) = |Le\Lme| FOR ALL ELEMENTS
+C=======================================================================
+
+C -------------------------------------------------------------
+C Scan 1: compute the external degrees of previous elements
+C with respect to the current element. That is:
+C (w (e) - wflg) = |Le \ Lme|
+C for each element e that appears in any supervariable in Lme.
+C The notation Le refers to the pattern (list of
+C supervariables) of a previous element e, where e is not yet
+C absorbed, stored in iw (pe (e) + 1 ... pe (e) + iw (pe (e))).
+C The notation Lme refers to the pattern of the current element
+C (stored in iw (pme1..pme2)). If (w (e) - wflg) becomes
+C zero, then the element e will be absorbed in scan 2.
+C -------------------------------------------------------------
+
+ DO 150 PME = PME1, PME2
+ I = IW (PME)
+ ELN = ELEN (I)
+ IF (ELN .GT. 0) THEN
+C note that nv (i) has been negated to denote i in Lme:
+ NVI = -NV (I)
+ WNVI = WFLG - NVI
+ DO 140 P = PE (I), PE (I) + ELN - 1
+ E = IW (P)
+ WE = W (E)
+ IF (WE .GE. WFLG) THEN
+C unabsorbed element e has been seen in this loop
+ WE = WE - NVI
+ ELSE IF (WE .NE. 0) THEN
+C e is an unabsorbed element
+C this is the first we have seen e in all of Scan 1
+ WE = DEGREE (E) + WNVI
+ ENDIF
+ W (E) = WE
+140 CONTINUE
+ ENDIF
+150 CONTINUE
+
+C=======================================================================
+C DEGREE UPDATE AND ELEMENT ABSORPTION
+C=======================================================================
+
+C -------------------------------------------------------------
+C Scan 2: for each i in Lme, sum up the degree of Lme (which
+C is degme), plus the sum of the external degrees of each Le
+C for the elements e appearing within i, plus the
+C supervariables in i. Place i in hash list.
+C -------------------------------------------------------------
+
+ DO 180 PME = PME1, PME2
+ I = IW (PME)
+ P1 = PE (I)
+ P2 = P1 + ELEN (I) - 1
+ PN = P1
+ HASH = 0
+ DEG = 0
+
+C ----------------------------------------------------------
+C scan the element list associated with supervariable i
+C ----------------------------------------------------------
+
+C UMFPACK/MA38-style approximate degree:
+ DO 160 P = P1, P2
+ E = IW (P)
+ WE = W (E)
+ IF (WE .NE. 0) THEN
+C e is an unabsorbed element
+ DEG = DEG + WE - WFLG
+ IW (PN) = E
+ PN = PN + 1
+ HASH = HASH + E
+ ENDIF
+160 CONTINUE
+
+C count the number of elements in i (including me):
+ ELEN (I) = PN - P1 + 1
+
+C ----------------------------------------------------------
+C scan the supervariables in the list associated with i
+C ----------------------------------------------------------
+
+ P3 = PN
+ DO 170 P = P2 + 1, P1 + LEN (I) - 1
+ J = IW (P)
+ NVJ = NV (J)
+ IF (NVJ .GT. 0) THEN
+C j is unabsorbed, and not in Lme.
+C add to degree and add to new list
+ DEG = DEG + NVJ
+ IW (PN) = J
+ PN = PN + 1
+ HASH = HASH + J
+ ENDIF
+170 CONTINUE
+
+C ----------------------------------------------------------
+C update the degree and check for mass elimination
+C ----------------------------------------------------------
+
+ IF (ELEN (I) .EQ. 1 .AND. P3 .EQ. PN) THEN
+
+C -------------------------------------------------------
+C mass elimination
+C -------------------------------------------------------
+
+C There is nothing left of this node except for an
+C edge to the current pivot element. elen (i) is 1,
+C and there are no variables adjacent to node i.
+C Absorb i into the current pivot element, me.
+
+ PE (I) = -ME
+ NVI = -NV (I)
+ DEGME = DEGME - NVI
+ NVPIV = NVPIV + NVI
+ NEL = NEL + NVI
+ NV (I) = 0
+ ELEN (I) = 0
+
+ ELSE
+
+C -------------------------------------------------------
+C update the upper-bound degree of i
+C -------------------------------------------------------
+
+C the following degree does not yet include the size
+C of the current element, which is added later:
+ DEGREE (I) = MIN (DEGREE (I), DEG)
+
+C -------------------------------------------------------
+C add me to the list for i
+C -------------------------------------------------------
+
+C move first supervariable to end of list
+ IW (PN) = IW (P3)
+C move first element to end of element part of list
+ IW (P3) = IW (P1)
+C add new element to front of list.
+ IW (P1) = ME
+C store the new length of the list in len (i)
+ LEN (I) = PN - P1 + 1
+
+C -------------------------------------------------------
+C place in hash bucket. Save hash key of i in last (i).
+C -------------------------------------------------------
+
+ HASH = MOD (HASH, HMOD) + 1
+ J = HEAD (HASH)
+ IF (J .LE. 0) THEN
+C the degree list is empty, hash head is -j
+ NEXT (I) = -J
+ HEAD (HASH) = -I
+ ELSE
+C degree list is not empty
+C use last (head (hash)) as hash head
+ NEXT (I) = LAST (J)
+ LAST (J) = I
+ ENDIF
+ LAST (I) = HASH
+ ENDIF
+180 CONTINUE
+
+ DEGREE (ME) = DEGME
+
+C -------------------------------------------------------------
+C Clear the counter array, w (...), by incrementing wflg.
+C -------------------------------------------------------------
+
+ DMAX = MAX (DMAX, DEGME)
+ WFLG = WFLG + DMAX
+
+C make sure that wflg+n does not cause integer overflow
+ IF (WFLG + N .LE. WFLG) THEN
+ DO 190 X = 1, N
+ IF (W (X) .NE. 0) W (X) = 1
+190 CONTINUE
+ WFLG = 2
+ ENDIF
+C at this point, w (1..n) .lt. wflg holds
+
+C=======================================================================
+C SUPERVARIABLE DETECTION
+C=======================================================================
+
+ DO 250 PME = PME1, PME2
+ I = IW (PME)
+ IF (NV (I) .LT. 0) THEN
+C i is a principal variable in Lme
+
+C -------------------------------------------------------
+C examine all hash buckets with 2 or more variables. We
+C do this by examing all unique hash keys for super-
+C variables in the pattern Lme of the current element, me
+C -------------------------------------------------------
+
+ HASH = LAST (I)
+C let i = head of hash bucket, and empty the hash bucket
+ J = HEAD (HASH)
+ IF (J .EQ. 0) GOTO 250
+ IF (J .LT. 0) THEN
+C degree list is empty
+ I = -J
+ HEAD (HASH) = 0
+ ELSE
+C degree list is not empty, restore last () of head
+ I = LAST (J)
+ LAST (J) = 0
+ ENDIF
+ IF (I .EQ. 0) GOTO 250
+
+C while loop:
+200 CONTINUE
+ IF (NEXT (I) .NE. 0) THEN
+
+C ----------------------------------------------------
+C this bucket has one or more variables following i.
+C scan all of them to see if i can absorb any entries
+C that follow i in hash bucket. Scatter i into w.
+C ----------------------------------------------------
+
+ LN = LEN (I)
+ ELN = ELEN (I)
+C do not flag the first element in the list (me)
+ DO 210 P = PE (I) + 1, PE (I) + LN - 1
+ W (IW (P)) = WFLG
+210 CONTINUE
+
+C ----------------------------------------------------
+C scan every other entry j following i in bucket
+C ----------------------------------------------------
+
+ JLAST = I
+ J = NEXT (I)
+
+C while loop:
+220 CONTINUE
+ IF (J .NE. 0) THEN
+
+C -------------------------------------------------
+C check if j and i have identical nonzero pattern
+C -------------------------------------------------
+
+ IF (LEN (J) .NE. LN) THEN
+C i and j do not have same size data structure
+ GOTO 240
+ ENDIF
+ IF (ELEN (J) .NE. ELN) THEN
+C i and j do not have same number of adjacent el
+ GOTO 240
+ ENDIF
+C do not flag the first element in the list (me)
+ DO 230 P = PE (J) + 1, PE (J) + LN - 1
+ IF (W (IW (P)) .NE. WFLG) THEN
+C an entry (iw(p)) is in j but not in i
+ GOTO 240
+ ENDIF
+230 CONTINUE
+
+C -------------------------------------------------
+C found it! j can be absorbed into i
+C -------------------------------------------------
+
+ PE (J) = -I
+C both nv (i) and nv (j) are negated since they
+C are in Lme, and the absolute values of each
+C are the number of variables in i and j:
+ NV (I) = NV (I) + NV (J)
+ NV (J) = 0
+ ELEN (J) = 0
+C delete j from hash bucket
+ J = NEXT (J)
+ NEXT (JLAST) = J
+ GOTO 220
+
+C -------------------------------------------------
+240 CONTINUE
+C j cannot be absorbed into i
+C -------------------------------------------------
+
+ JLAST = J
+ J = NEXT (J)
+ GOTO 220
+ ENDIF
+
+C ----------------------------------------------------
+C no more variables can be absorbed into i
+C go to next i in bucket and clear flag array
+C ----------------------------------------------------
+
+ WFLG = WFLG + 1
+ I = NEXT (I)
+ IF (I .NE. 0) GOTO 200
+ ENDIF
+ ENDIF
+250 CONTINUE
+
+C=======================================================================
+C RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVAR. FROM ELEMENT
+C=======================================================================
+
+ P = PME1
+ NLEFT = N - NEL
+ DO 260 PME = PME1, PME2
+ I = IW (PME)
+ NVI = -NV (I)
+ IF (NVI .GT. 0) THEN
+C i is a principal variable in Lme
+C restore nv (i) to signify that i is principal
+ NV (I) = NVI
+
+C -------------------------------------------------------
+C compute the external degree (add size of current elem)
+C -------------------------------------------------------
+
+ DEG = MAX (1, MIN (DEGREE (I) + DEGME-NVI, NLEFT-NVI))
+
+C -------------------------------------------------------
+C place the supervariable at the head of the degree list
+C -------------------------------------------------------
+
+ INEXT = HEAD (DEG)
+ IF (INEXT .NE. 0) LAST (INEXT) = I
+ NEXT (I) = INEXT
+ LAST (I) = 0
+ HEAD (DEG) = I
+
+C -------------------------------------------------------
+C save the new degree, and find the minimum degree
+C -------------------------------------------------------
+
+ MINDEG = MIN (MINDEG, DEG)
+ DEGREE (I) = DEG
+
+C -------------------------------------------------------
+C place the supervariable in the element pattern
+C -------------------------------------------------------
+
+ IW (P) = I
+ P = P + 1
+ ENDIF
+260 CONTINUE
+
+C=======================================================================
+C FINALIZE THE NEW ELEMENT
+C=======================================================================
+
+ NV (ME) = NVPIV + DEGME
+C nv (me) is now the degree of pivot (including diagonal part)
+C save the length of the list for the new element me
+ LEN (ME) = P - PME1
+ IF (LEN (ME) .EQ. 0) THEN
+C there is nothing left of the current pivot element
+ PE (ME) = 0
+ W (ME) = 0
+ ENDIF
+ IF (NEWMEM .NE. 0) THEN
+C element was not constructed in place: deallocate part
+C of it (final size is less than or equal to newmem,
+C since newly nonprincipal variables have been removed).
+ PFREE = P
+ MEM = MEM - NEWMEM + LEN (ME)
+ ENDIF
+
+C=======================================================================
+C END WHILE (selecting pivots)
+ GOTO 30
+ ENDIF
+C=======================================================================
+
+C=======================================================================
+C COMPUTE THE PERMUTATION VECTORS
+C=======================================================================
+
+C ----------------------------------------------------------------
+C The time taken by the following code is O(n). At this
+C point, elen (e) = -k has been done for all elements e,
+C and elen (i) = 0 has been done for all nonprincipal
+C variables i. At this point, there are no principal
+C supervariables left, and all elements are absorbed.
+C ----------------------------------------------------------------
+
+C ----------------------------------------------------------------
+C compute the ordering of unordered nonprincipal variables
+C ----------------------------------------------------------------
+
+ DO 290 I = 1, N
+ IF (ELEN (I) .EQ. 0) THEN
+
+C ----------------------------------------------------------
+C i is an un-ordered row. Traverse the tree from i until
+C reaching an element, e. The element, e, was the
+C principal supervariable of i and all nodes in the path
+C from i to when e was selected as pivot.
+C ----------------------------------------------------------
+
+ J = -PE (I)
+C while (j is a variable) do:
+270 CONTINUE
+ IF (ELEN (J) .GE. 0) THEN
+ J = -PE (J)
+ GOTO 270
+ ENDIF
+ E = J
+
+C ----------------------------------------------------------
+C get the current pivot ordering of e
+C ----------------------------------------------------------
+
+ K = -ELEN (E)
+
+C ----------------------------------------------------------
+C traverse the path again from i to e, and compress the
+C path (all nodes point to e). Path compression allows
+C this code to compute in O(n) time. Order the unordered
+C nodes in the path, and place the element e at the end.
+C ----------------------------------------------------------
+
+ J = I
+C while (j is a variable) do:
+280 CONTINUE
+ IF (ELEN (J) .GE. 0) THEN
+ JNEXT = -PE (J)
+ PE (J) = -E
+ IF (ELEN (J) .EQ. 0) THEN
+C j is an unordered row
+ ELEN (J) = K
+ K = K + 1
+ ENDIF
+ J = JNEXT
+ GOTO 280
+ ENDIF
+C leave elen (e) negative, so we know it is an element
+ ELEN (E) = -K
+ ENDIF
+290 CONTINUE
+
+C ----------------------------------------------------------------
+C reset the inverse permutation (elen (1..n)) to be positive,
+C and compute the permutation (last (1..n)).
+C ----------------------------------------------------------------
+
+ DO 300 I = 1, N
+ K = ABS (ELEN (I))
+ LAST (K) = I
+ ELEN (I) = K
+300 CONTINUE
+
+C=======================================================================
+C RETURN THE MEMORY USAGE IN IW
+C=======================================================================
+
+C If maxmem is less than or equal to iwlen, then no compressions
+C occurred, and iw (maxmem+1 ... iwlen) was unused. Otherwise
+C compressions did occur, and iwlen would have had to have been
+C greater than or equal to maxmem for no compressions to occur.
+C Return the value of maxmem in the pfree argument.
+
+ PFREE = MAXMEM
+
+ RETURN
+ END
+
diff --git a/BTF/Doc/ChangeLog b/BTF/Doc/ChangeLog
new file mode 100644
index 0000000..ee289d4
--- /dev/null
+++ b/BTF/Doc/ChangeLog
@@ -0,0 +1,38 @@
+Nov 1, 2007: version 1.0.1
+
+ * trivial change to BTF/MATLAB/btf.c mexFunction: unused variable removed.
+
+May 31, 2007: version 1.0 released
+
+ * the C application program interface has been modified (see below)
+
+ * maxtrans function renamed to btf_maxtrans
+
+ * strongcomp function renamed to btf_strongcomp
+
+ * full statement coverage tests (KLU/Tcov)
+
+ * maxwork parameter added to btf_maxtrans and btf_order
+
+ * btf_maxtrans modified; now returns Q[i] = -1 if row i is unmatched;
+ code to complete the permutation moved to btf_order. This also
+ changes the maxtrans mexFunction.
+
+ * btf_install added for easy MATLAB installation
+
+ * illustrative recursive version of maxtrans removed (see the recursive
+ version of cs_maxtrans in CSparse instead)
+
+ * MAXTRANS_* macros renamed BTF_*
+
+ * no bug fixes in this release
+
+Dec 12, 2006: version 0.11
+
+ * minor MATLAB cleanup
+
+Apr 30, 2006:
+
+ * minor editing of comments. dmperm.c moved to MATLAB directory, since
+ it requires MATLAB. Version number not changed.
+
diff --git a/BTF/Doc/lesser.txt b/BTF/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/BTF/Doc/lesser.txt
@@ -0,0 +1,504 @@
+ GNU LESSER GENERAL PUBLIC LICENSE
+ Version 2.1, February 1999
+
+ Copyright (C) 1991, 1999 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+[This is the first released version of the Lesser GPL. It also counts
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+ but WITHOUT ANY WARRANTY; without even the implied warranty of
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diff --git a/BTF/Include/btf.h b/BTF/Include/btf.h
new file mode 100644
index 0000000..b62d009
--- /dev/null
+++ b/BTF/Include/btf.h
@@ -0,0 +1,263 @@
+/* ========================================================================== */
+/* === BTF package ========================================================== */
+/* ========================================================================== */
+
+/* BTF_MAXTRANS: find a column permutation Q to give A*Q a zero-free diagonal
+ * BTF_STRONGCOMP: find a symmetric permutation P to put P*A*P' into block
+ * upper triangular form.
+ * BTF_ORDER: do both of the above (btf_maxtrans then btf_strongcomp).
+ *
+ * Copyright (c) 2004-2007. Tim Davis, University of Florida,
+ * with support from Sandia National Laboratories. All Rights Reserved.
+ */
+
+
+/* ========================================================================== */
+/* === BTF_MAXTRANS ========================================================= */
+/* ========================================================================== */
+
+/* BTF_MAXTRANS: finds a permutation of the columns of a matrix so that it has a
+ * zero-free diagonal. The input is an m-by-n sparse matrix in compressed
+ * column form. The array Ap of size n+1 gives the starting and ending
+ * positions of the columns in the array Ai. Ap[0] must be zero. The array Ai
+ * contains the row indices of the nonzeros of the matrix A, and is of size
+ * Ap[n]. The row indices of column j are located in Ai[Ap[j] ... Ap[j+1]-1].
+ * Row indices must be in the range 0 to m-1. Duplicate entries may be present
+ * in any given column. The input matrix is not checked for validity (row
+ * indices out of the range 0 to m-1 will lead to an undeterminate result -
+ * possibly a core dump, for example). Row indices in any given column need
+ * not be in sorted order. However, if they are sorted and the matrix already
+ * has a zero-free diagonal, then the identity permutation is returned.
+ *
+ * The output of btf_maxtrans is an array Match of size n. If row i is matched
+ * with column j, then A(i,j) is nonzero, and then Match[i] = j. If the matrix
+ * is structurally nonsingular, all entries in the Match array are unique, and
+ * Match can be viewed as a column permutation if A is square. That is, column
+ * k of the original matrix becomes column Match[k] of the permuted matrix. In
+ * MATLAB, this can be expressed as (for non-structurally singular matrices):
+ *
+ * Match = maxtrans (A) ;
+ * B = A (:, Match) ;
+ *
+ * except of course here the A matrix and Match vector are all 0-based (rows
+ * and columns in the range 0 to n-1), not 1-based (rows/cols in range 1 to n).
+ * The MATLAB dmperm routine returns a row permutation. See the maxtrans
+ * mexFunction for more details.
+ *
+ * If row i is not matched to any column, then Match[i] is == -1. The
+ * btf_maxtrans routine returns the number of nonzeros on diagonal of the
+ * permuted matrix.
+ *
+ * In the MATLAB mexFunction interface to btf_maxtrans, 1 is added to the Match
+ * array to obtain a 1-based permutation. Thus, in MATLAB where A is m-by-n:
+ *
+ * q = maxtrans (A) ; % has entries in the range 0:n
+ * q % a column permutation (only if sprank(A)==n)
+ * B = A (:, q) ; % permuted matrix (only if sprank(A)==n)
+ * sum (q > 0) ; % same as "sprank (A)"
+ *
+ * This behaviour differs from p = dmperm (A) in MATLAB, which returns the
+ * matching as p(j)=i if row i and column j are matched, and p(j)=0 if column j
+ * is unmatched.
+ *
+ * p = dmperm (A) ; % has entries in the range 0:m
+ * p % a row permutation (only if sprank(A)==m)
+ * B = A (p, :) ; % permuted matrix (only if sprank(A)==m)
+ * sum (p > 0) ; % definition of sprank (A)
+ *
+ * This algorithm is based on the paper "On Algorithms for obtaining a maximum
+ * transversal" by Iain Duff, ACM Trans. Mathematical Software, vol 7, no. 1,
+ * pp. 315-330, and "Algorithm 575: Permutations for a zero-free diagonal",
+ * same issue, pp. 387-390. Algorithm 575 is MC21A in the Harwell Subroutine
+ * Library. This code is not merely a translation of the Fortran code into C.
+ * It is a completely new implementation of the basic underlying method (depth
+ * first search over a subgraph with nodes corresponding to columns matched so
+ * far, and cheap matching). This code was written with minimal observation of
+ * the MC21A/B code itself. See comments below for a comparison between the
+ * maxtrans and MC21A/B codes.
+ *
+ * This routine operates on a column-form matrix and produces a column
+ * permutation. MC21A uses a row-form matrix and produces a row permutation.
+ * The difference is merely one of convention in the comments and interpretation
+ * of the inputs and outputs. If you want a row permutation, simply pass a
+ * compressed-row sparse matrix to this routine and you will get a row
+ * permutation (just like MC21A). Similarly, you can pass a column-oriented
+ * matrix to MC21A and it will happily return a column permutation.
+ */
+
+#ifndef _BTF_H
+#define _BTF_H
+
+/* make it easy for C++ programs to include BTF */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include "UFconfig.h"
+
+int btf_maxtrans /* returns # of columns matched */
+(
+ /* --- input, not modified: --- */
+ int nrow, /* A is nrow-by-ncol in compressed column form */
+ int ncol,
+ int Ap [ ], /* size ncol+1 */
+ int Ai [ ], /* size nz = Ap [ncol] */
+ double maxwork, /* maximum amount of work to do is maxwork*nnz(A); no limit
+ * if <= 0 */
+
+ /* --- output, not defined on input --- */
+ double *work, /* work = -1 if maxwork > 0 and the total work performed
+ * reached the maximum of maxwork*nnz(A).
+ * Otherwise, work = the total work performed. */
+
+ int Match [ ], /* size nrow. Match [i] = j if column j matched to row i
+ * (see above for the singular-matrix case) */
+
+ /* --- workspace, not defined on input or output --- */
+ int Work [ ] /* size 5*ncol */
+) ;
+
+/* long integer version (all "int" parameters become "UF_long") */
+UF_long btf_l_maxtrans (UF_long, UF_long, UF_long *, UF_long *, double,
+ double *, UF_long *, UF_long *) ;
+
+
+/* ========================================================================== */
+/* === BTF_STRONGCOMP ======================================================= */
+/* ========================================================================== */
+
+/* BTF_STRONGCOMP finds the strongly connected components of a graph, returning
+ * a symmetric permutation. The matrix A must be square, and is provided on
+ * input in compressed-column form (see BTF_MAXTRANS, above). The diagonal of
+ * the input matrix A (or A*Q if Q is provided on input) is ignored.
+ *
+ * If Q is not NULL on input, then the strongly connected components of A*Q are
+ * found. Q may be flagged on input, where Q[k] < 0 denotes a flagged column k.
+ * The permutation is j = BTF_UNFLIP (Q [k]). On output, Q is modified (the
+ * flags are preserved) so that P*A*Q is in block upper triangular form.
+ *
+ * If Q is NULL, then the permutation P is returned so that P*A*P' is in upper
+ * block triangular form.
+ *
+ * The vector R gives the block boundaries, where block b is in rows/columns
+ * R[b] to R[b+1]-1 of the permuted matrix, and where b ranges from 1 to the
+ * number of strongly connected components found.
+ */
+
+int btf_strongcomp /* return # of strongly connected components */
+(
+ /* input, not modified: */
+ int n, /* A is n-by-n in compressed column form */
+ int Ap [ ], /* size n+1 */
+ int Ai [ ], /* size nz = Ap [n] */
+
+ /* optional input, modified (if present) on output: */
+ int Q [ ], /* size n, input column permutation */
+
+ /* output, not defined on input */
+ int P [ ], /* size n. P [k] = j if row and column j are kth row/col
+ * in permuted matrix. */
+
+ int R [ ], /* size n+1. block b is in rows/cols R[b] ... R[b+1]-1 */
+
+ /* workspace, not defined on input or output */
+ int Work [ ] /* size 4n */
+) ;
+
+UF_long btf_l_strongcomp (UF_long, UF_long *, UF_long *, UF_long *, UF_long *,
+ UF_long *, UF_long *) ;
+
+
+/* ========================================================================== */
+/* === BTF_ORDER ============================================================ */
+/* ========================================================================== */
+
+/* BTF_ORDER permutes a square matrix into upper block triangular form. It
+ * does this by first finding a maximum matching (or perhaps a limited matching
+ * if the work is limited), via the btf_maxtrans function. If a complete
+ * matching is not found, BTF_ORDER completes the permutation, but flags the
+ * columns of P*A*Q to denote which columns are not matched. If the matrix is
+ * structurally rank deficient, some of the entries on the diagonal of the
+ * permuted matrix will be zero. BTF_ORDER then calls btf_strongcomp to find
+ * the strongly-connected components.
+ *
+ * On output, P and Q are the row and column permutations, where i = P[k] if
+ * row i of A is the kth row of P*A*Q, and j = BTF_UNFLIP(Q[k]) if column j of
+ * A is the kth column of P*A*Q. If Q[k] < 0, then the (k,k)th entry in P*A*Q
+ * is structurally zero.
+ *
+ * The vector R gives the block boundaries, where block b is in rows/columns
+ * R[b] to R[b+1]-1 of the permuted matrix, and where b ranges from 1 to the
+ * number of strongly connected components found.
+ */
+
+int btf_order /* returns number of blocks found */
+(
+ /* --- input, not modified: --- */
+ int n, /* A is n-by-n in compressed column form */
+ int Ap [ ], /* size n+1 */
+ int Ai [ ], /* size nz = Ap [n] */
+ double maxwork, /* do at most maxwork*nnz(A) work in the maximum
+ * transversal; no limit if <= 0 */
+
+ /* --- output, not defined on input --- */
+ double *work, /* return value from btf_maxtrans */
+ int P [ ], /* size n, row permutation */
+ int Q [ ], /* size n, column permutation */
+ int R [ ], /* size n+1. block b is in rows/cols R[b] ... R[b+1]-1 */
+ int *nmatch, /* # nonzeros on diagonal of P*A*Q */
+
+ /* --- workspace, not defined on input or output --- */
+ int Work [ ] /* size 5n */
+) ;
+
+UF_long btf_l_order (UF_long, UF_long *, UF_long *, double , double *,
+ UF_long *, UF_long *, UF_long *, UF_long *, UF_long *) ;
+
+
+/* ========================================================================== */
+/* === BTF marking of singular columns ====================================== */
+/* ========================================================================== */
+
+/* BTF_FLIP is a "negation about -1", and is used to mark an integer j
+ * that is normally non-negative. BTF_FLIP (-1) is -1. BTF_FLIP of
+ * a number > -1 is negative, and BTF_FLIP of a number < -1 is positive.
+ * BTF_FLIP (BTF_FLIP (j)) = j for all integers j. UNFLIP (j) acts
+ * like an "absolute value" operation, and is always >= -1. You can test
+ * whether or not an integer j is "flipped" with the BTF_ISFLIPPED (j)
+ * macro.
+ */
+
+#define BTF_FLIP(j) (-(j)-2)
+#define BTF_ISFLIPPED(j) ((j) < -1)
+#define BTF_UNFLIP(j) ((BTF_ISFLIPPED (j)) ? BTF_FLIP (j) : (j))
+
+/* ========================================================================== */
+/* === BTF version ========================================================== */
+/* ========================================================================== */
+
+/* All versions of BTF include these definitions.
+ * As an example, to test if the version you are using is 1.2 or later:
+ *
+ * if (BTF_VERSION >= BTF_VERSION_CODE (1,2)) ...
+ *
+ * This also works during compile-time:
+ *
+ * #if (BTF >= BTF_VERSION_CODE (1,2))
+ * printf ("This is version 1.2 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ */
+
+#define BTF_DATE "Nov 1, 2007"
+#define BTF_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define BTF_MAIN_VERSION 1
+#define BTF_SUB_VERSION 0
+#define BTF_SUBSUB_VERSION 1
+#define BTF_VERSION BTF_VERSION_CODE(BTF_MAIN_VERSION,BTF_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+#endif
diff --git a/BTF/Include/btf_internal.h b/BTF/Include/btf_internal.h
new file mode 100644
index 0000000..83f76f1
--- /dev/null
+++ b/BTF/Include/btf_internal.h
@@ -0,0 +1,64 @@
+/* ========================================================================== */
+/* === btf_internal include file ============================================ */
+/* ========================================================================== */
+
+#ifndef _BTF_INTERNAL_H
+#define _BTF_INTERNAL_H
+
+/*
+ * Copyright (c) 2004-2007. Tim Davis, University of Florida,
+ * with support from Sandia National Laboratories. All Rights Reserved.
+ */
+
+/* Not to be included in any user program. */
+
+#ifdef DLONG
+#define Int UF_long
+#define Int_id UF_long_id
+#define BTF(name) btf_l_ ## name
+#else
+#define Int int
+#define Int_id "%d"
+#define BTF(name) btf_ ## name
+#endif
+
+/* ========================================================================== */
+/* make sure debugging and printing is turned off */
+
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+#ifndef NPRINT
+#define NPRINT
+#endif
+
+/* To enable debugging and assertions, uncomment this line:
+ #undef NDEBUG
+*/
+/* To enable diagnostic printing, uncomment this line:
+ #undef NPRINT
+*/
+
+/* ========================================================================== */
+
+#include <stdio.h>
+#include <assert.h>
+#define ASSERT(a) assert(a)
+
+#undef TRUE
+#undef FALSE
+#undef PRINTF
+#undef MIN
+
+#ifndef NPRINT
+#define PRINTF(s) { printf s ; } ;
+#else
+#define PRINTF(s)
+#endif
+
+#define TRUE 1
+#define FALSE 0
+#define EMPTY (-1)
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+#endif
diff --git a/BTF/Lib/Makefile b/BTF/Lib/Makefile
new file mode 100644
index 0000000..a118002
--- /dev/null
+++ b/BTF/Lib/Makefile
@@ -0,0 +1,59 @@
+default: all
+
+ccode: all
+
+include ../../UFconfig/UFconfig.mk
+
+# for testing only:
+# TEST = -DTESTING
+
+C = $(CC) $(CFLAGS)
+
+INC = ../Include/btf.h ../Include/btf_internal.h
+
+I = -I../Include -I../../UFconfig
+
+all: library
+
+library: libbtf.a
+
+OBJ = btf_order.o btf_maxtrans.o btf_strongcomp.o \
+ btf_l_order.o btf_l_maxtrans.o btf_l_strongcomp.o
+
+libbtf.a: $(OBJ)
+ $(AR) libbtf.a $(OBJ)
+ $(RANLIB) libbtf.a
+
+$(OBJ): $(INC)
+
+#-------------------------------------------------------------------------------
+
+btf_order.o: ../Source/btf_order.c
+ $(C) -c $(I) $< -o $@
+
+btf_maxtrans.o: ../Source/btf_maxtrans.c
+ $(C) -c $(I) $< -o $@
+
+btf_strongcomp.o: ../Source/btf_strongcomp.c
+ $(C) -c $(I) $< -o $@
+
+#-------------------------------------------------------------------------------
+
+btf_l_order.o: ../Source/btf_order.c
+ $(C) -c $(I) -DDLONG $< -o $@
+
+btf_l_maxtrans.o: ../Source/btf_maxtrans.c
+ $(C) -c $(I) -DDLONG $< -o $@
+
+btf_l_strongcomp.o: ../Source/btf_strongcomp.c
+ $(C) -c $(I) -DDLONG $< -o $@
+
+#-------------------------------------------------------------------------------
+
+purge: distclean
+
+distclean: clean
+ - $(RM) libbtf.a
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/BTF/MATLAB/Contents.m b/BTF/MATLAB/Contents.m
new file mode 100644
index 0000000..9b6e0bc
--- /dev/null
+++ b/BTF/MATLAB/Contents.m
@@ -0,0 +1,20 @@
+% BTF ordering toolbox:
+%
+% Primary functions:
+%
+% btf - permute a square sparse matrix into upper block triangular form
+% maxtrans - permute the columns of a sparse matrix so it has a zero-free diagonal
+% strongcomp - symmetric permutation to upper block triangular form
+%
+% Other:
+% btf_install - compile and install BTF for use in MATLAB.
+% btf_demo - demo for BTF
+% drawbtf - plot the BTF form of a matrix
+% btf_make - compile BTF for use in MATLAB
+%
+% Example:
+% q = maxtrans (A)
+% [p,q,r] = btf (A)
+% [p,r] = strongcomp (A)
+
+% Copyright 2004-2007, Tim Davis, University of Florida
diff --git a/BTF/MATLAB/Makefile b/BTF/MATLAB/Makefile
new file mode 100644
index 0000000..7cb1bcf
--- /dev/null
+++ b/BTF/MATLAB/Makefile
@@ -0,0 +1,37 @@
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../Include -I../../UFconfig
+
+MX = $(MEX) $(I) -DDLONG
+
+all: maxtrans.mexglx strongcomp.mexglx btf.mexglx
+
+recursive: strongcomp_recursive.mexglx
+
+maxtrans.mexglx: ../Source/btf_maxtrans.c ../Include/btf.h maxtrans.c \
+ ../Include/btf_internal.h
+ $(MX) maxtrans.c ../Source/btf_maxtrans.c
+
+strongcomp.mexglx: ../Source/btf_strongcomp.c ../Include/btf.h \
+ strongcomp.c ../Include/btf_internal.h
+ $(MX) strongcomp.c ../Source/btf_strongcomp.c
+
+strongcomp_recursive.mexglx: ../Source/btf_strongcomp.c ../Include/btf.h \
+ strongcomp.c ../Include/btf_internal.h
+ $(MX) -DRECURSIVE -output strongcomp_recursive \
+ ../Source/btf_strongcomp.c strongcomp.c
+
+btf.mexglx: ../Source/btf_strongcomp.c ../Include/btf.h btf.c \
+ ../Include/btf_internal.h \
+ ../Source/btf_maxtrans.c ../Source/btf_order.c
+ $(MX) btf.c ../Source/btf_maxtrans.c \
+ ../Source/btf_strongcomp.c ../Source/btf_order.c
+
+distclean: purge
+
+purge: clean
+ - $(RM) *.o *.mex*
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/BTF/MATLAB/Test/btf_test.m b/BTF/MATLAB/Test/btf_test.m
new file mode 100644
index 0000000..9def379
--- /dev/null
+++ b/BTF/MATLAB/Test/btf_test.m
@@ -0,0 +1,19 @@
+function btf_test (nmat)
+%BTF_TEST test for BTF
+% Requires CSparse (or CXSparse) and UFget
+% Example:
+% btf_test
+% See also btf, maxtrans, strongcomp, dmperm, UFget,
+% test1, test2, test3, test4, test5, test6.
+
+if (nargin < 1)
+ nmat = 800 ;
+end
+
+test1 (nmat) ;
+test2 (nmat) ;
+test3 (nmat) ;
+test4 (nmat) ;
+test5 (nmat) ;
+test6 ;
+
diff --git a/BTF/MATLAB/Test/checkbtf.m b/BTF/MATLAB/Test/checkbtf.m
new file mode 100644
index 0000000..95bceca
--- /dev/null
+++ b/BTF/MATLAB/Test/checkbtf.m
@@ -0,0 +1,46 @@
+function checkbtf (A, p, q, r)
+%CHECKBTF ensure A(p,q) is in BTF form
+%
+% A(p,q) is in BTF form, r the block boundaries
+%
+% Example:
+% [p,q,r] = dmperm (A)
+% checkbtf (A, p, q, r)
+%
+% See also drawbtf, maxtrans, strongcomp.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+[m n] = size (A) ;
+if (m ~= n)
+ error ('A must be square') ;
+end
+
+if (any (sort (p) ~= 1:n))
+ error ('p not a permutation') ;
+end
+
+if (any (sort (q) ~= 1:n))
+ error ('q not a permutation') ;
+end
+
+nblocks = length (r) - 1 ;
+
+if (r (1) ~= 1)
+ error ('r(1) not one') ;
+end
+
+if (r (end) ~= n+1)
+ error ('r(end) not n+1') ;
+end
+
+if (nblocks < 1 | nblocks > n) %#ok
+ error ('nblocks wrong') ;
+end
+
+nblocks = length (r) - 1 ;
+rdiff = r (2:(nblocks+1)) - r (1:nblocks) ;
+if (any (rdiff < 1) | any (rdiff > n)) %#ok
+ error ('r bad')
+end
+
diff --git a/BTF/MATLAB/Test/test1.m b/BTF/MATLAB/Test/test1.m
new file mode 100644
index 0000000..c44e9db
--- /dev/null
+++ b/BTF/MATLAB/Test/test1.m
@@ -0,0 +1,141 @@
+function test1 (nmat)
+%TEST1 test for BTF
+% Requires CSparse and UFget
+% Example:
+% test1
+% See also btf, maxtrans, strongcomp, dmperm, UFget,
+% test1, test2, test3, test4, test5.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+index = UFget ;
+% f = find (index.sprank < min (index.nrows, index.ncols)) ;
+f = 1:length (index.nrows) ;
+
+% too much time:
+skip = [1514 1297 1876 1301] ;
+
+f = setdiff (f, skip) ;
+
+[ignore i] = sort (index.nnz (f)) ;
+f = f (i) ;
+
+if (nargin < 1)
+ nmat = 1000 ;
+end
+nmat = min (nmat, length (f)) ;
+f = f (1:nmat) ;
+
+T0 = zeros (nmat,1) ;
+T1 = zeros (nmat,1) ;
+Anz = zeros (nmat,1) ;
+figure (1) ;
+MN = zeros (nmat, 2) ;
+Nzdiag = zeros (nmat,1) ;
+
+% warmup
+p = maxtrans (sparse (1)) ; %#ok
+p = cs_dmperm (sparse (1)) ; %#ok
+a = cs_transpose (sparse (1)) ; %#ok
+
+h = waitbar (0, 'BTF test 1 of 6') ;
+
+try
+
+ for k = 1:nmat
+
+ Prob = UFget (f (k), index) ;
+ A = Prob.A ;
+ clear Prob
+ t = 0 ;
+
+ waitbar (k/nmat, h) ;
+
+ r = full (sum (spones (A), 2)) ;
+ c = full (sum (spones (A))) ;
+ m2 = length (find (r > 0)) ;
+ n2 = length (find (c > 0)) ;
+
+ if (m2 < n2)
+ tic
+ A = cs_transpose (A) ;
+ t = toc ;
+ end
+
+ Nzdiag (k) = nnz (diag (A)) ;
+
+ [m n] = size (A) ;
+ Anz (k) = nnz (A) ;
+ MN (k,:) = [m n] ;
+
+ tic
+ q = maxtrans (A) ;
+ t0 = toc ;
+ s0 = sum (q > 0) ;
+ T0 (k) = max (1e-9, t0) ;
+
+ tic
+ p = cs_dmperm (A) ;
+ t1 = toc ;
+ s1 = sum (p > 0) ;
+ T1 (k) = max (1e-9, t1) ;
+
+ fprintf (...
+ '%4d maxtrans %10.6f %10.6f cs_dmperm %10.6f m/n %8.2f', ...
+ f(k), t, t0, t1, m/n) ;
+ if (t1 ~= 0)
+ fprintf (' rel: %8.4f', t0 / t1) ;
+ end
+ fprintf ('\n') ;
+ if (s0 ~= s1)
+ error ('!') ;
+ end
+
+ if (s0 == n & m == n) %#ok
+ B = A (:, q) ;
+ subplot (2,2,1) ;
+ cspy (B) ;
+ if (nnz (diag (B)) ~= n)
+ error ('?')
+ end
+ clear B
+ else
+ cspy (0) ;
+ end
+
+ maxnz = nnz (A) ;
+
+ zfree = find (MN (1:k,1) == MN (1:k,2) & Nzdiag (1:k) == MN(1:k,1)) ;
+ square = find (MN (1:k,1) == MN (1:k,2) & Nzdiag (1:k) ~= MN(1:k,1)) ;
+ tall = find (MN (1:k,1) > MN (1:k,2)) ;
+ squat = find (MN (1:k,1) < MN (1:k,2)) ;
+
+ subplot (2,2,2) ;
+ loglog (Anz (square), T0 (square) ./ T1 (square), ...
+ 'o', [1 maxnz], [1 1], 'r-') ;
+ title ('square') ;
+ subplot (2,2,3) ;
+ loglog (Anz (tall), T0 (tall) ./ T1 (tall), ...
+ 'o', [1 maxnz], [1 1], 'r-') ;
+ title ('tall') ;
+ subplot (2,2,4) ;
+ title ('square, intially zero-free') ;
+ loglog (Anz (zfree), T0 (zfree) ./ T1 (zfree), ...
+ 'o', [1 maxnz], [1 1], 'r-') ;
+ title ('square, zero-free diag') ;
+
+ drawnow
+
+ end
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
diff --git a/BTF/MATLAB/Test/test2.m b/BTF/MATLAB/Test/test2.m
new file mode 100644
index 0000000..abcc3cd
--- /dev/null
+++ b/BTF/MATLAB/Test/test2.m
@@ -0,0 +1,109 @@
+function test2 (nmat)
+%TEST2 test for BTF
+% Requires CSparse and UFget
+% Example:
+% test2
+% See also btf, maxtrans, strongcomp, dmperm, UFget,
+% test1, test2, test3, test4, test5.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+index = UFget ;
+f = find (index.nrows == index.ncols) ;
+
+% too much time:
+skip = [1514 1297 1876 1301] ;
+f = setdiff (f, skip) ;
+
+[ignore i] = sort (index.nnz (f)) ;
+f = f (i) ;
+
+if (nargin < 1)
+ nmat = 1000 ;
+end
+nmat = min (nmat, length (f)) ;
+f = f (1:nmat) ;
+
+T0 = zeros (nmat,1) ;
+T1 = zeros (nmat,1) ;
+Anz = zeros (nmat,1) ;
+figure (1) ;
+clf
+MN = zeros (nmat, 2) ;
+Nzdiag = zeros (nmat,1) ;
+
+% warmup
+p = maxtrans (sparse (1)) ; %#ok
+p = btf (sparse (1)) ; %#ok
+p = cs_dmperm (sparse (1)) ; %#ok
+a = cs_transpose (sparse (1)) ; %#ok
+
+h = waitbar (0, 'BTF test 2 of 6') ;
+
+try
+ for k = 1:nmat
+
+ Prob = UFget (f (k), index) ;
+ A = Prob.A ;
+
+ waitbar (k/nmat, h) ;
+
+ Nzdiag (k) = nnz (diag (A)) ;
+
+ [m n] = size (A) ;
+ Anz (k) = nnz (A) ;
+ MN (k,:) = [m n] ;
+
+ tic
+ [p,q,r] = btf (A) ;
+ t0 = toc ;
+ s0 = sum (q > 0) ;
+ T0 (k) = max (1e-9, t0) ;
+
+ tic
+ [p2,q2,r2] = cs_dmperm (A) ;
+ t1 = toc ;
+ s1 = sum (dmperm (A) > 0) ;
+ T1 (k) = max (1e-9, t1) ;
+
+ fprintf ('%4d btf %10.6f cs_dmperm %10.6f', f(k), t0, t1) ;
+ if (t1 ~= 0)
+ fprintf (' rel: %8.4f', t0 / t1) ;
+ end
+ fprintf ('\n') ;
+
+ if (s0 ~= s1)
+ error ('!') ;
+ end
+
+ C = A (p, abs (q)) ;
+ subplot (1,2,1) ;
+ cspy (C) ;
+ z = find (q < 0) ;
+ zd = nnz (diag (C (z,z))) ;
+ if (zd > 0)
+ error ('?') ;
+ end
+
+ minnz = Anz (1) ;
+ maxnz = nnz (A) ;
+
+ subplot (1,2,2) ;
+ loglog (Anz (1:k), T0 (1:k) ./ T1 (1:k), ...
+ 'o', [minnz maxnz], [1 1], 'r-') ;
+ drawnow
+
+ clear C A Prob
+ end
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
diff --git a/BTF/MATLAB/Test/test3.m b/BTF/MATLAB/Test/test3.m
new file mode 100644
index 0000000..40b236e
--- /dev/null
+++ b/BTF/MATLAB/Test/test3.m
@@ -0,0 +1,530 @@
+function test3 (nmat)
+%TEST3 test for BTF
+% Requires UFget
+% Example:
+% test3
+% See also btf, maxtrans, strongcomp, dmperm, UFget,
+% test1, test2, test3, test4, test5.
+
+% Copyright 2007, Timothy A. Davis, Univ. of Florida
+
+doplot = 1 ;
+dopause = 0 ;
+dostrong = 1 ;
+
+index = UFget ;
+f = find (index.nrows == index.ncols) ;
+[ignore i] = sort (index.nnz (f)) ;
+f = f (i) ;
+clear i
+
+figure (1)
+
+% short test set: seg faults, lots of blocks, lots of work, and so on:
+nasty = [
+ % --- various test matrices (no seg fault, quick run time)
+ -(1:8)' % generated matrices
+ 904 % vanHeukelum/cage3 (5-by-5)
+ 819 % Simon/raefsky6 (permuted triangular matrix)
+ %
+ % --- older seg faults:
+ 264 % HB/west0156, causes older strongcomp_recursive to fail
+ 824 % TOKAMAK/utm300 (300-by-300), causes older code to fail
+ 868 % Pothen/bodyy4
+ %
+ % --- seg faults in old MATLAB dmperm
+ 290 % Averous/epb3
+ 983 % Sanghavi/ecl32
+ 885 % Pothen/tandem_dual
+ 879 % Pothen/onera_dual
+ 955 % Schenk_IBMSDS/2D_54019_highK
+ 957 % Schenk_IBMSDS/3D_51448_3D
+ 958 % Schenk_IBMSDS/ibm_matrix_2
+ 912 % vanHeukelum/cage11
+ 924 % Andrews/Andrews
+ 960 % Schenk_IBMSDS/matrix-new_3
+ 862 % Kim/kim1
+ 544 % Hamm/scircuit
+ 897 % Norris/torso2
+ 801 % Ronis/xenon1
+ 53 % HB/bcsstk31
+ 958 % Schenk_IBMSDS/matrix_9
+ 844 % Cunningham/qa8fk
+ 845 % Cunningham/qa8fk
+ 821 % Simon/venkat25
+ 822 % Simon/venkat50
+ 820 % Simon/venkat01
+ 812 % Simon/bbmat
+ 804 % Rothberg/cfd1
+ 54 % HB/bcsstk32
+ 913 % vanHeukelum/cage12
+ 846 % Boeing/bcsstk39
+ 972 % Schenk_IBMSDS/para-10
+ 974 % Schenk_IBMSDS/para-5
+ 975 % Schenk_IBMSDS/para-6
+ 976 % Schenk_IBMSDS/para-7
+ 977 % Schenk_IBMSDS/para-8
+ 978 % Schenk_IBMSDS/para-9
+ 961 % Schenk_ISEI/barrier2-10
+ 962 % Schenk_ISEI/barrier2-11
+ 963 % Schenk_ISEI/barrier2-12
+ 964 % Schenk_ISEI/barrier2-1
+ 965 % Schenk_ISEI/barrier2-2
+ 966 % Schenk_ISEI/barrier2-3
+ 967 % Schenk_ISEI/barrier2-4
+ 968 % Schenk_ISEI/barrier2-9
+ 851 % Chen/pkustk05
+ 979 % Kamvar/Stanford
+ 374 % Bova/rma10
+ %
+ % --- lots of time:
+ 395 % DRIVCAV/cavity16
+ 396 % DRIVCAV/cavity17
+ 397 % DRIVCAV/cavity18
+ 398 % DRIVCAV/cavity19
+ 399 % DRIVCAV/cavity20
+ 400 % DRIVCAV/cavity21
+ 401 % DRIVCAV/cavity22
+ 402 % DRIVCAV/cavity23
+ 403 % DRIVCAV/cavity24
+ 404 % DRIVCAV/cavity25
+ 405 % DRIVCAV/cavity26
+ 1109 % Sandia/mult_dcop_01
+ 1110 % Sandia/mult_dcop_02
+ 1111 % Sandia/mult_dcop_03
+ 376 % Brethour/coater2
+ 284 % ATandT/onetone2
+ 588 % Hollinger/mark3jac100
+ 589 % Hollinger/mark3jac100sc
+ 452 % Grund/bayer01
+ 920 % Hohn/sinc12
+ 590 % Hollinger/mark3jac120
+ 591 % Hollinger/mark3jac120sc
+ 809 % Shyy/shyy161
+ 448 % Graham/graham1
+ 283 % ATandT/onetone1
+ 445 % Garon/garon2
+ 541 % Hamm/bcircuit
+ 592 % Hollinger/mark3jac140
+ 593 % Hollinger/mark3jac140sc
+ 435 % FIDAP/ex40
+ 912 % Hohn/sinc15
+ 894 % Norris/lung2
+ 542 % Hamm/hcircuit
+ 752 % Mulvey/finan512
+ 753 % Mulvey/pfinan512
+ 564 % Hollinger/g7jac180
+ 565 % Hollinger/g7jac180sc
+ 566 % Hollinger/g7jac200
+ 567 % Hollinger/g7jac200sc
+ 748 % Mallya/lhr34
+ 749 % Mallya/lhr34c
+ 922 % Hohn/sinc18
+ 447 % Goodwin/rim
+ 807 % Rothberg/struct3
+ 286 % ATandT/twotone
+ 982 % Tromble/language
+ 953 % Schenk_IBMNA/c-73
+ 890 % Norris/heart1
+ 750 % Mallya/lhr71
+ 751 % Mallya/lhr71c
+ 925 % FEMLAB/ns3Da
+ 827 % Vavasis/av41092
+ 931 % FEMLAB/sme3Db
+ 1297 % GHS_index/boyd2
+ 1301 % GHS_indef/cont-300
+ %
+ % --- lots of time, and seg faults:
+ 285 % ATandT/pre2
+ % --- huge matrix, turn off plotting
+ 940 % Shenk/af_shell1, memory leak in plot, after call to btf, once.
+ % ----
+]' ;
+
+% maxtrans_recursive causes a seg fault on these matrices, because of
+% stack overflow (this is expected)
+skip_list_maxtrans_recursive = 285 ;
+
+% p = dmperm (A) in MATLAB 7.4 causes a seg fault on these matrices:
+skip_list_dmperm = [285 1301 1231 1251 1232 1241] ;
+
+% [p,q,r] = dmperm (A) in MATLAB 7.4 causes a seg fault on these matrices:
+skip_list_dmperm_btf = ...
+[ 285 879 885 290 955 957 958 924 960 897 959 844 845 ...
+ 821 822 820 804 913 846 972 974:978 961:968 979 940 ...
+ 1422 1513 1412 1510 1301 1231 1251 1434 1213 1232 1241 1357 1579 1431 1281] ;
+% length(skip_list_dmperm_btf)
+
+% time intensive
+skip_costly = [1514 1297 1876 1301] ;
+
+% strongcomp (recursive) causes a seg fault on these matrices because of
+% stack overflow (this is expected).
+skip_list_strongcomp_recursive = ...
+[983 285 879 885 290 955 957 958 912 924 960 862 544 897 801 53 959 844 845 ...
+ 821 822 820 812 804 54 913 846 972 974:978 961:968 851 374 940] ;
+skip_list_strongcomp_recursive = ...
+[ skip_list_strongcomp_recursive 592 593 752 753 807 286 982 855 566 567 ] ;
+
+% matrices with the largest # of nonzeros in the set (untested)
+toobig = [
+928 853 852 356 761 368 973 895 805 849 932 ...
+803 854 936 802 850 537 856 898 857 859 971 937 ...
+914 858 980 896 806 538 863 369 938 860 941 942 ...
+943 944 945 946 947 948 915 939 916 ] ;
+
+f = [ -(1:8) f ] ;
+% f = nasty ;
+
+h = waitbar (0, 'BTF test 3 of 6') ;
+
+if (nargin < 1)
+ nmat = 1000 ;
+end
+nmat = min (nmat, length (f)) ;
+f = f (1:nmat) ;
+
+try
+
+ for matnum = 1:nmat
+
+ waitbar (matnum/nmat, h) ;
+
+ j = f (matnum) ;
+
+ if (any (j == toobig) | any (j == skip_costly)) %#ok
+ fprintf ('\n%4d: %3d %s/%s too big\n', ...
+ matnum, j, index.Group{j}, index.Name{j}) ;
+ continue ;
+ end
+
+ rand ('state', 0) ;
+
+ % clear all unused variables.
+ % nothing here is left that is proportional to the matrix size
+ clear A p1 p2 p3 q3 r3 match1 match2 match4 pa ra sa qa B C pb rb pc rc
+ clear jumble B11 B12 B13 B21 B22 B23 B31 B32 B33 pjumble qjumble ans
+ clear c kbad kgood
+ % whos
+ % pause
+
+ if (j > 0)
+ Problem = UFget (j, index) ;
+ name = Problem.name ;
+ A = Problem.A ;
+ clear Problem
+ else
+ % construct the jth test matrix
+ j = -j ;
+ if (j == 1 | j == 2) %#ok
+ B11 = UFget ('Grund/b1_ss') ; % 7-by-7 diagonal block
+ B11 = B11.A ;
+ B12 = sparse (zeros (7,2)) ;
+ B12 (3,2) = 1 ;
+ B13 = sparse (ones (7,5)) ;
+ B21 = sparse (zeros (2,7)) ;
+ B22 = sparse (ones (2,2)) ; % 2-by-2 diagonal block
+ B23 = sparse (ones (2,5)) ;
+ B31 = sparse (zeros (5,7)) ;
+ B32 = sparse (zeros (5,2)) ;
+ B33 = UFget ('vanHeukelum/cage3') ; % 5-by-5 diagonal block
+ B33 = B33.A ;
+ A = [ B11 B12 B13 ; B21 B22 B23 ; B31 B32 B33 ] ;
+ name = '(j=1 test matrix)' ;
+ end
+ if (j == 2)
+ pjumble = [ 10 7 11 1 13 12 8 2 5 14 9 6 4 3 ] ;
+ qjumble = [ 3 14 2 11 1 8 5 7 10 12 4 13 9 6 ] ;
+ A = A (pjumble, qjumble) ;
+ name = '(j=2 test matrix)' ;
+ elseif (j == 3)
+ A = sparse (1) ;
+ elseif (j == 4)
+ A = sparse (0) ;
+ elseif (j == 5)
+ A = sparse (ones (2)) ;
+ elseif (j == 6)
+ A = sparse (2,2) ;
+ elseif (j == 7)
+ A = speye (2) ;
+ elseif (j == 8)
+ A = sparse (2,2) ;
+ A (2,1) = 1 ;
+ end
+ if (j > 2)
+ full (A)
+ end
+ end
+
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue ;
+ end
+ fprintf ('\n%4d: ', matnum) ;
+ fprintf (' =========================== Matrix: %3d %s\n', j, name) ;
+ fprintf ('n: %d nz: %d\n', n, nnz (A)) ;
+
+ if (nnz (A) > 6e6)
+ doplot = 0 ;
+ end
+
+ %-----------------------------------------------------------------------
+ % now try maxtrans
+ tic
+ match1 = maxtrans (A) ;
+ t = toc ;
+ s1 = sum (match1 > 0) ;
+ fprintf ('n-sprank: %d\n', n-s1) ;
+ fprintf ('maxtrans: %8.2f seconds\n', t) ;
+ singular = s1 < n ;
+
+ if (doplot)
+ % figure (1)
+ clf
+ subplot (2,4,1)
+ spy (A)
+ title (name) ;
+ end
+
+ p1 = match1 ;
+ if (any (p1 <= 0))
+ % complete the permutation
+ badrow = find (p1 <= 0) ;
+
+ badcol = ones (1,n) ;
+ badcol (p1 (p1 > 0)) = 0 ;
+ badcol = find (badcol) ;
+
+ p1 (badrow) = badcol ;
+
+ % construct the older form of match1
+ match1 (badrow) = -p1 (badrow) ;
+ end
+ if (any (sort (p1) ~= 1:n))
+ error ('!!') ;
+ end
+
+ B = A (:,p1) ;
+
+ if (doplot)
+ subplot (2,4,2)
+ hold off
+ spy (B)
+ hold on
+ badcol = find (match1 < 0) ;
+ Junk = sparse (badcol, badcol, ones (length (badcol), 1), n, n) ;
+ % if (~isempty (A))
+ % spy (Junk, 'ro') ;
+ % end
+ title ('maxtrans') ;
+ end
+
+ d = nnz (diag (B)) ;
+ if (d ~= s1)
+ error ('bad sprank') ;
+ end
+ clear B
+
+ %-----------------------------------------------------------------------
+ % try p = dmperm(A)
+ skip_dmperm = any (j == skip_list_dmperm) ;
+
+ if (~skip_dmperm)
+ tic
+ match4 = dmperm (A) ;
+ t = toc ;
+ fprintf ('p=dmperm(A): %8.2f seconds\n', t) ;
+ s4 = sum (match4 > 0) ;
+ singular4 = (s4 < n) ;
+
+ if (doplot)
+ if (~singular4)
+ subplot (2,4,3)
+ spy (A (match4,:))
+ title ('dmperm') ;
+ end
+ end
+ if (singular ~= singular4)
+ error ('s4?') ;
+ end
+ if (s1 ~= s4)
+ error ('bad sprank') ;
+ end
+ else
+ fprintf ('p=dmperm(A): skip\n') ;
+ end
+
+ %-----------------------------------------------------------------------
+ nblocks = -1 ;
+ skip_dmperm_btf = any (j == skip_list_dmperm_btf) ;
+ if (~skip_dmperm_btf)
+ % get btf form
+ tic
+ [pa,qa,ra,sa] = dmperm (A) ;
+ t = toc ;
+ fprintf ('[p,q,r,s]=dmperm(A): %8.2f seconds\n', t) ;
+ nblocks = length (ra) - 1 ;
+ fprintf ('nblocks: %d\n', nblocks) ;
+ if (~singular4)
+ checkbtf (A, pa, qa, ra) ;
+ if (doplot)
+ subplot (2,4,4)
+ drawbtf (A, pa, qa, ra)
+ title ('dmperm blocks')
+ end
+ end
+ else
+ fprintf ('[p,q,r,s]=dmperm(A): skip\n') ;
+ end
+
+ jumble = randperm (n) ;
+
+ %-----------------------------------------------------------------------
+ % try strongcomp, non-recursive version
+
+ %-------------------------------------------------------------------
+ % try strongcomp on original matrix
+ B = A (:,p1) ;
+ tic ;
+ [pb,rb] = strongcomp (B) ;
+ t = toc ;
+ fprintf ('strongcomp %8.2f seconds\n', t) ;
+ if (~singular & ~skip_dmperm_btf & (length (rb) ~= nblocks+1)) %#ok
+ error ('BTF:invalid (rb)') ;
+ end
+ checkbtf (B, pb, pb, rb) ;
+ if (doplot)
+ subplot (2,4,5)
+ drawbtf (B, pb, pb, rb) ;
+ title ('strongcomp') ;
+ end
+
+ %-------------------------------------------------------------------
+ % try btf on original matrix
+ tic ;
+ [pw,qw,rw] = btf (A) ;
+ t = toc ;
+ fprintf ('btf %8.2f seconds nblocks %d\n', ...
+ t, length (rw)-1) ;
+
+ if (any (pw ~= pb))
+ error ('pw') ;
+ end
+ if (any (rw ~= rb))
+ error ('rw') ;
+ end
+ if (any (abs (qw) ~= p1 (pw)))
+ error ('qw') ;
+ end
+ c = diag (A (pw,abs (qw))) ;
+ if (~singular & ~skip_dmperm_btf & (length (rw) ~= nblocks+1)) %#ok
+ error ('BTF:invalid (rw)') ;
+ end
+ checkbtf (A, pw, abs (qw), rw) ;
+
+ kbad = find (qw < 0) ;
+ kgood = find (qw > 0) ;
+ if (any (c (kbad) ~= 0))
+ error ('kbad') ;
+ end
+ if (any (c (kgood) == 0)) %#ok
+ error ('kgood') ;
+ end
+
+ if (doplot)
+ subplot (2,4,6)
+ drawbtf (A, pw, abs (qw), rw) ;
+ if (n < 500)
+ for k = kbad
+ plot ([k (k+1) (k+1) k k]-.5, ...
+ [k k (k+1) (k+1) k]-.5, 'r') ;
+ end
+ end
+ title ('btf') ;
+ end
+
+ %-------------------------------------------------------------------
+ % try [p,q,r] = strongcomp (A, qin) form
+ tic
+ [pz,qz,rz] = strongcomp (A, match1) ;
+ t = toc ;
+ fprintf ('[p,q,r]=strongcomp(A,qin)%8.2f seconds\n', t) ;
+ if (any (pz ~= pb))
+ error ('pz') ;
+ end
+ if (any (rz ~= rb))
+ error ('rz') ;
+ end
+ if (any (abs (qz) ~= p1 (pz)))
+ error ('qz') ;
+ end
+ c = diag (A (pz,abs (qz))) ;
+ if (~singular & ~skip_dmperm_btf & (length (rz) ~= nblocks+1)) %#ok
+ error ('BTF:invalid (rz)') ;
+ end
+ checkbtf (A, pz, abs (qz), rz) ;
+
+ kbad = find (qz < 0) ;
+ kgood = find (qz > 0) ;
+ if (any (c (kbad) ~= 0))
+ error ('kbad') ;
+ end
+ if (any (c (kgood) == 0)) %#ok
+ error ('kgood') ;
+ end
+
+ if (doplot)
+ subplot (2,4,7)
+ drawbtf (A, pz, abs (qz), rz) ;
+ if (n < 500)
+ for k = kbad
+ plot ([k (k+1) (k+1) k k]-.5, ...
+ [k k (k+1) (k+1) k]-.5, 'r') ;
+ end
+ end
+ title ('strongcomp(A,qin)') ;
+ end
+
+ %-------------------------------------------------------------------
+ % try strongcomp again, on a randomly jumbled matrix
+ C = sparse (B (jumble, jumble)) ;
+ tic ;
+ [pc,rc] = strongcomp (C) ;
+ t = toc ;
+ fprintf ('strongcomp (rand) %8.2f seconds\n', t) ;
+ if (~singular & ~skip_dmperm_btf & (length (rc) ~= nblocks+1)) %#ok
+ error ('BTF:invalid (rc)') ;
+ end
+ checkbtf (C, pc, pc, rc) ;
+ if (doplot)
+ subplot (2,4,8)
+ drawbtf (C, pc, pc, rc) ;
+ title ('strongcomp(rand)') ;
+ end
+
+ if (length (rc) ~= length (rb))
+ error ('strongcomp random mismatch') ;
+ end
+
+ %-----------------------------------------------------------------------
+ if (doplot)
+ drawnow
+ end
+
+ if (matnum ~= nmat & dopause) %#ok
+ input ('Hit enter: ') ;
+ end
+
+ end
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
diff --git a/BTF/MATLAB/Test/test4.m b/BTF/MATLAB/Test/test4.m
new file mode 100644
index 0000000..4e82083
--- /dev/null
+++ b/BTF/MATLAB/Test/test4.m
@@ -0,0 +1,86 @@
+function test4 (nmat)
+%TEST4 test for BTF
+% Requires UFget
+% Example:
+% test4
+% See also btf, maxtrans, strongcomp, dmperm, UFget,
+% test1, test2, test3, test4, test5.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+index = UFget ;
+f = find (index.nrows == index.ncols) ;
+[ignore i] = sort (index.nnz (f)) ;
+f = f (i) ;
+
+% time intensive
+skip_costly = [1514 1297 1876 1301] ;
+f = setdiff (f, skip_costly) ;
+
+if (nargin < 1)
+ nmat = 1000 ;
+end
+nmat = min (nmat, length (f)) ;
+f = f (1:nmat) ;
+
+h = waitbar (0, 'BTF test 4 of 6') ;
+
+try
+ for k = 1:nmat
+
+ Prob = UFget (f (k), index) ;
+ A = Prob.A ;
+
+ waitbar (k/nmat, h) ;
+
+ for tr = [1 -1]
+
+ if (tr == -1)
+ AT = A' ;
+ [m n] = size (A) ;
+ if (m == n)
+ if (nnz (spones (AT) - spones (A)) == 0)
+ fprintf ('skip transpose\n') ;
+ continue ;
+ end
+ end
+ A = AT ;
+ end
+
+ tic
+ [p1,q1,r1,work1] = btf (A) ;
+ t1 = toc ;
+ n1 = length (r1) - 1 ;
+
+ tic
+ [p2,q2,r2,work2] = btf (A, 10) ;
+ t2 = toc ;
+ n2 = length (r2) - 1 ;
+
+ fprintf (...
+ '%4d %4d : %10.4f %8d %8g : %10.4f %8d %8g :', ...
+ k, f(k), t1, n1, work1, t2, n2, work2) ;
+ if (t2 ~= 0)
+ fprintf (' rel %8.4f %8.4f' , t1 / t2, n2 / (max (1, n1))) ;
+ end
+ fprintf ('\n') ;
+
+ if (n1 ~= n2 | work1 ~= work2) %#ok
+ disp (Prob) ;
+ fprintf ('^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n') ;
+ end
+
+ end
+ end
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
diff --git a/BTF/MATLAB/Test/test5.m b/BTF/MATLAB/Test/test5.m
new file mode 100644
index 0000000..97358ac
--- /dev/null
+++ b/BTF/MATLAB/Test/test5.m
@@ -0,0 +1,86 @@
+function test5 (nmat)
+%TEST5 test for BTF
+% Requires UFget
+% Example:
+% test5
+% See also btf, maxtrans, strongcomp, dmperm, UFget,
+% test1, test2, test3, test4, test5.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+index = UFget ;
+
+[ignore f] = sort (index.nnz) ;
+
+% time intensive
+skip_costly = [1514 1297 1876 1301] ;
+f = setdiff (f, skip_costly) ;
+
+if (nargin < 1)
+ nmat = 1000 ;
+end
+nmat = min (nmat, length (f)) ;
+f = f (1:nmat) ;
+
+h = waitbar (0, 'BTF test 5 of 6') ;
+
+try
+ for k = 1:nmat
+
+ i = f(k) ;
+ Prob = UFget (i, index) ;
+ A = Prob.A ;
+
+ waitbar (k/nmat, h) ;
+
+ for tr = [1 -1]
+
+ if (tr == -1)
+ AT = A' ;
+ [m n] = size (A) ;
+ if (m == n)
+ if (nnz (spones (AT) - spones (A)) == 0)
+ fprintf ('skip test with transpose\n') ;
+ continue ;
+ end
+ end
+ A = AT ;
+ end
+
+ tic
+ q1 = maxtrans (A) ;
+ t1 = toc ;
+ r1 = sum (q1 > 0) ;
+
+ tic
+ q2 = maxtrans (A, 10) ;
+ t2 = toc ;
+ r2 = sum (q2 > 0) ;
+
+ fprintf (...
+ '%4d %4d : %10.4f %8d : %10.4f %8d', k, f(k), t1, r1, t2, r2) ;
+ fprintf (' rel sprank %8.4f', r2 / (max (1, r1))) ;
+ if (t2 ~= 0)
+ fprintf (': rel time %8.4f', t1 / t2) ;
+ end
+ fprintf ('\n') ;
+
+ if (r1 ~= r2)
+ disp (Prob) ;
+ fprintf ('^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n') ;
+ end
+
+ end
+ end
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
diff --git a/BTF/MATLAB/Test/test6.m b/BTF/MATLAB/Test/test6.m
new file mode 100644
index 0000000..c27ca82
--- /dev/null
+++ b/BTF/MATLAB/Test/test6.m
@@ -0,0 +1,138 @@
+function test6
+%TEST6 test for BTF
+% Requires UFget
+% Example:
+% test6
+% See also btf, maxtrans, strongcomp, dmperm, UFget,
+% test1, test2, test3, test4, test5.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+quick2 = [ ...
+ 1522 -272 1463 1521 460 1507 -838 1533 -1533 -1456 -1512 734 211 ...
+ -385 -735 394 -397 1109 -744 ...
+ -734 -375 -1200 -1536 -837 519 -519 520 -520 189 -189 454 385 ...
+ 387 -387 384 -384 386 -386 388 -388 525 -525 526 -526 735 ...
+ 1508 209 210 1243 -1243 1534 -840 1234 -1234 390 -390 392 -392 ...
+ -394 1472 1242 -1242 389 -389 391 -391 393 -393 1215 -1215 1216 ...
+-1216 736 -736 737 -737 455 -455 -224 -839 1426 -1426 -1473 396 ...
+ -396 398 -398 400 -400 402 -402 404 -404 -1531 395 -395 397 ...
+ 399 -399 401 -401 403 -403 405 -405 -738 -739 1459 -1459 1111 ...
+ 1110 376 -376 284 -284 -740 -742 -741 -743 1293 -1293 452 920 ...
+ -745 -446 1462 -1461 448 -448 283 -283 1502 -1502 1292 -1292 1503 ...
+-1503 1291 -1291 445 -445 -746 -747 1300 -1300 435 -435 -1343 -1345 ...
+-1344 1305 -1305 921 -1513 1307 -1307 1369 -1369 1374 -1374 1377 ...
+-1377 748 -748 -749 1510 922 -922 ] ;
+
+index = UFget ;
+nmat = length (quick2) ;
+dopause = 0 ;
+
+h = waitbar (0, 'BTF test 6 of 6') ;
+
+try
+
+ for k = 1:nmat
+
+ waitbar (k/nmat, h) ;
+
+ i = quick2 (k) ;
+ Prob = UFget (abs (i), index) ;
+ disp (Prob) ;
+ if (i < 0)
+ fprintf ('transposed\n') ;
+ A = Prob.A' ;
+ [m n] = size (A) ;
+ if (m == n)
+ if (nnz (spones (A) - spones (Prob.A)) == 0)
+ fprintf ('skip...\n') ;
+ continue ;
+ end
+ end
+ else
+ A = Prob.A ;
+ end
+
+ tic
+ [p1,q1,r1,work1] = btf (A) ;
+ t1 = toc ;
+ n1 = length (r1) - 1 ;
+ m1 = nnz (diag (A (p1, abs (q1)))) ;
+
+ limit = work1/nnz(A) ;
+
+ fprintf ('full search: %g * nnz(A)\n', limit) ;
+
+ works = linspace(0,limit,9) ;
+ works (1) = eps ;
+ nw = length (works) ;
+
+ T2 = zeros (nw, 1) ;
+ N2 = zeros (nw, 1) ;
+ M2 = zeros (nw, 1) ;
+
+ T2 (end) = t1 ;
+ N2 (end) = n1 ;
+ M2 (end) = m1 ;
+
+ fprintf ('full time %10.4f blocks %8d nnz(diag) %8d\n\n', t1, n1, m1) ;
+
+ subplot (3,4,4) ;
+ drawbtf (A, p1, abs (q1), r1) ;
+ title (Prob.name, 'Interpreter', 'none') ;
+
+ for j = 1:nw-1
+
+ maxwork = works (j) ;
+
+ tic
+ [p2,q2,r2,work2] = btf (A, maxwork) ;
+ t2 = toc ;
+ n2 = length (r2) - 1 ;
+ m2 = nnz (diag (A (p2, abs (q2)))) ;
+ T2 (j) = t2 ;
+ N2 (j) = n2 ;
+ M2 (j) = m2 ;
+
+ fprintf ('%9.1f %10.4f blocks %8d nnz(diag) %8d\n', ...
+ maxwork, t2, n2, m2) ;
+
+ subplot (3,4,4+j) ;
+ drawbtf (A, p2, abs (q2), r2) ;
+ title (sprintf ('%g', maxwork)) ;
+
+ ss = [1:j nw] ;
+
+ subplot (3,4,1) ;
+ plot (works(ss), T2(ss), 'o-') ; title ('time vs work') ;
+ axis ([0 limit 0 max(0.1,max(T2))]) ;
+
+ subplot (3,4,2) ;
+ plot (works(ss), N2(ss), 'o-') ; title ('blocks vs work') ;
+ axis ([0 limit 0 n1]) ;
+
+ subplot (3,4,3) ;
+ plot (works(ss), M2(ss), 'o-') ; title ('nnz(diag) vs work') ;
+ axis ([0 limit 0 m1]) ;
+ drawnow
+
+ end
+ fprintf ('full time %10.4f blocks %8d nnz(diag) %8d\n', t1, n1, m1) ;
+
+ if (dopause)
+ input ('hit enter: ') ;
+ end
+
+ end
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
diff --git a/BTF/MATLAB/btf.c b/BTF/MATLAB/btf.c
new file mode 100644
index 0000000..79d1ba2
--- /dev/null
+++ b/BTF/MATLAB/btf.c
@@ -0,0 +1,144 @@
+/* ========================================================================== */
+/* === btf mexFunction ====================================================== */
+/* ========================================================================== */
+
+/* BTF: Permute a square matrix to upper block triangular form with a zero-free
+ * diagonal, or with a maximum number of nonzeros along the diagonal if a
+ * zero-free permutation does not exist.
+ *
+ * Usage:
+ *
+ * [p,q,r] = btf (A) ;
+ * [p,q,r] = btf (A, maxwork) ;
+ *
+ * If the matrix has structural full rank, this is essentially identical to
+ *
+ * [p,q,r] = dmperm (A)
+ *
+ * except that p, q, and r will differ in trivial ways. Both return an upper
+ * block triangular form with a zero-free diagonal, if the matrix is
+ * structurally non-singular. The number and sizes of the blocks will be
+ * identical, but the order of the blocks, and the ordering within the blocks,
+ * can be different.
+ *
+ * If the matrix is structurally singular, q will contain negative entries.
+ * The permuted matrix is C = A(p,abs(q)), and find(q<0) gives a list of
+ * indices of the diagonal of C that are equal to zero. This differs from
+ * dmperm, which does not place the maximum matching along the main diagonal
+ * of C=A(p,q), but places it above the diagonal instead.
+ *
+ * See maxtrans, or btf.m, for a description of maxwork.
+ *
+ * An optional fourth output [p,q,r,work] = btf (...) returns the amount of
+ * work performed, or -1 if the maximum work limit is reached (in which case
+ * the maximum matching might not have been found).
+ *
+ * Copyright (c) 2004-2007. Tim Davis, University of Florida,
+ * with support from Sandia National Laboratories. All Rights Reserved.
+ *
+ * See also maxtrans, strongcomp, dmperm
+ */
+
+/* ========================================================================== */
+
+#include "mex.h"
+#include "btf.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double work, maxwork ;
+ UF_long b, n, k, *Ap, *Ai, *P, *R, nblocks, *Work, *Q, nmatch ;
+ double *Px, *Rx, *Qx, *w ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs and allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin < 1 || nargin > 2 || nargout > 4)
+ {
+ mexErrMsgTxt ("Usage: [p,q,r] = btf (A)") ;
+ }
+ n = mxGetM (pargin [0]) ;
+ if (!mxIsSparse (pargin [0]) || n != mxGetN (pargin [0]))
+ {
+ mexErrMsgTxt ("btf: A must be sparse, square, and non-empty") ;
+ }
+
+ /* get sparse matrix A */
+ Ap = (UF_long *) mxGetJc (pargin [0]) ;
+ Ai = (UF_long *) mxGetIr (pargin [0]) ;
+
+ /* get output arrays */
+ Q = mxMalloc (n * sizeof (UF_long)) ;
+ P = mxMalloc (n * sizeof (UF_long)) ;
+ R = mxMalloc ((n+1) * sizeof (UF_long)) ;
+
+ /* get workspace */
+ Work = mxMalloc (5*n * sizeof (UF_long)) ;
+
+ maxwork = 0 ;
+ if (nargin > 1)
+ {
+ maxwork = mxGetScalar (pargin [1]) ;
+ }
+ work = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the permutation to BTF */
+ /* ---------------------------------------------------------------------- */
+
+ nblocks = btf_l_order (n, Ap, Ai, maxwork, &work, P, Q, R, &nmatch, Work) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create outputs and free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* create P */
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ Px = mxGetPr (pargout [0]) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Px [k] = P [k] + 1 ; /* convert to 1-based */
+ }
+
+ /* create Q */
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ Qx = mxGetPr (pargout [1]) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Qx [k] = Q [k] + 1 ; /* convert to 1-based */
+ }
+ }
+
+ /* create R */
+ if (nargout > 2)
+ {
+ pargout [2] = mxCreateDoubleMatrix (1, nblocks+1, mxREAL) ;
+ Rx = mxGetPr (pargout [2]) ;
+ for (b = 0 ; b <= nblocks ; b++)
+ {
+ Rx [b] = R [b] + 1 ; /* convert to 1-based */
+ }
+ }
+
+ /* create work output */
+ if (nargout > 3)
+ {
+ pargout [3] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ w = mxGetPr (pargout [3]) ;
+ w [0] = work ;
+ }
+
+ mxFree (P) ;
+ mxFree (R) ;
+ mxFree (Work) ;
+ mxFree (Q) ;
+}
diff --git a/BTF/MATLAB/btf.m b/BTF/MATLAB/btf.m
new file mode 100644
index 0000000..14d7ac4
--- /dev/null
+++ b/BTF/MATLAB/btf.m
@@ -0,0 +1,38 @@
+function [p,q,r] = btf (A) %#ok
+%BTF permute a square sparse matrix into upper block triangular form
+% with a zero-free diagonal, or with a maximum number of nonzeros along the
+% diagonal if a zero-free permutation does not exist.
+%
+% Example:
+% [p,q,r] = btf (A) ;
+% [p,q,r] = btf (A,maxwork) ;
+%
+% If the matrix has structural full rank, this is essentially identical to
+%
+% [p,q,r] = dmperm (A)
+%
+% except that p, q, and r will differ in trivial ways. Both return an upper
+% block triangular form with a zero-free diagonal, if the matrix is
+% structurally non-singular. The number and sizes of the blocks will be
+% identical, but the order of the blocks, and the ordering within the blocks,
+% can be different.
+%
+% If the matrix is structurally singular, the q from btf will contain negative
+% entries. The permuted matrix is C = A(p,abs(q)), and find(q<0) gives a list
+% of indices of the diagonal of C that are equal to zero. This differs from
+% dmperm, which does not place the maximum matching along the main diagonal
+% of C=A(p,q), but places it above the diagonal instead.
+%
+% The second input limits the maximum amount of work the function does to
+% be maxwork*nnz(A), or no limit at all if maxwork <= 0. If the function
+% terminates early as a result, a maximum matching may not be found, and the
+% diagonal of A(p,abs(q)) might not have the maximum number of nonzeros
+% possible. Also, the number of blocks (length(r)-1) may be larger than
+% what btf(A) or dmperm(A) would compute.
+%
+% See also maxtrans, strongcomp, dmperm, sprank
+
+% Copyright 2004-2007, Tim Davis, University of Florida
+% with support from Sandia National Laboratories. All Rights Reserved.
+
+error ('btf mexFunction not found') ;
diff --git a/BTF/MATLAB/btf_demo.m b/BTF/MATLAB/btf_demo.m
new file mode 100644
index 0000000..8f2e7d4
--- /dev/null
+++ b/BTF/MATLAB/btf_demo.m
@@ -0,0 +1,48 @@
+%BTF_DEMO demo for BTF
+%
+% Example:
+% btf_demo
+%
+% See also btf, dmperm, strongcomp, maxtrans
+
+% Copyright 2004-2007, Tim Davis, University of Florida
+
+load west0479 ;
+A = west0479 ;
+
+figure (1)
+clf
+
+subplot (2,3,1) ;
+spy (A)
+title ('west0479') ;
+
+subplot (2,3,2) ;
+[p, q, r] = btf (A) ;
+% spy (A (p, abs(q))) ;
+drawbtf (A, p, q, r) ;
+title ('btf') ;
+
+fprintf ('\nbtf_demo: n %d nnz(A) %d # of blocks %d\n', ...
+ size (A,1), nnz (A), length (r) - 1) ;
+
+subplot (2,3,3) ;
+[p, q, r, s] = dmperm (A) ;
+drawbtf (A, p, q, r) ;
+title ('dmperm btf')
+
+subplot (2,3,4) ;
+[p, r] = strongcomp (A) ;
+% spy (A (p, abs(q))) ;
+drawbtf (A, p, p, r) ;
+title ('strongly conn. comp.') ;
+
+subplot (2,3,5) ;
+q = maxtrans (A) ;
+spy (A (:,q))
+title ('max transversal') ;
+
+subplot (2,3,6) ;
+p = dmperm (A) ;
+spy (A (p,:))
+title ('dmperm maxtrans') ;
diff --git a/BTF/MATLAB/btf_install.m b/BTF/MATLAB/btf_install.m
new file mode 100644
index 0000000..4507c6b
--- /dev/null
+++ b/BTF/MATLAB/btf_install.m
@@ -0,0 +1,17 @@
+function btf_install
+%BTF_INSTALL compile and install BTF for use in MATLAB.
+% Your current working directory must be BTF/MATLAB for this function to work.
+%
+% Example:
+% btf_install
+%
+% See also btf, maxtrans, stroncomp, dmperm.
+
+% Copyright 2004-2007, Tim Davis, University of Florida
+
+btf_make
+addpath (pwd) ;
+fprintf ('BTF has been compiled and installed. The path:\n') ;
+disp (pwd) ;
+fprintf ('has been added to your path. Use pathtool to add it permanently.\n');
+btf_demo
diff --git a/BTF/MATLAB/btf_make.m b/BTF/MATLAB/btf_make.m
new file mode 100644
index 0000000..a0c105d
--- /dev/null
+++ b/BTF/MATLAB/btf_make.m
@@ -0,0 +1,37 @@
+function btf_make
+%BTF_MAKE compile BTF for use in MATLAB
+% Your current working directory must be BTF/MATLAB for this function to work.
+%
+% Example:
+% btf_make
+%
+% See also btf, maxtrans, stroncomp, dmperm.
+
+% Copyright 2004-2007, Tim Davis, University of Florida
+
+details = 0 ; % if 1, print details of each command
+
+mexcmd = 'mex -O -DDLONG -I../Include -I../../UFconfig ' ;
+if (~isempty (strfind (computer, '64')))
+ mexcmd = [mexcmd '-largeArrayDims '] ;
+end
+
+s = [mexcmd 'maxtrans.c ../Source/btf_maxtrans.c'] ;
+if (details)
+ fprintf ('%s\n', s) ;
+end
+eval (s) ;
+
+s = [mexcmd 'strongcomp.c ../Source/btf_strongcomp.c'] ;
+if (details)
+ fprintf ('%s\n', s) ;
+end
+eval (s) ;
+
+s = [mexcmd 'btf.c ../Source/btf_maxtrans.c ../Source/btf_strongcomp.c ../Source/btf_order.c'] ;
+if (details)
+ fprintf ('%s\n', s) ;
+end
+eval (s) ;
+
+fprintf ('BTF successfully compiled.\n') ;
diff --git a/BTF/MATLAB/drawbtf.m b/BTF/MATLAB/drawbtf.m
new file mode 100644
index 0000000..55725b9
--- /dev/null
+++ b/BTF/MATLAB/drawbtf.m
@@ -0,0 +1,27 @@
+function drawbtf (A, p, q, r)
+%DRAWBTF plot the BTF form of a matrix
+%
+% A(p,q) is in BTF form, r the block boundaries
+%
+% Example:
+% [p,q,r] = dmperm (A)
+% drawbtf (A, p, q, r)
+%
+% See also btf, maxtrans, strongcomp, dmperm.
+
+% Copyright 2004-2007, Tim Davis, University of Florida
+
+nblocks = length (r) - 1 ;
+
+hold off
+spy (A (p,abs(q)))
+hold on
+
+for k = 1:nblocks
+ k1 = r (k) ;
+ k2 = r (k+1) ;
+ nk = k2 - k1 ;
+ if (nk > 1)
+ plot ([k1 k2 k2 k1 k1]-.5, [k1 k1 k2 k2 k1]-.5, 'r') ;
+ end
+end
diff --git a/BTF/MATLAB/maxtrans.c b/BTF/MATLAB/maxtrans.c
new file mode 100644
index 0000000..f89c2e8
--- /dev/null
+++ b/BTF/MATLAB/maxtrans.c
@@ -0,0 +1,101 @@
+/* ========================================================================== */
+/* === maxtrans mexFunction ================================================= */
+/* ========================================================================== */
+
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+/* MAXTRANS: Find a column permutation for a zero-free diagonal.
+ *
+ * Usage:
+ *
+ * q = maxtrans (A) ;
+ * q = maxtrans (A,maxwork) ;
+ *
+ * A (:,q) has a zero-free diagonal if sprank(A) == n.
+ * If the matrix is structurally singular, q will contain zeros. Similar
+ * to p = dmperm (A), except that dmperm returns a row permutation.
+ *
+ * An optional second output [q,work] = maxtrans (...) returns the amount of
+ * work performed, or -1 if the maximum work limit is reached (in which case
+ * the maximum matching might not have been found).
+ *
+ * Copyright (c) 2004-2007. Tim Davis, University of Florida,
+ * with support from Sandia National Laboratories. All Rights Reserved.
+ */
+
+/* ========================================================================== */
+
+#include "mex.h"
+#include "btf.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double maxwork, work ;
+ UF_long nrow, ncol, i, *Ap, *Ai, *Match, nmatch, *Work ;
+ double *Matchx, *w ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs and allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin < 1 || nargin > 2 || nargout > 2)
+ {
+ mexErrMsgTxt ("Usage: q = maxtrans (A)") ;
+ }
+ nrow = mxGetM (pargin [0]) ;
+ ncol = mxGetN (pargin [0]) ;
+ if (!mxIsSparse (pargin [0]))
+ {
+ mexErrMsgTxt ("maxtrans: A must be sparse, and non-empty") ;
+ }
+
+ /* get sparse matrix A */
+ Ap = (UF_long *) mxGetJc (pargin [0]) ;
+ Ai = (UF_long *) mxGetIr (pargin [0]) ;
+
+ /* get output array */
+ Match = mxMalloc (nrow * sizeof (UF_long)) ;
+
+ /* get workspace of size 5n (recursive version needs only 2n) */
+ Work = mxMalloc (5*ncol * sizeof (UF_long)) ;
+
+ maxwork = 0 ;
+ if (nargin > 1)
+ {
+ maxwork = mxGetScalar (pargin [1]) ;
+ }
+ work = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* perform the maximum transversal */
+ /* ---------------------------------------------------------------------- */
+
+ nmatch = btf_l_maxtrans (nrow, ncol, Ap, Ai, maxwork, &work, Match, Work) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create outputs and free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = mxCreateDoubleMatrix (1, nrow, mxREAL) ;
+ Matchx = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Matchx [i] = Match [i] + 1 ; /* convert to 1-based */
+ }
+
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ w = mxGetPr (pargout [1]) ;
+ w [0] = work ;
+ }
+
+ mxFree (Work) ;
+ mxFree (Match) ;
+}
diff --git a/BTF/MATLAB/maxtrans.m b/BTF/MATLAB/maxtrans.m
new file mode 100644
index 0000000..1fad193
--- /dev/null
+++ b/BTF/MATLAB/maxtrans.m
@@ -0,0 +1,30 @@
+function q = maxtrans (A) %#ok
+%MAXTRANS permute the columns of a sparse matrix so it has a zero-free diagonal
+% (if it exists). If no zero-free diagonal exists, then a maximum matching is
+% found. Note that this differs from p=dmperm(A), which returns a row
+% permutation.
+%
+% Example:
+% q = maxtrans (A)
+% q = maxtrans (A,maxwork)
+%
+% If row i and column j are matched, then q(i) = j. Otherwise, if row is
+% unmatched, then q(i) = 0. This is similar to dmperm, except that
+% p = dmperm(A) returns p(j)=i if row i and column j are matched, or p(j)=0 if
+% column j is unmatched.
+%
+% If A is structurally nonsingular, then A(:,maxtrans(A)) has a zero-free
+% diagonal, as does A (dmperm(A),:).
+%
+% The second input limits the maximum amount of work the function does
+% (excluding the O(nnz(A)) cheap match phase) to be maxwork*nnz(A), or no limit
+% at all if maxwork <= 0. If the function terminates early as a result, a
+% maximum matching may not be found. An optional second output
+% [q,work] = maxtrans (...) returns the amount of work performed, or -1 if the
+% maximum work limit is reached.
+%
+% See also: btf, strongcomp, dmperm, sprank
+
+% Copyright 2004-2007, Tim Davis, University of Florida
+
+error ('maxtrans mexfunction not found') ;
diff --git a/BTF/MATLAB/strongcomp.c b/BTF/MATLAB/strongcomp.c
new file mode 100644
index 0000000..16d7dc3
--- /dev/null
+++ b/BTF/MATLAB/strongcomp.c
@@ -0,0 +1,179 @@
+/* ========================================================================== */
+/* === stongcomp mexFunction ================================================ */
+/* ========================================================================== */
+
+/* STRONGCOMP: Find a symmetric permutation to upper block triangular form of
+ * a sparse square matrix.
+ *
+ * Usage:
+ *
+ * [p,r] = strongcomp (A) ;
+ *
+ * [p,q,r] = strongcomp (A,qin) ;
+ *
+ * In the first usage, the permuted matrix is C = A (p,p). In the second usage,
+ * the matrix A (:,qin) is symmetrically permuted to upper block triangular
+ * form, where qin is an input column permutation, and the final permuted
+ * matrix is C = A (p,q). This second usage is equivalent to
+ *
+ * [p,r] = strongcomp (A (:,qin)) ;
+ * q = qin (p) ;
+ *
+ * That is, if qin is not present it is assumed to be qin = 1:n.
+ *
+ * C is the permuted matrix, with a number of blocks equal to length(r)-1.
+ * The kth block is from row/col r(k) to row/col r(k+1)-1 of C.
+ * r(1) is one and the last entry in r is equal to n+1.
+ * The diagonal of A (or A (:,qin)) is ignored.
+ *
+ * strongcomp is normally proceeded by a maximum transversal:
+ *
+ * [p,q,r] = strongcomp (A, maxtrans (A))
+ *
+ * if the matrix has full structural rank. This is identical to
+ *
+ * [p,q,r] = btf (A)
+ *
+ * (except that btf handles the case when A is structurally rank-deficient).
+ * It essentially the same as
+ *
+ * [p,q,r] = dmperm (A)
+ *
+ * except that p, q, and r will differ between btf and dmperm. Both return an
+ * upper block triangular form with a zero-free diagonal. The number and sizes
+ * of the blocks will be identical, but the order of the blocks, and the
+ * ordering within the blocks, can be different. For structurally rank
+ * deficient matrices, dmpmerm returns the maximum matching as a zero-free
+ * diagonal that is above the main diagonal; btf always returns the matching as
+ * the main diagonal (which will thus contain zeros).
+ *
+ * Copyright (c) 2004-2007. Tim Davis, University of Florida,
+ * with support from Sandia National Laboratories. All Rights Reserved.
+ *
+ * See also maxtrans, btf, dmperm
+ */
+
+/* ========================================================================== */
+
+#include "mex.h"
+#include "btf.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout[],
+ int nargin,
+ const mxArray *pargin[]
+)
+{
+ UF_long b, n, i, k, j, *Ap, *Ai, *P, *R, nblocks, *Work, *Q, jj ;
+ double *Px, *Rx, *Qx ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs and allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ if (!((nargin == 1 && nargout <= 2) || (nargin == 2 && nargout <= 3)))
+ {
+ mexErrMsgTxt ("Usage: [p,r] = strongcomp (A)"
+ " or [p,q,r] = strongcomp (A,qin)") ;
+ }
+ n = mxGetM (pargin [0]) ;
+ if (!mxIsSparse (pargin [0]) || n != mxGetN (pargin [0]))
+ {
+ mexErrMsgTxt ("strongcomp: A must be sparse, square, and non-empty") ;
+ }
+
+ /* get sparse matrix A */
+ Ap = (UF_long *) mxGetJc (pargin [0]) ;
+ Ai = (UF_long *) mxGetIr (pargin [0]) ;
+
+ /* get output arrays */
+ P = mxMalloc (n * sizeof (UF_long)) ;
+ R = mxMalloc ((n+1) * sizeof (UF_long)) ;
+
+ /* get workspace of size 4n (recursive code only needs 2n) */
+ Work = mxMalloc (4*n * sizeof (UF_long)) ;
+
+ /* get the input column permutation Q */
+ if (nargin == 2)
+ {
+ if (mxGetNumberOfElements (pargin [1]) != n)
+ {
+ mexErrMsgTxt
+ ("strongcomp: qin must be a permutation vector of size n") ;
+ }
+ Qx = mxGetPr (pargin [1]) ;
+ Q = mxMalloc (n * sizeof (UF_long)) ;
+ /* connvert Qin to 0-based and check validity */
+ for (i = 0 ; i < n ; i++)
+ {
+ Work [i] = 0 ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ j = Qx [k] - 1 ; /* convert to 0-based */
+ jj = BTF_UNFLIP (j) ;
+ if (jj < 0 || jj >= n || Work [jj] == 1)
+ {
+ mexErrMsgTxt
+ ("strongcomp: qin must be a permutation vector of size n") ;
+ }
+ Work [jj] = 1 ;
+ Q [k] = j ;
+ }
+ }
+ else
+ {
+ /* no input column permutation */
+ Q = (UF_long *) NULL ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the strongly-connected components of A */
+ /* ---------------------------------------------------------------------- */
+
+ nblocks = btf_l_strongcomp (n, Ap, Ai, Q, P, R, Work) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create outputs and free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* create P */
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ Px = mxGetPr (pargout [0]) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Px [k] = P [k] + 1 ; /* convert to 1-based */
+ }
+
+ /* create Q */
+ if (nargin == 2 && nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ Qx = mxGetPr (pargout [1]) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Qx [k] = Q [k] + 1 ; /* convert to 1-based */
+ }
+ }
+
+ /* create R */
+ if (nargout == nargin + 1)
+ {
+ pargout [nargin] = mxCreateDoubleMatrix (1, nblocks+1, mxREAL) ;
+ Rx = mxGetPr (pargout [nargin]) ;
+ for (b = 0 ; b <= nblocks ; b++)
+ {
+ Rx [b] = R [b] + 1 ; /* convert to 1-based */
+ }
+ }
+
+ mxFree (P) ;
+ mxFree (R) ;
+ mxFree (Work) ;
+ if (nargin == 2)
+ {
+ mxFree (Q) ;
+ }
+}
diff --git a/BTF/MATLAB/strongcomp.m b/BTF/MATLAB/strongcomp.m
new file mode 100644
index 0000000..86546db
--- /dev/null
+++ b/BTF/MATLAB/strongcomp.m
@@ -0,0 +1,45 @@
+function [p,q,r] = strongcomp (A, qin) %#ok
+%STRONGCOMP symmetric permutation to upper block triangular form
+% The matrix must be sparse and square.
+%
+% Example:
+% [p,r] = strongcomp (A) ;
+% [p,q,r] = strongcomp (A,qin) ;
+%
+% In the first usage, the permuted matrix is C = A (p,p). In the second usage,
+% the matrix A (:,qin) is symmetrically permuted to upper block triangular
+% form, where qin is an input column permutation, and the final permuted
+% matrix is C = A (p,q). This second usage is equivalent to
+%
+% [p,r] = strongcomp (A (:,qin)) ;
+% q = qin (p) ;
+%
+% That is, if qin is not present it is assumed to be qin = 1:n.
+%
+% C is the permuted matrix, with a number of blocks equal to length(r)-1.
+% The kth block is from row/col r(k) to row/col r(k+1)-1 of C.
+% r(1) is one and the last entry in r is equal to n+1.
+% The diagonal of A (or A (:,qin)) is ignored.
+%
+% strongcomp is normally proceeded by a maximum transversal.
+% Assuming A is square and structurally nonsingular,
+%
+% [p,q,r] = strongcomp (A, maxtrans (A))
+%
+% is essentially identical to
+%
+% [p,q,r] = dmperm (A)
+%
+% except that p, q, and r will differ. Both return an upper block triangular
+% form with a zero-free diagonal. The number and sizes of the blocks will be
+% identical, but the order of the blocks, and the ordering within the blocks,
+% can be different. If the matrix is structurally singular, both strongcomp
+% and maxtrans return a vector q containing negative entries. abs(q) is a
+% permutation of 1:n, and find(q<0) gives a list of the indices of the
+% diagonal of A(p,q) that are zero.
+%
+% See also btf, maxtrans, dmperm
+
+% Copyright 2004-2007, Tim Davis, University of Florida
+
+error ('strongcomp mexFunction not found') ;
diff --git a/BTF/Makefile b/BTF/Makefile
new file mode 100644
index 0000000..796d8c1
--- /dev/null
+++ b/BTF/Makefile
@@ -0,0 +1,18 @@
+default: library
+
+include ../UFconfig/UFconfig.mk
+
+library:
+ ( cd Lib ; $(MAKE) )
+
+clean:
+ ( cd Lib ; $(MAKE) clean )
+
+distclean:
+ ( cd Lib ; $(MAKE) distclean )
+ ( cd MATLAB ; $(MAKE) distclean )
+
+mex:
+ ( cd MATLAB ; $(MAKE) )
+
+purge: distclean
diff --git a/BTF/README.txt b/BTF/README.txt
new file mode 100644
index 0000000..efc84f8
--- /dev/null
+++ b/BTF/README.txt
@@ -0,0 +1,109 @@
+BTF Version 1.0, May 31, 2007, by Timothy A. Davis
+Copyright (C) 2004-2007, University of Florida
+BTF is also available under other licenses; contact the author for details.
+http://www.cise.ufl.edu/research/sparse
+
+BTF is a software package for permuting a matrix into block upper triangular
+form. It includes a maximum transversal algorithm, which finds a permutation
+of a square or rectangular matrix so that it has a zero-free diagonal (if one
+exists); otherwise, it finds a maximal matching which maximizes the number of
+nonzeros on the diagonal. The package also includes a method for finding the
+strongly connected components of a graph. These two methods together give the
+permutation to block upper triangular form.
+
+Requires UFconfig, in the ../UFconfig directory relative to this directory.
+KLU relies on this package to permute
+
+To compile the libbtf.a library, type "make". The compiled library is located
+in BTF/Lib/libbtf.a. Compile code that uses BTF with -IBTF/Include.
+
+Type "make clean" to remove all but the compiled library, and "make distclean"
+to remove all files not in the original distribution.
+
+This package does not include a statement coverage test (Tcov directory) or
+demo program (Demo directory). See the KLU package for both. The BTF package
+does include a MATLAB interface, a MATLAB test suite (in the MATLAB/Test
+directory), and a MATLAB demo.
+
+See BTF/Include/btf.h for documentation on how to use the C-callable functions.
+Use "help btf", "help maxtrans" and "help strongcomp" in MATLAB, for details on
+how to use the MATLAB-callable functions. Additional details on the use of BTF
+are given in the KLU User Guide, normally in ../KLU/Doc/KLU_UserGuide.pdf
+relative to this directory.
+
+--------------------------------------------------------------------------------
+
+BTF is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+--------------------------------------------------------------------------------
+
+A full text of the license is in Doc/lesser.txt.
+
+--------------------------------------------------------------------------------
+
+Files and directories in the BTF package:
+
+ Doc documentation and license
+ Include include files
+ Lib compiled BTF library
+ Makefile Makefile for C and MATLAB versions
+ MATLAB MATLAB interface
+ README.txt this file
+ Source BTF source code
+
+./Doc:
+
+ ChangeLog changes in BTF
+ lesser.txt license
+
+./Include:
+
+ btf.h primary user include file
+ btf_internal.h internal include file, not for user programs
+
+./Lib:
+
+ Makefile Makefile for C library
+
+./MATLAB:
+
+ btf.c btf mexFunction
+ btf_install.m compile and install BTF for use in MATLAB
+ btf.m btf help
+ Contents.m contents of MATLAB interface
+ Makefile Makefile for MATLAB functions
+ maxtrans.c maxtrans mexFunction
+ maxtrans.m maxtrans help
+ strongcomp.c strongcomp mexFunction
+ strongcomp.m strongcomp help
+ Test MATLAB test directory
+
+./MATLAB/Test:
+
+ checkbtf.m check a BTF ordering
+ drawbtf.m plot a BTF ordering
+ test1.m compare maxtrans and cs_dmperm
+ test2.m compare btf and cs_dmperm
+ test3.m extensive test (maxtrans, strongcomp, and btf)
+ test4b.m test btf maxwork option
+ test4.m test btf maxwork option
+ test5.m test maxtrans maxwork option
+
+./Source:
+
+ btf_maxtrans.c btf_maxtrans C function
+ btf_order.c btf_order C function
+ btf_strongcomp.c btf_strongcomp C function
+
diff --git a/BTF/Source/btf_maxtrans.c b/BTF/Source/btf_maxtrans.c
new file mode 100644
index 0000000..7583e71
--- /dev/null
+++ b/BTF/Source/btf_maxtrans.c
@@ -0,0 +1,387 @@
+/* ========================================================================== */
+/* === BTF_MAXTRANS ========================================================= */
+/* ========================================================================== */
+
+/* Finds a column permutation that maximizes the number of entries on the
+ * diagonal of a sparse matrix. See btf.h for more information.
+ *
+ * This function is identical to cs_maxtrans in CSparse, with the following
+ * exceptions:
+ *
+ * (1) cs_maxtrans finds both jmatch and imatch, where jmatch [i] = j and
+ * imatch [j] = i if row i is matched to column j. This function returns
+ * just jmatch (the Match array). The MATLAB interface to cs_maxtrans
+ * (the single-output cs_dmperm) returns imatch, not jmatch to the MATLAB
+ * caller.
+ *
+ * (2) cs_maxtrans includes a pre-pass that counts the number of non-empty
+ * rows and columns (m2 and n2, respectively), and computes the matching
+ * using the transpose of A if m2 < n2. cs_maxtrans also returns quickly
+ * if the diagonal of the matrix is already zero-free. This pre-pass
+ * allows cs_maxtrans to be much faster than maxtrans, if the use of the
+ * transpose is warranted.
+ *
+ * However, for square structurally non-singular matrices with one or more
+ * zeros on the diagonal, the pre-pass is a waste of time, and for these
+ * matrices, maxtrans can be twice as fast as cs_maxtrans. Since the
+ * maxtrans function is intended primarily for square matrices that are
+ * typically structurally nonsingular, the pre-pass is not included here.
+ * If this maxtrans function is used on a matrix with many more columns
+ * than rows, consider passing the transpose to this function, or use
+ * cs_maxtrans instead.
+ *
+ * (3) cs_maxtrans can operate as a randomized algorithm, to help avoid
+ * rare cases of excessive run-time.
+ *
+ * (4) this maxtrans function includes an option that limits the total work
+ * performed. If this limit is reached, the maximum transveral might not
+ * be found.
+ *
+ * Thus, for general usage, cs_maxtrans is preferred. For square matrices that
+ * are typically structurally non-singular, maxtrans is preferred. A partial
+ * maxtrans can still be very useful when solving a sparse linear system.
+ *
+ * Copyright (c) 2004-2007. Tim Davis, University of Florida,
+ * with support from Sandia National Laboratories. All Rights Reserved.
+ */
+
+#include "btf.h"
+#include "btf_internal.h"
+
+
+/* ========================================================================== */
+/* === augment ============================================================== */
+/* ========================================================================== */
+
+/* Perform a depth-first-search starting at column k, to find an augmenting
+ * path. An augmenting path is a sequence of row/column pairs (i1,k), (i2,j1),
+ * (i3,j2), ..., (i(s+1), js), such that all of the following properties hold:
+ *
+ * * column k is not matched to any row
+ * * entries in the path are nonzero
+ * * the pairs (i1,j1), (i2,j2), (i3,j3) ..., (is,js) have been
+ * previously matched to each other
+ * * (i(s+1), js) is nonzero, and row i(s+1) is not matched to any column
+ *
+ * Once this path is found, the matching can be changed to the set of pairs
+ * path. An augmenting path is a sequence of row/column pairs
+ *
+ * (i1,k), (i2,j1), (i3,j2), ..., (i(s+1), js)
+ *
+ * Once a row is matched with a column it remains matched with some column, but
+ * not necessarily the column it was first matched with.
+ *
+ * In the worst case, this function can examine every nonzero in A. Since it
+ * is called n times by maxtrans, the total time of maxtrans can be as high as
+ * O(n*nnz(A)). To limit this work, pass a value of maxwork > 0. Then at
+ * most O((maxwork+1)*nnz(A)) work will be performed; the maximum matching might
+ * not be found, however.
+ *
+ * This routine is very similar to the dfs routine in klu_kernel.c, in the
+ * KLU sparse LU factorization package. It is essentially identical to the
+ * cs_augment routine in CSparse, and its recursive version (augment function
+ * in cs_maxtransr_mex.c), except that this routine allows for the search to be
+ * terminated early if too much work is being performed.
+ *
+ * The algorithm is based on the paper "On Algorithms for obtaining a maximum
+ * transversal" by Iain Duff, ACM Trans. Mathematical Software, vol 7, no. 1,
+ * pp. 315-330, and "Algorithm 575: Permutations for a zero-free diagonal",
+ * same issue, pp. 387-390. The code here is a new implementation of that
+ * algorithm, with different data structures and control flow. After writing
+ * this code, I carefully compared my algorithm with MC21A/B (ACM Algorithm 575)
+ * Some of the comparisons are partial because I didn't dig deeply into all of
+ * the details of MC21A/B, such as how the stack is maintained. The following
+ * arguments are essentially identical between this code and MC21A:
+ *
+ * maxtrans MC21A,B
+ * -------- -------
+ * n N identical
+ * k JORD identical
+ * Ap IP column / row pointers
+ * Ai ICN row / column indices
+ * Ap[n] LICN length of index array (# of nonzeros in A)
+ * Match IPERM output column / row permutation
+ * nmatch NUMNZ # of nonzeros on diagonal of permuted matrix
+ * Flag CV mark a node as visited by the depth-first-search
+ *
+ * The following are different, but analogous:
+ *
+ * Cheap ARP indicates what part of the a column / row has
+ * already been matched.
+ *
+ * The following arguments are very different:
+ *
+ * - LENR # of entries in each row/column (unused in maxtrans)
+ * Pstack OUT Pstack keeps track of where we are in the depth-
+ * first-search scan of column j. I think that OUT
+ * plays a similar role in MC21B, but I'm unsure.
+ * Istack PR keeps track of the rows in the path. PR is a link
+ * list, though, whereas Istack is a stack. Maxtrans
+ * does not use any link lists.
+ * Jstack OUT? PR? the stack for nodes in the path (unsure)
+ *
+ * The following control structures are roughly comparable:
+ *
+ * maxtrans MC21B
+ * -------- -----
+ * for (k = 0 ; k < n ; k++) DO 100 JORD=1,N
+ * while (head >= 0) DO 70 K=1,JORD
+ * for (p = Cheap [j] ; ...) DO 20 II=IN1,IN2
+ * for (p = head ; ...) DO 90 K=1,JORD
+ */
+
+static Int augment
+(
+ Int k, /* which stage of the main loop we're in */
+ Int Ap [ ], /* column pointers, size n+1 */
+ Int Ai [ ], /* row indices, size nz = Ap [n] */
+ Int Match [ ], /* size n, Match [i] = j if col j matched to i */
+ Int Cheap [ ], /* rows Ai [Ap [j] .. Cheap [j]-1] alread matched */
+ Int Flag [ ], /* Flag [j] = k if j already visited this stage */
+ Int Istack [ ], /* size n. Row index stack. */
+ Int Jstack [ ], /* size n. Column index stack. */
+ Int Pstack [ ], /* size n. Keeps track of position in adjacency list */
+ double *work, /* work performed by the depth-first-search */
+ double maxwork /* maximum work allowed */
+)
+{
+ /* local variables, but "global" to all DFS levels: */
+ Int found ; /* true if match found. */
+ Int head ; /* top of stack */
+
+ /* variables that are purely local to any one DFS level: */
+ Int j2 ; /* the next DFS goes to node j2 */
+ Int pend ; /* one past the end of the adjacency list for node j */
+ Int pstart ;
+ Int quick ;
+
+ /* variables that need to be pushed then popped from the stack: */
+ Int i ; /* the row tentatively matched to i if DFS successful */
+ Int j ; /* the DFS is at the current node j */
+ Int p ; /* current index into the adj. list for node j */
+ /* the variables i, j, and p are stacked in Istack, Jstack, and Pstack */
+
+ quick = (maxwork > 0) ;
+
+ /* start a DFS to find a match for column k */
+ found = FALSE ;
+ i = EMPTY ;
+ head = 0 ;
+ Jstack [0] = k ;
+ ASSERT (Flag [k] != k) ;
+
+ while (head >= 0)
+ {
+ j = Jstack [head] ;
+ pend = Ap [j+1] ;
+
+ if (Flag [j] != k) /* a node is not yet visited */
+ {
+
+ /* -------------------------------------------------------------- */
+ /* prework for node j */
+ /* -------------------------------------------------------------- */
+
+ /* first time that j has been visited */
+ Flag [j] = k ;
+ /* cheap assignment: find the next unmatched row in col j. This
+ * loop takes at most O(nnz(A)) time for the sum total of all
+ * calls to augment. */
+ for (p = Cheap [j] ; p < pend && !found ; p++)
+ {
+ i = Ai [p] ;
+ found = (Match [i] == EMPTY) ;
+ }
+ Cheap [j] = p ;
+
+ /* -------------------------------------------------------------- */
+
+ /* prepare for DFS */
+ if (found)
+ {
+ /* end of augmenting path, column j matched with row i */
+ Istack [head] = i ;
+ break ;
+ }
+ /* set Pstack [head] to the first entry in column j to scan */
+ Pstack [head] = Ap [j] ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* quick return if too much work done */
+ /* ------------------------------------------------------------------ */
+
+ if (quick && *work > maxwork)
+ {
+ /* too much work has been performed; abort the search */
+ return (EMPTY) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* DFS for nodes adjacent to j */
+ /* ------------------------------------------------------------------ */
+
+ /* If cheap assignment not made, continue the depth-first search. All
+ * rows in column j are already matched. Add the adjacent nodes to the
+ * stack by iterating through until finding another non-visited node.
+ *
+ * It is the following loop that can force maxtrans to take
+ * O(n*nnz(A)) time. */
+
+ pstart = Pstack [head] ;
+ for (p = pstart ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ j2 = Match [i] ;
+ ASSERT (j2 != EMPTY) ;
+ if (Flag [j2] != k)
+ {
+ /* Node j2 is not yet visited, start a depth-first search on
+ * node j2. Keep track of where we left off in the scan of adj
+ * list of node j so we can restart j where we left off. */
+ Pstack [head] = p + 1 ;
+ /* Push j2 onto the stack and immediately break so we can
+ * recurse on node j2. Also keep track of row i which (if this
+ * search for an augmenting path works) will be matched with the
+ * current node j. */
+ Istack [head] = i ;
+ Jstack [++head] = j2 ;
+ break ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* determine how much work was just performed */
+ /* ------------------------------------------------------------------ */
+
+ *work += (p - pstart + 1) ;
+
+ /* ------------------------------------------------------------------ */
+ /* node j is done, but the postwork is postponed - see below */
+ /* ------------------------------------------------------------------ */
+
+ if (p == pend)
+ {
+ /* If all adjacent nodes of j are already visited, pop j from
+ * stack and continue. We failed to find a match. */
+ head-- ;
+ }
+ }
+
+ /* postwork for all nodes j in the stack */
+ /* unwind the path and make the corresponding matches */
+ if (found)
+ {
+ for (p = head ; p >= 0 ; p--)
+ {
+ j = Jstack [p] ;
+ i = Istack [p] ;
+
+ /* -------------------------------------------------------------- */
+ /* postwork for node j */
+ /* -------------------------------------------------------------- */
+ /* if found, match row i with column j */
+ Match [i] = j ;
+ }
+ }
+ return (found) ;
+}
+
+
+/* ========================================================================== */
+/* === maxtrans ============================================================= */
+/* ========================================================================== */
+
+Int BTF(maxtrans) /* returns # of columns in the matching */
+(
+ /* --- input --- */
+ Int nrow, /* A is nrow-by-ncol in compressed column form */
+ Int ncol,
+ Int Ap [ ], /* size ncol+1 */
+ Int Ai [ ], /* size nz = Ap [ncol] */
+ double maxwork, /* do at most maxwork*nnz(A) work; no limit if <= 0. This
+ * work limit excludes the O(nnz(A)) cheap-match phase. */
+
+ /* --- output --- */
+ double *work, /* work = -1 if maxwork > 0 and the total work performed
+ * reached the maximum of maxwork*nnz(A)).
+ * Otherwise, work = the total work performed. */
+
+ Int Match [ ], /* size nrow. Match [i] = j if column j matched to row i */
+
+ /* --- workspace --- */
+ Int Work [ ] /* size 5*ncol */
+)
+{
+ Int *Cheap, *Flag, *Istack, *Jstack, *Pstack ;
+ Int i, j, k, nmatch, work_limit_reached, result ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace and initialize */
+ /* ---------------------------------------------------------------------- */
+
+ Cheap = Work ; Work += ncol ;
+ Flag = Work ; Work += ncol ;
+
+ /* stack for non-recursive depth-first search in augment function */
+ Istack = Work ; Work += ncol ;
+ Jstack = Work ; Work += ncol ;
+ Pstack = Work ;
+
+ /* in column j, rows Ai [Ap [j] .. Cheap [j]-1] are known to be matched */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Cheap [j] = Ap [j] ;
+ Flag [j] = EMPTY ;
+ }
+
+ /* all rows and columns are currently unmatched */
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Match [i] = EMPTY ;
+ }
+
+ if (maxwork > 0)
+ {
+ maxwork *= Ap [ncol] ;
+ }
+ *work = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find a matching row for each column k */
+ /* ---------------------------------------------------------------------- */
+
+ nmatch = 0 ;
+ work_limit_reached = FALSE ;
+ for (k = 0 ; k < ncol ; k++)
+ {
+ /* find an augmenting path to match some row i to column k */
+ result = augment (k, Ap, Ai, Match, Cheap, Flag, Istack, Jstack, Pstack,
+ work, maxwork) ;
+ if (result == TRUE)
+ {
+ /* we found it. Match [i] = k for some row i has been done. */
+ nmatch++ ;
+ }
+ else if (result == EMPTY)
+ {
+ /* augment gave up because of too much work, and no match found */
+ work_limit_reached = TRUE ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the Match, and the # of matches made */
+ /* ---------------------------------------------------------------------- */
+
+ /* At this point, row i is matched to j = Match [i] if j >= 0. i is an
+ * unmatched row if Match [i] == EMPTY. */
+
+ if (work_limit_reached)
+ {
+ /* return -1 if the work limit of maxwork*nnz(A) was reached */
+ *work = EMPTY ;
+ }
+
+ return (nmatch) ;
+}
diff --git a/BTF/Source/btf_order.c b/BTF/Source/btf_order.c
new file mode 100644
index 0000000..7ed04f1
--- /dev/null
+++ b/BTF/Source/btf_order.c
@@ -0,0 +1,132 @@
+/* ========================================================================== */
+/* === BTF_ORDER ============================================================ */
+/* ========================================================================== */
+
+/* Find a permutation P and Q to permute a square sparse matrix into upper block
+ * triangular form. A(P,Q) will contain a zero-free diagonal if A has
+ * structural full-rank. Otherwise, the number of nonzeros on the diagonal of
+ * A(P,Q) will be maximized, and will equal the structural rank of A.
+ *
+ * Q[k] will be "flipped" if a zero-free diagonal was not found. Q[k] will be
+ * negative, and j = BTF_UNFLIP (Q [k]) gives the corresponding permutation.
+ *
+ * R defines the block boundaries of A(P,Q). The kth block consists of rows
+ * and columns R[k] to R[k+1]-1.
+ *
+ * If maxwork > 0 on input, then the work performed in btf_maxtrans is limited
+ * to maxwork*nnz(A) (excluding the "cheap match" phase, which can take another
+ * nnz(A) work). On output, the work parameter gives the actual work performed,
+ * or -1 if the limit was reached. In the latter case, the diagonal of A(P,Q)
+ * might not be zero-free, and the number of nonzeros on the diagonal of A(P,Q)
+ * might not be equal to the structural rank.
+ *
+ * See btf.h for more details.
+ *
+ * Copyright (c) 2004-2007. Tim Davis, University of Florida,
+ * with support from Sandia National Laboratories. All Rights Reserved.
+ */
+
+#include "btf.h"
+#include "btf_internal.h"
+
+/* This function only operates on square matrices (either structurally full-
+ * rank, or structurally rank deficient). */
+
+Int BTF(order) /* returns number of blocks found */
+(
+ /* input, not modified: */
+ Int n, /* A is n-by-n in compressed column form */
+ Int Ap [ ], /* size n+1 */
+ Int Ai [ ], /* size nz = Ap [n] */
+ double maxwork, /* do at most maxwork*nnz(A) work in the maximum
+ * transversal; no limit if <= 0 */
+
+ /* output, not defined on input */
+ double *work, /* work performed in maxtrans, or -1 if limit reached */
+ Int P [ ], /* size n, row permutation */
+ Int Q [ ], /* size n, column permutation */
+ Int R [ ], /* size n+1. block b is in rows/cols R[b] ... R[b+1]-1 */
+ Int *nmatch, /* # nonzeros on diagonal of P*A*Q */
+
+ /* workspace, not defined on input or output */
+ Int Work [ ] /* size 5n */
+)
+{
+ Int *Flag ;
+ Int nblocks, i, j, nbadcol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the maximum matching */
+ /* ---------------------------------------------------------------------- */
+
+ /* if maxwork > 0, then a maximum matching might not be found */
+
+ *nmatch = BTF(maxtrans) (n, n, Ap, Ai, maxwork, work, Q, Work) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* complete permutation if the matrix is structurally singular */
+ /* ---------------------------------------------------------------------- */
+
+ /* Since the matrix is square, ensure BTF_UNFLIP(Q[0..n-1]) is a
+ * permutation of the columns of A so that A has as many nonzeros on the
+ * diagonal as possible.
+ */
+
+ if (*nmatch < n)
+ {
+ /* get a size-n work array */
+ Flag = Work + n ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Flag [j] = 0 ;
+ }
+
+ /* flag all matched columns */
+ for (i = 0 ; i < n ; i++)
+ {
+ j = Q [i] ;
+ if (j != EMPTY)
+ {
+ /* row i and column j are matched to each other */
+ Flag [j] = 1 ;
+ }
+ }
+
+ /* make a list of all unmatched columns, in Work [0..nbadcol-1] */
+ nbadcol = 0 ;
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ if (!Flag [j])
+ {
+ /* j is matched to nobody */
+ Work [nbadcol++] = j ;
+ }
+ }
+ ASSERT (*nmatch + nbadcol == n) ;
+
+ /* make an assignment for each unmatched row */
+ for (i = 0 ; i < n ; i++)
+ {
+ if (Q [i] == EMPTY && nbadcol > 0)
+ {
+ /* get an unmatched column j */
+ j = Work [--nbadcol] ;
+ /* assign j to row i and flag the entry by "flipping" it */
+ Q [i] = BTF_FLIP (j) ;
+ }
+ }
+ }
+
+ /* The permutation of a square matrix can be recovered as follows: Row i is
+ * matched with column j, where j = BTF_UNFLIP (Q [i]) and where j
+ * will always be in the valid range 0 to n-1. The entry A(i,j) is zero
+ * if BTF_ISFLIPPED (Q [i]) is true, and nonzero otherwise. nmatch
+ * is the number of entries in the Q array that are non-negative. */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the strongly connected components */
+ /* ---------------------------------------------------------------------- */
+
+ nblocks = BTF(strongcomp) (n, Ap, Ai, Q, P, R, Work) ;
+ return (nblocks) ;
+}
diff --git a/BTF/Source/btf_strongcomp.c b/BTF/Source/btf_strongcomp.c
new file mode 100644
index 0000000..4474bec
--- /dev/null
+++ b/BTF/Source/btf_strongcomp.c
@@ -0,0 +1,593 @@
+/* ========================================================================== */
+/* === BTF_STRONGCOMP ======================================================= */
+/* ========================================================================== */
+
+/* Finds the strongly connected components of a graph, or equivalently, permutes
+ * the matrix into upper block triangular form. See btf.h for more details.
+ * Input matrix and Q are not checked on input.
+ *
+ * Copyright (c) 2004-2007. Tim Davis, University of Florida,
+ * with support from Sandia National Laboratories. All Rights Reserved.
+ */
+
+#include "btf.h"
+#include "btf_internal.h"
+
+#define UNVISITED (-2) /* Flag [j] = UNVISITED if node j not visited yet */
+#define UNASSIGNED (-1) /* Flag [j] = UNASSIGNED if node j has been visited,
+ * but not yet assigned to a strongly-connected
+ * component (aka block). Flag [j] = k (k in the
+ * range 0 to nblocks-1) if node j has been visited
+ * (and completed, with its postwork done) and
+ * assigned to component k. */
+
+/* This file contains two versions of the depth-first-search, a recursive one
+ * and a non-recursive one. By default, the non-recursive one is used. */
+
+#ifndef RECURSIVE
+
+/* ========================================================================== */
+/* === dfs: non-recursive version (default) ================================= */
+/* ========================================================================== */
+
+/* Perform a depth-first-search of a graph, stored in an adjacency-list form.
+ * The row indices of column j (equivalently, the out-adjacency list of node j)
+ * are stored in Ai [Ap[j] ... Ap[j+1]-1]. Self-edge (diagonal entries) are
+ * ignored. Ap[0] must be zero, and thus nz = Ap[n] is the number of entries
+ * in the matrix (or edges in the graph). The row indices in each column need
+ * not be in any particular order. If an input column permutation is given,
+ * node j (in the permuted matrix A*Q) is located in
+ * Ai [Ap[Q[j]] ... Ap[Q[j]+1]-1]. This Q can be the same as the Match array
+ * output from the maxtrans routine, for a square matrix that is structurally
+ * full rank.
+ *
+ * The algorithm is from the paper by Robert E. Tarjan, "Depth-first search and
+ * linear graph algorithms," SIAM Journal on Computing, vol. 1, no. 2,
+ * pp. 146-160, 1972. The time taken by strongcomp is O(nnz(A)).
+ *
+ * See also MC13A/B in the Harwell subroutine library (Iain S. Duff and John
+ * K. Reid, "Algorithm 529: permutations to block triangular form," ACM Trans.
+ * on Mathematical Software, vol. 4, no. 2, pp. 189-192, 1978, and "An
+ * implementation of Tarjan's algorithm for the block triangular form of a
+ * matrix," same journal, pp. 137-147. This code is implements the same
+ * algorithm as MC13A/B, except that the data structures are very different.
+ * Also, unlike MC13A/B, the output permutation preserves the natural ordering
+ * within each block.
+ */
+
+static void dfs
+(
+ /* inputs, not modified on output: */
+ Int j, /* start the DFS at node j */
+ Int Ap [ ], /* size n+1, column pointers for the matrix A */
+ Int Ai [ ], /* row indices, size nz = Ap [n] */
+ Int Q [ ], /* input column permutation */
+
+ /* inputs, modified on output (each array is of size n): */
+ Int Time [ ], /* Time [j] = "time" that node j was first visited */
+ Int Flag [ ], /* Flag [j]: see above */
+ Int Low [ ], /* Low [j]: see definition below */
+ Int *p_nblocks, /* number of blocks (aka strongly-connected-comp.)*/
+ Int *p_timestamp, /* current "time" */
+
+ /* workspace, not defined on input or output: */
+ Int Cstack [ ], /* size n, output stack to hold nodes of components */
+ Int Jstack [ ], /* size n, stack for the variable j */
+ Int Pstack [ ] /* size n, stack for the variable p */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables, and initializations */
+ /* ---------------------------------------------------------------------- */
+
+ /* local variables, but "global" to all DFS levels: */
+ Int chead ; /* top of Cstack */
+ Int jhead ; /* top of Jstack and Pstack */
+
+ /* variables that are purely local to any one DFS level: */
+ Int i ; /* edge (j,i) considered; i can be next node to traverse */
+ Int parent ; /* parent of node j in the DFS tree */
+ Int pend ; /* one past the end of the adjacency list for node j */
+ Int jj ; /* column j of A*Q is column jj of the input matrix A */
+
+ /* variables that need to be pushed then popped from the stack: */
+ Int p ; /* current index into the adj. list for node j */
+ /* the variables j and p are stacked in Jstack and Pstack */
+
+ /* local copies of variables in the calling routine */
+ Int nblocks = *p_nblocks ;
+ Int timestamp = *p_timestamp ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start a DFS at node j (same as the recursive call dfs (EMPTY, j)) */
+ /* ---------------------------------------------------------------------- */
+
+ chead = 0 ; /* component stack is empty */
+ jhead = 0 ; /* Jstack and Pstack are empty */
+ Jstack [0] = j ; /* put the first node j on the Jstack */
+ ASSERT (Flag [j] == UNVISITED) ;
+
+ while (jhead >= 0)
+ {
+ j = Jstack [jhead] ; /* grab the node j from the top of Jstack */
+
+ /* determine which column jj of the A is column j of A*Q */
+ jj = (Q == (Int *) NULL) ? (j) : (BTF_UNFLIP (Q [j])) ;
+ pend = Ap [jj+1] ; /* j's row index list ends at Ai [pend-1] */
+
+ if (Flag [j] == UNVISITED)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* prework at node j */
+ /* -------------------------------------------------------------- */
+
+ /* node j is being visited for the first time */
+ Cstack [++chead] = j ; /* push j onto the stack */
+ timestamp++ ; /* get a timestamp */
+ Time [j] = timestamp ; /* give the timestamp to node j */
+ Low [j] = timestamp ;
+ Flag [j] = UNASSIGNED ; /* flag node j as visited */
+
+ /* -------------------------------------------------------------- */
+ /* set Pstack [jhead] to the first entry in column j to scan */
+ /* -------------------------------------------------------------- */
+
+ Pstack [jhead] = Ap [jj] ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* DFS rooted at node j (start it, or continue where left off) */
+ /* ------------------------------------------------------------------ */
+
+ for (p = Pstack [jhead] ; p < pend ; p++)
+ {
+ i = Ai [p] ; /* examine the edge from node j to node i */
+ if (Flag [i] == UNVISITED)
+ {
+ /* Node i has not been visited - start a DFS at node i.
+ * Keep track of where we left off in the scan of adjacency list
+ * of node j so we can restart j where we left off. */
+ Pstack [jhead] = p + 1 ;
+ /* Push i onto the stack and immediately break
+ * so we can recurse on node i. */
+ Jstack [++jhead] = i ;
+ ASSERT (Time [i] == EMPTY) ;
+ ASSERT (Low [i] == EMPTY) ;
+ /* break here to do what the recursive call dfs (j,i) does */
+ break ;
+ }
+ else if (Flag [i] == UNASSIGNED)
+ {
+ /* Node i has been visited, but still unassigned to a block
+ * this is a back or cross edge if Time [i] < Time [j].
+ * Note that i might equal j, in which case this code does
+ * nothing. */
+ ASSERT (Time [i] > 0) ;
+ ASSERT (Low [i] > 0) ;
+ Low [j] = MIN (Low [j], Time [i]) ;
+ }
+ }
+
+ if (p == pend)
+ {
+ /* If all adjacent nodes of j are already visited, pop j from
+ * Jstack and do the post work for node j. This also pops p
+ * from the Pstack. */
+ jhead-- ;
+
+ /* -------------------------------------------------------------- */
+ /* postwork at node j */
+ /* -------------------------------------------------------------- */
+
+ /* determine if node j is the head of a component */
+ if (Low [j] == Time [j])
+ {
+ /* pop all nodes in this SCC from Cstack */
+ while (TRUE)
+ {
+ ASSERT (chead >= 0) ; /* stack not empty (j in it) */
+ i = Cstack [chead--] ; /* pop a node from the Cstack */
+ ASSERT (i >= 0) ;
+ ASSERT (Flag [i] == UNASSIGNED) ;
+ Flag [i] = nblocks ; /* assign i to current block */
+ if (i == j) break ; /* current block ends at j */
+ }
+ nblocks++ ; /* one more block has been found */
+ }
+ /* update Low [parent], if the parent exists */
+ if (jhead >= 0)
+ {
+ parent = Jstack [jhead] ;
+ Low [parent] = MIN (Low [parent], Low [j]) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* cleanup: update timestamp and nblocks */
+ /* ---------------------------------------------------------------------- */
+
+ *p_timestamp = timestamp ;
+ *p_nblocks = nblocks ;
+}
+
+#else
+
+/* ========================================================================== */
+/* === dfs: recursive version (only for illustration) ======================= */
+/* ========================================================================== */
+
+/* The following is a recursive version of dfs, which computes identical results
+ * as the non-recursive dfs. It is included here because it is easier to read.
+ * Compare the comments in the code below with the identical comments in the
+ * non-recursive code above, and that will help you see the correlation between
+ * the two routines.
+ *
+ * This routine can cause stack overflow, and is thus not recommended for heavy
+ * usage, particularly for large matrices. To help in delaying stack overflow,
+ * global variables are used, reducing the amount of information each call to
+ * dfs places on the call/return stack (the integers i, j, p, parent, and the
+ * return address). Note that this means the recursive code is not thread-safe.
+ * To try this version, compile the code with -DRECURSIVE or include the
+ * following line at the top of this file:
+
+#define RECURSIVE
+
+ */
+
+static Int /* for recursive illustration only, not for production use */
+ chead, timestamp, nblocks, n, *Ap, *Ai, *Flag, *Cstack, *Time, *Low,
+ *P, *R, *Q ;
+
+static void dfs
+(
+ Int parent, /* came from parent node */
+ Int j /* at node j in the DFS */
+)
+{
+ Int p ; /* current index into the adj. list for node j */
+ Int i ; /* edge (j,i) considered; i can be next node to traverse */
+ Int jj ; /* column j of A*Q is column jj of the input matrix A */
+
+ /* ---------------------------------------------------------------------- */
+ /* prework at node j */
+ /* ---------------------------------------------------------------------- */
+
+ /* node j is being visited for the first time */
+ Cstack [++chead] = j ; /* push j onto the stack */
+ timestamp++ ; /* get a timestamp */
+ Time [j] = timestamp ; /* give the timestamp to node j */
+ Low [j] = timestamp ;
+ Flag [j] = UNASSIGNED ; /* flag node j as visited */
+
+ /* ---------------------------------------------------------------------- */
+ /* DFS rooted at node j */
+ /* ---------------------------------------------------------------------- */
+
+ /* determine which column jj of the A is column j of A*Q */
+ jj = (Q == (Int *) NULL) ? (j) : (BTF_UNFLIP (Q [j])) ;
+ for (p = Ap [jj] ; p < Ap [jj+1] ; p++)
+ {
+ i = Ai [p] ; /* examine the edge from node j to node i */
+ if (Flag [i] == UNVISITED)
+ {
+ /* Node i has not been visited - start a DFS at node i. */
+ dfs (j, i) ;
+ }
+ else if (Flag [i] == UNASSIGNED)
+ {
+ /* Node i has been visited, but still unassigned to a block
+ * this is a back or cross edge if Time [i] < Time [j].
+ * Note that i might equal j, in which case this code does
+ * nothing. */
+ Low [j] = MIN (Low [j], Time [i]) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* postwork at node j */
+ /* ---------------------------------------------------------------------- */
+
+ /* determine if node j is the head of a component */
+ if (Low [j] == Time [j])
+ {
+ /* pop all nodes in this strongly connected component from Cstack */
+ while (TRUE)
+ {
+ i = Cstack [chead--] ; /* pop a node from the Cstack */
+ Flag [i] = nblocks ; /* assign node i to current block */
+ if (i == j) break ; /* current block ends at node j */
+ }
+ nblocks++ ; /* one more block has been found */
+ }
+ /* update Low [parent] */
+ if (parent != EMPTY)
+ {
+ /* Note that this could be done with Low[j] = MIN(Low[j],Low[i]) just
+ * after the dfs (j,i) statement above, and then parent would not have
+ * to be an input argument. Putting it here places all the postwork
+ * for node j in one place, thus making the non-recursive DFS easier. */
+ Low [parent] = MIN (Low [parent], Low [j]) ;
+ }
+}
+
+#endif
+
+/* ========================================================================== */
+/* === btf_strongcomp ======================================================= */
+/* ========================================================================== */
+
+#ifndef RECURSIVE
+
+Int BTF(strongcomp) /* return # of strongly connected components */
+(
+ /* input, not modified: */
+ Int n, /* A is n-by-n in compressed column form */
+ Int Ap [ ], /* size n+1 */
+ Int Ai [ ], /* size nz = Ap [n] */
+
+ /* optional input, modified (if present) on output: */
+ Int Q [ ], /* size n, input column permutation. The permutation Q can
+ * include a flag which indicates an unmatched row.
+ * jold = BTF_UNFLIP (Q [jnew]) is the permutation;
+ * this function ingnores these flags. On output, it is
+ * modified according to the permutation P. */
+
+ /* output, not defined on input: */
+ Int P [ ], /* size n. P [k] = j if row and column j are kth row/col
+ * in permuted matrix. */
+ Int R [ ], /* size n+1. kth block is in rows/cols R[k] ... R[k+1]-1
+ * of the permuted matrix. */
+
+ /* workspace, not defined on input or output: */
+ Int Work [ ] /* size 4n */
+)
+
+#else
+
+Int BTF(strongcomp) /* recursive version - same as above except for Work size */
+(
+ Int n_in,
+ Int Ap_in [ ],
+ Int Ai_in [ ],
+ Int Q_in [ ],
+ Int P_in [ ],
+ Int R_in [ ],
+ Int Work [ ] /* size 2n */
+)
+
+#endif
+
+{
+ Int j, k, b ;
+
+#ifndef RECURSIVE
+ Int timestamp, nblocks, *Flag, *Cstack, *Time, *Low, *Jstack, *Pstack ;
+#else
+ n = n_in ;
+ Ap = Ap_in ;
+ Ai = Ai_in ;
+ Q = Q_in ;
+ P = P_in ;
+ R = R_in ;
+ chead = EMPTY ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get and initialize workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* timestamp is incremented each time a new node is visited.
+ *
+ * Time [j] is the timestamp given to node j.
+ *
+ * Low [j] is the lowest timestamp of any node reachable from j via either
+ * a path to any descendent of j in the DFS tree, or via a single edge to
+ * an either an ancestor (a back edge) or another node that's neither an
+ * ancestor nor a descendant (a cross edge). If Low [j] is equal to
+ * the timestamp of node j (Time [j]), then node j is the "head" of a
+ * strongly connected component (SCC). That is, it is the first node
+ * visited in its strongly connected component, and the DFS subtree rooted
+ * at node j spans all the nodes of the strongly connected component.
+ *
+ * The term "block" and "component" are used interchangebly in this code;
+ * "block" being a matrix term and "component" being a graph term for the
+ * same thing.
+ *
+ * When a node is visited, it is placed on the Cstack (for "component"
+ * stack). When node j is found to be an SCC head, all the nodes from the
+ * top of the stack to node j itself form the nodes in the SCC. This Cstack
+ * is used for both the recursive and non-recursive versions.
+ */
+
+ Time = Work ; Work += n ;
+ Flag = Work ; Work += n ;
+ Low = P ; /* use output array P as workspace for Low */
+ Cstack = R ; /* use output array R as workspace for Cstack */
+
+#ifndef RECURSIVE
+ /* stack for non-recursive dfs */
+ Jstack = Work ; Work += n ; /* stack for j */
+ Pstack = Work ; /* stack for p */
+#endif
+
+ for (j = 0 ; j < n ; j++)
+ {
+ Flag [j] = UNVISITED ;
+ Low [j] = EMPTY ;
+ Time [j] = EMPTY ;
+#ifndef NDEBUG
+ Cstack [j] = EMPTY ;
+#ifndef RECURSIVE
+ Jstack [j] = EMPTY ;
+ Pstack [j] = EMPTY ;
+#endif
+#endif
+ }
+
+ timestamp = 0 ; /* each node given a timestamp when it is visited */
+ nblocks = 0 ; /* number of blocks found so far */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the connected components via a depth-first-search */
+ /* ---------------------------------------------------------------------- */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* node j is unvisited or assigned to a block. Cstack is empty. */
+ ASSERT (Flag [j] == UNVISITED || (Flag [j] >= 0 && Flag [j] < nblocks));
+ if (Flag [j] == UNVISITED)
+ {
+#ifndef RECURSIVE
+ /* non-recursive dfs (default) */
+ dfs (j, Ap, Ai, Q, Time, Flag, Low, &nblocks, ×tamp,
+ Cstack, Jstack, Pstack) ;
+#else
+ /* recursive dfs (for illustration only) */
+ ASSERT (chead == EMPTY) ;
+ dfs (EMPTY, j) ;
+ ASSERT (chead == EMPTY) ;
+#endif
+ }
+ }
+ ASSERT (timestamp == n) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the block boundary array, R */
+ /* ---------------------------------------------------------------------- */
+
+ for (b = 0 ; b < nblocks ; b++)
+ {
+ R [b] = 0 ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ /* node j has been assigned to block b = Flag [j] */
+ ASSERT (Time [j] > 0 && Time [j] <= n) ;
+ ASSERT (Low [j] > 0 && Low [j] <= n) ;
+ ASSERT (Flag [j] >= 0 && Flag [j] < nblocks) ;
+ R [Flag [j]]++ ;
+ }
+ /* R [b] is now the number of nodes in block b. Compute cumulative sum
+ * of R, using Time [0 ... nblocks-1] as workspace. */
+ Time [0] = 0 ;
+ for (b = 1 ; b < nblocks ; b++)
+ {
+ Time [b] = Time [b-1] + R [b-1] ;
+ }
+ for (b = 0 ; b < nblocks ; b++)
+ {
+ R [b] = Time [b] ;
+ }
+ R [nblocks] = n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the permutation, preserving the natural order */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = EMPTY ;
+ }
+#endif
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* place column j in the permutation */
+ P [Time [Flag [j]]++] = j ;
+ }
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSERT (P [k] != EMPTY) ;
+ }
+#endif
+
+ /* Now block b consists of the nodes k1 to k2-1 in the permuted matrix,
+ * where k1 = R [b] and k2 = R [b+1]. Row and column j of the original
+ * matrix becomes row and column P [k] of the permuted matrix. The set of
+ * of rows/columns (nodes) in block b is given by P [k1 ... k2-1], and this
+ * set is sorted in ascending order. Thus, if the matrix consists of just
+ * one block, P is the identity permutation. */
+
+ /* ---------------------------------------------------------------------- */
+ /* if Q is present on input, set Q = Q*P' */
+ /* ---------------------------------------------------------------------- */
+
+ if (Q != (Int *) NULL)
+ {
+ /* We found a symmetric permutation P for the matrix A*Q. The overall
+ * permutation is thus P*(A*Q)*P'. Set Q=Q*P' so that the final
+ * permutation is P*A*Q. Use Time as workspace. Note that this
+ * preserves the negative values of Q if the matrix is structurally
+ * singular. */
+ for (k = 0 ; k < n ; k++)
+ {
+ Time [k] = Q [P [k]] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ Q [k] = Time [k] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* how to traverse the permuted matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* If Q is not present, the following code can be used to traverse the
+ * permuted matrix P*A*P'
+ *
+ * // compute the inverse of P
+ * for (knew = 0 ; knew < n ; knew++)
+ * {
+ * // row and column kold in the old matrix is row/column knew
+ * // in the permuted matrix P*A*P'
+ * kold = P [knew] ;
+ * Pinv [kold] = knew ;
+ * }
+ * for (b = 0 ; b < nblocks ; b++)
+ * {
+ * // traverse block b of the permuted matrix P*A*P'
+ * k1 = R [b] ;
+ * k2 = R [b+1] ;
+ * nk = k2 - k1 ;
+ * for (jnew = k1 ; jnew < k2 ; jnew++)
+ * {
+ * jold = P [jnew] ;
+ * for (p = Ap [jold] ; p < Ap [jold+1] ; p++)
+ * {
+ * iold = Ai [p] ;
+ * inew = Pinv [iold] ;
+ * // Entry in the old matrix is A (iold, jold), and its
+ * // position in the new matrix P*A*P' is (inew, jnew).
+ * // Let B be the bth diagonal block of the permuted
+ * // matrix. If inew >= k1, then this entry is in row/
+ * // column (inew-k1, jnew-k1) of the nk-by-nk matrix B.
+ * // Otherwise, the entry is in the upper block triangular
+ * // part, not in any diagonal block.
+ * }
+ * }
+ * }
+ *
+ * If Q is present replace the above statement
+ * jold = P [jnew] ;
+ * with
+ * jold = Q [jnew] ;
+ * or
+ * jold = BTF_UNFLIP (Q [jnew]) ;
+ *
+ * then entry A (iold,jold) in the old (unpermuted) matrix is at (inew,jnew)
+ * in the permuted matrix P*A*Q. Everything else remains the same as the
+ * above (simply replace P*A*P' with P*A*Q in the above comments).
+ */
+
+ /* ---------------------------------------------------------------------- */
+ /* return # of blocks / # of strongly connected components */
+ /* ---------------------------------------------------------------------- */
+
+ return (nblocks) ;
+}
diff --git a/CAMD/Demo/Makefile b/CAMD/Demo/Makefile
new file mode 100644
index 0000000..4eebb3d
--- /dev/null
+++ b/CAMD/Demo/Makefile
@@ -0,0 +1,57 @@
+#-----------------------------------------------------------------------------
+# compile the CAMD demo (for both GNU make or original make)
+#-----------------------------------------------------------------------------
+
+default: camd_simple camd_demo camd_demo2 camd_l_demo
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig
+
+UFCONFIG = ../../UFconfig/UFconfig.h
+
+INC = ../Include/camd.h $(UFCONFIG)
+
+library:
+ ( cd ../Lib ; $(MAKE) )
+
+#------------------------------------------------------------------------------
+# Create the demo program, run it, and compare the output
+#------------------------------------------------------------------------------
+
+dist:
+
+camd_demo: camd_demo.c library $(INC)
+ $(C) -o camd_demo camd_demo.c ../Lib/libcamd.a $(LIB)
+ ./camd_demo > my_camd_demo.out
+ - diff camd_demo.out my_camd_demo.out
+
+camd_l_demo: camd_l_demo.c library $(INC)
+ $(C) -o camd_l_demo camd_l_demo.c ../Lib/libcamd.a $(LIB)
+ ./camd_l_demo > my_camd_l_demo.out
+ - diff camd_l_demo.out my_camd_l_demo.out
+
+camd_demo2: camd_demo2.c library $(INC)
+ $(C) -o camd_demo2 camd_demo2.c ../Lib/libcamd.a $(LIB)
+ ./camd_demo2 > my_camd_demo2.out
+ - diff camd_demo2.out my_camd_demo2.out
+
+camd_simple: camd_simple.c library $(INC)
+ $(C) -o camd_simple camd_simple.c ../Lib/libcamd.a $(LIB)
+ ./camd_simple > my_camd_simple.out
+ - diff camd_simple.out my_camd_simple.out
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) camd_demo my_camd_demo.out
+ - $(RM) camd_l_demo my_camd_l_demo.out
+ - $(RM) camd_demo2 my_camd_demo2.out
+ - $(RM) camd_simple my_camd_simple.out
diff --git a/CAMD/Demo/camd_demo.c b/CAMD/Demo/camd_demo.c
new file mode 100644
index 0000000..7b3b9a3
--- /dev/null
+++ b/CAMD/Demo/camd_demo.c
@@ -0,0 +1,173 @@
+/* ========================================================================= */
+/* === CAMD demo main program ============================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* A simple C main program that illustrates the use of the ANSI C interface
+ * to CAMD.
+ */
+
+#include "camd.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+int main (void)
+{
+ /* The symmetric can_24 Harwell/Boeing matrix, including upper and lower
+ * triangular parts, and the diagonal entries. Note that this matrix is
+ * 0-based, with row and column indices in the range 0 to n-1. */
+ int n = 24, nz,
+ Ap [ ] = { 0, 9, 15, 21, 27, 33, 39, 48, 57, 61, 70, 76, 82, 88, 94, 100,
+ 106, 110, 119, 128, 137, 143, 152, 156, 160 },
+ Ai [ ] = {
+ /* column 0: */ 0, 5, 6, 12, 13, 17, 18, 19, 21,
+ /* column 1: */ 1, 8, 9, 13, 14, 17,
+ /* column 2: */ 2, 6, 11, 20, 21, 22,
+ /* column 3: */ 3, 7, 10, 15, 18, 19,
+ /* column 4: */ 4, 7, 9, 14, 15, 16,
+ /* column 5: */ 0, 5, 6, 12, 13, 17,
+ /* column 6: */ 0, 2, 5, 6, 11, 12, 19, 21, 23,
+ /* column 7: */ 3, 4, 7, 9, 14, 15, 16, 17, 18,
+ /* column 8: */ 1, 8, 9, 14,
+ /* column 9: */ 1, 4, 7, 8, 9, 13, 14, 17, 18,
+ /* column 10: */ 3, 10, 18, 19, 20, 21,
+ /* column 11: */ 2, 6, 11, 12, 21, 23,
+ /* column 12: */ 0, 5, 6, 11, 12, 23,
+ /* column 13: */ 0, 1, 5, 9, 13, 17,
+ /* column 14: */ 1, 4, 7, 8, 9, 14,
+ /* column 15: */ 3, 4, 7, 15, 16, 18,
+ /* column 16: */ 4, 7, 15, 16,
+ /* column 17: */ 0, 1, 5, 7, 9, 13, 17, 18, 19,
+ /* column 18: */ 0, 3, 7, 9, 10, 15, 17, 18, 19,
+ /* column 19: */ 0, 3, 6, 10, 17, 18, 19, 20, 21,
+ /* column 20: */ 2, 10, 19, 20, 21, 22,
+ /* column 21: */ 0, 2, 6, 10, 11, 19, 20, 21, 22,
+ /* column 22: */ 2, 20, 21, 22,
+ /* column 23: */ 6, 11, 12, 23 } ;
+
+ int P [24], Pinv [24], i, j, k, jnew, p, inew, result ;
+ double Control [CAMD_CONTROL], Info [CAMD_INFO] ;
+ char A [24][24] ;
+ int C [ ] = { 0, 0, 4, 0, 1, 0, 2, 2, 1, 1, 3, 4, 5, 5, 3, 4,
+ 5, 2, 5, 3, 4, 2, 1, 0 } ;
+
+ printf ("CAMD version %d.%d, date: %s\n", CAMD_MAIN_VERSION,
+ CAMD_SUB_VERSION, CAMD_DATE) ;
+ printf ("CAMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:\n") ;
+
+ /* get the default parameters, and print them */
+ camd_defaults (Control) ;
+ camd_control (Control) ;
+
+ /* print the input matrix */
+ nz = Ap [n] ;
+ printf ("\nInput matrix: %d-by-%d, with %d entries.\n"
+ " Note that for a symmetric matrix such as this one, only the\n"
+ " strictly lower or upper triangular parts would need to be\n"
+ " passed to CAMD, since CAMD computes the ordering of A+A'. The\n"
+ " diagonal entries are also not needed, since CAMD ignores them.\n"
+ , n, n, nz) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf ("\nColumn: %d, number of entries: %d, with row indices in"
+ " Ai [%d ... %d]:\n row indices:",
+ j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ printf (" %d", i) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* print a character plot of the input matrix. This is only reasonable
+ * because the matrix is small. */
+ printf ("\nPlot of input matrix pattern:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (i = 0 ; i < n ; i++) A [i][j] = '.' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ A [i][j] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2d: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* order the matrix */
+ result = camd_order (n, Ap, Ai, P, Control, Info, C) ;
+ printf ("return value from camd_order: %d (should be %d)\n",
+ result, CAMD_OK) ;
+
+ /* print the statistics */
+ camd_info (Info) ;
+
+ if (result != CAMD_OK)
+ {
+ printf ("CAMD failed\n") ;
+ exit (1) ;
+ }
+
+ /* print the permutation vector, P, and compute the inverse permutation */
+ printf ("Permutation vector:\n") ;
+ for (k = 0 ; k < n ; k++)
+ {
+ /* row/column j is the kth row/column in the permuted matrix */
+ j = P [k] ;
+ Pinv [j] = k ;
+ printf (" %2d", j) ;
+ }
+ printf ("\n\n") ;
+
+ printf ("Inverse permutation vector:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ k = Pinv [j] ;
+ printf (" %2d", k) ;
+ }
+ printf ("\n\n") ;
+
+ /* print a character plot of the permuted matrix. */
+ printf ("\nPlot of permuted matrix pattern:\n") ;
+ for (jnew = 0 ; jnew < n ; jnew++)
+ {
+ j = P [jnew] ;
+ for (inew = 0 ; inew < n ; inew++) A [inew][jnew] = '.' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ inew = Pinv [Ai [p]] ;
+ A [inew][jnew] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2d: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ return (0) ;
+}
diff --git a/CAMD/Demo/camd_demo.out b/CAMD/Demo/camd_demo.out
new file mode 100644
index 0000000..6ec7daf
--- /dev/null
+++ b/CAMD/Demo/camd_demo.out
@@ -0,0 +1,178 @@
+CAMD version 2.2, date: May 31, 2007
+CAMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:
+
+camd version 2.2, May 31, 2007: approximate minimum degree ordering:
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+
+
+Input matrix: 24-by-24, with 160 entries.
+ Note that for a symmetric matrix such as this one, only the
+ strictly lower or upper triangular parts would need to be
+ passed to CAMD, since CAMD computes the ordering of A+A'. The
+ diagonal entries are also not needed, since CAMD ignores them.
+
+Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]:
+ row indices: 0 5 6 12 13 17 18 19 21
+
+Column: 1, number of entries: 6, with row indices in Ai [9 ... 14]:
+ row indices: 1 8 9 13 14 17
+
+Column: 2, number of entries: 6, with row indices in Ai [15 ... 20]:
+ row indices: 2 6 11 20 21 22
+
+Column: 3, number of entries: 6, with row indices in Ai [21 ... 26]:
+ row indices: 3 7 10 15 18 19
+
+Column: 4, number of entries: 6, with row indices in Ai [27 ... 32]:
+ row indices: 4 7 9 14 15 16
+
+Column: 5, number of entries: 6, with row indices in Ai [33 ... 38]:
+ row indices: 0 5 6 12 13 17
+
+Column: 6, number of entries: 9, with row indices in Ai [39 ... 47]:
+ row indices: 0 2 5 6 11 12 19 21 23
+
+Column: 7, number of entries: 9, with row indices in Ai [48 ... 56]:
+ row indices: 3 4 7 9 14 15 16 17 18
+
+Column: 8, number of entries: 4, with row indices in Ai [57 ... 60]:
+ row indices: 1 8 9 14
+
+Column: 9, number of entries: 9, with row indices in Ai [61 ... 69]:
+ row indices: 1 4 7 8 9 13 14 17 18
+
+Column: 10, number of entries: 6, with row indices in Ai [70 ... 75]:
+ row indices: 3 10 18 19 20 21
+
+Column: 11, number of entries: 6, with row indices in Ai [76 ... 81]:
+ row indices: 2 6 11 12 21 23
+
+Column: 12, number of entries: 6, with row indices in Ai [82 ... 87]:
+ row indices: 0 5 6 11 12 23
+
+Column: 13, number of entries: 6, with row indices in Ai [88 ... 93]:
+ row indices: 0 1 5 9 13 17
+
+Column: 14, number of entries: 6, with row indices in Ai [94 ... 99]:
+ row indices: 1 4 7 8 9 14
+
+Column: 15, number of entries: 6, with row indices in Ai [100 ... 105]:
+ row indices: 3 4 7 15 16 18
+
+Column: 16, number of entries: 4, with row indices in Ai [106 ... 109]:
+ row indices: 4 7 15 16
+
+Column: 17, number of entries: 9, with row indices in Ai [110 ... 118]:
+ row indices: 0 1 5 7 9 13 17 18 19
+
+Column: 18, number of entries: 9, with row indices in Ai [119 ... 127]:
+ row indices: 0 3 7 9 10 15 17 18 19
+
+Column: 19, number of entries: 9, with row indices in Ai [128 ... 136]:
+ row indices: 0 3 6 10 17 18 19 20 21
+
+Column: 20, number of entries: 6, with row indices in Ai [137 ... 142]:
+ row indices: 2 10 19 20 21 22
+
+Column: 21, number of entries: 9, with row indices in Ai [143 ... 151]:
+ row indices: 0 2 6 10 11 19 20 21 22
+
+Column: 22, number of entries: 4, with row indices in Ai [152 ... 155]:
+ row indices: 2 20 21 22
+
+Column: 23, number of entries: 4, with row indices in Ai [156 ... 159]:
+ row indices: 6 11 12 23
+
+Plot of input matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . X X . . . . . X X . . . X X X . X . .
+ 1: . X . . . . . . X X . . . X X . . X . . . . . .
+ 2: . . X . . . X . . . . X . . . . . . . . X X X .
+ 3: . . . X . . . X . . X . . . . X . . X X . . . .
+ 4: . . . . X . . X . X . . . . X X X . . . . . . .
+ 5: X . . . . X X . . . . . X X . . . X . . . . . .
+ 6: X . X . . X X . . . . X X . . . . . . X . X . X
+ 7: . . . X X . . X . X . . . . X X X X X . . . . .
+ 8: . X . . . . . . X X . . . . X . . . . . . . . .
+ 9: . X . . X . . X X X . . . X X . . X X . . . . .
+10: . . . X . . . . . . X . . . . . . . X X X X . .
+11: . . X . . . X . . . . X X . . . . . . . . X . X
+12: X . . . . X X . . . . X X . . . . . . . . . . X
+13: X X . . . X . . . X . . . X . . . X . . . . . .
+14: . X . . X . . X X X . . . . X . . . . . . . . .
+15: . . . X X . . X . . . . . . . X X . X . . . . .
+16: . . . . X . . X . . . . . . . X X . . . . . . .
+17: X X . . . X . X . X . . . X . . . X X X . . . .
+18: X . . X . . . X . X X . . . . X . X X X . . . .
+19: X . . X . . X . . . X . . . . . . X X X X X . .
+20: . . X . . . . . . . X . . . . . . . . X X X X .
+21: X . X . . . X . . . X X . . . . . . . X X X X .
+22: . . X . . . . . . . . . . . . . . . . . X X X .
+23: . . . . . . X . . . . X X . . . . . . . . . . X
+return value from camd_order: 0 (should be 0)
+
+camd: approximate minimum degree ordering, results:
+ status: OK
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 1644
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 135
+ nonzeros in L (including diagonal): 159
+ # divide operations for LDL' or LU: 135
+ # multiply-subtract operations for LDL': 541
+ # multiply-subtract operations for LU: 947
+ max nz. in any column of L (incl. diagonal): 12
+
+ chol flop count for real A, sqrt counted as 1 flop: 1241
+ LDL' flop count for real A: 1217
+ LDL' flop count for complex A: 5543
+ LU flop count for real A (with no pivoting): 2029
+ LU flop count for complex A (with no pivoting): 8791
+
+Permutation vector:
+ 23 3 1 5 0 22 4 8 9 7 6 21 17 19 10 14 2 11 20 15 12 13 18 16
+
+Inverse permutation vector:
+ 4 2 16 1 6 3 10 9 7 8 14 17 20 21 15 19 23 12 22 13 18 11 5 0
+
+
+Plot of permuted matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . . . . . . X . . . . . . X . . X . . .
+ 1: . X . . . . . . . X . . . X X . . . . X . . X .
+ 2: . . X . . . . X X . . . X . . X . . . . . X . .
+ 3: . . . X X . . . . . X . X . . . . . . . X X . .
+ 4: . . . X X . . . . . X X X X . . . . . . X X X .
+ 5: . . . . . X . . . . . X . . . . X . X . . . . .
+ 6: . . . . . . X . X X . . . . . X . . . X . . . X
+ 7: . . X . . . . X X . . . . . . X . . . . . . . .
+ 8: . . X . . . X X X X . . X . . X . . . . . X X .
+ 9: . X . . . . X . X X . . X . . X . . . X . . X X
+10: X . . X X . . . . . X X . X . . X X . . X . . .
+11: . . . . X X . . . . X X . X X . X X X . . . . .
+12: . . X X X . . . X X . . X X . . . . . . . X X .
+13: . X . . X . . . . . X X X X X . . . X . . . X .
+14: . X . . . . . . . . . X . X X . . . X . . . X .
+15: . . X . . . X X X X . . . . . X . . . . . . . .
+16: . . . . . X . . . . X X . . . . X X X . . . . .
+17: X . . . . . . . . . X X . . . . X X . . X . . .
+18: . . . . . X . . . . . X . X X . X . X . . . . .
+19: . X . . . . X . . X . . . . . . . . . X . . X X
+20: X . . X X . . . . . X . . . . . . X . . X . . .
+21: . . X X X . . . X . . . X . . . . . . . . X . .
+22: . X . . X . . . X X . . X X X . . . . X . . X .
+23: . . . . . . X . . X . . . . . . . . . X . . . X
diff --git a/CAMD/Demo/camd_demo2.c b/CAMD/Demo/camd_demo2.c
new file mode 100644
index 0000000..fe6f675
--- /dev/null
+++ b/CAMD/Demo/camd_demo2.c
@@ -0,0 +1,217 @@
+/* ========================================================================= */
+/* === CAMD demo main program (jumbled matrix version) ===================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* A simple C main program that illustrates the use of the ANSI C interface
+ * to CAMD.
+ *
+ * Identical to camd_demo.c, except that it operates on an input matrix that has
+ * unsorted columns and duplicate entries.
+ */
+
+#include "camd.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+int main (void)
+{
+ /* The symmetric can_24 Harwell/Boeing matrix (jumbled, and not symmetric).
+ * Since CAMD operates on A+A', only A(i,j) or A(j,i) need to be specified,
+ * or both. The diagonal entries are optional (some are missing).
+ * There are many duplicate entries, which must be removed. */
+ int n = 24, nz,
+ Ap [ ] = { 0, 9, 14, 20, 28, 33, 37, 44, 53, 58, 63, 63, 66, 69, 72, 75,
+ 78, 82, 86, 91, 97, 101, 112, 112, 116 },
+ Ai [ ] = {
+ /* column 0: */ 0, 17, 18, 21, 5, 12, 5, 0, 13,
+ /* column 1: */ 14, 1, 8, 13, 17,
+ /* column 2: */ 2, 20, 11, 6, 11, 22,
+ /* column 3: */ 3, 3, 10, 7, 18, 18, 15, 19,
+ /* column 4: */ 7, 9, 15, 14, 16,
+ /* column 5: */ 5, 13, 6, 17,
+ /* column 6: */ 5, 0, 11, 6, 12, 6, 23,
+ /* column 7: */ 3, 4, 9, 7, 14, 16, 15, 17, 18,
+ /* column 8: */ 1, 9, 14, 14, 14,
+ /* column 9: */ 7, 13, 8, 1, 17,
+ /* column 10: */
+ /* column 11: */ 2, 12, 23,
+ /* column 12: */ 5, 11, 12,
+ /* column 13: */ 0, 13, 17,
+ /* column 14: */ 1, 9, 14,
+ /* column 15: */ 3, 15, 16,
+ /* column 16: */ 16, 4, 4, 15,
+ /* column 17: */ 13, 17, 19, 17,
+ /* column 18: */ 15, 17, 19, 9, 10,
+ /* column 19: */ 17, 19, 20, 0, 6, 10,
+ /* column 20: */ 22, 10, 20, 21,
+ /* column 21: */ 6, 2, 10, 19, 20, 11, 21, 22, 22, 22, 22,
+ /* column 22: */
+ /* column 23: */ 12, 11, 12, 23 } ;
+
+ int P [24], Pinv [24], i, j, k, jnew, p, inew, result ;
+ double Control [CAMD_CONTROL], Info [CAMD_INFO] ;
+ char A [24][24] ;
+ int C [ ] = { 3, 0, 4, 0, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 3, 4, 5, 2,
+ 8, 10, 4, 2, 2, 0 } ;
+
+ printf ("CAMD demo, with a jumbled version of the 24-by-24\n") ;
+ printf ("Harwell/Boeing matrix, can_24:\n") ;
+
+ /* get the default parameters, and print them */
+ camd_defaults (Control) ;
+ camd_control (Control) ;
+
+ /* print the input matrix */
+ nz = Ap [n] ;
+ printf ("\nJumbled input matrix: %d-by-%d, with %d entries.\n"
+ " Note that for a symmetric matrix such as this one, only the\n"
+ " strictly lower or upper triangular parts would need to be\n"
+ " passed to CAMD, since CAMD computes the ordering of A+A'. The\n"
+ " diagonal entries are also not needed, since CAMD ignores them.\n"
+ " This version of the matrix has jumbled columns and duplicate\n"
+ " row indices.\n", n, n, nz) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf ("\nColumn: %d, number of entries: %d, with row indices in"
+ " Ai [%d ... %d]:\n row indices:",
+ j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ printf (" %d", i) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* print a character plot of the input matrix. This is only reasonable
+ * because the matrix is small. */
+ printf ("\nPlot of (jumbled) input matrix pattern:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (i = 0 ; i < n ; i++) A [i][j] = '.' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ A [i][j] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2d: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* print a character plot of the matrix A+A'. */
+ printf ("\nPlot of symmetric matrix to be ordered by camd_order:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (i = 0 ; i < n ; i++) A [i][j] = '.' ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ A [j][j] = 'X' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ A [i][j] = 'X' ;
+ A [j][i] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2d: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* order the matrix */
+ result = camd_order (n, Ap, Ai, P, Control, Info, C) ;
+ printf ("return value from camd_order: %d (should be %d)\n",
+ result, CAMD_OK_BUT_JUMBLED) ;
+
+ /* print the statistics */
+ camd_info (Info) ;
+
+ if (result != CAMD_OK_BUT_JUMBLED)
+ {
+ printf ("CAMD failed\n") ;
+ exit (1) ;
+ }
+
+ /* print the permutation vector, P, and compute the inverse permutation */
+ printf ("Permutation vector:\n") ;
+ for (k = 0 ; k < n ; k++)
+ {
+ /* row/column j is the kth row/column in the permuted matrix */
+ j = P [k] ;
+ Pinv [j] = k ;
+ printf (" %2d", j) ;
+ }
+ printf ("\nPermuted constraints:\n") ;
+ for (k = 0 ; k < n ; k++)
+ {
+ /* row/column j is the kth row/column in the permuted matrix */
+ printf (" %2d", C [P [k]]) ;
+ }
+ printf ("\n\n") ;
+
+ printf ("Inverse permutation vector:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ k = Pinv [j] ;
+ printf (" %2d", k) ;
+ }
+ printf ("\n\n") ;
+
+ /* print a character plot of the permuted matrix. */
+ printf ("\nPlot of (symmetrized) permuted matrix pattern:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (i = 0 ; i < n ; i++) A [i][j] = '.' ;
+ }
+ for (jnew = 0 ; jnew < n ; jnew++)
+ {
+ j = P [jnew] ;
+ A [jnew][jnew] = 'X' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ inew = Pinv [Ai [p]] ;
+ A [inew][jnew] = 'X' ;
+ A [jnew][inew] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1d", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2d: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ return (0) ;
+}
diff --git a/CAMD/Demo/camd_demo2.out b/CAMD/Demo/camd_demo2.out
new file mode 100644
index 0000000..d3f67fd
--- /dev/null
+++ b/CAMD/Demo/camd_demo2.out
@@ -0,0 +1,209 @@
+CAMD demo, with a jumbled version of the 24-by-24
+Harwell/Boeing matrix, can_24:
+
+camd version 2.2, May 31, 2007: approximate minimum degree ordering:
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+
+
+Jumbled input matrix: 24-by-24, with 116 entries.
+ Note that for a symmetric matrix such as this one, only the
+ strictly lower or upper triangular parts would need to be
+ passed to CAMD, since CAMD computes the ordering of A+A'. The
+ diagonal entries are also not needed, since CAMD ignores them.
+ This version of the matrix has jumbled columns and duplicate
+ row indices.
+
+Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]:
+ row indices: 0 17 18 21 5 12 5 0 13
+
+Column: 1, number of entries: 5, with row indices in Ai [9 ... 13]:
+ row indices: 14 1 8 13 17
+
+Column: 2, number of entries: 6, with row indices in Ai [14 ... 19]:
+ row indices: 2 20 11 6 11 22
+
+Column: 3, number of entries: 8, with row indices in Ai [20 ... 27]:
+ row indices: 3 3 10 7 18 18 15 19
+
+Column: 4, number of entries: 5, with row indices in Ai [28 ... 32]:
+ row indices: 7 9 15 14 16
+
+Column: 5, number of entries: 4, with row indices in Ai [33 ... 36]:
+ row indices: 5 13 6 17
+
+Column: 6, number of entries: 7, with row indices in Ai [37 ... 43]:
+ row indices: 5 0 11 6 12 6 23
+
+Column: 7, number of entries: 9, with row indices in Ai [44 ... 52]:
+ row indices: 3 4 9 7 14 16 15 17 18
+
+Column: 8, number of entries: 5, with row indices in Ai [53 ... 57]:
+ row indices: 1 9 14 14 14
+
+Column: 9, number of entries: 5, with row indices in Ai [58 ... 62]:
+ row indices: 7 13 8 1 17
+
+Column: 10, number of entries: 0, with row indices in Ai [63 ... 62]:
+ row indices:
+
+Column: 11, number of entries: 3, with row indices in Ai [63 ... 65]:
+ row indices: 2 12 23
+
+Column: 12, number of entries: 3, with row indices in Ai [66 ... 68]:
+ row indices: 5 11 12
+
+Column: 13, number of entries: 3, with row indices in Ai [69 ... 71]:
+ row indices: 0 13 17
+
+Column: 14, number of entries: 3, with row indices in Ai [72 ... 74]:
+ row indices: 1 9 14
+
+Column: 15, number of entries: 3, with row indices in Ai [75 ... 77]:
+ row indices: 3 15 16
+
+Column: 16, number of entries: 4, with row indices in Ai [78 ... 81]:
+ row indices: 16 4 4 15
+
+Column: 17, number of entries: 4, with row indices in Ai [82 ... 85]:
+ row indices: 13 17 19 17
+
+Column: 18, number of entries: 5, with row indices in Ai [86 ... 90]:
+ row indices: 15 17 19 9 10
+
+Column: 19, number of entries: 6, with row indices in Ai [91 ... 96]:
+ row indices: 17 19 20 0 6 10
+
+Column: 20, number of entries: 4, with row indices in Ai [97 ... 100]:
+ row indices: 22 10 20 21
+
+Column: 21, number of entries: 11, with row indices in Ai [101 ... 111]:
+ row indices: 6 2 10 19 20 11 21 22 22 22 22
+
+Column: 22, number of entries: 0, with row indices in Ai [112 ... 111]:
+ row indices:
+
+Column: 23, number of entries: 4, with row indices in Ai [112 ... 115]:
+ row indices: 12 11 12 23
+
+Plot of (jumbled) input matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . . X . . . . . . X . . . . . X . . . .
+ 1: . X . . . . . . X X . . . . X . . . . . . . . .
+ 2: . . X . . . . . . . . X . . . . . . . . . X . .
+ 3: . . . X . . . X . . . . . . . X . . . . . . . .
+ 4: . . . . . . . X . . . . . . . . X . . . . . . .
+ 5: X . . . . X X . . . . . X . . . . . . . . . . .
+ 6: . . X . . X X . . . . . . . . . . . . X . X . .
+ 7: . . . X X . . X . X . . . . . . . . . . . . . .
+ 8: . X . . . . . . . X . . . . . . . . . . . . . .
+ 9: . . . . X . . X X . . . . . X . . . X . . . . .
+10: . . . X . . . . . . . . . . . . . . X X X X . .
+11: . . X . . . X . . . . . X . . . . . . . . X . X
+12: X . . . . . X . . . . X X . . . . . . . . . . X
+13: X X . . . X . . . X . . . X . . . X . . . . . .
+14: . X . . X . . X X . . . . . X . . . . . . . . .
+15: . . . X X . . X . . . . . . . X X . X . . . . .
+16: . . . . X . . X . . . . . . . X X . . . . . . .
+17: X X . . . X . X . X . . . X . . . X X X . . . .
+18: X . . X . . . X . . . . . . . . . . . . . . . .
+19: . . . X . . . . . . . . . . . . . X X X . X . .
+20: . . X . . . . . . . . . . . . . . . . X X X . .
+21: X . . . . . . . . . . . . . . . . . . . X X . .
+22: . . X . . . . . . . . . . . . . . . . . X X . .
+23: . . . . . . X . . . . X . . . . . . . . . . . X
+
+Plot of symmetric matrix to be ordered by camd_order:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . X X . . . . . X X . . . X X X . X . .
+ 1: . X . . . . . . X X . . . X X . . X . . . . . .
+ 2: . . X . . . X . . . . X . . . . . . . . X X X .
+ 3: . . . X . . . X . . X . . . . X . . X X . . . .
+ 4: . . . . X . . X . X . . . . X X X . . . . . . .
+ 5: X . . . . X X . . . . . X X . . . X . . . . . .
+ 6: X . X . . X X . . . . X X . . . . . . X . X . X
+ 7: . . . X X . . X . X . . . . X X X X X . . . . .
+ 8: . X . . . . . . X X . . . . X . . . . . . . . .
+ 9: . X . . X . . X X X . . . X X . . X X . . . . .
+10: . . . X . . . . . . X . . . . . . . X X X X . .
+11: . . X . . . X . . . . X X . . . . . . . . X . X
+12: X . . . . X X . . . . X X . . . . . . . . . . X
+13: X X . . . X . . . X . . . X . . . X . . . . . .
+14: . X . . X . . X X X . . . . X . . . . . . . . .
+15: . . . X X . . X . . . . . . . X X . X . . . . .
+16: . . . . X . . X . . . . . . . X X . . . . . . .
+17: X X . . . X . X . X . . . X . . . X X X . . . .
+18: X . . X . . . X . X X . . . . X . X X X . . . .
+19: X . . X . . X . . . X . . . . . . X X X X X . .
+20: . . X . . . . . . . X . . . . . . . . X X X X .
+21: X . X . . . X . . . X X . . . . . . . X X X X .
+22: . . X . . . . . . . . . . . . . . . . . X X X .
+23: . . . . . . X . . . . X X . . . . . . . . . . X
+return value from camd_order: 1 (should be 1)
+
+camd: approximate minimum degree ordering, results:
+ status: OK, but jumbled
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 102
+ symmetry of A: 0.4000
+ number of nonzeros on diagonal: 17
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2208
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 140
+ nonzeros in L (including diagonal): 164
+ # divide operations for LDL' or LU: 140
+ # multiply-subtract operations for LDL': 593
+ # multiply-subtract operations for LU: 1046
+ max nz. in any column of L (incl. diagonal): 13
+
+ chol flop count for real A, sqrt counted as 1 flop: 1350
+ LDL' flop count for real A: 1326
+ LDL' flop count for complex A: 6004
+ LU flop count for real A (with no pivoting): 2232
+ LU flop count for complex A (with no pivoting): 9628
+
+Permutation vector:
+ 23 3 1 5 4 8 9 7 17 22 21 6 10 14 0 2 11 15 20 13 16 12 18 19
+Permuted constraints:
+ 0 0 0 1 1 2 2 2 2 2 2 2 3 3 3 4 4 4 4 5 5 5 8 10
+
+Inverse permutation vector:
+ 14 2 15 1 4 3 11 7 5 6 12 16 21 19 13 17 20 8 22 23 18 10 9 0
+
+
+Plot of (symmetrized) permuted matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . . . . . . . X . . . . X . . . . X . .
+ 1: . X . . . . . X . . . . X . . . . X . . . . X X
+ 2: . . X . . X X . X . . . . X . . . . . X . . . .
+ 3: . . . X . . . . X . . X . . X . . . . X . X . .
+ 4: . . . . X . X X . . . . . X . . . X . . X . . .
+ 5: . . X . . X X . . . . . . X . . . . . . . . . .
+ 6: . . X . X X X X X . . . . X . . . . . X . . X .
+ 7: . X . . X . X X X . . . . X . . . X . . X . X .
+ 8: . . X X . . X X X . . . . . X . . . . X . . X X
+ 9: . . . . . . . . . X X . . . . X . . X . . . . .
+10: . . . . . . . . . X X X X . X X X . X . . . . X
+11: X . . X . . . . . . X X . . X X X . . . . X . X
+12: . X . . . . . . . . X . X . . . . . X . . . X X
+13: . . X . X X X X . . . . . X . . . . . . . . . .
+14: . . . X . . . . X . X X . . X . . . . X . X X X
+15: . . . . . . . . . X X X . . . X X . X . . . . .
+16: X . . . . . . . . . X X . . . X X . . . . X . .
+17: . X . . X . . X . . . . . . . . . X . . X . X .
+18: . . . . . . . . . X X . X . . X . . X . . . . X
+19: . . X X . . X . X . . . . . X . . . . X . . . .
+20: . . . . X . . X . . . . . . . . . X . . X . . .
+21: X . . X . . . . . . . X . . X . X . . . . X . .
+22: . X . . . . X X X . . . X . X . . X . . . . X X
+23: . X . . . . . . X . X X X . X . . . X . . . X X
diff --git a/CAMD/Demo/camd_l_demo.c b/CAMD/Demo/camd_l_demo.c
new file mode 100644
index 0000000..55491d6
--- /dev/null
+++ b/CAMD/Demo/camd_l_demo.c
@@ -0,0 +1,176 @@
+/* ========================================================================= */
+/* === CAMD demo main program (UF_long integer version) ==================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* A simple C main program that illustrates the use of the ANSI C interface
+ * to CAMD.
+ */
+
+#include "camd.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+/* define UF_long */
+#include "UFconfig.h"
+
+int main (void)
+{
+ /* The symmetric can_24 Harwell/Boeing matrix, including upper and lower
+ * triangular parts, and the diagonal entries. Note that this matrix is
+ * 0-based, with row and column indices in the range 0 to n-1. */
+ UF_long n = 24, nz,
+ Ap [ ] = { 0, 9, 15, 21, 27, 33, 39, 48, 57, 61, 70, 76, 82, 88, 94, 100,
+ 106, 110, 119, 128, 137, 143, 152, 156, 160 },
+ Ai [ ] = {
+ /* column 0: */ 0, 5, 6, 12, 13, 17, 18, 19, 21,
+ /* column 1: */ 1, 8, 9, 13, 14, 17,
+ /* column 2: */ 2, 6, 11, 20, 21, 22,
+ /* column 3: */ 3, 7, 10, 15, 18, 19,
+ /* column 4: */ 4, 7, 9, 14, 15, 16,
+ /* column 5: */ 0, 5, 6, 12, 13, 17,
+ /* column 6: */ 0, 2, 5, 6, 11, 12, 19, 21, 23,
+ /* column 7: */ 3, 4, 7, 9, 14, 15, 16, 17, 18,
+ /* column 8: */ 1, 8, 9, 14,
+ /* column 9: */ 1, 4, 7, 8, 9, 13, 14, 17, 18,
+ /* column 10: */ 3, 10, 18, 19, 20, 21,
+ /* column 11: */ 2, 6, 11, 12, 21, 23,
+ /* column 12: */ 0, 5, 6, 11, 12, 23,
+ /* column 13: */ 0, 1, 5, 9, 13, 17,
+ /* column 14: */ 1, 4, 7, 8, 9, 14,
+ /* column 15: */ 3, 4, 7, 15, 16, 18,
+ /* column 16: */ 4, 7, 15, 16,
+ /* column 17: */ 0, 1, 5, 7, 9, 13, 17, 18, 19,
+ /* column 18: */ 0, 3, 7, 9, 10, 15, 17, 18, 19,
+ /* column 19: */ 0, 3, 6, 10, 17, 18, 19, 20, 21,
+ /* column 20: */ 2, 10, 19, 20, 21, 22,
+ /* column 21: */ 0, 2, 6, 10, 11, 19, 20, 21, 22,
+ /* column 22: */ 2, 20, 21, 22,
+ /* column 23: */ 6, 11, 12, 23 } ;
+
+ UF_long P [24], Pinv [24], i, j, k, jnew, p, inew, result ;
+ double Control [CAMD_CONTROL], Info [CAMD_INFO] ;
+ char A [24][24] ;
+ UF_long C [ ] = { 0, 0, 4, 0, 1, 0, 2, 2, 1, 1, 3, 4, 5, 5, 3, 4,
+ 5, 2, 5, 3, 4, 2, 1, 0 };
+
+ printf ("CAMD version %d.%d, date: %s\n", CAMD_MAIN_VERSION,
+ CAMD_SUB_VERSION, CAMD_DATE) ;
+ printf ("CAMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:\n") ;
+
+ /* get the default parameters, and print them */
+ camd_l_defaults (Control) ;
+ camd_l_control (Control) ;
+
+ /* print the input matrix */
+ nz = Ap [n] ;
+ printf ("\nInput matrix: %ld-by-%ld, with %ld entries.\n"
+ " Note that for a symmetric matrix such as this one, only the\n"
+ " strictly lower or upper triangular parts would need to be\n"
+ " passed to CAMD, since CAMD computes the ordering of A+A'. The\n"
+ " diagonal entries are also not needed, since CAMD ignores them.\n"
+ , n, n, nz) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf ("\nColumn: %ld, number of entries: %ld, with row indices in"
+ " Ai [%ld ... %ld]:\n row indices:",
+ j, Ap [j+1] - Ap [j], Ap [j], Ap [j+1]-1) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ printf (" %ld", i) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* print a character plot of the input matrix. This is only reasonable
+ * because the matrix is small. */
+ printf ("\nPlot of input matrix pattern:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (i = 0 ; i < n ; i++) A [i][j] = '.' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ A [i][j] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1ld", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2ld: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ /* order the matrix */
+ result = camd_l_order (n, Ap, Ai, P, Control, Info, C) ;
+ printf ("return value from camd_l_order: %ld (should be %d)\n",
+ result, CAMD_OK) ;
+
+ /* print the statistics */
+ camd_l_info (Info) ;
+
+ if (result != CAMD_OK)
+ {
+ printf ("CAMD failed\n") ;
+ exit (1) ;
+ }
+
+ /* print the permutation vector, P, and compute the inverse permutation */
+ printf ("Permutation vector:\n") ;
+ for (k = 0 ; k < n ; k++)
+ {
+ /* row/column j is the kth row/column in the permuted matrix */
+ j = P [k] ;
+ Pinv [j] = k ;
+ printf (" %2ld", j) ;
+ }
+ printf ("\n\n") ;
+
+ printf ("Inverse permutation vector:\n") ;
+ for (j = 0 ; j < n ; j++)
+ {
+ k = Pinv [j] ;
+ printf (" %2ld", k) ;
+ }
+ printf ("\n\n") ;
+
+ /* print a character plot of the permuted matrix. */
+ printf ("\nPlot of permuted matrix pattern:\n") ;
+ for (jnew = 0 ; jnew < n ; jnew++)
+ {
+ j = P [jnew] ;
+ for (inew = 0 ; inew < n ; inew++) A [inew][jnew] = '.' ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ inew = Pinv [Ai [p]] ;
+ A [inew][jnew] = 'X' ;
+ }
+ }
+ printf (" ") ;
+ for (j = 0 ; j < n ; j++) printf (" %1ld", j % 10) ;
+ printf ("\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf ("%2ld: ", i) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" %c", A [i][j]) ;
+ }
+ printf ("\n") ;
+ }
+
+ return (0) ;
+}
diff --git a/CAMD/Demo/camd_l_demo.out b/CAMD/Demo/camd_l_demo.out
new file mode 100644
index 0000000..8899143
--- /dev/null
+++ b/CAMD/Demo/camd_l_demo.out
@@ -0,0 +1,178 @@
+CAMD version 2.2, date: May 31, 2007
+CAMD demo, with the 24-by-24 Harwell/Boeing matrix, can_24:
+
+camd version 2.2, May 31, 2007: approximate minimum degree ordering:
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+
+
+Input matrix: 24-by-24, with 160 entries.
+ Note that for a symmetric matrix such as this one, only the
+ strictly lower or upper triangular parts would need to be
+ passed to CAMD, since CAMD computes the ordering of A+A'. The
+ diagonal entries are also not needed, since CAMD ignores them.
+
+Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]:
+ row indices: 0 5 6 12 13 17 18 19 21
+
+Column: 1, number of entries: 6, with row indices in Ai [9 ... 14]:
+ row indices: 1 8 9 13 14 17
+
+Column: 2, number of entries: 6, with row indices in Ai [15 ... 20]:
+ row indices: 2 6 11 20 21 22
+
+Column: 3, number of entries: 6, with row indices in Ai [21 ... 26]:
+ row indices: 3 7 10 15 18 19
+
+Column: 4, number of entries: 6, with row indices in Ai [27 ... 32]:
+ row indices: 4 7 9 14 15 16
+
+Column: 5, number of entries: 6, with row indices in Ai [33 ... 38]:
+ row indices: 0 5 6 12 13 17
+
+Column: 6, number of entries: 9, with row indices in Ai [39 ... 47]:
+ row indices: 0 2 5 6 11 12 19 21 23
+
+Column: 7, number of entries: 9, with row indices in Ai [48 ... 56]:
+ row indices: 3 4 7 9 14 15 16 17 18
+
+Column: 8, number of entries: 4, with row indices in Ai [57 ... 60]:
+ row indices: 1 8 9 14
+
+Column: 9, number of entries: 9, with row indices in Ai [61 ... 69]:
+ row indices: 1 4 7 8 9 13 14 17 18
+
+Column: 10, number of entries: 6, with row indices in Ai [70 ... 75]:
+ row indices: 3 10 18 19 20 21
+
+Column: 11, number of entries: 6, with row indices in Ai [76 ... 81]:
+ row indices: 2 6 11 12 21 23
+
+Column: 12, number of entries: 6, with row indices in Ai [82 ... 87]:
+ row indices: 0 5 6 11 12 23
+
+Column: 13, number of entries: 6, with row indices in Ai [88 ... 93]:
+ row indices: 0 1 5 9 13 17
+
+Column: 14, number of entries: 6, with row indices in Ai [94 ... 99]:
+ row indices: 1 4 7 8 9 14
+
+Column: 15, number of entries: 6, with row indices in Ai [100 ... 105]:
+ row indices: 3 4 7 15 16 18
+
+Column: 16, number of entries: 4, with row indices in Ai [106 ... 109]:
+ row indices: 4 7 15 16
+
+Column: 17, number of entries: 9, with row indices in Ai [110 ... 118]:
+ row indices: 0 1 5 7 9 13 17 18 19
+
+Column: 18, number of entries: 9, with row indices in Ai [119 ... 127]:
+ row indices: 0 3 7 9 10 15 17 18 19
+
+Column: 19, number of entries: 9, with row indices in Ai [128 ... 136]:
+ row indices: 0 3 6 10 17 18 19 20 21
+
+Column: 20, number of entries: 6, with row indices in Ai [137 ... 142]:
+ row indices: 2 10 19 20 21 22
+
+Column: 21, number of entries: 9, with row indices in Ai [143 ... 151]:
+ row indices: 0 2 6 10 11 19 20 21 22
+
+Column: 22, number of entries: 4, with row indices in Ai [152 ... 155]:
+ row indices: 2 20 21 22
+
+Column: 23, number of entries: 4, with row indices in Ai [156 ... 159]:
+ row indices: 6 11 12 23
+
+Plot of input matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . X X . . . . . X X . . . X X X . X . .
+ 1: . X . . . . . . X X . . . X X . . X . . . . . .
+ 2: . . X . . . X . . . . X . . . . . . . . X X X .
+ 3: . . . X . . . X . . X . . . . X . . X X . . . .
+ 4: . . . . X . . X . X . . . . X X X . . . . . . .
+ 5: X . . . . X X . . . . . X X . . . X . . . . . .
+ 6: X . X . . X X . . . . X X . . . . . . X . X . X
+ 7: . . . X X . . X . X . . . . X X X X X . . . . .
+ 8: . X . . . . . . X X . . . . X . . . . . . . . .
+ 9: . X . . X . . X X X . . . X X . . X X . . . . .
+10: . . . X . . . . . . X . . . . . . . X X X X . .
+11: . . X . . . X . . . . X X . . . . . . . . X . X
+12: X . . . . X X . . . . X X . . . . . . . . . . X
+13: X X . . . X . . . X . . . X . . . X . . . . . .
+14: . X . . X . . X X X . . . . X . . . . . . . . .
+15: . . . X X . . X . . . . . . . X X . X . . . . .
+16: . . . . X . . X . . . . . . . X X . . . . . . .
+17: X X . . . X . X . X . . . X . . . X X X . . . .
+18: X . . X . . . X . X X . . . . X . X X X . . . .
+19: X . . X . . X . . . X . . . . . . X X X X X . .
+20: . . X . . . . . . . X . . . . . . . . X X X X .
+21: X . X . . . X . . . X X . . . . . . . X X X X .
+22: . . X . . . . . . . . . . . . . . . . . X X X .
+23: . . . . . . X . . . . X X . . . . . . . . . . X
+return value from camd_l_order: 0 (should be 0)
+
+camd: approximate minimum degree ordering, results:
+ status: OK
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 3288
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 135
+ nonzeros in L (including diagonal): 159
+ # divide operations for LDL' or LU: 135
+ # multiply-subtract operations for LDL': 541
+ # multiply-subtract operations for LU: 947
+ max nz. in any column of L (incl. diagonal): 12
+
+ chol flop count for real A, sqrt counted as 1 flop: 1241
+ LDL' flop count for real A: 1217
+ LDL' flop count for complex A: 5543
+ LU flop count for real A (with no pivoting): 2029
+ LU flop count for complex A (with no pivoting): 8791
+
+Permutation vector:
+ 23 3 1 5 0 22 4 8 9 7 6 21 17 19 10 14 2 11 20 15 12 13 18 16
+
+Inverse permutation vector:
+ 4 2 16 1 6 3 10 9 7 8 14 17 20 21 15 19 23 12 22 13 18 11 5 0
+
+
+Plot of permuted matrix pattern:
+ 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+ 0: X . . . . . . . . . X . . . . . . X . . X . . .
+ 1: . X . . . . . . . X . . . X X . . . . X . . X .
+ 2: . . X . . . . X X . . . X . . X . . . . . X . .
+ 3: . . . X X . . . . . X . X . . . . . . . X X . .
+ 4: . . . X X . . . . . X X X X . . . . . . X X X .
+ 5: . . . . . X . . . . . X . . . . X . X . . . . .
+ 6: . . . . . . X . X X . . . . . X . . . X . . . X
+ 7: . . X . . . . X X . . . . . . X . . . . . . . .
+ 8: . . X . . . X X X X . . X . . X . . . . . X X .
+ 9: . X . . . . X . X X . . X . . X . . . X . . X X
+10: X . . X X . . . . . X X . X . . X X . . X . . .
+11: . . . . X X . . . . X X . X X . X X X . . . . .
+12: . . X X X . . . X X . . X X . . . . . . . X X .
+13: . X . . X . . . . . X X X X X . . . X . . . X .
+14: . X . . . . . . . . . X . X X . . . X . . . X .
+15: . . X . . . X X X X . . . . . X . . . . . . . .
+16: . . . . . X . . . . X X . . . . X X X . . . . .
+17: X . . . . . . . . . X X . . . . X X . . X . . .
+18: . . . . . X . . . . . X . X X . X . X . . . . .
+19: . X . . . . X . . X . . . . . . . . . X . . X X
+20: X . . X X . . . . . X . . . . . . X . . X . . .
+21: . . X X X . . . X . . . X . . . . . . . . X . .
+22: . X . . X . . . X X . . X X X . . . . X . . X .
+23: . . . . . . X . . X . . . . . . . . . X . . . X
diff --git a/CAMD/Demo/camd_simple.c b/CAMD/Demo/camd_simple.c
new file mode 100644
index 0000000..54334a6
--- /dev/null
+++ b/CAMD/Demo/camd_simple.c
@@ -0,0 +1,24 @@
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+#include <stdio.h>
+#include "camd.h"
+
+int n = 5 ;
+int Ap [ ] = { 0, 2, 6, 10, 12, 14} ;
+int Ai [ ] = { 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 } ;
+int C [ ] = { 2, 0, 0, 0, 1 } ;
+int P [5] ;
+
+int main (void)
+{
+ int k ;
+ (void) camd_order (n, Ap, Ai, P, (double *) NULL, (double *) NULL, C) ;
+ for (k = 0 ; k < n ; k++) printf ("P [%d] = %d\n", k, P [k]) ;
+ return (0) ;
+}
+
diff --git a/CAMD/Demo/camd_simple.out b/CAMD/Demo/camd_simple.out
new file mode 100644
index 0000000..c94ebcd
--- /dev/null
+++ b/CAMD/Demo/camd_simple.out
@@ -0,0 +1,5 @@
+P [0] = 3
+P [1] = 2
+P [2] = 1
+P [3] = 4
+P [4] = 0
diff --git a/CAMD/Doc/CAMD_UserGuide.bib b/CAMD/Doc/CAMD_UserGuide.bib
new file mode 100644
index 0000000..03fbfa8
--- /dev/null
+++ b/CAMD/Doc/CAMD_UserGuide.bib
@@ -0,0 +1,98 @@
+ at string{SIREV = "{SIAM} Review"}
+ at string{SIMAX = "{SIAM} J. Matrix Anal. Applic."}
+ at string{SIAMJSC = "{SIAM} J. Sci. Comput."}
+ at string{TOMS = "{ACM} Trans. Math. Softw."}
+
+ at article{schu:01,
+ author = {J. Schulze},
+ title = {Towards a tighter coupling of bottom-up and top-down sparse matrix ordering methods},
+ journal = {BIT},
+ volume = {41},
+ number = {4},
+ pages = "800--841",
+ year = {2001}
+ }
+
+ at article{GeorgeLiu89,
+ author={George, A. and Liu, J. W. H.},
+ year={1989},
+ title={The Evolution of the Minimum Degree Ordering Algorithm},
+ journal=SIREV,
+ volume={31},
+ number={1},
+ pages={1--19}}
+
+ at article{AmestoyDavisDuff96,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={An approximate minimum degree ordering algorithm},
+ journal=SIMAX,
+ year={1996}
+ ,volume={17}
+ ,number={4}
+ ,pages={886-905}
+ }
+
+ at article{AmestoyDavisDuff04,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={Algorithm 837: An approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={381-388}
+ }
+
+ at misc{hsl:2002,
+ author = {HSL},
+ title = "{HSL} 2002: {A} collection of {F}ortran codes for large
+ scale scientific computation",
+ note = {{\tt www.cse.clrc.ac.uk/nag/hsl}},
+ year = 2002}
+
+
+ at article{RothbergEisenstat98,
+ author={Rothberg, E. and Eisenstat, S. C.},
+ title={Node selection strategies for bottom-up sparse matrix orderings},
+ journal=SIMAX,
+ year={1998}
+ ,volume={19}
+ ,number={3}
+ ,pages={682-695}
+ }
+
+ at article{KarypisKumar98e,
+ author={Karypis, G. and Kumar, V.},
+ title={A fast and high quality multilevel scheme for partitioning irregular graphs},
+ journal=SIAMJSC,
+ year={1998}
+ ,volume={20}
+ ,pages={359-392}
+ }
+
+ at article{Chaco,
+ author={B. Hendrickson and E. Rothberg},
+ title={Improving the runtime and quality of nested dissection ordering},
+ journal=SIAMJSC,
+ year={1999}
+ ,volume={20}
+ ,pages={468--489}
+ }
+
+ at article{PellegriniRomanAmestoy00,
+ author={Pellegrini, F. and Roman, J. and Amestoy, P.},
+ title={Hybridizing nested dissection and halo approximate minimum degree for efficient sparse matrix ordering},
+ journal={Concurrency: Practice and Experience},
+ year={2000}
+ ,volume={12}
+ ,pages={68-84}
+ }
+
+ at article{DavisGilbertLarimoreNg04,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={A column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,pages={353-376}
+ }
+
diff --git a/CAMD/Doc/CAMD_UserGuide.pdf b/CAMD/Doc/CAMD_UserGuide.pdf
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+\documentclass[11pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+%------------------------------------------------------------------------------
+\begin{document}
+%------------------------------------------------------------------------------
+
+\title{CAMD Version 2.2 User Guide}
+\author{Patrick R. Amestoy\thanks{ENSEEIHT-IRIT,
+2 rue Camichel 31017 Toulouse, France.
+email: amestoy at enseeiht.fr. http://www.enseeiht.fr/$\sim$amestoy.}
+\and Yanqing (Morris) Chen
+\and Timothy A. Davis\thanks{
+Dept.~of Computer and Information Science and Engineering,
+Univ.~of Florida, Gainesville, FL, USA.
+email: davis at cise.ufl.edu.
+http://www.cise.ufl.edu/$\sim$davis.
+This work was supported by the National
+Science Foundation, under grants ASC-9111263, DMS-9223088, and CCR-0203270.
+Portions of the work were done while on sabbatical at Stanford University
+and Lawrence Berkeley National Laboratory (with funding from Stanford
+University and the SciDAC program). Ordering constraints added with
+support from Sandia National Laboratory (Dept. of Energy).
+}
+\and Iain S. Duff\thanks{Rutherford Appleton Laboratory, Chilton, Didcot,
+Oxon OX11 0QX, England. email: i.s.duff at rl.ac.uk.
+http://www.numerical.rl.ac.uk/people/isd/isd.html.
+This work was supported by the EPSRC under grant GR/R46441.
+}}
+
+\date{May 31, 2007}
+\maketitle
+
+%------------------------------------------------------------------------------
+\begin{abstract}
+CAMD is a set of ANSI C routines that implements the approximate minimum degree
+ordering algorithm to permute sparse matrices prior to
+numerical factorization. Ordering constraints can be optionally provided.
+A MATLAB interface is included.
+\end{abstract}
+%------------------------------------------------------------------------------
+
+CAMD Version 2.2, Copyright\copyright 2007 by Timothy A. Davis,
+Yanqing (Morris) Chen,
+Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved.
+CAMD is available under alternate licences; contact T. Davis for details.
+
+{\bf CAMD License:}
+ Your use or distribution of CAMD or any modified version of
+ CAMD implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+{\bf Availability:}
+ http://www.cise.ufl.edu/research/sparse/camd
+
+{\bf Acknowledgments:}
+
+ This work was supported by the National Science Foundation, under
+ grants ASC-9111263 and DMS-9223088 and CCR-0203270, and by Sandia
+ National Labs (a grant from DOE).
+ The conversion to C, the addition of the elimination tree
+ post-ordering, and the handling of dense rows and columns
+ were done while Davis was on sabbatical at
+ Stanford University and Lawrence Berkeley National Laboratory.
+ The ordering constraints were added by Chen and Davis.
+
+%------------------------------------------------------------------------------
+\newpage
+\section{Overview}
+%------------------------------------------------------------------------------
+
+CAMD is a set of routines for preordering a sparse matrix prior to
+numerical factorization. It uses an approximate minimum degree ordering
+algorithm \cite{AmestoyDavisDuff96,AmestoyDavisDuff04}
+to find a permutation matrix $\m{P}$
+so that the Cholesky factorization $\m{PAP}\tr=\m{LL}\tr$ has fewer
+(often much fewer) nonzero entries than the Cholesky factorization of $\m{A}$.
+The algorithm is typically much faster than other ordering methods
+and minimum degree ordering
+algorithms that compute an exact degree \cite{GeorgeLiu89}.
+Some methods, such as approximate deficiency
+\cite{RothbergEisenstat98} and graph-partitioning based methods
+\cite{Chaco,KarypisKumar98e,PellegriniRomanAmestoy00,schu:01}
+can produce better orderings, depending on the matrix.
+
+The algorithm starts with an undirected graph representation of a
+symmetric sparse matrix $\m{A}$. Node $i$ in the graph corresponds to row
+and column $i$ of the matrix, and there is an edge $(i,j)$ in the graph if
+$a_{ij}$ is nonzero.
+The degree of a node is initialized to the number of off-diagonal nonzeros
+in row $i$, which is the size of the set of nodes
+adjacent to $i$ in the graph.
+
+The selection of a pivot $a_{ii}$ from the diagonal of $\m{A}$ and the first
+step of Gaussian elimination corresponds to one step of graph elimination.
+Numerical fill-in causes new nonzero entries in the matrix
+(fill-in refers to
+nonzeros in $\m{L}$ that are not in $\m{A}$).
+Node $i$ is eliminated and edges are added to its neighbors
+so that they form a clique (or {\em element}). To reduce fill-in,
+node $i$ is selected as the node of least degree in the graph.
+This process repeats until the graph is eliminated.
+
+The clique is represented implicitly. Rather than listing all the
+new edges in the graph, a single list of nodes is kept which represents
+the clique. This list corresponds to the nonzero pattern of the first
+column of $\m{L}$. As the elimination proceeds, some of these cliques
+become subsets of subsequent cliques, and are removed. This graph
+can be stored in place, that is
+using the same amount of memory as the original graph.
+
+The most costly part of the minimum degree algorithm is the recomputation
+of the degrees of nodes adjacent to the current pivot element.
+Rather than keep track of the exact degree, the approximate minimum degree
+algorithm finds an upper bound on the degree that is easier to compute.
+For nodes of least degree, this bound tends to be tight. Using the
+approximate degree instead of the exact degree leads to a substantial savings
+in run time, particularly for very irregularly structured matrices.
+It has no effect on the quality of the ordering.
+
+The elimination phase is followed by an
+elimination tree post-ordering. This has no effect on fill-in, but
+reorganizes the ordering so that the subsequent numerical factorization is
+more efficient. It also includes a pre-processing phase in which nodes of
+very high degree are removed (without causing fill-in), and placed last in the
+permutation $\m{P}$ (subject to the constraints).
+This reduces the run time substantially if the matrix
+has a few rows with many nonzero entries, and has little effect on the quality
+of the ordering.
+CAMD operates on the
+symmetric nonzero pattern of $\m{A}+\m{A}\tr$, so it can be given
+an unsymmetric matrix, or either the lower or upper triangular part of
+a symmetric matrix.
+
+CAMD has the ability to order the matrix with constraints. Each
+node $i$ in the graph (row/column $i$ in the matrix) has a constraint,
+{\tt C[i]}, which is in the range {\tt 0} to {\tt n-1}. All nodes with
+{\tt C[i] = 0} are
+ordered first, followed by all nodes with constraint {\tt 1}, and so on.
+That is, {\tt C[P[k]]} is monotonically non-decreasing as {\tt k} varies from
+{\tt 0} to {\tt n-1}. If {\tt C} is NULL, no
+constraints are used (the ordering will be similar to AMD's ordering,
+except that the postordering is different).
+The optional {\tt C} parameter is also provided in the MATLAB interface,
+({\tt p = camd (A,Control,C)}).
+
+For a discussion of the long history of the minimum degree algorithm,
+see \cite{GeorgeLiu89}.
+
+%------------------------------------------------------------------------------
+\section{Availability}
+%------------------------------------------------------------------------------
+
+CAMD is available at http://www.cise.ufl.edu/research/sparse.
+The Fortran version is available as the routine {\tt MC47} in HSL
+(formerly the Harwell Subroutine Library) \cite{hsl:2002}. {\tt MC47} does
+not include ordering constraints.
+
+%------------------------------------------------------------------------------
+\section{Using CAMD in MATLAB}
+%------------------------------------------------------------------------------
+
+To use CAMD in MATLAB, you must first compile the CAMD mexFunction.
+Just type {\tt make} in the Unix system shell, while in the {\tt CAMD}
+directory. You can also type {\tt camd\_make} in MATLAB, while in the
+{\tt CAMD/MATLAB} directory. Place the {\tt CAMD/MATLAB} directory in your
+MATLAB path. This can be done on any system with MATLAB, including Windows.
+See Section~\ref{Install} for more details on how to install CAMD.
+
+The MATLAB statement {\tt p=camd(A)} finds a permutation vector {\tt p} such
+that the Cholesky factorization {\tt chol(A(p,p))} is typically sparser than
+{\tt chol(A)}.
+If {\tt A} is unsymmetric, {\tt camd(A)} is identical to {\tt camd(A+A')}
+(ignoring numerical cancellation).
+If {\tt A} is not symmetric positive definite,
+but has substantial diagonal entries and a mostly symmetric nonzero pattern,
+then this ordering is also suitable for LU factorization. A partial pivoting
+threshold may be required to prevent pivots from being selected off the
+diagonal, such as the statement {\tt [L,U,P] = lu (A (p,p), 0.1)}.
+Type {\tt help lu} for more details.
+The statement {\tt [L,U,P,Q] = lu (A (p,p))} in MATLAB 6.5 is
+not suitable, however, because it uses UMFPACK Version 4.0 and thus
+does not attempt to select pivots from the diagonal.
+UMFPACK Version 4.1 in MATLAB 7.0 and later
+uses several strategies, including a symmetric pivoting strategy, and
+will give you better results if you want to factorize an unsymmetric matrix
+of this type. Refer to the UMFPACK User Guide for more details, at
+http://www.cise.ufl.edu/research/sparse/umfpack.
+
+The CAMD mexFunction is much faster than the built-in MATLAB symmetric minimum
+degree ordering methods, SYMAMD and SYMMMD. Its ordering quality is
+essentially identical to AMD, comparable to SYMAMD, and better than SYMMMD
+\cite{DavisGilbertLarimoreNg04}.
+
+An optional input argument can be used to modify the control parameters for
+CAMD (aggressive absorption, dense row/column handling, and printing of
+statistics). An optional output
+argument provides statistics on the ordering, including an analysis of the
+fill-in and the floating-point operation count for a subsequent factorization.
+For more details (once CAMD is installed),
+type {\tt help camd} in the MATLAB command window.
+
+%------------------------------------------------------------------------------
+\section{Using CAMD in a C program}
+\label{Cversion}
+%------------------------------------------------------------------------------
+
+The C-callable CAMD library consists of seven user-callable routines and one
+include file. There are two versions of each of the routines, with
+{\tt int} and {\tt long} integers.
+The routines with prefix
+{\tt camd\_l\_} use {\tt long} integer arguments; the others use
+{\tt int} integer arguments. If you compile CAMD in the standard
+ILP32 mode (32-bit {\tt int}'s, {\tt long}'s, and pointers) then the versions
+are essentially identical. You will be able to solve problems using up to 2GB
+of memory. If you compile CAMD in the standard LP64 mode, the size of an
+{\tt int} remains 32-bits, but the size of a {\tt long} and a pointer both get
+promoted to 64-bits.
+
+The following routines are fully described in Section~\ref{Primary}:
+
+\begin{itemize}
+\item {\tt camd\_order}
+({\tt long} version: {\tt camd\_l\_order})
+ {\footnotesize
+ \begin{verbatim}
+ #include "camd.h"
+ int n, Ap [n+1], Ai [nz], P [n], C [n] ;
+ double Control [CAMD_CONTROL], Info [CAMD_INFO] ;
+ int result = camd_order (n, Ap, Ai, P, Control, Info, C) ;
+ \end{verbatim}
+ }
+ Computes the approximate minimum degree ordering of an $n$-by-$n$ matrix
+ $\m{A}$. Returns a permutation vector {\tt P} of size {\tt n}, where
+ {\tt P[k] = i} if row and column {\tt i} are the {\tt k}th row and
+ column in the permuted matrix.
+ This routine allocates its own memory of size $1.2e+9n$ integers,
+ where $e$ is the number of nonzeros in $\m{A}+\m{A}\tr$.
+ It computes statistics about the matrix $\m{A}$, such as the symmetry of
+ its nonzero pattern, the number of nonzeros in $\m{L}$,
+ and the number of floating-point operations required for Cholesky and LU
+ factorizations (which are returned in the {\tt Info} array).
+ The user's input matrix is not modified.
+ It returns {\tt CAMD\_OK} if successful,
+ {\tt CAMD\_OK\_BUT\_JUMBLED} if successful (but the matrix had unsorted
+ and/or duplicate row indices),
+ {\tt CAMD\_INVALID} if the matrix is invalid,
+ {\tt CAMD\_OUT\_OF\_MEMORY} if out of memory.
+
+ The array {\tt C} provides the ordering constraints.
+ On input, {\tt C} may be null (to denote no constraints);
+ otherwise, it must be an array size {\tt n}, with entries in the range
+ {\tt 0} to {\tt n-1}.
+ On output, {\tt C[P[0..n-1]]} is monotonically non-descreasing.
+
+\item {\tt camd\_defaults}
+({\tt long} version: {\tt camd\_l\_defaults})
+ {\footnotesize
+ \begin{verbatim}
+ #include "camd.h"
+ double Control [CAMD_CONTROL] ;
+ camd_defaults (Control) ;
+ \end{verbatim}
+ }
+ Sets the default control parameters in the {\tt Control} array. These can
+ then be modified as desired before passing the array to the other CAMD
+ routines.
+
+\item {\tt camd\_control}
+({\tt long} version: {\tt camd\_l\_control})
+ {\footnotesize
+ \begin{verbatim}
+ #include "camd.h"
+ double Control [CAMD_CONTROL] ;
+ camd_control (Control) ;
+ \end{verbatim}
+ }
+ Prints a description of the control parameters, and their values.
+
+\item {\tt camd\_info}
+({\tt long} version: {\tt camd\_l\_info})
+ {\footnotesize
+ \begin{verbatim}
+ #include "camd.h"
+ double Info [CAMD_INFO] ;
+ camd_info (Info) ;
+ \end{verbatim}
+ }
+ Prints a description of the statistics computed by CAMD, and their values.
+
+\item {\tt camd\_valid}
+({\tt long} version: {\tt camd\_valid})
+ {\footnotesize
+ \begin{verbatim}
+ #include "camd.h"
+ int n, Ap [n+1], Ai [nz] ;
+ int result = camd_valid (n, n, Ap, Ai) ;
+ \end{verbatim}
+ }
+ Returns {\tt CAMD\_OK} or {\tt CAMD\_OK\_BUT\_JUMBLED}
+ if the matrix is valid as input to {\tt camd\_order};
+ the latter is returned if the matrix has unsorted and/or duplicate
+ row indices in one or more columns.
+ Returns {\tt CAMD\_INVALID} if the matrix cannot be passed to
+ {\tt camd\_order}.
+ For {\tt camd\_order}, the matrix must
+ also be square. The first two arguments are the number of rows and the
+ number of columns of the matrix. For its use in CAMD, these must both
+ equal {\tt n}.
+
+\item {\tt camd\_2}
+({\tt long} version: {\tt camd\_l2})
+ CAMD ordering kernel. It is faster than {\tt camd\_order}, and
+ can be called by the user, but it is difficult to use.
+ It does not check its inputs for errors.
+ It does not require the columns of its input matrix to be sorted,
+ but it destroys the matrix on output. Additional workspace must be passed.
+ Refer to the source file {\tt CAMD/Source/camd\_2.c} for a description.
+
+\end{itemize}
+
+The nonzero pattern of the matrix $\m{A}$ is represented in compressed column
+form.
+For an $n$-by-$n$ matrix $\m{A}$ with {\tt nz} nonzero entries, the
+representation consists of two arrays: {\tt Ap} of size {\tt n+1} and {\tt Ai}
+of size {\tt nz}. The row indices of entries in column {\tt j} are stored in
+ {\tt Ai[Ap[j]} $\ldots$ {\tt Ap[j+1]-1]}.
+For {\tt camd\_order},
+if duplicate row indices are present, or if the row indices in any given
+column are not sorted in ascending order, then {\tt camd\_order} creates
+an internal copy of the matrix with sorted rows and no duplicate entries,
+and orders the copy. This adds slightly to the time and memory usage of
+{\tt camd\_order}, but is not an error condition.
+
+The matrix is 0-based, and thus
+row indices must be in the range {\tt 0} to {\tt n-1}.
+The first entry {\tt Ap[0]} must be zero.
+The total number of entries in the matrix is thus {\tt nz = Ap[n]}.
+
+The matrix must be square, but it does not need to be symmetric.
+The {\tt camd\_order} routine constructs the nonzero pattern of
+$\m{B} = \m{A}+\m{A}\tr$ (without forming $\m{A}\tr$ explicitly if
+$\m{A}$ has sorted columns and no duplicate entries),
+and then orders the matrix $\m{B}$. Thus, either the
+lower triangular part of $\m{A}$, the upper triangular part,
+or any combination may be passed. The transpose $\m{A}\tr$ may also be
+passed to {\tt camd\_order}.
+The diagonal entries may be present, but are ignored.
+
+%------------------------------------------------------------------------------
+\subsection{Control parameters}
+\label{control_param}
+%------------------------------------------------------------------------------
+
+Control parameters are set in an optional {\tt Control} array.
+It is optional in the sense that if
+a {\tt NULL} pointer is passed for the {\tt Control} input argument,
+then default control parameters are used.
+%
+\begin{itemize}
+\item {\tt Control[CAMD\_DENSE]} (or {\tt Control(1)} in MATLAB):
+controls the threshold for ``dense''
+rows/columns. A dense row/column in $\m{A}+\m{A}\tr$
+can cause CAMD to spend significant time
+in ordering the matrix. If {\tt Control[CAMD\_DENSE]} $\ge 0$,
+rows/columns with
+more than {\tt Control[CAMD\_DENSE]} $\sqrt{n}$ entries are ignored during
+the ordering, and placed last in the output order. The default
+value of {\tt Control[CAMD\_DENSE]} is 10. If negative, no rows/columns
+are treated as ``dense.'' Rows/columns with 16 or fewer off-diagonal
+entries are never considered ``dense.''
+%
+\item {\tt Control[CAMD\_AGGRESSIVE]} (or {\tt Control(2)} in MATLAB):
+controls whether or not to use
+aggressive absorption, in which a prior element is absorbed into the current
+element if it is a subset of the current element, even if it is not
+adjacent to the current pivot element (refer
+to \cite{AmestoyDavisDuff96,AmestoyDavisDuff04}
+for more details). The default value is nonzero,
+which means that aggressive absorption will be performed. This nearly always
+leads to a better ordering (because the approximate degrees are more
+accurate) and a lower execution time. There are cases where it can
+lead to a slightly worse ordering, however. To turn it off, set
+{\tt Control[CAMD\_AGGRESSIVE]} to 0.
+%
+\end{itemize}
+
+Statistics are returned in the {\tt Info} array
+(if {\tt Info} is {\tt NULL}, then no statistics are returned).
+Refer to {\tt camd.h} file, for more details
+(14 different statistics are returned, so the list is not included here).
+
+%------------------------------------------------------------------------------
+\subsection{Sample C program}
+%------------------------------------------------------------------------------
+
+The following program, {\tt camd\_demo.c}, illustrates the basic use of CAMD.
+See Section~\ref{Synopsis} for a short description
+of each calling sequence.
+
+{\footnotesize
+\begin{verbatim}
+#include <stdio.h>
+#include "camd.h"
+
+int n = 5 ;
+int Ap [ ] = { 0, 2, 6, 10, 12, 14} ;
+int Ai [ ] = { 0,1, 0,1,2,4, 1,2,3,4, 2,3, 1,4 } ;
+int C [ ] = { 2, 0, 0, 0, 1 } ;
+int P [5] ;
+
+int main (void)
+{
+ int k ;
+ (void) camd_order (n, Ap, Ai, P, (double *) NULL, (double *) NULL, C) ;
+ for (k = 0 ; k < n ; k++) printf ("P [%d] = %d\n", k, P [k]) ;
+ return (0) ;
+}
+
+\end{verbatim}
+}
+
+The {\tt Ap} and {\tt Ai} arrays represent the binary matrix
+\[
+\m{A} = \left[
+\begin{array}{rrrrr}
+ 1 & 1 & 0 & 0 & 0 \\
+ 1 & 1 & 1 & 0 & 1 \\
+ 0 & 1 & 1 & 1 & 0 \\
+ 0 & 0 & 1 & 1 & 0 \\
+ 0 & 1 & 1 & 0 & 1 \\
+\end{array}
+\right].
+\]
+The diagonal entries are ignored.
+%
+CAMD constructs the pattern of $\m{A}+\m{A}\tr$,
+and returns a permutation vector of $(3, 2, 1, 4, 0)$.
+Note that nodes 1, 2, and 3 appear first (they are in the constraint set 0),
+node 4 appears next (since {\tt C[4] = 1}), and node 0 appears last.
+%
+Since the matrix is unsymmetric but with a mostly symmetric nonzero
+pattern, this would be a suitable permutation for an LU factorization of a
+matrix with this nonzero pattern and whose diagonal entries are not too small.
+The program uses default control settings and does not return any statistics
+about the ordering, factorization, or solution ({\tt Control} and {\tt Info}
+are both {\tt (double *) NULL}). It also ignores the status value returned by
+{\tt camd\_order}.
+
+More example programs are included with the CAMD package.
+The {\tt camd\_demo.c} program provides a more detailed demo of CAMD.
+Another example is the CAMD mexFunction, {\tt camd\_mex.c}.
+
+%------------------------------------------------------------------------------
+\subsection{A note about zero-sized arrays}
+%------------------------------------------------------------------------------
+
+CAMD uses several user-provided arrays of size {\tt n} or {\tt nz}.
+Either {\tt n} or {\tt nz} can be zero.
+If you attempt to {\tt malloc} an array of size zero,
+however, {\tt malloc} will return a null pointer which CAMD will report
+as invalid. If you {\tt malloc} an array of
+size {\tt n} or {\tt nz} to pass to CAMD, make sure that you handle the
+{\tt n} = 0 and {\tt nz = 0} cases correctly.
+
+%------------------------------------------------------------------------------
+\section{Synopsis of C-callable routines}
+\label{Synopsis}
+%------------------------------------------------------------------------------
+
+The matrix $\m{A}$ is {\tt n}-by-{\tt n} with {\tt nz} entries.
+
+{\footnotesize
+\begin{verbatim}
+#include "camd.h"
+int n, status, Ap [n+1], Ai [nz], P [n], C [n] ;
+double Control [CAMD_CONTROL], Info [CAMD_INFO] ;
+camd_defaults (Control) ;
+status = camd_order (n, Ap, Ai, P, Control, Info, C) ;
+camd_control (Control) ;
+camd_info (Info) ;
+status = camd_valid (n, n, Ap, Ai) ;
+\end{verbatim}
+}
+
+The {\tt camd\_l\_*} routines are identical, except that all {\tt int}
+arguments become {\tt long}:
+
+{\footnotesize
+\begin{verbatim}
+#include "camd.h"
+long n, status, Ap [n+1], Ai [nz], P [n], C [n] ;
+double Control [CAMD_CONTROL], Info [CAMD_INFO] ;
+camd_l_defaults (Control) ;
+status = camd_l_order (n, Ap, Ai, P, Control, Info, C) ;
+camd_l_control (Control) ;
+camd_l_info (Info) ;
+status = camd_l_valid (n, n, Ap, Ai) ;
+\end{verbatim}
+}
+
+%------------------------------------------------------------------------------
+\section{Installation}
+\label{Install}
+%------------------------------------------------------------------------------
+
+The following discussion assumes you have the {\tt make} program, either in
+Unix, or in Windows with Cygwin.
+
+System-dependent configurations are in the {\tt ../UFconfig/UFconfig.mk}
+file. You can edit that file to customize the compilation. The default
+settings will work on most systems.
+Sample configuration files are provided
+for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha.
+
+To compile and install the C-callable CAMD library,
+go to the {\tt CAMD} directory and type {\tt make}.
+The library will be placed in {\tt CAMD/Lib/libcamd.a}.
+Three demo programs of the CAMD ordering routine will be compiled and tested in
+the {\tt CAMD/Demo} directory.
+The outputs of these demo programs will then be compared with output
+files in the distribution.
+
+Typing {\tt make clean} will remove all but the final compiled libraries
+and demo programs. Typing {\tt make purge} or {\tt make distclean}
+removes all files not in the original distribution.
+If you compile CAMD and then later change the {\tt ../UFconfig/UFconfig.mk} file
+then you should type {\tt make purge} and then {\tt make} to recompile.
+
+When you compile your program that uses the C-callable CAMD library,
+you need to add the {\tt CAMD/Lib/libcamd.a} library
+and you need to tell your compiler to look in the
+{\tt CAMD/Include} directory for include
+files.
+See {\tt CAMD/Demo/Makefile} for an example.
+
+If all you want to use is the CAMD mexFunction in MATLAB, you can skip
+the use of the {\tt make} command entirely. Simply type
+{\tt camd\_make} in MATLAB while in the {\tt CAMD/MATLAB} directory.
+This works on any system with MATLAB, including Windows.
+Alternately, type {\tt make} in the {\tt CAMD/MATLAB} directory.
+
+If you have MATLAB 7.2 or earlier, you must first edit UFconfig/UFconfig.h to
+remove the "-largeArrayDims" option from the MEX command, prior to
+{\tt make mex} or {\tt make} in the MATLAB directory
+(or just use {\tt camd\_make.m} inside MATLAB.
+
+If you are including CAMD as a subset of a larger library and do not want
+to link the C standard I/O library, or if you simply do not need to use
+them, you can safely remove the {\tt camd\_control.c} and {\tt camd\_info.c}
+files. Similarly, if you use default parameters (or define your
+own {\tt Control} array), then you can exclude the {\tt camd\_defaults.c}
+file.
+Each of these files contains the user-callable routines of the same
+name. None of these auxiliary routines are directly called by
+{\tt camd\_order}.
+The {\tt camd\_dump.c} file contains debugging routines
+that are neither used nor compiled unless debugging is enabled.
+The {\tt camd\_internal.h} file must be edited to enable debugging;
+refer to the instructions in that file.
+The bare minimum files required to use just {\tt camd\_order} are
+{\tt camd.h} and {\tt camd\_internal.h}
+in the {\tt Include} directory,
+and
+{\tt camd\_1.c},
+{\tt camd\_2.c},
+{\tt camd\_aat.c},
+{\tt camd\_global.c},
+{\tt and\_order.c},
+{\tt camd\_postorder.c},
+{\tt camd\_preprocess.c},
+and
+{\tt camd\_valid.c}
+in the {\tt Source} directory.
+
+%------------------------------------------------------------------------------
+\newpage
+\section{The CAMD routines}
+\label{Primary}
+%------------------------------------------------------------------------------
+
+The file {\tt CAMD/Include/camd.h} listed below
+describes each user-callable routine in CAMD,
+and gives details on their use.
+
+{\footnotesize
+\begin{verbatim}
+/* ========================================================================= */
+/* === CAMD: approximate minimum degree ordering ========================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* CAMD finds a symmetric ordering P of a matrix A so that the Cholesky
+ * factorization of P*A*P' has fewer nonzeros and takes less work than the
+ * Cholesky factorization of A. If A is not symmetric, then it performs its
+ * ordering on the matrix A+A'. Two sets of user-callable routines are
+ * provided, one for int integers and the other for UF_long integers.
+ *
+ * The method is based on the approximate minimum degree algorithm, discussed
+ * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm",
+ * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp.
+ * 886-905, 1996.
+ */
+
+#ifndef CAMD_H
+#define CAMD_H
+
+/* make it easy for C++ programs to include CAMD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* get the definition of size_t: */
+#include <stddef.h>
+
+/* define UF_long */
+#include "UFconfig.h"
+
+int camd_order /* returns CAMD_OK, CAMD_OK_BUT_JUMBLED,
+ * CAMD_INVALID, or CAMD_OUT_OF_MEMORY */
+(
+ int n, /* A is n-by-n. n must be >= 0. */
+ const int Ap [ ], /* column pointers for A, of size n+1 */
+ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */
+ int P [ ], /* output permutation, of size n */
+ double Control [ ], /* input Control settings, of size CAMD_CONTROL */
+ double Info [ ], /* output Info statistics, of size CAMD_INFO */
+ const int C [ ] /* Constraint set of A, of size n; can be NULL */
+) ;
+
+UF_long camd_l_order /* see above for description of arguments */
+(
+ UF_long n,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ UF_long P [ ],
+ double Control [ ],
+ double Info [ ],
+ const UF_long C [ ]
+) ;
+
+/* Input arguments (not modified):
+ *
+ * n: the matrix A is n-by-n.
+ * Ap: an int/UF_long array of size n+1, containing column pointers of A.
+ * Ai: an int/UF_long array of size nz, containing the row indices of A,
+ * where nz = Ap [n].
+ * Control: a double array of size CAMD_CONTROL, containing control
+ * parameters. Defaults are used if Control is NULL.
+ *
+ * Output arguments (not defined on input):
+ *
+ * P: an int/UF_long array of size n, containing the output permutation. If
+ * row i is the kth pivot row, then P [k] = i. In MATLAB notation,
+ * the reordered matrix is A (P,P).
+ * Info: a double array of size CAMD_INFO, containing statistical
+ * information. Ignored if Info is NULL.
+ *
+ * On input, the matrix A is stored in column-oriented form. The row indices
+ * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1].
+ *
+ * If the row indices appear in ascending order in each column, and there
+ * are no duplicate entries, then camd_order is slightly more efficient in
+ * terms of time and memory usage. If this condition does not hold, a copy
+ * of the matrix is created (where these conditions do hold), and the copy is
+ * ordered.
+ *
+ * Row indices must be in the range 0 to
+ * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros
+ * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n].
+ * The matrix does not need to be symmetric, and the diagonal does not need to
+ * be present (if diagonal entries are present, they are ignored except for
+ * the output statistic Info [CAMD_NZDIAG]). The arrays Ai and Ap are not
+ * modified. This form of the Ap and Ai arrays to represent the nonzero
+ * pattern of the matrix A is the same as that used internally by MATLAB.
+ * If you wish to use a more flexible input structure, please see the
+ * umfpack_*_triplet_to_col routines in the UMFPACK package, at
+ * http://www.cise.ufl.edu/research/sparse/umfpack.
+ *
+ * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the
+ * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0
+ * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these
+ * restrictions are not met, CAMD returns CAMD_INVALID.
+ *
+ * CAMD returns:
+ *
+ * CAMD_OK if the matrix is valid and sufficient memory can be allocated to
+ * perform the ordering.
+ *
+ * CAMD_OUT_OF_MEMORY if not enough memory can be allocated.
+ *
+ * CAMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is
+ * NULL.
+ *
+ * CAMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate
+ * entries, but was otherwise valid.
+ *
+ * The CAMD routine first forms the pattern of the matrix A+A', and then
+ * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of
+ * the original is the kth pivotal row. In MATLAB notation, the permuted
+ * matrix is A (P,P), except that 0-based indexing is used instead of the
+ * 1-based indexing in MATLAB.
+ *
+ * The Control array is used to set various parameters for CAMD. If a NULL
+ * pointer is passed, default values are used. The Control array is not
+ * modified.
+ *
+ * Control [CAMD_DENSE]: controls the threshold for "dense" rows/columns.
+ * A dense row/column in A+A' can cause CAMD to spend a lot of time in
+ * ordering the matrix. If Control [CAMD_DENSE] >= 0, rows/columns
+ * with more than Control [CAMD_DENSE] * sqrt (n) entries are ignored
+ * during the ordering, and placed last in the output order. The
+ * default value of Control [CAMD_DENSE] is 10. If negative, no
+ * rows/columns are treated as "dense". Rows/columns with 16 or
+ * fewer off-diagonal entries are never considered "dense".
+ *
+ * Control [CAMD_AGGRESSIVE]: controls whether or not to use aggressive
+ * absorption, in which a prior element is absorbed into the current
+ * element if is a subset of the current element, even if it is not
+ * adjacent to the current pivot element (refer to Amestoy, Davis,
+ * & Duff, 1996, for more details). The default value is nonzero,
+ * which means to perform aggressive absorption. This nearly always
+ * leads to a better ordering (because the approximate degrees are
+ * more accurate) and a lower execution time. There are cases where
+ * it can lead to a slightly worse ordering, however. To turn it off,
+ * set Control [CAMD_AGGRESSIVE] to 0.
+ *
+ * Control [2..4] are not used in the current version, but may be used in
+ * future versions.
+ *
+ * The Info array provides statistics about the ordering on output. If it is
+ * not present, the statistics are not returned. This is not an error
+ * condition.
+ *
+ * Info [CAMD_STATUS]: the return value of CAMD, either CAMD_OK,
+ * CAMD_OK_BUT_JUMBLED, CAMD_OUT_OF_MEMORY, or CAMD_INVALID.
+ *
+ * Info [CAMD_N]: n, the size of the input matrix
+ *
+ * Info [CAMD_NZ]: the number of nonzeros in A, nz = Ap [n]
+ *
+ * Info [CAMD_SYMMETRY]: the symmetry of the matrix A. It is the number
+ * of "matched" off-diagonal entries divided by the total number of
+ * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also
+ * an entry, for any pair (i,j) for which i != j. In MATLAB notation,
+ * S = spones (A) ;
+ * B = tril (S, -1) + triu (S, 1) ;
+ * symmetry = nnz (B & B') / nnz (B) ;
+ *
+ * Info [CAMD_NZDIAG]: the number of entries on the diagonal of A.
+ *
+ * Info [CAMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the
+ * diagonal. If A is perfectly symmetric (Info [CAMD_SYMMETRY] = 1)
+ * with a fully nonzero diagonal, then Info [CAMD_NZ_A_PLUS_AT] = nz-n
+ * (the smallest possible value). If A is perfectly unsymmetric
+ * (Info [CAMD_SYMMETRY] = 0, for an upper triangular matrix, for
+ * example) with no diagonal, then Info [CAMD_NZ_A_PLUS_AT] = 2*nz
+ * (the largest possible value).
+ *
+ * Info [CAMD_NDENSE]: the number of "dense" rows/columns of A+A' that were
+ * removed from A prior to ordering. These are placed last in the
+ * output order P.
+ *
+ * Info [CAMD_MEMORY]: the amount of memory used by CAMD, in bytes. In the
+ * current version, this is 1.2 * Info [CAMD_NZ_A_PLUS_AT] + 9*n
+ * times the size of an integer. This is at most 2.4nz + 9n. This
+ * excludes the size of the input arguments Ai, Ap, and P, which have
+ * a total size of nz + 2*n + 1 integers.
+ *
+ * Info [CAMD_NCMPA]: the number of garbage collections performed.
+ *
+ * Info [CAMD_LNZ]: the number of nonzeros in L (excluding the diagonal).
+ * This is a slight upper bound because mass elimination is combined
+ * with the approximate degree update. It is a rough upper bound if
+ * there are many "dense" rows/columns. The rest of the statistics,
+ * below, are also slight or rough upper bounds, for the same reasons.
+ * The post-ordering of the assembly tree might also not exactly
+ * correspond to a true elimination tree postordering.
+ *
+ * Info [CAMD_NDIV]: the number of divide operations for a subsequent LDL'
+ * or LU factorization of the permuted matrix A (P,P).
+ *
+ * Info [CAMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a
+ * subsequent LDL' factorization of A (P,P).
+ *
+ * Info [CAMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a
+ * subsequent LU factorization of A (P,P), assuming that no numerical
+ * pivoting is required.
+ *
+ * Info [CAMD_DMAX]: the maximum number of nonzeros in any column of L,
+ * including the diagonal.
+ *
+ * Info [14..19] are not used in the current version, but may be used in
+ * future versions.
+ */
+
+/* ------------------------------------------------------------------------- */
+/* direct interface to CAMD */
+/* ------------------------------------------------------------------------- */
+
+/* camd_2 is the primary CAMD ordering routine. It is not meant to be
+ * user-callable because of its restrictive inputs and because it destroys
+ * the user's input matrix. It does not check its inputs for errors, either.
+ * However, if you can work with these restrictions it can be faster than
+ * camd_order and use less memory (assuming that you can create your own copy
+ * of the matrix for CAMD to destroy). Refer to CAMD/Source/camd_2.c for a
+ * description of each parameter. */
+
+void camd_2
+(
+ int n,
+ int Pe [ ],
+ int Iw [ ],
+ int Len [ ],
+ int iwlen,
+ int pfree,
+ int Nv [ ],
+ int Next [ ],
+ int Last [ ],
+ int Head [ ],
+ int Elen [ ],
+ int Degree [ ],
+ int W [ ],
+ double Control [ ],
+ double Info [ ],
+ const int C [ ],
+ int BucketSet [ ]
+) ;
+
+void camd_l2
+(
+ UF_long n,
+ UF_long Pe [ ],
+ UF_long Iw [ ],
+ UF_long Len [ ],
+ UF_long iwlen,
+ UF_long pfree,
+ UF_long Nv [ ],
+ UF_long Next [ ],
+ UF_long Last [ ],
+ UF_long Head [ ],
+ UF_long Elen [ ],
+ UF_long Degree [ ],
+ UF_long W [ ],
+ double Control [ ],
+ double Info [ ],
+ const UF_long C [ ],
+ UF_long BucketSet [ ]
+
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* camd_valid */
+/* ------------------------------------------------------------------------- */
+
+/* Returns CAMD_OK or CAMD_OK_BUT_JUMBLED if the matrix is valid as input to
+ * camd_order; the latter is returned if the matrix has unsorted and/or
+ * duplicate row indices in one or more columns. Returns CAMD_INVALID if the
+ * matrix cannot be passed to camd_order. For camd_order, the matrix must also
+ * be square. The first two arguments are the number of rows and the number
+ * of columns of the matrix. For its use in CAMD, these must both equal n.
+ */
+
+int camd_valid
+(
+ int n_row, /* # of rows */
+ int n_col, /* # of columns */
+ const int Ap [ ], /* column pointers, of size n_col+1 */
+ const int Ai [ ] /* row indices, of size Ap [n_col] */
+) ;
+
+UF_long camd_l_valid
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* camd_cvalid */
+/* ------------------------------------------------------------------------- */
+
+/* Returns TRUE if the constraint set is valid as input to camd_order,
+ * FALSE otherwise. */
+
+int camd_cvalid
+(
+ int n,
+ const int C [ ]
+) ;
+
+UF_long camd_l_cvalid
+(
+ UF_long n,
+ const UF_long C [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* CAMD memory manager and printf routines */
+/* ------------------------------------------------------------------------- */
+
+/* The user can redefine these to change the malloc, free, and printf routines
+ * that CAMD uses. */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN void *(*camd_malloc) (size_t) ; /* pointer to malloc */
+EXTERN void (*camd_free) (void *) ; /* pointer to free */
+EXTERN void *(*camd_realloc) (void *, size_t) ; /* pointer to realloc */
+EXTERN void *(*camd_calloc) (size_t, size_t) ; /* pointer to calloc */
+EXTERN int (*camd_printf) (const char *, ...) ; /* pointer to printf */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD Control and Info arrays */
+/* ------------------------------------------------------------------------- */
+
+/* camd_defaults: sets the default control settings */
+void camd_defaults (double Control [ ]) ;
+void camd_l_defaults (double Control [ ]) ;
+
+/* camd_control: prints the control settings */
+void camd_control (double Control [ ]) ;
+void camd_l_control (double Control [ ]) ;
+
+/* camd_info: prints the statistics */
+void camd_info (double Info [ ]) ;
+void camd_l_info (double Info [ ]) ;
+
+#define CAMD_CONTROL 5 /* size of Control array */
+#define CAMD_INFO 20 /* size of Info array */
+
+/* contents of Control */
+#define CAMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */
+#define CAMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */
+
+/* default Control settings */
+#define CAMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */
+#define CAMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */
+
+/* contents of Info */
+#define CAMD_STATUS 0 /* return value of camd_order and camd_l_order */
+#define CAMD_N 1 /* A is n-by-n */
+#define CAMD_NZ 2 /* number of nonzeros in A */
+#define CAMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */
+#define CAMD_NZDIAG 4 /* # of entries on diagonal */
+#define CAMD_NZ_A_PLUS_AT 5 /* nz in A+A' */
+#define CAMD_NDENSE 6 /* number of "dense" rows/columns in A */
+#define CAMD_MEMORY 7 /* amount of memory used by CAMD */
+#define CAMD_NCMPA 8 /* number of garbage collections in CAMD */
+#define CAMD_LNZ 9 /* approx. nz in L, excluding the diagonal */
+#define CAMD_NDIV 10 /* number of fl. point divides for LU and LDL' */
+#define CAMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */
+#define CAMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */
+#define CAMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */
+
+/* ------------------------------------------------------------------------- */
+/* return values of CAMD */
+/* ------------------------------------------------------------------------- */
+
+#define CAMD_OK 0 /* success */
+#define CAMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */
+#define CAMD_INVALID -2 /* input arguments are not valid */
+#define CAMD_OK_BUT_JUMBLED 1 /* input matrix is OK for camd_order, but
+ * columns were not sorted, and/or duplicate entries were present. CAMD had
+ * to do extra work before ordering the matrix. This is a warning, not an
+ * error. */
+
+/* ========================================================================== */
+/* === CAMD version ========================================================= */
+/* ========================================================================== */
+
+/*
+ * As an example, to test if the version you are using is 1.2 or later:
+ *
+ * if (CAMD_VERSION >= CAMD_VERSION_CODE (1,2)) ...
+ *
+ * This also works during compile-time:
+ *
+ * #if (CAMD_VERSION >= CAMD_VERSION_CODE (1,2))
+ * printf ("This is version 1.2 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ */
+
+#define CAMD_DATE "May 31, 2007"
+#define CAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define CAMD_MAIN_VERSION 2
+#define CAMD_SUB_VERSION 2
+#define CAMD_SUBSUB_VERSION 0
+#define CAMD_VERSION CAMD_VERSION_CODE(CAMD_MAIN_VERSION,CAMD_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
+\end{verbatim}
+}
+
+%------------------------------------------------------------------------------
+\newpage
+% References
+%------------------------------------------------------------------------------
+
+\bibliographystyle{plain}
+\bibliography{CAMD_UserGuide}
+
+\end{document}
diff --git a/CAMD/Doc/ChangeLog b/CAMD/Doc/ChangeLog
new file mode 100644
index 0000000..e3c5e12
--- /dev/null
+++ b/CAMD/Doc/ChangeLog
@@ -0,0 +1,54 @@
+May 31, 2007: version 2.2.0
+
+ * port to 64-bit MATLAB
+
+ * Makefile moved from Source/ to Lib/
+
+Dec 12, 2006, v2.1.3
+
+ * minor MATLAB cleanup
+
+Sept 28, 2006, v2.1.2
+
+ * #define SIZE_T_MAX not done if already defined (Mac OSX).
+
+Aug 31, 2006: v2.1.1
+
+ * trivial change to comments in camd.m
+
+June 27, 2006: CAMD Version 2.1
+
+ * bug fix. Ordering constraints not always met if dense and/or empty
+ nodes are present in the matrix.
+
+Apr. 30, 2006: CAMD Version 2.0
+
+ * CAMD released, based on AMD v2.0. To compare the two codes, type the
+ command ./docdiff in this directory (the "CAMD" and "camd" strings
+ are replaced with "AMD" and "amd" when the two packages are compared,
+ to make more evident the substantive differences between the packages).
+
+ Primary differences with AMD v2.0:
+
+ CAMD adds the ability to order the matrix with constraints. Each
+ node i in the graph (row/column i in the matrix) has a constraint,
+ C[i], which is in the range 0 to n-1. All nodes with C[i] = 0 are
+ ordered first, followed by all nodes with constraint 1, and so on.
+ That is, C[P[k]] is monotonically non-decreasing as k varies from 0
+ to n-1. camd_order has an additional C parameter; if NULL, no
+ constraints are used (the ordering will be similar to AMD's ordering).
+ The optional C parameter is also added to the MATLAB interface,
+ p = camd (A,Control,C).
+
+ Since the C parameter is optional, CAMD can replace AMD in any
+ application that uses AMD. Just pass C = NULL (or omit C in the MATLAB
+ interface). There is no Fortran version of CAMD, however.
+
+ The postordering is different, and there is no camd_post_tree.c file.
+
+ A new routine, camd_cvalid, has been added to check the validity of C.
+
+ CAMD requires more workspace than AMD (n+1 integers).
+
+ All user-visible names AMD* and amd* replaced with CAMD* and camd*.
+
diff --git a/CAMD/Doc/License b/CAMD/Doc/License
new file mode 100644
index 0000000..781b0f2
--- /dev/null
+++ b/CAMD/Doc/License
@@ -0,0 +1,40 @@
+CAMD, Copyright (c) by Timothy A. Davis,
+Yanqing Chen,
+Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved.
+CAMD is available under alternate licenses, contact T. Davis for details.
+
+CAMD License:
+
+ Your use or distribution of CAMD or any modified version of
+ CAMD implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/camd
+
+-------------------------------------------------------------------------------
diff --git a/CAMD/Doc/Makefile b/CAMD/Doc/Makefile
new file mode 100644
index 0000000..0598668
--- /dev/null
+++ b/CAMD/Doc/Makefile
@@ -0,0 +1,35 @@
+#------------------------------------------------------------------------------
+# CAMD Makefile for compiling on Unix systems (for GNU or original make)
+#------------------------------------------------------------------------------
+
+default: dist
+
+include ../../UFconfig/UFconfig.mk
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+ - $(RM) camd_temp
+
+purge: distclean
+
+distclean: clean
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+
+#------------------------------------------------------------------------------
+# Create the User Guide and Quick Start Guide
+#------------------------------------------------------------------------------
+
+CAMD_UserGuide.pdf: CAMD_UserGuide.tex CAMD_UserGuide.bib
+ pdflatex CAMD_UserGuide
+ bibtex CAMD_UserGuide
+ pdflatex CAMD_UserGuide
+ pdflatex CAMD_UserGuide
+
+dist: CAMD_UserGuide.pdf
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+ - $(RM) camd_temp
+
diff --git a/CAMD/Doc/camd.sed b/CAMD/Doc/camd.sed
new file mode 100644
index 0000000..877e3f0
--- /dev/null
+++ b/CAMD/Doc/camd.sed
@@ -0,0 +1,2 @@
+s/CAMD/AMD/g
+s/camd/amd/g
diff --git a/CAMD/Doc/cdiff b/CAMD/Doc/cdiff
new file mode 100755
index 0000000..7d477e2
--- /dev/null
+++ b/CAMD/Doc/cdiff
@@ -0,0 +1,4 @@
+#
+echo diff $1 $2
+sed -f camd.sed < $1 > camd_temp
+diff camd_temp $2
diff --git a/CAMD/Doc/docdiff b/CAMD/Doc/docdiff
new file mode 100755
index 0000000..942d993
--- /dev/null
+++ b/CAMD/Doc/docdiff
@@ -0,0 +1,37 @@
+./cdiff ../Demo/camd_demo2.c ../../AMD/Demo/amd_demo2.c
+./cdiff ../Demo/camd_demo.c ../../AMD/Demo/amd_demo.c
+./cdiff ../Demo/camd_l_demo.c ../../AMD/Demo/amd_l_demo.c
+./cdiff ../Demo/camd_simple.c ../../AMD/Demo/amd_simple.c
+./cdiff ../Demo/Makefile ../../AMD/Demo/Makefile
+./cdiff ../Doc/CAMD_UserGuide.bib ../../AMD/Doc/AMD_UserGuide.bib
+./cdiff ../Doc/CAMD_UserGuide.tex ../../AMD/Doc/AMD_UserGuide.tex
+./cdiff ../Doc/lesser.txt ../../AMD/Doc/lesser.txt
+./cdiff ../Doc/License ../../AMD/Doc/License
+./cdiff ../Doc/Makefile ../../AMD/Doc/Makefile
+./cdiff ../Include/camd.h ../../AMD/Include/amd.h
+./cdiff ../Include/camd_internal.h ../../AMD/Include/amd_internal.h
+./cdiff ../Lib/libcamd.def ../../AMD/Lib/libamd.def
+./cdiff ../MATLAB/camd_demo.m ../../AMD/MATLAB/amd_demo.m
+./cdiff ../MATLAB/camd.m ../../AMD/MATLAB/amd2.m
+./cdiff ../MATLAB/camd_make.m ../../AMD/MATLAB/amd_make.m
+./cdiff ../MATLAB/camd_mex.c ../../AMD/MATLAB/amd_mex.c
+./cdiff ../MATLAB/can_24 ../../AMD/MATLAB/can_24
+./cdiff ../MATLAB/Contents.m ../../AMD/MATLAB/Contents.m
+./cdiff ../MATLAB/Makefile ../../AMD/MATLAB/Makefile
+./cdiff ../Source/camd_1.c ../../AMD/Source/amd_1.c
+./cdiff ../Source/camd_2.c ../../AMD/Source/amd_2.c
+./cdiff ../Source/camd_aat.c ../../AMD/Source/amd_aat.c
+./cdiff ../Source/camd_control.c ../../AMD/Source/amd_control.c
+./cdiff ../Source/camd_defaults.c ../../AMD/Source/amd_defaults.c
+./cdiff ../Source/camd_dump.c ../../AMD/Source/amd_dump.c
+./cdiff ../Source/camd_global.c ../../AMD/Source/amd_global.c
+./cdiff ../Source/camd_info.c ../../AMD/Source/amd_info.c
+./cdiff ../Source/camd_order.c ../../AMD/Source/amd_order.c
+./cdiff ../Source/camd_postorder.c ../../AMD/Source/amd_postorder.c
+# ./cdiff ../Source/camd_post_tree.c ../../AMD/Source/amd_post_tree.c
+./cdiff ../Source/camd_preprocess.c ../../AMD/Source/amd_preprocess.c
+./cdiff ../Source/camd_valid.c ../../AMD/Source/amd_valid.c
+./cdiff ../Source/GNUmakefile ../../AMD/Source/GNUmakefile
+./cdiff ../Source/Makefile ../../AMD/Source/Makefile
+./cdiff ../Makefile ../../AMD/Makefile
+./cdiff ../README.txt ../../AMD/README.txt
diff --git a/CAMD/Doc/lesser.txt b/CAMD/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/CAMD/Doc/lesser.txt
@@ -0,0 +1,504 @@
+ GNU LESSER GENERAL PUBLIC LICENSE
+ Version 2.1, February 1999
+
+ Copyright (C) 1991, 1999 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
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+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+Also add information on how to contact you by electronic and paper mail.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the library, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the
+ library `Frob' (a library for tweaking knobs) written by James Random Hacker.
+
+ <signature of Ty Coon>, 1 April 1990
+ Ty Coon, President of Vice
+
+That's all there is to it!
+
+
diff --git a/CAMD/Include/camd.h b/CAMD/Include/camd.h
new file mode 100644
index 0000000..a822387
--- /dev/null
+++ b/CAMD/Include/camd.h
@@ -0,0 +1,419 @@
+/* ========================================================================= */
+/* === CAMD: approximate minimum degree ordering ========================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* CAMD finds a symmetric ordering P of a matrix A so that the Cholesky
+ * factorization of P*A*P' has fewer nonzeros and takes less work than the
+ * Cholesky factorization of A. If A is not symmetric, then it performs its
+ * ordering on the matrix A+A'. Two sets of user-callable routines are
+ * provided, one for int integers and the other for UF_long integers.
+ *
+ * The method is based on the approximate minimum degree algorithm, discussed
+ * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm",
+ * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp.
+ * 886-905, 1996.
+ */
+
+#ifndef CAMD_H
+#define CAMD_H
+
+/* make it easy for C++ programs to include CAMD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* get the definition of size_t: */
+#include <stddef.h>
+
+/* define UF_long */
+#include "UFconfig.h"
+
+int camd_order /* returns CAMD_OK, CAMD_OK_BUT_JUMBLED,
+ * CAMD_INVALID, or CAMD_OUT_OF_MEMORY */
+(
+ int n, /* A is n-by-n. n must be >= 0. */
+ const int Ap [ ], /* column pointers for A, of size n+1 */
+ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */
+ int P [ ], /* output permutation, of size n */
+ double Control [ ], /* input Control settings, of size CAMD_CONTROL */
+ double Info [ ], /* output Info statistics, of size CAMD_INFO */
+ const int C [ ] /* Constraint set of A, of size n; can be NULL */
+) ;
+
+UF_long camd_l_order /* see above for description of arguments */
+(
+ UF_long n,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ UF_long P [ ],
+ double Control [ ],
+ double Info [ ],
+ const UF_long C [ ]
+) ;
+
+/* Input arguments (not modified):
+ *
+ * n: the matrix A is n-by-n.
+ * Ap: an int/UF_long array of size n+1, containing column pointers of A.
+ * Ai: an int/UF_long array of size nz, containing the row indices of A,
+ * where nz = Ap [n].
+ * Control: a double array of size CAMD_CONTROL, containing control
+ * parameters. Defaults are used if Control is NULL.
+ *
+ * Output arguments (not defined on input):
+ *
+ * P: an int/UF_long array of size n, containing the output permutation. If
+ * row i is the kth pivot row, then P [k] = i. In MATLAB notation,
+ * the reordered matrix is A (P,P).
+ * Info: a double array of size CAMD_INFO, containing statistical
+ * information. Ignored if Info is NULL.
+ *
+ * On input, the matrix A is stored in column-oriented form. The row indices
+ * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1].
+ *
+ * If the row indices appear in ascending order in each column, and there
+ * are no duplicate entries, then camd_order is slightly more efficient in
+ * terms of time and memory usage. If this condition does not hold, a copy
+ * of the matrix is created (where these conditions do hold), and the copy is
+ * ordered.
+ *
+ * Row indices must be in the range 0 to
+ * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros
+ * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n].
+ * The matrix does not need to be symmetric, and the diagonal does not need to
+ * be present (if diagonal entries are present, they are ignored except for
+ * the output statistic Info [CAMD_NZDIAG]). The arrays Ai and Ap are not
+ * modified. This form of the Ap and Ai arrays to represent the nonzero
+ * pattern of the matrix A is the same as that used internally by MATLAB.
+ * If you wish to use a more flexible input structure, please see the
+ * umfpack_*_triplet_to_col routines in the UMFPACK package, at
+ * http://www.cise.ufl.edu/research/sparse/umfpack.
+ *
+ * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the
+ * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0
+ * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these
+ * restrictions are not met, CAMD returns CAMD_INVALID.
+ *
+ * CAMD returns:
+ *
+ * CAMD_OK if the matrix is valid and sufficient memory can be allocated to
+ * perform the ordering.
+ *
+ * CAMD_OUT_OF_MEMORY if not enough memory can be allocated.
+ *
+ * CAMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is
+ * NULL.
+ *
+ * CAMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate
+ * entries, but was otherwise valid.
+ *
+ * The CAMD routine first forms the pattern of the matrix A+A', and then
+ * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of
+ * the original is the kth pivotal row. In MATLAB notation, the permuted
+ * matrix is A (P,P), except that 0-based indexing is used instead of the
+ * 1-based indexing in MATLAB.
+ *
+ * The Control array is used to set various parameters for CAMD. If a NULL
+ * pointer is passed, default values are used. The Control array is not
+ * modified.
+ *
+ * Control [CAMD_DENSE]: controls the threshold for "dense" rows/columns.
+ * A dense row/column in A+A' can cause CAMD to spend a lot of time in
+ * ordering the matrix. If Control [CAMD_DENSE] >= 0, rows/columns
+ * with more than Control [CAMD_DENSE] * sqrt (n) entries are ignored
+ * during the ordering, and placed last in the output order. The
+ * default value of Control [CAMD_DENSE] is 10. If negative, no
+ * rows/columns are treated as "dense". Rows/columns with 16 or
+ * fewer off-diagonal entries are never considered "dense".
+ *
+ * Control [CAMD_AGGRESSIVE]: controls whether or not to use aggressive
+ * absorption, in which a prior element is absorbed into the current
+ * element if is a subset of the current element, even if it is not
+ * adjacent to the current pivot element (refer to Amestoy, Davis,
+ * & Duff, 1996, for more details). The default value is nonzero,
+ * which means to perform aggressive absorption. This nearly always
+ * leads to a better ordering (because the approximate degrees are
+ * more accurate) and a lower execution time. There are cases where
+ * it can lead to a slightly worse ordering, however. To turn it off,
+ * set Control [CAMD_AGGRESSIVE] to 0.
+ *
+ * Control [2..4] are not used in the current version, but may be used in
+ * future versions.
+ *
+ * The Info array provides statistics about the ordering on output. If it is
+ * not present, the statistics are not returned. This is not an error
+ * condition.
+ *
+ * Info [CAMD_STATUS]: the return value of CAMD, either CAMD_OK,
+ * CAMD_OK_BUT_JUMBLED, CAMD_OUT_OF_MEMORY, or CAMD_INVALID.
+ *
+ * Info [CAMD_N]: n, the size of the input matrix
+ *
+ * Info [CAMD_NZ]: the number of nonzeros in A, nz = Ap [n]
+ *
+ * Info [CAMD_SYMMETRY]: the symmetry of the matrix A. It is the number
+ * of "matched" off-diagonal entries divided by the total number of
+ * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also
+ * an entry, for any pair (i,j) for which i != j. In MATLAB notation,
+ * S = spones (A) ;
+ * B = tril (S, -1) + triu (S, 1) ;
+ * symmetry = nnz (B & B') / nnz (B) ;
+ *
+ * Info [CAMD_NZDIAG]: the number of entries on the diagonal of A.
+ *
+ * Info [CAMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the
+ * diagonal. If A is perfectly symmetric (Info [CAMD_SYMMETRY] = 1)
+ * with a fully nonzero diagonal, then Info [CAMD_NZ_A_PLUS_AT] = nz-n
+ * (the smallest possible value). If A is perfectly unsymmetric
+ * (Info [CAMD_SYMMETRY] = 0, for an upper triangular matrix, for
+ * example) with no diagonal, then Info [CAMD_NZ_A_PLUS_AT] = 2*nz
+ * (the largest possible value).
+ *
+ * Info [CAMD_NDENSE]: the number of "dense" rows/columns of A+A' that were
+ * removed from A prior to ordering. These are placed last in the
+ * output order P.
+ *
+ * Info [CAMD_MEMORY]: the amount of memory used by CAMD, in bytes. In the
+ * current version, this is 1.2 * Info [CAMD_NZ_A_PLUS_AT] + 9*n
+ * times the size of an integer. This is at most 2.4nz + 9n. This
+ * excludes the size of the input arguments Ai, Ap, and P, which have
+ * a total size of nz + 2*n + 1 integers.
+ *
+ * Info [CAMD_NCMPA]: the number of garbage collections performed.
+ *
+ * Info [CAMD_LNZ]: the number of nonzeros in L (excluding the diagonal).
+ * This is a slight upper bound because mass elimination is combined
+ * with the approximate degree update. It is a rough upper bound if
+ * there are many "dense" rows/columns. The rest of the statistics,
+ * below, are also slight or rough upper bounds, for the same reasons.
+ * The post-ordering of the assembly tree might also not exactly
+ * correspond to a true elimination tree postordering.
+ *
+ * Info [CAMD_NDIV]: the number of divide operations for a subsequent LDL'
+ * or LU factorization of the permuted matrix A (P,P).
+ *
+ * Info [CAMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a
+ * subsequent LDL' factorization of A (P,P).
+ *
+ * Info [CAMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a
+ * subsequent LU factorization of A (P,P), assuming that no numerical
+ * pivoting is required.
+ *
+ * Info [CAMD_DMAX]: the maximum number of nonzeros in any column of L,
+ * including the diagonal.
+ *
+ * Info [14..19] are not used in the current version, but may be used in
+ * future versions.
+ */
+
+/* ------------------------------------------------------------------------- */
+/* direct interface to CAMD */
+/* ------------------------------------------------------------------------- */
+
+/* camd_2 is the primary CAMD ordering routine. It is not meant to be
+ * user-callable because of its restrictive inputs and because it destroys
+ * the user's input matrix. It does not check its inputs for errors, either.
+ * However, if you can work with these restrictions it can be faster than
+ * camd_order and use less memory (assuming that you can create your own copy
+ * of the matrix for CAMD to destroy). Refer to CAMD/Source/camd_2.c for a
+ * description of each parameter. */
+
+void camd_2
+(
+ int n,
+ int Pe [ ],
+ int Iw [ ],
+ int Len [ ],
+ int iwlen,
+ int pfree,
+ int Nv [ ],
+ int Next [ ],
+ int Last [ ],
+ int Head [ ],
+ int Elen [ ],
+ int Degree [ ],
+ int W [ ],
+ double Control [ ],
+ double Info [ ],
+ const int C [ ],
+ int BucketSet [ ]
+) ;
+
+void camd_l2
+(
+ UF_long n,
+ UF_long Pe [ ],
+ UF_long Iw [ ],
+ UF_long Len [ ],
+ UF_long iwlen,
+ UF_long pfree,
+ UF_long Nv [ ],
+ UF_long Next [ ],
+ UF_long Last [ ],
+ UF_long Head [ ],
+ UF_long Elen [ ],
+ UF_long Degree [ ],
+ UF_long W [ ],
+ double Control [ ],
+ double Info [ ],
+ const UF_long C [ ],
+ UF_long BucketSet [ ]
+
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* camd_valid */
+/* ------------------------------------------------------------------------- */
+
+/* Returns CAMD_OK or CAMD_OK_BUT_JUMBLED if the matrix is valid as input to
+ * camd_order; the latter is returned if the matrix has unsorted and/or
+ * duplicate row indices in one or more columns. Returns CAMD_INVALID if the
+ * matrix cannot be passed to camd_order. For camd_order, the matrix must also
+ * be square. The first two arguments are the number of rows and the number
+ * of columns of the matrix. For its use in CAMD, these must both equal n.
+ */
+
+int camd_valid
+(
+ int n_row, /* # of rows */
+ int n_col, /* # of columns */
+ const int Ap [ ], /* column pointers, of size n_col+1 */
+ const int Ai [ ] /* row indices, of size Ap [n_col] */
+) ;
+
+UF_long camd_l_valid
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* camd_cvalid */
+/* ------------------------------------------------------------------------- */
+
+/* Returns TRUE if the constraint set is valid as input to camd_order,
+ * FALSE otherwise. */
+
+int camd_cvalid
+(
+ int n,
+ const int C [ ]
+) ;
+
+UF_long camd_l_cvalid
+(
+ UF_long n,
+ const UF_long C [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* CAMD memory manager and printf routines */
+/* ------------------------------------------------------------------------- */
+
+/* The user can redefine these to change the malloc, free, and printf routines
+ * that CAMD uses. */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN void *(*camd_malloc) (size_t) ; /* pointer to malloc */
+EXTERN void (*camd_free) (void *) ; /* pointer to free */
+EXTERN void *(*camd_realloc) (void *, size_t) ; /* pointer to realloc */
+EXTERN void *(*camd_calloc) (size_t, size_t) ; /* pointer to calloc */
+EXTERN int (*camd_printf) (const char *, ...) ; /* pointer to printf */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD Control and Info arrays */
+/* ------------------------------------------------------------------------- */
+
+/* camd_defaults: sets the default control settings */
+void camd_defaults (double Control [ ]) ;
+void camd_l_defaults (double Control [ ]) ;
+
+/* camd_control: prints the control settings */
+void camd_control (double Control [ ]) ;
+void camd_l_control (double Control [ ]) ;
+
+/* camd_info: prints the statistics */
+void camd_info (double Info [ ]) ;
+void camd_l_info (double Info [ ]) ;
+
+#define CAMD_CONTROL 5 /* size of Control array */
+#define CAMD_INFO 20 /* size of Info array */
+
+/* contents of Control */
+#define CAMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */
+#define CAMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */
+
+/* default Control settings */
+#define CAMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */
+#define CAMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */
+
+/* contents of Info */
+#define CAMD_STATUS 0 /* return value of camd_order and camd_l_order */
+#define CAMD_N 1 /* A is n-by-n */
+#define CAMD_NZ 2 /* number of nonzeros in A */
+#define CAMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */
+#define CAMD_NZDIAG 4 /* # of entries on diagonal */
+#define CAMD_NZ_A_PLUS_AT 5 /* nz in A+A' */
+#define CAMD_NDENSE 6 /* number of "dense" rows/columns in A */
+#define CAMD_MEMORY 7 /* amount of memory used by CAMD */
+#define CAMD_NCMPA 8 /* number of garbage collections in CAMD */
+#define CAMD_LNZ 9 /* approx. nz in L, excluding the diagonal */
+#define CAMD_NDIV 10 /* number of fl. point divides for LU and LDL' */
+#define CAMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */
+#define CAMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */
+#define CAMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */
+
+/* ------------------------------------------------------------------------- */
+/* return values of CAMD */
+/* ------------------------------------------------------------------------- */
+
+#define CAMD_OK 0 /* success */
+#define CAMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */
+#define CAMD_INVALID -2 /* input arguments are not valid */
+#define CAMD_OK_BUT_JUMBLED 1 /* input matrix is OK for camd_order, but
+ * columns were not sorted, and/or duplicate entries were present. CAMD had
+ * to do extra work before ordering the matrix. This is a warning, not an
+ * error. */
+
+/* ========================================================================== */
+/* === CAMD version ========================================================= */
+/* ========================================================================== */
+
+/*
+ * As an example, to test if the version you are using is 1.2 or later:
+ *
+ * if (CAMD_VERSION >= CAMD_VERSION_CODE (1,2)) ...
+ *
+ * This also works during compile-time:
+ *
+ * #if (CAMD_VERSION >= CAMD_VERSION_CODE (1,2))
+ * printf ("This is version 1.2 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ */
+
+#define CAMD_DATE "May 31, 2007"
+#define CAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define CAMD_MAIN_VERSION 2
+#define CAMD_SUB_VERSION 2
+#define CAMD_SUBSUB_VERSION 0
+#define CAMD_VERSION CAMD_VERSION_CODE(CAMD_MAIN_VERSION,CAMD_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/CAMD/Include/camd_internal.h b/CAMD/Include/camd_internal.h
new file mode 100644
index 0000000..2f0fe1f
--- /dev/null
+++ b/CAMD/Include/camd_internal.h
@@ -0,0 +1,337 @@
+/* ========================================================================= */
+/* === camd_internal.h ===================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* This file is for internal use in CAMD itself, and does not normally need to
+ * be included in user code (it is included in UMFPACK, however). All others
+ * should use camd.h instead.
+ *
+ * The following compile-time definitions affect how CAMD is compiled.
+ *
+ * -DNPRINT
+ *
+ * Disable all printing. stdio.h will not be included. Printing can
+ * be re-enabled at run-time by setting the global pointer camd_printf
+ * to printf (or mexPrintf for a MATLAB mexFunction).
+ *
+ * -DNMALLOC
+ *
+ * No memory manager is defined at compile-time. You MUST define the
+ * function pointers camd_malloc, camd_free, camd_realloc, and
+ * camd_calloc at run-time for CAMD to work properly.
+ */
+
+/* ========================================================================= */
+/* === NDEBUG ============================================================== */
+/* ========================================================================= */
+
+/*
+ * Turning on debugging takes some work (see below). If you do not edit this
+ * file, then debugging is always turned off, regardless of whether or not
+ * -DNDEBUG is specified in your compiler options.
+ *
+ * If CAMD is being compiled as a mexFunction, then MATLAB_MEX_FILE is defined,
+ * and mxAssert is used instead of assert. If debugging is not enabled, no
+ * MATLAB include files or functions are used. Thus, the CAMD library libcamd.a
+ * can be safely used in either a stand-alone C program or in another
+ * mexFunction, without any change.
+ */
+
+/*
+ CAMD will be exceedingly slow when running in debug mode. The next three
+ lines ensure that debugging is turned off.
+*/
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+
+/*
+ To enable debugging, uncomment the following line:
+#undef NDEBUG
+*/
+
+
+/* ------------------------------------------------------------------------- */
+/* ANSI include files */
+/* ------------------------------------------------------------------------- */
+
+/* from stdlib.h: size_t, malloc, free, realloc, and calloc */
+#include <stdlib.h>
+
+#if !defined(NPRINT) || !defined(NDEBUG)
+/* from stdio.h: printf. Not included if NPRINT is defined at compile time.
+ * fopen and fscanf are used when debugging. */
+#include <stdio.h>
+#endif
+
+/* from limits.h: INT_MAX and LONG_MAX */
+#include <limits.h>
+
+/* from math.h: sqrt */
+#include <math.h>
+
+/* ------------------------------------------------------------------------- */
+/* MATLAB include files (only if being used in or via MATLAB) */
+/* ------------------------------------------------------------------------- */
+
+#ifdef MATLAB_MEX_FILE
+#include "matrix.h"
+#include "mex.h"
+#endif
+
+/* ------------------------------------------------------------------------- */
+/* basic definitions */
+/* ------------------------------------------------------------------------- */
+
+#ifdef FLIP
+#undef FLIP
+#endif
+
+#ifdef MAX
+#undef MAX
+#endif
+
+#ifdef MIN
+#undef MIN
+#endif
+
+#ifdef EMPTY
+#undef EMPTY
+#endif
+
+#ifdef GLOBAL
+#undef GLOBAL
+#endif
+
+#ifdef PRIVATE
+#undef PRIVATE
+#endif
+
+/* FLIP is a "negation about -1", and is used to mark an integer i that is
+ * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY
+ * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i
+ * for all integers i. UNFLIP (i) is >= EMPTY. */
+#define EMPTY (-1)
+#define FLIP(i) (-(i)-2)
+#define UNFLIP(i) ((i < EMPTY) ? FLIP (i) : (i))
+
+/* for integer MAX/MIN, or for doubles when we don't care how NaN's behave: */
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+/* logical expression of p implies q: */
+#define IMPLIES(p,q) (!(p) || (q))
+
+/* Note that the IBM RS 6000 xlc predefines TRUE and FALSE in <types.h>. */
+/* The Compaq Alpha also predefines TRUE and FALSE. */
+#ifdef TRUE
+#undef TRUE
+#endif
+#ifdef FALSE
+#undef FALSE
+#endif
+
+#define TRUE (1)
+#define FALSE (0)
+#define PRIVATE static
+#define GLOBAL
+#define EMPTY (-1)
+
+/* Note that Linux's gcc 2.96 defines NULL as ((void *) 0), but other */
+/* compilers (even gcc 2.95.2 on Solaris) define NULL as 0 or (0). We */
+/* need to use the ANSI standard value of 0. */
+#ifdef NULL
+#undef NULL
+#endif
+
+#define NULL 0
+
+/* largest value of size_t */
+#ifndef SIZE_T_MAX
+#define SIZE_T_MAX ((size_t) (-1))
+#endif
+
+/* ------------------------------------------------------------------------- */
+/* integer type for CAMD: int or UF_long */
+/* ------------------------------------------------------------------------- */
+
+/* define UF_long */
+#include "UFconfig.h"
+
+#if defined (DLONG) || defined (ZLONG)
+
+#define Int UF_long
+#define ID UF_long_id
+#define Int_MAX UF_long_max
+
+#define CAMD_order camd_l_order
+#define CAMD_defaults camd_l_defaults
+#define CAMD_control camd_l_control
+#define CAMD_info camd_l_info
+#define CAMD_1 camd_l1
+#define CAMD_2 camd_l2
+#define CAMD_valid camd_l_valid
+#define CAMD_cvalid camd_l_cvalid
+#define CAMD_aat camd_l_aat
+#define CAMD_postorder camd_l_postorder
+#define CAMD_post_tree camd_l_post_tree
+#define CAMD_dump camd_l_dump
+#define CAMD_debug camd_l_debug
+#define CAMD_debug_init camd_l_debug_init
+#define CAMD_preprocess camd_l_preprocess
+
+#else
+
+#define Int int
+#define ID "%d"
+#define Int_MAX INT_MAX
+
+#define CAMD_order camd_order
+#define CAMD_defaults camd_defaults
+#define CAMD_control camd_control
+#define CAMD_info camd_info
+#define CAMD_1 camd_1
+#define CAMD_2 camd_2
+#define CAMD_valid camd_valid
+#define CAMD_cvalid camd_cvalid
+#define CAMD_aat camd_aat
+#define CAMD_postorder camd_postorder
+#define CAMD_post_tree camd_post_tree
+#define CAMD_dump camd_dump
+#define CAMD_debug camd_debug
+#define CAMD_debug_init camd_debug_init
+#define CAMD_preprocess camd_preprocess
+
+#endif
+
+/* ========================================================================= */
+/* === PRINTF macro ======================================================== */
+/* ========================================================================= */
+
+/* All output goes through the PRINTF macro. */
+#define PRINTF(params) { if (camd_printf != NULL) (void) camd_printf params ; }
+
+/* ------------------------------------------------------------------------- */
+/* CAMD routine definitions (user-callable) */
+/* ------------------------------------------------------------------------- */
+
+#include "camd.h"
+
+/* ------------------------------------------------------------------------- */
+/* CAMD routine definitions (not user-callable) */
+/* ------------------------------------------------------------------------- */
+
+GLOBAL size_t CAMD_aat
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int Len [ ],
+ Int Tp [ ],
+ double Info [ ]
+) ;
+
+GLOBAL void CAMD_1
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int P [ ],
+ Int Pinv [ ],
+ Int Len [ ],
+ Int slen,
+ Int S [ ],
+ double Control [ ],
+ double Info [ ],
+ const Int C [ ]
+) ;
+
+GLOBAL Int CAMD_postorder
+(
+ Int j, Int k, Int n, Int head [], Int next [], Int post [], Int stack []
+) ;
+
+GLOBAL void CAMD_preprocess
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int Rp [ ],
+ Int Ri [ ],
+ Int W [ ],
+ Int Flag [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* debugging definitions */
+/* ------------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+
+/* from assert.h: assert macro */
+#include <assert.h>
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN Int CAMD_debug ;
+
+GLOBAL void CAMD_debug_init ( char *s ) ;
+
+GLOBAL void CAMD_dump
+(
+ Int n,
+ Int Pe [ ],
+ Int Iw [ ],
+ Int Len [ ],
+ Int iwlen,
+ Int pfree,
+ Int Nv [ ],
+ Int Next [ ],
+ Int Last [ ],
+ Int Head [ ],
+ Int Elen [ ],
+ Int Degree [ ],
+ Int W [ ],
+ Int nel,
+ Int BucketSet [],
+ const Int C [],
+ Int Curc
+) ;
+
+#ifdef ASSERT
+#undef ASSERT
+#endif
+
+/* Use mxAssert if CAMD is compiled into a mexFunction */
+#ifdef MATLAB_MEX_FILE
+#define ASSERT(expression) (mxAssert ((expression), ""))
+#else
+#define ASSERT(expression) (assert (expression))
+#endif
+
+#define CAMD_DEBUG0(params) { PRINTF (params) ; }
+#define CAMD_DEBUG1(params) { if (CAMD_debug >= 1) PRINTF (params) ; }
+#define CAMD_DEBUG2(params) { if (CAMD_debug >= 2) PRINTF (params) ; }
+#define CAMD_DEBUG3(params) { if (CAMD_debug >= 3) PRINTF (params) ; }
+#define CAMD_DEBUG4(params) { if (CAMD_debug >= 4) PRINTF (params) ; }
+
+#else
+
+/* no debugging */
+#define ASSERT(expression)
+#define CAMD_DEBUG0(params)
+#define CAMD_DEBUG1(params)
+#define CAMD_DEBUG2(params)
+#define CAMD_DEBUG3(params)
+#define CAMD_DEBUG4(params)
+
+#endif
diff --git a/CAMD/Lib/GNUmakefile b/CAMD/Lib/GNUmakefile
new file mode 100644
index 0000000..1568e69
--- /dev/null
+++ b/CAMD/Lib/GNUmakefile
@@ -0,0 +1,60 @@
+#-------------------------------------------------------------------------------
+# CAMD Makefile for compiling on Unix systems (for GNU make only)
+#-------------------------------------------------------------------------------
+
+default: libcamd.a
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig
+
+#-------------------------------------------------------------------------------
+# source files
+#-------------------------------------------------------------------------------
+
+CAMD = camd_aat camd_1 camd_2 camd_dump camd_postorder camd_defaults \
+ camd_order camd_control camd_info camd_valid camd_preprocess
+
+UFCONFIG = ../../UFconfig/UFconfig.h
+
+INC = ../Include/camd.h ../Include/camd_internal.h $(UFCONFIG)
+
+#-------------------------------------------------------------------------------
+# object files for each version
+#-------------------------------------------------------------------------------
+
+CAMDI = $(addsuffix .o, $(subst camd_,camd_i_,$(CAMD)))
+CAMDL = $(addsuffix .o, $(subst camd_,camd_l_,$(CAMD)))
+
+#-------------------------------------------------------------------------------
+# compile each int and long routine (with no real/complex version)
+#-------------------------------------------------------------------------------
+
+camd_global.o: ../Source/camd_global.c $(INC)
+ $(C) -c $< -o $@
+
+camd_i_%.o: ../Source/camd_%.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+camd_l_%.o: ../Source/camd_%.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# Create the libcamd.a library (C versions only)
+#-------------------------------------------------------------------------------
+
+libcamd.a: camd_global.o $(CAMDI) $(CAMDL)
+ $(AR) libcamd.a $^
+ - $(RANLIB) libcamd.a
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) libcamd.a
diff --git a/CAMD/Lib/Makefile b/CAMD/Lib/Makefile
new file mode 100644
index 0000000..355202b
--- /dev/null
+++ b/CAMD/Lib/Makefile
@@ -0,0 +1,57 @@
+#-------------------------------------------------------------------------------
+# CAMD Makefile for compiling on Unix systems (for original Make ONLY)
+#-------------------------------------------------------------------------------
+
+# This is a very ugly Makefile, and is only provided for those who do not
+# have GNU make. Note that it is not used if you have GNU make. It ignores
+# dependency checking and just compiles everything.
+
+default: everything
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(CONFIG) -I../Include -I../../UFconfig
+
+everything:
+ $(C) -DDINT -c ../Source/camd_aat.c -o camd_i_aat.o
+ $(C) -DDINT -c ../Source/camd_1.c -o camd_i_1.o
+ $(C) -DDINT -c ../Source/camd_2.c -o camd_i_2.o
+ $(C) -DDINT -c ../Source/camd_dump.c -o camd_i_dump.o
+ $(C) -DDINT -c ../Source/camd_postorder.c -o camd_i_postorder.o
+ $(C) -DDINT -c ../Source/camd_defaults.c -o camd_i_defaults.o
+ $(C) -DDINT -c ../Source/camd_order.c -o camd_i_order.o
+ $(C) -DDINT -c ../Source/camd_control.c -o camd_i_control.o
+ $(C) -DDINT -c ../Source/camd_info.c -o camd_i_info.o
+ $(C) -DDINT -c ../Source/camd_valid.c -o camd_i_valid.o
+ $(C) -DDINT -c ../Source/camd_preprocess.c -o camd_i_preprocess.o
+ $(C) -DDLONG -c ../Source/camd_aat.c -o camd_l_aat.o
+ $(C) -DDLONG -c ../Source/camd_1.c -o camd_l_1.o
+ $(C) -DDLONG -c ../Source/camd_2.c -o camd_l_2.o
+ $(C) -DDLONG -c ../Source/camd_dump.c -o camd_l_dump.o
+ $(C) -DDLONG -c ../Source/camd_postorder.c -o camd_l_postorder.o
+ $(C) -DDLONG -c ../Source/camd_defaults.c -o camd_l_defaults.o
+ $(C) -DDLONG -c ../Source/camd_order.c -o camd_l_order.o
+ $(C) -DDLONG -c ../Source/camd_control.c -o camd_l_control.o
+ $(C) -DDLONG -c ../Source/camd_info.c -o camd_l_info.o
+ $(C) -DDLONG -c ../Source/camd_valid.c -o camd_l_valid.o
+ $(C) -DDLONG -c ../Source/camd_preprocess.c -o camd_l_preprocess.o
+ $(C) -c ../Source/camd_global.c
+ $(AR) libcamd.a camd_i_aat.o camd_i_1.o camd_i_2.o camd_i_dump.o \
+ camd_i_postorder.o camd_i_defaults.o camd_i_order.o \
+ camd_i_control.o camd_i_info.o camd_i_valid.o camd_l_aat.o \
+ camd_l_1.o camd_l_2.o camd_l_dump.o camd_l_postorder.o \
+ camd_l_defaults.o camd_l_order.o camd_l_control.o camd_l_info.o \
+ camd_l_valid.o camd_i_preprocess.o camd_l_preprocess.o camd_global.o
+ - $(RANLIB) libcamd.a
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) libcamd.a
diff --git a/CAMD/Lib/libcamd.def b/CAMD/Lib/libcamd.def
new file mode 100644
index 0000000..f0224f1
--- /dev/null
+++ b/CAMD/Lib/libcamd.def
@@ -0,0 +1,12 @@
+LIBRARY libcamd.dll
+EXPORTS
+camd_order
+camd_defaults
+camd_control
+camd_info
+camd_2
+camd_l_order
+camd_l_defaults
+camd_l_control
+camd_l_info
+camd_l2
diff --git a/CAMD/MATLAB/Contents.m b/CAMD/MATLAB/Contents.m
new file mode 100644
index 0000000..cb7b987
--- /dev/null
+++ b/CAMD/MATLAB/Contents.m
@@ -0,0 +1,15 @@
+%Contents of the CAMD sparse matrix ordering package:
+%
+% camd - p = camd (A), the approximate minimum degree ordering of A
+% camd_demo - a demo of camd, using the can_24 matrix
+% camd_make - to compile camd for use in MATLAB
+%
+% Example:
+% p = camd(A)
+%
+% See also: camd, amd, colamd, symamd, colmmd, symmmd, umfpack
+
+% Copyright 1994-2007, Tim Davis, University of Florida,
+% Patrick R. Amestoy, Iain S. Duff, and Yanqing Chen.
+
+help Contents
diff --git a/CAMD/MATLAB/Makefile b/CAMD/MATLAB/Makefile
new file mode 100644
index 0000000..a0bd541
--- /dev/null
+++ b/CAMD/MATLAB/Makefile
@@ -0,0 +1,34 @@
+#------------------------------------------------------------------------------
+# Makefile for the CAMD MATLAB mexFunction
+#------------------------------------------------------------------------------
+
+default: camd
+
+include ../../UFconfig/UFconfig.mk
+
+CAMD = ../Lib/libcamd.a
+
+I = -I../Include -I../../UFconfig
+
+INC = ../Include/camd.h ../Include/camd_internal.h ../../UFconfig/UFconfig.h
+
+SRC = ../Source/camd_1.c ../Source/camd_2.c ../Source/camd_aat.c \
+ ../Source/camd_control.c ../Source/camd_defaults.c ../Source/camd_dump.c \
+ ../Source/camd_global.c ../Source/camd_info.c ../Source/camd_order.c \
+ ../Source/camd_postorder.c \
+ ../Source/camd_preprocess.c ../Source/camd_valid.c
+
+camd: $(SRC) $(INC) camd_mex.c
+ $(MEX) -DDLONG $(I) -output camd camd_mex.c $(SRC)
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) camd.mex*
diff --git a/CAMD/MATLAB/camd.m b/CAMD/MATLAB/camd.m
new file mode 100644
index 0000000..72512b9
--- /dev/null
+++ b/CAMD/MATLAB/camd.m
@@ -0,0 +1,80 @@
+function [p, Info] = camd (A, Control, C) %#ok
+%CAMD p = camd (A), the approximate minimum degree ordering of A
+% P = CAMD (S) returns the approximate minimum degree permutation vector for
+% the sparse matrix C = S+S'. The Cholesky factorization of C (P,P), or
+% S (P,P), tends to be sparser than that of C or S. CAMD tends to be faster
+% than SYMMMD and SYMAMD, and tends to return better orderings than SYMMMD.
+% S must be square. If S is full, camd(S) is equivalent to camd(sparse(S)).
+%
+% Usage: P = camd (S) ; % finds the ordering
+% [P, Info] = camd (S,Control,C) ; % optional parameters & statistics
+% Control = camd ; % returns default parameters
+% camd ; % prints default parameters.
+%
+% Control (1); If S is n-by-n, then rows/columns with more than
+% max (16, (Control (1))* sqrt(n)) entries in S+S' are considered
+% "dense", and ignored during ordering. They are placed last in the
+% output permutation. The default is 10.0 if Control is not present.
+% Control (2): If nonzero, then aggressive absorption is performed.
+% This is the default if Control is not present.
+% Control (3): If nonzero, print statistics about the ordering.
+%
+% Info (1): status (0: ok, -1: out of memory, -2: matrix invalid)
+% Info (2): n = size (A,1)
+% Info (3): nnz (A)
+% Info (4): the symmetry of the matrix S (0.0 means purely unsymmetric,
+% 1.0 means purely symmetric). Computed as:
+% B = tril (S, -1) + triu (S, 1) ; symmetry = nnz (B & B') / nnz (B);
+% Info (5): nnz (diag (S))
+% Info (6): nnz in S+S', excluding the diagonal (= nnz (B+B'))
+% Info (7): number "dense" rows/columns in S+S'
+% Info (8): the amount of memory used by CAMD, in bytes
+% Info (9): the number of memory compactions performed by CAMD
+%
+% The following statistics are slight upper bounds because of the
+% approximate degree in CAMD. The bounds are looser if "dense" rows/columns
+% are ignored during ordering (Info (7) > 0). The statistics are for a
+% subsequent factorization of the matrix C (P,P). The LU factorization
+% statistics assume no pivoting.
+%
+% Info (10): the number of nonzeros in L, excluding the diagonal
+% Info (11): the number of divide operations for LL', LDL', or LU
+% Info (12): the number of multiply-subtract pairs for LL' or LDL'
+% Info (13): the number of multiply-subtract pairs for LU
+% Info (14): the max # of nonzeros in any column of L (incl. diagonal)
+% Info (15:20): unused, reserved for future use
+%
+% An assembly tree post-ordering is performed, which is typically the same
+% as an elimination tree post-ordering. It is not always identical because
+% of the approximate degree update used, and because "dense" rows/columns
+% do not take part in the post-order. It well-suited for a subsequent
+% "chol", however. If you require a precise elimination tree post-ordering,
+% then do the following:
+%
+% Example:
+% P = camd (S) ;
+% C = spones (S) + spones (S') ; % skip this if S already symmetric
+% [ignore, Q] = etree (C (P,P)) ;
+% P = P (Q) ;
+%
+% CAMD has the ability to order the matrix with constraints. Each
+% node i in the graph (row/column i in the matrix) has a constraint,
+% C(i), which is in the range 1 to n. All nodes with C(i) = 1 are
+% ordered first, followed by all nodes with constraint 2, and so on.
+% That is, C(P) is monotonically non-decreasing. If C is not provided,
+% no constraints are used (the ordering will be similar to AMD's ordering,
+% except that the postordering is different).
+%
+% See also AMD, COLMMD, COLAMD, COLPERM, SYMAMD, SYMMMD, SYMRCM.
+
+
+% Copyright 1994-2007, Tim Davis, University of Florida,
+% Patrick R. Amestoy, Iain S. Duff, and Yanqing Chen.
+%
+% Acknowledgements: This work was supported by the National Science
+% Foundation, under grants ASC-9111263, DMS-9223088, and CCR-0203270,
+% and by Sandia National Laboratories.
+%
+
+help camd
+error ('camd mexFunction not found! Type "camd_make" in MATLAB to compile camd');
diff --git a/CAMD/MATLAB/camd_demo.m b/CAMD/MATLAB/camd_demo.m
new file mode 100644
index 0000000..b8f3665
--- /dev/null
+++ b/CAMD/MATLAB/camd_demo.m
@@ -0,0 +1,116 @@
+function camd_demo
+%CAMD_DEMO a demo of camd, using the can_24 matrix
+%
+% A demo of CAMD for MATLAB.
+%
+% Example:
+% camd_demo
+%
+% See also: camd, camd_make
+
+% Copyright 1994-2007, Tim Davis, University of Florida,
+% Patrick R. Amestoy, Iain S. Duff, and Yanqing Chen.
+
+% This orders the same matrix as the ANSI C demo, camd_demo.c. It includes an
+% additional analysis of the matrix via MATLAB's symbfact routine.
+
+% First, print the help information for CAMD
+help camd
+
+% Get the Harwell/Boeing can_24 matrix.
+
+load can_24
+A = spconvert (can_24) ;
+
+n = size (A,1) ;
+
+rand ('state', 0) ;
+C = irand (6, n) ;
+
+figure (1)
+clf
+hold off
+subplot (2,2,1) ;
+spy (A)
+title ('HB/can24 matrix') ;
+
+% print the details during CAMD ordering and SYMBFACT
+% spparms ('spumoni', 1) ;
+
+% order the matrix. Note that the Info argument is optional.
+fprintf ('\nIf the next step fails, then you have\n') ;
+fprintf ('not yet compiled the CAMD mexFunction.\n') ;
+[p, Info] = camd (A) ; %#ok
+
+% order again, but this time print some statistics
+[p, camd_Info] = camd (A, [10 1 1], C) ;
+
+fprintf ('Permutation vector:\n') ;
+fprintf (' %2d', p) ;
+
+fprintf ('\n\n') ;
+fprintf ('Corresponding constraint sets:\n') ;
+
+if (any (sort (C (p)) ~= C (p)))
+ error ('Error!') ;
+end
+
+for j = 1:n
+ fprintf (' %2d', C (p (j))) ;
+end
+fprintf ('\n\n\n') ;
+
+subplot (2,2,2) ;
+spy (A (p,p)) ;
+title ('Permuted matrix') ;
+
+% The camd_demo.c program stops here.
+
+fprintf ('Analyze A(p,p) with MATLAB symbfact routine:\n') ;
+[cn, height, parent, post, R] = symbfact (A(p,p)) ;
+
+subplot (2,2,3) ;
+spy (R') ;
+title ('Cholesky factor L') ;
+
+subplot (2,2,4) ;
+treeplot (parent) ;
+title ('etree') ;
+
+% results from symbfact
+lnz = sum (cn) ; % number of nonzeros in L, incl. diagonal
+cn = cn - 1 ; % get the count of off-diagonal entries
+fl = n + sum (cn.^2 + 2*cn) ; % flop count for chol (A (p,p)
+fprintf ('number of nonzeros in L (including diagonal): %d\n', lnz) ;
+fprintf ('floating point operation count for chol (A (p,p)): %d\n', fl) ;
+
+% approximations from camd:
+lnz2 = n + camd_Info (10) ;
+fl2 = n + camd_Info (11) + 2 * camd_Info (12) ;
+fprintf ('\nResults from CAMD''s approximate analysis:\n') ;
+fprintf ('number of nonzeros in L (including diagonal): %d\n', lnz2) ;
+fprintf ('floating point operation count for chol (A (p,p)): %d\n\n', fl2) ;
+
+fprintf ('\nNote that the ordering quality is not as good as p=amd(A).\n') ;
+fprintf ('This is only because the ordering constraints, C, have been\n') ;
+fprintf ('randomly selected.\n') ;
+
+if (lnz2 ~= lnz | fl ~= fl2) %#ok
+ fprintf ('Note that the nonzero and flop counts from CAMD are slight\n') ;
+ fprintf ('upper bounds. This is due to the approximate minimum degree\n');
+ fprintf ('method used, in conjunction with "mass elimination".\n') ;
+ fprintf ('See the discussion about mass elimination in camd.h and\n') ;
+ fprintf ('camd_2.c for more details.\n') ;
+end
+
+% turn off diagnostic output in MATLAB's sparse matrix routines
+% spparms ('spumoni', 0) ;
+
+%-------------------------------------------------------------------------------
+
+function i = irand (n,s)
+% irand: return a random vector of size s, with values between 1 and n
+if (nargin == 1)
+ s = 1 ;
+end
+i = min (n, 1 + floor (rand (1,s) * n)) ;
diff --git a/CAMD/MATLAB/camd_demo.m.out b/CAMD/MATLAB/camd_demo.m.out
new file mode 100644
index 0000000..9cedeb5
--- /dev/null
+++ b/CAMD/MATLAB/camd_demo.m.out
@@ -0,0 +1,131 @@
+camd_demo
+ CAMD p = camd (A), the approximate minimum degree ordering of A
+ P = CAMD (S) returns the approximate minimum degree permutation vector for
+ the sparse matrix C = S+S'. The Cholesky factorization of C (P,P), or
+ S (P,P), tends to be sparser than that of C or S. CAMD tends to be faster
+ than SYMMMD and SYMAMD, and tends to return better orderings than SYMMMD.
+ S must be square. If S is full, camd(S) is equivalent to camd(sparse(S)).
+
+ Usage: P = camd (S) ; % finds the ordering
+ [P, Info] = camd (S,Control,C) ; % optional parameters & statistics
+ Control = camd ; % returns default parameters
+ camd ; % prints default parameters.
+
+ Control (1); If S is n-by-n, then rows/columns with more than
+ max (16, (Control (1))* sqrt(n)) entries in S+S' are considered
+ "dense", and ignored during ordering. They are placed last in the
+ output permutation. The default is 10.0 if Control is not present.
+ Control (2): If nonzero, then aggressive absorption is performed.
+ This is the default if Control is not present.
+ Control (3): If nonzero, print statistics about the ordering.
+
+ Info (1): status (0: ok, -1: out of memory, -2: matrix invalid)
+ Info (2): n = size (A,1)
+ Info (3): nnz (A)
+ Info (4): the symmetry of the matrix S (0.0 means purely unsymmetric,
+ 1.0 means purely symmetric). Computed as:
+ B = tril (S, -1) + triu (S, 1) ; symmetry = nnz (B & B') / nnz (B);
+ Info (5): nnz (diag (S))
+ Info (6): nnz in S+S', excluding the diagonal (= nnz (B+B'))
+ Info (7): number "dense" rows/columns in S+S'
+ Info (8): the amount of memory used by CAMD, in bytes
+ Info (9): the number of memory compactions performed by CAMD
+
+ The following statistics are slight upper bounds because of the
+ approximate degree in CAMD. The bounds are looser if "dense" rows/columns
+ are ignored during ordering (Info (7) > 0). The statistics are for a
+ subsequent factorization of the matrix C (P,P). The LU factorization
+ statistics assume no pivoting.
+
+ Info (10): the number of nonzeros in L, excluding the diagonal
+ Info (11): the number of divide operations for LL', LDL', or LU
+ Info (12): the number of multiply-subtract pairs for LL' or LDL'
+ Info (13): the number of multiply-subtract pairs for LU
+ Info (14): the max # of nonzeros in any column of L (incl. diagonal)
+ Info (15:20): unused, reserved for future use
+
+ An assembly tree post-ordering is performed, which is typically the same
+ as an elimination tree post-ordering. It is not always identical because
+ of the approximate degree update used, and because "dense" rows/columns
+ do not take part in the post-order. It well-suited for a subsequent
+ "chol", however. If you require a precise elimination tree post-ordering,
+ then do the following:
+
+ Example:
+ P = camd (S) ;
+ C = spones (S) + spones (S') ; % skip this if S already symmetric
+ [ignore, Q] = etree (C (P,P)) ;
+ P = P (Q) ;
+
+ CAMD has the ability to order the matrix with constraints. Each
+ node i in the graph (row/column i in the matrix) has a constraint,
+ C(i), which is in the range 1 to n. All nodes with C(i) = 1 are
+ ordered first, followed by all nodes with constraint 2, and so on.
+ That is, C(P) is monotonically non-decreasing. If C is not provided,
+ no constraints are used (the ordering will be similar to AMD's ordering,
+ except that the postordering is different).
+
+ See also AMD, COLMMD, COLAMD, COLPERM, SYMAMD, SYMMMD, SYMRCM.
+
+
+If the next step fails, then you have
+not yet compiled the CAMD mexFunction.
+
+camd version 2.2, May 31, 2007: approximate minimum degree ordering:
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+
+ input matrix A is 24-by-24
+ input matrix A has 160 nonzero entries
+
+camd: approximate minimum degree ordering, results:
+ status: OK
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 1644
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 149
+ nonzeros in L (including diagonal): 173
+ # divide operations for LDL' or LU: 149
+ # multiply-subtract operations for LDL': 631
+ # multiply-subtract operations for LU: 1113
+ max nz. in any column of L (incl. diagonal): 12
+
+ chol flop count for real A, sqrt counted as 1 flop: 1435
+ LDL' flop count for real A: 1411
+ LDL' flop count for complex A: 6389
+ LU flop count for real A (with no pivoting): 2375
+ LU flop count for complex A (with no pivoting): 10245
+
+Permutation vector:
+ 24 21 8 2 15 10 16 4 19 22 7 3 11 6 9 23 12 14 20 1 5 13 18 17
+
+Corresponding constraint sets:
+ 1 1 1 2 2 3 3 3 3 3 3 4 4 5 5 5 5 5 6 6 6 6 6 6
+
+
+Analyze A(p,p) with MATLAB symbfact routine:
+number of nonzeros in L (including diagonal): 173
+floating point operation count for chol (A (p,p)): 1435
+
+Results from CAMD's approximate analysis:
+number of nonzeros in L (including diagonal): 173
+floating point operation count for chol (A (p,p)): 1435
+
+
+Note that the ordering quality is not as good as p=amd(A).
+This is only because the ordering constraints, C, have been
+randomly selected.
+diary off
diff --git a/CAMD/MATLAB/camd_make.m b/CAMD/MATLAB/camd_make.m
new file mode 100644
index 0000000..0d59796
--- /dev/null
+++ b/CAMD/MATLAB/camd_make.m
@@ -0,0 +1,32 @@
+function camd_make
+%CAMD_MAKE to compile camd for use in MATLAB
+%
+% Example:
+% camd_make
+%
+% See also camd.
+
+% Copyright 1994-2007, Tim Davis, University of Florida,
+% Patrick R. Amestoy, Iain S. Duff, and Yanqing Chen.
+
+details = 0 ; % 1 if details of each command are to be printed
+
+d = '' ;
+if (~isempty (strfind (computer, '64')))
+ d = '-largeArrayDims' ;
+end
+
+i = sprintf ('-I..%sInclude -I..%s..%sUFconfig', filesep, filesep, filesep) ;
+cmd = sprintf ('mex -O %s -DDLONG -output camd %s camd_mex.c', d, i) ;
+files = {'camd_order', 'camd_dump', 'camd_postorder', ...
+ 'camd_aat', 'camd_2', 'camd_1', 'camd_defaults', 'camd_control', ...
+ 'camd_info', 'camd_valid', 'camd_global', 'camd_preprocess' } ;
+for i = 1 : length (files)
+ cmd = sprintf ('%s ..%sSource%s%s.c', cmd, filesep, filesep, files {i}) ;
+end
+if (details)
+ fprintf ('%s\n', cmd) ;
+end
+eval (cmd) ;
+
+fprintf ('CAMD successfully compiled.\n') ;
diff --git a/CAMD/MATLAB/camd_mex.c b/CAMD/MATLAB/camd_mex.c
new file mode 100644
index 0000000..03cbd25
--- /dev/null
+++ b/CAMD/MATLAB/camd_mex.c
@@ -0,0 +1,220 @@
+/* ========================================================================= */
+/* === CAMD mexFunction ===================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/*
+ * Usage:
+ * p = camd (A)
+ * p = camd (A, Control)
+ * [p, Info] = camd (A)
+ * [p, Info] = camd (A, Control, C)
+ * Control = camd ; % return the default Control settings for CAMD
+ * camd ; % print the default Control settings for CAMD
+ *
+ * Given a square matrix A, compute a permutation P suitable for a Cholesky
+ * factorization of the matrix B (P,P), where B = spones (A) + spones (A').
+ * The method used is the approximate minimum degree ordering method. See
+ * camd.m and camd.h for more information.
+ *
+ * The input matrix need not have sorted columns, and can have duplicate
+ * entries.
+ */
+
+#include "camd.h"
+#include "mex.h"
+#include "matrix.h"
+#include "UFconfig.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ UF_long i, m, n, *Ap, *Ai, *P, nc, result, spumoni, full, *C, Clen ;
+ double *Pout, *InfoOut, Control [CAMD_CONTROL], Info [CAMD_INFO],
+ *ControlIn, *Cin ;
+ mxArray *A ;
+
+ /* --------------------------------------------------------------------- */
+ /* get control parameters */
+ /* --------------------------------------------------------------------- */
+
+ camd_malloc = mxMalloc ;
+ camd_free = mxFree ;
+ camd_calloc = mxCalloc ;
+ camd_realloc = mxRealloc ;
+ camd_printf = mexPrintf ;
+
+ spumoni = 0 ;
+ if (nargin == 0)
+ {
+ /* get the default control parameters, and return */
+ pargout [0] = mxCreateDoubleMatrix (CAMD_CONTROL, 1, mxREAL) ;
+ camd_l_defaults (mxGetPr (pargout [0])) ;
+ if (nargout == 0)
+ {
+ camd_l_control (mxGetPr (pargout [0])) ;
+ }
+ return ;
+ }
+
+ camd_l_defaults (Control) ;
+ if (nargin > 1)
+ {
+ ControlIn = mxGetPr (pargin [1]) ;
+ nc = mxGetM (pargin [1]) * mxGetN (pargin [1]) ;
+ Control [CAMD_DENSE]
+ = (nc > 0) ? ControlIn [CAMD_DENSE] : CAMD_DEFAULT_DENSE ;
+ Control [CAMD_AGGRESSIVE]
+ = (nc > 1) ? ControlIn [CAMD_AGGRESSIVE] : CAMD_DEFAULT_AGGRESSIVE ;
+ spumoni = (nc > 2) ? (ControlIn [2] != 0) : 0 ;
+ }
+
+ if (spumoni > 0)
+ {
+ camd_l_control (Control) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* get inputs */
+ /* --------------------------------------------------------------------- */
+
+ if (nargout > 2 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: p = camd (A)\n"
+ "or [p, Info] = camd (A, Control, C)") ;
+ }
+
+ Clen = 0 ;
+ C = NULL ;
+ if (nargin > 2)
+ {
+ Cin = mxGetPr (pargin [2]) ;
+ Clen = mxGetNumberOfElements (pargin [2]) ;
+ if (Clen != 0)
+ {
+ C = (UF_long *) mxCalloc (Clen, sizeof (UF_long)) ;
+ for (i = 0 ; i < Clen ; i++)
+ {
+ /* convert c from 1-based to 0-based */
+ C [i] = (UF_long) Cin [i] - 1 ;
+ }
+ }
+ }
+
+ A = (mxArray *) pargin [0] ;
+ n = mxGetN (A) ;
+ m = mxGetM (A) ;
+ if (spumoni > 0)
+ {
+ mexPrintf (" input matrix A is %d-by-%d\n", m, n) ;
+ }
+
+ if (mxGetNumberOfDimensions (A) != 2)
+ {
+ mexErrMsgTxt ("camd: A must be 2-dimensional") ;
+ }
+ if (m != n)
+ {
+ mexErrMsgTxt ("camd: A must be square") ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* allocate workspace for output permutation */
+ /* --------------------------------------------------------------------- */
+
+ P = mxMalloc ((n+1) * sizeof (UF_long)) ;
+
+ /* --------------------------------------------------------------------- */
+ /* if A is full, convert to a sparse matrix */
+ /* --------------------------------------------------------------------- */
+
+ full = !mxIsSparse (A) ;
+ if (full)
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf (
+ " input matrix A is full (sparse copy of A will be created)\n");
+ }
+ mexCallMATLAB (1, &A, 1, (mxArray **) pargin, "sparse") ;
+ }
+ Ap = (UF_long *) mxGetJc (A) ;
+ Ai = (UF_long *) mxGetIr (A) ;
+ if (spumoni > 0)
+ {
+ mexPrintf (" input matrix A has %d nonzero entries\n", Ap [n]) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* order the matrix */
+ /* --------------------------------------------------------------------- */
+
+ result = camd_l_order (n, Ap, Ai, P, Control, Info, C) ;
+
+ /* --------------------------------------------------------------------- */
+ /* if A is full, free the sparse copy of A */
+ /* --------------------------------------------------------------------- */
+
+ if (full)
+ {
+ mxDestroyArray (A) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* print results (including return value) */
+ /* --------------------------------------------------------------------- */
+
+ if (spumoni > 0)
+ {
+ camd_l_info (Info) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* check error conditions */
+ /* --------------------------------------------------------------------- */
+
+ if (result == CAMD_OUT_OF_MEMORY)
+ {
+ mexErrMsgTxt ("camd: out of memory") ;
+ }
+ else if (result == CAMD_INVALID)
+ {
+ mexErrMsgTxt ("camd: input matrix A is corrupted") ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* copy the outputs to MATLAB */
+ /* --------------------------------------------------------------------- */
+
+ /* output permutation, P */
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ Pout = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Pout [i] = P [i] + 1 ; /* change to 1-based indexing for MATLAB */
+ }
+ mxFree (P) ;
+ if (nargin > 2) mxFree (C) ;
+
+ /* Info */
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (CAMD_INFO, 1, mxREAL) ;
+ InfoOut = mxGetPr (pargout [1]) ;
+ for (i = 0 ; i < CAMD_INFO ; i++)
+ {
+ InfoOut [i] = Info [i] ;
+ }
+ }
+}
diff --git a/CAMD/MATLAB/can_24 b/CAMD/MATLAB/can_24
new file mode 100644
index 0000000..38158a1
--- /dev/null
+++ b/CAMD/MATLAB/can_24
@@ -0,0 +1,160 @@
+ 1 1 1
+ 6 1 1
+ 7 1 1
+13 1 1
+14 1 1
+18 1 1
+19 1 1
+20 1 1
+22 1 1
+ 2 2 1
+ 9 2 1
+10 2 1
+14 2 1
+15 2 1
+18 2 1
+ 3 3 1
+ 7 3 1
+12 3 1
+21 3 1
+22 3 1
+23 3 1
+ 4 4 1
+ 8 4 1
+11 4 1
+16 4 1
+19 4 1
+20 4 1
+ 5 5 1
+ 8 5 1
+10 5 1
+15 5 1
+16 5 1
+17 5 1
+ 1 6 1
+ 6 6 1
+ 7 6 1
+13 6 1
+14 6 1
+18 6 1
+ 1 7 1
+ 3 7 1
+ 6 7 1
+ 7 7 1
+12 7 1
+13 7 1
+20 7 1
+22 7 1
+24 7 1
+ 4 8 1
+ 5 8 1
+ 8 8 1
+10 8 1
+15 8 1
+16 8 1
+17 8 1
+18 8 1
+19 8 1
+ 2 9 1
+ 9 9 1
+10 9 1
+15 9 1
+ 2 10 1
+ 5 10 1
+ 8 10 1
+ 9 10 1
+10 10 1
+14 10 1
+15 10 1
+18 10 1
+19 10 1
+ 4 11 1
+11 11 1
+19 11 1
+20 11 1
+21 11 1
+22 11 1
+ 3 12 1
+ 7 12 1
+12 12 1
+13 12 1
+22 12 1
+24 12 1
+ 1 13 1
+ 6 13 1
+ 7 13 1
+12 13 1
+13 13 1
+24 13 1
+ 1 14 1
+ 2 14 1
+ 6 14 1
+10 14 1
+14 14 1
+18 14 1
+ 2 15 1
+ 5 15 1
+ 8 15 1
+ 9 15 1
+10 15 1
+15 15 1
+ 4 16 1
+ 5 16 1
+ 8 16 1
+16 16 1
+17 16 1
+19 16 1
+ 5 17 1
+ 8 17 1
+16 17 1
+17 17 1
+ 1 18 1
+ 2 18 1
+ 6 18 1
+ 8 18 1
+10 18 1
+14 18 1
+18 18 1
+19 18 1
+20 18 1
+ 1 19 1
+ 4 19 1
+ 8 19 1
+10 19 1
+11 19 1
+16 19 1
+18 19 1
+19 19 1
+20 19 1
+ 1 20 1
+ 4 20 1
+ 7 20 1
+11 20 1
+18 20 1
+19 20 1
+20 20 1
+21 20 1
+22 20 1
+ 3 21 1
+11 21 1
+20 21 1
+21 21 1
+22 21 1
+23 21 1
+ 1 22 1
+ 3 22 1
+ 7 22 1
+11 22 1
+12 22 1
+20 22 1
+21 22 1
+22 22 1
+23 22 1
+ 3 23 1
+21 23 1
+22 23 1
+23 23 1
+ 7 24 1
+12 24 1
+13 24 1
+24 24 1
diff --git a/CAMD/Makefile b/CAMD/Makefile
new file mode 100644
index 0000000..58341b0
--- /dev/null
+++ b/CAMD/Makefile
@@ -0,0 +1,57 @@
+#------------------------------------------------------------------------------
+# CAMD Makefile (for GNU Make or original make)
+#------------------------------------------------------------------------------
+
+default: demo
+
+include ../UFconfig/UFconfig.mk
+
+# Compile all C code, including the C-callable routine and the mexFunctions.
+# Do not compile the FORTRAN versions, or MATLAB interface.
+demo:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+# Compile all C code, including the C-callable routine and the mexFunctions.
+# Do not compile the FORTRAN versions.
+all:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+ ( cd MATLAB ; $(MAKE) )
+
+# compile just the C-callable libraries (not mexFunctions or Demos)
+library:
+ ( cd Lib ; $(MAKE) )
+
+# remove object files, but keep the compiled programs and library archives
+clean:
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+ ( cd MATLAB ; $(MAKE) clean )
+ ( cd Doc ; $(MAKE) clean )
+
+# clean, and then remove compiled programs and library archives
+purge:
+ ( cd Lib ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd MATLAB ; $(MAKE) purge )
+ ( cd Doc ; $(MAKE) purge )
+
+distclean: purge
+
+# create PDF documents for the original distribution
+doc:
+ ( cd Doc ; $(MAKE) )
+
+# get ready for distribution
+dist: purge
+ ( cd Demo ; $(MAKE) dist )
+ ( cd Doc ; $(MAKE) )
+
+ccode: library
+
+lib: library
+
+# compile the MATLAB mexFunction
+mex:
+ ( cd MATLAB ; $(MAKE) )
diff --git a/CAMD/README.txt b/CAMD/README.txt
new file mode 100644
index 0000000..84702cc
--- /dev/null
+++ b/CAMD/README.txt
@@ -0,0 +1,204 @@
+CAMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, Yanqing Chen,
+Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved.
+CAMD is available under alternate licences; contact T. Davis for details.
+
+CAMD: a set of routines for permuting sparse matrices prior to
+ factorization. Includes a version in C, a version in Fortran, and a MATLAB
+ mexFunction.
+
+Requires UFconfig, in the ../UFconfig directory relative to this directory.
+
+Quick start (Unix, or Windows with Cygwin):
+
+ To compile, test, and install CAMD, you may wish to first configure the
+ installation by editting the ../UFconfig/UFconfig.mk file. Next, cd to
+ this directory (CAMD) and type "make" (or "make lib" if you do not have
+ MATLAB). When done, type "make clean" to remove unused *.o files
+ (keeps the compiled libraries and demo programs). See the User Guide
+ (Doc/CAMD_UserGuide.pdf), or ../UFconfig/UFconfig.mk for more details.
+
+Quick start (for MATLAB users);
+
+ To compile, test, and install the CAMD mexFunction, cd to the
+ CAMD/MATLAB directory and type camd_make at the MATLAB prompt.
+
+If you have MATLAB 7.2 or earlier and use "make mex", you must first edit
+UFconfig/UFconfig.h to remove the "-largeArrayDims" option from the MEX command
+(or just use camd_make.m inside MATLAB).
+
+-------------------------------------------------------------------------------
+
+CAMD License:
+
+ Your use or distribution of CAMD or any modified version of
+ CAMD implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/camd
+
+-------------------------------------------------------------------------------
+
+This is the CAMD README file. It is a terse overview of CAMD.
+Refer to the User Guide (Doc/CAMD_UserGuide.pdf) for how to install
+and use CAMD.
+
+Description:
+
+ CAMD is a set of routines for pre-ordering sparse matrices prior to Cholesky
+ or LU factorization, using the approximate minimum degree ordering
+ algorithm with optional ordering constraints. Written in ANSI/ISO C with
+ a MATLAB interface.
+
+Authors:
+
+ Timothy A. Davis (davis at cise.ufl.edu), University of Florida.
+ Patrick R. Amestory, ENSEEIHT, Toulouse, France.
+ Iain S. Duff, Rutherford Appleton Laboratory, UK.
+
+Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+
+ Portions of this work were done while on sabbatical at Stanford University
+ and Lawrence Berkeley National Laboratory (with funding from the SciDAC
+ program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon
+ for making this sabbatical possible.
+
+-------------------------------------------------------------------------------
+Files and directories in the CAMD distribution:
+-------------------------------------------------------------------------------
+
+ ---------------------------------------------------------------------------
+ Subdirectories of the CAMD directory:
+ ---------------------------------------------------------------------------
+
+ Doc documentation
+ Source primary source code
+ Include include file for use in your code that calls CAMD
+ Demo demo programs. also serves as test of the CAMD installation.
+ MATLAB CAMD mexFunction for MATLAB, and supporting m-files
+ Lib where the compiled C-callable and Fortran-callable
+ CAMD libraries placed.
+
+ ---------------------------------------------------------------------------
+ Files in the CAMD directory:
+ ---------------------------------------------------------------------------
+
+ Makefile top-level Makefile for GNU make or original make.
+ Windows users would require Cygwin to use "make"
+
+ README.txt this file
+
+ ---------------------------------------------------------------------------
+ Doc directory: documentation
+ ---------------------------------------------------------------------------
+
+ ChangeLog change log
+ License the CAMD License
+ Makefile for creating the documentation
+ CAMD_UserGuide.bib CAMD User Guide (references)
+ CAMD_UserGuide.tex CAMD User Guide (LaTeX)
+ CAMD_UserGuide.pdf CAMD User Guide (PDF)
+ lesser.txt the GNU LGPL license
+
+ docdiff tools for comparing CAMD with AMD
+ cdiff
+ camd.sed
+
+ ---------------------------------------------------------------------------
+ Source directory:
+ ---------------------------------------------------------------------------
+
+ camd_order.c user-callable, primary CAMD ordering routine
+ camd_control.c user-callable, prints the control parameters
+ camd_defaults.c user-callable, sets default control parameters
+ camd_info.c user-callable, prints the statistics from CAMD
+
+ camd_1.c non-user-callable, construct A+A'
+ camd_2.c user-callable, primary ordering kernel
+ (a C version of camd.f and camdbar.f, with
+ post-ordering added)
+ camd_aat.c non-user-callable, computes nnz (A+A')
+ camd_dump.c non-user-callable, debugging routines
+ camd_postorder.c non-user-callable, postorder
+ camd_valid.c non-user-callable, verifies a matrix
+ camd_preprocess.c non-user-callable, computes A', removes duplic
+
+ ---------------------------------------------------------------------------
+ Include directory:
+ ---------------------------------------------------------------------------
+
+ camd.h include file for C programs that use CAMD
+ camd_internal.h non-user-callable, include file for CAMD
+
+ ---------------------------------------------------------------------------
+ Demo directory:
+ ---------------------------------------------------------------------------
+
+ Makefile for GNU make or original make
+
+ camd_demo.c C demo program for CAMD
+ camd_demo.out output of camd_demo.c
+
+ camd_demo2.c C demo program for CAMD, jumbled matrix
+ camd_demo2.out output of camd_demo2.c
+
+ camd_l_demo.c C demo program for CAMD ("long" version)
+ camd_l_demo.out output of camd_l_demo.c
+
+ camd_simple.c simple C demo program for CAMD
+ camd_simple.out output of camd_simple.c
+
+ ---------------------------------------------------------------------------
+ MATLAB directory:
+ ---------------------------------------------------------------------------
+
+ GNUmakefile a nice Makefile, for GNU make
+ Makefile an ugly Unix Makefile (for older make's)
+
+ Contents.m for "help camd" listing of toolbox contents
+
+ camd.m MATLAB help file for CAMD
+ camd_make.m MATLAB m-file for compiling CAMD mexFunction
+ camd_install.m compile and install CAMD mexFunctions
+
+ camd_mex.c CAMD mexFunction for MATLAB
+
+ camd_demo.m MATLAB demo for CAMD
+ camd_demo.m.out diary output of camd_demo.m
+ can_24.mat input file for CAMD demo
+
+ ---------------------------------------------------------------------------
+ Lib directory: libcamd.a library placed here
+ ---------------------------------------------------------------------------
+
+ GNUmakefile a nice Makefile, for GNU make
+ Makefile an ugly Unix Makefile (for older make's)
+ libcamd.def CAMD definitions for Windows
diff --git a/CAMD/Source/camd_1.c b/CAMD/Source/camd_1.c
new file mode 100644
index 0000000..6ab1ac4
--- /dev/null
+++ b/CAMD/Source/camd_1.c
@@ -0,0 +1,184 @@
+/* ========================================================================= */
+/* === CAMD_1 ============================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* CAMD_1: Construct A+A' for a sparse matrix A and perform the CAMD ordering.
+ *
+ * The n-by-n sparse matrix A can be unsymmetric. It is stored in MATLAB-style
+ * compressed-column form, with sorted row indices in each column, and no
+ * duplicate entries. Diagonal entries may be present, but they are ignored.
+ * Row indices of column j of A are stored in Ai [Ap [j] ... Ap [j+1]-1].
+ * Ap [0] must be zero, and nz = Ap [n] is the number of entries in A. The
+ * size of the matrix, n, must be greater than or equal to zero.
+ *
+ * This routine must be preceded by a call to CAMD_aat, which computes the
+ * number of entries in each row/column in A+A', excluding the diagonal.
+ * Len [j], on input, is the number of entries in row/column j of A+A'. This
+ * routine constructs the matrix A+A' and then calls CAMD_2. No error checking
+ * is performed (this was done in CAMD_valid).
+ */
+
+#include "camd_internal.h"
+
+GLOBAL void CAMD_1
+(
+ Int n, /* n > 0 */
+ const Int Ap [ ], /* input of size n+1, not modified */
+ const Int Ai [ ], /* input of size nz = Ap [n], not modified */
+ Int P [ ], /* size n output permutation */
+ Int Pinv [ ], /* size n output inverse permutation */
+ Int Len [ ], /* size n input, undefined on output */
+ Int slen, /* slen >= sum (Len [0..n-1]) + 7n+2,
+ * ideally slen = 1.2 * sum (Len) + 8n+2 */
+ Int S [ ], /* size slen workspace */
+ double Control [ ], /* input array of size CAMD_CONTROL */
+ double Info [ ], /* output array of size CAMD_INFO */
+ const Int C [ ] /* Constraint set of size n */
+)
+{
+ Int i, j, k, p, pfree, iwlen, pj, p1, p2, pj2, *Iw, *Pe, *Nv, *Head,
+ *Elen, *Degree, *s, *W, *Sp, *Tp, *BucketSet ;
+
+ /* --------------------------------------------------------------------- */
+ /* construct the matrix for CAMD_2 */
+ /* --------------------------------------------------------------------- */
+
+ ASSERT (n > 0) ;
+
+ iwlen = slen - (7*n+2) ; /* allocate 7*n+2 workspace from S */
+ s = S ;
+ Pe = s ; s += n ;
+ Nv = s ; s += n ;
+ Head = s ; s += n+1 ; /* NOTE: was size n in AMD; size n+1 in CAMD */
+ Elen = s ; s += n ;
+ Degree = s ; s += n ;
+ W = s ; s += n+1 ; /* NOTE: was size n in AMD; size n+1 in CAMD */
+ BucketSet = s ; s += n ;
+ Iw = s ; s += iwlen ;
+
+ ASSERT (CAMD_valid (n, n, Ap, Ai) == CAMD_OK) ;
+ ASSERT (CAMD_cvalid (n, C)) ;
+
+ /* construct the pointers for A+A' */
+ Sp = Nv ; /* use Nv and W as workspace for Sp and Tp [ */
+ Tp = W ;
+ pfree = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Pe [j] = pfree ;
+ Sp [j] = pfree ;
+ pfree += Len [j] ;
+ }
+
+ /* Note that this restriction on iwlen is slightly more restrictive than
+ * what is strictly required in CAMD_2. CAMD_2 can operate with no elbow
+ * room at all, but it will be very slow. For better performance, at
+ * least size-n elbow room is enforced. */
+ ASSERT (iwlen >= pfree + n) ;
+
+#ifndef NDEBUG
+ for (p = 0 ; p < iwlen ; p++) Iw [p] = EMPTY ;
+#endif
+
+ for (k = 0 ; k < n ; k++)
+ {
+ CAMD_DEBUG1 (("Construct row/column k= "ID" of A+A'\n", k)) ;
+ p1 = Ap [k] ;
+ p2 = Ap [k+1] ;
+
+ /* construct A+A' */
+ for (p = p1 ; p < p2 ; )
+ {
+ /* scan the upper triangular part of A */
+ j = Ai [p] ;
+ ASSERT (j >= 0 && j < n) ;
+ if (j < k)
+ {
+ /* entry A (j,k) in the strictly upper triangular part */
+ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
+ ASSERT (Sp [k] < (k == n-1 ? pfree : Pe [k+1])) ;
+ Iw [Sp [j]++] = k ;
+ Iw [Sp [k]++] = j ;
+ p++ ;
+ }
+ else if (j == k)
+ {
+ /* skip the diagonal */
+ p++ ;
+ break ;
+ }
+ else /* j > k */
+ {
+ /* first entry below the diagonal */
+ break ;
+ }
+ /* scan lower triangular part of A, in column j until reaching
+ * row k. Start where last scan left off. */
+ ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ;
+ pj2 = Ap [j+1] ;
+ for (pj = Tp [j] ; pj < pj2 ; )
+ {
+ i = Ai [pj] ;
+ ASSERT (i >= 0 && i < n) ;
+ if (i < k)
+ {
+ /* A (i,j) is only in the lower part, not in upper */
+ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ;
+ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
+ Iw [Sp [i]++] = j ;
+ Iw [Sp [j]++] = i ;
+ pj++ ;
+ }
+ else if (i == k)
+ {
+ /* entry A (k,j) in lower part and A (j,k) in upper */
+ pj++ ;
+ break ;
+ }
+ else /* i > k */
+ {
+ /* consider this entry later, when k advances to i */
+ break ;
+ }
+ }
+ Tp [j] = pj ;
+ }
+ Tp [k] = p ;
+ }
+
+ /* clean up, for remaining mismatched entries */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (pj = Tp [j] ; pj < Ap [j+1] ; pj++)
+ {
+ i = Ai [pj] ;
+ ASSERT (i >= 0 && i < n) ;
+ /* A (i,j) is only in the lower part, not in upper */
+ ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ;
+ ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
+ Iw [Sp [i]++] = j ;
+ Iw [Sp [j]++] = i ;
+ }
+ }
+
+#ifndef NDEBUG
+ for (j = 0 ; j < n-1 ; j++) ASSERT (Sp [j] == Pe [j+1]) ;
+ ASSERT (Sp [n-1] == pfree) ;
+#endif
+
+ /* Tp and Sp no longer needed ] */
+
+ /* --------------------------------------------------------------------- */
+ /* order the matrix */
+ /* --------------------------------------------------------------------- */
+
+ CAMD_2 (n, Pe, Iw, Len, iwlen, pfree,
+ Nv, Pinv, P, Head, Elen, Degree, W, Control, Info, C, BucketSet) ;
+}
diff --git a/CAMD/Source/camd_2.c b/CAMD/Source/camd_2.c
new file mode 100644
index 0000000..bb9409c
--- /dev/null
+++ b/CAMD/Source/camd_2.c
@@ -0,0 +1,2013 @@
+/* ========================================================================= */
+/* === CAMD_2 ============================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* CAMD_2: performs the CAMD ordering on a symmetric sparse matrix A, followed
+ * by a postordering (via depth-first search) of the assembly tree using the
+ * CAMD_postorder routine.
+ */
+
+/* ========================================================================= */
+/* === Macros and definitions ============================================== */
+/* ========================================================================= */
+
+/* True if node i is in the current Constraint Set */
+#define IsInCurrentSet(C,i,curC) ((C == NULL) ? 1 : (C [i] == curC))
+
+/* True if i and j are in the same Constraint Set */
+#define InSameConstraintSet(C,i,j) ((C == NULL) ? 1 : (C [i] == C [j]))
+
+#include "camd_internal.h"
+
+/* ========================================================================= */
+/* === clear_flag ========================================================== */
+/* ========================================================================= */
+
+static Int clear_flag (Int wflg, Int wbig, Int W [ ], Int n)
+{
+ Int x ;
+ if (wflg < 2 || wflg >= wbig)
+ {
+ for (x = 0 ; x < n ; x++)
+ {
+ if (W [x] != 0) W [x] = 1 ;
+ }
+ wflg = 2 ;
+ }
+ /* at this point, W [0..n-1] < wflg holds */
+ return (wflg) ;
+}
+
+
+/* ========================================================================= */
+/* === CAMD_2 ============================================================== */
+/* ========================================================================= */
+
+GLOBAL void CAMD_2
+(
+ Int n, /* A is n-by-n, where n > 0 */
+ Int Pe [ ], /* Pe [0..n-1]: index in Iw of row i on input */
+ Int Iw [ ], /* workspace of size iwlen. Iw [0..pfree-1]
+ * holds the matrix on input */
+ Int Len [ ], /* Len [0..n-1]: length for row/column i on input */
+ Int iwlen, /* length of Iw. iwlen >= pfree + n */
+ Int pfree, /* Iw [pfree ... iwlen-1] is empty on input */
+
+ /* 7 size-n or size-n+1 workspaces, not defined on input: */
+ Int Nv [ ], /* size n, the size of each supernode on output */
+ Int Next [ ], /* size n, the output inverse permutation */
+ Int Last [ ], /* size n, the output permutation */
+ Int Head [ ], /* size n+1 (Note: it was size n in AMD) */
+ Int Elen [ ], /* size n, the size columns of L for each supernode */
+ Int Degree [ ], /* size n */
+ Int W [ ], /* size n+1 (Note: it was size n in AMD) */
+
+ /* control parameters and output statistics */
+ double Control [ ], /* array of size CAMD_CONTROL */
+ double Info [ ], /* array of size CAMD_INFO */
+
+ /* input, not modified: */
+ const Int C [ ], /* size n, C [i] is the constraint set of node i */
+
+ /* size-n workspace, not defined on input or output: */
+ Int BucketSet [ ] /* size n */
+)
+{
+
+/*
+ * Given a representation of the nonzero pattern of a symmetric matrix, A,
+ * (excluding the diagonal) perform an approximate minimum (UMFPACK/MA38-style)
+ * degree ordering to compute a pivot order such that the introduction of
+ * nonzeros (fill-in) in the Cholesky factors A = LL' is kept low. At each
+ * step, the pivot selected is the one with the minimum UMFAPACK/MA38-style
+ * upper-bound on the external degree. This routine can optionally perform
+ * aggresive absorption (as done by MC47B in the Harwell Subroutine
+ * Library).
+ *
+ * The approximate degree algorithm implemented here is the symmetric analog of
+ * the degree update algorithm in MA38 and UMFPACK (the Unsymmetric-pattern
+ * MultiFrontal PACKage, both by Davis and Duff). The routine is based on the
+ * MA27 minimum degree ordering algorithm by Iain Duff and John Reid.
+ *
+ * This routine is a translation of the original AMDBAR and MC47B routines,
+ * in Fortran, with the following modifications:
+ *
+ * (1) dense rows/columns are removed prior to ordering the matrix, and placed
+ * last in the output order. The presence of a dense row/column can
+ * increase the ordering time by up to O(n^2), unless they are removed
+ * prior to ordering.
+ *
+ * (2) the minimum degree ordering is followed by a postordering (depth-first
+ * search) of the assembly tree. Note that mass elimination (discussed
+ * below) combined with the approximate degree update can lead to the mass
+ * elimination of nodes with lower exact degree than the current pivot
+ * element. No additional fill-in is caused in the representation of the
+ * Schur complement. The mass-eliminated nodes merge with the current
+ * pivot element. They are ordered prior to the current pivot element.
+ * Because they can have lower exact degree than the current element, the
+ * merger of two or more of these nodes in the current pivot element can
+ * lead to a single element that is not a "fundamental supernode". The
+ * diagonal block can have zeros in it. Thus, the assembly tree used here
+ * is not guaranteed to be the precise supernodal elemination tree (with
+ * "funadmental" supernodes), and the postordering performed by this
+ * routine is not guaranteed to be a precise postordering of the
+ * elimination tree.
+ *
+ * (3) input parameters are added, to control aggressive absorption and the
+ * detection of "dense" rows/columns of A.
+ *
+ * (4) additional statistical information is returned, such as the number of
+ * nonzeros in L, and the flop counts for subsequent LDL' and LU
+ * factorizations. These are slight upper bounds, because of the mass
+ * elimination issue discussed above.
+ *
+ * (5) additional routines are added to interface this routine to MATLAB
+ * to provide a simple C-callable user-interface, to check inputs for
+ * errors, compute the symmetry of the pattern of A and the number of
+ * nonzeros in each row/column of A+A', to compute the pattern of A+A',
+ * to perform the assembly tree postordering, and to provide debugging
+ * ouput. Many of these functions are also provided by the Fortran
+ * Harwell Subroutine Library routine MC47A.
+ *
+ * (6) both "int" and "long" versions are provided. In the descriptions below
+ * and integer is and "int" or "long", depending on which version is
+ * being used.
+
+ **********************************************************************
+ ***** CAUTION: ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT. ******
+ **********************************************************************
+ ** If you want error checking, a more versatile input format, and a **
+ ** simpler user interface, use camd_order or camd_l_order instead. **
+ ** This routine is not meant to be user-callable. **
+ **********************************************************************
+
+ * ----------------------------------------------------------------------------
+ * References:
+ * ----------------------------------------------------------------------------
+ *
+ * [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern multifrontal
+ * method for sparse LU factorization", SIAM J. Matrix Analysis and
+ * Applications, vol. 18, no. 1, pp. 140-158. Discusses UMFPACK / MA38,
+ * which first introduced the approximate minimum degree used by this
+ * routine.
+ *
+ * [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff, "An approximate
+ * minimum degree ordering algorithm," SIAM J. Matrix Analysis and
+ * Applications, vol. 17, no. 4, pp. 886-905, 1996. Discusses AMDBAR and
+ * MC47B, which are the Fortran versions of this routine.
+ *
+ * [3] Alan George and Joseph Liu, "The evolution of the minimum degree
+ * ordering algorithm," SIAM Review, vol. 31, no. 1, pp. 1-19, 1989.
+ * We list below the features mentioned in that paper that this code
+ * includes:
+ *
+ * mass elimination:
+ * Yes. MA27 relied on supervariable detection for mass elimination.
+ *
+ * indistinguishable nodes:
+ * Yes (we call these "supervariables"). This was also in the MA27
+ * code - although we modified the method of detecting them (the
+ * previous hash was the true degree, which we no longer keep track
+ * of). A supervariable is a set of rows with identical nonzero
+ * pattern. All variables in a supervariable are eliminated together.
+ * Each supervariable has as its numerical name that of one of its
+ * variables (its principal variable).
+ *
+ * quotient graph representation:
+ * Yes. We use the term "element" for the cliques formed during
+ * elimination. This was also in the MA27 code. The algorithm can
+ * operate in place, but it will work more efficiently if given some
+ * "elbow room."
+ *
+ * element absorption:
+ * Yes. This was also in the MA27 code.
+ *
+ * external degree:
+ * Yes. The MA27 code was based on the true degree.
+ *
+ * incomplete degree update and multiple elimination:
+ * No. This was not in MA27, either. Our method of degree update
+ * within MC47B is element-based, not variable-based. It is thus
+ * not well-suited for use with incomplete degree update or multiple
+ * elimination.
+ *
+ * AMD Authors, and Copyright (C) 2004 by:
+ * Timothy A. Davis, Patrick Amestoy, Iain S. Duff, John K. Reid.
+ * Modifications for CAMD authored by Davis and Yanqing "Morris" Chen.
+ *
+ * Acknowledgements: This work (and the UMFPACK package) was supported by the
+ * National Science Foundation (ASC-9111263, DMS-9223088, and CCR-0203270).
+ * The UMFPACK/MA38 approximate degree update algorithm, the unsymmetric analog
+ * which forms the basis of CAMD, was developed while Tim Davis was supported by
+ * CERFACS (Toulouse, France) in a post-doctoral position. This C version, and
+ * the etree postorder, were written while Tim Davis was on sabbatical at
+ * Stanford University and Lawrence Berkeley National Laboratory.
+ * Ordering constraints were added with support from Sandia National Labs (DOE).
+
+ * ----------------------------------------------------------------------------
+ * INPUT ARGUMENTS (unaltered):
+ * ----------------------------------------------------------------------------
+
+ * n: The matrix order. Restriction: n >= 1.
+ *
+ * iwlen: The size of the Iw array. On input, the matrix is stored in
+ * Iw [0..pfree-1]. However, Iw [0..iwlen-1] should be slightly larger
+ * than what is required to hold the matrix, at least iwlen >= pfree + n.
+ * Otherwise, excessive compressions will take place. The recommended
+ * value of iwlen is 1.2 * pfree + n, which is the value used in the
+ * user-callable interface to this routine (camd_order.c). The algorithm
+ * will not run at all if iwlen < pfree. Restriction: iwlen >= pfree + n.
+ * Note that this is slightly more restrictive than the actual minimum
+ * (iwlen >= pfree), but CAMD_2 will be very slow with no elbow room.
+ * Thus, this routine enforces a bare minimum elbow room of size n.
+ *
+ * pfree: On input the tail end of the array, Iw [pfree..iwlen-1], is empty,
+ * and the matrix is stored in Iw [0..pfree-1]. During execution,
+ * additional data is placed in Iw, and pfree is modified so that
+ * Iw [pfree..iwlen-1] is always the unused part of Iw.
+ *
+ * Control: A double array of size CAMD_CONTROL containing input parameters
+ * that affect how the ordering is computed. If NULL, then default
+ * settings are used.
+ *
+ * Control [CAMD_DENSE] is used to determine whether or not a given input
+ * row is "dense". A row is "dense" if the number of entries in the row
+ * exceeds Control [CAMD_DENSE] times sqrt (n), except that rows with 16 or
+ * fewer entries are never considered "dense". To turn off the detection
+ * of dense rows, set Control [CAMD_DENSE] to a negative number, or to a
+ * number larger than sqrt (n). The default value of Control [CAMD_DENSE]
+ * is CAMD_DEFAULT_DENSE, which is defined in camd.h as 10.
+ *
+ * Control [CAMD_AGGRESSIVE] is used to determine whether or not aggressive
+ * absorption is to be performed. If nonzero, then aggressive absorption
+ * is performed (this is the default).
+ *
+ * C: defines the ordering constraints. s = C [j] gives the constraint set s
+ * that contains the row/column j (Restriction: 0 <= s < n).
+ * In the output row permutation, all rows in set 0 appear first, followed
+ * by all rows in set 1, and so on. If NULL, all rows are treated as if
+ * they were in a single constraint set, and you will obtain a similar
+ * ordering as AMD (slightly different because of the different
+ * postordering used).
+
+ * ----------------------------------------------------------------------------
+ * INPUT/OUPUT ARGUMENTS:
+ * ----------------------------------------------------------------------------
+ *
+ * Pe: An integer array of size n. On input, Pe [i] is the index in Iw of
+ * the start of row i. Pe [i] is ignored if row i has no off-diagonal
+ * entries. Thus Pe [i] must be in the range 0 to pfree-1 for non-empty
+ * rows.
+ *
+ * During execution, it is used for both supervariables and elements:
+ *
+ * Principal supervariable i: index into Iw of the description of
+ * supervariable i. A supervariable represents one or more rows of
+ * the matrix with identical nonzero pattern. In this case,
+ * Pe [i] >= 0.
+ *
+ * Non-principal supervariable i: if i has been absorbed into another
+ * supervariable j, then Pe [i] = FLIP (j), where FLIP (j) is defined
+ * as (-(j)-2). Row j has the same pattern as row i. Note that j
+ * might later be absorbed into another supervariable j2, in which
+ * case Pe [i] is still FLIP (j), and Pe [j] = FLIP (j2) which is
+ * < EMPTY, where EMPTY is defined as (-1) in camd_internal.h.
+ *
+ * Unabsorbed element e: the index into Iw of the description of element
+ * e, if e has not yet been absorbed by a subsequent element. Element
+ * e is created when the supervariable of the same name is selected as
+ * the pivot. In this case, Pe [i] >= 0.
+ *
+ * Absorbed element e: if element e is absorbed into element e2, then
+ * Pe [e] = FLIP (e2). This occurs when the pattern of e (which we
+ * refer to as Le) is found to be a subset of the pattern of e2 (that
+ * is, Le2). In this case, Pe [i] < EMPTY. If element e is "null"
+ * (it has no nonzeros outside its pivot block), then Pe [e] = EMPTY,
+ * and e is the root of an assembly subtree (or the whole tree if
+ * there is just one such root).
+ *
+ * Dense or empty variable i: if i is "dense" or empty (with zero degree),
+ * then Pe [i] = FLIP (n).
+ *
+ * On output, Pe holds the assembly tree/forest, which implicitly
+ * represents a pivot order with identical fill-in as the actual order
+ * (via a depth-first search of the tree), as follows. If Nv [i] > 0,
+ * then i represents a node in the assembly tree, and the parent of i is
+ * Pe [i], or EMPTY if i is a root. If Nv [i] = 0, then (i, Pe [i])
+ * represents an edge in a subtree, the root of which is a node in the
+ * assembly tree. Note that i refers to a row/column in the original
+ * matrix, not the permuted matrix.
+ *
+ * Info: A double array of size CAMD_INFO. If present, (that is, not NULL),
+ * then statistics about the ordering are returned in the Info array.
+ * See camd.h for a description.
+
+ * ----------------------------------------------------------------------------
+ * INPUT/MODIFIED (undefined on output):
+ * ----------------------------------------------------------------------------
+ *
+ * Len: An integer array of size n. On input, Len [i] holds the number of
+ * entries in row i of the matrix, excluding the diagonal. The contents
+ * of Len are undefined on output. Len also works as a temporary
+ * workspace in post ordering with dense nodes detected.
+ *
+ * Iw: An integer array of size iwlen. On input, Iw [0..pfree-1] holds the
+ * description of each row i in the matrix. The matrix must be symmetric,
+ * and both upper and lower triangular parts must be present. The
+ * diagonal must not be present. Row i is held as follows:
+ *
+ * Len [i]: the length of the row i data structure in the Iw array.
+ * Iw [Pe [i] ... Pe [i] + Len [i] - 1]:
+ * the list of column indices for nonzeros in row i (simple
+ * supervariables), excluding the diagonal. All supervariables
+ * start with one row/column each (supervariable i is just row i).
+ * If Len [i] is zero on input, then Pe [i] is ignored on input.
+ *
+ * Note that the rows need not be in any particular order, and there
+ * may be empty space between the rows.
+ *
+ * During execution, the supervariable i experiences fill-in. This is
+ * represented by placing in i a list of the elements that cause fill-in
+ * in supervariable i:
+ *
+ * Len [i]: the length of supervariable i in the Iw array.
+ * Iw [Pe [i] ... Pe [i] + Elen [i] - 1]:
+ * the list of elements that contain i. This list is kept short
+ * by removing absorbed elements.
+ * Iw [Pe [i] + Elen [i] ... Pe [i] + Len [i] - 1]:
+ * the list of supervariables in i. This list is kept short by
+ * removing nonprincipal variables, and any entry j that is also
+ * contained in at least one of the elements (j in Le) in the list
+ * for i (e in row i).
+ *
+ * When supervariable i is selected as pivot, we create an element e of
+ * the same name (e=i):
+ *
+ * Len [e]: the length of element e in the Iw array.
+ * Iw [Pe [e] ... Pe [e] + Len [e] - 1]:
+ * the list of supervariables in element e.
+ *
+ * An element represents the fill-in that occurs when supervariable i is
+ * selected as pivot (which represents the selection of row i and all
+ * non-principal variables whose principal variable is i). We use the
+ * term Le to denote the set of all supervariables in element e. Absorbed
+ * supervariables and elements are pruned from these lists when
+ * computationally convenient.
+ *
+ * CAUTION: THE INPUT MATRIX IS OVERWRITTEN DURING COMPUTATION.
+ * The contents of Iw are undefined on output.
+
+ * ----------------------------------------------------------------------------
+ * OUTPUT (need not be set on input):
+ * ----------------------------------------------------------------------------
+ *
+ *
+ * Nv: An integer array of size n. During execution, ABS (Nv [i]) is equal to
+ * the number of rows that are represented by the principal supervariable
+ * i. If i is a nonprincipal or dense variable, then Nv [i] = 0.
+ * Initially, Nv [i] = 1 for all i. Nv [i] < 0 signifies that i is a
+ * principal variable in the pattern Lme of the current pivot element me.
+ * After element me is constructed, Nv [i] is set back to a positive
+ * value.
+ *
+ * On output, Nv [i] holds the number of pivots represented by super
+ * row/column i of the original matrix, or Nv [i] = 0 for non-principal
+ * rows/columns. Note that i refers to a row/column in the original
+ * matrix, not the permuted matrix.
+ *
+ * Nv also works as a temporary workspace in initializing the BucketSet
+ * array.
+ *
+ * Elen: An integer array of size n. See the description of Iw above. At the
+ * start of execution, Elen [i] is set to zero for all rows i. During
+ * execution, Elen [i] is the number of elements in the list for
+ * supervariable i. When e becomes an element, Elen [e] = FLIP (esize) is
+ * set, where esize is the size of the element (the number of pivots, plus
+ * the number of nonpivotal entries). Thus Elen [e] < EMPTY.
+ * Elen (i) = EMPTY set when variable i becomes nonprincipal.
+ *
+ * For variables, Elen (i) >= EMPTY holds until just before the
+ * postordering and permutation vectors are computed. For elements,
+ * Elen [e] < EMPTY holds.
+ *
+ * On output, Elen [i] is the degree of the row/column in the Cholesky
+ * factorization of the permuted matrix, corresponding to the original row
+ * i, if i is a super row/column. It is equal to EMPTY if i is
+ * non-principal. Note that i refers to a row/column in the original
+ * matrix, not the permuted matrix.
+ *
+ * Note that the contents of Elen on output differ from the Fortran
+ * version (Elen holds the inverse permutation in the Fortran version,
+ * which is instead returned in the Next array in this C version,
+ * described below).
+ *
+ * Last: In a degree list, Last [i] is the supervariable preceding i, or EMPTY
+ * if i is the head of the list. In a hash bucket, Last [i] is the hash
+ * key for i.
+ *
+ * Last [Head [hash]] is also used as the head of a hash bucket if
+ * Head [hash] contains a degree list (see the description of Head,
+ * below).
+ *
+ * On output, Last [0..n-1] holds the permutation. That is, if
+ * i = Last [k], then row i is the kth pivot row (where k ranges from 0 to
+ * n-1). Row Last [k] of A is the kth row in the permuted matrix, PAP'.
+ *
+ * Next: Next [i] is the supervariable following i in a link list, or EMPTY if
+ * i is the last in the list. Used for two kinds of lists: degree lists
+ * and hash buckets (a supervariable can be in only one kind of list at a
+ * time).
+ *
+ * On output Next [0..n-1] holds the inverse permutation. That is, if
+ * k = Next [i], then row i is the kth pivot row. Row i of A appears as
+ * the (Next[i])-th row in the permuted matrix, PAP'.
+ *
+ * Note that the contents of Next on output differ from the Fortran
+ * version (Next is undefined on output in the Fortran version).
+
+ * ----------------------------------------------------------------------------
+ * LOCAL WORKSPACE (not input or output - used only during execution):
+ * ----------------------------------------------------------------------------
+ *
+ * Degree: An integer array of size n. If i is a supervariable, then
+ * Degree [i] holds the current approximation of the external degree of
+ * row i (an upper bound). The external degree is the number of nonzeros
+ * in row i, minus ABS (Nv [i]), the diagonal part. The bound is equal to
+ * the exact external degree if Elen [i] is less than or equal to two.
+ *
+ * We also use the term "external degree" for elements e to refer to
+ * |Le \ Lme|. If e is an element, then Degree [e] is |Le|, which is the
+ * degree of the off-diagonal part of the element e (not including the
+ * diagonal part).
+ *
+ * Head: An integer array of size n. Head is used for degree lists.
+ * Head [deg] is the first supervariable in a degree list. All
+ * supervariables i in a degree list Head [deg] have the same approximate
+ * degree, namely, deg = Degree [i]. If the list Head [deg] is empty then
+ * Head [deg] = EMPTY.
+ *
+ * During supervariable detection Head [hash] also serves as a pointer to
+ * a hash bucket. If Head [hash] >= 0, there is a degree list of degree
+ * hash. The hash bucket head pointer is Last [Head [hash]]. If
+ * Head [hash] = EMPTY, then the degree list and hash bucket are both
+ * empty. If Head [hash] < EMPTY, then the degree list is empty, and
+ * FLIP (Head [hash]) is the head of the hash bucket. After supervariable
+ * detection is complete, all hash buckets are empty, and the
+ * (Last [Head [hash]] = EMPTY) condition is restored for the non-empty
+ * degree lists.
+ *
+ * Head also workes as a temporary workspace in post ordering with dense
+ * nodes detected.
+ *
+ * W: An integer array of size n. The flag array W determines the status of
+ * elements and variables, and the external degree of elements.
+ *
+ * for elements:
+ * if W [e] = 0, then the element e is absorbed.
+ * if W [e] >= wflg, then W [e] - wflg is the size of the set
+ * |Le \ Lme|, in terms of nonzeros (the sum of ABS (Nv [i]) for
+ * each principal variable i that is both in the pattern of
+ * element e and NOT in the pattern of the current pivot element,
+ * me).
+ * if wflg > W [e] > 0, then e is not absorbed and has not yet been
+ * seen in the scan of the element lists in the computation of
+ * |Le\Lme| in Scan 1 below.
+ *
+ * for variables:
+ * during supervariable detection, if W [j] != wflg then j is
+ * not in the pattern of variable i.
+ *
+ * The W array is initialized by setting W [i] = 1 for all i, and by
+ * setting wflg = 2. It is reinitialized if wflg becomes too large (to
+ * ensure that wflg+n does not cause integer overflow).
+ *
+ * BucketSet: An integer array of size n.
+ * During execution it stores the rows that sorted in the ascending order
+ * based on C []. For instance: if C[]={0,2,1,0,1,0,2,1}, the
+ * Bucketset will be {0,3,5,2,4,7,1,6}.
+ * The elements in Bucketset are then modified, to maintain the order of
+ * roots (Pe[i]=-1) in each Constraint Set.
+
+ * ----------------------------------------------------------------------------
+ * LOCAL INTEGERS:
+ * ----------------------------------------------------------------------------
+ */
+
+ Int deg, degme, dext, lemax, e, elenme, eln, i, ilast, inext, j,
+ jlast, k, knt1, knt2, knt3, lenj, ln, me, mindeg, nel, nleft,
+ nvi, nvj, nvpiv, slenme, wbig, we, wflg, wnvi, ok, ndense, ncmpa, nnull,
+ dense, aggressive ;
+
+ unsigned Int hash ; /* unsigned, so that hash % n is well defined.*/
+
+/*
+ * deg: the degree of a variable or element
+ * degme: size, |Lme|, of the current element, me (= Degree [me])
+ * dext: external degree, |Le \ Lme|, of some element e
+ * lemax: largest |Le| seen so far (called dmax in Fortran version)
+ * e: an element
+ * elenme: the length, Elen [me], of element list of pivotal variable
+ * eln: the length, Elen [...], of an element list
+ * hash: the computed value of the hash function
+ * i: a supervariable
+ * ilast: the entry in a link list preceding i
+ * inext: the entry in a link list following i
+ * j: a supervariable
+ * jlast: the entry in a link list preceding j
+ * k: the pivot order of an element or variable
+ * knt1: loop counter used during element construction
+ * knt2: loop counter used during element construction
+ * knt3: loop counter used during compression
+ * lenj: Len [j]
+ * ln: length of a supervariable list
+ * me: current supervariable being eliminated, and the current
+ * element created by eliminating that supervariable
+ * mindeg: current minimum degree
+ * nel: number of pivots selected so far
+ * nleft: n - nel, the number of nonpivotal rows/columns remaining
+ * nvi: the number of variables in a supervariable i (= Nv [i])
+ * nvj: the number of variables in a supervariable j (= Nv [j])
+ * nvpiv: number of pivots in current element
+ * slenme: number of variables in variable list of pivotal variable
+ * wbig: = INT_MAX - n for the "int" version, LONG_MAX - n for the
+ * "long" version. wflg is not allowed to be >= wbig.
+ * we: W [e]
+ * wflg: used for flagging the W array. See description of Iw.
+ * wnvi: wflg - Nv [i]
+ * x: either a supervariable or an element
+ *
+ * ok: true if supervariable j can be absorbed into i
+ * ndense: number of "dense" rows/columns
+ * nnull: number of empty rows/columns
+ * dense: rows/columns with initial degree > dense are considered "dense"
+ * aggressive: true if aggressive absorption is being performed
+ * ncmpa: number of garbage collections
+
+ * ----------------------------------------------------------------------------
+ * LOCAL DOUBLES, used for statistical output only (except for alpha):
+ * ----------------------------------------------------------------------------
+ */
+
+ double f, r, ndiv, s, nms_lu, nms_ldl, dmax, alpha, lnz, lnzme ;
+
+/*
+ * f: nvpiv
+ * r: degme + nvpiv
+ * ndiv: number of divisions for LU or LDL' factorizations
+ * s: number of multiply-subtract pairs for LU factorization, for the
+ * current element me
+ * nms_lu number of multiply-subtract pairs for LU factorization
+ * nms_ldl number of multiply-subtract pairs for LDL' factorization
+ * dmax: the largest number of entries in any column of L, including the
+ * diagonal
+ * alpha: "dense" degree ratio
+ * lnz: the number of nonzeros in L (excluding the diagonal)
+ * lnzme: the number of nonzeros in L (excl. the diagonal) for the
+ * current element me
+
+ * ----------------------------------------------------------------------------
+ * LOCAL "POINTERS" (indices into the Iw array)
+ * ----------------------------------------------------------------------------
+*/
+
+ Int p, p1, p2, p3, p4, pdst, pend, pj, pme, pme1, pme2, pn, psrc ;
+
+/*
+ * Any parameter (Pe [...] or pfree) or local variable starting with "p" (for
+ * Pointer) is an index into Iw, and all indices into Iw use variables starting
+ * with "p." The only exception to this rule is the iwlen input argument.
+ *
+ * p: pointer into lots of things
+ * p1: Pe [i] for some variable i (start of element list)
+ * p2: Pe [i] + Elen [i] - 1 for some variable i
+ * p3: index of first supervariable in clean list
+ * p4:
+ * pdst: destination pointer, for compression
+ * pend: end of memory to compress
+ * pj: pointer into an element or variable
+ * pme: pointer into the current element (pme1...pme2)
+ * pme1: the current element, me, is stored in Iw [pme1...pme2]
+ * pme2: the end of the current element
+ * pn: pointer into a "clean" variable, also used to compress
+ * psrc: source pointer, for compression
+*/
+
+ Int curC, pBucket, pBucket2, degreeListCounter, c, cmax = 0,
+ ndense_or_null ;
+ Int *Bucket, *Perm ;
+
+/*
+ * curC: the current Constraint Set being ordered
+ * pBucket: pointer into Bucketset[] when building the degreelist for each
+ * Constraint Set
+ * pBucket2: pointer into Bucketset[] to tell the post ordering where to stop
+ * degreeListCounter: number of elements remaining in the
+ * degreelist of current Constraint Set
+ * Bucket: used to construct BucketSet
+ * Perm: permutation
+ */
+
+/* ========================================================================= */
+/* INITIALIZATIONS */
+/* ========================================================================= */
+
+ /* Note that this restriction on iwlen is slightly more restrictive than
+ * what is actually required in CAMD_2. CAMD_2 can operate with no elbow
+ * room at all, but it will be slow. For better performance, at least
+ * size-n elbow room is enforced. */
+ ASSERT (iwlen >= pfree + n) ;
+ ASSERT (n > 0) ;
+
+ /* initialize output statistics */
+ lnz = 0 ;
+ ndiv = 0 ;
+ nms_lu = 0 ;
+ nms_ldl = 0 ;
+ dmax = 1 ;
+ me = EMPTY ;
+
+ mindeg = 0 ;
+ ncmpa = 0 ;
+ nel = 0 ;
+ lemax = 0 ;
+ curC = 0 ;
+
+/* camd work initBucketSet using CountingSort
+ * BucketSort the index Array BucketSet According to Contrains Array C, Using
+ * Nv[] as a temporary workspace
+ * Input: Index Array from 0 to n.(index of rows)
+ * Output: Index Array sorted according to C. worked as a bucket set.
+ *
+ * All the value in C must be 0 <= C[i] <= n-1
+ * For instance: if C[]={0,2,1,0,1,0,2,1}, the output Bucketset should be
+ * {0,3,5,2,4,7,1,6}
+ */
+
+
+/* CountingSort BucketSet[] based on C[], It is O(n) linear time */
+
+ if (C == NULL)
+ {
+ /* store everything in bucket without changing order */
+ for (j = 0 ; j < n ; j++)
+ {
+ BucketSet [j] = j ;
+ }
+ }
+ else
+ {
+
+ Bucket = Nv ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Bucket [i] = 0 ;
+ }
+ cmax = C [0] ;
+ for (j = 0 ; j < n ; j++)
+ {
+ c = C [j] ;
+ CAMD_DEBUG1 (("C [%d] = "ID"\n", j, c)) ;
+ Bucket [c]++ ;
+ cmax = MAX (cmax, c) ;
+ ASSERT (c >= 0 && c < n) ;
+ }
+ CAMD_DEBUG1 (("Max constraint set: "ID"\n", cmax)) ;
+ for (i = 1 ; i < n ; i++)
+ {
+ Bucket [i] += Bucket [i-1] ;
+ }
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ BucketSet [--Bucket [C [j]]] = j ;
+ }
+
+#ifndef NDEBUG
+ CAMD_DEBUG3 (("\nConstraint Set "ID" :", C [BucketSet [0]]));
+ for (i = 0 ; i < n ; i++)
+ {
+ CAMD_DEBUG3 ((ID" ", BucketSet [i])) ;
+ if (i == n-1)
+ {
+ CAMD_DEBUG3 (("\n")) ;
+ break ;
+ }
+ if (C [BucketSet [i+1]] != C [BucketSet [i]])
+ {
+ CAMD_DEBUG3 (("\nConstraint Set "ID" :", C [BucketSet [i+1]])) ;
+ }
+ }
+#endif
+ }
+
+ /* get control parameters */
+ if (Control != (double *) NULL)
+ {
+ alpha = Control [CAMD_DENSE] ;
+ aggressive = (Control [CAMD_AGGRESSIVE] != 0) ;
+ }
+ else
+ {
+ alpha = CAMD_DEFAULT_DENSE ;
+ aggressive = CAMD_DEFAULT_AGGRESSIVE ;
+ }
+ /* Note: if alpha is NaN, this is undefined: */
+ if (alpha < 0)
+ {
+ /* only remove completely dense rows/columns */
+ dense = n-2 ;
+ }
+ else
+ {
+ dense = alpha * sqrt ((double) n) ;
+ }
+ dense = MAX (16, dense) ;
+ dense = MIN (n, dense) ;
+ CAMD_DEBUG1 (("\n\nCAMD (debug), alpha %g, aggr. "ID"\n",
+ alpha, aggressive)) ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ Last [i] = EMPTY ;
+ Head [i] = EMPTY ;
+ Next [i] = EMPTY ;
+ /* if separate Hhead array is used for hash buckets: *
+ Hhead [i] = EMPTY ;
+ */
+ Nv [i] = 1 ;
+ W [i] = 1 ;
+ Elen [i] = 0 ;
+ Degree [i] = Len [i] ;
+ }
+ Head [n] = EMPTY ;
+
+ /* initialize wflg */
+ wbig = Int_MAX - n ;
+ wflg = clear_flag (0, wbig, W, n) ;
+
+ /* --------------------------------------------------------------------- */
+ /* eliminate dense and empty rows */
+ /* --------------------------------------------------------------------- */
+
+ ndense = 0 ;
+ nnull = 0 ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ i = BucketSet [j] ;
+ deg = Degree [i] ;
+ ASSERT (deg >= 0 && deg < n) ;
+ if (deg > dense || deg == 0)
+ {
+
+ /* -------------------------------------------------------------
+ * Dense or empty variables are treated as non-principal variables
+ * represented by node n. That is, i is absorbed into n, just like
+ * j is absorbed into i in supervariable detection (see "found it!"
+ * comment, below).
+ * ------------------------------------------------------------- */
+
+ if (deg > dense)
+ {
+ CAMD_DEBUG1 (("Dense node "ID" degree "ID" bucket "ID"\n",
+ i, deg, j)) ;
+ ndense++ ;
+ }
+ else
+ {
+ CAMD_DEBUG1 (("Empty node "ID" degree "ID" bucket "ID"\n",
+ i, deg, j)) ;
+ nnull++ ;
+ }
+ Pe [i] = FLIP (n) ;
+ Nv [i] = 0 ; /* do not postorder this node */
+ Elen [i] = EMPTY ;
+ nel++ ;
+ }
+ }
+
+ ndense_or_null = ndense + nnull ;
+
+ pBucket = 0 ;
+ degreeListCounter = 0 ;
+ pBucket2 = 0 ;
+
+/* ========================================================================= */
+/* WHILE (selecting pivots) DO */
+/* ========================================================================= */
+
+ while (nel < n)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* if empty, fill the degree list with next non-empty constraint set */
+ /* ------------------------------------------------------------------ */
+
+ while (degreeListCounter == 0)
+ {
+ mindeg = n ;
+ /* determine the new constraint set */
+ curC = (C == NULL) ? 0 : C [BucketSet [pBucket]] ;
+ for ( ; pBucket < n ; pBucket++)
+ {
+ /* add i to the degree list, unless it's dead or not in curC */
+ i = BucketSet [pBucket] ;
+ if (!IsInCurrentSet (C, i, curC)) break ;
+ deg = Degree [i] ;
+ ASSERT (deg >= 0 && deg < n) ;
+ if (Pe [i] >= 0)
+ {
+
+ /* ------------------------------------------------------
+ * place i in the degree list corresponding to its degree
+ * ------------------------------------------------------ */
+
+ inext = Head [deg] ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = i ;
+ Next [i] = inext ;
+ Head [deg] = i ;
+ degreeListCounter++ ;
+ Last [i] = EMPTY ;
+ mindeg = MIN (mindeg, deg) ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ CAMD_DEBUG1 (("\n======Nel "ID"\n", nel)) ;
+ if (CAMD_debug >= 2)
+ {
+ CAMD_dump (n, Pe, Iw, Len, iwlen, pfree, Nv, Next,
+ Last, Head, Elen, Degree, W, nel, BucketSet, C, curC) ;
+ }
+#endif
+
+/* ========================================================================= */
+/* GET PIVOT OF MINIMUM DEGREE */
+/* ========================================================================= */
+
+ /* ----------------------------------------------------------------- */
+ /* find next supervariable for elimination */
+ /* ----------------------------------------------------------------- */
+
+ ASSERT (mindeg >= 0 && mindeg < n) ;
+ for (deg = mindeg ; deg < n ; deg++)
+ {
+ me = Head [deg] ;
+ if (me != EMPTY) break ;
+ }
+ mindeg = deg ;
+ ASSERT (me >= 0 && me < n) ;
+ CAMD_DEBUG1 (("=================me: "ID"\n", me)) ;
+
+ /* ----------------------------------------------------------------- */
+ /* remove chosen variable from link list */
+ /* ----------------------------------------------------------------- */
+
+ inext = Next [me] ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = EMPTY ;
+ Head [deg] = inext ;
+ degreeListCounter-- ;
+
+ /* ----------------------------------------------------------------- */
+ /* me represents the elimination of pivots nel to nel+Nv[me]-1. */
+ /* place me itself as the first in this set. */
+ /* ----------------------------------------------------------------- */
+
+ elenme = Elen [me] ;
+ nvpiv = Nv [me] ;
+ ASSERT (nvpiv > 0) ;
+ nel += nvpiv ;
+ CAMD_DEBUG1 (("nvpiv is initially "ID"\n", nvpiv)) ;
+
+/* ========================================================================= */
+/* CONSTRUCT NEW ELEMENT */
+/* ========================================================================= */
+
+ /* -----------------------------------------------------------------
+ * At this point, me is the pivotal supervariable. It will be
+ * converted into the current element. Scan list of the pivotal
+ * supervariable, me, setting tree pointers and constructing new list
+ * of supervariables for the new element, me. p is a pointer to the
+ * current position in the old list.
+ * ----------------------------------------------------------------- */
+
+ /* flag the variable "me" as being in Lme by negating Nv [me] */
+ Nv [me] = -nvpiv ;
+ degme = 0 ;
+ ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ;
+
+ if (elenme == 0)
+ {
+
+ /* ------------------------------------------------------------- */
+ /* construct the new element in place */
+ /* ------------------------------------------------------------- */
+
+ pme1 = Pe [me] ;
+ pme2 = pme1 - 1 ;
+
+ for (p = pme1 ; p <= pme1 + Len [me] - 1 ; p++)
+ {
+ i = Iw [p] ;
+ ASSERT (i >= 0 && i < n && Nv [i] >= 0) ;
+ nvi = Nv [i] ;
+ if (nvi > 0)
+ {
+
+ /* ----------------------------------------------------- */
+ /* i is a principal variable not yet placed in Lme. */
+ /* store i in new list */
+ /* ----------------------------------------------------- */
+
+ /* flag i as being in Lme by negating Nv [i] */
+ degme += nvi ;
+ Nv [i] = -nvi ;
+ Iw [++pme2] = i ;
+
+ /* ----------------------------------------------------- */
+ /* remove variable i from degree list. */
+ /* ----------------------------------------------------- */
+
+ if (IsInCurrentSet (C, i, curC))
+ {
+ ilast = Last [i] ;
+ inext = Next [i] ;
+ ASSERT (ilast >= EMPTY && ilast < n) ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = ilast ;
+ if (ilast != EMPTY)
+ {
+ Next [ilast] = inext ;
+ }
+ else
+ {
+ /* i is at the head of the degree list */
+ ASSERT (Degree [i] >= 0 && Degree [i] < n) ;
+ Head [Degree [i]] = inext ;
+ }
+ degreeListCounter-- ;
+ }
+ }
+ }
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------- */
+ /* construct the new element in empty space, Iw [pfree ...] */
+ /* ------------------------------------------------------------- */
+
+ p = Pe [me] ;
+ pme1 = pfree ;
+ slenme = Len [me] - elenme ;
+
+ for (knt1 = 1 ; knt1 <= elenme + 1 ; knt1++)
+ {
+
+ if (knt1 > elenme)
+ {
+ /* search the supervariables in me. */
+ e = me ;
+ pj = p ;
+ ln = slenme ;
+ CAMD_DEBUG2 (("Search sv: "ID" "ID" "ID"\n", me,pj,ln)) ;
+ }
+ else
+ {
+ /* search the elements in me. */
+ e = Iw [p++] ;
+ ASSERT (e >= 0 && e < n) ;
+ pj = Pe [e] ;
+ ln = Len [e] ;
+ CAMD_DEBUG2 (("Search element e "ID" in me "ID"\n", e,me)) ;
+ ASSERT (Elen [e] < EMPTY && W [e] > 0 && pj >= 0) ;
+ }
+ ASSERT (ln >= 0 && (ln == 0 || (pj >= 0 && pj < iwlen))) ;
+
+ /* ---------------------------------------------------------
+ * search for different supervariables and add them to the
+ * new list, compressing when necessary. this loop is
+ * executed once for each element in the list and once for
+ * all the supervariables in the list.
+ * --------------------------------------------------------- */
+
+ for (knt2 = 1 ; knt2 <= ln ; knt2++)
+ {
+ i = Iw [pj++] ;
+ ASSERT (i >= 0 && i < n && (i == me || Elen [i] >= EMPTY));
+ nvi = Nv [i] ;
+ CAMD_DEBUG2 ((": "ID" "ID" "ID" "ID"\n",
+ i, Elen [i], Nv [i], wflg)) ;
+
+ if (nvi > 0)
+ {
+
+ /* ------------------------------------------------- */
+ /* compress Iw, if necessary */
+ /* ------------------------------------------------- */
+
+ if (pfree >= iwlen)
+ {
+
+ CAMD_DEBUG1 (("GARBAGE COLLECTION\n")) ;
+
+ /* prepare for compressing Iw by adjusting pointers
+ * and lengths so that the lists being searched in
+ * the inner and outer loops contain only the
+ * remaining entries. */
+
+ Pe [me] = p ;
+ Len [me] -= knt1 ;
+ /* check if nothing left of supervariable me */
+ if (Len [me] == 0) Pe [me] = EMPTY ;
+ Pe [e] = pj ;
+ Len [e] = ln - knt2 ;
+ /* nothing left of element e */
+ if (Len [e] == 0) Pe [e] = EMPTY ;
+
+ ncmpa++ ; /* one more garbage collection */
+
+ /* store first entry of each object in Pe */
+ /* FLIP the first entry in each object */
+ for (j = 0 ; j < n ; j++)
+ {
+ pn = Pe [j] ;
+ if (pn >= 0)
+ {
+ ASSERT (pn >= 0 && pn < iwlen) ;
+ Pe [j] = Iw [pn] ;
+ Iw [pn] = FLIP (j) ;
+ }
+ }
+
+ /* psrc/pdst point to source/destination */
+ psrc = 0 ;
+ pdst = 0 ;
+ pend = pme1 - 1 ;
+
+ while (psrc <= pend)
+ {
+ /* search for next FLIP'd entry */
+ j = FLIP (Iw [psrc++]) ;
+ if (j >= 0)
+ {
+ CAMD_DEBUG2 (("Got object j: "ID"\n", j)) ;
+ Iw [pdst] = Pe [j] ;
+ Pe [j] = pdst++ ;
+ lenj = Len [j] ;
+ /* copy from source to destination */
+ for (knt3 = 0 ; knt3 <= lenj - 2 ; knt3++)
+ {
+ Iw [pdst++] = Iw [psrc++] ;
+ }
+ }
+ }
+
+ /* move the new partially-constructed element */
+ p1 = pdst ;
+ for (psrc = pme1 ; psrc <= pfree-1 ; psrc++)
+ {
+ Iw [pdst++] = Iw [psrc] ;
+ }
+ pme1 = p1 ;
+ pfree = pdst ;
+ pj = Pe [e] ;
+ p = Pe [me] ;
+
+ }
+
+ /* ------------------------------------------------- */
+ /* i is a principal variable not yet placed in Lme */
+ /* store i in new list */
+ /* ------------------------------------------------- */
+
+ /* flag i as being in Lme by negating Nv [i] */
+ degme += nvi ;
+ Nv [i] = -nvi ;
+ Iw [pfree++] = i ;
+ CAMD_DEBUG2 ((" s: "ID" nv "ID"\n", i, Nv [i]));
+
+ /* ------------------------------------------------- */
+ /* remove variable i from degree link list */
+ /* ------------------------------------------------- */
+
+ if (IsInCurrentSet (C, i, curC))
+ {
+ ilast = Last [i] ;
+ inext = Next [i] ;
+ ASSERT (ilast >= EMPTY && ilast < n) ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = ilast ;
+ if (ilast != EMPTY)
+ {
+ Next [ilast] = inext ;
+ }
+ else
+ {
+ /* i is at the head of the degree list */
+ ASSERT (Degree [i] >= 0 && Degree [i] < n) ;
+ Head [Degree [i]] = inext ;
+ }
+ degreeListCounter-- ;
+ }
+ }
+ }
+
+ if (e != me)
+ {
+ if (IsInCurrentSet (C, e, curC))
+ {
+ /* absorb element here if in same bucket */
+ /* set tree pointer and flag to indicate element e is
+ * absorbed into new element me (the parent of e is me)
+ */
+ CAMD_DEBUG1 ((" Element "ID" => "ID"\n", e, me)) ;
+ Pe [e] = FLIP (me) ;
+ W [e] = 0 ;
+ }
+ else
+ {
+ /* make element a root; kill it if not in same bucket */
+ CAMD_DEBUG1 (("2 Element "ID" => "ID"\n", e, me)) ;
+ Pe [e] = EMPTY ;
+ W [e] = 0 ;
+ }
+ }
+ }
+
+ pme2 = pfree - 1 ;
+ }
+
+ /* ----------------------------------------------------------------- */
+ /* me has now been converted into an element in Iw [pme1..pme2] */
+ /* ----------------------------------------------------------------- */
+
+ /* degme holds the external degree of new element */
+ Degree [me] = degme ;
+ Pe [me] = pme1 ;
+ Len [me] = pme2 - pme1 + 1 ;
+ ASSERT (Pe [me] >= 0 && Pe [me] < iwlen) ;
+
+ Elen [me] = FLIP (nvpiv + degme) ;
+ /* FLIP (Elen (me)) is now the degree of pivot (including
+ * diagonal part). */
+
+#ifndef NDEBUG
+ CAMD_DEBUG2 (("New element structure: length= "ID"\n", pme2-pme1+1)) ;
+ for (pme = pme1 ; pme <= pme2 ; pme++) CAMD_DEBUG3 ((" "ID"", Iw[pme]));
+ CAMD_DEBUG3 (("\n")) ;
+#endif
+
+ /* ----------------------------------------------------------------- */
+ /* make sure that wflg is not too large. */
+ /* ----------------------------------------------------------------- */
+
+ /* With the current value of wflg, wflg+n must not cause integer
+ * overflow */
+
+ wflg = clear_flag (wflg, wbig, W, n) ;
+
+/* ========================================================================= */
+/* COMPUTE (W [e] - wflg) = |Le\Lme| FOR ALL ELEMENTS */
+/* ========================================================================= */
+
+ /* -----------------------------------------------------------------
+ * Scan 1: compute the external degrees of previous elements with
+ * respect to the current element. That is:
+ * (W [e] - wflg) = |Le \ Lme|
+ * for each element e that appears in any supervariable in Lme. The
+ * notation Le refers to the pattern (list of supervariables) of a
+ * previous element e, where e is not yet absorbed, stored in
+ * Iw [Pe [e] + 1 ... Pe [e] + Len [e]]. The notation Lme
+ * refers to the pattern of the current element (stored in
+ * Iw [pme1..pme2]). If aggressive absorption is enabled, and
+ * (W [e] - wflg) becomes zero, then the element e will be absorbed
+ * in Scan 2.
+ * ----------------------------------------------------------------- */
+
+ CAMD_DEBUG2 (("me: ")) ;
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n) ;
+ eln = Elen [i] ;
+ CAMD_DEBUG3 ((""ID" Elen "ID": \n", i, eln)) ;
+ if (eln > 0)
+ {
+ /* note that Nv [i] has been negated to denote i in Lme: */
+ nvi = -Nv [i] ;
+ ASSERT (nvi > 0 && Pe [i] >= 0 && Pe [i] < iwlen) ;
+ wnvi = wflg - nvi ;
+ for (p = Pe [i] ; p <= Pe [i] + eln - 1 ; p++)
+ {
+ e = Iw [p] ;
+ ASSERT (e >= 0 && e < n) ;
+ we = W [e] ;
+ CAMD_DEBUG4 ((" e "ID" we "ID" ", e, we)) ;
+ if (we >= wflg)
+ {
+ /* unabsorbed element e has been seen in this loop */
+ CAMD_DEBUG4 ((" unabsorbed, first time seen")) ;
+ we -= nvi ;
+ }
+ else if (we != 0)
+ {
+ /* e is an unabsorbed element */
+ /* this is the first we have seen e in all of Scan 1 */
+ CAMD_DEBUG4 ((" unabsorbed")) ;
+ we = Degree [e] + wnvi ;
+ }
+ CAMD_DEBUG4 (("\n")) ;
+ W [e] = we ;
+ }
+ }
+ }
+ CAMD_DEBUG2 (("\n")) ;
+
+/* ========================================================================= */
+/* DEGREE UPDATE AND ELEMENT ABSORPTION */
+/* ========================================================================= */
+
+ /* -----------------------------------------------------------------
+ * Scan 2: for each i in Lme, sum up the degree of Lme (which is
+ * degme), plus the sum of the external degrees of each Le for the
+ * elements e appearing within i, plus the supervariables in i.
+ * Place i in hash list.
+ * ----------------------------------------------------------------- */
+
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n && Nv [i] < 0 && Elen [i] >= 0) ;
+ CAMD_DEBUG2 (("Updating: i "ID" "ID" "ID"\n", i, Elen[i], Len [i]));
+ p1 = Pe [i] ;
+ p2 = p1 + Elen [i] - 1 ;
+ pn = p1 ;
+ hash = 0 ;
+ deg = 0 ;
+ ASSERT (p1 >= 0 && p1 < iwlen && p2 >= -1 && p2 < iwlen) ;
+
+ /* ------------------------------------------------------------- */
+ /* scan the element list associated with supervariable i */
+ /* ------------------------------------------------------------- */
+
+ /* UMFPACK/MA38-style approximate degree: */
+ if (aggressive)
+ {
+ for (p = p1 ; p <= p2 ; p++)
+ {
+ e = Iw [p] ;
+ ASSERT (e >= 0 && e < n) ;
+ we = W [e] ;
+ if (we != 0)
+ {
+ /* e is an unabsorbed element */
+ /* dext = | Le \ Lme | */
+ dext = we - wflg ;
+ if (dext > 0)
+ {
+ deg += dext ;
+ Iw [pn++] = e ;
+ hash += e ;
+ CAMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ;
+ }
+ else
+ {
+ if (IsInCurrentSet (C, e, curC))
+ {
+ /* external degree of e is zero and if
+ * C[e] = curC; absorb e into me */
+ CAMD_DEBUG1 ((" Element "ID" =>"ID" (aggr)\n",
+ e, me)) ;
+ ASSERT (dext == 0) ;
+ Pe [e] = FLIP (me) ;
+ W [e] = 0 ;
+ }
+ else
+ {
+ /* make element a root; kill it if not in same
+ * bucket */
+ CAMD_DEBUG1 (("2 Element "ID" =>"ID" (aggr)\n",
+ e, me)) ;
+ ASSERT (dext == 0) ;
+ Pe [e] = EMPTY ;
+ W [e] = 0 ;
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ for (p = p1 ; p <= p2 ; p++)
+ {
+ e = Iw [p] ;
+ ASSERT (e >= 0 && e < n) ;
+ we = W [e] ;
+ if (we != 0)
+ {
+ /* e is an unabsorbed element */
+ dext = we - wflg ;
+ ASSERT (dext >= 0) ;
+ deg += dext ;
+ Iw [pn++] = e ;
+ hash += e ;
+ CAMD_DEBUG4 ((" e: "ID" hash = "ID"\n",e,hash)) ;
+ }
+ }
+ }
+
+ /* count the number of elements in i (including me): */
+ Elen [i] = pn - p1 + 1 ;
+
+ /* ------------------------------------------------------------- */
+ /* scan the supervariables in the list associated with i */
+ /* ------------------------------------------------------------- */
+
+ /* The bulk of the CAMD run time is typically spent in this loop,
+ * particularly if the matrix has many dense rows that are not
+ * removed prior to ordering. */
+ p3 = pn ;
+ p4 = p1 + Len [i] ;
+ for (p = p2 + 1 ; p < p4 ; p++)
+ {
+ j = Iw [p] ;
+ ASSERT (j >= 0 && j < n) ;
+ nvj = Nv [j] ;
+ if (nvj > 0)
+ {
+ /* j is unabsorbed, and not in Lme. */
+ /* add to degree and add to new list */
+ deg += nvj ;
+ Iw [pn++] = j ;
+ hash += j ;
+ CAMD_DEBUG4 ((" s: "ID" hash "ID" Nv[j]= "ID"\n",
+ j, hash, nvj)) ;
+ }
+ }
+
+ /* ------------------------------------------------------------- */
+ /* update the degree and check for mass elimination */
+ /* ------------------------------------------------------------- */
+
+ /* with aggressive absorption, deg==0 is identical to the
+ * Elen [i] == 1 && p3 == pn test, below. */
+ ASSERT (IMPLIES (aggressive, (deg==0) == (Elen[i]==1 && p3==pn))) ;
+
+ if (Elen [i] == 1 && p3 == pn && IsInCurrentSet (C, i, curC))
+ {
+
+ /* --------------------------------------------------------- */
+ /* mass elimination */
+ /* --------------------------------------------------------- */
+
+ /* There is nothing left of this node except for an edge to
+ * the current pivot element. Elen [i] is 1, and there are
+ * no variables adjacent to node i. Absorb i into the
+ * current pivot element, me. Note that if there are two or
+ * more mass eliminations, fillin due to mass elimination is
+ * possible within the nvpiv-by-nvpiv pivot block. It is this
+ * step that causes CAMD's analysis to be an upper bound.
+ *
+ * The reason is that the selected pivot has a lower
+ * approximate degree than the true degree of the two mass
+ * eliminated nodes. There is no edge between the two mass
+ * eliminated nodes. They are merged with the current pivot
+ * anyway.
+ *
+ * No fillin occurs in the Schur complement, in any case,
+ * and this effect does not decrease the quality of the
+ * ordering itself, just the quality of the nonzero and
+ * flop count analysis. It also means that the post-ordering
+ * is not an exact elimination tree post-ordering. */
+
+ CAMD_DEBUG1 ((" MASS i "ID" => parent e "ID"\n", i, me)) ;
+ Pe [i] = FLIP (me) ;
+ nvi = -Nv [i] ;
+ degme -= nvi ;
+ nvpiv += nvi ;
+ nel += nvi ;
+ Nv [i] = 0 ;
+ Elen [i] = EMPTY ;
+
+ }
+ else
+ {
+
+ /* --------------------------------------------------------- */
+ /* update the upper-bound degree of i */
+ /* --------------------------------------------------------- */
+
+ /* the following degree does not yet include the size
+ * of the current element, which is added later: */
+
+ Degree [i] = MIN (Degree [i], deg) ;
+
+ /* --------------------------------------------------------- */
+ /* add me to the list for i */
+ /* --------------------------------------------------------- */
+
+ /* move first supervariable to end of list */
+ Iw [pn] = Iw [p3] ;
+ /* move first element to end of element part of list */
+ Iw [p3] = Iw [p1] ;
+ /* add new element, me, to front of list. */
+ Iw [p1] = me ;
+ /* store the new length of the list in Len [i] */
+ Len [i] = pn - p1 + 1 ;
+
+ /* --------------------------------------------------------- */
+ /* place in hash bucket. Save hash key of i in Last [i]. */
+ /* --------------------------------------------------------- */
+
+ /* NOTE: this can fail if hash is negative, because the ANSI C
+ * standard does not define a % b when a and/or b are negative.
+ * That's why hash is defined as an unsigned Int, to avoid this
+ * problem. */
+ hash = hash % n ;
+ ASSERT (((Int) hash) >= 0 && ((Int) hash) < n) ;
+
+ /* if the Hhead array is not used: */
+ j = Head [hash] ;
+ if (j <= EMPTY)
+ {
+ /* degree list is empty, hash head is FLIP (j) */
+ Next [i] = FLIP (j) ;
+ Head [hash] = FLIP (i) ;
+ }
+ else
+ {
+ /* degree list is not empty, use Last [Head [hash]] as
+ * hash head. */
+ Next [i] = Last [j] ;
+ Last [j] = i ;
+ }
+
+ /* if a separate Hhead array is used: *
+ Next [i] = Hhead [hash] ;
+ Hhead [hash] = i ;
+ */
+
+ CAMD_DEBUG4 ((" s: "ID" hash "ID" \n", i, hash)) ;
+ Last [i] = hash ;
+ }
+ }
+
+ Degree [me] = degme ;
+
+ /* ----------------------------------------------------------------- */
+ /* Clear the counter array, W [...], by incrementing wflg. */
+ /* ----------------------------------------------------------------- */
+
+ /* make sure that wflg+n does not cause integer overflow */
+ lemax = MAX (lemax, degme) ;
+ wflg += lemax ;
+ wflg = clear_flag (wflg, wbig, W, n) ;
+ /* at this point, W [0..n-1] < wflg holds */
+
+/* ========================================================================= */
+/* SUPERVARIABLE DETECTION */
+/* ========================================================================= */
+
+ CAMD_DEBUG1 (("Detecting supervariables:\n")) ;
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n) ;
+ CAMD_DEBUG2 (("Consider i "ID" nv "ID"\n", i, Nv [i])) ;
+ if (Nv [i] < 0)
+ {
+ /* i is a principal variable in Lme */
+
+ /* ---------------------------------------------------------
+ * examine all hash buckets with 2 or more variables. We do
+ * this by examing all unique hash keys for supervariables in
+ * the pattern Lme of the current element, me
+ * --------------------------------------------------------- */
+
+ CAMD_DEBUG2 (("Last: "ID"\n", Last [i])) ;
+
+ /* let i = head of hash bucket, and empty the hash bucket */
+ ASSERT (Last [i] >= 0 && Last [i] < n) ;
+ hash = Last [i] ;
+
+ /* if Hhead array is not used: */
+ j = Head [hash] ;
+ if (j == EMPTY)
+ {
+ /* hash bucket and degree list are both empty */
+ i = EMPTY ;
+ }
+ else if (j < EMPTY)
+ {
+ /* degree list is empty */
+ i = FLIP (j) ;
+ Head [hash] = EMPTY ;
+ }
+ else
+ {
+ /* degree list is not empty, restore Last [j] of head j */
+ i = Last [j] ;
+ Last [j] = EMPTY ;
+ }
+
+ /* if separate Hhead array is used: *
+ i = Hhead [hash] ;
+ Hhead [hash] = EMPTY ;
+ */
+
+ ASSERT (i >= EMPTY && i < n) ;
+ CAMD_DEBUG2 (("----i "ID" hash "ID"\n", i, hash)) ;
+
+ while (i != EMPTY && Next [i] != EMPTY)
+ {
+
+ /* -----------------------------------------------------
+ * this bucket has one or more variables following i.
+ * scan all of them to see if i can absorb any entries
+ * that follow i in hash bucket. Scatter i into w.
+ * ----------------------------------------------------- */
+
+ ln = Len [i] ;
+ eln = Elen [i] ;
+ ASSERT (ln >= 0 && eln >= 0) ;
+ ASSERT (Pe [i] >= 0 && Pe [i] < iwlen) ;
+ /* do not flag the first element in the list (me) */
+ for (p = Pe [i] + 1 ; p <= Pe [i] + ln - 1 ; p++)
+ {
+ ASSERT (Iw [p] >= 0 && Iw [p] < n) ;
+ W [Iw [p]] = wflg ;
+ }
+
+ /* ----------------------------------------------------- */
+ /* scan every other entry j following i in bucket */
+ /* ----------------------------------------------------- */
+
+ jlast = i ;
+ j = Next [i] ;
+ ASSERT (j >= EMPTY && j < n) ;
+
+ while (j != EMPTY)
+ {
+ /* ------------------------------------------------- */
+ /* check if j and i have identical nonzero pattern */
+ /* ------------------------------------------------- */
+
+ CAMD_DEBUG3 (("compare i "ID" and j "ID"\n", i,j)) ;
+
+ /* check if i and j have the same Len and Elen */
+ /* and are in the same bucket */
+ ASSERT (Len [j] >= 0 && Elen [j] >= 0) ;
+ ASSERT (Pe [j] >= 0 && Pe [j] < iwlen) ;
+ ok = (Len [j] == ln) && (Elen [j] == eln) ;
+ ok = ok && InSameConstraintSet (C,i,j) ;
+
+ /* skip the first element in the list (me) */
+ for (p = Pe [j] + 1 ; ok && p <= Pe [j] + ln - 1 ; p++)
+ {
+ ASSERT (Iw [p] >= 0 && Iw [p] < n) ;
+ if (W [Iw [p]] != wflg) ok = 0 ;
+ }
+ if (ok)
+ {
+ /* --------------------------------------------- */
+ /* found it! j can be absorbed into i */
+ /* --------------------------------------------- */
+
+ CAMD_DEBUG1 (("found it! j "ID" => i "ID"\n", j,i));
+ Pe [j] = FLIP (i) ;
+ /* both Nv [i] and Nv [j] are negated since they */
+ /* are in Lme, and the absolute values of each */
+ /* are the number of variables in i and j: */
+ Nv [i] += Nv [j] ;
+ Nv [j] = 0 ;
+ Elen [j] = EMPTY ;
+ /* delete j from hash bucket */
+ ASSERT (j != Next [j]) ;
+ j = Next [j] ;
+ Next [jlast] = j ;
+
+ }
+ else
+ {
+ /* j cannot be absorbed into i */
+ jlast = j ;
+ ASSERT (j != Next [j]) ;
+ j = Next [j] ;
+ }
+ ASSERT (j >= EMPTY && j < n) ;
+ }
+
+ /* -----------------------------------------------------
+ * no more variables can be absorbed into i
+ * go to next i in bucket and clear flag array
+ * ----------------------------------------------------- */
+
+ wflg++ ;
+ i = Next [i] ;
+ ASSERT (i >= EMPTY && i < n) ;
+
+ }
+ }
+ }
+ CAMD_DEBUG2 (("detect done\n")) ;
+
+/* ========================================================================= */
+/* RESTORE DEGREE LISTS AND REMOVE NONPRINCIPAL SUPERVARIABLES FROM ELEMENT */
+/* ========================================================================= */
+
+ p = pme1 ;
+ nleft = n - nel ;
+ for (pme = pme1 ; pme <= pme2 ; pme++)
+ {
+ i = Iw [pme] ;
+ ASSERT (i >= 0 && i < n) ;
+ nvi = -Nv [i] ;
+ CAMD_DEBUG3 (("Restore i "ID" "ID"\n", i, nvi)) ;
+ if (nvi > 0)
+ {
+ /* i is a principal variable in Lme */
+ /* restore Nv [i] to signify that i is principal */
+ Nv [i] = nvi ;
+
+ /* --------------------------------------------------------- */
+ /* compute the external degree (add size of current element) */
+ /* --------------------------------------------------------- */
+
+ deg = Degree [i] + degme - nvi ;
+ deg = MIN (deg, nleft - nvi) ;
+ ASSERT (deg >= 0 && deg < n) ;
+
+ /* --------------------------------------------------------- */
+ /* place the supervariable at the head of the degree list */
+ /* --------------------------------------------------------- */
+
+ if (IsInCurrentSet (C, i, curC))
+ {
+ inext = Head [deg] ;
+ ASSERT (inext >= EMPTY && inext < n) ;
+ if (inext != EMPTY) Last [inext] = i ;
+ Next [i] = inext ;
+ Last [i] = EMPTY ;
+ Head [deg] = i ;
+ degreeListCounter++ ;
+ }
+
+ /* --------------------------------------------------------- */
+ /* save the new degree, and find the minimum degree */
+ /* --------------------------------------------------------- */
+
+ mindeg = MIN (mindeg, deg) ;
+ Degree [i] = deg ;
+
+ /* --------------------------------------------------------- */
+ /* place the supervariable in the element pattern */
+ /* --------------------------------------------------------- */
+
+ Iw [p++] = i ;
+ }
+ }
+ CAMD_DEBUG2 (("restore done\n")) ;
+
+/* ========================================================================= */
+/* FINALIZE THE NEW ELEMENT */
+/* ========================================================================= */
+
+ CAMD_DEBUG2 (("ME = "ID" DONE\n", me)) ;
+ Nv [me] = nvpiv ;
+ /* save the length of the list for the new element me */
+ Len [me] = p - pme1 ;
+ if (Len [me] == 0)
+ {
+ /* there is nothing left of the current pivot element */
+ /* it is a root of the assembly tree */
+ Pe [me] = EMPTY ;
+ W [me] = 0 ;
+ }
+ if (elenme != 0)
+ {
+ /* element was not constructed in place: deallocate part of */
+ /* it since newly nonprincipal variables may have been removed */
+ pfree = p ;
+ }
+
+ /* Store the element back into BucketSet. This is the way to maintain
+ * the order of roots (Pe[i]=-1) in each Constraint Set. */
+ BucketSet [pBucket2++] = me ;
+
+ /* The new element has nvpiv pivots and the size of the contribution
+ * block for a multifrontal method is degme-by-degme, not including
+ * the "dense" rows/columns. If the "dense" rows/columns are included,
+ * the frontal matrix is no larger than
+ * (degme+ndense)-by-(degme+ndense).
+ */
+
+ if (Info != (double *) NULL)
+ {
+ f = nvpiv ;
+ r = degme + ndense ;
+ dmax = MAX (dmax, f + r) ;
+
+ /* number of nonzeros in L (excluding the diagonal) */
+ lnzme = f*r + (f-1)*f/2 ;
+ lnz += lnzme ;
+
+ /* number of divide operations for LDL' and for LU */
+ ndiv += lnzme ;
+
+ /* number of multiply-subtract pairs for LU */
+ s = f*r*r + r*(f-1)*f + (f-1)*f*(2*f-1)/6 ;
+ nms_lu += s ;
+
+ /* number of multiply-subtract pairs for LDL' */
+ nms_ldl += (s + lnzme)/2 ;
+ }
+
+#ifndef NDEBUG
+ CAMD_DEBUG2 (("finalize done nel "ID" n "ID"\n ::::\n", nel, n)) ;
+ for (pme = Pe [me] ; pme <= Pe [me] + Len [me] - 1 ; pme++)
+ {
+ CAMD_DEBUG3 ((" "ID"", Iw [pme])) ;
+ }
+ CAMD_DEBUG3 (("\n")) ;
+#endif
+
+ }
+
+/* ========================================================================= */
+/* DONE SELECTING PIVOTS */
+/* ========================================================================= */
+
+ if (Info != (double *) NULL)
+ {
+
+ /* count the work to factorize the ndense-by-ndense submatrix */
+ f = ndense ;
+ dmax = MAX (dmax, (double) ndense) ;
+
+ /* number of nonzeros in L (excluding the diagonal) */
+ lnzme = (f-1)*f/2 ;
+ lnz += lnzme ;
+
+ /* number of divide operations for LDL' and for LU */
+ ndiv += lnzme ;
+
+ /* number of multiply-subtract pairs for LU */
+ s = (f-1)*f*(2*f-1)/6 ;
+ nms_lu += s ;
+
+ /* number of multiply-subtract pairs for LDL' */
+ nms_ldl += (s + lnzme)/2 ;
+
+ /* number of nz's in L (excl. diagonal) */
+ Info [CAMD_LNZ] = lnz ;
+
+ /* number of divide ops for LU and LDL' */
+ Info [CAMD_NDIV] = ndiv ;
+
+ /* number of multiply-subtract pairs for LDL' */
+ Info [CAMD_NMULTSUBS_LDL] = nms_ldl ;
+
+ /* number of multiply-subtract pairs for LU */
+ Info [CAMD_NMULTSUBS_LU] = nms_lu ;
+
+ /* number of "dense" rows/columns */
+ Info [CAMD_NDENSE] = ndense ;
+
+ /* largest front is dmax-by-dmax */
+ Info [CAMD_DMAX] = dmax ;
+
+ /* number of garbage collections in CAMD */
+ Info [CAMD_NCMPA] = ncmpa ;
+
+ /* successful ordering */
+ Info [CAMD_STATUS] = CAMD_OK ;
+ }
+
+/* ========================================================================= */
+/* POST-ORDERING */
+/* ========================================================================= */
+
+/* -------------------------------------------------------------------------
+ * Variables at this point:
+ *
+ * Pe: holds the elimination tree. The parent of j is FLIP (Pe [j]),
+ * or EMPTY if j is a root. The tree holds both elements and
+ * non-principal (unordered) variables absorbed into them.
+ * Dense and empty variables are non-principal and unordered. They are
+ * all represented by the fictitious node n (that is, Pe [i] = FLIP (n)
+ * and Elen [i] = EMPTY if i is a dense or empty node).
+ *
+ * Elen: holds the size of each element, including the diagonal part.
+ * FLIP (Elen [e]) > 0 if e is an element. For unordered
+ * variables i, Elen [i] is EMPTY.
+ *
+ * Nv: Nv [e] > 0 is the number of pivots represented by the element e.
+ * For unordered variables i, Nv [i] is zero.
+ *
+ * BucketSet: BucketSet [0.....pBucket2] holds all
+ * the elements that removed during the elimination, in eliminated order.
+ *
+ *
+ * Contents no longer needed:
+ * W, Iw, Len, Degree, Head, Next, Last.
+ *
+ * The matrix itself has been destroyed.
+ *
+ * n: the size of the matrix.
+ * ndense: the number of "dense" nodes.
+ * nnull: the number of empty nodes (zero degree)
+ * No other scalars needed (pfree, iwlen, etc.)
+ * ------------------------------------------------------------------------- */
+
+
+ /* restore Pe */
+ for (i = 0 ; i < n ; i++)
+ {
+ Pe [i] = FLIP (Pe [i]) ;
+ }
+
+ /* restore Elen, for output information only */
+ for (i = 0 ; i < n ; i++)
+ {
+ Elen [i] = FLIP (Elen [i]) ;
+ }
+
+ /* Now, Pe [j] is the parent of j, or EMPTY if j is a root.
+ * Pe [j] = n if j is a dense/empty node */
+
+ /* place all variables in the list of children of their parents */
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ if (Nv [j] > 0) continue ; /* skip if j is an element */
+ ASSERT (Pe [j] >= 0 && Pe [j] <= n) ;
+ Next [j] = Head [Pe [j]] ; /* place j in list of its parent */
+ Head [Pe [j]] = j ;
+ }
+
+ /* place all elements in the list of children of their parents */
+ for (e = n-1 ; e >= 0 ; e--)
+ {
+ if (Nv [e] <= 0) continue ; /* skip if e is a variable */
+ if (Pe [e] == EMPTY) continue ; /* skip if e is a root */
+ Next [e] = Head [Pe [e]] ; /* place e in list of its parent */
+ Head [Pe [e]] = e ;
+ }
+
+ /* determine where to put the postordering permutation */
+ if (C != NULL && ndense_or_null > 0)
+ {
+ /* Perm needs to be computed in a temporary workspace, and then
+ * transformed and copied into the output permutation, in Last */
+ Perm = Degree ;
+ }
+ else
+ {
+ /* the postorder computes the permutation directly, in Last */
+ Perm = Last ;
+ }
+
+ /* postorder the elements and their descendants (both elements and
+ * variables), but not (yet) the dense/empty nodes */
+ for (k = 0 , i = 0 ; i < pBucket2 ; i++)
+ {
+ j = BucketSet [i] ;
+ ASSERT (j >= 0 && j < n) ;
+ if (Pe [j] == EMPTY)
+ {
+ k = CAMD_postorder (j, k, n, Head, Next, Perm, W) ;
+ }
+ }
+
+ /* Perm [0..k-1] now contains a list of the nonempty/nondense nodes,
+ * ordered via minimum degree and following the constraints. */
+
+ CAMD_DEBUG1 (("before dense/empty, k = "ID"\n", k)) ;
+ fflush (stdout) ;
+ ASSERT (k + ndense_or_null == n) ;
+
+ if (ndense_or_null > 0)
+ {
+ if (C == NULL)
+ {
+ /* postorder the dense/empty nodes (the parent of all these is n) */
+ CAMD_postorder (n, k, n, Head, Next, Perm, W) ;
+ }
+ else
+ {
+ /* dense (or empty) nodes exist, AND C also exists. The dense/empty
+ * nodes are a link list whose head is Head[n], and Next[i] gives the
+ * next node after i in the list. They need to be sorted by their
+ * constraints, and then merged with Perm [0..k-1].*/
+
+ /* count how many dense/empty nodes are in each constraint set */
+
+ Bucket = W ; /* use W as workspace (it has size n+1) */
+
+ /* count the number of dense/empty nodes in each constraint set */
+ for (c = 0 ; c <= cmax ; c++)
+ {
+ Bucket [c] = 0 ;
+ }
+ i = 0 ;
+ for (j = Head [n] ; j != EMPTY ; j = Next [j])
+ {
+ CAMD_DEBUG1 (("Dense/empty node: "ID" : "ID" "ID"\n", j,
+ Pe [j], Elen [j])) ;
+ fflush (stdout) ;
+ ASSERT (Pe [j] == n && Elen [j] == EMPTY) ;
+ i++ ;
+ Bucket [C [j]]++ ;
+ }
+ ASSERT (i == ndense_or_null) ;
+
+ /* find the cumulative sum of Bucket */
+ knt1 = 0 ;
+ for (c = 0 ; c <= cmax ; c++)
+ {
+ i = Bucket [c] ;
+ Bucket [c] = knt1 ;
+ knt1 += i ;
+ }
+ CAMD_DEBUG1 (("knt1 "ID" dense/empty "ID"\n", knt1, ndense_or_null));
+ ASSERT (knt1 == ndense_or_null) ;
+
+ /* place dense/empty nodes in BucketSet, in constraint order,
+ * ties in natural order */
+ for (j = Head [n] ; j != EMPTY ; j = Next [j])
+ {
+ BucketSet [Bucket [C [j]]++] = j ;
+ }
+
+#ifndef NDEBUG
+ /* each set is in monotonically increasing order of constraints */
+ for (i = 1 ; i < k ; i++)
+ {
+ ASSERT (C [Perm [i]] >= C [Perm [i-1]]) ;
+ }
+ for (i = 1 ; i < ndense_or_null ; i++)
+ {
+ /* in order of constraints, with ties in natural order */
+ ASSERT (
+ (C [BucketSet [i]] > C [BucketSet [i-1]]) ||
+ (C [BucketSet [i]] == C [BucketSet [i-1]]
+ && (BucketSet [i] > BucketSet [i-1]))) ;
+ }
+#endif
+
+ /* merge Perm [0..k-1] and BucketSet [0..ndense+nnull] */
+ p1 = 0 ;
+ p2 = 0 ;
+ p3 = 0 ;
+ while (p1 < k && p2 < ndense_or_null)
+ {
+ /* place the dense/empty nodes at the end of each constraint
+ * set, after the non-dense/non-empty nodes in the same set */
+ if (C [Perm [p1]] <= C [BucketSet [p2]])
+ {
+ /* non-dense/non-empty node */
+ Last [p3++] = Perm [p1++] ;
+ }
+ else
+ {
+ /* dense/empty node */
+ Last [p3++] = BucketSet [p2++] ;
+ }
+ }
+ /* wrap up; either Perm[0..k-1] or BucketSet[ ] is used up */
+ while (p1 < k)
+ {
+ Last [p3++] = Perm [p1++] ;
+ }
+ while (p2 < ndense_or_null)
+ {
+ Last [p3++] = BucketSet [p2++] ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ CAMD_DEBUG1 (("\nFinal constrained ordering:\n")) ;
+ i = 0 ;
+ CAMD_DEBUG1 (("Last ["ID"] = "ID", C["ID"] = "ID"\n", i, Last [i],
+ Last [i], C [Last [i]])) ;
+ for (i = 1 ; i < n ; i++)
+ {
+ CAMD_DEBUG1 (("Last ["ID"] = "ID", C["ID"] = "ID"\n", i, Last [i],
+ Last [i], C [Last [i]])) ;
+
+ /* This is the critical assertion. It states that the permutation
+ * satisfies the constraints. */
+ ASSERT (C [Last [i]] >= C [Last [i-1]]) ;
+ }
+#endif
+}
diff --git a/CAMD/Source/camd_aat.c b/CAMD/Source/camd_aat.c
new file mode 100644
index 0000000..450ba34
--- /dev/null
+++ b/CAMD/Source/camd_aat.c
@@ -0,0 +1,184 @@
+/* ========================================================================= */
+/* === CAMD_aat ============================================================ */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* CAMD_aat: compute the symmetry of the pattern of A, and count the number of
+ * nonzeros each column of A+A' (excluding the diagonal). Assumes the input
+ * matrix has no errors, with sorted columns and no duplicates
+ * (CAMD_valid (n, n, Ap, Ai) must be CAMD_OK, but this condition is not
+ * checked).
+ */
+
+#include "camd_internal.h"
+
+GLOBAL size_t CAMD_aat /* returns nz in A+A' */
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int Len [ ], /* Len [j]: length of column j of A+A', excl diagonal*/
+ Int Tp [ ], /* workspace of size n */
+ double Info [ ]
+)
+{
+ Int p1, p2, p, i, j, pj, pj2, k, nzdiag, nzboth, nz ;
+ double sym ;
+ size_t nzaat ;
+
+#ifndef NDEBUG
+ CAMD_debug_init ("CAMD AAT") ;
+ for (k = 0 ; k < n ; k++) Tp [k] = EMPTY ;
+ ASSERT (CAMD_valid (n, n, Ap, Ai) == CAMD_OK) ;
+#endif
+
+ if (Info != (double *) NULL)
+ {
+ /* clear the Info array, if it exists */
+ for (i = 0 ; i < CAMD_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ Info [CAMD_STATUS] = CAMD_OK ;
+ }
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Len [k] = 0 ;
+ }
+
+ nzdiag = 0 ;
+ nzboth = 0 ;
+ nz = Ap [n] ;
+
+ for (k = 0 ; k < n ; k++)
+ {
+ p1 = Ap [k] ;
+ p2 = Ap [k+1] ;
+ CAMD_DEBUG2 (("\nAAT Column: "ID" p1: "ID" p2: "ID"\n", k, p1, p2)) ;
+
+ /* construct A+A' */
+ for (p = p1 ; p < p2 ; )
+ {
+ /* scan the upper triangular part of A */
+ j = Ai [p] ;
+ if (j < k)
+ {
+ /* entry A (j,k) is in the strictly upper triangular part,
+ * add both A (j,k) and A (k,j) to the matrix A+A' */
+ Len [j]++ ;
+ Len [k]++ ;
+ CAMD_DEBUG3 ((" upper ("ID","ID") ("ID","ID")\n", j,k, k,j));
+ p++ ;
+ }
+ else if (j == k)
+ {
+ /* skip the diagonal */
+ p++ ;
+ nzdiag++ ;
+ break ;
+ }
+ else /* j > k */
+ {
+ /* first entry below the diagonal */
+ break ;
+ }
+ /* scan lower triangular part of A, in column j until reaching
+ * row k. Start where last scan left off. */
+ ASSERT (Tp [j] != EMPTY) ;
+ ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ;
+ pj2 = Ap [j+1] ;
+ for (pj = Tp [j] ; pj < pj2 ; )
+ {
+ i = Ai [pj] ;
+ if (i < k)
+ {
+ /* A (i,j) is only in the lower part, not in upper.
+ * add both A (i,j) and A (j,i) to the matrix A+A' */
+ Len [i]++ ;
+ Len [j]++ ;
+ CAMD_DEBUG3 ((" lower ("ID","ID") ("ID","ID")\n",
+ i,j, j,i)) ;
+ pj++ ;
+ }
+ else if (i == k)
+ {
+ /* entry A (k,j) in lower part and A (j,k) in upper */
+ pj++ ;
+ nzboth++ ;
+ break ;
+ }
+ else /* i > k */
+ {
+ /* consider this entry later, when k advances to i */
+ break ;
+ }
+ }
+ Tp [j] = pj ;
+ }
+ /* Tp [k] points to the entry just below the diagonal in column k */
+ Tp [k] = p ;
+ }
+
+ /* clean up, for remaining mismatched entries */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (pj = Tp [j] ; pj < Ap [j+1] ; pj++)
+ {
+ i = Ai [pj] ;
+ /* A (i,j) is only in the lower part, not in upper.
+ * add both A (i,j) and A (j,i) to the matrix A+A' */
+ Len [i]++ ;
+ Len [j]++ ;
+ CAMD_DEBUG3 ((" lower cleanup ("ID","ID") ("ID","ID")\n",
+ i,j, j,i)) ;
+ }
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* compute the symmetry of the nonzero pattern of A */
+ /* --------------------------------------------------------------------- */
+
+ /* Given a matrix A, the symmetry of A is:
+ * B = tril (spones (A), -1) + triu (spones (A), 1) ;
+ * sym = nnz (B & B') / nnz (B) ;
+ * or 1 if nnz (B) is zero.
+ */
+
+ if (nz == nzdiag)
+ {
+ sym = 1 ;
+ }
+ else
+ {
+ sym = (2 * (double) nzboth) / ((double) (nz - nzdiag)) ;
+ }
+
+ nzaat = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ nzaat += Len [k] ;
+ }
+ CAMD_DEBUG1 (("CAMD nz in A+A', excluding diagonal (nzaat) = %g\n",
+ (double) nzaat)) ;
+ CAMD_DEBUG1 ((" nzboth: "ID" nz: "ID" nzdiag: "ID" symmetry: %g\n",
+ nzboth, nz, nzdiag, sym)) ;
+
+ if (Info != (double *) NULL)
+ {
+ Info [CAMD_STATUS] = CAMD_OK ;
+ Info [CAMD_N] = n ;
+ Info [CAMD_NZ] = nz ;
+ Info [CAMD_SYMMETRY] = sym ; /* symmetry of pattern of A */
+ Info [CAMD_NZDIAG] = nzdiag ; /* nonzeros on diagonal of A */
+ Info [CAMD_NZ_A_PLUS_AT] = nzaat ; /* nonzeros in A+A' */
+ }
+
+ return (nzaat) ;
+}
diff --git a/CAMD/Source/camd_control.c b/CAMD/Source/camd_control.c
new file mode 100644
index 0000000..f68eae9
--- /dev/null
+++ b/CAMD/Source/camd_control.c
@@ -0,0 +1,62 @@
+/* ========================================================================= */
+/* === CAMD_control ======================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable. Prints the control parameters for CAMD. See camd.h
+ * for details. If the Control array is not present, the defaults are
+ * printed instead.
+ */
+
+#include "camd_internal.h"
+
+GLOBAL void CAMD_control
+(
+ double Control [ ]
+)
+{
+ double alpha ;
+ Int aggressive ;
+
+ if (Control != (double *) NULL)
+ {
+ alpha = Control [CAMD_DENSE] ;
+ aggressive = Control [CAMD_AGGRESSIVE] != 0 ;
+ }
+ else
+ {
+ alpha = CAMD_DEFAULT_DENSE ;
+ aggressive = CAMD_DEFAULT_AGGRESSIVE ;
+ }
+
+ PRINTF (("\ncamd version %d.%d, %s: approximate minimum degree ordering:\n"
+ " dense row parameter: %g\n", CAMD_MAIN_VERSION, CAMD_SUB_VERSION,
+ CAMD_DATE, alpha)) ;
+
+ if (alpha < 0)
+ {
+ PRINTF ((" no rows treated as dense\n")) ;
+ }
+ else
+ {
+ PRINTF ((
+ " (rows with more than max (%g * sqrt (n), 16) entries are\n"
+ " considered \"dense\", and placed last in output permutation)\n",
+ alpha)) ;
+ }
+
+ if (aggressive)
+ {
+ PRINTF ((" aggressive absorption: yes\n\n")) ;
+ }
+ else
+ {
+ PRINTF ((" aggressive absorption: no\n\n")) ;
+ }
+}
diff --git a/CAMD/Source/camd_defaults.c b/CAMD/Source/camd_defaults.c
new file mode 100644
index 0000000..98002e8
--- /dev/null
+++ b/CAMD/Source/camd_defaults.c
@@ -0,0 +1,37 @@
+/* ========================================================================= */
+/* === CAMD_defaults ======================================================= */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable. Sets default control parameters for CAMD. See camd.h
+ * for details.
+ */
+
+#include "camd_internal.h"
+
+/* ========================================================================= */
+/* === CAMD defaults ======================================================= */
+/* ========================================================================= */
+
+GLOBAL void CAMD_defaults
+(
+ double Control [ ]
+)
+{
+ Int i ;
+ if (Control != (double *) NULL)
+ {
+ for (i = 0 ; i < CAMD_CONTROL ; i++)
+ {
+ Control [i] = 0 ;
+ }
+ Control [CAMD_DENSE] = CAMD_DEFAULT_DENSE ;
+ Control [CAMD_AGGRESSIVE] = CAMD_DEFAULT_AGGRESSIVE ;
+ }
+}
diff --git a/CAMD/Source/camd_dump.c b/CAMD/Source/camd_dump.c
new file mode 100644
index 0000000..deddeba
--- /dev/null
+++ b/CAMD/Source/camd_dump.c
@@ -0,0 +1,190 @@
+/* ========================================================================= */
+/* === CAMD_dump =========================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* Debugging routines for CAMD. Not used if NDEBUG is not defined at compile-
+ * time (the default). See comments in camd_internal.h on how to enable
+ * debugging. Not user-callable.
+ */
+
+#include "camd_internal.h"
+
+#ifndef NDEBUG
+
+/* This global variable is present only when debugging */
+GLOBAL Int CAMD_debug = -999 ; /* default is no debug printing */
+
+/* ========================================================================= */
+/* === CAMD_debug_init ===================================================== */
+/* ========================================================================= */
+
+/* Sets the debug print level, by reading the file debug.camd (if it exists) */
+
+GLOBAL void CAMD_debug_init ( char *s )
+{
+ FILE *f ;
+ f = fopen ("debug.camd", "r") ;
+ if (f == (FILE *) NULL)
+ {
+ CAMD_debug = -999 ;
+ }
+ else
+ {
+ fscanf (f, ID, &CAMD_debug) ;
+ fclose (f) ;
+ }
+ if (CAMD_debug >= 0)
+ {
+ printf ("%s: CAMD_debug_init, D= "ID"\n", s, CAMD_debug) ;
+ }
+}
+
+/* ========================================================================= */
+/* === CAMD_dump =========================================================== */
+/* ========================================================================= */
+
+/* Dump CAMD's data structure, except for the hash buckets. This routine
+ * cannot be called when the hash buckets are non-empty.
+ */
+
+GLOBAL void CAMD_dump (
+ Int n, /* A is n-by-n */
+ Int Pe [ ], /* pe [0..n-1]: index in iw of start of row i */
+ Int Iw [ ], /* workspace of size iwlen, iwlen [0..pfree-1]
+ * holds the matrix on input */
+ Int Len [ ], /* len [0..n-1]: length for row i */
+ Int iwlen, /* length of iw */
+ Int pfree, /* iw [pfree ... iwlen-1] is empty on input */
+ Int Nv [ ], /* nv [0..n-1] */
+ Int Next [ ], /* next [0..n-1] */
+ Int Last [ ], /* last [0..n-1] */
+ Int Head [ ], /* head [0..n-1] */
+ Int Elen [ ], /* size n */
+ Int Degree [ ], /* size n */
+ Int W [ ], /* size n */
+ Int nel,
+ Int BucketSet [ ],
+ const Int C [ ],
+ Int CurC
+)
+{
+ Int i, pe, elen, nv, len, e, p, k, j, deg, w, cnt, ilast ;
+
+ if (CAMD_debug < 0) return ;
+ ASSERT (pfree <= iwlen) ;
+ CAMD_DEBUG3 (("\nCAMD dump, pfree: "ID"\n", pfree)) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ pe = Pe [i] ;
+ elen = Elen [i] ;
+ nv = Nv [i] ;
+ len = Len [i] ;
+ w = W [i] ;
+
+ if (elen >= EMPTY)
+ {
+ if (nv == 0)
+ {
+ CAMD_DEBUG4 (("\nI "ID": nonprincipal: ", i)) ;
+ ASSERT (elen == EMPTY) ;
+ if (pe == FLIP(n))
+ {
+ CAMD_DEBUG4 ((" dense node\n")) ;
+ ASSERT (w == 1) ;
+ }
+ else
+ {
+ ASSERT (pe < EMPTY) ;
+ CAMD_DEBUG4 ((" i "ID" -> parent "ID"\n", i, FLIP (Pe[i])));
+ }
+ }
+ else
+ {
+ CAMD_DEBUG4 (("\nI "ID": active principal supervariable:\n",i));
+ CAMD_DEBUG4 ((" nv(i): "ID" Flag: %d\n", nv, (nv < 0))) ;
+ ASSERT (elen >= 0) ;
+ ASSERT (nv > 0 && pe >= 0) ;
+ p = pe ;
+ CAMD_DEBUG4 ((" e/s: ")) ;
+ if (elen == 0) CAMD_DEBUG4 ((" : ")) ;
+ ASSERT (pe + len <= pfree) ;
+ for (k = 0 ; k < len ; k++)
+ {
+ j = Iw [p] ;
+ CAMD_DEBUG4 ((" "ID"", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ if (k == elen-1) CAMD_DEBUG4 ((" : ")) ;
+ p++ ;
+ }
+ CAMD_DEBUG4 (("\n")) ;
+ }
+ }
+ else
+ {
+ e = i ;
+ if (w == 0)
+ {
+ CAMD_DEBUG4 (("\nE "ID": absorbed element: w "ID"\n", e, w)) ;
+ ASSERT (nv > 0 && pe < 0) ;
+ CAMD_DEBUG4 ((" e "ID" -> parent "ID"\n", e, FLIP (Pe [e]))) ;
+ }
+ else
+ {
+ CAMD_DEBUG4 (("\nE "ID": unabsorbed element: w "ID"\n", e, w)) ;
+ ASSERT (nv > 0 && pe >= 0) ;
+ p = pe ;
+ CAMD_DEBUG4 ((" : ")) ;
+ ASSERT (pe + len <= pfree) ;
+ for (k = 0 ; k < len ; k++)
+ {
+ j = Iw [p] ;
+ CAMD_DEBUG4 ((" "ID"", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ p++ ;
+ }
+ CAMD_DEBUG4 (("\n")) ;
+ }
+ }
+ CAMD_DEBUG4 (("C[i] is :"ID"\n", (C == NULL) ? 0 : C [i]));
+ }
+
+ /* this routine cannot be called when the hash buckets are non-empty */
+ CAMD_DEBUG4 (("\nDegree lists:\n")) ;
+ if (nel >= 0)
+ {
+ cnt = 0 ;
+ for (deg = 0 ; deg < n ; deg++)
+ {
+ if (Head [deg] == EMPTY) continue ;
+ ilast = EMPTY ;
+ CAMD_DEBUG4 ((ID": \n", deg)) ;
+ for (i = Head [deg] ; i != EMPTY ; i = Next [i])
+ {
+ CAMD_DEBUG4 ((" "ID" : next "ID" last "ID" deg "ID"\n",
+ i, Next [i], Last [i], Degree [i])) ;
+ ASSERT (i >= 0 && i < n && ilast == Last [i] &&
+ deg == Degree [i]) ;
+ cnt += Nv [i] ;
+ ilast = i ;
+ }
+ CAMD_DEBUG4 (("\n")) ;
+ }
+ }
+
+ CAMD_DEBUG4(("\nCurrent C[i] is "ID". current Buckets are:\n", CurC)) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ if ((C == NULL) ? 1 : (C [BucketSet [i]] <= CurC))
+ CAMD_DEBUG4((ID",",BucketSet [i]));
+ }
+ CAMD_DEBUG4 (("\n")) ;
+}
+
+#endif
diff --git a/CAMD/Source/camd_global.c b/CAMD/Source/camd_global.c
new file mode 100644
index 0000000..8a0a962
--- /dev/null
+++ b/CAMD/Source/camd_global.c
@@ -0,0 +1,84 @@
+/* ========================================================================= */
+/* === camd_global ========================================================= */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+#include <stdlib.h>
+
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#include "matrix.h"
+#endif
+
+#ifndef NULL
+#define NULL 0
+#endif
+
+/* ========================================================================= */
+/* === Default CAMD memory manager ========================================= */
+/* ========================================================================= */
+
+/* The user can redefine these global pointers at run-time to change the memory
+ * manager used by CAMD. CAMD only uses malloc and free; realloc and calloc are
+ * include for completeness, in case another package wants to use the same
+ * memory manager as CAMD.
+ *
+ * If compiling as a MATLAB mexFunction, the default memory manager is mxMalloc.
+ * You can also compile CAMD as a standard ANSI-C library and link a mexFunction
+ * against it, and then redefine these pointers at run-time, in your
+ * mexFunction.
+ *
+ * If -DNMALLOC is defined at compile-time, no memory manager is specified at
+ * compile-time. You must then define these functions at run-time, before
+ * calling CAMD, for CAMD to work properly.
+ */
+
+#ifndef NMALLOC
+#ifdef MATLAB_MEX_FILE
+/* MATLAB mexFunction: */
+void *(*camd_malloc) (size_t) = mxMalloc ;
+void (*camd_free) (void *) = mxFree ;
+void *(*camd_realloc) (void *, size_t) = mxRealloc ;
+void *(*camd_calloc) (size_t, size_t) = mxCalloc ;
+#else
+/* standard ANSI-C: */
+void *(*camd_malloc) (size_t) = malloc ;
+void (*camd_free) (void *) = free ;
+void *(*camd_realloc) (void *, size_t) = realloc ;
+void *(*camd_calloc) (size_t, size_t) = calloc ;
+#endif
+#else
+/* no memory manager defined at compile-time; you MUST define one at run-time */
+void *(*camd_malloc) (size_t) = NULL ;
+void (*camd_free) (void *) = NULL ;
+void *(*camd_realloc) (void *, size_t) = NULL ;
+void *(*camd_calloc) (size_t, size_t) = NULL ;
+#endif
+
+/* ========================================================================= */
+/* === Default CAMD printf routine ========================================= */
+/* ========================================================================= */
+
+/* The user can redefine this global pointer at run-time to change the printf
+ * routine used by CAMD. If NULL, no printing occurs.
+ *
+ * If -DNPRINT is defined at compile-time, stdio.h is not included. Printing
+ * can then be enabled at run-time by setting camd_printf to a non-NULL function.
+ */
+
+#ifndef NPRINT
+#ifdef MATLAB_MEX_FILE
+int (*camd_printf) (const char *, ...) = mexPrintf ;
+#else
+#include <stdio.h>
+int (*camd_printf) (const char *, ...) = printf ;
+#endif
+#else
+int (*camd_printf) (const char *, ...) = NULL ;
+#endif
diff --git a/CAMD/Source/camd_info.c b/CAMD/Source/camd_info.c
new file mode 100644
index 0000000..8451c1d
--- /dev/null
+++ b/CAMD/Source/camd_info.c
@@ -0,0 +1,119 @@
+/* ========================================================================= */
+/* === CAMD_info =========================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable. Prints the output statistics for CAMD. See camd.h
+ * for details. If the Info array is not present, nothing is printed.
+ */
+
+#include "camd_internal.h"
+
+#define PRI(format,x) { if (x >= 0) { PRINTF ((format, x)) ; }}
+
+GLOBAL void CAMD_info
+(
+ double Info [ ]
+)
+{
+ double n, ndiv, nmultsubs_ldl, nmultsubs_lu, lnz, lnzd ;
+
+ if (!Info)
+ {
+ return ;
+ }
+
+ n = Info [CAMD_N] ;
+ ndiv = Info [CAMD_NDIV] ;
+ nmultsubs_ldl = Info [CAMD_NMULTSUBS_LDL] ;
+ nmultsubs_lu = Info [CAMD_NMULTSUBS_LU] ;
+ lnz = Info [CAMD_LNZ] ;
+ lnzd = (n >= 0 && lnz >= 0) ? (n + lnz) : (-1) ;
+
+ /* CAMD return status */
+ PRINTF ((
+ "\ncamd: approximate minimum degree ordering, results:\n"
+ " status: ")) ;
+ if (Info [CAMD_STATUS] == CAMD_OK)
+ {
+ PRINTF (("OK\n")) ;
+ }
+ else if (Info [CAMD_STATUS] == CAMD_OUT_OF_MEMORY)
+ {
+ PRINTF (("out of memory\n")) ;
+ }
+ else if (Info [CAMD_STATUS] == CAMD_INVALID)
+ {
+ PRINTF (("invalid matrix\n")) ;
+ }
+ else if (Info [CAMD_STATUS] == CAMD_OK_BUT_JUMBLED)
+ {
+ PRINTF (("OK, but jumbled\n")) ;
+ }
+ else
+ {
+ PRINTF (("unknown\n")) ;
+ }
+
+ /* statistics about the input matrix */
+ PRI (" n, dimension of A: %.20g\n", n);
+ PRI (" nz, number of nonzeros in A: %.20g\n",
+ Info [CAMD_NZ]) ;
+ PRI (" symmetry of A: %.4f\n",
+ Info [CAMD_SYMMETRY]) ;
+ PRI (" number of nonzeros on diagonal: %.20g\n",
+ Info [CAMD_NZDIAG]) ;
+ PRI (" nonzeros in pattern of A+A' (excl. diagonal): %.20g\n",
+ Info [CAMD_NZ_A_PLUS_AT]) ;
+ PRI (" # dense rows/columns of A+A': %.20g\n",
+ Info [CAMD_NDENSE]) ;
+
+ /* statistics about CAMD's behavior */
+ PRI (" memory used, in bytes: %.20g\n",
+ Info [CAMD_MEMORY]) ;
+ PRI (" # of memory compactions: %.20g\n",
+ Info [CAMD_NCMPA]) ;
+
+ /* statistics about the ordering quality */
+ PRINTF (("\n"
+ " The following approximate statistics are for a subsequent\n"
+ " factorization of A(P,P) + A(P,P)'. They are slight upper\n"
+ " bounds if there are no dense rows/columns in A+A', and become\n"
+ " looser if dense rows/columns exist.\n\n")) ;
+
+ PRI (" nonzeros in L (excluding diagonal): %.20g\n",
+ lnz) ;
+ PRI (" nonzeros in L (including diagonal): %.20g\n",
+ lnzd) ;
+ PRI (" # divide operations for LDL' or LU: %.20g\n",
+ ndiv) ;
+ PRI (" # multiply-subtract operations for LDL': %.20g\n",
+ nmultsubs_ldl) ;
+ PRI (" # multiply-subtract operations for LU: %.20g\n",
+ nmultsubs_lu) ;
+ PRI (" max nz. in any column of L (incl. diagonal): %.20g\n",
+ Info [CAMD_DMAX]) ;
+
+ /* total flop counts for various factorizations */
+
+ if (n >= 0 && ndiv >= 0 && nmultsubs_ldl >= 0 && nmultsubs_lu >= 0)
+ {
+ PRINTF (("\n"
+ " chol flop count for real A, sqrt counted as 1 flop: %.20g\n"
+ " LDL' flop count for real A: %.20g\n"
+ " LDL' flop count for complex A: %.20g\n"
+ " LU flop count for real A (with no pivoting): %.20g\n"
+ " LU flop count for complex A (with no pivoting): %.20g\n\n",
+ n + ndiv + 2*nmultsubs_ldl,
+ ndiv + 2*nmultsubs_ldl,
+ 9*ndiv + 8*nmultsubs_ldl,
+ ndiv + 2*nmultsubs_lu,
+ 9*ndiv + 8*nmultsubs_lu)) ;
+ }
+}
diff --git a/CAMD/Source/camd_order.c b/CAMD/Source/camd_order.c
new file mode 100644
index 0000000..44bb809
--- /dev/null
+++ b/CAMD/Source/camd_order.c
@@ -0,0 +1,201 @@
+/* ========================================================================= */
+/* === CAMD_order ========================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* User-callable CAMD minimum degree ordering routine. See camd.h for
+ * documentation.
+ */
+
+#include "camd_internal.h"
+
+/* ========================================================================= */
+/* === CAMD_order ========================================================== */
+/* ========================================================================= */
+
+GLOBAL Int CAMD_order
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ Int P [ ],
+ double Control [ ],
+ double Info [ ],
+ const Int C [ ]
+)
+{
+ Int *Len, *S, nz, i, *Pinv, info, status, *Rp, *Ri, *Cp, *Ci, ok ;
+ size_t nzaat, slen ;
+ double mem = 0 ;
+
+#ifndef NDEBUG
+ CAMD_debug_init ("camd") ;
+#endif
+
+ /* clear the Info array, if it exists */
+ info = Info != (double *) NULL ;
+ if (info)
+ {
+ for (i = 0 ; i < CAMD_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ Info [CAMD_N] = n ;
+ Info [CAMD_STATUS] = CAMD_OK ;
+ }
+
+ /* make sure inputs exist and n is >= 0 */
+ if (Ai == (Int *) NULL || Ap == (Int *) NULL || P == (Int *) NULL || n < 0)
+ {
+ if (info) Info [CAMD_STATUS] = CAMD_INVALID ;
+ return (CAMD_INVALID) ; /* arguments are invalid */
+ }
+
+ if (n == 0)
+ {
+ return (CAMD_OK) ; /* n is 0 so there's nothing to do */
+ }
+
+ nz = Ap [n] ;
+ if (info)
+ {
+ Info [CAMD_NZ] = nz ;
+ }
+ if (nz < 0)
+ {
+ if (info) Info [CAMD_STATUS] = CAMD_INVALID ;
+ return (CAMD_INVALID) ;
+ }
+
+ /* check if n or nz will cause size_t overflow */
+ if ((size_t) n >= SIZE_T_MAX / sizeof (Int)
+ || (size_t) nz >= SIZE_T_MAX / sizeof (Int))
+ {
+ if (info) Info [CAMD_STATUS] = CAMD_OUT_OF_MEMORY ;
+ return (CAMD_OUT_OF_MEMORY) ; /* problem too large */
+ }
+
+ /* check the input matrix: CAMD_OK, CAMD_INVALID, or CAMD_OK_BUT_JUMBLED */
+ status = CAMD_valid (n, n, Ap, Ai) ;
+
+ if (status == CAMD_INVALID)
+ {
+ if (info) Info [CAMD_STATUS] = CAMD_INVALID ;
+ return (CAMD_INVALID) ; /* matrix is invalid */
+ }
+
+ /* allocate two size-n integer workspaces */
+ Len = camd_malloc (n * sizeof (Int)) ;
+ Pinv = camd_malloc (n * sizeof (Int)) ;
+ mem += n ;
+ mem += n ;
+ if (!Len || !Pinv)
+ {
+ /* :: out of memory :: */
+ camd_free (Len) ;
+ camd_free (Pinv) ;
+ if (info) Info [CAMD_STATUS] = CAMD_OUT_OF_MEMORY ;
+ return (CAMD_OUT_OF_MEMORY) ;
+ }
+
+ if (status == CAMD_OK_BUT_JUMBLED)
+ {
+ /* sort the input matrix and remove duplicate entries */
+ CAMD_DEBUG1 (("Matrix is jumbled\n")) ;
+ Rp = camd_malloc ((n+1) * sizeof (Int)) ;
+ Ri = camd_malloc (MAX (nz,1) * sizeof (Int)) ;
+ mem += (n+1) ;
+ mem += MAX (nz,1) ;
+ if (!Rp || !Ri)
+ {
+ /* :: out of memory :: */
+ camd_free (Rp) ;
+ camd_free (Ri) ;
+ camd_free (Len) ;
+ camd_free (Pinv) ;
+ if (info) Info [CAMD_STATUS] = CAMD_OUT_OF_MEMORY ;
+ return (CAMD_OUT_OF_MEMORY) ;
+ }
+ /* use Len and Pinv as workspace to create R = A' */
+ CAMD_preprocess (n, Ap, Ai, Rp, Ri, Len, Pinv) ;
+ Cp = Rp ;
+ Ci = Ri ;
+ }
+ else
+ {
+ /* order the input matrix as-is. No need to compute R = A' first */
+ Rp = NULL ;
+ Ri = NULL ;
+ Cp = (Int *) Ap ;
+ Ci = (Int *) Ai ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* determine the symmetry and count off-diagonal nonzeros in A+A' */
+ /* --------------------------------------------------------------------- */
+
+ nzaat = CAMD_aat (n, Cp, Ci, Len, P, Info) ;
+ CAMD_DEBUG1 (("nzaat: %g\n", (double) nzaat)) ;
+ ASSERT ((MAX (nz-n, 0) <= nzaat) && (nzaat <= 2 * (size_t) nz)) ;
+
+ /* --------------------------------------------------------------------- */
+ /* allocate workspace for matrix, elbow room, and 7 size-n vectors */
+ /* --------------------------------------------------------------------- */
+
+ S = NULL ;
+ slen = nzaat ; /* space for matrix */
+ ok = ((slen + nzaat/5) >= slen) ; /* check for size_t overflow */
+ slen += nzaat/5 ; /* add elbow room */
+ for (i = 0 ; ok && i < 8 ; i++)
+ {
+ ok = ((slen + n+1) > slen) ; /* check for size_t overflow */
+ slen += (n+1) ; /* size-n elbow room, 7 size-(n+1) workspace */
+ }
+ mem += slen ;
+ ok = ok && (slen < SIZE_T_MAX / sizeof (Int)) ; /* check for overflow */
+ ok = ok && (slen < Int_MAX) ; /* S[i] for Int i must be OK */
+ if (ok)
+ {
+ S = camd_malloc (slen * sizeof (Int)) ;
+ }
+ CAMD_DEBUG1 (("slen %g\n", (double) slen)) ;
+ if (!S)
+ {
+ /* :: out of memory :: (or problem too large) */
+ camd_free (Rp) ;
+ camd_free (Ri) ;
+ camd_free (Len) ;
+ camd_free (Pinv) ;
+ if (info) Info [CAMD_STATUS] = CAMD_OUT_OF_MEMORY ;
+ return (CAMD_OUT_OF_MEMORY) ;
+ }
+ if (info)
+ {
+ /* memory usage, in bytes. */
+ Info [CAMD_MEMORY] = mem * sizeof (Int) ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* order the matrix */
+ /* --------------------------------------------------------------------- */
+
+ CAMD_1 (n, Cp, Ci, P, Pinv, Len, slen, S, Control, Info, C) ;
+
+ /* --------------------------------------------------------------------- */
+ /* free the workspace */
+ /* --------------------------------------------------------------------- */
+
+ camd_free (Rp) ;
+ camd_free (Ri) ;
+ camd_free (Len) ;
+ camd_free (Pinv) ;
+ camd_free (S) ;
+ if (info) Info [CAMD_STATUS] = status ;
+ return (status) ; /* successful ordering */
+}
diff --git a/CAMD/Source/camd_postorder.c b/CAMD/Source/camd_postorder.c
new file mode 100644
index 0000000..b720856
--- /dev/null
+++ b/CAMD/Source/camd_postorder.c
@@ -0,0 +1,51 @@
+/* ========================================================================= */
+/* === CAMD_postorder ====================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* Perform a postordering (via depth-first search) of an assembly tree. */
+
+#include "camd_internal.h"
+
+GLOBAL Int CAMD_postorder
+(
+ Int j, /* start at node j, a root of the assembly tree */
+ Int k, /* on input, next node is the kth node */
+ Int n, /* normal nodes 0 to n-1, place-holder node n */
+ Int head [], /* head of link list of children of each node */
+ Int next [], /* next[i] is the next child after i in link list */
+ Int post [], /* postordering, post [k] = p if p is the kth node */
+ Int stack [] /* recursion stack */
+)
+{
+ int i, p, top = 0 ;
+ stack [0] = j ; /* place j on the stack, maybe place-holder node n */
+ while (top >= 0) /* while (stack is not empty) */
+ {
+ p = stack [top] ; /* p = top of stack */
+ i = head [p] ; /* i = youngest child of p */
+ if (i == -1)
+ {
+ top-- ; /* p has no unordered children left */
+ if (p != n)
+ {
+ /* node p is the kth postordered node. Do not postorder the
+ * place-holder node n, which is the root of a subtree
+ * containing all dense and empty nodes. */
+ post [k++] = p ;
+ }
+ }
+ else
+ {
+ head [p] = next [i] ; /* remove i from children of p */
+ stack [++top] = i ; /* start dfs on child node i */
+ }
+ }
+ return (k) ;
+}
diff --git a/CAMD/Source/camd_preprocess.c b/CAMD/Source/camd_preprocess.c
new file mode 100644
index 0000000..27c5942
--- /dev/null
+++ b/CAMD/Source/camd_preprocess.c
@@ -0,0 +1,119 @@
+/* ========================================================================= */
+/* === CAMD_preprocess ===================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* Sorts, removes duplicate entries, and transposes from the nonzero pattern of
+ * a column-form matrix A, to obtain the matrix R. The input matrix can have
+ * duplicate entries and/or unsorted columns (CAMD_valid (n,Ap,Ai) must not be
+ * CAMD_INVALID).
+ *
+ * This input condition is NOT checked. This routine is not user-callable.
+ */
+
+#include "camd_internal.h"
+
+/* ========================================================================= */
+/* === CAMD_preprocess ===================================================== */
+/* ========================================================================= */
+
+/* CAMD_preprocess does not check its input for errors or allocate workspace.
+ * On input, the condition (CAMD_valid (n,n,Ap,Ai) != CAMD_INVALID) must hold.
+ */
+
+GLOBAL void CAMD_preprocess
+(
+ Int n, /* input matrix: A is n-by-n */
+ const Int Ap [ ], /* size n+1 */
+ const Int Ai [ ], /* size nz = Ap [n] */
+
+ /* output matrix R: */
+ Int Rp [ ], /* size n+1 */
+ Int Ri [ ], /* size nz (or less, if duplicates present) */
+
+ Int W [ ], /* workspace of size n */
+ Int Flag [ ] /* workspace of size n */
+)
+{
+
+ /* --------------------------------------------------------------------- */
+ /* local variables */
+ /* --------------------------------------------------------------------- */
+
+ Int i, j, p, p2 ;
+
+ ASSERT (CAMD_valid (n, n, Ap, Ai) != CAMD_INVALID) ;
+
+ /* --------------------------------------------------------------------- */
+ /* count the entries in each row of A (excluding duplicates) */
+ /* --------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = 0 ; /* # of nonzeros in row i (excl duplicates) */
+ Flag [i] = EMPTY ; /* Flag [i] = j if i appears in column j */
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ p2 = Ap [j+1] ;
+ for (p = Ap [j] ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ if (Flag [i] != j)
+ {
+ /* row index i has not yet appeared in column j */
+ W [i]++ ; /* one more entry in row i */
+ Flag [i] = j ; /* flag row index i as appearing in col j*/
+ }
+ }
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* compute the row pointers for R */
+ /* --------------------------------------------------------------------- */
+
+ Rp [0] = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Rp [i+1] = Rp [i] + W [i] ;
+ }
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = Rp [i] ;
+ Flag [i] = EMPTY ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* construct the row form matrix R */
+ /* --------------------------------------------------------------------- */
+
+ /* R = row form of pattern of A */
+ for (j = 0 ; j < n ; j++)
+ {
+ p2 = Ap [j+1] ;
+ for (p = Ap [j] ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ if (Flag [i] != j)
+ {
+ /* row index i has not yet appeared in column j */
+ Ri [W [i]++] = j ; /* put col j in row i */
+ Flag [i] = j ; /* flag row index i as appearing in col j*/
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ ASSERT (CAMD_valid (n, n, Rp, Ri) == CAMD_OK) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (W [j] == Rp [j+1]) ;
+ }
+#endif
+}
diff --git a/CAMD/Source/camd_valid.c b/CAMD/Source/camd_valid.c
new file mode 100644
index 0000000..e628ddd
--- /dev/null
+++ b/CAMD/Source/camd_valid.c
@@ -0,0 +1,113 @@
+/* ========================================================================= */
+/* === CAMD_valid ========================================================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* CAMD, Copyright (c) Timothy A. Davis, Yanqing Chen, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: davis at cise.ufl.edu CISE Department, Univ. of Florida. */
+/* web: http://www.cise.ufl.edu/research/sparse/camd */
+/* ------------------------------------------------------------------------- */
+
+/* Check if a column-form matrix is valid or not. The matrix A is
+ * n_row-by-n_col. The row indices of entries in column j are in
+ * Ai [Ap [j] ... Ap [j+1]-1]. Required conditions are:
+ *
+ * n_row >= 0
+ * n_col >= 0
+ * nz = Ap [n_col] >= 0 number of entries in the matrix
+ * Ap [0] == 0
+ * Ap [j] <= Ap [j+1] for all j in the range 0 to n_col.
+ * Ai [0 ... nz-1] must be in the range 0 to n_row-1.
+ *
+ * If any of the above conditions hold, CAMD_INVALID is returned. If the
+ * following condition holds, CAMD_OK_BUT_JUMBLED is returned (a warning,
+ * not an error):
+ *
+ * row indices in Ai [Ap [j] ... Ap [j+1]-1] are not sorted in ascending
+ * order, and/or duplicate entries exist.
+ *
+ * Otherwise, CAMD_OK is returned.
+ */
+
+#include "camd_internal.h"
+
+GLOBAL Int CAMD_valid
+(
+ /* inputs, not modified on output: */
+ Int n_row, /* A is n_row-by-n_col */
+ Int n_col,
+ const Int Ap [ ], /* column pointers of A, of size n_col+1 */
+ const Int Ai [ ] /* row indices of A, of size nz = Ap [n_col] */
+)
+{
+ Int nz, j, p1, p2, ilast, i, p, result = CAMD_OK ;
+ if (n_row < 0 || n_col < 0 || Ap == NULL || Ai == NULL)
+ {
+ return (CAMD_INVALID) ;
+ }
+ nz = Ap [n_col] ;
+ if (Ap [0] != 0 || nz < 0)
+ {
+ /* column pointers must start at Ap [0] = 0, and Ap [n] must be >= 0 */
+ CAMD_DEBUG0 (("column 0 pointer bad or nz < 0\n")) ;
+ return (CAMD_INVALID) ;
+ }
+ for (j = 0 ; j < n_col ; j++)
+ {
+ p1 = Ap [j] ;
+ p2 = Ap [j+1] ;
+ CAMD_DEBUG2 (("\nColumn: "ID" p1: "ID" p2: "ID"\n", j, p1, p2)) ;
+ if (p1 > p2)
+ {
+ /* column pointers must be ascending */
+ CAMD_DEBUG0 (("column "ID" pointer bad\n", j)) ;
+ return (CAMD_INVALID) ;
+ }
+ ilast = EMPTY ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ CAMD_DEBUG3 (("row: "ID"\n", i)) ;
+ if (i < 0 || i >= n_row)
+ {
+ /* row index out of range */
+ CAMD_DEBUG0 (("index out of range, col "ID" row "ID"\n", j, i));
+ return (CAMD_INVALID) ;
+ }
+ if (i <= ilast)
+ {
+ /* row index unsorted, or duplicate entry present */
+ CAMD_DEBUG1 (("index unsorted/dupl col "ID" row "ID"\n", j, i));
+ result = CAMD_OK_BUT_JUMBLED ;
+ }
+ ilast = i ;
+ }
+ }
+ return (result) ;
+}
+
+
+GLOBAL Int CAMD_cvalid /* return TRUE if the Constraint set is valid,
+ * FALSE otherwise */
+(
+ /* inputs, not modified on output: */
+ Int n, /* the length of constraint set */
+ const Int C [ ] /* constraint set */
+)
+{
+ Int i ;
+ if (C != NULL)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ if (C [i] < 0 || C [i] > n - 1)
+ {
+ CAMD_DEBUG0 (("C["ID"] = "ID" invalid\n", i, C [i])) ;
+ return (FALSE) ;
+ }
+ }
+ }
+ return (TRUE) ;
+}
+
diff --git a/CCOLAMD/Demo/Makefile b/CCOLAMD/Demo/Makefile
new file mode 100644
index 0000000..2c02586
--- /dev/null
+++ b/CCOLAMD/Demo/Makefile
@@ -0,0 +1,43 @@
+#-----------------------------------------------------------------------------
+# compile the CCOLAMD demo
+#-----------------------------------------------------------------------------
+
+default: ccolamd_example ccolamd_l_example
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../Include -I../../UFconfig
+
+C = $(CC) $(CFLAGS) $(I)
+
+library:
+ ( cd ../Lib ; $(MAKE) )
+
+#------------------------------------------------------------------------------
+# Create the demo program, run it, and compare the output
+#------------------------------------------------------------------------------
+
+dist:
+
+ccolamd_example: ccolamd_example.c library
+ $(C) -o ccolamd_example ccolamd_example.c ../Lib/libccolamd.a -lm
+ - ./ccolamd_example > my_ccolamd_example.out
+ - diff ccolamd_example.out my_ccolamd_example.out
+
+ccolamd_l_example: ccolamd_l_example.c library
+ $(C) -o ccolamd_l_example ccolamd_l_example.c ../Lib/libccolamd.a -lm
+ - ./ccolamd_l_example > my_ccolamd_l_example.out
+ - diff ccolamd_example.out my_ccolamd_example.out
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) ccolamd_example ccolamd_l_example
+ - $(RM) my_ccolamd_example.out my_ccolamd_l_example.out
diff --git a/CCOLAMD/Demo/ccolamd_example.c b/CCOLAMD/Demo/ccolamd_example.c
new file mode 100644
index 0000000..253fdc9
--- /dev/null
+++ b/CCOLAMD/Demo/ccolamd_example.c
@@ -0,0 +1,185 @@
+/* ========================================================================== */
+/* === ccolamd and csymamd example ========================================== */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis,
+ * Sivasankaran Rajamanickam, and Stefan Larimore
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/*
+ * ccolamd example of use, to order the columns of a 5-by-4 matrix with
+ * 11 nonzero entries in the following nonzero pattern, with default knobs
+ * and no ordering constraints.
+ *
+ * x 0 x 0
+ * x 0 x x
+ * 0 x x 0
+ * 0 0 x x
+ * x x 0 0
+ *
+ * csymamd example of use, to order the rows and columns of a 5-by-5
+ * matrix with 13 nonzero entries in the following nonzero pattern,
+ * with default knobs and no ordering constraints.
+ *
+ * x x 0 0 0
+ * x x x x 0
+ * 0 x x 0 0
+ * 0 x 0 x x
+ * 0 0 0 x x
+ *
+ * (where x denotes a nonzero value).
+ */
+
+/* ========================================================================== */
+
+#include <stdio.h>
+#include "ccolamd.h"
+
+#define A_NNZ 11
+#define A_NROW 5
+#define A_NCOL 4
+#define ALEN 150 /* size max (2.2*nnz+17*ncol+7*nrow+6, 23*ncol+7*nrow+6) */
+
+#define B_NNZ 4
+#define B_N 5
+
+int main (void)
+{
+
+ /* ====================================================================== */
+ /* input matrix A definition */
+ /* ====================================================================== */
+
+ int A [ALEN] = {
+
+ 0, 1, 4, /* row indices of nonzeros in column 0 */
+ 2, 4, /* row indices of nonzeros in column 1 */
+ 0, 1, 2, 3, /* row indices of nonzeros in column 2 */
+ 1, 3} ; /* row indices of nonzeros in column 3 */
+
+ int p [ ] = {
+
+ 0, /* column 0 is in A [0..2] */
+ 3, /* column 1 is in A [3..4] */
+ 5, /* column 2 is in A [5..8] */
+ 9, /* column 3 is in A [9..10] */
+ A_NNZ} ; /* number of nonzeros in A */
+
+ /* ====================================================================== */
+ /* input matrix B definition */
+ /* ====================================================================== */
+
+ int B [ ] = { /* Note: only strictly lower triangular part */
+ /* is included, since symamd ignores the */
+ /* diagonal and upper triangular part of B. */
+
+ 1, /* row indices of nonzeros in column 0 */
+ 2, 3, /* row indices of nonzeros in column 1 */
+ /* row indices of nonzeros in column 2 (none) */
+ 4 /* row indices of nonzeros in column 3 */
+ } ; /* row indices of nonzeros in column 4 (none) */
+
+ int q [ ] = {
+
+ 0, /* column 0 is in B [0] */
+ 1, /* column 1 is in B [1..2] */
+ 3, /* column 2 is empty */
+ 3, /* column 3 is in B [3] */
+ 4, /* column 4 is empty */
+ B_NNZ} ; /* number of nonzeros in strictly lower B */
+
+ /* ====================================================================== */
+ /* other variable definitions */
+ /* ====================================================================== */
+
+ int perm [B_N+1] ; /* note the size is N+1 */
+ int stats [CCOLAMD_STATS] ; /* for ccolamd and csymamd output statistics */
+
+ int row, col, pp, length, ok ;
+
+ /* ====================================================================== */
+ /* dump the input matrix A */
+ /* ====================================================================== */
+
+ printf ("ccolamd %d-by-%d input matrix:\n", A_NROW, A_NCOL) ;
+ for (col = 0 ; col < A_NCOL ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ printf ("Column %d, with %d entries:\n", col, length) ;
+ for (pp = p [col] ; pp < p [col+1] ; pp++)
+ {
+ row = A [pp] ;
+ printf (" row %d\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix. Note that this destroys A and overwrites p */
+ /* ====================================================================== */
+
+ ok = ccolamd (A_NROW, A_NCOL, ALEN, A, p, (double *) NULL, stats, NULL) ;
+ ccolamd_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("ccolamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the column ordering */
+ /* ====================================================================== */
+
+ printf ("ccolamd column ordering:\n") ;
+ printf ("1st column: %d\n", p [0]) ;
+ printf ("2nd column: %d\n", p [1]) ;
+ printf ("3rd column: %d\n", p [2]) ;
+ printf ("4th column: %d\n", p [3]) ;
+
+ /* ====================================================================== */
+ /* dump the strictly lower triangular part of symmetric input matrix B */
+ /* ====================================================================== */
+
+ printf ("\n\ncsymamd %d-by-%d input matrix:\n", B_N, B_N) ;
+ printf ("Entries in strictly lower triangular part:\n") ;
+ for (col = 0 ; col < B_N ; col++)
+ {
+ length = q [col+1] - q [col] ;
+ printf ("Column %d, with %d entries:\n", col, length) ;
+ for (pp = q [col] ; pp < q [col+1] ; pp++)
+ {
+ row = B [pp] ;
+ printf (" row %d\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix B. Note that this does not modify B or q. */
+ /* ====================================================================== */
+
+ ok = csymamd (B_N, B, q, perm, (double *) NULL, stats, &calloc, &free,
+ NULL, -1) ;
+ csymamd_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("csymamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the symmetric ordering */
+ /* ====================================================================== */
+
+ printf ("csymamd column ordering:\n") ;
+ printf ("1st row/column: %d\n", perm [0]) ;
+ printf ("2nd row/column: %d\n", perm [1]) ;
+ printf ("3rd row/column: %d\n", perm [2]) ;
+ printf ("4th row/column: %d\n", perm [3]) ;
+ printf ("5th row/column: %d\n", perm [4]) ;
+
+ return (0) ;
+}
diff --git a/CCOLAMD/Demo/ccolamd_example.out b/CCOLAMD/Demo/ccolamd_example.out
new file mode 100644
index 0000000..c2139b2
--- /dev/null
+++ b/CCOLAMD/Demo/ccolamd_example.out
@@ -0,0 +1,50 @@
+ccolamd 5-by-4 input matrix:
+Column 0, with 3 entries:
+ row 0
+ row 1
+ row 4
+Column 1, with 2 entries:
+ row 2
+ row 4
+Column 2, with 4 entries:
+ row 0
+ row 1
+ row 2
+ row 3
+Column 3, with 2 entries:
+ row 1
+ row 3
+
+ccolamd version 2.7, Nov 1, 2007: OK.
+ccolamd: number of dense or empty rows ignored: 0
+ccolamd: number of dense or empty columns ignored: 0
+ccolamd: number of garbage collections performed: 0
+ccolamd column ordering:
+1st column: 1
+2nd column: 0
+3rd column: 3
+4th column: 2
+
+
+csymamd 5-by-5 input matrix:
+Entries in strictly lower triangular part:
+Column 0, with 1 entries:
+ row 1
+Column 1, with 2 entries:
+ row 2
+ row 3
+Column 2, with 0 entries:
+Column 3, with 1 entries:
+ row 4
+Column 4, with 0 entries:
+
+csymamd version 2.7, Nov 1, 2007: OK.
+csymamd: number of dense or empty rows ignored: 0
+csymamd: number of dense or empty columns ignored: 0
+csymamd: number of garbage collections performed: 0
+csymamd column ordering:
+1st row/column: 0
+2nd row/column: 2
+3rd row/column: 1
+4th row/column: 3
+5th row/column: 4
diff --git a/CCOLAMD/Demo/ccolamd_l_example.c b/CCOLAMD/Demo/ccolamd_l_example.c
new file mode 100644
index 0000000..b213aad
--- /dev/null
+++ b/CCOLAMD/Demo/ccolamd_l_example.c
@@ -0,0 +1,188 @@
+/* ========================================================================== */
+/* === ccolamd and csymamd example (UF_long integer version) ================ */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis,
+ * Sivasankaran Rajamanickam, and Stefan Larimore
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/*
+ * ccolamd example of use, to order the columns of a 5-by-4 matrix with
+ * 11 nonzero entries in the following nonzero pattern, with default knobs
+ * and no ordering constraints.
+ *
+ * x 0 x 0
+ * x 0 x x
+ * 0 x x 0
+ * 0 0 x x
+ * x x 0 0
+ *
+ * csymamd example of use, to order the rows and columns of a 5-by-5
+ * matrix with 13 nonzero entries in the following nonzero pattern,
+ * with default knobs and no ordering constraints.
+ *
+ * x x 0 0 0
+ * x x x x 0
+ * 0 x x 0 0
+ * 0 x 0 x x
+ * 0 0 0 x x
+ *
+ * (where x denotes a nonzero value).
+ */
+
+/* ========================================================================== */
+
+#include <stdio.h>
+#include "ccolamd.h"
+
+#define A_NNZ 11
+#define A_NROW 5
+#define A_NCOL 4
+#define ALEN 150 /* size max (2.2*nnz+17*ncol+7*nrow+6, 23*ncol+7*nrow+6) */
+
+#define B_NNZ 4
+#define B_N 5
+
+/* define UF_long */
+#include "UFconfig.h"
+
+int main (void)
+{
+
+ /* ====================================================================== */
+ /* input matrix A definition */
+ /* ====================================================================== */
+
+ UF_long A [ALEN] = {
+
+ 0, 1, 4, /* row indices of nonzeros in column 0 */
+ 2, 4, /* row indices of nonzeros in column 1 */
+ 0, 1, 2, 3, /* row indices of nonzeros in column 2 */
+ 1, 3} ; /* row indices of nonzeros in column 3 */
+
+ UF_long p [ ] = {
+
+ 0, /* column 0 is in A [0..2] */
+ 3, /* column 1 is in A [3..4] */
+ 5, /* column 2 is in A [5..8] */
+ 9, /* column 3 is in A [9..10] */
+ A_NNZ} ; /* number of nonzeros in A */
+
+ /* ====================================================================== */
+ /* input matrix B definition */
+ /* ====================================================================== */
+
+ UF_long B [ ] = { /* Note: only strictly lower triangular part */
+ /* is included, since symamd ignores the */
+ /* diagonal and upper triangular part of B. */
+
+ 1, /* row indices of nonzeros in column 0 */
+ 2, 3, /* row indices of nonzeros in column 1 */
+ /* row indices of nonzeros in column 2 (none) */
+ 4 /* row indices of nonzeros in column 3 */
+ } ; /* row indices of nonzeros in column 4 (none) */
+
+ UF_long q [ ] = {
+
+ 0, /* column 0 is in B [0] */
+ 1, /* column 1 is in B [1..2] */
+ 3, /* column 2 is empty */
+ 3, /* column 3 is in B [3] */
+ 4, /* column 4 is empty */
+ B_NNZ} ; /* number of nonzeros in strictly lower B */
+
+ /* ====================================================================== */
+ /* other variable definitions */
+ /* ====================================================================== */
+
+ UF_long perm [B_N+1] ; /* note the size is N+1 */
+ UF_long stats [CCOLAMD_STATS] ; /* for ccolamd and csymamd output stats */
+
+ UF_long row, col, pp, length, ok ;
+
+ /* ====================================================================== */
+ /* dump the input matrix A */
+ /* ====================================================================== */
+
+ printf ("ccolamd %d-by-%d input matrix:\n", A_NROW, A_NCOL) ;
+ for (col = 0 ; col < A_NCOL ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ printf ("Column %ld, with %ld entries:\n", col, length) ;
+ for (pp = p [col] ; pp < p [col+1] ; pp++)
+ {
+ row = A [pp] ;
+ printf (" row %ld\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix. Note that this destroys A and overwrites p */
+ /* ====================================================================== */
+
+ ok = ccolamd_l (A_NROW, A_NCOL, ALEN, A, p, (double *) NULL, stats, NULL) ;
+ ccolamd_l_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("ccolamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the column ordering */
+ /* ====================================================================== */
+
+ printf ("ccolamd_l column ordering:\n") ;
+ printf ("1st column: %ld\n", p [0]) ;
+ printf ("2nd column: %ld\n", p [1]) ;
+ printf ("3rd column: %ld\n", p [2]) ;
+ printf ("4th column: %ld\n", p [3]) ;
+
+ /* ====================================================================== */
+ /* dump the strictly lower triangular part of symmetric input matrix B */
+ /* ====================================================================== */
+
+ printf ("\n\ncsymamd_l %d-by-%d input matrix:\n", B_N, B_N) ;
+ printf ("Entries in strictly lower triangular part:\n") ;
+ for (col = 0 ; col < B_N ; col++)
+ {
+ length = q [col+1] - q [col] ;
+ printf ("Column %ld, with %ld entries:\n", col, length) ;
+ for (pp = q [col] ; pp < q [col+1] ; pp++)
+ {
+ row = B [pp] ;
+ printf (" row %ld\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix B. Note that this does not modify B or q. */
+ /* ====================================================================== */
+
+ ok = csymamd_l (B_N, B, q, perm, (double *) NULL, stats, &calloc, &free,
+ NULL, -1) ;
+ csymamd_l_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("csymamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the symmetric ordering */
+ /* ====================================================================== */
+
+ printf ("csymamd_l column ordering:\n") ;
+ printf ("1st row/column: %ld\n", perm [0]) ;
+ printf ("2nd row/column: %ld\n", perm [1]) ;
+ printf ("3rd row/column: %ld\n", perm [2]) ;
+ printf ("4th row/column: %ld\n", perm [3]) ;
+ printf ("5th row/column: %ld\n", perm [4]) ;
+
+ return (0) ;
+}
diff --git a/CCOLAMD/Demo/ccolamd_l_example.out b/CCOLAMD/Demo/ccolamd_l_example.out
new file mode 100644
index 0000000..5341d80
--- /dev/null
+++ b/CCOLAMD/Demo/ccolamd_l_example.out
@@ -0,0 +1,50 @@
+ccolamd 5-by-4 input matrix:
+Column 0, with 3 entries:
+ row 0
+ row 1
+ row 4
+Column 1, with 2 entries:
+ row 2
+ row 4
+Column 2, with 4 entries:
+ row 0
+ row 1
+ row 2
+ row 3
+Column 3, with 2 entries:
+ row 1
+ row 3
+
+ccolamd version 2.7, Nov 1, 2007: OK.
+ccolamd: number of dense or empty rows ignored: 0
+ccolamd: number of dense or empty columns ignored: 0
+ccolamd: number of garbage collections performed: 0
+ccolamd_l column ordering:
+1st column: 1
+2nd column: 0
+3rd column: 3
+4th column: 2
+
+
+csymamd_l 5-by-5 input matrix:
+Entries in strictly lower triangular part:
+Column 0, with 1 entries:
+ row 1
+Column 1, with 2 entries:
+ row 2
+ row 3
+Column 2, with 0 entries:
+Column 3, with 1 entries:
+ row 4
+Column 4, with 0 entries:
+
+csymamd version 2.7, Nov 1, 2007: OK.
+csymamd: number of dense or empty rows ignored: 0
+csymamd: number of dense or empty columns ignored: 0
+csymamd: number of garbage collections performed: 0
+csymamd_l column ordering:
+1st row/column: 0
+2nd row/column: 2
+3rd row/column: 1
+4th row/column: 3
+5th row/column: 4
diff --git a/CCOLAMD/Doc/ChangeLog b/CCOLAMD/Doc/ChangeLog
new file mode 100644
index 0000000..7a5f4a2
--- /dev/null
+++ b/CCOLAMD/Doc/ChangeLog
@@ -0,0 +1,35 @@
+Nov 1, 2007: version 2.7.1
+
+ * minor changes to MATLAB test code
+
+May 31, 2007: version 2.7.0
+
+ * ported to 64-bit MATLAB
+
+ * subdirectories added (Source/, Include/, Lib/, Doc/, MATLAB/, Demo/)
+
+Dec 12, 2006, version 2.5.2
+
+ * minor MATLAB clean up
+
+Apr 30, 2006: version 2.5
+
+ * ccolamd_recommended modified. Now returns size_t; 0 on error, > 0
+ if successful. Version number updated to synchronize with COLAMD.
+
+ * long replaced with UF_long integer, which is long except on WIN64
+
+Nov 15, 2005
+
+ * ccolamd_global.c added to ccolamd_make.m (version is still 1.0).
+
+Oct 10, 2005
+
+ * changed definition of ccolamd_printf to "extern"
+
+Version 1.0, released (Aug. 30, 2005)
+
+ * CCOLAMD version 1.0 is derived from COLAMD version 2.4. Refer to the
+ COLAMD ChangeLog file for the changes made to COLAMD since
+ COLAMD Version 1.0.
+
diff --git a/CCOLAMD/Doc/lesser.txt b/CCOLAMD/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/CCOLAMD/Doc/lesser.txt
@@ -0,0 +1,504 @@
+ GNU LESSER GENERAL PUBLIC LICENSE
+ Version 2.1, February 1999
+
+ Copyright (C) 1991, 1999 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+[This is the first released version of the Lesser GPL. It also counts
+ as the successor of the GNU Library Public License, version 2, hence
+ the version number 2.1.]
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+Licenses are intended to guarantee your freedom to share and change
+free software--to make sure the software is free for all its users.
+
+ This license, the Lesser General Public License, applies to some
+specially designated software packages--typically libraries--of the
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+can use it too, but we suggest you first think carefully about whether
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diff --git a/CCOLAMD/Include/ccolamd.h b/CCOLAMD/Include/ccolamd.h
new file mode 100644
index 0000000..ec8aaaa
--- /dev/null
+++ b/CCOLAMD/Include/ccolamd.h
@@ -0,0 +1,365 @@
+/* ========================================================================== */
+/* === CCOLAMD/ccolamd.h ==================================================== */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis,
+ * Sivasankaran Rajamanickam, and Stefan Larimore
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/*
+ * You must include this file (ccolamd.h) in any routine that uses ccolamd,
+ * csymamd, or the related macros and definitions.
+ */
+
+#ifndef CCOLAMD_H
+#define CCOLAMD_H
+
+/* make it easy for C++ programs to include CCOLAMD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* for size_t definition: */
+#include <stdlib.h>
+
+/* ========================================================================== */
+/* === CCOLAMD version ====================================================== */
+/* ========================================================================== */
+
+/* All versions of CCOLAMD will include the following definitions.
+ * As an example, to test if the version you are using is 1.3 or later:
+ *
+ * if (CCOLAMD_VERSION >= CCOLAMD_VERSION_CODE (1,3)) ...
+ *
+ * This also works during compile-time:
+ *
+ * #if CCOLAMD_VERSION >= CCOLAMD_VERSION_CODE (1,3)
+ * printf ("This is version 1.3 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ */
+
+#define CCOLAMD_DATE "Nov 1, 2007"
+#define CCOLAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define CCOLAMD_MAIN_VERSION 2
+#define CCOLAMD_SUB_VERSION 7
+#define CCOLAMD_SUBSUB_VERSION 1
+#define CCOLAMD_VERSION \
+ CCOLAMD_VERSION_CODE(CCOLAMD_MAIN_VERSION,CCOLAMD_SUB_VERSION)
+
+/* ========================================================================== */
+/* === Knob and statistics definitions ====================================== */
+/* ========================================================================== */
+
+/* size of the knobs [ ] array. Only knobs [0..3] are currently used. */
+#define CCOLAMD_KNOBS 20
+
+/* number of output statistics. Only stats [0..10] are currently used. */
+#define CCOLAMD_STATS 20
+
+/* knobs [0] and stats [0]: dense row knob and output statistic. */
+#define CCOLAMD_DENSE_ROW 0
+
+/* knobs [1] and stats [1]: dense column knob and output statistic. */
+#define CCOLAMD_DENSE_COL 1
+
+/* knobs [2]: aggressive absorption option */
+#define CCOLAMD_AGGRESSIVE 2
+
+/* knobs [3]: LU or Cholesky factorization option */
+#define CCOLAMD_LU 3
+
+/* stats [2]: memory defragmentation count output statistic */
+#define CCOLAMD_DEFRAG_COUNT 2
+
+/* stats [3]: ccolamd status: zero OK, > 0 warning or notice, < 0 error */
+#define CCOLAMD_STATUS 3
+
+/* stats [4..6]: error info, or info on jumbled columns */
+#define CCOLAMD_INFO1 4
+#define CCOLAMD_INFO2 5
+#define CCOLAMD_INFO3 6
+
+/* stats [7]: number of originally empty rows */
+#define CCOLAMD_EMPTY_ROW 7
+/* stats [8]: number of originally empty cols */
+#define CCOLAMD_EMPTY_COL 8
+/* stats [9]: number of rows with entries only in dense cols */
+#define CCOLAMD_NEWLY_EMPTY_ROW 9
+/* stats [10]: number of cols with entries only in dense rows */
+#define CCOLAMD_NEWLY_EMPTY_COL 10
+
+/* error codes returned in stats [3]: */
+#define CCOLAMD_OK (0)
+#define CCOLAMD_OK_BUT_JUMBLED (1)
+#define CCOLAMD_ERROR_A_not_present (-1)
+#define CCOLAMD_ERROR_p_not_present (-2)
+#define CCOLAMD_ERROR_nrow_negative (-3)
+#define CCOLAMD_ERROR_ncol_negative (-4)
+#define CCOLAMD_ERROR_nnz_negative (-5)
+#define CCOLAMD_ERROR_p0_nonzero (-6)
+#define CCOLAMD_ERROR_A_too_small (-7)
+#define CCOLAMD_ERROR_col_length_negative (-8)
+#define CCOLAMD_ERROR_row_index_out_of_bounds (-9)
+#define CCOLAMD_ERROR_out_of_memory (-10)
+#define CCOLAMD_ERROR_invalid_cmember (-11)
+#define CCOLAMD_ERROR_internal_error (-999)
+
+/* ========================================================================== */
+/* === Prototypes of user-callable routines ================================= */
+/* ========================================================================== */
+
+/* define UF_long */
+#include "UFconfig.h"
+
+size_t ccolamd_recommended /* returns recommended value of Alen, */
+ /* or 0 if input arguments are erroneous */
+(
+ int nnz, /* nonzeros in A */
+ int n_row, /* number of rows in A */
+ int n_col /* number of columns in A */
+) ;
+
+size_t ccolamd_l_recommended /* returns recommended value of Alen, */
+ /* or 0 if input arguments are erroneous */
+(
+ UF_long nnz, /* nonzeros in A */
+ UF_long n_row, /* number of rows in A */
+ UF_long n_col /* number of columns in A */
+) ;
+
+void ccolamd_set_defaults /* sets default parameters */
+( /* knobs argument is modified on output */
+ double knobs [CCOLAMD_KNOBS] /* parameter settings for ccolamd */
+) ;
+
+void ccolamd_l_set_defaults /* sets default parameters */
+( /* knobs argument is modified on output */
+ double knobs [CCOLAMD_KNOBS] /* parameter settings for ccolamd */
+) ;
+
+int ccolamd /* returns (1) if successful, (0) otherwise*/
+( /* A and p arguments are modified on output */
+ int n_row, /* number of rows in A */
+ int n_col, /* number of columns in A */
+ int Alen, /* size of the array A */
+ int A [ ], /* row indices of A, of size Alen */
+ int p [ ], /* column pointers of A, of size n_col+1 */
+ double knobs [CCOLAMD_KNOBS],/* parameter settings for ccolamd */
+ int stats [CCOLAMD_STATS], /* ccolamd output statistics and error codes */
+ int cmember [ ] /* Constraint set of A, of size n_col */
+) ;
+
+UF_long ccolamd_l /* same as ccolamd, but with UF_long integers */
+(
+ UF_long n_row,
+ UF_long n_col,
+ UF_long Alen,
+ UF_long A [ ],
+ UF_long p [ ],
+ double knobs [CCOLAMD_KNOBS],
+ UF_long stats [CCOLAMD_STATS],
+ UF_long cmember [ ]
+) ;
+
+int csymamd /* return (1) if OK, (0) otherwise */
+(
+ int n, /* number of rows and columns of A */
+ int A [ ], /* row indices of A */
+ int p [ ], /* column pointers of A */
+ int perm [ ], /* output permutation, size n_col+1 */
+ double knobs [CCOLAMD_KNOBS],/* parameters (uses defaults if NULL) */
+ int stats [CCOLAMD_STATS], /* output statistics and error codes */
+ void * (*allocate) (size_t, size_t), /* pointer to calloc (ANSI C) or */
+ /* mxCalloc (for MATLAB mexFunction) */
+ void (*release) (void *), /* pointer to free (ANSI C) or */
+ /* mxFree (for MATLAB mexFunction) */
+ int cmember [ ], /* Constraint set of A */
+ int stype /* 0: use both parts, >0: upper, <0: lower */
+) ;
+
+UF_long csymamd_l /* same as csymamd, but with UF_long integers */
+(
+ UF_long n,
+ UF_long A [ ],
+ UF_long p [ ],
+ UF_long perm [ ],
+ double knobs [CCOLAMD_KNOBS],
+ UF_long stats [CCOLAMD_STATS],
+ void * (*allocate) (size_t, size_t),
+ void (*release) (void *),
+ UF_long cmember [ ],
+ UF_long stype
+) ;
+
+void ccolamd_report
+(
+ int stats [CCOLAMD_STATS]
+) ;
+
+void ccolamd_l_report
+(
+ UF_long stats [CCOLAMD_STATS]
+) ;
+
+void csymamd_report
+(
+ int stats [CCOLAMD_STATS]
+) ;
+
+void csymamd_l_report
+(
+ UF_long stats [CCOLAMD_STATS]
+) ;
+
+
+/* ========================================================================== */
+/* === Prototypes of "expert" routines ====================================== */
+/* ========================================================================== */
+
+/* These routines are meant to be used internally, or in a future version of
+ * UMFPACK. They appear here so that UMFPACK can use them, but they should not
+ * be called directly by the user.
+ */
+
+int ccolamd2
+( /* A and p arguments are modified on output */
+ int n_row, /* number of rows in A */
+ int n_col, /* number of columns in A */
+ int Alen, /* size of the array A */
+ int A [ ], /* row indices of A, of size Alen */
+ int p [ ], /* column pointers of A, of size n_col+1 */
+ double knobs [CCOLAMD_KNOBS],/* parameter settings for ccolamd */
+ int stats [CCOLAMD_STATS], /* ccolamd output statistics and error codes */
+ /* each Front_ array is of size n_col+1: */
+ int Front_npivcol [ ], /* # pivot cols in each front */
+ int Front_nrows [ ], /* # of rows in each front (incl. pivot rows) */
+ int Front_ncols [ ], /* # of cols in each front (incl. pivot cols) */
+ int Front_parent [ ], /* parent of each front */
+ int Front_cols [ ], /* link list of pivot columns for each front */
+ int *p_nfr, /* total number of frontal matrices */
+ int InFront [ ], /* InFront [row] = f if row in front f */
+ int cmember [ ] /* Constraint set of A */
+) ;
+
+UF_long ccolamd2_l /* same as ccolamd2, but with UF_long integers */
+(
+ UF_long n_row,
+ UF_long n_col,
+ UF_long Alen,
+ UF_long A [ ],
+ UF_long p [ ],
+ double knobs [CCOLAMD_KNOBS],
+ UF_long stats [CCOLAMD_STATS],
+ UF_long Front_npivcol [ ],
+ UF_long Front_nrows [ ],
+ UF_long Front_ncols [ ],
+ UF_long Front_parent [ ],
+ UF_long Front_cols [ ],
+ UF_long *p_nfr,
+ UF_long InFront [ ],
+ UF_long cmember [ ]
+) ;
+
+void ccolamd_apply_order
+(
+ int Front [ ],
+ const int Order [ ],
+ int Temp [ ],
+ int nn,
+ int nfr
+) ;
+
+void ccolamd_l_apply_order
+(
+ UF_long Front [ ],
+ const UF_long Order [ ],
+ UF_long Temp [ ],
+ UF_long nn,
+ UF_long nfr
+) ;
+
+
+void ccolamd_fsize
+(
+ int nn,
+ int MaxFsize [ ],
+ int Fnrows [ ],
+ int Fncols [ ],
+ int Parent [ ],
+ int Npiv [ ]
+) ;
+
+void ccolamd_l_fsize
+(
+ UF_long nn,
+ UF_long MaxFsize [ ],
+ UF_long Fnrows [ ],
+ UF_long Fncols [ ],
+ UF_long Parent [ ],
+ UF_long Npiv [ ]
+) ;
+
+void ccolamd_postorder
+(
+ int nn,
+ int Parent [ ],
+ int Npiv [ ],
+ int Fsize [ ],
+ int Order [ ],
+ int Child [ ],
+ int Sibling [ ],
+ int Stack [ ],
+ int Front_cols [ ],
+ int cmember [ ]
+) ;
+
+void ccolamd_l_postorder
+(
+ UF_long nn,
+ UF_long Parent [ ],
+ UF_long Npiv [ ],
+ UF_long Fsize [ ],
+ UF_long Order [ ],
+ UF_long Child [ ],
+ UF_long Sibling [ ],
+ UF_long Stack [ ],
+ UF_long Front_cols [ ],
+ UF_long cmember [ ]
+) ;
+
+int ccolamd_post_tree
+(
+ int root,
+ int k,
+ int Child [ ],
+ const int Sibling [ ],
+ int Order [ ],
+ int Stack [ ]
+) ;
+
+UF_long ccolamd_l_post_tree
+(
+ UF_long root,
+ UF_long k,
+ UF_long Child [ ],
+ const UF_long Sibling [ ],
+ UF_long Order [ ],
+ UF_long Stack [ ]
+) ;
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN int (*ccolamd_printf) (const char *, ...) ;
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/CCOLAMD/Lib/Makefile b/CCOLAMD/Lib/Makefile
new file mode 100644
index 0000000..c5a0ce3
--- /dev/null
+++ b/CCOLAMD/Lib/Makefile
@@ -0,0 +1,32 @@
+#-------------------------------------------------------------------------------
+# CCOLAMD Makefile
+#-------------------------------------------------------------------------------
+
+default: libccolamd.a
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../Include -I../../UFconfig
+
+INC = ../Include/ccolamd.h ../../UFconfig/UFconfig.h
+
+SRC = ../Source/ccolamd.c ../Source/ccolamd_global.c
+
+# creates libccolamd.a, a C-callable COLAMD library
+libccolamd.a: $(SRC) $(INC)
+ $(CC) $(CFLAGS) $(I) -c ../Source/ccolamd_global.c
+ $(CC) $(CFLAGS) $(I) -c ../Source/ccolamd.c
+ $(CC) $(CFLAGS) $(I) -c ../Source/ccolamd.c -DDLONG -o ccolamd_l.o
+ $(AR) libccolamd.a ccolamd.o ccolamd_l.o ccolamd_global.o
+
+ccode: libccolamd.a
+
+library: libccolamd.a
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) libccolamd.a
diff --git a/CCOLAMD/MATLAB/Contents.m b/CCOLAMD/MATLAB/Contents.m
new file mode 100644
index 0000000..6ad7eb3
--- /dev/null
+++ b/CCOLAMD/MATLAB/Contents.m
@@ -0,0 +1,20 @@
+% CCOLAMD, constrained approximate minimum degree ordering
+%
+% Primary functions:
+% csymamd - constrained symmetric approximate minimum degree permutation
+% ccolamd - constrained column approximate minimum degree permutation.
+%
+% helper and test functions:
+% ccolamd_demo - demo for ccolamd and csymamd
+% ccolamd_make - compiles CCOLAMD and CSYMAMD for MATLAB
+% ccolamd_install - compiles and installs ccolamd and csymamd for MATLAB
+% ccolamd_test - extensive test of ccolamd and csymamd
+% luflops - compute the flop count for sparse LU factorization
+% ccolamdtestmex - test function for ccolamd
+% csymamdtestmex - test function for csymamd
+%
+% Example:
+% p = ccolamd (S, knobs, cmember)
+
+% Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam
+% Developed in collaboration with J. Gilbert and E. Ng.
diff --git a/CCOLAMD/MATLAB/Makefile b/CCOLAMD/MATLAB/Makefile
new file mode 100644
index 0000000..6bc82fc
--- /dev/null
+++ b/CCOLAMD/MATLAB/Makefile
@@ -0,0 +1,35 @@
+# CCOLAMD Makefile for MATLAB mexFunctions
+
+default: ccolamd2 csymamd2
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../../UFconfig -I../Include
+
+INC = ../Include/ccolamd.h ../../UFconfig/UFconfig.h
+
+SRC = ../Source/ccolamd.c ../Source/ccolamd_global.c
+
+MX = $(MEX) -DDLONG $(I)
+
+# Compiles the MATLAB-callable routines
+mex: ccolamd2 csymamd2
+
+csymamd2: csymamdmex.c $(INC) $(SRC)
+ $(MX) -output csymamd csymamdmex.c $(SRC)
+
+ccolamd2: ccolamdmex.c $(INC) $(SRC)
+ $(MX) -output ccolamd ccolamdmex.c $(SRC)
+
+# Compiles the extensive test code
+test: mex ccolamdtestmex.c csymamdtestmex.c $(INC) $(SRC)
+ $(MX) ccolamdtestmex.c $(SRC)
+ $(MX) csymamdtestmex.c $(SRC)
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) *.mex* *.dll
diff --git a/CCOLAMD/MATLAB/ccolamd.m b/CCOLAMD/MATLAB/ccolamd.m
new file mode 100644
index 0000000..e3234e9
--- /dev/null
+++ b/CCOLAMD/MATLAB/ccolamd.m
@@ -0,0 +1,48 @@
+function [p, stats] = ccolamd (S, knobs, cmember) %#ok
+%CCOLAMD constrained column approximate minimum degree permutation.
+% p = CCOLAMD(S) returns the column approximate minimum degree permutation
+% vector for the sparse matrix S. For a non-symmetric matrix S, S(:,p)
+% tends to have sparser LU factors than S. chol(S(:,p)'*S(:,p)) also tends
+% to be sparser than chol(S'*S). p=ccolamd(S,1) optimizes the ordering for
+% lu(S(:,p)). The ordering is followed by a column elimination tree post-
+% ordering.
+%
+% Example:
+% p = ccolamd (S)
+% p = ccolamd (S,knobs,cmember)
+%
+% knobs is an optional one- to five-element input vector, with a default
+% value of [0 10 10 1 0] if not present or empty ([ ]). Entries not present
+% are set to their defaults.
+%
+% knobs(1): if nonzero, the ordering is optimized for lu(S(:,p)). It will
+% be a poor ordering for chol(S(:,p)'*S(:,p)). This is the most
+% important knob for ccolamd.
+% knobs(2): if S is m-by-n, rows with more than max(16,knobs(2)*sqrt(n))
+% entries are ignored.
+% knobs(3): columns with more than max(16,knobs(3)*sqrt(min(m,n))) entries
+% are ignored and ordered last in the output permutation (subject to the
+% cmember constraints).
+% knobs(4): if nonzero, aggressive absorption is performed.
+% knobs(5): if nonzero, statistics and knobs are printed.
+%
+% cmember is an optional vector of length n. It defines the constraints on
+% the column ordering. If cmember(j)=s, then column j is in constraint set
+% s (s must be in the range 1 to n). In the output permutation p, all
+% columns in set 1 appear first, followed by all columns in set 2, and so
+% on. cmember=ones(1,n) if not present or empty. ccolamd(S,[],1:n) returns
+% 1:n.
+%
+% p = ccolamd(S) is about the same as p = colamd(S). knobs and its default
+% values differ. colamd always does aggressive absorption, and it finds an
+% ordering suitable for both lu(S(:,p)) and chol(S(:,p)'*S(:,p)); it cannot
+% optimize its ordering for lu(S(:,p)) to the extent that ccolamd(S,1) can.
+%
+% See also AMD, CSYMAMD, COLAMD, SYMAMD, SYMRCM.
+
+% Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam
+% Developed in collaboration with J. Gilbert and E. Ng.
+% Supported by the National Science Foundation (DMS-9504974, DMS-9803599,
+% CCR-0203270), and a grant from Sandia National Lab.
+
+error ('ccolamd: mexFunction not found') ;
diff --git a/CCOLAMD/MATLAB/ccolamd_demo.m b/CCOLAMD/MATLAB/ccolamd_demo.m
new file mode 100644
index 0000000..e2fd684
--- /dev/null
+++ b/CCOLAMD/MATLAB/ccolamd_demo.m
@@ -0,0 +1,209 @@
+%CCOLAMD_DEMO demo for ccolamd and csymamd
+% minimum degree ordering algorithm.
+%
+% Example:
+% ccolamd_demo
+%
+% See also ccolamd
+
+% Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+%-------------------------------------------------------------------------------
+% Print the introduction, the help info, and compile the mexFunctions
+%-------------------------------------------------------------------------------
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'ccolamd/csymamd demo.') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+help ccolamd_demo ;
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'ccolamd help information:') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+help ccolamd ;
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'csymamd help information:') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+help csymamd ;
+
+%-------------------------------------------------------------------------------
+% Solving Ax=b
+%-------------------------------------------------------------------------------
+
+n = 100 ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Solving Ax=b for a small %d-by-%d random matrix:', n, n) ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, '\nNote: Random sparse matrices are AWFUL test cases.\n') ;
+fprintf (1, 'They''re just easy to generate in a demo.\n') ;
+
+% set up the system
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+spparms ('default') ;
+A = sprandn (n, n, 2/n) + speye (n) ;
+b = (1:n)' ;
+
+figure (1)
+clf ;
+subplot (2,2,1)
+spy (A)
+title ('original matrix')
+
+fprintf (1, '\n\nSolving via lu (PAQ = LU), where Q is from ccolamd:\n') ;
+q = ccolamd (A, 1) ;
+I = speye (n) ;
+Q = I (:, q) ;
+[L,U,P] = lu (A*Q) ;
+fl = luflops (L, U) ;
+x = Q * (U \ (L \ (P * b))) ;
+fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ;
+fprintf (1, 'residual: %e\n', norm (A*x-b));
+subplot (2,2,2) ;
+spy (L|U) ;
+title ('LU with ccolamd') ;
+
+try
+fprintf (1, '\n\nSolving via lu (PAQ = LU), where Q is from colamd:\n') ;
+q = colamd (A) ;
+I = speye (n) ;
+Q = I (:, q) ;
+[L,U,P] = lu (A*Q) ;
+fl = luflops (L, U) ;
+x = Q * (U \ (L \ (P * b))) ;
+fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ;
+fprintf (1, 'residual: %e\n', norm (A*x-b));
+subplot (2,2,3) ;
+spy (L|U) ;
+title ('LU with colamd') ;
+catch
+fprintf (1, 'You have a very old version of MATLAB (no colamd) \n') ;
+end
+
+fprintf (1, '\n\nSolving via lu (PA = LU), without regard for sparsity:\n') ;
+[L,U,P] = lu (A) ;
+fl = luflops (L, U) ;
+x = U \ (L \ (P * b)) ;
+fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ;
+fprintf (1, 'residual: %e\n', norm (A*x-b));
+subplot (2,2,4) ;
+spy (L|U) ;
+title ('LU with no ordering') ;
+
+%-------------------------------------------------------------------------------
+% Large demo for ccolamd
+%-------------------------------------------------------------------------------
+
+% Since the analysis will be done on the Cholesky factorization of A'A,
+% set the knob to tell ccolamd to order for Cholesky, not LU.
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Large demo for ccolamd (symbolic analysis only):') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+spparms ('default') ;
+n = 1000 ;
+fprintf (1, 'Generating a random %d-by-%d sparse matrix.\n', n, n) ;
+A = sprandn (n, n, 2/n) + speye (n) ;
+
+figure (2)
+clf ;
+subplot (2,2,1)
+spy (A)
+title ('original matrix')
+
+fprintf (1, '\n\nUnordered matrix:\n') ;
+[lnz,h,parent,post,R] = symbfact (A, 'col') ;
+fprintf (1, 'nz in Cholesky factors of A''A: %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A''A: %d\n', sum (lnz.^2)) ;
+subplot (2,2,4) ;
+spy (R) ;
+title ('Cholesky with no ordering') ;
+
+tic ;
+p = ccolamd (A) ;
+t = toc ;
+[lnz,h,parent,post,R] = symbfact (A (:,p), 'col') ;
+fprintf (1, '\n\nccolamd run time: %f\n', t) ;
+fprintf (1, 'ccolamd ordering quality: \n') ;
+fprintf (1, 'nz in Cholesky factors of A(:,p)''A(:,p): %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A(:,p)''A(:,p): %d\n', sum (lnz.^2)) ;
+subplot (2,2,2) ;
+spy (R) ;
+title ('Cholesky with ccolamd') ;
+
+try
+tic ;
+p = colamd (A) ;
+t = toc ;
+[lnz,h,parent,post,R] = symbfact (A (:,p), 'col') ;
+fprintf (1, '\n\ncolamd run time: %f\n', t) ;
+fprintf (1, 'colamd ordering quality: \n') ;
+fprintf (1, 'nz in Cholesky factors of A(:,p)''A(:,p): %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A(:,p)''A(:,p): %d\n', sum (lnz.^2)) ;
+subplot (2,2,3) ;
+spy (R) ;
+title ('Cholesky with colamd') ;
+catch
+fprintf (1, 'You have a very old version of MATLAB (no colamd) \n') ;
+end
+
+%-------------------------------------------------------------------------------
+% Large demo for csymamd
+%-------------------------------------------------------------------------------
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Large demo for csymamd (symbolic analysis only):') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+
+fprintf (1, 'Generating a random symmetric %d-by-%d sparse matrix.\n', n, n) ;
+A = A+A' ;
+
+figure (3)
+clf ;
+subplot (2,2,1)
+spy (A)
+title ('original matrix')
+
+fprintf (1, '\n\nUnordered matrix:\n') ;
+[lnz,h,parent,post,R] = symbfact (A, 'sym') ;
+fprintf (1, 'nz in Cholesky factors of A: %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A: %d\n', sum (lnz.^2)) ;
+subplot (2,2,4) ;
+spy (R) ;
+title ('Cholesky with no ordering') ;
+
+tic ;
+p = csymamd (A) ;
+t = toc ;
+[lnz,h,parent,post,R] = symbfact (A (p,p), 'sym') ;
+fprintf (1, '\n\ncsymamd run time: %f\n', t) ;
+fprintf (1, 'csymamd ordering quality: \n') ;
+fprintf (1, 'nz in Cholesky factors of A(p,p): %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A(p,p): %d\n', sum (lnz.^2)) ;
+subplot (2,2,2) ;
+spy (R) ;
+title ('Cholesky with csymamd') ;
+
+try
+tic ;
+p = symamd (A) ;
+t = toc ;
+lnz = symbfact (A (p,p), 'sym') ;
+fprintf (1, '\n\nsymamd run time: %f\n', t) ;
+fprintf (1, 'symamd ordering quality: \n') ;
+fprintf (1, 'nz in Cholesky factors of A(p,p): %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A(p,p): %d\n', sum (lnz.^2)) ;
+subplot (2,2,3) ;
+spy (R) ;
+title ('Cholesky with symamd') ;
+catch
+fprintf (1, 'You have a very old version of MATLAB (no symamd) \n') ;
+end
+
+drawnow
diff --git a/CCOLAMD/MATLAB/ccolamd_install.m b/CCOLAMD/MATLAB/ccolamd_install.m
new file mode 100644
index 0000000..0d0428e
--- /dev/null
+++ b/CCOLAMD/MATLAB/ccolamd_install.m
@@ -0,0 +1,18 @@
+function ccolamd_install
+%CCOLAMD_INSTALL compiles and installs ccolamd and csymamd for MATLAB
+% Your current directory must be CCOLAMD/MATLAB for this function to work.
+%
+% Example:
+% ccolamd_install
+%
+% See also ccolamd, csymamd.
+
+% Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+ccolamd_make
+addpath (pwd)
+fprintf ('\nThe following path has been added. You may wish to add it\n') ;
+fprintf ('permanently, using the MATLAB pathtool command.\n') ;
+fprintf ('%s\n\n', pwd) ;
+ccolamd_demo
diff --git a/CCOLAMD/MATLAB/ccolamd_make.m b/CCOLAMD/MATLAB/ccolamd_make.m
new file mode 100644
index 0000000..4637f38
--- /dev/null
+++ b/CCOLAMD/MATLAB/ccolamd_make.m
@@ -0,0 +1,29 @@
+function ccolamd_make
+%CCOLAMD_MAKE compiles CCOLAMD and CSYMAMD for MATLAB
+%
+% Example:
+% ccolamd_make
+%
+% See also ccolamd, csymamd
+
+% Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+details = 0 ; % 1 if details of each command are to be printed
+d = '' ;
+if (~isempty (strfind (computer, '64')))
+ d = '-largeArrayDims' ;
+end
+src = '../Source/ccolamd.c ../Source/ccolamd_global.c' ;
+cmd = sprintf ('mex -DDLONG -O %s -I../../UFconfig -I../Include -output ', d) ;
+s = [cmd 'ccolamd ccolamdmex.c ' src] ;
+if (details)
+ fprintf ('%s\n', s) ;
+end
+eval (s) ;
+s = [cmd 'csymamd csymamdmex.c ' src] ;
+if (details)
+ fprintf ('%s\n', s) ;
+end
+eval (s) ;
+fprintf ('CCOLAMD and CSYMAMD successfully compiled.\n') ;
diff --git a/CCOLAMD/MATLAB/ccolamd_test.m b/CCOLAMD/MATLAB/ccolamd_test.m
new file mode 100644
index 0000000..e359b9f
--- /dev/null
+++ b/CCOLAMD/MATLAB/ccolamd_test.m
@@ -0,0 +1,485 @@
+function ccolamd_test
+%CCOLAMD_TEST extensive test of ccolamd and csymamd
+%
+% Example:
+% ccolamd_test
+%
+% See also csymamd, ccolamd, ccolamd_make.
+
+% Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+help ccolamd_test
+
+global ccolamd_default_knobs csymamd_default_knobs
+ccolamd_default_knobs = [0 10 10 1 0] ;
+csymamd_default_knobs = [10 1 0] ;
+
+ fprintf ('Compiling ccolamd, csymamd, and test mexFunctions.\n') ;
+ ccolamd_make ;
+
+ d = '' ;
+ if (~isempty (strfind (computer, '64')))
+ d = '-largeArrayDims' ;
+ end
+ src = '../Source/ccolamd.c ../Source/ccolamd_global.c' ;
+ cmd = sprintf ('mex -DDLONG -O %s -I../../UFconfig -I../Include ', d) ;
+ eval ([cmd 'ccolamdtestmex.c ' src]) ;
+ eval ([cmd 'csymamdtestmex.c ' src]) ;
+ fprintf ('Done compiling.\n') ;
+
+
+fprintf ('\nThe following codes will be tested:\n') ;
+which ccolamd
+which csymamd
+which ccolamdtestmex
+which csymamdtestmex
+
+fprintf ('\nStarting the tests. Please be patient.\n') ;
+
+h = waitbar (0, 'COLAMD test') ;
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+A = sprandn (500,500,0.4) ;
+
+p = ccolamd (A, [0 10 10 1 1]) ; check_perm (p, A) ;
+p = ccolamd (A, [1 2 7 1 1]) ; check_perm (p, A) ;
+p = ccolamd (A, [1 2 10 0 1]) ; check_perm (p, A) ;
+p = ccolamd (A, [9 2 3 1 1]) ; check_perm (p, A) ;
+
+p = csymamd (A, [10 1 1]) ; check_perm (p, A) ;
+p = csymamd (A, [4 1 1]) ; check_perm (p, A) ;
+p = csymamd (A, [9 0 1]) ; check_perm (p, A) ;
+
+fprintf ('Null matrices') ;
+A = zeros (0,0) ;
+A = sparse (A) ;
+
+p = ccolamd (A) ;
+check_perm (p, A) ;
+
+p = csymamd (A) ;
+check_perm (p, A) ;
+
+A = zeros (0, 100) ;
+A = sparse (A) ;
+p = ccolamd (A) ;
+check_perm (p, A) ;
+
+A = zeros (100, 0) ;
+A = sparse (A) ;
+p = ccolamd (A) ;
+check_perm (p, A) ;
+fprintf (' OK\n') ;
+
+
+fprintf ('Matrices with a few dense row/cols\n') ;
+for trial = 1:20
+
+ waitbar (trial/20, h, 'CCOLAMD: dense rows/cols') ;
+
+ % random square unsymmetric matrix
+ A = rand_matrix (1000, 1000, 1, 10, 20) ;
+ [m n] = size (A) ;
+
+ cmember = irand (min (trial,n), n) ;
+
+ for tol = [0:.1:2 3:20 1e6]
+ B = A + A' ;
+
+ p = ccolamd (A, [ ]) ; check_perm (p, A) ;
+ p = ccolamd (A, [1 tol tol 1]) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 tol tol 1]) ; check_perm (p, A) ;
+ p = ccolamd (A, [1 tol tol 0]) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 tol tol 1]) ; check_perm (p, A) ;
+ p = csymamd (A, [tol 1]) ; check_perm (p, A) ;
+ p = csymamd (A, tol) ; check_perm (p, A) ;
+ p = csymamd (A, [ ]) ; check_perm (p, A) ;
+ p = csymamd (B, [tol 0]) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 tol -1 1]) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 -1 tol 1]) ; check_perm (p, A) ;
+
+ % check with non-null cmember
+
+ p = ccolamd (A, [ ], cmember) ; check_perm (p, A) ;
+ p = ccolamd (A, [1 tol tol 1], cmember) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 tol tol 1], cmember) ; check_perm (p, A) ;
+ p = ccolamd (A, [1 tol tol 0], cmember) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 tol tol 1], cmember) ; check_perm (p, A) ;
+ p = csymamd (A, [tol 1], cmember) ; check_perm (p, A) ;
+ p = csymamd (A, tol, cmember) ; check_perm (p, A) ;
+ p = csymamd (A, [ ], cmember) ; check_perm (p, A) ;
+ p = csymamd (B, [tol 0], cmember) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 tol -1 1], cmember) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 -1 tol 1], cmember) ; check_perm (p, A) ;
+
+ p = ccolamd (A, [ ], [ ]) ; check_perm (p, A) ;
+ p = ccolamd (A, [1 tol tol 1], [ ]) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 tol tol 1], [ ]) ; check_perm (p, A) ;
+ p = ccolamd (A, [1 tol tol 0], [ ]) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 tol tol 1], [ ]) ; check_perm (p, A) ;
+ p = csymamd (A, [tol 1], [ ]) ; check_perm (p, A) ;
+ p = csymamd (A, tol, [ ]) ; check_perm (p, A) ;
+ p = csymamd (A, [ ], [ ]) ; check_perm (p, A) ;
+ p = csymamd (B, [tol 0], [ ]) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 tol -1 1], [ ]) ; check_perm (p, A) ;
+ p = ccolamd (A, [0 -1 tol 1], [ ]) ; check_perm (p, A) ;
+
+ end
+end
+fprintf (' OK\n') ;
+
+fprintf ('General matrices\n') ;
+for trial = 1:400
+
+ waitbar (trial/400, h, 'CCOLAMD: with dense rows/cols') ;
+
+ % matrix of random mtype
+ mtype = irand (3) ;
+ A = rand_matrix (2000, 2000, mtype, 0, 0) ;
+ p = ccolamd (A) ;
+ check_perm (p, A) ;
+
+ if (mtype == 3)
+ p = csymamd (A) ;
+ check_perm (p, A) ;
+ end
+
+end
+fprintf (' OK\n') ;
+
+
+
+fprintf ('Test error handling with invalid inputs\n') ;
+
+% Check different erroneous input.
+for trial = 1:30
+
+ waitbar (trial/30, h, 'CCOLAMD: error handling') ;
+
+ A = rand_matrix (1000, 1000, 2, 0, 0) ;
+
+ for err = 1:13
+
+ p = Tcolamd (A, [ccolamd_default_knobs 1 err], [ ]) ;
+ if (p(1) ~= -1) %#ok
+ check_perm (p, A) ;
+ end
+
+ if (err == 1)
+ % check different (valid) input args to ccolamd
+ p = Acolamd (A) ;
+ p2 = Acolamd (A, [ccolamd_default_knobs 0 0]) ;
+ if (any (p ~= p2))
+ error ('ccolamd: mismatch 1!') ;
+ end
+ end
+
+ B = A'*A ;
+ p = Tsymamd (B, [-1 1 0 err], [ ]) ;
+ if (p(1) ~= -1) %#ok
+ check_perm (p, A) ;
+ end
+
+ if (err == 1)
+
+ % check different (valid) input args to csymamd
+ p = Asymamd (B) ;
+ check_perm (p, A) ;
+ p2 = Asymamd (B, [csymamd_default_knobs 0]) ;
+ if (any (p ~= p2))
+ error ('symamd: mismatch 1!') ;
+ end
+ end
+
+ end
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('Matrices with a few empty columns\n') ;
+
+for trial = 1:400
+
+ waitbar (trial/400, h, 'CCOLAMD: with empty rows/cols') ;
+
+ % some are square, some are rectangular
+ n = 0 ;
+ while (n < 5)
+ A = rand_matrix (1000, 1000, irand (2), 0, 0) ;
+ [m n] = size (A) ;
+ end
+
+ % Add 5 null columns at random locations.
+ null_col = randperm (n) ;
+ A (:, null_col) = 0 ;
+
+ % Order the matrix and make sure that the null columns are ordered last.
+ p = ccolamd (A, [1 1e6 1e6 0]) ;
+ check_perm (p, A) ;
+
+ % find all null columns in A
+ null_col = find (sum (spones (A), 1) == 0) ;
+ nnull = length (null_col) ;
+ if (any (null_col ~= p ((n-nnull+1):n)))
+ error ('ccolamd: Null cols are not ordered last in natural order') ;
+ end
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('Matrices with a few empty rows and columns\n') ;
+
+for trial = 1:400
+
+ waitbar (trial/400, h, 'CCOLAMD: with empty rows/cols') ;
+
+ % symmetric matrices
+ n = 0 ;
+ while (n < 5)
+ A = rand_matrix (1000, 1000, 3, 0, 0) ;
+ [m n] = size (A) ;
+ end
+
+ % Add 5 null columns and rows at random locations.
+ null_col = randperm (n) ;
+ A (:, null_col) = 0 ;
+ A (null_col, :) = 0 ;
+
+ % Order the matrix and make sure that the null rows/cols are ordered last.
+ p = csymamd (A, -1) ;
+ check_perm (p, A) ;
+
+ % find all null rows/columns in A
+ Alo = tril (A, -1) ;
+ null_col = ...
+ find ((sum (spones (Alo), 1) == 0) & (sum (spones (Alo), 2) == 0)') ;
+ nnull = length (null_col) ;
+ if (any (null_col ~= p ((n-nnull+1):n)))
+ error ('csymamd: Null cols are not ordered last in natural order') ;
+ end
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('Matrices with a few empty rows\n') ;
+
+% Test matrices with null rows inserted.
+
+for trial = 1:400
+
+ waitbar (trial/400, h, 'CCOLAMD: with null rows') ;
+ m = 0 ;
+ while (m < 5)
+ A = rand_matrix (1000, 1000, 2, 0, 0) ;
+ m = size (A,1) ;
+ end
+
+ % Add 5 null rows at random locations.
+ null_row = randperm (m) ;
+ null_row = sort (null_row (1:5)) ;
+ A (null_row, :) = 0 ;
+
+ p = ccolamd (A) ;
+ check_perm (p, A) ;
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('\nccolamd and csymamd: all tests passed\n\n') ;
+close (h) ;
+
+%-------------------------------------------------------------------------------
+
+function p = Acolamd (S, knobs)
+% Acolamd: compare ccolamd and Tcolamd results
+
+global ccolamd_default_knobs
+
+if (nargin < 2)
+ p = ccolamd (S) ;
+ p1 = Tcolamd (S, [ccolamd_default_knobs 0 0], [ ]) ;
+else
+ p = ccolamd (S, knobs) ;
+ p1 = Tcolamd (S, knobs, [ ]) ;
+end
+
+check_perm (p, S) ;
+check_perm (p1, S) ;
+
+if (any (p1 ~= p))
+ narg = nargin ;
+ if (nargin == 2)
+ save bad S narg knobs
+ else
+ save bad S narg
+ end
+ error ('Acolamd mismatch!') ;
+end
+
+%-------------------------------------------------------------------------------
+
+function p = Asymamd (S, knobs)
+% Asymamd: compare csymamd and Tsymamd results
+
+global csymamd_default_knobs
+
+if (nargin < 2)
+ p = csymamd (S) ;
+ p1 = Tsymamd (S, [csymamd_default_knobs 0], [ ]) ;
+else
+ p = csymamd (S, knobs) ;
+ p1 = Tsymamd (S, knobs, [ ]) ;
+end
+
+if (any (p1 ~= p))
+ error ('Asymamd mismatch!') ;
+end
+
+
+%-------------------------------------------------------------------------------
+
+function check_perm (p, A, cmember)
+% check_perm: check for a valid permutation vector
+
+if (isempty (A) & isempty (p)) %#ok
+ % empty permutation vectors of empty matrices are OK
+ return
+end
+
+if (isempty (p))
+ error ('Bad permutation: cannot be empty') ;
+end
+
+[m n] = size (A) ;
+[p_m p_n] = size (p) ;
+if (p_n == 1)
+ % force p to be a row vector
+ p = p' ;
+ [p_m p_n] = size (p) ;
+end
+
+if (n ~= p_n)
+ error ('Bad permutation: wrong size') ;
+end
+
+if (p_m ~= 1) ;
+ % p must be a vector
+ error ('Bad permutation: not a vector') ;
+else
+ if (any (sort (p) - (1:p_n)))
+ error ('Bad permutation') ;
+ end
+end
+
+if (nargin > 2)
+ % check cmember
+ c = cmember (p) ;
+ % c must be monotonically non-decreasing
+ c = diff (c) ;
+ if (any (c < 0))
+ error ('permutation breaks the cmember constraints') ;
+ end
+end
+
+%-------------------------------------------------------------------------------
+
+function i = irand (n,s)
+% irand: return a random vector of size s, with values between 1 and n
+if (nargin == 1)
+ s = 1 ;
+end
+i = min (n, 1 + floor (rand (1,s) * n)) ;
+
+%-------------------------------------------------------------------------------
+
+function A = rand_matrix (n_max, m_max, mtype, d_rows, d_cols)
+% rand_matrix: return a random sparse matrix
+%
+% A = rand_matrix (n_max, m_max, mtype, d_rows, d_cols)
+%
+% A binary matrix of random size, at most n_max-by-m_max, with d_rows dense rows
+% and d_cols dense columns.
+%
+% mtype 1: square unsymmetric (m_max is ignored)
+% mtype 2: rectangular
+% mtype 3: symmetric (m_max is ignored)
+
+n = irand (n_max) ;
+if (mtype ~= 2)
+ % square
+ m = n ;
+else
+ m = irand (m_max) ;
+end
+
+A = sprand (m, n, 10 / max (m,n)) ;
+
+if (d_rows > 0)
+ % add dense rows
+ for k = 1:d_rows
+ i = irand (m) ;
+ nz = irand (n) ;
+ p = randperm (n) ;
+ p = p (1:nz) ;
+ A (i,p) = 1 ;
+ end
+end
+
+if (d_cols > 0)
+ % add dense cols
+ for k = 1:d_cols
+ j = irand (n) ;
+ nz = irand (m) ;
+ p = randperm (m) ;
+ p = p (1:nz) ;
+ A (p,j) = 1 ;
+ end
+end
+
+A = spones (A) ;
+
+% ensure that there are no empty columns
+d = find (full (sum (A,1)) == 0) ; %#ok
+A (m,d) = 1 ; %#ok
+
+% ensure that there are no empty rows
+d = find (full (sum (A,2)) == 0) ; %#ok
+A (d,n) = 1 ; %#ok
+
+if (mtype == 3)
+ % symmetric
+ A = A + A' + speye (n) ;
+end
+
+A = spones (A) ;
+
+%-------------------------------------------------------------------------------
+% Tcolamd: run ccolamd in a testing mode
+%-------------------------------------------------------------------------------
+
+function p = Tcolamd (S, knobs, cmember)
+
+% knobs (5) = 1 ;
+p = ccolamdtestmex (S, knobs, cmember) ;
+
+if (p (1) ~= -1)
+ check_perm (p, S) ;
+end
+
+
+%-------------------------------------------------------------------------------
+% Tsymamd: run csymamd in a testing mode
+%-------------------------------------------------------------------------------
+
+function p = Tsymamd (S, knobs, cmember)
+
+% knobs (2) = 1 ;
+p = csymamdtestmex (S, knobs, cmember) ;
+
+if (p (1) ~= -1)
+ check_perm (p, S) ;
+end
+
diff --git a/CCOLAMD/MATLAB/ccolamdmex.c b/CCOLAMD/MATLAB/ccolamdmex.c
new file mode 100644
index 0000000..fbcb878
--- /dev/null
+++ b/CCOLAMD/MATLAB/ccolamdmex.c
@@ -0,0 +1,228 @@
+/* ========================================================================== */
+/* === ccolamd mexFunction ================================================== */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * CCOLAMD, Copyright (C), Univ. of Florida. Authors: Timothy A. Davis,
+ * Sivasankaran Rajamanickam, and Stefan Larimore
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/*
+ * Usage:
+ * p = ccolamd (A) ;
+ * [p stats] = ccolamd (A, knobs, cmember) ;
+ *
+ * See ccolamd.m for a description.
+ */
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "ccolamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include <string.h>
+#include "UFconfig.h"
+
+/* ========================================================================== */
+/* === ccolamd mexFunction ================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ /* === Local variables ================================================== */
+
+ UF_long *A ; /* ccolamd's copy of the matrix and workspace */
+ UF_long *cmember ; /* ccolamd's copy of the constraint set */
+ double *in_cmember ; /* input constraint set */
+ UF_long *p ; /* ccolamd's copy of the column pointers */
+ UF_long Alen ; /* size of A */
+ UF_long cslen ; /* size of CS */
+ UF_long n_col ; /* number of columns of A */
+ UF_long n_row ; /* number of rows of A */
+ UF_long nnz ; /* number of entries in A */
+ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [CCOLAMD_KNOBS] ; /* ccolamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ UF_long i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ UF_long spumoni ; /* verbosity variable */
+ UF_long stats [CCOLAMD_STATS] ; /* stats for ccolamd */
+
+ /* === Check inputs ===================================================== */
+
+ if (nargin < 1 || nargin > 3 || nargout < 0 || nargout > 2)
+ {
+ mexErrMsgTxt ("Usage: [p stats] = ccolamd (A, knobs, cmember)") ;
+ }
+
+ /* === Get cmember ====================================================== */
+
+ cmember = NULL ;
+ cslen = 0 ;
+ if (nargin > 2)
+ {
+ in_cmember = mxGetPr (pargin [2]) ;
+ cslen = mxGetNumberOfElements (pargin [2]) ;
+ if (cslen != 0)
+ {
+ cmember = (UF_long *) mxCalloc (cslen, sizeof (UF_long)) ;
+ for (i = 0 ; i < cslen ; i++)
+ {
+ /* convert cmember from 1-based to 0-based */
+ cmember[i] = ((UF_long) in_cmember [i] - 1) ;
+ }
+ }
+ }
+
+ /* === Get knobs ======================================================== */
+
+ ccolamd_l_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ /* check for user-passed knobs */
+ if (nargin > 1)
+ {
+ in_knobs = mxGetPr (pargin [1]) ;
+ i = mxGetNumberOfElements (pargin [1]) ;
+ if (i > 0) knobs [CCOLAMD_LU] = (in_knobs [0] != 0) ;
+ if (i > 1) knobs [CCOLAMD_DENSE_ROW] = in_knobs [1] ;
+ if (i > 2) knobs [CCOLAMD_DENSE_COL] = in_knobs [2] ;
+ if (i > 3) knobs [CCOLAMD_AGGRESSIVE] = (in_knobs [3] != 0) ;
+ if (i > 4) spumoni = (in_knobs [4] != 0) ;
+ }
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\nccolamd version %d.%d, %s:\nknobs(1): %g, order for %s\n",
+ CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE,
+ in_knobs [0],
+ (knobs [CCOLAMD_LU] != 0) ? "lu(A)" : "chol(A'*A)") ;
+ if (knobs [CCOLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(2): %g, rows with > max(16,%g*sqrt(size(A,2)))"
+ " entries removed\n", in_knobs [1], knobs [CCOLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(2): %g, no dense rows removed\n", in_knobs [1]) ;
+ }
+ if (knobs [CCOLAMD_DENSE_COL] >= 0)
+ {
+ mexPrintf ("knobs(3): %g, cols with > max(16,%g*sqrt(min(size(A)))"
+ " entries removed\n", in_knobs [2], knobs [CCOLAMD_DENSE_COL]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(3): no dense columns removed\n", in_knobs [2]) ;
+ }
+ mexPrintf ("knobs(4): %g, aggressive absorption: %s\n",
+ in_knobs [3], (knobs [CCOLAMD_AGGRESSIVE] != 0) ? "yes" : "no") ;
+ mexPrintf ("knobs(5): %g, statistics and knobs printed\n",
+ in_knobs [4]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) pargin [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("ccolamd: input matrix must be 2-dimensional") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) pargin, "sparse") ;
+ }
+
+ /* === Allocate workspace for ccolamd =================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+
+ /* get column pointer vector */
+ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ;
+ (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ;
+ nnz = p [n_col] ;
+ Alen = (UF_long) ccolamd_l_recommended (nnz, n_row, n_col) ;
+ if (Alen == 0)
+ {
+ mexErrMsgTxt ("ccolamd: problem too large") ;
+ }
+
+ /* === Copy input matrix into workspace ================================= */
+
+ A = (UF_long *) mxCalloc (Alen, sizeof (UF_long)) ;
+ (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ;
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+ /* Check constraint set size */
+ if (cmember != NULL && cslen != n_col)
+ {
+ mexErrMsgTxt ("ccolamd: cmember must be of length equal to #cols of A");
+ }
+
+ /* === Order the columns (destroys A) =================================== */
+
+ if (!ccolamd_l (n_row, n_col, Alen, A, p, knobs, stats, cmember))
+ {
+ ccolamd_l_report (stats) ;
+ mexErrMsgTxt ("ccolamd error!") ;
+ }
+ mxFree (A) ;
+ mxFree (cmember) ;
+
+ /* === Return the permutation vector ==================================== */
+
+ pargout [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* ccolamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = p [i] + 1 ;
+ }
+ mxFree (p) ;
+
+ /* === Return the stats vector ========================================== */
+
+ /* print stats if spumoni is set */
+ if (spumoni)
+ {
+ ccolamd_l_report (stats) ;
+ }
+
+ if (nargout == 2)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, CCOLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (pargout [1]) ;
+ for (i = 0 ; i < CCOLAMD_STATS ; i++)
+ {
+ out_stats [i] = stats [i] ;
+ }
+
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if symamd returns FALSE */
+ out_stats [CCOLAMD_INFO1] ++ ;
+ out_stats [CCOLAMD_INFO2] ++ ;
+ }
+}
diff --git a/CCOLAMD/MATLAB/ccolamdtestmex.c b/CCOLAMD/MATLAB/ccolamdtestmex.c
new file mode 100644
index 0000000..b5b04da
--- /dev/null
+++ b/CCOLAMD/MATLAB/ccolamdtestmex.c
@@ -0,0 +1,533 @@
+/* ========================================================================== */
+/* === ccolamdtest mexFunction ============================================== */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis,
+ * Sivasankaran Rajamanickam, and Stefan Larimore
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/*
+ * This MATLAB mexFunction is for testing only. It is not meant for
+ * production use. See ccolamdmex.c and ccolamd.m instead.
+ *
+ * Usage:
+ *
+ * [ P, stats ] = ccolamdtest (A, knobs) ;
+ *
+ * The stats vector is optional. knobs is required:
+ *
+ * knobs (1) order for LU if nonzero, Cholesky otherwise. default 0
+ * knobs (2) spumoni, default 0.
+ * knobs (3) dense row control. default 10
+ * knobs (4) dense column control. default 10
+ * knobs (5) aggresive absorption if nonzero. default: 1
+ *
+ * knobs (6) for testing only. Controls the workspace used.
+ * knobs (7) for testing only. Controls how the input matrix is
+ * jumbled prior to calling colamd, to test its error
+ * handling capability.
+ *
+ * see ccolamd.c for a description of the stats array.
+ *
+ */
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "ccolamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include <string.h>
+#include "UFconfig.h"
+
+/* Here only for testing */
+#undef MIN
+#undef MAX
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define CCOLAMD_MIN_MEMORY(nnz,n_row,n_col) \
+ (MAX (2 * nnz, 4 * n_col) + \
+ 8*n_col + 6*n_row + n_col + (nnz / 5) \
+ + ((3 * n_col) + 1) + 5 * (n_col + 1) + n_row)
+
+/* ========================================================================== */
+/* === dump_matrix ========================================================== */
+/* ========================================================================== */
+
+static void dump_matrix
+(
+ UF_long A [ ],
+ UF_long p [ ],
+ UF_long n_row,
+ UF_long n_col,
+ UF_long Alen,
+ UF_long limit
+)
+{
+ UF_long col, k, row ;
+
+ mexPrintf ("dump matrix: nrow %d ncol %d Alen %d\n", n_row, n_col, Alen) ;
+
+ for (col = 0 ; col < MIN (n_col, limit) ; col++)
+ {
+ mexPrintf ("column %d, p[col] %d, p [col+1] %d, length %d\n",
+ col, p [col], p [col+1], p [col+1] - p [col]) ;
+ for (k = p [col] ; k < p [col+1] ; k++)
+ {
+ row = A [k] ;
+ mexPrintf (" %d", row) ;
+ }
+ mexPrintf ("\n") ;
+ }
+}
+
+/* ========================================================================== */
+/* === ccolamd mexFunction ================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nargout, /* number of left-hand sides */
+ mxArray *pargout [ ], /* left-hand side matrices */
+ int nargin, /* number of right--hand sides */
+ const mxArray *pargin [ ] /* right-hand side matrices */
+)
+{
+ /* === Local variables ================================================== */
+
+ UF_long *A ; /* ccolamd's copy of the matrix and workspace */
+ UF_long *p ; /* ccolamd's copy of the column pointers */
+ UF_long Alen ; /* size of A */
+ UF_long n_col ; /* number of columns of A */
+ UF_long n_row ; /* number of rows of A */
+ UF_long nnz ; /* number of entries in A */
+ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [CCOLAMD_KNOBS] ; /* ccolamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ UF_long i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ UF_long spumoni ; /* verbosity variable */
+ UF_long stats2 [CCOLAMD_STATS] ; /* stats for ccolamd */
+
+ UF_long *cp, *cp_end, result, col, length, ok ;
+ UF_long *stats ;
+ stats = stats2 ;
+
+ /* === Check inputs ===================================================== */
+
+ if (nargin != 3 || nargout < 0 || nargout > 2)
+ {
+ mexErrMsgTxt (
+ "ccolamdtest: incorrect number of input and/or output arguments") ;
+ }
+ /* for testing we require all 7 knobs */
+ if (mxGetNumberOfElements (pargin [1]) != 7)
+ {
+ mexErrMsgTxt ("ccolamdtest: must have all 7 knobs for testing") ;
+ }
+
+ /* === Get knobs ======================================================== */
+
+ ccolamd_l_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ in_knobs = mxGetPr (pargin [1]) ;
+ knobs [CCOLAMD_LU] = (in_knobs [0] != 0) ;
+ knobs [CCOLAMD_DENSE_ROW] = in_knobs [1] ;
+ knobs [CCOLAMD_DENSE_COL] = in_knobs [2] ;
+ knobs [CCOLAMD_AGGRESSIVE] = (in_knobs [3] != 0) ;
+ spumoni = (in_knobs [4] != 0) ;
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\nccolamd version %d.%d, %s:\nknobs(1): %g, order for %s\n",
+ CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE,
+ in_knobs [0],
+ (knobs [CCOLAMD_LU] != 0) ? "lu(A)" : "chol(A'*A)") ;
+ if (knobs [CCOLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(2): %g, rows with > max(16,%g*sqrt(size(A,2)))"
+ " entries removed\n", in_knobs [1], knobs [CCOLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(2): %g, no dense rows removed\n", in_knobs [1]) ;
+ }
+ if (knobs [CCOLAMD_DENSE_COL] >= 0)
+ {
+ mexPrintf ("knobs(3): %g, cols with > max(16,%g*sqrt(min(size(A)))"
+ " entries removed\n", in_knobs [2], knobs [CCOLAMD_DENSE_COL]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(3): no dense columns removed\n", in_knobs [2]) ;
+ }
+ mexPrintf ("knobs(4): %g, aggressive absorption: %s\n",
+ in_knobs [3], (knobs [CCOLAMD_AGGRESSIVE] != 0) ? "yes" : "no") ;
+ mexPrintf ("knobs(5): %g, statistics and knobs printed\n",
+ in_knobs [4]) ;
+ mexPrintf ("Testing: %g %g\n", in_knobs [5], in_knobs[6]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) pargin [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("ccolamd: input matrix must be 2-dimensional") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) pargin, "sparse") ;
+ }
+
+ /* === Allocate workspace for ccolamd =================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+
+ /* get column pointer vector so we can find nnz */
+ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ;
+ (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ;
+ nnz = p [n_col] ;
+ Alen = (UF_long) ccolamd_l_recommended (nnz, n_row, n_col) ;
+ if (Alen == 0)
+ {
+ mexErrMsgTxt ("ccolamd: problem too large") ;
+ }
+
+ /* === Modify size of Alen if testing =================================== */
+ /*
+ knobs [5] amount of workspace given to colamd.
+ < 0 : TIGHT memory
+ > 0 : MIN + knob [3] - 1
+ == 0 : RECOMMENDED memory
+ */
+
+ /* get knob [5], if negative */
+ if (in_knobs [5] < 0)
+ {
+ Alen = CCOLAMD_MIN_MEMORY (nnz, n_row, n_col) + n_col ;
+ }
+ else if (in_knobs [5] > 0)
+ {
+ Alen = CCOLAMD_MIN_MEMORY (nnz, n_row, n_col) + in_knobs [5] - 1 ;
+ }
+
+ /* otherwise, we use the recommended amount set above */
+
+ /* === Copy input matrix into workspace ================================= */
+
+ A = (UF_long *) mxCalloc (Alen, sizeof (UF_long)) ;
+ (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ;
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+
+ /* === Jumble matrix ==================================================== */
+
+ /*
+ knobs [6] FOR TESTING ONLY: Specifies how to jumble matrix
+ 0 : No jumbling
+ 1 : Make n_row less than zero
+ 2 : Make first pointer non-zero
+ 3 : Make column pointers not non-decreasing
+ 4 : Make a column pointer greater or equal to Alen
+ 5 : Make row indices not strictly increasing
+ 6 : Make a row index greater or equal to n_row
+ 7 : Set A = NULL
+ 8 : Set p = NULL
+ 9 : Repeat row index
+ 10: make row indices not sorted
+ 11: jumble columns massively (note this changes
+ the pattern of the matrix A.)
+ 12: Set stats = NULL
+ 13: Make n_col less than zero
+ */
+
+ /* jumble appropriately */
+ switch ((UF_long) in_knobs [6])
+ {
+
+ case 0 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: no errors expected\n") ;
+ }
+ result = 1 ; /* no errors */
+ break ;
+
+ case 1 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: nrow out of range\n") ;
+ }
+ result = 0 ; /* nrow out of range */
+ n_row = -1 ;
+ break ;
+
+ case 2 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: p [0] nonzero\n") ;
+ }
+ result = 0 ; /* p [0] must be zero */
+ p [0] = 1 ;
+ break ;
+
+ case 3 :
+ if (spumoni)
+ {
+ mexPrintf ("colamdtest: negative length last column\n") ;
+ }
+ result = (n_col == 0) ; /* p must be monotonically inc. */
+ p [n_col] = p [0] ;
+ break ;
+
+ case 4 :
+ if (spumoni)
+ {
+ mexPrintf ("colamdtest: Alen too small\n") ;
+ }
+ result = 0 ; /* out of memory */
+ p [n_col] = Alen ;
+ break ;
+
+ case 5 :
+ if (spumoni)
+ {
+ mexPrintf ("colamdtest: row index out of range (-1)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ result = 0 ;
+ A [nnz-1] = -1 ;
+ }
+ else
+ {
+ if (spumoni)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 6 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: row index out of range (n_row)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ if (spumoni)
+ {
+ mexPrintf ("Changing A[nnz-1] from %d to %d\n",
+ A [nnz-1], n_row) ;
+ }
+ result = 0 ;
+ A [nnz-1] = n_row ;
+ }
+ else
+ {
+ if (spumoni)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 7 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: A not present\n") ;
+ }
+ result = 0 ; /* A not present */
+ A = (UF_long *) NULL ;
+ break ;
+
+ case 8 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: p not present\n") ;
+ }
+ result = 0 ; /* p not present */
+ p = (UF_long *) NULL ;
+ break ;
+
+ case 9 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: duplicate row index\n") ;
+ }
+ result = 1 ; /* duplicate row index */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ A [p [col]] = A [p [col] + 1] ;
+ if (spumoni)
+ {
+ mexPrintf ("Made duplicate row %d in col %d\n",
+ A [p [col] + 1], col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, Alen, col+2) ;
+ }
+ break ;
+
+ case 10 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: unsorted column\n") ;
+ }
+ result = 1 ; /* jumbled columns */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ i = A[p [col]] ;
+ A [p [col]] = A[p [col] + 1] ;
+ A [p [col] + 1] = i ;
+ if (spumoni)
+ {
+ mexPrintf ("Unsorted column %d \n", col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, Alen, col+2) ;
+ }
+ break ;
+
+ case 11 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: massive jumbling\n") ;
+ }
+ result = 1 ; /* massive jumbling, but no errors */
+ srand (1) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ cp = &A [p [i]] ;
+ cp_end = &A [p [i+1]] ;
+ while (cp < cp_end)
+ {
+ *cp++ = rand() % n_row ;
+ }
+ }
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, Alen, n_col) ;
+ }
+ break ;
+
+ case 12 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: stats not present\n") ;
+ }
+ result = 0 ; /* stats not present */
+ stats = (UF_long *) NULL ;
+ break ;
+
+ case 13 :
+ if (spumoni)
+ {
+ mexPrintf ("ccolamdtest: ncol out of range\n") ;
+ }
+ result = 0 ; /* ncol out of range */
+ n_col = -1 ;
+ break ;
+
+ }
+
+
+ /* === Order the columns (destroys A) =================================== */
+
+ ok = ccolamd_l (n_row, n_col, Alen, A, p, knobs, stats, NULL) ;
+ if (spumoni)
+ {
+ ccolamd_l_report (stats) ;
+ }
+
+ /* === Return the stats vector ========================================== */
+
+ if (nargout == 2)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, CCOLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (pargout [1]) ;
+ for (i = 0 ; i < CCOLAMD_STATS ; i++)
+ {
+ out_stats [i] = (stats == NULL) ? (-1) : (stats [i]) ;
+ }
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if csymamd returns FALSE */
+ out_stats [CCOLAMD_INFO1] ++ ;
+ out_stats [CCOLAMD_INFO2] ++ ;
+ }
+
+ mxFree (A) ;
+
+ if (ok)
+ {
+
+ /* === Return the permutation vector ================================ */
+
+ pargout [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* ccolamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = p [i] + 1 ;
+ }
+ if (!result)
+ {
+ ccolamd_l_report (stats) ;
+ mexErrMsgTxt ("ccolamd should have returned TRUE\n") ;
+ }
+ }
+ else
+ {
+
+ /* return p = -1 if ccolamd failed */
+ pargout [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ out_perm = mxGetPr (pargout [0]) ;
+ out_perm [0] = -1 ;
+ if (result)
+ {
+ ccolamd_l_report (stats) ;
+ mexErrMsgTxt ("ccolamd should have returned FALSE\n") ;
+ }
+ }
+
+ mxFree (p) ;
+}
diff --git a/CCOLAMD/MATLAB/ccolamdtestmex.m b/CCOLAMD/MATLAB/ccolamdtestmex.m
new file mode 100644
index 0000000..9a56387
--- /dev/null
+++ b/CCOLAMD/MATLAB/ccolamdtestmex.m
@@ -0,0 +1,10 @@
+function [P, stats] = ccolamdtestmex (A, knobs) %#ok
+% CCOLAMDTESTMEX test function for ccolamd
+% Example:
+% [ P, stats ] = ccolamdtest (A, knobs) ;
+% See also ccolamd
+
+% Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+error ('ccolamdtestmex mexFunction not found') ;
diff --git a/CCOLAMD/MATLAB/csymamd.m b/CCOLAMD/MATLAB/csymamd.m
new file mode 100644
index 0000000..901040d
--- /dev/null
+++ b/CCOLAMD/MATLAB/csymamd.m
@@ -0,0 +1,48 @@
+function [p, stats] = csymamd (S, knobs, cmember) %#ok
+%CSYMAMD constrained symmetric approximate minimum degree permutation
+% P = CSYMAMD(S) for a symmetric positive definite matrix S, returns the
+% permutation vector p such that S(p,p) tends to have a sparser Cholesky
+% factor than S. Sometimes CSYMAMD works well for symmetric indefinite
+% matrices too. The matrix S is assumed to be symmetric; only the
+% strictly lower triangular part is referenced. S must be square. Note
+% that p=amd(S) is faster, but does not allow for a constrained ordering.
+% The ordering is followed by an elimination tree post-ordering.
+%
+% See also AMD, CCOLAMD, COLAMD, SYMAMD.
+%
+% Example:
+% p = csymamd (S)
+% p = csymamd (S,knobs,cmember)
+%
+% knobs is an optional one- to three-element input vector, with a default
+% value of [10 1 0] if present or empty ([ ]). Entries not present are set
+% to their defaults.
+%
+% knobs(1): If S is n-by-n, then rows and columns with more than
+% max(16,knobs(1)*sqrt(n)) entries are ignored, and ordered last in the
+% output permutation (subject to the cmember constraints).
+% knobs(2): if nonzero, aggressive absorption is performed.
+% knobs(3): if nonzero, statistics and knobs are printed.
+%
+% cmember is an optional vector of length n. It defines the constraints on
+% the ordering. If cmember(j)=s, then row/column j is in constraint set s
+% (s must be in the range 1 to n). In the output permutation p,
+% rows/columns in set 1 appear first, followed by all rows/columns in set 2,
+% and so on. cmember=ones(1,n) if not present or empty. csymamd(S,[],1:n)
+% returns 1:n.
+%
+% p = csymamd(S) is about the same as p = symamd(S). knobs and its default
+% values differ.
+%
+% Authors: S. Larimore, T. Davis (Univ of Florida), and S. Rajamanickam, in
+% collaboration with J. Gilbert and E. Ng. Supported by the National
+% Science Foundation (DMS-9504974, DMS-9803599, CCR-0203270), and a grant
+% from Sandia National Lab. See http://www.cise.ufl.edu/research/sparse
+% for ccolamd, csymamd, amd, colamd, symamd, and other related orderings.
+%
+% See also AMD, CCOLAMD, COLAMD, SYMAMD, SYMRCM.
+
+% Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+error ('csymamd: mexFunction not found') ;
diff --git a/CCOLAMD/MATLAB/csymamdmex.c b/CCOLAMD/MATLAB/csymamdmex.c
new file mode 100644
index 0000000..e52d926
--- /dev/null
+++ b/CCOLAMD/MATLAB/csymamdmex.c
@@ -0,0 +1,208 @@
+/* ========================================================================== */
+/* === csymamd mexFunction ================================================== */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * CCOLAMD, Copyright (C), Univ. of Florida. Authors: Timothy A. Davis,
+ * Sivasankaran Rajamanickam, and Stefan Larimore
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/*
+ * Usage:
+ * p = csymamd (A) ;
+ * [p stats] = csymamd (A, knobs, cmember) ;
+ *
+ * See csymamd.m for a description.
+ */
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "ccolamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include "UFconfig.h"
+
+/* ========================================================================== */
+/* === csymamd mexFunction ================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ /* === Local variables ================================================== */
+
+ UF_long *A ; /* row indices of input matrix A */
+ UF_long *perm ; /* column ordering of M and ordering of A */
+ UF_long *cmember ; /* csymamd's copy of the constraint set */
+ double *in_cmember ; /* input constraint set */
+ UF_long *p ; /* column pointers of input matrix A */
+ UF_long cslen ; /* size of constraint set */
+ UF_long n_col ; /* number of columns of A */
+ UF_long n_row ; /* number of rows of A */
+ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [CCOLAMD_KNOBS] ; /* csymamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ UF_long i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ UF_long spumoni ; /* verbosity variable */
+ UF_long stats [CCOLAMD_STATS] ; /* stats for symamd */
+
+ /* === Check inputs ===================================================== */
+
+ if (nargin < 1 || nargin > 3 || nargout < 0 || nargout > 2)
+ {
+ mexErrMsgTxt ("Usage: [p stats] = csymamd (S, knobs, cmember)") ;
+ }
+
+ /* === Get cmember ====================================================== */
+
+ cmember = NULL ;
+ cslen = 0 ;
+ if (nargin > 2)
+ {
+ in_cmember = mxGetPr (pargin [2]) ;
+ cslen = mxGetNumberOfElements (pargin [2]) ;
+ if (cslen != 0)
+ {
+ cmember = (UF_long *) mxCalloc (cslen, sizeof (UF_long)) ;
+ for (i = 0 ; i < cslen ; i++)
+ {
+ /* convert cmember from 1-based to 0-based */
+ cmember[i] = ((UF_long) in_cmember [i] - 1) ;
+ }
+ }
+ }
+
+ /* === Get knobs ======================================================== */
+
+ ccolamd_l_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ /* check for user-passed knobs */
+ i = 0 ;
+ if (nargin > 1)
+ {
+ in_knobs = mxGetPr (pargin [1]) ;
+ i = mxGetNumberOfElements (pargin [1]) ;
+ if (i > 0) knobs [CCOLAMD_DENSE_ROW] = in_knobs [0] ;
+ if (i > 1) knobs [CCOLAMD_AGGRESSIVE] = in_knobs [1] ;
+ if (i > 2) spumoni = (in_knobs [2] != 0) ;
+ }
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\ncsymamd version %d.%d, %s:\n",
+ CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE) ;
+ if (knobs [CCOLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(1): %g, rows/cols with > "
+ "max(16,%g*sqrt(size(A,2))) entries removed\n",
+ in_knobs [0], knobs [CCOLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(1): %g, no dense rows removed\n",
+ in_knobs [0]) ;
+ }
+ mexPrintf ("knobs(2): %g, aggressive absorption: %s\n",
+ in_knobs [1], (knobs [CCOLAMD_AGGRESSIVE] != 0) ? "yes" : "no") ;
+ mexPrintf ("knobs(3): %g, statistics and knobs printed\n",
+ in_knobs [2]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) pargin [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("csymamd: input matrix must be 2-dimensional.") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) pargin, "sparse") ;
+ }
+
+ /* === Allocate workspace for csymamd =================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+ if (n_col != n_row)
+ {
+ mexErrMsgTxt ("csymamd: matrix must be square.") ;
+ }
+
+ if (cmember != NULL && cslen != n_col)
+ {
+ mexErrMsgTxt ("csymamd: cmember must be of length equal to #cols of A");
+ }
+
+ A = (UF_long *) mxGetIr (Ainput) ;
+ p = (UF_long *) mxGetJc (Ainput) ;
+ perm = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ;
+
+ /* === Order the rows and columns of A (does not destroy A) ============= */
+
+ if (!csymamd_l (n_col, A, p, perm, knobs, stats, &mxCalloc, &mxFree,
+ cmember, -1))
+ {
+ csymamd_l_report (stats) ;
+ mexErrMsgTxt ("csymamd error!") ;
+ }
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+ /* === Return the permutation vector ==================================== */
+
+ pargout [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* symamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = perm [i] + 1 ;
+ }
+ mxFree (perm) ;
+ mxFree (cmember) ;
+
+ /* === Return the stats vector ========================================== */
+
+ /* print stats if spumoni is set */
+ if (spumoni)
+ {
+ csymamd_l_report (stats) ;
+ }
+
+ if (nargout == 2)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, CCOLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (pargout [1]) ;
+ for (i = 0 ; i < CCOLAMD_STATS ; i++)
+ {
+ out_stats [i] = stats [i] ;
+ }
+
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if symamd returns FALSE */
+ out_stats [CCOLAMD_INFO1] ++ ;
+ out_stats [CCOLAMD_INFO2] ++ ;
+ }
+}
diff --git a/CCOLAMD/MATLAB/csymamdtestmex.c b/CCOLAMD/MATLAB/csymamdtestmex.c
new file mode 100644
index 0000000..428b411
--- /dev/null
+++ b/CCOLAMD/MATLAB/csymamdtestmex.c
@@ -0,0 +1,502 @@
+/* ========================================================================== */
+/* === csymamdtest mexFunction ============================================== */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis,
+ * Sivasankaran Rajamanickam, and Stefan Larimore
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/*
+ * This MATLAB mexFunction is for testing only. It is not meant for
+ * production use. See csymamdmex.c and csymamd.m instead.
+ *
+ * Usage:
+ *
+ * [ P, stats ] = csymamdtest (A, knobs, cmember) ;
+ *
+ * The knobs and stats vectors are optional:
+ *
+ * knobs (1) dense row/col control. default 10
+ * knobs (2) spumoni, default 0.
+ * knobs (3) aggresive absorption if nonzero. default 1
+ *
+ * knobs (4) for testing only. Controls how the input matrix is
+ * jumbled prior to calling colamd, to test its error
+ * handling capability.
+ */
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "ccolamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include <string.h>
+#include "UFconfig.h"
+
+#ifdef MIN
+#undef MIN
+#endif
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+
+static void dump_matrix
+(
+ UF_long A [ ],
+ UF_long p [ ],
+ UF_long n_row,
+ UF_long n_col,
+ UF_long Alen,
+ UF_long limit
+)
+{
+ UF_long col, k, row ;
+
+ mexPrintf ("dump matrix: nrow %d ncol %d Alen %d\n", n_row, n_col, Alen) ;
+
+ if (!A)
+ {
+ mexPrintf ("A not present\n") ;
+ return ;
+ }
+
+ if (!p)
+ {
+ mexPrintf ("p not present\n") ;
+ return ;
+ }
+
+ for (col = 0 ; col < MIN (n_col, limit) ; col++)
+ {
+ mexPrintf ("column %d, p[col] %d, p [col+1] %d, length %d\n",
+ col, p [col], p [col+1], p [col+1] - p [col]) ;
+ for (k = p [col] ; k < p [col+1] ; k++)
+ {
+ row = A [k] ;
+ mexPrintf (" %d", row) ;
+ }
+ mexPrintf ("\n") ;
+ }
+}
+
+/* ========================================================================== */
+/* === csymamd mexFunction ================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nargout, /* number of left-hand sides */
+ mxArray *pargout [ ], /* left-hand side matrices */
+ int nargin, /* number of right--hand sides */
+ const mxArray *pargin [ ] /* right-hand side matrices */
+)
+{
+ /* === Local variables ================================================== */
+
+ UF_long *perm ; /* column ordering of M and ordering of A */
+ UF_long *A ; /* row indices of input matrix A */
+ UF_long *p ; /* column pointers of input matrix A */
+ UF_long n_col ; /* number of columns of A */
+ UF_long n_row ; /* number of rows of A */
+ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [CCOLAMD_KNOBS] ; /* ccolamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ UF_long i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ UF_long spumoni ; /* verbosity variable */
+ UF_long stats2 [CCOLAMD_STATS] ;/* stats for csymamd */
+
+ UF_long *cp, *cp_end, result, nnz, col, length, ok ;
+ UF_long *stats ;
+ stats = stats2 ;
+
+ /* === Check inputs ===================================================== */
+
+ if (nargin != 3 || nargout > 2)
+ {
+ mexErrMsgTxt (
+ "csymamdtest: incorrect number of input and/or output arguments.") ;
+ }
+ /* for testing we require all 4 knobs */
+ if (mxGetNumberOfElements (pargin [1]) != 4)
+ {
+ mexErrMsgTxt ("csymamdtest: must have 4 knobs for testing") ;
+ }
+
+ /* === Get knobs ======================================================== */
+
+ ccolamd_l_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ in_knobs = mxGetPr (pargin [1]) ;
+
+ i = mxGetNumberOfElements (pargin [1]) ;
+ knobs [CCOLAMD_DENSE_ROW] = in_knobs [0] ;
+ knobs [CCOLAMD_DENSE_COL] = in_knobs [0] ;
+ knobs [CCOLAMD_AGGRESSIVE] = (in_knobs [1] != 0) ;
+ spumoni = (in_knobs [2] != 0) ;
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\ncsymamd version %d.%d, %s:\n",
+ CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE) ;
+ if (knobs [CCOLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(1): %g, rows/cols with > "
+ "max(16,%g*sqrt(size(A,2))) entries removed\n",
+ in_knobs [0], knobs [CCOLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(1): %g, no dense rows removed\n",
+ in_knobs [0]) ;
+ }
+ mexPrintf ("knobs(2): %g, aggressive absorption: %s\n",
+ in_knobs [1], (knobs [CCOLAMD_AGGRESSIVE] != 0) ? "yes" : "no") ;
+ mexPrintf ("knobs(3): %g, statistics and knobs printed\n",
+ in_knobs [2]) ;
+ mexPrintf ("Testing: %g\n", in_knobs [3]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) pargin [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("csymamd: input matrix must be 2-dimensional.") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) pargin, "sparse") ;
+ }
+
+ /* === Allocate workspace for csymamd =================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+ if (n_col != n_row)
+ {
+ mexErrMsgTxt ("csymamd: matrix must be square.") ;
+ }
+
+ /* p = mxGetJc (Ainput) ; */
+ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ;
+ (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ;
+
+ nnz = p [n_col] ;
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: nnz %d\n", nnz) ;
+ }
+
+ /* A = mxGetIr (Ainput) ; */
+ A = (UF_long *) mxCalloc (nnz+1, sizeof (UF_long)) ;
+ (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ;
+
+ perm = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ;
+
+ /* === Jumble matrix ==================================================== */
+
+
+ /*
+ knobs [4] FOR TESTING ONLY: Specifies how to jumble matrix
+ 0 : No jumbling
+ 1 : (no errors)
+ 2 : Make first pointer non-zero
+ 3 : Make column pointers not non-decreasing
+ 4 : (no errors)
+ 5 : Make row indices not strictly increasing
+ 6 : Make a row index greater or equal to n_row
+ 7 : Set A = NULL
+ 8 : Set p = NULL
+ 9 : Repeat row index
+ 10: make row indices not sorted
+ 11: jumble columns massively (note this changes
+ the pattern of the matrix A.)
+ 12: Set stats = NULL
+ 13: Make n_col less than zero
+ */
+
+ /* jumble appropriately */
+ switch ((UF_long) in_knobs [3])
+ {
+
+ case 0 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: no errors expected\n") ;
+ }
+ result = 1 ; /* no errors */
+ break ;
+
+ case 1 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: no errors expected (1)\n") ;
+ }
+ result = 1 ;
+ break ;
+
+ case 2 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: p [0] nonzero\n") ;
+ }
+ result = 0 ; /* p [0] must be zero */
+ p [0] = 1 ;
+ break ;
+
+ case 3 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: negative length last column\n") ;
+ }
+ result = (n_col == 0) ; /* p must be monotonically inc. */
+ p [n_col] = p [0] ;
+ break ;
+
+ case 4 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: no errors expected (4)\n") ;
+ }
+ result = 1 ;
+ break ;
+
+ case 5 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: row index out of range (-1)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ result = 0 ;
+ A [nnz-1] = -1 ;
+ }
+ else
+ {
+ if (spumoni)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 6 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: row index out of range (ncol)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ result = 0 ;
+ A [nnz-1] = n_col ;
+ }
+ else
+ {
+ if (spumoni)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 7 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: A not present\n") ;
+ }
+ result = 0 ; /* A not present */
+ A = (UF_long *) NULL ;
+ break ;
+
+ case 8 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: p not present\n") ;
+ }
+ result = 0 ; /* p not present */
+ p = (UF_long *) NULL ;
+ break ;
+
+ case 9 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: duplicate row index\n") ;
+ }
+ result = 1 ; /* duplicate row index */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ A [p [col+1]-2] = A [p [col+1] - 1] ;
+ if (spumoni)
+ {
+ mexPrintf ("Made duplicate row %d in col %d\n",
+ A [p [col+1] - 1], col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, nnz, col+2) ;
+ }
+ break ;
+
+ case 10 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: unsorted column\n") ;
+ }
+ result = 1 ; /* jumbled columns */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ i = A[p [col]] ;
+ A [p [col]] = A[p [col] + 1] ;
+ A [p [col] + 1] = i ;
+ if (spumoni)
+ {
+ mexPrintf ("Unsorted column %d \n", col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, nnz, col+2) ;
+ }
+ break ;
+
+ case 11 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: massive jumbling\n") ;
+ }
+ result = 1 ; /* massive jumbling, but no errors */
+ srand (1) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ cp = &A [p [i]] ;
+ cp_end = &A [p [i+1]] ;
+ while (cp < cp_end)
+ {
+ *cp++ = rand() % n_row ;
+ }
+ }
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, nnz, n_col) ;
+ }
+ break ;
+
+ case 12 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: stats not present\n") ;
+ }
+ result = 0 ; /* stats not present */
+ stats = (UF_long *) NULL ;
+ break ;
+
+ case 13 :
+ if (spumoni)
+ {
+ mexPrintf ("csymamdtest: ncol out of range\n") ;
+ }
+ result = 0 ; /* ncol out of range */
+ n_col = -1 ;
+ break ;
+
+ }
+
+ /* === Order the rows and columns of A (does not destroy A) ============= */
+
+ ok = csymamd_l (n_col, A, p, perm, knobs, stats, &mxCalloc, &mxFree,
+ NULL, -1) ;
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+ if (spumoni)
+ {
+ csymamd_l_report (stats) ;
+ }
+
+ /* === Return the stats vector ========================================== */
+
+ if (nargout == 2)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, CCOLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (pargout [1]) ;
+ for (i = 0 ; i < CCOLAMD_STATS ; i++)
+ {
+ out_stats [i] = (stats == NULL) ? (-1) : (stats [i]) ;
+ }
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if csymamd returns FALSE */
+ out_stats [CCOLAMD_INFO1] ++ ;
+ out_stats [CCOLAMD_INFO2] ++ ;
+ }
+
+ mxFree (A) ;
+
+ if (ok)
+ {
+
+ /* === Return the permutation vector ================================ */
+
+ pargout [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* csymamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = perm [i] + 1 ;
+ }
+ if (!result)
+ {
+ csymamd_l_report (stats) ;
+ mexErrMsgTxt ("csymamd should have returned TRUE\n") ;
+ }
+ }
+ else
+ {
+
+ /* return p = -1 if csymamd failed */
+ pargout [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ out_perm = mxGetPr (pargout [0]) ;
+ out_perm [0] = -1 ;
+ if (result)
+ {
+ csymamd_l_report (stats) ;
+ mexErrMsgTxt ("csymamd should have returned FALSE\n") ;
+ }
+ }
+
+ mxFree (p) ;
+ mxFree (perm) ;
+}
diff --git a/CCOLAMD/MATLAB/csymamdtestmex.m b/CCOLAMD/MATLAB/csymamdtestmex.m
new file mode 100644
index 0000000..4510e6e
--- /dev/null
+++ b/CCOLAMD/MATLAB/csymamdtestmex.m
@@ -0,0 +1,10 @@
+function [P, stats] = csymamdtestmex (A, knobs) %#ok
+% CSYMAMDTESTMEX test function for csymamd
+% Example:
+% [ P, stats ] = csymamdtest (A, knobs) ;
+% See also csymamd
+
+% Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+error ('csymamdtestmex mexFunction not found') ;
diff --git a/CCOLAMD/MATLAB/luflops.m b/CCOLAMD/MATLAB/luflops.m
new file mode 100644
index 0000000..1ed7f30
--- /dev/null
+++ b/CCOLAMD/MATLAB/luflops.m
@@ -0,0 +1,33 @@
+function fl = luflops (L, U)
+%LUFLOPS compute the flop count for sparse LU factorization
+%
+% Example:
+% fl = luflops (L,U)
+%
+% Given a sparse LU factorization (L and U), return the flop count required
+% by a conventional LU factorization algorithm to compute it. L and U can
+% be either sparse or full matrices. L must be lower triangular and U must
+% be upper triangular. Do not attempt to use this on the permuted L from
+% [L,U] = lu (A). Instead, use [L,U,P] = lu (A) or [L,U,P,Q] = lu (A).
+%
+% Note that there is a subtle undercount in this estimate. Suppose A is
+% completely dense, but during LU factorization exact cancellation occurs,
+% causing some of the entries in L and U to become identically zero. The
+% flop count returned by this routine is an undercount. There is a simple
+% way to fix this (L = spones (L) + spones (tril (A))), but the fix is partial.
+% It can also occur that some entry in L is a "symbolic" fill-in (zero in
+% A, but a fill-in entry and thus must be computed), but numerically
+% zero. The only way to get a reliable LU factorization would be to do a
+% purely symbolic factorization of A. This cannot be done with
+% symbfact (A, 'col').
+%
+% See NA Digest, Vol 00, #50, Tuesday, Dec. 5, 2000
+%
+% See also symbfact
+
+% Copyright 1998-2007, Timothy A. Davis
+
+Lnz = full (sum (spones (L))) - 1 ; % off diagonal nz in cols of L
+Unz = full (sum (spones (U')))' - 1 ; % off diagonal nz in rows of U
+fl = 2*Lnz*Unz + sum (Lnz) ;
+
diff --git a/CCOLAMD/Makefile b/CCOLAMD/Makefile
new file mode 100644
index 0000000..a79f7eb
--- /dev/null
+++ b/CCOLAMD/Makefile
@@ -0,0 +1,49 @@
+#------------------------------------------------------------------------------
+# CCOLAMD Makefile
+#------------------------------------------------------------------------------
+
+default: demo
+
+include ../UFconfig/UFconfig.mk
+
+# Compile all C code, including the C-callable routine and the mexFunctions.
+# Do not the MATLAB interface.
+demo:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+# Compile all C code, including the C-callable routine and the mexFunctions.
+all:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+ ( cd MATLAB ; $(MAKE) )
+
+# compile just the C-callable libraries (not mexFunctions or Demos)
+library:
+ ( cd Lib ; $(MAKE) )
+
+# remove object files, but keep the compiled programs and library archives
+clean:
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+ ( cd MATLAB ; $(MAKE) clean )
+
+# clean, and then remove compiled programs and library archives
+purge:
+ ( cd Lib ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd MATLAB ; $(MAKE) purge )
+
+distclean: purge
+
+# get ready for distribution
+dist: purge
+ ( cd Demo ; $(MAKE) dist )
+
+ccode: library
+
+lib: library
+
+# compile the MATLAB mexFunction
+mex:
+ ( cd MATLAB ; $(MAKE) )
diff --git a/CCOLAMD/README.txt b/CCOLAMD/README.txt
new file mode 100644
index 0000000..f919208
--- /dev/null
+++ b/CCOLAMD/README.txt
@@ -0,0 +1,150 @@
+CCOLAMD version 2.7: constrained column approximate minimum degree ordering
+Copyright (C) 2005-2007, Univ. of Florida. Authors: Timothy A. Davis,
+Sivasankaran Rajamanickam, and Stefan Larimore. Closely based on COLAMD by
+Davis, Stefan Larimore, in collaboration with Esmond Ng, and John Gilbert.
+http://www.cise.ufl.edu/research/sparse
+-------------------------------------------------------------------------------
+
+The CCOLAMD column approximate minimum degree ordering algorithm computes
+a permutation vector P such that the LU factorization of A (:,P)
+tends to be sparser than that of A. The Cholesky factorization of
+(A (:,P))'*(A (:,P)) will also tend to be sparser than that of A'*A.
+CSYMAMD is a symmetric minimum degree ordering method based on CCOLAMD, also
+available as a MATLAB-callable function. It constructs a matrix M such
+that M'*M has the same pattern as A, and then uses CCOLAMD to compute a column
+ordering of M.
+
+Requires UFconfig, in the ../UFconfig directory relative to this directory.
+
+To compile and install the ccolamd m-files and mexFunctions, just cd to
+CCOLAMD/MATLAB and type ccolamd_install in the MATLAB command window.
+A short demo will run. Optionally, type ccolamd_test to run an extensive tests.
+Type "make" in Unix in the CCOLAMD directory to compile the C-callable
+library and to run a short demo.
+
+If you have MATLAB 7.2 or earlier, you must first edit UFconfig/UFconfig.h to
+remove the "-largeArrayDims" option from the MEX command (or just use
+ccolamd_install.m inside MATLAB).
+
+Other "make" targets:
+
+ make mex compiles MATLAB mexFunctions only
+ make libccolamd.a compiles a C-callable library containing ccolamd
+ make clean removes all files not in the distribution, except for
+ libccolamd.a
+ make distclean removes all files not in the distribution
+
+To use ccolamd and csymamd within an application written in C, all you need are
+ccolamd.c and ccolamd.h, which are the C-callable ccolamd/csymamd codes.
+See ccolamd.c for more information on how to call ccolamd from a C program.
+It contains a complete description of the C-interface to CCOLAMD and CSYMAMD.
+
+ Copyright (c) 1998-2007 by the University of Florida.
+ All Rights Reserved.
+
+ Licensed under the GNU LESSER GENERAL PUBLIC LICENSE.
+
+-------------------------------------------------------------------------------
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+-------------------------------------------------------------------------------
+
+
+Related papers:
+
+ T. A. Davis and W. W. Hager, Rajamanickam, Multiple-rank updates
+ to a supernodal sparse Cholesky factorization, submitted.
+
+ T. A. Davis, W. W. Hager, S. Rajamanickam, and Y. Chen, CHOLMOD: a
+ sparse Cholesky update/downdate package, submitted. CHOLMOD's
+ nested dissection ordering relies on CCOLAMD and CSYMAMD to order
+ the matrix after graph partitioning is used to find the ordering
+ constraints.
+
+ T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate column
+ minimum degree ordering algorithm, ACM Transactions on Mathematical
+ Software, vol. 30, no. 3., pp. 353-376, 2004.
+
+ T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD,
+ an approximate column minimum degree ordering algorithm, ACM
+ Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380,
+ 2004.
+
+ "An approximate minimum degree column ordering algorithm",
+ S. I. Larimore, MS Thesis, Dept. of Computer and Information
+ Science and Engineering, University of Florida, Gainesville, FL,
+ 1998. CISE Tech Report TR-98-016. Available at
+ ftp://ftp.cise.ufl.edu/cis/tech-reports/tr98/tr98-016.ps
+ via anonymous ftp.
+
+ Approximate Deficiency for Ordering the Columns of a Matrix,
+ J. L. Kern, Senior Thesis, Dept. of Computer and Information
+ Science and Engineering, University of Florida, Gainesville, FL,
+ 1999. Available at http://www.cise.ufl.edu/~davis/Kern/kern.ps
+
+Authors: Timothy A. Davis, Sivasankaran Rajamanickam, and Stefan Larimore.
+ Closely based on COLAMD by Stefan I. Larimore and Timothy A. Davis,
+ University of Florida, in collaboration with John Gilbert, Xerox PARC
+ (now at UC Santa Barbara), and Esmong Ng, Lawrence Berkeley National
+ Laboratory (much of this work he did while at Oak Ridge National
+ Laboratory).
+
+CCOLAMD files:
+
+ Demo simple demo
+ Doc additional documentation (see ccolamd.c for more)
+ Include include file
+ Lib compiled C-callable library
+ Makefile primary Unix Makefile
+ MATLAB MATLAB functions
+ README.txt this file
+ Source C source code
+
+ ./Demo:
+ ccolamd_example.c simple example
+ ccolamd_example.out output of colamd_example.c
+ ccolamd_l_example.c simple example, long integers
+ ccolamd_l_example.out output of colamd_l_example.c
+ Makefile Makefile for C demos
+
+ ./Doc:
+ ChangeLog change log
+ lesser.txt license
+
+ ./Include:
+ ccolamd.h include file
+
+ ./Lib:
+ Makefile Makefile for C-callable library
+
+ ./MATLAB:
+ ccolamd.m MATLAB interface for ccolamd
+ ccolamd_demo.m simple demo
+ ccolamd_install.m compile and install ccolamd and csymamd
+ ccolamd_make.m compile colamd2 and symamd2
+ ccolamdmex.c MATLAB mexFunction for ccolamd
+ ccolamd_test.m extensive test
+ ccolamdtestmex.c test function for ccolamd
+ Contents.m contents of the MATLAB directory
+ luflops.m test code
+ Makefile Makefile for MATLAB functions
+ csymamd.m MATLAB interface for csymamd
+ csymamdmex.c MATLAB mexFunction for csymamd
+ symamdtestmex.c test function for csymamd
+
+ ./Source:
+ ccolamd.c primary source code
+ ccolamd_global.c globally defined function pointers (malloc, free, ...)
diff --git a/CCOLAMD/Source/ccolamd.c b/CCOLAMD/Source/ccolamd.c
new file mode 100644
index 0000000..9247471
--- /dev/null
+++ b/CCOLAMD/Source/ccolamd.c
@@ -0,0 +1,4620 @@
+/* ========================================================================== */
+/* === CCOLAMD/CSYMAMD - a constrained column ordering algorithm ============ */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * CCOLAMD, Copyright (C) Univ. of Florida. Authors: Timothy A. Davis,
+ * Sivasankaran Rajamanickam, and Stefan Larimore
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/*
+ * ccolamd: a constrained approximate minimum degree column ordering
+ * algorithm, LU factorization of symmetric or unsymmetric matrices,
+ * QR factorization, least squares, interior point methods for
+ * linear programming problems, and other related problems.
+ *
+ * csymamd: a constrained approximate minimum degree ordering algorithm for
+ * Cholesky factorization of symmetric matrices.
+ *
+ * Purpose:
+ *
+ * CCOLAMD computes a permutation Q such that the Cholesky factorization of
+ * (AQ)'(AQ) has less fill-in and requires fewer floating point operations
+ * than A'A. This also provides a good ordering for sparse partial
+ * pivoting methods, P(AQ) = LU, where Q is computed prior to numerical
+ * factorization, and P is computed during numerical factorization via
+ * conventional partial pivoting with row interchanges. CCOLAMD is an
+ * extension of COLAMD, available as built-in function in MATLAB Version 6,
+ * available from MathWorks, Inc. (http://www.mathworks.com). This
+ * routine can be used in place of COLAMD in MATLAB.
+ *
+ * CSYMAMD computes a permutation P of a symmetric matrix A such that the
+ * Cholesky factorization of PAP' has less fill-in and requires fewer
+ * floating point operations than A. CSYMAMD constructs a matrix M such
+ * that M'M has the same nonzero pattern of A, and then orders the columns
+ * of M using colmmd. The column ordering of M is then returned as the
+ * row and column ordering P of A. CSYMAMD is an extension of SYMAMD.
+ *
+ * Authors:
+ *
+ * Timothy A. Davis and S. Rajamanickam wrote CCOLAMD, based directly on
+ * COLAMD by Stefan I. Larimore and Timothy A. Davis, University of
+ * Florida. The algorithm was developed in collaboration with John
+ * Gilbert, (UCSB, then at Xerox PARC), and Esmond Ng, (Lawrence Berkeley
+ * National Lab, then at Oak Ridge National Laboratory).
+ *
+ * Acknowledgements:
+ *
+ * This work was supported by the National Science Foundation, under
+ * grants DMS-9504974 and DMS-9803599, CCR-0203270, and a grant from the
+ * Sandia National Laboratory (Dept. of Energy).
+ *
+ * Copyright and License:
+ *
+ * Copyright (c) 1998-2005 by the University of Florida.
+ * All Rights Reserved.
+ * COLAMD is also available under alternate licenses, contact T. Davis
+ * for details.
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ * USA
+ *
+ * Permission is hereby granted to use or copy this program under the
+ * terms of the GNU LGPL, provided that the Copyright, this License,
+ * and the Availability of the original version is retained on all copies.
+ * User documentation of any code that uses this code or any modified
+ * version of this code must cite the Copyright, this License, the
+ * Availability note, and "Used by permission." Permission to modify
+ * the code and to distribute modified code is granted, provided the
+ * Copyright, this License, and the Availability note are retained,
+ * and a notice that the code was modified is included.
+ *
+ * Availability:
+ *
+ * The CCOLAMD/CSYMAMD library is available at
+ *
+ * http://www.cise.ufl.edu/research/sparse/ccolamd/
+ *
+ * This is the http://www.cise.ufl.edu/research/sparse/ccolamd/ccolamd.c
+ * file.
+ *
+ * See the ChangeLog file for changes since Version 1.0.
+ */
+
+/* ========================================================================== */
+/* === Description of user-callable routines ================================ */
+/* ========================================================================== */
+
+/* CCOLAMD includes both int and UF_long versions of all its routines. The
+ * description below is for the int version. For UF_long, all int arguments
+ * become UF_long integers. UF_long is normally defined as long, except for
+ * WIN64 */
+
+/* ----------------------------------------------------------------------------
+ * ccolamd_recommended:
+ * ----------------------------------------------------------------------------
+ *
+ * C syntax:
+ *
+ * #include "ccolamd.h"
+ * size_t ccolamd_recommended (int nnz, int n_row, int n_col) ;
+ * size_t ccolamd_l_recommended (UF_long nnz, UF_long n_row,
+ * UF_long n_col) ;
+ *
+ * Purpose:
+ *
+ * Returns recommended value of Alen for use by ccolamd. Returns 0
+ * if any input argument is negative. The use of this routine
+ * is optional. Not needed for csymamd, which dynamically allocates
+ * its own memory.
+ *
+ * Arguments (all input arguments):
+ *
+ * int nnz ; Number of nonzeros in the matrix A. This must
+ * be the same value as p [n_col] in the call to
+ * ccolamd - otherwise you will get a wrong value
+ * of the recommended memory to use.
+ *
+ * int n_row ; Number of rows in the matrix A.
+ *
+ * int n_col ; Number of columns in the matrix A.
+ *
+ * ----------------------------------------------------------------------------
+ * ccolamd_set_defaults:
+ * ----------------------------------------------------------------------------
+ *
+ * C syntax:
+ *
+ * #include "ccolamd.h"
+ * ccolamd_set_defaults (double knobs [CCOLAMD_KNOBS]) ;
+ * ccolamd_l_set_defaults (double knobs [CCOLAMD_KNOBS]) ;
+ *
+ * Purpose:
+ *
+ * Sets the default parameters. The use of this routine is optional.
+ * Passing a (double *) NULL pointer for the knobs results in the
+ * default parameter settings.
+ *
+ * Arguments:
+ *
+ * double knobs [CCOLAMD_KNOBS] ; Output only.
+ *
+ * knobs [0] and knobs [1] behave differently than they did in COLAMD.
+ * The other knobs are new to CCOLAMD.
+ *
+ * knobs [0]: dense row control
+ *
+ * For CCOLAMD, rows with more than
+ * max (16, knobs [CCOLAMD_DENSE_ROW] * sqrt (n_col))
+ * entries are removed prior to ordering.
+ *
+ * For CSYMAMD, rows and columns with more than
+ * max (16, knobs [CCOLAMD_DENSE_ROW] * sqrt (n))
+ * entries are removed prior to ordering, and placed last in the
+ * output ordering (subject to the constraints).
+ *
+ * If negative, only completely dense rows are removed. If you
+ * intend to use CCOLAMD for a Cholesky factorization of A*A', set
+ * knobs [CCOLAMD_DENSE_ROW] to -1, which is more appropriate for
+ * that case.
+ *
+ * Default: 10.
+ *
+ * knobs [1]: dense column control
+ *
+ * For CCOLAMD, columns with more than
+ * max (16, knobs [CCOLAMD_DENSE_COL] * sqrt (MIN (n_row,n_col)))
+ * entries are removed prior to ordering, and placed last in the
+ * output column ordering (subject to the constraints).
+ * Not used by CSYMAMD. If negative, only completely dense
+ * columns are removed. Default: 10.
+ *
+ * knobs [2]: aggressive absorption
+ *
+ * knobs [CCOLAMD_AGGRESSIVE] controls whether or not to do
+ * aggressive absorption during the ordering. Default is TRUE
+ * (nonzero). If zero, no aggressive absorption is performed.
+ *
+ * knobs [3]: optimize ordering for LU or Cholesky
+ *
+ * knobs [CCOLAMD_LU] controls an option that optimizes the
+ * ordering for the LU of A or the Cholesky factorization of A'A.
+ * If TRUE (nonzero), an ordering optimized for LU is performed.
+ * If FALSE (zero), an ordering for Cholesky is performed.
+ * Default is FALSE. CSYMAMD ignores this parameter; it always
+ * orders for Cholesky.
+ *
+ * ----------------------------------------------------------------------------
+ * ccolamd:
+ * ----------------------------------------------------------------------------
+ *
+ * C syntax:
+ *
+ * #include "ccolamd.h"
+ * int ccolamd (int n_row, int n_col, int Alen, int *A, int *p,
+ * double knobs [CCOLAMD_KNOBS], int stats [CCOLAMD_STATS],
+ * int *cmember) ;
+ *
+ * UF_long ccolamd_l (UF_long n_row, UF_long n_col, UF_long Alen,
+ * UF_long *A, UF_long *p, double knobs [CCOLAMD_KNOBS],
+ * UF_long stats [CCOLAMD_STATS], UF_long *cmember) ;
+ *
+ * Purpose:
+ *
+ * Computes a column ordering (Q) of A such that P(AQ)=LU or
+ * (AQ)'AQ=LL' have less fill-in and require fewer floating point
+ * operations than factorizing the unpermuted matrix A or A'A,
+ * respectively.
+ *
+ * Returns:
+ *
+ * TRUE (1) if successful, FALSE (0) otherwise.
+ *
+ * Arguments (for int version):
+ *
+ * int n_row ; Input argument.
+ *
+ * Number of rows in the matrix A.
+ * Restriction: n_row >= 0.
+ * ccolamd returns FALSE if n_row is negative.
+ *
+ * int n_col ; Input argument.
+ *
+ * Number of columns in the matrix A.
+ * Restriction: n_col >= 0.
+ * ccolamd returns FALSE if n_col is negative.
+ *
+ * int Alen ; Input argument.
+ *
+ * Restriction (see note):
+ * Alen >= MAX (2*nnz, 4*n_col) + 17*n_col + 7*n_row + 7, where
+ * nnz = p [n_col]. ccolamd returns FALSE if this condition is
+ * not met. We recommend about nnz/5 more space for better
+ * efficiency. This restriction makes an modest assumption
+ * regarding the size of two typedef'd structures in ccolamd.h.
+ * We do, however, guarantee that
+ *
+ * Alen >= ccolamd_recommended (nnz, n_row, n_col)
+ *
+ * will work efficiently.
+ *
+ * int A [Alen] ; Input argument, undefined on output.
+ *
+ * A is an integer array of size Alen. Alen must be at least as
+ * large as the bare minimum value given above, but this is very
+ * low, and can result in excessive run time. For best
+ * performance, we recommend that Alen be greater than or equal to
+ * ccolamd_recommended (nnz, n_row, n_col), which adds
+ * nnz/5 to the bare minimum value given above.
+ *
+ * On input, the row indices of the entries in column c of the
+ * matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices
+ * in a given column c need not be in ascending order, and
+ * duplicate row indices may be be present. However, ccolamd will
+ * work a little faster if both of these conditions are met
+ * (ccolamd puts the matrix into this format, if it finds that the
+ * the conditions are not met).
+ *
+ * The matrix is 0-based. That is, rows are in the range 0 to
+ * n_row-1, and columns are in the range 0 to n_col-1. ccolamd
+ * returns FALSE if any row index is out of range.
+ *
+ * The contents of A are modified during ordering, and are
+ * undefined on output.
+ *
+ * int p [n_col+1] ; Both input and output argument.
+ *
+ * p is an integer array of size n_col+1. On input, it holds the
+ * "pointers" for the column form of the matrix A. Column c of
+ * the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first
+ * entry, p [0], must be zero, and p [c] <= p [c+1] must hold
+ * for all c in the range 0 to n_col-1. The value nnz = p [n_col]
+ * is thus the total number of entries in the pattern of the
+ * matrix A. ccolamd returns FALSE if these conditions are not
+ * met.
+ *
+ * On output, if ccolamd returns TRUE, the array p holds the column
+ * permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is
+ * the first column index in the new ordering, and p [n_col-1] is
+ * the last. That is, p [k] = j means that column j of A is the
+ * kth pivot column, in AQ, where k is in the range 0 to n_col-1
+ * (p [0] = j means that column j of A is the first column in AQ).
+ *
+ * If ccolamd returns FALSE, then no permutation is returned, and
+ * p is undefined on output.
+ *
+ * double knobs [CCOLAMD_KNOBS] ; Input argument.
+ *
+ * See ccolamd_set_defaults for a description.
+ *
+ * int stats [CCOLAMD_STATS] ; Output argument.
+ *
+ * Statistics on the ordering, and error status.
+ * See ccolamd.h for related definitions.
+ * ccolamd returns FALSE if stats is not present.
+ *
+ * stats [0]: number of dense or empty rows ignored.
+ *
+ * stats [1]: number of dense or empty columns ignored (and
+ * ordered last in the output permutation p, subject to the
+ * constraints). Note that a row can become "empty" if it
+ * contains only "dense" and/or "empty" columns, and similarly
+ * a column can become "empty" if it only contains "dense"
+ * and/or "empty" rows.
+ *
+ * stats [2]: number of garbage collections performed. This can
+ * be excessively high if Alen is close to the minimum
+ * required value.
+ *
+ * stats [3]: status code. < 0 is an error code.
+ * > 1 is a warning or notice.
+ *
+ * 0 OK. Each column of the input matrix contained row
+ * indices in increasing order, with no duplicates.
+ *
+ * 1 OK, but columns of input matrix were jumbled (unsorted
+ * columns or duplicate entries). CCOLAMD had to do some
+ * extra work to sort the matrix first and remove
+ * duplicate entries, but it still was able to return a
+ * valid permutation (return value of ccolamd was TRUE).
+ *
+ * stats [4]: highest column index of jumbled columns
+ * stats [5]: last seen duplicate or unsorted row index
+ * stats [6]: number of duplicate or unsorted row indices
+ *
+ * -1 A is a null pointer
+ *
+ * -2 p is a null pointer
+ *
+ * -3 n_row is negative. stats [4]: n_row
+ *
+ * -4 n_col is negative. stats [4]: n_col
+ *
+ * -5 number of nonzeros in matrix is negative
+ *
+ * stats [4]: number of nonzeros, p [n_col]
+ *
+ * -6 p [0] is nonzero
+ *
+ * stats [4]: p [0]
+ *
+ * -7 A is too small
+ *
+ * stats [4]: required size
+ * stats [5]: actual size (Alen)
+ *
+ * -8 a column has a negative number of entries
+ *
+ * stats [4]: column with < 0 entries
+ * stats [5]: number of entries in col
+ *
+ * -9 a row index is out of bounds
+ *
+ * stats [4]: column with bad row index
+ * stats [5]: bad row index
+ * stats [6]: n_row, # of rows of matrx
+ *
+ * -10 (unused; see csymamd)
+ *
+ * int cmember [n_col] ; Input argument.
+ *
+ * cmember is new to CCOLAMD. It did not appear in COLAMD.
+ * It places contraints on the output ordering. s = cmember [j]
+ * gives the constraint set s that contains the column j
+ * (Restriction: 0 <= s < n_col). In the output column
+ * permutation, all columns in set 0 appear first, followed by
+ * all columns in set 1, and so on. If NULL, all columns are
+ * treated as if they were in a single constraint set, and you
+ * will obtain the same ordering as COLAMD (with one exception:
+ * the dense row/column threshold and other default knobs in
+ * CCOLAMD and COLAMD are different).
+ *
+ * Example:
+ *
+ * See
+ * http://www.cise.ufl.edu/research/sparse/ccolamd/ccolamd_example.c
+ * for a complete example.
+ *
+ * To order the columns of a 5-by-4 matrix with 11 nonzero entries in
+ * the following nonzero pattern
+ *
+ * x 0 x 0
+ * x 0 x x
+ * 0 x x 0
+ * 0 0 x x
+ * x x 0 0
+ *
+ * with default knobs, no output statistics, and no ordering
+ * constraints, do the following:
+ *
+ * #include "ccolamd.h"
+ * #define ALEN 144
+ * int A [ALEN] = {0, 1, 4, 2, 4, 0, 1, 2, 3, 1, 3} ;
+ * int p [ ] = {0, 3, 5, 9, 11} ;
+ * int stats [CCOLAMD_STATS] ;
+ * ccolamd (5, 4, ALEN, A, p, (double *) NULL, stats, NULL) ;
+ *
+ * The permutation is returned in the array p, and A is destroyed.
+ *
+ * ----------------------------------------------------------------------------
+ * csymamd:
+ * ----------------------------------------------------------------------------
+ *
+ * C syntax:
+ *
+ * #include "ccolamd.h"
+ *
+ * int csymamd (int n, int *A, int *p, int *perm,
+ * double knobs [CCOLAMD_KNOBS], int stats [CCOLAMD_STATS],
+ * void (*allocate) (size_t, size_t), void (*release) (void *),
+ * int *cmember, int stype) ;
+ *
+ * UF_long csymamd_l (UF_long n, UF_long *A, UF_long *p, UF_long *perm,
+ * double knobs [CCOLAMD_KNOBS], UF_long stats [CCOLAMD_STATS],
+ * void (*allocate) (size_t, size_t), void (*release) (void *),
+ * UF_long *cmember, UF_long stype) ;
+ *
+ * Purpose:
+ *
+ * The csymamd routine computes an ordering P of a symmetric sparse
+ * matrix A such that the Cholesky factorization PAP' = LL' remains
+ * sparse. It is based on a column ordering of a matrix M constructed
+ * so that the nonzero pattern of M'M is the same as A. Either the
+ * lower or upper triangular part of A can be used, or the pattern
+ * A+A' can be used. You must pass your selected memory allocator
+ * (usually calloc/free or mxCalloc/mxFree) to csymamd, for it to
+ * allocate memory for the temporary matrix M.
+ *
+ * Returns:
+ *
+ * TRUE (1) if successful, FALSE (0) otherwise.
+ *
+ * Arguments:
+ *
+ * int n ; Input argument.
+ *
+ * Number of rows and columns in the symmetrix matrix A.
+ * Restriction: n >= 0.
+ * csymamd returns FALSE if n is negative.
+ *
+ * int A [nnz] ; Input argument.
+ *
+ * A is an integer array of size nnz, where nnz = p [n].
+ *
+ * The row indices of the entries in column c of the matrix are
+ * held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a
+ * given column c need not be in ascending order, and duplicate
+ * row indices may be present. However, csymamd will run faster
+ * if the columns are in sorted order with no duplicate entries.
+ *
+ * The matrix is 0-based. That is, rows are in the range 0 to
+ * n-1, and columns are in the range 0 to n-1. csymamd
+ * returns FALSE if any row index is out of range.
+ *
+ * The contents of A are not modified.
+ *
+ * int p [n+1] ; Input argument.
+ *
+ * p is an integer array of size n+1. On input, it holds the
+ * "pointers" for the column form of the matrix A. Column c of
+ * the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first
+ * entry, p [0], must be zero, and p [c] <= p [c+1] must hold
+ * for all c in the range 0 to n-1. The value p [n] is
+ * thus the total number of entries in the pattern of the matrix A.
+ * csymamd returns FALSE if these conditions are not met.
+ *
+ * The contents of p are not modified.
+ *
+ * int perm [n+1] ; Output argument.
+ *
+ * On output, if csymamd returns TRUE, the array perm holds the
+ * permutation P, where perm [0] is the first index in the new
+ * ordering, and perm [n-1] is the last. That is, perm [k] = j
+ * means that row and column j of A is the kth column in PAP',
+ * where k is in the range 0 to n-1 (perm [0] = j means
+ * that row and column j of A are the first row and column in
+ * PAP'). The array is used as a workspace during the ordering,
+ * which is why it must be of length n+1, not just n.
+ *
+ * double knobs [CCOLAMD_KNOBS] ; Input argument.
+ *
+ * See colamd_set_defaults for a description.
+ *
+ * int stats [CCOLAMD_STATS] ; Output argument.
+ *
+ * Statistics on the ordering, and error status.
+ * See ccolamd.h for related definitions.
+ * csymand returns FALSE if stats is not present.
+ *
+ * stats [0]: number of dense or empty row and columns ignored
+ * (and ordered last in the output permutation perm, subject
+ * to the constraints). Note that a row/column can become
+ * "empty" if it contains only "dense" and/or "empty"
+ * columns/rows.
+ *
+ * stats [1]: (same as stats [0])
+ *
+ * stats [2]: number of garbage collections performed.
+ *
+ * stats [3]: status code. < 0 is an error code.
+ * > 1 is a warning or notice.
+ *
+ * 0 to -9: same as ccolamd, with n replacing n_col and n_row,
+ * and -3 and -7 are unused.
+ *
+ * -10 out of memory (unable to allocate temporary workspace
+ * for M or count arrays using the "allocate" routine
+ * passed into csymamd).
+ *
+ * void * (*allocate) (size_t, size_t)
+ *
+ * A pointer to a function providing memory allocation. The
+ * allocated memory must be returned initialized to zero. For a
+ * C application, this argument should normally be a pointer to
+ * calloc. For a MATLAB mexFunction, the routine mxCalloc is
+ * passed instead.
+ *
+ * void (*release) (size_t, size_t)
+ *
+ * A pointer to a function that frees memory allocated by the
+ * memory allocation routine above. For a C application, this
+ * argument should normally be a pointer to free. For a MATLAB
+ * mexFunction, the routine mxFree is passed instead.
+ *
+ * int cmember [n] ; Input argument.
+ *
+ * Same as ccolamd, except that cmember is of size n, and it places
+ * contraints symmetrically, on both the row and column ordering.
+ * Entries in cmember must be in the range 0 to n-1.
+ *
+ * int stype ; Input argument.
+ *
+ * If stype < 0, then only the strictly lower triangular part of
+ * A is accessed. The upper triangular part is assumed to be the
+ * transpose of the lower triangular part. This is the same as
+ * SYMAMD, which did not have an stype parameter.
+ *
+ * If stype > 0, only the strictly upper triangular part of A is
+ * accessed. The lower triangular part is assumed to be the
+ * transpose of the upper triangular part.
+ *
+ * If stype == 0, then the nonzero pattern of A+A' is ordered.
+ *
+ * ----------------------------------------------------------------------------
+ * ccolamd_report:
+ * ----------------------------------------------------------------------------
+ *
+ * C syntax:
+ *
+ * #include "ccolamd.h"
+ * ccolamd_report (int stats [CCOLAMD_STATS]) ;
+ * ccolamd_l_report (UF_long stats [CCOLAMD_STATS]) ;
+ *
+ * Purpose:
+ *
+ * Prints the error status and statistics recorded in the stats
+ * array on the standard error output (for a standard C routine)
+ * or on the MATLAB output (for a mexFunction).
+ *
+ * Arguments:
+ *
+ * int stats [CCOLAMD_STATS] ; Input only. Statistics from ccolamd.
+ *
+ *
+ * ----------------------------------------------------------------------------
+ * csymamd_report:
+ * ----------------------------------------------------------------------------
+ *
+ * C syntax:
+ *
+ * #include "ccolamd.h"
+ * csymamd_report (int stats [CCOLAMD_STATS]) ;
+ * csymamd_l_report (UF_long stats [CCOLAMD_STATS]) ;
+ *
+ * Purpose:
+ *
+ * Prints the error status and statistics recorded in the stats
+ * array on the standard error output (for a standard C routine)
+ * or on the MATLAB output (for a mexFunction).
+ *
+ * Arguments:
+ *
+ * int stats [CCOLAMD_STATS] ; Input only. Statistics from csymamd.
+ *
+ */
+
+
+/* ========================================================================== */
+/* === Scaffolding code definitions ======================================== */
+/* ========================================================================== */
+
+/* Ensure that debugging is turned off: */
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+
+/* turn on debugging by uncommenting the following line
+ #undef NDEBUG
+ */
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "ccolamd.h"
+
+#include <stdlib.h>
+#include <math.h>
+#include <limits.h>
+
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#include "matrix.h"
+#endif
+
+#if !defined (NPRINT) || !defined (NDEBUG)
+#include <stdio.h>
+#endif
+
+#ifndef NULL
+#define NULL ((void *) 0)
+#endif
+
+/* ========================================================================== */
+/* === int or UF_long ======================================================= */
+/* ========================================================================== */
+
+/* define UF_long */
+#include "UFconfig.h"
+
+#ifdef DLONG
+
+#define Int UF_long
+#define ID UF_long_id
+#define Int_MAX UF_long_max
+
+#define CCOLAMD_recommended ccolamd_l_recommended
+#define CCOLAMD_set_defaults ccolamd_l_set_defaults
+#define CCOLAMD_2 ccolamd2_l
+#define CCOLAMD_MAIN ccolamd_l
+#define CCOLAMD_apply_order ccolamd_l_apply_order
+#define CCOLAMD_postorder ccolamd_l_postorder
+#define CCOLAMD_post_tree ccolamd_l_post_tree
+#define CCOLAMD_fsize ccolamd_l_fsize
+#define CSYMAMD_MAIN csymamd_l
+#define CCOLAMD_report ccolamd_l_report
+#define CSYMAMD_report csymamd_l_report
+
+#else
+
+#define Int int
+#define ID "%d"
+#define Int_MAX INT_MAX
+
+#define CCOLAMD_recommended ccolamd_recommended
+#define CCOLAMD_set_defaults ccolamd_set_defaults
+#define CCOLAMD_2 ccolamd2
+#define CCOLAMD_MAIN ccolamd
+#define CCOLAMD_apply_order ccolamd_apply_order
+#define CCOLAMD_postorder ccolamd_postorder
+#define CCOLAMD_post_tree ccolamd_post_tree
+#define CCOLAMD_fsize ccolamd_fsize
+#define CSYMAMD_MAIN csymamd
+#define CCOLAMD_report ccolamd_report
+#define CSYMAMD_report csymamd_report
+
+#endif
+
+/* ========================================================================== */
+/* === Row and Column structures ============================================ */
+/* ========================================================================== */
+
+typedef struct CColamd_Col_struct
+{
+ /* size of this struct is 8 integers if no padding occurs */
+
+ Int start ; /* index for A of first row in this column, or DEAD */
+ /* if column is dead */
+ Int length ; /* number of rows in this column */
+ union
+ {
+ Int thickness ; /* number of original columns represented by this */
+ /* col, if the column is alive */
+ Int parent ; /* parent in parent tree super-column structure, if */
+ /* the column is dead */
+ } shared1 ;
+ union
+ {
+ Int score ;
+ Int order ;
+ } shared2 ;
+ union
+ {
+ Int headhash ; /* head of a hash bucket, if col is at the head of */
+ /* a degree list */
+ Int hash ; /* hash value, if col is not in a degree list */
+ Int prev ; /* previous column in degree list, if col is in a */
+ /* degree list (but not at the head of a degree list) */
+ } shared3 ;
+ union
+ {
+ Int degree_next ; /* next column, if col is in a degree list */
+ Int hash_next ; /* next column, if col is in a hash list */
+ } shared4 ;
+
+ Int nextcol ; /* next column in this supercolumn */
+ Int lastcol ; /* last column in this supercolumn */
+
+} CColamd_Col ;
+
+
+typedef struct CColamd_Row_struct
+{
+ /* size of this struct is 6 integers if no padding occurs */
+
+ Int start ; /* index for A of first col in this row */
+ Int length ; /* number of principal columns in this row */
+ union
+ {
+ Int degree ; /* number of principal & non-principal columns in row */
+ Int p ; /* used as a row pointer in init_rows_cols () */
+ } shared1 ;
+ union
+ {
+ Int mark ; /* for computing set differences and marking dead rows*/
+ Int first_column ;/* first column in row (used in garbage collection) */
+ } shared2 ;
+
+ Int thickness ; /* number of original rows represented by this row */
+ /* that are not yet pivotal */
+ Int front ; /* -1 if an original row */
+ /* k if this row represents the kth frontal matrix */
+ /* where k goes from 0 to at most n_col-1 */
+
+} CColamd_Row ;
+
+/* ========================================================================== */
+/* === basic definitions ==================================================== */
+/* ========================================================================== */
+
+#define EMPTY (-1)
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+/* Routines are either PUBLIC (user-callable) or PRIVATE (not user-callable) */
+#define GLOBAL
+#define PUBLIC
+#define PRIVATE static
+
+#define DENSE_DEGREE(alpha,n) \
+ ((Int) MAX (16.0, (alpha) * sqrt ((double) (n))))
+
+#define CMEMBER(c) ((cmember == (Int *) NULL) ? (0) : (cmember [c]))
+
+/* True if x is NaN */
+#define SCALAR_IS_NAN(x) ((x) != (x))
+
+/* true if an integer (stored in double x) would overflow (or if x is NaN) */
+#define INT_OVERFLOW(x) ((!((x) * (1.0+1e-8) <= (double) Int_MAX)) \
+ || SCALAR_IS_NAN (x))
+
+#define ONES_COMPLEMENT(r) (-(r)-1)
+#undef TRUE
+#undef FALSE
+#define TRUE (1)
+#define FALSE (0)
+
+/* Row and column status */
+#define ALIVE (0)
+#define DEAD (-1)
+
+/* Column status */
+#define DEAD_PRINCIPAL (-1)
+#define DEAD_NON_PRINCIPAL (-2)
+
+/* Macros for row and column status update and checking. */
+#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark)
+#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE)
+#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE)
+#define COL_IS_DEAD(c) (Col [c].start < ALIVE)
+#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE)
+#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL)
+#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; }
+#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; }
+#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }
+
+
+/* ========================================================================== */
+/* === ccolamd reporting mechanism ========================================== */
+/* ========================================================================== */
+
+#if defined (MATLAB_MEX_FILE) || defined (MATHWORKS)
+/* In MATLAB, matrices are 1-based to the user, but 0-based internally */
+#define INDEX(i) ((i)+1)
+#else
+/* In C, matrices are 0-based and indices are reported as such in *_report */
+#define INDEX(i) (i)
+#endif
+
+/* All output goes through the PRINTF macro. */
+#define PRINTF(params) { if (ccolamd_printf != NULL) (void) ccolamd_printf params ; }
+
+
+/* ========================================================================== */
+/* === Debugging prototypes and definitions ================================= */
+/* ========================================================================== */
+
+#ifndef NDEBUG
+
+#include <assert.h>
+
+/* debug print level, present only when debugging */
+PRIVATE Int ccolamd_debug ;
+
+/* debug print statements */
+#define DEBUG0(params) { PRINTF (params) ; }
+#define DEBUG1(params) { if (ccolamd_debug >= 1) PRINTF (params) ; }
+#define DEBUG2(params) { if (ccolamd_debug >= 2) PRINTF (params) ; }
+#define DEBUG3(params) { if (ccolamd_debug >= 3) PRINTF (params) ; }
+#define DEBUG4(params) { if (ccolamd_debug >= 4) PRINTF (params) ; }
+
+#ifdef MATLAB_MEX_FILE
+#define ASSERT(expression) (mxAssert ((expression), ""))
+#else
+#define ASSERT(expression) (assert (expression))
+#endif
+
+PRIVATE void ccolamd_get_debug
+(
+ char *method
+) ;
+
+PRIVATE void debug_mark
+(
+ Int n_row,
+ CColamd_Row Row [],
+ Int tag_mark,
+ Int max_mark
+) ;
+
+PRIVATE void debug_matrix
+(
+ Int n_row,
+ Int n_col,
+ CColamd_Row Row [],
+ CColamd_Col Col [],
+ Int A []
+) ;
+
+PRIVATE void debug_structures
+(
+ Int n_row,
+ Int n_col,
+ CColamd_Row Row [],
+ CColamd_Col Col [],
+ Int A [],
+ Int in_cset [],
+ Int cset_start []
+) ;
+
+PRIVATE void dump_super
+(
+ Int super_c,
+ CColamd_Col Col [],
+ Int n_col
+) ;
+
+PRIVATE void debug_deg_lists
+(
+ Int n_row,
+ Int n_col,
+ CColamd_Row Row [ ],
+ CColamd_Col Col [ ],
+ Int head [ ],
+ Int min_score,
+ Int should,
+ Int max_deg
+) ;
+
+#else
+
+/* === No debugging ========================================================= */
+
+#define DEBUG0(params) ;
+#define DEBUG1(params) ;
+#define DEBUG2(params) ;
+#define DEBUG3(params) ;
+#define DEBUG4(params) ;
+
+#define ASSERT(expression)
+
+#endif
+
+/* ========================================================================== */
+/* === Prototypes of PRIVATE routines ======================================= */
+/* ========================================================================== */
+
+PRIVATE Int init_rows_cols
+(
+ Int n_row,
+ Int n_col,
+ CColamd_Row Row [ ],
+ CColamd_Col Col [ ],
+ Int A [ ],
+ Int p [ ],
+ Int stats [CCOLAMD_STATS]
+) ;
+
+PRIVATE void init_scoring
+(
+ Int n_row,
+ Int n_col,
+ CColamd_Row Row [ ],
+ CColamd_Col Col [ ],
+ Int A [ ],
+ Int head [ ],
+ double knobs [CCOLAMD_KNOBS],
+ Int *p_n_row2,
+ Int *p_n_col2,
+ Int *p_max_deg,
+ Int cmember [ ],
+ Int n_cset,
+ Int cset_start [ ],
+ Int dead_cols [ ],
+ Int *p_ndense_row, /* number of dense rows */
+ Int *p_nempty_row, /* number of original empty rows */
+ Int *p_nnewlyempty_row, /* number of newly empty rows */
+ Int *p_ndense_col, /* number of dense cols (excl "empty" cols) */
+ Int *p_nempty_col, /* number of original empty cols */
+ Int *p_nnewlyempty_col /* number of newly empty cols */
+) ;
+
+PRIVATE Int find_ordering
+(
+ Int n_row,
+ Int n_col,
+ Int Alen,
+ CColamd_Row Row [ ],
+ CColamd_Col Col [ ],
+ Int A [ ],
+ Int head [ ],
+#ifndef NDEBUG
+ Int n_col2,
+#endif
+ Int max_deg,
+ Int pfree,
+ Int cset [ ],
+ Int cset_start [ ],
+#ifndef NDEBUG
+ Int n_cset,
+#endif
+ Int cmember [ ],
+ Int Front_npivcol [ ],
+ Int Front_nrows [ ],
+ Int Front_ncols [ ],
+ Int Front_parent [ ],
+ Int Front_cols [ ],
+ Int *p_nfr,
+ Int aggressive,
+ Int InFront [ ],
+ Int order_for_lu
+) ;
+
+PRIVATE void detect_super_cols
+(
+#ifndef NDEBUG
+ Int n_col,
+ CColamd_Row Row [ ],
+#endif
+ CColamd_Col Col [ ],
+ Int A [ ],
+ Int head [ ],
+ Int row_start,
+ Int row_length,
+ Int in_set [ ]
+) ;
+
+PRIVATE Int garbage_collection
+(
+ Int n_row,
+ Int n_col,
+ CColamd_Row Row [ ],
+ CColamd_Col Col [ ],
+ Int A [ ],
+ Int *pfree
+) ;
+
+PRIVATE Int clear_mark
+(
+ Int tag_mark,
+ Int max_mark,
+ Int n_row,
+ CColamd_Row Row [ ]
+) ;
+
+PRIVATE void print_report
+(
+ char *method,
+ Int stats [CCOLAMD_STATS]
+) ;
+
+
+/* ========================================================================== */
+/* === USER-CALLABLE ROUTINES: ============================================== */
+/* ========================================================================== */
+
+
+/* ========================================================================== */
+/* === ccolamd_recommended ================================================== */
+/* ========================================================================== */
+
+/*
+ * The ccolamd_recommended routine returns the suggested size for Alen. This
+ * value has been determined to provide good balance between the number of
+ * garbage collections and the memory requirements for ccolamd. If any
+ * argument is negative, or if integer overflow occurs, a 0 is returned as
+ * an error condition.
+ *
+ * 2*nnz space is required for the row and column indices of the matrix
+ * (or 4*n_col, which ever is larger).
+ *
+ * CCOLAMD_C (n_col) + CCOLAMD_R (n_row) space is required for the Col and Row
+ * arrays, respectively, which are internal to ccolamd. This is equal to
+ * 8*n_col + 6*n_row if the structures are not padded.
+ *
+ * An additional n_col space is the minimal amount of "elbow room",
+ * and nnz/5 more space is recommended for run time efficiency.
+ *
+ * The remaining (((3 * n_col) + 1) + 5 * (n_col + 1) + n_row) space is
+ * for other workspace used in ccolamd which did not appear in colamd.
+ */
+
+/* add two values of type size_t, and check for integer overflow */
+static size_t t_add (size_t a, size_t b, int *ok)
+{
+ (*ok) = (*ok) && ((a + b) >= MAX (a,b)) ;
+ return ((*ok) ? (a + b) : 0) ;
+}
+
+/* compute a*k where k is a small integer, and check for integer overflow */
+static size_t t_mult (size_t a, size_t k, int *ok)
+{
+ size_t i, s = 0 ;
+ for (i = 0 ; i < k ; i++)
+ {
+ s = t_add (s, a, ok) ;
+ }
+ return (s) ;
+}
+
+/* size of the Col and Row structures */
+#define CCOLAMD_C(n_col,ok) \
+ ((t_mult (t_add (n_col, 1, ok), sizeof (CColamd_Col), ok) / sizeof (Int)))
+
+#define CCOLAMD_R(n_row,ok) \
+ ((t_mult (t_add (n_row, 1, ok), sizeof (CColamd_Row), ok) / sizeof (Int)))
+
+/*
+#define CCOLAMD_RECOMMENDED(nnz, n_row, n_col) \
+ MAX (2 * nnz, 4 * n_col) + \
+ CCOLAMD_C (n_col) + CCOLAMD_R (n_row) + n_col + (nnz / 5) \
+ + ((3 * n_col) + 1) + 5 * (n_col + 1) + n_row
+ */
+
+static size_t ccolamd_need (Int nnz, Int n_row, Int n_col, int *ok)
+{
+
+ /* ccolamd_need, compute the following, and check for integer overflow:
+ need = MAX (2*nnz, 4*n_col) + n_col +
+ Col_size + Row_size +
+ (3*n_col+1) + (5*(n_col+1)) + n_row ;
+ */
+ size_t s, c, r, t ;
+
+ /* MAX (2*nnz, 4*n_col) */
+ s = t_mult (nnz, 2, ok) ; /* 2*nnz */
+ t = t_mult (n_col, 4, ok) ; /* 4*n_col */
+ s = MAX (s,t) ;
+
+ s = t_add (s, n_col, ok) ; /* bare minimum elbow room */
+
+ /* Col and Row arrays */
+ c = CCOLAMD_C (n_col, ok) ; /* size of column structures */
+ r = CCOLAMD_R (n_row, ok) ; /* size of row structures */
+ s = t_add (s, c, ok) ;
+ s = t_add (s, r, ok) ;
+
+ c = t_mult (n_col, 3, ok) ; /* 3*n_col + 1 */
+ c = t_add (c, 1, ok) ;
+ s = t_add (s, c, ok) ;
+
+ c = t_add (n_col, 1, ok) ; /* 5 * (n_col + 1) */
+ c = t_mult (c, 5, ok) ;
+ s = t_add (s, c, ok) ;
+
+ s = t_add (s, n_row, ok) ; /* n_row */
+
+ return (ok ? s : 0) ;
+}
+
+PUBLIC size_t CCOLAMD_recommended /* returns recommended value of Alen. */
+(
+ /* === Parameters ======================================================= */
+
+ Int nnz, /* number of nonzeros in A */
+ Int n_row, /* number of rows in A */
+ Int n_col /* number of columns in A */
+)
+{
+ size_t s ;
+ int ok = TRUE ;
+ if (nnz < 0 || n_row < 0 || n_col < 0)
+ {
+ return (0) ;
+ }
+ s = ccolamd_need (nnz, n_row, n_col, &ok) ; /* bare minimum needed */
+ s = t_add (s, nnz/5, &ok) ; /* extra elbow room */
+ ok = ok && (s < Int_MAX) ;
+ return (ok ? s : 0) ;
+}
+
+
+/* ========================================================================== */
+/* === ccolamd_set_defaults ================================================= */
+/* ========================================================================== */
+
+/*
+ * The ccolamd_set_defaults routine sets the default values of the user-
+ * controllable parameters for ccolamd.
+ */
+
+PUBLIC void CCOLAMD_set_defaults
+(
+ /* === Parameters ======================================================= */
+
+ double knobs [CCOLAMD_KNOBS] /* knob array */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ;
+
+ if (!knobs)
+ {
+ return ; /* no knobs to initialize */
+ }
+ for (i = 0 ; i < CCOLAMD_KNOBS ; i++)
+ {
+ knobs [i] = 0 ;
+ }
+ knobs [CCOLAMD_DENSE_ROW] = 10 ;
+ knobs [CCOLAMD_DENSE_COL] = 10 ;
+ knobs [CCOLAMD_AGGRESSIVE] = TRUE ; /* default: do aggressive absorption*/
+ knobs [CCOLAMD_LU] = FALSE ; /* default: order for Cholesky */
+}
+
+
+/* ========================================================================== */
+/* === symamd =============================================================== */
+/* ========================================================================== */
+
+PUBLIC Int CSYMAMD_MAIN /* return TRUE if OK, FALSE otherwise */
+(
+ /* === Parameters ======================================================= */
+
+ Int n, /* number of rows and columns of A */
+ Int A [ ], /* row indices of A */
+ Int p [ ], /* column pointers of A */
+ Int perm [ ], /* output permutation, size n+1 */
+ double knobs [CCOLAMD_KNOBS], /* parameters (uses defaults if NULL) */
+ Int stats [CCOLAMD_STATS], /* output statistics and error codes */
+ void * (*allocate) (size_t, size_t),/* pointer to calloc (ANSI C) or */
+ /* mxCalloc (for MATLAB mexFunction) */
+ void (*release) (void *), /* pointer to free (ANSI C) or */
+ /* mxFree (for MATLAB mexFunction) */
+ Int cmember [ ], /* constraint set */
+ Int stype /* stype of A */
+)
+{
+ /* === Local variables ================================================== */
+
+ double cknobs [CCOLAMD_KNOBS] ;
+ double default_knobs [CCOLAMD_KNOBS] ;
+
+ Int *count ; /* length of each column of M, and col pointer*/
+ Int *mark ; /* mark array for finding duplicate entries */
+ Int *M ; /* row indices of matrix M */
+ size_t Mlen ; /* length of M */
+ Int n_row ; /* number of rows in M */
+ Int nnz ; /* number of entries in A */
+ Int i ; /* row index of A */
+ Int j ; /* column index of A */
+ Int k ; /* row index of M */
+ Int mnz ; /* number of nonzeros in M */
+ Int pp ; /* index into a column of A */
+ Int last_row ; /* last row seen in the current column */
+ Int length ; /* number of nonzeros in a column */
+ Int both ; /* TRUE if ordering A+A' */
+ Int upper ; /* TRUE if ordering triu(A)+triu(A)' */
+ Int lower ; /* TRUE if ordering tril(A)+tril(A)' */
+
+#ifndef NDEBUG
+ ccolamd_get_debug ("csymamd") ;
+#endif
+
+ both = (stype == 0) ;
+ upper = (stype > 0) ;
+ lower = (stype < 0) ;
+
+ /* === Check the input arguments ======================================== */
+
+ if (!stats)
+ {
+ DEBUG1 (("csymamd: stats not present\n")) ;
+ return (FALSE) ;
+ }
+ for (i = 0 ; i < CCOLAMD_STATS ; i++)
+ {
+ stats [i] = 0 ;
+ }
+ stats [CCOLAMD_STATUS] = CCOLAMD_OK ;
+ stats [CCOLAMD_INFO1] = -1 ;
+ stats [CCOLAMD_INFO2] = -1 ;
+
+ if (!A)
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_A_not_present ;
+ DEBUG1 (("csymamd: A not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (!p) /* p is not present */
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p_not_present ;
+ DEBUG1 (("csymamd: p not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (n < 0) /* n must be >= 0 */
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_ncol_negative ;
+ stats [CCOLAMD_INFO1] = n ;
+ DEBUG1 (("csymamd: n negative "ID" \n", n)) ;
+ return (FALSE) ;
+ }
+
+ nnz = p [n] ;
+ if (nnz < 0) /* nnz must be >= 0 */
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nnz_negative ;
+ stats [CCOLAMD_INFO1] = nnz ;
+ DEBUG1 (("csymamd: number of entries negative "ID" \n", nnz)) ;
+ return (FALSE) ;
+ }
+
+ if (p [0] != 0)
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p0_nonzero ;
+ stats [CCOLAMD_INFO1] = p [0] ;
+ DEBUG1 (("csymamd: p[0] not zero "ID"\n", p [0])) ;
+ return (FALSE) ;
+ }
+
+ /* === If no knobs, set default knobs =================================== */
+
+ if (!knobs)
+ {
+ CCOLAMD_set_defaults (default_knobs) ;
+ knobs = default_knobs ;
+ }
+
+ /* === Allocate count and mark ========================================== */
+
+ count = (Int *) ((*allocate) (n+1, sizeof (Int))) ;
+ if (!count)
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ;
+ DEBUG1 (("csymamd: allocate count (size "ID") failed\n", n+1)) ;
+ return (FALSE) ;
+ }
+
+ mark = (Int *) ((*allocate) (n+1, sizeof (Int))) ;
+ if (!mark)
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ;
+ (*release) ((void *) count) ;
+ DEBUG1 (("csymamd: allocate mark (size "ID") failed\n", n+1)) ;
+ return (FALSE) ;
+ }
+
+ /* === Compute column counts of M, check if A is valid ================== */
+
+ stats [CCOLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/
+
+ for (i = 0 ; i < n ; i++)
+ {
+ mark [i] = -1 ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ last_row = -1 ;
+
+ length = p [j+1] - p [j] ;
+ if (length < 0)
+ {
+ /* column pointers must be non-decreasing */
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_col_length_negative ;
+ stats [CCOLAMD_INFO1] = j ;
+ stats [CCOLAMD_INFO2] = length ;
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ;
+ DEBUG1 (("csymamd: col "ID" negative length "ID"\n", j, length)) ;
+ return (FALSE) ;
+ }
+
+ for (pp = p [j] ; pp < p [j+1] ; pp++)
+ {
+ i = A [pp] ;
+ if (i < 0 || i >= n)
+ {
+ /* row index i, in column j, is out of bounds */
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_row_index_out_of_bounds ;
+ stats [CCOLAMD_INFO1] = j ;
+ stats [CCOLAMD_INFO2] = i ;
+ stats [CCOLAMD_INFO3] = n ;
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ;
+ DEBUG1 (("csymamd: row "ID" col "ID" out of bounds\n", i, j)) ;
+ return (FALSE) ;
+ }
+
+ if (i <= last_row || mark [i] == j)
+ {
+ /* row index is unsorted or repeated (or both), thus col */
+ /* is jumbled. This is a notice, not an error condition. */
+ stats [CCOLAMD_STATUS] = CCOLAMD_OK_BUT_JUMBLED ;
+ stats [CCOLAMD_INFO1] = j ;
+ stats [CCOLAMD_INFO2] = i ;
+ (stats [CCOLAMD_INFO3]) ++ ;
+ DEBUG1 (("csymamd: row "ID" col "ID" unsorted/dupl.\n", i, j)) ;
+ }
+
+ if (mark [i] != j)
+ {
+ if ((both && i != j) || (lower && i > j) || (upper && i < j))
+ {
+ /* row k of M will contain column indices i and j */
+ count [i]++ ;
+ count [j]++ ;
+ }
+ }
+
+ /* mark the row as having been seen in this column */
+ mark [i] = j ;
+
+ last_row = i ;
+ }
+ }
+
+ /* === Compute column pointers of M ===================================== */
+
+ /* use output permutation, perm, for column pointers of M */
+ perm [0] = 0 ;
+ for (j = 1 ; j <= n ; j++)
+ {
+ perm [j] = perm [j-1] + count [j-1] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ count [j] = perm [j] ;
+ }
+
+ /* === Construct M ====================================================== */
+
+ mnz = perm [n] ;
+ n_row = mnz / 2 ;
+ Mlen = CCOLAMD_recommended (mnz, n_row, n) ;
+ M = (Int *) ((*allocate) (Mlen, sizeof (Int))) ;
+ DEBUG1 (("csymamd: M is "ID"-by-"ID" with "ID" entries, Mlen = %g\n",
+ n_row, n, mnz, (double) Mlen)) ;
+
+ if (!M)
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ;
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ;
+ DEBUG1 (("csymamd: allocate M (size %g) failed\n", (double) Mlen)) ;
+ return (FALSE) ;
+ }
+
+ k = 0 ;
+
+ if (stats [CCOLAMD_STATUS] == CCOLAMD_OK)
+ {
+ /* Matrix is OK */
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (p [j+1] - p [j] >= 0) ;
+ for (pp = p [j] ; pp < p [j+1] ; pp++)
+ {
+ i = A [pp] ;
+ ASSERT (i >= 0 && i < n) ;
+ if ((both && i != j) || (lower && i > j) || (upper && i < j))
+ {
+ /* row k of M contains column indices i and j */
+ M [count [i]++] = k ;
+ M [count [j]++] = k ;
+ k++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* Matrix is jumbled. Do not add duplicates to M. Unsorted cols OK. */
+ DEBUG1 (("csymamd: Duplicates in A.\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ mark [i] = -1 ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (p [j+1] - p [j] >= 0) ;
+ for (pp = p [j] ; pp < p [j+1] ; pp++)
+ {
+ i = A [pp] ;
+ ASSERT (i >= 0 && i < n) ;
+ if (mark [i] != j)
+ {
+ if ((both && i != j) || (lower && i > j) || (upper && i<j))
+ {
+ /* row k of M contains column indices i and j */
+ M [count [i]++] = k ;
+ M [count [j]++] = k ;
+ k++ ;
+ mark [i] = j ;
+ }
+ }
+ }
+ }
+ }
+
+ /* count and mark no longer needed */
+ (*release) ((void *) mark) ;
+ (*release) ((void *) count) ;
+ ASSERT (k == n_row) ;
+
+ /* === Adjust the knobs for M =========================================== */
+
+ for (i = 0 ; i < CCOLAMD_KNOBS ; i++)
+ {
+ cknobs [i] = knobs [i] ;
+ }
+
+ /* there are no dense rows in M */
+ cknobs [CCOLAMD_DENSE_ROW] = -1 ;
+ cknobs [CCOLAMD_DENSE_COL] = knobs [CCOLAMD_DENSE_ROW] ;
+
+ /* ensure CCSYMAMD orders for Cholesky, not LU */
+ cknobs [CCOLAMD_LU] = FALSE ;
+
+ /* === Order the columns of M =========================================== */
+
+ (void) CCOLAMD_2 (n_row, n, (Int) Mlen, M, perm, cknobs, stats,
+ (Int *) NULL, (Int *) NULL, (Int *) NULL, (Int *) NULL,
+ (Int *) NULL, (Int *) NULL, (Int *) NULL, cmember) ;
+
+ /* === adjust statistics ================================================ */
+
+ /* a dense column in ccolamd means a dense row and col in csymamd */
+ stats [CCOLAMD_DENSE_ROW] = stats [CCOLAMD_DENSE_COL] ;
+
+ /* === Free M =========================================================== */
+
+ (*release) ((void *) M) ;
+ DEBUG1 (("csymamd: done.\n")) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === ccolamd ============================================================== */
+/* ========================================================================== */
+
+/*
+ * The colamd routine computes a column ordering Q of a sparse matrix
+ * A such that the LU factorization P(AQ) = LU remains sparse, where P is
+ * selected via partial pivoting. The routine can also be viewed as
+ * providing a permutation Q such that the Cholesky factorization
+ * (AQ)'(AQ) = LL' remains sparse.
+ */
+
+PUBLIC Int CCOLAMD_MAIN
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows in A */
+ Int n_col, /* number of columns in A */
+ Int Alen, /* length of A */
+ Int A [ ], /* row indices of A */
+ Int p [ ], /* pointers to columns in A */
+ double knobs [CCOLAMD_KNOBS],/* parameters (uses defaults if NULL) */
+ Int stats [CCOLAMD_STATS], /* output statistics and error codes */
+ Int cmember [ ] /* constraint set of A */
+)
+{
+ return (CCOLAMD_2 (n_row, n_col, Alen, A, p, knobs, stats,
+ (Int *) NULL, (Int *) NULL, (Int *) NULL, (Int *) NULL,
+ (Int *) NULL, (Int *) NULL, (Int *) NULL, cmember)) ;
+}
+
+
+/* ========================================================================== */
+/* === ccolamd2 ============================================================= */
+/* ========================================================================== */
+
+/* Identical to ccolamd, except that additional information about each frontal
+ * matrix is returned to the caller. Not intended to be directly called by
+ * the user.
+ */
+
+PUBLIC Int CCOLAMD_2 /* returns TRUE if successful, FALSE otherwise */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows in A */
+ Int n_col, /* number of columns in A */
+ Int Alen, /* length of A */
+ Int A [ ], /* row indices of A */
+ Int p [ ], /* pointers to columns in A */
+ double knobs [CCOLAMD_KNOBS],/* parameters (uses defaults if NULL) */
+ Int stats [CCOLAMD_STATS], /* output statistics and error codes */
+
+ /* each Front array is of size n_col+1. */
+ Int Front_npivcol [ ], /* # pivot cols in each front */
+ Int Front_nrows [ ], /* # of rows in each front (incl. pivot rows) */
+ Int Front_ncols [ ], /* # of cols in each front (incl. pivot cols) */
+ Int Front_parent [ ], /* parent of each front */
+ Int Front_cols [ ], /* link list of pivot columns for each front */
+ Int *p_nfr, /* total number of frontal matrices */
+ Int InFront [ ], /* InFront [row] = f if the original row was
+ * absorbed into front f. EMPTY if the row was
+ * empty, dense, or not absorbed. This array
+ * has size n_row+1 */
+ Int cmember [ ] /* constraint set of A */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ; /* loop index */
+ Int nnz ; /* nonzeros in A */
+ size_t Row_size ; /* size of Row [ ], in integers */
+ size_t Col_size ; /* size of Col [ ], in integers */
+ size_t need ; /* minimum required length of A */
+ CColamd_Row *Row ; /* pointer into A of Row [0..n_row] array */
+ CColamd_Col *Col ; /* pointer into A of Col [0..n_col] array */
+ Int n_col2 ; /* number of non-dense, non-empty columns */
+ Int n_row2 ; /* number of non-dense, non-empty rows */
+ Int ngarbage ; /* number of garbage collections performed */
+ Int max_deg ; /* maximum row degree */
+ double default_knobs [CCOLAMD_KNOBS] ; /* default knobs array */
+
+ Int n_cset ; /* number of constraint sets */
+ Int *cset ; /* cset of A */
+ Int *cset_start ; /* pointer into cset */
+ Int *temp_cstart ; /* temp pointer to start of cset */
+ Int *csize ; /* temp pointer to cset size */
+ Int ap ; /* column index */
+ Int order_for_lu ; /* TRUE: order for LU, FALSE: for Cholesky */
+
+ Int ndense_row, nempty_row, parent, ndense_col,
+ nempty_col, k, col, nfr, *Front_child, *Front_sibling, *Front_stack,
+ *Front_order, *Front_size ;
+ Int nnewlyempty_col, nnewlyempty_row ;
+ Int aggressive ;
+ Int row ;
+ Int *dead_cols ;
+ Int set1 ;
+ Int set2 ;
+ Int cs ;
+
+ int ok ;
+
+#ifndef NDEBUG
+ ccolamd_get_debug ("ccolamd") ;
+#endif
+
+ /* === Check the input arguments ======================================== */
+
+ if (!stats)
+ {
+ DEBUG1 (("ccolamd: stats not present\n")) ;
+ return (FALSE) ;
+ }
+ for (i = 0 ; i < CCOLAMD_STATS ; i++)
+ {
+ stats [i] = 0 ;
+ }
+ stats [CCOLAMD_STATUS] = CCOLAMD_OK ;
+ stats [CCOLAMD_INFO1] = -1 ;
+ stats [CCOLAMD_INFO2] = -1 ;
+
+ if (!A) /* A is not present */
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_A_not_present ;
+ DEBUG1 (("ccolamd: A not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (!p) /* p is not present */
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p_not_present ;
+ DEBUG1 (("ccolamd: p not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (n_row < 0) /* n_row must be >= 0 */
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nrow_negative ;
+ stats [CCOLAMD_INFO1] = n_row ;
+ DEBUG1 (("ccolamd: nrow negative "ID"\n", n_row)) ;
+ return (FALSE) ;
+ }
+
+ if (n_col < 0) /* n_col must be >= 0 */
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_ncol_negative ;
+ stats [CCOLAMD_INFO1] = n_col ;
+ DEBUG1 (("ccolamd: ncol negative "ID"\n", n_col)) ;
+ return (FALSE) ;
+ }
+
+ nnz = p [n_col] ;
+ if (nnz < 0) /* nnz must be >= 0 */
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nnz_negative ;
+ stats [CCOLAMD_INFO1] = nnz ;
+ DEBUG1 (("ccolamd: number of entries negative "ID"\n", nnz)) ;
+ return (FALSE) ;
+ }
+
+ if (p [0] != 0)
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p0_nonzero ;
+ stats [CCOLAMD_INFO1] = p [0] ;
+ DEBUG1 (("ccolamd: p[0] not zero "ID"\n", p [0])) ;
+ return (FALSE) ;
+ }
+
+ /* === If no knobs, set default knobs =================================== */
+
+ if (!knobs)
+ {
+ CCOLAMD_set_defaults (default_knobs) ;
+ knobs = default_knobs ;
+ }
+
+ aggressive = (knobs [CCOLAMD_AGGRESSIVE] != FALSE) ;
+ order_for_lu = (knobs [CCOLAMD_LU] != FALSE) ;
+
+ /* === Allocate workspace from array A ================================== */
+
+ ok = TRUE ;
+ Col_size = CCOLAMD_C (n_col, &ok) ;
+ Row_size = CCOLAMD_R (n_row, &ok) ;
+
+ /* min size of A is 2nnz+ncol. cset and cset_start are of size 2ncol+1 */
+ /* Each of the 5 fronts is of size n_col + 1. InFront is of size nrow. */
+
+ /*
+ need = MAX (2*nnz, 4*n_col) + n_col +
+ Col_size + Row_size +
+ (3*n_col+1) + (5*(n_col+1)) + n_row ;
+ */
+ need = ccolamd_need (nnz, n_row, n_col, &ok) ;
+
+ if (!ok || need > (size_t) Alen || need > Int_MAX)
+ {
+ /* not enough space in array A to perform the ordering */
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_A_too_small ;
+ stats [CCOLAMD_INFO1] = need ;
+ stats [CCOLAMD_INFO2] = Alen ;
+ DEBUG1 (("ccolamd: Need Alen >= "ID", given "ID"\n", need, Alen)) ;
+ return (FALSE) ;
+ }
+
+ /* since integer overflow has been check, the following cannot overflow: */
+ Alen -= Col_size + Row_size + (3*n_col + 1) + 5*(n_col+1) + n_row ;
+
+ /* Size of A is now Alen >= MAX (2*nnz, 4*n_col) + n_col. The ordering
+ * requires Alen >= 2*nnz + n_col, and the postorder requires
+ * Alen >= 5*n_col. */
+
+ ap = Alen ;
+
+ /* Front array workspace: 5*(n_col+1) + n_row */
+ if (!Front_npivcol || !Front_nrows || !Front_ncols || !Front_parent ||
+ !Front_cols || !Front_cols || !InFront)
+ {
+ Front_npivcol = &A [ap] ; ap += (n_col + 1) ;
+ Front_nrows = &A [ap] ; ap += (n_col + 1) ;
+ Front_ncols = &A [ap] ; ap += (n_col + 1) ;
+ Front_parent = &A [ap] ; ap += (n_col + 1) ;
+ Front_cols = &A [ap] ; ap += (n_col + 1) ;
+ InFront = &A [ap] ; ap += (n_row) ;
+ }
+ else
+ {
+ /* Fronts are present. Leave the additional space as elbow room. */
+ ap += 5*(n_col+1) + n_row ;
+ ap = Alen ;
+ }
+
+ /* Workspace for cset management: 3*n_col+1 */
+ /* cset_start is of size n_col + 1 */
+ cset_start = &A [ap] ;
+ ap += n_col + 1 ;
+
+ /* dead_col is of size n_col */
+ dead_cols = &A [ap] ;
+ ap += n_col ;
+
+ /* cset is of size n_col */
+ cset = &A [ap] ;
+ ap += n_col ;
+
+ /* Col is of size Col_size. The space is shared by temp_cstart and csize */
+ Col = (CColamd_Col *) &A [ap] ;
+ temp_cstart = (Int *) Col ; /* [ temp_cstart is of size n_col+1 */
+ csize = temp_cstart + (n_col+1) ; /* csize is of size n_col+1 */
+ ap += Col_size ;
+ ASSERT (Col_size >= 2*n_col+1) ;
+
+ /* Row is of size Row_size */
+ Row = (CColamd_Row *) &A [ap] ;
+ ap += Row_size ;
+
+ /* Initialize csize & dead_cols to zero */
+ for (i = 0 ; i < n_col ; i++)
+ {
+ csize [i] = 0 ;
+ dead_cols [i] = 0 ;
+ }
+
+ /* === Construct the constraint set ===================================== */
+
+ if (n_col == 0)
+ {
+ n_cset = 0 ;
+ }
+ else if (cmember == (Int *) NULL)
+ {
+ /* no constraint set; all columns belong to set zero */
+ n_cset = 1 ;
+ csize [0] = n_col ;
+ DEBUG1 (("no cmember present\n")) ;
+ }
+ else
+ {
+ n_cset = 0 ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ if (cmember [i] < 0 || cmember [i] > n_col)
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_invalid_cmember ;
+ DEBUG1 (("ccolamd: malformed cmember \n")) ;
+ return (FALSE) ;
+ }
+ n_cset = MAX (n_cset, cmember [i]) ;
+ csize [cmember [i]]++ ;
+ }
+ /* cset is zero based */
+ n_cset++ ;
+ }
+
+ ASSERT ((n_cset >= 0) && (n_cset <= n_col)) ;
+
+ cset_start [0] = temp_cstart [0] = 0 ;
+ for (i = 1 ; i <= n_cset ; i++)
+ {
+ cset_start [i] = cset_start [i-1] + csize [i-1] ;
+ DEBUG4 ((" cset_start ["ID"] = "ID" \n", i , cset_start [i])) ;
+ temp_cstart [i] = cset_start [i] ;
+ }
+
+ /* do in reverse order to encourage natural tie-breaking */
+ if (cmember == (Int *) NULL)
+ {
+ for (i = n_col-1 ; i >= 0 ; i--)
+ {
+ cset [temp_cstart [0]++] = i ;
+ }
+ }
+ else
+ {
+ for (i = n_col-1 ; i >= 0 ; i--)
+ {
+ cset [temp_cstart [cmember [i]]++] = i ;
+ }
+ }
+
+ /* ] temp_cstart and csize are no longer used */
+
+ /* === Construct the row and column data structures ===================== */
+
+ if (!init_rows_cols (n_row, n_col, Row, Col, A, p, stats))
+ {
+ /* input matrix is invalid */
+ DEBUG1 (("ccolamd: Matrix invalid\n")) ;
+ return (FALSE) ;
+ }
+
+ /* === Initialize front info ============================================ */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Front_npivcol [col] = 0 ;
+ Front_nrows [col] = 0 ;
+ Front_ncols [col] = 0 ;
+ Front_parent [col] = EMPTY ;
+ Front_cols [col] = EMPTY ;
+ }
+
+ /* === Initialize scores, kill dense rows/columns ======================= */
+
+ init_scoring (n_row, n_col, Row, Col, A, p, knobs,
+ &n_row2, &n_col2, &max_deg, cmember, n_cset, cset_start, dead_cols,
+ &ndense_row, &nempty_row, &nnewlyempty_row,
+ &ndense_col, &nempty_col, &nnewlyempty_col) ;
+
+ ASSERT (n_row2 == n_row - nempty_row - nnewlyempty_row - ndense_row) ;
+ ASSERT (n_col2 == n_col - nempty_col - nnewlyempty_col - ndense_col) ;
+ DEBUG1 (("# dense rows "ID" cols "ID"\n", ndense_row, ndense_col)) ;
+
+ /* === Order the supercolumns =========================================== */
+
+ ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p,
+#ifndef NDEBUG
+ n_col2,
+#endif
+ max_deg, 2*nnz, cset, cset_start,
+#ifndef NDEBUG
+ n_cset,
+#endif
+ cmember, Front_npivcol, Front_nrows, Front_ncols, Front_parent,
+ Front_cols, &nfr, aggressive, InFront, order_for_lu) ;
+
+ ASSERT (Alen >= 5*n_col) ;
+
+ /* === Postorder ======================================================== */
+
+ /* A is no longer needed, so use A [0..5*nfr-1] as workspace [ [ */
+ /* This step requires Alen >= 5*n_col */
+ Front_child = A ;
+ Front_sibling = Front_child + nfr ;
+ Front_stack = Front_sibling + nfr ;
+ Front_order = Front_stack + nfr ;
+ Front_size = Front_order + nfr ;
+
+ CCOLAMD_fsize (nfr, Front_size, Front_nrows, Front_ncols,
+ Front_parent, Front_npivcol) ;
+
+ CCOLAMD_postorder (nfr, Front_parent, Front_npivcol, Front_size,
+ Front_order, Front_child, Front_sibling, Front_stack, Front_cols,
+ cmember) ;
+
+ /* Front_size, Front_stack, Front_child, Front_sibling no longer needed ] */
+
+ /* use A [0..nfr-1] as workspace */
+ CCOLAMD_apply_order (Front_npivcol, Front_order, A, nfr, nfr) ;
+ CCOLAMD_apply_order (Front_nrows, Front_order, A, nfr, nfr) ;
+ CCOLAMD_apply_order (Front_ncols, Front_order, A, nfr, nfr) ;
+ CCOLAMD_apply_order (Front_parent, Front_order, A, nfr, nfr) ;
+ CCOLAMD_apply_order (Front_cols, Front_order, A, nfr, nfr) ;
+
+ /* fix the parent to refer to the new numbering */
+ for (i = 0 ; i < nfr ; i++)
+ {
+ parent = Front_parent [i] ;
+ if (parent != EMPTY)
+ {
+ Front_parent [i] = Front_order [parent] ;
+ }
+ }
+
+ /* fix InFront to refer to the new numbering */
+ for (row = 0 ; row < n_row ; row++)
+ {
+ i = InFront [row] ;
+ ASSERT (i >= EMPTY && i < nfr) ;
+ if (i != EMPTY)
+ {
+ InFront [row] = Front_order [i] ;
+ }
+ }
+
+ /* Front_order longer needed ] */
+
+ /* === Order the columns in the fronts ================================== */
+
+ /* use A [0..n_col-1] as inverse permutation */
+ for (i = 0 ; i < n_col ; i++)
+ {
+ A [i] = EMPTY ;
+ }
+
+ k = 0 ;
+ set1 = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ ASSERT (Front_npivcol [i] > 0) ;
+
+ set2 = CMEMBER (Front_cols [i]) ;
+ while (set1 < set2)
+ {
+ k += dead_cols [set1] ;
+ DEBUG3 (("Skip null/dense columns of set "ID"\n",set1)) ;
+ set1++ ;
+ }
+ set1 = set2 ;
+
+ for (col = Front_cols [i] ; col != EMPTY ; col = Col [col].nextcol)
+ {
+ ASSERT (col >= 0 && col < n_col) ;
+ DEBUG1 (("ccolamd output ordering: k "ID" col "ID"\n", k, col)) ;
+ p [k] = col ;
+ ASSERT (A [col] == EMPTY) ;
+
+ cs = CMEMBER (col) ;
+ ASSERT (k >= cset_start [cs] && k < cset_start [cs+1]) ;
+
+ A [col] = k ;
+ k++ ;
+ }
+ }
+
+ /* === Order the "dense" and null columns =============================== */
+
+ if (n_col2 < n_col)
+ {
+ for (col = 0 ; col < n_col ; col++)
+ {
+ if (A [col] == EMPTY)
+ {
+ k = Col [col].shared2.order ;
+ cs = CMEMBER (col) ;
+#ifndef NDEBUG
+ dead_cols [cs]-- ;
+#endif
+ ASSERT (k >= cset_start [cs] && k < cset_start [cs+1]) ;
+ DEBUG1 (("ccolamd output ordering: k "ID" col "ID
+ " (dense or null col)\n", k, col)) ;
+ p [k] = col ;
+ A [col] = k ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ for (i = 0 ; i < n_cset ; i++)
+ {
+ ASSERT (dead_cols [i] == 0) ;
+ }
+#endif
+
+ /* === Return statistics in stats ======================================= */
+
+ stats [CCOLAMD_DENSE_ROW] = ndense_row ;
+ stats [CCOLAMD_DENSE_COL] = nempty_row ;
+ stats [CCOLAMD_NEWLY_EMPTY_ROW] = nnewlyempty_row ;
+ stats [CCOLAMD_DENSE_COL] = ndense_col ;
+ stats [CCOLAMD_EMPTY_COL] = nempty_col ;
+ stats [CCOLAMD_NEWLY_EMPTY_COL] = nnewlyempty_col ;
+ ASSERT (ndense_col + nempty_col + nnewlyempty_col == n_col - n_col2) ;
+ if (p_nfr)
+ {
+ *p_nfr = nfr ;
+ }
+ stats [CCOLAMD_DEFRAG_COUNT] = ngarbage ;
+ DEBUG1 (("ccolamd: done.\n")) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === colamd_report ======================================================== */
+/* ========================================================================== */
+
+PUBLIC void CCOLAMD_report
+(
+ Int stats [CCOLAMD_STATS]
+)
+{
+ print_report ("ccolamd", stats) ;
+}
+
+
+/* ========================================================================== */
+/* === symamd_report ======================================================== */
+/* ========================================================================== */
+
+PUBLIC void CSYMAMD_report
+(
+ Int stats [CCOLAMD_STATS]
+)
+{
+ print_report ("csymamd", stats) ;
+}
+
+
+/* ========================================================================== */
+/* === NON-USER-CALLABLE ROUTINES: ========================================== */
+/* ========================================================================== */
+
+/* There are no user-callable routines beyond this point in the file */
+
+
+/* ========================================================================== */
+/* === init_rows_cols ======================================================= */
+/* ========================================================================== */
+
+/*
+ Takes the column form of the matrix in A and creates the row form of the
+ matrix. Also, row and column attributes are stored in the Col and Row
+ structs. If the columns are un-sorted or contain duplicate row indices,
+ this routine will also sort and remove duplicate row indices from the
+ column form of the matrix. Returns FALSE if the matrix is invalid,
+ TRUE otherwise. Not user-callable.
+*/
+
+PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ CColamd_Row Row [ ], /* of size n_row+1 */
+ CColamd_Col Col [ ], /* of size n_col+1 */
+ Int A [ ], /* row indices of A, of size Alen */
+ Int p [ ], /* pointers to columns in A, of size n_col+1 */
+ Int stats [CCOLAMD_STATS] /* colamd statistics */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int col ; /* a column index */
+ Int row ; /* a row index */
+ Int *cp ; /* a column pointer */
+ Int *cp_end ; /* a pointer to the end of a column */
+ Int *rp ; /* a row pointer */
+ Int *rp_end ; /* a pointer to the end of a row */
+ Int last_row ; /* previous row */
+
+ /* === Initialize columns, and check column pointers ==================== */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Col [col].start = p [col] ;
+ Col [col].length = p [col+1] - p [col] ;
+
+ if (Col [col].length < 0)
+ {
+ /* column pointers must be non-decreasing */
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_col_length_negative ;
+ stats [CCOLAMD_INFO1] = col ;
+ stats [CCOLAMD_INFO2] = Col [col].length ;
+ DEBUG1 (("ccolamd: col "ID" length "ID" < 0\n",
+ col, Col [col].length)) ;
+ return (FALSE) ;
+ }
+
+ Col [col].shared1.thickness = 1 ;
+ Col [col].shared2.score = 0 ;
+ Col [col].shared3.prev = EMPTY ;
+ Col [col].shared4.degree_next = EMPTY ;
+ Col [col].nextcol = EMPTY ;
+ Col [col].lastcol = col ;
+ }
+
+ /* p [0..n_col] no longer needed, used as "head" in subsequent routines */
+
+ /* === Scan columns, compute row degrees, and check row indices ========= */
+
+ stats [CCOLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].length = 0 ;
+ Row [row].shared2.mark = -1 ;
+ Row [row].thickness = 1 ;
+ Row [row].front = EMPTY ;
+ }
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ DEBUG1 (("\nCcolamd input column "ID":\n", col)) ;
+ last_row = -1 ;
+
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+ DEBUG1 (("row: "ID"\n", row)) ;
+
+ /* make sure row indices within range */
+ if (row < 0 || row >= n_row)
+ {
+ stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_row_index_out_of_bounds ;
+ stats [CCOLAMD_INFO1] = col ;
+ stats [CCOLAMD_INFO2] = row ;
+ stats [CCOLAMD_INFO3] = n_row ;
+ DEBUG1 (("row "ID" col "ID" out of bounds\n", row, col)) ;
+ return (FALSE) ;
+ }
+
+ if (row <= last_row || Row [row].shared2.mark == col)
+ {
+ /* row index are unsorted or repeated (or both), thus col */
+ /* is jumbled. This is a notice, not an error condition. */
+ stats [CCOLAMD_STATUS] = CCOLAMD_OK_BUT_JUMBLED ;
+ stats [CCOLAMD_INFO1] = col ;
+ stats [CCOLAMD_INFO2] = row ;
+ (stats [CCOLAMD_INFO3]) ++ ;
+ DEBUG1 (("row "ID" col "ID" unsorted/duplicate\n", row, col)) ;
+ }
+
+ if (Row [row].shared2.mark != col)
+ {
+ Row [row].length++ ;
+ }
+ else
+ {
+ /* this is a repeated entry in the column, */
+ /* it will be removed */
+ Col [col].length-- ;
+ }
+
+ /* mark the row as having been seen in this column */
+ Row [row].shared2.mark = col ;
+
+ last_row = row ;
+ }
+ }
+
+ /* === Compute row pointers ============================================= */
+
+ /* row form of the matrix starts directly after the column */
+ /* form of matrix in A */
+ Row [0].start = p [n_col] ;
+ Row [0].shared1.p = Row [0].start ;
+ Row [0].shared2.mark = -1 ;
+ for (row = 1 ; row < n_row ; row++)
+ {
+ Row [row].start = Row [row-1].start + Row [row-1].length ;
+ Row [row].shared1.p = Row [row].start ;
+ Row [row].shared2.mark = -1 ;
+ }
+
+ /* === Create row form ================================================== */
+
+ if (stats [CCOLAMD_STATUS] == CCOLAMD_OK_BUT_JUMBLED)
+ {
+ /* if cols jumbled, watch for repeated row indices */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+ if (Row [row].shared2.mark != col)
+ {
+ A [(Row [row].shared1.p)++] = col ;
+ Row [row].shared2.mark = col ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* if cols not jumbled, we don't need the mark (this is faster) */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ A [(Row [*cp++].shared1.p)++] = col ;
+ }
+ }
+ }
+
+ /* === Clear the row marks and set row degrees ========================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].shared2.mark = 0 ;
+ Row [row].shared1.degree = Row [row].length ;
+ }
+
+ /* === See if we need to re-create columns ============================== */
+
+ if (stats [CCOLAMD_STATUS] == CCOLAMD_OK_BUT_JUMBLED)
+ {
+ DEBUG1 (("ccolamd: reconstructing column form, matrix jumbled\n")) ;
+
+#ifndef NDEBUG
+ /* make sure column lengths are correct */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ p [col] = Col [col].length ;
+ }
+ for (row = 0 ; row < n_row ; row++)
+ {
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ p [*rp++]-- ;
+ }
+ }
+ for (col = 0 ; col < n_col ; col++)
+ {
+ ASSERT (p [col] == 0) ;
+ }
+ /* now p is all zero (different than when debugging is turned off) */
+#endif
+
+ /* === Compute col pointers ========================================= */
+
+ /* col form of the matrix starts at A [0]. */
+ /* Note, we may have a gap between the col form and the row */
+ /* form if there were duplicate entries, if so, it will be */
+ /* removed upon the first garbage collection */
+ Col [0].start = 0 ;
+ p [0] = Col [0].start ;
+ for (col = 1 ; col < n_col ; col++)
+ {
+ /* note that the lengths here are for pruned columns, i.e. */
+ /* no duplicate row indices will exist for these columns */
+ Col [col].start = Col [col-1].start + Col [col-1].length ;
+ p [col] = Col [col].start ;
+ }
+
+ /* === Re-create col form =========================================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ A [(p [*rp++])++] = row ;
+ }
+ }
+ }
+
+ /* === Done. Matrix is not (or no longer) jumbled ====================== */
+
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === init_scoring ========================================================= */
+/* ========================================================================== */
+
+/*
+ Kills dense or empty columns and rows, calculates an initial score for
+ each column, and places all columns in the degree lists. Not user-callable.
+*/
+
+PRIVATE void init_scoring
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ CColamd_Row Row [ ], /* of size n_row+1 */
+ CColamd_Col Col [ ], /* of size n_col+1 */
+ Int A [ ], /* column form and row form of A */
+ Int head [ ], /* of size n_col+1 */
+ double knobs [CCOLAMD_KNOBS],/* parameters */
+ Int *p_n_row2, /* number of non-dense, non-empty rows */
+ Int *p_n_col2, /* number of non-dense, non-empty columns */
+ Int *p_max_deg, /* maximum row degree */
+ Int cmember [ ],
+ Int n_cset,
+ Int cset_start [ ],
+ Int dead_cols [ ],
+ Int *p_ndense_row, /* number of dense rows */
+ Int *p_nempty_row, /* number of original empty rows */
+ Int *p_nnewlyempty_row, /* number of newly empty rows */
+ Int *p_ndense_col, /* number of dense cols (excl "empty" cols) */
+ Int *p_nempty_col, /* number of original empty cols */
+ Int *p_nnewlyempty_col /* number of newly empty cols */
+)
+{
+/* === Local variables ================================================== */
+
+ Int c ; /* a column index */
+ Int r, row ; /* a row index */
+ Int *cp ; /* a column pointer */
+ Int deg ; /* degree of a row or column */
+ Int *cp_end ; /* a pointer to the end of a column */
+ Int *new_cp ; /* new column pointer */
+ Int col_length ; /* length of pruned column */
+ Int score ; /* current column score */
+ Int n_col2 ; /* number of non-dense, non-empty columns */
+ Int n_row2 ; /* number of non-dense, non-empty rows */
+ Int dense_row_count ; /* remove rows with more entries than this */
+ Int dense_col_count ; /* remove cols with more entries than this */
+ Int max_deg ; /* maximum row degree */
+ Int s ; /* a cset index */
+ Int ndense_row ; /* number of dense rows */
+ Int nempty_row ; /* number of empty rows */
+ Int nnewlyempty_row ; /* number of newly empty rows */
+ Int ndense_col ; /* number of dense cols (excl "empty" cols) */
+ Int nempty_col ; /* number of original empty cols */
+ Int nnewlyempty_col ; /* number of newly empty cols */
+ Int ne ;
+
+#ifndef NDEBUG
+ Int debug_count ; /* debug only. */
+#endif
+
+ /* === Extract knobs ==================================================== */
+
+ /* Note: if knobs contains a NaN, this is undefined: */
+ if (knobs [CCOLAMD_DENSE_ROW] < 0)
+ {
+ /* only remove completely dense rows */
+ dense_row_count = n_col-1 ;
+ }
+ else
+ {
+ dense_row_count = DENSE_DEGREE (knobs [CCOLAMD_DENSE_ROW], n_col) ;
+ }
+ if (knobs [CCOLAMD_DENSE_COL] < 0)
+ {
+ /* only remove completely dense columns */
+ dense_col_count = n_row-1 ;
+ }
+ else
+ {
+ dense_col_count =
+ DENSE_DEGREE (knobs [CCOLAMD_DENSE_COL], MIN (n_row, n_col)) ;
+ }
+
+ DEBUG1 (("densecount: "ID" "ID"\n", dense_row_count, dense_col_count)) ;
+ max_deg = 0 ;
+
+ n_col2 = n_col ;
+ n_row2 = n_row ;
+
+ /* Set the head array for bookkeeping of dense and empty columns. */
+ /* This will be used as hash buckets later. */
+ for (s = 0 ; s < n_cset ; s++)
+ {
+ head [s] = cset_start [s+1] ;
+ }
+
+ ndense_col = 0 ;
+ nempty_col = 0 ;
+ nnewlyempty_col = 0 ;
+ ndense_row = 0 ;
+ nempty_row = 0 ;
+ nnewlyempty_row = 0 ;
+
+ /* === Kill empty columns =============================================== */
+
+ /* Put the empty columns at the end in their natural order, so that LU */
+ /* factorization can proceed as far as possible. */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ deg = Col [c].length ;
+ if (deg == 0)
+ {
+ /* this is a empty column, kill and order it last of its cset */
+ Col [c].shared2.order = --head [CMEMBER (c)] ;
+ --n_col2 ;
+ dead_cols [CMEMBER (c)] ++ ;
+ nempty_col++ ;
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ }
+ DEBUG1 (("ccolamd: null columns killed: "ID"\n", n_col - n_col2)) ;
+
+ /* === Kill dense columns =============================================== */
+
+ /* Put the dense columns at the end, in their natural order */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip any dead columns */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ deg = Col [c].length ;
+ if (deg > dense_col_count)
+ {
+ /* this is a dense column, kill and order it last of its cset */
+ Col [c].shared2.order = --head [CMEMBER (c)] ;
+ --n_col2 ;
+ dead_cols [CMEMBER (c)] ++ ;
+ ndense_col++ ;
+ /* decrement the row degrees */
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ Row [*cp++].shared1.degree-- ;
+ }
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ }
+ DEBUG1 (("Dense and null columns killed: "ID"\n", n_col - n_col2)) ;
+
+ /* === Kill dense and empty rows ======================================== */
+
+ /* Note that there can now be empty rows, since dense columns have
+ * been deleted. These are "newly" empty rows. */
+
+ ne = 0 ;
+ for (r = 0 ; r < n_row ; r++)
+ {
+ deg = Row [r].shared1.degree ;
+ ASSERT (deg >= 0 && deg <= n_col) ;
+ if (deg > dense_row_count)
+ {
+ /* There is at least one dense row. Continue ordering, but */
+ /* symbolic factorization will be redone after ccolamd is done.*/
+ ndense_row++ ;
+ }
+ if (deg == 0)
+ {
+ /* this is a newly empty row, or original empty row */
+ ne++ ;
+ }
+ if (deg > dense_row_count || deg == 0)
+ {
+ /* kill a dense or empty row */
+ KILL_ROW (r) ;
+ Row [r].thickness = 0 ;
+ --n_row2 ;
+ }
+ else
+ {
+ /* keep track of max degree of remaining rows */
+ max_deg = MAX (max_deg, deg) ;
+ }
+ }
+ nnewlyempty_row = ne - nempty_row ;
+ DEBUG1 (("ccolamd: Dense and null rows killed: "ID"\n", n_row - n_row2)) ;
+
+ /* === Compute initial column scores ==================================== */
+
+ /* At this point the row degrees are accurate. They reflect the number */
+ /* of "live" (non-dense) columns in each row. No empty rows exist. */
+ /* Some "live" columns may contain only dead rows, however. These are */
+ /* pruned in the code below. */
+
+ /* now find the initial COLMMD score for each column */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip dead column */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ score = 0 ;
+ cp = &A [Col [c].start] ;
+ new_cp = cp ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ /* skip if dead */
+ if (ROW_IS_DEAD (row))
+ {
+ continue ;
+ }
+ /* compact the column */
+ *new_cp++ = row ;
+ /* add row's external degree */
+ score += Row [row].shared1.degree - 1 ;
+ /* guard against integer overflow */
+ score = MIN (score, n_col) ;
+ }
+ /* determine pruned column length */
+ col_length = (Int) (new_cp - &A [Col [c].start]) ;
+ if (col_length == 0)
+ {
+ /* a newly-made null column (all rows in this col are "dense" */
+ /* and have already been killed) */
+ DEBUG1 (("Newly null killed: "ID"\n", c)) ;
+ Col [c].shared2.order = -- head [CMEMBER (c)] ;
+ --n_col2 ;
+ dead_cols [CMEMBER (c)] ++ ;
+ nnewlyempty_col++ ;
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ else
+ {
+ /* set column length and set score */
+ ASSERT (score >= 0) ;
+ ASSERT (score <= n_col) ;
+ Col [c].length = col_length ;
+ Col [c].shared2.score = score ;
+ }
+ }
+ DEBUG1 (("ccolamd: Dense, null, and newly-null columns killed: "ID"\n",
+ n_col-n_col2)) ;
+
+ /* At this point, all empty rows and columns are dead. All live columns */
+ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */
+ /* yet). Rows may contain dead columns, but all live rows contain at */
+ /* least one live column. */
+
+#ifndef NDEBUG
+ debug_count = 0 ;
+#endif
+
+ /* clear the hash buckets */
+ for (c = 0 ; c <= n_col ; c++)
+ {
+ head [c] = EMPTY ;
+ }
+
+#ifndef NDEBUG
+ debug_structures (n_row, n_col, Row, Col, A, cmember, cset_start) ;
+#endif
+
+ /* === Return number of remaining columns, and max row degree =========== */
+
+ *p_n_col2 = n_col2 ;
+ *p_n_row2 = n_row2 ;
+ *p_max_deg = max_deg ;
+ *p_ndense_row = ndense_row ;
+ *p_nempty_row = nempty_row ; /* original empty rows */
+ *p_nnewlyempty_row = nnewlyempty_row ;
+ *p_ndense_col = ndense_col ;
+ *p_nempty_col = nempty_col ; /* original empty cols */
+ *p_nnewlyempty_col = nnewlyempty_col ;
+}
+
+
+/* ========================================================================== */
+/* === find_ordering ======================================================== */
+/* ========================================================================== */
+
+/*
+ * Order the principal columns of the supercolumn form of the matrix
+ * (no supercolumns on input). Uses a minimum approximate column minimum
+ * degree ordering method. Not user-callable.
+ */
+
+PRIVATE Int find_ordering /* return the number of garbage collections */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Int Alen, /* size of A, 2*nnz + n_col or larger */
+ CColamd_Row Row [ ], /* of size n_row+1 */
+ CColamd_Col Col [ ], /* of size n_col+1 */
+ Int A [ ], /* column form and row form of A */
+ Int head [ ], /* of size n_col+1 */
+#ifndef NDEBUG
+ Int n_col2, /* Remaining columns to order */
+#endif
+ Int max_deg, /* Maximum row degree */
+ Int pfree, /* index of first free slot (2*nnz on entry) */
+ Int cset [ ], /* constraint set of A */
+ Int cset_start [ ], /* pointer to the start of every cset */
+#ifndef NDEBUG
+ Int n_cset, /* number of csets */
+#endif
+ Int cmember [ ], /* col -> cset mapping */
+ Int Front_npivcol [ ],
+ Int Front_nrows [ ],
+ Int Front_ncols [ ],
+ Int Front_parent [ ],
+ Int Front_cols [ ],
+ Int *p_nfr, /* number of fronts */
+ Int aggressive,
+ Int InFront [ ],
+ Int order_for_lu
+)
+{
+ /* === Local variables ================================================== */
+
+ Int k ; /* current pivot ordering step */
+ Int pivot_col ; /* current pivot column */
+ Int *cp ; /* a column pointer */
+ Int *rp ; /* a row pointer */
+ Int pivot_row ; /* current pivot row */
+ Int *new_cp ; /* modified column pointer */
+ Int *new_rp ; /* modified row pointer */
+ Int pivot_row_start ; /* pointer to start of pivot row */
+ Int pivot_row_degree ; /* number of columns in pivot row */
+ Int pivot_row_length ; /* number of supercolumns in pivot row */
+ Int pivot_col_score ; /* score of pivot column */
+ Int needed_memory ; /* free space needed for pivot row */
+ Int *cp_end ; /* pointer to the end of a column */
+ Int *rp_end ; /* pointer to the end of a row */
+ Int row ; /* a row index */
+ Int col ; /* a column index */
+ Int max_score ; /* maximum possible score */
+ Int cur_score ; /* score of current column */
+ unsigned Int hash ; /* hash value for supernode detection */
+ Int head_column ; /* head of hash bucket */
+ Int first_col ; /* first column in hash bucket */
+ Int tag_mark ; /* marker value for mark array */
+ Int row_mark ; /* Row [row].shared2.mark */
+ Int set_difference ; /* set difference size of row with pivot row */
+ Int min_score ; /* smallest column score */
+ Int col_thickness ; /* "thickness" (no. of columns in a supercol) */
+ Int max_mark ; /* maximum value of tag_mark */
+ Int pivot_col_thickness ; /* number of columns represented by pivot col */
+ Int prev_col ; /* Used by Dlist operations. */
+ Int next_col ; /* Used by Dlist operations. */
+ Int ngarbage ; /* number of garbage collections performed */
+ Int current_set ; /* consraint set that is being ordered */
+ Int score ; /* score of a column */
+ Int colstart ; /* pointer to first column in current cset */
+ Int colend ; /* pointer to last column in current cset */
+ Int deadcol ; /* number of dense & null columns in a cset */
+
+#ifndef NDEBUG
+ Int debug_d ; /* debug loop counter */
+ Int debug_step = 0 ; /* debug loop counter */
+ Int cols_thickness = 0 ; /* the thickness of the columns in current */
+ /* cset degreelist and in pivot row pattern. */
+#endif
+
+ Int pivot_row_thickness ; /* number of rows represented by pivot row */
+ Int nfr = 0 ; /* number of fronts */
+ Int child ;
+
+ /* === Initialization and clear mark ==================================== */
+
+ max_mark = Int_MAX - n_col ; /* Int_MAX defined in <limits.h> */
+ tag_mark = clear_mark (0, max_mark, n_row, Row) ;
+ min_score = 0 ;
+ ngarbage = 0 ;
+ current_set = -1 ;
+ deadcol = 0 ;
+ DEBUG1 (("ccolamd: Ordering, n_col2="ID"\n", n_col2)) ;
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ InFront [row] = EMPTY ;
+ }
+
+ /* === Order the columns ================================================ */
+
+ for (k = 0 ; k < n_col ; /* 'k' is incremented below */)
+ {
+
+ /* make sure degree list isn't empty */
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (head [min_score] >= EMPTY) ;
+
+#ifndef NDEBUG
+ for (debug_d = 0 ; debug_d < min_score ; debug_d++)
+ {
+ ASSERT (head [debug_d] == EMPTY) ;
+ }
+#endif
+
+ /* Initialize the degree list with columns from next non-empty cset */
+
+ while ((k+deadcol) == cset_start [current_set+1])
+ {
+ current_set++ ;
+ DEBUG1 (("\n\n\n============ CSET: "ID"\n", current_set)) ;
+ k += deadcol ; /* jump to start of next cset */
+ deadcol = 0 ; /* reset dead column count */
+
+ ASSERT ((current_set == n_cset) == (k == n_col)) ;
+
+ /* return if all columns are ordered. */
+ if (k == n_col)
+ {
+ *p_nfr = nfr ;
+ return (ngarbage) ;
+ }
+
+#ifndef NDEBUG
+ for (col = 0 ; col <= n_col ; col++)
+ {
+ ASSERT (head [col] == EMPTY) ;
+ }
+#endif
+
+ min_score = n_col ;
+ colstart = cset_start [current_set] ;
+ colend = cset_start [current_set+1] ;
+
+ while (colstart < colend)
+ {
+ col = cset [colstart++] ;
+
+ if (COL_IS_DEAD(col))
+ {
+ DEBUG1 (("Column "ID" is dead\n", col)) ;
+ /* count dense and null columns */
+ if (Col [col].shared2.order != EMPTY)
+ {
+ deadcol++ ;
+ }
+ continue ;
+ }
+
+ /* only add principal columns in current set to degree lists */
+ ASSERT (CMEMBER (col) == current_set) ;
+
+ score = Col [col].shared2.score ;
+ DEBUG1 (("Column "ID" is alive, score "ID"\n", col, score)) ;
+
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (score >= 0) ;
+ ASSERT (score <= n_col) ;
+ ASSERT (head [score] >= EMPTY) ;
+
+ /* now add this column to dList at proper score location */
+ next_col = head [score] ;
+ Col [col].shared3.prev = EMPTY ;
+ Col [col].shared4.degree_next = next_col ;
+
+ /* if there already was a column with the same score, set its */
+ /* previous pointer to this new column */
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = col ;
+ }
+ head [score] = col ;
+
+ /* see if this score is less than current min */
+ min_score = MIN (min_score, score) ;
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("degree lists initialized \n")) ;
+ debug_deg_lists (n_row, n_col, Row, Col, head, min_score,
+ ((cset_start [current_set+1]-cset_start [current_set])-deadcol),
+ max_deg) ;
+#endif
+ }
+
+#ifndef NDEBUG
+ if (debug_step % 100 == 0)
+ {
+ DEBUG2 (("\n... Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ;
+ }
+ else
+ {
+ DEBUG3 (("\n------Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ;
+ }
+ debug_step++ ;
+ DEBUG1 (("start of step k="ID": ", k)) ;
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, cset_start [current_set+1]-(k+deadcol), max_deg) ;
+ debug_matrix (n_row, n_col, Row, Col, A) ;
+#endif
+
+ /* === Select pivot column, and order it ============================ */
+
+ while (head [min_score] == EMPTY && min_score < n_col)
+ {
+ min_score++ ;
+ }
+
+ pivot_col = head [min_score] ;
+
+ ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;
+ next_col = Col [pivot_col].shared4.degree_next ;
+ head [min_score] = next_col ;
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = EMPTY ;
+ }
+
+ ASSERT (COL_IS_ALIVE (pivot_col)) ;
+
+ /* remember score for defrag check */
+ pivot_col_score = Col [pivot_col].shared2.score ;
+
+ /* the pivot column is the kth column in the pivot order */
+ Col [pivot_col].shared2.order = k ;
+
+ /* increment order count by column thickness */
+ pivot_col_thickness = Col [pivot_col].shared1.thickness ;
+ k += pivot_col_thickness ;
+ ASSERT (pivot_col_thickness > 0) ;
+ DEBUG3 (("Pivot col: "ID" thick "ID"\n", pivot_col,
+ pivot_col_thickness)) ;
+
+ /* === Garbage_collection, if necessary ============================= */
+
+ needed_memory = MIN (pivot_col_score, n_col - k) ;
+ if (pfree + needed_memory >= Alen)
+ {
+ pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;
+ ngarbage++ ;
+ /* after garbage collection we will have enough */
+ ASSERT (pfree + needed_memory < Alen) ;
+ /* garbage collection has wiped out Row [ ].shared2.mark array */
+ tag_mark = clear_mark (0, max_mark, n_row, Row) ;
+
+#ifndef NDEBUG
+ debug_matrix (n_row, n_col, Row, Col, A) ;
+#endif
+ }
+
+ /* === Compute pivot row pattern ==================================== */
+
+ /* get starting location for this new merged row */
+ pivot_row_start = pfree ;
+
+ /* initialize new row counts to zero */
+ pivot_row_degree = 0 ;
+ pivot_row_thickness = 0 ;
+
+ /* tag pivot column as having been visited so it isn't included */
+ /* in merged pivot row */
+ Col [pivot_col].shared1.thickness = -pivot_col_thickness ;
+
+ /* pivot row is the union of all rows in the pivot column pattern */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ ASSERT (row >= 0 && row < n_row) ;
+ DEBUG4 (("Pivcol pattern "ID" "ID"\n", ROW_IS_ALIVE (row), row)) ;
+ /* skip if row is dead */
+ if (ROW_IS_ALIVE (row))
+ {
+ /* sum the thicknesses of all the rows */
+ pivot_row_thickness += Row [row].thickness ;
+
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ /* add the column, if alive and untagged */
+ col_thickness = Col [col].shared1.thickness ;
+ if (col_thickness > 0 && COL_IS_ALIVE (col))
+ {
+ /* tag column in pivot row */
+ Col [col].shared1.thickness = -col_thickness ;
+ ASSERT (pfree < Alen) ;
+ /* place column in pivot row */
+ A [pfree++] = col ;
+ pivot_row_degree += col_thickness ;
+ DEBUG4 (("\t\t\tNew live col in pivrow: "ID"\n",col)) ;
+ }
+#ifndef NDEBUG
+ if (col_thickness < 0 && COL_IS_ALIVE (col))
+ {
+ DEBUG4 (("\t\t\tOld live col in pivrow: "ID"\n",col)) ;
+ }
+#endif
+ }
+ }
+ }
+
+ /* pivot_row_thickness is the number of rows in frontal matrix */
+ /* including both pivotal rows and nonpivotal rows */
+
+ /* clear tag on pivot column */
+ Col [pivot_col].shared1.thickness = pivot_col_thickness ;
+ max_deg = MAX (max_deg, pivot_row_degree) ;
+
+#ifndef NDEBUG
+ DEBUG3 (("check2\n")) ;
+ debug_mark (n_row, Row, tag_mark, max_mark) ;
+#endif
+
+ /* === Kill all rows used to construct pivot row ==================== */
+
+ /* also kill pivot row, temporarily */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* may be killing an already dead row */
+ row = *cp++ ;
+ DEBUG3 (("Kill row in pivot col: "ID"\n", row)) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ if (ROW_IS_ALIVE (row))
+ {
+ if (Row [row].front != EMPTY)
+ {
+ /* This row represents a frontal matrix. */
+ /* Row [row].front is a child of current front */
+ child = Row [row].front ;
+ Front_parent [child] = nfr ;
+ DEBUG1 (("Front "ID" => front "ID", normal\n", child, nfr));
+ }
+ else
+ {
+ /* This is an original row. Keep track of which front
+ * is its parent in the row-merge tree. */
+ InFront [row] = nfr ;
+ DEBUG1 (("Row "ID" => front "ID", normal\n", row, nfr)) ;
+ }
+ }
+
+ KILL_ROW (row) ;
+ Row [row].thickness = 0 ;
+ }
+
+ /* === Select a row index to use as the new pivot row =============== */
+
+ pivot_row_length = pfree - pivot_row_start ;
+ if (pivot_row_length > 0)
+ {
+ /* pick the "pivot" row arbitrarily (first row in col) */
+ pivot_row = A [Col [pivot_col].start] ;
+ DEBUG3 (("Pivotal row is "ID"\n", pivot_row)) ;
+ }
+ else
+ {
+ /* there is no pivot row, since it is of zero length */
+ pivot_row = EMPTY ;
+ ASSERT (pivot_row_length == 0) ;
+ }
+ ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;
+
+ /* === Approximate degree computation =============================== */
+
+ /* Here begins the computation of the approximate degree. The column */
+ /* score is the sum of the pivot row "length", plus the size of the */
+ /* set differences of each row in the column minus the pattern of the */
+ /* pivot row itself. The column ("thickness") itself is also */
+ /* excluded from the column score (we thus use an approximate */
+ /* external degree). */
+
+ /* The time taken by the following code (compute set differences, and */
+ /* add them up) is proportional to the size of the data structure */
+ /* being scanned - that is, the sum of the sizes of each column in */
+ /* the pivot row. Thus, the amortized time to compute a column score */
+ /* is proportional to the size of that column (where size, in this */
+ /* context, is the column "length", or the number of row indices */
+ /* in that column). The number of row indices in a column is */
+ /* monotonically non-decreasing, from the length of the original */
+ /* column on input to colamd. */
+
+ /* === Compute set differences ====================================== */
+
+ DEBUG3 (("** Computing set differences phase. **\n")) ;
+
+ /* pivot row is currently dead - it will be revived later. */
+
+ DEBUG3 (("Pivot row: ")) ;
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ DEBUG3 (("Col: "ID"\n", col)) ;
+
+ /* clear tags used to construct pivot row pattern */
+ col_thickness = -Col [col].shared1.thickness ;
+ ASSERT (col_thickness > 0) ;
+ Col [col].shared1.thickness = col_thickness ;
+
+ /* === Remove column from degree list =========================== */
+
+ /* only columns in current_set will be in degree list */
+ if (CMEMBER (col) == current_set)
+ {
+#ifndef NDEBUG
+ cols_thickness += col_thickness ;
+#endif
+ cur_score = Col [col].shared2.score ;
+ prev_col = Col [col].shared3.prev ;
+ next_col = Col [col].shared4.degree_next ;
+ DEBUG3 ((" cur_score "ID" prev_col "ID" next_col "ID"\n",
+ cur_score, prev_col, next_col)) ;
+ ASSERT (cur_score >= 0) ;
+ ASSERT (cur_score <= n_col) ;
+ ASSERT (cur_score >= EMPTY) ;
+ if (prev_col == EMPTY)
+ {
+ head [cur_score] = next_col ;
+ }
+ else
+ {
+ Col [prev_col].shared4.degree_next = next_col ;
+ }
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = prev_col ;
+ }
+ }
+
+ /* === Scan the column ========================================== */
+
+ cp = &A [Col [col].start] ;
+ cp_end = cp + Col [col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ continue ;
+ }
+ ASSERT (row != pivot_row) ;
+ set_difference = row_mark - tag_mark ;
+ /* check if the row has been seen yet */
+ if (set_difference < 0)
+ {
+ ASSERT (Row [row].shared1.degree <= max_deg) ;
+ set_difference = Row [row].shared1.degree ;
+ }
+ /* subtract column thickness from this row's set difference */
+ set_difference -= col_thickness ;
+ ASSERT (set_difference >= 0) ;
+ /* absorb this row if the set difference becomes zero */
+ if (set_difference == 0 && aggressive)
+ {
+ DEBUG3 (("aggressive absorption. Row: "ID"\n", row)) ;
+
+ if (Row [row].front != EMPTY)
+ {
+ /* Row [row].front is a child of current front. */
+ child = Row [row].front ;
+ Front_parent [child] = nfr ;
+ DEBUG1 (("Front "ID" => front "ID", aggressive\n",
+ child, nfr)) ;
+ }
+ else
+ {
+ /* this is an original row. Keep track of which front
+ * assembles it, for the row-merge tree */
+ InFront [row] = nfr ;
+ DEBUG1 (("Row "ID" => front "ID", aggressive\n",
+ row, nfr)) ;
+ }
+
+ KILL_ROW (row) ;
+
+ /* sum the thicknesses of all the rows */
+ pivot_row_thickness += Row [row].thickness ;
+ Row [row].thickness = 0 ;
+ }
+ else
+ {
+ /* save the new mark */
+ Row [row].shared2.mark = set_difference + tag_mark ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ debug_deg_lists (n_row, n_col, Row, Col, head, min_score,
+ cset_start [current_set+1]-(k+deadcol)-(cols_thickness),
+ max_deg) ;
+ cols_thickness = 0 ;
+#endif
+
+ /* === Add up set differences for each column ======================= */
+
+ DEBUG3 (("** Adding set differences phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ hash = 0 ;
+ cur_score = 0 ;
+ cp = &A [Col [col].start] ;
+ /* compact the column */
+ new_cp = cp ;
+ cp_end = cp + Col [col].length ;
+
+ DEBUG4 (("Adding set diffs for Col: "ID".\n", col)) ;
+
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ ASSERT (row >= 0 && row < n_row) ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ DEBUG4 ((" Row "ID", dead\n", row)) ;
+ continue ;
+ }
+ DEBUG4 ((" Row "ID", set diff "ID"\n", row, row_mark-tag_mark));
+ ASSERT (row_mark >= tag_mark) ;
+ /* compact the column */
+ *new_cp++ = row ;
+ /* compute hash function */
+ hash += row ;
+ /* add set difference */
+ cur_score += row_mark - tag_mark ;
+ /* integer overflow... */
+ cur_score = MIN (cur_score, n_col) ;
+ }
+
+ /* recompute the column's length */
+ Col [col].length = (Int) (new_cp - &A [Col [col].start]) ;
+
+ /* === Further mass elimination ================================= */
+
+ if (Col [col].length == 0 && CMEMBER (col) == current_set)
+ {
+ DEBUG4 (("further mass elimination. Col: "ID"\n", col)) ;
+ /* nothing left but the pivot row in this column */
+ KILL_PRINCIPAL_COL (col) ;
+ pivot_row_degree -= Col [col].shared1.thickness ;
+ ASSERT (pivot_row_degree >= 0) ;
+ /* order it */
+ Col [col].shared2.order = k ;
+ /* increment order count by column thickness */
+ k += Col [col].shared1.thickness ;
+ pivot_col_thickness += Col [col].shared1.thickness ;
+ /* add to column list of front */
+#ifndef NDEBUG
+ DEBUG1 (("Mass")) ;
+ dump_super (col, Col, n_col) ;
+#endif
+ Col [Col [col].lastcol].nextcol = Front_cols [nfr] ;
+ Front_cols [nfr] = col ;
+ }
+ else
+ {
+ /* === Prepare for supercolumn detection ==================== */
+
+ DEBUG4 (("Preparing supercol detection for Col: "ID".\n", col));
+
+ /* save score so far */
+ Col [col].shared2.score = cur_score ;
+
+ /* add column to hash table, for supercolumn detection */
+ hash %= n_col + 1 ;
+
+ DEBUG4 ((" Hash = "ID", n_col = "ID".\n", hash, n_col)) ;
+ ASSERT (((Int) hash) <= n_col) ;
+
+ head_column = head [hash] ;
+ if (head_column > EMPTY)
+ {
+ /* degree list "hash" is non-empty, use prev (shared3) of */
+ /* first column in degree list as head of hash bucket */
+ first_col = Col [head_column].shared3.headhash ;
+ Col [head_column].shared3.headhash = col ;
+ }
+ else
+ {
+ /* degree list "hash" is empty, use head as hash bucket */
+ first_col = - (head_column + 2) ;
+ head [hash] = - (col + 2) ;
+ }
+ Col [col].shared4.hash_next = first_col ;
+
+ /* save hash function in Col [col].shared3.hash */
+ Col [col].shared3.hash = (Int) hash ;
+ ASSERT (COL_IS_ALIVE (col)) ;
+ }
+ }
+
+ /* The approximate external column degree is now computed. */
+
+ /* === Supercolumn detection ======================================== */
+
+ DEBUG3 (("** Supercolumn detection phase. **\n")) ;
+
+ detect_super_cols (
+#ifndef NDEBUG
+ n_col, Row,
+#endif
+ Col, A, head, pivot_row_start, pivot_row_length, cmember) ;
+
+ /* === Kill the pivotal column ====================================== */
+
+ DEBUG1 ((" KILLING column detect supercols "ID" \n", pivot_col)) ;
+ KILL_PRINCIPAL_COL (pivot_col) ;
+
+ /* add columns to column list of front */
+#ifndef NDEBUG
+ DEBUG1 (("Pivot")) ;
+ dump_super (pivot_col, Col, n_col) ;
+#endif
+ Col [Col [pivot_col].lastcol].nextcol = Front_cols [nfr] ;
+ Front_cols [nfr] = pivot_col ;
+
+ /* === Clear mark =================================================== */
+
+ tag_mark = clear_mark (tag_mark+max_deg+1, max_mark, n_row, Row) ;
+
+#ifndef NDEBUG
+ DEBUG3 (("check3\n")) ;
+ debug_mark (n_row, Row, tag_mark, max_mark) ;
+#endif
+
+ /* === Finalize the new pivot row, and column scores ================ */
+
+ DEBUG3 (("** Finalize scores phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ /* compact the pivot row */
+ new_rp = rp ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ /* skip dead columns */
+ if (COL_IS_DEAD (col))
+ {
+ continue ;
+ }
+ *new_rp++ = col ;
+ /* add new pivot row to column */
+ A [Col [col].start + (Col [col].length++)] = pivot_row ;
+
+ /* retrieve score so far and add on pivot row's degree. */
+ /* (we wait until here for this in case the pivot */
+ /* row's degree was reduced due to mass elimination). */
+ cur_score = Col [col].shared2.score + pivot_row_degree ;
+
+ /* calculate the max possible score as the number of */
+ /* external columns minus the 'k' value minus the */
+ /* columns thickness */
+ max_score = n_col - k - Col [col].shared1.thickness ;
+
+ /* make the score the external degree of the union-of-rows */
+ cur_score -= Col [col].shared1.thickness ;
+
+ /* make sure score is less or equal than the max score */
+ cur_score = MIN (cur_score, max_score) ;
+ ASSERT (cur_score >= 0) ;
+
+ /* store updated score */
+ Col [col].shared2.score = cur_score ;
+
+ /* === Place column back in degree list ========================= */
+
+ if (CMEMBER (col) == current_set)
+ {
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (cur_score >= 0) ;
+ ASSERT (cur_score <= n_col) ;
+ ASSERT (head [cur_score] >= EMPTY) ;
+ next_col = head [cur_score] ;
+ Col [col].shared4.degree_next = next_col ;
+ Col [col].shared3.prev = EMPTY ;
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = col ;
+ }
+ head [cur_score] = col ;
+ /* see if this score is less than current min */
+ min_score = MIN (min_score, cur_score) ;
+ }
+ else
+ {
+ Col [col].shared4.degree_next = EMPTY ;
+ Col [col].shared3.prev = EMPTY ;
+ }
+ }
+
+#ifndef NDEBUG
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, cset_start [current_set+1]-(k+deadcol), max_deg) ;
+#endif
+
+ /* frontal matrix can have more pivot cols than pivot rows for */
+ /* singular matrices. */
+
+ /* number of candidate pivot columns */
+ Front_npivcol [nfr] = pivot_col_thickness ;
+
+ /* all rows (not just size of contrib. block) */
+ Front_nrows [nfr] = pivot_row_thickness ;
+
+ /* all cols */
+ Front_ncols [nfr] = pivot_col_thickness + pivot_row_degree ;
+
+ Front_parent [nfr] = EMPTY ;
+
+ pivot_row_thickness -= pivot_col_thickness ;
+ DEBUG1 (("Front "ID" Pivot_row_thickness after pivot cols elim: "ID"\n",
+ nfr, pivot_row_thickness)) ;
+ pivot_row_thickness = MAX (0, pivot_row_thickness) ;
+
+ /* === Resurrect the new pivot row ================================== */
+
+ if ((pivot_row_degree > 0 && pivot_row_thickness > 0 && (order_for_lu))
+ || (pivot_row_degree > 0 && (!order_for_lu)))
+ {
+ /* update pivot row length to reflect any cols that were killed */
+ /* during super-col detection and mass elimination */
+ Row [pivot_row].start = pivot_row_start ;
+ Row [pivot_row].length = (Int) (new_rp - &A[pivot_row_start]) ;
+ Row [pivot_row].shared1.degree = pivot_row_degree ;
+ Row [pivot_row].shared2.mark = 0 ;
+ Row [pivot_row].thickness = pivot_row_thickness ;
+ Row [pivot_row].front = nfr ;
+ /* pivot row is no longer dead */
+ DEBUG1 (("Resurrect Pivot_row "ID" deg: "ID"\n",
+ pivot_row, pivot_row_degree)) ;
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("Front "ID" : "ID" "ID" "ID" ", nfr,
+ Front_npivcol [nfr], Front_nrows [nfr], Front_ncols [nfr])) ;
+ DEBUG1 ((" cols:[ ")) ;
+ debug_d = 0 ;
+ for (col = Front_cols [nfr] ; col != EMPTY ; col = Col [col].nextcol)
+ {
+ DEBUG1 ((" "ID, col)) ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (COL_IS_DEAD (col)) ;
+ debug_d++ ;
+ ASSERT (debug_d <= pivot_col_thickness) ;
+ }
+ ASSERT (debug_d == pivot_col_thickness) ;
+ DEBUG1 ((" ]\n ")) ;
+#endif
+ nfr++ ; /* one more front */
+ }
+
+ /* === All principal columns have now been ordered ====================== */
+
+ *p_nfr = nfr ;
+ return (ngarbage) ;
+}
+
+
+/* ========================================================================== */
+/* === detect_super_cols ==================================================== */
+/* ========================================================================== */
+
+/*
+ * Detects supercolumns by finding matches between columns in the hash buckets.
+ * Check amongst columns in the set A [row_start ... row_start + row_length-1].
+ * The columns under consideration are currently *not* in the degree lists,
+ * and have already been placed in the hash buckets.
+ *
+ * The hash bucket for columns whose hash function is equal to h is stored
+ * as follows:
+ *
+ * if head [h] is >= 0, then head [h] contains a degree list, so:
+ *
+ * head [h] is the first column in degree bucket h.
+ * Col [head [h]].headhash gives the first column in hash bucket h.
+ *
+ * otherwise, the degree list is empty, and:
+ *
+ * -(head [h] + 2) is the first column in hash bucket h.
+ *
+ * For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous
+ * column" pointer. Col [c].shared3.hash is used instead as the hash number
+ * for that column. The value of Col [c].shared4.hash_next is the next column
+ * in the same hash bucket.
+ *
+ * Assuming no, or "few" hash collisions, the time taken by this routine is
+ * linear in the sum of the sizes (lengths) of each column whose score has
+ * just been computed in the approximate degree computation.
+ * Not user-callable.
+ */
+
+PRIVATE void detect_super_cols
+(
+ /* === Parameters ======================================================= */
+
+#ifndef NDEBUG
+ /* these two parameters are only needed when debugging is enabled: */
+ Int n_col, /* number of columns of A */
+ CColamd_Row Row [ ], /* of size n_row+1 */
+#endif
+
+ CColamd_Col Col [ ], /* of size n_col+1 */
+ Int A [ ], /* row indices of A */
+ Int head [ ], /* head of degree lists and hash buckets */
+ Int row_start, /* pointer to set of columns to check */
+ Int row_length, /* number of columns to check */
+ Int cmember [ ] /* col -> cset mapping */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int hash ; /* hash value for a column */
+ Int *rp ; /* pointer to a row */
+ Int c ; /* a column index */
+ Int super_c ; /* column index of the column to absorb into */
+ Int *cp1 ; /* column pointer for column super_c */
+ Int *cp2 ; /* column pointer for column c */
+ Int length ; /* length of column super_c */
+ Int prev_c ; /* column preceding c in hash bucket */
+ Int i ; /* loop counter */
+ Int *rp_end ; /* pointer to the end of the row */
+ Int col ; /* a column index in the row to check */
+ Int head_column ; /* first column in hash bucket or degree list */
+ Int first_col ; /* first column in hash bucket */
+
+ /* === Consider each column in the row ================================== */
+
+ rp = &A [row_start] ;
+ rp_end = rp + row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ if (COL_IS_DEAD (col))
+ {
+ continue ;
+ }
+
+ /* get hash number for this column */
+ hash = Col [col].shared3.hash ;
+ ASSERT (hash <= n_col) ;
+
+ /* === Get the first column in this hash bucket ===================== */
+
+ head_column = head [hash] ;
+ if (head_column > EMPTY)
+ {
+ first_col = Col [head_column].shared3.headhash ;
+ }
+ else
+ {
+ first_col = - (head_column + 2) ;
+ }
+
+ /* === Consider each column in the hash bucket ====================== */
+
+ for (super_c = first_col ; super_c != EMPTY ;
+ super_c = Col [super_c].shared4.hash_next)
+ {
+ ASSERT (COL_IS_ALIVE (super_c)) ;
+ ASSERT (Col [super_c].shared3.hash == hash) ;
+ length = Col [super_c].length ;
+
+ /* prev_c is the column preceding column c in the hash bucket */
+ prev_c = super_c ;
+
+ /* === Compare super_c with all columns after it ================ */
+
+ for (c = Col [super_c].shared4.hash_next ;
+ c != EMPTY ; c = Col [c].shared4.hash_next)
+ {
+ ASSERT (c != super_c) ;
+ ASSERT (COL_IS_ALIVE (c)) ;
+ ASSERT (Col [c].shared3.hash == hash) ;
+
+ /* not identical if lengths or scores are different, */
+ /* or if in different constraint sets */
+ if (Col [c].length != length ||
+ Col [c].shared2.score != Col [super_c].shared2.score
+ || CMEMBER (c) != CMEMBER (super_c))
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* compare the two columns */
+ cp1 = &A [Col [super_c].start] ;
+ cp2 = &A [Col [c].start] ;
+
+ for (i = 0 ; i < length ; i++)
+ {
+ /* the columns are "clean" (no dead rows) */
+ ASSERT (ROW_IS_ALIVE (*cp1)) ;
+ ASSERT (ROW_IS_ALIVE (*cp2)) ;
+ /* row indices will same order for both supercols, */
+ /* no gather scatter nessasary */
+ if (*cp1++ != *cp2++)
+ {
+ break ;
+ }
+ }
+
+ /* the two columns are different if the for-loop "broke" */
+ /* super columns should belong to the same constraint set */
+ if (i != length)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* === Got it! two columns are identical =================== */
+
+ ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;
+
+ Col [super_c].shared1.thickness += Col [c].shared1.thickness ;
+ Col [c].shared1.parent = super_c ;
+ KILL_NON_PRINCIPAL_COL (c) ;
+ /* order c later, in order_children() */
+ Col [c].shared2.order = EMPTY ;
+ /* remove c from hash bucket */
+ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;
+
+ /* add c to end of list of super_c */
+ ASSERT (Col [super_c].lastcol >= 0) ;
+ ASSERT (Col [super_c].lastcol < n_col) ;
+ Col [Col [super_c].lastcol].nextcol = c ;
+ Col [super_c].lastcol = Col [c].lastcol ;
+#ifndef NDEBUG
+ /* dump the supercolumn */
+ DEBUG1 (("Super")) ;
+ dump_super (super_c, Col, n_col) ;
+#endif
+ }
+ }
+
+ /* === Empty this hash bucket ======================================= */
+
+ if (head_column > EMPTY)
+ {
+ /* corresponding degree list "hash" is not empty */
+ Col [head_column].shared3.headhash = EMPTY ;
+ }
+ else
+ {
+ /* corresponding degree list "hash" is empty */
+ head [hash] = EMPTY ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === garbage_collection =================================================== */
+/* ========================================================================== */
+
+/*
+ * Defragments and compacts columns and rows in the workspace A. Used when
+ * all avaliable memory has been used while performing row merging. Returns
+ * the index of the first free position in A, after garbage collection. The
+ * time taken by this routine is linear is the size of the array A, which is
+ * itself linear in the number of nonzeros in the input matrix.
+ * Not user-callable.
+ */
+
+PRIVATE Int garbage_collection /* returns the new value of pfree */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows */
+ Int n_col, /* number of columns */
+ CColamd_Row Row [ ], /* row info */
+ CColamd_Col Col [ ], /* column info */
+ Int A [ ], /* A [0 ... Alen-1] holds the matrix */
+ Int *pfree /* &A [0] ... pfree is in use */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int *psrc ; /* source pointer */
+ Int *pdest ; /* destination pointer */
+ Int j ; /* counter */
+ Int r ; /* a row index */
+ Int c ; /* a column index */
+ Int length ; /* length of a row or column */
+
+#ifndef NDEBUG
+ Int debug_rows ;
+ DEBUG2 (("Defrag..\n")) ;
+ for (psrc = &A[0] ; psrc < pfree ; psrc++) ASSERT (*psrc >= 0) ;
+ debug_rows = 0 ;
+#endif
+
+ /* === Defragment the columns =========================================== */
+
+ pdest = &A[0] ;
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ psrc = &A [Col [c].start] ;
+
+ /* move and compact the column */
+ ASSERT (pdest <= psrc) ;
+ Col [c].start = (Int) (pdest - &A [0]) ;
+ length = Col [c].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ r = *psrc++ ;
+ if (ROW_IS_ALIVE (r))
+ {
+ *pdest++ = r ;
+ }
+ }
+ Col [c].length = (Int) (pdest - &A [Col [c].start]) ;
+ }
+ }
+
+ /* === Prepare to defragment the rows =================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_DEAD (r) || (Row [r].length == 0))
+ {
+ /* This row is already dead, or is of zero length. Cannot compact
+ * a row of zero length, so kill it. NOTE: in the current version,
+ * there are no zero-length live rows. Kill the row (for the first
+ * time, or again) just to be safe. */
+ KILL_ROW (r) ;
+ }
+ else
+ {
+ /* save first column index in Row [r].shared2.first_column */
+ psrc = &A [Row [r].start] ;
+ Row [r].shared2.first_column = *psrc ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ /* flag the start of the row with the one's complement of row */
+ *psrc = ONES_COMPLEMENT (r) ;
+#ifndef NDEBUG
+ debug_rows++ ;
+#endif
+ }
+ }
+
+ /* === Defragment the rows ============================================== */
+
+ psrc = pdest ;
+ while (psrc < pfree)
+ {
+ /* find a negative number ... the start of a row */
+ if (*psrc++ < 0)
+ {
+ psrc-- ;
+ /* get the row index */
+ r = ONES_COMPLEMENT (*psrc) ;
+ ASSERT (r >= 0 && r < n_row) ;
+ /* restore first column index */
+ *psrc = Row [r].shared2.first_column ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+
+ /* move and compact the row */
+ ASSERT (pdest <= psrc) ;
+ Row [r].start = (Int) (pdest - &A [0]) ;
+ length = Row [r].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ c = *psrc++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ *pdest++ = c ;
+ }
+ }
+ Row [r].length = (Int) (pdest - &A [Row [r].start]) ;
+#ifndef NDEBUG
+ debug_rows-- ;
+#endif
+ }
+ }
+
+ /* ensure we found all the rows */
+ ASSERT (debug_rows == 0) ;
+
+ /* === Return the new value of pfree ==================================== */
+
+ return ((Int) (pdest - &A [0])) ;
+}
+
+
+/* ========================================================================== */
+/* === clear_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ * Clears the Row [ ].shared2.mark array, and returns the new tag_mark.
+ * Return value is the new tag_mark. Not user-callable.
+ */
+
+PRIVATE Int clear_mark /* return the new value for tag_mark */
+(
+ /* === Parameters ======================================================= */
+
+ Int tag_mark, /* new value of tag_mark */
+ Int max_mark, /* max allowed value of tag_mark */
+
+ Int n_row, /* number of rows in A */
+ CColamd_Row Row [ ] /* Row [0 ... n_row-1].shared2.mark is set to zero */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+
+ if (tag_mark <= 0 || tag_mark >= max_mark)
+ {
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ Row [r].shared2.mark = 0 ;
+ }
+ }
+ tag_mark = 1 ;
+ }
+
+ return (tag_mark) ;
+}
+
+
+/* ========================================================================== */
+/* === print_report ========================================================= */
+/* ========================================================================== */
+
+/* No printing occurs if NPRINT is defined at compile time. */
+
+PRIVATE void print_report
+(
+ char *method,
+ Int stats [CCOLAMD_STATS]
+)
+{
+
+ Int i1, i2, i3 ;
+
+ PRINTF (("\n%s version %d.%d, %s: ", method,
+ CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE)) ;
+
+ if (!stats)
+ {
+ PRINTF (("No statistics available.\n")) ;
+ return ;
+ }
+
+ i1 = stats [CCOLAMD_INFO1] ;
+ i2 = stats [CCOLAMD_INFO2] ;
+ i3 = stats [CCOLAMD_INFO3] ;
+
+ if (stats [CCOLAMD_STATUS] >= 0)
+ {
+ PRINTF(("OK. ")) ;
+ }
+ else
+ {
+ PRINTF(("ERROR. ")) ;
+ }
+
+ switch (stats [CCOLAMD_STATUS])
+ {
+
+ case CCOLAMD_OK_BUT_JUMBLED:
+
+ PRINTF(("Matrix has unsorted or duplicate row indices.\n")) ;
+
+ PRINTF(("%s: duplicate or out-of-order row indices: "ID"\n",
+ method, i3)) ;
+
+ PRINTF(("%s: last seen duplicate or out-of-order row: "ID"\n",
+ method, INDEX (i2))) ;
+
+ PRINTF(("%s: last seen in column: "ID"",
+ method, INDEX (i1))) ;
+
+ /* no break - fall through to next case instead */
+
+ case CCOLAMD_OK:
+
+ PRINTF(("\n")) ;
+
+ PRINTF(("%s: number of dense or empty rows ignored: "ID"\n",
+ method, stats [CCOLAMD_DENSE_ROW])) ;
+
+ PRINTF(("%s: number of dense or empty columns ignored: "ID"\n",
+ method, stats [CCOLAMD_DENSE_COL])) ;
+
+ PRINTF(("%s: number of garbage collections performed: "ID"\n",
+ method, stats [CCOLAMD_DEFRAG_COUNT])) ;
+ break ;
+
+ case CCOLAMD_ERROR_A_not_present:
+
+ PRINTF(("Array A (row indices of matrix) not present.\n")) ;
+ break ;
+
+ case CCOLAMD_ERROR_p_not_present:
+
+ PRINTF(("Array p (column pointers for matrix) not present.\n")) ;
+ break ;
+
+ case CCOLAMD_ERROR_nrow_negative:
+
+ PRINTF(("Invalid number of rows ("ID").\n", i1)) ;
+ break ;
+
+ case CCOLAMD_ERROR_ncol_negative:
+
+ PRINTF(("Invalid number of columns ("ID").\n", i1)) ;
+ break ;
+
+ case CCOLAMD_ERROR_nnz_negative:
+
+ PRINTF(("Invalid number of nonzero entries ("ID").\n", i1)) ;
+ break ;
+
+ case CCOLAMD_ERROR_p0_nonzero:
+
+ PRINTF(("Invalid column pointer, p [0] = "ID", must be 0.\n", i1)) ;
+ break ;
+
+ case CCOLAMD_ERROR_A_too_small:
+
+ PRINTF(("Array A too small.\n")) ;
+ PRINTF((" Need Alen >= "ID", but given only Alen = "ID".\n",
+ i1, i2)) ;
+ break ;
+
+ case CCOLAMD_ERROR_col_length_negative:
+
+ PRINTF(("Column "ID" has a negative number of entries ("ID").\n",
+ INDEX (i1), i2)) ;
+ break ;
+
+ case CCOLAMD_ERROR_row_index_out_of_bounds:
+
+ PRINTF(("Row index (row "ID") out of bounds ("ID" to "ID") in"
+ "column "ID".\n", INDEX (i2), INDEX (0), INDEX (i3-1),
+ INDEX (i1))) ;
+ break ;
+
+ case CCOLAMD_ERROR_out_of_memory:
+
+ PRINTF(("Out of memory.\n")) ;
+ break ;
+
+ case CCOLAMD_ERROR_invalid_cmember:
+
+ PRINTF(("cmember invalid\n")) ;
+ break ;
+ }
+}
+
+
+/* ========================================================================= */
+/* === "Expert" routines =================================================== */
+/* ========================================================================= */
+
+/* The following routines are visible outside this routine, but are not meant
+ * to be called by the user. They are meant for a future version of UMFPACK,
+ * to replace UMFPACK internal routines with a similar name.
+ */
+
+
+/* ========================================================================== */
+/* === CCOLAMD_apply_order ================================================== */
+/* ========================================================================== */
+
+/*
+ * Apply post-ordering of supernodal elimination tree.
+ */
+
+GLOBAL void CCOLAMD_apply_order
+(
+ Int Front [ ], /* of size nn on input, size nfr on output */
+ const Int Order [ ], /* Order [i] = k, i in the range 0..nn-1,
+ * and k in the range 0..nfr-1, means that node
+ * i is the kth node in the postordered tree. */
+ Int Temp [ ], /* workspace of size nfr */
+ Int nn, /* nodes are numbered in the range 0..nn-1 */
+ Int nfr /* the number of nodes actually in use */
+)
+{
+ Int i, k ;
+ for (i = 0 ; i < nn ; i++)
+ {
+ k = Order [i] ;
+ ASSERT (k >= EMPTY && k < nfr) ;
+ if (k != EMPTY)
+ {
+ Temp [k] = Front [i] ;
+ }
+ }
+
+ for (k = 0 ; k < nfr ; k++)
+ {
+ Front [k] = Temp [k] ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === CCOLAMD_fsize ======================================================== */
+/* ========================================================================== */
+
+/* Determine the largest frontal matrix size for each subtree.
+ * Only required to sort the children of each
+ * node prior to postordering the column elimination tree. */
+
+GLOBAL void CCOLAMD_fsize
+(
+ Int nn,
+ Int Fsize [ ],
+ Int Fnrows [ ],
+ Int Fncols [ ],
+ Int Parent [ ],
+ Int Npiv [ ]
+)
+{
+ double dr, dc ;
+ Int j, parent, frsize, r, c ;
+
+ for (j = 0 ; j < nn ; j++)
+ {
+ Fsize [j] = EMPTY ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find max front size for tree rooted at node j, for each front j */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG1 (("\n\n========================================FRONTS:\n")) ;
+ for (j = 0 ; j < nn ; j++)
+ {
+ if (Npiv [j] > 0)
+ {
+ /* this is a frontal matrix */
+ parent = Parent [j] ;
+ r = Fnrows [j] ;
+ c = Fncols [j] ;
+ /* avoid integer overflow */
+ dr = (double) r ;
+ dc = (double) c ;
+ frsize = (INT_OVERFLOW (dr * dc)) ? Int_MAX : (r * c) ;
+ DEBUG1 ((""ID" : npiv "ID" size "ID" parent "ID" ",
+ j, Npiv [j], frsize, parent)) ;
+ Fsize [j] = MAX (Fsize [j], frsize) ;
+ DEBUG1 (("Fsize [j = "ID"] = "ID"\n", j, Fsize [j])) ;
+ if (parent != EMPTY)
+ {
+ /* find the maximum frontsize of self and children */
+ ASSERT (Npiv [parent] > 0) ;
+ ASSERT (parent > j) ;
+ Fsize [parent] = MAX (Fsize [parent], Fsize [j]) ;
+ DEBUG1 (("Fsize [parent = "ID"] = "ID"\n",
+ parent, Fsize [parent]));
+ }
+ }
+ }
+ DEBUG1 (("fsize done\n")) ;
+}
+
+
+/* ========================================================================= */
+/* === CCOLAMD_postorder =================================================== */
+/* ========================================================================= */
+
+/* Perform a postordering (via depth-first search) of an assembly tree. */
+
+GLOBAL void CCOLAMD_postorder
+(
+ /* inputs, not modified on output: */
+ Int nn, /* nodes are in the range 0..nn-1 */
+ Int Parent [ ], /* Parent [j] is the parent of j, or EMPTY if root */
+ Int Nv [ ], /* Nv [j] > 0 number of pivots represented by node j,
+ * or zero if j is not a node. */
+ Int Fsize [ ], /* Fsize [j]: size of node j */
+
+ /* output, not defined on input: */
+ Int Order [ ], /* output post-order */
+
+ /* workspaces of size nn: */
+ Int Child [ ],
+ Int Sibling [ ],
+ Int Stack [ ],
+ Int Front_cols [ ],
+
+ /* input, not modified on output: */
+ Int cmember [ ]
+)
+{
+ Int i, j, k, parent, frsize, f, fprev, maxfrsize, bigfprev, bigf, fnext ;
+
+ for (j = 0 ; j < nn ; j++)
+ {
+ Child [j] = EMPTY ;
+ Sibling [j] = EMPTY ;
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* place the children in link lists - bigger elements tend to be last */
+ /* --------------------------------------------------------------------- */
+
+ for (j = nn-1 ; j >= 0 ; j--)
+ {
+ if (Nv [j] > 0)
+ {
+ /* this is an element */
+ parent = Parent [j] ;
+ if (parent != EMPTY)
+ {
+ /* place the element in link list of the children its parent */
+ /* bigger elements will tend to be at the end of the list */
+ Sibling [j] = Child [parent] ;
+ if (CMEMBER (Front_cols[parent]) == CMEMBER (Front_cols[j]))
+ {
+ Child [parent] = j ;
+ }
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ {
+ Int nels, ff, nchild ;
+ DEBUG1 (("\n\n================================ ccolamd_postorder:\n"));
+ nels = 0 ;
+ for (j = 0 ; j < nn ; j++)
+ {
+ if (Nv [j] > 0)
+ {
+ DEBUG1 ((""ID" : nels "ID" npiv "ID" size "ID
+ " parent "ID" maxfr "ID"\n", j, nels,
+ Nv [j], Fsize [j], Parent [j], Fsize [j])) ;
+ /* this is an element */
+ /* dump the link list of children */
+ nchild = 0 ;
+ DEBUG1 ((" Children: ")) ;
+ for (ff = Child [j] ; ff != EMPTY ; ff = Sibling [ff])
+ {
+ DEBUG1 ((ID" ", ff)) ;
+ nchild++ ;
+ ASSERT (nchild < nn) ;
+ }
+ DEBUG1 (("\n")) ;
+ parent = Parent [j] ;
+ nels++ ;
+ }
+ }
+ }
+#endif
+
+ /* --------------------------------------------------------------------- */
+ /* place the largest child last in the list of children for each node */
+ /* --------------------------------------------------------------------- */
+
+ for (i = 0 ; i < nn ; i++)
+ {
+ if (Nv [i] > 0 && Child [i] != EMPTY)
+ {
+
+#ifndef NDEBUG
+ Int nchild ;
+ DEBUG1 (("Before partial sort, element "ID"\n", i)) ;
+ nchild = 0 ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ DEBUG1 ((" f: "ID" size: "ID"\n", f, Fsize [f])) ;
+ nchild++ ;
+ }
+#endif
+
+ /* find the biggest element in the child list */
+ fprev = EMPTY ;
+ maxfrsize = EMPTY ;
+ bigfprev = EMPTY ;
+ bigf = EMPTY ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ frsize = Fsize [f] ;
+ if (frsize >= maxfrsize)
+ {
+ /* this is the biggest seen so far */
+ maxfrsize = frsize ;
+ bigfprev = fprev ;
+ bigf = f ;
+ }
+ fprev = f ;
+ }
+
+ fnext = Sibling [bigf] ;
+
+ DEBUG1 (("bigf "ID" maxfrsize "ID" bigfprev "ID" fnext "ID
+ " fprev " ID"\n", bigf, maxfrsize, bigfprev, fnext, fprev)) ;
+
+ if (fnext != EMPTY)
+ {
+ /* if fnext is EMPTY then bigf is already at the end of list */
+
+ if (bigfprev == EMPTY)
+ {
+ /* delete bigf from the element of the list */
+ Child [i] = fnext ;
+ }
+ else
+ {
+ /* delete bigf from the middle of the list */
+ Sibling [bigfprev] = fnext ;
+ }
+
+ /* put bigf at the end of the list */
+ Sibling [bigf] = EMPTY ;
+ Sibling [fprev] = bigf ;
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("After partial sort, element "ID"\n", i)) ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ DEBUG1 ((" "ID" "ID"\n", f, Fsize [f])) ;
+ nchild-- ;
+ }
+#endif
+ }
+ }
+
+ /* --------------------------------------------------------------------- */
+ /* postorder the assembly tree */
+ /* --------------------------------------------------------------------- */
+
+ for (i = 0 ; i < nn ; i++)
+ {
+ Order [i] = EMPTY ;
+ }
+
+ k = 0 ;
+
+ for (i = 0 ; i < nn ; i++)
+ {
+ if ((Parent [i] == EMPTY
+ || (CMEMBER (Front_cols [Parent [i]]) != CMEMBER (Front_cols [i])))
+ && Nv [i] > 0)
+ {
+ DEBUG1 (("Root of assembly tree "ID"\n", i)) ;
+ k = CCOLAMD_post_tree (i, k, Child, Sibling, Order, Stack) ;
+ }
+ }
+}
+
+
+/* ========================================================================= */
+/* === CCOLAMD_post_tree =================================================== */
+/* ========================================================================= */
+
+/* Post-ordering of a supernodal column elimination tree. */
+
+GLOBAL Int CCOLAMD_post_tree
+(
+ Int root, /* root of the tree */
+ Int k, /* start numbering at k */
+ Int Child [ ], /* input argument of size nn, undefined on
+ * output. Child [i] is the head of a link
+ * list of all nodes that are children of node
+ * i in the tree. */
+ const Int Sibling [ ], /* input argument of size nn, not modified.
+ * If f is a node in the link list of the
+ * children of node i, then Sibling [f] is the
+ * next child of node i.
+ */
+ Int Order [ ], /* output order, of size nn. Order [i] = k
+ * if node i is the kth node of the reordered
+ * tree. */
+ Int Stack [ ] /* workspace of size nn */
+)
+{
+ Int f, head, h, i ;
+
+#if 0
+ /* --------------------------------------------------------------------- */
+ /* recursive version (Stack [ ] is not used): */
+ /* --------------------------------------------------------------------- */
+
+ /* this is simple, but can cause stack overflow if nn is large */
+ i = root ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ k = CCOLAMD_post_tree (f, k, Child, Sibling, Order, Stack, nn) ;
+ }
+ Order [i] = k++ ;
+ return (k) ;
+#endif
+
+ /* --------------------------------------------------------------------- */
+ /* non-recursive version, using an explicit stack */
+ /* --------------------------------------------------------------------- */
+
+ /* push root on the stack */
+ head = 0 ;
+ Stack [0] = root ;
+
+ while (head >= 0)
+ {
+ /* get head of stack */
+ i = Stack [head] ;
+ DEBUG1 (("head of stack "ID" \n", i)) ;
+
+ if (Child [i] != EMPTY)
+ {
+ /* the children of i are not yet ordered */
+ /* push each child onto the stack in reverse order */
+ /* so that small ones at the head of the list get popped first */
+ /* and the biggest one at the end of the list gets popped last */
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ head++ ;
+ }
+ h = head ;
+ for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
+ {
+ ASSERT (h > 0) ;
+ Stack [h--] = f ;
+ DEBUG1 (("push "ID" on stack\n", f)) ;
+ }
+ ASSERT (Stack [h] == i) ;
+
+ /* delete child list so that i gets ordered next time we see it */
+ Child [i] = EMPTY ;
+ }
+ else
+ {
+ /* the children of i (if there were any) are already ordered */
+ /* remove i from the stack and order it. Front i is kth front */
+ head-- ;
+ DEBUG1 (("pop "ID" order "ID"\n", i, k)) ;
+ Order [i] = k++ ;
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("\nStack:")) ;
+ for (h = head ; h >= 0 ; h--)
+ {
+ Int j = Stack [h] ;
+ DEBUG1 ((" "ID, j)) ;
+ }
+ DEBUG1 (("\n\n")) ;
+#endif
+
+ }
+ return (k) ;
+}
+
+
+
+/* ========================================================================== */
+/* === CCOLAMD debugging routines =========================================== */
+/* ========================================================================== */
+
+/* When debugging is disabled, the remainder of this file is ignored. */
+
+#ifndef NDEBUG
+
+
+/* ========================================================================== */
+/* === debug_structures ===================================================== */
+/* ========================================================================== */
+
+/*
+ * At this point, all empty rows and columns are dead. All live columns
+ * are "clean" (containing no dead rows) and simplicial (no supercolumns
+ * yet). Rows may contain dead columns, but all live rows contain at
+ * least one live column.
+ */
+
+PRIVATE void debug_structures
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ CColamd_Row Row [ ],
+ CColamd_Col Col [ ],
+ Int A [ ],
+ Int cmember [ ],
+ Int cset_start [ ]
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ;
+ Int c ;
+ Int *cp ;
+ Int *cp_end ;
+ Int len ;
+ Int score ;
+ Int r ;
+ Int *rp ;
+ Int *rp_end ;
+ Int deg ;
+ Int cs ;
+
+ /* === Check A, Row, and Col ============================================ */
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ len = Col [c].length ;
+ score = Col [c].shared2.score ;
+ DEBUG4 (("initial live col %5d %5d %5d\n", c, len, score)) ;
+ ASSERT (len > 0) ;
+ ASSERT (score >= 0) ;
+ ASSERT (Col [c].shared1.thickness == 1) ;
+ cp = &A [Col [c].start] ;
+ cp_end = cp + len ;
+ while (cp < cp_end)
+ {
+ r = *cp++ ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ }
+ }
+ else
+ {
+ i = Col [c].shared2.order ;
+ cs = CMEMBER (c) ;
+ ASSERT (i >= cset_start [cs] && i < cset_start [cs+1]) ;
+ }
+ }
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ i = 0 ;
+ len = Row [r].length ;
+ deg = Row [r].shared1.degree ;
+ ASSERT (len > 0) ;
+ ASSERT (deg > 0) ;
+ rp = &A [Row [r].start] ;
+ rp_end = rp + len ;
+ while (rp < rp_end)
+ {
+ c = *rp++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ i++ ;
+ }
+ }
+ ASSERT (i > 0) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_deg_lists ====================================================== */
+/* ========================================================================== */
+
+/*
+ * Prints the contents of the degree lists. Counts the number of columns
+ * in the degree list and compares it to the total it should have. Also
+ * checks the row degrees.
+ */
+
+PRIVATE void debug_deg_lists
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ CColamd_Row Row [ ],
+ CColamd_Col Col [ ],
+ Int head [ ],
+ Int min_score,
+ Int should,
+ Int max_deg
+)
+
+{
+ /* === Local variables ================================================== */
+
+ Int deg ;
+ Int col ;
+ Int have ;
+ Int row ;
+
+ /* === Check the degree lists =========================================== */
+
+ if (n_col > 10000 && ccolamd_debug <= 0)
+ {
+ return ;
+ }
+ have = 0 ;
+ DEBUG4 (("Degree lists: "ID"\n", min_score)) ;
+ for (deg = 0 ; deg <= n_col ; deg++)
+ {
+ col = head [deg] ;
+ if (col == EMPTY)
+ {
+ continue ;
+ }
+ DEBUG4 (("%d:", deg)) ;
+ ASSERT (Col [col].shared3.prev == EMPTY) ;
+ while (col != EMPTY)
+ {
+ DEBUG4 ((" "ID"", col)) ;
+ have += Col [col].shared1.thickness ;
+ ASSERT (COL_IS_ALIVE (col)) ;
+ col = Col [col].shared4.degree_next ;
+ }
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("should "ID" have "ID"\n", should, have)) ;
+ ASSERT (should == have) ;
+
+ /* === Check the row degrees ============================================ */
+
+ if (n_row > 10000 && ccolamd_debug <= 0)
+ {
+ return ;
+ }
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (ROW_IS_ALIVE (row))
+ {
+ ASSERT (Row [row].shared1.degree <= max_deg) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ * Ensures that the tag_mark is less that the maximum and also ensures that
+ * each entry in the mark array is less than the tag mark.
+ */
+
+PRIVATE void debug_mark
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ CColamd_Row Row [ ],
+ Int tag_mark,
+ Int max_mark
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+
+ /* === Check the Row marks ============================================== */
+
+ ASSERT (tag_mark > 0 && tag_mark <= max_mark) ;
+ if (n_row > 10000 && ccolamd_debug <= 0)
+ {
+ return ;
+ }
+ for (r = 0 ; r < n_row ; r++)
+ {
+ ASSERT (Row [r].shared2.mark < tag_mark) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_matrix ========================================================= */
+/* ========================================================================== */
+
+/* Prints out the contents of the columns and the rows. */
+
+PRIVATE void debug_matrix
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ CColamd_Row Row [ ],
+ CColamd_Col Col [ ],
+ Int A [ ]
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+ Int c ;
+ Int *rp ;
+ Int *rp_end ;
+ Int *cp ;
+ Int *cp_end ;
+
+ /* === Dump the rows and columns of the matrix ========================== */
+
+ if (ccolamd_debug < 3)
+ {
+ return ;
+ }
+ DEBUG3 (("DUMP MATRIX:\n")) ;
+ for (r = 0 ; r < n_row ; r++)
+ {
+ DEBUG3 (("Row "ID" alive? "ID"\n", r, ROW_IS_ALIVE (r))) ;
+ if (ROW_IS_DEAD (r))
+ {
+ continue ;
+ }
+
+ DEBUG3 (("start "ID" length "ID" degree "ID"\nthickness "ID"\n",
+ Row [r].start, Row [r].length, Row [r].shared1.degree,
+ Row [r].thickness)) ;
+
+ rp = &A [Row [r].start] ;
+ rp_end = rp + Row [r].length ;
+ while (rp < rp_end)
+ {
+ c = *rp++ ;
+ DEBUG4 ((" "ID" col "ID"\n", COL_IS_ALIVE (c), c)) ;
+ }
+ }
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ DEBUG3 (("Col "ID" alive? "ID"\n", c, COL_IS_ALIVE (c))) ;
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ DEBUG3 (("start "ID" length "ID" shared1 "ID" shared2 "ID"\n",
+ Col [c].start, Col [c].length,
+ Col [c].shared1.thickness, Col [c].shared2.score)) ;
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ r = *cp++ ;
+ DEBUG4 ((" "ID" row "ID"\n", ROW_IS_ALIVE (r), r)) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === dump_super =========================================================== */
+/* ========================================================================== */
+
+PRIVATE void dump_super
+(
+ Int super_c,
+ CColamd_Col Col [ ],
+ Int n_col
+)
+{
+ Int col, ncols ;
+
+ DEBUG1 ((" =[ ")) ;
+ ncols = 0 ;
+ for (col = super_c ; col != EMPTY ; col = Col [col].nextcol)
+ {
+ DEBUG1 ((" "ID, col)) ;
+ ASSERT (col >= 0 && col < n_col) ;
+ if (col != super_c)
+ {
+ ASSERT (COL_IS_DEAD (col)) ;
+ }
+ if (Col [col].nextcol == EMPTY)
+ {
+ ASSERT (col == Col [super_c].lastcol) ;
+ }
+ ncols++ ;
+ ASSERT (ncols <= Col [super_c].shared1.thickness) ;
+ }
+ ASSERT (ncols == Col [super_c].shared1.thickness) ;
+ DEBUG1 (("]\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === ccolamd_get_debug ==================================================== */
+/* ========================================================================== */
+
+PRIVATE void ccolamd_get_debug
+(
+ char *method
+)
+{
+ FILE *debug_file ;
+ ccolamd_debug = 0 ; /* no debug printing */
+
+ /* Read debug info from the debug file. */
+ debug_file = fopen ("debug", "r") ;
+ if (debug_file)
+ {
+ (void) fscanf (debug_file, ""ID"", &ccolamd_debug) ;
+ (void) fclose (debug_file) ;
+ }
+
+ DEBUG0 ((":")) ;
+ DEBUG1 (("%s: debug version, D = "ID" (THIS WILL BE SLOW!)\n",
+ method, ccolamd_debug)) ;
+ DEBUG1 ((" Debug printing level: "ID"\n", ccolamd_debug)) ;
+}
+
+#endif
diff --git a/CCOLAMD/Source/ccolamd_global.c b/CCOLAMD/Source/ccolamd_global.c
new file mode 100644
index 0000000..d439851
--- /dev/null
+++ b/CCOLAMD/Source/ccolamd_global.c
@@ -0,0 +1,25 @@
+/* ========================================================================== */
+/* === ccolamd_global.c ===================================================== */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis,
+ * Sivasankaran Rajamanickam, and Stefan Larimore
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Global variables for CCOLAMD */
+
+#ifndef NPRINT
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+int (*ccolamd_printf) (const char *, ...) = mexPrintf ;
+#else
+#include <stdio.h>
+int (*ccolamd_printf) (const char *, ...) = printf ;
+#endif
+#else
+int (*ccolamd_printf) (const char *, ...) = ((void *) 0) ;
+#endif
+
diff --git a/CHOLMOD/Check/License.txt b/CHOLMOD/Check/License.txt
new file mode 100644
index 0000000..8a20b17
--- /dev/null
+++ b/CHOLMOD/Check/License.txt
@@ -0,0 +1,24 @@
+CHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Check module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
diff --git a/CHOLMOD/Check/cholmod_check.c b/CHOLMOD/Check/cholmod_check.c
new file mode 100644
index 0000000..13a092d
--- /dev/null
+++ b/CHOLMOD/Check/cholmod_check.c
@@ -0,0 +1,2627 @@
+/* ========================================================================== */
+/* === Check/cholmod_check ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Check Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Routines to check and print the contents of the 5 CHOLMOD objects:
+ *
+ * No CHOLMOD routine calls the check or print routines. If a user wants to
+ * check CHOLMOD's input parameters, a separate call to the appropriate check
+ * routine should be used before calling other CHOLMOD routines.
+ *
+ * cholmod_check_common check statistics and workspace in Common
+ * cholmod_check_sparse check sparse matrix in compressed column form
+ * cholmod_check_dense check dense matrix
+ * cholmod_check_factor check factorization
+ * cholmod_check_triplet check sparse matrix in triplet form
+ *
+ * cholmod_print_common print statistics in Common
+ * cholmod_print_sparse print sparse matrix in compressed column form
+ * cholmod_print_dense print dense matrix
+ * cholmod_print_factor print factorization
+ * cholmod_print_triplet print sparse matrix in triplet form
+ *
+ * In addition, this file contains routines to check and print three types of
+ * integer vectors:
+ *
+ * cholmod_check_perm check a permutation of 0:n-1 (no duplicates)
+ * cholmod_check_subset check a subset of 0:n-1 (duplicates OK)
+ * cholmod_check_parent check an elimination tree
+ *
+ * cholmod_print_perm print a permutation
+ * cholmod_print_subset print a subset
+ * cholmod_print_parent print an elimination tree
+ *
+ * Each Common->print level prints the items at or below the given level:
+ *
+ * 0: print nothing; just check the data structures and return TRUE/FALSE
+ * 1: error messages
+ * 2: warning messages
+ * 3: one-line summary of each object printed
+ * 4: short summary of each object (first and last few entries)
+ * 5: entire contents of the object
+ *
+ * No CHOLMOD routine calls these routines, so no printing occurs unless
+ * the user specifically calls a cholmod_print_* routine. Thus, the default
+ * print level is 3.
+ *
+ * Common->precise controls the # of digits printed for numerical entries
+ * (5 if FALSE, 15 if TRUE).
+ *
+ * If Common->print_function is NULL, then no printing occurs. The
+ * cholmod_check_* and cholmod_print_* routines still check their inputs and
+ * return TRUE/FALSE if the object is valid or not.
+ *
+ * This file also includes debugging routines that are enabled only when
+ * NDEBUG is defined in cholmod_internal.h (cholmod_dump_*).
+ */
+
+#ifndef NCHECK
+
+#include "cholmod_internal.h"
+#include "cholmod_check.h"
+
+/* ========================================================================== */
+/* === printing definitions ================================================= */
+/* ========================================================================== */
+
+#ifdef LONG
+#define I8 "%8ld"
+#define I_8 "%-8ld"
+#else
+#define I8 "%8d"
+#define I_8 "%-8d"
+#endif
+
+#define PR(i,format,arg) \
+{ \
+ if (print >= i && Common->print_function != NULL) \
+ { \
+ (Common->print_function) (format, arg) ; \
+ } \
+}
+
+#define P1(format,arg) PR(1,format,arg)
+#define P2(format,arg) PR(2,format,arg)
+#define P3(format,arg) PR(3,format,arg)
+#define P4(format,arg) PR(4,format,arg)
+
+#define ERR(msg) \
+{ \
+ P1 ("\nCHOLMOD ERROR: %s: ", type) ; \
+ if (name != NULL) \
+ { \
+ P1 ("%s", name) ; \
+ } \
+ P1 (": %s\n", msg) ; \
+ ERROR (CHOLMOD_INVALID, "invalid") ; \
+ return (FALSE) ; \
+}
+
+/* print a numerical value */
+#define PRINTVALUE(value) \
+{ \
+ if (Common->precise) \
+ { \
+ P4 (" %23.15e", value) ; \
+ } \
+ else \
+ { \
+ P4 (" %.5g", value) ; \
+ } \
+}
+
+/* start printing */
+#define ETC_START(count,limit) \
+{ \
+ count = (init_print == 4) ? (limit) : (-1) ; \
+}
+
+/* re-enable printing if condition is met */
+#define ETC_ENABLE(condition,count,limit) \
+{ \
+ if ((condition) && init_print == 4) \
+ { \
+ count = limit ; \
+ print = 4 ; \
+ } \
+}
+
+/* turn off printing if limit is reached */
+#define ETC_DISABLE(count) \
+{ \
+ if ((count >= 0) && (count-- == 0) && print == 4) \
+ { \
+ P4 ("%s", " ...\n") ; \
+ print = 3 ; \
+ } \
+}
+
+/* re-enable printing, or turn if off after limit is reached */
+#define ETC(condition,count,limit) \
+{ \
+ ETC_ENABLE (condition, count, limit) ; \
+ ETC_DISABLE (count) ; \
+}
+
+#define BOOLSTR(x) ((x) ? "true " : "false")
+
+/* ========================================================================== */
+/* === print_value ========================================================== */
+/* ========================================================================== */
+
+static void print_value
+(
+ Int print,
+ Int xtype,
+ double *Xx,
+ double *Xz,
+ Int p,
+ cholmod_common *Common)
+{
+ if (xtype == CHOLMOD_REAL)
+ {
+ PRINTVALUE (Xx [p]) ;
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ P4 ("%s", "(") ;
+ PRINTVALUE (Xx [2*p ]) ;
+ P4 ("%s", " , ") ;
+ PRINTVALUE (Xx [2*p+1]) ;
+ P4 ("%s", ")") ;
+ }
+ else if (xtype == CHOLMOD_ZOMPLEX)
+ {
+ P4 ("%s", "(") ;
+ PRINTVALUE (Xx [p]) ;
+ P4 ("%s", " , ") ;
+ PRINTVALUE (Xz [p]) ;
+ P4 ("%s", ")") ;
+ }
+}
+
+/* ========================================================================== */
+/* === cholmod_check_common ================================================= */
+/* ========================================================================== */
+
+/* Print and verify the contents of Common */
+
+static int check_common
+(
+ Int print,
+ char *name,
+ cholmod_common *Common
+)
+{
+ double fl, lnz ;
+ double *Xwork ;
+ Int *Flag, *Head ;
+ UF_long mark ;
+ Int i, nrow, nmethods, ordering, xworksize, amd_printed, init_print ;
+ char *type = "common" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print control parameters and statistics */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ init_print = print ;
+
+ P2 ("%s", "\n") ;
+
+ P1 ("CHOLMOD version %d", CHOLMOD_MAIN_VERSION) ;
+ P1 (".%d", CHOLMOD_SUB_VERSION) ;
+ P1 (".%d", CHOLMOD_SUBSUB_VERSION) ;
+ P1 (", %s: ", CHOLMOD_DATE) ;
+
+ if (name != NULL)
+ {
+ P1 ("%s: ", name) ;
+ }
+ switch (Common->status)
+ {
+
+ case CHOLMOD_OK:
+ P1 ("%s", "status: OK\n") ;
+ break ;
+
+ case CHOLMOD_OUT_OF_MEMORY:
+ P1 ("%s", "status: ERROR, out of memory\n") ;
+ break ;
+
+ case CHOLMOD_INVALID:
+ P1 ("%s", "status: ERROR, invalid parameter\n") ;
+ break ;
+
+ case CHOLMOD_TOO_LARGE:
+ P1 ("%s", "status: ERROR, problem too large\n") ;
+ break ;
+
+ case CHOLMOD_NOT_INSTALLED:
+ P1 ("%s", "status: ERROR, method not installed\n") ;
+ break ;
+
+ case CHOLMOD_NOT_POSDEF:
+ P1 ("%s", "status: warning, matrix not positive definite\n") ;
+ break ;
+
+ case CHOLMOD_DSMALL:
+ P1 ("%s", "status: warning, diagonal entry has tiny abs. value\n") ;
+ break ;
+
+ default:
+ ERR ("unknown status") ;
+ }
+
+ P2 (" Architecture: %s\n", CHOLMOD_ARCHITECTURE) ;
+ P3 (" sizeof(int): %d\n", (int) sizeof (int)) ;
+ P3 (" sizeof(UF_long): %d\n", (int) sizeof (UF_long)) ;
+ P3 (" sizeof(void *): %d\n", (int) sizeof (void *)) ;
+ P3 (" sizeof(double): %d\n", (int) sizeof (double)) ;
+ P3 (" sizeof(Int): %d (CHOLMOD's basic integer)\n", (int) sizeof (Int)) ;
+ P3 (" sizeof(BLAS_INT): %d (integer used in the BLAS)\n",
+ (int) sizeof (BLAS_INT)) ;
+
+ if (Common->fl != EMPTY)
+ {
+ P2 ("%s", " Results from most recent analysis:\n") ;
+ P2 (" Cholesky flop count: %.5g\n", Common->fl) ;
+ P2 (" Nonzeros in L: %.5g\n", Common->lnz) ;
+ }
+ if (Common->modfl != EMPTY)
+ {
+ P2 (" Update/downdate flop count: %.5g\n", Common->modfl) ;
+ }
+
+ P2 (" memory blocks in use: %8.0f\n", (double) (Common->malloc_count)) ;
+ P2 (" memory in use (MB): %8.1f\n",
+ (double) (Common->memory_inuse) / 1048576.) ;
+ P2 (" peak memory usage (MB): %8.1f\n",
+ (double) (Common->memory_usage) / 1048576.) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* primary control parameters and related ordering statistics */
+ /* ---------------------------------------------------------------------- */
+
+ P3 (" maxrank: update/downdate rank: "ID"\n",
+ (Int) CHOLMOD(maxrank) (0, Common)) ;
+ P3 (" supernodal control: %d", Common->supernodal) ;
+ P3 (" %g ", Common->supernodal_switch) ;
+ if (Common->supernodal <= CHOLMOD_SIMPLICIAL)
+ {
+ P3 ("%s", "(always do simplicial)\n") ;
+ }
+ else if (Common->supernodal == CHOLMOD_AUTO)
+ {
+ P3 ("(supernodal if flops/lnz >= %g)\n", Common->supernodal_switch) ;
+ }
+ else
+ {
+ P3 ("%s", "(always do supernodal)\n") ;
+ }
+
+ nmethods = MIN (Common->nmethods, CHOLMOD_MAXMETHODS) ;
+ nmethods = MAX (0, nmethods) ;
+
+ if (nmethods > 0)
+ {
+ P3 ("%s", " nmethods: number of ordering methods to try: ") ;
+ P3 (""ID"\n", nmethods) ;
+ }
+ else
+ {
+ P3 ("%s", " nmethods=0: default strategy: Try user permutation if "
+ "given. Try AMD.\n") ;
+#ifndef NPARTITION
+ if (Common->default_nesdis)
+ {
+ P3 ("%s", " Try NESDIS if AMD reports flops/nnz(L) >= 500 and "
+ "nnz(L)/nnz(A) >= 5.\n") ;
+ }
+ else
+ {
+ P3 ("%s", " Try METIS if AMD reports flops/nnz(L) >= 500 and "
+ "nnz(L)/nnz(A) >= 5.\n") ;
+ }
+#endif
+ P3 ("%s", " Select best ordering tried.\n") ;
+ Common->method [0].ordering = CHOLMOD_GIVEN ;
+ Common->method [1].ordering = CHOLMOD_AMD ;
+ Common->method [2].ordering = CHOLMOD_METIS ;
+#ifndef NPARTITION
+ nmethods = 3 ;
+#else
+ nmethods = 2 ;
+#endif
+ }
+
+ amd_printed = FALSE ;
+ for (i = 0 ; i < nmethods ; i++)
+ {
+ P3 (" method "ID": ", i) ;
+ ordering = Common->method [i].ordering ;
+ fl = Common->method [i].fl ;
+ lnz = Common->method [i].lnz ;
+ switch (ordering)
+ {
+
+ case CHOLMOD_NATURAL:
+ P3 ("%s", "natural\n") ;
+ break ;
+
+ case CHOLMOD_GIVEN:
+ P3 ("%s", "user permutation (if given)\n") ;
+ break ;
+
+ case CHOLMOD_AMD:
+ P3 ("%s", "AMD (or COLAMD if factorizing AA')\n") ;
+ amd_printed = TRUE ;
+ break ;
+
+ case CHOLMOD_COLAMD:
+ P3 ("%s", "AMD if factorizing A, COLAMD if factorizing AA')\n");
+ amd_printed = TRUE ;
+ break ;
+
+ case CHOLMOD_METIS:
+ P3 ("%s", "METIS_NodeND nested dissection\n") ;
+ break ;
+
+ case CHOLMOD_NESDIS:
+ P3 ("%s", "CHOLMOD nested dissection\n") ;
+
+ P3 (" nd_small: # nodes in uncut subgraph: "ID"\n",
+ (Int) (Common->method [i].nd_small)) ;
+ P3 (" nd_compress: compress the graph: %s\n",
+ BOOLSTR (Common->method [i].nd_compress)) ;
+ P3 (" nd_camd: use constrained min degree: %s\n",
+ BOOLSTR (Common->method [i].nd_camd)) ;
+ break ;
+
+ default:
+ P3 (ID, ordering) ;
+ ERR ("unknown ordering method") ;
+ break ;
+
+ }
+
+ if (!(ordering == CHOLMOD_NATURAL || ordering == CHOLMOD_GIVEN))
+ {
+ if (Common->method [i].prune_dense < 0)
+ {
+ P3 (" prune_dense: for pruning dense nodes: %s\n",
+ " none pruned") ;
+ }
+ else
+ {
+ P3 (" prune_dense: for pruning dense nodes: "
+ "%.5g\n",
+ Common->method [i].prune_dense) ;
+ P3 (" a dense node has degree "
+ ">= max(16,(%.5g)*sqrt(n))\n",
+ Common->method [i].prune_dense) ;
+ }
+ }
+
+ if (ordering == CHOLMOD_COLAMD || ordering == CHOLMOD_NESDIS)
+ {
+ if (Common->method [i].prune_dense2 < 0)
+ {
+ P3 (" prune_dense2: for pruning dense rows for AA':"
+ " %s\n", " none pruned") ;
+ }
+ else
+ {
+ P3 (" prune_dense2: for pruning dense rows for AA':"
+ " %.5g\n", Common->method [i].prune_dense2) ;
+ P3 (" a dense row has degree "
+ ">= max(16,(%.5g)*sqrt(ncol))\n",
+ Common->method [i].prune_dense2) ;
+ }
+ }
+
+ if (fl != EMPTY) P3 (" flop count: %.5g\n", fl) ;
+ if (lnz != EMPTY) P3 (" nnz(L): %.5g\n", lnz) ;
+ }
+
+ /* backup AMD results, if any */
+ if (!amd_printed)
+ {
+ P3 ("%s", " backup method: ") ;
+ P3 ("%s", "AMD (or COLAMD if factorizing AA')\n") ;
+ fl = Common->method [nmethods].fl ;
+ lnz = Common->method [nmethods].lnz ;
+ if (fl != EMPTY) P3 (" AMD flop count: %.5g\n", fl) ;
+ if (lnz != EMPTY) P3 (" AMD nnz(L): %.5g\n", lnz) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* arcane control parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->final_asis)
+ {
+ P4 ("%s", " final_asis: TRUE, leave as is\n") ;
+ }
+ else
+ {
+ P4 ("%s", " final_asis: FALSE, convert when done\n") ;
+ if (Common->final_super)
+ {
+ P4 ("%s", " final_super: TRUE, leave in supernodal form\n") ;
+ }
+ else
+ {
+ P4 ("%s", " final_super: FALSE, convert to simplicial form\n") ;
+ }
+ if (Common->final_ll)
+ {
+ P4 ("%s", " final_ll: TRUE, convert to LL' form\n") ;
+ }
+ else
+ {
+ P4 ("%s", " final_ll: FALSE, convert to LDL' form\n") ;
+ }
+ if (Common->final_pack)
+ {
+ P4 ("%s", " final_pack: TRUE, pack when done\n") ;
+ }
+ else
+ {
+ P4 ("%s", " final_pack: FALSE, do not pack when done\n") ;
+ }
+ if (Common->final_monotonic)
+ {
+ P4 ("%s", " final_monotonic: TRUE, ensure L is monotonic\n") ;
+ }
+ else
+ {
+ P4 ("%s",
+ " final_monotonic: FALSE, do not ensure L is monotonic\n") ;
+ }
+ P4 (" final_resymbol: remove zeros from amalgamation: %s\n",
+ BOOLSTR (Common->final_resymbol)) ;
+ }
+
+ P4 (" dbound: LDL' diagonal threshold: % .5g\n Entries with abs. value"
+ " less than dbound are replaced with +/- dbound.\n",
+ Common->dbound) ;
+
+ P4 (" grow0: memory reallocation: % .5g\n", Common->grow0) ;
+ P4 (" grow1: memory reallocation: % .5g\n", Common->grow1) ;
+ P4 (" grow2: memory reallocation: %g\n", (double) (Common->grow2)) ;
+
+ P4 ("%s", " nrelax, zrelax: supernodal amalgamation rule:\n") ;
+ P4 ("%s", " s = # columns in two adjacent supernodes\n") ;
+ P4 ("%s", " z = % of zeros in new supernode if they are merged.\n") ;
+ P4 ("%s", " Two supernodes are merged if") ;
+ P4 (" (s <= %g) or (no new zero entries) or\n",
+ (double) (Common->nrelax [0])) ;
+ P4 (" (s <= %g and ", (double) (Common->nrelax [1])) ;
+ P4 ("z < %.5g%%) or", Common->zrelax [0] * 100) ;
+ P4 (" (s <= %g and ", (double) (Common->nrelax [2])) ;
+ P4 ("z < %.5g%%) or", Common->zrelax [1] * 100) ;
+ P4 (" (z < %.5g%%)\n", Common->zrelax [2] * 100) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check workspace */
+ /* ---------------------------------------------------------------------- */
+
+ mark = Common->mark ;
+ nrow = Common->nrow ;
+ Flag = Common->Flag ;
+ Head = Common->Head ;
+ if (nrow > 0)
+ {
+ if (mark < 0 || Flag == NULL || Head == NULL)
+ {
+ ERR ("workspace corrupted (Flag and/or Head missing)") ;
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ if (Flag [i] >= mark)
+ {
+ PRINT0 (("Flag ["ID"]="ID", mark = %ld\n", i, Flag [i], mark)) ;
+ ERR ("workspace corrupted (Flag)") ;
+ }
+ }
+ for (i = 0 ; i <= nrow ; i++)
+ {
+ if (Head [i] != EMPTY)
+ {
+ PRINT0 (("Head ["ID"] = "ID",\n", i, Head [i])) ;
+ ERR ("workspace corrupted (Head)") ;
+ }
+ }
+ }
+ xworksize = Common->xworksize ;
+ Xwork = Common->Xwork ;
+ if (xworksize > 0)
+ {
+ if (Xwork == NULL)
+ {
+ ERR ("workspace corrupted (Xwork missing)") ;
+ }
+ for (i = 0 ; i < xworksize ; i++)
+ {
+ if (Xwork [i] != 0.)
+ {
+ PRINT0 (("Xwork ["ID"] = %g\n", i, Xwork [i])) ;
+ ERR ("workspace corrupted (Xwork)") ;
+ }
+ }
+ }
+
+ /* workspace and parameters are valid */
+ P3 ("%s", " OK\n") ;
+ P4 ("%s", "\n") ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_common)
+(
+ cholmod_common *Common
+)
+{
+ return (check_common (0, NULL, Common)) ;
+}
+
+
+int CHOLMOD(print_common)
+(
+ /* ---- input ---- */
+ char *name, /* printed name of Common object */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int print = (Common == NULL) ? 3 : (Common->print) ;
+ return (check_common (print, name, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_sparse ================================================= */
+/* ========================================================================== */
+
+/* Ensure that a sparse matrix in column-oriented form is valid, and optionally
+ * print it. Returns the number of entries on the diagonal or -1 if error.
+ *
+ * workspace: Iwork (nrow)
+ */
+
+static UF_long check_sparse
+(
+ Int *Wi,
+ Int print,
+ char *name,
+ cholmod_sparse *A,
+ UF_long *nnzdiag,
+ cholmod_common *Common
+)
+{
+ double *Ax, *Az ;
+ Int *Ap, *Ai, *Anz ;
+ Int nrow, ncol, nzmax, sorted, packed, j, p, pend, i, nz, ilast,
+ space, init_print, dnz, count, xtype ;
+ char *type = "sparse" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print header information */
+ /* ---------------------------------------------------------------------- */
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD sparse: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ if (A == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ nzmax = A->nzmax ;
+ sorted = A->sorted ;
+ packed = A->packed ;
+ xtype = A->xtype ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+ nz = CHOLMOD(nnz) (A, Common) ;
+
+ P3 (" "ID"", nrow) ;
+ P3 ("-by-"ID", ", ncol) ;
+ P3 ("nz "ID",", nz) ;
+ if (A->stype > 0)
+ {
+ P3 ("%s", " upper.") ;
+ }
+ else if (A->stype < 0)
+ {
+ P3 ("%s", " lower.") ;
+ }
+ else
+ {
+ P3 ("%s", " up/lo.") ;
+ }
+
+ P4 ("\n nzmax "ID", ", nzmax) ;
+ if (nz > nzmax)
+ {
+ ERR ("nzmax too small") ;
+ }
+ if (!sorted)
+ {
+ P4 ("%s", "un") ;
+ }
+ P4 ("%s", "sorted, ") ;
+ if (!packed)
+ {
+ P4 ("%s", "un") ;
+ }
+ P4 ("%s", "packed, ") ;
+
+ switch (A->itype)
+ {
+ case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ;
+ case CHOLMOD_INTLONG: ERR ("mixed int/UF_long type unsupported") ;
+ case CHOLMOD_LONG: P4 ("%s", "\n scalar types: UF_long, ") ; break ;
+ default: ERR ("unknown itype") ;
+ }
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ;
+ case CHOLMOD_REAL: P4 ("%s", "real") ; break ;
+ case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ;
+ case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ;
+ default: ERR ("unknown xtype") ;
+ }
+
+ switch (A->dtype)
+ {
+ case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ;
+ case CHOLMOD_SINGLE: ERR ("float unsupported") ;
+ default: ERR ("unknown dtype") ;
+ }
+
+ if (A->itype != ITYPE || A->dtype != DTYPE)
+ {
+ ERR ("integer and real type must match routine") ;
+ }
+
+ if (A->stype && nrow != ncol)
+ {
+ ERR ("symmetric but not square") ;
+ }
+
+ /* check for existence of Ap, Ai, Anz, Ax, and Az arrays */
+ if (Ap == NULL)
+ {
+ ERR ("p array not present") ;
+ }
+ if (Ai == NULL)
+ {
+ ERR ("i array not present") ;
+ }
+ if (!packed && Anz == NULL)
+ {
+ ERR ("nz array not present") ;
+ }
+ if (xtype != CHOLMOD_PATTERN && Ax == NULL)
+ {
+ ERR ("x array not present") ;
+ }
+ if (xtype == CHOLMOD_ZOMPLEX && Az == NULL)
+ {
+ ERR ("z array not present") ;
+ }
+
+ /* packed matrices must start at Ap [0] = 0 */
+ if (packed && Ap [0] != 0)
+ {
+ ERR ("p [0] must be zero") ;
+ }
+ if (packed && (Ap [ncol] < Ap [0] || Ap [ncol] > nzmax))
+ {
+ ERR ("p [ncol] invalid") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace if needed */
+ /* ---------------------------------------------------------------------- */
+
+ if (!sorted)
+ {
+ if (Wi == NULL)
+ {
+ CHOLMOD(allocate_work) (0, nrow, 0, Common) ;
+ Wi = Common->Iwork ; /* size nrow, (i/i/l) */
+ }
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [i] = EMPTY ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check and print each column */
+ /* ---------------------------------------------------------------------- */
+
+ init_print = print ;
+ dnz = 0 ;
+ ETC_START (count, 8) ;
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ ETC (j == ncol-1, count, 4) ;
+ p = Ap [j] ;
+ if (packed)
+ {
+ pend = Ap [j+1] ;
+ nz = pend - p ;
+ }
+ else
+ {
+ /* Note that Anz [j] < 0 is treated as zero */
+ nz = MAX (0, Anz [j]) ;
+ pend = p + nz ;
+ }
+ /* Note that space can be negative if the matrix is non-monotonic */
+ space = Ap [j+1] - p ;
+ P4 (" col "ID":", j) ;
+ P4 (" nz "ID"", nz) ;
+ P4 (" start "ID"", p) ;
+ P4 (" end "ID"", pend) ;
+ if (!packed)
+ {
+ P4 (" space "ID"", space) ;
+ }
+ P4 ("%s", ":\n") ;
+ if (p < 0 || pend > nzmax)
+ {
+ ERR ("pointer invalid") ;
+ }
+ if (nz < 0 || nz > nrow)
+ {
+ ERR ("nz invalid") ;
+ }
+ ilast = EMPTY ;
+
+ for ( ; p < pend ; p++)
+ {
+ ETC (j == ncol-1 && p >= pend-4, count, -1) ;
+ i = Ai [p] ;
+ P4 (" "I8":", i) ;
+
+ print_value (print, xtype, Ax, Az, p, Common) ;
+
+ if (i == j)
+ {
+ dnz++ ;
+ }
+ if (i < 0 || i >= nrow)
+ {
+ ERR ("row index out of range") ;
+ }
+ if (sorted && i <= ilast)
+ {
+ ERR ("row indices out of order") ;
+ }
+ if (!sorted && Wi [i] == j)
+ {
+ ERR ("duplicate row index") ;
+ }
+ P4 ("%s", "\n") ;
+ ilast = i ;
+ if (!sorted)
+ {
+ Wi [i] = j ;
+ }
+ }
+ }
+
+ /* matrix is valid */
+ P4 (" nnz on diagonal: "ID"\n", dnz) ;
+ P3 ("%s", " OK\n") ;
+ P4 ("%s", "\n") ;
+ *nnzdiag = dnz ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_sparse)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ UF_long nnzdiag ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_sparse (NULL, 0, NULL, A, &nnzdiag, Common)) ;
+}
+
+
+int CHOLMOD(print_sparse)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to print */
+ char *name, /* printed name of sparse matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ UF_long nnzdiag ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_sparse (NULL, Common->print, name, A, &nnzdiag, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_dense ================================================== */
+/* ========================================================================== */
+
+/* Ensure a dense matrix is valid, and optionally print it. */
+
+static int check_dense
+(
+ Int print,
+ char *name,
+ cholmod_dense *X,
+ cholmod_common *Common
+)
+{
+ double *Xx, *Xz ;
+ Int i, j, d, nrow, ncol, nzmax, nz, init_print, count, xtype ;
+ char *type = "dense" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print header information */
+ /* ---------------------------------------------------------------------- */
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD dense: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ if (X == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ nrow = X->nrow ;
+ ncol = X->ncol ;
+ nzmax = X->nzmax ;
+ d = X->d ;
+ Xx = X->x ;
+ Xz = X->z ;
+ xtype = X->xtype ;
+
+ P3 (" "ID"", nrow) ;
+ P3 ("-by-"ID", ", ncol) ;
+ P4 ("\n leading dimension "ID", ", d) ;
+ P4 ("nzmax "ID", ", nzmax) ;
+ if (d * ncol > nzmax)
+ {
+ ERR ("nzmax too small") ;
+ }
+ if (d < nrow)
+ {
+ ERR ("leading dimension must be >= # of rows") ;
+ }
+ if (Xx == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ switch (X->xtype)
+ {
+ case CHOLMOD_PATTERN: ERR ("pattern unsupported") ; break ;
+ case CHOLMOD_REAL: P4 ("%s", "real") ; break ;
+ case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ;
+ case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ;
+ default: ERR ("unknown xtype") ;
+ }
+
+ switch (X->dtype)
+ {
+ case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ;
+ case CHOLMOD_SINGLE: ERR ("single unsupported") ;
+ default: ERR ("unknown dtype") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check and print each entry */
+ /* ---------------------------------------------------------------------- */
+
+ if (print >= 4)
+ {
+ init_print = print ;
+ ETC_START (count, 9) ;
+ nz = nrow * ncol ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ ETC (j == ncol-1, count, 5) ;
+ P4 (" col "ID":\n", j) ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ ETC (j == ncol-1 && i >= nrow-4, count, -1) ;
+ P4 (" "I8":", i) ;
+
+ print_value (print, xtype, Xx, Xz, i+j*d, Common) ;
+
+ P4 ("%s", "\n") ;
+ }
+ }
+ }
+
+ /* dense is valid */
+ P3 ("%s", " OK\n") ;
+ P4 ("%s", "\n") ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_dense)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* dense matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_dense (0, NULL, X, Common)) ;
+}
+
+
+int CHOLMOD(print_dense)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* dense matrix to print */
+ char *name, /* printed name of dense matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_dense (Common->print, name, X, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_subset ================================================= */
+/* ========================================================================== */
+
+/* Ensure S (0:len-1) is a subset of 0:n-1. Duplicates are allowed. S may be
+ * NULL. A negative len denotes the set 0:n-1.
+ *
+ * To check the rset and cset for A(rset,cset), where nc and nr are the length
+ * of cset and rset respectively:
+ *
+ * cholmod_check_subset (cset, nc, A->ncol, Common) ;
+ * cholmod_check_subset (rset, nr, A->nrow, Common) ;
+ *
+ * workspace: none
+ */
+
+static int check_subset
+(
+ Int *S,
+ UF_long len,
+ size_t n,
+ Int print,
+ char *name,
+ cholmod_common *Common
+)
+{
+ Int i, k, init_print, count ;
+ char *type = "subset" ;
+
+ init_print = print ;
+
+ if (S == NULL)
+ {
+ /* zero len denotes S = [ ], negative len denotes S = 0:n-1 */
+ len = (len < 0) ? (-1) : 0 ;
+ }
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD subset: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ P3 (" len: %ld ", len) ;
+ if (len < 0)
+ {
+ P3 ("%s", "(denotes 0:n-1) ") ;
+ }
+ P3 ("n: "ID"", (Int) n) ;
+ P4 ("%s", "\n") ;
+
+ if (len <= 0 || S == NULL)
+ {
+ P3 ("%s", " OK\n") ;
+ P4 ("%s", "\n") ;
+ return (TRUE) ;
+ }
+
+ if (print >= 4)
+ {
+ ETC_START (count, 8) ;
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ ETC (k == ((Int) len) - 4, count, -1) ;
+ i = S [k] ;
+ P4 (" "I8":", k) ;
+ P4 (" "ID"\n", i) ;
+ if (i < 0 || i >= ((Int) n))
+ {
+ ERR ("entry out range") ;
+ }
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ i = S [k] ;
+ if (i < 0 || i >= ((Int) n))
+ {
+ ERR ("entry out range") ;
+ }
+ }
+ }
+ P3 ("%s", " OK\n") ;
+ P4 ("%s", "\n") ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_subset)
+(
+ /* ---- input ---- */
+ Int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */
+ UF_long len, /* size of Set (an integer array), or < 0 if 0:n-1 */
+ size_t n, /* 0:n-1 is valid range */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_subset (Set, len, n, 0, NULL, Common)) ;
+}
+
+
+int CHOLMOD(print_subset)
+(
+ /* ---- input ---- */
+ Int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */
+ UF_long len, /* size of Set (an integer array), or < 0 if 0:n-1 */
+ size_t n, /* 0:n-1 is valid range */
+ char *name, /* printed name of Set */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_subset (Set, len, n, Common->print, name, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_perm =================================================== */
+/* ========================================================================== */
+
+/* Ensure that Perm [0..len-1] is a permutation of a subset of 0:n-1. Perm
+ * may be NULL, which is interpreted as the identity permutation. There can
+ * be no duplicate entries (len must be <= n).
+ *
+ * If n <= Common->nrow, then this routine takes O(len) time and does not
+ * allocate any memory, by using Common->Flag. Otherwise, it takes O(n) time
+ * and ensures that Common->Iwork is at least n*sizeof(Int) in size.
+ *
+ * To check the fset: cholmod_check_perm (fset, fsize, ncol, Common) ;
+ * To check a permutation: cholmod_check_perm (Perm, n, n, Common) ;
+ *
+ * workspace: Flag (n) if n <= Common->nrow, Iwork (n) otherwise.
+ */
+
+static int check_perm
+(
+ Int *Wi,
+ Int print,
+ char *name,
+ Int *Perm,
+ size_t len,
+ size_t n,
+ cholmod_common *Common
+)
+{
+ Int *Flag ;
+ Int i, k, mark, init_print, count ;
+ char *type = "perm" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* checks that take O(1) time */
+ /* ---------------------------------------------------------------------- */
+
+ if (Perm == NULL || n == 0)
+ {
+ /* Perm is valid implicit identity, or empty */
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* checks that take O(n) time or require memory allocation */
+ /* ---------------------------------------------------------------------- */
+
+ init_print = print ;
+ ETC_START (count, 8) ;
+
+ if (Wi == NULL && n <= Common->nrow)
+ {
+ /* use the Common->Flag array if it's big enough */
+ mark = CHOLMOD(clear_flag) (Common) ;
+ Flag = Common->Flag ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ;
+ if (print >= 4)
+ {
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ ETC (k >= ((Int) len) - 4, count, -1) ;
+ i = Perm [k] ;
+ P4 (" "I8":", k) ;
+ P4 (""ID"\n", i) ;
+ if (i < 0 || i >= ((Int) n) || Flag [i] == mark)
+ {
+ CHOLMOD(clear_flag) (Common) ;
+ ERR ("invalid permutation") ;
+ }
+ Flag [i] = mark ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ i = Perm [k] ;
+ if (i < 0 || i >= ((Int) n) || Flag [i] == mark)
+ {
+ CHOLMOD(clear_flag) (Common) ;
+ ERR ("invalid permutation") ;
+ }
+ Flag [i] = mark ;
+ }
+ }
+ CHOLMOD(clear_flag) (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ;
+ }
+ else
+ {
+ if (Wi == NULL)
+ {
+ /* use Common->Iwork instead, but initialize it first */
+ CHOLMOD(allocate_work) (0, n, 0, Common) ;
+ Wi = Common->Iwork ; /* size n, (i/i/i) is OK */
+ }
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+ for (i = 0 ; i < ((Int) n) ; i++)
+ {
+ Wi [i] = FALSE ;
+ }
+ if (print >= 4)
+ {
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ ETC (k >= ((Int) len) - 4, count, -1) ;
+ i = Perm [k] ;
+ P4 (" "I8":", k) ;
+ P4 (""ID"\n", i) ;
+ if (i < 0 || i >= ((Int) n) || Wi [i])
+ {
+ ERR ("invalid permutation") ;
+ }
+ Wi [i] = TRUE ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < ((Int) len) ; k++)
+ {
+ i = Perm [k] ;
+ if (i < 0 || i >= ((Int) n) || Wi [i])
+ {
+ ERR ("invalid permutation") ;
+ }
+ Wi [i] = TRUE ;
+ }
+ }
+ }
+
+ /* perm is valid */
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_perm)
+(
+ /* ---- input ---- */
+ Int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */
+ size_t len, /* size of Perm (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_perm (NULL, 0, NULL, Perm, len, n, Common)) ;
+}
+
+
+int CHOLMOD(print_perm)
+(
+ /* ---- input ---- */
+ Int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */
+ size_t len, /* size of Perm (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ char *name, /* printed name of Perm */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int ok, print ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ print = Common->print ;
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD perm: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+ P3 (" len: "ID"", (Int) len) ;
+ P3 (" n: "ID"", (Int) n) ;
+ P4 ("%s", "\n") ;
+ ok = check_perm (NULL, print, name, Perm, len, n, Common) ;
+ if (ok)
+ {
+ P3 ("%s", " OK\n") ;
+ P4 ("%s", "\n") ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_parent ================================================= */
+/* ========================================================================== */
+
+/* Ensure that Parent is a valid elimination tree of nodes 0 to n-1.
+ * If j is a root of the tree then Parent [j] is EMPTY (-1).
+ *
+ * NOTE: this check will fail if applied to the component tree (CParent) in
+ * cholmod_nested_dissection, unless it has been postordered and renumbered.
+ *
+ * workspace: none
+ */
+
+static int check_parent
+(
+ Int *Parent,
+ size_t n,
+ Int print,
+ char *name,
+ cholmod_common *Common
+)
+{
+ Int j, p, init_print, count ;
+ char *type = "parent" ;
+
+ init_print = print ;
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD parent: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ P3 (" n: "ID"", (Int) n) ;
+ P4 ("%s", "\n") ;
+
+ if (Parent == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* checks that take O(n) time */
+ /* ---------------------------------------------------------------------- */
+
+ ETC_START (count, 8) ;
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ ETC (j == ((Int) n) - 4, count, -1) ;
+ p = Parent [j] ;
+ P4 (" "I8":", j) ;
+ P4 (" "ID"\n", p) ;
+ if (!(p == EMPTY || p > j))
+ {
+ ERR ("invalid") ;
+ }
+ }
+ P3 ("%s", " OK\n") ;
+ P4 ("%s", "\n") ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_parent)
+(
+ /* ---- input ---- */
+ Int *Parent, /* Parent [0:n-1] is an elimination tree */
+ size_t n, /* size of Parent */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_parent (Parent, n, 0, NULL, Common)) ;
+}
+
+
+int CHOLMOD(print_parent)
+(
+ /* ---- input ---- */
+ Int *Parent, /* Parent [0:n-1] is an elimination tree */
+ size_t n, /* size of Parent */
+ char *name, /* printed name of Parent */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_parent (Parent, n, Common->print, name, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_factor ================================================= */
+/* ========================================================================== */
+
+static int check_factor
+(
+ Int *Wi,
+ Int print,
+ char *name,
+ cholmod_factor *L,
+ cholmod_common *Common
+)
+{
+ double *Lx, *Lz ;
+ Int *Lp, *Li, *Lnz, *Lnext, *Lprev, *Perm, *ColCount, *Lpi, *Lpx, *Super,
+ *Ls ;
+ Int n, nzmax, j, p, pend, i, nz, ordering, space, is_monotonic, minor,
+ count, precise, init_print, ilast, lnz, head, tail, jprev, plast,
+ jnext, examine_super, nsuper, s, k1, k2, psi, psend, psx, nsrow, nscol,
+ ps2, psxend, ssize, xsize, maxcsize, maxesize, nsrow2, jj, ii, xtype ;
+ char *type = "factor" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print header information */
+ /* ---------------------------------------------------------------------- */
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD factor: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ if (L == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ n = L->n ;
+ minor = L->minor ;
+ ordering = L->ordering ;
+ xtype = L->xtype ;
+
+ Perm = L->Perm ;
+ ColCount = L->ColCount ;
+ lnz = 0 ;
+
+ precise = Common->precise ;
+
+ P3 (" "ID"", n) ;
+ P3 ("-by-"ID"", n) ;
+
+ if (minor < n)
+ {
+ P3 (" not positive definite (column "ID")", minor) ;
+ }
+
+ switch (L->itype)
+ {
+ case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ;
+ case CHOLMOD_INTLONG: ERR ("mixed int/UF_long type unsupported") ;
+ case CHOLMOD_LONG: P4 ("%s", "\n scalar types: UF_long, ") ; break ;
+ default: ERR ("unknown itype") ;
+ }
+
+ switch (L->xtype)
+ {
+ case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ;
+ case CHOLMOD_REAL: P4 ("%s", "real") ; break ;
+ case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ;
+ case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ;
+ default: ERR ("unknown xtype") ;
+ }
+
+ switch (L->dtype)
+ {
+ case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ;
+ case CHOLMOD_SINGLE: ERR ("single unsupported") ;
+ default: ERR ("unknown dtype") ;
+ }
+
+ if (L->itype != ITYPE || L->dtype != DTYPE)
+ {
+ ERR ("integer and real type must match routine") ;
+ }
+
+ if (L->is_super)
+ {
+ P3 ("%s", " supernodal") ;
+ }
+ else
+ {
+ P3 ("%s", " simplicial") ;
+ }
+
+ if (L->is_ll)
+ {
+ P3 ("%s", ", LL'.") ;
+ }
+ else
+ {
+ P3 ("%s", ", LDL'.") ;
+ }
+
+ P4 ("%s", "\n ordering method used: ") ;
+ switch (L->ordering)
+ {
+ case CHOLMOD_POSTORDERED:P4 ("%s", "natural (postordered)") ; break ;
+ case CHOLMOD_NATURAL: P4 ("%s", "natural") ; break ;
+ case CHOLMOD_GIVEN: P4 ("%s", "user-provided") ; break ;
+ case CHOLMOD_AMD: P4 ("%s", "AMD") ; break ;
+ case CHOLMOD_COLAMD: P4 ("%s", "AMD for A, COLAMD for A*A'") ;break ;
+#ifndef NPARTITION
+ case CHOLMOD_METIS: P4 ("%s", "METIS NodeND") ; break ;
+ case CHOLMOD_NESDIS: P4 ("%s", "CHOLMOD nested dissection") ; break ;
+#endif
+ default: ERR ("unknown ordering") ;
+ }
+
+ P4 ("%s", "\n") ;
+
+ init_print = print ;
+
+ if (L->is_super && L->xtype == CHOLMOD_ZOMPLEX)
+ {
+ ERR ("Supernodal zomplex L not supported") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check L->Perm */
+ /* ---------------------------------------------------------------------- */
+
+ if (!check_perm (Wi, print, name, Perm, n, n, Common))
+ {
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check L->ColCount */
+ /* ---------------------------------------------------------------------- */
+
+ if (ColCount == NULL)
+ {
+ ERR ("ColCount vector invalid") ;
+ }
+
+ ETC_START (count, 8) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ ETC (j >= n-4, count, -1) ;
+ P4 (" col: "ID" ", j) ;
+ nz = ColCount [j] ;
+ P4 ("colcount: "ID"\n", nz) ;
+ if (nz < 0 || nz > n-j)
+ {
+ ERR ("ColCount out of range") ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check factor */
+ /* ---------------------------------------------------------------------- */
+
+ if (L->xtype == CHOLMOD_PATTERN && !(L->is_super))
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* check simplicial symbolic factor */
+ /* ------------------------------------------------------------------ */
+
+ /* nothing else to do */ ;
+
+ }
+ else if (L->xtype != CHOLMOD_PATTERN && !(L->is_super))
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* check simplicial numerical factor */
+ /* ------------------------------------------------------------------ */
+
+ P4 ("monotonic: %d\n", L->is_monotonic) ;
+ nzmax = L->nzmax ;
+ P3 (" nzmax "ID".", nzmax) ;
+ P4 ("%s", "\n") ;
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lnz = L->nz ;
+ Lnext = L->next ;
+ Lprev = L->prev ;
+
+ /* check for existence of Lp, Li, Lnz, Lnext, Lprev, and Lx arrays */
+ if (Lp == NULL)
+ {
+ ERR ("p array not present") ;
+ }
+ if (Li == NULL)
+ {
+ ERR ("i array not present") ;
+ }
+ if (Lnz == NULL)
+ {
+ ERR ("nz array not present") ;
+ }
+ if (Lx == NULL)
+ {
+ ERR ("x array not present") ;
+ }
+ if (xtype == CHOLMOD_ZOMPLEX && Lz == NULL)
+ {
+ ERR ("z array not present") ;
+ }
+ if (Lnext == NULL)
+ {
+ ERR ("next array not present") ;
+ }
+ if (Lprev == NULL)
+ {
+ ERR ("prev array not present") ;
+ }
+
+ ETC_START (count, 8) ;
+
+ /* check each column of L */
+ plast = 0 ;
+ is_monotonic = TRUE ;
+ for (j = 0 ; j < n ; j++)
+ {
+ ETC (j >= n-3, count, -1) ;
+ p = Lp [j] ;
+ nz = Lnz [j] ;
+ pend = p + nz ;
+ lnz += nz ;
+
+ P4 (" col "ID":", j) ;
+ P4 (" nz "ID"", nz) ;
+ P4 (" start "ID"", p) ;
+ P4 (" end "ID"", pend) ;
+
+ if (Lnext [j] < 0 || Lnext [j] > n)
+ {
+ ERR ("invalid link list") ;
+ }
+ space = Lp [Lnext [j]] - p ;
+
+ P4 (" space "ID"", space) ;
+ P4 (" free "ID":\n", space - nz) ;
+
+ if (p < 0 || pend > nzmax || space < 1)
+ {
+ ERR ("pointer invalid") ;
+ }
+ if (nz < 1 || nz > (n-j) || nz > space)
+ {
+ ERR ("nz invalid") ;
+ }
+ ilast = j-1 ;
+
+ if (p < plast)
+ {
+ is_monotonic = FALSE ;
+ }
+ plast = p ;
+
+ i = Li [p] ;
+ P4 (" "I8":", i) ;
+ if (i != j)
+ {
+ ERR ("diagonal missing") ;
+ }
+
+ print_value (print, xtype, Lx, Lz, p, Common) ;
+
+ P4 ("%s", "\n") ;
+ ilast = j ;
+ for (p++ ; p < pend ; p++)
+ {
+ ETC_DISABLE (count) ;
+ i = Li [p] ;
+ P4 (" "I8":", i) ;
+ if (i < j || i >= n)
+ {
+ ERR ("row index out of range") ;
+ }
+ if (i <= ilast)
+ {
+ ERR ("row indices out of order") ;
+ }
+
+ print_value (print, xtype, Lx, Lz, p, Common) ;
+
+ P4 ("%s", "\n") ;
+ ilast = i ;
+ }
+ }
+
+ if (L->is_monotonic && !is_monotonic)
+ {
+ ERR ("columns not monotonic") ;
+ }
+
+ /* check the link list */
+ head = n+1 ;
+ tail = n ;
+ j = head ;
+ jprev = EMPTY ;
+ count = 0 ;
+ for ( ; ; )
+ {
+ if (j < 0 || j > n+1 || count > n+2)
+ {
+ ERR ("invalid link list") ;
+ }
+ jnext = Lnext [j] ;
+ if (j >= 0 && j < n)
+ {
+ if (jprev != Lprev [j])
+ {
+ ERR ("invalid link list") ;
+ }
+ }
+ count++ ;
+ if (j == tail)
+ {
+ break ;
+ }
+ jprev = j ;
+ j = jnext ;
+ }
+ if (Lnext [tail] != EMPTY || count != n+2)
+ {
+ ERR ("invalid link list") ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* check supernodal numeric or symbolic factor */
+ /* ------------------------------------------------------------------ */
+
+ nsuper = L->nsuper ;
+ ssize = L->ssize ;
+ xsize = L->xsize ;
+ maxcsize = L->maxcsize ;
+ maxesize = L->maxesize ;
+ Ls = L->s ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Super = L->super ;
+ Lx = L->x ;
+ ETC_START (count, 8) ;
+
+ P4 (" ssize "ID" ", ssize) ;
+ P4 ("xsize "ID" ", xsize) ;
+ P4 ("maxcsize "ID" ", maxcsize) ;
+ P4 ("maxesize "ID"\n", maxesize) ;
+
+ if (Ls == NULL)
+ {
+ ERR ("invalid: L->s missing") ;
+ }
+ if (Lpi == NULL)
+ {
+ ERR ("invalid: L->pi missing") ;
+ }
+ if (Lpx == NULL)
+ {
+ ERR ("invalid: L->px missing") ;
+ }
+ if (Super == NULL)
+ {
+ ERR ("invalid: L->super missing") ;
+ }
+
+ if (L->xtype != CHOLMOD_PATTERN)
+ {
+ /* numerical supernodal factor */
+ if (Lx == NULL)
+ {
+ ERR ("invalid: L->x missing") ;
+ }
+ if (Ls [0] == EMPTY)
+ {
+ ERR ("invalid: L->s not defined") ;
+ }
+ examine_super = TRUE ;
+ }
+ else
+ {
+ /* symbolic supernodal factor, but only if it has been computed */
+ examine_super = (Ls [0] != EMPTY) ;
+ }
+
+ if (examine_super)
+ {
+ if (Lpi [0] != 0 || MAX (1, Lpi [nsuper]) != ssize)
+ {
+ PRINT0 (("Lpi [0] "ID", Lpi [nsuper = "ID"] = "ID"\n",
+ Lpi [0], nsuper, Lpi [nsuper])) ;
+ ERR ("invalid: L->pi invalid") ;
+ }
+ if (Lpx [0] != 0 || MAX (1, Lpx [nsuper]) != xsize)
+ {
+ ERR ("invalid: L->px invalid") ;
+ }
+
+ /* check and print each supernode */
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ nsrow2 = nsrow - nscol ;
+ ps2 = psi + nscol ;
+ psxend = Lpx [s+1] ;
+
+ ETC (s == nsuper-1, count, 4) ;
+
+ P4 (" supernode "ID", ", s) ;
+ P4 ("col "ID" ", k1) ;
+ P4 ("to "ID". ", k2-1) ;
+ P4 ("nz in first col: "ID".\n", nsrow) ;
+ P4 (" values start "ID", ", psx) ;
+ P4 ("end "ID"\n", psxend) ;
+
+ if (k1 > k2 || k1 < 0 || k2 > n || nsrow < nscol || nsrow2 < 0
+ || psxend - psx != nsrow * nscol)
+ {
+ ERR ("invalid supernode") ;
+ }
+
+ lnz += nscol * nsrow - (nscol*nscol - nscol)/2 ;
+
+ if (L->xtype != CHOLMOD_PATTERN)
+ {
+ /* print each column of the supernode */
+ for (jj = 0 ; jj < nscol ; jj++)
+ {
+ ETC_ENABLE (s == nsuper-1 && jj >= nscol-3, count, -1) ;
+ j = k1 + jj ;
+ P4 (" col "ID"\n", j) ;
+ ilast = j ;
+ i = Ls [psi + jj] ;
+ P4 (" "I8":", i) ;
+ if (i != j)
+ {
+ ERR ("row index invalid") ;
+ }
+
+ /* PRINTVALUE (Lx [psx + jj + jj*nsrow]) ; */
+ print_value (print, xtype, Lx, NULL,
+ psx + jj + jj*nsrow, Common) ;
+
+ P4 ("%s", "\n") ;
+ for (ii = jj + 1 ; ii < nsrow ; ii++)
+ {
+ ETC_DISABLE (count) ;
+ i = Ls [psi + ii] ;
+ P4 (" "I8":", i) ;
+ if (i <= ilast || i > n)
+ {
+ ERR ("row index out of range") ;
+ }
+
+ /* PRINTVALUE (Lx [psx + ii + jj*nsrow]) ; */
+ print_value (print, xtype, Lx, NULL,
+ psx + ii + jj*nsrow, Common) ;
+
+ P4 ("%s", "\n") ;
+ ilast = i ;
+ }
+ }
+ }
+ else
+ {
+ /* just print the leading column of the supernode */
+ P4 (" col "ID"\n", k1) ;
+ for (jj = 0 ; jj < nscol ; jj++)
+ {
+ ETC (s == nsuper-1 && jj >= nscol-3, count, -1) ;
+ j = k1 + jj ;
+ i = Ls [psi + jj] ;
+ P4 (" "I8"", i) ;
+ if (i != j)
+ {
+ ERR ("row index invalid") ;
+ }
+ P4 ("%s", "\n") ;
+ }
+ ilast = j ;
+ for (ii = nscol ; ii < nsrow ; ii++)
+ {
+ ETC_DISABLE (count) ;
+ i = Ls [psi + ii] ;
+ P4 (" "I8"", i) ;
+ if (i <= ilast || i > n)
+ {
+ ERR ("row index out of range") ;
+ }
+ P4 ("%s", "\n") ;
+ ilast = i ;
+ }
+ }
+ }
+ }
+ }
+
+ /* factor is valid */
+ P3 (" nz "ID"", lnz) ;
+ P3 ("%s", " OK\n") ;
+ P4 ("%s", "\n") ;
+ return (TRUE) ;
+}
+
+
+int CHOLMOD(check_factor)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to check */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_factor (NULL, 0, NULL, L, Common)) ;
+}
+
+
+int CHOLMOD(print_factor)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to print */
+ char *name, /* printed name of factor */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_factor (NULL, Common->print, name, L, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_check_triplet ================================================ */
+/* ========================================================================== */
+
+/* Ensure a triplet matrix is valid, and optionally print it. */
+
+static int check_triplet
+(
+ Int print,
+ char *name,
+ cholmod_triplet *T,
+ cholmod_common *Common
+)
+{
+ double *Tx, *Tz ;
+ Int *Ti, *Tj ;
+ Int i, j, p, nrow, ncol, nzmax, nz, xtype, init_print, count ;
+ char *type = "triplet" ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print header information */
+ /* ---------------------------------------------------------------------- */
+
+ P4 ("%s", "\n") ;
+ P3 ("%s", "CHOLMOD triplet: ") ;
+ if (name != NULL)
+ {
+ P3 ("%s: ", name) ;
+ }
+
+ if (T == NULL)
+ {
+ ERR ("null") ;
+ }
+
+ nrow = T->nrow ;
+ ncol = T->ncol ;
+ nzmax = T->nzmax ;
+ nz = T->nnz ;
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ Tz = T->z ;
+ xtype = T->xtype ;
+
+
+ P3 (" "ID"", nrow) ;
+ P3 ("-by-"ID", ", ncol) ;
+ P3 ("nz "ID",", nz) ;
+ if (T->stype > 0)
+ {
+ P3 ("%s", " upper.") ;
+ }
+ else if (T->stype < 0)
+ {
+ P3 ("%s", " lower.") ;
+ }
+ else
+ {
+ P3 ("%s", " up/lo.") ;
+ }
+
+ P4 ("\n nzmax "ID", ", nzmax) ;
+ if (nz > nzmax)
+ {
+ ERR ("nzmax too small") ;
+ }
+
+ switch (T->itype)
+ {
+ case CHOLMOD_INT: P4 ("%s", "\n scalar types: int, ") ; break ;
+ case CHOLMOD_INTLONG: ERR ("mixed int/UF_long type unsupported") ;
+ case CHOLMOD_LONG: P4 ("%s", "\n scalar types: UF_long, ") ; break ;
+ default: ERR ("unknown itype") ;
+ }
+
+ switch (T->xtype)
+ {
+ case CHOLMOD_PATTERN: P4 ("%s", "pattern") ; break ;
+ case CHOLMOD_REAL: P4 ("%s", "real") ; break ;
+ case CHOLMOD_COMPLEX: P4 ("%s", "complex") ; break ;
+ case CHOLMOD_ZOMPLEX: P4 ("%s", "zomplex") ; break ;
+ default: ERR ("unknown xtype") ;
+ }
+
+ switch (T->dtype)
+ {
+ case CHOLMOD_DOUBLE: P4 ("%s", ", double\n") ; break ;
+ case CHOLMOD_SINGLE: ERR ("single unsupported") ;
+ default: ERR ("unknown dtype") ;
+ }
+
+ if (T->itype != ITYPE || T->dtype != DTYPE)
+ {
+ ERR ("integer and real type must match routine") ;
+ }
+
+ if (T->stype && nrow != ncol)
+ {
+ ERR ("symmetric but not square") ;
+ }
+
+ /* check for existence of Ti, Tj, Tx arrays */
+ if (Tj == NULL)
+ {
+ ERR ("j array not present") ;
+ }
+ if (Ti == NULL)
+ {
+ ERR ("i array not present") ;
+ }
+
+ if (xtype != CHOLMOD_PATTERN && Tx == NULL)
+ {
+ ERR ("x array not present") ;
+ }
+ if (xtype == CHOLMOD_ZOMPLEX && Tz == NULL)
+ {
+ ERR ("z array not present") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check and print each entry */
+ /* ---------------------------------------------------------------------- */
+
+ init_print = print ;
+ ETC_START (count, 8) ;
+
+ for (p = 0 ; p < nz ; p++)
+ {
+ ETC (p >= nz-4, count, -1) ;
+ i = Ti [p] ;
+ P4 (" "I8":", p) ;
+ P4 (" "I_8"", i) ;
+ if (i < 0 || i >= nrow)
+ {
+ ERR ("row index out of range") ;
+ }
+ j = Tj [p] ;
+ P4 (" "I_8"", j) ;
+ if (j < 0 || j >= ncol)
+ {
+ ERR ("column index out of range") ;
+ }
+
+ print_value (print, xtype, Tx, Tz, p, Common) ;
+
+ P4 ("%s", "\n") ;
+ }
+
+ /* triplet matrix is valid */
+ P3 ("%s", " OK\n") ;
+ P4 ("%s", "\n") ;
+ return (TRUE) ;
+}
+
+
+
+int CHOLMOD(check_triplet)
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* triplet matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_triplet (0, NULL, T, Common)) ;
+}
+
+
+int CHOLMOD(print_triplet)
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* triplet matrix to print */
+ char *name, /* printed name of triplet matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ return (check_triplet (Common->print, name, T, Common)) ;
+}
+
+
+
+/* ========================================================================== */
+/* === CHOLMOD debugging routines =========================================== */
+/* ========================================================================== */
+
+#ifndef NDEBUG
+
+/* The global variables present only when debugging enabled. */
+int CHOLMOD(dump) = 0 ;
+int CHOLMOD(dump_malloc) = -1 ;
+
+/* workspace: no debug routines use workspace in Common */
+
+/* ========================================================================== */
+/* === cholmod_dump_init ==================================================== */
+/* ========================================================================== */
+
+void CHOLMOD(dump_init) (char *s, cholmod_common *Common)
+{
+ FILE *f ;
+ f = fopen ("debug", "r") ;
+ if (f == NULL)
+ {
+ CHOLMOD(dump) = 0 ;
+ }
+ else
+ {
+ fscanf (f, "%d", &CHOLMOD(dump)) ;
+ fclose (f) ;
+ }
+ PRINT1 (("%s: cholmod_dump_init, D = %d\n", s, CHOLMOD(dump))) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_sparse ================================================== */
+/* ========================================================================== */
+
+UF_long CHOLMOD(dump_sparse) /* returns nnz (diag (A)) or EMPTY if error */
+(
+ cholmod_sparse *A,
+ char *name,
+ cholmod_common *Common
+)
+{
+ Int *Wi ;
+ UF_long nnzdiag ;
+ Int ok ;
+
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (0) ;
+ }
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ Wi = malloc (MAX (1, A->nrow) * sizeof (Int)) ;
+ ok = check_sparse (Wi, CHOLMOD(dump), name, A, &nnzdiag, Common) ;
+ if (Wi != NULL) free (Wi) ;
+ return (ok ? nnzdiag : EMPTY) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_factor ================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_factor)
+(
+ cholmod_factor *L,
+ char *name,
+ cholmod_common *Common
+)
+{
+ Int *Wi ;
+ int ok ;
+
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ Wi = malloc (MAX (1, L->n) * sizeof (Int)) ;
+ ok = check_factor (Wi, CHOLMOD(dump), name, L, Common) ;
+ if (Wi != NULL) free (Wi) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_perm ==================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_perm)
+(
+ Int *Perm,
+ size_t len,
+ size_t n,
+ char *name,
+ cholmod_common *Common
+)
+{
+ Int *Wi ;
+ int ok ;
+
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Wi = malloc (MAX (1, n) * sizeof (Int)) ;
+ ok = check_perm (Wi, CHOLMOD(dump), name, Perm, len, n,Common) ;
+ if (Wi != NULL) free (Wi) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_dense =================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_dense)
+(
+ cholmod_dense *X,
+ char *name,
+ cholmod_common *Common
+)
+{
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ return (check_dense (CHOLMOD(dump), name, X, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_triplet ================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(dump_triplet)
+(
+ cholmod_triplet *T,
+ char *name,
+ cholmod_common *Common
+)
+{
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ return (check_triplet (CHOLMOD(dump), name, T, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_subset ================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_subset)
+(
+ Int *S,
+ size_t len,
+ size_t n,
+ char *name,
+ cholmod_common *Common
+)
+{
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ return (check_subset (S, len, n, CHOLMOD(dump), name, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_parent ================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_parent)
+(
+ Int *Parent,
+ size_t n,
+ char *name,
+ cholmod_common *Common
+)
+{
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ return (check_parent (Parent, n, CHOLMOD(dump), name, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_real ==================================================== */
+/* ========================================================================== */
+
+void CHOLMOD(dump_real)
+(
+ char *name, Real *X, UF_long nrow, UF_long ncol, int lower, int xentry,
+ cholmod_common *Common
+)
+{
+ /* dump an nrow-by-ncol real dense matrix */
+ UF_long i, j ;
+ double x, z ;
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return ;
+ }
+ PRINT1 (("%s: dump_real, nrow: %ld ncol: %ld lower: %d\n",
+ name, nrow, ncol, lower)) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ PRINT2 ((" col %ld\n", j)) ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ /* X is stored in column-major form */
+ if (lower && i < j)
+ {
+ PRINT2 ((" %5ld: -", i)) ;
+ }
+ else
+ {
+ x = *X ;
+ PRINT2 ((" %5ld: %e", i, x)) ;
+ if (xentry == 2)
+ {
+ z = *(X+1) ;
+ PRINT2 ((", %e", z)) ;
+ }
+ }
+ PRINT2 (("\n")) ;
+ X += xentry ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_super =================================================== */
+/* ========================================================================== */
+
+void CHOLMOD(dump_super)
+(
+ UF_long s,
+ Int *Super, Int *Lpi, Int *Ls, Int *Lpx, double *Lx,
+ int xentry,
+ cholmod_common *Common
+)
+{
+ Int k1, k2, do_values, psi, psx, nsrow, nscol, psend, ilast, p, i ;
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return ;
+ }
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ nscol = k2 - k1 ;
+ do_values = (Lpx != NULL) && (Lx != NULL) ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ nsrow = psend - psi ;
+ PRINT1 (("\nSuper %ld, columns "ID" to "ID", "ID" rows "ID" cols\n",
+ s, k1, k2-1, nsrow, nscol)) ;
+ ilast = -1 ;
+ for (p = psi ; p < psend ; p++)
+ {
+ i = Ls [p] ;
+ PRINT2 ((" "ID" : p-psi "ID"\n", i, p-psi)) ;
+ ASSERT (IMPLIES (p-psi < nscol, i == k1 + (p-psi))) ;
+ if (p-psi == nscol-1) PRINT2 (("------\n")) ;
+ ASSERT (i > ilast) ;
+ ilast = i ;
+ }
+ if (do_values)
+ {
+ psx = Lpx [s] ;
+ CHOLMOD(dump_real) ("Supernode", Lx + xentry*psx, nsrow, nscol, TRUE,
+ xentry, Common) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_mem ===================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_mem) (char *where, UF_long should, cholmod_common *Common)
+{
+ UF_long diff = should - Common->memory_inuse ;
+ if (diff != 0)
+ {
+ PRINT0 (("mem: %-15s peak %10g inuse %10g should %10g\n",
+ where, (double) Common->memory_usage, (double) Common->memory_inuse,
+ (double) should)) ;
+ PRINT0 (("mem: %s diff %ld !\n", where, diff)) ;
+ }
+ return (diff == 0) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_partition =============================================== */
+/* ========================================================================== */
+
+/* make sure we have a proper separator (for debugging only)
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(dump_partition)
+(
+ UF_long n,
+ Int *Cp,
+ Int *Ci,
+ Int *Cnw,
+ Int *Part,
+ UF_long sepsize,
+ cholmod_common *Common
+)
+{
+ Int chek [3], which, ok, i, j, p ;
+ PRINT1 (("bisect sepsize %ld\n", sepsize)) ;
+ ok = TRUE ;
+ chek [0] = 0 ;
+ chek [1] = 0 ;
+ chek [2] = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ PRINT2 (("--------j "ID" in part "ID" nw "ID"\n", j, Part [j], Cnw[j]));
+ which = Part [j] ;
+ for (p = Cp [j] ; p < Cp [j+1] ; p++)
+ {
+ i = Ci [p] ;
+ PRINT3 (("i "ID", part "ID"\n", i, Part [i])) ;
+ if (which == 0)
+ {
+ if (Part [i] == 1)
+ {
+ PRINT0 (("Error! "ID" "ID"\n", i, j)) ;
+ ok = FALSE ;
+ }
+ }
+ else if (which == 1)
+ {
+ if (Part [i] == 0)
+ {
+ PRINT0 (("Error! "ID" "ID"\n", i, j)) ;
+ ok = FALSE ;
+ }
+ }
+ }
+ if (which < 0 || which > 2)
+ {
+ PRINT0 (("Part out of range\n")) ;
+ ok = FALSE ;
+ }
+ chek [which] += Cnw [j] ;
+ }
+ PRINT1 (("sepsize %ld check "ID" "ID" "ID"\n",
+ sepsize, chek[0], chek[1],chek[2]));
+ if (sepsize != chek[2])
+ {
+ PRINT0 (("mismatch!\n")) ;
+ ok = FALSE ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dump_work ==================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(dump_work) (int flag, int head, UF_long wsize,
+ cholmod_common *Common)
+{
+ double *W ;
+ Int *Flag, *Head ;
+ Int k, nrow, mark ;
+
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return (TRUE) ;
+ }
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ nrow = Common->nrow ;
+ Flag = Common->Flag ;
+ Head = Common->Head ;
+ W = Common->Xwork ;
+ mark = Common->mark ;
+
+ if (wsize < 0)
+ {
+ /* check all of Xwork */
+ wsize = Common->xworksize ;
+ }
+ else
+ {
+ /* check on the first wsize doubles in Xwork */
+ wsize = MIN (wsize, (Int) (Common->xworksize)) ;
+ }
+
+ if (flag)
+ {
+ for (k = 0 ; k < nrow ; k++)
+ {
+ if (Flag [k] >= mark)
+ {
+ PRINT0 (("Flag invalid, Flag ["ID"] = "ID", mark = "ID"\n",
+ k, Flag [k], mark)) ;
+ ASSERT (0) ;
+ return (FALSE) ;
+ }
+ }
+ }
+
+ if (head)
+ {
+ for (k = 0 ; k < nrow ; k++)
+ {
+ if (Head [k] != EMPTY)
+ {
+ PRINT0 (("Head invalid, Head ["ID"] = "ID"\n", k, Head [k])) ;
+ ASSERT (0) ;
+ return (FALSE) ;
+ }
+ }
+ }
+
+ for (k = 0 ; k < wsize ; k++)
+ {
+ if (W [k] != 0.)
+ {
+ PRINT0 (("W invalid, W ["ID"] = %g\n", k, W [k])) ;
+ ASSERT (0) ;
+ return (FALSE) ;
+ }
+ }
+
+ return (TRUE) ;
+}
+#endif
+#endif
diff --git a/CHOLMOD/Check/cholmod_read.c b/CHOLMOD/Check/cholmod_read.c
new file mode 100644
index 0000000..089f524
--- /dev/null
+++ b/CHOLMOD/Check/cholmod_read.c
@@ -0,0 +1,1320 @@
+/* ========================================================================== */
+/* === Check/cholmod_read =================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Check Module. Copyright (C) 2005-2006, Timothy A. Davis.
+ * The CHOLMOD/Check Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Read a sparse matrix in triplet or dense form. A triplet matrix can be
+ * returned as compressed-column sparse matrix. The file format is compatible
+ * with all variations of the Matrix Market "coordinate" and "array" format
+ * (http://www.nist.gov/MatrixMarket). The format supported by these routines
+ * also allow other formats, where the Matrix Market header is optional.
+ *
+ * Although the Matrix Market header is optional, I recommend that users stick
+ * with the strict Matrix Market format. The optional format appears here to
+ * support the reading of symmetric matrices stored with just their upper
+ * triangular parts present, for testing and development of the A->stype > 0
+ * format in CHOLMOD. That format is not included in the Matrix Market format.
+ *
+ * If the first line of the file starts with %%MatrixMarket, then it is
+ * interpretted as a file in Matrix Market format. This line must have
+ * the following format:
+ *
+ * %%MatrixMarket matrix <fmt> <type> <storage>
+ *
+ * <fmt> is one of: coordinate or array. The former is a sparse matrix in
+ * triplet form. The latter is a dense matrix in column-major form.
+ *
+ * <type> is one of: real, complex, pattern, or integer.
+ * The functions here convert the "integer" and "pattern" types to real.
+ *
+ * <storage> is one of: general, hermitian, symmetric, or skew-symmetric
+ *
+ * The strings are case-insensitive. Only the first character is
+ * significant (or the first two for skew-symmetric).
+ *
+ * <type> is ignored for all matrices; the actual type (real, complex,
+ * or pattern) is inferred from the number of tokens in each line of the
+ * file. For a "coordinate" matrix: 2: pattern, 3: real, 4: complex; for
+ * a dense "array" matrix: 1: real, 2: complex. This is compatible with
+ * the Matrix Market format, since pattern matrices must have two tokens
+ * per line, real matrices must have 3, and complex matrices must have 4.
+ * A storage of "general" implies an stype of zero (see below).
+ * "symmetric" and "hermitian" imply an stype of -1. Skew-symmetric and
+ * complex symmetric matrices are always returned with both upper and lower
+ * triangular parts present, with an stype of zero, since CHOLMOD does not
+ * have a method for representing skew-symmetric and complex symmetric
+ * matrices. Real symmetric and complex Hermitian matrices may optionally
+ * be returned with both parts present.
+ *
+ * Any other lines starting with "%" are treated as comments, and are ignored.
+ * Blank lines are ignored. The Matrix Market header is optional in this
+ * routine (it is not optional in the Matrix Market format).
+ *
+ * Note that complex matrices are always returned in CHOLMOD_COMPLEX format,
+ * not CHOLMOD_ZOMPLEX.
+ *
+ * -----------------------------------------------------------------------------
+ * Triplet matrices:
+ * -----------------------------------------------------------------------------
+ *
+ * The first data line of a triplet matrix contains 3 or 4 integers:
+ *
+ * nrow ncol nnz stype
+ *
+ * where stype is optional (stype does not appear in the Matrix Market format).
+ * The matrix is nrow-by-ncol. The following nnz lines (excluding comments
+ * and blank lines) each contain a single entry. Duplicates are permitted,
+ * and are summed in the output matrix.
+ *
+ * The stype is first derived from the Matrix Market header. If the stype
+ * appears as the fourth integer in the first data line, it is determined from
+ * that line.
+ *
+ * If stype is present, it denotes the storage format for the matrix.
+ * stype = 0 denotes an unsymmetric matrix (same as Matrix Market "general").
+ * stype = -1 denotes a real symmetric or complex Hermitian matrix whose lower
+ * triangular entries are stored. Entries may be present in the upper
+ * triangular part, but these are ignored (same as Matrix Market
+ * "real symmetric" and "complex Hermitian").
+ * stype = 1 denotes a real symmetric or complex Hermitian matrix whose upper
+ * triangular entries are stored. Entries may be present in the lower
+ * triangular part, but these are ignored. This option is not present
+ * in the Matrix Market format.
+ *
+ * If stype is not present (no Matrix Market header and not in the first data
+ * line) it is inferred from the rest of the data. If the matrix is
+ * rectangular, or has entries in both the upper and lower triangular parts,
+ * then it is assumed to be unsymmetric (stype=0). If only entries in the
+ * lower triangular part are present, the matrix is assumed to have stype = -1.
+ * If only entries in the upper triangular part are present, the matrix is
+ * assumed to have stype = 1.
+ *
+ * After the first data line (with nrow, ncol, nnz, and optionally stype),
+ * each nonzero consists of one line with 2, 3, or 4 entries. All lines must
+ * have the same number of entries. The first two entries are the row and
+ * column indices of the nonzero. If 3 entries are present, the 3rd entry is
+ * the numerical value, and the matrix is real. If 4 entries are present,
+ * the 3rd and 4th entries in the line are the real and imaginary parts of
+ * a complex value.
+ *
+ * The matrix can be either 0-based or 1-based. It is first assumed to be
+ * one-based (all matrices in the Matrix Market are one-based), with row indices
+ * in the range 1 to ncol and column indices in the range 1 to nrow. If a row
+ * or column index of zero is found, the matrix is assumed to be zero-based
+ * (with row indices in the range 0 to ncol-1 and column indices in the range 0
+ * to nrow-1).
+ *
+ * If Common->prefer_binary is set to its default value of FALSE, then
+ * for symmetric pattern-only matrices, the kth diagonal (if present) is set to
+ * one plus the degree of the row/column k, and the off-diagonal entries are set
+ * to -1. A symmetric pattern-only matrix with a zero-free diagonal is thus
+ * converted into a symmetric positive definite matrix. All entries are set to
+ * one for an unsymmetric pattern-only matrix. This differs from the
+ * Matrix Market format (A = mmread ('file') returns a binary pattern for A for
+ * symmetric pattern-only matrices). If Common->prefer_binary is TRUE, then
+ * this function returns a binary matrix (just like mmread('file')).
+ *
+ * -----------------------------------------------------------------------------
+ * Dense matrices:
+ * -----------------------------------------------------------------------------
+ *
+ * A dense matrix is specified by the Matrix Market "array" format. The
+ * Matrix Market header is optional; if not present, the matrix is assumed to
+ * be in the Matrix Market "general" format. The first data line contains just
+ * two integers:
+ *
+ * nrow ncol
+ *
+ * The <type> can be real, integer, or complex (not pattern). These functions
+ * convert an integer type to real. The entries in the matrix are stored in
+ * column-major format, with one line per entry. Two entries are present in
+ * each line for complex matrices, one for real and integer matrices. In
+ * rectangular and unsymmetric matrices, all entries are present. For real
+ * symmetric or complex Hermitian matrices, only entries in the lower triangular
+ * part appear. For skew-symmetric matrices, only entries in the strictly
+ * lower triangular part appear.
+ *
+ * Since CHOLMOD does not have a data structure for presenting dense symmetric/
+ * Hermitian matrices, these functions always return a dense matrix in its
+ * general form, with both upper and lower parts present.
+ */
+
+#ifndef NCHECK
+
+#include "cholmod_internal.h"
+#include "cholmod_check.h"
+#include <string.h>
+#include <ctype.h>
+
+/* The MatrixMarket format specificies a maximum line length of 1024 */
+#define MAXLINE 1030
+
+/* ========================================================================== */
+/* === get_line ============================================================= */
+/* ========================================================================== */
+
+/* Read one line of the file, return TRUE if successful, FALSE if EOF. */
+
+static int get_line (FILE *f, char *buf)
+{
+ buf [0] = '\0' ;
+ buf [1] = '\0' ;
+ buf [MAXLINE] = '\0' ;
+ return (fgets (buf, MAXLINE, f) != NULL) ;
+}
+
+/* ========================================================================== */
+/* === fix_inf ============================================================== */
+/* ========================================================================== */
+
+/* Replace huge values with +/- Inf's, since scanf and printf don't deal
+ * with Inf's properly.
+ */
+
+static double fix_inf (double x)
+{
+ if ((x >= HUGE_DOUBLE) || (x <= -HUGE_DOUBLE))
+ {
+ /* treat this as +/- Inf (assume 2*x leads to overflow) */
+ x = 2*x ;
+ }
+ return (x) ;
+}
+
+/* ========================================================================== */
+/* === is_blank_line ======================================================== */
+/* ========================================================================== */
+
+/* TRUE if s is a blank line or comment, FALSE otherwise */
+
+static int is_blank_line
+(
+ char *s
+)
+{
+ int c, k ;
+ if (s [0] == '%')
+ {
+ /* a comment line */
+ return (TRUE) ;
+ }
+ for (k = 0 ; k <= MAXLINE ; k++)
+ {
+ c = s [k] ;
+ if (c == '\0')
+ {
+ /* end of line */
+ break ;
+ }
+ if (!isspace (c))
+ {
+ /* non-space character */
+ return (FALSE) ;
+ }
+ }
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === read_header ========================================================== */
+/* ========================================================================== */
+
+/* Read the header. This consists of zero or more comment lines (blank, or
+ * starting with a "%" in the first column), followed by a single data line
+ * containing up to four numerical values.
+ *
+ * The first line may optionally be a Matrix Market header line, of the form
+ *
+ * %%MatrixMarket matrix <fmt> <type> <storage>
+ *
+ * The first data line of a sparse matrix in triplet form consists of 3 or 4
+ * numerical values:
+ *
+ * nrow ncol nnz stype
+ *
+ * where stype is optional (it does not appear in the Matrix Market file
+ * format). The first line of a dense matrix in column-major form consists of
+ * two numerical values:
+ *
+ * nrow ncol
+ *
+ * The stype of the matrix is determine either from the Matrix Market header,
+ * or (optionally) from the first data line. stypes of 0 to -3 directly
+ * correlate with the Matrix Market format; stype = 1 is an extension to that
+ * format.
+ *
+ * 999: unknown (will be inferred from the data)
+ * 1: real symmetric or complex Hermitian with upper part stored
+ * (not in the Matrix Market format)
+ * 0: unsymmetric (same as Matrix Market "general")
+ * -1: real symmetric or complex Hermitian, with lower part stored
+ * (Matrix Market "real symmetric" or "complex hermitian")
+ * -2: real or complex skew symmetric (lower part stored, can only be
+ * specified by Matrix Market header)
+ * -3: complex symmetric (lower part stored)
+ * specified by Matrix Market header)
+ *
+ * The Matrix Market header is optional. If stype appears in the first data
+ * line, it is determine by that data line. Otherwise, if the Matrix Market
+ * header appears, stype is determined from that header. If stype does not
+ * appear, it is set to "unknown" (999).
+ */
+
+#define STYPE_UNKNOWN 999
+#define STYPE_SYMMETRIC_UPPER 1
+#define STYPE_UNSYMMETRIC 0
+#define STYPE_SYMMETRIC_LOWER -1
+#define STYPE_SKEW_SYMMETRIC -2
+#define STYPE_COMPLEX_SYMMETRIC_LOWER -3
+
+static int read_header /* returns TRUE if successful, FALSE on error */
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from */
+ /* ---- output --- */
+ char *buf, /* a character array of size MAXLINE+1 */
+ int *mtype, /* CHOLMOD_TRIPLET or CHOLMOD_DENSE */
+ size_t *nrow, /* number of rows in the matrix */
+ size_t *ncol, /* number of columns in the matrix */
+ size_t *nnz, /* number of entries in a triplet matrix (0 for dense)*/
+ int *stype /* stype (see above) */
+)
+{
+ char *p ;
+ int first = TRUE, got_mm_header = FALSE, c, c2, is_complex, nitems ;
+ double l1, l2, l3, l4 ;
+
+ *mtype = CHOLMOD_TRIPLET ;
+ *nrow = 0 ;
+ *ncol = 0 ;
+ *nnz = 0 ;
+ *stype = STYPE_UNKNOWN ;
+
+ for ( ; ; )
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the next line */
+ /* ------------------------------------------------------------------ */
+
+ if (!get_line (f, buf))
+ {
+ /* premature end of file */
+ return (FALSE) ;
+ }
+
+ if (first && (strncmp (buf, "%%MatrixMarket", 14) == 0))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* read a Matrix Market header */
+ /* -------------------------------------------------------------- */
+
+ got_mm_header = TRUE ;
+ p = buf ;
+
+ /* -------------------------------------------------------------- */
+ /* get "matrix" token */
+ /* -------------------------------------------------------------- */
+
+ while (*p && !isspace (*p)) p++ ;
+ while (*p && isspace (*p)) p++ ;
+ c = tolower (*p) ;
+ if (c != 'm')
+ {
+ /* bad format */
+ return (FALSE) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* get the fmt token ("coord" or "array") */
+ /* -------------------------------------------------------------- */
+
+ while (*p && !isspace (*p)) p++ ;
+ while (*p && isspace (*p)) p++ ;
+ c = tolower (*p) ;
+ if (c == 'c')
+ {
+ *mtype = CHOLMOD_TRIPLET ;
+ }
+ else if (c == 'a')
+ {
+ *mtype = CHOLMOD_DENSE ;
+ }
+ else
+ {
+ /* bad format, neither "coordinate" nor "array" */
+ return (FALSE) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* get type token (real, pattern, complex, integer) */
+ /* -------------------------------------------------------------- */
+
+ while (*p && !isspace (*p)) p++ ;
+ while (*p && isspace (*p)) p++ ;
+ c = tolower (*p) ;
+ if (!(c == 'r' || c == 'p' || c == 'c' || c == 'i'))
+ {
+ /* bad format */
+ return (FALSE) ;
+ }
+ is_complex = (c == 'c') ;
+
+ /* -------------------------------------------------------------- */
+ /* get storage token (general, hermitian, symmetric, skew) */
+ /* -------------------------------------------------------------- */
+
+ while (*p && !isspace (*p)) p++ ;
+ while (*p && isspace (*p)) p++ ;
+ c = tolower (*p) ;
+ c2 = tolower (*(p+1)) ;
+ if (c == 'g')
+ {
+ /* "general" storage (unsymmetric matrix), both parts present */
+ *stype = STYPE_UNSYMMETRIC ;
+ }
+ else if (c == 's' && c2 == 'y')
+ {
+ /* "symmetric" */
+ if (is_complex)
+ {
+ /* complex symmetric, lower triangular part present */
+ *stype = STYPE_COMPLEX_SYMMETRIC_LOWER ;
+ }
+ else
+ {
+ /* real symmetric, lower triangular part present */
+ *stype = STYPE_SYMMETRIC_LOWER ;
+ }
+ }
+ else if (c == 'h')
+ {
+ /* "hermitian" matrix, lower triangular part present */
+ *stype = STYPE_SYMMETRIC_LOWER ;
+ }
+ else if (c == 's' && c2 == 'k')
+ {
+ /* "skew-symmetric" (real or complex), lower part present */
+ *stype = STYPE_SKEW_SYMMETRIC ;
+ }
+ else
+ {
+ /* bad format */
+ return (FALSE) ;
+ }
+
+ }
+ else if (is_blank_line (buf))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* blank line or comment line */
+ /* -------------------------------------------------------------- */
+
+ continue ;
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* read the first data line and return */
+ /* -------------------------------------------------------------- */
+
+ /* format: nrow ncol nnz stype */
+ l1 = EMPTY ;
+ l2 = EMPTY ;
+ l3 = 0 ;
+ l4 = 0 ;
+ nitems = sscanf (buf, "%lg %lg %lg %lg\n", &l1, &l2, &l3, &l4) ;
+ if (nitems < 2 || nitems > 4 || l1 > Int_max || l2 > Int_max)
+ {
+ /* invalid matrix */
+ return (FALSE) ;
+ }
+ *nrow = l1 ;
+ *ncol = l2 ;
+ if (nitems == 2)
+ {
+ /* a dense matrix */
+ if (!got_mm_header)
+ {
+ *mtype = CHOLMOD_DENSE ;
+ *stype = STYPE_UNSYMMETRIC ;
+ }
+ }
+ if (nitems == 3 || nitems == 4)
+ {
+ /* a sparse triplet matrix */
+ *nnz = l3 ;
+ if (!got_mm_header)
+ {
+ *mtype = CHOLMOD_TRIPLET ;
+ }
+ }
+ if (nitems == 4)
+ {
+ /* an stype specified here can only be 1, 0, or -1 */
+ if (l4 < 0)
+ {
+ *stype = STYPE_SYMMETRIC_LOWER ;
+ }
+ else if (l4 > 0)
+ {
+ *stype = STYPE_SYMMETRIC_UPPER ;
+ }
+ else
+ {
+ *stype = STYPE_UNSYMMETRIC ;
+ }
+ }
+ if (*nrow != *ncol)
+ {
+ /* a rectangular matrix must be unsymmetric */
+ *stype = STYPE_UNSYMMETRIC ;
+ }
+ return (TRUE) ;
+ }
+
+ first = FALSE ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === read_triplet ========================================================= */
+/* ========================================================================== */
+
+/* Header has already been read in, including first line (nrow ncol nnz stype).
+ * Read the triplets. */
+
+static cholmod_triplet *read_triplet
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ size_t nrow, /* number of rows */
+ size_t ncol, /* number of columns */
+ size_t nnz, /* number of triplets in file to read */
+ int stype, /* stype from header, or "unknown" */
+ int prefer_unsym, /* if TRUE, always return T->stype of zero */
+ /* ---- workspace */
+ char *buf, /* of size MAXLINE+1 */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double x, z ;
+ double *Tx ;
+ Int *Ti, *Tj, *Rdeg, *Cdeg ;
+ cholmod_triplet *T ;
+ double l1, l2 ;
+ Int nitems, xtype, unknown, k, nshould, is_lower, is_upper, one_based, i, j,
+ imax, jmax, skew_symmetric, p, complex_symmetric ;
+ size_t s, nnz2, extra ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* quick return for empty matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow == 0 || ncol == 0 || nnz == 0)
+ {
+ /* return an empty matrix */
+ return (CHOLMOD(allocate_triplet) (nrow, ncol, 0, 0, CHOLMOD_REAL,
+ Common)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* special stype cases: unknown, skew symmetric, and complex symmetric */
+ /* ---------------------------------------------------------------------- */
+
+ unknown = (stype == STYPE_UNKNOWN) ;
+ skew_symmetric = (stype == STYPE_SKEW_SYMMETRIC) ;
+ complex_symmetric = (stype == STYPE_COMPLEX_SYMMETRIC_LOWER) ;
+
+ extra = 0 ;
+ if (stype < STYPE_SYMMETRIC_LOWER
+ || (prefer_unsym && stype != STYPE_UNSYMMETRIC))
+ {
+ /* 999: unknown might be converted to unsymmetric */
+ /* 1: symmetric upper converted to unsym. if prefer_unsym is TRUE */
+ /* -1: symmetric lower converted to unsym. if prefer_unsym is TRUE */
+ /* -2: real or complex skew symmetric converted to unsymmetric */
+ /* -3: complex symmetric converted to unsymmetric */
+ stype = STYPE_UNSYMMETRIC ;
+ extra = nnz ;
+ }
+ nnz2 = CHOLMOD(add_size_t) (nnz, extra, &ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = nrow + ncol */
+ s = CHOLMOD(add_size_t) (nrow, ncol, &ok) ;
+ if (!ok || nrow > Int_max || ncol > Int_max || nnz > Int_max)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ Rdeg = Common->Iwork ; /* size nrow */
+ Cdeg = Rdeg + nrow ; /* size ncol */
+
+ /* ---------------------------------------------------------------------- */
+ /* read the triplets */
+ /* ---------------------------------------------------------------------- */
+
+ is_lower = TRUE ;
+ is_upper = TRUE ;
+ one_based = TRUE ;
+ imax = 0 ;
+ jmax = 0 ;
+
+ Tx = NULL ;
+ Ti = NULL ;
+ Tj = NULL ;
+ xtype = 999 ;
+ nshould = 0 ;
+
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the next triplet, skipping blank lines and comment lines */
+ /* ------------------------------------------------------------------ */
+
+ l1 = EMPTY ;
+ l2 = EMPTY ;
+ x = 0 ;
+ z = 0 ;
+
+ for ( ; ; )
+ {
+ if (!get_line (f, buf))
+ {
+ /* premature end of file - not enough triplets read in */
+ ERROR (CHOLMOD_INVALID, "premature EOF") ;
+ return (NULL) ;
+ }
+ if (is_blank_line (buf))
+ {
+ /* blank line or comment */
+ continue ;
+ }
+ nitems = sscanf (buf, "%lg %lg %lg %lg\n", &l1, &l2, &x, &z) ;
+ x = fix_inf (x) ;
+ z = fix_inf (z) ;
+ break ;
+ }
+
+ nitems = (nitems == EOF) ? 0 : nitems ;
+ i = l1 ;
+ j = l2 ;
+
+ /* ------------------------------------------------------------------ */
+ /* for first triplet: determine type and allocate triplet matrix */
+ /* ------------------------------------------------------------------ */
+
+ if (k == 0)
+ {
+ if (nitems < 2 || nitems > 4)
+ {
+ /* invalid matrix */
+ ERROR (CHOLMOD_INVALID, "invalid format") ;
+ return (NULL) ;
+ }
+ else if (nitems == 2)
+ {
+ /* this will be converted into a real matrix later */
+ xtype = CHOLMOD_PATTERN ;
+ }
+ else if (nitems == 3)
+ {
+ xtype = CHOLMOD_REAL ;
+ }
+ else if (nitems == 4)
+ {
+ xtype = CHOLMOD_COMPLEX ;
+ }
+
+ /* the rest of the lines should have the same number of entries */
+ nshould = nitems ;
+
+ /* allocate triplet matrix */
+ T = CHOLMOD(allocate_triplet) (nrow, ncol, nnz2, stype,
+ (xtype == CHOLMOD_PATTERN ? CHOLMOD_REAL : xtype), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ T->nnz = nnz ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* save the entry in the triplet matrix */
+ /* ------------------------------------------------------------------ */
+
+ if (nitems != nshould || i < 0 || j < 0)
+ {
+ /* wrong format, premature end-of-file, or negative indices */
+ CHOLMOD(free_triplet) (&T, Common) ;
+ ERROR (CHOLMOD_INVALID, "invalid matrix file") ;
+ return (NULL) ;
+ }
+
+ Ti [k] = i ;
+ Tj [k] = j ;
+
+ if (i < j)
+ {
+ /* this entry is in the upper triangular part */
+ is_lower = FALSE ;
+ }
+ if (i > j)
+ {
+ /* this entry is in the lower triangular part */
+ is_upper = FALSE ;
+ }
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ Tx [k] = x ;
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ Tx [2*k ] = x ; /* real part */
+ Tx [2*k+1] = z ; /* imaginary part */
+ }
+
+ if (i == 0 || j == 0)
+ {
+ one_based = FALSE ;
+ }
+
+ imax = MAX (i, imax) ;
+ jmax = MAX (j, jmax) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to zero-based */
+ /* ---------------------------------------------------------------------- */
+
+ if (one_based)
+ {
+ /* input matrix is one-based; convert matrix to zero-based */
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+ Ti [k]-- ;
+ Tj [k]-- ;
+ }
+ }
+
+ if (one_based ?
+ (imax > (Int) nrow || jmax > (Int) ncol) :
+ (imax >= (Int) nrow || jmax >= (Int) ncol))
+ {
+ /* indices out of range */
+ CHOLMOD(free_triplet) (&T, Common) ;
+ ERROR (CHOLMOD_INVALID, "indices out of range") ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the stype, if not yet known */
+ /* ---------------------------------------------------------------------- */
+
+ if (unknown)
+ {
+ if (is_lower && is_upper)
+ {
+ /* diagonal matrix, symmetric with upper part present */
+ stype = STYPE_SYMMETRIC_UPPER ;
+ }
+ else if (is_lower && !is_upper)
+ {
+ /* symmetric, lower triangular part present */
+ stype = STYPE_SYMMETRIC_LOWER ;
+ }
+ else if (!is_lower && is_upper)
+ {
+ /* symmetric, upper triangular part present */
+ stype = STYPE_SYMMETRIC_UPPER ;
+ }
+ else
+ {
+ /* unsymmetric */
+ stype = STYPE_UNSYMMETRIC ;
+ extra = 0 ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* add the remainder of symmetric, skew-symmetric or Hermitian matrices */
+ /* ---------------------------------------------------------------------- */
+
+ /* note that this step is not done for real symmetric or complex Hermitian
+ * matrices, unless prefer_unsym is TRUE */
+ if (extra > 0)
+ {
+ p = nnz ;
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i != j)
+ {
+ Ti [p] = j ;
+ Tj [p] = i ;
+ if (xtype == CHOLMOD_REAL)
+ {
+ if (skew_symmetric)
+ {
+ Tx [p] = -Tx [k] ;
+ }
+ else
+ {
+ Tx [p] = Tx [k] ;
+ }
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ if (skew_symmetric)
+ {
+ Tx [2*p ] = -Tx [2*k ] ;
+ Tx [2*p+1] = -Tx [2*k+1] ;
+ }
+ else if (complex_symmetric)
+ {
+ Tx [2*p ] = Tx [2*k ] ;
+ Tx [2*p+1] = Tx [2*k+1] ;
+ }
+ else /* Hermitian */
+ {
+ Tx [2*p ] = Tx [2*k ] ;
+ Tx [2*p+1] = -Tx [2*k+1] ;
+ }
+ }
+ p++ ;
+ }
+ }
+ T->nnz = p ;
+ nnz = p ;
+ }
+
+ T->stype = stype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create values for a pattern-only matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (xtype == CHOLMOD_PATTERN)
+ {
+ if (stype == STYPE_UNSYMMETRIC || Common->prefer_binary)
+ {
+ /* unsymmetric case, or binary case */
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+ Tx [k] = 1 ;
+ }
+ }
+ else
+ {
+ /* compute the row and columm degrees (excluding the diagonal) */
+ for (i = 0 ; i < (Int) nrow ; i++)
+ {
+ Rdeg [i] = 0 ;
+ }
+ for (j = 0 ; j < (Int) ncol ; j++)
+ {
+ Cdeg [j] = 0 ;
+ }
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if ((stype < 0 && i > j) || (stype > 0 && i < j))
+ {
+ /* both a(i,j) and a(j,i) appear in the matrix */
+ Rdeg [i]++ ;
+ Cdeg [j]++ ;
+ Rdeg [j]++ ;
+ Cdeg [i]++ ;
+ }
+ }
+ /* assign the numerical values */
+ for (k = 0 ; k < (Int) nnz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ Tx [k] = (i == j) ? (1 + MAX (Rdeg [i], Cdeg [j])) : (-1) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the new triplet matrix */
+ /* ---------------------------------------------------------------------- */
+
+ return (T) ;
+}
+
+
+/* ========================================================================== */
+/* === read_dense =========================================================== */
+/* ========================================================================== */
+
+/* Header has already been read in, including first line (nrow ncol).
+ * Read a dense matrix. */
+
+static cholmod_dense *read_dense
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ size_t nrow, /* number of rows */
+ size_t ncol, /* number of columns */
+ int stype, /* stype from header */
+ /* ---- workspace */
+ char *buf, /* of size MAXLINE+1 */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double x, z ;
+ double *Xx = NULL ;
+ cholmod_dense *X ;
+ Int nitems, xtype = -1, nshould = 0, i, j, k, kup, first ;
+
+ /* ---------------------------------------------------------------------- */
+ /* quick return for empty matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow == 0 || ncol == 0)
+ {
+ /* return an empty dense matrix */
+ return (CHOLMOD(zeros) (nrow, ncol, CHOLMOD_REAL, Common)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the entries */
+ /* ---------------------------------------------------------------------- */
+
+ first = TRUE ;
+
+ for (j = 0 ; j < (Int) ncol ; j++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the row index of the first entry in the file for column j */
+ /* ------------------------------------------------------------------ */
+
+ if (stype == STYPE_UNSYMMETRIC)
+ {
+ i = 0 ;
+ }
+ else if (stype == STYPE_SKEW_SYMMETRIC)
+ {
+ i = j+1 ;
+ }
+ else /* real symmetric or complex Hermitian lower */
+ {
+ i = j ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* get column j */
+ /* ------------------------------------------------------------------ */
+
+ for ( ; i < (Int) nrow ; i++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* get the next entry, skipping blank lines and comment lines */
+ /* -------------------------------------------------------------- */
+
+ x = 0 ;
+ z = 0 ;
+ for ( ; ; )
+ {
+
+ if (!get_line (f, buf))
+ {
+ /* premature end of file - not enough entries read in */
+ ERROR (CHOLMOD_INVALID, "premature EOF") ;
+ return (NULL) ;
+ }
+
+ if (is_blank_line (buf))
+ {
+ /* blank line or comment */
+ continue ;
+ }
+ nitems = sscanf (buf, "%lg %lg\n", &x, &z) ;
+ x = fix_inf (x) ;
+ z = fix_inf (z) ;
+ break ;
+ }
+
+ nitems = (nitems == EOF) ? 0 : nitems ;
+
+ /* -------------------------------------------------------------- */
+ /* for first entry: determine type and allocate dense matrix */
+ /* -------------------------------------------------------------- */
+
+ if (first)
+ {
+ first = FALSE ;
+
+ if (nitems < 1 || nitems > 2)
+ {
+ /* invalid matrix */
+ ERROR (CHOLMOD_INVALID, "invalid format") ;
+ return (NULL) ;
+ }
+ else if (nitems == 1)
+ {
+ /* a real matrix */
+ xtype = CHOLMOD_REAL ;
+ }
+ else if (nitems == 2)
+ {
+ /* a complex matrix */
+ xtype = CHOLMOD_COMPLEX ;
+ }
+
+ /* the rest of the lines should have same number of entries */
+ nshould = nitems ;
+
+ /* allocate the result */
+ X = CHOLMOD(zeros) (nrow, ncol, xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+ Xx = X->x ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* save the entry in the dense matrix */
+ /* -------------------------------------------------------------- */
+
+ if (nitems != nshould)
+ {
+ /* wrong format or premature end-of-file */
+ CHOLMOD(free_dense) (&X, Common) ;
+ ERROR (CHOLMOD_INVALID, "invalid matrix file") ;
+ return (NULL) ;
+ }
+
+ k = i + j*nrow ;
+ kup = j + i*nrow ;
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ /* real matrix */
+ Xx [k] = x ;
+ if (k != kup)
+ {
+ if (stype == STYPE_SYMMETRIC_LOWER)
+ {
+ /* real symmetric matrix */
+ Xx [kup] = x ;
+ }
+ else if (stype == STYPE_SKEW_SYMMETRIC)
+ {
+ /* real skew symmetric matrix */
+ Xx [kup] = -x ;
+ }
+ }
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ Xx [2*k ] = x ; /* real part */
+ Xx [2*k+1] = z ; /* imaginary part */
+ if (k != kup)
+ {
+ if (stype == STYPE_SYMMETRIC_LOWER)
+ {
+ /* complex Hermitian */
+ Xx [2*kup ] = x ; /* real part */
+ Xx [2*kup+1] = -z ; /* imaginary part */
+ }
+ else if (stype == STYPE_SKEW_SYMMETRIC)
+ {
+ /* complex skew symmetric */
+ Xx [2*kup ] = -x ; /* real part */
+ Xx [2*kup+1] = -z ; /* imaginary part */
+ }
+ if (stype == STYPE_COMPLEX_SYMMETRIC_LOWER)
+ {
+ /* complex symmetric */
+ Xx [2*kup ] = x ; /* real part */
+ Xx [2*kup+1] = z ; /* imaginary part */
+ }
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the new dense matrix */
+ /* ---------------------------------------------------------------------- */
+
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_read_triplet ================================================= */
+/* ========================================================================== */
+
+/* Read in a triplet matrix from a file. */
+
+cholmod_triplet *CHOLMOD(read_triplet)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ char buf [MAXLINE+1] ;
+ size_t nrow, ncol, nnz ;
+ int stype, mtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (f, NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* read the header and first data line */
+ /* ---------------------------------------------------------------------- */
+
+ if (!read_header (f, buf, &mtype, &nrow, &ncol, &nnz, &stype) ||
+ mtype != CHOLMOD_TRIPLET)
+ {
+ /* invalid matrix - this function can only read in a triplet matrix */
+ ERROR (CHOLMOD_INVALID, "invalid format") ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the triplet matrix */
+ /* ---------------------------------------------------------------------- */
+
+ return (read_triplet (f, nrow, ncol, nnz, stype, FALSE, buf, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_read_sparse ================================================== */
+/* ========================================================================== */
+
+/* Read a sparse matrix from a file. See cholmod_read_triplet for a discussion
+ * of the file format.
+ *
+ * If Common->prefer_upper is TRUE (the default case), a symmetric matrix is
+ * returned stored in upper-triangular form (A->stype == 1).
+ */
+
+cholmod_sparse *CHOLMOD(read_sparse)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *A, *A2 ;
+ cholmod_triplet *T ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (f, NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to a sparse matrix in compressed-column form */
+ /* ---------------------------------------------------------------------- */
+
+ T = CHOLMOD(read_triplet) (f, Common) ;
+ A = CHOLMOD(triplet_to_sparse) (T, 0, Common) ;
+ CHOLMOD(free_triplet) (&T, Common) ;
+
+ if (Common->prefer_upper && A != NULL && A->stype == -1)
+ {
+ /* A=A' */
+ A2 = CHOLMOD(transpose) (A, 2, Common) ;
+ CHOLMOD(free_sparse) (&A, Common) ;
+ A = A2 ;
+ }
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_read_dense =================================================== */
+/* ========================================================================== */
+
+/* Read a dense matrix from a file. */
+
+cholmod_dense *CHOLMOD(read_dense)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ char buf [MAXLINE+1] ;
+ size_t nrow, ncol, nnz ;
+ int stype, mtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (f, NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* read the header and first data line */
+ /* ---------------------------------------------------------------------- */
+
+ if (!read_header (f, buf, &mtype, &nrow, &ncol, &nnz, &stype) ||
+ mtype != CHOLMOD_DENSE)
+ {
+ /* invalid matrix - this function can only read in a dense matrix */
+ ERROR (CHOLMOD_INVALID, "invalid format") ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the dense matrix */
+ /* ---------------------------------------------------------------------- */
+
+ return (read_dense (f, nrow, ncol, stype, buf, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_read_matrix ================================================== */
+/* ========================================================================== */
+
+/* Read a triplet matrix, sparse matrix or a dense matrix from a file. Returns
+ * a void pointer to either a cholmod_triplet, cholmod_sparse, or cholmod_dense
+ * object. The type of object is passed back to the caller as the mtype
+ * argument. */
+
+void *CHOLMOD(read_matrix)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ int prefer, /* If 0, a sparse matrix is always return as a
+ * cholmod_triplet form. It can have any stype
+ * (symmetric-lower, unsymmetric, or
+ * symmetric-upper).
+ * If 1, a sparse matrix is returned as an unsymmetric
+ * cholmod_sparse form (A->stype == 0), with both
+ * upper and lower triangular parts present.
+ * This is what the MATLAB mread mexFunction does,
+ * since MATLAB does not have an stype.
+ * If 2, a sparse matrix is returned with an stype of 0
+ * or 1 (unsymmetric, or symmetric with upper part
+ * stored).
+ * This argument has no effect for dense matrices.
+ */
+ /* ---- output---- */
+ int *mtype, /* CHOLMOD_TRIPLET, CHOLMOD_SPARSE or CHOLMOD_DENSE */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ void *G = NULL ;
+ cholmod_sparse *A, *A2 ;
+ cholmod_triplet *T ;
+ char buf [MAXLINE+1] ;
+ size_t nrow, ncol, nnz ;
+ int stype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (f, NULL) ;
+ RETURN_IF_NULL (mtype, NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* read the header to determine the mtype */
+ /* ---------------------------------------------------------------------- */
+
+ if (!read_header (f, buf, mtype, &nrow, &ncol, &nnz, &stype))
+ {
+ /* invalid matrix */
+ ERROR (CHOLMOD_INVALID, "invalid format") ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read a matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (*mtype == CHOLMOD_TRIPLET)
+ {
+ /* read in the triplet matrix, converting to unsymmetric format if
+ * prefer == 1 */
+ T = read_triplet (f, nrow, ncol, nnz, stype, prefer == 1, buf, Common) ;
+ if (prefer == 0)
+ {
+ /* return matrix in its original triplet form */
+ G = T ;
+ }
+ else
+ {
+ /* return matrix in a compressed-column form */
+ A = CHOLMOD(triplet_to_sparse) (T, 0, Common) ;
+ CHOLMOD(free_triplet) (&T, Common) ;
+ if (A != NULL && prefer == 2 && A->stype == -1)
+ {
+ /* convert A from symmetric-lower to symmetric-upper */
+ A2 = CHOLMOD(transpose) (A, 2, Common) ;
+ CHOLMOD(free_sparse) (&A, Common) ;
+ A = A2 ;
+ }
+ *mtype = CHOLMOD_SPARSE ;
+ G = A ;
+ }
+ }
+ else if (*mtype == CHOLMOD_DENSE)
+ {
+ /* return a dense matrix */
+ G = read_dense (f, nrow, ncol, stype, buf, Common) ;
+ }
+ return (G) ;
+}
+#endif
diff --git a/CHOLMOD/Check/cholmod_write.c b/CHOLMOD/Check/cholmod_write.c
new file mode 100644
index 0000000..0c2d83f
--- /dev/null
+++ b/CHOLMOD/Check/cholmod_write.c
@@ -0,0 +1,744 @@
+/* ========================================================================== */
+/* === Check/cholmod_write ================================================== */
+/* ========================================================================== */
+
+/* Write a matrix to a file in Matrix Market form.
+ *
+ * A can be sparse or full.
+ *
+ * If present and non-empty, A and Z must have the same dimension. Z contains
+ * the explicit zero entries in the matrix (which MATLAB drops). The entries
+ * of Z appear as explicit zeros in the output file. Z is optional. If it is
+ * an empty matrix it is ignored. Z must be sparse or empty, if present.
+ * It is ignored if A is full.
+ *
+ * filename is the name of the output file. comments is file whose
+ * contents are include after the Matrix Market header and before the first
+ * data line. Ignored if an empty string or not present.
+ *
+ * Except for the workspace used by cholmod_symmetry (ncol integers) for
+ * the sparse case, these routines use no workspace at all.
+ */
+
+#ifndef NCHECK
+
+#include "cholmod_internal.h"
+#include "cholmod_check.h"
+#include "cholmod_matrixops.h"
+#include <string.h>
+#include <ctype.h>
+
+#define MMLEN 1024
+#define MAXLINE MMLEN+6
+
+/* ========================================================================== */
+/* === include_comments ===================================================== */
+/* ========================================================================== */
+
+/* Read in the comments file, if it exists, and copy it to the Matrix Market
+ * file. A "%" is prepended to each line. Returns TRUE if successful, FALSE
+ * otherwise.
+ */
+
+static int include_comments (FILE *f, char *comments)
+{
+ FILE *cf = NULL ;
+ char buffer [MAXLINE] ;
+ int ok = TRUE ;
+ if (comments != NULL && comments [0] != '\0')
+ {
+ cf = fopen (comments, "r") ;
+ if (cf == NULL)
+ {
+ return (FALSE) ;
+ }
+ while (ok && fgets (buffer, MAXLINE, cf) != NULL)
+ {
+ /* ensure the line is not too long */
+ buffer [MMLEN-1] = '\0' ;
+ buffer [MMLEN-2] = '\n' ;
+ ok = ok && (fprintf (f, "%%%s", buffer) > 0) ;
+ }
+ fclose (cf) ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === get_value ============================================================ */
+/* ========================================================================== */
+
+/* Get the pth value in the matrix. */
+
+static void get_value
+(
+ double *Ax, /* real values, or real/imag. for CHOLMOD_COMPLEX type */
+ double *Az, /* imaginary values for CHOLMOD_ZOMPLEX type */
+ Int p, /* get the pth entry */
+ Int xtype, /* A->xtype: pattern, real, complex, or zomplex */
+ double *x, /* the real part */
+ double *z /* the imaginary part */
+)
+{
+ switch (xtype)
+ {
+ case CHOLMOD_PATTERN:
+ *x = 1 ;
+ *z = 0 ;
+ break ;
+
+ case CHOLMOD_REAL:
+ *x = Ax [p] ;
+ *z = 0 ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ *x = Ax [2*p] ;
+ *z = Ax [2*p+1] ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ *x = Ax [p] ;
+ *z = Az [p] ;
+ break ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === print_value ========================================================== */
+/* ========================================================================== */
+
+/* Print a numeric value to the file, using the shortest format that ensures
+ * the value is written precisely. Returns TRUE if successful, FALSE otherwise.
+ */
+
+static int print_value
+(
+ FILE *f, /* file to print to */
+ double x, /* value to print */
+ Int is_integer /* TRUE if printing as an integer */
+)
+{
+ double y ;
+ char s [MAXLINE], *p ;
+ Int i, dest = 0, src = 0 ;
+ int width, ok ;
+
+ if (is_integer)
+ {
+ i = (Int) x ;
+ ok = (fprintf (f, ID, i) > 0) ;
+ return (ok) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* handle Inf and NaN */
+ /* ---------------------------------------------------------------------- */
+
+ /* change -inf to -HUGE_DOUBLE, and change +inf and nan to +HUGE_DOUBLE */
+ if (CHOLMOD_IS_NAN (x) || x >= HUGE_DOUBLE)
+ {
+ x = HUGE_DOUBLE ;
+ }
+ else if (x <= -HUGE_DOUBLE)
+ {
+ x = -HUGE_DOUBLE ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the smallest acceptable precision */
+ /* ---------------------------------------------------------------------- */
+
+ for (width = 6 ; width < 20 ; width++)
+ {
+ sprintf (s, "%.*g", width, x) ;
+ sscanf (s, "%lg", &y) ;
+ if (x == y) break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* shorten the string */
+ /* ---------------------------------------------------------------------- */
+
+ /* change "e+0" to "e", change "e+" to "e", and change "e-0" to "e-" */
+ for (i = 0 ; i < MAXLINE && s [i] != '\0' ; i++)
+ {
+ if (s [i] == 'e')
+ {
+ if (s [i+1] == '+')
+ {
+ dest = i+1 ;
+ if (s [i+2] == '0')
+ {
+ /* delete characters s[i+1] and s[i+2] */
+ src = i+3 ;
+ }
+ else
+ {
+ /* delete characters s[i+1] */
+ src = i+2 ;
+ }
+ }
+ else if (s [i+1] == '-')
+ {
+ dest = i+2 ;
+ if (s [i+2] == '0')
+ {
+ /* delete character s[i+2] */
+ src = i+3 ;
+ }
+ else
+ {
+ /* no change */
+ break ;
+ }
+ }
+ while (s [src] != '\0')
+ {
+ s [dest++] = s [src++] ;
+ }
+ s [dest] = '\0' ;
+ break ;
+ }
+ }
+
+ /* delete the leading "0" if present and not necessary */
+ p = s ;
+ s [MAXLINE-1] = '\0' ;
+ i = strlen (s) ;
+ if (i > 2 && s [0] == '0' && s [1] == '.')
+ {
+ /* change "0.x" to ".x" */
+ p = s + 1 ;
+ }
+ else if (i > 3 && s [0] == '-' && s [1] == '0' && s [2] == '.')
+ {
+ /* change "-0.x" to "-.x" */
+ s [1] = '-' ;
+ p = s + 1 ;
+ }
+
+#if 0
+ /* double-check */
+ i = sscanf (p, "%lg", &z) ;
+ if (i != 1 || y != z)
+ {
+ /* oops! something went wrong in the "e+0" edit, above. */
+ /* this "cannot" happen */
+ sprintf (s, "%.*g", width, x) ;
+ p = s ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* print the value to the file */
+ /* ---------------------------------------------------------------------- */
+
+ ok = (fprintf (f, "%s", p) > 0) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === print_triplet ======================================================== */
+/* ========================================================================== */
+
+/* Print a triplet, converting it to one-based. Returns TRUE if successful,
+ * FALSE otherwise.
+ */
+
+static int print_triplet
+(
+ FILE *f, /* file to print to */
+ Int is_binary, /* TRUE if file is "pattern" */
+ Int is_complex, /* TRUE if file is "complex" */
+ Int is_integer, /* TRUE if file is "integer" */
+ Int i, /* row index (zero-based) */
+ Int j, /* column index (zero-based) */
+ double x, /* real part */
+ double z /* imaginary part */
+)
+{
+ int ok ;
+ ok = (fprintf (f, ID " " ID, 1+i, 1+j) > 0) ;
+ if (!is_binary)
+ {
+ fprintf (f, " ") ;
+ ok = ok && print_value (f, x, is_integer) ;
+ if (is_complex)
+ {
+ fprintf (f, " ") ;
+ ok = ok && print_value (f, z, is_integer) ;
+ }
+ }
+ ok = ok && (fprintf (f, "\n") > 0) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === ntriplets ============================================================ */
+/* ========================================================================== */
+
+/* Compute the number of triplets that will be printed to the file
+ * from the matrix A. */
+
+static Int ntriplets
+(
+ cholmod_sparse *A, /* matrix that will be printed */
+ Int is_sym /* TRUE if the file is symmetric (lower part only)*/
+)
+{
+ Int *Ap, *Ai, *Anz, packed, i, j, p, pend, ncol, stype, nz = 0 ;
+ if (A == NULL)
+ {
+ /* the Z matrix is NULL */
+ return (0) ;
+ }
+ stype = A->stype ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ ncol = A->ncol ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? Ap [j+1] : p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if ((stype < 0 && i >= j) || (stype == 0 && (i >= j || !is_sym)))
+ {
+ /* CHOLMOD matrix is symmetric-lower (and so is the file);
+ * or CHOLMOD matrix is unsymmetric and either A(i,j) is in
+ * the lower part or the file is unsymmetric. */
+ nz++ ;
+ }
+ else if (stype > 0 && i <= j)
+ {
+ /* CHOLMOD matrix is symmetric-upper, but the file is
+ * symmetric-lower. Need to transpose the entry. */
+ nz++ ;
+ }
+ }
+ }
+ return (nz) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_write_sparse ================================================= */
+/* ========================================================================== */
+
+/* Write a sparse matrix to a file in Matrix Market format. Optionally include
+ * comments, and print explicit zero entries given by the pattern of the Z
+ * matrix. If not NULL, the Z matrix must have the same dimensions and stype
+ * as A.
+ *
+ * Returns the symmetry in which the matrix was printed (1 to 7, see the
+ * CHOLMOD_MM_* codes in CHOLMOD/Include/cholmod_core.h), or -1 on failure.
+ *
+ * If A and Z are sorted on input, and either unsymmetric (stype = 0) or
+ * symmetric-lower (stype < 0), and if A and Z do not overlap, then the triplets
+ * are sorted, first by column and then by row index within each column, with
+ * no duplicate entries. If all the above holds except stype > 0, then the
+ * triplets are sorted by row first and then column.
+ */
+
+int CHOLMOD(write_sparse)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to write to, must already be open */
+ cholmod_sparse *A, /* matrix to print */
+ cholmod_sparse *Z, /* optional matrix with pattern of explicit zeros */
+ char *comments, /* optional filename of comments to include */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double x = 0, z = 0 ;
+ double *Ax, *Az ;
+ Int *Ap, *Ai, *Anz, *Zp, *Zi, *Znz ;
+ Int nrow, ncol, is_complex, symmetry, i, j, q, iz, p, nz, is_binary, stype,
+ is_integer, asym, is_sym, xtype, apacked, zpacked, pend, qend, zsym ;
+ int ok ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (f, EMPTY) ;
+ RETURN_IF_NULL (A, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ if (Z != NULL && (Z->nrow == 0 || Z->ncol == 0))
+ {
+ /* Z is non-NULL but empty, so treat it as a NULL matrix */
+ Z = NULL ;
+ }
+ if (Z != NULL)
+ {
+ RETURN_IF_XTYPE_INVALID (Z, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ if (Z->nrow != A->nrow || Z->ncol != A->ncol || Z->stype != A->stype)
+ {
+ ERROR (CHOLMOD_INVALID, "dimension or type of A and Z mismatch") ;
+ return (EMPTY) ;
+ }
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the A matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ xtype = A->xtype ;
+ apacked = A->packed ;
+
+ if (xtype == CHOLMOD_PATTERN)
+ {
+ /* a CHOLMOD pattern matrix is printed as "pattern" in the file */
+ is_binary = TRUE ;
+ is_integer = FALSE ;
+ is_complex = FALSE ;
+ }
+ else if (xtype == CHOLMOD_REAL)
+ {
+ /* determine if a real matrix is in fact binary or integer */
+ is_binary = TRUE ;
+ is_integer = TRUE ;
+ is_complex = FALSE ;
+ for (j = 0 ; (is_binary || is_integer) && j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (apacked) ? Ap [j+1] : p + Anz [j] ;
+ for ( ; (is_binary || is_integer) && p < pend ; p++)
+ {
+ x = Ax [p] ;
+ if (x != 1)
+ {
+ is_binary = FALSE ;
+ }
+ /* convert to Int and then back to double */
+ i = (Int) x ;
+ z = (double) i ;
+ if (z != x)
+ {
+ is_integer = FALSE ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* a CHOLMOD complex matrix is printed as "complex" in the file */
+ is_binary = FALSE ;
+ is_integer = FALSE ;
+ is_complex = TRUE ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the Z matrix (only consider the pattern) */
+ /* ---------------------------------------------------------------------- */
+
+ Zp = NULL ;
+ Zi = NULL ;
+ Znz = NULL ;
+ zpacked = TRUE ;
+ if (Z != NULL)
+ {
+ Zp = Z->p ;
+ Zi = Z->i ;
+ Znz = Z->nz ;
+ zpacked = Z->packed ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the symmetry of A and Z */
+ /* ---------------------------------------------------------------------- */
+
+ stype = A->stype ;
+ if (A->nrow != A->ncol)
+ {
+ asym = CHOLMOD_MM_RECTANGULAR ;
+ }
+ else if (stype != 0)
+ {
+ /* CHOLMOD's A and Z matrices have a symmetric (and matching) stype.
+ * Note that the diagonal is not checked. */
+ asym = is_complex ? CHOLMOD_MM_HERMITIAN : CHOLMOD_MM_SYMMETRIC ;
+ }
+ else if (!A->sorted)
+ {
+ /* A is in unsymmetric storage, but unsorted */
+ asym = CHOLMOD_MM_UNSYMMETRIC ;
+ }
+ else
+ {
+ /* CHOLMOD's stype is zero (stored in unsymmetric form) */
+ asym = EMPTY ;
+ zsym = EMPTY ;
+
+#ifndef NMATRIXOPS
+ /* determine if the matrices are in fact symmetric or Hermitian */
+ asym = CHOLMOD(symmetry) (A, 1, NULL, NULL, NULL, NULL, Common) ;
+ zsym = (Z == NULL) ? 999 :
+ CHOLMOD(symmetry) (Z, 1, NULL, NULL, NULL, NULL, Common) ;
+#endif
+
+ if (asym == EMPTY || zsym <= CHOLMOD_MM_UNSYMMETRIC)
+ {
+ /* not computed, out of memory, or Z is unsymmetric */
+ asym = CHOLMOD_MM_UNSYMMETRIC ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* write the Matrix Market header */
+ /* ---------------------------------------------------------------------- */
+
+ ok = fprintf (f, "%%%%MatrixMarket matrix coordinate") > 0 ;
+
+ if (is_complex)
+ {
+ ok = ok && (fprintf (f, " complex") > 0) ;
+ }
+ else if (is_binary)
+ {
+ ok = ok && (fprintf (f, " pattern") > 0) ;
+ }
+ else if (is_integer)
+ {
+ ok = ok && (fprintf (f, " integer") > 0) ;
+ }
+ else
+ {
+ ok = ok && (fprintf (f, " real") > 0) ;
+ }
+
+ is_sym = FALSE ;
+
+ switch (asym)
+ {
+ case CHOLMOD_MM_RECTANGULAR:
+ case CHOLMOD_MM_UNSYMMETRIC:
+ /* A is rectangular or unsymmetric */
+ ok = ok && (fprintf (f, " general\n") > 0) ;
+ is_sym = FALSE ;
+ symmetry = CHOLMOD_MM_UNSYMMETRIC ;
+ break ;
+
+ case CHOLMOD_MM_SYMMETRIC:
+ case CHOLMOD_MM_SYMMETRIC_POSDIAG:
+ /* A is symmetric */
+ ok = ok && (fprintf (f, " symmetric\n") > 0) ;
+ is_sym = TRUE ;
+ symmetry = CHOLMOD_MM_SYMMETRIC ;
+ break ;
+
+ case CHOLMOD_MM_HERMITIAN:
+ case CHOLMOD_MM_HERMITIAN_POSDIAG:
+ /* A is Hermitian */
+ ok = ok && (fprintf (f, " Hermitian\n") > 0) ;
+ is_sym = TRUE ;
+ symmetry = CHOLMOD_MM_HERMITIAN ;
+ break ;
+
+ case CHOLMOD_MM_SKEW_SYMMETRIC:
+ /* A is skew symmetric */
+ ok = ok && (fprintf (f, " skew-symmetric\n") > 0) ;
+ is_sym = TRUE ;
+ symmetry = CHOLMOD_MM_SKEW_SYMMETRIC ;
+ break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* include the comments if present */
+ /* ---------------------------------------------------------------------- */
+
+ ok = ok && include_comments (f, comments) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* write a sparse matrix (A and Z) */
+ /* ---------------------------------------------------------------------- */
+
+ nz = ntriplets (A, is_sym) + ntriplets (Z, is_sym) ;
+
+ /* write the first data line, with nrow, ncol, and # of triplets */
+ ok = ok && (fprintf (f, ID " " ID " " ID "\n", nrow, ncol, nz) > 0) ;
+
+ for (j = 0 ; ok && j < ncol ; j++)
+ {
+ /* merge column of A and Z */
+ p = Ap [j] ;
+ pend = (apacked) ? Ap [j+1] : p + Anz [j] ;
+ q = (Z == NULL) ? 0 : Zp [j] ;
+ qend = (Z == NULL) ? 0 : ((zpacked) ? Zp [j+1] : q + Znz [j]) ;
+ while (ok)
+ {
+ /* get the next row index from A and Z */
+ i = (p < pend) ? Ai [p] : (nrow+1) ;
+ iz = (q < qend) ? Zi [q] : (nrow+2) ;
+ if (i <= iz)
+ {
+ /* get A(i,j), or quit if both A and Z are exhausted */
+ if (i == nrow+1) break ;
+ get_value (Ax, Az, p, xtype, &x, &z) ;
+ p++ ;
+ }
+ else
+ {
+ /* get Z(i,j) */
+ i = iz ;
+ x = 0 ;
+ z = 0 ;
+ q++ ;
+ }
+ if ((stype < 0 && i >= j) || (stype == 0 && (i >= j || !is_sym)))
+ {
+ /* CHOLMOD matrix is symmetric-lower (and so is the file);
+ * or CHOLMOD matrix is unsymmetric and either A(i,j) is in
+ * the lower part or the file is unsymmetric. */
+ ok = ok && print_triplet (f, is_binary, is_complex, is_integer,
+ i,j, x,z) ;
+ }
+ else if (stype > 0 && i <= j)
+ {
+ /* CHOLMOD matrix is symmetric-upper, but the file is
+ * symmetric-lower. Need to transpose the entry. If the
+ * matrix is real, the complex part is ignored. If the matrix
+ * is complex, it Hermitian.
+ */
+ ASSERT (IMPLIES (is_complex, asym == CHOLMOD_MM_HERMITIAN)) ;
+ if (z != 0)
+ {
+ z = -z ;
+ }
+ ok = ok && print_triplet (f, is_binary, is_complex, is_integer,
+ j,i, x,z) ;
+ }
+ }
+ }
+
+ if (!ok)
+ {
+ ERROR (CHOLMOD_INVALID, "error reading/writing file") ;
+ return (EMPTY) ;
+ }
+
+ return (asym) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_write_dense ================================================== */
+/* ========================================================================== */
+
+/* Write a dense matrix to a file in Matrix Market format. Optionally include
+ * comments. Returns > 0 if successful, -1 otherwise (1 if rectangular, 2 if
+ * square). Future versions may return 1 to 7 on success (a CHOLMOD_MM_* code,
+ * just as cholmod_write_sparse does).
+ *
+ * A dense matrix is written in "general" format; symmetric formats in the
+ * Matrix Market standard are not exploited.
+ */
+
+int CHOLMOD(write_dense)
+(
+ /* ---- input ---- */
+ FILE *f, /* file to write to, must already be open */
+ cholmod_dense *X, /* matrix to print */
+ char *comments, /* optional filename of comments to include */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double x = 0, z = 0 ;
+ double *Xx, *Xz ;
+ Int nrow, ncol, is_complex, i, j, xtype, p ;
+ int ok ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (f, EMPTY) ;
+ RETURN_IF_NULL (X, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the X matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Xx = X->x ;
+ Xz = X->z ;
+ nrow = X->nrow ;
+ ncol = X->ncol ;
+ xtype = X->xtype ;
+ is_complex = (xtype == CHOLMOD_COMPLEX) || (xtype == CHOLMOD_ZOMPLEX) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* write the Matrix Market header */
+ /* ---------------------------------------------------------------------- */
+
+ ok = (fprintf (f, "%%%%MatrixMarket matrix array") > 0) ;
+ if (is_complex)
+ {
+ ok = ok && (fprintf (f, " complex general\n") > 0) ;
+ }
+ else
+ {
+ ok = ok && (fprintf (f, " real general\n") > 0) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* include the comments if present */
+ /* ---------------------------------------------------------------------- */
+
+ ok = ok && include_comments (f, comments) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* write a dense matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* write the first data line, with nrow and ncol */
+ ok = ok && (fprintf (f, ID " " ID "\n", nrow, ncol) > 0) ;
+
+ Xx = X->x ;
+ Xz = X->z ;
+ for (j = 0 ; ok && j < ncol ; j++)
+ {
+ for (i = 0 ; ok && i < nrow ; i++)
+ {
+ p = i + j*nrow ;
+ get_value (Xx, Xz, p, xtype, &x, &z) ;
+ ok = ok && print_value (f, x, FALSE) ;
+ if (is_complex)
+ {
+ ok = ok && (fprintf (f, " ") > 0) ;
+ ok = ok && print_value (f, z, FALSE) ;
+ }
+ ok = ok && (fprintf (f, "\n") > 0) ;
+ }
+ }
+
+ if (!ok)
+ {
+ ERROR (CHOLMOD_INVALID, "error reading/writing file") ;
+ return (EMPTY) ;
+ }
+
+ return ((nrow == ncol) ? CHOLMOD_MM_UNSYMMETRIC : CHOLMOD_MM_RECTANGULAR) ;
+}
+#endif
diff --git a/CHOLMOD/Check/lesser.txt b/CHOLMOD/Check/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/CHOLMOD/Check/lesser.txt
@@ -0,0 +1,504 @@
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+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the
+ library `Frob' (a library for tweaking knobs) written by James Random Hacker.
+
+ <signature of Ty Coon>, 1 April 1990
+ Ty Coon, President of Vice
+
+That's all there is to it!
+
+
diff --git a/CHOLMOD/Cholesky/License.txt b/CHOLMOD/Cholesky/License.txt
new file mode 100644
index 0000000..b444856
--- /dev/null
+++ b/CHOLMOD/Cholesky/License.txt
@@ -0,0 +1,24 @@
+CHOLMOD/Cholesky module, Copyright (C) 2005-2006, Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Cholesky module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
diff --git a/CHOLMOD/Cholesky/cholmod_amd.c b/CHOLMOD/Cholesky/cholmod_amd.c
new file mode 100644
index 0000000..09f8ec1
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_amd.c
@@ -0,0 +1,212 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_amd ================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD interface to the AMD ordering routine. Orders A if the matrix is
+ * symmetric. On output, Perm [k] = i if row/column i of A is the kth
+ * row/column of P*A*P'. This corresponds to A(p,p) in MATLAB notation.
+ *
+ * If A is unsymmetric, cholmod_amd orders A*A'. On output, Perm [k] = i if
+ * row/column i of A*A' is the kth row/column of P*A*A'*P'. This corresponds to
+ * A(p,:)*A(p,:)' in MATLAB notation. If f is present, A(p,f)*A(p,f)' is
+ * ordered.
+ *
+ * Computes the flop count for a subsequent LL' factorization, the number
+ * of nonzeros in L, and the number of nonzeros in the matrix ordered (A,
+ * A*A' or A(:,f)*A(:,f)').
+ *
+ * workspace: Iwork (6*nrow). Head (nrow).
+ *
+ * Allocates a temporary copy of A+A' or A*A' (with
+ * both upper and lower triangular parts) as input to AMD.
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex)
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "amd.h"
+#include "cholmod_cholesky.h"
+
+#if (!defined (AMD_VERSION) || (AMD_VERSION < AMD_VERSION_CODE (2,0)))
+#error "AMD v2.0 or later is required"
+#endif
+
+/* ========================================================================== */
+/* === cholmod_amd ========================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(amd)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ Int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double Info [AMD_INFO], Control2 [AMD_CONTROL], *Control ;
+ Int *Cp, *Len, *Nv, *Head, *Elen, *Degree, *Wi, *Iwork, *Next ;
+ cholmod_sparse *C ;
+ Int j, n, cnz ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ n = A->nrow ;
+
+ RETURN_IF_NULL (Perm, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ if (n == 0)
+ {
+ /* nothing to do */
+ Common->fl = 0 ;
+ Common->lnz = 0 ;
+ Common->anz = 0 ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note: this is less than the space used in cholmod_analyze, so if
+ * cholmod_amd is being called by that routine, no space will be
+ * allocated.
+ */
+
+ /* s = MAX (6*n, A->ncol) */
+ s = CHOLMOD(mult_size_t) (n, 6, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+ s = MAX (s, A->ncol) ;
+
+ CHOLMOD(allocate_work) (n, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ Iwork = Common->Iwork ;
+ Degree = Iwork ; /* size n */
+ Wi = Iwork + n ; /* size n */
+ Len = Iwork + 2*((size_t) n) ; /* size n */
+ Nv = Iwork + 3*((size_t) n) ; /* size n */
+ Next = Iwork + 4*((size_t) n) ; /* size n */
+ Elen = Iwork + 5*((size_t) n) ; /* size n */
+
+ Head = Common->Head ; /* size n+1, but only n is used */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the input matrix for AMD */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0)
+ {
+ /* C = A*A' or A(:,f)*A(:,f)', add extra space of nnz(C)/2+n to C */
+ C = CHOLMOD(aat) (A, fset, fsize, -2, Common) ;
+ }
+ else
+ {
+ /* C = A+A', but use only the upper triangular part of A if A->stype = 1
+ * and only the lower part of A if A->stype = -1. Add extra space of
+ * nnz(C)/2+n to C. */
+ C = CHOLMOD(copy) (A, 0, -2, Common) ;
+ }
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory, fset invalid, or other error */
+ return (FALSE) ;
+ }
+
+ Cp = C->p ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Len [j] = Cp [j+1] - Cp [j] ;
+ }
+
+ /* C does not include the diagonal, and both upper and lower parts.
+ * Common->anz includes the diagonal, and just the lower part of C */
+ cnz = Cp [n] ;
+ Common->anz = cnz / 2 + n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order C using AMD */
+ /* ---------------------------------------------------------------------- */
+
+ /* get parameters */
+ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS)
+ {
+ /* use AMD defaults */
+ Control = NULL ;
+ }
+ else
+ {
+ Control = Control2 ;
+ Control [AMD_DENSE] = Common->method [Common->current].prune_dense ;
+ Control [AMD_AGGRESSIVE] = Common->method [Common->current].aggressive ;
+ }
+
+ /* AMD_2 does not use amd_malloc and amd_free, but set these pointers just
+ * be safe. */
+ amd_malloc = Common->malloc_memory ;
+ amd_free = Common->free_memory ;
+ amd_calloc = Common->calloc_memory ;
+ amd_realloc = Common->realloc_memory ;
+
+ /* AMD_2 doesn't print anything either, but future versions might,
+ * so set the amd_printf pointer too. */
+ amd_printf = Common->print_function ;
+
+#ifdef LONG
+ amd_l2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen,
+ Degree, Wi, Control, Info) ;
+#else
+ amd_2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen,
+ Degree, Wi, Control, Info) ;
+#endif
+
+ /* LL' flop count. Need to subtract n for LL' flop count. Note that this
+ * is a slight upper bound which is often exact (see AMD/Source/amd_2.c for
+ * details). cholmod_analyze computes an exact flop count and fill-in. */
+ Common->fl = Info [AMD_NDIV] + 2 * Info [AMD_NMULTSUBS_LDL] + n ;
+
+ /* Info [AMD_LNZ] excludes the diagonal */
+ Common->lnz = n + Info [AMD_LNZ] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the AMD workspace and clear the persistent workspace in Common */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (IMPLIES (Common->status == CHOLMOD_OK,
+ CHOLMOD(dump_perm) (Perm, n, n, "AMD2 perm", Common))) ;
+ CHOLMOD(free_sparse) (&C, Common) ;
+ for (j = 0 ; j <= n ; j++)
+ {
+ Head [j] = EMPTY ;
+ }
+ return (TRUE) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_analyze.c b/CHOLMOD/Cholesky/cholmod_analyze.c
new file mode 100644
index 0000000..19ce5b4
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_analyze.c
@@ -0,0 +1,896 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_analyze ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Order and analyze a matrix (either simplicial or supernodal), in prepartion
+ * for numerical factorization via cholmod_factorize or via the "expert"
+ * routines cholmod_rowfac and cholmod_super_numeric.
+ *
+ * symmetric case: A or A(p,p)
+ * unsymmetric case: AA', A(p,:)*A(p,:)', A(:,f)*A(:,f)', or A(p,f)*A(p,f)'
+ *
+ * For the symmetric case, only the upper or lower triangular part of A is
+ * accessed (depending on the type of A). LL'=A (or permuted A) is analzed.
+ * For the unsymmetric case (LL'=AA' or permuted A).
+ *
+ * There can be no duplicate entries in p or f. p is of length m if A is
+ * m-by-n. f can be length 0 to n.
+ *
+ * In both cases, the columns of A need not be sorted. A can be in packed
+ * or unpacked form.
+ *
+ * Ordering options include:
+ *
+ * natural: A is not permuted to reduce fill-in
+ * given: a permutation can be provided to this routine (UserPerm)
+ * AMD: approximate minumum degree (AMD for the symmetric case,
+ * COLAMD for the AA' case).
+ * METIS: nested dissection with METIS_NodeND
+ * NESDIS: nested dissection using METIS_NodeComputeSeparator,
+ * typically followed by a constrained minimum degree
+ * (CAMD for the symmetric case, CCOLAMD for the AA' case).
+ *
+ * Multiple ordering options can be tried (up to 9 of them), and the best one
+ * is selected (the one that gives the smallest number of nonzeros in the
+ * simplicial factor L). If one method fails, cholmod_analyze keeps going, and
+ * picks the best among the methods that succeeded. This routine fails (and
+ * returns NULL) if either initial memory allocation fails, all ordering methods
+ * fail, or the supernodal analysis (if requested) fails. By default, the 9
+ * methods available are:
+ *
+ * 1) given permutation (skipped if UserPerm is NULL)
+ * 2) AMD (symmetric case) or COLAMD (unsymmetric case)
+ * 3) METIS with default parameters
+ * 4) NESDIS with default parameters (stopping the partitioning when
+ * the graph is of size nd_small = 200 or less, remove nodes with
+ * more than max (16, prune_dense * sqrt (n)) nodes where
+ * prune_dense = 10, and follow partitioning with CCOLAMD, a
+ * constrained minimum degree ordering).
+ * 5) natural
+ * 6) NESDIS, nd_small = 20000, prune_dense = 10
+ * 7) NESDIS, nd_small = 4, prune_dense = 10, no min degree
+ * 8) NESDIS, nd_small = 200, prune_dense = 0
+ * 9) COLAMD for A*A' or AMD for A
+ *
+ * By default, the first two are tried, and METIS is tried if AMD reports a high
+ * flop count and fill-in. Let fl denote the flop count for the AMD, ordering,
+ * nnz(L) the # of nonzeros in L, and nnz(tril(A)) (or A*A'). If
+ * fl/nnz(L) >= 500 and nnz(L)/nnz(tril(A)) >= 5, then METIS is attempted. The
+ * best ordering is used (UserPerm if given, AMD, and METIS if attempted). If
+ * you do not have METIS, only the first two will be tried (user permutation,
+ * if provided, and AMD/COLAMD). This default behavior is obtained when
+ * Common->nmethods is zero. In this case, methods 0, 1, and 2 in
+ * Common->method [..] are reset to User-provided, AMD, and METIS (or NESDIS
+ * if Common->default_nesdis is set to the non-default value of TRUE),
+ * respectively.
+ *
+ * You can modify these 9 methods and the number of methods tried by changing
+ * parameters in the Common argument. If you know the best ordering for your
+ * matrix, set Common->nmethods to 1 and set Common->method[0].ordering to the
+ * requested ordering method. Parameters for each method can also be modified
+ * (refer to cholmod.h for details).
+ *
+ * Note that it is possible for METIS to terminate your program if it runs out
+ * of memory. This is not the case for any CHOLMOD or minimum degree ordering
+ * routine (AMD, COLAMD, CAMD, CCOLAMD, or CSYMAMD). Since NESDIS relies on
+ * METIS, it too can terminate your program.
+ *
+ * The factor L is returned as simplicial symbolic (L->is_super FALSE) if
+ * Common->supernodal <= CHOLMOD_SIMPLICIAL (0) or as supernodal symbolic if
+ * Common->supernodal >= CHOLMOD_SUPERNODAL (2). If Common->supernodal is
+ * equal to CHOLMOD_AUTO (1), then L is simplicial if the flop count per
+ * nonzero in L is less than Common->supernodal_switch (default: 40), and
+ * is returned as a supernodal factor otherwise.
+ *
+ * In both cases, L->xtype is CHOLMOD_PATTERN.
+ * A subsequent call to cholmod_factorize will perform a
+ * simplicial or supernodal factorization, depending on the type of L.
+ *
+ * For the simplicial case, L contains the fill-reducing permutation (L->Perm)
+ * and the counts of nonzeros in each column of L (L->ColCount). For the
+ * supernodal case, L also contains the nonzero pattern of each supernode.
+ *
+ * workspace: Flag (nrow), Head (nrow+1)
+ * if symmetric: Iwork (6*nrow)
+ * if unsymmetric: Iwork (6*nrow+ncol).
+ * calls various ordering routines, which typically allocate O(nnz(A))
+ * temporary workspace ((2 to 3)*nnz(A) * sizeof (Int) is typical, but it
+ * can be much higher if A*A' must be explicitly formed for METIS). Also
+ * allocates up to 2 temporary (permuted/transpose) copies of the nonzero
+ * pattern of A, and up to 3*n*sizeof(Int) additional workspace.
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex)
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+#ifndef NSUPERNODAL
+#include "cholmod_supernodal.h"
+#endif
+
+#ifndef NPARTITION
+#include "cholmod_partition.h"
+#endif
+
+
+/* ========================================================================== */
+/* === cholmod_analyze ====================================================== */
+/* ========================================================================== */
+
+/* Orders and analyzes A, AA', PAP', or PAA'P' and returns a symbolic factor
+ * that can later be passed to cholmod_factorize. */
+
+cholmod_factor *CHOLMOD(analyze)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order and analyze */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(analyze_p) (A, NULL, NULL, 0, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === permute_matrices ===================================================== */
+/* ========================================================================== */
+
+/* Permute and transpose a matrix. Allocates the A1 and A2 matrices, if needed,
+ * or returns them as NULL if not needed.
+ */
+
+static int permute_matrices
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to permute */
+ Int ordering, /* ordering method used */
+ Int *Perm, /* fill-reducing permutation */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ Int do_rowcolcounts,/* if TRUE, compute both S and F. If FALSE, only
+ * S is needed for the symmetric case, and only F for
+ * the unsymmetric case */
+ /* ---- output --- */
+ cholmod_sparse **A1_handle, /* see comments below for A1, A2, S, F */
+ cholmod_sparse **A2_handle,
+ cholmod_sparse **S_handle,
+ cholmod_sparse **F_handle,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *A1, *A2, *S, *F ;
+
+ *A1_handle = NULL ;
+ *A2_handle = NULL ;
+ *S_handle = NULL ;
+ *F_handle = NULL ;
+ A1 = NULL ;
+ A2 = NULL ;
+
+ if (ordering == CHOLMOD_NATURAL)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* natural ordering of A */
+ /* ------------------------------------------------------------------ */
+
+ if (A->stype < 0)
+ {
+ /* symmetric lower case: A already in lower form, so S=A' */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (A, 0, NULL, NULL, 0, Common) ;
+ F = A ;
+ S = A2 ;
+ }
+ else if (A->stype > 0)
+ {
+ /* symmetric upper case: F = pattern of triu (A)', S = A */
+ /* workspace: Iwork (nrow) */
+ if (do_rowcolcounts)
+ {
+ /* F not needed for symmetric case if do_rowcolcounts FALSE */
+ A1 = CHOLMOD(ptranspose) (A, 0, NULL, fset, fsize, Common) ;
+ }
+ F = A1 ;
+ S = A ;
+ }
+ else
+ {
+ /* unsymmetric case: F = pattern of A (:,f)', S = A */
+ /* workspace: Iwork (nrow if no fset, MAX(nrow,ncol) if fset) */
+ A1 = CHOLMOD(ptranspose) (A, 0, NULL, fset, fsize, Common) ;
+ F = A1 ;
+ S = A ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A is permuted */
+ /* ------------------------------------------------------------------ */
+
+ if (A->stype < 0)
+ {
+ /* symmetric lower case: S = tril (A (p,p))' and F = S' */
+ /* workspace: Iwork (2*nrow) */
+ A2 = CHOLMOD(ptranspose) (A, 0, Perm, NULL, 0, Common) ;
+ S = A2 ;
+ /* workspace: Iwork (nrow) */
+ if (do_rowcolcounts)
+ {
+ /* F not needed for symmetric case if do_rowcolcounts FALSE */
+ A1 = CHOLMOD(ptranspose) (A2, 0, NULL, NULL, 0, Common) ;
+ }
+ F = A1 ;
+ }
+ else if (A->stype > 0)
+ {
+ /* symmetric upper case: F = triu (A (p,p))' and S = F' */
+ /* workspace: Iwork (2*nrow) */
+ A1 = CHOLMOD(ptranspose) (A, 0, Perm, NULL, 0, Common) ;
+ F = A1 ;
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (A1, 0, NULL, NULL, 0, Common) ;
+ S = A2 ;
+ }
+ else
+ {
+ /* unsymmetric case: F = A (p,f)' and S = F' */
+ /* workspace: Iwork (nrow if no fset, MAX(nrow,ncol) if fset) */
+ A1 = CHOLMOD(ptranspose) (A, 0, Perm, fset, fsize, Common) ;
+ F = A1 ;
+ if (do_rowcolcounts)
+ {
+ /* S not needed for unsymmetric case if do_rowcolcounts FALSE */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (A1, 0, NULL, NULL, 0, Common) ;
+ }
+ S = A2 ;
+ }
+ }
+
+ /* If any cholmod_*transpose fails, one or more matrices will be NULL */
+ *A1_handle = A1 ;
+ *A2_handle = A2 ;
+ *S_handle = S ;
+ *F_handle = F ;
+ return (Common->status == CHOLMOD_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_analyze_ordering ============================================= */
+/* ========================================================================== */
+
+/* Given a matrix A and its fill-reducing permutation, compute the elimination
+ * tree, its (non-weighted) postordering, and the number of nonzeros in each
+ * column of L. Also computes the flop count, the total nonzeros in L, and
+ * the nonzeros in A (Common->fl, Common->lnz, and Common->anz).
+ *
+ * The column counts of L, flop count, and other statistics from
+ * cholmod_rowcolcounts are not computed if ColCount is NULL.
+ *
+ * workspace: Iwork (2*nrow if symmetric, 2*nrow+ncol if unsymmetric),
+ * Flag (nrow), Head (nrow+1)
+ */
+
+int CHOLMOD(analyze_ordering)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int ordering, /* ordering method used */
+ Int *Perm, /* size n, fill-reducing permutation to analyze */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ Int *Parent, /* size n, elimination tree */
+ Int *Post, /* size n, postordering of elimination tree */
+ Int *ColCount, /* size n, nnz in each column of L */
+ /* ---- workspace */
+ Int *First, /* size nworkspace for cholmod_postorder */
+ Int *Level, /* size n workspace for cholmod_postorder */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *A1, *A2, *S, *F ;
+ Int n, ok, do_rowcolcounts ;
+
+ /* check inputs */
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+
+ n = A->nrow ;
+
+ do_rowcolcounts = (ColCount != NULL) ;
+
+ /* permute A according to Perm and fset */
+ ok = permute_matrices (A, ordering, Perm, fset, fsize, do_rowcolcounts,
+ &A1, &A2, &S, &F, Common) ;
+
+ /* find etree of S (symmetric upper/lower case) or F (unsym case) */
+ /* workspace: symmmetric: Iwork (nrow), unsym: Iwork (nrow+ncol) */
+ ok = ok && CHOLMOD(etree) (A->stype ? S:F, Parent, Common) ;
+
+ /* postorder the etree (required by cholmod_rowcolcounts) */
+ /* workspace: Iwork (2*nrow) */
+ ok = ok && (CHOLMOD(postorder) (Parent, n, NULL, Post, Common) == n) ;
+
+ /* cholmod_postorder doesn't set Common->status if it returns < n */
+ Common->status = (!ok && Common->status == CHOLMOD_OK) ?
+ CHOLMOD_INVALID : Common->status ;
+
+ /* analyze LL'=S or SS' or S(:,f)*S(:,f)' */
+ /* workspace:
+ * if symmetric: Flag (nrow), Iwork (2*nrow)
+ * if unsymmetric: Flag (nrow), Iwork (2*nrow+ncol), Head (nrow+1)
+ */
+ if (do_rowcolcounts)
+ {
+ ok = ok && CHOLMOD(rowcolcounts) (A->stype ? F:S, fset, fsize, Parent,
+ Post, NULL, ColCount, First, Level, Common) ;
+ }
+
+ /* free temporary matrices and return result */
+ CHOLMOD(free_sparse) (&A1, Common) ;
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === Free workspace and return L ========================================== */
+/* ========================================================================== */
+
+#define FREE_WORKSPACE_AND_RETURN \
+{ \
+ Common->no_workspace_reallocate = FALSE ; \
+ CHOLMOD(free) (n, sizeof (Int), Lparent, Common) ; \
+ CHOLMOD(free) (n, sizeof (Int), Perm, Common) ; \
+ CHOLMOD(free) (n, sizeof (Int), ColCount, Common) ; \
+ if (Common->status < CHOLMOD_OK) \
+ { \
+ CHOLMOD(free_factor) (&L, Common) ; \
+ } \
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; \
+ return (L) ; \
+}
+
+
+/* ========================================================================== */
+/* === cholmod_analyze_p ==================================================== */
+/* ========================================================================== */
+
+/* Orders and analyzes A, AA', PAP', PAA'P', FF', or PFF'P and returns a
+ * symbolic factor that can later be passed to cholmod_factorize, where
+ * F = A(:,fset) if fset is not NULL and A->stype is zero.
+ * UserPerm is tried if non-NULL. */
+
+cholmod_factor *CHOLMOD(analyze_p)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order and analyze */
+ Int *UserPerm, /* user-provided permutation, size A->nrow */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double lnz_best ;
+ Int *First, *Level, *Work4n, *Cmember, *CParent, *ColCount, *Lperm, *Parent,
+ *Post, *Perm, *Lparent, *Lcolcount ;
+ cholmod_factor *L ;
+ Int k, n, ordering, method, nmethods, status, default_strategy, ncol, uncol,
+ skip_analysis, skip_best ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ Common->status = CHOLMOD_OK ;
+ status = CHOLMOD_OK ;
+ Common->selected = EMPTY ;
+ Common->called_nd = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+ ncol = A->ncol ;
+ uncol = (A->stype == 0) ? (A->ncol) : 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* set the default strategy */
+ /* ---------------------------------------------------------------------- */
+
+ lnz_best = (double) EMPTY ;
+ skip_best = FALSE ;
+ nmethods = MIN (Common->nmethods, CHOLMOD_MAXMETHODS) ;
+ nmethods = MAX (0, nmethods) ;
+ PRINT1 (("nmethods "ID"\n", nmethods)) ;
+
+ default_strategy = (nmethods == 0) ;
+ if (default_strategy)
+ {
+ /* default strategy: try UserPerm, if given. Try AMD for A, or COLAMD
+ * to order A*A'. Try METIS for the symmetric case only if AMD reports
+ * a high degree of fill-in and flop count. Always try METIS for the
+ * unsymmetric case. METIS is not tried if the Partition Module
+ * isn't installed. If Common->default_nesdis is TRUE, then NESDIS
+ * is used as the 3rd ordering instead. */
+ Common->method [0].ordering = CHOLMOD_GIVEN ;/* skip if UserPerm NULL */
+ Common->method [1].ordering = CHOLMOD_AMD ;
+ Common->method [2].ordering =
+ (Common->default_nesdis ? CHOLMOD_NESDIS : CHOLMOD_METIS) ;
+#ifndef NPARTITION
+ nmethods = 3 ;
+#else
+ nmethods = 2 ;
+#endif
+ }
+
+#ifdef NSUPERNODAL
+ /* CHOLMOD Supernodal module not installed, just do simplicial analysis */
+ Common->supernodal = CHOLMOD_SIMPLICIAL ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note: enough space needs to be allocated here so that routines called by
+ * cholmod_analyze do not reallocate the space.
+ */
+
+ /* s = 6*n + uncol */
+ s = CHOLMOD(mult_size_t) (n, 6, &ok) ;
+ s = CHOLMOD(add_size_t) (s, uncol, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+
+ CHOLMOD(allocate_work) (n, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ensure that subsequent routines, called by cholmod_analyze, do not
+ * reallocate any workspace. This is set back to FALSE in the
+ * FREE_WORKSPACE_AND_RETURN macro, which is the only way this function
+ * returns to its caller. */
+ Common->no_workspace_reallocate = TRUE ;
+
+ /* Use the last 4*n Int's in Iwork for Parent, First, Level, and Post, since
+ * other CHOLMOD routines will use the first 2n+uncol space. The ordering
+ * routines (cholmod_amd, cholmod_colamd, cholmod_ccolamd, cholmod_metis)
+ * are an exception. They can use all 6n + ncol space, since the contents
+ * of Parent, First, Level, and Post are not needed across calls to those
+ * routines. */
+ Work4n = Common->Iwork ;
+ Work4n += 2*((size_t) n) + uncol ;
+ Parent = Work4n ;
+ First = Work4n + n ;
+ Level = Work4n + 2*((size_t) n) ;
+ Post = Work4n + 3*((size_t) n) ;
+
+ /* note that this assignment means that cholmod_nested_dissection,
+ * cholmod_ccolamd, and cholmod_camd can use only the first 4n+uncol
+ * space in Common->Iwork */
+ Cmember = Post ;
+ CParent = Level ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate more workspace, and an empty simplicial symbolic factor */
+ /* ---------------------------------------------------------------------- */
+
+ L = CHOLMOD(allocate_factor) (n, Common) ;
+ Lparent = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+ Perm = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+ ColCount = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ FREE_WORKSPACE_AND_RETURN ;
+ }
+ Lperm = L->Perm ;
+ Lcolcount = L->ColCount ;
+ Common->anz = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* try all the requested ordering options and backup to AMD if needed */
+ /* ---------------------------------------------------------------------- */
+
+ /* turn off error handling [ */
+ Common->try_catch = TRUE ;
+
+ for (method = 0 ; method <= nmethods ; method++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* determine the method to try */
+ /* ------------------------------------------------------------------ */
+
+ Common->fl = EMPTY ;
+ Common->lnz = EMPTY ;
+ skip_analysis = FALSE ;
+
+ if (method == nmethods)
+ {
+ /* All methods failed: backup to AMD */
+ if (Common->selected == EMPTY && !default_strategy)
+ {
+ PRINT1 (("All methods requested failed: backup to AMD\n")) ;
+ ordering = CHOLMOD_AMD ;
+ }
+ else
+ {
+ break ;
+ }
+ }
+ else
+ {
+ ordering = Common->method [method].ordering ;
+ }
+ Common->current = method ;
+ PRINT1 (("method "ID": Try method: "ID"\n", method, ordering)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* find the fill-reducing permutation */
+ /* ------------------------------------------------------------------ */
+
+ if (ordering == CHOLMOD_NATURAL)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* natural ordering */
+ /* -------------------------------------------------------------- */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Perm [k] = k ;
+ }
+
+ }
+ else if (ordering == CHOLMOD_GIVEN)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* use given ordering of A, if provided */
+ /* -------------------------------------------------------------- */
+
+ if (UserPerm == NULL)
+ {
+ /* this is not an error condition */
+ PRINT1 (("skip, no user perm given\n")) ;
+ continue ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ /* UserPerm is checked in cholmod_ptranspose */
+ Perm [k] = UserPerm [k] ;
+ }
+
+ }
+ else if (ordering == CHOLMOD_AMD)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* AMD ordering of A, A*A', or A(:,f)*A(:,f)' */
+ /* -------------------------------------------------------------- */
+
+ CHOLMOD(amd) (A, fset, fsize, Perm, Common) ;
+ skip_analysis = TRUE ;
+
+ }
+ else if (ordering == CHOLMOD_COLAMD)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* AMD for symmetric case, COLAMD for A*A' or A(:,f)*A(:,f)' */
+ /* -------------------------------------------------------------- */
+
+ if (A->stype)
+ {
+ CHOLMOD(amd) (A, fset, fsize, Perm, Common) ;
+ skip_analysis = TRUE ;
+ }
+ else
+ {
+ /* Alternative:
+ CHOLMOD(ccolamd) (A, fset, fsize, NULL, Perm, Common) ;
+ */
+ /* do not postorder, it is done later, below */
+ /* workspace: Iwork (4*nrow+uncol), Flag (nrow), Head (nrow+1)*/
+ CHOLMOD(colamd) (A, fset, fsize, FALSE, Perm, Common) ;
+ }
+
+ }
+ else if (ordering == CHOLMOD_METIS)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* use METIS_NodeND directly (via a CHOLMOD wrapper) */
+ /* -------------------------------------------------------------- */
+
+#ifndef NPARTITION
+ /* postorder parameter is false, because it will be later, below */
+ /* workspace: Iwork (4*nrow+uncol), Flag (nrow), Head (nrow+1) */
+ Common->called_nd = TRUE ;
+ CHOLMOD(metis) (A, fset, fsize, FALSE, Perm, Common) ;
+#else
+ Common->status = CHOLMOD_NOT_INSTALLED ;
+#endif
+
+ }
+ else if (ordering == CHOLMOD_NESDIS)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* use CHOLMOD's nested dissection */
+ /* -------------------------------------------------------------- */
+
+ /* this method is based on METIS' node bissection routine
+ * (METIS_NodeComputeSeparator). In contrast to METIS_NodeND,
+ * it calls CAMD or CCOLAMD on the whole graph, instead of MMD
+ * on just the leaves. */
+#ifndef NPARTITION
+ /* workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow) */
+ Common->called_nd = TRUE ;
+ CHOLMOD(nested_dissection) (A, fset, fsize, Perm, CParent, Cmember,
+ Common) ;
+#else
+ Common->status = CHOLMOD_NOT_INSTALLED ;
+#endif
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* invalid ordering method */
+ /* -------------------------------------------------------------- */
+
+ Common->status = CHOLMOD_INVALID ;
+ PRINT1 (("No such ordering: "ID"\n", ordering)) ;
+ }
+
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory, or method failed */
+ status = MIN (status, Common->status) ;
+ Common->status = CHOLMOD_OK ;
+ continue ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* analyze the ordering */
+ /* ------------------------------------------------------------------ */
+
+ if (!skip_analysis)
+ {
+ if (!CHOLMOD(analyze_ordering) (A, ordering, Perm, fset, fsize,
+ Parent, Post, ColCount, First, Level, Common))
+ {
+ /* ordering method failed; clear status and try next method */
+ status = MIN (status, Common->status) ;
+ Common->status = CHOLMOD_OK ;
+ continue ;
+ }
+ }
+
+ ASSERT (Common->fl >= 0 && Common->lnz >= 0) ;
+ Common->method [method].fl = Common->fl ;
+ Common->method [method].lnz = Common->lnz ;
+ PRINT1 (("lnz %g fl %g\n", Common->lnz, Common->fl)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* pick the best method */
+ /* ------------------------------------------------------------------ */
+
+ /* fl.pt. compare, but lnz can never be NaN */
+ if (Common->selected == EMPTY || Common->lnz < lnz_best)
+ {
+ Common->selected = method ;
+ PRINT1 (("this is best so far, method "ID"\n", method)) ;
+ L->ordering = ordering ;
+ lnz_best = Common->lnz ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Lperm [k] = Perm [k] ;
+ }
+ /* save the results of cholmod_analyze_ordering, if it was called */
+ skip_best = skip_analysis ;
+ if (!skip_analysis)
+ {
+ /* save the column count; becomes permanent part of L */
+ for (k = 0 ; k < n ; k++)
+ {
+ Lcolcount [k] = ColCount [k] ;
+ }
+ /* Parent is needed for weighted postordering and for supernodal
+ * analysis. Does not become a permanent part of L */
+ for (k = 0 ; k < n ; k++)
+ {
+ Lparent [k] = Parent [k] ;
+ }
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* determine if METIS is to be skipped */
+ /* ------------------------------------------------------------------ */
+
+ if (default_strategy && ordering == CHOLMOD_AMD)
+ {
+ if ((Common->fl < 500 * Common->lnz) ||
+ (Common->lnz < 5 * Common->anz))
+ {
+ /* AMD found an ordering with less than 500 flops per nonzero in
+ * L, or one with a fill-in ratio (nnz(L)/nnz(A)) of less than
+ * 5. This is pretty good, and it's unlikely that METIS will do
+ * better (this heuristic is based on tests on all symmetric
+ * positive definite matrices in the UF sparse matrix
+ * collection, and it works well across a wide range of
+ * problems). METIS can take much more time and AMD. */
+ break ;
+ }
+ }
+ }
+
+ /* turn error printing back on ] */
+ Common->try_catch = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return if no ordering method succeeded */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->selected == EMPTY)
+ {
+ /* All methods failed.
+ * If two or more methods failed, they may have failed for different
+ * reasons. Both would clear Common->status and skip to the next
+ * method. Common->status needs to be restored here to the worst error
+ * obtained in any of the methods. CHOLMOD_INVALID is worse
+ * than CHOLMOD_OUT_OF_MEMORY, since the former implies something may
+ * be wrong with the user's input. CHOLMOD_OUT_OF_MEMORY is simply an
+ * indication of lack of resources. */
+ ASSERT (status < CHOLMOD_OK) ;
+ ERROR (status, "all methods failed") ;
+ FREE_WORKSPACE_AND_RETURN ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* do the analysis for AMD, if skipped */
+ /* ---------------------------------------------------------------------- */
+
+ Common->fl = Common->method [Common->selected].fl ;
+ Common->lnz = Common->method [Common->selected].lnz ;
+ ASSERT (Common->lnz >= 0) ;
+
+ if (skip_best)
+ {
+ if (!CHOLMOD(analyze_ordering) (A, L->ordering, Lperm, fset, fsize,
+ Lparent, Post, Lcolcount, First, Level, Common))
+ {
+ /* out of memory, or method failed */
+ FREE_WORKSPACE_AND_RETURN ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* postorder the etree, weighted by the column counts */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->postorder)
+ {
+ /* combine the fill-reducing ordering with the weighted postorder */
+ /* workspace: Iwork (2*nrow) */
+ if (CHOLMOD(postorder) (Lparent, n, Lcolcount, Post, Common) == n)
+ {
+ /* use First and Level as workspace [ */
+ Int *Wi = First, *InvPost = Level ;
+ Int newchild, oldchild, newparent, oldparent ;
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Wi [k] = Lperm [Post [k]] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ Lperm [k] = Wi [k] ;
+ }
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Wi [k] = Lcolcount [Post [k]] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ Lcolcount [k] = Wi [k] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ InvPost [Post [k]] = k ;
+ }
+
+ /* updated Lparent needed only for supernodal case */
+ for (newchild = 0 ; newchild < n ; newchild++)
+ {
+ oldchild = Post [newchild] ;
+ oldparent = Lparent [oldchild] ;
+ newparent = (oldparent == EMPTY) ? EMPTY : InvPost [oldparent] ;
+ Wi [newchild] = newparent ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ Lparent [k] = Wi [k] ;
+ }
+ /* done using Iwork as workspace ] */
+
+ /* L is now postordered, no longer in natural ordering */
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+ L->ordering = CHOLMOD_POSTORDERED ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal analysis, if requested or if selected automatically */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NSUPERNODAL
+ if (Common->supernodal > CHOLMOD_AUTO
+ || (Common->supernodal == CHOLMOD_AUTO &&
+ Common->lnz > 0 &&
+ (Common->fl / Common->lnz) >= Common->supernodal_switch))
+ {
+ cholmod_sparse *S, *F, *A2, *A1 ;
+
+ permute_matrices (A, L->ordering, Lperm, fset, fsize, TRUE,
+ &A1, &A2, &S, &F, Common) ;
+
+ /* workspace: Flag (nrow), Head (nrow), Iwork (5*nrow) */
+ CHOLMOD(super_symbolic) (S, F, Lparent, L, Common) ;
+ PRINT1 (("status %d\n", Common->status)) ;
+
+ CHOLMOD(free_sparse) (&A1, Common) ;
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* free temporary matrices and workspace, and return result L */
+ /* ---------------------------------------------------------------------- */
+
+ FREE_WORKSPACE_AND_RETURN ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_colamd.c b/CHOLMOD/Cholesky/cholmod_colamd.c
new file mode 100644
index 0000000..1f20101
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_colamd.c
@@ -0,0 +1,210 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_colamd ============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD interface to the COLAMD ordering routine (version 2.4 or later).
+ * Finds a permutation p such that the Cholesky factorization of PAA'P' is
+ * sparser than AA' using colamd. If the postorder input parameter is TRUE,
+ * the column etree is found and postordered, and the colamd ordering is then
+ * combined with its postordering. A must be unsymmetric.
+ *
+ * There can be no duplicate entries in f.
+ * f can be length 0 to n if A is m-by-n.
+ *
+ * workspace: Iwork (4*nrow+ncol), Head (nrow+1), Flag (nrow)
+ * Allocates a copy of its input matrix, which
+ * is then used as CCOLAMD's workspace.
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex)
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "colamd.h"
+#include "cholmod_cholesky.h"
+
+#if (!defined (COLAMD_VERSION) || (COLAMD_VERSION < COLAMD_VERSION_CODE (2,5)))
+#error "COLAMD v2.5 or later is required"
+#endif
+
+/* ========================================================================== */
+/* === cholmod_colamd ======================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(colamd)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int postorder, /* if TRUE, follow with a coletree postorder */
+ /* ---- output --- */
+ Int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double knobs [COLAMD_KNOBS] ;
+ cholmod_sparse *C ;
+ Int *NewPerm, *Parent, *Post, *Work2n ;
+ Int k, nrow, ncol ;
+ size_t s, alen ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (Perm, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (A->stype != 0)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix must be unsymmetric") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note: this is less than the space used in cholmod_analyze, so if
+ * cholmod_colamd is being called by that routine, no space will be
+ * allocated.
+ */
+
+ /* s = 4*nrow + ncol */
+ s = CHOLMOD(mult_size_t) (nrow, 4, &ok) ;
+ s = CHOLMOD(add_size_t) (s, ncol, &ok) ;
+
+#ifdef LONG
+ alen = colamd_l_recommended (A->nzmax, ncol, nrow) ;
+ colamd_l_set_defaults (knobs) ;
+#else
+ alen = colamd_recommended (A->nzmax, ncol, nrow) ;
+ colamd_set_defaults (knobs) ;
+#endif
+
+ if (!ok || alen == 0)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "matrix invalid or too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate COLAMD workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* colamd_printf is only available in colamd v2.4 or later */
+ colamd_printf = Common->print_function ;
+
+ C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0,
+ CHOLMOD_PATTERN, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy (and transpose) the input matrix A into the colamd workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* C = A (:,f)', which also packs A if needed. */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset) */
+ ok = CHOLMOD(transpose_unsym) (A, 0, NULL, fset, fsize, C, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order the matrix (destroys the contents of C->i and C->p) */
+ /* ---------------------------------------------------------------------- */
+
+ /* get parameters */
+ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS)
+ {
+ /* this is the CHOLMOD default, not the COLAMD default */
+ knobs [COLAMD_DENSE_ROW] = -1 ;
+ }
+ else
+ {
+ /* get the knobs from the Common parameters */
+ knobs [COLAMD_DENSE_COL] = Common->method[Common->current].prune_dense ;
+ knobs [COLAMD_DENSE_ROW] = Common->method[Common->current].prune_dense2;
+ knobs [COLAMD_AGGRESSIVE] = Common->method[Common->current].aggressive ;
+ }
+
+ if (ok)
+ {
+ Int *Cp ;
+ Int stats [COLAMD_STATS] ;
+ Cp = C->p ;
+
+#ifdef LONG
+ colamd_l (ncol, nrow, alen, C->i, Cp, knobs, stats) ;
+#else
+ colamd (ncol, nrow, alen, C->i, Cp, knobs, stats) ;
+#endif
+
+ ok = stats [COLAMD_STATUS] ;
+ ok = (ok == COLAMD_OK || ok == COLAMD_OK_BUT_JUMBLED) ;
+ /* permutation returned in C->p, if the ordering succeeded */
+ for (k = 0 ; k < nrow ; k++)
+ {
+ Perm [k] = Cp [k] ;
+ }
+ }
+
+ CHOLMOD(free_sparse) (&C, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* column etree postordering */
+ /* ---------------------------------------------------------------------- */
+
+ if (postorder)
+ {
+ /* use the last 2*n space in Iwork for Parent and Post */
+ Work2n = Common->Iwork ;
+ Work2n += 2*((size_t) nrow) + ncol ;
+ Parent = Work2n ; /* size nrow (i/i/l) */
+ Post = Work2n + nrow ; /* size nrow (i/i/l) */
+
+ /* workspace: Iwork (2*nrow+ncol), Flag (nrow), Head (nrow+1) */
+ ok = ok && CHOLMOD(analyze_ordering) (A, CHOLMOD_COLAMD, Perm, fset,
+ fsize, Parent, Post, NULL, NULL, NULL, Common) ;
+
+ /* combine the colamd permutation with its postordering */
+ if (ok)
+ {
+ NewPerm = Common->Iwork ; /* size nrow (i/i/l) */
+ for (k = 0 ; k < nrow ; k++)
+ {
+ NewPerm [k] = Perm [Post [k]] ;
+ }
+ for (k = 0 ; k < nrow ; k++)
+ {
+ Perm [k] = NewPerm [k] ;
+ }
+ }
+ }
+
+ return (ok) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_etree.c b/CHOLMOD/Cholesky/cholmod_etree.c
new file mode 100644
index 0000000..592cba8
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_etree.c
@@ -0,0 +1,227 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_etree =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Compute the elimination tree of A or A'*A
+ *
+ * In the symmetric case, the upper triangular part of A is used. Entries not
+ * in this part of the matrix are ignored. Computing the etree of a symmetric
+ * matrix from just its lower triangular entries is not supported.
+ *
+ * In the unsymmetric case, all of A is used, and the etree of A'*A is computed.
+ *
+ * References:
+ *
+ * J. Liu, "A compact row storage scheme for Cholesky factors", ACM Trans.
+ * Math. Software, vol 12, 1986, pp. 127-148.
+ *
+ * J. Liu, "The role of elimination trees in sparse factorization", SIAM J.
+ * Matrix Analysis & Applic., vol 11, 1990, pp. 134-172.
+ *
+ * J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for
+ * sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710.
+ *
+ * workspace: symmetric: Iwork (nrow), unsymmetric: Iwork (nrow+ncol)
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex)
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === update_etree ========================================================= */
+/* ========================================================================== */
+
+static void update_etree
+(
+ /* inputs, not modified */
+ Int k, /* process the edge (k,i) in the input graph */
+ Int i,
+ /* inputs, modified on output */
+ Int Parent [ ], /* Parent [t] = p if p is the parent of t */
+ Int Ancestor [ ] /* Ancestor [t] is the ancestor of node t in the
+ partially-constructed etree */
+)
+{
+ Int a ;
+ for ( ; ; ) /* traverse the path from k to the root of the tree */
+ {
+ a = Ancestor [k] ;
+ if (a == i)
+ {
+ /* final ancestor reached; no change to tree */
+ return ;
+ }
+ /* perform path compression */
+ Ancestor [k] = i ;
+ if (a == EMPTY)
+ {
+ /* final ancestor undefined; this is a new edge in the tree */
+ Parent [k] = i ;
+ return ;
+ }
+ /* traverse up to the ancestor of k */
+ k = a ;
+ }
+}
+
+/* ========================================================================== */
+/* === cholmod_etree ======================================================== */
+/* ========================================================================== */
+
+/* Find the elimination tree of A or A'*A */
+
+int CHOLMOD(etree)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ /* ---- output --- */
+ Int *Parent, /* size ncol. Parent [j] = p if p is the parent of j */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap, *Ai, *Anz, *Ancestor, *Prev, *Iwork ;
+ Int i, j, jprev, p, pend, nrow, ncol, packed, stype ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (Parent, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ stype = A->stype ;
+
+ /* s = A->nrow + (stype ? 0 : A->ncol) */
+ s = CHOLMOD(add_size_t) (A->nrow, (stype ? 0 : A->ncol), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "etree", Common) >= 0) ;
+ Iwork = Common->Iwork ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = A->ncol ; /* the number of columns of A */
+ nrow = A->nrow ; /* the number of rows of A */
+ Ap = A->p ; /* size ncol+1, column pointers for A */
+ Ai = A->i ; /* the row indices of A */
+ Anz = A->nz ; /* number of nonzeros in each column of A */
+ packed = A->packed ;
+ Ancestor = Iwork ; /* size ncol (i/i/l) */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Parent [j] = EMPTY ;
+ Ancestor [j] = EMPTY ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the etree */
+ /* ---------------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* symmetric (upper) case: compute etree (A) */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* for each row i in column j of triu(A), excluding the diagonal */
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i < j)
+ {
+ update_etree (i, j, Parent, Ancestor) ;
+ }
+ }
+ }
+
+ }
+ else if (stype == 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* unsymmetric case: compute etree (A'*A) */
+ /* ------------------------------------------------------------------ */
+
+ Prev = Iwork + ncol ; /* size nrow (i/i/l) */
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Prev [i] = EMPTY ;
+ }
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* for each row i in column j of A */
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ /* a graph is constructed dynamically with one path per row
+ * of A. If the ith row of A contains column indices
+ * (j1,j2,j3,j4) then the new graph has edges (j1,j2), (j2,j3),
+ * and (j3,j4). When at node i of this path-graph, all edges
+ * (jprev,j) are considered, where jprev<j */
+ i = Ai [p] ;
+ jprev = Prev [i] ;
+ if (jprev != EMPTY)
+ {
+ update_etree (jprev, j, Parent, Ancestor) ;
+ }
+ Prev [i] = j ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* symmetric case with lower triangular part not supported */
+ /* ------------------------------------------------------------------ */
+
+ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ;
+ return (FALSE) ;
+ }
+
+ ASSERT (CHOLMOD(dump_parent) (Parent, ncol, "Parent", Common)) ;
+ return (TRUE) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_factorize.c b/CHOLMOD/Cholesky/cholmod_factorize.c
new file mode 100644
index 0000000..15544d3
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_factorize.c
@@ -0,0 +1,429 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_factorize =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Computes the numerical factorization of a symmetric matrix. The primary
+ * inputs to this routine are a sparse matrix A and the symbolic factor L from
+ * cholmod_analyze or a prior numerical factor L. If A is symmetric, this
+ * routine factorizes A(p,p)+beta*I (beta can be zero), where p is the
+ * fill-reducing permutation (L->Perm). If A is unsymmetric, either
+ * A(p,:)*A(p,:)'+beta*I or A(p,f)*A(p,f)'+beta*I is factorized. The set f and
+ * the nonzero pattern of the matrix A must be the same as the matrix passed to
+ * cholmod_analyze for the supernodal case. For the simplicial case, it can
+ * be different, but it should be the same for best performance. beta is real.
+ *
+ * A simplicial factorization or supernodal factorization is chosen, based on
+ * the type of the factor L. If L->is_super is TRUE, a supernodal LL'
+ * factorization is computed. Otherwise, a simplicial numeric factorization
+ * is computed, either LL' or LDL', depending on Common->final_ll.
+ *
+ * Once the factorization is complete, it can be left as is or optionally
+ * converted into any simplicial numeric type, depending on the
+ * Common->final_* parameters. If converted from a supernodal to simplicial
+ * type, and the Common->final_resymbol parameter is true, then numerically
+ * zero entries in L due to relaxed supernodal amalgamation are removed from
+ * the simplicial factor (they are always left in the supernodal form of L).
+ * Entries that are numerically zero but present in the simplicial symbolic
+ * pattern of L are left in place (that is, the graph of L remains chordal).
+ * This is required for the update/downdate/rowadd/rowdel routines to work
+ * properly.
+ *
+ * workspace: Flag (nrow), Head (nrow+1),
+ * if symmetric: Iwork (2*nrow+2*nsuper)
+ * if unsymmetric: Iwork (2*nrow+MAX(2*nsuper,ncol))
+ * where nsuper is 0 if simplicial, or the # of relaxed supernodes in
+ * L otherwise (nsuper <= nrow).
+ * if simplicial: W (nrow).
+ * Allocates up to two temporary copies of its input matrix (including
+ * both pattern and numerical values).
+ *
+ * If the matrix is not positive definite the routine returns TRUE, but
+ * sets Common->status to CHOLMOD_NOT_POSDEF and L->minor is set to the
+ * column at which the failure occurred. Columns L->minor to L->n-1 are
+ * set to zero.
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex), except that the
+ * input matrix A cannot be pattern-only. If L is simplicial, its numeric
+ * xtype matches A on output. If L is supernodal, its xtype is real if A is
+ * real, or complex if A is complex or zomplex.
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+#ifndef NSUPERNODAL
+#include "cholmod_supernodal.h"
+#endif
+
+
+/* ========================================================================== */
+/* === cholmod_factorize ==================================================== */
+/* ========================================================================== */
+
+/* Factorizes PAP' (or PAA'P' if A->stype is 0), using a factor obtained
+ * from cholmod_analyze. The analysis can be re-used simply by calling this
+ * routine a second time with another matrix. A must have the same nonzero
+ * pattern as that passed to cholmod_analyze. */
+
+int CHOLMOD(factorize)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* resulting factorization */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double zero [2] ;
+ zero [0] = 0 ;
+ zero [1] = 0 ;
+ return (CHOLMOD(factorize_p) (A, zero, NULL, 0, L, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_factorize_p ================================================== */
+/* ========================================================================== */
+
+/* Same as cholmod_factorize, but with more options. */
+
+int CHOLMOD(factorize_p)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ double beta [2], /* factorize beta*I+A or beta*I+A'*A */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* resulting factorization */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *S, *F, *A1, *A2 ;
+ Int nrow, ncol, stype, convert, n, nsuper, grow2, status ;
+ size_t s, t, uncol ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ n = L->n ;
+ stype = A->stype ;
+ if (L->n != A->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ;
+ return (FALSE) ;
+ }
+ if (stype != 0 && nrow != ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (FALSE) ;
+ }
+ DEBUG (CHOLMOD(dump_sparse) (A, "A for cholmod_factorize", Common)) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nsuper = (L->is_super ? L->nsuper : 0) ;
+ uncol = ((stype != 0) ? 0 : ncol) ;
+
+ /* s = 2*nrow + MAX (uncol, 2*nsuper) */
+ s = CHOLMOD(mult_size_t) (nsuper, 2, &ok) ;
+ s = MAX (uncol, s) ;
+ t = CHOLMOD(mult_size_t) (nrow, 2, &ok) ;
+ s = CHOLMOD(add_size_t) (s, t, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (nrow, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ S = NULL ;
+ F = NULL ;
+ A1 = NULL ;
+ A2 = NULL ;
+
+ /* convert to another form when done, if requested */
+ convert = !(Common->final_asis) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* perform supernodal LL' or simplicial LDL' factorization */
+ /* ---------------------------------------------------------------------- */
+
+ if (L->is_super)
+ {
+
+#ifndef NSUPERNODAL
+
+ /* ------------------------------------------------------------------ */
+ /* supernodal factorization */
+ /* ------------------------------------------------------------------ */
+
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* natural ordering */
+ /* -------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+ /* S = tril (A'), F not needed */
+ /* workspace: Iwork (nrow) */
+ A1 = CHOLMOD(ptranspose) (A, 2, NULL, NULL, 0, Common) ;
+ S = A1 ;
+ }
+ else if (stype < 0)
+ {
+ /* This is the fastest option for the natural ordering */
+ /* S = A; F not needed */
+ S = A ;
+ }
+ else
+ {
+ /* F = A(:,f)' */
+ /* workspace: Iwork (nrow) */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ A1 = CHOLMOD(ptranspose) (A, 2, NULL, fset, fsize, Common) ;
+ F = A1 ;
+ /* S = A */
+ S = A ;
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* permute the input matrix before factorization */
+ /* -------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+ /* This is the fastest option for factoring a permuted matrix */
+ /* S = tril (PAP'); F not needed */
+ /* workspace: Iwork (2*nrow) */
+ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ;
+ S = A1 ;
+ }
+ else if (stype < 0)
+ {
+ /* A2 = triu (PAP') */
+ /* workspace: Iwork (2*nrow) */
+ A2 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ;
+ /* S = tril (A2'); F not needed */
+ /* workspace: Iwork (nrow) */
+ A1 = CHOLMOD(ptranspose) (A2, 2, NULL, NULL, 0, Common) ;
+ S = A1 ;
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ ASSERT (A2 == NULL) ;
+ }
+ else
+ {
+ /* F = A(p,f)' */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, fset, fsize, Common) ;
+ F = A1 ;
+ /* S = F' */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (F, 2, NULL, NULL, 0, Common) ;
+ S = A2 ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* supernodal factorization */
+ /* ------------------------------------------------------------------ */
+
+ /* workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow+2*nsuper) */
+ if (Common->status == CHOLMOD_OK)
+ {
+ CHOLMOD(super_numeric) (S, F, beta, L, Common) ;
+ }
+ status = Common->status ;
+ ASSERT (IMPLIES (status >= CHOLMOD_OK, L->xtype != CHOLMOD_PATTERN)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* convert to final form, if requested */
+ /* ------------------------------------------------------------------ */
+
+ if (Common->status >= CHOLMOD_OK && convert)
+ {
+ /* workspace: none */
+ ok = CHOLMOD(change_factor) (L->xtype, Common->final_ll,
+ Common->final_super, Common->final_pack,
+ Common->final_monotonic, L, Common) ;
+ if (ok && Common->final_resymbol && !(L->is_super))
+ {
+ /* workspace: Flag (nrow), Head (nrow+1),
+ * if symmetric: Iwork (2*nrow)
+ * if unsymmetric: Iwork (2*nrow+ncol) */
+ CHOLMOD(resymbol_noperm) (S, fset, fsize, Common->final_pack,
+ L, Common) ;
+ }
+ }
+
+#else
+
+ /* ------------------------------------------------------------------ */
+ /* CHOLMOD Supernodal module not installed */
+ /* ------------------------------------------------------------------ */
+
+ status = CHOLMOD_NOT_INSTALLED ;
+ ERROR (CHOLMOD_NOT_INSTALLED,"Supernodal module not installed") ;
+
+#endif
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* simplicial LDL' factorization */
+ /* ------------------------------------------------------------------ */
+
+ /* Permute the input matrix A if necessary. cholmod_rowfac requires
+ * triu(A) in column form for the symmetric case, and A in column form
+ * for the unsymmetric case (the matrix S). The unsymmetric case
+ * requires A in row form, or equivalently A' in column form (the
+ * matrix F).
+ */
+
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* natural ordering */
+ /* -------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+ /* F is not needed, S = A */
+ S = A ;
+ }
+ else if (stype < 0)
+ {
+ /* F is not needed, S = A' */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (A, 2, NULL, NULL, 0, Common) ;
+ S = A2 ;
+ }
+ else
+ {
+ /* F = A (:,f)' */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ A1 = CHOLMOD(ptranspose) (A, 2, NULL, fset, fsize, Common) ;
+ F = A1 ;
+ S = A ;
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* permute the input matrix before factorization */
+ /* -------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+ /* F = tril (A (p,p)') */
+ /* workspace: Iwork (2*nrow) */
+ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ;
+ /* A2 = triu (F') */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (A1, 2, NULL, NULL, 0, Common) ;
+ /* the symmetric case does not need F, free it and set to NULL*/
+ CHOLMOD(free_sparse) (&A1, Common) ;
+ }
+ else if (stype < 0)
+ {
+ /* A2 = triu (A (p,p)'), F not needed. This is the fastest
+ * way to factorize a matrix using the simplicial routine
+ * (cholmod_rowfac). */
+ /* workspace: Iwork (2*nrow) */
+ A2 = CHOLMOD(ptranspose) (A, 2, L->Perm, NULL, 0, Common) ;
+ }
+ else
+ {
+ /* F = A (p,f)' */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ A1 = CHOLMOD(ptranspose) (A, 2, L->Perm, fset, fsize, Common) ;
+ F = A1 ;
+ /* A2 = F' */
+ /* workspace: Iwork (nrow) */
+ A2 = CHOLMOD(ptranspose) (F, 2, NULL, NULL, 0, Common) ;
+ }
+ S = A2 ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* simplicial LDL' or LL' factorization */
+ /* ------------------------------------------------------------------ */
+
+ /* factorize beta*I+S (symmetric) or beta*I+F*F' (unsymmetric) */
+ /* workspace: Flag (nrow), W (nrow), Iwork (2*nrow) */
+ if (Common->status == CHOLMOD_OK)
+ {
+ grow2 = Common->grow2 ;
+ L->is_ll = BOOLEAN (Common->final_ll) ;
+ if (L->xtype == CHOLMOD_PATTERN && Common->final_pack)
+ {
+ /* allocate a factor with exactly the space required */
+ Common->grow2 = 0 ;
+ }
+ CHOLMOD(rowfac) (S, F, beta, 0, nrow, L, Common) ;
+ Common->grow2 = grow2 ;
+ }
+ status = Common->status ;
+
+ /* ------------------------------------------------------------------ */
+ /* convert to final form, if requested */
+ /* ------------------------------------------------------------------ */
+
+ if (Common->status >= CHOLMOD_OK && convert)
+ {
+ /* workspace: none */
+ CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE,
+ Common->final_pack, Common->final_monotonic, L, Common) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free A1 and A2 if they exist */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&A1, Common) ;
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ Common->status = MAX (Common->status, status) ;
+ return (Common->status >= CHOLMOD_OK) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_postorder.c b/CHOLMOD/Cholesky/cholmod_postorder.c
new file mode 100644
index 0000000..d9b44c5
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_postorder.c
@@ -0,0 +1,292 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_postorder =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Compute the postorder of a tree. */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+
+/* ========================================================================== */
+/* === dfs ================================================================== */
+/* ========================================================================== */
+
+/* The code below includes both a recursive and non-recursive depth-first-search
+ * of a tree. The recursive code is simpler, but can lead to stack overflow.
+ * It is left here for reference, to understand what the non-recursive code
+ * is computing. To try the recursive version, uncomment the following
+ * #define, or compile the code with -DRECURSIVE. Be aware that stack
+ * overflow may occur.
+#define RECURSIVE
+ */
+
+#ifdef RECURSIVE
+
+/* recursive version: a working code for reference only, not actual use */
+
+static Int dfs /* return the new value of k */
+(
+ Int p, /* start a DFS at node p */
+ Int k, /* start the node numbering at k */
+ Int Post [ ], /* Post ordering, modified on output */
+ Int Head [ ], /* Head [p] = youngest child of p; EMPTY on output */
+ Int Next [ ], /* Next [j] = sibling of j; unmodified */
+ Int Pstack [ ] /* unused */
+)
+{
+ Int j ;
+ /* start a DFS at each child of node p */
+ for (j = Head [p] ; j != EMPTY ; j = Next [j])
+ {
+ /* start a DFS at child node j */
+ k = dfs (j, k, Post, Head, Next, Pstack) ;
+ }
+ Post [k++] = p ; /* order node p as the kth node */
+ Head [p] = EMPTY ; /* link list p no longer needed */
+ return (k) ; /* the next node will be numbered k */
+}
+
+#else
+
+/* non-recursive version for actual use */
+
+static Int dfs /* return the new value of k */
+(
+ Int p, /* start the DFS at a root node p */
+ Int k, /* start the node numbering at k */
+ Int Post [ ], /* Post ordering, modified on output */
+ Int Head [ ], /* Head [p] = youngest child of p; EMPTY on output */
+ Int Next [ ], /* Next [j] = sibling of j; unmodified */
+ Int Pstack [ ] /* workspace of size n, undefined on input or output */
+)
+{
+ Int j, phead ;
+
+ /* put the root node on the stack */
+ Pstack [0] = p ;
+ phead = 0 ;
+
+ /* while the stack is not empty, do: */
+ while (phead >= 0)
+ {
+ /* grab the node p from top of the stack and get its youngest child j */
+ p = Pstack [phead] ;
+ j = Head [p] ;
+ if (j == EMPTY)
+ {
+ /* all children of p ordered. remove p from stack and order it */
+ phead-- ;
+ Post [k++] = p ; /* order node p as the kth node */
+ }
+ else
+ {
+ /* leave p on the stack. Start a DFS at child node j by putting
+ * j on the stack and removing j from the list of children of p. */
+ Head [p] = Next [j] ;
+ Pstack [++phead] = j ;
+ }
+ }
+ return (k) ; /* the next node will be numbered k */
+}
+
+#endif
+
+/* ========================================================================== */
+/* === cholmod_postorder ==================================================== */
+/* ========================================================================== */
+
+/* Postorder a tree. The tree is either an elimination tree (the output from
+ * from cholmod_etree) or a component tree (from cholmod_nested_dissection).
+ *
+ * An elimination tree is a complete tree of n nodes with Parent [j] > j or
+ * Parent [j] = EMPTY if j is a root. On output Post [0..n-1] is a complete
+ * permutation vector.
+ *
+ * A component tree is a subset of 0..n-1. Parent [j] = -2 if node j is not
+ * in the component tree. Parent [j] = EMPTY if j is a root of the component
+ * tree, and Parent [j] is in the range 0 to n-1 if j is in the component
+ * tree but not a root. On output, Post [k] is defined only for nodes in
+ * the component tree. Post [k] = j if node j is the kth node in the
+ * postordered component tree, where k is in the range 0 to the number of
+ * components minus 1.
+ *
+ * Node j is ignored and not included in the postorder if Parent [j] < EMPTY.
+ *
+ * As a result, check_parent (Parent, n,...) may fail on input, since
+ * cholmod_check_parent assumes Parent is an elimination tree. Similarly,
+ * cholmod_check_perm (Post, ...) may fail on output, since Post is a partial
+ * permutation if Parent is a component tree.
+ *
+ * An optional node weight can be given. When starting a postorder at node j,
+ * the children of j are ordered in decreasing order of their weight.
+ * If no weights are given (Weight is NULL) then children are ordered in
+ * decreasing order of their node number. The weight of a node must be in the
+ * range 0 to n-1. Weights outside that range are silently converted to that
+ * range (weights < 0 are treated as zero, and weights >= n are treated as n-1).
+ *
+ *
+ * workspace: Head (n), Iwork (2*n)
+ */
+
+UF_long CHOLMOD(postorder) /* return # of nodes postordered */
+(
+ /* ---- input ---- */
+ Int *Parent, /* size n. Parent [j] = p if p is the parent of j */
+ size_t n,
+ Int *Weight, /* size n, optional. Weight [j] is weight of node j */
+ /* ---- output --- */
+ Int *Post, /* size n. Post [k] = j is kth in postordered tree */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Head, *Next, *Pstack, *Iwork ;
+ Int j, p, k, w, nextj ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (Parent, EMPTY) ;
+ RETURN_IF_NULL (Post, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = 2*n */
+ s = CHOLMOD(mult_size_t) (n, 2, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (EMPTY) ;
+ }
+
+ CHOLMOD(allocate_work) (n, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (EMPTY) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Head = Common->Head ; /* size n+1, initially all EMPTY */
+ Iwork = Common->Iwork ;
+ Next = Iwork ; /* size n (i/i/l) */
+ Pstack = Iwork + n ; /* size n (i/i/l) */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct a link list of children for each node */
+ /* ---------------------------------------------------------------------- */
+
+ if (Weight == NULL)
+ {
+
+ /* in reverse order so children are in ascending order in each list */
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ p = Parent [j] ;
+ if (p >= 0 && p < ((Int) n))
+ {
+ /* add j to the list of children for node p */
+ Next [j] = Head [p] ;
+ Head [p] = j ;
+ }
+ }
+
+ /* Head [p] = j if j is the youngest (least-numbered) child of p */
+ /* Next [j1] = j2 if j2 is the next-oldest sibling of j1 */
+
+ }
+ else
+ {
+
+ /* First, construct a set of link lists according to Weight.
+ *
+ * Whead [w] = j if node j is the first node in bucket w.
+ * Next [j1] = j2 if node j2 follows j1 in a link list.
+ */
+
+ Int *Whead = Pstack ; /* use Pstack as workspace for Whead [ */
+
+ for (w = 0 ; w < ((Int) n) ; w++)
+ {
+ Whead [w] = EMPTY ;
+ }
+ /* do in forward order, so nodes that ties are ordered by node index */
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ p = Parent [j] ;
+ if (p >= 0 && p < ((Int) n))
+ {
+ w = Weight [j] ;
+ w = MAX (0, w) ;
+ w = MIN (w, ((Int) n) - 1) ;
+ /* place node j at the head of link list for weight w */
+ Next [j] = Whead [w] ;
+ Whead [w] = j ;
+ }
+ }
+
+ /* traverse weight buckets, placing each node in its parent's list */
+ for (w = n-1 ; w >= 0 ; w--)
+ {
+ for (j = Whead [w] ; j != EMPTY ; j = nextj)
+ {
+ nextj = Next [j] ;
+ /* put node j in the link list of its parent */
+ p = Parent [j] ;
+ ASSERT (p >= 0 && p < ((Int) n)) ;
+ Next [j] = Head [p] ;
+ Head [p] = j ;
+ }
+ }
+
+ /* Whead no longer needed ] */
+ /* Head [p] = j if j is the lightest child of p */
+ /* Next [j1] = j2 if j2 is the next-heaviest sibling of j1 */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* start a DFS at each root node of the etree */
+ /* ---------------------------------------------------------------------- */
+
+ k = 0 ;
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ if (Parent [j] == EMPTY)
+ {
+ /* j is the root of a tree; start a DFS here */
+ k = dfs (j, k, Post, Head, Next, Pstack) ;
+ }
+ }
+
+ /* this would normally be EMPTY already, unless Parent is invalid */
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ Head [j] = EMPTY ;
+ }
+
+ PRINT1 (("postordered "ID" nodes\n", k)) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (k) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_rcond.c b/CHOLMOD/Cholesky/cholmod_rcond.c
new file mode 100644
index 0000000..69f7412
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_rcond.c
@@ -0,0 +1,161 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_rcond =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Return a rough estimate of the reciprocal of the condition number:
+ * the minimum entry on the diagonal of L (or absolute entry of D for an LDL'
+ * factorization) divided by the maximum entry (squared for LL'). L can be
+ * real, complex, or zomplex. Returns -1 on error, 0 if the matrix is singular
+ * or has a zero entry on the diagonal of L, 1 if the matrix is 0-by-0, or
+ * min(diag(L))/max(diag(L)) otherwise. Never returns NaN; if L has a NaN on
+ * the diagonal it returns zero instead.
+ *
+ * For an LL' factorization, (min(diag(L))/max(diag(L)))^2 is returned.
+ * For an LDL' factorization, (min(diag(D))/max(diag(D))) is returned.
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === LMINMAX ============================================================== */
+/* ========================================================================== */
+
+/* Update lmin and lmax for one entry L(j,j) */
+
+#define FIRST_LMINMAX(Ljj,lmin,lmax) \
+{ \
+ double ljj = Ljj ; \
+ if (IS_NAN (ljj)) \
+ { \
+ return (0) ; \
+ } \
+ lmin = ljj ; \
+ lmax = ljj ; \
+}
+
+#define LMINMAX(Ljj,lmin,lmax) \
+{ \
+ double ljj = Ljj ; \
+ if (IS_NAN (ljj)) \
+ { \
+ return (0) ; \
+ } \
+ if (ljj < lmin) \
+ { \
+ lmin = ljj ; \
+ } \
+ else if (ljj > lmax) \
+ { \
+ lmax = ljj ; \
+ } \
+}
+
+/* ========================================================================== */
+/* === cholmod_rcond ======================================================== */
+/* ========================================================================== */
+
+double CHOLMOD(rcond) /* return min(diag(L)) / max(diag(L)) */
+(
+ /* ---- input ---- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double lmin, lmax, rcond ;
+ double *Lx ;
+ Int *Lpi, *Lpx, *Super, *Lp ;
+ Int n, e, nsuper, s, k1, k2, psi, psend, psx, nsrow, nscol, jj, j ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (L, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ n = L->n ;
+ if (n == 0)
+ {
+ return (1) ;
+ }
+ if (L->minor < L->n)
+ {
+ return (0) ;
+ }
+
+ e = (L->xtype == CHOLMOD_COMPLEX) ? 2 : 1 ;
+
+ if (L->is_super)
+ {
+ /* L is supernodal */
+ nsuper = L->nsuper ; /* number of supernodes in L */
+ Lpi = L->pi ; /* column pointers for integer pattern */
+ Lpx = L->px ; /* column pointers for numeric values */
+ Super = L->super ; /* supernode sizes */
+ Lx = L->x ; /* numeric values */
+ FIRST_LMINMAX (Lx [0], lmin, lmax) ; /* first diagonal entry of L */
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ; /* first column in supernode s */
+ k2 = Super [s+1] ; /* last column in supernode is k2-1 */
+ psi = Lpi [s] ; /* first row index is L->s [psi] */
+ psend = Lpi [s+1] ; /* last row index is L->s [psend-1] */
+ psx = Lpx [s] ; /* first numeric entry is Lx [psx] */
+ nsrow = psend - psi ; /* supernode is nsrow-by-nscol */
+ nscol = k2 - k1 ;
+ for (jj = 0 ; jj < nscol ; jj++)
+ {
+ LMINMAX (Lx [e * (psx + jj + jj*nsrow)], lmin, lmax) ;
+ }
+ }
+ }
+ else
+ {
+ /* L is simplicial */
+ Lp = L->p ;
+ Lx = L->x ;
+ if (L->is_ll)
+ {
+ /* LL' factorization */
+ FIRST_LMINMAX (Lx [Lp [0]], lmin, lmax) ;
+ for (j = 1 ; j < n ; j++)
+ {
+ LMINMAX (Lx [e * Lp [j]], lmin, lmax) ;
+ }
+ }
+ else
+ {
+ /* LDL' factorization, the diagonal might be negative */
+ FIRST_LMINMAX (fabs (Lx [Lp [0]]), lmin, lmax) ;
+ for (j = 1 ; j < n ; j++)
+ {
+ LMINMAX (fabs (Lx [e * Lp [j]]), lmin, lmax) ;
+ }
+ }
+ }
+ rcond = lmin / lmax ;
+ if (L->is_ll)
+ {
+ rcond = rcond*rcond ;
+ }
+ return (rcond) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_resymbol.c b/CHOLMOD/Cholesky/cholmod_resymbol.c
new file mode 100644
index 0000000..c1c0018
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_resymbol.c
@@ -0,0 +1,609 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_resymbol ============================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Recompute the symbolic pattern of L. Entries not in the symbolic pattern
+ * are dropped. L->Perm can be used (or not) to permute the input matrix A.
+ *
+ * These routines are used after a supernodal factorization is converted into
+ * a simplicial one, to remove zero entries that were added due to relaxed
+ * supernode amalgamation. They can also be used after a series of downdates
+ * to remove entries that would no longer be present if the matrix were
+ * factorized from scratch. A downdate (cholmod_updown) does not remove any
+ * entries from L.
+ *
+ * workspace: Flag (nrow), Head (nrow+1),
+ * if symmetric: Iwork (2*nrow)
+ * if unsymmetric: Iwork (2*nrow+ncol).
+ * Allocates up to 2 copies of its input matrix A (pattern only).
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === cholmod_resymbol ===================================================== */
+/* ========================================================================== */
+
+/* Remove entries from L that are not in the factorization of P*A*P', P*A*A'*P',
+ * or P*F*F'*P' (depending on A->stype and whether fset is NULL or not).
+ *
+ * cholmod_resymbol is the same as cholmod_resymbol_noperm, except that it
+ * first permutes A according to L->Perm. A can be upper/lower/unsymmetric,
+ * in contrast to cholmod_resymbol_noperm (which can be lower or unsym). */
+
+int CHOLMOD(resymbol)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int pack, /* if TRUE, pack the columns of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization, entries pruned on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *H, *F, *G ;
+ Int stype, nrow, ncol ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ if (L->is_super)
+ {
+ /* cannot operate on a supernodal factorization */
+ ERROR (CHOLMOD_INVALID, "cannot operate on supernodal L") ;
+ return (FALSE) ;
+ }
+ if (L->n != A->nrow)
+ {
+ /* dimensions must agree */
+ ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ stype = A->stype ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ /* s = 2*nrow + (stype ? 0 : ncol) */
+ s = CHOLMOD(mult_size_t) (nrow, 2, &ok) ;
+ s = CHOLMOD(add_size_t) (s, (stype ? 0 : ncol), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (nrow, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* permute the input matrix if necessary */
+ /* ---------------------------------------------------------------------- */
+
+ H = NULL ;
+ G = NULL ;
+
+ if (stype > 0)
+ {
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+ /* F = triu(A)' */
+ /* workspace: Iwork (nrow) */
+ G = CHOLMOD(ptranspose) (A, 0, NULL, NULL, 0, Common) ;
+ }
+ else
+ {
+ /* F = triu(A(p,p))' */
+ /* workspace: Iwork (2*nrow) */
+ G = CHOLMOD(ptranspose) (A, 0, L->Perm, NULL, 0, Common) ;
+ }
+ F = G ;
+ }
+ else if (stype < 0)
+ {
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+ F = A ;
+ }
+ else
+ {
+ /* G = triu(A(p,p))' */
+ /* workspace: Iwork (2*nrow) */
+ G = CHOLMOD(ptranspose) (A, 0, L->Perm, NULL, 0, Common) ;
+ /* H = G' */
+ /* workspace: Iwork (nrow) */
+ H = CHOLMOD(ptranspose) (G, 0, NULL, NULL, 0, Common) ;
+ F = H ;
+ }
+ }
+ else
+ {
+ if (L->ordering == CHOLMOD_NATURAL)
+ {
+ F = A ;
+ }
+ else
+ {
+ /* G = A(p,f)' */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ G = CHOLMOD(ptranspose) (A, 0, L->Perm, fset, fsize, Common) ;
+ /* H = G' */
+ /* workspace: Iwork (ncol) */
+ H = CHOLMOD(ptranspose) (G, 0, NULL, NULL, 0, Common) ;
+ F = H ;
+ }
+ }
+
+ /* No need to check for failure here. cholmod_resymbol_noperm will return
+ * FALSE if F is NULL. */
+
+ /* ---------------------------------------------------------------------- */
+ /* resymbol */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(resymbol_noperm) (F, fset, fsize, pack, L, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the temporary matrices, if they exist */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&H, Common) ;
+ CHOLMOD(free_sparse) (&G, Common) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_resymbol_noperm ============================================== */
+/* ========================================================================== */
+
+/* Redo symbolic LDL' or LL' factorization of I + F*F' or I+A, where F=A(:,f).
+ *
+ * L already exists, but is a superset of the true dynamic pattern (simple
+ * column downdates and row deletions haven't pruned anything). Just redo the
+ * symbolic factorization and drop entries that are no longer there. The
+ * diagonal is not modified. The number of nonzeros in column j of L
+ * (L->nz[j]) can decrease. The column pointers (L->p[j]) remain unchanged if
+ * pack is FALSE or if L is not monotonic. Otherwise, the columns of L are
+ * packed in place.
+ *
+ * For the symmetric case, the columns of the lower triangular part of A
+ * are accessed by column. NOTE that this the transpose of the general case.
+ *
+ * For the unsymmetric case, F=A(:,f) is accessed by column.
+ *
+ * A need not be sorted, and can be packed or unpacked. If L->Perm is not
+ * identity, then A must already be permuted according to the permutation used
+ * to factorize L. The advantage of using this routine is that it does not
+ * need to create permuted copies of A first.
+ *
+ * This routine can be called if L is only partially factored via cholmod_rowfac
+ * since all it does is prune. If an entry is in F*F' or A, but not in L, it
+ * isn't added to L.
+ *
+ * L must be simplicial LDL' or LL'; it cannot be supernodal or symbolic.
+ *
+ * The set f is held in fset and fsize.
+ * fset = NULL means ":" in MATLAB. fset is ignored.
+ * fset != NULL means f = fset [0..fset-1].
+ * fset != NULL and fsize = 0 means f is the empty set.
+ * There can be no duplicates in fset.
+ * Common->status is set to CHOLMOD_INVALID if fset is invalid.
+ *
+ * workspace: Flag (nrow), Head (nrow+1),
+ * if symmetric: Iwork (2*nrow)
+ * if unsymmetric: Iwork (2*nrow+ncol).
+ * Unlike cholmod_resymbol, this routine does not allocate any temporary
+ * copies of its input matrix.
+ */
+
+int CHOLMOD(resymbol_noperm)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int pack, /* if TRUE, pack the columns of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization, entries pruned on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Lx, *Lz ;
+ Int i, j, k, row, parent, p, pend, pdest, ncol, apacked, sorted, nrow, nf,
+ use_fset, mark, jj, stype, xtype ;
+ Int *Ap, *Ai, *Anz, *Li, *Lp, *Lnz, *Flag, *Head, *Link, *Anext, *Iwork ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ ncol = A->ncol ;
+ nrow = A->nrow ;
+ stype = A->stype ;
+ ASSERT (IMPLIES (stype != 0, nrow == ncol)) ;
+ if (stype > 0)
+ {
+ /* symmetric, with upper triangular part, not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric upper not supported ") ;
+ return (FALSE) ;
+ }
+ if (L->is_super)
+ {
+ /* cannot operate on a supernodal or symbolic factorization */
+ ERROR (CHOLMOD_INVALID, "cannot operate on supernodal L") ;
+ return (FALSE) ;
+ }
+ if (L->n != A->nrow)
+ {
+ /* dimensions must agree */
+ ERROR (CHOLMOD_INVALID, "A and L dimensions do not match") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = 2*nrow + (stype ? 0 : ncol) */
+ s = CHOLMOD(mult_size_t) (nrow, 2, &ok) ;
+ if (stype != 0)
+ {
+ s = CHOLMOD(add_size_t) (s, ncol, &ok) ;
+ }
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (nrow, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ai = A->i ;
+ Ap = A->p ;
+ Anz = A->nz ;
+ apacked = A->packed ;
+ sorted = A->sorted ;
+
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lp = L->p ;
+ Lnz = L->nz ;
+ xtype = L->xtype ;
+
+ /* If L is monotonic on input, then it can be packed or
+ * unpacked on output, depending on the pack input parameter. */
+
+ /* cannot pack a non-monotonic matrix */
+ if (!(L->is_monotonic))
+ {
+ pack = FALSE ;
+ }
+
+ ASSERT (L->nzmax >= (size_t) (Lp [L->n])) ;
+
+ pdest = 0 ;
+
+ PRINT1 (("\n\n===================== Resymbol pack %d Apacked %d\n",
+ pack, A->packed)) ;
+ ASSERT (CHOLMOD(dump_sparse) (A, "ReSymbol A:", Common) >= 0) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "ReSymbol initial L (i, x):", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Flag = Common->Flag ; /* size nrow */
+ Head = Common->Head ; /* size nrow+1 */
+ Iwork = Common->Iwork ;
+ Link = Iwork ; /* size nrow (i/i/l) [ */
+ Lnz = Iwork + nrow ; /* size nrow (i/i/l), if L not packed */
+ Anext = Iwork + 2*((size_t) nrow) ; /* size ncol (i/i/l), unsym. only */
+ for (j = 0 ; j < nrow ; j++)
+ {
+ Link [j] = EMPTY ;
+ }
+
+ /* use Lnz in L itself */
+ Lnz = L->nz ;
+ ASSERT (Lnz != NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* for the unsymmetric case, queue each column of A (:,f) */
+ /* ---------------------------------------------------------------------- */
+
+ /* place each column of the basis set on the link list corresponding to */
+ /* the smallest row index in that column */
+
+ if (stype == 0)
+ {
+ use_fset = (fset != NULL) ;
+ if (use_fset)
+ {
+ nf = fsize ;
+ /* This is the only O(ncol) loop in cholmod_resymbol.
+ * It is required only to check the fset. */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Anext [j] = -2 ;
+ }
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = fset [jj] ;
+ if (j < 0 || j > ncol || Anext [j] != -2)
+ {
+ /* out-of-range or duplicate entry in fset */
+ ERROR (CHOLMOD_INVALID, "fset invalid") ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (FALSE) ;
+ }
+ /* flag column j as having been seen */
+ Anext [j] = EMPTY ;
+ }
+ /* the fset is now valid */
+ ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ;
+ }
+ else
+ {
+ nf = ncol ;
+ }
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = (use_fset) ? (fset [jj]) : jj ;
+ /* column j is the fset; find the smallest row (if any) */
+ p = Ap [j] ;
+ pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ if (pend > p)
+ {
+ k = Ai [p] ;
+ if (!sorted)
+ {
+ for ( ; p < pend ; p++)
+ {
+ k = MIN (k, Ai [p]) ;
+ }
+ }
+ /* place column j on link list k */
+ ASSERT (k >= 0 && k < nrow) ;
+ Anext [j] = Head [k] ;
+ Head [k] = j ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* recompute symbolic LDL' factorization */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < nrow ; k++)
+ {
+
+#ifndef NDEBUG
+ PRINT1 (("\n\n================== Initial column k = "ID"\n", k)) ;
+ for (p = Lp [k] ; p < Lp [k] + Lnz [k] ; p++)
+ {
+ PRINT1 ((" row: "ID" value: ", Li [p])) ;
+ PRINT1 (("\n")) ;
+ }
+ PRINT1 (("Recomputing LDL, column k = "ID"\n", k)) ;
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* compute column k of I+F*F' or I+A */
+ /* ------------------------------------------------------------------ */
+
+ /* flag the diagonal entry */
+ /* mark = CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+
+ Flag [k] = mark ;
+ PRINT1 ((" row: "ID" (diagonal)\n", k)) ;
+
+ if (stype != 0)
+ {
+ /* merge column k of A into Flag (lower triangular part only) */
+ p = Ap [k] ;
+ pend = (apacked) ? (Ap [k+1]) : (p + Anz [k]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i > k)
+ {
+ Flag [i] = mark ;
+ }
+ }
+ }
+ else
+ {
+ /* for each column j whos first row index is in row k */
+ for (j = Head [k] ; j != EMPTY ; j = Anext [j])
+ {
+ /* merge column j of A into Flag */
+ PRINT1 ((" ---- A column "ID"\n", j)) ;
+ p = Ap [j] ;
+ pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ PRINT1 ((" length "ID" adding\n", pend-p)) ;
+ for ( ; p < pend ; p++)
+ {
+#ifndef NDEBUG
+ ASSERT (Ai [p] >= k && Ai [p] < nrow) ;
+ if (Flag [Ai [p]] < mark) PRINT1 ((" row "ID"\n", Ai [p])) ;
+#endif
+ Flag [Ai [p]] = mark ;
+ }
+ }
+ /* clear the kth link list */
+ Head [k] = EMPTY ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* compute pruned pattern of kth column of L = union of children */
+ /* ------------------------------------------------------------------ */
+
+ /* for each column j of L whose parent is k */
+ for (j = Link [k] ; j != EMPTY ; j = Link [j])
+ {
+ /* merge column j of L into Flag */
+ PRINT1 ((" ---- L column "ID"\n", k)) ;
+ ASSERT (j < k) ;
+ ASSERT (Lnz [j] > 0) ;
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+ ASSERT (Li [p] == j && Li [p+1] == k) ;
+ p++ ; /* skip past the diagonal entry */
+ for ( ; p < pend ; p++)
+ {
+ /* add to pattern */
+ ASSERT (Li [p] >= k && Li [p] < nrow) ;
+ Flag [Li [p]] = mark ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* prune the kth column of L */
+ /* ------------------------------------------------------------------ */
+
+ PRINT1 (("Final column of L:\n")) ;
+ p = Lp [k] ;
+ pend = p + Lnz [k] ;
+
+ if (pack)
+ {
+ /* shift column k upwards */
+ Lp [k] = pdest ;
+ }
+ else
+ {
+ /* leave column k in place, just reduce Lnz [k] */
+ pdest = p ;
+ }
+
+ for ( ; p < pend ; p++)
+ {
+ ASSERT (pdest < pend) ;
+ ASSERT (pdest <= p) ;
+ row = Li [p] ;
+ ASSERT (row >= k && row < nrow) ;
+ if (Flag [row] == mark)
+ {
+ /* keep this entry */
+ Li [pdest] = row ;
+ if (xtype == CHOLMOD_REAL)
+ {
+ Lx [pdest] = Lx [p] ;
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ Lx [2*pdest ] = Lx [2*p ] ;
+ Lx [2*pdest+1] = Lx [2*p+1] ;
+ }
+ else if (xtype == CHOLMOD_ZOMPLEX)
+ {
+ Lx [pdest] = Lx [p] ;
+ Lz [pdest] = Lz [p] ;
+ }
+ pdest++ ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* prepare this column for its parent */
+ /* ------------------------------------------------------------------ */
+
+ Lnz [k] = pdest - Lp [k] ;
+
+ PRINT1 ((" L("ID") length "ID"\n", k, Lnz [k])) ;
+ ASSERT (Lnz [k] > 0) ;
+
+ /* parent is the first entry in the column after the diagonal */
+ parent = (Lnz [k] > 1) ? (Li [Lp [k] + 1]) : EMPTY ;
+
+ PRINT1 (("parent ("ID") = "ID"\n", k, parent)) ;
+ ASSERT ((parent > k && parent < nrow) || (parent == EMPTY)) ;
+
+ if (parent != EMPTY)
+ {
+ Link [k] = Link [parent] ;
+ Link [parent] = k ;
+ }
+ }
+
+ /* done using Iwork for Link, Lnz (if needed), and Anext ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to packed, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ if (pack)
+ {
+ /* finalize Lp */
+ Lp [nrow] = pdest ;
+ /* Shrink L to be just large enough. It cannot fail. */
+ /* workspace: none */
+ ASSERT ((size_t) (Lp [nrow]) <= L->nzmax) ;
+ CHOLMOD(reallocate_factor) (Lp [nrow], L, Common) ;
+ ASSERT (Common->status >= CHOLMOD_OK) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* clear workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "ReSymbol final L (i, x):", Common)) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (TRUE) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_rowcolcounts.c b/CHOLMOD/Cholesky/cholmod_rowcolcounts.c
new file mode 100644
index 0000000..62d5770
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_rowcolcounts.c
@@ -0,0 +1,537 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_rowcolcounts ======================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Compute the row and column counts of the Cholesky factor L of the matrix
+ * A or A*A'. The etree and its postordering must already be computed (see
+ * cholmod_etree and cholmod_postorder) and given as inputs to this routine.
+ *
+ * For the symmetric case (LL'=A), A is accessed by column. Only the lower
+ * triangular part of A is used. Entries not in this part of the matrix are
+ * ignored. This is the same as storing the upper triangular part of A by
+ * rows, with entries in the lower triangular part being ignored. NOTE: this
+ * representation is the TRANSPOSE of the input to cholmod_etree.
+ *
+ * For the unsymmetric case (LL'=AA'), A is accessed by column. Equivalently,
+ * if A is viewed as a matrix in compressed-row form, this routine computes
+ * the row and column counts for L where LL'=A'A. If the input vector f is
+ * present, then F*F' is analyzed instead, where F = A(:,f).
+ *
+ * The set f is held in fset and fsize.
+ * fset = NULL means ":" in MATLAB. fset is ignored.
+ * fset != NULL means f = fset [0..fset-1].
+ * fset != NULL and fsize = 0 means f is the empty set.
+ * Common->status is set to CHOLMOD_INVALID if fset is invalid.
+ *
+ * In both cases, the columns of A need not be sorted.
+ * A can be packed or unpacked.
+ *
+ * References:
+ * J. Gilbert, E. Ng, B. Peyton, "An efficient algorithm to compute row and
+ * column counts for sparse Cholesky factorization", SIAM J. Matrix Analysis &
+ * Applic., vol 15, 1994, pp. 1075-1091.
+ *
+ * J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for
+ * sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710.
+ *
+ * workspace:
+ * if symmetric: Flag (nrow), Iwork (2*nrow)
+ * if unsymmetric: Flag (nrow), Iwork (2*nrow+ncol), Head (nrow+1)
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex).
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === initialize_node ====================================================== */
+/* ========================================================================== */
+
+static int initialize_node /* initial work for kth node in postordered etree */
+(
+ Int k, /* at the kth step of the algorithm (and kth node) */
+ Int Post [ ], /* Post [k] = i, the kth node in postordered etree */
+ Int Parent [ ], /* Parent [i] is the parent of i in the etree */
+ Int ColCount [ ], /* ColCount [c] is the current weight of node c */
+ Int PrevNbr [ ] /* PrevNbr [u] = k if u was last considered at step k */
+)
+{
+ Int p, parent ;
+ /* determine p, the kth node in the postordered etree */
+ p = Post [k] ;
+ /* adjust the weight if p is not a root of the etree */
+ parent = Parent [p] ;
+ if (parent != EMPTY)
+ {
+ ColCount [parent]-- ;
+ }
+ /* flag node p to exclude self edges (p,p) */
+ PrevNbr [p] = k ;
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === process_edge ========================================================= */
+/* ========================================================================== */
+
+/* edge (p,u) is being processed. p < u is a descendant of its ancestor u in
+ * the etree. node p is the kth node in the postordered etree. */
+
+static void process_edge
+(
+ Int p, /* process edge (p,u) of the matrix */
+ Int u,
+ Int k, /* we are at the kth node in the postordered etree */
+ Int First [ ], /* First [i] = k if the postordering of first
+ * descendent of node i is k */
+ Int PrevNbr [ ], /* u was last considered at step k = PrevNbr [u] */
+ Int ColCount [ ], /* ColCount [c] is the current weight of node c */
+ Int PrevLeaf [ ], /* s = PrevLeaf [u] means that s was the last leaf
+ * seen in the subtree rooted at u. */
+ Int RowCount [ ], /* RowCount [i] is # of nonzeros in row i of L,
+ * including the diagonal. Not computed if NULL. */
+ Int SetParent [ ], /* the FIND/UNION data structure, which forms a set
+ * of trees. A root i has i = SetParent [i]. Following
+ * a path from i to the root q of the subtree containing
+ * i means that q is the SetParent representative of i.
+ * All nodes in the tree could have their SetParent
+ * equal to the root q; the tree representation is used
+ * to save time. When a path is traced from i to its
+ * root q, the path is re-traversed to set the SetParent
+ * of the whole path to be the root q. */
+ Int Level [ ] /* Level [i] = length of path from node i to root */
+)
+{
+ Int prevleaf, q, s, sparent ;
+ if (First [p] > PrevNbr [u])
+ {
+ /* p is a leaf of the subtree of u */
+ ColCount [p]++ ;
+ prevleaf = PrevLeaf [u] ;
+ if (prevleaf == EMPTY)
+ {
+ /* p is the first leaf of subtree of u; RowCount will be incremented
+ * by the length of the path in the etree from p up to u. */
+ q = u ;
+ }
+ else
+ {
+ /* q = FIND (prevleaf): find the root q of the
+ * SetParent tree containing prevleaf */
+ for (q = prevleaf ; q != SetParent [q] ; q = SetParent [q])
+ {
+ ;
+ }
+ /* the root q has been found; re-traverse the path and
+ * perform path compression */
+ s = prevleaf ;
+ for (s = prevleaf ; s != q ; s = sparent)
+ {
+ sparent = SetParent [s] ;
+ SetParent [s] = q ;
+ }
+ /* adjust the RowCount and ColCount; RowCount will be incremented by
+ * the length of the path from p to the SetParent root q, and
+ * decrement the ColCount of q by one. */
+ ColCount [q]-- ;
+ }
+ if (RowCount != NULL)
+ {
+ /* if RowCount is being computed, increment it by the length of
+ * the path from p to q */
+ RowCount [u] += (Level [p] - Level [q]) ;
+ }
+ /* p is a leaf of the subtree of u, so mark PrevLeaf [u] to be p */
+ PrevLeaf [u] = p ;
+ }
+ /* flag u has having been processed at step k */
+ PrevNbr [u] = k ;
+}
+
+
+/* ========================================================================== */
+/* === finalize_node ======================================================== */
+/* ========================================================================== */
+
+static void finalize_node /* compute UNION (p, Parent [p]) */
+(
+ Int p,
+ Int Parent [ ], /* Parent [p] is the parent of p in the etree */
+ Int SetParent [ ] /* see process_edge, above */
+)
+{
+ /* all nodes in the SetParent tree rooted at p now have as their final
+ * root the node Parent [p]. This computes UNION (p, Parent [p]) */
+ if (Parent [p] != EMPTY)
+ {
+ SetParent [p] = Parent [p] ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === cholmod_rowcolcounts ================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(rowcolcounts)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ Int *Parent, /* size nrow. Parent [i] = p if p is the parent of i */
+ Int *Post, /* size nrow. Post [k] = i if i is the kth node in
+ * the postordered etree. */
+ /* ---- output --- */
+ Int *RowCount, /* size nrow. RowCount [i] = # entries in the ith row of
+ * L, including the diagonal. */
+ Int *ColCount, /* size nrow. ColCount [i] = # entries in the ith
+ * column of L, including the diagonal. */
+ Int *First, /* size nrow. First [i] = k is the least postordering
+ * of any descendant of i. */
+ Int *Level, /* size nrow. Level [i] is the length of the path from
+ * i to the root, with Level [root] = 0. */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double fl, ff ;
+ Int *Ap, *Ai, *Anz, *PrevNbr, *SetParent, *Head, *PrevLeaf, *Anext, *Ipost,
+ *Iwork ;
+ Int i, j, r, k, len, s, p, pend, inew, stype, nf, anz, inode, parent,
+ nrow, ncol, packed, use_fset, jj ;
+ size_t w ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (Parent, FALSE) ;
+ RETURN_IF_NULL (Post, FALSE) ;
+ RETURN_IF_NULL (ColCount, FALSE) ;
+ RETURN_IF_NULL (First, FALSE) ;
+ RETURN_IF_NULL (Level, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ stype = A->stype ;
+ if (stype > 0)
+ {
+ /* symmetric with upper triangular part not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric upper not supported") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ; /* the number of rows of A */
+ ncol = A->ncol ; /* the number of columns of A */
+
+ /* w = 2*nrow + (stype ? 0 : ncol) */
+ w = CHOLMOD(mult_size_t) (nrow, 2, &ok) ;
+ w = CHOLMOD(add_size_t) (w, (stype ? 0 : ncol), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (nrow, w, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ ASSERT (CHOLMOD(dump_perm) (Post, nrow, nrow, "Post", Common)) ;
+ ASSERT (CHOLMOD(dump_parent) (Parent, nrow, "Parent", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ; /* size ncol+1, column pointers for A */
+ Ai = A->i ; /* the row indices of A, of size nz=Ap[ncol+1] */
+ Anz = A->nz ;
+ packed = A->packed ;
+ ASSERT (IMPLIES (!packed, Anz != NULL)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ SetParent = Iwork ; /* size nrow (i/i/l) */
+ PrevNbr = Iwork + nrow ; /* size nrow (i/i/l) */
+ Anext = Iwork + 2*((size_t) nrow) ; /* size ncol (i/i/l) (unsym only) */
+ PrevLeaf = Common->Flag ; /* size nrow */
+ Head = Common->Head ; /* size nrow+1 (unsym only)*/
+
+ /* ---------------------------------------------------------------------- */
+ /* find the first descendant and level of each node in the tree */
+ /* ---------------------------------------------------------------------- */
+
+ /* First [i] = k if the postordering of first descendent of node i is k */
+ /* Level [i] = length of path from node i to the root (Level [root] = 0) */
+
+ for (i = 0 ; i < nrow ; i++)
+ {
+ First [i] = EMPTY ;
+ }
+
+ /* postorder traversal of the etree */
+ for (k = 0 ; k < nrow ; k++)
+ {
+ /* node i of the etree is the kth node in the postordered etree */
+ i = Post [k] ;
+
+ /* i is a leaf if First [i] is still EMPTY */
+ /* ColCount [i] starts at 1 if i is a leaf, zero otherwise */
+ ColCount [i] = (First [i] == EMPTY) ? 1 : 0 ;
+
+ /* traverse the path from node i to the root, stopping if we find a
+ * node r whose First [r] is already defined. */
+ len = 0 ;
+ for (r = i ; (r != EMPTY) && (First [r] == EMPTY) ; r = Parent [r])
+ {
+ First [r] = k ;
+ len++ ;
+ }
+ if (r == EMPTY)
+ {
+ /* we hit a root node, the level of which is zero */
+ len-- ;
+ }
+ else
+ {
+ /* we stopped at node r, where Level [r] is already defined */
+ len += Level [r] ;
+ }
+ /* re-traverse the path from node i to r; set the level of each node */
+ for (s = i ; s != r ; s = Parent [s])
+ {
+ Level [s] = len-- ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* AA' case: sort columns of A according to first postordered row index */
+ /* ---------------------------------------------------------------------- */
+
+ fl = 0.0 ;
+ if (stype == 0)
+ {
+ /* [ use PrevNbr [0..nrow-1] as workspace for Ipost */
+ Ipost = PrevNbr ;
+ /* Ipost [i] = k if i is the kth node in the postordered etree. */
+ for (k = 0 ; k < nrow ; k++)
+ {
+ Ipost [Post [k]] = k ;
+ }
+ use_fset = (fset != NULL) ;
+ if (use_fset)
+ {
+ nf = fsize ;
+ /* clear Anext to check fset */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Anext [j] = -2 ;
+ }
+ /* find the first postordered row in each column of A (post,f)
+ * and place the column in the corresponding link list */
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = fset [jj] ;
+ if (j < 0 || j > ncol || Anext [j] != -2)
+ {
+ /* out-of-range or duplicate entry in fset */
+ ERROR (CHOLMOD_INVALID, "fset invalid") ;
+ return (FALSE) ;
+ }
+ /* flag column j as having been seen */
+ Anext [j] = EMPTY ;
+ }
+ /* fset is now valid */
+ ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ;
+ }
+ else
+ {
+ nf = ncol ;
+ }
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = (use_fset) ? (fset [jj]) : jj ;
+ /* column j is in the fset; find the smallest row (if any) */
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ ff = (double) MAX (0, pend - p) ;
+ fl += ff*ff + ff ;
+ if (pend > p)
+ {
+ k = Ipost [Ai [p]] ;
+ for ( ; p < pend ; p++)
+ {
+ inew = Ipost [Ai [p]] ;
+ k = MIN (k, inew) ;
+ }
+ /* place column j in link list k */
+ ASSERT (k >= 0 && k < nrow) ;
+ Anext [j] = Head [k] ;
+ Head [k] = j ;
+ }
+ }
+ /* Ipost no longer needed for inverse postordering ]
+ * Head [k] contains a link list of all columns whose first
+ * postordered row index is equal to k, for k = 0 to nrow-1. */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row counts and node weights */
+ /* ---------------------------------------------------------------------- */
+
+ if (RowCount != NULL)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ RowCount [i] = 1 ;
+ }
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ PrevLeaf [i] = EMPTY ;
+ PrevNbr [i] = EMPTY ;
+ SetParent [i] = i ; /* every node is in its own set, by itself */
+ }
+
+ if (stype != 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* symmetric case: LL' = A */
+ /* ------------------------------------------------------------------ */
+
+ /* also determine the number of entries in triu(A) */
+ anz = nrow ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ /* j is the kth node in the postordered etree */
+ j = initialize_node (k, Post, Parent, ColCount, PrevNbr) ;
+
+ /* for all nonzeros A(i,j) below the diagonal, in column j of A */
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i > j)
+ {
+ /* j is a descendant of i in etree(A) */
+ anz++ ;
+ process_edge (j, i, k, First, PrevNbr, ColCount,
+ PrevLeaf, RowCount, SetParent, Level) ;
+ }
+ }
+ /* update SetParent: UNION (j, Parent [j]) */
+ finalize_node (j, Parent, SetParent) ;
+ }
+ Common->anz = anz ;
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* unsymmetric case: LL' = AA' */
+ /* ------------------------------------------------------------------ */
+
+ for (k = 0 ; k < nrow ; k++)
+ {
+ /* inode is the kth node in the postordered etree */
+ inode = initialize_node (k, Post, Parent, ColCount, PrevNbr) ;
+
+ /* for all cols j whose first postordered row is k: */
+ for (j = Head [k] ; j != EMPTY ; j = Anext [j])
+ {
+ /* k is the first postordered row in column j of A */
+ /* for all rows i in column j: */
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ /* has i already been considered at this step k */
+ if (PrevNbr [i] < k)
+ {
+ /* inode is a descendant of i in etree(AA') */
+ /* process edge (inode,i) and set PrevNbr[i] to k */
+ process_edge (inode, i, k, First, PrevNbr, ColCount,
+ PrevLeaf, RowCount, SetParent, Level) ;
+ }
+ }
+ }
+ /* clear link list k */
+ Head [k] = EMPTY ;
+ /* update SetParent: UNION (inode, Parent [inode]) */
+ finalize_node (inode, Parent, SetParent) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finish computing the column counts */
+ /* ---------------------------------------------------------------------- */
+
+ for (j = 0 ; j < nrow ; j++)
+ {
+ parent = Parent [j] ;
+ if (parent != EMPTY)
+ {
+ /* add the ColCount of j to its parent */
+ ColCount [parent] += ColCount [j] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* clear workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Common->mark = EMPTY ;
+ /* CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* flop count and nnz(L) for subsequent LL' numerical factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* use double to avoid integer overflow. lnz cannot be NaN. */
+ Common->aatfl = fl ;
+ Common->lnz = 0. ;
+ fl = 0 ;
+ for (j = 0 ; j < nrow ; j++)
+ {
+ ff = (double) (ColCount [j]) ;
+ Common->lnz += ff ;
+ fl += ff*ff ;
+ }
+
+ Common->fl = fl ;
+ PRINT1 (("rowcol fl %g lnz %g\n", Common->fl, Common->lnz)) ;
+
+ return (TRUE) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_rowfac.c b/CHOLMOD/Cholesky/cholmod_rowfac.c
new file mode 100644
index 0000000..255bb9b
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_rowfac.c
@@ -0,0 +1,679 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_rowfac ============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Full or incremental numerical LDL' or LL' factorization (simplicial, not
+ * supernodal) cholmod_factorize is the "easy" wrapper for this code, but it
+ * does not provide access to incremental factorization.
+ *
+ * cholmod_rowfac computes the full or incremental LDL' or LL' factorization of
+ * A+beta*I (where A is symmetric) or A*F+beta*I (where A and F are unsymmetric
+ * and only the upper triangular part of A*F+beta*I is used). It computes
+ * L (and D, for LDL') one row at a time. beta is real.
+ *
+ * A is nrow-by-ncol or nrow-by-nrow. In "packed" form it is a conventional
+ * column-oriented sparse matrix. Row indices of column j are in
+ * Ai [Ap [j] ... Ap [j+1]-1] and values in the same locations of Ax.
+ * will be faster if A has sorted columns. In "unpacked" form the column
+ * of A ends at Ap [j] + Anz [j] - 1 instead of Ap [j+1] - 1.
+ *
+ * Row indices in each column of A can be sorted or unsorted, but the routine
+ * routine works fastest if A is sorted, or if only triu(A) is provided
+ * for the symmetric case.
+ *
+ * The unit-diagonal nrow-by-nrow output matrix L is returned in "unpacked"
+ * column form, with row indices of column j in Li [Lp [j] ...
+ * Lp [j] + Lnz [j] - 1] and values in the same location in Lx. The row
+ * indices in each column of L are in sorted order. The unit diagonal of L
+ * is not stored.
+ *
+ * L can be a simplicial symbolic or numeric (L->is_super must be FALSE).
+ * A symbolic factor is converted immediately into a numeric factor containing
+ * the identity matrix.
+ *
+ * For a full factorization, kstart = 0 and kend = nrow. The existing nonzero
+ * entries (numerical values in L->x and L->z for the zomplex case, and indices
+ * in L->i), if any, are overwritten.
+ *
+ * To compute an incremental factorization, select kstart and kend as the range
+ * of rows of L you wish to compute. A correct factorization will be computed
+ * only if all descendants of all nodes k = kstart to kend-1 in the etree have
+ * been factorized by a prior call to this routine, and if rows kstart to kend-1
+ * have not been factorized. This condition is NOT checked on input.
+ *
+ * ---------------
+ * Symmetric case:
+ * ---------------
+ *
+ * The factorization (in MATLAB notation) is:
+ *
+ * S = beta*I + A
+ * S = triu (S) + triu (S,1)'
+ * L*D*L' = S, or L*L' = S
+ *
+ * A is a conventional sparse matrix in compressed column form. Only the
+ * diagonal and upper triangular part of A is accessed; the lower
+ * triangular part is ignored and assumed to be equal to the upper
+ * triangular part. For an incremental factorization, only columns kstart
+ * to kend-1 of A are accessed. F is not used.
+ *
+ * ---------------
+ * Unsymmetric case:
+ * ---------------
+ *
+ * The factorization (in MATLAB notation) is:
+ *
+ * S = beta*I + A*F
+ * S = triu (S) + triu (S,1)'
+ * L*D*L' = S, or L*L' = S
+ *
+ * The typical case is F=A'. Alternatively, if F=A(:,f)', then this
+ * routine factorizes S = beta*I + A(:,f)*A(:,f)'.
+ *
+ * All of A and F are accessed, but only the upper triangular part of A*F
+ * is used. F must be of size A->ncol by A->nrow. F is used for the
+ * unsymmetric case only. F can be packed or unpacked and it need not be
+ * sorted.
+ *
+ * For a complete factorization of beta*I + A*A',
+ * this routine performs a number of flops exactly equal to:
+ *
+ * sum (for each column j of A) of (Anz (j)^2 + Anz (j)), to form S
+ * +
+ * sum (for each column j of L) of (Lnz (j)^2 + 3*Lnz (j)), to factorize S
+ *
+ * where Anz (j) is the number of nonzeros in column j of A, and Lnz (j)
+ * is the number of nonzero in column j of L below the diagonal.
+ *
+ *
+ * workspace: Flag (nrow), W (nrow if real, 2*nrow if complex/zomplex),
+ * Iwork (nrow)
+ *
+ * Supports any xtype, except a pattern-only input matrix A cannot be
+ * factorized.
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === subtree ============================================================== */
+/* ========================================================================== */
+
+/* Compute the nonzero pattern of the sparse triangular solve Lx=b, where L in
+ * this case is L(0:k-1,0:k-1), and b is a column of A. This is done by
+ * traversing the kth row-subtree of the elimination tree of L, starting from
+ * each nonzero entry in b. The pattern is returned postordered, and is valid
+ * for a subsequent numerical triangular solve of Lx=b. The elimination tree
+ * can be provided in a Parent array, or extracted from the pattern of L itself.
+ *
+ * The pattern of x = inv(L)*b is returned in Stack [top...].
+ * Also scatters b, or a multiple of b, into the work vector W.
+ *
+ * The SCATTER macro is defines how the numerical values of A or A*A' are to be
+ * scattered.
+ *
+ * PARENT(i) is a macro the defines how the etree is accessed. It is either:
+ * #define PARENT(i) Parent [i]
+ * #define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY
+ */
+
+#define SUBTREE \
+ for ( ; p < pend ; p++) \
+ { \
+ i = Ai [p] ; \
+ if (i <= k) \
+ { \
+ /* scatter the column of A, or A*A' into Wx and Wz */ \
+ SCATTER ; \
+ /* start at node i and traverse up the subtree, stop at node k */ \
+ for (len = 0 ; i < k && i != EMPTY && Flag [i] < mark ; i = parent) \
+ { \
+ /* L(k,i) is nonzero, and seen for the first time */ \
+ Stack [len++] = i ; /* place i on the stack */ \
+ Flag [i] = mark ; /* mark i as visited */ \
+ parent = PARENT (i) ; /* traverse up the etree to the parent */ \
+ } \
+ /* move the path down to the bottom of the stack */ \
+ while (len > 0) \
+ { \
+ Stack [--top] = Stack [--len] ; \
+ } \
+ } \
+ else if (sorted) \
+ { \
+ break ; \
+ } \
+ }
+
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_rowfac.c"
+#define COMPLEX
+#include "t_cholmod_rowfac.c"
+#define ZOMPLEX
+#include "t_cholmod_rowfac.c"
+
+#define MASK
+#define REAL
+#include "t_cholmod_rowfac.c"
+#define COMPLEX
+#include "t_cholmod_rowfac.c"
+#define ZOMPLEX
+#include "t_cholmod_rowfac.c"
+#undef MASK
+
+
+/* ========================================================================== */
+/* === cholmod_row_subtree ================================================== */
+/* ========================================================================== */
+
+/* Compute the nonzero pattern of the solution to the lower triangular system
+ * L(0:k-1,0:k-1) * x = A (0:k-1,k) if A is symmetric, or
+ * L(0:k-1,0:k-1) * x = A (0:k-1,:) * A (:,k)' if A is unsymmetric.
+ * This gives the nonzero pattern of row k of L (excluding the diagonal).
+ * The pattern is returned postordered.
+ *
+ * The symmetric case requires A to be in symmetric-upper form.
+ *
+ * The result is returned in R, a pre-allocated sparse matrix of size nrow-by-1,
+ * with R->nzmax >= nrow. R is assumed to be packed (Rnz [0] is not updated);
+ * the number of entries in R is given by Rp [0].
+ *
+ * FUTURE WORK: a very minor change to this routine could allow it to compute
+ * the nonzero pattern of x for any system Lx=b. The SUBTREE macro would need
+ * to change, to eliminate its dependence on k.
+ *
+ * workspace: Flag (nrow)
+ */
+
+int CHOLMOD(row_subtree)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */
+ size_t krow, /* row k of L */
+ Int *Parent, /* elimination tree */
+ /* ---- output --- */
+ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Rp, *Stack, *Flag, *Ap, *Ai, *Anz, *Fp, *Fi, *Fnz ;
+ Int p, pend, parent, t, stype, nrow, k, pf, pfend, Fpacked, packed,
+ sorted, top, len, i, mark ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (R, FALSE) ;
+ RETURN_IF_NULL (Parent, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ stype = A->stype ;
+ if (stype == 0)
+ {
+ RETURN_IF_NULL (F, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ }
+ if (krow >= A->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "subtree: k invalid") ;
+ return (FALSE) ;
+ }
+ if (R->ncol != 1 || A->nrow != R->nrow || A->nrow > R->nzmax)
+ {
+ ERROR (CHOLMOD_INVALID, "subtree: R invalid") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ CHOLMOD(allocate_work) (nrow, 0, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (stype > 0)
+ {
+ /* symmetric upper case: F is not needed. It may be NULL */
+ Fp = NULL ;
+ Fi = NULL ;
+ Fnz = NULL ;
+ Fpacked = TRUE ;
+ }
+ else if (stype == 0)
+ {
+ /* unsymmetric case: F is required. */
+ Fp = F->p ;
+ Fi = F->i ;
+ Fnz = F->nz ;
+ Fpacked = F->packed ;
+ }
+ else
+ {
+ /* symmetric lower triangular form not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ;
+ return (FALSE) ;
+ }
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ sorted = A->sorted ;
+
+ k = krow ;
+ Stack = R->i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Flag = Common->Flag ; /* size nrow, Flag [i] < mark must hold */
+ /* mark = CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the pattern of L(k,:) */
+ /* ---------------------------------------------------------------------- */
+
+ top = nrow ; /* Stack is empty */
+ Flag [k] = mark ; /* do not include diagonal entry in Stack */
+
+#define SCATTER /* do not scatter numerical values */
+#define PARENT(i) Parent [i] /* use Parent for etree */
+
+ if (stype != 0)
+ {
+ /* scatter kth col of triu (A), get pattern L(k,:) */
+ p = Ap [k] ;
+ pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ;
+ SUBTREE ;
+ }
+ else
+ {
+ /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */
+ pf = Fp [k] ;
+ pfend = (Fpacked) ? (Fp [k+1]) : (pf + Fnz [k]) ;
+ for ( ; pf < pfend ; pf++)
+ {
+ /* get nonzero entry F (t,k) */
+ t = Fi [pf] ;
+ p = Ap [t] ;
+ pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ;
+ SUBTREE ;
+ }
+ }
+
+#undef SCATTER
+#undef PARENT
+
+ /* shift the stack upwards, to the first part of R */
+ len = nrow - top ;
+ for (i = 0 ; i < len ; i++)
+ {
+ Stack [i] = Stack [top + i] ;
+ }
+
+ Rp = R->p ;
+ Rp [0] = 0 ;
+ Rp [1] = len ;
+ R->sorted = FALSE ;
+
+ CHOLMOD(clear_flag) (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_row_lsubtree ================================================= */
+/* ========================================================================== */
+
+/* Identical to cholmod_row_subtree, except that the elimination tree is
+ * obtained from L itself, as the first off-diagonal entry in each column.
+ * L must be simplicial, not supernodal */
+
+int CHOLMOD(row_lsubtree)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ Int *Fi, size_t fnz, /* nonzero pattern of kth row of A', not required
+ * for the symmetric case. Need not be sorted. */
+ size_t krow, /* row k of L */
+ cholmod_factor *L, /* the factor L from which parent(i) is derived */
+ /* ---- output --- */
+ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Rp, *Stack, *Flag, *Ap, *Ai, *Anz, *Lp, *Li, *Lnz ;
+ Int p, pend, parent, t, stype, nrow, k, pf, packed, sorted, top, len, i,
+ mark ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (R, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ stype = A->stype ;
+ if (stype == 0)
+ {
+ RETURN_IF_NULL (Fi, FALSE) ;
+ }
+ if (krow >= A->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "lsubtree: k invalid") ;
+ return (FALSE) ;
+ }
+ if (R->ncol != 1 || A->nrow != R->nrow || A->nrow > R->nzmax)
+ {
+ ERROR (CHOLMOD_INVALID, "lsubtree: R invalid") ;
+ return (FALSE) ;
+ }
+ if (L->is_super)
+ {
+ ERROR (CHOLMOD_INVALID, "lsubtree: L invalid (cannot be supernodal)") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ CHOLMOD(allocate_work) (nrow, 0, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (stype < 0)
+ {
+ /* symmetric lower triangular form not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ;
+ return (FALSE) ;
+ }
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ sorted = A->sorted ;
+
+ k = krow ;
+ Stack = R->i ;
+
+ Lp = L->p ;
+ Li = L->i ;
+ Lnz = L->nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Flag = Common->Flag ; /* size nrow, Flag [i] < mark must hold */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the pattern of L(k,:) */
+ /* ---------------------------------------------------------------------- */
+
+ top = nrow ; /* Stack is empty */
+ Flag [k] = mark ; /* do not include diagonal entry in Stack */
+
+#define SCATTER /* do not scatter numerical values */
+#define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY
+
+ if (stype != 0)
+ {
+ /* scatter kth col of triu (A), get pattern L(k,:) */
+ p = Ap [k] ;
+ pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ;
+ SUBTREE ;
+ }
+ else
+ {
+ /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */
+ for (pf = 0 ; pf < (Int) fnz ; pf++)
+ {
+ /* get nonzero entry F (t,k) */
+ t = Fi [pf] ;
+ p = Ap [t] ;
+ pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ;
+ SUBTREE ;
+ }
+ }
+
+#undef SCATTER
+#undef PARENT
+
+ /* shift the stack upwards, to the first part of R */
+ len = nrow - top ;
+ for (i = 0 ; i < len ; i++)
+ {
+ Stack [i] = Stack [top + i] ;
+ }
+
+ Rp = R->p ;
+ Rp [0] = 0 ;
+ Rp [1] = len ;
+ R->sorted = FALSE ;
+
+ CHOLMOD(clear_flag) (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_rowfac ======================================================= */
+/* ========================================================================== */
+
+/* This is the incremental factorization for general purpose usage. */
+
+int CHOLMOD(rowfac)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */
+ double beta [2], /* factorize beta*I+A or beta*I+AA' */
+ size_t kstart, /* first row to factorize */
+ size_t kend, /* last row to factorize is kend-1 */
+ /* ---- in/out --- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(rowfac_mask) (A, F, beta, kstart, kend, NULL, NULL, L,
+ Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_rowfac_mask ================================================== */
+/* ========================================================================== */
+
+/* This is meant for use in LPDASA only. */
+
+int CHOLMOD(rowfac_mask)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */
+ double beta [2], /* factorize beta*I+A or beta*I+AA' */
+ size_t kstart, /* first row to factorize */
+ size_t kend, /* last row to factorize is kend-1 */
+ Int *mask, /* size A->nrow. if mask[i] >= 0 row i is set to zero */
+ Int *RLinkUp, /* size A->nrow. link list of rows to compute */
+ /* ---- in/out --- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int n ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (L->xtype != CHOLMOD_PATTERN && A->xtype != L->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype of A and L do not match") ;
+ return (FALSE) ;
+ }
+ if (L->is_super)
+ {
+ ERROR (CHOLMOD_INVALID, "can only do simplicial factorization");
+ return (FALSE) ;
+ }
+ if (A->stype == 0)
+ {
+ RETURN_IF_NULL (F, FALSE) ;
+ if (A->xtype != F->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype of A and F do not match") ;
+ return (FALSE) ;
+ }
+ }
+ if (A->stype < 0)
+ {
+ /* symmetric lower triangular form not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ;
+ return (FALSE) ;
+ }
+ if (kend > L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "kend invalid") ;
+ return (FALSE) ;
+ }
+ if (A->nrow != L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "dimensions of A and L do not match") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ Common->rowfacfl = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Xwork is of size n for the real case, 2*n for complex/zomplex */
+ n = L->n ;
+
+ /* s = ((A->xtype != CHOLMOD_REAL) ? 2:1)*n */
+ s = CHOLMOD(mult_size_t) (n, ((A->xtype != CHOLMOD_REAL) ? 2:1), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (n, n, s, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, A->nrow, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize the matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ if (RLinkUp == NULL)
+ {
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_REAL:
+ ok = r_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ ok = c_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ ok = z_cholmod_rowfac (A, F, beta, kstart, kend, L, Common) ;
+ break ;
+ }
+
+ }
+ else
+ {
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_REAL:
+ ok = r_cholmod_rowfac_mask (A, F, beta, kstart, kend,
+ mask, RLinkUp, L, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ ok = c_cholmod_rowfac_mask (A, F, beta, kstart, kend,
+ mask, RLinkUp, L, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ ok = z_cholmod_rowfac_mask (A, F, beta, kstart, kend,
+ mask, RLinkUp, L, Common) ;
+ break ;
+ }
+ }
+
+ return (ok) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_solve.c b/CHOLMOD/Cholesky/cholmod_solve.c
new file mode 100644
index 0000000..b51fc80
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_solve.c
@@ -0,0 +1,1202 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_solve =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Solve one of the following systems:
+ *
+ * Ax=b 0: CHOLMOD_A also applies the permutation L->Perm
+ * LDL'x=b 1: CHOLMOD_LDLt does not apply L->Perm
+ * LDx=b 2: CHOLMOD_LD
+ * DL'x=b 3: CHOLMOD_DLt
+ * Lx=b 4: CHOLMOD_L
+ * L'x=b 5: CHOLMOD_Lt
+ * Dx=b 6: CHOLMOD_D
+ * x=Pb 7: CHOLMOD_P apply a permutation (P is L->Perm)
+ * x=P'b 8: CHOLMOD_Pt apply an inverse permutation
+ *
+ * The factorization can be simplicial LDL', simplicial LL', or supernodal LL'.
+ * For an LL' factorization, D is the identity matrix. Thus CHOLMOD_LD and
+ * CHOLMOD_L solve the same system if an LL' factorization was performed,
+ * for example.
+ *
+ * The supernodal solver uses BLAS routines dtrsv, dgemv, dtrsm, and dgemm,
+ * or their complex counterparts ztrsv, zgemv, ztrsm, and zgemm.
+ *
+ * If both L and B are real, then X is returned real. If either is complex
+ * or zomplex, X is returned as either complex or zomplex, depending on the
+ * Common->prefer_zomplex parameter.
+ *
+ * Supports any numeric xtype (pattern-only matrices not supported).
+ *
+ * This routine does not check to see if the diagonal of L or D is zero,
+ * because sometimes a partial solve can be done with indefinite or singular
+ * matrix. If you wish to check in your own code, test L->minor. If
+ * L->minor == L->n, then the matrix has no zero diagonal entries.
+ * If k = L->minor < L->n, then L(k,k) is zero for an LL' factorization, or
+ * D(k,k) is zero for an LDL' factorization.
+ *
+ * This routine returns X as NULL only if it runs out of memory. If L is
+ * indefinite or singular, then X may contain Inf's or NaN's, but it will
+ * exist on output.
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+#ifndef NSUPERNODAL
+#include "cholmod_supernodal.h"
+#endif
+
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_solve.c"
+
+#define COMPLEX
+#include "t_cholmod_solve.c"
+
+#define ZOMPLEX
+#include "t_cholmod_solve.c"
+
+/* ========================================================================== */
+/* === Permutation macro ==================================================== */
+/* ========================================================================== */
+
+/* If Perm is NULL, it is interpretted as the identity permutation */
+
+#define P(k) ((Perm == NULL) ? (k) : Perm [k])
+
+
+/* ========================================================================== */
+/* === perm ================================================================= */
+/* ========================================================================== */
+
+/* Y = B (P (1:nrow), k1 : min (k1+ncols,ncol)-1) where B is nrow-by-ncol.
+ *
+ * Creates a permuted copy of a contiguous set of columns of B.
+ * Y is already allocated on input. Y must be of sufficient size. Let nk be
+ * the number of columns accessed in B. Y->xtype determines the complexity of
+ * the result.
+ *
+ * If B is real and Y is complex (or zomplex), only the real part of B is
+ * copied into Y. The imaginary part of Y is set to zero.
+ *
+ * If B is complex (or zomplex) and Y is real, both the real and imaginary and
+ * parts of B are returned in Y. Y is returned as nrow-by-2*nk. The even
+ * columns of Y contain the real part of B and the odd columns contain the
+ * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is
+ * returned as nrow-by-nk with leading dimension nrow. Y->nzmax must be >=
+ * nrow*nk.
+ *
+ * The case where the input (B) is real and the output (Y) is zomplex is
+ * not used.
+ */
+
+static void perm
+(
+ /* ---- input ---- */
+ cholmod_dense *B, /* input matrix B */
+ Int *Perm, /* optional input permutation (can be NULL) */
+ Int k1, /* first column of B to copy */
+ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */
+ /* ---- in/out --- */
+ cholmod_dense *Y /* output matrix Y, already allocated */
+)
+{
+ double *Yx, *Yz, *Bx, *Bz ;
+ Int k2, nk, p, k, j, nrow, ncol, d, dual, dj, j2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = B->ncol ;
+ nrow = B->nrow ;
+ k2 = MIN (k1+ncols, ncol) ;
+ nk = MAX (k2 - k1, 0) ;
+ dual = (Y->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ;
+ d = B->d ;
+ Bx = B->x ;
+ Bz = B->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ Y->nrow = nrow ;
+ Y->ncol = dual*nk ;
+ Y->d = nrow ;
+ ASSERT (((Int) Y->nzmax) >= nrow*nk*dual) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Y = B (P (1:nrow), k1:k2-1) */
+ /* ---------------------------------------------------------------------- */
+
+ switch (Y->xtype)
+ {
+
+ case CHOLMOD_REAL:
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y real, B real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [k + j2] = Bx [p] ; /* real */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y real, B complex. Y is nrow-by-2*nk */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [k + j2 ] = Bx [2*p ] ; /* real */
+ Yx [k + j2 + nrow] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y real, B zomplex. Y is nrow-by-2*nk */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [k + j2 ] = Bx [p] ; /* real */
+ Yx [k + j2 + nrow] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y complex, B real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [2*k + j2] = Bx [p] ; /* real */
+ Yx [2*k+1 + j2] = 0 ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y complex, B complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [2*k + j2] = Bx [2*p ] ; /* real */
+ Yx [2*k+1 + j2] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y complex, B zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [2*k + j2] = Bx [p] ; /* real */
+ Yx [2*k+1 + j2] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+
+ switch (B->xtype)
+ {
+
+#if 0
+ case CHOLMOD_REAL:
+ /* this case is not used */
+ break ;
+#endif
+
+ case CHOLMOD_COMPLEX:
+ /* Y zomplex, B complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [k + j2] = Bx [2*p ] ; /* real */
+ Yz [k + j2] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y zomplex, B zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [k + j2] = Bx [p] ; /* real */
+ Yz [k + j2] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ }
+}
+
+
+/* ========================================================================== */
+/* === iperm ================================================================ */
+/* ========================================================================== */
+
+/* X (P (1:nrow), k1 : min (k1+ncols,ncol)-1) = Y where X is nrow-by-ncol.
+ *
+ * Copies and permutes Y into a contiguous set of columns of X. X is already
+ * allocated on input. Y must be of sufficient size. Let nk be the number
+ * of columns accessed in X. X->xtype determines the complexity of the result.
+ *
+ * If X is real and Y is complex (or zomplex), only the real part of B is
+ * copied into X. The imaginary part of Y is ignored.
+ *
+ * If X is complex (or zomplex) and Y is real, both the real and imaginary and
+ * parts of Y are returned in X. Y is nrow-by-2*nk. The even
+ * columns of Y contain the real part of B and the odd columns contain the
+ * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is
+ * nrow-by-nk with leading dimension nrow. Y->nzmax must be >= nrow*nk.
+ *
+ * The case where the input (Y) is complex and the output (X) is real,
+ * and the case where the input (Y) is zomplex and the output (X) is real,
+ * are not used.
+ */
+
+static void iperm
+(
+ /* ---- input ---- */
+ cholmod_dense *Y, /* input matrix Y */
+ Int *Perm, /* optional input permutation (can be NULL) */
+ Int k1, /* first column of B to copy */
+ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */
+ /* ---- in/out --- */
+ cholmod_dense *X /* output matrix X, already allocated */
+)
+{
+ double *Yx, *Yz, *Xx, *Xz ;
+ Int k2, nk, p, k, j, nrow, ncol, d, dj, j2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = X->ncol ;
+ nrow = X->nrow ;
+ k2 = MIN (k1+ncols, ncol) ;
+ nk = MAX (k2 - k1, 0) ;
+ d = X->d ;
+ Xx = X->x ;
+ Xz = X->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ ASSERT (((Int) Y->nzmax) >= nrow*nk*
+ ((X->xtype != CHOLMOD_REAL && Y->xtype == CHOLMOD_REAL) ? 2:1)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* X (P (1:nrow), k1:k2-1) = Y */
+ /* ---------------------------------------------------------------------- */
+
+ switch (Y->xtype)
+ {
+
+ case CHOLMOD_REAL:
+
+ switch (X->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y real, X real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [k + j2] ; /* real */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y real, X complex. Y is nrow-by-2*nk */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [k + j2 ] ; /* real */
+ Xx [2*p+1] = Yx [k + j2 + nrow] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y real, X zomplex. Y is nrow-by-2*nk */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [k + j2 ] ; /* real */
+ Xz [p] = Yx [k + j2 + nrow] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+
+ switch (X->xtype)
+ {
+
+#if 0
+ case CHOLMOD_REAL:
+ /* this case is not used */
+ break ;
+#endif
+
+ case CHOLMOD_COMPLEX:
+ /* Y complex, X complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [2*k + j2] ; /* real */
+ Xx [2*p+1] = Yx [2*k+1 + j2] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y complex, X zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * 2 * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [2*k + j2] ; /* real */
+ Xz [p] = Yx [2*k+1 + j2] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+
+ switch (X->xtype)
+ {
+
+#if 0
+ case CHOLMOD_REAL:
+ /* this case is not used */
+ break ;
+#endif
+
+ case CHOLMOD_COMPLEX:
+ /* Y zomplex, X complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [k + j2] ; /* real */
+ Xx [2*p+1] = Yz [k + j2] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y zomplex, X zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = nrow * (j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [k + j2] ; /* real */
+ Xz [p] = Yz [k + j2] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ }
+}
+
+
+/* ========================================================================== */
+/* === ptrans =============================================================== */
+/* ========================================================================== */
+
+/* Y = B (P (1:nrow), k1 : min (k1+ncols,ncol)-1)' where B is nrow-by-ncol.
+ *
+ * Creates a permuted and transposed copy of a contiguous set of columns of B.
+ * Y is already allocated on input. Y must be of sufficient size. Let nk be
+ * the number of columns accessed in B. Y->xtype determines the complexity of
+ * the result.
+ *
+ * If B is real and Y is complex (or zomplex), only the real part of B is
+ * copied into Y. The imaginary part of Y is set to zero.
+ *
+ * If B is complex (or zomplex) and Y is real, both the real and imaginary and
+ * parts of B are returned in Y. Y is returned as 2*nk-by-nrow. The even
+ * rows of Y contain the real part of B and the odd rows contain the
+ * imaginary part of B. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is
+ * returned as nk-by-nrow with leading dimension nk. Y->nzmax must be >=
+ * nrow*nk.
+ *
+ * The array transpose is performed, not the complex conjugate transpose.
+ */
+
+static void ptrans
+(
+ /* ---- input ---- */
+ cholmod_dense *B, /* input matrix B */
+ Int *Perm, /* optional input permutation (can be NULL) */
+ Int k1, /* first column of B to copy */
+ Int ncols, /* last column to copy is min(k1+ncols,B->ncol)-1 */
+ /* ---- in/out --- */
+ cholmod_dense *Y /* output matrix Y, already allocated */
+)
+{
+ double *Yx, *Yz, *Bx, *Bz ;
+ Int k2, nk, p, k, j, nrow, ncol, d, dual, dj, j2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = B->ncol ;
+ nrow = B->nrow ;
+ k2 = MIN (k1+ncols, ncol) ;
+ nk = MAX (k2 - k1, 0) ;
+ dual = (Y->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ;
+ d = B->d ;
+ Bx = B->x ;
+ Bz = B->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ Y->nrow = dual*nk ;
+ Y->ncol = nrow ;
+ Y->d = dual*nk ;
+ ASSERT (((Int) Y->nzmax) >= nrow*nk*dual) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Y = B (P (1:nrow), k1:k2-1)' */
+ /* ---------------------------------------------------------------------- */
+
+ switch (Y->xtype)
+ {
+
+ case CHOLMOD_REAL:
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y real, B real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*nk] = Bx [p] ; /* real */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y real, B complex. Y is 2*nk-by-nrow */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*2*nk] = Bx [2*p ] ; /* real */
+ Yx [j2+1 + k*2*nk] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y real, B zomplex. Y is 2*nk-by-nrow */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*2*nk] = Bx [p] ; /* real */
+ Yx [j2+1 + k*2*nk] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y complex, B real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*2*nk] = Bx [p] ; /* real */
+ Yx [j2+1 + k*2*nk] = 0 ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y complex, B complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*2*nk] = Bx [2*p ] ; /* real */
+ Yx [j2+1 + k*2*nk] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y complex, B zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*2*nk] = Bx [p] ; /* real */
+ Yx [j2+1 + k*2*nk] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y zomplex, B real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*nk] = Bx [p] ; /* real */
+ Yz [j2 + k*nk] = 0 ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y zomplex, B complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*nk] = Bx [2*p ] ; /* real */
+ Yz [j2 + k*nk] = Bx [2*p+1] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y zomplex, B zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Yx [j2 + k*nk] = Bx [p] ; /* real */
+ Yz [j2 + k*nk] = Bz [p] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ }
+}
+
+
+/* ========================================================================== */
+/* === iptrans ============================================================== */
+/* ========================================================================== */
+
+/* X (P (1:nrow), k1 : min (k1+ncols,ncol)-1) = Y' where X is nrow-by-ncol.
+ *
+ * Copies into a permuted and transposed contiguous set of columns of X.
+ * X is already allocated on input. Y must be of sufficient size. Let nk be
+ * the number of columns accessed in X. X->xtype determines the complexity of
+ * the result.
+ *
+ * If X is real and Y is complex (or zomplex), only the real part of Y is
+ * copied into X. The imaginary part of Y is ignored.
+ *
+ * If X is complex (or zomplex) and Y is real, both the real and imaginary and
+ * parts of X are returned in Y. Y is 2*nk-by-nrow. The even
+ * rows of Y contain the real part of X and the odd rows contain the
+ * imaginary part of X. Y->nzmax must be >= 2*nrow*nk. Otherise, Y is
+ * nk-by-nrow with leading dimension nk. Y->nzmax must be >= nrow*nk.
+ *
+ * The case where Y is complex or zomplex, and X is real, is not used.
+ *
+ * The array transpose is performed, not the complex conjugate transpose.
+ */
+
+static void iptrans
+(
+ /* ---- input ---- */
+ cholmod_dense *Y, /* input matrix Y */
+ Int *Perm, /* optional input permutation (can be NULL) */
+ Int k1, /* first column of X to copy into */
+ Int ncols, /* last column to copy is min(k1+ncols,X->ncol)-1 */
+ /* ---- in/out --- */
+ cholmod_dense *X /* output matrix X, already allocated */
+)
+{
+ double *Yx, *Yz, *Xx, *Xz ;
+ Int k2, nk, p, k, j, nrow, ncol, d, dj, j2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = X->ncol ;
+ nrow = X->nrow ;
+ k2 = MIN (k1+ncols, ncol) ;
+ nk = MAX (k2 - k1, 0) ;
+ d = X->d ;
+ Xx = X->x ;
+ Xz = X->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ ASSERT (((Int) Y->nzmax) >= nrow*nk*
+ ((X->xtype != CHOLMOD_REAL && Y->xtype == CHOLMOD_REAL) ? 2:1)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* X (P (1:nrow), k1:k2-1) = Y' */
+ /* ---------------------------------------------------------------------- */
+
+ switch (Y->xtype)
+ {
+
+ case CHOLMOD_REAL:
+
+ switch (X->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ /* Y real, X real */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [j2 + k*nk] ; /* real */
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ /* Y real, X complex. Y is 2*nk-by-nrow */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [j2 + k*2*nk] ; /* real */
+ Xx [2*p+1] = Yx [j2+1 + k*2*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y real, X zomplex. Y is 2*nk-by-nrow */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [j2 + k*2*nk] ; /* real */
+ Xz [p] = Yx [j2+1 + k*2*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+
+ switch (X->xtype)
+ {
+
+#if 0
+ case CHOLMOD_REAL:
+ /* this case is not used */
+ break ;
+#endif
+
+ case CHOLMOD_COMPLEX:
+ /* Y complex, X complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [j2 + k*2*nk] ; /* real */
+ Xx [2*p+1] = Yx [j2+1 + k*2*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y complex, X zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = 2*(j-k1) ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [j2 + k*2*nk] ; /* real */
+ Xz [p] = Yx [j2+1 + k*2*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+
+ switch (X->xtype)
+ {
+
+#if 0
+ case CHOLMOD_REAL:
+ /* this case is not used */
+ break ;
+#endif
+
+ case CHOLMOD_COMPLEX:
+ /* Y zomplex, X complex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [2*p ] = Yx [j2 + k*nk] ; /* real */
+ Xx [2*p+1] = Yz [j2 + k*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* Y zomplex, X zomplex */
+ for (j = k1 ; j < k2 ; j++)
+ {
+ dj = d*j ;
+ j2 = j-k1 ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ p = P(k) + dj ;
+ Xx [p] = Yx [j2 + k*nk] ; /* real */
+ Xz [p] = Yz [j2 + k*nk] ; /* imag */
+ }
+ }
+ break ;
+
+ }
+ break ;
+
+ }
+}
+
+
+/* ========================================================================== */
+/* === cholmod_solve ======================================================== */
+/* ========================================================================== */
+
+/* Solve a linear system.
+ *
+ * The factorization can be simplicial LDL', simplicial LL', or supernodal LL'.
+ * The Dx=b solve returns silently for the LL' factorizations (it is implicitly
+ * identity).
+ */
+
+cholmod_dense *CHOLMOD(solve)
+(
+ /* ---- input ---- */
+ int sys, /* system to solve */
+ cholmod_factor *L, /* factorization to use */
+ cholmod_dense *B, /* right-hand-side */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *Y = NULL, *X = NULL ;
+ Int *Perm ;
+ Int n, nrhs, ncols, ctype, xtype, k1, nr, ytype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (L, NULL) ;
+ RETURN_IF_NULL (B, NULL) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ RETURN_IF_XTYPE_INVALID (B, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ if (sys < CHOLMOD_A || sys > CHOLMOD_Pt)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid system") ;
+ return (NULL) ;
+ }
+ if (B->d < L->n || B->nrow != L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "dimensions of L and B do not match") ;
+ return (NULL) ;
+ }
+ DEBUG (CHOLMOD(dump_factor) (L, "L", Common)) ;
+ DEBUG (CHOLMOD(dump_dense) (B, "B", Common)) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if ((sys == CHOLMOD_P || sys == CHOLMOD_Pt || sys == CHOLMOD_A)
+ && L->ordering != CHOLMOD_NATURAL)
+ {
+ Perm = L->Perm ;
+ }
+ else
+ {
+ /* do not use L->Perm; use the identity permutation instead */
+ Perm = NULL ;
+ }
+
+ nrhs = B->ncol ;
+ n = L->n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the result X */
+ /* ---------------------------------------------------------------------- */
+
+ ctype = (Common->prefer_zomplex) ? CHOLMOD_ZOMPLEX : CHOLMOD_COMPLEX ;
+
+ if (sys == CHOLMOD_P || sys == CHOLMOD_Pt)
+ {
+ /* x=Pb and x=P'b return X real if B is real; X is the preferred
+ * complex/zcomplex type if B is complex or zomplex */
+ xtype = (B->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL : ctype ;
+ }
+ else if (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL)
+ {
+ /* X is real if both L and B are real */
+ xtype = CHOLMOD_REAL ;
+ }
+ else
+ {
+ /* X is complex, use the preferred complex/zomplex type */
+ xtype = ctype ;
+ }
+
+ X = CHOLMOD(allocate_dense) (n, nrhs, n, xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve using L, D, L', P, or some combination */
+ /* ---------------------------------------------------------------------- */
+
+ if (sys == CHOLMOD_P)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* x = P*b */
+ /* ------------------------------------------------------------------ */
+
+ perm (B, Perm, 0, nrhs, X) ;
+
+ }
+ else if (sys == CHOLMOD_Pt)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* x = P'*b */
+ /* ------------------------------------------------------------------ */
+
+ iperm (B, Perm, 0, nrhs, X) ;
+
+ }
+ else if (L->is_super)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve using a supernodal LL' factorization */
+ /* ------------------------------------------------------------------ */
+
+#ifndef NSUPERNODAL
+ Int blas_ok = TRUE ;
+
+ /* allocate workspace */
+ cholmod_dense *E ;
+ Int dual ;
+ dual = (L->xtype == CHOLMOD_REAL && B->xtype != CHOLMOD_REAL) ? 2 : 1 ;
+ Y = CHOLMOD(allocate_dense) (n, dual*nrhs, n, L->xtype, Common) ;
+ E = CHOLMOD(allocate_dense) (dual*nrhs, L->maxesize, dual*nrhs,
+ L->xtype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_dense) (&X, Common) ;
+ CHOLMOD(free_dense) (&Y, Common) ;
+ CHOLMOD(free_dense) (&E, Common) ;
+ return (NULL) ;
+ }
+
+ perm (B, Perm, 0, nrhs, Y) ; /* Y = P*B */
+
+ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt)
+ {
+ blas_ok = CHOLMOD(super_lsolve) (L, Y, E, Common) ; /* Y = L\Y */
+ blas_ok = blas_ok &&
+ CHOLMOD(super_ltsolve) (L, Y, E, Common) ; /* Y = L'\Y*/
+ }
+ else if (sys == CHOLMOD_L || sys == CHOLMOD_LD)
+ {
+ blas_ok = CHOLMOD(super_lsolve) (L, Y, E, Common) ; /* Y = L\Y */
+ }
+ else if (sys == CHOLMOD_Lt || sys == CHOLMOD_DLt)
+ {
+ blas_ok = CHOLMOD(super_ltsolve) (L, Y, E, Common) ; /* Y = L'\Y*/
+ }
+ CHOLMOD(free_dense) (&E, Common) ;
+
+ iperm (Y, Perm, 0, nrhs, X) ; /* X = P'*Y */
+
+ if (CHECK_BLAS_INT && !blas_ok)
+ {
+ /* Integer overflow in the BLAS. This is probably impossible,
+ * since the BLAS were used to create the supernodal factorization.
+ * It might be possible for the calls to the BLAS to differ between
+ * factorization and forward/backsolves, however. This statement
+ * is untested; it does not appear in the compiled code if
+ * CHECK_BLAS_INT is true (when the same integer is used in CHOLMOD
+ * and the BLAS. */
+ CHOLMOD(free_dense) (&X, Common) ;
+ }
+
+#else
+ /* CHOLMOD Supernodal module not installed */
+ ERROR (CHOLMOD_NOT_INSTALLED,"Supernodal module not installed") ;
+#endif
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve using a simplicial LL' or LDL' factorization */
+ /* ------------------------------------------------------------------ */
+
+ if (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL)
+ {
+ /* L, B, and Y are all real */
+ /* solve with up to 4 columns of B at a time */
+ ncols = 4 ;
+ nr = MAX (4, nrhs) ;
+ ytype = CHOLMOD_REAL ;
+ }
+ else if (L->xtype == CHOLMOD_REAL)
+ {
+ /* solve with one column of B (real/imag), at a time */
+ ncols = 1 ;
+ nr = 2 ;
+ ytype = CHOLMOD_REAL ;
+ }
+ else
+ {
+ /* L is complex or zomplex, B is real/complex/zomplex, Y has the
+ * same complexity as L. Solve with one column of B at a time. */
+ ncols = 1 ;
+ nr = 1 ;
+ ytype = L->xtype ;
+ }
+
+ Y = CHOLMOD(allocate_dense) (nr, n, nr, ytype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_dense) (&X, Common) ;
+ CHOLMOD(free_dense) (&Y, Common) ;
+ return (NULL) ;
+ }
+
+ for (k1 = 0 ; k1 < nrhs ; k1 += ncols)
+ {
+ /* -------------------------------------------------------------- */
+ /* Y = B (P, k1:k1+ncols-1)' = (P * B (:,...))' */
+ /* -------------------------------------------------------------- */
+
+ ptrans (B, Perm, k1, ncols, Y) ;
+
+ /* -------------------------------------------------------------- */
+ /* solve Y = (L' \ (L \ Y'))', or other system, with template */
+ /* -------------------------------------------------------------- */
+
+ switch (L->xtype)
+ {
+ case CHOLMOD_REAL:
+ r_simplicial_solver (sys, L, Y) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ c_simplicial_solver (sys, L, Y) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ z_simplicial_solver (sys, L, Y) ;
+ break ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* X (P, k1:k2+ncols-1) = Y' */
+ /* -------------------------------------------------------------- */
+
+ iptrans (Y, Perm, k1, ncols, X) ;
+ }
+ }
+
+ CHOLMOD(free_dense) (&Y, Common) ;
+ DEBUG (CHOLMOD(dump_dense) (X, "X result", Common)) ;
+ return (X) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/cholmod_spsolve.c b/CHOLMOD/Cholesky/cholmod_spsolve.c
new file mode 100644
index 0000000..a9c34f9
--- /dev/null
+++ b/CHOLMOD/Cholesky/cholmod_spsolve.c
@@ -0,0 +1,397 @@
+/* ========================================================================== */
+/* === Cholesky/cholmod_spsolve ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Given an LL' or LDL' factorization of A, solve one of the following systems:
+ *
+ * Ax=b 0: CHOLMOD_A also applies the permutation L->Perm
+ * LDL'x=b 1: CHOLMOD_LDLt does not apply L->Perm
+ * LDx=b 2: CHOLMOD_LD
+ * DL'x=b 3: CHOLMOD_DLt
+ * Lx=b 4: CHOLMOD_L
+ * L'x=b 5: CHOLMOD_Lt
+ * Dx=b 6: CHOLMOD_D
+ * x=Pb 7: CHOLMOD_P apply a permutation (P is L->Perm)
+ * x=P'b 8: CHOLMOD_Pt apply an inverse permutation
+ *
+ * where b and x are sparse. If L and b are real, then x is real. Otherwise,
+ * x is complex or zomplex, depending on the Common->prefer_zomplex parameter.
+ * All xtypes of x and b are supported (real, complex, and zomplex).
+ */
+
+#ifndef NCHOLESKY
+
+#include "cholmod_internal.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === EXPAND_AS_NEEDED ===================================================== */
+/* ========================================================================== */
+
+/* Double the size of the sparse matrix X, if we have run out of space. */
+
+#define EXPAND_AS_NEEDED \
+if (xnz >= nzmax) \
+{ \
+ nzmax *= 2 ; \
+ CHOLMOD(reallocate_sparse) (nzmax, X, Common) ; \
+ if (Common->status < CHOLMOD_OK) \
+ { \
+ CHOLMOD(free_sparse) (&X, Common) ; \
+ CHOLMOD(free_dense) (&X4, Common) ; \
+ CHOLMOD(free_dense) (&B4, Common) ; \
+ return (NULL) ; \
+ } \
+ Xi = X->i ; \
+ Xx = X->x ; \
+ Xz = X->z ; \
+}
+
+
+/* ========================================================================== */
+/* === cholmod_spolve ======================================================= */
+/* ========================================================================== */
+
+cholmod_sparse *CHOLMOD(spsolve) /* returns the sparse solution X */
+(
+ /* ---- input ---- */
+ int sys, /* system to solve */
+ cholmod_factor *L, /* factorization to use */
+ cholmod_sparse *B, /* right-hand-side */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double x, z ;
+ cholmod_dense *X4, *B4 ;
+ cholmod_sparse *X ;
+ double *Bx, *Bz, *Xx, *Xz, *B4x, *B4z, *X4x, *X4z ;
+ Int *Bi, *Bp, *Xp, *Xi, *Bnz ;
+ Int n, nrhs, q, p, i, j, jfirst, jlast, packed, block, pend, j_n, xtype ;
+ size_t xnz, nzmax ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (L, NULL) ;
+ RETURN_IF_NULL (B, NULL) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ RETURN_IF_XTYPE_INVALID (B, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ if (L->n != B->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "dimensions of L and B do not match") ;
+ return (NULL) ;
+ }
+ if (B->stype)
+ {
+ ERROR (CHOLMOD_INVALID, "B cannot be stored in symmetric mode") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace B4 and initial result X */
+ /* ---------------------------------------------------------------------- */
+
+ n = L->n ;
+ nrhs = B->ncol ;
+
+ /* X is real if both L and B are real, complex/zomplex otherwise */
+ xtype = (L->xtype == CHOLMOD_REAL && B->xtype == CHOLMOD_REAL) ?
+ CHOLMOD_REAL :
+ (Common->prefer_zomplex ? CHOLMOD_ZOMPLEX : CHOLMOD_COMPLEX) ;
+
+ /* solve up to 4 columns at a time */
+ block = MIN (nrhs, 4) ;
+
+ /* initial size of X is at most 4*n */
+ nzmax = n*block ;
+
+ X = CHOLMOD(spzeros) (n, nrhs, nzmax, xtype, Common) ;
+ B4 = CHOLMOD(zeros) (n, block, B->xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&X, Common) ;
+ CHOLMOD(free_dense) (&B4, Common) ;
+ return (NULL) ;
+ }
+
+ Bp = B->p ;
+ Bi = B->i ;
+ Bx = B->x ;
+ Bz = B->z ;
+ Bnz = B->nz ;
+ packed = B->packed ;
+
+ Xp = X->p ;
+ Xi = X->i ;
+ Xx = X->x ;
+ Xz = X->z ;
+
+ xnz = 0 ;
+
+ B4x = B4->x ;
+ B4z = B4->z ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve in chunks of 4 columns at a time */
+ /* ---------------------------------------------------------------------- */
+
+ for (jfirst = 0 ; jfirst < nrhs ; jfirst += block)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* adjust the number of columns of B4 */
+ /* ------------------------------------------------------------------ */
+
+ jlast = MIN (nrhs, jfirst + block) ;
+ B4->ncol = jlast - jfirst ;
+
+ /* ------------------------------------------------------------------ */
+ /* scatter B(jfirst:jlast-1) into B4 */
+ /* ------------------------------------------------------------------ */
+
+ for (j = jfirst ; j < jlast ; j++)
+ {
+ p = Bp [j] ;
+ pend = (packed) ? (Bp [j+1]) : (p + Bnz [j]) ;
+ j_n = (j-jfirst)*n ;
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ for ( ; p < pend ; p++)
+ {
+ B4x [Bi [p] + j_n] = Bx [p] ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for ( ; p < pend ; p++)
+ {
+ q = Bi [p] + j_n ;
+ B4x [2*q ] = Bx [2*p ] ;
+ B4x [2*q+1] = Bx [2*p+1] ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for ( ; p < pend ; p++)
+ {
+ q = Bi [p] + j_n ;
+ B4x [q] = Bx [p] ;
+ B4z [q] = Bz [p] ;
+ }
+ break ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* solve the system (X4 = A\B4 or other system) */
+ /* ------------------------------------------------------------------ */
+
+ X4 = CHOLMOD(solve) (sys, L, B4, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&X, Common) ;
+ CHOLMOD(free_dense) (&B4, Common) ;
+ CHOLMOD(free_dense) (&X4, Common) ;
+ return (NULL) ;
+ }
+ ASSERT (X4->xtype == xtype) ;
+ X4x = X4->x ;
+ X4z = X4->z ;
+
+ /* ------------------------------------------------------------------ */
+ /* append the solution onto X */
+ /* ------------------------------------------------------------------ */
+
+ for (j = jfirst ; j < jlast ; j++)
+ {
+ Xp [j] = xnz ;
+ j_n = (j-jfirst)*n ;
+ if ( xnz + n <= nzmax)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* X is guaranteed to be large enough */
+ /* ---------------------------------------------------------- */
+
+ switch (xtype)
+ {
+
+ case CHOLMOD_REAL:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [i + j_n] ;
+ if (IS_NONZERO (x))
+ {
+ Xi [xnz] = i ;
+ Xx [xnz] = x ;
+ xnz++ ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [2*(i + j_n) ] ;
+ z = X4x [2*(i + j_n)+1] ;
+ if (IS_NONZERO (x) || IS_NONZERO (z))
+ {
+ Xi [xnz] = i ;
+ Xx [2*xnz ] = x ;
+ Xx [2*xnz+1] = z ;
+ xnz++ ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [i + j_n] ;
+ z = X4z [i + j_n] ;
+ if (IS_NONZERO (x) || IS_NONZERO (z))
+ {
+ Xi [xnz] = i ;
+ Xx [xnz] = x ;
+ Xz [xnz] = z ;
+ xnz++ ;
+ }
+ }
+ break ;
+ }
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* X may need to increase in size */
+ /* ---------------------------------------------------------- */
+
+ switch (xtype)
+ {
+
+ case CHOLMOD_REAL:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [i + j_n] ;
+ if (IS_NONZERO (x))
+ {
+ EXPAND_AS_NEEDED ;
+ Xi [xnz] = i ;
+ Xx [xnz] = x ;
+ xnz++ ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [2*(i + j_n) ] ;
+ z = X4x [2*(i + j_n)+1] ;
+ if (IS_NONZERO (x) || IS_NONZERO (z))
+ {
+ EXPAND_AS_NEEDED ;
+ Xi [xnz] = i ;
+ Xx [2*xnz ] = x ;
+ Xx [2*xnz+1] = z ;
+ xnz++ ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ x = X4x [i + j_n] ;
+ z = X4z [i + j_n] ;
+ if (IS_NONZERO (x) || IS_NONZERO (z))
+ {
+ EXPAND_AS_NEEDED ;
+ Xi [xnz] = i ;
+ Xx [xnz] = x ;
+ Xz [xnz] = z ;
+ xnz++ ;
+ }
+ }
+ break ;
+ }
+
+ }
+ }
+ CHOLMOD(free_dense) (&X4, Common) ;
+
+ /* ------------------------------------------------------------------ */
+ /* clear B4 for next iteration */
+ /* ------------------------------------------------------------------ */
+
+ if (jlast < nrhs)
+ {
+
+ for (j = jfirst ; j < jlast ; j++)
+ {
+ p = Bp [j] ;
+ pend = (packed) ? (Bp [j+1]) : (p + Bnz [j]) ;
+ j_n = (j-jfirst)*n ;
+
+ switch (B->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ for ( ; p < pend ; p++)
+ {
+ B4x [Bi [p] + j_n] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for ( ; p < pend ; p++)
+ {
+ q = Bi [p] + j_n ;
+ B4x [2*q ] = 0 ;
+ B4x [2*q+1] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for ( ; p < pend ; p++)
+ {
+ q = Bi [p] + j_n ;
+ B4x [q] = 0 ;
+ B4z [q] = 0 ;
+ }
+ break ;
+ }
+ }
+ }
+ }
+
+ Xp [nrhs] = xnz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce X in size, free workspace, and return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (xnz <= X->nzmax) ;
+ CHOLMOD(reallocate_sparse) (xnz, X, Common) ;
+ ASSERT (Common->status == CHOLMOD_OK) ;
+ CHOLMOD(free_dense) (&B4, Common) ;
+ return (X) ;
+}
+#endif
diff --git a/CHOLMOD/Cholesky/lesser.txt b/CHOLMOD/Cholesky/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/CHOLMOD/Cholesky/lesser.txt
@@ -0,0 +1,504 @@
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+DAMAGES.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Libraries
+
+ If you develop a new library, and you want it to be of the greatest
+possible use to the public, we recommend making it free software that
+everyone can redistribute and change. You can do so by permitting
+redistribution under these terms (or, alternatively, under the terms of the
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+
+ To apply these terms, attach the following notices to the library. It is
+safest to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least the
+"copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the library's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+Also add information on how to contact you by electronic and paper mail.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the library, if
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+
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+ library `Frob' (a library for tweaking knobs) written by James Random Hacker.
+
+ <signature of Ty Coon>, 1 April 1990
+ Ty Coon, President of Vice
+
+That's all there is to it!
+
+
diff --git a/CHOLMOD/Cholesky/t_cholmod_lsolve.c b/CHOLMOD/Cholesky/t_cholmod_lsolve.c
new file mode 100644
index 0000000..1ab79b9
--- /dev/null
+++ b/CHOLMOD/Cholesky/t_cholmod_lsolve.c
@@ -0,0 +1,843 @@
+/* ========================================================================== */
+/* === Cholesky/t_cholmod_lsolve ============================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine to solve Lx=b with unit or non-unit diagonal, or
+ * solve LDx=b.
+ *
+ * The numeric xtype of L and Y must match. Y contains b on input and x on
+ * output, stored in row-form. Y is nrow-by-n, where nrow must equal 1 for the
+ * complex or zomplex cases, and nrow <= 4 for the real case.
+ *
+ * This file is not compiled separately. It is included in t_cholmod_solve.c
+ * instead. It contains no user-callable routines.
+ *
+ * workspace: none
+ *
+ * Supports real, complex, and zomplex factors.
+ */
+
+/* undefine all prior definitions */
+#undef FORM_NAME
+#undef LSOLVE
+
+/* -------------------------------------------------------------------------- */
+/* define the method */
+/* -------------------------------------------------------------------------- */
+
+#ifdef LL
+/* LL': solve Lx=b with non-unit diagonal */
+#define FORM_NAME(prefix,rank) prefix ## ll_lsolve_ ## rank
+
+#elif defined (LD)
+/* LDL': solve LDx=b */
+#define FORM_NAME(prefix,rank) prefix ## ldl_ldsolve_ ## rank
+
+#else
+/* LDL': solve Lx=b with unit diagonal */
+#define FORM_NAME(prefix,rank) prefix ## ldl_lsolve_ ## rank
+
+#endif
+
+/* LSOLVE(k) defines the name of a routine for an n-by-k right-hand-side. */
+
+#define LSOLVE(prefix,rank) FORM_NAME(prefix,rank)
+
+#ifdef REAL
+
+/* ========================================================================== */
+/* === LSOLVE (1) =========================================================== */
+/* ========================================================================== */
+
+/* Solve Lx=b, where b has 1 column */
+
+static void LSOLVE (PREFIX,1)
+(
+ cholmod_factor *L,
+ double X [ ] /* n-by-1 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = 0 ; j < n ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j+1, and j+2) */
+ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y = X [j] ;
+#ifdef LL
+ y /= Lx [p] ;
+ X [j] = y ;
+#elif defined (LD)
+ X [j] = y / Lx [p] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ X [Li [p]] -= Lx [p] * y ;
+ }
+ j++ ; /* advance to next column of L */
+
+ }
+ else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2] ;
+ Int q = Lp [j+1] ;
+#ifdef LL
+ y [0] = X [j] / Lx [p] ;
+ y [1] = (X [j+1] - Lx [p+1] * y [0]) / Lx [q] ;
+ X [j ] = y [0] ;
+ X [j+1] = y [1] ;
+#elif defined (LD)
+ y [0] = X [j] ;
+ y [1] = X [j+1] - Lx [p+1] * y [0] ;
+ X [j ] = y [0] / Lx [p] ;
+ X [j+1] = y [1] / Lx [q] ;
+#else
+ y [0] = X [j] ;
+ y [1] = X [j+1] - Lx [p+1] * y [0] ;
+ X [j+1] = y [1] ;
+#endif
+ for (p += 2, q++ ; p < pend ; p++, q++)
+ {
+ X [Li [p]] -= Lx [p] * y [0] + Lx [q] * y [1] ;
+ }
+ j += 2 ; /* advance to next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3] ;
+ Int q = Lp [j+1] ;
+ Int r = Lp [j+2] ;
+#ifdef LL
+ y [0] = X [j] / Lx [p] ;
+ y [1] = (X [j+1] - Lx [p+1] * y [0]) / Lx [q] ;
+ y [2] = (X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1]) / Lx [r] ;
+ X [j ] = y [0] ;
+ X [j+1] = y [1] ;
+ X [j+2] = y [2] ;
+#elif defined (LD)
+ y [0] = X [j] ;
+ y [1] = X [j+1] - Lx [p+1] * y [0] ;
+ y [2] = X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1] ;
+ X [j ] = y [0] / Lx [p] ;
+ X [j+1] = y [1] / Lx [q] ;
+ X [j+2] = y [2] / Lx [r] ;
+#else
+ y [0] = X [j] ;
+ y [1] = X [j+1] - Lx [p+1] * y [0] ;
+ y [2] = X [j+2] - Lx [p+2] * y [0] - Lx [q+1] * y [1] ;
+ X [j+1] = y [1] ;
+ X [j+2] = y [2] ;
+#endif
+ for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++)
+ {
+ X [Li [p]] -= Lx [p] * y [0] + Lx [q] * y [1] + Lx [r] * y [2] ;
+ }
+ j += 3 ; /* advance to next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (2) =========================================================== */
+/* ========================================================================== */
+
+/* Solve Lx=b, where b has 2 columns */
+
+static void LSOLVE (PREFIX,2)
+(
+ cholmod_factor *L,
+ double X [ ][2] /* n-by-2 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = 0 ; j < n ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j+1, and j+2) */
+ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2] ;
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+#ifdef LL
+ y [0] /= Lx [p] ;
+ y [1] /= Lx [p] ;
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+#elif defined (LD)
+ X [j][0] = y [0] / Lx [p] ;
+ X [j][1] = y [1] / Lx [p] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ X [i][0] -= Lx [p] * y [0] ;
+ X [i][1] -= Lx [p] * y [1] ;
+ }
+ j++ ; /* advance to next column of L */
+
+ }
+ else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][2] ;
+ Int q = Lp [j+1] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ;
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+#endif
+ for (p += 2, q++ ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ X [i][0] -= Lx [p] * y [0][0] + Lx [q] * y [1][0] ;
+ X [i][1] -= Lx [p] * y [0][1] + Lx [q] * y [1][1] ;
+ }
+ j += 2 ; /* advance to next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3][2] ;
+ Int q = Lp [j+1] ;
+ Int r = Lp [j+2] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ;
+ y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r];
+ y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r];
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+ X [j+2][0] = y [2][0] / Lx [r] ;
+ X [j+2][1] = y [2][1] / Lx [r] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+#endif
+ for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ X[i][0] -= Lx[p] * y[0][0] + Lx[q] * y[1][0] + Lx[r] * y[2][0] ;
+ X[i][1] -= Lx[p] * y[0][1] + Lx[q] * y[1][1] + Lx[r] * y[2][1] ;
+ }
+ j += 3 ; /* advance to next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (3) =========================================================== */
+/* ========================================================================== */
+
+/* Solve Lx=b, where b has 3 columns */
+
+static void LSOLVE (PREFIX,3)
+(
+ cholmod_factor *L,
+ double X [ ][3] /* n-by-3 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = 0 ; j < n ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j+1, and j+2) */
+ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3] ;
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+ y [2] = X [j][2] ;
+#ifdef LL
+ y [0] /= Lx [p] ;
+ y [1] /= Lx [p] ;
+ y [2] /= Lx [p] ;
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+ X [j][2] = y [2] ;
+#elif defined (LD)
+ X [j][0] = y [0] / Lx [p] ;
+ X [j][1] = y [1] / Lx [p] ;
+ X [j][2] = y [2] / Lx [p] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ double lx = Lx [p] ;
+ X [i][0] -= lx * y [0] ;
+ X [i][1] -= lx * y [1] ;
+ X [i][2] -= lx * y [2] ;
+ }
+ j++ ; /* advance to next column of L */
+
+ }
+ else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][3] ;
+ Int q = Lp [j+1] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+ y [0][2] = X [j][2] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [0][2] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ;
+ y [1][2] = (X [j+1][2] - Lx [p+1] * y [0][2]) / Lx [q] ;
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j ][2] = y [0][2] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+ X [j+1][2] = y [1][2] / Lx [q] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+#endif
+ for (p += 2, q++ ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ double lx [2] ;
+ lx [0] = Lx [p] ;
+ lx [1] = Lx [q] ;
+ X [i][0] -= lx [0] * y [0][0] + lx [1] * y [1][0] ;
+ X [i][1] -= lx [0] * y [0][1] + lx [1] * y [1][1] ;
+ X [i][2] -= lx [0] * y [0][2] + lx [1] * y [1][2] ;
+ }
+ j += 2 ; /* advance to next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3][3] ;
+ Int q = Lp [j+1] ;
+ Int r = Lp [j+2] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+ y [0][2] = X [j][2] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [0][2] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ;
+ y [1][2] = (X [j+1][2] - Lx[p+1] * y[0][2]) / Lx [q] ;
+ y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r];
+ y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r];
+ y [2][2] = (X [j+2][2] - Lx[p+2] * y[0][2] - Lx[q+1]*y[1][2])/Lx[r];
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+ X [j+2][2] = y [2][2] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j ][2] = y [0][2] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+ X [j+1][2] = y [1][2] / Lx [q] ;
+ X [j+2][0] = y [2][0] / Lx [r] ;
+ X [j+2][1] = y [2][1] / Lx [r] ;
+ X [j+2][2] = y [2][2] / Lx [r] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+ X [j+2][2] = y [2][2] ;
+#endif
+ for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ double lx [3] ;
+ lx [0] = Lx [p] ;
+ lx [1] = Lx [q] ;
+ lx [2] = Lx [r] ;
+ X [i][0] -= lx[0] * y[0][0] + lx[1] * y[1][0] + lx[2] * y[2][0];
+ X [i][1] -= lx[0] * y[0][1] + lx[1] * y[1][1] + lx[2] * y[2][1];
+ X [i][2] -= lx[0] * y[0][2] + lx[1] * y[1][2] + lx[2] * y[2][2];
+ }
+ j += 3 ; /* advance to next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (4) =========================================================== */
+/* ========================================================================== */
+
+/* Solve Lx=b, where b has 4 columns */
+
+static void LSOLVE (PREFIX,4)
+(
+ cholmod_factor *L,
+ double X [ ][4] /* n-by-4 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = 0 ; j < n ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j+1, and j+2) */
+ if (lnz < 4 || lnz != Lnz [j+1] + 1 || Li [p+1] != j+1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [4] ;
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+ y [2] = X [j][2] ;
+ y [3] = X [j][3] ;
+#ifdef LL
+ y [0] /= Lx [p] ;
+ y [1] /= Lx [p] ;
+ y [2] /= Lx [p] ;
+ y [3] /= Lx [p] ;
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+ X [j][2] = y [2] ;
+ X [j][3] = y [3] ;
+#elif defined (LD)
+ X [j][0] = y [0] / Lx [p] ;
+ X [j][1] = y [1] / Lx [p] ;
+ X [j][2] = y [2] / Lx [p] ;
+ X [j][3] = y [3] / Lx [p] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ double lx = Lx [p] ;
+ X [i][0] -= lx * y [0] ;
+ X [i][1] -= lx * y [1] ;
+ X [i][2] -= lx * y [2] ;
+ X [i][3] -= lx * y [3] ;
+ }
+ j++ ; /* advance to next column of L */
+
+ }
+ else if (lnz != Lnz [j+2] + 2 || Li [p+2] != j+2)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][4] ;
+ Int q = Lp [j+1] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+ y [0][2] = X [j][2] ;
+ y [0][3] = X [j][3] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [0][2] /= Lx [p] ;
+ y [0][3] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx [p+1] * y [0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx [p+1] * y [0][1]) / Lx [q] ;
+ y [1][2] = (X [j+1][2] - Lx [p+1] * y [0][2]) / Lx [q] ;
+ y [1][3] = (X [j+1][3] - Lx [p+1] * y [0][3]) / Lx [q] ;
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j ][3] = y [0][3] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+1][3] = y [1][3] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j ][2] = y [0][2] / Lx [p] ;
+ X [j ][3] = y [0][3] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+ X [j+1][2] = y [1][2] / Lx [q] ;
+ X [j+1][3] = y [1][3] / Lx [q] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+1][3] = y [1][3] ;
+#endif
+ for (p += 2, q++ ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ double lx [2] ;
+ lx [0] = Lx [p] ;
+ lx [1] = Lx [q] ;
+ X [i][0] -= lx [0] * y [0][0] + lx [1] * y [1][0] ;
+ X [i][1] -= lx [0] * y [0][1] + lx [1] * y [1][1] ;
+ X [i][2] -= lx [0] * y [0][2] + lx [1] * y [1][2] ;
+ X [i][3] -= lx [0] * y [0][3] + lx [1] * y [1][3] ;
+ }
+ j += 2 ; /* advance to next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3][4] ;
+ Int q = Lp [j+1] ;
+ Int r = Lp [j+2] ;
+ y [0][0] = X [j][0] ;
+ y [0][1] = X [j][1] ;
+ y [0][2] = X [j][2] ;
+ y [0][3] = X [j][3] ;
+#ifdef LL
+ y [0][0] /= Lx [p] ;
+ y [0][1] /= Lx [p] ;
+ y [0][2] /= Lx [p] ;
+ y [0][3] /= Lx [p] ;
+ y [1][0] = (X [j+1][0] - Lx[p+1] * y[0][0]) / Lx [q] ;
+ y [1][1] = (X [j+1][1] - Lx[p+1] * y[0][1]) / Lx [q] ;
+ y [1][2] = (X [j+1][2] - Lx[p+1] * y[0][2]) / Lx [q] ;
+ y [1][3] = (X [j+1][3] - Lx[p+1] * y[0][3]) / Lx [q] ;
+ y [2][0] = (X [j+2][0] - Lx[p+2] * y[0][0] - Lx[q+1]*y[1][0])/Lx[r];
+ y [2][1] = (X [j+2][1] - Lx[p+2] * y[0][1] - Lx[q+1]*y[1][1])/Lx[r];
+ y [2][2] = (X [j+2][2] - Lx[p+2] * y[0][2] - Lx[q+1]*y[1][2])/Lx[r];
+ y [2][3] = (X [j+2][3] - Lx[p+2] * y[0][3] - Lx[q+1]*y[1][3])/Lx[r];
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j ][3] = y [0][3] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+1][3] = y [1][3] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+ X [j+2][2] = y [2][2] ;
+ X [j+2][3] = y [2][3] ;
+#elif defined (LD)
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ;
+ y [2][3] = X [j+2][3] - Lx [p+2] * y [0][3] - Lx [q+1] * y [1][3] ;
+ X [j ][0] = y [0][0] / Lx [p] ;
+ X [j ][1] = y [0][1] / Lx [p] ;
+ X [j ][2] = y [0][2] / Lx [p] ;
+ X [j ][3] = y [0][3] / Lx [p] ;
+ X [j+1][0] = y [1][0] / Lx [q] ;
+ X [j+1][1] = y [1][1] / Lx [q] ;
+ X [j+1][2] = y [1][2] / Lx [q] ;
+ X [j+1][3] = y [1][3] / Lx [q] ;
+ X [j+2][0] = y [2][0] / Lx [r] ;
+ X [j+2][1] = y [2][1] / Lx [r] ;
+ X [j+2][2] = y [2][2] / Lx [r] ;
+ X [j+2][3] = y [2][3] / Lx [r] ;
+#else
+ y [1][0] = X [j+1][0] - Lx [p+1] * y [0][0] ;
+ y [1][1] = X [j+1][1] - Lx [p+1] * y [0][1] ;
+ y [1][2] = X [j+1][2] - Lx [p+1] * y [0][2] ;
+ y [1][3] = X [j+1][3] - Lx [p+1] * y [0][3] ;
+ y [2][0] = X [j+2][0] - Lx [p+2] * y [0][0] - Lx [q+1] * y [1][0] ;
+ y [2][1] = X [j+2][1] - Lx [p+2] * y [0][1] - Lx [q+1] * y [1][1] ;
+ y [2][2] = X [j+2][2] - Lx [p+2] * y [0][2] - Lx [q+1] * y [1][2] ;
+ y [2][3] = X [j+2][3] - Lx [p+2] * y [0][3] - Lx [q+1] * y [1][3] ;
+ X [j+1][0] = y [1][0] ;
+ X [j+1][1] = y [1][1] ;
+ X [j+1][2] = y [1][2] ;
+ X [j+1][3] = y [1][3] ;
+ X [j+2][0] = y [2][0] ;
+ X [j+2][1] = y [2][1] ;
+ X [j+2][2] = y [2][2] ;
+ X [j+2][3] = y [2][3] ;
+#endif
+ for (p += 3, q += 2, r++ ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ double lx [3] ;
+ lx [0] = Lx [p] ;
+ lx [1] = Lx [q] ;
+ lx [2] = Lx [r] ;
+ X [i][0] -= lx[0] * y[0][0] + lx[1] * y[1][0] + lx[2] * y[2][0];
+ X [i][1] -= lx[0] * y[0][1] + lx[1] * y[1][1] + lx[2] * y[2][1];
+ X [i][2] -= lx[0] * y[0][2] + lx[1] * y[1][2] + lx[2] * y[2][2];
+ X [i][3] -= lx[0] * y[0][3] + lx[1] * y[1][3] + lx[2] * y[2][3];
+ }
+ j += 3 ; /* advance to next column of L */
+ }
+ }
+}
+
+#endif
+
+
+/* ========================================================================== */
+/* === LSOLVE (k) =========================================================== */
+/* ========================================================================== */
+
+static void LSOLVE (PREFIX,k)
+(
+ cholmod_factor *L,
+ cholmod_dense *Y /* nr-by-n where nr is 1 to 4 */
+)
+{
+
+#ifndef REAL
+ double yx [2] ;
+#ifdef ZOMPLEX
+ double yz [1] ;
+ double *Lz = L->z ;
+ double *Xz = Y->z ;
+#endif
+ double *Lx = L->x ;
+ double *Xx = Y->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int i, j, n = L->n ;
+#endif
+
+ ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */
+ ASSERT (L->n == Y->ncol) ; /* dimensions must match */
+ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */
+ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */
+ ASSERT (!(L->is_super)) ; /* L is simplicial LL' or LDL' */
+
+#ifdef REAL
+
+ /* ---------------------------------------------------------------------- */
+ /* solve a real linear system, with 1 to 4 RHS's and dynamic supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (Y->nrow <= 4) ;
+
+ switch (Y->nrow)
+ {
+ case 1: LSOLVE (PREFIX,1) (L, Y->x) ; break ;
+ case 2: LSOLVE (PREFIX,2) (L, Y->x) ; break ;
+ case 3: LSOLVE (PREFIX,3) (L, Y->x) ; break ;
+ case 4: LSOLVE (PREFIX,4) (L, Y->x) ; break ;
+ }
+
+#else
+
+ /* ---------------------------------------------------------------------- */
+ /* solve a complex linear system, with just one right-hand-side */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (Y->nrow == 1) ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* y = X [j] ; */
+ ASSIGN (yx,yz,0, Xx,Xz,j) ;
+
+#ifdef LL
+ /* y /= Lx [p] ; */
+ /* X [j] = y ; */
+ DIV_REAL (yx,yz,0, yx,yz,0, Lx,p) ;
+ ASSIGN (Xx,Xz,j, yx,yz,0) ;
+#elif defined (LD)
+ /* X [j] = y / Lx [p] ; */
+ DIV_REAL (Xx,Xz,j, yx,yz,0, Lx,p) ;
+#endif
+
+ for (p++ ; p < pend ; p++)
+ {
+ /* X [Li [p]] -= Lx [p] * y ; */
+ i = Li [p] ;
+ MULTSUB (Xx,Xz,i, Lx,Lz,p, yx,yz,0) ;
+ }
+ }
+
+#endif
+}
+
+/* prepare for the next inclusion of this file in cholmod_solve.c */
+#undef LL
+#undef LD
diff --git a/CHOLMOD/Cholesky/t_cholmod_ltsolve.c b/CHOLMOD/Cholesky/t_cholmod_ltsolve.c
new file mode 100644
index 0000000..e58d1cd
--- /dev/null
+++ b/CHOLMOD/Cholesky/t_cholmod_ltsolve.c
@@ -0,0 +1,841 @@
+/* ========================================================================== */
+/* === Cholesky/t_cholmod_ltsolve =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine to solve L'x=b with unit or non-unit diagonal, or
+ * solve DL'x=b.
+ *
+ * The numeric xtype of L and Y must match. Y contains b on input and x on
+ * output, stored in row-form. Y is nrow-by-n, where nrow must equal 1 for the
+ * complex or zomplex cases, and nrow <= 4 for the real case.
+ *
+ * This file is not compiled separately. It is included in t_cholmod_solve.c
+ * instead. It contains no user-callable routines.
+ *
+ * workspace: none
+ *
+ * Supports real, complex, and zomplex factors.
+ */
+
+/* undefine all prior definitions */
+#undef FORM_NAME
+#undef LSOLVE
+#undef DIAG
+
+/* -------------------------------------------------------------------------- */
+/* define the method */
+/* -------------------------------------------------------------------------- */
+
+#ifdef LL
+/* LL': solve Lx=b with non-unit diagonal */
+#define FORM_NAME(prefix,rank) prefix ## ll_ltsolve_ ## rank
+#define DIAG
+
+#elif defined (LD)
+/* LDL': solve LDx=b */
+#define FORM_NAME(prefix,rank) prefix ## ldl_dltsolve_ ## rank
+#define DIAG
+
+#else
+/* LDL': solve Lx=b with unit diagonal */
+#define FORM_NAME(prefix,rank) prefix ## ldl_ltsolve_ ## rank
+
+#endif
+
+/* LSOLVE(k) defines the name of a routine for an n-by-k right-hand-side. */
+#define LSOLVE(prefix,rank) FORM_NAME(prefix,rank)
+
+#ifdef REAL
+
+/* ========================================================================== */
+/* === LSOLVE (1) =========================================================== */
+/* ========================================================================== */
+
+/* Solve L'x=b, where b has 1 column */
+
+static void LSOLVE (PREFIX,1)
+(
+ cholmod_factor *L,
+ double X [ ] /* n-by-1 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = n-1 ; j >= 0 ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j-1, and j-2) */
+ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y = X [j] ;
+#ifdef DIAG
+ double d = Lx [p] ;
+#endif
+#ifdef LD
+ y /= d ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ y -= Lx [p] * X [Li [p]] ;
+ }
+#ifdef LL
+ X [j] = y / d ;
+#else
+ X [j] = y ;
+#endif
+ j-- ; /* advance to the next column of L */
+
+ }
+ else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2], t ;
+ Int q = Lp [j-1] ;
+#ifdef DIAG
+ double d [2] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+#endif
+ t = Lx [q+1] ;
+#ifdef LD
+ y [0] = X [j ] / d [0] ;
+ y [1] = X [j-1] / d [1] ;
+#else
+ y [0] = X [j ] ;
+ y [1] = X [j-1] ;
+#endif
+ for (p++, q += 2 ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ y [0] -= Lx [p] * X [i] ;
+ y [1] -= Lx [q] * X [i] ;
+ }
+#ifdef LL
+ y [0] /= d [0] ;
+ y [1] = (y [1] - t * y [0]) / d [1] ;
+#else
+ y [1] -= t * y [0] ;
+#endif
+ X [j ] = y [0] ;
+ X [j-1] = y [1] ;
+ j -= 2 ; /* advance to the next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3], t [3] ;
+ Int q = Lp [j-1] ;
+ Int r = Lp [j-2] ;
+#ifdef DIAG
+ double d [3] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+ d [2] = Lx [r] ;
+#endif
+ t [0] = Lx [q+1] ;
+ t [1] = Lx [r+1] ;
+ t [2] = Lx [r+2] ;
+#ifdef LD
+ y [0] = X [j] / d [0] ;
+ y [1] = X [j-1] / d [1] ;
+ y [2] = X [j-2] / d [2] ;
+#else
+ y [0] = X [j] ;
+ y [1] = X [j-1] ;
+ y [2] = X [j-2] ;
+#endif
+ for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ y [0] -= Lx [p] * X [i] ;
+ y [1] -= Lx [q] * X [i] ;
+ y [2] -= Lx [r] * X [i] ;
+ }
+#ifdef LL
+ y [0] /= d [0] ;
+ y [1] = (y [1] - t [0] * y [0]) / d [1] ;
+ y [2] = (y [2] - t [2] * y [0] - t [1] * y [1]) / d [2] ;
+#else
+ y [1] -= t [0] * y [0] ;
+ y [2] -= t [2] * y [0] + t [1] * y [1] ;
+#endif
+ X [j-2] = y [2] ;
+ X [j-1] = y [1] ;
+ X [j ] = y [0] ;
+ j -= 3 ; /* advance to the next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (2) =========================================================== */
+/* ========================================================================== */
+
+/* Solve L'x=b, where b has 2 columns */
+
+static void LSOLVE (PREFIX,2)
+(
+ cholmod_factor *L,
+ double X [ ][2] /* n-by-2 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = n-1 ; j >= 0 ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j-1, and j-2) */
+ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2] ;
+#ifdef DIAG
+ double d = Lx [p] ;
+#endif
+#ifdef LD
+ y [0] = X [j][0] / d ;
+ y [1] = X [j][1] / d ;
+#else
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ y [0] -= Lx [p] * X [i][0] ;
+ y [1] -= Lx [p] * X [i][1] ;
+ }
+#ifdef LL
+ X [j][0] = y [0] / d ;
+ X [j][1] = y [1] / d ;
+#else
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+#endif
+ j-- ; /* advance to the next column of L */
+
+ }
+ else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][2], t ;
+ Int q = Lp [j-1] ;
+#ifdef DIAG
+ double d [2] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+#endif
+ t = Lx [q+1] ;
+#ifdef LD
+ y [0][0] = X [j ][0] / d [0] ;
+ y [0][1] = X [j ][1] / d [0] ;
+ y [1][0] = X [j-1][0] / d [1] ;
+ y [1][1] = X [j-1][1] / d [1] ;
+#else
+ y [0][0] = X [j ][0] ;
+ y [0][1] = X [j ][1] ;
+ y [1][0] = X [j-1][0] ;
+ y [1][1] = X [j-1][1] ;
+#endif
+ for (p++, q += 2 ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ y [0][0] -= Lx [p] * X [i][0] ;
+ y [0][1] -= Lx [p] * X [i][1] ;
+ y [1][0] -= Lx [q] * X [i][0] ;
+ y [1][1] -= Lx [q] * X [i][1] ;
+ }
+#ifdef LL
+ y [0][0] /= d [0] ;
+ y [0][1] /= d [0] ;
+ y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ;
+ y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ;
+#else
+ y [1][0] -= t * y [0][0] ;
+ y [1][1] -= t * y [0][1] ;
+#endif
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j-1][0] = y [1][0] ;
+ X [j-1][1] = y [1][1] ;
+ j -= 2 ; /* advance to the next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3][2], t [3] ;
+ Int q = Lp [j-1] ;
+ Int r = Lp [j-2] ;
+#ifdef DIAG
+ double d [3] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+ d [2] = Lx [r] ;
+#endif
+ t [0] = Lx [q+1] ;
+ t [1] = Lx [r+1] ;
+ t [2] = Lx [r+2] ;
+#ifdef LD
+ y [0][0] = X [j ][0] / d [0] ;
+ y [0][1] = X [j ][1] / d [0] ;
+ y [1][0] = X [j-1][0] / d [1] ;
+ y [1][1] = X [j-1][1] / d [1] ;
+ y [2][0] = X [j-2][0] / d [2] ;
+ y [2][1] = X [j-2][1] / d [2] ;
+#else
+ y [0][0] = X [j ][0] ;
+ y [0][1] = X [j ][1] ;
+ y [1][0] = X [j-1][0] ;
+ y [1][1] = X [j-1][1] ;
+ y [2][0] = X [j-2][0] ;
+ y [2][1] = X [j-2][1] ;
+#endif
+ for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ y [0][0] -= Lx [p] * X [i][0] ;
+ y [0][1] -= Lx [p] * X [i][1] ;
+ y [1][0] -= Lx [q] * X [i][0] ;
+ y [1][1] -= Lx [q] * X [i][1] ;
+ y [2][0] -= Lx [r] * X [i][0] ;
+ y [2][1] -= Lx [r] * X [i][1] ;
+ }
+#ifdef LL
+ y [0][0] /= d [0] ;
+ y [0][1] /= d [0] ;
+ y [1][0] = (y [1][0] - t [0] * y [0][0]) / d [1] ;
+ y [1][1] = (y [1][1] - t [0] * y [0][1]) / d [1] ;
+ y [2][0] = (y [2][0] - t [2] * y [0][0] - t [1] * y [1][0]) / d [2];
+ y [2][1] = (y [2][1] - t [2] * y [0][1] - t [1] * y [1][1]) / d [2];
+#else
+ y [1][0] -= t [0] * y [0][0] ;
+ y [1][1] -= t [0] * y [0][1] ;
+ y [2][0] -= t [2] * y [0][0] + t [1] * y [1][0] ;
+ y [2][1] -= t [2] * y [0][1] + t [1] * y [1][1] ;
+#endif
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j-1][0] = y [1][0] ;
+ X [j-1][1] = y [1][1] ;
+ X [j-2][0] = y [2][0] ;
+ X [j-2][1] = y [2][1] ;
+ j -= 3 ; /* advance to the next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (3) =========================================================== */
+/* ========================================================================== */
+
+/* Solve L'x=b, where b has 3 columns */
+
+static void LSOLVE (PREFIX,3)
+(
+ cholmod_factor *L,
+ double X [ ][3] /* n-by-3 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = n-1 ; j >= 0 ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j-1, and j-2) */
+ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3] ;
+#ifdef DIAG
+ double d = Lx [p] ;
+#endif
+#ifdef LD
+ y [0] = X [j][0] / d ;
+ y [1] = X [j][1] / d ;
+ y [2] = X [j][2] / d ;
+#else
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+ y [2] = X [j][2] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ y [0] -= Lx [p] * X [i][0] ;
+ y [1] -= Lx [p] * X [i][1] ;
+ y [2] -= Lx [p] * X [i][2] ;
+ }
+#ifdef LL
+ X [j][0] = y [0] / d ;
+ X [j][1] = y [1] / d ;
+ X [j][2] = y [2] / d ;
+#else
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+ X [j][2] = y [2] ;
+#endif
+ j-- ; /* advance to the next column of L */
+
+ }
+ else if (lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][3], t ;
+ Int q = Lp [j-1] ;
+#ifdef DIAG
+ double d [2] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+#endif
+ t = Lx [q+1] ;
+#ifdef LD
+ y [0][0] = X [j ][0] / d [0] ;
+ y [0][1] = X [j ][1] / d [0] ;
+ y [0][2] = X [j ][2] / d [0] ;
+ y [1][0] = X [j-1][0] / d [1] ;
+ y [1][1] = X [j-1][1] / d [1] ;
+ y [1][2] = X [j-1][2] / d [1] ;
+#else
+ y [0][0] = X [j ][0] ;
+ y [0][1] = X [j ][1] ;
+ y [0][2] = X [j ][2] ;
+ y [1][0] = X [j-1][0] ;
+ y [1][1] = X [j-1][1] ;
+ y [1][2] = X [j-1][2] ;
+#endif
+ for (p++, q += 2 ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ y [0][0] -= Lx [p] * X [i][0] ;
+ y [0][1] -= Lx [p] * X [i][1] ;
+ y [0][2] -= Lx [p] * X [i][2] ;
+ y [1][0] -= Lx [q] * X [i][0] ;
+ y [1][1] -= Lx [q] * X [i][1] ;
+ y [1][2] -= Lx [q] * X [i][2] ;
+ }
+#ifdef LL
+ y [0][0] /= d [0] ;
+ y [0][1] /= d [0] ;
+ y [0][2] /= d [0] ;
+ y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ;
+ y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ;
+ y [1][2] = (y [1][2] - t * y [0][2]) / d [1] ;
+#else
+ y [1][0] -= t * y [0][0] ;
+ y [1][1] -= t * y [0][1] ;
+ y [1][2] -= t * y [0][2] ;
+#endif
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j-1][0] = y [1][0] ;
+ X [j-1][1] = y [1][1] ;
+ X [j-1][2] = y [1][2] ;
+ j -= 2 ; /* advance to the next column of L */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of three columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [3][3], t [3] ;
+ Int q = Lp [j-1] ;
+ Int r = Lp [j-2] ;
+#ifdef DIAG
+ double d [3] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+ d [2] = Lx [r] ;
+#endif
+ t [0] = Lx [q+1] ;
+ t [1] = Lx [r+1] ;
+ t [2] = Lx [r+2] ;
+#ifdef LD
+ y [0][0] = X [j ][0] / d [0] ;
+ y [0][1] = X [j ][1] / d [0] ;
+ y [0][2] = X [j ][2] / d [0] ;
+ y [1][0] = X [j-1][0] / d [1] ;
+ y [1][1] = X [j-1][1] / d [1] ;
+ y [1][2] = X [j-1][2] / d [1] ;
+ y [2][0] = X [j-2][0] / d [2] ;
+ y [2][1] = X [j-2][1] / d [2] ;
+ y [2][2] = X [j-2][2] / d [2] ;
+#else
+ y [0][0] = X [j ][0] ;
+ y [0][1] = X [j ][1] ;
+ y [0][2] = X [j ][2] ;
+ y [1][0] = X [j-1][0] ;
+ y [1][1] = X [j-1][1] ;
+ y [1][2] = X [j-1][2] ;
+ y [2][0] = X [j-2][0] ;
+ y [2][1] = X [j-2][1] ;
+ y [2][2] = X [j-2][2] ;
+#endif
+ for (p++, q += 2, r += 3 ; p < pend ; p++, q++, r++)
+ {
+ Int i = Li [p] ;
+ y [0][0] -= Lx [p] * X [i][0] ;
+ y [0][1] -= Lx [p] * X [i][1] ;
+ y [0][2] -= Lx [p] * X [i][2] ;
+ y [1][0] -= Lx [q] * X [i][0] ;
+ y [1][1] -= Lx [q] * X [i][1] ;
+ y [1][2] -= Lx [q] * X [i][2] ;
+ y [2][0] -= Lx [r] * X [i][0] ;
+ y [2][1] -= Lx [r] * X [i][1] ;
+ y [2][2] -= Lx [r] * X [i][2] ;
+ }
+#ifdef LL
+ y [0][0] /= d [0] ;
+ y [0][1] /= d [0] ;
+ y [0][2] /= d [0] ;
+ y [1][0] = (y [1][0] - t [0] * y [0][0]) / d [1] ;
+ y [1][1] = (y [1][1] - t [0] * y [0][1]) / d [1] ;
+ y [1][2] = (y [1][2] - t [0] * y [0][2]) / d [1] ;
+ y [2][0] = (y [2][0] - t [2] * y [0][0] - t [1] * y [1][0]) / d [2];
+ y [2][1] = (y [2][1] - t [2] * y [0][1] - t [1] * y [1][1]) / d [2];
+ y [2][2] = (y [2][2] - t [2] * y [0][2] - t [1] * y [1][2]) / d [2];
+#else
+ y [1][0] -= t [0] * y [0][0] ;
+ y [1][1] -= t [0] * y [0][1] ;
+ y [1][2] -= t [0] * y [0][2] ;
+ y [2][0] -= t [2] * y [0][0] + t [1] * y [1][0] ;
+ y [2][1] -= t [2] * y [0][1] + t [1] * y [1][1] ;
+ y [2][2] -= t [2] * y [0][2] + t [1] * y [1][2] ;
+#endif
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j-1][0] = y [1][0] ;
+ X [j-1][1] = y [1][1] ;
+ X [j-1][2] = y [1][2] ;
+ X [j-2][0] = y [2][0] ;
+ X [j-2][1] = y [2][1] ;
+ X [j-2][2] = y [2][2] ;
+ j -= 3 ; /* advance to the next column of L */
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === LSOLVE (4) =========================================================== */
+/* ========================================================================== */
+
+/* Solve L'x=b, where b has 4 columns */
+
+static void LSOLVE (PREFIX,4)
+(
+ cholmod_factor *L,
+ double X [ ][4] /* n-by-4 in row form */
+)
+{
+ double *Lx = L->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int j, n = L->n ;
+
+ for (j = n-1 ; j >= 0 ; )
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* find a chain of supernodes (up to j, j-1, and j-2) */
+ if (j < 4 || lnz != Lnz [j-1] - 1 || Li [Lp [j-1]+1] != j)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a single column of L */
+ /* -------------------------------------------------------------- */
+
+ double y [4] ;
+#ifdef DIAG
+ double d = Lx [p] ;
+#endif
+#ifdef LD
+ y [0] = X [j][0] / d ;
+ y [1] = X [j][1] / d ;
+ y [2] = X [j][2] / d ;
+ y [3] = X [j][3] / d ;
+#else
+ y [0] = X [j][0] ;
+ y [1] = X [j][1] ;
+ y [2] = X [j][2] ;
+ y [3] = X [j][3] ;
+#endif
+ for (p++ ; p < pend ; p++)
+ {
+ Int i = Li [p] ;
+ y [0] -= Lx [p] * X [i][0] ;
+ y [1] -= Lx [p] * X [i][1] ;
+ y [2] -= Lx [p] * X [i][2] ;
+ y [3] -= Lx [p] * X [i][3] ;
+ }
+#ifdef LL
+ X [j][0] = y [0] / d ;
+ X [j][1] = y [1] / d ;
+ X [j][2] = y [2] / d ;
+ X [j][3] = y [3] / d ;
+#else
+ X [j][0] = y [0] ;
+ X [j][1] = y [1] ;
+ X [j][2] = y [2] ;
+ X [j][3] = y [3] ;
+#endif
+ j-- ; /* advance to the next column of L */
+
+ }
+ else /* if (j == 1 || lnz != Lnz [j-2]-2 || Li [Lp [j-2]+2] != j) */
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve with a supernode of two columns of L */
+ /* -------------------------------------------------------------- */
+
+ double y [2][4], t ;
+ Int q = Lp [j-1] ;
+#ifdef DIAG
+ double d [2] ;
+ d [0] = Lx [p] ;
+ d [1] = Lx [q] ;
+#endif
+ t = Lx [q+1] ;
+#ifdef LD
+ y [0][0] = X [j ][0] / d [0] ;
+ y [0][1] = X [j ][1] / d [0] ;
+ y [0][2] = X [j ][2] / d [0] ;
+ y [0][3] = X [j ][3] / d [0] ;
+ y [1][0] = X [j-1][0] / d [1] ;
+ y [1][1] = X [j-1][1] / d [1] ;
+ y [1][2] = X [j-1][2] / d [1] ;
+ y [1][3] = X [j-1][3] / d [1] ;
+#else
+ y [0][0] = X [j ][0] ;
+ y [0][1] = X [j ][1] ;
+ y [0][2] = X [j ][2] ;
+ y [0][3] = X [j ][3] ;
+ y [1][0] = X [j-1][0] ;
+ y [1][1] = X [j-1][1] ;
+ y [1][2] = X [j-1][2] ;
+ y [1][3] = X [j-1][3] ;
+#endif
+ for (p++, q += 2 ; p < pend ; p++, q++)
+ {
+ Int i = Li [p] ;
+ y [0][0] -= Lx [p] * X [i][0] ;
+ y [0][1] -= Lx [p] * X [i][1] ;
+ y [0][2] -= Lx [p] * X [i][2] ;
+ y [0][3] -= Lx [p] * X [i][3] ;
+ y [1][0] -= Lx [q] * X [i][0] ;
+ y [1][1] -= Lx [q] * X [i][1] ;
+ y [1][2] -= Lx [q] * X [i][2] ;
+ y [1][3] -= Lx [q] * X [i][3] ;
+ }
+#ifdef LL
+ y [0][0] /= d [0] ;
+ y [0][1] /= d [0] ;
+ y [0][2] /= d [0] ;
+ y [0][3] /= d [0] ;
+ y [1][0] = (y [1][0] - t * y [0][0]) / d [1] ;
+ y [1][1] = (y [1][1] - t * y [0][1]) / d [1] ;
+ y [1][2] = (y [1][2] - t * y [0][2]) / d [1] ;
+ y [1][3] = (y [1][3] - t * y [0][3]) / d [1] ;
+#else
+ y [1][0] -= t * y [0][0] ;
+ y [1][1] -= t * y [0][1] ;
+ y [1][2] -= t * y [0][2] ;
+ y [1][3] -= t * y [0][3] ;
+#endif
+ X [j ][0] = y [0][0] ;
+ X [j ][1] = y [0][1] ;
+ X [j ][2] = y [0][2] ;
+ X [j ][3] = y [0][3] ;
+ X [j-1][0] = y [1][0] ;
+ X [j-1][1] = y [1][1] ;
+ X [j-1][2] = y [1][2] ;
+ X [j-1][3] = y [1][3] ;
+ j -= 2 ; /* advance to the next column of L */
+ }
+
+ /* NOTE: with 4 right-hand-sides, it suffices to exploit dynamic
+ * supernodes of just size 1 and 2. 3-column supernodes are not
+ * needed. */
+ }
+}
+
+#endif
+
+/* ========================================================================== */
+/* === LSOLVE (k) =========================================================== */
+/* ========================================================================== */
+
+static void LSOLVE (PREFIX,k)
+(
+ cholmod_factor *L,
+ cholmod_dense *Y /* nr-by-n where nr is 1 to 4 */
+)
+{
+
+#ifndef REAL
+#ifdef DIAG
+ double d [1] ;
+#endif
+ double yx [2] ;
+#ifdef ZOMPLEX
+ double yz [1] ;
+ double *Lz = L->z ;
+ double *Xz = Y->z ;
+#endif
+ double *Lx = L->x ;
+ double *Xx = Y->x ;
+ Int *Li = L->i ;
+ Int *Lp = L->p ;
+ Int *Lnz = L->nz ;
+ Int i, j, n = L->n ;
+#endif
+
+ ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */
+ ASSERT (L->n == Y->ncol) ; /* dimensions must match */
+ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */
+ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */
+ ASSERT (!(L->is_super)) ; /* L is simplicial LL' or LDL' */
+
+#ifdef REAL
+
+ /* ---------------------------------------------------------------------- */
+ /* solve a real linear system, with 1 to 4 RHS's and dynamic supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (Y->nrow <= 4) ;
+ switch (Y->nrow)
+ {
+ case 1: LSOLVE (PREFIX,1) (L, Y->x) ; break ;
+ case 2: LSOLVE (PREFIX,2) (L, Y->x) ; break ;
+ case 3: LSOLVE (PREFIX,3) (L, Y->x) ; break ;
+ case 4: LSOLVE (PREFIX,4) (L, Y->x) ; break ;
+ }
+
+#else
+
+ /* ---------------------------------------------------------------------- */
+ /* solve a complex linear system, with just one right-hand-side */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (Y->nrow == 1) ;
+
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ /* get the start, end, and length of column j */
+ Int p = Lp [j] ;
+ Int lnz = Lnz [j] ;
+ Int pend = p + lnz ;
+
+ /* y = X [j] ; */
+ ASSIGN (yx,yz,0, Xx,Xz,j) ;
+
+#ifdef DIAG
+ /* d = Lx [p] ; */
+ ASSIGN_REAL (d,0, Lx,p) ;
+#endif
+#ifdef LD
+ /* y /= d ; */
+ DIV_REAL (yx,yz,0, yx,yz,0, d,0) ;
+#endif
+
+ for (p++ ; p < pend ; p++)
+ {
+ /* y -= conj (Lx [p]) * X [Li [p]] ; */
+ i = Li [p] ;
+ MULTSUBCONJ (yx,yz,0, Lx,Lz,p, Xx,Xz,i) ;
+ }
+
+#ifdef LL
+ /* X [j] = y / d ; */
+ DIV_REAL (Xx,Xz,j, yx,yz,0, d,0) ;
+#else
+ /* X [j] = y ; */
+ ASSIGN (Xx,Xz,j, yx,yz,0) ;
+#endif
+
+ }
+
+#endif
+}
+
+/* prepare for the next inclusion of this file in cholmod_solve.c */
+#undef LL
+#undef LD
diff --git a/CHOLMOD/Cholesky/t_cholmod_rowfac.c b/CHOLMOD/Cholesky/t_cholmod_rowfac.c
new file mode 100644
index 0000000..38120ce
--- /dev/null
+++ b/CHOLMOD/Cholesky/t_cholmod_rowfac.c
@@ -0,0 +1,458 @@
+/* ========================================================================== */
+/* === Cholesky/t_cholmod_rowfac ============================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_rowfac. Supports any numeric xtype
+ * (real, complex, or zomplex).
+ *
+ * workspace: Iwork (n), Flag (n), Xwork (n if real, 2*n if complex)
+ */
+
+#include "cholmod_template.h"
+
+#ifdef MASK
+static int TEMPLATE (cholmod_rowfac_mask)
+#else
+static int TEMPLATE (cholmod_rowfac)
+#endif
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,f)' */
+ double beta [2], /* factorize beta*I+A or beta*I+AA' (beta [0] only) */
+ size_t kstart, /* first row to factorize */
+ size_t kend, /* last row to factorize is kend-1 */
+#ifdef MASK
+ /* These inputs are used for cholmod_rowfac_mask only */
+ Int *mask, /* size A->nrow. if mask[i] then W(i) is set to zero */
+ Int *RLinkUp, /* size A->nrow. link list of rows to compute */
+#endif
+ /* ---- in/out --- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double yx [2], lx [2], fx [2], dk [1], di [1], fl = 0 ;
+#ifdef ZOMPLEX
+ double yz [1], lz [1], fz [1] ;
+#endif
+ double *Ax, *Az, *Lx, *Lz, *Wx, *Wz, *Fx, *Fz ;
+ Int *Ap, *Anz, *Ai, *Lp, *Lnz, *Li, *Lnext, *Flag, *Stack, *Fp, *Fi, *Fnz,
+ *Iwork ;
+ Int i, p, k, t, pf, pfend, top, s, mark, pend, n, lnz, is_ll, multadds,
+ use_dbound, packed, stype, Fpacked, sorted, nzmax, len, parent ;
+#ifndef REAL
+ Int dk_imaginary ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ PRINT1 (("\nin cholmod_rowfac, kstart %d kend %d stype %d\n",
+ kstart, kend, A->stype)) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "Initial L", Common)) ;
+
+ n = A->nrow ;
+ stype = A->stype ;
+
+ if (stype > 0)
+ {
+ /* symmetric upper case: F is not needed. It may be NULL */
+ Fp = NULL ;
+ Fi = NULL ;
+ Fx = NULL ;
+ Fz = NULL ;
+ Fnz = NULL ;
+ Fpacked = TRUE ;
+ }
+ else
+ {
+ /* unsymmetric case: F is required. */
+ Fp = F->p ;
+ Fi = F->i ;
+ Fx = F->x ;
+ Fz = F->z ;
+ Fnz = F->nz ;
+ Fpacked = F->packed ;
+ }
+
+ Ap = A->p ; /* size A->ncol+1, column pointers of A */
+ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */
+ Ax = A->x ; /* size nz, numeric values of A */
+ Az = A->z ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ sorted = A->sorted ;
+
+ use_dbound = IS_GT_ZERO (Common->dbound) ;
+
+ /* get the current factors L (and D for LDL'); allocate space if needed */
+ is_ll = L->is_ll ;
+ if (L->xtype == CHOLMOD_PATTERN)
+ {
+ /* ------------------------------------------------------------------ */
+ /* L is symbolic only; allocate and initialize L (and D for LDL') */
+ /* ------------------------------------------------------------------ */
+
+ /* workspace: none */
+ CHOLMOD(change_factor) (A->xtype, is_ll, FALSE, FALSE, TRUE, L, Common);
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (FALSE) ;
+ }
+ ASSERT (L->minor == (size_t) n) ;
+ }
+ else if (kstart == 0 && kend == (size_t) n)
+ {
+ /* ------------------------------------------------------------------ */
+ /* refactorization; reset L->nz and L->minor to restart factorization */
+ /* ------------------------------------------------------------------ */
+
+ L->minor = n ;
+ Lnz = L->nz ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Lnz [k] = 1 ;
+ }
+ }
+
+ ASSERT (is_ll == L->is_ll) ;
+ ASSERT (L->xtype != CHOLMOD_PATTERN) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "L ready", Common)) ;
+ DEBUG (CHOLMOD(dump_sparse) (A, "A ready", Common)) ;
+ DEBUG (if (stype == 0) CHOLMOD(dump_sparse) (F, "F ready", Common)) ;
+
+ /* inputs, can be modified on output: */
+ Lp = L->p ; /* size n+1 */
+ ASSERT (Lp != NULL) ;
+
+ /* outputs, contents defined on input for incremental case only: */
+ Lnz = L->nz ; /* size n */
+ Lnext = L->next ; /* size n+2 */
+ Li = L->i ; /* size L->nzmax, can change in size */
+ Lx = L->x ; /* size L->nzmax or 2*L->nzmax, can change in size */
+ Lz = L->z ; /* size L->nzmax for zomplex case, can change in size */
+ nzmax = L->nzmax ;
+ ASSERT (Lnz != NULL && Li != NULL && Lx != NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Stack = Iwork ; /* size n (i/i/l) */
+ Flag = Common->Flag ; /* size n, Flag [i] < mark must hold */
+ Wx = Common->Xwork ; /* size n if real, 2*n if complex or
+ * zomplex. Xwork [i] == 0 must hold. */
+ Wz = Wx + n ; /* size n for zomplex case only */
+ mark = Common->mark ;
+ ASSERT ((Int) Common->xworksize >= (L->xtype == CHOLMOD_REAL ? 1:2)*n) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute LDL' or LL' factorization by rows */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef MASK
+#define NEXT(k) k = RLinkUp [k]
+#else
+#define NEXT(k) k++
+#endif
+
+ for (k = kstart ; k < ((Int) kend) ; NEXT(k))
+ {
+ PRINT1 (("\n===============K "ID" Lnz [k] "ID"\n", k, Lnz [k])) ;
+
+ /* ------------------------------------------------------------------ */
+ /* compute pattern of kth row of L and scatter kth input column */
+ /* ------------------------------------------------------------------ */
+
+ /* column k of L is currently empty */
+ ASSERT (Lnz [k] == 1) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ;
+
+ top = n ; /* Stack is empty */
+ Flag [k] = mark ; /* do not include diagonal entry in Stack */
+
+ /* use Li [Lp [i]+1] for etree */
+#define PARENT(i) (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY
+
+ if (stype > 0)
+ {
+ /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */
+ p = Ap [k] ;
+ pend = (packed) ? (Ap [k+1]) : (p + Anz [k]) ;
+ /* W [i] = Ax [i] ; scatter column of A */
+#define SCATTER ASSIGN(Wx,Wz,i, Ax,Az,p)
+ SUBTREE ;
+#undef SCATTER
+ }
+ else
+ {
+ /* scatter kth col of triu (beta*I+AA'), get pattern L(k,:) */
+ pf = Fp [k] ;
+ pfend = (Fpacked) ? (Fp [k+1]) : (pf + Fnz [k]) ;
+ for ( ; pf < pfend ; pf++)
+ {
+ /* get nonzero entry F (t,k) */
+ t = Fi [pf] ;
+ /* fk = Fx [pf] */
+ ASSIGN (fx, fz, 0, Fx, Fz, pf) ;
+ p = Ap [t] ;
+ pend = (packed) ? (Ap [t+1]) : (p + Anz [t]) ;
+ multadds = 0 ;
+ /* W [i] += Ax [p] * fx ; scatter column of A*A' */
+#define SCATTER MULTADD (Wx,Wz,i, Ax,Az,p, fx,fz,0) ; multadds++ ;
+ SUBTREE ;
+#undef SCATTER
+#ifdef REAL
+ fl += 2 * ((double) multadds) ;
+#else
+ fl += 8 * ((double) multadds) ;
+#endif
+ }
+ }
+
+#undef PARENT
+
+ /* ------------------------------------------------------------------ */
+ /* if mask is present, set the corresponding entries in W to zero */
+ /* ------------------------------------------------------------------ */
+
+#ifdef MASK
+ /* remove the dead element of Wx */
+ if (mask != NULL)
+ {
+
+#if 0
+ /* older version */
+ for (p = n; p > top;)
+ {
+ i = Stack [--p] ;
+ if ( mask [i] >= 0 )
+ {
+ CLEAR (Wx,Wz,i) ; /* set W(i) to zero */
+ }
+ }
+#endif
+
+ for (s = top ; s < n ; s++)
+ {
+ i = Stack [s] ;
+ if (mask [i] >= 0)
+ {
+ CLEAR (Wx,Wz,i) ; /* set W(i) to zero */
+ }
+ }
+
+ }
+#endif
+
+ /* nonzero pattern of kth row of L is now in Stack [top..n-1].
+ * Flag [Stack [top..n-1]] is equal to mark, but no longer needed */
+
+ /* mark = CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+
+ /* ------------------------------------------------------------------ */
+ /* compute kth row of L and store in column form */
+ /* ------------------------------------------------------------------ */
+
+ /* Solve L (0:k-1, 0:k-1) * y (0:k-1) = b (0:k-1) where
+ * b (0:k) = A (0:k,k) or A(0:k,:) * F(:,k) is in W and Stack.
+ *
+ * For LDL' factorization:
+ * L (k, 0:k-1) = y (0:k-1) ./ D (0:k-1)
+ * D (k) = b (k) - L (k, 0:k-1) * y (0:k-1)
+ *
+ * For LL' factorization:
+ * L (k, 0:k-1) = y (0:k-1)
+ * L (k,k) = sqrt (b (k) - L (k, 0:k-1) * L (0:k-1, k))
+ */
+
+ /* dk = W [k] + beta */
+ ADD_REAL (dk,0, Wx,k, beta,0) ;
+
+#ifndef REAL
+ /* In the unsymmetric case, the imaginary part of W[k] must be real,
+ * since F is assumed to be the complex conjugate transpose of A. In
+ * the symmetric case, W[k] is the diagonal of A. If the imaginary part
+ * of W[k] is nonzero, then the Cholesky factorization cannot be
+ * computed; A is not positive definite */
+ dk_imaginary = (stype > 0) ? (IMAG_IS_NONZERO (Wx,Wz,k)) : FALSE ;
+#endif
+
+ /* W [k] = 0.0 ; */
+ CLEAR (Wx,Wz,k) ;
+
+ for (s = top ; s < n ; s++)
+ {
+ /* get i for each nonzero entry L(k,i) */
+ i = Stack [s] ;
+
+ /* y = W [i] ; */
+ ASSIGN (yx,yz,0, Wx,Wz,i) ;
+
+ /* W [i] = 0.0 ; */
+ CLEAR (Wx,Wz,i) ;
+
+ lnz = Lnz [i] ;
+ p = Lp [i] ;
+ ASSERT (lnz > 0 && Li [p] == i) ;
+ pend = p + lnz ;
+
+ /* di = Lx [p] ; the diagonal entry L or D(i,i), which is real */
+ ASSIGN_REAL (di,0, Lx,p) ;
+
+ if (i >= (Int) L->minor || IS_ZERO (di [0]))
+ {
+ /* For the LL' factorization, L(i,i) is zero. For the LDL',
+ * D(i,i) is zero. Skip column i of L, and set L(k,i) = 0. */
+ CLEAR (lx,lz,0) ;
+ p = pend ;
+ }
+ else if (is_ll)
+ {
+#ifdef REAL
+ fl += 2 * ((double) (pend - p - 1)) + 3 ;
+#else
+ fl += 8 * ((double) (pend - p - 1)) + 6 ;
+#endif
+ /* forward solve using L (i:(k-1),i) */
+ /* divide by L(i,i), which must be real and nonzero */
+ /* y /= di [0] */
+ DIV_REAL (yx,yz,0, yx,yz,0, di,0) ;
+ for (p++ ; p < pend ; p++)
+ {
+ /* W [Li [p]] -= Lx [p] * y ; */
+ MULTSUB (Wx,Wz,Li[p], Lx,Lz,p, yx,yz,0) ;
+ }
+ /* do not scale L; compute dot product for L(k,k) */
+ /* L(k,i) = conj(y) ; */
+ ASSIGN_CONJ (lx,lz,0, yx,yz,0) ;
+ /* d -= conj(y) * y ; */
+ LLDOT (dk,0, yx,yz,0) ;
+ }
+ else
+ {
+#ifdef REAL
+ fl += 2 * ((double) (pend - p - 1)) + 3 ;
+#else
+ fl += 8 * ((double) (pend - p - 1)) + 6 ;
+#endif
+ /* forward solve using D (i,i) and L ((i+1):(k-1),i) */
+ for (p++ ; p < pend ; p++)
+ {
+ /* W [Li [p]] -= Lx [p] * y ; */
+ MULTSUB (Wx,Wz,Li[p], Lx,Lz,p, yx,yz,0) ;
+ }
+ /* Scale L (k,0:k-1) for LDL' factorization, compute D (k,k)*/
+#ifdef REAL
+ /* L(k,i) = y/d */
+ lx [0] = yx [0] / di [0] ;
+ /* d -= L(k,i) * y */
+ dk [0] -= lx [0] * yx [0] ;
+#else
+ /* L(k,i) = conj(y) ; */
+ ASSIGN_CONJ (lx,lz,0, yx,yz,0) ;
+ /* L(k,i) /= di ; */
+ DIV_REAL (lx,lz,0, lx,lz,0, di,0) ;
+ /* d -= conj(y) * y / di */
+ LDLDOT (dk,0, yx,yz,0, di,0) ;
+#endif
+ }
+
+ /* determine if column i of L can hold the new L(k,i) entry */
+ if (p >= Lp [Lnext [i]])
+ {
+ /* column i needs to grow */
+ PRINT1 (("Factor Colrealloc "ID", old Lnz "ID"\n", i, Lnz [i]));
+ if (!CHOLMOD(reallocate_column) (i, lnz + 1, L, Common))
+ {
+ /* out of memory, L is now simplicial symbolic */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = 0 ; */
+ CLEAR (Wx,Wz,i) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, n, Common)) ;
+ return (FALSE) ;
+ }
+ Li = L->i ; /* L->i, L->x, L->z may have moved */
+ Lx = L->x ;
+ Lz = L->z ;
+ p = Lp [i] + lnz ; /* contents of L->p changed */
+ ASSERT (p < Lp [Lnext [i]]) ;
+ }
+
+ /* store L (k,i) in the column form matrix of L */
+ Li [p] = k ;
+ /* Lx [p] = L(k,i) ; */
+ ASSIGN (Lx,Lz,p, lx,lz,0) ;
+ Lnz [i]++ ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* ensure abs (d) >= dbound if dbound is given, and store it in L */
+ /* ------------------------------------------------------------------ */
+
+ p = Lp [k] ;
+ Li [p] = k ;
+
+ if (k >= (Int) L->minor)
+ {
+ /* the matrix is already not positive definite */
+ dk [0] = 0 ;
+ }
+ else if (use_dbound)
+ {
+ /* modify the diagonal to force LL' or LDL' to exist */
+ dk [0] = CHOLMOD(dbound) (is_ll ? fabs (dk [0]) : dk [0], Common) ;
+ }
+ else if ((is_ll ? (IS_LE_ZERO (dk [0])) : (IS_ZERO (dk [0])))
+#ifndef REAL
+ || dk_imaginary
+#endif
+ )
+ {
+ /* the matrix has just been found to be not positive definite */
+ dk [0] = 0 ;
+ L->minor = k ;
+ ERROR (CHOLMOD_NOT_POSDEF, "not positive definite") ;
+ }
+
+ if (is_ll)
+ {
+ /* this is counted as one flop, below */
+ dk [0] = sqrt (dk [0]) ;
+ }
+
+ /* Lx [p] = D(k,k) = d ; real part only */
+ ASSIGN_REAL (Lx,p, dk,0) ;
+ CLEAR_IMAG (Lx,Lz,p) ;
+ }
+
+#undef NEXT
+
+ if (is_ll) fl += MAX ((Int) kend - (Int) kstart, 0) ; /* count sqrt's */
+ Common->rowfacfl = fl ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "final cholmod_rowfac", Common)) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, n, Common)) ;
+ return (TRUE) ;
+}
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/CHOLMOD/Cholesky/t_cholmod_solve.c b/CHOLMOD/Cholesky/t_cholmod_solve.c
new file mode 100644
index 0000000..a70594a
--- /dev/null
+++ b/CHOLMOD/Cholesky/t_cholmod_solve.c
@@ -0,0 +1,164 @@
+/* ========================================================================== */
+/* === Cholesky/t_cholmod_solve ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Cholesky Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Cholesky Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_solve. Supports any numeric xtype (real,
+ * complex, or zomplex). The xtypes of all matrices (L and Y) must match.
+ */
+
+#include "cholmod_template.h"
+
+/* ========================================================================== */
+/* === simplicial template solvers ========================================== */
+/* ========================================================================== */
+
+/* LL': solve Lx=b with non-unit diagonal */
+#define LL
+#include "t_cholmod_lsolve.c"
+
+/* LDL': solve LDx=b */
+#define LD
+#include "t_cholmod_lsolve.c"
+
+/* LDL': solve Lx=b with unit diagonal */
+#include "t_cholmod_lsolve.c"
+
+/* LL': solve L'x=b with non-unit diagonal */
+#define LL
+#include "t_cholmod_ltsolve.c"
+
+/* LDL': solve DL'x=b */
+#define LD
+#include "t_cholmod_ltsolve.c"
+
+/* LDL': solve L'x=b with unit diagonal */
+#include "t_cholmod_ltsolve.c"
+
+
+/* ========================================================================== */
+/* === t_ldl_dsolve ========================================================= */
+/* ========================================================================== */
+
+/* Solve Dx=b for an LDL' factorization, where Y holds b' on input and x' on
+ * output. */
+
+static void TEMPLATE (ldl_dsolve)
+(
+ cholmod_factor *L,
+ cholmod_dense *Y /* nr-by-n with leading dimension nr */
+)
+{
+ double d [1] ;
+ double *Lx, *Yx, *Yz ;
+ Int *Lp ;
+ Int n, nrhs, k, p, k1, k2 ;
+
+ ASSERT (L->xtype == Y->xtype) ; /* L and Y must have the same xtype */
+ ASSERT (L->n == Y->ncol) ; /* dimensions must match */
+ ASSERT (Y->nrow == Y->d) ; /* leading dimension of Y = # rows of Y */
+ ASSERT (L->xtype != CHOLMOD_PATTERN) ; /* L is not symbolic */
+ ASSERT (!(L->is_super) && !(L->is_ll)) ; /* L is simplicial LDL' */
+
+ nrhs = Y->nrow ;
+ n = L->n ;
+ Lp = L->p ;
+ Lx = L->x ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ for (k = 0 ; k < n ; k++)
+ {
+ k1 = k*nrhs ;
+ k2 = (k+1)*nrhs ;
+ ASSIGN_REAL (d,0, Lx,Lp[k]) ;
+ for (p = k1 ; p < k2 ; p++)
+ {
+ DIV_REAL (Yx,Yz,p, Yx,Yz,p, d,0) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === t_simplicial_solver ================================================== */
+/* ========================================================================== */
+
+/* Solve a linear system, where Y' contains the (array-transposed) right-hand
+ * side on input, and the solution on output. No permutations are applied;
+ * these must have already been applied to Y on input. */
+
+static void TEMPLATE (simplicial_solver)
+(
+ int sys, /* system to solve */
+ cholmod_factor *L, /* factor to use, a simplicial LL' or LDL' */
+ cholmod_dense *Y /* right-hand-side on input, solution on output */
+)
+{
+ if (L->is_ll)
+ {
+ /* The factorization is LL' */
+ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt)
+ {
+ /* Solve Ax=b or LL'x=b */
+ TEMPLATE (ll_lsolve_k) (L, Y) ;
+ TEMPLATE (ll_ltsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_L || sys == CHOLMOD_LD)
+ {
+ /* Solve Lx=b */
+ TEMPLATE (ll_lsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_Lt || sys == CHOLMOD_DLt)
+ {
+ /* Solve L'x=b */
+ TEMPLATE (ll_ltsolve_k) (L, Y) ;
+ }
+ }
+ else
+ {
+ /* The factorization is LDL' */
+ if (sys == CHOLMOD_A || sys == CHOLMOD_LDLt)
+ {
+ /* Solve Ax=b or LDL'x=b */
+ TEMPLATE (ldl_lsolve_k) (L, Y) ;
+ TEMPLATE (ldl_dltsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_LD)
+ {
+ /* Solve LDx=b */
+ TEMPLATE (ldl_ldsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_L)
+ {
+ /* Solve Lx=b */
+ TEMPLATE (ldl_lsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_Lt)
+ {
+ /* Solve L'x=b */
+ TEMPLATE (ldl_ltsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_DLt)
+ {
+ /* Solve DL'x=b */
+ TEMPLATE (ldl_dltsolve_k) (L, Y) ;
+ }
+ else if (sys == CHOLMOD_D)
+ {
+ /* Solve Dx=b */
+ TEMPLATE (ldl_dsolve) (L, Y) ;
+ }
+ }
+}
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/CHOLMOD/Core/License.txt b/CHOLMOD/Core/License.txt
new file mode 100644
index 0000000..51b795e
--- /dev/null
+++ b/CHOLMOD/Core/License.txt
@@ -0,0 +1,25 @@
+CHOLMOD/Core Module. Copyright (C) 2005-2006, Univ. of Florida.
+Author: Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Core module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
diff --git a/CHOLMOD/Core/cholmod_aat.c b/CHOLMOD/Core/cholmod_aat.c
new file mode 100644
index 0000000..7514edf
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_aat.c
@@ -0,0 +1,302 @@
+/* ========================================================================== */
+/* === Core/cholmod_aat ===================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* C = A*A' or C = A(:,f)*A(:,f)'
+ *
+ * A can be packed or unpacked, sorted or unsorted, but must be stored with
+ * both upper and lower parts (A->stype of zero). C is returned as packed,
+ * C->stype of zero (both upper and lower parts present), and unsorted. See
+ * cholmod_ssmult in the MatrixOps Module for a more general matrix-matrix
+ * multiply.
+ *
+ * You can trivially convert C into a symmetric upper/lower matrix by
+ * changing C->stype = 1 or -1 after calling this routine.
+ *
+ * workspace:
+ * Flag (A->nrow),
+ * Iwork (max (A->nrow, A->ncol)) if fset present,
+ * Iwork (A->nrow) if no fset,
+ * W (A->nrow) if mode > 0,
+ * allocates temporary copy for A'.
+ *
+ * A can be pattern or real. Complex or zomplex cases are supported only
+ * if the mode is <= 0 (in which case the numerical values are ignored).
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+cholmod_sparse *CHOLMOD(aat)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* input matrix; C=A*A' is constructed */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag)
+ * -2: pattern only, no diagonal, add 50% + n extra
+ * space to C */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double fjt ;
+ double *Ax, *Fx, *Cx, *W ;
+ Int *Ap, *Anz, *Ai, *Fp, *Fi, *Cp, *Ci, *Flag ;
+ cholmod_sparse *C, *F ;
+ Int packed, j, i, pa, paend, pf, pfend, n, mark, cnz, t, p, values, diag,
+ extra ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->stype)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix cannot be symmetric") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ diag = (mode >= 0) ;
+ n = A->nrow ;
+ CHOLMOD(allocate_work) (n, MAX (A->ncol, A->nrow), values ? n : 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n : 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ;
+
+ /* get the A matrix */
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ packed = A->packed ;
+
+ /* get workspace */
+ W = Common->Xwork ; /* size n, unused if values is FALSE */
+ Flag = Common->Flag ; /* size n, Flag [0..n-1] < mark on input*/
+
+ /* ---------------------------------------------------------------------- */
+ /* F = A' or A(:,f)' */
+ /* ---------------------------------------------------------------------- */
+
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset)*/
+ F = CHOLMOD(ptranspose) (A, values, NULL, fset, fsize, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ Fp = F->p ;
+ Fi = F->i ;
+ Fx = F->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the number of entries in the result C */
+ /* ---------------------------------------------------------------------- */
+
+ cnz = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ /* clear the Flag array */
+ /* mark = CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+
+ /* exclude the diagonal, if requested */
+ if (!diag)
+ {
+ Flag [j] = mark ;
+ }
+
+ /* for each nonzero F(t,j) in column j, do: */
+ pfend = Fp [j+1] ;
+ for (pf = Fp [j] ; pf < pfend ; pf++)
+ {
+ /* F(t,j) is nonzero */
+ t = Fi [pf] ;
+
+ /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */
+ pa = Ap [t] ;
+ paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ;
+ for ( ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ;
+ if (Flag [i] != mark)
+ {
+ Flag [i] = mark ;
+ cnz++ ;
+ }
+ }
+ }
+ if (cnz < 0)
+ {
+ break ; /* integer overflow case */
+ }
+ }
+
+ extra = (mode == -2) ? (cnz/2 + n) : 0 ;
+
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check for integer overflow */
+ /* ---------------------------------------------------------------------- */
+
+ if (cnz < 0 || (cnz + extra) < 0)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ CHOLMOD(clear_flag) (Common) ;
+ CHOLMOD(free_sparse) (&F, Common) ;
+ return (NULL) ; /* problem too large */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate C */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_sparse) (n, n, cnz + extra, FALSE, TRUE, 0,
+ values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&F, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = A*A' */
+ /* ---------------------------------------------------------------------- */
+
+ cnz = 0 ;
+
+ if (values)
+ {
+
+ /* pattern and values */
+ for (j = 0 ; j < n ; j++)
+ {
+ /* clear the Flag array */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* start column j of C */
+ Cp [j] = cnz ;
+
+ /* for each nonzero F(t,j) in column j, do: */
+ pfend = Fp [j+1] ;
+ for (pf = Fp [j] ; pf < pfend ; pf++)
+ {
+ /* F(t,j) is nonzero */
+ t = Fi [pf] ;
+ fjt = Fx [pf] ;
+
+ /* add the nonzero pattern of A(:,t) to the pattern of C(:,j)
+ * and scatter the values into W */
+ pa = Ap [t] ;
+ paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ;
+ for ( ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ;
+ if (Flag [i] != mark)
+ {
+ Flag [i] = mark ;
+ Ci [cnz++] = i ;
+ }
+ W [i] += Ax [pa] * fjt ;
+ }
+ }
+
+ /* gather the values into C(:,j) */
+ for (p = Cp [j] ; p < cnz ; p++)
+ {
+ i = Ci [p] ;
+ Cx [p] = W [i] ;
+ W [i] = 0 ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* pattern only */
+ for (j = 0 ; j < n ; j++)
+ {
+ /* clear the Flag array */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* exclude the diagonal, if requested */
+ if (!diag)
+ {
+ Flag [j] = mark ;
+ }
+
+ /* start column j of C */
+ Cp [j] = cnz ;
+
+ /* for each nonzero F(t,j) in column j, do: */
+ pfend = Fp [j+1] ;
+ for (pf = Fp [j] ; pf < pfend ; pf++)
+ {
+ /* F(t,j) is nonzero */
+ t = Fi [pf] ;
+
+ /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */
+ pa = Ap [t] ;
+ paend = (packed) ? (Ap [t+1]) : (pa + Anz [t]) ;
+ for ( ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ;
+ if (Flag [i] != mark)
+ {
+ Flag [i] = mark ;
+ Ci [cnz++] = i ;
+ }
+ }
+ }
+ }
+ }
+
+ Cp [n] = cnz ;
+ ASSERT (IMPLIES (mode != -2, MAX (1,cnz) == C->nzmax)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* clear workspace and free temporary matrices and return result */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&F, Common) ;
+ CHOLMOD(clear_flag) (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n : 0, Common)) ;
+ DEBUG (i = CHOLMOD(dump_sparse) (C, "aat", Common)) ;
+ ASSERT (IMPLIES (mode < 0, i == 0)) ;
+ return (C) ;
+}
diff --git a/CHOLMOD/Core/cholmod_add.c b/CHOLMOD/Core/cholmod_add.c
new file mode 100644
index 0000000..04eca8b
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_add.c
@@ -0,0 +1,282 @@
+/* ========================================================================== */
+/* === Core/cholmod_add ===================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* C = alpha*A + beta*B, or spones(A+B). Result is packed, with sorted or
+ * unsorted columns. This routine is much faster and takes less memory if C
+ * is allowed to have unsorted columns.
+ *
+ * If A and B are both symmetric (in upper form) then C is the same. Likewise,
+ * if A and B are both symmetric (in lower form) then C is the same.
+ * Otherwise, C is unsymmetric. A and B must have the same dimension.
+ *
+ * workspace: Flag (nrow), W (nrow) if values, Iwork (max (nrow,ncol)).
+ * allocates temporary copies for A and B if they are symmetric.
+ * allocates temporary copy of C if it is to be returned sorted.
+ *
+ * A and B can have an xtype of pattern or real. Complex or zomplex cases
+ * are supported only if the "values" input parameter is FALSE.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+cholmod_sparse *CHOLMOD(add)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to add */
+ cholmod_sparse *B, /* matrix to add */
+ double alpha [2], /* scale factor for A */
+ double beta [2], /* scale factor for B */
+ int values, /* if TRUE compute the numerical values of C */
+ int sorted, /* if TRUE, sort columns of C */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Bx, *Cx, *W ;
+ Int apacked, up, lo, nrow, ncol, bpacked, nzmax, pa, paend, pb, pbend, i,
+ j, p, mark, nz ;
+ Int *Ap, *Ai, *Anz, *Bp, *Bi, *Bnz, *Flag, *Cp, *Ci ;
+ cholmod_sparse *A2, *B2, *C ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_NULL (B, NULL) ;
+ values = values &&
+ (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->nrow != B->nrow || A->ncol != B->ncol)
+ {
+ /* A and B must have the same dimensions */
+ ERROR (CHOLMOD_INVALID, "A and B dimesions do not match") ;
+ return (NULL) ;
+ }
+ /* A and B must have the same numerical type if values is TRUE (both must
+ * be CHOLMOD_REAL, this is implicitly checked above) */
+
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ CHOLMOD(allocate_work) (nrow, MAX (nrow,ncol), values ? nrow : 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow <= 1)
+ {
+ /* C will be implicitly sorted, so no need to sort it here */
+ sorted = FALSE ;
+ }
+
+ /* convert A or B to unsymmetric, if necessary */
+ A2 = NULL ;
+ B2 = NULL ;
+
+ if (A->stype != B->stype)
+ {
+ if (A->stype)
+ {
+ /* workspace: Iwork (max (nrow,ncol)) */
+ A2 = CHOLMOD(copy) (A, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ A = A2 ;
+ }
+ if (B->stype)
+ {
+ /* workspace: Iwork (max (nrow,ncol)) */
+ B2 = CHOLMOD(copy) (B, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+ B = B2 ;
+ }
+ }
+
+ /* get the A matrix */
+ ASSERT (A->stype == B->stype) ;
+ up = (A->stype > 0) ;
+ lo = (A->stype < 0) ;
+
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ apacked = A->packed ;
+
+ /* get the B matrix */
+ Bp = B->p ;
+ Bnz = B->nz ;
+ Bi = B->i ;
+ Bx = B->x ;
+ bpacked = B->packed ;
+
+ /* get workspace */
+ W = Common->Xwork ; /* size nrow, used if values is TRUE */
+ Flag = Common->Flag ; /* size nrow, Flag [0..nrow-1] < mark on input */
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the result C */
+ /* ---------------------------------------------------------------------- */
+
+ /* If integer overflow occurs, nzmax < 0 and the allocate fails properly
+ * (likewise in most other matrix manipulation routines). */
+
+ nzmax = CHOLMOD(nnz) (A, Common) + CHOLMOD(nnz) (B, Common) ;
+
+ C = CHOLMOD(allocate_sparse) (nrow, ncol, nzmax, FALSE, TRUE,
+ SIGN (A->stype), values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute C = alpha*A + beta*B */
+ /* ---------------------------------------------------------------------- */
+
+ nz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Cp [j] = nz ;
+
+ /* clear the Flag array */
+ /* mark = CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+
+ /* scatter B into W */
+ pb = Bp [j] ;
+ pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ;
+ for (p = pb ; p < pbend ; p++)
+ {
+ i = Bi [p] ;
+ if ((up && i > j) || (lo && i < j))
+ {
+ continue ;
+ }
+ Flag [i] = mark ;
+ if (values)
+ {
+ W [i] = beta [0] * Bx [p] ;
+ }
+ }
+
+ /* add A and gather from W into C(:,j) */
+ pa = Ap [j] ;
+ paend = (apacked) ? (Ap [j+1]) : (pa + Anz [j]) ;
+ for (p = pa ; p < paend ; p++)
+ {
+ i = Ai [p] ;
+ if ((up && i > j) || (lo && i < j))
+ {
+ continue ;
+ }
+ Flag [i] = EMPTY ;
+ Ci [nz] = i ;
+ if (values)
+ {
+ Cx [nz] = W [i] + alpha [0] * Ax [p] ;
+ W [i] = 0 ;
+ }
+ nz++ ;
+ }
+
+ /* gather remaining entries into C(:,j), using pattern of B */
+ for (p = pb ; p < pbend ; p++)
+ {
+ i = Bi [p] ;
+ if ((up && i > j) || (lo && i < j))
+ {
+ continue ;
+ }
+ if (Flag [i] == mark)
+ {
+ Ci [nz] = i ;
+ if (values)
+ {
+ Cx [nz] = W [i] ;
+ W [i] = 0 ;
+ }
+ nz++ ;
+ }
+ }
+ }
+
+ Cp [ncol] = nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce C in size and free temporary matrices */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (MAX (1,nz) <= C->nzmax) ;
+ CHOLMOD(reallocate_sparse) (nz, C, Common) ;
+ ASSERT (Common->status >= CHOLMOD_OK) ;
+
+ /* clear the Flag array */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* sort C, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ if (sorted)
+ {
+ /* workspace: Iwork (max (nrow,ncol)) */
+ if (!CHOLMOD(sort) (C, Common))
+ {
+ CHOLMOD(free_sparse) (&C, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (C, "add", Common) >= 0) ;
+ return (C) ;
+}
diff --git a/CHOLMOD/Core/cholmod_band.c b/CHOLMOD/Core/cholmod_band.c
new file mode 100644
index 0000000..2e5f0ac
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_band.c
@@ -0,0 +1,374 @@
+/* ========================================================================== */
+/* === Core/cholmod_band ==================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* C = tril (triu (A,k1), k2)
+ *
+ * C is a matrix consisting of the diagonals of A from k1 to k2.
+ *
+ * k=0 is the main diagonal of A, k=1 is the superdiagonal, k=-1 is the
+ * subdiagonal, and so on. If A is m-by-n, then:
+ *
+ * k1=-m C = tril (A,k2)
+ * k2=n C = triu (A,k1)
+ * k1=0 and k2=0 C = diag(A), except C is a matrix, not a vector
+ *
+ * Values of k1 and k2 less than -m are treated as -m, and values greater
+ * than n are treated as n.
+ *
+ * A can be of any symmetry (upper, lower, or unsymmetric); C is returned in
+ * the same form, and packed. If A->stype > 0, entries in the lower
+ * triangular part of A are ignored, and the opposite is true if
+ * A->stype < 0. If A has sorted columns, then so does C.
+ * C has the same size as A.
+ *
+ * If inplace is TRUE, then the matrix A is modified in place.
+ * Only packed matrices can be converted in place.
+ *
+ * C can be returned as a numerical valued matrix (if A has numerical values
+ * and mode > 0), as a pattern-only (mode == 0), or as a pattern-only but with
+ * the diagonal entries removed (mode < 0).
+ *
+ * workspace: none
+ *
+ * A can have an xtype of pattern or real. Complex and zomplex cases supported
+ * only if mode <= 0 (in which case the numerical values are ignored).
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+static cholmod_sparse *band /* returns C, or NULL if failure */
+(
+ /* ---- input or in/out if inplace is TRUE --- */
+ cholmod_sparse *A,
+ /* ---- input ---- */
+ UF_long k1, /* ignore entries below the k1-st diagonal */
+ UF_long k2, /* ignore entries above the k2-nd diagonal */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diagonal) */
+ int inplace, /* if TRUE, then convert A in place */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Cx ;
+ Int packed, nz, j, p, pend, i, ncol, nrow, jlo, jhi, ilo, ihi, sorted,
+ values, diag ;
+ Int *Ap, *Anz, *Ai, *Cp, *Ci ;
+ cholmod_sparse *C ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ packed = A->packed ;
+ diag = (mode >= 0) ;
+ if (inplace && !packed)
+ {
+ /* cannot operate on an unpacked matrix in place */
+ ERROR (CHOLMOD_INVALID, "cannot operate on unpacked matrix in-place") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+
+ PRINT1 (("k1 %ld k2 %ld\n", k1, k2)) ;
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ sorted = A->sorted ;
+
+
+ if (A->stype > 0)
+ {
+ /* ignore any entries in strictly lower triangular part of A */
+ k1 = MAX (k1, 0) ;
+ }
+ if (A->stype < 0)
+ {
+ /* ignore any entries in strictly upper triangular part of A */
+ k2 = MIN (k2, 0) ;
+ }
+ ncol = A->ncol ;
+ nrow = A->nrow ;
+
+ /* ensure k1 and k2 are in the range -nrow to +ncol to
+ * avoid possible integer overflow if k1 and k2 are huge */
+ k1 = MAX (-nrow, k1) ;
+ k1 = MIN (k1, ncol) ;
+ k2 = MAX (-nrow, k2) ;
+ k2 = MIN (k2, ncol) ;
+
+ /* consider columns jlo to jhi. columns outside this range are empty */
+ jlo = MAX (k1, 0) ;
+ jhi = MIN (k2+nrow, ncol) ;
+
+ if (k1 > k2)
+ {
+ /* nothing to do */
+ jlo = ncol ;
+ jhi = ncol ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate C, or operate on A in place */
+ /* ---------------------------------------------------------------------- */
+
+ if (inplace)
+ {
+ /* convert A in place */
+ C = A ;
+ }
+ else
+ {
+ /* count the number of entries in the result C */
+ nz = 0 ;
+ if (sorted)
+ {
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i > ihi)
+ {
+ break ;
+ }
+ if (i >= ilo && (diag || i != j))
+ {
+ nz++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= ilo && i <= ihi && (diag || i != j))
+ {
+ nz++ ;
+ }
+ }
+ }
+ }
+ /* allocate C; A will not be modified. C is sorted if A is sorted */
+ C = CHOLMOD(allocate_sparse) (A->nrow, ncol, nz, sorted, TRUE,
+ A->stype, values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct C */
+ /* ---------------------------------------------------------------------- */
+
+ /* columns 0 to jlo-1 are empty */
+ for (j = 0 ; j < jlo ; j++)
+ {
+ Cp [j] = 0 ;
+ }
+
+ nz = 0 ;
+ if (sorted)
+ {
+ if (values)
+ {
+ /* pattern and values */
+ ASSERT (diag) ;
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cp [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i > ihi)
+ {
+ break ;
+ }
+ if (i >= ilo)
+ {
+ Ci [nz] = i ;
+ Cx [nz] = Ax [p] ;
+ nz++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* pattern only, perhaps with no diagonal */
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cp [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i > ihi)
+ {
+ break ;
+ }
+ if (i >= ilo && (diag || i != j))
+ {
+ Ci [nz++] = i ;
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ if (values)
+ {
+ /* pattern and values */
+ ASSERT (diag) ;
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cp [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= ilo && i <= ihi)
+ {
+ Ci [nz] = i ;
+ Cx [nz] = Ax [p] ;
+ nz++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* pattern only, perhaps with no diagonal */
+ for (j = jlo ; j < jhi ; j++)
+ {
+ ilo = j-k2 ;
+ ihi = j-k1 ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cp [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= ilo && i <= ihi && (diag || i != j))
+ {
+ Ci [nz++] = i ;
+ }
+ }
+ }
+ }
+ }
+
+ /* columns jhi to ncol-1 are empty */
+ for (j = jhi ; j <= ncol ; j++)
+ {
+ Cp [j] = nz ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce A in size if done in place */
+ /* ---------------------------------------------------------------------- */
+
+ if (inplace)
+ {
+ /* free the unused parts of A, and reduce A->i and A->x in size */
+ ASSERT (MAX (1,nz) <= A->nzmax) ;
+ CHOLMOD(reallocate_sparse) (nz, A, Common) ;
+ ASSERT (Common->status >= CHOLMOD_OK) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result C */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG (i = CHOLMOD(dump_sparse) (C, "band", Common)) ;
+ ASSERT (IMPLIES (mode < 0, i == 0)) ;
+ return (C) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_band ========================================================= */
+/* ========================================================================== */
+
+cholmod_sparse *CHOLMOD(band)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to extract band matrix from */
+ UF_long k1, /* ignore entries below the k1-st diagonal */
+ UF_long k2, /* ignore entries above the k2-nd diagonal */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (band (A, k1, k2, mode, FALSE, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_band_inplace ================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(band_inplace)
+(
+ /* ---- input ---- */
+ UF_long k1, /* ignore entries below the k1-st diagonal */
+ UF_long k2, /* ignore entries above the k2-nd diagonal */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix from which entries not in band are removed */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (band (A, k1, k2, mode, TRUE, Common) != NULL) ;
+}
diff --git a/CHOLMOD/Core/cholmod_change_factor.c b/CHOLMOD/Core/cholmod_change_factor.c
new file mode 100644
index 0000000..cc90b0e
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_change_factor.c
@@ -0,0 +1,1227 @@
+/* ========================================================================== */
+/* === Core/cholmod_change_factor =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Change the numeric/symbolic, LL/LDL, simplicial/super, packed/unpacked,
+ * monotonic/non-monotonic status of a cholmod_factor object.
+ *
+ * There are four basic classes of factor types:
+ *
+ * (1) simplicial symbolic: Consists of two size-n arrays: the fill-reducing
+ * permutation (L->Perm) and the nonzero count for each column of L
+ * (L->ColCount). All other factor types also include this information.
+ * L->ColCount may be exact (obtained from the analysis routines), or
+ * it may be a guess. During factorization, and certainly after update/
+ * downdate, the columns of L can have a different number of nonzeros.
+ * L->ColCount is used to allocate space. L->ColCount is exact for the
+ * supernodal factorizations. The nonzero pattern of L is not kept.
+ *
+ * (2) simplicial numeric: These represent L in a compressed column form. The
+ * variants of this type are:
+ *
+ * LDL': L is unit diagonal. Row indices in column j are located in
+ * L->i [L->p [j] ... L->p [j] + L->nz [j]], and corresponding numeric
+ * values are in the same locations in L->x. The total number of
+ * entries is the sum of L->nz [j]. The unit diagonal is not stored;
+ * D is stored on the diagonal of L instead. L->p may or may not be
+ * monotonic. The order of storage of the columns in L->i and L->x is
+ * given by a doubly-linked list (L->prev and L->next). L->p is of
+ * size n+1, but only the first n entries are used (it is used if L
+ * is converted to a sparse matrix via cholmod_factor_to_sparse).
+ *
+ * For the complex case, L->x is stored interleaved with real/imag
+ * parts, and is of size 2*lnz*sizeof(double). For the zomplex case,
+ * L->x is of size lnz*sizeof(double) and holds the real part; L->z
+ * is the same size and holds the imaginary part.
+ *
+ * LL': This is identical to the LDL' form, except that the non-unit
+ * diagonal of L is stored as the first entry in each column of L.
+ *
+ * (3) supernodal symbolic: A representation of the nonzero pattern of the
+ * supernodes for a supernodal factorization. There are L->nsuper
+ * supernodes. Columns L->super [k] to L->super [k+1]-1 are in the kth
+ * supernode. The row indices for the kth supernode are in
+ * L->s [L->pi [k] ... L->pi [k+1]-1]. The numerical values are not
+ * allocated (L->x), but when they are they will be located in
+ * L->x [L->px [k] ... L->px [k+1]-1], and the L->px array is defined
+ * in this factor type.
+ *
+ * For the complex case, L->x is stored interleaved with real/imag parts,
+ * and is of size 2*L->xsize*sizeof(double). The zomplex supernodal case
+ * is not supported, since it is not compatible with LAPACK and the BLAS.
+ *
+ * (4) supernodal numeric: Always an LL' factorization. L is non-unit
+ * diagonal. L->x contains the numerical values of the supernodes, as
+ * described above for the supernodal symbolic factor.
+ * For the complex case, L->x is stored interleaved, and is of size
+ * 2*L->xsize*sizeof(double). The zomplex supernodal case is not
+ * supported, since it is not compatible with LAPACK and the BLAS.
+ *
+ * FUTURE WORK: support a supernodal LDL' factor.
+ *
+ *
+ * In all cases, the row indices in each column (L->i for simplicial L and
+ * L->s for supernodal L) are kept sorted from low indices to high indices.
+ * This means the diagonal of L (or D for LDL' factors) is always kept as the
+ * first entry in each column.
+ *
+ * The cholmod_change_factor routine can do almost all possible conversions.
+ * It cannot do the following conversions:
+ *
+ * (1) Simplicial numeric types cannot be converted to a supernodal
+ * symbolic type. This would simultaneously deallocate the
+ * simplicial pattern and numeric values and reallocate uninitialized
+ * space for the supernodal pattern. This isn't useful for the user,
+ * and not needed by CHOLMOD's own routines either.
+ *
+ * (2) Only a symbolic factor (simplicial to supernodal) can be converted
+ * to a supernodal numeric factor.
+ *
+ * Some conversions are meant only to be used internally by other CHOLMOD
+ * routines, and should not be performed by the end user. They allocate space
+ * whose contents are undefined:
+ *
+ * (1) converting from simplicial symbolic to supernodal symbolic.
+ * (2) converting any factor to supernodal numeric.
+ *
+ * workspace: no conversion routine uses workspace in Common. No temporary
+ * workspace is allocated.
+ *
+ * Supports all xtypes, except that there is no supernodal zomplex L.
+ *
+ * The to_xtype parameter is used only when converting from symbolic to numeric
+ * or numeric to symbolic. It cannot be used to convert a numeric xtype (real,
+ * complex, or zomplex) to a different numeric xtype. For that conversion,
+ * use cholmod_factor_xtype instead.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+static void natural_list (cholmod_factor *L) ;
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_change_factor.c"
+#define COMPLEX
+#include "t_cholmod_change_factor.c"
+#define ZOMPLEX
+#include "t_cholmod_change_factor.c"
+
+
+/* ========================================================================== */
+/* === L_is_packed ========================================================== */
+/* ========================================================================== */
+
+/* Return TRUE if the columns of L are packed, FALSE otherwise. For debugging
+ * only. */
+
+#ifndef NDEBUG
+static int L_is_packed (cholmod_factor *L, cholmod_common *Common)
+{
+ Int j ;
+ Int *Lnz = L->nz ;
+ Int *Lp = L->p ;
+ Int n = L->n ;
+
+ if (L->xtype == CHOLMOD_PATTERN || L->is_super)
+ {
+ return (TRUE) ;
+ }
+
+ if (Lnz == NULL || Lp == NULL)
+ {
+ return (TRUE) ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ PRINT3 (("j: "ID" Lnz "ID" Lp[j+1] "ID" Lp[j] "ID"\n", j, Lnz [j],
+ Lp [j+1], Lp [j])) ;
+ if (Lnz [j] != (Lp [j+1] - Lp [j]))
+ {
+ PRINT2 (("L is not packed\n")) ;
+ return (FALSE) ;
+ }
+ }
+ return (TRUE) ;
+}
+#endif
+
+
+/* ========================================================================== */
+/* === natural_list ========================================================= */
+/* ========================================================================== */
+
+/* Create a naturally-ordered doubly-linked list of columns. */
+
+static void natural_list (cholmod_factor *L)
+{
+ Int head, tail, n, j ;
+ Int *Lnext, *Lprev ;
+ Lnext = L->next ;
+ Lprev = L->prev ;
+ ASSERT (Lprev != NULL && Lnext != NULL) ;
+ n = L->n ;
+ head = n+1 ;
+ tail = n ;
+ Lnext [head] = 0 ;
+ Lprev [head] = EMPTY ;
+ Lnext [tail] = EMPTY ;
+ Lprev [tail] = n-1 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Lnext [j] = j+1 ;
+ Lprev [j] = j-1 ;
+ }
+ Lprev [0] = head ;
+ L->is_monotonic = TRUE ;
+}
+
+
+/* ========================================================================== */
+/* === allocate_simplicial_numeric ========================================== */
+/* ========================================================================== */
+
+/* Allocate O(n) arrays for simplicial numeric factorization. Initializes
+ * the link lists only. Does not allocate the L->i, L->x, or L->z arrays. */
+
+static int allocate_simplicial_numeric
+(
+ cholmod_factor *L,
+ cholmod_common *Common
+)
+{
+ Int n ;
+ Int *Lp, *Lnz, *Lprev, *Lnext ;
+ size_t n1, n2 ;
+
+ PRINT1 (("Allocate simplicial\n")) ;
+
+ ASSERT (L->xtype == CHOLMOD_PATTERN || L->is_super) ;
+ ASSERT (L->p == NULL) ;
+ ASSERT (L->nz == NULL) ;
+ ASSERT (L->prev == NULL) ;
+ ASSERT (L->next == NULL) ;
+
+ n = L->n ;
+
+ /* this cannot cause size_t overflow */
+ n1 = ((size_t) n) + 1 ;
+ n2 = ((size_t) n) + 2 ;
+
+ Lp = CHOLMOD(malloc) (n1, sizeof (Int), Common) ;
+ Lnz = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+ Lprev = CHOLMOD(malloc) (n2, sizeof (Int), Common) ;
+ Lnext = CHOLMOD(malloc) (n2, sizeof (Int), Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free) (n1, sizeof (Int), Lp, Common) ;
+ CHOLMOD(free) (n, sizeof (Int), Lnz, Common) ;
+ CHOLMOD(free) (n2, sizeof (Int), Lprev, Common) ;
+ CHOLMOD(free) (n2, sizeof (Int), Lnext, Common) ;
+ PRINT1 (("Allocate simplicial failed\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ============================================== commit the changes to L */
+
+ L->p = Lp ;
+ L->nz = Lnz ;
+ L->prev = Lprev ;
+ L->next = Lnext ;
+ /* initialize a doubly linked list for columns in natural order */
+ natural_list (L) ;
+ PRINT1 (("Allocate simplicial done\n")) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === simplicial_symbolic_to_super_symbolic ================================ */
+/* ========================================================================== */
+
+/* Convert a simplicial symbolic factor supernodal symbolic factor. Does not
+ * initialize the new space. */
+
+static int simplicial_symbolic_to_super_symbolic
+(
+ cholmod_factor *L,
+ cholmod_common *Common
+)
+{
+ Int nsuper, xsize, ssize ;
+ Int *Lsuper, *Lpi, *Lpx, *Ls ;
+ size_t nsuper1 ;
+
+ ASSERT (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) ;
+
+ xsize = L->xsize ;
+ ssize = L->ssize ;
+ nsuper = L->nsuper ;
+ nsuper1 = ((size_t) nsuper) + 1 ;
+
+ PRINT1 (("simple sym to super sym: ssize "ID" xsize "ID" nsuper "ID""
+ " status %d\n", ssize, xsize, nsuper, Common->status)) ;
+
+ /* O(nsuper) arrays, where nsuper <= n */
+ Lsuper = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ;
+ Lpi = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ;
+ Lpx = CHOLMOD(malloc) (nsuper1, sizeof (Int), Common) ;
+
+ /* O(ssize) array, where ssize <= nnz(L), and usually much smaller */
+ Ls = CHOLMOD(malloc) (ssize, sizeof (Int), Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free) (nsuper1, sizeof (Int), Lsuper, Common) ;
+ CHOLMOD(free) (nsuper1, sizeof (Int), Lpi, Common) ;
+ CHOLMOD(free) (nsuper1, sizeof (Int), Lpx, Common) ;
+ CHOLMOD(free) (ssize, sizeof (Int), Ls, Common) ;
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ============================================== commit the changes to L */
+
+ ASSERT (Lsuper != NULL && Lpi != NULL && Lpx != NULL && Ls != NULL) ;
+
+ L->maxcsize = 0 ;
+ L->maxesize = 0 ;
+
+ L->super = Lsuper ;
+ L->pi = Lpi ;
+ L->px = Lpx ;
+ L->s = Ls ;
+ Ls [0] = EMPTY ; /* supernodal pattern undefined */
+
+ L->is_super = TRUE ;
+ L->is_ll = TRUE ; /* supernodal LDL' not supported */
+ L->xtype = CHOLMOD_PATTERN ;
+ L->dtype = DTYPE ;
+ L->minor = L->n ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === any_to_simplicial_symbolic =========================================== */
+/* ========================================================================== */
+
+/* Convert any factor L to a simplicial symbolic factor, leaving only L->Perm
+ * and L->ColCount. Cannot fail. Any of the components of L (except Perm and
+ * ColCount) may already be free'd. */
+
+static void any_to_simplicial_symbolic
+(
+ cholmod_factor *L,
+ int to_ll,
+ cholmod_common *Common
+)
+{
+ Int n, lnz, xs, ss, s, e ;
+ size_t n1, n2 ;
+
+ /* ============================================== commit the changes to L */
+
+ n = L->n ;
+ lnz = L->nzmax ;
+ s = L->nsuper + 1 ;
+ xs = (L->is_super) ? ((Int) (L->xsize)) : (lnz) ;
+ e = (L->xtype == CHOLMOD_COMPLEX ? 2 : 1) ;
+ ss = L->ssize ;
+
+ /* this cannot cause size_t overflow */
+ n1 = ((size_t) n) + 1 ;
+ n2 = ((size_t) n) + 2 ;
+
+ /* free all but the symbolic analysis (Perm and ColCount) */
+ L->p = CHOLMOD(free) (n1, sizeof (Int), L->p, Common) ;
+ L->i = CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ;
+ L->x = CHOLMOD(free) (xs, e*sizeof (double), L->x, Common) ;
+ L->z = CHOLMOD(free) (lnz, sizeof (double), L->z, Common) ;
+ L->nz = CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ;
+ L->next = CHOLMOD(free) (n2, sizeof (Int), L->next, Common) ;
+ L->prev = CHOLMOD(free) (n2, sizeof (Int), L->prev, Common) ;
+ L->super = CHOLMOD(free) (s, sizeof (Int), L->super, Common) ;
+ L->pi = CHOLMOD(free) (s, sizeof (Int), L->pi, Common) ;
+ L->px = CHOLMOD(free) (s, sizeof (Int), L->px, Common) ;
+ L->s = CHOLMOD(free) (ss, sizeof (Int), L->s, Common) ;
+ L->nzmax = 0 ;
+ L->is_super = FALSE ;
+ L->xtype = CHOLMOD_PATTERN ;
+ L->dtype = DTYPE ;
+ L->minor = n ;
+ L->is_ll = to_ll ;
+}
+
+
+/* ========================================================================== */
+/* === ll_super_to_super_symbolic =========================================== */
+/* ========================================================================== */
+
+/* Convert a numerical supernodal L to symbolic supernodal. Cannot fail. */
+
+static void ll_super_to_super_symbolic
+(
+ cholmod_factor *L,
+ cholmod_common *Common
+)
+{
+
+ /* ============================================== commit the changes to L */
+
+ /* free all but the supernodal numerical factor */
+ ASSERT (L->xtype != CHOLMOD_PATTERN && L->is_super && L->is_ll) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "start to super symbolic", Common)) ;
+ L->x = CHOLMOD(free) (L->xsize,
+ (L->xtype == CHOLMOD_COMPLEX ? 2 : 1) * sizeof (double), L->x,
+ Common) ;
+ L->xtype = CHOLMOD_PATTERN ;
+ L->dtype = DTYPE ;
+ L->minor = L->n ;
+ L->is_ll = TRUE ; /* supernodal LDL' not supported */
+ DEBUG (CHOLMOD(dump_factor) (L, "done to super symbolic", Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === simplicial_symbolic_to_simplicial_numeric ============================ */
+/* ========================================================================== */
+
+/* Convert a simplicial symbolic L to a simplicial numeric L; allocate space
+ * for L using L->ColCount from symbolic analysis, and set L to identity.
+ *
+ * If packed < 0, then this routine is creating a copy of another factor
+ * (via cholmod_copy_factor). In this case, the space is not initialized. */
+
+static void simplicial_symbolic_to_simplicial_numeric
+(
+ cholmod_factor *L,
+ int to_ll,
+ int packed,
+ int to_xtype,
+ cholmod_common *Common
+)
+{
+ double grow0, grow1, xlen, xlnz ;
+ double *Lx, *Lz ;
+ Int *Li, *Lp, *Lnz, *ColCount ;
+ Int n, grow, grow2, p, j, lnz, len, ok, e ;
+
+ ASSERT (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) ;
+ if (!allocate_simplicial_numeric (L, Common))
+ {
+ PRINT1 (("out of memory, allocate simplicial numeric\n")) ;
+ return ; /* out of memory */
+ }
+ ASSERT (L->ColCount != NULL && L->nz != NULL && L->p != NULL) ;
+ ASSERT (L->x == NULL && L->z == NULL && L->i == NULL) ;
+
+ ColCount = L->ColCount ;
+ Lnz = L->nz ;
+ Lp = L->p ;
+ ok = TRUE ;
+ n = L->n ;
+
+ if (packed < 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* used by cholmod_copy_factor to allocate a copy of a factor object */
+ /* ------------------------------------------------------------------ */
+
+ lnz = L->nzmax ;
+ L->nzmax = 0 ;
+
+ }
+ else if (packed)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* LDL' or LL' packed */
+ /* ------------------------------------------------------------------ */
+
+ PRINT1 (("convert to packed LL' or LDL'\n")) ;
+ lnz = 0 ;
+ for (j = 0 ; ok && j < n ; j++)
+ {
+ /* ensure len is in the range 1 to n-j */
+ len = ColCount [j] ;
+ len = MAX (1, len) ;
+ len = MIN (len, n-j) ;
+ lnz += len ;
+ ok = (lnz >= 0) ;
+ }
+ for (j = 0 ; j <= n ; j++)
+ {
+ Lp [j] = j ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ Lnz [j] = 1 ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* LDL' unpacked */
+ /* ------------------------------------------------------------------ */
+
+ PRINT1 (("convert to unpacked\n")) ;
+ /* compute new lnzmax */
+ /* if any parameter is NaN, grow is false */
+ grow0 = Common->grow0 ;
+ grow1 = Common->grow1 ;
+ grow2 = Common->grow2 ;
+ grow0 = IS_NAN (grow0) ? 1 : grow0 ;
+ grow1 = IS_NAN (grow1) ? 1 : grow1 ;
+ /* fl.pt. compare, but no NaN's: */
+ grow = (grow0 >= 1.0) && (grow1 >= 1.0) && (grow2 > 0) ;
+ PRINT1 (("init, grow1 %g grow2 "ID"\n", grow1, grow2)) ;
+ /* initialize Lp and Lnz for each column */
+ lnz = 0 ;
+ for (j = 0 ; ok && j < n ; j++)
+ {
+ Lp [j] = lnz ;
+ Lnz [j] = 1 ;
+
+ /* ensure len is in the range 1 to n-j */
+ len = ColCount [j] ;
+ len = MAX (1, len) ;
+ len = MIN (len, n-j) ;
+
+ /* compute len in double to avoid integer overflow */
+ PRINT1 (("ColCount ["ID"] = "ID"\n", j, len)) ;
+ if (grow)
+ {
+ xlen = (double) len ;
+ xlen = grow1 * xlen + grow2 ;
+ xlen = MIN (xlen, n-j) ;
+ len = (Int) xlen ;
+ }
+ ASSERT (len >= 1 && len <= n-j) ;
+ lnz += len ;
+ ok = (lnz >= 0) ;
+ }
+ if (ok)
+ {
+ Lp [n] = lnz ;
+ if (grow)
+ {
+ /* add extra space */
+ xlnz = (double) lnz ;
+ xlnz *= grow0 ;
+ xlnz = MIN (xlnz, Size_max) ;
+ xlnz = MIN (xlnz, ((double) n * (double) n + (double) n) / 2) ;
+ lnz = (Int) xlnz ;
+ }
+ }
+ }
+
+ lnz = MAX (1, lnz) ;
+
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ }
+
+ /* allocate L->i, L->x, and L->z */
+ PRINT1 (("resizing from zero size to lnz "ID"\n", lnz)) ;
+ ASSERT (L->nzmax == 0) ;
+ e = (to_xtype == CHOLMOD_COMPLEX ? 2 : 1) ;
+ if (!ok || !CHOLMOD(realloc_multiple) (lnz, 1, to_xtype, &(L->i), NULL,
+ &(L->x), &(L->z), &(L->nzmax), Common))
+ {
+ L->p = CHOLMOD(free) (n+1, sizeof (Int), L->p, Common) ;
+ L->nz = CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ;
+ L->prev = CHOLMOD(free) (n+2, sizeof (Int), L->prev, Common) ;
+ L->next = CHOLMOD(free) (n+2, sizeof (Int), L->next, Common) ;
+ L->i = CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ;
+ L->x = CHOLMOD(free) (lnz, e*sizeof (double), L->x, Common) ;
+ L->z = CHOLMOD(free) (lnz, sizeof (double), L->z, Common) ;
+ PRINT1 (("cannot realloc simplicial numeric\n")) ;
+ return ; /* out of memory */
+ }
+
+ /* ============================================== commit the changes to L */
+
+ /* initialize L to be the identity matrix */
+ L->xtype = to_xtype ;
+ L->dtype = DTYPE ;
+ L->minor = n ;
+
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+
+#if 0
+ if (lnz == 1)
+ {
+ /* the user won't expect to access this entry, but some CHOLMOD
+ * routines may. Set it to zero so that valgrind doesn't complain. */
+ switch (to_xtype)
+ {
+ case CHOLMOD_REAL:
+ Lx [0] = 0 ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ Lx [0] = 0 ;
+ Lx [1] = 0 ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ Lx [0] = 0 ;
+ Lz [0] = 0 ;
+ break ;
+ }
+ }
+#endif
+
+ if (packed >= 0)
+ {
+ /* create the unit diagonal for either the LL' or LDL' case */
+
+ switch (L->xtype)
+ {
+ case CHOLMOD_REAL:
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (Lp [j] < Lp [j+1]) ;
+ p = Lp [j] ;
+ Li [p] = j ;
+ Lx [p] = 1 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (Lp [j] < Lp [j+1]) ;
+ p = Lp [j] ;
+ Li [p] = j ;
+ Lx [2*p ] = 1 ;
+ Lx [2*p+1] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (Lp [j] < Lp [j+1]) ;
+ p = Lp [j] ;
+ Li [p] = j ;
+ Lx [p] = 1 ;
+ Lz [p] = 0 ;
+ }
+ break ;
+ }
+ }
+
+ L->is_ll = to_ll ;
+
+ PRINT1 (("done convert simplicial symbolic to numeric\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === change_simplicial_numeric ============================================ */
+/* ========================================================================== */
+
+/* Change LL' to LDL', LDL' to LL', or leave as-is.
+ *
+ * If to_packed is TRUE, then the columns of L are packed and made monotonic
+ * (to_monotonic is ignored; it is implicitly TRUE).
+ *
+ * If to_monotonic is TRUE but to_packed is FALSE, the columns of L are made
+ * monotonic but not packed.
+ *
+ * If both to_packed and to_monotonic are FALSE, then the columns of L are
+ * left as-is, and the conversion is done in place.
+ *
+ * If L is already monotonic, or if it is to be left non-monotonic, then this
+ * conversion always succeeds.
+ *
+ * When converting an LDL' to LL' factorization, any column with a negative
+ * or zero diagonal entry is not modified so that conversion back to LDL' will
+ * succeed. This can result in a matrix L with a negative entry on the diagonal
+ * If the kth entry on the diagonal of D is negative, it and the kth column of
+ * L are left unchanged. A subsequent conversion back to an LDL' form will also
+ * leave the column unchanged, so the correct LDL' factorization will be
+ * restored. L->minor is set to the smallest k for which D (k,k) is negative.
+ */
+
+static void change_simplicial_numeric
+(
+ cholmod_factor *L,
+ int to_ll,
+ int to_packed,
+ int to_monotonic,
+ cholmod_common *Common
+)
+{
+ double grow0, grow1, xlen, xlnz ;
+ void *newLi, *newLx, *newLz ;
+ double *Lx, *Lz ;
+ Int *Lp, *Li, *Lnz ;
+ Int make_monotonic, grow2, n, j, lnz, len, grow, ok, make_ll, make_ldl ;
+ size_t nzmax0 ;
+
+ PRINT1 (("\n===Change simplicial numeric: %d %d %d\n",
+ to_ll, to_packed, to_monotonic)) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "change simplicial numeric", Common)) ;
+ ASSERT (L->xtype != CHOLMOD_PATTERN && !(L->is_super)) ;
+
+ make_monotonic = ((to_packed || to_monotonic) && !(L->is_monotonic)) ;
+ make_ll = (to_ll && !(L->is_ll)) ;
+ make_ldl = (!to_ll && L->is_ll) ;
+
+ n = L->n ;
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lnz = L->nz ;
+
+ grow = FALSE ;
+ grow0 = Common->grow0 ;
+ grow1 = Common->grow1 ;
+ grow2 = Common->grow2 ;
+ grow0 = IS_NAN (grow0) ? 1 : grow0 ;
+ grow1 = IS_NAN (grow1) ? 1 : grow1 ;
+ ok = TRUE ;
+ newLi = NULL ;
+ newLx = NULL ;
+ newLz = NULL ;
+ lnz = 0 ;
+
+ if (make_monotonic)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Columns out of order, but will be reordered and optionally packed. */
+ /* ------------------------------------------------------------------ */
+
+ PRINT1 (("L is non-monotonic\n")) ;
+
+ /* compute new L->nzmax */
+ if (!to_packed)
+ {
+ /* if any parameter is NaN, grow is false */
+ /* fl.pt. comparisons below are false if any parameter is NaN */
+ grow = (grow0 >= 1.0) && (grow1 >= 1.0) && (grow2 > 0) ;
+ }
+ for (j = 0 ; ok && j < n ; j++)
+ {
+ len = Lnz [j] ;
+ ASSERT (len >= 1 && len <= n-j) ;
+
+ /* compute len in double to avoid integer overflow */
+ if (grow)
+ {
+ xlen = (double) len ;
+ xlen = grow1 * xlen + grow2 ;
+ xlen = MIN (xlen, n-j) ;
+ len = (Int) xlen ;
+ }
+ ASSERT (len >= Lnz [j] && len <= n-j) ;
+
+ PRINT2 (("j: "ID" Lnz[j] "ID" len "ID" p "ID"\n",
+ j, Lnz [j], len, lnz)) ;
+
+ lnz += len ;
+ ok = (lnz >= 0) ;
+ }
+
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return ;
+ }
+
+ if (grow)
+ {
+ xlnz = (double) lnz ;
+ xlnz *= grow0 ;
+ xlnz = MIN (xlnz, Size_max) ;
+ xlnz = MIN (xlnz, ((double) n * (double) n + (double) n) / 2) ;
+ lnz = (Int) xlnz ;
+ }
+
+ lnz = MAX (1, lnz) ;
+ PRINT1 (("final lnz "ID"\n", lnz)) ;
+ nzmax0 = 0 ;
+
+ CHOLMOD(realloc_multiple) (lnz, 1, L->xtype, &newLi, NULL,
+ &newLx, &newLz, &nzmax0, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return ; /* out of memory */
+ }
+ }
+
+ /* ============================================== commit the changes to L */
+
+ /* ---------------------------------------------------------------------- */
+ /* convert the simplicial L, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (L->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ r_change_simplicial_numeric (L, to_ll, to_packed,
+ newLi, newLx, newLz, lnz, grow, grow1, grow2,
+ make_ll, make_monotonic, make_ldl, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ c_change_simplicial_numeric (L, to_ll, to_packed,
+ newLi, newLx, newLz, lnz, grow, grow1, grow2,
+ make_ll, make_monotonic, make_ldl, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ z_change_simplicial_numeric (L, to_ll, to_packed,
+ newLi, newLx, newLz, lnz, grow, grow1, grow2,
+ make_ll, make_monotonic, make_ldl, Common) ;
+ break ;
+ }
+
+ DEBUG (CHOLMOD(dump_factor) (L, "L simplicial changed", Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === ll_super_to_simplicial_numeric ======================================= */
+/* ========================================================================== */
+
+/* Convert a supernodal numeric factorization to any simplicial numeric one.
+ * Leaves L->xtype unchanged (real or complex, not zomplex since there is
+ * no supernodal zomplex L). */
+
+static void ll_super_to_simplicial_numeric
+(
+ cholmod_factor *L,
+ int to_packed,
+ int to_ll,
+ cholmod_common *Common
+)
+{
+ Int *Ls, *Lpi, *Lpx, *Super, *Li ;
+ Int n, lnz, s, nsuper, psi, psend, nsrow, nscol, k1, k2, erows ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "start LL super to simplicial", Common)) ;
+ PRINT1 (("super -> simplicial (%d %d)\n", to_packed, to_ll)) ;
+ ASSERT (L->xtype != CHOLMOD_PATTERN && L->is_ll && L->is_super) ;
+ ASSERT (L->x != NULL && L->i == NULL) ;
+
+ n = L->n ;
+ nsuper = L->nsuper ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Super = L->super ;
+
+ /* Int overflow cannot occur since supernodal L already exists */
+
+ if (to_packed)
+ {
+ /* count the number of nonzeros in L. Each supernode is of the form
+ *
+ * l . . . For this example, nscol = 4 (# columns). nsrow = 9.
+ * l l . . The "." entries are allocated in the supernodal
+ * l l l . factor, but not used. They are not copied to the
+ * l l l l simplicial factor. Some "l" and "e" entries may be
+ * e e e e numerically zero and even symbolically zero if a
+ * e e e e tight simplicial factorization or resymbol were
+ * e e e e done, because of numerical cancellation and relaxed
+ * e e e e supernode amalgamation, respectively.
+ * e e e e
+ */
+ lnz = 0 ;
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ ASSERT (nsrow >= nscol) ;
+ erows = nsrow - nscol ;
+
+ /* lower triangular part, including the diagonal,
+ * counting the "l" terms in the figure above. */
+ lnz += nscol * (nscol+1) / 2 ;
+
+ /* rectangular part, below the diagonal block (the "e" terms) */
+ lnz += nscol * erows ;
+ }
+ ASSERT (lnz <= (Int) (L->xsize)) ;
+ }
+ else
+ {
+ /* Li will be the same size as Lx */
+ lnz = L->xsize ;
+ }
+ ASSERT (lnz >= 0) ;
+ PRINT1 (("simplicial lnz = "ID" to_packed: %d to_ll: %d L->xsize %g\n",
+ lnz, to_ll, to_packed, (double) L->xsize)) ;
+
+ Li = CHOLMOD(malloc) (lnz, sizeof (Int), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return ; /* out of memory */
+ }
+
+ if (!allocate_simplicial_numeric (L, Common))
+ {
+ CHOLMOD(free) (lnz, sizeof (Int), Li, Common) ;
+ return ; /* out of memory */
+ }
+
+ /* ============================================== commit the changes to L */
+
+ L->i = Li ;
+ L->nzmax = lnz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert the supernodal L, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (L->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ r_ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ c_ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ;
+ break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free unused parts of L */
+ /* ---------------------------------------------------------------------- */
+
+ L->super = CHOLMOD(free) (nsuper+1, sizeof (Int), L->super, Common) ;
+ L->pi = CHOLMOD(free) (nsuper+1, sizeof (Int), L->pi, Common) ;
+ L->px = CHOLMOD(free) (nsuper+1, sizeof (Int), L->px, Common) ;
+ L->s = CHOLMOD(free) (L->ssize, sizeof (Int), L->s, Common) ;
+
+ L->ssize = 0 ;
+ L->xsize = 0 ;
+ L->nsuper = 0 ;
+ L->maxesize = 0 ;
+ L->maxcsize = 0 ;
+
+ L->is_super = FALSE ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "done LL super to simplicial", Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === super_symbolic_to_ll_super =========================================== */
+/* ========================================================================== */
+
+/* Convert a supernodal symbolic factorization to a supernodal numeric
+ * factorization by allocating L->x. Contents of L->x are undefined.
+ */
+
+static int super_symbolic_to_ll_super
+(
+ int to_xtype,
+ cholmod_factor *L,
+ cholmod_common *Common
+)
+{
+ double *Lx ;
+ Int wentry = (to_xtype == CHOLMOD_REAL) ? 1 : 2 ;
+ PRINT1 (("convert super sym to num\n")) ;
+ ASSERT (L->xtype == CHOLMOD_PATTERN && L->is_super) ;
+ Lx = CHOLMOD(malloc) (L->xsize, wentry * sizeof (double), Common) ;
+ PRINT1 (("xsize %g\n", (double) L->xsize)) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ============================================== commit the changes to L */
+
+ if (L->xsize == 1)
+ {
+ /* the caller won't expect to access this entry, but some CHOLMOD
+ * routines may. Set it to zero so that valgrind doesn't complain. */
+ switch (to_xtype)
+ {
+ case CHOLMOD_REAL:
+ Lx [0] = 0 ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ Lx [0] = 0 ;
+ Lx [1] = 0 ;
+ break ;
+ }
+ }
+
+ L->x = Lx ;
+ L->xtype = to_xtype ;
+ L->dtype = DTYPE ;
+ L->minor = L->n ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_change_factor ================================================ */
+/* ========================================================================== */
+
+/* Convert a factor L. Some conversions simply allocate uninitialized space
+ * that meant to be filled later.
+ *
+ * If the conversion fails, the factor is left in its original form, with one
+ * exception. Converting a supernodal symbolic factor to a simplicial numeric
+ * one (with L=D=I) may leave the factor in simplicial symbolic form.
+ *
+ * Memory allocated for each conversion is listed below.
+ */
+
+int CHOLMOD(change_factor)
+(
+ /* ---- input ---- */
+ int to_xtype, /* convert to CHOLMOD_PATTERN, _REAL, _COMPLEX, or
+ * _ZOMPLEX */
+ int to_ll, /* TRUE: convert to LL', FALSE: LDL' */
+ int to_super, /* TRUE: convert to supernodal, FALSE: simplicial */
+ int to_packed, /* TRUE: pack simplicial columns, FALSE: do not pack */
+ int to_monotonic, /* TRUE: put simplicial columns in order, FALSE: not */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (to_xtype < CHOLMOD_PATTERN || to_xtype > CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype invalid") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ PRINT1 (("-----convert from (%d,%d,%d,%d,%d) to (%d,%d,%d,%d,%d)\n",
+ L->xtype, L->is_ll, L->is_super, L_is_packed (L, Common), L->is_monotonic,
+ to_xtype, to_ll, to_super, to_packed, to_monotonic)) ;
+
+ /* ensure all parameters are TRUE/FALSE */
+ to_ll = BOOLEAN (to_ll) ;
+ to_super = BOOLEAN (to_super) ;
+
+ ASSERT (BOOLEAN (L->is_ll) == L->is_ll) ;
+ ASSERT (BOOLEAN (L->is_super) == L->is_super) ;
+
+ if (to_super && to_xtype == CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "supernodal zomplex L not supported") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert */
+ /* ---------------------------------------------------------------------- */
+
+ if (to_xtype == CHOLMOD_PATTERN)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert to symbolic */
+ /* ------------------------------------------------------------------ */
+
+ if (!to_super)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* convert any factor into a simplicial symbolic factor */
+ /* -------------------------------------------------------------- */
+
+ any_to_simplicial_symbolic (L, to_ll, Common) ; /* cannot fail */
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* convert to a supernodal symbolic factor */
+ /* -------------------------------------------------------------- */
+
+ if (L->xtype != CHOLMOD_PATTERN && L->is_super)
+ {
+ /* convert from supernodal numeric to supernodal symbolic.
+ * this preserves symbolic pattern of L, discards numeric
+ * values */
+ ll_super_to_super_symbolic (L, Common) ; /* cannot fail */
+ }
+ else if (L->xtype == CHOLMOD_PATTERN && !(L->is_super))
+ {
+ /* convert from simplicial symbolic to supernodal symbolic.
+ * contents of supernodal pattern are uninitialized. Not meant
+ * for the end user. */
+ simplicial_symbolic_to_super_symbolic (L, Common) ;
+ }
+ else
+ {
+ /* cannot convert from simplicial numeric to supernodal
+ * symbolic */
+ ERROR (CHOLMOD_INVALID,
+ "cannot convert L to supernodal symbolic") ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert to numeric */
+ /* ------------------------------------------------------------------ */
+
+ if (to_super)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* convert to supernodal numeric factor */
+ /* -------------------------------------------------------------- */
+
+ if (L->xtype == CHOLMOD_PATTERN)
+ {
+ if (L->is_super)
+ {
+ /* Convert supernodal symbolic to supernodal numeric.
+ * Contents of supernodal numeric values are uninitialized.
+ * This is used by cholmod_super_numeric. Not meant for
+ * the end user. */
+ super_symbolic_to_ll_super (to_xtype, L, Common) ;
+ }
+ else
+ {
+ /* Convert simplicial symbolic to supernodal numeric.
+ * Contents not defined. This is used by
+ * Core/cholmod_copy_factor only. Not meant for the end
+ * user. */
+ if (!simplicial_symbolic_to_super_symbolic (L, Common))
+ {
+ /* failure, convert back to simplicial symbolic */
+ any_to_simplicial_symbolic (L, to_ll, Common) ;
+ }
+ else
+ {
+ /* conversion to super symbolic OK, allocate numeric
+ * part */
+ super_symbolic_to_ll_super (to_xtype, L, Common) ;
+ }
+ }
+ }
+ else
+ {
+ /* nothing to do if L is already in supernodal numeric form */
+ if (!(L->is_super))
+ {
+ ERROR (CHOLMOD_INVALID,
+ "cannot convert simplicial L to supernodal") ;
+ }
+ /* FUTURE WORK: convert to/from supernodal LL' and LDL' */
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* convert any factor to simplicial numeric */
+ /* -------------------------------------------------------------- */
+
+ if (L->xtype == CHOLMOD_PATTERN && !(L->is_super))
+ {
+
+ /* ---------------------------------------------------------- */
+ /* convert simplicial symbolic to simplicial numeric (L=I,D=I)*/
+ /* ---------------------------------------------------------- */
+
+ simplicial_symbolic_to_simplicial_numeric (L, to_ll, to_packed,
+ to_xtype, Common) ;
+
+ }
+ else if (L->xtype != CHOLMOD_PATTERN && L->is_super)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* convert a supernodal LL' to simplicial numeric */
+ /* ---------------------------------------------------------- */
+
+ ll_super_to_simplicial_numeric (L, to_packed, to_ll, Common) ;
+
+ }
+ else if (L->xtype == CHOLMOD_PATTERN && L->is_super)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* convert a supernodal symbolic to simplicial numeric (L=D=I)*/
+ /* ---------------------------------------------------------- */
+
+ any_to_simplicial_symbolic (L, to_ll, Common) ;
+ /* if the following fails, it leaves the factor in simplicial
+ * symbolic form */
+ simplicial_symbolic_to_simplicial_numeric (L, to_ll, to_packed,
+ to_xtype, Common) ;
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* change a simplicial numeric factor */
+ /* ---------------------------------------------------------- */
+
+ /* change LL' to LDL', LDL' to LL', or leave as-is. pack the
+ * columns of L, or leave as-is. Ensure the columns are
+ * monotonic, or leave as-is. */
+
+ change_simplicial_numeric (L, to_ll, to_packed, to_monotonic,
+ Common) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ return (Common->status >= CHOLMOD_OK) ;
+}
diff --git a/CHOLMOD/Core/cholmod_common.c b/CHOLMOD/Core/cholmod_common.c
new file mode 100644
index 0000000..9b00b8d
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_common.c
@@ -0,0 +1,657 @@
+/* ========================================================================== */
+/* === Core/cholmod_common ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_common object:
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_start the first call to CHOLMOD
+ * cholmod_finish the last call to CHOLMOD
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_defaults restore (most) default control parameters
+ * cholmod_allocate_work allocate (or reallocate) workspace in Common
+ * cholmod_free_work free workspace in Common
+ * cholmod_clear_flag clear Common->Flag in workspace
+ * cholmod_maxrank column dimension of Common->Xwork workspace
+ *
+ * The Common object is unique. It cannot be allocated or deallocated by
+ * CHOLMOD, since it contains the definition of the memory management routines
+ * used (pointers to malloc, free, realloc, and calloc, or their equivalent).
+ * The Common object contains workspace that is used between calls to
+ * CHOLMOD routines. This workspace allocated by CHOLMOD as needed, by
+ * cholmod_allocate_work and cholmod_free_work.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+/* ========================================================================== */
+/* === cholmod_start ======================================================== */
+/* ========================================================================== */
+
+/* Initialize Common default parameters and statistics. Sets workspace
+ * pointers to NULL.
+ *
+ * This routine must be called just once, prior to calling any other CHOLMOD
+ * routine. Do not call this routine after any other CHOLMOD routine (except
+ * cholmod_finish, to start a new CHOLMOD session), or a memory leak will
+ * occur.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(start)
+(
+ cholmod_common *Common
+)
+{
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* user error handling routine */
+ /* ---------------------------------------------------------------------- */
+
+ Common->error_handler = NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* integer and numerical types */
+ /* ---------------------------------------------------------------------- */
+
+ Common->itype = ITYPE ;
+ Common->dtype = DTYPE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* default control parameters */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(defaults) (Common) ;
+ Common->try_catch = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* memory management routines */
+ /* ---------------------------------------------------------------------- */
+
+ /* The user can replace cholmod's memory management routines by redefining
+ * these function pointers. */
+
+#ifndef NMALLOC
+ /* stand-alone ANSI C program */
+ Common->malloc_memory = malloc ;
+ Common->free_memory = free ;
+ Common->realloc_memory = realloc ;
+ Common->calloc_memory = calloc ;
+#else
+ /* no memory manager defined at compile-time; MUST define one at run-time */
+ Common->malloc_memory = NULL ;
+ Common->free_memory = NULL ;
+ Common->realloc_memory = NULL ;
+ Common->calloc_memory = NULL ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* complex arithmetic routines */
+ /* ---------------------------------------------------------------------- */
+
+ Common->complex_divide = CHOLMOD(divcomplex) ;
+ Common->hypotenuse = CHOLMOD(hypot) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print routine */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NPRINT
+ /* stand-alone ANSI C program */
+ Common->print_function = printf ;
+#else
+ /* printing disabled */
+ Common->print_function = NULL ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* This code assumes the workspace held in Common is not initialized. If
+ * it is, then a memory leak will occur because the pointers are
+ * overwritten with NULL. */
+
+ Common->nrow = 0 ;
+ Common->mark = EMPTY ;
+ Common->xworksize = 0 ;
+ Common->iworksize = 0 ;
+ Common->Flag = NULL ;
+ Common->Head = NULL ;
+ Common->Iwork = NULL ;
+ Common->Xwork = NULL ;
+ Common->no_workspace_reallocate = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics */
+ /* ---------------------------------------------------------------------- */
+
+ /* fl and lnz are computed in cholmod_analyze and cholmod_rowcolcounts */
+ Common->fl = EMPTY ;
+ Common->lnz = EMPTY ;
+
+ /* modfl is computed in cholmod_updown, cholmod_rowadd, and cholmod_rowdel*/
+ Common->modfl = EMPTY ;
+
+ /* all routines use status as their error-report code */
+ Common->status = CHOLMOD_OK ;
+
+ Common->malloc_count = 0 ; /* # calls to malloc minus # calls to free */
+ Common->memory_usage = 0 ; /* peak memory usage (in bytes) */
+ Common->memory_inuse = 0 ; /* current memory in use (in bytes) */
+
+ Common->nrealloc_col = 0 ;
+ Common->nrealloc_factor = 0 ;
+ Common->ndbounds_hit = 0 ;
+ Common->rowfacfl = 0 ;
+ Common->aatfl = EMPTY ;
+
+ /* Common->called_nd is TRUE if cholmod_analyze called or NESDIS */
+ Common->called_nd = FALSE ;
+
+ DEBUG_INIT ("cholmod start", Common) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_defaults ===================================================== */
+/* ========================================================================== */
+
+/* Set Common default parameters, except for the function pointers.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(defaults)
+(
+ cholmod_common *Common
+)
+{
+ Int i ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* default control parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Common->dbound = 0.0 ;
+ Common->grow0 = 1.2 ;
+ Common->grow1 = 1.2 ;
+ Common->grow2 = 5 ;
+ Common->maxrank = 8 ;
+
+ Common->final_asis = TRUE ;
+ Common->final_super = TRUE ;
+ Common->final_ll = FALSE ;
+ Common->final_pack = TRUE ;
+ Common->final_monotonic = TRUE ;
+ Common->final_resymbol = FALSE ;
+
+ /* use simplicial factorization if flop/nnz(L) < 40, supernodal otherwise */
+ Common->supernodal = CHOLMOD_AUTO ;
+ Common->supernodal_switch = 40 ;
+
+ Common->nrelax [0] = 4 ;
+ Common->nrelax [1] = 16 ;
+ Common->nrelax [2] = 48 ;
+ Common->zrelax [0] = 0.8 ;
+ Common->zrelax [1] = 0.1 ;
+ Common->zrelax [2] = 0.05 ;
+
+ Common->prefer_zomplex = FALSE ;
+ Common->prefer_upper = TRUE ;
+ Common->prefer_binary = FALSE ;
+ Common->quick_return_if_not_posdef = FALSE ;
+
+ /* METIS workarounds */
+ Common->metis_memory = 0.0 ; /* > 0 for memory guard (2 is reasonable) */
+ Common->metis_nswitch = 3000 ;
+ Common->metis_dswitch = 0.66 ;
+
+ Common->print = 3 ;
+ Common->precise = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* default ordering methods */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that if the Partition module is not installed, the CHOLMOD_METIS
+ * and CHOLMOD_NESDIS methods will not be available. cholmod_analyze will
+ * report the CHOLMOD_NOT_INSTALLED error, and safely skip over them.
+ */
+
+#if (CHOLMOD_MAXMETHODS < 9)
+#error "CHOLMOD_MAXMETHODS must be 9 or more (defined in cholmod_core.h)."
+#endif
+
+ /* default strategy: try given, AMD, and then METIS if AMD reports high
+ * fill-in. NESDIS can be used instead, if Common->default_nesdis is TRUE.
+ */
+ Common->nmethods = 0 ; /* use default strategy */
+ Common->default_nesdis = FALSE ; /* use METIS in default strategy */
+
+ Common->current = 0 ; /* current method being tried */
+ Common->selected = 0 ; /* the best method selected */
+
+ /* first, fill each method with default parameters */
+ for (i = 0 ; i <= CHOLMOD_MAXMETHODS ; i++)
+ {
+ /* CHOLMOD's default method is AMD for A or AA' */
+ Common->method [i].ordering = CHOLMOD_AMD ;
+
+ /* CHOLMOD nested dissection and minimum degree parameter */
+ Common->method [i].prune_dense = 10.0 ; /* dense row/col control */
+
+ /* min degree parameters (AMD, COLAMD, SYMAMD, CAMD, CCOLAMD, CSYMAMD)*/
+ Common->method [i].prune_dense2 = -1 ; /* COLAMD dense row control */
+ Common->method [i].aggressive = TRUE ; /* aggressive absorption */
+ Common->method [i].order_for_lu = FALSE ;/* order for Cholesky not LU */
+
+ /* CHOLMOD's nested dissection (METIS + constrained AMD) */
+ Common->method [i].nd_small = 200 ; /* small graphs aren't cut */
+ Common->method [i].nd_compress = TRUE ; /* compress graph & subgraphs */
+ Common->method [i].nd_camd = 1 ; /* use CAMD */
+ Common->method [i].nd_components = FALSE ; /* lump connected comp. */
+ Common->method [i].nd_oksep = 1.0 ; /* sep ok if < oksep*n */
+
+ /* statistics for each method are not yet computed */
+ Common->method [i].fl = EMPTY ;
+ Common->method [i].lnz = EMPTY ;
+ }
+
+ Common->postorder = TRUE ; /* follow ordering with weighted postorder */
+
+ /* Next, define some methods. The first five use default parameters. */
+ Common->method [0].ordering = CHOLMOD_GIVEN ; /* skip if UserPerm NULL */
+ Common->method [1].ordering = CHOLMOD_AMD ;
+ Common->method [2].ordering = CHOLMOD_METIS ;
+ Common->method [3].ordering = CHOLMOD_NESDIS ;
+ Common->method [4].ordering = CHOLMOD_NATURAL ;
+
+ /* CHOLMOD's nested dissection with large leaves of separator tree */
+ Common->method [5].ordering = CHOLMOD_NESDIS ;
+ Common->method [5].nd_small = 20000 ;
+
+ /* CHOLMOD's nested dissection with tiny leaves, and no AMD ordering */
+ Common->method [6].ordering = CHOLMOD_NESDIS ;
+ Common->method [6].nd_small = 4 ;
+ Common->method [6].nd_camd = 0 ; /* no CSYMAMD or CAMD */
+
+ /* CHOLMOD's nested dissection with no dense node removal */
+ Common->method [7].ordering = CHOLMOD_NESDIS ;
+ Common->method [7].prune_dense = -1. ;
+
+ /* COLAMD for A*A', AMD for A */
+ Common->method [8].ordering = CHOLMOD_COLAMD ;
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_finish ======================================================= */
+/* ========================================================================== */
+
+/* The last call to CHOLMOD must be cholmod_finish. You may call this routine
+ * more than once, and can safely call any other CHOLMOD routine after calling
+ * it (including cholmod_start).
+ *
+ * The statistics and parameter settings in Common are preserved. The
+ * workspace in Common is freed. This routine is just another name for
+ * cholmod_free_work.
+ */
+
+int CHOLMOD(finish)
+(
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(free_work) (Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_allocate_work ================================================ */
+/* ========================================================================== */
+
+/* Allocate and initialize workspace for CHOLMOD routines, or increase the size
+ * of already-allocated workspace. If enough workspace is already allocated,
+ * then nothing happens.
+ *
+ * workspace: Flag (nrow), Head (nrow+1), Iwork (iworksize), Xwork (xworksize)
+ */
+
+int CHOLMOD(allocate_work)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows in the matrix A */
+ size_t iworksize, /* size of Iwork */
+ size_t xworksize, /* size of Xwork */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *W ;
+ Int *Head ;
+ Int i ;
+ size_t nrow1 ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Allocate Flag (nrow) and Head (nrow+1) */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = MAX (1, nrow) ;
+
+ /* nrow1 = nrow + 1 */
+ nrow1 = CHOLMOD(add_size_t) (nrow, 1, &ok) ;
+ if (!ok)
+ {
+ /* nrow+1 causes size_t overflow ; problem is too large */
+ Common->status = CHOLMOD_TOO_LARGE ;
+ CHOLMOD(free_work) (Common) ;
+ return (FALSE) ;
+ }
+
+ if (nrow > Common->nrow)
+ {
+
+ if (Common->no_workspace_reallocate)
+ {
+ /* CHOLMOD is not allowed to change the workspace here */
+ Common->status = CHOLMOD_INVALID ;
+ return (FALSE) ;
+ }
+
+ /* free the old workspace (if any) and allocate new space */
+ Common->Flag = CHOLMOD(free) (Common->nrow, sizeof (Int), Common->Flag,
+ Common) ;
+ Common->Head = CHOLMOD(free) (Common->nrow+1,sizeof (Int), Common->Head,
+ Common) ;
+ Common->Flag = CHOLMOD(malloc) (nrow, sizeof (Int), Common) ;
+ Common->Head = CHOLMOD(malloc) (nrow1, sizeof (Int), Common) ;
+
+ /* record the new size of Flag and Head */
+ Common->nrow = nrow ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_work) (Common) ;
+ return (FALSE) ;
+ }
+
+ /* initialize Flag and Head */
+ Common->mark = EMPTY ;
+ CHOLMOD(clear_flag) (Common) ;
+ Head = Common->Head ;
+ for (i = 0 ; i <= (Int) (nrow) ; i++)
+ {
+ Head [i] = EMPTY ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Allocate Iwork (iworksize) */
+ /* ---------------------------------------------------------------------- */
+
+ iworksize = MAX (1, iworksize) ;
+ if (iworksize > Common->iworksize)
+ {
+
+ if (Common->no_workspace_reallocate)
+ {
+ /* CHOLMOD is not allowed to change the workspace here */
+ Common->status = CHOLMOD_INVALID ;
+ return (FALSE) ;
+ }
+
+ /* free the old workspace (if any) and allocate new space.
+ * integer overflow safely detected in cholmod_malloc */
+ CHOLMOD(free) (Common->iworksize, sizeof (Int), Common->Iwork, Common) ;
+ Common->Iwork = CHOLMOD(malloc) (iworksize, sizeof (Int), Common) ;
+
+ /* record the new size of Iwork */
+ Common->iworksize = iworksize ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_work) (Common) ;
+ return (FALSE) ;
+ }
+
+ /* note that Iwork does not need to be initialized */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Allocate Xwork (xworksize) and set it to ((double) 0.) */
+ /* ---------------------------------------------------------------------- */
+
+ /* make sure xworksize is >= 1 */
+ xworksize = MAX (1, xworksize) ;
+ if (xworksize > Common->xworksize)
+ {
+
+ if (Common->no_workspace_reallocate)
+ {
+ /* CHOLMOD is not allowed to change the workspace here */
+ Common->status = CHOLMOD_INVALID ;
+ return (FALSE) ;
+ }
+
+ /* free the old workspace (if any) and allocate new space */
+ CHOLMOD(free) (Common->xworksize, sizeof (double), Common->Xwork,
+ Common) ;
+ Common->Xwork = CHOLMOD(malloc) (xworksize, sizeof (double), Common) ;
+
+ /* record the new size of Xwork */
+ Common->xworksize = xworksize ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_work) (Common) ;
+ return (FALSE) ;
+ }
+
+ /* initialize Xwork */
+ W = Common->Xwork ;
+ for (i = 0 ; i < (Int) xworksize ; i++)
+ {
+ W [i] = 0. ;
+ }
+ }
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_free_work ==================================================== */
+/* ========================================================================== */
+
+/* Deallocate the CHOLMOD workspace.
+ *
+ * workspace: deallocates all workspace in Common
+ */
+
+int CHOLMOD(free_work)
+(
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->Flag = CHOLMOD(free) (Common->nrow, sizeof (Int),
+ Common->Flag, Common) ;
+ Common->Head = CHOLMOD(free) (Common->nrow+1, sizeof (Int),
+ Common->Head, Common) ;
+ Common->Iwork = CHOLMOD(free) (Common->iworksize, sizeof (Int),
+ Common->Iwork, Common) ;
+ Common->Xwork = CHOLMOD(free) (Common->xworksize, sizeof (double),
+ Common->Xwork, Common) ;
+ Common->nrow = 0 ;
+ Common->iworksize = 0 ;
+ Common->xworksize = 0 ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_clear_flag =================================================== */
+/* ========================================================================== */
+
+/* Increment mark to ensure Flag [0..nrow-1] < mark. If integer overflow
+ * occurs, or mark was initially negative, reset the entire array. This is
+ * not an error condition, but an intended function of the Flag workspace.
+ *
+ * workspace: Flag (nrow). Does not modify Flag if nrow is zero.
+ */
+
+UF_long CHOLMOD(clear_flag)
+(
+ cholmod_common *Common
+)
+{
+ Int i, nrow, *Flag ;
+
+ RETURN_IF_NULL_COMMON (-1) ;
+
+ Common->mark++ ;
+ if (Common->mark <= 0)
+ {
+ nrow = Common->nrow ;
+ Flag = Common->Flag ;
+ PRINT2 (("reset Flag: nrow "ID"\n", nrow)) ;
+ PRINT2 (("reset Flag: mark %ld\n", Common->mark)) ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Flag [i] = EMPTY ;
+ }
+ Common->mark = 0 ;
+ }
+ return (Common->mark) ;
+}
+
+
+/* ========================================================================== */
+/* ==== cholmod_maxrank ===================================================== */
+/* ========================================================================== */
+
+/* Find a valid value of Common->maxrank. Returns 0 if error, or 2, 4, or 8
+ * if successful. */
+
+size_t CHOLMOD(maxrank) /* returns validated value of Common->maxrank */
+(
+ /* ---- input ---- */
+ size_t n, /* A and L will have n rows */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ size_t maxrank ;
+ RETURN_IF_NULL_COMMON (0) ;
+ maxrank = Common->maxrank ;
+ if (n > 0)
+ {
+ /* Ensure maxrank*n*sizeof(double) does not result in integer overflow.
+ * If n is so large that 2*n*sizeof(double) results in integer overflow
+ * (n = 268,435,455 if an Int is 32 bits), then maxrank will be 0 or 1,
+ * but maxrank will be set to 2 below. 2*n will not result in integer
+ * overflow, and CHOLMOD will run out of memory or safely detect integer
+ * overflow elsewhere.
+ */
+ maxrank = MIN (maxrank, Size_max / (n * sizeof (double))) ;
+ }
+ if (maxrank <= 2)
+ {
+ maxrank = 2 ;
+ }
+ else if (maxrank <= 4)
+ {
+ maxrank = 4 ;
+ }
+ else
+ {
+ maxrank = 8 ;
+ }
+ return (maxrank) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dbound ======================================================= */
+/* ========================================================================== */
+
+/* Ensure the absolute value of a diagonal entry, D (j,j), is greater than
+ * Common->dbound. This routine is not meant for the user to call. It is used
+ * by the various LDL' factorization and update/downdate routines. The
+ * default value of Common->dbound is zero, and in that case this routine is not
+ * called at all. No change is made if D (j,j) is NaN. CHOLMOD does not call
+ * this routine if Common->dbound is NaN.
+ */
+
+double CHOLMOD(dbound) /* returns modified diagonal entry of D */
+(
+ /* ---- input ---- */
+ double dj, /* diagonal entry of D, for LDL' factorization */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double dbound ;
+ RETURN_IF_NULL_COMMON (0) ;
+ if (!IS_NAN (dj))
+ {
+ dbound = Common->dbound ;
+ if (dj < 0)
+ {
+ if (dj > -dbound)
+ {
+ dj = -dbound ;
+ Common->ndbounds_hit++ ;
+ if (Common->status == CHOLMOD_OK)
+ {
+ ERROR (CHOLMOD_DSMALL, "diagonal below threshold") ;
+ }
+ }
+ }
+ else
+ {
+ if (dj < dbound)
+ {
+ dj = dbound ;
+ Common->ndbounds_hit++ ;
+ if (Common->status == CHOLMOD_OK)
+ {
+ ERROR (CHOLMOD_DSMALL, "diagonal below threshold") ;
+ }
+ }
+ }
+ }
+ return (dj) ;
+}
diff --git a/CHOLMOD/Core/cholmod_complex.c b/CHOLMOD/Core/cholmod_complex.c
new file mode 100644
index 0000000..8bef584
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_complex.c
@@ -0,0 +1,547 @@
+/* ========================================================================== */
+/* === Core/cholmod_complex ================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* If you convert a matrix that contains uninitialized data, valgrind will
+ * complain. This can occur in a factor L which has gaps (a partial
+ * factorization, or after updates that change the nonzero pattern), an
+ * unpacked sparse matrix, a dense matrix with leading dimension d > # of rows,
+ * or any matrix (dense, sparse, triplet, or factor) with more space allocated
+ * than is used. You can safely ignore any of these complaints by valgrind. */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+/* ========================================================================== */
+/* === cholmod_hypot ======================================================== */
+/* ========================================================================== */
+
+/* There is an equivalent routine called hypot in <math.h>, which conforms
+ * to ANSI C99. However, CHOLMOD does not assume that ANSI C99 is available.
+ * You can use the ANSI C99 hypot routine with:
+ *
+ * #include <math.h>
+ * Common->hypotenuse = hypot ;
+ *
+ * Default value of the Common->hypotenuse pointer is cholmod_hypot.
+ *
+ * s = hypot (x,y) computes s = sqrt (x*x + y*y) but does so more accurately.
+ * The NaN cases for the double relops x >= y and x+y == x are safely ignored.
+ */
+
+double CHOLMOD(hypot) (double x, double y)
+{
+ double s, r ;
+ x = fabs (x) ;
+ y = fabs (y) ;
+ if (x >= y)
+ {
+ if (x + y == x)
+ {
+ s = x ;
+ }
+ else
+ {
+ r = y / x ;
+ s = x * sqrt (1.0 + r*r) ;
+ }
+ }
+ else
+ {
+ if (y + x == y)
+ {
+ s = y ;
+ }
+ else
+ {
+ r = x / y ;
+ s = y * sqrt (1.0 + r*r) ;
+ }
+ }
+ return (s) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_divcomplex =================================================== */
+/* ========================================================================== */
+
+/* c = a/b where c, a, and b are complex. The real and imaginary parts are
+ * passed as separate arguments to this routine. The NaN case is ignored
+ * for the double relop br >= bi. Returns 1 if the denominator is zero,
+ * 0 otherwise. Note that this return value is the single exception to the
+ * rule that all CHOLMOD routines that return int return TRUE if successful
+ * or FALSE otherise.
+ *
+ * This uses ACM Algo 116, by R. L. Smith, 1962, which tries to avoid
+ * underflow and overflow.
+ *
+ * c can be the same variable as a or b.
+ *
+ * Default value of the Common->complex_divide pointer is cholmod_divcomplex.
+ */
+
+int CHOLMOD(divcomplex)
+(
+ double ar, double ai, /* real and imaginary parts of a */
+ double br, double bi, /* real and imaginary parts of b */
+ double *cr, double *ci /* real and imaginary parts of c */
+)
+{
+ double tr, ti, r, den ;
+ if (fabs (br) >= fabs (bi))
+ {
+ r = bi / br ;
+ den = br + r * bi ;
+ tr = (ar + ai * r) / den ;
+ ti = (ai - ar * r) / den ;
+ }
+ else
+ {
+ r = br / bi ;
+ den = r * br + bi ;
+ tr = (ar * r + ai) / den ;
+ ti = (ai * r - ar) / den ;
+ }
+ *cr = tr ;
+ *ci = ti ;
+ return (IS_ZERO (den)) ;
+}
+
+
+/* ========================================================================== */
+/* === change_complexity ==================================================== */
+/* ========================================================================== */
+
+/* X and Z represent an array of size nz, with numeric xtype given by xtype_in.
+ *
+ * If xtype_in is:
+ * CHOLMOD_PATTERN: X and Z must be NULL.
+ * CHOLMOD_REAL: X is of size nz, Z must be NULL.
+ * CHOLMOD_COMPLEX: X is of size 2*nz, Z must be NULL.
+ * CHOLMOD_ZOMPLEX: X is of size nz, Z is of size nz.
+ *
+ * The array is changed into the numeric xtype given by xtype_out, with the
+ * same definitions of X and Z above. Note that the input conditions, above,
+ * are not checked. These are checked in the caller routine.
+ *
+ * Returns TRUE if successful, FALSE otherwise. X and Z are not modified if
+ * not successful.
+ */
+
+static int change_complexity
+(
+ /* ---- input ---- */
+ Int nz, /* size of X and/or Z */
+ int xtype_in, /* xtype of X and Z on input */
+ int xtype_out, /* requested xtype of X and Z on output */
+ int xtype1, /* xtype_out must be in the range [xtype1 .. xtype2] */
+ int xtype2,
+ /* ---- in/out --- */
+ void **XX, /* old X on input, new X on output */
+ void **ZZ, /* old Z on input, new Z on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Xold, *Zold, *Xnew, *Znew ;
+ Int k ;
+ size_t nz2 ;
+
+ if (xtype_out < xtype1 || xtype_out > xtype2)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid xtype") ;
+ return (FALSE) ;
+ }
+
+ Common->status = CHOLMOD_OK ;
+ Xold = *XX ;
+ Zold = *ZZ ;
+
+ switch (xtype_in)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* converting from pattern */
+ /* ------------------------------------------------------------------ */
+
+ case CHOLMOD_PATTERN:
+
+ switch (xtype_out)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* pattern -> real */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_REAL:
+ /* allocate X and set to all ones */
+ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [k] = 1 ;
+ }
+ *XX = Xnew ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* pattern -> complex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_COMPLEX:
+ /* allocate X and set to all ones */
+ Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [2*k ] = 1 ;
+ Xnew [2*k+1] = 0 ;
+ }
+ *XX = Xnew ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* pattern -> zomplex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_ZOMPLEX:
+ /* allocate X and Z and set to all ones */
+ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free) (nz, sizeof (double), Xnew, Common) ;
+ CHOLMOD(free) (nz, sizeof (double), Znew, Common) ;
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [k] = 1 ;
+ Znew [k] = 0 ;
+ }
+ *XX = Xnew ;
+ *ZZ = Znew ;
+ break ;
+ }
+ break ;
+
+ /* ------------------------------------------------------------------ */
+ /* converting from real */
+ /* ------------------------------------------------------------------ */
+
+ case CHOLMOD_REAL:
+
+ switch (xtype_out)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* real -> pattern */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_PATTERN:
+ /* free X */
+ *XX = CHOLMOD(free) (nz, sizeof (double), *XX, Common) ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* real -> complex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_COMPLEX:
+ /* allocate a new X and copy the old X */
+ Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [2*k ] = Xold [k] ;
+ Xnew [2*k+1] = 0 ;
+ }
+ CHOLMOD(free) (nz, sizeof (double), *XX, Common) ;
+ *XX = Xnew ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* real -> zomplex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_ZOMPLEX:
+ /* allocate a new Z and set it to zero */
+ Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Znew [k] = 0 ;
+ }
+ *ZZ = Znew ;
+ break ;
+ }
+ break ;
+
+ /* ------------------------------------------------------------------ */
+ /* converting from complex */
+ /* ------------------------------------------------------------------ */
+
+ case CHOLMOD_COMPLEX:
+
+ switch (xtype_out)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* complex -> pattern */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_PATTERN:
+ /* free X */
+ *XX = CHOLMOD(free) (nz, 2*sizeof (double), *XX, Common) ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* complex -> real */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_REAL:
+ /* pack the real part of X, discarding the imaginary part */
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xold [k] = Xold [2*k] ;
+ }
+ /* shrink X in half (this cannot fail) */
+ nz2 = 2*nz ;
+ *XX = CHOLMOD(realloc) (nz, sizeof (double), *XX, &nz2,
+ Common) ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* complex -> zomplex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_ZOMPLEX:
+ /* allocate X and Z and copy the old X into them */
+ Xnew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ Znew = CHOLMOD(malloc) (nz, sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free) (nz, sizeof (double), Xnew, Common) ;
+ CHOLMOD(free) (nz, sizeof (double), Znew, Common) ;
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [k] = Xold [2*k ] ;
+ Znew [k] = Xold [2*k+1] ;
+ }
+ CHOLMOD(free) (nz, 2*sizeof (double), *XX, Common) ;
+ *XX = Xnew ;
+ *ZZ = Znew ;
+ break ;
+ }
+ break ;
+
+ /* ------------------------------------------------------------------ */
+ /* converting from zomplex */
+ /* ------------------------------------------------------------------ */
+
+ case CHOLMOD_ZOMPLEX:
+
+ switch (xtype_out)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* zomplex -> pattern */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_PATTERN:
+ /* free X and Z */
+ *XX = CHOLMOD(free) (nz, sizeof (double), *XX, Common) ;
+ *ZZ = CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* zomplex -> real */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_REAL:
+ /* free the imaginary part */
+ *ZZ = CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ;
+ break ;
+
+ /* ---------------------------------------------------------- */
+ /* zomplex -> complex */
+ /* ---------------------------------------------------------- */
+
+ case CHOLMOD_COMPLEX:
+ Xnew = CHOLMOD(malloc) (nz, 2*sizeof (double), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Xnew [2*k ] = Xold [k] ;
+ Xnew [2*k+1] = Zold [k] ;
+ }
+ CHOLMOD(free) (nz, sizeof (double), *XX, Common) ;
+ CHOLMOD(free) (nz, sizeof (double), *ZZ, Common) ;
+ *XX = Xnew ;
+ *ZZ = NULL ;
+ break ;
+
+ }
+ break ;
+ }
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_sparse_xtype ================================================= */
+/* ========================================================================== */
+
+/* Change the numeric xtype of a sparse matrix. Supports any type on input
+ * and output (pattern, real, complex, or zomplex). */
+
+int CHOLMOD(sparse_xtype)
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* sparse matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int ok ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+
+ ok = change_complexity (A->nzmax, A->xtype, to_xtype,
+ CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, &(A->x), &(A->z), Common) ;
+ if (ok)
+ {
+ A->xtype = to_xtype ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_triplet_xtype ================================================ */
+/* ========================================================================== */
+
+/* Change the numeric xtype of a triplet matrix. Supports any type on input
+ * and output (pattern, real, complex, or zomplex). */
+
+int CHOLMOD(triplet_xtype)
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype */
+ /* ---- in/out --- */
+ cholmod_triplet *T, /* triplet matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int ok ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (T, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ ok = change_complexity (T->nzmax, T->xtype, to_xtype,
+ CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, &(T->x), &(T->z), Common) ;
+ if (ok)
+ {
+ T->xtype = to_xtype ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dense_xtype ================================================= */
+/* ========================================================================== */
+
+/* Change the numeric xtype of a dense matrix. Supports real, complex or
+ * zomplex on input and output */
+
+int CHOLMOD(dense_xtype)
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype */
+ /* ---- in/out --- */
+ cholmod_dense *X, /* dense matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int ok ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (X, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ ok = change_complexity (X->nzmax, X->xtype, to_xtype,
+ CHOLMOD_REAL, CHOLMOD_ZOMPLEX, &(X->x), &(X->z), Common) ;
+ if (ok)
+ {
+ X->xtype = to_xtype ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_factor_xtype ================================================= */
+/* ========================================================================== */
+
+/* Change the numeric xtype of a factor. Supports real, complex or zomplex on
+ * input and output. Supernodal zomplex factors are not supported. */
+
+int CHOLMOD(factor_xtype)
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to change */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int ok ;
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (L->is_super &&
+ (L->xtype == CHOLMOD_ZOMPLEX || to_xtype == CHOLMOD_ZOMPLEX))
+ {
+ ERROR (CHOLMOD_INVALID, "invalid xtype for supernodal L") ;
+ return (FALSE) ;
+ }
+ ok = change_complexity ((L->is_super ? L->xsize : L->nzmax), L->xtype,
+ to_xtype, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, &(L->x), &(L->z), Common) ;
+ if (ok)
+ {
+ L->xtype = to_xtype ;
+ }
+ return (ok) ;
+}
diff --git a/CHOLMOD/Core/cholmod_copy.c b/CHOLMOD/Core/cholmod_copy.c
new file mode 100644
index 0000000..d4532ad
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_copy.c
@@ -0,0 +1,407 @@
+/* ========================================================================== */
+/* === Core/cholmod_copy ==================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* C = A, which allocates C and copies A into C, with possible change of
+ * stype. The diagonal can optionally be removed. The numerical entries
+ * can optionally be copied. This routine differs from cholmod_copy_sparse,
+ * which makes an exact copy of a sparse matrix.
+ *
+ * A can be of any type (packed/unpacked, upper/lower/unsymmetric). C is
+ * packed and can be of any stype (upper/lower/unsymmetric), except that if
+ * A is rectangular C can only be unsymmetric. If the stype of A and C
+ * differ, then the appropriate conversion is made.
+ *
+ * Symmetry of A (A->stype):
+ * <0: lower: assume A is symmetric with just tril(A); the rest of A is ignored
+ * 0 unsym: assume A is unsymmetric; consider all entries in A
+ * >0 upper: assume A is symmetric with just triu(A); the rest of A is ignored
+ *
+ * Symmetry of C (stype parameter):
+ * <0 lower: return just tril(C)
+ * 0 unsym: return all of C
+ * >0 upper: return just triu(C)
+ *
+ * In MATLAB: Using cholmod_copy:
+ * ---------- ----------------------------
+ * C = A ; A unsymmetric, C unsymmetric
+ * C = tril (A) ; A unsymmetric, C lower
+ * C = triu (A) ; A unsymmetric, C upper
+ * U = triu (A) ; L = tril (U',-1) ; C = L+U ; A upper, C unsymmetric
+ * C = triu (A)' ; A upper, C lower
+ * C = triu (A) ; A upper, C upper
+ * L = tril (A) ; U = triu (L',1) ; C = L+U ; A lower, C unsymmetric
+ * C = tril (A) ; A lower, C lower
+ * C = tril (A)' ; A lower, C upper
+ *
+ * workspace: Iwork (max (nrow,ncol))
+ *
+ * A can have an xtype of pattern or real. Complex and zomplex cases only
+ * supported when mode <= 0 (in which case the numerical values are ignored).
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+
+/* ========================================================================== */
+/* === copy_sym_to_unsym ==================================================== */
+/* ========================================================================== */
+
+/* Construct an unsymmetric copy of a symmetric sparse matrix. This does the
+ * work for as C = cholmod_copy (A, 0, mode, Common) when A is symmetric.
+ * In this case, extra space can be added to C.
+ */
+
+static cholmod_sparse *copy_sym_to_unsym
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag)
+ * -2: pattern only, no diagonal, add 50% + n extra
+ * space to C */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double aij ;
+ double *Ax, *Cx ;
+ Int *Ap, *Ai, *Anz, *Cp, *Ci, *Wj, *Iwork ;
+ cholmod_sparse *C ;
+ Int nrow, ncol, nz, packed, j, p, pend, i, pc, up, lo, values, diag,
+ astype, extra ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ packed = A->packed ;
+ values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ;
+ diag = (mode >= 0) ;
+
+ astype = SIGN (A->stype) ;
+ up = (astype > 0) ;
+ lo = (astype < 0) ;
+ ASSERT (astype != 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create an unsymmetric copy of a symmetric matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Wj = Iwork ; /* size ncol (i/i/l) */
+
+ /* In MATLAB notation, for converting a symmetric/upper matrix:
+ * U = triu (A) ;
+ * L = tril (U',-1) ;
+ * C = L + U ;
+ *
+ * For converting a symmetric/lower matrix to unsymmetric:
+ * L = tril (A) ;
+ * U = triu (L',1) ;
+ * C = L + U ;
+ */
+ ASSERT (up || lo) ;
+ PRINT1 (("copy: convert symmetric to unsym\n")) ;
+
+ /* count the number of entries in each column of C */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Wj [j] = 0 ;
+ }
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i == j)
+ {
+ /* the diagonal entry A(i,i) will appear just once
+ * (unless it is excluded with mode < 0) */
+ if (diag)
+ {
+ Wj [j]++ ;
+ }
+ }
+ else if ((up && i < j) || (lo && i > j))
+ {
+ /* upper case: A(i,j) is in the strictly upper part;
+ * A(j,i) will be added to the strictly lower part of C.
+ * lower case is the opposite. */
+ Wj [j]++ ;
+ Wj [i]++ ;
+ }
+ }
+ }
+ nz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ nz += Wj [j] ;
+ }
+
+ extra = (mode == -2) ? (nz/2 + ncol) : 0 ;
+
+ /* allocate C. C is sorted if and only if A is sorted */
+ C = CHOLMOD(allocate_sparse) (nrow, ncol, nz + extra, A->sorted, TRUE, 0,
+ values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ;
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* construct the column pointers for C */
+ p = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Cp [j] = p ;
+ p += Wj [j] ;
+ }
+ Cp [ncol] = p ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Wj [j] = Cp [j] ;
+ }
+
+ /* construct C */
+ if (values)
+ {
+
+ /* pattern and values */
+ ASSERT (diag) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ aij = Ax [p] ;
+ if (i == j)
+ {
+ /* add diagonal entry A(i,i) to column i */
+ pc = Wj [i]++ ;
+ Ci [pc] = i ;
+ Cx [pc] = aij ;
+ }
+ else if ((up && i < j) || (lo && i > j))
+ {
+ /* add A(i,j) to column j */
+ pc = Wj [j]++ ;
+ Ci [pc] = i ;
+ Cx [pc] = aij ;
+ /* add A(j,i) to column i */
+ pc = Wj [i]++ ;
+ Ci [pc] = j ;
+ Cx [pc] = aij ;
+ }
+ }
+ }
+
+ }
+ else
+ {
+
+ /* pattern only, possibly excluding the diagonal */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i == j)
+ {
+ /* add diagonal entry A(i,i) to column i
+ * (unless it is excluded with mode < 0) */
+ if (diag)
+ {
+ Ci [Wj [i]++] = i ;
+ }
+ }
+ else if ((up && i < j) || (lo && i > j))
+ {
+ /* add A(i,j) to column j */
+ Ci [Wj [j]++] = i ;
+ /* add A(j,i) to column i */
+ Ci [Wj [i]++] = j ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG (i = CHOLMOD(dump_sparse) (C, "copy_sym_to_unsym", Common)) ;
+ PRINT1 (("mode %d nnzdiag "ID"\n", mode, i)) ;
+ ASSERT (IMPLIES (mode < 0, i == 0)) ;
+ return (C) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy ========================================================= */
+/* ========================================================================== */
+
+cholmod_sparse *CHOLMOD(copy)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ int stype, /* requested stype of C */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *C ;
+ Int nrow, ncol, up, lo, values, diag, astype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ values = (mode > 0) && (A->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ if ((stype || A->stype) && nrow != ncol)
+ {
+ /* inputs invalid */
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(allocate_work) (0, MAX (nrow,ncol), 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ diag = (mode >= 0) ;
+ astype = SIGN (A->stype) ;
+ stype = SIGN (stype) ;
+ up = (astype > 0) ;
+ lo = (astype < 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (astype == stype)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* symmetry of A and C are the same */
+ /* ------------------------------------------------------------------ */
+
+ /* copy A into C, keeping the same symmetry. If A is symmetric
+ * entries in the ignored part of A are not copied into C */
+ C = CHOLMOD(band) (A, -nrow, ncol, mode, Common) ;
+
+ }
+ else if (!astype)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert unsymmetric matrix A into a symmetric matrix C */
+ /* ------------------------------------------------------------------ */
+
+ if (stype > 0)
+ {
+ /* C = triu (A) */
+ C = CHOLMOD(band) (A, 0, ncol, mode, Common) ;
+ }
+ else
+ {
+ /* C = tril (A) */
+ C = CHOLMOD(band) (A, -nrow, 0, mode, Common) ;
+ }
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+ C->stype = stype ;
+
+ }
+ else if (astype == -stype)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* transpose a symmetric matrix */
+ /* ------------------------------------------------------------------ */
+
+ /* converting upper to lower or lower to upper */
+ /* workspace: Iwork (nrow) */
+ C = CHOLMOD(transpose) (A, values, Common) ;
+ if (!diag)
+ {
+ /* remove diagonal, if requested */
+ CHOLMOD(band_inplace) (-nrow, ncol, -1, C, Common) ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* create an unsymmetric copy of a symmetric matrix */
+ /* ------------------------------------------------------------------ */
+
+ C = copy_sym_to_unsym (A, mode, Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return if error */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG (diag = CHOLMOD(dump_sparse) (C, "copy", Common)) ;
+ PRINT1 (("mode %d nnzdiag "ID"\n", mode, diag)) ;
+ ASSERT (IMPLIES (mode < 0, diag == 0)) ;
+ return (C) ;
+}
diff --git a/CHOLMOD/Core/cholmod_dense.c b/CHOLMOD/Core/cholmod_dense.c
new file mode 100644
index 0000000..57cb6de
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_dense.c
@@ -0,0 +1,640 @@
+/* ========================================================================== */
+/* === Core/cholmod_dense =================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_dense object:
+ *
+ * The solve routines and some of the MatrixOps and Modify routines use dense
+ * matrices as inputs. These are held in column-major order. With a leading
+ * dimension of d, the entry in row i and column j is held in x [i+j*d].
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_allocate_dense allocate a dense matrix
+ * cholmod_free_dense free a dense matrix
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_zeros allocate a dense matrix of all zeros
+ * cholmod_ones allocate a dense matrix of all ones
+ * cholmod_eye allocate a dense identity matrix
+ * cholmod_sparse_to_dense create a dense matrix copy of a sparse matrix
+ * cholmod_dense_to_sparse create a sparse matrix copy of a dense matrix
+ * cholmod_copy_dense create a copy of a dense matrix
+ * cholmod_copy_dense2 copy a dense matrix (pre-allocated)
+ *
+ * All routines in this file can handle the real, complex, and zomplex cases.
+ * Pattern-only dense matrices are not supported. cholmod_sparse_to_dense can
+ * take a pattern-only input sparse matrix, however, and cholmod_dense_to_sparse
+ * can generate a pattern-only output sparse matrix.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define PATTERN
+#include "t_cholmod_dense.c"
+#define REAL
+#include "t_cholmod_dense.c"
+#define COMPLEX
+#include "t_cholmod_dense.c"
+#define ZOMPLEX
+#include "t_cholmod_dense.c"
+
+
+/* ========================================================================== */
+/* === cholmod_allocate_dense =============================================== */
+/* ========================================================================== */
+
+/* Allocate a dense matrix with leading dimension d. The space is not
+ * initialized.
+ */
+
+cholmod_dense *CHOLMOD(allocate_dense)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ size_t d, /* leading dimension */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X ;
+ size_t nzmax, nzmax0 ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (d < nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "leading dimension invalid") ;
+ return (NULL) ;
+ }
+ if (xtype < CHOLMOD_REAL || xtype > CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype invalid") ;
+ return (NULL) ;
+ }
+
+ /* ensure the dimensions do not cause integer overflow */
+ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ;
+
+ /* nzmax = MAX (1, d*ncol) ; */
+ nzmax = CHOLMOD(mult_size_t) (d, ncol, &ok) ;
+ nzmax = MAX (1, nzmax) ;
+
+ if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate header */
+ /* ---------------------------------------------------------------------- */
+
+ X = CHOLMOD(malloc) (sizeof (cholmod_dense), 1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ PRINT1 (("cholmod_allocate_dense %d-by-%d nzmax %d xtype %d\n",
+ nrow, ncol, nzmax, xtype)) ;
+
+ X->nrow = nrow ;
+ X->ncol = ncol ;
+ X->nzmax = nzmax ;
+ X->xtype = xtype ;
+ X->dtype = DTYPE ;
+ X->x = NULL ;
+ X->z = NULL ;
+ X->d = d ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the matrix itself */
+ /* ---------------------------------------------------------------------- */
+
+ nzmax0 = 0 ;
+ CHOLMOD(realloc_multiple) (nzmax, 0, xtype, NULL, NULL, &(X->x), &(X->z),
+ &nzmax0, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_dense) (&X, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_zeros ======================================================== */
+/* ========================================================================== */
+
+/* Allocate a dense matrix and set it to zero */
+
+cholmod_dense *CHOLMOD(zeros)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X ;
+ double *Xx, *Xz ;
+ Int i, nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate a dense matrix and set it to zero */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ X = CHOLMOD(allocate_dense) (nrow, ncol, nrow, xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* NULL Common, out of memory, or inputs invalid */
+ }
+
+ Xx = X->x ;
+ Xz = X->z ;
+ nz = MAX (1, X->nzmax) ;
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [i] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < 2*nz ; i++)
+ {
+ Xx [i] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [i] = 0 ;
+ }
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xz [i] = 0 ;
+ }
+ break ;
+ }
+
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_ones ========================================================= */
+/* ========================================================================== */
+
+/* Allocate a dense matrix and set it to zero */
+
+cholmod_dense *CHOLMOD(ones)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X ;
+ double *Xx, *Xz ;
+ Int i, nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate a dense matrix and set it to all ones */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ X = CHOLMOD(allocate_dense) (nrow, ncol, nrow, xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* NULL Common, out of memory, or inputs invalid */
+ }
+
+ Xx = X->x ;
+ Xz = X->z ;
+ nz = MAX (1, X->nzmax) ;
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [i] = 1 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [2*i ] = 1 ;
+ Xx [2*i+1] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [i] = 1 ;
+ }
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xz [i] = 0 ;
+ }
+ break ;
+ }
+
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_eye ========================================================== */
+/* ========================================================================== */
+
+/* Allocate a dense matrix and set it to the identity matrix */
+
+cholmod_dense *CHOLMOD(eye)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X ;
+ double *Xx, *Xz ;
+ Int i, n, nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate a dense matrix and set it to the identity matrix */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ X = CHOLMOD(zeros) (nrow, ncol, xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* NULL Common, out of memory, or inputs invalid */
+ }
+
+ nz = MAX (1, nrow*ncol) ;
+ Xx = X->x ;
+ Xz = X->z ;
+
+ n = MIN (nrow, ncol) ;
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i + i*nrow] = 1 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [2 * (i + i*nrow)] = 1 ;
+ }
+ break ;
+ }
+
+ return (X) ;
+}
+
+/* ========================================================================== */
+/* === cholmod_free_dense =================================================== */
+/* ========================================================================== */
+
+/* free a dense matrix
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(free_dense)
+(
+ /* ---- in/out --- */
+ cholmod_dense **XHandle, /* dense matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ if (XHandle == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ X = *XHandle ;
+ if (X == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ switch (X->xtype)
+ {
+ case CHOLMOD_REAL:
+ X->x = CHOLMOD(free) (X->nzmax, sizeof (double), X->x, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ X->x = CHOLMOD(free) (X->nzmax, 2*sizeof (double), X->x, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ X->x = CHOLMOD(free) (X->nzmax, sizeof (double), X->x, Common) ;
+ X->z = CHOLMOD(free) (X->nzmax, sizeof (double), X->z, Common) ;
+ break ;
+ }
+
+ *XHandle = CHOLMOD(free) (1, sizeof (cholmod_dense), (*XHandle), Common) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_sparse_to_dense ============================================== */
+/* ========================================================================== */
+
+/* Convert a sparse matrix to a dense matrix.
+ * The output dense matrix has the same xtype as the input sparse matrix,
+ * except that a pattern-only sparse matrix A is converted into a real dense
+ * matrix X, with 1's and 0's. All xtypes are supported.
+ */
+
+cholmod_dense *CHOLMOD(sparse_to_dense)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *X = NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->stype && A->nrow != A->ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert the matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_PATTERN:
+ X = p_cholmod_sparse_to_dense (A, Common) ;
+ break ;
+
+ case CHOLMOD_REAL:
+ X = r_cholmod_sparse_to_dense (A, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ X = c_cholmod_sparse_to_dense (A, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ X = z_cholmod_sparse_to_dense (A, Common) ;
+ break ;
+ }
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_dense_to_sparse ============================================== */
+/* ========================================================================== */
+
+/* Convert a dense matrix to a sparse matrix, similar to the MATLAB statements:
+ *
+ * C = sparse (X) values = TRUE
+ * C = spones (sparse (X)) values = FALSE
+ *
+ * except that X must be double (it can be of many different types in MATLAB)
+ *
+ * The resulting sparse matrix C has the same numeric xtype as the input dense
+ * matrix X, unless "values" is FALSE (in which case C is real, where C(i,j)=1
+ * if (i,j) is an entry in X.
+ */
+
+cholmod_sparse *CHOLMOD(dense_to_sparse)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ int values, /* TRUE if values to be copied, FALSE otherwise */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *C = NULL ;
+
+ DEBUG (CHOLMOD(dump_dense) (X, "X", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (X, NULL) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ if (X->d < X->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert the matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (X->xtype)
+ {
+ case CHOLMOD_REAL:
+ C = r_cholmod_dense_to_sparse (X, values, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ C = c_cholmod_dense_to_sparse (X, values, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ C = z_cholmod_dense_to_sparse (X, values, Common) ;
+ break ;
+ }
+ return (C) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy_dense2 ================================================== */
+/* ========================================================================== */
+
+/* Y = X, where X and Y are both already allocated. The leading dimensions of
+ * X and Y may differ, but both must be >= the # of rows in X and Y.
+ * Entries in rows nrow to d-1 are not copied from X, since the space might not
+ * be initialized. Y->nzmax is unchanged. X->nzmax is typically
+ * (X->d)*(X->ncol), but a user might modify that condition outside of any
+ * CHOLMOD routine.
+ *
+ * The two dense matrices X and Y must have the same numeric xtype.
+ */
+
+int CHOLMOD(copy_dense2)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ /* ---- output --- */
+ cholmod_dense *Y, /* copy of matrix X */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (X, FALSE) ;
+ RETURN_IF_NULL (Y, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (Y, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (X->nrow != Y->nrow || X->ncol != Y->ncol || X->xtype != Y->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "X and Y must have same dimensions and xtype") ;
+ return (FALSE) ;
+ }
+ if (X->d < X->nrow || Y->d < Y->nrow
+ || (X->d * X->ncol) > X->nzmax || (Y->d * Y->ncol) > Y->nzmax)
+ {
+ ERROR (CHOLMOD_INVALID, "X and/or Y invalid") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (X->xtype)
+ {
+ case CHOLMOD_REAL:
+ r_cholmod_copy_dense2 (X, Y) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ c_cholmod_copy_dense2 (X, Y) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ z_cholmod_copy_dense2 (X, Y) ;
+ break ;
+ }
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy_dense =================================================== */
+/* ========================================================================== */
+
+/* Y = X, copy a dense matrix */
+
+cholmod_dense *CHOLMOD(copy_dense)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *Y ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (X, NULL) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate result */
+ /* ---------------------------------------------------------------------- */
+
+ Y = CHOLMOD(allocate_dense) (X->nrow, X->ncol, X->d, X->xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory or X invalid */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Y = X */
+ /* ---------------------------------------------------------------------- */
+
+ /* This cannot fail (X and Y are allocated, and have the same nrow, ncol
+ * d, and xtype) */
+ CHOLMOD(copy_dense2) (X, Y, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ return (Y) ;
+}
diff --git a/CHOLMOD/Core/cholmod_error.c b/CHOLMOD/Core/cholmod_error.c
new file mode 100644
index 0000000..b1e5d4c
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_error.c
@@ -0,0 +1,80 @@
+/* ========================================================================== */
+/* === Core/cholmod_error =================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD error-handling routine. */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+/* ========================================================================== */
+/* ==== cholmod_error ======================================================= */
+/* ========================================================================== */
+
+/* An error has occurred. Set the status, optionally print an error message,
+ * and call the user error-handling routine (if it exists). If
+ * Common->try_catch is TRUE, then CHOLMOD is inside a try/catch block.
+ * The status is set, but no message is printed and the user error handler
+ * is not called. This is not (yet) an error, since CHOLMOD may recover.
+ *
+ * In the current version, this try/catch mechanism is used internally only in
+ * cholmod_analyze, which tries multiple ordering methods and picks the best
+ * one. If one or more ordering method fails, it keeps going. Only one
+ * ordering needs to succeed for cholmod_analyze to succeed.
+ */
+
+int CHOLMOD(error)
+(
+ /* ---- input ---- */
+ int status, /* error status */
+ char *file, /* name of source code file where error occured */
+ int line, /* line number in source code file where error occured*/
+ char *message, /* error message */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ Common->status = status ;
+
+ if (!(Common->try_catch))
+ {
+
+#ifndef NPRINT
+ /* print a warning or error message */
+ if (Common->print_function != NULL)
+ {
+ if (status > 0 && Common->print > 1)
+ {
+ (Common->print_function) ("CHOLMOD warning: %s\n", message) ;
+ fflush (stdout) ;
+ fflush (stderr) ;
+ }
+ else if (Common->print > 0)
+ {
+ (Common->print_function) ("CHOLMOD error: %s\n", message) ;
+ fflush (stdout) ;
+ fflush (stderr) ;
+ }
+ }
+#endif
+
+ /* call the user error handler, if it exists */
+ if (Common->error_handler != NULL)
+ {
+ Common->error_handler (status, file, line, message) ;
+ }
+ }
+
+ return (TRUE) ;
+}
diff --git a/CHOLMOD/Core/cholmod_factor.c b/CHOLMOD/Core/cholmod_factor.c
new file mode 100644
index 0000000..0185ce4
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_factor.c
@@ -0,0 +1,935 @@
+/* ========================================================================== */
+/* === Core/cholmod_factor ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_factor object:
+ *
+ * The data structure for an LL' or LDL' factorization is too complex to
+ * describe in one sentence. This object can hold the symbolic analysis alone,
+ * or in combination with a "simplicial" (similar to a sparse matrix) or
+ * "supernodal" form of the numerical factorization. Only the routine to free
+ * a factor is primary, since a factor object is created by the factorization
+ * routine (cholmod_factorize). It must be freed with cholmod_free_factor.
+ *
+ * Primary routine:
+ * ----------------
+ * cholmod_free_factor free a factor
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_allocate_factor allocate a symbolic factor (LL' or LDL')
+ * cholmod_reallocate_factor change the # entries in a factor
+ * cholmod_change_factor change the type of factor (e.g., LDL' to LL')
+ * cholmod_pack_factor pack the columns of a factor
+ * cholmod_reallocate_column resize a single column of a factor
+ * cholmod_factor_to_sparse create a sparse matrix copy of a factor
+ * cholmod_copy_factor create a copy of a factor
+ *
+ * Note that there is no cholmod_sparse_to_factor routine to create a factor
+ * as a copy of a sparse matrix. It could be done, after a fashion, but a
+ * lower triangular sparse matrix would not necessarily have a chordal graph,
+ * which would break the many CHOLMOD routines that rely on this property.
+ *
+ * The cholmod_factor_to_sparse routine is provided so that matrix operations
+ * in the MatrixOps module may be applied to L. Those operations operate on
+ * cholmod_sparse objects, and they are not guaranteed to maintain the chordal
+ * property of L. Such a modified L cannot be safely converted back to a
+ * cholmod_factor object.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+
+/* ========================================================================== */
+/* === cholmod_allocate_factor ============================================== */
+/* ========================================================================== */
+
+/* Allocate a simplicial symbolic factor, with L->Perm and L->ColCount allocated
+ * and initialized to "empty" values (Perm [k] = k, and ColCount[k] = 1).
+ * The integer and numerical parts of L are not allocated. L->xtype is returned
+ * as CHOLMOD_PATTERN and L->is_super are returned as FALSE. L->is_ll is also
+ * returned FALSE, but this may be modified when the matrix is factorized.
+ *
+ * This is sufficient (but far from ideal) for input to cholmod_factorize,
+ * since the simplicial LL' or LDL' factorization (cholmod_rowfac) can
+ * reallocate the columns of L as needed. The primary purpose of this routine
+ * is to allocate space for a symbolic factorization, for the "expert" user to
+ * do his or her own symbolic analysis. The typical user should use
+ * cholmod_analyze instead of this routine.
+ *
+ * workspace: none
+ */
+
+cholmod_factor *CHOLMOD(allocate_factor)
+(
+ /* ---- input ---- */
+ size_t n, /* L is n-by-n */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int j ;
+ Int *Perm, *ColCount ;
+ cholmod_factor *L ;
+ int ok = TRUE ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ensure the dimension does not cause integer overflow */
+ (void) CHOLMOD(add_size_t) (n, 2, &ok) ;
+ if (!ok || n > Int_max)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+
+ L = CHOLMOD(malloc) (sizeof (cholmod_factor), 1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ L->n = n ;
+ L->is_ll = FALSE ;
+ L->is_super = FALSE ;
+ L->is_monotonic = TRUE ;
+ L->itype = ITYPE ;
+ L->xtype = CHOLMOD_PATTERN ;
+ L->dtype = DTYPE ;
+
+ /* allocate the purely symbolic part of L */
+ L->ordering = CHOLMOD_NATURAL ;
+ L->Perm = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+ L->ColCount = CHOLMOD(malloc) (n, sizeof (Int), Common) ;
+
+ /* simplicial part of L is empty */
+ L->nzmax = 0 ;
+ L->p = NULL ;
+ L->i = NULL ;
+ L->x = NULL ;
+ L->z = NULL ;
+ L->nz = NULL ;
+ L->next = NULL ;
+ L->prev = NULL ;
+
+ /* supernodal part of L is also empty */
+ L->nsuper = 0 ;
+ L->ssize = 0 ;
+ L->xsize = 0 ;
+ L->maxesize = 0 ;
+ L->maxcsize = 0 ;
+ L->super = NULL ;
+ L->pi = NULL ;
+ L->px = NULL ;
+ L->s = NULL ;
+
+ /* L has not been factorized */
+ L->minor = n ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_factor) (&L, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ /* initialize Perm and ColCount */
+ Perm = L->Perm ;
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ Perm [j] = j ;
+ }
+ ColCount = L->ColCount ;
+ for (j = 0 ; j < ((Int) n) ; j++)
+ {
+ ColCount [j] = 1 ;
+ }
+
+ return (L) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_free_factor ================================================== */
+/* ========================================================================== */
+
+/* Free a factor object.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(free_factor)
+(
+ /* ---- in/out --- */
+ cholmod_factor **LHandle, /* factor to free, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int n, lnz, xs, ss, s ;
+ cholmod_factor *L ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ if (LHandle == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ L = *LHandle ;
+ if (L == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ n = L->n ;
+ lnz = L->nzmax ;
+ s = L->nsuper + 1 ;
+ xs = (L->is_super) ? ((Int) (L->xsize)) : (lnz) ;
+ ss = L->ssize ;
+
+ /* symbolic part of L */
+ CHOLMOD(free) (n, sizeof (Int), L->Perm, Common) ;
+ CHOLMOD(free) (n, sizeof (Int), L->ColCount, Common) ;
+
+ /* simplicial form of L */
+ CHOLMOD(free) (n+1, sizeof (Int), L->p, Common) ;
+ CHOLMOD(free) (lnz, sizeof (Int), L->i, Common) ;
+ CHOLMOD(free) (n, sizeof (Int), L->nz, Common) ;
+ CHOLMOD(free) (n+2, sizeof (Int), L->next, Common) ;
+ CHOLMOD(free) (n+2, sizeof (Int), L->prev, Common) ;
+
+ /* supernodal form of L */
+ CHOLMOD(free) (s, sizeof (Int), L->pi, Common) ;
+ CHOLMOD(free) (s, sizeof (Int), L->px, Common) ;
+ CHOLMOD(free) (s, sizeof (Int), L->super, Common) ;
+ CHOLMOD(free) (ss, sizeof (Int), L->s, Common) ;
+
+ /* numerical values for both simplicial and supernodal L */
+ if (L->xtype == CHOLMOD_REAL)
+ {
+ CHOLMOD(free) (xs, sizeof (double), L->x, Common) ;
+ }
+ else if (L->xtype == CHOLMOD_COMPLEX)
+ {
+ CHOLMOD(free) (xs, 2*sizeof (double), L->x, Common) ;
+ }
+ else if (L->xtype == CHOLMOD_ZOMPLEX)
+ {
+ CHOLMOD(free) (xs, sizeof (double), L->x, Common) ;
+ CHOLMOD(free) (xs, sizeof (double), L->z, Common) ;
+ }
+
+ *LHandle = CHOLMOD(free) (1, sizeof (cholmod_factor), (*LHandle), Common) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_reallocate_factor ============================================ */
+/* ========================================================================== */
+
+/* Change the size of L->i and L->x, or allocate them if their current size
+ * is zero. L must be simplicial.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(reallocate_factor)
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ PRINT1 (("realloc factor: xtype %d\n", L->xtype)) ;
+ if (L->is_super)
+ {
+ /* L must be simplicial, and not symbolic */
+ ERROR (CHOLMOD_INVALID, "L invalid") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ PRINT1 (("realloc factor %g to %g\n", (double) L->nzmax, (double) nznew)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* resize (or allocate) the L->i and L->x components of the factor */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(realloc_multiple) (nznew, 1, L->xtype, &(L->i), NULL,
+ &(L->x), &(L->z), &(L->nzmax), Common) ;
+ return (Common->status == CHOLMOD_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_reallocate_column =========================================== */
+/* ========================================================================== */
+
+/* Column j needs more space, reallocate it at the end of L->i and L->x.
+ * If the reallocation fails, the factor is converted to a simplicial
+ * symbolic factor (no pattern, just L->Perm and L->ColCount).
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(reallocate_column)
+(
+ /* ---- input ---- */
+ size_t j, /* the column to reallocate */
+ size_t need, /* required size of column j */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double xneed ;
+ double *Lx, *Lz ;
+ Int *Lp, *Lprev, *Lnext, *Li, *Lnz ;
+ Int n, pold, pnew, len, k, tail ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (L->is_super)
+ {
+ ERROR (CHOLMOD_INVALID, "L must be simplicial") ;
+ return (FALSE) ;
+ }
+ n = L->n ;
+ if (j >= L->n || need == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "j invalid") ;
+ return (FALSE) ; /* j out of range */
+ }
+ Common->status = CHOLMOD_OK ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "start colrealloc", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* increase the size of L if needed */
+ /* ---------------------------------------------------------------------- */
+
+ /* head = n+1 ; */
+ tail = n ;
+ Lp = L->p ;
+ Lnz = L->nz ;
+ Lprev = L->prev ;
+ Lnext = L->next ;
+
+ ASSERT (Lnz != NULL) ;
+ ASSERT (Lnext != NULL && Lprev != NULL) ;
+ PRINT1 (("col %g need %g\n", (double) j, (double) need)) ;
+
+ /* column j cannot have more than n-j entries if all entries are present */
+ need = MIN (need, n-j) ;
+
+ /* compute need in double to avoid integer overflow */
+ if (Common->grow1 >= 1.0)
+ {
+ xneed = (double) need ;
+ xneed = Common->grow1 * xneed + Common->grow2 ;
+ xneed = MIN (xneed, n-j) ;
+ need = (Int) xneed ;
+ }
+ PRINT1 (("really new need %g current %g\n", (double) need,
+ (double) (Lp [Lnext [j]] - Lp [j]))) ;
+ ASSERT (need >= 1 && need <= n-j) ;
+
+ if (Lp [Lnext [j]] - Lp [j] >= (Int) need)
+ {
+ /* no need to reallocate the column, it's already big enough */
+ PRINT1 (("colrealloc: quick return %g %g\n",
+ (double) (Lp [Lnext [j]] - Lp [j]), (double) need)) ;
+ return (TRUE) ;
+
+ }
+
+ if (Lp [tail] + need > L->nzmax)
+ {
+ /* use double to avoid integer overflow */
+ xneed = (double) need ;
+ if (Common->grow0 < 1.2) /* fl. pt. compare, false if NaN */
+ {
+ /* if grow0 is less than 1.2 or NaN, don't use it */
+ xneed = 1.2 * (((double) L->nzmax) + xneed + 1) ;
+ }
+ else
+ {
+ xneed = Common->grow0 * (((double) L->nzmax) + xneed + 1) ;
+ }
+ if (xneed > Size_max ||
+ !CHOLMOD(reallocate_factor) ((Int) xneed, L, Common))
+ {
+ /* out of memory, convert to simplicial symbolic */
+ CHOLMOD(change_factor) (CHOLMOD_PATTERN, L->is_ll, FALSE, TRUE,
+ TRUE, L, Common) ;
+ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory; L now symbolic") ;
+ return (FALSE) ; /* out of memory */
+ }
+ PRINT1 (("\n=== GROW L from %g to %g\n",
+ (double) L->nzmax, (double) xneed)) ;
+ /* pack all columns so that each column has at most grow2 free space */
+ CHOLMOD(pack_factor) (L, Common) ;
+ ASSERT (Common->status == CHOLMOD_OK) ;
+ Common->nrealloc_factor++ ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* reallocate the column */
+ /* ---------------------------------------------------------------------- */
+
+ Common->nrealloc_col++ ;
+
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+
+ /* remove j from its current position in the list */
+ Lnext [Lprev [j]] = Lnext [j] ;
+ Lprev [Lnext [j]] = Lprev [j] ;
+
+ /* place j at the end of the list */
+ Lnext [Lprev [tail]] = j ;
+ Lprev [j] = Lprev [tail] ;
+ Lnext [j] = n ;
+ Lprev [tail] = j ;
+
+ /* L is no longer monotonic; columns are out-of-order */
+ L->is_monotonic = FALSE ;
+
+ /* allocate space for column j */
+ pold = Lp [j] ;
+ pnew = Lp [tail] ;
+ Lp [j] = pnew ;
+ Lp [tail] += need ;
+
+ /* copy column j to the new space */
+ len = Lnz [j] ;
+ for (k = 0 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ }
+
+ if (L->xtype == CHOLMOD_REAL)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [pnew + k] = Lx [pold + k] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_COMPLEX)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [2*(pnew + k) ] = Lx [2*(pold + k) ] ;
+ Lx [2*(pnew + k)+1] = Lx [2*(pold + k)+1] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_ZOMPLEX)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [pnew + k] = Lx [pold + k] ;
+ Lz [pnew + k] = Lz [pold + k] ;
+ }
+ }
+
+ DEBUG (CHOLMOD(dump_factor) (L, "colrealloc done", Common)) ;
+
+ /* successful reallocation of column j of L */
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_pack_factor ================================================== */
+/* ========================================================================== */
+
+/* Pack the columns of a simplicial LDL' or LL' factor. This can be followed
+ * by a call to cholmod_reallocate_factor to reduce the size of L to the exact
+ * size required by the factor, if desired. Alternatively, you can leave the
+ * size of L->i and L->x the same, to allow space for future updates/rowadds.
+ *
+ * Each column is reduced in size so that it has at most Common->grow2 free
+ * space at the end of the column.
+ *
+ * Does nothing and returns silently if given any other type of factor.
+ *
+ * Does NOT force the columns of L to be monotonic. It thus differs from
+ * cholmod_change_factor (xtype, -, FALSE, TRUE, TRUE, L, Common), which
+ * packs the columns and ensures that they appear in monotonic order.
+ */
+
+int CHOLMOD(pack_factor)
+(
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Lx, *Lz ;
+ Int *Lp, *Li, *Lnz, *Lnext ;
+ Int pnew, j, k, pold, len, n, head, tail, grow2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ DEBUG (CHOLMOD(dump_factor) (L, "start pack", Common)) ;
+ PRINT1 (("PACK factor %d\n", L->is_super)) ;
+
+ if (L->xtype == CHOLMOD_PATTERN || L->is_super)
+ {
+ /* nothing to do unless L is simplicial numeric */
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* pack */
+ /* ---------------------------------------------------------------------- */
+
+ grow2 = Common->grow2 ;
+ PRINT1 (("\nPACK grow2 "ID"\n", grow2)) ;
+
+ pnew = 0 ;
+ n = L->n ;
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lnz = L->nz ;
+ Lnext = L->next ;
+
+ head = n+1 ;
+ tail = n ;
+
+ for (j = Lnext [head] ; j != tail ; j = Lnext [j])
+ {
+ /* pack column j */
+ pold = Lp [j] ;
+ len = Lnz [j] ;
+ ASSERT (len > 0) ;
+ PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ;
+ if (pnew < pold)
+ {
+ PRINT2 ((" pack this column\n")) ;
+
+ for (k = 0 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ }
+
+ if (L->xtype == CHOLMOD_REAL)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [pnew + k] = Lx [pold + k] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_COMPLEX)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [2*(pnew + k) ] = Lx [2*(pold + k) ] ;
+ Lx [2*(pnew + k)+1] = Lx [2*(pold + k)+1] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_ZOMPLEX)
+ {
+ for (k = 0 ; k < len ; k++)
+ {
+ Lx [pnew + k] = Lx [pold + k] ;
+ Lz [pnew + k] = Lz [pold + k] ;
+ }
+ }
+
+ Lp [j] = pnew ;
+ }
+ len = MIN (len + grow2, n - j) ;
+ pnew = MIN (Lp [j] + len, Lp [Lnext [j]]) ;
+ }
+ PRINT2 (("final pnew = "ID"\n", pnew)) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_factor_to_sparse ============================================= */
+/* ========================================================================== */
+
+/* Constructs a column-oriented sparse matrix containing the pattern and values
+ * of a simplicial or supernodal numerical factor, and then converts the factor
+ * into a simplicial symbolic factor. If L is already packed, monotonic,
+ * and simplicial (which is the case when cholmod_factorize uses the simplicial
+ * Cholesky factorization algorithm) then this routine requires only O(1)
+ * memory and takes O(1) time.
+ *
+ * Only operates on numeric factors (real, complex, or zomplex). Does not
+ * change the numeric L->xtype (the resulting sparse matrix has the same xtype
+ * as L). If this routine fails, L is left unmodified.
+ */
+
+cholmod_sparse *CHOLMOD(factor_to_sparse)
+(
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to copy, converted to symbolic on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *Lsparse ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (L, NULL) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, NULL) ;
+ Common->status = CHOLMOD_OK ;
+ DEBUG (CHOLMOD(dump_factor) (L, "start convert to matrix", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to packed, monotonic, simplicial, numeric */
+ /* ---------------------------------------------------------------------- */
+
+ /* leave as LL or LDL' */
+ if (!CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE, TRUE, TRUE, L,
+ Common))
+ {
+ ERROR (CHOLMOD_INVALID, "cannot convert L") ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create Lsparse */
+ /* ---------------------------------------------------------------------- */
+
+ /* allocate the header for Lsparse, the sparse matrix version of L */
+ Lsparse = CHOLMOD(malloc) (sizeof (cholmod_sparse), 1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* transfer the contents from L to Lsparse */
+ Lsparse->nrow = L->n ;
+ Lsparse->ncol = L->n ;
+ Lsparse->p = L->p ;
+ Lsparse->i = L->i ;
+ Lsparse->x = L->x ;
+ Lsparse->z = L->z ;
+ Lsparse->nz = NULL ;
+ Lsparse->stype = 0 ;
+ Lsparse->itype = L->itype ;
+ Lsparse->xtype = L->xtype ;
+ Lsparse->dtype = L->dtype ;
+ Lsparse->sorted = TRUE ;
+ Lsparse->packed = TRUE ;
+ Lsparse->nzmax = L->nzmax ;
+ ASSERT (CHOLMOD(dump_sparse) (Lsparse, "Lsparse", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to symbolic, but do not free contents transfered to Lsparse */
+ /* ---------------------------------------------------------------------- */
+
+ L->p = NULL ;
+ L->i = NULL ;
+ L->x = NULL ;
+ L->z = NULL ;
+ L->xtype = CHOLMOD_PATTERN ;
+ CHOLMOD(change_factor) (CHOLMOD_PATTERN, FALSE, FALSE, TRUE, TRUE, L,
+ Common) ;
+
+ return (Lsparse) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy_factor ================================================== */
+/* ========================================================================== */
+
+/* Create an exact copy of a factor, with one exception:
+ *
+ * Entries in unused space are not copied (they might not be initialized,
+ * and copying them would cause program checkers such as purify and
+ * valgrind to complain).
+ *
+ * Note that a supernodal L cannot be zomplex.
+ */
+
+cholmod_factor *CHOLMOD(copy_factor)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_factor *L2 ;
+ double *Lx, *L2x, *Lz, *L2z ;
+ Int *Perm, *ColCount, *Lp, *Li, *Lnz, *Lnext, *Lprev, *Lsuper, *Lpi, *Lpx,
+ *Ls, *Perm2, *ColCount2, *L2p, *L2i, *L2nz, *L2next, *L2prev, *L2super,
+ *L2pi, *L2px, *L2s ;
+ Int n, j, p, pend, s, xsize, ssize, nsuper ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (L, NULL) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ Common->status = CHOLMOD_OK ;
+ DEBUG (CHOLMOD(dump_factor) (L, "start copy", Common)) ;
+
+ n = L->n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate a simplicial symbolic factor */
+ /* ---------------------------------------------------------------------- */
+
+ /* allocates L2->Perm and L2->ColCount */
+ L2 = CHOLMOD(allocate_factor) (n, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ ASSERT (L2->xtype == CHOLMOD_PATTERN && !(L2->is_super)) ;
+
+ Perm = L->Perm ;
+ ColCount = L->ColCount ;
+ Perm2 = L2->Perm ;
+ ColCount2 = L2->ColCount ;
+ L2->ordering = L->ordering ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ Perm2 [j] = Perm [j] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ ColCount2 [j] = ColCount [j] ;
+ }
+ L2->is_ll = L->is_ll ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the rest of the factor */
+ /* ---------------------------------------------------------------------- */
+
+ if (L->xtype != CHOLMOD_PATTERN && !(L->super))
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* allocate a simplicial numeric factor */
+ /* ------------------------------------------------------------------ */
+
+ /* allocate L2->p, L2->nz, L2->prev, L2->next, L2->i, and L2->x.
+ * packed = -1 so that cholmod_change_factor allocates space of
+ * size L2->nzmax */
+ L2->nzmax = L->nzmax ;
+ if (!CHOLMOD(change_factor) (L->xtype, L->is_ll, FALSE, -1, TRUE,
+ L2, Common))
+ {
+ CHOLMOD(free_factor) (&L2, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+ ASSERT (MAX (1, L->nzmax) == L2->nzmax) ;
+
+ /* ------------------------------------------------------------------ */
+ /* copy the contents of a simplicial numeric factor */
+ /* ------------------------------------------------------------------ */
+
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lnz = L->nz ;
+ Lnext = L->next ;
+ Lprev = L->prev ;
+
+ L2p = L2->p ;
+ L2i = L2->i ;
+ L2x = L2->x ;
+ L2z = L2->z ;
+ L2nz = L2->nz ;
+ L2next = L2->next ;
+ L2prev = L2->prev ;
+ L2->xtype = L->xtype ;
+ L2->dtype = L->dtype ;
+
+ for (j = 0 ; j <= n ; j++)
+ {
+ L2p [j] = Lp [j] ;
+ }
+
+ for (j = 0 ; j < n+2 ; j++)
+ {
+ L2prev [j] = Lprev [j] ;
+ }
+
+ for (j = 0 ; j < n+2 ; j++)
+ {
+ L2next [j] = Lnext [j] ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ L2nz [j] = Lnz [j] ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ L2i [p] = Li [p] ;
+ }
+ p = Lp [j] ;
+
+ if (L->xtype == CHOLMOD_REAL)
+ {
+ for ( ; p < pend ; p++)
+ {
+ L2x [p] = Lx [p] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_COMPLEX)
+ {
+ for ( ; p < pend ; p++)
+ {
+ L2x [2*p ] = Lx [2*p ] ;
+ L2x [2*p+1] = Lx [2*p+1] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_ZOMPLEX)
+ {
+ for ( ; p < pend ; p++)
+ {
+ L2x [p] = Lx [p] ;
+ L2z [p] = Lz [p] ;
+ }
+ }
+
+ }
+
+ }
+ else if (L->is_super)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* copy a supernodal factor */
+ /* ------------------------------------------------------------------ */
+
+ xsize = L->xsize ;
+ ssize = L->ssize ;
+ nsuper = L->nsuper ;
+
+ L2->xsize = xsize ;
+ L2->ssize = ssize ;
+ L2->nsuper = nsuper ;
+
+ /* allocate L2->super, L2->pi, L2->px, and L2->s. Allocate L2->x if
+ * L is numeric */
+ if (!CHOLMOD(change_factor) (L->xtype, TRUE, TRUE, TRUE, TRUE, L2,
+ Common))
+ {
+ CHOLMOD(free_factor) (&L2, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ ASSERT (L2->s != NULL) ;
+
+ /* ------------------------------------------------------------------ */
+ /* copy the contents of a supernodal factor */
+ /* ------------------------------------------------------------------ */
+
+ Lsuper = L->super ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Lx = L->x ;
+
+ L2super = L2->super ;
+ L2pi = L2->pi ;
+ L2px = L2->px ;
+ L2s = L2->s ;
+ L2x = L2->x ;
+
+ L2->maxcsize = L->maxcsize ;
+ L2->maxesize = L->maxesize ;
+
+ for (s = 0 ; s <= nsuper ; s++)
+ {
+ L2super [s] = Lsuper [s] ;
+ }
+ for (s = 0 ; s <= nsuper ; s++)
+ {
+ L2pi [s] = Lpi [s] ;
+ }
+ for (s = 0 ; s <= nsuper ; s++)
+ {
+ L2px [s] = Lpx [s] ;
+ }
+
+ L2s [0] = 0 ;
+ for (p = 0 ; p < ssize ; p++)
+ {
+ L2s [p] = Ls [p] ;
+ }
+
+ if (L->xtype == CHOLMOD_REAL)
+ {
+ for (p = 0 ; p < xsize ; p++)
+ {
+ L2x [p] = Lx [p] ;
+ }
+ }
+ else if (L->xtype == CHOLMOD_COMPLEX)
+ {
+ for (p = 0 ; p < 2*xsize ; p++)
+ {
+ L2x [p] = Lx [p] ;
+ }
+ }
+ }
+
+ L2->minor = L->minor ;
+ L2->is_monotonic = L->is_monotonic ;
+
+ DEBUG (CHOLMOD(dump_factor) (L2, "L2 got copied", Common)) ;
+ ASSERT (L2->xtype == L->xtype && L2->is_super == L->is_super) ;
+ return (L2) ;
+}
diff --git a/CHOLMOD/Core/cholmod_memory.c b/CHOLMOD/Core/cholmod_memory.c
new file mode 100644
index 0000000..f6a1f00
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_memory.c
@@ -0,0 +1,563 @@
+/* ========================================================================== */
+/* === Core/cholmod_memory ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core memory management routines:
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_malloc malloc wrapper
+ * cholmod_free free wrapper
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_calloc calloc wrapper
+ * cholmod_realloc realloc wrapper
+ * cholmod_realloc_multiple realloc wrapper for multiple objects
+ *
+ * The user may make use of these, just like malloc and free. You can even
+ * malloc an object and safely free it with cholmod_free, and visa versa
+ * (except that the memory usage statistics will be corrupted). These routines
+ * do differ from malloc and free. If cholmod_free is given a NULL pointer,
+ * for example, it does nothing (unlike the ANSI free). cholmod_realloc does
+ * not return NULL if given a non-NULL pointer and a nonzero size, even if it
+ * fails (it sets an error code in Common->status instead).
+ *
+ * CHOLMOD keeps track of the amount of memory it has allocated, and so the
+ * cholmod_free routine includes as a parameter the size of the object being
+ * freed. This is only used for memory usage statistics, which are very useful
+ * in finding memory leaks in your program. If you, the user of CHOLMOD, pass
+ * the wrong size, the only consequence is that the memory usage statistics
+ * will be invalid. This will causes assertions to fail if CHOLMOD is
+ * compiled with debugging enabled, but otherwise it will cause no errors.
+ *
+ * The cholmod_free_* routines for each CHOLMOD object keep track of the size
+ * of the blocks they free, so they do not require you to pass their sizes
+ * as a parameter.
+ *
+ * If a block of size zero is requested, these routines allocate a block of
+ * size one instead.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+/* ========================================================================== */
+/* === cholmod_add_size_t =================================================== */
+/* ========================================================================== */
+
+/* Safely compute a+b, and check for integer overflow. If overflow occurs,
+ * return 0 and set OK to FALSE. Also return 0 if OK is FALSE on input. */
+
+size_t CHOLMOD(add_size_t) (size_t a, size_t b, int *ok)
+{
+ size_t s = a + b ;
+ (*ok) = (*ok) && (s >= a) ;
+ return ((*ok) ? s : 0) ;
+}
+
+/* ========================================================================== */
+/* === cholmod_mult_size_t ================================================== */
+/* ========================================================================== */
+
+/* Safely compute a*k, where k should be small, and check for integer overflow.
+ * If overflow occurs, return 0 and set OK to FALSE. Also return 0 if OK is
+ * FALSE on input. */
+
+size_t CHOLMOD(mult_size_t) (size_t a, size_t k, int *ok)
+{
+ size_t p = 0, s ;
+ while (*ok)
+ {
+ if (k % 2)
+ {
+ p = p + a ;
+ (*ok) = (*ok) && (p >= a) ;
+ }
+ k = k / 2 ;
+ if (!k) return (p) ;
+ s = a + a ;
+ (*ok) = (*ok) && (s >= a) ;
+ a = s ;
+ }
+ return (0) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_malloc ======================================================= */
+/* ========================================================================== */
+
+/* Wrapper around malloc routine. Allocates space of size MAX(1,n)*size, where
+ * size is normally a sizeof (...).
+ *
+ * This routine, cholmod_calloc, and cholmod_realloc do not set Common->status
+ * to CHOLMOD_OK on success, so that a sequence of cholmod_malloc's, _calloc's,
+ * or _realloc's can be used. If any of them fails, the Common->status will
+ * hold the most recent error status.
+ *
+ * Usage, for a pointer to int:
+ *
+ * p = cholmod_malloc (n, sizeof (int), Common)
+ *
+ * Uses a pointer to the malloc routine (or its equivalent) defined in Common.
+ */
+
+void *CHOLMOD(malloc) /* returns pointer to the newly malloc'd block */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ void *p ;
+ size_t s ;
+ int ok = TRUE ;
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (size == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ;
+ p = NULL ;
+ }
+ else if (n >= (Size_max / size) || n >= Int_max)
+ {
+ /* object is too big to allocate without causing integer overflow */
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ p = NULL ;
+ }
+ else
+ {
+ /* call malloc, or its equivalent */
+ s = CHOLMOD(mult_size_t) (MAX (1,n), size, &ok) ;
+ p = ok ? ((Common->malloc_memory) (s)) : NULL ;
+ if (p == NULL)
+ {
+ /* failure: out of memory */
+ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ;
+ }
+ else
+ {
+ /* success: increment the count of objects allocated */
+ Common->malloc_count++ ;
+ Common->memory_inuse += (n * size) ;
+ Common->memory_usage =
+ MAX (Common->memory_usage, Common->memory_inuse) ;
+ PRINTM (("cholmod_malloc %p %d cnt: %d inuse %d\n",
+ p, n*size, Common->malloc_count, Common->memory_inuse)) ;
+ }
+ }
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_free ========================================================= */
+/* ========================================================================== */
+
+/* Wrapper around free routine. Returns NULL, which can be assigned to the
+ * pointer being freed, as in:
+ *
+ * p = cholmod_free (n, sizeof (int), p, Common) ;
+ *
+ * In CHOLMOD, the syntax:
+ *
+ * cholmod_free (n, sizeof (int), p, Common) ;
+ *
+ * is used if p is a local pointer and the routine is returning shortly.
+ * Uses a pointer to the free routine (or its equivalent) defined in Common.
+ * Nothing is freed if the pointer is NULL.
+ */
+
+void *CHOLMOD(free) /* always returns NULL */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* ---- in/out --- */
+ void *p, /* block of memory to free */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (p != NULL)
+ {
+ /* only free the object if the pointer is not NULL */
+ /* call free, or its equivalent */
+ (Common->free_memory) (p) ;
+ Common->malloc_count-- ;
+ Common->memory_inuse -= (n * size) ;
+ PRINTM (("cholmod_free %p %d cnt: %d inuse %d\n",
+ p, n*size, Common->malloc_count, Common->memory_inuse)) ;
+ /* This assertion will fail if the user calls cholmod_malloc and
+ * cholmod_free with mismatched memory sizes. It shouldn't fail
+ * otherwise. */
+ ASSERT (IMPLIES (Common->malloc_count == 0, Common->memory_inuse == 0));
+ }
+ /* return NULL, and the caller should assign this to p. This avoids
+ * freeing the same pointer twice. */
+ return (NULL) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_calloc ======================================================= */
+/* ========================================================================== */
+
+/* Wrapper around calloc routine.
+ *
+ * Uses a pointer to the calloc routine (or its equivalent) defined in Common.
+ * This routine is identical to malloc, except that it zeros the newly allocated
+ * block to zero.
+ */
+
+void *CHOLMOD(calloc) /* returns pointer to the newly calloc'd block */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ void *p ;
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (size == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ;
+ p = NULL ;
+ }
+ else if (n >= (Size_max / size) || n >= Int_max)
+ {
+ /* object is too big to allocate without causing integer overflow */
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ p = NULL ;
+ }
+ else
+ {
+ /* call calloc, or its equivalent */
+ p = (Common->calloc_memory) (MAX (1,n), size) ;
+ if (p == NULL)
+ {
+ /* failure: out of memory */
+ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ;
+ }
+ else
+ {
+ /* success: increment the count of objects allocated */
+ Common->malloc_count++ ;
+ Common->memory_inuse += (n * size) ;
+ Common->memory_usage =
+ MAX (Common->memory_usage, Common->memory_inuse) ;
+ PRINTM (("cholmod_calloc %p %d cnt: %d inuse %d\n",
+ p, n*size, Common->malloc_count, Common->memory_inuse)) ;
+ }
+ }
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_realloc ====================================================== */
+/* ========================================================================== */
+
+/* Wrapper around realloc routine. Given a pointer p to a block of size
+ * (*n)*size memory, it changes the size of the block pointed to by p to be
+ * MAX(1,nnew)*size in size. It may return a pointer different than p. This
+ * should be used as (for a pointer to int):
+ *
+ * p = cholmod_realloc (nnew, sizeof (int), p, *n, Common) ;
+ *
+ * If p is NULL, this is the same as p = cholmod_malloc (...).
+ * A size of nnew=0 is treated as nnew=1.
+ *
+ * If the realloc fails, p is returned unchanged and Common->status is set
+ * to CHOLMOD_OUT_OF_MEMORY. If successful, Common->status is not modified,
+ * and p is returned (possibly changed) and pointing to a large block of memory.
+ *
+ * Uses a pointer to the realloc routine (or its equivalent) defined in Common.
+ */
+
+void *CHOLMOD(realloc) /* returns pointer to reallocated block */
+(
+ /* ---- input ---- */
+ size_t nnew, /* requested # of items in reallocated block */
+ size_t size, /* size of each item */
+ /* ---- in/out --- */
+ void *p, /* block of memory to realloc */
+ size_t *n, /* current size on input, nnew on output if successful*/
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ size_t nold = (*n) ;
+ void *pnew ;
+ size_t s ;
+ int ok = TRUE ;
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (size == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "sizeof(item) must be > 0") ;
+ p = NULL ;
+ }
+ else if (p == NULL)
+ {
+ /* A fresh object is being allocated. */
+ PRINT1 (("realloc fresh: %d %d\n", nnew, size)) ;
+ p = CHOLMOD(malloc) (nnew, size, Common) ;
+ *n = (p == NULL) ? 0 : nnew ;
+ }
+ else if (nold == nnew)
+ {
+ /* Nothing to do. Do not change p or n. */
+ PRINT1 (("realloc nothing: %d %d\n", nnew, size)) ;
+ }
+ else if (nnew >= (Size_max / size) || nnew >= Int_max)
+ {
+ /* failure: nnew is too big. Do not change p or n. */
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ }
+ else
+ {
+ /* The object exists, and is changing to some other nonzero size. */
+ /* call realloc, or its equivalent */
+ PRINT1 (("realloc : %d to %d, %d\n", nold, nnew, size)) ;
+ pnew = NULL ;
+
+ s = CHOLMOD(mult_size_t) (MAX (1,nnew), size, &ok) ;
+ pnew = ok ? ((Common->realloc_memory) (p, s)) : NULL ;
+
+ if (pnew == NULL)
+ {
+ /* Do not change p, since it still points to allocated memory */
+ if (nnew <= nold)
+ {
+ /* The attempt to reduce the size of the block from n to
+ * nnew has failed. The current block is not modified, so
+ * pretend to succeed, but do not change p. Do change
+ * CHOLMOD's notion of the size of the block, however. */
+ *n = nnew ;
+ PRINTM (("nnew <= nold failed, pretend to succeed\n")) ;
+ PRINTM (("cholmod_realloc_old: %p %d cnt: %d inuse %d\n"
+ "cholmod_realloc_new: %p %d cnt: %d inuse %d\n",
+ p, nold*size, Common->malloc_count-1,
+ Common->memory_inuse - nold*size,
+ p, nnew*size, Common->malloc_count,
+ Common->memory_inuse + (nnew-nold)*size)) ;
+ Common->memory_inuse += ((nnew-nold) * size) ;
+ }
+ else
+ {
+ /* Increasing the size of the block has failed.
+ * Do not change n. */
+ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ;
+ }
+ }
+ else
+ {
+ /* success: return revised p and change the size of the block */
+ PRINTM (("cholmod_realloc_old: %p %d cnt: %d inuse %d\n"
+ "cholmod_realloc_new: %p %d cnt: %d inuse %d\n",
+ p, nold*size, Common->malloc_count-1,
+ Common->memory_inuse - nold*size,
+ pnew, nnew*size, Common->malloc_count,
+ Common->memory_inuse + (nnew-nold)*size)) ;
+ p = pnew ;
+ *n = nnew ;
+ Common->memory_inuse += ((nnew-nold) * size) ;
+ }
+ Common->memory_usage = MAX (Common->memory_usage, Common->memory_inuse);
+ }
+
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_realloc_multiple ============================================= */
+/* ========================================================================== */
+
+/* reallocate multiple blocks of memory, all of the same size (up to two integer
+ * and two real blocks). Either reallocations all succeed, or all are returned
+ * in the original size (they are freed if the original size is zero). The nnew
+ * blocks are of size 1 or more.
+ */
+
+int CHOLMOD(realloc_multiple)
+(
+ /* ---- input ---- */
+ size_t nnew, /* requested # of items in reallocated blocks */
+ int nint, /* number of int/UF_long blocks */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* ---- in/out --- */
+ void **I, /* int or UF_long block */
+ void **J, /* int or UF_long block */
+ void **X, /* complex or double block */
+ void **Z, /* zomplex case only: double block */
+ size_t *nold_p, /* current size of the I,J,X,Z blocks on input,
+ * nnew on output if successful */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *xx, *zz ;
+ size_t i, j, x, z, nold ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid xtype") ;
+ return (FALSE) ;
+ }
+
+ nold = *nold_p ;
+
+ if (nint < 1 && xtype == CHOLMOD_PATTERN)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ i = nold ;
+ j = nold ;
+ x = nold ;
+ z = nold ;
+
+ if (nint > 0)
+ {
+ *I = CHOLMOD(realloc) (nnew, sizeof (Int), *I, &i, Common) ;
+ }
+ if (nint > 1)
+ {
+ *J = CHOLMOD(realloc) (nnew, sizeof (Int), *J, &j, Common) ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ *X = CHOLMOD(realloc) (nnew, sizeof (double), *X, &x, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ *X = CHOLMOD(realloc) (nnew, 2*sizeof (double), *X, &x, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ *X = CHOLMOD(realloc) (nnew, sizeof (double), *X, &x, Common) ;
+ *Z = CHOLMOD(realloc) (nnew, sizeof (double), *Z, &z, Common) ;
+ break ;
+ }
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* one or more realloc's failed. Resize all back down to nold. */
+
+ if (nold == 0)
+ {
+
+ if (nint > 0)
+ {
+ *I = CHOLMOD(free) (i, sizeof (Int), *I, Common) ;
+ }
+ if (nint > 1)
+ {
+ *J = CHOLMOD(free) (j, sizeof (Int), *J, Common) ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ *X = CHOLMOD(free) (x, sizeof (double), *X, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ *X = CHOLMOD(free) (x, 2*sizeof (double), *X, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ *X = CHOLMOD(free) (x, sizeof (double), *X, Common) ;
+ *Z = CHOLMOD(free) (x, sizeof (double), *Z, Common) ;
+ break ;
+ }
+
+ }
+ else
+ {
+ if (nint > 0)
+ {
+ *I = CHOLMOD(realloc) (nold, sizeof (Int), *I, &i, Common) ;
+ }
+ if (nint > 1)
+ {
+ *J = CHOLMOD(realloc) (nold, sizeof (Int), *J, &j, Common) ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ *X = CHOLMOD(realloc) (nold, sizeof (double), *X, &x,
+ Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ *X = CHOLMOD(realloc) (nold, 2*sizeof (double), *X, &x,
+ Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ *X = CHOLMOD(realloc) (nold, sizeof (double), *X, &x,
+ Common) ;
+ *Z = CHOLMOD(realloc) (nold, sizeof (double), *Z, &z,
+ Common) ;
+ break ;
+ }
+
+ }
+
+ return (FALSE) ;
+ }
+
+ if (nold == 0)
+ {
+ /* New space was allocated. Clear the first entry so that valgrind
+ * doesn't complain about its access in change_complexity
+ * (Core/cholmod_complex.c). */
+ xx = *X ;
+ zz = *Z ;
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ xx [0] = 0 ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ xx [0] = 0 ;
+ xx [1] = 0 ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ xx [0] = 0 ;
+ zz [0] = 0 ;
+ break ;
+ }
+ }
+
+ /* all realloc's succeeded, change size to reflect realloc'ed size. */
+ *nold_p = nnew ;
+ return (TRUE) ;
+}
diff --git a/CHOLMOD/Core/cholmod_sparse.c b/CHOLMOD/Core/cholmod_sparse.c
new file mode 100644
index 0000000..059f855
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_sparse.c
@@ -0,0 +1,652 @@
+/* ========================================================================== */
+/* === Core/cholmod_sparse ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_sparse object:
+ *
+ * A sparse matrix is held in compressed column form. In the basic type
+ * ("packed", which corresponds to a MATLAB sparse matrix), an n-by-n matrix
+ * with nz entries is held in three arrays: p of size n+1, i of size nz, and x
+ * of size nz. Row indices of column j are held in i [p [j] ... p [j+1]-1] and
+ * in the same locations in x. There may be no duplicate entries in a column.
+ * Row indices in each column may be sorted or unsorted (CHOLMOD keeps track).
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_allocate_sparse allocate a sparse matrix
+ * cholmod_free_sparse free a sparse matrix
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_reallocate_sparse change the size (# entries) of sparse matrix
+ * cholmod_nnz number of nonzeros in a sparse matrix
+ * cholmod_speye sparse identity matrix
+ * cholmod_spzeros sparse zero matrix
+ * cholmod_copy_sparse create a copy of a sparse matrix
+ *
+ * All xtypes are supported (pattern, real, complex, and zomplex)
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+
+/* ========================================================================== */
+/* === cholmod_allocate_sparse ============================================== */
+/* ========================================================================== */
+
+/* Allocate space for a matrix. A->i and A->x are not initialized. A->p
+ * (and A->nz if A is not packed) are set to zero, so a matrix containing no
+ * entries (all zero) is returned. See also cholmod_spzeros.
+ *
+ * workspace: none
+ */
+
+cholmod_sparse *CHOLMOD(allocate_sparse)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ size_t nzmax, /* max # of nonzeros of A */
+ int sorted, /* TRUE if columns of A sorted, FALSE otherwise */
+ int packed, /* TRUE if A will be packed, FALSE otherwise */
+ int stype, /* stype of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *A ;
+ Int *Ap, *Anz ;
+ size_t nzmax0 ;
+ Int j ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (stype != 0 && nrow != ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "rectangular matrix with stype != 0 invalid") ;
+ return (NULL) ;
+ }
+ if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype invalid") ;
+ return (NULL) ;
+ }
+ /* ensure the dimensions do not cause integer overflow */
+ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ;
+ if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate header */
+ /* ---------------------------------------------------------------------- */
+
+ A = CHOLMOD(malloc) (sizeof (cholmod_sparse), 1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ PRINT1 (("cholmod_allocate_sparse %d-by-%d nzmax %d sorted %d packed %d"
+ " xtype %d\n", nrow, ncol, nzmax, sorted, packed, xtype)) ;
+
+ nzmax = MAX (1, nzmax) ;
+
+ A->nrow = nrow ;
+ A->ncol = ncol ;
+ A->nzmax = nzmax ;
+ A->packed = packed ; /* default is packed (A->nz not present) */
+ A->stype = stype ;
+ A->itype = ITYPE ;
+ A->xtype = xtype ;
+ A->dtype = DTYPE ;
+
+ A->nz = NULL ;
+ A->p = NULL ;
+ A->i = NULL ;
+ A->x = NULL ;
+ A->z = NULL ;
+
+ /* A 1-by-m matrix always has sorted columns */
+ A->sorted = (nrow <= 1) ? TRUE : sorted ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the matrix itself */
+ /* ---------------------------------------------------------------------- */
+
+ /* allocate O(ncol) space */
+ A->p = CHOLMOD(malloc) (((size_t) ncol)+1, sizeof (Int), Common) ;
+ if (!packed)
+ {
+ A->nz = CHOLMOD(malloc) (ncol, sizeof (Int), Common) ;
+ }
+
+ /* allocate O(nz) space */
+ nzmax0 = 0 ;
+ CHOLMOD(realloc_multiple) (nzmax, 1, xtype, &(A->i), NULL, &(A->x), &(A->z),
+ &nzmax0, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&A, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize A->p and A->nz so that A is an empty matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ for (j = 0 ; j <= (Int) ncol ; j++)
+ {
+ Ap [j] = 0 ;
+ }
+ if (!packed)
+ {
+ Anz = A->nz ;
+ for (j = 0 ; j < (Int) ncol ; j++)
+ {
+ Anz [j] = 0 ;
+ }
+ }
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_free_sparse ================================================== */
+/* ========================================================================== */
+
+/* free a sparse matrix
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(free_sparse)
+(
+ /* ---- in/out --- */
+ cholmod_sparse **AHandle, /* matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int n, nz ;
+ cholmod_sparse *A ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ if (AHandle == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ A = *AHandle ;
+ if (A == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ n = A->ncol ;
+ nz = A->nzmax ;
+ A->p = CHOLMOD(free) (n+1, sizeof (Int), A->p, Common) ;
+ A->i = CHOLMOD(free) (nz, sizeof (Int), A->i, Common) ;
+ A->nz = CHOLMOD(free) (n, sizeof (Int), A->nz, Common) ;
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_REAL:
+ A->x = CHOLMOD(free) (nz, sizeof (double), A->x, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ A->x = CHOLMOD(free) (nz, 2*sizeof (double), A->x, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ A->x = CHOLMOD(free) (nz, sizeof (double), A->x, Common) ;
+ A->z = CHOLMOD(free) (nz, sizeof (double), A->z, Common) ;
+ break ;
+ }
+
+ *AHandle = CHOLMOD(free) (1, sizeof (cholmod_sparse), (*AHandle), Common) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_reallocate_sparse ============================================ */
+/* ========================================================================== */
+
+/* Change the size of A->i, A->x, and A->z, or allocate them if their current
+ * size is zero. A->x and A->z are not modified if A->xtype is CHOLMOD_PATTERN.
+ * A->z is not modified unless A->xtype is CHOLMOD_ZOMPLEX.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(reallocate_sparse)
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in A */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to reallocate */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ PRINT1 (("realloc matrix %d to %d, xtype: %d\n",
+ A->nzmax, nznew, A->xtype)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* resize the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(realloc_multiple) (MAX (1,nznew), 1, A->xtype, &(A->i), NULL,
+ &(A->x), &(A->z), &(A->nzmax), Common) ;
+
+ return (Common->status == CHOLMOD_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_speye ======================================================== */
+/* ========================================================================== */
+
+/* Return a sparse identity matrix. */
+
+cholmod_sparse *CHOLMOD(speye)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Az ;
+ cholmod_sparse *A ;
+ Int *Ap, *Ai ;
+ Int j, n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ n = MIN (nrow, ncol) ;
+ A = CHOLMOD(allocate_sparse) (nrow, ncol, n, TRUE, TRUE, 0, xtype,
+ Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory or inputs invalid */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create the identity matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ Ap [j] = j ;
+ }
+ for (j = n ; j <= ((Int) ncol) ; j++)
+ {
+ Ap [j] = n ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ Ai [j] = j ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ for (j = 0 ; j < n ; j++)
+ {
+ Ax [j] = 1 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (j = 0 ; j < n ; j++)
+ {
+ Ax [2*j ] = 1 ;
+ Ax [2*j+1] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (j = 0 ; j < n ; j++)
+ {
+ Ax [j] = 1 ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ Az [j] = 0 ;
+ }
+ break ;
+ }
+
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_spzeros ====================================================== */
+/* ========================================================================== */
+
+/* Return a sparse zero matrix. */
+
+cholmod_sparse *CHOLMOD(spzeros)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ size_t nzmax, /* max # of nonzeros of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ return (CHOLMOD(allocate_sparse) (nrow, ncol, nzmax, TRUE, TRUE, 0, xtype,
+ Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_nnz ========================================================== */
+/* ========================================================================== */
+
+/* Return the number of entries in a sparse matrix.
+ *
+ * workspace: none
+ * integer overflow cannot occur, since the matrix is already allocated.
+ */
+
+UF_long CHOLMOD(nnz)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap, *Anz ;
+ size_t nz ;
+ Int j, ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (A, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return nnz (A) */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = A->ncol ;
+ if (A->packed)
+ {
+ Ap = A->p ;
+ RETURN_IF_NULL (Ap, EMPTY) ;
+ nz = Ap [ncol] ;
+ }
+ else
+ {
+ Anz = A->nz ;
+ RETURN_IF_NULL (Anz, EMPTY) ;
+ nz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ nz += MAX (0, Anz [j]) ;
+ }
+ }
+ return (nz) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy_sparse ================================================== */
+/* ========================================================================== */
+
+/* C = A. Create an exact copy of a sparse matrix, with one exception.
+ * Entries in unused space are not copied (they might not be initialized,
+ * and copying them would cause program checkers such as purify and
+ * valgrind to complain). The xtype of the resulting matrix C is the same as
+ * the xtype of the input matrix A.
+ *
+ * See also Core/cholmod_copy, which copies a matrix with possible changes
+ * in stype, presence of diagonal entries, pattern vs. numerical values,
+ * real and/or imaginary parts, and so on.
+ */
+
+cholmod_sparse *CHOLMOD(copy_sparse)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Cx, *Az, *Cz ;
+ Int *Ap, *Ai, *Anz, *Cp, *Ci, *Cnz ;
+ cholmod_sparse *C ;
+ Int p, pend, j, ncol, packed, nzmax, nz, xtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->stype != 0 && A->nrow != A->ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "rectangular matrix with stype != 0 invalid") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ ASSERT (CHOLMOD(dump_sparse) (A, "A original", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = A->ncol ;
+ nzmax = A->nzmax ;
+ packed = A->packed ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+ xtype = A->xtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the copy */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_sparse) (A->nrow, A->ncol, A->nzmax, A->sorted,
+ A->packed, A->stype, A->xtype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+ Cz = C->z ;
+ Cnz = C->nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ for (j = 0 ; j <= ncol ; j++)
+ {
+ Cp [j] = Ap [j] ;
+ }
+
+ if (packed)
+ {
+ nz = Ap [ncol] ;
+ for (p = 0 ; p < nz ; p++)
+ {
+ Ci [p] = Ai [p] ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ for (p = 0 ; p < nz ; p++)
+ {
+ Cx [p] = Ax [p] ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (p = 0 ; p < 2*nz ; p++)
+ {
+ Cx [p] = Ax [p] ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (p = 0 ; p < nz ; p++)
+ {
+ Cx [p] = Ax [p] ;
+ Cz [p] = Az [p] ;
+ }
+ break ;
+ }
+
+ }
+ else
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Cnz [j] = Anz [j] ;
+ }
+
+ switch (xtype)
+ {
+ case CHOLMOD_PATTERN:
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [p] = Ai [p] ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_REAL:
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [p] = Ai [p] ;
+ Cx [p] = Ax [p] ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [p] = Ai [p] ;
+ Cx [2*p ] = Ax [2*p ] ;
+ Cx [2*p+1] = Ax [2*p+1] ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [p] = Ai [p] ;
+ Cx [p] = Ax [p] ;
+ Cz [p] = Az [p] ;
+ }
+ }
+ break ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (C, "C copy", Common) >= 0) ;
+ return (C) ;
+}
diff --git a/CHOLMOD/Core/cholmod_transpose.c b/CHOLMOD/Core/cholmod_transpose.c
new file mode 100644
index 0000000..7e94aa8
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_transpose.c
@@ -0,0 +1,1139 @@
+/* ========================================================================== */
+/* === Core/cholmod_transpose =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_sparse object to
+ * compute the transpose or permuted transpose of a matrix:
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_transpose transpose sparse matrix
+ * cholmod_ptranspose transpose and permute sparse matrix
+ * cholmod_sort sort row indices in each column of sparse matrix
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_transpose_unsym transpose unsymmetric sparse matrix
+ * cholmod_transpose_sym transpose symmetric sparse matrix
+ *
+ * All xtypes (pattern, real, complex, and zomplex) are supported.
+ *
+ * ---------------------------------------
+ * Unsymmetric case: A->stype is zero.
+ * ---------------------------------------
+ *
+ * Computes F = A', F = A (:,f)' or F = A (p,f)', except that the indexing by
+ * f does not work the same as the MATLAB notation (see below). A->stype
+ * is zero, which denotes that both the upper and lower triangular parts of
+ * A are present (and used). A may in fact be symmetric in pattern and/or
+ * value; A->stype just denotes which part of A are stored. A may be
+ * rectangular.
+ *
+ * p is a permutation of 0:m-1, and f is a subset of 0:n-1, where A is m-by-n.
+ * There can be no duplicate entries in p or f.
+ *
+ * The set f is held in fset and fsize.
+ * fset = NULL means ":" in MATLAB. fsize is ignored.
+ * fset != NULL means f = fset [0..fsize-1].
+ * fset != NULL and fsize = 0 means f is the empty set.
+ *
+ * Columns not in the set f are considered to be zero. That is,
+ * if A is 5-by-10 then F = A (:,[3 4])' is not 2-by-5, but 10-by-5, and rows
+ * 3 and 4 of F are equal to columns 3 and 4 of A (the other rows of F are
+ * zero). More precisely, in MATLAB notation:
+ *
+ * [m n] = size (A) ;
+ * F = A ;
+ * notf = ones (1,n) ;
+ * notf (f) = 0 ;
+ * F (:, find (notf)) = 0
+ * F = F'
+ *
+ * If you want the MATLAB equivalent F=A(p,f) operation, use cholmod_submatrix
+ * instead (which does not compute the transpose).
+ *
+ * F->nzmax must be large enough to hold the matrix F. It is not modified.
+ * If F->nz is present then F->nz [j] = # of entries in column j of F.
+ *
+ * A can be sorted or unsorted, with packed or unpacked columns.
+ *
+ * If f is present and not sorted in ascending order, then F is unsorted
+ * (that is, it may contain columns whose row indices do not appear in
+ * ascending order). Otherwise, F is sorted (the row indices in each
+ * column of F appear in strictly ascending order).
+ *
+ * F is returned in packed or unpacked form, depending on F->packed on input.
+ * If F->packed is false, then F is returned in unpacked form (F->nz must be
+ * present). Each row i of F is large enough to hold all the entries in row i
+ * of A, even if f is provided. That is, F->i and
+ * F->x [F->p [i] .. F->p [i] + F->nz [i] - 1] contain all entries in A (i,f),
+ * but F->p [i+1] - F->p [i] is equal to the number of nonzeros in A (i,:),
+ * not just A (i,f).
+ *
+ * The cholmod_transpose_unsym routine is the only operation in CHOLMOD that
+ * can produce an unpacked matrix.
+ *
+ * ---------------------------------------
+ * Symmetric case: A->stype is nonzero.
+ * ---------------------------------------
+ *
+ * Computes F = A' or F = A(p,p)', the transpose or permuted transpose, where
+ * A->stype is nonzero.
+ *
+ * If A->stype > 0, then A is a symmetric matrix where just the upper part
+ * of the matrix is stored. Entries in the lower triangular part may be
+ * present, but are ignored. A must be square. If F=A', then F is returned
+ * sorted; otherwise F is unsorted for the F=A(p,p)' case.
+ *
+ * There can be no duplicate entries in p.
+ * The fset and fsize parameters are not used.
+ *
+ * Three kinds of transposes are available, depending on the "values" parameter:
+ * 0: do not transpose the numerical values; create a CHOLMOD_PATTERN matrix
+ * 1: array transpose
+ * 2: complex conjugate transpose (same as 2 if input is real or pattern)
+ *
+ * -----------------------------------------------------------------------------
+ *
+ * For cholmod_transpose_unsym and cholmod_transpose_sym, the output matrix
+ * F must already be pre-allocated by the caller, with the correct dimensions.
+ * If F is not valid or has the wrong dimensions, it is not modified.
+ * Otherwise, if F is too small, the transpose is not computed; the contents
+ * of F->p contain the column pointers of the resulting matrix, where
+ * F->p [F->ncol] > F->nzmax. In this case, the remaining contents of F are
+ * not modified. F can still be properly free'd with cholmod_free_sparse.
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define PATTERN
+#include "t_cholmod_transpose.c"
+#define REAL
+#include "t_cholmod_transpose.c"
+#define COMPLEX
+#include "t_cholmod_transpose.c"
+#define COMPLEX
+#define NCONJUGATE
+#include "t_cholmod_transpose.c"
+#define ZOMPLEX
+#include "t_cholmod_transpose.c"
+#define ZOMPLEX
+#define NCONJUGATE
+#include "t_cholmod_transpose.c"
+
+
+/* ========================================================================== */
+/* === cholmod_transpose_unsym ============================================== */
+/* ========================================================================== */
+
+/* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is
+ * already allocated. See cholmod_transpose for a simpler routine.
+ *
+ * workspace:
+ * Iwork (MAX (nrow,ncol)) if fset is present
+ * Iwork (nrow) if fset is NULL
+ *
+ * The xtype of A and F must match, unless values is zero or F->xtype is
+ * CHOLMOD_PATTERN (in which case only the pattern of A is transpose into F).
+ */
+
+int CHOLMOD(transpose_unsym)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 2: complex conj. transpose, 1: array transpose,
+ 0: do not transpose the numerical values */
+ Int *Perm, /* size nrow, if present (can be NULL) */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Fp, *Fnz, *Ap, *Ai, *Anz, *Wi ;
+ Int nrow, ncol, permute, use_fset, Apacked, Fpacked, p, pend,
+ i, j, k, Fsorted, nf, jj, jlast ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (F, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (A->nrow != F->ncol || A->ncol != F->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "F has the wrong dimensions") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nf = fsize ;
+ use_fset = (fset != NULL) ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ Ap = A->p ; /* size A->ncol+1, column pointers of A */
+ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */
+ Anz = A->nz ;
+ Apacked = A->packed ;
+ ASSERT (IMPLIES (!Apacked, Anz != NULL)) ;
+
+ permute = (Perm != NULL) ;
+
+ Fp = F->p ; /* size A->nrow+1, row pointers of F */
+ Fnz = F->nz ;
+ Fpacked = F->packed ;
+ ASSERT (IMPLIES (!Fpacked, Fnz != NULL)) ;
+
+ nf = (use_fset) ? nf : ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = nrow + ((fset != NULL) ? ncol : 0) */
+ s = CHOLMOD(add_size_t) (nrow, ((fset != NULL) ? ncol : 0), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ Wi = Common->Iwork ; /* size nrow (i/l/l) */
+
+ /* ---------------------------------------------------------------------- */
+ /* check Perm and fset */
+ /* ---------------------------------------------------------------------- */
+
+ if (permute)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [i] = 1 ;
+ }
+ for (k = 0 ; k < nrow ; k++)
+ {
+ i = Perm [k] ;
+ if (i < 0 || i > nrow || Wi [i] == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid permutation") ;
+ return (FALSE) ;
+ }
+ Wi [i] = 0 ;
+ }
+ }
+
+ if (use_fset)
+ {
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Wi [j] = 1 ;
+ }
+ for (k = 0 ; k < nf ; k++)
+ {
+ j = fset [k] ;
+ if (j < 0 || j > ncol || Wi [j] == 0)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid fset") ;
+ return (FALSE) ;
+ }
+ Wi [j] = 0 ;
+ }
+ }
+
+ /* Perm and fset are now valid */
+ ASSERT (CHOLMOD(dump_perm) (Perm, nrow, nrow, "Perm", Common)) ;
+ ASSERT (CHOLMOD(dump_perm) (fset, nf, ncol, "fset", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each row of A or A(:,f) */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [i] = 0 ;
+ }
+
+ jlast = EMPTY ;
+ Fsorted = TRUE ;
+
+ if (use_fset)
+ {
+ /* count entries in each row of A(:,f) */
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = fset [jj] ;
+ if (j <= jlast)
+ {
+ Fsorted = FALSE ;
+ }
+ p = Ap [j] ;
+ pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Wi [Ai [p]]++ ;
+ }
+ jlast = j ;
+ }
+
+ /* save the nz counts if F is unpacked, and recount all of A */
+ if (!Fpacked)
+ {
+ if (permute)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fnz [i] = Wi [Perm [i]] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fnz [i] = Wi [i] ;
+ }
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [i] = 0 ;
+ }
+
+ /* count entries in each row of A */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Wi [Ai [p]]++ ;
+ }
+ }
+ }
+
+ }
+ else
+ {
+
+ /* count entries in each row of A */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Wi [Ai [p]]++ ;
+ }
+ }
+
+ /* save the nz counts if F is unpacked */
+ if (!Fpacked)
+ {
+ if (permute)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fnz [i] = Wi [Perm [i]] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fnz [i] = Wi [i] ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row pointers */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ if (permute)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fp [i] = p ;
+ p += Wi [Perm [i]] ;
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [Perm [i]] = Fp [i] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Fp [i] = p ;
+ p += Wi [i] ;
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wi [i] = Fp [i] ;
+ }
+ }
+ Fp [nrow] = p ;
+
+ if (p > (Int) (F->nzmax))
+ {
+ ERROR (CHOLMOD_INVALID, "F is too small") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* transpose matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ ok = FALSE ;
+ if (values == 0 || F->xtype == CHOLMOD_PATTERN)
+ {
+ ok = p_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ else if (F->xtype == CHOLMOD_REAL)
+ {
+ ok = r_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ else if (F->xtype == CHOLMOD_COMPLEX)
+ {
+ if (values == 1)
+ {
+ /* array transpose */
+ ok = ct_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ else
+ {
+ /* complex conjugate transpose */
+ ok = c_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ }
+ else if (F->xtype == CHOLMOD_ZOMPLEX)
+ {
+ if (values == 1)
+ {
+ /* array transpose */
+ ok = zt_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ else
+ {
+ /* complex conjugate transpose */
+ ok = z_cholmod_transpose_unsym (A, Perm, fset, nf, F, Common) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize result F */
+ /* ---------------------------------------------------------------------- */
+
+ if (ok)
+ {
+ F->sorted = Fsorted ;
+ }
+ ASSERT (CHOLMOD(dump_sparse) (F, "output F unsym", Common) >= 0) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_transpose_sym ================================================ */
+/* ========================================================================== */
+
+/* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated.
+ * See cholmod_transpose for a simpler routine.
+ *
+ * workspace: Iwork (nrow) if Perm NULL, Iwork (2*nrow) if Perm non-NULL.
+ */
+
+int CHOLMOD(transpose_sym)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 2: complex conj. transpose, 1: array transpose,
+ 0: do not transpose the numerical values */
+ Int *Perm, /* size nrow, if present (can be NULL) */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A' or A(p,p)' */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap, *Anz, *Ai, *Fp, *Wi, *Pinv, *Iwork ;
+ Int p, pend, packed, upper, permute, jold, n, i, j, k, iold ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (F, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (F, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (A->nrow != A->ncol || A->stype == 0)
+ {
+ /* this routine handles square symmetric matrices only */
+ ERROR (CHOLMOD_INVALID, "matrix must be symmetric") ;
+ return (FALSE) ;
+ }
+ if (A->nrow != F->ncol || A->ncol != F->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "F has the wrong dimensions") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ permute = (Perm != NULL) ;
+ n = A->nrow ;
+ Ap = A->p ; /* size A->ncol+1, column pointers of A */
+ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */
+ Anz = A->nz ;
+ packed = A->packed ;
+ ASSERT (IMPLIES (!packed, Anz != NULL)) ;
+ upper = (A->stype > 0) ;
+
+ Fp = F->p ; /* size A->nrow+1, row pointers of F */
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = (Perm != NULL) ? 2*n : n */
+ s = CHOLMOD(add_size_t) (n, ((Perm != NULL) ? n : 0), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Wi = Iwork ; /* size n (i/l/l) */
+ Pinv = Iwork + n ; /* size n (i/i/l) , unused if Perm NULL */
+
+ /* ---------------------------------------------------------------------- */
+ /* check Perm and construct inverse permutation */
+ /* ---------------------------------------------------------------------- */
+
+ if (permute)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Pinv [i] = EMPTY ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Perm [k] ;
+ if (i < 0 || i > n || Pinv [i] != EMPTY)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid permutation") ;
+ return (FALSE) ;
+ }
+ Pinv [i] = k ;
+ }
+ }
+
+ /* Perm is now valid */
+ ASSERT (CHOLMOD(dump_perm) (Perm, n, n, "Perm", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each row of F */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ Wi [i] = 0 ;
+ }
+
+ if (packed)
+ {
+ if (permute)
+ {
+ if (upper)
+ {
+ /* packed, permuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ pend = Ap [jold+1] ;
+ for (p = Ap [jold] ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold <= jold)
+ {
+ i = Pinv [iold] ;
+ Wi [MIN (i, j)]++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* packed, permuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ pend = Ap [jold+1] ;
+ for (p = Ap [jold] ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold >= jold)
+ {
+ i = Pinv [iold] ;
+ Wi [MAX (i, j)]++ ;
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ if (upper)
+ {
+ /* packed, unpermuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ pend = Ap [j+1] ;
+ for (p = Ap [j] ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i <= j)
+ {
+ Wi [i]++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* packed, unpermuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ pend = Ap [j+1] ;
+ for (p = Ap [j] ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= j)
+ {
+ Wi [i]++ ;
+ }
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ if (permute)
+ {
+ if (upper)
+ {
+ /* unpacked, permuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ p = Ap [jold] ;
+ pend = p + Anz [jold] ;
+ for ( ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold <= jold)
+ {
+ i = Pinv [iold] ;
+ Wi [MIN (i, j)]++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* unpacked, permuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ p = Ap [jold] ;
+ pend = p + Anz [jold] ;
+ for ( ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold >= jold)
+ {
+ i = Pinv [iold] ;
+ Wi [MAX (i, j)]++ ;
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ if (upper)
+ {
+ /* unpacked, unpermuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i <= j)
+ {
+ Wi [i]++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* unpacked, unpermuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Ap [j] ;
+ pend = p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= j)
+ {
+ Wi [i]++ ;
+ }
+ }
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row pointers */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Fp [i] = p ;
+ p += Wi [i] ;
+ }
+ Fp [n] = p ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Wi [i] = Fp [i] ;
+ }
+
+ if (p > (Int) (F->nzmax))
+ {
+ ERROR (CHOLMOD_INVALID, "F is too small") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* transpose matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ ok = FALSE ;
+ if (values == 0 || F->xtype == CHOLMOD_PATTERN)
+ {
+ PRINT2 (("\n:::: p_transpose_sym Perm %p\n", Perm)) ;
+ ok = p_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ else if (F->xtype == CHOLMOD_REAL)
+ {
+ PRINT2 (("\n:::: r_transpose_sym Perm %p\n", Perm)) ;
+ ok = r_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ else if (F->xtype == CHOLMOD_COMPLEX)
+ {
+ if (values == 1)
+ {
+ /* array transpose */
+ PRINT2 (("\n:::: ct_transpose_sym Perm %p\n", Perm)) ;
+ ok = ct_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ else
+ {
+ /* complex conjugate transpose */
+ PRINT2 (("\n:::: c_transpose_sym Perm %p\n", Perm)) ;
+ ok = c_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ }
+ else if (F->xtype == CHOLMOD_ZOMPLEX)
+ {
+ if (values == 1)
+ {
+ /* array transpose */
+ PRINT2 (("\n:::: zt_transpose_sym Perm %p\n", Perm)) ;
+ ok = zt_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ else
+ {
+ /* complex conjugate transpose */
+ PRINT2 (("\n:::: z_transpose_sym Perm %p\n", Perm)) ;
+ ok = z_cholmod_transpose_sym (A, Perm, F, Common) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize result F */
+ /* ---------------------------------------------------------------------- */
+
+ /* F is sorted if there is no permutation vector */
+ if (ok)
+ {
+ F->sorted = !permute ;
+ F->packed = TRUE ;
+ F->stype = - SIGN (A->stype) ; /* flip the stype */
+ ASSERT (CHOLMOD(dump_sparse) (F, "output F sym", Common) >= 0) ;
+ }
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_transpose ==================================================== */
+/* ========================================================================== */
+
+/* Returns A'. See also cholmod_ptranspose below. */
+
+cholmod_sparse *CHOLMOD(transpose)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 2: complex conj. transpose, 1: array transpose,
+ 0: do not transpose the numerical values
+ (returns its result as CHOLMOD_PATTERN) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(ptranspose) (A, values, NULL, NULL, 0, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_ptranspose =================================================== */
+/* ========================================================================== */
+
+/* Return A' or A(p,p)' if A is symmetric. Return A', A(:,f)', or A(p,f)' if
+ * A is unsymmetric.
+ *
+ * workspace:
+ * Iwork (MAX (nrow,ncol)) if unsymmetric and fset is non-NULL
+ * Iwork (nrow) if unsymmetric and fset is NULL
+ * Iwork (2*nrow) if symmetric and Perm is non-NULL.
+ * Iwork (nrow) if symmetric and Perm is NULL.
+ *
+ * A simple worst-case upper bound on the workspace is nrow+ncol.
+ */
+
+cholmod_sparse *CHOLMOD(ptranspose)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 2: complex conj. transpose, 1: array transpose,
+ 0: do not transpose the numerical values */
+ Int *Perm, /* if non-NULL, F = A(p,f) or A(p,p) */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap, *Anz ;
+ cholmod_sparse *F ;
+ Int nrow, ncol, use_fset, j, jj, fnz, packed, stype, nf, xtype ;
+ size_t ineed ;
+ int ok = TRUE ;
+
+ nf = fsize ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ stype = A->stype ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ if (stype != 0)
+ {
+ use_fset = FALSE ;
+ if (Perm != NULL)
+ {
+ ineed = CHOLMOD(mult_size_t) (A->nrow, 2, &ok) ;
+ }
+ else
+ {
+ ineed = A->nrow ;
+ }
+ }
+ else
+ {
+ use_fset = (fset != NULL) ;
+ if (use_fset)
+ {
+ ineed = MAX (A->nrow, A->ncol) ;
+ }
+ else
+ {
+ ineed = A->nrow ;
+ }
+ }
+
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+
+ CHOLMOD(allocate_work) (0, ineed, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ ASSERT (IMPLIES (!packed, Anz != NULL)) ;
+ xtype = values ? A->xtype : CHOLMOD_PATTERN ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate F */
+ /* ---------------------------------------------------------------------- */
+
+ /* determine # of nonzeros in F */
+ if (stype != 0)
+ {
+ /* F=A' or F=A(p,p)', fset is ignored */
+ fnz = CHOLMOD(nnz) (A, Common) ;
+ }
+ else
+ {
+ nf = (use_fset) ? nf : ncol ;
+ if (use_fset)
+ {
+ fnz = 0 ;
+ /* F=A(:,f)' or F=A(p,f)' */
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ /* The fset is not yet checked; it will be thoroughly checked
+ * in cholmod_transpose_unsym. For now, just make sure we don't
+ * access Ap and Anz out of bounds. */
+ j = fset [jj] ;
+ if (j >= 0 && j < ncol)
+ {
+ fnz += packed ? (Ap [j+1] - Ap [j]) : MAX (0, Anz [j]) ;
+ }
+ }
+ }
+ else
+ {
+ /* F=A' or F=A(p,:)' */
+ fnz = CHOLMOD(nnz) (A, Common) ;
+ }
+ }
+
+ /* F is ncol-by-nrow, fnz nonzeros, sorted unless f is present and unsorted,
+ * packed, of opposite stype as A, and with/without numerical values */
+ F = CHOLMOD(allocate_sparse) (ncol, nrow, fnz, TRUE, TRUE, -SIGN(stype),
+ xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* transpose and optionally permute the matrix A */
+ /* ---------------------------------------------------------------------- */
+
+ if (stype != 0)
+ {
+ /* F = A (p,p)', using upper or lower triangular part of A only */
+ ok = CHOLMOD(transpose_sym) (A, values, Perm, F, Common) ;
+ }
+ else
+ {
+ /* F = A (p,f)' */
+ ok = CHOLMOD(transpose_unsym) (A, values, Perm, fset, nf, F, Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the matrix F, or NULL if an error occured */
+ /* ---------------------------------------------------------------------- */
+
+ if (!ok)
+ {
+ CHOLMOD(free_sparse) (&F, Common) ;
+ }
+ return (F) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_sort ========================================================= */
+/* ========================================================================== */
+
+/* Sort the columns of A, in place. Returns A in packed form, even if it
+ * starts as unpacked. Removes entries in the ignored part of a symmetric
+ * matrix.
+ *
+ * workspace: Iwork (max (nrow,ncol)). Allocates additional workspace for a
+ * temporary copy of A'.
+ */
+
+int CHOLMOD(sort)
+(
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to sort */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap ;
+ cholmod_sparse *F ;
+ Int anz, ncol, nrow, stype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ nrow = A->nrow ;
+ if (nrow <= 1)
+ {
+ /* a 1-by-n sparse matrix must be sorted */
+ A->sorted = TRUE ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ ncol = A->ncol ;
+ CHOLMOD(allocate_work) (0, MAX (nrow, ncol), 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ anz = CHOLMOD(nnz) (A, Common) ;
+ stype = A->stype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* sort the columns of the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* allocate workspace for transpose: ncol-by-nrow, same # of nonzeros as A,
+ * sorted, packed, same stype as A, and of the same numeric type as A. */
+ F = CHOLMOD(allocate_sparse) (ncol, nrow, anz, TRUE, TRUE, stype,
+ A->xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ if (stype != 0)
+ {
+ /* F = A', upper or lower triangular part only */
+ CHOLMOD(transpose_sym) (A, 1, NULL, F, Common) ;
+ A->packed = TRUE ;
+ /* A = F' */
+ CHOLMOD(transpose_sym) (F, 1, NULL, A, Common) ;
+ }
+ else
+ {
+ /* F = A' */
+ CHOLMOD(transpose_unsym) (A, 1, NULL, NULL, 0, F, Common) ;
+ A->packed = TRUE ;
+ /* A = F' */
+ CHOLMOD(transpose_unsym) (F, 1, NULL, NULL, 0, A, Common) ;
+ }
+
+ ASSERT (A->sorted && A->packed) ;
+ ASSERT (CHOLMOD(dump_sparse) (A, "Asorted", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce A in size, if needed. This must succeed. */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ anz = Ap [ncol] ;
+ ASSERT ((size_t) anz <= A->nzmax) ;
+ CHOLMOD(reallocate_sparse) (anz, A, Common) ;
+ ASSERT (Common->status >= CHOLMOD_OK) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&F, Common) ;
+ return (TRUE) ;
+}
diff --git a/CHOLMOD/Core/cholmod_triplet.c b/CHOLMOD/Core/cholmod_triplet.c
new file mode 100644
index 0000000..5ce7ad8
--- /dev/null
+++ b/CHOLMOD/Core/cholmod_triplet.c
@@ -0,0 +1,773 @@
+/* ========================================================================== */
+/* === Core/cholmod_triplet ================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Core utility routines for the cholmod_triplet object:
+ *
+ * A sparse matrix held in triplet form is the simplest one for a user to
+ * create. It consists of a list of nz entries in arbitrary order, held in
+ * three arrays: i, j, and x, each of length nk. The kth entry is in row i[k],
+ * column j[k], with value x[k]. There may be duplicate values; if A(i,j)
+ * appears more than once, its value is the sum of the entries with those row
+ * and column indices.
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_allocate_triplet allocate a triplet matrix
+ * cholmod_free_triplet free a triplet matrix
+ *
+ * Secondary routines:
+ * -------------------
+ * cholmod_reallocate_triplet reallocate a triplet matrix
+ * cholmod_sparse_to_triplet create a triplet matrix copy of a sparse matrix
+ * cholmod_triplet_to_sparse create a sparse matrix copy of a triplet matrix
+ * cholmod_copy_triplet create a copy of a triplet matrix
+ *
+ * The relationship between an m-by-n cholmod_sparse matrix A and a
+ * cholmod_triplet matrix (i, j, and x) is identical to how they are used in
+ * the MATLAB "sparse" and "find" functions:
+ *
+ * [i j x] = find (A)
+ * [m n] = size (A)
+ * A = sparse (i,j,x,m,n)
+ *
+ * with the exception that the cholmod_sparse matrix may be "unpacked", may
+ * have either sorted or unsorted columns (depending on the option selected),
+ * and may be symmetric with just the upper or lower triangular part stored.
+ * Likewise, the cholmod_triplet matrix may contain just the entries in the
+ * upper or lower triangular part of a symmetric matrix.
+ *
+ * MATLAB sparse matrices are always "packed", always have sorted columns,
+ * and always store both parts of a symmetric matrix. In some cases, MATLAB
+ * behaves like CHOLMOD by ignoring entries in the upper or lower triangular
+ * part of a matrix that is otherwise assumed to be symmetric (such as the
+ * input to chol). In CHOLMOD, that option is a characteristic of the object.
+ * In MATLAB, that option is based on how a matrix is used as the input to
+ * a function.
+ *
+ * The triplet matrix is provided to give the user a simple way of constructing
+ * a sparse matrix. There are very few operations supported for triplet
+ * matrices. The assumption is that they will be converted to cholmod_sparse
+ * matrix form first.
+ *
+ * Adding two triplet matrices simply involves concatenating the contents of
+ * the three arrays (i, j, and x). To permute a triplet matrix, just replace
+ * the row and column indices with their permuted values. For example, if
+ * P is a permutation vector, then P [k] = j means row/column j is the kth
+ * row/column in C=P*A*P'. In MATLAB notation, C=A(p,p). If Pinv is an array
+ * of size n and T is the triplet form of A, then:
+ *
+ * Ti = T->i ;
+ * Tj = T->j ;
+ * for (k = 0 ; k < n ; k++) Pinv [P [k]] = k ;
+ * for (k = 0 ; k < nz ; k++) Ti [k] = Pinv [Ti [k]] ;
+ * for (k = 0 ; k < nz ; k++) Tj [k] = Pinv [Tj [k]] ;
+ *
+ * overwrites T with the triplet form of C=P*A*P'. The conversion
+ *
+ * C = cholmod_triplet_to_sparse (T, 0, &Common) ;
+ *
+ * will then return the matrix C = P*A*P'.
+ *
+ * Note that T->stype > 0 means that entries in the lower triangular part of
+ * T are transposed into the upper triangular part when T is converted to
+ * sparse matrix (cholmod_sparse) form with cholmod_triplet_to_sparse. The
+ * opposite is true for T->stype < 0.
+ *
+ * Since the triplet matrix T is so simple to generate, it's quite easy
+ * to remove entries that you do not want, prior to converting T to the
+ * cholmod_sparse form. So if you include these entries in T, CHOLMOD
+ * assumes that there must be a reason (such as the one above). Thus,
+ * no entry in a triplet matrix is ever ignored.
+ *
+ * Other operations, such as extacting a submatrix, horizontal and vertical
+ * concatenation, multiply a triplet matrix times a dense matrix, are also
+ * simple. Multiplying two triplet matrices is not trivial; the simplest
+ * method is to convert them to cholmod_sparse matrices first.
+ *
+ * Supports all xtypes (pattern, real, complex, and zomplex).
+ */
+
+#include "cholmod_internal.h"
+#include "cholmod_core.h"
+
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define PATTERN
+#include "t_cholmod_triplet.c"
+#define REAL
+#include "t_cholmod_triplet.c"
+#define COMPLEX
+#include "t_cholmod_triplet.c"
+#define ZOMPLEX
+#include "t_cholmod_triplet.c"
+
+
+/* ========================================================================== */
+/* === cholmod_allocate_triplet ============================================= */
+/* ========================================================================== */
+
+/* allocate space for a triplet matrix
+ *
+ * workspace: none
+ */
+
+cholmod_triplet *CHOLMOD(allocate_triplet)
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of T */
+ size_t ncol, /* # of columns of T */
+ size_t nzmax, /* max # of nonzeros of T */
+ int stype, /* stype of T */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_triplet *T ;
+ size_t nzmax0 ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ if (xtype < CHOLMOD_PATTERN || xtype > CHOLMOD_ZOMPLEX)
+ {
+ ERROR (CHOLMOD_INVALID, "xtype invalid") ;
+ return (NULL) ;
+ }
+ /* ensure the dimensions do not cause integer overflow */
+ (void) CHOLMOD(add_size_t) (ncol, 2, &ok) ;
+ if (!ok || nrow > Int_max || ncol > Int_max || nzmax > Int_max)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate header */
+ /* ---------------------------------------------------------------------- */
+
+ T = CHOLMOD(malloc) (sizeof (cholmod_triplet), 1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ PRINT1 (("cholmod_allocate_triplet %d-by-%d nzmax %d xtype %d\n",
+ nrow, ncol, nzmax, xtype)) ;
+
+ nzmax = MAX (1, nzmax) ;
+
+ T->nrow = nrow ;
+ T->ncol = ncol ;
+ T->nzmax = nzmax ;
+ T->nnz = 0 ;
+ T->stype = stype ;
+ T->itype = ITYPE ;
+ T->xtype = xtype ;
+ T->dtype = DTYPE ;
+
+ T->j = NULL ;
+ T->i = NULL ;
+ T->x = NULL ;
+ T->z = NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the matrix itself */
+ /* ---------------------------------------------------------------------- */
+
+ nzmax0 = 0 ;
+ CHOLMOD(realloc_multiple) (nzmax, 2, xtype, &(T->i), &(T->j),
+ &(T->x), &(T->z), &nzmax0, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_triplet) (&T, Common) ;
+ return (NULL) ; /* out of memory */
+ }
+
+ return (T) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_free_triplet ================================================= */
+/* ========================================================================== */
+
+/* free a triplet matrix
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(free_triplet)
+(
+ /* ---- in/out --- */
+ cholmod_triplet **THandle, /* matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int nz ;
+ cholmod_triplet *T ;
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+
+ if (THandle == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ T = *THandle ;
+ if (T == NULL)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+ nz = T->nzmax ;
+ T->j = CHOLMOD(free) (nz, sizeof (Int), T->j, Common) ;
+ T->i = CHOLMOD(free) (nz, sizeof (Int), T->i, Common) ;
+ if (T->xtype == CHOLMOD_REAL)
+ {
+ T->x = CHOLMOD(free) (nz, sizeof (double), T->x, Common) ;
+ }
+ else if (T->xtype == CHOLMOD_COMPLEX)
+ {
+ T->x = CHOLMOD(free) (nz, 2*sizeof (double), T->x, Common) ;
+ }
+ else if (T->xtype == CHOLMOD_ZOMPLEX)
+ {
+ T->x = CHOLMOD(free) (nz, sizeof (double), T->x, Common) ;
+ T->z = CHOLMOD(free) (nz, sizeof (double), T->z, Common) ;
+ }
+ *THandle = CHOLMOD(free) (1, sizeof (cholmod_triplet), (*THandle), Common) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_reallocate_triplet =========================================== */
+/* ========================================================================== */
+
+/* Change the size of T->i, T->j, and T->x, or allocate them if their current
+ * size is zero. T->x is not modified if T->xtype is CHOLMOD_PATTERN.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(reallocate_triplet)
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in T */
+ /* ---- in/out --- */
+ cholmod_triplet *T, /* triplet matrix to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (T, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ PRINT1 (("realloc triplet %d to %d, xtype: %d\n",
+ T->nzmax, nznew, T->xtype)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* resize the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(realloc_multiple) (MAX (1,nznew), 2, T->xtype, &(T->i), &(T->j),
+ &(T->x), &(T->z), &(T->nzmax), Common) ;
+
+ return (Common->status == CHOLMOD_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_triplet_to_sparse ============================================ */
+/* ========================================================================== */
+
+/* Convert a set of triplets into a cholmod_sparse matrix. In MATLAB notation,
+ * for unsymmetric matrices:
+ *
+ * A = sparse (Ti, Tj, Tx, nrow, ncol, nzmax) ;
+ *
+ * For the symmetric upper case:
+ *
+ * A = sparse (min(Ti,Tj), max(Ti,Tj), Tx, nrow, ncol, nzmax) ;
+ *
+ * For the symmetric lower case:
+ *
+ * A = sparse (max(Ti,Tj), min(Ti,Tj), Tx, nrow, ncol, nzmax) ;
+ *
+ * If Tx is NULL, then A->x is not allocated, and only the pattern of A is
+ * computed. A is returned in packed form, and can be of any stype
+ * (upper/lower/unsymmetric). It has enough space to hold the values in T,
+ * or nzmax, whichever is larger.
+ *
+ * workspace: Iwork (max (nrow,ncol))
+ * allocates a temporary copy of its output matrix.
+ *
+ * The resulting sparse matrix has the same xtype as the input triplet matrix.
+ */
+
+cholmod_sparse *CHOLMOD(triplet_to_sparse)
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* matrix to copy */
+ size_t nzmax, /* allocate at least this much space in output matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *R, *A = NULL ;
+ Int *Wj, *Rp, *Ri, *Rnz, *Ti, *Tj ;
+ Int i, j, p, k, stype, nrow, ncol, nz, ok ;
+ size_t anz = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (T, NULL) ;
+ Ti = T->i ;
+ Tj = T->j ;
+ RETURN_IF_NULL (Ti, NULL) ;
+ RETURN_IF_NULL (Tj, NULL) ;
+ RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ stype = SIGN (T->stype) ;
+ if (stype && T->nrow != T->ncol)
+ {
+ /* inputs invalid */
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ DEBUG (CHOLMOD(dump_triplet) (T, "T", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = T->nrow ;
+ ncol = T->ncol ;
+ nz = T->nnz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(allocate_work) (0, MAX (nrow, ncol), 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate temporary matrix R */
+ /* ---------------------------------------------------------------------- */
+
+ R = CHOLMOD(allocate_sparse) (ncol, nrow, nz, FALSE, FALSE, -stype,
+ T->xtype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ Rp = R->p ;
+ Ri = R->i ;
+ Rnz = R->nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each row of A (also counting duplicates) */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Rnz [i] = 0 ;
+ }
+
+ if (stype > 0)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i < 0 || i >= nrow || j < 0 || j >= ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "index out of range") ;
+ break ;
+ }
+ /* A will be symmetric with just the upper triangular part stored.
+ * Create a matrix R that is lower triangular. Entries in the
+ * upper part of R are transposed to the lower part. */
+ Rnz [MIN (i,j)]++ ;
+ }
+ }
+ else if (stype < 0)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i < 0 || i >= nrow || j < 0 || j >= ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "index out of range") ;
+ break ;
+ }
+ /* A will be symmetric with just the lower triangular part stored.
+ * Create a matrix R that is upper triangular. Entries in the
+ * lower part of R are transposed to the upper part. */
+ Rnz [MAX (i,j)]++ ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i < 0 || i >= nrow || j < 0 || j >= ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "index out of range") ;
+ break ;
+ }
+ /* constructing an unsymmetric matrix */
+ Rnz [i]++ ;
+ }
+ }
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* triplet matrix is invalid */
+ CHOLMOD(free_sparse) (&R, Common) ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the row pointers */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Rp [i] = p ;
+ p += Rnz [i] ;
+ }
+ Rp [nrow] = p ;
+
+ /* use Wj (i/l/l) as temporary row pointers */
+ Wj = Common->Iwork ; /* size MAX (nrow,ncol) FUTURE WORK: (i/l/l) */
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Wj [i] = Rp [i] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct triplet matrix, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (T->xtype)
+ {
+ case CHOLMOD_PATTERN:
+ anz = p_cholmod_triplet_to_sparse (T, R, Common) ;
+ break ;
+
+ case CHOLMOD_REAL:
+ anz = r_cholmod_triplet_to_sparse (T, R, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ anz = c_cholmod_triplet_to_sparse (T, R, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ anz = z_cholmod_triplet_to_sparse (T, R, Common) ;
+ break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* A = R' (array transpose, not complex conjugate transpose) */
+ /* ---------------------------------------------------------------------- */
+
+ /* workspace: Iwork (R->nrow), which is A->ncol */
+
+ ASSERT (CHOLMOD(dump_sparse) (R, "R", Common) >= 0) ;
+
+ A = CHOLMOD(allocate_sparse) (nrow, ncol, MAX (anz, nzmax), TRUE, TRUE,
+ stype, T->xtype, Common) ;
+
+ if (stype)
+ {
+ ok = CHOLMOD(transpose_sym) (R, 1, NULL, A, Common) ;
+ }
+ else
+ {
+ ok = CHOLMOD(transpose_unsym) (R, 1, NULL, NULL, 0, A, Common) ;
+ }
+
+ CHOLMOD(free_sparse) (&R, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free_sparse) (&A, Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "A = triplet(T) result", Common) >= 0) ;
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_sparse_to_triplet ============================================ */
+/* ========================================================================== */
+
+/* Converts a sparse column-oriented matrix to triplet form.
+ * The resulting triplet matrix has the same xtype as the sparse matrix.
+ *
+ * workspace: none
+ */
+
+cholmod_triplet *CHOLMOD(sparse_to_triplet)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Az, *Tx, *Tz ;
+ Int *Ap, *Ai, *Ti, *Tj, *Anz ;
+ cholmod_triplet *T ;
+ Int i, xtype, p, pend, k, j, nrow, ncol, nz, stype, packed, up, lo,
+ both ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ stype = SIGN (A->stype) ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ if (stype && nrow != ncol)
+ {
+ /* inputs invalid */
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (NULL) ;
+ }
+ Ax = A->x ;
+ Az = A->z ;
+ xtype = A->xtype ;
+ Common->status = CHOLMOD_OK ;
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate triplet matrix */
+ /* ---------------------------------------------------------------------- */
+
+ nz = CHOLMOD(nnz) (A, Common) ;
+ T = CHOLMOD(allocate_triplet) (nrow, ncol, nz, A->stype, A->xtype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to a sparse matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+ packed = A->packed ;
+
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ Tz = T->z ;
+ T->stype = A->stype ;
+
+ both = (A->stype == 0) ;
+ up = (A->stype > 0) ;
+ lo = (A->stype < 0) ;
+
+ k = 0 ;
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (both || (up && i <= j) || (lo && i >= j))
+ {
+ Ti [k] = Ai [p] ;
+ Tj [k] = j ;
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ Tx [k] = Ax [p] ;
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ Tx [2*k ] = Ax [2*p ] ;
+ Tx [2*k+1] = Ax [2*p+1] ;
+ }
+ else if (xtype == CHOLMOD_ZOMPLEX)
+ {
+ Tx [k] = Ax [p] ;
+ Tz [k] = Az [p] ;
+ }
+
+ k++ ;
+ ASSERT (k <= nz) ;
+ }
+ }
+ }
+
+ T->nnz = k ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_triplet) (T, "T", Common)) ;
+ return (T) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_copy_triplet ================================================= */
+/* ========================================================================== */
+
+/* Create an exact copy of a triplet matrix, except that entries in unused
+ * space are not copied (they might not be initialized, and copying them would
+ * cause program checkers such as purify and valgrind to complain).
+ * The output triplet matrix has the same xtype as the input triplet matrix.
+ */
+
+cholmod_triplet *CHOLMOD(copy_triplet)
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Tx, *Tz, *Cx, *Cz ;
+ Int *Ci, *Cj, *Ti, *Tj ;
+ cholmod_triplet *C ;
+ Int xtype, k, nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (T, NULL) ;
+ RETURN_IF_XTYPE_INVALID (T, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, NULL) ;
+ nz = T->nnz ;
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ Tz = T->z ;
+ xtype = T->xtype ;
+ RETURN_IF_NULL (Ti, NULL) ;
+ RETURN_IF_NULL (Tj, NULL) ;
+ Common->status = CHOLMOD_OK ;
+ DEBUG (CHOLMOD(dump_triplet) (T, "T input", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate copy */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_triplet) (T->nrow, T->ncol, T->nzmax, T->stype,
+ xtype, Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the triplet matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Ci = C->i ;
+ Cj = C->j ;
+ Cx = C->x ;
+ Cz = C->z ;
+ C->nnz = nz ;
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Ci [k] = Ti [k] ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Cj [k] = Tj [k] ;
+ }
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ Cx [k] = Tx [k] ;
+ }
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ Cx [2*k ] = Tx [2*k ] ;
+ Cx [2*k+1] = Tx [2*k+1] ;
+ }
+ }
+ else if (xtype == CHOLMOD_ZOMPLEX)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ Cx [k] = Tx [k] ;
+ Cz [k] = Tz [k] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_triplet) (C, "C triplet copy", Common)) ;
+ return (C) ;
+}
diff --git a/CHOLMOD/Core/lesser.txt b/CHOLMOD/Core/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/CHOLMOD/Core/lesser.txt
@@ -0,0 +1,504 @@
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+This section is intended to make thoroughly clear what is believed to
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+
+ 12. If the distribution and/or use of the Library is restricted in
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+so that distribution is permitted only in or among countries not thus
+excluded. In such case, this License incorporates the limitation as if
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+
+ 13. The Free Software Foundation may publish revised and/or new
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+the Free Software Foundation. If the Library does not specify a
+license version number, you may choose any version ever published by
+the Free Software Foundation.
+
+ 14. If you wish to incorporate parts of the Library into other free
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+Software Foundation; we sometimes make exceptions for this. Our
+decision will be guided by the two goals of preserving the free status
+of all derivatives of our free software and of promoting the sharing
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+ 15. BECAUSE THE LIBRARY IS LICENSED FREE OF CHARGE, THERE IS NO
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+DAMAGES.
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+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Libraries
+
+ If you develop a new library, and you want it to be of the greatest
+possible use to the public, we recommend making it free software that
+everyone can redistribute and change. You can do so by permitting
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+ To apply these terms, attach the following notices to the library. It is
+safest to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least the
+"copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the library's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
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+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+Also add information on how to contact you by electronic and paper mail.
+
+You should also get your employer (if you work as a programmer) or your
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+ library `Frob' (a library for tweaking knobs) written by James Random Hacker.
+
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+ Ty Coon, President of Vice
+
+That's all there is to it!
+
+
diff --git a/CHOLMOD/Core/t_cholmod_change_factor.c b/CHOLMOD/Core/t_cholmod_change_factor.c
new file mode 100644
index 0000000..548f883
--- /dev/null
+++ b/CHOLMOD/Core/t_cholmod_change_factor.c
@@ -0,0 +1,661 @@
+/* ========================================================================== */
+/* === Core/t_cholmod_change_factor ========================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_change_factor. All xtypes supported. */
+
+#include "cholmod_template.h"
+
+/* ========================================================================== */
+/* === t_change_simplicial_numeric ========================================== */
+/* ========================================================================== */
+
+static void TEMPLATE (change_simplicial_numeric)
+(
+ cholmod_factor *L,
+ Int to_ll,
+ Int to_packed,
+ Int *newLi,
+ double *newLx,
+ double *newLz,
+ Int lnz,
+ Int grow,
+ double grow1,
+ Int grow2,
+ Int make_ll,
+ Int make_monotonic,
+ Int make_ldl,
+ cholmod_common *Common
+)
+{
+ double xlen, dj [1], ljj [1], lj2 [1] ;
+ double *Lx, *Lz ;
+ Int *Lp, *Li, *Lnz ;
+ Int n, j, len, pnew, pold, k, p, pend ;
+
+ n = L->n ;
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lz = L->z ;
+ Lnz = L->nz ;
+
+ if (make_ll)
+ {
+ L->minor = n ;
+ }
+
+ if (make_monotonic)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* reorder the columns to make them monotonic */
+ /* ------------------------------------------------------------------ */
+
+ pnew = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ /* copy and pack column j */
+ len = Lnz [j] ;
+ PRINT2 (("j: "ID" Lnz[j] "ID" len "ID" p "ID"\n",
+ j, Lnz [j], len, pnew)) ;
+ pold = Lp [j] ;
+ ASSERT (Li [pold] == j) ;
+
+ if (make_ll)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* copy and convert LDL' to LL' */
+ /* ---------------------------------------------------------- */
+
+ /* dj = Lx [pold] ; */
+ ASSIGN_REAL (dj,0, Lx,pold) ;
+
+ if (IS_LE_ZERO (dj [0]))
+ {
+ /* Conversion has failed; matrix is not positive definite.
+ * Do not modify the column so that the LDL' factorization
+ * can be restored if desired, by converting back to LDL'.
+ * Continue the conversion, but flag the error. */
+ if (L->minor == (size_t) n)
+ {
+ ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ;
+ L->minor = j ;
+ }
+ for (k = 0 ; k < len ; k++)
+ {
+ newLi [pnew + k] = Li [pold + k] ;
+ /* newLx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ }
+ else
+ {
+ ljj [0] = sqrt (dj [0]) ;
+ newLi [pnew] = j ;
+ /* newLx [pnew] = ljj ; */
+ ASSIGN_REAL (newLx, pnew, ljj, 0) ;
+ CLEAR_IMAG (newLx, newLz, pnew) ;
+
+ for (k = 1 ; k < len ; k++)
+ {
+ newLi [pnew + k] = Li [pold + k] ;
+ /* newLx [pnew + k] = Lx [pold + k] * ljj ; */
+ MULT_REAL (newLx, newLz, pnew+k, Lx, Lz, pold+k, ljj,0);
+ }
+ }
+
+ }
+ else if (make_ldl)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* copy and convert LL' to LDL' */
+ /* ---------------------------------------------------------- */
+
+ /* ljj = Lx [pold] ; */
+ ASSIGN_REAL (ljj, 0, Lx, pold) ;
+
+ if (ljj [0] <= 0)
+ {
+ /* matrix is not positive-definite; copy column as-is */
+ for (k = 0 ; k < len ; k++)
+ {
+ newLi [pnew + k] = Li [pold + k] ;
+ /* newLx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ }
+ else
+ {
+ newLi [pnew] = j ;
+ /* newLx [pnew] = ljj*ljj ; */
+ lj2 [0] = ljj [0] * ljj [0] ;
+ ASSIGN_REAL (newLx, pnew, lj2, 0) ;
+ CLEAR_IMAG (newLx, newLz, pnew) ;
+
+ for (k = 1 ; k < len ; k++)
+ {
+ newLi [pnew + k] = Li [pold + k] ;
+ /* newLx [pnew + k] = Lx [pold + k] / ljj ; */
+ DIV_REAL (newLx, newLz, pnew+k, Lx, Lz, pold+k, ljj,0) ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* copy and leave LL' or LDL' as-is */
+ /* ---------------------------------------------------------- */
+
+ for (k = 0 ; k < len ; k++)
+ {
+ newLi [pnew + k] = Li [pold + k] ;
+ /* newLx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (newLx, newLz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ }
+
+ Lp [j] = pnew ;
+
+ /* compute len in double to avoid integer overflow */
+ if (grow)
+ {
+ xlen = (double) len ;
+ xlen = grow1 * xlen + grow2 ;
+ xlen = MIN (xlen, n-j) ;
+ len = (Int) xlen ;
+ }
+ ASSERT (len >= Lnz [j] && len <= n-j) ;
+ pnew += len ;
+ ASSERT (pnew > 0) ; /* integer overflow case already covered */
+ }
+ Lp [n] = pnew ;
+ PRINT1 (("final pnew = "ID", lnz "ID" lnzmax %g\n",
+ pnew, lnz, (double) L->nzmax)) ;
+ ASSERT (pnew <= lnz) ;
+
+ /* free the old L->i and L->x and replace with the new ones */
+ CHOLMOD(free) (L->nzmax, sizeof (Int), L->i, Common) ;
+
+#ifdef REAL
+ CHOLMOD(free) (L->nzmax, sizeof (double), L->x, Common) ;
+#elif defined (COMPLEX)
+ CHOLMOD(free) (L->nzmax, 2*sizeof (double), L->x, Common) ;
+#else
+ CHOLMOD(free) (L->nzmax, sizeof (double), L->x, Common) ;
+ CHOLMOD(free) (L->nzmax, sizeof (double), L->z, Common) ;
+#endif
+
+ L->i = newLi ;
+ L->x = newLx ;
+ L->z = newLz ;
+ L->nzmax = lnz ;
+
+ /* reconstruct the link list */
+ natural_list (L) ;
+
+ }
+ else if (to_packed)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* already monotonic, just pack the columns of L */
+ /* ------------------------------------------------------------------ */
+
+ pnew = 0 ;
+
+ if (make_ll)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* pack and convert LDL' to LL' */
+ /* -------------------------------------------------------------- */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* pack column j */
+ pold = Lp [j] ;
+ len = Lnz [j] ;
+ ASSERT (len > 0) ;
+ ASSERT (Li [pold] == j) ;
+ PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ;
+
+ /* dj = Lx [pold] ; */
+ ASSIGN_REAL (dj,0, Lx,pold) ;
+
+ if (IS_LE_ZERO (dj [0]))
+ {
+ /* Conversion has failed; matrix is not positive definite.
+ * Do not modify the column so that the LDL' factorization
+ * can be restored if desired, by converting back to LDL'.
+ * Continue the conversion, but flag the error. */
+ if (L->minor == (size_t) n)
+ {
+ ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ;
+ L->minor = j ;
+ }
+ for (k = 0 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ /* Lx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ }
+ else
+ {
+ ljj [0] = sqrt (dj [0]) ;
+ Li [pnew] = j ;
+
+ /* Lx [pnew] = ljj ; */
+ ASSIGN_REAL (Lx, pnew, ljj, 0) ;
+ CLEAR_IMAG (Lx, Lz, pnew) ;
+
+ for (k = 1 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ /* Lx [pnew + k] = Lx [pold + k] * ljj ; */
+ MULT_REAL (Lx, Lz, pnew+k, Lx, Lz, pold+k, ljj,0) ;
+ }
+ }
+ Lp [j] = pnew ;
+ pnew += len ;
+ }
+
+ }
+ else if (make_ldl)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* pack and convert LL' to LDL' */
+ /* -------------------------------------------------------------- */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* pack column j */
+ pold = Lp [j] ;
+ len = Lnz [j] ;
+
+ /* ljj = Lx [pold] ; */
+ ASSIGN_REAL (ljj, 0, Lx, pold) ;
+
+ ASSERT (len > 0) ;
+ PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ;
+ if (ljj [0] <= 0)
+ {
+ /* matrix is not positive-definite; pack column as-is */
+ for (k = 0 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ /* Lx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ }
+ else
+ {
+ Li [pnew] = Li [pold] ;
+
+ /* Lx [pnew] = ljj*ljj ; */
+ lj2 [0] = ljj [0] * ljj [0] ;
+ ASSIGN_REAL (Lx, pnew, lj2, 0) ;
+ CLEAR_IMAG (Lx, Lz, pnew) ;
+
+ for (k = 1 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ /* Lx [pnew + k] = Lx [pold + k] / ljj ; */
+ DIV_REAL (Lx, Lz, pnew+k, Lx, Lz, pold+k, ljj,0) ;
+ }
+ }
+ Lp [j] = pnew ;
+ pnew += len ;
+ }
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* pack and leave LL' or LDL' as-is */
+ /* ---------------------------------------------------------- */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* pack column j */
+ pold = Lp [j] ;
+ len = Lnz [j] ;
+ ASSERT (len > 0) ;
+ PRINT2 (("col "ID" pnew "ID" pold "ID"\n", j, pnew, pold)) ;
+ if (pnew < pold)
+ {
+ PRINT2 ((" pack this column\n")) ;
+ for (k = 0 ; k < len ; k++)
+ {
+ Li [pnew + k] = Li [pold + k] ;
+ /* Lx [pnew + k] = Lx [pold + k] ; */
+ ASSIGN (Lx, Lz, pnew+k, Lx, Lz, pold+k) ;
+ }
+ Lp [j] = pnew ;
+ }
+ pnew += len ;
+ }
+ }
+
+ Lp [n] = pnew ;
+ PRINT2 (("Lp [n] = "ID"\n", pnew)) ;
+
+ }
+ else if (make_ll)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert LDL' to LL', but do so in-place */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+
+ /* dj = Lx [p] ; */
+ ASSIGN_REAL (dj,0, Lx,p) ;
+
+ if (IS_LE_ZERO (dj [0]))
+ {
+ /* Conversion has failed; matrix is not positive definite.
+ * Do not modify the column so that the LDL' factorization
+ * can be restored if desired, by converting back to LDL'.
+ * Continue the conversion, but flag the error. */
+ if (L->minor == (size_t) n)
+ {
+ ERROR (CHOLMOD_NOT_POSDEF, "L not positive definite") ;
+ L->minor = j ;
+ }
+ }
+ else
+ {
+ ljj [0] = sqrt (dj [0]) ;
+ /* Lx [p] = ljj ; */
+ ASSIGN_REAL (Lx,p, ljj,0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+
+ for (p++ ; p < pend ; p++)
+ {
+ /* Lx [p] *= ljj ; */
+ MULT_REAL (Lx,Lz,p, Lx,Lz,p, ljj,0) ;
+ }
+ }
+ }
+
+ }
+ else if (make_ldl)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert LL' to LDL', but do so in-place */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+
+ /* ljj = Lx [p] ; */
+ ASSIGN_REAL (ljj, 0, Lx, p) ;
+
+ if (ljj [0] > 0)
+ {
+ /* Lx [p] = ljj*ljj ; */
+ lj2 [0] = ljj [0] * ljj [0] ;
+ ASSIGN_REAL (Lx, p, lj2, 0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+
+ for (p++ ; p < pend ; p++)
+ {
+ /* Lx [p] /= ljj ; */
+ DIV_REAL (Lx,Lz,p, Lx,Lz,p, ljj,0) ;
+ }
+ }
+ }
+ }
+
+ L->is_ll = to_ll ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "done change simplicial numeric", Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === t_ll_super_to_simplicial_numeric ===================================== */
+/* ========================================================================== */
+
+/* A supernodal L can only be real or complex, not zomplex */
+
+#ifndef ZOMPLEX
+
+static void TEMPLATE (ll_super_to_simplicial_numeric)
+(
+ cholmod_factor *L,
+ Int to_packed,
+ Int to_ll,
+ cholmod_common *Common
+)
+{
+ double ljj [1], lj2 [1] ;
+ double *Lx ;
+ Int *Ls, *Lpi, *Lpx, *Super, *Lp, *Li, *Lnz ;
+ Int n, lnz, s, nsuper, p, psi, psx, psend, nsrow, nscol, ii, jj, j, k1, k2,
+ q ;
+
+ L->is_ll = to_ll ;
+
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lnz = L->nz ;
+ lnz = L->nzmax ;
+
+ n = L->n ;
+ nsuper = L->nsuper ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Super = L->super ;
+
+ p = 0 ;
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+
+ for (jj = 0 ; jj < nscol ; jj++)
+ {
+ /* column j of L starts here */
+ j = jj + k1 ;
+
+ if (to_ll)
+ {
+ if (to_packed)
+ {
+
+ /* ------------------------------------------------------ */
+ /* convert to LL' packed */
+ /* ------------------------------------------------------ */
+
+ Lp [j] = p ;
+ PRINT2 (("Col j "ID" p "ID"\n", j, p)) ;
+ for (ii = jj ; ii < nsrow ; ii++)
+ {
+ /* get L(i,j) from supernode and store in column j */
+ ASSERT (p < (Int) (L->xsize) && p <= psx+ii+jj*nsrow) ;
+ Li [p] = Ls [psi + ii] ;
+ /* Lx [p] = Lx [psx + ii + jj*nsrow] ; */
+ q = psx + ii + jj*nsrow ;
+ ASSIGN (Lx,-,p, Lx,-,q) ;
+ PRINT2 ((" i "ID" ", Li [p])) ;
+ XPRINT2 (Lx,-,q) ;
+ PRINT2 (("\n")) ;
+ p++ ;
+ }
+ Lnz [j] = p - Lp [j] ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------ */
+ /* convert to LL' unpacked */
+ /* ------------------------------------------------------ */
+
+ p = psx + jj + jj*nsrow ;
+ Lp [j] = p ;
+ Li [p] = j ;
+ Lnz [j] = nsrow - jj ;
+ p++ ;
+ for (ii = jj + 1 ; ii < nsrow ; ii++)
+ {
+ /* get L(i,j) from supernode and store in column j */
+ Li [psx + ii + jj*nsrow] = Ls [psi + ii] ;
+ }
+
+ }
+ }
+ else
+ {
+ if (to_packed)
+ {
+
+ /* ------------------------------------------------------ */
+ /* convert to LDL' packed */
+ /* ------------------------------------------------------ */
+
+ Lp [j] = p ;
+ PRINT2 (("Col j "ID" p "ID"\n", Lp [j], p)) ;
+ /* ljj = Lx [psx + jj + jj*nsrow] ; */
+ ASSIGN_REAL (ljj, 0, Lx, psx + jj + jj*nsrow) ;
+
+ if (ljj [0] <= 0)
+ {
+ /* the matrix is not positive definite; do not divide */
+ /* Lx [p] = ljj ; */
+ ASSIGN_REAL (Lx, p, ljj, 0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+ ljj [0] = 1 ;
+ }
+ else
+ {
+ lj2 [0] = ljj [0] * ljj [0] ;
+ /* Lx [p] = ljj*ljj ; */
+ ASSIGN_REAL (Lx, p, lj2, 0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+ }
+ Li [p] = j ;
+ p++ ;
+ for (ii = jj + 1 ; ii < nsrow ; ii++)
+ {
+ /* get L(i,j) from supernode and store in column j */
+ ASSERT (p < (Int) (L->xsize) && p <= psx+ii+jj*nsrow) ;
+ Li [p] = Ls [psi + ii] ;
+
+ /* Lx [p] = Lx [psx + ii + jj*nsrow] / ljj ; */
+ q = psx + ii + jj*nsrow ;
+ DIV_REAL (Lx, Lz, p, Lx, Lz, q, ljj,0) ;
+
+ PRINT2 ((" i "ID" %g\n", Li [p], Lx [p])) ;
+ p++ ;
+ }
+ Lnz [j] = p - Lp [j] ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------ */
+ /* convert to LDL' unpacked */
+ /* ------------------------------------------------------ */
+
+ p = psx + jj + jj*nsrow ;
+ Lp [j] = p ;
+
+ /* ljj = Lx [p] ; */
+ ASSIGN_REAL (ljj,0, Lx,p) ;
+
+ if (ljj [0] <= 0)
+ {
+ /* the matrix is not positive definite; do not divide */
+ /* Lx [p] = ljj ; */
+ ASSIGN_REAL (Lx, p, ljj, 0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+ ljj [0] = 1 ;
+ }
+ else
+ {
+ lj2 [0] = ljj [0] * ljj [0] ;
+ /* Lx [p] = ljj*ljj ; */
+ ASSIGN_REAL (Lx, p, lj2, 0) ;
+ CLEAR_IMAG (Lx, Lz, p) ;
+ }
+ Li [p] = j ;
+ Lnz [j] = nsrow - jj ;
+ p++ ;
+ for (ii = jj + 1 ; ii < nsrow ; ii++)
+ {
+ /* get L(i,j) from supernode and store in column j */
+ Li [psx + ii + jj*nsrow] = Ls [psi + ii] ;
+
+ /* Lx [psx + ii + jj*nsrow] /= ljj ; */
+ q = psx + ii + jj*nsrow ;
+ DIV_REAL (Lx, Lz, q, Lx, Lz, q, ljj,0) ;
+ }
+ }
+ }
+ }
+ }
+
+ if (to_packed)
+ {
+ Lp [n] = p ;
+ PRINT1 (("Final Lp "ID" n "ID" lnz "ID"\n", p, n, lnz)) ;
+ ASSERT (Lp [n] == lnz) ;
+ ASSERT (lnz <= (Int) (L->xsize)) ;
+ /* reduce size of L->x to match L->i. This cannot fail. */
+ L->x = CHOLMOD(realloc) (lnz,
+#ifdef COMPLEX
+ 2 *
+#endif
+ sizeof (double), L->x, &(L->xsize), Common) ;
+ ASSERT (lnz == (Int) (L->xsize)) ;
+ Common->status = CHOLMOD_OK ;
+ }
+ else
+ {
+ Lp [n] = Lpx [nsuper] ;
+ ASSERT (MAX (1,Lp [n]) == (Int) (L->xsize)) ;
+ ASSERT (MAX (1,Lp [n]) == (Int) (L->nzmax)) ;
+ }
+}
+
+#endif
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/CHOLMOD/Core/t_cholmod_dense.c b/CHOLMOD/Core/t_cholmod_dense.c
new file mode 100644
index 0000000..6be9e6d
--- /dev/null
+++ b/CHOLMOD/Core/t_cholmod_dense.c
@@ -0,0 +1,266 @@
+/* ========================================================================== */
+/* === Core/t_cholmod_dense ================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_dense. All xtypes supported, except that there
+ * are no dense matrices with an xtype of pattern. */
+
+#include "cholmod_template.h"
+
+/* ========================================================================== */
+/* === t_cholmod_sparse_to_dense ============================================ */
+/* ========================================================================== */
+
+static cholmod_dense *TEMPLATE (cholmod_sparse_to_dense)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Xx, *Az, *Xz ;
+ Int *Ap, *Ai, *Anz ;
+ cholmod_dense *X ;
+ Int i, j, p, pend, nrow, ncol, packed ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ packed = A->packed ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate result */
+ /* ---------------------------------------------------------------------- */
+
+ X = CHOLMOD(zeros) (nrow, ncol, XTYPE2, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ Xx = X->x ;
+ Xz = X->z ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy into dense matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype < 0)
+ {
+ /* A is symmetric with lower stored, but both parts of X are present */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= j)
+ {
+ ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ;
+ ASSIGN2_CONJ (Xx, Xz, j+i*nrow, Ax, Az, p) ;
+ }
+ }
+ }
+ }
+ else if (A->stype > 0)
+ {
+ /* A is symmetric with upper stored, but both parts of X are present */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i <= j)
+ {
+ ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ;
+ ASSIGN2_CONJ (Xx, Xz, j+i*nrow, Ax, Az, p) ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* both parts of A and X are present */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ ASSIGN2 (Xx, Xz, i+j*nrow, Ax, Az, p) ;
+ }
+ }
+ }
+
+ return (X) ;
+}
+
+
+#ifndef PATTERN
+
+/* There are no dense matrices of xtype CHOLMOD_PATTERN */
+
+/* ========================================================================== */
+/* === t_cholmod_dense_to_sparse ============================================ */
+/* ========================================================================== */
+
+static cholmod_sparse *TEMPLATE (cholmod_dense_to_sparse)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ int values, /* TRUE if values to be copied, FALSE otherwise */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Xx, *Cx, *Xz, *Cz ;
+ Int *Ci, *Cp ;
+ cholmod_sparse *C ;
+ Int i, j, p, d, nrow, ncol, nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = X->nrow ;
+ ncol = X->ncol ;
+ d = X->d ;
+ Xx = X->x ;
+ Xz = X->z ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the number of nonzeros in the result */
+ /* ---------------------------------------------------------------------- */
+
+ nz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ if (ENTRY_IS_NONZERO (Xx, Xz, i+j*d))
+ {
+ nz++ ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the result C */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_sparse) (nrow, ncol, nz, TRUE, TRUE, 0,
+ values ? XTYPE : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+ Cz = C->z ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the dense matrix X into the sparse matrix C */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Cp [j] = p ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ if (ENTRY_IS_NONZERO (Xx, Xz, i+j*d))
+ {
+ Ci [p] = i ;
+ if (values)
+ {
+ ASSIGN (Cx, Cz, p, Xx, Xz, i+j*d) ;
+ }
+ p++ ;
+ }
+ }
+ }
+ ASSERT (p == nz) ;
+ Cp [ncol] = nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (C, "C", Common) >= 0) ;
+ return (C) ;
+}
+
+
+/* ========================================================================== */
+/* === t_cholmod_copy_dense2 ================================================ */
+/* ========================================================================== */
+
+/* Y = X, where X and Y are both already allocated. */
+
+static int TEMPLATE (cholmod_copy_dense2)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ /* ---- output --- */
+ cholmod_dense *Y /* copy of matrix X */
+)
+{
+ double *Xx, *Xz, *Yx, *Yz ;
+ Int i, j, nrow, ncol, dy, dx ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Xx = X->x ;
+ Xz = X->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ dx = X->d ;
+ dy = Y->d ;
+ nrow = X->nrow ;
+ ncol = X->ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy */
+ /* ---------------------------------------------------------------------- */
+
+ CLEAR (Yx, Yz, 0) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ ASSIGN (Yx, Yz, i+j*dy, Xx, Xz, i+j*dx) ;
+ }
+ }
+ return (TRUE) ;
+}
+
+#endif
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/CHOLMOD/Core/t_cholmod_transpose.c b/CHOLMOD/Core/t_cholmod_transpose.c
new file mode 100644
index 0000000..f36a20b
--- /dev/null
+++ b/CHOLMOD/Core/t_cholmod_transpose.c
@@ -0,0 +1,318 @@
+/* ========================================================================== */
+/* === Core/t_cholmod_transpose ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_transpose. All xtypes are supported. For
+ * complex matrices, either the array tranpose or complex conjugate transpose
+ * can be computed. */
+
+#include "cholmod_template.h"
+
+/* ========================================================================== */
+/* === t_cholmod_transpose_unsym ============================================ */
+/* ========================================================================== */
+
+/* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is
+ * already allocated. The complex case performs either the array transpose
+ * or complex conjugate transpose.
+ *
+ * workspace:
+ * Iwork (MAX (nrow,ncol)) if fset is present
+ * Iwork (nrow) if fset is NULL
+ */
+
+static int TEMPLATE (cholmod_transpose_unsym)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ Int *Perm, /* size nrow, if present (can be NULL) */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ Int nf, /* size of fset */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Az, *Fx, *Fz ;
+ Int *Ap, *Anz, *Ai, *Fp, *Fnz, *Fj, *Wi, *Iwork ;
+ Int j, p, pend, nrow, ncol, Apacked, use_fset, fp, Fpacked, jj, permute ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* ensure the xtype of A and F match (ignored if this is pattern version) */
+ if (!XTYPE_OK (A->xtype))
+ {
+ ERROR (CHOLMOD_INVALID, "real/complex mismatch") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ use_fset = (fset != NULL) ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ Ap = A->p ; /* size A->ncol+1, column pointers of A */
+ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */
+ Ax = A->x ; /* size nz, real values of A */
+ Az = A->z ; /* size nz, imag values of A */
+ Anz = A->nz ;
+ Apacked = A->packed ;
+ ASSERT (IMPLIES (!Apacked, Anz != NULL)) ;
+
+ permute = (Perm != NULL) ;
+
+ Fp = F->p ; /* size A->nrow+1, row pointers of F */
+ Fj = F->i ; /* size nz, column indices of F */
+ Fx = F->x ; /* size nz, real values of F */
+ Fz = F->z ; /* size nz, imag values of F */
+ Fnz = F->nz ;
+ Fpacked = F->packed ;
+ ASSERT (IMPLIES (!Fpacked, Fnz != NULL)) ;
+
+ nf = (use_fset) ? nf : ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Wi = Iwork ; /* size nrow (i/l/l) */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the transpose */
+ /* ---------------------------------------------------------------------- */
+
+ for (jj = 0 ; jj < nf ; jj++)
+ {
+ j = (use_fset) ? (fset [jj]) : jj ;
+ p = Ap [j] ;
+ pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ fp = Wi [Ai [p]]++ ;
+ Fj [fp] = j ;
+#ifdef NCONJUGATE
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+#else
+ ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ;
+#endif
+ }
+ }
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === t_cholmod_transpose_sym ============================================== */
+/* ========================================================================== */
+
+/* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated.
+ * The complex case performs either the array transpose or complex conjugate
+ * transpose.
+ *
+ * workspace: Iwork (nrow) if Perm NULL, Iwork (2*nrow) if Perm non-NULL.
+ */
+
+static int TEMPLATE (cholmod_transpose_sym)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ Int *Perm, /* size n, if present (can be NULL) */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A' or A(p,p)' */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Az, *Fx, *Fz ;
+ Int *Ap, *Anz, *Ai, *Fp, *Fj, *Wi, *Pinv, *Iwork ;
+ Int p, pend, packed, fp, upper, permute, jold, n, i, j, iold ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* ensure the xtype of A and F match (ignored if this is pattern version) */
+ if (!XTYPE_OK (A->xtype))
+ {
+ ERROR (CHOLMOD_INVALID, "real/complex mismatch") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ permute = (Perm != NULL) ;
+ n = A->nrow ;
+ Ap = A->p ; /* size A->ncol+1, column pointers of A */
+ Ai = A->i ; /* size nz = Ap [A->ncol], row indices of A */
+ Ax = A->x ; /* size nz, real values of A */
+ Az = A->z ; /* size nz, imag values of A */
+ Anz = A->nz ;
+ packed = A->packed ;
+ ASSERT (IMPLIES (!packed, Anz != NULL)) ;
+ upper = (A->stype > 0) ;
+
+ Fp = F->p ; /* size A->nrow+1, row pointers of F */
+ Fj = F->i ; /* size nz, column indices of F */
+ Fx = F->x ; /* size nz, real values of F */
+ Fz = F->z ; /* size nz, imag values of F */
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Wi = Iwork ; /* size n (i/l/l) */
+ Pinv = Iwork + n ; /* size n (i/i/l) , unused if Perm NULL */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the transpose */
+ /* ---------------------------------------------------------------------- */
+
+ if (permute)
+ {
+ if (upper)
+ {
+ /* permuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ p = Ap [jold] ;
+ pend = (packed) ? Ap [jold+1] : p + Anz [jold] ;
+ for ( ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold <= jold)
+ {
+ i = Pinv [iold] ;
+ if (i < j)
+ {
+ fp = Wi [i]++ ;
+ Fj [fp] = j ;
+#ifdef NCONJUGATE
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+#else
+ ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ;
+#endif
+ }
+ else
+ {
+ fp = Wi [j]++ ;
+ Fj [fp] = i ;
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ /* permuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ jold = Perm [j] ;
+ p = Ap [jold] ;
+ pend = (packed) ? Ap [jold+1] : p + Anz [jold] ;
+ for ( ; p < pend ; p++)
+ {
+ iold = Ai [p] ;
+ if (iold >= jold)
+ {
+ i = Pinv [iold] ;
+ if (i > j)
+ {
+ fp = Wi [i]++ ;
+ Fj [fp] = j ;
+#ifdef NCONJUGATE
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+#else
+ ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ;
+#endif
+ }
+ else
+ {
+ fp = Wi [j]++ ;
+ Fj [fp] = i ;
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+ }
+ }
+ }
+ }
+ }
+ }
+ else
+ {
+ if (upper)
+ {
+ /* unpermuted, upper */
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? Ap [j+1] : p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i <= j)
+ {
+ fp = Wi [i]++ ;
+ Fj [fp] = j ;
+#ifdef NCONJUGATE
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+#else
+ ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ;
+#endif
+ }
+ }
+ }
+ }
+ else
+ {
+ /* unpermuted, lower */
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? Ap [j+1] : p + Anz [j] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= j)
+ {
+ fp = Wi [i]++ ;
+ Fj [fp] = j ;
+#ifdef NCONJUGATE
+ ASSIGN (Fx, Fz, fp, Ax, Az, p) ;
+#else
+ ASSIGN_CONJ (Fx, Fz, fp, Ax, Az, p) ;
+#endif
+ }
+ }
+ }
+ }
+ }
+
+ return (TRUE) ;
+}
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
+#undef NCONJUGATE
diff --git a/CHOLMOD/Core/t_cholmod_triplet.c b/CHOLMOD/Core/t_cholmod_triplet.c
new file mode 100644
index 0000000..d917175
--- /dev/null
+++ b/CHOLMOD/Core/t_cholmod_triplet.c
@@ -0,0 +1,176 @@
+/* ========================================================================== */
+/* === Core/t_cholmod_triplet =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Core Module. Copyright (C) 2005-2006,
+ * Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Core Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_triplet. All xtypes supported */
+
+#include "cholmod_template.h"
+
+/* ========================================================================== */
+/* === t_cholmod_triplet_to_sparse ========================================== */
+/* ========================================================================== */
+
+static size_t TEMPLATE (cholmod_triplet_to_sparse)
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* matrix to copy */
+ /* ---- in/out --- */
+ cholmod_sparse *R, /* output matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Rx, *Rz, *Tx, *Tz ;
+ Int *Wj, *Rp, *Ri, *Rnz, *Ti, *Tj ;
+ Int i, j, p, p1, p2, pdest, pj, k, stype, nrow, ncol, nz ;
+ size_t anz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* Wj contains a copy of Rp on input [ */
+ Wj = Common->Iwork ; /* size MAX (nrow,ncol). (i/l/l) */
+
+ Rp = R->p ;
+ Ri = R->i ;
+ Rnz = R->nz ;
+ Rx = R->x ;
+ Rz = R->z ;
+
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ Tz = T->z ;
+ nz = T->nnz ;
+ nrow = T->nrow ;
+ ncol = T->ncol ;
+ stype = SIGN (T->stype) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the row form */
+ /* ---------------------------------------------------------------------- */
+
+ /* if Ti is jumbled, this part dominates the run time */
+
+ if (stype > 0)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i < j)
+ {
+ /* place triplet (j,i,x) in column i of R */
+ p = Wj [i]++ ;
+ Ri [p] = j ;
+ }
+ else
+ {
+ /* place triplet (i,j,x) in column j of R */
+ p = Wj [j]++ ;
+ Ri [p] = i ;
+ }
+ ASSIGN (Rx, Rz, p, Tx, Tz, k) ;
+ }
+ }
+ else if (stype < 0)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i > j)
+ {
+ /* place triplet (j,i,x) in column i of R */
+ p = Wj [i]++ ;
+ Ri [p] = j ;
+ }
+ else
+ {
+ /* place triplet (i,j,x) in column j of R */
+ p = Wj [j]++ ;
+ Ri [p] = i ;
+ }
+ ASSIGN (Rx, Rz, p, Tx, Tz, k) ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ /* place triplet (i,j,x) in column i of R */
+ p = Wj [Ti [k]]++ ;
+ Ri [p] = Tj [k] ;
+ ASSIGN (Rx, Rz, p, Tx, Tz, k) ;
+ }
+ }
+
+ /* done using Wj (i/l/l) as temporary row pointers ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* sum up duplicates */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Wj (i/l/l) of size ncol to keep track of duplicates in each row [ */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Wj [j] = EMPTY ;
+ }
+
+ anz = 0 ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ p1 = Rp [i] ;
+ p2 = Rp [i+1] ;
+ pdest = p1 ;
+ /* at this point Wj [j] < p1 holds true for all columns j, because
+ * Ri/Rx is stored in row oriented manner */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ j = Ri [p] ;
+ pj = Wj [j] ;
+ if (pj >= p1)
+ {
+ /* this column index j is already in row i at position pj;
+ * sum up the duplicate entry */
+ /* Rx [pj] += Rx [p] ; */
+ ASSEMBLE (Rx, Rz, pj, Rx, Rz, p) ;
+ }
+ else
+ {
+ /* keep the entry and keep track in Wj [j] for case above */
+ Wj [j] = pdest ;
+ if (pdest != p)
+ {
+ Ri [pdest] = j ;
+ ASSIGN (Rx, Rz, pdest, Rx, Rz, p) ;
+ }
+ pdest++ ;
+ }
+ }
+ Rnz [i] = pdest - p1 ;
+ anz += (pdest - p1) ;
+ }
+ /* done using Wj to keep track of duplicate entries in each row ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* return number of entries after summing up duplicates */
+ /* ---------------------------------------------------------------------- */
+
+ return (anz) ;
+}
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/CHOLMOD/Demo/License.txt b/CHOLMOD/Demo/License.txt
new file mode 100644
index 0000000..256c3e0
--- /dev/null
+++ b/CHOLMOD/Demo/License.txt
@@ -0,0 +1,24 @@
+CHOLMOD/Demo Module. Copyright (C) 2005-2006, Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Demo module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
diff --git a/CHOLMOD/Demo/Makefile b/CHOLMOD/Demo/Makefile
new file mode 100644
index 0000000..3681f0b
--- /dev/null
+++ b/CHOLMOD/Demo/Makefile
@@ -0,0 +1,85 @@
+#===============================================================================
+# CHOLMOD/Demo/Makefile
+#===============================================================================
+
+# If you compile CHOLMOD with -DNPARTITION, then you do not need METIS or
+# CCOLAMD.
+
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+#-------------------------------------------------------------------------------
+# With METIS, CCOLAMD, CAMD, and the Partition Module:
+LIB2 = ../Lib/libcholmod.a ../../AMD/Lib/libamd.a ../../COLAMD/Lib/libcolamd.a \
+ ../../CCOLAMD/Lib/libccolamd.a ../../CAMD/Lib/libcamd.a \
+ $(METIS) $(LAPACK) $(BLAS) $(XERBLA) $(LIB)
+# Use this instead, if you compile with -DNPARTITION:
+# LIB2 = ../Lib/libcholmod.a ../../AMD/Lib/libamd.a ../../COLAMD/libcolamd.a \
+ $(LAPACK) $(BLAS) $(XERBLA) $(LIB)
+#-------------------------------------------------------------------------------
+
+C = $(CC) $(CFLAGS) $(CHOLMOD_CONFIG)
+
+code: library cholmod_demo cholmod_l_demo cholmod_simple
+
+fortran: readhb readhb2 reade
+
+all: code
+ ./cholmod_demo < Matrix/bcsstk01.tri
+ ./cholmod_l_demo < Matrix/bcsstk01.tri
+ ./cholmod_demo < Matrix/lp_afiro.tri
+ ./cholmod_l_demo < Matrix/lp_afiro.tri
+ ./cholmod_demo < Matrix/can___24.mtx
+ ./cholmod_l_demo < Matrix/can___24.mtx
+ ./cholmod_demo < Matrix/c.tri
+ ./cholmod_l_demo < Matrix/c.tri
+ ./cholmod_simple < Matrix/c.tri
+ ./cholmod_simple < Matrix/can___24.mtx
+ ./cholmod_simple < Matrix/bcsstk01.tri
+
+distclean: purge
+
+purge: clean
+ - $(RM) cholmod_demo cholmod_l_demo readhb readhb2 reade
+ - $(RM) cholmod_simple
+
+clean:
+ - $(RM) $(CLEAN)
+
+#-------------------------------------------------------------------------------
+# See below if you compile with -DNPARTITION
+library:
+ ( cd ../../UFconfig/xerbla ; $(MAKE) )
+ ( cd ../Lib ; $(MAKE) )
+ ( cd ../../AMD ; $(MAKE) library )
+ ( cd ../../CAMD ; $(MAKE) library )
+ ( cd ../../COLAMD ; $(MAKE) library )
+ ( cd ../../CCOLAMD ; $(MAKE) library )
+# use this rule instead, if you compile with -DNPARTITION:
+# library:
+# ( cd ../../UFconfig/xerbla ; $(MAKE) )
+# ( cd ../Lib ; $(MAKE) )
+# ( cd ../../AMD ; $(MAKE) library )
+# ( cd ../../COLAMD ; $(MAKE) )
+#-------------------------------------------------------------------------------
+
+I = -I../Include -I../../UFconfig
+
+cholmod_demo: library cholmod_demo.c cholmod_demo.h
+ $(C) -o cholmod_demo $(I) cholmod_demo.c $(LIB2)
+
+cholmod_simple: library cholmod_simple.c
+ $(C) -o cholmod_simple $(I) cholmod_simple.c $(LIB2)
+
+cholmod_l_demo: library cholmod_l_demo.c cholmod_demo.h
+ $(C) -o cholmod_l_demo $(I) cholmod_l_demo.c $(LIB2)
+
+readhb: readhb.f
+ $(F77) $(FFLAGS) -o readhb readhb.f
+
+readhb2: readhb2.f
+ $(F77) $(FFLAGS) -O -o readhb2 readhb2.f
+
+reade: reade.f
+ $(F77) $(FFLAGS) -O -o reade reade.f
diff --git a/CHOLMOD/Demo/Matrix/0.tri b/CHOLMOD/Demo/Matrix/0.tri
new file mode 100644
index 0000000..6a20ce4
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/0.tri
@@ -0,0 +1 @@
+0 0 0 0
diff --git a/CHOLMOD/Demo/Matrix/bcsstk01.rsa b/CHOLMOD/Demo/Matrix/bcsstk01.rsa
new file mode 100644
index 0000000..3d420ed
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/bcsstk01.rsa
@@ -0,0 +1,78 @@
+1SYMMETRIC STIFFNESS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM BCSSTK01
+ 74 4 14 56 0
+RSA 48 48 224 0
+(16I5) (16I5) (4E20.12)
+ 1 9 17 25 31 37 43 49 55 62 66 70 75 85 95 104
+ 112 120 127 132 136 141 144 146 149 154 158 161 164 167 169 173
+ 178 183 185 188 191 196 201 205 208 211 213 216 219 221 222 224
+ 225
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+ 3 4 5 9 21 23 27 28 4 8 10 22 27 28 5 7
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+ 8 10 12 14 18 32 9 10 11 15 17 33 34 10 16 33
+ 34 11 15 17 35 12 14 18 31 36 13 17 18 19 23 37
+ 42 43 47 48 14 15 16 18 20 22 38 44 45 46 15 16
+ 17 21 39 40 44 45 46 16 20 22 39 40 44 45 46 17
+ 18 19 23 41 43 47 48 18 24 37 42 43 47 48 19 23
+ 24 43 48 20 22 24 44 21 22 23 45 46 22 45 46 23
+ 47 24 43 48 25 29 30 31 35 26 28 32 34 27 28 33
+ 28 32 34 29 31 35 30 36 31 35 36 37 32 34 36 38
+ 42 33 34 35 39 41 34 40 35 39 41 36 38 42 37 41
+ 42 43 47 38 40 42 44 46 39 40 41 45 40 44 46 41
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+ .647105806113E+05 .239928529451E+07 .140838195984E+06 .350487988027E+07
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+ .247238730198E+10 .961679848804E+09 -.109779731332E+09 .531278103775E+09
diff --git a/CHOLMOD/Demo/Matrix/bcsstk01.tri b/CHOLMOD/Demo/Matrix/bcsstk01.tri
new file mode 100644
index 0000000..a5124d2
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/bcsstk01.tri
@@ -0,0 +1,227 @@
+% title:1SYMMETRIC STIFFNESS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM
+% key: BCSSTK01
+ 48 48 224 -1
+ 1 1 0.283226851851999993E+007
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diff --git a/CHOLMOD/Demo/Matrix/bcsstk02.rsa b/CHOLMOD/Demo/Matrix/bcsstk02.rsa
new file mode 100644
index 0000000..9b25574
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/bcsstk02.rsa
@@ -0,0 +1,701 @@
+1SYMMETRIC STIFFNESS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED BCSSTK02
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diff --git a/CHOLMOD/Demo/Matrix/bcsstk02.tri b/CHOLMOD/Demo/Matrix/bcsstk02.tri
new file mode 100644
index 0000000..4569afa
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/bcsstk02.tri
@@ -0,0 +1,2214 @@
+% title:1SYMMETRIC STIFFNESS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED
+% key: BCSSTK02
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diff --git a/CHOLMOD/Demo/Matrix/c.mtx b/CHOLMOD/Demo/Matrix/c.mtx
new file mode 100644
index 0000000..d63456d
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/c.mtx
@@ -0,0 +1,8 @@
+%%MatrixMarket matrix coordinate complex hermitian
+3 3 5
+1 1 1. 0.
+3 1 2. -1.
+2 2 1. 0.
+3 2 3. 0.
+3 3 42. 0.
+
diff --git a/CHOLMOD/Demo/Matrix/c.tri b/CHOLMOD/Demo/Matrix/c.tri
new file mode 100644
index 0000000..5bd417c
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/c.tri
@@ -0,0 +1,7 @@
+3 3 5 -1
+1 1 1. 0.
+3 1 2. -1.
+2 2 1. 0.
+3 2 3. 0.
+3 3 42. 0.
+
diff --git a/CHOLMOD/Demo/Matrix/can___24.mtx b/CHOLMOD/Demo/Matrix/can___24.mtx
new file mode 100644
index 0000000..6e8be53
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/can___24.mtx
@@ -0,0 +1,94 @@
+%%MatrixMarket matrix coordinate pattern symmetric
+24 24 92
+1 1
+6 1
+7 1
+13 1
+14 1
+18 1
+19 1
+20 1
+22 1
+2 2
+9 2
+10 2
+14 2
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+3 3
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+5 5
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+6 6
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+7 7
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+8 8
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+9 9
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diff --git a/CHOLMOD/Demo/Matrix/d.tri b/CHOLMOD/Demo/Matrix/d.tri
new file mode 100644
index 0000000..235c803
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/d.tri
@@ -0,0 +1,7 @@
+3 3 5 0
+1 1 1. 0.
+3 1 2. -1.
+2 2 1. 0.
+3 2 3. 0.
+3 3 42. 0.
+
diff --git a/CHOLMOD/Demo/Matrix/empty.tri b/CHOLMOD/Demo/Matrix/empty.tri
new file mode 100644
index 0000000..e69de29
diff --git a/CHOLMOD/Demo/Matrix/lp_afiro.rra b/CHOLMOD/Demo/Matrix/lp_afiro.rra
new file mode 100644
index 0000000..54860ac
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/lp_afiro.rra
@@ -0,0 +1,55 @@
+LP problem: min c'*x, where Ax=b, l<=x<=u (c,l,u,z0 in lp_afiro.clu )AFIRO
+ 58 3 4 34 17
+RRA 27 51 102 0
+(20i4) (26i3) (3e26.18) (3e26.18)
+F 1 0
+ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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+ 0.000000000000000000E+00 0.000000000000000000E+00 0.000000000000000000E+00
+ 0.800000000000000000E+02 0.000000000000000000E+00 0.000000000000000000E+00
+ 0.000000000000000000E+00 0.000000000000000000E+00 0.000000000000000000E+00
+ 0.500000000000000000E+03 0.000000000000000000E+00 0.000000000000000000E+00
+ 0.440000000000000000E+02 0.500000000000000000E+03 0.000000000000000000E+00
+ 0.000000000000000000E+00 0.000000000000000000E+00 0.000000000000000000E+00
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diff --git a/CHOLMOD/Demo/Matrix/lp_afiro.tri b/CHOLMOD/Demo/Matrix/lp_afiro.tri
new file mode 100644
index 0000000..5e90c05
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/lp_afiro.tri
@@ -0,0 +1,105 @@
+% title:LP problem: min c'*x, where Ax=b, l<=x<=u (c,l,u,z0 in lp_afiro.clu )
+% key: AFIRO
+ 27 51 102 0
+ 3 1 0.100000000000000000E+001
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diff --git a/CHOLMOD/Demo/Matrix/mangle1.mtx b/CHOLMOD/Demo/Matrix/mangle1.mtx
new file mode 100644
index 0000000..15ca279
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/mangle1.mtx
@@ -0,0 +1 @@
+%%MatrixMarket junk coordinate real general
diff --git a/CHOLMOD/Demo/Matrix/mangle2.mtx b/CHOLMOD/Demo/Matrix/mangle2.mtx
new file mode 100644
index 0000000..f710563
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/mangle2.mtx
@@ -0,0 +1 @@
+%%MatrixMarket matrix junk real general
diff --git a/CHOLMOD/Demo/Matrix/mangle3.mtx b/CHOLMOD/Demo/Matrix/mangle3.mtx
new file mode 100644
index 0000000..5d8402a
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/mangle3.mtx
@@ -0,0 +1 @@
+%%MatrixMarket matrix coordinate junk general
diff --git a/CHOLMOD/Demo/Matrix/mangle4.mtx b/CHOLMOD/Demo/Matrix/mangle4.mtx
new file mode 100644
index 0000000..539f5be
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/mangle4.mtx
@@ -0,0 +1 @@
+%%MatrixMarket matrix coordinate real junk
diff --git a/CHOLMOD/Demo/Matrix/mangle5.tri b/CHOLMOD/Demo/Matrix/mangle5.tri
new file mode 100644
index 0000000..3349161
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/mangle5.tri
@@ -0,0 +1,7 @@
+-3 3 5 1
+1 1 1. 0.
+1 3 2. -1.
+2 2 1. 0.
+2 3 3. 0.
+3 3 42. 0.
+
diff --git a/CHOLMOD/Demo/Matrix/mangle6.tri b/CHOLMOD/Demo/Matrix/mangle6.tri
new file mode 100644
index 0000000..63d1832
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/mangle6.tri
@@ -0,0 +1,2 @@
+3 3 1 0
+5
diff --git a/CHOLMOD/Demo/Matrix/mangle7.tri b/CHOLMOD/Demo/Matrix/mangle7.tri
new file mode 100644
index 0000000..78ac168
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/mangle7.tri
@@ -0,0 +1,2 @@
+3 3 1 0
+999 999 3.14
diff --git a/CHOLMOD/Demo/Matrix/mangle8.tri b/CHOLMOD/Demo/Matrix/mangle8.tri
new file mode 100644
index 0000000..cba7166
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/mangle8.tri
@@ -0,0 +1,2 @@
+3 3 1 0
+-999 999 3.14
diff --git a/CHOLMOD/Demo/Matrix/n5 b/CHOLMOD/Demo/Matrix/n5
new file mode 100644
index 0000000..b3f24d5
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/n5
@@ -0,0 +1,4061 @@
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diff --git a/CHOLMOD/Demo/Matrix/one.tri b/CHOLMOD/Demo/Matrix/one.tri
new file mode 100644
index 0000000..a2f25f6
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/one.tri
@@ -0,0 +1,3 @@
+%%MatrixMarket matrix coord pattern general
+1 1 1
+1 1
diff --git a/CHOLMOD/Demo/Matrix/pts5ldd03.mtx b/CHOLMOD/Demo/Matrix/pts5ldd03.mtx
new file mode 100644
index 0000000..ea51f3a
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/pts5ldd03.mtx
@@ -0,0 +1,755 @@
+%%MatrixMarket matrix coordinate real general
+%Laplacian of uniform grid on L-shaped domain of 3 unit squares
+%(interior points only have non-zero values,) matrix order N=3*n^2+2*n
+%meshsize h=1/(n+1), count begins from rectangle corner furthest from
+%attached square, (thus long columns first). Function value
+%is 1 except over attached square where f=M1, and f=(1+M1)/2
+%on boundary between rectangle and square. Here let M1=1 and n=7,
+%and eigmin = 9.69316221355115459.
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+ 91 76 -64
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+ 144 145 -64
+ 145 144 -64
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+ 146 145 -64
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+ 148 141 -64
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+ 149 142 -64
+ 149 156 -64
+ 150 143 -64
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+ 151 144 -64
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+ 152 145 -64
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+ 153 146 -64
+ 153 160 -64
+ 154 147 -64
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+ 150 149 -64
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+ 151 150 -64
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+ 153 152 -64
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+ 160 159 -64
+ 160 161 -64
+ 161 160 -64
+
diff --git a/CHOLMOD/Demo/Matrix/up.tri b/CHOLMOD/Demo/Matrix/up.tri
new file mode 100644
index 0000000..39f7572
--- /dev/null
+++ b/CHOLMOD/Demo/Matrix/up.tri
@@ -0,0 +1,7 @@
+3 3 5 1
+1 1 1. 0.
+1 3 2. -1.
+2 2 1. 0.
+2 3 3. 0.
+3 3 42. 0.
+
diff --git a/CHOLMOD/Demo/cholmod_demo.c b/CHOLMOD/Demo/cholmod_demo.c
new file mode 100644
index 0000000..73dbacf
--- /dev/null
+++ b/CHOLMOD/Demo/cholmod_demo.c
@@ -0,0 +1,400 @@
+/* ========================================================================== */
+/* === Demo/cholmod_demo ==================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Demo Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Demo Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Read in a matrix from a file, and use CHOLMOD to solve Ax=b if A is
+ * symmetric, or (AA'+beta*I)x=b otherwise. The file format is a simple
+ * triplet format, compatible with most files in the Matrix Market format.
+ * See cholmod_read.c for more details. The readhb.f program reads a
+ * Harwell/Boeing matrix (excluding element-types) and converts it into the
+ * form needed by this program. reade.f reads a matrix in Harwell/Boeing
+ * finite-element form.
+ *
+ * Usage:
+ * cholmod_demo matrixfile
+ * cholmod_demo < matrixfile
+ *
+ * The matrix is assumed to be positive definite (a supernodal LL' or simplicial
+ * LDL' factorization is used).
+ *
+ * Requires the Core, Cholesky, MatrixOps, and Check Modules.
+ * Optionally uses the Partition and Supernodal Modules.
+ * Does not use the Modify Module.
+ *
+ * See cholmod_simple.c for a simpler demo program.
+ */
+
+#include "cholmod_demo.h"
+
+/* ff is a global variable so that it can be closed by my_handler */
+FILE *ff ;
+
+/* halt if an error occurs */
+static void my_handler (int status, char *file, int line, char *message)
+{
+ printf ("cholmod error: file: %s line: %d status: %d: %s\n",
+ file, line, status, message) ;
+ if (status < 0)
+ {
+ if (ff != NULL) fclose (ff) ;
+ exit (0) ;
+ }
+}
+
+int main (int argc, char **argv)
+{
+ double resid, t, ta, tf, ts, tot, bnorm, xnorm, anorm, rnorm, fl, anz,
+ axbnorm, rnorm2, resid2 ;
+ FILE *f ;
+ cholmod_sparse *A ;
+ cholmod_dense *X, *B, *W, *R ;
+ double one [2], zero [2], minusone [2], beta [2], xlnz ;
+ cholmod_common Common, *cm ;
+ cholmod_factor *L ;
+ double *Bx, *Rx, *Xx ;
+ int i, n, isize, xsize, ordering, xtype, s, ss, lnz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the file containing the input matrix */
+ /* ---------------------------------------------------------------------- */
+
+ ff = NULL ;
+ if (argc > 1)
+ {
+ if ((f = fopen (argv [1], "r")) == NULL)
+ {
+ my_handler (CHOLMOD_INVALID, __FILE__, __LINE__,
+ "unable to open file") ;
+ }
+ ff = f ;
+ }
+ else
+ {
+ f = stdin ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_start (cm) ;
+
+ /* use default parameter settings, except for the error handler. This
+ * demo program terminates if an error occurs (out of memory, not positive
+ * definite, ...). It makes the demo program simpler (no need to check
+ * CHOLMOD error conditions). This non-default parameter setting has no
+ * effect on performance. */
+ cm->error_handler = my_handler ;
+
+ /* Note that CHOLMOD will do a supernodal LL' or a simplicial LDL' by
+ * default, automatically selecting the latter if flop/nnz(L) < 40. */
+
+ /* ---------------------------------------------------------------------- */
+ /* create basic scalars */
+ /* ---------------------------------------------------------------------- */
+
+ zero [0] = 0 ;
+ zero [1] = 0 ;
+ one [0] = 1 ;
+ one [1] = 0 ;
+ minusone [0] = -1 ;
+ minusone [1] = 0 ;
+ beta [0] = 1e-6 ;
+ beta [1] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* read in a matrix */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\n---------------------------------- cholmod_demo:\n") ;
+ A = cholmod_read_sparse (f, cm) ;
+ if (ff != NULL) fclose (ff) ;
+ anorm = cholmod_norm_sparse (A, 0, cm) ;
+ xtype = A->xtype ;
+ printf ("norm (A,inf) = %g\n", anorm) ;
+ printf ("norm (A,1) = %g\n", cholmod_norm_sparse (A, 1, cm)) ;
+ cholmod_print_sparse (A, "A", cm) ;
+
+ if (A->nrow > A->ncol)
+ {
+ /* Transpose A so that A'A+beta*I will be factorized instead */
+ cholmod_sparse *C = cholmod_transpose (A, 2, cm) ;
+ cholmod_free_sparse (&A, cm) ;
+ A = C ;
+ printf ("transposing input matrix\n") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create an arbitrary right-hand-side */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+ B = cholmod_zeros (n, 1, xtype, cm) ;
+ Bx = B->x ;
+
+#if GHS
+ {
+ /* b = A*ones(n,1), used by Gould, Hu, and Scott in their experiments */
+ cholmod_dense *X0 ;
+ X0 = cholmod_ones (A->ncol, 1, xtype, cm) ;
+ cholmod_sdmult (A, 0, one, zero, X0, B, cm) ;
+ cholmod_free_dense (&X0, cm) ;
+ }
+#else
+ if (xtype == CHOLMOD_REAL)
+ {
+ /* real case */
+ for (i = 0 ; i < n ; i++)
+ {
+ double x = n ;
+ Bx [i] = 1 + i / x ;
+ }
+ }
+ else
+ {
+ /* complex case */
+ for (i = 0 ; i < n ; i++)
+ {
+ double x = n ;
+ Bx [2*i ] = 1 + i / x ; /* real part of B(i) */
+ Bx [2*i+1] = (x/2 - i) / (3*x) ; /* imag part of B(i) */
+ }
+ }
+#endif
+
+ cholmod_print_dense (B, "B", cm) ;
+ bnorm = cholmod_norm_dense (B, 0, cm) ; /* max norm */
+ printf ("bnorm %g\n", bnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* analyze, factorize, and solve */
+ /* ---------------------------------------------------------------------- */
+
+ t = CPUTIME ;
+ L = cholmod_analyze (A, cm) ;
+ ta = CPUTIME - t ;
+ ta = MAX (ta, 0) ;
+
+ printf ("Analyze: flop %g lnz %g\n", cm->fl, cm->lnz) ;
+
+ if (A->stype == 0)
+ {
+ printf ("Factorizing A*A'+beta*I\n") ;
+ t = CPUTIME ;
+ cholmod_factorize_p (A, beta, NULL, 0, L, cm) ;
+ tf = CPUTIME - t ;
+ tf = MAX (tf, 0) ;
+ }
+ else
+ {
+ printf ("Factorizing A\n") ;
+ t = CPUTIME ;
+ cholmod_factorize (A, L, cm) ;
+ tf = CPUTIME - t ;
+ tf = MAX (tf, 0) ;
+ }
+
+ t = CPUTIME ;
+
+ X = cholmod_solve (CHOLMOD_A, L, B, cm) ;
+ ts = CPUTIME - t ;
+ ts = MAX (ts, 0) ;
+ tot = ta + tf + ts ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the residual */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0)
+ {
+ /* (AA'+beta*I)x=b is the linear system that was solved */
+ /* W = A'*X */
+ W = cholmod_allocate_dense (A->ncol, 1, A->ncol, xtype, cm) ;
+ cholmod_sdmult (A, 2, one, zero, X, W, cm) ;
+ /* R = B - beta*X */
+ R = cholmod_zeros (n, 1, xtype, cm) ;
+ Rx = R->x ;
+ Xx = X->x ;
+ if (xtype == CHOLMOD_REAL)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Rx [i] = Bx [i] - beta [0] * Xx [i] ;
+ }
+ }
+ else
+ {
+ /* complex case */
+ for (i = 0 ; i < n ; i++)
+ {
+ Rx [2*i ] = Bx [2*i ] - beta [0] * Xx [2*i ] ;
+ Rx [2*i+1] = Bx [2*i+1] - beta [0] * Xx [2*i+1] ;
+ }
+ }
+ /* R = A*W - R */
+ cholmod_sdmult (A, 0, one, minusone, W, R, cm) ;
+ cholmod_free_dense (&W, cm) ;
+ }
+ else
+ {
+ /* Ax=b was factorized and solved, R = B-A*X */
+ R = cholmod_copy_dense (B, cm) ;
+ cholmod_sdmult (A, 0, minusone, one, X, R, cm) ;
+ }
+ rnorm = cholmod_norm_dense (R, 0, cm) ; /* max abs. entry */
+ xnorm = cholmod_norm_dense (X, 0, cm) ; /* max abs. entry */
+
+ axbnorm = (anorm * xnorm + bnorm + ((n == 0) ? 1 : 0)) ;
+ resid = rnorm / axbnorm ;
+
+ /* ---------------------------------------------------------------------- */
+ /* iterative refinement (real symmetric case only) */
+ /* ---------------------------------------------------------------------- */
+
+ resid2 = -1 ;
+ if (A->stype != 0 && A->xtype == CHOLMOD_REAL)
+ {
+ cholmod_dense *R2 ;
+
+ /* R2 = A\(B-A*X) */
+ R2 = cholmod_solve (CHOLMOD_A, L, R, cm) ;
+ /* compute X = X + A\(B-A*X) */
+ Xx = X->x ;
+ Rx = R2->x ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Xx [i] + Rx [i] ;
+ }
+ cholmod_free_dense (&R2, cm) ;
+ cholmod_free_dense (&R, cm) ;
+
+ /* compute the new residual, R = B-A*X */
+ R = cholmod_copy_dense (B, cm) ;
+ cholmod_sdmult (A, 0, minusone, one, X, R, cm) ;
+ rnorm2 = cholmod_norm_dense (R, 0, cm) ;
+ resid2 = rnorm2 / axbnorm ;
+ }
+
+ cholmod_free_dense (&R, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print results */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_print_factor (L, "L", cm) ;
+
+ /* determine the # of integers's and reals's in L. See cholmod_free */
+ if (L->is_super)
+ {
+ s = L->nsuper + 1 ;
+ xsize = L->xsize ;
+ ss = L->ssize ;
+ isize =
+ n /* L->Perm */
+ + n /* L->ColCount, nz in each column of 'pure' L */
+ + s /* L->pi, column pointers for L->s */
+ + s /* L->px, column pointers for L->x */
+ + s /* L->super, starting column index of each supernode */
+ + ss ; /* L->s, the pattern of the supernodes */
+ }
+ else
+ {
+ /* this space can increase if you change parameters to their non-
+ * default values (cm->final_pack, for example). */
+ lnz = L->nzmax ;
+ xsize = lnz ;
+ isize =
+ n /* L->Perm */
+ + n /* L->ColCount, nz in each column of 'pure' L */
+ + n+1 /* L->p, column pointers */
+ + lnz /* L->i, integer row indices */
+ + n /* L->nz, nz in each column of L */
+ + n+2 /* L->next, link list */
+ + n+2 ; /* L->prev, link list */
+ }
+
+ anz = cm->anz ;
+ for (i = 0 ; i < CHOLMOD_MAXMETHODS ; i++)
+ {
+ fl = cm->method [i].fl ;
+ xlnz = cm->method [i].lnz ;
+ cm->method [i].fl = -1 ;
+ cm->method [i].lnz = -1 ;
+ ordering = cm->method [i].ordering ;
+ if (fl >= 0)
+ {
+ printf ("Ordering: ") ;
+ if (ordering == CHOLMOD_POSTORDERED) printf ("postordered ") ;
+ if (ordering == CHOLMOD_NATURAL) printf ("natural ") ;
+ if (ordering == CHOLMOD_GIVEN) printf ("user ") ;
+ if (ordering == CHOLMOD_AMD) printf ("AMD ") ;
+ if (ordering == CHOLMOD_METIS) printf ("METIS ") ;
+ if (ordering == CHOLMOD_NESDIS) printf ("NESDIS ") ;
+ if (xlnz > 0)
+ {
+ printf ("fl/lnz %10.1f", fl / xlnz) ;
+ }
+ if (anz > 0)
+ {
+ printf (" lnz/anz %10.1f", xlnz / anz) ;
+ }
+ printf ("\n") ;
+ }
+ }
+
+ printf ("ints in L: %d, doubles in L: %d\n", isize, xsize) ;
+ printf ("factor flops %g nnz(L) %15.0f (w/no amalgamation)\n",
+ cm->fl, cm->lnz) ;
+ if (A->stype == 0)
+ {
+ printf ("nnz(A): %15.0f\n", cm->anz) ;
+ }
+ else
+ {
+ printf ("nnz(A*A'): %15.0f\n", cm->anz) ;
+ }
+ if (cm->lnz > 0)
+ {
+ printf ("flops / nnz(L): %8.1f\n", cm->fl / cm->lnz) ;
+ }
+ if (anz > 0)
+ {
+ printf ("nnz(L) / nnz(A): %8.1f\n", cm->lnz / cm->anz) ;
+ }
+ printf ("analyze cputime: %12.4f\n", ta) ;
+ printf ("factor cputime: %12.4f mflop: %8.1f\n", tf,
+ (tf == 0) ? 0 : (1e-6*cm->fl / tf)) ;
+ printf ("solve cputime: %12.4f mflop: %8.1f\n", ts,
+ (ts == 0) ? 0 : (1e-6*4*cm->lnz / ts)) ;
+ printf ("overall cputime: %12.4f mflop: %8.1f\n",
+ tot, (tot == 0) ? 0 : (1e-6 * (cm->fl + 4 * cm->lnz) / tot)) ;
+ printf ("peak memory usage: %12.0f (MB)\n",
+ (double) (cm->memory_usage) / 1048576.) ;
+ printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))\n", resid) ;
+ if (resid2 >= 0)
+ {
+ printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))"
+ " after iterative refinement\n", resid2) ;
+ }
+ printf ("rcond %8.1e\n\n", cholmod_rcond (L, cm)) ;
+ cholmod_free_factor (&L, cm) ;
+ cholmod_free_dense (&X, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free matrices and finish CHOLMOD */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_free_sparse (&A, cm) ;
+ cholmod_free_dense (&B, cm) ;
+ cholmod_finish (cm) ;
+ return (0) ;
+}
diff --git a/CHOLMOD/Demo/cholmod_demo.h b/CHOLMOD/Demo/cholmod_demo.h
new file mode 100644
index 0000000..147f270
--- /dev/null
+++ b/CHOLMOD/Demo/cholmod_demo.h
@@ -0,0 +1,25 @@
+/* ========================================================================== */
+/* === Demo/cholmod_demo.h ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Demo Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Demo Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+#include "cholmod.h"
+#include <string.h>
+#include <ctype.h>
+#include <stdio.h>
+#include <time.h>
+#include <stdlib.h>
+#define TRUE 1
+#define FALSE 0
+
+#define CPUTIME ((double) (clock ( )) / CLOCKS_PER_SEC)
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+
diff --git a/CHOLMOD/Demo/cholmod_l_demo.c b/CHOLMOD/Demo/cholmod_l_demo.c
new file mode 100644
index 0000000..a011b47
--- /dev/null
+++ b/CHOLMOD/Demo/cholmod_l_demo.c
@@ -0,0 +1,402 @@
+/* ========================================================================== */
+/* === Demo/cholmod_l_demo ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Demo Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Demo Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Read in a matrix from a file, and use CHOLMOD to solve Ax=b if A is
+ * symmetric, or (AA'+beta*I)x=b otherwise. The file format is a simple
+ * triplet format, compatible with most files in the Matrix Market format.
+ * See cholmod_read.c for more details. The readhb.f format reads a
+ * Harwell/Boeing matrix (excluding element-types) and converts it into the
+ * form needed by this program. reade.f reads a matrix in Harwell/Boeing
+ * finite-element form.
+ *
+ * Usage:
+ * cholmod_l_demo matrixfile
+ * cholmod_l_demo < matrixfile
+ *
+ * The matrix is assumed to be positive definite (a supernodal LL' or simplicial
+ * LDL' factorization is used).
+ *
+ * Requires the Core, Cholesky, MatrixOps, and Check Modules.
+ * Optionally uses the Partition and Supernodal Modules.
+ * Does not use the Modify Module.
+ *
+ * See cholmod_simple.c for a simpler demo program.
+ *
+ * UF_long is normally defined as long, except for WIN64.
+ */
+
+#include "cholmod_demo.h"
+
+/* ff is a global variable so that it can be closed by my_handler */
+FILE *ff ;
+
+/* halt if an error occurs */
+static void my_handler (int status, char *file, int line, char *message)
+{
+ printf ("cholmod error: file: %s line: %d status: %d: %s\n",
+ file, line, status, message) ;
+ if (status < 0)
+ {
+ if (ff != NULL) fclose (ff) ;
+ exit (0) ;
+ }
+}
+
+int main (int argc, char **argv)
+{
+ double resid, t, ta, tf, ts, tot, bnorm, xnorm, anorm, rnorm, fl, anz,
+ axbnorm, rnorm2, resid2 ;
+ FILE *f ;
+ cholmod_sparse *A ;
+ cholmod_dense *X, *B, *W, *R ;
+ double one [2], zero [2], minusone [2], beta [2], xlnz ;
+ cholmod_common Common, *cm ;
+ cholmod_factor *L ;
+ double *Bx, *Rx, *Xx ;
+ UF_long i, n, isize, xsize, ordering, xtype, s, ss, lnz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the file containing the input matrix */
+ /* ---------------------------------------------------------------------- */
+
+ ff = NULL ;
+ if (argc > 1)
+ {
+ if ((f = fopen (argv [1], "r")) == NULL)
+ {
+ my_handler (CHOLMOD_INVALID, __FILE__, __LINE__,
+ "unable to open file") ;
+ }
+ ff = f ;
+ }
+ else
+ {
+ f = stdin ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+
+ /* use default parameter settings, except for the error handler. This
+ * demo program terminates if an error occurs (out of memory, not positive
+ * definite, ...). It makes the demo program simpler (no need to check
+ * CHOLMOD error conditions). This non-default parameter setting has no
+ * effect on performance. */
+ cm->error_handler = my_handler ;
+
+ /* Note that CHOLMOD will do a supernodal LL' or a simplicial LDL' by
+ * default, automatically selecting the latter if flop/nnz(L) < 40. */
+
+ /* ---------------------------------------------------------------------- */
+ /* create basic scalars */
+ /* ---------------------------------------------------------------------- */
+
+ zero [0] = 0 ;
+ zero [1] = 0 ;
+ one [0] = 1 ;
+ one [1] = 0 ;
+ minusone [0] = -1 ;
+ minusone [1] = 0 ;
+ beta [0] = 1e-6 ;
+ beta [1] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* read in a matrix */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\n---------------------------------- cholmod_l_demo:\n") ;
+ A = cholmod_l_read_sparse (f, cm) ;
+ if (ff != NULL) fclose (ff) ;
+ anorm = cholmod_l_norm_sparse (A, 0, cm) ;
+ xtype = A->xtype ;
+ printf ("norm (A,inf) = %g\n", anorm) ;
+ printf ("norm (A,1) = %g\n", cholmod_l_norm_sparse (A, 1, cm)) ;
+ cholmod_l_print_sparse (A, "A", cm) ;
+
+ if (A->nrow > A->ncol)
+ {
+ /* Transpose A so that A'A+beta*I will be factorized instead */
+ cholmod_sparse *C = cholmod_l_transpose (A, 2, cm) ;
+ cholmod_l_free_sparse (&A, cm) ;
+ A = C ;
+ printf ("transposing input matrix\n") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create an arbitrary right-hand-side */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+ B = cholmod_l_zeros (n, 1, xtype, cm) ;
+ Bx = B->x ;
+
+#if GHS
+ {
+ /* b = A*ones(n,1), used by Gould, Hu, and Scott in their experiments */
+ cholmod_dense *X0 ;
+ X0 = cholmod_l_ones (A->ncol, 1, xtype, cm) ;
+ cholmod_l_sdmult (A, 0, one, zero, X0, B, cm) ;
+ cholmod_l_free_dense (&X0, cm) ;
+ }
+#else
+ if (xtype == CHOLMOD_REAL)
+ {
+ /* real case */
+ for (i = 0 ; i < n ; i++)
+ {
+ double x = n ;
+ Bx [i] = 1 + i / x ;
+ }
+ }
+ else
+ {
+ /* complex case */
+ for (i = 0 ; i < n ; i++)
+ {
+ double x = n ;
+ Bx [2*i ] = 1 + i / x ; /* real part of B(i) */
+ Bx [2*i+1] = (x/2 - i) / (3*x) ; /* imag part of B(i) */
+ }
+ }
+#endif
+
+ cholmod_l_print_dense (B, "B", cm) ;
+ bnorm = cholmod_l_norm_dense (B, 0, cm) ; /* max norm */
+ printf ("bnorm %g\n", bnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* analyze, factorize, and solve */
+ /* ---------------------------------------------------------------------- */
+
+ t = CPUTIME ;
+ L = cholmod_l_analyze (A, cm) ;
+ ta = CPUTIME - t ;
+ ta = MAX (ta, 0) ;
+
+ printf ("Analyze: flop %g lnz %g\n", cm->fl, cm->lnz) ;
+
+ if (A->stype == 0)
+ {
+ printf ("Factorizing A*A'+beta*I\n") ;
+ t = CPUTIME ;
+ cholmod_l_factorize_p (A, beta, NULL, 0, L, cm) ;
+ tf = CPUTIME - t ;
+ tf = MAX (tf, 0) ;
+ }
+ else
+ {
+ printf ("Factorizing A\n") ;
+ t = CPUTIME ;
+ cholmod_l_factorize (A, L, cm) ;
+ tf = CPUTIME - t ;
+ tf = MAX (tf, 0) ;
+ }
+
+ t = CPUTIME ;
+
+ X = cholmod_l_solve (CHOLMOD_A, L, B, cm) ;
+ ts = CPUTIME - t ;
+ ts = MAX (ts, 0) ;
+ tot = ta + tf + ts ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the residual */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0)
+ {
+ /* (AA'+beta*I)x=b is the linear system that was solved */
+ /* W = A'*X */
+ W = cholmod_l_allocate_dense (A->ncol, 1, A->ncol, xtype, cm) ;
+ cholmod_l_sdmult (A, 2, one, zero, X, W, cm) ;
+ /* R = B - beta*X */
+ R = cholmod_l_zeros (n, 1, xtype, cm) ;
+ Rx = R->x ;
+ Xx = X->x ;
+ if (xtype == CHOLMOD_REAL)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Rx [i] = Bx [i] - beta [0] * Xx [i] ;
+ }
+ }
+ else
+ {
+ /* complex case */
+ for (i = 0 ; i < n ; i++)
+ {
+ Rx [2*i ] = Bx [2*i ] - beta [0] * Xx [2*i ] ;
+ Rx [2*i+1] = Bx [2*i+1] - beta [0] * Xx [2*i+1] ;
+ }
+ }
+ /* R = A*W - R */
+ cholmod_l_sdmult (A, 0, one, minusone, W, R, cm) ;
+ cholmod_l_free_dense (&W, cm) ;
+ }
+ else
+ {
+ /* Ax=b was factorized and solved, R = B-A*X */
+ R = cholmod_l_copy_dense (B, cm) ;
+ cholmod_l_sdmult (A, 0, minusone, one, X, R, cm) ;
+ }
+ rnorm = cholmod_l_norm_dense (R, 0, cm) ; /* max abs. entry */
+ xnorm = cholmod_l_norm_dense (X, 0, cm) ; /* max abs. entry */
+
+ axbnorm = (anorm * xnorm + bnorm + ((n == 0) ? 1 : 0)) ;
+ resid = rnorm / axbnorm ;
+
+ /* ---------------------------------------------------------------------- */
+ /* iterative refinement (real symmetric case only) */
+ /* ---------------------------------------------------------------------- */
+
+ resid2 = -1 ;
+ if (A->stype != 0 && A->xtype == CHOLMOD_REAL)
+ {
+ cholmod_dense *R2 ;
+
+ /* R2 = A\(B-A*X) */
+ R2 = cholmod_l_solve (CHOLMOD_A, L, R, cm) ;
+ /* compute X = X + A\(B-A*X) */
+ Xx = X->x ;
+ Rx = R2->x ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Xx [i] + Rx [i] ;
+ }
+ cholmod_l_free_dense (&R2, cm) ;
+ cholmod_l_free_dense (&R, cm) ;
+
+ /* compute the new residual, R = B-A*X */
+ R = cholmod_l_copy_dense (B, cm) ;
+ cholmod_l_sdmult (A, 0, minusone, one, X, R, cm) ;
+ rnorm2 = cholmod_l_norm_dense (R, 0, cm) ;
+ resid2 = rnorm2 / axbnorm ;
+ }
+
+ cholmod_l_free_dense (&R, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print results */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_print_factor (L, "L", cm) ;
+
+ /* determine the # of integers's and reals's in L. See cholmod_free */
+ if (L->is_super)
+ {
+ s = L->nsuper + 1 ;
+ xsize = L->xsize ;
+ ss = L->ssize ;
+ isize =
+ n /* L->Perm */
+ + n /* L->ColCount, nz in each column of 'pure' L */
+ + s /* L->pi, column pointers for L->s */
+ + s /* L->px, column pointers for L->x */
+ + s /* L->super, starting column index of each supernode */
+ + ss ; /* L->s, the pattern of the supernodes */
+ }
+ else
+ {
+ /* this space can increase if you change parameters to their non-
+ * default values (cm->final_pack, for example). */
+ lnz = L->nzmax ;
+ xsize = lnz ;
+ isize =
+ n /* L->Perm */
+ + n /* L->ColCount, nz in each column of 'pure' L */
+ + n+1 /* L->p, column pointers */
+ + lnz /* L->i, integer row indices */
+ + n /* L->nz, nz in each column of L */
+ + n+2 /* L->next, link list */
+ + n+2 ; /* L->prev, link list */
+ }
+
+ anz = cm->anz ;
+ for (i = 0 ; i < CHOLMOD_MAXMETHODS ; i++)
+ {
+ fl = cm->method [i].fl ;
+ xlnz = cm->method [i].lnz ;
+ cm->method [i].fl = -1 ;
+ cm->method [i].lnz = -1 ;
+ ordering = cm->method [i].ordering ;
+ if (fl >= 0)
+ {
+ printf ("Ordering: ") ;
+ if (ordering == CHOLMOD_POSTORDERED) printf ("postordered ") ;
+ if (ordering == CHOLMOD_NATURAL) printf ("natural ") ;
+ if (ordering == CHOLMOD_GIVEN) printf ("user ") ;
+ if (ordering == CHOLMOD_AMD) printf ("AMD ") ;
+ if (ordering == CHOLMOD_METIS) printf ("METIS ") ;
+ if (ordering == CHOLMOD_NESDIS) printf ("NESDIS ") ;
+ if (xlnz > 0)
+ {
+ printf ("fl/lnz %10.1f", fl / xlnz) ;
+ }
+ if (anz > 0)
+ {
+ printf (" lnz/anz %10.1f", xlnz / anz) ;
+ }
+ printf ("\n") ;
+ }
+ }
+
+ printf ("ints in L: %ld, doubles in L: %ld\n", isize, xsize) ;
+ printf ("factor flops %g nnz(L) %15.0f (w/no amalgamation)\n",
+ cm->fl, cm->lnz) ;
+ if (A->stype == 0)
+ {
+ printf ("nnz(A): %15.0f\n", cm->anz) ;
+ }
+ else
+ {
+ printf ("nnz(A*A'): %15.0f\n", cm->anz) ;
+ }
+ if (cm->lnz > 0)
+ {
+ printf ("flops / nnz(L): %8.1f\n", cm->fl / cm->lnz) ;
+ }
+ if (anz > 0)
+ {
+ printf ("nnz(L) / nnz(A): %8.1f\n", cm->lnz / cm->anz) ;
+ }
+ printf ("analyze cputime: %12.4f\n", ta) ;
+ printf ("factor cputime: %12.4f mflop: %8.1f\n", tf,
+ (tf == 0) ? 0 : (1e-6*cm->fl / tf)) ;
+ printf ("solve cputime: %12.4f mflop: %8.1f\n", ts,
+ (ts == 0) ? 0 : (1e-6*4*cm->lnz / ts)) ;
+ printf ("overall cputime: %12.4f mflop: %8.1f\n",
+ tot, (tot == 0) ? 0 : (1e-6 * (cm->fl + 4 * cm->lnz) / tot)) ;
+ printf ("peak memory usage: %12.0f (MB)\n",
+ (double) (cm->memory_usage) / 1048576.) ;
+ printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))\n", resid) ;
+ if (resid2 >= 0)
+ {
+ printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))"
+ " after iterative refinement\n", resid2) ;
+ }
+ printf ("rcond %8.1e\n\n", cholmod_l_rcond (L, cm)) ;
+ cholmod_l_free_factor (&L, cm) ;
+ cholmod_l_free_dense (&X, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free matrices and finish CHOLMOD */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free_sparse (&A, cm) ;
+ cholmod_l_free_dense (&B, cm) ;
+ cholmod_l_finish (cm) ;
+ return (0) ;
+}
diff --git a/CHOLMOD/Demo/cholmod_simple.c b/CHOLMOD/Demo/cholmod_simple.c
new file mode 100644
index 0000000..a997147
--- /dev/null
+++ b/CHOLMOD/Demo/cholmod_simple.c
@@ -0,0 +1,50 @@
+/* ========================================================================== */
+/* === Demo/cholmod_simple ================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Demo Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Demo Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Read in a real symmetric or complex Hermitian matrix from stdin in
+ * MatrixMarket format, solve Ax=b where b=[1 1 ... 1]', and print the residual.
+ * Usage: cholmod_simple < matrixfile
+ */
+
+#include "cholmod.h"
+int main (void)
+{
+ cholmod_sparse *A ;
+ cholmod_dense *x, *b, *r ;
+ cholmod_factor *L ;
+ double one [2] = {1,0}, m1 [2] = {-1,0} ; /* basic scalars */
+ cholmod_common c ;
+ cholmod_start (&c) ; /* start CHOLMOD */
+ A = cholmod_read_sparse (stdin, &c) ; /* read in a matrix */
+ cholmod_print_sparse (A, "A", &c) ; /* print the matrix */
+ if (A == NULL || A->stype == 0) /* A must be symmetric */
+ {
+ cholmod_free_sparse (&A, &c) ;
+ cholmod_finish (&c) ;
+ return (0) ;
+ }
+ b = cholmod_ones (A->nrow, 1, A->xtype, &c) ; /* b = ones(n,1) */
+ L = cholmod_analyze (A, &c) ; /* analyze */
+ cholmod_factorize (A, L, &c) ; /* factorize */
+ x = cholmod_solve (CHOLMOD_A, L, b, &c) ; /* solve Ax=b */
+ r = cholmod_copy_dense (b, &c) ; /* r = b */
+ cholmod_sdmult (A, 0, m1, one, x, r, &c) ; /* r = r-Ax */
+ printf ("norm(b-Ax) %8.1e\n",
+ cholmod_norm_dense (r, 0, &c)) ; /* print norm(r) */
+ cholmod_free_factor (&L, &c) ; /* free matrices */
+ cholmod_free_sparse (&A, &c) ;
+ cholmod_free_dense (&r, &c) ;
+ cholmod_free_dense (&x, &c) ;
+ cholmod_free_dense (&b, &c) ;
+ cholmod_finish (&c) ; /* finish CHOLMOD */
+ return (0) ;
+}
diff --git a/CHOLMOD/Demo/gpl.txt b/CHOLMOD/Demo/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/CHOLMOD/Demo/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it. (Some other Free Software Foundation software is covered by
+the GNU Library General Public License instead.) You can apply it to
+your programs, too.
+
+ When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+this service if you wish), that you receive source code or can get it
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+the limitation as if written in the body of this License.
+
+ 9. The Free Software Foundation may publish revised and/or new versions
+of the General Public License from time to time. Such new versions will
+be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+Each version is given a distinguishing version number. If the Program
+specifies a version number of this License which applies to it and "any
+later version", you have the option of following the terms and conditions
+either of that version or of any later version published by the Free
+Software Foundation. If the Program does not specify a version number of
+this License, you may choose any version ever published by the Free Software
+Foundation.
+
+ 10. If you wish to incorporate parts of the Program into other free
+programs whose distribution conditions are different, write to the author
+to ask for permission. For software which is copyrighted by the Free
+Software Foundation, write to the Free Software Foundation; we sometimes
+make exceptions for this. Our decision will be guided by the two goals
+of preserving the free status of all derivatives of our free software and
+of promoting the sharing and reuse of software generally.
+
+ NO WARRANTY
+
+ 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
+FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
+OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
+PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
+OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
+TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
+PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
+REPAIR OR CORRECTION.
+
+ 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
+REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
+INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
+OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
+TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
+YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
+PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGES.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+
+Also add information on how to contact you by electronic and paper mail.
+
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
+
+ Gnomovision version 69, Copyright (C) year name of author
+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ <signature of Ty Coon>, 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Library General
+Public License instead of this License.
diff --git a/CHOLMOD/Demo/make.out b/CHOLMOD/Demo/make.out
new file mode 100644
index 0000000..0b1980f
--- /dev/null
+++ b/CHOLMOD/Demo/make.out
@@ -0,0 +1,213 @@
+./cholmod_demo < Matrix/bcsstk01.tri
+
+---------------------------------- cholmod_demo:
+norm (A,inf) = 3.57095e+09
+norm (A,1) = 3.57095e+09
+CHOLMOD sparse: A: 48-by-48, nz 224, upper. OK
+CHOLMOD dense: B: 48-by-1, OK
+bnorm 1.97917
+Analyze: flop 6009 lnz 489
+Factorizing A
+CHOLMOD factor: L: 48-by-48 simplicial, LDL'. nzmax 489. nz 489 OK
+Ordering: AMD fl/lnz 12.3 lnz/anz 2.2
+ints in L: 782, doubles in L: 489
+factor flops 6009 nnz(L) 489 (w/no amalgamation)
+nnz(A*A'): 224
+flops / nnz(L): 12.3
+nnz(L) / nnz(A): 2.2
+analyze cputime: 0.0000
+factor cputime: 0.0000 mflop: 0.0
+solve cputime: 0.0000 mflop: 0.0
+overall cputime: 0.0000 mflop: 0.0
+peak memory usage: 0 (MB)
+residual 2.5e-19 (|Ax-b|/(|A||x|+|b|))
+residual 1.3e-19 (|Ax-b|/(|A||x|+|b|)) after iterative refinement
+rcond 9.5e-06
+
+./cholmod_l_demo < Matrix/bcsstk01.tri
+
+---------------------------------- cholmod_l_demo:
+norm (A,inf) = 3.57095e+09
+norm (A,1) = 3.57095e+09
+CHOLMOD sparse: A: 48-by-48, nz 224, upper. OK
+CHOLMOD dense: B: 48-by-1, OK
+bnorm 1.97917
+Analyze: flop 6009 lnz 489
+Factorizing A
+CHOLMOD factor: L: 48-by-48 simplicial, LDL'. nzmax 489. nz 489 OK
+Ordering: AMD fl/lnz 12.3 lnz/anz 2.2
+ints in L: 782, doubles in L: 489
+factor flops 6009 nnz(L) 489 (w/no amalgamation)
+nnz(A*A'): 224
+flops / nnz(L): 12.3
+nnz(L) / nnz(A): 2.2
+analyze cputime: 0.0000
+factor cputime: 0.0000 mflop: 0.0
+solve cputime: 0.0000 mflop: 0.0
+overall cputime: 0.0000 mflop: 0.0
+peak memory usage: 0 (MB)
+residual 2.5e-19 (|Ax-b|/(|A||x|+|b|))
+residual 1.3e-19 (|Ax-b|/(|A||x|+|b|)) after iterative refinement
+rcond 9.5e-06
+
+./cholmod_demo < Matrix/lp_afiro.tri
+
+---------------------------------- cholmod_demo:
+norm (A,inf) = 20.525
+norm (A,1) = 3.429
+CHOLMOD sparse: A: 27-by-51, nz 102, up/lo. OK
+CHOLMOD dense: B: 27-by-1, OK
+bnorm 1.96296
+Analyze: flop 529 lnz 113
+Factorizing A*A'+beta*I
+CHOLMOD factor: L: 27-by-27 simplicial, LDL'. nzmax 113. nz 113 OK
+Ordering: AMD fl/lnz 4.7 lnz/anz 1.3
+ints in L: 280, doubles in L: 113
+factor flops 529 nnz(L) 113 (w/no amalgamation)
+nnz(A): 90
+flops / nnz(L): 4.7
+nnz(L) / nnz(A): 1.3
+analyze cputime: 0.0000
+factor cputime: 0.0000 mflop: 0.0
+solve cputime: 0.0000 mflop: 0.0
+overall cputime: 0.0000 mflop: 0.0
+peak memory usage: 0 (MB)
+residual 7.4e-17 (|Ax-b|/(|A||x|+|b|))
+rcond 3.0e-02
+
+./cholmod_l_demo < Matrix/lp_afiro.tri
+
+---------------------------------- cholmod_l_demo:
+norm (A,inf) = 20.525
+norm (A,1) = 3.429
+CHOLMOD sparse: A: 27-by-51, nz 102, up/lo. OK
+CHOLMOD dense: B: 27-by-1, OK
+bnorm 1.96296
+Analyze: flop 529 lnz 113
+Factorizing A*A'+beta*I
+CHOLMOD factor: L: 27-by-27 simplicial, LDL'. nzmax 113. nz 113 OK
+Ordering: AMD fl/lnz 4.7 lnz/anz 1.3
+ints in L: 280, doubles in L: 113
+factor flops 529 nnz(L) 113 (w/no amalgamation)
+nnz(A): 90
+flops / nnz(L): 4.7
+nnz(L) / nnz(A): 1.3
+analyze cputime: 0.0000
+factor cputime: 0.0000 mflop: 0.0
+solve cputime: 0.0000 mflop: 0.0
+overall cputime: 0.0000 mflop: 0.0
+peak memory usage: 0 (MB)
+residual 7.4e-17 (|Ax-b|/(|A||x|+|b|))
+rcond 3.0e-02
+
+./cholmod_demo < Matrix/can___24.mtx
+
+---------------------------------- cholmod_demo:
+norm (A,inf) = 17
+norm (A,1) = 17
+CHOLMOD sparse: A: 24-by-24, nz 92, upper. OK
+CHOLMOD dense: B: 24-by-1, OK
+bnorm 1.95833
+Analyze: flop 656 lnz 120
+Factorizing A
+CHOLMOD factor: L: 24-by-24 simplicial, LDL'. nzmax 120. nz 120 OK
+Ordering: AMD fl/lnz 5.5 lnz/anz 1.3
+ints in L: 269, doubles in L: 120
+factor flops 656 nnz(L) 120 (w/no amalgamation)
+nnz(A*A'): 92
+flops / nnz(L): 5.5
+nnz(L) / nnz(A): 1.3
+analyze cputime: 0.0000
+factor cputime: 0.0000 mflop: 0.0
+solve cputime: 0.0000 mflop: 0.0
+overall cputime: 0.0000 mflop: 0.0
+peak memory usage: 0 (MB)
+residual 1.3e-16 (|Ax-b|/(|A||x|+|b|))
+residual 7.5e-17 (|Ax-b|/(|A||x|+|b|)) after iterative refinement
+rcond 5.0e-01
+
+./cholmod_l_demo < Matrix/can___24.mtx
+
+---------------------------------- cholmod_l_demo:
+norm (A,inf) = 17
+norm (A,1) = 17
+CHOLMOD sparse: A: 24-by-24, nz 92, upper. OK
+CHOLMOD dense: B: 24-by-1, OK
+bnorm 1.95833
+Analyze: flop 656 lnz 120
+Factorizing A
+CHOLMOD factor: L: 24-by-24 simplicial, LDL'. nzmax 120. nz 120 OK
+Ordering: AMD fl/lnz 5.5 lnz/anz 1.3
+ints in L: 269, doubles in L: 120
+factor flops 656 nnz(L) 120 (w/no amalgamation)
+nnz(A*A'): 92
+flops / nnz(L): 5.5
+nnz(L) / nnz(A): 1.3
+analyze cputime: 0.0000
+factor cputime: 0.0000 mflop: 0.0
+solve cputime: 0.0000 mflop: 0.0
+overall cputime: 0.0000 mflop: 0.0
+peak memory usage: 0 (MB)
+residual 1.3e-16 (|Ax-b|/(|A||x|+|b|))
+residual 7.5e-17 (|Ax-b|/(|A||x|+|b|)) after iterative refinement
+rcond 5.0e-01
+
+./cholmod_demo < Matrix/c.tri
+
+---------------------------------- cholmod_demo:
+norm (A,inf) = 47.2361
+norm (A,1) = 47.2361
+CHOLMOD sparse: A: 3-by-3, nz 5, upper. OK
+CHOLMOD dense: B: 3-by-1, OK
+bnorm 1.66759
+Analyze: flop 9 lnz 5
+Factorizing A
+CHOLMOD factor: L: 3-by-3 simplicial, LDL'. nzmax 5. nz 5 OK
+Ordering: AMD fl/lnz 1.8 lnz/anz 1.0
+ints in L: 28, doubles in L: 5
+factor flops 9 nnz(L) 5 (w/no amalgamation)
+nnz(A*A'): 5
+flops / nnz(L): 1.8
+nnz(L) / nnz(A): 1.0
+analyze cputime: 0.0000
+factor cputime: 0.0000 mflop: 0.0
+solve cputime: 0.0000 mflop: 0.0
+overall cputime: 0.0000 mflop: 0.0
+peak memory usage: 0 (MB)
+residual 2.0e-17 (|Ax-b|/(|A||x|+|b|))
+rcond 3.6e-02
+
+./cholmod_l_demo < Matrix/c.tri
+
+---------------------------------- cholmod_l_demo:
+norm (A,inf) = 47.2361
+norm (A,1) = 47.2361
+CHOLMOD sparse: A: 3-by-3, nz 5, upper. OK
+CHOLMOD dense: B: 3-by-1, OK
+bnorm 1.66759
+Analyze: flop 9 lnz 5
+Factorizing A
+CHOLMOD factor: L: 3-by-3 simplicial, LDL'. nzmax 5. nz 5 OK
+Ordering: AMD fl/lnz 1.8 lnz/anz 1.0
+ints in L: 28, doubles in L: 5
+factor flops 9 nnz(L) 5 (w/no amalgamation)
+nnz(A*A'): 5
+flops / nnz(L): 1.8
+nnz(L) / nnz(A): 1.0
+analyze cputime: 0.0000
+factor cputime: 0.0000 mflop: 0.0
+solve cputime: 0.0000 mflop: 0.0
+overall cputime: 0.0000 mflop: 0.0
+peak memory usage: 0 (MB)
+residual 2.0e-17 (|Ax-b|/(|A||x|+|b|))
+rcond 3.6e-02
+
+./cholmod_simple < Matrix/c.tri
+CHOLMOD sparse: A: 3-by-3, nz 5, upper. OK
+norm(b-Ax) 5.6e-17
+./cholmod_simple < Matrix/can___24.mtx
+CHOLMOD sparse: A: 24-by-24, nz 92, upper. OK
+norm(b-Ax) 2.0e-15
+./cholmod_simple < Matrix/bcsstk01.tri
+CHOLMOD sparse: A: 48-by-48, nz 224, upper. OK
+norm(b-Ax) 2.7e-13
diff --git a/CHOLMOD/Demo/reade.f b/CHOLMOD/Demo/reade.f
new file mode 100644
index 0000000..2010d5c
--- /dev/null
+++ b/CHOLMOD/Demo/reade.f
@@ -0,0 +1,182 @@
+c-----------------------------------------------------------------------
+c Read a sparse matrix in the Harwell/Boeing format and output a
+c matrix in triplet format.
+c
+c not for: **A
+c use for: RSE and PSE
+c-----------------------------------------------------------------------
+
+ integer nzmax, nmax
+ parameter (nzmax = 50000000, nmax = 1000000)
+ integer Ptr (nmax), Index (nzmax), n, nz, totcrd, ptrcrd,
+ $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, row, col, p,
+ $ nguess, nexact, nrhsix, nrhsvl
+ character title*72, key*30, type*3, ptrfmt*16,
+ $ indfmt*16, valfmt*20, rhsfmt*20
+ logical sym, unsorted
+ double precision Value (nzmax)
+ double precision skew
+ character rhstyp*3
+ integer nel
+ integer lastrow
+
+ integer prow, el, pval, hasval
+ integer stype
+
+c-----------------------------------------------------------------------
+c read header information from Harwell/Boeing matrix
+c-----------------------------------------------------------------------
+
+ nrhs = 0
+ nrhsix = 0
+
+ read (5, 10, err = 998)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd, rhscrd,
+ $ type, nrow, ncol, nz, nel,
+ $ ptrfmt, indfmt, valfmt, rhsfmt
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+ read (5, 20, err = 998) rhstyp,nrhs,nrhsix
+ endif
+10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+20 format (a3, 11x, 2i14)
+
+ skew = 0.0
+ if (type (2:2) .eq. 'Z' .or. type (2:2) .eq. 'z') then
+ write (0, *) '*ZE not supported!'
+ stop
+ endif
+ if (type (2:2) .eq. 'S' .or. type (2:2) .eq. 's') skew = 1.0
+ if (type (2:2) .eq. 'H' .or. type (2:2) .eq. 'h') then
+ write (0, *) '*HE not supported!'
+ stop
+ endif
+ sym = skew .ne. 0.0
+
+c write (0, 30) title, key, type, nrow, ncol, nz
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+c write (0, 40) rhstyp,nrhs,nzrhs
+ endif
+30 format (
+ $ ' title: ', a72 /
+ $ ' key: ', a8 /
+ $ ' type: ', a3, ' nrow: ', i14, ' ncol: ', i14 /
+ $ ' nz: ', i14)
+40 format (' rhstyp: ', a3, ' nrhs: ', i14, ' nzrhs: ', i14)
+
+ n = max (nrow, ncol)
+
+ if (n .ge. nmax .or. nz .gt. nzmax) then
+ write (0, *) 'Matrix too big!'
+ stop
+ endif
+
+ if (type (3:3) .ne. 'E' .and. type (3:3) .ne. 'a') then
+ write (0, *) 'Can only handle **E types!'
+ stop
+ endif
+
+ if (.not. (
+ $ type (1:1) .eq. 'P' .or.
+ $ type (1:1) .eq. 'p' .or.
+ $ type (1:1) .eq. 'R' .or.
+ $ type (1:1) .eq. 'r')) then
+ write (0, *) 'Can only handle R*E or P*E types!'
+ stop
+ endif
+
+c-----------------------------------------------------------------------
+c read the pattern
+c-----------------------------------------------------------------------
+
+ read (5, ptrfmt, err = 998) (Ptr (p), p = 1, ncol+1)
+ read (5, indfmt, err = 998) (Index (p), p = 1, nz)
+
+c-----------------------------------------------------------------------
+c check if the columns are sorted
+c-----------------------------------------------------------------------
+
+ unsorted = .false.
+ do 101 col = 1, ncol
+ lastrow = 0
+ do 91 p = Ptr (col), Ptr (col+1) - 1
+ row = Index (p)
+ if (row .lt. lastrow) then
+ unsorted = .true.
+ write (0,*) ' ********* Columns are unsorted'
+ goto 102
+ endif
+ lastrow = row
+91 continue
+101 continue
+102 continue
+
+c-----------------------------------------------------------------------
+c read the values
+c-----------------------------------------------------------------------
+
+ if (valcrd .gt. 0) then
+ read (5, valfmt, err = 998) (Value (p), p = 1, nel)
+ endif
+
+c-----------------------------------------------------------------------
+c write the triplet form of the input matrix
+c-----------------------------------------------------------------------
+
+c stype = 0: unsymmetric
+c stype = -1: symmetric, lower triangular part present
+
+ stype = -1
+
+ nz = 0
+ do 300 el = 1, ncol
+ do 390 p = Ptr (el), Ptr (el+1) - 1
+ do 392 prow = p, Ptr (el+1) - 1
+ nz = nz + 1
+392 continue
+390 continue
+300 continue
+
+ write (6, 701) title
+ write (6, 702) key
+701 format ('% title:', a72)
+702 format ('% key: ', a8)
+ write (6, 710) nrow, nrow, nz, stype
+710 format (2i8, i12, i3)
+
+ pval = 0
+ do 100 el = 1, ncol
+ do 90 p = Ptr (el), Ptr (el+1) - 1
+ col = Index (p)
+ do 92 prow = p, Ptr (el+1) - 1
+ row = Index (prow)
+ if (row .lt. col) then
+ write (0, *) 'bad format!'
+ stop
+ endif
+ if (valcrd .gt. 0) then
+ pval = pval + 1
+ if (pval .gt. nel) then
+ write (0, *) 'bad format!'
+ stop
+ endif
+ write (6, 200) row, col, Value (pval)
+ else
+ write (6, 201) row, col
+ endif
+92 continue
+90 continue
+100 continue
+
+200 format (2i8, e30.18e3)
+201 format (2i8)
+
+c-----------------------------------------------------------------------
+ stop
+
+998 write (0,*) 'Read error: Harwell/Boeing matrix'
+ stop
+ end
+
diff --git a/CHOLMOD/Demo/readhb.f b/CHOLMOD/Demo/readhb.f
new file mode 100644
index 0000000..d4cd2dc
--- /dev/null
+++ b/CHOLMOD/Demo/readhb.f
@@ -0,0 +1,105 @@
+c-----------------------------------------------------------------------
+c Read a sparse matrix in the Harwell/Boeing format and output a
+c matrix in triplet format. Only the lower triangular part of a
+c symmetric matrix is provided. Does not handle skew-symmetric
+c matrices.
+c-----------------------------------------------------------------------
+
+ integer nzmax, nmax
+ parameter (nzmax = 100000000, nmax = 1000000)
+ integer Ptr (nmax), Index (nzmax), n, nz, totcrd, ptrcrd,
+ $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, row, col, p
+ character title*72, key*30, type*3, ptrfmt*16,
+ $ indfmt*16, valfmt*20, rhsfmt*20
+ logical sym
+ double precision Value (nzmax), skew
+ character rhstyp*3
+ integer nzrhs, nel, stype
+
+c-----------------------------------------------------------------------
+
+c read header information from Harwell/Boeing matrix
+
+ read (5, 10, err = 998)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd, rhscrd,
+ $ type, nrow, ncol, nz, nel,
+ $ ptrfmt, indfmt, valfmt, rhsfmt
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+ read (5, 20, err = 998) rhstyp,nrhs,nzrhs
+ endif
+10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+20 format (a3, 11x, 2i14)
+
+ skew = 0.0
+ if (type (2:2) .eq. 'Z' .or. type (2:2) .eq. 'z') skew = -1.0
+ if (type (2:2) .eq. 'S' .or. type (2:2) .eq. 's') skew = 1.0
+ sym = skew .ne. 0.0
+
+c write (0, 30) title, key, type, nrow, ncol, nz
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+c write (0, 40) rhstyp,nrhs,nzrhs
+ endif
+30 format (
+ $ ' title: ', a72 /
+ $ ' key: ', a8 /
+ $ ' type: ', a3, ' nrow: ', i14, ' ncol: ', i14 /
+ $ ' nz: ', i14)
+40 format (' rhstyp: ', a3, ' nrhs: ', i14, ' nzrhs: ', i14)
+* write (0, *) ' sym: ', sym, ' skew: ', skew
+
+ if (skew .eq. -1) then
+ write (0, *) 'Cannot handle skew-symmetric matrices'
+ stop
+ endif
+
+ n = max (nrow, ncol)
+
+ if (ncol .ge. nmax .or. nz .gt. nzmax) then
+ write (0, *) ' Matrix too big!'
+ stop
+ endif
+
+ read (5, ptrfmt, err = 998) (Ptr (p), p = 1, ncol+1)
+ read (5, indfmt, err = 998) (Index (p), p = 1, nz)
+
+c read the values
+ if (valcrd .gt. 0) then
+ read (5, valfmt, err = 998) (Value (p), p = 1, nz)
+ endif
+
+c create the triplet form of the input matrix
+c stype = 0: unsymmetric
+c stype = -1: symmetric, lower triangular part present
+
+ stype = -skew
+
+ write (6, 101) title
+ write (6, 102) key
+101 format ('% title:', a72)
+102 format ('% key: ', a8)
+ write (6, 110) nrow, ncol, nz, stype
+110 format (2i8, i12, i3)
+
+ do 100 col = 1, ncol
+ do 90 p = Ptr (col), Ptr (col+1) - 1
+ row = Index (p)
+ if (valcrd .gt. 0) then
+ write (6, 200) row, col, Value (p)
+c if (sym .and. row .ne. col) then
+c write (6, 200) col, row, skew * Value (p)
+c endif
+ else
+ write (6, 201) row, col
+ endif
+90 continue
+100 continue
+200 format (2i8, e30.18e3)
+201 format (2i8)
+ stop
+
+998 write (0,*) 'Read error: Harwell/Boeing matrix'
+ stop
+ end
diff --git a/CHOLMOD/Demo/readhb2.f b/CHOLMOD/Demo/readhb2.f
new file mode 100644
index 0000000..6fc0f69
--- /dev/null
+++ b/CHOLMOD/Demo/readhb2.f
@@ -0,0 +1,121 @@
+c-----------------------------------------------------------------------
+c Read a sparse matrix in the Harwell/Boeing format and output a
+c matrix in triplet format. Only the lower triangular part of a
+c symmetric matrix is provided. Does not handle skew-symmetric
+c matrices.
+c
+c This version assumes the matrix is symmetric. Only the
+c lower triangular part is printed.
+c-----------------------------------------------------------------------
+
+ integer nzmax, nmax
+ parameter (nzmax = 100000000, nmax = 1000000)
+ integer Ptr (nmax), Index (nzmax), n, nz, totcrd, ptrcrd,
+ $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, row, col, p
+ character title*72, key*30, type*3, ptrfmt*16,
+ $ indfmt*16, valfmt*20, rhsfmt*20
+ logical sym
+ double precision Value (nzmax), skew
+ character rhstyp*3
+ integer nzrhs, nel, stype
+
+c-----------------------------------------------------------------------
+
+c read header information from Harwell/Boeing matrix
+
+ read (5, 10, err = 998)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd, rhscrd,
+ $ type, nrow, ncol, nz, nel,
+ $ ptrfmt, indfmt, valfmt, rhsfmt
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+ read (5, 20, err = 998) rhstyp,nrhs,nzrhs
+ endif
+10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+20 format (a3, 11x, 2i14)
+
+ skew = 0.0
+ if (type (2:2) .eq. 'Z' .or. type (2:2) .eq. 'z') skew = -1.0
+ if (type (2:2) .eq. 'S' .or. type (2:2) .eq. 's') skew = 1.0
+ sym = skew .ne. 0.0
+
+c write (0, 30) title, key, type, nrow, ncol, nz
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+c write (0, 40) rhstyp,nrhs,nzrhs
+ endif
+30 format (
+ $ ' title: ', a72 /
+ $ ' key: ', a8 /
+ $ ' type: ', a3, ' nrow: ', i14, ' ncol: ', i14 /
+ $ ' nz: ', i14)
+40 format (' rhstyp: ', a3, ' nrhs: ', i14, ' nzrhs: ', i14)
+* write (0, *) ' sym: ', sym, ' skew: ', skew
+
+ if (skew .eq. -1) then
+ write (0, *) 'Cannot handle skew-symmetric matrices'
+ stop
+ endif
+
+ n = max (nrow, ncol)
+
+ if (ncol .ge. nmax .or. nz .gt. nzmax) then
+ write (0, *) ' Matrix too big!'
+ stop
+ endif
+
+ read (5, ptrfmt, err = 998) (Ptr (p), p = 1, ncol+1)
+ read (5, indfmt, err = 998) (Index (p), p = 1, nz)
+
+c read the values
+ if (valcrd .gt. 0) then
+ read (5, valfmt, err = 998) (Value (p), p = 1, nz)
+ endif
+
+c create the triplet form of the input matrix
+c stype = 0: unsymmetric
+c stype = -1: symmetric, lower triangular part present
+
+c stype = -skew
+ stype = -1
+
+ nz = 0 ;
+ do 300 col = 1, ncol
+ do 390 p = Ptr (col), Ptr (col+1) - 1
+ row = Index (p)
+ if (row .ge. col) then
+ nz = nz + 1
+ endif
+390 continue
+300 continue
+
+ write (6, 101) title
+ write (6, 102) key
+101 format ('% title:', a72)
+102 format ('% key: ', a8)
+ write (6, 110) nrow, ncol, nz, stype
+110 format (2i8, i12, i3)
+
+ do 100 col = 1, ncol
+ do 90 p = Ptr (col), Ptr (col+1) - 1
+ row = Index (p)
+ if (row .ge. col) then
+ if (valcrd .gt. 0) then
+ write (6, 200) row, col, Value (p)
+c if (sym .and. row .ne. col) then
+c write (6, 200) col, row, skew * Value (p)
+c endif
+ else
+ write (6, 201) row, col
+ endif
+ endif
+90 continue
+100 continue
+200 format (2i8, e30.18e3)
+201 format (2i8)
+ stop
+
+998 write (0,*) 'Read error: Harwell/Boeing matrix'
+ stop
+ end
diff --git a/CHOLMOD/Doc/ChangeLog b/CHOLMOD/Doc/ChangeLog
new file mode 100644
index 0000000..487ba9a
--- /dev/null
+++ b/CHOLMOD/Doc/ChangeLog
@@ -0,0 +1,190 @@
+Nov 1, 2007, version 1.6.0
+
+ * minor lint cleanup (no bugs)
+
+ * new CHOLMOD_CLEAR_FLAG macro, which speeds up the calls to
+ cholmod_clear_flag, avoiding the function call if not needed. Note
+ that this leads to untested lines in the Tcov test, but the lines of
+ the macro are tested in several places, just not everywhere it appers.
+
+ * port to MATLAB 7.5 (mex -lmwblas option now required for Linux)
+
+ * minor bug fix to cholmod_add.c to avoid potential Int overflow
+
+ * extra option added to cholmod2 mexFunction
+
+ * sparse2 mexFunction modified to ensure nnz(A) == nzmax(A) always holds
+ (It didn't in v1.5.0 if numerically zero entries were dropped in A).
+
+ * correction to Help comments for spsym function
+
+ * bug fix to cholmod_symmetry.c: determination of Hermitian vs non-Hermitian
+ matrices was incorrect if the diagonal was imaginary.
+
+ * performance fix for cholmod_nesdis.c and nesdis mexFunction
+
+May 31, 2007, version 1.5.0
+
+ * 64-bit MATLAB interface
+
+ * MATLAB interface back-ported to MATLAB 6.1.
+
+ * bug fix: solving Dx=b using a supernodal factorization, in
+ cholmod_l_solve, when sizeof(UF_long) > sizeof(BLAS integer)
+
+ * changes to Makefiles to reflect directory changes in COLAMD and CCOLAMD
+ v2.7.0 directory structure (CHOLMOD v1.5 requires v2.7.0 of those
+ two packages)
+
+ * update to Modify/cholmod_updown.c, to allow input vector R to be packed
+ or unpacked.
+
+ * bug fix to Tcov/huge.c test code, for 64-bit case (this has no effect
+ on the CHOLMOD library itself, just the test code)
+
+Dec 12, 2006, version 1.4.0
+
+ * added support for large files (larger than 2GB)
+
+ * minor MATLAB cleanup
+
+ * renamed MATLAB function from cholmod to cholmod2, to avoid filename clash
+ with itself (the built-in version of cholmod).
+
+Dec 2, 2006, version 1.3.0
+
+ * Major modification to cholmod_read.c; now fully supports all forms of the
+ Matrix Market format. Added cholmod_read_dense and cholmod_read_matrix
+ functions to cholmod_read.c. Major changes to mread MATLAB function.
+ Added Common->prefer_binary option for cholmod_read.
+
+ * Added cholmod_write.c (cholmod_write_sparse and cholmod_write_dense
+ functions). Added mwrite MATLAB function.
+
+ * Added 2nd output argument to sparse2 (Z, binary pattern of explicit
+ zero entries).
+
+ * Added the function cholmod_symmetry to the MatrixOps module.
+ Added spsym MATLAB function.
+
+ * 2nd argument to cholmod_triplet_to_sparse changed from int to size_t.
+
+ * minor correction to cholmod_analyze_ordering, cholmod_dense.c
+
+ * minor change to cholmod_rowfac.c, cholmod_solve.c, ...
+ to allow for easier testing.
+
+Sept 28, 2006, version 1.2.1
+
+ * bug fix to cholmod_matlab.c, when working with sparse INT64 matrices
+ in the "sparse2" function
+
+Aug 31, 2006, version 1.2
+
+ * Common->default_nesdis parameter and Common->called_nd statistic added.
+ Otherwise, no change to user interface. v1.2 is fully upward
+ compatible with v1.1 (even binary compatible).
+
+ * non-supernodal Lx=b and L'x=b solves simplified, slight increase in
+ performance.
+
+ * update/downdate performance improved.
+
+ * ordering options and output statistics added to MATLAB/cholmod
+ mexFunction.
+
+July 27, 2006, version 1.1.1
+
+ * bug fix for cholmod_rowfac_mask, for the complex case. Has no
+ effect on MATLAB.
+
+June 27, 2006:
+
+ * trivial changes to nested dissection code, and cholmod_read.c (for
+ debugging, and to add explicit typecasts so compilers don't complain).
+
+May, 2006:
+
+ * Added new routines for LPDASA: cholmod_rowfac_mask, cholmod_updown_mask.
+ Added cholmod_collapse_septree. Added nd_oksep, nd_components
+ parameters to Common.
+
+Apr 30, 2006: version 1.1
+
+ * added interface to CAMD. cholmod_nested_dissection can now call
+ CCOLAMD, CSYMAMD, and CAMD. Common->nd_camd usage extended.
+ New argument added to nesdis mexFunction. New cholmod_camd function
+ added. No other changes to CHOLMOD user interface.
+
+ * more careful integer overflow checks. Added non-user-callable functions
+ to add and multiply size_t integers, with overflow checks.
+
+ * added Common->no_workspace_reallocate
+
+ * flop count is now correct for A*A' case (Common->rowfacfl).
+
+Jan 18, 2006: version 1.0.2
+
+ * bug fix: MATLAB interface incorrect for full logical matrices.
+
+ * Tcov tests modified to generate fewer intentional nan's, to make it
+ easier to look for errors in BLAS libraries that incorrectly
+ generate nan's.
+
+Dec 16, 2005: version 1.0.1
+
+ * bug fix: cholmod_amd allocated too small of a workspace when ordering A*A'
+
+Dec 8, 2005: version 1.0
+
+ * no real changes. Version 1.0 is the same as version 0.8. Version 1.0 is
+ simply the formal stable release.
+
+ * known issue: the floating point operation count, Common->rowfacfl, is
+ statistic is incorrect when factorizing A*A'. This will be fixed in
+ version 1.1.
+
+Nov 15, 2005: version 0.8
+
+ * bug fix in t_cholmod_super_numeric, for [R,p]=chol(A) usage.
+
+ * Common->quick_return_if_not_posdef added.
+
+ * Added cholmod_row_lsubtree (required for LPDASA)
+
+ * bug fix: cholmod_rcond returned sqrt(1/cond) for an LL' factorization;
+ 1/cond is required.
+
+ * new statistics added: flop counts for cholmod_rowfac, # of factor column
+ reallocations, # of factor reallocations due to column reallocations,
+ and # of times the (non-default) bounds on diag(L) are hit.
+
+ * factor column reallocation skipped if space already big enough.
+
+ * bug fix: cholmod_copy_factor did not copy L->is_monotonic.
+
+ * bug fix: cholmod_change_factor (diagonal entry was wrong in one case)
+
+ * rcond added to cholmod mexFunction ([x,rcond] = cholmod(A,b)).
+
+ * cholmod_rowadd, cholmod_rowdel modified. rowdel no longer removes
+ entries from the matrix; it sets them to zero instead.
+
+Oct 10, 2005: version 0.7
+
+ * minor changes: minor change to Check/cholmod_check.c (coerce
+ sizeof(...) to (int) when printing. Less strict check on A->p for
+ unpacked matrices) , removed a few unused variables in
+ Check/cholmod_read.c and Demo/cholmod*demo.c, changed "exit(0)" to
+ "return(0)" in Demo/cholmod_simple.c. Changed Makefile so that "." is
+ not assumed to be on the $path. Added Cygwin to architecture detection
+ in Include/cholmod_blas.h. Added cparent and cmember to nesdis.m.
+ Space for future expansion added to cholmod_common.
+
+ * removed "rowmark" from the Modify module, which affects how partial
+ updates to Lx=b solves are done during update/downdate. Should only
+ affect LPDASA.
+
+ * added CHOLMOD_SUBSUB_VERSION
+
+Aug 31, 2005: version 0.6 released.
diff --git a/CHOLMOD/Doc/Makefile b/CHOLMOD/Doc/Makefile
new file mode 100644
index 0000000..6945903
--- /dev/null
+++ b/CHOLMOD/Doc/Makefile
@@ -0,0 +1,225 @@
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+all: UserGuide.pdf
+
+I = \
+ ../Include/cholmod.h \
+ ../Include/cholmod_blas.h \
+ ../Include/cholmod_check.h \
+ ../Include/cholmod_cholesky.h \
+ ../Include/cholmod_complexity.h \
+ ../Include/cholmod_config.h \
+ ../Include/cholmod_core.h \
+ ../Include/cholmod_internal.h \
+ ../Include/cholmod_matrixops.h \
+ ../Include/cholmod_modify.h \
+ ../Include/cholmod_partition.h \
+ ../Include/cholmod_supernodal.h \
+ ../Include/cholmod_template.h
+
+C = ../Demo/cholmod_simple.c
+
+M = \
+ ../MATLAB/analyze.m \
+ ../MATLAB/bisect.m \
+ ../MATLAB/chol2.m \
+ ../MATLAB/cholmod2.m \
+ ../MATLAB/cholmod_demo.m \
+ ../MATLAB/cholmod_make.m \
+ ../MATLAB/etree2.m \
+ ../MATLAB/graph_demo.m \
+ ../MATLAB/lchol.m \
+ ../MATLAB/ldlchol.m \
+ ../MATLAB/ldl_normest.m \
+ ../MATLAB/ldlsolve.m \
+ ../MATLAB/ldlsplit.m \
+ ../MATLAB/ldlupdate.m \
+ ../MATLAB/metis.m \
+ ../MATLAB/nesdis.m \
+ ../MATLAB/resymbol.m \
+ ../MATLAB/sdmult.m \
+ ../MATLAB/sparse2.m \
+ ../MATLAB/spsym.m \
+ ../MATLAB/mread.m \
+ ../MATLAB/mwrite.m \
+ ../MATLAB/symbfact2.m
+
+UserGuide.pdf: UserGuide.tex UserGuide.bib $(I) $(C) $(M) Makefile getproto rule.awk header.tex footer.tex getmproto mfooter.tex mheader.tex mfile.awk
+ ./getmproto ../MATLAB/analyze.m > _analyze_m.tex
+ ./getmproto ../MATLAB/bisect.m > _bisect_m.tex
+ ./getmproto ../MATLAB/chol2.m > _chol2_m.tex
+ ./getmproto ../MATLAB/cholmod2.m > _cholmod2_m.tex
+ ./getmproto ../MATLAB/cholmod_demo.m > _cholmod_demo_m.tex
+ ./getmproto ../MATLAB/cholmod_make.m > _cholmod_make_m.tex
+ ./getmproto ../MATLAB/etree2.m > _etree2_m.tex
+ ./getmproto ../MATLAB/graph_demo.m > _graph_demo_m.tex
+ ./getmproto ../MATLAB/lchol.m > _lchol_m.tex
+ ./getmproto ../MATLAB/ldlchol.m > _ldlchol_m.tex
+ ./getmproto ../MATLAB/ldl_normest.m > _ldl_normest_m.tex
+ ./getmproto ../MATLAB/ldlsolve.m > _ldlsolve_m.tex
+ ./getmproto ../MATLAB/ldlsplit.m > _ldlsplit_m.tex
+ ./getmproto ../MATLAB/ldlupdate.m > _ldlupdate_m.tex
+ ./getmproto ../MATLAB/metis.m > _metis_m.tex
+ ./getmproto ../MATLAB/mread.m > _mread_m.tex
+ ./getmproto ../MATLAB/spsym.m > _spsym_m.tex
+ ./getmproto ../MATLAB/mwrite.m > _mwrite_m.tex
+ ./getmproto ../MATLAB/nesdis.m > _nesdis_m.tex
+ ./getmproto ../MATLAB/resymbol.m > _resymbol_m.tex
+ ./getmproto ../MATLAB/sdmult.m > _sdmult_m.tex
+ ./getmproto ../MATLAB/sparse2.m > _sparse2_m.tex
+ ./getmproto ../MATLAB/symbfact2.m > _symbfact2_m.tex
+ ./getproto '/include/, /^}/' ../Demo/cholmod_simple.c > _simple.tex
+ ./getproto '/typedef struct cholmod_common/, /^}/' ../Include/cholmod_core.h > _common.tex
+ ./getproto '/int cholmod_start/, /\*\) ;/' ../Include/cholmod_core.h > _start.tex
+ ./getproto '/int cholmod_finish/, /\*\) ;/' ../Include/cholmod_core.h > _finish.tex
+ ./getproto '/int cholmod_defaults/, /\*\) ;/' ../Include/cholmod_core.h > _defaults.tex
+ ./getproto '/size_t cholmod_maxrank/, /\*\) ;/' ../Include/cholmod_core.h > _maxrank.tex
+ ./getproto '/int cholmod_allocate_work/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_work.tex
+ ./getproto '/int cholmod_free_work/, /\*\) ;/' ../Include/cholmod_core.h > _free_work.tex
+ ./getproto '/long cholmod_clear_flag/, /\*\) ;/' ../Include/cholmod_core.h > _clear_flag.tex
+ ./getproto '/int cholmod_error/, /\*\) ;/' ../Include/cholmod_core.h > _error.tex
+ ./getproto '/double cholmod_dbound/, /\*\) ;/' ../Include/cholmod_core.h > _dbound.tex
+ ./getproto '/double cholmod_hypot/, /double\) ;/' ../Include/cholmod_core.h > _hypot.tex
+ ./getproto '/int cholmod_divcomplex/, /\*\) ;/' ../Include/cholmod_core.h > _divcomplex.tex
+ ./getproto '/typedef struct cholmod_sparse/, /^}/' ../Include/cholmod_core.h > _sparse.tex
+ ./getproto '/cholmod_sparse \*cholmod_allocate_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_sparse.tex
+ ./getproto '/int cholmod_free_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _free_sparse.tex
+ ./getproto '/int cholmod_reallocate_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_sparse.tex
+ ./getproto '/long cholmod_nnz/, /\*\) ;/' ../Include/cholmod_core.h > _nnz.tex
+ ./getproto '/cholmod_sparse \*cholmod_speye/, /\*\) ;/' ../Include/cholmod_core.h > _speye.tex
+ ./getproto '/cholmod_sparse \*cholmod_spzeros/, /\*\) ;/' ../Include/cholmod_core.h > _spzeros.tex
+ ./getproto '/cholmod_sparse \*cholmod_transpose/, /\*\) ;/' ../Include/cholmod_core.h > _transpose.tex
+ ./getproto '/int cholmod_transpose_unsym/, /\*\) ;/' ../Include/cholmod_core.h > _transpose_unsym.tex
+ ./getproto '/int cholmod_transpose_sym/, /\*\) ;/' ../Include/cholmod_core.h > _transpose_sym.tex
+ ./getproto '/cholmod_sparse \*cholmod_ptranspose/, /\*\) ;/' ../Include/cholmod_core.h > _ptranspose.tex
+ ./getproto '/int cholmod_sort/, /\*\) ;/' ../Include/cholmod_core.h > _sort.tex
+ ./getproto '/cholmod_sparse \*cholmod_band/, /\*\) ;/' ../Include/cholmod_core.h > _band.tex
+ ./getproto '/int cholmod_band_inplace/, /\*\) ;/' ../Include/cholmod_core.h > _band_inplace.tex
+ ./getproto '/cholmod_sparse \*cholmod_aat/, /\*\) ;/' ../Include/cholmod_core.h > _aat.tex
+ ./getproto '/cholmod_sparse \*cholmod_copy_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _copy_sparse.tex
+ ./getproto '/cholmod_sparse \*cholmod_copy /, /\*\) ;/' ../Include/cholmod_core.h > _copy.tex
+ ./getproto '/cholmod_sparse \*cholmod_add/, /\*\) ;/' ../Include/cholmod_core.h > _add.tex
+ ./getproto '/int cholmod_sparse_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _sparse_xtype.tex
+ ./getproto '/typedef struct cholmod_factor/, /^}/' ../Include/cholmod_core.h > _factor.tex
+ ./getproto '/cholmod_factor \*cholmod_allocate_factor/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_factor.tex
+ ./getproto '/int cholmod_free_factor/, /\*\) ;/' ../Include/cholmod_core.h > _free_factor.tex
+ ./getproto '/int cholmod_reallocate_factor/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_factor.tex
+ ./getproto '/int cholmod_change_factor/, /\*\) ;/' ../Include/cholmod_core.h > _change_factor.tex
+ ./getproto '/int cholmod_pack_factor/, /\*\) ;/' ../Include/cholmod_core.h > _pack_factor.tex
+ ./getproto '/int cholmod_reallocate_column/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_column.tex
+ ./getproto '/cholmod_sparse \*cholmod_factor_to_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _factor_to_sparse.tex
+ ./getproto '/cholmod_factor \*cholmod_copy_factor/, /\*\) ;/' ../Include/cholmod_core.h > _copy_factor.tex
+ ./getproto '/int cholmod_factor_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _factor_xtype.tex
+ ./getproto '/typedef struct cholmod_dense/, /^}/' ../Include/cholmod_core.h > _dense.tex
+ ./getproto '/cholmod_dense \*cholmod_allocate_dense/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_dense.tex
+ ./getproto '/cholmod_dense \*cholmod_zeros/, /\*\) ;/' ../Include/cholmod_core.h > _zeros.tex
+ ./getproto '/cholmod_dense \*cholmod_ones/, /\*\) ;/' ../Include/cholmod_core.h > _ones.tex
+ ./getproto '/cholmod_dense \*cholmod_eye/, /\*\) ;/' ../Include/cholmod_core.h > _eye.tex
+ ./getproto '/int cholmod_free_dense/, /\*\) ;/' ../Include/cholmod_core.h > _free_dense.tex
+ ./getproto '/cholmod_dense \*cholmod_sparse_to_dense/, /\*\) ;/' ../Include/cholmod_core.h > _sparse_to_dense.tex
+ ./getproto '/cholmod_sparse \*cholmod_dense_to_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _dense_to_sparse.tex
+ ./getproto '/cholmod_dense \*cholmod_copy_dense/, /\*\) ;/' ../Include/cholmod_core.h > _copy_dense.tex
+ ./getproto '/int cholmod_copy_dense2/, /\*\) ;/' ../Include/cholmod_core.h > _copy_dense2.tex
+ ./getproto '/int cholmod_dense_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _dense_xtype.tex
+ ./getproto '/typedef struct cholmod_triplet/, /^}/' ../Include/cholmod_core.h > _triplet.tex
+ ./getproto '/cholmod_triplet \*cholmod_allocate_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _allocate_triplet.tex
+ ./getproto '/int cholmod_free_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _free_triplet.tex
+ ./getproto '/int cholmod_reallocate_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _reallocate_triplet.tex
+ ./getproto '/cholmod_triplet \*cholmod_sparse_to_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _sparse_to_triplet.tex
+ ./getproto '/cholmod_sparse \*cholmod_triplet_to_sparse/, /\*\) ;/' ../Include/cholmod_core.h > _triplet_to_sparse.tex
+ ./getproto '/cholmod_triplet \*cholmod_copy_triplet/, /\*\) ;/' ../Include/cholmod_core.h > _copy_triplet.tex
+ ./getproto '/int cholmod_triplet_xtype/, /\*\) ;/' ../Include/cholmod_core.h > _triplet_xtype.tex
+ ./getproto '/void \*cholmod_malloc/, /\*\) ;/' ../Include/cholmod_core.h > _malloc.tex
+ ./getproto '/void \*cholmod_calloc/, /\*\) ;/' ../Include/cholmod_core.h > _calloc.tex
+ ./getproto '/void \*cholmod_free/, /\*\) ;/' ../Include/cholmod_core.h > _free.tex
+ ./getproto '/void \*cholmod_realloc/, /\*\) ;/' ../Include/cholmod_core.h > _realloc.tex
+ ./getproto '/int cholmod_realloc_multiple/, /\*\) ;/' ../Include/cholmod_core.h > _realloc_multiple.tex
+ ./getproto '/itype defines the/, /define CHOLMOD_SUPERNODAL/' ../Include/cholmod_core.h > _defn.tex
+ ./getproto '/int cholmod_check_common/, /\*\) ;/' ../Include/cholmod_check.h > _check_common.tex
+ ./getproto '/int cholmod_print_common/, /\*\) ;/' ../Include/cholmod_check.h > _print_common.tex
+ ./getproto '/int cholmod_check_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _check_sparse.tex
+ ./getproto '/int cholmod_print_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _print_sparse.tex
+ ./getproto '/int cholmod_check_dense/, /\*\) ;/' ../Include/cholmod_check.h > _check_dense.tex
+ ./getproto '/int cholmod_print_dense/, /\*\) ;/' ../Include/cholmod_check.h > _print_dense.tex
+ ./getproto '/int cholmod_check_factor/, /\*\) ;/' ../Include/cholmod_check.h > _check_factor.tex
+ ./getproto '/int cholmod_print_factor/, /\*\) ;/' ../Include/cholmod_check.h > _print_factor.tex
+ ./getproto '/int cholmod_check_triplet/, /\*\) ;/' ../Include/cholmod_check.h > _check_triplet.tex
+ ./getproto '/int cholmod_print_triplet/, /\*\) ;/' ../Include/cholmod_check.h > _print_triplet.tex
+ ./getproto '/int cholmod_check_subset/, /\*\) ;/' ../Include/cholmod_check.h > _check_subset.tex
+ ./getproto '/int cholmod_print_subset/, /\*\) ;/' ../Include/cholmod_check.h > _print_subset.tex
+ ./getproto '/int cholmod_check_perm/, /\*\) ;/' ../Include/cholmod_check.h > _check_perm.tex
+ ./getproto '/int cholmod_print_perm/, /\*\) ;/' ../Include/cholmod_check.h > _print_perm.tex
+ ./getproto '/int cholmod_check_parent/, /\*\) ;/' ../Include/cholmod_check.h > _check_parent.tex
+ ./getproto '/int cholmod_print_parent/, /\*\) ;/' ../Include/cholmod_check.h > _print_parent.tex
+ ./getproto '/cholmod_triplet \*cholmod_read_triplet/, /\*\) ;/' ../Include/cholmod_check.h > _read_triplet.tex
+ ./getproto '/cholmod_sparse \*cholmod_read_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _read_sparse.tex
+ ./getproto '/cholmod_dense \*cholmod_read_dense/, /\*\) ;/' ../Include/cholmod_check.h > _read_dense.tex
+ ./getproto '/void \*cholmod_read_matrix/, /\*\) ;/' ../Include/cholmod_check.h > _read_matrix.tex
+ ./getproto '/int cholmod_write_sparse/, /\*\) ;/' ../Include/cholmod_check.h > _write_sparse.tex
+ ./getproto '/int cholmod_write_dense/, /\*\) ;/' ../Include/cholmod_check.h > _write_dense.tex
+ ./getproto '/cholmod_factor \*cholmod_analyze /, /\*\) ;/' ../Include/cholmod_cholesky.h > _analyze.tex
+ ./getproto '/cholmod_factor \*cholmod_analyze_p/, /\*\) ;/' ../Include/cholmod_cholesky.h > _analyze_p.tex
+ ./getproto '/int cholmod_factorize /, /\*\) ;/' ../Include/cholmod_cholesky.h > _factorize.tex
+ ./getproto '/int cholmod_factorize_p/, /\*\) ;/' ../Include/cholmod_cholesky.h > _factorize_p.tex
+ ./getproto '/cholmod_dense \*cholmod_solve/, /\*\) ;/' ../Include/cholmod_cholesky.h > _solve.tex
+ ./getproto '/cholmod_sparse \*cholmod_spsolve/, /\*\) ;/' ../Include/cholmod_cholesky.h > _spsolve.tex
+ ./getproto '/int cholmod_etree/, /\*\) ;/' ../Include/cholmod_cholesky.h > _etree.tex
+ ./getproto '/int cholmod_rowcolcounts/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rowcolcounts.tex
+ ./getproto '/int cholmod_analyze_ordering/, /\*\) ;/' ../Include/cholmod_cholesky.h > _analyze_ordering.tex
+ ./getproto '/int cholmod_amd/, /\*\) ;/' ../Include/cholmod_cholesky.h > _amd.tex
+ ./getproto '/int cholmod_colamd/, /\*\) ;/' ../Include/cholmod_cholesky.h > _colamd.tex
+ ./getproto '/int cholmod_rowfac/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rowfac.tex
+ ./getproto '/int cholmod_rowfac_mask/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rowfac_mask.tex
+ ./getproto '/int cholmod_row_subtree/, /\*\) ;/' ../Include/cholmod_cholesky.h > _row_subtree.tex
+ ./getproto '/int cholmod_row_lsubtree/, /\*\) ;/' ../Include/cholmod_cholesky.h > _row_lsubtree.tex
+ ./getproto '/int cholmod_resymbol /, /\*\) ;/' ../Include/cholmod_cholesky.h > _resymbol.tex
+ ./getproto '/int cholmod_resymbol_noperm/, /\*\) ;/' ../Include/cholmod_cholesky.h > _resymbol_noperm.tex
+ ./getproto '/double cholmod_rcond/, /\*\) ;/' ../Include/cholmod_cholesky.h > _rcond.tex
+ ./getproto '/long cholmod_postorder/, /\*\) ;/' ../Include/cholmod_cholesky.h > _postorder.tex
+ ./getproto '/int cholmod_updown /, /\*\) ;/' ../Include/cholmod_modify.h > _updown.tex
+ ./getproto '/int cholmod_updown_solve/, /\*\) ;/' ../Include/cholmod_modify.h > _updown_solve.tex
+ ./getproto '/int cholmod_updown_mark/, /\*\) ;/' ../Include/cholmod_modify.h > _updown_mark.tex
+ ./getproto '/int cholmod_updown_mask/, /\*\) ;/' ../Include/cholmod_modify.h > _updown_mask.tex
+ ./getproto '/int cholmod_rowadd /, /\*\) ;/' ../Include/cholmod_modify.h > _rowadd.tex
+ ./getproto '/int cholmod_rowadd_solve/, /\*\) ;/' ../Include/cholmod_modify.h > _rowadd_solve.tex
+ ./getproto '/int cholmod_rowadd_mark/, /\*\) ;/' ../Include/cholmod_modify.h > _rowadd_mark.tex
+ ./getproto '/int cholmod_rowdel /, /\*\) ;/' ../Include/cholmod_modify.h > _rowdel.tex
+ ./getproto '/int cholmod_rowdel_solve/, /\*\) ;/' ../Include/cholmod_modify.h > _rowdel_solve.tex
+ ./getproto '/int cholmod_rowdel_mark/, /\*\) ;/' ../Include/cholmod_modify.h > _rowdel_mark.tex
+ ./getproto '/int cholmod_drop/, /\*\) ;/' ../Include/cholmod_matrixops.h > _drop.tex
+ ./getproto '/double cholmod_norm_dense/, /\*\) ;/' ../Include/cholmod_matrixops.h > _norm_dense.tex
+ ./getproto '/double cholmod_norm_sparse/, /\*\) ;/' ../Include/cholmod_matrixops.h > _norm_sparse.tex
+ ./getproto '/cholmod_sparse \*cholmod_horzcat/, /\*\) ;/' ../Include/cholmod_matrixops.h > _horzcat.tex
+ ./getproto '/define CHOLMOD_SCALAR/, /\*\) ;/' ../Include/cholmod_matrixops.h > _scale.tex
+ ./getproto '/int cholmod_sdmult/, /\*\) ;/' ../Include/cholmod_matrixops.h > _sdmult.tex
+ ./getproto '/cholmod_sparse \*cholmod_ssmult/, /\*\) ;/' ../Include/cholmod_matrixops.h > _ssmult.tex
+ ./getproto '/cholmod_sparse \*cholmod_submatrix/, /\*\) ;/' ../Include/cholmod_matrixops.h > _submatrix.tex
+ ./getproto '/cholmod_sparse \*cholmod_vertcat/, /\*\) ;/' ../Include/cholmod_matrixops.h > _vertcat.tex
+ ./getproto '/int cholmod_symmetry/, /\*\) ;/' ../Include/cholmod_matrixops.h > _symmetry.tex
+ ./getproto '/int cholmod_super_symbolic/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_symbolic.tex
+ ./getproto '/int cholmod_super_numeric/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_numeric.tex
+ ./getproto '/int cholmod_super_lsolve/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_lsolve.tex
+ ./getproto '/int cholmod_super_ltsolve/, /\*\) ;/' ../Include/cholmod_supernodal.h > _super_ltsolve.tex
+ ./getproto '/long cholmod_nested_dissection/, /\*\) ;/' ../Include/cholmod_partition.h > _nested_dissection.tex
+ ./getproto '/int cholmod_metis/, /\*\) ;/' ../Include/cholmod_partition.h > _metis.tex
+ ./getproto '/int cholmod_ccolamd/, /\*\) ;/' ../Include/cholmod_partition.h > _ccolamd.tex
+ ./getproto '/int cholmod_camd/, /\*\) ;/' ../Include/cholmod_partition.h > _camd.tex
+ ./getproto '/int cholmod_csymamd/, /\*\) ;/' ../Include/cholmod_partition.h > _csymamd.tex
+ ./getproto '/int cholmod_csymamd/, /\*\) ;/' ../Include/cholmod_partition.h > _csymamd.tex
+ ./getproto '/long cholmod_bisect/, /\*\) ;/' ../Include/cholmod_partition.h > _bisect.tex
+ ./getproto '/long cholmod_metis_bisector/, /\*\) ;/' ../Include/cholmod_partition.h > _metis_bisector.tex
+ ./getproto '/long cholmod_collapse_septree/, /\*\) ;/' ../Include/cholmod_partition.h > _collapse_septree.tex
+ pdflatex UserGuide
+ bibtex UserGuide
+ pdflatex UserGuide
+ pdflatex UserGuide
+
+distclean: purge
+
+purge: clean
+ - $(RM) _temp.awk _*.tex *.dvi *.aux *.log *.lof *.lot *.toc *.bak *.bbl *.blg
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/CHOLMOD/Doc/UserGuide.bib b/CHOLMOD/Doc/UserGuide.bib
new file mode 100644
index 0000000..c804ad2
--- /dev/null
+++ b/CHOLMOD/Doc/UserGuide.bib
@@ -0,0 +1,196 @@
+ at string{SIMAX = "{SIAM} J. Matrix Anal. Applic."}
+ at string{TOMS = "{ACM} Trans. Math. Softw."}
+ at string{SIAMJSC = "{SIAM} J. Sci. Comput."}
+
+ at article{DavisHager06,
+ author={Davis, T. A. and Hager, W. W.},
+ title={Dynamic supernodes in sparse {Cholesky} update/downdate and triangular
+ solves},
+ journal=TOMS,
+ year={submitted in 2006}
+ }
+
+ at article{ChenDavisHagerRajamanickam06,
+ author={Chen, Y. and Davis, T. A. and Hager, W. W. and Rajamanickam, S.},
+ title={Algorithm 8xx: {CHOLMOD}, supernodal sparse {Cholesky} factorization and
+ update/downdate},
+ journal=TOMS,
+ year={submitted in 2006}
+ }
+
+ at article{DavisHager99,
+ author={Davis, T. A. and Hager, W. W.},
+ title={Modifying a sparse {C}holesky factorization},
+ journal=SIMAX,
+ year={1999}
+ ,volume={20}
+ ,number={3}
+ ,pages={606--627}
+ }
+
+ at article{DavisHager01,
+ author={Davis, T. A. and Hager, W. W.},
+ title={Multiple-Rank Modifications of a Sparse {C}holesky Factorization},
+ journal=SIMAX,
+ year={2001}
+ ,volume={22}
+ ,number={4}
+ ,pages={997--1013}
+ }
+
+ at article{DavisHager05,
+ author={Davis, T. A. and Hager, W. W.},
+ title={Row modifications of a sparse {Cholesky} factorization},
+ journal=SIMAX,
+ year={2005}
+ ,volume={26}
+ ,number={3}
+ ,pages={621--639}
+ }
+
+ at article{AmestoyDavisDuff96,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={An approximate minimum degree ordering algorithm},
+ journal=SIMAX,
+ year={1996}
+ ,volume={17}
+ ,number={4}
+ ,pages={886--905}
+ }
+
+ at article{Davis05,
+ author={Davis, T. A.},
+ title={Algorithm 849: A concise sparse {Cholesky} algorithm},
+ journal=TOMS,
+ year={2005},volume={31},number={4},pages={587--591}}
+
+ at article{DavisGilbertLarimoreNg00,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={A column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={353--376}}
+
+ at article{DavisGilbertLarimoreNg00_algo,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={Algorithm 836: {COLAMD}, a column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={377--380}}
+
+ at article{NgPeyton91b,
+ author={Ng, E. and Peyton, B.},
+ title={Block sparse {C}holesky algorithms on advanced uniprocessor computers},
+ journal=SIAMJSC,
+ year={1993}
+ ,volume={14}
+ ,pages={1034--1056}
+ }
+
+ at article{Liu86c,
+ author={Liu, J. W. H.},
+ title={A Compact Row Storage Scheme for {C}holesky Factors Using Elimination Trees},
+ journal=TOMS,
+ year={1986},
+ volume={12},
+ number={2},
+ pages={127--148},
+ }
+
+ at article{Liu90a,
+ author={Liu, J. W. H.},
+ title={The Role of Elimination Trees in Sparse Factorization},
+ journal=SIMAX,
+ year={1990}
+ ,volume={11}
+ ,number={1}
+ ,pages={134--172}
+ }
+
+ at article{GilbertNgPeyton94,
+ author={Gilbert, J. R. and Ng, E. G. and Peyton, B. W.},
+ title={An efficient algorithm to compute row and column counts for sparse {C}holesky factorization},
+ journal=SIMAX,
+ year={1994}
+ ,volume={15}
+ ,number={4}
+ ,pages={1075--1091}
+ }
+
+ at article{GilbertLiNgPeyton01,
+ author={Gilbert, J. R. and Li, X. S. and Ng, E. G. and Peyton, B. W.},
+ title={Computing row and column counts for sparse {QR} and {LU} factorization},
+ journal={{BIT}},
+ year={2001}
+ ,volume={41}
+ ,number={4}
+ ,pages={693--710}
+ }
+
+ at book{LAPACK,
+ author={Anderson, E. and Bai, Z. and Bischof, C. and Blackford, S. and Demmel, J. and Dongarra, J. and {Du Croz}, J. and Greenbaum, A. and Hammarling, S. and McKenny, A. and Sorensen, D.},
+ title={{LAPACK} Users' Guide, 3rd ed.},
+ publisher={{SIAM}},
+ year={1999}
+ }
+
+ at article{ACM679a,
+ author={Dongarra, J. J. and {Du Croz}, J. and Duff, I. S. and Hammarling, S.},
+ title={A set of level-3 basic linear algebra subprograms},
+ journal=TOMS,
+ year={1990}
+ ,volume={16}
+ ,number={1}
+ ,pages={1--17}
+ }
+
+
+ at article{KarypisKumar98,
+ author={Karypis, G. and Kumar, V.},
+ title={A fast and high quality multilevel scheme for partitioning irregular graphs},
+ journal=SIAMJSC,
+ year=1998
+ ,volume={20}
+ ,number={1}
+ ,pages={359--392}
+ }
+
+ at article{GilbertMolerSchreiber,
+ author={Gilbert, J. R. and Moler, C. and Schreiber, R.},
+ title={Sparse matrices in {MATLAB}: design and implementation},
+ journal=SIMAX,
+ year={1992}
+ ,volume={13}
+ ,number={1}
+ ,pages={333--356}
+ }
+
+ at article{AmestoyDavisDuff03,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={381-388}}
+
+
+ at article{GouldHuScott05,
+ author={Gould, N. I. M. and Hu, Y. and Scott, J. A.},
+ title={A numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations},
+ journal=TOMS,
+ year={to appear}
+ }
+
+ at techreport{GouldHuScott05b,
+ author={Gould, N. I. M. and Hu, Y. and Scott, J. A.},
+ title={Complete results from a numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations},
+ institution={CCLRC, Rutherford Appleton Laboratory},
+ number={Internal report 2005-1 (revision 1)},
+ year={2005},
+ howpublished={www.numerical.rl.ac.uk/reports/reports.shtml}
+ }
diff --git a/CHOLMOD/Doc/UserGuide.pdf b/CHOLMOD/Doc/UserGuide.pdf
new file mode 100644
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diff --git a/CHOLMOD/Doc/UserGuide.tex b/CHOLMOD/Doc/UserGuide.tex
new file mode 100644
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+++ b/CHOLMOD/Doc/UserGuide.tex
@@ -0,0 +1,3369 @@
+%-------------------------------------------------------------------------------
+% The CHOLMOD/Doc/UserGuide.tex file.
+%-------------------------------------------------------------------------------
+
+\documentclass[11pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+\newcommand{\new}[1]{\overline{#1}}
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+\begin{document}
+
+\author{Timothy A. Davis \\
+Dept. of Computer and Information Science and Engineering \\
+Univ. of Florida, Gainesville, FL}
+\title{User Guide for CHOLMOD: a sparse Cholesky factorization and
+modification package}
+\date{Version 1.6, Nov 1, 2007}
+\maketitle
+
+%-------------------------------------------------------------------------------
+\begin{abstract}
+ CHOLMOD\footnote{CHOLMOD is short for CHOLesky MODification,
+ since a key feature of the package is its ability to update/downdate
+ a sparse Cholesky factorization}
+ is a set of routines for factorizing sparse symmetric positive
+ definite matrices of the form $\m{A}$ or $\m{AA}\tr$, updating/downdating
+ a sparse Cholesky factorization, solving linear systems, updating/downdating
+ the solution to the triangular system $\m{Lx}=\m{b}$, and many other sparse
+ matrix functions for both symmetric and unsymmetric matrices.
+ Its supernodal Cholesky factorization
+ relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction
+ of the peak performance of the BLAS. Both real and complex matrices
+ are supported. CHOLMOD is written in ANSI/ISO C, with both
+ C and MATLAB interfaces. This code works on Microsoft Windows and many versions
+ of Unix and Linux.
+\end{abstract}
+%-------------------------------------------------------------------------------
+
+CHOLMOD Copyright\copyright 2005-2006 by Timothy A. Davis. Portions are also
+copyrighted by William W. Hager (the {\tt Modify} Module),
+and the University of Florida (the {\tt Partition} and {\tt Core} Modules).
+All Rights Reserved. Some of CHOLMOD's Modules are distributed under the GNU
+General Public License, and others under the GNU Lesser General Public License.
+Refer to each Module for details.
+CHOLMOD is also available under other licenses that permit its use in
+proprietary applications; contact the authors for details.
+See http://www.cise.ufl.edu/research/sparse for the code and all documentation,
+including this User Guide.
+
+\newpage
+\tableofcontents
+
+%-------------------------------------------------------------------------------
+\newpage \section{Overview}
+%-------------------------------------------------------------------------------
+
+CHOLMOD is a set of ANSI C routines for solving systems of linear
+equations, $\m{Ax}=\m{b}$, when $\m{A}$ is sparse and symmetric positive definite,
+and $\m{x}$ and $\m{b}$ can be either sparse or dense.\footnote{Some support
+is provided for symmetric indefinite matrices.}
+Complex matrices are supported, in two different formats.
+CHOLMOD includes high-performance left-looking supernodal factorization
+and solve methods \cite{NgPeyton91b},
+based on LAPACK \cite{LAPACK} and the BLAS \cite{ACM679a}.
+After a matrix is factorized, its factors can be updated or downdated using
+the techniques described by Davis and Hager
+in \cite{DavisHager99,DavisHager01,DavisHager05}.
+Many additional sparse matrix operations are provided, for both
+symmetric and unsymmetric matrices (square or rectangular), including
+sparse matrix multiply, add, transpose, permutation, scaling,
+norm, concatenation, sub-matrix access, and converting to alternate data structures.
+Interfaces to many ordering methods are provided, including minimum degree
+(AMD \cite{AmestoyDavisDuff96,AmestoyDavisDuff03},
+COLAMD \cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00}),
+constrained minimum degree (CSYMAMD, CCOLAMD, CAMD), and
+graph-partitioning-based nested dissection (METIS \cite{KarypisKumar98}).
+Most of its operations are available within MATLAB via mexFunction interfaces.
+
+A pair of articles on CHOLMOD has been submitted to the ACM Transactions
+on Mathematical Softare:
+\cite{ChenDavisHagerRajamanickam06,DavisHager06}.
+
+CHOLMOD 1.0 replaces {\tt chol} (the sparse case), {\tt symbfact}, and {\tt etree}
+in MATLAB 7.2 (R2006a), and is used for {\tt x=A}$\backslash${\tt b}
+when {\tt A} is symmetric positive definite \cite{GilbertMolerSchreiber}.
+It will replace {\tt sparse} in a future version of MATLAB.
+
+The C-callable CHOLMOD library consists of 133 user-callable routines and one
+include file. Each routine comes in two versions, one for {\tt int} integers
+and another for {\tt long}. Many of the routines can support either real or
+complex matrices, simply by passing a matrix of the appropriate type.
+
+Nick Gould, Yifan Hu, and Jennifer Scott have independently tested CHOLMOD's
+performance, comparing it with nearly a dozen or so other solvers
+\cite{GouldHuScott05,GouldHuScott05b}. Its performance was quite competitive.
+
+%-------------------------------------------------------------------------------
+\newpage \section{Primary routines and data structures}
+%-------------------------------------------------------------------------------
+
+Five primary CHOLMOD routines are required to factorize $\m{A}$ or $\m{AA}\tr$
+and solve the related system $\m{Ax}=\m{b}$ or $\m{AA}\tr\m{x}=\m{b}$,
+for either the real or complex cases:
+\begin{enumerate}
+\item {\tt cholmod\_start}:
+ This must be the first call to CHOLMOD.
+
+\item {\tt cholmod\_analyze}:
+ Finds a fill-reducing ordering, and performs the symbolic factorization,
+ either simplicial (non-supernodal) or supernodal.
+
+\item {\tt cholmod\_factorize}:
+ Numerical factorization, either simplicial or supernodal, $\m{LL}\tr$ or $\m{LDL}\tr$
+ using either the symbolic factorization from {\tt cholmod\_analyze} or the numerical
+ factorization from a prior call to {\tt cholmod\_factorize}.
+
+\item {\tt cholmod\_solve}:
+ Solves $\m{Ax}=\m{b}$, or many other related systems, where $\m{x}$ and
+ $\m{b}$ are dense matrices. The {\tt cholmod\_spsolve} routine handles
+ the sparse case. Any mixture of real and complex $\m{A}$ and $\m{b}$ are
+ allowed.
+
+\item {\tt cholmod\_finish}:
+ This must be the last call to CHOLMOD.
+\end{enumerate}
+
+Additional routines are also required to create and destroy
+the matrices $\m{A}$, $\m{x}$, $\m{b}$, and the $\m{LL}\tr$ or $\m{LDL}\tr$ factorization.
+CHOLMOD has five kinds of data structures, referred to as objects and implemented
+as pointers to {\tt struct}'s:
+
+\begin{enumerate}
+\item {\tt cholmod\_common}: parameter settings, statistics, and workspace
+ used internally by CHOLMOD.
+ See Section~\ref{cholmod_common} for details.
+
+\item {\tt cholmod\_sparse}: a sparse matrix in compressed-column form,
+ either pattern-only, real, complex, or ``zomplex.'' In its basic form,
+ the matrix {\tt A} contains:
+ \begin{itemize}
+ \item {\tt A->p}, an integer array of size {\tt A->ncol+1}.
+ \item {\tt A->i}, an integer array of size {\tt A->nzmax}.
+ \item {\tt A->x}, a {\tt double} array of size {\tt A->nzmax} or twice that for the complex case.
+ This is compatible with the Fortran and ANSI C99 complex data type.
+ \item {\tt A->z}, a {\tt double} array of size {\tt A->nzmax} if {\tt A} is zomplex.
+ A zomplex matrix has a {\tt z} array, thus the name.
+ This is compatible with the MATLAB representation of complex matrices.
+ \end{itemize}
+ For all four types of matrices, the row indices of entries of column {\tt j}
+ are located in {\tt A->i [A->p [j] ... A->p [j+1]-1]}.
+ For a real matrix, the corresponding numerical values are in {\tt A->x} at the same location.
+ For a complex matrix, the entry whose row index is {\tt A->i [p]} is contained in
+ {\tt A->x [2*p]} (the real part) and {\tt A->x [2*p+1]} (the imaginary part).
+ For a zomplex matrix, the real part is in {\tt A->x [p]} and imaginary part is in {\tt A->z [p]}.
+ See Section~\ref{cholmod_sparse} for more details.
+
+\item {\tt cholmod\_factor}:
+ A symbolic or numeric factorization, either real, complex, or zomplex.
+ It can be either an $\m{LL}\tr$ or $\m{LDL}\tr$ factorization, and either
+ simplicial or supernodal. You will normally not need to examine its contents.
+ See Section~\ref{cholmod_factor} for more details.
+
+\item {\tt cholmod\_dense}:
+ A dense matrix, either real, complex or zomplex, in column-major order.
+ This differs from the row-major convention used in C. A dense matrix {\tt X} contains
+ \begin{itemize}
+ \item {\tt X->x}, a double array of size {\tt X->nzmax} or twice that for the complex case.
+ \item {\tt X->z}, a double array of size {\tt X->nzmax} if {\tt X} is zomplex.
+ \end{itemize}
+ For a real dense matrix $x_{ij}$ is {\tt X->x [i+j*d]} where {\tt d = X->d} is the leading dimension of {\tt X}.
+ For a complex dense matrix, the real part of $x_{ij}$ is {\tt X->x [2*(i+j*d)]} and the imaginary part is {\tt X->x [2*(i+j*d)+1]}.
+ For a zomplex dense matrix, the real part of $x_{ij}$ is {\tt X->x [i+j*d]} and the imaginary part is {\tt X->z [i+j*d]}.
+ Real and complex dense matrices can be passed to LAPACK and the BLAS.
+ See Section~\ref{cholmod_dense} for more details.
+
+\item {\tt cholmod\_triplet}:
+ CHOLMOD's sparse matrix ({\tt cholmod\_sparse}) is the primary input for nearly all CHOLMOD
+ routines, but it can be difficult for the user to construct.
+ A simpler method of creating a sparse matrix is to first create a {\tt cholmod\_triplet} matrix,
+ and then convert it to a {\tt cholmod\_sparse} matrix via
+ the {\tt cholmod\_triplet\_to\_sparse} routine.
+ In its basic form, the triplet matrix {\tt T} contains
+ \begin{itemize}
+ \item {\tt T->i} and {\tt T->j}, integer arrays of size {\tt T->nzmax}.
+ \item {\tt T->x}, a double array of size {\tt T->nzmax} or twice that for the complex case.
+ \item {\tt T->z}, a double array of size {\tt T->nzmax} if {\tt T} is zomplex.
+ \end{itemize}
+ The {\tt k}th entry in the data structure has row index
+ {\tt T->i [k]} and column index {\tt T->j [k]}.
+ For a real triplet matrix, its numerical value is {\tt T->x [k]}.
+ For a complex triplet matrix, its real part is {\tt T->x [2*k]} and its imaginary part is {\tt T->x [2*k+1]}.
+ For a zomplex matrix, the real part is {\tt T->x [k]} and imaginary part is {\tt T->z [k]}.
+ The entries can be in any order, and duplicates are permitted.
+ See Section~\ref{cholmod_triplet} for more details.
+
+\end{enumerate}
+
+Each of the five objects has a routine in CHOLMOD to create and destroy it.
+CHOLMOD provides many other operations on these objects as well.
+A few of the most important ones are illustrated in the sample program in the
+next section.
+
+%-------------------------------------------------------------------------------
+\newpage \section{Simple example program}
+%-------------------------------------------------------------------------------
+
+\input{_simple.tex}
+The {\tt Demo/cholmod\_simple.c} program illustrates the
+basic usage of CHOLMOD. It reads a triplet matrix from a file
+(in Matrix Market format), converts it into a sparse matrix,
+creates a linear system, solves it, and prints the norm of the residual.
+
+See the {\tt CHOLMOD/Demo/cholmod\_demo.c} program for a more elaborate
+example, and \newline
+{\tt CHOLMOD/Demo/cholmod\_l\_demo.c} for its {\tt long} integer version.
+
+%-------------------------------------------------------------------------------
+\newpage \section{Installation of the C-callable library}
+\label{Install}
+%-------------------------------------------------------------------------------
+
+CHOLMOD requires a suite of external packages, many of which are distributed
+along with CHOLMOD, but three of which are not. Those included with CHOLMOD are:
+\begin{itemize}
+\item AMD: an approximate minimum degree ordering algorithm,
+ by Tim Davis, Patrick Amestoy, and Iain Duff
+ \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}.
+\item COLAMD: an approximate column minimum degree ordering algorithm,
+ by Tim Davis, Stefan Larimore, John Gilbert, and Esmond Ng
+ \cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00}.
+\item CCOLAMD: a constrained approximate column minimum degree ordering
+ algorithm,
+ by Tim Davis and Siva Rajamanickam, based directly on COLAMD.
+ This package is not required if CHOLMOD is compiled with the
+ {\tt -DNPARTITION} flag.
+\item CAMD: a constrained approximate minimum degree ordering
+ algorithm,
+ by Tim Davis and Yanqing Chen, based directly on AMD.
+ This package is not required if CHOLMOD is compiled with the
+ {\tt -DNPARTITION} flag.
+\item {\tt UFconfig}: a single place where all sparse matrix packages authored
+ or co-authored by Davis are configured. Also includes a version of the
+ {\tt xerbla} routine for the BLAS.
+\end{itemize}
+
+Three other packages are required for optimal performance:
+\begin{itemize}
+\item {\tt METIS 4.0.1}: a graph partitioning package by George Karypis,
+ Univ. of Minnesota. Not needed if {\tt -DNPARTITION} is used.
+ See http://www-users.cs.umn.edu/$\sim$karypis/metis.
+\item BLAS: the Basic Linear Algebra Subprograms.
+ Not needed if {\tt -DNSUPERNODAL} is used.
+ See http://www.netlib.org for the reference BLAS (not meant for production
+ use). For Kazushige Goto's optimized BLAS (highly recommended for CHOLMOD)
+ see \newline
+ http://www.tacc.utexas.edu/$\sim$kgoto/ or
+ http://www.cs.utexas.edu/users/flame/goto/.
+ I recommend that you avoid the Intel MKL BLAS; one recent
+ version returns NaN's, where both the Goto BLAS and the standard
+ Fortran reference BLAS return the correct answer.
+ See {\tt CHOLMOD/README} for more information.
+\item LAPACK: the Basic Linear Algebra Subprograms.
+ Not needed if {\tt -DNSUPERNODAL} is used.
+ See http://www.netlib.org.
+\end{itemize}
+
+You must first obtain and install METIS, LAPACK, and the BLAS.
+Next edit the system-dependent configurations in the
+{\tt UFconfig/UFconfig.mk} file. Sample configurations are provided
+for Linux, Macintosh, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha.
+The most important configuration is the location of the BLAS, LAPACK, and METIS
+packages, since in its default configuration CHOLMOD cannot be compiled without them.
+
+\noindent
+Here are the various parameters that you can control in your {\tt UFconfig/UFconfig.mk} file:
+\begin{itemize}
+\item {\tt CC = } your C compiler, such as {\tt cc}.
+\item {\tt CFLAGS = } optimization flags, such as {\tt -O}.
+\item {\tt RANLIB = } your system's {\tt ranlib} program, if needed.
+\item {\tt AR =} the command to create a library (such as {\tt ar}).
+\item {\tt RM =} the command to delete a file.
+\item {\tt MV =} the command to rename a file.
+\item {\tt F77 =} the command to compile a Fortran program (optional).
+\item {\tt F77FLAGS =} the Fortran compiler flags (optional).
+\item {\tt F77LIB =} the Fortran libraries (optional).
+\item {\tt LIB = } basic libraries, such as {\tt -lm}.
+\item {\tt MEX =} the command to compile a MATLAB mexFunction.
+\item {\tt BLAS =} your BLAS library.
+\item {\tt LAPACK =} your LAPACK library.
+\item {\tt XERBLA =} a library containing the BLAS {\tt xerbla} routine, if required.
+\item {\tt METIS\_PATH =} the path to your copy of the METIS 4.0.1 source code.
+\item {\tt METIS =} your METIS library.
+\item {\tt CHOLMOD\_CONFIG = } configuration settings specific to CHOLMOD.
+\end{itemize}
+
+\noindent
+CHOLMOD's specific settings are given by the {\tt CHOLMOD\_CONFIG} string:
+\begin{itemize}
+\item {\tt -DNCHECK}: do not include the Check module. License: GNU LGPL.
+\item {\tt -DNCHOLESKY}: do not include the Cholesky module. License: GNU LGPL.
+\item {\tt -DNPARTITION}: do not include the Partition module. License: GNU LGPL.
+\item {\tt -DNGPL}: do not include any GNU GPL Modules in the CHOLMOD library.
+\item {\tt -DNMATRIXOPS}: do not include the MatrixOps module. License: GNU GPL.
+\item {\tt -DNMODIFY}: do not include the Modify module. License: GNU GPL.
+\item {\tt -DNSUPERNODAL}: do not include the Supernodal module. License: GNU GPL.
+\item {\tt -DNPRINT}: do not print anything.
+\item {\tt -D'LONGBLAS=long'} or {\tt -DLONGBLAS='long long'}
+ defines the integers used by LAPACK and the BLAS (defaults to {\tt int}).
+\item {\tt -DNSUNPERF}: for Solaris only. If defined, do not use the Sun Performance Library.
+\item {\tt -DNLARGEFILE}: CHOLMOD now assumes support for large files (2GB or
+larger). If this causes problems, you can compile CHOLMOD with -DNLARGEFILE.
+To use large files, you should {\tt \#include "cholmod.h"} (or at least
+{\tt \#include "cholmod\_io64.h"}) before any other {\tt \#include} statements,
+in your application that uses CHOLMOD. You may need to use {\tt fopen64}
+to create a file pointer to pass to CHOLMOD, if you are using a non-gcc
+compiler.
+\end{itemize}
+
+Type {\tt make} in the {\tt CHOLMOD} directory. The AMD,
+COLAMD, CAMD, CCOLAMD, and {\tt CHOLMOD} libraries will be compiled,
+as will the C version of the null-output {\tt xerbla} routine in case you need it.
+No Fortran compiler is required in this case. A short demo program will
+be compiled and tested on a few matrices. The residuals should all be small.
+Compare your output with the {\tt CHOLMOD/Demo/make.out} file.
+
+CHOLMOD is now ready for use in your own applications. You must link
+your programs with the
+{\tt CHOLMOD/Lib/libcholmod.a},
+{\tt AMD/Lib/libamd.a},
+{\tt COLAMD/libcolamd.a},
+{\tt CAMD/libcamd.a}, \newline
+{\tt CCOLAMD/libccolamd.a},
+{\tt metis-4.0/libmetis.a},
+LAPACK,
+and
+BLAS libraries,
+as well as the {\tt xerbla} library if you need it
+({\tt UFconfig/xerlib/libcerbla.a} for the C version or
+\newline
+ {\tt UFconfig/xerlib/libxerbla.a} for the Fortran version).
+Your compiler needs to know the location of the CHOLMOD {\tt Include} directory,
+so that it can find the {\tt cholmod.h} include file, by
+adding the {\tt -ICHOLMOD/Include} to your C compiler options
+(modified appropriately to reflect the location of your copy of CHOLMOD).
+
+%-------------------------------------------------------------------------------
+\newpage \section{Using CHOLMOD in MATLAB}
+%-------------------------------------------------------------------------------
+
+CHOLMOD includes a set of m-files and mexFunctions in the CHOLMOD/MATLAB
+directory. The following functions are provided:
+
+\vspace{0.1in}
+\begin{tabular}{ll}
+\hline
+{\tt analyze} & order and analyze a matrix \\
+{\tt bisect} & find a node separator \\
+{\tt chol2} & same as {\tt chol} \\
+{\tt cholmod2} & same as {\tt x=A}$\backslash${\tt b} if {\tt A} is symmetric positive definite \\
+{\tt cholmod\_demo} & a short demo program \\
+{\tt cholmod\_make} & compiles CHOLMOD for use in MATLAB \\
+{\tt etree2} & same as {\tt etree} \\
+{\tt graph\_demo} & graph partitioning demo \\
+{\tt lchol} & {\tt L*L'} factorization \\
+{\tt ldlchol} & {\tt L*D*L'} factorization \\
+{\tt ldl\_normest} & estimate {\tt norm(A-L*D*L')} \\
+{\tt ldlsolve} & {\tt x = L'}$\backslash${\tt (D}$\backslash${\tt (L}$\backslash${\tt b))} \\
+{\tt ldlsplit} & split the output of {\tt ldlchol} into {\tt L} and {\tt D} \\
+{\tt ldlupdate} & update/downdate an {\tt L*D*L'} factorization \\
+{\tt metis} & interface to {\tt METIS\_NodeND} ordering \\
+{\tt mread} & read a sparse or dense Matrix Market file \\
+{\tt mwrite} & write a sparse or dense Matrix Market file \\
+{\tt nesdis} & CHOLMOD's nested dissection ordering \\
+{\tt resymbol} & recomputes the symbolic factorization \\
+{\tt sdmult} & {\tt S*F} where {\tt S} is sparse and {\tt F} is dense \\
+{\tt spsym} & determine symmetry \\
+{\tt sparse2} & same as {\tt sparse} \\
+{\tt symbfact2} & same as {\tt symbfact} \\
+\hline
+\end{tabular}
+
+\vspace{0.1in}\noindent
+Each function is described in the next sections.
+
+\newpage
+\subsection{{\tt analyze}: order and analyze} \input{_analyze_m.tex}
+\subsection{{\tt bisect}: find a node separator} \input{_bisect_m.tex}
+\subsection{{\tt chol2}: same as {\tt chol}} \input{_chol2_m.tex}
+\newpage
+\subsection{{\tt cholmod2}: supernodal backslash} \input{_cholmod2_m.tex}
+\newpage
+\subsection{{\tt cholmod\_demo}: a short demo program} \input{_cholmod_demo_m.tex}
+\subsection{{\tt cholmod\_make}: compile CHOLMOD in MATLAB} \input{_cholmod_make_m.tex}
+\newpage
+\subsection{{\tt etree2}: same as {\tt etree}} \input{_etree2_m.tex}
+\subsection{{\tt graph\_demo}: graph partitioning demo} \input{_graph_demo_m.tex}
+\newpage
+\subsection{{\tt lchol}: $\m{LL}\tr$ factorization} \input{_lchol_m.tex}
+\subsection{{\tt ldlchol}: $\m{LDL}\tr$ factorization} \input{_ldlchol_m.tex}
+\newpage
+\subsection{{\tt ldlsolve}: solve using an $\m{LDL}\tr$ factorization} \input{_ldlsolve_m.tex}
+\subsection{{\tt ldlsplit}: split an $\m{LDL}\tr$ factorization} \input{_ldlsplit_m.tex}
+\newpage
+\subsection{{\tt ldlupdate}: update/downdate an $\m{LDL}\tr$ factorization} \input{_ldlupdate_m.tex}
+\newpage
+\subsection{{\tt mread}: read a sparse or dense matrix from a Matrix Market file}\input{_mread_m.tex}
+\subsection{{\tt mwrite}: write a sparse or densematrix to a Matrix Market file} \input{_mwrite_m.tex}
+\newpage
+\subsection{{\tt metis}: order with METIS} \input{_metis_m.tex}
+\newpage
+\subsection{{\tt nesdis}: order with CHOLMOD nested dissection} \input{_nesdis_m.tex}
+\newpage
+\subsection{{\tt resymbol}: re-do symbolic factorization} \input{_resymbol_m.tex}
+\subsection{{\tt sdmult}: sparse matrix times dense matrix} \input{_sdmult_m.tex}
+\newpage
+\subsection{{\tt spsym}: determine symmetry} \input{_spsym_m.tex}
+\newpage
+\subsection{{\tt sparse2}: same as {\tt sparse}} \input{_sparse2_m.tex}
+\newpage
+\subsection{{\tt symbfact2}: same as {\tt symbfact}} \input{_symbfact2_m.tex}
+
+%-------------------------------------------------------------------------------
+\newpage \section{Installation for use in MATLAB}
+%-------------------------------------------------------------------------------
+
+If you wish to use METIS within CHOLMOD, you should first obtain a copy of METIS 4.0.1.
+See http://www-users.cs.umn.edu/$\sim$karypis/metis. Place your copy
+of the {\tt metis-4.0} directory (folder, for Windows users) in the same directory
+that contains your copy of the {\tt CHOLMOD} directory. If you do not have
+METIS, however, you can still use CHOLMOD. Some of the CHOLMOD functions will not
+be available ({\tt metis}, {\tt bisect}, and {\tt nesdis}),
+and you may experience higher fill-in for large matrices
+(particularly those arising in 3D finite-element problems) when using
+{\tt analyze}, {\tt chol2}, {\tt cholmod2}, {\tt lchol}, and {\tt ldlchol}.
+There are two methods for compiling CHOLMOD for use in MATLAB; both
+are described below.
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt cholmod\_make}: compiling CHOLMOD in MATLAB}
+%-------------------------------------------------------------------------------
+
+This is the preferred method, since it allows METIS to be reconfigured to
+use the MATLAB memory-management functions instead of {\tt malloc} and {\tt free};
+this avoids the issue of METIS terminating MATLAB if it runs out of memory.
+It is also simpler for Windows users, who do not have the {\tt make}
+command (unless you obtain a copy of {\tt Cygwin}).
+
+Start MATLAB, {\tt cd} to the {\tt CHOLMOD/MATLAB} directory, and
+type {\tt cholmod\_make} in the MATLAB command window. This will compile
+the MATLAB interfaces for AMD, COLAMD, CAMD, CCOLAMD, METIS, and CHOLMOD.
+If you do not have METIS, type {\tt cholmod\_make('')}.
+If your copy of METIS is in another location, type
+{\tt cholmod\_make ('path')} where {\tt path} is the pathname
+of your copy of the {\tt metis-4.0} directory.
+
+When METIS is compiled {\tt malloc}, {\tt free}, {\tt calloc}, and {\tt realloc}
+are redefined to the MATLAB-equivalents ({\tt mxMalloc}, ...).
+These memory-management functions safely terminate a mexFunction if they
+fail, and will free all memory allocated by the mexFunction.
+Thus, METIS will safely abort without terminating MATLAB, if it runs out
+of memory.
+The {\tt cholmod\_make} handles this redefinition without making any
+changes to your METIS source code.
+
+%-------------------------------------------------------------------------------
+\subsection{Unix {\tt make} for compiling CHOLMOD}
+%-------------------------------------------------------------------------------
+
+You can also compile the CHOLMOD mexFunctions using the Unix/Linux {\tt make}
+command. When using the {\tt gcc} compiler, I strongly recommend editing the
+{\tt metis-4.0/Makefile.in} file and changing {\tt COPTIONS} to
+\begin{verbatim}
+ COPTIONS = -fexceptions
+\end{verbatim}
+Also ensure {\tt -fexceptions} is in the {\tt CFLAGS} option in the
+{\tt UFconfig/UFconfig.mk} file that comes with CHOLMOD.
+If you do not make these modifications, the CHOLMOD mexFunctions
+will terminate MATLAB if they encounter an error.
+
+If you have MATLAB 7.2 or earlier and use {\tt make mex} in the
+{\tt CHOLMOD} directory (equivalently, {\tt make} in {\tt CHOLMOD/MATLAB}),
+you must first edit
+{\tt UFconfig/UFconfig.h} to remove the {\tt -largeArrayDims}
+option from the MEX command
+(or just use {\tt cholmod\_make.m} inside MATLAB).
+
+Next, compile your METIS 4.0.1 library by typing {\tt make} in the
+{\tt metis-4.0} directory. Then type {\tt make} in the {\tt CHOLMOD/MATLAB}
+directory. This will compile the C-callable libraries for
+AMD, COLAMD, CAMD, CCOLAMD, METIS, and CHOLMOD, and then compile the
+mexFunction interfaces to those libraries.
+If METIS tries {\tt malloc} and encounters an out-of-memory condition,
+it calls {\tt abort}, which will terminate MATLAB. This problem does not
+occur using the method described in the previous section.
+
+%-------------------------------------------------------------------------------
+\newpage \section{Integer and floating-point types, and notation used}
+%-------------------------------------------------------------------------------
+
+CHOLMOD supports both {\tt int} and {\tt long} integers. CHOLMOD
+routines with the prefix {\tt cholmod\_} use {\tt int} integers,
+{\tt cholmod\_l\_} routines use {\tt long}. All floating-point
+values are {\tt double}.
+
+The {\tt long} integer is redefinable, via {\tt UFconfig.h}.
+That file defines a C preprocessor token {\tt UF\_long} which is
+{\tt long} on all systems except for Windows-64, in which case it is
+defined as {\tt \_\_int64}. The intent is that with suitable compile-time
+switches, {\tt int} is a 32-bit integer and {\tt UF\_long} is a 64-bit
+integer. The term {\tt long} is used to describe the latter
+integer throughout this document (except in the prototypes).
+
+Two kinds of complex matrices are supported: complex and zomplex.
+A complex matrix is held in a manner that is compatible with the
+Fortran and ANSI C99 complex data type. A complex array of size {\tt n}
+is a {\tt double} array {\tt x} of size {\tt 2*n}, with the real and imaginary
+parts interleaved (the real part comes first, as a {\tt double}, followed the
+imaginary part, also as a {\tt double}. Thus, the real part of the {\tt k}th
+entry is {\tt x[2*k]} and the imaginary part is {\tt x[2*k+1]}.
+
+A zomplex matrix of size {\tt n} stores its real part in one
+{\tt double} array of size {\tt n} called {\tt x} and its imaginary part
+in another {\tt double} array of size {\tt n} called {\tt z} (thus the
+name ``zomplex''). This also how MATLAB stores its complex matrices.
+The real part of the {\tt k}th entry is {\tt x[k]} and the imaginary part is
+{\tt z[k]}.
+
+Unlike {\tt UMFPACK}, the same routine name in CHOLMOD is used for pattern-only,
+real, complex, and zomplex matrices. For example, the statement
+\begin{verbatim}
+ C = cholmod_copy_sparse (A, &Common) ;
+\end{verbatim}
+creates a copy of a pattern, real, complex, or zomplex sparse matrix {\tt A}.
+The xtype (pattern, real, complex, or zomplex) of the resulting sparse matrix {\tt C}
+is the same as {\tt A} (a pattern-only sparse matrix contains no floating-point
+values). In the above case, {\tt C} and {\tt A} use {\tt int} integers.
+For {\tt long} integers, the statement would become:
+\begin{verbatim}
+ C = cholmod_l_copy_sparse (A, &Common) ;
+\end{verbatim}
+The last parameter of all CHOLMOD routines is always {\tt \&Common},
+a pointer to the
+{\tt cholmod\_common} object, which contains parameters, statistics,
+and workspace used throughout CHOLMOD.
+
+The {\tt xtype} of a CHOLMOD object (sparse matrix, triplet matrix, dense
+matrix, or factorization) determines whether it is pattern-only,
+real, complex, or zomplex.
+
+The names of the {\tt int} versions are primarily used in this document.
+To obtain the name of the {\tt long} version of the same routine, simply
+replace {\tt cholmod\_} with {\tt cholmod\_l\_}.
+
+MATLAB matrix notation is used throughout this document and in
+the comments in the CHOLMOD code itself. If you are not familiar with
+MATLAB, here is a short introduction to the notation, and a few
+minor variations used in CHOLMOD:
+
+\begin{itemize}
+ \item {\tt C=A+B} and {\tt C=A*B}, respectively are a matrix add and multiply if both
+ {\tt A} and {\tt B} are matrices of appropriate size. If {\tt A} is
+ a scalar, then it is added to or multiplied with every entry in {\tt B}.
+ \item {\tt a:b} where {\tt a} and {\tt b} are integers refers to the
+ sequence {\tt a}, {\tt a+1}, ... {\tt b}.
+ \item {\tt [A B]} and {\tt [A,B]} are the horizontal concatenation of {\tt A} and {\tt B}.
+ \item {\tt [A;B]} is the vertical concatenation of {\tt A} and {\tt B}.
+ \item {\tt A(i,j)} can refer either to a scalar or a submatrix.
+ For example: \newline
+ \vspace{0.05in}
+ \begin{tabular}{ll}
+ \hline
+ {\tt A(1,1)} & a scalar. \\
+ {\tt A(:,j)} & column {\tt j} of {\tt A}. \\
+ {\tt A(i,:)} & row {\tt i} of {\tt A}. \\
+ {\tt A([1 2], [1 2])} & a 2-by-2 matrix containing the 2-by-2 leading minor of {\tt A}. \\
+ \hline
+ \end{tabular} \newline
+ \vspace{0.1in}
+ If {\tt p} is a permutation of {\tt 1:n}, and {\tt A} is {\tt n}-by-{\tt n},
+ then {\tt A(p,p)} corresponds to the permuted matrix $\m{PAP}\tr$.
+ \item {\tt tril(A)} is the lower triangular part of {\tt A}, including the diagonal.
+ \item {\tt tril(A,k)} is the lower triangular part of {\tt A}, including entries
+ on and below the $k$th diagonal.
+ \item {\tt triu(A)} is the upper triangular part of {\tt A}, including the diagonal.
+ \item {\tt triu(A,k)} is the upper triangular part of {\tt A}, including entries
+ on and above the $k$th diagonal.
+ \item {\tt size(A)} returns the dimensions of {\tt A}.
+ \item {\tt find(x)} if {\tt x} is a vector returns a list of indices {\tt i}
+ for which {\tt x(i)} is nonzero.
+ \item {\tt A'} is the transpose of {\tt A} if {\tt A} is real, or
+ the complex conjugate transpose if {\tt A} is complex.
+ \item {\tt A.'} is the array transpose of {\tt A}.
+ \item {\tt diag(A)} is the diagonal of {\tt A} if {\tt A} is a matrix.
+ \item {\tt C=diag(s)} is a diagonal matrix if {\tt s} is a vector,
+ with the values of {\tt s} on the diagonal of {\tt C}.
+ \item {\tt S=spones(A)} returns a binary matrix {\tt S} with the
+ same nonzero pattern of {\tt A}.
+ \item {\tt nnz(A)} is the number of nonzero entries in {\tt A}.
+\end{itemize}
+
+\noindent Variations to MATLAB notation used in this document:
+\begin{itemize}
+ \item CHOLMOD uses 0-based notation (the first entry in the matrix is
+ {\tt A(0,0)}). MATLAB is 1-based. The context is usually clear.
+ \item {\tt I} is the identity matrix.
+ \item {\tt A(:,f)}, where {\tt f} is a set of columns, is interpreted
+ differently in CHOLMOD, but just for the set named {\tt f}.
+ See {\tt cholmod\_transpose\_unsym} for details.
+\end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \section{The CHOLMOD Modules, objects, and functions}
+\label{Modules}
+%-------------------------------------------------------------------------------
+
+CHOLMOD contains a total of 133 {\tt int}-based routines (and the same number
+of {\tt long} routines), divided into a set of inter-related
+Modules. Each Module contains a set of related functions. The functions
+are divided into two types: Primary and Secondary, to reflect how a user will
+typically use CHOLMOD. Most users will find the Primary routines to be
+sufficient to use CHOLMOD in their programs. Each Module exists as a
+sub-directory (a folder for Windows users) within the CHOLMOD directory
+(or folder).
+
+\vspace{0.1in}
+\noindent There are seven Modules that provide user-callable routines for CHOLMOD.
+ \begin{enumerate}
+ \item {\tt Core}: basic data structures and definitions
+ \item {\tt Check}: prints/checks each of CHOLMOD's objects
+ \item {\tt Cholesky}: sparse Cholesky factorization
+ \item {\tt Modify}: sparse Cholesky update/downdate and row-add/row-delete
+ \item {\tt MatrixOps}: sparse matrix operators (add, multiply, norm, scale)
+ \item {\tt Supernodal}: supernodal sparse Cholesky factorization
+ \item {\tt Partition}: graph-partitioning-based orderings
+ \end{enumerate}
+
+\noindent Two additional Modules are required to compile the CHOLMOD library:
+ \begin{enumerate}
+ \item {\tt Include}: include files for CHOLMOD and programs that use CHOLMOD
+ \item {\tt Lib}: where the CHOLMOD library is built
+ \end{enumerate}
+
+\noindent Five additional Modules provide support functions and documentation:
+ \begin{enumerate}
+ \item {\tt Demo}: simple programs that illustrate the use of CHOLMOD
+ \item {\tt Doc}: documentation (including this document)
+ \item {\tt MATLAB}: CHOLMOD's interface to MATLAB
+ \item {\tt Tcov}: an exhaustive test coverage (requires Linux or Solaris)
+ \item {\tt Valgrind}: runs the {\tt Tcov} test under {\tt valgrind} (requires Linux)
+ \end{enumerate}
+
+The following Modules are licensed under the GNU Lesser General Public
+License: {\tt Check}, {\tt Cholesky}, {\tt Core}, and {\tt Partition}.
+The following Modules are licensed under the GNU General Public
+License: {\tt Demo}, {\tt Modify}, {\tt MatrixOps}, {\tt Supernodal},
+the {\tt MATLAB} Module (not MATLAB itself!), {\tt Tcov}, and {\tt Valgrind}.
+The files in the {\tt Include} Module are licensed according to
+their respective Modules. The {\tt Lib} and {\tt Doc} Modules need
+no license; the compiled binaries are licensed the same as their source code.
+
+%-------------------------------------------------------------------------------
+\newpage \subsection{{\tt Core} Module: basic data structures and definitions}
+%-------------------------------------------------------------------------------
+
+CHOLMOD includes five basic objects, defined in the {\tt Core} Module.
+The {\tt Core Module} provides basic operations for these objects
+and is required by all six other CHOLMOD library Modules:
+
+\subsubsection{{\tt cholmod\_common}: parameters, statistics, and workspace}
+ You must call {\tt cholmod\_start} before calling any other
+ CHOLMOD routine, and you must call {\tt cholmod\_finish} as your
+ last call to CHOLMOD (with the exception of
+ {\tt cholmod\_print\_common} and {\tt cholmod\_check\_common}
+ in the {\tt Check} Module).
+ Once the {\tt cholmod\_common} object is initialized,
+ the user may modify CHOLMOD's parameters held in this object,
+ and obtain statistics on CHOLMOD's activity.
+
+\vspace{0.1in}
+\noindent Primary routines for the {\tt cholmod\_common} object:
+% 2
+ \begin{itemize}
+ \item {\tt cholmod\_start}: the first call to CHOLMOD.
+ \item {\tt cholmod\_finish}: the last call to CHOLMOD (frees workspace in the {\tt cholmod\_common} object).
+ \end{itemize}
+
+\noindent Secondary routines for the {\tt cholmod\_common} object:
+% 9
+ \begin{itemize}
+ \item {\tt cholmod\_defaults}: restores default parameters
+ \item {\tt cholmod\_maxrank}: determine maximum rank for update/downdate.
+ \item {\tt cholmod\_allocate\_work}: allocate workspace.
+ \item {\tt cholmod\_free\_work}: free workspace.
+ \item {\tt cholmod\_clear\_flag}: clear {\tt Flag} array.
+ \item {\tt cholmod\_error}: called when CHOLMOD encounters and error.
+ \item {\tt cholmod\_dbound}: bounds the diagonal of $\m{L}$ or $\m{D}$.
+ \item {\tt cholmod\_hypot}: compute {\tt sqrt(x*x+y*y)} accurately.
+ \item {\tt cholmod\_divcomplex}: complex divide.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsubsection{{\tt cholmod\_sparse}: a sparse matrix in compressed column form}
+%-------------------------------------------------------------------------------
+ A sparse matrix {\tt A} is held in compressed column form. In the basic
+ type (``packed,'' which corresponds to how MATLAB stores its sparse
+ matrices), and {\tt nrow}-by-{\tt ncol} matrix with {\tt nzmax} entries
+ is held in three arrays: {\tt p} of size {\tt ncol+1},
+ {\tt i} of size {\tt nzmax}, and {\tt x} of size {\tt nzmax}.
+ Row indices of nonzero entries in column {\tt j} are held in
+ {\tt i [p[j] ... p[j+1]-1]}, and their corresponding numerical values
+ are held in {\tt x [p[j] ... p[j+1]-1]}. The first column starts at
+ location zero ({\tt p[0]=0}).
+ There may be no duplicate entries. Row indices in each column may
+ be sorted or unsorted (the {\tt A->sorted} flag must be false if
+ the columns are unsorted). The {\tt A->stype} determines the
+ storage mode: 0 if the matrix is unsymmetric, 1 if the matrix is
+ symmetric with just the upper triangular part stored, and -1 if
+ the matrix is symmetric with just the lower triangular part stored.
+
+ In ``unpacked'' form, an additional array {\tt nz} of size {\tt ncol}
+ is used. The end of column {\tt j} in {\tt i} and {\tt x}
+ is given by {\tt p[j]+nz[j]}. Columns not need be in any particular
+ order ({\tt p[0]} need not be zero), and there may be gaps between
+ the columns.
+
+\vspace{0.1in}
+\noindent Primary routines for the {\tt cholmod\_sparse} object:
+% 2
+ \begin{itemize}
+ \item {\tt cholmod\_allocate\_sparse}: allocate a sparse matrix
+ \item {\tt cholmod\_free\_sparse}: free a sparse matrix
+ \end{itemize}
+
+\noindent Secondary routines for the {\tt cholmod\_sparse} object:
+% 16
+ \begin{itemize}
+ \item {\tt cholmod\_reallocate\_sparse}: change the size (number of entries) of a sparse matrix.
+ \item {\tt cholmod\_nnz}: number of nonzeros in a sparse matrix.
+ \item {\tt cholmod\_speye}: sparse identity matrix.
+ \item {\tt cholmod\_spzeros}: sparse zero matrix.
+ \item {\tt cholmod\_transpose}: transpose a sparse matrix.
+ \item {\tt cholmod\_ptranspose}: transpose/permute a sparse matrix.
+ \item {\tt cholmod\_transpose\_unsym}: transpose/permute an unsymmetric sparse matrix.
+ \item {\tt cholmod\_transpose\_sym}: transpose/permute a symmetric sparse matrix.
+ \item {\tt cholmod\_sort}: sort row indices in each column of a sparse matrix.
+ \item {\tt cholmod\_band}: extract a band of a sparse matrix.
+ \item {\tt cholmod\_band\_inplace}: remove entries not with a band.
+ \item {\tt cholmod\_aat}: {\tt C = A*A'}.
+ \item {\tt cholmod\_copy\_sparse}: {\tt C = A}, create an exact copy of a sparse matrix.
+ \item {\tt cholmod\_copy}: {\tt C = A}, with possible change of {\tt stype}.
+ \item {\tt cholmod\_add}: {\tt C = alpha*A + beta*B}.
+ \item {\tt cholmod\_sparse\_xtype}: change the {\tt xtype} of a sparse matrix.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsubsection{{\tt cholmod\_factor}: a symbolic or numeric factorization}
+%-------------------------------------------------------------------------------
+
+ A factor can be in $\m{LL}\tr$ or $\m{LDL}\tr$ form, and either supernodal
+ or simplicial form. In simplicial form, this is very much like a
+ packed or unpacked {\tt cholmod\_sparse} matrix. In supernodal
+ form, adjacent columns with similar nonzero pattern are stored as
+ a single block (a supernode).
+
+\vspace{0.1in}
+\noindent Primary routine for the {\tt cholmod\_factor} object:
+% 1
+ \begin{itemize}
+ \item {\tt cholmod\_free\_factor}: free a factor
+ \end{itemize}
+
+\noindent Secondary routines for the {\tt cholmod\_factor} object:
+% 8
+ \begin{itemize}
+ \item {\tt cholmod\_allocate\_factor}: allocate a factor. You will normally use {\tt cholmod\_analyze} to create a factor.
+ \item {\tt cholmod\_reallocate\_factor}: change the number of entries in a factor.
+ \item {\tt cholmod\_change\_factor}: change the type of a factor ($\m{LDL}\tr$ to $\m{LL}\tr$, supernodal to simplicial, etc.).
+ \item {\tt cholmod\_pack\_factor}: pack the columns of a factor.
+ \item {\tt cholmod\_reallocate\_column}: resize a single column of a factor.
+ \item {\tt cholmod\_factor\_to\_sparse}: create a sparse matrix copy of a factor.
+ \item {\tt cholmod\_copy\_factor}: create a copy of a factor.
+ \item {\tt cholmod\_factor\_xtype}: change the xtype of a factor.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsubsection{{\tt cholmod\_dense}: a dense matrix}
+%-------------------------------------------------------------------------------
+ This consists of a dense array of numerical values and its dimensions.
+
+\vspace{0.1in}
+\noindent Primary routines for the {\tt cholmod\_dense} object:
+% 2
+ \begin{itemize}
+ \item {\tt cholmod\_allocate\_dense}: allocate a dense matrix.
+ \item {\tt cholmod\_free\_dense}: free a dense matrix.
+ \end{itemize}
+
+\vspace{0.1in}
+\noindent Secondary routines for the {\tt cholmod\_dense} object:
+% 8
+ \begin{itemize}
+ \item {\tt cholmod\_zeros}: allocate a dense matrix of all zeros.
+ \item {\tt cholmod\_ones}: allocate a dense matrix of all ones.
+ \item {\tt cholmod\_eye}: allocate a dense identity matrix .
+ \item {\tt cholmod\_sparse\_to\_dense}: create a dense matrix copy of a sparse matrix.
+ \item {\tt cholmod\_dense\_to\_sparse}: create a sparse matrix copy of a dense matrix.
+ \item {\tt cholmod\_copy\_dense}: create a copy of a dense matrix.
+ \item {\tt cholmod\_copy\_dense2}: copy a dense matrix (pre-allocated).
+ \item {\tt cholmod\_dense\_xtype}: change the {\tt xtype} of a dense matrix.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsubsection{{\tt cholmod\_triplet}: a sparse matrix in ``triplet'' form}
+%-------------------------------------------------------------------------------
+ The {\tt cholmod\_sparse} matrix is the basic sparse matrix used in
+ CHOLMOD, but it can be difficult for the user to construct. It also
+ does not easily support the inclusion of new entries in the matrix.
+ The {\tt cholmod\_triplet} matrix is provided to address these issues.
+ A sparse matrix in triplet form consists of three arrays of size
+ {\tt nzmax}: {\tt i}, {\tt j}, and {\tt x}, and a {\tt z} array
+ for the zomplex case.
+
+\vspace{0.1in}
+\noindent Primary routines for the {\tt cholmod\_triplet} object:
+% 3
+ \begin{itemize}
+ \item {\tt cholmod\_allocate\_triplet}: allocate a triplet matrix.
+ \item {\tt cholmod\_free\_triplet}: free a triplet matrix.
+ \item {\tt cholmod\_triplet\_to\_sparse}: create a sparse matrix copy of a triplet matrix.
+ \end{itemize}
+
+\noindent Secondary routines for the {\tt cholmod\_triplet} object:
+% 4
+ \begin{itemize}
+ \item {\tt cholmod\_reallocate\_triplet}: change the number of entries in a triplet matrix.
+ \item {\tt cholmod\_sparse\_to\_triplet}: create a triplet matrix copy of a sparse matrix.
+ \item {\tt cholmod\_copy\_triplet}: create a copy of a triplet matrix.
+ \item {\tt cholmod\_triplet\_xtype}: change the {\tt xtype} of a triplet matrix.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsubsection{Memory management routines}
+%-------------------------------------------------------------------------------
+ By default, CHOLMOD uses the ANSI C {\tt malloc}, {\tt free},
+ {\tt calloc}, and {\tt realloc} routines. You may use different
+ routines by modifying function pointers in the {\tt cholmod\_common} object.
+
+\vspace{0.1in}
+\noindent Primary routines:
+% 2
+ \begin{itemize}
+ \item {\tt cholmod\_malloc}: {\tt malloc} wrapper.
+ \item {\tt cholmod\_free}: {\tt free} wrapper.
+ \end{itemize}
+
+\noindent Secondary routines:
+% 3
+ \begin{itemize}
+ \item {\tt cholmod\_calloc}: {\tt calloc} wrapper.
+ \item {\tt cholmod\_realloc}: {\tt realloc} wrapper.
+ \item {\tt cholmod\_realloc\_multiple}: {\tt realloc} wrapper for multiple objects.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsection{{\tt Check} Module: print/check the CHOLMOD objects}
+%-------------------------------------------------------------------------------
+ The {\tt Check} Module contains routines that check and print the five
+ basic objects in CHOLMOD, and three kinds of integer vectors (a set,
+ a permutation, and a tree). It also provides a routine to read a sparse
+ matrix from a file in Matrix Market format (http://www.nist.gov/MatrixMarket).
+ Requires the {\tt Core} Module.
+
+\vspace{0.1in}
+\noindent Primary routines:
+% 4
+ \begin{itemize}
+ \item {\tt cholmod\_print\_common}: print the {\tt cholmod\_common} object,
+ including statistics on CHOLMOD's behavior (fill-in, flop count,
+ ordering methods used, and so on).
+ \item {\tt cholmod\_write\_sparse}: write a sparse matrix to a file
+ in Matrix Market format.
+ \item {\tt cholmod\_write\_dense}: write a sparse matrix to a file
+ in Matrix Market format.
+ \item {\tt cholmod\_read\_matrix}: read a sparse or dense matrix from a file
+ in Matrix Market format.
+ \end{itemize}
+
+\vspace{0.1in}
+\noindent Secondary routines:
+% 18
+ \begin{itemize}
+ \item {\tt cholmod\_check\_common}: check the {\tt cholmod\_common} object
+ \item {\tt cholmod\_check\_sparse}: check a sparse matrix
+ \item {\tt cholmod\_print\_sparse}: print a sparse matrix
+ \item {\tt cholmod\_check\_dense}: check a dense matrix
+ \item {\tt cholmod\_print\_dense}: print a dense matrix
+ \item {\tt cholmod\_check\_factor}: check a Cholesky factorization
+ \item {\tt cholmod\_print\_factor}: print a Cholesky factorization
+ \item {\tt cholmod\_check\_triplet}: check a triplet matrix
+ \item {\tt cholmod\_print\_triplet}: print a triplet matrix
+ \item {\tt cholmod\_check\_subset}: check a subset (integer vector in given range)
+ \item {\tt cholmod\_print\_subset}: print a subset (integer vector in given range)
+ \item {\tt cholmod\_check\_perm}: check a permutation (an integer vector)
+ \item {\tt cholmod\_print\_perm}: print a permutation (an integer vector)
+ \item {\tt cholmod\_check\_parent}: check an elimination tree (an integer vector)
+ \item {\tt cholmod\_print\_parent}: print an elimination tree (an integer vector)
+ \item {\tt cholmod\_read\_triplet}: read a triplet matrix from a file
+ \item {\tt cholmod\_read\_sparse}: read a sparse matrix from a file
+ \item {\tt cholmod\_read\_dense}: read a dense matrix from a file
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsection{{\tt Cholesky} Module: sparse Cholesky factorization}
+%-------------------------------------------------------------------------------
+
+The primary routines are all that a user requires to order, analyze, and
+factorize a sparse symmetric positive definite matrix $\m{A}$ (or $\m{AA}\tr$), and
+to solve $\m{Ax}=\m{b}$ (or $\m{AA}\tr\m{x}=\m{b}$). The primary routines rely on the secondary
+routines, the {\tt Core} Module, and the AMD and COLAMD packages. They
+make optional use of the {\tt Supernodal} and {\tt Partition} Modules, the
+METIS package, the CAMD package, and
+the CCOLAMD package. The {\tt Cholesky} Module is
+required by the {\tt Partition} Module.
+
+\vspace{0.1in}
+\noindent Primary routines:
+% 4
+ \begin{itemize}
+ \item {\tt cholmod\_analyze}: order and analyze (simplicial or supernodal).
+ \item {\tt cholmod\_factorize}: simplicial or supernodal Cholesky factorization.
+ \item {\tt cholmod\_solve}: solve a linear system (simplicial or supernodal, dense $\m{x}$ and $\m{b}$).
+ \item {\tt cholmod\_spsolve}: solve a linear system (simplicial or supernodal, sparse $\m{x}$ and $\m{b}$ ).
+ \end{itemize}
+
+\noindent Secondary routines:
+% 15
+ \begin{itemize}
+ \item {\tt cholmod\_analyze\_p}: analyze, with user-provided permutation or $\m{f}$ set.
+ \item {\tt cholmod\_factorize\_p}: factorize, with user-provided permutation or $\m{f}$.
+ \item {\tt cholmod\_analyze\_ordering}: analyze a permutation
+ \item {\tt cholmod\_etree}: find the elimination tree.
+ \item {\tt cholmod\_rowcolcounts}: compute the row/column counts of $\m{L}$.
+ \item {\tt cholmod\_amd}: order using AMD.
+ \item {\tt cholmod\_colamd}: order using COLAMD.
+ \item {\tt cholmod\_rowfac}: incremental simplicial factorization.
+ \item {\tt cholmod\_row\_subtree}: find the nonzero pattern of a row of $\m{L}$.
+ \item {\tt cholmod\_row\_lsubtree}: find the nonzero pattern of a row of $\m{L}$.
+ \item {\tt cholmod\_resymbol}: recompute the symbolic pattern of $\m{L}$.
+ \item {\tt cholmod\_resymbol\_noperm}: recompute the symbolic pattern of $\m{L}$, no permutation.
+ \item {\tt cholmod\_postorder}: postorder a tree.
+ \item {\tt cholmod\_rcond}: compute the reciprocal condition number estimate.
+ \item {\tt cholmod\_rowfac\_mask}: for use in LPDASA only.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsection{{\tt Modify} Module: update/downdate a sparse Cholesky factorization}
+%-------------------------------------------------------------------------------
+
+The {\tt Modify} Module contains sparse Cholesky modification routines:
+update, downdate, row-add, and row-delete.
+It can also modify a corresponding solution to $\m{Lx}=\m{b}$ when L is modified.
+This module is most useful when applied on a Cholesky factorization computed by
+the {\tt Cholesky} module, but it does not actually require the {\tt Cholesky} module.
+The {\tt Core} module can create an identity Cholesky factorization ($\m{LDL}\tr$ where
+$\m{L}=\m{D}=\m{I}$) that can then be modified by these routines.
+Requires the {\tt Core} module. Not required by any other CHOLMOD Module.
+
+\vspace{0.1in}
+\noindent Primary routine:
+% 1
+ \begin{itemize}
+ \item {\tt cholmod\_updown}: multiple rank update/downdate
+ \end{itemize}
+
+\noindent Secondary routines:
+% 8
+ \begin{itemize}
+ \item {\tt cholmod\_updown\_solve}: update/downdate, and modify solution to $\m{Lx=b}$
+ \item {\tt cholmod\_updown\_mark}: update/downdate, and modify solution to partial $\m{Lx=b}$
+ \item {\tt cholmod\_updown\_mask}: for use in LPDASA only.
+ \item {\tt cholmod\_rowadd}: add a row to an $\m{LDL}\tr$ factorization
+ \item {\tt cholmod\_rowadd\_solve}: add a row, and update solution to $\m{Lx=b}$
+ \item {\tt cholmod\_rowadd\_mark}: add a row, and update solution to partial $\m{Lx=b}$
+ \item {\tt cholmod\_rowdel}: delete a row from an $\m{LDL}\tr$ factorization
+ \item {\tt cholmod\_rowdel\_solve}: delete a row, and downdate $\m{Lx=b}$
+ \item {\tt cholmod\_rowdel\_mark}: delete a row, and downdate solution to partial $\m{Lx=b}$
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt MatrixOps} Module: basic sparse matrix operations}
+%-------------------------------------------------------------------------------
+
+The {\tt MatrixOps} Module provides
+basic operations on sparse and dense matrices.
+Requires the {\tt Core} module. Not required by any other CHOLMOD module.
+In the descriptions below,
+{\tt A}, {\tt B}, and {\tt C:} are sparse matrices ({\tt cholmod\_sparse}),
+{\tt X} and {\tt Y} are dense matrices ({\tt cholmod\_dense}),
+{\tt s} is a scalar or vector, and
+{\tt alpha} {\tt beta} are scalars.
+
+% 10
+ \begin{itemize}
+ \item {\tt cholmod\_drop}: drop entries from A with absolute value $\ge$ a given tolerance.
+ \item {\tt cholmod\_norm\_dense}: {\tt s = norm (X)}, 1-norm, infinity-norm, or 2-norm
+ \item {\tt cholmod\_norm\_sparse}: {\tt s = norm (A)}, 1-norm or infinity-norm
+ \item {\tt cholmod\_horzcat}: {\tt C = [A,B]}
+ \item {\tt cholmod\_scale}: {\tt A = diag(s)*A}, {\tt A*diag(s)}, {\tt s*A} or {\tt diag(s)*A*diag(s)}.
+ \item {\tt cholmod\_sdmult}: {\tt Y = alpha*(A*X) + beta*Y} or {\tt alpha*(A'*X) + beta*Y}.
+ \item {\tt cholmod\_ssmult}: {\tt C = A*B}
+ \item {\tt cholmod\_submatrix}: {\tt C = A (i,j)}, where {\tt i} and {\tt j} are arbitrary integer vectors.
+ \item {\tt cholmod\_vertcat}: {\tt C = [A ; B]}.
+ \item {\tt cholmod\_symmetry}: determine symmetry of a matrix.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \subsection{{\tt Supernodal} Module: supernodal sparse Cholesky factorization}
+%-------------------------------------------------------------------------------
+
+The {\tt Supernodal} Module performs
+supernodal analysis, factorization, and solve. The simplest way to use
+these routines is via the {\tt Cholesky} Module. This Module does not provide any
+fill-reducing orderings. It normally operates on matrices ordered by the
+{\tt Cholesky} Module.
+It does not require the {\tt Cholesky} Module itself, however.
+Requires the {\tt Core} Module, and two external packages: LAPACK and the BLAS.
+Optionally used by the {\tt Cholesky} Module. All are secondary routines
+since these functions are more easily used via the {\tt Cholesky} Module.
+
+\vspace{0.1in}
+\noindent Secondary routines:
+% 4
+ \begin{itemize}
+ \item {\tt cholmod\_super\_symbolic}: supernodal symbolic analysis
+ \item {\tt cholmod\_super\_numeric}: supernodal numeric factorization
+ \item {\tt cholmod\_super\_lsolve}: supernodal $\m{Lx}=\m{b}$ solve
+ \item {\tt cholmod\_super\_ltsolve}: supernodal $\m{L}\tr\m{x}=\m{b}$ solve
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt Partition} Module: graph-partitioning-based orderings}
+%-------------------------------------------------------------------------------
+
+The {\tt Partition} Module provides
+graph partitioning and graph-partition-based orderings. It includes an
+interface to CAMD, CCOLAMD, and CSYMAMD, constrained minimum degree ordering
+methods which order a matrix following constraints determined via nested
+dissection.
+Requires the {\tt Core} and {\tt Cholesky} Modules, and two packages: {\tt METIS 4.0.1}, CAMD, and CCOLAMD.
+Optionally used by the {\tt Cholesky} Module. All are secondary routines since
+these are more easily used by the {\tt Cholesky} Module.
+
+Note that METIS does not have a version that uses {\tt long} integers. If you try to use
+these routines (except the CAMD, CCOLAMD, and CSYMAMD interfaces)
+on a matrix that is too large, an error code will be returned.
+
+\vspace{0.1in}
+\noindent Secondary routines:
+% 8
+ \begin{itemize}
+ \item {\tt cholmod\_nested\_dissection}: CHOLMOD nested dissection ordering
+ \item {\tt cholmod\_metis}: METIS nested dissection ordering ({\tt METIS\_NodeND})
+ \item {\tt cholmod\_camd}: interface to CAMD ordering
+ \item {\tt cholmod\_ccolamd}: interface to CCOLAMD ordering
+ \item {\tt cholmod\_csymamd}: interface to CSYMAMD ordering
+ \item {\tt cholmod\_bisect}: graph partitioner (currently based on METIS)
+ \item {\tt cholmod\_metis\_bisector}: direct interface to {\tt METIS\_NodeComputeSeparator}.
+ \item {\tt cholmod\_collapse\_septree}: pruned a separator tree from
+ {\tt cholmod\_nested\_dissection}.
+ \end{itemize}
+
+%-------------------------------------------------------------------------------
+\newpage \section{CHOLMOD naming convention, parameters, and return values}
+%-------------------------------------------------------------------------------
+
+All routine names, data types, and CHOLMOD library files use the
+{\tt cholmod\_} prefix. All macros and other {\tt \#define} statements
+visible to the user program use the {\tt CHOLMOD} prefix.
+The {\tt cholmod.h} file must be included in user programs that use CHOLMOD:
+
+{\footnotesize
+\begin{verbatim}
+ #include "cholmod.h"
+\end{verbatim}
+}
+
+\noindent
+All CHOLMOD routines (in all modules) use the following protocol for return values:
+\begin{itemize}
+\item {\tt int}: {\tt TRUE} (1) if successful, or {\tt FALSE} (0) otherwise. (exception: {\tt cholmod\_divcomplex}).
+\item {\tt long}: a value $\ge 0$ if successful, or -1 otherwise.
+\item {\tt double}: a value $\ge 0$ if successful, or -1 otherwise.
+\item {\tt size\_t}: a value $>$ 0 if successful, or 0 otherwise.
+\item {\tt void *}: a non-{\tt NULL} pointer to newly allocated memory if successful, or {\tt NULL} otherwise.
+\item {\tt cholmod\_sparse *}: a non-{\tt NULL} pointer to a newly allocated sparse matrix if successful, or {\tt NULL} otherwise.
+\item {\tt cholmod\_factor *}: a non-{\tt NULL} pointer to a newly allocated factor if successful, or {\tt NULL} otherwise.
+\item {\tt cholmod\_triplet *}: a non-{\tt NULL} pointer to a newly allocated triplet matrix if successful, or {\tt NULL} otherwise.
+\item {\tt cholmod\_dense *}: a non-{\tt NULL} pointer to a newly allocated dense matrix if successful, or {\tt NULL} otherwise.
+\end{itemize}
+
+{\tt TRUE} and {\tt FALSE} are not defined in {\tt cholmod.h},
+since they may conflict with the user program. A routine that described
+here returning {\tt TRUE} or {\tt FALSE} returns 1 or 0, respectively.
+Any {\tt TRUE}/{\tt FALSE} parameter is true if nonzero, false if zero.
+
+\noindent
+Input, output, and input/output parameters:
+\begin{itemize}
+\item Input parameters appear first in the parameter lists of all CHOLMOD routines.
+They are not modified by CHOLMOD.
+\item Input/output parameters (except for {\tt Common}) appear next.
+They must be defined on input, and are modified on output.
+\item Output parameters are listed next. If they are pointers, they must
+point to allocated space on input, but their contents are not defined on input.
+\item Workspace parameters appear next. They are used in only two routines in the Supernodal module.
+\item The {\tt cholmod\_common *Common} parameter always appears as the last parameter
+(with two exceptions: {\tt cholmod\_hypot} and {\tt cholmod\_divcomplex}).
+It is always an input/output parameter.
+\end{itemize}
+
+A floating-point scalar is passed to CHOLMOD as a pointer to a {\tt double}
+array of size two. The first entry in this array is the real part of the
+scalar, and the second entry is the imaginary part. The imaginary part is
+only accessed if the other inputs are complex or zomplex. In some cases
+the imaginary part is always ignored ({\tt cholmod\_factor\_p}, for example).
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: {\tt cholmod\_common} object}
+\label{cholmod_common}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{Constant definitions}
+%---------------------------------------
+
+\input{_defn.tex}
+These definitions are used within the {\tt cholmod\_common} object,
+called {\tt Common} both here and throughout the code.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_common}: parameters, statistics, and workspace}
+%---------------------------------------
+
+\input{_common.tex}
+The {\tt cholmod\_common Common} object contains parameters, statistics, and
+workspace used within CHOLMOD. The first call to CHOLMOD must be
+{\tt cholmod\_start}, which initializes this object.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_start}: start CHOLMOD}
+%---------------------------------------
+
+\input{_start.tex}
+Sets the default parameters, clears the statistics, and initializes all
+workspace pointers to {\tt NULL}. The {\tt int}/{\tt long} type
+is set in {\tt Common->itype}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_finish}: finish CHOLMOD}
+%---------------------------------------
+
+\input{_finish.tex}
+This must be the last call to CHOLMOD.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_defaults}: set default parameters}
+%---------------------------------------
+
+\input{_defaults.tex}
+Sets the default parameters.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_maxrank}: maximum update/downdate rank}
+%---------------------------------------
+
+\input{_maxrank.tex}
+Returns the maximum rank for an update/downdate.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_allocate\_work}: allocate workspace}
+%---------------------------------------
+
+\input{_allocate_work.tex}
+Allocates workspace in {\tt Common}. The workspace consists
+of the integer {\tt Head}, {\tt Flag}, and {\tt Iwork} arrays,
+of size {\tt nrow+1}, {\tt nrow}, and {\tt iworksize},
+respectively, and a {\tt double} array {\tt Xwork} of size
+{\tt xworksize}. The {\tt Head} array is normally equal to -1
+when it is cleared. If the {\tt Flag} array is cleared,
+all entries are less than {\tt Common->mark}. The {\tt Iwork} array is
+not kept in any particular state.
+The integer type is {\tt int} or {\tt long}, depending
+on whether the {\tt cholmod\_} or {\tt cholmod\_l\_} routines
+are used.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_free\_work}: free workspace}
+%---------------------------------------
+
+\input{_free_work.tex}
+Frees the workspace in {\tt Common}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_clear\_flag}: clear Flag array}
+%---------------------------------------
+
+\input{_clear_flag.tex}
+Increments {\tt Common->mark} so that the {\tt Flag} array is now cleared.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_error}: report error}
+%---------------------------------------
+
+\input{_error.tex}
+This routine is called when CHOLMOD encounters an error.
+It prints a message (if printing is enabled), sets
+{\tt Common->status}. It then calls the
+user error handler routine {\tt Common->error\_handler},
+if it is not {\tt NULL}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_dbound}: bound diagonal of $\m{L}$}
+%---------------------------------------
+
+\input{_dbound.tex}
+Ensures that entries on the diagonal of $\m{L}$ for an $\m{LL}\tr$
+factorization are greater than or equal to {\tt Common->dbound}.
+For an $\m{LDL}\tr$ factorization, it ensures that the magnitude
+of the entries of $\m{D}$ are greater than or equal to {\tt Common->dbound}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_hypot}: {\tt sqrt(x*x+y*y)}}
+%---------------------------------------
+
+\input{_hypot.tex}
+Computes the magnitude of a complex number.
+This routine is the default value for the {\tt Common->hypotenuse} function pointer.
+See also {\tt hypot}, in the standard {\tt math.h} header. If you have
+the ANSI C99 {\tt hypot}, you can use {\tt Common->hypotenuse = hypot}.
+The {\tt cholmod\_hypot} routine is provided in case you are using the
+ANSI C89 standard, which does not have {\tt hypot}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_divcomplex}: complex divide}
+%---------------------------------------
+
+\input{_divcomplex.tex}
+Divides two complex numbers. It returns 1 if a divide-by-zero occurred, or 0 otherwise.
+This routine is the default value for the {\tt Common->complex\_divide} function pointer.
+This return value is the single exception to the CHOLMOD rule that states all {\tt int} return
+values are {\tt TRUE} if successful or {\tt FALSE} otherwise.
+The exception is made to match the return value of a different complex divide routine
+that is not a part of CHOLMOD, but can be used via the function pointer.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: {\tt cholmod\_sparse} object}
+\label{cholmod_sparse}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_sparse}: compressed-column sparse matrix}
+%---------------------------------------
+
+\input{_sparse.tex}
+Stores a sparse matrix in compressed-column form.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_allocate\_sparse}: allocate sparse matrix}
+%---------------------------------------
+
+\input{_allocate_sparse.tex}
+Allocates a sparse matrix. {\tt A->i}, {\tt A->x}, and {\tt A->z} are not initialized.
+The matrix returned is all zero, but it contains space enough for {\tt nzmax} entries.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_free\_sparse}: free sparse matrix}
+%---------------------------------------
+
+\input{_free_sparse.tex}
+Frees a sparse matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_reallocate\_sparse}: reallocate sparse matrix}
+%---------------------------------------
+
+\input{_reallocate_sparse.tex}
+Reallocates a sparse matrix, so that it can contain {\tt nznew} entries.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_nnz}: number of entries in sparse matrix}
+%---------------------------------------
+
+\input{_nnz.tex}
+Returns the number of entries in a sparse matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_speye}: sparse identity matrix}
+%---------------------------------------
+
+\input{_speye.tex}
+Returns the sparse identity matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_spzeros}: sparse zero matrix}
+%---------------------------------------
+
+\input{_spzeros.tex}
+Returns the sparse zero matrix. This is another name
+for {\tt cholmod\_allocate\_sparse}, but with fewer parameters
+(the matrix is packed, sorted, and unsymmetric).
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_transpose}: transpose sparse matrix}
+%---------------------------------------
+
+\input{_transpose.tex}
+Returns the transpose or complex conjugate transpose of a sparse matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_ptranspose}: transpose/permute sparse matrix}
+%---------------------------------------
+
+\input{_ptranspose.tex}
+Returns {\tt A'} or {\tt A(p,p)'} if {\tt A} is symmetric.
+Returns {\tt A'}, {\tt A(:,f)'}, or {\tt A(p,f)'} if {\tt A} is unsymmetric.
+See {\tt cholmod\_transpose\_unsym} for a discussion of how {\tt f} is used;
+this usage deviates from the MATLAB notation.
+Can also return the array transpose.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_sort}: sort columns of a sparse matrix}
+%---------------------------------------
+
+\input{_sort.tex}
+Sorts the columns of the matrix {\tt A}. Returns {\tt A} in packed form, even if it
+starts as unpacked. Removes entries in the ignored part of a symmetric matrix.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_transpose\_unsym}: transpose/permute unsymmetric sparse matrix}
+%---------------------------------------
+
+\input{_transpose_unsym.tex}
+Transposes and optionally permutes an unsymmetric sparse matrix.
+The output matrix must be preallocated before calling this routine.
+
+Computes {\tt F=A'}, {\tt F=A(:,f)'} or {\tt F=A(p,f)'}, except that the
+indexing by {\tt f} does not work the same as the MATLAB notation (see below).
+{\tt A->stype} is zero, which denotes that both the upper and lower triangular
+parts of A are present (and used). The matrix {\tt A} may in fact be symmetric in pattern
+and/or value; {\tt A->stype} just denotes which part of {\tt A} are stored. {\tt A} may be
+rectangular.
+
+The integer vector
+{\tt p} is a permutation of {\tt 0:m-1}, and {\tt f} is a subset of {\tt 0:n-1},
+where A is {\tt m}-by-{\tt n}.
+There can be no duplicate entries in {\tt p} or {\tt f}.
+
+\noindent
+Three kinds of transposes are available, depending on the {\tt values} parameter:
+\begin{itemize}
+\item 0: do not transpose the numerical values; create a {\tt CHOLMOD\_PATTERN} matrix
+\item 1: array transpose
+\item 2: complex conjugate transpose (same as 2 if input is real or pattern)
+\end{itemize}
+
+\noindent
+The set {\tt f} is held in fset and fsize:
+\begin{itemize}
+\item {\tt fset = NULL} means ``{\tt :}'' in MATLAB. {\tt fset} is ignored.
+\item {\tt fset != NULL} means {\tt f = fset [0..fsize-1]}.
+\item {\tt fset != NULL} and {\tt fsize = 0} means {\tt f} is the empty set.
+\end{itemize}
+
+Columns not in the set {\tt f} are considered to be zero. That is,
+if {\tt A} is 5-by-10 then {\tt F=A(:,[3 4])'} is not 2-by-5, but 10-by-5,
+and rows 3 and 4 of {\tt F} are equal to columns 3 and 4 of {\tt A} (the other
+rows of {\tt F} are zero). More precisely, in MATLAB notation:
+
+\begin{verbatim}
+ [m n] = size (A)
+ F = A
+ notf = ones (1,n)
+ notf (f) = 0
+ F (:, find (notf)) = 0
+ F = F'
+\end{verbatim}
+
+If you want the MATLAB equivalent {\tt F=A(p,f)} operation, use
+{\tt cholmod\_submatrix} instead (which does not compute the transpose).
+{\tt F->nzmax} must be large enough to hold the matrix {\tt F}.
+If {\tt F->nz} is present then {\tt F->nz [j]} is equal to the number of entries in column {\tt j} of {\tt F}.
+{\tt A} can be sorted or unsorted, with packed or unpacked columns.
+If {\tt f} is present and not sorted in ascending order, then {\tt F} is unsorted
+(that is, it may contain columns whose row indices do not appear in
+ascending order). Otherwise, {\tt F} is sorted (the row indices in each
+column of {\tt F} appear in strictly ascending order).
+
+{\tt F} is returned in packed or unpacked form, depending on {\tt F->packed} on input.
+If {\tt F->packed} is {\tt FALSE}, then {\tt F} is returned in unpacked form ({\tt F->nz} must be
+present). Each row {\tt i} of {\tt F} is large enough to hold all the entries in row {\tt i}
+of {\tt A}, even if {\tt f} is provided. That is, {\tt F->i} and
+{\tt F->x [F->p [i] .. F->p [i] + F->nz [i] - 1]} contain all entries in {\tt A(i,f)},
+but {\tt F->p [i+1] - F->p [i]} is equal to the number of nonzeros in {\tt A (i,:)},
+not just {\tt A (i,f)}.
+The {\tt cholmod\_transpose\_unsym} routine is the only operation in CHOLMOD that
+can produce an unpacked matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_transpose\_sym}: transpose/permute symmetric sparse matrix}
+%---------------------------------------
+
+\input{_transpose_sym.tex}
+Computes {\tt F = A'} or {\tt F = A(p,p)'}, the transpose or permuted transpose, where
+{\tt A->stype} is nonzero. {\tt A} must be square and symmetric.
+If {\tt A->stype} $> 0$, then {\tt A} is a symmetric matrix where just the upper part
+of the matrix is stored. Entries in the lower triangular part may be
+present, but are ignored.
+If {\tt A->stype} $< 0$, then {\tt A} is a symmetric matrix where just the lower part
+of the matrix is stored. Entries in the upper triangular part may be present, but are ignored.
+If {\tt F=A'}, then {\tt F} is returned
+sorted; otherwise {\tt F} is unsorted for the {\tt F=A(p,p)'} case.
+There can be no duplicate entries in {\tt p}.
+
+Three kinds of transposes are available, depending on the {\tt values} parameter:
+\begin{itemize}
+\item 0: do not transpose the numerical values; create a {\tt CHOLMOD\_PATTERN} matrix
+\item 1: array transpose
+\item 2: complex conjugate transpose (same as 2 if input is real or pattern)
+\end{itemize}
+
+For {\tt cholmod\_transpose\_unsym} and {\tt cholmod\_transpose\_sym}, the output matrix
+{\tt F} must already be pre-allocated by the caller, with the correct dimensions.
+If {\tt F} is not valid or has the wrong dimensions, it is not modified.
+Otherwise, if {\tt F} is too small, the transpose is not computed; the contents
+of {\tt F->p} contain the column pointers of the resulting matrix, where
+{\tt F->p [F->ncol] > F->nzmax}. In this case, the remaining contents of {\tt F} are
+not modified. {\tt F} can still be properly freed with {\tt cholmod\_free\_sparse}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_band}: extract band of a sparse matrix}
+%---------------------------------------
+
+\input{_band.tex}
+Returns {\tt C = tril (triu (A,k1), k2)}.
+{\tt C} is a matrix consisting of the diagonals of A from {\tt k1} to {\tt k2}.
+{\tt k=0} is the main diagonal of {\tt A}, {\tt k=1} is the superdiagonal, {\tt k=-1} is the
+subdiagonal, and so on. If {\tt A} is {\tt m}-by-{\tt n}, then:
+\begin{itemize}
+\item {\tt k1=-m} means {\tt C = tril (A,k2)}
+\item {\tt k2=n} means {\tt C = triu (A,k1)}
+\item {\tt k1=0} and {\tt k2=0} means {\tt C = diag(A)}, except {\tt C} is a matrix, not a vector
+\end{itemize}
+Values of {\tt k1} and {\tt k2} less than {\tt -m} are treated as {\tt -m}, and values greater
+than {\tt n} are treated as {\tt n}.
+
+{\tt A} can be of any symmetry (upper, lower, or unsymmetric); {\tt C} is returned in
+the same form, and packed. If {\tt A->stype} $> 0$, entries in the lower
+triangular part of {\tt A} are ignored, and the opposite is true if
+{\tt A->stype} $< 0$. If {\tt A} has sorted columns, then so does {\tt C}.
+{\tt C} has the same size as {\tt A}.
+
+{\tt C} can be returned as a numerical valued matrix (if {\tt A} has numerical values
+and {\tt mode} $> 0$), as a pattern-only ({\tt mode} $=0$), or as a pattern-only but with
+the diagonal entries removed ({\tt mode} $< 0$).
+
+The xtype of {\tt A} can be pattern or real. Complex or zomplex cases are supported only
+if {\tt mode} is $\le 0$ (in which case the numerical values are ignored).
+
+%---------------------------------------
+\subsection{{\tt cholmod\_band\_inplace}: extract band, in place}
+%---------------------------------------
+
+\input{_band_inplace.tex}
+Same as {\tt cholmod\_band}, except that it always operates in place.
+Only packed matrices can be converted in place.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_aat}: compute $\m{AA}\tr$}
+%---------------------------------------
+
+\input{_aat.tex}
+Computes {\tt C = A*A'} or {\tt C = A(:,f)*A(:,f)'}.
+{\tt A} can be packed or unpacked, sorted or unsorted, but must be stored with
+both upper and lower parts ({\tt A->stype} of zero). {\tt C} is returned as packed,
+{\tt C->stype} of zero (both upper and lower parts present), and unsorted. See
+{\tt cholmod\_ssmult} in the {\tt MatrixOps} Module for a more general matrix-matrix
+multiply.
+The xtype of {\tt A} can be pattern or real. Complex or zomplex cases are supported only
+if {\tt mode} is $\le 0$ (in which case the numerical values are ignored).
+You can trivially convert {\tt C} to a symmetric upper/lower matrix
+by changing {\tt C->stype} to 1 or -1, respectively, after calling this routine.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_copy\_sparse}: copy sparse matrix}
+%---------------------------------------
+
+\input{_copy_sparse.tex}
+Returns an exact copy of the input sparse matrix {\tt A}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_copy}: copy (and change) sparse matrix}
+%---------------------------------------
+
+\input{_copy.tex}
+{\tt C = A}, which allocates {\tt C} and copies {\tt A} into {\tt C}, with possible change of
+{\tt stype}. The diagonal can optionally be removed. The numerical entries
+can optionally be copied. This routine differs from {\tt cholmod\_copy\_sparse},
+which makes an exact copy of a sparse matrix.
+
+{\tt A} can be of any type (packed/unpacked, upper/lower/unsymmetric). {\tt C} is
+packed and can be of any stype (upper/lower/unsymmetric), except that if
+{\tt A} is rectangular {\tt C} can only be unsymmetric. If the stype of A and C
+differ, then the appropriate conversion is made.
+
+\noindent
+There are three cases for {\tt A->stype}:
+\begin{itemize}
+\item $<0$, lower: assume {\tt A} is symmetric with just {\tt tril(A)} stored; the rest of {\tt A} is ignored
+\item $ 0$, unsymmetric: assume {\tt A} is unsymmetric; consider all entries in A
+\item $>0$, upper: assume {\tt A} is symmetric with just {\tt triu(A)} stored; the rest of {\tt A} is ignored
+\end{itemize}
+
+\noindent
+There are three cases for the requested symmetry of {\tt C} ({\tt stype} parameter):
+\begin{itemize}
+\item $<0$, lower: return just {\tt tril(C)}
+\item $0$, unsymmetric: return all of {\tt C}
+\item $>0$, upper: return just {\tt triu(C)}
+\end{itemize}
+
+\noindent
+This gives a total of nine combinations: \newline
+\begin{tabular}{ll}
+\hline
+Equivalent MATLAB statements & Using {\tt cholmod\_copy} \\
+\hline
+{\tt C = A ; }& {\tt A} unsymmetric, {\tt C} unsymmetric \\
+{\tt C = tril (A) ; }& {\tt A} unsymmetric, {\tt C} lower \\
+{\tt C = triu (A) ; }& {\tt A} unsymmetric, {\tt C} upper \\
+{\tt U = triu (A) ; L = tril (U',-1) ; C = L+U ; }& {\tt A} upper, {\tt C} unsymmetric \\
+{\tt C = triu (A)' ; }& {\tt A} upper, {\tt C} lower \\
+{\tt C = triu (A) ; }& {\tt A} upper, {\tt C} upper \\
+{\tt L = tril (A) ; U = triu (L',1) ; C = L+U ; }& {\tt A} lower, {\tt C} unsymmetric \\
+{\tt C = tril (A) ; }& {\tt A} lower, {\tt C} lower \\
+{\tt C = tril (A)' ; }& {\tt A} lower, {\tt C} upper \\
+\hline
+\end{tabular}
+
+\vspace{0.1in}
+The xtype of {\tt A} can be pattern or real. Complex or zomplex cases are supported only
+if {\tt values} is {\tt FALSE} (in which case the numerical values are ignored).
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_add}: add sparse matrices}
+%---------------------------------------
+
+\input{_add.tex}
+Returns {\tt C = alpha*A + beta*B}.
+If the {\tt stype} of {\tt A} and {\tt B} match, then {\tt C} has
+the same {\tt stype}. Otherwise, {\tt C->stype} is zero ({\tt C} is
+unsymmetric).
+
+%---------------------------------------
+\subsection{{\tt cholmod\_sparse\_xtype}: change sparse xtype}
+%---------------------------------------
+
+\input{_sparse_xtype.tex}
+Changes the {\tt xtype} of a sparse matrix, to pattern, real, complex, or zomplex.
+Changing from complex or zomplex to real discards the imaginary part.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: {\tt cholmod\_factor} object}
+\label{cholmod_factor}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_factor} object: a sparse Cholesky factorization}
+%---------------------------------------
+
+\input{_factor.tex}
+An $\m{LL}\tr$ or $\m{LDL}\tr$ factorization in simplicial or supernodal form.
+A simplicial factor is very similar to a {\tt cholmod\_sparse} matrix.
+For an $\m{LDL}\tr$ factorization, the diagonal matrix $\m{D}$ is stored
+as the diagonal of $\m{L}$; the unit-diagonal of $\m{L}$ is not stored.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_free\_factor}: free factor}
+%---------------------------------------
+
+\input{_free_factor.tex}
+Frees a factor.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_allocate\_factor}: allocate factor}
+%---------------------------------------
+
+\input{_allocate_factor.tex}
+Allocates a factor and sets it to identity.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_reallocate\_factor}: reallocate factor}
+%---------------------------------------
+
+\input{_reallocate_factor.tex}
+Reallocates a simplicial factor so that it can contain {\tt nznew} entries.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_change\_factor}: change factor}
+%---------------------------------------
+
+\input{_change_factor.tex}
+Change the numeric or symbolic, $\m{LL}\tr$ or $\m{LDL}\tr$, simplicial or super, packed or unpacked, and
+monotonic or non-monotonic status of a {\tt cholmod\_factor} object.
+
+There are four basic classes of factor types:
+\begin{enumerate}
+\item simplicial symbolic: Consists of two size-{\tt n} arrays: the fill-reducing
+permutation ({\tt L->Perm}) and the nonzero count for each column of L
+({\tt L->ColCount}). All other factor types also include this information.
+{\tt L->ColCount} may be exact (obtained from the analysis routines), or
+it may be a guess. During factorization, and certainly after update/downdate,
+the columns of {\tt L} can have a different number of nonzeros.
+{\tt L->ColCount} is used to allocate space. {\tt L->ColCount} is exact for the
+supernodal factorizations. The nonzero pattern of {\tt L} is not kept.
+
+\item simplicial numeric: These represent {\tt L} in a compressed column form. The
+variants of this type are:
+
+\begin{itemize}
+\item $\m{LDL}\tr$: {\tt L} is unit diagonal. Row indices in column {\tt j} are located in
+ {\tt L->i [L->p [j] ... L->p [j] + L->nz [j]]}, and corresponding numeric
+ values are in the same locations in {\tt L->x}. The total number of
+ entries is the sum of {\tt L->nz [j]}. The unit diagonal is not stored;
+ {\tt D} is stored on the diagonal of {\tt L} instead. {\tt L->p} may or may not be
+ monotonic. The order of storage of the columns in {\tt L->i} and {\tt L->x} is
+ given by a doubly-linked list ({\tt L->prev} and {\tt L->next}). {\tt L->p} is of
+ size {\tt n+1}, but only the first {\tt n} entries are used.
+
+ For the complex case, {\tt L->x} is stored interleaved with real and imaginary
+ parts, and is of size {\tt 2*lnz*sizeof(double)}. For the zomplex case,
+ {\tt L->x} is of size {\tt lnz*sizeof(double)} and holds the real part; {\tt L->z}
+ is the same size and holds the imaginary part.
+
+\item $\m{LL}\tr$: This is identical to the $\m{LDL}\tr$ form, except that the non-unit
+ diagonal of {\tt L} is stored as the first entry in each column of {\tt L}.
+\end{itemize}
+
+\item supernodal symbolic: A representation of the nonzero pattern of the
+supernodes for a supernodal factorization. There are {\tt L->nsuper}
+supernodes. Columns {\tt L->super [k]} to {\tt L->super [k+1]-1} are in the {\tt k}th
+supernode. The row indices for the {\tt k}th supernode are in
+{\tt L->s [L->pi [k] ... L->pi [k+1]-1]}. The numerical values are not
+allocated ({\tt L->x}), but when they are they will be located in
+{\tt L->x [L->px [k] ... L->px [k+1]-1]}, and the {\tt L->px} array is defined
+in this factor type.
+
+For the complex case, {\tt L->x} is stored interleaved with real/imaginary parts,
+and is of size \newline
+{\tt 2*L->xsize*sizeof(double)}. The zomplex supernodal case
+is not supported, since it is not compatible with LAPACK and the BLAS.
+
+\item supernodal numeric: Always an $\m{LL}\tr$ factorization. {\tt L} has a non-unit
+ diagonal. {\tt L->x} contains the numerical values of the supernodes, as
+ described above for the supernodal symbolic factor.
+ For the complex case, {\tt L->x} is stored interleaved, and is of size
+ {\tt 2*L->xsize*sizeof(double)}. The zomplex supernodal case is not
+ supported, since it is not compatible with LAPACK and the BLAS.
+\end{enumerate}
+
+
+In all cases, the row indices in each column ({\tt L->i} for simplicial {\tt L} and
+{\tt L->s} for supernodal {\tt L}) are kept sorted from low indices to high indices.
+This means the diagonal of {\tt L} (or {\tt D} for a $\m{LDL}\tr$ factorization) is always kept as the
+first entry in each column. The elimination tree is not kept. The parent
+of node {\tt j} can be found as the second row index in the {\tt j}th column.
+If column {\tt j} has no off-diagonal entries then node {\tt j} is a root
+of the elimination tree.
+
+The {\tt cholmod\_change\_factor} routine can do almost all possible conversions.
+It cannot do the following conversions:
+
+\begin{itemize}
+\item Simplicial numeric types cannot be converted to a supernodal
+ symbolic type. This would simultaneously deallocate the
+ simplicial pattern and numeric values and reallocate uninitialized
+ space for the supernodal pattern. This isn't useful for the user,
+ and not needed by CHOLMOD's own routines either.
+\item Only a symbolic factor (simplicial to supernodal) can be converted
+ to a supernodal numeric factor.
+\end{itemize}
+
+Some conversions are meant only to be used internally by other CHOLMOD
+routines, and should not be performed by the end user. They allocate space
+whose contents are undefined:
+
+\begin{itemize}
+\item converting from simplicial symbolic to supernodal symbolic.
+\item converting any factor to supernodal numeric.
+\end{itemize}
+
+Supports all xtypes, except that there is no supernodal zomplex L.
+
+The {\tt to\_xtype} parameter is used only when converting from symbolic to numeric
+or numeric to symbolic. It cannot be used to convert a numeric xtype (real,
+complex, or zomplex) to a different numeric xtype. For that conversion,
+use {\tt cholmod\_factor\_xtype} instead.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_pack\_factor}: pack the columns of a factor}
+%---------------------------------------
+
+\input{_pack_factor.tex}
+Pack the columns of a simplicial $\m{LDL}\tr$ or $\m{LL}\tr$ factorization. This can be followed
+by a call to {\tt cholmod\_reallocate\_factor} to reduce the size of {\tt L} to the exact
+size required by the factor, if desired. Alternatively, you can leave the
+size of {\tt L->i} and {\tt L->x} the same, to allow space for future updates/rowadds.
+Each column is reduced in size so that it has at most {\tt Common->grow2} free
+space at the end of the column.
+Does nothing and returns silently if given any other type of factor.
+Does not force the columns of {\tt L} to be monotonic. It thus differs from
+\begin{verbatim}
+ cholmod_change_factor (xtype, L->is_ll, FALSE, TRUE, TRUE, L, Common)
+\end{verbatim}
+which packs the columns and ensures that they appear in monotonic order.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_reallocate\_column}: reallocate one column of a factor}
+%---------------------------------------
+
+\input{_reallocate_column.tex}
+Reallocates the space allotted to a single column of $\m{L}$.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_factor\_to\_sparse}: sparse matrix copy of a factor}
+%---------------------------------------
+
+\input{_factor_to_sparse.tex}
+Returns a column-oriented sparse matrix containing the pattern and values
+of a simplicial or supernodal numerical factor, and then converts the factor
+into a simplicial symbolic factor. If {\tt L} is already packed, monotonic,
+and simplicial (which is the case when {\tt cholmod\_factorize} uses the simplicial
+Cholesky factorization algorithm) then this routine requires only a small
+amount of time and memory, independent of {\tt n}.
+It only operates on numeric factors (real, complex, or zomplex). It does not
+change {\tt L->xtype} (the resulting sparse matrix has the same {\tt xtype}
+as {\tt L}). If this routine fails, {\tt L} is left unmodified.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_copy\_factor}: copy factor}
+%---------------------------------------
+
+\input{_copy_factor.tex}
+Returns an exact copy of a factor.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_factor\_xtype}: change factor xtype}
+%---------------------------------------
+
+\input{_factor_xtype.tex}
+Changes the {\tt xtype} of a factor, to pattern, real, complex, or zomplex.
+Changing from complex or zomplex to real discards the imaginary part.
+You cannot change a supernodal factor to the zomplex xtype.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: {\tt cholmod\_dense} object}
+\label{cholmod_dense}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_dense} object: a dense matrix}
+%---------------------------------------
+
+\input{_dense.tex}
+Contains a dense matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_allocate\_dense}: allocate dense matrix}
+%---------------------------------------
+
+\input{_allocate_dense.tex}
+Allocates a dense matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_free\_dense}: free dense matrix}
+%---------------------------------------
+
+\input{_free_dense.tex}
+Frees a dense matrix.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_zeros}: dense zero matrix}
+%---------------------------------------
+
+\input{_zeros.tex}
+Returns an all-zero dense matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_ones}: dense matrix, all ones}
+%---------------------------------------
+
+\input{_ones.tex}
+Returns a dense matrix with each entry equal to one.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_eye}: dense identity matrix}
+%---------------------------------------
+
+\input{_eye.tex}
+Returns a dense identity matrix.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_sparse\_to\_dense}: dense matrix copy of a sparse matrix}
+%---------------------------------------
+
+\input{_sparse_to_dense.tex}
+Returns a dense copy of a sparse matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_dense\_to\_sparse}: sparse matrix copy of a dense matrix}
+%---------------------------------------
+
+\input{_dense_to_sparse.tex}
+Returns a sparse copy of a dense matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_copy\_dense}: copy dense matrix}
+%---------------------------------------
+
+\input{_copy_dense.tex}
+Returns a copy of a dense matrix.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_copy\_dense2}: copy dense matrix (preallocated)}
+%---------------------------------------
+
+\input{_copy_dense2.tex}
+Returns a copy of a dense matrix, placing the result in a preallocated matrix {\tt Y}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_dense\_xtype}: change dense matrix xtype}
+%---------------------------------------
+
+\input{_dense_xtype.tex}
+Changes the {\tt xtype} of a dense matrix, to real, complex, or zomplex.
+Changing from complex or zomplex to real discards the imaginary part.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: {\tt cholmod\_triplet} object}
+\label{cholmod_triplet}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_triplet} object: sparse matrix in triplet form}
+%---------------------------------------
+
+\input{_triplet.tex}
+Contains a sparse matrix in triplet form.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_allocate\_triplet}: allocate triplet matrix}
+%---------------------------------------
+
+\input{_allocate_triplet.tex}
+Allocates a triplet matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_free\_triplet}: free triplet matrix}
+%---------------------------------------
+
+\input{_free_triplet.tex}
+Frees a triplet matrix.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_reallocate\_triplet}: reallocate triplet matrix}
+%---------------------------------------
+
+\input{_reallocate_triplet.tex}
+Reallocates a triplet matrix so that it can hold {\tt nznew} entries.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_sparse\_to\_triplet}: triplet matrix copy of a sparse matrix}
+%---------------------------------------
+
+\input{_sparse_to_triplet.tex}
+Returns a triplet matrix copy of a sparse matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_triplet\_to\_sparse}: sparse matrix copy of a triplet matrix}
+%---------------------------------------
+
+\input{_triplet_to_sparse.tex}
+Returns a sparse matrix copy of a triplet matrix.
+If the triplet matrix is symmetric with just the lower part present ({\tt T->stype} $< 0$),
+then entries in the upper part are transposed and placed in the lower part when
+converting to a sparse matrix. Similarly,
+if the triplet matrix is symmetric with just the upper part present ({\tt T->stype} $> 0$),
+then entries in the lower part are transposed and placed in the upper part when
+converting to a sparse matrix.
+Any duplicate entries are summed.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_copy\_triplet}: copy triplet matrix}
+%---------------------------------------
+
+\input{_copy_triplet.tex}
+Returns an exact copy of a triplet matrix.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_triplet\_xtype}: change triplet xtype}
+%---------------------------------------
+
+\input{_triplet_xtype.tex}
+Changes the {\tt xtype} of a dense matrix, to real, complex, or zomplex.
+Changing from complex or zomplex to real discards the imaginary part.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Core} Module: memory management}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_malloc}: allocate memory}
+%---------------------------------------
+
+\input{_malloc.tex}
+Allocates a block of memory of size {\tt n*size},
+using the {\tt Common->malloc\_memory}
+function pointer (default is to use the ANSI C {\tt malloc} routine).
+A value of {\tt n=0} is treated as {\tt n=1}.
+If not successful, {\tt NULL} is returned and {\tt Common->status} is set to {\tt CHOLMOD\_OUT\_OF\_MEMORY}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_calloc}: allocate and clear memory}
+%---------------------------------------
+
+\input{_calloc.tex}
+Allocates a block of memory of size {\tt n*size},
+using the {\tt Common->calloc\_memory}
+function pointer (default is to use the ANSI C {\tt calloc} routine).
+A value of {\tt n=0} is treated as {\tt n=1}.
+If not successful, {\tt NULL} is returned and {\tt Common->status} is set to {\tt CHOLMOD\_OUT\_OF\_MEMORY}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_free}: free memory}
+%---------------------------------------
+
+\input{_free.tex}
+Frees a block of memory of size {\tt n*size},
+using the {\tt Common->free\_memory}
+function pointer (default is to use the ANSI C {\tt free} routine).
+The size of the block ({\tt n} and {\tt size}) is only required so that CHOLMOD
+can keep track of its current and peak memory usage. This is a useful statistic,
+and it can also help in tracking down memory leaks. After the call to
+{\tt cholmod\_finish}, the count of allocated blocks ({\tt Common->malloc\_count})
+should be zero, and the count of bytes in use ({\tt Common->memory\_inuse}) also
+should be zero. If you allocate a block with one size and free it with another,
+the {\tt Common->memory\_inuse} count will be wrong, but CHOLMOD will not
+have a memory leak.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_realloc}: reallocate memory}
+%---------------------------------------
+
+\input{_realloc.tex}
+Reallocates a block of memory whose current size {\tt n*size},
+and whose new size will be {\tt nnew*size} if successful,
+using the {\tt Common->calloc\_memory}
+function pointer (default is to use the ANSI C {\tt realloc} routine).
+If the reallocation is not successful, {\tt p} is returned unchanged
+and {\tt Common->status} is set to {\tt CHOLMOD\_OUT\_OF\_MEMORY}.
+The value of {\tt n} is set to {\tt nnew} if successful, or left
+unchanged otherwise.
+A value of {\tt nnew=0} is treated as {\tt nnew=1}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_realloc\_multiple}: reallocate memory}
+%---------------------------------------
+
+\input{_realloc_multiple.tex}
+Reallocates multiple blocks of memory, all with the same number of items
+(but with different item sizes). Either all reallocations succeed,
+or all are returned to their original size.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Check} Module routines}
+%-------------------------------------------------------------------------------
+
+No CHOLMOD routines print anything, except for the {\tt cholmod\_print\_*}
+routines in the {\tt Check} Module, and the {\tt cholmod\_error} routine. The
+{\tt Common->print\_function} is a pointer to {\tt printf} by default;
+you can redirect the output of CHOLMOD by redefining this pointer.
+If {\tt Common->print\_function} is {\tt NULL}, CHOLMOD does not print anything.
+
+The {\tt Common->print} parameter determines how much detail is printed.
+Each value of {\tt Common->print} listed below also prints the items listed
+for smaller values of {\tt Common->print}:
+\begin{itemize}
+\item 0: print nothing; check the data structures and return {\tt TRUE} or {\tt FALSE}.
+\item 1: print error messages.
+\item 2: print warning messages.
+\item 3: print a one-line summary of the object.
+\item 4: print a short summary of the object (first and last few entries).
+\item 5: print the entire contents of the object.
+\end{itemize}
+Values less than zero are treated as zero, and values greater than five are
+treated as five.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_check\_common}: check Common object}
+%---------------------------------------
+
+\input{_check_common.tex}
+Check if the {\tt Common} object is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_common}: print Common object}
+%---------------------------------------
+
+\input{_print_common.tex}
+Print the {\tt Common} object and check if it is valid.
+This prints the CHOLMOD parameters and statistics.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_sparse}: check sparse matrix}
+%---------------------------------------
+
+\input{_check_sparse.tex}
+Check if a sparse matrix is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_sparse}: print sparse matrix}
+%---------------------------------------
+
+\input{_print_sparse.tex}
+Print a sparse matrix and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_dense}: check dense matrix}
+%---------------------------------------
+
+\input{_check_dense.tex}
+Check if a dense matrix is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_dense}: print dense matrix}
+%---------------------------------------
+
+\input{_print_dense.tex}
+Print a dense matrix and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_factor}: check factor}
+%---------------------------------------
+
+\input{_check_factor.tex}
+Check if a factor is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_factor}: print factor}
+%---------------------------------------
+
+\input{_print_factor.tex}
+Print a factor and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_triplet}: check triplet matrix}
+%---------------------------------------
+
+\input{_check_triplet.tex}
+Check if a triplet matrix is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_triplet}: print triplet matrix}
+%---------------------------------------
+
+\input{_print_triplet.tex}
+Print a triplet matrix and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_subset}: check subset}
+%---------------------------------------
+
+\input{_check_subset.tex}
+Check if a subset is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_subset}: print subset}
+%---------------------------------------
+
+\input{_print_subset.tex}
+Print a subset and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_perm}: check permutation}
+%---------------------------------------
+
+\input{_check_perm.tex}
+Check if a permutation is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_perm}: print permutation}
+%---------------------------------------
+
+\input{_print_perm.tex}
+Print a permutation and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_check\_parent}: check elimination tree}
+%---------------------------------------
+
+\input{_check_parent.tex}
+Check if an elimination tree is valid.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_print\_parent}: print elimination tree}
+%---------------------------------------
+
+\input{_print_parent.tex}
+Print an elimination tree and check if it is valid.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_read\_triplet}: read triplet matrix from file}
+%---------------------------------------
+
+\input{_read_triplet.tex}
+Read a sparse matrix in triplet form, using the the {\tt coord}
+Matrix Market format (http://www.nist.gov/MatrixMarket).
+Skew-symmetric and complex symmetric matrices are returned with
+both upper and lower triangular parts present (an stype of zero).
+Real symmetric and complex Hermitian matrices are returned with just
+their upper or lower triangular part, depending on their stype.
+The Matrix Market {\tt array} data type for dense matrices is not supported
+(use {\tt cholmod\_read\_dense} for that case).
+
+If the first line of the file starts with {\tt \%\%MatrixMarket}, then it is
+interpreted as a file in Matrix Market format. The header line is optional.
+If present, this line must have the following format:
+\vspace{0.1in}
+
+ {\tt \%\%MatrixMarket matrix coord} {\em type storage}
+
+\vspace{0.1in}
+\noindent
+where {\em type} is one of: {\tt real}, {\tt complex}, {\tt pattern},
+or {\tt integer}, and {\em storage} is one of: {\tt general}, {\tt hermitian},
+{\tt symmetric}, or {\tt skew-symmetric}.
+In CHOLMOD, these roughly correspond to the {\tt xtype}
+(pattern, real, complex, or zomplex) and {\tt stype}
+(unsymmetric, symmetric/upper, and symmetric/lower).
+The strings are case-insensitive. Only the first character (or the
+first two for skew-symmetric) is significant.
+The {\tt coord} token can be replaced with {\tt array} in the Matrix Market format, but
+this format not supported by {\tt cholmod\_read\_triplet}.
+The {\tt integer} type is converted to real.
+The {\em type} is ignored; the actual type (real, complex, or pattern) is
+inferred from the number of tokens in each line of the file (2: pattern,
+3: real, 4: complex). This is compatible with the Matrix Market format.
+
+A storage of {\tt general} implies an stype of zero
+(see below). A storage of {\tt symmetric} and {\tt hermitian} imply an stype of -1.
+Skew-symmetric and complex symmetric matrices are returned with an stype of 0.
+Blank lines, any other lines starting with ``{\tt \%}'' are treated as comments, and are ignored.
+
+The first non-comment line contains 3 or 4 integers:
+\vspace{0.1in}
+
+ {\em nrow ncol nnz stype}
+
+\vspace{0.1in}
+\noindent
+where {\em stype} is optional (stype does not appear in the Matrix Market format).
+The matrix is {\em nrow}-by-{\em ncol}. The following {\em nnz} lines (excluding comments)
+each contain a single entry. Duplicates are permitted, and are summed in
+the output matrix.
+
+If stype is present, it denotes the storage format for the matrix.
+\begin{itemize}
+\item stype = 0 denotes an unsymmetric matrix (same as Matrix Market {\tt general}).
+\item stype = -1 denotes a symmetric or Hermitian matrix whose lower triangular
+ entries are stored. Entries may be present in the upper triangular
+ part, but these are ignored (same as Matrix Market {\tt symmetric}
+ for the real case, {\tt hermitian} for the complex case).
+\item stype = 1 denotes a symmetric or Hermitian matrix whose upper triangular
+ entries are stored. Entries may be present in the lower triangular
+ part, but these are ignored. This format is not available in the Matrix
+ Market format.
+\end{itemize}
+
+If neither the stype nor the Matrix Market header are present, then
+the stype is inferred from the rest of the data. If the matrix is
+rectangular, or has
+entries in both the upper and lower triangular parts, then it is assumed to
+be unsymmetric (stype=0). If only entries in the lower triangular part are
+present, the matrix is assumed to have stype = -1. If only entries in the
+upper triangular part are present, the matrix is assumed to have stype = 1.
+
+Each nonzero consists of one line with 2, 3, or 4 entries. All lines must
+have the same number of entries. The first two entries are the row and
+column indices of the nonzero. If 3 entries are present, the 3rd entry is
+the numerical value, and the matrix is real. If 4 entries are present,
+the 3rd and 4th entries in the line are the real and imaginary parts of
+a complex value.
+
+The matrix can be either 0-based or 1-based. It is first assumed to be
+one-based (compatible with Matrix Market), with row indices in the range
+1 to ncol and column indices in the range 1 to nrow. If a row or column
+index of zero is found, the matrix is assumed to be zero-based (with row
+indices in the range 0 to ncol-1 and column indices in the range 0 to
+nrow-1). This test correctly determines that all Matrix Market
+matrices are in 1-based form.
+
+For symmetric pattern-only matrices, the kth diagonal (if present) is set to
+one plus the degree of the row k or column k (whichever is larger), and the
+off-diagonals are set to -1. A symmetric pattern-only matrix with a
+zero-free diagonal is thus converted into a symmetric positive definite
+matrix. All entries are set to one for an unsymmetric pattern-only matrix.
+This differs from the MatrixMarket format ({\tt A = mmread ('file')} returns
+a binary pattern for A for symmetric pattern-only matrices).
+To return a binary format for all pattern-only matrices, use
+{\tt A = mread('file',1)}.
+
+Example matrices that follow this format can be found in the
+{\tt CHOLMOD/Demo/Matrix} and \newline
+{\tt CHOLMOD/Tcov/Matrix} directories.
+You can also try any of the matrices in the Matrix Market collection
+at http://www.nist.gov/MatrixMarket.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_read\_sparse}: read sparse matrix from file}
+%---------------------------------------
+
+\input{_read_sparse.tex}
+Read a sparse matrix in triplet form from a file (using {\tt cholmod\_read\_triplet})
+and convert to a CHOLMOD sparse matrix.
+The Matrix Market format is used.
+If {\tt Common->prefer\_upper} is {\tt TRUE} (the default case), a symmetric matrix is
+returned stored in upper-triangular form ({\tt A->stype} is 1).
+Otherwise, it is left in its original form, either upper or lower.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_read\_dense}: read dense matrix from file}
+%---------------------------------------
+
+\input{_read_dense.tex}
+Read a dense matrix from a file, using the the {\tt array}
+Matrix Market format
+\newline (http://www.nist.gov/MatrixMarket).
+
+%---------------------------------------
+\subsection{{\tt cholmod\_read\_matrix}: read a matrix from file}
+%---------------------------------------
+
+\input{_read_matrix.tex}
+Read a sparse or dense matrix from a file, in Matrix Market format.
+Returns a {\tt void} pointer to either a
+{\tt cholmod\_triplet},
+{\tt cholmod\_sparse}, or
+{\tt cholmod\_dense} object.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_write\_sparse}: write a sparse matrix to a file}
+%---------------------------------------
+
+\input{_write_sparse.tex}
+Write a sparse matrix to a file in Matrix Market format. Optionally include
+comments, and print explicit zero entries given by the pattern of the {\tt Z}
+matrix. If not NULL, the {\tt Z} matrix must have the same dimensions and stype
+as {\tt A}.
+
+Returns the symmetry in which the matrix was printed
+(1 to 7) or -1 on failure. See the {\tt cholmod\_symmetry} function for
+a description of the return codes.
+
+If {\tt A} and {\tt Z} are sorted on input, and either unsymmetric (stype = 0) or
+symmetric-lower (stype < 0), and if {\tt A} and {\tt Z} do not overlap,
+then the triplets
+are sorted, first by column and then by row index within each column, with
+no duplicate entries. If all the above holds except stype > 0, then the
+triplets are sorted by row first and then column.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_write\_dense}: write a dense matrix to a file}
+%---------------------------------------
+
+\input{_write_dense.tex}
+Write a dense matrix to a file in Matrix Market format. Optionally include
+comments. Returns > 0 if successful, -1 otherwise (1 if rectangular, 2 if
+square).
+A dense matrix is written in "general" format; symmetric formats in the
+Matrix Market standard are not exploited.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Cholesky} Module routines}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_analyze}: symbolic factorization}
+%---------------------------------------
+
+\input{_analyze.tex}
+Orders and analyzes a matrix (either simplicial or supernodal), in preparation
+for numerical factorization via {\tt cholmod\_factorize} or via the ``expert''
+routines {\tt cholmod\_rowfac} and {\tt cholmod\_super\_numeric}.
+
+In the symmetric case, {\tt A} or {\tt A(p,p)} is analyzed,
+where {\tt p} is the fill-reducing ordering.
+In the unsymmetric case, {\tt A*A'} or {\tt A(p,:)*A(p,:)'} is analyzed.
+The {\tt cholmod\_analyze\_p} routine can be given a user-provided permutation {\tt p}
+(see below).
+
+The default ordering strategy is to first try AMD.
+The ordering quality is analyzed, and if AMD obtains an ordering where
+{\tt nnz(L)} is greater than or equal to {\tt 5*nnz(tril(A))}
+(or {\tt 5*nnz(tril(A*A'))} if {\tt A} is unsymmetric) and
+the floating-point operation count for the subsequent factorization is
+greater than or equal to {\tt 500*nnz(L)}, then METIS is tried (if installed).
+For {\tt cholmod\_analyze\_p}, the user-provided ordering is also tried.
+This default behavior is obtained when {\tt Common->nmethods} is zero.
+In this case, methods 0, 1, and 2 in {\tt Common->method[...]} are reset
+to user-provided, AMD, and METIS, respectively.
+The ordering with the smallest {\tt nnz(L)} is kept.
+
+If {\tt Common->default\_nesdis} is true (nonzero), then CHOLMOD's
+nested dissection (NESDIS) is used for the default strategy described
+above, in place of METIS.
+
+Other ordering options can be requested. These include:
+\begin{enumerate}
+\item natural: A is not permuted to reduce fill-in.
+\item user-provided: a permutation can be provided to {\tt cholmod\_analyze\_p}.
+\item AMD: approximate minimum degree (AMD for the symmetric case, COLAMD for the {\tt A*A'} case).
+\item METIS: nested dissection with {\tt METIS\_NodeND}
+\item {\tt NESDIS}: CHOLMOD's nested dissection using
+ {\tt METIS\_NodeComputeSeparator},
+ followed by a constrained minimum degree
+ (CAMD or CSYMAMD for the symmetric case, CCOLAMD for the {\tt A*A'} case).
+ This is typically slower than METIS, but typically provides better orderings.
+\end{enumerate}
+
+Multiple ordering options can be tried (up to 9 of them), and the best one
+is selected (the one that gives the smallest number of nonzeros in the
+simplicial factor L). If one method fails, {\tt cholmod\_analyze} keeps going, and
+picks the best among the methods that succeeded. This routine fails (and
+returns {\tt NULL}) if either the initial memory allocation fails, all ordering methods
+fail, or the supernodal analysis (if requested) fails. Change {\tt Common->nmethods} to the
+number of methods you wish to try. By default, the 9 methods available are:
+
+\begin{enumerate}
+\item user-provided permutation (only for {\tt cholmod\_analyze\_p}).
+\item AMD with default parameters.
+\item METIS with default parameters.
+\item {\tt NESDIS} with default parameters: stopping the partitioning when
+ the graph is of size {\tt nd\_small} = 200 or less, remove nodes with
+ more than {\tt max (16, prune\_dense * sqrt (n))} nodes where
+ {\tt prune\_dense} = 10, and follow partitioning with
+ constrained minimum degree ordering
+ (CAMD for the symmetric case,
+ CCOLAMD for the unsymmetric case).
+\item natural ordering (with weighted postorder).
+\item NESDIS, {\tt nd\_small} = 20000, {\tt prune\_dense} = 10.
+\item NESDIS, {\tt nd\_small} = 4, {\tt prune\_dense} = 10,
+ no constrained minimum degree.
+\item NESDIS, {\tt nd\_small} = 200, {\tt prune\_dense} = 0.
+\item COLAMD for {\tt A*A'} or AMD for {\tt A}
+\end{enumerate}
+
+You can modify these 9 methods and the number of methods tried by changing
+parameters in the {\tt Common} argument. If you know the best ordering for your
+matrix, set {\tt Common->nmethods} to 1 and set {\tt Common->method[0].ordering} to the
+requested ordering method. Parameters for each method can also be modified
+(refer to the description of {\tt cholmod\_common} for details).
+
+Note that it is possible for METIS to terminate your program if it runs out
+of memory. This is not the case for any CHOLMOD or minimum degree ordering
+routine (AMD, COLAMD, CAMD, CCOLAMD, or CSYMAMD).
+Since {\tt NESDIS} relies on METIS, it too can terminate your program.
+
+The selected ordering is followed by a weighted postorder of the elimination
+tree by default (see {\tt cholmod\_postorder} for details),
+unless {\tt Common->postorder} is set to {\tt FALSE}.
+The postorder does not change the number of nonzeros in $\m{L}$ or
+the floating-point operation count. It does improve performance,
+particularly for the supernodal factorization.
+If you truly want the natural ordering with no postordering,
+you must set {\tt Common->postorder} to {\tt FALSE}.
+
+The factor {\tt L} is returned as simplicial symbolic if
+{\tt Common->supernodal} is {\tt CHOLMOD\_SIMPLICIAL} (zero) or as supernodal symbolic if
+{\tt Common->supernodal} is {\tt CHOLMOD\_SUPERNODAL} (two). If \newline
+{\tt Common->supernodal} is {\tt CHOLMOD\_AUTO} (one),
+then {\tt L} is simplicial if the flop count per nonzero in {\tt L} is less than
+{\tt Common->supernodal\_switch} (default: 40), and
+supernodal otherwise. In both cases, {\tt L->xtype} is {\tt CHOLMOD\_PATTERN}.
+A subsequent call to {\tt cholmod\_factorize} will perform a
+simplicial or supernodal factorization, depending on the type of {\tt L}.
+
+For the simplicial case, {\tt L} contains the fill-reducing permutation ({\tt L->Perm})
+and the counts of nonzeros in each column of {\tt L} ({\tt L->ColCount}). For the
+supernodal case, {\tt L} also contains the nonzero pattern of each supernode.
+
+If a simplicial factorization is selected, it will be $\m{LDL}\tr$ by default, since
+this is the kind required by the {\tt Modify} Module. CHOLMOD does not include a
+supernodal $\m{LDL}\tr$ factorization, so if a supernodal factorization is selected,
+it will be in the form $\m{LL}\tr$. The $\m{LDL}\tr$ method can be used to
+factorize positive definite matrices and indefinite matrices whose leading minors
+are well-conditioned (2-by-2 pivoting is not supported). The $\m{LL}\tr$ method
+is restricted to positive definite matrices. To factorize a large indefinite matrix,
+set {\tt Common->supernodal} to {\tt CHOLMOD\_SIMPLICIAL}, and the simplicial
+$\m{LDL}\tr$ method will always be used. This will be significantly slower than
+a supernodal $\m{LL}\tr$ factorization, however.
+
+Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_factorize}: numeric factorization}
+%---------------------------------------
+
+\input{_factorize.tex}
+Computes the numerical factorization of a symmetric matrix. The % primary
+inputs to this routine are a sparse matrix {\tt A} and the symbolic factor {\tt L} from
+{\tt cholmod\_analyze} or a prior numerical factor {\tt L}. If {\tt A} is symmetric, this
+routine factorizes {\tt A(p,p)}. %+beta*I (beta can be zero),
+where p is the fill-reducing permutation ({\tt L->Perm}). If {\tt A} is unsymmetric,
+% either
+{\tt A(p,:)*A(p,:)'} % +beta*I or A(p,f)*A(p,f)'+beta*I
+is factorized. % The set f and
+The nonzero pattern of the matrix {\tt A} must be the same as the matrix passed to
+{\tt cholmod\_analyze} for the supernodal case. For the simplicial case, it can
+be different, but it should be the same for best performance. % beta is real.
+
+A simplicial factorization or supernodal factorization is chosen, based on
+the type of the factor {\tt L}. If {\tt L->is\_super} is {\tt TRUE}, a supernodal $\m{LL}\tr$
+factorization is computed. Otherwise, a simplicial numeric factorization
+is computed, either $\m{LL}\tr$ or $\m{LDL}\tr$, depending on {\tt Common->final\_ll}
+(the default for the simplicial case is to compute an $\m{LDL}\tr$ factorization).
+
+Once the factorization is complete, it can be left as is or optionally
+converted into any simplicial numeric type, depending on the
+{\tt Common->final\_*} parameters. If converted from a supernodal to simplicial
+type, and {\tt Common->final\_resymbol} is {\tt TRUE}, then numerically
+zero entries in {\tt L} due to relaxed supernodal amalgamation are removed from
+the simplicial factor (they are always left in the supernodal form of {\tt L}).
+Entries that are numerically zero but present in the simplicial symbolic
+pattern of {\tt L} are left in place (the graph of {\tt L} remains chordal).
+This is required for the update/downdate/rowadd/rowdel routines to work
+properly.
+
+If the matrix is not positive definite the routine returns {\tt TRUE}, but
+{\tt Common->status} is set to {\tt CHOLMOD\_NOT\_POSDEF} and {\tt L->minor} is set to the
+column at which the failure occurred. Columns {\tt L->minor} to {\tt L->n-1}
+are set to zero.
+
+Supports any xtype (pattern, real, complex, or zomplex), except that the
+input matrix {\tt A} cannot be pattern-only. If {\tt L} is simplicial, its numeric
+xtype matches {\tt A} on output. If {\tt L} is supernodal, its xtype is real if {\tt A} is
+real, or complex if {\tt A} is complex or zomplex. CHOLMOD does not provide
+a supernodal zomplex factor, since it is incompatible with how complex numbers are
+stored in LAPACK and the BLAS.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_analyze\_p}: symbolic factorization, given permutation}
+%---------------------------------------
+
+\input{_analyze_p.tex}
+Identical to {\tt cholmod\_analyze}, except that a user-provided
+permutation {\tt p} can be provided, and the set {\tt f} for the unsymmetric case
+can be provided. The matrices {\tt A(:,f)*A(:,f)'} or {\tt A(p,f)*A(p,f)'}
+can be analyzed in the the unsymmetric case.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_factorize\_p}: numeric factorization, given permutation}
+%---------------------------------------
+
+\input{_factorize_p.tex}
+Identical to {\tt cholmod\_factorize}, but with additional options.
+The set {\tt f} can be provided for the unsymmetric case;
+{\tt A(p,f)*A(p,f)'} is factorized. The term {\tt beta*I} can be added to
+the matrix before it is factorized, where {\tt beta} is real.
+Only the real part, {\tt beta[0]}, is used.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_solve}: solve a linear system}
+%---------------------------------------
+
+\input{_solve.tex}
+Returns a solution {\tt X} that solves one of the following systems:
+
+\begin{tabular}{ll|ll}
+ \hline
+ system & {\tt sys} parameter & system & {\tt sys} parameter \\
+ $\m{Ax}=\m{b}$ & 0: {\tt CHOLMOD\_A} & & \\
+ $\m{LDL}\tr\m{x}=\m{b}$ & 1: {\tt CHOLMOD\_LDLt} & $\m{L}\tr\m{x}=\m{b}$ & 5: {\tt CHOLMOD\_Lt} \\
+ $\m{LDx}=\m{b}$ & 2: {\tt CHOLMOD\_LD} & $\m{Dx}=\m{b}$ & 6: {\tt CHOLMOD\_D} \\
+ $\m{DL}\tr\m{x}=\m{b}$ & 3: {\tt CHOLMOD\_DLt} & $\m{x}=\m{Pb}$ & 7: {\tt CHOLMOD\_P} \\
+ $\m{Lx}=\m{b}$ & 4: {\tt CHOLMOD\_L} & $\m{x}=\m{P}\tr\m{b}$ & 8: {\tt CHOLMOD\_Pt} \\
+ \hline
+\end{tabular}
+
+The factorization can be simplicial $\m{LDL}\tr$, simplicial $\m{LL}\tr$, or supernodal $\m{LL}\tr$.
+For an $\m{LL}\tr$ factorization, $\m{D}$ is the identity matrix. Thus {\tt CHOLMOD\_LD} and
+{\tt CHOLMOD\_L} solve the same system if an $\m{LL}\tr$ factorization was performed,
+for example.
+This is one of the few routines in CHOLMOD for which the xtype of the input
+arguments need not match.
+If both {\tt L} and {\tt B} are real, then {\tt X} is returned real. If either is complex
+or zomplex, {\tt X} is returned as either complex or zomplex, depending on the
+{\tt Common->prefer\_zomplex} parameter (default is complex).
+
+This routine does not check to see if the diagonal of $\m{L}$ or $\m{D}$ is zero,
+because sometimes a partial solve can be done with an indefinite or singular
+matrix. If you wish to check in your own code, test {\tt L->minor}. If
+{\tt L->minor == L->n}, then the matrix has no zero diagonal entries.
+If {\tt k = L->minor < L->n}, then {\tt L(k,k)} is zero for an $\m{LL}\tr$ factorization, or
+{\tt D(k,k)} is zero for an $\m{LDL}\tr$ factorization.
+
+Iterative refinement is not performed, but this can be easily done with
+the {\tt MatrixOps} Module. See {\tt Demo/cholmod\_demo.c} for an example.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_spsolve}: solve a linear system}
+%---------------------------------------
+
+\input{_spsolve.tex}
+Identical to {\tt cholmod\_spsolve}, except that {\tt B} and {\tt X} are sparse.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_etree}: find elimination tree}
+%---------------------------------------
+
+\input{_etree.tex}
+Computes the elimination tree of {\tt A} or {\tt A'*A}.
+In the symmetric case, the upper triangular part of {\tt A} is used. Entries not
+in this part of the matrix are ignored. Computing the etree of a symmetric
+matrix from just its lower triangular entries is not supported.
+In the unsymmetric case, all of {\tt A} is used, and the etree of {\tt A'*A} is computed.
+Refer to \cite{Liu90a} for a discussion of the elimination tree
+and its use in sparse Cholesky factorization.
+% J. Liu, "The role of elimination trees in sparse factorization", SIAM J.
+% Matrix Analysis \& Applic., vol 11, 1990, pp. 134-172.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rowcolcounts}: nonzeros counts of a factor}
+%---------------------------------------
+
+\input{_rowcolcounts.tex}
+Compute the row and column counts of the Cholesky factor {\tt L} of the matrix
+{\tt A} or {\tt A*A'}. The etree and its postordering must already be computed (see
+{\tt cholmod\_etree} and {\tt cholmod\_postorder}) and given as inputs to this routine.
+For the symmetric case ($\m{LL}\tr=\m{A}$), {\tt A} must be stored in
+symmetric/lower form ({\tt A->stype = -1}).
+In the unsymmetric case, {\tt A*A'} or {\tt A(:,f)*A(:,f)'} can be analyzed.
+The fundamental floating-point operation count is returned in {\tt Common->fl}
+(this excludes extra flops due to relaxed supernodal amalgamation).
+Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}.
+The algorithm is described in \cite{GilbertLiNgPeyton01,GilbertNgPeyton94}.
+
+% J. Gilbert, E. Ng, B. Peyton, "An efficient algorithm to compute row and
+% column counts for sparse Cholesky factorization", SIAM J. Matrix Analysis \&
+% Applic., vol 15, 1994, pp. 1075-1091.
+%
+% J. Gilbert, X. Li, E. Ng, B. Peyton, "Computing row and column counts for
+% sparse QR and LU factorization", BIT, vol 41, 2001, pp. 693-710.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_analyze\_ordering}: analyze a permutation}
+%---------------------------------------
+
+\input{_analyze_ordering.tex}
+Given a matrix {\tt A} and its fill-reducing permutation, compute the elimination
+tree, its (non-weighted) postordering, and the number of nonzeros in each
+column of {\tt L}. Also computes the flop count, the total nonzeros in {\tt L}, and
+the nonzeros in {\tt tril(A)} ({\tt Common->fl}, {\tt Common->lnz}, and {\tt Common->anz}).
+In the unsymmetric case, {\tt A(p,f)*A(p,f)'} is analyzed, and {\tt Common->anz}
+is the number of nonzero entries in the lower triangular part of the product,
+not in {\tt A} itself.
+
+Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}.
+
+The column counts of {\tt L}, flop count, and other statistics from
+{\tt cholmod\_rowcolcounts} are not computed if {\tt ColCount} is {\tt NULL}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_amd}: interface to AMD}
+%---------------------------------------
+
+\input{_amd.tex}
+CHOLMOD interface to the AMD ordering package. Orders {\tt A} if the matrix is
+symmetric. On output, {\tt Perm [k] = i} if row/column {\tt i} of {\tt A} is the {\tt k}th
+row/column of {\tt P*A*P'}. This corresponds to {\tt A(p,p)} in MATLAB notation.
+If A is unsymmetric, {\tt cholmod\_amd} orders {\tt A*A'} or {\tt A(:,f)*A(:,f)'}.
+On output, {\tt Perm [k] = i} if
+row/column {\tt i} of {\tt A*A'} is the {\tt k}th row/column of {\tt P*A*A'*P'}.
+This corresponds to {\tt A(p,:)*A(p,:)'} in MATLAB notation.
+If {\tt f} is present, {\tt A(p,f)*A(p,f)'} is the permuted matrix.
+Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}.
+
+Computes the flop count for a subsequent $\m{LL}\tr$ factorization, the number
+of nonzeros in {\tt L}, and the number of nonzeros in the matrix ordered
+({\tt A}, {\tt A*A'} or {\tt A(:,f)*A(:,f)'}).
+These statistics are returned in
+{\tt Common->fl}, {\tt Common->lnz}, and {\tt Common->anz}, respectively.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_colamd}: interface to COLAMD}
+%---------------------------------------
+
+\input{_colamd.tex}
+CHOLMOD interface to the COLAMD ordering package.
+Finds a permutation {\tt p} such that the Cholesky factorization of {\tt P*A*A'*P'} is
+sparser than {\tt A*A'}, using COLAMD. If the {\tt postorder} input parameter is {\tt TRUE},
+the column elimination tree is found and postordered, and the COLAMD ordering is then
+combined with its postordering (COLAMD itself does not perform this postordering).
+{\tt A} must be unsymmetric ({\tt A->stype = 0}).
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_rowfac}: row-oriented Cholesky factorization}
+%---------------------------------------
+
+\input{_rowfac.tex}
+Full or incremental numerical $\m{LDL}\tr$ or $\m{LL}\tr$ factorization (simplicial, not
+supernodal). {\tt cholmod\_factorize} is the ``easy'' wrapper for this code, but it
+does not provide access to incremental factorization.
+The algorithm is the row-oriented, up-looking method described in \cite{Davis05}.
+See also \cite{Liu86c}. No 2-by-2 pivoting (or any other pivoting) is performed.
+
+{\tt cholmod\_rowfac} computes the full or incremental $\m{LDL}\tr$ or $\m{LL}\tr$ factorization of
+{\tt A+beta*I} (where {\tt A} is symmetric) or {\tt A*F+beta*I}
+(where {\tt A} and {\tt F} are unsymmetric
+and only the upper triangular part of {\tt A*F+beta*I} is used). It computes
+{\tt L} (and {\tt D}, for $\m{LDL}\tr$) one row at a time.
+The input scalar {\tt beta} is real; only the real part ({\tt beta[0]}) is used.
+
+{\tt L} can be a simplicial symbolic or numeric ({\tt L->is\_super} must be {\tt FALSE}).
+A symbolic factor is converted immediately into a numeric factor containing
+the identity matrix.
+
+For a full factorization, use {\tt kstart = 0} and {\tt kend = nrow}. The existing nonzero
+entries (numerical values in {\tt L->x} and {\tt L->z} for the zomplex case, and indices
+in {\tt L->i}) are overwritten.
+
+To compute an incremental factorization, select {\tt kstart} and {\tt kend} as the range
+of rows of {\tt L} you wish to compute. Rows {\tt kstart} to {\tt kend-1} of {\tt L}
+will be computed. A correct factorization will be computed
+only if all descendants of all nodes {\tt kstart} to {\tt kend-1} in the elimination tree have
+been factorized by a prior call to this routine, and if rows {\tt kstart} to {\tt kend-1}
+have not been factorized. This condition is {\bf not} checked on input.
+
+In the symmetric case, {\tt A} must be stored in upper form ({\tt A->stype} is greater than zero).
+The matrix {\tt F} is not accessed and may be {\tt NULL}. Only
+columns {\tt kstart} to {\tt kend-1} of {\tt A} are accessed.
+
+In the unsymmetric case,
+ the typical case is {\tt F=A'}. Alternatively, if {\tt F=A(:,f)'}, then this
+ routine factorizes the matrix {\tt S = beta*I + A(:,f)*A(:,f)'}.
+ The product {\tt A*F} is assumed to be symmetric;
+ only the upper triangular part of {\tt A*F} is used.
+ {\tt F} must be of size {\tt A->ncol} by {\tt A->nrow}.
+
+% J. Liu, "A compact row storage scheme for Cholesky factors", ACM Trans.
+% Math. Software, vol 12, 1986, pp. 127-148.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rowfac\_mask}: row-oriented Cholesky factorization}
+%---------------------------------------
+
+\input{_rowfac_mask.tex}
+For use in LPDASA only.
+
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_row\_subtree}: pattern of row of a factor}
+%---------------------------------------
+
+\input{_row_subtree.tex}
+Compute the nonzero pattern of the solution to the lower triangular system
+\begin{verbatim}
+ L(0:k-1,0:k-1) * x = A (0:k-1,k)
+\end{verbatim}
+if {\tt A} is symmetric, or
+\begin{verbatim}
+ L(0:k-1,0:k-1) * x = A (0:k-1,:) * A (:,k)'
+\end{verbatim}
+if {\tt A} is unsymmetric.
+This gives the nonzero pattern of row {\tt k} of {\tt L} (excluding the diagonal).
+The pattern is returned postordered, according to the subtree of the elimination
+tree rooted at node {\tt k}.
+
+The symmetric case requires {\tt A} to be in symmetric-upper form.
+
+The result is returned in {\tt R}, a pre-allocated sparse matrix of size {\tt nrow}-by-1,
+with {\tt R->nzmax >= nrow}. {\tt R} is assumed to be packed ({\tt Rnz [0]} is not updated);
+the number of entries in {\tt R} is given by {\tt Rp [0]}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_row\_lsubtree}: pattern of row of a factor}
+%---------------------------------------
+
+\input{_row_lsubtree.tex}
+Identical to {\tt cholmod\_row\_subtree}, except the elimination tree is
+found from {\tt L} itself, not {\tt Parent}. Also, {\tt F=A'} is not provided;
+the nonzero pattern of the {\tt k}th column of {\tt F} is given by
+{\tt Fi} and {\tt fnz} instead.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_resymbol}: re-do symbolic factorization}
+%---------------------------------------
+
+\input{_resymbol.tex}
+Recompute the symbolic pattern of {\tt L}. Entries not in the symbolic pattern
+of the factorization of {\tt A(p,p)} or {\tt F*F'}, where
+{\tt F=A(p,f)} or {\tt F=A(:,f)}, are dropped, where
+{\tt p = L->Perm} is used to permute the input matrix {\tt A}.
+
+Refer to {\tt cholmod\_transpose\_unsym} for a description of {\tt f}.
+
+If an entry in {\tt L} is kept, its numerical value does not change.
+
+This routine is used after a supernodal factorization is converted into
+a simplicial one, to remove zero entries that were added due to relaxed
+supernode amalgamation. It can also be used after a series of downdates
+to remove entries that would no longer be present if the matrix were
+factorized from scratch. A downdate ({\tt cholmod\_updown}) does not remove any
+entries from {\tt L}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_resymbol\_noperm}: re-do symbolic factorization}
+%---------------------------------------
+
+\input{_resymbol_noperm.tex}
+Identical to {\tt cholmod\_resymbol}, except that the fill-reducing
+ordering {\tt L->Perm} is not used.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_postorder}: tree postorder}
+%---------------------------------------
+
+\input{_postorder.tex}
+Postorder a tree. The tree is either an elimination tree (the output from
+{\tt cholmod\_etree}) or a component tree (from {\tt cholmod\_nested\_dissection}).
+
+An elimination tree is a complete tree of {\tt n} nodes with {\tt Parent [j] > j} or
+{\tt Parent [j] = -1} if j is a root. On output {\tt Post [0..n-1]} is a complete
+permutation vector;
+{\tt Post [k] = j} if node {\tt j} is the {\tt k}th node in the
+postordered elimination tree, where {\tt k} is in the range 0 to {\tt n-1}.
+
+A component tree is a subset of {\tt 0:n-1}. {\tt Parent [j] = -2} if node {\tt j} is not
+in the component tree. {\tt Parent [j] = -1} if {\tt j} is a root of the component
+tree, and {\tt Parent [j]} is in the range 0 to {\tt n-1} if {\tt j} is in the component
+tree but not a root. On output, {\tt Post [k]} is defined only for nodes in
+the component tree. {\tt Post [k] = j} if node {\tt j} is the {\tt k}th node in the
+postordered component tree, where {\tt k} is in the range 0 to the number of
+components minus 1.
+Node {\tt j} is ignored and not included in the postorder if {\tt Parent [j] < -1}.
+As a result, {\tt cholmod\_check\_parent (Parent, ...)} and {\tt cholmod\_check\_perm (Post, ...)}
+fail if used for a component tree and its postordering.
+
+An optional node weight can be given. When starting a postorder at node {\tt j},
+the children of {\tt j} are ordered in decreasing order of their weight.
+If no weights are given ({\tt Weight} is {\tt NULL}) then children are ordered in
+decreasing order of their node number. The weight of a node must be in the
+range 0 to {\tt n-1}. Weights outside that range are silently converted to that
+range (weights $<$ 0 are treated as zero, and weights $\ge$ {\tt n} are treated as {\tt n-1}).
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rcond}: reciprocal condition number}
+%---------------------------------------
+
+\input{_rcond.tex}
+Returns a rough estimate of the reciprocal of the condition number:
+the minimum entry on the diagonal of {\tt L} (or absolute entry of {\tt D} for an $\m{LDL}\tr$
+factorization) divided by the maximum entry. {\tt L} can be real, complex, or
+zomplex. Returns -1 on error, 0 if the matrix is singular or has a zero or NaN
+entry on the diagonal of {\tt L}, 1 if the matrix is 0-by-0, or
+{\tt min(diag(L))/max(diag(L))} otherwise. Never returns NaN; if {\tt L} has a NaN on
+the diagonal it returns zero instead.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Modify} Module routines}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_updown}: update/downdate}
+%---------------------------------------
+
+\input{_updown.tex}
+Updates/downdates the $\m{LDL}\tr$ factorization (symbolic, then numeric), by
+computing a new factorization of
+\[
+\new{\m{L}}\new{\m{D}}\new{\m{L}}\tr = \m{LDL}\tr \pm \m{CC}\tr
+\]
+where $\new{\m{L}}$ denotes the new factor.
+{\tt C} must be sorted. It can be either packed or unpacked. As in all CHOLMOD
+routines, the columns of {\tt L} are sorted on input, and also on output.
+If {\tt L} does not contain a simplicial numeric $\m{LDL}\tr$ factorization, it
+is converted into one. Thus, a supernodal $\m{LL}\tr$ factorization
+can be passed to {\tt cholmod\_updown}.
+A symbolic {\tt L} is converted into a numeric identity matrix.
+If the initial conversion fails, the factor is returned unchanged.
+
+If memory runs out during the update, the factor is returned as a simplicial
+symbolic factor. That is, everything is freed except for the fill-reducing
+ordering and its corresponding column counts (typically computed by
+{\tt cholmod\_analyze}).
+
+Note that the fill-reducing permutation {\tt L->Perm} is not used. The row
+indices of {\tt C} refer to the rows of {\tt L}, not {\tt A}. If your original system is
+$\m{LDL}\tr = \m{PAP}\tr$ (where $\m{P} =$ {\tt L->Perm}), and you want to compute the $\m{LDL}\tr$
+factorization of $\m{A}+\m{CC}\tr$, then you must permute $\m{C}$ first. That is,
+if
+\[
+ \m{PAP}\tr = \m{LDL}\tr
+\]
+is the initial factorization, then
+\[
+\m{P}(\m{A}+\m{CC}\tr)\m{P}\tr
+ = \m{PAP}\tr+\m{PCC}\tr\m{P}\tr
+ = \m{LDL}\tr + (\m{PC})(\m{PC})\tr
+ = \m{LDL}\tr + \new{\m{C}}\new{\m{C}}\tr
+\]
+where $\new{\m{C}} = \m{PC}$.
+
+You can use the {\tt cholmod\_submatrix} routine in the {\tt MatrixOps} Module
+to permute {\tt C}, with:
+\begin{verbatim}
+ Cnew = cholmod_submatrix (C, L->Perm, L->n, NULL, -1, TRUE, TRUE, Common) ;
+\end{verbatim}
+
+Note that the {\tt sorted} input parameter to {\tt cholmod\_submatrix} must be {\tt TRUE},
+because {\tt cholmod\_updown} requires {\tt C} with sorted columns.
+Only real matrices are supported.
+The algorithms are described in \cite{DavisHager99,DavisHager01}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_updown\_solve}: update/downdate}
+%---------------------------------------
+
+\input{_updown_solve.tex}
+Identical to {\tt cholmod\_updown}, except
+the system $\m{Lx}=\m{b}$ is also updated/downdated.
+The new system is $\new{\m{L}}\new{\m{x}}=\m{b} + \Delta \m{b}$. The old solution $\m{x}$ is overwritten
+with $\new{\m{x}}$. Note that as in the update/downdate of $\m{L}$ itself, the fill-
+reducing permutation {\tt L->Perm} is not used. The vectors $\m{x}$ and $\m{b}$ are in the permuted
+ordering, not your original ordering. This routine does not handle multiple right-hand-sides.
+
+%---------------------------------------
+\newpage
+\subsection{{\tt cholmod\_updown\_mark}: update/downdate}
+%---------------------------------------
+
+\input{_updown_mark.tex}
+Identical to {\tt cholmod\_updown\_solve}, except that only part of $\m{L}$
+is used in the update of the solution to $\m{Lx}=\m{b}$. For more details,
+see the source code file {\tt CHOLMOD/Modify/cholmod\_updown.c}.
+This routine is meant for use in the {\tt LPDASA} linear program solver only,
+by Hager and Davis.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_updown\_mask}: update/downdate}
+%---------------------------------------
+
+\input{_updown_mask.tex}
+For use in LPDASA only.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_rowadd}: add row to factor}
+%---------------------------------------
+
+\input{_rowadd.tex}
+Adds a row and column to an $\m{LDL}\tr$ factorization. The {\tt k}th
+row and column of {\tt L} must be equal to the {\tt k}th row and
+column of the identity matrix on input.
+Only real matrices are supported.
+The algorithm is described in \cite{DavisHager05}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rowadd\_solve}: add row to factor}
+%---------------------------------------
+
+\input{_rowadd_solve.tex}
+Identical to {\tt cholmod\_rowadd}, except the system $\m{Lx}=\m{b}$ is also updated/downdated, just like {\tt cholmod\_updown\_solve}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_rowdel}: delete row from factor}
+%---------------------------------------
+
+\input{_rowdel.tex}
+Deletes a row and column from an $\m{LDL}\tr$ factorization. The {\tt k}th
+row and column of {\tt L} is equal to the {\tt k}th row and
+column of the identity matrix on output.
+Only real matrices are supported.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rowdel\_solve}: delete row from factor}
+%---------------------------------------
+
+\input{_rowdel_solve.tex}
+Identical to {\tt cholmod\_rowdel}, except the system $\m{Lx}=\m{b}$ is also updated/downdated, just like {\tt cholmod\_updown\_solve}.
+When row/column $k$ of $\m{A}$ is deleted from the system $\m{Ay}=\m{b}$, this can induce
+a change to $\m{x}$, in addition to changes arising when $\m{L}$ and $\m{b}$ are modified.
+If this is the case, the kth entry of $\m{y}$ is required as input ({\tt yk}).
+The algorithm is described in \cite{DavisHager05}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_rowadd\_mark}: add row to factor}
+%---------------------------------------
+
+\input{_rowadd_mark.tex}
+Identical to {\tt cholmod\_rowadd\_solve}, except that only part of $\m{L}$
+is used in the update of the solution to $\m{Lx}=\m{b}$. For more details,
+see the source code file {\tt CHOLMOD/Modify/cholmod\_rowadd.c}.
+This routine is meant for use in the {\tt LPDASA} linear program solver only.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_rowdel\_mark}: delete row from factor}
+%---------------------------------------
+
+\input{_rowdel_mark.tex}
+Identical to {\tt cholmod\_rowadd\_solve}, except that only part of $\m{L}$
+is used in the update of the solution to $\m{Lx}=\m{b}$. For more details,
+see the source code file {\tt CHOLMOD/Modify/cholmod\_rowdel.c}.
+This routine is meant for use in the {\tt LPDASA} linear program solver only.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt MatrixOps} Module routines}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_drop}: drop small entries}
+%---------------------------------------
+
+\input{_drop.tex}
+Drop small entries from {\tt A}, and entries in the ignored part of {\tt A} if {\tt A}
+is symmetric. No CHOLMOD routine drops small numerical entries
+from a matrix, except for this one. NaN's and Inf's are kept.
+
+Supports pattern and real matrices; complex and zomplex matrices are not supported.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_norm\_dense}: dense matrix norm}
+%---------------------------------------
+
+\input{_norm_dense.tex}
+Returns the infinity-norm, 1-norm, or 2-norm of a dense matrix.
+Can compute the 2-norm only for a dense column vector.
+All xtypes are supported.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_norm\_sparse}: sparse matrix norm}
+%---------------------------------------
+
+\input{_norm_sparse.tex}
+Returns the infinity-norm or 1-norm of a sparse matrix.
+All xtypes are supported.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_scale}: scale sparse matrix}
+%---------------------------------------
+
+\input{_scale.tex}
+Scales a matrix: {\tt A = diag(s)*A}, {\tt A*diag(s)}, {\tt s*A}, or {\tt diag(s)*A*diag(s)}.
+
+{\tt A} can be of any type (packed/unpacked, upper/lower/unsymmetric).
+The symmetry of {\tt A} is ignored; all entries in the matrix are modified.
+
+If {\tt A} is {\tt m}-by-{\tt n} unsymmetric but scaled symmetrically, the result is
+\begin{verbatim}
+ A = diag (s (1:m)) * A * diag (s (1:n))
+\end{verbatim}
+
+Row or column scaling of a symmetric matrix still results in a symmetric
+matrix, since entries are still ignored by other routines.
+For example, when row-scaling a symmetric matrix where just the upper
+triangular part is stored (and lower triangular entries ignored)
+{\tt A = diag(s)*triu(A)} is performed, where the result {\tt A} is also
+symmetric-upper. This has the effect of modifying the implicit lower
+triangular part. In MATLAB notation:
+\begin{verbatim}
+ U = diag(s)*triu(A) ;
+ L = tril (U',-1)
+ A = L + U ;
+\end{verbatim}
+
+The scale parameter determines the kind of scaling to perform and the size of {\tt S}:
+
+\begin{tabular}{lll}
+\hline
+{\tt scale} & operation & size of {\tt S} \\
+\hline
+{\tt CHOLMOD\_SCALAR} & {\tt s[0]*A} & 1 \\
+{\tt CHOLMOD\_ROW} & {\tt diag(s)*A} & {\tt nrow}-by-1 or 1-by-{\tt nrow} \\
+{\tt CHOLMOD\_COL} & {\tt A*diag(s)} & {\tt ncol}-by-1 or 1-by-{\tt ncol} \\
+{\tt CHOLMOD\_SYM} & {\tt diag(s)*A*diag(s)} & {\tt max(nrow,ncol)}-by-1, or 1-by-{\tt max(nrow,ncol)} \\
+\hline
+\end{tabular}
+
+Only real matrices are supported.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_sdmult}: sparse-times-dense matrix}
+%---------------------------------------
+
+\input{_sdmult.tex}
+Sparse matrix times dense matrix:
+{\tt Y = alpha*(A*X) + beta*Y} or {\tt Y = alpha*(A'*X) + beta*Y},
+where {\tt A} is sparse and {\tt X} and {\tt Y} are dense.
+When using {\tt A}, {\tt X} has {\tt A->ncol} columns and {\tt Y} has {\tt A->nrow} rows.
+When using {\tt A'}, {\tt X} has {\tt A->nrow} columns and {\tt Y} has {\tt A->ncol} rows.
+If {\tt transpose = 0}, then {\tt A} is used;
+otherwise, {\tt A'} is used (the complex conjugate transpose).
+The {\tt transpose} parameter is ignored if the matrix is symmetric or Hermitian.
+(the array transpose {\tt A.'} is not supported).
+Supports real, complex, and zomplex matrices, but the xtypes of {\tt A}, {\tt X}, and {\tt Y} must all match.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_ssmult}: sparse-times-sparse matrix}
+%---------------------------------------
+
+\input{_ssmult.tex}
+Computes {\tt C = A*B}; multiplying two sparse matrices.
+{\tt C} is returned as packed, and either unsorted or sorted, depending on the
+{\tt sorted} input parameter. If {\tt C} is returned sorted, then either {\tt C = (B'*A')'}
+or {\tt C = (A*B)''} is computed, depending on the number of nonzeros in {\tt A}, {\tt B}, and {\tt C}.
+The stype of {\tt C} is determined by the {\tt stype} parameter.
+Only pattern and real matrices are supported. Complex and zomplex matrices
+are supported only when the numerical values are not computed ({\tt values}
+is {\tt FALSE}).
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_submatrix}: sparse submatrix}
+%---------------------------------------
+
+\input{_submatrix.tex}
+Returns {\tt C = A (rset,cset)}, where {\tt C} becomes {\tt length(rset)}-by-{\tt length(cset)} in dimension.
+{\tt rset} and {\tt cset} can have duplicate entries. {\tt A} must be unsymmetric. {\tt C} unsymmetric and
+is packed. If {\tt sorted} is {\tt TRUE} on input, or {\tt rset} is sorted and {\tt A} is
+sorted, then {\tt C} is sorted; otherwise {\tt C} is unsorted.
+
+If {\tt rset} is {\tt NULL}, it means ``{\tt [ ]}'' in MATLAB notation, the empty set.
+The number of rows in the result {\tt C} will be zero if {\tt rset} is {\tt NULL}.
+Likewise if {\tt cset} means the empty set; the number of columns in the result {\tt C} will be zero if {\tt cset} is {\tt NULL}.
+If {\tt rsize} or {\tt csize} is negative, it denotes ``{\tt :}'' in MATLAB notation.
+Thus, if both {\tt rsize} and {\tt csize} are negative {\tt C = A(:,:) = A} is returned.
+
+For permuting a matrix, this routine is an alternative to {\tt cholmod\_ptranspose}
+(which permutes and transposes a matrix and can work on symmetric matrices).
+
+The time taken by this routine is O({\tt A->nrow}) if the {\tt Common} workspace needs
+to be initialized, plus O({\tt C->nrow + C->ncol + nnz (A (:,cset))}). Thus, if {\tt C}
+is small and the workspace is not initialized, the time can be dominated by
+the call to {\tt cholmod\_allocate\_work}. However, once the workspace is
+allocated, subsequent calls take less time.
+
+Only pattern and real matrices are supported. Complex and zomplex matrices
+are supported only when {\tt values} is {\tt FALSE}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_horzcat}: horizontal concatenation}
+%---------------------------------------
+
+\input{_horzcat.tex}
+Horizontal concatenation, returns {\tt C = [A,B]} in MATLAB notation.
+{\tt A} and {\tt B} can have any stype. {\tt C} is returned unsymmetric and packed.
+{\tt A} and {\tt B} must have the same number of rows.
+{\tt C} is sorted if both {\tt A} and {\tt B} are sorted.
+{\tt A} and {\tt B} must have the same numeric xtype, unless {\tt values} is {\tt FALSE}.
+{\tt A} and {\tt B} cannot be complex or zomplex, unless {\tt values} is {\tt FALSE}.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_vertcat}: vertical concatenation}
+%---------------------------------------
+
+\input{_vertcat.tex}
+Vertical concatenation, returns {\tt C = [A;B]} in MATLAB notation.
+{\tt A} and {\tt B} can have any stype. {\tt C} is returned unsymmetric and packed.
+{\tt A} and {\tt B} must have the same number of columns.
+{\tt C} is sorted if both {\tt A} and {\tt B} are sorted.
+{\tt A} and {\tt B} must have the same numeric xtype, unless {\tt values} is {\tt FALSE}.
+{\tt A} and {\tt B} cannot be complex or zomplex, unless {\tt values} is {\tt FALSE}.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_symmetry}: compute the symmetry of a matrix}
+%---------------------------------------
+
+\input{_symmetry.tex}
+
+Determines if a sparse matrix is rectangular, unsymmetric, symmetric,
+skew-symmetric, or Hermitian. It does so by looking at its numerical values
+of both upper and lower triangular parts of a CHOLMOD "unsymmetric"
+matrix, where A->stype == 0. The transpose of A is NOT constructed.
+
+If not unsymmetric, it also determines if the matrix has a diagonal whose
+entries are all real and positive (and thus a candidate for sparse Cholesky
+if A->stype is changed to a nonzero value).
+
+Note that a Matrix Market "general" matrix is either rectangular or
+unsymmetric.
+
+The row indices in the column of each matrix MUST be sorted for this function
+to work properly (A->sorted must be TRUE). This routine returns EMPTY if
+A->stype is not zero, or if A->sorted is FALSE. The exception to this rule
+is if A is rectangular.
+
+If option == 0, then this routine returns immediately when it finds a
+non-positive diagonal entry (or one with nonzero imaginary part). If the
+matrix is not a candidate for sparse Cholesky, it returns the value
+{\tt CHOLMOD\_MM\_UNSYMMETRIC}, even if the matrix might in fact be symmetric or
+Hermitian.
+
+This routine is useful inside the MATLAB backslash, which must look at an
+arbitrary matrix (A->stype == 0) and determine if it is a candidate for
+sparse Cholesky. In that case, option should be 0.
+
+This routine is also useful when writing a MATLAB matrix to a file in
+Rutherford/Boeing or Matrix Market format. Those formats require a
+determination as to the symmetry of the matrix, and thus this routine should
+not return upon encountering the first non-positive diagonal. In this case,
+option should be 1.
+
+If option is 2, this function can be used to compute the numerical and
+pattern symmetry, where 0 is a completely unsymmetric matrix, and 1 is a
+perfectly symmetric matrix. This option is used when computing the following
+statistics for the matrices in the UF Sparse Matrix Collection.
+
+ numerical symmetry: number of matched offdiagonal nonzeros over
+ the total number of offdiagonal entries. A real entry $a_{ij}$, $i \ne j$,
+ is matched if $a_{ji} = a_{ij}$, but this is only counted if both
+ $a_{ji}$ and $a_{ij}$ are nonzero. This does not depend on {\tt Z}.
+ (If A is complex, then the above test is modified; $a_{ij}$ is matched
+ if $\mbox{conj}(a_{ji}) = a_{ij}$.
+
+ Then numeric symmetry = xmatched / nzoffdiag, or 1 if nzoffdiag = 0.
+
+ pattern symmetry: number of matched offdiagonal entries over the
+ total number of offdiagonal entries. An entry $a_{ij}$, $i \ne j$, is
+ matched if $a_{ji}$ is also an entry.
+
+ Then pattern symmetry = pmatched / nzoffdiag, or 1 if nzoffdiag = 0.
+
+The symmetry of a matrix with no offdiagonal entries is equal to 1.
+
+A workspace of size ncol integers is allocated; EMPTY is returned if this
+allocation fails.
+
+Summary of return values:
+
+\begin{tabular}{ll}
+{\tt EMPTY (-1)} & out of memory, stype not zero, A not sorted \\
+{\tt CHOLMOD\_MM\_RECTANGULAR 1} & A is rectangular \\
+{\tt CHOLMOD\_MM\_UNSYMMETRIC 2} & A is unsymmetric \\
+{\tt CHOLMOD\_MM\_SYMMETRIC 3} & A is symmetric, but with non-pos. diagonal \\
+{\tt CHOLMOD\_MM\_HERMITIAN 4} & A is Hermitian, but with non-pos. diagonal \\
+{\tt CHOLMOD\_MM\_SKEW\_SYMMETRIC 5} & A is skew symmetric \\
+{\tt CHOLMOD\_MM\_SYMMETRIC\_POSDIAG 6} & A is symmetric with positive diagonal \\
+{\tt CHOLMOD\_MM\_HERMITIAN\_POSDIAG 7} & A is Hermitian with positive diagonal \\
+\end{tabular}
+
+See also the {\tt spsym} mexFunction, which is a MATLAB interface for this code.
+
+If the matrix is a candidate for sparse Cholesky, it will return a result
+\newline
+{\tt CHOLMOD\_MM\_SYMMETRIC\_POSDIAG} if real, or {\tt CHOLMOD\_MM\_HERMITIAN\_POSDIAG} if
+complex. Otherwise, it will return a value less than this. This is true
+regardless of the value of the option parameter.
+
+
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Supernodal} Module routines}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_super\_symbolic}: supernodal symbolic factorization}
+%---------------------------------------
+
+\input{_super_symbolic.tex}
+Supernodal symbolic analysis of the $\m{LL}\tr$ factorization of {\tt A}, {\tt A*A'}, or {\tt A(:,f)*A(:,f)'}.
+This routine must be preceded by a simplicial symbolic analysis
+({\tt cholmod\_rowcolcounts}). See {\tt Cholesky/cholmod\_analyze.c} for an example of how to use
+this routine.
+The user need not call this directly; {\tt cholmod\_analyze} is a ``simple'' wrapper for this routine.
+{\tt A} can be symmetric (upper), or unsymmetric. The symmetric/lower form is not supported.
+In the unsymmetric case {\tt F} is the normally transpose of {\tt A}.
+Alternatively, if {\tt F=A(:,f)'} then {\tt F*F'} is analyzed.
+Requires {\tt Parent} and {\tt L->ColCount} to be defined on input; these are the
+simplicial {\tt Parent} and {\tt ColCount} arrays as computed by {\tt cholmod\_rowcolcounts}.
+Does not use {\tt L->Perm}; the input matrices {\tt A} and {\tt F} must already be properly
+permuted. Allocates and computes the supernodal pattern of {\tt L}
+({\tt L->super}, {\tt L->pi}, {\tt L->px}, and {\tt L->s}).
+Does not allocate the real part ({\tt L->x}).
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_super\_numeric}: supernodal numeric factorization}
+%---------------------------------------
+
+\input{_super_numeric.tex}
+Computes the numerical Cholesky factorization of {\tt A+beta*I} or {\tt A*F+beta*I}. Only the
+lower triangular part of {\tt A+beta*I} or {\tt A*F+beta*I} is accessed. The
+matrices {\tt A} and {\tt F} must already be permuted according to the fill-reduction
+permutation {\tt L->Perm}. {\tt cholmod\_factorize} is an "easy" wrapper for this code
+which applies that permutation.
+The input scalar {\tt beta} is real; only the real part ({\tt beta[0]} is used.
+
+Symmetric case: {\tt A} is a symmetric (lower) matrix. {\tt F} is not accessed and may be {\tt NULL}.
+With a fill-reducing permutation, {\tt A(p,p)} should be passed for {\tt A}, where is
+{\tt p} is {\tt L->Perm}.
+
+Unsymmetric case: {\tt A} is unsymmetric, and {\tt F} must be present. Normally, {\tt F=A'}.
+With a fill-reducing permutation, {\tt A(p,f)} and {\tt A(p,f)'} should be passed as the
+parameters {\tt A} and {\tt F}, respectively, where {\tt f} is a list of the subset of the columns of {\tt A}.
+
+The input factorization {\tt L} must be supernodal ({\tt L->is\_super} is {\tt TRUE}). It can
+either be symbolic or numeric. In the first case, {\tt L} has been analyzed by
+{\tt cholmod\_analyze} or {\tt cholmod\_super\_symbolic}, but the matrix has not yet been
+numerically factorized. The numerical values are allocated here and the
+factorization is computed. In the second case, a prior matrix has been
+analyzed and numerically factorized, and a new matrix is being factorized.
+The numerical values of {\tt L} are replaced with the new numerical factorization.
+
+{\tt L->is\_ll} is ignored on input, and set to {\tt TRUE} on output. This routine always computes an $\m{LL}\tr$
+factorization. Supernodal $\m{LDL}\tr$ factorization is not supported.
+
+If the matrix is not positive definite the routine returns {\tt TRUE}, but sets
+{\tt Common->status} to {\tt CHOLMOD\_NOT\_POSDEF} and {\tt L->minor} is set to the column at
+which the failure occurred. Columns {\tt L->minor} to {\tt L->n-1} are set to zero.
+
+If {\tt L} is supernodal symbolic on input, it is converted to a supernodal numeric
+factor on output, with an xtype of real if {\tt A} is real, or complex if {\tt A} is
+complex or zomplex. If {\tt L} is supernodal numeric on input, its xtype must
+match {\tt A} (except that {\tt L} can be complex and {\tt A} zomplex). The xtype of {\tt A} and {\tt F}
+must match.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_super\_lsolve}: supernodal forward solve}
+%---------------------------------------
+
+\input{_super_lsolve.tex}
+Solve $\m{Lx}=\m{b}$ for a supernodal factorization. This routine does not
+apply the permutation {\tt L->Perm}. See {\tt cholmod\_solve} for a more general
+interface that performs that operation.
+Only real and complex xtypes are supported.
+{\tt L}, {\tt X}, and {\tt E} must have the same xtype.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_super\_ltsolve}: supernodal backsolve}
+%---------------------------------------
+
+\input{_super_ltsolve.tex}
+Solve $\m{L}\tr\m{x}=\m{b}$ for a supernodal factorization. This routine does not
+apply the permutation {\tt L->Perm}. See {\tt cholmod\_solve} for a more general
+interface that performs that operation.
+Only real and complex xtypes are supported.
+{\tt L}, {\tt X}, and {\tt E} must have the same xtype.
+
+%-------------------------------------------------------------------------------
+\newpage \section{{\tt Partition} Module routines}
+%-------------------------------------------------------------------------------
+
+%---------------------------------------
+\subsection{{\tt cholmod\_nested\_dissection}: nested dissection ordering}
+%---------------------------------------
+
+\input{_nested_dissection.tex}
+CHOLMOD's nested dissection algorithm:
+ using its own compression and connected-components
+ algorithms, an external graph partitioner (METIS), and a constrained
+ minimum degree ordering algorithm (CAMD, CCOLAMD, or CSYMAMD). Typically
+ gives better orderings than {\tt METIS\_NodeND} (about 5\% to 10\% fewer
+ nonzeros in {\tt L}).
+
+This method uses a node bisector, applied recursively (but using a
+non-recursive implementation). Once the graph is partitioned, it calls a
+constrained minimum degree code (CAMD or CSYMAMD for {\tt A+A'},
+and CCOLAMD for {\tt A*A'}) to
+order all the nodes in the graph - but obeying the constraints determined
+by the separators. This routine is similar to {\tt METIS\_NodeND}, except for
+how
+it treats the leaf nodes. {\tt METIS\_NodeND} orders the leaves of the separator
+tree with {\tt MMD}, ignoring the rest of the matrix when ordering a single leaf.
+This routine orders the whole matrix with CAMD, CSYMAMD, or CCOLAMD, all at once,
+when the graph partitioning is done.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_metis}: interface to METIS nested dissection}
+%---------------------------------------
+
+\input{_metis.tex}
+CHOLMOD wrapper for the {\tt METIS\_NodeND} ordering routine. Creates {\tt A+A'},
+{\tt A*A'} or {\tt A(:,f)*A(:,f)'} and then calls {\tt METIS\_NodeND} on the resulting graph.
+This routine is comparable to {\tt cholmod\_nested\_dissection}, except that it
+calls {\tt METIS\_NodeND} directly, and it does not return the separator tree.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_camd}: interface to CAMD}
+%---------------------------------------
+
+\input{_camd.tex}
+CHOLMOD interface to the CAMD ordering routine. Finds a permutation
+{\tt p} such that the Cholesky factorization of {\tt A(p,p)}
+is sparser than {\tt A}. If {\tt A} is unsymmetric,
+{\tt A*A'} is ordered.
+If {\tt Cmember[i]=c} then node {\tt i} is in set {\tt c}.
+All nodes in set 0 are ordered first, followed by all nodes in set 1, and so on.
+
+%---------------------------------------
+\newpage \subsection{{\tt cholmod\_ccolamd}: interface to CCOLAMD}
+%---------------------------------------
+
+\input{_ccolamd.tex}
+CHOLMOD interface to the CCOLAMD ordering routine. Finds a permutation
+{\tt p} such that the Cholesky factorization of {\tt A(p,:)*A(p,:)'} is sparser than {\tt A*A'}.
+The column elimination is found and postordered, and the CCOLAMD ordering is then
+combined with its postordering. {\tt A} must be unsymmetric.
+If {\tt Cmember[i]=c} then node {\tt i} is in set {\tt c}.
+All nodes in set 0 are ordered first, followed by all nodes in set 1, and so on.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_csymamd}: interface to CSYMAMD}
+%---------------------------------------
+
+\input{_csymamd.tex}
+CHOLMOD interface to the CSYMAMD ordering routine. Finds a permutation
+{\tt p} such that the Cholesky factorization of {\tt A(p,p)} is sparser than {\tt A}.
+The elimination tree is found and postordered, and the CSYMAMD
+ordering is then combined with its postordering. If {\tt A} is unsymmetric,
+{\tt A+A'} is ordered ({\tt A} must be square).
+If {\tt Cmember[i]=c} then node {\tt i} is in set {\tt c}.
+All nodes in set 0 are ordered first, followed by all nodes in set 1, and so on.
+
+%---------------------------------------
+\newpage
+\subsection{{\tt cholmod\_bisect}: graph bisector}
+%---------------------------------------
+
+\input{_bisect.tex}
+Finds a node bisector of {\tt A}, {\tt A*A'}, {\tt A(:,f)*A(:,f)'}:
+a set of nodes that partitions the graph into two parts.
+Compresses the graph first, and then calls METIS.
+
+%---------------------------------------
+\subsection{{\tt cholmod\_metis\_bisector}: interface to METIS node bisector}
+%---------------------------------------
+
+\input{_metis_bisector.tex}
+Finds a set of nodes that bisects the graph of {\tt A} or {\tt A*A'} (a direct interface to \newline
+{\tt METIS\_NodeComputeSeparator}).
+
+The input matrix {\tt A} must be square, symmetric (with both upper and lower
+parts present) and with no diagonal entries. These conditions are not
+checked.
+
+%---------------------------------------
+\newpage
+\subsection{{\tt cholmod\_collapse\_septree}: prune a separator tree}
+%---------------------------------------
+
+\input{_collapse_septree.tex}
+Prunes a separator tree obtained from {\tt cholmod\_nested\_dissection}.
+
+\newpage
+\bibliographystyle{plain}
+\bibliography{UserGuide}
+\end{document}
diff --git a/CHOLMOD/Doc/footer.tex b/CHOLMOD/Doc/footer.tex
new file mode 100644
index 0000000..112a2d1
--- /dev/null
+++ b/CHOLMOD/Doc/footer.tex
@@ -0,0 +1,6 @@
+\end{verbatim}
+}
+\noindent\hspace{0.85in}\rule[0.25in]{5.2in}{1pt}
+\vspace{-0.15in}
+
+\noindent {\bf Purpose:}
diff --git a/CHOLMOD/Doc/getmproto b/CHOLMOD/Doc/getmproto
new file mode 100755
index 0000000..644a48c
--- /dev/null
+++ b/CHOLMOD/Doc/getmproto
@@ -0,0 +1,4 @@
+#!/bin/sh
+cat mheader.tex
+expand -8 $1 | awk -f mfile.awk
+cat mfooter.tex
diff --git a/CHOLMOD/Doc/getproto b/CHOLMOD/Doc/getproto
new file mode 100755
index 0000000..b3b30a6
--- /dev/null
+++ b/CHOLMOD/Doc/getproto
@@ -0,0 +1,6 @@
+#!/bin/sh
+echo -n $1 > _temp.awk
+cat rule.awk >> _temp.awk
+cat header.tex
+expand -8 $2 | awk -f _temp.awk
+cat footer.tex
diff --git a/CHOLMOD/Doc/header.tex b/CHOLMOD/Doc/header.tex
new file mode 100644
index 0000000..4f28f1b
--- /dev/null
+++ b/CHOLMOD/Doc/header.tex
@@ -0,0 +1,4 @@
+\noindent\hspace{0.85in}\rule[0.05in]{5.2in}{1pt}
+\vspace{-0.15in}
+{\footnotesize
+\begin{verbatim}
diff --git a/CHOLMOD/Doc/mfile.awk b/CHOLMOD/Doc/mfile.awk
new file mode 100644
index 0000000..5106442
--- /dev/null
+++ b/CHOLMOD/Doc/mfile.awk
@@ -0,0 +1 @@
+/^%/ { print " ", substr ($0,2) }
diff --git a/CHOLMOD/Doc/mfooter.tex b/CHOLMOD/Doc/mfooter.tex
new file mode 100644
index 0000000..4bce503
--- /dev/null
+++ b/CHOLMOD/Doc/mfooter.tex
@@ -0,0 +1,4 @@
+\end{verbatim}
+}
+\noindent\hspace{0.85in}\rule[0.25in]{5.2in}{1pt}
+\vspace{-0.15in}
diff --git a/CHOLMOD/Doc/mheader.tex b/CHOLMOD/Doc/mheader.tex
new file mode 100644
index 0000000..90d3203
--- /dev/null
+++ b/CHOLMOD/Doc/mheader.tex
@@ -0,0 +1,5 @@
+
+\noindent\hspace{0.85in}\rule[0.05in]{5.2in}{1pt}
+\vspace{-0.15in}
+{\footnotesize
+\begin{verbatim}
diff --git a/CHOLMOD/Doc/rule.awk b/CHOLMOD/Doc/rule.awk
new file mode 100644
index 0000000..16e6ac1
--- /dev/null
+++ b/CHOLMOD/Doc/rule.awk
@@ -0,0 +1 @@
+{ print " ", $0 }
diff --git a/CHOLMOD/Include/License.txt b/CHOLMOD/Include/License.txt
new file mode 100644
index 0000000..cfca615
--- /dev/null
+++ b/CHOLMOD/Include/License.txt
@@ -0,0 +1,9 @@
+CHOLMOD/Include/* files.
+Copyright (C) 2005-2006, either Univ. of Florida or T. Davis,
+depending on the file.
+http://www.cise.ufl.edu/research/sparse
+
+Refer to each include file in this directory; each file is licensed
+separately, according to the Module for which it contains definitions
+and prototypes.
+
diff --git a/CHOLMOD/Include/README.txt b/CHOLMOD/Include/README.txt
new file mode 100644
index 0000000..387eb6e
--- /dev/null
+++ b/CHOLMOD/Include/README.txt
@@ -0,0 +1,25 @@
+CHOLMOD: a sparse Cholesky factorization package.
+
+The Include/*.h files in this directory provide a basic documentation of all
+user-callable routines and user-visible data structures in the CHOLMOD
+package. Start with cholmod.h, which describes the general structure of
+the parameter lists of CHOLMOD routines. cholmod_core.h describes the
+data structures and basic operations on them (creating and deleting them).
+
+cholmod.h single include file for all user programs
+cholmod_config.h CHOLMOD compile-time configuration
+
+cholmod_core.h Core module: data structures and basic support routines
+cholmod_check.h Check module: check/print CHOLMOD data structures
+cholmod_cholesky.h Cholesky module: LL' and LDL' factorization
+cholmod_matrixops.h MatrixOps module: sparse matrix operators (add, mult,..)
+cholmod_modify.h Modify module: update/downdate/...
+cholmod_partition.h Partition module: nested dissection ordering
+cholmod_supernodal.h Supernodal module: supernodal Cholesky
+
+These include files are not used in user programs, but in CHOLMOD only:
+
+cholmod_blas.h BLAS definitions
+cholmod_complexity.h complex arithmetic
+cholmod_template.h complex arithmetic for template routines
+cholmod_internal.h internal definitions, not visible to user program
diff --git a/CHOLMOD/Include/cholmod.h b/CHOLMOD/Include/cholmod.h
new file mode 100644
index 0000000..1332516
--- /dev/null
+++ b/CHOLMOD/Include/cholmod.h
@@ -0,0 +1,122 @@
+/* ========================================================================== */
+/* === Include/cholmod.h ==================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ *
+ * Portions of CHOLMOD (the Core and Partition Modules) are copyrighted by the
+ * University of Florida. The Modify Module is co-authored by William W.
+ * Hager, Univ. of Florida.
+ *
+ * Acknowledgements: this work was supported in part by the National Science
+ * Foundation (NFS CCR-0203270 and DMS-9803599), and a grant from Sandia
+ * National Laboratories (Dept. of Energy) which supported the development of
+ * CHOLMOD's Partition Module.
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD include file, for inclusion user programs.
+ *
+ * The include files listed below include a short description of each user-
+ * callable routine. Each routine in CHOLMOD has a consistent interface.
+ * More details about the CHOLMOD data types is in the cholmod_core.h file.
+ *
+ * Naming convention:
+ * ------------------
+ *
+ * All routine names, data types, and CHOLMOD library files use the
+ * cholmod_ prefix. All macros and other #define's use the CHOLMOD
+ * prefix.
+ *
+ * Return value:
+ * -------------
+ *
+ * Most CHOLMOD routines return an int (TRUE (1) if successful, or FALSE
+ * (0) otherwise. A UF_long or double return value is >= 0 if successful,
+ * or -1 otherwise. A size_t return value is > 0 if successful, or 0
+ * otherwise.
+ *
+ * If a routine returns a pointer, it is a pointer to a newly allocated
+ * object or NULL if a failure occured, with one exception. cholmod_free
+ * always returns NULL.
+ *
+ * "Common" parameter:
+ * ------------------
+ *
+ * The last parameter in all CHOLMOD routines is a pointer to the CHOLMOD
+ * "Common" object. This contains control parameters, statistics, and
+ * workspace used between calls to CHOLMOD. It is always an input/output
+ * parameter.
+ *
+ * Input, Output, and Input/Output parameters:
+ * -------------------------------------------
+ *
+ * Input parameters are listed first. They are not modified by CHOLMOD.
+ *
+ * Input/output are listed next. They must be defined on input, and
+ * are modified on output.
+ *
+ * Output parameters are listed next. If they are pointers, they must
+ * point to allocated space on input, but their contents are not defined
+ * on input.
+ *
+ * Workspace parameters appear next. They are used in only two routines
+ * in the Supernodal module.
+ *
+ * The cholmod_common *Common parameter always appears as the last
+ * parameter. It is always an input/output parameter.
+ */
+
+#ifndef CHOLMOD_H
+#define CHOLMOD_H
+
+/* make it easy for C++ programs to include CHOLMOD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* assume large file support. If problems occur, compile with -DNLARGEFILE */
+#include "cholmod_io64.h"
+
+/* define UF_long */
+#include "UFconfig.h"
+
+#include "cholmod_config.h"
+
+/* CHOLMOD always includes the Core module. */
+#include "cholmod_core.h"
+
+#ifndef NCHECK
+#include "cholmod_check.h"
+#endif
+
+#ifndef NCHOLESKY
+#include "cholmod_cholesky.h"
+#endif
+
+#ifndef NMATRIXOPS
+#include "cholmod_matrixops.h"
+#endif
+
+#ifndef NMODIFY
+#include "cholmod_modify.h"
+#endif
+
+#ifndef NPARTITION
+#include "cholmod_partition.h"
+#endif
+
+#ifndef NSUPERNODAL
+#include "cholmod_supernodal.h"
+#endif
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_blas.h b/CHOLMOD/Include/cholmod_blas.h
new file mode 100644
index 0000000..7957968
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_blas.h
@@ -0,0 +1,451 @@
+/* ========================================================================== */
+/* === Include/cholmod_blas.h =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_blas.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_blas.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* This does not need to be included in the user's program. */
+
+#ifndef CHOLMOD_BLAS_H
+#define CHOLMOD_BLAS_H
+
+/* ========================================================================== */
+/* === Architecture ========================================================= */
+/* ========================================================================== */
+
+#if defined (__sun) || defined (MSOL2) || defined (ARCH_SOL2)
+#define CHOLMOD_SOL2
+#define CHOLMOD_ARCHITECTURE "Sun Solaris"
+
+#elif defined (__sgi) || defined (MSGI) || defined (ARCH_SGI)
+#define CHOLMOD_SGI
+#define CHOLMOD_ARCHITECTURE "SGI Irix"
+
+#elif defined (__linux) || defined (MGLNX86) || defined (ARCH_GLNX86)
+#define CHOLMOD_LINUX
+#define CHOLMOD_ARCHITECTURE "Linux"
+
+#elif defined (_AIX) || defined (MIBM_RS) || defined (ARCH_IBM_RS)
+#define CHOLMOD_AIX
+#define CHOLMOD_ARCHITECTURE "IBM AIX"
+#define BLAS_NO_UNDERSCORE
+
+#elif defined (__alpha) || defined (MALPHA) || defined (ARCH_ALPHA)
+#define CHOLMOD_ALPHA
+#define CHOLMOD_ARCHITECTURE "Compaq Alpha"
+
+#elif defined (_WIN32) || defined (WIN32) || defined (_WIN64) || defined (WIN64)
+#if defined (__MINGW32__) || defined (__MINGW32__)
+#define CHOLMOD_MINGW
+#elif defined (__CYGWIN32__) || defined (__CYGWIN32__)
+#define CHOLMOD_CYGWIN
+#else
+#define CHOLMOD_WINDOWS
+#define BLAS_NO_UNDERSCORE
+#endif
+#define CHOLMOD_ARCHITECTURE "Microsoft Windows"
+
+#elif defined (__hppa) || defined (__hpux) || defined (MHPUX) || defined (ARCH_HPUX)
+#define CHOLMOD_HP
+#define CHOLMOD_ARCHITECTURE "HP Unix"
+#define BLAS_NO_UNDERSCORE
+
+#elif defined (__hp700) || defined (MHP700) || defined (ARCH_HP700)
+#define CHOLMOD_HP
+#define CHOLMOD_ARCHITECTURE "HP 700 Unix"
+#define BLAS_NO_UNDERSCORE
+
+#else
+/* If the architecture is unknown, and you call the BLAS, you may need to */
+/* define BLAS_BY_VALUE, BLAS_NO_UNDERSCORE, and/or BLAS_CHAR_ARG yourself. */
+#define CHOLMOD_ARCHITECTURE "unknown"
+#endif
+
+
+/* ========================================================================== */
+/* === BLAS and LAPACK names ================================================ */
+/* ========================================================================== */
+
+/* Prototypes for the various versions of the BLAS. */
+
+/* Determine if the 64-bit Sun Performance BLAS is to be used */
+#if defined(CHOLMOD_SOL2) && !defined(NSUNPERF) && defined(LONG) && defined(LONGBLAS)
+#define SUN64
+#endif
+
+#ifdef SUN64
+
+#define BLAS_DTRSV dtrsv_64_
+#define BLAS_DGEMV dgemv_64_
+#define BLAS_DTRSM dtrsm_64_
+#define BLAS_DGEMM dgemm_64_
+#define BLAS_DSYRK dsyrk_64_
+#define BLAS_DGER dger_64_
+#define BLAS_DSCAL dscal_64_
+#define LAPACK_DPOTRF dpotrf_64_
+
+#define BLAS_ZTRSV ztrsv_64_
+#define BLAS_ZGEMV zgemv_64_
+#define BLAS_ZTRSM ztrsm_64_
+#define BLAS_ZGEMM zgemm_64_
+#define BLAS_ZHERK zherk_64_
+#define BLAS_ZGER zgeru_64_
+#define BLAS_ZSCAL zscal_64_
+#define LAPACK_ZPOTRF zpotrf_64_
+
+#elif defined (BLAS_NO_UNDERSCORE)
+
+#define BLAS_DTRSV dtrsv
+#define BLAS_DGEMV dgemv
+#define BLAS_DTRSM dtrsm
+#define BLAS_DGEMM dgemm
+#define BLAS_DSYRK dsyrk
+#define BLAS_DGER dger
+#define BLAS_DSCAL dscal
+#define LAPACK_DPOTRF dpotrf
+
+#define BLAS_ZTRSV ztrsv
+#define BLAS_ZGEMV zgemv
+#define BLAS_ZTRSM ztrsm
+#define BLAS_ZGEMM zgemm
+#define BLAS_ZHERK zherk
+#define BLAS_ZGER zgeru
+#define BLAS_ZSCAL zscal
+#define LAPACK_ZPOTRF zpotrf
+
+#else
+
+#define BLAS_DTRSV dtrsv_
+#define BLAS_DGEMV dgemv_
+#define BLAS_DTRSM dtrsm_
+#define BLAS_DGEMM dgemm_
+#define BLAS_DSYRK dsyrk_
+#define BLAS_DGER dger_
+#define BLAS_DSCAL dscal_
+#define LAPACK_DPOTRF dpotrf_
+
+#define BLAS_ZTRSV ztrsv_
+#define BLAS_ZGEMV zgemv_
+#define BLAS_ZTRSM ztrsm_
+#define BLAS_ZGEMM zgemm_
+#define BLAS_ZHERK zherk_
+#define BLAS_ZGER zgeru_
+#define BLAS_ZSCAL zscal_
+#define LAPACK_ZPOTRF zpotrf_
+
+#endif
+
+/* ========================================================================== */
+/* === BLAS and LAPACK integer arguments ==================================== */
+/* ========================================================================== */
+
+/* CHOLMOD can be compiled with -D'LONGBLAS=long' for the Sun Performance
+ * Library, or -D'LONGBLAS=long long' for SGI's SCSL BLAS. This defines the
+ * integer used in the BLAS for the cholmod_l_* routines.
+ *
+ * The "int" version of CHOLMOD always uses the "int" version of the BLAS.
+ */
+
+#if defined (LONGBLAS) && defined (LONG)
+#define BLAS_INT LONGBLAS
+#else
+#define BLAS_INT int
+#endif
+
+/* If the BLAS integer is smaller than the basic CHOLMOD integer, then we need
+ * to check for integer overflow when converting from one to the other. If
+ * any integer overflows, the externally-defined blas_ok variable is set to
+ * FALSE. blas_ok should be set to TRUE before calling any BLAS_* macro.
+ */
+
+#define CHECK_BLAS_INT (sizeof (BLAS_INT) < sizeof (Int))
+#define EQ(K,k) (((BLAS_INT) K) == ((Int) k))
+
+/* ========================================================================== */
+/* === BLAS and LAPACK prototypes and macros ================================ */
+/* ========================================================================== */
+
+void BLAS_DGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta,
+ double *Y, BLAS_INT *incy) ;
+
+#define BLAS_dgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_ZGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta,
+ double *Y, BLAS_INT *incy) ;
+
+#define BLAS_zgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_DTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A,
+ BLAS_INT *lda, double *X, BLAS_INT *incx) ;
+
+#define BLAS_dtrsv(uplo,trans,diag,n,A,lda,X,incx) \
+{ \
+ BLAS_INT N = n, LDA = lda, INCX = incx ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \
+ } \
+}
+
+void BLAS_ZTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A,
+ BLAS_INT *lda, double *X, BLAS_INT *incx) ;
+
+#define BLAS_ztrsv(uplo,trans,diag,n,A,lda,X,incx) \
+{ \
+ BLAS_INT N = n, LDA = lda, INCX = incx ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \
+ } \
+}
+
+void BLAS_DTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m,
+ BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb) ;
+
+#define BLAS_dtrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\
+ } \
+}
+
+void BLAS_ZTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m,
+ BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb) ;
+
+#define BLAS_ztrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\
+ } \
+}
+
+void BLAS_DGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n,
+ BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ;
+
+#define BLAS_dgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \
+{ \
+ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \
+ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \
+ C, &LDC) ; \
+ } \
+}
+
+void BLAS_ZGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n,
+ BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ;
+
+#define BLAS_zgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \
+{ \
+ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \
+ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \
+ C, &LDC) ; \
+ } \
+}
+
+void BLAS_DSYRK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k,
+ double *alpha, double *A, BLAS_INT *lda, double *beta, double *C,
+ BLAS_INT *ldc) ;
+
+#define BLAS_dsyrk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \
+{ \
+ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DSYRK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \
+ } \
+} \
+
+void BLAS_ZHERK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k,
+ double *alpha, double *A, BLAS_INT *lda, double *beta, double *C,
+ BLAS_INT *ldc) ;
+
+#define BLAS_zherk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \
+{ \
+ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZHERK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \
+ } \
+} \
+
+void LAPACK_DPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda,
+ BLAS_INT *info) ;
+
+#define LAPACK_dpotrf(uplo,n,A,lda,info) \
+{ \
+ BLAS_INT N = n, LDA = lda, INFO = 1 ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \
+ } \
+ if (blas_ok) \
+ { \
+ LAPACK_DPOTRF (uplo, &N, A, &LDA, &INFO) ; \
+ } \
+ info = INFO ; \
+}
+
+void LAPACK_ZPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda,
+ BLAS_INT *info) ;
+
+#define LAPACK_zpotrf(uplo,n,A,lda,info) \
+{ \
+ BLAS_INT N = n, LDA = lda, INFO = 1 ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \
+ } \
+ if (blas_ok) \
+ { \
+ LAPACK_ZPOTRF (uplo, &N, A, &LDA, &INFO) ; \
+ } \
+ info = INFO ; \
+}
+
+/* ========================================================================== */
+
+void BLAS_DSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ;
+
+#define BLAS_dscal(n,alpha,Y,incy) \
+{ \
+ BLAS_INT N = n, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DSCAL (&N, alpha, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_ZSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ;
+
+#define BLAS_zscal(n,alpha,Y,incy) \
+{ \
+ BLAS_INT N = n, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZSCAL (&N, alpha, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_DGER (BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy,
+ double *A, BLAS_INT *lda) ;
+
+#define BLAS_dger(m,n,alpha,X,incx,Y,incy,A,lda) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \
+ } \
+}
+
+void BLAS_ZGER (BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy,
+ double *A, BLAS_INT *lda) ;
+
+#define BLAS_zgeru(m,n,alpha,X,incx,Y,incy,A,lda) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \
+ } \
+}
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_check.h b/CHOLMOD/Include/cholmod_check.h
new file mode 100644
index 0000000..58e4ad0
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_check.h
@@ -0,0 +1,417 @@
+/* ========================================================================== */
+/* === Include/cholmod_check.h ============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_check.h. Copyright (C) 2005-2006, Timothy A. Davis
+ * CHOLMOD/Include/cholmod_check.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Check module.
+ *
+ * Routines that check and print the 5 basic data types in CHOLMOD, and 3 kinds
+ * of integer vectors (subset, perm, and parent), and read in matrices from a
+ * file:
+ *
+ * cholmod_check_common check/print the Common object
+ * cholmod_print_common
+ *
+ * cholmod_check_sparse check/print a sparse matrix in column-oriented form
+ * cholmod_print_sparse
+ *
+ * cholmod_check_dense check/print a dense matrix
+ * cholmod_print_dense
+ *
+ * cholmod_check_factor check/print a Cholesky factorization
+ * cholmod_print_factor
+ *
+ * cholmod_check_triplet check/print a sparse matrix in triplet form
+ * cholmod_print_triplet
+ *
+ * cholmod_check_subset check/print a subset (integer vector in given range)
+ * cholmod_print_subset
+ *
+ * cholmod_check_perm check/print a permutation (an integer vector)
+ * cholmod_print_perm
+ *
+ * cholmod_check_parent check/print an elimination tree (an integer vector)
+ * cholmod_print_parent
+ *
+ * cholmod_read_triplet read a matrix in triplet form (any Matrix Market
+ * "coordinate" format, or a generic triplet format).
+ *
+ * cholmod_read_sparse read a matrix in sparse form (same file format as
+ * cholmod_read_triplet).
+ *
+ * cholmod_read_dense read a dense matrix (any Matrix Market "array"
+ * format, or a generic dense format).
+ *
+ * cholmod_write_sparse write a sparse matrix to a Matrix Market file.
+ *
+ * cholmod_write_dense write a dense matrix to a Matrix Market file.
+ *
+ * cholmod_print_common and cholmod_check_common are the only two routines that
+ * you may call after calling cholmod_finish.
+ *
+ * Requires the Core module. Not required by any CHOLMOD module, except when
+ * debugging is enabled (in which case all modules require the Check module).
+ *
+ * See cholmod_read.c for a description of the file formats supported by the
+ * cholmod_read_* routines.
+ */
+
+#ifndef CHOLMOD_CHECK_H
+#define CHOLMOD_CHECK_H
+
+#include "cholmod_core.h"
+#include <stdio.h>
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_common: check the Common object */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_common
+(
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_common (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_common: print the Common object */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_common
+(
+ /* ---- input ---- */
+ char *name, /* printed name of Common object */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_common (char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_sparse: check a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_sparse
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_sparse (cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_sparse */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_sparse
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to print */
+ char *name, /* printed name of sparse matrix */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_sparse (cholmod_sparse *, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_dense: check a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_dense
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* dense matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_dense (cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_dense: print a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_dense
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* dense matrix to print */
+ char *name, /* printed name of dense matrix */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_dense (cholmod_dense *, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_factor: check a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_factor
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to check */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_factor (cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_factor: print a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_factor
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to print */
+ char *name, /* printed name of factor */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_factor (cholmod_factor *, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_triplet: check a sparse matrix in triplet form */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_triplet
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* triplet matrix to check */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_triplet (cholmod_triplet *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_triplet: print a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_triplet
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* triplet matrix to print */
+ char *name, /* printed name of triplet matrix */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_triplet (cholmod_triplet *, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_subset: check a subset */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_subset
+(
+ /* ---- input ---- */
+ int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */
+ UF_long len, /* size of Set (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_subset (UF_long *, UF_long, size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_subset: print a subset */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_subset
+(
+ /* ---- input ---- */
+ int *Set, /* Set [0:len-1] is a subset of 0:n-1. Duplicates OK */
+ UF_long len, /* size of Set (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ char *name, /* printed name of Set */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_subset (UF_long *, UF_long, size_t, char *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_perm: check a permutation */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_perm
+(
+ /* ---- input ---- */
+ int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */
+ size_t len, /* size of Perm (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_perm (UF_long *, size_t, size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_perm: print a permutation vector */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_perm
+(
+ /* ---- input ---- */
+ int *Perm, /* Perm [0:len-1] is a permutation of subset of 0:n-1 */
+ size_t len, /* size of Perm (an integer array) */
+ size_t n, /* 0:n-1 is valid range */
+ char *name, /* printed name of Perm */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_perm (UF_long *, size_t, size_t, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_check_parent: check an elimination tree */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_check_parent
+(
+ /* ---- input ---- */
+ int *Parent, /* Parent [0:n-1] is an elimination tree */
+ size_t n, /* size of Parent */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_check_parent (UF_long *, size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_print_parent */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_print_parent
+(
+ /* ---- input ---- */
+ int *Parent, /* Parent [0:n-1] is an elimination tree */
+ size_t n, /* size of Parent */
+ char *name, /* printed name of Parent */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_print_parent (UF_long *, size_t, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_read_sparse: read a sparse matrix from a file */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_read_sparse
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_read_sparse (FILE *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_read_triplet: read a triplet matrix from a file */
+/* -------------------------------------------------------------------------- */
+
+cholmod_triplet *cholmod_read_triplet
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_triplet *cholmod_l_read_triplet (FILE *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_read_dense: read a dense matrix from a file */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_read_dense
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_read_dense (FILE *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_read_matrix: read a sparse or dense matrix from a file */
+/* -------------------------------------------------------------------------- */
+
+void *cholmod_read_matrix
+(
+ /* ---- input ---- */
+ FILE *f, /* file to read from, must already be open */
+ int prefer, /* If 0, a sparse matrix is always return as a
+ * cholmod_triplet form. It can have any stype
+ * (symmetric-lower, unsymmetric, or
+ * symmetric-upper).
+ * If 1, a sparse matrix is returned as an unsymmetric
+ * cholmod_sparse form (A->stype == 0), with both
+ * upper and lower triangular parts present.
+ * This is what the MATLAB mread mexFunction does,
+ * since MATLAB does not have an stype.
+ * If 2, a sparse matrix is returned with an stype of 0
+ * or 1 (unsymmetric, or symmetric with upper part
+ * stored).
+ * This argument has no effect for dense matrices.
+ */
+ /* ---- output---- */
+ int *mtype, /* CHOLMOD_TRIPLET, CHOLMOD_SPARSE or CHOLMOD_DENSE */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+void *cholmod_l_read_matrix (FILE *, int, int *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_write_sparse: write a sparse matrix to a file */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_write_sparse
+(
+ /* ---- input ---- */
+ FILE *f, /* file to write to, must already be open */
+ cholmod_sparse *A, /* matrix to print */
+ cholmod_sparse *Z, /* optional matrix with pattern of explicit zeros */
+ char *comments, /* optional filename of comments to include */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_write_sparse (FILE *, cholmod_sparse *, cholmod_sparse *,
+ char *c, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_write_dense: write a dense matrix to a file */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_write_dense
+(
+ /* ---- input ---- */
+ FILE *f, /* file to write to, must already be open */
+ cholmod_dense *X, /* matrix to print */
+ char *comments, /* optional filename of comments to include */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_write_dense (FILE *, cholmod_dense *, char *, cholmod_common *) ;
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_cholesky.h b/CHOLMOD/Include/cholmod_cholesky.h
new file mode 100644
index 0000000..7388afb
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_cholesky.h
@@ -0,0 +1,498 @@
+/* ========================================================================== */
+/* === Include/cholmod_cholesky.h =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_cholesky.h. Copyright (C) 2005-2006, Timothy A. Davis
+ * CHOLMOD/Include/cholmod_cholesky.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Cholesky module.
+ *
+ * Sparse Cholesky routines: analysis, factorization, and solve.
+ *
+ * The primary routines are all that a user requires to order, analyze, and
+ * factorize a sparse symmetric positive definite matrix A (or A*A'), and
+ * to solve Ax=b (or A*A'x=b). The primary routines rely on the secondary
+ * routines, the CHOLMOD Core module, and the AMD and COLAMD packages. They
+ * make optional use of the CHOLMOD Supernodal and Partition modules, the
+ * METIS package, and the CCOLAMD package.
+ *
+ * Primary routines:
+ * -----------------
+ *
+ * cholmod_analyze order and analyze (simplicial or supernodal)
+ * cholmod_factorize simplicial or supernodal Cholesky factorization
+ * cholmod_solve solve a linear system (simplicial or supernodal)
+ * cholmod_spsolve solve a linear system (sparse x and b)
+ *
+ * Secondary routines:
+ * ------------------
+ *
+ * cholmod_analyze_p analyze, with user-provided permutation or f set
+ * cholmod_factorize_p factorize, with user-provided permutation or f
+ * cholmod_analyze_ordering analyze a fill-reducing ordering
+ * cholmod_etree find the elimination tree
+ * cholmod_rowcolcounts compute the row/column counts of L
+ * cholmod_amd order using AMD
+ * cholmod_colamd order using COLAMD
+ * cholmod_rowfac incremental simplicial factorization
+ * cholmod_rowfac_mask rowfac, specific to LPDASA
+ * cholmod_row_subtree find the nonzero pattern of a row of L
+ * cholmod_resymbol recompute the symbolic pattern of L
+ * cholmod_resymbol_noperm recompute the symbolic pattern of L, no L->Perm
+ * cholmod_postorder postorder a tree
+ *
+ * Requires the Core module, and two packages: AMD and COLAMD.
+ * Optionally uses the Supernodal and Partition modules.
+ * Required by the Partition module.
+ */
+
+#ifndef CHOLMOD_CHOLESKY_H
+#define CHOLMOD_CHOLESKY_H
+
+#include "cholmod_config.h"
+#include "cholmod_core.h"
+
+#ifndef NPARTITION
+#include "cholmod_partition.h"
+#endif
+
+#ifndef NSUPERNODAL
+#include "cholmod_supernodal.h"
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_analyze: order and analyze (simplicial or supernodal) */
+/* -------------------------------------------------------------------------- */
+
+/* Orders and analyzes A, AA', PAP', or PAA'P' and returns a symbolic factor
+ * that can later be passed to cholmod_factorize. */
+
+cholmod_factor *cholmod_analyze
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order and analyze */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_factor *cholmod_l_analyze (cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_analyze_p: analyze, with user-provided permutation or f set */
+/* -------------------------------------------------------------------------- */
+
+/* Orders and analyzes A, AA', PAP', PAA'P', FF', or PFF'P and returns a
+ * symbolic factor that can later be passed to cholmod_factorize, where
+ * F = A(:,fset) if fset is not NULL and A->stype is zero.
+ * UserPerm is tried if non-NULL. */
+
+cholmod_factor *cholmod_analyze_p
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order and analyze */
+ int *UserPerm, /* user-provided permutation, size A->nrow */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_factor *cholmod_l_analyze_p (cholmod_sparse *, UF_long *, UF_long *,
+ size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_factorize: simplicial or supernodal Cholesky factorization */
+/* -------------------------------------------------------------------------- */
+
+/* Factorizes PAP' (or PAA'P' if A->stype is 0), using a factor obtained
+ * from cholmod_analyze. The analysis can be re-used simply by calling this
+ * routine a second time with another matrix. A must have the same nonzero
+ * pattern as that passed to cholmod_analyze. */
+
+int cholmod_factorize
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* resulting factorization */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_factorize (cholmod_sparse *, cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_factorize_p: factorize, with user-provided permutation or fset */
+/* -------------------------------------------------------------------------- */
+
+/* Same as cholmod_factorize, but with more options. */
+
+int cholmod_factorize_p
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ double beta [2], /* factorize beta*I+A or beta*I+A'*A */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* resulting factorization */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_factorize_p (cholmod_sparse *, double *, UF_long *, size_t,
+ cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_solve: solve a linear system (simplicial or supernodal) */
+/* -------------------------------------------------------------------------- */
+
+/* Solves one of many linear systems with a dense right-hand-side, using the
+ * factorization from cholmod_factorize (or as modified by any other CHOLMOD
+ * routine). D is identity for LL' factorizations. */
+
+#define CHOLMOD_A 0 /* solve Ax=b */
+#define CHOLMOD_LDLt 1 /* solve LDL'x=b */
+#define CHOLMOD_LD 2 /* solve LDx=b */
+#define CHOLMOD_DLt 3 /* solve DL'x=b */
+#define CHOLMOD_L 4 /* solve Lx=b */
+#define CHOLMOD_Lt 5 /* solve L'x=b */
+#define CHOLMOD_D 6 /* solve Dx=b */
+#define CHOLMOD_P 7 /* permute x=Px */
+#define CHOLMOD_Pt 8 /* permute x=P'x */
+
+cholmod_dense *cholmod_solve /* returns the solution X */
+(
+ /* ---- input ---- */
+ int sys, /* system to solve */
+ cholmod_factor *L, /* factorization to use */
+ cholmod_dense *B, /* right-hand-side */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_solve (int, cholmod_factor *, cholmod_dense *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_spsolve: solve a linear system with a sparse right-hand-side */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_spsolve
+(
+ /* ---- input ---- */
+ int sys, /* system to solve */
+ cholmod_factor *L, /* factorization to use */
+ cholmod_sparse *B, /* right-hand-side */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_spsolve (int, cholmod_factor *, cholmod_sparse *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_etree: find the elimination tree of A or A'*A */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_etree
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ /* ---- output --- */
+ int *Parent, /* size ncol. Parent [j] = p if p is the parent of j */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_etree (cholmod_sparse *, UF_long *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowcolcounts: compute the row/column counts of L */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_rowcolcounts
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int *Parent, /* size nrow. Parent [i] = p if p is the parent of i */
+ int *Post, /* size nrow. Post [k] = i if i is the kth node in
+ * the postordered etree. */
+ /* ---- output --- */
+ int *RowCount, /* size nrow. RowCount [i] = # entries in the ith row of
+ * L, including the diagonal. */
+ int *ColCount, /* size nrow. ColCount [i] = # entries in the ith
+ * column of L, including the diagonal. */
+ int *First, /* size nrow. First [i] = k is the least postordering
+ * of any descendant of i. */
+ int *Level, /* size nrow. Level [i] is the length of the path from
+ * i to the root, with Level [root] = 0. */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowcolcounts (cholmod_sparse *, UF_long *, size_t, UF_long *,
+ UF_long *, UF_long *, UF_long *, UF_long *, UF_long *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_analyze_ordering: analyze a fill-reducing ordering */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_analyze_ordering
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int ordering, /* ordering method used */
+ int *Perm, /* size n, fill-reducing permutation to analyze */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ int *Parent, /* size n, elimination tree */
+ int *Post, /* size n, postordering of elimination tree */
+ int *ColCount, /* size n, nnz in each column of L */
+ /* ---- workspace */
+ int *First, /* size nworkspace for cholmod_postorder */
+ int *Level, /* size n workspace for cholmod_postorder */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_analyze_ordering (cholmod_sparse *, int, UF_long *, UF_long *,
+ size_t, UF_long *, UF_long *, UF_long *, UF_long *, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_amd: order using AMD */
+/* -------------------------------------------------------------------------- */
+
+/* Finds a permutation P to reduce fill-in in the factorization of P*A*P'
+ * or P*A*A'P' */
+
+int cholmod_amd
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_amd (cholmod_sparse *, UF_long *, size_t, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_colamd: order using COLAMD */
+/* -------------------------------------------------------------------------- */
+
+/* Finds a permutation P to reduce fill-in in the factorization of P*A*A'*P'.
+ * Orders F*F' where F = A (:,fset) if fset is not NULL */
+
+int cholmod_colamd
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int postorder, /* if TRUE, follow with a coletree postorder */
+ /* ---- output --- */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_colamd (cholmod_sparse *, UF_long *, size_t, int, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowfac: incremental simplicial factorization */
+/* -------------------------------------------------------------------------- */
+
+/* Partial or complete simplicial factorization. Rows and columns kstart:kend-1
+ * of L and D must be initially equal to rows/columns kstart:kend-1 of the
+ * identity matrix. Row k can only be factorized if all descendants of node
+ * k in the elimination tree have been factorized. */
+
+int cholmod_rowfac
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */
+ double beta [2], /* factorize beta*I+A or beta*I+A'*A */
+ size_t kstart, /* first row to factorize */
+ size_t kend, /* last row to factorize is kend-1 */
+ /* ---- in/out --- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowfac (cholmod_sparse *, cholmod_sparse *, double *, size_t,
+ size_t, cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowfac_mask: incremental simplicial factorization */
+/* -------------------------------------------------------------------------- */
+
+/* cholmod_rowfac_mask is a version of cholmod_rowfac that is specific to
+ * LPDASA. It is unlikely to be needed by any other application. */
+
+int cholmod_rowfac_mask
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */
+ double beta [2], /* factorize beta*I+A or beta*I+A'*A */
+ size_t kstart, /* first row to factorize */
+ size_t kend, /* last row to factorize is kend-1 */
+ int *mask, /* if mask[i] >= 0, then set row i to zero */
+ int *RLinkUp, /* link list of rows to compute */
+ /* ---- in/out --- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowfac_mask (cholmod_sparse *, cholmod_sparse *, double *, size_t,
+ size_t, UF_long *, UF_long *, cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_row_subtree: find the nonzero pattern of a row of L */
+/* -------------------------------------------------------------------------- */
+
+/* Find the nonzero pattern of x for the system Lx=b where L = (0:k-1,0:k-1)
+ * and b = kth column of A or A*A' (rows 0 to k-1 only) */
+
+int cholmod_row_subtree
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ cholmod_sparse *F, /* used for A*A' case only. F=A' or A(:,fset)' */
+ size_t k, /* row k of L */
+ int *Parent, /* elimination tree */
+ /* ---- output --- */
+ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_row_subtree (cholmod_sparse *, cholmod_sparse *, size_t,
+ UF_long *, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_row_lsubtree: find the nonzero pattern of a row of L */
+/* -------------------------------------------------------------------------- */
+
+/* Identical to cholmod_row_subtree, except that it finds the elimination tree
+ * from L itself. */
+
+int cholmod_row_lsubtree
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int *Fi, size_t fnz, /* nonzero pattern of kth row of A', not required
+ * for the symmetric case. Need not be sorted. */
+ size_t k, /* row k of L */
+ cholmod_factor *L, /* the factor L from which parent(i) is derived */
+ /* ---- output --- */
+ cholmod_sparse *R, /* pattern of L(k,:), 1-by-n with R->nzmax >= n */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_row_lsubtree (cholmod_sparse *, UF_long *, size_t,
+ size_t, cholmod_factor *, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_resymbol: recompute the symbolic pattern of L */
+/* -------------------------------------------------------------------------- */
+
+/* Remove entries from L that are not in the factorization of P*A*P', P*A*A'*P',
+ * or P*F*F'*P' (depending on A->stype and whether fset is NULL or not).
+ *
+ * cholmod_resymbol is the same as cholmod_resymbol_noperm, except that it
+ * first permutes A according to L->Perm. A can be upper/lower/unsymmetric,
+ * in contrast to cholmod_resymbol_noperm (which can be lower or unsym). */
+
+int cholmod_resymbol
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int pack, /* if TRUE, pack the columns of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization, entries pruned on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_resymbol (cholmod_sparse *, UF_long *, size_t, int,
+ cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_resymbol_noperm: recompute the symbolic pattern of L, no L->Perm */
+/* -------------------------------------------------------------------------- */
+
+/* Remove entries from L that are not in the factorization of A, A*A',
+ * or F*F' (depending on A->stype and whether fset is NULL or not). */
+
+int cholmod_resymbol_noperm
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int pack, /* if TRUE, pack the columns of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization, entries pruned on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_resymbol_noperm (cholmod_sparse *, UF_long *, size_t, int,
+ cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rcond: compute rough estimate of reciprocal of condition number */
+/* -------------------------------------------------------------------------- */
+
+double cholmod_rcond /* return min(diag(L)) / max(diag(L)) */
+(
+ /* ---- input ---- */
+ cholmod_factor *L,
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+double cholmod_l_rcond (cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_postorder: Compute the postorder of a tree */
+/* -------------------------------------------------------------------------- */
+
+UF_long cholmod_postorder /* return # of nodes postordered */
+(
+ /* ---- input ---- */
+ int *Parent, /* size n. Parent [j] = p if p is the parent of j */
+ size_t n,
+ int *Weight_p, /* size n, optional. Weight [j] is weight of node j */
+ /* ---- output --- */
+ int *Post, /* size n. Post [k] = j is kth in postordered tree */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_postorder (UF_long *, size_t, UF_long *, UF_long *,
+ cholmod_common *) ;
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_complexity.h b/CHOLMOD/Include/cholmod_complexity.h
new file mode 100644
index 0000000..a84583a
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_complexity.h
@@ -0,0 +1,264 @@
+/* ========================================================================== */
+/* === Include/cholmod_complexity.h ========================================= */
+/* ========================================================================== */
+
+/* Define operations on pattern, real, complex, and zomplex objects.
+ *
+ * The xtype of an object defines it numerical type. A qttern object has no
+ * numerical values (A->x and A->z are NULL). A real object has no imaginary
+ * qrt (A->x is used, A->z is NULL). A complex object has an imaginary qrt
+ * that is stored interleaved with its real qrt (A->x is of size 2*nz, A->z
+ * is NULL). A zomplex object has both real and imaginary qrts, which are
+ * stored seqrately, as in MATLAB (A->x and A->z are both used).
+ *
+ * XTYPE is CHOLMOD_PATTERN, _REAL, _COMPLEX or _ZOMPLEX, and is the xtype of
+ * the template routine under construction. XTYPE2 is equal to XTYPE, except
+ * if XTYPE is CHOLMOD_PATTERN, in which case XTYPE is CHOLMOD_REAL.
+ * XTYPE and XTYPE2 are defined in cholmod_template.h.
+ */
+
+/* -------------------------------------------------------------------------- */
+/* pattern */
+/* -------------------------------------------------------------------------- */
+
+#define P_TEMPLATE(name) p_ ## name
+#define P_ASSIGN2(x,z,p,ax,az,q) x [p] = 1
+#define P_PRINT(k,x,z,p) PRK(k, ("1"))
+
+/* -------------------------------------------------------------------------- */
+/* real */
+/* -------------------------------------------------------------------------- */
+
+#define R_TEMPLATE(name) r_ ## name
+#define R_ASSEMBLE(x,z,p,ax,az,q) x [p] += ax [q]
+#define R_ASSIGN(x,z,p,ax,az,q) x [p] = ax [q]
+#define R_ASSIGN_CONJ(x,z,p,ax,az,q) x [p] = ax [q]
+#define R_ASSIGN_REAL(x,p,ax,q) x [p] = ax [q]
+#define R_XTYPE_OK(type) ((type) == CHOLMOD_REAL)
+#define R_IS_NONZERO(ax,az,q) IS_NONZERO (ax [q])
+#define R_IS_ZERO(ax,az,q) IS_ZERO (ax [q])
+#define R_IS_ONE(ax,az,q) (ax [q] == 1)
+#define R_MULT(x,z,p, ax,az,q, bx,bz,r) x [p] = ax [q] * bx [r]
+#define R_MULTADD(x,z,p, ax,az,q, bx,bz,r) x [p] += ax [q] * bx [r]
+#define R_MULTSUB(x,z,p, ax,az,q, bx,bz,r) x [p] -= ax [q] * bx [r]
+#define R_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) x [p] += ax [q] * bx [r]
+#define R_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) x [p] -= ax [q] * bx [r]
+#define R_ADD(x,z,p, ax,az,q, bx,bz,r) x [p] = ax [q] + bx [r]
+#define R_ADD_REAL(x,p, ax,q, bx,r) x [p] = ax [q] + bx [r]
+#define R_CLEAR(x,z,p) x [p] = 0
+#define R_CLEAR_IMAG(x,z,p)
+#define R_DIV(x,z,p,ax,az,q) x [p] /= ax [q]
+#define R_LLDOT(x,p, ax,az,q) x [p] -= ax [q] * ax [q]
+#define R_PRINT(k,x,z,p) PRK(k, ("%24.16e", x [p]))
+
+#define R_DIV_REAL(x,z,p, ax,az,q, bx,r) x [p] = ax [q] / bx [r]
+#define R_MULT_REAL(x,z,p, ax,az,q, bx,r) x [p] = ax [q] * bx [r]
+
+#define R_LDLDOT(x,p, ax,az,q, bx,r) x [p] -=(ax[q] * ax[q])/ bx[r]
+
+/* -------------------------------------------------------------------------- */
+/* complex */
+/* -------------------------------------------------------------------------- */
+
+#define C_TEMPLATE(name) c_ ## name
+#define CT_TEMPLATE(name) ct_ ## name
+
+#define C_ASSEMBLE(x,z,p,ax,az,q) \
+ x [2*(p) ] += ax [2*(q) ] ; \
+ x [2*(p)+1] += ax [2*(q)+1]
+
+#define C_ASSIGN(x,z,p,ax,az,q) \
+ x [2*(p) ] = ax [2*(q) ] ; \
+ x [2*(p)+1] = ax [2*(q)+1]
+
+#define C_ASSIGN_REAL(x,p,ax,q) x [2*(p)] = ax [2*(q)]
+
+#define C_ASSIGN_CONJ(x,z,p,ax,az,q) \
+ x [2*(p) ] = ax [2*(q) ] ; \
+ x [2*(p)+1] = -ax [2*(q)+1]
+
+#define C_XTYPE_OK(type) ((type) == CHOLMOD_COMPLEX)
+
+#define C_IS_NONZERO(ax,az,q) \
+ (IS_NONZERO (ax [2*(q)]) || IS_NONZERO (ax [2*(q)+1]))
+
+#define C_IS_ZERO(ax,az,q) \
+ (IS_ZERO (ax [2*(q)]) && IS_ZERO (ax [2*(q)+1]))
+
+#define C_IS_ONE(ax,az,q) \
+ ((ax [2*(q)] == 1) && IS_ZERO (ax [2*(q)+1]))
+
+#define C_IMAG_IS_NONZERO(ax,az,q) (IS_NONZERO (ax [2*(q)+1]))
+
+#define C_MULT(x,z,p, ax,az,q, bx,bz,r) \
+x [2*(p) ] = ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \
+x [2*(p)+1] = ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1]
+
+#define C_MULTADD(x,z,p, ax,az,q, bx,bz,r) \
+x [2*(p) ] += ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \
+x [2*(p)+1] += ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1]
+
+#define C_MULTSUB(x,z,p, ax,az,q, bx,bz,r) \
+x [2*(p) ] -= ax [2*(q) ] * bx [2*(r)] - ax [2*(q)+1] * bx [2*(r)+1] ; \
+x [2*(p)+1] -= ax [2*(q)+1] * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1]
+
+/* s += conj(a)*b */
+#define C_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) \
+x [2*(p) ] += ax [2*(q) ] * bx [2*(r)] + ax [2*(q)+1] * bx [2*(r)+1] ; \
+x [2*(p)+1] += (-ax [2*(q)+1]) * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1]
+
+/* s -= conj(a)*b */
+#define C_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) \
+x [2*(p) ] -= ax [2*(q) ] * bx [2*(r)] + ax [2*(q)+1] * bx [2*(r)+1] ; \
+x [2*(p)+1] -= (-ax [2*(q)+1]) * bx [2*(r)] + ax [2*(q) ] * bx [2*(r)+1]
+
+#define C_ADD(x,z,p, ax,az,q, bx,bz,r) \
+ x [2*(p) ] = ax [2*(q) ] + bx [2*(r) ] ; \
+ x [2*(p)+1] = ax [2*(q)+1] + bx [2*(r)+1]
+
+#define C_ADD_REAL(x,p, ax,q, bx,r) \
+ x [2*(p)] = ax [2*(q)] + bx [2*(r)]
+
+#define C_CLEAR(x,z,p) \
+ x [2*(p) ] = 0 ; \
+ x [2*(p)+1] = 0
+
+#define C_CLEAR_IMAG(x,z,p) \
+ x [2*(p)+1] = 0
+
+/* s = s / a */
+#define C_DIV(x,z,p,ax,az,q) \
+ Common->complex_divide ( \
+ x [2*(p)], x [2*(p)+1], \
+ ax [2*(q)], ax [2*(q)+1], \
+ &x [2*(p)], &x [2*(p)+1])
+
+/* s -= conj(a)*a ; note that the result of conj(a)*a is real */
+#define C_LLDOT(x,p, ax,az,q) \
+ x [2*(p)] -= ax [2*(q)] * ax [2*(q)] + ax [2*(q)+1] * ax [2*(q)+1]
+
+#define C_PRINT(k,x,z,p) PRK(k, ("(%24.16e,%24.16e)", x [2*(p)], x [2*(p)+1]))
+
+#define C_DIV_REAL(x,z,p, ax,az,q, bx,r) \
+ x [2*(p) ] = ax [2*(q) ] / bx [2*(r)] ; \
+ x [2*(p)+1] = ax [2*(q)+1] / bx [2*(r)]
+
+#define C_MULT_REAL(x,z,p, ax,az,q, bx,r) \
+ x [2*(p) ] = ax [2*(q) ] * bx [2*(r)] ; \
+ x [2*(p)+1] = ax [2*(q)+1] * bx [2*(r)]
+
+/* s -= conj(a)*a/t */
+#define C_LDLDOT(x,p, ax,az,q, bx,r) \
+ x [2*(p)] -= (ax [2*(q)] * ax [2*(q)] + ax [2*(q)+1] * ax [2*(q)+1]) / bx[r]
+
+/* -------------------------------------------------------------------------- */
+/* zomplex */
+/* -------------------------------------------------------------------------- */
+
+#define Z_TEMPLATE(name) z_ ## name
+#define ZT_TEMPLATE(name) zt_ ## name
+
+#define Z_ASSEMBLE(x,z,p,ax,az,q) \
+ x [p] += ax [q] ; \
+ z [p] += az [q]
+
+#define Z_ASSIGN(x,z,p,ax,az,q) \
+ x [p] = ax [q] ; \
+ z [p] = az [q]
+
+#define Z_ASSIGN_REAL(x,p,ax,q) x [p] = ax [q]
+
+#define Z_ASSIGN_CONJ(x,z,p,ax,az,q) \
+ x [p] = ax [q] ; \
+ z [p] = -az [q]
+
+#define Z_XTYPE_OK(type) ((type) == CHOLMOD_ZOMPLEX)
+
+#define Z_IS_NONZERO(ax,az,q) \
+ (IS_NONZERO (ax [q]) || IS_NONZERO (az [q]))
+
+#define Z_IS_ZERO(ax,az,q) \
+ (IS_ZERO (ax [q]) && IS_ZERO (az [q]))
+
+#define Z_IS_ONE(ax,az,q) \
+ ((ax [q] == 1) && IS_ZERO (az [q]))
+
+#define Z_IMAG_IS_NONZERO(ax,az,q) (IS_NONZERO (az [q]))
+
+#define Z_MULT(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] = ax [q] * bx [r] - az [q] * bz [r] ; \
+ z [p] = az [q] * bx [r] + ax [q] * bz [r]
+
+#define Z_MULTADD(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] += ax [q] * bx [r] - az [q] * bz [r] ; \
+ z [p] += az [q] * bx [r] + ax [q] * bz [r]
+
+#define Z_MULTSUB(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] -= ax [q] * bx [r] - az [q] * bz [r] ; \
+ z [p] -= az [q] * bx [r] + ax [q] * bz [r]
+
+#define Z_MULTADDCONJ(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] += ax [q] * bx [r] + az [q] * bz [r] ; \
+ z [p] += (-az [q]) * bx [r] + ax [q] * bz [r]
+
+#define Z_MULTSUBCONJ(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] -= ax [q] * bx [r] + az [q] * bz [r] ; \
+ z [p] -= (-az [q]) * bx [r] + ax [q] * bz [r]
+
+#define Z_ADD(x,z,p, ax,az,q, bx,bz,r) \
+ x [p] = ax [q] + bx [r] ; \
+ z [p] = az [q] + bz [r]
+
+#define Z_ADD_REAL(x,p, ax,q, bx,r) \
+ x [p] = ax [q] + bx [r]
+
+#define Z_CLEAR(x,z,p) \
+ x [p] = 0 ; \
+ z [p] = 0
+
+#define Z_CLEAR_IMAG(x,z,p) \
+ z [p] = 0
+
+/* s = s/a */
+#define Z_DIV(x,z,p,ax,az,q) \
+ Common->complex_divide (x [p], z [p], ax [q], az [q], &x [p], &z [p])
+
+/* s -= conj(a)*a ; note that the result of conj(a)*a is real */
+#define Z_LLDOT(x,p, ax,az,q) \
+ x [p] -= ax [q] * ax [q] + az [q] * az [q]
+
+#define Z_PRINT(k,x,z,p) PRK(k, ("(%24.16e,%24.16e)", x [p], z [p]))
+
+#define Z_DIV_REAL(x,z,p, ax,az,q, bx,r) \
+ x [p] = ax [q] / bx [r] ; \
+ z [p] = az [q] / bx [r]
+
+#define Z_MULT_REAL(x,z,p, ax,az,q, bx,r) \
+ x [p] = ax [q] * bx [r] ; \
+ z [p] = az [q] * bx [r]
+
+/* s -= conj(a)*a/t */
+#define Z_LDLDOT(x,p, ax,az,q, bx,r) \
+ x [p] -= (ax [q] * ax [q] + az [q] * az [q]) / bx[r]
+
+/* -------------------------------------------------------------------------- */
+/* all classes */
+/* -------------------------------------------------------------------------- */
+
+/* Check if A->xtype and the two arrays A->x and A->z are valid. Set status to
+ * invalid, unless status is already "out of memory". A can be a sparse matrix,
+ * dense matrix, factor, or triplet. */
+
+#define RETURN_IF_XTYPE_INVALID(A,xtype1,xtype2,result) \
+{ \
+ if ((A)->xtype < (xtype1) || (A)->xtype > (xtype2) || \
+ ((A)->xtype != CHOLMOD_PATTERN && ((A)->x) == NULL) || \
+ ((A)->xtype == CHOLMOD_ZOMPLEX && ((A)->z) == NULL)) \
+ { \
+ if (Common->status != CHOLMOD_OUT_OF_MEMORY) \
+ { \
+ ERROR (CHOLMOD_INVALID, "invalid xtype") ; \
+ } \
+ return (result) ; \
+ } \
+}
diff --git a/CHOLMOD/Include/cholmod_config.h b/CHOLMOD/Include/cholmod_config.h
new file mode 100644
index 0000000..b9de51b
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_config.h
@@ -0,0 +1,83 @@
+/* ========================================================================== */
+/* === Include/cholmod_config.h ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_config.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_config.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD configuration file, for inclusion in user programs.
+ *
+ * You do not have to edit any CHOLMOD files to compile and install CHOLMOD.
+ * However, if you do not use all of CHOLMOD's modules, you need to compile
+ * with the appropriate flag, or edit this file to add the appropriate #define.
+ *
+ * If you wish to use CHOLMOD under the GNU LGPL license only, then you must
+ * compile CHOLMOD with -DNMATRIXOPS -DNSUPERNODAL and -DNMODIFY. This can
+ * be done using just -DNGPL.
+ *
+ * Compiler flags for CHOLMOD:
+ *
+ * -DNCHECK do not include the Check module. License: GNU LGPL
+ * -DNCHOLESKY do not include the Cholesky module. License: GNU LGPL
+ * -DNPARTITION do not include the Partition module. License: GNU LGPL
+ *
+ * -DNGPL do not include any GNU GPL Modules in the CHOLMOD library.
+ * -DNMATRIXOPS do not include the MatrixOps module. License: GNU GPL
+ * -DNMODIFY do not include the Modify module. License: GNU GPL
+ * -DNSUPERNODAL do not include the Supernodal module. License: GNU GPL
+ *
+ * -DNPRINT do not print anything
+ *
+ * -D'LONGBLAS=long' or -DLONGBLAS='long long' defines the integers used by
+ * LAPACK and the BLAS. Use LONGBLAS=long on Solaris to use
+ * the 64-bit Sun Performance BLAS in cholmod_l_* routines.
+ * You may need to use -D'LONGBLAS=long long' on the SGI
+ * (this is not tested).
+ *
+ * -DNSUNPERF for Solaris only. If defined, do not use the Sun
+ * Performance Library. The default is to use SunPerf.
+ * You must compile CHOLMOD with -xlic_lib=sunperf.
+ *
+ * The Core Module (License GNU LGPL) is always included in the CHOLMOD library.
+ */
+
+#ifndef CHOLMOD_CONFIG_H
+#define CHOLMOD_CONFIG_H
+
+/* Use the compiler flag, or uncomment the definition(s), if you want to use
+ * one or more non-default installation options: */
+
+/*
+#define NCHECK
+#define NCHOLESKY
+#define NPARTITION
+
+#define NGPL
+#define NMATRIXOPS
+#define NMODIFY
+#define NSUPERNODAL
+
+#define NPRINT
+
+#define LONGBLAS long
+#define LONGBLAS long long
+#define NSUNPERF
+*/
+
+/* -------------------------------------------------------------------------- */
+/* if NGPL is defined, disable all GNU GPL Modules */
+/* -------------------------------------------------------------------------- */
+
+#ifdef NGPL
+#define NMATRIXOPS
+#define NMODIFY
+#define NSUPERNODAL
+#endif
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_core.h b/CHOLMOD/Include/cholmod_core.h
new file mode 100644
index 0000000..523f505
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_core.h
@@ -0,0 +1,2268 @@
+/* ========================================================================== */
+/* === Include/cholmod_core.h =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_core.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_core.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Core module: basic CHOLMOD objects and routines.
+ * Required by all CHOLMOD modules. Requires no other module or package.
+ *
+ * The CHOLMOD modules are:
+ *
+ * Core basic data structures and definitions
+ * Check check/print the 5 CHOLMOD objects, & 3 types of integer vectors
+ * Cholesky sparse Cholesky factorization
+ * Modify sparse Cholesky update/downdate/row-add/row-delete
+ * MatrixOps sparse matrix functions (add, multiply, norm, ...)
+ * Supernodal supernodal sparse Cholesky factorization
+ * Partition graph-partitioning based orderings
+ *
+ * The CHOLMOD objects:
+ * --------------------
+ *
+ * cholmod_common parameters, statistics, and workspace
+ * cholmod_sparse a sparse matrix in compressed column form
+ * cholmod_factor an LL' or LDL' factorization
+ * cholmod_dense a dense matrix
+ * cholmod_triplet a sparse matrix in "triplet" form
+ *
+ * The Core module described here defines the CHOLMOD data structures, and
+ * basic operations on them. To create and solve a sparse linear system Ax=b,
+ * the user must create A and b, populate them with values, and then pass them
+ * to the routines in the CHOLMOD Cholesky module. There are two primary
+ * methods for creating A: (1) allocate space for a column-oriented sparse
+ * matrix and fill it with pattern and values, or (2) create a triplet form
+ * matrix and convert it to a sparse matrix. The latter option is simpler.
+ *
+ * The matrices b and x are typically dense matrices, but can also be sparse.
+ * You can allocate and free them as dense matrices with the
+ * cholmod_allocate_dense and cholmod_free_dense routines.
+ *
+ * The cholmod_factor object contains the symbolic and numeric LL' or LDL'
+ * factorization of sparse symmetric matrix. The matrix must be positive
+ * definite for an LL' factorization. It need only be symmetric and have well-
+ * conditioned leading submatrices for it to have an LDL' factorization
+ * (CHOLMOD does not pivot for numerical stability). It is typically created
+ * with the cholmod_factorize routine in the Cholesky module, but can also
+ * be initialized to L=D=I in the Core module and then modified by the Modify
+ * module. It must be freed with cholmod_free_factor, defined below.
+ *
+ * The Core routines for each object are described below. Each list is split
+ * into two parts: the primary routines and secondary routines.
+ *
+ * ============================================================================
+ * === cholmod_common =========================================================
+ * ============================================================================
+ *
+ * The Common object contains control parameters, statistics, and
+ * You must call cholmod_start before calling any other CHOLMOD routine, and
+ * must call cholmod_finish as your last call to CHOLMOD, with two exceptions:
+ * you may call cholmod_print_common and cholmod_check_common in the Check
+ * module after calling cholmod_finish.
+ *
+ * cholmod_start first call to CHOLMOD
+ * cholmod_finish last call to CHOLMOD
+ * -----------------------------
+ * cholmod_defaults restore default parameters
+ * cholmod_maxrank maximum rank for update/downdate
+ * cholmod_allocate_work allocate workspace in Common
+ * cholmod_free_work free workspace in Common
+ * cholmod_clear_flag clear Flag workspace in Common
+ * cholmod_error called when CHOLMOD encounters an error
+ * cholmod_dbound for internal use in CHOLMOD only
+ * cholmod_hypot compute sqrt (x*x + y*y) accurately
+ * cholmod_divcomplex complex division, c = a/b
+ *
+ * ============================================================================
+ * === cholmod_sparse =========================================================
+ * ============================================================================
+ *
+ * A sparse matrix is held in compressed column form. In the basic type
+ * ("packed", which corresponds to a MATLAB sparse matrix), an n-by-n matrix
+ * with nz entries is held in three arrays: p of size n+1, i of size nz, and x
+ * of size nz. Row indices of column j are held in i [p [j] ... p [j+1]-1] and
+ * in the same locations in x. There may be no duplicate entries in a column.
+ * Row indices in each column may be sorted or unsorted (CHOLMOD keeps track).
+ * A->stype determines the storage mode: 0 if both upper/lower parts are stored,
+ * -1 if A is symmetric and just tril(A) is stored, +1 if symmetric and triu(A)
+ * is stored.
+ *
+ * cholmod_allocate_sparse allocate a sparse matrix
+ * cholmod_free_sparse free a sparse matrix
+ * -----------------------------
+ * cholmod_reallocate_sparse change the size (# entries) of sparse matrix
+ * cholmod_nnz number of nonzeros in a sparse matrix
+ * cholmod_speye sparse identity matrix
+ * cholmod_spzeros sparse zero matrix
+ * cholmod_transpose transpose a sparse matrix
+ * cholmod_ptranspose transpose/permute a sparse matrix
+ * cholmod_transpose_unsym transpose/permute an unsymmetric sparse matrix
+ * cholmod_transpose_sym transpose/permute a symmetric sparse matrix
+ * cholmod_sort sort row indices in each column of sparse matrix
+ * cholmod_band C = tril (triu (A,k1), k2)
+ * cholmod_band_inplace A = tril (triu (A,k1), k2)
+ * cholmod_aat C = A*A'
+ * cholmod_copy_sparse C = A, create an exact copy of a sparse matrix
+ * cholmod_copy C = A, with possible change of stype
+ * cholmod_add C = alpha*A + beta*B
+ * cholmod_sparse_xtype change the xtype of a sparse matrix
+ *
+ * ============================================================================
+ * === cholmod_factor =========================================================
+ * ============================================================================
+ *
+ * The data structure for an LL' or LDL' factorization is too complex to
+ * describe in one sentence. This object can hold the symbolic analysis alone,
+ * or in combination with a "simplicial" (similar to a sparse matrix) or
+ * "supernodal" form of the numerical factorization. Only the routine to free
+ * a factor is primary, since a factor object is created by the factorization
+ * routine (cholmod_factorize). It must be freed with cholmod_free_factor.
+ *
+ * cholmod_free_factor free a factor
+ * -----------------------------
+ * cholmod_allocate_factor allocate a factor (LL' or LDL')
+ * cholmod_reallocate_factor change the # entries in a factor
+ * cholmod_change_factor change the type of factor (e.g., LDL' to LL')
+ * cholmod_pack_factor pack the columns of a factor
+ * cholmod_reallocate_column resize a single column of a factor
+ * cholmod_factor_to_sparse create a sparse matrix copy of a factor
+ * cholmod_copy_factor create a copy of a factor
+ * cholmod_factor_xtype change the xtype of a factor
+ *
+ * Note that there is no cholmod_sparse_to_factor routine to create a factor
+ * as a copy of a sparse matrix. It could be done, after a fashion, but a
+ * lower triangular sparse matrix would not necessarily have a chordal graph,
+ * which would break the many CHOLMOD routines that rely on this property.
+ *
+ * ============================================================================
+ * === cholmod_dense ==========================================================
+ * ============================================================================
+ *
+ * The solve routines and some of the MatrixOps and Modify routines use dense
+ * matrices as inputs. These are held in column-major order. With a leading
+ * dimension of d, the entry in row i and column j is held in x [i+j*d].
+ *
+ * cholmod_allocate_dense allocate a dense matrix
+ * cholmod_free_dense free a dense matrix
+ * -----------------------------
+ * cholmod_zeros allocate a dense matrix of all zeros
+ * cholmod_ones allocate a dense matrix of all ones
+ * cholmod_eye allocate a dense identity matrix
+ * cholmod_sparse_to_dense create a dense matrix copy of a sparse matrix
+ * cholmod_dense_to_sparse create a sparse matrix copy of a dense matrix
+ * cholmod_copy_dense create a copy of a dense matrix
+ * cholmod_copy_dense2 copy a dense matrix (pre-allocated)
+ * cholmod_dense_xtype change the xtype of a dense matrix
+ *
+ * ============================================================================
+ * === cholmod_triplet ========================================================
+ * ============================================================================
+ *
+ * A sparse matrix held in triplet form is the simplest one for a user to
+ * create. It consists of a list of nz entries in arbitrary order, held in
+ * three arrays: i, j, and x, each of length nk. The kth entry is in row i[k],
+ * column j[k], with value x[k]. There may be duplicate values; if A(i,j)
+ * appears more than once, its value is the sum of the entries with those row
+ * and column indices.
+ *
+ * cholmod_allocate_triplet allocate a triplet matrix
+ * cholmod_triplet_to_sparse create a sparse matrix copy of a triplet matrix
+ * cholmod_free_triplet free a triplet matrix
+ * -----------------------------
+ * cholmod_reallocate_triplet change the # of entries in a triplet matrix
+ * cholmod_sparse_to_triplet create a triplet matrix copy of a sparse matrix
+ * cholmod_copy_triplet create a copy of a triplet matrix
+ * cholmod_triplet_xtype change the xtype of a triplet matrix
+ *
+ * ============================================================================
+ * === memory management ======================================================
+ * ============================================================================
+ *
+ * cholmod_malloc malloc wrapper
+ * cholmod_calloc calloc wrapper
+ * cholmod_free free wrapper
+ * cholmod_realloc realloc wrapper
+ * cholmod_realloc_multiple realloc wrapper for multiple objects
+ *
+ * ============================================================================
+ * === Core CHOLMOD prototypes ================================================
+ * ============================================================================
+ *
+ * All CHOLMOD routines (in all modules) use the following protocol for return
+ * values, with one exception:
+ *
+ * int TRUE (1) if successful, or FALSE (0) otherwise.
+ * (exception: cholmod_divcomplex)
+ * UF_long a value >= 0 if successful, or -1 otherwise.
+ * double a value >= 0 if successful, or -1 otherwise.
+ * size_t a value > 0 if successful, or 0 otherwise.
+ * void * a non-NULL pointer to newly allocated memory if
+ * successful, or NULL otherwise.
+ * cholmod_sparse * a non-NULL pointer to a newly allocated matrix
+ * if successful, or NULL otherwise.
+ * cholmod_factor * a non-NULL pointer to a newly allocated factor
+ * if successful, or NULL otherwise.
+ * cholmod_triplet * a non-NULL pointer to a newly allocated triplet
+ * matrix if successful, or NULL otherwise.
+ * cholmod_dense * a non-NULL pointer to a newly allocated triplet
+ * matrix if successful, or NULL otherwise.
+ *
+ * The last parameter to all routines is always a pointer to the CHOLMOD
+ * Common object.
+ *
+ * TRUE and FALSE are not defined here, since they may conflict with the user
+ * program. A routine that described here returning TRUE or FALSE returns 1
+ * or 0, respectively. Any TRUE/FALSE parameter is true if nonzero, false if
+ * zero.
+ */
+
+#ifndef CHOLMOD_CORE_H
+#define CHOLMOD_CORE_H
+
+/* ========================================================================== */
+/* === CHOLMOD version ====================================================== */
+/* ========================================================================== */
+
+/* All versions of CHOLMOD will include the following definitions.
+ * As an example, to test if the version you are using is 1.3 or later:
+ *
+ * if (CHOLMOD_VERSION >= CHOLMOD_VER_CODE (1,3)) ...
+ *
+ * This also works during compile-time:
+ *
+ * #if CHOLMOD_VERSION >= CHOLMOD_VER_CODE (1,3)
+ * printf ("This is version 1.3 or later\n") ;
+ * #else
+ * printf ("This is version is earlier than 1.3\n") ;
+ * #endif
+ */
+
+#define CHOLMOD_DATE "Nov 1, 2007"
+#define CHOLMOD_VER_CODE(main,sub) ((main) * 1000 + (sub))
+#define CHOLMOD_MAIN_VERSION 1
+#define CHOLMOD_SUB_VERSION 6
+#define CHOLMOD_SUBSUB_VERSION 0
+#define CHOLMOD_VERSION \
+ CHOLMOD_VER_CODE(CHOLMOD_MAIN_VERSION,CHOLMOD_SUB_VERSION)
+
+
+/* ========================================================================== */
+/* === non-CHOLMOD include files ============================================ */
+/* ========================================================================== */
+
+/* This is the only non-CHOLMOD include file imposed on the user program.
+ * It required for size_t definition used here. CHOLMOD itself includes other
+ * ANSI C89 standard #include files, but does not expose them to the user.
+ *
+ * CHOLMOD assumes that your C compiler is ANSI C89 compliant. It does not make
+ * use of ANSI C99 features.
+ */
+
+#include <stddef.h>
+#include <stdlib.h>
+
+/* ========================================================================== */
+/* === CHOLMOD objects ====================================================== */
+/* ========================================================================== */
+
+/* Each CHOLMOD object has its own type code. */
+
+#define CHOLMOD_COMMON 0
+#define CHOLMOD_SPARSE 1
+#define CHOLMOD_FACTOR 2
+#define CHOLMOD_DENSE 3
+#define CHOLMOD_TRIPLET 4
+
+/* ========================================================================== */
+/* === CHOLMOD Common ======================================================= */
+/* ========================================================================== */
+
+/* itype defines the types of integer used: */
+#define CHOLMOD_INT 0 /* all integer arrays are int */
+#define CHOLMOD_INTLONG 1 /* most are int, some are UF_long */
+#define CHOLMOD_LONG 2 /* all integer arrays are UF_long */
+
+/* The itype of all parameters for all CHOLMOD routines must match.
+ * FUTURE WORK: CHOLMOD_INTLONG is not yet supported.
+ */
+
+/* dtype defines what the numerical type is (double or float): */
+#define CHOLMOD_DOUBLE 0 /* all numerical values are double */
+#define CHOLMOD_SINGLE 1 /* all numerical values are float */
+
+/* The dtype of all parameters for all CHOLMOD routines must match.
+ *
+ * Scalar floating-point values are always passed as double arrays of size 2
+ * (for the real and imaginary parts). They are typecast to float as needed.
+ * FUTURE WORK: the float case is not supported yet.
+ */
+
+/* xtype defines the kind of numerical values used: */
+#define CHOLMOD_PATTERN 0 /* pattern only, no numerical values */
+#define CHOLMOD_REAL 1 /* a real matrix */
+#define CHOLMOD_COMPLEX 2 /* a complex matrix (ANSI C99 compatible) */
+#define CHOLMOD_ZOMPLEX 3 /* a complex matrix (MATLAB compatible) */
+
+/* The xtype of all parameters for all CHOLMOD routines must match.
+ *
+ * CHOLMOD_PATTERN: x and z are ignored.
+ * CHOLMOD_DOUBLE: x is non-null of size nzmax, z is ignored.
+ * CHOLMOD_COMPLEX: x is non-null of size 2*nzmax doubles, z is ignored.
+ * CHOLMOD_ZOMPLEX: x and z are non-null of size nzmax
+ *
+ * In the real case, z is ignored. The kth entry in the matrix is x [k].
+ * There are two methods for the complex case. In the ANSI C99-compatible
+ * CHOLMOD_COMPLEX case, the real and imaginary parts of the kth entry
+ * are in x [2*k] and x [2*k+1], respectively. z is ignored. In the
+ * MATLAB-compatible CHOLMOD_ZOMPLEX case, the real and imaginary
+ * parts of the kth entry are in x [k] and z [k].
+ *
+ * Scalar floating-point values are always passed as double arrays of size 2
+ * (real and imaginary parts). The imaginary part of a scalar is ignored if
+ * the routine operates on a real matrix.
+ *
+ * These Modules support complex and zomplex matrices, with a few exceptions:
+ *
+ * Check all routines
+ * Cholesky all routines
+ * Core all except cholmod_aat, add, band, copy
+ * Demo all routines
+ * Partition all routines
+ * Supernodal all routines support any real, complex, or zomplex input.
+ * There will never be a supernodal zomplex L; a complex
+ * supernodal L is created if A is zomplex.
+ * Tcov all routines
+ * Valgrind all routines
+ *
+ * These Modules provide partial support for complex and zomplex matrices:
+ *
+ * MATLAB all routines support real and zomplex only, not complex,
+ * with the exception of ldlupdate, which supports
+ * real matrices only. This is a minor constraint since
+ * MATLAB's matrices are all real or zomplex.
+ * MatrixOps only norm_dense, norm_sparse, and sdmult support complex
+ * and zomplex
+ *
+ * These Modules do not support complex and zomplex matrices at all:
+ *
+ * Modify all routines support real matrices only
+ */
+
+/* Definitions for cholmod_common: */
+#define CHOLMOD_MAXMETHODS 9 /* maximum number of different methods that
+ * cholmod_analyze can try. Must be >= 9. */
+
+/* Common->status values. zero means success, negative means a fatal error,
+ * positive is a warning. */
+#define CHOLMOD_OK 0 /* success */
+#define CHOLMOD_NOT_INSTALLED (-1) /* failure: method not installed */
+#define CHOLMOD_OUT_OF_MEMORY (-2) /* failure: out of memory */
+#define CHOLMOD_TOO_LARGE (-3) /* failure: integer overflow occured */
+#define CHOLMOD_INVALID (-4) /* failure: invalid input */
+#define CHOLMOD_NOT_POSDEF (1) /* warning: matrix not pos. def. */
+#define CHOLMOD_DSMALL (2) /* warning: D for LDL' or diag(L) or
+ * LL' has tiny absolute value */
+
+/* ordering method (also used for L->ordering) */
+#define CHOLMOD_NATURAL 0 /* use natural ordering */
+#define CHOLMOD_GIVEN 1 /* use given permutation */
+#define CHOLMOD_AMD 2 /* use minimum degree (AMD) */
+#define CHOLMOD_METIS 3 /* use METIS' nested dissection */
+#define CHOLMOD_NESDIS 4 /* use CHOLMOD's version of nested dissection:
+ * node bisector applied recursively, followed
+ * by constrained minimum degree (CSYMAMD or
+ * CCOLAMD) */
+#define CHOLMOD_COLAMD 5 /* use AMD for A, COLAMD for A*A' */
+
+/* POSTORDERED is not a method, but a result of natural ordering followed by a
+ * weighted postorder. It is used for L->ordering, not method [ ].ordering. */
+#define CHOLMOD_POSTORDERED 6 /* natural ordering, postordered. */
+
+/* supernodal strategy (for Common->supernodal) */
+#define CHOLMOD_SIMPLICIAL 0 /* always do simplicial */
+#define CHOLMOD_AUTO 1 /* select simpl/super depending on matrix */
+#define CHOLMOD_SUPERNODAL 2 /* always do supernodal */
+
+typedef struct cholmod_common_struct
+{
+ /* ---------------------------------------------------------------------- */
+ /* parameters for symbolic/numeric factorization and update/downdate */
+ /* ---------------------------------------------------------------------- */
+
+ double dbound ; /* Smallest absolute value of diagonal entries of D
+ * for LDL' factorization and update/downdate/rowadd/
+ * rowdel, or the diagonal of L for an LL' factorization.
+ * Entries in the range 0 to dbound are replaced with dbound.
+ * Entries in the range -dbound to 0 are replaced with -dbound. No
+ * changes are made to the diagonal if dbound <= 0. Default: zero */
+
+ double grow0 ; /* For a simplicial factorization, L->i and L->x can
+ * grow if necessary. grow0 is the factor by which
+ * it grows. For the initial space, L is of size MAX (1,grow0) times
+ * the required space. If L runs out of space, the new size of L is
+ * MAX(1.2,grow0) times the new required space. If you do not plan on
+ * modifying the LDL' factorization in the Modify module, set grow0 to
+ * zero (or set grow2 to 0, see below). Default: 1.2 */
+
+ double grow1 ;
+
+ size_t grow2 ; /* For a simplicial factorization, each column j of L
+ * is initialized with space equal to
+ * grow1*L->ColCount[j] + grow2. If grow0 < 1, grow1 < 1, or grow2 == 0,
+ * then the space allocated is exactly equal to L->ColCount[j]. If the
+ * column j runs out of space, it increases to grow1*need + grow2 in
+ * size, where need is the total # of nonzeros in that column. If you do
+ * not plan on modifying the factorization in the Modify module, set
+ * grow2 to zero. Default: grow1 = 1.2, grow2 = 5. */
+
+ size_t maxrank ; /* rank of maximum update/downdate. Valid values:
+ * 2, 4, or 8. A value < 2 is set to 2, and a
+ * value > 8 is set to 8. It is then rounded up to the next highest
+ * power of 2, if not already a power of 2. Workspace (Xwork, below) of
+ * size nrow-by-maxrank double's is allocated for the update/downdate.
+ * If an update/downdate of rank-k is requested, with k > maxrank,
+ * it is done in steps of maxrank. Default: 8, which is fastest.
+ * Memory usage can be reduced by setting maxrank to 2 or 4.
+ */
+
+ double supernodal_switch ; /* supernodal vs simplicial factorization */
+ int supernodal ; /* If Common->supernodal <= CHOLMOD_SIMPLICIAL
+ * (0) then cholmod_analyze performs a
+ * simplicial analysis. If >= CHOLMOD_SUPERNODAL (2), then a supernodal
+ * analysis is performed. If == CHOLMOD_AUTO (1) and
+ * flop/nnz(L) < Common->supernodal_switch, then a simplicial analysis
+ * is done. A supernodal analysis done otherwise.
+ * Default: CHOLMOD_AUTO. Default supernodal_switch = 40 */
+
+ int final_asis ; /* If TRUE, then ignore the other final_* parameters
+ * (except for final_pack).
+ * The factor is left as-is when done. Default: TRUE.*/
+
+ int final_super ; /* If TRUE, leave a factor in supernodal form when
+ * supernodal factorization is finished. If FALSE,
+ * then convert to a simplicial factor when done.
+ * Default: TRUE */
+
+ int final_ll ; /* If TRUE, leave factor in LL' form when done.
+ * Otherwise, leave in LDL' form. Default: FALSE */
+
+ int final_pack ; /* If TRUE, pack the columns when done. If TRUE, and
+ * cholmod_factorize is called with a symbolic L, L is
+ * allocated with exactly the space required, using L->ColCount. If you
+ * plan on modifying the factorization, set Common->final_pack to FALSE,
+ * and each column will be given a little extra slack space for future
+ * growth in fill-in due to updates. Default: TRUE */
+
+ int final_monotonic ; /* If TRUE, ensure columns are monotonic when done.
+ * Default: TRUE */
+
+ int final_resymbol ;/* if cholmod_factorize performed a supernodal
+ * factorization, final_resymbol is true, and
+ * final_super is FALSE (convert a simplicial numeric factorization),
+ * then numerically zero entries that resulted from relaxed supernodal
+ * amalgamation are removed. This does not remove entries that are zero
+ * due to exact numeric cancellation, since doing so would break the
+ * update/downdate rowadd/rowdel routines. Default: FALSE. */
+
+ /* supernodal relaxed amalgamation parameters: */
+ double zrelax [3] ;
+ size_t nrelax [3] ;
+
+ /* Let ns be the total number of columns in two adjacent supernodes.
+ * Let z be the fraction of zero entries in the two supernodes if they
+ * are merged (z includes zero entries from prior amalgamations). The
+ * two supernodes are merged if:
+ * (ns <= nrelax [0]) || (no new zero entries added) ||
+ * (ns <= nrelax [1] && z < zrelax [0]) ||
+ * (ns <= nrelax [2] && z < zrelax [1]) || (z < zrelax [2])
+ *
+ * Default parameters result in the following rule:
+ * (ns <= 4) || (no new zero entries added) ||
+ * (ns <= 16 && z < 0.8) || (ns <= 48 && z < 0.1) || (z < 0.05)
+ */
+
+ int prefer_zomplex ; /* X = cholmod_solve (sys, L, B, Common) computes
+ * x=A\b or solves a related system. If L and B are
+ * both real, then X is real. Otherwise, X is returned as
+ * CHOLMOD_COMPLEX if Common->prefer_zomplex is FALSE, or
+ * CHOLMOD_ZOMPLEX if Common->prefer_zomplex is TRUE. This parameter
+ * is needed because there is no supernodal zomplex L. Suppose the
+ * caller wants all complex matrices to be stored in zomplex form
+ * (MATLAB, for example). A supernodal L is returned in complex form
+ * if A is zomplex. B can be real, and thus X = cholmod_solve (L,B)
+ * should return X as zomplex. This cannot be inferred from the input
+ * arguments L and B. Default: FALSE, since all data types are
+ * supported in CHOLMOD_COMPLEX form and since this is the native type
+ * of LAPACK and the BLAS. Note that the MATLAB/cholmod.c mexFunction
+ * sets this parameter to TRUE, since MATLAB matrices are in
+ * CHOLMOD_ZOMPLEX form.
+ */
+
+ int prefer_upper ; /* cholmod_analyze and cholmod_factorize work
+ * fastest when a symmetric matrix is stored in
+ * upper triangular form when a fill-reducing ordering is used. In
+ * MATLAB, this corresponds to how x=A\b works. When the matrix is
+ * ordered as-is, they work fastest when a symmetric matrix is in lower
+ * triangular form. In MATLAB, R=chol(A) does the opposite. This
+ * parameter affects only how cholmod_read returns a symmetric matrix.
+ * If TRUE (the default case), a symmetric matrix is always returned in
+ * upper-triangular form (A->stype = 1). */
+
+ int quick_return_if_not_posdef ; /* if TRUE, the supernodal numeric
+ * factorization will return quickly if
+ * the matrix is not positive definite. Default: FALSE. */
+
+ /* ---------------------------------------------------------------------- */
+ /* printing and error handling options */
+ /* ---------------------------------------------------------------------- */
+
+ int print ; /* print level. Default: 3 */
+ int precise ; /* if TRUE, print 16 digits. Otherwise print 5 */
+ int (*print_function) (const char *, ...) ; /* pointer to printf */
+
+ int try_catch ; /* if TRUE, then ignore errors; CHOLMOD is in the middle
+ * of a try/catch block. No error message is printed
+ * and the Common->error_handler function is not called. */
+
+ void (*error_handler) (int status, char *file, int line, char *message) ;
+
+ /* Common->error_handler is the user's error handling routine. If not
+ * NULL, this routine is called if an error occurs in CHOLMOD. status
+ * can be CHOLMOD_OK (0), negative for a fatal error, and positive for
+ * a warning. file is a string containing the name of the source code
+ * file where the error occured, and line is the line number in that
+ * file. message is a string describing the error in more detail. */
+
+ /* ---------------------------------------------------------------------- */
+ /* ordering options */
+ /* ---------------------------------------------------------------------- */
+
+ /* The cholmod_analyze routine can try many different orderings and select
+ * the best one. It can also try one ordering method multiple times, with
+ * different parameter settings. The default is to use three orderings,
+ * the user's permutation (if provided), AMD which is the fastest ordering
+ * and generally gives good fill-in, and METIS. CHOLMOD's nested dissection
+ * (METIS with a constrained AMD) usually gives a better ordering than METIS
+ * alone (by about 5% to 10%) but it takes more time.
+ *
+ * If you know the method that is best for your matrix, set Common->nmethods
+ * to 1 and set Common->method [0] to the set of parameters for that method.
+ * If you set it to 1 and do not provide a permutation, then only AMD will
+ * be called.
+ *
+ * If METIS is not available, the default # of methods tried is 2 (the user
+ * permutation, if any, and AMD).
+ *
+ * To try other methods, set Common->nmethods to the number of methods you
+ * want to try. The suite of default methods and their parameters is
+ * described in the cholmod_defaults routine, and summarized here:
+ *
+ * Common->method [i]:
+ * i = 0: user-provided ordering (cholmod_analyze_p only)
+ * i = 1: AMD (for both A and A*A')
+ * i = 2: METIS
+ * i = 3: CHOLMOD's nested dissection (NESDIS), default parameters
+ * i = 4: natural
+ * i = 5: NESDIS with nd_small = 20000
+ * i = 6: NESDIS with nd_small = 4, no constrained minimum degree
+ * i = 7: NESDIS with no dense node removal
+ * i = 8: AMD for A, COLAMD for A*A'
+ *
+ * You can modify the suite of methods you wish to try by modifying
+ * Common.method [...] after calling cholmod_start or cholmod_defaults.
+ *
+ * For example, to use AMD, followed by a weighted postordering:
+ *
+ * Common->nmethods = 1 ;
+ * Common->method [0].ordering = CHOLMOD_AMD ;
+ * Common->postorder = TRUE ;
+ *
+ * To use the natural ordering (with no postordering):
+ *
+ * Common->nmethods = 1 ;
+ * Common->method [0].ordering = CHOLMOD_NATURAL ;
+ * Common->postorder = FALSE ;
+ *
+ * If you are going to factorize hundreds or more matrices with the same
+ * nonzero pattern, you may wish to spend a great deal of time finding a
+ * good permutation. In this case, try setting Common->nmethods to 9.
+ * The time spent in cholmod_analysis will be very high, but you need to
+ * call it only once.
+ *
+ * cholmod_analyze sets Common->current to a value between 0 and nmethods-1.
+ * Each ordering method uses the set of options defined by this parameter.
+ */
+
+ int nmethods ; /* The number of ordering methods to try. Default: 0.
+ * nmethods = 0 is a special case. cholmod_analyze
+ * will try the user-provided ordering (if given) and AMD. Let fl and
+ * lnz be the flop count and nonzeros in L from AMD's ordering. Let
+ * anz be the number of nonzeros in the upper or lower triangular part
+ * of the symmetric matrix A. If fl/lnz < 500 or lnz/anz < 5, then this
+ * is a good ordering, and METIS is not attempted. Otherwise, METIS is
+ * tried. The best ordering found is used. If nmethods > 0, the
+ * methods used are given in the method[ ] array, below. The first
+ * three methods in the default suite of orderings is (1) use the given
+ * permutation (if provided), (2) use AMD, and (3) use METIS. Maximum
+ * allowed value is CHOLMOD_MAXMETHODS. */
+
+ int current ; /* The current method being tried. Default: 0. Valid
+ * range is 0 to nmethods-1. */
+
+ int selected ; /* The best method found. */
+
+ /* The suite of ordering methods and parameters: */
+
+ struct cholmod_method_struct
+ {
+ /* statistics for this method */
+ double lnz ; /* nnz(L) excl. zeros from supernodal amalgamation,
+ * for a "pure" L */
+
+ double fl ; /* flop count for a "pure", real simplicial LL'
+ * factorization, with no extra work due to
+ * amalgamation. Subtract n to get the LDL' flop count. Multiply
+ * by about 4 if the matrix is complex or zomplex. */
+
+ /* ordering method parameters */
+ double prune_dense ;/* dense row/col control for AMD, SYMAMD, CSYMAMD,
+ * and NESDIS (cholmod_nested_dissection). For a
+ * symmetric n-by-n matrix, rows/columns with more than
+ * MAX (16, prune_dense * sqrt (n)) entries are removed prior to
+ * ordering. They appear at the end of the re-ordered matrix.
+ *
+ * If prune_dense < 0, only completely dense rows/cols are removed.
+ *
+ * This paramater is also the dense column control for COLAMD and
+ * CCOLAMD. For an m-by-n matrix, columns with more than
+ * MAX (16, prune_dense * sqrt (MIN (m,n))) entries are removed prior
+ * to ordering. They appear at the end of the re-ordered matrix.
+ * CHOLMOD factorizes A*A', so it calls COLAMD and CCOLAMD with A',
+ * not A. Thus, this parameter affects the dense *row* control for
+ * CHOLMOD's matrix, and the dense *column* control for COLAMD and
+ * CCOLAMD.
+ *
+ * Removing dense rows and columns improves the run-time of the
+ * ordering methods. It has some impact on ordering quality
+ * (usually minimal, sometimes good, sometimes bad).
+ *
+ * Default: 10. */
+
+ double prune_dense2 ;/* dense row control for COLAMD and CCOLAMD.
+ * Rows with more than MAX (16, dense2 * sqrt (n))
+ * for an m-by-n matrix are removed prior to ordering. CHOLMOD's
+ * matrix is transposed before ordering it with COLAMD or CCOLAMD,
+ * so this controls the dense *columns* of CHOLMOD's matrix, and
+ * the dense *rows* of COLAMD's or CCOLAMD's matrix.
+ *
+ * If prune_dense2 < 0, only completely dense rows/cols are removed.
+ *
+ * Default: -1. Note that this is not the default for COLAMD and
+ * CCOLAMD. -1 is best for Cholesky. 10 is best for LU. */
+
+ double nd_oksep ; /* in NESDIS, when a node separator is computed, it
+ * discarded if nsep >= nd_oksep*n, where nsep is
+ * the number of nodes in the separator, and n is the size of the
+ * graph being cut. Valid range is 0 to 1. If 1 or greater, the
+ * separator is discarded if it consists of the entire graph.
+ * Default: 1 */
+
+ double other1 [4] ; /* future expansion */
+
+ size_t nd_small ; /* do not partition graphs with fewer nodes than
+ * nd_small, in NESDIS. Default: 200 (same as
+ * METIS) */
+
+ size_t other2 [4] ; /* future expansion */
+
+ int aggressive ; /* Aggresive absorption in AMD, COLAMD, SYMAMD,
+ * CCOLAMD, and CSYMAMD. Default: TRUE */
+
+ int order_for_lu ; /* CCOLAMD can be optimized to produce an ordering
+ * for LU or Cholesky factorization. CHOLMOD only
+ * performs a Cholesky factorization. However, you may wish to use
+ * CHOLMOD as an interface for CCOLAMD but use it for your own LU
+ * factorization. In this case, order_for_lu should be set to FALSE.
+ * When factorizing in CHOLMOD itself, you should *** NEVER *** set
+ * this parameter FALSE. Default: TRUE. */
+
+ int nd_compress ; /* If TRUE, compress the graph and subgraphs before
+ * partitioning them in NESDIS. Default: TRUE */
+
+ int nd_camd ; /* If 1, follow the nested dissection ordering
+ * with a constrained minimum degree ordering that
+ * respects the partitioning just found (using CAMD). If 2, use
+ * CSYMAMD instead. If you set nd_small very small, you may not need
+ * this ordering, and can save time by setting it to zero (no
+ * constrained minimum degree ordering). Default: 1. */
+
+ int nd_components ; /* The nested dissection ordering finds a node
+ * separator that splits the graph into two parts,
+ * which may be unconnected. If nd_components is TRUE, each of
+ * these connected components is split independently. If FALSE,
+ * each part is split as a whole, even if it consists of more than
+ * one connected component. Default: FALSE */
+
+ /* fill-reducing ordering to use */
+ int ordering ;
+
+ size_t other3 [4] ; /* future expansion */
+
+ } method [CHOLMOD_MAXMETHODS + 1] ;
+
+ int postorder ; /* If TRUE, cholmod_analyze follows the ordering with a
+ * weighted postorder of the elimination tree. Improves
+ * supernode amalgamation. Does not affect fundamental nnz(L) and
+ * flop count. Default: TRUE. */
+
+ /* ---------------------------------------------------------------------- */
+ /* memory management routines */
+ /* ---------------------------------------------------------------------- */
+
+ void *(*malloc_memory) (size_t) ; /* pointer to malloc */
+ void *(*realloc_memory) (void *, size_t) ; /* pointer to realloc */
+ void (*free_memory) (void *) ; /* pointer to free */
+ void *(*calloc_memory) (size_t, size_t) ; /* pointer to calloc */
+
+ /* ---------------------------------------------------------------------- */
+ /* routines for complex arithmetic */
+ /* ---------------------------------------------------------------------- */
+
+ int (*complex_divide) (double ax, double az, double bx, double bz,
+ double *cx, double *cz) ;
+
+ /* flag = complex_divide (ax, az, bx, bz, &cx, &cz) computes the complex
+ * division c = a/b, where ax and az hold the real and imaginary part
+ * of a, and b and c are stored similarly. flag is returned as 1 if
+ * a divide-by-zero occurs, or 0 otherwise. By default, the function
+ * pointer Common->complex_divide is set equal to cholmod_divcomplex.
+ */
+
+ double (*hypotenuse) (double x, double y) ;
+
+ /* s = hypotenuse (x,y) computes s = sqrt (x*x + y*y), but does so more
+ * accurately. By default, the function pointer Common->hypotenuse is
+ * set equal to cholmod_hypot. See also the hypot function in the C99
+ * standard, which has an identical syntax and function. If you have
+ * a C99-compliant compiler, you can set Common->hypotenuse = hypot. */
+
+ /* ---------------------------------------------------------------------- */
+ /* METIS workarounds */
+ /* ---------------------------------------------------------------------- */
+
+ double metis_memory ; /* This is a parameter for CHOLMOD's interface to
+ * METIS, not a parameter to METIS itself. METIS
+ * uses an amount of memory that is difficult to estimate precisely
+ * beforehand. If it runs out of memory, it terminates your program.
+ * All routines in CHOLMOD except for CHOLMOD's interface to METIS
+ * return an error status and safely return to your program if they run
+ * out of memory. To mitigate this problem, the CHOLMOD interface
+ * can allocate a single block of memory equal in size to an empirical
+ * upper bound of METIS's memory usage times the Common->metis_memory
+ * parameter, and then immediately free it. It then calls METIS. If
+ * this pre-allocation fails, it is possible that METIS will fail as
+ * well, and so CHOLMOD returns with an out-of-memory condition without
+ * calling METIS.
+ *
+ * METIS_NodeND (used in the CHOLMOD_METIS ordering option) with its
+ * default parameter settings typically uses about (4*nz+40n+4096)
+ * times sizeof(int) memory, where nz is equal to the number of entries
+ * in A for the symmetric case or AA' if an unsymmetric matrix is
+ * being ordered (where nz includes both the upper and lower parts
+ * of A or AA'). The observed "upper bound" (with 2 exceptions),
+ * measured in an instrumented copy of METIS 4.0.1 on thousands of
+ * matrices, is (10*nz+50*n+4096) * sizeof(int). Two large matrices
+ * exceeded this bound, one by almost a factor of 2 (Gupta/gupta2).
+ *
+ * If your program is terminated by METIS, try setting metis_memory to
+ * 2.0, or even higher if needed. By default, CHOLMOD assumes that METIS
+ * does not have this problem (so that CHOLMOD will work correctly when
+ * this issue is fixed in METIS). Thus, the default value is zero.
+ * This work-around is not guaranteed anyway.
+ *
+ * If a matrix exceeds this predicted memory usage, AMD is attempted
+ * instead. It, too, may run out of memory, but if it does so it will
+ * not terminate your program.
+ */
+
+ double metis_dswitch ; /* METIS_NodeND in METIS 4.0.1 gives a seg */
+ size_t metis_nswitch ; /* fault with one matrix of order n = 3005 and
+ * nz = 6,036,025. This is a very dense graph.
+ * The workaround is to use AMD instead of METIS for matrices of dimension
+ * greater than Common->metis_nswitch (default 3000) or more and with
+ * density of Common->metis_dswitch (default 0.66) or more.
+ * cholmod_nested_dissection has no problems with the same matrix, even
+ * though it uses METIS_NodeComputeSeparator on this matrix. If this
+ * seg fault does not affect you, set metis_nswitch to zero or less,
+ * and CHOLMOD will not switch to AMD based just on the density of the
+ * matrix (it will still switch to AMD if the metis_memory parameter
+ * causes the switch).
+ */
+
+ /* ---------------------------------------------------------------------- */
+ /* workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* CHOLMOD has several routines that take less time than the size of
+ * workspace they require. Allocating and initializing the workspace would
+ * dominate the run time, unless workspace is allocated and initialized
+ * just once. CHOLMOD allocates this space when needed, and holds it here
+ * between calls to CHOLMOD. cholmod_start sets these pointers to NULL
+ * (which is why it must be the first routine called in CHOLMOD).
+ * cholmod_finish frees the workspace (which is why it must be the last
+ * call to CHOLMOD).
+ */
+
+ size_t nrow ; /* size of Flag and Head */
+ UF_long mark ; /* mark value for Flag array */
+ size_t iworksize ; /* size of Iwork. Upper bound: 6*nrow+ncol */
+ size_t xworksize ; /* size of Xwork, in bytes.
+ * maxrank*nrow*sizeof(double) for update/downdate.
+ * 2*nrow*sizeof(double) otherwise */
+
+ /* initialized workspace: contents needed between calls to CHOLMOD */
+ void *Flag ; /* size nrow, an integer array. Kept cleared between
+ * calls to cholmod rouines (Flag [i] < mark) */
+
+ void *Head ; /* size nrow+1, an integer array. Kept cleared between
+ * calls to cholmod routines (Head [i] = EMPTY) */
+
+ void *Xwork ; /* a double array. Its size varies. It is nrow for
+ * most routines (cholmod_rowfac, cholmod_add,
+ * cholmod_aat, cholmod_norm, cholmod_ssmult) for the real case, twice
+ * that when the input matrices are complex or zomplex. It is of size
+ * 2*nrow for cholmod_rowadd and cholmod_rowdel. For cholmod_updown,
+ * its size is maxrank*nrow where maxrank is 2, 4, or 8. Kept cleared
+ * between calls to cholmod (set to zero). */
+
+ /* uninitialized workspace, contents not needed between calls to CHOLMOD */
+ void *Iwork ; /* size iworksize, 2*nrow+ncol for most routines,
+ * up to 6*nrow+ncol for cholmod_analyze. */
+
+ int itype ; /* If CHOLMOD_LONG, Flag, Head, and Iwork are UF_long.
+ * Otherwise all three arrays are int. */
+
+ int dtype ; /* double or float */
+
+ /* Common->itype and Common->dtype are used to define the types of all
+ * sparse matrices, triplet matrices, dense matrices, and factors
+ * created using this Common struct. The itypes and dtypes of all
+ * parameters to all CHOLMOD routines must match. */
+
+ int no_workspace_reallocate ; /* this is an internal flag, used as a
+ * precaution by cholmod_analyze. It is normally false. If true,
+ * cholmod_allocate_work is not allowed to reallocate any workspace;
+ * they must use the existing workspace in Common (Iwork, Flag, Head,
+ * and Xwork). Added for CHOLMOD v1.1 */
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics */
+ /* ---------------------------------------------------------------------- */
+
+ /* fl and lnz are set only in cholmod_analyze and cholmod_rowcolcounts,
+ * in the Cholesky modudle. modfl is set only in the Modify module. */
+
+ int status ; /* error code */
+ double fl ; /* LL' flop count from most recent analysis */
+ double lnz ; /* fundamental nz in L */
+ double anz ; /* nonzeros in tril(A) if A is symmetric/lower,
+ * triu(A) if symmetric/upper, or tril(A*A') if
+ * unsymmetric, in last call to cholmod_analyze. */
+ double modfl ; /* flop count from most recent update/downdate/
+ * rowadd/rowdel (excluding flops to modify the
+ * solution to Lx=b, if computed) */
+ size_t malloc_count ; /* # of objects malloc'ed minus the # free'd*/
+ size_t memory_usage ; /* peak memory usage in bytes */
+ size_t memory_inuse ; /* current memory usage in bytes */
+
+ double nrealloc_col ; /* # of column reallocations */
+ double nrealloc_factor ;/* # of factor reallocations due to col. reallocs */
+ double ndbounds_hit ; /* # of times diagonal modified by dbound */
+
+ double rowfacfl ; /* # of flops in last call to cholmod_rowfac */
+ double aatfl ; /* # of flops to compute A(:,f)*A(:,f)' */
+
+ /* ---------------------------------------------------------------------- */
+ /* future expansion */
+ /* ---------------------------------------------------------------------- */
+
+ /* To allow CHOLMOD to be updated without recompiling the user application,
+ * additional space is set aside here for future statistics, parameters,
+ * and workspace. Note: additional entries were added in v1.1 to the
+ * method array, above, and thus v1.0 and v1.1 are not binary compatible.
+ *
+ * v1.1 to the current version are binary compatible.
+ */
+
+ double other1 [16] ;
+ UF_long other2 [16] ;
+ int other3 [13] ; /* reduced from size 16 in v1.1. */
+
+ int prefer_binary ; /* cholmod_read_triplet converts a symmetric
+ * pattern-only matrix into a real matrix. If
+ * prefer_binary is FALSE, the diagonal entries are set to 1 + the degree
+ * of the row/column, and off-diagonal entries are set to -1 (resulting
+ * in a positive definite matrix if the diagonal is zero-free). Most
+ * symmetric patterns are the pattern a positive definite matrix. If
+ * this parameter is TRUE, then the matrix is returned with a 1 in each
+ * entry, instead. Default: FALSE. Added in v1.3. */
+
+ /* control parameter (added for v1.2): */
+ int default_nesdis ; /* Default: FALSE. If FALSE, then the default
+ * ordering strategy (when Common->nmethods == 0)
+ * is to try the given ordering (if present), AMD, and then METIS if AMD
+ * reports high fill-in. If Common->default_nesdis is TRUE then NESDIS
+ * is used instead in the default strategy. */
+
+ /* statistic (added for v1.2): */
+ int called_nd ; /* TRUE if the last call to
+ * cholmod_analyze called NESDIS or METIS. */
+
+ size_t other4 [16] ;
+ void *other5 [16] ;
+
+} cholmod_common ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_start: first call to CHOLMOD */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_start
+(
+ cholmod_common *Common
+) ;
+
+int cholmod_l_start (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_finish: last call to CHOLMOD */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_finish
+(
+ cholmod_common *Common
+) ;
+
+int cholmod_l_finish (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_defaults: restore default parameters */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_defaults
+(
+ cholmod_common *Common
+) ;
+
+int cholmod_l_defaults (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_maxrank: return valid maximum rank for update/downdate */
+/* -------------------------------------------------------------------------- */
+
+size_t cholmod_maxrank /* returns validated value of Common->maxrank */
+(
+ /* ---- input ---- */
+ size_t n, /* A and L will have n rows */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+size_t cholmod_l_maxrank (size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_allocate_work: allocate workspace in Common */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_allocate_work
+(
+ /* ---- input ---- */
+ size_t nrow, /* size: Common->Flag (nrow), Common->Head (nrow+1) */
+ size_t iworksize, /* size of Common->Iwork */
+ size_t xworksize, /* size of Common->Xwork */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_allocate_work (size_t, size_t, size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_free_work: free workspace in Common */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_free_work
+(
+ cholmod_common *Common
+) ;
+
+int cholmod_l_free_work (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_clear_flag: clear Flag workspace in Common */
+/* -------------------------------------------------------------------------- */
+
+/* use a macro for speed */
+#define CHOLMOD_CLEAR_FLAG(Common) \
+{ \
+ Common->mark++ ; \
+ if (Common->mark <= 0) \
+ { \
+ Common->mark = EMPTY ; \
+ CHOLMOD (clear_flag) (Common) ; \
+ } \
+}
+
+UF_long cholmod_clear_flag
+(
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_clear_flag (cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_error: called when CHOLMOD encounters an error */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_error
+(
+ /* ---- input ---- */
+ int status, /* error status */
+ char *file, /* name of source code file where error occured */
+ int line, /* line number in source code file where error occured*/
+ char *message, /* error message */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_error (int, char *, int, char *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_dbound: for internal use in CHOLMOD only */
+/* -------------------------------------------------------------------------- */
+
+double cholmod_dbound /* returns modified diagonal entry of D or L */
+(
+ /* ---- input ---- */
+ double dj, /* diagonal entry of D for LDL' or L for LL' */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+double cholmod_l_dbound (double, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_hypot: compute sqrt (x*x + y*y) accurately */
+/* -------------------------------------------------------------------------- */
+
+double cholmod_hypot
+(
+ /* ---- input ---- */
+ double x, double y
+) ;
+
+double cholmod_l_hypot (double, double) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_divcomplex: complex division, c = a/b */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_divcomplex /* return 1 if divide-by-zero, 0 otherise */
+(
+ /* ---- input ---- */
+ double ar, double ai, /* real and imaginary parts of a */
+ double br, double bi, /* real and imaginary parts of b */
+ /* ---- output --- */
+ double *cr, double *ci /* real and imaginary parts of c */
+) ;
+
+int cholmod_l_divcomplex (double, double, double, double, double *, double *) ;
+
+
+/* ========================================================================== */
+/* === Core/cholmod_sparse ================================================== */
+/* ========================================================================== */
+
+/* A sparse matrix stored in compressed-column form. */
+
+typedef struct cholmod_sparse_struct
+{
+ size_t nrow ; /* the matrix is nrow-by-ncol */
+ size_t ncol ;
+ size_t nzmax ; /* maximum number of entries in the matrix */
+
+ /* pointers to int or UF_long: */
+ void *p ; /* p [0..ncol], the column pointers */
+ void *i ; /* i [0..nzmax-1], the row indices */
+
+ /* for unpacked matrices only: */
+ void *nz ; /* nz [0..ncol-1], the # of nonzeros in each col. In
+ * packed form, the nonzero pattern of column j is in
+ * A->i [A->p [j] ... A->p [j+1]-1]. In unpacked form, column j is in
+ * A->i [A->p [j] ... A->p [j]+A->nz[j]-1] instead. In both cases, the
+ * numerical values (if present) are in the corresponding locations in
+ * the array x (or z if A->xtype is CHOLMOD_ZOMPLEX). */
+
+ /* pointers to double or float: */
+ void *x ; /* size nzmax or 2*nzmax, if present */
+ void *z ; /* size nzmax, if present */
+
+ int stype ; /* Describes what parts of the matrix are considered:
+ *
+ * 0: matrix is "unsymmetric": use both upper and lower triangular parts
+ * (the matrix may actually be symmetric in pattern and value, but
+ * both parts are explicitly stored and used). May be square or
+ * rectangular.
+ * >0: matrix is square and symmetric, use upper triangular part.
+ * Entries in the lower triangular part are ignored.
+ * <0: matrix is square and symmetric, use lower triangular part.
+ * Entries in the upper triangular part are ignored.
+ *
+ * Note that stype>0 and stype<0 are different for cholmod_sparse and
+ * cholmod_triplet. See the cholmod_triplet data structure for more
+ * details.
+ */
+
+ int itype ; /* CHOLMOD_INT: p, i, and nz are int.
+ * CHOLMOD_INTLONG: p is UF_long, i and nz are int.
+ * CHOLMOD_LONG: p, i, and nz are UF_long. */
+
+ int xtype ; /* pattern, real, complex, or zomplex */
+ int dtype ; /* x and z are double or float */
+ int sorted ; /* TRUE if columns are sorted, FALSE otherwise */
+ int packed ; /* TRUE if packed (nz ignored), FALSE if unpacked
+ * (nz is required) */
+
+} cholmod_sparse ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_allocate_sparse: allocate a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_allocate_sparse
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ size_t nzmax, /* max # of nonzeros of A */
+ int sorted, /* TRUE if columns of A sorted, FALSE otherwise */
+ int packed, /* TRUE if A will be packed, FALSE otherwise */
+ int stype, /* stype of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_allocate_sparse (size_t, size_t, size_t, int, int,
+ int, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_free_sparse: free a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_free_sparse
+(
+ /* ---- in/out --- */
+ cholmod_sparse **A, /* matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_free_sparse (cholmod_sparse **, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_reallocate_sparse: change the size (# entries) of sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_reallocate_sparse
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in A */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to reallocate */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_reallocate_sparse ( size_t, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_nnz: return number of nonzeros in a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+UF_long cholmod_nnz
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_nnz (cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_speye: sparse identity matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_speye
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_speye (size_t, size_t, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_spzeros: sparse zero matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_spzeros
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of A */
+ size_t ncol, /* # of columns of A */
+ size_t nzmax, /* max # of nonzeros of A */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_spzeros (size_t, size_t, size_t, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_transpose: transpose a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+/* Return A' or A.' The "values" parameter is 0, 1, or 2 to denote the pattern
+ * transpose, the array transpose (A.'), and the complex conjugate transpose
+ * (A').
+ */
+
+cholmod_sparse *cholmod_transpose
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_transpose (cholmod_sparse *, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_transpose_unsym: transpose an unsymmetric sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+/* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is
+ * already allocated. See cholmod_transpose for a simpler routine. */
+
+int cholmod_transpose_unsym
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
+ int *Perm, /* size nrow, if present (can be NULL) */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_transpose_unsym (cholmod_sparse *, int, UF_long *, UF_long *,
+ size_t, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_transpose_sym: transpose a symmetric sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+/* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated.
+ * See cholmod_transpose for a simpler routine. */
+
+int cholmod_transpose_sym
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
+ int *Perm, /* size nrow, if present (can be NULL) */
+ /* ---- output --- */
+ cholmod_sparse *F, /* F = A' or A(p,p)' */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_transpose_sym (cholmod_sparse *, int, UF_long *, cholmod_sparse *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_ptranspose: transpose a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+/* Return A' or A(p,p)' if A is symmetric. Return A', A(:,f)', or A(p,f)' if
+ * A is unsymmetric. */
+
+cholmod_sparse *cholmod_ptranspose
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to transpose */
+ int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
+ int *Perm, /* if non-NULL, F = A(p,f) or A(p,p) */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_ptranspose (cholmod_sparse *, int, UF_long *,
+ UF_long *, size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_sort: sort row indices in each column of sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_sort
+(
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to sort */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_sort (cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_band: C = tril (triu (A,k1), k2) */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_band
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to extract band matrix from */
+ UF_long k1, /* ignore entries below the k1-st diagonal */
+ UF_long k2, /* ignore entries above the k2-nd diagonal */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_band (cholmod_sparse *, UF_long, UF_long, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_band_inplace: A = tril (triu (A,k1), k2) */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_band_inplace
+(
+ /* ---- input ---- */
+ UF_long k1, /* ignore entries below the k1-st diagonal */
+ UF_long k2, /* ignore entries above the k2-nd diagonal */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix from which entries not in band are removed */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_band_inplace (UF_long, UF_long, int, cholmod_sparse *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_aat: C = A*A' or A(:,f)*A(:,f)' */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_aat
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* input matrix; C=A*A' is constructed */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag),
+ * -2: pattern only, no diagonal, add 50%+n extra
+ * space to C */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_aat (cholmod_sparse *, UF_long *, size_t, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy_sparse: C = A, create an exact copy of a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_copy_sparse
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_copy_sparse (cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy: C = A, with possible change of stype */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_copy
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ int stype, /* requested stype of C */
+ int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_copy (cholmod_sparse *, int, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_add: C = alpha*A + beta*B */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_add
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to add */
+ cholmod_sparse *B, /* matrix to add */
+ double alpha [2], /* scale factor for A */
+ double beta [2], /* scale factor for B */
+ int values, /* if TRUE compute the numerical values of C */
+ int sorted, /* if TRUE, sort columns of C */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_add (cholmod_sparse *, cholmod_sparse *, double *,
+ double *, int, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_sparse_xtype: change the xtype of a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_sparse_xtype
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype (pattern, real, complex, zomplex) */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* sparse matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_sparse_xtype (int, cholmod_sparse *, cholmod_common *) ;
+
+
+/* ========================================================================== */
+/* === Core/cholmod_factor ================================================== */
+/* ========================================================================== */
+
+/* A symbolic and numeric factorization, either simplicial or supernodal.
+ * In all cases, the row indices in the columns of L are kept sorted. */
+
+typedef struct cholmod_factor_struct
+{
+ /* ---------------------------------------------------------------------- */
+ /* for both simplicial and supernodal factorizations */
+ /* ---------------------------------------------------------------------- */
+
+ size_t n ; /* L is n-by-n */
+
+ size_t minor ; /* If the factorization failed, L->minor is the column
+ * at which it failed (in the range 0 to n-1). A value
+ * of n means the factorization was successful or
+ * the matrix has not yet been factorized. */
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic ordering and analysis */
+ /* ---------------------------------------------------------------------- */
+
+ void *Perm ; /* size n, permutation used */
+ void *ColCount ; /* size n, column counts for simplicial L */
+
+ /* ---------------------------------------------------------------------- */
+ /* simplicial factorization */
+ /* ---------------------------------------------------------------------- */
+
+ size_t nzmax ; /* size of i and x */
+
+ void *p ; /* p [0..ncol], the column pointers */
+ void *i ; /* i [0..nzmax-1], the row indices */
+ void *x ; /* x [0..nzmax-1], the numerical values */
+ void *z ;
+ void *nz ; /* nz [0..ncol-1], the # of nonzeros in each column.
+ * i [p [j] ... p [j]+nz[j]-1] contains the row indices,
+ * and the numerical values are in the same locatins
+ * in x. The value of i [p [k]] is always k. */
+
+ void *next ; /* size ncol+2. next [j] is the next column in i/x */
+ void *prev ; /* size ncol+2. prev [j] is the prior column in i/x.
+ * head of the list is ncol+1, and the tail is ncol. */
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that L->x is shared with the simplicial data structure. L->x has
+ * size L->nzmax for a simplicial factor, and size L->xsize for a supernodal
+ * factor. */
+
+ size_t nsuper ; /* number of supernodes */
+ size_t ssize ; /* size of s, integer part of supernodes */
+ size_t xsize ; /* size of x, real part of supernodes */
+ size_t maxcsize ; /* size of largest update matrix */
+ size_t maxesize ; /* max # of rows in supernodes, excl. triangular part */
+
+ void *super ; /* size nsuper+1, first col in each supernode */
+ void *pi ; /* size nsuper+1, pointers to integer patterns */
+ void *px ; /* size nsuper+1, pointers to real parts */
+ void *s ; /* size ssize, integer part of supernodes */
+
+ /* ---------------------------------------------------------------------- */
+ /* factorization type */
+ /* ---------------------------------------------------------------------- */
+
+ int ordering ; /* ordering method used */
+
+ int is_ll ; /* TRUE if LL', FALSE if LDL' */
+ int is_super ; /* TRUE if supernodal, FALSE if simplicial */
+ int is_monotonic ; /* TRUE if columns of L appear in order 0..n-1.
+ * Only applicable to simplicial numeric types. */
+
+ /* There are 8 types of factor objects that cholmod_factor can represent
+ * (only 6 are used):
+ *
+ * Numeric types (xtype is not CHOLMOD_PATTERN)
+ * --------------------------------------------
+ *
+ * simplicial LDL': (is_ll FALSE, is_super FALSE). Stored in compressed
+ * column form, using the simplicial components above (nzmax, p, i,
+ * x, z, nz, next, and prev). The unit diagonal of L is not stored,
+ * and D is stored in its place. There are no supernodes.
+ *
+ * simplicial LL': (is_ll TRUE, is_super FALSE). Uses the same storage
+ * scheme as the simplicial LDL', except that D does not appear.
+ * The first entry of each column of L is the diagonal entry of
+ * that column of L.
+ *
+ * supernodal LDL': (is_ll FALSE, is_super TRUE). Not used.
+ * FUTURE WORK: add support for supernodal LDL'
+ *
+ * supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal factor,
+ * using the supernodal components described above (nsuper, ssize,
+ * xsize, maxcsize, maxesize, super, pi, px, s, x, and z).
+ *
+ *
+ * Symbolic types (xtype is CHOLMOD_PATTERN)
+ * -----------------------------------------
+ *
+ * simplicial LDL': (is_ll FALSE, is_super FALSE). Nothing is present
+ * except Perm and ColCount.
+ *
+ * simplicial LL': (is_ll TRUE, is_super FALSE). Identical to the
+ * simplicial LDL', except for the is_ll flag.
+ *
+ * supernodal LDL': (is_ll FALSE, is_super TRUE). Not used.
+ * FUTURE WORK: add support for supernodal LDL'
+ *
+ * supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal symbolic
+ * factorization. The simplicial symbolic information is present
+ * (Perm and ColCount), as is all of the supernodal factorization
+ * except for the numerical values (x and z).
+ */
+
+ int itype ; /* The integer arrays are Perm, ColCount, p, i, nz,
+ * next, prev, super, pi, px, and s. If itype is
+ * CHOLMOD_INT, all of these are int arrays.
+ * CHOLMOD_INTLONG: p, pi, px are UF_long, others int.
+ * CHOLMOD_LONG: all integer arrays are UF_long. */
+ int xtype ; /* pattern, real, complex, or zomplex */
+ int dtype ; /* x and z double or float */
+
+} cholmod_factor ;
+
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_allocate_factor: allocate a factor (symbolic LL' or LDL') */
+/* -------------------------------------------------------------------------- */
+
+cholmod_factor *cholmod_allocate_factor
+(
+ /* ---- input ---- */
+ size_t n, /* L is n-by-n */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_factor *cholmod_l_allocate_factor (size_t, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_free_factor: free a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_free_factor
+(
+ /* ---- in/out --- */
+ cholmod_factor **L, /* factor to free, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_free_factor (cholmod_factor **, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_reallocate_factor: change the # entries in a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_reallocate_factor
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_reallocate_factor (size_t, cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_change_factor: change the type of factor (e.g., LDL' to LL') */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_change_factor
+(
+ /* ---- input ---- */
+ int to_xtype, /* to CHOLMOD_PATTERN, _REAL, _COMPLEX, _ZOMPLEX */
+ int to_ll, /* TRUE: convert to LL', FALSE: LDL' */
+ int to_super, /* TRUE: convert to supernodal, FALSE: simplicial */
+ int to_packed, /* TRUE: pack simplicial columns, FALSE: do not pack */
+ int to_monotonic, /* TRUE: put simplicial columns in order, FALSE: not */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_change_factor ( int, int, int, int, int, cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_pack_factor: pack the columns of a factor */
+/* -------------------------------------------------------------------------- */
+
+/* Pack the columns of a simplicial factor. Unlike cholmod_change_factor,
+ * it can pack the columns of a factor even if they are not stored in their
+ * natural order (non-monotonic). */
+
+int cholmod_pack_factor
+(
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_pack_factor (cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_reallocate_column: resize a single column of a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_reallocate_column
+(
+ /* ---- input ---- */
+ size_t j, /* the column to reallocate */
+ size_t need, /* required size of column j */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_reallocate_column (size_t, size_t, cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_factor_to_sparse: create a sparse matrix copy of a factor */
+/* -------------------------------------------------------------------------- */
+
+/* Only operates on numeric factors, not symbolic ones */
+
+cholmod_sparse *cholmod_factor_to_sparse
+(
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to copy, converted to symbolic on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_factor_to_sparse (cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy_factor: create a copy of a factor */
+/* -------------------------------------------------------------------------- */
+
+cholmod_factor *cholmod_copy_factor
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_factor *cholmod_l_copy_factor (cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_factor_xtype: change the xtype of a factor */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_factor_xtype
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype (real, complex, or zomplex) */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to change */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_factor_xtype (int, cholmod_factor *, cholmod_common *) ;
+
+
+/* ========================================================================== */
+/* === Core/cholmod_dense =================================================== */
+/* ========================================================================== */
+
+/* A dense matrix in column-oriented form. It has no itype since it contains
+ * no integers. Entry in row i and column j is located in x [i+j*d].
+ */
+
+typedef struct cholmod_dense_struct
+{
+ size_t nrow ; /* the matrix is nrow-by-ncol */
+ size_t ncol ;
+ size_t nzmax ; /* maximum number of entries in the matrix */
+ size_t d ; /* leading dimension (d >= nrow must hold) */
+ void *x ; /* size nzmax or 2*nzmax, if present */
+ void *z ; /* size nzmax, if present */
+ int xtype ; /* pattern, real, complex, or zomplex */
+ int dtype ; /* x and z double or float */
+
+} cholmod_dense ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_allocate_dense: allocate a dense matrix (contents uninitialized) */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_allocate_dense
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ size_t d, /* leading dimension */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_allocate_dense (size_t, size_t, size_t, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_zeros: allocate a dense matrix and set it to zero */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_zeros
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_zeros (size_t, size_t, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_ones: allocate a dense matrix and set it to all ones */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_ones
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_ones (size_t, size_t, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_eye: allocate a dense matrix and set it to the identity matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_eye
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of matrix */
+ size_t ncol, /* # of columns of matrix */
+ int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_eye (size_t, size_t, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_free_dense: free a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_free_dense
+(
+ /* ---- in/out --- */
+ cholmod_dense **X, /* dense matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_free_dense (cholmod_dense **, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_sparse_to_dense: create a dense matrix copy of a sparse matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_sparse_to_dense
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_sparse_to_dense (cholmod_sparse *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_dense_to_sparse: create a sparse matrix copy of a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_dense_to_sparse
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ int values, /* TRUE if values to be copied, FALSE otherwise */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_dense_to_sparse (cholmod_dense *, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy_dense: create a copy of a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_dense *cholmod_copy_dense
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_dense *cholmod_l_copy_dense (cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy_dense2: copy a dense matrix (pre-allocated) */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_copy_dense2
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to copy */
+ /* ---- output --- */
+ cholmod_dense *Y, /* copy of matrix X */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_copy_dense2 (cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_dense_xtype: change the xtype of a dense matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_dense_xtype
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype (real, complex,or zomplex) */
+ /* ---- in/out --- */
+ cholmod_dense *X, /* dense matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_dense_xtype (int, cholmod_dense *, cholmod_common *) ;
+
+
+/* ========================================================================== */
+/* === Core/cholmod_triplet ================================================= */
+/* ========================================================================== */
+
+/* A sparse matrix stored in triplet form. */
+
+typedef struct cholmod_triplet_struct
+{
+ size_t nrow ; /* the matrix is nrow-by-ncol */
+ size_t ncol ;
+ size_t nzmax ; /* maximum number of entries in the matrix */
+ size_t nnz ; /* number of nonzeros in the matrix */
+
+ void *i ; /* i [0..nzmax-1], the row indices */
+ void *j ; /* j [0..nzmax-1], the column indices */
+ void *x ; /* size nzmax or 2*nzmax, if present */
+ void *z ; /* size nzmax, if present */
+
+ int stype ; /* Describes what parts of the matrix are considered:
+ *
+ * 0: matrix is "unsymmetric": use both upper and lower triangular parts
+ * (the matrix may actually be symmetric in pattern and value, but
+ * both parts are explicitly stored and used). May be square or
+ * rectangular.
+ * >0: matrix is square and symmetric. Entries in the lower triangular
+ * part are transposed and added to the upper triangular part when
+ * the matrix is converted to cholmod_sparse form.
+ * <0: matrix is square and symmetric. Entries in the upper triangular
+ * part are transposed and added to the lower triangular part when
+ * the matrix is converted to cholmod_sparse form.
+ *
+ * Note that stype>0 and stype<0 are different for cholmod_sparse and
+ * cholmod_triplet. The reason is simple. You can permute a symmetric
+ * triplet matrix by simply replacing a row and column index with their
+ * new row and column indices, via an inverse permutation. Suppose
+ * P = L->Perm is your permutation, and Pinv is an array of size n.
+ * Suppose a symmetric matrix A is represent by a triplet matrix T, with
+ * entries only in the upper triangular part. Then the following code:
+ *
+ * Ti = T->i ;
+ * Tj = T->j ;
+ * for (k = 0 ; k < n ; k++) Pinv [P [k]] = k ;
+ * for (k = 0 ; k < nz ; k++) Ti [k] = Pinv [Ti [k]] ;
+ * for (k = 0 ; k < nz ; k++) Tj [k] = Pinv [Tj [k]] ;
+ *
+ * creates the triplet form of C=P*A*P'. However, if T initially
+ * contains just the upper triangular entries (T->stype = 1), after
+ * permutation it has entries in both the upper and lower triangular
+ * parts. These entries should be transposed when constructing the
+ * cholmod_sparse form of A, which is what cholmod_triplet_to_sparse
+ * does. Thus:
+ *
+ * C = cholmod_triplet_to_sparse (T, 0, &Common) ;
+ *
+ * will return the matrix C = P*A*P'.
+ *
+ * Since the triplet matrix T is so simple to generate, it's quite easy
+ * to remove entries that you do not want, prior to converting T to the
+ * cholmod_sparse form. So if you include these entries in T, CHOLMOD
+ * assumes that there must be a reason (such as the one above). Thus,
+ * no entry in a triplet matrix is ever ignored.
+ */
+
+ int itype ; /* CHOLMOD_LONG: i and j are UF_long. Otherwise int. */
+ int xtype ; /* pattern, real, complex, or zomplex */
+ int dtype ; /* x and z are double or float */
+
+} cholmod_triplet ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_allocate_triplet: allocate a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_triplet *cholmod_allocate_triplet
+(
+ /* ---- input ---- */
+ size_t nrow, /* # of rows of T */
+ size_t ncol, /* # of columns of T */
+ size_t nzmax, /* max # of nonzeros of T */
+ int stype, /* stype of T */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_triplet *cholmod_l_allocate_triplet (size_t, size_t, size_t, int, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_free_triplet: free a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_free_triplet
+(
+ /* ---- in/out --- */
+ cholmod_triplet **T, /* triplet matrix to deallocate, NULL on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_free_triplet (cholmod_triplet **, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_reallocate_triplet: change the # of entries in a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_reallocate_triplet
+(
+ /* ---- input ---- */
+ size_t nznew, /* new # of entries in T */
+ /* ---- in/out --- */
+ cholmod_triplet *T, /* triplet matrix to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_reallocate_triplet (size_t, cholmod_triplet *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_sparse_to_triplet: create a triplet matrix copy of a sparse matrix*/
+/* -------------------------------------------------------------------------- */
+
+cholmod_triplet *cholmod_sparse_to_triplet
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_triplet *cholmod_l_sparse_to_triplet (cholmod_sparse *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_triplet_to_sparse: create a sparse matrix copy of a triplet matrix*/
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_triplet_to_sparse
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* matrix to copy */
+ size_t nzmax, /* allocate at least this much space in output matrix */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_triplet_to_sparse (cholmod_triplet *, size_t,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_copy_triplet: create a copy of a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+cholmod_triplet *cholmod_copy_triplet
+(
+ /* ---- input ---- */
+ cholmod_triplet *T, /* matrix to copy */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_triplet *cholmod_l_copy_triplet (cholmod_triplet *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_triplet_xtype: change the xtype of a triplet matrix */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_triplet_xtype
+(
+ /* ---- input ---- */
+ int to_xtype, /* requested xtype (pattern, real, complex,or zomplex)*/
+ /* ---- in/out --- */
+ cholmod_triplet *T, /* triplet matrix to change */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_triplet_xtype (int, cholmod_triplet *, cholmod_common *) ;
+
+
+/* ========================================================================== */
+/* === Core/cholmod_memory ================================================== */
+/* ========================================================================== */
+
+/* The user may make use of these, just like malloc and free. You can even
+ * malloc an object and safely free it with cholmod_free, and visa versa
+ * (except that the memory usage statistics will be corrupted). These routines
+ * do differ from malloc and free. If cholmod_free is given a NULL pointer,
+ * for example, it does nothing (unlike the ANSI free). cholmod_realloc does
+ * not return NULL if given a non-NULL pointer and a nonzero size, even if it
+ * fails (it returns the original pointer and sets an error code in
+ * Common->status instead).
+ *
+ * CHOLMOD keeps track of the amount of memory it has allocated, and so the
+ * cholmod_free routine also takes the size of the object being freed. This
+ * is only used for statistics. If you, the user of CHOLMOD, pass the wrong
+ * size, the only consequence is that the memory usage statistics will be
+ * corrupted.
+ */
+
+void *cholmod_malloc /* returns pointer to the newly malloc'd block */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+void *cholmod_l_malloc (size_t, size_t, cholmod_common *) ;
+
+void *cholmod_calloc /* returns pointer to the newly calloc'd block */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+void *cholmod_l_calloc (size_t, size_t, cholmod_common *) ;
+
+void *cholmod_free /* always returns NULL */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* ---- in/out --- */
+ void *p, /* block of memory to free */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+void *cholmod_l_free (size_t, size_t, void *, cholmod_common *) ;
+
+void *cholmod_realloc /* returns pointer to reallocated block */
+(
+ /* ---- input ---- */
+ size_t nnew, /* requested # of items in reallocated block */
+ size_t size, /* size of each item */
+ /* ---- in/out --- */
+ void *p, /* block of memory to realloc */
+ size_t *n, /* current size on input, nnew on output if successful*/
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+void *cholmod_l_realloc (size_t, size_t, void *, size_t *, cholmod_common *) ;
+
+int cholmod_realloc_multiple
+(
+ /* ---- input ---- */
+ size_t nnew, /* requested # of items in reallocated blocks */
+ int nint, /* number of int/UF_long blocks */
+ int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
+ /* ---- in/out --- */
+ void **I, /* int or UF_long block */
+ void **J, /* int or UF_long block */
+ void **X, /* complex, double, or float block */
+ void **Z, /* zomplex case only: double or float block */
+ size_t *n, /* current size of the I,J,X,Z blocks on input,
+ * nnew on output if successful */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_realloc_multiple (size_t, int, int, void **, void **, void **,
+ void **, size_t *, cholmod_common *) ;
+
+/* ========================================================================== */
+/* === symmetry types ======================================================= */
+/* ========================================================================== */
+
+#define CHOLMOD_MM_RECTANGULAR 1
+#define CHOLMOD_MM_UNSYMMETRIC 2
+#define CHOLMOD_MM_SYMMETRIC 3
+#define CHOLMOD_MM_HERMITIAN 4
+#define CHOLMOD_MM_SKEW_SYMMETRIC 5
+#define CHOLMOD_MM_SYMMETRIC_POSDIAG 6
+#define CHOLMOD_MM_HERMITIAN_POSDIAG 7
+
+/* ========================================================================== */
+/* === Numerical relop macros =============================================== */
+/* ========================================================================== */
+
+/* These macros correctly handle the NaN case.
+ *
+ * CHOLMOD_IS_NAN(x):
+ * True if x is NaN. False otherwise. The commonly-existing isnan(x)
+ * function could be used, but it's not in Kernighan & Ritchie 2nd edition
+ * (ANSI C89). It may appear in <math.h>, but I'm not certain about
+ * portability. The expression x != x is true if and only if x is NaN,
+ * according to the IEEE 754 floating-point standard.
+ *
+ * CHOLMOD_IS_ZERO(x):
+ * True if x is zero. False if x is nonzero, NaN, or +/- Inf.
+ * This is (x == 0) if the compiler is IEEE 754 compliant.
+ *
+ * CHOLMOD_IS_NONZERO(x):
+ * True if x is nonzero, NaN, or +/- Inf. False if x zero.
+ * This is (x != 0) if the compiler is IEEE 754 compliant.
+ *
+ * CHOLMOD_IS_LT_ZERO(x):
+ * True if x is < zero or -Inf. False if x is >= 0, NaN, or +Inf.
+ * This is (x < 0) if the compiler is IEEE 754 compliant.
+ *
+ * CHOLMOD_IS_GT_ZERO(x):
+ * True if x is > zero or +Inf. False if x is <= 0, NaN, or -Inf.
+ * This is (x > 0) if the compiler is IEEE 754 compliant.
+ *
+ * CHOLMOD_IS_LE_ZERO(x):
+ * True if x is <= zero or -Inf. False if x is > 0, NaN, or +Inf.
+ * This is (x <= 0) if the compiler is IEEE 754 compliant.
+ */
+
+#ifdef CHOLMOD_WINDOWS
+
+/* Yes, this is exceedingly ugly. Blame Microsoft, which hopelessly */
+/* violates the IEEE 754 floating-point standard in a bizarre way. */
+/* If you're using an IEEE 754-compliant compiler, then x != x is true */
+/* iff x is NaN. For Microsoft, (x < x) is true iff x is NaN. */
+/* So either way, this macro safely detects a NaN. */
+#define CHOLMOD_IS_NAN(x) (((x) != (x)) || (((x) < (x))))
+#define CHOLMOD_IS_ZERO(x) (((x) == 0.) && !CHOLMOD_IS_NAN(x))
+#define CHOLMOD_IS_NONZERO(x) (((x) != 0.) || CHOLMOD_IS_NAN(x))
+#define CHOLMOD_IS_LT_ZERO(x) (((x) < 0.) && !CHOLMOD_IS_NAN(x))
+#define CHOLMOD_IS_GT_ZERO(x) (((x) > 0.) && !CHOLMOD_IS_NAN(x))
+#define CHOLMOD_IS_LE_ZERO(x) (((x) <= 0.) && !CHOLMOD_IS_NAN(x))
+
+#else
+
+/* These all work properly, according to the IEEE 754 standard ... except on */
+/* a PC with windows. Works fine in Linux on the same PC... */
+#define CHOLMOD_IS_NAN(x) ((x) != (x))
+#define CHOLMOD_IS_ZERO(x) ((x) == 0.)
+#define CHOLMOD_IS_NONZERO(x) ((x) != 0.)
+#define CHOLMOD_IS_LT_ZERO(x) ((x) < 0.)
+#define CHOLMOD_IS_GT_ZERO(x) ((x) > 0.)
+#define CHOLMOD_IS_LE_ZERO(x) ((x) <= 0.)
+
+#endif
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_internal.h b/CHOLMOD/Include/cholmod_internal.h
new file mode 100644
index 0000000..383eecb
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_internal.h
@@ -0,0 +1,396 @@
+/* ========================================================================== */
+/* === Include/cholmod_internal.h =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_internal.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_internal.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD internal include file.
+ *
+ * This file contains internal definitions for CHOLMOD, not meant to be included
+ * in user code. They define macros that are not prefixed with CHOLMOD_. This
+ * file can safely #include'd in user code if you want to make use of the
+ * macros defined here, and don't mind the possible name conflicts with your
+ * code, however.
+ *
+ * Required by all CHOLMOD routines. Not required by any user routine that
+ * uses CHOLMOMD. Unless debugging is enabled, this file does not require any
+ * CHOLMOD module (not even the Core module).
+ *
+ * If debugging is enabled, all CHOLMOD modules require the Check module.
+ * Enabling debugging requires that this file be editted. Debugging cannot be
+ * enabled with a compiler flag. This is because CHOLMOD is exceedingly slow
+ * when debugging is enabled. Debugging is meant for development of CHOLMOD
+ * itself, not by users of CHOLMOD.
+ */
+
+#ifndef CHOLMOD_INTERNAL_H
+#define CHOLMOD_INTERNAL_H
+
+/* ========================================================================== */
+/* === large file I/O ======================================================= */
+/* ========================================================================== */
+
+/* Definitions for large file I/O must come before any other #includes. If
+ * this causes problems (may not be portable to all platforms), then compile
+ * CHOLMOD with -DNLARGEFILE. You must do this for MATLAB 6.5 and earlier,
+ * for example. */
+
+#include "cholmod_io64.h"
+
+/* ========================================================================== */
+/* === debugging and basic includes ========================================= */
+/* ========================================================================== */
+
+/* turn off debugging */
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+
+/* Uncomment this line to enable debugging. CHOLMOD will be very slow.
+#undef NDEBUG
+ */
+
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#endif
+
+#if !defined(NPRINT) || !defined(NDEBUG)
+#include <stdio.h>
+#endif
+
+#include <stddef.h>
+#include <math.h>
+#include <limits.h>
+#include <float.h>
+#include <stdlib.h>
+
+/* ========================================================================== */
+/* === basic definitions ==================================================== */
+/* ========================================================================== */
+
+/* Some non-conforming compilers insist on defining TRUE and FALSE. */
+#undef TRUE
+#undef FALSE
+#define TRUE 1
+#define FALSE 0
+#define BOOLEAN(x) ((x) ? TRUE : FALSE)
+
+/* NULL should already be defined, but ensure it is here. */
+#ifndef NULL
+#define NULL ((void *) 0)
+#endif
+
+/* FLIP is a "negation about -1", and is used to mark an integer i that is
+ * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY
+ * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i
+ * for all integers i. UNFLIP (i) is >= EMPTY. */
+#define EMPTY (-1)
+#define FLIP(i) (-(i)-2)
+#define UNFLIP(i) (((i) < EMPTY) ? FLIP (i) : (i))
+
+/* MAX and MIN are not safe to use for NaN's */
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MAX3(a,b,c) (((a) > (b)) ? (MAX (a,c)) : (MAX (b,c)))
+#define MAX4(a,b,c,d) (((a) > (b)) ? (MAX3 (a,c,d)) : (MAX3 (b,c,d)))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+#define IMPLIES(p,q) (!(p) || (q))
+
+/* find the sign: -1 if x < 0, 1 if x > 0, zero otherwise.
+ * Not safe for NaN's */
+#define SIGN(x) (((x) < 0) ? (-1) : (((x) > 0) ? 1 : 0))
+
+/* round up an integer x to a multiple of s */
+#define ROUNDUP(x,s) ((s) * (((x) + ((s) - 1)) / (s)))
+
+#define ERROR(status,msg) \
+ CHOLMOD(error) (status, __FILE__, __LINE__, msg, Common)
+
+/* Check a pointer and return if null. Set status to invalid, unless the
+ * status is already "out of memory" */
+#define RETURN_IF_NULL(A,result) \
+{ \
+ if ((A) == NULL) \
+ { \
+ if (Common->status != CHOLMOD_OUT_OF_MEMORY) \
+ { \
+ ERROR (CHOLMOD_INVALID, "argument missing") ; \
+ } \
+ return (result) ; \
+ } \
+}
+
+/* Return if Common is NULL or invalid */
+#define RETURN_IF_NULL_COMMON(result) \
+{ \
+ if (Common == NULL) \
+ { \
+ return (result) ; \
+ } \
+ if (Common->itype != ITYPE || Common->dtype != DTYPE) \
+ { \
+ Common->status = CHOLMOD_INVALID ; \
+ return (result) ; \
+ } \
+}
+
+#define IS_NAN(x) CHOLMOD_IS_NAN(x)
+#define IS_ZERO(x) CHOLMOD_IS_ZERO(x)
+#define IS_NONZERO(x) CHOLMOD_IS_NONZERO(x)
+#define IS_LT_ZERO(x) CHOLMOD_IS_LT_ZERO(x)
+#define IS_GT_ZERO(x) CHOLMOD_IS_GT_ZERO(x)
+#define IS_LE_ZERO(x) CHOLMOD_IS_LE_ZERO(x)
+
+/* 1e308 is a huge number that doesn't take many characters to print in a
+ * file, in CHOLMOD/Check/cholmod_read and _write. Numbers larger than this
+ * are interpretted as Inf, since sscanf doesn't read in Inf's properly.
+ * This assumes IEEE double precision arithmetic. DBL_MAX would be a little
+ * better, except that it takes too many digits to print in a file. */
+#define HUGE_DOUBLE 1e308
+
+/* ========================================================================== */
+/* === int/UF_long and double/float definitions ============================= */
+/* ========================================================================== */
+
+/* CHOLMOD is designed for 3 types of integer variables:
+ *
+ * (1) all integers are int
+ * (2) most integers are int, some are UF_long
+ * (3) all integers are UF_long
+ *
+ * and two kinds of floating-point values:
+ *
+ * (1) double
+ * (2) float
+ *
+ * the complex types (ANSI-compatible complex, and MATLAB-compatable zomplex)
+ * are based on the double or float type, and are not selected here. They
+ * are typically selected via template routines.
+ *
+ * This gives 6 different modes in which CHOLMOD can be compiled (only the
+ * first two are currently supported):
+ *
+ * DINT double, int prefix: cholmod_
+ * DLONG double, UF_long prefix: cholmod_l_
+ * DMIX double, mixed int/UF_long prefix: cholmod_m_
+ * SINT float, int prefix: cholmod_si_
+ * SLONG float, UF_long prefix: cholmod_sl_
+ * SMIX float, mixed int/log prefix: cholmod_sm_
+ *
+ * These are selected with compile time flags (-DDLONG, for example). If no
+ * flag is selected, the default is DINT.
+ *
+ * All six versions use the same include files. The user-visible include files
+ * are completely independent of which int/UF_long/double/float version is being
+ * used. The integer / real types in all data structures (sparse, triplet,
+ * dense, common, and triplet) are defined at run-time, not compile-time, so
+ * there is only one "cholmod_sparse" data type. Void pointers are used inside
+ * that data structure to point to arrays of the proper type. Each data
+ * structure has an itype and dtype field which determines the kind of basic
+ * types used. These are defined in Include/cholmod_core.h.
+ *
+ * FUTURE WORK: support all six types (float, and mixed int/UF_long)
+ *
+ * UF_long is normally defined as long. However, for WIN64 it is __int64.
+ * It can also be redefined for other platforms, by modifying UFconfig.h.
+ */
+
+#include "UFconfig.h"
+
+/* -------------------------------------------------------------------------- */
+/* Size_max: the largest value of size_t */
+/* -------------------------------------------------------------------------- */
+
+#define Size_max ((size_t) (-1))
+
+/* routines for doing arithmetic on size_t, and checking for overflow */
+size_t cholmod_add_size_t (size_t a, size_t b, int *ok) ;
+size_t cholmod_mult_size_t (size_t a, size_t k, int *ok) ;
+size_t cholmod_l_add_size_t (size_t a, size_t b, int *ok) ;
+size_t cholmod_l_mult_size_t (size_t a, size_t k, int *ok) ;
+
+/* -------------------------------------------------------------------------- */
+/* double (also complex double), UF_long */
+/* -------------------------------------------------------------------------- */
+
+#ifdef DLONG
+#define Real double
+#define Int UF_long
+#define Int_max UF_long_max
+#define CHOLMOD(name) cholmod_l_ ## name
+#define LONG
+#define DOUBLE
+#define ITYPE CHOLMOD_LONG
+#define DTYPE CHOLMOD_DOUBLE
+#define ID UF_long_id
+
+/* -------------------------------------------------------------------------- */
+/* double, int/UF_long */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (DMIX)
+#error "mixed int/UF_long not yet supported"
+
+/* -------------------------------------------------------------------------- */
+/* single, int */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (SINT)
+#error "single-precision not yet supported"
+
+/* -------------------------------------------------------------------------- */
+/* single, UF_long */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (SLONG)
+#error "single-precision not yet supported"
+
+/* -------------------------------------------------------------------------- */
+/* single, int/UF_long */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (SMIX)
+#error "single-precision not yet supported"
+
+/* -------------------------------------------------------------------------- */
+/* double (also complex double), int: this is the default */
+/* -------------------------------------------------------------------------- */
+
+#else
+
+#ifndef DINT
+#define DINT
+#endif
+#define INT
+#define DOUBLE
+
+#define Real double
+#define Int int
+#define Int_max INT_MAX
+#define CHOLMOD(name) cholmod_ ## name
+#define ITYPE CHOLMOD_INT
+#define DTYPE CHOLMOD_DOUBLE
+#define ID "%d"
+
+#endif
+
+
+/* ========================================================================== */
+/* === real/complex arithmetic ============================================== */
+/* ========================================================================== */
+
+#include "cholmod_complexity.h"
+
+/* ========================================================================== */
+/* === Architecture and BLAS ================================================ */
+/* ========================================================================== */
+
+#include "cholmod_blas.h"
+
+/* ========================================================================== */
+/* === debugging definitions ================================================ */
+/* ========================================================================== */
+
+#ifndef NDEBUG
+
+#include <assert.h>
+#include "cholmod.h"
+
+/* The cholmod_dump routines are in the Check module. No CHOLMOD routine
+ * calls the cholmod_check_* or cholmod_print_* routines in the Check module,
+ * since they use Common workspace that may already be in use. Instead, they
+ * use the cholmod_dump_* routines defined there, which allocate their own
+ * workspace if they need it. */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+/* double, int */
+EXTERN int cholmod_dump ;
+EXTERN int cholmod_dump_malloc ;
+UF_long cholmod_dump_sparse (cholmod_sparse *, char *, cholmod_common *) ;
+int cholmod_dump_factor (cholmod_factor *, char *, cholmod_common *) ;
+int cholmod_dump_triplet (cholmod_triplet *, char *, cholmod_common *) ;
+int cholmod_dump_dense (cholmod_dense *, char *, cholmod_common *) ;
+int cholmod_dump_subset (int *, size_t, size_t, char *, cholmod_common *) ;
+int cholmod_dump_perm (int *, size_t, size_t, char *, cholmod_common *) ;
+int cholmod_dump_parent (int *, size_t, char *, cholmod_common *) ;
+void cholmod_dump_init (char *, cholmod_common *) ;
+int cholmod_dump_mem (char *, UF_long, cholmod_common *) ;
+void cholmod_dump_real (char *, Real *, UF_long, UF_long, int, int,
+ cholmod_common *) ;
+void cholmod_dump_super (UF_long, int *, int *, int *, int *, double *, int,
+ cholmod_common *) ;
+int cholmod_dump_partition (UF_long, int *, int *, int *, int *, UF_long,
+ cholmod_common *) ;
+int cholmod_dump_work(int, int, UF_long, cholmod_common *) ;
+
+/* double, UF_long */
+EXTERN int cholmod_l_dump ;
+EXTERN int cholmod_l_dump_malloc ;
+UF_long cholmod_l_dump_sparse (cholmod_sparse *, char *, cholmod_common *) ;
+int cholmod_l_dump_factor (cholmod_factor *, char *, cholmod_common *) ;
+int cholmod_l_dump_triplet (cholmod_triplet *, char *, cholmod_common *) ;
+int cholmod_l_dump_dense (cholmod_dense *, char *, cholmod_common *) ;
+int cholmod_l_dump_subset (UF_long *, size_t, size_t, char *,
+ cholmod_common *) ;
+int cholmod_l_dump_perm (UF_long *, size_t, size_t, char *, cholmod_common *) ;
+int cholmod_l_dump_parent (UF_long *, size_t, char *, cholmod_common *) ;
+void cholmod_l_dump_init (char *, cholmod_common *) ;
+int cholmod_l_dump_mem (char *, UF_long, cholmod_common *) ;
+void cholmod_l_dump_real (char *, Real *, UF_long, UF_long, int, int,
+ cholmod_common *) ;
+void cholmod_l_dump_super (UF_long, UF_long *, UF_long *, UF_long *, UF_long *,
+ double *, int, cholmod_common *) ;
+int cholmod_l_dump_partition (UF_long, UF_long *, UF_long *, UF_long *,
+ UF_long *, UF_long, cholmod_common *) ;
+int cholmod_l_dump_work(int, int, UF_long, cholmod_common *) ;
+
+#define DEBUG_INIT(s,Common) { CHOLMOD(dump_init)(s, Common) ; }
+#define ASSERT(expression) (assert (expression))
+
+#define PRK(k,params) \
+{ \
+ if (CHOLMOD(dump) >= (k) && Common->print_function != NULL) \
+ { \
+ (Common->print_function) params ; \
+ } \
+}
+
+#define PRINT0(params) PRK (0, params)
+#define PRINT1(params) PRK (1, params)
+#define PRINT2(params) PRK (2, params)
+#define PRINT3(params) PRK (3, params)
+
+#define PRINTM(params) \
+{ \
+ if (CHOLMOD(dump_malloc) > 0) \
+ { \
+ printf params ; \
+ } \
+}
+
+#define DEBUG(statement) statement
+
+#else
+
+/* Debugging disabled (the normal case) */
+#define PRK(k,params)
+#define DEBUG_INIT(s,Common)
+#define PRINT0(params)
+#define PRINT1(params)
+#define PRINT2(params)
+#define PRINT3(params)
+#define PRINTM(params)
+#define ASSERT(expression)
+#define DEBUG(statement)
+#endif
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_io64.h b/CHOLMOD/Include/cholmod_io64.h
new file mode 100644
index 0000000..98bf2b3
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_io64.h
@@ -0,0 +1,46 @@
+/* ========================================================================== */
+/* === Include/cholmod_io64 ================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_io64.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_io64.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Definitions required for large file I/O, which must come before any other
+ * #includes. These are not used if -DNLARGEFILE is defined at compile time.
+ * Large file support may not be portable across all platforms and compilers;
+ * if you encounter an error here, compile your code with -DNLARGEFILE. In
+ * particular, you must use -DNLARGEFILE for MATLAB 6.5 or earlier (which does
+ * not have the io64.h include file).
+ */
+
+#ifndef CHOLMOD_IO_H
+#define CHOLMOD_IO_H
+
+/* skip all of this if NLARGEFILE is defined at the compiler command line */
+#ifndef NLARGEFILE
+
+#if defined(MATLAB_MEX_FILE) || defined(MATHWORKS)
+
+/* CHOLMOD is being compiled as a MATLAB MEX file, or for use inside MATLAB */
+#include "io64.h"
+
+#else
+
+/* CHOLMOD is being compiled in a stand-alone library */
+#undef _LARGEFILE64_SOURCE
+#define _LARGEFILE64_SOURCE
+#undef _FILE_OFFSET_BITS
+#define _FILE_OFFSET_BITS 64
+
+#endif
+
+#endif
+
+#endif
+
diff --git a/CHOLMOD/Include/cholmod_matrixops.h b/CHOLMOD/Include/cholmod_matrixops.h
new file mode 100644
index 0000000..b4d090b
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_matrixops.h
@@ -0,0 +1,235 @@
+/* ========================================================================== */
+/* === Include/cholmod_matrixops.h ========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_matrixops.h.
+ * Copyright (C) 2005-2006, Timothy A. Davis
+ * CHOLMOD/Include/cholmod_matrixops.h is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD MatrixOps module.
+ *
+ * Basic operations on sparse and dense matrices.
+ *
+ * cholmod_drop A = entries in A with abs. value >= tol
+ * cholmod_norm_dense s = norm (X), 1-norm, inf-norm, or 2-norm
+ * cholmod_norm_sparse s = norm (A), 1-norm or inf-norm
+ * cholmod_horzcat C = [A,B]
+ * cholmod_scale A = diag(s)*A, A*diag(s), s*A or diag(s)*A*diag(s)
+ * cholmod_sdmult Y = alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y
+ * cholmod_ssmult C = A*B
+ * cholmod_submatrix C = A (i,j), where i and j are arbitrary vectors
+ * cholmod_vertcat C = [A ; B]
+ *
+ * A, B, C: sparse matrices (cholmod_sparse)
+ * X, Y: dense matrices (cholmod_dense)
+ * s: scalar or vector
+ *
+ * Requires the Core module. Not required by any other CHOLMOD module.
+ */
+
+#ifndef CHOLMOD_MATRIXOPS_H
+#define CHOLMOD_MATRIXOPS_H
+
+#include "cholmod_core.h"
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_drop: drop entries with small absolute value */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_drop
+(
+ /* ---- input ---- */
+ double tol, /* keep entries with absolute value > tol */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to drop entries from */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_drop (double, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_norm_dense: s = norm (X), 1-norm, inf-norm, or 2-norm */
+/* -------------------------------------------------------------------------- */
+
+double cholmod_norm_dense
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to compute the norm of */
+ int norm, /* type of norm: 0: inf. norm, 1: 1-norm, 2: 2-norm */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+double cholmod_l_norm_dense (cholmod_dense *, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_norm_sparse: s = norm (A), 1-norm or inf-norm */
+/* -------------------------------------------------------------------------- */
+
+double cholmod_norm_sparse
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to compute the norm of */
+ int norm, /* type of norm: 0: inf. norm, 1: 1-norm */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+double cholmod_l_norm_sparse (cholmod_sparse *, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_horzcat: C = [A,B] */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_horzcat
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* left matrix to concatenate */
+ cholmod_sparse *B, /* right matrix to concatenate */
+ int values, /* if TRUE compute the numerical values of C */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_horzcat (cholmod_sparse *, cholmod_sparse *, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_scale: A = diag(s)*A, A*diag(s), s*A or diag(s)*A*diag(s) */
+/* -------------------------------------------------------------------------- */
+
+/* scaling modes, selected by the scale input parameter: */
+#define CHOLMOD_SCALAR 0 /* A = s*A */
+#define CHOLMOD_ROW 1 /* A = diag(s)*A */
+#define CHOLMOD_COL 2 /* A = A*diag(s) */
+#define CHOLMOD_SYM 3 /* A = diag(s)*A*diag(s) */
+
+int cholmod_scale
+(
+ /* ---- input ---- */
+ cholmod_dense *S, /* scale factors (scalar or vector) */
+ int scale, /* type of scaling to compute */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to scale */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_scale (cholmod_dense *, int, cholmod_sparse *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_sdmult: Y = alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y */
+/* -------------------------------------------------------------------------- */
+
+/* Sparse matrix times dense matrix */
+
+int cholmod_sdmult
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to multiply */
+ int transpose, /* use A if 0, or A' otherwise */
+ double alpha [2], /* scale factor for A */
+ double beta [2], /* scale factor for Y */
+ cholmod_dense *X, /* dense matrix to multiply */
+ /* ---- in/out --- */
+ cholmod_dense *Y, /* resulting dense matrix */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_sdmult (cholmod_sparse *, int, double *, double *,
+ cholmod_dense *, cholmod_dense *Y, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_ssmult: C = A*B */
+/* -------------------------------------------------------------------------- */
+
+/* Sparse matrix times sparse matrix */
+
+cholmod_sparse *cholmod_ssmult
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* left matrix to multiply */
+ cholmod_sparse *B, /* right matrix to multiply */
+ int stype, /* requested stype of C */
+ int values, /* TRUE: do numerical values, FALSE: pattern only */
+ int sorted, /* if TRUE then return C with sorted columns */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_ssmult (cholmod_sparse *, cholmod_sparse *, int, int,
+ int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_submatrix: C = A (r,c), where i and j are arbitrary vectors */
+/* -------------------------------------------------------------------------- */
+
+/* rsize < 0 denotes ":" in MATLAB notation, or more precisely 0:(A->nrow)-1.
+ * In this case, r can be NULL. An rsize of zero, or r = NULL and rsize >= 0,
+ * denotes "[ ]" in MATLAB notation (the empty set).
+ * Similar rules hold for csize.
+ */
+
+cholmod_sparse *cholmod_submatrix
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to subreference */
+ int *rset, /* set of row indices, duplicates OK */
+ UF_long rsize, /* size of r; rsize < 0 denotes ":" */
+ int *cset, /* set of column indices, duplicates OK */
+ UF_long csize, /* size of c; csize < 0 denotes ":" */
+ int values, /* if TRUE compute the numerical values of C */
+ int sorted, /* if TRUE then return C with sorted columns */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_submatrix (cholmod_sparse *, UF_long *, UF_long,
+ UF_long *, UF_long, int, int, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_vertcat: C = [A ; B] */
+/* -------------------------------------------------------------------------- */
+
+cholmod_sparse *cholmod_vertcat
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* left matrix to concatenate */
+ cholmod_sparse *B, /* right matrix to concatenate */
+ int values, /* if TRUE compute the numerical values of C */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+cholmod_sparse *cholmod_l_vertcat (cholmod_sparse *, cholmod_sparse *, int,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_symmetry: determine if a sparse matrix is symmetric */
+/* -------------------------------------------------------------------------- */
+
+int cholmod_symmetry
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ int option,
+ /* ---- output ---- */
+ int *xmatched,
+ int *pmatched,
+ int *nzoffdiag,
+ int *nzdiag,
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_symmetry (cholmod_sparse *, int, UF_long *, UF_long *, UF_long *,
+ UF_long *, cholmod_common *) ;
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_modify.h b/CHOLMOD/Include/cholmod_modify.h
new file mode 100644
index 0000000..bb7dd5a
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_modify.h
@@ -0,0 +1,304 @@
+/* ========================================================================== */
+/* === Include/cholmod_modify.h ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_modify.h.
+ * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager
+ * CHOLMOD/Include/cholmod_modify.h is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Modify module.
+ *
+ * Sparse Cholesky modification routines: update / downdate / rowadd / rowdel.
+ * Can also modify a corresponding solution to Lx=b when L is modified. This
+ * module is most useful when applied on a Cholesky factorization computed by
+ * the Cholesky module, but it does not actually require the Cholesky module.
+ * The Core module can create an identity Cholesky factorization (LDL' where
+ * L=D=I) that can then by modified by these routines.
+ *
+ * Primary routines:
+ * -----------------
+ *
+ * cholmod_updown multiple rank update/downdate
+ * cholmod_rowadd add a row to an LDL' factorization
+ * cholmod_rowdel delete a row from an LDL' factorization
+ *
+ * Secondary routines:
+ * -------------------
+ *
+ * cholmod_updown_solve update/downdate, and modify solution to Lx=b
+ * cholmod_updown_mark update/downdate, and modify solution to partial Lx=b
+ * cholmod_updown_mask update/downdate for LPDASA
+ * cholmod_rowadd_solve add a row, and update solution to Lx=b
+ * cholmod_rowadd_mark add a row, and update solution to partial Lx=b
+ * cholmod_rowdel_solve delete a row, and downdate Lx=b
+ * cholmod_rowdel_mark delete a row, and downdate solution to partial Lx=b
+ *
+ * Requires the Core module. Not required by any other CHOLMOD module.
+ */
+
+#ifndef CHOLMOD_MODIFY_H
+#define CHOLMOD_MODIFY_H
+
+#include "cholmod_core.h"
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_updown: multiple rank update/downdate */
+/* -------------------------------------------------------------------------- */
+
+/* Compute the new LDL' factorization of LDL'+CC' (an update) or LDL'-CC'
+ * (a downdate). The factor object L need not be an LDL' factorization; it
+ * is converted to one if it isn't. */
+
+int cholmod_updown
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_updown (int, cholmod_sparse *, cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_updown_solve: update/downdate, and modify solution to Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_updown, except that it also updates/downdates the
+ * solution to Lx=b+DeltaB. x and b must be n-by-1 dense matrices. b is not
+ * need as input to this routine, but a sparse change to b is (DeltaB). Only
+ * entries in DeltaB corresponding to columns modified in L are accessed; the
+ * rest must be zero. */
+
+int cholmod_updown_solve
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_updown_solve (int, cholmod_sparse *, cholmod_factor *,
+ cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_updown_mark: update/downdate, and modify solution to partial Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_updown_solve, except only part of L is used in
+ * the update/downdate of the solution to Lx=b. This routine is an "expert"
+ * routine. It is meant for use in LPDASA only. See cholmod_updown.c for
+ * a description of colmark. */
+
+int cholmod_updown_mark
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ int *colmark, /* int array of size n. See cholmod_updown.c */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_updown_mark (int, cholmod_sparse *, UF_long *, cholmod_factor *,
+ cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_updown_mask: update/downdate, for LPDASA */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_updown_mark, except has an additional "mask"
+ * argument. This routine is an "expert" routine. It is meant for use in
+ * LPDASA only. See cholmod_updown.c for a description of mask. */
+
+int cholmod_updown_mask
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ int *colmark, /* int array of size n. See cholmod_updown.c */
+ int *mask, /* size n */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_updown_mask (int, cholmod_sparse *, UF_long *, UF_long *,
+ cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowadd: add a row to an LDL' factorization (a rank-2 update) */
+/* -------------------------------------------------------------------------- */
+
+/* cholmod_rowadd adds a row to the LDL' factorization. It computes the kth
+ * row and kth column of L, and then updates the submatrix L (k+1:n,k+1:n)
+ * accordingly. The kth row and column of L must originally be equal to the
+ * kth row and column of the identity matrix. The kth row/column of L is
+ * computed as the factorization of the kth row/column of the matrix to
+ * factorize, which is provided as a single n-by-1 sparse matrix R. */
+
+int cholmod_rowadd
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to add */
+ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowadd (size_t, cholmod_sparse *, cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowadd_solve: add a row, and update solution to Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_rowadd, and also updates the solution to Lx=b
+ * See cholmod_updown for a description of how Lx=b is updated. There is on
+ * additional parameter: bk specifies the new kth entry of b. */
+
+int cholmod_rowadd_solve
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to add */
+ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */
+ double bk [2], /* kth entry of the right-hand-side b */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowadd_solve (size_t, cholmod_sparse *, double *,
+ cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowadd_mark: add a row, and update solution to partial Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_rowadd_solve, except only part of L is used in
+ * the update/downdate of the solution to Lx=b. This routine is an "expert"
+ * routine. It is meant for use in LPDASA only. */
+
+int cholmod_rowadd_mark
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to add */
+ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */
+ double bk [2], /* kth entry of the right hand side, b */
+ int *colmark, /* int array of size n. See cholmod_updown.c */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowadd_mark (size_t, cholmod_sparse *, double *, UF_long *,
+ cholmod_factor *, cholmod_dense *, cholmod_dense *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowdel: delete a row from an LDL' factorization (a rank-2 update) */
+/* -------------------------------------------------------------------------- */
+
+/* Sets the kth row and column of L to be the kth row and column of the identity
+ * matrix, and updates L(k+1:n,k+1:n) accordingly. To reduce the running time,
+ * the caller can optionally provide the nonzero pattern (or an upper bound) of
+ * kth row of L, as the sparse n-by-1 vector R. Provide R as NULL if you want
+ * CHOLMOD to determine this itself, which is easier for the caller, but takes
+ * a little more time.
+ */
+
+int cholmod_rowdel
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to delete */
+ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowdel (size_t, cholmod_sparse *, cholmod_factor *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowdel_solve: delete a row, and downdate Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_rowdel, but also downdates the solution to Lx=b.
+ * When row/column k of A is "deleted" from the system A*y=b, this can induce
+ * a change to x, in addition to changes arising when L and b are modified.
+ * If this is the case, the kth entry of y is required as input (yk) */
+
+int cholmod_rowdel_solve
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to delete */
+ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */
+ double yk [2], /* kth entry in the solution to A*y=b */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowdel_solve (size_t, cholmod_sparse *, double *,
+ cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_rowdel_mark: delete a row, and downdate solution to partial Lx=b */
+/* -------------------------------------------------------------------------- */
+
+/* Does the same as cholmod_rowdel_solve, except only part of L is used in
+ * the update/downdate of the solution to Lx=b. This routine is an "expert"
+ * routine. It is meant for use in LPDASA only. */
+
+int cholmod_rowdel_mark
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to delete */
+ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */
+ double yk [2], /* kth entry in the solution to A*y=b */
+ int *colmark, /* int array of size n. See cholmod_updown.c */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_rowdel_mark (size_t, cholmod_sparse *, double *, UF_long *,
+ cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_partition.h b/CHOLMOD/Include/cholmod_partition.h
new file mode 100644
index 0000000..1adbc46
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_partition.h
@@ -0,0 +1,233 @@
+/* ========================================================================== */
+/* === Include/cholmod_partition.h ========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_partition.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_partition.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Partition module.
+ *
+ * Graph partitioning and graph-partition-based orderings. Includes an
+ * interface to CCOLAMD and CSYMAMD, constrained minimum degree ordering
+ * methods which order a matrix following constraints determined via nested
+ * dissection.
+ *
+ * cholmod_nested_dissection CHOLMOD nested dissection ordering
+ * cholmod_metis METIS nested dissection ordering (METIS_NodeND)
+ * cholmod_ccolamd interface to CCOLAMD ordering
+ * cholmod_csymamd interface to CSYMAMD ordering
+ * cholmod_camd interface to CAMD ordering
+ * cholmod_bisect graph partitioner (currently based on METIS)
+ * cholmod_metis_bisector direct interface to METIS_NodeComputeSeparator
+ *
+ * Requires the Core and Cholesky modules, and three packages: METIS, CAMD,
+ * and CCOLAMD. Optionally used by the Cholesky module.
+ *
+ * Note that METIS does not have a version that uses UF_long integers. If you
+ * try to use cholmod_nested_dissection, cholmod_metis, cholmod_bisect, or
+ * cholmod_metis_bisector on a matrix that is too large, an error code will be
+ * returned. METIS does have an "idxtype", which could be redefined as UF_long,
+ * if you wish to edit METIS or use compile-time flags to redefine idxtype.
+ */
+
+#ifndef CHOLMOD_PARTITION_H
+#define CHOLMOD_PARTITION_H
+
+#include "cholmod_core.h"
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_nested_dissection */
+/* -------------------------------------------------------------------------- */
+
+/* Order A, AA', or A(:,f)*A(:,f)' using CHOLMOD's nested dissection method
+ * (METIS's node bisector applied recursively to compute the separator tree
+ * and constraint sets, followed by CCOLAMD using the constraints). Usually
+ * finds better orderings than METIS_NodeND, but takes longer.
+ */
+
+UF_long cholmod_nested_dissection /* returns # of components */
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ int *Perm, /* size A->nrow, output permutation */
+ int *CParent, /* size A->nrow. On output, CParent [c] is the parent
+ * of component c, or EMPTY if c is a root, and where
+ * c is in the range 0 to # of components minus 1 */
+ int *Cmember, /* size A->nrow. Cmember [j] = c if node j of A is
+ * in component c */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_nested_dissection (cholmod_sparse *, UF_long *, size_t,
+ UF_long *, UF_long *, UF_long *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_metis */
+/* -------------------------------------------------------------------------- */
+
+/* Order A, AA', or A(:,f)*A(:,f)' using METIS_NodeND. */
+
+int cholmod_metis
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int postorder, /* if TRUE, follow with etree or coletree postorder */
+ /* ---- output --- */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_metis (cholmod_sparse *, UF_long *, size_t, int, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_ccolamd */
+/* -------------------------------------------------------------------------- */
+
+/* Order AA' or A(:,f)*A(:,f)' using CCOLAMD. */
+
+int cholmod_ccolamd
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int *Cmember, /* size A->nrow. Cmember [i] = c if row i is in the
+ * constraint set c. c must be >= 0. The # of
+ * constraint sets is max (Cmember) + 1. If Cmember is
+ * NULL, then it is interpretted as Cmember [i] = 0 for
+ * all i */
+ /* ---- output --- */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_ccolamd (cholmod_sparse *, UF_long *, size_t, UF_long *,
+ UF_long *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_csymamd */
+/* -------------------------------------------------------------------------- */
+
+/* Order A using CSYMAMD. */
+
+int cholmod_csymamd
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ /* ---- output --- */
+ int *Cmember, /* size nrow. see cholmod_ccolamd above */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_csymamd (cholmod_sparse *, UF_long *, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_camd */
+/* -------------------------------------------------------------------------- */
+
+/* Order A using CAMD. */
+
+int cholmod_camd
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ int *Cmember, /* size nrow. see cholmod_ccolamd above */
+ int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_camd (cholmod_sparse *, UF_long *, size_t, UF_long *, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_bisect */
+/* -------------------------------------------------------------------------- */
+
+/* Finds a node bisector of A, A*A', A(:,f)*A(:,f)'. */
+
+UF_long cholmod_bisect /* returns # of nodes in separator */
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to bisect */
+ int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int compress, /* if TRUE, compress the graph first */
+ /* ---- output --- */
+ int *Partition, /* size A->nrow. Node i is in the left graph if
+ * Partition [i] = 0, the right graph if 1, and in the
+ * separator if 2. */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_bisect (cholmod_sparse *, UF_long *, size_t, int, UF_long *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_metis_bisector */
+/* -------------------------------------------------------------------------- */
+
+/* Find a set of nodes that bisects the graph of A or AA' (direct interface
+ * to METIS_NodeComputeSeparator). */
+
+UF_long cholmod_metis_bisector /* returns separator size */
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to bisect */
+ int *Anw, /* size A->nrow, node weights */
+ int *Aew, /* size nz, edge weights */
+ /* ---- output --- */
+ int *Partition, /* size A->nrow. see cholmod_bisect above. */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_metis_bisector (cholmod_sparse *, UF_long *, UF_long *,
+ UF_long *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_collapse_septree */
+/* -------------------------------------------------------------------------- */
+
+/* Collapse nodes in a separator tree. */
+
+UF_long cholmod_collapse_septree
+(
+ /* ---- input ---- */
+ size_t n, /* # of nodes in the graph */
+ size_t ncomponents, /* # of nodes in the separator tree (must be <= n) */
+ double nd_oksep, /* collapse if #sep >= nd_oksep * #nodes in subtree */
+ size_t nd_small, /* collapse if #nodes in subtree < nd_small */
+ /* ---- in/out --- */
+ int *CParent, /* size ncomponents; from cholmod_nested_dissection */
+ int *Cmember, /* size n; from cholmod_nested_dissection */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+UF_long cholmod_l_collapse_septree (size_t, size_t, double, size_t, UF_long *,
+ UF_long *, cholmod_common *) ;
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_supernodal.h b/CHOLMOD/Include/cholmod_supernodal.h
new file mode 100644
index 0000000..cfb483e
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_supernodal.h
@@ -0,0 +1,147 @@
+/* ========================================================================== */
+/* === Include/cholmod_supernodal.h ========================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_supernodal.h.
+ * Copyright (C) 2005-2006, Timothy A. Davis
+ * CHOLMOD/Include/cholmod_supernodal.h is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD Supernodal module.
+ *
+ * Supernodal analysis, factorization, and solve. The simplest way to use
+ * these routines is via the Cholesky module. It does not provide any
+ * fill-reducing orderings, but does accept the orderings computed by the
+ * Cholesky module. It does not require the Cholesky module itself, however.
+ *
+ * Primary routines:
+ * -----------------
+ * cholmod_super_symbolic supernodal symbolic analysis
+ * cholmod_super_numeric supernodal numeric factorization
+ * cholmod_super_lsolve supernodal Lx=b solve
+ * cholmod_super_ltsolve supernodal L'x=b solve
+ *
+ * Prototypes for the BLAS and LAPACK routines that CHOLMOD uses are listed
+ * below, including how they are used in CHOLMOD.
+ *
+ * BLAS routines:
+ * --------------
+ * dtrsv solve Lx=b or L'x=b, L non-unit diagonal, x and b stride-1
+ * dtrsm solve LX=B or L'X=b, L non-unit diagonal
+ * dgemv y=y-A*x or y=y-A'*x (x and y stride-1)
+ * dgemm C=A*B', C=C-A*B, or C=C-A'*B
+ * dsyrk C=tril(A*A')
+ *
+ * LAPACK routines:
+ * ----------------
+ * dpotrf LAPACK: A=chol(tril(A))
+ *
+ * Requires the Core module, and two external packages: LAPACK and the BLAS.
+ * Optionally used by the Cholesky module.
+ */
+
+#ifndef CHOLMOD_SUPERNODAL_H
+#define CHOLMOD_SUPERNODAL_H
+
+#include "cholmod_core.h"
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_super_symbolic */
+/* -------------------------------------------------------------------------- */
+
+/* Analyzes A, AA', or A(:,f)*A(:,f)' in preparation for a supernodal numeric
+ * factorization. The user need not call this directly; cholmod_analyze is
+ * a "simple" wrapper for this routine.
+ */
+
+int cholmod_super_symbolic
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ cholmod_sparse *F, /* F = A' or A(:,f)' */
+ int *Parent, /* elimination tree */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* simplicial symbolic on input,
+ * supernodal symbolic on output */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_super_symbolic (cholmod_sparse *, cholmod_sparse *, UF_long *,
+ cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_super_numeric */
+/* -------------------------------------------------------------------------- */
+
+/* Computes the numeric LL' factorization of A, AA', or A(:,f)*A(:,f)' using
+ * a BLAS-based supernodal method. The user need not call this directly;
+ * cholmod_factorize is a "simple" wrapper for this routine.
+ */
+
+int cholmod_super_numeric
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* F = A' or A(:,f)' */
+ double beta [2], /* beta*I is added to diagonal of matrix to factorize */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_super_numeric (cholmod_sparse *, cholmod_sparse *, double *,
+ cholmod_factor *, cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_super_lsolve */
+/* -------------------------------------------------------------------------- */
+
+/* Solve Lx=b where L is from a supernodal numeric factorization. The user
+ * need not call this routine directly. cholmod_solve is a "simple" wrapper
+ * for this routine. */
+
+int cholmod_super_lsolve
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the forward solve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to Lx=b on output */
+ /* ---- workspace */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_super_lsolve (cholmod_factor *, cholmod_dense *, cholmod_dense *,
+ cholmod_common *) ;
+
+/* -------------------------------------------------------------------------- */
+/* cholmod_super_ltsolve */
+/* -------------------------------------------------------------------------- */
+
+/* Solve L'x=b where L is from a supernodal numeric factorization. The user
+ * need not call this routine directly. cholmod_solve is a "simple" wrapper
+ * for this routine. */
+
+int cholmod_super_ltsolve
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the backsolve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to L'x=b on output */
+ /* ---- workspace */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+) ;
+
+int cholmod_l_super_ltsolve (cholmod_factor *, cholmod_dense *, cholmod_dense *,
+ cholmod_common *) ;
+
+#endif
diff --git a/CHOLMOD/Include/cholmod_template.h b/CHOLMOD/Include/cholmod_template.h
new file mode 100644
index 0000000..aa45b4d
--- /dev/null
+++ b/CHOLMOD/Include/cholmod_template.h
@@ -0,0 +1,238 @@
+/* ========================================================================== */
+/* === Include/cholmod_template.h =========================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* undefine current xtype macros, and then define macros for current type */
+/* -------------------------------------------------------------------------- */
+
+#undef TEMPLATE
+#undef XTYPE
+#undef XTYPE2
+#undef XTYPE_OK
+#undef ENTRY_IS_NONZERO
+#undef ENTRY_IS_ZERO
+#undef ENTRY_IS_ONE
+#undef IMAG_IS_NONZERO
+
+#undef ASSEMBLE
+#undef ASSIGN
+#undef ASSIGN_CONJ
+#undef ASSIGN2
+#undef ASSIGN2_CONJ
+#undef ASSIGN_REAL
+#undef MULT
+#undef MULTADD
+#undef ADD
+#undef ADD_REAL
+#undef MULTSUB
+#undef MULTADDCONJ
+#undef MULTSUBCONJ
+#undef LLDOT
+#undef CLEAR
+#undef DIV
+#undef DIV_REAL
+#undef MULT_REAL
+#undef CLEAR_IMAG
+#undef LDLDOT
+#undef PREFIX
+
+#undef ENTRY_SIZE
+
+#undef XPRINT0
+#undef XPRINT1
+#undef XPRINT2
+#undef XPRINT3
+
+/* -------------------------------------------------------------------------- */
+/* pattern */
+/* -------------------------------------------------------------------------- */
+
+
+#ifdef PATTERN
+
+#define PREFIX p_
+#define TEMPLATE(name) P_TEMPLATE(name)
+#define XTYPE CHOLMOD_PATTERN
+#define XTYPE2 CHOLMOD_REAL
+#define XTYPE_OK(type) (TRUE)
+#define ENTRY_IS_NONZERO(ax,az,q) (TRUE)
+#define ENTRY_IS_ZERO(ax,az,q) (FALSE)
+#define ENTRY_IS_ONE(ax,az,q) (TRUE)
+#define IMAG_IS_NONZERO(ax,az,q) (FALSE)
+#define ENTRY_SIZE 0
+
+#define ASSEMBLE(x,z,p,ax,az,q)
+#define ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN_CONJ(x,z,p,ax,az,q)
+#define ASSIGN2(x,z,p,ax,az,q) P_ASSIGN2(x,z,p,ax,az,q)
+#define ASSIGN2_CONJ(x,z,p,ax,az,q) P_ASSIGN2(x,z,p,ax,az,q)
+#define ASSIGN_REAL(x,p,ax,q)
+#define MULT(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD_REAL(x,p, ax,q, bx,r)
+#define MULTSUB(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define LLDOT(x,p,ax,az,q)
+#define CLEAR(x,z,p)
+#define CLEAR_IMAG(x,z,p)
+#define DIV(x,z,p,ax,az,q)
+#define DIV_REAL(x,z,p, ax,az,q, bx,r)
+#define MULT_REAL(x,z,p, ax,az,q, bx,r)
+#define LDLDOT(x,p, ax,az,q, bx,r)
+
+#define XPRINT0(x,z,p) P_PRINT(0,x,z,p)
+#define XPRINT1(x,z,p) P_PRINT(1,x,z,p)
+#define XPRINT2(x,z,p) P_PRINT(2,x,z,p)
+#define XPRINT3(x,z,p) P_PRINT(3,x,z,p)
+
+/* -------------------------------------------------------------------------- */
+/* real */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (REAL)
+
+#define PREFIX r_
+#define TEMPLATE(name) R_TEMPLATE(name)
+#define XTYPE CHOLMOD_REAL
+#define XTYPE2 CHOLMOD_REAL
+#define XTYPE_OK(type) R_XTYPE_OK(type)
+#define ENTRY_IS_NONZERO(ax,az,q) R_IS_NONZERO(ax,az,q)
+#define ENTRY_IS_ZERO(ax,az,q) R_IS_ZERO(ax,az,q)
+#define ENTRY_IS_ONE(ax,az,q) R_IS_ONE(ax,az,q)
+#define IMAG_IS_NONZERO(ax,az,q) (FALSE)
+#define ENTRY_SIZE 1
+
+#define ASSEMBLE(x,z,p,ax,az,q) R_ASSEMBLE(x,z,p,ax,az,q)
+#define ASSIGN(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN_CONJ(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN2(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN2_CONJ(x,z,p,ax,az,q) R_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN_REAL(x,p,ax,q) R_ASSIGN_REAL(x,p,ax,q)
+#define MULT(x,z,p,ax,az,q,bx,bz,pb) R_MULT(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADD(x,z,p,ax,az,q,bx,bz,pb) R_MULTADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD(x,z,p,ax,az,q,bx,bz,pb) R_ADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD_REAL(x,p, ax,q, bx,r) R_ADD_REAL(x,p, ax,q, bx,r)
+#define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) R_MULTSUB(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ R_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ R_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define LLDOT(x,p,ax,az,q) R_LLDOT(x,p,ax,az,q)
+#define CLEAR(x,z,p) R_CLEAR(x,z,p)
+#define CLEAR_IMAG(x,z,p) R_CLEAR_IMAG(x,z,p)
+#define DIV(x,z,p,ax,az,q) R_DIV(x,z,p,ax,az,q)
+#define DIV_REAL(x,z,p, ax,az,q, bx,r) R_DIV_REAL(x,z,p, ax,az,q, bx,r)
+#define MULT_REAL(x,z,p, ax,az,q, bx,r) R_MULT_REAL(x,z,p, ax,az,q, bx,r)
+#define LDLDOT(x,p, ax,az,q, bx,r) R_LDLDOT(x,p, ax,az,q, bx,r)
+
+#define XPRINT0(x,z,p) R_PRINT(0,x,z,p)
+#define XPRINT1(x,z,p) R_PRINT(1,x,z,p)
+#define XPRINT2(x,z,p) R_PRINT(2,x,z,p)
+#define XPRINT3(x,z,p) R_PRINT(3,x,z,p)
+
+/* -------------------------------------------------------------------------- */
+/* complex */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (COMPLEX)
+
+#define PREFIX c_
+
+#ifdef NCONJUGATE
+#define TEMPLATE(name) CT_TEMPLATE(name)
+#else
+#define TEMPLATE(name) C_TEMPLATE(name)
+#endif
+
+#define ASSEMBLE(x,z,p,ax,az,q) C_ASSEMBLE(x,z,p,ax,az,q)
+#define ASSIGN(x,z,p,ax,az,q) C_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN_CONJ(x,z,p,ax,az,q) C_ASSIGN_CONJ(x,z,p,ax,az,q)
+#define ASSIGN2(x,z,p,ax,az,q) C_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN2_CONJ(x,z,p,ax,az,q) C_ASSIGN_CONJ(x,z,p,ax,az,q)
+#define ASSIGN_REAL(x,p,ax,q) C_ASSIGN_REAL(x,p,ax,q)
+#define XTYPE CHOLMOD_COMPLEX
+#define XTYPE2 CHOLMOD_COMPLEX
+#define XTYPE_OK(type) C_XTYPE_OK(type)
+#define ENTRY_IS_NONZERO(ax,az,q) C_IS_NONZERO(ax,az,q)
+#define ENTRY_IS_ZERO(ax,az,q) C_IS_ZERO(ax,az,q)
+#define ENTRY_IS_ONE(ax,az,q) C_IS_ONE(ax,az,q)
+#define IMAG_IS_NONZERO(ax,az,q) C_IMAG_IS_NONZERO(ax,az,q)
+#define ENTRY_SIZE 2
+
+#define MULTADD(x,z,p,ax,az,q,bx,bz,pb) C_MULTADD(x,z,p,ax,az,q,bx,bz,pb)
+#define MULT(x,z,p,ax,az,q,bx,bz,pb) C_MULT(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD(x,z,p,ax,az,q,bx,bz,pb) C_ADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD_REAL(x,p, ax,q, bx,r) C_ADD_REAL(x,p, ax,q, bx,r)
+#define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) C_MULTSUB(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ C_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ C_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define LLDOT(x,p,ax,az,q) C_LLDOT(x,p,ax,az,q)
+#define CLEAR(x,z,p) C_CLEAR(x,z,p)
+#define CLEAR_IMAG(x,z,p) C_CLEAR_IMAG(x,z,p)
+#define DIV(x,z,p,ax,az,q) C_DIV(x,z,p,ax,az,q)
+#define DIV_REAL(x,z,p, ax,az,q, bx,r) C_DIV_REAL(x,z,p, ax,az,q, bx,r)
+#define MULT_REAL(x,z,p, ax,az,q, bx,r) C_MULT_REAL(x,z,p, ax,az,q, bx,r)
+#define LDLDOT(x,p, ax,az,q, bx,r) C_LDLDOT(x,p, ax,az,q, bx,r)
+
+#define XPRINT0(x,z,p) C_PRINT(0,x,z,p)
+#define XPRINT1(x,z,p) C_PRINT(1,x,z,p)
+#define XPRINT2(x,z,p) C_PRINT(2,x,z,p)
+#define XPRINT3(x,z,p) C_PRINT(3,x,z,p)
+
+/* -------------------------------------------------------------------------- */
+/* zomplex */
+/* -------------------------------------------------------------------------- */
+
+#elif defined (ZOMPLEX)
+
+#define PREFIX z_
+
+#ifdef NCONJUGATE
+#define TEMPLATE(name) ZT_TEMPLATE(name)
+#else
+#define TEMPLATE(name) Z_TEMPLATE(name)
+#endif
+
+#define ASSEMBLE(x,z,p,ax,az,q) Z_ASSEMBLE(x,z,p,ax,az,q)
+#define ASSIGN(x,z,p,ax,az,q) Z_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN_CONJ(x,z,p,ax,az,q) Z_ASSIGN_CONJ(x,z,p,ax,az,q)
+#define ASSIGN2(x,z,p,ax,az,q) Z_ASSIGN(x,z,p,ax,az,q)
+#define ASSIGN2_CONJ(x,z,p,ax,az,q) Z_ASSIGN_CONJ(x,z,p,ax,az,q)
+#define ASSIGN_REAL(x,p,ax,q) Z_ASSIGN_REAL(x,p,ax,q)
+#define XTYPE CHOLMOD_ZOMPLEX
+#define XTYPE2 CHOLMOD_ZOMPLEX
+#define XTYPE_OK(type) Z_XTYPE_OK(type)
+#define ENTRY_IS_NONZERO(ax,az,q) Z_IS_NONZERO(ax,az,q)
+#define ENTRY_IS_ZERO(ax,az,q) Z_IS_ZERO(ax,az,q)
+#define ENTRY_IS_ONE(ax,az,q) Z_IS_ONE(ax,az,q)
+#define IMAG_IS_NONZERO(ax,az,q) Z_IMAG_IS_NONZERO(ax,az,q)
+#define ENTRY_SIZE 1
+
+#define MULTADD(x,z,p,ax,az,q,bx,bz,pb) Z_MULTADD(x,z,p,ax,az,q,bx,bz,pb)
+#define MULT(x,z,p,ax,az,q,bx,bz,pb) Z_MULT(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD(x,z,p,ax,az,q,bx,bz,pb) Z_ADD(x,z,p,ax,az,q,bx,bz,pb)
+#define ADD_REAL(x,p, ax,q, bx,r) Z_ADD_REAL(x,p, ax,q, bx,r)
+#define MULTSUB(x,z,p,ax,az,q,bx,bz,pb) Z_MULTSUB(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ Z_MULTADDCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb) \
+ Z_MULTSUBCONJ(x,z,p,ax,az,q,bx,bz,pb)
+#define LLDOT(x,p,ax,az,q) Z_LLDOT(x,p,ax,az,q)
+#define CLEAR(x,z,p) Z_CLEAR(x,z,p)
+#define CLEAR_IMAG(x,z,p) Z_CLEAR_IMAG(x,z,p)
+#define DIV(x,z,p,ax,az,q) Z_DIV(x,z,p,ax,az,q)
+#define DIV_REAL(x,z,p, ax,az,q, bx,r) Z_DIV_REAL(x,z,p, ax,az,q, bx,r)
+#define MULT_REAL(x,z,p, ax,az,q, bx,r) Z_MULT_REAL(x,z,p, ax,az,q, bx,r)
+#define LDLDOT(x,p, ax,az,q, bx,r) Z_LDLDOT(x,p, ax,az,q, bx,r)
+
+#define XPRINT0(x,z,p) Z_PRINT(0,x,z,p)
+#define XPRINT1(x,z,p) Z_PRINT(1,x,z,p)
+#define XPRINT2(x,z,p) Z_PRINT(2,x,z,p)
+#define XPRINT3(x,z,p) Z_PRINT(3,x,z,p)
+
+#endif
diff --git a/CHOLMOD/Lib/Makefile b/CHOLMOD/Lib/Makefile
new file mode 100644
index 0000000..7d736d3
--- /dev/null
+++ b/CHOLMOD/Lib/Makefile
@@ -0,0 +1,472 @@
+#===============================================================================
+# CHOLOMD/Lib/Makefile: for compiling the CHOLMOD library
+#===============================================================================
+
+default: all
+
+ccode: all
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(CHOLMOD_CONFIG)
+
+all: libcholmod.a
+
+library: libcholmod.a
+
+purge: distclean
+
+distclean: clean
+ - $(RM) libcholmod.a
+
+clean:
+ - $(RM) $(CLEAN)
+
+#-------------------------------------------------------------------------------
+# ../Include/ directory contains all include files:
+#-------------------------------------------------------------------------------
+
+INC = ../Include/cholmod.h \
+ ../Include/cholmod_blas.h \
+ ../Include/cholmod_check.h \
+ ../Include/cholmod_cholesky.h \
+ ../Include/cholmod_complexity.h \
+ ../Include/cholmod_config.h \
+ ../Include/cholmod_core.h \
+ ../Include/cholmod_internal.h \
+ ../Include/cholmod_matrixops.h \
+ ../Include/cholmod_modify.h \
+ ../Include/cholmod_partition.h \
+ ../Include/cholmod_supernodal.h \
+ ../Include/cholmod_template.h
+
+#-------------------------------------------------------------------------------
+# The 7 CHOLMOD library modules (int, double)
+#-------------------------------------------------------------------------------
+
+CORE = cholmod_aat.o cholmod_add.o cholmod_band.o \
+ cholmod_change_factor.o cholmod_common.o cholmod_complex.o \
+ cholmod_copy.o cholmod_dense.o cholmod_error.o cholmod_factor.o \
+ cholmod_memory.o cholmod_sparse.o \
+ cholmod_transpose.o cholmod_triplet.o
+
+CHECK = cholmod_check.o cholmod_read.o cholmod_write.o
+
+CHOLESKY = cholmod_amd.o cholmod_analyze.o cholmod_colamd.o \
+ cholmod_etree.o cholmod_factorize.o cholmod_postorder.o \
+ cholmod_rcond.o cholmod_resymbol.o cholmod_rowcolcounts.o \
+ cholmod_rowfac.o cholmod_solve.o cholmod_spsolve.o
+
+MATRIXOPS = cholmod_drop.o cholmod_horzcat.o cholmod_norm.o \
+ cholmod_scale.o cholmod_sdmult.o cholmod_ssmult.o \
+ cholmod_submatrix.o cholmod_vertcat.o cholmod_symmetry.o
+
+PARTITION = cholmod_ccolamd.o cholmod_csymamd.o \
+ cholmod_metis.o cholmod_nesdis.o cholmod_camd.o
+
+MODIFY = cholmod_rowadd.o cholmod_rowdel.o cholmod_updown.o
+
+SUPERNODAL = cholmod_super_numeric.o cholmod_super_solve.o \
+ cholmod_super_symbolic.o
+
+DI = $(CORE) $(CHECK) $(CHOLESKY) $(MATRIXOPS) $(MODIFY) $(SUPERNODAL) \
+ $(PARTITION)
+
+#-------------------------------------------------------------------------------
+# CHOLMOD library modules (long, double)
+#-------------------------------------------------------------------------------
+
+LCORE = cholmod_l_aat.o cholmod_l_add.o cholmod_l_band.o \
+ cholmod_l_change_factor.o cholmod_l_common.o cholmod_l_complex.o \
+ cholmod_l_copy.o cholmod_l_dense.o cholmod_l_error.o \
+ cholmod_l_factor.o cholmod_l_memory.o \
+ cholmod_l_sparse.o cholmod_l_transpose.o cholmod_l_triplet.o
+
+LCHECK = cholmod_l_check.o cholmod_l_read.o cholmod_l_write.o
+
+LCHOLESKY = cholmod_l_amd.o cholmod_l_analyze.o cholmod_l_colamd.o \
+ cholmod_l_etree.o cholmod_l_factorize.o cholmod_l_postorder.o \
+ cholmod_l_rcond.o cholmod_l_resymbol.o cholmod_l_rowcolcounts.o \
+ cholmod_l_rowfac.o cholmod_l_solve.o cholmod_l_spsolve.o
+
+LMATRIXOPS = cholmod_l_drop.o cholmod_l_horzcat.o cholmod_l_norm.o \
+ cholmod_l_scale.o cholmod_l_sdmult.o cholmod_l_ssmult.o \
+ cholmod_l_submatrix.o cholmod_l_vertcat.o cholmod_l_symmetry.o
+
+LPARTITION = cholmod_l_ccolamd.o cholmod_l_csymamd.o \
+ cholmod_l_metis.o cholmod_l_nesdis.o cholmod_l_camd.o
+
+LMODIFY = cholmod_l_rowadd.o cholmod_l_rowdel.o cholmod_l_updown.o
+
+LSUPERNODAL = cholmod_l_super_numeric.o cholmod_l_super_solve.o \
+ cholmod_l_super_symbolic.o
+
+DL = $(LCORE) $(LCHECK) $(LCHOLESKY) $(LMATRIXOPS) $(LMODIFY) $(LSUPERNODAL) \
+ $(LPARTITION)
+
+#-------------------------------------------------------------------------------
+
+# to compile just the double/int version, use OBJ = $(DI)
+OBJ = $(DI) $(DL)
+
+libcholmod.a: $(OBJ)
+ $(AR) libcholmod.a $(OBJ)
+ $(RANLIB) libcholmod.a
+
+$(OBJ): $(INC)
+
+I = -I../../AMD/Include -I../../AMD/Source -I../../COLAMD/Include \
+ -I$(METIS_PATH)/Lib -I../../CCOLAMD/Include -I../../CAMD/Include \
+ -I../Include -I../../UFconfig
+
+#-------------------------------------------------------------------------------
+# Check Module:
+#-------------------------------------------------------------------------------
+
+cholmod_check.o: ../Check/cholmod_check.c
+ $(C) -c $(I) $<
+
+cholmod_read.o: ../Check/cholmod_read.c
+ $(C) -c $(I) $<
+
+cholmod_write.o: ../Check/cholmod_write.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_check.o: ../Check/cholmod_check.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_read.o: ../Check/cholmod_read.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_write.o: ../Check/cholmod_write.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+
+#-------------------------------------------------------------------------------
+# Core Module:
+#-------------------------------------------------------------------------------
+
+cholmod_common.o: ../Core/cholmod_common.c
+ $(C) -c $(I) $<
+
+cholmod_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c
+ $(C) -c $(I) $<
+
+cholmod_factor.o: ../Core/cholmod_factor.c
+ $(C) -c $(I) $<
+
+cholmod_change_factor.o: ../Core/cholmod_change_factor.c \
+ ../Core/t_cholmod_change_factor.c
+ $(C) -c $(I) $<
+
+cholmod_memory.o: ../Core/cholmod_memory.c
+ $(C) -c $(I) $<
+
+cholmod_sparse.o: ../Core/cholmod_sparse.c
+ $(C) -c $(I) $<
+
+cholmod_complex.o: ../Core/cholmod_complex.c
+ $(C) -c $(I) $<
+
+cholmod_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c
+ $(C) -c $(I) $<
+
+cholmod_band.o: ../Core/cholmod_band.c
+ $(C) -c $(I) $<
+
+cholmod_copy.o: ../Core/cholmod_copy.c
+ $(C) -c $(I) $<
+
+cholmod_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c
+ $(C) -c $(I) $<
+
+cholmod_error.o: ../Core/cholmod_error.c
+ $(C) -c $(I) $<
+
+cholmod_aat.o: ../Core/cholmod_aat.c
+ $(C) -c $(I) $<
+
+cholmod_add.o: ../Core/cholmod_add.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_common.o: ../Core/cholmod_common.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_factor.o: ../Core/cholmod_factor.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_change_factor.o: ../Core/cholmod_change_factor.c \
+ ../Core/t_cholmod_change_factor.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_memory.o: ../Core/cholmod_memory.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_sparse.o: ../Core/cholmod_sparse.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_complex.o: ../Core/cholmod_complex.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_band.o: ../Core/cholmod_band.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_copy.o: ../Core/cholmod_copy.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_error.o: ../Core/cholmod_error.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_aat.o: ../Core/cholmod_aat.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_add.o: ../Core/cholmod_add.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+
+#-------------------------------------------------------------------------------
+# Cholesky Module:
+#-------------------------------------------------------------------------------
+
+cholmod_amd.o: ../Cholesky/cholmod_amd.c
+ $(C) -c $(I) $<
+
+cholmod_analyze.o: ../Cholesky/cholmod_analyze.c
+ $(C) -c $(I) $<
+
+cholmod_colamd.o: ../Cholesky/cholmod_colamd.c
+ $(C) -c $(I) $<
+
+cholmod_etree.o: ../Cholesky/cholmod_etree.c
+ $(C) -c $(I) $<
+
+cholmod_factorize.o: ../Cholesky/cholmod_factorize.c
+ $(C) -c $(I) $<
+
+cholmod_postorder.o: ../Cholesky/cholmod_postorder.c
+ $(C) -c $(I) $<
+
+cholmod_rcond.o: ../Cholesky/cholmod_rcond.c
+ $(C) -c $(I) $<
+
+cholmod_resymbol.o: ../Cholesky/cholmod_resymbol.c
+ $(C) -c $(I) $<
+
+cholmod_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c
+ $(C) -c $(I) $<
+
+cholmod_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \
+ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c
+ $(C) -c $(I) $<
+
+cholmod_spsolve.o: ../Cholesky/cholmod_spsolve.c
+ $(C) -c $(I) $<
+
+cholmod_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_amd.o: ../Cholesky/cholmod_amd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_analyze.o: ../Cholesky/cholmod_analyze.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_colamd.o: ../Cholesky/cholmod_colamd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_etree.o: ../Cholesky/cholmod_etree.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_factorize.o: ../Cholesky/cholmod_factorize.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_postorder.o: ../Cholesky/cholmod_postorder.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_rcond.o: ../Cholesky/cholmod_rcond.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_resymbol.o: ../Cholesky/cholmod_resymbol.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \
+ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_spsolve.o: ../Cholesky/cholmod_spsolve.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+#-------------------------------------------------------------------------------
+# Partition Module:
+#-------------------------------------------------------------------------------
+
+cholmod_ccolamd.o: ../Partition/cholmod_ccolamd.c
+ $(C) -c $(I) $<
+
+cholmod_csymamd.o: ../Partition/cholmod_csymamd.c
+ $(C) -c $(I) $<
+
+cholmod_camd.o: ../Partition/cholmod_camd.c
+ $(C) -c $(I) $<
+
+cholmod_metis.o: ../Partition/cholmod_metis.c
+ $(C) -c $(I) $<
+
+cholmod_nesdis.o: ../Partition/cholmod_nesdis.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_ccolamd.o: ../Partition/cholmod_ccolamd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_csymamd.o: ../Partition/cholmod_csymamd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_camd.o: ../Partition/cholmod_camd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_metis.o: ../Partition/cholmod_metis.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_nesdis.o: ../Partition/cholmod_nesdis.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+
+#-------------------------------------------------------------------------------
+# MatrixOps Module:
+#-------------------------------------------------------------------------------
+
+cholmod_horzcat.o: ../MatrixOps/cholmod_horzcat.c
+ $(C) -c $(I) $<
+
+cholmod_norm.o: ../MatrixOps/cholmod_norm.c
+ $(C) -c $(I) $<
+
+cholmod_scale.o: ../MatrixOps/cholmod_scale.c
+ $(C) -c $(I) $<
+
+cholmod_drop.o: ../MatrixOps/cholmod_drop.c
+ $(C) -c $(I) $<
+
+cholmod_sdmult.o: ../MatrixOps/cholmod_sdmult.c \
+ ../MatrixOps/t_cholmod_sdmult.c
+ $(C) -c $(I) $<
+
+cholmod_ssmult.o: ../MatrixOps/cholmod_ssmult.c
+ $(C) -c $(I) $<
+
+cholmod_submatrix.o: ../MatrixOps/cholmod_submatrix.c
+ $(C) -c $(I) $<
+
+cholmod_vertcat.o: ../MatrixOps/cholmod_vertcat.c
+ $(C) -c $(I) $<
+
+cholmod_symmetry.o: ../MatrixOps/cholmod_symmetry.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_horzcat.o: ../MatrixOps/cholmod_horzcat.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_norm.o: ../MatrixOps/cholmod_norm.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_scale.o: ../MatrixOps/cholmod_scale.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_drop.o: ../MatrixOps/cholmod_drop.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_sdmult.o: ../MatrixOps/cholmod_sdmult.c \
+ ../MatrixOps/t_cholmod_sdmult.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_ssmult.o: ../MatrixOps/cholmod_ssmult.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_submatrix.o: ../MatrixOps/cholmod_submatrix.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_vertcat.o: ../MatrixOps/cholmod_vertcat.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_symmetry.o: ../MatrixOps/cholmod_symmetry.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+#-------------------------------------------------------------------------------
+# Modify Module:
+#-------------------------------------------------------------------------------
+
+cholmod_rowadd.o: ../Modify/cholmod_rowadd.c
+ $(C) -c $(I) $<
+
+cholmod_rowdel.o: ../Modify/cholmod_rowdel.c
+ $(C) -c $(I) $<
+
+cholmod_updown.o: ../Modify/cholmod_updown.c \
+ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_rowadd.o: ../Modify/cholmod_rowadd.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_rowdel.o: ../Modify/cholmod_rowdel.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_updown.o: ../Modify/cholmod_updown.c \
+ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+
+#-------------------------------------------------------------------------------
+# Supernodal Module:
+#-------------------------------------------------------------------------------
+
+cholmod_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \
+ ../Supernodal/t_cholmod_super_numeric.c
+ $(C) -c $(I) $<
+
+cholmod_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c
+ $(C) -c $(I) $<
+
+cholmod_super_solve.o: ../Supernodal/cholmod_super_solve.c \
+ ../Supernodal/t_cholmod_super_solve.c
+ $(C) -c $(I) $<
+
+#-------------------------------------------------------------------------------
+
+cholmod_l_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \
+ ../Supernodal/t_cholmod_super_numeric.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c
+ $(C) -DDLONG -c $(I) $< -o $@
+
+cholmod_l_super_solve.o: ../Supernodal/cholmod_super_solve.c \
+ ../Supernodal/t_cholmod_super_solve.c
+ $(C) -DDLONG -c $(I) $< -o $@
diff --git a/CHOLMOD/MATLAB/Contents.m b/CHOLMOD/MATLAB/Contents.m
new file mode 100644
index 0000000..d1fd3e7
--- /dev/null
+++ b/CHOLMOD/MATLAB/Contents.m
@@ -0,0 +1,37 @@
+% CHOLMOD: a sparse supernodal Cholesky update/downdate package
+%
+% cholmod2 - supernodal sparse Cholesky backslash, x = A\b
+% chol2 - sparse Cholesky factorization, A=R'R.
+% lchol - sparse A=L*L' factorization.
+% ldlchol - sparse A=LDL' factorization
+% ldlupdate - multiple-rank update or downdate of a sparse LDL' factorization.
+% resymbol - recomputes the symbolic Cholesky factorization of the matrix A.
+% ldlsolve - solve LDL'x=b using a sparse LDL' factorization
+% ldlsplit - split an LDL' factorization into L and D.
+% metis - nested dissection ordering via METIS_NodeND.
+% nesdis - nested dissection ordering via CHOLMOD's nested dissection.
+% septree - prune a separator tree.
+% bisect - computes a node separator based on METIS_NodeComputeSeparator.
+% analyze - order and analyze a matrix using CHOLMOD's best-effort ordering.
+% etree2 - sparse elimination tree.
+% sparse2 - replacement for SPARSE
+% symbfact2 - symbolic factorization
+% sdmult - sparse matrix times dense matrix
+% mread - read a sparse matrix from a file in Matrix Market format.
+% mwrite - write a matrix to a file in Matrix Market form.
+% spsym - determine if a sparse matrix is symmetric, Hermitian, or skew-symmetric.
+% ldl_normest - estimate the 1-norm of A-L*D*L' without computing L*D*L'
+% cholmod_demo - a demo for CHOLMOD
+% cholmod_install - compile and install CHOLMOD, AMD, COLAMD, CCOLAMD, CAMD
+% cholmod_make - compiles the CHOLMOD mexFunctions
+% graph_demo - graph partitioning demo
+%
+%
+% Example:
+% x = cholmod2(A,b)
+
+% Note: cholmod has been renamed cholmod2, so as not to conflict with itself
+% (the MATLAB built-in cholmod function).
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
diff --git a/CHOLMOD/MATLAB/License.txt b/CHOLMOD/MATLAB/License.txt
new file mode 100644
index 0000000..916cc31
--- /dev/null
+++ b/CHOLMOD/MATLAB/License.txt
@@ -0,0 +1,26 @@
+CHOLMOD/MATLAB Module.
+Copyright (C) 2005-2006, Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+MATLAB(tm) is a Registered Trademark of The MathWorks, Inc.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/MATLAB module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
diff --git a/CHOLMOD/MATLAB/Makefile b/CHOLMOD/MATLAB/Makefile
new file mode 100644
index 0000000..884aabe
--- /dev/null
+++ b/CHOLMOD/MATLAB/Makefile
@@ -0,0 +1,700 @@
+#===============================================================================
+# CHOLMOD/MATLAB/Makefile
+#===============================================================================
+
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I. -I../../AMD/Include -I../../COLAMD/Include -I../../CCOLAMD/Include \
+ -I../../CAMD/Include -I../Include -I../../UFconfig -I$(METIS_PATH)/Lib
+
+all: mread sdmult ldlsolve resymbol symbfact2 chol2 lchol \
+ ldlchol cholmod2 ldlupdate metis bisect nesdis etree2 sparse2 analyze \
+ septree spsym mwrite other
+
+MX = $(MEX) $(CHOLMOD_CONFIG) -DDLONG -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE $(I)
+
+distclean: purge
+
+purge: clean
+ - $(RM) *.mex* *.dll
+
+clean:
+ - $(RM) $(CLEAN)
+
+#===============================================================================
+
+AMD_INC = ../../AMD/Include/amd.h ../../AMD/Include/amd_internal.h
+
+AMD = \
+ amd_1.o \
+ amd_2.o \
+ amd_aat.o \
+ amd_control.o \
+ amd_defaults.o \
+ amd_dump.o \
+ amd_global.o \
+ amd_info.o \
+ amd_order.o \
+ amd_postorder.o \
+ amd_post_tree.o \
+ amd_preprocess.o \
+ amd_valid.o
+
+amd_1.o: ../../AMD/Source/amd_1.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_2.o: ../../AMD/Source/amd_2.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_aat.o: ../../AMD/Source/amd_aat.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_control.o: ../../AMD/Source/amd_control.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_defaults.o: ../../AMD/Source/amd_defaults.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_dump.o: ../../AMD/Source/amd_dump.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_global.o: ../../AMD/Source/amd_global.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_info.o: ../../AMD/Source/amd_info.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_order.o: ../../AMD/Source/amd_order.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_postorder.o: ../../AMD/Source/amd_postorder.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_post_tree.o: ../../AMD/Source/amd_post_tree.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_preprocess.o: ../../AMD/Source/amd_preprocess.c $(AMD_INC)
+ $(MX) -c $<
+
+amd_valid.o: ../../AMD/Source/amd_valid.c $(AMD_INC)
+ $(MX) -c $<
+
+#===============================================================================
+
+CAMD_INC = ../../CAMD/Include/camd.h ../../CAMD/Include/camd_internal.h
+
+CAMD = \
+ camd_1.o \
+ camd_2.o \
+ camd_aat.o \
+ camd_control.o \
+ camd_defaults.o \
+ camd_dump.o \
+ camd_global.o \
+ camd_info.o \
+ camd_order.o \
+ camd_postorder.o \
+ camd_preprocess.o \
+ camd_valid.o
+
+camd_1.o: ../../CAMD/Source/camd_1.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_2.o: ../../CAMD/Source/camd_2.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_aat.o: ../../CAMD/Source/camd_aat.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_control.o: ../../CAMD/Source/camd_control.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_defaults.o: ../../CAMD/Source/camd_defaults.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_dump.o: ../../CAMD/Source/camd_dump.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_global.o: ../../CAMD/Source/camd_global.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_info.o: ../../CAMD/Source/camd_info.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_order.o: ../../CAMD/Source/camd_order.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_postorder.o: ../../CAMD/Source/camd_postorder.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_post_tree.o: ../../CAMD/Source/camd_post_tree.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_preprocess.o: ../../CAMD/Source/camd_preprocess.c $(CAMD_INC)
+ $(MX) -c $<
+
+camd_valid.o: ../../CAMD/Source/camd_valid.c $(CAMD_INC)
+ $(MX) -c $<
+
+#===============================================================================
+
+COLAMD_INC = ../../COLAMD/Include/colamd.h
+
+COLAMD = colamd.o colamd_global.o
+
+colamd.o: ../../COLAMD/Source/colamd.c $(COLAMD_INC)
+ $(MX) -c $<
+
+colamd_global.o: ../../COLAMD/Source/colamd_global.c $(COLAMD_INC)
+ $(MX) -c $<
+
+#===============================================================================
+
+CCOLAMD_INC = ../../CCOLAMD/Include/ccolamd.h
+
+CCOLAMD = ccolamd.o ccolamd_global.o
+
+ccolamd.o: ../../CCOLAMD/Source/ccolamd.c $(CCOLAMD_INC)
+ $(MX) -c $<
+
+ccolamd_global.o: ../../CCOLAMD/Source/ccolamd_global.c $(CCOLAMD_INC)
+ $(MX) -c $<
+
+#===============================================================================
+
+# patch METIS 4.0.1
+rename.h: Makefile $(METIS_PATH)/Lib/rename.h
+ echo '/* do not edit this file; generated by CHOLMOD/MATLAB/Makefile */' > rename.h
+ echo '#undef log2' >> rename.h
+ echo '#include "$(METIS_PATH)/Lib/rename.h"' >> rename.h
+ echo '#undef log2' >> rename.h
+ echo '#define log2 METIS__log2' >> rename.h
+ echo '#include "mex.h"' >> rename.h
+ echo '#define malloc mxMalloc' >> rename.h
+ echo '#define free mxFree' >> rename.h
+ echo '#define calloc mxCalloc' >> rename.h
+ echo '#define realloc mxRealloc' >> rename.h
+
+METIS_INC = rename.h \
+ $(METIS_PATH)/Lib/defs.h \
+ $(METIS_PATH)/Lib/macros.h \
+ $(METIS_PATH)/Lib/metis.h \
+ $(METIS_PATH)/Lib/proto.h \
+ $(METIS_PATH)/Lib/rename.h \
+ $(METIS_PATH)/Lib/struct.h
+
+METIS = \
+ balance.o \
+ bucketsort.o \
+ ccgraph.o \
+ coarsen.o \
+ compress.o \
+ debug.o \
+ estmem.o \
+ fm.o \
+ fortran.o \
+ frename.o \
+ graph.o \
+ initpart.o \
+ kmetis.o \
+ kvmetis.o \
+ kwayfm.o \
+ kwayrefine.o \
+ kwayvolfm.o \
+ kwayvolrefine.o \
+ match.o \
+ mbalance2.o \
+ mbalance.o \
+ mcoarsen.o \
+ memory.o \
+ mesh.o \
+ meshpart.o \
+ mfm2.o \
+ mfm.o \
+ mincover.o \
+ minitpart2.o \
+ minitpart.o \
+ mkmetis.o \
+ mkwayfmh.o \
+ mkwayrefine.o \
+ mmatch.o \
+ mmd.o \
+ mpmetis.o \
+ mrefine2.o \
+ mrefine.o \
+ mutil.o \
+ myqsort.o \
+ ometis.o \
+ parmetis.o \
+ pmetis.o \
+ pqueue.o \
+ refine.o \
+ separator.o \
+ sfm.o \
+ srefine.o \
+ stat.o \
+ subdomains.o \
+ timing.o \
+ util.o
+
+balance.o: $(METIS_PATH)/Lib/balance.c $(METIS_INC)
+ $(MX) -c $<
+
+bucketsort.o: $(METIS_PATH)/Lib/bucketsort.c $(METIS_INC)
+ $(MX) -c $<
+
+ccgraph.o: $(METIS_PATH)/Lib/ccgraph.c $(METIS_INC)
+ $(MX) -c $<
+
+coarsen.o: $(METIS_PATH)/Lib/coarsen.c $(METIS_INC)
+ $(MX) -c $<
+
+compress.o: $(METIS_PATH)/Lib/compress.c $(METIS_INC)
+ $(MX) -c $<
+
+debug.o: $(METIS_PATH)/Lib/debug.c $(METIS_INC)
+ $(MX) -c $<
+
+estmem.o: $(METIS_PATH)/Lib/estmem.c $(METIS_INC)
+ $(MX) -c $<
+
+fm.o: $(METIS_PATH)/Lib/fm.c $(METIS_INC)
+ $(MX) -c $<
+
+fortran.o: $(METIS_PATH)/Lib/fortran.c $(METIS_INC)
+ $(MX) -c $<
+
+frename.o: $(METIS_PATH)/Lib/frename.c $(METIS_INC)
+ $(MX) -c $<
+
+graph.o: $(METIS_PATH)/Lib/graph.c $(METIS_INC)
+ $(MX) -c $<
+
+initpart.o: $(METIS_PATH)/Lib/initpart.c $(METIS_INC)
+ $(MX) -c $<
+
+kmetis.o: $(METIS_PATH)/Lib/kmetis.c $(METIS_INC)
+ $(MX) -c $<
+
+kvmetis.o: $(METIS_PATH)/Lib/kvmetis.c $(METIS_INC)
+ $(MX) -c $<
+
+kwayfm.o: $(METIS_PATH)/Lib/kwayfm.c $(METIS_INC)
+ $(MX) -c $<
+
+kwayrefine.o: $(METIS_PATH)/Lib/kwayrefine.c $(METIS_INC)
+ $(MX) -c $<
+
+kwayvolfm.o: $(METIS_PATH)/Lib/kwayvolfm.c $(METIS_INC)
+ $(MX) -c $<
+
+kwayvolrefine.o: $(METIS_PATH)/Lib/kwayvolrefine.c $(METIS_INC)
+ $(MX) -c $<
+
+match.o: $(METIS_PATH)/Lib/match.c $(METIS_INC)
+ $(MX) -c $<
+
+mbalance2.o: $(METIS_PATH)/Lib/mbalance2.c $(METIS_INC)
+ $(MX) -c $<
+
+mbalance.o: $(METIS_PATH)/Lib/mbalance.c $(METIS_INC)
+ $(MX) -c $<
+
+mcoarsen.o: $(METIS_PATH)/Lib/mcoarsen.c $(METIS_INC)
+ $(MX) -c $<
+
+memory.o: $(METIS_PATH)/Lib/memory.c $(METIS_INC)
+ $(MX) -c $<
+
+mesh.o: $(METIS_PATH)/Lib/mesh.c $(METIS_INC)
+ $(MX) -c $<
+
+meshpart.o: $(METIS_PATH)/Lib/meshpart.c $(METIS_INC)
+ $(MX) -c $<
+
+mfm2.o: $(METIS_PATH)/Lib/mfm2.c $(METIS_INC)
+ $(MX) -c $<
+
+mfm.o: $(METIS_PATH)/Lib/mfm.c $(METIS_INC)
+ $(MX) -c $<
+
+mincover.o: $(METIS_PATH)/Lib/mincover.c $(METIS_INC)
+ $(MX) -c $<
+
+minitpart2.o: $(METIS_PATH)/Lib/minitpart2.c $(METIS_INC)
+ $(MX) -c $<
+
+minitpart.o: $(METIS_PATH)/Lib/minitpart.c $(METIS_INC)
+ $(MX) -c $<
+
+mkmetis.o: $(METIS_PATH)/Lib/mkmetis.c $(METIS_INC)
+ $(MX) -c $<
+
+mkwayfmh.o: $(METIS_PATH)/Lib/mkwayfmh.c $(METIS_INC)
+ $(MX) -c $<
+
+mkwayrefine.o: $(METIS_PATH)/Lib/mkwayrefine.c $(METIS_INC)
+ $(MX) -c $<
+
+mmatch.o: $(METIS_PATH)/Lib/mmatch.c $(METIS_INC)
+ $(MX) -c $<
+
+mmd.o: $(METIS_PATH)/Lib/mmd.c $(METIS_INC)
+ $(MX) -c $<
+
+mpmetis.o: $(METIS_PATH)/Lib/mpmetis.c $(METIS_INC)
+ $(MX) -c $<
+
+mrefine2.o: $(METIS_PATH)/Lib/mrefine2.c $(METIS_INC)
+ $(MX) -c $<
+
+mrefine.o: $(METIS_PATH)/Lib/mrefine.c $(METIS_INC)
+ $(MX) -c $<
+
+mutil.o: $(METIS_PATH)/Lib/mutil.c $(METIS_INC)
+ $(MX) -c $<
+
+myqsort.o: $(METIS_PATH)/Lib/myqsort.c $(METIS_INC)
+ $(MX) -c $<
+
+ometis.o: $(METIS_PATH)/Lib/ometis.c $(METIS_INC)
+ $(MX) -c $<
+
+parmetis.o: $(METIS_PATH)/Lib/parmetis.c $(METIS_INC)
+ $(MX) -c $<
+
+pmetis.o: $(METIS_PATH)/Lib/pmetis.c $(METIS_INC)
+ $(MX) -c $<
+
+pqueue.o: $(METIS_PATH)/Lib/pqueue.c $(METIS_INC)
+ $(MX) -c $<
+
+refine.o: $(METIS_PATH)/Lib/refine.c $(METIS_INC)
+ $(MX) -c $<
+
+separator.o: $(METIS_PATH)/Lib/separator.c $(METIS_INC)
+ $(MX) -c $<
+
+sfm.o: $(METIS_PATH)/Lib/sfm.c $(METIS_INC)
+ $(MX) -c $<
+
+srefine.o: $(METIS_PATH)/Lib/srefine.c $(METIS_INC)
+ $(MX) -c $<
+
+stat.o: $(METIS_PATH)/Lib/stat.c $(METIS_INC)
+ $(MX) -c $<
+
+subdomains.o: $(METIS_PATH)/Lib/subdomains.c $(METIS_INC)
+ $(MX) -c $<
+
+timing.o: $(METIS_PATH)/Lib/timing.c $(METIS_INC)
+ $(MX) -c $<
+
+util.o: $(METIS_PATH)/Lib/util.c $(METIS_INC)
+ $(MX) -c $<
+
+#===============================================================================
+
+CHOLMOD_INC = \
+ cholmod_matlab.h \
+ ../Include/cholmod_blas.h \
+ ../Include/cholmod_check.h \
+ ../Include/cholmod_cholesky.h \
+ ../Include/cholmod_complexity.h \
+ ../Include/cholmod_config.h \
+ ../Include/cholmod_core.h \
+ ../Include/cholmod.h \
+ ../Include/cholmod_internal.h \
+ ../Include/cholmod_io64.h \
+ ../Include/cholmod_matrixops.h \
+ ../Include/cholmod_modify.h \
+ ../Include/cholmod_partition.h \
+ ../Include/cholmod_supernodal.h \
+ ../Include/cholmod_template.h
+
+CHOLMOD = \
+ cholmod_matlab.o \
+ cholmod_check.o \
+ cholmod_read.o \
+ cholmod_write.o \
+ cholmod_amd.o \
+ cholmod_analyze.o \
+ cholmod_colamd.o \
+ cholmod_etree.o \
+ cholmod_factorize.o \
+ cholmod_postorder.o \
+ cholmod_rcond.o \
+ cholmod_resymbol.o \
+ cholmod_rowcolcounts.o \
+ cholmod_rowfac.o \
+ cholmod_solve.o \
+ cholmod_spsolve.o \
+ cholmod_aat.o \
+ cholmod_add.o \
+ cholmod_band.o \
+ cholmod_change_factor.o \
+ cholmod_common.o \
+ cholmod_complex.o \
+ cholmod_copy.o \
+ cholmod_dense.o \
+ cholmod_error.o \
+ cholmod_factor.o \
+ cholmod_memory.o \
+ cholmod_sparse.o \
+ cholmod_transpose.o \
+ cholmod_triplet.o \
+ cholmod_drop.o \
+ cholmod_horzcat.o \
+ cholmod_norm.o \
+ cholmod_scale.o \
+ cholmod_sdmult.o \
+ cholmod_ssmult.o \
+ cholmod_submatrix.o \
+ cholmod_symmetry.o \
+ cholmod_vertcat.o \
+ cholmod_rowadd.o \
+ cholmod_rowdel.o \
+ cholmod_updown.o \
+ cholmod_camd.o \
+ cholmod_ccolamd.o \
+ cholmod_csymamd.o \
+ cholmod_metis.o \
+ cholmod_nesdis.o \
+ cholmod_super_numeric.o \
+ cholmod_super_solve.o \
+ cholmod_super_symbolic.o
+
+cholmod_matlab.o: cholmod_matlab.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_check.o: ../Check/cholmod_check.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_read.o: ../Check/cholmod_read.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_write.o: ../Check/cholmod_write.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_amd.o: ../Cholesky/cholmod_amd.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_analyze.o: ../Cholesky/cholmod_analyze.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_colamd.o: ../Cholesky/cholmod_colamd.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_etree.o: ../Cholesky/cholmod_etree.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_factorize.o: ../Cholesky/cholmod_factorize.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_postorder.o: ../Cholesky/cholmod_postorder.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_rcond.o: ../Cholesky/cholmod_rcond.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_resymbol.o: ../Cholesky/cholmod_resymbol.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_rowfac.o: ../Cholesky/cholmod_rowfac.c \
+ ../Cholesky/t_cholmod_rowfac.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_solve.o: ../Cholesky/cholmod_solve.c \
+ ../Cholesky/t_cholmod_lsolve.c \
+ ../Cholesky/t_cholmod_ltsolve.c \
+ ../Cholesky/t_cholmod_solve.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_spsolve.o: ../Cholesky/cholmod_spsolve.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_aat.o: ../Core/cholmod_aat.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_add.o: ../Core/cholmod_add.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_band.o: ../Core/cholmod_band.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_change_factor.o: ../Core/cholmod_change_factor.c \
+ ../Core/t_cholmod_change_factor.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_common.o: ../Core/cholmod_common.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_complex.o: ../Core/cholmod_complex.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_copy.o: ../Core/cholmod_copy.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_dense.o: ../Core/cholmod_dense.c \
+ ../Core/t_cholmod_dense.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_error.o: ../Core/cholmod_error.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_factor.o: ../Core/cholmod_factor.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_memory.o: ../Core/cholmod_memory.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_sparse.o: ../Core/cholmod_sparse.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_transpose.o: ../Core/cholmod_transpose.c \
+ ../Core/t_cholmod_transpose.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_triplet.o: ../Core/cholmod_triplet.c \
+ ../Core/t_cholmod_triplet.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_drop.o: ../MatrixOps/cholmod_drop.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_horzcat.o: ../MatrixOps/cholmod_horzcat.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_norm.o: ../MatrixOps/cholmod_norm.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_scale.o: ../MatrixOps/cholmod_scale.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_sdmult.o: ../MatrixOps/cholmod_sdmult.c \
+ ../MatrixOps/t_cholmod_sdmult.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_ssmult.o: ../MatrixOps/cholmod_ssmult.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_submatrix.o: ../MatrixOps/cholmod_submatrix.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_symmetry.o: ../MatrixOps/cholmod_symmetry.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_vertcat.o: ../MatrixOps/cholmod_vertcat.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_rowadd.o: ../Modify/cholmod_rowadd.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_rowdel.o: ../Modify/cholmod_rowdel.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_updown.o: ../Modify/cholmod_updown.c \
+ ../Modify/t_cholmod_updown.c \
+ ../Modify/t_cholmod_updown_numkr.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_camd.o: ../Partition/cholmod_camd.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_ccolamd.o: ../Partition/cholmod_ccolamd.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_csymamd.o: ../Partition/cholmod_csymamd.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_metis.o: ../Partition/cholmod_metis.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_nesdis.o: ../Partition/cholmod_nesdis.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \
+ ../Supernodal/t_cholmod_super_numeric.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_super_solve.o: ../Supernodal/cholmod_super_solve.c \
+ ../Supernodal/t_cholmod_super_solve.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+cholmod_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c $(CHOLMOD_INC)
+ $(MX) -c $<
+
+
+#===============================================================================
+
+OBJ = $(AMD) $(CAMD) $(COLAMD) $(CCOLAMD) $(METIS) $(CHOLMOD)
+
+analyze: analyze.c $(OBJ)
+ $(MX) analyze.c $(OBJ)
+
+mread: mread.c $(OBJ)
+ $(MX) mread.c $(OBJ)
+
+mwrite: mwrite.c $(OBJ)
+ $(MX) mwrite.c $(OBJ)
+
+spsym: spsym.c $(OBJ)
+ $(MX) spsym.c $(OBJ)
+
+chol2: chol2.c $(OBJ)
+ $(MX) chol2.c $(OBJ)
+
+lchol: lchol.c $(OBJ)
+ $(MX) lchol.c $(OBJ)
+
+ldlchol: ldlchol.c $(OBJ)
+ $(MX) ldlchol.c $(OBJ)
+
+ldlupdate: ldlupdate.c $(OBJ)
+ $(MX) ldlupdate.c $(OBJ)
+
+ldlsolve: ldlsolve.c $(OBJ)
+ $(MX) ldlsolve.c $(OBJ)
+
+sdmult: sdmult.c $(OBJ)
+ $(MX) sdmult.c $(OBJ)
+
+resymbol: resymbol.c $(OBJ)
+ $(MX) resymbol.c $(OBJ)
+
+cholmod2: cholmod2.c $(OBJ)
+ $(MX) cholmod2.c $(OBJ)
+
+nesdis: nesdis.c $(OBJ)
+ $(MX) nesdis.c $(OBJ)
+
+septree: septree.c $(OBJ)
+ $(MX) septree.c $(OBJ)
+
+metis: metis.c $(OBJ)
+ $(MX) metis.c $(OBJ)
+
+etree2: etree2.c $(OBJ)
+ $(MX) etree2.c $(OBJ)
+
+bisect: bisect.c $(OBJ)
+ $(MX) bisect.c $(OBJ)
+
+symbfact2: symbfact2.c $(OBJ)
+ $(MX) symbfact2.c $(OBJ)
+
+sparse2: sparse2.c $(OBJ)
+ $(MX) sparse2.c $(OBJ)
+
+#-------------------------------------------------------------------------------
+
+other:
+ ( cd ../../AMD ; $(MAKE) mex )
+ ( cd ../../CAMD ; $(MAKE) mex )
+ ( cd ../../COLAMD ; $(MAKE) mex )
+ ( cd ../../CCOLAMD ; $(MAKE) mex )
diff --git a/CHOLMOD/MATLAB/README.txt b/CHOLMOD/MATLAB/README.txt
new file mode 100644
index 0000000..18f1637
--- /dev/null
+++ b/CHOLMOD/MATLAB/README.txt
@@ -0,0 +1,67 @@
+-----------------------
+Using CHOLMOD in MATLAB
+-----------------------
+
+See Contents.m for a description of each CHOLMOD function.
+
+To compile CHOLMOD for use in MATLAB, you may optionally use METIS. If you
+do not use METIS, compile CHOLMOD with the -DNPARTITION flag.
+
+There are two ways of compiling the CHOLMOD mexFunctions. The 2nd one is best.
+
+(1) Using the Unix "make" command. This will compile the AMD, COLAMD, CCOLAMD,
+ and CHOLMOD libraries (*.a). You must first add -fexceptions to the
+ CFLAGS definition in UFconfig/UFconfig.mk first (for Linux). Otherwise,
+ MATLAB will not be able to handle exceptions properly (CHOLMOD may terminate
+ MATLAB if it encounters an error). The METIS library must also be compiled
+ with -fexceptions (see metis-4.0/Makefile.in).
+ For other operating systems, see your default MATLAB mexopts.sh file
+ (type "mex -v"). Next, simply type "make" in the operating system command
+ window in this directory.
+
+ On Linux (with gcc), you must compile all codes with the -fexceptions flag.
+ See option (2) if you have problems compiling METIS.
+
+(2) using the "cholmod_make" m-file in MATLAB. First, place a copy of
+ METIS 4.0.1 in the ../../metis-4.0 directory (the same directory that
+ contains AMD, COLAMD, CCOLAMD, and CHOLMOD).
+ Then, type "cholmod_make" in the MATLAB command window.
+ All source files (including METIS) will be compiled with the MATLAB mex
+ commnand. This works on all operating systems, including Windows.
+ You can use an alternate location for METIS, if you pass the pathname
+ as the first argument to cholmod_make, as in
+
+ cholmod_make ('path to your copy of metis-4.0 goes here') ;
+
+ Option (2) is better because it allows for several workarounds for METIS.
+ With Option (1), METIS terminates MATLAB if it runs out of memory. That
+ does not happen with Option (2).
+
+You should also add CHOLMOD/MATLAB to your MATLAB path.
+
+cholmod_demo is a short demo program for CHOLMOD. Type "cholmod_demo" in
+your MATLAB command window to test your newly compiling CHOLMOD functions.
+Test/cholmod_test.m runs the test suite for the MATLAB interface to CHOLMOD.
+It requires the "UFget" interface to the UF sparse matrix collection, but
+provides a more extensive test for CHOLMOD. To obtain a copy of UFget, see
+http://www.cise.ufl.edu/research/sparse .
+
+----------------------------------------
+Using AMD, CCOLAMD, and COLAMD in MATLAB
+----------------------------------------
+
+The following steps are not required to use CHOLMOD in MATLAB.
+
+To use AMD in MATLAB, go to the AMD/MATLAB directory and either type "amd_make"
+in the MATLAB command window, or type "make" in the Unix shell. Add AMD/MATLAB
+to your MATLAB path.
+
+To use CCOLAMD in MATLAB, go to the CCOLAMD directory and either type
+"ccolamd_demo" in the MATLAB command window, or type "make" in the Unix shell.
+Add CCOLAMD to your MATLAB path.
+
+COLAMD is already an integral part of MATLAB, but you can upgrade to the most
+recent version. Go to the COLAMD directory and either type "colamd_demo" in
+the MATLAB command window, or type "make" in the Unix shell.
+Add COLAMD to your MATLAB path.
+
diff --git a/CHOLMOD/MATLAB/Test/Contents.m b/CHOLMOD/MATLAB/Test/Contents.m
new file mode 100644
index 0000000..828f1e7
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/Contents.m
@@ -0,0 +1,44 @@
+% CHOLMOD TEST functions
+%
+% cholmod_test - test the CHOLMOD mexFunctions
+% dg - order and plot A*A', using CHOLMOD's nested dissection
+% n2 - script to test CHOLMOD septree function
+% nn - Compare nesdis with metis, in both quality and run time
+% test0 - test most CHOLMOD functions
+% test1 - test sparse2
+% test2 - test sparse2
+% test3 - test sparse on int8, int16, and logical
+% test4 - test cholmod2 with multiple and sparse right-hand-sides
+% test5 - test sparse2
+% test6 - test sparse with large matrix, both real and complex
+% test7 - test sparse2
+% test8 - order a large range of sparse matrices, test symbfact2
+% test9 - test metis, etree, bisect, nesdis
+% test10 - test cholmod2's backslash on real and complex matrices
+% test11 - compare CHOLMOD and MATLAB, save results in Results.mat
+% test11results - analyze results from test11.m
+% test12 - test etree2 and compare with etree
+% test13 - test cholmod2 and MATLAB on large tridiagonal matrices
+% test14 - test metis, symbfact2, and etree2
+% test15 - test symbfact2 vs MATLAB
+% test16 - test cholmod2 on a large matrix
+% test17 - test lchol on a few large matrices
+% test18 - test cholmod2 on a few large matrices
+% test19 - look for NaN's from lchol (caused by Intel MKL 7.x bug)
+% test20 - test symbfact2, cholmod2, and lu on a few large matrices
+% test21 - test cholmod2 on diagonal or ill-conditioned matrices
+% test22 - test pos.def and indef. matrices
+% test23 - test chol and cholmod2 on the sparse matrix used in "bench"
+% test24 - test sdmult
+% test25 - test sdmult on a large matrix
+% test26 - test logical full and sparse matrices
+% test27 - test nesdis with one matrix (HB/west0479)
+% test28 - test nesdis
+% testmm - compare mread and mmread for entire Matrix Market collection
+% testsolve - test CHOLMOD and compare with x=A\b
+%
+% Example:
+% cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
diff --git a/CHOLMOD/MATLAB/Test/Results.mat b/CHOLMOD/MATLAB/Test/Results.mat
new file mode 100644
index 0000000..63f83a3
Binary files /dev/null and b/CHOLMOD/MATLAB/Test/Results.mat differ
diff --git a/CHOLMOD/MATLAB/Test/cholmod_test.m b/CHOLMOD/MATLAB/Test/cholmod_test.m
new file mode 100644
index 0000000..9f8eed2
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/cholmod_test.m
@@ -0,0 +1,181 @@
+function cholmod_test (nmat, do_diary)
+%CHOLMOD_TEST test the CHOLMOD mexFunctions
+%
+% Example:
+% cholmod_test(nmat,do_diary)
+%
+% The UFget interface to the UF sparse matrix collection is required.
+%
+% nmat is optional. If present, it is the # of matrices used in
+% tests 0, 8, 10, 11, 12, and 12. tests 14 and 15 use 2*nmat matrices.
+% default nmat is 50.
+%
+% do_diary: 1 to save results in a diary, 0 otherwise. Default 0.
+%
+% cholmod_demo: run tests on a few random matrices
+% graph_demo: graph partitioning demo
+% test0: test most CHOLMOD functions
+% test1: test sparse2
+% test2: test sparse2
+% test3: test sparse on int8, int16, and logical
+% test4: test cholmod2 with multiple and sparse right-hand-sides
+% test5: test sparse2
+% test6: test sparse with large matrix, both real and complex, compare w/MATLAB
+% test7: test sparse2
+% test8: order many sparse matrices, test symbfact2, compare amd and metis
+% test9: test metis, etree, bisect, nesdis
+% test10: test cholmod2's backslash on real and complex matrices
+% test11: test analyze, compare CHOLMOD and MATLAB, save results in Results.mat
+% test12: test etree2 and compare with etree
+% test13: test cholmod2 and MATLAB on large tridiagonal matrices
+% test14: test metis, symbfact2, and etree2
+% test15: test symbfact2 vs MATLAB
+% test16: test cholmod2 on a large matrix
+% test17: test lchol on a few large matrices
+% test18: test cholmod2 on a few large matrices
+% test19: look for NaN's from lchol (caused by Intel MKL 7.x bug)
+% test20: test symbfact2, cholmod2, and lu on a few large matrices
+% test21: test cholmod2 on diagonal or ill-conditioned matrices
+% test22: test chol and chol2 and singular and indefinite matrices
+% test23: test chol and cholmod2 on the sparse matrix used in "bench"
+% test24: test sdmult
+% test25: test sdmult on a large matrix
+% test26: test logical full and sparse matrices
+% test27: test nesdis
+%
+% See also test0, test1, ... test28.
+
+% This extensive test is not included:
+% test28: test nesdis
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+if (nargin < 2)
+ do_diary = 0 ;
+end
+
+if (do_diary)
+ diary off
+ s = date ;
+ t = clock ;
+ s = sprintf ('diary cholmod_test_%s_%d-%d-%d.txt\n', s, t (4), t(5), fix(t(6)));
+ eval (s) ;
+end
+
+fprintf ('Running CHOLMOD tests.\n') ;
+help cholmod_test
+
+test_path = pwd ;
+% addpath (test_path) ;
+cd ('..') ;
+cholmod_path = pwd ;
+addpath (cholmod_path)
+cd ('../../AMD/MATLAB') ;
+amd_path = pwd ;
+addpath (amd_path)
+cd ('../../COLAMD') ;
+colamd_path = pwd ;
+addpath (colamd_path)
+cd ('../CCOLAMD') ;
+ccolamd_path = pwd ;
+addpath (ccolamd_path)
+cd ('../CAMD/MATLAB') ;
+camd_path = pwd ;
+addpath (camd_path)
+
+cd (test_path)
+fprintf ('Added the following paths. You may wish to add them\n') ;
+fprintf ('permanently using the MATLAB pathtool command.\n') ;
+fprintf ('%s\n', cholmod_path) ;
+fprintf ('%s\n', amd_path) ;
+fprintf ('%s\n', colamd_path) ;
+fprintf ('%s\n', ccolamd_path) ;
+fprintf ('%s\n', camd_path) ;
+
+if (nargin < 1)
+ nmat = 50 ;
+end
+
+try
+ s = metis (sparse (1)) ;
+ do_metis = 1 ;
+catch
+ fprintf ('METIS not installed\n') ;
+ do_metis = 0 ;
+end
+
+h = waitbar (0.5/32, 'CHOLMOD demo:') ;
+
+try
+
+ cholmod_demo ; waitbar ( 1/32, h, 'CHOLMOD graph demo');
+ if (do_metis)
+ graph_demo ;
+ end
+ waitbar ( 2/32, h, 'CHOLMOD test0') ;
+ test0 (nmat) ; waitbar ( 3/32, h, 'CHOLMOD test1') ;
+ test1 ; waitbar ( 4/32, h, 'CHOLMOD test2') ;
+ test2 ; waitbar ( 5/32, h, 'CHOLMOD test3') ;
+ test3 ; waitbar ( 6/32, h, 'CHOLMOD test4') ;
+ test4 ; waitbar ( 7/32, h, 'CHOLMOD test5') ;
+ test5 ; waitbar ( 8/32, h, 'CHOLMOD test6') ;
+ test6 ; waitbar ( 9/32, h, 'CHOLMOD test7') ;
+ test7 ; waitbar (10/32, h, 'CHOLMOD test8') ;
+
+ if (do_metis)
+ % these tests require METIS
+ test8 (nmat) ; waitbar (11/32, h, 'CHOLMOD test9') ;
+ test9 ;
+ end
+
+ waitbar (12/32, h, 'CHOLMOD test10') ;
+ test10 (nmat) ; waitbar (13/32, h, 'CHOLMOD test11') ;
+ test11 (nmat) ; waitbar (14/32, h, 'CHOLMOD test12') ;
+ test12 (nmat) ; waitbar (15/32, h, 'CHOLMOD test13') ;
+ test13 ; waitbar (16/32, h, 'CHOLMOD test14') ;
+
+ if (do_metis)
+ % this test requires METIS
+ test14 (2*nmat) ;
+ end
+
+ waitbar (17/32, h, 'CHOLMOD test15') ;
+ test15 (2*nmat) ; waitbar (18/32, h, 'CHOLMOD test16') ;
+ test16 ; waitbar (19/32, h, 'CHOLMOD test17') ;
+ test17 ; waitbar (20/32, h, 'CHOLMOD test18') ;
+ test18 ; waitbar (21/32, h, 'CHOLMOD test19') ;
+ test19 ; waitbar (22/32, h, 'CHOLMOD test20') ;
+ test20 ; waitbar (23/32, h, 'CHOLMOD test21') ;
+ test21 ; waitbar (24/32, h, 'CHOLMOD test22a') ;
+ test22 (nmat) ; waitbar (25/32, h, 'CHOLMOD test22b') ;
+ test22 (0) ; waitbar (26/32, h, 'CHOLMOD test23') ;
+ test23 ; waitbar (27/32, h, 'CHOLMOD test24') ;
+ test24 ; waitbar (28/32, h, 'CHOLMOD test25') ;
+ test25 ; waitbar (29/32, h, 'CHOLMOD test26') ;
+ test26 (do_metis) ; waitbar (31/32, h, 'CHOLMOD test27') ;
+
+ if (do_metis)
+ test27 ;
+ end
+
+ % this test requires METIS
+ % test28 ; % (disabled)
+
+ waitbar (32/32, h, 'CHOLMOD test done') ;
+ fprintf ('=============================================================\n');
+ fprintf ('all tests passed\n') ;
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
+if (do_diary)
+ diary off
+end
diff --git a/CHOLMOD/MATLAB/Test/cholmod_test_11-May-2007_13-29-15.txt b/CHOLMOD/MATLAB/Test/cholmod_test_11-May-2007_13-29-15.txt
new file mode 100644
index 0000000..08b4651
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/cholmod_test_11-May-2007_13-29-15.txt
@@ -0,0 +1,12324 @@
+Running CHOLMOD tests.
+diary cholmod_test_11-May-2007_13-29-15.txt
+
+ CHOLMOD_TEST test the CHOLMOD mexFunctions
+
+ Example:
+ cholmod_test(nmat)
+
+ The UFget interface to the UF sparse matrix collection is required.
+
+ nmat is optional. If present, it is the # of matrices used in
+ tests 0, 8, 10, 11, 12, and 12. tests 14 and 15 use 2*nmat matrices.
+ default nmat is 50.
+
+ cholmod_demo: run tests on a few random matrices
+ graph_demo: graph partitioning demo
+ test0: test most CHOLMOD functions
+ test1: test sparse2
+ test2: test sparse2
+ test3: test sparse on int8, int16, and logical
+ test4: test cholmod2 with multiple and sparse right-hand-sides
+ test5: test sparse2
+ test6: test sparse with large matrix, both real and complex, compare w/MATLAB
+ test7: test sparse2
+ test8: order many sparse matrices, test symbfact2, compare amd and metis
+ test9: test metis, etree, bisect, nesdis
+ test10: test cholmod2's backslash on real and complex matrices
+ test11: test analyze, compare CHOLMOD and MATLAB, save results in Results.mat
+ test12: test etree2 and compare with etree
+ test13: test cholmod2 and MATLAB on large tridiagonal matrices
+ test14: test metis, symbfact2, and etree2
+ test15: test symbfact2 vs MATLAB
+ test16: test cholmod2 on a large matrix
+ test17: test lchol on a few large matrices
+ test18: test cholmod2 on a few large matrices
+ test19: look for NaN's from lchol (caused by Intel MKL 7.x bug)
+ test20: test symbfact2, cholmod2, and lu on a few large matrices
+ test21: test cholmod2 on diagonal or ill-conditioned matrices
+ test22: test chol and chol2 and singular and indefinite matrices
+ test23: test chol and cholmod2 on the sparse matrix used in "bench"
+ test24: test sdmult
+ test25: test sdmult on a large matrix
+ test26: test logical full and sparse matrices
+ test27: test nesdis
+
+ See also test0, test1, ... test28.
+
+Added the following paths. You may wish to add them
+permanently using the MATLAB pathtool command.
+/amd/birch/export/research07/sparse/SuiteSparse/CHOLMOD/MATLAB
+/amd/birch/export/research07/sparse/SuiteSparse/AMD/MATLAB
+/amd/birch/export/research07/sparse/SuiteSparse/COLAMD
+/amd/birch/export/research07/sparse/SuiteSparse/CCOLAMD
+/amd/birch/export/research07/sparse/SuiteSparse/CAMD/MATLAB
+
+
+--------- Hit enter to contine:
+ CHOLMOD_DEMO a demo for CHOLMOD
+
+ Tests CHOLMOD with various randomly-generated matrices, and the west0479
+ matrix distributed with MATLAB. Random matrices are not good test cases,
+ but they are easily generated. It also compares CHOLMOD and MATLAB on the
+ sparse matrix problem used in the MATLAB BENCH command.
+
+ See CHOLMOD/MATLAB/Test/test_all.m for a lengthy test using matrices from
+ the UF sparse matrix collection.
+
+ Example:
+ cholmod_demo
+
+ See also BENCH
+
+
+--------------------------------------------------------------
+cholmod_demo: sparse matrix, n 479 nnz 7551
+CHOLMOD lchol(sparse(A)) time: 0.00 mflop 83.4
+CHOLMOD ldlchol(sparse(A)) time: 0.00 mflop 78.5
+CHOLMOD ldlupdate(sparse(A),C) time: 0.01 (rank-1, C dense)
+err: 8.87659e-16
+MATLAB chol(sparse(A)) time: 0.00 mflop 133.1
+MATLAB chol(full(A)) time: 0.02 mflop 16.0
+MATLAB cholupdate(full(A),C) time: 0.00 (rank-1)
+err: 2.78134e-16
+CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): 0.6
+CHOLMOD sparse update speedup vs MATLAB DENSE update: 0.3
+
+--------------------------------------------------------------
+cholmod_demo: sparse matrix, n 2000 nnz 17946
+CHOLMOD lchol(sparse(A)) time: 0.13 mflop 1720.7
+CHOLMOD ldlchol(sparse(A)) time: 0.13 mflop 1697.2
+CHOLMOD ldlupdate(sparse(A),C) time: 0.16 (rank-1, C dense)
+err: 1.10497e-14
+MATLAB chol(sparse(A)) time: 0.43 mflop 518.5
+MATLAB chol(full(A)) time: 1.61 mflop 138.4
+MATLAB cholupdate(full(A),C) time: 0.16 (rank-1)
+err: 2.58727e-14
+CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): 3.3
+CHOLMOD sparse update speedup vs MATLAB DENSE update: 1.0
+
+--------------------------------------------------------------
+cholmod_demo: dense matrix, n 100
+CHOLMOD lchol(sparse(A)) time: 0.00 mflop 419.8
+CHOLMOD ldlchol(sparse(A)) time: 0.00 mflop 373.9
+CHOLMOD ldlupdate(sparse(A),C) time: 0.00 (rank-1, C dense)
+err: 2.67101e-16
+MATLAB chol(sparse(A)) time: 0.00 mflop 313.0
+MATLAB chol(full(A)) time: 0.00 mflop 735.5
+MATLAB cholupdate(full(A),C) time: 0.00 (rank-1)
+err: 2.63339e-16
+CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): 1.3
+CHOLMOD sparse update speedup vs MATLAB DENSE update: 1.0
+
+--------------------------------------------------------------
+cholmod_demo: dense matrix, n 2000
+CHOLMOD lchol(sparse(A)) time: 2.21 mflop 1208.8
+CHOLMOD ldlchol(sparse(A)) time: 2.24 mflop 1192.4
+CHOLMOD ldlupdate(sparse(A),C) time: 0.15 (rank-1, C dense)
+err: 1.45631e-15
+MATLAB chol(sparse(A)) time: 2.66 mflop 1004.9
+MATLAB chol(full(A)) time: 1.60 mflop 1672.4
+MATLAB cholupdate(full(A),C) time: 0.16 (rank-1)
+err: 1.42948e-15
+CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): 1.2
+CHOLMOD sparse update speedup vs MATLAB DENSE update: 1.1
+
+--------------------------------------------------------------
+
+With the matrix used in the MATLAB 7.2 "bench" program.
+No fill-reducing orderings are used; type "help bench" for more information.
+MATLAB x=A\b time: 4.4297 resid: 2e-13
+CHOLMOD x=A\b time: 2.3991 resid: 2e-13
+CHOLMOD speedup: 1.85
+
+cholmod_demo finished: all tests passed
+
+For more accurate timings, run this test again.
+=================================================================
+test0: test most CHOLMOD functions
+Testing CHOLMOD with AMD and the UF sparse matrix collection
+test matrices sorted by dimension:
+1440: Oberwolfach LFAT5 14 1
+1438: Oberwolfach LF10 18 1
+ 436: FIDAP ex5 27 1
+ 23: HB bcsstk01 48 1
+ 872: Pothen mesh1e1 48 1
+ 873: Pothen mesh1em1 48 1
+ 874: Pothen mesh1em6 48 1
+ 24: HB bcsstk02 66 1
+ 57: HB bcsstm02 66 1
+ 220: HB nos4 100 1
+ 25: HB bcsstk03 112 1
+1506: Pajek Journals 124 1
+ 26: HB bcsstk04 132 1
+ 44: HB bcsstk22 138 1
+ 72: HB bcsstm22 138 1
+ 206: HB lund_a 147 1
+ 207: HB lund_b 147 1
+ 27: HB bcsstk05 153 1
+ 60: HB bcsstm05 153 1
+ 217: HB nos1 237 1
+ 877: Pothen mesh3e1 289 1
+ 878: Pothen mesh3em5 289 1
+ 875: Pothen mesh2e1 306 1
+ 876: Pothen mesh2em5 306 1
+ 229: HB plat362 362 1
+ 315: Bai mhdb416 416 1
+ 28: HB bcsstk06 420 1
+ 29: HB bcsstk07 420 1
+ 61: HB bcsstm06 420 1
+ 62: HB bcsstm07 420 1
+ 221: HB nos5 468 1
+ 42: HB bcsstk20 485 1
+ 70: HB bcsstm20 485 1
+ 2: HB 494_bus 494 1
+ 339: Boeing bcsstk34 588 1
+ 3: HB 662_bus 662 1
+ 222: HB nos6 675 1
+ 4: HB 685_bus 685 1
+ 357: Boeing msc00726 726 1
+ 223: HB nos7 729 1
+ 41: HB bcsstk19 817 1
+ 69: HB bcsstm19 817 1
+ 159: HB gr_30_30 900 1
+ 218: HB nos2 957 1
+ 219: HB nos3 960 1
+ 358: Boeing msc01050 1050 1
+ 30: HB bcsstk08 1074 1
+ 63: HB bcsstm08 1074 1
+ 31: HB bcsstk09 1083 1
+ 64: HB bcsstm09 1083 1
+
+================== Problem: 1440: Oberwolfach/LFAT5 n: 14 nnz: 46
+title: Oberwolfach: linear 1D beam
+time: amd 0.0002
+CHOLMOD time: L=lchol 0.0002 nnz(L): 33
+CHOLMOD time: R=chol2 0.0002 nnz(R): 33
+MATLAB time: R=chol 0.0002 nnz(R): 33
+MATLAB [..,R]=symbfact 0.0004 nnz(R): 33
+
+CHOLMOD speedup vs MATLAB chol: R: 0.88 L: 0.91
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.79
+CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 33
+CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 33
+
+CHOLMOD time: rank-8 ldlupdate 0.0002 nnz(L) 33 no fill-in
+CHOLMOD time: rank-4 ldldowndate 0.0002 nnz(L) 33 no fill-in
+after resymbol: 33
+CHOLMOD residual: 2.3e-21
+MATLAB residual: 6.0e-21
+CHOLMOD residual: 6.7e-21 (sparse b)
+MATLAB residual: 1.1e-20 (sparse b)
+
+================== Problem: 1438: Oberwolfach/LF10 n: 18 nnz: 82
+title: Oberwolfach: linear 1D beam
+time: amd 0.0000
+CHOLMOD time: L=lchol 0.0000 nnz(L): 58
+CHOLMOD time: R=chol2 0.0000 nnz(R): 58
+MATLAB time: R=chol 0.0000 nnz(R): 58
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 58
+
+CHOLMOD speedup vs MATLAB chol: R: 0.84 L: 1.09
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 4.67
+CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 58
+CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 58
+
+CHOLMOD time: rank-6 ldlupdate 0.0001 nnz(L) 65 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0000 nnz(L) 65 no fill-in
+after resymbol: 58
+CHOLMOD residual: 5.8e-18
+MATLAB residual: 3.3e-18
+CHOLMOD residual: 8.9e-18 (sparse b)
+MATLAB residual: 3.0e-18 (sparse b)
+
+================== Problem: 436: FIDAP/ex5 n: 27 nnz: 279
+title: TEST MATRIX FROM FIDAP: EX5.MAT
+time: amd 0.0000
+CHOLMOD time: L=lchol 0.0000 nnz(L): 153
+CHOLMOD time: R=chol2 0.0001 nnz(R): 153
+MATLAB time: R=chol 0.0001 nnz(R): 153
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 153
+
+CHOLMOD speedup vs MATLAB chol: R: 0.91 L: 1.11
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 3.83
+CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 153
+CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 153
+
+CHOLMOD time: rank-4 ldlupdate 0.0001 nnz(L) 213 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0000 nnz(L) 213 no fill-in
+after resymbol: 153
+CHOLMOD residual: 2.0e-15
+MATLAB residual: 2.0e-15
+CHOLMOD residual: 1.5e-15 (sparse b)
+MATLAB residual: 1.2e-15 (sparse b)
+
+================== Problem: 23: HB/bcsstk01 n: 48 nnz: 400
+title: SYMMETRIC STIFFNESS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0001 nnz(L): 489
+CHOLMOD time: R=chol2 0.0001 nnz(R): 489
+MATLAB time: R=chol 0.0001 nnz(R): 489
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 489
+
+CHOLMOD speedup vs MATLAB chol: R: 0.93 L: 1.04
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 2.45
+CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 489
+CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 489
+
+CHOLMOD time: rank-3 ldlupdate 0.0001 nnz(L) 518 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0000 nnz(L) 518 no fill-in
+after resymbol: 489
+CHOLMOD residual: 4.9e-22
+MATLAB residual: 3.8e-22
+CHOLMOD residual: 2.8e-22 (sparse b)
+MATLAB residual: 3.7e-22 (sparse b)
+
+================== Problem: 872: Pothen/mesh1e1 n: 48 nnz: 306
+title: mesh1e1, with coordinates. From NASA, collected by Alex Pothen
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0001 nnz(L): 336
+CHOLMOD time: R=chol2 0.0001 nnz(R): 336
+MATLAB time: R=chol 0.0001 nnz(R): 336
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 336
+
+CHOLMOD speedup vs MATLAB chol: R: 0.87 L: 1.02
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 2.80
+CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 336
+CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 336
+
+CHOLMOD time: rank-1 ldlupdate 0.0001 nnz(L) 337 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0000 nnz(L) 337 no fill-in
+after resymbol: 336
+CHOLMOD residual: 3.1e-16
+MATLAB residual: 4.4e-16
+CHOLMOD residual: 3.9e-16 (sparse b)
+MATLAB residual: 4.1e-16 (sparse b)
+
+================== Problem: 873: Pothen/mesh1em1 n: 48 nnz: 306
+title: mesh1em1, with coordinates. From NASA, collected by Alex Pothen
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0001 nnz(L): 336
+CHOLMOD time: R=chol2 0.0001 nnz(R): 336
+MATLAB time: R=chol 0.0001 nnz(R): 336
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 336
+
+CHOLMOD speedup vs MATLAB chol: R: 0.87 L: 0.99
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 2.82
+CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 336
+CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 336
+
+CHOLMOD time: rank-2 ldlupdate 0.0001 nnz(L) 370 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0000 nnz(L) 370 no fill-in
+after resymbol: 336
+CHOLMOD residual: 1.7e-16
+MATLAB residual: 1.4e-16
+CHOLMOD residual: 1.5e-16 (sparse b)
+MATLAB residual: 1.9e-16 (sparse b)
+
+================== Problem: 874: Pothen/mesh1em6 n: 48 nnz: 306
+title: mesh1em6, with coordinates. From NASA, collected by Alex Pothen
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0001 nnz(L): 336
+CHOLMOD time: R=chol2 0.0001 nnz(R): 336
+MATLAB time: R=chol 0.0001 nnz(R): 336
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 336
+
+CHOLMOD speedup vs MATLAB chol: R: 0.87 L: 0.68
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.89
+CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 336
+CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 336
+
+CHOLMOD time: rank-4 ldlupdate 0.0001 nnz(L) 371 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0000 nnz(L) 371 no fill-in
+after resymbol: 336
+CHOLMOD residual: 4.8e-16
+MATLAB residual: 4.8e-16
+CHOLMOD residual: 5.3e-16 (sparse b)
+MATLAB residual: 4.4e-16 (sparse b)
+
+================== Problem: 24: HB/bcsstk02 n: 66 nnz: 4356
+title: SYMMETRIC STIFFNESS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0003 nnz(L): 2211
+CHOLMOD time: R=chol2 0.0004 nnz(R): 2211
+MATLAB time: R=chol 0.0004 nnz(R): 2211
+MATLAB [..,R]=symbfact 0.0004 nnz(R): 2211
+
+CHOLMOD speedup vs MATLAB chol: R: 0.93 L: 1.12
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.16
+CHOLMOD time: [L,,q]=lchol 0.0005 nnz(L): 2211
+CHOLMOD time: [L,,q]=ldlchol 0.0005 nnz(L): 2211
+
+CHOLMOD time: rank-4 ldlupdate 0.0001 nnz(L) 2211 no fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0001 nnz(L) 2211 no fill-in
+after resymbol: 2211
+CHOLMOD residual: 9.8e-17
+MATLAB residual: 1.0e-16
+CHOLMOD residual: 4.3e-17 (sparse b)
+MATLAB residual: 3.8e-17 (sparse b)
+
+================== Problem: 57: HB/bcsstm02 n: 66 nnz: 66
+title: SYMMETRIC MASS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED
+time: amd 0.0000
+CHOLMOD time: L=lchol 0.0000 nnz(L): 66
+CHOLMOD time: R=chol2 0.0000 nnz(R): 66
+MATLAB time: R=chol 0.0000 nnz(R): 66
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 66
+
+CHOLMOD speedup vs MATLAB chol: R: 0.84 L: 1.06
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 5.44
+CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 66
+CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 66
+
+CHOLMOD time: rank-7 ldlupdate 0.0001 nnz(L) 67 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0000 nnz(L) 67 no fill-in
+after resymbol: 66
+CHOLMOD residual: 2.4e-14
+MATLAB residual: 3.2e-15
+CHOLMOD residual: 1.0e-14 (sparse b)
+MATLAB residual: 6.4e-16 (sparse b)
+
+================== Problem: 220: HB/nos4 n: 100 nnz: 594
+title: SYMMETRIC MATRIX OF BEAM STRUCTURE, NOVEMBER 1982.
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0001 nnz(L): 630
+CHOLMOD time: R=chol2 0.0001 nnz(R): 630
+MATLAB time: R=chol 0.0001 nnz(R): 630
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 632
+
+CHOLMOD speedup vs MATLAB chol: R: 0.89 L: 0.99
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 2.13
+CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 632
+CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 632
+
+CHOLMOD time: rank-3 ldlupdate 0.0001 nnz(L) 654 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0000 nnz(L) 654 no fill-in
+after resymbol: 632
+CHOLMOD residual: 9.2e-13
+MATLAB residual: 8.5e-13
+CHOLMOD residual: 3.2e-13 (sparse b)
+MATLAB residual: 2.4e-13 (sparse b)
+
+================== Problem: 25: HB/bcsstk03 n: 112 nnz: 640
+title: SYMMETRIC STIFFNESS MATRIX, SMALL TEST STRUCTURE
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0001 nnz(L): 380
+CHOLMOD time: R=chol2 0.0001 nnz(R): 380
+MATLAB time: R=chol 0.0001 nnz(R): 380
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 384
+
+CHOLMOD speedup vs MATLAB chol: R: 0.88 L: 0.96
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 2.86
+CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 380
+CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 384
+
+CHOLMOD time: rank-6 ldlupdate 0.0001 nnz(L) 445 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0000 nnz(L) 445 no fill-in
+after resymbol: 384
+CHOLMOD residual: 1.4e-22
+MATLAB residual: 2.2e-22
+CHOLMOD residual: 9.8e-23 (sparse b)
+MATLAB residual: 2.2e-22 (sparse b)
+
+================== Problem: 1506: Pajek/Journals n: 124 nnz: 12068
+title: Pajek network: Slovenian journals 1999-2000
+time: amd 0.0003
+CHOLMOD time: L=lchol 0.0010 nnz(L): 6990
+CHOLMOD time: R=chol2 0.0013 nnz(R): 6990
+MATLAB time: R=chol 0.0013 nnz(R): 6990
+MATLAB [..,R]=symbfact 0.0009 nnz(R): 6990
+
+CHOLMOD speedup vs MATLAB chol: R: 1.04 L: 1.25
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.84
+CHOLMOD time: [L,,q]=lchol 0.0017 nnz(L): 6990
+CHOLMOD time: [L,,q]=ldlchol 0.0017 nnz(L): 6990
+
+CHOLMOD time: rank-8 ldlupdate 0.0002 nnz(L) 6990 no fill-in
+CHOLMOD time: rank-4 ldldowndate 0.0002 nnz(L) 6990 no fill-in
+after resymbol: 6990
+CHOLMOD residual: 5.1e-19
+MATLAB residual: 5.3e-19
+CHOLMOD residual: 2.5e-19 (sparse b)
+MATLAB residual: 2.7e-19 (sparse b)
+
+================== Problem: 26: HB/bcsstk04 n: 132 nnz: 3648
+title: SYMMETRIC STIFFNESS MATRIX, OIL RIG, NOT CONDENSED (SAME MODEL AS X02)
+time: amd 0.0002
+CHOLMOD time: L=lchol 0.0005 nnz(L): 3291
+CHOLMOD time: R=chol2 0.0005 nnz(R): 3291
+MATLAB time: R=chol 0.0005 nnz(R): 3291
+MATLAB [..,R]=symbfact 0.0004 nnz(R): 3293
+
+CHOLMOD speedup vs MATLAB chol: R: 1.02 L: 1.01
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.85
+CHOLMOD time: [L,,q]=lchol 0.0007 nnz(L): 3291
+CHOLMOD time: [L,,q]=ldlchol 0.0007 nnz(L): 3293
+
+CHOLMOD time: rank-1 ldlupdate 0.0002 nnz(L) 3570 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0001 nnz(L) 3570 no fill-in
+after resymbol: 3293
+CHOLMOD residual: 1.4e-18
+MATLAB residual: 1.6e-18
+CHOLMOD residual: 4.2e-19 (sparse b)
+MATLAB residual: 3.5e-19 (sparse b)
+
+================== Problem: 44: HB/bcsstk22 n: 138 nnz: 696
+title: SYMMETRIC STIFFNESS MATRIX - TEXTILE LOOM FRAME
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0001 nnz(L): 680
+CHOLMOD time: R=chol2 0.0001 nnz(R): 680
+MATLAB time: R=chol 0.0001 nnz(R): 680
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 680
+
+CHOLMOD speedup vs MATLAB chol: R: 0.91 L: 0.99
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 2.08
+CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 680
+CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 680
+
+CHOLMOD time: rank-6 ldlupdate 0.0001 nnz(L) 685 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 685 no fill-in
+after resymbol: 680
+CHOLMOD residual: 1.3e-18
+MATLAB residual: 1.2e-18
+CHOLMOD residual: 2.3e-19 (sparse b)
+MATLAB residual: 2.2e-19 (sparse b)
+
+================== Problem: 72: HB/bcsstm22 n: 138 nnz: 138
+title: SYMMETRIC MASS MATRIX - TEXTILE LOOM FRAME
+time: amd 0.0000
+CHOLMOD time: L=lchol 0.0000 nnz(L): 138
+CHOLMOD time: R=chol2 0.0001 nnz(R): 138
+MATLAB time: R=chol 0.0001 nnz(R): 138
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 138
+
+CHOLMOD speedup vs MATLAB chol: R: 0.90 L: 1.08
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 3.65
+CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 138
+CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 138
+
+CHOLMOD time: rank-5 ldlupdate 0.0001 nnz(L) 139 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0000 nnz(L) 139 no fill-in
+after resymbol: 138
+CHOLMOD residual: 5.7e-10
+MATLAB residual: 1.2e-13
+CHOLMOD residual: 1.5e-11 (sparse b)
+MATLAB residual: 6.7e-14 (sparse b)
+
+================== Problem: 206: HB/lund_a n: 147 nnz: 2449
+title: SYMMETRIC MATRIX A OF LUND EIGENVALUE PROBLEM, MAY 1974
+time: amd 0.0002
+CHOLMOD time: L=lchol 0.0003 nnz(L): 2339
+CHOLMOD time: R=chol2 0.0003 nnz(R): 2339
+MATLAB time: R=chol 0.0003 nnz(R): 2339
+MATLAB [..,R]=symbfact 0.0003 nnz(R): 2339
+
+CHOLMOD speedup vs MATLAB chol: R: 0.99 L: 0.96
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.09
+CHOLMOD time: [L,,q]=lchol 0.0004 nnz(L): 2339
+CHOLMOD time: [L,,q]=ldlchol 0.0004 nnz(L): 2339
+
+CHOLMOD time: rank-5 ldlupdate 0.0001 nnz(L) 2354 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0001 nnz(L) 2354 no fill-in
+after resymbol: 2339
+CHOLMOD residual: 1.1e-18
+MATLAB residual: 8.2e-19
+CHOLMOD residual: 5.8e-20 (sparse b)
+MATLAB residual: 6.4e-20 (sparse b)
+
+================== Problem: 207: HB/lund_b n: 147 nnz: 2441
+title: SYMMETRIC MATRIX B OF LUND EIGENVALUE PROBLEM, MAY 1974
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0003 nnz(L): 2340
+CHOLMOD time: R=chol2 0.0003 nnz(R): 2340
+MATLAB time: R=chol 0.0003 nnz(R): 2340
+MATLAB [..,R]=symbfact 0.0003 nnz(R): 2340
+
+CHOLMOD speedup vs MATLAB chol: R: 1.07 L: 1.07
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.12
+CHOLMOD time: [L,,q]=lchol 0.0004 nnz(L): 2340
+CHOLMOD time: [L,,q]=ldlchol 0.0004 nnz(L): 2340
+
+CHOLMOD time: rank-6 ldlupdate 0.0001 nnz(L) 2481 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 2481 no fill-in
+after resymbol: 2340
+CHOLMOD residual: 1.2e-16
+MATLAB residual: 1.2e-16
+CHOLMOD residual: 8.7e-17 (sparse b)
+MATLAB residual: 8.7e-17 (sparse b)
+
+================== Problem: 27: HB/bcsstk05 n: 153 nnz: 2423
+title: SYMMETRIC STIFFNESS MATRIX, TRANSMISSION TOWER, LUMPED MASSES
+time: amd 0.0002
+CHOLMOD time: L=lchol 0.0003 nnz(L): 2326
+CHOLMOD time: R=chol2 0.0003 nnz(R): 2326
+MATLAB time: R=chol 0.0003 nnz(R): 2326
+MATLAB [..,R]=symbfact 0.0003 nnz(R): 2326
+
+CHOLMOD speedup vs MATLAB chol: R: 0.97 L: 0.90
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.05
+CHOLMOD time: [L,,q]=lchol 0.0005 nnz(L): 2326
+CHOLMOD time: [L,,q]=ldlchol 0.0005 nnz(L): 2326
+
+CHOLMOD time: rank-4 ldlupdate 0.0002 nnz(L) 2572 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0001 nnz(L) 2572 no fill-in
+after resymbol: 2326
+CHOLMOD residual: 1.5e-18
+MATLAB residual: 1.2e-18
+CHOLMOD residual: 3.8e-19 (sparse b)
+MATLAB residual: 3.3e-19 (sparse b)
+
+================== Problem: 60: HB/bcsstm05 n: 153 nnz: 153
+title: SYMMETRIC MASS MATRIX, TRANSMISSION TOWER, LUMPED MASSES
+time: amd 0.0000
+CHOLMOD time: L=lchol 0.0001 nnz(L): 153
+CHOLMOD time: R=chol2 0.0001 nnz(R): 153
+MATLAB time: R=chol 0.0001 nnz(R): 153
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 153
+
+CHOLMOD speedup vs MATLAB chol: R: 0.81 L: 0.94
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 3.33
+CHOLMOD time: [L,,q]=lchol 0.0001 nnz(L): 153
+CHOLMOD time: [L,,q]=ldlchol 0.0001 nnz(L): 153
+
+CHOLMOD time: rank-1 ldlupdate 0.0001 nnz(L) 154 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0000 nnz(L) 154 no fill-in
+after resymbol: 153
+CHOLMOD residual: 1.8e-15
+MATLAB residual: 1.7e-15
+CHOLMOD residual: 8.8e-16 (sparse b)
+MATLAB residual: 8.8e-16 (sparse b)
+
+================== Problem: 217: HB/nos1 n: 237 nnz: 1017
+title: SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON BEAM.
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0001 nnz(L): 704
+CHOLMOD time: R=chol2 0.0001 nnz(R): 704
+MATLAB time: R=chol 0.0001 nnz(R): 704
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 704
+
+CHOLMOD speedup vs MATLAB chol: R: 0.88 L: 0.92
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 2.11
+CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 704
+CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 704
+
+CHOLMOD time: rank-3 ldlupdate 0.0001 nnz(L) 896 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0001 nnz(L) 896 no fill-in
+after resymbol: 704
+CHOLMOD residual: 2.1e-18
+MATLAB residual: 2.2e-18
+CHOLMOD residual: 2.5e-19 (sparse b)
+MATLAB residual: 2.7e-19 (sparse b)
+
+================== Problem: 877: Pothen/mesh3e1 n: 289 nnz: 1377
+title: mesh3e1, with coordinates. From NASA, collected by Alex Pothen
+time: amd 0.0002
+CHOLMOD time: L=lchol 0.0003 nnz(L): 2433
+CHOLMOD time: R=chol2 0.0003 nnz(R): 2433
+MATLAB time: R=chol 0.0003 nnz(R): 2433
+MATLAB [..,R]=symbfact 0.0003 nnz(R): 2433
+
+CHOLMOD speedup vs MATLAB chol: R: 0.92 L: 0.94
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.18
+CHOLMOD time: [L,,q]=lchol 0.0006 nnz(L): 2433
+CHOLMOD time: [L,,q]=ldlchol 0.0005 nnz(L): 2433
+
+CHOLMOD time: rank-4 ldlupdate 0.0001 nnz(L) 2433 no fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0001 nnz(L) 2433 no fill-in
+after resymbol: 2433
+CHOLMOD residual: 2.8e-15
+MATLAB residual: 2.9e-15
+CHOLMOD residual: 3.9e-15 (sparse b)
+MATLAB residual: 3.8e-15 (sparse b)
+
+================== Problem: 878: Pothen/mesh3em5 n: 289 nnz: 1377
+title: mesh3em5, with coordinates. From NASA, collected by Alex Pothen
+time: amd 0.0002
+CHOLMOD time: L=lchol 0.0003 nnz(L): 2433
+CHOLMOD time: R=chol2 0.0003 nnz(R): 2433
+MATLAB time: R=chol 0.0003 nnz(R): 2433
+MATLAB [..,R]=symbfact 0.0003 nnz(R): 2433
+
+CHOLMOD speedup vs MATLAB chol: R: 0.92 L: 0.93
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.17
+CHOLMOD time: [L,,q]=lchol 0.0006 nnz(L): 2433
+CHOLMOD time: [L,,q]=ldlchol 0.0006 nnz(L): 2433
+
+CHOLMOD time: rank-7 ldlupdate 0.0002 nnz(L) 2538 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 2538 no fill-in
+after resymbol: 2433
+CHOLMOD residual: 4.7e-15
+MATLAB residual: 4.9e-15
+CHOLMOD residual: 5.3e-15 (sparse b)
+MATLAB residual: 5.1e-15 (sparse b)
+
+================== Problem: 875: Pothen/mesh2e1 n: 306 nnz: 2018
+title: mesh2e1, with coordinates. From NASA, collected by Alex Pothen
+time: amd 0.0003
+CHOLMOD time: L=lchol 0.0004 nnz(L): 3224
+CHOLMOD time: R=chol2 0.0004 nnz(R): 3224
+MATLAB time: R=chol 0.0004 nnz(R): 3224
+MATLAB [..,R]=symbfact 0.0004 nnz(R): 3224
+
+CHOLMOD speedup vs MATLAB chol: R: 0.96 L: 0.96
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.06
+CHOLMOD time: [L,,q]=lchol 0.0007 nnz(L): 3224
+CHOLMOD time: [L,,q]=ldlchol 0.0007 nnz(L): 3224
+
+CHOLMOD time: rank-7 ldlupdate 0.0002 nnz(L) 3508 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 3508 no fill-in
+after resymbol: 3224
+CHOLMOD residual: 1.8e-16
+MATLAB residual: 2.2e-16
+CHOLMOD residual: 4.0e-16 (sparse b)
+MATLAB residual: 3.9e-16 (sparse b)
+
+================== Problem: 876: Pothen/mesh2em5 n: 306 nnz: 2018
+title: mesh2em5, with coordinates. From NASA, collected by Alex Pothen
+time: amd 0.0003
+CHOLMOD time: L=lchol 0.0004 nnz(L): 3224
+CHOLMOD time: R=chol2 0.0004 nnz(R): 3224
+MATLAB time: R=chol 0.0004 nnz(R): 3224
+MATLAB [..,R]=symbfact 0.0004 nnz(R): 3224
+
+CHOLMOD speedup vs MATLAB chol: R: 1.03 L: 1.04
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.01
+CHOLMOD time: [L,,q]=lchol 0.0007 nnz(L): 3224
+CHOLMOD time: [L,,q]=ldlchol 0.0007 nnz(L): 3224
+
+CHOLMOD time: rank-7 ldlupdate 0.0001 nnz(L) 3224 no fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 3224 no fill-in
+after resymbol: 3224
+CHOLMOD residual: 1.7e-16
+MATLAB residual: 2.2e-16
+CHOLMOD residual: 2.2e-16 (sparse b)
+MATLAB residual: 3.0e-16 (sparse b)
+
+================== Problem: 229: HB/plat362 n: 362 nnz: 5786
+title: SPLATZMAN FINITE DIFFERENCE MODEL OF ATLANTICOCEAN
+time: amd 0.0004
+CHOLMOD time: L=lchol 0.0010 nnz(L): 8060
+CHOLMOD time: R=chol2 0.0010 nnz(R): 8060
+MATLAB time: R=chol 0.0011 nnz(R): 8060
+MATLAB [..,R]=symbfact 0.0007 nnz(R): 8060
+
+CHOLMOD speedup vs MATLAB chol: R: 1.07 L: 1.12
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.70
+CHOLMOD time: [L,,q]=lchol 0.0015 nnz(L): 8060
+CHOLMOD time: [L,,q]=ldlchol 0.0015 nnz(L): 8060
+
+CHOLMOD time: rank-5 ldlupdate 0.0007 nnz(L) 9872 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0002 nnz(L) 9872 no fill-in
+after resymbol: 8060
+CHOLMOD residual: 3.5e-05
+MATLAB residual: 1.4e-05
+CHOLMOD residual: 2.6e-05 (sparse b)
+MATLAB residual: 1.0e-05 (sparse b)
+
+================== Problem: 315: Bai/mhdb416 n: 416 nnz: 2312
+title: MAGNETO-HYDRO-DYNAMICS ALFVEN SPECTRAL PROBLEM
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0002 nnz(L): 1364
+CHOLMOD time: R=chol2 0.0002 nnz(R): 1364
+MATLAB time: R=chol 0.0002 nnz(R): 1364
+MATLAB [..,R]=symbfact 0.0003 nnz(R): 1364
+
+CHOLMOD speedup vs MATLAB chol: R: 0.87 L: 0.85
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.53
+CHOLMOD time: [L,,q]=lchol 0.0004 nnz(L): 1364
+CHOLMOD time: [L,,q]=ldlchol 0.0004 nnz(L): 1364
+
+CHOLMOD time: rank-5 ldlupdate 0.0001 nnz(L) 1369 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0001 nnz(L) 1369 no fill-in
+after resymbol: 1364
+CHOLMOD residual: 6.7e-11
+MATLAB residual: 7.0e-11
+CHOLMOD residual: 3.4e-11 (sparse b)
+MATLAB residual: 1.6e-11 (sparse b)
+
+================== Problem: 28: HB/bcsstk06 n: 420 nnz: 7860
+title: SYMMETRIC STIFFNESS MATRIX, MEDIUM TEST PROBLEM, LUMPED MASSES
+time: amd 0.0004
+CHOLMOD time: L=lchol 0.0015 nnz(L): 11345
+CHOLMOD time: R=chol2 0.0016 nnz(R): 11345
+MATLAB time: R=chol 0.0017 nnz(R): 11345
+MATLAB [..,R]=symbfact 0.0009 nnz(R): 11345
+
+CHOLMOD speedup vs MATLAB chol: R: 1.06 L: 1.10
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.58
+CHOLMOD time: [L,,q]=lchol 0.0021 nnz(L): 11345
+CHOLMOD time: [L,,q]=ldlchol 0.0020 nnz(L): 11345
+
+CHOLMOD time: rank-5 ldlupdate 0.0008 nnz(L) 12897 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0003 nnz(L) 12897 no fill-in
+after resymbol: 11345
+CHOLMOD residual: 4.8e-20
+MATLAB residual: 4.8e-20
+CHOLMOD residual: 2.4e-20 (sparse b)
+MATLAB residual: 2.6e-20 (sparse b)
+
+================== Problem: 29: HB/bcsstk07 n: 420 nnz: 7860
+title: SYMMETRIC STIFFNESS MATRIX, MEDIUM TEST PROBLEM, CONSISTENT MASSES
+time: amd 0.0004
+CHOLMOD time: L=lchol 0.0015 nnz(L): 11345
+CHOLMOD time: R=chol2 0.0016 nnz(R): 11345
+MATLAB time: R=chol 0.0017 nnz(R): 11345
+MATLAB [..,R]=symbfact 0.0009 nnz(R): 11345
+
+CHOLMOD speedup vs MATLAB chol: R: 1.11 L: 1.17
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.60
+CHOLMOD time: [L,,q]=lchol 0.0021 nnz(L): 11345
+CHOLMOD time: [L,,q]=ldlchol 0.0020 nnz(L): 11345
+
+CHOLMOD time: rank-1 ldlupdate 0.0006 nnz(L) 11385 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0002 nnz(L) 11385 no fill-in
+after resymbol: 11345
+CHOLMOD residual: 3.9e-20
+MATLAB residual: 4.1e-20
+CHOLMOD residual: 1.5e-20 (sparse b)
+MATLAB residual: 1.4e-20 (sparse b)
+
+================== Problem: 61: HB/bcsstm06 n: 420 nnz: 420
+title: SYMMETRIC MASS MATRIX, MEDIUM TEST PROBLEM, LUMPED MASSES
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0001 nnz(L): 420
+CHOLMOD time: R=chol2 0.0001 nnz(R): 420
+MATLAB time: R=chol 0.0001 nnz(R): 420
+MATLAB [..,R]=symbfact 0.0003 nnz(R): 420
+
+CHOLMOD speedup vs MATLAB chol: R: 0.83 L: 0.90
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 2.86
+CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 420
+CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 420
+
+CHOLMOD time: rank-5 ldlupdate 0.0001 nnz(L) 421 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0000 nnz(L) 421 no fill-in
+after resymbol: 420
+CHOLMOD residual: 4.2e-19
+MATLAB residual: 4.0e-19
+CHOLMOD residual: 2.0e-19 (sparse b)
+MATLAB residual: 2.0e-19 (sparse b)
+
+================== Problem: 62: HB/bcsstm07 n: 420 nnz: 7252
+title: SYMMETRIC MASS MATRIX, MEDIUM TEST PROBLEM, CONSISTENT MASSES
+time: amd 0.0004
+CHOLMOD time: L=lchol 0.0014 nnz(L): 10654
+CHOLMOD time: R=chol2 0.0015 nnz(R): 10654
+MATLAB time: R=chol 0.0015 nnz(R): 10654
+MATLAB [..,R]=symbfact 0.0009 nnz(R): 10654
+
+CHOLMOD speedup vs MATLAB chol: R: 1.03 L: 1.08
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.61
+CHOLMOD time: [L,,q]=lchol 0.0020 nnz(L): 10654
+CHOLMOD time: [L,,q]=ldlchol 0.0019 nnz(L): 10654
+
+CHOLMOD time: rank-6 ldlupdate 0.0005 nnz(L) 10730 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0003 nnz(L) 10730 no fill-in
+after resymbol: 10654
+CHOLMOD residual: 2.0e-16
+MATLAB residual: 1.8e-16
+CHOLMOD residual: 1.7e-16 (sparse b)
+MATLAB residual: 1.4e-16 (sparse b)
+
+================== Problem: 221: HB/nos5 n: 468 nnz: 5172
+title: SYMMETRIC MATRIX, FE APPROXIMATION OF BUILDING.
+time: amd 0.0008
+CHOLMOD time: L=lchol 0.0024 nnz(L): 18436
+CHOLMOD time: R=chol2 0.0028 nnz(R): 18436
+MATLAB time: R=chol 0.0028 nnz(R): 18436
+MATLAB [..,R]=symbfact 0.0012 nnz(R): 18437
+
+CHOLMOD speedup vs MATLAB chol: R: 1.00 L: 1.20
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.53
+CHOLMOD time: [L,,q]=lchol 0.0036 nnz(L): 18436
+CHOLMOD time: [L,,q]=ldlchol 0.0038 nnz(L): 18437
+
+CHOLMOD time: rank-7 ldlupdate 0.0016 nnz(L) 19563 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0004 nnz(L) 19563 no fill-in
+after resymbol: 18437
+CHOLMOD residual: 2.0e-17
+MATLAB residual: 1.8e-17
+CHOLMOD residual: 3.2e-18 (sparse b)
+MATLAB residual: 3.8e-18 (sparse b)
+
+================== Problem: 42: HB/bcsstk20 n: 485 nnz: 3135
+title: SYMMETRIC STIFFNESS MATRIX - FRAME WITHIN A SUSPENSION BRIDGE
+time: amd 0.0002
+CHOLMOD time: L=lchol 0.0003 nnz(L): 2310
+CHOLMOD time: R=chol2 0.0003 nnz(R): 2310
+MATLAB time: R=chol 0.0003 nnz(R): 2310
+MATLAB [..,R]=symbfact 0.0004 nnz(R): 2336
+
+CHOLMOD speedup vs MATLAB chol: R: 0.91 L: 0.90
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.31
+CHOLMOD time: [L,,q]=lchol 0.0006 nnz(L): 2310
+CHOLMOD time: [L,,q]=ldlchol 0.0006 nnz(L): 2336
+
+CHOLMOD time: rank-7 ldlupdate 0.0002 nnz(L) 2548 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 2548 no fill-in
+after resymbol: 2336
+CHOLMOD residual: 7.4e-22
+MATLAB residual: 7.1e-22
+CHOLMOD residual: 5.6e-23 (sparse b)
+MATLAB residual: 9.0e-23 (sparse b)
+
+================== Problem: 70: HB/bcsstm20 n: 485 nnz: 485
+title: SYMMETRIC MASS MATRIX - FRAME WITHIN A SUSPENSION BRIDGE
+time: amd 0.0004
+CHOLMOD time: L=lchol 0.0001 nnz(L): 485
+CHOLMOD time: R=chol2 0.0001 nnz(R): 485
+MATLAB time: R=chol 0.0001 nnz(R): 485
+MATLAB [..,R]=symbfact 0.0002 nnz(R): 485
+
+CHOLMOD speedup vs MATLAB chol: R: 0.83 L: 0.81
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 2.04
+CHOLMOD time: [L,,q]=lchol 0.0002 nnz(L): 485
+CHOLMOD time: [L,,q]=ldlchol 0.0002 nnz(L): 485
+
+CHOLMOD time: rank-8 ldlupdate 0.0001 nnz(L) 486 with fill-in
+CHOLMOD time: rank-4 ldldowndate 0.0000 nnz(L) 486 no fill-in
+after resymbol: 485
+CHOLMOD residual: 1.0e-22
+MATLAB residual: 9.8e-23
+CHOLMOD residual: 5.0e-23 (sparse b)
+MATLAB residual: 4.5e-23 (sparse b)
+
+================== Problem: 2: HB/494_bus n: 494 nnz: 1666
+title: S ADMITTANCE MATRIX 494 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985.
+time: amd 0.0002
+CHOLMOD time: L=lchol 0.0002 nnz(L): 1414
+CHOLMOD time: R=chol2 0.0002 nnz(R): 1414
+MATLAB time: R=chol 0.0002 nnz(R): 1414
+MATLAB [..,R]=symbfact 0.0004 nnz(R): 1414
+
+CHOLMOD speedup vs MATLAB chol: R: 0.88 L: 0.87
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.46
+CHOLMOD time: [L,,q]=lchol 0.0006 nnz(L): 1414
+CHOLMOD time: [L,,q]=ldlchol 0.0005 nnz(L): 1414
+
+CHOLMOD time: rank-6 ldlupdate 0.0001 nnz(L) 1499 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 1499 no fill-in
+after resymbol: 1414
+CHOLMOD residual: 2.5e-14
+MATLAB residual: 2.0e-14
+CHOLMOD residual: 1.4e-15 (sparse b)
+MATLAB residual: 1.8e-15 (sparse b)
+
+================== Problem: 339: Boeing/bcsstk34 n: 588 nnz: 21418
+title: NASTRAN BUCKLING PROBLEM STIFFNESS MATRIX
+time: amd 0.0010
+CHOLMOD time: L=lchol 0.0055 nnz(L): 43351
+CHOLMOD time: R=chol2 0.0069 nnz(R): 43351
+MATLAB time: R=chol 0.0070 nnz(R): 43351
+MATLAB [..,R]=symbfact 0.0036 nnz(R): 43366
+
+CHOLMOD speedup vs MATLAB chol: R: 1.02 L: 1.28
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.65
+CHOLMOD time: [L,,q]=lchol 0.0073 nnz(L): 43351
+CHOLMOD time: [L,,q]=ldlchol 0.0076 nnz(L): 43366
+
+CHOLMOD time: rank-4 ldlupdate 0.0036 nnz(L) 48749 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0012 nnz(L) 48749 no fill-in
+after resymbol: 43366
+CHOLMOD residual: 2.9e-20
+MATLAB residual: 3.0e-20
+CHOLMOD residual: 2.6e-20 (sparse b)
+MATLAB residual: 2.6e-20 (sparse b)
+
+================== Problem: 3: HB/662_bus n: 662 nnz: 2474
+title: S ADMITTANCE MATRIX 662 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985.
+time: amd 0.0004
+CHOLMOD time: L=lchol 0.0004 nnz(L): 2549
+CHOLMOD time: R=chol2 0.0004 nnz(R): 2549
+MATLAB time: R=chol 0.0003 nnz(R): 2549
+MATLAB [..,R]=symbfact 0.0005 nnz(R): 2549
+
+CHOLMOD speedup vs MATLAB chol: R: 0.89 L: 0.88
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.20
+CHOLMOD time: [L,,q]=lchol 0.0009 nnz(L): 2549
+CHOLMOD time: [L,,q]=ldlchol 0.0008 nnz(L): 2549
+
+CHOLMOD time: rank-6 ldlupdate 0.0002 nnz(L) 2589 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 2589 no fill-in
+after resymbol: 2549
+CHOLMOD residual: 1.4e-13
+MATLAB residual: 2.0e-13
+CHOLMOD residual: 7.1e-15 (sparse b)
+MATLAB residual: 8.7e-15 (sparse b)
+
+================== Problem: 222: HB/nos6 n: 675 nnz: 3255
+title: SYMMETRIC MATRIX, POISSON'S EQUATION IN L SHAPE, MIXED BC.
+time: amd 0.0005
+CHOLMOD time: L=lchol 0.0007 nnz(L): 6453
+CHOLMOD time: R=chol2 0.0007 nnz(R): 6453
+MATLAB time: R=chol 0.0007 nnz(R): 6453
+MATLAB [..,R]=symbfact 0.0006 nnz(R): 6453
+
+CHOLMOD speedup vs MATLAB chol: R: 1.01 L: 1.00
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.85
+CHOLMOD time: [L,,q]=lchol 0.0013 nnz(L): 6453
+CHOLMOD time: [L,,q]=ldlchol 0.0013 nnz(L): 6453
+
+CHOLMOD time: rank-2 ldlupdate 0.0004 nnz(L) 6600 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0001 nnz(L) 6600 no fill-in
+after resymbol: 6453
+CHOLMOD residual: 3.3e-15
+MATLAB residual: 3.6e-15
+CHOLMOD residual: 2.1e-16 (sparse b)
+MATLAB residual: 2.1e-16 (sparse b)
+
+================== Problem: 4: HB/685_bus n: 685 nnz: 3249
+title: S ADMITTANCE MATRIX 685 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985.
+time: amd 0.0005
+CHOLMOD time: L=lchol 0.0005 nnz(L): 3650
+CHOLMOD time: R=chol2 0.0005 nnz(R): 3650
+MATLAB time: R=chol 0.0005 nnz(R): 3650
+MATLAB [..,R]=symbfact 0.0005 nnz(R): 3650
+
+CHOLMOD speedup vs MATLAB chol: R: 0.98 L: 0.98
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.07
+CHOLMOD time: [L,,q]=lchol 0.0011 nnz(L): 3650
+CHOLMOD time: [L,,q]=ldlchol 0.0011 nnz(L): 3650
+
+CHOLMOD time: rank-1 ldlupdate 0.0002 nnz(L) 3717 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0001 nnz(L) 3717 no fill-in
+after resymbol: 3650
+CHOLMOD residual: 4.5e-15
+MATLAB residual: 6.8e-15
+CHOLMOD residual: 2.4e-16 (sparse b)
+MATLAB residual: 3.3e-16 (sparse b)
+
+================== Problem: 357: Boeing/msc00726 n: 726 nnz: 34518
+title: SYMMETRIC TEST MATRIX FROM MSC/NASTRAN BC4F8.OUT2
+time: amd 0.0021
+CHOLMOD time: L=lchol 0.0173 nnz(L): 110707
+CHOLMOD time: R=chol2 0.0214 nnz(R): 110707
+MATLAB time: R=chol 0.0218 nnz(R): 110707
+MATLAB [..,R]=symbfact 0.0085 nnz(R): 110707
+
+CHOLMOD speedup vs MATLAB chol: R: 1.02 L: 1.26
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.49
+CHOLMOD time: [L,,q]=lchol 0.0213 nnz(L): 110707
+CHOLMOD time: [L,,q]=ldlchol 0.1228 nnz(L): 110707
+
+CHOLMOD time: rank-6 ldlupdate 0.0058 nnz(L) 110715 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0028 nnz(L) 110715 no fill-in
+after resymbol: 110707
+CHOLMOD residual: 2.7e-21
+MATLAB residual: 2.8e-21
+CHOLMOD residual: 3.9e-22 (sparse b)
+MATLAB residual: 3.9e-22 (sparse b)
+
+================== Problem: 223: HB/nos7 n: 729 nnz: 4617
+title: SYMMETRIC MATRIX, POISSON'S EQUATION IN UNIT CUBE.
+time: amd 0.0008
+CHOLMOD time: L=lchol 0.0027 nnz(L): 18945
+CHOLMOD time: R=chol2 0.0035 nnz(R): 18945
+MATLAB time: R=chol 0.0034 nnz(R): 18945
+MATLAB [..,R]=symbfact 0.0013 nnz(R): 18945
+
+CHOLMOD speedup vs MATLAB chol: R: 0.99 L: 1.24
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.48
+CHOLMOD time: [L,,q]=lchol 0.0042 nnz(L): 18945
+CHOLMOD time: [L,,q]=ldlchol 0.0044 nnz(L): 18945
+
+CHOLMOD time: rank-3 ldlupdate 0.0012 nnz(L) 19170 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0005 nnz(L) 19170 no fill-in
+after resymbol: 18945
+CHOLMOD residual: 2.2e-13
+MATLAB residual: 2.6e-13
+CHOLMOD residual: 9.3e-15 (sparse b)
+MATLAB residual: 9.4e-15 (sparse b)
+
+================== Problem: 41: HB/bcsstk19 n: 817 nnz: 6853
+title: SYMMETRIC STIFFNESS MATRIX - PART OF A SUSPENSION BRIDGE
+time: amd 0.0005
+CHOLMOD time: L=lchol 0.0009 nnz(L): 7528
+CHOLMOD time: R=chol2 0.0009 nnz(R): 7528
+MATLAB time: R=chol 0.0009 nnz(R): 7528
+MATLAB [..,R]=symbfact 0.0008 nnz(R): 7528
+
+CHOLMOD speedup vs MATLAB chol: R: 0.98 L: 0.95
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.90
+CHOLMOD time: [L,,q]=lchol 0.0016 nnz(L): 7528
+CHOLMOD time: [L,,q]=ldlchol 0.0016 nnz(L): 7528
+
+CHOLMOD time: rank-6 ldlupdate 0.0006 nnz(L) 7558 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0002 nnz(L) 7558 no fill-in
+after resymbol: 7528
+CHOLMOD residual: 2.8e-20
+MATLAB residual: 3.2e-20
+CHOLMOD residual: 7.6e-21 (sparse b)
+MATLAB residual: 5.7e-21 (sparse b)
+
+================== Problem: 69: HB/bcsstm19 n: 817 nnz: 817
+title: SYMMETRIC MASS MATRIX - PART OF A SUSPENSION BRIDGE
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0002 nnz(L): 817
+CHOLMOD time: R=chol2 0.0002 nnz(R): 817
+MATLAB time: R=chol 0.0002 nnz(R): 817
+MATLAB [..,R]=symbfact 0.0003 nnz(R): 817
+
+CHOLMOD speedup vs MATLAB chol: R: 0.81 L: 0.79
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.67
+CHOLMOD time: [L,,q]=lchol 0.0003 nnz(L): 817
+CHOLMOD time: [L,,q]=ldlchol 0.0003 nnz(L): 817
+
+CHOLMOD time: rank-2 ldlupdate 0.0001 nnz(L) 818 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0001 nnz(L) 818 no fill-in
+after resymbol: 817
+CHOLMOD residual: 2.0e-22
+MATLAB residual: 2.0e-22
+CHOLMOD residual: 1.0e-22 (sparse b)
+MATLAB residual: 1.0e-22 (sparse b)
+
+================== Problem: 159: HB/gr_30_30 n: 900 nnz: 7744
+title: SYMMETRIC MATRIX FROM NINE POINT START ON A 30 X 30 GRID.
+time: amd 0.0007
+CHOLMOD time: L=lchol 0.0020 nnz(L): 16348
+CHOLMOD time: R=chol2 0.0021 nnz(R): 16348
+MATLAB time: R=chol 0.0022 nnz(R): 16348
+MATLAB [..,R]=symbfact 0.0012 nnz(R): 16348
+
+CHOLMOD speedup vs MATLAB chol: R: 1.02 L: 1.10
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.61
+CHOLMOD time: [L,,q]=lchol 0.0030 nnz(L): 16348
+CHOLMOD time: [L,,q]=ldlchol 0.0029 nnz(L): 16348
+
+CHOLMOD time: rank-8 ldlupdate 0.0013 nnz(L) 17998 with fill-in
+CHOLMOD time: rank-4 ldldowndate 0.0004 nnz(L) 17998 no fill-in
+after resymbol: 16348
+CHOLMOD residual: 4.1e-13
+MATLAB residual: 4.4e-13
+CHOLMOD residual: 2.4e-14 (sparse b)
+MATLAB residual: 2.7e-14 (sparse b)
+
+================== Problem: 218: HB/nos2 n: 957 nnz: 4137
+title: SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON BEAM.
+time: amd 0.0003
+CHOLMOD time: L=lchol 0.0004 nnz(L): 2864
+CHOLMOD time: R=chol2 0.0004 nnz(R): 2864
+MATLAB time: R=chol 0.0003 nnz(R): 2864
+MATLAB [..,R]=symbfact 0.0005 nnz(R): 2864
+
+CHOLMOD speedup vs MATLAB chol: R: 0.88 L: 0.83
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.25
+CHOLMOD time: [L,,q]=lchol 0.0008 nnz(L): 2864
+CHOLMOD time: [L,,q]=ldlchol 0.0008 nnz(L): 2864
+
+CHOLMOD time: rank-8 ldlupdate 0.0003 nnz(L) 3124 with fill-in
+CHOLMOD time: rank-4 ldldowndate 0.0002 nnz(L) 3124 no fill-in
+after resymbol: 2864
+CHOLMOD residual: 3.5e-17
+MATLAB residual: 3.8e-17
+CHOLMOD residual: 4.8e-18 (sparse b)
+MATLAB residual: 4.6e-18 (sparse b)
+
+================== Problem: 219: HB/nos3 n: 960 nnz: 15844
+title: SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON PLATE
+time: amd 0.0009
+CHOLMOD time: L=lchol 0.0039 nnz(L): 31309
+CHOLMOD time: R=chol2 0.0049 nnz(R): 31309
+MATLAB time: R=chol 0.0049 nnz(R): 31309
+MATLAB [..,R]=symbfact 0.0027 nnz(R): 31314
+
+CHOLMOD speedup vs MATLAB chol: R: 0.99 L: 1.24
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.70
+CHOLMOD time: [L,,q]=lchol 0.0055 nnz(L): 31311
+CHOLMOD time: [L,,q]=ldlchol 0.0057 nnz(L): 31314
+
+CHOLMOD time: rank-7 ldlupdate 0.0026 nnz(L) 36618 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0010 nnz(L) 36618 no fill-in
+after resymbol: 31314
+CHOLMOD residual: 1.9e-13
+MATLAB residual: 1.9e-13
+CHOLMOD residual: 7.0e-15 (sparse b)
+MATLAB residual: 7.0e-15 (sparse b)
+
+================== Problem: 358: Boeing/msc01050 n: 1050 nnz: 26198
+title: SYMMETRIC TEST MATRIX FROM MSC/NASTRAN STARF8.OUT2
+time: amd 0.0019
+CHOLMOD time: L=lchol 0.0051 nnz(L): 28305
+CHOLMOD time: R=chol2 0.0054 nnz(R): 28305
+MATLAB time: R=chol 0.0057 nnz(R): 28305
+MATLAB [..,R]=symbfact 0.0032 nnz(R): 28305
+
+CHOLMOD speedup vs MATLAB chol: R: 1.06 L: 1.13
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.64
+CHOLMOD time: [L,,q]=lchol 0.0074 nnz(L): 28305
+CHOLMOD time: [L,,q]=ldlchol 0.0072 nnz(L): 28305
+
+CHOLMOD time: rank-5 ldlupdate 0.0016 nnz(L) 28411 with fill-in
+CHOLMOD time: rank-2 ldldowndate 0.0007 nnz(L) 28411 no fill-in
+after resymbol: 28305
+CHOLMOD residual: 5.3e-14
+MATLAB residual: 5.1e-14
+CHOLMOD residual: 4.3e-15 (sparse b)
+MATLAB residual: 4.3e-15 (sparse b)
+
+================== Problem: 30: HB/bcsstk08 n: 1074 nnz: 12960
+title: SYMMETRIC STIFFNESS MATRIX, FRAME BUILDING (TV STUDIO)
+time: amd 0.0024
+CHOLMOD time: L=lchol 0.0056 nnz(L): 31150
+CHOLMOD time: R=chol2 0.0068 nnz(R): 31150
+MATLAB time: R=chol 0.0070 nnz(R): 31150
+MATLAB [..,R]=symbfact 0.0027 nnz(R): 31153
+
+CHOLMOD speedup vs MATLAB chol: R: 1.04 L: 1.25
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.48
+CHOLMOD time: [L,,q]=lchol 0.0089 nnz(L): 31150
+CHOLMOD time: [L,,q]=ldlchol 0.0092 nnz(L): 31153
+
+CHOLMOD time: rank-8 ldlupdate 0.0021 nnz(L) 31639 with fill-in
+CHOLMOD time: rank-4 ldldowndate 0.0009 nnz(L) 31639 no fill-in
+after resymbol: 31153
+CHOLMOD residual: 4.0e-22
+MATLAB residual: 3.0e-22
+CHOLMOD residual: 4.3e-22 (sparse b)
+MATLAB residual: 2.7e-22 (sparse b)
+
+================== Problem: 63: HB/bcsstm08 n: 1074 nnz: 1074
+title: SYMMETRIC MASS MATRIX, FRAME BUILDING (TV STUDIO)
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0002 nnz(L): 1074
+CHOLMOD time: R=chol2 0.0002 nnz(R): 1074
+MATLAB time: R=chol 0.0002 nnz(R): 1074
+MATLAB [..,R]=symbfact 0.0004 nnz(R): 1074
+
+CHOLMOD speedup vs MATLAB chol: R: 0.83 L: 0.81
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.81
+CHOLMOD time: [L,,q]=lchol 0.0004 nnz(L): 1074
+CHOLMOD time: [L,,q]=ldlchol 0.0004 nnz(L): 1074
+
+CHOLMOD time: rank-8 ldlupdate 0.0001 nnz(L) 1075 with fill-in
+CHOLMOD time: rank-4 ldldowndate 0.0001 nnz(L) 1075 no fill-in
+after resymbol: 1074
+CHOLMOD residual: 3.2e-21
+MATLAB residual: 3.0e-21
+CHOLMOD residual: 1.4e-21 (sparse b)
+MATLAB residual: 1.2e-21 (sparse b)
+
+================== Problem: 31: HB/bcsstk09 n: 1083 nnz: 18437
+title: SYMMETRIC STIFFNESS MATRIX, SQUARE PLATE CLAMPED
+time: amd 0.0018
+CHOLMOD time: L=lchol 0.0076 nnz(L): 58341
+CHOLMOD time: R=chol2 0.0095 nnz(R): 58341
+MATLAB time: R=chol 0.0095 nnz(R): 58341
+MATLAB [..,R]=symbfact 0.0045 nnz(R): 58416
+
+CHOLMOD speedup vs MATLAB chol: R: 1.01 L: 1.26
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 0.60
+CHOLMOD time: [L,,q]=lchol 0.0103 nnz(L): 58339
+CHOLMOD time: [L,,q]=ldlchol 0.0107 nnz(L): 58416
+
+CHOLMOD time: rank-1 ldlupdate 0.0040 nnz(L) 64019 with fill-in
+CHOLMOD time: rank-1 ldldowndate 0.0015 nnz(L) 64019 no fill-in
+after resymbol: 58416
+CHOLMOD residual: 1.7e-18
+MATLAB residual: 1.3e-18
+CHOLMOD residual: 1.1e-19 (sparse b)
+MATLAB residual: 8.9e-20 (sparse b)
+
+================== Problem: 64: HB/bcsstm09 n: 1083 nnz: 1083
+title: SYMMETRIC MASS MATRIX, SQUARE PLATE CLAMPED
+time: amd 0.0001
+CHOLMOD time: L=lchol 0.0002 nnz(L): 1083
+CHOLMOD time: R=chol2 0.0002 nnz(R): 1083
+MATLAB time: R=chol 0.0002 nnz(R): 1083
+MATLAB [..,R]=symbfact 0.0004 nnz(R): 1083
+
+CHOLMOD speedup vs MATLAB chol: R: 0.86 L: 0.84
+
+
+CHOLMOD numeric lchol vs MATLAB symbfact: 1.61
+CHOLMOD time: [L,,q]=lchol 0.0004 nnz(L): 1083
+CHOLMOD time: [L,,q]=ldlchol 0.0004 nnz(L): 1083
+
+CHOLMOD time: rank-7 ldlupdate 0.0001 nnz(L) 1084 with fill-in
+CHOLMOD time: rank-3 ldldowndate 0.0001 nnz(L) 1084 no fill-in
+after resymbol: 1083
+CHOLMOD residual: 1.5e-05
+MATLAB residual: 3.4e-11
+CHOLMOD residual: 1.2e-06 (sparse b)
+MATLAB residual: 1.8e-11 (sparse b)
+test0 passed
+=================================================================
+test1: test sparse2
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 1
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (1,1) 1
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (1,1) 1
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (1,1) 1
+
+size B1: 1 1
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (1,1) 1
+
+size B2: 1 1
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 1
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (1,1) 5
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (1,1) 5
+
+size B2: 1 1
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 1
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (1,1) 3.1416
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (1,1) 3.1416
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (1,1) 3.1416
+
+size B1: 1 1
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (1,1) 3.1416
+
+size B2: 1 1
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 1
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 1-by-1
+
+size B2: 1 1
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (1,2) 1
+ (1,3) 1
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (1,2) 1
+ (1,3) 1
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (1,2) 1
+ (1,3) 1
+
+size B1: 1 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (1,2) 1
+ (1,3) 1
+
+size B2: 1 3
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (1,2) 2
+ (1,3) 3
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (1,2) 2
+ (1,3) 3
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (1,2) 2
+ (1,3) 3
+
+size B1: 1 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (1,2) 2
+ (1,3) 3
+
+size B2: 1 3
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (1,2) 3.1416
+ (1,3) 3.1416
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (1,2) 3.1416
+ (1,3) 3.1416
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (1,2) 3.1416
+ (1,3) 3.1416
+
+size B1: 1 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (1,2) 3.1416
+ (1,3) 3.1416
+
+size B2: 1 3
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 3
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (1,3) 1
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (1,3) 1
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (1,3) 1
+
+size B1: 1 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (1,3) 1
+
+size B2: 1 3
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 3
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (1,3) 5
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (1,3) 5
+
+size B2: 1 3
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 3
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (1,3) 3.1416
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (1,3) 3.1416
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (1,3) 3.1416
+
+size B1: 1 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (1,3) 3.1416
+
+size B2: 1 3
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ 3
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 1-by-3
+
+size B2: 1 3
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ []
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 1-by-0
+
+size B2: 1 0
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ []
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ []
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 1-by-0
+
+size B2: 1 0
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 1
+
+
+j =
+
+ []
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 1-by-0
+
+size B2: 1 0
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 1
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,1) 1
+ (3,1) 1
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,1) 1
+ (3,1) 1
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,1) 1
+ (3,1) 1
+
+size B1: 3 1
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,1) 1
+ (3,1) 1
+
+size B2: 3 1
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 1
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,1) 2
+ (3,1) 3
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,1) 2
+ (3,1) 3
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,1) 2
+ (3,1) 3
+
+size B1: 3 1
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,1) 2
+ (3,1) 3
+
+size B2: 3 1
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 1
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,1) 3.1416
+ (3,1) 3.1416
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,1) 3.1416
+ (3,1) 3.1416
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,1) 3.1416
+ (3,1) 3.1416
+
+size B1: 3 1
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,1) 3.1416
+ (3,1) 3.1416
+
+size B2: 3 1
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 1
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,2) 1
+ (3,3) 1
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,2) 1
+ (3,3) 1
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,2) 1
+ (3,3) 1
+
+size B1: 3 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,2) 1
+ (3,3) 1
+
+size B2: 3 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,2) 2
+ (3,3) 3
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,2) 2
+ (3,3) 3
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,2) 2
+ (3,3) 3
+
+size B1: 3 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,2) 2
+ (3,3) 3
+
+size B2: 3 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,2) 3.1416
+ (3,3) 3.1416
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,2) 3.1416
+ (3,3) 3.1416
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,2) 3.1416
+ (3,3) 3.1416
+
+size B1: 3 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,2) 3.1416
+ (3,3) 3.1416
+
+size B2: 3 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 3
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,3) 1
+ (3,3) 1
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,3) 1
+ (3,3) 1
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,3) 1
+ (3,3) 1
+
+size B1: 3 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,3) 1
+ (3,3) 1
+
+size B2: 3 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 3
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,3) 2
+ (3,3) 3
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,3) 2
+ (3,3) 3
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,3) 2
+ (3,3) 3
+
+size B1: 3 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,3) 2
+ (3,3) 3
+
+size B2: 3 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 3
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,3) 3.1416
+ (3,3) 3.1416
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,3) 3.1416
+ (3,3) 3.1416
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,3) 3.1416
+ (3,3) 3.1416
+
+size B1: 3 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,3) 3.1416
+ (3,3) 3.1416
+
+size B2: 3 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ 3
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ []
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ []
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ []
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 2
+ 3
+
+
+j =
+
+ []
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 1
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,1) 1
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,1) 1
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,1) 1
+
+size B1: 2 1
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,1) 1
+
+size B2: 2 1
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 1
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,1) 5
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,1) 5
+
+size B2: 2 1
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 1
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,1) 3.1416
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,1) 3.1416
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,1) 3.1416
+
+size B1: 2 1
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,1) 3.1416
+
+size B2: 2 1
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 1
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 2-by-1
+
+size B2: 2 1
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,2) 1
+ (2,3) 1
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,2) 1
+ (2,3) 1
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,2) 1
+ (2,3) 1
+
+size B1: 2 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,2) 1
+ (2,3) 1
+
+size B2: 2 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,2) 2
+ (2,3) 3
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,2) 2
+ (2,3) 3
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,2) 2
+ (2,3) 3
+
+size B1: 2 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,2) 2
+ (2,3) 3
+
+size B2: 2 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,2) 3.1416
+ (2,3) 3.1416
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,2) 3.1416
+ (2,3) 3.1416
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,2) 3.1416
+ (2,3) 3.1416
+
+size B1: 2 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,2) 3.1416
+ (2,3) 3.1416
+
+size B2: 2 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 3
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,3) 1
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,3) 1
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,3) 1
+
+size B1: 2 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,3) 1
+
+size B2: 2 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 3
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,3) 5
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,3) 5
+
+size B2: 2 3
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 3
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ (2,3) 3.1416
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ (2,3) 3.1416
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ (2,3) 3.1416
+
+size B1: 2 3
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ (2,3) 3.1416
+
+size B2: 2 3
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ 3
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 2-by-3
+
+size B2: 2 3
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ []
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 2-by-0
+
+size B2: 2 0
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ []
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ []
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 2-by-0
+
+size B2: 2 0
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ 2
+
+
+j =
+
+ []
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 2-by-0
+
+size B2: 2 0
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 1
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 0-by-1
+
+size B2: 0 1
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 1
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 1
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 0-by-1
+
+size B2: 0 1
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 1
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 0-by-1
+
+size B2: 0 1
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 2
+ 3
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 3
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 0-by-3
+
+size B2: 0 3
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 3
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 3
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 0-by-3
+
+size B2: 0 3
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ 3
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 0-by-3
+
+size B2: 0 3
+========================== SPARSE AND SPARSE2 DIFFER
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ []
+
+
+s =
+
+ 1
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 0-by-0
+
+size B2: 0 0
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ []
+
+
+s =
+
+ 2
+ 3
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+sparse failed
+
+A2 = sparse2 (i,j,s,m,n)
+sparse2 failed
+
+B1 = sparse (i,j,s)
+sparse failed
+
+B2 = sparse2 (i,j,s)
+sparse2 failed
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ []
+
+
+s =
+
+ 3.1416
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 0-by-0
+
+size B2: 0 0
+
+-----------------------------------------------
+
+i =
+
+ []
+
+
+j =
+
+ []
+
+
+s =
+
+ []
+
+
+m =
+
+ 3
+
+
+n =
+
+ 4
+
+
+A1 = sparse (i,j,s,m,n)
+
+A1 =
+
+ All zero sparse: 3-by-4
+
+size A1: 3 4
+
+A2 = sparse2 (i,j,s,m,n)
+
+A2 =
+
+ All zero sparse: 3-by-4
+
+size A2: 3 4
+
+B1 = sparse (i,j,s)
+
+B1 =
+
+ All zero sparse: 0-by-0
+
+size B1: 0 0
+
+B2 = sparse2 (i,j,s)
+
+B2 =
+
+ All zero sparse: 0-by-0
+
+size B2: 0 0
+test1 passed (review the above results)
+=================================================================
+test2: test sparse2
+
+i =
+
+ 2 3
+
+
+j =
+
+ 3 4
+
+
+s =
+
+ 11.4000 + 3.4000i 9.2000 + 1.2000i
+
+
+ans =
+
+ (2,3) 11.4000 + 3.4000i
+ (3,4) 9.2000 + 1.2000i
+
+
+ans =
+
+ (2,3) 11.4000 + 3.4000i
+ (3,4) 9.2000 + 1.2000i
+
+
+ans =
+
+ 3290
+
+test2 passed
+=================================================================
+test3: test sparse on int8, int16, and logical
+
+c =
+
+ab d
+
+Warning: SPARSE with a character array input returns a sparse double result.
+ This behavior will change in a future release.
+> In test3 at 14
+ In cholmod_test at 100
+
+ans =
+
+ (1,1) 97
+ (1,2) 98
+ (1,4) 100
+
+
+ans =
+
+ (1,1) 97
+ (1,2) 98
+ (1,4) 100
+
+Warning: SPARSE with a character array input returns a sparse double result.
+ This behavior will change in a future release.
+> In test3 at 16
+ In cholmod_test at 100
+
+ans =
+
+ (1,1) 97
+ (2,1) 98
+ (4,1) 100
+
+
+ans =
+
+ (1,1) 97
+ (2,1) 98
+ (4,1) 100
+
+ Name Size Bytes Class Attributes
+
+ ans 4x1 64 double sparse
+ c 1x4 8 char
+
+
+ans =
+
+ 3
+
+sparse(int8(c)) fails in MATLAB
+
+ans =
+
+ (1,1) 97
+ (1,2) 98
+ (1,4) 100
+
+
+ans =
+
+ (1,1) 97
+ (1,2) 98
+ (1,4) 100
+
+ Name Size Bytes Class Attributes
+
+ ans 1x4 88 double sparse
+ c 1x4 8 char
+
+
+s =
+
+ 1 0 1 1
+ 0 0 0 1
+ 0 1 1 1
+ 1 0 0 0
+
+
+ans =
+
+ (1,1) 1
+ (4,1) 1
+ (3,2) 1
+ (1,3) 1
+ (3,3) 1
+ (1,4) 1
+ (2,4) 1
+ (3,4) 1
+
+ Name Size Bytes Class Attributes
+
+ ans 4x4 112 logical sparse
+ c 1x4 8 char
+ s 4x4 16 logical
+
+
+ans =
+
+ (1,1) 1
+ (4,1) 1
+ (3,2) 1
+ (1,3) 1
+ (3,3) 1
+ (1,4) 1
+ (2,4) 1
+ (3,4) 1
+
+ Name Size Bytes Class Attributes
+
+ ans 4x4 112 logical sparse
+ c 1x4 8 char
+ s 4x4 16 logical
+
+
+x =
+
+ 0.1013 0.2280 0.1095 0.9468
+ 0.2648 0.0281 0.8211 0.8138
+ 0.2595 0.6996 0.4195 0.7779
+ 0.5345 0.8071 0.8422 0.8768
+
+
+ans =
+
+ (4,1) 1
+ (3,2) 1
+ (4,2) 1
+ (2,3) 1
+ (4,3) 1
+ (1,4) 1
+ (2,4) 1
+ (3,4) 1
+ (4,4) 1
+
+ Name Size Bytes Class Attributes
+
+ ans 4x4 121 logical sparse
+ c 1x4 8 char
+ s 4x4 16 logical
+ x 4x4 128 double
+
+
+ans =
+
+ (4,1) 1
+ (3,2) 1
+ (4,2) 1
+ (2,3) 1
+ (4,3) 1
+ (1,4) 1
+ (2,4) 1
+ (3,4) 1
+ (4,4) 1
+
+ Name Size Bytes Class Attributes
+
+ ans 4x4 121 logical sparse
+ c 1x4 8 char
+ s 4x4 16 logical
+ x 4x4 128 double
+
+test3 passed
+=================================================================
+test4: test cholmod2 with multiple and sparse right-hand-sides
+maxerr 2.363058e-12 2.350665e-12
+test4 passed
+=================================================================
+test5: test sparse2
+test5 passed
+=================================================================
+test6: test sparse with large matrix, both real and complex
+do_complex = 0
+
+Prob =
+
+ title: 'Light hydrocarbon recovery. OK if illconditioned,from a nonlinear solvr'
+ A: [70304x70304 double]
+ Zeros: [70304x70304 double]
+ b: [70304x1 double]
+ name: 'Mallya/lhr71'
+ id: 750
+ date: '1994'
+ author: 'J. Mallya'
+ ed: 'T. Davis'
+ kind: 'chemical process simulation problem'
+
+find time 0.0573
+dtri time: cholmod2 0.154045 matlab 0.143959
+dtri time: cholmod2 0.155702 matlab 0.144404 (jumbled)
+dtri time: cholmod2 0.740039 matlab 3.960841 (duplicates)
+length 2988012 nz 1494006
+
+err =
+
+ 0
+
+dtri time: cholmod2 1.054730 matlab 3.971992 (upper)
+
+err =
+
+ 0
+
+dtri time: cholmod2 1.170586 matlab 3.867817 (lower)
+dtri time: cholmod2 0.564294 matlab 3.392247 (sorted, dupl)
+do_complex = 1
+
+Prob =
+
+ title: 'Light hydrocarbon recovery. OK if illconditioned,from a nonlinear solvr'
+ A: [70304x70304 double]
+ Zeros: [70304x70304 double]
+ b: [70304x1 double]
+ name: 'Mallya/lhr71'
+ id: 750
+ date: '1994'
+ author: 'J. Mallya'
+ ed: 'T. Davis'
+ kind: 'chemical process simulation problem'
+
+find time 0.0776
+dtri time: cholmod2 0.205535 matlab 0.171580
+dtri time: cholmod2 0.396889 matlab 0.269580 (jumbled)
+dtri time: cholmod2 1.634356 matlab 4.170549 (duplicates)
+length 2988012 nz 1494006
+
+err =
+
+ 0
+
+dtri time: cholmod2 1.754138 matlab 4.164494 (upper)
+
+err =
+
+ 0
+
+dtri time: cholmod2 1.633999 matlab 4.168737 (lower)
+dtri time: cholmod2 0.635309 matlab 3.554928 (sorted, dupl)
+test6 passed
+=================================================================
+test7: test sparse2
+
+Prob =
+
+ title: 'Light hydrocarbon recovery. OK if illconditioned,from a nonlinear solvr'
+ A: [70304x70304 double]
+ Zeros: [70304x70304 double]
+ b: [70304x1 double]
+ name: 'Mallya/lhr71'
+ id: 750
+ date: '1994'
+ author: 'J. Mallya'
+ ed: 'T. Davis'
+ kind: 'chemical process simulation problem'
+
+find time 0.0574
+tot: 0.154660
+tot: 0.156477 again
+tot: 0.153834 (i,j,x)
+tot: 0.156731 (jumbled)
+tot 0.634492 (duplicates)
+test7 passed
+=================================================================
+test8: factorize a large range of sparse matrices
+test matrices sorted by dimension:
+1440: Oberwolfach LFAT5 14 1
+1438: Oberwolfach LF10 18 1
+ 97: HB can_24 24 0
+1177: HB lap_25 25 0
+ 436: FIDAP ex5 27 1
+ 13: HB bcspwr01 39 0
+ 23: HB bcsstk01 48 1
+ 872: Pothen mesh1e1 48 1
+ 873: Pothen mesh1em1 48 1
+ 874: Pothen mesh1em6 48 1
+ 14: HB bcspwr02 49 0
+ 129: HB dwt_59 59 0
+ 102: HB can_61 61 0
+ 103: HB can_62 62 0
+ 24: HB bcsstk02 66 1
+ 132: HB dwt_66 66 0
+ 883: Pothen sphere2 66 0
+ 133: HB dwt_72 72 0
+ 106: HB can_73 73 0
+ 11: HB ash85 85 0
+ 136: HB dwt_87 87 0
+ 108: HB can_96 96 0
+ 220: HB nos4 100 1
+ 25: HB bcsstk03 112 1
+ 15: HB bcspwr03 118 0
+1506: Pajek Journals 124 1
+ 26: HB bcsstk04 132 1
+ 44: HB bcsstk22 138 1
+ 93: HB can_144 144 0
+ 206: HB lund_a 147 1
+ 207: HB lund_b 147 1
+ 27: HB bcsstk05 153 1
+ 94: HB can_161 161 0
+ 113: HB dwt_162 162 0
+ 95: HB can_187 187 0
+ 114: HB dwt_193 193 0
+ 115: HB dwt_198 198 0
+ 116: HB dwt_209 209 0
+ 117: HB dwt_221 221 0
+ 96: HB can_229 229 0
+ 118: HB dwt_234 234 0
+ 217: HB nos1 237 1
+ 119: HB dwt_245 245 0
+ 98: HB can_256 256 0
+ 884: Pothen sphere3 258 0
+ 202: HB lshp_265 265 0
+ 99: HB can_268 268 0
+ 16: HB bcspwr04 274 0
+ 877: Pothen mesh3e1 289 1
+ 878: Pothen mesh3em5 289 1
+
+================== Problem: Oberwolfach/LFAT5 n: 14 nnz: 46
+title: Oberwolfach: linear 1D beam
+
+symbfact time: MATLAB 0.0133 CHOLMOD 0.0005 speedup 27.72
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.8
+time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.8
+
+metis/amd time: 1.5023 nnz(L): 1.0000
+
+================== Problem: Oberwolfach/LF10 n: 18 nnz: 82
+title: Oberwolfach: linear 1D beam
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.64
+time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.4
+time: metis 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.4
+
+metis/amd time: 4.7692 nnz(L): 1.2414
+
+================== Problem: HB/can_24 n: 24 nnz: 160
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.66
+time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 5.5
+time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 5.8
+
+metis/amd time: 5.4865 nnz(L): 1.0417
+
+================== Problem: HB/lap_25 n: 25 nnz: 169
+title: FINITE ELEMENT PROBLEM. LAPLACIAN ON A 5 BY 5 GRID.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.86
+time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.3
+time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 5.7
+
+metis/amd time: 4.8421 nnz(L): 0.9493
+
+================== Problem: FIDAP/ex5 n: 27 nnz: 279
+title: TEST MATRIX FROM FIDAP: EX5.MAT
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.73
+time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.4
+time: metis 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.4
+
+metis/amd time: 3.0526 nnz(L): 1.0000
+
+================== Problem: HB/bcspwr01 n: 39 nnz: 131
+title: SYMMETRIC STRUCTURE (STANDARD TEST POWER SYSTEM - NEW ENGLAND)
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.65
+time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.8
+time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.0
+
+metis/amd time: 3.8750 nnz(L): 1.0385
+
+================== Problem: HB/bcsstk01 n: 48 nnz: 400
+title: SYMMETRIC STIFFNESS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.84
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.3
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.0
+
+metis/amd time: 6.5909 nnz(L): 0.9898
+
+================== Problem: Pothen/mesh1e1 n: 48 nnz: 306
+title: mesh1e1, with coordinates. From NASA, collected by Alex Pothen
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.65
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.0
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.3
+
+metis/amd time: 5.4697 nnz(L): 1.0357
+
+================== Problem: Pothen/mesh1em1 n: 48 nnz: 306
+title: mesh1em1, with coordinates. From NASA, collected by Alex Pothen
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.53
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.0
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.3
+
+metis/amd time: 5.9667 nnz(L): 1.0357
+
+================== Problem: Pothen/mesh1em6 n: 48 nnz: 306
+title: mesh1em6, with coordinates. From NASA, collected by Alex Pothen
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.56
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.0
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 8.3
+
+metis/amd time: 5.8361 nnz(L): 1.0357
+
+================== Problem: HB/bcspwr02 n: 49 nnz: 167
+title: SYMMETRIC STRUCTURE OF A SMALL TEST POWER SYSTEM
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.59
+time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.8
+time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.2
+
+metis/amd time: 5.7907 nnz(L): 1.0775
+
+================== Problem: HB/dwt_59 n: 59 nnz: 267
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.59
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.5
+time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.7
+
+metis/amd time: 3.8286 nnz(L): 1.0492
+
+================== Problem: HB/can_61 n: 61 nnz: 557
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.83
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.2
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.0
+
+metis/amd time: 6.6721 nnz(L): 1.0997
+
+================== Problem: HB/can_62 n: 62 nnz: 218
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.57
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.2
+time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.5
+
+metis/amd time: 5.4118 nnz(L): 1.0870
+
+================== Problem: HB/bcsstk02 n: 66 nnz: 4356
+title: SYMMETRIC STIFFNESS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED
+
+symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 1.89
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 44.3
+time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 44.3
+
+metis/amd time: 2.6044 nnz(L): 1.0000
+
+================== Problem: HB/dwt_66 n: 66 nnz: 320
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.58
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.0
+time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.6
+
+metis/amd time: 4.5455 nnz(L): 1.4767
+
+================== Problem: Pothen/sphere2 n: 66 nnz: 450
+title: sphere2, with coordinates. From NASA, collected by Alex Pothen
+
+symbfact time: MATLAB 0.0004 CHOLMOD 0.0001 speedup 3.69
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.6
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 11.8
+
+metis/amd time: 5.2329 nnz(L): 0.9736
+
+================== Problem: HB/dwt_72 n: 72 nnz: 222
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.69
+time: amd 0.0000 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.7
+time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 2.9
+
+metis/amd time: 5.6383 nnz(L): 1.0924
+
+================== Problem: HB/can_73 n: 73 nnz: 377
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.59
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.9
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.4
+
+metis/amd time: 5.5857 nnz(L): 1.0434
+
+================== Problem: HB/ash85 n: 85 nnz: 523
+title: SYMMETRIC PATTERN OF NORMAL MATRIX OF HOLLAND SURVEY. ASHKENAZI, 1974
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.45
+time: amd 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.6
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.6
+
+metis/amd time: 1.4360 nnz(L): 1.1089
+
+================== Problem: HB/dwt_87 n: 87 nnz: 541
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.19
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 5.3
+time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.8
+
+metis/amd time: 3.2791 nnz(L): 1.1739
+
+================== Problem: HB/can_96 n: 96 nnz: 768
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.36
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 11.6
+time: metis 0.0005 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.3
+
+metis/amd time: 4.6700 nnz(L): 1.0467
+
+================== Problem: HB/nos4 n: 100 nnz: 594
+title: SYMMETRIC MATRIX OF BEAM STRUCTURE, NOVEMBER 1982.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.40
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.0
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 9.7
+
+metis/amd time: 3.6610 nnz(L): 1.2168
+
+================== Problem: HB/bcsstk03 n: 112 nnz: 640
+title: SYMMETRIC STIFFNESS MATRIX, SMALL TEST STRUCTURE
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.44
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.5
+time: metis 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.9
+
+metis/amd time: 2.9107 nnz(L): 1.3385
+
+================== Problem: HB/bcspwr03 n: 118 nnz: 476
+title: SYMMETRIC STRUCTURE OF 118 BUS IEEE STANDARD TEST CASE POWER NETWORK
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.40
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.4
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.9
+
+metis/amd time: 4.0326 nnz(L): 1.0862
+
+================== Problem: Pajek/Journals n: 124 nnz: 12068
+title: Pajek network: Slovenian journals 1999-2000
+
+symbfact time: MATLAB 0.0006 CHOLMOD 0.0004 speedup 1.71
+time: amd 0.0003 mnnz(L) 0.0 mfl 1 fl/nnz(L) 72.3
+time: metis 0.0020 mnnz(L) 0.0 mfl 0 fl/nnz(L) 70.1
+
+metis/amd time: 5.8776 nnz(L): 0.9744
+
+================== Problem: HB/bcsstk04 n: 132 nnz: 3648
+title: SYMMETRIC STIFFNESS MATRIX, OIL RIG, NOT CONDENSED (SAME MODEL AS X02)
+
+symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 2.05
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 27.5
+time: metis 0.0008 mnnz(L) 0.0 mfl 0 fl/nnz(L) 32.2
+
+metis/amd time: 3.8689 nnz(L): 1.1072
+
+================== Problem: HB/bcsstk22 n: 138 nnz: 696
+title: SYMMETRIC STIFFNESS MATRIX - TEXTILE LOOM FRAME
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.34
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.2
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.7
+
+metis/amd time: 2.3333 nnz(L): 1.0632
+
+================== Problem: HB/can_144 n: 144 nnz: 1296
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.27
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.6
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.2
+
+metis/amd time: 3.3840 nnz(L): 1.0706
+
+================== Problem: HB/lund_a n: 147 nnz: 2449
+title: SYMMETRIC MATRIX A OF LUND EIGENVALUE PROBLEM, MAY 1974
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.12
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 18.1
+time: metis 0.0005 mnnz(L) 0.0 mfl 0 fl/nnz(L) 21.2
+
+metis/amd time: 4.4622 nnz(L): 1.1475
+
+================== Problem: HB/lund_b n: 147 nnz: 2441
+title: SYMMETRIC MATRIX B OF LUND EIGENVALUE PROBLEM, MAY 1974
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.11
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 18.1
+time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 22.1
+
+metis/amd time: 4.4160 nnz(L): 1.1833
+
+================== Problem: HB/bcsstk05 n: 153 nnz: 2423
+title: SYMMETRIC STIFFNESS MATRIX, TRANSMISSION TOWER, LUMPED MASSES
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.02
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 16.8
+time: metis 0.0007 mnnz(L) 0.0 mfl 0 fl/nnz(L) 21.7
+
+metis/amd time: 4.0545 nnz(L): 1.2055
+
+================== Problem: HB/can_161 n: 161 nnz: 1377
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0003 speedup 0.93
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 19.1
+time: metis 0.0005 mnnz(L) 0.0 mfl 0 fl/nnz(L) 15.9
+
+metis/amd time: 2.7914 nnz(L): 0.8795
+
+================== Problem: HB/dwt_162 n: 162 nnz: 1182
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.17
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 9.2
+time: metis 0.0004 mnnz(L) 0.0 mfl 0 fl/nnz(L) 9.5
+
+metis/amd time: 2.6013 nnz(L): 1.0291
+
+================== Problem: HB/can_187 n: 187 nnz: 1491
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.16
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 13.8
+time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.8
+
+metis/amd time: 3.7267 nnz(L): 0.9683
+
+================== Problem: HB/dwt_193 n: 193 nnz: 3493
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 2.01
+time: amd 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 28.3
+time: metis 0.0011 mnnz(L) 0.0 mfl 0 fl/nnz(L) 29.6
+
+metis/amd time: 4.1051 nnz(L): 1.0422
+
+================== Problem: HB/dwt_198 n: 198 nnz: 1392
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.11
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.4
+time: metis 0.0005 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.1
+
+metis/amd time: 2.9815 nnz(L): 0.9694
+
+================== Problem: HB/dwt_209 n: 209 nnz: 1743
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.09
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 11.0
+time: metis 0.0008 mnnz(L) 0.0 mfl 0 fl/nnz(L) 13.6
+
+metis/amd time: 3.5598 nnz(L): 1.1378
+
+================== Problem: HB/dwt_221 n: 221 nnz: 1629
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.11
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 9.1
+time: metis 0.0007 mnnz(L) 0.0 mfl 0 fl/nnz(L) 10.7
+
+metis/amd time: 2.7893 nnz(L): 1.1089
+
+================== Problem: HB/can_229 n: 229 nnz: 1777
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.08
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 17.2
+time: metis 0.0008 mnnz(L) 0.0 mfl 0 fl/nnz(L) 18.8
+
+metis/amd time: 3.7621 nnz(L): 1.0619
+
+================== Problem: HB/dwt_234 n: 234 nnz: 834
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.26
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.5
+time: metis 0.0005 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.9
+
+metis/amd time: 3.5515 nnz(L): 1.0641
+
+================== Problem: HB/nos1 n: 237 nnz: 1017
+title: SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON BEAM.
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0001 speedup 2.22
+time: amd 0.0001 mnnz(L) 0.0 mfl 0 fl/nnz(L) 3.2
+time: metis 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 4.4
+
+metis/amd time: 3.7444 nnz(L): 1.3537
+
+================== Problem: HB/dwt_245 n: 245 nnz: 1461
+title: SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.14
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.3
+time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 9.0
+
+metis/amd time: 2.7129 nnz(L): 1.1176
+
+================== Problem: HB/can_256 n: 256 nnz: 2916
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 1.94
+time: amd 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 17.7
+time: metis 0.0008 mnnz(L) 0.0 mfl 0 fl/nnz(L) 20.2
+
+metis/amd time: 2.9789 nnz(L): 1.0937
+
+================== Problem: Pothen/sphere3 n: 258 nnz: 1794
+title: sphere3, with coordinates. From NASA, collected by Alex Pothen
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 1.97
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 24.5
+time: metis 0.0007 mnnz(L) 0.0 mfl 0 fl/nnz(L) 21.5
+
+metis/amd time: 2.8970 nnz(L): 0.9353
+
+================== Problem: HB/lshp_265 n: 265 nnz: 1753
+title: SYMMETRIC MATRIX FROM ALAN GEORGE'S L-SHAPE PROBLEMS, 1978.
+
+symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 2.02
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 14.4
+time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 17.5
+
+metis/amd time: 2.8216 nnz(L): 1.1213
+
+================== Problem: HB/can_268 n: 268 nnz: 3082
+title: SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.
+
+symbfact time: MATLAB 0.0004 CHOLMOD 0.0002 speedup 1.96
+time: amd 0.0003 mnnz(L) 0.0 mfl 0 fl/nnz(L) 18.1
+time: metis 0.0009 mnnz(L) 0.0 mfl 0 fl/nnz(L) 21.3
+
+metis/amd time: 3.2102 nnz(L): 1.0960
+
+================== Problem: HB/bcspwr04 n: 274 nnz: 1612
+title: SYMMETRIC STRUCTURE EQUIVALENCED REPRESENTATION OF U.S. POWER NETWORK
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 1.99
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 6.2
+time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 7.1
+
+metis/amd time: 3.2887 nnz(L): 1.0819
+
+================== Problem: Pothen/mesh3e1 n: 289 nnz: 1377
+title: mesh3e1, with coordinates. From NASA, collected by Alex Pothen
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 2.11
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 11.3
+time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.7
+
+metis/amd time: 2.3906 nnz(L): 1.0908
+
+================== Problem: Pothen/mesh3em5 n: 289 nnz: 1377
+title: mesh3em5, with coordinates. From NASA, collected by Alex Pothen
+
+symbfact time: MATLAB 0.0003 CHOLMOD 0.0002 speedup 1.71
+time: amd 0.0002 mnnz(L) 0.0 mfl 0 fl/nnz(L) 11.3
+time: metis 0.0006 mnnz(L) 0.0 mfl 0 fl/nnz(L) 12.7
+
+metis/amd time: 2.4410 nnz(L): 1.0908
+test8 passed
+=================================================================
+test9: test metis, etree, bisect, nesdis
+
+Prob =
+
+ title: 'S STIFFNESS MATRIX - MODULE OF AN OFFSHORE PLATFORM'
+ A: [3948x3948 double]
+ name: 'HB/bcsstk15'
+ id: 37
+ date: '1985'
+ author: 'M. Will'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+
+metis:
+Elapsed time is 0.100277 seconds.
+Elapsed time is 0.100283 seconds.
+Elapsed time is 0.101989 seconds.
+Elapsed time is 0.113528 seconds.
+Elapsed time is 0.115154 seconds.
+
+metis(A):
+Elapsed time is 0.058451 seconds.
+
+lnz0 =
+
+ 492391
+
+
+amd:
+Elapsed time is 0.009234 seconds.
+
+lnz =
+
+ 614590
+
+
+bisect:
+Elapsed time is 0.040865 seconds.
+Elapsed time is 0.039559 seconds.
+Elapsed time is 0.040628 seconds.
+Elapsed time is 0.061155 seconds.
+Elapsed time is 0.063285 seconds.
+
+nested dissection:
+Elapsed time is 0.137077 seconds.
+Elapsed time is 0.135862 seconds.
+Elapsed time is 0.136597 seconds.
+Elapsed time is 0.174602 seconds.
+Elapsed time is 0.175804 seconds.
+
+nested_dissection(A):
+Elapsed time is 0.078392 seconds.
+
+lnz1 =
+
+ 485679
+
+test9 passed
+=================================================================
+test10: test cholmod2's backslash
+test matrices sorted by dimension:
+1440: Oberwolfach LFAT5 14 1
+1438: Oberwolfach LF10 18 1
+ 436: FIDAP ex5 27 1
+ 23: HB bcsstk01 48 1
+ 872: Pothen mesh1e1 48 1
+ 873: Pothen mesh1em1 48 1
+ 874: Pothen mesh1em6 48 1
+ 24: HB bcsstk02 66 1
+ 57: HB bcsstm02 66 1
+ 220: HB nos4 100 1
+ 25: HB bcsstk03 112 1
+1506: Pajek Journals 124 1
+ 26: HB bcsstk04 132 1
+ 44: HB bcsstk22 138 1
+ 72: HB bcsstm22 138 1
+ 206: HB lund_a 147 1
+ 207: HB lund_b 147 1
+ 27: HB bcsstk05 153 1
+ 60: HB bcsstm05 153 1
+ 217: HB nos1 237 1
+ 877: Pothen mesh3e1 289 1
+ 878: Pothen mesh3em5 289 1
+ 875: Pothen mesh2e1 306 1
+ 876: Pothen mesh2em5 306 1
+ 229: HB plat362 362 1
+ 315: Bai mhdb416 416 1
+ 28: HB bcsstk06 420 1
+ 29: HB bcsstk07 420 1
+ 61: HB bcsstm06 420 1
+ 62: HB bcsstm07 420 1
+ 221: HB nos5 468 1
+ 42: HB bcsstk20 485 1
+ 70: HB bcsstm20 485 1
+ 2: HB 494_bus 494 1
+ 339: Boeing bcsstk34 588 1
+ 3: HB 662_bus 662 1
+ 222: HB nos6 675 1
+ 4: HB 685_bus 685 1
+ 357: Boeing msc00726 726 1
+ 223: HB nos7 729 1
+ 41: HB bcsstk19 817 1
+ 69: HB bcsstm19 817 1
+ 159: HB gr_30_30 900 1
+ 218: HB nos2 957 1
+ 219: HB nos3 960 1
+ 358: Boeing msc01050 1050 1
+ 30: HB bcsstk08 1074 1
+ 63: HB bcsstm08 1074 1
+ 31: HB bcsstk09 1083 1
+ 64: HB bcsstm09 1083 1
+
+nn =
+
+ 1440
+
+
+Prob =
+
+ name: 'Oberwolfach/LFAT5'
+ title: 'Oberwolfach: linear 1D beam'
+ A: [14x14 double]
+ id: 1440
+ notes: 'Primary matrix in this model reduction problem is the Oberwolfach K matrix'
+ aux: [1x1 struct]
+ date: '2004'
+ author: 'J. Lienemann, A. Greiner, J. Korvink'
+ ed: 'E. Rudnyi'
+ kind: 'model reduction problem'
+
+A: [n 14 real 1] B: [sp:0 nrhs 1 real 1] [e1: 4e-14 : -0.6] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 14 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-14 : -1.2] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 14 real 1] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 14 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 14 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : -0.3] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 14 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 14 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-14 : 0.5] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 14 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 14 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 14 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 14 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 14 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 14 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 14 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 14 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 14 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-18 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 14 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-16 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 14 real 0] B: [sp:1 nrhs 9 real 1] [e1: 7e-16 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 14 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 14 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 2.4]
+
+nn =
+
+ 1438
+
+
+Prob =
+
+ name: 'Oberwolfach/LF10'
+ title: 'Oberwolfach: linear 1D beam'
+ A: [18x18 double]
+ id: 1438
+ notes: 'Primary matrix in this model reduction problem is the Oberwolfach K matrix'
+ aux: [1x1 struct]
+ date: '2004'
+ author: 'J. Lienemann, A. Greiner, J. Korvink'
+ ed: 'E. Rudnyi'
+ kind: 'model reduction problem'
+
+A: [n 18 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-13 : -2.6] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-12 : -1.0] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-12 : -1.3] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-12 : -0.6] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-12 : -1.2] [t1: 0.00 t2 0.00 : 0.7]
+A: [n 18 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-12 : -0.7] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-12 : -0.7] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-12 : 0.1] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-12 : -1.3] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 1] B: [sp:1 nrhs 9 real 0] [e1: 5e-12 : -0.8] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 0] B: [sp:0 nrhs 1 real 1] [e1: 9e-16 : -0.2] [t1: 0.00 t2 0.00 : 0.6]
+A: [n 18 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-15 : -0.5] [t1: 0.00 t2 0.00 : 0.7]
+A: [n 18 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -0.3] [t1: 0.00 t2 0.00 : 0.6]
+A: [n 18 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-15 : 0.1] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 0] B: [sp:0 nrhs 9 real 0] [e1: 3e-15 : -0.2] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 18 real 0] B: [sp:1 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 0] B: [sp:1 nrhs 4 real 1] [e1: 6e-16 : 0.3] [t1: 0.00 t2 0.00 : 0.6]
+A: [n 18 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-16 : 0.1] [t1: 0.00 t2 0.00 : 0.6]
+A: [n 18 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-16 : 0.8] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 18 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-15 : 0.1] [t1: 0.00 t2 0.00 : 0.8]
+
+nn =
+
+ 436
+
+
+Prob =
+
+ title: ' TEST MATRIX FROM FIDAP: EX5.MAT'
+ A: [27x27 double]
+ name: 'FIDAP/ex5'
+ id: 436
+ date: '1994'
+ author: 'A. Baggag, Y. Saad'
+ ed: 'A. Baggag, Y. Saad'
+ kind: 'computational fluid dynamics problem'
+
+A: [n 27 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 27 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-08 : -0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 27 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-08 : 0.3] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 1] B: [sp:0 nrhs 1 real 0] [e1: 5e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 1] B: [sp:0 nrhs 9 real 0] [e1: 5e-08 : -0.0] [t1: 0.00 t2 0.00 : 0.6]
+A: [n 27 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-09 : 0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-09 : -0.7] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 27 real 1] B: [sp:1 nrhs 9 real 1] [e1: 7e-09 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 27 real 1] B: [sp:1 nrhs 9 real 0] [e1: 8e-09 : -0.1] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 27 real 0] B: [sp:0 nrhs 1 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 27 real 0] B: [sp:0 nrhs 1 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 0] B: [sp:0 nrhs 9 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 27 real 0] B: [sp:1 nrhs 1 real 0] [e1: 6e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 27 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 23
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM'
+ A: [48x48 double]
+ name: 'HB/bcsstk01'
+ id: 23
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 48 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 48 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-12 : 0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 0.7]
+A: [n 48 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 48 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 1 real 0] [e1: 8e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 48 real 1] B: [sp:1 nrhs 9 real 0] [e1: 8e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 4 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:0 nrhs 9 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 1 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 9 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 48 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 48 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 48 real 0] B: [sp:1 nrhs 9 real 0] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 872
+
+
+Prob =
+
+ A: [48x48 double]
+ title: 'mesh1e1, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/mesh1e1'
+ id: 872
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+A: [n 48 real 1] B: [sp:0 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 1] B: [sp:0 nrhs 1 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:0 nrhs 9 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 9 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 48 real 0] B: [sp:0 nrhs 4 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 9 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 1 real 0] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 9 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 1 real 1] [e1: 7e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 48 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+
+nn =
+
+ 873
+
+
+Prob =
+
+ A: [48x48 double]
+ title: 'mesh1em1, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/mesh1em1'
+ id: 873
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+A: [n 48 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:0 nrhs 4 real 1] [e1: 7e-15 : 0.1] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 1] B: [sp:0 nrhs 9 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 1] B: [sp:0 nrhs 1 real 0] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 48 real 1] B: [sp:1 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 4 real 1] [e1: 4e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 1 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 48 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:0 nrhs 4 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:0 nrhs 9 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 1 real 0] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 9 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+
+nn =
+
+ 874
+
+
+Prob =
+
+ A: [48x48 double]
+ title: 'mesh1em6, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/mesh1em6'
+ id: 874
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+A: [n 48 real 1] B: [sp:0 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 48 real 1] B: [sp:0 nrhs 1 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:0 nrhs 9 real 0] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 48 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:0 nrhs 4 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 9 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 1 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:0 nrhs 9 real 0] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 48 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 48 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 24
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED'
+ A: [66x66 double]
+ name: 'HB/bcsstk02'
+ id: 24
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 66 real 1] B: [sp:0 nrhs 1 real 1] [e1: 4e-12 : -0.3] [t1: 0.00 t2 0.00 : 0.6]
+A: [n 66 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-12 : -0.2] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 66 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-12 : -0.1] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 66 real 1] B: [sp:0 nrhs 1 real 0] [e1: 7e-12 : -0.1] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 66 real 1] B: [sp:0 nrhs 9 real 0] [e1: 7e-12 : -0.1] [t1: 0.00 t2 0.00 : 0.7]
+A: [n 66 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-13 : 0.2] [t1: 0.00 t2 0.00 : 0.6]
+A: [n 66 real 1] B: [sp:1 nrhs 4 real 1] [e1: 7e-13 : -0.1] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 66 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-12 : -0.3] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 66 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-12 : -0.0] [t1: 0.00 t2 0.00 : 0.6]
+A: [n 66 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-12 : -0.2] [t1: 0.00 t2 0.00 : 0.6]
+A: [n 66 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.3] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 66 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.2] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 66 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 66 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-14 : 0.2] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 66 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 66 real 0] B: [sp:1 nrhs 1 real 1] [e1: 9e-16 : -0.1] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 66 real 0] B: [sp:1 nrhs 4 real 1] [e1: 3e-15 : 0.2] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 66 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-15 : 0.2] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 66 real 0] B: [sp:1 nrhs 1 real 0] [e1: 4e-15 : 0.1] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 66 real 0] B: [sp:1 nrhs 9 real 0] [e1: 7e-15 : 0.2] [t1: 0.00 t2 0.00 : 0.8]
+
+nn =
+
+ 57
+
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED'
+ A: [66x66 double]
+ name: 'HB/bcsstm02'
+ id: 57
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 66 real 1] B: [sp:0 nrhs 1 real 1] [e1: 6e-16 : -2.2] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-15 : -1.8] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 66 real 1] B: [sp:0 nrhs 9 real 1] [e1: 6e-16 : -2.5] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-15 : -2.5] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 66 real 1] B: [sp:1 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-17 : -5.7] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 66 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-16 : -1.7] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 66 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-16 : -2.2] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-16 : -2.0] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:0 nrhs 1 real 1] [e1: 7e-16 : -2.1] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:0 nrhs 4 real 1] [e1: 7e-16 : -2.4] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:0 nrhs 9 real 1] [e1: 8e-16 : -2.3] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 66 real 1] B: [sp:0 nrhs 1 real 0] [e1: 6e-16 : -3.3] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-15 : -2.4] [t1: 0.00 t2 0.00 : 0.4]
+A: [n 66 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-16 : -2.1] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-16 : -2.3] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-16 : -2.1] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-16 : -1.1] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 66 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-16 : -1.9] [t1: 0.00 t2 0.00 : 0.3]
+
+nn =
+
+ 220
+
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX OF BEAM STRUCTURE, NOVEMBER 1982.'
+ A: [100x100 double]
+ name: 'HB/nos4'
+ id: 220
+ date: '1982'
+ author: 'H. Simon'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 100 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-12 : 0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 100 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 100 real 1] B: [sp:1 nrhs 1 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-14 : -0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-13 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 0] B: [sp:0 nrhs 1 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 100 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 100 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 100 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 100 real 0] B: [sp:1 nrhs 1 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 0] B: [sp:1 nrhs 4 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 100 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 100 real 0] B: [sp:1 nrhs 9 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 25
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX, SMALL TEST STRUCTURE'
+ A: [112x112 double]
+ name: 'HB/bcsstk03'
+ id: 25
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 112 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 112 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-11 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 112 real 1] B: [sp:0 nrhs 9 real 0] [e1: 6e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 1] B: [sp:1 nrhs 1 real 1] [e1: 9e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 1] B: [sp:1 nrhs 4 real 1] [e1: 9e-12 : 0.1] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 112 real 1] B: [sp:1 nrhs 9 real 1] [e1: 8e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-12 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 0] B: [sp:0 nrhs 1 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 112 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 112 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 112 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 112 real 0] B: [sp:1 nrhs 4 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 112 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 0] B: [sp:1 nrhs 1 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 112 real 0] B: [sp:1 nrhs 9 real 0] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+
+nn =
+
+ 1506
+
+
+Prob =
+
+ name: 'Pajek/Journals'
+ title: 'Pajek network: Slovenian journals 1999-2000'
+ A: [124x124 double]
+ id: 1506
+ kind: 'undirected weighted graph'
+ notes: [14x78 char]
+ aux: [1x1 struct]
+ date: '2000'
+ author: 'CATI Center Ljubljana'
+ ed: 'V. Batagelj'
+
+A: [n 124 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-14 : -0.2] [t1: 0.00 t2 0.00 : 0.7]
+A: [n 124 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-14 : -0.2] [t1: 0.10 t2 0.00 : 57.8]
+A: [n 124 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-14 : -0.2] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 124 real 1] B: [sp:0 nrhs 1 real 0] [e1: 8e-14 : 0.2] [t1: 0.00 t2 0.00 : 0.7]
+A: [n 124 real 1] B: [sp:0 nrhs 9 real 0] [e1: 8e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 124 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.5] [t1: 0.00 t2 0.00 : 0.7]
+A: [n 124 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.7]
+A: [n 124 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.6]
+A: [n 124 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.7]
+A: [n 124 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.7]
+A: [n 124 real 0] B: [sp:0 nrhs 1 real 1] [e1: 3e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 124 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : 0.1] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 124 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 124 real 0] B: [sp:0 nrhs 1 real 0] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 124 real 0] B: [sp:0 nrhs 9 real 0] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 124 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-15 : -0.4] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 124 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.3] [t1: 0.00 t2 0.10 : 0.0]
+A: [n 124 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : -0.2] [t1: 0.00 t2 0.01 : 0.7]
+A: [n 124 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : -0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 124 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.2] [t1: 0.00 t2 0.01 : 0.7]
+
+nn =
+
+ 26
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX, OIL RIG, NOT CONDENSED (SAME MODEL AS X02)'
+ A: [132x132 double]
+ name: 'HB/bcsstk04'
+ id: 26
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 132 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 132 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-11 : -0.1] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 132 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-11 : 0.4] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 132 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 132 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 132 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 132 real 1] B: [sp:1 nrhs 4 real 1] [e1: 4e-12 : 0.1] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 132 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-12 : -0.1] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 132 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 132 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-12 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 132 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 132 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 132 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 132 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 132 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 132 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 132 real 0] B: [sp:1 nrhs 4 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 132 real 0] B: [sp:1 nrhs 9 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 132 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 132 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 44
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX - TEXTILE LOOM FRAME'
+ A: [138x138 double]
+ name: 'HB/bcsstk22'
+ id: 44
+ date: '1984'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 138 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.3]
+A: [n 138 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-11 : -0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-11 : 0.2] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 1] B: [sp:1 nrhs 1 real 0] [e1: 8e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 138 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 138 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 138 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-16 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 0] B: [sp:1 nrhs 4 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 0] B: [sp:1 nrhs 1 real 0] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 138 real 0] B: [sp:1 nrhs 9 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 72
+
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX - TEXTILE LOOM FRAME'
+ A: [138x138 double]
+ name: 'HB/bcsstm22'
+ id: 72
+ date: '1984'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 138 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-15 : -1.8] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 138 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-15 : -1.9] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 138 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 138 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 138 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-15 : -1.9] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 138 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-16 : -1.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 138 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-16 : -1.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 138 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-16 : -1.9] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 138 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-16 : -3.7] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 138 real 1] B: [sp:1 nrhs 9 real 0] [e1: 9e-16 : -1.7] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 138 real 1] B: [sp:0 nrhs 1 real 1] [e1: 7e-16 : -3.5] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 138 real 1] B: [sp:0 nrhs 4 real 1] [e1: 7e-16 : -3.5] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 138 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-15 : -3.0] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 138 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-15 : -3.7] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 138 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-15 : -2.9] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 138 real 1] B: [sp:1 nrhs 1 real 1] [e1: 7e-16 : -1.4] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 138 real 1] B: [sp:1 nrhs 4 real 1] [e1: 7e-16 : -1.4] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 138 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-16 : -2.5] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 138 real 1] B: [sp:1 nrhs 1 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 138 real 1] B: [sp:1 nrhs 9 real 0] [e1: 5e-16 : -2.3] [t1: 0.00 t2 0.00 : 0.1]
+
+nn =
+
+ 206
+
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX A OF LUND EIGENVALUE PROBLEM, MAY 1974'
+ A: [147x147 double]
+ name: 'HB/lund_a'
+ id: 206
+ date: '1974'
+ author: 'T. Johansson'
+ ed: 'A. Curtis, I. Duff, J. Reid'
+ kind: 'structural problem'
+
+A: [n 147 real 1] B: [sp:0 nrhs 1 real 1] [e1: 3e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-10 : -0.1] [t1: 0.00 t2 0.00 : 1.4]
+A: [n 147 real 1] B: [sp:0 nrhs 9 real 1] [e1: 3e-10 : 0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 1] B: [sp:0 nrhs 9 real 0] [e1: 5e-10 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 1] B: [sp:1 nrhs 4 real 1] [e1: 5e-11 : 0.1] [t1: 0.00 t2 0.00 : 1.3]
+A: [n 147 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-11 : 0.2] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 147 real 0] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 147 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 147 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 0] B: [sp:1 nrhs 4 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 0] B: [sp:1 nrhs 9 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 207
+
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX B OF LUND EIGENVALUE PROBLEM, MAY 1974'
+ A: [147x147 double]
+ name: 'HB/lund_b'
+ id: 207
+ date: '1974'
+ author: 'T. Johansson'
+ ed: 'A. Curtis, I. Duff, J. Reid'
+ kind: 'structural problem'
+
+A: [n 147 real 1] B: [sp:0 nrhs 1 real 1] [e1: 8e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 147 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-12 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 1] B: [sp:1 nrhs 9 real 0] [e1: 5e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 147 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 147 real 0] B: [sp:1 nrhs 1 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 0] B: [sp:1 nrhs 4 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 147 real 0] B: [sp:1 nrhs 9 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 147 real 0] B: [sp:1 nrhs 1 real 0] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 147 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 27
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX, TRANSMISSION TOWER, LUMPED MASSES'
+ A: [153x153 double]
+ name: 'HB/bcsstk05'
+ id: 27
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 153 real 1] B: [sp:0 nrhs 1 real 1] [e1: 9e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 153 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 153 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 153 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 153 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 153 real 1] B: [sp:1 nrhs 1 real 1] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 153 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-12 : 0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 153 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 153 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 153 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 153 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 153 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 153 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 153 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 153 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 153 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 153 real 0] B: [sp:1 nrhs 4 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 153 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 153 real 0] B: [sp:1 nrhs 1 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 153 real 0] B: [sp:1 nrhs 9 real 0] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 60
+
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX, TRANSMISSION TOWER, LUMPED MASSES'
+ A: [153x153 double]
+ name: 'HB/bcsstm05'
+ id: 60
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 153 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-15 : -2.8] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 153 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-15 : -2.5] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 153 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 153 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-15 : -2.3] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 153 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-15 : -2.2] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 153 real 1] B: [sp:1 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 153 real 1] B: [sp:1 nrhs 4 real 1] [e1: 4e-16 : -2.3] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 153 real 1] B: [sp:1 nrhs 9 real 1] [e1: 9e-16 : -1.6] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 153 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-17 : -8.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 153 real 1] B: [sp:1 nrhs 9 real 0] [e1: 5e-16 : -2.6] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 153 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 153 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 153 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -2.6] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 153 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 153 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 153 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-16 : -3.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 153 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-16 : -2.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 153 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-16 : -3.9] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 153 real 1] B: [sp:1 nrhs 1 real 0] [e1: 5e-16 : -2.2] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 153 real 1] B: [sp:1 nrhs 9 real 0] [e1: 9e-16 : -1.6] [t1: 0.00 t2 0.00 : 0.1]
+
+nn =
+
+ 217
+
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON BEAM.'
+ A: [237x237 double]
+ name: 'HB/nos1'
+ id: 217
+ date: '1982'
+ author: 'H. Simon'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 237 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 1] B: [sp:0 nrhs 1 real 0] [e1: 8e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 1] B: [sp:0 nrhs 9 real 0] [e1: 8e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 237 real 1] B: [sp:1 nrhs 4 real 1] [e1: 9e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 1] B: [sp:1 nrhs 9 real 1] [e1: 7e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 237 real 1] B: [sp:1 nrhs 1 real 0] [e1: 7e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 237 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-10 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 237 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 237 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 0] B: [sp:0 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 237 real 0] B: [sp:1 nrhs 4 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 237 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 237 real 0] B: [sp:1 nrhs 1 real 0] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 237 real 0] B: [sp:1 nrhs 9 real 0] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 877
+
+
+Prob =
+
+ A: [289x289 double]
+ title: 'mesh3e1, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/mesh3e1'
+ Zeros: [289x289 double]
+ id: 877
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+A: [n 289 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 289 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 1] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 289 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:0 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:1 nrhs 1 real 1] [e1: 3e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:1 nrhs 4 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:1 nrhs 9 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.10 t2 0.00 : 96.1]
+
+nn =
+
+ 878
+
+
+Prob =
+
+ A: [289x289 double]
+ title: 'mesh3em5, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/mesh3em5'
+ Zeros: [289x289 double]
+ id: 878
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+A: [n 289 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 1] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 1] B: [sp:1 nrhs 1 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.10 : 0.0]
+A: [n 289 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 0] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+A: [n 289 real 0] B: [sp:0 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:1 nrhs 1 real 1] [e1: 4e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 289 real 0] B: [sp:1 nrhs 4 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:1 nrhs 9 real 1] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 289 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 875
+
+
+Prob =
+
+ A: [306x306 double]
+ title: 'mesh2e1, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/mesh2e1'
+ id: 875
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+A: [n 306 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.10 : 0.0]
+A: [n 306 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-13 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-13 : -0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 1] B: [sp:1 nrhs 1 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-13 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:0 nrhs 1 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:0 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 0] B: [sp:0 nrhs 1 real 0] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:0 nrhs 9 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 0] B: [sp:1 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:1 nrhs 4 real 1] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 876
+
+
+Prob =
+
+ A: [306x306 double]
+ title: 'mesh2em5, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/mesh2em5'
+ id: 876
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+A: [n 306 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 306 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-14 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 1] B: [sp:0 nrhs 1 real 0] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 1] B: [sp:0 nrhs 9 real 0] [e1: 9e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-14 : -0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 1] B: [sp:1 nrhs 9 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:0 nrhs 1 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:0 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.5]
+A: [n 306 real 0] B: [sp:0 nrhs 1 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 0] B: [sp:0 nrhs 9 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 0] B: [sp:1 nrhs 1 real 1] [e1: 5e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:1 nrhs 4 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 306 real 0] B: [sp:1 nrhs 1 real 0] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 306 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 229
+
+
+Prob =
+
+ title: 'SPLATZMAN FINITE DIFFERENCE MODEL OF ATLANTICOCEAN'
+ A: [362x362 double]
+ name: 'HB/plat362'
+ id: 229
+ date: '1975'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: '2D/3D problem'
+
+A: [n 362 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 362 real 1] B: [sp:0 nrhs 4 real 1] [e1: 8e-05 : -0.2] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 1] B: [sp:0 nrhs 9 real 1] [e1: 8e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 1] B: [sp:0 nrhs 1 real 0] [e1: 9e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-04 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 362 real 1] B: [sp:1 nrhs 1 real 1] [e1: 4e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 362 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-04 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-04 : -0.1] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 362 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-04 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 362 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-04 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 0] B: [sp:0 nrhs 4 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 362 real 0] B: [sp:0 nrhs 9 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 362 real 0] B: [sp:0 nrhs 1 real 0] [e1: 9e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 0] B: [sp:0 nrhs 9 real 0] [e1: 9e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 362 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 362 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 315
+
+
+Prob =
+
+ title: 'MAGNETO-HYDRO-DYNAMICS ALFVEN SPECTRAL PROBLEM'
+ A: [416x416 double]
+ name: 'Bai/mhdb416'
+ id: 315
+ date: '1994'
+ author: 'A. Booten, M. Kooper, H. van der Vorst, S. Poedts, J. Goedbloed'
+ ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra'
+ kind: 'electromagnetics problem'
+
+A: [n 416 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 416 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-12 : -0.1] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 416 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-12 : -0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 416 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 416 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 416 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 416 real 1] B: [sp:1 nrhs 4 real 1] [e1: 5e-13 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 416 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 416 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 416 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 416 real 0] B: [sp:0 nrhs 1 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 416 real 0] B: [sp:0 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 416 real 0] B: [sp:0 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 416 real 0] B: [sp:0 nrhs 1 real 0] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 416 real 0] B: [sp:0 nrhs 9 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 416 real 0] B: [sp:1 nrhs 1 real 1] [e1: 6e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 416 real 0] B: [sp:1 nrhs 4 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.3]
+A: [n 416 real 0] B: [sp:1 nrhs 9 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 416 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.10 t2 0.00 : 206.5]
+A: [n 416 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+
+nn =
+
+ 28
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX, MEDIUM TEST PROBLEM, LUMPED MASSES'
+ A: [420x420 double]
+ name: 'HB/bcsstk06'
+ id: 28
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 420 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 420 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-10 : 0.1] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 420 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 1] B: [sp:1 nrhs 1 real 1] [e1: 8e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-11 : -0.1] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 9 real 1] [e1: 5e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 9 real 0] [e1: 8e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 0] B: [sp:0 nrhs 1 real 1] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 4 real 1] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 420 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.10 : 0.0]
+A: [n 420 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 420 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 0] B: [sp:1 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 29
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX, MEDIUM TEST PROBLEM, CONSISTENT MASSES'
+ A: [420x420 double]
+ name: 'HB/bcsstk07'
+ id: 29
+ kind: 'duplicate structural problem'
+ notes: 'duplicate of HB/bcsstk06'
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+
+A: [n 420 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 420 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 420 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-10 : 0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-10 : -0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 1] B: [sp:1 nrhs 1 real 1] [e1: 4e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-11 : 0.1] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 9 real 0] [e1: 8e-11 : -0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 0] B: [sp:0 nrhs 1 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 4 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.10 : 0.0]
+A: [n 420 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 420 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 420 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 420 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 61
+
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX, MEDIUM TEST PROBLEM, LUMPED MASSES'
+ A: [420x420 double]
+ name: 'HB/bcsstm06'
+ id: 61
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 420 real 1] B: [sp:0 nrhs 1 real 1] [e1: 3e-15 : -2.8] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-15 : -2.7] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 420 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-15 : -2.6] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 420 real 1] B: [sp:0 nrhs 1 real 0] [e1: 6e-15 : -2.6] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:0 nrhs 9 real 0] [e1: 6e-15 : -2.5] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 420 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-16 : -3.9] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-16 : -3.9] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:1 nrhs 9 real 1] [e1: 9e-16 : -2.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-16 : -4.4] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-15 : -2.8] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-15 : -3.9] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-15 : -3.8] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 420 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -3.7] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 420 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-15 : -3.5] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 420 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-15 : -3.3] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 420 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-16 : -4.8] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-16 : -3.7] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-16 : -4.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-16 : -4.5] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 420 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-16 : -4.0] [t1: 0.00 t2 0.00 : 0.1]
+
+nn =
+
+ 62
+
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX, MEDIUM TEST PROBLEM, CONSISTENT MASSES'
+ A: [420x420 double]
+ name: 'HB/bcsstm07'
+ id: 62
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 420 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:0 nrhs 4 real 1] [e1: 6e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:0 nrhs 9 real 1] [e1: 6e-13 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 1] B: [sp:0 nrhs 1 real 0] [e1: 7e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 420 real 1] B: [sp:0 nrhs 9 real 0] [e1: 9e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-13 : -0.1] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 420 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 420 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 1 real 1] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 4 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 420 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 420 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 420 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 420 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 221
+
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX, FE APPROXIMATION OF BUILDING.'
+ A: [468x468 double]
+ name: 'HB/nos5'
+ id: 221
+ date: '1982'
+ author: 'H. Simon'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 468 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 468 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 468 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 468 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 468 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 468 real 1] B: [sp:1 nrhs 1 real 1] [e1: 5e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 468 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 468 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.01 : 1.0]
+A: [n 468 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 468 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 468 real 0] B: [sp:0 nrhs 1 real 1] [e1: 6e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 468 real 0] B: [sp:0 nrhs 4 real 1] [e1: 9e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 468 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 468 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 468 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.1]
+A: [n 468 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 468 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 468 real 0] B: [sp:1 nrhs 9 real 1] Warning: Matrix is indefinite or singular to working precision
+ [e1: 2e-14 : NaN] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 468 real 0] B: [sp:1 nrhs 1 real 0] Warning: Matrix is singular to working precision.
+> In testsolve at 15
+ In test10 at 116
+ In cholmod_test at 112
+Warning: Matrix is indefinite or singular to working precision
+ [e1: NaN : NaN] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 468 real 0] B: [sp:1 nrhs 9 real 0] Warning: Matrix is singular to working precision.
+> In testsolve at 15
+ In test10 at 117
+ In cholmod_test at 112
+Warning: Matrix is indefinite or singular to working precision
+ [e1: NaN : NaN] [t1: 0.02 t2 0.02 : 1.0]
+
+nn =
+
+ 42
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX - FRAME WITHIN A SUSPENSION BRIDGE'
+ A: [485x485 double]
+ name: 'HB/bcsstk20'
+ id: 42
+ date: '1984'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 485 real 1] B: [sp:0 nrhs 1 real 1] [e1: 9e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-05 : 0.4] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 1] B: [sp:0 nrhs 9 real 1] [e1: 9e-06 : -0.3] [t1: 0.00 t2 0.00 : 1.3]
+A: [n 485 real 1] B: [sp:0 nrhs 1 real 0] [e1: 9e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.2]
+A: [n 485 real 1] B: [sp:1 nrhs 4 real 1] [e1: 8e-07 : 0.4] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 1] B: [sp:1 nrhs 9 real 1] [e1: 7e-07 : 0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 485 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-06 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 485 real 0] B: [sp:0 nrhs 1 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 485 real 0] B: [sp:0 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 485 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 0] B: [sp:0 nrhs 1 real 0] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 0] B: [sp:0 nrhs 9 real 0] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 0] B: [sp:1 nrhs 1 real 1] [e1: 7e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 485 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 485 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 485 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+
+nn =
+
+ 70
+
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX - FRAME WITHIN A SUSPENSION BRIDGE'
+ A: [485x485 double]
+ name: 'HB/bcsstm20'
+ id: 70
+ date: '1984'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 485 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-15 : -2.2] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:0 nrhs 4 real 1] [e1: 6e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 485 real 1] B: [sp:0 nrhs 9 real 1] [e1: 6e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 485 real 1] B: [sp:0 nrhs 1 real 0] [e1: 9e-15 : -2.2] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-14 : -1.8] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 485 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-16 : -3.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:1 nrhs 4 real 1] [e1: 8e-16 : -2.6] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:1 nrhs 9 real 1] [e1: 9e-16 : -2.3] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-16 : -7.4] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-16 : -6.3] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 485 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-16 : -6.2] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 485 real 1] B: [sp:0 nrhs 1 real 0] [e1: 6e-16 : -6.2] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:0 nrhs 9 real 0] [e1: 7e-16 : -6.2] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 485 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-16 : -5.6] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-16 : -5.6] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-17 : -8.7] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:1 nrhs 1 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 485 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-16 : -4.1] [t1: 0.00 t2 0.00 : 0.1]
+
+nn =
+
+ 2
+
+
+Prob =
+
+ title: 'S ADMITTANCE MATRIX 494 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985.'
+ A: [494x494 double]
+ name: 'HB/494_bus'
+ id: 2
+ date: '1985'
+ author: 'D. Tylavsky'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'power network problem'
+
+A: [n 494 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-09 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 1] B: [sp:1 nrhs 1 real 1] [e1: 6e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-11 : -0.1] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 494 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 494 real 1] B: [sp:1 nrhs 9 real 0] [e1: 7e-11 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 494 real 0] B: [sp:0 nrhs 1 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 0] B: [sp:0 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 0] B: [sp:0 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 0] B: [sp:0 nrhs 1 real 0] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 0] B: [sp:0 nrhs 9 real 0] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 0] B: [sp:1 nrhs 1 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 494 real 0] B: [sp:1 nrhs 4 real 1] [e1: 8e-15 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 494 real 0] B: [sp:1 nrhs 9 real 1] [e1: 9e-15 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 494 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 494 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+
+nn =
+
+ 339
+
+
+Prob =
+
+ title: 'NASTRAN BUCKLING PROBLEM STIFFNESS MATRIX'
+ A: [588x588 double]
+ name: 'Boeing/bcsstk34'
+ id: 339
+ date: '1995'
+ author: 'R. Grimes'
+ ed: 'T. Davis'
+ kind: 'structural problem'
+
+A: [n 588 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 588 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 588 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 588 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 588 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 588 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 588 real 1] B: [sp:1 nrhs 4 real 1] [e1: 4e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 588 real 1] B: [sp:1 nrhs 9 real 1] [e1: 6e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 588 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.1]
+A: [n 588 real 1] B: [sp:1 nrhs 9 real 0] [e1: 9e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 588 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 588 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 588 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 588 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 588 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 588 real 0] B: [sp:1 nrhs 1 real 1] [e1: 3e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 588 real 0] B: [sp:1 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 588 real 0] B: [sp:1 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 588 real 0] B: [sp:1 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 588 real 0] B: [sp:1 nrhs 9 real 0] [e1: 7e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+
+nn =
+
+ 3
+
+
+Prob =
+
+ title: 'S ADMITTANCE MATRIX 662 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985.'
+ A: [662x662 double]
+ name: 'HB/662_bus'
+ id: 3
+ date: '1985'
+ author: 'D. Tylavsky'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'power network problem'
+
+A: [n 662 real 1] B: [sp:0 nrhs 1 real 1] [e1: 9e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 1] B: [sp:0 nrhs 4 real 1] [e1: 9e-10 : -0.1] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 662 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-09 : -0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-09 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 662 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-09 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 662 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-11 : -0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 1] B: [sp:1 nrhs 9 real 0] [e1: 5e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 0] B: [sp:0 nrhs 1 real 1] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 0] B: [sp:0 nrhs 4 real 1] [e1: 5e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 662 real 0] B: [sp:0 nrhs 9 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 662 real 0] B: [sp:0 nrhs 1 real 0] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 0] B: [sp:0 nrhs 9 real 0] [e1: 9e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 662 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 662 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 222
+
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX, POISSON'S EQUATION IN L SHAPE, MIXED BC.'
+ A: [675x675 double]
+ name: 'HB/nos6'
+ id: 222
+ date: '1982'
+ author: 'H. Simon'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: '2D/3D problem'
+
+A: [n 675 real 1] B: [sp:0 nrhs 1 real 1] [e1: 3e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-08 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 1] B: [sp:0 nrhs 9 real 1] [e1: 3e-08 : -0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 1] B: [sp:1 nrhs 1 real 1] [e1: 9e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-09 : 0.1] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 0] B: [sp:0 nrhs 1 real 1] [e1: 7e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 0] B: [sp:0 nrhs 4 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 675 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 675 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 675 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 675 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 675 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 675 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 675 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 675 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 4
+
+
+Prob =
+
+ title: 'S ADMITTANCE MATRIX 685 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985.'
+ A: [685x685 double]
+ name: 'HB/685_bus'
+ id: 4
+ date: '1985'
+ author: 'D. Tylavsky'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'power network problem'
+
+A: [n 685 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-10 : -0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 685 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-10 : -0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 685 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-10 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 685 real 1] B: [sp:1 nrhs 9 real 1] [e1: 5e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 1] B: [sp:1 nrhs 9 real 0] [e1: 9e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 0] B: [sp:0 nrhs 1 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 0] B: [sp:0 nrhs 4 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 685 real 0] B: [sp:0 nrhs 9 real 1] [e1: 6e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 685 real 0] B: [sp:0 nrhs 1 real 0] [e1: 9e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 685 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 685 real 0] B: [sp:1 nrhs 9 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 685 real 0] B: [sp:1 nrhs 1 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 685 real 0] B: [sp:1 nrhs 9 real 0] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 357
+
+
+Prob =
+
+ title: 'SYMMETRIC TEST MATRIX FROM MSC/NASTRAN BC4F8.OUT2'
+ A: [726x726 double]
+ name: 'Boeing/msc00726'
+ id: 357
+ date: '1995'
+ author: 'R. Grimes'
+ ed: 'T. Davis'
+ kind: 'structural problem'
+
+A: [n 726 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.1]
+A: [n 726 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 726 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 726 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 726 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 726 real 1] B: [sp:1 nrhs 1 real 1] [e1: 5e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 726 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-12 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 726 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-12 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 726 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-12 : 0.0] [t1: 0.12 t2 0.02 : 5.4]
+A: [n 726 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-12 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 726 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-13 : 0.0] [t1: 0.06 t2 0.16 : 0.4]
+A: [n 726 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.17 t2 0.07 : 2.3]
+A: [n 726 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.18 t2 0.18 : 1.0]
+A: [n 726 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.16 t2 0.06 : 2.6]
+A: [n 726 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-13 : 0.0] [t1: 0.18 t2 0.18 : 1.0]
+A: [n 726 real 0] B: [sp:1 nrhs 1 real 1] [e1: 5e-14 : 0.0] [t1: 0.16 t2 0.06 : 2.6]
+A: [n 726 real 0] B: [sp:1 nrhs 4 real 1] [e1: 6e-14 : 0.0] [t1: 0.18 t2 0.17 : 1.0]
+A: [n 726 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-14 : 0.0] [t1: 0.19 t2 0.09 : 2.2]
+A: [n 726 real 0] B: [sp:1 nrhs 1 real 0] [e1: 7e-14 : 0.0] [t1: 0.06 t2 0.16 : 0.4]
+A: [n 726 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.19 t2 0.19 : 1.0]
+
+nn =
+
+ 223
+
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX, POISSON'S EQUATION IN UNIT CUBE.'
+ A: [729x729 double]
+ name: 'HB/nos7'
+ id: 223
+ date: '1982'
+ author: 'H. Simon'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: '2D/3D problem'
+
+A: [n 729 real 1] B: [sp:0 nrhs 1 real 1] [e1: 2e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 729 real 1] B: [sp:0 nrhs 4 real 1] [e1: 3e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 729 real 1] B: [sp:0 nrhs 9 real 1] [e1: 3e-06 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 729 real 1] B: [sp:0 nrhs 1 real 0] [e1: 4e-06 : 0.0] [t1: 0.00 t2 0.01 : 0.9]
+A: [n 729 real 1] B: [sp:0 nrhs 9 real 0] [e1: 4e-06 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 729 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-09 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 729 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 729 real 1] B: [sp:1 nrhs 9 real 1] [e1: 9e-08 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 729 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-07 : 0.0] [t1: 0.10 t2 0.01 : 18.0]
+A: [n 729 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-07 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 729 real 0] B: [sp:0 nrhs 1 real 1] [e1: 9e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 729 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-13 : 0.0] [t1: 0.02 t2 0.12 : 0.2]
+A: [n 729 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 729 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 729 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.13 t2 0.03 : 5.0]
+A: [n 729 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 729 real 0] B: [sp:1 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.02 t2 0.12 : 0.2]
+A: [n 729 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.04 t2 0.04 : 1.0]
+A: [n 729 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.11 t2 0.01 : 8.6]
+A: [n 729 real 0] B: [sp:1 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.04 t2 0.04 : 1.0]
+
+nn =
+
+ 41
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX - PART OF A SUSPENSION BRIDGE'
+ A: [817x817 double]
+ name: 'HB/bcsstk19'
+ id: 41
+ date: '1984'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 817 real 1] B: [sp:0 nrhs 1 real 1] [e1: 7e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 1] B: [sp:0 nrhs 4 real 1] [e1: 7e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 1] B: [sp:0 nrhs 9 real 1] [e1: 7e-06 : -0.2] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-05 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 1] B: [sp:1 nrhs 1 real 1] [e1: 4e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 1] B: [sp:1 nrhs 4 real 1] [e1: 5e-07 : -0.1] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 817 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-06 : -0.2] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 1] B: [sp:1 nrhs 1 real 0] [e1: 1e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-06 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 817 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 817 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 817 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 817 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 817 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 817 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 817 real 0] B: [sp:1 nrhs 9 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.8]
+
+nn =
+
+ 69
+
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX - PART OF A SUSPENSION BRIDGE'
+ A: [817x817 double]
+ name: 'HB/bcsstm19'
+ id: 69
+ date: '1984'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 817 real 1] B: [sp:0 nrhs 1 real 1] [e1: 8e-15 : -2.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:0 nrhs 4 real 1] [e1: 8e-15 : -2.2] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:0 nrhs 9 real 1] [e1: 9e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 817 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-14 : -2.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : -1.9] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 817 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-15 : -2.8] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-15 : -2.9] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : -2.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-15 : -1.8] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-15 : -1.9] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:0 nrhs 1 real 1] [e1: 9e-16 : -5.8] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:0 nrhs 4 real 1] [e1: 9e-16 : -5.8] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 817 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-15 : -4.9] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 817 real 1] B: [sp:0 nrhs 1 real 0] [e1: 3e-15 : -4.9] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:0 nrhs 9 real 0] [e1: 3e-15 : -5.0] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 817 real 1] B: [sp:1 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:1 nrhs 4 real 1] [e1: 2e-16 : -5.6] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-16 : -4.5] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-16 : -6.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 817 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-16 : -6.3] [t1: 0.00 t2 0.00 : 0.1]
+
+nn =
+
+ 159
+
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX FROM NINE POINT START ON A 30 X 30 GRID.'
+ A: [900x900 double]
+ name: 'HB/gr_30_30'
+ id: 159
+ date: '1983'
+ author: 'R. Grimes'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: '2D/3D problem'
+
+A: [n 900 real 1] B: [sp:0 nrhs 1 real 1] [e1: 9e-12 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 900 real 1] B: [sp:0 nrhs 4 real 1] [e1: 9e-12 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 900 real 1] B: [sp:0 nrhs 9 real 1] [e1: 9e-12 : -0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 900 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 900 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 900 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 900 real 1] B: [sp:1 nrhs 4 real 1] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 900 real 1] B: [sp:1 nrhs 9 real 1] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 900 real 1] B: [sp:1 nrhs 1 real 0] [e1: 4e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 900 real 1] B: [sp:1 nrhs 9 real 0] [e1: 6e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 900 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 900 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 900 real 0] B: [sp:0 nrhs 9 real 1] [e1: 1e-13 : 0.0] [t1: 0.01 t2 0.01 : 0.7]
+A: [n 900 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 900 real 0] B: [sp:0 nrhs 9 real 0] [e1: 2e-13 : 0.0] [t1: 0.01 t2 0.01 : 0.9]
+A: [n 900 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 900 real 0] B: [sp:1 nrhs 4 real 1] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 900 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.01 t2 0.01 : 0.9]
+A: [n 900 real 0] B: [sp:1 nrhs 1 real 0] [e1: 4e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 900 real 0] B: [sp:1 nrhs 9 real 0] [e1: 5e-14 : 0.0] [t1: 0.01 t2 0.01 : 0.9]
+
+nn =
+
+ 218
+
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON BEAM.'
+ A: [957x957 double]
+ name: 'HB/nos2'
+ id: 218
+ date: '1982'
+ author: 'H. Simon'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 957 real 1] B: [sp:0 nrhs 1 real 1] [e1: 5e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 957 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 957 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 957 real 1] B: [sp:0 nrhs 1 real 0] [e1: 7e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 957 real 1] B: [sp:0 nrhs 9 real 0] [e1: 8e-06 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 957 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 957 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 957 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 957 real 1] B: [sp:1 nrhs 1 real 0] [e1: 9e-08 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 957 real 1] B: [sp:1 nrhs 9 real 0] [e1: 6e-07 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 957 real 0] B: [sp:0 nrhs 1 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 957 real 0] B: [sp:0 nrhs 4 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.0]
+A: [n 957 real 0] B: [sp:0 nrhs 9 real 1] [e1: 8e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 957 real 0] B: [sp:0 nrhs 1 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 957 real 0] B: [sp:0 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 957 real 0] B: [sp:1 nrhs 1 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 957 real 0] B: [sp:1 nrhs 4 real 1] [e1: 1e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 957 real 0] B: [sp:1 nrhs 9 real 1] [e1: 2e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+A: [n 957 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 1.1]
+A: [n 957 real 0] B: [sp:1 nrhs 9 real 0] [e1: 3e-14 : 0.0] [t1: 0.00 t2 0.00 : 0.9]
+
+nn =
+
+ 219
+
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX, FE APPROXIMATION TO BIHARMONIC OPERATOR ON PLATE'
+ A: [960x960 double]
+ name: 'HB/nos3'
+ id: 219
+ date: '1982'
+ author: 'H. Simon'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 960 real 1] B: [sp:0 nrhs 1 real 1] [e1: 4e-10 : 0.0] [t1: 0.01 t2 0.00 : 1.0]
+A: [n 960 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 1] B: [sp:0 nrhs 1 real 0] [e1: 6e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 1] B: [sp:0 nrhs 9 real 0] [e1: 7e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 1] B: [sp:1 nrhs 1 real 1] [e1: 1e-11 : 0.0] [t1: 0.00 t2 0.01 : 1.0]
+A: [n 960 real 1] B: [sp:1 nrhs 4 real 1] [e1: 3e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 1] B: [sp:1 nrhs 9 real 1] [e1: 3e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 1] B: [sp:1 nrhs 1 real 0] [e1: 2e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 960 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 960 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 0] B: [sp:0 nrhs 9 real 0] [e1: 3e-13 : 0.0] [t1: 0.03 t2 0.02 : 1.0]
+A: [n 960 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 0] B: [sp:1 nrhs 4 real 1] [e1: 4e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 960 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 960 real 0] B: [sp:1 nrhs 1 real 0] [e1: 5e-14 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 960 real 0] B: [sp:1 nrhs 9 real 0] [e1: 7e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+
+nn =
+
+ 358
+
+
+Prob =
+
+ title: 'SYMMETRIC TEST MATRIX FROM MSC/NASTRAN STARF8.OUT2'
+ A: [1050x1050 double]
+ Zeros: [1050x1050 double]
+ name: 'Boeing/msc01050'
+ id: 358
+ date: '1995'
+ author: 'R. Grimes'
+ ed: 'T. Davis'
+ kind: 'structural problem'
+
+A: [n 1050 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-00 : 0.0] [t1: 0.01 t2 0.01 : 1.1]
+A: [n 1050 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e+00 : -0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1050 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e+00 : -0.0] [t1: 0.01 t2 0.01 : 1.1]
+A: [n 1050 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e+00 : -0.0] [t1: 0.01 t2 0.01 : 1.1]
+A: [n 1050 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e+00 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1050 real 1] B: [sp:1 nrhs 1 real 1] [e1: 3e-02 : 0.0] [t1: 0.01 t2 0.01 : 1.1]
+A: [n 1050 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-01 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1050 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-01 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1050 real 1] B: [sp:1 nrhs 1 real 0] [e1: 3e-02 : 0.0] [t1: 0.01 t2 0.01 : 1.1]
+A: [n 1050 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-01 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1050 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 1050 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 1050 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 1050 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 1050 real 0] B: [sp:0 nrhs 9 real 0] [e1: 3e-13 : 0.0] [t1: 0.03 t2 0.12 : 0.2]
+A: [n 1050 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 1050 real 0] B: [sp:1 nrhs 4 real 1] [e1: 5e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 1050 real 0] B: [sp:1 nrhs 9 real 1] [e1: 4e-14 : 0.0] [t1: 0.03 t2 0.03 : 0.9]
+A: [n 1050 real 0] B: [sp:1 nrhs 1 real 0] [e1: 5e-14 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 1050 real 0] B: [sp:1 nrhs 9 real 0] [e1: 6e-14 : 0.0] [t1: 0.03 t2 0.03 : 0.9]
+
+nn =
+
+ 30
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX, FRAME BUILDING (TV STUDIO)'
+ A: [1074x1074 double]
+ name: 'HB/bcsstk08'
+ id: 30
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 1074 real 1] B: [sp:0 nrhs 1 real 1] [e1: 3e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1074 real 1] B: [sp:0 nrhs 4 real 1] [e1: 4e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1074 real 1] B: [sp:0 nrhs 9 real 1] [e1: 4e-11 : 0.0] [t1: 0.01 t2 0.11 : 0.1]
+A: [n 1074 real 1] B: [sp:0 nrhs 1 real 0] [e1: 5e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1074 real 1] B: [sp:0 nrhs 9 real 0] [e1: 7e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1074 real 1] B: [sp:1 nrhs 1 real 1] [e1: 2e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1074 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-11 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1074 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-11 : 0.0] [t1: 0.11 t2 0.01 : 8.7]
+A: [n 1074 real 1] B: [sp:1 nrhs 1 real 0] [e1: 8e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1074 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 1074 real 0] B: [sp:0 nrhs 1 real 1] [e1: 1e-13 : 0.0] [t1: 0.13 t2 0.03 : 4.9]
+A: [n 1074 real 0] B: [sp:0 nrhs 4 real 1] [e1: 1e-13 : 0.0] [t1: 0.04 t2 0.14 : 0.3]
+A: [n 1074 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.05 t2 0.15 : 0.3]
+A: [n 1074 real 0] B: [sp:0 nrhs 1 real 0] [e1: 2e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 1074 real 0] B: [sp:0 nrhs 9 real 0] [e1: 3e-13 : 0.0] [t1: 0.15 t2 0.05 : 3.2]
+A: [n 1074 real 0] B: [sp:1 nrhs 1 real 1] [e1: 2e-14 : 0.0] [t1: 0.13 t2 0.03 : 4.9]
+A: [n 1074 real 0] B: [sp:1 nrhs 4 real 1] [e1: 2e-14 : 0.0] [t1: 0.04 t2 0.14 : 0.3]
+A: [n 1074 real 0] B: [sp:1 nrhs 9 real 1] [e1: 3e-14 : 0.0] [t1: 0.06 t2 0.16 : 0.4]
+A: [n 1074 real 0] B: [sp:1 nrhs 1 real 0] [e1: 3e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 1074 real 0] B: [sp:1 nrhs 9 real 0] [e1: 5e-14 : 0.0] [t1: 0.06 t2 0.16 : 0.4]
+
+nn =
+
+ 63
+
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX, FRAME BUILDING (TV STUDIO)'
+ A: [1074x1074 double]
+ name: 'HB/bcsstm08'
+ id: 63
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 1074 real 1] B: [sp:0 nrhs 1 real 1] [e1: 3e-15 : -3.5] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:0 nrhs 4 real 1] [e1: 5e-15 : -2.8] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 1074 real 1] B: [sp:0 nrhs 9 real 1] [e1: 5e-15 : -3.0] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 1074 real 1] B: [sp:0 nrhs 1 real 0] [e1: 8e-15 : -2.9] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-14 : -2.7] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 1074 real 1] B: [sp:1 nrhs 1 real 1] [e1: 5e-16 : -3.2] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:1 nrhs 4 real 1] [e1: 5e-16 : -3.5] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-15 : -2.5] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:1 nrhs 1 real 0] [e1: 7e-16 : -3.8] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:1 nrhs 9 real 0] [e1: 1e-15 : -3.2] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:0 nrhs 1 real 1] [e1: 6e-17 : -9.2] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:0 nrhs 4 real 1] [e1: 2e-16 : -7.3] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 1074 real 1] B: [sp:0 nrhs 9 real 1] [e1: 2e-16 : -7.7] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 1074 real 1] B: [sp:0 nrhs 1 real 0] [e1: 7e-18 : -13.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:0 nrhs 9 real 0] [e1: 6e-16 : -6.8] [t1: 0.00 t2 0.00 : 0.4]
+A: [n 1074 real 1] B: [sp:1 nrhs 1 real 1] [e1: 6e-17 : -6.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:1 nrhs 4 real 1] [e1: 6e-17 : -6.6] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-16 : -6.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:1 nrhs 1 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1074 real 1] B: [sp:1 nrhs 9 real 0] [e1: 4e-16 : -4.6] [t1: 0.00 t2 0.00 : 0.1]
+
+nn =
+
+ 31
+
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX, SQUARE PLATE CLAMPED'
+ A: [1083x1083 double]
+ name: 'HB/bcsstk09'
+ id: 31
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 1083 real 1] B: [sp:0 nrhs 1 real 1] [e1: 1e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1083 real 1] B: [sp:0 nrhs 4 real 1] [e1: 1e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1083 real 1] B: [sp:0 nrhs 9 real 1] [e1: 1e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1083 real 1] B: [sp:0 nrhs 1 real 0] [e1: 2e-10 : 0.0] [t1: 0.01 t2 0.11 : 0.1]
+A: [n 1083 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-10 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1083 real 1] B: [sp:1 nrhs 1 real 1] [e1: 5e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1083 real 1] B: [sp:1 nrhs 4 real 1] [e1: 5e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1083 real 1] B: [sp:1 nrhs 9 real 1] [e1: 1e-11 : 0.0] [t1: 0.01 t2 0.11 : 0.1]
+A: [n 1083 real 1] B: [sp:1 nrhs 1 real 0] [e1: 9e-12 : 0.0] [t1: 0.01 t2 0.01 : 1.0]
+A: [n 1083 real 1] B: [sp:1 nrhs 9 real 0] [e1: 2e-11 : 0.0] [t1: 0.02 t2 0.02 : 1.0]
+A: [n 1083 real 0] B: [sp:0 nrhs 1 real 1] [e1: 2e-13 : 0.0] [t1: 0.13 t2 0.03 : 4.6]
+A: [n 1083 real 0] B: [sp:0 nrhs 4 real 1] [e1: 2e-13 : 0.0] [t1: 0.04 t2 0.14 : 0.3]
+A: [n 1083 real 0] B: [sp:0 nrhs 9 real 1] [e1: 2e-13 : 0.0] [t1: 0.04 t2 0.14 : 0.3]
+A: [n 1083 real 0] B: [sp:0 nrhs 1 real 0] [e1: 3e-13 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 1083 real 0] B: [sp:0 nrhs 9 real 0] [e1: 4e-13 : 0.0] [t1: 0.14 t2 0.04 : 3.3]
+A: [n 1083 real 0] B: [sp:1 nrhs 1 real 1] [e1: 3e-14 : 0.0] [t1: 0.03 t2 0.13 : 0.2]
+A: [n 1083 real 0] B: [sp:1 nrhs 4 real 1] [e1: 5e-14 : 0.0] [t1: 0.04 t2 0.14 : 0.3]
+A: [n 1083 real 0] B: [sp:1 nrhs 9 real 1] [e1: 5e-14 : 0.0] [t1: 0.05 t2 0.15 : 0.4]
+A: [n 1083 real 0] B: [sp:1 nrhs 1 real 0] [e1: 8e-14 : 0.0] [t1: 0.03 t2 0.03 : 1.0]
+A: [n 1083 real 0] B: [sp:1 nrhs 9 real 0] [e1: 1e-13 : 0.0] [t1: 0.16 t2 0.05 : 2.9]
+
+nn =
+
+ 64
+
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX, SQUARE PLATE CLAMPED'
+ A: [1083x1083 double]
+ name: 'HB/bcsstm09'
+ id: 64
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+A: [n 1083 real 1] B: [sp:0 nrhs 1 real 1] [e1: 7e-15 : -3.4] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 1083 real 1] B: [sp:0 nrhs 4 real 1] [e1: 8e-15 : -3.2] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 1083 real 1] B: [sp:0 nrhs 9 real 1] [e1: 9e-15 : -3.1] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 1083 real 1] B: [sp:0 nrhs 1 real 0] [e1: 1e-14 : -3.1] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:0 nrhs 9 real 0] [e1: 2e-14 : -2.9] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 1083 real 1] B: [sp:1 nrhs 1 real 1] [e1: 7e-16 : -4.3] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:1 nrhs 4 real 1] [e1: 1e-15 : -3.7] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:1 nrhs 9 real 1] [e1: 2e-15 : -3.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:1 nrhs 1 real 0] [e1: 8e-16 : -4.8] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:1 nrhs 9 real 0] [e1: 3e-15 : -3.6] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:0 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:0 nrhs 4 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:0 nrhs 9 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.2]
+A: [n 1083 real 1] B: [sp:0 nrhs 1 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:0 nrhs 9 real 0] [e1: 1e-16 : -10.4] [t1: 0.00 t2 0.00 : 0.3]
+A: [n 1083 real 1] B: [sp:1 nrhs 1 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:1 nrhs 4 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:1 nrhs 9 real 1] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:1 nrhs 1 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+A: [n 1083 real 1] B: [sp:1 nrhs 9 real 0] [e1: 0e+00 : 0.0] [t1: 0.00 t2 0.00 : 0.1]
+=================================================================
+test11 : compare CHOLMOD and MATLAB, save results in Results.mat
+test matrices sorted by dimension:
+1440: Oberwolfach LFAT5 14 1
+1438: Oberwolfach LF10 18 1
+ 436: FIDAP ex5 27 1
+ 23: HB bcsstk01 48 1
+ 872: Pothen mesh1e1 48 1
+ 873: Pothen mesh1em1 48 1
+ 874: Pothen mesh1em6 48 1
+ 24: HB bcsstk02 66 1
+ 57: HB bcsstm02 66 1
+ 220: HB nos4 100 1
+ 25: HB bcsstk03 112 1
+1506: Pajek Journals 124 1
+ 26: HB bcsstk04 132 1
+ 44: HB bcsstk22 138 1
+ 72: HB bcsstm22 138 1
+ 206: HB lund_a 147 1
+ 207: HB lund_b 147 1
+ 27: HB bcsstk05 153 1
+ 60: HB bcsstm05 153 1
+ 217: HB nos1 237 1
+ 877: Pothen mesh3e1 289 1
+ 878: Pothen mesh3em5 289 1
+ 875: Pothen mesh2e1 306 1
+ 876: Pothen mesh2em5 306 1
+ 229: HB plat362 362 1
+ 315: Bai mhdb416 416 1
+ 28: HB bcsstk06 420 1
+ 29: HB bcsstk07 420 1
+ 61: HB bcsstm06 420 1
+ 62: HB bcsstm07 420 1
+ 221: HB nos5 468 1
+ 42: HB bcsstk20 485 1
+ 70: HB bcsstm20 485 1
+ 2: HB 494_bus 494 1
+ 339: Boeing bcsstk34 588 1
+ 3: HB 662_bus 662 1
+ 222: HB nos6 675 1
+ 4: HB 685_bus 685 1
+ 357: Boeing msc00726 726 1
+ 223: HB nos7 729 1
+ 41: HB bcsstk19 817 1
+ 69: HB bcsstm19 817 1
+ 159: HB gr_30_30 900 1
+ 218: HB nos2 957 1
+ 219: HB nos3 960 1
+ 358: Boeing msc01050 1050 1
+ 30: HB bcsstk08 1074 1
+ 63: HB bcsstm08 1074 1
+ 31: HB bcsstk09 1083 1
+ 64: HB bcsstm09 1083 1
+
+1440: Oberwolfach/LFAT5
+n 14 lnz 33 fl 91
+cholmod2: t: 0.00003 e: 6.4e-14 mflop 3
+matlab: t: 0.00003 e: 4.3e-14 mflop 3 cholmod2 speedup: 1.1
+
+1438: Oberwolfach/LF10
+n 18 lnz 58 fl 198
+cholmod2: t: 0.00003 e: 1.8e-12 mflop 6
+matlab: t: 0.00002 e: 1.1e-12 mflop 9 cholmod2 speedup: 0.6
+
+436: FIDAP/ex5
+n 27 lnz 153 fl 981
+cholmod2: t: 0.00009 e: 3.5e-08 mflop 11
+matlab: t: 0.00012 e: 3.5e-08 mflop 8 cholmod2 speedup: 1.3
+
+ 23: HB/bcsstk01
+n 48 lnz 489 fl 6009
+cholmod2: t: 0.00027 e: 1.2e-12 mflop 22
+matlab: t: 0.00023 e: 1.2e-12 mflop 26 cholmod2 speedup: 0.8
+
+872: Pothen/mesh1e1
+n 48 lnz 336 fl 2678
+cholmod2: t: 0.00011 e: 4.1e-15 mflop 25
+matlab: t: 0.00009 e: 4.1e-15 mflop 28 cholmod2 speedup: 0.9
+
+873: Pothen/mesh1em1
+n 48 lnz 336 fl 2678
+cholmod2: t: 0.00021 e: 5.7e-15 mflop 13
+matlab: t: 0.00018 e: 5.7e-15 mflop 15 cholmod2 speedup: 0.8
+
+874: Pothen/mesh1em6
+n 48 lnz 336 fl 2678
+cholmod2: t: 0.00023 e: 2.5e-15 mflop 12
+matlab: t: 0.00019 e: 2.5e-15 mflop 14 cholmod2 speedup: 0.8
+
+ 24: HB/bcsstk02
+n 66 lnz 2211 fl 98021
+cholmod2: t: 0.00071 e: 5.7e-12 mflop 138
+matlab: t: 0.00032 e: 5.7e-12 mflop 302 cholmod2 speedup: 0.5
+
+ 57: HB/bcsstm02
+n 66 lnz 66 fl 66
+cholmod2: t: 0.00004 e: 3.3e-15 mflop 2
+matlab: t: 0.00001 e: 2.5e-16 mflop 7 cholmod2 speedup: 0.2
+
+220: HB/nos4
+n 100 lnz 632 fl 4438
+cholmod2: t: 0.00040 e: 1.3e-12 mflop 11
+matlab: t: 0.00037 e: 1.3e-12 mflop 12 cholmod2 speedup: 0.9
+
+ 25: HB/bcsstk03
+n 112 lnz 384 fl 1360
+cholmod2: t: 0.00027 e: 2.4e-11 mflop 5
+matlab: t: 0.00021 e: 2.4e-11 mflop 7 cholmod2 speedup: 0.8
+
+1506: Pajek/Journals
+n 124 lnz 6990 fl 505314
+cholmod2: t: 0.00131 e: 4.2e-14 mflop 386
+matlab: t: 0.00087 e: 4.1e-14 mflop 580 cholmod2 speedup: 0.7
+
+ 26: HB/bcsstk04
+n 132 lnz 3293 fl 90567
+cholmod2: t: 0.00092 e: 1.5e-11 mflop 98
+matlab: t: 0.00132 e: 1.5e-11 mflop 68 cholmod2 speedup: 1.4
+
+ 44: HB/bcsstk22
+n 138 lnz 680 fl 4224
+cholmod2: t: 0.00040 e: 8.2e-12 mflop 10
+matlab: t: 0.00037 e: 8.2e-12 mflop 11 cholmod2 speedup: 0.9
+
+ 72: HB/bcsstm22
+n 138 lnz 138 fl 138
+cholmod2: t: 0.00013 e: 5.4e-15 mflop 1
+matlab: t: 0.00002 e: 1.1e-15 mflop 7 cholmod2 speedup: 0.1
+
+206: HB/lund_a
+n 147 lnz 2339 fl 42287
+cholmod2: t: 0.00040 e: 3.4e-10 mflop 105
+matlab: t: 0.00041 e: 3.4e-10 mflop 104 cholmod2 speedup: 1.0
+
+207: HB/lund_b
+n 147 lnz 2340 fl 42320
+cholmod2: t: 0.00066 e: 1.4e-12 mflop 65
+matlab: t: 0.00076 e: 1.4e-12 mflop 56 cholmod2 speedup: 1.2
+
+ 27: HB/bcsstk05
+n 153 lnz 2326 fl 39118
+cholmod2: t: 0.00091 e: 9.7e-12 mflop 43
+matlab: t: 0.00090 e: 9.7e-12 mflop 44 cholmod2 speedup: 1.0
+
+ 60: HB/bcsstm05
+n 153 lnz 153 fl 153
+cholmod2: t: 0.00015 e: 7.8e-15 mflop 1
+matlab: t: 0.00002 e: 1.3e-15 mflop 7 cholmod2 speedup: 0.1
+
+217: HB/nos1
+n 237 lnz 704 fl 2254
+cholmod2: t: 0.00020 e: 4.0e-09 mflop 11
+matlab: t: 0.00018 e: 4.0e-09 mflop 12 cholmod2 speedup: 0.9
+
+877: Pothen/mesh3e1
+n 289 lnz 2433 fl 27549
+cholmod2: t: 0.00077 e: 2.8e-14 mflop 36
+matlab: t: 0.00096 e: 2.8e-14 mflop 29 cholmod2 speedup: 1.3
+
+878: Pothen/mesh3em5
+n 289 lnz 2433 fl 27549
+cholmod2: t: 0.00108 e: 2.6e-14 mflop 25
+matlab: t: 0.00096 e: 2.6e-14 mflop 29 cholmod2 speedup: 0.9
+
+875: Pothen/mesh2e1
+n 306 lnz 3224 fl 43648
+cholmod2: t: 0.00148 e: 1.5e-13 mflop 29
+matlab: t: 0.00124 e: 1.5e-13 mflop 35 cholmod2 speedup: 0.8
+
+876: Pothen/mesh2em5
+n 306 lnz 3224 fl 43648
+cholmod2: t: 0.00068 e: 4.9e-14 mflop 65
+matlab: t: 0.00062 e: 4.9e-14 mflop 70 cholmod2 speedup: 0.9
+
+229: HB/plat362
+n 362 lnz 8060 fl 220156
+cholmod2: t: 0.00242 e: 2.1e-05 mflop 91
+matlab: t: 0.00298 e: 2.1e-05 mflop 74 cholmod2 speedup: 1.2
+
+315: Bai/mhdb416
+n 416 lnz 1364 fl 4998
+cholmod2: t: 0.00076 e: 2.0e-12 mflop 7
+matlab: t: 0.00081 e: 2.0e-12 mflop 6 cholmod2 speedup: 1.1
+
+ 28: HB/bcsstk06
+n 420 lnz 11345 fl 400973
+cholmod2: t: 0.00396 e: 1.9e-10 mflop 101
+matlab: t: 0.00423 e: 1.9e-10 mflop 95 cholmod2 speedup: 1.1
+
+ 29: HB/bcsstk07
+n 420 lnz 11345 fl 400973
+cholmod2: t: 0.00200 e: 1.9e-10 mflop 201
+matlab: t: 0.00211 e: 1.9e-10 mflop 190 cholmod2 speedup: 1.1
+
+ 61: HB/bcsstm06
+n 420 lnz 420 fl 420
+cholmod2: t: 0.00027 e: 2.1e-14 mflop 2
+matlab: t: 0.00003 e: 3.0e-15 mflop 14 cholmod2 speedup: 0.1
+
+ 62: HB/bcsstm07
+n 420 lnz 10654 fl 353996
+cholmod2: t: 0.00375 e: 5.7e-13 mflop 94
+matlab: t: 0.00392 e: 5.7e-13 mflop 90 cholmod2 speedup: 1.0
+
+221: HB/nos5
+n 468 lnz 18437 fl 1.07298e+06
+cholmod2: t: 0.00672 e: 9.8e-12 mflop 160
+matlab: t: 0.00647 e: 9.8e-12 mflop 166 cholmod2 speedup: 1.0
+
+ 42: HB/bcsstk20
+n 485 lnz 2336 fl 13864
+cholmod2: t: 0.00056 e: 5.6e-06 mflop 25
+matlab: t: 0.00053 e: 5.6e-06 mflop 26 cholmod2 speedup: 0.9
+
+ 70: HB/bcsstm20
+n 485 lnz 485 fl 485
+cholmod2: t: 0.00034 e: 2.7e-14 mflop 1
+matlab: t: 0.00004 e: 5.7e-15 mflop 13 cholmod2 speedup: 0.1
+
+ 2: HB/494_bus
+n 494 lnz 1414 fl 4812
+cholmod2: t: 0.00105 e: 8.0e-10 mflop 5
+matlab: t: 0.00098 e: 8.0e-10 mflop 5 cholmod2 speedup: 0.9
+
+339: Boeing/bcsstk34
+n 588 lnz 43366 fl 3.91893e+06
+cholmod2: t: 0.01322 e: 1.1e-12 mflop 296
+matlab: t: 0.01341 e: 1.1e-12 mflop 292 cholmod2 speedup: 1.0
+
+ 3: HB/662_bus
+n 662 lnz 2549 fl 12937
+cholmod2: t: 0.00185 e: 9.6e-10 mflop 7
+matlab: t: 0.00156 e: 9.6e-10 mflop 8 cholmod2 speedup: 0.8
+
+222: HB/nos6
+n 675 lnz 6453 fl 85577
+cholmod2: t: 0.00129 e: 2.7e-08 mflop 66
+matlab: t: 0.00117 e: 2.7e-08 mflop 73 cholmod2 speedup: 0.9
+
+ 4: HB/685_bus
+n 685 lnz 3650 fl 25150
+cholmod2: t: 0.00158 e: 1.6e-10 mflop 16
+matlab: t: 0.00200 e: 1.6e-10 mflop 13 cholmod2 speedup: 1.3
+
+357: Boeing/msc00726
+n 726 lnz 110707 fl 2.31244e+07
+cholmod2: t: 0.02436 e: 1.8e-11 mflop 949
+matlab: t: 0.03762 e: 1.8e-11 mflop 615 cholmod2 speedup: 1.5
+
+223: HB/nos7
+n 729 lnz 18945 fl 1.0875e+06
+cholmod2: t: 0.00748 e: 2.5e-06 mflop 145
+matlab: t: 0.00720 e: 2.5e-06 mflop 151 cholmod2 speedup: 1.0
+
+ 41: HB/bcsstk19
+n 817 lnz 7528 fl 77096
+cholmod2: t: 0.00342 e: 6.7e-06 mflop 23
+matlab: t: 0.00297 e: 6.7e-06 mflop 26 cholmod2 speedup: 0.9
+
+ 69: HB/bcsstm19
+n 817 lnz 817 fl 817
+cholmod2: t: 0.00030 e: 3.8e-14 mflop 3
+matlab: t: 0.00003 e: 6.0e-15 mflop 31 cholmod2 speedup: 0.1
+
+159: HB/gr_30_30
+n 900 lnz 16348 fl 405796
+cholmod2: t: 0.00557 e: 8.7e-12 mflop 73
+matlab: t: 0.00560 e: 8.7e-12 mflop 73 cholmod2 speedup: 1.0
+
+218: HB/nos2
+n 957 lnz 2864 fl 9214
+cholmod2: t: 0.00152 e: 4.4e-06 mflop 6
+matlab: t: 0.00144 e: 4.4e-06 mflop 6 cholmod2 speedup: 0.9
+
+219: HB/nos3
+n 960 lnz 31314 fl 1.38676e+06
+cholmod2: t: 0.00953 e: 4.3e-10 mflop 145
+matlab: t: 0.00984 e: 4.3e-10 mflop 141 cholmod2 speedup: 1.0
+
+358: Boeing/msc01050
+n 1050 lnz 28305 fl 1.01711e+06
+cholmod2: t: 0.00768 e: 1.1e+00 mflop 133
+matlab: t: 0.00809 e: 1.1e+00 mflop 126 cholmod2 speedup: 1.1
+
+ 30: HB/bcsstk08
+n 1074 lnz 31153 fl 1.80924e+06
+cholmod2: t: 0.01337 e: 4.5e-11 mflop 135
+matlab: t: 0.01572 e: 4.5e-11 mflop 115 cholmod2 speedup: 1.2
+
+ 63: HB/bcsstm08
+n 1074 lnz 1074 fl 1074
+cholmod2: t: 0.00086 e: 3.6e-14 mflop 1
+matlab: t: 0.00005 e: 4.4e-15 mflop 22 cholmod2 speedup: 0.1
+
+ 31: HB/bcsstk09
+n 1083 lnz 58416 fl 4.50027e+06
+cholmod2: t: 0.01767 e: 1.3e-10 mflop 255
+matlab: t: 0.01763 e: 1.3e-10 mflop 255 cholmod2 speedup: 1.0
+
+ 64: HB/bcsstm09
+n 1083 lnz 1083 fl 1083
+cholmod2: t: 0.00040 e: 8.1e-14 mflop 3
+matlab: t: 0.00003 e: 8.2e-15 mflop 34 cholmod2 speedup: 0.1
+test11 passed
+=================================================================
+test12: test etree2 and compare with etree
+Matrices to test: 50
+
+ 904: vanHeukelum/cage3 nrow: 5 ncol: 5 nnz: 19
+etree(A,'col'): 0.0004 0.0003 speedup 1.36
+etree(A,'row'): 0.0003 0.0003 speedup 1.12
+etree(A): 0.0003 0.0003 speedup 1.24
+etree(A'): 0.0003 0.0003 speedup 0.96
+after amd:
+etree(A): 0.0002 0.0000 speedup 10.05
+etree(A'): 0.0001 0.0000 speedup 5.48
+
+ 449: Grund/b1_ss nrow: 7 ncol: 7 nnz: 15
+etree(A,'col'): 0.0001 0.0000 speedup 7.28
+etree(A,'row'): 0.0001 0.0000 speedup 3.83
+etree(A): 0.0001 0.0000 speedup 8.14
+etree(A'): 0.0001 0.0000 speedup 5.74
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.71
+etree(A'): 0.0001 0.0000 speedup 6.41
+
+1710: Meszaros/farm nrow: 7 ncol: 17 nnz: 41
+etree(A,'col'): 0.0002 0.0000 speedup 7.70
+etree(A,'row'): 0.0001 0.0000 speedup 3.93
+
+ 715: LPnetlib/lpi_galenet nrow: 8 ncol: 14 nnz: 22
+etree(A,'col'): 0.0001 0.0000 speedup 6.39
+etree(A,'row'): 0.0001 0.0000 speedup 5.57
+
+1817: Meszaros/kleemin nrow: 8 ncol: 16 nnz: 44
+etree(A,'col'): 0.0001 0.0000 speedup 5.80
+etree(A,'row'): 0.0001 0.0000 speedup 5.45
+
+ 185: HB/jgl009 nrow: 9 ncol: 9 nnz: 50
+etree(A,'col'): 0.0001 0.0000 speedup 6.39
+etree(A,'row'): 0.0001 0.0000 speedup 4.07
+etree(A): 0.0001 0.0000 speedup 7.47
+etree(A'): 0.0001 0.0000 speedup 5.45
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.93
+etree(A'): 0.0001 0.0000 speedup 6.06
+
+ 719: LPnetlib/lpi_itest2 nrow: 9 ncol: 13 nnz: 26
+etree(A,'col'): 0.0001 0.0000 speedup 6.05
+etree(A,'row'): 0.0001 0.0000 speedup 5.60
+
+ 905: vanHeukelum/cage4 nrow: 9 ncol: 9 nnz: 49
+etree(A,'col'): 0.0001 0.0000 speedup 6.11
+etree(A,'row'): 0.0001 0.0000 speedup 5.36
+etree(A): 0.0001 0.0000 speedup 7.79
+etree(A'): 0.0001 0.0000 speedup 5.50
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.79
+etree(A'): 0.0001 0.0000 speedup 8.11
+
+ 238: HB/rgg010 nrow: 10 ncol: 10 nnz: 76
+etree(A,'col'): 0.0001 0.0000 speedup 6.37
+etree(A,'row'): 0.0001 0.0000 speedup 5.55
+etree(A): 0.0001 0.0000 speedup 5.10
+etree(A'): 0.0001 0.0000 speedup 5.14
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.79
+etree(A'): 0.0001 0.0000 speedup 5.63
+
+1524: Pajek/Stranke94 nrow: 10 ncol: 10 nnz: 90
+etree(A,'col'): 0.0001 0.0000 speedup 6.21
+etree(A,'row'): 0.0001 0.0000 speedup 3.97
+etree(A): 0.0001 0.0000 speedup 7.53
+etree(A'): 0.0001 0.0000 speedup 5.43
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.36
+etree(A'): 0.0001 0.0000 speedup 5.58
+
+ 186: HB/jgl011 nrow: 11 ncol: 11 nnz: 76
+etree(A,'col'): 0.0001 0.0000 speedup 6.21
+etree(A,'row'): 0.0001 0.0000 speedup 5.55
+etree(A): 0.0001 0.0000 speedup 7.40
+etree(A'): 0.0001 0.0000 speedup 4.00
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.64
+etree(A'): 0.0001 0.0000 speedup 4.42
+
+ 720: LPnetlib/lpi_itest6 nrow: 11 ncol: 17 nnz: 29
+etree(A,'col'): 0.0001 0.0000 speedup 6.11
+etree(A,'row'): 0.0001 0.0000 speedup 5.48
+
+1525: Pajek/Tina_AskCal nrow: 11 ncol: 11 nnz: 29
+etree(A,'col'): 0.0001 0.0000 speedup 6.11
+etree(A,'row'): 0.0001 0.0000 speedup 5.62
+etree(A): 0.0001 0.0000 speedup 7.33
+etree(A'): 0.0001 0.0000 speedup 5.53
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.79
+etree(A'): 0.0001 0.0000 speedup 5.72
+
+1526: Pajek/Tina_AskCog nrow: 11 ncol: 11 nnz: 36
+etree(A,'col'): 0.0001 0.0000 speedup 6.60
+etree(A,'row'): 0.0001 0.0000 speedup 5.27
+etree(A): 0.0001 0.0000 speedup 7.67
+etree(A'): 0.0001 0.0000 speedup 5.70
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.64
+etree(A'): 0.0001 0.0000 speedup 5.79
+
+1527: Pajek/Tina_DisCal nrow: 11 ncol: 11 nnz: 41
+etree(A,'col'): 0.0001 0.0000 speedup 6.50
+etree(A,'row'): 0.0001 0.0000 speedup 5.62
+etree(A): 0.0001 0.0000 speedup 7.00
+etree(A'): 0.0001 0.0000 speedup 4.28
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.86
+etree(A'): 0.0001 0.0000 speedup 4.42
+
+1528: Pajek/Tina_DisCog nrow: 11 ncol: 11 nnz: 48
+etree(A,'col'): 0.0001 0.0000 speedup 6.11
+etree(A,'row'): 0.0001 0.0000 speedup 4.91
+etree(A): 0.0001 0.0000 speedup 9.87
+etree(A'): 0.0001 0.0000 speedup 5.00
+after amd:
+etree(A): 0.0001 0.0000 speedup 8.31
+etree(A'): 0.0001 0.0000 speedup 5.67
+
+1755: Meszaros/problem nrow: 12 ncol: 46 nnz: 86
+etree(A,'col'): 0.0001 0.0000 speedup 5.30
+etree(A,'row'): 0.0001 0.0000 speedup 5.17
+
+1440: Oberwolfach/LFAT5 nrow: 14 ncol: 14 nnz: 46
+etree(A,'col'): 0.0001 0.0000 speedup 6.39
+etree(A,'row'): 0.0001 0.0000 speedup 5.29
+etree(A): 0.0002 0.0000 speedup 15.20
+etree(A'): 0.0001 0.0000 speedup 5.48
+after amd:
+etree(A): 0.0001 0.0000 speedup 5.10
+etree(A'): 0.0001 0.0000 speedup 6.11
+
+1741: Meszaros/p0033 nrow: 15 ncol: 48 nnz: 113
+etree(A,'col'): 0.0001 0.0000 speedup 5.43
+etree(A,'row'): 0.0001 0.0000 speedup 3.87
+
+1438: Oberwolfach/LF10 nrow: 18 ncol: 18 nnz: 82
+etree(A,'col'): 0.0001 0.0000 speedup 6.00
+etree(A,'row'): 0.0001 0.0000 speedup 4.88
+etree(A): 0.0001 0.0000 speedup 7.73
+etree(A'): 0.0001 0.0000 speedup 4.95
+after amd:
+etree(A): 0.0001 0.0000 speedup 5.75
+etree(A'): 0.0001 0.0000 speedup 5.14
+
+1479: Pajek/GD01_b nrow: 18 ncol: 18 nnz: 37
+etree(A,'col'): 0.0001 0.0000 speedup 5.80
+etree(A,'row'): 0.0001 0.0000 speedup 5.18
+etree(A): 0.0001 0.0000 speedup 7.47
+etree(A'): 0.0001 0.0000 speedup 5.33
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.27
+etree(A'): 0.0002 0.0000 speedup 9.05
+
+ 706: LPnetlib/lpi_bgprtr nrow: 20 ncol: 40 nnz: 70
+etree(A,'col'): 0.0001 0.0000 speedup 5.48
+etree(A,'row'): 0.0001 0.0000 speedup 5.21
+
+1481: Pajek/GD02_a nrow: 23 ncol: 23 nnz: 87
+etree(A,'col'): 0.0001 0.0000 speedup 5.71
+etree(A,'row'): 0.0001 0.0000 speedup 5.12
+etree(A): 0.0001 0.0000 speedup 7.56
+etree(A'): 0.0001 0.0000 speedup 5.23
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.47
+etree(A'): 0.0001 0.0000 speedup 5.70
+
+1516: Pajek/Ragusa18 nrow: 23 ncol: 23 nnz: 64
+etree(A,'col'): 0.0001 0.0000 speedup 6.00
+etree(A,'row'): 0.0001 0.0000 speedup 5.12
+etree(A): 0.0001 0.0000 speedup 4.70
+etree(A'): 0.0001 0.0000 speedup 5.27
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.27
+etree(A'): 0.0001 0.0000 speedup 5.60
+
+1742: Meszaros/p0040 nrow: 23 ncol: 63 nnz: 133
+etree(A,'col'): 0.0001 0.0000 speedup 5.39
+etree(A,'row'): 0.0001 0.0000 speedup 3.94
+
+ 97: HB/can_24 nrow: 24 ncol: 24 nnz: 160
+etree(A,'col'): 0.0001 0.0000 speedup 6.10
+etree(A,'row'): 0.0001 0.0000 speedup 3.72
+etree(A): 0.0001 0.0000 speedup 6.88
+etree(A'): 0.0001 0.0000 speedup 5.13
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.06
+etree(A'): 0.0001 0.0000 speedup 5.24
+
+ 624: LPnetlib/lp_fit1d nrow: 24 ncol: 1049 nnz: 13427
+etree(A,'col'): 0.0004 0.0002 speedup 2.25
+etree(A,'row'): 0.0008 0.0002 speedup 3.34
+
+1515: Pajek/Ragusa16 nrow: 24 ncol: 24 nnz: 81
+etree(A,'col'): 0.0001 0.0000 speedup 5.71
+etree(A,'row'): 0.0001 0.0000 speedup 5.08
+etree(A): 0.0001 0.0000 speedup 4.95
+etree(A'): 0.0001 0.0000 speedup 4.96
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.60
+etree(A'): 0.0001 0.0000 speedup 5.60
+
+ 626: LPnetlib/lp_fit2d nrow: 25 ncol: 10524 nnz: 129042
+etree(A,'col'): 0.0056 0.0020 speedup 2.74
+etree(A,'row'): 0.0107 0.0032 speedup 3.33
+
+1177: HB/lap_25 nrow: 25 ncol: 25 nnz: 169
+etree(A,'col'): 0.0001 0.0000 speedup 5.76
+etree(A,'row'): 0.0001 0.0000 speedup 3.53
+etree(A): 0.0001 0.0000 speedup 7.44
+etree(A'): 0.0001 0.0000 speedup 5.18
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.93
+etree(A'): 0.0001 0.0000 speedup 5.19
+
+ 436: FIDAP/ex5 nrow: 27 ncol: 27 nnz: 279
+etree(A,'col'): 0.0001 0.0000 speedup 5.59
+etree(A,'row'): 0.0001 0.0000 speedup 5.04
+etree(A): 0.0001 0.0000 speedup 6.59
+etree(A'): 0.0001 0.0000 speedup 4.88
+after amd:
+etree(A): 0.0001 0.0000 speedup 6.59
+etree(A'): 0.0001 0.0000 speedup 5.45
+
+ 597: LPnetlib/lp_afiro nrow: 27 ncol: 51 nnz: 102
+etree(A,'col'): 0.0001 0.0000 speedup 5.21
+etree(A,'row'): 0.0002 0.0000 speedup 6.27
+
+1759: Meszaros/refine nrow: 29 ncol: 62 nnz: 153
+etree(A,'col'): 0.0001 0.0000 speedup 4.96
+etree(A,'row'): 0.0001 0.0000 speedup 5.08
+
+ 232: HB/pores_1 nrow: 30 ncol: 30 nnz: 180
+etree(A,'col'): 0.0001 0.0000 speedup 5.76
+etree(A,'row'): 0.0001 0.0000 speedup 5.04
+etree(A): 0.0001 0.0000 speedup 6.82
+etree(A'): 0.0001 0.0000 speedup 5.35
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.06
+etree(A'): 0.0001 0.0000 speedup 4.11
+
+ 168: HB/ibm32 nrow: 32 ncol: 32 nnz: 126
+etree(A,'col'): 0.0001 0.0000 speedup 5.76
+etree(A,'row'): 0.0001 0.0000 speedup 4.58
+etree(A): 0.0001 0.0000 speedup 6.82
+etree(A'): 0.0001 0.0000 speedup 5.23
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.33
+etree(A'): 0.0001 0.0000 speedup 5.29
+
+1199: Hamrle/Hamrle1 nrow: 32 ncol: 32 nnz: 98
+etree(A,'col'): 0.0001 0.0000 speedup 5.71
+etree(A,'row'): 0.0001 0.0000 speedup 5.17
+etree(A): 0.0001 0.0000 speedup 6.88
+etree(A'): 0.0001 0.0000 speedup 5.00
+after amd:
+etree(A): 0.0001 0.0000 speedup 6.41
+etree(A'): 0.0001 0.0000 speedup 5.65
+
+1480: Pajek/GD01_c nrow: 33 ncol: 33 nnz: 135
+etree(A,'col'): 0.0001 0.0000 speedup 5.81
+etree(A,'row'): 0.0001 0.0000 speedup 4.70
+etree(A): 0.0001 0.0000 speedup 6.44
+etree(A'): 0.0001 0.0000 speedup 5.05
+after amd:
+etree(A): 0.0001 0.0000 speedup 7.06
+etree(A'): 0.0001 0.0000 speedup 3.93
+
+ 731: LPnetlib/lpi_woodinfe nrow: 35 ncol: 89 nnz: 140
+etree(A,'col'): 0.0001 0.0000 speedup 5.00
+etree(A,'row'): 0.0001 0.0000 speedup 5.12
+
+1474: Pajek/football nrow: 35 ncol: 35 nnz: 118
+etree(A,'col'): 0.0001 0.0000 speedup 5.68
+etree(A,'row'): 0.0001 0.0000 speedup 4.74
+etree(A): 0.0001 0.0000 speedup 6.21
+etree(A'): 0.0001 0.0000 speedup 5.16
+after amd:
+etree(A): 0.0001 0.0000 speedup 6.33
+etree(A'): 0.0001 0.0000 speedup 4.15
+
+1485: Pajek/GD95_a nrow: 36 ncol: 36 nnz: 57
+etree(A,'col'): 0.0001 0.0000 speedup 5.50
+etree(A,'row'): 0.0001 0.0000 speedup 5.00
+etree(A): 0.0001 0.0000 speedup 6.33
+etree(A'): 0.0001 0.0000 speedup 4.83
+after amd:
+etree(A): 0.0001 0.0000 speedup 6.53
+etree(A'): 0.0001 0.0000 speedup 4.04
+
+ 906: vanHeukelum/cage5 nrow: 37 ncol: 37 nnz: 233
+etree(A,'col'): 0.0001 0.0000 speedup 5.25
+etree(A,'row'): 0.0001 0.0000 speedup 4.78
+etree(A): 0.0001 0.0000 speedup 6.00
+etree(A'): 0.0001 0.0000 speedup 4.73
+after amd:
+etree(A): 0.0001 0.0000 speedup 6.65
+etree(A'): 0.0001 0.0000 speedup 5.00
+
+1495: Pajek/GD98_a nrow: 38 ncol: 38 nnz: 50
+etree(A,'col'): 0.0001 0.0000 speedup 5.45
+etree(A,'row'): 0.0001 0.0000 speedup 4.88
+etree(A): 0.0001 0.0000 speedup 6.44
+etree(A'): 0.0001 0.0000 speedup 5.04
+after amd:
+etree(A): 0.0001 0.0000 speedup 6.71
+etree(A'): 0.0001 0.0000 speedup 5.48
+
+ 13: HB/bcspwr01 nrow: 39 ncol: 39 nnz: 131
+etree(A,'col'): 0.0001 0.0000 speedup 5.25
+etree(A,'row'): 0.0001 0.0000 speedup 4.89
+etree(A): 0.0001 0.0000 speedup 6.26
+etree(A'): 0.0001 0.0000 speedup 3.80
+after amd:
+etree(A): 0.0001 0.0000 speedup 6.53
+etree(A'): 0.0001 0.0000 speedup 5.17
+
+ 636: LPnetlib/lp_kb2 nrow: 43 ncol: 68 nnz: 313
+etree(A,'col'): 0.0001 0.0000 speedup 4.67
+etree(A,'row'): 0.0001 0.0000 speedup 3.39
+
+1493: Pajek/GD97_b nrow: 47 ncol: 47 nnz: 264
+etree(A,'col'): 0.0001 0.0000 speedup 5.08
+etree(A,'row'): 0.0001 0.0000 speedup 4.13
+etree(A): 0.0001 0.0000 speedup 6.32
+etree(A'): 0.0001 0.0000 speedup 4.58
+after amd:
+etree(A): 0.0001 0.0000 speedup 6.11
+etree(A'): 0.0002 0.0000 speedup 6.08
+
+ 23: HB/bcsstk01 nrow: 48 ncol: 48 nnz: 400
+etree(A,'col'): 0.0001 0.0000 speedup 4.92
+etree(A,'row'): 0.0001 0.0000 speedup 4.28
+etree(A): 0.0001 0.0000 speedup 5.86
+etree(A'): 0.0001 0.0000 speedup 4.54
+after amd:
+etree(A): 0.0001 0.0000 speedup 5.33
+etree(A'): 0.0001 0.0000 speedup 4.70
+
+ 56: HB/bcsstm01 nrow: 48 ncol: 48 nnz: 24
+etree(A,'col'): 0.0001 0.0000 speedup 5.86
+etree(A,'row'): 0.0001 0.0000 speedup 5.17
+etree(A): 0.0001 0.0000 speedup 4.58
+etree(A'): 0.0001 0.0000 speedup 5.32
+after amd:
+etree(A): 0.0001 0.0000 speedup 5.15
+etree(A'): 0.0001 0.0000 speedup 5.48
+
+ 872: Pothen/mesh1e1 nrow: 48 ncol: 48 nnz: 306
+etree(A,'col'): 0.0001 0.0000 speedup 5.12
+etree(A,'row'): 0.0001 0.0000 speedup 3.51
+etree(A): 0.0001 0.0000 speedup 5.81
+etree(A'): 0.0002 0.0000 speedup 5.67
+after amd:
+etree(A): 0.0001 0.0000 speedup 5.95
+etree(A'): 0.0001 0.0000 speedup 5.04
+
+ 873: Pothen/mesh1em1 nrow: 48 ncol: 48 nnz: 306
+etree(A,'col'): 0.0001 0.0000 speedup 4.88
+etree(A,'row'): 0.0001 0.0000 speedup 4.63
+etree(A): 0.0001 0.0000 speedup 6.00
+etree(A'): 0.0001 0.0000 speedup 3.67
+after amd:
+etree(A): 0.0001 0.0000 speedup 6.53
+etree(A'): 0.0001 0.0000 speedup 5.12
+
+ 874: Pothen/mesh1em6 nrow: 48 ncol: 48 nnz: 306
+etree(A,'col'): 0.0001 0.0000 speedup 5.16
+etree(A,'row'): 0.0001 0.0000 speedup 4.53
+etree(A): 0.0001 0.0000 speedup 6.00
+etree(A'): 0.0001 0.0000 speedup 4.25
+after amd:
+etree(A): 0.0001 0.0000 speedup 6.26
+etree(A'): 0.0001 0.0000 speedup 5.00
+test12 passed
+=================================================================
+test13: test cholmod2 and MATLAB on large tridiagonal matrices
+n 10000 cholmod2 0.01 err 3.5e-13
+n 10000 matlab 0.00 err 2.6e-13
+n 10000 cholmod2 0.01 err 3.6e-13
+n 10000 matlab 0.00 err 2.6e-13
+n 100000 cholmod2 0.14 err 3.6e-12
+n 100000 matlab 0.01 err 2.6e-12
+n 1000000 cholmod2 2.84 err 3.6e-11
+n 1000000 matlab 0.18 err 2.6e-11
+=================================================================
+test14: test metis, symbfact2, and etree2
+904:
+
+Prob =
+
+ title: 'DNA electrophoresis, 3 monomers in polymer. A. van Heukelum, Utrecht U.'
+ A: [5x5 double]
+ name: 'vanHeukelum/cage3'
+ id: 904
+ date: '2003'
+ author: 'A. van Heukelum'
+ ed: 'T. Davis'
+ kind: 'directed weighted graph'
+
+nnz(A) 19
+nnz(S) 19
+nnz(A*A') 25
+nnz(A'*A) 25
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+449:
+
+Prob =
+
+ title: 'Unsymmetric Matrix b1_ss, F. Grund, Dec 1994.'
+ A: [7x7 double]
+ b: [7x1 double]
+ name: 'Grund/b1_ss'
+ id: 449
+ date: '1997'
+ author: 'F. Grund'
+ ed: 'F. Grund'
+ kind: 'chemical process simulation problem'
+
+nnz(A) 15
+nnz(S) 24
+nnz(A*A') 25
+nnz(A'*A) 25
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+185:
+
+Prob =
+
+ title: 'U JOHN G. LEWIS P4 COUNTEREXAMPLE WHICH REQUIRES FILL IN SPIKES'
+ A: [9x9 double]
+ name: 'HB/jgl009'
+ id: 185
+ date: '1983'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'counter-example problem'
+
+nnz(A) 50
+nnz(S) 72
+nnz(A*A') 81
+nnz(A'*A) 81
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+905:
+
+Prob =
+
+ title: 'DNA electrophoresis, 4 monomers in polymer. A. van Heukelum, Utrecht U.'
+ A: [9x9 double]
+ name: 'vanHeukelum/cage4'
+ id: 905
+ date: '2003'
+ author: 'A. van Heukelum'
+ ed: 'T. Davis'
+ kind: 'directed weighted graph'
+
+nnz(A) 49
+nnz(S) 49
+nnz(A*A') 81
+nnz(A'*A) 81
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+238:
+
+Prob =
+
+ title: 'S EXAMPLE TO DEMONSTRATE THE CHIMNEY EFFECT IN P4 - BY R.G. GRIMES'
+ A: [10x10 double]
+ name: 'HB/rgg010'
+ id: 238
+ date: '1983'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'counter-example problem'
+
+nnz(A) 76
+nnz(S) 100
+nnz(A*A') 100
+nnz(A'*A) 100
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1524:
+
+Prob =
+
+ name: 'Pajek/Stranke94'
+ title: 'Pajek network: Slovene Parliamentary Parties 1994'
+ A: [10x10 double]
+ id: 1524
+ kind: 'undirected weighted graph'
+ notes: [22x78 char]
+ aux: [1x1 struct]
+ date: '1994'
+ author: 'V. Batagelj'
+ ed: 'V. Batagelj'
+
+nnz(A) 90
+nnz(S) 90
+nnz(A*A') 100
+nnz(A'*A) 100
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+186:
+
+Prob =
+
+ title: 'U JOHN G. LEWIS P4 COUNTEREXAMPLE WHICH REQUIRES FILL IN SPIKES'
+ A: [11x11 double]
+ name: 'HB/jgl011'
+ id: 186
+ date: '1983'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'counter-example problem'
+
+nnz(A) 76
+nnz(S) 108
+nnz(A*A') 115
+nnz(A'*A) 121
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1525:
+
+Prob =
+
+ name: 'Pajek/Tina_AskCal'
+ title: 'Pajek network: student govt, Univ. Ljubljana, 1992 (ask opin., recall)'
+ A: [11x11 double]
+ id: 1525
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1992'
+ author: 'V. Batagelj'
+ ed: 'V. Batagelj'
+
+nnz(A) 29
+nnz(S) 50
+nnz(A*A') 85
+nnz(A'*A) 58
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1526:
+
+Prob =
+
+ name: 'Pajek/Tina_AskCog'
+ title: 'Pajek network: student govt, Univ. Ljubljana, 1992 (ask, recognized)'
+ A: [11x11 double]
+ id: 1526
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1992'
+ author: 'V. Batagelj'
+ ed: 'V. Batagelj'
+
+nnz(A) 36
+nnz(S) 54
+nnz(A*A') 95
+nnz(A'*A) 75
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1527:
+
+Prob =
+
+ name: 'Pajek/Tina_DisCal'
+ title: 'Pajek network: student govt, Univ. Ljubljana, 1992 (discuss, recall)'
+ A: [11x11 double]
+ id: 1527
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1992'
+ author: 'V. Batagelj'
+ ed: 'V. Batagelj'
+
+nnz(A) 41
+nnz(S) 64
+nnz(A*A') 103
+nnz(A'*A) 76
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1528:
+
+Prob =
+
+ name: 'Pajek/Tina_DisCog'
+ title: 'Pajek network: student govt, Univ. Ljubljana, 1992 (discuss, recog.)'
+ A: [11x11 double]
+ id: 1528
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1992'
+ author: 'V. Batagelj'
+ ed: 'V. Batagelj'
+
+nnz(A) 48
+nnz(S) 72
+nnz(A*A') 109
+nnz(A'*A) 97
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+719:
+
+Prob =
+
+ title: 'Netlib LP problem itest2: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lpi_itest2'
+ A: [9x13 double]
+ b: [9x1 double]
+ id: 719
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: '1991'
+ author: 'J. Chinneck, E. Dravnieks'
+ ed: 'J. Chinneck'
+ notes: [33x76 char]
+
+nnz(A) 26
+nnz(S) 9
+nnz(A*A') 9
+nnz(A'*A) 9
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+715:
+
+Prob =
+
+ title: 'Netlib LP problem galenet: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lpi_galenet'
+ A: [8x14 double]
+ b: [8x1 double]
+ id: 715
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: ''
+ author: 'H. Greenberg'
+ ed: 'J. Chinneck'
+ notes: [19x76 char]
+
+nnz(A) 22
+nnz(S) 17
+nnz(A*A') 11
+nnz(A'*A) 14
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1440:
+
+Prob =
+
+ name: 'Oberwolfach/LFAT5'
+ title: 'Oberwolfach: linear 1D beam'
+ A: [14x14 double]
+ id: 1440
+ notes: 'Primary matrix in this model reduction problem is the Oberwolfach K matrix'
+ aux: [1x1 struct]
+ date: '2004'
+ author: 'J. Lienemann, A. Greiner, J. Korvink'
+ ed: 'E. Rudnyi'
+ kind: 'model reduction problem'
+
+nnz(A) 46
+nnz(S) 46
+nnz(A*A') 72
+nnz(A'*A) 72
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1817:
+
+Prob =
+
+ name: 'Meszaros/kleemin'
+ title: 'LP sequence: kleemin3, 4, 5, 6, 7, 8'
+ id: 1817
+ kind: 'linear programming problem sequence'
+ date: '2004'
+ author: ''
+ ed: 'C. Meszaros'
+ A: [8x16 double]
+ notes: [3x57 char]
+ aux: [1x1 struct]
+
+nnz(A) 44
+nnz(S) 8
+nnz(A*A') 8
+nnz(A'*A) 8
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+720:
+
+Prob =
+
+ title: 'Netlib LP problem itest6: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lpi_itest6'
+ A: [11x17 double]
+ b: [11x1 double]
+ id: 720
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: '1991'
+ author: 'J. Chinneck, E. Dravnieks'
+ ed: 'J. Chinneck'
+ notes: [33x76 char]
+
+nnz(A) 29
+nnz(S) 19
+nnz(A*A') 31
+nnz(A'*A) 19
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1710:
+
+Prob =
+
+ name: 'Meszaros/farm'
+ title: 'linear programming problem, C. Meszaros test set'
+ id: 1710
+ kind: 'linear programming problem'
+ date: '2004'
+ author: ''
+ ed: 'C. Meszaros'
+ A: [7x17 double]
+ b: [7x1 double]
+ aux: [1x1 struct]
+ notes: [3x57 char]
+
+nnz(A) 41
+nnz(S) 21
+nnz(A*A') 18
+nnz(A'*A) 21
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1438:
+
+Prob =
+
+ name: 'Oberwolfach/LF10'
+ title: 'Oberwolfach: linear 1D beam'
+ A: [18x18 double]
+ id: 1438
+ notes: 'Primary matrix in this model reduction problem is the Oberwolfach K matrix'
+ aux: [1x1 struct]
+ date: '2004'
+ author: 'J. Lienemann, A. Greiner, J. Korvink'
+ ed: 'E. Rudnyi'
+ kind: 'model reduction problem'
+
+nnz(A) 82
+nnz(S) 82
+nnz(A*A') 154
+nnz(A'*A) 154
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1479:
+
+Prob =
+
+ name: 'Pajek/GD01_b'
+ title: 'Pajek network: Graph Drawing contest 2001'
+ A: [18x18 double]
+ id: 1479
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '2001'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 37
+nnz(S) 54
+nnz(A*A') 62
+nnz(A'*A) 56
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1481:
+
+Prob =
+
+ name: 'Pajek/GD02_a'
+ title: 'Pajek network: Graph Drawing contest 2002'
+ A: [23x23 double]
+ id: 1481
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '2002'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 87
+nnz(S) 118
+nnz(A*A') 272
+nnz(A'*A) 376
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1516:
+
+Prob =
+
+ name: 'Pajek/Ragusa18'
+ title: 'Pajek network: Ragusa set'
+ A: [23x23 double]
+ id: 1516
+ kind: 'directed weighted graph'
+ notes: [5x78 char]
+ aux: [1x1 struct]
+ date: '2006'
+ author: 'V. Batagelj'
+ ed: 'V. Batagelj'
+
+nnz(A) 64
+nnz(S) 105
+nnz(A*A') 263
+nnz(A'*A) 158
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+97:
+
+Prob =
+
+ title: 'SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.'
+ A: [24x24 double]
+ name: 'HB/can_24'
+ id: 97
+ date: '1981'
+ author: 'L. Marro'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 160
+nnz(S) 160
+nnz(A*A') 336
+nnz(A'*A) 336
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1515:
+
+Prob =
+
+ name: 'Pajek/Ragusa16'
+ title: 'Pajek network: Ragusa set'
+ A: [24x24 double]
+ id: 1515
+ kind: 'directed weighted graph'
+ notes: [5x78 char]
+ aux: [1x1 struct]
+ date: '2006'
+ author: 'V. Batagelj'
+ ed: 'V. Batagelj'
+
+nnz(A) 81
+nnz(S) 126
+nnz(A*A') 271
+nnz(A'*A) 250
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1177:
+
+Prob =
+
+ title: 'FINITE ELEMENT PROBLEM. LAPLACIAN ON A 5 BY 5 GRID.'
+ A: [25x25 double]
+ name: 'HB/lap_25'
+ id: 1177
+ date: '1980'
+ author: 'I. Duff'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 169
+nnz(S) 169
+nnz(A*A') 361
+nnz(A'*A) 361
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+436:
+
+Prob =
+
+ title: ' TEST MATRIX FROM FIDAP: EX5.MAT'
+ A: [27x27 double]
+ name: 'FIDAP/ex5'
+ id: 436
+ date: '1994'
+ author: 'A. Baggag, Y. Saad'
+ ed: 'A. Baggag, Y. Saad'
+ kind: 'computational fluid dynamics problem'
+
+nnz(A) 279
+nnz(S) 279
+nnz(A*A') 495
+nnz(A'*A) 495
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+232:
+
+Prob =
+
+ title: 'UNSYMMETRIC MATRIX FROM PORES'
+ A: [30x30 double]
+ name: 'HB/pores_1'
+ id: 232
+ date: '1980'
+ author: 'J. Appleyard'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'computational fluid dynamics problem'
+
+nnz(A) 180
+nnz(S) 236
+nnz(A*A') 476
+nnz(A'*A) 388
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+168:
+
+Prob =
+
+ title: 'UNSYMMETRIC PATTERN ON LEAFLET ADVERTISING IBM 1971 CONFERENCE'
+ A: [32x32 double]
+ name: 'HB/ibm32'
+ id: 168
+ date: '1971'
+ author: 'IBM'
+ ed: 'A. Curtis, I. Duff, J. Reid'
+ kind: 'directed graph'
+
+nnz(A) 126
+nnz(S) 212
+nnz(A*A') 392
+nnz(A'*A) 390
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1199:
+
+Prob =
+
+ name: 'Hamrle/Hamrle1'
+ title: 'Hamrle/Hamrle1 circuit simulation matrix'
+ A: [32x32 double]
+ b: [32x1 double]
+ id: 1199
+ date: '2004'
+ author: 'J. Hamrle'
+ ed: 'T. Davis'
+ kind: 'circuit simulation problem'
+
+nnz(A) 98
+nnz(S) 185
+nnz(A*A') 222
+nnz(A'*A) 220
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1480:
+
+Prob =
+
+ name: 'Pajek/GD01_c'
+ title: 'Pajek network: Graph Drawing contest 2001'
+ A: [33x33 double]
+ id: 1480
+ kind: 'directed multigraph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '2001'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 135
+nnz(S) 270
+nnz(A*A') 312
+nnz(A'*A) 374
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1474:
+
+Prob =
+
+ name: 'Pajek/football'
+ title: 'Pajek network: World Soccer, Paris 1998'
+ A: [35x35 double]
+ id: 1474
+ kind: 'directed weighted graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1998'
+ author: 'L. Krempel'
+ ed: 'V. Batagelj'
+
+nnz(A) 118
+nnz(S) 236
+nnz(A*A') 568
+nnz(A'*A) 234
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1485:
+
+Prob =
+
+ name: 'Pajek/GD95_a'
+ title: 'Pajek network: Graph Drawing contest 1995'
+ A: [36x36 double]
+ id: 1485
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1995'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 57
+nnz(S) 112
+nnz(A*A') 80
+nnz(A'*A) 101
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+906:
+
+Prob =
+
+ title: 'DNA electrophoresis, 5 monomers in polymer. A. van Heukelum, Utrecht U.'
+ A: [37x37 double]
+ name: 'vanHeukelum/cage5'
+ id: 906
+ date: '2003'
+ author: 'A. van Heukelum'
+ ed: 'T. Davis'
+ kind: 'directed weighted graph'
+
+nnz(A) 233
+nnz(S) 233
+nnz(A*A') 653
+nnz(A'*A) 653
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1495:
+
+Prob =
+
+ name: 'Pajek/GD98_a'
+ title: 'Pajek network: Graph Drawing contest 1998'
+ A: [38x38 double]
+ id: 1495
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1998'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 50
+nnz(S) 92
+nnz(A*A') 78
+nnz(A'*A) 241
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+13:
+
+Prob =
+
+ title: 'SYMMETRIC STRUCTURE (STANDARD TEST POWER SYSTEM - NEW ENGLAND)'
+ A: [39x39 double]
+ name: 'HB/bcspwr01'
+ id: 13
+ date: '1981'
+ author: 'B. Dembart, J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'power network problem'
+
+nnz(A) 131
+nnz(S) 131
+nnz(A*A') 275
+nnz(A'*A) 275
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+706:
+
+Prob =
+
+ title: 'Netlib LP problem bgprtr: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lpi_bgprtr'
+ A: [20x40 double]
+ b: [20x1 double]
+ id: 706
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: '1993'
+ author: 'L. Schrage'
+ ed: 'J. Chinneck'
+ notes: [23x76 char]
+
+nnz(A) 70
+nnz(S) 52
+nnz(A*A') 37
+nnz(A'*A) 44
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1755:
+
+Prob =
+
+ name: 'Meszaros/problem'
+ title: 'linear programming problem, C. Meszaros test set'
+ id: 1755
+ kind: 'linear programming problem'
+ date: '2004'
+ author: ''
+ ed: 'C. Meszaros'
+ A: [12x46 double]
+ b: [12x1 double]
+ aux: [1x1 struct]
+ notes: [3x57 char]
+
+nnz(A) 86
+nnz(S) 44
+nnz(A*A') 14
+nnz(A'*A) 80
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1493:
+
+Prob =
+
+ name: 'Pajek/GD97_b'
+ title: 'Pajek network: Graph Drawing contest 1997'
+ A: [47x47 double]
+ id: 1493
+ kind: 'undirected weighted graph'
+ notes: [12x78 char]
+ aux: [1x1 struct]
+ date: '1997'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 264
+nnz(S) 264
+nnz(A*A') 1274
+nnz(A'*A) 1274
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+23:
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM'
+ A: [48x48 double]
+ name: 'HB/bcsstk01'
+ id: 23
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 400
+nnz(S) 400
+nnz(A*A') 1292
+nnz(A'*A) 1292
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+56:
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX SMALL GENERALIZED EIGENVALUE PROBLEM, B MATRIX'
+ A: [48x48 double]
+ Zeros: [48x48 double]
+ name: 'HB/bcsstm01'
+ id: 56
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 24
+nnz(S) 24
+nnz(A*A') 24
+nnz(A'*A) 24
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+872:
+
+Prob =
+
+ A: [48x48 double]
+ title: 'mesh1e1, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/mesh1e1'
+ id: 872
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+nnz(A) 306
+nnz(S) 306
+nnz(A*A') 772
+nnz(A'*A) 772
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+873:
+
+Prob =
+
+ A: [48x48 double]
+ title: 'mesh1em1, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/mesh1em1'
+ id: 873
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+nnz(A) 306
+nnz(S) 306
+nnz(A*A') 772
+nnz(A'*A) 772
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+874:
+
+Prob =
+
+ A: [48x48 double]
+ title: 'mesh1em6, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/mesh1em6'
+ id: 874
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+nnz(A) 306
+nnz(S) 306
+nnz(A*A') 772
+nnz(A'*A) 772
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1741:
+
+Prob =
+
+ name: 'Meszaros/p0033'
+ title: 'linear programming problem, C. Meszaros test set'
+ id: 1741
+ kind: 'linear programming problem'
+ date: '2004'
+ author: ''
+ ed: 'C. Meszaros'
+ A: [15x48 double]
+ b: [15x1 double]
+ aux: [1x1 struct]
+ notes: [3x57 char]
+
+nnz(A) 113
+nnz(S) 15
+nnz(A*A') 15
+nnz(A'*A) 15
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+14:
+
+Prob =
+
+ title: 'SYMMETRIC STRUCTURE OF A SMALL TEST POWER SYSTEM'
+ A: [49x49 double]
+ name: 'HB/bcspwr02'
+ id: 14
+ date: '1981'
+ author: 'B. Dembart, J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'power network problem'
+
+nnz(A) 167
+nnz(S) 167
+nnz(A*A') 403
+nnz(A'*A) 403
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1460:
+
+Prob =
+
+ name: 'Pajek/divorce'
+ title: 'Pajek network: divorce laws in the 50 US states'
+ A: [50x9 double]
+ id: 1460
+ kind: 'bipartite graph'
+ notes: [6x78 char]
+ aux: [1x1 struct]
+ date: '2006'
+ author: ''
+ ed: 'V. Batagelj'
+
+nnz(A) 225
+nnz(S) 57
+nnz(A*A') 77
+nnz(A'*A) 81
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+597:
+
+Prob =
+
+ title: 'Netlib LP problem afiro: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lp_afiro'
+ A: [27x51 double]
+ b: [27x1 double]
+ id: 597
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: ''
+ author: 'M. Saunders'
+ ed: 'D. Gay'
+ notes: [48x78 char]
+
+nnz(A) 102
+nnz(S) 88
+nnz(A*A') 71
+nnz(A'*A) 73
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+464:
+
+Prob =
+
+ title: 'Unsymmetric Matrix d_ss, F. Grund, Dec 1994.'
+ A: [53x53 double]
+ Zeros: [53x53 double]
+ b: [53x1 double]
+ name: 'Grund/d_ss'
+ id: 464
+ date: '1997'
+ author: 'F. Grund'
+ ed: 'F. Grund'
+ kind: 'chemical process simulation problem'
+
+nnz(A) 144
+nnz(S) 278
+nnz(A*A') 311
+nnz(A'*A) 315
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+109:
+
+Prob =
+
+ title: 'UNSYMMETRIC PATTERN OF CURTIS, 1971'
+ A: [54x54 double]
+ name: 'HB/curtis54'
+ id: 109
+ date: '1971'
+ author: 'A. Curtis'
+ ed: 'A. Curtis, I. Duff, J. Reid'
+ kind: '2D/3D problem'
+
+nnz(A) 291
+nnz(S) 302
+nnz(A*A') 794
+nnz(A'*A) 728
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1457:
+
+Prob =
+
+ name: 'Pajek/Cities'
+ title: 'Pajek network: www.lboro.ac.uk/gawc, data set 6'
+ A: [55x46 double]
+ id: 1457
+ kind: 'weighted bipartite graph'
+ notes: [10x78 char]
+ aux: [1x1 struct]
+ date: '2001'
+ author: 'P. Taylor, D. Walker'
+ ed: 'V. Batagelj'
+
+nnz(A) 1342
+nnz(S) 1626
+nnz(A*A') 2116
+nnz(A'*A) 2114
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+274:
+
+Prob =
+
+ title: 'UNSYMMETRIC PATTERN OF ORDER 57 GIVEN BY WILLOUGHBY IN REID, 1970'
+ A: [57x57 double]
+ name: 'HB/will57'
+ id: 274
+ date: '1970'
+ author: 'R. Willoughby'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'semiconductor device problem'
+
+nnz(A) 281
+nnz(S) 311
+nnz(A*A') 647
+nnz(A'*A) 665
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+129:
+
+Prob =
+
+ title: 'SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON'
+ A: [59x59 double]
+ name: 'HB/dwt_59'
+ id: 129
+ date: '1980'
+ author: 'G. Everstine, D. Taylor'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 267
+nnz(S) 267
+nnz(A*A') 571
+nnz(A'*A) 571
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+172:
+
+Prob =
+
+ title: 'UNSYMMETRIC MATRIX - CAVETT'S PROCESS (CHEM ENG),1982'
+ A: [59x59 double]
+ Zeros: [59x59 double]
+ name: 'HB/impcol_b'
+ id: 172
+ date: '1982'
+ author: 'D. Bogle'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'chemical process simulation problem'
+
+nnz(A) 271
+nnz(S) 497
+nnz(A*A') 783
+nnz(A'*A) 627
+metis (S):
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+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+102:
+
+Prob =
+
+ title: 'SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.'
+ A: [61x61 double]
+ name: 'HB/can_61'
+ id: 102
+ date: '1981'
+ author: 'L. Marro'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 557
+nnz(S) 557
+nnz(A*A') 1793
+nnz(A'*A) 1793
+metis (S):
+metis (A,row):
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+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+103:
+
+Prob =
+
+ title: 'SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.'
+ A: [62x62 double]
+ name: 'HB/can_62'
+ id: 103
+ date: '1981'
+ author: 'L. Marro'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 218
+nnz(S) 218
+nnz(A*A') 482
+nnz(A'*A) 482
+metis (S):
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+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+293:
+
+Prob =
+
+ title: 'BOUNDED FINLINE WAVEGUIDE EIGENMODES B SHULTZ AND S GEDNEY'
+ A: [62x62 double]
+ name: 'Bai/bfwa62'
+ id: 293
+ date: '1994'
+ author: 'B. Schultz, S. Gedney'
+ ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra'
+ kind: 'electromagnetics problem'
+
+nnz(A) 450
+nnz(S) 462
+nnz(A*A') 1306
+nnz(A'*A) 1340
+metis (S):
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+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+296:
+
+Prob =
+
+ title: 'BOUNDED FINLINE WAVEGUIDE EIGENMODES B SHULTZ AND S GEDNEY'
+ A: [62x62 double]
+ name: 'Bai/bfwb62'
+ id: 296
+ date: '1994'
+ author: 'B. Schultz, S. Gedney'
+ ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra'
+ kind: 'electromagnetics problem'
+
+nnz(A) 342
+nnz(S) 342
+nnz(A*A') 992
+nnz(A'*A) 992
+metis (S):
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+turning off postorder:
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+metis (A,col):
+analyzing results:
+1487:
+
+Prob =
+
+ name: 'Pajek/GD95_c'
+ title: 'Pajek network: Graph Drawing contest 1995'
+ A: [62x62 double]
+ id: 1487
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1995'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 287
+nnz(S) 288
+nnz(A*A') 998
+nnz(A'*A) 996
+metis (S):
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+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1759:
+
+Prob =
+
+ name: 'Meszaros/refine'
+ title: 'linear programming problem, C. Meszaros test set'
+ id: 1759
+ kind: 'linear programming problem'
+ date: '2004'
+ author: ''
+ ed: 'C. Meszaros'
+ A: [29x62 double]
+ b: [29x1 double]
+ aux: [1x1 struct]
+ notes: [3x57 char]
+
+nnz(A) 153
+nnz(S) 29
+nnz(A*A') 29
+nnz(A'*A) 29
+metis (S):
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+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1742:
+
+Prob =
+
+ name: 'Meszaros/p0040'
+ title: 'linear programming problem, C. Meszaros test set'
+ id: 1742
+ kind: 'linear programming problem'
+ date: '2004'
+ author: ''
+ ed: 'C. Meszaros'
+ A: [23x63 double]
+ b: [23x1 double]
+ aux: [1x1 struct]
+ notes: [3x57 char]
+
+nnz(A) 133
+nnz(S) 23
+nnz(A*A') 23
+nnz(A'*A) 23
+metis (S):
+metis (A,row):
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+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1498:
+
+Prob =
+
+ name: 'Pajek/GD99_b'
+ title: 'Pajek network: Graph Drawing contest 1999'
+ A: [64x64 double]
+ id: 1498
+ kind: 'undirected multigraph'
+ notes: [5x78 char]
+ aux: [1x1 struct]
+ date: '1999'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 252
+nnz(S) 252
+nnz(A*A') 668
+nnz(A'*A) 668
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1490:
+
+Prob =
+
+ name: 'Pajek/GD96_c'
+ title: 'Pajek network: Graph Drawing contest 1996'
+ A: [65x65 double]
+ id: 1490
+ kind: 'undirected graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1996'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 250
+nnz(S) 250
+nnz(A*A') 695
+nnz(A'*A) 695
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+24:
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED'
+ A: [66x66 double]
+ name: 'HB/bcsstk02'
+ id: 24
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 4356
+nnz(S) 4356
+nnz(A*A') 4356
+nnz(A'*A) 4356
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+57:
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX, SMALL OIL RIG, STATICALLY CONDENSED'
+ A: [66x66 double]
+ name: 'HB/bcsstm02'
+ id: 57
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 66
+nnz(S) 66
+nnz(A*A') 66
+nnz(A'*A) 66
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+132:
+
+Prob =
+
+ title: 'SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON'
+ A: [66x66 double]
+ name: 'HB/dwt_66'
+ id: 132
+ date: '1980'
+ author: 'G. Everstine, D. Taylor'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 320
+nnz(S) 320
+nnz(A*A') 576
+nnz(A'*A) 576
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+883:
+
+Prob =
+
+ A: [66x66 double]
+ title: 'sphere2, with coordinates. From NASA, collected by Alex Pothen'
+ name: 'Pothen/sphere2'
+ id: 883
+ aux: [1x1 struct]
+ date: '2003'
+ author: 'NASA'
+ ed: 'G. Kumfert, A. Pothen'
+ kind: 'structural problem'
+
+nnz(A) 450
+nnz(S) 450
+nnz(A*A') 1170
+nnz(A'*A) 1170
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+262:
+
+Prob =
+
+ title: 'U CAVETT PROBLEM WITH 5 COMPONENTS ( CHEM. ENG. FROM WESTERBERG )'
+ A: [67x67 double]
+ name: 'HB/west0067'
+ id: 262
+ date: '1983'
+ author: 'A. Westerberg'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'chemical process simulation problem'
+
+nnz(A) 294
+nnz(S) 576
+nnz(A*A') 1041
+nnz(A'*A) 889
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+636:
+
+Prob =
+
+ title: 'Netlib LP problem kb2: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lp_kb2'
+ A: [43x68 double]
+ b: [43x1 double]
+ id: 636
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: '1989'
+ author: 'J. Tomlin'
+ ed: 'D. Gay'
+ notes: [39x74 char]
+
+nnz(A) 313
+nnz(S) 318
+nnz(A*A') 513
+nnz(A'*A) 355
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+133:
+
+Prob =
+
+ title: 'SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON'
+ A: [72x72 double]
+ name: 'HB/dwt_72'
+ id: 133
+ date: '1980'
+ author: 'G. Everstine, D. Taylor'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 222
+nnz(S) 222
+nnz(A*A') 412
+nnz(A'*A) 412
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1501:
+
+Prob =
+
+ name: 'Pajek/GlossGT'
+ title: 'Pajek network: graph and digraph glossary'
+ A: [72x72 double]
+ id: 1501
+ kind: 'directed graph'
+ notes: [10x78 char]
+ aux: [1x1 struct]
+ date: '2001'
+ author: 'W. Cherowitzo'
+ ed: 'V. Batagelj'
+
+nnz(A) 122
+nnz(S) 236
+nnz(A*A') 798
+nnz(A'*A) 161
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+106:
+
+Prob =
+
+ title: 'SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.'
+ A: [73x73 double]
+ name: 'HB/can_73'
+ id: 106
+ date: '1981'
+ author: 'L. Marro'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 377
+nnz(S) 377
+nnz(A*A') 1377
+nnz(A'*A) 1377
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1486:
+
+Prob =
+
+ name: 'Pajek/GD95_b'
+ title: 'Pajek network: Graph Drawing contest 1995'
+ A: [73x73 double]
+ id: 1486
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1995'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 96
+nnz(S) 191
+nnz(A*A') 148
+nnz(A'*A) 875
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+666:
+
+Prob =
+
+ title: 'Netlib LP problem sc50a: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lp_sc50a'
+ A: [50x78 double]
+ b: [50x1 double]
+ id: 666
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: '1989'
+ author: 'N. Gould'
+ ed: 'D. Gay'
+ notes: [30x74 char]
+
+nnz(A) 160
+nnz(S) 163
+nnz(A*A') 136
+nnz(A'*A) 174
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+667:
+
+Prob =
+
+ title: 'Netlib LP problem sc50b: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lp_sc50b'
+ A: [50x78 double]
+ b: [50x1 double]
+ id: 667
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: '1989'
+ author: 'N. Gould'
+ ed: 'D. Gay'
+ notes: [30x74 char]
+
+nnz(A) 148
+nnz(S) 155
+nnz(A*A') 132
+nnz(A'*A) 162
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+253:
+
+Prob =
+
+ title: 'UNSYMMETRIC - 1D STEAM MODEL OF OIL RES. - 20 POINTS - 4 DOF MAY 1983'
+ A: [80x80 double]
+ Zeros: [80x80 double]
+ name: 'HB/steam3'
+ id: 253
+ date: '1983'
+ author: 'R. Grimes'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'computational fluid dynamics problem'
+
+nnz(A) 314
+nnz(S) 392
+nnz(A*A') 688
+nnz(A'*A) 768
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1482:
+
+Prob =
+
+ name: 'Pajek/GD02_b'
+ title: 'Pajek network: Graph Drawing contest 2002'
+ A: [80x80 double]
+ id: 1482
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '2002'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 232
+nnz(S) 464
+nnz(A*A') 570
+nnz(A'*A) 630
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1492:
+
+Prob =
+
+ name: 'Pajek/GD97_a'
+ title: 'Pajek network: Graph Drawing contest 1997'
+ A: [84x84 double]
+ id: 1492
+ kind: 'directed graph'
+ notes: [5x78 char]
+ aux: [1x1 struct]
+ date: '1997'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 332
+nnz(S) 332
+nnz(A*A') 860
+nnz(A'*A) 860
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+11:
+
+Prob =
+
+ title: 'SYMMETRIC PATTERN OF NORMAL MATRIX OF HOLLAND SURVEY. ASHKENAZI, 1974'
+ A: [85x85 double]
+ name: 'HB/ash85'
+ id: 11
+ date: '1974'
+ author: 'V. Askenazi'
+ ed: 'A. Curtis, I. Duff, J. Reid'
+ kind: 'least squares problem'
+
+nnz(A) 523
+nnz(S) 523
+nnz(A*A') 1317
+nnz(A'*A) 1317
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1519:
+
+Prob =
+
+ name: 'Pajek/Sandi_authors'
+ title: 'Pajek network: Klavzar bibliography'
+ A: [86x86 double]
+ id: 1519
+ kind: 'undirected weighted graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1999'
+ author: 'I. Klavzar'
+ ed: 'V. Batagelj'
+
+nnz(A) 248
+nnz(S) 248
+nnz(A*A') 908
+nnz(A'*A) 908
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+136:
+
+Prob =
+
+ title: 'SYMMETRIC CONNECTION TABLE FROM DTNSRDC, WASHINGTON'
+ A: [87x87 double]
+ name: 'HB/dwt_87'
+ id: 136
+ date: '1980'
+ author: 'G. Everstine, D. Taylor'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 541
+nnz(S) 541
+nnz(A*A') 1539
+nnz(A'*A) 1539
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+462:
+
+Prob =
+
+ title: 'Unsymmetric Matrix d_dyn, F. Grund, Dec 1994.'
+ A: [87x87 double]
+ Zeros: [87x87 double]
+ b: [87x1 double]
+ name: 'Grund/d_dyn'
+ id: 462
+ date: '1997'
+ author: 'F. Grund'
+ ed: 'F. Grund'
+ kind: 'chemical process simulation problem'
+
+nnz(A) 230
+nnz(S) 438
+nnz(A*A') 497
+nnz(A'*A) 525
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+463:
+
+Prob =
+
+ title: 'Unsymmetric Matrix d_dyn1, F. Grund, Oct 1995.'
+ A: [87x87 double]
+ Zeros: [87x87 double]
+ name: 'Grund/d_dyn1'
+ id: 463
+ date: '1997'
+ author: 'F. Grund'
+ ed: 'F. Grund'
+ kind: 'chemical process simulation problem'
+
+nnz(A) 232
+nnz(S) 442
+nnz(A*A') 503
+nnz(A'*A) 535
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+731:
+
+Prob =
+
+ title: 'Netlib LP problem woodinfe: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lpi_woodinfe'
+ A: [35x89 double]
+ b: [35x1 double]
+ id: 731
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: '1989'
+ author: 'H. Greenberg'
+ ed: 'J. Chinneck'
+ notes: [35x76 char]
+
+nnz(A) 140
+nnz(S) 67
+nnz(A*A') 32
+nnz(A'*A) 41
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1641:
+
+Prob =
+
+ name: 'Bai/tols90'
+ title: 'TOLOSA MATRIX'
+ A: [90x90 double]
+ id: 1641
+ date: '1991'
+ author: 'S. Godet-Thobie'
+ ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra'
+ kind: 'computational fluid dynamics problem'
+
+nnz(A) 1746
+nnz(S) 2970
+nnz(A*A') 3204
+nnz(A'*A) 8100
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+907:
+
+Prob =
+
+ title: 'DNA electrophoresis, 6 monomers in polymer. A. van Heukelum, Utrecht U.'
+ A: [93x93 double]
+ name: 'vanHeukelum/cage6'
+ id: 907
+ date: '2003'
+ author: 'A. van Heukelum'
+ ed: 'T. Davis'
+ kind: 'directed weighted graph'
+
+nnz(A) 785
+nnz(S) 785
+nnz(A*A') 2849
+nnz(A'*A) 2849
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+108:
+
+Prob =
+
+ title: 'SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.'
+ A: [96x96 double]
+ name: 'HB/can_96'
+ id: 108
+ date: '1981'
+ author: 'L. Marro'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 768
+nnz(S) 768
+nnz(A*A') 1920
+nnz(A'*A) 1920
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+220:
+
+Prob =
+
+ title: 'SYMMETRIC MATRIX OF BEAM STRUCTURE, NOVEMBER 1982.'
+ A: [100x100 double]
+ name: 'HB/nos4'
+ id: 220
+ date: '1982'
+ author: 'H. Simon'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 594
+nnz(S) 594
+nnz(A*A') 1802
+nnz(A'*A) 1802
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+318:
+
+Prob =
+
+ title: 'OLMSTEAD FLOW MODEL'
+ A: [100x100 double]
+ name: 'Bai/olm100'
+ id: 318
+ date: '1994'
+ author: 'K. Meerbergen'
+ ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra'
+ kind: 'computational fluid dynamics problem'
+
+nnz(A) 396
+nnz(S) 494
+nnz(A*A') 590
+nnz(A'*A) 976
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+337:
+
+Prob =
+
+ title: 'TUBULAR REACTOR MODEL'
+ A: [100x100 double]
+ name: 'Bai/tub100'
+ id: 337
+ date: '1994'
+ author: 'K. Meerbergen, D. Roose'
+ ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra'
+ kind: 'computational fluid dynamics problem'
+
+nnz(A) 396
+nnz(S) 396
+nnz(A*A') 784
+nnz(A'*A) 784
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1326:
+
+Prob =
+
+ name: 'Morandini/rotor1'
+ title: 'Marco Morandini, small helicoptor rotor model'
+ A: [100x100 double]
+ id: 1326
+ date: '2006'
+ author: 'M. Morandini'
+ ed: 'T. Davis'
+ kind: 'structural problem'
+
+nnz(A) 708
+nnz(S) 1020
+nnz(A*A') 3346
+nnz(A'*A) 3634
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1484:
+
+Prob =
+
+ name: 'Pajek/GD06_theory'
+ title: 'Pajek network: Graph Drawing contest 2006'
+ A: [101x101 double]
+ id: 1484
+ kind: 'undirected graph'
+ notes: [9x78 char]
+ date: '2006'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 380
+nnz(S) 380
+nnz(A*A') 3341
+nnz(A'*A) 3341
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+861:
+
+Prob =
+
+ A: [102x102 double]
+ b: [102x3 double]
+ title: 'Spline toolbox. Pivot tol 0.1 fails, needs >= 0.26. MathWorks,Inc'
+ name: 'MathWorks/pivtol'
+ id: 861
+ date: '2002'
+ author: 'B. Cheng'
+ ed: 'T. Davis'
+ kind: 'statistical/mathematical problem'
+
+nnz(A) 306
+nnz(S) 308
+nnz(A*A') 510
+nnz(A'*A) 512
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+306:
+
+Prob =
+
+ title: 'CHUCK MATRIX (MULTIPLE EIGENVALUES) J. CULLUM'
+ A: [104x104 double]
+ name: 'Bai/ck104'
+ id: 306
+ date: '1986'
+ author: 'J. Cullum'
+ ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra'
+ kind: '2D/3D problem'
+
+nnz(A) 992
+nnz(S) 992
+nnz(A*A') 1712
+nnz(A'*A) 1712
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1499:
+
+Prob =
+
+ name: 'Pajek/GD99_c'
+ title: 'Pajek network: Graph Drawing contest 1999'
+ A: [105x105 double]
+ id: 1499
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1999'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 149
+nnz(S) 240
+nnz(A*A') 177
+nnz(A'*A) 352
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+721:
+
+Prob =
+
+ title: 'Netlib LP problem klein1: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lpi_klein1'
+ A: [54x108 double]
+ b: [54x1 double]
+ id: 721
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: ''
+ author: 'E. Klotz'
+ ed: 'J. Chinneck'
+ notes: [19x76 char]
+
+nnz(A) 750
+nnz(S) 54
+nnz(A*A') 54
+nnz(A'*A) 54
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1489:
+
+Prob =
+
+ name: 'Pajek/GD96_b'
+ title: 'Pajek network: Graph Drawing contest 1996'
+ A: [111x111 double]
+ id: 1489
+ kind: 'directed graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1996'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 193
+nnz(S) 386
+nnz(A*A') 3021
+nnz(A'*A) 100
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+25:
+
+Prob =
+
+ title: 'SYMMETRIC STIFFNESS MATRIX, SMALL TEST STRUCTURE'
+ A: [112x112 double]
+ name: 'HB/bcsstk03'
+ id: 25
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 640
+nnz(S) 640
+nnz(A*A') 1072
+nnz(A'*A) 1072
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+58:
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX, SMALL TEST STRUCTURE'
+ A: [112x112 double]
+ Zeros: [112x112 double]
+ name: 'HB/bcsstm03'
+ id: 58
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz(A) 72
+nnz(S) 72
+nnz(A*A') 72
+nnz(A'*A) 72
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+1497:
+
+Prob =
+
+ name: 'Pajek/GD98_c'
+ title: 'Pajek network: Graph Drawing contest 1998'
+ A: [112x112 double]
+ id: 1497
+ kind: 'undirected graph'
+ notes: [7x78 char]
+ aux: [1x1 struct]
+ date: '1998'
+ author: 'Graph Drawing Contest'
+ ed: 'V. Batagelj'
+
+nnz(A) 336
+nnz(S) 336
+nnz(A*A') 784
+nnz(A'*A) 784
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+158:
+
+Prob =
+
+ title: 'UNSYMMETRIC PATTERN SUPPLIED BY MORVEN GENTLEMAN, SUMMER 1973'
+ A: [113x113 double]
+ name: 'HB/gent113'
+ id: 158
+ date: '1973'
+ author: 'W. Gentleman'
+ ed: 'A. Curtis, I. Duff, J. Reid'
+ kind: 'statistical/mathematical problem'
+
+nnz(A) 655
+nnz(S) 1188
+nnz(A*A') 2683
+nnz(A'*A) 2351
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+603:
+
+Prob =
+
+ title: 'Netlib LP problem blend: minimize c'*x, where Ax=b, lo<=x<=hi'
+ name: 'LPnetlib/lp_blend'
+ A: [74x114 double]
+ b: [74x1 double]
+ id: 603
+ aux: [1x1 struct]
+ kind: 'linear programming problem'
+ date: '1989'
+ author: 'N. Gould'
+ ed: 'D. Gay'
+ notes: [36x76 char]
+
+nnz(A) 522
+nnz(S) 749
+nnz(A*A') 1319
+nnz(A'*A) 1062
+metis (S):
+metis (A,row):
+metis (A,col):
+turning off postorder:
+metis (S):
+metis (A,row):
+metis (A,col):
+analyzing results:
+test14 passed
+=================================================================
+Matrices to test: 100
+
+ 904: vanHeukelum/cage3 nrow: 5 ncol: 5 nnz: 19
+c=symbfact(A): 0.0003 0.0001 speedup 2.57 lnz 12
+R=symbfact(A): 0.0004 0.0002 speedup 2.66
+c=symbfact(A'): 0.0004 0.0001 speedup 2.89 lnz 12
+R=symbfact(A'): 0.0004 0.0002 speedup 2.77
+c=symbfact(A,'col'): 0.0004 0.0002 speedup 2.38 lnz 15
+R=symbfact(A,'col'): 0.0004 0.0002 speedup 2.86
+
+ 449: Grund/b1_ss nrow: 7 ncol: 7 nnz: 15
+c=symbfact(A): 0.0001 0.0000 speedup 6.25 lnz 13
+R=symbfact(A): 0.0001 0.0000 speedup 4.36
+c=symbfact(A'): 0.0001 0.0000 speedup 5.84 lnz 10
+R=symbfact(A'): 0.0001 0.0000 speedup 5.04
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.80 lnz 19
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.77
+
+ 185: HB/jgl009 nrow: 9 ncol: 9 nnz: 50
+c=symbfact(A): 0.0001 0.0000 speedup 5.61 lnz 23
+R=symbfact(A): 0.0001 0.0000 speedup 3.74
+c=symbfact(A'): 0.0001 0.0000 speedup 5.52 lnz 39
+R=symbfact(A'): 0.0003 0.0000 speedup 8.63
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.90 lnz 45
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.07
+
+ 905: vanHeukelum/cage4 nrow: 9 ncol: 9 nnz: 49
+c=symbfact(A): 0.0001 0.0000 speedup 5.94 lnz 36
+R=symbfact(A): 0.0001 0.0000 speedup 3.50
+c=symbfact(A'): 0.0001 0.0000 speedup 5.52 lnz 36
+R=symbfact(A'): 0.0001 0.0000 speedup 4.57
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.67 lnz 45
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.55
+
+ 238: HB/rgg010 nrow: 10 ncol: 10 nnz: 76
+c=symbfact(A): 0.0001 0.0000 speedup 5.37 lnz 31
+R=symbfact(A): 0.0001 0.0000 speedup 4.55
+c=symbfact(A'): 0.0001 0.0000 speedup 3.93 lnz 55
+R=symbfact(A'): 0.0001 0.0000 speedup 3.57
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.62 lnz 55
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.37
+
+1524: Pajek/Stranke94 nrow: 10 ncol: 10 nnz: 90
+c=symbfact(A): 0.0001 0.0000 speedup 5.37 lnz 55
+R=symbfact(A): 0.0001 0.0000 speedup 4.65
+c=symbfact(A'): 0.0002 0.0000 speedup 6.65 lnz 55
+R=symbfact(A'): 0.0001 0.0000 speedup 4.69
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.76 lnz 55
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.22
+
+ 186: HB/jgl011 nrow: 11 ncol: 11 nnz: 76
+c=symbfact(A): 0.0001 0.0000 speedup 5.72 lnz 31
+R=symbfact(A): 0.0001 0.0000 speedup 4.47
+c=symbfact(A'): 0.0001 0.0000 speedup 3.96 lnz 59
+R=symbfact(A'): 0.0001 0.0000 speedup 3.57
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.45 lnz 66
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.32
+
+1525: Pajek/Tina_AskCal nrow: 11 ncol: 11 nnz: 29
+c=symbfact(A): 0.0001 0.0000 speedup 5.44 lnz 33
+R=symbfact(A): 0.0001 0.0000 speedup 4.48
+c=symbfact(A'): 0.0001 0.0000 speedup 5.65 lnz 25
+R=symbfact(A'): 0.0001 0.0000 speedup 5.04
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.62 lnz 35
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.21
+
+1526: Pajek/Tina_AskCog nrow: 11 ncol: 11 nnz: 36
+c=symbfact(A): 0.0001 0.0000 speedup 5.61 lnz 36
+R=symbfact(A): 0.0001 0.0000 speedup 3.69
+c=symbfact(A'): 0.0001 0.0000 speedup 5.36 lnz 35
+R=symbfact(A'): 0.0001 0.0000 speedup 4.36
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.50 lnz 44
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.23
+
+1527: Pajek/Tina_DisCal nrow: 11 ncol: 11 nnz: 41
+c=symbfact(A): 0.0001 0.0000 speedup 5.61 lnz 47
+R=symbfact(A): 0.0001 0.0000 speedup 4.32
+c=symbfact(A'): 0.0001 0.0000 speedup 5.36 lnz 34
+R=symbfact(A'): 0.0001 0.0000 speedup 4.54
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.71 lnz 46
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.33
+
+1528: Pajek/Tina_DisCog nrow: 11 ncol: 11 nnz: 48
+c=symbfact(A): 0.0001 0.0000 speedup 5.61 lnz 45
+R=symbfact(A): 0.0001 0.0000 speedup 4.55
+c=symbfact(A'): 0.0001 0.0000 speedup 5.14 lnz 39
+R=symbfact(A'): 0.0001 0.0000 speedup 4.43
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.45 lnz 55
+R=symbfact(A,'col'): 0.0002 0.0000 speedup 4.78
+
+ 719: LPnetlib/lpi_itest2 nrow: 9 ncol: 13 nnz: 26
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.64 lnz 35
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.09
+
+ 715: LPnetlib/lpi_galenet nrow: 8 ncol: 14 nnz: 22
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.64 lnz 37
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.09
+
+1440: Oberwolfach/LFAT5 nrow: 14 ncol: 14 nnz: 46
+c=symbfact(A): 0.0001 0.0000 speedup 5.61 lnz 33
+R=symbfact(A): 0.0001 0.0000 speedup 3.57
+c=symbfact(A'): 0.0001 0.0000 speedup 5.52 lnz 33
+R=symbfact(A'): 0.0001 0.0000 speedup 4.61
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.50 lnz 43
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.26
+
+1817: Meszaros/kleemin nrow: 8 ncol: 16 nnz: 44
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.77 lnz 86
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.03
+
+ 720: LPnetlib/lpi_itest6 nrow: 11 ncol: 17 nnz: 29
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.48 lnz 38
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.12
+
+1710: Meszaros/farm nrow: 7 ncol: 17 nnz: 41
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.61 lnz 101
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.89
+
+1438: Oberwolfach/LF10 nrow: 18 ncol: 18 nnz: 82
+c=symbfact(A): 0.0001 0.0000 speedup 5.00 lnz 58
+R=symbfact(A): 0.0001 0.0000 speedup 4.24
+c=symbfact(A'): 0.0001 0.0000 speedup 5.32 lnz 58
+R=symbfact(A'): 0.0001 0.0000 speedup 4.03
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.17 lnz 86
+R=symbfact(A,'col'): 0.0002 0.0000 speedup 4.78
+
+1479: Pajek/GD01_b nrow: 18 ncol: 18 nnz: 37
+c=symbfact(A): 0.0001 0.0000 speedup 5.47 lnz 43
+R=symbfact(A): 0.0001 0.0001 speedup 0.92
+c=symbfact(A'): 0.0001 0.0000 speedup 4.03 lnz 37
+R=symbfact(A'): 0.0001 0.0000 speedup 3.50
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.43 lnz 43
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 4.06
+
+1481: Pajek/GD02_a nrow: 23 ncol: 23 nnz: 87
+c=symbfact(A): 0.0001 0.0000 speedup 5.05 lnz 83
+R=symbfact(A): 0.0001 0.0000 speedup 4.14
+c=symbfact(A'): 0.0001 0.0000 speedup 3.65 lnz 83
+R=symbfact(A'): 0.0001 0.0000 speedup 3.25
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.92 lnz 208
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.38
+
+1516: Pajek/Ragusa18 nrow: 23 ncol: 23 nnz: 64
+c=symbfact(A): 0.0001 0.0000 speedup 5.05 lnz 69
+R=symbfact(A): 0.0001 0.0001 speedup 2.10
+c=symbfact(A'): 0.0001 0.0000 speedup 3.74 lnz 61
+R=symbfact(A'): 0.0001 0.0000 speedup 3.28
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.25 lnz 96
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.83
+
+ 97: HB/can_24 nrow: 24 ncol: 24 nnz: 160
+c=symbfact(A): 0.0001 0.0000 speedup 4.65 lnz 120
+R=symbfact(A): 0.0001 0.0000 speedup 3.09
+c=symbfact(A'): 0.0001 0.0000 speedup 4.73 lnz 120
+R=symbfact(A'): 0.0001 0.0001 speedup 1.96
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.93 lnz 196
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.36
+
+1515: Pajek/Ragusa16 nrow: 24 ncol: 24 nnz: 81
+c=symbfact(A): 0.0001 0.0000 speedup 5.05 lnz 71
+R=symbfact(A): 0.0001 0.0000 speedup 3.36
+c=symbfact(A'): 0.0001 0.0000 speedup 5.04 lnz 70
+R=symbfact(A'): 0.0001 0.0000 speedup 4.00
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.12 lnz 144
+R=symbfact(A,'col'): 0.0002 0.0000 speedup 5.54
+
+1177: HB/lap_25 nrow: 25 ncol: 25 nnz: 169
+c=symbfact(A): 0.0001 0.0000 speedup 4.65 lnz 138
+R=symbfact(A): 0.0002 0.0000 speedup 3.87
+c=symbfact(A'): 0.0001 0.0000 speedup 3.62 lnz 138
+R=symbfact(A'): 0.0001 0.0000 speedup 3.86
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.44 lnz 235
+R=symbfact(A,'col'): 0.0002 0.0000 speedup 3.21
+
+ 436: FIDAP/ex5 nrow: 27 ncol: 27 nnz: 279
+c=symbfact(A): 0.0001 0.0000 speedup 4.58 lnz 153
+R=symbfact(A): 0.0002 0.0000 speedup 3.80
+c=symbfact(A'): 0.0001 0.0000 speedup 4.64 lnz 153
+R=symbfact(A'): 0.0001 0.0000 speedup 3.92
+c=symbfact(A,'col'): 0.0002 0.0000 speedup 6.69 lnz 261
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 3.21
+
+ 232: HB/pores_1 nrow: 30 ncol: 30 nnz: 180
+c=symbfact(A): 0.0005 0.0000 speedup 20.28 lnz 133
+R=symbfact(A): 0.0002 0.0001 speedup 3.04
+c=symbfact(A'): 0.0001 0.0000 speedup 5.04 lnz 183
+R=symbfact(A'): 0.0001 0.0000 speedup 3.16
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.82 lnz 253
+R=symbfact(A,'col'): 0.0001 0.0001 speedup 2.65
+
+ 168: HB/ibm32 nrow: 32 ncol: 32 nnz: 126
+c=symbfact(A): 0.0001 0.0000 speedup 4.70 lnz 155
+R=symbfact(A): 0.0001 0.0000 speedup 3.00
+c=symbfact(A'): 0.0001 0.0000 speedup 5.00 lnz 135
+R=symbfact(A'): 0.0001 0.0000 speedup 3.75
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.66 lnz 325
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.08
+
+1199: Hamrle/Hamrle1 nrow: 32 ncol: 32 nnz: 98
+c=symbfact(A): 0.0001 0.0000 speedup 4.86 lnz 173
+R=symbfact(A): 0.0001 0.0002 speedup 0.88
+c=symbfact(A'): 0.0001 0.0000 speedup 4.96 lnz 112
+R=symbfact(A'): 0.0001 0.0000 speedup 3.12
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.93 lnz 176
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.34
+
+1480: Pajek/GD01_c nrow: 33 ncol: 33 nnz: 135
+c=symbfact(A): 0.0001 0.0000 speedup 4.50 lnz 139
+R=symbfact(A): 0.0962 0.0000 speedup 1963.43
+c=symbfact(A'): 0.0002 0.0000 speedup 6.00 lnz 144
+R=symbfact(A'): 0.0001 0.0000 speedup 3.87
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.82 lnz 214
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.04
+
+1474: Pajek/football nrow: 35 ncol: 35 nnz: 118
+c=symbfact(A): 0.0001 0.0000 speedup 4.40 lnz 144
+R=symbfact(A): 0.0002 0.0000 speedup 3.49
+c=symbfact(A'): 0.0002 0.0000 speedup 5.72 lnz 97
+R=symbfact(A'): 0.0001 0.0000 speedup 3.09
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.63 lnz 146
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.13
+
+1485: Pajek/GD95_a nrow: 36 ncol: 36 nnz: 57
+c=symbfact(A): 0.0001 0.0000 speedup 4.42 lnz 69
+R=symbfact(A): 0.0001 0.0000 speedup 2.96
+c=symbfact(A'): 0.0001 0.0000 speedup 4.73 lnz 71
+R=symbfact(A'): 0.0001 0.0011 speedup 0.12
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.07 lnz 69
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.72
+
+ 906: vanHeukelum/cage5 nrow: 37 ncol: 37 nnz: 233
+c=symbfact(A): 0.0001 0.0000 speedup 4.19 lnz 198
+R=symbfact(A): 0.0002 0.0001 speedup 2.00
+c=symbfact(A'): 0.0001 0.0000 speedup 4.67 lnz 198
+R=symbfact(A'): 0.0001 0.0000 speedup 3.36
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.38 lnz 472
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.37
+
+1495: Pajek/GD98_a nrow: 38 ncol: 38 nnz: 50
+c=symbfact(A): 0.0001 0.0000 speedup 4.65 lnz 59
+R=symbfact(A): 0.0001 0.0000 speedup 3.69
+c=symbfact(A'): 0.0001 0.0000 speedup 5.19 lnz 74
+R=symbfact(A'): 0.0001 0.0000 speedup 3.16
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.04 lnz 144
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.49
+
+ 13: HB/bcspwr01 nrow: 39 ncol: 39 nnz: 131
+c=symbfact(A): 0.0001 0.0000 speedup 4.40 lnz 104
+R=symbfact(A): 0.0001 0.0001 speedup 2.92
+c=symbfact(A'): 0.0001 0.0000 speedup 4.70 lnz 104
+R=symbfact(A'): 0.0001 0.0000 speedup 3.54
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.47 lnz 190
+R=symbfact(A,'col'): 0.0001 0.0001 speedup 2.65
+
+ 706: LPnetlib/lpi_bgprtr nrow: 20 ncol: 40 nnz: 70
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.96 lnz 155
+R=symbfact(A,'col'): 0.0001 0.0001 speedup 2.72
+
+1755: Meszaros/problem nrow: 12 ncol: 46 nnz: 86
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.93 lnz 377
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 3.04
+
+1493: Pajek/GD97_b nrow: 47 ncol: 47 nnz: 264
+c=symbfact(A): 0.0001 0.0000 speedup 3.87 lnz 211
+R=symbfact(A): 0.0002 0.0001 speedup 2.71
+c=symbfact(A'): 0.0001 0.0000 speedup 4.25 lnz 211
+R=symbfact(A'): 0.0002 0.0001 speedup 2.75
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.19 lnz 713
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.17
+
+ 23: HB/bcsstk01 nrow: 48 ncol: 48 nnz: 400
+c=symbfact(A): 0.0001 0.0000 speedup 3.75 lnz 489
+R=symbfact(A): 0.0002 0.0001 speedup 2.56
+c=symbfact(A'): 0.0001 0.0000 speedup 4.45 lnz 489
+R=symbfact(A'): 0.0002 0.0001 speedup 2.98
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.98 lnz 944
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 1.97
+
+ 56: HB/bcsstm01 nrow: 48 ncol: 48 nnz: 24
+c=symbfact(A): 0.0001 0.0000 speedup 4.73 lnz 48
+R=symbfact(A): 0.0001 0.0000 speedup 4.00
+c=symbfact(A'): 0.0001 0.0000 speedup 4.96 lnz 48
+R=symbfact(A'): 0.0002 0.0001 speedup 3.67
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 4.33 lnz 48
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.74
+
+ 872: Pothen/mesh1e1 nrow: 48 ncol: 48 nnz: 306
+c=symbfact(A): 0.0001 0.0000 speedup 4.30 lnz 336
+R=symbfact(A): 0.0002 0.0001 speedup 3.04
+c=symbfact(A'): 0.0001 0.0000 speedup 4.34 lnz 336
+R=symbfact(A'): 0.0002 0.0001 speedup 2.72
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.11 lnz 769
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.40
+
+ 873: Pothen/mesh1em1 nrow: 48 ncol: 48 nnz: 306
+c=symbfact(A): 0.0001 0.0000 speedup 3.90 lnz 336
+R=symbfact(A): 0.0002 0.0001 speedup 3.13
+c=symbfact(A'): 0.0001 0.0000 speedup 4.27 lnz 336
+R=symbfact(A'): 0.0002 0.0001 speedup 2.70
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.19 lnz 769
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.45
+
+ 874: Pothen/mesh1em6 nrow: 48 ncol: 48 nnz: 306
+c=symbfact(A): 0.0001 0.0000 speedup 3.90 lnz 336
+R=symbfact(A): 0.0002 0.0001 speedup 3.17
+c=symbfact(A'): 0.0002 0.0000 speedup 5.35 lnz 336
+R=symbfact(A'): 0.0002 0.0001 speedup 3.04
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.08 lnz 769
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.30
+
+1741: Meszaros/p0033 nrow: 15 ncol: 48 nnz: 113
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.61 lnz 364
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.91
+
+ 14: HB/bcspwr02 nrow: 49 ncol: 49 nnz: 167
+c=symbfact(A): 0.0001 0.0000 speedup 4.04 lnz 129
+R=symbfact(A): 0.0002 0.0001 speedup 3.06
+c=symbfact(A'): 0.0001 0.0000 speedup 4.59 lnz 129
+R=symbfact(A'): 0.0001 0.0000 speedup 2.92
+c=symbfact(A,'col'): 0.0002 0.0000 speedup 4.97 lnz 275
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.50
+
+1460: Pajek/divorce nrow: 50 ncol: 9 nnz: 225
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.96 lnz 45
+R=symbfact(A,'col'): 0.0001 0.0001 speedup 2.71
+
+ 597: LPnetlib/lp_afiro nrow: 27 ncol: 51 nnz: 102
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.68 lnz 293
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.52
+
+ 464: Grund/d_ss nrow: 53 ncol: 53 nnz: 144
+c=symbfact(A): 0.0001 0.0000 speedup 4.15 lnz 238
+R=symbfact(A): 0.0002 0.0001 speedup 2.74
+c=symbfact(A'): 0.0001 0.0000 speedup 4.29 lnz 243
+R=symbfact(A'): 0.0003 0.0000 speedup 5.36
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.39 lnz 259
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.96
+
+ 109: HB/curtis54 nrow: 54 ncol: 54 nnz: 291
+c=symbfact(A): 0.0001 0.0000 speedup 3.81 lnz 222
+R=symbfact(A): 0.0002 0.0001 speedup 3.11
+c=symbfact(A'): 0.0001 0.0001 speedup 2.09 lnz 208
+R=symbfact(A'): 0.0002 0.0001 speedup 3.34
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.13 lnz 556
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.22
+
+1457: Pajek/Cities nrow: 55 ncol: 46 nnz: 1342
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.76 lnz 1081
+R=symbfact(A,'col'): 0.0003 0.0002 speedup 1.78
+
+ 274: HB/will57 nrow: 57 ncol: 57 nnz: 281
+c=symbfact(A): 0.0001 0.0000 speedup 4.03 lnz 179
+R=symbfact(A): 0.0002 0.0001 speedup 3.30
+c=symbfact(A'): 0.0001 0.0000 speedup 4.15 lnz 178
+R=symbfact(A'): 0.0002 0.0000 speedup 4.41
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.11 lnz 450
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.17
+
+ 129: HB/dwt_59 nrow: 59 ncol: 59 nnz: 267
+c=symbfact(A): 0.0001 0.0000 speedup 3.77 lnz 244
+R=symbfact(A): 0.0002 0.0001 speedup 3.13
+c=symbfact(A'): 0.0001 0.0001 speedup 2.22 lnz 244
+R=symbfact(A'): 0.0002 0.0001 speedup 3.30
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.03 lnz 492
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.25
+
+ 172: HB/impcol_b nrow: 59 ncol: 59 nnz: 271
+c=symbfact(A): 0.0001 0.0000 speedup 3.75 lnz 394
+R=symbfact(A): 0.0002 0.0001 speedup 2.52
+c=symbfact(A'): 0.0002 0.0000 speedup 6.14 lnz 269
+R=symbfact(A'): 0.0002 0.0001 speedup 2.78
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.19 lnz 468
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.25
+
+ 102: HB/can_61 nrow: 61 ncol: 61 nnz: 557
+c=symbfact(A): 0.0001 0.0000 speedup 3.50 lnz 361
+R=symbfact(A): 0.0002 0.0001 speedup 2.07
+c=symbfact(A'): 0.0002 0.0000 speedup 3.92 lnz 361
+R=symbfact(A'): 0.0002 0.0001 speedup 2.54
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.84 lnz 966
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.09
+
+ 103: HB/can_62 nrow: 62 ncol: 62 nnz: 218
+c=symbfact(A): 0.0001 0.0000 speedup 3.87 lnz 184
+R=symbfact(A): 0.0002 0.0001 speedup 2.64
+c=symbfact(A'): 0.0001 0.0000 speedup 4.13 lnz 184
+R=symbfact(A'): 0.0001 0.0000 speedup 3.19
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.19 lnz 358
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.74
+
+ 293: Bai/bfwa62 nrow: 62 ncol: 62 nnz: 450
+c=symbfact(A): 0.0001 0.0000 speedup 3.43 lnz 317
+R=symbfact(A): 0.0002 0.0001 speedup 3.02
+c=symbfact(A'): 0.0001 0.0000 speedup 3.97 lnz 327
+R=symbfact(A'): 0.0002 0.0001 speedup 3.00
+c=symbfact(A,'col'): 0.0002 0.0000 speedup 3.57 lnz 743
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.24
+
+ 296: Bai/bfwb62 nrow: 62 ncol: 62 nnz: 342
+c=symbfact(A): 0.0001 0.0000 speedup 3.64 lnz 288
+R=symbfact(A): 0.0002 0.0001 speedup 2.98
+c=symbfact(A'): 0.0001 0.0000 speedup 4.00 lnz 288
+R=symbfact(A'): 0.0002 0.0001 speedup 2.62
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.72 lnz 589
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.64
+
+1487: Pajek/GD95_c nrow: 62 ncol: 62 nnz: 287
+c=symbfact(A): 0.0002 0.0000 speedup 4.67 lnz 234
+R=symbfact(A): 0.0002 0.0001 speedup 3.27
+c=symbfact(A'): 0.0001 0.0000 speedup 4.03 lnz 234
+R=symbfact(A'): 0.0002 0.0001 speedup 3.13
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.05 lnz 598
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.49
+
+1759: Meszaros/refine nrow: 29 ncol: 62 nnz: 153
+c=symbfact(A,'col'): 0.0002 0.0000 speedup 6.03 lnz 628
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.74
+
+1742: Meszaros/p0040 nrow: 23 ncol: 63 nnz: 133
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.71 lnz 515
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.71
+
+1498: Pajek/GD99_b nrow: 64 ncol: 64 nnz: 252
+c=symbfact(A): 0.0001 0.0000 speedup 3.75 lnz 461
+R=symbfact(A): 0.0002 0.0001 speedup 2.82
+c=symbfact(A'): 0.0002 0.0000 speedup 4.46 lnz 461
+R=symbfact(A'): 0.0002 0.0001 speedup 2.98
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.95 lnz 1001
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.81
+
+1490: Pajek/GD96_c nrow: 65 ncol: 65 nnz: 250
+c=symbfact(A): 0.0001 0.0000 speedup 3.69 lnz 341
+R=symbfact(A): 0.0002 0.0001 speedup 3.00
+c=symbfact(A'): 0.0001 0.0000 speedup 4.06 lnz 341
+R=symbfact(A'): 0.0002 0.0001 speedup 3.00
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.00 lnz 626
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.16
+
+ 24: HB/bcsstk02 nrow: 66 ncol: 66 nnz: 4356
+c=symbfact(A): 0.0002 0.0001 speedup 2.47 lnz 2211
+R=symbfact(A): 0.0934 0.0002 speedup 411.51
+c=symbfact(A'): 0.0004 0.0001 speedup 4.48 lnz 2211
+R=symbfact(A'): 0.0004 0.0002 speedup 2.47
+c=symbfact(A,'col'): 0.0002 0.0001 speedup 2.09 lnz 2211
+R=symbfact(A,'col'): 0.0010 0.0008 speedup 1.27
+
+ 57: HB/bcsstm02 nrow: 66 ncol: 66 nnz: 66
+c=symbfact(A): 0.0001 0.0000 speedup 4.82 lnz 66
+R=symbfact(A): 0.0001 0.0000 speedup 3.57
+c=symbfact(A'): 0.0001 0.0000 speedup 4.92 lnz 66
+R=symbfact(A'): 0.0001 0.0001 speedup 1.07
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.96 lnz 66
+R=symbfact(A,'col'): 0.0001 0.0000 speedup 3.60
+
+ 132: HB/dwt_66 nrow: 66 ncol: 66 nnz: 320
+c=symbfact(A): 0.0001 0.0000 speedup 4.11 lnz 193
+R=symbfact(A): 0.0002 0.0000 speedup 3.59
+c=symbfact(A'): 0.0001 0.0000 speedup 4.77 lnz 193
+R=symbfact(A'): 0.0002 0.0001 speedup 2.96
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.17 lnz 321
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.89
+
+ 883: Pothen/sphere2 nrow: 66 ncol: 66 nnz: 450
+c=symbfact(A): 0.0001 0.0000 speedup 3.44 lnz 682
+R=symbfact(A): 0.0002 0.0001 speedup 2.76
+c=symbfact(A'): 0.0002 0.0000 speedup 4.63 lnz 682
+R=symbfact(A'): 0.0002 0.0001 speedup 2.82
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.91 lnz 1368
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 1.89
+
+ 262: HB/west0067 nrow: 67 ncol: 67 nnz: 294
+c=symbfact(A): 0.0001 0.0000 speedup 3.56 lnz 701
+R=symbfact(A): 0.0002 0.0001 speedup 2.56
+c=symbfact(A'): 0.0001 0.0000 speedup 4.11 lnz 569
+R=symbfact(A'): 0.0002 0.0001 speedup 2.80
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.83 lnz 872
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.36
+
+ 636: LPnetlib/lp_kb2 nrow: 43 ncol: 68 nnz: 313
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.00 lnz 589
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.39
+
+ 133: HB/dwt_72 nrow: 72 ncol: 72 nnz: 222
+c=symbfact(A): 0.0001 0.0000 speedup 4.00 lnz 184
+R=symbfact(A): 0.0002 0.0001 speedup 2.78
+c=symbfact(A'): 0.0001 0.0000 speedup 4.35 lnz 184
+R=symbfact(A'): 0.0002 0.0001 speedup 3.12
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.14 lnz 329
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.76
+
+1501: Pajek/GlossGT nrow: 72 ncol: 72 nnz: 122
+c=symbfact(A): 0.0001 0.0000 speedup 3.66 lnz 219
+R=symbfact(A): 0.0002 0.0001 speedup 3.09
+c=symbfact(A'): 0.0001 0.0000 speedup 3.32 lnz 96
+R=symbfact(A'): 0.0001 0.0000 speedup 3.44
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.36 lnz 147
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 3.06
+
+ 106: HB/can_73 nrow: 73 ncol: 73 nnz: 377
+c=symbfact(A): 0.0001 0.0000 speedup 3.62 lnz 392
+R=symbfact(A): 0.0002 0.0001 speedup 2.60
+c=symbfact(A'): 0.0002 0.0000 speedup 4.21 lnz 392
+R=symbfact(A'): 0.0002 0.0001 speedup 2.73
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.90 lnz 1438
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.05
+
+1486: Pajek/GD95_b nrow: 73 ncol: 73 nnz: 96
+c=symbfact(A): 0.0001 0.0000 speedup 4.04 lnz 105
+R=symbfact(A): 0.0002 0.0000 speedup 3.29
+c=symbfact(A'): 0.0001 0.0000 speedup 4.00 lnz 147
+R=symbfact(A'): 0.0002 0.0000 speedup 3.30
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.41 lnz 476
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.76
+
+ 666: LPnetlib/lp_sc50a nrow: 50 ncol: 78 nnz: 160
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.08 lnz 332
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.62
+
+ 667: LPnetlib/lp_sc50b nrow: 50 ncol: 78 nnz: 148
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.59 lnz 316
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.70
+
+ 253: HB/steam3 nrow: 80 ncol: 80 nnz: 314
+c=symbfact(A): 0.0001 0.0000 speedup 4.00 lnz 208
+R=symbfact(A): 0.0002 0.0001 speedup 3.20
+c=symbfact(A'): 0.0001 0.0000 speedup 4.09 lnz 205
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+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.11 lnz 424
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.49
+
+1482: Pajek/GD02_b nrow: 80 ncol: 80 nnz: 232
+c=symbfact(A): 0.0001 0.0000 speedup 3.56 lnz 326
+R=symbfact(A): 0.0002 0.0001 speedup 2.88
+c=symbfact(A'): 0.0002 0.0000 speedup 4.31 lnz 317
+R=symbfact(A'): 0.0002 0.0001 speedup 2.93
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.88 lnz 497
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+
+1492: Pajek/GD97_a nrow: 84 ncol: 84 nnz: 332
+c=symbfact(A): 0.0001 0.0000 speedup 3.41 lnz 677
+R=symbfact(A): 0.0002 0.0001 speedup 2.60
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+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.71 lnz 1608
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+
+ 11: HB/ash85 nrow: 85 ncol: 85 nnz: 523
+c=symbfact(A): 0.0001 0.0000 speedup 3.26 lnz 505
+R=symbfact(A): 0.0002 0.0001 speedup 2.73
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+R=symbfact(A'): 0.0002 0.0001 speedup 2.71
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.59 lnz 1109
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+
+1519: Pajek/Sandi_authors nrow: 86 ncol: 86 nnz: 248
+c=symbfact(A): 0.0001 0.0000 speedup 3.46 lnz 221
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+c=symbfact(A'): 0.0001 0.0000 speedup 3.94 lnz 221
+R=symbfact(A'): 0.0002 0.0001 speedup 2.52
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.95 lnz 533
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+
+ 136: HB/dwt_87 nrow: 87 ncol: 87 nnz: 541
+c=symbfact(A): 0.0001 0.0000 speedup 3.37 lnz 414
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+R=symbfact(A'): 0.0002 0.0001 speedup 2.46
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.65 lnz 921
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+
+ 462: Grund/d_dyn nrow: 87 ncol: 87 nnz: 230
+c=symbfact(A): 0.0001 0.0000 speedup 3.33 lnz 442
+R=symbfact(A): 0.0002 0.0001 speedup 2.74
+c=symbfact(A'): 0.0001 0.0000 speedup 3.84 lnz 450
+R=symbfact(A'): 0.0002 0.0001 speedup 2.85
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.81 lnz 432
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.01
+
+ 463: Grund/d_dyn1 nrow: 87 ncol: 87 nnz: 232
+c=symbfact(A): 0.0001 0.0000 speedup 3.43 lnz 476
+R=symbfact(A): 0.0002 0.0001 speedup 2.64
+c=symbfact(A'): 0.0001 0.0000 speedup 3.74 lnz 441
+R=symbfact(A'): 0.0002 0.0001 speedup 2.38
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.74 lnz 439
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 1.80
+
+ 731: LPnetlib/lpi_woodinfe nrow: 35 ncol: 89 nnz: 140
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.11 lnz 402
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.58
+
+1641: Bai/tols90 nrow: 90 ncol: 90 nnz: 1746
+c=symbfact(A): 0.0001 0.0000 speedup 3.33 lnz 315
+R=symbfact(A): 0.0002 0.0001 speedup 2.75
+c=symbfact(A'): 0.0002 0.0001 speedup 2.96 lnz 1539
+R=symbfact(A'): 0.0003 0.0001 speedup 2.25
+c=symbfact(A,'col'): 0.0002 0.0001 speedup 2.33 lnz 4095
+R=symbfact(A,'col'): 0.0007 0.0005 speedup 1.46
+
+ 907: vanHeukelum/cage6 nrow: 93 ncol: 93 nnz: 785
+c=symbfact(A): 0.0001 0.0000 speedup 3.07 lnz 1170
+R=symbfact(A): 0.0002 0.0001 speedup 2.27
+c=symbfact(A'): 0.0002 0.0000 speedup 3.65 lnz 1170
+R=symbfact(A'): 0.0002 0.0001 speedup 2.42
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.34 lnz 2665
+R=symbfact(A,'col'): 0.0003 0.0002 speedup 1.82
+
+ 108: HB/can_96 nrow: 96 ncol: 96 nnz: 768
+c=symbfact(A): 0.0002 0.0000 speedup 3.42 lnz 984
+R=symbfact(A): 0.0002 0.0001 speedup 2.26
+c=symbfact(A'): 0.0002 0.0001 speedup 1.20 lnz 984
+R=symbfact(A'): 0.0002 0.0001 speedup 2.57
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.46 lnz 2620
+R=symbfact(A,'col'): 0.0003 0.0002 speedup 1.78
+
+ 220: HB/nos4 nrow: 100 ncol: 100 nnz: 594
+c=symbfact(A): 0.0001 0.0000 speedup 3.02 lnz 632
+R=symbfact(A): 0.0002 0.0001 speedup 2.39
+c=symbfact(A'): 0.0002 0.0000 speedup 3.50 lnz 632
+R=symbfact(A'): 0.0002 0.0001 speedup 2.59
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.53 lnz 1414
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.05
+
+ 318: Bai/olm100 nrow: 100 ncol: 100 nnz: 396
+c=symbfact(A): 0.0001 0.0000 speedup 3.67 lnz 247
+R=symbfact(A): 0.0002 0.0001 speedup 3.04
+c=symbfact(A'): 0.0001 0.0000 speedup 4.15 lnz 249
+R=symbfact(A'): 0.0002 0.0001 speedup 3.18
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.95 lnz 538
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.10
+
+ 337: Bai/tub100 nrow: 100 ncol: 100 nnz: 396
+c=symbfact(A): 0.0001 0.0000 speedup 3.73 lnz 297
+R=symbfact(A): 0.0002 0.0001 speedup 2.55
+c=symbfact(A'): 0.0001 0.0000 speedup 4.11 lnz 297
+R=symbfact(A'): 0.0002 0.0001 speedup 3.05
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.93 lnz 490
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.55
+
+1326: Morandini/rotor1 nrow: 100 ncol: 100 nnz: 708
+c=symbfact(A): 0.0001 0.0000 speedup 3.02 lnz 551
+R=symbfact(A): 0.0002 0.0001 speedup 2.44
+c=symbfact(A'): 0.0002 0.0000 speedup 4.18 lnz 714
+R=symbfact(A'): 0.0002 0.0001 speedup 2.52
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.41 lnz 2049
+R=symbfact(A,'col'): 0.0003 0.0002 speedup 1.76
+
+1484: Pajek/GD06_theory nrow: 101 ncol: 101 nnz: 380
+c=symbfact(A): 0.0001 0.0000 speedup 3.61 lnz 336
+R=symbfact(A): 0.0002 0.0001 speedup 2.89
+c=symbfact(A'): 0.0001 0.0000 speedup 3.94 lnz 336
+R=symbfact(A'): 0.0002 0.0001 speedup 2.56
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.75 lnz 3401
+R=symbfact(A,'col'): 0.0003 0.0001 speedup 1.99
+
+ 861: MathWorks/pivtol nrow: 102 ncol: 102 nnz: 306
+c=symbfact(A): 0.0001 0.0000 speedup 3.93 lnz 302
+R=symbfact(A): 0.0002 0.0001 speedup 2.57
+c=symbfact(A'): 0.0001 0.0000 speedup 4.12 lnz 303
+R=symbfact(A'): 0.0002 0.0001 speedup 3.00
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.03 lnz 500
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.62
+
+ 306: Bai/ck104 nrow: 104 ncol: 104 nnz: 992
+c=symbfact(A): 0.0001 0.0000 speedup 3.11 lnz 548
+R=symbfact(A): 0.0002 0.0001 speedup 2.61
+c=symbfact(A'): 0.0002 0.0000 speedup 3.71 lnz 548
+R=symbfact(A'): 0.0002 0.0001 speedup 3.12
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.48 lnz 912
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 1.89
+
+1499: Pajek/GD99_c nrow: 105 ncol: 105 nnz: 149
+c=symbfact(A): 0.0002 0.0000 speedup 5.75 lnz 166
+R=symbfact(A): 0.0002 0.0001 speedup 3.15
+c=symbfact(A'): 0.0001 0.0000 speedup 3.76 lnz 221
+R=symbfact(A'): 0.0002 0.0001 speedup 2.61
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.08 lnz 231
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.83
+
+ 721: LPnetlib/lpi_klein1 nrow: 54 ncol: 108 nnz: 750
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.35 lnz 2132
+R=symbfact(A,'col'): 0.0003 0.0002 speedup 1.82
+
+1489: Pajek/GD96_b nrow: 111 ncol: 111 nnz: 193
+c=symbfact(A): 0.0001 0.0000 speedup 3.49 lnz 303
+R=symbfact(A): 0.0003 0.0001 speedup 4.68
+c=symbfact(A'): 0.0001 0.0000 speedup 4.45 lnz 132
+R=symbfact(A'): 0.0001 0.0001 speedup 2.68
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.14 lnz 168
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.83
+
+ 25: HB/bcsstk03 nrow: 112 ncol: 112 nnz: 640
+c=symbfact(A): 0.0002 0.0000 speedup 4.18 lnz 384
+R=symbfact(A): 0.0002 0.0001 speedup 2.46
+c=symbfact(A'): 0.0002 0.0000 speedup 3.72 lnz 384
+R=symbfact(A'): 0.0002 0.0001 speedup 2.88
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.65 lnz 592
+R=symbfact(A,'col'): 0.0002 0.0001 speedup 2.13
+
+ 58: HB/bcsstm03 nrow: 112 ncol: 112 nnz: 72
+c=symbfact(A): 0.0001 0.0000 speedup 4.19 lnz 112
+R=symbfact(A): 0.0002 0.0000 speedup 3.40
+c=symbfact(A'): 0.0001 0.0000 speedup 4.86 lnz 112
+R=symbfact(A'): 0.0001 0.0000 speedup 3.31
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 3.52 lnz 112
+R=symbfact(A,'col'): 0.0002 0.0000 speedup 3.23
+
+1497: Pajek/GD98_c nrow: 112 ncol: 112 nnz: 336
+c=symbfact(A): 0.0001 0.0000 speedup 3.12 lnz 967
+R=symbfact(A): 0.0002 0.0001 speedup 2.43
+c=symbfact(A'): 0.0002 0.0000 speedup 3.58 lnz 967
+R=symbfact(A'): 0.0002 0.0001 speedup 2.43
+c=symbfact(A,'col'): 0.0001 0.0000 speedup 2.63 lnz 2064
+R=symbfact(A,'col'): 0.0003 0.0001 speedup 2.16
+
+ 158: HB/gent113 nrow: 113 ncol: 113 nnz: 655
+c=symbfact(A): 0.0001 0.0000 speedup 2.94 lnz 791
+R=symbfact(A): 0.0002 0.0001 speedup 2.33
+c=symbfact(A'): 0.0002 0.0000 speedup 3.73 lnz 643
+R=symbfact(A'): 0.0002 0.0001 speedup 2.56
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.36 lnz 1433
+R=symbfact(A,'col'): 0.0003 0.0001 speedup 2.06
+
+ 603: LPnetlib/lp_blend nrow: 74 ncol: 114 nnz: 522
+c=symbfact(A,'col'): 0.0001 0.0001 speedup 2.57 lnz 1459
+R=symbfact(A,'col'): 0.0002 0.0002 speedup 1.14
+test15 passed
+=================================================================
+test16: test cholmod2 on a large matrix
+
+Prob =
+
+ A: [9000x9000 double]
+ name: 'ND/nd3k'
+ title: 'ND problem set, matrix nd3k'
+ id: 936
+ date: '2003'
+ author: 'author unknown'
+ ed: 'T. Davis'
+ kind: '2D/3D problem'
+
+time 17.5518
+test16 passed
+=================================================================
+test17: test lchol on a few large matrices
+
+Prob =
+
+ title: 'S.Norris, Univ. Auckland. FEM, Laplace eqn 2D 100x100 mesh'
+ A: [9604x9604 double]
+ name: 'Norris/fv1'
+ id: 887
+ date: '2003'
+ author: 'S. Norris'
+ ed: 'T. Davis'
+ kind: '2D/3D problem'
+
+
+ans =
+
+ 3.4748
+
+
+Prob =
+
+ A: [9000x9000 double]
+ name: 'ND/nd3k'
+ title: 'ND problem set, matrix nd3k'
+ id: 936
+ date: '2003'
+ author: 'author unknown'
+ ed: 'T. Davis'
+ kind: '2D/3D problem'
+
+
+ans =
+
+ 30.1030
+
+
+Prob =
+
+ title: 'S.Norris, Univ. Auckland. FEM, Laplace eqn 2D 100x100 mesh'
+ A: [9604x9604 double]
+ name: 'Norris/fv1'
+ id: 887
+ date: '2003'
+ author: 'S. Norris'
+ ed: 'T. Davis'
+ kind: '2D/3D problem'
+
+
+ans =
+
+ 3.4748
+
+=================================================================
+test18: test cholmod2 on a few large matrices
+
+Prob =
+
+ title: 'S.Norris, Univ. Auckland. FEM, Laplace eqn 2D 100x100 mesh'
+ A: [9604x9604 double]
+ name: 'Norris/fv1'
+ id: 887
+ date: '2003'
+ author: 'S. Norris'
+ ed: 'T. Davis'
+ kind: '2D/3D problem'
+
+
+ans =
+
+ 4.9310e-12
+
+
+Prob =
+
+ A: [9000x9000 double]
+ name: 'ND/nd3k'
+ title: 'ND problem set, matrix nd3k'
+ id: 936
+ date: '2003'
+ author: 'author unknown'
+ ed: 'T. Davis'
+ kind: '2D/3D problem'
+
+
+ans =
+
+ 1.6330e-05
+
+
+Prob =
+
+ title: 'S.Norris, Univ. Auckland. FEM, Laplace eqn 2D 100x100 mesh'
+ A: [9604x9604 double]
+ name: 'Norris/fv1'
+ id: 887
+ date: '2003'
+ author: 'S. Norris'
+ ed: 'T. Davis'
+ kind: '2D/3D problem'
+
+
+ans =
+
+ 4.9453e-12
+
+test18 passed
+=================================================================
+test19: look for NaN's from lchol (caused by Intel MKL 7.x bug)
+
+Prob =
+
+ A: [9000x9000 double]
+ name: 'ND/nd3k'
+ title: 'ND problem set, matrix nd3k'
+ id: 936
+ date: '2003'
+ author: 'author unknown'
+ ed: 'T. Davis'
+ kind: '2D/3D problem'
+
+mflop rate: 1287.30
+test19 passed; you have a NaN-free BLAS (must not be MKL 7.x...)
+=================================================================
+test20: test symbfact2, cholmod2, and lu on a few large matrices
+
+Prob =
+
+ title: 'STRUCTURE FROM NASA LANGLEY, ACCURACY PROBLEM ON Y-MP'
+ A: [16146x16146 double]
+ b: [16146x1 double]
+ name: 'Simon/olafu'
+ id: 813
+ date: '1993'
+ author: 'H. Simon'
+ ed: 'H. Simon'
+ kind: 'structural problem'
+
+lnz 3095636 unz 3095636 nnz(L+U) 6175126 fl 1.13063e+09 gflop 1.84307
+ t 0.613446 err 5.225120e-04
+
+Prob =
+
+ title: 'BUCKLING PROBLEM FOR CONTAINER MODEL, ARTHUR RAEFSKY, CENTRIC ENG.'
+ A: [19779x19779 double]
+ Zeros: [19779x19779 double]
+ b: [19779x1 double]
+ name: 'Simon/raefsky4'
+ id: 817
+ date: '1993'
+ author: 'A. Raefsky'
+ ed: 'H. Simon'
+ kind: 'structural problem'
+
+lnz 7304797 unz 7304797 nnz(L+U) 14589815 fl 5.30769e+09 gflop 4.02389
+ t 1.31904 err 6.031010e-03
+=================================================================
+test21: test cholmod2 on diagonal or ill-conditioned matrices
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX - TEXTILE LOOM FRAME'
+ A: [138x138 double]
+ name: 'HB/bcsstm22'
+ id: 72
+ date: '1984'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz: 138
+MATLAB resid 0.0e+00 err 0.0e+00
+CHOLMOD resid 1.1e-17 err 1.3e-14
+condest 9.4e+02
+
+Prob =
+
+ title: 'MAGNETO-HYDRO-DYNAMICS ALFVEN SPECTRAL PROBLEM'
+ A: [416x416 double]
+ name: 'Bai/mhdb416'
+ id: 315
+ date: '1994'
+ author: 'A. Booten, M. Kooper, H. van der Vorst, S. Poedts, J. Goedbloed'
+ ed: 'Z. Bai, D. Day, J. Demmel, J. Dongarra'
+ kind: 'electromagnetics problem'
+
+nnz: 2312
+MATLAB resid 2.3e-18 err 2.8e-12
+CHOLMOD resid 2.3e-18 err 2.8e-12
+condest 5.1e+09
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX, SQUARE PLATE CLAMPED'
+ A: [1083x1083 double]
+ name: 'HB/bcsstm09'
+ id: 64
+ date: '1982'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz: 1083
+MATLAB resid 0.0e+00 err 0.0e+00
+CHOLMOD resid 5.2e-17 err 2.4e-13
+condest 1.0e+04
+
+Prob =
+
+ title: 'SYMMETRIC MASS MATRIX - CLAMPED SQUARE PLATE'
+ A: [3600x3600 double]
+ name: 'HB/bcsstm21'
+ id: 71
+ date: '1984'
+ author: 'J. Lewis'
+ ed: 'I. Duff, R. Grimes, J. Lewis'
+ kind: 'structural problem'
+
+nnz: 3600
+MATLAB resid 0.0e+00 err 0.0e+00
+CHOLMOD resid 2.5e-18 err 2.7e-13
+condest 2.4e+01
+
+Prob =
+
+ name: 'Oberwolfach/t2dal_e'
+ title: 'Oberwolfach: micropyros thruster, E matrix'
+ A: [4257x4257 double]
+ id: 1207
+ kind: 'duplicate model reduction problem'
+ date: '2004'
+ author: 'E. Rudnyi'
+ ed: 'E. Rudnyi'
+
+nnz: 4257
+MATLAB resid 0.0e+00 err 0.0e+00
+CHOLMOD resid 1.3e-17 err 3.9e-13
+condest 3.8e+07
+
+Prob =
+
+ title: 'FEM CRYSTAL FREE VIBRATION MASS MATRIX'
+ A: [13965x13965 double]
+ name: 'Boeing/crystm02'
+ id: 354
+ date: '1995'
+ author: 'R. Grimes'
+ ed: 'T. Davis'
+ kind: 'materials problem'
+
+nnz: 322905
+MATLAB resid 9.5e-17 err 2.3e-11
+CHOLMOD resid 9.5e-17 err 2.3e-11
+condest 4.5e+02
+
+Prob =
+
+ name: 'Oberwolfach/t3dl_e'
+ title: 'Oberwolfach: micropyros thruster, E matrix'
+ A: [20360x20360 double]
+ id: 1211
+ kind: 'duplicate model reduction problem'
+ date: '2004'
+ author: 'E. Rudnyi'
+ ed: 'E. Rudnyi'
+
+nnz: 20360
+MATLAB resid 0.0e+00 err 0.0e+00
+CHOLMOD resid 3.2e-17 err 2.0e-12
+condest 6.0e+03
+=================================================================
+test22: test pos.def and indef. matrices
+test22: chol and chol2 are repeated so each take >= 0.1 sec
+
+================== 904: Problem: vanHeukelum/cage3 m: 5 n: 5 nnz: 19 19
+rcond: 4.25263103233630423983e-01
+p: 0 0 MATLAB: 0.0003 CHOLMOD: 0.0003 speedup 1.08 err: 0 0
+
+================== 449: Problem: Grund/b1_ss m: 7 n: 7 nnz: 15 24
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.76 err: 0 0
+
+================== 1710: Problem: Meszaros/farm m: 7 n: 17 nnz: 41 39
+rcond: 2.52948218857096309570e-03
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.88 err: 0 0
+
+================== 715: Problem: LPnetlib/lpi_galenet m: 8 n: 14 nnz: 22 24
+rcond: 8.16496580927726145482e-01
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.75 err: 0 0
+
+================== 1817: Problem: Meszaros/kleemin m: 8 n: 16 nnz: 44 64
+rcond: 9.94982371447397095920e-02
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0
+
+================== 185: Problem: HB/jgl009 m: 9 n: 9 nnz: 50 72
+rcond: 0.00000000000000000000e+00
+p: 3 3 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.78 err: 0 0
+
+================== 719: Problem: LPnetlib/lpi_itest2 m: 9 n: 13 nnz: 26 51
+rcond: 4.47109297966382157608e-01
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.73 err: 0 0
+
+================== 905: Problem: vanHeukelum/cage4 m: 9 n: 9 nnz: 49 49
+rcond: 4.78114120908413264832e-01
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.92 err: 0 0
+
+================== 238: Problem: HB/rgg010 m: 10 n: 10 nnz: 76 100
+rcond: 0.00000000000000000000e+00
+p: 3 3 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.90 err: 0 0
+
+================== 1524: Problem: Pajek/Stranke94 m: 10 n: 10 nnz: 90 90
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.76 err: 0 0
+
+================== 186: Problem: HB/jgl011 m: 11 n: 11 nnz: 76 108
+rcond: 0.00000000000000000000e+00
+p: 6 6 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.80 err: 0 0
+
+================== 720: Problem: LPnetlib/lpi_itest6 m: 11 n: 17 nnz: 29 51
+rcond: 9.45751723210471600956e-03
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.87 err: 0 0
+
+================== 1525: Problem: Pajek/Tina_AskCal m: 11 n: 11 nnz: 29 50
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0
+
+================== 1526: Problem: Pajek/Tina_AskCog m: 11 n: 11 nnz: 36 54
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.79 err: 0 0
+
+================== 1527: Problem: Pajek/Tina_DisCal m: 11 n: 11 nnz: 41 64
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.84 err: 0 0
+
+================== 1528: Problem: Pajek/Tina_DisCog m: 11 n: 11 nnz: 48 72
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.85 err: 0 0
+
+================== 1755: Problem: Meszaros/problem m: 12 n: 46 nnz: 86 42
+rcond: 5.37847998878130950651e-01
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 1.08 err: 0 0
+
+================== 1440: Problem: Oberwolfach/LFAT5 m: 14 n: 14 nnz: 46 46
+rcond: 1.55639238128393175712e-04
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.76 err: 0 0
+
+================== 1741: Problem: Meszaros/p0033 m: 15 n: 48 nnz: 113 95
+rcond: 1.48172008456599587148e-03
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.78 err: 0 0
+
+================== 1438: Problem: Oberwolfach/LF10 m: 18 n: 18 nnz: 82 82
+rcond: 5.27046276694730000262e-03
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0
+
+================== 1479: Problem: Pajek/GD01_b m: 18 n: 18 nnz: 37 54
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.92 err: 0 0
+
+================== 706: Problem: LPnetlib/lpi_bgprtr m: 20 n: 40 nnz: 70 96
+rcond: 1.25918385245936273811e-03
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.76 err: 0 0
+
+================== 1481: Problem: Pajek/GD02_a m: 23 n: 23 nnz: 87 118
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.78 err: 0 0
+
+================== 1516: Problem: Pajek/Ragusa18 m: 23 n: 23 nnz: 64 105
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.93 err: 0 0
+
+================== 1742: Problem: Meszaros/p0040 m: 23 n: 63 nnz: 133 163
+rcond: 2.52390925692451309308e-04
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0
+
+================== 97: Problem: HB/can_24 m: 24 n: 24 nnz: 160 160
+rcond: 0.00000000000000000000e+00
+p: 2 2 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.82 err: 0 0
+
+================== 624: Problem: LPnetlib/lp_fit1d m: 24 n: 1049 nnz: 13427 558
+rcond: 7.36202451773845909129e-04
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.98 err: 0 0
+
+================== 1515: Problem: Pajek/Ragusa16 m: 24 n: 24 nnz: 81 126
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.92 err: 0 0
+
+================== 626: Problem: LPnetlib/lp_fit2d m: 25 n: 10524 nnz: 129042 617
+rcond: 2.18529247214663312551e-03
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.95 err: 0 0
+
+================== 1177: Problem: HB/lap_25 m: 25 n: 25 nnz: 169 169
+rcond: 0.00000000000000000000e+00
+p: 2 2 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.80 err: 0 0
+
+================== 436: Problem: FIDAP/ex5 m: 27 n: 27 nnz: 279 279
+rcond: 8.27464239340425602477e-04
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.86 err: 0 0
+
+================== 597: Problem: LPnetlib/lp_afiro m: 27 n: 51 nnz: 102 153
+rcond: 1.72386001683099310267e-01
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.83 err: 0 0
+
+================== 1759: Problem: Meszaros/refine m: 29 n: 62 nnz: 153 217
+rcond: 1.81514831282913007005e-02
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0
+
+================== 232: Problem: HB/pores_1 m: 30 n: 30 nnz: 180 236
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0
+
+================== 168: Problem: HB/ibm32 m: 32 n: 32 nnz: 126 212
+rcond: 0.00000000000000000000e+00
+p: 18 18 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.84 err: 0 0
+
+================== 1199: Problem: Hamrle/Hamrle1 m: 32 n: 32 nnz: 98 181
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.79 err: 0 0
+
+================== 1480: Problem: Pajek/GD01_c m: 33 n: 33 nnz: 135 270
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.92 err: 0 0
+
+================== 731: Problem: LPnetlib/lpi_woodinfe m: 35 n: 89 nnz: 140 137
+rcond: 4.26401432711220829130e-01
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.86 err: 0 0
+
+================== 1474: Problem: Pajek/football m: 35 n: 35 nnz: 118 236
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.84 err: 0 0
+
+================== 1485: Problem: Pajek/GD95_a m: 36 n: 36 nnz: 57 112
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.80 err: 0 0
+
+================== 906: Problem: vanHeukelum/cage5 m: 37 n: 37 nnz: 233 233
+rcond: 2.54392381006308010427e-01
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.82 err: 0 0
+
+================== 1495: Problem: Pajek/GD98_a m: 38 n: 38 nnz: 50 92
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.91 err: 0 0
+
+================== 13: Problem: HB/bcspwr01 m: 39 n: 39 nnz: 131 131
+rcond: 0.00000000000000000000e+00
+p: 2 2 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.83 err: 0 0
+
+================== 636: Problem: LPnetlib/lp_kb2 m: 43 n: 68 nnz: 313 847
+rcond: 4.57208742551626703965e-04
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.93 err: 0 0
+
+================== 1493: Problem: Pajek/GD97_b m: 47 n: 47 nnz: 264 264
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.99 err: 0 0
+
+================== 23: Problem: HB/bcsstk01 m: 48 n: 48 nnz: 400 400
+rcond: 3.07546526042088742836e-03
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.88 err: 0 0
+
+================== 56: Problem: HB/bcsstm01 m: 48 n: 48 nnz: 24 24
+rcond: 0.00000000000000000000e+00
+p: 4 4 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.79 err: 0 0
+
+================== 872: Problem: Pothen/mesh1e1 m: 48 n: 48 nnz: 306 306
+rcond: 5.92447279051849906573e-01
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 1.07 err: 0 0
+
+================== 873: Problem: Pothen/mesh1em1 m: 48 n: 48 nnz: 306 306
+rcond: 2.99182771005118530727e-01
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.88 err: 0 0
+
+================== 874: Problem: Pothen/mesh1em6 m: 48 n: 48 nnz: 306 306
+rcond: 5.98061003584390182830e-01
+p: 0 0 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.88 err: 0 0
+test22: all tests passed
+=================================================================
+test22: test pos.def and indef. matrices
+testing matrices for which MATLAB and CHOLMOD differ
+test22: chol and chol2 are repeated so each take >= 0.1 sec
+
+================== 186: Problem: HB/jgl011 m: 11 n: 11 nnz: 76 108
+rcond: 0.00000000000000000000e+00
+p: 6 6 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.78 err: 0 0
+
+================== 109: Problem: HB/curtis54 m: 54 n: 54 nnz: 291 302
+rcond: 0.00000000000000000000e+00
+p: 4 4 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.96 err: 0 0
+
+================== 793: Problem: Qaplib/lp_nug05 m: 210 n: 225 nnz: 1050 4060
+rcond: 0.00000000000000000000e+00
+p: 75 75 MATLAB: 0.0015 CHOLMOD: 0.0014 speedup 1.12 err: 0 0
+
+================== 607: Problem: LPnetlib/lp_brandy m: 220 n: 303 nnz: 2202 5275
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0004 CHOLMOD: 0.0003 speedup 1.18 err: 0 0
+
+================== 707: Problem: LPnetlib/lpi_box1 m: 231 n: 261 nnz: 651 1401
+rcond: 0.00000000000000000000e+00
+p: 22 22 MATLAB: 0.0003 CHOLMOD: 0.0002 speedup 1.80 err: 0 0
+
+================== 231: Problem: HB/plskz362 m: 362 n: 362 nnz: 1760 0
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0001 CHOLMOD: 0.0001 speedup 0.87 err: 0 0
+
+================== 794: Problem: Qaplib/lp_nug06 m: 372 n: 486 nnz: 2232 8724
+rcond: 0.00000000000000000000e+00
+p: 260 260 MATLAB: 0.0089 CHOLMOD: 0.1089 speedup 0.08 err: 0 0
+
+================== 673: Problem: LPnetlib/lp_scorpion m: 388 n: 466 nnz: 1534 3814
+rcond: 0.00000000000000000000e+00
+p: 35 35 MATLAB: 0.0003 CHOLMOD: 0.0004 speedup 0.79 err: 0 0
+
+================== 1156: Problem: Sandia/oscil_dcop_45 m: 430 n: 430 nnz: 1544 1572
+rcond: 0.00000000000000000000e+00
+p: 31 31 MATLAB: 0.0002 CHOLMOD: 0.0002 speedup 0.90 err: 0 0
+
+================== 795: Problem: Qaplib/lp_nug07 m: 602 n: 931 nnz: 4214 16576
+rcond: 0.00000000000000000000e+00
+p: 218 218 MATLAB: 0.0171 CHOLMOD: 0.0170 speedup 1.01 err: 0 0
+
+================== 796: Problem: Qaplib/lp_nug08 m: 912 n: 1632 nnz: 7296 28816
+rcond: 0.00000000000000000000e+00
+p: 388 388 MATLAB: 0.1514 CHOLMOD: 0.0512 speedup 2.96 err: 0 0
+
+================== 260: Problem: HB/well1033 m: 1033 n: 320 nnz: 4732 182679
+rcond: 0.00000000000000000000e+00
+p: 15 15 MATLAB: 0.0148 CHOLMOD: 0.0149 speedup 0.99 err: 0 0
+
+================== 261: Problem: HB/well1850 m: 1850 n: 712 nnz: 8755 522902
+rcond: 0.00000000000000000000e+00
+p: 6 6 MATLAB: 0.0454 CHOLMOD: 0.0440 speedup 1.03 err: 0 0
+
+================== 230: Problem: HB/plsk1919 m: 1919 n: 1919 nnz: 9662 0
+rcond: 0.00000000000000000000e+00
+p: 1 1 MATLAB: 0.0003 CHOLMOD: 0.0003 speedup 0.92 err: 0 0
+
+================== 649: Problem: LPnetlib/lp_pds_02 m: 2953 n: 7716 nnz: 16571 23281
+rcond: 2.12687604726321055632e-08
+p: 0 0 MATLAB: 0.0140 CHOLMOD: 0.0144 speedup 0.97 err: 0 0
+
+================== 660: Problem: LPnetlib/lp_qap12 m: 3192 n: 8856 nnz: 38304 152376
+rcond: 0.00000000000000000000e+00
+p: 1424 1424 MATLAB: 0.9041 CHOLMOD: 1.2285 speedup 0.74 err: 0 0
+
+================== 609: Problem: LPnetlib/lp_cre_a m: 3516 n: 7248 nnz: 18168 44866
+rcond: 0.00000000000000000000e+00
+p: 3407 3407 MATLAB: 0.0077 CHOLMOD: 0.0069 speedup 1.11 err: 0 0
+
+================== 619: Problem: LPnetlib/lp_dfl001 m: 6071 n: 12230 nnz: 35632 81917
+rcond: 0.00000000000000000000e+00
+p: 5652 5652 MATLAB: 1.0070 CHOLMOD: 1.3922 speedup 0.72 err: 0 0
+
+================== 661: Problem: LPnetlib/lp_qap15 m: 6330 n: 22275 nnz: 94950 378480
+rcond: 0.00000000000000000000e+00
+p: 617 617 MATLAB: 0.3764 CHOLMOD: 0.7196 speedup 0.52 err: 0 0
+
+================== 650: Problem: LPnetlib/lp_pds_06 m: 9881 n: 29351 nnz: 63220 88003
+rcond: 0.00000000000000000000e+00
+p: 9316 9316 MATLAB: 0.1965 CHOLMOD: 0.1951 speedup 1.01 err: 0 0
+
+================== 379: Problem: Cote/vibrobox m: 12328 n: 12328 nnz: 301700 301700
+rcond: 0.00000000000000000000e+00
+p: 11561 11561 MATLAB: 0.6442 CHOLMOD: 0.6420 speedup 1.00 err: 0 0
+
+================== 638: Problem: LPnetlib/lp_ken_11 m: 14694 n: 21349 nnz: 49058 82454
+rcond: 0.00000000000000000000e+00
+p: 14626 14626 MATLAB: 0.0411 CHOLMOD: 0.0413 speedup 0.99 err: 0 0
+test22: all tests passed
+=================================================================
+test23: test chol & cholmod2 on the sparse matrix used in "bench"
+Using each method's internal fill-reducing ordering:
+MATLAB x=A\b time: 0.0467 resid: 6e-14
+CHOLMOD x=A\b time: 0.0472 resid: 6e-14
+CHOLMOD speedup: 0.99
+
+S = A(p,p) where p is CHOLMOD's ordering:
+MATLAB R=chol(S) time: 0.0434 resid: 5e-14
+CHOLMOD L=lchol(S) time: 0.0363 resid: 5e-14
+CHOLMOD speedup: 1.20
+Warning: SYMMMD is obsolete and will be removed in a future version. Use SYMAMD instead.
+> In symmmd at 16
+ In test23 at 60
+ In cholmod_test at 131
+
+S = A(p,p) where p is MATLAB's ordering in x=A\b (symmmd):
+MATLAB R=chol(S) time: 0.0449 resid: 5e-14
+CHOLMOD L=lchol(S) time: 0.0369 resid: 5e-14
+CHOLMOD speedup: 1.22
+
+
+With no fill-reducing orderings:
+MATLAB R=chol(A) time: 0.1380 resid: 1e-13
+CHOLMOD L=lchol(A) time: 0.1098 resid: 1e-13
+CHOLMOD speedup: 1.26
+
+
+With no fill-reducing orderings (as used in "bench"):
+MATLAB x=A\b time: 0.0822 resid: 6e-14
+CHOLMOD x=A\b time: 0.0899 resid: 8e-14
+CHOLMOD speedup: 0.91
+=================================================================
+test24: test sdmult
+test 24 passed, maxerr 0
+=================================================================
+test25: test sdmult on a large matrix
+
+Test matrix: 9000-by-9000, nnz 3279690
+
+A*X where X is 9000-by-k
+k: 0 time: MATLAB 0.00 CHOLMOD 0.00 speedup 0.90 err 0e+00 mflop: MATLAB 0.0 CHOLMOD 0.0
+k: 1 time: MATLAB 0.02 CHOLMOD 0.02 speedup 1.00 err 0e+00 mflop: MATLAB 402.6 CHOLMOD 403.3
+k: 2 time: MATLAB 0.02 CHOLMOD 0.02 speedup 0.72 err 0e+00 mflop: MATLAB 740.2 CHOLMOD 535.8
+k: 3 time: MATLAB 0.12 CHOLMOD 0.03 speedup 4.51 err 0e+00 mflop: MATLAB 163.9 CHOLMOD 739.9
+k: 4 time: MATLAB 0.02 CHOLMOD 0.16 speedup 0.15 err 0e+00 mflop: MATLAB 1132.3 CHOLMOD 165.1
+k: 5 time: MATLAB 0.04 CHOLMOD 0.18 speedup 0.23 err 0e+00 mflop: MATLAB 828.0 CHOLMOD 187.1
+k: 6 time: MATLAB 0.04 CHOLMOD 0.18 speedup 0.22 err 0e+00 mflop: MATLAB 960.9 CHOLMOD 213.6
+k: 7 time: MATLAB 0.14 CHOLMOD 0.09 speedup 1.68 err 0e+00 mflop: MATLAB 320.6 CHOLMOD 537.6
+k: 8 time: MATLAB 0.05 CHOLMOD 0.22 speedup 0.21 err 0e+00 mflop: MATLAB 1127.1 CHOLMOD 240.8
+k: 9 time: MATLAB 0.16 CHOLMOD 0.23 speedup 0.69 err 0e+00 mflop: MATLAB 363.5 CHOLMOD 251.4
+k: 10 time: MATLAB 0.16 CHOLMOD 0.24 speedup 0.68 err 0e+00 mflop: MATLAB 398.6 CHOLMOD 271.1
+k: 10 time: MATLAB 0.16 CHOLMOD 0.24 speedup 0.68 err 0e+00 mflop: MATLAB 398.1 CHOLMOD 270.3
+k: 20 time: MATLAB 0.32 CHOLMOD 0.59 speedup 0.53 err 0e+00 mflop: MATLAB 412.6 CHOLMOD 220.7
+k: 30 time: MATLAB 0.28 CHOLMOD 0.94 speedup 0.30 err 0e+00 mflop: MATLAB 696.3 CHOLMOD 210.1
+k: 40 time: MATLAB 0.43 CHOLMOD 1.19 speedup 0.37 err 0e+00 mflop: MATLAB 604.7 CHOLMOD 220.8
+k: 50 time: MATLAB 0.60 CHOLMOD 1.43 speedup 0.42 err 0e+00 mflop: MATLAB 549.5 CHOLMOD 229.5
+k: 100 time: MATLAB 1.08 CHOLMOD 2.97 speedup 0.36 err 0e+00 mflop: MATLAB 606.6 CHOLMOD 221.0
+k: 200 time: MATLAB 2.26 CHOLMOD 5.95 speedup 0.38 err 0e+00 mflop: MATLAB 579.4 CHOLMOD 220.6
+k: 300 time: MATLAB 3.55 CHOLMOD 8.80 speedup 0.40 err 0e+00 mflop: MATLAB 554.7 CHOLMOD 223.5
+k: 400 time: MATLAB 4.65 CHOLMOD 12.36 speedup 0.38 err 0e+00 mflop: MATLAB 564.5 CHOLMOD 212.3
+k: 500 time: MATLAB 5.81 CHOLMOD 14.75 speedup 0.39 err 0e+00 mflop: MATLAB 564.7 CHOLMOD 222.3
+
+For comparison, here is CHOLMOD's x=A\b time:
+CHOLMOD x=A\b time: 18.82 (b is n-by-1) resid 2e-05
+CHOLMOD x=A\b time: 22.40 (b is n-by-100) resid 2e-05
+CHOLMOD x=A\b time: 26.86 (b is n-by-200) resid 2e-05
+CHOLMOD x=A\b time: 29.62 (b is n-by-300) resid 2e-05
+CHOLMOD x=A\b time: 33.93 (b is n-by-400) resid 2e-05
+CHOLMOD x=A\b time: 38.16 (b is n-by-500) resid 2e-05
+
+MATLAB x=A\b time: 24.45 (b is n-by-1) resid 1e-05
+test25 passed
+=================================================================
+test26: test logical full and sparse matrices
+test26 passed
+=================================================================
+test27: test nesdis
+# of components: 7
+size of root 32 out of 479 rows
+node 1 : parent 3 size 105 work 40598
+node 2 : parent 3 size 99 work 32753
+node 3 : parent 7 size 11 work 2584
+node 4 : parent 6 size 108 work 99359
+node 5 : parent 6 size 105 work 54811
+node 6 : parent 7 size 19 work 8846
+node 7 : parent 0 size 32 work 15983
+test27 passed
+=================================================================
+all tests passed
diff --git a/CHOLMOD/MATLAB/Test/dg.m b/CHOLMOD/MATLAB/Test/dg.m
new file mode 100644
index 0000000..433bdbd
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/dg.m
@@ -0,0 +1,76 @@
+function dg(A)
+%DG order and plot A*A', using CHOLMOD's nested dissection
+% used by test27.m
+% Example:
+% dg(A)
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+A = spones (A) ;
+[p cp cm] = nesdis (A, 'row') ;
+
+% get the corresponding column ordering. Order the columns
+% in increasing order of min(find(A(:,j)))
+
+[m n] = size (A) ;
+C = A (p,:) ;
+qmin = zeros (1,n) ;
+for j = 1:n
+ qmin (j) = min (find (C (:,j))) ; %#ok
+end
+[ignore q] = sort (qmin) ;
+
+C = C (:,q) ;
+% figure (1)
+clf
+subplot (2,3,1) ; treeplot (cp)
+drawnow
+subplot (2,3,2) ; spy (C)
+drawnow
+% axis off
+subplot (2,3,3) ; spy (C*C')
+drawnow
+% axis off
+
+ncomp = max(cm) ;
+fprintf ('# of components: %d\n', ncomp)
+
+% cs = [cm(p) n+1] ;
+% cboundaries = find (diff (cs)) ;
+
+fprintf ('size of root %d out of %d rows\n', length (find (cm == ncomp)), m);
+
+[cnt h pa po R] = symbfact2 (A (p,:), 'row') ;
+% rc = full (sum (R)) ;
+
+for k = 1:ncomp
+ fprintf ('node %4d : parent %4d size %6d work %g\n', ...
+ k, cp (k), length (find (cm == k)), sum (cnt (find (cm == k)).^2) ) ; %#ok
+end
+
+subplot (2,3,4) ; spy (A*A') ;
+drawnow
+
+subplot (2,3,5) ; spy (R+R') ;
+drawnow
+
+pamd = amd2 (A*A') ; % use AMD from SuiteSparse, not built-in
+[cnt h pa po R] = symbfact2 (A (pamd,:), 'row') ;
+subplot (2,3,6) ; spy (R+R') ;
+drawnow
+
+% s = bisect (A, 'row') ;
+% [ignore pp] = sort (s) ;
+% E = A(pp,:) ;
+% subplot (2,3,4) ; spy (E*E')
+% fprintf ('bisect: %d\n', length (find (s == 2))) ;
+
+% figure (2)
+% spy (C*C')
+% hold on
+% for j = cboundaries
+% plot ([1 n], [j j], 'r', [j j], [1 n], 'r') ;
+% end
+
+
diff --git a/CHOLMOD/MATLAB/Test/n2.m b/CHOLMOD/MATLAB/Test/n2.m
new file mode 100644
index 0000000..64239cb
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/n2.m
@@ -0,0 +1,74 @@
+%N2 script to test CHOLMOD septree function
+% Example:
+% n2
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+index = UFget ;
+f = find ((index.amd_lnz > 0) & (index.nrows > 200)) ;
+[ignore i] = sort (index.amd_lnz (f)) ;
+f = f (i) ;
+nmat = length (f) ;
+
+for i = f
+
+ Prob = UFget (i, index) ;
+ disp (Prob) ;
+ A = spones (Prob.A) ;
+ [m n] = size (A) ;
+ name = Prob.name ;
+ clear Prob
+
+ if (m == n)
+ mode = 'sym' ;
+ A = A + A' ;
+ len = n ;
+ elseif (m < n)
+ mode = 'row' ;
+ len = m ;
+ else
+ mode = 'col' ;
+ len = n ;
+ end
+
+ [p cp cmem] = nesdis (A, mode) ;
+
+ subplot (2,4,1) ;
+ treeplot (cp) ;
+
+ [cp2 cmem2] = septree (cp, cmem, 0.5, 200) ; %#ok
+ subplot (2,4,2) ;
+ treeplot (cp2) ;
+
+ [cp3 cmem3] = septree (cp, cmem, 0.2, 300) ; %#ok
+ subplot (2,4,3) ;
+ treeplot (cp3) ;
+
+ [cp4 cmem4] = septree (cp, cmem, 0.12, 500) ; %#ok
+ subplot (2,4,4) ;
+ treeplot (cp4) ;
+
+
+ [p cp cmem] = nesdis (A, mode, [200 1]) ;
+
+ subplot (2,4,5) ;
+ treeplot (cp) ;
+
+ [cp2 cmem2] = septree (cp, cmem, 0.5, 200) ; %#ok
+ subplot (2,4,6) ;
+ treeplot (cp2) ;
+
+ [cp3 cmem3] = septree (cp, cmem, 0.2, 300) ; %#ok
+ subplot (2,4,7) ;
+ treeplot (cp3) ;
+
+ [cp4 cmem4] = septree (cp, cmem, 0.12, 500) ; %#ok
+ subplot (2,4,8) ;
+ treeplot (cp4) ;
+
+ drawnow
+ % pause
+
+end
+
diff --git a/CHOLMOD/MATLAB/Test/nn.m b/CHOLMOD/MATLAB/Test/nn.m
new file mode 100644
index 0000000..10b55ff
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/nn.m
@@ -0,0 +1,159 @@
+%NN Compare nesdis with metis, in both quality and run time
+%
+% Example:
+% nn
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+index = UFget ;
+f = find (index.amd_lnz > 0) ;
+[ignore i] = sort (index.amd_lnz (f)) ;
+f = f (i) ;
+nmat = length (f) ;
+
+T1 = zeros (1,nmat) ;
+T2 = zeros (1,nmat) ;
+TM = zeros (1,nmat) ;
+Lnz1 = zeros (1,nmat) ;
+Lnz2 = zeros (1,nmat) ;
+LnzM = zeros (1,nmat) ;
+Fl1 = zeros (1,nmat) ;
+Fl2 = zeros (1,nmat) ;
+FlM = zeros (1,nmat) ;
+
+for k = 1:nmat
+
+ i = f (k) ;
+ Prob = UFget (i,index) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+
+ if (m ~= n)
+ continue ;
+ end
+
+ fprintf ('%35s: ', Prob.name) ;
+
+ if (m == n)
+ mode = 'sym' ;
+ A = A + A' ;
+ len = n ;
+ elseif (m < n)
+ mode = 'row' ;
+ len = m ;
+ else
+ mode = 'col' ;
+ len = n ;
+ end
+
+ fprintf (' %s ', mode) ;
+
+ % try nesdis using camd, and splitting connected components
+ tic
+ [p2 cparent2 cmember2] = nesdis (A, mode, [200 1]) ;
+ t2 = toc ;
+
+ % subplot (3,3,7) ; treeplot (cparent2) ;
+
+ % try nesdis using camd
+ tic
+ [p1 cparent1 cmember1] = nesdis (A, mode) ;
+ t1 = toc ;
+
+ % subplot (3,3,8) ; treeplot (cparent1) ;
+
+ % try metis
+ tic
+ pm = metis (A, mode) ;
+ tm = toc ;
+
+ if (any (sort (p1) ~= 1:len))
+ error ('p1!') ;
+ end
+
+ if (any (sort (p2) ~= 1:len))
+ error ('p2!') ;
+ end
+
+ % compare ordering quality
+
+ if (m == n)
+ c2 = symbfact2 (A (p2,p2), mode) ; fl2 = sum (c2.^2) ; c2 = sum (c2) ;
+ c1 = symbfact2 (A (p1,p1), mode) ; fl1 = sum (c1.^2) ; c1 = sum (c1) ;
+ cm = symbfact2 (A (pm,pm), mode) ; flm = sum (cm.^2) ; cm = sum (cm) ;
+ elseif (m < n)
+ c2 = symbfact2 (A (p2, :), mode) ; fl2 = sum (c2.^2) ; c2 = sum (c2) ;
+ c1 = symbfact2 (A (p1, :), mode) ; fl1 = sum (c1.^2) ; c1 = sum (c1) ;
+ cm = symbfact2 (A (pm, :), mode) ; flm = sum (cm.^2) ; cm = sum (cm) ;
+ else
+ c2 = symbfact2 (A ( :,p2), mode) ; fl2 = sum (c2.^2) ; c2 = sum (c2) ;
+ c1 = symbfact2 (A ( :,p1), mode) ; fl1 = sum (c1.^2) ; c1 = sum (c1) ;
+ cm = symbfact2 (A ( :,pm), mode) ; flm = sum (cm.^2) ; cm = sum (cm) ;
+ end
+
+ T1 (k) = t1 ;
+ T2 (k) = t2 ;
+ TM (k) = tm ;
+ Lnz1 (k) = c1 ;
+ Lnz2 (k) = c2 ;
+ LnzM (k) = cm ;
+ Fl1 (k) = fl1 ;
+ Fl2 (k) = fl2 ;
+ FlM (k) = flm ;
+ tmax = max ([max(T1 (1:k)) max(T2 (1:k)) max(TM (1:k))]) ;
+ tmin = min ([min(T1 (1:k)) min(T2 (1:k)) min(TM (1:k))]) ;
+ cmax = max ([max(Lnz1 (1:k)) max(Lnz2 (1:k)) max(LnzM (1:k))]) ;
+ flmax =max ([max(Fl1 (1:k)) max(Fl2 (1:k)) max(FlM (1:k))]) ;
+
+ fprintf (...
+ 'time %8.2f %8.2f %8.2f speedup %8.2f flop %8.2e %8.2e %8.2e ratio %8.2f\n', ...
+ t2, t1, tm, tm/t1, fl2, fl1, flm, flm/fl1) ;
+
+ if (mod (k, 20) ~= 0)
+ continue
+ end
+
+ subplot (3,3,1) ;
+ x = T1 (1:k) ./ T2 (1:k) ;
+ semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ;
+ axis tight
+ title (sprintf ('(nesdis default)/(with split) time, median: %g', ...
+ median (x))) ;
+
+ subplot (3,3,2) ;
+ x = (Lnz1 (1:k) ./ Lnz2 (1:k)) ;
+ semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ;
+ axis tight
+ title (sprintf ('(nesdis default)/(with split) lnz, median: %g', ...
+ median (x))) ;
+
+ subplot (3,3,3) ;
+ x = (Fl1 (1:k) ./ Fl2 (1:k)) ;
+ semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ;
+ axis tight
+ title (sprintf ('(nesdis default)/(with split) flops, median: %g', ...
+ median (x))) ;
+
+ subplot (3,3,4) ;
+ x = T1 (1:k) ./ TM (1:k) ;
+ semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ;
+ axis tight
+ title (sprintf ('(nesdis default)/metis time, median %g', median (x))) ;
+
+ subplot (3,3,5) ;
+ x = (Lnz1 (1:k) ./ LnzM (1:k)) ;
+ semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ;
+ axis tight
+ title (sprintf ('(nesdis default)/metis lnz, median: %g', median (x))) ;
+
+ subplot (3,3,6) ;
+ x = (Fl1 (1:k) ./ FlM (1:k)) ;
+ semilogy (1:k, x, 'o', [1 k], [1 1], 'r-') ;
+ axis tight
+ title (sprintf ('(nesdis default)/metis flops, median: %g', median (x))) ;
+
+ drawnow
+
+ % pause
+end
diff --git a/CHOLMOD/MATLAB/Test/test0.m b/CHOLMOD/MATLAB/Test/test0.m
new file mode 100644
index 0000000..35ae12a
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test0.m
@@ -0,0 +1,287 @@
+function test0 (nmat)
+%TEST0 test most CHOLMOD functions
+% Example:
+% test0(nmat)
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test0: test most CHOLMOD functions\n') ;
+
+% This test requires UFget, the MATLAB interface to the UF sparse matrix
+% collection. You can obtain UFget from
+% http://www.cise.ufl.edu/research/sparse/matrices.
+
+try % load UF index
+ index = UFget ;
+catch
+ error ('Test aborted. UF sparse matrix collection not available.\n') ;
+end
+
+f = find (index.posdef) ;
+[ignore i] = sort (index.nrows (f)) ;
+f = f (i) ;
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+doplots = 0 ;
+
+if (doplots)
+ clf
+end
+
+% skip = [937:939 1202:1211] ;
+skip = 937:939 ;
+if (nargin > 0)
+ nmat = max (0,nmat) ;
+ nmat = min (nmat, length (f)) ;
+ f = f (1:nmat) ;
+end
+
+% f= 229
+
+fprintf ('test matrices sorted by dimension:\n') ;
+for i = f
+ if (any (i == skip))
+ continue
+ end
+ fprintf ('%4d: %-20s %-20s %12d %d\n', i, ...
+ index.Group {i}, index.Name {i}, index.nrows (i), index.posdef (i)) ;
+end
+
+% pause
+
+for i = f
+
+ if (any (i == skip))
+ continue
+ end
+
+ % try
+
+ Problem = UFget (i) ;
+ A = Problem.A ;
+ fprintf ('\n================== Problem: %d: %s n: %d nnz: %d\n', ...
+ i, Problem.name, size (A,1), nnz (A)) ;
+ fprintf ('title: %s\n', Problem.title) ;
+ clear Problem
+ n = size (A,1) ;
+
+ % use AMD from SuiteSparse
+ tic
+ p = amd2 (A) ;
+ t0 = toc ;
+ fprintf ('time: amd %10.4f\n', t0) ;
+
+ S = A (p,p) ;
+
+ if (doplots)
+ subplot (3,2,1) ; spy (A) ; title ('A original') ;
+ subplot (3,2,2) ; spy (S) ; title ('A permuted') ;
+ drawnow ;
+ end
+
+ % ensure chol, chol2, and lchol are loaded, for more accurate timing
+ R = chol2 (sparse (1)) ; %#ok
+ R = chol (sparse (1)) ; %#ok
+ R = lchol (sparse (1)) ; %#ok
+ R = ldlchol (sparse (1)) ; %#ok
+ R = ldlupdate (sparse (1), sparse (1)) ; %#ok
+ c = symbfact (sparse (1)) ; %#ok
+
+ tic ;
+ L = lchol (S) ;
+ t3 = toc ;
+ if (doplots)
+ subplot (3,2,5) ; spy (L) ; title ('L=lchol') ;
+ drawnow ;
+ end
+ fprintf ('CHOLMOD time: L=lchol %10.4f nnz(L): %d\n', t3, nnz (L)) ;
+ lnorm = norm (L, 1) ;
+
+ err = ldl_normest (S, L) / lnorm ;
+ if (err > 1e-6)
+ error ('!') ;
+ end
+ clear L
+
+ tic ;
+ R = chol2 (S) ;
+ t2 = toc ;
+ if (doplots)
+ subplot (3,2,3) ; spy (R) ; title ('R=chol2') ;
+ drawnow ;
+ end
+ fprintf ('CHOLMOD time: R=chol2 %10.4f nnz(R): %d\n', t2, nnz (R)) ;
+
+ err = ldl_normest (S, R') / lnorm ;
+ if (err > 1e-6)
+ error ('!') ;
+ end
+ clear R
+
+ tic ;
+ R = chol (S) ;
+ t1 = toc ;
+ fprintf ('MATLAB time: R=chol %10.4f nnz(R): %d\n', t1, nnz (R)) ;
+ if (doplots)
+ subplot (3,2,4) ; spy (R) ; title ('chol') ;
+ drawnow ;
+ end
+
+ err = ldl_normest (S, R') / lnorm ;
+ if (err > 1e-6)
+ error ('!') ;
+ end
+ clear R
+
+ tic ;
+ [count,h,parent,post,R] = symbfact (S) ;
+ t7 = toc ;
+ fprintf ('MATLAB [..,R]=symbfact %10.4f nnz(R): %d\n', t7, nnz (R)) ;
+
+ fprintf ('\nCHOLMOD speedup vs MATLAB chol: R: %8.2f L: %8.2f\n\n', ...
+ t1/t2, t1/t3) ;
+
+ fprintf ('\nCHOLMOD numeric lchol vs MATLAB symbfact: %8.2f\n', t7/t3) ;
+
+ clear R S
+
+ % use AMD or METIS, doing the ordering in CHOLMOD
+ tic
+ [L,p,q] = lchol (A) ;
+ t4 = toc ;
+ fprintf ('CHOLMOD time: [L,,q]=lchol %10.4f nnz(L): %d\n', ...
+ t4, nnz (L)) ;
+ if (doplots)
+ subplot (3,2,6) ; spy (L) ; title ('[L,p,q]=lchol') ;
+ drawnow ;
+ end
+
+ err = ldl_normest (A (q,q), L) / lnorm ;
+ if (err > 1e-6)
+ error ('!') ;
+ end
+ clear L
+
+ % try an LDL' factorization, LD has LDL' factorization of S = A(q,q)
+ tic
+ [LD,p,q] = ldlchol (A) ;
+ t5 = toc ;
+ fprintf ('CHOLMOD time: [L,,q]=ldlchol %10.4f nnz(L): %d\n', ...
+ t5, nnz (LD)) ;
+ [L,D] = ldlsplit (LD) ;
+ S = A (q,q) ;
+
+ err = ldl_normest (S, L, D) / lnorm ;
+ if (err > 1e-6)
+ error ('!') ;
+ end
+ clear L D A
+
+ % update the LDL' factorization (rank 1 to 8). Pick a C that has
+ % the same pattern as a random set of columns of L, so no fill-in
+ % occurs. Then add one arbitrary entry, to add some fill-in to L.
+ k = 1 + floor (rand (1) * 8) ;
+ cols = randperm (n) ;
+ cols = cols (1:k) ;
+ C = sprandn (LD (:,cols)) ;
+ row = 1 + floor (rand (1) * n) ;
+ C (row,1) = 1 ;
+
+ if (~isreal (C) | ~isreal (LD)) %#ok
+ fprintf ('skip update/downdate of complex matrix ...\n') ;
+ continue ;
+ end
+
+ tic
+ LD2 = ldlupdate (LD, C) ;
+ t = toc ;
+ fprintf ('\nCHOLMOD time: rank-%d ldlupdate %10.4f nnz(L) %d', ...
+ k, t, nnz (LD2)) ;
+
+ if (nnz (LD2) > nnz (LD))
+ fprintf (' with fill-in\n') ;
+ else
+ fprintf (' no fill-in\n') ;
+ end
+ clear LD
+
+ % check the factorization, LD2 has LDL' factorization of S+C*C'
+ [L,D] = ldlsplit (LD2) ;
+ err = ldl_normest (S + C*C', L, D) / lnorm ;
+ if (err > 1e-6)
+ error ('!') ;
+ end
+ clear L D
+
+ % downate the LDL' factorization, with just part of C
+ % no change to the pattern occurs.
+ k = max (1, floor (k/2)) ;
+ C1 = C (:, 1:k) ;
+ C2 = C (:, k+1:end) ; %#ok
+ tic
+ LD3 = ldlupdate (LD2, C1, '-') ;
+ t = toc ;
+ clear LD2
+ fprintf ('CHOLMOD time: rank-%d ldldowndate %10.4f nnz(L) %d', ...
+ k, t, nnz (LD3)) ;
+ fprintf (' no fill-in\n') ;
+
+ % check the factorization, LD3 has LDL' factorization of A(q,q)+C2*C2'
+ [L,D] = ldlsplit (LD3) ;
+ S2 = S + C*C' - C1*C1' ;
+ err = ldl_normest (S2, L, D) / lnorm ;
+ if (err > 1e-6)
+ error ('!') ;
+ end
+
+ % now test resymbol
+ LD4 = resymbol (LD3, S2) ;
+ [L,D] = ldlsplit (LD4) ;
+ err = ldl_normest (S2, L, D) / lnorm ;
+ if (err > 1e-6)
+ error ('!') ;
+ end
+ fprintf ('after resymbol: %d\n', nnz (LD4)) ;
+
+ % compare resymbol with ldlchol
+ LD5 = ldlchol (S2) ;
+ if (nnz (LD5) ~= nnz (LD4))
+ error ('!') ;
+ end
+ if (nnz (spones (LD5) - spones (LD4)) ~= 0)
+ error ('!') ;
+ end
+
+ b = rand (n,2) ;
+ x = ldlsolve (LD4, b) ;
+ err1 = norm (S2*x-b,1) / norm (S,1) ;
+
+ fprintf ('CHOLMOD residual: %6.1e\n', err1) ;
+
+ x = S2\b ;
+ err2 = norm (S2*x-b,1) / norm (S,1) ;
+ fprintf ('MATLAB residual: %6.1e\n', err2) ;
+
+ b = sprandn (n,3,0.4) ;
+ x = ldlsolve (LD4, b) ;
+ err1 = norm (S2*x-b,1) / norm (S,1) ;
+
+ fprintf ('CHOLMOD residual: %6.1e (sparse b)\n', err1) ;
+
+ x = S2\b ;
+ err2 = norm (S2*x-b,1) / norm (S,1) ;
+ fprintf ('MATLAB residual: %6.1e (sparse b)\n', err2) ;
+
+ % catch
+ % fprintf ('failed\n') ;
+ % end
+
+ clear A S C L R LD LD2 LD3 D p q C1 C2 LD3 S2 LD4 b x LD5
+
+end
+
+fprintf ('test0 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test1.m b/CHOLMOD/MATLAB/Test/test1.m
new file mode 100644
index 0000000..73e2a10
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test1.m
@@ -0,0 +1,84 @@
+function test1 (wait)
+%TEST1 test sparse2
+% Example:
+% test1
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test1: test sparse2\n') ;
+
+if (nargin == 0)
+ wait = 0 ;
+end
+
+m = 3 ;
+n = 4 ;
+
+ii = { 1, [2 3]', 2, [ ] } ;
+jj = { 1, [2 3]', 3, [ ] } ;
+ss = { 1, [2 3]', pi, [ ] } ;
+
+for ki = 1:length (ii)
+ for kj = 1:length (jj)
+ for ks = 1:length (ss)
+
+ fprintf ('\n-----------------------------------------------\n') ;
+ i = ii {ki} %#ok
+ j = jj {kj} %#ok
+ s = ss {ks} %#ok
+ m %#ok
+ n %#ok
+ clear A1 A2 B1 B2
+
+ fprintf ('\nA1 = sparse (i,j,s,m,n)\n') ;
+ try % sparse, possibly with invalid inputs
+ A1 = sparse (i,j,s,m,n) %#ok
+ fprintf ('size A1: %d %d\n', size (A1)) ;
+ catch
+ A1 = 'A failed' ;
+ fprintf ('sparse failed\n') ;
+ end
+
+ fprintf ('\nA2 = sparse2 (i,j,s,m,n)\n') ;
+ try % sparse2, possibly with invalid inputs
+ A2 = sparse2 (i,j,s,m,n) %#ok
+ fprintf ('size A2: %d %d\n', size (A2)) ;
+ catch
+ A2 = 'A failed' ;
+ fprintf ('sparse2 failed\n') ;
+ end
+
+ fprintf ('\nB1 = sparse (i,j,s)\n') ;
+ try % sparse, possibly with invalid inputs
+ B1 = sparse (i,j,s) %#ok
+ fprintf ('size B1: %d %d\n', size (B1)) ;
+ catch
+ B1 = 'B failed' ;
+ fprintf ('sparse failed\n') ;
+ end
+
+ fprintf ('\nB2 = sparse2 (i,j,s)\n') ;
+ try % sparse2, possibly with invalid inputs
+ B2 = sparse2 (i,j,s) %#ok
+ fprintf ('size B2: %d %d\n', size (B2)) ;
+ catch
+ B2 = 'B failed' ;
+ fprintf ('sparse2 failed\n') ;
+ end
+
+ if (wait)
+ pause
+ end
+
+ if (~isequal (A1,A2) | ~isequal (B1,B2)) %#ok
+ fprintf (...
+ '========================== SPARSE AND SPARSE2 DIFFER\n') ;
+ end
+
+ end
+ end
+end
+
+fprintf ('test1 passed (review the above results)\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test10.m b/CHOLMOD/MATLAB/Test/test10.m
new file mode 100644
index 0000000..95a3ad3
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test10.m
@@ -0,0 +1,124 @@
+function test10 (nmat)
+%TEST10 test cholmod2's backslash on real and complex matrices
+% Example:
+% test10(nmat)
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test10: test cholmod2''s backslash\n') ;
+
+rand ('state',0) ;
+randn ('state',0) ;
+
+index = UFget ;
+f = find (index.posdef) ;
+[ignore i] = sort (index.nrows (f)) ;
+f = f (i) ;
+
+% start after nd6k
+% f = f ((find (f == 937) + 1):end) ;
+
+skip = [937:939 1202:1211] ;
+if (nargin > 0)
+ nmat = max (0,nmat) ;
+ nmat = min (nmat, length (f)) ;
+ f = f (1:nmat) ;
+end
+
+fprintf ('test matrices sorted by dimension:\n') ;
+for i = f
+ if (any (i == skip))
+ continue
+ end
+ fprintf ('%4d: %-20s %-20s %12d %d\n', i, ...
+ index.Group {i}, index.Name {i}, index.nrows (i), index.posdef (i)) ;
+end
+
+
+for nn = f
+ % for nn = 23
+
+ if (any (nn == skip))
+ continue
+ end
+
+ % try
+
+ for complexity = 0:1
+
+ if nn < 0
+ n = -nn ;
+ A = rand (n) + (complexity * rand(n) * 1i) ;
+ A=A*A' ;
+ full (A)
+ A = sparse (A) ;
+
+ elseif (nn == 0)
+
+ i = 1i ;
+ A = [ 11 4-i 1+i 2+2*i
+ 4+i 22 0 0
+ 1-i 0 33 0
+ 2-2*i 0 0 44 ] ;
+ A = sparse (A) ;
+ p = [4 3 2 1] ; %#ok
+ full (A)
+ A = sparse (A) ;
+
+ else
+
+ if (~complexity)
+ nn %#ok
+ Prob = UFget (nn) %#ok
+ end
+ A = Prob.A ;
+ if (complexity)
+ A = A / norm(A,1) ;
+ Z = .1 * sprandn (A) * 1i ;
+ Z = Z+Z' ;
+ A = A + Z ;
+ A = A + norm(A,1) * speye (size(A,1)) ;
+ end
+ n = size (A,1) ;
+ end
+
+ for sparsity = 0:1
+
+ if (sparsity)
+ b = sprandn (n,4,0.1) ;
+ else
+ b = rand (n,4) ;
+ end
+
+ b1 = b (:,1) ;
+
+ [x1,x2,e1,e2] = testsolve (A,b1) ; %#ok
+ [x1,x2,e1,e2] = testsolve (A,b) ; %#ok
+
+ if (sparsity)
+ b = sprandn (n,9,0.1) ;
+ else
+ b = rand (n,9) ;
+ end
+
+ [x1,x2,e1,e2] = testsolve (A,b) ; %#ok
+
+ if (sparsity)
+ b = sprandn (n,9,0.1) + sprandn (n,9,0.1)*1i ;
+ else
+ b = rand (n,9) + rand(n,9)*1i ;
+ end
+
+ b1 = b (:,1) ;
+
+ [x1,x2,e1,e2] = testsolve (A,b1) ; %#ok
+ [x1,x2,e1,e2] = testsolve (A,b) ; %#ok
+
+ end
+ end
+ % catch
+ % fprintf (' failed\n') ;
+ % end
+end
diff --git a/CHOLMOD/MATLAB/Test/test11.m b/CHOLMOD/MATLAB/Test/test11.m
new file mode 100644
index 0000000..99e4b18
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test11.m
@@ -0,0 +1,138 @@
+function test11 (nmat)
+%TEST11 compare CHOLMOD and MATLAB, save results in Results.mat
+% also tests analyze
+% Example:
+% test11(nmat)
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test11 : compare CHOLMOD and MATLAB, save results in Results.mat\n');
+
+rand ('state',0) ;
+randn ('state',0) ;
+
+index = UFget ;
+f = find (index.posdef) ;
+[ignore i] = sort (index.nrows (f)) ;
+f = f (i) ;
+clear ignore
+
+% start after nd6k
+% f = f ((find (f == 937) + 1):end) ;
+
+skip = [937:939 1202:1211] ;
+
+if (nargin > 0)
+ nmat = max (0,nmat) ;
+ nmat = min (nmat, length (f)) ;
+ f = f (1:nmat) ;
+end
+
+fprintf ('test matrices sorted by dimension:\n') ;
+for i = f
+ if (any (i == skip))
+ continue
+ end
+ fprintf ('%4d: %-20s %-20s %12d %d\n', i, ...
+ index.Group {i}, index.Name {i}, index.nrows (i), index.posdef (i)) ;
+end
+
+kk = 0 ;
+nmat = length (f) ;
+T1 = zeros (1,nmat) ; % matlab time
+T2 = zeros (1,nmat) ; % cholmod2 time
+E1 = zeros (1,nmat) ; % matlab residual
+E2 = zeros (1,nmat) ; % cholmod2 residual
+FL = zeros (1,nmat) ; % cholmod2 flop count
+LNZ = zeros (1,nmat) ; % cholmod2 lnz
+
+for kkk = 1:length(f)
+
+ nn = f (kkk) ;
+
+ if (any (nn == skip))
+ continue
+ end
+
+ % try
+
+ fprintf ('\n%3d: %s/%s\n', nn, index.Group {nn}, index.Name {nn}) ;
+ Prob = UFget (nn) ;
+ A = Prob.A ;
+ clear Prob
+ n = size (A,1) ;
+ b = rand (n,1) ;
+
+ % analyze
+ [p count] = analyze (A) ;
+ % LDL' flop count
+ % fl = sum ((count-1).*(count-1) + 2*(count-1)) ;
+ % LL' flop count
+ fl = sum (count.^2) ;
+ lnz = sum (count) ;
+ fprintf ('n %d lnz %g fl %g\n', n, lnz, fl) ;
+ clear p count
+
+ % try
+ k2 = 0 ;
+ t2 = 0 ;
+ while (t2 < 1)
+ tic
+ x = cholmod2 (A,b) ;
+ t = toc ;
+ t2 = t2 + t ;
+ k2 = k2 + 1 ;
+ end
+ t2 = t2 / k2 ;
+ e2 = norm (A*x-b,1) ;
+ % catch
+ % e2 = Inf ;
+ % k2 = Inf ;
+ % t2 = Inf ;
+ % end
+ fprintf ('cholmod2: t: %10.5f e: %6.1e mflop %6.0f\n', ...
+ t2, e2, 1e-6 * fl / t2) ;
+
+ % try
+ k1 = 0 ;
+ t1 = 0 ;
+ while (t1 < 1)
+ tic
+ x = A\b ;
+ t = toc ;
+ t1 = t1 + t ;
+ k1 = k1 + 1 ;
+ end
+ t1 = t1 / k1 ;
+ e1 = norm (A*x-b,1) ;
+ % catch
+ % e1 = Inf ;
+ % k1 = Inf ;
+ % t1 = Inf ;
+ % end
+ fprintf ('matlab: t: %10.5f e: %6.1e mflop %6.0f', ...
+ t1, e1, 1e-6 * fl / t1) ;
+
+ fprintf (' cholmod2 speedup: %5.1f\n', t1/t2) ;
+
+ kk = kk + 1 ;
+ T1 (kk) = t1 ;
+ T2 (kk) = t2 ;
+ E1 (kk) = e1 ;
+ E2 (kk) = e2 ;
+ FL (kk) = fl ;
+ LNZ (kk) = lnz ;
+ save Results T1 T2 E1 E2 FL LNZ f kkk
+
+ % catch
+ % fprintf (' failed\n') ;
+ % end
+
+ clear A x b
+
+end
+
+% test11results
+fprintf ('test11 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test11results.m b/CHOLMOD/MATLAB/Test/test11results.m
new file mode 100644
index 0000000..5ffd69c
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test11results.m
@@ -0,0 +1,50 @@
+function test11results
+%TEST11RESULTS analyze results from test11.m
+% Example:
+% test11results
+% See also test11, cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+load Results
+index = UFget ;
+
+c = E1(1:kkk) < 1 & T1(1:kkk) > 0 ;
+m = E2(1:kkk) < 1 & T2(1:kkk) > 0 ;
+cgood = find (c) ; %#ok
+mgood = find (m) ; %#ok
+good = find (c | m) ;
+bad = find (~(c|m)) ;
+
+fl_per_lnz = FL(1:kkk) ./ LNZ(1:kkk) ;
+speedup = T1(1:kkk) ./ T2(1:kkk) ;
+
+[ignore ii] = sort (fl_per_lnz (good)) ;
+good = good (ii) ;
+
+fprintf ('MATLABtime CHOLMOD(time,flop,nnz(L)) speedup problem\n') ;
+for k = good
+ i = f (k) ;
+% fprintf ('%4d: t1 %10.2f t2 %10.2f fl %6.1e lnz %6.1e %s/%s\n', ...
+% i, T1(k), T2(k), FL(k), LNZ(k), index.Group{i}, index.Name{i}) ;
+ fprintf ('%10.4f %10.4f %6.1e %6.1e %5.2f %s/%s\n', ...
+ T1(k), T2(k), FL(k), LNZ(k), speedup(k), ...
+ index.Group{i}, index.Name{i}) ;
+end
+
+fprintf ('\nfailed in both:\n') ;
+for k = bad
+ i = f (k) ;
+ fprintf ('%10.4f %10.4f %6.1e %6.1e %5.2f %s/%s\n', ...
+ T1(k), T2(k), FL(k), LNZ(k), speedup(k), ...
+ index.Group{i}, index.Name{i}) ;
+end
+
+% figure (3)
+clf
+loglog (fl_per_lnz (good), speedup (good), 'x') ;
+axis ([1 4000 .1 50]) ;
+xlabel ('Cholesky flop count / nnz(L)') ;
+ylabel ('(MATLAB x=A\\b time) / (CHOLMOD time)') ;
+
+drawnow
diff --git a/CHOLMOD/MATLAB/Test/test12.m b/CHOLMOD/MATLAB/Test/test12.m
new file mode 100644
index 0000000..fb81d1d
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test12.m
@@ -0,0 +1,214 @@
+function test12 (nmat)
+%TEST12 test etree2 and compare with etree
+% Example:
+% test12(nmat)
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test12: test etree2 and compare with etree\n') ;
+
+index = UFget ;
+
+% only test matrices with nrows = 109000 or less. large ones nearly always
+% cause a MATLAB segfault.
+% f = find (index.nrows < 109000) ;
+f = 1:length (index.nrows) ;
+
+% sort by row dimension
+[ignore i] = sort (index.nrows (f)) ;
+f = f (i) ;
+
+if (nargin > 0)
+ nmat = max (0,nmat) ;
+ nmat = min (nmat, length (f)) ;
+ f = f (1:nmat) ;
+end
+
+% MATLAB 7.0 (R14, sp2, linux) etree gives a segfault for these matrices:
+s_skip = [ 803 374 1287 1311 1308 957 958 1257 955 761 1282 1230 1256 ...
+ 924 1302 537 820 821 822 1258 ...
+ 844 845 1238 804 939 1270 1305 1208 1209 290 879 928 1307 1244 ...
+ 1275 1276 1296 885 1269 959 542 1290 ] ;
+
+sym_skip = s_skip ;
+
+p_sym_skip = 1296 ;
+p_symt_skip = 1296 ;
+
+symt_skip= [ s_skip 592 593 809 ] ;
+
+rowcol_skip = [ 646 ...
+ 1224 803 588 589 374 1287 562 563 801 1311 1246 951 1308 950 ...
+ 957 958 800 1257 564 565 955 761 1282 590 591 1230 1256 952 566 ...
+ 567 924 1302 1293 1294 537 820 821 822 1306 849 1258 592 593 ...
+ 1225 844 845 1226 1238 1227 804 939 1270 752 753 1305 809 1228 ...
+ 1208 1209 1291 1292 1300 856 1229 290 879 928 1307 857 1244 ...
+ 1275 1276 1296 885 858 859 1269 1263 959 542 1290 ] ;
+
+col_skip = [ rowcol_skip 647 612 610 648 799 651 652 750 751 640 ] ;
+
+row_skip= [ rowcol_skip 903 373 ] ;
+
+% f = f (find (f == 1290) : end) ;
+
+fprintf ('Matrices to test: %d\n', length (f)) ;
+
+
+for i = f
+
+ % try
+
+ Problem = UFget (i) ;
+ A = spones (Problem.A) ;
+ [m n] = size (A) ;
+ fprintf ('\n%4d: %-20s nrow: %6d ncol: %6d nnz: %10d\n', ...
+ i, Problem.name, m, n, nnz(A)) ;
+
+ % if (max (m,n) < 500)
+ % A = full (A) ;
+ % end
+
+ % warmup, for accurate timing
+ etree (sparse (1)) ;
+ etree2 (sparse (1)) ;
+ amd2 (sparse (1)) ;
+
+ % test column etree
+ skip = any (i == col_skip) | m > 109000 ; %#ok
+ if (~skip)
+ tic ;
+ [parent post] = etree (A, 'col') ;
+ t1 = toc ;
+ else
+ t1 = Inf ;
+ end
+
+ tic ;
+ [my_parent my_post] = etree2 (A, 'col') ;
+ t2 = toc ;
+
+ if (~skip)
+ if (any (parent ~= my_parent))
+ error ('parent invalid!') ;
+ end
+ end
+ fprintf ('etree(A,''col''): %8.4f %8.4f speedup %8.2f ',...
+ t1, t2, t1/t2);
+ if (~skip)
+ if (any (post ~= my_post))
+ fprintf ('postorder differs') ;
+ end
+ end
+ fprintf ('\n') ;
+
+ % test row etree
+ skip = any (i == row_skip) | m > 109000 ; %#ok
+ if (~skip)
+ tic ;
+ [parent post] = etree (A', 'col') ;
+ t1 = toc ;
+ else
+ t1 = Inf ;
+ end
+
+ tic ;
+ [my_parent my_post] = etree2 (A, 'row') ;
+ t2 = toc ;
+
+ if (~skip)
+ if (any (parent ~= my_parent))
+ error ('parent invalid!') ;
+ end
+ end
+ fprintf ('etree(A,''row''): %8.4f %8.4f speedup %8.2f ',...
+ t1, t2, t1/t2);
+ if (~skip)
+ if (any (post ~= my_post))
+ fprintf ('postorder differs') ;
+ end
+ end
+ fprintf ('\n') ;
+
+
+
+ if (m == n)
+
+ for trial = 1:2
+
+ if (trial == 1)
+ skip1 = any (i == sym_skip) | m > 109000 ; %#ok
+ skip2 = any (i == symt_skip) | m > 109000 ; %#ok
+ else
+ skip1 = any (i == p_sym_skip) | m > 109000 ; %#ok
+ skip2 = any (i == p_symt_skip) | m > 109000 ; %#ok
+ fprintf ('after amd:\n') ;
+ p = amd2 (A) ; % use AMD from SuiteSparse
+ A = A (p,p) ;
+ end
+
+ % test symmetric etree, using triu(A)
+ if (~skip1)
+ tic ;
+ [parent post] = etree (A) ;
+ t1 = toc ;
+ else
+ t1 = Inf ;
+ end
+
+ tic ;
+ [my_parent my_post] = etree2 (A) ;
+ t2 = toc ;
+
+ if (~skip1)
+ if (any (parent ~= my_parent))
+ error ('parent invalid!') ;
+ end
+ end
+ fprintf ('etree(A): %8.4f %8.4f speedup %8.2f ',...
+ t1, t2, t1/t2);
+ if (~skip1)
+ if (any (post ~= my_post))
+ fprintf ('postorder differs') ;
+ end
+ end
+ fprintf ('\n') ;
+
+ % test symmetric etree, using tril(A)
+ if (~skip2)
+ tic ;
+ [parent post] = etree (A') ;
+ t1 = toc ;
+ else
+ t1 = Inf ;
+ end
+
+ tic ;
+ [my_parent my_post] = etree2 (A, 'lo') ;
+ t2 = toc ;
+
+ if (~skip2)
+ if (any (parent ~= my_parent))
+ error ('parent invalid!') ;
+ end
+ end
+ fprintf('etree(A''): %8.4f %8.4f speedup %8.2f ',...
+ t1, t2, t1/t2);
+ if (~skip2)
+ if (any (post ~= my_post))
+ fprintf ('postorder differs') ;
+ end
+ end
+ fprintf ('\n') ;
+
+ end
+
+ end
+
+ % catch
+ % fprintf ('%d: failed\n', i) ;
+ % end
+end
+
+fprintf ('test12 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test13.m b/CHOLMOD/MATLAB/Test/test13.m
new file mode 100644
index 0000000..0f53009
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test13.m
@@ -0,0 +1,35 @@
+function test13
+%TEST13 test cholmod2 and MATLAB on large tridiagonal matrices
+% Example:
+% test13
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test13: test cholmod2 and MATLAB on large tridiagonal matrices\n') ;
+
+for n = [10000 1e4 1e5 1e6]
+
+ e = ones (n,1) ;
+ A = spdiags ([e 4*e e], -1:1, n, n) ;
+ clear e
+ b = rand (n,1) ;
+
+ tic ;
+ x = cholmod2 (A,b) ;
+ t2 = toc ;
+ e = norm (A*x-b,1) ;
+ fprintf ('n %9d cholmod2 %8.2f err %6.1e\n', n, t2, e) ;
+
+ tic ;
+ x = A\b ;
+ t1 = toc ;
+ e = norm (A*x-b,1) ;
+ fprintf ('n %9d matlab %8.2f err %6.1e\n', n, t1, e) ;
+
+ clear A b
+
+end
+
+
diff --git a/CHOLMOD/MATLAB/Test/test14.m b/CHOLMOD/MATLAB/Test/test14.m
new file mode 100644
index 0000000..58ee672
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test14.m
@@ -0,0 +1,127 @@
+function test14 (nmat)
+%TEST14 test metis, symbfact2, and etree2
+% Example:
+% test14(nmat)
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test14: test metis, symbfact2, and etree2\n') ;
+
+index = UFget ;
+
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+
+% f1 = find (max (index.nrows (f), index.ncols (f)) > 55500) ;
+% f1 = f1 (1) ;
+% f = f (f1:end) ;
+
+% These bugs show up when Common->metis_memory is set to zero:
+% skip = [ 1298 ] ; % runs out of memory in metis(A,'row')
+skip = 1257 ; %#ok % GHS_psdef/crankseg_1: segfault in metis(A,'row') ;
+skip = 850 ; %#ok % Chen/pkustk04: segfault in metis(A,'row') ;
+skip = [ ] ; %#ok
+
+if (nargin > 0)
+ nmat = max (0,nmat) ;
+ nmat = min (nmat, length (f)) ;
+ f = f (1:nmat) ;
+end
+
+for i = f
+
+ fprintf ('%d:\n', i) ;
+ if (any (skip == i))
+ fprintf ('skip %s / %s\n', index.Group {i}, index.Name {i}) ;
+ continue
+ end
+
+ % try
+
+ Prob = UFget (i) %#ok
+ A = Prob.A ;
+ [m n] = size (A) ;
+
+ if (m == n)
+ S = spones (A) ;
+ else
+ n = min (m,n) ;
+ S = spones (A (1:n,1:n)) ;
+ end
+
+ try % compute nnz(S*S')
+ nzaat = nnz (S*S') ;
+ catch
+ nzaat = -1 ;
+ end
+ try % compute nnz(S'*S)
+ nzata = nnz (S'*S) ;
+ catch
+ nzata = -1 ;
+ end
+ S = S | S' ;
+
+ fprintf ('nnz(A) %d\n', nnz (A)) ;
+ fprintf ('nnz(S) %d\n', nnz (S)) ;
+ fprintf ('nnz(A*A'') %d\n', nzaat) ;
+ fprintf ('nnz(A''*A) %d\n', nzata) ;
+
+ fprintf ('metis (S):\n') ; p1 = metis (S) ;
+ fprintf ('metis (A,row):\n') ; p2 = metis (A, 'row') ;
+ fprintf ('metis (A,col):\n') ; p3 = metis (A, 'col') ;
+
+ fprintf ('turning off postorder:\n') ;
+ fprintf ('metis (S):\n') ; n1 = metis (S, 'sym', 'no postorder') ;
+ fprintf ('metis (A,row):\n') ; n2 = metis (A, 'row', 'no postorder') ;
+ fprintf ('metis (A,col):\n') ; n3 = metis (A, 'col', 'no postorder') ;
+
+ fprintf ('analyzing results:\n') ;
+
+ [pa1 po1] = etree2 (S (n1,n1)) ;
+ [pa2 po2] = etree2 (A (n2,:), 'row') ;
+ [pa3 po3] = etree2 (A (:,n3), 'col') ;
+
+ q1 = n1 (po1) ;
+ q2 = n2 (po2) ;
+ q3 = n3 (po3) ;
+
+ if (any (p1 ~= q1))
+ error ('1!') ;
+ end
+
+ if (any (p2 ~= q2))
+ error ('2!') ;
+ end
+
+ if (any (p3 ~= q3))
+ error ('3!') ;
+ end
+
+ s1 = symbfact2 (S (p1,p1)) ;
+ s2 = symbfact2 (A (p2,:), 'row') ;
+ s3 = symbfact2 (A (:,p3), 'col') ;
+
+ t1 = symbfact2 (S (n1,n1)) ;
+ t2 = symbfact2 (A (n2,:), 'row') ;
+ t3 = symbfact2 (A (:,n3), 'col') ;
+
+ if (any (s1 ~= t1 (po1)))
+ error ('s1!') ;
+ end
+
+ if (any (s2 ~= t2 (po2)))
+ error ('s2!') ;
+ end
+
+ if (any (s3 ~= t3 (po3)))
+ error ('s3!') ;
+ end
+
+ % catch
+ % fprintf ('%d failed\n') ;
+ % end
+end
+
+
+fprintf ('test14 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test15.m b/CHOLMOD/MATLAB/Test/test15.m
new file mode 100644
index 0000000..7b5ac81
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test15.m
@@ -0,0 +1,180 @@
+function test15 (nmat)
+%TEST15 test symbfact2 vs MATLAB
+% Example:
+% test15(nmat)
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+
+index = UFget ;
+
+% only test matrices with nrows = 109000 or less. large ones nearly always
+% cause a MATLAB segfault.
+f = find (index.nrows < 109000 & index.ncols < 109000) ;
+
+% sort by row /col dimension
+s = max (index.nrows, index.ncols) ;
+[ignore i] = sort (s (f)) ;
+f = f (i) ;
+
+if (nargin > 0)
+ nmat = max (0,nmat) ;
+ nmat = min (nmat, length (f)) ;
+ f = f (1:nmat) ;
+end
+
+fprintf ('Matrices to test: %d\n', length (f)) ;
+
+for i = f
+
+ % try
+
+ Problem = UFget (i) ;
+ A = spones (Problem.A) ;
+ [m n] = size (A) ;
+ fprintf ('\n%4d: %-20s nrow: %6d ncol: %6d nnz: %10d\n', ...
+ i, Problem.name, m, n, nnz(A)) ;
+
+ % warmup, for accurate timing
+ etree (sparse (1)) ;
+ etree2 (sparse (1)) ;
+ amd2 (sparse (1)) ;
+ symbfact (sparse (1)) ;
+ symbfact2 (sparse (1)) ;
+
+ % test symmetric case
+ if (m == n)
+
+ % permute the matrix first
+ p = amd2 (A) ;
+ A = A (p,p) ;
+
+ % test with triu(A)
+ tic
+ co = symbfact (A) ;
+ t1 = toc ;
+ tic
+ co2 = symbfact2 (A) ;
+ t2 = toc ;
+
+ fprintf ('c=symbfact(A): %10.4f %10.4f speedup %8.2f lnz %d\n', ...
+ t1, t2, t1/t2, sum (co)) ;
+
+ if (any (co ~= co2))
+ error ('!') ;
+ end
+
+ tic
+ [co h parent post R] = symbfact (A) ;
+ t1 = toc ;
+ tic
+ [co2 h2 parent2 post2 R2] = symbfact2 (A) ;
+ t2 = toc ;
+
+ fprintf ('R=symbfact(A): %10.4f %10.4f speedup %8.2f\n',...
+ t1, t2, t1/t2) ;
+
+ checkem(co,co2,parent,parent2,post,post2,R,R2,h,h2) ;
+
+ % test with tril(A)
+ tic
+ co = symbfact (A') ;
+ t1 = toc ;
+ tic
+ co2 = symbfact2 (A,'lo') ;
+ t2 = toc ;
+
+ fprintf (...
+ 'c=symbfact(A''): %10.4f %10.4f speedup %8.2f lnz %d\n',...
+ t1, t2, t1/t2, sum (co)) ;
+
+ if (any (co ~= co2))
+ error ('!') ;
+ end
+
+ tic
+ [co h parent post R] = symbfact (A') ;
+ t1 = toc ;
+ tic
+ [co2 h2 parent2 post2 R2] = symbfact2 (A,'lo') ;
+ t2 = toc ;
+
+ fprintf (...
+ 'R=symbfact(A''): %10.4f %10.4f speedup %8.2f\n',...
+ t1, t2, t1/t2) ;
+
+ checkem(co,co2,parent,parent2,post,post2,R,R2,h,h2) ;
+
+ end
+
+ % permute the matrix first
+ p = colamd (A) ;
+ [parent post] = etree2 (A (:,p), 'col') ;
+ p = p (post) ;
+ A = A (:,p) ;
+
+ % test column case
+ tic
+ co = symbfact (A,'col') ;
+ t1 = toc ;
+ tic
+ co2 = symbfact2 (A,'col') ;
+ t2 = toc ;
+
+ fprintf ('c=symbfact(A,''col''): %10.4f %10.4f speedup %8.2f lnz %d\n', ...
+ t1, t2, t1/t2, sum (co)) ;
+
+ if (any (co ~= co2))
+ error ('!') ;
+ end
+
+ tic
+ [co h parent post R] = symbfact (A,'col') ;
+ t1 = toc ;
+ tic
+ [co2 h2 parent2 post2 R2] = symbfact2 (A,'col') ;
+ t2 = toc ;
+
+ fprintf ('R=symbfact(A,''col''): %10.4f %10.4f speedup %8.2f\n', ...
+ t1, t2, t1/t2) ;
+
+ checkem(co,co2,parent,parent2,post,post2,R,R2,h,h2) ;
+
+% catch
+% fprintf ('%d failed\n', i) ;
+% end
+end
+
+fprintf ('test15 passed\n') ;
+
+%-------------------------------------------------------------------------------
+
+function checkem(co,co2,parent,parent2,post,post2,R,R2,h,h2)
+% checkem compare results from symbfact and symbfact2
+if (any (co ~= co2))
+ error ('count!') ;
+end
+if (any (parent ~= parent2))
+ error ('parent!') ;
+end
+if (any (post ~= post2))
+ error ('post!') ;
+end
+if (nnz (R2) ~= nnz (R))
+ error ('lnz!') ;
+end
+if (h ~= h2)
+ error ('h!') ;
+end
+% this may run out of memory
+try % compute nnz(R-R2)
+ err = nnz (R-R2) ;
+catch
+ err = -1 ;
+ fprintf ('nnz(R-R2) not computed\n') ;
+end
+if (err > 0)
+ error ('R!') ;
+end
diff --git a/CHOLMOD/MATLAB/Test/test16.m b/CHOLMOD/MATLAB/Test/test16.m
new file mode 100644
index 0000000..65f0151
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test16.m
@@ -0,0 +1,35 @@
+function test16
+%TEST16 test cholmod2 on a large matrix
+% Example:
+% test16
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+
+fprintf ('=================================================================\n');
+fprintf ('test16: test cholmod2 on a large matrix\n') ;
+
+rand ('state',1) ;
+randn ('state',1) ;
+
+Prob = UFget (936) %#ok
+A = Prob.A ;
+% tic
+% [L,s,p] = lchol (A) ;
+% toc
+% norm (L,1)
+
+n = size (A,1) ;
+b = rand (n,1) ;
+tic
+x = cholmod2(A,b) ;
+t = toc ;
+fprintf ('time %g\n', t) ;
+err = norm (A*x-b) ;
+
+if (err > 1e-5)
+ error ('!') ;
+end
+
+fprintf ('test16 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test17.m b/CHOLMOD/MATLAB/Test/test17.m
new file mode 100644
index 0000000..a833cfd
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test17.m
@@ -0,0 +1,32 @@
+function test17
+%TEST17 test lchol on a few large matrices
+% Example:
+% test17
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test17: test lchol on a few large matrices\n') ;
+
+rand ('state',1) ;
+randn ('state',1) ;
+
+Prob = UFget (887) %#ok
+A = Prob.A ;
+[L,s,p] = lchol (A) ; %#ok
+norm (L,1)
+
+clear all
+
+Prob = UFget (936) %#ok
+A = Prob.A ;
+[L,s,p] = lchol (A) ; %#ok
+norm (L,1) %#ok
+
+clear all
+
+Prob = UFget (887) %#ok
+A = Prob.A ;
+[L,s,p] = lchol (A) ; %#ok
+norm (L,1) %#ok
diff --git a/CHOLMOD/MATLAB/Test/test18.m b/CHOLMOD/MATLAB/Test/test18.m
new file mode 100644
index 0000000..06bcf8f
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test18.m
@@ -0,0 +1,40 @@
+function test18
+%TEST18 test cholmod2 on a few large matrices
+% Example:
+% test18
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test18: test cholmod2 on a few large matrices\n') ;
+
+rand ('state',1) ;
+randn ('state',1) ;
+
+Prob = UFget (887) %#ok
+A = Prob.A ;
+n = size (A,1) ;
+b = rand (n,1) ;
+x = cholmod2 (A,b) ;
+norm (A*x-b,1)
+
+clear all
+
+Prob = UFget (936) %#ok
+A = Prob.A ;
+n = size (A,1) ;
+b = rand (n,1) ;
+x = cholmod2 (A,b) ;
+norm (A*x-b,1)
+
+clear all
+
+Prob = UFget (887) %#ok
+A = Prob.A ;
+n = size (A,1) ;
+b = rand (n,1) ;
+x = cholmod2 (A,b) ;
+norm (A*x-b,1)
+
+fprintf ('test18 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test19.m b/CHOLMOD/MATLAB/Test/test19.m
new file mode 100644
index 0000000..f3349e2
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test19.m
@@ -0,0 +1,29 @@
+function test19
+%TEST19 look for NaN's from lchol (caused by Intel MKL 7.x bug)
+% Example:
+% test19
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test19: look for NaN''s from lchol (caused by Intel MKL 7.x bug)\n') ;
+
+Prob = UFget (936) %#ok
+A = Prob.A ;
+[p count] = analyze (A) ;
+A = A (p,p) ;
+tic
+L = lchol (A) ;
+t = toc ;
+fl = sum (count.^2) ;
+fprintf ('mflop rate: %8.2f\n', 1e-6*fl/t) ;
+n = size (L,1) ;
+for k = 1:n
+ if (any (isnan (L (:,k))))
+ k %#ok
+ error ('!') ;
+ end
+end
+
+fprintf ('test19 passed; you have a NaN-free BLAS (must not be MKL 7.x...)\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test2.m b/CHOLMOD/MATLAB/Test/test2.m
new file mode 100644
index 0000000..dd26e92
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test2.m
@@ -0,0 +1,42 @@
+function test2
+%TEST2 test sparse2
+% Example:
+% test2
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test2: test sparse2\n') ;
+
+i = [ 2 3 ] %#ok
+j = [ 3 4 ] %#ok
+s = [11.4 9.2] + 1i * [3.4 1.2] %#ok
+sparse (i,j,s) %#ok
+sparse2 (i,j,s) %#ok
+
+n = 100 ;
+nz = 4000 ;
+
+i = fix (n * rand (nz,1)) + 1 ;
+j = fix (n * rand (nz,1)) + 1 ;
+s = rand (nz,1) + 1i * rand (nz,1) ;
+A = sparse (i,j,s,n,n) ;
+B = sparse2 (i,j,s,n,n) ;
+nnz(A)
+
+if (norm (A-B,1) > 1e-14)
+ A_minus_B = A-B %#ok
+ error ('!') ;
+end
+
+C = sparse (A) ;
+D = sparse2 (B) ;
+
+if (norm (C-D,1) > 1e-14)
+ C_minus_D = C-D %#ok
+ error ('!') ;
+end
+% spy(C)
+
+fprintf ('test2 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test20.m b/CHOLMOD/MATLAB/Test/test20.m
new file mode 100644
index 0000000..0f0f53a
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test20.m
@@ -0,0 +1,56 @@
+function test20
+%TEST20 test symbfact2, cholmod2, and lu on a few large matrices
+% Example:
+% test20
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test20: test symbfact2, cholmod2, and lu on a few large matrices\n') ;
+
+unsym = [409 899 901 291 827] ; %#ok
+spd = [813 817] ;
+% f = [ unsym spd ] ;
+f = spd ;
+spparms ('spumoni',0) ;
+
+for i = f
+ Prob = UFget (i) %#ok
+ A = Prob.A ;
+ clear Prob ;
+ n = size (A,1) ;
+ b = A*ones (n,1) ;
+ if (any (i == spd))
+ p = amd2 (A) ;
+ count = symbfact2 (A (p,p)) ;
+ count2 = symbfact (A (p,p)) ;
+ if (any (count ~= count2))
+ error ('!') ;
+ end
+ fl = sum (count.^2) ;
+ lnz = sum (count) ;
+ unz = lnz ;
+ tic
+ x = cholmod2 (A,b) ;
+ t = toc ;
+ else
+ % spparms ('spumoni',2) ;
+ [L, U, P, Q] = lu (A) ; %#ok
+ % fl = luflop (L,U) ;
+ Lnz = full (sum (spones (L))) - 1 ;
+ Unz = full (sum (spones (U')))' - 1 ;
+ fl = 2*Lnz*Unz + sum (Lnz) ;
+ lnz = nnz(L) ;
+ unz = nnz(U) ;
+ tic
+ x=A\b ;
+ t = toc ;
+ end
+ err = norm (A*x-b,1) ;
+ clear L U P Q A x b
+ fprintf ('lnz %d unz %d nnz(L+U) %d fl %g gflop %g\n t %g err %e\n', ...
+ lnz, unz, lnz+unz-n, fl, 1e-9*fl/t, t, err) ;
+ % pause
+end
+
diff --git a/CHOLMOD/MATLAB/Test/test21.m b/CHOLMOD/MATLAB/Test/test21.m
new file mode 100644
index 0000000..c24de77
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test21.m
@@ -0,0 +1,45 @@
+function test21
+%TEST21 test cholmod2 on diagonal or ill-conditioned matrices
+% Example:
+% test21
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test21: test cholmod2 on diagonal or ill-conditioned matrices\n') ;
+
+f = [
+ 72 % HB/bcsstm22
+ 315 % Bai/mhdb416
+ 64 % HB/bcsstm09
+ 71 % HB/bcsstm21
+ 1207 % Oberwolfach/t2dal_e
+ 354 % Boeing/crystm02
+ 1211 % Oberwolfach/t3dl_e
+ ]' ;
+
+for i = f
+
+ Prob = UFget (i) %#ok
+ A = Prob.A ;
+ n = size (A,1) ;
+ x = ones (n,2) ;
+ b = A*x ;
+ fprintf ('nnz: %d\n', nnz (A)) ;
+
+ x1 = A\b ;
+ x2 = cholmod2 (A,b) ;
+
+ s = norm (A,1) * norm (x,1) + norm (b,1) ;
+ resid1 = norm (A*x1-b,1) / s ;
+ resid2 = norm (A*x2-b,1) / s ;
+
+ err1 = norm (x-x1,1) ;
+ err2 = norm (x-x2,1) ;
+
+ fprintf ('MATLAB resid %6.1e err %6.1e\n', resid1, err1) ;
+ fprintf ('CHOLMOD resid %6.1e err %6.1e\n', resid2, err2) ;
+ fprintf ('condest %6.1e\n', condest (A)) ;
+
+end
diff --git a/CHOLMOD/MATLAB/Test/test22.m b/CHOLMOD/MATLAB/Test/test22.m
new file mode 100644
index 0000000..d77c861
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test22.m
@@ -0,0 +1,209 @@
+function test22(nmat)
+%TEST22 test pos.def and indef. matrices
+% Example:
+% test22(nmat)
+%
+% if nmat <= 0, just test problematic matrices
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test22: test pos.def and indef. matrices\n') ;
+
+index = UFget ;
+
+[ignore f] = sort (index.nrows) ;
+
+if (nargin > 0)
+ problematic = (nmat <= 0) ;
+ if (problematic)
+ % Matrices for which MATLAB and CHOLMOD differ, for which the error
+ % is high, or other issues arose during debugging
+ fprintf ('testing matrices for which MATLAB and CHOLMOD differ\n') ;
+ f = [
+ 186 % HB/jgl011
+ 109 % HB/curtis54
+ 793 % Qaplib/lp_nug05
+ 607 % LPnetlib/lp_brandy
+ 707 % LPnetlib/lp_bore3d
+ 231 % HB/plskz362
+ 794 % Qaplib/lp_nug06
+ 673 % LPnetlib/lp_scorpion
+ 1156 % Sandia/oscil_dcop_45 (also 1157:1168)
+ 795 % Qaplib/lp_nug07
+ 796 % Qaplib/lp_nug08
+ 260 % HB/well1033
+ 261 % HB/well1850
+ 230 % HB/plsk1919
+ 649 % LPnetlib/lp_pds_02
+ 660 % LPnetlib/lp_qap12
+ 609 % LPnetlib/lp_cre_a
+ 619 % LPnetlib/lp_dfl001
+ 661 % LPnetlib/lp_qap15
+ 650 % LPnetlib/lp_pds_06
+ 379 % Cote/vibrobox
+ 638 % LPnetlib/lp_ken_11
+ 799 % Qaplib/lp_nug20
+ ]' ;
+ else
+ nmat = max (0,nmat) ;
+ nmat = min (nmat, length (f)) ;
+ f = f (1:nmat) ;
+ end
+end
+
+skip = [
+ 811, ... % Simon/appu, which is a random matrix
+ 937:939, ... % large ND/ problems
+ 1157:1168 ... % duplicates
+ 799 % rather large: Qaplib/lp_nug20
+ ] ;
+
+tlimit = 0.1 ;
+fprintf ('test22: chol and chol2 are repeated so each take >= %g sec\n',tlimit);
+
+klimit = 1 ;
+
+% warmup, for more accurate timing
+[R,p] = chol (sparse (1)) ; %#ok
+[R,p] = chol2 (sparse (1)) ; %#ok
+clear R p
+
+for i = f
+
+ if (any (i == skip))
+ continue ;
+ end
+
+ Problem = UFget (i) ;
+ A = Problem.A ;
+ [m n] = size (A) ;
+ fprintf ('\n================== %4d: Problem: %s m: %d n: %d nnz: %d', ...
+ i, Problem.name, m, n, nnz (A)) ;
+ clear Problem ;
+
+ try % create a symmetric version of the matrix
+ if (m == n)
+ if (nnz (A-A') > 0)
+ A = A+A' ;
+ end
+ else
+ A = A*A' ;
+ end
+ catch
+ fprintf ('skip\n') ;
+ continue
+ end
+
+ fprintf (' %d\n', nnz (A)) ;
+
+ p = amd2 (A) ;
+ A = A (p,p) ;
+ anorm = norm (A,1) ;
+
+ % Run each code for at least 'tlimit' seconds
+
+ % MATLAB
+ k = 0 ;
+ t1 = 0 ;
+ while (t1 < tlimit & k < klimit) %#ok
+ tic ;
+ [R1,p1] = chol (A) ;
+ t = toc ;
+ t1 = t1 + t ;
+ k = k + 1 ;
+ end
+ t1 = t1 / k ;
+
+ % CHOLMOD
+ k = 0 ;
+ t2 = 0 ;
+ while (t2 < tlimit & k < klimit) %#ok
+ tic ;
+ [R2,p2] = chol2 (A) ;
+ t = toc ;
+ t2 = t2 + t ;
+ k = k + 1 ;
+ end
+ t2 = t2 / k ;
+
+ if (klimit == 1)
+ rmin = full (min (abs (diag (R2)))) ;
+ rmax = full (max (abs (diag (R2)))) ;
+ if (p2 ~= 0 | isnan (rmin) | isnan (rmax) | rmax == 0) %#ok
+ rcond = 0 ;
+ else
+ rcond = rmin / rmax ;
+ end
+ fprintf ('rcond: %30.20e\n', rcond) ;
+ end
+
+ if (p1 == 1)
+ % MATLAB does not follow its own definitions. If p is 1, then R is
+ % supposed to be 0-by-n, not 0-by-0. CHOLMOD fixes this bug.
+ % Here, A is m-by-m
+ R1 = sparse (0,m) ;
+ end
+
+ kerr = 0 ;
+ if (p1 ~= p2)
+ % MATLAB and CHOLMOD don't agree. See if both are correct,
+ % because differences in roundoff errors can make one go
+ % a little farther than the other.
+
+ % if p1 is zero, it means MATLAB was fully successful
+ k1 = p1 ;
+ if (k1 == 0)
+ k1 = n ;
+ end
+
+ % if p2 is zero, it means CHOLMOD was fully successful
+ k2 = p2 ;
+ if (k2 == 0)
+ k2 = n ;
+ end
+
+ if (k1 > k2)
+ % MATLAB went further than CHOLMOD. This is OK if MATLAB found
+ % a small entry where CHOLMOD stopped.
+ k = k2 ;
+ kerr = R1 (k,k) ;
+ % now reduce R1 in size, to compare with R2
+ R1 = R1 (1:k2-1,:) ;
+ else
+ % CHOLMOD went further than MATLAB. This is OK if CHOLMOD found
+ % a small entry where MATLAB stopped.
+ k = k1 ;
+ kerr = R2 (k,k) ;
+ % now reduce R2 in size, to compare with R1
+ R2 = R2 (1:k1-1,:) ;
+ end
+ end
+
+ err = norm (R1-R2,1) / max (anorm,1) ;
+ fprintf ('p: %6d %6d MATLAB: %10.4f CHOLMOD: %10.4f speedup %6.2f err:', ...
+ p1, p2, t1, t2, t1/t2) ;
+
+ if (err == 0)
+ fprintf (' 0') ;
+ else
+ fprintf (' %6.0e', err) ;
+ end
+
+ if (kerr == 0)
+ fprintf (' 0\n') ;
+ else
+ fprintf (' %6.0e\n', kerr) ;
+ end
+
+% if (err > 1e-6)
+% error ('!') ;
+% end
+
+% pause
+ clear R1 R2 p1 p2 p A
+
+end
+
+fprintf ('test22: all tests passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test23.m b/CHOLMOD/MATLAB/Test/test23.m
new file mode 100644
index 0000000..b1cafb9
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test23.m
@@ -0,0 +1,122 @@
+function test23
+%TEST23 test chol and cholmod2 on the sparse matrix used in "bench"
+% Example:
+% test23
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test23: test chol & cholmod2 on the sparse matrix used in "bench"\n');
+
+n = 120 ;
+A = delsq (numgrid ('L', n)) ;
+b = sum (A)' ;
+
+fprintf ('Using each method''s internal fill-reducing ordering:\n') ;
+
+tic ;
+x = A\b ;
+t1 = toc ;
+e1 = norm (A*x-b) ;
+
+tic ;
+x = cholmod2 (A,b) ;
+t2 = toc ;
+e2 = norm (A*x-b) ;
+
+fprintf ('MATLAB x=A\\b time: %8.4f resid: %8.0e\n', t1, e1) ;
+fprintf ('CHOLMOD x=A\\b time: %8.4f resid: %8.0e\n', t2, e2) ;
+fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ;
+
+% get CHOLMOD's ordering (best of AMD and METIS)
+p = analyze (A) ;
+S = A (p,p) ;
+
+tic ;
+R = chol (S) ;
+t1 = toc ;
+x = R \ (R' \ b (p)) ;
+x (p) = x ;
+e1 = norm (A*x-b) ;
+
+tic ;
+L = lchol (S) ;
+t2 = toc ;
+x = L' \ (L \ b (p)) ;
+x (p) = x ;
+e2 = norm (A*x-b) ;
+
+fprintf ('\nS = A(p,p) where p is CHOLMOD''s ordering:\n') ;
+fprintf ('MATLAB R=chol(S) time: %8.4f resid: %8.0e\n', t1, e1) ;
+fprintf ('CHOLMOD L=lchol(S) time: %8.4f resid: %8.0e\n', t2, e2) ;
+fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ;
+
+% get MATLABS's ordering (symmmd in v7.0.4). If that fails then use amd.
+% A future version of MATLAB will remove symmmd, since it is declared
+% "deprecated" in v7.0.4.
+try % symmmd, use amd if it fails
+ method = 'symmmd' ;
+ p = symmmd (A) ;
+catch
+ % use AMD from SuiteSparse
+ method = 'amd' ;
+ fprintf ('\nsymmmd not available, using amd instead.\n') ;
+ p = amd2 (A) ;
+end
+S = A (p,p) ;
+
+tic ;
+R = chol (S) ;
+t1 = toc ;
+x = R \ (R' \ b (p)) ;
+x (p) = x ;
+e1 = norm (A*x-b) ;
+
+tic ;
+L = lchol (S) ;
+t2 = toc ;
+x = L' \ (L \ b (p)) ;
+x (p) = x ;
+e2 = norm (A*x-b) ;
+
+fprintf ('\nS = A(p,p) where p is MATLAB''s ordering in x=A\\b (%s):\n',method);
+fprintf ('MATLAB R=chol(S) time: %8.4f resid: %8.0e\n', t1, e1) ;
+fprintf ('CHOLMOD L=lchol(S) time: %8.4f resid: %8.0e\n', t2, e2) ;
+fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ;
+
+fprintf ('\n\nWith no fill-reducing orderings:\n') ;
+tic ;
+R = chol (A) ;
+t1 = toc ;
+x = R \ (R' \ b) ;
+e1 = norm (A*x-b) ;
+
+tic ;
+L = lchol (A) ;
+t2 = toc ;
+x = L' \ (L \ b) ;
+e2 = norm (A*x-b) ;
+
+fprintf ('MATLAB R=chol(A) time: %8.4f resid: %8.0e\n', t1, e1) ;
+fprintf ('CHOLMOD L=lchol(A) time: %8.4f resid: %8.0e\n', t2, e2) ;
+fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ;
+
+fprintf ('\n\nWith no fill-reducing orderings (as used in "bench"):\n') ;
+
+spparms ('autommd',0) ;
+tic ;
+x = A\b ;
+t1 = toc ;
+e1 = norm (A*x-b) ;
+
+tic ;
+x = cholmod2 (A,b,0) ;
+t2 = toc ;
+e2 = norm (A*x-b) ;
+
+fprintf ('MATLAB x=A\\b time: %8.4f resid: %8.0e\n', t1, e1) ;
+fprintf ('CHOLMOD x=A\\b time: %8.4f resid: %8.0e\n', t2, e2) ;
+fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ;
+
+spparms ('default') ;
diff --git a/CHOLMOD/MATLAB/Test/test24.m b/CHOLMOD/MATLAB/Test/test24.m
new file mode 100644
index 0000000..56000ad
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test24.m
@@ -0,0 +1,60 @@
+function test24
+%TEST24 test sdmult
+% Example:
+% test24
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test24: test sdmult\n') ;
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+maxerr = 0 ;
+
+for trials = 1:1000
+
+ sm = fix (20 * rand (1)) ;
+ sn = fix (20 * rand (1)) ;
+ fn = fix (20 * rand (1)) ;
+
+ for complexity = 0:1
+ for transpose = 0:1
+ if (transpose)
+ fm = sm ;
+ else
+ fm = sn ;
+ end
+ S = sprand (sm,sn,0.5) ;
+ F = rand (fm,fn) ;
+
+ if (complexity)
+ S = S + 1i * sprand (S) ;
+ F = F + 1i * rand (fm,fn) ;
+ end
+
+ % MATLAB does not support empty complex matrices
+ if (isempty (S) | isempty (F)) %#ok
+ S = sparse (real (S)) ;
+ F = real (F) ;
+ end
+
+ C = sdmult (S,F,transpose) ;
+
+ if (transpose)
+ D = S'*F ;
+ else
+ D = S*F ;
+ end
+
+ err = norm (C-D,1) ;
+ maxerr = max (err, maxerr) ;
+ if (err > 1e-13)
+ error ('!') ;
+ end
+ end
+ end
+end
+
+fprintf ('test 24 passed, maxerr %g\n', maxerr) ;
diff --git a/CHOLMOD/MATLAB/Test/test25.m b/CHOLMOD/MATLAB/Test/test25.m
new file mode 100644
index 0000000..4253951
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test25.m
@@ -0,0 +1,66 @@
+function test25
+%TEST25 test sdmult on a large matrix
+% Example:
+% test25
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test25: test sdmult on a large matrix\n') ;
+
+Prob = UFget (936) ;
+A = Prob.A ;
+n = size (A,1) ;
+
+nz = nnz (A) ;
+fprintf ('\nTest matrix: %d-by-%d, nnz %d\n', n, n, nz) ;
+
+Z = rand (n, 500) ;
+
+fprintf ('\nA*X where X is %d-by-k\n', n) ;
+
+for k = [0:10 10:10:50 100:100:500]
+
+ X = Z (:, 1:k) ;
+
+ tic ;
+ D = A*X ;
+ t1 = toc ;
+
+ tic ;
+ C = sdmult (A,X) ;
+ t2 = toc ;
+
+ err = norm (C-D,1) ;
+ fprintf (...
+ 'k: %3d time: MATLAB %8.2f CHOLMOD %8.2f speedup %8.2f err %6.0e',...
+ k, t1, t2, t1/t2, err) ;
+ fl = 2*nz*k ;
+ fprintf (' mflop: MATLAB %8.1f CHOLMOD %8.1f\n', 1e-6*fl/t1, 1e-6*fl/t2) ;
+
+ clear C D X
+end
+
+fprintf ('\nFor comparison, here is CHOLMOD''s x=A\\b time:\n') ;
+for k = [1 100:100:500]
+ B = Z (:, 1:k) ;
+ tic
+ x = cholmod2 (A,B) ;
+ t2 = toc ;
+ err2 = norm (sdmult(A,x)-B,1) ;
+ fprintf (...
+ 'CHOLMOD x=A\\b time: %8.2f (b is n-by-%d) resid %6.0e\n', t2, k, err2) ;
+ clear x B
+end
+
+b = Z (:,1) ;
+clear Z
+
+tic
+x = A\b ;
+t1 = toc ;
+err1 = norm (A*x-b,1) ;
+fprintf ('\nMATLAB x=A\\b time: %8.2f (b is n-by-1) resid %6.0e\n', t1, err1) ;
+
+fprintf ('test25 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test26.m b/CHOLMOD/MATLAB/Test/test26.m
new file mode 100644
index 0000000..76b55e2
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test26.m
@@ -0,0 +1,90 @@
+function test26 (do_metis)
+%TEST26 test logical full and sparse matrices
+% Example:
+% test26
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test26: test logical full and sparse matrices\n') ;
+
+if (nargin < 1)
+ do_metis = 1 ;
+end
+
+Prob = UFget ('HB/bcsstk01') ;
+A = Prob.A ;
+p = amd2 (A) ;
+n = size (A,1) ;
+A = A (p,p) + 10*speye (n) ;
+C = logical (A ~= 0) ;
+
+test26b (A,C,do_metis) ;
+test26b (full (A),C,do_metis) ;
+test26b (full (A), full (C),do_metis) ;
+test26b (A, full(C),do_metis) ;
+
+A = A + 0.001 * (spones (tril (A,-1) + triu (A,1))) * 1i ;
+
+test26b (A,C,do_metis) ;
+test26b (full (A),C,do_metis) ;
+test26b (full (A), full (C),do_metis) ;
+test26b (A, full(C),do_metis) ;
+fprintf ('test26 passed\n') ;
+
+%-------------------------------------------------------------------------------
+
+function test26b (A,C,do_metis)
+% test26b test bisect, analyze, etree2, metis, nesdis, symbfact2, and resymbol
+
+p1 = analyze (A) ;
+p2 = analyze (C) ;
+if (any (p1 ~= p2))
+ error ('test 26 failed (analyze)!') ;
+end
+
+p1 = etree2 (A) ;
+p2 = etree2 (C) ;
+if (any (p1 ~= p2))
+ error ('test 26 failed (etree2)!') ;
+end
+
+if (do_metis)
+
+ s1 = bisect (A) ;
+ s2 = bisect (C) ;
+ if (any (s1 ~= s2))
+ error ('test 26 failed (bisect)!') ;
+ end
+
+ p1 = metis (A) ;
+ p2 = metis (C) ;
+ if (any (p1 ~= p2))
+ error ('test 26 failed (metis)!') ;
+ end
+
+ p1 = nesdis (A) ;
+ p2 = nesdis (C) ;
+ if (any (p1 ~= p2))
+ error ('test 26 failed (nesdis)!') ;
+ end
+
+end
+
+c1 = symbfact2 (A) ;
+c2 = symbfact2 (C) ;
+if (any (c1 ~= c2))
+ error ('test 26 failed (symbfact2)!') ;
+end
+
+A (1,2) = 0 ;
+A (2,1) = 0 ;
+C = logical (A ~= 0) ;
+
+L = chol (sparse (A))' ;
+L1 = resymbol (L, A) ;
+L2 = resymbol (L, C) ;
+if (norm (L1 - L2, 1) ~= 0)
+ error ('test 26 failed (resymbol)!') ;
+end
diff --git a/CHOLMOD/MATLAB/Test/test27.m b/CHOLMOD/MATLAB/Test/test27.m
new file mode 100644
index 0000000..06f1a0d
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test27.m
@@ -0,0 +1,15 @@
+function test27
+%TEST27 test nesdis with one matrix (HB/west0479)
+% Example:
+% test27
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test27: test nesdis\n') ;
+
+Prob = UFget ('HB/west0479') ;
+dg (Prob.A) ;
+
+fprintf ('test27 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test28.m b/CHOLMOD/MATLAB/Test/test28.m
new file mode 100644
index 0000000..708d749
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test28.m
@@ -0,0 +1,61 @@
+function test28
+%TEST28 test nesdis
+% Example:
+% test28
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+index = UFget ;
+
+[ignore f] = sort (index.nnz) ;
+
+% f = find (index.nrows < index.ncols) ;
+% [ignore i] = sort (index.nnz (f)) ;
+% f = f (i) ;
+
+f = f (1:100) ;
+
+for i = f
+
+ try
+
+ Prob = UFget (i, index) ;
+ A = spones (Prob.A) ;
+ [m n] = size (A) ;
+
+ if (m < n)
+ A = A*A' ;
+ elseif (m > n) ;
+ A = A'*A ;
+ else
+ A = A+A' ;
+ end
+
+ % default: do not split connected components
+ [p1 cp1 cmem1] = nesdis (A) ; %#ok
+
+ % order connected components separately
+ [p2 cp2 cmem2] = nesdis (A, 'sym', [200 1]) ; %#ok
+ c1 = symbfact (A (p1,p1)) ;
+ c2 = symbfact (A (p2,p2)) ;
+ lnz1 = sum (c1) ;
+ lnz2 = sum (c2) ;
+ fprintf ('%35s %8d %8d ', Prob.name, lnz1, lnz2)
+ if (lnz1 == lnz2)
+ fprintf (' 1\n') ;
+ else
+ fprintf (' %8.3f\n', lnz1/lnz2) ;
+ end
+
+ subplot (2,3,1) ; spy (A) ;
+ subplot (2,3,2) ; spy (A (p1,p1)) ;
+ subplot (2,3,3) ; treeplot (cp1) ;
+ subplot (2,3,5) ; spy (A (p2,p2)) ;
+ subplot (2,3,6) ; treeplot (cp2) ;
+ drawnow
+
+ catch
+ fprintf ('%4d failed\n', i) ;
+ end
+end
diff --git a/CHOLMOD/MATLAB/Test/test3.m b/CHOLMOD/MATLAB/Test/test3.m
new file mode 100644
index 0000000..f84b902
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test3.m
@@ -0,0 +1,42 @@
+function test3
+%TEST3 test sparse on int8, int16, and logical
+% Example:
+% test3
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test3: test sparse on int8, int16, and logical\n') ;
+
+clear all
+c = ['a' 'b' 0 'd'] %#ok
+sparse(c)
+sparse2(c)
+sparse(c')
+sparse2(c')
+whos
+nzmax(ans) %#ok
+
+try % this will fail
+ sparse(int8(c))
+catch
+ fprintf ('sparse(int8(c)) fails in MATLAB\n') ;
+end
+sparse2(int8(c))
+
+sparse2 (int16(c))
+whos
+s = logical(rand(4) > .5) %#ok
+sparse (s)
+whos
+sparse2(s)
+whos
+
+x = rand(4) %#ok
+sparse (x > .5) %#ok
+whos
+sparse2 (x > .5) %#ok
+whos
+
+fprintf ('test3 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test4.m b/CHOLMOD/MATLAB/Test/test4.m
new file mode 100644
index 0000000..5b0872e
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test4.m
@@ -0,0 +1,56 @@
+function test4
+%TEST4 test cholmod2 with multiple and sparse right-hand-sides
+% Example:
+% test4
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test4: test cholmod2 with multiple and sparse right-hand-sides\n') ;
+
+Prob = UFget ('HB/bcsstk01') ;
+A = Prob.A ;
+n = size (A,1) ;
+b = rand (n,1) ;
+x = cholmod2 (A,b) ;
+m2 = norm (A*x-b,1) ;
+b = sparse (b) ;
+x = cholmod2 (A,b) ;
+m2 = max (m2, norm (A*x-b,1)) ;
+m1 = 0 ;
+
+for nrhs = 1:80
+ b = sparse (rand (n,nrhs)) ;
+ x = A\b ;
+ e1 = norm (A*x-b,1) ;
+ x = cholmod2 (A,b) ;
+ e2 = norm (A*x-b,1) ;
+ if (e2 > 1e-11)
+ error ('!') ;
+ end
+ m1 = max (m1, e1) ;
+ m2 = max (m2, e2) ;
+end
+
+for nrhs = 1:80
+ b = sprandn (n, nrhs, 0.01) ;
+ x = A\b ;
+ % nnz (x) / (n*nrhs)
+ e1 = norm (A*x-b,1) ;
+ x = cholmod2 (A,b) ;
+ e2 = norm (A*x-b,1) ;
+ if (e2 > 1e-11)
+ error ('!') ;
+ end
+ m1 = max (m1, e1) ;
+ m2 = max (m2, e2) ;
+end
+
+fprintf ('maxerr %e %e\n', m1, m2) ;
+
+if (m1 > 1e-11 | m2 > 1e-11) %#ok
+ error ('!') ;
+end
+
+fprintf ('test4 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test5.m b/CHOLMOD/MATLAB/Test/test5.m
new file mode 100644
index 0000000..3fd8cc7
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test5.m
@@ -0,0 +1,95 @@
+function test5
+%TEST5 test sparse2
+% Example:
+% test5
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test5: test sparse2\n') ;
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+A = sprandn (10,20,0.2) ;
+[m n ] = size (A) ;
+
+[i j x] = find (A) ;
+% [i2 j2 x2] = cholmod_find (A) ;
+% if (any (i ~= i2))
+% error ('i!') ;
+%end
+%if (any (j ~= j2))
+% error ('j!') ;
+%end
+%if (any (x ~= x2))
+% error ('x!') ;
+%end
+
+% full (sum (spones (A')))
+
+C = sparse (i,j,x,m,n) ;
+B = sparse2 (i,j,x,m,n) ;
+err = norm(A-B,1) ;
+if (err > 0)
+ error ('dtri 1') ;
+end
+err = norm(C-B,1) ;
+if (err > 0)
+ error ('dtri 1b') ;
+end
+
+nz = length (x) ;
+p = randperm (nz) ;
+
+i2 = i(p) ;
+j2 = j(p) ;
+x2 = x(p) ; %#ok
+
+B = sparse2 (i,j,x,m,n) ;
+err = norm(A-B,1) ;
+if (err > 0)
+ error ('dtri 2') ;
+end
+
+ii = [i2 ; i2] ;
+jj = [j2 ; j2] ;
+xx = rand (2*nz,1) ;
+
+C = sparse (ii,jj,xx,m,n) ;
+D = sparse2 (ii,jj,xx,m,n) ;
+err = norm (C-D,1) ;
+if (err > 0)
+ error ('dtri 3') ;
+end
+
+% E = sparse2 (ii,jj,xx,n,n,+1) ;
+E = sparse (min(ii,jj), max(ii,jj), xx, n, n) ;
+F = sparse (min(ii,jj), max(ii,jj), xx, n, n) ;
+err = norm (E-F,1) ;
+if (err > 0)
+ error ('dtri 4') ;
+end
+
+% E = sparse2 (ii,jj,xx,n,n,-1) ;
+E = sparse (max(ii,jj), min(ii,jj), xx, n, n) ;
+F = sparse (max(ii,jj), min(ii,jj), xx, n, n) ;
+err = norm (E-F,1) ;
+if (err > 0)
+ error ('dtri 5') ;
+end
+
+[i1 j1 x1] = find (F) ; %#ok
+% [i2 j2 x2] = cholmod_find (F) ;
+% if (any (i1 ~= i2))
+% error ('i!') ;
+% end
+% if (any (j1 ~= j2))
+% error ('j!') ;
+% end
+% if (any (x1 ~= x2))
+% error ('x!') ;
+% end
+
+fprintf ('test5 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test6.m b/CHOLMOD/MATLAB/Test/test6.m
new file mode 100644
index 0000000..3a217c4
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test6.m
@@ -0,0 +1,167 @@
+function test6
+%TEST6 test sparse with large matrix, both real and complex
+% compare times with MATLAB
+% Example:
+% test6
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test6: test sparse with large matrix, both real and complex\n') ;
+
+for do_complex = 0:1
+
+ fprintf ('do_complex = %d\n', do_complex) ;
+ randn ('state', 0) ;
+ rand ('state', 0) ;
+
+ % Prob = UFget (437)
+ Prob = UFget (749) %#ok
+ A = Prob.A ;
+ [m n] = size (A) ; %#ok
+
+ if (do_complex)
+% A = A + 1i*sprand(A) ;
+% patch for MATLAB 7.2
+ A = A + sparse(1:m,1:m,1i)*sprand(A) ;
+ end
+
+ tic
+ [i j x] = find (A) ;
+ t = toc ;
+ fprintf ('find time %8.4f\n', t) ;
+
+ % tic
+ % [i1 j1 x1] = cholmod_find (A) ;
+ % t = toc ;
+ % fprintf ('cholmod_find time %8.4f (for testing only, it should be slow)\n', t) ;
+
+ % if (any (i ~= i1))
+ % error ('i!') ;
+ % end
+ % if (any (j ~= j1))
+ % error ('j!') ;
+ % end
+ % if (any (x ~= x1))
+ % error ('x!') ;
+ % end
+
+ [m n ] = size (A) ;
+
+ tic ;
+ B = sparse2 (i,j,x,m,n) ;
+ t1 = toc ;
+ tic ;
+ C = sparse (i,j,x,m,n) ;
+ t2 = toc ;
+
+ fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f\n', t1, t2) ;
+
+ err = norm(A-B,1) ;
+ if (err > 0)
+ error ('dtri2 1') ;
+ end
+
+ err = norm(A-C,1) ;
+ if (err > 0)
+ error ('dtri2 1') ;
+ end
+
+ nz = length (x) ;
+ p = randperm (nz) ;
+
+ i2 = i(p) ;
+ j2 = j(p) ;
+ x2 = x(p) ; %#ok
+
+ tic ;
+ B = sparse2 (i,j,x,m,n) ;
+ t1 = toc ;
+ tic ;
+ C = sparse (i,j,x,m,n) ;
+ t2 = toc ;
+
+ fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f (jumbled)\n', t1, t2) ;
+
+ err = norm(A-B,1) ;
+ if (err > 0)
+ error ('dtri2 2') ;
+ end
+
+ err = norm(A-C,1) ;
+ if (err > 0)
+ error ('dtri2 1') ;
+ end
+
+ ii = [i2 ; i2] ;
+ jj = [j2 ; j2] ;
+ xx = rand (2*nz,1) ;
+ if (do_complex)
+ xx = xx + 1i* rand (2*nz,1) ;
+ end
+
+ tic ;
+ D = sparse2 (ii,jj,xx,m,n) ;
+ t1 = toc ;
+ tic ;
+ C = sparse (ii,jj,xx,m,n) ;
+ t2 = toc ;
+ err = norm (C-D,1) ;
+ if (err > 0)
+ error ('dtri2 3') ;
+ end
+ fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f (duplicates)\n', t1, t2) ;
+
+ fprintf ('length %d nz %d\n', length (xx), nnz(D)) ;
+
+ i2 = min (ii,jj) ;
+ j2 = max (ii,jj) ;
+
+ tic ;
+ E = sparse2 (i2,j2,xx,n,n) ;
+ t1 = toc ;
+ tic ;
+ F = sparse (i2, j2, xx, n, n) ;
+ t2 = toc ;
+ err = norm (E-F,1) %#ok
+ if (err > 1e-13)
+ error ('dtri2 4') ;
+ end
+ fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f (upper)\n', t1, t2) ;
+
+ i2 = max (ii,jj) ;
+ j2 = min (ii,jj) ;
+
+ tic ;
+ E = sparse2 (i2,j2,xx,n,n) ;
+ t1 = toc ;
+ tic ;
+ F = sparse (i2, j2, xx, n, n) ;
+ t2 = toc ;
+ err = norm (E-F,1) %#ok
+ if (err > 1e-13)
+ error ('dtri2 5') ;
+ end
+ fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f (lower)\n', t1, t2) ;
+
+ [ignore, i] = sort (ii) ;
+ ii = ii (i) ;
+ jj = jj (i) ;
+ xx = xx (i) ;
+
+ tic ;
+ D = sparse2 (ii,jj,xx,m,n) ;
+ t1 = toc ;
+ tic ;
+ C = sparse (ii,jj,xx,m,n) ;
+ t2 = toc ;
+ err = norm (C-D,1) ;
+ if (err > 0)
+ error ('dtri2 6') ;
+ end
+ fprintf ('dtri time: cholmod2 %8.6f matlab %8.6f (sorted, dupl)\n', t1, t2) ;
+
+end
+
+fprintf ('test6 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test7.m b/CHOLMOD/MATLAB/Test/test7.m
new file mode 100644
index 0000000..8403dbc
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test7.m
@@ -0,0 +1,63 @@
+function test7
+%TEST7 test sparse2
+% Example:
+% test7
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test7: test sparse2\n') ;
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+% Prob = UFget (437)
+Prob = UFget (750) %#ok
+A = Prob.A ;
+[m n] = size (A) ;
+
+tic
+[i j x] = find (A) ;
+t = toc ;
+fprintf ('find time %8.4f\n', t) ;
+
+tic ;
+B = sparse2 (i,j,x,m,n) ; %#ok
+t1 = toc ;
+fprintf ('tot: %8.6f\n', t1)
+
+tic ;
+B = sparse2 (i,j,x,m,n) ; %#ok
+t1 = toc ;
+fprintf ('tot: %8.6f again \n', t1) ;
+
+tic ;
+B1 = sparse2 (i,j,x) ; %#ok
+t1 = toc ;
+fprintf ('tot: %8.6f (i,j,x)\n', t1) ;
+
+nz = length (x) ;
+p = randperm (nz) ;
+
+i2 = i(p) ;
+j2 = j(p) ;
+x2 = x(p) ; %#ok
+
+tic ;
+B = sparse2 (i,j,x,m,n) ; %#ok
+t1 = toc ;
+
+fprintf ('tot: %8.6f (jumbled)\n', t1) ;
+
+ii = [i2 ; i2] ;
+jj = [j2 ; j2] ;
+xx = rand (2*nz,1) ;
+
+tic ;
+D = sparse2 (ii,jj,xx,m,n) ; %#ok
+t1 = toc ;
+
+fprintf ('tot %8.6f (duplicates)\n', t1) ;
+
+fprintf ('test7 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test8.m b/CHOLMOD/MATLAB/Test/test8.m
new file mode 100644
index 0000000..19465e5
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test8.m
@@ -0,0 +1,121 @@
+function test8 (nmat)
+%TEST8 order a large range of sparse matrices, test symbfact2
+% compare AMD and METIS
+% Example:
+% test8(nmat)
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test8: factorize a large range of sparse matrices\n') ;
+
+% get list of test matrices
+
+index = UFget ;
+
+% GHS posdef test set (more or less)
+f = find (...
+ ((index.numerical_symmetry == 1 & index.isBinary) | (index.posdef)) ...
+ & (index.nnzdiag == index.nrows) ...
+ & (index.nrows > 10000 | index.nrows == 9000) ...
+ & (index.nrows < 600000) & (index.nnz > index.nrows)) ; %#ok
+
+% include small matrices
+f = find (...
+ ((index.numerical_symmetry == 1 & index.isBinary) | (index.posdef)) ...
+ & (index.nnzdiag == index.nrows) ...
+ & (index.nrows < 600000) & (index.nnz > index.nrows)) ;
+
+for k = 1:length (f)
+ names {k} = index.Name {f(k)} ; %#ok
+end
+
+[ignore i] = sort (names) ;
+
+f = f (i) ;
+
+% fprintf ('test matrices sorted by name:\n') ;
+% for i = f
+% fprintf ('%4d: %-20s %-20s %12d %d\n', i, ...
+% index.Group {i}, index.Name {i}, index.nrows (i), index.posdef (i)) ;
+% end
+
+[ignore i] = sort (index.nrows (f)) ;
+f = f (i) ;
+
+if (nargin > 0)
+ nmat = max (0,nmat) ;
+ nmat = min (nmat, length (f)) ;
+ f = f (1:nmat) ;
+end
+
+fprintf ('test matrices sorted by dimension:\n') ;
+for i = f
+ fprintf ('%4d: %-20s %-20s %12d %d\n', i, ...
+ index.Group {i}, index.Name {i}, index.nrows (i), index.posdef (i)) ;
+end
+
+junk = sparse (1) ;
+
+% input ('hit enter to continue: ') ;
+
+for k = 1:length (f)
+
+ Problem = UFget (f(k)) ;
+ A = Problem.A ;
+ fprintf ('\n================== Problem: %s n: %d nnz: %d\n', ...
+ Problem.name, size (A,1), nnz (A)) ;
+ fprintf ('title: %s\n\n', Problem.title) ;
+ clear Problem
+ n = size (A,1) ; %#ok
+
+ amd2 (junk) ;
+ metis (junk) ;
+
+ tic ;
+ [p1,info] = amd2 (A) ; %#ok
+ t1 = toc ;
+ S1 = A (p1,p1) ;
+ tic ;
+ c1 = symbfact (S1) ;
+ ts1 = toc ;
+ tic ;
+ d1 = symbfact (S1) ;
+ ts2 = toc ;
+ if (any (c1 ~= d1))
+ error ('!')
+ end
+ fprintf ('symbfact time: MATLAB %9.4f CHOLMOD %9.4f speedup %8.2f\n', ...
+ ts1, ts2, ts1/ts2) ;
+
+ lnz1 = sum (c1) ;
+ fl1 = sum (c1.^2) ;
+ fprintf ('time: amd %10.4f mnnz(L) %8.1f mfl %8.0f fl/nnz(L) %8.1f\n', ...
+ t1, lnz1/1e6, fl1 /1e6, fl1/lnz1) ;
+
+ tic ;
+ p2 = metis (A) ;
+ t2 = toc ;
+ S2 = A (p2,p2) ;
+ c2 = symbfact (S2) ;
+ lnz2 = sum (c2) ;
+ fl2 = sum (c2.^2) ;
+
+ fprintf ('time: metis %10.4f mnnz(L) %8.1f mfl %8.0f fl/nnz(L) %8.1f\n', ...
+ t2, lnz2/1e6, fl2/1e6, fl2/lnz2) ;
+
+ r = lnz2 / lnz1 ; %#ok
+ fprintf ('\nmetis/amd time: %8.4f nnz(L): %8.4f\n', t2/t1, lnz2/lnz1) ;
+
+ % save results
+ lnz (k,1) = lnz1 ; %#ok
+ lnz (k,2) = lnz2 ; %#ok
+ fl1 (k,1) = fl1 ; %#ok
+ fl2 (k,2) = fl2 ; %#ok
+ t (k,1) = t1 ; %#ok
+ t (k,2) = t2 ; %#ok
+
+end
+
+fprintf ('test8 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/test9.m b/CHOLMOD/MATLAB/Test/test9.m
new file mode 100644
index 0000000..f514dfb
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/test9.m
@@ -0,0 +1,80 @@
+function test9
+%TEST9 test metis, etree, bisect, nesdis
+% Example:
+% test9
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('=================================================================\n');
+fprintf ('test9: test metis, etree, bisect, nesdis\n') ;
+
+% Prob = UFget ('LPnetlib/lp_qap15') ;
+Prob = UFget ('HB/bcsstk15') %#ok
+A = Prob.A ;
+C = A'*A ;
+R = A*A' ;
+
+fprintf ('\nmetis:\n') ;
+tic ; p0 = metis (R) ; toc %#ok
+% [pa po] = etree2 (R (p0,p0)) ; sparse (po - (1:size(R,1)))
+
+tic ; p1 = metis (C) ; toc %#ok
+% [pa po] = etree2 (C (p1,p1)) ; sparse (po - (1:size(C,1)))
+
+tic ; p2 = metis (C, 'sym') ; toc %#ok
+% [pa po] = etree2 (C (p1,p1)) ; sparse (po - (1:size(C,1)))
+
+tic ; p3 = metis (A, 'row') ; toc %#ok
+% [pa po] = etree2 (A (p1,:), 'row') ; sparse (po - (1:size(A,1)))
+
+tic ; p4 = metis (A, 'col') ; toc %#ok
+% [pa po] = etree2 (A (:,p1), 'col') ; sparse (po - (1:size(A,2)))
+
+fprintf ('\nmetis(A):\n') ;
+[m n] = size(A) ;
+if (m == n)
+ if (nnz (A-A') == 0)
+ tic ; p5 = metis (A) ; toc
+ % figure (1)
+ % spy (A (p5,p5)) ;
+ [ignore q] = etree (A(p5,p5)) ;
+ p5post = p5 (q) ; %#ok
+ % figure (2)
+ % spy (A (p5post,p5post)) ;
+ lnz0 = sum (symbfact (A (p5,p5))) %#ok
+ end
+end
+
+fprintf ('\namd:\n') ;
+if (m == n)
+ if (nnz (A-A') == 0)
+ tic ; z0 = amd2 (A) ; toc %#ok
+ lnz = sum (symbfact (A (z0,z0))) %#ok
+ end
+end
+
+fprintf ('\nbisect:\n') ;
+tic ; s0 = bisect (R) ; toc %#ok
+tic ; s1 = bisect (C) ; toc %#ok
+tic ; s2 = bisect (C, 'sym') ; toc %#ok
+tic ; s3 = bisect (A, 'row') ; toc %#ok
+tic ; s4 = bisect (A, 'col') ; toc %#ok
+
+
+fprintf ('\nnested dissection:\n') ;
+tic ; [c0 cp0 cmem0] = nesdis (R) ; toc %#ok
+tic ; [c1 cp1 cmem1] = nesdis (C) ; toc %#ok
+tic ; [c2 cp2 cmem2] = nesdis (C, 'sym') ; toc %#ok
+tic ; [c3 cp3 cmem3] = nesdis (A, 'row') ; toc %#ok
+tic ; [c4 cp4 cmem4] = nesdis (A, 'col') ; toc %#ok
+
+fprintf ('\nnested_dissection(A):\n') ;
+if (m == n)
+ if (nnz (A-A') == 0)
+ tic ; c5 = nesdis (A) ; toc %#ok
+ lnz1 = sum (symbfact (A (c5,c5))) %#ok
+ end
+end
+
+fprintf ('test9 passed\n') ;
diff --git a/CHOLMOD/MATLAB/Test/testmm.m b/CHOLMOD/MATLAB/Test/testmm.m
new file mode 100644
index 0000000..c45f03b
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/testmm.m
@@ -0,0 +1,549 @@
+%TESTMM compare mread and mmread for entire Matrix Market collection
+% Example:
+% testmm
+% See also mread.
+% Requires the mmread MATLAB m-file from http://www.nist.gov
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+matrices = {
+ 'M/Harwell-Boeing/acoust/young1c.mtx', ...
+ 'M/Harwell-Boeing/acoust/young2c.mtx', ...
+ 'M/Harwell-Boeing/acoust/young3c.mtx', ...
+ 'M/Harwell-Boeing/acoust/young4c.mtx', ...
+ 'M/Harwell-Boeing/airtfc/zenios.mtx', ...
+ 'M/Harwell-Boeing/astroph/mcca.mtx', ...
+ 'M/Harwell-Boeing/astroph/mcfe.mtx', ...
+ 'M/Harwell-Boeing/bcspwr/bcspwr01.mtx', ...
+ 'M/Harwell-Boeing/bcspwr/bcspwr02.mtx', ...
+ 'M/Harwell-Boeing/bcspwr/bcspwr03.mtx', ...
+ 'M/Harwell-Boeing/bcspwr/bcspwr04.mtx', ...
+ 'M/Harwell-Boeing/bcspwr/bcspwr05.mtx', ...
+ 'M/Harwell-Boeing/bcspwr/bcspwr06.mtx', ...
+ 'M/Harwell-Boeing/bcspwr/bcspwr07.mtx', ...
+ 'M/Harwell-Boeing/bcspwr/bcspwr08.mtx', ...
+ 'M/Harwell-Boeing/bcspwr/bcspwr09.mtx', ...
+ 'M/Harwell-Boeing/bcspwr/bcspwr10.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk01.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk02.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk03.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk04.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk05.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk06.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk07.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk08.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk09.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk10.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk11.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk12.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstk13.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm01.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm02.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm03.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm04.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm05.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm06.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm07.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm08.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm09.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm10.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm11.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm12.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc1/bcsstm13.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc2/bcsstk14.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc2/bcsstk15.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc2/bcsstk16.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc2/bcsstk17.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc2/bcsstk18.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstk19.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstk20.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstk21.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstk22.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstk23.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstk24.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstk25.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstm19.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstm20.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstm21.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstm22.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstm23.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstm24.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc3/bcsstm25.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc4/bcsstk26.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc4/bcsstk27.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc4/bcsstk28.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc4/bcsstm26.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc4/bcsstm27.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc5/bcsstk29.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc5/bcsstk30.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc5/bcsstk31.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc5/bcsstk32.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc5/bcsstk33.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc6/blckhole.mtx', ...
+ 'M/Harwell-Boeing/bcsstruc6/sstmodel.mtx', ...
+ 'M/Harwell-Boeing/cannes/can_1054.mtx', ...
+ 'M/Harwell-Boeing/cannes/can_1072.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__144.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__161.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__187.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__229.mtx', ...
+ 'M/Harwell-Boeing/cannes/can___24.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__256.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__268.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__292.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__445.mtx', ...
+ 'M/Harwell-Boeing/cannes/can___61.mtx', ...
+ 'M/Harwell-Boeing/cannes/can___62.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__634.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__715.mtx', ...
+ 'M/Harwell-Boeing/cannes/can___73.mtx', ...
+ 'M/Harwell-Boeing/cannes/can__838.mtx', ...
+ 'M/Harwell-Boeing/cannes/can___96.mtx', ...
+ 'M/Harwell-Boeing/chemimp/impcol_a.mtx', ...
+ 'M/Harwell-Boeing/chemimp/impcol_b.mtx', ...
+ 'M/Harwell-Boeing/chemimp/impcol_c.mtx', ...
+ 'M/Harwell-Boeing/chemimp/impcol_d.mtx', ...
+ 'M/Harwell-Boeing/chemimp/impcol_e.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west0067.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west0132.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west0156.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west0167.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west0381.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west0479.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west0497.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west0655.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west0989.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west1505.mtx', ...
+ 'M/Harwell-Boeing/chemwest/west2021.mtx', ...
+ 'M/Harwell-Boeing/cirphys/jpwh_991.mtx', ...
+ 'M/Harwell-Boeing/counterx/jgl009.mtx', ...
+ 'M/Harwell-Boeing/counterx/jgl011.mtx', ...
+ 'M/Harwell-Boeing/counterx/rgg010.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt_1005.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt_1007.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt_1242.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__162.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__193.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__198.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__209.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__221.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__234.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__245.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt_2680.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__307.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__310.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__346.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__361.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__419.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__492.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__503.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__512.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__592.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt___59.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__607.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt___66.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt___72.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__758.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__869.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__878.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt___87.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__918.mtx', ...
+ 'M/Harwell-Boeing/dwt/dwt__992.mtx', ...
+ 'M/Harwell-Boeing/econaus/mahindas.mtx', ...
+ 'M/Harwell-Boeing/econaus/orani678.mtx', ...
+ 'M/Harwell-Boeing/econiea/beacxc.mtx', ...
+ 'M/Harwell-Boeing/econiea/beaflw.mtx', ...
+ 'M/Harwell-Boeing/econiea/beause.mtx', ...
+ 'M/Harwell-Boeing/econiea/mbeacxc.mtx', ...
+ 'M/Harwell-Boeing/econiea/mbeaflw.mtx', ...
+ 'M/Harwell-Boeing/econiea/mbeause.mtx', ...
+ 'M/Harwell-Boeing/econiea/wm1.mtx', ...
+ 'M/Harwell-Boeing/econiea/wm2.mtx', ...
+ 'M/Harwell-Boeing/econiea/wm3.mtx', ...
+ 'M/Harwell-Boeing/facsimile/fs_183_1.mtx', ...
+ 'M/Harwell-Boeing/facsimile/fs_183_3.mtx', ...
+ 'M/Harwell-Boeing/facsimile/fs_183_4.mtx', ...
+ 'M/Harwell-Boeing/facsimile/fs_183_6.mtx', ...
+ 'M/Harwell-Boeing/facsimile/fs_680_1.mtx', ...
+ 'M/Harwell-Boeing/facsimile/fs_680_2.mtx', ...
+ 'M/Harwell-Boeing/facsimile/fs_680_3.mtx', ...
+ 'M/Harwell-Boeing/facsimile/fs_760_1.mtx', ...
+ 'M/Harwell-Boeing/facsimile/fs_760_2.mtx', ...
+ 'M/Harwell-Boeing/facsimile/fs_760_3.mtx', ...
+ 'M/Harwell-Boeing/gemat/gemat11.mtx', ...
+ 'M/Harwell-Boeing/gemat/gemat12.mtx', ...
+ 'M/Harwell-Boeing/gemat/gemat1.mtx', ...
+ 'M/Harwell-Boeing/grenoble/gre_1107.mtx', ...
+ 'M/Harwell-Boeing/grenoble/gre__115.mtx', ...
+ 'M/Harwell-Boeing/grenoble/gre__185.mtx', ...
+ 'M/Harwell-Boeing/grenoble/gre_216a.mtx', ...
+ 'M/Harwell-Boeing/grenoble/gre_216b.mtx', ...
+ 'M/Harwell-Boeing/grenoble/gre__343.mtx', ...
+ 'M/Harwell-Boeing/grenoble/gre__512.mtx', ...
+ 'M/Harwell-Boeing/jagmesh/jagmesh1.mtx', ...
+ 'M/Harwell-Boeing/jagmesh/jagmesh2.mtx', ...
+ 'M/Harwell-Boeing/jagmesh/jagmesh3.mtx', ...
+ 'M/Harwell-Boeing/jagmesh/jagmesh4.mtx', ...
+ 'M/Harwell-Boeing/jagmesh/jagmesh5.mtx', ...
+ 'M/Harwell-Boeing/jagmesh/jagmesh6.mtx', ...
+ 'M/Harwell-Boeing/jagmesh/jagmesh7.mtx', ...
+ 'M/Harwell-Boeing/jagmesh/jagmesh8.mtx', ...
+ 'M/Harwell-Boeing/jagmesh/jagmesh9.mtx', ...
+ 'M/Harwell-Boeing/lanpro/nos1.mtx', ...
+ 'M/Harwell-Boeing/lanpro/nos2.mtx', ...
+ 'M/Harwell-Boeing/lanpro/nos3.mtx', ...
+ 'M/Harwell-Boeing/lanpro/nos4.mtx', ...
+ 'M/Harwell-Boeing/lanpro/nos5.mtx', ...
+ 'M/Harwell-Boeing/lanpro/nos6.mtx', ...
+ 'M/Harwell-Boeing/lanpro/nos7.mtx', ...
+ 'M/Harwell-Boeing/laplace/gr_30_30.mtx', ...
+ 'M/Harwell-Boeing/lns/lns__131.mtx', ...
+ 'M/Harwell-Boeing/lns/lns_3937.mtx', ...
+ 'M/Harwell-Boeing/lns/lns__511.mtx', ...
+ 'M/Harwell-Boeing/lns/lnsp_131.mtx', ...
+ 'M/Harwell-Boeing/lns/lnsp3937.mtx', ...
+ 'M/Harwell-Boeing/lns/lnsp_511.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp1009.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp1270.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp1561.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp1882.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp2233.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp2614.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp_265.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp3025.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp3466.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp_406.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp_577.mtx', ...
+ 'M/Harwell-Boeing/lshape/lshp_778.mtx', ...
+ 'M/Harwell-Boeing/lsq/illc1033.mtx', ...
+ 'M/Harwell-Boeing/lsq/illc1850.mtx', ...
+ 'M/Harwell-Boeing/lsq/well1033.mtx', ...
+ 'M/Harwell-Boeing/lsq/well1850.mtx', ...
+ 'M/Harwell-Boeing/nnceng/hor__131.mtx', ...
+ 'M/Harwell-Boeing/nucl/nnc1374.mtx', ...
+ 'M/Harwell-Boeing/nucl/nnc261.mtx', ...
+ 'M/Harwell-Boeing/nucl/nnc666.mtx', ...
+ 'M/Harwell-Boeing/oilgen/orsirr_1.mtx', ...
+ 'M/Harwell-Boeing/oilgen/orsirr_2.mtx', ...
+ 'M/Harwell-Boeing/oilgen/orsreg_1.mtx', ...
+ 'M/Harwell-Boeing/platz/plat1919.mtx', ...
+ 'M/Harwell-Boeing/platz/plat362.mtx', ...
+ 'M/Harwell-Boeing/platz/plsk1919.mtx', ...
+ 'M/Harwell-Boeing/platz/plskz362.mtx', ...
+ 'M/Harwell-Boeing/pores/pores_1.mtx', ...
+ 'M/Harwell-Boeing/pores/pores_2.mtx', ...
+ 'M/Harwell-Boeing/pores/pores_3.mtx', ...
+ 'M/Harwell-Boeing/psadmit/1138_bus.mtx', ...
+ 'M/Harwell-Boeing/psadmit/494_bus.mtx', ...
+ 'M/Harwell-Boeing/psadmit/662_bus.mtx', ...
+ 'M/Harwell-Boeing/psadmit/685_bus.mtx', ...
+ 'M/Harwell-Boeing/psmigr/psmigr_1.mtx', ...
+ 'M/Harwell-Boeing/psmigr/psmigr_2.mtx', ...
+ 'M/Harwell-Boeing/psmigr/psmigr_3.mtx', ...
+ 'M/Harwell-Boeing/saylor/saylr1.mtx', ...
+ 'M/Harwell-Boeing/saylor/saylr3.mtx', ...
+ 'M/Harwell-Boeing/saylor/saylr4.mtx', ...
+ 'M/Harwell-Boeing/sherman/sherman1.mtx', ...
+ 'M/Harwell-Boeing/sherman/sherman2.mtx', ...
+ 'M/Harwell-Boeing/sherman/sherman3.mtx', ...
+ 'M/Harwell-Boeing/sherman/sherman4.mtx', ...
+ 'M/Harwell-Boeing/sherman/sherman5.mtx', ...
+ 'M/Harwell-Boeing/smtape/abb313.mtx', ...
+ 'M/Harwell-Boeing/smtape/arc130.mtx', ...
+ 'M/Harwell-Boeing/smtape/ash219.mtx', ...
+ 'M/Harwell-Boeing/smtape/ash292.mtx', ...
+ 'M/Harwell-Boeing/smtape/ash331.mtx', ...
+ 'M/Harwell-Boeing/smtape/ash608.mtx', ...
+ 'M/Harwell-Boeing/smtape/ash85.mtx', ...
+ 'M/Harwell-Boeing/smtape/bp_____0.mtx', ...
+ 'M/Harwell-Boeing/smtape/bp__1000.mtx', ...
+ 'M/Harwell-Boeing/smtape/bp__1200.mtx', ...
+ 'M/Harwell-Boeing/smtape/bp__1400.mtx', ...
+ 'M/Harwell-Boeing/smtape/bp__1600.mtx', ...
+ 'M/Harwell-Boeing/smtape/bp___200.mtx', ...
+ 'M/Harwell-Boeing/smtape/bp___400.mtx', ...
+ 'M/Harwell-Boeing/smtape/bp___600.mtx', ...
+ 'M/Harwell-Boeing/smtape/bp___800.mtx', ...
+ 'M/Harwell-Boeing/smtape/curtis54.mtx', ...
+ 'M/Harwell-Boeing/smtape/eris1176.mtx', ...
+ 'M/Harwell-Boeing/smtape/fs_541_1.mtx', ...
+ 'M/Harwell-Boeing/smtape/fs_541_2.mtx', ...
+ 'M/Harwell-Boeing/smtape/fs_541_3.mtx', ...
+ 'M/Harwell-Boeing/smtape/fs_541_4.mtx', ...
+ 'M/Harwell-Boeing/smtape/gent113.mtx', ...
+ 'M/Harwell-Boeing/smtape/ibm32.mtx', ...
+ 'M/Harwell-Boeing/smtape/lund_a.mtx', ...
+ 'M/Harwell-Boeing/smtape/lund_b.mtx', ...
+ 'M/Harwell-Boeing/smtape/shl____0.mtx', ...
+ 'M/Harwell-Boeing/smtape/shl__200.mtx', ...
+ 'M/Harwell-Boeing/smtape/shl__400.mtx', ...
+ 'M/Harwell-Boeing/smtape/str____0.mtx', ...
+ 'M/Harwell-Boeing/smtape/str__200.mtx', ...
+ 'M/Harwell-Boeing/smtape/str__400.mtx', ...
+ 'M/Harwell-Boeing/smtape/str__600.mtx', ...
+ 'M/Harwell-Boeing/smtape/will199.mtx', ...
+ 'M/Harwell-Boeing/smtape/will57.mtx', ...
+ 'M/Harwell-Boeing/steam/steam1.mtx', ...
+ 'M/Harwell-Boeing/steam/steam2.mtx', ...
+ 'M/Harwell-Boeing/steam/steam3.mtx', ...
+ 'M/Harwell-Boeing/watt/watt__1.mtx', ...
+ 'M/Harwell-Boeing/watt/watt__2.mtx', ...
+ 'M/misc/cylshell/s1rmq4m1.mtx', ...
+ 'M/misc/cylshell/s1rmt3m1.mtx', ...
+ 'M/misc/cylshell/s2rmq4m1.mtx', ...
+ 'M/misc/cylshell/s3dkq4m2.mtx', ...
+ 'M/misc/cylshell/s3dkt3m2.mtx', ...
+ 'M/misc/cylshell/s3rmq4m1.mtx', ...
+ 'M/misc/cylshell/s3rmt3m1.mtx', ...
+ 'M/misc/cylshell/s3rmt3m3.mtx', ...
+ 'M/misc/hamm/add20.mtx', ...
+ 'M/misc/hamm/add32.mtx', ...
+ 'M/misc/hamm/memplus.mtx', ...
+ 'M/misc/pts5ldd0/pts5ldd03.mtx', ...
+ 'M/misc/pts5ldd0/pts5ldd04.mtx', ...
+ 'M/misc/pts5ldd0/pts5ldd05.mtx', ...
+ 'M/misc/pts5ldd0/pts5ldd06.mtx', ...
+ 'M/misc/pts5ldd0/pts5ldd07.mtx', ...
+ 'M/misc/pts5ldd1/pts5ldd13.mtx', ...
+ 'M/misc/pts5ldd1/pts5ldd14.mtx', ...
+ 'M/misc/pts5ldd1/pts5ldd15.mtx', ...
+ 'M/misc/pts5ldd1/pts5ldd16.mtx', ...
+ 'M/misc/pts5ldd1/pts5ldd17.mtx', ...
+ 'M/misc/pts5ldd2/pts5ldd23.mtx', ...
+ 'M/misc/pts5ldd2/pts5ldd24.mtx', ...
+ 'M/misc/pts5ldd2/pts5ldd25.mtx', ...
+ 'M/misc/pts5ldd2/pts5ldd26.mtx', ...
+ 'M/misc/pts5ldd2/pts5ldd27.mtx', ...
+ 'M/misc/qcd/conf5.0-00l4x4-1000.mtx', ...
+ 'M/misc/qcd/conf5.0-00l4x4-1400.mtx', ...
+ 'M/misc/qcd/conf5.0-00l4x4-1800.mtx', ...
+ 'M/misc/qcd/conf5.0-00l4x4-2200.mtx', ...
+ 'M/misc/qcd/conf5.0-00l4x4-2600.mtx', ...
+ 'M/misc/qcd/conf5.4-00l8x8-0500.mtx', ...
+ 'M/misc/qcd/conf5.4-00l8x8-1000.mtx', ...
+ 'M/misc/qcd/conf5.4-00l8x8-1500.mtx', ...
+ 'M/misc/qcd/conf5.4-00l8x8-2000.mtx', ...
+ 'M/misc/qcd/conf6.0-00l4x4-2000.mtx', ...
+ 'M/misc/qcd/conf6.0-00l4x4-3000.mtx', ...
+ 'M/misc/qcd/conf6.0-00l8x8-2000.mtx', ...
+ 'M/misc/qcd/conf6.0-00l8x8-3000.mtx', ...
+ 'M/misc/qcd/conf6.0-00l8x8-8000.mtx', ...
+ 'M/NEP/airfoil/af23560.mtx', ...
+ 'M/NEP/bfwave/bfw398a.mtx', ...
+ 'M/NEP/bfwave/bfw398b.mtx', ...
+ 'M/NEP/bfwave/bfw62a.mtx', ...
+ 'M/NEP/bfwave/bfw62b.mtx', ...
+ 'M/NEP/bfwave/bfw782a.mtx', ...
+ 'M/NEP/bfwave/bfw782b.mtx', ...
+ 'M/NEP/brussel/rdb1250l.mtx', ...
+ 'M/NEP/brussel/rdb1250.mtx', ...
+ 'M/NEP/brussel/rdb200l.mtx', ...
+ 'M/NEP/brussel/rdb200.mtx', ...
+ 'M/NEP/brussel/rdb2048l.mtx', ...
+ 'M/NEP/brussel/rdb2048.mtx', ...
+ 'M/NEP/brussel/rdb3200l.mtx', ...
+ 'M/NEP/brussel/rdb450l.mtx', ...
+ 'M/NEP/brussel/rdb450.mtx', ...
+ 'M/NEP/brussel/rdb800l.mtx', ...
+ 'M/NEP/brussel/rdb968.mtx', ...
+ 'M/NEP/chuck/ck104.mtx', ...
+ 'M/NEP/chuck/ck400.mtx', ...
+ 'M/NEP/chuck/ck656.mtx', ...
+ 'M/NEP/crystal/cry10000.mtx', ...
+ 'M/NEP/crystal/cry2500.mtx', ...
+ 'M/NEP/dwave/dw2048.mtx', ...
+ 'M/NEP/dwave/dw8192.mtx', ...
+ 'M/NEP/dwave/dwa512.mtx', ...
+ 'M/NEP/dwave/dwb512.mtx', ...
+ 'M/NEP/gedney/dwg961a.mtx', ...
+ 'M/NEP/gedney/dwg961b.mtx', ...
+ 'M/NEP/h2plus/qc2534.mtx', ...
+ 'M/NEP/h2plus/qc324.mtx', ...
+ 'M/NEP/matpde/pde225.mtx', ...
+ 'M/NEP/matpde/pde2961.mtx', ...
+ 'M/NEP/matpde/pde900.mtx', ...
+ 'M/NEP/mhd/mhd1280a.mtx', ...
+ 'M/NEP/mhd/mhd1280b.mtx', ...
+ 'M/NEP/mhd/mhd3200a.mtx', ...
+ 'M/NEP/mhd/mhd3200b.mtx', ...
+ 'M/NEP/mhd/mhd416a.mtx', ...
+ 'M/NEP/mhd/mhd416b.mtx', ...
+ 'M/NEP/mhd/mhd4800a.mtx', ...
+ 'M/NEP/mhd/mhd4800b.mtx', ...
+ 'M/NEP/mvmbwm/bwm2000.mtx', ...
+ 'M/NEP/mvmbwm/bwm200.mtx', ...
+ 'M/NEP/mvmmcd/cdde1.mtx', ...
+ 'M/NEP/mvmmcd/cdde2.mtx', ...
+ 'M/NEP/mvmmcd/cdde3.mtx', ...
+ 'M/NEP/mvmmcd/cdde4.mtx', ...
+ 'M/NEP/mvmmcd/cdde5.mtx', ...
+ 'M/NEP/mvmmcd/cdde6.mtx', ...
+ 'M/NEP/mvmode/odep400a.mtx', ...
+ 'M/NEP/mvmode/odep400b.mtx', ...
+ 'M/NEP/mvmrwk/rw136.mtx', ...
+ 'M/NEP/mvmrwk/rw496.mtx', ...
+ 'M/NEP/mvmrwk/rw5151.mtx', ...
+ 'M/NEP/mvmtls/tols1090.mtx', ...
+ 'M/NEP/mvmtls/tols2000.mtx', ...
+ 'M/NEP/mvmtls/tols340.mtx', ...
+ 'M/NEP/mvmtls/tols4000.mtx', ...
+ 'M/NEP/mvmtls/tols90.mtx', ...
+ 'M/NEP/olmstead/olm1000.mtx', ...
+ 'M/NEP/olmstead/olm100.mtx', ...
+ 'M/NEP/olmstead/olm2000.mtx', ...
+ 'M/NEP/olmstead/olm5000.mtx', ...
+ 'M/NEP/olmstead/olm500.mtx', ...
+ 'M/NEP/quebec/qh1484.mtx', ...
+ 'M/NEP/quebec/qh768.mtx', ...
+ 'M/NEP/quebec/qh882.mtx', ...
+ 'M/NEP/robotics/rbs480a.mtx', ...
+ 'M/NEP/robotics/rbs480b.mtx', ...
+ 'M/NEP/stoch/lop163.mtx', ...
+ 'M/NEP/tubular/tub1000.mtx', ...
+ 'M/NEP/tubular/tub100.mtx', ...
+ 'M/SPARSKIT/drivcav/e05r0000.mtx', ...
+ 'M/SPARSKIT/drivcav/e05r0100.mtx', ...
+ 'M/SPARSKIT/drivcav/e05r0200.mtx', ...
+ 'M/SPARSKIT/drivcav/e05r0300.mtx', ...
+ 'M/SPARSKIT/drivcav/e05r0400.mtx', ...
+ 'M/SPARSKIT/drivcav/e05r0500.mtx', ...
+ 'M/SPARSKIT/drivcav/e20r0000.mtx', ...
+ 'M/SPARSKIT/drivcav/e20r0100.mtx', ...
+ 'M/SPARSKIT/drivcav/e20r0500.mtx', ...
+ 'M/SPARSKIT/drivcav/e20r1000.mtx', ...
+ 'M/SPARSKIT/drivcav/e20r2000.mtx', ...
+ 'M/SPARSKIT/drivcav/e20r3000.mtx', ...
+ 'M/SPARSKIT/drivcav/e20r4000.mtx', ...
+ 'M/SPARSKIT/drivcav/e20r5000.mtx', ...
+ 'M/SPARSKIT/drivcav/e30r0000.mtx', ...
+ 'M/SPARSKIT/drivcav/e30r0100.mtx', ...
+ 'M/SPARSKIT/drivcav/e30r0500.mtx', ...
+ 'M/SPARSKIT/drivcav/e30r1000.mtx', ...
+ 'M/SPARSKIT/drivcav/e30r2000.mtx', ...
+ 'M/SPARSKIT/drivcav/e30r3000.mtx', ...
+ 'M/SPARSKIT/drivcav/e30r4000.mtx', ...
+ 'M/SPARSKIT/drivcav/e30r5000.mtx', ...
+ 'M/SPARSKIT/drivcav/e40r0000.mtx', ...
+ 'M/SPARSKIT/drivcav/e40r0100.mtx', ...
+ 'M/SPARSKIT/drivcav/e40r0500.mtx', ...
+ 'M/SPARSKIT/drivcav/e40r1000.mtx', ...
+ 'M/SPARSKIT/drivcav/e40r2000.mtx', ...
+ 'M/SPARSKIT/drivcav/e40r3000.mtx', ...
+ 'M/SPARSKIT/drivcav/e40r4000.mtx', ...
+ 'M/SPARSKIT/drivcav/e40r5000.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity01.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity02.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity03.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity04.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity05.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity06.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity07.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity08.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity09.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity10.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity11.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity12.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity13.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity14.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity15.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity16.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity17.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity18.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity19.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity20.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity21.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity22.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity23.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity24.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity25.mtx', ...
+ 'M/SPARSKIT/drivcav_old/cavity26.mtx', ...
+ 'M/SPARSKIT/fidap/fidap001.mtx', ...
+ 'M/SPARSKIT/fidap/fidap002.mtx', ...
+ 'M/SPARSKIT/fidap/fidap003.mtx', ...
+ 'M/SPARSKIT/fidap/fidap004.mtx', ...
+ 'M/SPARSKIT/fidap/fidap005.mtx', ...
+ 'M/SPARSKIT/fidap/fidap006.mtx', ...
+ 'M/SPARSKIT/fidap/fidap007.mtx', ...
+ 'M/SPARSKIT/fidap/fidap008.mtx', ...
+ 'M/SPARSKIT/fidap/fidap009.mtx', ...
+ 'M/SPARSKIT/fidap/fidap010.mtx', ...
+ 'M/SPARSKIT/fidap/fidap011.mtx', ...
+ 'M/SPARSKIT/fidap/fidap012.mtx', ...
+ 'M/SPARSKIT/fidap/fidap013.mtx', ...
+ 'M/SPARSKIT/fidap/fidap014.mtx', ...
+ 'M/SPARSKIT/fidap/fidap015.mtx', ...
+ 'M/SPARSKIT/fidap/fidap018.mtx', ...
+ 'M/SPARSKIT/fidap/fidap019.mtx', ...
+ 'M/SPARSKIT/fidap/fidap020.mtx', ...
+ 'M/SPARSKIT/fidap/fidap021.mtx', ...
+ 'M/SPARSKIT/fidap/fidap022.mtx', ...
+ 'M/SPARSKIT/fidap/fidap023.mtx', ...
+ 'M/SPARSKIT/fidap/fidap024.mtx', ...
+ 'M/SPARSKIT/fidap/fidap025.mtx', ...
+ 'M/SPARSKIT/fidap/fidap026.mtx', ...
+ 'M/SPARSKIT/fidap/fidap027.mtx', ...
+ 'M/SPARSKIT/fidap/fidap028.mtx', ...
+ 'M/SPARSKIT/fidap/fidap029.mtx', ...
+ 'M/SPARSKIT/fidap/fidap031.mtx', ...
+ 'M/SPARSKIT/fidap/fidap032.mtx', ...
+ 'M/SPARSKIT/fidap/fidap033.mtx', ...
+ 'M/SPARSKIT/fidap/fidap035.mtx', ...
+ 'M/SPARSKIT/fidap/fidap036.mtx', ...
+ 'M/SPARSKIT/fidap/fidap037.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm02.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm03.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm05.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm07.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm08.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm09.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm10.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm11.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm13.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm15.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm29.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm33.mtx', ...
+ 'M/SPARSKIT/fidap/fidapm37.mtx', ...
+ 'M/SPARSKIT/tokamak/utm1700a.mtx', ...
+ 'M/SPARSKIT/tokamak/utm1700b.mtx', ...
+ 'M/SPARSKIT/tokamak/utm300.mtx', ...
+ 'M/SPARSKIT/tokamak/utm3060.mtx', ...
+ 'M/SPARSKIT/tokamak/utm5940.mtx', ...
+} ;
+
+
+for i = 1:length(matrices)
+
+ filename = matrices {i} ;
+ fprintf ('\nfile: %s\n', filename) ;
+ tic
+ [A,rows,cols,entries,rep,field,symm] = mmread(filename) ;
+ t1 = toc ;
+ fprintf (' %d by %d, nz %d %s %s %s\n', ...
+ rows, cols, entries, rep, field, symm) ;
+% try
+ tic
+ B = mread (filename) ;
+ t2 = toc ;
+% catch
+% B = [ ] ;
+% end
+
+ fprintf ('speedup %6.2f nnz %d\n', t1/t2, nnz(A)) ;
+
+ % mread add values to a pattern-only matrix. Remove them
+ if (strcmp (field, 'pattern'))
+ B = spones (B) ;
+ end
+
+ if (isempty (B))
+ fprintf ('============================ could not read with CHOLMOD\n') ;
+ error ('!') ;
+ else
+ err = norm (A-B,1) ;
+ if (err ~= 0)
+ fprintf ('=================================== %8.1e\n', err) ;
+ error ('!') ;
+ end
+ end
+end
+
diff --git a/CHOLMOD/MATLAB/Test/testsolve.m b/CHOLMOD/MATLAB/Test/testsolve.m
new file mode 100644
index 0000000..22ad363
--- /dev/null
+++ b/CHOLMOD/MATLAB/Test/testsolve.m
@@ -0,0 +1,43 @@
+function [x1,x2,e1,e2] = testsolve (A,b)
+%TESTSOLVE test CHOLMOD and compare with x=A\b
+% [x1,x2,e1,e2] = testsolve (A,b) ;
+% Compare CHOLMOD and MATLAB's x=A\b
+% x1 = A\b, x2 = cholmod2(A,b), e1 = norm(A*x1-b), e2 = norm(A*x2-b)
+% Example:
+% [x1,x2,e1,e2] = testsolve (A,b) ;
+% See also cholmod_test
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida
+
+fprintf ('A: [n %6d real %d] B: [sp:%d nrhs %d real %d] ', ...
+ size(A,1), isreal(A), issparse(b), size(b,2), isreal(b)) ;
+tic
+x1 = A\b ;
+t1 = toc ;
+tic
+x2 = cholmod2(A,b) ;
+t2 = toc ;
+tic
+e1 = norm (A*x1-b,1) ;
+t3 = toc ;
+e2 = norm (A*x2-b,1) ;
+if (e2 == 0 | e1 == 0) %#ok
+ e12 = 0 ;
+else
+ e12 = log2 (e1/e2) ;
+end
+if (t2 == 0)
+ t12 = 1 ;
+else
+ t12 = t1 / t2 ;
+end
+if (t2 == 0)
+ t32 = 1 ; %#ok
+else
+ t32 = t3 / t2 ; %#ok
+end
+fprintf (' [e1: %5.0e : %5.1f] [t1: %8.2f t2 %8.2f : %5.1f]\n', ...
+ e1, e12, t1, t2, t12) ;
+if (e2 > max (1e-8, 1e3*e1))
+ error ('!') ;
+end
diff --git a/CHOLMOD/MATLAB/Windows/README.txt b/CHOLMOD/MATLAB/Windows/README.txt
new file mode 100644
index 0000000..165a532
--- /dev/null
+++ b/CHOLMOD/MATLAB/Windows/README.txt
@@ -0,0 +1 @@
+These files are need to compile METIS on Windows.
diff --git a/CHOLMOD/MATLAB/Windows/rand48.c b/CHOLMOD/MATLAB/Windows/rand48.c
new file mode 100644
index 0000000..e8f6af7
--- /dev/null
+++ b/CHOLMOD/MATLAB/Windows/rand48.c
@@ -0,0 +1,24 @@
+/* ========================================================================== */
+/* === MATLAB/rand48.c ====================================================== */
+/* ========================================================================== */
+
+/* METIS uses drand48 and srand48, which conform to the SVID standard. The
+ * lcc compiler for Windows shipped with MATLAB does not include the drand48
+ * and srand48 routines. This file is a cheap replacement using the
+ * more-common rand and srand instead (which lcc does have).
+ *
+ * This file is only used when compiling CHOLMOD with the cholmod_make.m,
+ * on the PC, with the lcc compiler.
+ */
+
+#include <stdlib.h>
+
+double drand48 (void)
+{
+ return (((double) (rand ( ))) / ((double) RAND_MAX)) ;
+}
+
+void srand48 (long int seed)
+{
+ srand ((unsigned int) seed) ;
+}
diff --git a/CHOLMOD/MATLAB/Windows/strings.h b/CHOLMOD/MATLAB/Windows/strings.h
new file mode 100644
index 0000000..302c607
--- /dev/null
+++ b/CHOLMOD/MATLAB/Windows/strings.h
@@ -0,0 +1,8 @@
+/* ========================================================================== */
+/* === MATLAB/strings.h ===================================================== */
+/* ========================================================================== */
+
+/* This is an empty strings.h file, for compiling METIS 4.0.1 properly. METIS
+ * does not need the Unix <strings.h>, but includes it in metis.h anyway.
+ * This empty file is needed to successfully compile METIS using cholmod_make.
+ */
diff --git a/CHOLMOD/MATLAB/analyze.c b/CHOLMOD/MATLAB/analyze.c
new file mode 100644
index 0000000..e806fe7
--- /dev/null
+++ b/CHOLMOD/MATLAB/analyze.c
@@ -0,0 +1,189 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/analyze mexFunction =================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Order a matrix and then analyze it, using CHOLMOD's best-effort ordering.
+ * Returns the count of the number of nonzeros in each column of L for the
+ * permuted matrix A.
+ *
+ * Usage:
+ *
+ * [p count] = analyze (A) orders A, using just tril(A)
+ * [p count] = analyze (A,'sym') orders A, using just tril(A)
+ * [p count] = analyze (A,'row') orders A*A'
+ * [p count] = analyze (A,'col') orders A'*A
+ *
+ * with an optional 3rd parameter:
+ *
+ * [p count] = analyze (A,'sym',k) orders A, using just tril(A)
+ * [p count] = analyze (A,'row',k) orders A*A'
+ * [p count] = analyze (A,'col',k) orders A'*A
+ *
+ * k=0 is the default. k != 0 selects the ordering strategy.
+ *
+ * See analyze.m for more details.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0 ;
+ cholmod_factor *L ;
+ cholmod_sparse *A, Amatrix, *C, *S ;
+ cholmod_common Common, *cm ;
+ Int n, transpose, c ;
+ char buf [LEN] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set defaults */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* only do the simplicial analysis (L->Perm and L->ColCount) */
+ cm->supernodal = CHOLMOD_SIMPLICIAL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 2 || nargin < 1 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: [p count] = analyze (A, mode)") ;
+ }
+ if (nargin == 3)
+ {
+ cm->nmethods = mxGetScalar (pargin [2]) ;
+ if (cm->nmethods == -1)
+ {
+ /* use AMD only */
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_AMD ;
+ cm->postorder = TRUE ;
+ }
+ else if (cm->nmethods == -2)
+ {
+ /* use METIS only */
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_METIS ;
+ cm->postorder = TRUE ;
+ }
+ else if (cm->nmethods == -3)
+ {
+ /* use NESDIS only */
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NESDIS ;
+ cm->postorder = TRUE ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get input matrix A */
+ /* ---------------------------------------------------------------------- */
+
+ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ;
+ S = (A == &Amatrix) ? NULL : A ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get A->stype, default is to use tril(A) */
+ /* ---------------------------------------------------------------------- */
+
+ A->stype = -1 ;
+ transpose = FALSE ;
+
+ if (nargin > 1)
+ {
+ buf [0] = '\0' ;
+ if (mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], buf, LEN) ;
+ }
+ c = buf [0] ;
+ if (tolower (c) == 'r')
+ {
+ /* unsymmetric case (A*A') if string starts with 'r' */
+ transpose = FALSE ;
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 'c')
+ {
+ /* unsymmetric case (A'*A) if string starts with 'c' */
+ transpose = TRUE ;
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 's')
+ {
+ /* symmetric case (A) if string starts with 's' */
+ transpose = FALSE ;
+ A->stype = -1 ;
+ }
+ else
+ {
+ mexErrMsgTxt ("analyze: unrecognized mode") ;
+ }
+ }
+
+ if (A->stype && A->nrow != A->ncol)
+ {
+ mexErrMsgTxt ("analyze: A must be square") ;
+ }
+
+ C = NULL ;
+ if (transpose)
+ {
+ /* C = A', and then order C*C' */
+ C = cholmod_l_transpose (A, 0, cm) ;
+ if (C == NULL)
+ {
+ mexErrMsgTxt ("analyze failed") ;
+ }
+ A = C ;
+ }
+
+ n = A->nrow ;
+
+ /* ---------------------------------------------------------------------- */
+ /* analyze and order the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ L = cholmod_l_analyze (A, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return Perm */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = sputil_put_int (L->Perm, n, 1) ;
+ if (nargout > 1)
+ {
+ pargout [1] = sputil_put_int (L->ColCount, n, 0) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free_factor (&L, cm) ;
+ cholmod_l_free_sparse (&C, cm) ;
+ cholmod_l_free_sparse (&S, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /* if (cm->malloc_count != 0) mexErrMsgTxt ("!") ; */
+}
diff --git a/CHOLMOD/MATLAB/analyze.m b/CHOLMOD/MATLAB/analyze.m
new file mode 100644
index 0000000..323e8c4
--- /dev/null
+++ b/CHOLMOD/MATLAB/analyze.m
@@ -0,0 +1,65 @@
+function [p, count] = analyze (A, mode, k) %#ok
+%ANALYZE order and analyze a matrix using CHOLMOD's best-effort ordering.
+%
+% Example:
+% [p count] = analyze (A) orders A, using just tril(A)
+% [p count] = analyze (A,'sym') orders A, using just tril(A)
+% [p count] = analyze (A,'row') orders A*A'
+% [p count] = analyze (A,'col') orders A'*A
+%
+% an optional 3rd parameter modifies the ordering strategy:
+%
+% [p count] = analyze (A,'sym',k) orders A, using just tril(A)
+% [p count] = analyze (A,'row',k) orders A*A'
+% [p count] = analyze (A,'col',k) orders A'*A
+%
+% Returns a permutation and the count of the number of nonzeros in each
+% column of L for the permuted matrix A. That is, count is returned as:
+%
+% count = symbfact2 (A (p,p)) if ordering A
+% count = symbfact2 (A (p,:),'row') if ordering A*A'
+% count = symbfact2 (A (:,p),'col') if ordering A'*A
+%
+% CHOLMOD uses the following ordering strategy:
+%
+% k = 0: Try AMD. If that ordering gives a flop count >= 500 * nnz(L)
+% and a fill-in of nnz(L) >= 5*nnz(C), then try METIS_NodeND (where
+% C = A, A*A', or A'*A is the matrix being ordered. Selects the best
+% ordering tried. This is the default.
+%
+% if k > 0, then multiple orderings are attempted.
+%
+% k = 1 or 2: just try AMD
+% k = 3: also try METIS_NodeND
+% k = 4: also try NESDIS, CHOLMOD's nested dissection (NESDIS), with
+% default parameters. Uses METIS's node bisector and CCOLAMD.
+% k = 5: also try the natural ordering (p = 1:n)
+% k = 6: also try NESDIS with large leaves of the separator tree
+% k = 7: also try NESDIS with tiny leaves and no CCOLAMD ordering
+% k = 8: also try NESDIS with no dense-node removal
+% k = 9: also try COLAMD if ordering A'*A or A*A', (AMD if ordering A).
+% k > 9 is treated as k = 9
+%
+% k = -1: just use AMD
+% k = -2: just use METIS
+% k = -3: just use NESDIS
+%
+% The method returning the smallest nnz(L) is used for p and count.
+% k = 4 takes much longer than (say) k = 0, but it can reduce nnz(L) by
+% a typical 5% to 10%. k = 5 to 9 is getting extreme, but if you have
+% lots of time and want to find the best ordering possible, set k = 9.
+%
+% If METIS is not installed for use in CHOLMOD, then the strategy is
+% different:
+%
+% k = 1 to 4: just try AMD
+% k = 5 to 8: also try the natural ordering (p = 1:n)
+% k = 9: also try COLAMD if ordering A'*A or A*A', (AMD if ordering A).
+% k > 9 is treated as k = 9
+%
+% See also METIS, NESDIS, BISECT, SYMBFACT, AMD
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('analyze mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/bisect.c b/CHOLMOD/MATLAB/bisect.c
new file mode 100644
index 0000000..5e48090
--- /dev/null
+++ b/CHOLMOD/MATLAB/bisect.c
@@ -0,0 +1,168 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/bisect mexFunction ==================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * METIS (Copyright 1998, G. Karypis) is not distributed with CHOLMOD.
+ * -------------------------------------------------------------------------- */
+
+/* Find an node separator of an undirected graph, using
+ * METIS_NodeComputeSeparator.
+ *
+ * Usage:
+ *
+ * s = bisect (A) bisects A, uses tril(A)
+ * s = bisect (A, 'sym') bisects A, uses tril(A)
+ * s = bisect (A, 'row') bisects A*A'
+ * s = bisect (A, 'col') bisects A'*A
+ *
+ * Node i of the graph is in the left graph if s(i)=0, the right graph if
+ * s(i)=1, and in the separator if s(i)=2.
+ *
+ * Requirse METIS and the CHOLMOD Partition Module.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+
+#ifndef NPARTITION
+
+ double dummy = 0 ;
+ Int *Partition ;
+ cholmod_sparse *A, Amatrix, *C, *S ;
+ cholmod_common Common, *cm ;
+ Int n, transpose, c ;
+ char buf [LEN] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set defaults */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: p = bisect (A, mode)") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get input matrix A */
+ /* ---------------------------------------------------------------------- */
+
+ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ;
+ S = (A == &Amatrix) ? NULL : A ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get A->stype, default is to use tril(A) */
+ /* ---------------------------------------------------------------------- */
+
+ A->stype = -1 ;
+ transpose = FALSE ;
+
+ if (nargin > 1)
+ {
+ buf [0] = '\0' ;
+ if (mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], buf, LEN) ;
+ }
+ c = buf [0];
+ if (tolower (c) == 'r')
+ {
+ /* unsymmetric case (A*A') if string starts with 'r' */
+ transpose = FALSE ;
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 'c')
+ {
+ /* unsymmetric case (A'*A) if string starts with 'c' */
+ transpose = TRUE ;
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 's')
+ {
+ /* symmetric case (A) if string starts with 's' */
+ transpose = FALSE ;
+ A->stype = -1 ;
+ }
+ else
+ {
+ mexErrMsgTxt ("bisect: p=bisect(A,mode) ; unrecognized mode") ;
+ }
+ }
+
+ if (A->stype && A->nrow != A->ncol)
+ {
+ mexErrMsgTxt ("bisect: A must be square") ;
+ }
+
+ C = NULL ;
+ if (transpose)
+ {
+ /* C = A', and then bisect C*C' */
+ C = cholmod_l_transpose (A, 0, cm) ;
+ if (C == NULL)
+ {
+ mexErrMsgTxt ("bisect failed") ;
+ }
+ A = C ;
+ }
+
+ n = A->nrow ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Partition = cholmod_l_malloc (n, sizeof (Int), cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order the matrix with CHOLMOD's interface to METIS_NodeND */
+ /* ---------------------------------------------------------------------- */
+
+ if (cholmod_l_bisect (A, NULL, 0, TRUE, Partition, cm) < 0)
+ {
+ mexErrMsgTxt ("bisect failed") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return Partition */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = sputil_put_int (Partition, n, 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free (n, sizeof (Int), Partition, cm) ;
+ cholmod_l_free_sparse (&C, cm) ;
+ cholmod_l_free_sparse (&S, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /* if (cm->malloc_count != 0) mexErrMsgTxt ("!") ; */
+
+#else
+ mexErrMsgTxt ("METIS and the CHOLMOD Partition Module not installed\n") ;
+#endif
+}
diff --git a/CHOLMOD/MATLAB/bisect.m b/CHOLMOD/MATLAB/bisect.m
new file mode 100644
index 0000000..36b928a
--- /dev/null
+++ b/CHOLMOD/MATLAB/bisect.m
@@ -0,0 +1,25 @@
+function p = bisect (A, mode) %#ok
+%BISECT computes a node separator based on METIS_NodeComputeSeparator.
+%
+% Example:
+% s = bisect(A) bisects A. Uses tril(A) and assumes A is symmetric.
+% s = bisect(A,'sym') the same as p=bisect(A).
+% s = bisect(A,'col') bisects A'*A.
+% s = bisect(A,'row') bisects A*A'.
+%
+% A must be square for p=bisect(A) and bisect(A,'sym').
+%
+% s is a vector of length equal to the dimension of A, A'*A, or A*A',
+% depending on the matrix bisected. s(i)=0 if node i is in the left subgraph,
+% s(i)=1 if it is in the right subgraph, and s(i)=2 if node i is in the node
+% separator.
+%
+% Requires METIS, authored by George Karypis, Univ. of Minnesota. This
+% MATLAB interface, via CHOLMOD, is by Tim Davis.
+%
+% See also METIS, NESDIS
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('bisect mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/chol2.c b/CHOLMOD/MATLAB/chol2.c
new file mode 100644
index 0000000..4313ebd
--- /dev/null
+++ b/CHOLMOD/MATLAB/chol2.c
@@ -0,0 +1,164 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/chol2 mexFunction ===================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Numeric R'R factorization. Note that LL' and LDL' are faster than R'R
+ * and use less memory. The R'R factorization methods use triu(A), just like
+ * MATLAB's built-in chol.
+ *
+ * R = chol2 (A) same as R = chol (A), just faster
+ * [R,p] = chol2 (A) save as [R,p] = chol(A), just faster
+ * [R,p,q] = chol2 (A) factorizes A(q,q) into R'*R
+ *
+ * A must be sparse. It can be complex or real.
+ *
+ * R is returned with no explicit zero entries. This means it might not be
+ * chordal, and R cannot be passed back to CHOLMOD for an update/downdate or
+ * for a fast simplicial solve. spones (R) will be equal to the R returned
+ * by symbfact2 if no numerically zero entries are dropped, or a subset
+ * otherwise.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0, *px ;
+ cholmod_sparse Amatrix, *A, *Lsparse, *R ;
+ cholmod_factor *L ;
+ cholmod_common Common, *cm ;
+ Int n, minor ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* convert to packed LL' when done */
+ cm->final_asis = FALSE ;
+ cm->final_super = FALSE ;
+ cm->final_ll = TRUE ;
+ cm->final_pack = TRUE ;
+ cm->final_monotonic = TRUE ;
+
+ /* no need to prune entries due to relaxed supernodal amalgamation, since
+ * zeros are dropped with sputil_drop_zeros instead */
+ cm->final_resymbol = FALSE ;
+
+ cm->quick_return_if_not_posdef = (nargout < 2) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin != 1 || nargout > 3)
+ {
+ mexErrMsgTxt ("usage: [R,p,q] = chol2 (A)") ;
+ }
+
+ n = mxGetN (pargin [0]) ;
+
+ if (!mxIsSparse (pargin [0]) || n != mxGetM (pargin [0]))
+ {
+ mexErrMsgTxt ("A must be square and sparse") ;
+ }
+
+ /* get input sparse matrix A. Use triu(A) only */
+ A = sputil_get_sparse (pargin [0], &Amatrix, &dummy, 1) ;
+
+ /* use natural ordering if no q output parameter */
+ if (nargout < 3)
+ {
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NATURAL ;
+ cm->postorder = FALSE ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* analyze and factorize */
+ /* ---------------------------------------------------------------------- */
+
+ L = cholmod_l_analyze (A, cm) ;
+ cholmod_l_factorize (A, L, cm) ;
+
+ if (nargout < 2 && cm->status != CHOLMOD_OK)
+ {
+ mexErrMsgTxt ("matrix is not positive definite") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to a sparse matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* the conversion sets L->minor back to n, so get a copy of it first */
+ minor = L->minor ;
+ Lsparse = cholmod_l_factor_to_sparse (L, cm) ;
+ if (Lsparse->xtype == CHOLMOD_COMPLEX)
+ {
+ /* convert Lsparse from complex to zomplex */
+ cholmod_l_sparse_xtype (CHOLMOD_ZOMPLEX, Lsparse, cm) ;
+ }
+
+ if (minor < n)
+ {
+ /* remove columns minor to n-1 from Lsparse */
+ sputil_trim (Lsparse, minor, cm) ;
+ }
+
+ /* drop zeros from Lsparse */
+ sputil_drop_zeros (Lsparse) ;
+
+ /* Lsparse is lower triangular; conjugate transpose to get R */
+ R = cholmod_l_transpose (Lsparse, 2, cm) ;
+ cholmod_l_free_sparse (&Lsparse, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return results to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ /* return R */
+ pargout [0] = sputil_put_sparse (&R, cm) ;
+
+ /* return minor (translate to MATLAB convention) */
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ px = mxGetPr (pargout [1]) ;
+ px [0] = ((minor == n) ? 0 : (minor+1)) ;
+ }
+
+ /* return permutation */
+ if (nargout > 2)
+ {
+ pargout [2] = sputil_put_int (L->Perm, n, 1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free_factor (&L, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != (3 + mxIsComplex (pargout[0]))) mexErrMsgTxt ("!") ;
+ */
+}
diff --git a/CHOLMOD/MATLAB/chol2.m b/CHOLMOD/MATLAB/chol2.m
new file mode 100644
index 0000000..2279ec8
--- /dev/null
+++ b/CHOLMOD/MATLAB/chol2.m
@@ -0,0 +1,21 @@
+function [R,p,q] = chol2 (A) %#ok
+%CHOL2 sparse Cholesky factorization, A=R'R.
+% Note that A=L*L' (LCHOL) and A=L*D*L' (LDLCHOL) factorizations are faster
+% than R'*R (CHOL2 and CHOL) and use less memory. The LL' and LDL'
+% factorization methods use tril(A). This method uses triu(A), just like
+% the built-in CHOL.
+%
+% Example:
+% R = chol2 (A) same as R = chol (A), just faster
+% [R,p] = chol2 (A) save as [R,p] = chol(A), just faster
+% [R,p,q] = chol2 (A) factorizes A(q,q) into R'*R, where q is
+% a fill-reducing ordering
+%
+% A must be sparse.
+%
+% See also LCHOL, LDLCHOL, CHOL, LDLUPDATE.
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('chol2 mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/cholmod2.c b/CHOLMOD/MATLAB/cholmod2.c
new file mode 100644
index 0000000..4a784ac
--- /dev/null
+++ b/CHOLMOD/MATLAB/cholmod2.c
@@ -0,0 +1,273 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/cholmod mexFunction =================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Supernodal sparse Cholesky backslash, x = A\b. Factorizes PAP' in LL' then
+ * solves a sparse linear system. Uses the diagonal and upper triangular part
+ * of A only. A must be sparse. b can be sparse or dense.
+ *
+ * Usage:
+ *
+ * x = cholmod2 (A, b)
+ * [x stats] = cholmod2 (A, b, ordering) % a scalar: 0,-1,-2, or -3
+ * [x stats] = cholmod2 (A, b, p) % a permutation vector
+ *
+ * The 3rd argument select the ordering method to use. If not present or -1,
+ * the default ordering strategy is used (AMD, and then try METIS if AMD finds
+ * an ordering with high fill-in, and use the best method tried).
+ *
+ * Other options for the ordering parameter:
+ *
+ * 0 natural (no etree postordering)
+ * -1 use CHOLMOD's default ordering strategy (AMD, then try METIS)
+ * -2 AMD, and then try NESDIS (not METIS) if AMD has high fill-in
+ * -3 use AMD only
+ * -4 use METIS only
+ * -5 use NESDIS only
+ * -6 natural, but with etree postordering
+ * p user permutation (vector of size n, with a permutation of 1:n)
+ *
+ * stats(1) estimate of the reciprocal of the condition number
+ * stats(2) ordering used:
+ * 0: natural, 1: given, 2:amd, 3:metis, 4:nesdis, 5:colamd,
+ * 6: natural but postordered.
+ * stats(3) nnz(L)
+ * stats(4) flop count in Cholesky factorization. Excludes solution
+ * of upper/lower triangular systems, which can be easily
+ * computed from stats(3) (roughly 4*nnz(L)*size(b,2)).
+ * stats(5) memory usage in MB.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0, rcond, *p ;
+ cholmod_sparse Amatrix, Bspmatrix, *A, *Bs, *Xs ;
+ cholmod_dense Bmatrix, *X, *B ;
+ cholmod_factor *L ;
+ cholmod_common Common, *cm ;
+ Int n, B_is_sparse, ordering, k, *Perm ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* There is no supernodal LDL'. If cm->final_ll = FALSE (the default), then
+ * this mexFunction will use a simplicial LDL' when flops/lnz < 40, and a
+ * supernodal LL' otherwise. This may give suprising results to the MATLAB
+ * user, so always perform an LL' factorization by setting cm->final_ll
+ * to TRUE. */
+
+ cm->final_ll = TRUE ;
+ cm->quick_return_if_not_posdef = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 2 || nargin < 2 || nargin > 3)
+ {
+ mexErrMsgTxt ("usage: [x,rcond] = cholmod2 (A,b,ordering)") ;
+ }
+ n = mxGetM (pargin [0]) ;
+ if (!mxIsSparse (pargin [0]) || (n != mxGetN (pargin [0])))
+ {
+ mexErrMsgTxt ("A must be square and sparse") ;
+ }
+ if (n != mxGetM (pargin [1]))
+ {
+ mexErrMsgTxt ("# of rows of A and B must match") ;
+ }
+
+ /* get sparse matrix A. Use triu(A) only. */
+ A = sputil_get_sparse (pargin [0], &Amatrix, &dummy, 1) ;
+
+ /* get sparse or dense matrix B */
+ B = NULL ;
+ Bs = NULL ;
+ B_is_sparse = mxIsSparse (pargin [1]) ;
+ if (B_is_sparse)
+ {
+ /* get sparse matrix B (unsymmetric) */
+ Bs = sputil_get_sparse (pargin [1], &Bspmatrix, &dummy, 0) ;
+ }
+ else
+ {
+ /* get dense matrix B */
+ B = sputil_get_dense (pargin [1], &Bmatrix, &dummy) ;
+ }
+
+ /* get the ordering option */
+ if (nargin < 3)
+ {
+ /* use default ordering */
+ ordering = -1 ;
+ }
+ else
+ {
+ /* use a non-default option */
+ ordering = mxGetScalar (pargin [2]) ;
+ }
+
+ p = NULL ;
+ Perm = NULL ;
+
+ if (ordering == 0)
+ {
+ /* natural ordering */
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NATURAL ;
+ cm->postorder = FALSE ;
+ }
+ else if (ordering == -1)
+ {
+ /* default strategy ... nothing to change */
+ }
+ else if (ordering == -2)
+ {
+ /* default strategy, but with NESDIS in place of METIS */
+ cm->default_nesdis = TRUE ;
+ }
+ else if (ordering == -3)
+ {
+ /* use AMD only */
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_AMD ;
+ cm->postorder = TRUE ;
+ }
+ else if (ordering == -4)
+ {
+ /* use METIS only */
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_METIS ;
+ cm->postorder = TRUE ;
+ }
+ else if (ordering == -5)
+ {
+ /* use NESDIS only */
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NESDIS ;
+ cm->postorder = TRUE ;
+ }
+ else if (ordering == -6)
+ {
+ /* natural ordering, but with etree postordering */
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NATURAL ;
+ cm->postorder = TRUE ;
+ }
+ else if (ordering == -7)
+ {
+ /* always try both AMD and METIS, and pick the best */
+ cm->nmethods = 2 ;
+ cm->method [0].ordering = CHOLMOD_AMD ;
+ cm->method [1].ordering = CHOLMOD_METIS ;
+ cm->postorder = TRUE ;
+ }
+ else if (ordering >= 1)
+ {
+ /* assume the 3rd argument is a user-provided permutation of 1:n */
+ if (mxGetNumberOfElements (pargin [2]) != n)
+ {
+ mexErrMsgTxt ("invalid input permutation") ;
+ }
+ /* copy from double to integer, and convert to 0-based */
+ p = mxGetPr (pargin [2]) ;
+ Perm = cholmod_l_malloc (n, sizeof (Int), cm) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Perm [k] = p [k] - 1 ;
+ }
+ /* check the permutation */
+ if (!cholmod_l_check_perm (Perm, n, n, cm))
+ {
+ mexErrMsgTxt ("invalid input permutation") ;
+ }
+ /* use only the given permutation */
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_GIVEN ;
+ cm->postorder = FALSE ;
+ }
+ else
+ {
+ mexErrMsgTxt ("invalid ordering option") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* analyze and factorize */
+ /* ---------------------------------------------------------------------- */
+
+ L = cholmod_l_analyze_p (A, Perm, NULL, 0, cm) ;
+ cholmod_l_free (n, sizeof (Int), Perm, cm) ;
+ cholmod_l_factorize (A, L, cm) ;
+
+ rcond = cholmod_l_rcond (L, cm) ;
+
+ if (rcond == 0)
+ {
+ mexWarnMsgTxt ("Matrix is indefinite or singular to working precision");
+ }
+ else if (rcond < DBL_EPSILON)
+ {
+ mexWarnMsgTxt ("Matrix is close to singular or badly scaled.") ;
+ mexPrintf (" Results may be inaccurate. RCOND = %g.\n", rcond) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve and return solution to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ if (B_is_sparse)
+ {
+ /* solve AX=B with sparse X and B; return sparse X to MATLAB */
+ Xs = cholmod_l_spsolve (CHOLMOD_A, L, Bs, cm) ;
+ pargout [0] = sputil_put_sparse (&Xs, cm) ;
+ }
+ else
+ {
+ /* solve AX=B with dense X and B; return dense X to MATLAB */
+ X = cholmod_l_solve (CHOLMOD_A, L, B, cm) ;
+ pargout [0] = sputil_put_dense (&X, cm) ;
+ }
+
+ /* return statistics, if requested */
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, 5, mxREAL) ;
+ p = mxGetPr (pargout [1]) ;
+ p [0] = rcond ;
+ p [1] = L->ordering ;
+ p [2] = cm->lnz ;
+ p [3] = cm->fl ;
+ p [4] = cm->memory_usage / 1048576. ;
+ }
+
+ cholmod_l_free_factor (&L, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count !=
+ (mxIsComplex (pargout [0]) + (mxIsSparse (pargout[0]) ? 3:1)))
+ mexErrMsgTxt ("memory leak!") ;
+ */
+}
diff --git a/CHOLMOD/MATLAB/cholmod2.m b/CHOLMOD/MATLAB/cholmod2.m
new file mode 100644
index 0000000..759d545
--- /dev/null
+++ b/CHOLMOD/MATLAB/cholmod2.m
@@ -0,0 +1,42 @@
+function [x,stats] = cholmod2 (A, b, ordering) %#ok
+%CHOLMOD2 supernodal sparse Cholesky backslash, x = A\b
+%
+% Example:
+% x = cholmod2 (A,b)
+%
+% Computes the LL' factorization of A(p,p), where p is a fill-reducing
+% ordering, then solves a sparse linear system Ax=b. A must be sparse,
+% symmetric, and positive definite). Uses only the upper triangular part
+% of A. A second output, [x,stats]=cholmod2(A,b), returns statistics:
+%
+% stats(1) estimate of the reciprocal of the condition number
+% stats(2) ordering used:
+% 0: natural, 1: given, 2:amd, 3:metis, 4:nesdis,
+% 5:colamd, 6: natural but postordered.
+% stats(3) nnz(L)
+% stats(4) flop count in Cholesky factorization. Excludes solution
+% of upper/lower triangular systems, which can be easily
+% computed from stats(3) (roughly 4*nnz(L)*size(b,2)).
+% stats(5) memory usage in MB.
+%
+% The 3rd argument select the ordering method to use. If not present or -1,
+% the default ordering strategy is used (AMD, and then try METIS if AMD finds
+% an ordering with high fill-in, and use the best method tried).
+%
+% Other options for the ordering parameter:
+%
+% 0 natural (no etree postordering)
+% -1 use CHOLMOD's default ordering strategy (AMD, then try METIS)
+% -2 AMD, and then try NESDIS (not METIS) if AMD has high fill-in
+% -3 use AMD only
+% -4 use METIS only
+% -5 use NESDIS only
+% -6 natural, but with etree postordering
+% p user permutation (vector of size n, with a permutation of 1:n)
+%
+% See also CHOL, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cholmod2 mexFunction not found\n') ;
diff --git a/CHOLMOD/MATLAB/cholmod_demo.m b/CHOLMOD/MATLAB/cholmod_demo.m
new file mode 100644
index 0000000..159c68a
--- /dev/null
+++ b/CHOLMOD/MATLAB/cholmod_demo.m
@@ -0,0 +1,164 @@
+function cholmod_demo
+%CHOLMOD_DEMO a demo for CHOLMOD
+%
+% Tests CHOLMOD with various randomly-generated matrices, and the west0479
+% matrix distributed with MATLAB. Random matrices are not good test cases,
+% but they are easily generated. It also compares CHOLMOD and MATLAB on the
+% sparse matrix problem used in the MATLAB BENCH command.
+%
+% See CHOLMOD/MATLAB/Test/cholmod_test.m for a lengthy test using matrices from
+% the UF sparse matrix collection.
+%
+% Example:
+% cholmod_demo
+%
+% See also BENCH
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+help cholmod_demo
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+load west0479
+A = west0479 ;
+n = size (A,1) ;
+A = A*A'+100*speye (n) ;
+try_matrix (A) ;
+clear A
+
+n = 2000 ;
+A = sprandn (n, n, 0.002) ;
+A = A+A'+100*speye (n) ;
+try_matrix (A) ;
+clear A
+
+for n = [100 2000]
+ A = rand (n) ;
+ A = A*A' + 10 * eye (n) ;
+ try_matrix (A) ;
+ clear A
+end
+
+fprintf ('\n--------------------------------------------------------------\n') ;
+fprintf ('\nWith the matrix used in the MATLAB 7.2 "bench" program.\n') ;
+fprintf ('No fill-reducing orderings are used; type "help bench" for more') ;
+fprintf (' information.\n') ;
+
+n = 300 ;
+A = delsq (numgrid ('L', n)) ;
+b = sum (A)' ;
+
+spparms ('default') ;
+spparms ('autommd',0) ;
+spparms ('autoamd',0) ;
+tic ;
+x = A\b ;
+t1 = toc ;
+e1 = norm (A*x-b) ;
+
+tic ;
+x = cholmod2 (A,b,0) ;
+t2 = toc ;
+e2 = norm (A*x-b) ;
+
+fprintf ('MATLAB x=A\\b time: %8.4f resid: %8.0e\n', t1, e1) ;
+fprintf ('CHOLMOD x=A\\b time: %8.4f resid: %8.0e\n', t2, e2) ;
+fprintf ('CHOLMOD speedup: %8.2f\n', t1/t2) ;
+
+spparms ('default') ;
+
+fprintf ('\ncholmod_demo finished: all tests passed\n') ;
+fprintf ('\nFor more accurate timings, run this test again.\n') ;
+
+
+
+
+
+
+function try_matrix (A)
+% try_matrix: try a matrix with CHOLMOD
+
+n = size (A,1) ;
+S = sparse (A) ;
+
+fprintf ('\n--------------------------------------------------------------\n') ;
+if (issparse (A))
+ fprintf ('cholmod_demo: sparse matrix, n %d nnz %d\n', n, nnz (A)) ;
+else
+ fprintf ('cholmod_demo: dense matrix, n %d\n', n) ;
+end
+
+X = rand (n,1) ;
+C = sparse (X) ;
+try
+ % use built-in AMD
+ p = amd (S) ;
+catch
+ try
+ % use AMD from SuiteSparse (../../AMD)
+ p = amd2 (S) ;
+ catch
+ % use SYMAMD
+ p = symamd (S) ;
+ end
+end
+S = S (p,p) ;
+
+lnz = symbfact2 (S) ;
+fl = sum (lnz.^2) ;
+
+tic
+L = lchol (S) ; %#ok
+t1 = toc ;
+fprintf ('CHOLMOD lchol(sparse(A)) time: %6.2f mflop %8.1f\n', ...
+ t1, 1e-6 * fl / t1) ;
+
+tic
+LD = ldlchol (S) ; %#ok
+t2 = toc ;
+fprintf ('CHOLMOD ldlchol(sparse(A)) time: %6.2f mflop %8.1f\n', ...
+ t2, 1e-6 * fl / t2) ;
+
+tic
+LD = ldlupdate (LD,C) ;
+t3 = toc ;
+fprintf ('CHOLMOD ldlupdate(sparse(A),C) time: %6.2f (rank-1, C dense)\n', t3) ;
+
+[L,D] = ldlsplit (LD) ;
+L = full (L) ;
+err = norm ((S+C*C') - L*D*L', 1) / norm (S,1) ;
+fprintf ('err: %g\n', err) ;
+
+tic
+R = chol (S) ; %#ok
+s1 = toc ;
+fprintf ('MATLAB chol(sparse(A)) time: %6.2f mflop %8.1f\n', ...
+ s1, 1e-6 * fl / s1) ;
+
+E = full (A) ;
+tic
+R = chol (E) ;
+s2 = toc ;
+fprintf ('MATLAB chol(full(A)) time: %6.2f mflop %8.1f\n', ...
+ s2, 1e-6 * fl / s2) ;
+
+Z = full (R) ;
+tic
+Z = cholupdate (Z,X) ;
+s3 = toc ;
+fprintf ('MATLAB cholupdate(full(A),C) time: %6.2f (rank-1)\n', s3) ;
+
+err = norm ((E+X*X') - Z'*Z, 1) / norm (E,1) ;
+fprintf ('err: %g\n', err) ;
+
+fprintf ('CHOLMOD lchol(sparse(A)) speedup over chol(sparse(A)): %6.1f\n', ...
+ s1 / t1) ;
+
+fprintf ('CHOLMOD sparse update speedup vs MATLAB DENSE update: %6.1f\n', ...
+ s3 / t3) ;
+
+clear E S L R LD X C D Z
+clear err s1 s2 s3 t1 t2 t3 n
diff --git a/CHOLMOD/MATLAB/cholmod_install.m b/CHOLMOD/MATLAB/cholmod_install.m
new file mode 100644
index 0000000..5f50730
--- /dev/null
+++ b/CHOLMOD/MATLAB/cholmod_install.m
@@ -0,0 +1,70 @@
+function cholmod_install (metis_path)
+%CHOLMOD_INSTALL compile and install CHOLMOD, AMD, COLAMD, CCOLAMD, CAMD
+%
+% Example:
+% cholmod_install % compiles using ../../metis-4.0
+% cholmod_install ('/my/metis') % using non-default path to METIS
+% cholmod_install ('no metis') % do not use METIS at all
+%
+% CHOLMOD relies on AMD and COLAMD, for its ordering options, and can
+% optionally use CCOLAMD, CAMD, and METIS as well. By default, CCOLAMD, CAMD,
+% and METIS are used. METIS is assumed to be in the ../../metis-4.0 directory.
+%
+% See http://www-users.cs.umn.edu/~karypis/metis for a copy of METIS 4.0.1.
+%
+% You can only use cholmod_install while in the CHOLMOD/MATLAB directory.
+%
+% See also analyze, bisect, chol2, cholmod2, etree2, lchol, ldlchol, ldlsolve,
+% ldlupdate, metis, spsym, nesdis, septree, resymbol, sdmult, sparse2,
+% symbfact2, mread, mwrite, amd2, colamd2, camd, ccolamd
+
+% Copyright 2006-2007, Timothy A. Davis
+
+if (nargin < 1)
+ metis_path = '../../metis-4.0' ;
+end
+
+% compile CHOLMOD and add to the path
+cholmod_make (metis_path) ;
+cholmod_path = pwd ;
+addpath (cholmod_path)
+
+fprintf ('\nNow compiling the AMD, COLAMD, CCOLAMD, and CAMD mexFunctions:\n') ;
+
+% compile AMD and add to the path
+cd ../../AMD/MATLAB
+amd_make
+amd_path = pwd ;
+addpath (amd_path)
+
+% compile COLAMD and add to the path
+cd ../../COLAMD/MATLAB
+colamd_make
+colamd_path = pwd ;
+addpath (colamd_path)
+
+% compile CCOLAMD and add to the path
+cd ../../CCOLAMD/MATLAB
+ccolamd_make
+ccolamd_path = pwd ;
+addpath (ccolamd_path)
+
+% compile CAMD and add to the path
+cd ../../CAMD/MATLAB
+camd_make
+camd_path = pwd ;
+addpath (camd_path)
+
+cd (cholmod_path)
+
+fprintf ('\nThe following paths have been added. You may wish to add them\n') ;
+fprintf ('permanently, using the MATLAB pathtool command.\n') ;
+fprintf ('%s\n', cholmod_path) ;
+fprintf ('%s\n', amd_path) ;
+fprintf ('%s\n', colamd_path) ;
+fprintf ('%s\n', ccolamd_path) ;
+fprintf ('%s\n', camd_path) ;
+
+fprintf ('\nTo try your new mexFunctions, cut-and-paste this command:\n') ;
+fprintf ('amd_demo, colamd_demo, ccolamd_demo, camd_demo, graph_demo, cholmod_demo\n') ;
+
diff --git a/CHOLMOD/MATLAB/cholmod_make.m b/CHOLMOD/MATLAB/cholmod_make.m
new file mode 100644
index 0000000..44d22dc
--- /dev/null
+++ b/CHOLMOD/MATLAB/cholmod_make.m
@@ -0,0 +1,361 @@
+function cholmod_make (metis_path)
+%CHOLMOD_MAKE compiles the CHOLMOD mexFunctions
+%
+% Example:
+% cholmod_make
+%
+% CHOLMOD relies on AMD and COLAMD, and optionally CCOLAMD, CAMD, and METIS.
+% All but METIS are distributed with CHOLMOD. To compile CHOLMOD to use METIS
+% you must first place a copy of the metis-4.0 directory (METIS version 4.0.1)
+% in same directory that contains the AMD, COLAMD, CCOLAMD, and CHOLMOD
+% directories. Next, type
+%
+% cholmod_make
+%
+% in the MATLAB command window. Alternatively, use this command:
+%
+% cholmod_make ('path to your copy of metis-4.0 here') ;
+%
+% See http://www-users.cs.umn.edu/~karypis/metis for a copy of
+% METIS 4.0.1. If you do not have METIS, use either of the following:
+%
+% cholmod_make ('')
+% cholmod_make ('no metis')
+%
+% You must type the cholmod_make command while in the CHOLMOD/MATLAB directory.
+%
+% See also analyze, bisect, chol2, cholmod2, etree2, lchol, ldlchol, ldlsolve,
+% ldlupdate, metis, spsym, nesdis, septree, resymbol, sdmult, sparse2,
+% symbfact2, mread, mwrite
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+details = 0 ; % 1 if details of each command are to be printed
+
+v = getversion ;
+try
+ % ispc does not appear in MATLAB 5.3
+ pc = ispc ;
+catch
+ % if ispc fails, assume we are on a Windows PC if it's not unix
+ pc = ~isunix ;
+end
+
+d = '' ;
+if (~isempty (strfind (computer, '64')))
+ % 64-bit MATLAB
+ d = '-largeArrayDims' ;
+end
+
+include = '-I. -I../../AMD/Include -I../../COLAMD/Include -I../../CCOLAMD/Include -I../../CAMD/Include -I../Include -I../../UFconfig' ;
+
+if (v < 7.0)
+ % do not attempt to compile CHOLMOD with large file support
+ include = [include ' -DNLARGEFILE'] ;
+elseif (~pc)
+ % Linux/Unix require these flags for large file support
+ include = [include ' -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE'] ;
+end
+
+if (v < 6.5)
+ % logical class does not exist in MATLAB 6.1 or earlie
+ include = [include ' -DMATLAB6p1_OR_EARLIER'] ;
+end
+
+% Determine the METIS path, and whether or not METIS is available
+if (nargin == 0)
+ metis_path = '../../metis-4.0' ;
+end
+if (strcmp (metis_path, 'no metis'))
+ metis_path = '' ;
+end
+have_metis = (~isempty (metis_path)) ;
+
+% fix the METIS 4.0.1 rename.h file
+if (have_metis)
+ fprintf ('Compiling CHOLMOD with METIS on MATLAB Version %g\n', v) ;
+ f = fopen ('rename.h', 'w') ;
+ if (f == -1)
+ error ('unable to create rename.h in current directory') ;
+ end
+ fprintf (f, '/* do not edit this file; generated by cholmod_make */\n') ;
+ fprintf (f, '#undef log2\n') ;
+ fprintf (f, '#include "%s/Lib/rename.h"\n', metis_path) ;
+ fprintf (f, '#undef log2\n') ;
+ fprintf (f, '#define log2 METIS__log2\n') ;
+ fprintf (f, '#include "mex.h"\n') ;
+ fprintf (f, '#define malloc mxMalloc\n') ;
+ fprintf (f, '#define free mxFree\n') ;
+ fprintf (f, '#define calloc mxCalloc\n') ;
+ fprintf (f, '#define realloc mxRealloc\n') ;
+ fclose (f) ;
+ include = [include ' -I' metis_path '/Lib'] ;
+else
+ fprintf ('Compiling CHOLMOD without METIS on MATLAB Version %g\n', v) ;
+ include = ['-DNPARTITION ' include] ;
+end
+
+
+%-------------------------------------------------------------------------------
+% BLAS option
+%-------------------------------------------------------------------------------
+
+% This is exceedingly ugly. The MATLAB mex command needs to be told where to
+% fine the LAPACK and BLAS libraries, which is a real portability nightmare.
+
+if (pc)
+ if (v < 6.5)
+ % MATLAB 6.1 and earlier: use the version supplied here
+ lapack = 'lcc_lib/libmwlapack.lib' ;
+ elseif (v < 7.5)
+ lapack = 'libmwlapack.lib' ;
+ else
+ lapack = 'libmwlapack.lib libmwblas.lib' ;
+ end
+else
+ if (v < 7.5)
+ lapack = '-lmwlapack' ;
+ else
+ lapack = '-lmwlapack -lmwblas' ;
+ end
+end
+
+%-------------------------------------------------------------------------------
+
+include = strrep (include, '/', filesep) ;
+
+amd_src = { ...
+ '../../AMD/Source/amd_1', ...
+ '../../AMD/Source/amd_2', ...
+ '../../AMD/Source/amd_aat', ...
+ '../../AMD/Source/amd_control', ...
+ '../../AMD/Source/amd_defaults', ...
+ '../../AMD/Source/amd_dump', ...
+ '../../AMD/Source/amd_global', ...
+ '../../AMD/Source/amd_info', ...
+ '../../AMD/Source/amd_order', ...
+ '../../AMD/Source/amd_postorder', ...
+ '../../AMD/Source/amd_post_tree', ...
+ '../../AMD/Source/amd_preprocess', ...
+ '../../AMD/Source/amd_valid' } ;
+
+camd_src = { ...
+ '../../CAMD/Source/camd_1', ...
+ '../../CAMD/Source/camd_2', ...
+ '../../CAMD/Source/camd_aat', ...
+ '../../CAMD/Source/camd_control', ...
+ '../../CAMD/Source/camd_defaults', ...
+ '../../CAMD/Source/camd_dump', ...
+ '../../CAMD/Source/camd_global', ...
+ '../../CAMD/Source/camd_info', ...
+ '../../CAMD/Source/camd_order', ...
+ '../../CAMD/Source/camd_postorder', ...
+ '../../CAMD/Source/camd_preprocess', ...
+ '../../CAMD/Source/camd_valid' } ;
+
+colamd_src = {
+ '../../COLAMD/Source/colamd', ...
+ '../../COLAMD/Source/colamd_global' } ;
+
+ccolamd_src = {
+ '../../CCOLAMD/Source/ccolamd', ...
+ '../../CCOLAMD/Source/ccolamd_global' } ;
+
+metis_src = {
+ 'Lib/balance', ...
+ 'Lib/bucketsort', ...
+ 'Lib/ccgraph', ...
+ 'Lib/coarsen', ...
+ 'Lib/compress', ...
+ 'Lib/debug', ...
+ 'Lib/estmem', ...
+ 'Lib/fm', ...
+ 'Lib/fortran', ...
+ 'Lib/frename', ...
+ 'Lib/graph', ...
+ 'Lib/initpart', ...
+ 'Lib/kmetis', ...
+ 'Lib/kvmetis', ...
+ 'Lib/kwayfm', ...
+ 'Lib/kwayrefine', ...
+ 'Lib/kwayvolfm', ...
+ 'Lib/kwayvolrefine', ...
+ 'Lib/match', ...
+ 'Lib/mbalance2', ...
+ 'Lib/mbalance', ...
+ 'Lib/mcoarsen', ...
+ 'Lib/memory', ...
+ 'Lib/mesh', ...
+ 'Lib/meshpart', ...
+ 'Lib/mfm2', ...
+ 'Lib/mfm', ...
+ 'Lib/mincover', ...
+ 'Lib/minitpart2', ...
+ 'Lib/minitpart', ...
+ 'Lib/mkmetis', ...
+ 'Lib/mkwayfmh', ...
+ 'Lib/mkwayrefine', ...
+ 'Lib/mmatch', ...
+ 'Lib/mmd', ...
+ 'Lib/mpmetis', ...
+ 'Lib/mrefine2', ...
+ 'Lib/mrefine', ...
+ 'Lib/mutil', ...
+ 'Lib/myqsort', ...
+ 'Lib/ometis', ...
+ 'Lib/parmetis', ...
+ 'Lib/pmetis', ...
+ 'Lib/pqueue', ...
+ 'Lib/refine', ...
+ 'Lib/separator', ...
+ 'Lib/sfm', ...
+ 'Lib/srefine', ...
+ 'Lib/stat', ...
+ 'Lib/subdomains', ...
+ 'Lib/timing', ...
+ 'Lib/util' } ;
+
+for i = 1:length (metis_src)
+ metis_src {i} = [metis_path '/' metis_src{i}] ;
+end
+
+cholmod_matlab = { 'cholmod_matlab' } ;
+
+cholmod_src = {
+ '../Core/cholmod_aat', ...
+ '../Core/cholmod_add', ...
+ '../Core/cholmod_band', ...
+ '../Core/cholmod_change_factor', ...
+ '../Core/cholmod_common', ...
+ '../Core/cholmod_complex', ...
+ '../Core/cholmod_copy', ...
+ '../Core/cholmod_dense', ...
+ '../Core/cholmod_error', ...
+ '../Core/cholmod_factor', ...
+ '../Core/cholmod_memory', ...
+ '../Core/cholmod_sparse', ...
+ '../Core/cholmod_transpose', ...
+ '../Core/cholmod_triplet', ...
+ '../Check/cholmod_check', ...
+ '../Check/cholmod_read', ...
+ '../Check/cholmod_write', ...
+ '../Cholesky/cholmod_amd', ...
+ '../Cholesky/cholmod_analyze', ...
+ '../Cholesky/cholmod_colamd', ...
+ '../Cholesky/cholmod_etree', ...
+ '../Cholesky/cholmod_factorize', ...
+ '../Cholesky/cholmod_postorder', ...
+ '../Cholesky/cholmod_rcond', ...
+ '../Cholesky/cholmod_resymbol', ...
+ '../Cholesky/cholmod_rowcolcounts', ...
+ '../Cholesky/cholmod_rowfac', ...
+ '../Cholesky/cholmod_solve', ...
+ '../Cholesky/cholmod_spsolve', ...
+ '../MatrixOps/cholmod_drop', ...
+ '../MatrixOps/cholmod_horzcat', ...
+ '../MatrixOps/cholmod_norm', ...
+ '../MatrixOps/cholmod_scale', ...
+ '../MatrixOps/cholmod_sdmult', ...
+ '../MatrixOps/cholmod_ssmult', ...
+ '../MatrixOps/cholmod_submatrix', ...
+ '../MatrixOps/cholmod_vertcat', ...
+ '../MatrixOps/cholmod_symmetry', ...
+ '../Modify/cholmod_rowadd', ...
+ '../Modify/cholmod_rowdel', ...
+ '../Modify/cholmod_updown', ...
+ '../Supernodal/cholmod_super_numeric', ...
+ '../Supernodal/cholmod_super_solve', ...
+ '../Supernodal/cholmod_super_symbolic', ...
+ '../Partition/cholmod_ccolamd', ...
+ '../Partition/cholmod_csymamd', ...
+ '../Partition/cholmod_camd', ...
+ '../Partition/cholmod_metis', ...
+ '../Partition/cholmod_nesdis' } ;
+
+cholmod_mex_src = { ...
+ 'analyze', ...
+ 'bisect', ...
+ 'chol2', ...
+ 'cholmod2', ...
+ 'etree2', ...
+ 'lchol', ...
+ 'ldlchol', ...
+ 'ldlsolve', ...
+ 'ldlupdate', ...
+ 'metis', ...
+ 'spsym', ...
+ 'nesdis', ...
+ 'septree', ...
+ 'resymbol', ...
+ 'sdmult', ...
+ 'sparse2', ...
+ 'symbfact2', ...
+ 'mread', ...
+ 'mwrite' } ;
+
+if (pc)
+ % Windows does not have drand48 and srand48, required by METIS. Use
+ % drand48 and srand48 in CHOLMOD/MATLAB/Windows/rand48.c instead.
+ obj_extension = '.obj' ;
+ cholmod_matlab = [cholmod_matlab {'Windows/rand48'}] ;
+ include = [include ' -IWindows'] ;
+else
+ obj_extension = '.o' ;
+end
+
+% compile each library source file
+obj = '' ;
+
+source = [amd_src colamd_src ccolamd_src camd_src cholmod_src cholmod_matlab] ;
+if (have_metis)
+ source = [metis_src source] ;
+end
+
+kk = 0 ;
+
+for f = source
+ ff = strrep (f {1}, '/', filesep) ;
+ slash = strfind (ff, filesep) ;
+ if (isempty (slash))
+ slash = 1 ;
+ else
+ slash = slash (end) + 1 ;
+ end
+ o = ff (slash:end) ;
+ obj = [obj ' ' o obj_extension] ; %#ok
+ s = sprintf ('mex %s -DDLONG -O %s -c %s.c', d, include, ff) ;
+ kk = do_cmd (s, kk, details) ;
+end
+
+% compile each mexFunction
+for f = cholmod_mex_src
+ s = sprintf ('mex %s -DDLONG -O %s %s.c', d, include, f{1}) ;
+ s = [s obj ' ' lapack] ; %#ok
+ kk = do_cmd (s, kk, details) ;
+end
+
+% clean up
+s = ['delete ' obj] ;
+do_cmd (s, kk, details) ;
+fprintf ('\nCHOLMOD successfully compiled\n') ;
+
+%-------------------------------------------------------------------------------
+function kk = do_cmd (s, kk, details)
+%DO_CMD: evaluate a command, and either print it or print a "."
+if (details)
+ fprintf ('%s\n', s) ;
+else
+ if (mod (kk, 60) == 0)
+ fprintf ('\n') ;
+ end
+ kk = kk + 1 ;
+ fprintf ('.') ;
+end
+eval (s) ;
+
+%-------------------------------------------------------------------------------
+function v = getversion
+% determine the MATLAB version, and return it as a double.
+v = sscanf (version, '%d.%d.%d') ;
+v = 10.^(0:-1:-(length(v)-1)) * v ;
diff --git a/CHOLMOD/MATLAB/cholmod_matlab.c b/CHOLMOD/MATLAB/cholmod_matlab.c
new file mode 100644
index 0000000..a1cda98
--- /dev/null
+++ b/CHOLMOD/MATLAB/cholmod_matlab.c
@@ -0,0 +1,2162 @@
+/* ========================================================================== */
+/* === MATLAB/cholmod_matlab ================================================ */
+/* ========================================================================== */
+
+/* Utility routines for the CHOLMOD MATLAB mexFunctions.
+ *
+ * If CHOLMOD runs out of memory, MATLAB will terminate the mexFunction
+ * immediately since it uses mxMalloc (see sputil_config, below). Likewise,
+ * if mxCreate* or mxMalloc (as called in this file) fails, MATLAB will also
+ * terminate the mexFunction. When this occurs, MATLAB frees all allocated
+ * memory, so we don't have to worry about memory leaks. If this were not the
+ * case, the routines in this file would suffer from memory leaks whenever an
+ * error occurred.
+ */
+
+#include "cholmod_matlab.h"
+
+#ifndef INT64_T
+#define INT64_T long long
+#endif
+
+/* This file pointer is used for the mread and mwrite mexFunctions. It must
+ * be a global variable, because the file pointer is not passed to the
+ * sputil_error_handler function when an error occurs. */
+FILE *sputil_file = NULL ;
+
+/* ========================================================================== */
+/* === sputil_config ======================================================== */
+/* ========================================================================== */
+
+/* Define function pointers and other parameters for a mexFunction */
+
+void sputil_config (Int spumoni, cholmod_common *cm)
+{
+ /* cholmod_l_solve must return a real or zomplex X for MATLAB */
+ cm->prefer_zomplex = TRUE ;
+
+ /* use mxMalloc and related memory management routines */
+ cm->malloc_memory = mxMalloc ;
+ cm->free_memory = mxFree ;
+ cm->realloc_memory = mxRealloc ;
+ cm->calloc_memory = mxCalloc ;
+
+ /* printing and error handling */
+ if (spumoni == 0)
+ {
+ /* do not print anything from within CHOLMOD */
+ cm->print = -1 ;
+ cm->print_function = NULL ;
+ }
+ else
+ {
+ /* spumoni = 1: print warning and error messages. cholmod_l_print_*
+ * routines will print a one-line summary of each object printed.
+ * spumoni = 2: also print a short summary of each object.
+ */
+ cm->print = spumoni + 2 ;
+ cm->print_function = mexPrintf ;
+ }
+
+ /* error handler */
+ cm->error_handler = sputil_error_handler ;
+
+ /* complex arithmetic */
+ cm->complex_divide = cholmod_l_divcomplex ;
+ cm->hypotenuse = cholmod_l_hypot ;
+
+#ifndef NPARTITION
+#if defined(METIS_VERSION)
+#if (METIS_VERSION >= METIS_VER(4,0,2))
+ /* METIS 4.0.2 uses function pointers for malloc and free */
+ METIS_malloc = cm->malloc_memory ;
+ METIS_free = cm->free_memory ;
+#endif
+#endif
+#endif
+
+ /* Turn off METIS memory guard. It is not needed, because mxMalloc will
+ * safely terminate the mexFunction and free any workspace without killing
+ * all of MATLAB. This assumes cholmod_make was used to compile CHOLMOD
+ * for MATLAB. */
+ cm->metis_memory = 0.0 ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_error_handler ================================================= */
+/* ========================================================================== */
+
+void sputil_error_handler (int status, char *file, int line, char *message)
+{
+ if (status < CHOLMOD_OK)
+ {
+ /*
+ mexPrintf ("ERROR: file %s line %d, status %d\n", file, line, status) ;
+ */
+ if (sputil_file != NULL)
+ {
+ fclose (sputil_file) ;
+ sputil_file = NULL ;
+ }
+ mexErrMsgTxt (message) ;
+ }
+ /*
+ else
+ {
+ mexPrintf ("Warning: file %s line %d, status %d\n", file, line, status);
+ }
+ */
+}
+
+
+/* ========================================================================== */
+/* === sputil_get_sparse ==================================================== */
+/* ========================================================================== */
+
+/* Create a shallow CHOLMOD copy of a MATLAB sparse matrix. No memory is
+ * allocated. The resulting matrix A must not be modified.
+ */
+
+cholmod_sparse *sputil_get_sparse
+(
+ const mxArray *Amatlab, /* MATLAB version of the matrix */
+ cholmod_sparse *A, /* CHOLMOD version of the matrix */
+ double *dummy, /* a pointer to a valid scalar double */
+ Int stype /* -1: lower, 0: unsymmetric, 1: upper */
+)
+{
+ Int *Ap ;
+ A->nrow = mxGetM (Amatlab) ;
+ A->ncol = mxGetN (Amatlab) ;
+ A->p = (Int *) mxGetJc (Amatlab) ;
+ A->i = (Int *) mxGetIr (Amatlab) ;
+ Ap = A->p ;
+ A->nzmax = Ap [A->ncol] ;
+ A->packed = TRUE ;
+ A->sorted = TRUE ;
+ A->nz = NULL ;
+ A->itype = CHOLMOD_INT ;
+ A->dtype = CHOLMOD_DOUBLE ;
+ A->stype = stype ;
+
+#ifndef MATLAB6p1_OR_EARLIER
+
+ if (mxIsLogical (Amatlab))
+ {
+ A->x = NULL ;
+ A->z = NULL ;
+ A->xtype = CHOLMOD_PATTERN ;
+ }
+ else if (mxIsEmpty (Amatlab))
+ {
+ /* this is not dereferenced, but the existence (non-NULL) of these
+ * pointers is checked in CHOLMOD */
+ A->x = dummy ;
+ A->z = dummy ;
+ A->xtype = mxIsComplex (Amatlab) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ;
+ }
+ else if (mxIsDouble (Amatlab))
+ {
+ A->x = mxGetPr (Amatlab) ;
+ A->z = mxGetPi (Amatlab) ;
+ A->xtype = mxIsComplex (Amatlab) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ;
+ }
+ else
+ {
+ /* only logical and complex/real double matrices supported */
+ sputil_error (ERROR_INVALID_TYPE, 0) ;
+ }
+
+#else
+
+ if (mxIsEmpty (Amatlab))
+ {
+ /* this is not dereferenced, but the existence (non-NULL) of these
+ * pointers is checked in CHOLMOD */
+ A->x = dummy ;
+ A->z = dummy ;
+ A->xtype = mxIsComplex (Amatlab) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ;
+ }
+ else
+ {
+ /* in MATLAB 6.1, the matrix is sparse, so it must be double */
+ A->x = mxGetPr (Amatlab) ;
+ A->z = mxGetPi (Amatlab) ;
+ A->xtype = mxIsComplex (Amatlab) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ;
+ }
+
+#endif
+
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_get_dense ===================================================== */
+/* ========================================================================== */
+
+/* Create a shallow CHOLMOD copy of a MATLAB dense matrix. No memory is
+ * allocated. Only double (real and zomplex) matrices are supported. The
+ * resulting matrix B must not be modified.
+ */
+
+cholmod_dense *sputil_get_dense
+(
+ const mxArray *Amatlab, /* MATLAB version of the matrix */
+ cholmod_dense *A, /* CHOLMOD version of the matrix */
+ double *dummy /* a pointer to a valid scalar double */
+)
+{
+ A->nrow = mxGetM (Amatlab) ;
+ A->ncol = mxGetN (Amatlab) ;
+ A->d = A->nrow ;
+ A->nzmax = A->nrow * A->ncol ;
+ A->dtype = CHOLMOD_DOUBLE ;
+
+ if (mxIsEmpty (Amatlab))
+ {
+ A->x = dummy ;
+ A->z = dummy ;
+ }
+ else if (mxIsDouble (Amatlab))
+ {
+ A->x = mxGetPr (Amatlab) ;
+ A->z = mxGetPi (Amatlab) ;
+ }
+ else
+ {
+ /* only full double matrices supported by sputil_get_dense */
+ sputil_error (ERROR_INVALID_TYPE, 0) ;
+ }
+ A->xtype = mxIsComplex (Amatlab) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ;
+
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_get_sparse_pattern ============================================ */
+/* ========================================================================== */
+
+/* Create a CHOLMOD_PATTERN sparse matrix for a MATLAB matrix, depending on the
+ * type:
+ *
+ * (1) MATLAB full real double: duplicate CHOLMOD_REAL sparse matrix.
+ * (2) MATLAB full complex double: duplicate CHOLMOD_ZOMPLEX sparse matrix.
+ * (3) MATLAB full logical: duplicate CHOLMOD_PATTERN sparse matrix.
+ * (4) MATLAB sparse real double: shallow CHOLMOD_REAL copy.
+ * (5) MATLAB sparse complex double: shallow CHOLMOD_ZOMPLEX copy.
+ * (6) MATLAB sparse logical: shallow CHOLMOD_PATTERN copy.
+ *
+ * A shallow copy or duplicate is returned; the shallow copy must not be freed.
+ * For a shallow copy, the return value A is the same as Ashallow. For a
+ * complete duplicate, A and Ashallow will differ.
+ */
+
+cholmod_sparse *sputil_get_sparse_pattern
+(
+ const mxArray *Amatlab, /* MATLAB version of the matrix */
+ cholmod_sparse *Ashallow, /* shallow CHOLMOD version of the matrix */
+ double *dummy, /* a pointer to a valid scalar double */
+ cholmod_common *cm
+)
+{
+ cholmod_sparse *A = NULL ;
+
+ if (!mxIsSparse (Amatlab))
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A = sparse (X) where X is full */
+ /* ------------------------------------------------------------------ */
+
+ if (mxIsDouble (Amatlab))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* convert full double X into sparse matrix A (pattern only) */
+ /* -------------------------------------------------------------- */
+
+ cholmod_dense Xmatrix, *X ;
+ X = sputil_get_dense (Amatlab, &Xmatrix, dummy) ;
+ A = cholmod_l_dense_to_sparse (X, FALSE, cm) ;
+
+ }
+
+#ifndef MATLAB6p1_OR_EARLIER
+
+ else if (mxIsLogical (Amatlab))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* convert full logical MATLAB matrix into CHOLMOD_PATTERN */
+ /* -------------------------------------------------------------- */
+
+ /* (this is copied and modified from t_cholmod_dense.c) */
+
+ char *x ;
+ Int *Ap, *Ai ;
+ Int nrow, ncol, i, j, nz, nzmax, p ;
+
+ /* -------------------------------------------------------------- */
+ /* count the number of nonzeros in the result */
+ /* -------------------------------------------------------------- */
+
+ nrow = mxGetM (Amatlab) ;
+ ncol = mxGetN (Amatlab) ;
+ x = (char *) mxGetData (Amatlab) ;
+ nzmax = nrow * ncol ;
+ for (nz = 0, j = 0 ; j < nzmax ; j++)
+ {
+ if (x [j])
+ {
+ nz++ ;
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* allocate the result A */
+ /* -------------------------------------------------------------- */
+
+ A = cholmod_l_allocate_sparse (nrow, ncol, nz, TRUE, TRUE, 0,
+ CHOLMOD_PATTERN, cm) ;
+
+ if (cm->status < CHOLMOD_OK)
+ {
+ return (NULL) ; /* out of memory */
+ }
+ Ap = A->p ;
+ Ai = A->i ;
+
+ /* -------------------------------------------------------------- */
+ /* copy the full logical matrix into the sparse matrix A */
+ /* -------------------------------------------------------------- */
+
+ p = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Ap [j] = p ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ if (x [i+j*nrow])
+ {
+ Ai [p++] = i ;
+ }
+ }
+ }
+ /* ASSERT (p == nz) ; */
+ Ap [ncol] = nz ;
+ }
+
+#endif
+
+ else
+ {
+ /* only double and logical matrices supported */
+ sputil_error (ERROR_INVALID_TYPE, 0) ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* create a shallow copy of sparse matrix A (default stype is zero) */
+ /* ------------------------------------------------------------------ */
+
+ A = sputil_get_sparse (Amatlab, Ashallow, dummy, 0) ;
+ A->x = NULL ;
+ A->z = NULL ;
+ A->xtype = CHOLMOD_PATTERN ;
+ }
+
+ return (A) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_put_sparse ==================================================== */
+/* ========================================================================== */
+
+/* Creates a true MATLAB version of a CHOLMOD sparse matrix. The CHOLMOD sparse
+ * matrix is destroyed. Both real and zomplex matrices are supported.
+ */
+
+mxArray *sputil_put_sparse
+(
+ cholmod_sparse **Ahandle, /* CHOLMOD version of the matrix */
+ cholmod_common *cm
+)
+{
+ mxArray *Amatlab ;
+ cholmod_sparse *A ;
+ A = *Ahandle ;
+ Amatlab = mxCreateSparse (0, 0, 0,
+ (A->xtype != CHOLMOD_REAL) ? mxCOMPLEX: mxREAL) ;
+ mxSetM (Amatlab, A->nrow) ;
+ mxSetN (Amatlab, A->ncol) ;
+ mxSetNzmax (Amatlab, A->nzmax) ;
+ mxFree (mxGetJc (Amatlab)) ;
+ mxFree (mxGetIr (Amatlab)) ;
+ mxFree (mxGetPr (Amatlab)) ;
+ mxSetJc (Amatlab, A->p) ;
+ mxSetIr (Amatlab, A->i) ;
+ mxSetPr (Amatlab, A->x) ;
+ mexMakeMemoryPersistent (A->p) ;
+ mexMakeMemoryPersistent (A->i) ;
+ mexMakeMemoryPersistent (A->x) ;
+ if (A->xtype != CHOLMOD_REAL)
+ {
+ mxFree (mxGetPi (Amatlab)) ;
+ mxSetPi (Amatlab, A->z) ;
+ mexMakeMemoryPersistent (A->z) ;
+ }
+ A->p = NULL ;
+ A->i = NULL ;
+ A->x = NULL ;
+ A->z = NULL ;
+ cholmod_l_free_sparse (Ahandle, cm) ;
+ return (Amatlab) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_put_dense ===================================================== */
+/* ========================================================================== */
+
+/* Creates a true MATLAB version of a CHOLMOD dense matrix. The CHOLMOD dense
+ * matrix is destroyed. Both real and zomplex matrices are supported.
+ */
+
+mxArray *sputil_put_dense
+(
+ cholmod_dense **Ahandle, /* CHOLMOD version of the matrix */
+ cholmod_common *cm
+)
+{
+ mxArray *Amatlab ;
+ cholmod_dense *A ;
+ A = *Ahandle ;
+ Amatlab = mxCreateDoubleMatrix (0, 0,
+ (A->xtype != CHOLMOD_REAL) ? mxCOMPLEX: mxREAL) ;
+ mxSetM (Amatlab, A->nrow) ;
+ mxSetN (Amatlab, A->ncol) ;
+ mxFree (mxGetPr (Amatlab)) ;
+ mxSetPr (Amatlab, A->x) ;
+ mexMakeMemoryPersistent (A->x) ;
+ if (A->xtype != CHOLMOD_REAL)
+ {
+ mxFree (mxGetPi (Amatlab)) ;
+ mxSetPi (Amatlab, A->z) ;
+ mexMakeMemoryPersistent (A->z) ;
+ }
+ A->x = NULL ;
+ A->z = NULL ;
+ cholmod_l_free_dense (Ahandle, cm) ;
+ return (Amatlab) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_put_int ======================================================= */
+/* ========================================================================== */
+
+/* Convert an Int vector into a double mxArray */
+
+mxArray *sputil_put_int
+(
+ Int *P, /* vector to convert */
+ Int n, /* length of P */
+ Int one_based /* 1 if convert from 0-based to 1-based, 0 otherwise */
+)
+{
+ double *p ;
+ mxArray *Q ;
+ Int i ;
+ Q = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ p = mxGetPr (Q) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ p [i] = (double) (P [i] + one_based) ;
+ }
+ return (Q) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_error ========================================================= */
+/* ========================================================================== */
+
+/* An integer is out of range, or other error has occurred. */
+
+void sputil_error
+(
+ Int error, /* kind of error */
+ Int is_index /* TRUE if a matrix index, FALSE if a matrix dimension */
+)
+{
+ if (error == ERROR_TOO_SMALL)
+ {
+ mexErrMsgTxt (is_index ?
+ "sparse: index into matrix must be positive" :
+ "sparse: sparse matrix sizes must be non-negative integers") ;
+ }
+ else if (error == ERROR_HUGE)
+ {
+ mexErrMsgTxt (is_index ?
+ "sparse: index into matrix is too large" :
+ "sparse: sparse matrix size is too large") ;
+ }
+ else if (error == ERROR_NOT_INTEGER)
+ {
+ mexErrMsgTxt (is_index ?
+ "sparse: index into matrix must be an integer" :
+ "sparse: sparse matrix size must be an integer") ;
+ }
+ else if (error == ERROR_TOO_LARGE)
+ {
+ mexErrMsgTxt ("sparse: index exceeds matrix dimensions") ;
+ }
+ else if (error == ERROR_USAGE)
+ {
+ mexErrMsgTxt (
+ "Usage:\n"
+ "A = sparse (S)\n"
+ "A = sparse (i,j,s,m,n,nzmax)\n"
+ "A = sparse (i,j,s,m,n)\n"
+ "A = sparse (i,j,s)\n"
+ "A = sparse (m,n)\n") ;
+ }
+ else if (error == ERROR_LENGTH)
+ {
+ mexErrMsgTxt ("sparse: vectors must be the same lengths") ;
+ }
+ else if (error == ERROR_INVALID_TYPE)
+ {
+ mexErrMsgTxt ("matrix class not supported") ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === sputil_double_to_int ================================================= */
+/* ========================================================================== */
+
+/* convert a double into an integer */
+
+Int sputil_double_to_int /* returns integer value of x */
+(
+ double x, /* double value to convert */
+ Int is_index, /* TRUE if a matrix index, FALSE if a matrix dimension */
+ Int n /* if a matrix index, x cannot exceed this dimension,
+ * except that -1 is treated as infinity */
+)
+{
+ Int i ;
+ if (x > INT_MAX)
+ {
+ /* x is way too big for an integer */
+ sputil_error (ERROR_HUGE, is_index) ;
+ }
+ else if (x < 0)
+ {
+ /* x must be non-negative */
+ sputil_error (ERROR_TOO_SMALL, is_index) ;
+ }
+ i = (Int) x ;
+ if (x != (double) i)
+ {
+ /* x must be an integer */
+ sputil_error (ERROR_NOT_INTEGER, is_index) ;
+ }
+ if (is_index)
+ {
+ if (i < 1)
+ {
+ sputil_error (ERROR_TOO_SMALL, is_index) ;
+ }
+ else if (i > n && n != EMPTY)
+ {
+ sputil_error (ERROR_TOO_LARGE, is_index) ;
+ }
+ }
+ return (i) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_nelements ===================================================== */
+/* ========================================================================== */
+
+/* return the number of elements in an mxArray. Trigger an error on integer
+ * overflow (in case the argument is sparse) */
+
+Int sputil_nelements (const mxArray *arg)
+{
+ double size ;
+ const Int *dims ;
+ Int k, ndims ;
+ ndims = mxGetNumberOfDimensions (arg) ;
+ dims = (Int *) mxGetDimensions (arg) ;
+ size = 1 ;
+ for (k = 0 ; k < ndims ; k++)
+ {
+ size *= dims [k] ;
+ }
+ return (sputil_double_to_int (size, FALSE, 0)) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_get_double ==================================================== */
+/* ========================================================================== */
+
+double sputil_get_double (const mxArray *arg)
+{
+ if (sputil_nelements (arg) < 1)
+ {
+ /* [] is not a scalar, but its value is zero so that
+ * sparse ([],[],[]) is a 0-by-0 matrix */
+ return (0) ;
+ }
+ return (mxGetScalar (arg)) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_get_integer =================================================== */
+/* ========================================================================== */
+
+/* return an argument as a non-negative integer scalar, or -1 if error */
+
+Int sputil_get_integer
+(
+ const mxArray *arg, /* MATLAB argument to convert */
+ Int is_index, /* TRUE if an index, FALSE if a matrix dimension */
+ Int n /* maximum value, if an index */
+)
+{
+ double x = sputil_get_double (arg) ;
+ if (mxIsInf (x) || mxIsNaN (x))
+ {
+ /* arg is Inf or NaN, return -1 */
+ return (EMPTY) ;
+ }
+ return (sputil_double_to_int (x, is_index, n)) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_trim ========================================================== */
+/* ========================================================================== */
+
+/* Remove columns k to n-1 from a sparse matrix S, leaving columns 0 to k-1.
+ * S must be packed (there can be no S->nz array). This condition is not
+ * checked, since only packed matrices are passed to this routine. */
+
+void sputil_trim
+(
+ cholmod_sparse *S,
+ Int k,
+ cholmod_common *cm
+)
+{
+ Int *Sp ;
+ Int ncol ;
+ size_t n1, nznew ;
+
+ if (S == NULL)
+ {
+ return ;
+ }
+
+ ncol = S->ncol ;
+ if (k < 0 || k >= ncol)
+ {
+ /* do not modify S */
+ return ;
+ }
+
+ /* reduce S->p in size. This cannot fail. */
+ n1 = ncol + 1 ;
+ S->p = cholmod_l_realloc (k+1, sizeof (Int), S->p, &n1, cm) ;
+
+ /* get the new number of entries in S */
+ Sp = S->p ;
+ nznew = Sp [k] ;
+
+ /* reduce S->i, S->x, and S->z (if present) to size nznew */
+ cholmod_l_reallocate_sparse (nznew, S, cm) ;
+
+ /* S now has only k columns */
+ S->ncol = k ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_extract_zeros ================================================= */
+/* ========================================================================== */
+
+/* Create a sparse binary (real double) matrix Z that contains the pattern
+ * of explicit zeros in the sparse real/zomplex double matrix A. */
+
+cholmod_sparse *sputil_extract_zeros
+(
+ cholmod_sparse *A,
+ cholmod_common *cm
+)
+{
+ Int *Ap, *Ai, *Zp, *Zi ;
+ double *Ax, *Az, *Zx ;
+ Int j, p, nzeros = 0, is_complex, pz, nrow, ncol ;
+ cholmod_sparse *Z ;
+
+ if (A == NULL || A->xtype == CHOLMOD_PATTERN || A->xtype == CHOLMOD_COMPLEX)
+ {
+ /* only sparse real/zomplex double matrices supported */
+ sputil_error (ERROR_INVALID_TYPE, 0) ;
+ }
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ ncol = A->ncol ;
+ nrow = A->nrow ;
+ is_complex = (A->xtype == CHOLMOD_ZOMPLEX) ;
+
+ /* count the number of zeros in a sparse matrix A */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ if (CHOLMOD_IS_ZERO (Ax [p]) &&
+ ((is_complex) ? CHOLMOD_IS_ZERO (Az [p]) : TRUE))
+ {
+ nzeros++ ;
+ }
+ }
+ }
+
+ /* allocate the Z matrix with space for all the zero entries */
+ Z = cholmod_l_spzeros (nrow, ncol, nzeros, CHOLMOD_REAL, cm) ;
+
+ /* extract the zeros from A and store them in Z as binary values */
+ if (nzeros > 0)
+ {
+ Zp = Z->p ;
+ Zi = Z->i ;
+ Zx = Z->x ;
+ pz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Zp [j] = pz ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ if (CHOLMOD_IS_ZERO (Ax [p]) &&
+ ((is_complex) ? CHOLMOD_IS_ZERO (Az [p]) : TRUE))
+ {
+ Zi [pz] = Ai [p] ;
+ Zx [pz] = 1 ;
+ pz++ ;
+ }
+ }
+ }
+ Zp [ncol] = pz ;
+ }
+
+ return (Z) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_drop_zeros ==================================================== */
+/* ========================================================================== */
+
+/* Drop zeros from a packed CHOLMOD sparse matrix (zomplex or real). This is
+ * very similar to CHOLMOD/MatrixOps/cholmod_drop, except that this routine has
+ * no tolerance parameter and it can handle zomplex matrices. NaN's are left
+ * in the matrix. If this is used on the sparse matrix version of the factor
+ * L, then the update/downdate methods cannot be applied to L (ldlupdate).
+ * Returns the number of entries dropped.
+ */
+
+Int sputil_drop_zeros
+(
+ cholmod_sparse *S
+)
+{
+ double sik, zik ;
+ Int *Sp, *Si ;
+ double *Sx, *Sz ;
+ Int pdest, k, ncol, p, pend, nz ;
+
+ if (S == NULL)
+ {
+ return (0) ;
+ }
+
+ Sp = S->p ;
+ Si = S->i ;
+ Sx = S->x ;
+ Sz = S->z ;
+ pdest = 0 ;
+ ncol = S->ncol ;
+ nz = Sp [ncol] ;
+
+ if (S->xtype == CHOLMOD_ZOMPLEX)
+ {
+ for (k = 0 ; k < ncol ; k++)
+ {
+ p = Sp [k] ;
+ pend = Sp [k+1] ;
+ Sp [k] = pdest ;
+ for ( ; p < pend ; p++)
+ {
+ sik = Sx [p] ;
+ zik = Sz [p] ;
+ if (CHOLMOD_IS_NONZERO (sik) || CHOLMOD_IS_NONZERO (zik))
+ {
+ if (p != pdest)
+ {
+ Si [pdest] = Si [p] ;
+ Sx [pdest] = sik ;
+ Sz [pdest] = zik ;
+ }
+ pdest++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < ncol ; k++)
+ {
+ p = Sp [k] ;
+ pend = Sp [k+1] ;
+ Sp [k] = pdest ;
+ for ( ; p < pend ; p++)
+ {
+ sik = Sx [p] ;
+ if (CHOLMOD_IS_NONZERO (sik))
+ {
+ if (p != pdest)
+ {
+ Si [pdest] = Si [p] ;
+ Sx [pdest] = sik ;
+ }
+ pdest++ ;
+ }
+ }
+ }
+ }
+ Sp [ncol] = pdest ;
+ return (nz - pdest) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_copy_ij ======================================================= */
+/* ========================================================================== */
+
+/* copy i or j arguments into an Int vector. For small integer types, i and
+ * and j can be returned with negative entries; this error condition is caught
+ * later, in cholmod_triplet_to_sparse.
+ *
+ * TODO: if the mxClassID matches the default Int integer (INT32 for 32-bit
+ * MATLAB and INT64 for 64-bit), then it would save memory to patch in the
+ * vector with a pointer copy, rather than making a copy of the whole vector.
+ * This would require that the 1-based i and j vectors be converted on the fly
+ * to 0-based vectors in cholmod_triplet_to_sparse.
+ */
+
+Int sputil_copy_ij /* returns the dimension, n */
+(
+ Int is_scalar, /* TRUE if argument is a scalar, FALSE otherwise */
+ Int scalar, /* scalar value of the argument */
+ void *vector, /* vector value of the argument */
+ mxClassID category, /* type of vector */
+ Int nz, /* length of output vector I */
+ Int n, /* maximum dimension, EMPTY if not yet known */
+ Int *I /* vector of length nz to copy into */
+)
+{
+ Int i, k, ok, ok2, ok3, n2 ;
+
+ if (is_scalar)
+ {
+ n2 = scalar ;
+ if (n == EMPTY)
+ {
+ n = scalar ;
+ }
+ i = scalar - 1 ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ I [k] = i ;
+ }
+ }
+ else
+ {
+ /* copy double input into Int vector (convert to 0-based) */
+ ok = TRUE ;
+ ok2 = TRUE ;
+ ok3 = TRUE ;
+ n2 = 0 ;
+
+ switch (category)
+ {
+
+#ifndef MATLAB6p1_OR_EARLIER
+
+ /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */
+ case mxLOGICAL_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = (Int) (((mxLogical *) vector) [k]) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+#endif
+
+ case mxCHAR_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = (Int) (((mxChar *) vector) [k]) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+ case mxINT8_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = (Int) (((INT8_T *) vector) [k]) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+ case mxUINT8_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = (Int) (((UINT8_T *) vector) [k]) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+ case mxINT16_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = (Int) (((INT16_T *) vector) [k]) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+ case mxUINT16_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = (Int) (((UINT16_T *) vector) [k]) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+ case mxINT32_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = (Int) (((INT32_T *) vector) [k]) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+ case mxUINT32_CLASS:
+
+ for (k = 0 ; ok3 && k < nz ; k++)
+ {
+ double y = (((UINT32_T *) vector) [k]) ;
+ i = (Int) y ;
+ ok3 = (y < Int_max) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+ case mxINT64_CLASS:
+
+ for (k = 0 ; ok2 && ok3 && k < nz ; k++)
+ {
+ INT64_T y = ((INT64_T *) vector) [k] ;
+ i = (Int) y ;
+ ok2 = (y > 0) ;
+ ok3 = (y < Int_max) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+ case mxUINT64_CLASS:
+
+ for (k = 0 ; ok2 && ok3 && k < nz ; k++)
+ {
+ unsigned INT64_T y = ((unsigned INT64_T *) vector) [k] ;
+ i = (Int) y ;
+ ok2 = (y > 0) ;
+ ok3 = (y < Int_max) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+ case mxSINGLE_CLASS:
+
+ for (k = 0 ; ok && ok2 && ok3 && k < nz ; k++)
+ {
+ float y = ((float *) vector) [k] ;
+ i = (Int) y ;
+ ok = (y == (float) i) ;
+ ok2 = (y > 0) ;
+ ok3 = (y < Int_max) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+ break ;
+
+ case mxDOUBLE_CLASS:
+
+ for (k = 0 ; ok && ok2 && ok3 && k < nz ; k++)
+ {
+ double y = ((double *) vector) [k] ;
+ i = (Int) y ;
+ ok = (y == (double) i) ;
+ ok2 = (y > 0) ;
+ ok3 = (y < Int_max) ;
+ I [k] = i - 1 ;
+ n2 = MAX (n2, i) ;
+ }
+
+ break ;
+
+ default:
+
+ sputil_error (ERROR_INVALID_TYPE, FALSE) ;
+ break ;
+ }
+
+ if (!ok)
+ {
+ sputil_error (ERROR_NOT_INTEGER, TRUE) ;
+ }
+
+ if (!ok2)
+ {
+ sputil_error (ERROR_TOO_SMALL, TRUE) ;
+ }
+
+ if (!ok3)
+ {
+ sputil_error (ERROR_HUGE, TRUE) ;
+ }
+
+ }
+ return ((n == EMPTY) ? n2 : n) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_dense_to_sparse =============================================== */
+/* ========================================================================== */
+
+/* Convert a dense matrix of any numeric type into a
+ * sparse double or sparse logical matrix.
+ */
+
+#define COUNT_NZ \
+{ \
+ for (j = 0 ; j < ncol ; j++) \
+ { \
+ for (i = 0 ; i < nrow ; i++) \
+ { \
+ xij = X [i + j*nrow] ; \
+ if (CHOLMOD_IS_NONZERO (xij)) \
+ { \
+ nz++ ; \
+ } \
+ } \
+ } \
+}
+
+#define COPY_DENSE_TO_SPARSE(stype) \
+{ \
+ stype *Sx ; \
+ Sp = (Int *) mxGetJc (S) ; \
+ Si = (Int *) mxGetIr (S) ; \
+ Sx = (stype *) mxGetData (S) ; \
+ nz = 0 ; \
+ for (j = 0 ; j < ncol ; j++) \
+ { \
+ Sp [j] = nz ; \
+ for (i = 0 ; i < nrow ; i++) \
+ { \
+ xij = X [i + j*nrow] ; \
+ if (CHOLMOD_IS_NONZERO (xij)) \
+ { \
+ Si [nz] = i ; \
+ Sx [nz] = (stype) xij ; \
+ nz++ ; \
+ } \
+ } \
+ } \
+ Sp [ncol] = nz ; \
+}
+
+#define DENSE_TO_SPARSE(type) \
+{ \
+ type *X, xij ; \
+ X = (type *) mxGetData (arg) ; \
+ COUNT_NZ ; \
+ S = mxCreateSparse (nrow, ncol, nz, mxREAL) ; \
+ COPY_DENSE_TO_SPARSE (double) ; \
+}
+
+mxArray *sputil_dense_to_sparse (const mxArray *arg)
+{
+ mxArray *S = NULL ;
+ Int *Sp, *Si ;
+ Int nrow, ncol, nz, i, j ;
+
+ nrow = mxGetM (arg) ;
+ ncol = mxGetN (arg) ;
+ nz = 0 ;
+
+ if (mxIsComplex (arg))
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert a complex dense matrix into a complex sparse matrix */
+ /* ------------------------------------------------------------------ */
+
+ double xij, zij ;
+ double *X, *Z, *Sx, *Sz ;
+
+ if (mxGetClassID (arg) != mxDOUBLE_CLASS)
+ {
+ /* A complex matrix can have any class (int8, int16, single, etc),
+ * but this function only supports complex double. This condition
+ * is not checked in the caller. */
+ sputil_error (ERROR_INVALID_TYPE, FALSE) ;
+ }
+
+ X = mxGetPr (arg) ;
+ Z = mxGetPi (arg) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ xij = X [i + j*nrow] ;
+ zij = Z [i + j*nrow] ;
+ if (CHOLMOD_IS_NONZERO (xij) || CHOLMOD_IS_NONZERO (zij))
+ {
+ nz++ ;
+ }
+ }
+ }
+ S = mxCreateSparse (nrow, ncol, nz, mxCOMPLEX) ;
+ Sp = (Int *) mxGetJc (S) ;
+ Si = (Int *) mxGetIr (S) ;
+ Sx = mxGetPr (S) ;
+ Sz = mxGetPi (S) ;
+ nz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Sp [j] = nz ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ xij = X [i + j*nrow] ;
+ zij = Z [i + j*nrow] ;
+ if (CHOLMOD_IS_NONZERO (xij) || CHOLMOD_IS_NONZERO (zij))
+ {
+ Si [nz] = i ;
+ Sx [nz] = xij ;
+ Sz [nz] = zij ;
+ nz++ ;
+ }
+ }
+ }
+ Sp [ncol] = nz ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert real matrix (any class) to sparse double or logical */
+ /* ------------------------------------------------------------------ */
+
+ switch (mxGetClassID (arg))
+ {
+
+#ifndef MATLAB6p1_OR_EARLIER
+
+ /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */
+ case mxLOGICAL_CLASS:
+ {
+ mxLogical *X, xij ;
+ X = (mxLogical *) mxGetData (arg) ;
+ COUNT_NZ ;
+ S = mxCreateSparseLogicalMatrix (nrow, ncol, nz) ;
+ COPY_DENSE_TO_SPARSE (mxLogical) ;
+ }
+ break ;
+#endif
+
+ case mxCHAR_CLASS:
+
+ DENSE_TO_SPARSE (mxChar) ;
+ break ;
+
+ case mxINT8_CLASS:
+
+ DENSE_TO_SPARSE (char) ;
+ break ;
+
+ case mxUINT8_CLASS:
+
+ DENSE_TO_SPARSE (unsigned char) ;
+ break ;
+
+ case mxINT16_CLASS:
+
+ DENSE_TO_SPARSE (short) ;
+ break ;
+
+ case mxUINT16_CLASS:
+
+ DENSE_TO_SPARSE (unsigned short) ;
+ break ;
+
+ case mxINT32_CLASS:
+
+ DENSE_TO_SPARSE (INT32_T) ;
+ break ;
+
+ case mxUINT32_CLASS:
+
+ DENSE_TO_SPARSE (unsigned INT32_T) ;
+ break ;
+
+ case mxINT64_CLASS:
+
+ DENSE_TO_SPARSE (INT64_T) ;
+ break ;
+
+ case mxUINT64_CLASS:
+
+ DENSE_TO_SPARSE (unsigned INT64_T) ;
+ break ;
+
+ case mxSINGLE_CLASS:
+
+ DENSE_TO_SPARSE (float) ;
+ break ;
+
+ case mxDOUBLE_CLASS:
+
+ DENSE_TO_SPARSE (double) ;
+ break ;
+
+ default:
+
+ sputil_error (ERROR_INVALID_TYPE, FALSE) ;
+ break ;
+ }
+ }
+
+ return (S) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_triplet_to_sparse ============================================= */
+/* ========================================================================== */
+
+/* Convert a triplet form into a sparse matrix. If complex, s must be double.
+ * If real, s can be of any class.
+ */
+
+cholmod_sparse *sputil_triplet_to_sparse
+(
+ Int nrow, Int ncol, Int nz, Int nzmax,
+ Int i_is_scalar, Int i, void *i_vector, mxClassID i_class,
+ Int j_is_scalar, Int j, void *j_vector, mxClassID j_class,
+ Int s_is_scalar, double x, double z, void *x_vector, double *z_vector,
+ mxClassID s_class, Int s_complex,
+ cholmod_common *cm
+)
+{
+ double dummy = 0 ;
+ cholmod_triplet *T ;
+ cholmod_sparse *S ;
+ double *Tx, *Tz ;
+ Int *Ti, *Tj ;
+ Int k, x_patch ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the triplet form */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that nrow and ncol may be EMPTY; this is not an error condition.
+ * Allocate the numerical part of T only if s is a scalar. */
+ x_patch = (!s_is_scalar && (s_class == mxDOUBLE_CLASS || s_complex)) ;
+
+ T = cholmod_l_allocate_triplet (MAX (0,nrow), MAX (0,ncol), nz, 0,
+ x_patch ? CHOLMOD_PATTERN :
+ (s_complex ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL), cm) ;
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ Tz = T->z ;
+
+ /* ---------------------------------------------------------------------- */
+ /* fill the triplet form */
+ /* ---------------------------------------------------------------------- */
+
+ if (s_is_scalar)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* fill T->x and T->z with a scalar value */
+ /* ------------------------------------------------------------------ */
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = x ;
+ }
+ if (s_complex)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tz [k] = z ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* copy x/z_vector into T->x and T->z, and convert to double */
+ /* ------------------------------------------------------------------ */
+
+ if (s_complex)
+ {
+
+ /* Patch in s as the numerical values of the triplet matrix.
+ * Note that T->x and T->z must not be free'd when done. */
+ T->x = (x_vector == NULL) ? &dummy : x_vector ;
+ T->z = (z_vector == NULL) ? &dummy : z_vector ;
+ T->xtype = CHOLMOD_ZOMPLEX ;
+
+ }
+ else switch (s_class)
+ {
+
+#ifndef MATLAB6p1_OR_EARLIER
+
+ /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */
+ case mxLOGICAL_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((mxLogical *) x_vector) [k]) ;
+ }
+ break ;
+
+#endif
+
+ case mxCHAR_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((mxChar *) x_vector) [k]) ;
+ }
+ break ;
+
+ case mxINT8_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((INT8_T *) x_vector) [k]) ;
+ }
+ break ;
+
+ case mxUINT8_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((UINT8_T *) x_vector) [k]) ;
+ }
+ break ;
+
+ case mxINT16_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((INT16_T *) x_vector) [k]) ;
+ }
+ break ;
+
+ case mxUINT16_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((UINT16_T *) x_vector) [k]) ;
+ }
+ break ;
+
+ case mxINT32_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((INT32_T *) x_vector) [k]) ;
+ }
+ break ;
+
+ case mxUINT32_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((UINT32_T *) x_vector) [k]) ;
+ }
+ break ;
+
+ case mxINT64_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((INT64_T *) x_vector) [k]) ;
+ }
+ break ;
+
+ case mxUINT64_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((unsigned INT64_T *) x_vector) [k]) ;
+ }
+ break ;
+
+ case mxSINGLE_CLASS:
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Tx [k] = (double) (((float *) x_vector) [k]) ;
+ }
+ break ;
+
+ case mxDOUBLE_CLASS:
+
+ /* Patch in s as the numerical values of the triplet matrix.
+ * Note that T->x must not be free'd when done. */
+ T->x = (x_vector == NULL) ? &dummy : x_vector ;
+ T->xtype = CHOLMOD_REAL ;
+ break ;
+
+ default:
+
+ sputil_error (ERROR_INVALID_TYPE, FALSE) ;
+ break ;
+ }
+ }
+
+ /* copy i in to the integer vector T->i */
+ nrow = sputil_copy_ij (i_is_scalar, i, i_vector, i_class, nz, nrow, Ti) ;
+
+ /* copy j in to the integer vector T->j */
+ ncol = sputil_copy_ij (j_is_scalar, j, j_vector, j_class, nz, ncol, Tj) ;
+
+ /* nrow and ncol are known */
+ T->nrow = nrow ;
+ T->ncol = ncol ;
+ T->nnz = nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert triplet to sparse matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* If the triplet matrix T is invalid, or if CHOLMOD runs out of memory,
+ * then S is NULL. */
+ S = cholmod_l_triplet_to_sparse (T, nzmax, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* do not free T->x or T->z if it points to input x_vector */
+ if (x_patch)
+ {
+ T->x = NULL ;
+ T->z = NULL ;
+ T->xtype = CHOLMOD_PATTERN ;
+ }
+ cholmod_l_free_triplet (&T, cm) ;
+ return (S) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_copy_sparse =================================================== */
+/* ========================================================================== */
+
+/* copy a sparse matrix, S = sparse(A), dropping any zero entries and ensuring
+ * the nzmax(S) == nnz(S). Explicit zero entries in A "cannot" occur, in
+ * the current version of MATLAB ... but a user mexFunction might generate a
+ * matrix with explicit zeros. This function ensures S=sparse(A) drops those
+ * explicit zeros. */
+
+mxArray *sputil_copy_sparse (const mxArray *A)
+{
+ double aij, zij ;
+ mxArray *S ;
+ double *Ax, *Az, *Sx, *Sz ;
+ Int *Ap, *Ai, *Sp, *Si ;
+ Int anz, snz, p, j, nrow, ncol, pend ;
+
+#ifndef MATLAB6p1_OR_EARLIER
+
+ /* MATLAB 6.1 or earlier : all sparse matrices are OK */
+ if (! (mxGetClassID (A) == mxLOGICAL_CLASS ||
+ mxGetClassID (A) == mxDOUBLE_CLASS))
+ {
+ /* Only sparse logical and real/complex double matrices supported.
+ * This condition is not checked in the caller. */
+ sputil_error (ERROR_INVALID_TYPE, 0) ;
+ }
+
+#endif
+
+ nrow = mxGetM (A) ;
+ ncol = mxGetN (A) ;
+ Ap = (Int *) mxGetJc (A) ;
+ Ai = (Int *) mxGetIr (A) ;
+ anz = Ap [ncol] ;
+
+ snz = 0 ;
+
+#ifndef MATLAB6p1_OR_EARLIER
+
+ /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */
+ if (mxIsLogical (A))
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* copy a sparse logical matrix */
+ /* ------------------------------------------------------------------ */
+
+ /* count the number of nonzeros in A */
+ mxLogical *Al, *Sl ;
+ Al = mxGetLogicals (A) ;
+ for (p = 0 ; p < anz ; p++)
+ {
+ if (Al [p])
+ {
+ snz++ ;
+ }
+ }
+
+ /* allocate S */
+ S = mxCreateSparseLogicalMatrix (nrow, ncol, snz) ;
+ Sp = (Int *) mxGetJc (S) ;
+ Si = (Int *) mxGetIr (S) ;
+ Sl = mxGetLogicals (S) ;
+
+ /* copy A into S, dropping zero entries */
+ snz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Sp [j] = snz ;
+ pend = Ap [j+1] ;
+ for (p = Ap [j] ; p < pend ; p++)
+ {
+ if (Al [p])
+ {
+ Si [snz] = Ai [p] ;
+ Sl [snz] = 1 ;
+ snz++ ;
+ }
+ }
+ }
+
+ }
+ else
+
+#endif
+
+ if (mxIsComplex (A))
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* copy a sparse complex double matrix */
+ /* ------------------------------------------------------------------ */
+
+ /* count the number of nonzeros in A */
+ Ax = mxGetPr (A) ;
+ Az = mxGetPi (A) ;
+ for (p = 0 ; p < anz ; p++)
+ {
+ aij = Ax [p] ;
+ zij = Az [p] ;
+ if (CHOLMOD_IS_NONZERO (aij) || CHOLMOD_IS_NONZERO (zij))
+ {
+ snz++ ;
+ }
+ }
+
+ /* allocate S */
+ S = mxCreateSparse (nrow, ncol, snz, mxCOMPLEX) ;
+ Sp = (Int *) mxGetJc (S) ;
+ Si = (Int *) mxGetIr (S) ;
+ Sx = mxGetPr (S) ;
+ Sz = mxGetPi (S) ;
+
+ /* copy A into S, dropping zero entries */
+ snz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Sp [j] = snz ;
+ pend = Ap [j+1] ;
+ for (p = Ap [j] ; p < pend ; p++)
+ {
+ aij = Ax [p] ;
+ zij = Az [p] ;
+ if (CHOLMOD_IS_NONZERO (aij) || CHOLMOD_IS_NONZERO (zij))
+ {
+ Si [snz] = Ai [p] ;
+ Sx [snz] = aij ;
+ Sz [snz] = zij ;
+ snz++ ;
+ }
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* copy a sparse real double matrix */
+ /* ------------------------------------------------------------------ */
+
+ /* count the number of nonzeros in A */
+ Ax = mxGetPr (A) ;
+ for (p = 0 ; p < anz ; p++)
+ {
+ aij = Ax [p] ;
+ if (CHOLMOD_IS_NONZERO (aij))
+ {
+ snz++ ;
+ }
+ }
+
+ /* allocate S */
+ S = mxCreateSparse (nrow, ncol, snz, mxREAL) ;
+ Sp = (Int *) mxGetJc (S) ;
+ Si = (Int *) mxGetIr (S) ;
+ Sx = mxGetPr (S) ;
+
+ /* copy A into S, dropping zero entries */
+ snz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Sp [j] = snz ;
+ pend = Ap [j+1] ;
+ for (p = Ap [j] ; p < pend ; p++)
+ {
+ aij = Ax [p] ;
+ if (CHOLMOD_IS_NONZERO (aij))
+ {
+ Si [snz] = Ai [p] ;
+ Sx [snz] = aij ;
+ snz++ ;
+ }
+ }
+ }
+ }
+
+ Sp [ncol] = snz ;
+ return (S) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_sparse_to_dense =============================================== */
+/* ========================================================================== */
+
+/* convert a sparse double or logical array to a dense double array */
+
+mxArray *sputil_sparse_to_dense (const mxArray *S)
+{
+ mxArray *X ;
+ double *Sx, *Sz, *Xx, *Xz ;
+ Int *Sp, *Si ;
+ Int nrow, ncol, i, j, p, pend, j2 ;
+
+#ifndef MATLAB6p1_OR_EARLIER
+
+ /* MATLAB 6.1 or earlier : all sparse matrices are OK */
+ if (! (mxGetClassID (S) == mxLOGICAL_CLASS ||
+ mxGetClassID (S) == mxDOUBLE_CLASS))
+ {
+ /* only sparse logical and real/complex double matrices supported */
+ sputil_error (ERROR_INVALID_TYPE, 0) ;
+ }
+
+#endif
+
+ nrow = mxGetM (S) ;
+ ncol = mxGetN (S) ;
+ Sp = (Int *) mxGetJc (S) ;
+ Si = (Int *) mxGetIr (S) ;
+
+#ifndef MATLAB6p1_OR_EARLIER
+
+ /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */
+ if (mxIsLogical (S))
+ {
+ /* logical */
+ mxLogical *Sl ;
+ Sl = (mxLogical *) mxGetData (S) ;
+ X = mxCreateDoubleMatrix (nrow, ncol, mxREAL) ;
+ Xx = mxGetPr (X) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ pend = Sp [j+1] ;
+ j2 = j*nrow ;
+ for (p = Sp [j] ; p < pend ; p++)
+ {
+ Xx [Si [p] + j2] = (double) (Sl [p]) ;
+ }
+ }
+ }
+ else
+
+#endif
+
+ if (mxIsComplex (S))
+ {
+ /* complex */
+ Sx = mxGetPr (S) ;
+ Sz = mxGetPi (S) ;
+ X = mxCreateDoubleMatrix (nrow, ncol, mxCOMPLEX) ;
+ Xx = mxGetPr (X) ;
+ Xz = mxGetPi (X) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ pend = Sp [j+1] ;
+ j2 = j*nrow ;
+ for (p = Sp [j] ; p < pend ; p++)
+ {
+ i = Si [p] ;
+ Xx [i + j2] = Sx [p] ;
+ Xz [i + j2] = Sz [p] ;
+ }
+ }
+ }
+ else
+ {
+ /* real */
+ Sx = mxGetPr (S) ;
+ X = mxCreateDoubleMatrix (nrow, ncol, mxREAL) ;
+ Xx = mxGetPr (X) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ pend = Sp [j+1] ;
+ j2 = j*nrow ;
+ for (p = Sp [j] ; p < pend ; p++)
+ {
+ Xx [Si [p] + j2] = Sx [p] ;
+ }
+ }
+ }
+
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === sputil_check_ijvector ================================================ */
+/* ========================================================================== */
+
+/* Check a sparse i or j input argument */
+
+void sputil_check_ijvector (const mxArray *arg)
+{
+ if (mxIsComplex (arg))
+ {
+ /* i and j cannot be complex */
+ sputil_error (ERROR_NOT_INTEGER, TRUE) ;
+ }
+ if (mxIsSparse (arg))
+ {
+ /* the i and j arguments for sparse(i,j,s,...) can be sparse, but if so
+ * they must have no zero entries. */
+ double mn, m, nz ;
+ Int *p, n ;
+ m = (double) mxGetM (arg) ;
+ n = mxGetN (arg) ;
+ mn = m*n ;
+ p = (Int *) mxGetJc (arg) ;
+ nz = p [n] ;
+ if (mn != nz)
+ {
+ /* i or j contains at least one zero, which is invalid */
+ sputil_error (ERROR_TOO_SMALL, TRUE) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === sputil_sparse ======================================================== */
+/* ========================================================================== */
+
+/* Implements the sparse2 mexFunction */
+
+void sputil_sparse
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double x, z ;
+ double *z_vector ;
+ void *i_vector, *j_vector, *x_vector ;
+ mxArray *s_array ;
+ cholmod_sparse *S, *Z ;
+ cholmod_common Common, *cm ;
+ Int nrow, ncol, k, nz, i_is_scalar, j_is_scalar, s_is_sparse,
+ s_is_scalar, ilen, jlen, slen, nzmax, i, j, s_complex, ndropped ;
+ mxClassID i_class, j_class, s_class ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set defaults */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 2 || nargin > 6 || nargin == 4 || nargin == 0)
+ {
+ sputil_error (ERROR_USAGE, FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert inputs into a sparse matrix S */
+ /* ---------------------------------------------------------------------- */
+
+ S = NULL ;
+ Z = NULL ;
+
+ if (nargin == 1)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* S = sparse (A) where A is sparse or full */
+ /* ------------------------------------------------------------------ */
+
+ nrow = mxGetM (pargin [0]) ;
+ ncol = mxGetN (pargin [0]) ;
+
+ if (mxIsSparse (pargin [0]))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* S = sparse (A) where A is sparse (double, complex, or logical) */
+ /* -------------------------------------------------------------- */
+
+ pargout [0] = sputil_copy_sparse (pargin [0]) ;
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* S = sparse (A) where A is full (real or complex) */
+ /* -------------------------------------------------------------- */
+
+ /* A can be of any numeric type (mxLogical, int8, ..., double),
+ * except that if A is complex, it must also be double. */
+ pargout [0] = sputil_dense_to_sparse (pargin [0]) ;
+ }
+
+ }
+ else if (nargin == 2)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* S = sparse (m,n) */
+ /* ------------------------------------------------------------------ */
+
+ Int *Sp ;
+ nrow = sputil_get_integer (pargin [0], FALSE, 0) ;
+ ncol = sputil_get_integer (pargin [1], FALSE, 0) ;
+ pargout [0] = mxCreateSparse (nrow, ncol, 1, mxREAL) ;
+ Sp = (Int *) mxGetJc (pargout [0]) ;
+ Sp [0] = 0 ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* S = sparse (i,j,s), sparse (i,j,s,m,n) or sparse (i,j,s,m,n,nzmax) */
+ /* ------------------------------------------------------------------ */
+
+ /* i, j, and s can be of any numeric type */
+
+ /* ensure i and j are valid (i and j cannot be complex) */
+ sputil_check_ijvector (pargin [0]) ;
+ sputil_check_ijvector (pargin [1]) ;
+
+ /* convert s from sparse to dense (double), if necessary */
+ s_is_sparse = mxIsSparse (pargin [2]) ;
+ if (s_is_sparse)
+ {
+ /* s must be double (real/complex) or logical */
+ s_array = sputil_sparse_to_dense (pargin [2]) ;
+ }
+ else
+ {
+ s_array = (mxArray *) pargin [2] ;
+ }
+
+ /* s is now full. It can be any class, except if complex it must also
+ * be double */
+ s_class = mxGetClassID (s_array) ;
+ s_complex = mxIsComplex (s_array) ;
+ if (s_complex && s_class != mxDOUBLE_CLASS)
+ {
+ /* for complex case, only double class is supported */
+ sputil_error (ERROR_INVALID_TYPE, 0) ;
+ }
+
+ /* get sizes of inputs */
+ ilen = sputil_nelements (pargin [0]) ;
+ jlen = sputil_nelements (pargin [1]) ;
+ slen = sputil_nelements (s_array) ;
+
+ /* if i, j, s are scalars, they "float" to sizes of non-scalar args */
+ i_is_scalar = (ilen == 1) ;
+ j_is_scalar = (jlen == 1) ;
+ s_is_scalar = (slen == 1) ;
+
+ /* find the length */
+ if (!i_is_scalar)
+ {
+ /* if i is not a scalar, let it determine the length */
+ nz = ilen ;
+ }
+ else if (!j_is_scalar)
+ {
+ /* otherwise, if j is not a scalar, let it determine the length */
+ nz = jlen ;
+ }
+ else
+ {
+ /* finally, i and j are both scalars, so let s determine length */
+ nz = slen ;
+ }
+
+ /* make sure the sizes are compatible */
+ if (!((i_is_scalar || ilen == nz) &&
+ (j_is_scalar || jlen == nz) &&
+ (s_is_scalar || slen == nz)))
+ {
+ sputil_error (ERROR_LENGTH, FALSE) ;
+ }
+
+ if (nargin > 4)
+ {
+ nrow = sputil_get_integer (pargin [3], FALSE, 0) ;
+ ncol = sputil_get_integer (pargin [4], FALSE, 0) ;
+ }
+ else
+ {
+ /* nrow and ncol will be discovered by scanning i and j */
+ nrow = EMPTY ;
+ ncol = EMPTY ;
+ }
+
+ if (nargin > 5)
+ {
+ nzmax = sputil_get_integer (pargin [5], FALSE, 0) ;
+ nzmax = MAX (nzmax, nz) ;
+ }
+ else
+ {
+ nzmax = nz ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* convert triplet form to sparse form */
+ /* ------------------------------------------------------------------ */
+
+ i = i_is_scalar ? sputil_get_integer (pargin [0], TRUE, nrow) : 0 ;
+ i_vector = mxGetData (pargin [0]) ;
+ i_class = mxGetClassID (pargin [0]) ;
+
+ j = j_is_scalar ? sputil_get_integer (pargin [1], TRUE, ncol) : 0 ;
+ j_vector = mxGetData (pargin [1]) ;
+ j_class = mxGetClassID (pargin [1]) ;
+
+ x_vector = mxGetData (s_array) ;
+ z_vector = mxGetPi (s_array) ;
+ x = sputil_get_double (s_array) ;
+ z = (s_complex && z_vector != NULL) ? (z_vector [0]) : 0 ;
+
+ S = sputil_triplet_to_sparse (nrow, ncol, nz, nzmax,
+ i_is_scalar, i, i_vector, i_class,
+ j_is_scalar, j, j_vector, j_class,
+ s_is_scalar, x, z, x_vector, z_vector,
+ s_class, s_complex,
+ cm) ;
+
+ /* set nzmax(S) to nnz(S), unless nzmax is specified on input */
+ if (nargin <= 5 && S != NULL)
+ {
+ cholmod_l_reallocate_sparse (cholmod_l_nnz (S, cm), S, cm) ;
+ }
+
+ if (nargout > 1)
+ {
+ /* return a binary pattern of the explicit zero entries, for the
+ * [S Z] = sparse(i,j,x, ...) form. */
+ Z = sputil_extract_zeros (S, cm) ;
+ }
+
+ /* drop explicit zeros from S */
+ ndropped = sputil_drop_zeros (S) ;
+
+ /* if entries dropped, set nzmax(S) to nnz(S), unless nzmax specified */
+ if (ndropped > 0 && nargin <= 5 && S != NULL)
+ {
+ cholmod_l_reallocate_sparse (cholmod_l_nnz (S, cm), S, cm) ;
+ }
+
+ if (s_is_sparse)
+ {
+ mxDestroyArray (s_array) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert S into a MATLAB sparse matrix */
+ /* ---------------------------------------------------------------------- */
+
+ k = 0 ;
+ if (S != NULL)
+ {
+
+#ifndef MATLAB6p1_OR_EARLIER
+
+ /* MATLAB 6.1 or earlier do not have mxLOGICAL_CLASS */
+ if (mxIsLogical (pargin [2]))
+ {
+ /* copy S into a MATLAB sparse logical matrix */
+ mxLogical *s_logical ;
+ pargout [0] = mxCreateSparseLogicalMatrix (0, 0, 0) ;
+ s_logical = cholmod_l_malloc (S->nzmax, sizeof (mxLogical), cm) ;
+ for (k = 0 ; k < (Int) (S->nzmax) ; k++)
+ {
+ s_logical [k] = 1 ;
+ }
+ mxFree (mxGetData (pargout [0])) ;
+ mxSetData (pargout [0], s_logical) ;
+ mexMakeMemoryPersistent (s_logical) ;
+ k++ ;
+ }
+ else
+
+#endif
+
+ if (mxIsComplex (pargin [2]))
+ {
+ /* copy S into a MATLAB sparse complex double matrix */
+ pargout [0] = mxCreateSparse (0, 0, 0, mxCOMPLEX) ;
+ mxFree (mxGetPr (pargout [0])) ;
+ mxFree (mxGetPi (pargout [0])) ;
+ mxSetPr (pargout [0], S->x) ;
+ mxSetPi (pargout [0], S->z) ;
+ mexMakeMemoryPersistent (S->x) ;
+ mexMakeMemoryPersistent (S->z) ;
+ k += 2 ;
+ S->x = NULL ;
+ S->z = NULL ;
+ }
+ else
+ {
+ /* copy S into a MATLAB sparse real double matrix */
+ pargout [0] = mxCreateSparse (0, 0, 0, mxREAL) ;
+ mxSetPr (pargout [0], S->x) ;
+ mexMakeMemoryPersistent (S->x) ;
+ k++ ;
+ S->x = NULL ;
+ }
+
+ mxSetM (pargout [0], S->nrow) ;
+ mxSetN (pargout [0], S->ncol) ;
+ mxSetNzmax (pargout [0], S->nzmax) ;
+ mxFree (mxGetJc (pargout [0])) ;
+ mxFree (mxGetIr (pargout [0])) ;
+ mxSetJc (pargout [0], S->p) ;
+ mxSetIr (pargout [0], S->i) ;
+ mexMakeMemoryPersistent (S->p) ;
+ mexMakeMemoryPersistent (S->i) ;
+ k += 2 ;
+
+ /* free cholmod_sparse S, except for what has been given to MATLAB */
+ S->p = NULL ;
+ S->i = NULL ;
+ cholmod_l_free_sparse (&S, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return Z to MATLAB, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 1)
+ {
+ if (Z == NULL)
+ {
+ /* Z not computed; return an empty matrix */
+ Z = cholmod_l_spzeros (nrow, ncol, 0, CHOLMOD_REAL, cm) ;
+ }
+ pargout [1] = sputil_put_sparse (&Z, cm) ;
+ }
+
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != k) mexErrMsgTxt ("!") ;
+ */
+}
diff --git a/CHOLMOD/MATLAB/cholmod_matlab.h b/CHOLMOD/MATLAB/cholmod_matlab.h
new file mode 100644
index 0000000..34207d3
--- /dev/null
+++ b/CHOLMOD/MATLAB/cholmod_matlab.h
@@ -0,0 +1,178 @@
+/* ========================================================================== */
+/* === MATLAB/cholmod_matlab.h ============================================== */
+/* ========================================================================== */
+
+/* Shared prototypes and definitions for CHOLMOD mexFunctions */
+
+#include "UFconfig.h"
+#ifndef DLONG
+#define DLONG
+#endif
+#define Int UF_long
+#define Int_max UF_long_max
+
+/* Ensure cholmod_read_* and cholmod_write_* work for large files. This
+ * requires MATLAB 7.0 or later. If you are using MATLAB 6.5 or earlier,
+ * you must delete the following line, or compile CHOLMOD with -DNLARGEFILE */
+#include "cholmod_io64.h"
+
+#ifndef NPARTITION
+#include "metis.h"
+#endif
+#undef ASSERT
+
+#include "cholmod.h"
+#include <limits.h>
+#include <string.h>
+#include <ctype.h>
+#include <float.h>
+#include "mex.h"
+#define EMPTY (-1)
+#define TRUE 1
+#define FALSE 0
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define LEN 16
+
+#define ERROR_TOO_SMALL 0
+#define ERROR_HUGE 1
+#define ERROR_NOT_INTEGER 2
+#define ERROR_TOO_LARGE 3
+#define ERROR_USAGE 4
+#define ERROR_LENGTH 5
+#define ERROR_INVALID_TYPE 6
+#define ERROR_OUT_OF_MEMORY 7
+
+/* getting spumoni at run-time takes way too much time */
+#ifndef SPUMONI
+#define SPUMONI 0
+#endif
+
+/* closed by sputil_error_handler if not NULL */
+extern FILE *sputil_file ;
+
+void sputil_error /* reports an error */
+(
+ Int error, /* kind of error */
+ Int is_index /* TRUE if a matrix index, FALSE if a matrix dimension */
+) ;
+
+Int sputil_double_to_int /* returns integer value of x */
+(
+ double x, /* double value to convert */
+ Int is_index, /* TRUE if a matrix index, FALSE if a matrix dimension */
+ Int n /* if a matrix index, x cannot exceed this dimension */
+) ;
+
+double sputil_get_double (const mxArray *arg) ; /* like mxGetScalar */
+
+Int sputil_get_integer /* returns the integer value of a MATLAB argument */
+(
+ const mxArray *arg, /* MATLAB argument to convert */
+ Int is_index, /* TRUE if an index, FALSE if a matrix dimension */
+ Int n /* maximum value, if an index */
+) ;
+
+
+Int sputil_copy_ij /* returns the dimension, n */
+(
+ Int is_scalar, /* TRUE if argument is a scalar, FALSE otherwise */
+ Int scalar, /* scalar value of the argument */
+ void *vector, /* vector value of the argument */
+ mxClassID category, /* type of vector */
+ Int nz, /* length of output vector I */
+ Int n, /* maximum dimension, EMPTY if not yet known */
+ Int *I /* vector of length nz to copy into */
+) ;
+
+/* converts a triplet matrix to a compressed-column matrix */
+cholmod_sparse *sputil_triplet_to_sparse
+(
+ Int nrow, Int ncol, Int nz, Int nzmax,
+ Int i_is_scalar, Int i, void *i_vector, mxClassID i_class,
+ Int j_is_scalar, Int j, void *j_vector, mxClassID j_class,
+ Int s_is_scalar, double x, double z, void *x_vector, double *z_vector,
+ mxClassID s_class, Int s_complex,
+ cholmod_common *cm
+) ;
+
+mxArray *sputil_copy_sparse (const mxArray *A) ; /* copy a sparse matrix */
+
+Int sputil_nelements (const mxArray *arg) ; /* like mxGetNumberOfElements */
+
+void sputil_sparse /* top-level wrapper for "sparse" function */
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+) ;
+
+void sputil_error_handler (int status, char *file, int line, char *message) ;
+
+void sputil_config (Int spumoni, cholmod_common *cm) ;
+
+mxArray *sputil_sparse_to_dense (const mxArray *S) ;
+
+cholmod_sparse *sputil_get_sparse
+(
+ const mxArray *Amatlab, /* MATLAB version of the matrix */
+ cholmod_sparse *A, /* CHOLMOD version of the matrix */
+ double *dummy, /* a pointer to a valid scalar double */
+ Int stype /* -1: lower, 0: unsymmetric, 1: upper */
+) ;
+
+cholmod_dense *sputil_get_dense
+(
+ const mxArray *Amatlab, /* MATLAB version of the matrix */
+ cholmod_dense *A, /* CHOLMOD version of the matrix */
+ double *dummy /* a pointer to a valid scalar double */
+) ;
+
+mxArray *sputil_put_dense /* returns the MATLAB version */
+(
+ cholmod_dense **Ahandle, /* CHOLMOD version of the matrix */
+ cholmod_common *cm
+) ;
+
+mxArray *sputil_put_sparse
+(
+ cholmod_sparse **Ahandle, /* CHOLMOD version of the matrix */
+ cholmod_common *cm
+) ;
+
+Int sputil_drop_zeros /* drop numerical zeros from a CHOLMOD matrix */
+(
+ cholmod_sparse *S
+) ;
+
+mxArray *sputil_put_int /* copy Int vector to mxArray */
+(
+ Int *P, /* vector to convert */
+ Int n, /* length of P */
+ Int one_based /* 1 if convert from 0-based to 1-based, 0 otherwise */
+) ;
+
+mxArray *sputil_dense_to_sparse (const mxArray *arg) ;
+
+void sputil_check_ijvector (const mxArray *arg) ;
+
+void sputil_trim
+(
+ cholmod_sparse *S,
+ Int k,
+ cholmod_common *cm
+) ;
+
+cholmod_sparse *sputil_get_sparse_pattern
+(
+ const mxArray *Amatlab, /* MATLAB version of the matrix */
+ cholmod_sparse *Ashallow, /* shallow CHOLMOD version of the matrix */
+ double *dummy, /* a pointer to a valid scalar double */
+ cholmod_common *cm
+) ;
+
+cholmod_sparse *sputil_extract_zeros
+(
+ cholmod_sparse *A,
+ cholmod_common *cm
+) ;
diff --git a/CHOLMOD/MATLAB/etree2.c b/CHOLMOD/MATLAB/etree2.c
new file mode 100644
index 0000000..13f7e82
--- /dev/null
+++ b/CHOLMOD/MATLAB/etree2.c
@@ -0,0 +1,178 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/etree2 mexFunction ==================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Usage:
+ *
+ * parent = etree2 (A) returns etree of A, uses triu(A)
+ * parent = etree2 (A, 'col') returns etree of A'*A
+ * parent = etree2 (A, 'sym') same as etree2 (A)
+ * parent = etree2 (A, 'row') same as etree2 (A', 'col')
+ * parent = etree2 (A, 'lo') returns etree of A, uses tril(A)
+ *
+ * [parent post] = etree2(...) also returns a postorder of the tree
+ *
+ * etree2 (A, 'col') does not form A'*A and is thus faster than etree2 (A'*A)
+ * and takes less memory. Likewise, etree (A, 'row') does not
+ * form A*A', and is thus faster than etree2 (A*A') and takes less memory.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0 ;
+ Int *Parent ;
+ cholmod_sparse *A, Amatrix, *S ;
+ cholmod_common Common, *cm ;
+ Int n, coletree, c ;
+ char buf [LEN] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set defaults */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 2 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: [parent post] = etree2 (A, mode)") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get input matrix A */
+ /* ---------------------------------------------------------------------- */
+
+ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ;
+ S = (A == &Amatrix) ? NULL : A ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get A->stype, default is to use triu(A) */
+ /* ---------------------------------------------------------------------- */
+
+ A->stype = 1 ;
+ n = A->nrow ;
+ coletree = FALSE ;
+ if (nargin > 1)
+ {
+ buf [0] = '\0' ;
+ if (mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], buf, LEN) ;
+ }
+ c = buf [0] ;
+ if (tolower (c) == 'r')
+ {
+ /* unsymmetric case (A*A') if string starts with 'r' */
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 'c')
+ {
+ /* unsymmetric case (A'*A) if string starts with 'c' */
+ n = A->ncol ;
+ coletree = TRUE ;
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 's')
+ {
+ /* symmetric upper case (A) if string starts with 's' */
+ A->stype = 1 ;
+ }
+ else if (tolower (c) == 'l')
+ {
+ /* symmetric lower case (A) if string starts with 'l' */
+ A->stype = -1 ;
+ }
+ else
+ {
+ mexErrMsgTxt ("etree2: unrecognized mode") ;
+ }
+ }
+
+ if (A->stype && A->nrow != A->ncol)
+ {
+ mexErrMsgTxt ("etree2: A must be square") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the etree */
+ /* ---------------------------------------------------------------------- */
+
+ Parent = cholmod_l_malloc (n, sizeof (Int), cm) ;
+ if (A->stype == 1 || coletree)
+ {
+ /* symmetric case: find etree of A, using triu(A) */
+ /* column case: find column etree of A, which is etree of A'*A */
+ cholmod_l_etree (A, Parent, cm) ;
+ }
+ else
+ {
+ /* symmetric case: find etree of A, using tril(A) */
+ /* row case: find row etree of A, which is etree of A*A' */
+ /* R = A' */
+ cholmod_sparse *R ;
+ R = cholmod_l_transpose (A, 0, cm) ;
+ cholmod_l_etree (R, Parent, cm) ;
+ cholmod_l_free_sparse (&R, cm) ;
+ }
+
+ if (cm->status < CHOLMOD_OK)
+ {
+ /* out of memory or matrix invalid */
+ mexErrMsgTxt ("etree2 failed: matrix corrupted!") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return Parent to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = sputil_put_int (Parent, n, 1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* postorder the tree and return results to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 1)
+ {
+ Int *Post ;
+ Post = cholmod_l_malloc (n, sizeof (Int), cm) ;
+ if (cholmod_l_postorder (Parent, n, NULL, Post, cm) != n)
+ {
+ /* out of memory or Parent invalid */
+ mexErrMsgTxt ("etree2 postorder failed!") ;
+ }
+ pargout [1] = sputil_put_int (Post, n, 1) ;
+ cholmod_l_free (n, sizeof (Int), Post, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free (n, sizeof (Int), Parent, cm) ;
+ cholmod_l_free_sparse (&S, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /* if (cm->malloc_count != 0) mexErrMsgTxt ("!") ; */
+}
diff --git a/CHOLMOD/MATLAB/etree2.m b/CHOLMOD/MATLAB/etree2.m
new file mode 100644
index 0000000..15ad182
--- /dev/null
+++ b/CHOLMOD/MATLAB/etree2.m
@@ -0,0 +1,42 @@
+function [parent, post] = etree2 (A, mode) %#ok
+%ETREE2 sparse elimination tree.
+% Finds the elimination tree of A, A'*A, or A*A', and optionaly postorders
+% the tree. parent(j) is the parent of node j in the tree, or 0 if j is a
+% root. The symmetric case uses only the upper or lower triangular part of
+% A (etree2(A) uses the upper part, and etree2(A,'lo') uses the lower part).
+%
+% Example:
+% parent = etree2 (A) finds the elimination tree of A, using triu(A)
+% parent = etree2 (A,'sym') same as etree2(A)
+% parent = etree2 (A,'col') finds the elimination tree of A'*A
+% parent = etree2 (A,'row') finds the elimination tree of A*A'
+% parent = etree2 (A,'lo') finds the elimination tree of A, using tril(A)
+%
+% [parent,post] = etree2 (...) also returns a post-ordering of the tree.
+%
+% If you have a fill-reducing permutation p, you can combine it with an
+% elimination tree post-ordering using the following code. Post-ordering has
+% no effect on fill-in (except for lu), but it does improve the performance
+% of the subsequent factorization.
+%
+% For the symmetric case, suitable for chol(A(p,p)):
+%
+% [parent post] = etree2 (A (p,p)) ;
+% p = p (post) ;
+%
+% For the column case, suitable for qr(A(:,p)) or lu(A(:,p)):
+%
+% [parent post] = etree2 (A (:,p), 'col') ;
+% p = p (post) ;
+%
+% For the row case, suitable for qr(A(p,:)') or chol(A(p,:)*A(p,:)'):
+%
+% [parent post] = etree2 (A (p,:), 'row') ;
+% p = p (post) ;
+%
+% See also TREELAYOUT, TREEPLOT, ETREEPLOT, ETREE
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('etree2 mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/gpl.txt b/CHOLMOD/MATLAB/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/CHOLMOD/MATLAB/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it. (Some other Free Software Foundation software is covered by
+the GNU Library General Public License instead.) You can apply it to
+your programs, too.
+
+ When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
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+ 10. If you wish to incorporate parts of the Program into other free
+programs whose distribution conditions are different, write to the author
+to ask for permission. For software which is copyrighted by the Free
+Software Foundation, write to the Free Software Foundation; we sometimes
+make exceptions for this. Our decision will be guided by the two goals
+of preserving the free status of all derivatives of our free software and
+of promoting the sharing and reuse of software generally.
+
+ NO WARRANTY
+
+ 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
+FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
+OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
+PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
+OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
+TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
+PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
+REPAIR OR CORRECTION.
+
+ 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
+REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
+INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
+OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
+TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
+YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
+PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGES.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+
+Also add information on how to contact you by electronic and paper mail.
+
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
+
+ Gnomovision version 69, Copyright (C) year name of author
+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ <signature of Ty Coon>, 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Library General
+Public License instead of this License.
diff --git a/CHOLMOD/MATLAB/graph_demo.m b/CHOLMOD/MATLAB/graph_demo.m
new file mode 100644
index 0000000..36ab539
--- /dev/null
+++ b/CHOLMOD/MATLAB/graph_demo.m
@@ -0,0 +1,105 @@
+function graph_demo (n)
+%GRAPH_DEMO graph partitioning demo
+% graph_demo(n) constructs an set of n-by-n 2D grids, partitions them, and
+% plots them in one-second intervals. n is optional; it defaults to 60.
+%
+% Example:
+% graph_demo
+%
+% See also DELSQ, NUMGRID, GPLOT, TREEPLOT
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 1)
+ % construct a 60-by-60 grid
+ n = 60 ;
+end
+
+figure (1)
+clf
+
+for regions = {'Square', 'C' 'Disc', 'Annulus', 'Heart', 'Butterfly', 'L'}
+
+ % construct the grid
+ region = regions {1} ;
+ g = numgrid (region (1), n) ;
+ x = repmat (0:n-1, n, 1) ;
+ y = repmat (((n-1):-1:0)', 1, n) ;
+ A = delsq (g) ;
+ x = x (find (g)) ; %#ok
+ y = y (find (g)) ; %#ok
+
+ % plot the original grid
+ clf
+ subplot (2,2,1)
+ my_gplot (A, x, y)
+ title (sprintf ('%s-shaped 2D grid', region)) ;
+ axis equal
+ axis off
+
+ % bisect the graph
+ s = bisect (A) ;
+ [i j] = find (A) ;
+ subplot (2,2,2)
+ my_gplot (sparse (i, j, s(i) == s(j)), x, y) ;
+ title ('node bisection') ;
+ axis equal
+ axis off
+
+ % nested dissection
+ nsmall = floor (size (A,1) / 2) ;
+ defaults = 0 ;
+ while (1)
+ if (defaults)
+ % use defaults
+ [p cp cmember] = nesdis (A) ;
+ else
+ [p cp cmember] = nesdis (A, 'sym', nsmall) ;
+ end
+
+ % plot the components
+ subplot (2,2,3)
+ my_gplot (sparse (i, j, cmember(i) == cmember (j)), x, y) ;
+ if (defaults)
+ title ('nested dissection (defaults)') ;
+ else
+ title (sprintf ('nested dissection, nsmall %d', nsmall)) ;
+ end
+ axis equal
+ axis off
+
+ % plot the separator tree
+ subplot (2,2,4)
+ treeplot (cp, 'ko')
+ title ('separator tree') ;
+ axis equal
+ axis off
+
+ drawnow
+ pause (0.1)
+
+ if (defaults)
+ break ;
+ end
+
+ nsmall = floor (nsmall / 2) ;
+ if (nsmall < 20)
+ defaults = 1 ;
+ pause (0.2)
+ end
+ end
+end
+
+%-------------------------------------------------------------------------------
+
+function my_gplot (A, x, y)
+% my_gplot : like gplot, just a lot faster
+[i, j] = find (A) ;
+[ignore, p] = sort (max(i, j)) ;
+i = i (p) ;
+j = j (p) ;
+nans = repmat (NaN, size (i)) ;
+x = [ x(i) x(j) nans ]' ;
+y = [ y(i) y(j) nans ]' ;
+plot (x (:), y (:)) ;
diff --git a/CHOLMOD/MATLAB/lcc_lib/lapacksyms.def b/CHOLMOD/MATLAB/lcc_lib/lapacksyms.def
new file mode 100644
index 0000000..7f8563c
--- /dev/null
+++ b/CHOLMOD/MATLAB/lcc_lib/lapacksyms.def
@@ -0,0 +1,718 @@
+LIBRARY liblapack.dll
+EXPORTS
+dasum
+daxpy
+dbdsdc
+dbdsqr
+dcopy
+ddisna
+ddot
+dgbbrd
+dgbcon
+dgbequ
+dgbmv
+dgbrfs
+dgbsv
+dgbsvx
+dgbtf2
+dgbtrf
+dgbtrs
+dgebak
+dgebal
+dgebd2
+dgebrd
+dgecon
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+dgees
+dgeesx
+dgeev
+dgeevx
+dgegs
+dgegv
+dgehd2
+dgehrd
+dgelq2
+dgelqf
+dgels
+dgelsd
+dgelss
+dgelsx
+dgelsy
+dgemm
+dgemv
+dgeql2
+dgeqlf
+dgeqp3
+dgeqpf
+dgeqr2
+dgeqrf
+dger
+dgerfs
+dgerq2
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+dgesc2
+dgesdd
+dgesv
+dgesvd
+dgesvx
+dgetc2
+dgetf2
+dgetrf
+dgetri
+dgetrs
+dggbak
+dggbal
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+dggesx
+dggev
+dggevx
+dggglm
+dgghrd
+dgglse
+dggqrf
+dggrqf
+dggsvd
+dggsvp
+dgtcon
+dgtrfs
+dgtsv
+dgtsvx
+dgttrf
+dgttrs
+dgtts2
+dhgeqz
+dhsein
+dhseqr
+dlabad
+dlabrd
+dlacon
+dlacpy
+dladiv
+dlae2
+dlaebz
+dlaed0
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+dlaed9
+dlaeda
+dlaein
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+dlagts
+dlagv2
+dlahqr
+dlahrd
+dlaic1
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+dlals0
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+dlamch
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+dlarft
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+dlargv
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+dlauum
+dnrm2
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+dzasum
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+idamax
+ieeeck
+ilaenv
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+izmax1
+lsame
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+xerbla
+zaxpy
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diff --git a/CHOLMOD/MATLAB/lcc_lib/libmwlapack.lib b/CHOLMOD/MATLAB/lcc_lib/libmwlapack.lib
new file mode 100644
index 0000000..ba94c1b
Binary files /dev/null and b/CHOLMOD/MATLAB/lcc_lib/libmwlapack.lib differ
diff --git a/CHOLMOD/MATLAB/lchol.c b/CHOLMOD/MATLAB/lchol.c
new file mode 100644
index 0000000..95a23aa
--- /dev/null
+++ b/CHOLMOD/MATLAB/lchol.c
@@ -0,0 +1,159 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/lchol mexFunction ===================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Numeric LL' factorization. Note that LL' and LDL' are faster than R'R
+ * and use less memory. The LL' factorization methods use tril(A).
+ *
+ * L = lchol (A) same as L = chol (A)', just faster
+ * [L,p] = lchol (A) save as [R,p] = chol(A) ; L=R', just faster
+ * [L,p,q] = lchol (A) factorizes A(q,q) into L*L'
+ *
+ * A must be sparse. It can be complex or real.
+ *
+ * L is returned with no explicit zero entries. This means it might not be
+ * chordal, and L cannot be passed back to CHOLMOD for an update/downdate or
+ * for a fast simplicial solve. spones (L) will be equal to the L returned
+ * by symbfact2 if no numerically zero entries are dropped, or a subset
+ * otherwise.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0, *px ;
+ cholmod_sparse Amatrix, *A, *Lsparse ;
+ cholmod_factor *L ;
+ cholmod_common Common, *cm ;
+ Int n, minor ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* convert to packed LL' when done */
+ cm->final_asis = FALSE ;
+ cm->final_super = FALSE ;
+ cm->final_ll = TRUE ;
+ cm->final_pack = TRUE ;
+ cm->final_monotonic = TRUE ;
+
+ /* no need to prune entries due to relaxed supernodal amalgamation, since
+ * zeros are dropped with sputil_drop_zeros instead */
+ cm->final_resymbol = FALSE ;
+
+ cm->quick_return_if_not_posdef = (nargout < 2) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin != 1 || nargout > 3)
+ {
+ mexErrMsgTxt ("usage: [L,p,q] = lchol (A)") ;
+ }
+
+ n = mxGetN (pargin [0]) ;
+
+ if (!mxIsSparse (pargin [0]) || n != mxGetM (pargin [0]))
+ {
+ mexErrMsgTxt ("A must be square and sparse") ;
+ }
+
+ /* get sparse matrix A, use tril(A) */
+ A = sputil_get_sparse (pargin [0], &Amatrix, &dummy, -1) ;
+
+ /* use natural ordering if no q output parameter */
+ if (nargout < 3)
+ {
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NATURAL ;
+ cm->postorder = FALSE ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* analyze and factorize */
+ /* ---------------------------------------------------------------------- */
+
+ L = cholmod_l_analyze (A, cm) ;
+ cholmod_l_factorize (A, L, cm) ;
+
+ if (nargout < 2 && cm->status != CHOLMOD_OK)
+ {
+ mexErrMsgTxt ("matrix is not positive definite") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to a sparse matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* the conversion sets L->minor back to n, so get a copy of it first */
+ minor = L->minor ;
+ Lsparse = cholmod_l_factor_to_sparse (L, cm) ;
+ if (Lsparse->xtype == CHOLMOD_COMPLEX)
+ {
+ /* convert Lsparse from complex to zomplex */
+ cholmod_l_sparse_xtype (CHOLMOD_ZOMPLEX, Lsparse, cm) ;
+ }
+
+ if (minor < n)
+ {
+ /* remove columns minor to n-1 from Lsparse */
+ sputil_trim (Lsparse, minor, cm) ;
+ }
+
+ /* drop zeros from Lsparse */
+ sputil_drop_zeros (Lsparse) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return results to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ /* return L as a sparse matrix */
+ pargout [0] = sputil_put_sparse (&Lsparse, cm) ;
+
+ /* return minor (translate to MATLAB convention) */
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ px = mxGetPr (pargout [1]) ;
+ px [0] = ((minor == n) ? 0 : (minor+1)) ;
+ }
+
+ /* return permutation */
+ if (nargout > 2)
+ {
+ pargout [2] = sputil_put_int (L->Perm, n, 1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free_factor (&L, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != 3 + mxIsComplex (pargout[0])) mexErrMsgTxt ("!") ;
+ */
+}
diff --git a/CHOLMOD/MATLAB/lchol.m b/CHOLMOD/MATLAB/lchol.m
new file mode 100644
index 0000000..9ffb004
--- /dev/null
+++ b/CHOLMOD/MATLAB/lchol.m
@@ -0,0 +1,18 @@
+function [L,p,q] = lchol (A) %#ok
+%LCHOL sparse A=L*L' factorization.
+% Note that L*L' (LCHOL) and L*D*L' (LDLCHOL) factorizations are faster than
+% R'*R (CHOL2 and CHOL) and use less memory. The LL' and LDL' factorization
+% methods use tril(A). A must be sparse.
+%
+% Example:
+% L = lchol (A) same as L = chol (A')', just faster
+% [L,p] = lchol (A) save as [R,p] = chol(A') ; L=R', just faster
+% [L,p,q] = lchol (A) factorizes A(q,q) into L*L', where q is a
+% fill-reducing ordering
+%
+% See also CHOL2, LDLCHOL, CHOL.
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('lchol mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/ldl_normest.m b/CHOLMOD/MATLAB/ldl_normest.m
new file mode 100644
index 0000000..858f5e7
--- /dev/null
+++ b/CHOLMOD/MATLAB/ldl_normest.m
@@ -0,0 +1,86 @@
+function rho = ldl_normest (A, L, D)
+%LDL_NORMEST estimate the 1-norm of A-L*D*L' without computing L*D*L'
+%
+% Example:
+%
+% rho = ldl_normest (A, L, D)
+%
+% which estimates the computation of the 1-norm:
+%
+% rho = norm (A-L*D*L', 1)
+%
+% Authors: William W. Hager, Math Dept., Univ. of Florida
+% Timothy A. Davis, CISE Dept., Univ. of Florida
+% Gainesville, FL, 32611, USA.
+% based on normest1, contributed on November, 1997
+%
+% See also condest, normest
+
+% Copyright 2006-2007, William W. Hager and Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+
+if (m ~= n)
+ error ('A must be square') ;
+end
+if (nnz (A-A') ~= 0)
+ error ('A must be symmetric') ;
+end
+
+if (nargin < 3)
+ D = speye (n) ;
+end
+
+notvisited = ones (m, 1) ; % nonvisited(j) is zero if j is visited, 1 otherwise
+rho = 0 ; % the global rho
+
+for trial = 1:3 % {
+
+ x = notvisited ./ sum (notvisited) ;
+ rho1 = 0 ; % the current rho for this trial
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%% COMPUTE Ex1 = E*x EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ % Ex1 = (A*x) - L*(U*x) ;
+ Ex1 = (A*x) - L*(D*(L'*x)) ;
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ rho2 = norm (Ex1, 1) ;
+
+ while rho2 > rho1 % {
+
+ rho1 = rho2 ;
+ y = 2*(Ex1 >= 0) - 1 ;
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%% COMPUTE z = E'*y EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ % z = (A'*y) - U'*(L'*y) ;
+ z = (A*y) - L*(D*(L'*x)) ;
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ [zj, j] = max (abs (z .* notvisited)) ;
+ j = j (1) ;
+ if (abs (z (j)) > z'*x) % {
+ x = zeros (m, 1) ;
+ x (j) = 1 ;
+ notvisited (j) = 0 ;
+ else % } {
+ break ;
+ end % }
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%% COMPUTE Ex1 = E*x EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ Ex1 = (A*x) - L*(D*(L'*x)) ;
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ rho2 = norm (Ex1, 1) ;
+
+ end % }
+
+ rho = max (rho, rho1) ;
+
+end % }
diff --git a/CHOLMOD/MATLAB/ldlchol.c b/CHOLMOD/MATLAB/ldlchol.c
new file mode 100644
index 0000000..d1a3159
--- /dev/null
+++ b/CHOLMOD/MATLAB/ldlchol.c
@@ -0,0 +1,202 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/ldlchol mexFunction =================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Numeric LDL' factorization. Note that LL' and LDL' are faster than R'R
+ * and use less memory. The LDL' factorization methods use tril(A).
+ * The unit diagonal L can be obtained with tril(LD,-1)+speye(n) and the
+ * diagonal D can be obtained with D = diag(diag(LD)) ;
+ *
+ * LD = ldlchol (A) return the LDL' factorization of A
+ * [LD,p] = ldlchol (A) like [R,p] = chol(A), except LD is always square
+ * [LD,p,q] = ldlchol (A) factorizes A(q,q) into L*D*L'
+ *
+ * LD = ldlchol (A,beta) return the LDL' factorization of A*A'+beta*I
+ * [LD,p] = ldlchol (A,beta) like [R,p] = chol(A*A'+beta+I)
+ * [LD,p,q] = ldlchol (A,beta) factorizes A(q,:)*A(q,:)'+beta*I into L*D*L'
+ *
+ * Explicit zeros may appear in the LD matrix. The pattern of LD matches the
+ * pattern of L as computed by symbfact2, even if some entries in LD are
+ * explicitly zero. This is to ensure that ldlupdate works properly. You must
+ * NOT modify LD in MATLAB itself and then use ldlupdate if LD contains
+ * explicit zero entries; ldlupdate will fail catastrophically in this case.
+ *
+ * You MAY modify LD in MATLAB if you do not pass it back to ldlupdate. Just be
+ * aware that LD contains explicit zero entries, contrary to the standard
+ * practice in MATLAB of removing those entries from all sparse matrices.
+ *
+ * Note that CHOLMOD uses a supernodal LL' factorization and then converts it
+ * to LDL' for large matrices, and a simplicial LDL' factorization otherwise.
+ * Two-by-two block pivoting is not performed, in any case. Thus, ldlchol
+ * will not be able to perform an LDL' factorization of an arbitrary indefinite
+ * matrix. The matrix
+ *
+ * 0 1
+ * 1 0
+ *
+ * will fail, for example. You can tell CHOLMOD to always use its simplicial
+ * LDL' factorization by adding the statement
+ *
+ * cm->supernodal = CHOLMOD_SIMPLICIAL ;
+ *
+ * but ldlchol will be much slower for large matrices. It still will not be
+ * able to handle the above matrix, but it can then handle matrices such as
+ *
+ * -2 1
+ * 1 -2
+ *
+ * or any other symmetric matrix for which all leading minors are
+ * well-conditioned.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0, beta [2], *px ;
+ cholmod_sparse Amatrix, *A, *Lsparse ;
+ cholmod_factor *L ;
+ cholmod_common Common, *cm ;
+ Int n, minor ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* convert to packed LDL' when done */
+ cm->final_asis = FALSE ;
+ cm->final_super = FALSE ;
+ cm->final_ll = FALSE ;
+ cm->final_pack = TRUE ;
+ cm->final_monotonic = TRUE ;
+
+ /* since numerically zero entries are NOT dropped from the symbolic
+ * pattern, we DO need to drop entries that result from supernodal
+ * amalgamation. */
+ cm->final_resymbol = TRUE ;
+
+ cm->quick_return_if_not_posdef = (nargout < 2) ;
+
+ /* This will disable the supernodal LL', which will be slow. */
+ /* cm->supernodal = CHOLMOD_SIMPLICIAL ; */
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin > 2 || nargout > 3)
+ {
+ mexErrMsgTxt ("usage: [L,p,q] = ldlchol (A,beta)") ;
+ }
+
+ n = mxGetM (pargin [0]) ;
+
+ if (!mxIsSparse (pargin [0]))
+ {
+ mexErrMsgTxt ("A must be sparse") ;
+ }
+ if (nargin == 1 && n != mxGetN (pargin [0]))
+ {
+ mexErrMsgTxt ("A must be square") ;
+ }
+
+ /* get sparse matrix A, use tril(A) */
+ A = sputil_get_sparse (pargin [0], &Amatrix, &dummy, -1) ;
+
+ if (nargin == 1)
+ {
+ A->stype = -1 ; /* use lower part of A */
+ beta [0] = 0 ;
+ beta [1] = 0 ;
+ }
+ else
+ {
+ A->stype = 0 ; /* use all of A, factorizing A*A' */
+ beta [0] = mxGetScalar (pargin [1]) ;
+ beta [1] = 0 ;
+ }
+
+ /* use natural ordering if no q output parameter */
+ if (nargout < 3)
+ {
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NATURAL ;
+ cm->postorder = FALSE ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* analyze and factorize */
+ /* ---------------------------------------------------------------------- */
+
+ L = cholmod_l_analyze (A, cm) ;
+ cholmod_l_factorize_p (A, beta, NULL, 0, L, cm) ;
+
+ if (nargout < 2 && cm->status != CHOLMOD_OK)
+ {
+ mexErrMsgTxt ("matrix is not positive definite") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to a sparse matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* the conversion sets L->minor back to n, so get a copy of it first */
+ minor = L->minor ;
+ Lsparse = cholmod_l_factor_to_sparse (L, cm) ;
+ if (Lsparse->xtype == CHOLMOD_COMPLEX)
+ {
+ /* convert Lsparse from complex to zomplex */
+ cholmod_l_sparse_xtype (CHOLMOD_ZOMPLEX, Lsparse, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return results to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ /* return L as a sparse matrix (it may contain numerically zero entries) */
+ pargout [0] = sputil_put_sparse (&Lsparse, cm) ;
+
+ /* return minor (translate to MATLAB convention) */
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ px = mxGetPr (pargout [1]) ;
+ px [0] = ((minor == n) ? 0 : (minor+1)) ;
+ }
+
+ /* return permutation */
+ if (nargout > 2)
+ {
+ pargout [2] = sputil_put_int (L->Perm, n, 1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free_factor (&L, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != 3 + mxIsComplex (pargout[0])) mexErrMsgTxt ("!") ;
+ */
+}
diff --git a/CHOLMOD/MATLAB/ldlchol.m b/CHOLMOD/MATLAB/ldlchol.m
new file mode 100644
index 0000000..fe2b7ff
--- /dev/null
+++ b/CHOLMOD/MATLAB/ldlchol.m
@@ -0,0 +1,39 @@
+function [LD,p,q] = ldlchol (A,beta) %#ok
+%LDLCHOL sparse A=LDL' factorization
+% Note that L*L' (LCHOL) and L*D*L' (LDLCHOL) factorizations are faster than
+% R'*R (CHOL2 and CHOL) and use less memory. The LL' and LDL' factorization
+% methods use tril(A). A must be sparse.
+%
+% Example:
+% LD = ldlchol (A) return the LDL' factorization of A
+% [LD,p] = ldlchol (A) similar [R,p] = chol(A), but for L*D*L'
+% [LD,p,q] = ldlchol (A) factorizes A(q,q) into L*D*L', where q is a
+% fill-reducing ordering
+%
+% LD = ldlchol (A,beta) return the LDL' factorization of A*A'+beta*I
+% [LD,p] = ldlchol (A,beta) like [R,p] = chol(A*A'+beta+I)
+% [LD,p,q] = ldlchol (A,beta) factorizes A(q,:)*A(q,:)'+beta*I into L*D*L'
+%
+% The output matrix LD contains both L and D. D is on the diagonal of LD, and
+% L is contained in the strictly lower triangular part of LD. The unit-
+% diagonal of L is not stored. You can obtain the L and D matrices with
+% [L,D] = ldlsplit (LD). LD is in the form needed by ldlupdate.
+%
+% Explicit zeros may appear in the LD matrix. The pattern of LD matches the
+% pattern of L as computed by symbfact2, even if some entries in LD are
+% explicitly zero. This is to ensure that ldlupdate and ldlsolve work
+% properly. You must NOT modify LD in MATLAB itself and then use ldlupdate
+% or ldlsolve if LD contains explicit zero entries; ldlupdate and ldlsolve
+% will fail catastrophically in this case.
+%
+% You MAY modify LD in MATLAB if you do not pass it back to ldlupdate or
+% ldlsolve. Just be aware that LD contains explicit zero entries, contrary
+% to the standard practice in MATLAB of removing those entries from all
+% sparse matrices. LD = sparse2 (LD) will remove any zero entries in LD.
+%
+% See also LDLUPDATE, LDLSOLVE, LDLSPLIT, CHOL2, LCHOL, CHOL, SPARSE2
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('ldlchol mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/ldlsolve.c b/CHOLMOD/MATLAB/ldlsolve.c
new file mode 100644
index 0000000..d6579d7
--- /dev/null
+++ b/CHOLMOD/MATLAB/ldlsolve.c
@@ -0,0 +1,178 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/ldlsolve mexFunction ================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Solve LDL'x=b given an LDL' factorization computed by ldlchol.
+ *
+ * Usage:
+ *
+ * x = ldlsolve (LD,b)
+ *
+ * b can be dense or sparse.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0, rcond ;
+ Int *Lp, *Lnz, *Lprev, *Lnext ;
+ cholmod_sparse *Bs, Bspmatrix, *Xs ;
+ cholmod_dense *B, Bmatrix, *X ;
+ cholmod_factor *L ;
+ cholmod_common Common, *cm ;
+ Int j, k, n, B_is_sparse, head, tail ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = ldlsolve (LD, b)") ;
+ }
+
+ n = mxGetN (pargin [0]) ;
+ k = mxGetN (pargin [1]) ;
+
+ if (!mxIsSparse (pargin [0]) || n != mxGetM (pargin [0]))
+ {
+ mexErrMsgTxt ("ldlsolve: LD must be sparse and square") ;
+ }
+ if (n != mxGetM (pargin [1]))
+ {
+ mexErrMsgTxt ("ldlsolve: b wrong dimension") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get b */
+ /* ---------------------------------------------------------------------- */
+
+ /* get sparse or dense matrix B */
+ B = NULL ;
+ Bs = NULL ;
+ B_is_sparse = mxIsSparse (pargin [1]) ;
+ if (B_is_sparse)
+ {
+ /* get sparse matrix B (unsymmetric) */
+ Bs = sputil_get_sparse (pargin [1], &Bspmatrix, &dummy, 0) ;
+ }
+ else
+ {
+ /* get dense matrix B */
+ B = sputil_get_dense (pargin [1], &Bmatrix, &dummy) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct a shallow copy of the input sparse matrix L */
+ /* ---------------------------------------------------------------------- */
+
+ /* the construction of the CHOLMOD takes O(n) time and memory */
+
+ /* allocate the CHOLMOD symbolic L */
+ L = cholmod_l_allocate_factor (n, cm) ;
+ L->ordering = CHOLMOD_NATURAL ;
+
+ /* get the MATLAB L */
+ L->p = mxGetJc (pargin [0]) ;
+ L->i = mxGetIr (pargin [0]) ;
+ L->x = mxGetPr (pargin [0]) ;
+ L->z = mxGetPi (pargin [0]) ;
+
+ /* allocate and initialize the rest of L */
+ L->nz = cholmod_l_malloc (n, sizeof (Int), cm) ;
+ Lp = L->p ;
+ Lnz = L->nz ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Lnz [j] = Lp [j+1] - Lp [j] ;
+ }
+ L->prev = cholmod_l_malloc (n+2, sizeof (Int), cm) ;
+ L->next = cholmod_l_malloc (n+2, sizeof (Int), cm) ;
+ Lprev = L->prev ;
+ Lnext = L->next ;
+
+ head = n+1 ;
+ tail = n ;
+ Lnext [head] = 0 ;
+ Lprev [head] = -1 ;
+ Lnext [tail] = -1 ;
+ Lprev [tail] = n-1 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Lnext [j] = j+1 ;
+ Lprev [j] = j-1 ;
+ }
+ Lprev [0] = head ;
+
+ L->xtype = (mxIsComplex (pargin [0])) ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL ;
+ L->nzmax = Lp [n] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve and return solution to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ if (B_is_sparse)
+ {
+ /* solve LDL'X=B with sparse X and B; return sparse X to MATLAB */
+ Xs = cholmod_l_spsolve (CHOLMOD_LDLt, L, Bs, cm) ;
+ pargout [0] = sputil_put_sparse (&Xs, cm) ;
+ }
+ else
+ {
+ /* solve AX=B with dense X and B; return dense X to MATLAB */
+ X = cholmod_l_solve (CHOLMOD_LDLt, L, B, cm) ;
+ pargout [0] = sputil_put_dense (&X, cm) ;
+ }
+
+ rcond = cholmod_l_rcond (L, cm) ;
+ if (rcond == 0)
+ {
+ mexWarnMsgTxt ("Matrix is indefinite or singular to working precision");
+ }
+ else if (rcond < DBL_EPSILON)
+ {
+ mexWarnMsgTxt ("Matrix is close to singular or badly scaled.") ;
+ mexPrintf (" Results may be inaccurate. RCOND = %g.\n", rcond) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ L->p = NULL ;
+ L->i = NULL ;
+ L->x = NULL ;
+ L->z = NULL ;
+ cholmod_l_free_factor (&L, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count !=
+ (mxIsComplex (pargout [0]) + (mxIsSparse (pargout[0]) ? 3:1)))
+ mexErrMsgTxt ("!") ;
+ */
+}
diff --git a/CHOLMOD/MATLAB/ldlsolve.m b/CHOLMOD/MATLAB/ldlsolve.m
new file mode 100644
index 0000000..0bb97c0
--- /dev/null
+++ b/CHOLMOD/MATLAB/ldlsolve.m
@@ -0,0 +1,21 @@
+function x = ldlsolve (LD,b) %#ok
+%LDLSOLVE solve LDL'x=b using a sparse LDL' factorization
+%
+% Example:
+% x = ldlsolve (LD,b)
+%
+% solves the system L*D*L'*x=b for x. This is equivalent to
+%
+% [L,D] = ldlsplit (LD) ;
+% x = L' \ (D \ (L \ b)) ;
+%
+% LD is from ldlchol, or as updated by ldlupdate. You must not modify LD as
+% obtained from ldlchol or ldlupdate prior to passing it to this function.
+% See ldlupdate for more details.
+%
+% See also LDLCHOL, LDLUPDATE, LDLSPLIT
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('ldlsolve mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/ldlsplit.m b/CHOLMOD/MATLAB/ldlsplit.m
new file mode 100644
index 0000000..5f86c32
--- /dev/null
+++ b/CHOLMOD/MATLAB/ldlsplit.m
@@ -0,0 +1,19 @@
+function [L,D] = ldlsplit (LD) %#ok
+%LDLSPLIT split an LDL' factorization into L and D.
+%
+% Example:
+% [L,D] = ldlsplit (LD)
+%
+% LD contains an LDL' factorization, computed with LD = ldlchol(A),
+% for example. The diagonal of LD contains D, and the entries below
+% the diagonal contain L (which has a unit diagonal). This function
+% splits LD into its two components L and D so that L*D*L' = A.
+%
+% See also LDLCHOL, LDLSOLVE, LDLUPDATE.
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (LD,1) ;
+D = diag (diag (LD)) ;
+L = tril (LD,-1) + speye (n) ;
diff --git a/CHOLMOD/MATLAB/ldlupdate.c b/CHOLMOD/MATLAB/ldlupdate.c
new file mode 100644
index 0000000..34035d6
--- /dev/null
+++ b/CHOLMOD/MATLAB/ldlupdate.c
@@ -0,0 +1,174 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/ldlupdate mexFunction ================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Multiple-rank update or downdate of a sparse LDL' factorization.
+ *
+ * Usage:
+ *
+ * LD = ldlupdate (LD,C) update an LDL' factorization
+ * LD = ldlupdate (LD,C,'+') update an LDL' factorization
+ * LD = ldlupdate (LD,C,'-') downdate an LDL' factorization
+ *
+ * See ldlupdate.m for details. LD and C must be real and sparse.
+ *
+ * The bulk of the time is spent copying the input LD to the output LD. This
+ * mexFunction could be much faster if it could safely modify its input LD.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0 ;
+ double *Lx, *Lx2 ;
+ Int *Li, *Lp, *Li2, *Lp2, *Lnz2, *ColCount ;
+ cholmod_sparse Cmatrix, *C, *Lsparse ;
+ cholmod_factor *L ;
+ cholmod_common Common, *cm ;
+ Int j, k, s, update, n, lnz ;
+ char buf [LEN] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 1 || nargin < 2 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: L = ldlupdate (L, C, '+')") ;
+ }
+
+ n = mxGetN (pargin [0]) ;
+ k = mxGetN (pargin [1]) ;
+
+ if (!mxIsSparse (pargin [0]) || !mxIsSparse (pargin [1])
+ || n != mxGetM (pargin [0]) || n != mxGetM (pargin [1])
+ || mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+ mexErrMsgTxt ("ldlupdate: C and/or L not sparse, complex, or wrong"
+ " dimensions") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine if we're doing an update or downdate */
+ /* ---------------------------------------------------------------------- */
+
+ update = TRUE ;
+ if (nargin > 2 && mxIsChar (pargin [2]))
+ {
+ mxGetString (pargin [2], buf, LEN) ;
+ if (buf [0] == '-')
+ {
+ update = FALSE ;
+ }
+ else if (buf [0] != '+')
+ {
+ mexErrMsgTxt ("ldlupdate: update string must be '+' or '-'") ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get C: sparse matrix of incoming/outgoing columns */
+ /* ---------------------------------------------------------------------- */
+
+ C = sputil_get_sparse (pargin [1], &Cmatrix, &dummy, 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct a copy of the input sparse matrix L */
+ /* ---------------------------------------------------------------------- */
+
+ /* get the MATLAB L */
+ Lp = (Int *) mxGetJc (pargin [0]) ;
+ Li = (Int *) mxGetIr (pargin [0]) ;
+ Lx = mxGetPr (pargin [0]) ;
+
+ /* allocate the CHOLMOD symbolic L */
+ L = cholmod_l_allocate_factor (n, cm) ;
+ L->ordering = CHOLMOD_NATURAL ;
+ ColCount = L->ColCount ;
+ for (j = 0 ; j < n ; j++)
+ {
+ ColCount [j] = Lp [j+1] - Lp [j] ;
+ }
+
+ /* allocate space for a CHOLMOD LDL' packed factor */
+ cholmod_l_change_factor (CHOLMOD_REAL, FALSE, FALSE, TRUE, TRUE, L, cm) ;
+
+ /* copy MATLAB L into CHOLMOD L */
+ Lp2 = L->p ;
+ Li2 = L->i ;
+ Lx2 = L->x ;
+ Lnz2 = L->nz ;
+ lnz = L->nzmax ;
+ for (j = 0 ; j <= n ; j++)
+ {
+ Lp2 [j] = Lp [j] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ Lnz2 [j] = Lp [j+1] - Lp [j] ;
+ }
+ for (s = 0 ; s < lnz ; s++)
+ {
+ Li2 [s] = Li [s] ;
+ }
+ for (s = 0 ; s < lnz ; s++)
+ {
+ Lx2 [s] = Lx [s] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* update/downdate the LDL' factorization */
+ /* ---------------------------------------------------------------------- */
+
+ if (!cholmod_l_updown (update, C, L, cm))
+ {
+ mexErrMsgTxt ("ldlupdate failed\n") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the results back to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ /* change L back to packed LDL' (it may have become unpacked if the
+ * sparsity pattern changed). This change takes O(n) time if the pattern
+ * of L wasn't updated. */
+ Lsparse = cholmod_l_factor_to_sparse (L, cm) ;
+
+ /* return L as a sparse matrix */
+ pargout [0] = sputil_put_sparse (&Lsparse, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free_factor (&L, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != 3 + mxIsComplex (pargout[0])) mexErrMsgTxt ("!") ;
+ */
+}
diff --git a/CHOLMOD/MATLAB/ldlupdate.m b/CHOLMOD/MATLAB/ldlupdate.m
new file mode 100644
index 0000000..a7cb0df
--- /dev/null
+++ b/CHOLMOD/MATLAB/ldlupdate.m
@@ -0,0 +1,55 @@
+function LD = ldlupdate (LD,C,updown) %#ok
+%LDLUPDATE multiple-rank update or downdate of a sparse LDL' factorization.
+%
+% On input, LD contains the LDL' factorization of A (L*D*L'=A or A(q,q)).
+% The unit-diagonal of L is not stored. In its place is the diagonal matrix
+% D. LD can be computed using the CHOLMOD mexFunctions:
+%
+% LD = ldlchol (A) ;
+% or
+% [LD,p,q] = ldlchol (A) ;
+%
+% With this LD, either of the following MATLAB statements,
+%
+% Example:
+% LD = ldlupdate (LD,C)
+% LD = ldlupdate (LD,C,'+')
+%
+% return the LDL' factorization of A+C*C' or A(q,q)-C*C' if LD holds the LDL'
+% factorization of A(q,q) on input. For a downdate:
+%
+% LD = ldlupdate (LD,C,'-')
+%
+% returns the LDL' factorization of A-C*C' or A(q,q)-C*C'.
+%
+% LD and C must be sparse and real. LD must be square, and C must have the
+% same number of rows as LD. You must not modify LD in MATLAB (see the
+% WARNING below).
+%
+% Note that if C is sparse with few columns, most of the time spent in this
+% routine is taken by copying the input LD to the output LD. If MATLAB
+% allowed mexFunctions to safely modify its inputs, this mexFunction would
+% be much faster, since not all of LD changes.
+%
+% See also LDLCHOL, LDLSPLIT, LDLSOLVE, CHOLUPDATE
+%
+% ===========================================================================
+% =============================== WARNING ===================================
+% ===========================================================================
+% MATLAB drops zero entries from its sparse matrices. LD can contain
+% numerically zero entries that are symbolically present in the sparse matrix
+% data structure. These are essential for ldlupdate and ldlsolve to work
+% properly, since they exploit the graph-theoretic structure of a sparse
+% Cholesky factorization. If you modify LD in MATLAB, those zero entries may
+% get dropped and the required graph property will be destroyed. In this
+% case, ldlupdate and ldlsolve will fail catastrophically (possibly with a
+% segmentation fault, terminating MATLAB). It takes much more time to ensure
+% this property holds than the time it takes to do the update/downdate or the
+% solve, so ldlupdate and ldlsolve simply assume the propertly holds.
+% ===========================================================================
+
+% Copyright 2006-2007, Timothy A. Davis, William W. Hager
+% http://www.cise.ufl.edu/research/sparse
+
+error ('ldlupdate mexFunction not found') ;
+
diff --git a/CHOLMOD/MATLAB/metis.c b/CHOLMOD/MATLAB/metis.c
new file mode 100644
index 0000000..0696ae0
--- /dev/null
+++ b/CHOLMOD/MATLAB/metis.c
@@ -0,0 +1,166 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/metis mexFunction ===================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * METIS (Copyright 1998, G. Karypis) is not distributed with CHOLMOD.
+ * -------------------------------------------------------------------------- */
+
+/* Nested dissection using METIS_NodeND
+ *
+ * Usage:
+ *
+ * p = metis (A) orders A, using just tril(A)
+ * p = metis (A,'sym') orders A, using just tril(A)
+ * p = metis (A,'row') orders A*A'
+ * p = metis (A,'col') orders A'*A
+ *
+ * METIS_NodeND's ordering is followed by CHOLMOD's etree or column etree
+ * postordering. Requires METIS and the CHOLMOD Partition Module.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+#ifndef NPARTITION
+ double dummy = 0 ;
+ Int *Perm ;
+ cholmod_sparse *A, Amatrix, *C, *S ;
+ cholmod_common Common, *cm ;
+ Int n, transpose, c, postorder ;
+ char buf [LEN] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set defaults */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 1 || nargin < 1 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: p = metis (A, mode)") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get input matrix A */
+ /* ---------------------------------------------------------------------- */
+
+ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ;
+ S = (A == &Amatrix) ? NULL : A ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get A->stype, default is to use tril(A) */
+ /* ---------------------------------------------------------------------- */
+
+ A->stype = -1 ;
+ transpose = FALSE ;
+
+ if (nargin > 1)
+ {
+ buf [0] = '\0' ;
+ if (mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], buf, LEN) ;
+ }
+ c = buf [0] ;
+ if (tolower (c) == 'r')
+ {
+ /* unsymmetric case (A*A') if string starts with 'r' */
+ transpose = FALSE ;
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 'c')
+ {
+ /* unsymmetric case (A'*A) if string starts with 'c' */
+ transpose = TRUE ;
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 's')
+ {
+ /* symmetric case (A) if string starts with 's' */
+ transpose = FALSE ;
+ A->stype = -1 ;
+ }
+ else
+ {
+ mexErrMsgTxt ("metis: p=metis(A,mode) ; unrecognized mode") ;
+ }
+ }
+
+ if (A->stype && A->nrow != A->ncol)
+ {
+ mexErrMsgTxt ("metis: A must be square") ;
+ }
+
+ C = NULL ;
+ if (transpose)
+ {
+ /* C = A', and then order C*C' with METIS */
+ C = cholmod_l_transpose (A, 0, cm) ;
+ if (C == NULL)
+ {
+ mexErrMsgTxt ("metis failed") ;
+ }
+ A = C ;
+ }
+
+ n = A->nrow ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Perm = cholmod_l_malloc (n, sizeof (Int), cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order the matrix with CHOLMOD's interface to METIS_NodeND */
+ /* ---------------------------------------------------------------------- */
+
+ postorder = (nargin < 3) ;
+ if (!cholmod_l_metis (A, NULL, 0, postorder, Perm, cm))
+ {
+ mexErrMsgTxt ("metis failed") ;
+ return ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return Perm */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = sputil_put_int (Perm, n, 1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free (n, sizeof (Int), Perm, cm) ;
+ cholmod_l_free_sparse (&C, cm) ;
+ cholmod_l_free_sparse (&S, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != 0) mexErrMsgTxt ("!") ;
+ */
+#else
+ mexErrMsgTxt ("METIS and the CHOLMOD Partition Module not installed\n") ;
+#endif
+}
diff --git a/CHOLMOD/MATLAB/metis.m b/CHOLMOD/MATLAB/metis.m
new file mode 100644
index 0000000..8df183a
--- /dev/null
+++ b/CHOLMOD/MATLAB/metis.m
@@ -0,0 +1,23 @@
+function p = metis (A, mode) %#ok
+%METIS nested dissection ordering via METIS_NodeND.
+%
+% Example:
+% p = metis(A) returns p such chol(A(p,p)) is typically sparser than
+% chol(A). Uses tril(A) and assumes A is symmetric.
+% p = metis(A,'sym') the same as p=metis(A).
+% p = metis(A,'col') returns p so that chol(A(:,p)'*A(:,p)) is typically
+% sparser than chol(A'*A).
+% p = metis(A,'row') returns p so that chol(A(p,:)*A(p,:)') is typically
+% sparser than chol(A'*A).
+%
+% A must be square for p=metis(A) or metis(A,'sym')
+%
+% Requires METIS, authored by George Karypis, Univ. of Minnesota. This
+% MATLAB interface, via CHOLMOD, is by Tim Davis.
+%
+% See also NESDIS, BISECT
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('metis mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/mread.c b/CHOLMOD/MATLAB/mread.c
new file mode 100644
index 0000000..5a0e047
--- /dev/null
+++ b/CHOLMOD/MATLAB/mread.c
@@ -0,0 +1,219 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/mread mexFunction ===================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* [A Z] = mread (filename, prefer_binary)
+ *
+ * Read a sparse or dense matrix from a file in Matrix Market format.
+ *
+ * All MatrixMarket formats are supported.
+ * The Matrix Market "integer" format is converted into real, but the values
+ * are preserved. The "pattern" format is converted into real. If a pattern
+ * matrix is unsymmetric, all of its values are equal to one. If a pattern is
+ * symmetric, the kth diagonal entry is set to one plus the number of
+ * off-diagonal nonzeros in row/column k, and off-diagonal entries are set to
+ * -1.
+ *
+ * Explicit zero entries are returned as the binary pattern of the matrix Z.
+ */
+
+#include "cholmod_matlab.h"
+
+/* maximum file length */
+#define MAXLEN 1030
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ void *G ;
+ cholmod_dense *X = NULL ;
+ cholmod_sparse *A = NULL, *Z = NULL ;
+ cholmod_common Common, *cm ;
+ Int *Ap = NULL, *Ai ;
+ double *Ax, *Az = NULL ;
+ char filename [MAXLEN] ;
+ Int nz, k, is_complex = FALSE, nrow = 0, ncol = 0, allzero ;
+ int mtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin > 2 || nargout > 2)
+ {
+ mexErrMsgTxt ("usage: [A Z] = mread (filename, prefer_binary)") ;
+ }
+ if (!mxIsChar (pargin [0]))
+ {
+ mexErrMsgTxt ("mread requires a filename") ;
+ }
+ mxGetString (pargin [0], filename, MAXLEN) ;
+ sputil_file = fopen (filename, "r") ;
+ if (sputil_file == NULL)
+ {
+ mexErrMsgTxt ("cannot open file") ;
+ }
+ if (nargin > 1)
+ {
+ cm->prefer_binary = (mxGetScalar (pargin [1]) != 0) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the matrix, as either a dense or sparse matrix */
+ /* ---------------------------------------------------------------------- */
+
+ G = cholmod_l_read_matrix (sputil_file, 1, &mtype, cm) ;
+ fclose (sputil_file) ;
+ sputil_file = NULL ;
+ if (G == NULL)
+ {
+ mexErrMsgTxt ("could not read file") ;
+ }
+
+ /* get the specific matrix (A or X), and change to ZOMPLEX if needed */
+ if (mtype == CHOLMOD_SPARSE)
+ {
+ A = (cholmod_sparse *) G ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ is_complex = (A->xtype == CHOLMOD_COMPLEX) ;
+ Ap = A->p ;
+ Ai = A->i ;
+ if (is_complex)
+ {
+ /* if complex, ensure A is ZOMPLEX */
+ cholmod_l_sparse_xtype (CHOLMOD_ZOMPLEX, A, cm) ;
+ }
+ Ax = A->x ;
+ Az = A->z ;
+ }
+ else if (mtype == CHOLMOD_DENSE)
+ {
+ X = (cholmod_dense *) G ;
+ nrow = X->nrow ;
+ ncol = X->ncol ;
+ is_complex = (X->xtype == CHOLMOD_COMPLEX) ;
+ if (is_complex)
+ {
+ /* if complex, ensure X is ZOMPLEX */
+ cholmod_l_dense_xtype (CHOLMOD_ZOMPLEX, X, cm) ;
+ }
+ Ax = X->x ;
+ Az = X->z ;
+ }
+ else
+ {
+ mexErrMsgTxt ("invalid file") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* if requested, extract the zero entries and place them in Z */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 1)
+ {
+ if (mtype == CHOLMOD_SPARSE)
+ {
+ /* A is a sparse real/zomplex double matrix */
+ Z = sputil_extract_zeros (A, cm) ;
+ }
+ else
+ {
+ /* input is full; just return an empty Z matrix */
+ Z = cholmod_l_spzeros (nrow, ncol, 0, CHOLMOD_REAL, cm) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* prune the zero entries from A and set nzmax(A) to nnz(A) */
+ /* ---------------------------------------------------------------------- */
+
+ if (mtype == CHOLMOD_SPARSE)
+ {
+ sputil_drop_zeros (A) ;
+ cholmod_l_reallocate_sparse (cholmod_l_nnz (A, cm), A, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* change a complex matrix to real if its imaginary part is all zero */
+ /* ---------------------------------------------------------------------- */
+
+ if (is_complex)
+ {
+ if (mtype == CHOLMOD_SPARSE)
+ {
+ nz = Ap [ncol] ;
+ }
+ else
+ {
+ nz = nrow * ncol ;
+ }
+ allzero = TRUE ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ if (Az [k] != 0)
+ {
+ allzero = FALSE ;
+ break ;
+ }
+ }
+ if (allzero)
+ {
+ /* discard the all-zero imaginary part */
+ if (mtype == CHOLMOD_SPARSE)
+ {
+ cholmod_l_sparse_xtype (CHOLMOD_REAL, A, cm) ;
+ }
+ else
+ {
+ cholmod_l_dense_xtype (CHOLMOD_REAL, X, cm) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return results to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ if (mtype == CHOLMOD_SPARSE)
+ {
+ pargout [0] = sputil_put_sparse (&A, cm) ;
+ }
+ else
+ {
+ pargout [0] = sputil_put_dense (&X, cm) ;
+ }
+ if (nargout > 1)
+ {
+ pargout [1] = sputil_put_sparse (&Z, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+}
diff --git a/CHOLMOD/MATLAB/mread.m b/CHOLMOD/MATLAB/mread.m
new file mode 100644
index 0000000..1490013
--- /dev/null
+++ b/CHOLMOD/MATLAB/mread.m
@@ -0,0 +1,24 @@
+function [A, Z] = mread (filename,prefer_binary) %#ok
+%MREAD read a sparse matrix from a file in Matrix Market format.
+%
+% Example:
+% A = mread (filename)
+% [A Z] = mread (filename, prefer_binary)
+%
+% Unlike MMREAD, only the matrix is returned; the file format is not
+% returned. Explicit zero entries can be present in the file; these are not
+% included in A. They appear as the nonzero pattern of the binary matrix Z.
+%
+% If prefer_binary is not present, or zero, a symmetric pattern-only matrix
+% is returned with A(i,i) = 1+length(find(A(:,i))) if it is present in the
+% pattern, and A(i,j) = -1 for off-diagonal entries. If you want the original
+% Matrix Market matrix in this case, simply use A = mread (filename,1).
+%
+% Compare with mmread.m at http://math.nist.gov/MatrixMarket
+%
+% See also load
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('mread mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/mwrite.c b/CHOLMOD/MATLAB/mwrite.c
new file mode 100644
index 0000000..46f4390
--- /dev/null
+++ b/CHOLMOD/MATLAB/mwrite.c
@@ -0,0 +1,183 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/mwrite mexFunction ==================================== */
+/* ========================================================================== */
+
+/* Write a matrix to a file in Matrix Market form.
+ *
+ * symmetry = mwrite (filename, A, Z, comments_filename)
+ *
+ * A can be sparse or full.
+ *
+ * If present and non-empty, A and Z must have the same dimension. Z contains
+ * the explicit zero entries in the matrix (which MATLAB drops). The entries
+ * of Z appear as explicit zeros in the output file. Z is optional. If it is
+ * an empty matrix it is ignored. Z must be sparse or empty, if present.
+ * It is ignored if A is full.
+ *
+ * filename is the name of the output file. comments_file is file whose
+ * contents are include after the Matrix Market header and before the first
+ * data line. Ignored if an empty string or not present.
+ */
+
+#include "cholmod_matlab.h"
+
+#define MAXLEN 1030
+
+/* -------------------------------------------------------------------------- */
+/* mwrite mexFunction */
+/* -------------------------------------------------------------------------- */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0 ;
+ cholmod_sparse Amatrix, Zmatrix, *A, *Z ;
+ cholmod_dense Xmatrix, *X ;
+ cholmod_common Common, *cm ;
+ Int arg_z, arg_comments, sym ;
+ char filename [MAXLEN], comments [MAXLEN] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin < 2 || nargin > 4 || nargout > 1)
+ {
+ mexErrMsgTxt ("Usage: mwrite (filename, A, Z, comments_filename)") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the output filename */
+ /* ---------------------------------------------------------------------- */
+
+ if (!mxIsChar (pargin [0]))
+ {
+ mexErrMsgTxt ("first parameter must be a filename") ;
+ }
+ mxGetString (pargin [0], filename, MAXLEN) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the A matrix (sparse or dense) */
+ /* ---------------------------------------------------------------------- */
+
+ if (mxIsSparse (pargin [1]))
+ {
+ A = sputil_get_sparse (pargin [1], &Amatrix, &dummy, 0) ;
+ X = NULL ;
+ }
+ else
+ {
+ X = sputil_get_dense (pargin [1], &Xmatrix, &dummy) ;
+ A = NULL ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine if the Z matrix and comments_file are present */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin == 3)
+ {
+ if (mxIsChar (pargin [2]))
+ {
+ /* mwrite (file, A, comments) */
+ arg_z = -1 ;
+ arg_comments = 2 ;
+ }
+ else
+ {
+ /* mwrite (file, A, Z). Ignore Z if A is full */
+ arg_z = (A == NULL) ? -1 : 2 ;
+ arg_comments = -1 ;
+ }
+ }
+ else if (nargin == 4)
+ {
+ /* mwrite (file, A, Z, comments). Ignore Z is A is full */
+ arg_z = (A == NULL) ? -1 : 2 ;
+ arg_comments = 3 ;
+ }
+ else
+ {
+ arg_z = -1 ;
+ arg_comments = -1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the Z matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (arg_z == -1 ||
+ mxGetM (pargin [arg_z]) == 0 || mxGetN (pargin [arg_z]) == 0)
+ {
+ /* A is dense, Z is not present, or Z is empty. Ignore Z. */
+ Z = NULL ;
+ }
+ else
+ {
+ /* A is sparse and Z is present and not empty */
+ if (!mxIsSparse (pargin [arg_z]))
+ {
+ mexErrMsgTxt ("Z must be sparse") ;
+ }
+ Z = sputil_get_sparse (pargin [arg_z], &Zmatrix, &dummy, 0) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the comments filename */
+ /* ---------------------------------------------------------------------- */
+
+ comments [0] = '\0' ;
+ if (arg_comments != -1)
+ {
+ if (!mxIsChar (pargin [arg_comments]))
+ {
+ mexErrMsgTxt ("comments filename must be a string") ;
+ }
+ mxGetString (pargin [arg_comments], comments, MAXLEN) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* write the matrix to the file */
+ /* ---------------------------------------------------------------------- */
+
+ sputil_file = fopen (filename, "w") ;
+ if (sputil_file == NULL)
+ {
+ mexErrMsgTxt ("error opening file") ;
+ }
+ if (A != NULL)
+ {
+ sym = cholmod_l_write_sparse (sputil_file, A, Z, comments, cm) ;
+ }
+ else
+ {
+ sym = cholmod_l_write_dense (sputil_file, X, comments, cm) ;
+ }
+ fclose (sputil_file) ;
+ sputil_file = NULL ;
+ if (sym < 0)
+ {
+ mexErrMsgTxt ("mwrite failed") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace and return symmetry */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = sputil_put_int (&sym, 1, 0) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+}
diff --git a/CHOLMOD/MATLAB/mwrite.m b/CHOLMOD/MATLAB/mwrite.m
new file mode 100644
index 0000000..e3e9776
--- /dev/null
+++ b/CHOLMOD/MATLAB/mwrite.m
@@ -0,0 +1,23 @@
+function mtype = mwrite (filename, A, Z, comments_filename) %#ok
+%MWRITE write a matrix to a file in Matrix Market form.
+%
+% Example:
+% mtype = mwrite (filename, A, Z, comments_filename)
+%
+% A can be sparse or full.
+%
+% If present and non-empty, A and Z must have the same dimension. Z contains
+% the explicit zero entries in the matrix (which MATLAB drops). The entries
+% of Z appear as explicit zeros in the output file. Z is optional. If it is
+% an empty matrix it is ignored. Z must be sparse or empty, if present.
+% It is ignored if A is full.
+%
+% filename is the name of the output file. comments_filename is the file
+% whose contents are include after the Matrix Market header and before the
+% first data line. Ignored if an empty string or not present.
+%
+% See also mread.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+error ('mwrite mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/nesdis.c b/CHOLMOD/MATLAB/nesdis.c
new file mode 100644
index 0000000..3e8150c
--- /dev/null
+++ b/CHOLMOD/MATLAB/nesdis.c
@@ -0,0 +1,213 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/nesdis mexFunction ==================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * METIS (Copyright 1998, G. Karypis) is not distributed with CHOLMOD.
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD's nested dissection, based on METIS_NodeComputerSeparator, CAMD, and
+ * CCOLAMD.
+ *
+ * Usage:
+ *
+ * [p, cp, cmember] = nesdis (A) orders A, using tril(A)
+ * [p, cp, cmember] = nesdis (A,'sym') orders A, using tril(A)
+ * [p, cp, cmember] = nesdis (A,'row') orders A*A'
+ * [p, cp, cmember] = nesdis (A,'col') orders A'*A
+ *
+ * Nested dissection ordering. Returns a permutation p such that the Cholesky
+ * factorization of A(p,p), A(p,:)*A(p,:)', or A(:,p)'*A(:,p) is sparser than
+ * the unpermuted system. 'mode' defaults to 'sym'.
+ *
+ * An optional 3rd input argument:
+ *
+ * nesdis (A,mode,opts)
+ *
+ * specifies control parameters. opts(1) is the smallest subgraph that should
+ * not be partitioned (default is 200), opts(2) is 1 if connected components are
+ * to be split independently (default is 0). opts(3) controls when a separator
+ * is kept; it is kept if nsep < opts(3)*n, where nsep is the number of nodes in
+ * the separator and n is the number of nodes in the graph being cut (default is
+ * 1).
+ *
+ * opts(4) is 0 if the smallest subgraphs are not to be ordered. For the 'sym'
+ * case, or if mode is not present: 1 if to be ordered by CAMD, or 2 if to be
+ * ordered with CSYMAMD (default is 1). For the other cases: 0 for natural
+ * ordering, 1 if to be ordered by CCOLAMD.
+ *
+ * cp and cmember are optional. cmember(i)=c means that node i is in component
+ * c, where c is in the range of 1 to the number of components. length(cp) is
+ * the number of components found. cp is the separator tree; cp(c) is the
+ * parent of component c, or 0 if c is a root. There can be anywhere from
+ * 1 to n components, where n is the number of rows of A, A*A', or A'*A.
+ *
+ * Requires METIS and the CHOLMOD Partition Module.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+#ifndef NPARTITION
+ double dummy = 0 ;
+ Int *Perm, *Cmember, *CParent ;
+ cholmod_sparse *A, Amatrix, *C, *S ;
+ cholmod_common Common, *cm ;
+ Int n, transpose, c, ncomp ;
+ char buf [LEN] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set defaults */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 3 || nargin < 1 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: [p cp cmember] = nesdis (A, mode, opts)") ;
+ }
+ if (nargin > 2)
+ {
+ double *x = mxGetPr (pargin [2]) ;
+ n = mxGetNumberOfElements (pargin [2]) ;
+ if (n > 0) cm->method [0].nd_small = x [0] ;
+ if (n > 1) cm->method [0].nd_components = x [1] ;
+ if (n > 2) cm->method [0].nd_oksep = x [2] ;
+ if (n > 3) cm->method [0].nd_camd = x [3] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get input matrix A */
+ /* ---------------------------------------------------------------------- */
+
+ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ;
+ S = (A == &Amatrix) ? NULL : A ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get A->stype, default is to use tril(A) */
+ /* ---------------------------------------------------------------------- */
+
+ A->stype = -1 ;
+ transpose = FALSE ;
+
+ if (nargin > 1)
+ {
+ buf [0] = '\0' ;
+ if (mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], buf, LEN) ;
+ }
+ c = buf [0] ;
+ if (tolower (c) == 'r')
+ {
+ /* unsymmetric case (A*A') if string starts with 'r' */
+ transpose = FALSE ;
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 'c')
+ {
+ /* unsymmetric case (A'*A) if string starts with 'c' */
+ transpose = TRUE ;
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 's')
+ {
+ /* symmetric case (A) if string starts with 's' */
+ transpose = FALSE ;
+ A->stype = -1 ;
+ }
+ else
+ {
+ mexErrMsgTxt ("nesdis: unrecognized mode") ;
+ }
+ }
+
+ if (A->stype && A->nrow != A->ncol)
+ {
+ mexErrMsgTxt ("nesdis: A must be square") ;
+ }
+
+ C = NULL ;
+ if (transpose)
+ {
+ /* C = A', and then order C*C' with cholmod_l_nested_dissection */
+ C = cholmod_l_transpose (A, 0, cm) ;
+ if (C == NULL)
+ {
+ mexErrMsgTxt ("nesdis failed") ;
+ }
+ A = C ;
+ }
+
+ n = A->nrow ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CParent = cholmod_l_malloc (n, sizeof (Int), cm) ;
+ Cmember = cholmod_l_malloc (n, sizeof (Int), cm) ;
+ Perm = cholmod_l_malloc (n, sizeof (Int), cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order the matrix with CHOLMOD's nested dissection */
+ /* ---------------------------------------------------------------------- */
+
+ ncomp = cholmod_l_nested_dissection (A, NULL, 0, Perm, CParent, Cmember,cm);
+ if (ncomp < 0)
+ {
+ mexErrMsgTxt ("nesdis failed") ;
+ return ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return Perm, CParent, and Cmember */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = sputil_put_int (Perm, n, 1) ;
+ if (nargout > 1)
+ {
+ pargout [1] = sputil_put_int (CParent, ncomp, 1) ;
+ }
+ if (nargout > 2)
+ {
+ pargout [2] = sputil_put_int (Cmember, n, 1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free (n, sizeof (Int), Perm, cm) ;
+ cholmod_l_free (n, sizeof (Int), CParent, cm) ;
+ cholmod_l_free (n, sizeof (Int), Cmember, cm) ;
+ cholmod_l_free_sparse (&C, cm) ;
+ cholmod_l_free_sparse (&S, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != 0) mexErrMsgTxt ("!") ;
+ */
+#else
+ mexErrMsgTxt ("METIS and the CHOLMOD Partition Module not installed\n") ;
+#endif
+}
diff --git a/CHOLMOD/MATLAB/nesdis.m b/CHOLMOD/MATLAB/nesdis.m
new file mode 100644
index 0000000..b439861
--- /dev/null
+++ b/CHOLMOD/MATLAB/nesdis.m
@@ -0,0 +1,54 @@
+function [p, cparent, cmember] = nesdis (A, mode, opts) %#ok
+%NESDIS nested dissection ordering via CHOLMOD's nested dissection.
+%
+% Example:
+% p = nesdis(A) returns p such chol(A(p,p)) is typically sparser than
+% chol(A). Uses tril(A) and assumes A is symmetric.
+% p = nesdis(A,'sym') the same as p=nesdis(A).
+% p = nesdis(A,'col') returns p so that chol(A(:,p)'*A(:,p)) is typically
+% sparser than chol(A'*A).
+% p = nesdis(A,'row') returns p so that chol(A(p,:)*A(p,:)') is typically
+% sparser than chol(A'*A).
+%
+% A must be square for p=nesdis(A) or nesdis(A,'sym').
+%
+% With three output arguments, [p cp cmember] = nesdis(...), the separator
+% tree and node-to-component mapping is returned. cmember(i)=c means that
+% node i is in component c, where c is in the range of 1 to the number of
+% components. length(cp) is the number of components found. cp is the
+% separator tree; cp(c) is the parent of component c, or 0 if c is a root.
+% There can be anywhere from 1 to n components, where n is dimension of A,
+% A*A', or A'*A. cmember is a vector of length n.
+%
+% An optional 3rd input argument, nesdis (A,mode,opts), modifies the default
+% parameters. opts(1) specifies the smallest subgraph that should not be
+% partitioned (default is 200). opts(2) is 0 by default; if nonzero,
+% connected components (formed after the node separator is removed) are
+% partitioned independently. The default value tends to lead to a more
+% balanced separator tree, cp. opts(3) defines when a separator is kept; it
+% is kept if the separator size is < opts(3) times the number of nodes in the
+% graph being cut (valid range is 0 to 1, default is 1).
+%
+% opts(4) specifies graph is to be ordered after it is dissected. For the
+% 'sym' case: 0: natural ordering, 1: CAMD, 2: CSYMAMD. For other cases:
+% 0: natural ordering, nonzero: CCOLAMD. The default is 1, to use CAMD for
+% the symmetric case and CCOLAMD for the other cases.
+%
+% If opts is shorter than length 4, defaults are used for entries
+% that are not present.
+%
+% NESDIS uses METIS' node separator algorithm to recursively partition the
+% graph. This gives a set of constraints (cmember) that is then passed to
+% CCOLAMD, CSYMAMD, or CAMD, constrained minimum degree ordering algorithms.
+% NESDIS typically takes slightly more time than METIS (METIS_NodeND), but
+% tends to produce better orderings.
+%
+% Requires METIS, authored by George Karypis, Univ. of Minnesota. This
+% MATLAB interface, via CHOLMOD, is by Tim Davis.
+%
+% See also METIS, BISECT, AMD
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('nesdis mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/rename.h b/CHOLMOD/MATLAB/rename.h
new file mode 100644
index 0000000..bd8aace
--- /dev/null
+++ b/CHOLMOD/MATLAB/rename.h
@@ -0,0 +1,10 @@
+/* do not edit this file; generated by cholmod_make */
+#undef log2
+#include "../../metis-4.0/Lib/rename.h"
+#undef log2
+#define log2 METIS__log2
+#include "mex.h"
+#define malloc mxMalloc
+#define free mxFree
+#define calloc mxCalloc
+#define realloc mxRealloc
diff --git a/CHOLMOD/MATLAB/resymbol.c b/CHOLMOD/MATLAB/resymbol.c
new file mode 100644
index 0000000..83426ee
--- /dev/null
+++ b/CHOLMOD/MATLAB/resymbol.c
@@ -0,0 +1,164 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/resymbol mexFunction ================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Usage:
+ * L = resymbol (L, A)
+ *
+ * Recompute the symbolic Cholesky factorization of the matrix A. A must be
+ * symmetric. Only tril(A) is used. Entries in L that are not in the Cholesky
+ * factorization of A are removed from L. L can be from an LL' or LDL'
+ * factorization. The numerical values of A are ignored; only its nonzero
+ * pattern is used.
+ */
+
+/* ========================================================================== */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0 ;
+ double *Lx, *Lx2, *Lz, *Lz2 ;
+ Int *Li, *Lp, *Lnz2, *Li2, *Lp2, *ColCount ;
+ cholmod_sparse *A, Amatrix, *Lsparse, *S ;
+ cholmod_factor *L ;
+ cholmod_common Common, *cm ;
+ Int j, s, n, lnz, is_complex ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("usage: L = resymbol (L, A)\n") ;
+ }
+
+ n = mxGetN (pargin [0]) ;
+ if (!mxIsSparse (pargin [0]) || n != mxGetM (pargin [0]))
+ {
+ mexErrMsgTxt ("resymbol: L must be sparse and square") ;
+ }
+ if (n != mxGetM (pargin [1]) || n != mxGetN (pargin [1]))
+ {
+ mexErrMsgTxt ("resymbol: A and L must have same dimensions") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the sparse matrix A */
+ /* ---------------------------------------------------------------------- */
+
+ A = sputil_get_sparse_pattern (pargin [1], &Amatrix, &dummy, cm) ;
+ S = (A == &Amatrix) ? NULL : A ;
+
+ A->stype = -1 ;
+
+ /* A = sputil_get_sparse (pargin [1], &Amatrix, &dummy, -1) ; */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct a copy of the input sparse matrix L */
+ /* ---------------------------------------------------------------------- */
+
+ /* get the MATLAB L */
+ Lp = (Int *) mxGetJc (pargin [0]) ;
+ Li = (Int *) mxGetIr (pargin [0]) ;
+ Lx = mxGetPr (pargin [0]) ;
+ Lz = mxGetPi (pargin [0]) ;
+ is_complex = mxIsComplex (pargin [0]) ;
+
+ /* allocate the CHOLMOD symbolic L */
+ L = cholmod_l_allocate_factor (n, cm) ;
+ L->ordering = CHOLMOD_NATURAL ;
+ ColCount = L->ColCount ;
+ for (j = 0 ; j < n ; j++)
+ {
+ ColCount [j] = Lp [j+1] - Lp [j] ;
+ }
+
+ /* allocate space for a CHOLMOD LDL' packed factor */
+ /* (LL' and LDL' are treated identically) */
+ cholmod_l_change_factor (is_complex ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL,
+ FALSE, FALSE, TRUE, TRUE, L, cm) ;
+
+ /* copy MATLAB L into CHOLMOD L */
+ Lp2 = L->p ;
+ Li2 = L->i ;
+ Lx2 = L->x ;
+ Lz2 = L->z ;
+ Lnz2 = L->nz ;
+ lnz = L->nzmax ;
+ for (j = 0 ; j <= n ; j++)
+ {
+ Lp2 [j] = Lp [j] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ Lnz2 [j] = Lp [j+1] - Lp [j] ;
+ }
+ for (s = 0 ; s < lnz ; s++)
+ {
+ Li2 [s] = Li [s] ;
+ }
+ for (s = 0 ; s < lnz ; s++)
+ {
+ Lx2 [s] = Lx [s] ;
+ }
+ if (is_complex)
+ {
+ for (s = 0 ; s < lnz ; s++)
+ {
+ Lz2 [s] = Lz [s] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* resymbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_resymbol (A, NULL, 0, TRUE, L, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the results back to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ Lsparse = cholmod_l_factor_to_sparse (L, cm) ;
+
+ /* return L as a sparse matrix */
+ pargout [0] = sputil_put_sparse (&Lsparse, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free_factor (&L, cm) ;
+ cholmod_l_free_sparse (&S, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != 3 + mxIsComplex (pargout[0])) mexErrMsgTxt ("!") ;
+ */
+}
diff --git a/CHOLMOD/MATLAB/resymbol.m b/CHOLMOD/MATLAB/resymbol.m
new file mode 100644
index 0000000..e80d9d9
--- /dev/null
+++ b/CHOLMOD/MATLAB/resymbol.m
@@ -0,0 +1,19 @@
+function L = resymbol (L, A) %#ok
+%RESYMBOL recomputes the symbolic Cholesky factorization of the matrix A.
+%
+% Example:
+% L = resymbol (L, A)
+%
+% Recompute the symbolic Cholesky factorization of the matrix A. A must be
+% symmetric. Only tril(A) is used. Entries in L that are not in the Cholesky
+% factorization of A are removed from L. L can be from an LL' or LDL'
+% factorization (lchol or ldlchol). resymbol is useful after a series of
+% downdates via ldlupdate, since downdates do not remove any entries in L.
+% The numerical values of A are ignored; only its nonzero pattern is used.
+%
+% See also LCHOL, LDLUPDATE
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('resymbol not found') ;
diff --git a/CHOLMOD/MATLAB/sdmult.c b/CHOLMOD/MATLAB/sdmult.c
new file mode 100644
index 0000000..47dd766
--- /dev/null
+++ b/CHOLMOD/MATLAB/sdmult.c
@@ -0,0 +1,99 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/sdmult mexFunction ==================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Compute C = S*F or S'*F where S is sparse and F is full (C is also sparse).
+ * S and F must both be real or both be complex.
+ *
+ * Usage:
+ *
+ * C = sdmult (S,F) ; C = S*F
+ * C = sdmult (S,F,0) ; C = S*F
+ * C = sdmult (S,F,1) ; C = S'*F
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0, one [2] = {1,0}, zero [2] = {0,0} ;
+ cholmod_sparse *S, Smatrix ;
+ cholmod_dense *F, Fmatrix, *C ;
+ cholmod_common Common, *cm ;
+ Int srow, scol, frow, fcol, crow, transpose ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 1 || nargin < 2 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: C = sdmult (S,F,transpose)") ;
+ }
+
+ srow = mxGetM (pargin [0]) ;
+ scol = mxGetN (pargin [0]) ;
+ frow = mxGetM (pargin [1]) ;
+ fcol = mxGetN (pargin [1]) ;
+
+ transpose = !((nargin == 2) || (mxGetScalar (pargin [2]) == 0)) ;
+
+ if (frow != (transpose ? srow : scol))
+ {
+ mexErrMsgTxt ("invalid inner dimensions") ;
+ }
+
+ if (!mxIsSparse (pargin [0]) || mxIsSparse (pargin [1]))
+ {
+ mexErrMsgTxt ("sdmult (S,F): S must be sparse, F must be full") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get S and F */
+ /* ---------------------------------------------------------------------- */
+
+ S = sputil_get_sparse (pargin [0], &Smatrix, &dummy, 0) ;
+ F = sputil_get_dense (pargin [1], &Fmatrix, &dummy) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = S*F or S'*F */
+ /* ---------------------------------------------------------------------- */
+
+ crow = transpose ? scol : srow ;
+ C = cholmod_l_allocate_dense (crow, fcol, crow, F->xtype, cm) ;
+ cholmod_l_sdmult (S, transpose, one, zero, F, C, cm) ;
+ pargout [0] = sputil_put_dense (&C, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace and the CHOLMOD L, except for what is copied to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != (mxIsComplex (pargout [0]) + 1)) mexErrMsgTxt ("!");
+ */
+}
diff --git a/CHOLMOD/MATLAB/sdmult.m b/CHOLMOD/MATLAB/sdmult.m
new file mode 100644
index 0000000..e49bff9
--- /dev/null
+++ b/CHOLMOD/MATLAB/sdmult.m
@@ -0,0 +1,20 @@
+function C = sdmult (S,F,transpose) %#ok
+%SDMULT sparse matrix times dense matrix
+% Compute C = S*F or S'*F where S is sparse and F is full (C is also sparse).
+% S and F must both be real or both be complex. This function is
+% substantially faster than the MATLAB expression C=S*F when F has many
+% columns.
+%
+% Example:
+% C = sdmult (S,F) ; C = S*F
+% C = sdmult (S,F,0) ; C = S*F
+% C = sdmult (S,F,1) ; C = S'*F
+%
+% See also MTIMES
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('sdmult mexFunction not found') ;
+
+
diff --git a/CHOLMOD/MATLAB/septree.c b/CHOLMOD/MATLAB/septree.c
new file mode 100644
index 0000000..b7bd25b
--- /dev/null
+++ b/CHOLMOD/MATLAB/septree.c
@@ -0,0 +1,141 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/septree mexFunction =================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * METIS (Copyright 1998, G. Karypis) is not distributed with CHOLMOD.
+ * -------------------------------------------------------------------------- */
+
+/* Prune a separator tree.
+ *
+ * Usage:
+ *
+ * [cp_new, cmember_new] = septree (cp, cmember, nd_oksep, nd_small) ;
+ *
+ * cp and cmember are outputs of the nesdis mexFunction.
+ *
+ * cmember(i)=c means that node i is in component
+ * c, where c is in the range of 1 to the number of components. length(cp) is
+ * the number of components found. cp is the separator tree; cp(c) is the
+ * parent of component c, or 0 if c is a root. There can be anywhere from
+ * 1 to n components, where n is the number of rows of A, A*A', or A'*A.
+ *
+ * On output, cp_new and cmember_new are the new tree and graph-to-tree mapping.
+ * A subtree is collapsed into a single node if the number of nodes in the
+ * separator is > nd_oksep times the total size of the subtree, or if the
+ * subtree has fewer than nd_small nodes.
+ *
+ * Requires the CHOLMOD Partition Module.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+#ifndef NPARTITION
+ double *p ;
+ Int *Cmember, *CParent ;
+ cholmod_common Common, *cm ;
+ double nd_oksep ;
+ Int nd_small, nc, n, c, j, nc_new ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set defaults */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 2 || nargin != 4)
+ {
+ mexErrMsgTxt ("Usage: [cp_new, cmember_new] = "
+ "septree (cp, cmember, nd_oksep, nd_small)") ;
+ }
+
+ nc = mxGetNumberOfElements (pargin [0]) ;
+ n = mxGetNumberOfElements (pargin [1]) ;
+ nd_oksep = mxGetScalar (pargin [2]) ;
+ nd_small = mxGetScalar (pargin [3]) ;
+
+ if (n < nc)
+ {
+ mexErrMsgTxt ("invalid inputs") ;
+ }
+
+ CParent = cholmod_l_malloc (nc, sizeof (Int), cm) ;
+ Cmember = cholmod_l_malloc (n, sizeof (Int), cm) ;
+
+ p = mxGetPr (pargin [0]) ;
+ for (c = 0 ; c < nc ; c++)
+ {
+ CParent [c] = p [c] - 1 ;
+ if (CParent [c] < EMPTY || CParent [c] > nc)
+ {
+ mexErrMsgTxt ("cp invalid") ;
+ }
+ }
+
+ p = mxGetPr (pargin [1]) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Cmember [j] = p [j] - 1 ;
+ if (Cmember [j] < 0 || Cmember [j] > nc)
+ {
+ mexErrMsgTxt ("cmember invalid") ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* collapse the tree */
+ /* ---------------------------------------------------------------------- */
+
+ nc_new = cholmod_l_collapse_septree (n, nc, nd_oksep, nd_small, CParent,
+ Cmember, cm) ;
+ if (nc_new < 0)
+ {
+ mexErrMsgTxt ("septree failed") ;
+ return ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return CParent and Cmember */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = sputil_put_int (CParent, nc_new, 1) ;
+ if (nargout > 1)
+ {
+ pargout [1] = sputil_put_int (Cmember, n, 1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free (nc, sizeof (Int), CParent, cm) ;
+ cholmod_l_free (n, sizeof (Int), Cmember, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != 0) mexErrMsgTxt ("!") ;
+ */
+#else
+ mexErrMsgTxt ("CHOLMOD Partition Module not installed\n") ;
+#endif
+}
diff --git a/CHOLMOD/MATLAB/septree.m b/CHOLMOD/MATLAB/septree.m
new file mode 100644
index 0000000..23dc58e
--- /dev/null
+++ b/CHOLMOD/MATLAB/septree.m
@@ -0,0 +1,26 @@
+function [cp_new, cmember_new] = septree (cp, cmember, nd_oksep, nd_small) %#ok
+%SEPTREE prune a separator tree.
+%
+% Example:
+% [cp_new, cmember_new] = septree (cp, cmember, nd_oksep, nd_small) ;
+%
+% cp and cmember are outputs of nesdis. cmember(i)=c means that node i is in
+% component c, where c is in the range of 1 to the number of components.
+% length(cp) is the number of components found. cp is the separator tree;
+% cp(c) is the parent of component c, or 0 if c is a root. There can be
+% anywhere from 1 to n components, where n is the number of rows of A, A*A',
+% or A'*A.
+%
+% On output, cp_new and cmember_new are the new tree and graph-to-tree
+% mapping. A subtree is collapsed into a single node if the number of nodes
+% in the separator is > nd_oksep times the total size of the subtree, or if
+% the subtree has fewer than nd_small nodes.
+%
+% Requires the CHOLMOD Partition Module.
+%
+% See also NESDIS.
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('septree mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/sparse2.c b/CHOLMOD/MATLAB/sparse2.c
new file mode 100644
index 0000000..764a425
--- /dev/null
+++ b/CHOLMOD/MATLAB/sparse2.c
@@ -0,0 +1,18 @@
+/* ========================================================================== */
+/* === MATLAB/sparse2 mexFunction =========================================== */
+/* ========================================================================== */
+
+/* Identical to the "sparse" function in MATLAB, just faster. */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ sputil_sparse (nargout, pargout, nargin, pargin) ;
+}
diff --git a/CHOLMOD/MATLAB/sparse2.m b/CHOLMOD/MATLAB/sparse2.m
new file mode 100644
index 0000000..f19e656
--- /dev/null
+++ b/CHOLMOD/MATLAB/sparse2.m
@@ -0,0 +1,28 @@
+function S = sparse2 (i,j,s,m,n,nzmax) %#ok
+%SPARSE2 replacement for SPARSE
+%
+% Example:
+% S = sparse2 (i,j,s,m,n,nzmax)
+%
+% Identical to the MATLAB sparse function (just faster).
+% An additional feature is added that is not part of the MATLAB sparse
+% function, the Z matrix. With an extra output,
+%
+% [S Z] = sparse2 (i,j,s,m,n,nzmax)
+%
+% the matrix Z is a binary real matrix whose nonzero pattern contains the
+% explicit zero entries that were dropped from S. Z only contains entries
+% for the sparse2(i,j,s,...) usage. [S Z]=sparse2(X) where X is full always
+% returns Z with nnz(Z) = 0, as does [S Z]=sparse2(m,n). More precisely,
+% Z is the following matrix (where ... means the optional m, n, and nzmax
+% parameters).
+%
+% S = sparse (i,j,s, ...)
+% Z = spones (sparse (i,j,1, ...)) - spones (S)
+%
+% See also sparse.
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('sparse2 mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/spsym.c b/CHOLMOD/MATLAB/spsym.c
new file mode 100644
index 0000000..e693852
--- /dev/null
+++ b/CHOLMOD/MATLAB/spsym.c
@@ -0,0 +1,102 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/spsym mexFunction ===================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* [result xmatched pmatched nzoffdiag nzdiag] = spsym (A, quick).
+ * See the spsym.m file for a description of what it computes.
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0 ;
+ cholmod_sparse Amatrix, *A ;
+ cholmod_common Common, *cm ;
+ Int result, quick, option, xmatched, pmatched, nzoffdiag, nzdiag ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set parameters */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin > 2 || nargin < 1 || nargout > 5)
+ {
+ mexErrMsgTxt ("usage: [s xmatch pmatch nzoff nzd] = spsym (A,quick)") ;
+ }
+ if (!mxIsSparse (pargin [0]))
+ {
+ mexErrMsgTxt ("A must be sparse and double") ;
+ }
+
+ /* get sparse matrix A */
+ A = sputil_get_sparse (pargin [0], &Amatrix, &dummy, 0) ;
+
+ /* get the "quick" parameter */
+ quick = (nargin > 1) ? (mxGetScalar (pargin [1]) != 0) : FALSE ;
+
+ if (nargout > 1)
+ {
+ option = 2 ;
+ }
+ else if (quick)
+ {
+ option = 0 ;
+ }
+ else
+ {
+ option = 1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine symmetry */
+ /* ---------------------------------------------------------------------- */
+
+ xmatched = 0 ;
+ pmatched = 0 ;
+ nzoffdiag = 0 ;
+ nzdiag = 0 ;
+
+ result = cholmod_l_symmetry (A, option, &xmatched, &pmatched, &nzoffdiag,
+ &nzdiag, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return results to MATLAB */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = sputil_put_int (&result, 1, 0) ;
+
+ if (nargout > 1) pargout [1] = sputil_put_int (&xmatched, 1, 0) ;
+ if (nargout > 2) pargout [2] = sputil_put_int (&pmatched, 1, 0) ;
+ if (nargout > 3) pargout [3] = sputil_put_int (&nzoffdiag, 1, 0) ;
+ if (nargout > 4) pargout [4] = sputil_put_int (&nzdiag, 1, 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+}
diff --git a/CHOLMOD/MATLAB/spsym.m b/CHOLMOD/MATLAB/spsym.m
new file mode 100644
index 0000000..6221a9b
--- /dev/null
+++ b/CHOLMOD/MATLAB/spsym.m
@@ -0,0 +1,84 @@
+function result = spsym (A, quick) %#ok
+%SPSYM determine if a sparse matrix is symmetric, Hermitian, or skew-symmetric.
+% If so, also determine if its diagonal has all positive real entries.
+% A must be sparse.
+%
+% Example:
+% result = spsym (A) ;
+% result = spsym (A,quick) ;
+%
+% If quick = 0, or is not present, then this routine returns:
+%
+% 1: if A is rectangular
+% 2: if A is unsymmetric
+% 3: if A is symmetric, but with one or more A(j,j) <= 0
+% 4: if A is Hermitian, but with one or more A(j,j) <= 0 or with
+% nonzero imaginary part
+% 5: if A is skew symmetric (and thus the diagonal is all zero as well)
+% 6: if A is symmetric with real positive diagonal
+% 7: if A is Hermitian with real positive diagonal
+%
+% If quick is nonzero, then the function can return more quickly, as soon as
+% it finds a diagonal entry that is <= 0 or with a nonzero imaginary part. In
+% this case, it returns 1, even if the matrix might otherwise be symmetric or
+% Hermitian.
+%
+% Regardless of the value of "quick", this function returns 6 or 7 if A is
+% a candidate for sparse Cholesky.
+%
+% For an MATLAB M-file function that computes the same thing as this
+% mexFunction (but much slower), see the get_symmetry function by typing
+% "type spsym".
+%
+% This spsym function does not compute the transpose of A, nor does it need
+% to examine the entire matrix if it is unsymmetric. It uses very little
+% memory as well (just size-n workspace, where n = size (A,1)).
+%
+% Examples:
+% load west0479
+% A = west0479 ;
+% spsym (A)
+% spsym (A+A')
+% spsym (A-A')
+% spsym (A+A'+3*speye(size(A,1)))
+%
+% See also mldivide.
+
+% function result = get_symmetry (A,quick)
+% %GET_SYMMETRY: does the same thing as the spsym mexFunction.
+% % It's just a lot slower and uses much more memory. This function
+% % is meant for testing and documentation only.
+% [m n] = size (A) ;
+% if (m ~= n)
+% result = 1 ; % rectangular
+% return
+% end
+% if (nargin < 2)
+% quick = 0 ;
+% end
+% d = diag (A) ;
+% posdiag = all (real (d) > 0) & all (imag (d) == 0) ;
+% if (quick & ~posdiag)
+% result = 2 ; % Not a candidate for sparse Cholesky.
+% elseif (~isreal (A) & nnz (A-A') == 0)
+% if (posdiag)
+% result = 7 ; % complex Hermitian, with positive diagonal
+% else
+% result = 4 ; % complex Hermitian, nonpositive diagonal
+% end
+% elseif (nnz (A-A.') == 0)
+% if (posdiag)
+% result = 6 ; % symmetric with positive diagonal
+% else
+% result = 3 ; % symmetric, nonpositive diagonal
+% end
+% elseif (nnz (A+A.') == 0)
+% result = 5 ; % skew symmetric
+% else
+% result = 2 ; % unsymmetric
+% end
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('spsym mexFunction not found') ;
diff --git a/CHOLMOD/MATLAB/symbfact2.c b/CHOLMOD/MATLAB/symbfact2.c
new file mode 100644
index 0000000..c56dda1
--- /dev/null
+++ b/CHOLMOD/MATLAB/symbfact2.c
@@ -0,0 +1,336 @@
+/* ========================================================================== */
+/* === CHOLMOD/MATLAB/symbfact2 mexFunction ================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MATLAB Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MATLAB Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * MATLAB(tm) is a Trademark of The MathWorks, Inc.
+ * -------------------------------------------------------------------------- */
+
+/* Usage:
+ *
+ * count = symbfact2 (A) returns row counts of R=chol(A)
+ * count = symbfact2 (A,'col') returns row counts of R=chol(A'*A)
+ * count = symbfact2 (A,'sym') same as symbfact2(A)
+ * count = symbfact2 (A,'lo') same as symbfact2(A'), uses tril(A)
+ * count = symbfact2 (A,'row') returns row counts of R=chol(A*A')
+ *
+ * [count, h, parent, post, R] = symbfact2 (...)
+ *
+ * h: height of the elimination tree
+ * parent: the elimination tree itself
+ * post: postordering of the elimination tree
+ * R: a 0-1 matrix whose structure is that of chol(A) or chol(A'*A)
+ * for the 'col' case
+ *
+ * symbfact2(A) and symbfact2(A,'sym') uses triu(A).
+ * symbfact2(A,'lo') uses tril(A).
+ *
+ * These forms return L = R' instead of R. They are faster and take less
+ * memory. They return the same count, h, parent, and post outputs.
+ *
+ * [count, h, parent, post, L] = symbfact2 (A,'col','L')
+ * [count, h, parent, post, L] = symbfact2 (A,'sym','L')
+ * [count, h, parent, post, L] = symbfact2 (A,'lo', 'L')
+ * [count, h, parent, post, L] = symbfact2 (A,'row','L')
+ */
+
+#include "cholmod_matlab.h"
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double dummy = 0 ;
+ double *Lx, *px ;
+ Int *Parent, *Post, *ColCount, *First, *Level, *Rp, *Ri, *Lp, *Li, *W ;
+ cholmod_sparse *A, Amatrix, *F, *Aup, *Alo, *R, *A1, *A2, *L, *S ;
+ cholmod_common Common, *cm ;
+ Int n, i, coletree, j, lnz, p, k, height, c ;
+ char buf [LEN] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD and set defaults */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ cholmod_l_start (cm) ;
+ sputil_config (SPUMONI, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 5 || nargin < 1 || nargin > 3)
+ {
+ mexErrMsgTxt (
+ "Usage: [count h parent post R] = symbfact2 (A, mode, Lmode)") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get input matrix A */
+ /* ---------------------------------------------------------------------- */
+
+ A = sputil_get_sparse_pattern (pargin [0], &Amatrix, &dummy, cm) ;
+ S = (A == &Amatrix) ? NULL : A ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get A->stype, default is to use triu(A) */
+ /* ---------------------------------------------------------------------- */
+
+ A->stype = 1 ;
+ n = A->nrow ;
+ coletree = FALSE ;
+ if (nargin > 1)
+ {
+ buf [0] = '\0' ;
+ if (mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], buf, LEN) ;
+ }
+ c = buf [0] ;
+ if (tolower (c) == 'r')
+ {
+ /* unsymmetric case (A*A') if string starts with 'r' */
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 'c')
+ {
+ /* unsymmetric case (A'*A) if string starts with 'c' */
+ n = A->ncol ;
+ coletree = TRUE ;
+ A->stype = 0 ;
+ }
+ else if (tolower (c) == 's')
+ {
+ /* symmetric upper case (A) if string starts with 's' */
+ A->stype = 1 ;
+ }
+ else if (tolower (c) == 'l')
+ {
+ /* symmetric lower case (A) if string starts with 'l' */
+ A->stype = -1 ;
+ }
+ else
+ {
+ mexErrMsgTxt ("symbfact2: unrecognized mode") ;
+ }
+ }
+
+ if (A->stype && A->nrow != A->ncol)
+ {
+ mexErrMsgTxt ("symbfact2: A must be square") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the etree, its postorder, and the row/column counts */
+ /* ---------------------------------------------------------------------- */
+
+ Parent = cholmod_l_malloc (n, sizeof (Int), cm) ;
+ Post = cholmod_l_malloc (n, sizeof (Int), cm) ;
+ ColCount = cholmod_l_malloc (n, sizeof (Int), cm) ;
+ First = cholmod_l_malloc (n, sizeof (Int), cm) ;
+ Level = cholmod_l_malloc (n, sizeof (Int), cm) ;
+
+ /* F = A' */
+ F = cholmod_l_transpose (A, 0, cm) ;
+
+ if (A->stype == 1 || coletree)
+ {
+ /* symmetric upper case: find etree of A, using triu(A) */
+ /* column case: find column etree of A, which is etree of A'*A */
+ Aup = A ;
+ Alo = F ;
+ }
+ else
+ {
+ /* symmetric lower case: find etree of A, using tril(A) */
+ /* row case: find row etree of A, which is etree of A*A' */
+ Aup = F ;
+ Alo = A ;
+ }
+
+ cholmod_l_etree (Aup, Parent, cm) ;
+
+ if (cm->status < CHOLMOD_OK)
+ {
+ /* out of memory or matrix invalid */
+ mexErrMsgTxt ("symbfact2 failed: matrix corrupted!") ;
+ }
+
+ if (cholmod_l_postorder (Parent, n, NULL, Post, cm) != n)
+ {
+ /* out of memory or Parent invalid */
+ mexErrMsgTxt ("symbfact2 postorder failed!") ;
+ }
+
+ /* symmetric upper case: analyze tril(F), which is triu(A) */
+ /* column case: analyze F*F', which is A'*A */
+ /* symmetric lower case: analyze tril(A) */
+ /* row case: analyze A*A' */
+ cholmod_l_rowcolcounts (Alo, NULL, 0, Parent, Post, NULL, ColCount,
+ First, Level, cm) ;
+
+ if (cm->status < CHOLMOD_OK)
+ {
+ /* out of memory or matrix invalid */
+ mexErrMsgTxt ("symbfact2 failed: matrix corrupted!") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return results to MATLAB: count, h, parent, and post */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = sputil_put_int (ColCount, n, 0) ;
+ if (nargout > 1)
+ {
+ /* compute the elimination tree height */
+ height = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ height = MAX (height, Level [i]) ;
+ }
+ height++ ;
+ pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ px = mxGetPr (pargout [1]) ;
+ px [0] = height ;
+ }
+ if (nargout > 2)
+ {
+ pargout [2] = sputil_put_int (Parent, n, 1) ;
+ }
+ if (nargout > 3)
+ {
+ pargout [3] = sputil_put_int (Post, n, 1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct L, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 4)
+ {
+
+ if (A->stype == 1)
+ {
+ /* symmetric upper case: use triu(A) only, A2 not needed */
+ A1 = A ;
+ A2 = NULL ;
+ }
+ else if (A->stype == -1)
+ {
+ /* symmetric lower case: use tril(A) only, A2 not needed */
+ A1 = F ;
+ A2 = NULL ;
+ }
+ else if (coletree)
+ {
+ /* column case: analyze F*F' */
+ A1 = F ;
+ A2 = A ;
+ }
+ else
+ {
+ /* row case: analyze A*A' */
+ A1 = A ;
+ A2 = F ;
+ }
+
+ /* count the total number of entries in L */
+ lnz = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ lnz += ColCount [j] ;
+ }
+
+ /* allocate the output matrix L (pattern-only) */
+ L = cholmod_l_allocate_sparse (n, n, lnz, TRUE, TRUE, 0,
+ CHOLMOD_PATTERN, cm) ;
+ Lp = L->p ;
+ Li = L->i ;
+
+ /* initialize column pointers */
+ lnz = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Lp [j] = lnz ;
+ lnz += ColCount [j] ;
+ }
+ Lp [j] = lnz ;
+
+ /* create a copy of the column pointers */
+ W = First ;
+ for (j = 0 ; j < n ; j++)
+ {
+ W [j] = Lp [j] ;
+ }
+
+ /* get workspace for computing one row of L */
+ R = cholmod_l_allocate_sparse (n, 1, n, FALSE, TRUE, 0, CHOLMOD_PATTERN,
+ cm) ;
+ Rp = R->p ;
+ Ri = R->i ;
+
+ /* compute L one row at a time */
+ for (k = 0 ; k < n ; k++)
+ {
+ /* get the kth row of L and store in the columns of L */
+ cholmod_l_row_subtree (A1, A2, k, Parent, R, cm) ;
+ for (p = 0 ; p < Rp [1] ; p++)
+ {
+ Li [W [Ri [p]]++] = k ;
+ }
+ /* add the diagonal entry */
+ Li [W [k]++] = k ;
+ }
+
+ /* free workspace */
+ cholmod_l_free_sparse (&R, cm) ;
+
+ /* transpose L to get R, or leave as is */
+ if (nargin < 3)
+ {
+ /* R = L' */
+ R = cholmod_l_transpose (L, 0, cm) ;
+ cholmod_l_free_sparse (&L, cm) ;
+ L = R ;
+ }
+
+ /* fill numerical values of L with one's (only MATLAB needs this...) */
+ L->x = cholmod_l_malloc (lnz, sizeof (double), cm) ;
+ Lx = L->x ;
+ for (p = 0 ; p < lnz ; p++)
+ {
+ Lx [p] = 1 ;
+ }
+ L->xtype = CHOLMOD_REAL ;
+
+ /* return L (or R) to MATLAB */
+ pargout [4] = sputil_put_sparse (&L, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ cholmod_l_free (n, sizeof (Int), Parent, cm) ;
+ cholmod_l_free (n, sizeof (Int), Post, cm) ;
+ cholmod_l_free (n, sizeof (Int), ColCount, cm) ;
+ cholmod_l_free (n, sizeof (Int), First, cm) ;
+ cholmod_l_free (n, sizeof (Int), Level, cm) ;
+ cholmod_l_free_sparse (&F, cm) ;
+ cholmod_l_free_sparse (&S, cm) ;
+ cholmod_l_finish (cm) ;
+ cholmod_l_print_common (" ", cm) ;
+ /*
+ if (cm->malloc_count != ((nargout == 5) ? 3:0)) mexErrMsgTxt ("!") ;
+ */
+}
diff --git a/CHOLMOD/MATLAB/symbfact2.m b/CHOLMOD/MATLAB/symbfact2.m
new file mode 100644
index 0000000..f8348b4
--- /dev/null
+++ b/CHOLMOD/MATLAB/symbfact2.m
@@ -0,0 +1,48 @@
+function [count, h, parent, post, L] = symbfact2 (A, mode, Lmode) %#ok
+%SYMBFACT2 symbolic factorization
+%
+% Analyzes the Cholesky factorization of A, A'*A, or A*A'.
+%
+% Example:
+% count = symbfact2 (A) returns row counts of R=chol(A)
+% count = symbfact2 (A,'col') returns row counts of R=chol(A'*A)
+% count = symbfact2 (A,'sym') same as symbfact2(A)
+% count = symbfact2 (A,'lo') same as symbfact2(A'), uses tril(A)
+% count = symbfact2 (A,'row') returns row counts of R=chol(A*A')
+%
+% The flop count for a subsequent LL' factorization is sum(count.^2)
+%
+% [count, h, parent, post, R] = symbfact2 (...) returns:
+%
+% h: height of the elimination tree
+% parent: the elimination tree itself
+% post: postordering of the elimination tree
+% R: a 0-1 matrix whose structure is that of chol(A) for the symmetric
+% case, chol(A'*A) for the 'col' case, or chol(A*A') for the
+% 'row' case.
+%
+% symbfact2(A) and symbfact2(A,'sym') uses the upper triangular part of A
+% (triu(A)) and assumes the lower triangular part is the transpose of
+% the upper triangular part. symbfact2(A,'lo') uses tril(A) instead.
+%
+% With one to four output arguments, symbfact2 takes time almost proportional
+% to nnz(A)+n where n is the dimension of R, and memory proportional to
+% nnz(A). Computing the 5th argument takes more time and memory, both
+% O(nnz(L)). Internally, the pattern of L is computed and R=L' is returned.
+%
+% The following forms return L = R' instead of R. They are faster and take
+% less memory than the forms above. They return the same count, h, parent,
+% and post outputs.
+%
+% [count, h, parent, post, L] = symbfact2 (A,'col','L')
+% [count, h, parent, post, L] = symbfact2 (A,'sym','L')
+% [count, h, parent, post, L] = symbfact2 (A,'lo', 'L')
+% [count, h, parent, post, L] = symbfact2 (A,'row','L')
+%
+% See also CHOL, ETREE, TREELAYOUT, SYMBFACT
+
+% Copyright 2006-2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+error ('symbfact2 mexFunction not found!') ;
+
diff --git a/CHOLMOD/Makefile b/CHOLMOD/Makefile
new file mode 100644
index 0000000..1916688
--- /dev/null
+++ b/CHOLMOD/Makefile
@@ -0,0 +1,59 @@
+#-------------------------------------------------------------------------------
+# CHOLMOD Makefile
+#-------------------------------------------------------------------------------
+
+# Note: If you do not have METIS, or do not wish to use it in CHOLMOD, you must
+# compile CHOLMOD with the -DNPARTITION flag. See ../UFconfig/UFconfig.mk.
+
+default: all
+
+include ../UFconfig/UFconfig.mk
+
+# Compile the C-callable libraries and the Demo programs.
+all:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+# Compile the C-callable libraries only.
+library:
+ ( cd Lib ; $(MAKE) )
+
+# Remove all files not in the original distribution
+purge:
+ ( cd MATLAB ; $(MAKE) purge )
+ ( cd Tcov ; $(MAKE) purge )
+ ( cd Lib ; $(MAKE) purge )
+# ( cd Valgrind ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd Doc ; $(MAKE) purge )
+
+# Remove all files not in the original distribution, except keep the
+# compiled libraries.
+clean:
+ ( cd MATLAB ; $(MAKE) clean )
+ ( cd Tcov ; $(MAKE) clean )
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Valgrind ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+
+distclean: purge
+
+ccode: all
+
+# Compile the MATLAB mexFunctions (you can also use cholmod_make.m in MATLAB)
+mex:
+ ( cd MATLAB ; $(MAKE) )
+
+# Run the test coverage suite. Takes about 40 minutes on a 3.2GHz Pentium.
+# Requires Linux (gcc, gcov).
+cov:
+ ( cd Tcov ; $(MAKE) go )
+
+# Run the test coverage suite using Valgrind. This takes a *** long *** time.
+valgrind:
+ ( cd Valgrind ; $(MAKE) )
+
+# Compile the C-callable libraries and the Demo programs.
+demo:
+ ( cd Demo ; $(MAKE) )
+
diff --git a/CHOLMOD/MatrixOps/License.txt b/CHOLMOD/MatrixOps/License.txt
new file mode 100644
index 0000000..3db84d9
--- /dev/null
+++ b/CHOLMOD/MatrixOps/License.txt
@@ -0,0 +1,25 @@
+CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006,
+Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/MatrixOps module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
diff --git a/CHOLMOD/MatrixOps/cholmod_drop.c b/CHOLMOD/MatrixOps/cholmod_drop.c
new file mode 100644
index 0000000..adba83d
--- /dev/null
+++ b/CHOLMOD/MatrixOps/cholmod_drop.c
@@ -0,0 +1,183 @@
+/* ========================================================================== */
+/* === MatrixOps/cholmod_drop =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Drop small entries from A, and entries in the ignored part of A if A
+ * is symmetric. None of the matrix operations drop small numerical entries
+ * from a matrix, except for this one. NaN's and Inf's are kept.
+ *
+ * workspace: none
+ *
+ * Supports pattern and real matrices, complex and zomplex not supported.
+ */
+
+#ifndef NMATRIXOPS
+
+#include "cholmod_internal.h"
+#include "cholmod_matrixops.h"
+
+
+/* ========================================================================== */
+/* === cholmod_drop ========================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(drop)
+(
+ /* ---- input ---- */
+ double tol, /* keep entries with absolute value > tol */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to drop entries from */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double aij ;
+ double *Ax ;
+ Int *Ap, *Ai, *Anz ;
+ Int packed, i, j, nrow, ncol, p, pend, nz, values ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ ASSERT (CHOLMOD(dump_sparse) (A, "A predrop", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ ncol = A->ncol ;
+ nrow = A->nrow ;
+ values = (A->xtype != CHOLMOD_PATTERN) ;
+ nz = 0 ;
+
+ if (values)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* drop small numerical entries from A, and entries in ignored part */
+ /* ------------------------------------------------------------------ */
+
+ if (A->stype > 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* A is symmetric, with just upper triangular part stored */
+ /* -------------------------------------------------------------- */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Ap [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ aij = Ax [p] ;
+ if (i <= j && (fabs (aij) > tol || IS_NAN (aij)))
+ {
+ Ai [nz] = i ;
+ Ax [nz] = aij ;
+ nz++ ;
+ }
+ }
+ }
+
+ }
+ else if (A->stype < 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* A is symmetric, with just lower triangular part stored */
+ /* -------------------------------------------------------------- */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Ap [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ aij = Ax [p] ;
+ if (i >= j && (fabs (aij) > tol || IS_NAN (aij)))
+ {
+ Ai [nz] = i ;
+ Ax [nz] = aij ;
+ nz++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* both parts of A present, just drop small entries */
+ /* -------------------------------------------------------------- */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Ap [j] = nz ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ aij = Ax [p] ;
+ if (fabs (aij) > tol || IS_NAN (aij))
+ {
+ Ai [nz] = i ;
+ Ax [nz] = aij ;
+ nz++ ;
+ }
+ }
+ }
+ }
+ Ap [ncol] = nz ;
+
+ /* reduce A->i and A->x in size */
+ ASSERT (MAX (1,nz) <= A->nzmax) ;
+ CHOLMOD(reallocate_sparse) (nz, A, Common) ;
+ ASSERT (Common->status >= CHOLMOD_OK) ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* consider only the pattern of A */
+ /* ------------------------------------------------------------------ */
+
+ /* Note that cholmod_band_inplace calls cholmod_reallocate_sparse */
+ if (A->stype > 0)
+ {
+ CHOLMOD(band_inplace) (0, ncol, 0, A, Common) ;
+ }
+ else if (A->stype < 0)
+ {
+ CHOLMOD(band_inplace) (-nrow, 0, 0, A, Common) ;
+ }
+ }
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "A dropped", Common) >= 0) ;
+ return (TRUE) ;
+}
+#endif
diff --git a/CHOLMOD/MatrixOps/cholmod_horzcat.c b/CHOLMOD/MatrixOps/cholmod_horzcat.c
new file mode 100644
index 0000000..0c731a0
--- /dev/null
+++ b/CHOLMOD/MatrixOps/cholmod_horzcat.c
@@ -0,0 +1,203 @@
+/* ========================================================================== */
+/* === MatrixOps/cholmod_horzcat ============================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Horizontal concatenation, C = [A , B] in MATLAB notation.
+ *
+ * A and B can be up/lo/unsym; C is unsymmetric and packed.
+ * A and B must have the same number of rows.
+ * C is sorted if both A and B are sorted.
+ *
+ * workspace: Iwork (max (A->nrow, A->ncol, B->nrow, B->ncol)).
+ * allocates temporary copies of A and B if they are symmetric.
+ *
+ * A and B must have the same numeric xtype, unless values is FALSE.
+ * A and B cannot be complex or zomplex, unless values is FALSE.
+ */
+
+#ifndef NMATRIXOPS
+
+#include "cholmod_internal.h"
+#include "cholmod_matrixops.h"
+
+
+/* ========================================================================== */
+/* === cholmod_horzcat ====================================================== */
+/* ========================================================================== */
+
+cholmod_sparse *CHOLMOD(horzcat)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* left matrix to concatenate */
+ cholmod_sparse *B, /* right matrix to concatenate */
+ int values, /* if TRUE compute the numerical values of C */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Bx, *Cx ;
+ Int *Ap, *Ai, *Anz, *Bp, *Bi, *Bnz, *Cp, *Ci ;
+ cholmod_sparse *C, *A2, *B2 ;
+ Int apacked, bpacked, ancol, bncol, ncol, nrow, anz, bnz, nz, j, p, pend,
+ pdest ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_NULL (B, NULL) ;
+ values = values &&
+ (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->nrow != B->nrow)
+ {
+ /* A and B must have the same number of rows */
+ ERROR (CHOLMOD_INVALID, "A and B must have same # rows") ;
+ return (NULL) ;
+ }
+ /* A and B must have the same numerical type if values is TRUE (both must
+ * be CHOLMOD_REAL, this is implicitly checked above) */
+
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ ancol = A->ncol ;
+ bncol = B->ncol ;
+ nrow = A->nrow ;
+ CHOLMOD(allocate_work) (0, MAX3 (nrow, ancol, bncol), 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* convert A to unsymmetric, if necessary */
+ A2 = NULL ;
+ if (A->stype != 0)
+ {
+ /* workspace: Iwork (max (A->nrow,A->ncol)) */
+ A2 = CHOLMOD(copy) (A, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+ A = A2 ;
+ }
+
+ /* convert B to unsymmetric, if necessary */
+ B2 = NULL ;
+ if (B->stype != 0)
+ {
+ /* workspace: Iwork (max (B->nrow,B->ncol)) */
+ B2 = CHOLMOD(copy) (B, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ return (NULL) ;
+ }
+ B = B2 ;
+ }
+
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ apacked = A->packed ;
+
+ Bp = B->p ;
+ Bnz = B->nz ;
+ Bi = B->i ;
+ Bx = B->x ;
+ bpacked = B->packed ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate C */
+ /* ---------------------------------------------------------------------- */
+
+ anz = CHOLMOD(nnz) (A, Common) ;
+ bnz = CHOLMOD(nnz) (B, Common) ;
+ ncol = ancol + bncol ;
+ nz = anz + bnz ;
+
+ C = CHOLMOD(allocate_sparse) (nrow, ncol, nz, A->sorted && B->sorted, TRUE,
+ 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ return (NULL) ;
+ }
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = [A , B] */
+ /* ---------------------------------------------------------------------- */
+
+ pdest = 0 ;
+
+ /* copy A as the first A->ncol columns of C */
+ for (j = 0 ; j < ancol ; j++)
+ {
+ /* A(:,j) is the jth column of C */
+ p = Ap [j] ;
+ pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cp [j] = pdest ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [pdest] = Ai [p] ;
+ if (values) Cx [pdest] = Ax [p] ;
+ pdest++ ;
+ }
+ }
+
+ /* copy B as the next B->ncol columns of C */
+ for (j = 0 ; j < bncol ; j++)
+ {
+ /* B(:,j) is the (ancol+j)th column of C */
+ p = Bp [j] ;
+ pend = (bpacked) ? (Bp [j+1]) : (p + Bnz [j]) ;
+ Cp [ancol + j] = pdest ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [pdest] = Bi [p] ;
+ if (values) Cx [pdest] = Bx [p] ;
+ pdest++ ;
+ }
+ }
+ Cp [ncol] = pdest ;
+ ASSERT (pdest == anz + bnz) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the unsymmetric copies of A and B, and return C */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ return (C) ;
+}
+#endif
diff --git a/CHOLMOD/MatrixOps/cholmod_norm.c b/CHOLMOD/MatrixOps/cholmod_norm.c
new file mode 100644
index 0000000..d4ed600
--- /dev/null
+++ b/CHOLMOD/MatrixOps/cholmod_norm.c
@@ -0,0 +1,452 @@
+/* ========================================================================== */
+/* === MatrixOps/cholmod_norm =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* r = norm (A), compute the infinity-norm, 1-norm, or 2-norm of a sparse or
+ * dense matrix. Can compute the 2-norm only for a dense column vector.
+ * Returns -1 if an error occurs.
+ *
+ * Pattern, real, complex, and zomplex sparse matrices are supported.
+ */
+
+#ifndef NMATRIXOPS
+
+#include "cholmod_internal.h"
+#include "cholmod_matrixops.h"
+
+
+/* ========================================================================== */
+/* === abs_value ============================================================ */
+/* ========================================================================== */
+
+/* Compute the absolute value of a real, complex, or zomplex value */
+
+static double abs_value
+(
+ int xtype,
+ double *Ax,
+ double *Az,
+ Int p,
+ cholmod_common *Common
+)
+{
+ double s = 0 ;
+ switch (xtype)
+ {
+ case CHOLMOD_PATTERN:
+ s = 1 ;
+ break ;
+
+ case CHOLMOD_REAL:
+ s = fabs (Ax [p]) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ s = Common->hypotenuse (Ax [2*p], Ax [2*p+1]) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ s = Common->hypotenuse (Ax [p], Az [p]) ;
+ break ;
+ }
+ return (s) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_norm_dense =================================================== */
+/* ========================================================================== */
+
+double CHOLMOD(norm_dense)
+(
+ /* ---- input ---- */
+ cholmod_dense *X, /* matrix to compute the norm of */
+ int norm, /* type of norm: 0: inf. norm, 1: 1-norm, 2: 2-norm */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double xnorm, s, x, z ;
+ double *Xx, *Xz, *W ;
+ Int nrow, ncol, d, i, j, use_workspace, xtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (X, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+ ncol = X->ncol ;
+ if (norm < 0 || norm > 2 || (norm == 2 && ncol > 1))
+ {
+ ERROR (CHOLMOD_INVALID, "invalid norm") ;
+ return (EMPTY) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = X->nrow ;
+ d = X->d ;
+ Xx = X->x ;
+ Xz = X->z ;
+ xtype = X->xtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace, if needed */
+ /* ---------------------------------------------------------------------- */
+
+ W = NULL ;
+ use_workspace = (norm == 0 && ncol > 4) ;
+ if (use_workspace)
+ {
+ CHOLMOD(allocate_work) (0, 0, nrow, Common) ;
+ W = Common->Xwork ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* oops, no workspace */
+ use_workspace = FALSE ;
+ }
+ }
+
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the norm */
+ /* ---------------------------------------------------------------------- */
+
+ xnorm = 0 ;
+
+ if (use_workspace)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* infinity-norm = max row sum, using stride-1 access of X */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG (for (i = 0 ; i < nrow ; i++) ASSERT (W [i] == 0)) ;
+
+ /* this is faster than stride-d, but requires O(nrow) workspace */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ W [i] += abs_value (xtype, Xx, Xz, i+j*d, Common) ;
+ }
+ }
+ for (i = 0 ; i < nrow ; i++)
+ {
+ s = W [i] ;
+ if ((IS_NAN (s) || s > xnorm) && !IS_NAN (xnorm))
+ {
+ xnorm = s ;
+ }
+ W [i] = 0 ;
+ }
+
+ }
+ else if (norm == 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* infinity-norm = max row sum, using stride-d access of X */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < nrow ; i++)
+ {
+ s = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ s += abs_value (xtype, Xx, Xz, i+j*d, Common) ;
+ }
+ if ((IS_NAN (s) || s > xnorm) && !IS_NAN (xnorm))
+ {
+ xnorm = s ;
+ }
+ }
+
+ }
+ else if (norm == 1)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* 1-norm = max column sum */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ s = 0 ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ s += abs_value (xtype, Xx, Xz, i+j*d, Common) ;
+ }
+ if ((IS_NAN (s) || s > xnorm) && !IS_NAN (xnorm))
+ {
+ xnorm = s ;
+ }
+ }
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* 2-norm = sqrt (sum (X.^2)) */
+ /* ------------------------------------------------------------------ */
+
+ switch (xtype)
+ {
+
+ case CHOLMOD_REAL:
+ for (i = 0 ; i < nrow ; i++)
+ {
+ x = Xx [i] ;
+ xnorm += x*x ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < nrow ; i++)
+ {
+ x = Xx [2*i ] ;
+ z = Xx [2*i+1] ;
+ xnorm += x*x + z*z ;
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < nrow ; i++)
+ {
+ x = Xx [i] ;
+ z = Xz [i] ;
+ xnorm += x*x + z*z ;
+ }
+ break ;
+ }
+
+ xnorm = sqrt (xnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ return (xnorm) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_norm_sparse ================================================== */
+/* ========================================================================== */
+
+double CHOLMOD(norm_sparse)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to compute the norm of */
+ int norm, /* type of norm: 0: inf. norm, 1: 1-norm */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double anorm, s ;
+ double *Ax, *Az, *W ;
+ Int *Ap, *Ai, *Anz ;
+ Int i, j, p, pend, nrow, ncol, packed, xtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (A, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+ ncol = A->ncol ;
+ nrow = A->nrow ;
+ if (norm < 0 || norm > 1)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid norm") ;
+ return (EMPTY) ;
+ }
+ if (A->stype && nrow != ncol)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix invalid") ;
+ return (EMPTY) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ xtype = A->xtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace, if needed */
+ /* ---------------------------------------------------------------------- */
+
+ W = NULL ;
+ if (A->stype || norm == 0)
+ {
+ CHOLMOD(allocate_work) (0, 0, nrow, Common) ;
+ W = Common->Xwork ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (EMPTY) ;
+ }
+ DEBUG (for (i = 0 ; i < nrow ; i++) ASSERT (W [i] == 0)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the norm */
+ /* ---------------------------------------------------------------------- */
+
+ anorm = 0 ;
+
+ if (A->stype > 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A is symmetric with upper triangular part stored */
+ /* ------------------------------------------------------------------ */
+
+ /* infinity-norm = 1-norm = max row/col sum */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ s = abs_value (xtype, Ax, Az, p, Common) ;
+ if (i == j)
+ {
+ W [i] += s ;
+ }
+ else if (i < j)
+ {
+ W [i] += s ;
+ W [j] += s ;
+ }
+ }
+ }
+
+ }
+ else if (A->stype < 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A is symmetric with lower triangular part stored */
+ /* ------------------------------------------------------------------ */
+
+ /* infinity-norm = 1-norm = max row/col sum */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ s = abs_value (xtype, Ax, Az, p, Common) ;
+ if (i == j)
+ {
+ W [i] += s ;
+ }
+ else if (i > j)
+ {
+ W [i] += s ;
+ W [j] += s ;
+ }
+ }
+ }
+
+ }
+ else if (norm == 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A is unsymmetric, compute the infinity-norm */
+ /* ------------------------------------------------------------------ */
+
+ /* infinity-norm = max row sum */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ W [Ai [p]] += abs_value (xtype, Ax, Az, p, Common) ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A is unsymmetric, compute the 1-norm */
+ /* ------------------------------------------------------------------ */
+
+ /* 1-norm = max column sum */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ if (xtype == CHOLMOD_PATTERN)
+ {
+ s = pend - p ;
+ }
+ else
+ {
+ s = 0 ;
+ for ( ; p < pend ; p++)
+ {
+ s += abs_value (xtype, Ax, Az, p, Common) ;
+ }
+ }
+ if ((IS_NAN (s) || s > anorm) && !IS_NAN (anorm))
+ {
+ anorm = s ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the max row sum */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype || norm == 0)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ s = W [i] ;
+ if ((IS_NAN (s) || s > anorm) && !IS_NAN (anorm))
+ {
+ anorm = s ;
+ }
+ W [i] = 0 ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ return (anorm) ;
+}
+#endif
diff --git a/CHOLMOD/MatrixOps/cholmod_scale.c b/CHOLMOD/MatrixOps/cholmod_scale.c
new file mode 100644
index 0000000..22bc249
--- /dev/null
+++ b/CHOLMOD/MatrixOps/cholmod_scale.c
@@ -0,0 +1,217 @@
+/* ========================================================================== */
+/* === MatrixOps/cholmod_scale ============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* scale a matrix: A = diag(s)*A, A*diag(s), s*A, or diag(s)*A*diag(s)
+ *
+ * A can be of any type (packed/unpacked, upper/lower/unsymmetric).
+ * The symmetry of A is ignored; all entries in the matrix are modified.
+ *
+ * If A is m-by-n unsymmetric but scaled symmtrically, the result is
+ * A = diag (s (1:m)) * A * diag (s (1:n)).
+ *
+ * Note: diag(s) should be interpretted as spdiags(s,0,n,n) where n=length(s).
+ *
+ * Row or column scaling of a symmetric matrix still results in a symmetric
+ * matrix, since entries are still ignored by other routines.
+ * For example, when row-scaling a symmetric matrix where just the upper
+ * triangular part is stored (and lower triangular entries ignored)
+ * A = diag(s)*triu(A) is performed, where the result A is also
+ * symmetric-upper. This has the effect of modifying the implicit lower
+ * triangular part. In MATLAB notation:
+ *
+ * U = diag(s)*triu(A) ;
+ * L = tril (U',-1)
+ * A = L + U ;
+ *
+ * The scale parameter determines the kind of scaling to perform:
+ *
+ * CHOLMOD_SCALAR: s[0]*A
+ * CHOLMOD_ROW: diag(s)*A
+ * CHOLMOD_COL: A*diag(s)
+ * CHOLMOD_SYM: diag(s)*A*diag(s)
+ *
+ * The size of S depends on the scale parameter:
+ *
+ * CHOLMOD_SCALAR: size 1
+ * CHOLMOD_ROW: size nrow-by-1 or 1-by-nrow
+ * CHOLMOD_COL: size ncol-by-1 or 1-by-ncol
+ * CHOLMOD_SYM: size max(nrow,ncol)-by-1, or 1-by-max(nrow,ncol)
+ *
+ * workspace: none
+ *
+ * Only real matrices are supported.
+ */
+
+#ifndef NMATRIXOPS
+
+#include "cholmod_internal.h"
+#include "cholmod_matrixops.h"
+
+
+/* ========================================================================== */
+/* === cholmod_scale ======================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(scale)
+(
+ /* ---- input ---- */
+ cholmod_dense *S, /* scale factors (scalar or vector) */
+ int scale, /* type of scaling to compute */
+ /* ---- in/out --- */
+ cholmod_sparse *A, /* matrix to scale */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double t ;
+ double *Ax, *s ;
+ Int *Ap, *Anz, *Ai ;
+ Int packed, j, ncol, nrow, p, pend, sncol, snrow, nn, ok ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (S, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (S, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ;
+ ncol = A->ncol ;
+ nrow = A->nrow ;
+ sncol = S->ncol ;
+ snrow = S->nrow ;
+ if (scale == CHOLMOD_SCALAR)
+ {
+ ok = (snrow == 1 && sncol == 1) ;
+ }
+ else if (scale == CHOLMOD_ROW)
+ {
+ ok = (snrow == nrow && sncol == 1) || (snrow == 1 && sncol == nrow) ;
+ }
+ else if (scale == CHOLMOD_COL)
+ {
+ ok = (snrow == ncol && sncol == 1) || (snrow == 1 && sncol == ncol) ;
+ }
+ else if (scale == CHOLMOD_SYM)
+ {
+ nn = MAX (nrow, ncol) ;
+ ok = (snrow == nn && sncol == 1) || (snrow == 1 && sncol == nn) ;
+ }
+ else
+ {
+ /* scale invalid */
+ ERROR (CHOLMOD_INVALID, "invalid scaling option") ;
+ return (FALSE) ;
+ }
+ if (!ok)
+ {
+ /* S is wrong size */
+ ERROR (CHOLMOD_INVALID, "invalid scale factors") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ packed = A->packed ;
+ s = S->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* scale the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (scale == CHOLMOD_ROW)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A = diag(s)*A, row scaling */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Ax [p] *= s [Ai [p]] ;
+ }
+ }
+
+ }
+ else if (scale == CHOLMOD_COL)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A = A*diag(s), column scaling */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ t = s [j] ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Ax [p] *= t ;
+ }
+ }
+
+ }
+ else if (scale == CHOLMOD_SYM)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A = diag(s)*A*diag(s), symmetric scaling */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ t = s [j] ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Ax [p] *= t * s [Ai [p]] ;
+ }
+ }
+
+ }
+ else if (scale == CHOLMOD_SCALAR)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* A = s[0] * A, scalar scaling */
+ /* ------------------------------------------------------------------ */
+
+ t = s [0] ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Ax [p] *= t ;
+ }
+ }
+ }
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "A scaled", Common) >= 0) ;
+ return (TRUE) ;
+}
+#endif
diff --git a/CHOLMOD/MatrixOps/cholmod_sdmult.c b/CHOLMOD/MatrixOps/cholmod_sdmult.c
new file mode 100644
index 0000000..6e85174
--- /dev/null
+++ b/CHOLMOD/MatrixOps/cholmod_sdmult.c
@@ -0,0 +1,149 @@
+/* ========================================================================== */
+/* === MatrixOps/cholmod_sdmult ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Sparse matrix times dense matrix:
+ * Y = alpha*(A*X) + beta*Y or Y = alpha*(A'*X) + beta*Y,
+ * where A is sparse and X and Y are dense.
+ *
+ * when using A, X has A->ncol columns and Y has A->nrow rows
+ * when using A', X has A->nrow columns and Y has A->ncol rows
+ *
+ * workspace: none in Common. Temporary workspace of size 4*(X->nrow) is used
+ * if A is stored in symmetric form and X has four columns or more. If the
+ * workspace is not available, a slower method is used instead that requires
+ * no workspace.
+ *
+ * transpose = 0: use A
+ * otherwise, use A' (complex conjugate transpose)
+ *
+ * transpose is ignored if the matrix is symmetric or Hermitian.
+ * (the array transpose A.' is not supported).
+ *
+ * Supports real, complex, and zomplex matrices, but the xtypes of A, X, and Y
+ * must all match.
+ */
+
+#ifndef NMATRIXOPS
+
+#include "cholmod_internal.h"
+#include "cholmod_matrixops.h"
+
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_sdmult.c"
+#define COMPLEX
+#include "t_cholmod_sdmult.c"
+#define ZOMPLEX
+#include "t_cholmod_sdmult.c"
+
+/* ========================================================================== */
+/* === cholmod_sdmult ======================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(sdmult)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to multiply */
+ int transpose, /* use A if 0, otherwise use A' */
+ double alpha [2], /* scale factor for A */
+ double beta [2], /* scale factor for Y */
+ cholmod_dense *X, /* dense matrix to multiply */
+ /* ---- in/out --- */
+ cholmod_dense *Y, /* resulting dense matrix */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *w ;
+ size_t nx, ny ;
+ Int e ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (X, FALSE) ;
+ RETURN_IF_NULL (Y, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (Y, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ ny = transpose ? A->ncol : A->nrow ; /* required length of Y */
+ nx = transpose ? A->nrow : A->ncol ; /* required length of X */
+ if (X->nrow != nx || X->ncol != Y->ncol || Y->nrow != ny)
+ {
+ /* X and/or Y have the wrong dimension */
+ ERROR (CHOLMOD_INVALID, "X and/or Y have wrong dimensions") ;
+ return (FALSE) ;
+ }
+ if (A->xtype != X->xtype || A->xtype != Y->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "A, X, and Y must have same xtype") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace, if required */
+ /* ---------------------------------------------------------------------- */
+
+ w = NULL ;
+ e = (A->xtype == CHOLMOD_REAL ? 1:2) ;
+ if (A->stype && X->ncol >= 4)
+ {
+ w = CHOLMOD(malloc) (nx, 4*e*sizeof (double), Common) ;
+ }
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Y = alpha*op(A)*X + beta*Y via template routine */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ;
+ DEBUG (CHOLMOD(dump_dense) (X, "X", Common)) ;
+ DEBUG (if (IS_NONZERO (beta [0])
+ || (IS_NONZERO (beta [1]) && A->xtype != CHOLMOD_REAL))
+ CHOLMOD(dump_dense) (Y, "Y", Common)) ;
+
+ switch (A->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ r_cholmod_sdmult (A, transpose, alpha, beta, X, Y, w) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ c_cholmod_sdmult (A, transpose, alpha, beta, X, Y, w) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ z_cholmod_sdmult (A, transpose, alpha, beta, X, Y, w) ;
+ break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free) (4*nx, e*sizeof (double), w, Common) ;
+ DEBUG (CHOLMOD(dump_dense) (Y, "Y", Common)) ;
+ return (TRUE) ;
+}
+#endif
diff --git a/CHOLMOD/MatrixOps/cholmod_ssmult.c b/CHOLMOD/MatrixOps/cholmod_ssmult.c
new file mode 100644
index 0000000..aa02326
--- /dev/null
+++ b/CHOLMOD/MatrixOps/cholmod_ssmult.c
@@ -0,0 +1,487 @@
+/* ========================================================================== */
+/* === MatrixOps/cholmod_ssmult ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* C = A*B. Multiply two sparse matrices.
+ *
+ * A and B can be packed or unpacked, sorted or unsorted, and of any stype.
+ * If A or B are symmetric, an internal unsymmetric copy is made first, however.
+ * C is computed as if A and B are unsymmetric, and then if the stype input
+ * parameter requests a symmetric form (upper or lower) the matrix is converted
+ * into that form.
+ *
+ * C is returned as packed, and either unsorted or sorted, depending on the
+ * "sorted" input parameter. If C is returned sorted, then either C = (B'*A')'
+ * or C = (A*B)'' is computed, depending on the number of nonzeros in A, B, and
+ * C.
+ *
+ * workspace:
+ * if C unsorted: Flag (A->nrow), W (A->nrow) if values
+ * if C sorted: Flag (B->ncol), W (B->ncol) if values
+ * Iwork (max (A->ncol, A->nrow, B->nrow, B->ncol))
+ * allocates temporary copies for A, B, and C, if required.
+ *
+ * Only pattern and real matrices are supported. Complex and zomplex matrices
+ * are supported only when the numerical values are not computed ("values"
+ * is FALSE).
+ */
+
+#ifndef NMATRIXOPS
+
+#include "cholmod_internal.h"
+#include "cholmod_matrixops.h"
+
+
+/* ========================================================================== */
+/* === cholmod_ssmult ======================================================= */
+/* ========================================================================== */
+
+cholmod_sparse *CHOLMOD(ssmult)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* left matrix to multiply */
+ cholmod_sparse *B, /* right matrix to multiply */
+ int stype, /* requested stype of C */
+ int values, /* TRUE: do numerical values, FALSE: pattern only */
+ int sorted, /* if TRUE then return C with sorted columns */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double bjt ;
+ double *Ax, *Bx, *Cx, *W ;
+ Int *Ap, *Anz, *Ai, *Bp, *Bnz, *Bi, *Cp, *Ci, *Flag ;
+ cholmod_sparse *C, *A2, *B2, *A3, *B3, *C2 ;
+ Int apacked, bpacked, j, i, pa, paend, pb, pbend, ncol, mark, cnz, t, p,
+ nrow, anz, bnz, do_swap_and_transpose, n1, n2 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_NULL (B, NULL) ;
+ values = values &&
+ (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->ncol != B->nrow)
+ {
+ /* inner dimensions must agree */
+ ERROR (CHOLMOD_INVALID, "A and B inner dimensions must match") ;
+ return (NULL) ;
+ }
+ /* A and B must have the same numerical type if values is TRUE (both must
+ * be CHOLMOD_REAL, this is implicitly checked above) */
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->nrow <= 1)
+ {
+ /* C will be implicitly sorted, so no need to sort it here */
+ sorted = FALSE ;
+ }
+ if (sorted)
+ {
+ n1 = MAX (A->nrow, B->ncol) ;
+ }
+ else
+ {
+ n1 = A->nrow ;
+ }
+ n2 = MAX4 (A->ncol, A->nrow, B->nrow, B->ncol) ;
+ CHOLMOD(allocate_work) (n1, n2, values ? n1 : 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1 : 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* convert A to unsymmetric, if necessary */
+ A2 = NULL ;
+ B2 = NULL ;
+ if (A->stype)
+ {
+ /* workspace: Iwork (max (A->nrow,A->ncol)) */
+ A2 = CHOLMOD(copy) (A, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ;
+ return (NULL) ;
+ }
+ A = A2 ;
+ }
+
+ /* convert B to unsymmetric, if necessary */
+ if (B->stype)
+ {
+ /* workspace: Iwork (max (B->nrow,B->ncol)) */
+ B2 = CHOLMOD(copy) (B, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ;
+ return (NULL) ;
+ }
+ B = B2 ;
+ }
+
+ ASSERT (CHOLMOD(dump_sparse) (A, "A", Common) >= 0) ;
+ ASSERT (CHOLMOD(dump_sparse) (B, "B", Common) >= 0) ;
+
+ /* get the A matrix */
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ apacked = A->packed ;
+
+ /* get the B matrix */
+ Bp = B->p ;
+ Bnz = B->nz ;
+ Bi = B->i ;
+ Bx = B->x ;
+ bpacked = B->packed ;
+
+ /* get the size of C */
+ nrow = A->nrow ;
+ ncol = B->ncol ;
+
+ /* get workspace */
+ W = Common->Xwork ; /* size nrow, unused if values is FALSE */
+ Flag = Common->Flag ; /* size nrow, Flag [0..nrow-1] < mark on input*/
+
+ /* ---------------------------------------------------------------------- */
+ /* count the number of entries in the result C */
+ /* ---------------------------------------------------------------------- */
+
+ cnz = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* clear the Flag array */
+ /* mark = CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+
+ /* for each nonzero B(t,j) in column j, do: */
+ pb = Bp [j] ;
+ pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ;
+ for ( ; pb < pbend ; pb++)
+ {
+ /* B(t,j) is nonzero */
+ t = Bi [pb] ;
+
+ /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */
+ pa = Ap [t] ;
+ paend = (apacked) ? (Ap [t+1]) : (pa + Anz [t]) ;
+ for ( ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ;
+ if (Flag [i] != mark)
+ {
+ Flag [i] = mark ;
+ cnz++ ;
+ }
+ }
+ }
+ if (cnz < 0)
+ {
+ break ; /* integer overflow case */
+ }
+ }
+
+ /* mark = CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check for integer overflow */
+ /* ---------------------------------------------------------------------- */
+
+ if (cnz < 0)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Determine how to return C sorted (if requested) */
+ /* ---------------------------------------------------------------------- */
+
+ do_swap_and_transpose = FALSE ;
+
+ if (sorted)
+ {
+ /* Determine the best way to return C with sorted columns. Computing
+ * C = (B'*A')' takes cnz + anz + bnz time (ignoring O(n) terms).
+ * Sorting C when done, C = (A*B)'', takes 2*cnz time. Pick the one
+ * with the least amount of work. */
+
+ anz = CHOLMOD(nnz) (A, Common) ;
+ bnz = CHOLMOD(nnz) (B, Common) ;
+
+ do_swap_and_transpose = (anz + bnz < cnz) ;
+
+ if (do_swap_and_transpose)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* C = (B'*A')' */
+ /* -------------------------------------------------------------- */
+
+ /* workspace: Iwork (A->nrow) */
+ A3 = CHOLMOD(ptranspose) (A, values, NULL, NULL, 0, Common) ;
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ A2 = A3 ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common));
+ return (NULL) ;
+ }
+ /* workspace: Iwork (B->nrow) */
+ B3 = CHOLMOD(ptranspose) (B, values, NULL, NULL, 0, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ B2 = B3 ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common));
+ return (NULL) ;
+ }
+ A = B2 ;
+ B = A2 ;
+
+ /* get the new A matrix */
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ apacked = A->packed ;
+
+ /* get the new B matrix */
+ Bp = B->p ;
+ Bnz = B->nz ;
+ Bi = B->i ;
+ Bx = B->x ;
+ bpacked = B->packed ;
+
+ /* get the size of C' */
+ nrow = A->nrow ;
+ ncol = B->ncol ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate C */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_sparse) (nrow, ncol, cnz, FALSE, TRUE, 0,
+ values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ;
+ return (NULL) ;
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = A*B */
+ /* ---------------------------------------------------------------------- */
+
+ cnz = 0 ;
+
+ if (values)
+ {
+
+ /* pattern and values */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* clear the Flag array */
+ /* mark = CHOLMOD(clear_flag (Common)) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+
+ /* start column j of C */
+ Cp [j] = cnz ;
+
+ /* for each nonzero B(t,j) in column j, do: */
+ pb = Bp [j] ;
+ pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ;
+ for ( ; pb < pbend ; pb++)
+ {
+ /* B(t,j) is nonzero */
+ t = Bi [pb] ;
+ bjt = Bx [pb] ;
+
+ /* add the nonzero pattern of A(:,t) to the pattern of C(:,j)
+ * and scatter the values into W */
+ pa = Ap [t] ;
+ paend = (apacked) ? (Ap [t+1]) : (pa + Anz [t]) ;
+ for ( ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ;
+ if (Flag [i] != mark)
+ {
+ Flag [i] = mark ;
+ Ci [cnz++] = i ;
+ }
+ W [i] += Ax [pa] * bjt ;
+ }
+ }
+
+ /* gather the values into C(:,j) */
+ for (p = Cp [j] ; p < cnz ; p++)
+ {
+ i = Ci [p] ;
+ Cx [p] = W [i] ;
+ W [i] = 0 ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* pattern only */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* clear the Flag array */
+ /* mark = CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+
+ /* start column j of C */
+ Cp [j] = cnz ;
+
+ /* for each nonzero B(t,j) in column j, do: */
+ pb = Bp [j] ;
+ pbend = (bpacked) ? (Bp [j+1]) : (pb + Bnz [j]) ;
+ for ( ; pb < pbend ; pb++)
+ {
+ /* B(t,j) is nonzero */
+ t = Bi [pb] ;
+
+ /* add the nonzero pattern of A(:,t) to the pattern of C(:,j) */
+ pa = Ap [t] ;
+ paend = (apacked) ? (Ap [t+1]) : (pa + Anz [t]) ;
+ for ( ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ;
+ if (Flag [i] != mark)
+ {
+ Flag [i] = mark ;
+ Ci [cnz++] = i ;
+ }
+ }
+ }
+ }
+ }
+
+ Cp [ncol] = cnz ;
+ ASSERT (MAX (1,cnz) == C->nzmax) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* clear workspace and free temporary matrices */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ /* CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert C to a symmetric upper/lower matrix if requested */
+ /* ---------------------------------------------------------------------- */
+
+ /* convert C in place, which cannot fail since no memory is allocated */
+ if (stype > 0)
+ {
+ /* C = triu (C), in place */
+ (void) CHOLMOD(band_inplace) (0, ncol, values, C, Common) ;
+ C->stype = 1 ;
+ }
+ else if (stype < 0)
+ {
+ /* C = tril (C), in place */
+ (void) CHOLMOD(band_inplace) (-nrow, 0, values, C, Common) ;
+ C->stype = -1 ;
+ }
+ ASSERT (Common->status >= CHOLMOD_OK) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* sort C, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ if (sorted)
+ {
+ if (do_swap_and_transpose)
+ {
+ /* workspace: Iwork (C->ncol), which is A->nrow since C=(B'*A') */
+ C2 = CHOLMOD(ptranspose) (C, values, NULL, NULL, 0, Common) ;
+ CHOLMOD(free_sparse) (&C, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common));
+ return (NULL) ;
+ }
+ C = C2 ;
+ }
+ else
+ {
+ /* workspace: Iwork (max (C->nrow,C->ncol)) */
+ if (!CHOLMOD(sort) (C, Common))
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&C, Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common));
+ return (NULL) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG (CHOLMOD(dump_sparse) (C, "ssmult", Common) >= 0) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, values ? n1:0, Common)) ;
+ return (C) ;
+}
+#endif
diff --git a/CHOLMOD/MatrixOps/cholmod_submatrix.c b/CHOLMOD/MatrixOps/cholmod_submatrix.c
new file mode 100644
index 0000000..467b679
--- /dev/null
+++ b/CHOLMOD/MatrixOps/cholmod_submatrix.c
@@ -0,0 +1,425 @@
+/* ========================================================================== */
+/* === MatrixOps/cholmod_submatrix ========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* C = A (rset,cset), where C becomes length(rset)-by-length(cset) in dimension.
+ * rset and cset can have duplicate entries. A and C must be unsymmetric. C
+ * is packed. If the sorted flag is TRUE on input, or rset is sorted and A is
+ * sorted, then C is sorted; otherwise C is unsorted.
+ *
+ * A NULL rset or cset means "[ ]" in MATLAB notation.
+ * If the length of rset or cset is negative, it denotes ":" in MATLAB notation.
+ *
+ * For permuting a matrix, this routine is an alternative to cholmod_ptranspose
+ * (which permutes and transposes a matrix and can work on symmetric matrices).
+ *
+ * The time taken by this routine is O(A->nrow) if the Common workspace needs
+ * to be initialized, plus O(C->nrow + C->ncol + nnz (A (:,cset))). Thus, if C
+ * is small and the workspace is not initialized, the time can be dominated by
+ * the call to cholmod_allocate_work. However, once the workspace is
+ * allocated, subsequent calls take less time.
+ *
+ * workspace: Iwork (max (A->nrow + length (rset), length (cset))).
+ * allocates temporary copy of C if it is to be returned sorted.
+ *
+ * Future work: A common case occurs where A has sorted columns, and rset is in
+ * the form lo:hi in MATLAB notation. This routine could exploit that case
+ * to run even faster when the matrix is sorted, particularly when lo is small.
+ *
+ * Only pattern and real matrices are supported. Complex and zomplex matrices
+ * are supported only when "values" is FALSE.
+ */
+
+#ifndef NMATRIXOPS
+
+#include "cholmod_internal.h"
+#include "cholmod_matrixops.h"
+
+/* ========================================================================== */
+/* === check_subset ========================================================= */
+/* ========================================================================== */
+
+/* Check the rset or cset, and return TRUE if valid, FALSE if invalid */
+
+static int check_subset (Int *set, Int len, Int n)
+{
+ Int k ;
+ if (set == NULL)
+ {
+ return (TRUE) ;
+ }
+ for (k = 0 ; k < len ; k++)
+ {
+ if (set [k] < 0 || set [k] >= n)
+ {
+ return (FALSE) ;
+ }
+ }
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_submatrix ==================================================== */
+/* ========================================================================== */
+
+cholmod_sparse *CHOLMOD(submatrix)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to subreference */
+ Int *rset, /* set of row indices, duplicates OK */
+ UF_long rsize, /* size of rset, or -1 for ":" */
+ Int *cset, /* set of column indices, duplicates OK */
+ UF_long csize, /* size of cset, or -1 for ":" */
+ int values, /* if TRUE compute the numerical values of C */
+ int sorted, /* if TRUE then return C with sorted columns */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double aij = 0 ;
+ double *Ax, *Cx ;
+ Int *Ap, *Ai, *Anz, *Ci, *Cp, *Head, *Rlen, *Rnext, *Iwork ;
+ cholmod_sparse *C ;
+ Int packed, ancol, anrow, cnrow, cncol, nnz, i, j, csorted, ilast, p,
+ pend, pdest, ci, cj, head, nr, nc ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ values = (values && (A->xtype != CHOLMOD_PATTERN)) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->stype != 0)
+ {
+ /* A must be unsymmetric */
+ ERROR (CHOLMOD_INVALID, "symmetric upper or lower case not supported") ;
+ return (NULL) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ ancol = A->ncol ;
+ anrow = A->nrow ;
+ nr = rsize ;
+ nc = csize ;
+ if (rset == NULL)
+ {
+ /* nr = 0 denotes rset = [ ], nr < 0 denotes rset = 0:anrow-1 */
+ nr = (nr < 0) ? (-1) : 0 ;
+ }
+ if (cset == NULL)
+ {
+ /* nr = 0 denotes cset = [ ], nr < 0 denotes cset = 0:ancol-1 */
+ nc = (nc < 0) ? (-1) : 0 ;
+ }
+ cnrow = (nr < 0) ? anrow : nr ; /* negative rset means rset = 0:anrow-1 */
+ cncol = (nc < 0) ? ancol : nc ; /* negative cset means cset = 0:ancol-1 */
+
+ if (nr < 0 && nc < 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* C = A (:,:), use cholmod_copy instead */
+ /* ------------------------------------------------------------------ */
+
+ /* workspace: Iwork (max (C->nrow,C->ncol)) */
+ PRINT1 (("submatrix C = A (:,:)\n")) ;
+ C = CHOLMOD(copy) (A, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+ return (C) ;
+ }
+ PRINT1 (("submatrix nr "ID" nc "ID" Cnrow "ID" Cncol "ID""
+ " Anrow "ID" Ancol "ID"\n", nr, nc, cnrow, cncol, anrow, ancol)) ;
+
+ /* s = MAX3 (anrow+MAX(0,nr), cncol, cnrow) ; */
+ s = CHOLMOD(add_size_t) (anrow, MAX (0,nr), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (NULL) ;
+ }
+ s = MAX3 (s, ((size_t) cncol), ((size_t) cnrow)) ;
+
+ CHOLMOD(allocate_work) (anrow, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ packed = A->packed ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Head = Common->Head ; /* size anrow */
+ Iwork = Common->Iwork ;
+ Rlen = Iwork ; /* size anrow (i/i/l) */
+ Rnext = Iwork + anrow ; /* size nr (i/i/l), not used if nr < 0 */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct inverse of rset and compute nnz (C) */
+ /* ---------------------------------------------------------------------- */
+
+ PRINT1 (("nr "ID" nc "ID"\n", nr, nc)) ;
+ PRINT1 (("anrow "ID" ancol "ID"\n", anrow, ancol)) ;
+ PRINT1 (("cnrow "ID" cncol "ID"\n", cnrow, cncol)) ;
+ DEBUG (for (i = 0 ; i < nr ; i++) PRINT2 (("rset ["ID"] = "ID"\n",
+ i, rset [i])));
+ DEBUG (for (i = 0 ; i < nc ; i++) PRINT2 (("cset ["ID"] = "ID"\n",
+ i, cset [i])));
+
+ /* C is sorted if A and rset are sorted, or if C has one row or less */
+ csorted = A->sorted || (cnrow <= 1) ;
+
+ if (!check_subset (rset, nr, anrow))
+ {
+ ERROR (CHOLMOD_INVALID, "invalid rset") ;
+ return (NULL) ;
+ }
+
+ if (!check_subset (cset, nc, ancol))
+ {
+ ERROR (CHOLMOD_INVALID, "invalid cset") ;
+ return (NULL) ;
+ }
+
+ nnz = 0 ;
+ if (nr < 0)
+ {
+ /* C = A (:,cset) where cset = [ ] or cset is not empty */
+ ASSERT (IMPLIES (cncol > 0, cset != NULL)) ;
+ for (cj = 0 ; cj < cncol ; cj++)
+ {
+ /* construct column cj of C, which is column j of A */
+ j = cset [cj] ;
+ nnz += (packed) ? (Ap [j+1] - Ap [j]) : MAX (0, Anz [j]) ;
+ }
+ }
+ else
+ {
+ /* C = A (rset,cset), where rset is not empty but cset might be empty */
+ /* create link lists in reverse order to preserve natural order */
+ ilast = anrow ;
+ for (ci = nr-1 ; ci >= 0 ; ci--)
+ {
+ /* row i of A becomes row ci of C; add ci to ith link list */
+ i = rset [ci] ;
+ head = Head [i] ;
+ Rlen [i] = (head == EMPTY) ? 1 : (Rlen [i] + 1) ;
+ Rnext [ci] = head ;
+ Head [i] = ci ;
+ if (i > ilast)
+ {
+ /* row indices in columns of C will not be sorted */
+ csorted = FALSE ;
+ }
+ ilast = i ;
+ }
+
+#ifndef NDEBUG
+ for (i = 0 ; i < anrow ; i++)
+ {
+ Int k = 0 ;
+ Int rlen = (Head [i] != EMPTY) ? Rlen [i] : -1 ;
+ PRINT1 (("Row "ID" Rlen "ID": ", i, rlen)) ;
+ for (ci = Head [i] ; ci != EMPTY ; ci = Rnext [ci])
+ {
+ k++ ;
+ PRINT2 ((""ID" ", ci)) ;
+ }
+ PRINT1 (("\n")) ;
+ ASSERT (IMPLIES (Head [i] != EMPTY, k == Rlen [i])) ;
+ }
+#endif
+
+ /* count nonzeros in C */
+ for (cj = 0 ; cj < cncol ; cj++)
+ {
+ /* count rows in column cj of C, which is column j of A */
+ j = (nc < 0) ? cj : (cset [cj]) ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ /* row i of A becomes multiple rows (ci) of C */
+ i = Ai [p] ;
+ ASSERT (i >= 0 && i < anrow) ;
+ if (Head [i] != EMPTY)
+ {
+ nnz += Rlen [i] ;
+ }
+ }
+ }
+ }
+ PRINT1 (("nnz (C) "ID"\n", nnz)) ;
+
+ /* rset and cset are now valid */
+ DEBUG (CHOLMOD(dump_subset) (rset, rsize, anrow, "rset", Common)) ;
+ DEBUG (CHOLMOD(dump_subset) (cset, csize, ancol, "cset", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate C */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_sparse) (cnrow, cncol, nnz, csorted, TRUE, 0,
+ values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ for (i = 0 ; i < anrow ; i++)
+ {
+ Head [i] = EMPTY ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (NULL) ;
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = A (rset,cset) */
+ /* ---------------------------------------------------------------------- */
+
+ pdest = 0 ;
+ if (nnz == 0)
+ {
+ /* C has no nonzeros */
+ for (cj = 0 ; cj <= cncol ; cj++)
+ {
+ Cp [cj] = 0 ;
+ }
+ }
+ else if (nr < 0)
+ {
+ /* C = A (:,cset), where cset is not empty */
+ for (cj = 0 ; cj < cncol ; cj++)
+ {
+ /* construct column cj of C, which is column j of A */
+ PRINT1 (("construct cj = j = "ID"\n", cj)) ;
+ j = cset [cj] ;
+ Cp [cj] = pdest ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [pdest] = Ai [p] ;
+ if (values)
+ {
+ Cx [pdest] = Ax [p] ;
+ }
+ pdest++ ;
+ ASSERT (pdest <= nnz) ;
+ }
+ }
+ }
+ else
+ {
+ /* C = A (rset,cset), where rset is not empty but cset might be empty */
+ for (cj = 0 ; cj < cncol ; cj++)
+ {
+ /* construct column cj of C, which is column j of A */
+ PRINT1 (("construct cj = "ID"\n", cj)) ;
+ j = (nc < 0) ? cj : (cset [cj]) ;
+ PRINT1 (("cj = "ID"\n", j)) ;
+ Cp [cj] = pdest ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ /* row (Ai [p]) of A becomes multiple rows (ci) of C */
+ PRINT2 (("i: "ID" becomes: ", Ai [p])) ;
+ if (values)
+ {
+ aij = Ax [p] ;
+ }
+ for (ci = Head [Ai [p]] ; ci != EMPTY ; ci = Rnext [ci])
+ {
+ PRINT3 ((""ID" ", ci)) ;
+ Ci [pdest] = ci ;
+ if (values)
+ {
+ Cx [pdest] = aij ;
+ }
+ pdest++ ;
+ ASSERT (pdest <= nnz) ;
+ }
+ PRINT2 (("\n")) ;
+ }
+ }
+ }
+ Cp [cncol] = pdest ;
+ ASSERT (nnz == pdest) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* clear workspace */
+ /* ---------------------------------------------------------------------- */
+
+ for (ci = 0 ; ci < nr ; ci++)
+ {
+ Head [rset [ci]] = EMPTY ;
+ }
+
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* sort C, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (C , "C before sort", Common) >= 0) ;
+
+ if (sorted && !csorted)
+ {
+ /* workspace: Iwork (max (C->nrow,C->ncol)) */
+ if (!CHOLMOD(sort) (C, Common))
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&C, Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (NULL) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_sparse) (C , "Final C", Common) >= 0) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (C) ;
+}
+#endif
diff --git a/CHOLMOD/MatrixOps/cholmod_symmetry.c b/CHOLMOD/MatrixOps/cholmod_symmetry.c
new file mode 100644
index 0000000..6770346
--- /dev/null
+++ b/CHOLMOD/MatrixOps/cholmod_symmetry.c
@@ -0,0 +1,482 @@
+/* ========================================================================== */
+/* === MatrixOps/cholmod_symmetry =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Determines if a sparse matrix is rectangular, unsymmetric, symmetric,
+ * skew-symmetric, or Hermitian. It does so by looking at its numerical values
+ * of both upper and lower triangular parts of a CHOLMOD "unsymmetric"
+ * matrix, where A->stype == 0. The transpose of A is NOT constructed.
+ *
+ * If not unsymmetric, it also determines if the matrix has a diagonal whose
+ * entries are all real and positive (and thus a candidate for sparse Cholesky
+ * if A->stype is changed to a nonzero value).
+ *
+ * Note that a Matrix Market "general" matrix is either rectangular or
+ * unsymmetric.
+ *
+ * The row indices in the column of each matrix MUST be sorted for this function
+ * to work properly (A->sorted must be TRUE). This routine returns EMPTY if
+ * A->stype is not zero, or if A->sorted is FALSE. The exception to this rule
+ * is if A is rectangular.
+ *
+ * If option == 0, then this routine returns immediately when it finds a
+ * non-positive diagonal entry (or one with nonzero imaginary part). If the
+ * matrix is not a candidate for sparse Cholesky, it returns the value
+ * CHOLMOD_MM_UNSYMMETRIC, even if the matrix might in fact be symmetric or
+ * Hermitian.
+ *
+ * This routine is useful inside the MATLAB backslash, which must look at an
+ * arbitrary matrix (A->stype == 0) and determine if it is a candidate for
+ * sparse Cholesky. In that case, option should be 0.
+ *
+ * This routine is also useful when writing a MATLAB matrix to a file in
+ * Rutherford/Boeing or Matrix Market format. Those formats require a
+ * determination as to the symmetry of the matrix, and thus this routine should
+ * not return upon encountering the first non-positive diagonal. In this case,
+ * option should be 1.
+ *
+ * If option is 2, this function can be used to compute the numerical and
+ * pattern symmetry, where 0 is a completely unsymmetric matrix, and 1 is a
+ * perfectly symmetric matrix. This option is used when computing the following
+ * statistics for the matrices in the UF Sparse Matrix Collection.
+ *
+ * numerical symmetry: number of matched offdiagonal nonzeros over
+ * the total number of offdiagonal entries. A real entry A(i,j), i ~= j,
+ * is matched if A (j,i) == A (i,j), but this is only counted if both
+ * A(j,i) and A(i,j) are nonzero. This does not depend on Z.
+ * (If A is complex, then the above test is modified; A (i,j) is matched
+ * if conj (A (j,i)) == A (i,j)).
+ *
+ * Then numeric symmetry = xmatched / nzoffdiag, or 1 if nzoffdiag = 0.
+ *
+ * pattern symmetry: number of matched offdiagonal entries over the
+ * total number of offdiagonal entries. An entry A(i,j), i ~= j, is
+ * matched if A (j,i) is also an entry.
+ *
+ * Then pattern symmetry = pmatched / nzoffdiag, or 1 if nzoffdiag = 0.
+ *
+ * The symmetry of a matrix with no offdiagonal entries is equal to 1.
+ *
+ * A workspace of size ncol integers is allocated; EMPTY is returned if this
+ * allocation fails.
+ *
+ * Summary of return values:
+ *
+ * EMPTY (-1) out of memory, stype not zero, A not sorted
+ * CHOLMOD_MM_RECTANGULAR 1 A is rectangular
+ * CHOLMOD_MM_UNSYMMETRIC 2 A is unsymmetric
+ * CHOLMOD_MM_SYMMETRIC 3 A is symmetric, but with non-pos. diagonal
+ * CHOLMOD_MM_HERMITIAN 4 A is Hermitian, but with non-pos. diagonal
+ * CHOLMOD_MM_SKEW_SYMMETRIC 5 A is skew symmetric
+ * CHOLMOD_MM_SYMMETRIC_POSDIAG 6 A is symmetric with positive diagonal
+ * CHOLMOD_MM_HERMITIAN_POSDIAG 7 A is Hermitian with positive diagonal
+ *
+ * See also the spsym mexFunction, which is a MATLAB interface for this code.
+ *
+ * If the matrix is a candidate for sparse Cholesky, it will return a result
+ * CHOLMOD_MM_SYMMETRIC_POSDIAG if real, or CHOLMOD_MM_HERMITIAN_POSDIAG if
+ * complex. Otherwise, it will return a value less than this. This is true
+ * regardless of the value of the option parameter.
+ */
+
+#ifndef NMATRIXOPS
+
+#include "cholmod_internal.h"
+#include "cholmod_matrixops.h"
+
+
+/* ========================================================================== */
+/* === get_value ============================================================ */
+/* ========================================================================== */
+
+/* Get the pth value in the matrix. */
+
+static void get_value
+(
+ double *Ax, /* real values, or real/imag. for CHOLMOD_COMPLEX type */
+ double *Az, /* imaginary values for CHOLMOD_ZOMPLEX type */
+ Int p, /* get the pth entry */
+ Int xtype, /* A->xtype: pattern, real, complex, or zomplex */
+ double *x, /* the real part */
+ double *z /* the imaginary part */
+)
+{
+ switch (xtype)
+ {
+ case CHOLMOD_PATTERN:
+ *x = 1 ;
+ *z = 0 ;
+ break ;
+
+ case CHOLMOD_REAL:
+ *x = Ax [p] ;
+ *z = 0 ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ *x = Ax [2*p] ;
+ *z = Ax [2*p+1] ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ *x = Ax [p] ;
+ *z = Az [p] ;
+ break ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === cholmod_symmetry ===================================================== */
+/* ========================================================================== */
+
+/* Determine the symmetry of a matrix, and check its diagonal.
+ *
+ * option 0: Do not count # of matched pairs. Quick return if the
+ * the matrix has a zero, negative, or imaginary diagonal entry.
+ *
+ * option 1: Do not count # of matched pairs. Do not return quickly if
+ * the matrix has a zero, negative, or imaginary diagonal entry.
+ * The result 1 to 7 is accurately computed:
+ *
+ * EMPTY (-1) out of memory, stype not zero, A not sorted
+ * CHOLMOD_MM_RECTANGULAR 1 A is rectangular
+ * CHOLMOD_MM_UNSYMMETRIC 2 A is unsymmetric
+ * CHOLMOD_MM_SYMMETRIC 3 A is symmetric, with non-pos. diagonal
+ * CHOLMOD_MM_HERMITIAN 4 A is Hermitian, with non-pos. diagonal
+ * CHOLMOD_MM_SKEW_SYMMETRIC 5 A is skew symmetric
+ * CHOLMOD_MM_SYMMETRIC_POSDIAG 6 is symmetric with positive diagonal
+ * CHOLMOD_MM_HERMITIAN_POSDIAG 7 A is Hermitian with positive diagonal
+ *
+ * The routine returns as soon as the above is determined (that is, it
+ * can return as soon as it determines the matrix is unsymmetric).
+ *
+ * option 2: All of the above, but also compute the number of matched off-
+ * diagonal entries (of two types). xmatched is the number of
+ * nonzero entries for which A(i,j) = conj(A(j,i)). pmatched is
+ * the number of entries (i,j) for which A(i,j) and A(j,i) are both in
+ * the pattern of A (the value doesn't matter). nzoffdiag is the total
+ * number of off-diagonal entries in the pattern. nzdiag is the number of
+ * diagonal entries in the pattern.
+ *
+ * With option 0 or 1, or if the matrix is rectangular, xmatched, pmatched,
+ * nzoffdiag, and nzdiag are not computed.
+ *
+ * Note that a matched pair, A(i,j) and A(j,i) for i != j, is counted twice
+ * (once per entry).
+ */
+
+int CHOLMOD(symmetry)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A,
+ int option, /* option 0, 1, or 2 (see above) */
+ /* ---- output --- */ /* outputs ignored if any are NULL */
+ Int *p_xmatched, /* # of matched numerical entries */
+ Int *p_pmatched, /* # of matched entries in pattern */
+ Int *p_nzoffdiag, /* # of off diagonal entries */
+ Int *p_nzdiag, /* # of diagonal entries */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double aij_real = 0, aij_imag = 0, aji_real = 0, aji_imag = 0 ;
+ double *Ax, *Az ;
+ Int *Ap, *Ai, *Anz, *munch ;
+ Int packed, nrow, ncol, xtype, is_symmetric, is_skew, is_hermitian, posdiag,
+ j, p, pend, i, piend, result, xmatched, pmatched, nzdiag, i2, found ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (A, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+ ASSERT (CHOLMOD(dump_sparse) (A, "cholmod_symmetry", Common) >= 0) ;
+
+ if (p_xmatched == NULL || p_pmatched == NULL
+ || p_nzoffdiag == NULL || p_nzdiag == NULL)
+ {
+ /* option 2 is not performed if any output parameter is NULL */
+ option = MAX (option, 1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ ncol = A->ncol ;
+ nrow = A->nrow ;
+ xtype = A->xtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check if rectangular, unsorted, or stype is not zero */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow != ncol)
+ {
+ /* matrix is rectangular */
+ return (CHOLMOD_MM_RECTANGULAR) ;
+ }
+
+ if (!(A->sorted) || A->stype != 0)
+ {
+ /* this function cannot determine the type or symmetry */
+ return (EMPTY) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* this function requires uninitialized Int workspace of size ncol */
+ CHOLMOD(allocate_work) (0, ncol, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (EMPTY) ;
+ }
+
+ munch = Common->Iwork ; /* the munch array is size ncol */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine symmetry of a square matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* a complex or zomplex matrix is Hermitian until proven otherwise */
+ is_hermitian = (xtype >= CHOLMOD_COMPLEX) ;
+
+ /* any matrix is symmetric until proven otherwise */
+ is_symmetric = TRUE ;
+
+ /* a non-pattern matrix is skew-symmetric until proven otherwise */
+ is_skew = (xtype != CHOLMOD_PATTERN) ;
+
+ /* a matrix has positive diagonal entries until proven otherwise */
+ posdiag = TRUE ;
+
+ /* munch pointers start at the top of each column */
+ for (j = 0 ; j < ncol ; j++)
+ {
+ munch [j] = Ap [j] ;
+ }
+
+ xmatched = 0 ;
+ pmatched = 0 ;
+ nzdiag = 0 ;
+
+ for (j = 0 ; j < ncol ; j++) /* examine each column of A */
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* look at the entire munch column j */
+ /* ------------------------------------------------------------------ */
+
+ /* start at the munch point of column j, and go to end of the column */
+ p = munch [j] ;
+ pend = (packed) ? (Ap [j+1]) : (Ap [j] + Anz [j]) ;
+
+ for ( ; p < pend ; p++)
+ {
+ /* get the row index of A(i,j) */
+ i = Ai [p] ;
+
+ if (i < j)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* A(i,j) in triu(A), but matching A(j,i) not in tril(A) */
+ /* ---------------------------------------------------------- */
+
+ /* entry A(i,j) is unmatched; it appears in the upper triangular
+ * part, but not the lower triangular part. The matrix is
+ * unsymmetric. */
+ is_hermitian = FALSE ;
+ is_symmetric = FALSE ;
+ is_skew = FALSE ;
+
+ }
+ else if (i == j)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* the diagonal A(j,j) is present; check its value */
+ /* ---------------------------------------------------------- */
+
+ get_value (Ax, Az, p, xtype, &aij_real, &aij_imag) ;
+ if (aij_real != 0. || aij_imag != 0.)
+ {
+ /* diagonal is nonzero; matrix is not skew-symmetric */
+ nzdiag++ ;
+ is_skew = FALSE ;
+ }
+ if (aij_real <= 0. || aij_imag != 0.)
+ {
+ /* diagonal negative or imaginary; not chol candidate */
+ posdiag = FALSE ;
+ }
+ if (aij_imag != 0.)
+ {
+ /* imaginary part is present; not Hermitian */
+ is_hermitian = FALSE ;
+ }
+
+ }
+ else /* i > j */
+ {
+
+ /* ---------------------------------------------------------- */
+ /* consider column i, up to and including row j */
+ /* ---------------------------------------------------------- */
+
+ /* munch the entry at top of column i up to and incl row j */
+ piend = (packed) ? (Ap [i+1]) : (Ap [i] + Anz [i]) ;
+
+ found = FALSE ;
+
+ for ( ; munch [i] < piend ; munch [i]++)
+ {
+
+ i2 = Ai [munch [i]] ;
+
+ if (i2 < j)
+ {
+
+ /* -------------------------------------------------- */
+ /* A(i2,i) in triu(A) but A(i,i2) not in tril(A) */
+ /* -------------------------------------------------- */
+
+ /* The matrix is unsymmetric. */
+ is_hermitian = FALSE ;
+ is_symmetric = FALSE ;
+ is_skew = FALSE ;
+
+ }
+ else if (i2 == j)
+ {
+
+ /* -------------------------------------------------- */
+ /* both A(i,j) and A(j,i) exist in the matrix */
+ /* -------------------------------------------------- */
+
+ /* this is one more matching entry in the pattern */
+ pmatched += 2 ;
+ found = TRUE ;
+
+ /* get the value of A(i,j) */
+ get_value (Ax, Az, p, xtype, &aij_real, &aij_imag) ;
+
+ /* get the value of A(j,i) */
+ get_value (Ax, Az, munch [i],
+ xtype, &aji_real, &aji_imag) ;
+
+ /* compare A(i,j) with A(j,i) */
+ if (aij_real != aji_real || aij_imag != aji_imag)
+ {
+ /* the matrix cannot be symmetric */
+ is_symmetric = FALSE ;
+ }
+ if (aij_real != -aji_real || aij_imag != aji_imag)
+ {
+ /* the matrix cannot be skew-symmetric */
+ is_skew = FALSE ;
+ }
+ if (aij_real != aji_real || aij_imag != -aji_imag)
+ {
+ /* the matrix cannot be Hermitian */
+ is_hermitian = FALSE ;
+ }
+ else
+ {
+ /* A(i,j) and A(j,i) are numerically matched */
+ xmatched += 2 ;
+ }
+
+ }
+ else /* i2 > j */
+ {
+
+ /* -------------------------------------------------- */
+ /* entry A(i2,i) is not munched; consider it later */
+ /* -------------------------------------------------- */
+
+ break ;
+ }
+ }
+
+ if (!found)
+ {
+ /* A(i,j) in tril(A) but A(j,i) not in triu(A).
+ * The matrix is unsymmetric. */
+ is_hermitian = FALSE ;
+ is_symmetric = FALSE ;
+ is_skew = FALSE ;
+ }
+ }
+
+ if (option < 2 && !(is_symmetric || is_skew || is_hermitian))
+ {
+ /* matrix is unsymmetric; terminate the test */
+ return (CHOLMOD_MM_UNSYMMETRIC) ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* quick return if not Cholesky candidate */
+ /* ------------------------------------------------------------------ */
+
+ if (option < 1 && (!posdiag || nzdiag < ncol))
+ {
+ /* Diagonal entry not present, or present but negative or with
+ * nonzero imaginary part. Quick return for option 0. */
+ return (CHOLMOD_MM_UNSYMMETRIC) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the results */
+ /* ---------------------------------------------------------------------- */
+
+ if (option >= 2)
+ {
+ *p_xmatched = xmatched ;
+ *p_pmatched = pmatched ;
+ *p_nzoffdiag = CHOLMOD(nnz) (A, Common) - nzdiag ;
+ *p_nzdiag = nzdiag ;
+ }
+
+ result = CHOLMOD_MM_UNSYMMETRIC ;
+ if (is_hermitian)
+ {
+ /* complex Hermitian matrix, with either pos. or non-pos. diagonal */
+ result = posdiag ? CHOLMOD_MM_HERMITIAN_POSDIAG : CHOLMOD_MM_HERMITIAN ;
+ }
+ else if (is_symmetric)
+ {
+ /* real or complex symmetric matrix, with pos. or non-pos. diagonal */
+ result = posdiag ? CHOLMOD_MM_SYMMETRIC_POSDIAG : CHOLMOD_MM_SYMMETRIC ;
+ }
+ else if (is_skew)
+ {
+ /* real or complex skew-symmetric matrix */
+ result = CHOLMOD_MM_SKEW_SYMMETRIC ;
+ }
+ return (result) ;
+}
+#endif
diff --git a/CHOLMOD/MatrixOps/cholmod_vertcat.c b/CHOLMOD/MatrixOps/cholmod_vertcat.c
new file mode 100644
index 0000000..e04d5b2
--- /dev/null
+++ b/CHOLMOD/MatrixOps/cholmod_vertcat.c
@@ -0,0 +1,201 @@
+/* ========================================================================== */
+/* === MatrixOps/cholmod_vertcat ============================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Vertical concatenation, C = [A ; B] in MATLAB notation.
+ *
+ * A and B can be up/lo/unsym; C is unsymmetric and packed.
+ * A and B must have the same number of columns.
+ * C is sorted if both A and B are sorted.
+ *
+ * workspace: Iwork (max (A->nrow, A->ncol, B->nrow, B->ncol)).
+ * allocates temporary copies of A and B if they are symmetric.
+ *
+ * Only pattern and real matrices are supported. Complex and zomplex matrices
+ * are supported only if "values" is FALSE.
+ */
+
+#ifndef NMATRIXOPS
+
+#include "cholmod_internal.h"
+#include "cholmod_matrixops.h"
+
+
+/* ========================================================================== */
+/* === cholmod_vertcat ====================================================== */
+/* ========================================================================== */
+
+cholmod_sparse *CHOLMOD(vertcat)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* left matrix to concatenate */
+ cholmod_sparse *B, /* right matrix to concatenate */
+ int values, /* if TRUE compute the numerical values of C */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Ax, *Bx, *Cx ;
+ Int *Ap, *Ai, *Anz, *Bp, *Bi, *Bnz, *Cp, *Ci ;
+ cholmod_sparse *C, *A2, *B2 ;
+ Int apacked, bpacked, anrow, bnrow, ncol, nrow, anz, bnz, nz, j, p, pend,
+ pdest ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (NULL) ;
+ RETURN_IF_NULL (A, NULL) ;
+ RETURN_IF_NULL (B, NULL) ;
+ values = values &&
+ (A->xtype != CHOLMOD_PATTERN) && (B->xtype != CHOLMOD_PATTERN) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ RETURN_IF_XTYPE_INVALID (B, CHOLMOD_PATTERN,
+ values ? CHOLMOD_REAL : CHOLMOD_ZOMPLEX, NULL) ;
+ if (A->ncol != B->ncol)
+ {
+ /* A and B must have the same number of columns */
+ ERROR (CHOLMOD_INVALID, "A and B must have same # of columns") ;
+ return (NULL) ;
+ }
+ /* A and B must have the same numerical type if values is TRUE (both must
+ * be CHOLMOD_REAL, this is implicitly checked above) */
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ anrow = A->nrow ;
+ bnrow = B->nrow ;
+ ncol = A->ncol ;
+ CHOLMOD(allocate_work) (0, MAX3 (anrow, bnrow, ncol), 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* convert A to unsymmetric, if necessary */
+ A2 = NULL ;
+ if (A->stype != 0)
+ {
+ /* workspace: Iwork (max (A->nrow,A->ncol)) */
+ A2 = CHOLMOD(copy) (A, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (NULL) ;
+ }
+ A = A2 ;
+ }
+
+ /* convert B to unsymmetric, if necessary */
+ B2 = NULL ;
+ if (B->stype != 0)
+ {
+ /* workspace: Iwork (max (B->nrow,B->ncol)) */
+ B2 = CHOLMOD(copy) (B, 0, values, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ return (NULL) ;
+ }
+ B = B2 ;
+ }
+
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ apacked = A->packed ;
+
+ Bp = B->p ;
+ Bnz = B->nz ;
+ Bi = B->i ;
+ Bx = B->x ;
+ bpacked = B->packed ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate C */
+ /* ---------------------------------------------------------------------- */
+
+ anz = CHOLMOD(nnz) (A, Common) ;
+ bnz = CHOLMOD(nnz) (B, Common) ;
+ nrow = anrow + bnrow ;
+ nz = anz + bnz ;
+
+ C = CHOLMOD(allocate_sparse) (nrow, ncol, nz, A->sorted && B->sorted, TRUE,
+ 0, values ? A->xtype : CHOLMOD_PATTERN, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ return (NULL) ;
+ }
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = [A ; B] */
+ /* ---------------------------------------------------------------------- */
+
+ pdest = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* attach A(:,j) as the first part of C(:,j) */
+ p = Ap [j] ;
+ pend = (apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cp [j] = pdest ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [pdest] = Ai [p] ;
+ if (values)
+ {
+ Cx [pdest] = Ax [p] ;
+ }
+ pdest++ ;
+ }
+
+ /* attach B(:,j) as the second part of C(:,j) */
+ p = Bp [j] ;
+ pend = (bpacked) ? (Bp [j+1]) : (p + Bnz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [pdest] = Bi [p] + anrow ;
+ if (values)
+ {
+ Cx [pdest] = Bx [p] ;
+ }
+ pdest++ ;
+ }
+ }
+ Cp [ncol] = pdest ;
+ ASSERT (pdest == nz) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the unsymmetric copies of A and B, and return C */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&A2, Common) ;
+ CHOLMOD(free_sparse) (&B2, Common) ;
+ return (C) ;
+}
+#endif
diff --git a/CHOLMOD/MatrixOps/gpl.txt b/CHOLMOD/MatrixOps/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/CHOLMOD/MatrixOps/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it. (Some other Free Software Foundation software is covered by
+the GNU Library General Public License instead.) You can apply it to
+your programs, too.
+
+ When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
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+
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+ 10. If you wish to incorporate parts of the Program into other free
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+ This program is free software; you can redistribute it and/or modify
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+ (at your option) any later version.
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+
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+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
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+Public License instead of this License.
diff --git a/CHOLMOD/MatrixOps/t_cholmod_sdmult.c b/CHOLMOD/MatrixOps/t_cholmod_sdmult.c
new file mode 100644
index 0000000..b653285
--- /dev/null
+++ b/CHOLMOD/MatrixOps/t_cholmod_sdmult.c
@@ -0,0 +1,726 @@
+/* ========================================================================== */
+/* === MatrixOps/t_cholmod_sdmult =========================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/MatrixOps Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/MatrixOps Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_sdmult */
+
+#include "cholmod_template.h"
+
+#undef ADVANCE
+
+#ifdef REAL
+#define ADVANCE(x,z,d) x += d
+#elif defined (COMPLEX)
+#define ADVANCE(x,z,d) x += 2*d
+#else
+#define ADVANCE(x,z,d) x += d ; z += d
+#endif
+
+/* ========================================================================== */
+/* === t_cholmod_sdmult ===================================================== */
+/* ========================================================================== */
+
+static void TEMPLATE (cholmod_sdmult)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* sparse matrix to multiply */
+ int transpose, /* use A if 0, or A' otherwise */
+ double alpha [2], /* scale factor for A */
+ double beta [2], /* scale factor for Y */
+ cholmod_dense *X, /* dense matrix to multiply */
+ /* ---- in/out --- */
+ cholmod_dense *Y, /* resulting dense matrix */
+ /* -- workspace -- */
+ double *W /* size 4*nx if needed, twice that for c/zomplex case */
+)
+{
+
+ double yx [8], xx [8], ax [2] ;
+#ifdef ZOMPLEX
+ double yz [4], xz [4], az [1] ;
+ double betaz [1], alphaz [1] ;
+#endif
+
+ double *Ax, *Az, *Xx, *Xz, *Yx, *Yz, *w, *Wz ;
+ Int *Ap, *Ai, *Anz ;
+ size_t nx, ny, dx, dy ;
+ Int packed, nrow, ncol, j, k, p, pend, kcol, i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef ZOMPLEX
+ betaz [0] = beta [1] ;
+ alphaz [0] = alpha [1] ;
+#endif
+
+ ny = transpose ? A->ncol : A->nrow ; /* required length of Y */
+ nx = transpose ? A->nrow : A->ncol ; /* required length of X */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ Ap = A->p ;
+ Anz = A->nz ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ packed = A->packed ;
+ Xx = X->x ;
+ Xz = X->z ;
+ Yx = Y->x ;
+ Yz = Y->z ;
+ kcol = X->ncol ;
+ dy = Y->d ;
+ dx = X->d ;
+ w = W ;
+ Wz = W + 4*nx ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Y = beta * Y */
+ /* ---------------------------------------------------------------------- */
+
+ if (ENTRY_IS_ZERO (beta, betaz, 0))
+ {
+ for (k = 0 ; k < kcol ; k++)
+ {
+ for (i = 0 ; i < ((Int) ny) ; i++)
+ {
+ /* y [i] = 0. ; */
+ CLEAR (Yx, Yz, i) ;
+ }
+ /* y += dy ; */
+ ADVANCE (Yx,Yz,dy) ;
+ }
+ }
+ else if (!ENTRY_IS_ONE (beta, betaz, 0))
+ {
+ for (k = 0 ; k < kcol ; k++)
+ {
+ for (i = 0 ; i < ((Int) ny) ; i++)
+ {
+ /* y [i] *= beta [0] ; */
+ MULT (Yx,Yz,i, Yx,Yz,i, beta,betaz, 0) ;
+ }
+ /* y += dy ; */
+ ADVANCE (Yx,Yz,dy) ;
+ }
+ }
+
+ if (ENTRY_IS_ZERO (alpha, alphaz, 0))
+ {
+ /* nothing else to do */
+ return ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Y += alpha * op(A) * X, where op(A)=A or A' */
+ /* ---------------------------------------------------------------------- */
+
+ Yx = Y->x ;
+ Yz = Y->z ;
+
+ k = 0 ;
+
+ if (A->stype == 0)
+ {
+
+ if (transpose)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Y += alpha * A' * x, unsymmetric case */
+ /* -------------------------------------------------------------- */
+
+ if (kcol % 4 == 1)
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* yj = 0. ; */
+ CLEAR (yx, yz, 0) ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ /* yj += conj(Ax [p]) * x [Ai [p]] ; */
+ i = Ai [p] ;
+ ASSIGN_CONJ (ax,az,0, Ax,Az,p) ;
+ MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ;
+ }
+ /* y [j] += alpha [0] * yj ; */
+ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ;
+ }
+ /* y += dy ; */
+ /* x += dx ; */
+ ADVANCE (Yx,Yz,dy) ;
+ ADVANCE (Xx,Xz,dx) ;
+ k++ ;
+
+ }
+ else if (kcol % 4 == 2)
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* yj0 = 0. ; */
+ /* yj1 = 0. ; */
+ CLEAR (yx,yz,0) ;
+ CLEAR (yx,yz,1) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ /* aij = conj (Ax [p]) ; */
+ ASSIGN_CONJ (ax,az,0, Ax,Az,p) ;
+
+ /* yj0 += aij * x [i ] ; */
+ /* yj1 += aij * x [i+dx] ; */
+ MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ;
+ MULTADD (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ;
+ }
+ /* y [j ] += alpha [0] * yj0 ; */
+ /* y [j+dy] += alpha [0] * yj1 ; */
+ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ;
+ MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ;
+ }
+ /* y += 2*dy ; */
+ /* x += 2*dx ; */
+ ADVANCE (Yx,Yz,2*dy) ;
+ ADVANCE (Xx,Xz,2*dx) ;
+ k += 2 ;
+
+ }
+ else if (kcol % 4 == 3)
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* yj0 = 0. ; */
+ /* yj1 = 0. ; */
+ /* yj2 = 0. ; */
+ CLEAR (yx,yz,0) ;
+ CLEAR (yx,yz,1) ;
+ CLEAR (yx,yz,2) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ /* aij = conj (Ax [p]) ; */
+ ASSIGN_CONJ (ax,az,0, Ax,Az,p) ;
+
+ /* yj0 += aij * x [i ] ; */
+ /* yj1 += aij * x [i+ dx] ; */
+ /* yj2 += aij * x [i+2*dx] ; */
+ MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ;
+ MULTADD (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ;
+ MULTADD (yx,yz,2, ax,az,0, Xx,Xz,i+2*dx) ;
+ }
+ /* y [j ] += alpha [0] * yj0 ; */
+ /* y [j+ dy] += alpha [0] * yj1 ; */
+ /* y [j+2*dy] += alpha [0] * yj2 ; */
+ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ;
+ MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ;
+ MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ;
+ }
+ /* y += 3*dy ; */
+ /* x += 3*dx ; */
+ ADVANCE (Yx,Yz,3*dy) ;
+ ADVANCE (Xx,Xz,3*dx) ;
+ k += 3 ;
+ }
+
+ for ( ; k < kcol ; k += 4)
+ {
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* yj0 = 0. ; */
+ /* yj1 = 0. ; */
+ /* yj2 = 0. ; */
+ /* yj3 = 0. ; */
+ CLEAR (yx,yz,0) ;
+ CLEAR (yx,yz,1) ;
+ CLEAR (yx,yz,2) ;
+ CLEAR (yx,yz,3) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ /* aij = conj(Ax [p]) ; */
+ ASSIGN_CONJ (ax,az,0, Ax,Az,p) ;
+
+ /* yj0 += aij * x [i ] ; */
+ /* yj1 += aij * x [i+ dx] ; */
+ /* yj2 += aij * x [i+2*dx] ; */
+ /* yj3 += aij * x [i+3*dx] ; */
+ MULTADD (yx,yz,0, ax,az,0, Xx,Xz,i) ;
+ MULTADD (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ;
+ MULTADD (yx,yz,2, ax,az,0, Xx,Xz,i+2*dx) ;
+ MULTADD (yx,yz,3, ax,az,0, Xx,Xz,i+3*dx) ;
+
+ }
+ /* y [j ] += alpha [0] * yj0 ; */
+ /* y [j+ dy] += alpha [0] * yj1 ; */
+ /* y [j+2*dy] += alpha [0] * yj2 ; */
+ /* y [j+3*dy] += alpha [0] * yj3 ; */
+ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ;
+ MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ;
+ MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ;
+ MULTADD (Yx,Yz,j+3*dy, alpha,alphaz,0, yx,yz,3) ;
+ }
+ /* y += 4*dy ; */
+ /* x += 4*dx ; */
+ ADVANCE (Yx,Yz,4*dy) ;
+ ADVANCE (Xx,Xz,4*dx) ;
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Y += alpha * A * x, unsymmetric case */
+ /* -------------------------------------------------------------- */
+
+ if (kcol % 4 == 1)
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* xj = alpha [0] * x [j] ; */
+ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ /* y [Ai [p]] += Ax [p] * xj ; */
+ i = Ai [p] ;
+ MULTADD (Yx,Yz,i, Ax,Az,p, xx,xz,0) ;
+ }
+ }
+ /* y += dy ; */
+ /* x += dx ; */
+ ADVANCE (Yx,Yz,dy) ;
+ ADVANCE (Xx,Xz,dx) ;
+ k++ ;
+
+ }
+ else if (kcol % 4 == 2)
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* xj0 = alpha [0] * x [j ] ; */
+ /* xj1 = alpha [0] * x [j+dx] ; */
+ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ;
+ MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ /* aij = Ax [p] ; */
+ ASSIGN (ax,az,0, Ax,Az,p) ;
+
+ /* y [i ] += aij * xj0 ; */
+ /* y [i+dy] += aij * xj1 ; */
+ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ;
+ MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ;
+ }
+ }
+ /* y += 2*dy ; */
+ /* x += 2*dx ; */
+ ADVANCE (Yx,Yz,2*dy) ;
+ ADVANCE (Xx,Xz,2*dx) ;
+ k += 2 ;
+
+ }
+ else if (kcol % 4 == 3)
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* xj0 = alpha [0] * x [j ] ; */
+ /* xj1 = alpha [0] * x [j+ dx] ; */
+ /* xj2 = alpha [0] * x [j+2*dx] ; */
+ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ;
+ MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ;
+ MULT (xx,xz,2, alpha,alphaz,0, Xx,Xz,j+2*dx) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ /* aij = Ax [p] ; */
+ ASSIGN (ax,az,0, Ax,Az,p) ;
+
+ /* y [i ] += aij * xj0 ; */
+ /* y [i+ dy] += aij * xj1 ; */
+ /* y [i+2*dy] += aij * xj2 ; */
+ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ;
+ MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ;
+ MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ;
+ }
+ }
+ /* y += 3*dy ; */
+ /* x += 3*dx ; */
+ ADVANCE (Yx,Yz,3*dy) ;
+ ADVANCE (Xx,Xz,3*dx) ;
+ k += 3 ;
+ }
+
+ for ( ; k < kcol ; k += 4)
+ {
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* xj0 = alpha [0] * x [j ] ; */
+ /* xj1 = alpha [0] * x [j+ dx] ; */
+ /* xj2 = alpha [0] * x [j+2*dx] ; */
+ /* xj3 = alpha [0] * x [j+3*dx] ; */
+ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ;
+ MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ;
+ MULT (xx,xz,2, alpha,alphaz,0, Xx,Xz,j+2*dx) ;
+ MULT (xx,xz,3, alpha,alphaz,0, Xx,Xz,j+3*dx) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ /* aij = Ax [p] ; */
+ ASSIGN (ax,az,0, Ax,Az,p) ;
+
+ /* y [i ] += aij * xj0 ; */
+ /* y [i+ dy] += aij * xj1 ; */
+ /* y [i+2*dy] += aij * xj2 ; */
+ /* y [i+3*dy] += aij * xj3 ; */
+ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ;
+ MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ;
+ MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ;
+ MULTADD (Yx,Yz,i+3*dy, ax,az,0, xx,xz,3) ;
+ }
+ }
+ /* y += 4*dy ; */
+ /* x += 4*dx ; */
+ ADVANCE (Yx,Yz,4*dy) ;
+ ADVANCE (Xx,Xz,4*dx) ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Y += alpha * (A or A') * x, symmetric case (upper/lower) */
+ /* ------------------------------------------------------------------ */
+
+ /* Only the upper/lower triangular part and the diagonal of A is used.
+ * Since both x and y are written to in the innermost loop, this
+ * code can experience cache bank conflicts if x is used directly.
+ * Thus, a copy is made of x, four columns at a time, if x has
+ * four or more columns.
+ */
+
+ if (kcol % 4 == 1)
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* yj = 0. ; */
+ CLEAR (yx,yz,0) ;
+
+ /* xj = alpha [0] * x [j] ; */
+ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i == j)
+ {
+ /* y [i] += Ax [p] * xj ; */
+ MULTADD (Yx,Yz,i, Ax,Az,p, xx,xz,0) ;
+ }
+ else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j))
+ {
+ /* aij = Ax [p] ; */
+ ASSIGN (ax,az,0, Ax,Az,p) ;
+
+ /* y [i] += aij * xj ; */
+ /* yj += aij * x [i] ; */
+ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ;
+ MULTADDCONJ (yx,yz,0, ax,az,0, Xx,Xz,i) ;
+
+
+ }
+ }
+ /* y [j] += alpha [0] * yj ; */
+ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ;
+
+ }
+ /* y += dy ; */
+ /* x += dx ; */
+ ADVANCE (Yx,Yz,dy) ;
+ ADVANCE (Xx,Xz,dx) ;
+ k++ ;
+
+ }
+ else if (kcol % 4 == 2)
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* yj0 = 0. ; */
+ /* yj1 = 0. ; */
+ CLEAR (yx,yz,0) ;
+ CLEAR (yx,yz,1) ;
+
+ /* xj0 = alpha [0] * x [j ] ; */
+ /* xj1 = alpha [0] * x [j+dx] ; */
+ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ;
+ MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i == j)
+ {
+ /* aij = Ax [p] ; */
+ ASSIGN (ax,az,0, Ax,Az,p) ;
+
+ /* y [i ] += aij * xj0 ; */
+ /* y [i+dy] += aij * xj1 ; */
+ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ;
+ MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ;
+
+ }
+ else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j))
+ {
+ /* aij = Ax [p] ; */
+ ASSIGN (ax,az,0, Ax,Az,p) ;
+
+ /* y [i ] += aij * xj0 ; */
+ /* y [i+dy] += aij * xj1 ; */
+ /* yj0 += aij * x [i ] ; */
+ /* yj1 += aij * x [i+dx] ; */
+ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ;
+ MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ;
+ MULTADDCONJ (yx,yz,0, ax,az,0, Xx,Xz,i) ;
+ MULTADDCONJ (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ;
+
+ }
+ }
+ /* y [j ] += alpha [0] * yj0 ; */
+ /* y [j+dy] += alpha [0] * yj1 ; */
+ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ;
+ MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ;
+
+ }
+ /* y += 2*dy ; */
+ /* x += 2*dx ; */
+ ADVANCE (Yx,Yz,2*dy) ;
+ ADVANCE (Xx,Xz,2*dx) ;
+ k += 2 ;
+
+ }
+ else if (kcol % 4 == 3)
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* yj0 = 0. ; */
+ /* yj1 = 0. ; */
+ /* yj2 = 0. ; */
+ CLEAR (yx,yz,0) ;
+ CLEAR (yx,yz,1) ;
+ CLEAR (yx,yz,2) ;
+
+ /* xj0 = alpha [0] * x [j ] ; */
+ /* xj1 = alpha [0] * x [j+ dx] ; */
+ /* xj2 = alpha [0] * x [j+2*dx] ; */
+ MULT (xx,xz,0, alpha,alphaz,0, Xx,Xz,j) ;
+ MULT (xx,xz,1, alpha,alphaz,0, Xx,Xz,j+dx) ;
+ MULT (xx,xz,2, alpha,alphaz,0, Xx,Xz,j+2*dx) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i == j)
+ {
+
+ /* aij = Ax [p] ; */
+ ASSIGN (ax,az,0, Ax,Az,p) ;
+
+ /* y [i ] += aij * xj0 ; */
+ /* y [i+ dy] += aij * xj1 ; */
+ /* y [i+2*dy] += aij * xj2 ; */
+ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ;
+ MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ;
+ MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ;
+
+ }
+ else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j))
+ {
+
+ /* aij = Ax [p] ; */
+ ASSIGN (ax,az,0, Ax,Az,p) ;
+
+ /* y [i ] += aij * xj0 ; */
+ /* y [i+ dy] += aij * xj1 ; */
+ /* y [i+2*dy] += aij * xj2 ; */
+ /* yj0 += aij * x [i ] ; */
+ /* yj1 += aij * x [i+ dx] ; */
+ /* yj2 += aij * x [i+2*dx] ; */
+ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ;
+ MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ;
+ MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ;
+ MULTADDCONJ (yx,yz,0, ax,az,0, Xx,Xz,i) ;
+ MULTADDCONJ (yx,yz,1, ax,az,0, Xx,Xz,i+dx) ;
+ MULTADDCONJ (yx,yz,2, ax,az,0, Xx,Xz,i+2*dx) ;
+
+ }
+ }
+ /* y [j ] += alpha [0] * yj0 ; */
+ /* y [j+ dy] += alpha [0] * yj1 ; */
+ /* y [j+2*dy] += alpha [0] * yj2 ; */
+ MULTADD (Yx,Yz,j, alpha,alphaz,0, yx,yz,0) ;
+ MULTADD (Yx,Yz,j+dy, alpha,alphaz,0, yx,yz,1) ;
+ MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ;
+
+ }
+ /* y += 3*dy ; */
+ /* x += 3*dx ; */
+ ADVANCE (Yx,Yz,3*dy) ;
+ ADVANCE (Xx,Xz,3*dx) ;
+
+ k += 3 ;
+ }
+
+ /* copy four columns of X into W, and put in row form */
+ for ( ; k < kcol ; k += 4)
+ {
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* w [4*j ] = x [j ] ; */
+ /* w [4*j+1] = x [j+ dx] ; */
+ /* w [4*j+2] = x [j+2*dx] ; */
+ /* w [4*j+3] = x [j+3*dx] ; */
+ ASSIGN (w,Wz,4*j , Xx,Xz,j ) ;
+ ASSIGN (w,Wz,4*j+1, Xx,Xz,j+dx ) ;
+ ASSIGN (w,Wz,4*j+2, Xx,Xz,j+2*dx) ;
+ ASSIGN (w,Wz,4*j+3, Xx,Xz,j+3*dx) ;
+ }
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* yj0 = 0. ; */
+ /* yj1 = 0. ; */
+ /* yj2 = 0. ; */
+ /* yj3 = 0. ; */
+ CLEAR (yx,yz,0) ;
+ CLEAR (yx,yz,1) ;
+ CLEAR (yx,yz,2) ;
+ CLEAR (yx,yz,3) ;
+
+ /* xj0 = alpha [0] * w [4*j ] ; */
+ /* xj1 = alpha [0] * w [4*j+1] ; */
+ /* xj2 = alpha [0] * w [4*j+2] ; */
+ /* xj3 = alpha [0] * w [4*j+3] ; */
+ MULT (xx,xz,0, alpha,alphaz,0, w,Wz,4*j) ;
+ MULT (xx,xz,1, alpha,alphaz,0, w,Wz,4*j+1) ;
+ MULT (xx,xz,2, alpha,alphaz,0, w,Wz,4*j+2) ;
+ MULT (xx,xz,3, alpha,alphaz,0, w,Wz,4*j+3) ;
+
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i == j)
+ {
+ /* aij = Ax [p] ; */
+ ASSIGN (ax,az,0, Ax,Az,p) ;
+
+ /* y [i ] += aij * xj0 ; */
+ /* y [i+ dy] += aij * xj1 ; */
+ /* y [i+2*dy] += aij * xj2 ; */
+ /* y [i+3*dy] += aij * xj3 ; */
+ MULTADD (Yx,Yz,i , ax,az,0, xx,xz,0) ;
+ MULTADD (Yx,Yz,i+dy , ax,az,0, xx,xz,1) ;
+ MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ;
+ MULTADD (Yx,Yz,i+3*dy, ax,az,0, xx,xz,3) ;
+
+ }
+ else if ((A->stype > 0 && i < j) || (A->stype < 0 && i > j))
+ {
+ /* aij = Ax [p] ; */
+ ASSIGN (ax,az,0, Ax,Az,p) ;
+
+ /* y [i ] += aij * xj0 ; */
+ /* y [i+ dy] += aij * xj1 ; */
+ /* y [i+2*dy] += aij * xj2 ; */
+ /* y [i+3*dy] += aij * xj3 ; */
+ /* yj0 += aij * w [4*i ] ; */
+ /* yj1 += aij * w [4*i+1] ; */
+ /* yj2 += aij * w [4*i+2] ; */
+ /* yj3 += aij * w [4*i+3] ; */
+ MULTADD (Yx,Yz,i, ax,az,0, xx,xz,0) ;
+ MULTADD (Yx,Yz,i+dy, ax,az,0, xx,xz,1) ;
+ MULTADD (Yx,Yz,i+2*dy, ax,az,0, xx,xz,2) ;
+ MULTADD (Yx,Yz,i+3*dy, ax,az,0, xx,xz,3) ;
+ MULTADDCONJ (yx,yz,0, ax,az,0, w,Wz,4*i) ;
+ MULTADDCONJ (yx,yz,1, ax,az,0, w,Wz,4*i+1) ;
+ MULTADDCONJ (yx,yz,2, ax,az,0, w,Wz,4*i+2) ;
+ MULTADDCONJ (yx,yz,3, ax,az,0, w,Wz,4*i+3) ;
+
+ }
+ }
+ /* y [j ] += alpha [0] * yj0 ; */
+ /* y [j+ dy] += alpha [0] * yj1 ; */
+ /* y [j+2*dy] += alpha [0] * yj2 ; */
+ /* y [j+3*dy] += alpha [0] * yj3 ; */
+ MULTADD (Yx,Yz,j , alpha,alphaz,0, yx,yz,0) ;
+ MULTADD (Yx,Yz,j+dy , alpha,alphaz,0, yx,yz,1) ;
+ MULTADD (Yx,Yz,j+2*dy, alpha,alphaz,0, yx,yz,2) ;
+ MULTADD (Yx,Yz,j+3*dy, alpha,alphaz,0, yx,yz,3) ;
+
+ }
+ /* y += 4*dy ; */
+ /* x += 4*dx ; */
+ ADVANCE (Yx,Yz,4*dy) ;
+ ADVANCE (Xx,Xz,4*dx) ;
+
+ }
+ }
+}
+
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/CHOLMOD/Modify/License.txt b/CHOLMOD/Modify/License.txt
new file mode 100644
index 0000000..cbcf9b3
--- /dev/null
+++ b/CHOLMOD/Modify/License.txt
@@ -0,0 +1,25 @@
+CHOLMOD/Modify Module.
+Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Modify module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
diff --git a/CHOLMOD/Modify/cholmod_rowadd.c b/CHOLMOD/Modify/cholmod_rowadd.c
new file mode 100644
index 0000000..f0adc9c
--- /dev/null
+++ b/CHOLMOD/Modify/cholmod_rowadd.c
@@ -0,0 +1,678 @@
+/* ========================================================================== */
+/* === Modify/cholmod_rowadd ================================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Modify Module.
+ * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager.
+ * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Adds a row and column to an LDL' factorization, and optionally updates the
+ * solution to Lx=b.
+ *
+ * workspace: Flag (nrow), Head (nrow+1), W (2*nrow), Iwork (2*nrow)
+ *
+ * Only real matrices are supported. A symbolic L is converted into a
+ * numeric identity matrix before the row is added.
+ */
+
+#ifndef NMODIFY
+
+#include "cholmod_internal.h"
+#include "cholmod_modify.h"
+
+
+/* ========================================================================== */
+/* === cholmod_rowadd ======================================================= */
+/* ========================================================================== */
+
+/* cholmod_rowadd adds a row to the LDL' factorization. It computes the kth
+ * row and kth column of L, and then updates the submatrix L (k+1:n,k+1:n)
+ * accordingly. The kth row and column of L should originally be equal to the
+ * kth row and column of the identity matrix (they are treated as such, if they
+ * are not). The kth row/column of L is computed as the factorization of the
+ * kth row/column of the matrix to factorize, which is provided as a single
+ * n-by-1 sparse matrix R. The sparse vector R need not be sorted.
+ */
+
+int CHOLMOD(rowadd)
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to add */
+ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double bk [2] ;
+ bk [0] = 0. ;
+ bk [1] = 0. ;
+ return (CHOLMOD(rowadd_mark) (k, R, bk, NULL, L, NULL, NULL, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_rowadd_solve ================================================= */
+/* ========================================================================== */
+
+/* Does the same as cholmod_rowadd, and also updates the solution to Lx=b
+ * See cholmod_updown for a description of how Lx=b is updated. There is on
+ * additional parameter: bk specifies the new kth entry of b.
+ */
+
+int CHOLMOD(rowadd_solve)
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to add */
+ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */
+ double bk [2], /* kth entry of the right-hand-side b */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(rowadd_mark) (k, R, bk, NULL, L, X, DeltaB, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === icomp ================================================================ */
+/* ========================================================================== */
+
+/* for sorting by qsort */
+static int icomp (Int *i, Int *j)
+{
+ if (*i < *j)
+ {
+ return (-1) ;
+ }
+ else
+ {
+ return (1) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === cholmod_rowadd_mark ================================================== */
+/* ========================================================================== */
+
+/* Does the same as cholmod_rowadd_solve, except only part of L is used in
+ * the update/downdate of the solution to Lx=b. This routine is an "expert"
+ * routine. It is meant for use in LPDASA only. */
+
+int CHOLMOD(rowadd_mark)
+(
+ /* ---- input ---- */
+ size_t kadd, /* row/column index to add */
+ cholmod_sparse *R, /* row/column of matrix to factorize (n-by-1) */
+ double bk [2], /* kth entry of the right hand side, b */
+ Int *colmark, /* Int array of size 1. See cholmod_updown.c */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double dk, yj, l_kj, lx, l_ij, sqrt_dk, dj, xk, rnz, fl ;
+ double *Lx, *W, *Cx, *Rx, *Xx, *Nx ;
+ Int *Li, *Lp, *Lnz, *Flag, *Stack, *Ci, *Rj, *Rp, *Lnext, *Iwork, *Rnz ;
+ cholmod_sparse *C, Cmatrix ;
+ Int i, j, p, pend, top, len, kk, li, lnz, mark, k, n, parent, Cp [2],
+ do_solve, do_update ;
+ size_t s ;
+ int ok = TRUE ;
+ DEBUG (Int lastrow) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_NULL (R, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (R, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ;
+ n = L->n ;
+ k = kadd ;
+ if (kadd >= L->n || k < 0)
+ {
+ ERROR (CHOLMOD_INVALID, "k invalid") ;
+ return (FALSE) ;
+ }
+ if (R->ncol != 1 || R->nrow != L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "R invalid") ;
+ return (FALSE) ;
+ }
+ Rj = R->i ;
+ Rx = R->x ;
+ Rp = R->p ;
+ Rnz = R->nz ;
+ rnz = (R->packed) ? (Rp [1]) : (Rnz [0]) ;
+ do_solve = (X != NULL) && (DeltaB != NULL) ;
+ if (do_solve)
+ {
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (DeltaB, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ;
+ Xx = X->x ;
+ Nx = DeltaB->x ;
+ if (X->nrow != L->n || X->ncol != 1 || DeltaB->nrow != L->n ||
+ DeltaB->ncol != 1 || Xx == NULL || Nx == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "X and/or DeltaB invalid") ;
+ return (FALSE) ;
+ }
+ }
+ else
+ {
+ Xx = NULL ;
+ Nx = NULL ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = 2*n */
+ s = CHOLMOD(mult_size_t) (n, 2, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (n, s, s, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, s, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to simplicial numeric LDL' factor, if not already */
+ /* ---------------------------------------------------------------------- */
+
+ if (L->xtype == CHOLMOD_PATTERN || L->is_super || L->is_ll)
+ {
+ /* can only update/downdate a simplicial LDL' factorization */
+ CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, FALSE, L,
+ Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory, L is returned unchanged */
+ return (FALSE) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* inputs, not modified on output: */
+ Lp = L->p ; /* size n+1. input, not modified on output */
+
+ /* outputs, contents defined on input for incremental case only: */
+ Lnz = L->nz ; /* size n */
+ Li = L->i ; /* size L->nzmax. Can change in size. */
+ Lx = L->x ; /* size L->nzmax. Can change in size. */
+ Lnext = L->next ; /* size n+2 */
+
+ ASSERT (L->nz != NULL) ;
+
+ PRINT1 (("rowadd:\n")) ;
+ fl = 0 ;
+
+#if 0
+#ifndef NDEBUG
+ /* column k of L should be zero, except for the diagonal. This test is
+ * overly cautious. */
+ for (p = Lp [k] + 1 ; p < Lp [k] + Lnz [k] ; p++) ASSERT (Lx [p] == 0) ;
+#endif
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Flag = Common->Flag ; /* size n */
+ W = Common->Xwork ; /* size n */
+ Cx = W + n ; /* size n (use 2nd column of Xwork for C) */
+ Iwork = Common->Iwork ;
+ Stack = Iwork ; /* size n (i/i/l), also in cholmod_updown */
+ Ci = Iwork + n ; /* size n (i/i/l) */
+ /* NOTE: cholmod_updown uses Iwork [0..n-1] (i/i/l) as Stack as well */
+
+ mark = Common->mark ;
+
+ /* copy Rj/Rx into W/Ci */
+ for (p = 0 ; p < rnz ; p++)
+ {
+ i = Rj [p] ;
+ ASSERT (i >= 0 && i < n) ;
+ W [i] = Rx [p] ;
+ Ci [p] = i ;
+ }
+
+ /* At this point, W [Ci [0..rnz-1]] holds the sparse vector to add */
+ /* The nonzero pattern of column W is held in Ci (it may be unsorted). */
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization to get pattern of kth row of L */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG (for (p = 0 ; p < rnz ; p++)
+ PRINT1 (("C ("ID",%g)\n", Ci [p], W [Ci [p]]))) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* flag the diagonal */
+ Flag [k] = mark ;
+
+ /* find the union of all the paths */
+ top = n ;
+ lnz = 0 ; /* # of nonzeros in column k of L, excluding diagonal */
+ for (p = 0 ; p < rnz ; p++)
+ {
+ i = Ci [p] ;
+
+ if (i < k)
+ {
+
+ /* walk from i = entry in Ci to root (and stop if i marked)*/
+ PRINT2 (("\nwalk from i = "ID" towards k = "ID"\n", i, k)) ;
+ len = 0 ;
+
+ /* walk up tree, but stop if we go below the diagonal */
+ while (i < k && i != EMPTY && Flag [i] < mark)
+ {
+ PRINT2 ((" Add "ID" to path\n", i)) ;
+ ASSERT (i >= 0 && i < k) ;
+ Stack [len++] = i ; /* place i on the stack */
+ Flag [i] = mark ; /* mark i as visited */
+ /* parent is the first entry in the column after the diagonal */
+ ASSERT (Lnz [i] > 0) ;
+ parent = (Lnz [i] > 1) ? (Li [Lp [i] + 1]) : EMPTY ;
+ PRINT2 ((" parent: "ID"\n", parent)) ;
+ i = parent ; /* go up the tree */
+ }
+ ASSERT (len <= top) ;
+
+ /* move the path down to the bottom of the stack */
+ /* this shifts Stack [0..len-1] down to [ ... oldtop-1] */
+ while (len > 0)
+ {
+ Stack [--top] = Stack [--len] ;
+ }
+ }
+ else if (i > k)
+ {
+ /* prune the diagonal and upper triangular entries from Ci */
+ Ci [lnz++] = i ;
+ Flag [i] = mark ;
+ }
+ }
+
+#ifndef NDEBUG
+ PRINT1 (("length of S after prune: "ID"\n", lnz)) ;
+ for (p = 0 ; p < lnz ; p++)
+ {
+ PRINT1 (("After prune Ci ["ID"] = "ID"\n", p, Ci [p])) ;
+ ASSERT (Ci [p] > k) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* ensure each column of L has enough space to grow */
+ /* ---------------------------------------------------------------------- */
+
+ for (kk = top ; kk < n ; kk++)
+ {
+ /* could skip this if we knew column j already included row k */
+ j = Stack [kk] ;
+ if (Lp [j] + Lnz [j] >= Lp [Lnext [j]])
+ {
+ PRINT1 (("Col "ID" realloc, old Lnz "ID"\n", j, Lnz [j])) ;
+ if (!CHOLMOD(reallocate_column) (j, Lnz [j] + 1, L, Common))
+ {
+ /* out of memory, L is now simplicial symbolic */
+ /* CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = 0 ;
+ }
+ return (FALSE) ;
+ }
+ /* L->i and L->x may have moved */
+ Li = L->i ;
+ Lx = L->x ;
+ }
+ ASSERT (Lp [j] + Lnz [j] < Lp [Lnext [j]]
+ || (Lp [Lnext [j]] - Lp [j] == n-j)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute kth row of L and store in column form */
+ /* ---------------------------------------------------------------------- */
+
+ /* solve L (1:k-1, 1:k-1) * y (1:k-1) = b (1:k-1) */
+ /* where b (1:k) is in W and Ci */
+
+ /* L (k, 1:k-1) = y (1:k-1) ./ D (1:k-1) */
+ /* D (k) = B (k,k) - L (k, 1:k-1) * y (1:k-1) */
+
+ PRINT2 (("\nForward solve: "ID" to "ID"\n", top, n)) ;
+ ASSERT (Lnz [k] >= 1 && Li [Lp [k]] == k) ;
+ DEBUG (for (i = top ; i < n ; i++) PRINT2 ((" Path: "ID"\n", Stack [i]))) ;
+
+ dk = W [k] ;
+ W [k] = 0.0 ;
+
+ /* if do_solve: compute x (k) = b (k) - L (k, 1:k-1) * x (1:k-1) */
+ xk = bk [0] ;
+ PRINT2 (("B [k] = %g\n", xk)) ;
+
+ for (kk = top ; kk < n ; kk++)
+ {
+ j = Stack [kk] ;
+ i = j ;
+ PRINT2 (("Forward solve col j = "ID":\n", j)) ;
+ ASSERT (j >= 0 && j < k) ;
+
+ /* forward solve using L (j+1:k-1,j) */
+ yj = W [j] ;
+ W [j] = 0.0 ;
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+ ASSERT (Lnz [j] > 0) ;
+ dj = Lx [p++] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Li [p] ;
+ PRINT2 ((" row "ID"\n", i)) ;
+ ASSERT (i > j) ;
+ ASSERT (i < n) ;
+ /* stop at row k */
+ if (i >= k)
+ {
+ break ;
+ }
+ W [i] -= Lx [p] * yj ;
+ }
+
+ /* each iteration of the above for loop did 2 flops, and 3 flops
+ * are done below. so: fl += 2 * (Lp [j] - p - 1) + 3 becomes: */
+ fl += 2 * (Lp [j] - p) + 1 ;
+
+ /* scale L (k,1:k-1) and compute dot product for D (k,k) */
+ l_kj = yj / dj ;
+ dk -= l_kj * yj ;
+
+ /* compute dot product for X(k) */
+ if (do_solve)
+ {
+ xk -= l_kj * Xx [j] ;
+ }
+
+ /* store l_kj in the jth column of L */
+ /* and shift the rest of the column down */
+
+ li = k ;
+ lx = l_kj ;
+
+ if (i == k)
+ {
+ /* no need to modify the nonzero pattern of L, since it already
+ * contains row index k. */
+ ASSERT (Li [p] == k) ;
+ Lx [p] = l_kj ;
+
+ for (p++ ; p < pend ; p++)
+ {
+ i = Li [p] ;
+ l_ij = Lx [p] ;
+ ASSERT (i > k && i < n) ;
+ PRINT2 ((" apply to row "ID" of column k of L\n", i)) ;
+
+ /* add to the pattern of the kth column of L */
+ if (Flag [i] < mark)
+ {
+ PRINT2 ((" add Ci["ID"] = "ID"\n", lnz, i)) ;
+ ASSERT (i > k) ;
+ Ci [lnz++] = i ;
+ Flag [i] = mark ;
+ }
+
+ /* apply the update to the kth column of L */
+ /* yj is equal to l_kj * d_j */
+
+ W [i] -= l_ij * yj ;
+ }
+
+ }
+ else
+ {
+
+ PRINT2 (("Shift col j = "ID", apply saxpy to col k of L\n", j)) ;
+ for ( ; p < pend ; p++)
+ {
+ /* swap (Li [p],Lx [p]) with (li,lx) */
+ i = Li [p] ;
+ l_ij = Lx [p] ;
+ Li [p] = li ;
+ Lx [p] = lx ;
+ li = i ;
+ lx = l_ij ;
+ ASSERT (i > k && i < n) ;
+ PRINT2 ((" apply to row "ID" of column k of L\n", i)) ;
+
+ /* add to the pattern of the kth column of L */
+ if (Flag [i] < mark)
+ {
+ PRINT2 ((" add Ci["ID"] = "ID"\n", lnz, i)) ;
+ ASSERT (i > k) ;
+ Ci [lnz++] = i ;
+ Flag [i] = mark ;
+ }
+
+ /* apply the update to the kth column of L */
+ /* yj is equal to l_kj * d_j */
+
+ W [i] -= l_ij * yj ;
+ }
+
+ /* store the last value in the jth column of L */
+ Li [p] = li ;
+ Lx [p] = lx ;
+ Lnz [j]++ ;
+
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* merge C with the pattern of the existing column of L */
+ /* ---------------------------------------------------------------------- */
+
+ /* This column should be zero, but it may contain explicit zero entries.
+ * These entries should be kept, not dropped. */
+ p = Lp [k] ;
+ pend = p + Lnz [k] ;
+ for (p++ ; p < pend ; p++)
+ {
+ i = Li [p] ;
+ /* add to the pattern of the kth column of L */
+ if (Flag [i] < mark)
+ {
+ PRINT2 ((" add Ci["ID"] = "ID" from existing col k\n", lnz, i)) ;
+ ASSERT (i > k) ;
+ Ci [lnz++] = i ;
+ Flag [i] = mark ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+
+ if (do_solve)
+ {
+ Xx [k] = xk ;
+ PRINT2 (("Xx [k] = %g\n", Xx [k])) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* ensure abs (dk) >= dbound, if dbound is given */
+ /* ---------------------------------------------------------------------- */
+
+ dk = (IS_GT_ZERO (Common->dbound)) ? (CHOLMOD(dbound) (dk, Common)) : dk ;
+
+ PRINT2 (("D [k = "ID"] = %g\n", k, dk)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* store the kth column of L */
+ /* ---------------------------------------------------------------------- */
+
+ /* ensure the new column of L has enough space */
+ if (Lp [k] + lnz + 1 > Lp [Lnext [k]])
+ {
+ PRINT1 (("New Col "ID" realloc, old Lnz "ID"\n", k, Lnz [k])) ;
+ if (!CHOLMOD(reallocate_column) (k, lnz + 1, L, Common))
+ {
+ /* out of memory, L is now simplicial symbolic */
+ CHOLMOD(clear_flag) (Common) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = 0 ;
+ }
+ return (FALSE) ;
+ }
+ /* L->i and L->x may have moved */
+ Li = L->i ;
+ Lx = L->x ;
+ }
+ ASSERT (Lp [k] + lnz + 1 <= Lp [Lnext [k]]) ;
+
+#ifndef NDEBUG
+ PRINT2 (("\nPrior to sort: lnz "ID" (excluding diagonal)\n", lnz)) ;
+ for (kk = 0 ; kk < lnz ; kk++)
+ {
+ i = Ci [kk] ;
+ PRINT2 (("L ["ID"] kept: "ID" %e\n", kk, i, W [i] / dk)) ;
+ }
+#endif
+
+ /* sort Ci */
+ qsort (Ci, lnz, sizeof (Int), (int (*) (const void *, const void *)) icomp);
+
+ /* store the kth column of L */
+ DEBUG (lastrow = k) ;
+ p = Lp [k] ;
+ Lx [p++] = dk ;
+ Lnz [k] = lnz + 1 ;
+ fl += lnz ;
+ for (kk = 0 ; kk < lnz ; kk++, p++)
+ {
+ i = Ci [kk] ;
+ PRINT2 (("L ["ID"] after sort: "ID", %e\n", kk, i, W [i] / dk)) ;
+ ASSERT (i > lastrow) ;
+ Li [p] = i ;
+ Lx [p] = W [i] / dk ;
+ W [i] = 0.0 ;
+ DEBUG (lastrow = i) ;
+ }
+
+ /* compute DeltaB for updown (in DeltaB) */
+ if (do_solve)
+ {
+ p = Lp [k] ;
+ pend = p + Lnz [k] ;
+ for (p++ ; p < pend ; p++)
+ {
+ ASSERT (Li [p] > k) ;
+ Nx [Li [p]] -= Lx [p] * xk ;
+ }
+ }
+
+ /* clear the flag for the update */
+ mark = CHOLMOD(clear_flag) (Common) ;
+
+ /* workspaces are now cleared */
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* update/downdate */
+ /* ---------------------------------------------------------------------- */
+
+ /* update or downdate L (k+1:n, k+1:n) with the vector
+ * C = L (:,k) * sqrt (abs (D [k])).
+ * Do a numeric update if D[k] < 0, numeric downdate otherwise.
+ */
+
+ ok = TRUE ;
+ Common->modfl = 0 ;
+
+ PRINT1 (("rowadd update lnz = "ID"\n", lnz)) ;
+ if (lnz > 0)
+ {
+ do_update = IS_LT_ZERO (dk) ;
+ if (do_update)
+ {
+ dk = -dk ;
+ }
+ sqrt_dk = sqrt (dk) ;
+ p = Lp [k] + 1 ;
+ for (kk = 0 ; kk < lnz ; kk++, p++)
+ {
+ Cx [kk] = Lx [p] * sqrt_dk ;
+ }
+ fl += lnz + 1 ;
+
+ /* create a n-by-1 sparse matrix to hold the single column */
+ C = &Cmatrix ;
+ C->nrow = n ;
+ C->ncol = 1 ;
+ C->nzmax = lnz ;
+ C->sorted = TRUE ;
+ C->packed = TRUE ;
+ C->p = Cp ;
+ C->i = Ci ;
+ C->x = Cx ;
+ C->nz = NULL ;
+ C->itype = L->itype ;
+ C->xtype = L->xtype ;
+ C->dtype = L->dtype ;
+ C->z = NULL ;
+ C->stype = 0 ;
+
+ Cp [0] = 0 ;
+ Cp [1] = lnz ;
+
+ /* numeric downdate if dk > 0, and optional Lx=b change */
+ /* workspace: Flag (nrow), Head (nrow+1), W (nrow), Iwork (2*nrow) */
+ ok = CHOLMOD(updown_mark) (do_update ? (1) : (0), C, colmark,
+ L, X, DeltaB, Common) ;
+
+ /* clear workspace */
+ for (kk = 0 ; kk < lnz ; kk++)
+ {
+ Cx [kk] = 0 ;
+ }
+ }
+
+ Common->modfl += fl ;
+
+ DEBUG (CHOLMOD(dump_factor) (L, "LDL factorization, L:", Common)) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ;
+ return (ok) ;
+}
+#endif
diff --git a/CHOLMOD/Modify/cholmod_rowdel.c b/CHOLMOD/Modify/cholmod_rowdel.c
new file mode 100644
index 0000000..ee0c1a2
--- /dev/null
+++ b/CHOLMOD/Modify/cholmod_rowdel.c
@@ -0,0 +1,461 @@
+/* ========================================================================== */
+/* === Modify/cholmod_rowdel ================================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Modify Module.
+ * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager.
+ * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Deletes a row and column from an LDL' factorization. The row and column k
+ * is set to the kth row and column of the identity matrix. Optionally
+ * downdates the solution to Lx=b.
+ *
+ * workspace: Flag (nrow), Head (nrow+1), W (nrow*2), Iwork (2*nrow)
+ *
+ * Only real matrices are supported (exception: since only the pattern of R
+ * is used, it can have any valid xtype).
+ */
+
+#ifndef NMODIFY
+
+#include "cholmod_internal.h"
+#include "cholmod_modify.h"
+
+
+/* ========================================================================== */
+/* === cholmod_rowdel ======================================================= */
+/* ========================================================================== */
+
+/* Sets the kth row and column of L to be the kth row and column of the identity
+ * matrix, and updates L(k+1:n,k+1:n) accordingly. To reduce the running time,
+ * the caller can optionally provide the nonzero pattern (or an upper bound) of
+ * kth row of L, as the sparse n-by-1 vector R. Provide R as NULL if you want
+ * CHOLMOD to determine this itself, which is easier for the caller, but takes
+ * a little more time.
+ */
+
+int CHOLMOD(rowdel)
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to delete */
+ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double yk [2] ;
+ yk [0] = 0. ;
+ yk [1] = 0. ;
+ return (CHOLMOD(rowdel_mark) (k, R, yk, NULL, L, NULL, NULL, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_rowdel_solve ================================================= */
+/* ========================================================================== */
+
+/* Does the same as cholmod_rowdel, but also downdates the solution to Lx=b.
+ * When row/column k of A is "deleted" from the system A*y=b, this can induce
+ * a change to x, in addition to changes arising when L and b are modified.
+ * If this is the case, the kth entry of y is required as input (yk) */
+
+int CHOLMOD(rowdel_solve)
+(
+ /* ---- input ---- */
+ size_t k, /* row/column index to delete */
+ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */
+ double yk [2], /* kth entry in the solution to A*y=b */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(rowdel_mark) (k, R, yk, NULL, L, X, DeltaB, Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_rowdel_mark ================================================== */
+/* ========================================================================== */
+
+/* Does the same as cholmod_rowdel_solve, except only part of L is used in
+ * the update/downdate of the solution to Lx=b. This routine is an "expert"
+ * routine. It is meant for use in LPDASA only.
+ *
+ * if R == NULL then columns 0:k-1 of L are searched for row k. Otherwise, it
+ * searches columns in the set defined by the pattern of the first column of R.
+ * This is meant to be the pattern of row k of L (a superset of that pattern is
+ * OK too). R must be a permutation of a subset of 0:k-1.
+ */
+
+int CHOLMOD(rowdel_mark)
+(
+ /* ---- input ---- */
+ size_t kdel, /* row/column index to delete */
+ cholmod_sparse *R, /* NULL, or the nonzero pattern of kth row of L */
+ double yk [2], /* kth entry in the solution to A*y=b */
+ Int *colmark, /* Int array of size 1. See cholmod_updown.c */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double dk, sqrt_dk, xk, dj, fl ;
+ double *Lx, *Cx, *W, *Xx, *Nx ;
+ Int *Li, *Lp, *Lnz, *Ci, *Rj, *Rp, *Iwork ;
+ cholmod_sparse *C, Cmatrix ;
+ Int j, p, pend, kk, lnz, n, Cp [2], do_solve, do_update, left, k,
+ right, middle, i, klast, given_row, rnz ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ;
+ n = L->n ;
+ k = kdel ;
+ if (kdel >= L->n || k < 0)
+ {
+ ERROR (CHOLMOD_INVALID, "k invalid") ;
+ return (FALSE) ;
+ }
+ if (R == NULL)
+ {
+ Rj = NULL ;
+ rnz = EMPTY ;
+ }
+ else
+ {
+ RETURN_IF_XTYPE_INVALID (R, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (R->ncol != 1 || R->nrow != L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "R invalid") ;
+ return (FALSE) ;
+ }
+ Rj = R->i ;
+ Rp = R->p ;
+ rnz = Rp [1] ;
+ }
+ do_solve = (X != NULL) && (DeltaB != NULL) ;
+ if (do_solve)
+ {
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (DeltaB, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ;
+ Xx = X->x ;
+ Nx = DeltaB->x ;
+ if (X->nrow != L->n || X->ncol != 1 || DeltaB->nrow != L->n ||
+ DeltaB->ncol != 1 || Xx == NULL || Nx == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "X and/or DeltaB invalid") ;
+ return (FALSE) ;
+ }
+ }
+ else
+ {
+ Xx = NULL ;
+ Nx = NULL ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = 2*n */
+ s = CHOLMOD(mult_size_t) (n, 2, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (n, s, s, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to simplicial numeric LDL' factor, if not already */
+ /* ---------------------------------------------------------------------- */
+
+ if (L->xtype == CHOLMOD_PATTERN || L->is_super || L->is_ll)
+ {
+ /* can only update/downdate a simplicial LDL' factorization */
+ CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, FALSE, L,
+ Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory, L is returned unchanged */
+ return (FALSE) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* inputs, not modified on output: */
+ Lp = L->p ; /* size n+1 */
+
+ /* outputs, contents defined on input for incremental case only: */
+ Lnz = L->nz ; /* size n */
+ Li = L->i ; /* size L->nzmax. Can change in size. */
+ Lx = L->x ; /* size L->nzmax. Can change in size. */
+
+ ASSERT (L->nz != NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ W = Common->Xwork ; /* size n, used only in cholmod_updown */
+ Cx = W + n ; /* use 2nd column of Xwork for C (size n) */
+ Iwork = Common->Iwork ;
+ Ci = Iwork + n ; /* size n (i/i/l) */
+ /* NOTE: cholmod_updown uses Iwork [0..n-1] (i/i/l) as Stack */
+
+ /* ---------------------------------------------------------------------- */
+ /* prune row k from all columns of L */
+ /* ---------------------------------------------------------------------- */
+
+ given_row = (rnz >= 0) ;
+ klast = given_row ? rnz : k ;
+ PRINT2 (("given_row "ID"\n", given_row)) ;
+
+ for (kk = 0 ; kk < klast ; kk++)
+ {
+ /* either search j = 0:k-1 or j = Rj [0:rnz-1] */
+ j = given_row ? (Rj [kk]) : (kk) ;
+
+ if (j < 0 || j >= k)
+ {
+ ERROR (CHOLMOD_INVALID, "R invalid") ;
+ return (FALSE) ;
+ }
+
+ PRINT2 (("Prune col j = "ID":\n", j)) ;
+
+ lnz = Lnz [j] ;
+ dj = Lx [Lp [j]] ;
+ ASSERT (Lnz [j] > 0 && Li [Lp [j]] == j) ;
+
+ if (lnz > 1)
+ {
+ left = Lp [j] ;
+ pend = left + lnz ;
+ right = pend - 1 ;
+
+ i = Li [right] ;
+
+ if (i < k)
+ {
+ /* row k is not in column j */
+ continue ;
+ }
+ else if (i == k)
+ {
+ /* k is the last row index in this column (quick delete) */
+ if (do_solve)
+ {
+ Xx [j] -= yk [0] * dj * Lx [right] ;
+ }
+ Lx [right] = 0 ;
+ }
+ else
+ {
+ /* binary search for row k in column j */
+ PRINT2 (("\nBinary search: lnz "ID" k = "ID"\n", lnz, k)) ;
+ while (left < right)
+ {
+ middle = (left + right) / 2 ;
+ PRINT2 (("left "ID" right "ID" middle "ID": ["ID" "ID""
+ ""ID"]\n", left, right, middle,
+ Li [left], Li [middle], Li [right])) ;
+ if (k > Li [middle])
+ {
+ left = middle + 1 ;
+ }
+ else
+ {
+ right = middle ;
+ }
+ }
+ ASSERT (left >= Lp [j] && left < pend) ;
+
+#ifndef NDEBUG
+ /* brute force, linear-time search */
+ {
+ Int p3 = Lp [j] ;
+ i = EMPTY ;
+ PRINT2 (("Brute force:\n")) ;
+ for ( ; p3 < pend ; p3++)
+ {
+ i = Li [p3] ;
+ PRINT2 (("p "ID" ["ID"]\n", p3, i)) ;
+ if (i >= k)
+ {
+ break ;
+ }
+ }
+ if (i == k)
+ {
+ ASSERT (k == Li [p3]) ;
+ ASSERT (p3 == left) ;
+ }
+ }
+#endif
+
+ if (k == Li [left])
+ {
+ if (do_solve)
+ {
+ Xx [j] -= yk [0] * dj * Lx [left] ;
+ }
+ /* found row k in column j. Prune it from the column.*/
+ Lx [left] = 0 ;
+ }
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ /* ensure that row k has been deleted from the matrix L */
+ for (j = 0 ; j < k ; j++)
+ {
+ Int lasti ;
+ lasti = EMPTY ;
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+ /* look for row k in column j */
+ PRINT1 (("Pruned column "ID"\n", j)) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Li [p] ;
+ PRINT2 ((" "ID"", i)) ;
+ PRINT2 ((" %g\n", Lx [p])) ;
+ ASSERT (IMPLIES (i == k, Lx [p] == 0)) ;
+ ASSERT (i > lasti) ;
+ lasti = i ;
+ }
+ PRINT1 (("\n")) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* set diagonal and clear column k of L */
+ /* ---------------------------------------------------------------------- */
+
+ lnz = Lnz [k] - 1 ;
+ ASSERT (Lnz [k] > 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* update/downdate */
+ /* ---------------------------------------------------------------------- */
+
+ /* update or downdate L (k+1:n, k+1:n) with the vector
+ * C = L (:,k) * sqrt (abs (D [k]))
+ * Do a numeric update if D[k] > 0, numeric downdate otherwise.
+ */
+
+ PRINT1 (("rowdel downdate lnz = "ID"\n", lnz)) ;
+
+ /* store the new unit diagonal */
+ p = Lp [k] ;
+ pend = p + lnz + 1 ;
+ dk = Lx [p] ;
+ Lx [p++] = 1 ;
+ PRINT2 (("D [k = "ID"] = %g\n", k, dk)) ;
+ ok = TRUE ;
+ fl = 0 ;
+
+ if (lnz > 0)
+ {
+ /* compute DeltaB for updown (in DeltaB) */
+ if (do_solve)
+ {
+ xk = Xx [k] - yk [0] * dk ;
+ for ( ; p < pend ; p++)
+ {
+ Nx [Li [p]] += Lx [p] * xk ;
+ }
+ }
+
+ do_update = IS_GT_ZERO (dk) ;
+ if (!do_update)
+ {
+ dk = -dk ;
+ }
+ sqrt_dk = sqrt (dk) ;
+ p = Lp [k] + 1 ;
+ for (kk = 0 ; kk < lnz ; kk++, p++)
+ {
+ Ci [kk] = Li [p] ;
+ Cx [kk] = Lx [p] * sqrt_dk ;
+ Lx [p] = 0 ; /* clear column k */
+ }
+ fl = lnz + 1 ;
+
+ /* create a n-by-1 sparse matrix to hold the single column */
+ C = &Cmatrix ;
+ C->nrow = n ;
+ C->ncol = 1 ;
+ C->nzmax = lnz ;
+ C->sorted = TRUE ;
+ C->packed = TRUE ;
+ C->p = Cp ;
+ C->i = Ci ;
+ C->x = Cx ;
+ C->nz = NULL ;
+ C->itype = L->itype ;
+ C->xtype = L->xtype ;
+ C->dtype = L->dtype ;
+ C->z = NULL ;
+ C->stype = 0 ;
+
+ Cp [0] = 0 ;
+ Cp [1] = lnz ;
+
+ /* numeric update if dk > 0, and with Lx=b change */
+ /* workspace: Flag (nrow), Head (nrow+1), W (nrow), Iwork (2*nrow) */
+ ok = CHOLMOD(updown_mark) (do_update ? (1) : (0), C, colmark,
+ L, X, DeltaB, Common) ;
+
+ /* clear workspace */
+ for (kk = 0 ; kk < lnz ; kk++)
+ {
+ Cx [kk] = 0 ;
+ }
+ }
+
+ Common->modfl += fl ;
+
+ if (do_solve)
+ {
+ /* kth equation becomes identity, so X(k) is now Y(k) */
+ Xx [k] = yk [0] ;
+ }
+
+ DEBUG (CHOLMOD(dump_factor) (L, "LDL factorization, L:", Common)) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 2*n, Common)) ;
+ return (ok) ;
+}
+#endif
diff --git a/CHOLMOD/Modify/cholmod_updown.c b/CHOLMOD/Modify/cholmod_updown.c
new file mode 100644
index 0000000..1b220c9
--- /dev/null
+++ b/CHOLMOD/Modify/cholmod_updown.c
@@ -0,0 +1,1570 @@
+/* ========================================================================== */
+/* === Modify/cholmod_updown ================================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Modify Module.
+ * Copyright (C) 2005-2006, Timothy A. Davis and William W. Hager.
+ * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Updates/downdates the LDL' factorization (symbolic, then numeric), by
+ * computing a new factorization of
+ *
+ * Lnew * Dnew * Lnew' = Lold * Dold * Lold' +/- C*C'
+ *
+ * C must be sorted. It can be either packed or unpacked. As in all CHOLMOD
+ * routines, the columns of L are sorted on input, and also on output.
+ *
+ * If the factor is not an unpacked LDL' or dynamic LDL', it is converted
+ * to an LDL' dynamic factor. An unpacked LDL' factor may be updated, but if
+ * any one column runs out of space, the factor is converted to an LDL'
+ * dynamic one. If the initial conversion fails, the factor is returned
+ * unchanged.
+ *
+ * If memory runs out during the update, the factor is returned as a simplicial
+ * symbolic factor. That is, everything is freed except for the fill-reducing
+ * ordering and its corresponding column counts (typically computed by
+ * cholmod_analyze).
+ *
+ * Note that the fill-reducing permutation L->Perm is NOT used. The row
+ * indices of C refer to the rows of L, not A. If your original system is
+ * LDL' = PAP' (where P = L->Perm), and you want to compute the LDL'
+ * factorization of A+CC', then you must permute C first. That is:
+ *
+ * PAP' = LDL'
+ * P(A+CC')P' = PAP'+PCC'P' = LDL' + (PC)(PC)' = LDL' + Cnew*Cnew'
+ * where Cnew = P*C.
+ *
+ * You can use the cholmod_submatrix routine in the MatrixOps module
+ * to permute C, with:
+ *
+ * Cnew = cholmod_submatrix (C, L->Perm, L->n, NULL, -1, TRUE, TRUE, Common) ;
+ *
+ * Note that the sorted input parameter to cholmod_submatrix must be TRUE,
+ * because cholmod_updown requires C with sorted columns.
+ *
+ * The system Lx=b can also be updated/downdated. The old system was Lold*x=b.
+ * The new system is Lnew*xnew = b + deltab. The old solution x is overwritten
+ * with xnew. Note that as in the update/downdate of L itself, the fill-
+ * reducing permutation L->Perm is not used. x and b are in the permuted
+ * ordering, not your original ordering. x and b are n-by-1; this routine
+ * does not handle multiple right-hand-sides.
+ *
+ * workspace: Flag (nrow), Head (nrow+1), W (maxrank*nrow), Iwork (nrow),
+ * where maxrank is 2, 4, or 8.
+ *
+ * Only real matrices are supported. A symbolic L is converted into a
+ * numeric identity matrix.
+ */
+
+#ifndef NMODIFY
+
+#include "cholmod_internal.h"
+#include "cholmod_modify.h"
+
+
+/* ========================================================================== */
+/* === cholmod_updown ======================================================= */
+/* ========================================================================== */
+
+/* Compute the new LDL' factorization of LDL'+CC' (an update) or LDL'-CC'
+ * (a downdate). The factor object L need not be an LDL' factorization; it
+ * is converted to one if it isn't. */
+
+int CHOLMOD(updown)
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(updown_mask) (update, C, NULL, NULL, L, NULL, NULL,
+ Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_updown_solve ================================================= */
+/* ========================================================================== */
+
+/* Does the same as cholmod_updown, except that it also updates/downdates the
+ * solution to Lx=b+DeltaB. x and b must be n-by-1 dense matrices. b is not
+ * need as input to this routine, but a sparse change to b is (DeltaB). Only
+ * entries in DeltaB corresponding to columns modified in L are accessed; the
+ * rest are ignored.
+ */
+
+int CHOLMOD(updown_solve)
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(updown_mask) (update, C, NULL, NULL, L, X, DeltaB,
+ Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === Power2 =============================================================== */
+/* ========================================================================== */
+
+/* Power2 [i] is smallest power of 2 that is >= i (for i in range 0 to 8) */
+
+static Int Power2 [ ] =
+{
+/* 0 1 2 3 4 5 6 7 8 */
+ 0, 1, 2, 4, 4, 8, 8, 8, 8
+} ;
+
+/* ========================================================================== */
+/* === debug routines ======================================================= */
+/* ========================================================================== */
+
+#ifndef NDEBUG
+
+static void dump_set (Int s, Int **Set_ps1, Int **Set_ps2, Int j, Int n,
+ cholmod_common *Common)
+{
+ Int *p, len, i, ilast ;
+
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return ;
+ }
+
+ len = Set_ps2 [s] - Set_ps1 [s] ;
+ PRINT2 (("Set s: "ID" len: "ID":", s, len)) ;
+ ASSERT (len > 0) ;
+ ilast = j ;
+ for (p = Set_ps1 [s] ; p < Set_ps2 [s] ; p++)
+ {
+ i = *p ;
+ PRINT3 ((" "ID"", i)) ;
+ ASSERT (i > ilast && i < n) ;
+ ilast = i ;
+ }
+ PRINT3 (("\n")) ;
+}
+
+static void dump_col
+(
+ char *w, Int j, Int p1, Int p2, Int *Li, double *Lx, Int n,
+ cholmod_common *Common
+)
+{
+ Int p, row, lastrow ;
+
+ if (CHOLMOD(dump) < -1)
+ {
+ /* no checks if debug level is -2 or less */
+ return ;
+ }
+
+ PRINT3 (("\n\nDUMP COL==== j = "ID" %s: p1="ID" p2="ID" \n", j, w, p1,p2));
+ lastrow = -1 ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ PRINT3 ((" "ID": ", p)) ;
+ row = Li [p] ;
+ PRINT3 ((""ID" ", Li [p])) ;
+ PRINT3 (("%g ", Lx [p])) ;
+ PRINT3 (("\n")) ;
+ ASSERT (row > lastrow && row < n) ;
+ lastrow = row ;
+ }
+ ASSERT (p1 < p2) ;
+ ASSERT (Li [p1] == j) ;
+ PRINT3 (("\n")) ;
+}
+#endif
+
+
+/* ========================================================================== */
+/* === a path =============================================================== */
+/* ========================================================================== */
+
+/* A path is a set of nodes of the etree which are all affected by the same
+ * columns of C. */
+
+typedef struct Path_struct
+{
+ Int start ; /* column at which to start, or EMPTY if initial */
+ Int end ; /* column at which to end, or EMPTY if initial */
+ Int ccol ; /* column of C to which path refers */
+ Int parent ; /* parent path */
+ Int c ; /* child of j along this path */
+ Int next ; /* next path in link list */
+ Int rank ; /* number of rank-1 paths merged onto this path */
+ Int order ; /* dfs order of this path */
+ Int wfirst ; /* first column of W to affect this path */
+ Int pending ; /* column at which the path is pending */
+ Int botrow ; /* for partial update/downdate of solution to Lx=b */
+
+} Path_type ;
+
+
+/* ========================================================================== */
+/* === dfs ================================================================== */
+/* ========================================================================== */
+
+/* Compute the DFS order of the set of paths. This can be recursive because
+ * there are at most 23 paths to sort: one for each column of C (8 at most),
+ * and one for each node in a balanced binary tree with 8 leaves (15).
+ * Stack overflow is thus not a problem. */
+
+static void dfs
+(
+ Path_type *Path, /* the set of Paths */
+ Int k, /* the rank of the update/downdate */
+ Int path, /* which path to work on */
+ Int *path_order, /* the current path order */
+ Int *w_order, /* the current order of the columns of W */
+ Int depth,
+ Int npaths /* total number of paths */
+)
+{
+ Int c ; /* child path */
+
+ ASSERT (path >= 0 && path < npaths) ;
+ if (path < k)
+ {
+ /* this is a leaf node, corresponding to column W (:,path) */
+ /* and column C (:, Path [path].ccol) */
+ ASSERT (Path [path].ccol >= 0) ;
+ Path [path].wfirst = *w_order ;
+ Path [path].order = *w_order ;
+ (*w_order)++ ;
+ }
+ else
+ {
+ /* this is a non-leaf path, within the tree */
+ ASSERT (Path [path].c != EMPTY) ;
+ ASSERT (Path [path].ccol == EMPTY) ;
+ /* order each child path */
+ for (c = Path [path].c ; c != EMPTY ; c = Path [c].next)
+ {
+ dfs (Path, k, c, path_order, w_order, depth+1, npaths) ;
+ if (Path [path].wfirst == EMPTY)
+ {
+ Path [path].wfirst = Path [c].wfirst ;
+ }
+ }
+ /* order this path next */
+ Path [path].order = (*path_order)++ ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === numeric update/downdate routines ===================================== */
+/* ========================================================================== */
+
+#define WDIM 1
+#include "t_cholmod_updown.c"
+#define WDIM 2
+#include "t_cholmod_updown.c"
+#define WDIM 4
+#include "t_cholmod_updown.c"
+#define WDIM 8
+#include "t_cholmod_updown.c"
+
+
+/* ========================================================================== */
+/* === cholmod_updown_mark ================================================== */
+/* ========================================================================== */
+
+/* Update/downdate LDL' +/- C*C', and update/downdate selected portions of the
+ * solution to Lx=b.
+ *
+ * The original system is L*x = b. The new system is Lnew*xnew = b + deltab.
+ * deltab(i) can be nonzero only if column i of L is modified by the update/
+ * downdate. If column i is not modified, the deltab(i) is not accessed.
+ *
+ * The solution to Lx=b is not modified if either X or DeltaB are NULL.
+ *
+ * Rowmark and colmark:
+ * --------------------
+ *
+ * rowmark and colmark affect which portions of L take part in the update/
+ * downdate of the solution to Lx=b. They do not affect how L itself is
+ * updated/downdated. They are both ignored if X or DeltaB are NULL.
+ *
+ * If not NULL, rowmark is an integer array of size n where L is n-by-n.
+ * rowmark [j] defines the part of column j of L that takes part in the update/
+ * downdate of the forward solve, Lx=b. Specifically, if i = rowmark [j],
+ * then L(j:i-1,j) is used, and L(i:end,j) is ignored.
+ *
+ * If not NULL, colmark is an integer array of size C->ncol. colmark [ccol]
+ * for a column C(:,ccol) redefines those parts of L that take part in the
+ * update/downdate of Lx=b. Each column of C affects a set of columns of L.
+ * If column ccol of C affects column j of L, then the new rowmark [j] of
+ * column j of L is defined as colmark [ccol]. In a multiple-rank update/
+ * downdate, if two or more columns of C affect column j, its new rowmark [j]
+ * is the colmark of the least-numbered column of C. colmark is ignored if
+ * it is NULL, in which case rowmark is not modified. If colmark [ccol] is
+ * EMPTY (-1), then rowmark is not modified for that particular column of C.
+ * colmark is ignored if it is NULL, or rowmark, X, or DeltaB are NULL.
+ *
+ * The algorithm for modifying the solution to Lx=b when rowmark and colmark
+ * are NULL is as follows:
+ *
+ * for each column j of L that is modified:
+ * deltab (j:end) += L (j:end,j) * x(j)
+ * modify L
+ * for each column j of L that is modified:
+ * x (j) = deltab (j)
+ * deltab (j) = 0
+ * deltab (j+1:end) -= L (j+1:end,j) * x(j)
+ *
+ * If rowmark is non-NULL but colmark is NULL:
+ *
+ * for each column j of L that is modified:
+ * deltab (j:rowmark(j)-1) += L (j:rowmark(j)-1,j) * x(j)
+ * modify L
+ * for each column j of L that is modified:
+ * x (j) = deltab (j)
+ * deltab (j) = 0
+ * deltab (j+1:rowmark(j)-1) -= L (j+1:rowmark(j)-1,j) * x(j)
+ *
+ * If both rowmark and colmark are non-NULL:
+ *
+ * for each column j of L that is modified:
+ * deltab (j:rowmark(j)-1) += L (j:rowmark(j)-1,j) * x(j)
+ * modify L
+ * for each column j of L that is modified:
+ * modify rowmark (j) according to colmark
+ * for each column j of L that is modified:
+ * x (j) = deltab (j)
+ * deltab (j) = 0
+ * deltab (j+1:rowmark(j)-1) -= L (j+1:rowmark(j)-1,j) * x(j)
+ *
+ * Note that if the rank of C exceeds k = Common->maxrank (which is 2, 4, or 8),
+ * then the update/downdate is done as a series of rank-k updates. In this
+ * case, the above algorithm is repeated for each block of k columns of C.
+ *
+ * Unless it leads to no changes in rowmark, colmark should be used only if
+ * C->ncol <= Common->maxrank, because the update/downdate is done with maxrank
+ * columns at a time. Otherwise, the results are undefined.
+ *
+ * This routine is an "expert" routine. It is meant for use in LPDASA only.
+ */
+
+int CHOLMOD(updown_mark)
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ Int *colmark, /* Int array of size n. */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ return (CHOLMOD(updown_mask) (update, C, colmark, NULL, L, X, DeltaB,
+ Common)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_updown_mask ================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(updown_mask)
+(
+ /* ---- input ---- */
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* the incoming sparse update */
+ Int *colmark, /* Int array of size n. See cholmod_updown.c */
+ Int *mask, /* size n */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factor to modify */
+ cholmod_dense *X, /* solution to Lx=b (size n-by-1) */
+ cholmod_dense *DeltaB, /* change in b, zero on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double xj, fl ;
+ double *Lx, *W, *Xx, *Nx ;
+ Int *Li, *Lp, *Lnz, *Cp, *Ci, *Cnz, *Head, *Flag, *Stack, *Lnext, *Iwork,
+ *Set_ps1 [32], *Set_ps2 [32], *ps1, *ps2 ;
+ size_t maxrank ;
+ Path_type OrderedPath [32], Path [32] ;
+ Int n, wdim, k1, k2, npaths, i, j, row, packed, ccol, p, cncol, do_solve,
+ mark, jj, j2, kk, nextj, p1, p2, c, use_colmark, newlnz,
+ k, newpath, path_order, w_order, scattered, path, newparent, pp1, pp2,
+ smax, maxrow, row1, nsets, s, p3, newlnz1, Set [32], top, len, lnz, m,
+ botrow ;
+ size_t w ;
+ int ok = TRUE ;
+ DEBUG (Int oldparent) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (C, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_REAL, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (C, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ;
+ n = L->n ;
+ cncol = C->ncol ;
+ if (!(C->sorted))
+ {
+ ERROR (CHOLMOD_INVALID, "C must have sorted columns") ;
+ return (FALSE) ;
+ }
+ if (n != (Int) (C->nrow))
+ {
+ ERROR (CHOLMOD_INVALID, "C and L dimensions do not match") ;
+ return (FALSE) ;
+ }
+ do_solve = (X != NULL) && (DeltaB != NULL) ;
+ if (do_solve)
+ {
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (DeltaB, CHOLMOD_REAL, CHOLMOD_REAL, FALSE) ;
+ Xx = X->x ;
+ Nx = DeltaB->x ;
+ if (X->nrow != L->n || X->ncol != 1 || DeltaB->nrow != L->n ||
+ DeltaB->ncol != 1 || Xx == NULL || Nx == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "X and/or DeltaB invalid") ;
+ return (FALSE) ;
+ }
+ }
+ else
+ {
+ Xx = NULL ;
+ Nx = NULL ;
+ }
+ Common->status = CHOLMOD_OK ;
+ Common->modfl = 0 ;
+
+ fl = 0 ;
+ use_colmark = (colmark != NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note: cholmod_rowadd and cholmod_rowdel use the second n doubles in
+ * Common->Xwork for Cx, and then perform a rank-1 update here, which uses
+ * the first n doubles in Common->Xwork. Both the rowadd and rowdel
+ * routines allocate enough workspace so that Common->Xwork isn't destroyed
+ * below. Also, both cholmod_rowadd and cholmod_rowdel use the second n
+ * ints in Common->Iwork for Ci.
+ */
+
+ /* make sure maxrank is in the proper range */
+ maxrank = CHOLMOD(maxrank) (n, Common) ;
+ k = MIN (cncol, (Int) maxrank) ; /* maximum k is wdim */
+ wdim = Power2 [k] ; /* number of columns needed in W */
+ ASSERT (wdim <= (Int) maxrank) ;
+ PRINT1 (("updown wdim final "ID" k "ID"\n", wdim, k)) ;
+
+ /* w = wdim * n */
+ w = CHOLMOD(mult_size_t) (n, wdim, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (n, n, w, Common) ;
+ if (Common->status < CHOLMOD_OK || maxrank == 0)
+ {
+ /* out of memory, L is returned unchanged */
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to simplicial numeric LDL' factor, if not already */
+ /* ---------------------------------------------------------------------- */
+
+ if (L->xtype == CHOLMOD_PATTERN || L->is_super || L->is_ll)
+ {
+ /* can only update/downdate a simplicial LDL' factorization */
+ CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE, FALSE, L,
+ Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory, L is returned unchanged */
+ return (FALSE) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* mark = CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+
+ PRINT1 (("updown, rank %g update %d\n", (double) C->ncol, update)) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "input L for updown", Common)) ;
+ ASSERT (CHOLMOD(dump_sparse) (C, "input C for updown", Common) >= 0) ;
+
+ Ci = C->i ;
+ Cp = C->p ;
+ Cnz = C->nz ;
+ packed = C->packed ;
+ ASSERT (IMPLIES (!packed, Cnz != NULL)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* quick return */
+ /* ---------------------------------------------------------------------- */
+
+ if (cncol <= 0 || n == 0)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get L */
+ /* ---------------------------------------------------------------------- */
+
+ Li = L->i ;
+ Lx = L->x ;
+ Lp = L->p ;
+ Lnz = L->nz ;
+ Lnext = L->next ;
+ ASSERT (Lnz != NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Flag = Common->Flag ; /* size n, Flag [i] <= mark must hold */
+ Head = Common->Head ; /* size n, Head [i] == EMPTY must hold */
+ W = Common->Xwork ; /* size n-by-wdim, zero on input and output*/
+
+ /* note that Iwork [n .. 2*n-1] (i/i/l) may be in use in rowadd/rowdel: */
+ Iwork = Common->Iwork ;
+ Stack = Iwork ; /* size n, uninitialized (i/i/l) */
+
+ /* ---------------------------------------------------------------------- */
+ /* entire rank-cncol update, done as a sequence of rank-k updates */
+ /* ---------------------------------------------------------------------- */
+
+ ps1 = NULL ;
+ ps2 = NULL ;
+
+ for (k1 = 0 ; k1 < cncol ; k1 += k)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the next k columns of C for the update/downdate */
+ /* ------------------------------------------------------------------ */
+
+ /* the last update/downdate might be less than rank-k */
+ if (k > cncol - k1)
+ {
+ k = cncol - k1 ;
+ wdim = Power2 [k] ;
+ }
+ k2 = k1 + k - 1 ;
+
+ /* workspaces are in the following state, on input and output */
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* create a zero-length path for each column of W */
+ /* ------------------------------------------------------------------ */
+
+ nextj = n ;
+ path = 0 ;
+ for (ccol = k1 ; ccol <= k2 ; ccol++)
+ {
+ PRINT1 (("Column ["ID"]: "ID"\n", path, ccol)) ;
+ ASSERT (ccol >= 0 && ccol <= cncol) ;
+ pp1 = Cp [ccol] ;
+ pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ;
+ /* get the row index j of the first entry in C (:,ccol) */
+ if (pp2 > pp1)
+ {
+ /* Column ccol of C has at least one entry. */
+ j = Ci [pp1] ;
+ }
+ else
+ {
+ /* Column ccol of C is empty. Pretend it has one entry in
+ * the last column with numerical value of zero. */
+ j = n-1 ;
+ }
+ ASSERT (j >= 0 && j < n) ;
+
+ /* find first column to work on */
+ nextj = MIN (nextj, j) ;
+
+ Path [path].ccol = ccol ; /* which column of C this path is for */
+ Path [path].start = EMPTY ; /* paths for C have zero length */
+ Path [path].end = EMPTY ;
+ Path [path].parent = EMPTY ; /* no parent yet */
+ Path [path].rank = 1 ; /* one column of W */
+ Path [path].c = EMPTY ; /* no child of this path (case A) */
+ Path [path].next = Head [j] ; /* this path is pending at col j */
+ Path [path].pending = j ; /* this path is pending at col j */
+ Head [j] = path ; /* this path is pending at col j */
+ PRINT1(("Path "ID" starts: start "ID" end "ID" parent "ID" c "ID""
+ "j "ID" ccol "ID"\n", path, Path [path].start,
+ Path [path].end, Path [path].parent,
+ Path [path].c, j, ccol)) ;
+
+ /* initialize botrow for this path */
+ Path [path].botrow = (use_colmark) ? colmark [ccol] : n ;
+
+ path++ ;
+ }
+
+ /* we start with paths 0 to k-1. Next one (now unused) is npaths */
+ npaths = k ;
+
+ j = nextj ;
+ ASSERT (j < n) ;
+ scattered = FALSE ;
+
+ /* ------------------------------------------------------------------ */
+ /* symbolic update of columns of L */
+ /* ------------------------------------------------------------------ */
+
+ while (j < n)
+ {
+ ASSERT (j >= 0 && j < n && Lnz [j] > 0) ;
+
+ /* the old column, Li [p1..p2-1]. D (j,j) is stored in Lx [p1] */
+ p1 = Lp [j] ;
+ newlnz = Lnz [j] ;
+ p2 = p1 + newlnz ;
+
+#ifndef NDEBUG
+ PRINT1 (("\n=========Column j="ID" p1 "ID" p2 "ID" lnz "ID" \n",
+ j, p1, p2, newlnz)) ;
+ dump_col ("Old", j, p1, p2, Li, Lx, n, Common) ;
+ oldparent = (Lnz [j] > 1) ? (Li [p1 + 1]) : EMPTY ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, FALSE, 0, Common)) ;
+ ASSERT (!scattered) ;
+ PRINT1 (("Col "ID": Checking paths, npaths: "ID"\n", j, npaths)) ;
+ for (kk = 0 ; kk < npaths ; kk++)
+ {
+ Int kk2, found, j3 = Path [kk].pending ;
+ PRINT2 (("Path "ID" pending at "ID".\n", kk, j3)) ;
+ if (j3 != EMPTY)
+ {
+ /* Path kk must be somewhere in link list for column j3 */
+ ASSERT (Head [j3] != EMPTY) ;
+ PRINT3 ((" List at "ID": ", j3)) ;
+ found = FALSE ;
+ for (kk2 = Head [j3] ; kk2 != EMPTY ; kk2 = Path [kk2].next)
+ {
+ PRINT3 ((""ID" ", kk2)) ;
+ ASSERT (Path [kk2].pending == j3) ;
+ found = found || (kk2 == kk) ;
+ }
+ PRINT3 (("\n")) ;
+ ASSERT (found) ;
+ }
+ }
+ PRINT1 (("\nCol "ID": Paths at this column, head "ID"\n",
+ j, Head [j]));
+ ASSERT (Head [j] != EMPTY) ;
+ for (kk = Head [j] ; kk != EMPTY ; kk = Path [kk].next)
+ {
+ PRINT1 (("path "ID": (c="ID" j="ID") npaths "ID"\n",
+ kk, Path[kk].c, j, npaths)) ;
+ ASSERT (kk >= 0 && kk < npaths) ;
+ ASSERT (Path [kk].pending == j) ;
+ }
+#endif
+
+ /* -------------------------------------------------------------- */
+ /* determine the path we're on */
+ /* -------------------------------------------------------------- */
+
+ /* get the first old path at column j */
+ path = Head [j] ;
+
+ /* -------------------------------------------------------------- */
+ /* update/downdate of forward solve, Lx=b */
+ /* -------------------------------------------------------------- */
+
+ if (do_solve)
+ {
+ xj = Xx [j] ;
+ if (IS_NONZERO (xj))
+ {
+ xj = Xx [j] ;
+ /* This is first time column j has been seen for entire */
+ /* rank-k update/downdate. */
+
+ /* DeltaB += Lold (j:botrow-1,j) * X (j) */
+ Nx [j] += xj ; /* diagonal of L */
+
+ /* find the botrow for this column */
+ botrow = (use_colmark) ? Path [path].botrow : n ;
+
+ for (p = p1 + 1 ; p < p2 ; p++)
+ {
+ i = Li [p] ;
+ if (i >= botrow)
+ {
+ break ;
+ }
+ Nx [i] += Lx [p] * xj ;
+ }
+
+ /* clear X[j] to flag col j of Lold as having been seen. If
+ * X (j) was initially zero, then the above code is never
+ * executed for column j. This is safe, since if xj=0 the
+ * code above does not do anything anyway. */
+ Xx [j] = 0.0 ;
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* start a new path at this column if two or more paths merge */
+ /* -------------------------------------------------------------- */
+
+ newpath =
+ /* start a new path if paths have merged */
+ (Path [path].next != EMPTY)
+ /* or if j is the first node on a path (case A). */
+ || (Path [path].c == EMPTY) ;
+
+ if (newpath)
+ {
+ /* get the botrow of the first path at column j */
+ botrow = (use_colmark) ? Path [path].botrow : n ;
+
+ path = npaths++ ;
+ ASSERT (npaths <= 3*k) ;
+ Path [path].ccol = EMPTY ; /* no single col of C for this path*/
+ Path [path].start = j ; /* path starts at this column j */
+ Path [path].end = EMPTY ; /* don't know yet where it ends */
+ Path [path].parent = EMPTY ;/* don't know parent path yet */
+ Path [path].rank = 0 ; /* rank is sum of child path ranks */
+ PRINT1 (("Path "ID" starts: start "ID" end "ID" parent "ID"\n",
+ path, Path [path].start, Path [path].end, Path [path].parent)) ;
+
+ /* set the botrow of the new path */
+ Path [path].botrow = (use_colmark) ? botrow : n ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* for each path kk pending at column j */
+ /* -------------------------------------------------------------- */
+
+ /* make a list of the sets that need to be merged into column j */
+ nsets = 0 ;
+
+ for (kk = Head [j] ; kk != EMPTY ; kk = Path [kk].next)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* path kk is at (c,j) */
+ /* ---------------------------------------------------------- */
+
+ c = Path [kk].c ;
+ ASSERT (c < j) ;
+ PRINT1 (("TUPLE on path "ID" (c="ID" j="ID")\n", kk, c, j)) ;
+ ASSERT (Path [kk].pending == j) ;
+
+ if (newpath)
+ {
+ /* finalize path kk and find rank of this path */
+ Path [kk].end = c ; /* end of old path is previous node c */
+ Path [kk].parent = path ; /* parent is this path */
+ Path [path].rank += Path [kk].rank ; /* sum up ranks */
+ Path [kk].pending = EMPTY ;
+ PRINT1 (("Path "ID" done:start "ID" end "ID" parent "ID"\n",
+ kk, Path [kk].start, Path [kk].end, Path [kk].parent)) ;
+ }
+
+ if (c == EMPTY)
+ {
+
+ /* ------------------------------------------------------ */
+ /* CASE A: first node in path */
+ /* ------------------------------------------------------ */
+
+ /* update: add pattern of incoming column */
+
+ /* Column ccol of C is in Ci [pp1 ... pp2-1] */
+ ccol = Path [kk].ccol ;
+ pp1 = Cp [ccol] ;
+ pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ;
+ PRINT1 (("Case A, ccol = "ID" len "ID"\n", ccol, pp2-pp1)) ;
+ ASSERT (IMPLIES (pp2 > pp1, Ci [pp1] == j)) ;
+
+ if (!scattered)
+ {
+ /* scatter the original pattern of column j of L */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ Flag [Li [p]] = mark ;
+ }
+ scattered = TRUE ;
+ }
+
+ /* scatter column ccol of C (skip first entry, j) */
+ newlnz1 = newlnz ;
+ for (p = pp1 + 1 ; p < pp2 ; p++)
+ {
+ row = Ci [p] ;
+ if (Flag [row] < mark)
+ {
+ /* this is a new entry in Lj' */
+ Flag [row] = mark ;
+ newlnz++ ;
+ }
+ }
+ if (newlnz1 != newlnz)
+ {
+ /* column ccol of C adds something to column j of L */
+ Set [nsets++] = FLIP (ccol) ;
+ }
+
+ }
+ else if (Head [c] == 1)
+ {
+
+ /* ------------------------------------------------------ */
+ /* CASE B: c is old, but changed, child of j */
+ /* CASE C: new child of j */
+ /* ------------------------------------------------------ */
+
+ /* Head [c] is 1 if col c of L has new entries,
+ * EMPTY otherwise */
+ Flag [c] = 0 ;
+ Head [c] = EMPTY ;
+
+ /* update: add Lc' */
+
+ /* column c of L is in Li [pp1 .. pp2-1] */
+ pp1 = Lp [c] ;
+ pp2 = pp1 + Lnz [c] ;
+ PRINT1 (("Case B/C: c = "ID"\n", c)) ;
+ DEBUG (dump_col ("Child", c, pp1, pp2, Li, Lx, n, Common)) ;
+ ASSERT (j == Li [pp1 + 1]) ; /* j is new parent of c */
+
+ if (!scattered)
+ {
+ /* scatter the original pattern of column j of L */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ Flag [Li [p]] = mark ;
+ }
+ scattered = TRUE ;
+ }
+
+ /* scatter column c of L (skip first two entries, c and j)*/
+ newlnz1 = newlnz ;
+ for (p = pp1 + 2 ; p < pp2 ; p++)
+ {
+ row = Li [p] ;
+ if (Flag [row] < mark)
+ {
+ /* this is a new entry in Lj' */
+ Flag [row] = mark ;
+ newlnz++ ;
+ }
+ }
+ PRINT2 (("\n")) ;
+
+ if (newlnz1 != newlnz)
+ {
+ /* column c of L adds something to column j of L */
+ Set [nsets++] = c ;
+ }
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* update the pattern of column j of L */
+ /* -------------------------------------------------------------- */
+
+ /* Column j of L will be in Li/Lx [p1 .. p3-1] */
+ p3 = p1 + newlnz ;
+ ASSERT (IMPLIES (nsets == 0, newlnz == Lnz [j])) ;
+ PRINT1 (("p1 "ID" p2 "ID" p3 "ID" nsets "ID"\n", p1, p2, p3,nsets));
+
+ /* -------------------------------------------------------------- */
+ /* ensure we have enough space for the longer column */
+ /* -------------------------------------------------------------- */
+
+ if (nsets > 0 && p3 > Lp [Lnext [j]])
+ {
+ PRINT1 (("Col realloc: j "ID" newlnz "ID"\n", j, newlnz)) ;
+ if (!CHOLMOD(reallocate_column) (j, newlnz, L, Common))
+ {
+ /* out of memory, L is now simplicial symbolic */
+ CHOLMOD(clear_flag) (Common) ;
+ for (j = 0 ; j <= n ; j++)
+ {
+ Head [j] = EMPTY ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ;
+ return (FALSE) ;
+ }
+ /* L->i and L->x may have moved. Column j has moved too */
+ Li = L->i ;
+ Lx = L->x ;
+ p1 = Lp [j] ;
+ p2 = p1 + Lnz [j] ;
+ p3 = p1 + newlnz ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* create set pointers */
+ /* -------------------------------------------------------------- */
+
+ for (s = 0 ; s < nsets ; s++)
+ {
+ /* Pattern of Set s is *(Set_ps1 [s] ... Set_ps2 [s]-1) */
+ c = Set [s] ;
+ if (c < EMPTY)
+ {
+ /* column ccol of C, skip first entry (j) */
+ ccol = FLIP (c) ;
+ pp1 = Cp [ccol] ;
+ pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ;
+ ASSERT (pp2 - pp1 > 1) ;
+ Set_ps1 [s] = &(Ci [pp1 + 1]) ;
+ Set_ps2 [s] = &(Ci [pp2]) ;
+ PRINT1 (("set "ID" is ccol "ID"\n", s, ccol)) ;
+ }
+ else
+ {
+ /* column c of L, skip first two entries (c and j) */
+ pp1 = Lp [c] ;
+ pp2 = pp1 + Lnz [c] ;
+ ASSERT (Lnz [c] > 2) ;
+ Set_ps1 [s] = &(Li [pp1 + 2]) ;
+ Set_ps2 [s] = &(Li [pp2]) ;
+ PRINT1 (("set "ID" is L "ID"\n", s, c)) ;
+ }
+ DEBUG (dump_set (s, Set_ps1, Set_ps2, j, n, Common)) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* multiset merge */
+ /* -------------------------------------------------------------- */
+
+ /* Merge the sets into a single sorted set, Lj'. Before the merge
+ * starts, column j is located in Li/Lx [p1 ... p2-1] and the
+ * space Li/Lx [p2 ... p3-1] is empty. p1 is Lp [j], p2 is
+ * Lp [j] + Lnz [j] (the old length of the column), and p3 is
+ * Lp [j] + newlnz (the new and longer length of the column).
+ *
+ * The sets 0 to nsets-1 are defined by the Set_ps1 and Set_ps2
+ * pointers. Set s is located in *(Set_ps1 [s] ... Set_ps2 [s]-1).
+ * It may be a column of C, or a column of L. All row indices i in
+ * the sets are in the range i > j and i < n. All sets are sorted.
+ *
+ * The merge into column j of L is done in place.
+ *
+ * During the merge, p2 and p3 are updated. Li/Lx [p1..p2-1]
+ * reflects the indices of the old column j of L that are yet to
+ * be merged into the new column. Entries in their proper place in
+ * the new column j of L are located in Li/Lx [p3 ... p1+newlnz-1].
+ * The merge finishes when p2 == p3.
+ *
+ * During the merge, set s consumed as it is merged into column j of
+ * L. Its unconsumed contents are *(Set_ps1 [s] ... Set_ps2 [s]-1).
+ * When a set is completely consumed, it is removed from the set of
+ * sets, and nsets is decremented.
+ *
+ * The multiset merge and 2-set merge finishes when p2 == p3.
+ */
+
+ PRINT1 (("Multiset merge p3 "ID" p2 "ID" nsets "ID"\n",
+ p3, p2, nsets)) ;
+
+ while (p3 > p2 && nsets > 1)
+ {
+
+#ifndef NDEBUG
+ PRINT2 (("\nMultiset merge. nsets = "ID"\n", nsets)) ;
+ PRINT2 (("Source col p1 = "ID", p2 = "ID", p3= "ID"\n",
+ p1, p2, p3)) ;
+ for (p = p1 + 1 ; p < p2 ; p++)
+ {
+ PRINT2 ((" p: "ID" source row "ID" %g\n",
+ p, Li[p], Lx[p])) ;
+ ASSERT (Li [p] > j && Li [p] < n) ;
+ }
+ PRINT2 (("---\n")) ;
+ for (p = p3 ; p < p1 + newlnz ; p++)
+ {
+ PRINT2 ((" p: "ID" target row "ID" %g\n",
+ p, Li[p], Lx[p])) ;
+ ASSERT (Li [p] > j && Li [p] < n) ;
+ }
+ for (s = 0 ; s < nsets ; s++)
+ {
+ dump_set (s, Set_ps1, Set_ps2, j, n, Common) ;
+ }
+#endif
+
+ /* get the entry at the tail end of source column Lj */
+ row1 = Li [p2 - 1] ;
+ ASSERT (row1 >= j && p2 >= p1) ;
+
+ /* find the largest row in all the sets */
+ maxrow = row1 ;
+ smax = EMPTY ;
+ for (s = nsets-1 ; s >= 0 ; s--)
+ {
+ ASSERT (Set_ps1 [s] < Set_ps2 [s]) ;
+ row = *(Set_ps2 [s] - 1) ;
+ if (row == maxrow)
+ {
+ /* skip past this entry in set s (it is a duplicate) */
+ Set_ps2 [s]-- ;
+ if (Set_ps1 [s] == Set_ps2 [s])
+ {
+ /* nothing more in this set */
+ nsets-- ;
+ Set_ps1 [s] = Set_ps1 [nsets] ;
+ Set_ps2 [s] = Set_ps2 [nsets] ;
+ if (smax == nsets)
+ {
+ /* Set smax redefined; it is now this set */
+ smax = s ;
+ }
+ }
+ }
+ else if (row > maxrow)
+ {
+ maxrow = row ;
+ smax = s ;
+ }
+ }
+ ASSERT (maxrow > j) ;
+
+ /* move the row onto the stack of the target column */
+ if (maxrow == row1)
+ {
+ /* next entry is in Lj, move to the bottom of Lj' */
+ ASSERT (smax == EMPTY) ;
+ p2-- ;
+ p3-- ;
+ Li [p3] = maxrow ;
+ Lx [p3] = Lx [p2] ;
+ }
+ else
+ {
+ /* new entry in Lj' */
+ ASSERT (smax >= 0 && smax < nsets) ;
+ Set_ps2 [smax]-- ;
+ p3-- ;
+ Li [p3] = maxrow ;
+ Lx [p3] = 0.0 ;
+ if (Set_ps1 [smax] == Set_ps2 [smax])
+ {
+ /* nothing more in this set */
+ nsets-- ;
+ Set_ps1 [smax] = Set_ps1 [nsets] ;
+ Set_ps2 [smax] = Set_ps2 [nsets] ;
+ PRINT1 (("Set "ID" now empty\n", smax)) ;
+ }
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* 2-set merge: */
+ /* -------------------------------------------------------------- */
+
+ /* This the same as the multi-set merge, except there is only one
+ * set s = 0 left. The source column j and the set 0 are being
+ * merged into the target column j. */
+
+ if (nsets > 0)
+ {
+ ps1 = Set_ps1 [0] ;
+ ps2 = Set_ps2 [0] ;
+ }
+
+ while (p3 > p2)
+ {
+
+#ifndef NDEBUG
+ PRINT2 (("\n2-set merge.\n")) ;
+ ASSERT (nsets == 1) ;
+ PRINT2 (("Source col p1 = "ID", p2 = "ID", p3= "ID"\n",
+ p1, p2, p3)) ;
+ for (p = p1 + 1 ; p < p2 ; p++)
+ {
+ PRINT2 ((" p: "ID" source row "ID" %g\n",
+ p, Li[p], Lx[p])) ;
+ ASSERT (Li [p] > j && Li [p] < n) ;
+ }
+ PRINT2 (("---\n")) ;
+ for (p = p3 ; p < p1 + newlnz ; p++)
+ {
+ PRINT2 ((" p: "ID" target row "ID" %g\n",
+ p, Li[p], Lx[p])) ;
+ ASSERT (Li [p] > j && Li [p] < n) ;
+ }
+ dump_set (0, Set_ps1, Set_ps2, j, n, Common) ;
+#endif
+
+ if (p2 == p1 + 1)
+ {
+ /* the top of Lj is empty; copy the set and quit */
+ while (p3 > p2)
+ {
+ /* new entry in Lj' */
+ row = *(--ps2) ;
+ p3-- ;
+ Li [p3] = row ;
+ Lx [p3] = 0.0 ;
+ }
+ }
+ else
+ {
+ /* get the entry at the tail end of Lj */
+ row1 = Li [p2 - 1] ;
+ ASSERT (row1 > j && row1 < n) ;
+ /* get the entry at the tail end of the incoming set */
+ ASSERT (ps1 < ps2) ;
+ row = *(ps2-1) ;
+ ASSERT (row > j && row1 < n) ;
+ /* move the larger of the two entries to the target set */
+ if (row1 >= row)
+ {
+ /* next entry is in Lj, move to the bottom */
+ if (row1 == row)
+ {
+ /* skip past this entry in the set */
+ ps2-- ;
+ }
+ p2-- ;
+ p3-- ;
+ Li [p3] = row1 ;
+ Lx [p3] = Lx [p2] ;
+ }
+ else
+ {
+ /* new entry in Lj' */
+ ps2-- ;
+ p3-- ;
+ Li [p3] = row ;
+ Lx [p3] = 0.0 ;
+ }
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* The new column j of L is now in Li/Lx [p1 ... p2-1] */
+ /* -------------------------------------------------------------- */
+
+ p2 = p1 + newlnz ;
+ DEBUG (dump_col ("After merge: ", j, p1, p2, Li, Lx, n, Common)) ;
+
+ fl += Path [path].rank * (6 + 4 * (double) newlnz) ;
+
+ /* -------------------------------------------------------------- */
+ /* clear Flag; original pattern of column j L no longer marked */
+ /* -------------------------------------------------------------- */
+
+ mark = CHOLMOD(clear_flag) (Common) ;
+ scattered = FALSE ;
+
+ /* -------------------------------------------------------------- */
+ /* find the new parent */
+ /* -------------------------------------------------------------- */
+
+ newparent = (newlnz > 1) ? (Li [p1 + 1]) : EMPTY ;
+ PRINT1 (("\nNew parent, Lnz: "ID": "ID" "ID"\n",
+ j, newparent,newlnz));
+ ASSERT (oldparent == EMPTY || newparent <= oldparent) ;
+
+ /* -------------------------------------------------------------- */
+ /* go to the next node in the path */
+ /* -------------------------------------------------------------- */
+
+ /* path moves to (j,nextj) unless j is a root */
+ nextj = (newparent == EMPTY) ? n : newparent ;
+
+ /* place path at head of list for nextj, or terminate the path */
+ PRINT1 (("\n j = "ID" nextj = "ID"\n\n", j, nextj)) ;
+ Path [path].c = j ;
+ if (nextj < n)
+ {
+ /* put path on link list of pending paths at column nextj */
+ Path [path].next = Head [nextj] ;
+ Path [path].pending = nextj ;
+ Head [nextj] = path ;
+ PRINT1 (("Path "ID" continues to ("ID","ID"). Rank "ID"\n",
+ path, Path [path].c, nextj, Path [path].rank)) ;
+ }
+ else
+ {
+ /* path has ended here, at a root */
+ Path [path].next = EMPTY ;
+ Path [path].pending = EMPTY ;
+ Path [path].end = j ;
+ PRINT1 (("Path "ID" ends at root ("ID"). Rank "ID"\n",
+ path, Path [path].end, Path [path].rank)) ;
+ }
+
+ /* The link list Head [j] can now be emptied. Set Head [j] to 1
+ * if column j has changed (it is no longer used as a link list). */
+ PRINT1 (("column "ID", oldlnz = "ID"\n", j, Lnz [j])) ;
+ Head [j] = (Lnz [j] != newlnz) ? 1 : EMPTY ;
+ Lnz [j] = newlnz ;
+ PRINT1 (("column "ID", newlnz = "ID"\n", j, newlnz)) ;
+ DEBUG (dump_col ("New", j, p1, p2, Li, Lx, n, Common)) ;
+
+ /* move to the next column */
+ if (k == Path [path].rank)
+ {
+ /* only one path left */
+ j = nextj ;
+ }
+ else
+ {
+ /* The current path is moving from column j to column nextj
+ * (nextj is n if the path has ended). However, there may be
+ * other paths pending in columns j+1 to nextj-1. There are
+ * two methods for looking for the next column with a pending
+ * update. The first one looks at all columns j+1 to nextj-1
+ * for a non-empty link list. This can be costly if j and
+ * nextj differ by a large amount (it can be O(n), but this
+ * entire routine may take Omega(1) time). The second method
+ * looks at all paths and finds the smallest column at which any
+ * path is pending. It takes O(# of paths), which is bounded
+ * by 23: one for each column of C (up to 8), and then 15 for a
+ * balanced binary tree with 8 leaves. However, if j and
+ * nextj differ by a tiny amount (nextj is often j+1 near
+ * the end of the matrix), looking at columns j+1 to nextj
+ * would be faster. Both methods give the same answer. */
+
+ if (nextj - j < npaths)
+ {
+ /* there are fewer columns to search than paths */
+ PRINT1 (("check j="ID" to nextj="ID"\n", j, nextj)) ;
+ for (j2 = j + 1 ; j2 < nextj ; j2++)
+ {
+ PRINT1 (("check j="ID" "ID"\n", j2, Head [j2])) ;
+ if (Head [j2] != EMPTY)
+ {
+ PRINT1 (("found, j="ID"\n", j2)) ;
+ ASSERT (Path [Head [j2]].pending == j2) ;
+ break ;
+ }
+ }
+ }
+ else
+ {
+ /* there are fewer paths than columns to search */
+ j2 = nextj ;
+ for (kk = 0 ; kk < npaths ; kk++)
+ {
+ jj = Path [kk].pending ;
+ PRINT2 (("Path "ID" pending at "ID"\n", kk, jj)) ;
+ if (jj != EMPTY) j2 = MIN (j2, jj) ;
+ }
+ }
+ j = j2 ;
+ }
+ }
+
+ /* ensure workspaces are back to the values required on input */
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, TRUE, Common)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* depth-first-search of tree to order the paths */
+ /* ------------------------------------------------------------------ */
+
+ /* create lists of child paths */
+ PRINT1 (("\n\nDFS search:\n\n")) ;
+ for (path = 0 ; path < npaths ; path++)
+ {
+ Path [path].c = EMPTY ; /* first child of path */
+ Path [path].next = EMPTY ; /* next sibling of path */
+ Path [path].order = EMPTY ; /* path is not ordered yet */
+ Path [path].wfirst = EMPTY ; /* 1st column of W not found yet */
+
+#ifndef NDEBUG
+ j = Path [path].start ;
+ PRINT1 (("Path "ID" : start "ID" end "ID" parent "ID" ccol "ID"\n",
+ path, j, Path [path].end, Path [path].parent, Path [path].ccol)) ;
+ for ( ; ; )
+ {
+ PRINT1 ((" column "ID"\n", j)) ;
+ ASSERT (j == EMPTY || (j >= 0 && j < n)) ;
+ if (j == Path [path].end)
+ {
+ break ;
+ }
+ ASSERT (j >= 0 && j < n) ;
+ j = (Lnz [j] > 1) ? (Li [Lp [j] + 1]) : EMPTY ;
+ }
+#endif
+ }
+
+ for (path = 0 ; path < npaths ; path++)
+ {
+ p = Path [path].parent ; /* add path to child list of parent */
+ if (p != EMPTY)
+ {
+ ASSERT (p < npaths) ;
+ Path [path].next = Path [p].c ;
+ Path [p].c = path ;
+ }
+ }
+
+ path_order = k ;
+ w_order = 0 ;
+ for (path = npaths-1 ; path >= 0 ; path--)
+ {
+ if (Path [path].order == EMPTY)
+ {
+ /* this path is the root of a subtree of Tbar */
+ PRINT1 (("Root path "ID"\n", path)) ;
+ ASSERT (path >= k) ;
+ dfs (Path, k, path, &path_order, &w_order, 0, npaths) ;
+ }
+ }
+ ASSERT (path_order == npaths) ;
+ ASSERT (w_order == k) ;
+
+ /* reorder the paths */
+ for (path = 0 ; path < npaths ; path++)
+ {
+ /* old order is path, new order is Path [path].order */
+ OrderedPath [Path [path].order] = Path [path] ;
+ }
+
+#ifndef NDEBUG
+ for (path = 0 ; path < npaths ; path++)
+ {
+ PRINT1 (("Ordered Path "ID": start "ID" end "ID" wfirst "ID" rank "
+ ""ID" ccol "ID"\n", path, OrderedPath [path].start,
+ OrderedPath [path].end, OrderedPath [path].wfirst,
+ OrderedPath [path].rank, OrderedPath [path].ccol)) ;
+ if (path < k)
+ {
+ ASSERT (OrderedPath [path].ccol >= 0) ;
+ }
+ else
+ {
+ ASSERT (OrderedPath [path].ccol == EMPTY) ;
+ }
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* numeric update/downdate for all paths */
+ /* ------------------------------------------------------------------ */
+
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ;
+
+ switch (wdim)
+ {
+ case 1:
+ updown_1_r (update, C, k, L, W, OrderedPath, npaths, mask,
+ Common) ;
+ break ;
+ case 2:
+ updown_2_r (update, C, k, L, W, OrderedPath, npaths, mask,
+ Common) ;
+ break ;
+ case 4:
+ updown_4_r (update, C, k, L, W, OrderedPath, npaths, mask,
+ Common) ;
+ break ;
+ case 8:
+ updown_8_r (update, C, k, L, W, OrderedPath, npaths, mask,
+ Common) ;
+ break ;
+ }
+
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, wdim, Common)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* update/downdate the forward solve */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_solve)
+ {
+ /* We now have DeltaB += Lold (:,j) * X (j) for all columns j in union
+ * of all paths seen during the entire rank-cncol update/downdate. For
+ * each j in path, do DeltaB -= Lnew (:,j)*DeltaB(j)
+ * in topological order. */
+
+#ifndef NDEBUG
+ PRINT1 (("\ndo_solve, DeltaB + Lold(:,Path)*X(Path):\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ PRINT1 (("do_solve: "ID" %30.20e\n", i, Nx [i])) ;
+ }
+#endif
+
+ /* Note that the downdate, if it deleted entries, would need to compute
+ * the Stack prior to doing any downdates. */
+
+ /* find the union of all the paths in the new L */
+ top = n ; /* "top" is stack pointer, not a row or column index */
+ for (ccol = 0 ; ccol < cncol ; ccol++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* j = first row index of C (:,ccol) */
+ /* -------------------------------------------------------------- */
+
+ pp1 = Cp [ccol] ;
+ pp2 = (packed) ? (Cp [ccol+1]) : (pp1 + Cnz [ccol]) ;
+ if (pp2 > pp1)
+ {
+ /* Column ccol of C has at least one entry. */
+ j = Ci [pp1] ;
+ }
+ else
+ {
+ /* Column ccol of C is empty */
+ j = n-1 ;
+ }
+ PRINT1 (("\ndo_solve: ccol= "ID"\n", ccol)) ;
+ ASSERT (j >= 0 && j < n) ;
+ len = 0 ;
+
+ /* -------------------------------------------------------------- */
+ /* find the new rowmark */
+ /* -------------------------------------------------------------- */
+
+ /* Each column of C can redefine the region of L that takes part in
+ * the update/downdate of the triangular solve Lx=b. If
+ * i = colmark [ccol] for column C(:,ccol), then i = rowmark [j] is
+ * redefined for all columns along the path modified by C(:,ccol).
+ * If more than one column modifies any given column j of L, then
+ * the rowmark of j is determined by the colmark of the least-
+ * numbered column that affects column j. That is, if both
+ * C(:,ccol1) and C(:,ccol2) affect column j of L, then
+ * rowmark [j] = colmark [MIN (ccol1, ccol2)].
+ *
+ * rowmark [j] is not modified if rowmark or colmark are NULL,
+ * or if colmark [ccol] is EMPTY.
+ */
+
+ botrow = (use_colmark) ? (colmark [ccol]) : EMPTY ;
+
+ /* -------------------------------------------------------------- */
+ /* traverse from j towards root, stopping if node already visited */
+ /* -------------------------------------------------------------- */
+
+ while (j != EMPTY && Flag [j] < mark)
+ {
+ PRINT1 (("do_solve: subpath j= "ID"\n", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ Stack [len++] = j ; /* place j on the stack */
+ Flag [j] = mark ; /* flag j as visited */
+
+ /* if using colmark, mark column j with botrow */
+ ASSERT (Li [Lp [j]] == j) ; /* diagonal is always present */
+ if (use_colmark)
+ {
+ Li [Lp [j]] = botrow ; /* use the space for botrow */
+ }
+
+ /* go up the tree, to the parent of j */
+ j = (Lnz [j] > 1) ? (Li [Lp [j] + 1]) : EMPTY ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* move the path down to the bottom of the stack */
+ /* -------------------------------------------------------------- */
+
+ ASSERT (len <= top) ;
+ while (len > 0)
+ {
+ Stack [--top] = Stack [--len] ;
+ }
+ }
+
+#ifndef NDEBUG
+ /* Union of paths now in Stack [top..n-1] in topological order */
+ PRINT1 (("\nTopological order:\n")) ;
+ for (i = top ; i < n ; i++)
+ {
+ PRINT1 (("column "ID" in full path\n", Stack [i])) ;
+ }
+#endif
+
+ /* Do the forward solve for the full path part of L */
+ for (m = top ; m < n ; m++)
+ {
+ j = Stack [m] ;
+ ASSERT (j >= 0 && j < n) ;
+ PRINT1 (("do_solve: path j= "ID"\n", j)) ;
+ p1 = Lp [j] ;
+ lnz = Lnz [j] ;
+ p2 = p1 + lnz ;
+ xj = Nx [j] ;
+
+ /* copy new solution onto old one, for all cols in full path */
+ Xx [j] = xj ;
+ Nx [j] = 0. ;
+
+ /* DeltaB -= Lnew (j+1:botrow-1,j) * deltab(j) */
+ if (use_colmark)
+ {
+ botrow = Li [p1] ; /* get botrow */
+ Li [p1] = j ; /* restore diagonal entry */
+ for (p = p1 + 1 ; p < p2 ; p++)
+ {
+ i = Li [p] ;
+ if (i >= botrow) break ;
+ Nx [i] -= Lx [p] * xj ;
+ }
+ }
+ else
+ {
+ for (p = p1 + 1 ; p < p2 ; p++)
+ {
+ Nx [Li [p]] -= Lx [p] * xj ;
+ }
+ }
+ }
+
+ /* clear the Flag */
+ mark = CHOLMOD(clear_flag) (Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* successful update/downdate */
+ /* ---------------------------------------------------------------------- */
+
+ Common->modfl = fl ;
+ DEBUG (for (j = 0 ; j < n ; j++) ASSERT (IMPLIES (do_solve, Nx[j] == 0.))) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, TRUE, Common)) ;
+ DEBUG (CHOLMOD(dump_factor) (L, "output L for updown", Common)) ;
+ return (TRUE) ;
+}
+#endif
diff --git a/CHOLMOD/Modify/gpl.txt b/CHOLMOD/Modify/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/CHOLMOD/Modify/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
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diff --git a/CHOLMOD/Modify/t_cholmod_updown.c b/CHOLMOD/Modify/t_cholmod_updown.c
new file mode 100644
index 0000000..094c290
--- /dev/null
+++ b/CHOLMOD/Modify/t_cholmod_updown.c
@@ -0,0 +1,214 @@
+/* ========================================================================== */
+/* === Modify/t_cholmod_updown ============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Modify Module. Copyright (C) 2005-2006,
+ * Timothy A. Davis and William W. Hager.
+ * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Updates/downdates the LDL' factorization, by computing a new factorization of
+ *
+ * Lnew * Dnew * Lnew' = Lold * Dold * Lold' +/- C*C'
+ *
+ * This file is not compiled separately. It is included into
+ * cholmod_updown.c. There are no user-callable routines in this file.
+ *
+ * The next include statements, below, create the numerical update/downdate
+ * kernels from t_cholmod_updown_numkr.c. There are 4 compiled versions of this
+ * file, one for each value of WDIM in the set 1, 2, 4, and 8. Each calls
+ * multiple versions of t_cholmod_updown_numkr; the number of versions of each
+ * is equal to WDIM. Each t_cholmod_updown_numkr version is included as a
+ * static function within its t_cholmod_updown.c caller routine. Thus:
+ *
+ * t*_updown.c creates these versions of t_cholmod_updown_numkr.c:
+ * --------- ---------------------------------------------------
+ *
+ * updown_1_r updown_1_1
+ *
+ * updown_2_r updown_2_1 updown_2_2
+ *
+ * updown_4_r updown_4_1 updown_4_2 updown_4_3 updown_4_4
+ *
+ * updown_8_r updown_8_1 updown_8_2 updown_8_3 updown_8_4
+ * updown_8_5 updown_8_6 updown_8_7 updown_8_8
+ *
+ * workspace: Xwork (nrow*wdim)
+ */
+
+/* ========================================================================== */
+/* === routines for numeric update/downdate along one path ================== */
+/* ========================================================================== */
+
+#undef FORM_NAME
+#undef NUMERIC
+
+#define FORM_NAME(k,rank) updown_ ## k ## _ ## rank
+#define NUMERIC(k,rank) FORM_NAME(k,rank)
+
+#define RANK 1
+#include "t_cholmod_updown_numkr.c"
+
+#if WDIM >= 2
+#define RANK 2
+#include "t_cholmod_updown_numkr.c"
+#endif
+
+#if WDIM >= 4
+#define RANK 3
+#include "t_cholmod_updown_numkr.c"
+#define RANK 4
+#include "t_cholmod_updown_numkr.c"
+#endif
+
+#if WDIM == 8
+#define RANK 5
+#include "t_cholmod_updown_numkr.c"
+#define RANK 6
+#include "t_cholmod_updown_numkr.c"
+#define RANK 7
+#include "t_cholmod_updown_numkr.c"
+#define RANK 8
+#include "t_cholmod_updown_numkr.c"
+#endif
+
+
+/* ========================================================================== */
+/* === numeric update/downdate for all paths ================================ */
+/* ========================================================================== */
+
+static void NUMERIC (WDIM, r)
+(
+ int update, /* TRUE for update, FALSE for downdate */
+ cholmod_sparse *C, /* in packed or unpacked, and sorted form */
+ /* no empty columns */
+ Int rank, /* rank of the update/downdate */
+ cholmod_factor *L, /* with unit diagonal (diagonal not stored) */
+ /* temporary workspaces: */
+ double W [ ], /* n-by-WDIM dense matrix, initially zero */
+ Path_type Path [ ],
+ Int npaths,
+ Int mask [ ], /* size n */
+ cholmod_common *Common
+)
+{
+ double Alpha [8] ;
+ double *Cx, *Wpath, *W1, *a ;
+ Int i, j, p, ccol, pend, wfirst, e, path, packed ;
+ Int *Ci, *Cp, *Cnz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ci = C->i ;
+ Cx = C->x ;
+ Cp = C->p ;
+ Cnz = C->nz ;
+ packed = C->packed ;
+ ASSERT (IMPLIES (!packed, Cnz != NULL)) ;
+ ASSERT (L->n == C->nrow) ;
+ DEBUG (CHOLMOD(dump_real) ("num_d: in W:", W, WDIM, L->n, FALSE, 1,Common));
+
+ /* ---------------------------------------------------------------------- */
+ /* scatter C into W */
+ /* ---------------------------------------------------------------------- */
+
+ for (path = 0 ; path < rank ; path++)
+ {
+ /* W (:, path) = C (:, Path [path].col) */
+ ccol = Path [path].ccol ;
+ Wpath = W + path ;
+ PRINT1 (("Ordered Columns [path = "ID"] = "ID"\n", path, ccol)) ;
+ p = Cp [ccol] ;
+ pend = (packed) ? (Cp [ccol+1]) : (p + Cnz [ccol]) ;
+ /* column C can be empty */
+ for ( ; p < pend ; p++)
+ {
+ i = Ci [p] ;
+ ASSERT (i >= 0 && i < (Int) (C->nrow)) ;
+ if (mask == NULL || mask [i] < 0)
+ {
+ Wpath [WDIM * i] = Cx [p] ;
+ }
+ PRINT1 ((" row "ID" : %g mask "ID"\n", i, Cx [p],
+ (mask) ? mask [i] : 0)) ;
+ }
+ Alpha [path] = 1.0 ;
+ }
+ DEBUG (CHOLMOD(dump_real) ("num_d: W:", W, WDIM, L->n, FALSE, 1,Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric update/downdate of the paths */
+ /* ---------------------------------------------------------------------- */
+
+ /* for each disjoint subpath in Tbar in DFS order do */
+ for (path = rank ; path < npaths ; path++)
+ {
+
+ /* determine which columns of W to use */
+ wfirst = Path [path].wfirst ;
+ e = Path [path].end ;
+ j = Path [path].start ;
+ ASSERT (e >= 0 && e < (Int) (L->n)) ;
+ ASSERT (j >= 0 && j < (Int) (L->n)) ;
+
+ W1 = W + wfirst ; /* pointer to row 0, column wfirst of W */
+ a = Alpha + wfirst ; /* pointer to Alpha [wfirst] */
+
+ PRINT1 (("Numerical update/downdate of path "ID"\n", path)) ;
+ PRINT1 (("start "ID" end "ID" wfirst "ID" rank "ID" ccol "ID"\n", j, e,
+ wfirst, Path [path].rank, Path [path].ccol)) ;
+
+#if WDIM == 1
+ NUMERIC (WDIM,1) (update, j, e, a, W1, L, Common) ;
+#else
+
+ switch (Path [path].rank)
+ {
+ case 1:
+ NUMERIC (WDIM,1) (update, j, e, a, W1, L, Common) ;
+ break ;
+
+#if WDIM >= 2
+ case 2:
+ NUMERIC (WDIM,2) (update, j, e, a, W1, L, Common) ;
+ break ;
+#endif
+
+#if WDIM >= 4
+ case 3:
+ NUMERIC (WDIM,3) (update, j, e, a, W1, L, Common) ;
+ break ;
+ case 4:
+ NUMERIC (WDIM,4) (update, j, e, a, W1, L, Common) ;
+ break ;
+#endif
+
+#if WDIM == 8
+ case 5:
+ NUMERIC (WDIM,5) (update, j, e, a, W1, L, Common) ;
+ break ;
+ case 6:
+ NUMERIC (WDIM,6) (update, j, e, a, W1, L, Common) ;
+ break ;
+ case 7:
+ NUMERIC (WDIM,7) (update, j, e, a, W1, L, Common) ;
+ break ;
+ case 8:
+ NUMERIC (WDIM,8) (update, j, e, a, W1, L, Common) ;
+ break ;
+#endif
+
+ }
+#endif
+
+ }
+}
+
+/* prepare for the next inclusion of this file in cholmod_updown.c */
+#undef WDIM
diff --git a/CHOLMOD/Modify/t_cholmod_updown_numkr.c b/CHOLMOD/Modify/t_cholmod_updown_numkr.c
new file mode 100644
index 0000000..33060e9
--- /dev/null
+++ b/CHOLMOD/Modify/t_cholmod_updown_numkr.c
@@ -0,0 +1,746 @@
+/* ========================================================================== */
+/* === Modify/t_cholmod_updown_numkr ======================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Modify Module. Copyright (C) 2005-2006,
+ * Timothy A. Davis and William W. Hager.
+ * The CHOLMOD/Modify Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Supernodal numerical update/downdate of rank K = RANK, along a single path.
+ * This routine operates on a simplicial factor, but operates on adjacent
+ * columns of L that would fit within a single supernode. "Adjacent" means
+ * along a single path in the elimination tree; they may or may not be
+ * adjacent in the matrix L.
+ *
+ * external defines: NUMERIC, WDIM, RANK.
+ *
+ * WDIM is 1, 2, 4, or 8. RANK can be 1 to WDIM.
+ *
+ * A simple method is included (#define SIMPLE). The code works, but is slow.
+ * It is meant only to illustrate what this routine is doing.
+ *
+ * A rank-K update proceeds along a single path, using single-column, dual-
+ * column, or quad-column updates of L. If a column j and the next column
+ * in the path (its parent) do not have the same nonzero pattern, a single-
+ * column update is used. If they do, but the 3rd and 4th column from j do
+ * not have the same pattern, a dual-column update is used, in which the two
+ * columns are treated as if they were a single supernode of two columns. If
+ * there are 4 columns in the path that all have the same nonzero pattern, then
+ * a quad-column update is used. All three kinds of updates can be used along
+ * a single path, in a single call to this function.
+ *
+ * Single-column update:
+ *
+ * When updating a single column of L, each iteration of the for loop,
+ * below, processes four rows of W (all columns involved) and one column
+ * of L. Suppose we have a rank-5 update, and columns 2 through 6 of W
+ * are involved. In this case, W in this routine is a pointer to column
+ * 2 of the matrix W in the caller. W (in the caller, shown as 'W') is
+ * held in row-major order, and is 8-by-n (a dense matrix storage format),
+ * but shown below in column form to match the column of L. Suppose there
+ * are 13 nonzero entries in column 27 of L, with row indices 27 (the
+ * diagonal, D), 28, 30, 31, 42, 43, 44, 50, 51, 67, 81, 83, and 84. This
+ * pattern is held in Li [Lp [27] ... Lp [27 + Lnz [27] - 1], where
+ * Lnz [27] = 13. The modification of the current column j of L is done
+ * in the following order. A dot (.) means the entry of W is not accessed.
+ *
+ * W0 points to row 27 of W, and G is a 1-by-8 temporary vector.
+ *
+ * G[0] G[4]
+ * G x x x x x . . .
+ *
+ * W0
+ * |
+ * v
+ * 27 . . x x x x x . W0 points to W (27,2)
+ *
+ *
+ * row 'W' W column j = 27
+ * | | | of L
+ * v v v |
+ * first iteration of for loop: v
+ *
+ * 28 . . 1 5 9 13 17 . x
+ * 30 . . 2 6 10 14 18 . x
+ * 31 . . 3 7 11 15 19 . x
+ * 42 . . 4 8 12 16 20 . x
+ *
+ * second iteration of for loop:
+ *
+ * 43 . . 1 5 9 13 17 . x
+ * 44 . . 2 6 10 14 18 . x
+ * 50 . . 3 7 11 15 19 . x
+ * 51 . . 4 8 12 16 20 . x
+ *
+ * third iteration of for loop:
+ *
+ * 67 . . 1 5 9 13 17 . x
+ * 81 . . 2 6 10 14 18 . x
+ * 83 . . 3 7 11 15 19 . x
+ * 84 . . 4 8 12 16 20 . x
+ *
+ * If the number of offdiagonal nonzeros in column j of L is not divisible
+ * by 4, then the switch-statement does the work for the first nz % 4 rows.
+ *
+ * Dual-column update:
+ *
+ * In this case, two columns of L that are adjacent in the path are being
+ * updated, by 1 to 8 columns of W. Suppose columns j=27 and j=28 are
+ * adjacent columns in the path (they need not be j and j+1). Two rows
+ * of G and W are used as coefficients during the update: (G0, G1) and
+ * (W0, W1).
+ *
+ * G0 x x x x x . . .
+ * G1 x x x x x . . .
+ *
+ * 27 . . x x x x x . W0 points to W (27,2)
+ * 28 . . x x x x x . W1 points to W (28,2)
+ *
+ *
+ * row 'W' W0,W1 column j = 27
+ * | | | of L
+ * v v v |
+ * | |-- column j = 28 of L
+ * v v
+ * update L (j1,j):
+ *
+ * 28 . . 1 2 3 4 5 . x - ("-" is not stored in L)
+ *
+ * cleanup iteration since length is odd:
+ *
+ * 30 . . 1 2 3 4 5 . x x
+ *
+ * then each iteration does two rows of both columns of L:
+ *
+ * 31 . . 1 3 5 7 9 . x x
+ * 42 . . 2 4 6 8 10 . x x
+ *
+ * 43 . . 1 3 5 7 9 . x x
+ * 44 . . 2 4 6 8 10 . x x
+ *
+ * 50 . . 1 3 5 7 9 . x x
+ * 51 . . 2 4 6 8 10 . x x
+ *
+ * 67 . . 1 3 5 7 9 . x x
+ * 81 . . 2 4 6 8 10 . x x
+ *
+ * 83 . . 1 3 5 7 9 . x x
+ * 84 . . 2 4 6 8 10 . x x
+ *
+ * If the number of offdiagonal nonzeros in column j of L is not even,
+ * then the cleanup iteration does the work for the first row.
+ *
+ * Quad-column update:
+ *
+ * In this case, four columns of L that are adjacent in the path are being
+ * updated, by 1 to 8 columns of W. Suppose columns j=27, 28, 30, and 31
+ * are adjacent columns in the path (they need not be j, j+1, ...). Four
+ * rows of G and W are used as coefficients during the update: (G0 through
+ * G3) and (W0 through W3). j=27, j1=28, j2=30, and j3=31.
+ *
+ * G0 x x x x x . . .
+ * G1 x x x x x . . .
+ * G3 x x x x x . . .
+ * G4 x x x x x . . .
+ *
+ * 27 . . x x x x x . W0 points to W (27,2)
+ * 28 . . x x x x x . W1 points to W (28,2)
+ * 30 . . x x x x x . W2 points to W (30,2)
+ * 31 . . x x x x x . W3 points to W (31,2)
+ *
+ *
+ * row 'W' W0,W1,.. column j = 27
+ * | | | of L
+ * v v v |
+ * | |-- column j = 28 of L
+ * | | |-- column j = 30 of L
+ * | | | |-- column j = 31 of L
+ * v v v v
+ * update L (j1,j):
+ * 28 . . 1 2 3 4 5 . x - - -
+ *
+ * update L (j2,j):
+ * 30 . . 1 2 3 4 5 . # x - - (# denotes modified)
+ *
+ * update L (j2,j1)
+ * 30 . . 1 2 3 4 5 . x # - -
+ *
+ * update L (j3,j)
+ * 31 . . 1 2 3 4 5 . # x x -
+ *
+ * update L (j3,j1)
+ * 31 . . 1 2 3 4 5 . x # x -
+ *
+ * update L (j3,j2)
+ * 31 . . 1 2 3 4 5 . x x # -
+ *
+ * cleanup iteration since length is odd:
+ * 42 . . 1 2 3 4 5 . x x x x
+ *
+ *
+ * ----- CHOLMOD v1.1.1 did the following --------------------------------------
+ * then each iteration does two rows of all four colummns of L:
+ *
+ * 43 . . 1 3 5 7 9 . x x x x
+ * 44 . . 2 4 6 8 10 . x x x x
+ *
+ * 50 . . 1 3 5 7 9 . x x x x
+ * 51 . . 2 4 6 8 10 . x x x x
+ *
+ * 67 . . 1 3 5 7 9 . x x x x
+ * 81 . . 2 4 6 8 10 . x x x x
+ *
+ * 83 . . 1 3 5 7 9 . x x x x
+ * 84 . . 2 4 6 8 10 . x x x x
+ *
+ * ----- CHOLMOD v1.2.0 does the following -------------------------------------
+ * then each iteration does one rows of all four colummns of L:
+ *
+ * 43 . . 1 2 3 4 5 . x x x x
+ * 44 . . 1 2 3 4 5 . x x x x
+ * 50 . . 1 3 5 4 5 . x x x x
+ * 51 . . 1 2 3 4 5 . x x x x
+ * 67 . . 1 3 5 4 5 . x x x x
+ * 81 . . 1 2 3 4 5 . x x x x
+ * 83 . . 1 3 5 4 5 . x x x x
+ * 84 . . 1 2 3 4 5 . x x x x
+ *
+ * This file is included in t_cholmod_updown.c, only.
+ * It is not compiled separately. It contains no user-callable routines.
+ *
+ * workspace: Xwork (WDIM*nrow)
+ */
+
+/* ========================================================================== */
+/* === loop unrolling macros ================================================ */
+/* ========================================================================== */
+
+#undef RANK1
+#undef RANK2
+#undef RANK3
+#undef RANK4
+#undef RANK5
+#undef RANK6
+#undef RANK7
+#undef RANK8
+
+#define RANK1(statement) statement
+
+#if RANK < 2
+#define RANK2(statement)
+#else
+#define RANK2(statement) statement
+#endif
+
+#if RANK < 3
+#define RANK3(statement)
+#else
+#define RANK3(statement) statement
+#endif
+
+#if RANK < 4
+#define RANK4(statement)
+#else
+#define RANK4(statement) statement
+#endif
+
+#if RANK < 5
+#define RANK5(statement)
+#else
+#define RANK5(statement) statement
+#endif
+
+#if RANK < 6
+#define RANK6(statement)
+#else
+#define RANK6(statement) statement
+#endif
+
+#if RANK < 7
+#define RANK7(statement)
+#else
+#define RANK7(statement) statement
+#endif
+
+#if RANK < 8
+#define RANK8(statement)
+#else
+#define RANK8(statement) statement
+#endif
+
+#define FOR_ALL_K \
+ RANK1 (DO (0)) \
+ RANK2 (DO (1)) \
+ RANK3 (DO (2)) \
+ RANK4 (DO (3)) \
+ RANK5 (DO (4)) \
+ RANK6 (DO (5)) \
+ RANK7 (DO (6)) \
+ RANK8 (DO (7))
+
+/* ========================================================================== */
+/* === alpha/gamma ========================================================== */
+/* ========================================================================== */
+
+#undef ALPHA_GAMMA
+
+#define ALPHA_GAMMA(Dj,Alpha,Gamma,W) \
+{ \
+ double dj = Dj ; \
+ if (update) \
+ { \
+ for (k = 0 ; k < RANK ; k++) \
+ { \
+ double w = W [k] ; \
+ double alpha = Alpha [k] ; \
+ double a = alpha + (w * w) / dj ; \
+ dj *= a ; \
+ Alpha [k] = a ; \
+ Gamma [k] = (- w / dj) ; \
+ dj /= alpha ; \
+ } \
+ } \
+ else \
+ { \
+ for (k = 0 ; k < RANK ; k++) \
+ { \
+ double w = W [k] ; \
+ double alpha = Alpha [k] ; \
+ double a = alpha - (w * w) / dj ; \
+ dj *= a ; \
+ Alpha [k] = a ; \
+ Gamma [k] = w / dj ; \
+ dj /= alpha ; \
+ } \
+ } \
+ Dj = ((use_dbound) ? (CHOLMOD(dbound) (dj, Common)) : (dj)) ; \
+}
+
+/* ========================================================================== */
+/* === numeric update/downdate along one path =============================== */
+/* ========================================================================== */
+
+static void NUMERIC (WDIM, RANK)
+(
+ int update, /* TRUE for update, FALSE for downdate */
+ Int j, /* first column in the path */
+ Int e, /* last column in the path */
+ double Alpha [ ], /* alpha, for each column of W */
+ double W [ ], /* W is an n-by-WDIM array, stored in row-major order */
+ cholmod_factor *L, /* with unit diagonal (diagonal not stored) */
+ cholmod_common *Common
+)
+{
+
+#ifdef SIMPLE
+#define w(row,col) W [WDIM*(row) + (col)]
+
+ /* ---------------------------------------------------------------------- */
+ /* concise but slow version for illustration only */
+ /* ---------------------------------------------------------------------- */
+
+ double Gamma [WDIM] ;
+ double *Lx ;
+ Int *Li, *Lp, *Lnz ;
+ Int p, k ;
+ Int use_dbound = IS_GT_ZERO (Common->dbound) ;
+
+ Li = L->i ;
+ Lx = L->x ;
+ Lp = L->p ;
+ Lnz = L->nz ;
+
+ /* walk up the etree from node j to its ancestor e */
+ for ( ; j <= e ; j = (Lnz [j] > 1) ? (Li [Lp [j] + 1]) : Int_max)
+ {
+ /* update the diagonal entry D (j,j) with each column of W */
+ ALPHA_GAMMA (Lx [Lp [j]], Alpha, Gamma, (&(w (j,0)))) ;
+ /* update column j of L */
+ for (p = Lp [j] + 1 ; p < Lp [j] + Lnz [j] ; p++)
+ {
+ /* update row Li [p] of column j of L with each column of W */
+ Int i = Li [p] ;
+ for (k = 0 ; k < RANK ; k++)
+ {
+ w (i,k) -= w (j,k) * Lx [p] ;
+ Lx [p] -= Gamma [k] * w (i,k) ;
+ }
+ }
+ /* clear workspace W */
+ for (k = 0 ; k < RANK ; k++)
+ {
+ w (j,k) = 0 ;
+ }
+ }
+
+#else
+
+ /* ---------------------------------------------------------------------- */
+ /* dynamic supernodal version: supernodes detected dynamically */
+ /* ---------------------------------------------------------------------- */
+
+ double G0 [RANK], G1 [RANK], G2 [RANK], G3 [RANK] ;
+ double Z0 [RANK], Z1 [RANK], Z2 [RANK], Z3 [RANK] ;
+ double *W0, *W1, *W2, *W3, *Lx ;
+ Int *Li, *Lp, *Lnz ;
+ Int j1, j2, j3, p0, p1, p2, p3, parent, lnz, pend, k ;
+ Int use_dbound = IS_GT_ZERO (Common->dbound) ;
+
+ Li = L->i ;
+ Lx = L->x ;
+ Lp = L->p ;
+ Lnz = L->nz ;
+
+ /* walk up the etree from node j to its ancestor e */
+ for ( ; j <= e ; j = parent)
+ {
+
+ p0 = Lp [j] ; /* col j is Li,Lx [p0 ... p0+lnz-1] */
+ lnz = Lnz [j] ;
+
+ W0 = W + WDIM * j ; /* pointer to row j of W */
+ pend = p0 + lnz ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) Z0 [k] = W0 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) W0 [k] = 0 ;
+ FOR_ALL_K
+ #undef DO
+
+ /* update D (j,j) */
+ ALPHA_GAMMA (Lx [p0], Alpha, G0, Z0) ;
+ p0++ ;
+
+ /* determine how many columns of L to update at the same time */
+ parent = (lnz > 1) ? (Li [p0]) : Int_max ;
+ if (parent <= e && lnz == Lnz [parent] + 1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* node j and its parent j1 can be updated at the same time */
+ /* -------------------------------------------------------------- */
+
+ j1 = parent ;
+ j2 = (lnz > 2) ? (Li [p0+1]) : Int_max ;
+ j3 = (lnz > 3) ? (Li [p0+2]) : Int_max ;
+ W1 = W + WDIM * j1 ; /* pointer to row j1 of W */
+ p1 = Lp [j1] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) Z1 [k] = W1 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) W1 [k] = 0 ;
+ FOR_ALL_K
+ #undef DO
+
+ /* update L (j1,j) */
+ {
+ double lx = Lx [p0] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) \
+ Z1 [k] -= Z0 [k] * lx ; \
+ lx -= G0 [k] * Z1 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ Lx [p0++] = lx ;
+ }
+
+ /* update D (j1,j1) */
+ ALPHA_GAMMA (Lx [p1], Alpha, G1, Z1) ;
+ p1++ ;
+
+ /* -------------------------------------------------------------- */
+ /* update 2 or 4 columns of L */
+ /* -------------------------------------------------------------- */
+
+ if ((j2 <= e) && /* j2 in the current path */
+ (j3 <= e) && /* j3 in the current path */
+ (lnz == Lnz [j2] + 2) && /* column j2 matches */
+ (lnz == Lnz [j3] + 3)) /* column j3 matches */
+ {
+
+ /* ---------------------------------------------------------- */
+ /* update 4 columns of L */
+ /* ---------------------------------------------------------- */
+
+ /* p0 and p1 currently point to row j2 in cols j and j1 of L */
+
+ parent = (lnz > 4) ? (Li [p0+2]) : Int_max ;
+ W2 = W + WDIM * j2 ; /* pointer to row j2 of W */
+ W3 = W + WDIM * j3 ; /* pointer to row j3 of W */
+ p2 = Lp [j2] ;
+ p3 = Lp [j3] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) Z2 [k] = W2 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) Z3 [k] = W3 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) W2 [k] = 0 ;
+ FOR_ALL_K
+ #undef DO
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) W3 [k] = 0 ;
+ FOR_ALL_K
+ #undef DO
+
+ /* update L (j2,j) and update L (j2,j1) */
+ {
+ double lx [2] ;
+ lx [0] = Lx [p0] ;
+ lx [1] = Lx [p1] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) \
+ Z2 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * Z2 [k] ; \
+ Z2 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * Z2 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ Lx [p0++] = lx [0] ;
+ Lx [p1++] = lx [1] ;
+ }
+
+ /* update D (j2,j2) */
+ ALPHA_GAMMA (Lx [p2], Alpha, G2, Z2) ;
+ p2++ ;
+
+ /* update L (j3,j), L (j3,j1), and L (j3,j2) */
+ {
+ double lx [3] ;
+ lx [0] = Lx [p0] ;
+ lx [1] = Lx [p1] ;
+ lx [2] = Lx [p2] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) \
+ Z3 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * Z3 [k] ; \
+ Z3 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * Z3 [k] ; \
+ Z3 [k] -= Z2 [k] * lx [2] ; lx [2] -= G2 [k] * Z3 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ Lx [p0++] = lx [0] ;
+ Lx [p1++] = lx [1] ;
+ Lx [p2++] = lx [2] ;
+ }
+
+ /* update D (j3,j3) */
+ ALPHA_GAMMA (Lx [p3], Alpha, G3, Z3) ;
+ p3++ ;
+
+ /* each iteration updates L (i, [j j1 j2 j3]) */
+ for ( ; p0 < pend ; p0++, p1++, p2++, p3++)
+ {
+ double lx [4], *w0 ;
+ lx [0] = Lx [p0] ;
+ lx [1] = Lx [p1] ;
+ lx [2] = Lx [p2] ;
+ lx [3] = Lx [p3] ;
+ w0 = W + WDIM * Li [p0] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) \
+ w0 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * w0 [k] ; \
+ w0 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * w0 [k] ; \
+ w0 [k] -= Z2 [k] * lx [2] ; lx [2] -= G2 [k] * w0 [k] ; \
+ w0 [k] -= Z3 [k] * lx [3] ; lx [3] -= G3 [k] * w0 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ Lx [p0] = lx [0] ;
+ Lx [p1] = lx [1] ;
+ Lx [p2] = lx [2] ;
+ Lx [p3] = lx [3] ;
+ }
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* update 2 columns of L */
+ /* ---------------------------------------------------------- */
+
+ parent = j2 ;
+
+ /* cleanup iteration if length is odd */
+ if ((lnz - 2) % 2)
+ {
+ double lx [2] , *w0 ;
+ lx [0] = Lx [p0] ;
+ lx [1] = Lx [p1] ;
+ w0 = W + WDIM * Li [p0] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) \
+ w0 [k] -= Z0 [k] * lx [0] ; lx [0] -= G0 [k] * w0 [k] ; \
+ w0 [k] -= Z1 [k] * lx [1] ; lx [1] -= G1 [k] * w0 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ Lx [p0++] = lx [0] ;
+ Lx [p1++] = lx [1] ;
+ }
+
+ for ( ; p0 < pend ; p0 += 2, p1 += 2)
+ {
+ double lx [2][2], w [2], *w0, *w1 ;
+ lx [0][0] = Lx [p0 ] ;
+ lx [1][0] = Lx [p0+1] ;
+ lx [0][1] = Lx [p1 ] ;
+ lx [1][1] = Lx [p1+1] ;
+ w0 = W + WDIM * Li [p0 ] ;
+ w1 = W + WDIM * Li [p0+1] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) \
+ w [0] = w0 [k] - Z0 [k] * lx [0][0] ; \
+ w [1] = w1 [k] - Z0 [k] * lx [1][0] ; \
+ lx [0][0] -= G0 [k] * w [0] ; \
+ lx [1][0] -= G0 [k] * w [1] ; \
+ w0 [k] = w [0] -= Z1 [k] * lx [0][1] ; \
+ w1 [k] = w [1] -= Z1 [k] * lx [1][1] ; \
+ lx [0][1] -= G1 [k] * w [0] ; \
+ lx [1][1] -= G1 [k] * w [1] ;
+ FOR_ALL_K
+ #undef DO
+
+ Lx [p0 ] = lx [0][0] ;
+ Lx [p0+1] = lx [1][0] ;
+ Lx [p1 ] = lx [0][1] ;
+ Lx [p1+1] = lx [1][1] ;
+ }
+ }
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* update one column of L */
+ /* -------------------------------------------------------------- */
+
+ /* cleanup iteration if length is not a multiple of 4 */
+ switch ((lnz - 1) % 4)
+ {
+ case 1:
+ {
+ double lx , *w0 ;
+ lx = Lx [p0] ;
+ w0 = W + WDIM * Li [p0] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) \
+ w0 [k] -= Z0 [k] * lx ; lx -= G0 [k] * w0 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ Lx [p0++] = lx ;
+ }
+ break ;
+
+ case 2:
+ {
+ double lx [2], *w0, *w1 ;
+ lx [0] = Lx [p0 ] ;
+ lx [1] = Lx [p0+1] ;
+ w0 = W + WDIM * Li [p0 ] ;
+ w1 = W + WDIM * Li [p0+1] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) \
+ w0 [k] -= Z0 [k] * lx [0] ; \
+ w1 [k] -= Z0 [k] * lx [1] ; \
+ lx [0] -= G0 [k] * w0 [k] ; \
+ lx [1] -= G0 [k] * w1 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ Lx [p0++] = lx [0] ;
+ Lx [p0++] = lx [1] ;
+ }
+ break ;
+
+ case 3:
+ {
+ double lx [3], *w0, *w1, *w2 ;
+ lx [0] = Lx [p0 ] ;
+ lx [1] = Lx [p0+1] ;
+ lx [2] = Lx [p0+2] ;
+ w0 = W + WDIM * Li [p0 ] ;
+ w1 = W + WDIM * Li [p0+1] ;
+ w2 = W + WDIM * Li [p0+2] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) \
+ w0 [k] -= Z0 [k] * lx [0] ; \
+ w1 [k] -= Z0 [k] * lx [1] ; \
+ w2 [k] -= Z0 [k] * lx [2] ; \
+ lx [0] -= G0 [k] * w0 [k] ; \
+ lx [1] -= G0 [k] * w1 [k] ; \
+ lx [2] -= G0 [k] * w2 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ Lx [p0++] = lx [0] ;
+ Lx [p0++] = lx [1] ;
+ Lx [p0++] = lx [2] ;
+ }
+ }
+
+ for ( ; p0 < pend ; p0 += 4)
+ {
+ double lx [4], *w0, *w1, *w2, *w3 ;
+ lx [0] = Lx [p0 ] ;
+ lx [1] = Lx [p0+1] ;
+ lx [2] = Lx [p0+2] ;
+ lx [3] = Lx [p0+3] ;
+ w0 = W + WDIM * Li [p0 ] ;
+ w1 = W + WDIM * Li [p0+1] ;
+ w2 = W + WDIM * Li [p0+2] ;
+ w3 = W + WDIM * Li [p0+3] ;
+
+ /* for k = 0 to RANK-1 do: */
+ #define DO(k) \
+ w0 [k] -= Z0 [k] * lx [0] ; \
+ w1 [k] -= Z0 [k] * lx [1] ; \
+ w2 [k] -= Z0 [k] * lx [2] ; \
+ w3 [k] -= Z0 [k] * lx [3] ; \
+ lx [0] -= G0 [k] * w0 [k] ; \
+ lx [1] -= G0 [k] * w1 [k] ; \
+ lx [2] -= G0 [k] * w2 [k] ; \
+ lx [3] -= G0 [k] * w3 [k] ;
+ FOR_ALL_K
+ #undef DO
+
+ Lx [p0 ] = lx [0] ;
+ Lx [p0+1] = lx [1] ;
+ Lx [p0+2] = lx [2] ;
+ Lx [p0+3] = lx [3] ;
+ }
+ }
+ }
+#endif
+}
+/* prepare this file for another inclusion in t_cholmod_updown.c: */
+#undef RANK
diff --git a/CHOLMOD/Partition/License.txt b/CHOLMOD/Partition/License.txt
new file mode 100644
index 0000000..8a2bd21
--- /dev/null
+++ b/CHOLMOD/Partition/License.txt
@@ -0,0 +1,25 @@
+CHOLMOD/Partition Module.
+Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Partition module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
diff --git a/CHOLMOD/Partition/cholmod_camd.c b/CHOLMOD/Partition/cholmod_camd.c
new file mode 100644
index 0000000..51ec0a7
--- /dev/null
+++ b/CHOLMOD/Partition/cholmod_camd.c
@@ -0,0 +1,227 @@
+/* ========================================================================== */
+/* === Partition/cholmod_camd =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Partition Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD interface to the CAMD ordering routine. Orders A if the matrix is
+ * symmetric. On output, Perm [k] = i if row/column i of A is the kth
+ * row/column of P*A*P'. This corresponds to A(p,p) in MATLAB notation.
+ *
+ * If A is unsymmetric, cholmod_camd orders A*A'. On output, Perm [k] = i if
+ * row/column i of A*A' is the kth row/column of P*A*A'*P'. This corresponds to
+ * A(p,:)*A(p,:)' in MATLAB notation. If f is present, A(p,f)*A(p,f)' is
+ * ordered.
+ *
+ * Computes the flop count for a subsequent LL' factorization, the number
+ * of nonzeros in L, and the number of nonzeros in the matrix ordered (A,
+ * A*A' or A(:,f)*A(:,f)').
+ *
+ * workspace: Iwork (4*nrow). Head (nrow).
+ *
+ * Allocates a temporary copy of A+A' or A*A' (with
+ * both upper and lower triangular parts) as input to CAMD.
+ * Also allocates 3*(n+1) additional integer workspace (not in Common).
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex)
+ */
+
+#ifndef NPARTITION
+
+#include "cholmod_internal.h"
+#include "camd.h"
+#include "cholmod_partition.h"
+
+#if (CAMD_VERSION < CAMD_VERSION_CODE (2,0))
+#error "CAMD v2.0 or later is required"
+#endif
+
+/* ========================================================================== */
+/* === cholmod_camd ========================================================= */
+/* ========================================================================== */
+
+int CHOLMOD(camd)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ Int *Cmember, /* size nrow. see cholmod_ccolamd.c for description.*/
+ /* ---- output ---- */
+ Int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double Info [CAMD_INFO], Control2 [CAMD_CONTROL], *Control ;
+ Int *Cp, *Len, *Nv, *Head, *Elen, *Degree, *Wi, *Next, *BucketSet,
+ *Work3n, *p ;
+ cholmod_sparse *C ;
+ Int j, n, cnz ;
+ size_t s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ n = A->nrow ;
+
+ /* s = 4*n */
+ s = CHOLMOD(mult_size_t) (n, 4, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ RETURN_IF_NULL (Perm, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+ if (n == 0)
+ {
+ /* nothing to do */
+ Common->fl = 0 ;
+ Common->lnz = 0 ;
+ Common->anz = 0 ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* cholmod_analyze has allocated Cmember at Common->Iwork + 5*n+uncol, and
+ * CParent at Common->Iwork + 4*n+uncol, where uncol is 0 if A is symmetric
+ * or A->ncol otherwise. Thus, only the first 4n integers in Common->Iwork
+ * can be used here. */
+
+ CHOLMOD(allocate_work) (n, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ p = Common->Iwork ;
+ Degree = p ; p += n ; /* size n */
+ Elen = p ; p += n ; /* size n */
+ Len = p ; p += n ; /* size n */
+ Nv = p ; p += n ; /* size n */
+
+ Work3n = CHOLMOD(malloc) (n+1, 3*sizeof (Int), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ p = Work3n ;
+ Next = p ; p += n ; /* size n */
+ Wi = p ; p += (n+1) ; /* size n+1 */
+ BucketSet = p ; /* size n */
+
+ Head = Common->Head ; /* size n+1 */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the input matrix for CAMD */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0)
+ {
+ /* C = A*A' or A(:,f)*A(:,f)', add extra space of nnz(C)/2+n to C */
+ C = CHOLMOD(aat) (A, fset, fsize, -2, Common) ;
+ }
+ else
+ {
+ /* C = A+A', but use only the upper triangular part of A if A->stype = 1
+ * and only the lower part of A if A->stype = -1. Add extra space of
+ * nnz(C)/2+n to C. */
+ C = CHOLMOD(copy) (A, 0, -2, Common) ;
+ }
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory, fset invalid, or other error */
+ CHOLMOD(free) (n+1, 3*sizeof (Int), Work3n, Common) ;
+ return (FALSE) ;
+ }
+
+ Cp = C->p ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Len [j] = Cp [j+1] - Cp [j] ;
+ }
+
+ /* C does not include the diagonal, and both upper and lower parts.
+ * Common->anz includes the diagonal, and just the lower part of C */
+ cnz = Cp [n] ;
+ Common->anz = cnz / 2 + n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order C using CAMD */
+ /* ---------------------------------------------------------------------- */
+
+ /* get parameters */
+ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS)
+ {
+ /* use CAMD defaults */
+ Control = NULL ;
+ }
+ else
+ {
+ Control = Control2 ;
+ Control [CAMD_DENSE] = Common->method [Common->current].prune_dense ;
+ Control [CAMD_AGGRESSIVE] = Common->method [Common->current].aggressive;
+ }
+
+ /* CAMD_2 does not use camd_malloc and camd_free, but set these pointers
+ * just be safe. */
+ camd_malloc = Common->malloc_memory ;
+ camd_free = Common->free_memory ;
+ camd_calloc = Common->calloc_memory ;
+ camd_realloc = Common->realloc_memory ;
+
+ /* CAMD_2 doesn't print anything either, but future versions might,
+ * so set the camd_printf pointer too. */
+ camd_printf = Common->print_function ;
+
+#ifdef LONG
+ /* DEBUG (camd_l_debug_init ("cholmod_l_camd")) ; */
+ camd_l2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen,
+ Degree, Wi, Control, Info, Cmember, BucketSet) ;
+#else
+ /* DEBUG (camd_debug_init ("cholmod_camd")) ; */
+ camd_2 (n, C->p, C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen,
+ Degree, Wi, Control, Info, Cmember, BucketSet) ;
+#endif
+
+ /* LL' flop count. Need to subtract n for LL' flop count. Note that this
+ * is a slight upper bound which is often exact (see CAMD/Source/camd_2.c
+ * for details). cholmod_analyze computes an exact flop count and
+ * fill-in. */
+ Common->fl = Info [CAMD_NDIV] + 2 * Info [CAMD_NMULTSUBS_LDL] + n ;
+
+ /* Info [CAMD_LNZ] excludes the diagonal */
+ Common->lnz = n + Info [CAMD_LNZ] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the CAMD workspace and clear the persistent workspace in Common */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (IMPLIES (Common->status == CHOLMOD_OK,
+ CHOLMOD(dump_perm) (Perm, n, n, "CAMD2 perm", Common))) ;
+ CHOLMOD(free_sparse) (&C, Common) ;
+ for (j = 0 ; j <= n ; j++)
+ {
+ Head [j] = EMPTY ;
+ }
+ CHOLMOD(free) (n+1, 3*sizeof (Int), Work3n, Common) ;
+ return (TRUE) ;
+}
+#endif
diff --git a/CHOLMOD/Partition/cholmod_ccolamd.c b/CHOLMOD/Partition/cholmod_ccolamd.c
new file mode 100644
index 0000000..06d4fd0
--- /dev/null
+++ b/CHOLMOD/Partition/cholmod_ccolamd.c
@@ -0,0 +1,205 @@
+/* ========================================================================== */
+/* === Partition/cholmod_ccolamd ============================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Partition Module.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD interface to the CCOLAMD ordering routine. Finds a permutation
+ * p such that the Cholesky factorization of PAA'P' is sparser than AA'.
+ * The column etree is found and postordered, and the ccolamd ordering is then
+ * combined with its postordering. A must be unsymmetric.
+ *
+ * workspace: Iwork (MAX (nrow,ncol))
+ * Allocates a copy of its input matrix, which is
+ * then used as CCOLAMD's workspace.
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex).
+ */
+
+#ifndef NPARTITION
+
+#include "cholmod_internal.h"
+#include "ccolamd.h"
+#include "cholmod_partition.h"
+
+#if (CCOLAMD_VERSION < CCOLAMD_VERSION_CODE (2,5))
+#error "CCOLAMD v2.0 or later is required"
+#endif
+
+/* ========================================================================== */
+/* === ccolamd_interface ==================================================== */
+/* ========================================================================== */
+
+/* Order with ccolamd */
+
+static int ccolamd_interface
+(
+ cholmod_sparse *A,
+ size_t alen,
+ Int *Perm,
+ Int *Cmember,
+ Int *fset,
+ Int fsize,
+ cholmod_sparse *C,
+ cholmod_common *Common
+)
+{
+ double knobs [CCOLAMD_KNOBS] ;
+ Int *Cp = NULL ;
+ Int ok, k, nrow, ncol, stats [CCOLAMD_STATS] ;
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy (and transpose) the input matrix A into the ccolamd workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* C = A (:,f)', which also packs A if needed. */
+ /* workspace: Iwork (nrow if no fset; MAX (nrow,ncol) if fset non-NULL) */
+ ok = CHOLMOD(transpose_unsym) (A, 0, NULL, fset, fsize, C, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order the matrix (destroys the contents of C->i and C->p) */
+ /* ---------------------------------------------------------------------- */
+
+ /* get parameters */
+#ifdef LONG
+ ccolamd_l_set_defaults (knobs) ;
+#else
+ ccolamd_set_defaults (knobs) ;
+#endif
+
+ if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS)
+ {
+ /* this is the CHOLMOD default, not the CCOLAMD default */
+ knobs [CCOLAMD_DENSE_ROW] = -1 ;
+ }
+ else
+ {
+ /* get the knobs from the Common parameters */
+ knobs [CCOLAMD_DENSE_COL] =Common->method[Common->current].prune_dense ;
+ knobs [CCOLAMD_DENSE_ROW] =Common->method[Common->current].prune_dense2;
+ knobs [CCOLAMD_AGGRESSIVE]=Common->method[Common->current].aggressive ;
+ knobs [CCOLAMD_LU] =Common->method[Common->current].order_for_lu;
+ }
+
+ if (ok)
+ {
+
+#ifdef LONG
+ ccolamd_l (ncol, nrow, alen, C->i, C->p, knobs, stats, Cmember) ;
+#else
+ ccolamd (ncol, nrow, alen, C->i, C->p, knobs, stats, Cmember) ;
+#endif
+
+ ok = stats [CCOLAMD_STATUS] ;
+
+ ok = (ok == CCOLAMD_OK || ok == CCOLAMD_OK_BUT_JUMBLED) ;
+ /* permutation returned in C->p, if the ordering succeeded */
+ Cp = C->p ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ Perm [k] = Cp [k] ;
+ }
+ }
+
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_ccolamd ====================================================== */
+/* ========================================================================== */
+
+/* Order AA' or A(:,f)*A(:,f)' using CCOLAMD. */
+
+int CHOLMOD(ccolamd)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ Int *Cmember, /* size A->nrow. Cmember [i] = c if row i is in the
+ * constraint set c. c must be >= 0. The # of
+ * constraint sets is max (Cmember) + 1. If Cmember is
+ * NULL, then it is interpretted as Cmember [i] = 0 for
+ * all i */
+ /* ---- output --- */
+ Int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_sparse *C ;
+ Int ok, nrow, ncol ;
+ size_t alen ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (Perm, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (A->stype != 0)
+ {
+ ERROR (CHOLMOD_INVALID, "matrix must be unsymmetric") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef LONG
+ alen = ccolamd_l_recommended (A->nzmax, ncol, nrow) ;
+#else
+ alen = ccolamd_recommended (A->nzmax, ncol, nrow) ;
+#endif
+
+ if (alen == 0)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "matrix invalid or too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (0, MAX (nrow,ncol), 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0,
+ CHOLMOD_PATTERN, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order with ccolamd */
+ /* ---------------------------------------------------------------------- */
+
+ ok = ccolamd_interface (A, alen, Perm, Cmember, fset, fsize, C, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the workspace and return result */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&C, Common) ;
+ return (ok) ;
+}
+#endif
diff --git a/CHOLMOD/Partition/cholmod_csymamd.c b/CHOLMOD/Partition/cholmod_csymamd.c
new file mode 100644
index 0000000..7b8044a
--- /dev/null
+++ b/CHOLMOD/Partition/cholmod_csymamd.c
@@ -0,0 +1,141 @@
+/* ========================================================================== */
+/* === Partition/cholmod_csymamd ============================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Partition Module.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD interface to the CSYMAMD ordering routine. Finds a permutation
+ * p such that the Cholesky factorization of PAP' is sparser than A.
+ * The column etree is found and postordered, and the CSYMAMD
+ * ordering is then combined with its postordering. If A is unsymmetric,
+ * A+A' is ordered (A must be square).
+ *
+ * workspace: Head (nrow+1)
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex).
+ */
+
+#ifndef NPARTITION
+
+#include "cholmod_internal.h"
+#include "ccolamd.h"
+#include "cholmod_partition.h"
+
+#if (CCOLAMD_VERSION < CCOLAMD_VERSION_CODE (2,5))
+#error "CCOLAMD v2.0 or later is required"
+#endif
+
+/* ========================================================================== */
+/* === cholmod_csymamd ====================================================== */
+/* ========================================================================== */
+
+int CHOLMOD(csymamd)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ /* ---- output --- */
+ Int *Cmember, /* size nrow. see cholmod_ccolamd.c for description */
+ Int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double knobs [CCOLAMD_KNOBS] ;
+ Int *perm, *Head ;
+ Int ok, i, nrow, stats [CCOLAMD_STATS] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (Perm, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+
+ if (A->nrow != A->ncol || !(A->packed))
+ {
+ ERROR (CHOLMOD_INVALID, "matrix must be square and packed") ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(allocate_work) (nrow, 0, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* order the matrix (does not affect A->p or A->i) */
+ /* ---------------------------------------------------------------------- */
+
+ perm = Common->Head ; /* size nrow+1 (i/l/l) */
+
+ /* get parameters */
+#ifdef LONG
+ ccolamd_l_set_defaults (knobs) ;
+#else
+ ccolamd_set_defaults (knobs) ;
+#endif
+ if (Common->current >= 0 && Common->current < CHOLMOD_MAXMETHODS)
+ {
+ /* get the knobs from the Common parameters */
+ knobs [CCOLAMD_DENSE_ROW] =Common->method[Common->current].prune_dense ;
+ knobs [CCOLAMD_AGGRESSIVE]=Common->method[Common->current].aggressive ;
+ }
+
+ {
+#ifdef LONG
+ csymamd_l (nrow, A->i, A->p, perm, knobs, stats, Common->calloc_memory,
+ Common->free_memory, Cmember, A->stype) ;
+#else
+ csymamd (nrow, A->i, A->p, perm, knobs, stats, Common->calloc_memory,
+ Common->free_memory, Cmember, A->stype) ;
+#endif
+ ok = stats [CCOLAMD_STATUS] ;
+ }
+
+ if (ok == CCOLAMD_ERROR_out_of_memory)
+ {
+ ERROR (CHOLMOD_OUT_OF_MEMORY, "out of memory") ;
+ }
+ ok = (ok == CCOLAMD_OK || ok == CCOLAMD_OK_BUT_JUMBLED) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the workspace and return result */
+ /* ---------------------------------------------------------------------- */
+
+ /* permutation returned in perm [0..n-1] */
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Perm [i] = perm [i] ;
+ }
+
+ /* clear Head workspace (used for perm, in csymamd): */
+ Head = Common->Head ;
+ for (i = 0 ; i <= nrow ; i++)
+ {
+ Head [i] = EMPTY ;
+ }
+
+ return (ok) ;
+}
+#endif
diff --git a/CHOLMOD/Partition/cholmod_metis.c b/CHOLMOD/Partition/cholmod_metis.c
new file mode 100644
index 0000000..0351543
--- /dev/null
+++ b/CHOLMOD/Partition/cholmod_metis.c
@@ -0,0 +1,792 @@
+/* ========================================================================== */
+/* === Partition/cholmod_metis ============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Partition Module.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD interface to the METIS package (Version 4.0.1):
+ *
+ * cholmod_metis_bisector:
+ *
+ * Wrapper for METIS_NodeComputeSeparator. Finds a set of nodes that
+ * partitions the graph into two parts.
+ *
+ * cholmod_metis:
+ *
+ * Wrapper for METIS_NodeND, METIS's own nested dissection algorithm.
+ * Typically faster than cholmod_nested_dissection, mostly because it
+ * uses minimum degree on just the leaves of the separator tree, rather
+ * than the whole matrix.
+ *
+ * Note that METIS does not return an error if it runs out of memory. Instead,
+ * it terminates the program. This interface attempts to avoid that problem
+ * by preallocating space that should be large enough for any memory allocations
+ * within METIS, and then freeing that space, just before the call to METIS.
+ * While this is not guaranteed to work, it is very unlikely to fail. If you
+ * encounter this problem, increase Common->metis_memory. If you don't mind
+ * having your program terminated, set Common->metis_memory to zero (a value of
+ * 2.0 is usually safe). Several other METIS workarounds are made in the
+ * routines in this file. See the description of metis_memory_ok, just below,
+ * for more details.
+ *
+ * FUTURE WORK: interfaces to other partitioners (CHACO, SCOTCH, JOSTLE, ... )
+ *
+ * workspace: several size-nz and size-n temporary arrays. Uses no workspace
+ * in Common.
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex).
+ */
+
+#ifndef NPARTITION
+
+#include "cholmod_internal.h"
+#undef ASSERT
+
+#include "metis.h"
+/* METIS has its own ASSERT that it reveals to the user, so remove it here: */
+#undef ASSERT
+
+/* and redefine it back again */
+#ifndef NDEBUG
+#define ASSERT(expression) (assert (expression))
+#else
+#define ASSERT(expression)
+#endif
+
+#include "cholmod_partition.h"
+#include "cholmod_cholesky.h"
+
+
+/* ========================================================================== */
+/* === dumpgraph ============================================================ */
+/* ========================================================================== */
+
+/* For dumping the input graph to METIS_NodeND, to check with METIS's onmetis
+ * and graphchk programs. For debugging only. To use, uncomment this #define:
+#define DUMP_GRAPH
+ */
+
+#ifdef DUMP_GRAPH
+#include <stdio.h>
+/* After dumping the graph with this routine, run "onmetis metisgraph" */
+static void dumpgraph (idxtype *Mp, idxtype *Mi, UF_long n,
+ cholmod_common *Common)
+{
+ UF_long i, j, p, nz ;
+ FILE *f ;
+ nz = Mp [n] ;
+ printf ("Dumping METIS graph n %ld nz %ld\n", n, nz) ; /* DUMP_GRAPH */
+ f = fopen ("metisgraph", "w") ;
+ if (f == NULL)
+ {
+ ERROR (-99, "cannot open metisgraph") ;
+ return ;
+ }
+ fprintf (f, "%ld %ld\n", n, nz/2) ; /* DUMP_GRAPH */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Mp [j] ; p < Mp [j+1] ; p++)
+ {
+ i = Mi [p] ;
+ fprintf (f, " %ld", i+1) ; /* DUMP_GRAPH */
+ }
+ fprintf (f, "\n") ; /* DUMP_GRAPH */
+ }
+ fclose (f) ;
+}
+#endif
+
+
+/* ========================================================================== */
+/* === metis_memory_ok ====================================================== */
+/* ========================================================================== */
+
+/* METIS_NodeND and METIS_NodeComputeSeparator will terminate your program it
+ * they run out of memory. In an attempt to workaround METIS' behavior, this
+ * routine allocates a single block of memory of size equal to an observed
+ * upper bound on METIS' memory usage. It then immediately deallocates the
+ * block. If the allocation fails, METIS is not called.
+ *
+ * Median memory usage for a graph with n nodes and nz edges (counting each
+ * edge twice, or both upper and lower triangular parts of a matrix) is
+ * 4*nz + 40*n + 4096 integers. A "typical" upper bound is 10*nz + 50*n + 4096
+ * integers. Nearly all matrices tested fit within that upper bound, with the
+ * exception two in the UF sparse matrix collection: Schenk_IBMNA/c-64 and
+ * Gupta/gupta2. The latter exceeds the "upper bound" by a factor of just less
+ * than 2.
+ *
+ * If you do not mind having your program terminated if it runs out of memory,
+ * set Common->metis_memory to zero. Its default value is 2, which allows for
+ * some memory fragmentation, and also accounts for the Gupta/gupta2 matrix.
+ *
+ * An alternative, if CHOLMOD is used in MATLAB, is to use a version of METIS
+ * (4.0.2, perhaps) proposed to George Karypis. This version uses function
+ * pointer for malloc and free. They can be set to mxMalloc and mxFree
+ * (see sputil_config in MATLAB/sputil.c). On Linux, with gcc, you must also
+ * compile CHOLMOD, METIS, AMD, COLAMD, and CCOLAMD with the -fexceptions
+ * compiler flag. With this configuration, mxMalloc safely aborts the
+ * mexFunction, frees all memory allocted by METIS, and safely returns to
+ * MATLAB. You may then set Common->metis_memory = 0.
+ */
+
+#define GUESS(nz,n) (10 * (nz) + 50 * (n) + 4096)
+
+static int metis_memory_ok
+(
+ Int n,
+ Int nz,
+ cholmod_common *Common
+)
+{
+ double s ;
+ void *p ;
+ size_t metis_guard ;
+
+ if (Common->metis_memory <= 0)
+ {
+ /* do not prevent METIS from running out of memory */
+ return (TRUE) ;
+ }
+
+ n = MAX (1, n) ;
+ nz = MAX (0, nz) ;
+
+ /* compute in double, to avoid integer overflow */
+ s = GUESS ((double) nz, (double) n) ;
+ s *= Common->metis_memory ;
+
+ if (s * sizeof (idxtype) >= ((double) Size_max))
+ {
+ /* don't even attempt to malloc such a large block */
+ return (FALSE) ;
+ }
+
+ /* recompute in size_t */
+ metis_guard = GUESS ((size_t) nz, (size_t) n) ;
+ metis_guard *= Common->metis_memory ;
+
+ /* attempt to malloc the block */
+ p = CHOLMOD(malloc) (metis_guard, sizeof (idxtype), Common) ;
+ if (p == NULL)
+ {
+ /* failure - return out-of-memory condition */
+ return (FALSE) ;
+ }
+
+ /* success - free the block */
+ CHOLMOD(free) (metis_guard, sizeof (idxtype), p, Common) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_metis_bisector =============================================== */
+/* ========================================================================== */
+
+/* Finds a set of nodes that bisects the graph of A or AA' (direct interface
+ * to METIS_NodeComputeSeparator).
+ *
+ * The input matrix A must be square, symmetric (with both upper and lower
+ * parts present) and with no diagonal entries. These conditions are NOT
+ * checked.
+ */
+
+UF_long CHOLMOD(metis_bisector) /* returns separator size */
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to bisect */
+ Int *Anw, /* size A->nrow, node weights */
+ Int *Aew, /* size nz, edge weights */
+ /* ---- output --- */
+ Int *Partition, /* size A->nrow */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Ap, *Ai ;
+ idxtype *Mp, *Mi, *Mnw, *Mew, *Mpart ;
+ Int n, nleft, nright, j, p, csep, total_weight, lightest, nz ;
+ int Opt [8], nn, csp ;
+ size_t n1 ;
+ DEBUG (Int nsep) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (A, EMPTY) ;
+ RETURN_IF_NULL (Anw, EMPTY) ;
+ RETURN_IF_NULL (Aew, EMPTY) ;
+ RETURN_IF_NULL (Partition, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ if (A->stype || A->nrow != A->ncol)
+ {
+ /* A must be square, with both upper and lower parts present */
+ ERROR (CHOLMOD_INVALID, "matrix must be square, symmetric,"
+ " and with both upper/lower parts present") ;
+ return (EMPTY) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* quick return */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+ if (n == 0)
+ {
+ return (0) ;
+ }
+ n1 = ((size_t) n) + 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ nz = Ap [n] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* METIS does not have a 64-bit integer version */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef LONG
+ if (sizeof (Int) > sizeof (idxtype) && MAX (n,nz) > INT_MAX / sizeof (int))
+ {
+ /* CHOLMOD's matrix is too large for METIS */
+ return (EMPTY) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* set default options */
+ /* ---------------------------------------------------------------------- */
+
+ Opt [0] = 0 ; /* use defaults */
+ Opt [1] = 3 ; /* matching type */
+ Opt [2] = 1 ; /* init. partitioning algo*/
+ Opt [3] = 2 ; /* refinement algorithm */
+ Opt [4] = 0 ; /* no debug */
+ Opt [5] = 0 ; /* unused */
+ Opt [6] = 0 ; /* unused */
+ Opt [7] = -1 ; /* random seed */
+
+ DEBUG (for (j = 0 ; j < n ; j++) ASSERT (Anw [j] > 0)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy Int to METIS idxtype, if necessary */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG (for (j = 0 ; j < nz ; j++) ASSERT (Aew [j] > 0)) ;
+ if (sizeof (Int) == sizeof (idxtype))
+ {
+ /* this is the typical case */
+ Mi = (idxtype *) Ai ;
+ Mew = (idxtype *) Aew ;
+ Mp = (idxtype *) Ap ;
+ Mnw = (idxtype *) Anw ;
+ Mpart = (idxtype *) Partition ;
+ }
+ else
+ {
+ /* idxtype and Int differ; copy the graph into the METIS idxtype */
+ Mi = CHOLMOD(malloc) (nz, sizeof (idxtype), Common) ;
+ Mew = CHOLMOD(malloc) (nz, sizeof (idxtype), Common) ;
+ Mp = CHOLMOD(malloc) (n1, sizeof (idxtype), Common) ;
+ Mnw = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ;
+ Mpart = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ;
+ CHOLMOD(free) (nz, sizeof (idxtype), Mew, Common) ;
+ CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ;
+ CHOLMOD(free) (n, sizeof (idxtype), Mnw, Common) ;
+ CHOLMOD(free) (n, sizeof (idxtype), Mpart, Common) ;
+ return (EMPTY) ;
+ }
+ for (p = 0 ; p < nz ; p++)
+ {
+ Mi [p] = Ai [p] ;
+ }
+ for (p = 0 ; p < nz ; p++)
+ {
+ Mew [p] = Aew [p] ;
+ }
+ for (j = 0 ; j <= n ; j++)
+ {
+ Mp [j] = Ap [j] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ Mnw [j] = Anw [j] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* METIS workaround: try to ensure METIS doesn't run out of memory */
+ /* ---------------------------------------------------------------------- */
+
+ if (!metis_memory_ok (n, nz, Common))
+ {
+ /* METIS might ask for too much memory and thus terminate the program */
+ if (sizeof (Int) != sizeof (idxtype))
+ {
+ CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ;
+ CHOLMOD(free) (nz, sizeof (idxtype), Mew, Common) ;
+ CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ;
+ CHOLMOD(free) (n, sizeof (idxtype), Mnw, Common) ;
+ CHOLMOD(free) (n, sizeof (idxtype), Mpart, Common) ;
+ }
+ return (EMPTY) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* partition the graph */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ PRINT1 (("Metis graph, n = "ID"\n", n)) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Int ppp ;
+ PRINT2 (("M(:,"ID") node weight "ID"\n", j, (Int) Mnw [j])) ;
+ ASSERT (Mnw [j] > 0) ;
+ for (ppp = Mp [j] ; ppp < Mp [j+1] ; ppp++)
+ {
+ PRINT3 ((" "ID" : "ID"\n", (Int) Mi [ppp], (Int) Mew [ppp])) ;
+ ASSERT (Mi [ppp] != j) ;
+ ASSERT (Mew [ppp] > 0) ;
+ }
+ }
+#endif
+
+ nn = n ;
+ METIS_NodeComputeSeparator (&nn, Mp, Mi, Mnw, Mew, Opt, &csp, Mpart) ;
+ n = nn ;
+ csep = csp ;
+
+ PRINT1 (("METIS csep "ID"\n", csep)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the results back from idxtype, if required */
+ /* ---------------------------------------------------------------------- */
+
+ if (sizeof (Int) != sizeof (idxtype))
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ Partition [j] = Mpart [j] ;
+ }
+ CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ;
+ CHOLMOD(free) (nz, sizeof (idxtype), Mew, Common) ;
+ CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ;
+ CHOLMOD(free) (n, sizeof (idxtype), Mnw, Common) ;
+ CHOLMOD(free) (n, sizeof (idxtype), Mpart, Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* ensure a reasonable separator */
+ /* ---------------------------------------------------------------------- */
+
+ /* METIS can return a valid separator with no nodes in (for example) the
+ * left part. In this case, there really is no separator. CHOLMOD
+ * prefers, in this case, for all nodes to be in the separator (and both
+ * left and right parts to be empty). Also, if the graph is unconnected,
+ * METIS can return a valid empty separator. CHOLMOD prefers at least one
+ * node in the separator. Note that cholmod_nested_dissection only calls
+ * this routine on connected components, but cholmod_bisect can call this
+ * routine for any graph. */
+
+ if (csep == 0)
+ {
+ /* The separator is empty, select lightest node as separator. If
+ * ties, select the highest numbered node. */
+ lightest = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Anw [j] <= Anw [lightest])
+ {
+ lightest = j ;
+ }
+ }
+ PRINT1 (("Force "ID" as sep\n", lightest)) ;
+ Partition [lightest] = 2 ;
+ csep = Anw [lightest] ;
+ }
+
+ /* determine the node weights in the left and right part of the graph */
+ nleft = 0 ;
+ nright = 0 ;
+ DEBUG (nsep = 0) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ PRINT1 (("Partition ["ID"] = "ID"\n", j, Partition [j])) ;
+ if (Partition [j] == 0)
+ {
+ nleft += Anw [j] ;
+ }
+ else if (Partition [j] == 1)
+ {
+ nright += Anw [j] ;
+ }
+#ifndef NDEBUG
+ else
+ {
+ ASSERT (Partition [j] == 2) ;
+ nsep += Anw [j] ;
+ }
+#endif
+ }
+ ASSERT (csep == nsep) ;
+
+ total_weight = nleft + nright + csep ;
+
+ if (csep < total_weight)
+ {
+ /* The separator is less than the whole graph. Make sure the left and
+ * right parts are either both empty or both non-empty. */
+ PRINT1 (("nleft "ID" nright "ID" csep "ID" tot "ID"\n",
+ nleft, nright, csep, total_weight)) ;
+ ASSERT (nleft + nright + csep == total_weight) ;
+ ASSERT (nleft > 0 || nright > 0) ;
+ if ((nleft == 0 && nright > 0) || (nleft > 0 && nright == 0))
+ {
+ /* left or right is empty; put all nodes in the separator */
+ PRINT1 (("Force all in sep\n")) ;
+ csep = total_weight ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Partition [j] = 2 ;
+ }
+ }
+ }
+
+ ASSERT (CHOLMOD(dump_partition) (n, Ap, Ai, Anw, Partition, csep, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return the sum of the weights of nodes in the separator */
+ /* ---------------------------------------------------------------------- */
+
+ return (csep) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_metis ======================================================== */
+/* ========================================================================== */
+
+/* CHOLMOD wrapper for the METIS_NodeND ordering routine. Creates A+A',
+ * A*A' or A(:,f)*A(:,f)' and then calls METIS_NodeND on the resulting graph.
+ * This routine is comparable to cholmod_nested_dissection, except that it
+ * calls METIS_NodeND directly, and it does not return the separator tree.
+ *
+ * workspace: Flag (nrow), Iwork (4*n+uncol)
+ * Allocates a temporary matrix B=A*A' or B=A.
+ */
+
+int CHOLMOD(metis)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int postorder, /* if TRUE, follow with etree or coletree postorder */
+ /* ---- output --- */
+ Int *Perm, /* size A->nrow, output permutation */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double d ;
+ Int *Iperm, *Iwork, *Bp, *Bi ;
+ idxtype *Mp, *Mi, *Mperm, *Miperm ;
+ cholmod_sparse *B ;
+ Int i, j, n, nz, p, identity, uncol ;
+ int Opt [8], nn, zero = 0 ;
+ size_t n1, s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (Perm, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* quick return */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+ if (n == 0)
+ {
+ return (TRUE) ;
+ }
+ n1 = ((size_t) n) + 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = 4*n + uncol */
+ uncol = (A->stype == 0) ? A->ncol : 0 ;
+ s = CHOLMOD(mult_size_t) (n, 4, &ok) ;
+ s = CHOLMOD(add_size_t) (s, uncol, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (n, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert the matrix to adjacency list form */
+ /* ---------------------------------------------------------------------- */
+
+ /* The input graph for METIS must be symmetric, with both upper and lower
+ * parts present, and with no diagonal entries. The columns need not be
+ * sorted.
+ * B = A+A', A*A', or A(:,f)*A(:,f)', upper and lower parts present */
+ if (A->stype)
+ {
+ /* Add the upper/lower part to a symmetric lower/upper matrix by
+ * converting to unsymmetric mode */
+ /* workspace: Iwork (nrow) */
+ B = CHOLMOD(copy) (A, 0, -1, Common) ;
+ }
+ else
+ {
+ /* B = A*A' or A(:,f)*A(:,f)', no diagonal */
+ /* workspace: Flag (nrow), Iwork (max (nrow,ncol)) */
+ B = CHOLMOD(aat) (A, fset, fsize, -1, Common) ;
+ }
+ ASSERT (CHOLMOD(dump_sparse) (B, "B for NodeND", Common) >= 0) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (B->nrow == A->nrow) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Iwork = Common->Iwork ;
+ Iperm = Iwork ; /* size n (i/i/l) */
+
+ Bp = B->p ;
+ Bi = B->i ;
+ nz = Bp [n] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* METIS does not have a UF_long integer version */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef LONG
+ if (sizeof (Int) > sizeof (idxtype) && MAX (n,nz) > INT_MAX / sizeof (int))
+ {
+ /* CHOLMOD's matrix is too large for METIS */
+ CHOLMOD(free_sparse) (&B, Common) ;
+ return (FALSE) ;
+ }
+#endif
+
+ /* B does not include the diagonal, and both upper and lower parts.
+ * Common->anz includes the diagonal, and just the lower part of B */
+ Common->anz = nz / 2 + n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* set control parameters for METIS_NodeND */
+ /* ---------------------------------------------------------------------- */
+
+ Opt [0] = 0 ; /* use defaults */
+ Opt [1] = 3 ; /* matching type */
+ Opt [2] = 1 ; /* init. partitioning algo*/
+ Opt [3] = 2 ; /* refinement algorithm */
+ Opt [4] = 0 ; /* no debug */
+ Opt [5] = 1 ; /* initial compression */
+ Opt [6] = 0 ; /* no dense node removal */
+ Opt [7] = 1 ; /* number of separators @ each step */
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the METIS input arrays, if needed */
+ /* ---------------------------------------------------------------------- */
+
+ if (sizeof (Int) == sizeof (idxtype))
+ {
+ /* This is the typical case. */
+ Miperm = (idxtype *) Iperm ;
+ Mperm = (idxtype *) Perm ;
+ Mp = (idxtype *) Bp ;
+ Mi = (idxtype *) Bi ;
+ }
+ else
+ {
+ /* allocate graph for METIS only if Int and idxtype differ */
+ Miperm = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ;
+ Mperm = CHOLMOD(malloc) (n, sizeof (idxtype), Common) ;
+ Mp = CHOLMOD(malloc) (n1, sizeof (idxtype), Common) ;
+ Mi = CHOLMOD(malloc) (nz, sizeof (idxtype), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&B, Common) ;
+ CHOLMOD(free) (n, sizeof (idxtype), Miperm, Common) ;
+ CHOLMOD(free) (n, sizeof (idxtype), Mperm, Common) ;
+ CHOLMOD(free) (n1, sizeof (idxtype), Mp, Common) ;
+ CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ;
+ return (FALSE) ;
+ }
+ for (j = 0 ; j <= n ; j++)
+ {
+ Mp [j] = Bp [j] ;
+ }
+ for (p = 0 ; p < nz ; p++)
+ {
+ Mi [p] = Bi [p] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* METIS workarounds */
+ /* ---------------------------------------------------------------------- */
+
+ identity = FALSE ;
+ if (nz == 0)
+ {
+ /* The matrix has no off-diagonal entries. METIS_NodeND fails in this
+ * case, so avoid using it. The best permutation is identity anyway,
+ * so this is an easy fix. */
+ identity = TRUE ;
+ PRINT1 (("METIS:: no nz\n")) ;
+ }
+ else if (Common->metis_nswitch > 0)
+ {
+ /* METIS_NodeND in METIS 4.0.1 gives a seg fault with one matrix of
+ * order n = 3005 and nz = 6,036,025, including the diagonal entries.
+ * The workaround is to return the identity permutation instead of using
+ * METIS for matrices of dimension 3000 or more and with density of 66%
+ * or more - admittedly an uncertain fix, but such matrices are so dense
+ * that any reasonable ordering will do, even identity (n^2 is only 50%
+ * higher than nz in this case). CHOLMOD's nested dissection method
+ * (cholmod_nested_dissection) has no problems with the same matrix,
+ * even though it too uses METIS_NodeComputeSeparator. The matrix is
+ * derived from LPnetlib/lpi_cplex1 in the UF sparse matrix collection.
+ * If C is the lpi_cplex matrix (of order 3005-by-5224), A = (C*C')^2
+ * results in the seg fault. The seg fault also occurs in the stand-
+ * alone onmetis program that comes with METIS. If a future version of
+ * METIS fixes this problem, then set Common->metis_nswitch to zero.
+ */
+ d = ((double) nz) / (((double) n) * ((double) n)) ;
+ if (n > (Int) (Common->metis_nswitch) && d > Common->metis_dswitch)
+ {
+ identity = TRUE ;
+ PRINT1 (("METIS:: nswitch/dswitch activated\n")) ;
+ }
+ }
+
+ if (!identity && !metis_memory_ok (n, nz, Common))
+ {
+ /* METIS might ask for too much memory and thus terminate the program */
+ identity = TRUE ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the permutation */
+ /* ---------------------------------------------------------------------- */
+
+ if (identity)
+ {
+ /* no need to do the postorder */
+ postorder = FALSE ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Mperm [i] = i ;
+ }
+ }
+ else
+ {
+#ifdef DUMP_GRAPH
+ /* DUMP_GRAPH */ printf ("Calling METIS_NodeND n "ID" nz "ID""
+ "density %g\n", n, nz, ((double) nz) / (((double) n) * ((double) n)));
+ dumpgraph (Mp, Mi, n, Common) ;
+#endif
+
+ nn = n ;
+ METIS_NodeND (&nn, Mp, Mi, &zero, Opt, Mperm, Miperm) ;
+ n = nn ;
+
+ PRINT0 (("METIS_NodeND done\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the METIS input arrays */
+ /* ---------------------------------------------------------------------- */
+
+ if (sizeof (Int) != sizeof (idxtype))
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Perm [i] = (Int) (Mperm [i]) ;
+ }
+ CHOLMOD(free) (n, sizeof (idxtype), Miperm, Common) ;
+ CHOLMOD(free) (n, sizeof (idxtype), Mperm, Common) ;
+ CHOLMOD(free) (n+1, sizeof (idxtype), Mp, Common) ;
+ CHOLMOD(free) (nz, sizeof (idxtype), Mi, Common) ;
+ }
+
+ CHOLMOD(free_sparse) (&B, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* etree or column-etree postordering, using the Cholesky Module */
+ /* ---------------------------------------------------------------------- */
+
+ if (postorder)
+ {
+ Int *Parent, *Post, *NewPerm ;
+ Int k ;
+
+ Parent = Iwork + 2*((size_t) n) + uncol ; /* size n = nrow */
+ Post = Parent + n ; /* size n */
+
+ /* workspace: Iwork (2*nrow+uncol), Flag (nrow), Head (nrow+1) */
+ CHOLMOD(analyze_ordering) (A, CHOLMOD_METIS, Perm, fset, fsize,
+ Parent, Post, NULL, NULL, NULL, Common) ;
+ if (Common->status == CHOLMOD_OK)
+ {
+ /* combine the METIS permutation with its postordering */
+ NewPerm = Parent ; /* use Parent as workspace */
+ for (k = 0 ; k < n ; k++)
+ {
+ NewPerm [k] = Perm [Post [k]] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ Perm [k] = NewPerm [k] ;
+ }
+ }
+ }
+
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ PRINT1 (("cholmod_metis done\n")) ;
+ return (Common->status == CHOLMOD_OK) ;
+}
+#endif
diff --git a/CHOLMOD/Partition/cholmod_nesdis.c b/CHOLMOD/Partition/cholmod_nesdis.c
new file mode 100644
index 0000000..7def8b9
--- /dev/null
+++ b/CHOLMOD/Partition/cholmod_nesdis.c
@@ -0,0 +1,2164 @@
+/* ========================================================================== */
+/* === Partition/cholmod_nesdis ============================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Partition Module.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * The CHOLMOD/Partition Module is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* CHOLMOD nested dissection and graph partitioning.
+ *
+ * cholmod_bisect:
+ *
+ * Finds a set of nodes that partitions the graph into two parts.
+ * Compresses the graph first. Requires METIS.
+ *
+ * cholmod_nested_dissection:
+ *
+ * Nested dissection, using its own compression and connected-commponents
+ * algorithms, an external graph partitioner (METIS), and a constrained
+ * minimum degree ordering algorithm (CCOLAMD or CSYMAMD). Typically
+ * gives better orderings than METIS_NodeND (about 5% to 10% fewer
+ * nonzeros in L).
+ *
+ * cholmod_collapse_septree:
+ *
+ * Prune the separator tree returned by cholmod_nested_dissection.
+ *
+ * This file contains several routines private to this file:
+ *
+ * partition compress and partition a graph
+ * clear_flag clear Common->Flag, but do not modify negative entries
+ * find_components find the connected components of a graph
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex).
+ */
+
+#ifndef NPARTITION
+
+#include "cholmod_internal.h"
+#include "cholmod_partition.h"
+#include "cholmod_cholesky.h"
+
+/* ========================================================================== */
+/* === partition ============================================================ */
+/* ========================================================================== */
+
+/* Find a set of nodes that partition a graph. The graph must be symmetric
+ * with no diagonal entries. To compress the graph first, compress is TRUE
+ * and on input Hash [j] holds the hash key for node j, which must be in the
+ * range 0 to csize-1. The input graph (Cp, Ci) is destroyed. Cew is all 1's
+ * on input and output. Cnw [j] > 0 is the initial weight of node j. On
+ * output, Cnw [i] = 0 if node i is absorbed into j and the original weight
+ * Cnw [i] is added to Cnw [j]. If compress is FALSE, the graph is not
+ * compressed and Cnw and Hash are unmodified. The partition itself is held in
+ * the output array Part of size n. Part [j] is 0, 1, or 2, depending on
+ * whether node j is in the left part of the graph, the right part, or the
+ * separator, respectively. Note that the input graph need not be connected,
+ * and the output subgraphs (the three parts) may also be unconnected.
+ *
+ * Returns the size of the separator, in terms of the sum of the weights of
+ * the nodes. It is guaranteed to be between 1 and the total weight of all
+ * the nodes. If it is of size less than the total weight, then both the left
+ * and right parts are guaranteed to be non-empty (this guarantee depends on
+ * cholmod_metis_bisector).
+ */
+
+static UF_long partition /* size of separator or -1 if failure */
+(
+ /* inputs, not modified on output */
+#ifndef NDEBUG
+ Int csize, /* upper bound on # of edges in the graph;
+ * csize >= MAX (n, nnz(C)) must hold. */
+#endif
+ int compress, /* if TRUE the compress the graph first */
+
+ /* input/output */
+ Int Hash [ ], /* Hash [i] = hash >= 0 is the hash function for node
+ * i on input. On output, Hash [i] = FLIP (j) if node
+ * i is absorbed into j. Hash [i] >= 0 if i has not
+ * been absorbed. */
+
+ /* input graph, compressed graph of cn nodes on output */
+ cholmod_sparse *C,
+
+ /* input/output */
+ Int Cnw [ ], /* size n. Cnw [j] > 0 is the weight of node j on
+ * input. On output, if node i is absorbed into
+ * node j, then Cnw [i] = 0 and the original weight of
+ * node i is added to Cnw [j]. The sum of Cnw [0..n-1]
+ * is not modified. */
+
+ /* workspace */
+ Int Cew [ ], /* size csize, all 1's on input and output */
+
+ /* more workspace, undefined on input and output */
+ Int Cmap [ ], /* size n (i/i/l) */
+
+ /* output */
+ Int Part [ ], /* size n, Part [j] = 0, 1, or 2. */
+
+ cholmod_common *Common
+)
+{
+ Int n, hash, head, i, j, k, p, pend, ilen, ilast, pi, piend,
+ jlen, ok, cn, csep, pdest, nodes_pruned, nz, total_weight, jscattered ;
+ Int *Cp, *Ci, *Next, *Hhead ;
+
+#ifndef NDEBUG
+ Int cnt, pruned ;
+ double work = 0, goodwork = 0 ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* quick return for small or empty graphs */
+ /* ---------------------------------------------------------------------- */
+
+ n = C->nrow ;
+ Cp = C->p ;
+ Ci = C->i ;
+ nz = Cp [n] ;
+
+ PRINT2 (("Partition start, n "ID" nz "ID"\n", n, nz)) ;
+
+ total_weight = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (Cnw [j] > 0) ;
+ total_weight += Cnw [j] ;
+ }
+
+ if (n <= 2)
+ {
+ /* very small graph */
+ for (j = 0 ; j < n ; j++)
+ {
+ Part [j] = 2 ;
+ }
+ return (total_weight) ;
+ }
+ else if (nz <= 0)
+ {
+ /* no edges, this is easy */
+ PRINT2 (("diagonal matrix\n")) ;
+ k = n/2 ;
+ for (j = 0 ; j < k ; j++)
+ {
+ Part [j] = 0 ;
+ }
+ for ( ; j < n ; j++)
+ {
+ Part [j] = 1 ;
+ }
+ /* ensure the separator is not empty (required by nested dissection) */
+ Part [n-1] = 2 ;
+ return (Cnw [n-1]) ;
+ }
+
+#ifndef NDEBUG
+ ASSERT (n > 1 && nz > 0) ;
+ PRINT2 (("original graph:\n")) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ PRINT2 ((""ID": ", j)) ;
+ for (p = Cp [j] ; p < Cp [j+1] ; p++)
+ {
+ i = Ci [p] ;
+ PRINT3 ((""ID" ", i)) ;
+ ASSERT (i >= 0 && i < n && i != j) ;
+ }
+ PRINT2 (("hash: "ID"\n", Hash [j])) ;
+ }
+ DEBUG (for (p = 0 ; p < csize ; p++) ASSERT (Cew [p] == 1)) ;
+#endif
+
+ nodes_pruned = 0 ;
+
+ if (compress)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get workspace */
+ /* ------------------------------------------------------------------ */
+
+ Next = Part ; /* use Part as workspace for Next [ */
+ Hhead = Cew ; /* use Cew as workspace for Hhead [ */
+
+ /* ------------------------------------------------------------------ */
+ /* create the hash buckets */
+ /* ------------------------------------------------------------------ */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* get the hash key for node j */
+ hash = Hash [j] ;
+ ASSERT (hash >= 0 && hash < csize) ;
+ head = Hhead [hash] ;
+ if (head > EMPTY)
+ {
+ /* hash bucket for this hash key is empty. */
+ head = EMPTY ;
+ }
+ else
+ {
+ /* hash bucket for this hash key is not empty. get old head */
+ head = FLIP (head) ;
+ ASSERT (head >= 0 && head < n) ;
+ }
+ /* node j becomes the new head of the hash bucket. FLIP it so that
+ * we can tell the difference between an empty or non-empty hash
+ * bucket. */
+ Hhead [hash] = FLIP (j) ;
+ Next [j] = head ;
+ ASSERT (head >= EMPTY && head < n) ;
+ }
+
+#ifndef NDEBUG
+ for (cnt = 0, k = 0 ; k < n ; k++)
+ {
+ ASSERT (Hash [k] >= 0 && Hash [k] < csize) ; /* k is alive */
+ hash = Hash [k] ;
+ ASSERT (hash >= 0 && hash < csize) ;
+ head = Hhead [hash] ;
+ ASSERT (head < EMPTY) ; /* hash bucket not empty */
+ j = FLIP (head) ;
+ ASSERT (j >= 0 && j < n) ;
+ if (j == k)
+ {
+ PRINT2 (("hash "ID": ", hash)) ;
+ for ( ; j != EMPTY ; j = Next [j])
+ {
+ PRINT3 ((" "ID"", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ ASSERT (Hash [j] == hash) ;
+ cnt++ ;
+ ASSERT (cnt <= n) ;
+ }
+ PRINT2 (("\n")) ;
+ }
+ }
+ ASSERT (cnt == n) ;
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* scan the non-empty hash buckets for indistinguishable nodes */
+ /* ------------------------------------------------------------------ */
+
+ /* If there are no hash collisions and no compression occurs, this takes
+ * O(n) time. If no hash collisions, but some nodes are removed, this
+ * takes time O(n+e) where e is the sum of the degress of the nodes
+ * that are removed. Even with many hash collisions (a rare case),
+ * this algorithm has never been observed to perform more than nnz(A)
+ * useless work.
+ *
+ * Cmap is used as workspace to mark nodes of the graph, [
+ * for comparing the nonzero patterns of two nodes i and j.
+ */
+
+#define Cmap_MARK(i) Cmap [i] = j
+#define Cmap_MARKED(i) (Cmap [i] == j)
+
+ for (i = 0 ; i < n ; i++)
+ {
+ Cmap [i] = EMPTY ;
+ }
+
+ for (k = 0 ; k < n ; k++)
+ {
+ hash = Hash [k] ;
+ ASSERT (hash >= FLIP (n-1) && hash < csize) ;
+ if (hash < 0)
+ {
+ /* node k has already been absorbed into some other node */
+ ASSERT (FLIP (Hash [k]) >= 0 && FLIP (Hash [k] < n)) ;
+ continue ;
+ }
+ head = Hhead [hash] ;
+ ASSERT (head < EMPTY || head == 1) ;
+ if (head == 1)
+ {
+ /* hash bucket is already empty */
+ continue ;
+ }
+ PRINT2 (("\n--------------------hash "ID":\n", hash)) ;
+ for (j = FLIP (head) ; j != EMPTY && Next[j] > EMPTY ; j = Next [j])
+ {
+ /* compare j with all nodes i following it in hash bucket */
+ ASSERT (j >= 0 && j < n && Hash [j] == hash) ;
+ p = Cp [j] ;
+ pend = Cp [j+1] ;
+ jlen = pend - p ;
+ jscattered = FALSE ;
+ DEBUG (for (i = 0 ; i < n ; i++) ASSERT (!Cmap_MARKED (i))) ;
+ DEBUG (pruned = FALSE) ;
+ ilast = j ;
+ for (i = Next [j] ; i != EMPTY ; i = Next [i])
+ {
+ ASSERT (i >= 0 && i < n && Hash [i] == hash && i != j) ;
+ pi = Cp [i] ;
+ piend = Cp [i+1] ;
+ ilen = piend - pi ;
+ DEBUG (work++) ;
+ if (ilen != jlen)
+ {
+ /* i and j have different degrees */
+ ilast = i ;
+ continue ;
+ }
+ /* scatter the pattern of node j, if not already */
+ if (!jscattered)
+ {
+ Cmap_MARK (j) ;
+ for ( ; p < pend ; p++)
+ {
+ Cmap_MARK (Ci [p]) ;
+ }
+ jscattered = TRUE ;
+ DEBUG (work += jlen) ;
+ }
+ for (ok = Cmap_MARKED (i) ; ok && pi < piend ; pi++)
+ {
+ ok = Cmap_MARKED (Ci [pi]) ;
+ DEBUG (work++) ;
+ }
+ if (ok)
+ {
+ /* found it. kill node i and merge it into j */
+ PRINT2 (("found "ID" absorbed into "ID"\n", i, j)) ;
+ Hash [i] = FLIP (j) ;
+ Cnw [j] += Cnw [i] ;
+ Cnw [i] = 0 ;
+ ASSERT (ilast != i && ilast >= 0 && ilast < n) ;
+ Next [ilast] = Next [i] ; /* delete i from bucket */
+ nodes_pruned++ ;
+ DEBUG (goodwork += (ilen+1)) ;
+ DEBUG (pruned = TRUE) ;
+ }
+ else
+ {
+ /* i and j are different */
+ ilast = i ;
+ }
+ }
+ DEBUG (if (pruned) goodwork += jlen) ;
+ }
+ /* empty the hash bucket, restoring Cew */
+ Hhead [hash] = 1 ;
+ }
+
+ DEBUG (if (((work - goodwork) / (double) nz) > 0.20) PRINT0 ((
+ "work %12g good %12g nz %12g (wasted work/nz: %6.2f )\n",
+ work, goodwork, (double) nz, (work - goodwork) / ((double) nz)))) ;
+
+ /* All hash buckets now empty. Cmap no longer needed as workspace. ]
+ * Cew no longer needed as Hhead; Cew is now restored to all ones. ]
+ * Part no longer needed as workspace for Next. ] */
+ }
+
+ /* Edge weights are all one, node weights reflect node absorption */
+ DEBUG (for (p = 0 ; p < csize ; p++) ASSERT (Cew [p] == 1)) ;
+ DEBUG (for (cnt = 0, j = 0 ; j < n ; j++) cnt += Cnw [j]) ;
+ ASSERT (cnt == total_weight) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compress and partition the graph */
+ /* ---------------------------------------------------------------------- */
+
+ if (nodes_pruned == 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* no pruning done at all. Do not create the compressed graph */
+ /* ------------------------------------------------------------------ */
+
+ /* FUTURE WORK: could call CHACO, SCOTCH, ... here too */
+ csep = CHOLMOD(metis_bisector) (C, Cnw, Cew, Part, Common) ;
+
+ }
+ else if (nodes_pruned == n-1)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* only one node left. This is a dense graph */
+ /* ------------------------------------------------------------------ */
+
+ PRINT2 (("completely dense graph\n")) ;
+ csep = total_weight ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Part [j] = 2 ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* compress the graph and partition the compressed graph */
+ /* ------------------------------------------------------------------ */
+
+ /* ------------------------------------------------------------------ */
+ /* create the map from the uncompressed graph to the compressed graph */
+ /* ------------------------------------------------------------------ */
+
+ /* Cmap [j] = k if node j is alive and the kth node of compressed graph.
+ * The mapping is done monotonically (that is, k <= j) to simplify the
+ * uncompression later on. Cmap [j] = EMPTY if node j is dead. */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ Cmap [j] = EMPTY ;
+ }
+ k = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Cnw [j] > 0)
+ {
+ ASSERT (k <= j) ;
+ Cmap [j] = k++ ;
+ }
+ }
+ cn = k ; /* # of nodes in compressed graph */
+ PRINT2 (("compressed graph from "ID" to "ID" nodes\n", n, cn)) ;
+ ASSERT (cn > 1 && cn == n - nodes_pruned) ;
+
+ /* ------------------------------------------------------------------ */
+ /* create the compressed graph */
+ /* ------------------------------------------------------------------ */
+
+ k = 0 ;
+ pdest = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Cnw [j] > 0)
+ {
+ /* node j in the full graph is node k in the compressed graph */
+ ASSERT (k <= j && Cmap [j] == k) ;
+ p = Cp [j] ;
+ pend = Cp [j+1] ;
+ Cp [k] = pdest ;
+ Cnw [k] = Cnw [j] ;
+ for ( ; p < pend ; p++)
+ {
+ /* prune dead nodes, and remap to new node numbering */
+ i = Ci [p] ;
+ ASSERT (i >= 0 && i < n && i != j) ;
+ i = Cmap [i] ;
+ ASSERT (i >= EMPTY && i < cn && i != k) ;
+ if (i > EMPTY)
+ {
+ ASSERT (pdest <= p) ;
+ Ci [pdest++] = i ;
+ }
+ }
+ k++ ;
+ }
+ }
+ Cp [cn] = pdest ;
+ C->nrow = cn ;
+ C->ncol = cn ; /* affects mem stats unless restored when C free'd */
+
+#ifndef NDEBUG
+ PRINT2 (("pruned graph ("ID"/"ID") nodes, ("ID"/"ID") edges\n",
+ cn, n, pdest, nz)) ;
+ PRINT2 (("compressed graph:\n")) ;
+ for (cnt = 0, j = 0 ; j < cn ; j++)
+ {
+ PRINT2 ((""ID": ", j)) ;
+ for (p = Cp [j] ; p < Cp [j+1] ; p++)
+ {
+ i = Ci [p] ;
+ PRINT3 ((""ID" ", i)) ;
+ ASSERT (i >= 0 && i < cn && i != j) ;
+ }
+ PRINT2 (("weight: "ID"\n", Cnw [j])) ;
+ ASSERT (Cnw [j] > 0) ;
+ cnt += Cnw [j] ;
+ }
+ ASSERT (cnt == total_weight) ;
+ for (j = 0 ; j < n ; j++) PRINT2 (("Cmap ["ID"] = "ID"\n", j, Cmap[j]));
+ ASSERT (k == cn) ;
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* find the separator of the compressed graph */
+ /* ------------------------------------------------------------------ */
+
+ /* FUTURE WORK: could call CHACO, SCOTCH, ... here too */
+ csep = CHOLMOD(metis_bisector) (C, Cnw, Cew, Part, Common) ;
+
+ if (csep < 0)
+ {
+ /* failed */
+ return (-1) ;
+ }
+
+ PRINT2 (("Part: ")) ;
+ DEBUG (for (j = 0 ; j < cn ; j++) PRINT2 ((""ID" ", Part [j]))) ;
+ PRINT2 (("\n")) ;
+
+ /* Cp and Ci no longer needed */
+
+ /* ------------------------------------------------------------------ */
+ /* find the separator of the uncompressed graph */
+ /* ------------------------------------------------------------------ */
+
+ /* expand the separator to live nodes in the uncompressed graph */
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ /* do this in reverse order so that Cnw can be expanded in place */
+ k = Cmap [j] ;
+ ASSERT (k >= EMPTY && k < n) ;
+ if (k > EMPTY)
+ {
+ /* node k in compressed graph and is node j in full graph */
+ ASSERT (k <= j) ;
+ ASSERT (Hash [j] >= EMPTY) ;
+ Part [j] = Part [k] ;
+ Cnw [j] = Cnw [k] ;
+ }
+ else
+ {
+ /* node j is a dead node */
+ Cnw [j] = 0 ;
+ DEBUG (Part [j] = EMPTY) ;
+ ASSERT (Hash [j] < EMPTY) ;
+ }
+ }
+
+ /* find the components for the dead nodes */
+ for (i = 0 ; i < n ; i++)
+ {
+ if (Hash [i] < EMPTY)
+ {
+ /* node i has been absorbed into node j */
+ j = FLIP (Hash [i]) ;
+ ASSERT (Part [i] == EMPTY && j >= 0 && j < n && Cnw [i] == 0) ;
+ Part [i] = Part [j] ;
+ }
+ ASSERT (Part [i] >= 0 && Part [i] <= 2) ;
+ }
+
+#ifndef NDEBUG
+ PRINT2 (("Part: ")) ;
+ for (cnt = 0, j = 0 ; j < n ; j++)
+ {
+ ASSERT (Part [j] != EMPTY) ;
+ PRINT2 ((""ID" ", Part [j])) ;
+ if (Part [j] == 2) cnt += Cnw [j] ;
+ }
+ PRINT2 (("\n")) ;
+ PRINT2 (("csep "ID" "ID"\n", cnt, csep)) ;
+ ASSERT (cnt == csep) ;
+ for (cnt = 0, j = 0 ; j < n ; j++) cnt += Cnw [j] ;
+ ASSERT (cnt == total_weight) ;
+#endif
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the separator (or -1 if error) */
+ /* ---------------------------------------------------------------------- */
+
+ PRINT2 (("Partition done, n "ID" csep "ID"\n", n, csep)) ;
+ return (csep) ;
+}
+
+
+/* ========================================================================== */
+/* === clear_flag =========================================================== */
+/* ========================================================================== */
+
+/* A node j has been removed from the graph if Flag [j] < EMPTY.
+ * If Flag [j] >= EMPTY && Flag [j] < mark, then node j is alive but unmarked.
+ * Flag [j] == mark means that node j is alive and marked. Incrementing mark
+ * means that all nodes are either (still) dead, or live but unmarked.
+ *
+ * If Map is NULL, then on output, Common->mark < Common->Flag [i] for all i
+ * from 0 to Common->nrow. This is the same output condition as
+ * cholmod_clear_flag, except that this routine maintains the Flag [i] < EMPTY
+ * condition as well, if that condition was true on input.
+ *
+ * If Map is non-NULL, then on output, Common->mark < Common->Flag [i] for all
+ * i in the set Map [0..cn-1].
+ *
+ * workspace: Flag (nrow)
+ */
+
+static UF_long clear_flag (Int *Map, Int cn, cholmod_common *Common)
+{
+ Int nrow, i ;
+ Int *Flag ;
+ PRINT2 (("old mark %ld\n", Common->mark)) ;
+ Common->mark++ ;
+ PRINT2 (("new mark %ld\n", Common->mark)) ;
+ if (Common->mark <= 0)
+ {
+ nrow = Common->nrow ;
+ Flag = Common->Flag ;
+ if (Map != NULL)
+ {
+ for (i = 0 ; i < cn ; i++)
+ {
+ /* if Flag [Map [i]] < EMPTY, leave it alone */
+ if (Flag [Map [i]] >= EMPTY)
+ {
+ Flag [Map [i]] = EMPTY ;
+ }
+ }
+ /* now Flag [Map [i]] <= EMPTY for all i */
+ }
+ else
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ /* if Flag [i] < EMPTY, leave it alone */
+ if (Flag [i] >= EMPTY)
+ {
+ Flag [i] = EMPTY ;
+ }
+ }
+ /* now Flag [i] <= EMPTY for all i */
+ }
+ Common->mark = 0 ;
+ }
+ return (Common->mark) ;
+}
+
+
+/* ========================================================================== */
+/* === find_components ====================================================== */
+/* ========================================================================== */
+
+/* Find all connected components of the current subgraph C. The subgraph C
+ * consists of the nodes of B that appear in the set Map [0..cn-1]. If Map
+ * is NULL, then it is assumed to be the identity mapping
+ * (Map [0..cn-1] = 0..cn-1).
+ *
+ * A node j does not appear in B if it has been ordered (Flag [j] < EMPTY,
+ * which means that j has been ordered and is "deleted" from B).
+ *
+ * If the size of a component is large, it is placed on the component stack,
+ * Cstack. Otherwise, its nodes are ordered and it is not placed on the Cstack.
+ *
+ * A component S is defined by a "representative node" (repnode for short)
+ * called the snode, which is one of the nodes in the subgraph. Likewise, the
+ * subgraph C is defined by its repnode, called cnode.
+ *
+ * If Part is not NULL on input, then Part [i] determines how the components
+ * are placed on the stack. Components containing nodes i with Part [i] == 0
+ * are placed first, followed by components with Part [i] == 1.
+ *
+ * The first node placed in each of the two parts is flipped when placed in
+ * the Cstack. This allows the components of the two parts to be found simply
+ * by traversing the Cstack.
+ *
+ * workspace: Flag (nrow)
+ */
+
+static void find_components
+(
+ /* inputs, not modified on output */
+ cholmod_sparse *B,
+ Int Map [ ], /* size n, only Map [0..cn-1] used */
+ Int cn, /* # of nodes in C */
+ Int cnode, /* root node of component C, or EMPTY if C is the
+ * entire graph B */
+
+ Int Part [ ], /* size cn, optional */
+
+ /* input/output */
+ Int Bnz [ ], /* size n. Bnz [j] = # nonzeros in column j of B.
+ * Reduce since B is pruned of dead nodes. */
+
+ Int CParent [ ], /* CParent [i] = j if component with repnode j is
+ * the parent of the component with repnode i.
+ * CParent [i] = EMPTY if the component with
+ * repnode i is a root of the separator tree.
+ * CParent [i] is -2 if i is not a repnode. */
+ Int Cstack [ ], /* component stack for nested dissection */
+ Int *top, /* Cstack [0..top] contains root nodes of the
+ * the components currently in the stack */
+
+ /* workspace, undefined on input and output: */
+ Int Queue [ ], /* size n, for breadth-first search */
+
+ cholmod_common *Common
+)
+{
+ Int n, mark, cj, j, sj, sn, p, i, snode, pstart, pdest, pend, nd_components,
+ part, first, save_mark ;
+ Int *Bp, *Bi, *Flag ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ PRINT2 (("find components: cn %d\n", cn)) ;
+ Flag = Common->Flag ; /* size n */
+
+ /* force initialization of Flag [Map [0..cn-1]] */
+ save_mark = Common->mark ; /* save the current mark */
+ Common->mark = EMPTY ;
+
+ /* clear Flag; preserve Flag [Map [i]] if Flag [Map [i]] already < EMPTY */
+ /* this takes O(cn) time */
+ mark = clear_flag (Map, cn, Common) ;
+
+ Bp = B->p ;
+ Bi = B->i ;
+ n = B->nrow ;
+ ASSERT (cnode >= EMPTY && cnode < n) ;
+ ASSERT (IMPLIES (cnode >= 0, Flag [cnode] < EMPTY)) ;
+
+ /* get ordering parameters */
+ nd_components = Common->method [Common->current].nd_components ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the connected components of C via a breadth-first search */
+ /* ---------------------------------------------------------------------- */
+
+ part = (Part == NULL) ? 0 : 1 ;
+
+ /* examine each part (part 1 and then part 0) */
+ for (part = (Part == NULL) ? 0 : 1 ; part >= 0 ; part--)
+ {
+
+ /* first is TRUE for the first connected component in each part */
+ first = TRUE ;
+
+ /* find all connected components in the current part */
+ for (cj = 0 ; cj < cn ; cj++)
+ {
+ /* get node snode, which is node cj of C. It might already be in
+ * the separator of C (and thus ordered, with Flag [snode] < EMPTY)
+ */
+ snode = (Map == NULL) ? (cj) : (Map [cj]) ;
+ ASSERT (snode >= 0 && snode < n) ;
+
+ if (Flag [snode] >= EMPTY && Flag [snode] < mark
+ && ((Part == NULL) || Part [cj] == part))
+ {
+
+ /* ---------------------------------------------------------- */
+ /* find new connected component S */
+ /* ---------------------------------------------------------- */
+
+ /* node snode is the repnode of a connected component S, the
+ * parent of which is cnode, the repnode of C. If cnode is
+ * EMPTY then C is the original graph B. */
+ PRINT2 (("----------:::snode "ID" cnode "ID"\n", snode, cnode));
+
+ ASSERT (CParent [snode] == -2) ;
+ if (first || nd_components)
+ {
+ /* If this is the first node in this part, then it becomes
+ * the repnode of all components in this part, and all
+ * components in this part form a single node in the
+ * separator tree. If nd_components is TRUE, then all
+ * connected components form their own node in the
+ * separator tree.
+ */
+ CParent [snode] = cnode ;
+ }
+
+ /* place j in the queue and mark it */
+ Queue [0] = snode ;
+ Flag [snode] = mark ;
+ sn = 1 ;
+
+ /* breadth-first traversal, starting at node j */
+ for (sj = 0 ; sj < sn ; sj++)
+ {
+ /* get node j from head of Queue and traverse its edges */
+ j = Queue [sj] ;
+ PRINT2 ((" j: "ID"\n", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ ASSERT (Flag [j] == mark) ;
+ pstart = Bp [j] ;
+ pdest = pstart ;
+ pend = pstart + Bnz [j] ;
+ for (p = pstart ; p < pend ; p++)
+ {
+ i = Bi [p] ;
+ if (i != j && Flag [i] >= EMPTY)
+ {
+ /* node is still in the graph */
+ Bi [pdest++] = i ;
+ if (Flag [i] < mark)
+ {
+ /* node i is in this component S, and unflagged
+ * (first time node i has been seen in this BFS)
+ * place node i in the queue and mark it */
+ Queue [sn++] = i ;
+ Flag [i] = mark ;
+ }
+ }
+ }
+ /* edges to dead nodes have been removed */
+ Bnz [j] = pdest - pstart ;
+ }
+
+ /* ---------------------------------------------------------- */
+ /* order S if it is small; place it on Cstack otherwise */
+ /* ---------------------------------------------------------- */
+
+ PRINT2 (("sn "ID"\n", sn)) ;
+
+ /* place the new component on the Cstack. Flip the node if
+ * is the first connected component of the current part,
+ * or if all components are treated as their own node in
+ * the separator tree. */
+ Cstack [++(*top)] =
+ (first || nd_components) ? FLIP (snode) : snode ;
+ first = FALSE ;
+ }
+ }
+ }
+
+ /* restore the flag (normally taking O(1) time except for Int overflow) */
+ Common->mark = save_mark++ ;
+ clear_flag (NULL, 0, Common) ;
+ DEBUG (for (i = 0 ; i < n ; i++) ASSERT (Flag [i] < Common->mark)) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_bisect ======================================================= */
+/* ========================================================================== */
+
+/* Finds a node bisector of A, A*A', A(:,f)*A(:,f)'.
+ *
+ * workspace: Flag (nrow),
+ * Iwork (nrow if symmetric, max (nrow,ncol) if unsymmetric).
+ * Allocates a temporary matrix B=A*A' or B=A,
+ * and O(nnz(A)) temporary memory space.
+ */
+
+UF_long CHOLMOD(bisect) /* returns # of nodes in separator */
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to bisect */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ int compress, /* if TRUE, compress the graph first */
+ /* ---- output --- */
+ Int *Partition, /* size A->nrow. Node i is in the left graph if
+ * Partition [i] = 0, the right graph if 1, and in the
+ * separator if 2. */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *Bp, *Bi, *Hash, *Cmap, *Bnw, *Bew, *Iwork ;
+ cholmod_sparse *B ;
+ unsigned Int hash ;
+ Int j, n, bnz, sepsize, p, pend ;
+ size_t csize, s ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (A, EMPTY) ;
+ RETURN_IF_NULL (Partition, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* quick return */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+ if (n == 0)
+ {
+ return (0) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = n + MAX (n, A->ncol) */
+ s = CHOLMOD(add_size_t) (A->nrow, MAX (A->nrow, A->ncol), &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (EMPTY) ;
+ }
+
+ CHOLMOD(allocate_work) (n, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (EMPTY) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ Iwork = Common->Iwork ;
+ Hash = Iwork ; /* size n, (i/l/l) */
+ Cmap = Iwork + n ; /* size n, (i/i/l) */
+
+ /* ---------------------------------------------------------------------- */
+ /* convert the matrix to adjacency list form */
+ /* ---------------------------------------------------------------------- */
+
+ /* The input graph to must be symmetric, with no diagonal entries
+ * present. The columns need not be sorted. */
+
+ /* B = A, A*A', or A(:,f)*A(:,f)', upper and lower parts present */
+
+ if (A->stype)
+ {
+ /* Add the upper/lower part to a symmetric lower/upper matrix by
+ * converting to unsymmetric mode */
+ /* workspace: Iwork (nrow) */
+ B = CHOLMOD(copy) (A, 0, -1, Common) ;
+ }
+ else
+ {
+ /* B = A*A' or A(:,f)*A(:,f)', no diagonal */
+ /* workspace: Flag (nrow), Iwork (max (nrow,ncol)) */
+ B = CHOLMOD(aat) (A, fset, fsize, -1, Common) ;
+ }
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (EMPTY) ;
+ }
+ Bp = B->p ;
+ Bi = B->i ;
+ bnz = Bp [n] ;
+ ASSERT ((Int) (B->nrow) == n && (Int) (B->ncol) == n) ;
+
+ /* B does not include the diagonal, and both upper and lower parts.
+ * Common->anz includes the diagonal, and just the lower part of B */
+ Common->anz = bnz / 2 + ((double) n) ;
+
+ /* Bew should be at least size n for the hash function to work well */
+ /* this cannot cause overflow, because the matrix is already created */
+ csize = MAX (((size_t) n) + 1, (size_t) bnz) ;
+
+ /* create the graph using Flag as workspace for node weights [ */
+ Bnw = Common->Flag ; /* size n workspace */
+
+ /* compute hash for each node if compression requested */
+ if (compress)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ hash = j ;
+ pend = Bp [j+1] ;
+ for (p = Bp [j] ; p < pend ; p++)
+ {
+ hash += Bi [p] ;
+ ASSERT (Bi [p] != j) ;
+ }
+ /* finalize the hash key for node j */
+ hash %= csize ;
+ Hash [j] = (Int) hash ;
+ ASSERT (Hash [j] >= 0 && Hash [j] < csize) ;
+ }
+ }
+
+ /* allocate edge weights */
+ Bew = CHOLMOD(malloc) (csize, sizeof (Int), Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&B, Common) ;
+ CHOLMOD(free) (csize, sizeof (Int), Bew, Common) ;
+ return (EMPTY) ;
+ }
+
+ /* graph has unit node and edge weights */
+ for (j = 0 ; j < n ; j++)
+ {
+ Bnw [j] = 1 ;
+ }
+ for (s = 0 ; s < csize ; s++)
+ {
+ Bew [s] = 1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compress and partition the graph */
+ /* ---------------------------------------------------------------------- */
+
+ sepsize = partition (
+#ifndef NDEBUG
+ csize,
+#endif
+ compress, Hash, B, Bnw, Bew, Cmap, Partition, Common) ;
+
+ /* contents of Bp, Bi, Bnw, and Bew no longer needed ] */
+
+ /* If partition fails, free the workspace below and return sepsize < 0 */
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ B->ncol = n ; /* restore size for memory usage statistics */
+ CHOLMOD(free_sparse) (&B, Common) ;
+ Common->mark = EMPTY ;
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ CHOLMOD(free) (csize, sizeof (Int), Bew, Common) ;
+ return (sepsize) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_nested_dissection ============================================ */
+/* ========================================================================== */
+
+/* This method uses a node bisector, applied recursively (but using a
+ * non-recursive algorithm). Once the graph is partitioned, it calls a
+ * constrained min degree code (CAMD or CSYMAMD for A+A', and CCOLAMD for A*A')
+ * to order all the nodes in the graph - but obeying the constraints determined
+ * by the separators. This routine is similar to METIS_NodeND, except for how
+ * it treats the leaf nodes. METIS_NodeND orders the leaves of the separator
+ * tree with MMD, ignoring the rest of the matrix when ordering a single leaf.
+ * This routine orders the whole matrix with CSYMAMD or CCOLAMD, all at once,
+ * when the graph partitioning is done.
+ *
+ * This function also returns a postorderd separator tree (CParent), and a
+ * mapping of nodes in the graph to nodes in the separator tree (Cmember).
+ *
+ * workspace: Flag (nrow), Head (nrow+1), Iwork (4*nrow + (ncol if unsymmetric))
+ * Allocates a temporary matrix B=A*A' or B=A,
+ * and O(nnz(A)) temporary memory space.
+ * Allocates an additional 3*n*sizeof(Int) temporary workspace
+ */
+
+UF_long CHOLMOD(nested_dissection) /* returns # of components, or -1 if error */
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to order */
+ Int *fset, /* subset of 0:(A->ncol)-1 */
+ size_t fsize, /* size of fset */
+ /* ---- output --- */
+ Int *Perm, /* size A->nrow, output permutation */
+ Int *CParent, /* size A->nrow. On output, CParent [c] is the parent
+ * of component c, or EMPTY if c is a root, and where
+ * c is in the range 0 to # of components minus 1 */
+ Int *Cmember, /* size A->nrow. Cmember [j] = c if node j of A is
+ * in component c */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double prune_dense, nd_oksep ;
+ Int *Bp, *Bi, *Bnz, *Cstack, *Imap, *Map, *Flag, *Head, *Next, *Bnw, *Iwork,
+ *Ipost, *NewParent, *Hash, *Cmap, *Cp, *Ci, *Cew, *Cnw, *Part, *Post,
+ *Work3n ;
+ unsigned Int hash ;
+ Int n, bnz, top, i, j, k, cnode, cdense, p, cj, cn, ci, cnz, mark, c, uncol,
+ sepsize, parent, ncomponents, threshold, ndense, pstart, pdest, pend,
+ nd_compress, nd_camd, csize, jnext, nd_small, total_weight,
+ nchild, child = EMPTY ;
+ cholmod_sparse *B, *C ;
+ size_t s ;
+ int ok = TRUE ;
+ DEBUG (Int cnt) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (A, EMPTY) ;
+ RETURN_IF_NULL (Perm, EMPTY) ;
+ RETURN_IF_NULL (CParent, EMPTY) ;
+ RETURN_IF_NULL (Cmember, EMPTY) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, EMPTY) ;
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* quick return */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+ if (n == 0)
+ {
+ return (1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* get ordering parameters */
+ prune_dense = Common->method [Common->current].prune_dense ;
+ nd_compress = Common->method [Common->current].nd_compress ;
+ nd_oksep = Common->method [Common->current].nd_oksep ;
+ nd_oksep = MAX (0, nd_oksep) ;
+ nd_oksep = MIN (1, nd_oksep) ;
+ nd_camd = Common->method [Common->current].nd_camd ;
+ nd_small = Common->method [Common->current].nd_small ;
+ nd_small = MAX (4, nd_small) ;
+
+ PRINT0 (("nd_components %d nd_small %d nd_oksep %g\n",
+ Common->method [Common->current].nd_components,
+ nd_small, nd_oksep)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = 4*n + uncol */
+ uncol = (A->stype == 0) ? A->ncol : 0 ;
+ s = CHOLMOD(mult_size_t) (n, 4, &ok) ;
+ s = CHOLMOD(add_size_t) (s, uncol, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (EMPTY) ;
+ }
+
+ CHOLMOD(allocate_work) (n, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (EMPTY) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Flag = Common->Flag ; /* size n */
+ Head = Common->Head ; /* size n+1, all equal to -1 */
+
+ Iwork = Common->Iwork ;
+ Imap = Iwork ; /* size n, same as Queue in find_components */
+ Map = Iwork + n ; /* size n */
+ Bnz = Iwork + 2*((size_t) n) ; /* size n */
+ Hash = Iwork + 3*((size_t) n) ; /* size n */
+
+ Work3n = CHOLMOD(malloc) (n, 3*sizeof (Int), Common) ;
+ Part = Work3n ; /* size n */
+ Bnw = Part + n ; /* size n */
+ Cnw = Bnw + n ; /* size n */
+
+ Cstack = Perm ; /* size n, use Perm as workspace for Cstack [ */
+ Cmap = Cmember ; /* size n, use Cmember as workspace [ */
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (EMPTY) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert B to symmetric form with both upper/lower parts present */
+ /* ---------------------------------------------------------------------- */
+
+ /* B = A+A', A*A', or A(:,f)*A(:,f)', upper and lower parts present */
+
+ if (A->stype)
+ {
+ /* Add the upper/lower part to a symmetric lower/upper matrix by
+ * converting to unsymmetric mode */
+ /* workspace: Iwork (nrow) */
+ B = CHOLMOD(copy) (A, 0, -1, Common) ;
+ }
+ else
+ {
+ /* B = A*A' or A(:,f)*A(:,f)', no diagonal */
+ /* workspace: Flag (nrow), Iwork (max (nrow,ncol)) */
+ B = CHOLMOD(aat) (A, fset, fsize, -1, Common) ;
+ }
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ;
+ return (EMPTY) ;
+ }
+ Bp = B->p ;
+ Bi = B->i ;
+ bnz = CHOLMOD(nnz) (B, Common) ;
+ ASSERT ((Int) (B->nrow) == n && (Int) (B->ncol) == n) ;
+ csize = MAX (n, bnz) ;
+ ASSERT (CHOLMOD(dump_sparse) (B, "B for nd:", Common) >= 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+ /* all nodes start out unmarked and unordered (Type 4, see below) */
+ Common->mark = EMPTY ;
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ ASSERT (Flag == Common->Flag) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ CParent [j] = -2 ;
+ }
+
+ /* prune dense nodes from B */
+ if (IS_NAN (prune_dense) || prune_dense < 0)
+ {
+ /* only remove completely dense nodes */
+ threshold = n-2 ;
+ }
+ else
+ {
+ /* remove nodes with degree more than threshold */
+ threshold = (Int) (MAX (16, prune_dense * sqrt ((double) (n)))) ;
+ threshold = MIN (n, threshold) ;
+ }
+ ndense = 0 ;
+ cnode = EMPTY ;
+ cdense = EMPTY ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ Bnz [j] = Bp [j+1] - Bp [j] ;
+ if (Bnz [j] > threshold)
+ {
+ /* node j is dense, prune it from B */
+ PRINT2 (("j is dense %d\n", j)) ;
+ ndense++ ;
+ if (cnode == EMPTY)
+ {
+ /* first dense node found becomes root of this component,
+ * which contains all of the dense nodes found here */
+ cdense = j ;
+ cnode = j ;
+ CParent [cnode] = EMPTY ;
+ }
+ Flag [j] = FLIP (cnode) ;
+ }
+ }
+ B->packed = FALSE ;
+ ASSERT (B->nz == NULL) ;
+
+ if (ndense == n)
+ {
+ /* all nodes removed: Perm is identity, all nodes in component zero,
+ * and the separator tree has just one node. */
+ PRINT2 (("all nodes are dense\n")) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Perm [k] = k ;
+ Cmember [k] = 0 ;
+ }
+ CParent [0] = EMPTY ;
+ CHOLMOD(free_sparse) (&B, Common) ;
+ CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ;
+ Common->mark = EMPTY ;
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ return (1) ;
+ }
+
+ /* Cp and Ci are workspace to construct the subgraphs to partition */
+ C = CHOLMOD(allocate_sparse) (n, n, csize, FALSE, TRUE, 0, CHOLMOD_PATTERN,
+ Common) ;
+ Cew = CHOLMOD(malloc) (csize, sizeof (Int), Common) ;
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ CHOLMOD(free_sparse) (&C, Common) ;
+ CHOLMOD(free_sparse) (&B, Common) ;
+ CHOLMOD(free) (csize, sizeof (Int), Cew, Common) ;
+ CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ;
+ Common->mark = EMPTY ;
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ PRINT2 (("out of memory for C, etc\n")) ;
+ return (EMPTY) ;
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+
+ /* create initial unit node and edge weights */
+ for (j = 0 ; j < n ; j++)
+ {
+ Bnw [j] = 1 ;
+ }
+ for (p = 0 ; p < csize ; p++)
+ {
+ Cew [p] = 1 ;
+ }
+
+ /* push the initial connnected components of B onto the Cstack */
+ top = EMPTY ; /* Cstack is empty */
+ /* workspace: Flag (nrow), Iwork (nrow); use Imap as workspace for Queue [*/
+ find_components (B, NULL, n, cnode, NULL,
+ Bnz, CParent, Cstack, &top, Imap, Common) ;
+ /* done using Imap as workspace for Queue ] */
+
+ /* Nodes can now be of Type 0, 1, 2, or 4 (see definition below) */
+
+ /* ---------------------------------------------------------------------- */
+ /* while Cstack is not empty, do: */
+ /* ---------------------------------------------------------------------- */
+
+ while (top >= 0)
+ {
+
+ /* clear the Flag array, but do not modify negative entries in Flag */
+ mark = clear_flag (NULL, 0, Common) ;
+
+ DEBUG (for (i = 0 ; i < n ; i++) Imap [i] = EMPTY) ;
+
+ /* ------------------------------------------------------------------ */
+ /* get node(s) from the top of the Cstack */
+ /* ------------------------------------------------------------------ */
+
+ /* i is the repnode of its (unordered) connected component. Get
+ * all repnodes for all connected components of a single part. If
+ * each connected component is to be ordered separately (nd_components
+ * is TRUE), then this while loop iterates just once. */
+
+ cnode = EMPTY ;
+ cn = 0 ;
+ while (cnode == EMPTY)
+ {
+ i = Cstack [top--] ;
+
+ if (i < 0)
+ {
+ /* this is the last node in this component */
+ i = FLIP (i) ;
+ cnode = i ;
+ }
+
+ ASSERT (i >= 0 && i < n && Flag [i] >= EMPTY) ;
+
+ /* place i in the queue and mark it */
+ Map [cn] = i ;
+ Flag [i] = mark ;
+ Imap [i] = cn ;
+ cn++ ;
+ }
+
+ ASSERT (cnode != EMPTY) ;
+
+ /* During ordering, there are five kinds of nodes in the graph of B,
+ * based on Flag [j] and CParent [j] for nodes j = 0 to n-1:
+ *
+ * Type 0: If cnode is a repnode of an unordered component, then
+ * CParent [cnode] is in the range EMPTY to n-1 and
+ * Flag [cnode] >= EMPTY. This is a "live" node.
+ *
+ * Type 1: If cnode is a repnode of an ordered separator component,
+ * then Flag [cnode] < EMPTY and FLAG [cnode] = FLIP (cnode).
+ * CParent [cnode] is in the range EMPTY to n-1. cnode is a root of
+ * the separator tree if CParent [cnode] == EMPTY. This node is dead.
+ *
+ * Type 2: If node j isn't a repnode, has not been absorbed via
+ * graph compression into another node, but is in an ordered separator
+ * component, then cnode = FLIP (Flag [j]) gives the repnode of the
+ * component that contains j and CParent [j] is -2. This node is dead.
+ * Note that Flag [j] < EMPTY.
+ *
+ * Type 3: If node i has been absorbed via graph compression into some
+ * other node j = FLIP (Flag [i]) where j is not a repnode.
+ * CParent [j] is -2. Node i may or may not be in an ordered
+ * component. This node is dead. Note that Flag [j] < EMPTY.
+ *
+ * Type 4: If node j is "live" (not in an ordered component, and not
+ * absorbed into any other node), then Flag [j] >= EMPTY.
+ *
+ * Only "live" nodes (of type 0 or 4) are placed in a subgraph to be
+ * partitioned. Node j is alive if Flag [j] >= EMPTY, and dead if
+ * Flag [j] < EMPTY.
+ */
+
+ /* ------------------------------------------------------------------ */
+ /* create the subgraph for this connected component C */
+ /* ------------------------------------------------------------------ */
+
+ /* Do a breadth-first search of the graph starting at cnode.
+ * use Map [0..cn-1] for nodes in the component C [
+ * use Cnw and Cew for node and edge weights of the resulting subgraph [
+ * use Cp and Ci for the resulting subgraph [
+ * use Imap [i] for all nodes i in B that are in the component C [
+ */
+
+ cnz = 0 ;
+ total_weight = 0 ;
+ for (cj = 0 ; cj < cn ; cj++)
+ {
+ /* get node j from the head of the queue; it is node cj of C */
+ j = Map [cj] ;
+ ASSERT (Flag [j] == mark) ;
+ Cp [cj] = cnz ;
+ Cnw [cj] = Bnw [j] ;
+ ASSERT (Cnw [cj] >= 0) ;
+ total_weight += Cnw [cj] ;
+ pstart = Bp [j] ;
+ pdest = pstart ;
+ pend = pstart + Bnz [j] ;
+ hash = cj ;
+ for (p = pstart ; p < pend ; p++)
+ {
+ i = Bi [p] ;
+ /* prune diagonal entries and dead edges from B */
+ if (i != j && Flag [i] >= EMPTY)
+ {
+ /* live node i is in the current component */
+ Bi [pdest++] = i ;
+ if (Flag [i] != mark)
+ {
+ /* First time node i has been seen, it is a new node
+ * of C. place node i in the queue and mark it */
+ Map [cn] = i ;
+ Flag [i] = mark ;
+ Imap [i] = cn ;
+ cn++ ;
+ }
+ /* place the edge (cj,ci) in the adjacency list of cj */
+ ci = Imap [i] ;
+ ASSERT (ci >= 0 && ci < cn && ci != cj && cnz < csize) ;
+ Ci [cnz++] = ci ;
+ hash += ci ;
+ }
+ }
+ /* edges to dead nodes have been removed */
+ Bnz [j] = pdest - pstart ;
+ /* finalize the hash key for column j */
+ hash %= csize ;
+ Hash [cj] = (Int) hash ;
+ ASSERT (Hash [cj] >= 0 && Hash [cj] < csize) ;
+ }
+ Cp [cn] = cnz ;
+ C->nrow = cn ;
+ C->ncol = cn ; /* affects mem stats unless restored when C free'd */
+
+ /* contents of Imap no longer needed ] */
+
+#ifndef NDEBUG
+ for (cj = 0 ; cj < cn ; cj++)
+ {
+ j = Map [cj] ;
+ PRINT2 (("----------------------------C column cj: "ID" j: "ID"\n",
+ cj, j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ ASSERT (Flag [j] >= EMPTY) ;
+ for (p = Cp [cj] ; p < Cp [cj+1] ; p++)
+ {
+ ci = Ci [p] ;
+ i = Map [ci] ;
+ PRINT3 (("ci: "ID" i: "ID"\n", ci, i)) ;
+ ASSERT (ci != cj && ci >= 0 && ci < cn) ;
+ ASSERT (i != j && i >= 0 && i < n) ;
+ ASSERT (Flag [i] >= EMPTY) ;
+ }
+ }
+#endif
+
+ PRINT0 (("consider cn %d nd_small %d ", cn, nd_small)) ;
+ if (cn < nd_small) /* could be 'total_weight < nd_small' instead */
+ {
+ /* place all nodes in the separator */
+ PRINT0 ((" too small\n")) ;
+ sepsize = total_weight ;
+ }
+ else
+ {
+
+ /* Cp and Ci now contain the component, with cn nodes and cnz
+ * nonzeros. The mapping of a node cj into node j the main graph
+ * B is given by Map [cj] = j */
+ PRINT0 ((" cut\n")) ;
+
+ /* -------------------------------------------------------------- */
+ /* compress and partition the graph C */
+ /* -------------------------------------------------------------- */
+
+ /* The edge weights Cew [0..csize-1] are all 1's on input to and
+ * output from the partition routine. */
+
+ sepsize = partition (
+#ifndef NDEBUG
+ csize,
+#endif
+ nd_compress, Hash, C, Cnw, Cew,
+ Cmap, Part, Common) ;
+
+ /* contents of Cp and Ci no longer needed ] */
+
+ if (sepsize < 0)
+ {
+ /* failed */
+ C->ncol = n ; /* restore size for memory usage statistics */
+ CHOLMOD(free_sparse) (&C, Common) ;
+ CHOLMOD(free_sparse) (&B, Common) ;
+ CHOLMOD(free) (csize, sizeof (Int), Cew, Common) ;
+ CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ;
+ Common->mark = EMPTY ;
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ return (EMPTY) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* compress B based on how C was compressed */
+ /* -------------------------------------------------------------- */
+
+ for (ci = 0 ; ci < cn ; ci++)
+ {
+ if (Hash [ci] < EMPTY)
+ {
+ /* ci is dead in C, having been absorbed into cj */
+ cj = FLIP (Hash [ci]) ;
+ PRINT2 (("In C, "ID" absorbed into "ID" (wgt now "ID")\n",
+ ci, cj, Cnw [cj])) ;
+ /* i is dead in B, having been absorbed into j */
+ i = Map [ci] ;
+ j = Map [cj] ;
+ PRINT2 (("In B, "ID" (wgt "ID") => "ID" (wgt "ID")\n",
+ i, Bnw [i], j, Bnw [j], Cnw [cj])) ;
+ /* more than one node may be absorbed into j. This is
+ * accounted for in Cnw [cj]. Assign it here rather
+ * than += Bnw [i] */
+ Bnw [i] = 0 ;
+ Bnw [j] = Cnw [cj] ;
+ Flag [i] = FLIP (j) ;
+ }
+ }
+
+ DEBUG (for (cnt = 0, j = 0 ; j < n ; j++) cnt += Bnw [j]) ;
+ ASSERT (cnt == n) ;
+ }
+
+ /* contents of Cnw [0..cn-1] no longer needed ] */
+
+ /* ------------------------------------------------------------------ */
+ /* order the separator, and stack the components when C is split */
+ /* ------------------------------------------------------------------ */
+
+ /* one more component has been found: either the separator of C,
+ * or all of C */
+
+ ASSERT (sepsize >= 0 && sepsize <= total_weight) ;
+
+ PRINT0 (("sepsize %d tot %d : %8.4f ", sepsize, total_weight,
+ ((double) sepsize) / ((double) total_weight))) ;
+
+ if (sepsize == total_weight || sepsize == 0 ||
+ sepsize > nd_oksep * total_weight)
+ {
+ /* Order the nodes in the component. The separator is too large,
+ * or empty. Note that the partition routine cannot return a
+ * sepsize of zero, but it can return a separator consisting of the
+ * whole graph. The "sepsize == 0" test is kept, above, in case the
+ * partition routine changes. In either case, this component
+ * remains unsplit, and becomes a leaf of the separator tree. */
+ PRINT2 (("cnode %d sepsize zero or all of graph: "ID"\n",
+ cnode, sepsize)) ;
+ for (cj = 0 ; cj < cn ; cj++)
+ {
+ j = Map [cj] ;
+ Flag [j] = FLIP (cnode) ;
+ PRINT2 ((" node cj: "ID" j: "ID" ordered\n", cj, j)) ;
+ }
+ ASSERT (Flag [cnode] == FLIP (cnode)) ;
+ ASSERT (cnode != EMPTY && Flag [cnode] < EMPTY) ;
+ PRINT0 (("discarded\n")) ;
+
+ }
+ else
+ {
+
+ /* Order the nodes in the separator of C and find a new repnode
+ * cnode that is in the separator of C. This requires the separator
+ * to be non-empty. */
+ PRINT0 (("sepsize not tiny: "ID"\n", sepsize)) ;
+ parent = CParent [cnode] ;
+ ASSERT (parent >= EMPTY && parent < n) ;
+ CParent [cnode] = -2 ;
+ cnode = EMPTY ;
+ for (cj = 0 ; cj < cn ; cj++)
+ {
+ j = Map [cj] ;
+ if (Part [cj] == 2)
+ {
+ /* All nodes in the separator become part of a component
+ * whose repnode is cnode */
+ PRINT2 (("node cj: "ID" j: "ID" ordered\n", cj, j)) ;
+ if (cnode == EMPTY)
+ {
+ PRINT2(("------------new cnode: cj "ID" j "ID"\n",
+ cj, j)) ;
+ cnode = j ;
+ }
+ Flag [j] = FLIP (cnode) ;
+ }
+ else
+ {
+ PRINT2 ((" node cj: "ID" j: "ID" not ordered\n",
+ cj, j)) ;
+ }
+ }
+ ASSERT (cnode != EMPTY && Flag [cnode] < EMPTY) ;
+ ASSERT (CParent [cnode] == -2) ;
+ CParent [cnode] = parent ;
+
+ /* find the connected components when C is split, and push
+ * them on the Cstack. Use Imap as workspace for Queue. [ */
+ /* workspace: Flag (nrow) */
+ find_components (B, Map, cn, cnode, Part, Bnz,
+ CParent, Cstack, &top, Imap, Common) ;
+ /* done using Imap as workspace for Queue ] */
+ }
+ /* contents of Map [0..cn-1] no longer needed ] */
+ }
+
+ /* done using Cmember as workspace for Cmap ] */
+ /* done using Perm as workspace for Cstack ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* place nodes removed via compression into their proper component */
+ /* ---------------------------------------------------------------------- */
+
+ /* At this point, all nodes are of Type 1, 2, or 3, as defined above. */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* find the repnode cnode that contains node i */
+ j = FLIP (Flag [i]) ;
+ PRINT2 (("\nfind component for "ID", in: "ID"\n", i, j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ DEBUG (cnt = 0) ;
+ while (CParent [j] == -2)
+ {
+ j = FLIP (Flag [j]) ;
+ PRINT2 ((" walk up to "ID" ", j)) ;
+ ASSERT (j >= 0 && j < n) ;
+ PRINT2 ((" CParent "ID"\n", CParent [j])) ;
+ ASSERT (cnt < n) ;
+ DEBUG (cnt++) ;
+ }
+ cnode = j ;
+ ASSERT (cnode >= 0 && cnode < n) ;
+ ASSERT (CParent [cnode] >= EMPTY && CParent [cnode] < n) ;
+ PRINT2 (("i "ID" is in component with cnode "ID"\n", i, cnode)) ;
+ ASSERT (Flag [cnode] == FLIP (cnode)) ;
+
+ /* Mark all nodes along the path from i to cnode as being in the
+ * component whos repnode is cnode. Perform path compression. */
+ j = FLIP (Flag [i]) ;
+ Flag [i] = FLIP (cnode) ;
+ DEBUG (cnt = 0) ;
+ while (CParent [j] == -2)
+ {
+ ASSERT (j >= 0 && j < n) ;
+ jnext = FLIP (Flag [j]) ;
+ PRINT2 ((" "ID" walk "ID" set cnode to "ID"\n", i, j, cnode)) ;
+ ASSERT (cnt < n) ;
+ DEBUG (cnt++) ;
+ Flag [j] = FLIP (cnode) ;
+ j = jnext ;
+ }
+ }
+
+ /* At this point, all nodes fall into Types 1 or 2, as defined above. */
+
+#ifndef NDEBUG
+ for (j = 0 ; j < n ; j++)
+ {
+ PRINT2 (("j %d CParent %d ", j, CParent [j])) ;
+ if (CParent [j] >= EMPTY && CParent [j] < n)
+ {
+ /* case 1: j is a repnode of a component */
+ cnode = j ;
+ PRINT2 ((" a repnode\n")) ;
+ }
+ else
+ {
+ /* case 2: j is not a repnode of a component */
+ cnode = FLIP (Flag [j]) ;
+ PRINT2 ((" repnode is %d\n", cnode)) ;
+ ASSERT (cnode >= 0 && cnode < n) ;
+ ASSERT (CParent [cnode] >= EMPTY && CParent [cnode] < n) ;
+ }
+ ASSERT (Flag [cnode] == FLIP (cnode)) ;
+ /* case 3 no longer holds */
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ C->ncol = n ; /* restore size for memory usage statistics */
+ CHOLMOD(free_sparse) (&C, Common) ;
+ CHOLMOD(free_sparse) (&B, Common) ;
+ CHOLMOD(free) (csize, sizeof (Int), Cew, Common) ;
+ CHOLMOD(free) (3*n, sizeof (Int), Work3n, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* handle dense nodes */
+ /* ---------------------------------------------------------------------- */
+
+ /* The separator tree has nodes with either no children or two or more
+ * children - with one exception. There may exist a single root node with
+ * exactly one child, which holds the dense rows/columns of the matrix.
+ * Delete this node if it exists. */
+
+ if (ndense > 0)
+ {
+ ASSERT (CParent [cdense] == EMPTY) ; /* cdense has no parent */
+ /* find the children of cdense */
+ nchild = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (CParent [j] == cdense)
+ {
+ nchild++ ;
+ child = j ;
+ }
+ }
+ if (nchild == 1)
+ {
+ /* the cdense node has just one child; merge the two nodes */
+ PRINT1 (("root has one child\n")) ;
+ CParent [cdense] = -2 ; /* cdense is deleted */
+ CParent [child] = EMPTY ; /* child becomes a root */
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Flag [j] == FLIP (cdense))
+ {
+ /* j is a dense node */
+ PRINT1 (("dense %d\n", j)) ;
+ Flag [j] = FLIP (child) ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* postorder the components */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG (for (cnt = 0, j = 0 ; j < n ; j++) if (CParent [j] != -2) cnt++) ;
+
+ /* use Cmember as workspace for Post [ */
+ Post = Cmember ;
+
+ /* cholmod_postorder uses Head and Iwork [0..2n]. It does not use Flag,
+ * which here holds the mapping of nodes to repnodes. It ignores all nodes
+ * for which CParent [j] < -1, so it operates just on the repnodes. */
+ /* workspace: Head (n), Iwork (2*n) */
+ ncomponents = CHOLMOD(postorder) (CParent, n, NULL, Post, Common) ;
+ ASSERT (cnt == ncomponents) ;
+
+ /* use Iwork [0..n-1] as workspace for Ipost ( */
+ Ipost = Iwork ;
+ DEBUG (for (j = 0 ; j < n ; j++) Ipost [j] = EMPTY) ;
+
+ /* compute inverse postorder */
+ for (c = 0 ; c < ncomponents ; c++)
+ {
+ cnode = Post [c] ;
+ ASSERT (cnode >= 0 && cnode < n) ;
+ Ipost [cnode] = c ;
+ ASSERT (Head [c] == EMPTY) ;
+ }
+
+ /* adjust the parent array */
+ /* Iwork [n..2n-1] used for NewParent [ */
+ NewParent = Iwork + n ;
+ for (c = 0 ; c < ncomponents ; c++)
+ {
+ parent = CParent [Post [c]] ;
+ NewParent [c] = (parent == EMPTY) ? EMPTY : (Ipost [parent]) ;
+ }
+ for (c = 0 ; c < ncomponents ; c++)
+ {
+ CParent [c] = NewParent [c] ;
+ }
+ ASSERT (CHOLMOD(dump_parent) (CParent, ncomponents, "CParent", Common)) ;
+
+ /* Iwork [n..2n-1] no longer needed for NewParent ] */
+ /* Cmember no longer needed for Post ] */
+
+#ifndef NDEBUG
+ /* count the number of children of each node */
+ for (c = 0 ; c < ncomponents ; c++)
+ {
+ Cmember [c] = 0 ;
+ }
+ for (c = 0 ; c < ncomponents ; c++)
+ {
+ if (CParent [c] != EMPTY) Cmember [CParent [c]]++ ;
+ }
+ for (c = 0 ; c < ncomponents ; c++)
+ {
+ /* a node is either a leaf, or has 2 or more children */
+ ASSERT (Cmember [c] == 0 || Cmember [c] >= 2) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* place each node in its component */
+ /* ---------------------------------------------------------------------- */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* node j is in the cth component, whose repnode is cnode */
+ cnode = FLIP (Flag [j]) ;
+ PRINT2 (("j "ID" flag "ID" cnode "ID"\n",
+ j, Flag [j], FLIP (Flag [j]))) ;
+ ASSERT (cnode >= 0 && cnode < n) ;
+ c = Ipost [cnode] ;
+ ASSERT (c >= 0 && c < ncomponents) ;
+ Cmember [j] = c ;
+ }
+
+ /* Flag no longer needed for the node-to-component mapping */
+
+ /* done using Iwork [0..n-1] as workspace for Ipost ) */
+
+ /* ---------------------------------------------------------------------- */
+ /* clear the Flag array */
+ /* ---------------------------------------------------------------------- */
+
+ Common->mark = EMPTY ;
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the permutation */
+ /* ---------------------------------------------------------------------- */
+
+ PRINT1 (("nd_camd: %d A->stype %d\n", nd_camd, A->stype)) ;
+
+ if (nd_camd)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* apply camd, csymamd, or ccolamd using the Cmember constraints */
+ /* ------------------------------------------------------------------ */
+
+ if (A->stype != 0)
+ {
+ /* ordering A+A', so fset and fsize are ignored.
+ * Add the upper/lower part to a symmetric lower/upper matrix by
+ * converting to unsymmetric mode
+ * workspace: Iwork (nrow) */
+ B = CHOLMOD(copy) (A, 0, -1, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ PRINT0 (("make symmetric failed\n")) ;
+ return (EMPTY) ;
+ }
+ ASSERT ((Int) (B->nrow) == n && (Int) (B->ncol) == n) ;
+ PRINT2 (("nested dissection (2)\n")) ;
+ B->stype = -1 ;
+ if (nd_camd == 2)
+ {
+ /* workspace: Head (nrow+1), Iwork (nrow) if symmetric-upper */
+ ok = CHOLMOD(csymamd) (B, Cmember, Perm, Common) ;
+ }
+ else
+ {
+ /* workspace: Head (nrow), Iwork (4*nrow) */
+ ok = CHOLMOD(camd) (B, NULL, 0, Cmember, Perm, Common) ;
+ }
+ CHOLMOD(free_sparse) (&B, Common) ;
+ if (!ok)
+ {
+ /* failed */
+ PRINT0 (("camd/csymamd failed\n")) ;
+ return (EMPTY) ;
+ }
+ }
+ else
+ {
+ /* ordering A*A' or A(:,f)*A(:,f)' */
+ /* workspace: Iwork (nrow if no fset; MAX(nrow,ncol) if fset) */
+ if (!CHOLMOD(ccolamd) (A, fset, fsize, Cmember, Perm, Common))
+ {
+ /* ccolamd failed */
+ PRINT2 (("ccolamd failed\n")) ;
+ return (EMPTY) ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* natural ordering of each component */
+ /* ------------------------------------------------------------------ */
+
+ /* use Iwork [0..n-1] for Next [ */
+ Next = Iwork ;
+
+ /* ------------------------------------------------------------------ */
+ /* place the nodes in link lists, one list per component */
+ /* ------------------------------------------------------------------ */
+
+ /* do so in reverse order, to preserve original ordering */
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ /* node j is in the cth component */
+ c = Cmember [j] ;
+ ASSERT (c >= 0 && c < ncomponents) ;
+ /* place node j in link list for component c */
+ Next [j] = Head [c] ;
+ Head [c] = j ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* order each node in each component */
+ /* ------------------------------------------------------------------ */
+
+ k = 0 ;
+ for (c = 0 ; c < ncomponents ; c++)
+ {
+ for (j = Head [c] ; j != EMPTY ; j = Next [j])
+ {
+ Perm [k++] = j ;
+ }
+ Head [c] = EMPTY ;
+ }
+ ASSERT (k == n) ;
+
+ /* done using Iwork [0..n-1] for Next ] */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* clear workspace and return number of components */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ return (ncomponents) ;
+}
+
+/* ========================================================================== */
+/* === cholmod_collapse_septree ============================================= */
+/* ========================================================================== */
+
+/* cholmod_nested_dissection returns the separator tree that was used in the
+ * constrained minimum degree algorithm. Parameter settings (nd_small,
+ * nd_oksep, etc) that give a good fill-reducing ordering may give too fine of
+ * a separator tree for other uses (parallelism, multi-level LPDASA, etc). This
+ * function takes as input the separator tree computed by
+ * cholmod_nested_dissection, and collapses selected subtrees into single
+ * nodes. A subtree is collapsed if its root node (the separator) is large
+ * compared to the total number of nodes in the subtree, or if the subtree is
+ * small. Note that the separator tree may actually be a forest.
+ *
+ * nd_oksep and nd_small act just like the ordering parameters in Common.
+ * Returns the new number of nodes in the separator tree.
+ */
+
+UF_long CHOLMOD(collapse_septree)
+(
+ /* ---- input ---- */
+ size_t n, /* # of nodes in the graph */
+ size_t ncomponents, /* # of nodes in the separator tree (must be <= n) */
+ double nd_oksep, /* collapse if #sep >= nd_oksep * #nodes in subtree */
+ size_t nd_small, /* collapse if #nodes in subtree < nd_small */
+ /* ---- in/out --- */
+ Int *CParent, /* size ncomponents; from cholmod_nested_dissection */
+ Int *Cmember, /* size n; from cholmod_nested_dissection */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ Int *First, *Count, *Csubtree, *W, *Map ;
+ Int c, j, k, nc, sepsize, total_weight, parent, nc_new, first ;
+ int collapse = FALSE, ok = TRUE ;
+ size_t s ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (EMPTY) ;
+ RETURN_IF_NULL (CParent, EMPTY) ;
+ RETURN_IF_NULL (Cmember, EMPTY) ;
+ if (n < ncomponents)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid separator tree") ;
+ return (EMPTY) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ nc = ncomponents ;
+ if (n <= 1 || ncomponents <= 1)
+ {
+ /* no change; tree is one node already */
+ return (nc) ;
+ }
+
+ nd_oksep = MAX (0, nd_oksep) ;
+ nd_oksep = MIN (1, nd_oksep) ;
+ nd_small = MAX (4, nd_small) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* s = 3*ncomponents */
+ s = CHOLMOD(mult_size_t) (ncomponents, 3, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (EMPTY) ;
+ }
+ CHOLMOD(allocate_work) (0, s, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (EMPTY) ;
+ }
+ W = Common->Iwork ;
+ Count = W ; W += ncomponents ; /* size ncomponents */
+ Csubtree = W ; W += ncomponents ; /* size ncomponents */
+ First = W ; W += ncomponents ; /* size ncomponents */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the first descendant of each node of the separator tree */
+ /* ---------------------------------------------------------------------- */
+
+ for (c = 0 ; c < nc ; c++)
+ {
+ First [c] = EMPTY ;
+ }
+ for (k = 0 ; k < nc ; k++)
+ {
+ for (c = k ; c != EMPTY && First [c] == -1 ; c = CParent [c])
+ {
+ ASSERT (c >= 0 && c < nc) ;
+ First [c] = k ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the number of nodes of the graph in each node of the tree */
+ /* ---------------------------------------------------------------------- */
+
+ for (c = 0 ; c < nc ; c++)
+ {
+ Count [c] = 0 ;
+ }
+ for (j = 0 ; j < (Int) n ; j++)
+ {
+ ASSERT (Cmember [j] >= 0 && Cmember [j] < nc) ;
+ Count [Cmember [j]]++ ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the number of nodes in each subtree */
+ /* ---------------------------------------------------------------------- */
+
+ for (c = 0 ; c < nc ; c++)
+ {
+ /* each subtree includes its root */
+ Csubtree [c] = Count [c] ;
+ PRINT1 ((ID" size "ID" parent "ID" first "ID"\n",
+ c, Count [c], CParent [c], First [c])) ;
+ }
+
+ for (c = 0 ; c < nc ; c++)
+ {
+ /* add the subtree of the child, c, into the count of its parent */
+ parent = CParent [c] ;
+ ASSERT (parent >= EMPTY && parent < nc) ;
+ if (parent != EMPTY)
+ {
+ Csubtree [parent] += Csubtree [c] ;
+ }
+ }
+
+#ifndef NDEBUG
+ /* the sum of the roots should be n */
+ j = 0 ;
+ for (c = 0 ; c < nc ; c++) if (CParent [c] == EMPTY) j += Csubtree [c] ;
+ ASSERT (j == (Int) n) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* find subtrees to collapse */
+ /* ---------------------------------------------------------------------- */
+
+ /* consider all nodes in reverse post-order */
+ for (c = nc-1 ; c >= 0 ; c--)
+ {
+ /* consider the subtree rooted at node c */
+ sepsize = Count [c] ;
+ total_weight = Csubtree [c] ;
+ PRINT1 (("Node "ID" sepsize "ID" subtree "ID" ratio %g\n", c, sepsize,
+ total_weight, ((double) sepsize)/((double) total_weight))) ;
+ first = First [c] ;
+ if (first < c && /* c must not be a leaf */
+ (sepsize > nd_oksep * total_weight || total_weight < (int) nd_small))
+ {
+ /* this separator is too large, or the subtree is too small.
+ * collapse the tree, by converting the entire subtree rooted at
+ * c into a single node. The subtree consists of all nodes from
+ * First[c] to the root c. Flag all nodes from First[c] to c-1
+ * as dead.
+ */
+ collapse = TRUE ;
+ for (k = first ; k < c ; k++)
+ {
+ CParent [k] = -2 ;
+ PRINT1 ((" collapse node "ID"\n", k)) ;
+ }
+ /* continue at the next node, first-1 */
+ c = first ;
+ }
+ }
+
+ PRINT1 (("collapse: %d\n", collapse)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compress the tree */
+ /* ---------------------------------------------------------------------- */
+
+ Map = Count ; /* Count no longer needed */
+
+ nc_new = nc ;
+ if (collapse)
+ {
+ nc_new = 0 ;
+ for (c = 0 ; c < nc ; c++)
+ {
+ Map [c] = nc_new ;
+ if (CParent [c] >= EMPTY)
+ {
+ /* node c is alive, and becomes node Map[c] in the new tree.
+ * Increment nc_new for the next node c. */
+ nc_new++ ;
+ }
+ }
+ PRINT1 (("Collapse the tree from "ID" to "ID" nodes\n", nc, nc_new)) ;
+ ASSERT (nc_new > 0) ;
+ for (c = 0 ; c < nc ; c++)
+ {
+ parent = CParent [c] ;
+ if (parent >= EMPTY)
+ {
+ /* node c is alive */
+ CParent [Map [c]] = (parent == EMPTY) ? EMPTY : Map [parent] ;
+ }
+ }
+ for (j = 0 ; j < (Int) n ; j++)
+ {
+ PRINT1 (("j "ID" Cmember[j] "ID" Map[Cmember[j]] "ID"\n",
+ j, Cmember [j], Map [Cmember [j]])) ;
+ Cmember [j] = Map [Cmember [j]] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return new size of separator tree */
+ /* ---------------------------------------------------------------------- */
+
+ return (nc_new) ;
+}
+#endif
diff --git a/CHOLMOD/Partition/lesser.txt b/CHOLMOD/Partition/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/CHOLMOD/Partition/lesser.txt
@@ -0,0 +1,504 @@
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diff --git a/CHOLMOD/README.txt b/CHOLMOD/README.txt
new file mode 100644
index 0000000..193d758
--- /dev/null
+++ b/CHOLMOD/README.txt
@@ -0,0 +1,84 @@
+CHOLMOD: a sparse CHOLesky MODification package
+Version 1.6, Nov 1, 2007. Copyright (c) 2005-2007.
+-----------------------------------------------
+
+ CHOLMOD is a set of routines for factorizing sparse symmetric positive
+ definite matrices of the form A or AA', updating/downdating a sparse
+ Cholesky factorization, solving linear systems, updating/downdating
+ the solution to the triangular system Lx=b, and many other sparse matrix
+ functions for both symmetric and unsymmetric matrices. Its supernodal
+ Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains
+ a substantial fraction of the peak performance of the BLAS. Both real and
+ complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both
+ C and MATLAB interfaces. This code works on Microsoft Windows and many
+ versions of Unix and Linux.
+
+
+Some Modules of CHOLMOD are copyrighted by the University of Florida (the
+Core and Partition Modules). The rest are copyrighted by the authors:
+Timothy A. Davis (all of them), and William W. Hager (the Modify Module).
+
+CHOLMOD relies on several other packages: AMD, CAMD, COLAMD, CCOLAMD, UFconfig,
+METIS, the BLAS, and LAPACK. All but METIS, the BLAS, and LAPACK are part of
+SuiteSparse.
+
+AMD is authored by T. Davis, Iain Duff, and Patrick Amestoy.
+COLAMD is authored by T. Davis and Stefan Larimore, with algorithmic design
+in collaboration with John Gilbert and Esmond Ng.
+CCOLAMD is authored by T. Davis and Siva Rajamanickam.
+CAMD is authored by T. Davis and Y. Chen.
+
+LAPACK and the BLAS are authored by Jack Dongarra and many others.
+LAPACK is available at http://www.netlib.org/lapack
+
+METIS is authored by George Karypis, Univ. of Minnesota. Its use in CHOLMOD
+is optional. See http://www-users.cs.umn.edu/~karypis/metis.
+Place a copy of the metis-4.0 directory in the same directory that
+contains the CHOLMOD, AMD, COLAMD, and CCOLAMD directories prior to compiling
+with "make".
+
+If you do not wish to use METIS, you must edit UFconfig and change the line:
+
+ CHOLMOD_CONFIG =
+
+to
+
+ CHOLMOD_CONFIG = -DNPARTITION
+
+The CHOLMOD, AMD, COLAMD, CCOLAMD, and UFconfig directories must all reside
+in a common parent directory. To compile all these libraries,
+edit UFconfig/UFconfig.mk to reflect your environment (C compiler, location
+of the BLAS, and so on) and then type "make" in either the CHOLMOD directory
+or in the parent directory of CHOLMOD. See each package for more details on
+how to compile them.
+
+For use in MATLAB (on any system, including Windows): start MATLAB,
+cd to the CHOLMOD/MATLAB directory, and type cholmod_make in the MATLAB
+Command Window. This is the best way to compile CHOLMOD for MATLAB; it
+provides a workaround for a METIS design feature, in which METIS terminates
+your program (and thus MATLAB) if it runs out of memory. Using cholmod_make
+also ensures your mexFunctions are compiled with -fexceptions, so that
+exceptions are handled properly (when hitting control-C in the MATLAB command
+window, for example).
+
+If you have MATLAB 7.2 or earlier and use "make mex", you must first edit
+UFconfig/UFconfig.h to remove the "-largeArrayDims" option from the MEX command
+(or just use cholmod_make.m inside MATLAB).
+
+On the Pentium, do NOT use the Intel MKL BLAS prior to MKL Version 8.0 with
+CHOLMOD. Older versions (prior to 8.0) have a bug in dgemm when computing
+A*B'. The bug generates a NaN result, when the inputs are well-defined. Use
+the Goto BLAS or the MKL v8.0 BLAS instead. The Goto BLAS is faster and more
+reliable. See http://www.tacc.utexas.edu/~kgoto/ or
+http://www.cs.utexas.edu/users/flame/goto/.
+Sadly, the Intel MKL BLAS 7.x is the default for MATLAB 7.0.4. See
+http://www.mathworks.com/support/bugreports/details.html?rp=252103 for more
+details. To workaround this problem on Linux, set environment variable
+BLAS_VERSION to libmkl_p3.so:libguide.so. On Windows, set environment variable
+BLAS_VERSION to mkl_p3.dll. Better yet, get MATLAB 7sp3 (MATLAB 7.1) or later.
+
+Acknowledgements: this work was supported in part by the National Science
+Foundation (NFS CCR-0203270 and DMS-9803599), and a grant from Sandia National
+Laboratories (Dept. of Energy) which supported the development of CHOLMOD's
+Partition Module.
+
diff --git a/CHOLMOD/Supernodal/License.txt b/CHOLMOD/Supernodal/License.txt
new file mode 100644
index 0000000..668c929
--- /dev/null
+++ b/CHOLMOD/Supernodal/License.txt
@@ -0,0 +1,25 @@
+CHOLMOD/Supernodal Module.
+Copyright (C) 2005-2006, Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Supernodal module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
diff --git a/CHOLMOD/Supernodal/cholmod_super_numeric.c b/CHOLMOD/Supernodal/cholmod_super_numeric.c
new file mode 100644
index 0000000..93d33a2
--- /dev/null
+++ b/CHOLMOD/Supernodal/cholmod_super_numeric.c
@@ -0,0 +1,296 @@
+/* ========================================================================== */
+/* === Supernodal/cholmod_super_numeric ===================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Computes the Cholesky factorization of A+beta*I or A*F+beta*I. Only the
+ * the lower triangular part of A+beta*I or A*F+beta*I is accessed. The
+ * matrices A and F must already be permuted according to the fill-reduction
+ * permutation L->Perm. cholmod_factorize is an "easy" wrapper for this code
+ * which applies that permutation. beta is real.
+ *
+ * Symmetric case: A is a symmetric (lower) matrix. F is not accessed.
+ * With a fill-reducing permutation, A(p,p) should be passed instead, where is
+ * p is L->Perm.
+ *
+ * Unsymmetric case: A is unsymmetric, and F must be present. Normally, F=A'.
+ * With a fill-reducing permutation, A(p,f) and A(p,f)' should be passed as A
+ * and F, respectively, where f is a list of the subset of the columns of A.
+ *
+ * The input factorization L must be supernodal (L->is_super is TRUE). It can
+ * either be symbolic or numeric. In the first case, L has been analyzed by
+ * cholmod_analyze or cholmod_super_symbolic, but the matrix has not yet been
+ * numerically factorized. The numerical values are allocated here and the
+ * factorization is computed. In the second case, a prior matrix has been
+ * analyzed and numerically factorized, and a new matrix is being factorized.
+ * The numerical values of L are replaced with the new numerical factorization.
+ *
+ * L->is_ll is ignored, and set to TRUE. This routine always computes an LL'
+ * factorization. Supernodal LDL' factorization is not (yet) supported.
+ * FUTURE WORK: perform a supernodal LDL' factorization if L->is_ll is FALSE.
+ *
+ * Uses BLAS routines dsyrk, dgemm, dtrsm, and the LAPACK routine dpotrf.
+ * The supernodal solver uses BLAS routines dtrsv, dgemv, dtrsm, and dgemm.
+ *
+ * If the matrix is not positive definite the routine returns TRUE, but sets
+ * Common->status to CHOLMOD_NOT_POSDEF and L->minor is set to the column at
+ * which the failure occurred. The supernode containing the non-positive
+ * diagonal entry is set to zero (this includes columns to the left of L->minor
+ * in the same supernode), as are all subsequent supernodes.
+ *
+ * workspace: Flag (nrow), Head (nrow+1), Iwork (2*nrow + 4*nsuper).
+ * Allocates temporary space of size L->maxcsize * sizeof(double)
+ * (twice that for the complex/zomplex case).
+ *
+ * If L is supernodal symbolic on input, it is converted to a supernodal numeric
+ * factor on output, with an xtype of real if A is real, or complex if A is
+ * complex or zomplex. If L is supernodal numeric on input, its xtype must
+ * match A (except that L can be complex and A zomplex). The xtype of A and F
+ * must match.
+ */
+
+#ifndef NSUPERNODAL
+
+#include "cholmod_internal.h"
+#include "cholmod_supernodal.h"
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_super_numeric.c"
+#define COMPLEX
+#include "t_cholmod_super_numeric.c"
+#define ZOMPLEX
+#include "t_cholmod_super_numeric.c"
+
+/* ========================================================================== */
+/* === cholmod_super_numeric ================================================ */
+/* ========================================================================== */
+
+/* Returns TRUE if successful, or if the matrix is not positive definite.
+ * Returns FALSE if out of memory, inputs are invalid, or other fatal error
+ * occurs.
+ */
+
+int CHOLMOD(super_numeric)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* F = A' or A(:,f)' */
+ double beta [2], /* beta*I is added to diagonal of matrix to factorize */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ cholmod_dense *C ;
+ Int *Super, *Map, *SuperMap ;
+ size_t maxcsize ;
+ Int nsuper, n, i, k, s, stype, nrow ;
+ int ok = TRUE, symbolic ;
+ size_t t, w ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_COMPLEX, FALSE) ;
+ stype = A->stype ;
+ if (stype < 0)
+ {
+ if (A->nrow != A->ncol || A->nrow != L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid dimensions") ;
+ return (FALSE) ;
+ }
+ }
+ else if (stype == 0)
+ {
+ if (A->nrow != L->n)
+ {
+ ERROR (CHOLMOD_INVALID, "invalid dimensions") ;
+ return (FALSE) ;
+ }
+ RETURN_IF_NULL (F, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (F, CHOLMOD_REAL, CHOLMOD_ZOMPLEX, FALSE) ;
+ if (A->nrow != F->ncol || A->ncol != F->nrow || F->stype != 0)
+ {
+ ERROR (CHOLMOD_INVALID, "F invalid") ;
+ return (FALSE) ;
+ }
+ if (A->xtype != F->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "A and F must have same xtype") ;
+ return (FALSE) ;
+ }
+ }
+ else
+ {
+ /* symmetric upper case not suppored */
+ ERROR (CHOLMOD_INVALID, "symmetric upper case not supported") ;
+ return (FALSE) ;
+ }
+ if (!(L->is_super))
+ {
+ ERROR (CHOLMOD_INVALID, "L not supernodal") ;
+ return (FALSE) ;
+ }
+ if (L->xtype != CHOLMOD_PATTERN)
+ {
+ if (! ((A->xtype == CHOLMOD_REAL && L->xtype == CHOLMOD_REAL)
+ || (A->xtype == CHOLMOD_COMPLEX && L->xtype == CHOLMOD_COMPLEX)
+ || (A->xtype == CHOLMOD_ZOMPLEX && L->xtype == CHOLMOD_COMPLEX)))
+ {
+ ERROR (CHOLMOD_INVALID, "complex type mismatch") ;
+ return (FALSE) ;
+ }
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace in Common */
+ /* ---------------------------------------------------------------------- */
+
+ nsuper = L->nsuper ;
+ maxcsize = L->maxcsize ;
+ nrow = A->nrow ;
+ n = nrow ;
+
+ PRINT1 (("nsuper "ID" maxcsize %g\n", nsuper, (double) maxcsize)) ;
+ ASSERT (nsuper >= 0 && maxcsize > 0) ;
+
+ /* w = 2*n + 4*nsuper */
+ w = CHOLMOD(mult_size_t) (n, 2, &ok) ;
+ t = CHOLMOD(mult_size_t) (nsuper, 4, &ok) ;
+ w = CHOLMOD(add_size_t) (w, t, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (n, w, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the current factor L and allocate numerical part, if needed */
+ /* ---------------------------------------------------------------------- */
+
+ Super = L->super ;
+ symbolic = (L->xtype == CHOLMOD_PATTERN) ;
+ if (symbolic)
+ {
+ /* convert to supernodal numeric by allocating L->x */
+ CHOLMOD(change_factor) (
+ (A->xtype == CHOLMOD_REAL) ? CHOLMOD_REAL : CHOLMOD_COMPLEX,
+ TRUE, TRUE, TRUE, TRUE, L, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* the factor L remains in symbolic supernodal form */
+ return (FALSE) ;
+ }
+ }
+ ASSERT (L->dtype == DTYPE) ;
+ ASSERT (L->xtype == CHOLMOD_REAL || L->xtype == CHOLMOD_COMPLEX) ;
+
+ /* supernodal LDL' is not supported */
+ L->is_ll = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get more workspace */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_dense) (maxcsize, 1, maxcsize, L->xtype, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ int status = Common->status ;
+ if (symbolic)
+ {
+ /* Change L back to symbolic, since the numeric values are not
+ * initialized. This cannot fail. */
+ CHOLMOD(change_factor) (CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE,
+ L, Common) ;
+ }
+ /* the factor L is now back to the form it had on input */
+ Common->status = status ;
+ return (FALSE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ SuperMap = Common->Iwork ; /* size n (i/i/l) */
+ Map = Common->Flag ; /* size n, use Flag as workspace for Map array */
+ for (i = 0 ; i < n ; i++)
+ {
+ Map [i] = EMPTY ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the mapping of nodes to relaxed supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ /* SuperMap [k] = s if column k is contained in supernode s */
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ PRINT1 (("Super ["ID"] "ID" ncols "ID"\n",
+ s, Super[s], Super[s+1]-Super[s]));
+ for (k = Super [s] ; k < Super [s+1] ; k++)
+ {
+ SuperMap [k] = s ;
+ PRINT2 (("relaxed SuperMap ["ID"] = "ID"\n", k, SuperMap [k])) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal numerical factorization, using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (A->xtype)
+ {
+ case CHOLMOD_REAL:
+ ok = r_cholmod_super_numeric (A, F, beta, L, C, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ ok = c_cholmod_super_numeric (A, F, beta, L, C, Common) ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ /* This operates on complex L, not zomplex */
+ ok = z_cholmod_super_numeric (A, F, beta, L, C, Common) ;
+ break ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* clear Common workspace, free temp workspace C, and return */
+ /* ---------------------------------------------------------------------- */
+
+ /* Flag array was used as workspace, clear it */
+ Common->mark = EMPTY ;
+ /* CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+ CHOLMOD(free_dense) (&C, Common) ;
+ return (ok) ;
+}
+#endif
diff --git a/CHOLMOD/Supernodal/cholmod_super_solve.c b/CHOLMOD/Supernodal/cholmod_super_solve.c
new file mode 100644
index 0000000..2d81222
--- /dev/null
+++ b/CHOLMOD/Supernodal/cholmod_super_solve.c
@@ -0,0 +1,221 @@
+/* ========================================================================== */
+/* === Supernodal/cholmod_super_solve ======================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Solve Lx=b or L'x=b for a supernodal factorization. These routines do not
+ * apply the permutation L->Perm. See cholmod_solve for a more general
+ * interface that performs that operation.
+ */
+
+#ifndef NSUPERNODAL
+
+#include "cholmod_internal.h"
+#include "cholmod_supernodal.h"
+
+/* ========================================================================== */
+/* === TEMPLATE ============================================================= */
+/* ========================================================================== */
+
+#define REAL
+#include "t_cholmod_super_solve.c"
+#define COMPLEX
+#include "t_cholmod_super_solve.c"
+
+/* ========================================================================== */
+/* === cholmod_super_lsolve ================================================= */
+/* ========================================================================== */
+
+/* Solve Lx=b where x and b are of size n-by-nrhs. b is overwritten by the
+ * solution x. On input, b is stored in col-major order with leading dimension
+ * of d, and on output x is stored in the same manner.
+ *
+ * The contents of the workspace E are undefined on both input and output.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(super_lsolve) /* TRUE if OK, FALSE if BLAS overflow occured */
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the forward solve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to Lx=b on output */
+ /* ---- workspace ---- */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ int blas_ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_NULL (X, FALSE) ;
+ RETURN_IF_NULL (E, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (E, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ if (L->xtype != X->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "L and X must have the same xtype") ;
+ return (FALSE) ;
+ }
+ if (L->xtype != E->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "L and E must have the same xtype") ;
+ return (FALSE) ;
+ }
+ if (X->d < X->nrow || L->n != X->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "X and L dimensions must match") ;
+ return (FALSE) ;
+ }
+ if (E->nzmax < X->ncol * (L->maxesize))
+ {
+ ERROR (CHOLMOD_INVALID, "workspace E not large enough") ;
+ return (FALSE) ;
+ }
+ if (!(L->is_ll) || !(L->is_super))
+ {
+ ERROR (CHOLMOD_INVALID, "L not supernodal") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ ASSERT (IMPLIES (L->n == 0, L->nsuper == 0)) ;
+ if (L->n == 0 || X->ncol == 0)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Lx=b using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (L->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ blas_ok = r_cholmod_super_lsolve (L, X, E, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ blas_ok = c_cholmod_super_lsolve (L, X, E, Common) ;
+ break ;
+ }
+
+ if (CHECK_BLAS_INT && !blas_ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ;
+ }
+ return (blas_ok) ;
+}
+
+
+/* ========================================================================== */
+/* === cholmod_super_ltsolve ================================================ */
+/* ========================================================================== */
+
+/* Solve L'x=b where x and b are of size n-by-nrhs. b is overwritten by the
+ * solution x. On input, b is stored in col-major order with leading dimension
+ * of d, and on output x is stored in the same manner.
+ *
+ * The contents of the workspace E are undefined on both input and output.
+ *
+ * workspace: none
+ */
+
+int CHOLMOD(super_ltsolve) /* TRUE if OK, FALSE if BLAS overflow occured */
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the backsolve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to L'x=b on output */
+ /* ---- workspace ---- */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ int blas_ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_NULL (X, FALSE) ;
+ RETURN_IF_NULL (E, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (X, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (E, CHOLMOD_REAL, CHOLMOD_COMPLEX, FALSE) ;
+ if (L->xtype != X->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "L and X must have the same xtype") ;
+ return (FALSE) ;
+ }
+ if (L->xtype != E->xtype)
+ {
+ ERROR (CHOLMOD_INVALID, "L and E must have the same xtype") ;
+ return (FALSE) ;
+ }
+ if (X->d < X->nrow || L->n != X->nrow)
+ {
+ ERROR (CHOLMOD_INVALID, "X and L dimensions must match") ;
+ return (FALSE) ;
+ }
+ if (E->nzmax < X->ncol * (L->maxesize))
+ {
+ ERROR (CHOLMOD_INVALID, "workspace E not large enough") ;
+ return (FALSE) ;
+ }
+ if (!(L->is_ll) || !(L->is_super))
+ {
+ ERROR (CHOLMOD_INVALID, "L not supernodal") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+ ASSERT (IMPLIES (L->n == 0, L->nsuper == 0)) ;
+ if (L->n == 0 || X->ncol == 0)
+ {
+ /* nothing to do */
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Lx=b using template routine */
+ /* ---------------------------------------------------------------------- */
+
+ switch (L->xtype)
+ {
+
+ case CHOLMOD_REAL:
+ blas_ok = r_cholmod_super_ltsolve (L, X, E, Common) ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ blas_ok = c_cholmod_super_ltsolve (L, X, E, Common) ;
+ break ;
+ }
+
+ if (CHECK_BLAS_INT && !blas_ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ;
+ }
+
+ return (blas_ok) ;
+}
+#endif
diff --git a/CHOLMOD/Supernodal/cholmod_super_symbolic.c b/CHOLMOD/Supernodal/cholmod_super_symbolic.c
new file mode 100644
index 0000000..c7cd0c7
--- /dev/null
+++ b/CHOLMOD/Supernodal/cholmod_super_symbolic.c
@@ -0,0 +1,794 @@
+/* ========================================================================== */
+/* === Supernodal/cholmod_super_symbolic ==================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Supernodal symbolic analysis of the LL' factorization of A, A*A',
+ * A(:,f)*A(:,f)'.
+ *
+ * This routine must be preceded by a simplicial symbolic analysis
+ * (cholmod_rowcolcounts). See cholmod_analyze.c for an example of how to use
+ * this routine.
+ *
+ * The user need not call this directly; cholmod_analyze is a "simple" wrapper
+ * for this routine.
+ *
+ * Symmetric case:
+ *
+ * A is stored in column form, with entries stored in the upper triangular
+ * part. Entries in the lower triangular part are ignored.
+ *
+ * Unsymmetric case:
+ *
+ * A is stored in column form. If F is equal to the transpose of A, then
+ * A*A' is analyzed. F can include a subset of the columns of A
+ * (F=A(:,f)'), in which case F*F' is analyzed.
+ *
+ * Requires Parent and L->ColCount to be defined on input; these are the
+ * simplicial Parent and ColCount arrays as computed by cholmod_rowcolcounts.
+ * Does not use L->Perm; the input matrices A and F must already be properly
+ * permuted. Allocates and computes the supernodal pattern of L (L->super,
+ * L->pi, L->px, and L->s). Does not allocate the real part (L->x).
+ *
+ * Supports any xtype (pattern, real, complex, or zomplex).
+ */
+
+#ifndef NSUPERNODAL
+
+#include "cholmod_internal.h"
+#include "cholmod_supernodal.h"
+
+
+/* ========================================================================== */
+/* === subtree ============================================================== */
+/* ========================================================================== */
+
+/* In the symmetric case, traverse the kth row subtree from the nonzeros in
+ * A (0:k,k) and add the new entries found to the pattern of the kth row of L.
+ *
+ * In the unsymmetric case, the nonzero pattern of A*F is computed one column at
+ * one column at a time. The kth column is A*F(:,k), or the set union of all
+ * columns A(:,j) for which F(j,k) is nonzero. This routine is called once
+ * for each entry j. Only the upper triangular part is needed, so only
+ * A (0:k,j) is accessed.
+ *
+ * Only adds column indices corresponding to the leading columns of each
+ * relaxed supernode.
+ */
+
+static void subtree
+(
+ /* inputs, not modified: */
+ Int j, /* j = k for symmetric case */
+ Int k,
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Anz [ ],
+ Int SuperMap [ ],
+ Int Sparent [ ],
+ Int mark,
+
+ /* input/output: */
+ Int Flag [ ],
+ Int Ls [ ],
+ Int Lpi2 [ ]
+)
+{
+ Int p, pend, i, si ;
+ p = Ap [j] ;
+ pend = (Anz == NULL) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i < k)
+ {
+ /* (i,k) is an entry in the upper triangular part of A or A*F'.
+ * symmetric case: A(i,k) is nonzero (j=k).
+ * unsymmetric case: A(i,j) and F(j,k) are both nonzero.
+ *
+ * Column i is in supernode si = SuperMap [i]. Follow path from si
+ * to root of supernodal etree, stopping at the first flagged
+ * supernode. The root of the row subtree is supernode SuperMap[k],
+ * which is flagged already. This traversal will stop there, or it
+ * might stop earlier if supernodes have been flagged by previous
+ * calls to this routine for the same k. */
+ for (si = SuperMap [i] ; Flag [si] < mark ; si = Sparent [si])
+ {
+ ASSERT (si <= SuperMap [k]) ;
+ Ls [Lpi2 [si]++] = k ;
+ Flag [si] = mark ;
+ }
+ }
+ }
+}
+
+
+/* clear workspace used by cholmod_super_symbolic */
+#define FREE_WORKSPACE \
+{ \
+ /* CHOLMOD(clear_flag) (Common) ; */ \
+ CHOLMOD_CLEAR_FLAG (Common) ; \
+ for (k = 0 ; k <= nfsuper ; k++) \
+ { \
+ Head [k] = EMPTY ; \
+ } \
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ; \
+} \
+
+
+/* ========================================================================== */
+/* === cholmod_super_symbolic =============================================== */
+/* ========================================================================== */
+
+/* Analyzes A, AA', or A(:,f)*A(:,f)' in preparation for a supernodal numeric
+ * factorization. The user need not call this directly; cholmod_analyze is
+ * a "simple" wrapper for this routine.
+ *
+ * workspace: Flag (nrow), Head (nrow), Iwork (2*nrow),
+ * and temporary space of size 3*nfsuper*sizeof(Int), where nfsuper <= n
+ * is the number of fundamental supernodes.
+ */
+
+int CHOLMOD(super_symbolic)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to analyze */
+ cholmod_sparse *F, /* F = A' or A(:,f)' */
+ Int *Parent, /* elimination tree */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* simplicial symbolic on input,
+ * supernodal symbolic on output */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double zrelax0, zrelax1, zrelax2, xxsize ;
+ Int *Wi, *Wj, *Super, *Snz, *Ap, *Ai, *Flag, *Head, *Ls, *Lpi, *Lpx, *Fnz,
+ *Sparent, *Anz, *SuperMap, *Merged, *Nscol, *Zeros, *Fp, *Fj,
+ *ColCount, *Lpi2, *Lsuper, *Iwork ;
+ Int nsuper, d, n, j, k, s, mark, parent, p, pend, k1, k2, packed, nscol,
+ nsrow, ndrow1, ndrow2, stype, ssize, xsize, sparent, plast, slast,
+ csize, maxcsize, ss, nscol0, nscol1, ns, nfsuper, newzeros, totzeros,
+ merge, snext, esize, maxesize, nrelax0, nrelax1, nrelax2 ;
+ size_t w ;
+ int ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ RETURN_IF_NULL_COMMON (FALSE) ;
+ RETURN_IF_NULL (A, FALSE) ;
+ RETURN_IF_NULL (L, FALSE) ;
+ RETURN_IF_NULL (Parent, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
+ RETURN_IF_XTYPE_INVALID (L, CHOLMOD_PATTERN, CHOLMOD_PATTERN, FALSE) ;
+ stype = A->stype ;
+ if (stype < 0)
+ {
+ /* invalid symmetry; symmetric lower form not supported */
+ ERROR (CHOLMOD_INVALID, "symmetric lower not supported") ;
+ return (FALSE) ;
+ }
+ if (stype == 0)
+ {
+ /* F must be present in the unsymmetric case */
+ RETURN_IF_NULL (F, FALSE) ;
+ }
+ if (L->is_super)
+ {
+ /* L must be a simplicial symbolic factor */
+ ERROR (CHOLMOD_INVALID, "L must be symbolic on input") ;
+ return (FALSE) ;
+ }
+ Common->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+
+ /* w = 5*n */
+ w = CHOLMOD(mult_size_t) (n, 5, &ok) ;
+ if (!ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ return (FALSE) ;
+ }
+
+ CHOLMOD(allocate_work) (n, w, 0, Common) ;
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory */
+ return (FALSE) ;
+ }
+ ASSERT (CHOLMOD(dump_work) (TRUE, TRUE, 0, Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* A is now either A or triu(A(p,p)) for the symmetric case. It is either
+ * A or A(p,f) for the unsymmetric case (both in column form). It can be
+ * either packed or unpacked, and either sorted or unsorted. Entries in
+ * the lower triangular part may be present if A is symmetric, but these
+ * are ignored. */
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+
+ if (stype != 0)
+ {
+ /* F not accessed */
+ Fp = NULL ;
+ Fj = NULL ;
+ Fnz = NULL ;
+ packed = TRUE ;
+ }
+ else
+ {
+ /* F = A(:,f) or A(p,f) in packed row form, either sorted or unsorted */
+ Fp = F->p ;
+ Fj = F->i ;
+ Fnz = F->nz ;
+ packed = F->packed ;
+ }
+
+ ColCount = L->ColCount ;
+
+ nrelax0 = Common->nrelax [0] ;
+ nrelax1 = Common->nrelax [1] ;
+ nrelax2 = Common->nrelax [2] ;
+
+ zrelax0 = Common->zrelax [0] ;
+ zrelax1 = Common->zrelax [1] ;
+ zrelax2 = Common->zrelax [2] ;
+
+ zrelax0 = IS_NAN (zrelax0) ? 0 : zrelax0 ;
+ zrelax1 = IS_NAN (zrelax1) ? 0 : zrelax1 ;
+ zrelax2 = IS_NAN (zrelax2) ? 0 : zrelax2 ;
+
+ ASSERT (CHOLMOD(dump_parent) (Parent, n, "Parent", Common)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* Sparent, Snz, and Merged could be allocated later, of size nfsuper */
+
+ Iwork = Common->Iwork ;
+ Wi = Iwork ; /* size n (i/l/l). Lpi2 is i/l/l */
+ Wj = Iwork + n ; /* size n (i/l/l). Zeros is i/l/l */
+ Sparent = Iwork + 2*((size_t) n) ; /* size nfsuper <= n [ */
+ Snz = Iwork + 3*((size_t) n) ; /* size nfsuper <= n [ */
+ Merged = Iwork + 4*((size_t) n) ; /* size nfsuper <= n [ */
+
+ Flag = Common->Flag ; /* size n */
+ Head = Common->Head ; /* size n+1 */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the fundamental supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ /* count the number of children of each node, using Wi [ */
+ for (j = 0 ; j < n ; j++)
+ {
+ Wi [j] = 0 ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ parent = Parent [j] ;
+ if (parent != EMPTY)
+ {
+ Wi [parent]++ ;
+ }
+ }
+
+ Super = Head ; /* use Head [0..nfsuper] as workspace for Super list ( */
+
+ /* column 0 always starts a new supernode */
+ nfsuper = (n == 0) ? 0 : 1 ; /* number of fundamental supernodes */
+ Super [0] = 0 ;
+
+ for (j = 1 ; j < n ; j++)
+ {
+ /* check if j starts new supernode, or in the same supernode as j-1 */
+ if (Parent [j-1] != j /* parent of j-1 is not j */
+ || (ColCount [j-1] != ColCount [j] + 1) /* j-1 not subset of j*/
+ || Wi [j] > 1) /* j has more than one child */
+ {
+ /* j is the leading node of a supernode */
+ Super [nfsuper++] = j ;
+ }
+ }
+ Super [nfsuper] = n ;
+
+ /* contents of Wi no longer needed for child count ] */
+
+ Nscol = Wi ; /* use Wi as size-nfsuper workspace for Nscol [ */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the mapping of fundamental nodes to supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ SuperMap = Wj ; /* use Wj as workspace for SuperMap [ */
+
+ /* SuperMap [k] = s if column k is contained in supernode s */
+ for (s = 0 ; s < nfsuper ; s++)
+ {
+ for (k = Super [s] ; k < Super [s+1] ; k++)
+ {
+ SuperMap [k] = s ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the fundamental supernodal etree */
+ /* ---------------------------------------------------------------------- */
+
+ for (s = 0 ; s < nfsuper ; s++)
+ {
+ j = Super [s+1] - 1 ; /* last node in supernode s */
+ parent = Parent [j] ; /* parent of last node */
+ Sparent [s] = (parent == EMPTY) ? EMPTY : SuperMap [parent] ;
+ PRINT1 (("Sparent ["ID"] = "ID"\n", s, Sparent [s])) ;
+ }
+
+ /* contents of Wj no longer needed as workspace for SuperMap ]
+ * SuperMap will be recomputed below, for the relaxed supernodes. */
+
+ Zeros = Wj ; /* use Wj for Zeros, workspace of size nfsuper [ */
+
+ /* ---------------------------------------------------------------------- */
+ /* relaxed amalgamation */
+ /* ---------------------------------------------------------------------- */
+
+ for (s = 0 ; s < nfsuper ; s++)
+ {
+ Merged [s] = EMPTY ; /* s not merged into another */
+ Nscol [s] = Super [s+1] - Super [s] ; /* # of columns in s */
+ Zeros [s] = 0 ; /* # of zero entries in s */
+ ASSERT (s <= Super [s]) ;
+ Snz [s] = ColCount [Super [s]] ; /* # of entries in leading col of s */
+ PRINT2 (("lnz ["ID"] "ID"\n", s, Snz [s])) ;
+ }
+
+ for (s = nfsuper-2 ; s >= 0 ; s--)
+ {
+ /* should supernodes s and s+1 merge into a new node s? */
+ PRINT1 (("\n========= Check relax of s "ID" and s+1 "ID"\n", s, s+1)) ;
+
+ ss = Sparent [s] ;
+ if (ss == EMPTY)
+ {
+ PRINT1 (("s "ID" is a root, no merge with s+1 = "ID"\n", s, s+1)) ;
+ continue ;
+ }
+
+ /* find the current parent of s (perform path compression as needed) */
+ for (ss = Sparent [s] ; Merged [ss] != EMPTY ; ss = Merged [ss]) ;
+ sparent = ss ;
+ PRINT2 (("Current sparent of s "ID" is "ID"\n", s, sparent)) ;
+
+ /* ss is the current parent of s */
+ for (ss = Sparent [s] ; Merged [ss] != EMPTY ; ss = snext)
+ {
+ snext = Merged [ss] ;
+ PRINT2 (("ss "ID" is dead, merged into snext "ID"\n", ss, snext)) ;
+ Merged [ss] = sparent ;
+ }
+
+ /* if s+1 is not the current parent of s, do not merge */
+ if (sparent != s+1)
+ {
+ continue ;
+ }
+
+ nscol0 = Nscol [s] ; /* # of columns in s */
+ nscol1 = Nscol [s+1] ; /* # of columns in s+1 */
+ ns = nscol0 + nscol1 ;
+ PRINT2 (("ns "ID" nscol0 "ID" nscol1 "ID"\n", ns, nscol0, nscol1)) ;
+
+ totzeros = Zeros [s+1] ; /* current # of zeros in s+1 */
+
+ /* determine if supernodes s and s+1 should merge */
+ if (ns <= nrelax0)
+ {
+ PRINT2 (("ns is tiny ("ID"), so go ahead and merge\n", ns)) ;
+ merge = TRUE ;
+ }
+ else
+ {
+ /* use double to avoid integer overflow */
+ double lnz0 = Snz [s] ; /* # entries in leading column of s */
+ double lnz1 = Snz [s+1] ; /* # entries in leading column of s+1 */
+ double xnewzeros = nscol0 * (lnz1 + nscol0 - lnz0) ;
+
+ /* use Int for the final update of Zeros [s] below */
+ newzeros = nscol0 * (Snz [s+1] + nscol0 - Snz [s]) ;
+ ASSERT (newzeros == xnewzeros) ;
+
+ PRINT2 (("lnz0 %g lnz1 %g xnewzeros %g\n", lnz0, lnz1, xnewzeros)) ;
+ if (xnewzeros == 0)
+ {
+ /* no new zeros, so go ahead and merge */
+ PRINT2 (("no new fillin, so go ahead and merge\n")) ;
+ merge = TRUE ;
+ }
+ else
+ {
+ /* # of zeros if merged */
+ double xtotzeros = ((double) totzeros) + xnewzeros ;
+
+ /* xtotsize: total size of merged supernode, if merged: */
+ double xns = (double) ns ;
+ double xtotsize = (xns * (xns+1) / 2) + xns * (lnz1 - nscol1) ;
+ double z = xtotzeros / xtotsize ;
+
+ Int totsize ;
+ totsize = (ns * (ns+1) / 2) + ns * (Snz [s+1] - nscol1) ;
+
+ PRINT2 (("oldzeros "ID" newzeros "ID" xtotsize %g z %g\n",
+ Zeros [s+1], newzeros, xtotsize, z)) ;
+
+ /* use Int for the final update of Zeros [s] below */
+ totzeros += newzeros ;
+
+ /* do not merge if supernode would become too big
+ * (Int overflow). Continue computing; not (yet) an error. */
+ /* fl.pt. compare, but no NaN's can occur here */
+ merge = ((ns <= nrelax1 && z < zrelax0) ||
+ (ns <= nrelax2 && z < zrelax1) ||
+ (z < zrelax2)) &&
+ (xtotsize < Int_max / sizeof (double)) ;
+
+ }
+ }
+
+ if (merge)
+ {
+ PRINT1 (("Merge node s ("ID") and s+1 ("ID")\n", s, s+1)) ;
+ Zeros [s] = totzeros ;
+ Merged [s+1] = s ;
+ Snz [s] = nscol0 + Snz [s+1] ;
+ Nscol [s] += Nscol [s+1] ;
+ }
+ }
+
+ /* contents of Wj no longer needed for Zeros ] */
+ /* contents of Wi no longer needed for Nscol ] */
+ /* contents of Sparent no longer needed (recomputed below) */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the relaxed supernode list */
+ /* ---------------------------------------------------------------------- */
+
+ nsuper = 0 ;
+ for (s = 0 ; s < nfsuper ; s++)
+ {
+ if (Merged [s] == EMPTY)
+ {
+ PRINT1 (("live supernode: "ID" snz "ID"\n", s, Snz [s])) ;
+ Super [nsuper] = Super [s] ;
+ Snz [nsuper] = Snz [s] ;
+ nsuper++ ;
+ }
+ }
+ Super [nsuper] = n ;
+ PRINT1 (("Fundamental supernodes: "ID" relaxed "ID"\n", nfsuper, nsuper)) ;
+
+ /* Merged no longer needed ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the mapping of relaxed nodes to supernodes */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Wj as workspace for SuperMap { */
+
+ /* SuperMap [k] = s if column k is contained in supernode s */
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ for (k = Super [s] ; k < Super [s+1] ; k++)
+ {
+ SuperMap [k] = s ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the relaxed supernodal etree */
+ /* ---------------------------------------------------------------------- */
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ j = Super [s+1] - 1 ; /* last node in supernode s */
+ parent = Parent [j] ; /* parent of last node */
+ Sparent [s] = (parent == EMPTY) ? EMPTY : SuperMap [parent] ;
+ PRINT1 (("new Sparent ["ID"] = "ID"\n", s, Sparent [s])) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the size of L->s and L->x */
+ /* ---------------------------------------------------------------------- */
+
+ ssize = 0 ;
+ xsize = 0 ;
+ xxsize = 0 ;
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ nscol = Super [s+1] - Super [s] ;
+ nsrow = Snz [s] ;
+ ASSERT (nscol > 0) ;
+ ssize += nsrow ;
+ xsize += nscol * nsrow ;
+ /* also compute xsize in double to guard against Int overflow */
+ xxsize += ((double) nscol) * ((double) nsrow) ;
+ if (xxsize > Int_max)
+ {
+ /* Int overflow, clear workspace and return */
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
+ FREE_WORKSPACE ;
+ return (FALSE) ;
+ }
+ ASSERT (ssize > 0 && xsize > 0) ;
+ }
+ xsize = MAX (1, xsize) ;
+ ssize = MAX (1, ssize) ;
+ PRINT1 (("ix sizes: "ID" "ID" nsuper "ID"\n", ssize, xsize, nsuper)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate L (all except real part L->x) */
+ /* ---------------------------------------------------------------------- */
+
+ L->ssize = ssize ;
+ L->xsize = xsize ;
+ L->nsuper = nsuper ;
+
+ CHOLMOD(change_factor) (CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE, L, Common);
+
+ if (Common->status < CHOLMOD_OK)
+ {
+ /* out of memory; L is still a valid simplicial symbolic factor */
+ FREE_WORKSPACE ;
+ return (FALSE) ;
+ }
+
+ DEBUG (CHOLMOD(dump_factor) (L, "L to symbolic super", Common)) ;
+ ASSERT (L->is_ll && L->xtype == CHOLMOD_PATTERN && L->is_super) ;
+
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Ls [0] = 0 ; /* flag for cholmod_check_factor; supernodes are defined */
+ Lsuper = L->super ;
+
+ /* copy the list of relaxed supernodes into the final list in L */
+ for (s = 0 ; s <= nsuper ; s++)
+ {
+ Lsuper [s] = Super [s] ;
+ }
+
+ /* Head no longer needed as workspace for fundamental Super list ) */
+
+ Super = Lsuper ; /* Super is now the list of relaxed supernodes */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct column pointers of relaxed supernodal pattern (L->pi) */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ Lpi [s] = p ;
+ p += Snz [s] ;
+ PRINT1 (("Snz ["ID"] = "ID", Super ["ID"] = "ID"\n",
+ s, Snz [s], s, Super[s])) ;
+ }
+ Lpi [nsuper] = p ;
+ ASSERT ((Int) (L->ssize) == MAX (1,p)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct pointers for supernodal values (L->px) */
+ /* ---------------------------------------------------------------------- */
+
+ p = 0 ;
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ nscol = Super [s+1] - Super [s] ; /* number of columns in s */
+ nsrow = Snz [s] ; /* # of rows, incl triangular part*/
+ Lpx [s] = p ; /* pointer to numerical part of s */
+ p += nscol * nsrow ;
+ }
+ Lpx [s] = p ;
+ ASSERT ((Int) (L->xsize) == MAX (1,p)) ;
+
+ /* Snz no longer needed ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic analysis to construct the relaxed supernodal pattern (L->s) */
+ /* ---------------------------------------------------------------------- */
+
+ Lpi2 = Wi ; /* copy Lpi into Lpi2, using Wi as workspace for Lpi2 [ */
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ Lpi2 [s] = Lpi [s] ;
+ }
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ /* sth supernode is in columns k1 to k2-1.
+ * compute nonzero pattern of L (k1:k2-1,:). */
+
+ /* place rows k1 to k2-1 in leading column of supernode s */
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ PRINT1 (("=========>>> Supernode "ID" k1 "ID" k2-1 "ID"\n",
+ s, k1, k2-1)) ;
+ for (k = k1 ; k < k2 ; k++)
+ {
+ Ls [Lpi2 [s]++] = k ;
+ }
+
+ /* compute nonzero pattern each row k1 to k2-1 */
+ for (k = k1 ; k < k2 ; k++)
+ {
+ /* compute row k of L. In the symmetric case, the pattern of L(k,:)
+ * is the set of nodes reachable in the supernodal etree from any
+ * row i in the nonzero pattern of A(0:k,k). In the unsymmetric
+ * case, the pattern of the kth column of A*A' is the set union
+ * of all columns A(0:k,j) for each nonzero F(j,k). */
+
+ /* clear the Flag array and mark the current supernode */
+ /* mark = CHOLMOD(clear_flag) (Common) ; */
+ CHOLMOD_CLEAR_FLAG (Common) ;
+ mark = Common->mark ;
+ Flag [s] = mark ;
+ ASSERT (s == SuperMap [k]) ;
+
+ /* traverse the row subtree for each nonzero in A or AA' */
+ if (stype != 0)
+ {
+ subtree (k, k, Ap, Ai, Anz, SuperMap, Sparent, mark,
+ Flag, Ls, Lpi2) ;
+ }
+ else
+ {
+ /* for each nonzero in F (k,:) do */
+ p = Fp [k] ;
+ pend = (packed) ? (Fp [k+1]) : (p + Fnz [k]) ;
+ for ( ; p < pend ; p++)
+ {
+ subtree (Fj [p], k, Ap, Ai, Anz, SuperMap, Sparent, mark,
+ Flag, Ls, Lpi2) ;
+ }
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ PRINT1 (("Lpi2[s] "ID" Lpi[s+1] "ID"\n", Lpi2 [s], Lpi [s+1])) ;
+ ASSERT (Lpi2 [s] == Lpi [s+1]) ;
+ CHOLMOD(dump_super) (s, Super, Lpi, Ls, NULL, NULL, 0, Common) ;
+ }
+#endif
+
+ /* contents of Wi no longer needed for Lpi2 ] */
+ /* Sparent no longer needed ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the largest update matrix (L->maxcsize) */
+ /* ---------------------------------------------------------------------- */
+
+ /* maxcsize could be determined before L->s is allocated and defined, which
+ * would mean that all memory requirements for both the symbolic and numeric
+ * factorizations could be computed using O(nnz(A)+O(n)) space. However, it
+ * would require a lot of extra work. The analysis phase, above, would need
+ * to be duplicated, but with Ls not kept; instead, the algorithm would keep
+ * track of the current s and slast for each supernode d, and update them
+ * when a new row index appears in supernode d. An alternative would be to
+ * do this computation only if the allocation of L->s failed, in which case
+ * the following code would be skipped.
+ *
+ * The csize for a supernode is the size of its largest contribution to
+ * a subsequent ancestor supernode. For example, suppose the rows of #'s
+ * in the figure below correspond to the columns of a subsequent supernode,
+ * and the dots are the entries in that ancestore.
+ *
+ * c
+ * c c
+ * c c c
+ * x x x
+ * x x x
+ * # # # .
+ * # # # . .
+ * * * * . .
+ * * * * . .
+ * * * * . .
+ * . .
+ *
+ * Then for this update, the csize is 3-by-2, or 6, because there are 3
+ * rows of *'s which is the number of rows in the update, and there are
+ * 2 rows of #'s, which is the number columns in the update. The csize
+ * of a supernode is the largest such contribution for any ancestor
+ * supernode. maxcsize, for the whole matrix, has a rough upper bound of
+ * the maximum size of any supernode. This bound is loose, because the
+ * the contribution must be less than the size of the ancestor supernodal
+ * that it's updating. maxcsize of a completely dense matrix, with one
+ * supernode, is zero.
+ *
+ * maxesize is the column dimension for the workspace E needed for the
+ * solve. E is of size nrhs-by-maxesize, where the nrhs is the number of
+ * columns in the right-hand-side. The maxesize is the largest esize of
+ * any supernode. The esize of a supernode is the number of row indices
+ * it contains, excluding the column indices of the supernode itself.
+ * For the following example, esize is 4:
+ *
+ * c
+ * c c
+ * c c c
+ * x x x
+ * x x x
+ * x x x
+ * x x x
+ *
+ * maxesize can be no bigger than n.
+ */
+
+ maxcsize = 1 ;
+ maxesize = 1 ;
+
+ /* do not need to guard csize against Int overflow if xsize is OK */
+
+ for (d = 0 ; d < nsuper ; d++)
+ {
+ nscol = Super [d+1] - Super [d] ;
+ p = Lpi [d] + nscol ;
+ plast = p ;
+ pend = Lpi [d+1] ;
+ esize = pend - p ;
+ maxesize = MAX (maxesize, esize) ;
+ slast = (p == pend) ? (EMPTY) : (SuperMap [Ls [p]]) ;
+ for ( ; p <= pend ; p++)
+ {
+ s = (p == pend) ? (EMPTY) : (SuperMap [Ls [p]]) ;
+ if (s != slast)
+ {
+ /* row i is the start of a new supernode */
+ ndrow1 = p - plast ;
+ ndrow2 = pend - plast ;
+ csize = ndrow2 * ndrow1 ;
+ PRINT1 (("Supernode "ID" ancestor "ID" C: "ID"-by-"ID" csize "
+ ""ID"\n", d, slast, ndrow1, ndrow2, csize)) ;
+ maxcsize = MAX (maxcsize, csize) ;
+ plast = p ;
+ slast = s ;
+ }
+ }
+ }
+ PRINT1 (("max csize "ID"\n", maxcsize)) ;
+
+ /* Wj no longer needed for SuperMap } */
+
+ L->maxcsize = maxcsize ;
+ L->maxesize = maxesize ;
+ L->is_super = TRUE ;
+ ASSERT (L->xtype == CHOLMOD_PATTERN && L->is_ll) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal symbolic factorization is complete */
+ /* ---------------------------------------------------------------------- */
+
+ FREE_WORKSPACE ;
+ return (TRUE) ;
+}
+#endif
diff --git a/CHOLMOD/Supernodal/gpl.txt b/CHOLMOD/Supernodal/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/CHOLMOD/Supernodal/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
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diff --git a/CHOLMOD/Supernodal/t_cholmod_super_numeric.c b/CHOLMOD/Supernodal/t_cholmod_super_numeric.c
new file mode 100644
index 0000000..4757721
--- /dev/null
+++ b/CHOLMOD/Supernodal/t_cholmod_super_numeric.c
@@ -0,0 +1,741 @@
+/* ========================================================================== */
+/* === Supernodal/t_cholmod_super_numeric =================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_super_numeric. All xtypes supported, except
+ * that a zomplex A and F result in a complex L (there is no supernodal
+ * zomplex L).
+ */
+
+/* ========================================================================== */
+/* === complex arithmetic =================================================== */
+/* ========================================================================== */
+
+#include "cholmod_template.h"
+
+#undef L_ENTRY
+#undef L_CLEAR
+#undef L_ASSIGN
+#undef L_MULTADD
+#undef L_ASSEMBLE
+#undef L_ASSEMBLESUB
+
+#ifdef REAL
+
+/* -------------------------------------------------------------------------- */
+/* A, F, and L are all real */
+/* -------------------------------------------------------------------------- */
+
+#define L_ENTRY 1
+#define L_CLEAR(Lx,p) Lx [p] = 0
+#define L_ASSIGN(Lx,q, Ax,Az,p) Lx [q] = Ax [p]
+#define L_MULTADD(Lx,q, Ax,Az,p, f) Lx [q] += Ax [p] * f [0]
+#define L_ASSEMBLE(Lx,q,b) Lx [q] += b [0]
+#define L_ASSEMBLESUB(Lx,q,C,p) Lx [q] -= C [p]
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* A and F are complex or zomplex, L and C are complex */
+/* -------------------------------------------------------------------------- */
+
+#define L_ENTRY 2
+#define L_CLEAR(Lx,p) Lx [2*(p)] = 0 ; Lx [2*(p)+1] = 0
+#define L_ASSEMBLE(Lx,q,b) Lx [2*(q)] += b [0] ;
+#define L_ASSEMBLESUB(Lx,q,C,p) \
+ Lx [2*(q) ] -= C [2*(p) ] ; \
+ Lx [2*(q)+1] -= C [2*(p)+1] ;
+
+#ifdef COMPLEX
+
+/* -------------------------------------------------------------------------- */
+/* A, F, L, and C are all complex */
+/* -------------------------------------------------------------------------- */
+
+#define L_ASSIGN(Lx,q, Ax,Az,p) \
+ Lx [2*(q) ] = Ax [2*(p) ] ; \
+ Lx [2*(q)+1] = Ax [2*(p)+1]
+
+#define L_MULTADD(Lx,q, Ax,Az,p, f) \
+ Lx [2*(q) ] += Ax [2*(p) ] * f [0] - Ax [2*(p)+1] * f [1] ; \
+ Lx [2*(q)+1] += Ax [2*(p)+1] * f [0] + Ax [2*(p) ] * f [1]
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* A and F are zomplex, L and C is complex */
+/* -------------------------------------------------------------------------- */
+
+#define L_ASSIGN(Lx,q, Ax,Az,p) \
+ Lx [2*(q) ] = Ax [p] ; \
+ Lx [2*(q)+1] = Az [p] ;
+
+#define L_MULTADD(Lx,q, Ax,Az,p, f) \
+ Lx [2*(q) ] += Ax [p] * f [0] - Az [p] * f [1] ; \
+ Lx [2*(q)+1] += Az [p] * f [0] + Ax [p] * f [1]
+
+#endif
+#endif
+
+
+/* ========================================================================== */
+/* === t_cholmod_super_numeric ============================================== */
+/* ========================================================================== */
+
+/* This function returns FALSE only if integer overflow occurs in the BLAS.
+ * It returns TRUE otherwise whether or not the matrix is positive definite. */
+
+static int TEMPLATE (cholmod_super_numeric)
+(
+ /* ---- input ---- */
+ cholmod_sparse *A, /* matrix to factorize */
+ cholmod_sparse *F, /* F = A' or A(:,f)' */
+ double beta [2], /* beta*I is added to diagonal of matrix to factorize */
+ /* ---- in/out --- */
+ cholmod_factor *L, /* factorization */
+ /* -- workspace -- */
+ cholmod_dense *Cwork, /* size (L->maxcsize)-by-1 */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double one [2], zero [2], fjk [2] ;
+ double *Lx, *Ax, *Fx, *Az, *Fz, *C ;
+ Int *Super, *Head, *Ls, *Lpi, *Lpx, *Map, *SuperMap, *RelativeMap, *Next,
+ *Lpos, *Fp, *Fi, *Fnz, *Ap, *Ai, *Anz, *Iwork, *Next_save, *Lpos_save ;
+ Int nsuper, n, j, i, k, s, p, pend, k1, k2, nscol, psi, psx, psend, nsrow,
+ pj, d, kd1, kd2, info, ndcol, ndrow, pdi, pdx, pdend, pdi1, pdi2, pdx1,
+ ndrow1, ndrow2, px, dancestor, sparent, dnext, nsrow2, ndrow3, pk, pf,
+ pfend, stype, Apacked, Fpacked, q, imap, repeat_supernode, nscol2, ss,
+ nscol_new = 0 ;
+
+ /* If integer overflow occurs in the BLAS, Common->status is set to
+ * CHOLMOD_TOO_LARGE, and the contents of Lx are undefined. */
+ int blas_ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nsuper = L->nsuper ;
+ n = L->n ;
+
+ C = Cwork->x ; /* workspace of size L->maxcsize */
+
+ one [0] = 1.0 ; /* ALPHA for *syrk, *herk, *gemm, and *trsm */
+ one [1] = 0. ;
+
+ zero [0] = 0. ; /* BETA for *syrk, *herk, and *gemm */
+ zero [1] = 0. ;
+
+ Iwork = Common->Iwork ;
+ SuperMap = Iwork ; /* size n (i/i/l) */
+ RelativeMap = Iwork + n ; /* size n (i/i/l) */
+ Next = Iwork + 2*((size_t) n) ; /* size nsuper*/
+ Lpos = Iwork + 2*((size_t) n) + nsuper ; /* size nsuper*/
+ Next_save = Iwork + 2*((size_t) n) + 2*((size_t) nsuper) ;/* size nsuper*/
+ Lpos_save = Iwork + 2*((size_t) n) + 3*((size_t) nsuper) ;/* size nsuper*/
+
+ Map = Common->Flag ; /* size n, use Flag as workspace for Map array */
+ Head = Common->Head ; /* size n+1, only Head [0..nsuper-1] used */
+
+ Ls = L->s ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+
+ Super = L->super ;
+
+ Lx = L->x ;
+
+ stype = A->stype ;
+
+ if (stype != 0)
+ {
+ /* F not accessed */
+ Fp = NULL ;
+ Fi = NULL ;
+ Fx = NULL ;
+ Fz = NULL ;
+ Fnz = NULL ;
+ Fpacked = TRUE ;
+ }
+ else
+ {
+ Fp = F->p ;
+ Fi = F->i ;
+ Fx = F->x ;
+ Fz = F->z ;
+ Fnz = F->nz ;
+ Fpacked = F->packed ;
+ }
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+ Apacked = A->packed ;
+
+ /* clear the Map so that changes in the pattern of A can be detected */
+ for (i = 0 ; i < n ; i++)
+ {
+ Map [i] = EMPTY ;
+ }
+
+ /* If the matrix is not positive definite, the supernode s containing the
+ * first zero or negative diagonal entry of L is repeated (but factorized
+ * only up to just before the problematic diagonal entry). The purpose is
+ * to provide MATLAB with [R,p]=chol(A); columns 1 to p-1 of L=R' are
+ * required, where L(p,p) is the problematic diagonal entry. The
+ * repeat_supernode flag tells us whether this is the repeated supernode.
+ * Once supernode s is repeated, the factorization is terminated. */
+ repeat_supernode = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal numerical factorization */
+ /* ---------------------------------------------------------------------- */
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the size of supernode s */
+ /* ------------------------------------------------------------------ */
+
+ k1 = Super [s] ; /* s contains columns k1 to k2-1 of L */
+ k2 = Super [s+1] ;
+ nscol = k2 - k1 ; /* # of columns in all of s */
+ psi = Lpi [s] ; /* pointer to first row of s in Ls */
+ psx = Lpx [s] ; /* pointer to first row of s in Lx */
+ psend = Lpi [s+1] ; /* pointer just past last row of s in Ls */
+ nsrow = psend - psi ; /* # of rows in all of s */
+
+ PRINT1 (("====================================================\n"
+ "S "ID" k1 "ID" k2 "ID" nsrow "ID" nscol "ID" psi "ID" psend "
+ ""ID" psx "ID"\n", s, k1, k2, nsrow, nscol, psi, psend, psx)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* zero the supernode s */
+ /* ------------------------------------------------------------------ */
+
+ ASSERT ((size_t) (psx + nsrow*nscol) <= L->xsize) ;
+
+ pend = psx + nsrow * nscol ; /* s is nsrow-by-nscol */
+ for (p = psx ; p < pend ; p++)
+ {
+ /* Lx [p] = 0 ; */
+ L_CLEAR (Lx,p) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* construct the scattered Map for supernode s */
+ /* ------------------------------------------------------------------ */
+
+ /* If row i is the kth row in s, then Map [i] = k. Similarly, if
+ * column j is the kth column in s, then Map [j] = k. */
+
+ for (k = 0 ; k < nsrow ; k++)
+ {
+ PRINT1 ((" "ID" map "ID"\n", Ls [psi+k], k)) ;
+ Map [Ls [psi + k]] = k ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* copy matrix into supernode s (lower triangular part only) */
+ /* ------------------------------------------------------------------ */
+
+ pk = psx ;
+ for (k = k1 ; k < k2 ; k++)
+ {
+ if (stype != 0)
+ {
+ /* copy the kth column of A into the supernode */
+ p = Ap [k] ;
+ pend = (Apacked) ? (Ap [k+1]) : (p + Anz [k]) ;
+ for ( ; p < pend ; p++)
+ {
+ /* row i of L is located in row Map [i] of s */
+ i = Ai [p] ;
+ if (i >= k)
+ {
+ /* This test is here simply to avoid a segfault. If
+ * the test is false, the numeric factorization of A
+ * is undefined. It does not detect all invalid
+ * entries, only some of them (when debugging is
+ * enabled, and Map is cleared after each step, then
+ * all entries not in the pattern of L are detected). */
+ imap = Map [i] ;
+ if (imap >= 0 && imap < nsrow)
+ {
+ /* Lx [Map [i] + pk] = Ax [p] ; */
+ L_ASSIGN (Lx,(imap+pk), Ax,Az,p) ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* copy the kth column of A*F into the supernode */
+ pf = Fp [k] ;
+ pfend = (Fpacked) ? (Fp [k+1]) : (p + Fnz [k]) ;
+ for ( ; pf < pfend ; pf++)
+ {
+ j = Fi [pf] ;
+
+ /* fjk = Fx [pf] ; */
+ L_ASSIGN (fjk,0, Fx,Fz,pf) ;
+
+ p = Ap [j] ;
+ pend = (Apacked) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i >= k)
+ {
+ /* See the discussion of imap above. */
+ imap = Map [i] ;
+ if (imap >= 0 && imap < nsrow)
+ {
+ /* Lx [Map [i] + pk] += Ax [p] * fjk ; */
+ L_MULTADD (Lx,(imap+pk), Ax,Az,p, fjk) ;
+ }
+ }
+ }
+ }
+ }
+ pk += nsrow ; /* advance to the next column of the supernode */
+ }
+
+ /* add beta to the diagonal of the supernode, if nonzero */
+ if (beta [0] != 0.0)
+ {
+ /* note that only the real part of beta is used */
+ pk = psx ;
+ for (k = k1 ; k < k2 ; k++)
+ {
+ /* Lx [pk] += beta [0] ; */
+ L_ASSEMBLE (Lx,pk, beta) ;
+ pk += nsrow + 1 ; /* advance to the next diagonal entry */
+ }
+ }
+
+ PRINT1 (("Supernode with just A: repeat: "ID"\n", repeat_supernode)) ;
+ DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY,
+ Common)) ;
+ PRINT1 (("\n\n")) ;
+
+ /* ------------------------------------------------------------------ */
+ /* save/restore the list of supernodes */
+ /* ------------------------------------------------------------------ */
+
+ if (!repeat_supernode)
+ {
+ /* Save the list of pending descendants in case s is not positive
+ * definite. Also save Lpos for each descendant d, so that we can
+ * find which part of d is used to update s. */
+ for (d = Head [s] ; d != EMPTY ; d = Next [d])
+ {
+ Lpos_save [d] = Lpos [d] ;
+ Next_save [d] = Next [d] ;
+ }
+ }
+ else
+ {
+ /* s is not positive definite, and is being repeated. Restore
+ * the list of supernodes. This can be done with pointer assignment
+ * because all 4 arrays are held within Common->Iwork. */
+ Lpos = Lpos_save ;
+ Next = Next_save ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* update supernode s with each pending descendant d */
+ /* ------------------------------------------------------------------ */
+
+#ifndef NDEBUG
+ for (d = Head [s] ; d != EMPTY ; d = Next [d])
+ {
+ PRINT1 (("\nWill update "ID" with Child: "ID"\n", s, d)) ;
+ DEBUG (CHOLMOD(dump_super) (d, Super, Lpi, Ls, Lpx, Lx, L_ENTRY,
+ Common)) ;
+ }
+ PRINT1 (("\nNow factorizing supernode "ID":\n", s)) ;
+#endif
+
+ for (d = Head [s] ; d != EMPTY ; d = dnext)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* get the size of supernode d */
+ /* -------------------------------------------------------------- */
+
+ kd1 = Super [d] ; /* d contains cols kd1 to kd2-1 of L */
+ kd2 = Super [d+1] ;
+ ndcol = kd2 - kd1 ; /* # of columns in all of d */
+ pdi = Lpi [d] ; /* pointer to first row of d in Ls */
+ pdx = Lpx [d] ; /* pointer to first row of d in Lx */
+ pdend = Lpi [d+1] ; /* pointer just past last row of d in Ls */
+ ndrow = pdend - pdi ; /* # rows in all of d */
+
+ PRINT1 (("Child: ")) ;
+ DEBUG (CHOLMOD(dump_super) (d, Super, Lpi, Ls, Lpx, Lx, L_ENTRY,
+ Common)) ;
+
+ /* -------------------------------------------------------------- */
+ /* find the range of rows of d that affect rows k1 to k2-1 of s */
+ /* -------------------------------------------------------------- */
+
+ p = Lpos [d] ; /* offset of 1st row of d affecting s */
+ pdi1 = pdi + p ; /* ptr to 1st row of d affecting s in Ls */
+ pdx1 = pdx + p ; /* ptr to 1st row of d affecting s in Lx */
+
+ /* there must be at least one row remaining in d to update s */
+ ASSERT (pdi1 < pdend) ;
+ PRINT1 (("Lpos[d] "ID" pdi1 "ID" Ls[pdi1] "ID"\n",
+ Lpos[d], pdi1, Ls [pdi1])) ;
+ ASSERT (Ls [pdi1] >= k1 && Ls [pdi1] < k2) ;
+
+ for (pdi2 = pdi1 ; pdi2 < pdend && Ls [pdi2] < k2 ; pdi2++) ;
+ ndrow1 = pdi2 - pdi1 ; /* # rows in first part of d */
+ ndrow2 = pdend - pdi1 ; /* # rows in remaining d */
+
+ /* rows Ls [pdi1 ... pdi2-1] are in the range k1 to k2-1. Since d
+ * affects s, this set cannot be empty. */
+ ASSERT (pdi1 < pdi2 && pdi2 <= pdend) ;
+ PRINT1 (("ndrow1 "ID" ndrow2 "ID"\n", ndrow1, ndrow2)) ;
+ DEBUG (for (p = pdi1 ; p < pdi2 ; p++)
+ PRINT1 (("Ls["ID"] "ID"\n", p, Ls[p]))) ;
+
+ /* -------------------------------------------------------------- */
+ /* construct the update matrix C for this supernode d */
+ /* -------------------------------------------------------------- */
+
+ /* C = L (k1:n-1, kd1:kd2-1) * L (k1:k2-1, kd1:kd2-1)', except
+ * that k1:n-1 refers to all of the rows in L, but many of the
+ * rows are all zero. Supernode d holds columns kd1 to kd2-1 of L.
+ * Nonzero rows in the range k1:k2-1 are in the list
+ * Ls [pdi1 ... pdi2-1], of size ndrow1. Nonzero rows in the range
+ * k2:n-1 are in the list Ls [pdi2 ... pdend], of size ndrow2. Let
+ * L1 = L (Ls [pdi1 ... pdi2-1], kd1:kd2-1), and let
+ * L2 = L (Ls [pdi2 ... pdend], kd1:kd2-1). C is ndrow2-by-ndcol.
+ * Let C1 be the first ndrow1 rows of C and let C2 be the last
+ * ndrow2-ndrow1 rows of C. Only the lower triangular part of C1
+ * needs to be computed since C1 is symmetric.
+ */
+
+ /* maxcsize is the largest size of C for all pairs (d,s) */
+ ASSERT (ndrow2 * ndrow1 <= ((Int) L->maxcsize)) ;
+
+ /* compute leading ndrow1-by-ndrow1 lower triangular block of C,
+ * C1 = L1*L1' */
+
+#ifdef REAL
+ BLAS_dsyrk ("L", "N",
+ ndrow1, ndcol, /* N, K: L1 is ndrow1-by-ndcol*/
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*pdx1, ndrow, /* A, LDA: L1, ndrow */
+ zero, /* BETA: 0 */
+ C, ndrow2) ; /* C, LDC: C1 */
+#else
+ BLAS_zherk ("L", "N",
+ ndrow1, ndcol, /* N, K: L1 is ndrow1-by-ndcol*/
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*pdx1, ndrow, /* A, LDA: L1, ndrow */
+ zero, /* BETA: 0 */
+ C, ndrow2) ; /* C, LDC: C1 */
+#endif
+
+ /* compute remaining (ndrow3-ndrow1)-by-ndrow1 block of C,
+ * C2 = L2*L1' */
+ ndrow3 = ndrow2 - ndrow1 ;
+ if (ndrow3 > 0)
+ {
+
+#ifdef REAL
+ BLAS_dgemm ("N", "C",
+ ndrow3, ndrow1, ndcol, /* M, N, K */
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*(pdx1 + ndrow1),/* A, LDA: L2, ndrow */
+ ndrow,
+ Lx + L_ENTRY*pdx1, /* B, LDB: L1, ndrow */
+ ndrow,
+ zero, /* BETA: 0 */
+ C + L_ENTRY*ndrow1, /* C, LDC: C2 */
+ ndrow2) ;
+#else
+ BLAS_zgemm ("N", "C",
+ ndrow3, ndrow1, ndcol, /* M, N, K */
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*(pdx1 + ndrow1),/* A, LDA: L2, ndrow */
+ ndrow,
+ Lx + L_ENTRY*pdx1, /* B, LDB: L1, ndrow */
+ ndrow,
+ zero, /* BETA: 0 */
+ C + L_ENTRY*ndrow1, /* C, LDC: C2 */
+ ndrow2) ;
+#endif
+
+ }
+
+ DEBUG (CHOLMOD(dump_real) ("C", C, ndrow2, ndrow1, TRUE, L_ENTRY,
+ Common)) ;
+
+ /* -------------------------------------------------------------- */
+ /* construct relative map to assemble d into s */
+ /* -------------------------------------------------------------- */
+
+ for (i = 0 ; i < ndrow2 ; i++)
+ {
+ RelativeMap [i] = Map [Ls [pdi1 + i]] ;
+ ASSERT (RelativeMap [i] >= 0 && RelativeMap [i] < nsrow) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* assemble C into supernode s using the relative map */
+ /* -------------------------------------------------------------- */
+
+ pj = 0 ;
+ for (j = 0 ; j < ndrow1 ; j++) /* cols k1:k2-1 */
+ {
+ ASSERT (RelativeMap [j] == Map [Ls [pdi1 + j]]) ;
+ ASSERT (RelativeMap [j] >= 0 && RelativeMap [j] < nscol) ;
+ px = psx + RelativeMap [j] * nsrow ;
+ for (i = j ; i < ndrow2 ; i++) /* rows k1:n-1 */
+ {
+ ASSERT (RelativeMap [i] == Map [Ls [pdi1 + i]]) ;
+ ASSERT (RelativeMap [i] >= j && RelativeMap [i] < nsrow) ;
+ /* Lx [px + RelativeMap [i]] -= C [i + pj] ; */
+ q = px + RelativeMap [i] ;
+ L_ASSEMBLESUB (Lx,q, C, i+pj) ;
+ }
+ pj += ndrow2 ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* prepare this supernode d for its next ancestor */
+ /* -------------------------------------------------------------- */
+
+ dnext = Next [d] ;
+
+ if (!repeat_supernode)
+ {
+ /* If node s is being repeated, Head [dancestor] has already
+ * been cleared (set to EMPTY). It must remain EMPTY. The
+ * dancestor will not be factorized since the factorization
+ * terminates at node s. */
+ Lpos [d] = pdi2 - pdi ;
+ if (Lpos [d] < ndrow)
+ {
+ dancestor = SuperMap [Ls [pdi2]] ;
+ ASSERT (dancestor > s && dancestor < nsuper) ;
+ /* place d in the link list of its next ancestor */
+ Next [d] = Head [dancestor] ;
+ Head [dancestor] = d ;
+ }
+ }
+ }
+
+ PRINT1 (("\nSupernode with contributions A: repeat: "ID"\n",
+ repeat_supernode)) ;
+ DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY,
+ Common)) ;
+ PRINT1 (("\n\n")) ;
+
+ /* ------------------------------------------------------------------ */
+ /* factorize diagonal block of supernode s in LL' */
+ /* ------------------------------------------------------------------ */
+
+ /* The current supernode s is ready to factorize. It has been updated
+ * by all descendant supernodes. Let S = the current supernode, which
+ * holds rows k1:n-1 and columns k1:k2-1 of the updated matrix. It
+ * splits into two parts: the square diagonal block S1, and the
+ * rectangular part S2. Here, S1 is factorized into L1*L1' and
+ * overwritten by S1.
+ *
+ * If supernode s is being repeated, only factorize it up to but not
+ * including the column containing the problematic entry.
+ */
+
+ nscol2 = (repeat_supernode) ? (nscol_new) : (nscol) ;
+
+#ifdef REAL
+ LAPACK_dpotrf ("L",
+ nscol2, /* N: nscol2 */
+ Lx + L_ENTRY*psx, nsrow, /* A, LDA: S1, nsrow */
+ info) ; /* INFO */
+#else
+ LAPACK_zpotrf ("L",
+ nscol2, /* N: nscol2 */
+ Lx + L_ENTRY*psx, nsrow, /* A, LDA: S1, nsrow */
+ info) ; /* INFO */
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* check if the matrix is not positive definite */
+ /* ------------------------------------------------------------------ */
+
+ if (repeat_supernode)
+ {
+ /* the leading part has been refactorized; it must have succeeded */
+ info = 0 ;
+
+ /* zero out the rest of this supernode */
+ p = psx + nsrow * nscol_new ;
+ pend = psx + nsrow * nscol ; /* s is nsrow-by-nscol */
+ for ( ; p < pend ; p++)
+ {
+ /* Lx [p] = 0 ; */
+ L_CLEAR (Lx,p) ;
+ }
+ }
+
+ /* info is set to one in LAPACK_*potrf if blas_ok is FALSE. It is
+ * set to zero in dpotrf/zpotrf if the factorization was successful. */
+ if (CHECK_BLAS_INT && !blas_ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ;
+ }
+
+ if (info != 0)
+ {
+ /* Matrix is not positive definite. dpotrf/zpotrf do NOT report an
+ * error if the diagonal of L has NaN's, only if it has a zero. */
+ if (Common->status == CHOLMOD_OK)
+ {
+ ERROR (CHOLMOD_NOT_POSDEF, "matrix not positive definite") ;
+ }
+
+ /* L->minor is the column of L that contains a zero or negative
+ * diagonal term. */
+ L->minor = k1 + info - 1 ;
+
+ /* clear the link lists of all subsequent supernodes */
+ for (ss = s+1 ; ss < nsuper ; ss++)
+ {
+ Head [ss] = EMPTY ;
+ }
+
+ /* zero this supernode, and all remaining supernodes */
+ pend = L->xsize ;
+ for (p = psx ; p < pend ; p++)
+ {
+ /* Lx [p] = 0. ; */
+ L_CLEAR (Lx,p) ;
+ }
+
+ /* If L is indefinite, it still contains useful information.
+ * Supernodes 0 to s-1 are valid, similar to MATLAB [R,p]=chol(A),
+ * where the 1-based p is identical to the 0-based L->minor. Since
+ * L->minor is in the current supernode s, it and any columns to the
+ * left of it in supernode s are also all zero. This differs from
+ * [R,p]=chol(A), which contains nonzero rows 1 to p-1. Fix this
+ * by setting repeat_supernode to TRUE, and repeating supernode s.
+ *
+ * If Common->quick_return_if_not_posdef is true, then the entire
+ * supernode s is not factorized; it is left as all zero.
+ */
+
+ if (info == 1 || Common->quick_return_if_not_posdef)
+ {
+ /* If the first column of supernode s contains a zero or
+ * negative diagonal entry, then it is already properly set to
+ * zero. Also, info will be 1 if integer overflow occured in
+ * the BLAS. */
+ Head [s] = EMPTY ;
+ return (Common->status >= CHOLMOD_OK) ;
+ }
+ else
+ {
+ /* Repeat supernode s, but only factorize it up to but not
+ * including the column containing the problematic diagonal
+ * entry. */
+ repeat_supernode = TRUE ;
+ s-- ;
+ nscol_new = info - 1 ;
+ continue ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* compute the subdiagonal block and prepare supernode for its parent */
+ /* ------------------------------------------------------------------ */
+
+ nsrow2 = nsrow - nscol2 ;
+ if (nsrow2 > 0)
+ {
+ /* The current supernode is columns k1 to k2-1 of L. Let L1 be the
+ * diagonal block (factorized by dpotrf/zpotrf above; rows/cols
+ * k1:k2-1), and L2 be rows k2:n-1 and columns k1:k2-1 of L. The
+ * triangular system to solve is L2*L1' = S2, where S2 is
+ * overwritten with L2. More precisely, L2 = S2 / L1' in MATLAB
+ * notation.
+ */
+
+#ifdef REAL
+ BLAS_dtrsm ("R", "L", "C", "N",
+ nsrow2, nscol2, /* M, N */
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*psx, nsrow, /* A, LDA: L1, nsrow */
+ Lx + L_ENTRY*(psx + nscol2), /* B, LDB, L2, nsrow */
+ nsrow) ;
+#else
+ BLAS_ztrsm ("R", "L", "C", "N",
+ nsrow2, nscol2, /* M, N */
+ one, /* ALPHA: 1 */
+ Lx + L_ENTRY*psx, nsrow, /* A, LDA: L1, nsrow */
+ Lx + L_ENTRY*(psx + nscol2), /* B, LDB, L2, nsrow */
+ nsrow) ;
+#endif
+
+ if (CHECK_BLAS_INT && !blas_ok)
+ {
+ ERROR (CHOLMOD_TOO_LARGE, "problem too large for the BLAS") ;
+ }
+
+ if (!repeat_supernode)
+ {
+ /* Lpos [s] is offset of first row of s affecting its parent */
+ Lpos [s] = nscol ;
+ sparent = SuperMap [Ls [psi + nscol]] ;
+ ASSERT (sparent != EMPTY) ;
+ ASSERT (Ls [psi + nscol] >= Super [sparent]) ;
+ ASSERT (Ls [psi + nscol] < Super [sparent+1]) ;
+ ASSERT (SuperMap [Ls [psi + nscol]] == sparent) ;
+ ASSERT (sparent > s && sparent < nsuper) ;
+ /* place s in link list of its parent */
+ Next [s] = Head [sparent] ;
+ Head [sparent] = s ;
+ }
+ }
+
+ Head [s] = EMPTY ; /* link list for supernode s no longer needed */
+
+ /* clear the Map (debugging only, to detect changes in pattern of A) */
+ DEBUG (for (k = 0 ; k < nsrow ; k++) Map [Ls [psi + k]] = EMPTY) ;
+ DEBUG (CHOLMOD(dump_super) (s, Super, Lpi, Ls, Lpx, Lx, L_ENTRY,
+ Common)) ;
+
+ if (repeat_supernode)
+ {
+ /* matrix is not positive definite; finished clean-up for supernode
+ * containing negative diagonal */
+ return (Common->status >= CHOLMOD_OK) ;
+ }
+ }
+
+ /* success; matrix is positive definite */
+ L->minor = n ;
+ return (Common->status >= CHOLMOD_OK) ;
+}
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/CHOLMOD/Supernodal/t_cholmod_super_solve.c b/CHOLMOD/Supernodal/t_cholmod_super_solve.c
new file mode 100644
index 0000000..2f5e792
--- /dev/null
+++ b/CHOLMOD/Supernodal/t_cholmod_super_solve.c
@@ -0,0 +1,430 @@
+/* ========================================================================== */
+/* === Supernodal/t_cholmod_super_solve ===================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Supernodal Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Supernodal Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Template routine for cholmod_super_solve. Supports real or complex L. */
+
+#include "cholmod_template.h"
+
+static int TEMPLATE (cholmod_super_lsolve)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the forward solve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to Lx=b on output */
+ /* ---- workspace ---- */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Lx, *Xx, *Ex ;
+ double minus_one [2], one [2] ;
+ Int *Lpi, *Lpx, *Ls, *Super ;
+ Int nsuper, k1, k2, psi, psend, psx, nsrow, nscol, ii, s,
+ nsrow2, n, ps2, j, i, d, nrhs ;
+
+ /* If integer overflow occurs in the BLAS, Common->status is set to
+ * CHOLMOD_TOO_LARGE in the caller, and the contents of X are undefined. */
+ int blas_ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrhs = X->ncol ;
+ Ex = E->x ;
+ Xx = X->x ;
+ n = L->n ;
+ d = X->d ;
+
+ nsuper = L->nsuper ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Super = L->super ;
+ Lx = L->x ;
+ minus_one [0] = -1.0 ;
+ minus_one [1] = 0 ;
+ one [0] = 1.0 ;
+ one [1] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Lx=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrhs == 1)
+ {
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ nsrow2 = nsrow - nscol ;
+ ps2 = psi + nscol ;
+ ASSERT ((size_t) nsrow2 <= L->maxesize) ;
+
+ /* L1 is nscol-by-nscol, lower triangular with non-unit diagonal.
+ * L2 is nsrow2-by-nscol. L1 and L2 have leading dimension of
+ * nsrow. x1 is nscol-by-nsrow, with leading dimension n.
+ * E is nsrow2-by-1, with leading dimension nsrow2.
+ */
+
+ /* gather X into E */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ /* Ex [ii] = Xx [Ls [ps2 + ii]] ; */
+ ASSIGN (Ex,-,ii, Xx,-,Ls [ps2 + ii]) ;
+ }
+
+#ifdef REAL
+
+ /* solve L1*x1 (that is, x1 = L1\x1) */
+ BLAS_dtrsv ("L", "N", "N",
+ nscol, /* N: L1 is nscol-by-nscol */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */
+
+ /* E = E - L2*x1 */
+ BLAS_dgemv ("N",
+ nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Xx + ENTRY_SIZE*k1, 1, /* X, INCX: x1 */
+ one, /* BETA: 1 */
+ Ex, 1) ; /* Y, INCY: E */
+
+#else
+
+ /* solve L1*x1 (that is, x1 = L1\x1) */
+ BLAS_ztrsv ("L", "N", "N",
+ nscol, /* N: L1 is nscol-by-nscol */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */
+
+ /* E = E - L2*x1 */
+ BLAS_zgemv ("N",
+ nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Xx + ENTRY_SIZE*k1, 1, /* X, INCX: x1 */
+ one, /* BETA: 1 */
+ Ex, 1) ; /* Y, INCY: E */
+
+#endif
+
+ /* scatter E back into X */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ /* Xx [Ls [ps2 + ii]] = Ex [ii] ; */
+ ASSIGN (Xx,-,Ls [ps2 + ii], Ex,-,ii) ;
+ }
+ }
+ }
+ else
+ {
+
+ for (s = 0 ; s < nsuper ; s++)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ nsrow2 = nsrow - nscol ;
+ ps2 = psi + nscol ;
+ ASSERT ((size_t) nsrow2 <= L->maxesize) ;
+
+ /* E is nsrow2-by-nrhs, with leading dimension nsrow2. */
+
+ /* gather X into E */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ i = Ls [ps2 + ii] ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ /* Ex [ii + j*nsrow2] = Xx [i + j*d] ; */
+ ASSIGN (Ex,-,ii+j*nsrow2, Xx,-,i+j*d) ;
+ }
+ }
+
+#ifdef REAL
+
+ /* solve L1*x1 */
+ BLAS_dtrsm ("L", "L", "N", "N",
+ nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */
+ one, /* ALPHA: 1 */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */
+
+ /* E = E - L2*x1 */
+ if (nsrow2 > 0)
+ {
+ BLAS_dgemm ("N", "N",
+ nsrow2, nrhs, nscol, /* M, N, K */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Xx + ENTRY_SIZE*k1, d, /* B, LDB: X1 */
+ one, /* BETA: 1 */
+ Ex, nsrow2) ; /* C, LDC: E */
+ }
+
+#else
+
+ /* solve L1*x1 */
+ BLAS_ztrsm ("L", "L", "N", "N",
+ nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */
+ one, /* ALPHA: 1 */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */
+
+ /* E = E - L2*x1 */
+ if (nsrow2 > 0)
+ {
+ BLAS_zgemm ("N", "N",
+ nsrow2, nrhs, nscol, /* M, N, K */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Xx + ENTRY_SIZE*k1, d, /* B, LDB: X1 */
+ one, /* BETA: 1 */
+ Ex, nsrow2) ; /* C, LDC: E */
+ }
+
+#endif
+
+ /* scatter E back into X */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ i = Ls [ps2 + ii] ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ /* Xx [i + j*d] = Ex [ii + j*nsrow2] ; */
+ ASSIGN (Xx,-,i+j*d, Ex,-,ii+j*nsrow2) ;
+ }
+ }
+ }
+ }
+
+ Common->status = CHOLMOD_OK ;
+ return (blas_ok) ;
+}
+
+
+static int TEMPLATE (cholmod_super_ltsolve)
+(
+ /* ---- input ---- */
+ cholmod_factor *L, /* factor to use for the forward solve */
+ /* ---- output ---- */
+ cholmod_dense *X, /* b on input, solution to Lx=b on output */
+ /* ---- workspace ---- */
+ cholmod_dense *E, /* workspace of size nrhs*(L->maxesize) */
+ /* --------------- */
+ cholmod_common *Common
+)
+{
+ double *Lx, *Xx, *Ex ;
+ double minus_one [2], one [2] ;
+ Int *Lpi, *Lpx, *Ls, *Super ;
+ Int nsuper, k1, k2, psi, psend, psx, nsrow, nscol, ii, s,
+ nsrow2, n, ps2, j, i, d, nrhs ;
+ int blas_ok = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ nrhs = X->ncol ;
+ Ex = E->x ;
+ Xx = X->x ;
+ n = L->n ;
+ d = X->d ;
+
+ nsuper = L->nsuper ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Ls = L->s ;
+ Super = L->super ;
+ Lx = L->x ;
+ minus_one [0] = -1.0 ;
+ minus_one [1] = 0 ;
+ one [0] = 1.0 ;
+ one [1] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve L'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrhs == 1)
+ {
+
+ for (s = nsuper-1 ; s >= 0 ; s--)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ nsrow2 = nsrow - nscol ;
+ ps2 = psi + nscol ;
+ ASSERT ((size_t) nsrow2 <= L->maxesize) ;
+
+ /* L1 is nscol-by-nscol, lower triangular with non-unit diagonal.
+ * L2 is nsrow2-by-nscol. L1 and L2 have leading dimension of
+ * nsrow. x1 is nscol-by-nsrow, with leading dimension n.
+ * E is nsrow2-by-1, with leading dimension nsrow2.
+ */
+
+ /* gather X into E */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ /* Ex [ii] = Xx [Ls [ps2 + ii]] ; */
+ ASSIGN (Ex,-,ii, Xx,-,Ls [ps2 + ii]) ;
+ }
+
+#ifdef REAL
+
+ /* x1 = x1 - L2'*E */
+ BLAS_dgemv ("C",
+ nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Ex, 1, /* X, INCX: Ex */
+ one, /* BETA: 1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* Y, INCY: x1 */
+
+ /* solve L1'*x1 */
+ BLAS_dtrsv ("L", "C", "N",
+ nscol, /* N: L1 is nscol-by-nscol */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */
+
+#else
+
+ /* x1 = x1 - L2'*E */
+ BLAS_zgemv ("C",
+ nsrow2, nscol, /* M, N: L2 is nsrow2-by-nscol */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Ex, 1, /* X, INCX: Ex */
+ one, /* BETA: 1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* Y, INCY: x1 */
+
+ /* solve L1'*x1 */
+ BLAS_ztrsv ("L", "C", "N",
+ nscol, /* N: L1 is nscol-by-nscol */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, 1) ; /* X, INCX: x1 */
+
+#endif
+
+ }
+ }
+ else
+ {
+
+ for (s = nsuper-1 ; s >= 0 ; s--)
+ {
+ k1 = Super [s] ;
+ k2 = Super [s+1] ;
+ psi = Lpi [s] ;
+ psend = Lpi [s+1] ;
+ psx = Lpx [s] ;
+ nsrow = psend - psi ;
+ nscol = k2 - k1 ;
+ nsrow2 = nsrow - nscol ;
+ ps2 = psi + nscol ;
+ ASSERT ((size_t) nsrow2 <= L->maxesize) ;
+
+ /* E is nsrow2-by-nrhs, with leading dimension nsrow2. */
+
+ /* gather X into E */
+ for (ii = 0 ; ii < nsrow2 ; ii++)
+ {
+ i = Ls [ps2 + ii] ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ /* Ex [ii + j*nsrow2] = Xx [i + j*d] ; */
+ ASSIGN (Ex,-,ii+j*nsrow2, Xx,-,i+j*d) ;
+ }
+ }
+
+#ifdef REAL
+
+ /* x1 = x1 - L2'*E */
+ if (nsrow2 > 0)
+ {
+ BLAS_dgemm ("C", "N",
+ nscol, nrhs, nsrow2, /* M, N, K */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Ex, nsrow2, /* B, LDB: E */
+ one, /* BETA: 1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* C, LDC: x1 */
+ }
+
+ /* solve L1'*x1 */
+ BLAS_dtrsm ("L", "L", "C", "N",
+ nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */
+ one, /* ALPHA: 1 */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */
+
+#else
+
+ /* x1 = x1 - L2'*E */
+ if (nsrow2 > 0)
+ {
+ BLAS_zgemm ("C", "N",
+ nscol, nrhs, nsrow2, /* M, N, K */
+ minus_one, /* ALPHA: -1 */
+ Lx + ENTRY_SIZE*(psx + nscol), /* A, LDA: L2 */
+ nsrow,
+ Ex, nsrow2, /* B, LDB: E */
+ one, /* BETA: 1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* C, LDC: x1 */
+ }
+
+ /* solve L1'*x1 */
+ BLAS_ztrsm ("L", "L", "C", "N",
+ nscol, nrhs, /* M, N: x1 is nscol-by-nrhs */
+ one, /* ALPHA: 1 */
+ Lx + ENTRY_SIZE*psx, nsrow, /* A, LDA: L1 */
+ Xx + ENTRY_SIZE*k1, d) ; /* B, LDB: x1 */
+
+#endif
+
+ }
+ }
+
+ Common->status = CHOLMOD_OK ;
+ return (blas_ok) ;
+}
+
+#undef PATTERN
+#undef REAL
+#undef COMPLEX
+#undef ZOMPLEX
diff --git a/CHOLMOD/Tcov/License.txt b/CHOLMOD/Tcov/License.txt
new file mode 100644
index 0000000..b2246d2
--- /dev/null
+++ b/CHOLMOD/Tcov/License.txt
@@ -0,0 +1,24 @@
+CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Tcov module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
diff --git a/CHOLMOD/Tcov/Make.inc b/CHOLMOD/Tcov/Make.inc
new file mode 100644
index 0000000..5e571e0
--- /dev/null
+++ b/CHOLMOD/Tcov/Make.inc
@@ -0,0 +1,8 @@
+# valgrind is not used
+V =
+
+# covall is used
+COVER = ./covall
+
+# with test coverage
+CFLAGS = -O0 -g --coverage
diff --git a/CHOLMOD/Tcov/Makefile b/CHOLMOD/Tcov/Makefile
new file mode 100644
index 0000000..663697e
--- /dev/null
+++ b/CHOLMOD/Tcov/Makefile
@@ -0,0 +1,1212 @@
+#===============================================================================
+# CHOLMOD/Tcov/Makefile
+#===============================================================================
+
+# If you compile CHOLMOD with -DNPARTITION, then you do not need METIS,
+# CCOLAMD, or the Partition module.
+
+include ../../UFconfig/UFconfig.mk
+include Make.inc
+
+# Tcov requires gcc
+CC = gcc
+
+C = $(CC) $(CFLAGS) $(CHOLMOD_CONFIG) $(NANTESTS)
+
+# optimized LAPACK and BLAS
+# LIB = $(METIS) -lm $(LAPACK) $(BLAS) $(XERBLA)
+
+# LAPACK and the Fortran reference BLAS, compiled with gfortran -g -O:
+# LIB = $(METIS) -lm -llapack_plain -lblas_plain -lg2c
+LIB = $(METIS) -lm -llapack_plain -lblas_plain -lgfortran -lgfortranbegin
+LIB = $(METIS) -lm -llapack -lblas -lgfortran -lgfortranbegin
+
+# Solaris
+# LIB = $(METIS) -xlic_lib=sunperf
+
+# Use "grep" only, if you do not have "indent"
+PRETTY = grep -v "^\#" | indent -bl -nce -ss -bli0 -i4 -sob -l120
+# PRETTY = grep -v "^\#" | ssh persimmon indent -bl -nce -ss -bli0 -i4 -sob -l120
+# PRETTY = grep -v "^\#"
+
+I = -I../../AMD/Include -I../../COLAMD/Include \
+ -I$(METIS_PATH)/Lib -I../../CCOLAMD/Include -I../../CAMD/Include \
+ -I../Include -I../../UFconfig
+
+default: cm cl z_demo l_demo cmread clread
+
+TEST = cm.c test_ops.c null.c null2.c lpdemo.c memory.c solve.c aug.c unpack.c \
+ raw_factor.c cctest.c ctest.c amdtest.c camdtest.c huge.c
+
+INC = ../Include/cholmod.h \
+ ../Include/cholmod_blas.h \
+ ../Include/cholmod_check.h \
+ ../Include/cholmod_cholesky.h \
+ ../Include/cholmod_complexity.h \
+ ../Include/cholmod_config.h \
+ ../Include/cholmod_core.h \
+ ../Include/cholmod_internal.h \
+ ../Include/cholmod_matrixops.h \
+ ../Include/cholmod_modify.h \
+ ../Include/cholmod_partition.h \
+ ../Include/cholmod_supernodal.h \
+ ../Include/cholmod_template.h
+
+AMDSRC = ../../AMD/Source/amd_1.c \
+ ../../AMD/Source/amd_2.c \
+ ../../AMD/Source/amd_aat.c \
+ ../../AMD/Source/amd_control.c \
+ ../../AMD/Source/amd_defaults.c \
+ ../../AMD/Source/amd_global.c \
+ ../../AMD/Source/amd_info.c \
+ ../../AMD/Source/amd_order.c \
+ ../../AMD/Source/amd_postorder.c \
+ ../../AMD/Source/amd_post_tree.c \
+ ../../AMD/Source/amd_preprocess.c \
+ ../../AMD/Source/amd_valid.c \
+ ../../AMD/Include/amd.h \
+ ../../AMD/Include/amd_internal.h
+
+AMDOBJ = \
+ zz_amd_1.o \
+ zz_amd_2.o \
+ zz_amd_aat.o \
+ zz_amd_control.o \
+ zz_amd_defaults.o \
+ zz_amd_global.o \
+ zz_amd_info.o \
+ zz_amd_dump.o \
+ zz_amd_order.o \
+ zz_amd_postorder.o \
+ zz_amd_post_tree.o \
+ zz_amd_preprocess.o \
+ zz_amd_valid.o
+
+LAMDOBJ = \
+ zl_amd_1.o \
+ zl_amd_2.o \
+ zl_amd_aat.o \
+ zl_amd_control.o \
+ zl_amd_defaults.o \
+ zl_amd_global.o \
+ zl_amd_info.o \
+ zl_amd_dump.o \
+ zl_amd_order.o \
+ zl_amd_postorder.o \
+ zl_amd_post_tree.o \
+ zl_amd_preprocess.o \
+ zl_amd_valid.o
+
+COLAMDSRC = ../../COLAMD/Source/colamd.c ../../COLAMD/Source/colamd_global.c
+
+COLAMDOBJ = zz_colamd.o yz_colamd_global.o
+
+LCOLAMDOBJ = zl_colamd.o yl_colamd_global.o
+
+#-------------------------------------------------------------------------------
+# When using the Partition Module:
+
+CCOLAMDSRC = \
+ ../../CCOLAMD/Source/ccolamd.c \
+ ../../CCOLAMD/Source/ccolamd_global.c \
+ ../../CCOLAMD/Include/ccolamd.h
+
+CCOLAMDOBJ = zz_ccolamd.o yz_ccolamd_global.o
+
+LCCOLAMDOBJ = zl_ccolamd.o yl_ccolamd_global.o
+
+$(CCOLAMDOBJ): $(CCOLAMDSRC)
+
+$(LCCOLAMDOBJ): $(CCOLAMDSRC)
+
+IPARTITION_OBJ = \
+ z_ccolamd.o \
+ z_csymamd.o \
+ z_camd.o \
+ z_metis.o \
+ z_nesdis.o
+
+LPARTITION_OBJ = \
+ l_ccolamd.o \
+ l_csymamd.o \
+ l_camd.o \
+ l_metis.o \
+ l_nesdis.o
+
+CAMDSRC = ../../CAMD/Source/camd_1.c \
+ ../../CAMD/Source/camd_2.c \
+ ../../CAMD/Source/camd_aat.c \
+ ../../CAMD/Source/camd_control.c \
+ ../../CAMD/Source/camd_defaults.c \
+ ../../CAMD/Source/camd_global.c \
+ ../../CAMD/Source/camd_info.c \
+ ../../CAMD/Source/camd_order.c \
+ ../../CAMD/Source/camd_postorder.c \
+ ../../CAMD/Source/camd_preprocess.c \
+ ../../CAMD/Source/camd_valid.c \
+ ../../CAMD/Include/camd.h \
+ ../../CAMD/Include/camd_internal.h
+
+CAMDOBJ = \
+ zz_camd_1.o \
+ zz_camd_2.o \
+ zz_camd_aat.o \
+ zz_camd_control.o \
+ zz_camd_defaults.o \
+ zz_camd_global.o \
+ zz_camd_info.o \
+ zz_camd_order.o \
+ zz_camd_postorder.o \
+ zz_camd_preprocess.o \
+ zz_camd_valid.o \
+ zz_camd_dump.o
+
+LCAMDOBJ = \
+ zl_camd_1.o \
+ zl_camd_2.o \
+ zl_camd_aat.o \
+ zl_camd_control.o \
+ zl_camd_defaults.o \
+ zl_camd_global.o \
+ zl_camd_info.o \
+ zl_camd_order.o \
+ zl_camd_postorder.o \
+ zl_camd_preprocess.o \
+ zl_camd_valid.o \
+ zl_camd_dump.o
+
+$(CAMDOBJ): $(CAMDSRC)
+
+$(LCAMDOBJ): $(CAMDSRC)
+
+#-------------------------------------------------------------------------------
+# If you compile with -DNPARTITION, you may replace the above definitions
+# with empty ones (see immediately below), and then you do not need a copy of
+# CCOLAMD:
+# CCOLAMDSRC =
+# CCOLAMDOBJ =
+# LCCOLAMDOBJ =
+# IPARTITION_OBJ =
+# LPARTITION_OBJ =
+# CAMDSRC =
+# CAMDOBJ =
+# LCAMDOBJ =
+#-------------------------------------------------------------------------------
+
+IOBJ = \
+ z_common.o \
+ z_dense.o \
+ z_factor.o \
+ z_change_factor.o \
+ z_memory.o \
+ z_sparse.o \
+ z_complex.o \
+ z_transpose.o \
+ z_band.o \
+ z_copy.o \
+ z_triplet.o \
+ z_error.o \
+ z_aat.o \
+ z_add.o \
+ z_check.o \
+ z_read.o \
+ z_write.o \
+ z_amd.o \
+ z_analyze.o \
+ z_colamd.o \
+ z_etree.o \
+ z_factorize.o \
+ z_postorder.o \
+ z_rcond.o \
+ z_resymbol.o \
+ z_rowcolcounts.o \
+ z_rowfac.o \
+ z_solve.o \
+ z_spsolve.o \
+ z_drop.o \
+ z_horzcat.o \
+ z_norm.o \
+ z_scale.o \
+ z_sdmult.o \
+ z_ssmult.o \
+ z_submatrix.o \
+ z_vertcat.o \
+ z_symmetry.o \
+ z_rowadd.o \
+ z_rowdel.o \
+ z_updown.o \
+ z_super_numeric.o \
+ z_super_solve.o \
+ z_super_symbolic.o \
+ $(IPARTITION_OBJ)
+
+LOBJ = \
+ l_common.o \
+ l_dense.o \
+ l_factor.o \
+ l_change_factor.o \
+ l_memory.o \
+ l_sparse.o \
+ l_complex.o \
+ l_transpose.o \
+ l_band.o \
+ l_copy.o \
+ l_triplet.o \
+ l_error.o \
+ l_aat.o \
+ l_add.o \
+ l_check.o \
+ l_read.o \
+ l_write.o \
+ l_amd.o \
+ l_analyze.o \
+ l_colamd.o \
+ l_etree.o \
+ l_factorize.o \
+ l_postorder.o \
+ l_rcond.o \
+ l_resymbol.o \
+ l_rowcolcounts.o \
+ l_rowfac.o \
+ l_solve.o \
+ l_spsolve.o \
+ l_drop.o \
+ l_horzcat.o \
+ l_norm.o \
+ l_scale.o \
+ l_sdmult.o \
+ l_ssmult.o \
+ l_submatrix.o \
+ l_vertcat.o \
+ l_symmetry.o \
+ l_rowadd.o \
+ l_rowdel.o \
+ l_updown.o \
+ l_super_numeric.o \
+ l_super_solve.o \
+ l_super_symbolic.o \
+ $(LPARTITION_OBJ)
+
+IALL = $(IOBJ) $(AMDOBJ) $(COLAMDOBJ) $(CCOLAMDOBJ) $(CAMDOBJ)
+
+LALL = $(LOBJ) $(LAMDOBJ) $(LCOLAMDOBJ) $(LCCOLAMDOBJ) $(LCAMDOBJ)
+
+
+cm: $(IALL) $(TEST) cm.h Makefile
+ $(C) $(I) $(TEST) -o cm $(IALL) $(LIB)
+
+cl: $(LALL) $(TEST) cm.h Makefile
+ $(C) -DDLONG $(I) $(TEST) -o cl $(LALL) $(LIB)
+
+cmread: $(IALL) cmread.c Makefile
+ $(C) $(I) cmread.c -o cmread $(IALL) $(LIB)
+
+clread: $(LALL) cmread.c Makefile
+ $(C) -DDLONG $(I) cmread.c -o clread $(LALL) $(LIB)
+
+z_demo: $(IALL) ../Demo/cholmod_demo.c cm.h Makefile \
+ ../Demo/cholmod_demo.h
+ cat ../Demo/cholmod_demo.c > z_demo.c
+ $(C) $(I) -I../Demo z_demo.c -o z_demo $(IALL) $(LIB)
+
+l_demo: $(LALL) ../Demo/cholmod_l_demo.c cm.h Makefile \
+ ../Demo/cholmod_demo.h
+ cat ../Demo/cholmod_l_demo.c > l_demo.c
+ $(C) -DDLONG $(I) -I../Demo l_demo.c -o l_demo $(LALL) $(LIB)
+
+go: z_demo l_demo cmread clread cm cl
+ $(V) ./z_demo ../Demo/Matrix/bcsstk01.tri > tmp/demo_k1.out
+ $(V) ./z_demo ../Demo/Matrix/bcsstk02.tri > tmp/demo_k2.out
+ $(V) ./z_demo < ../Demo/Matrix/lp_afiro.tri > tmp/demo_afiro.out
+ $(V) ./z_demo < ../Demo/Matrix/can___24.mtx > tmp/demo_can24.out
+ $(V) ./z_demo < ../Demo/Matrix/c.tri > tmp/demo_c.out
+ $(V) ./z_demo < ../Demo/Matrix/d.tri > tmp/demo_d.out
+ $(V) ./z_demo < ../Demo/Matrix/up.tri > tmp/demo_up.out
+ $(V) ./z_demo < ../Demo/Matrix/c.mtx > tmp/demo_c_mtx.out
+ $(V) ./z_demo < ../Demo/Matrix/0.tri > tmp/demo_0.out
+ $(V) ./z_demo < Matrix/3_2 > tmp/demo_3_2.out
+ $(V) ./z_demo < Matrix/c5lo > tmp/demo_c5lo.out
+ $(V) ./z_demo < Matrix/c10 > tmp/demo_c10.out
+ $(V) ./z_demo no_such_file > tmp/demo_no_such_file.out
+ $(V) ./z_demo ../Demo/Matrix/mangle1.mtx > tmp/demo_mangle1.out
+ $(V) ./z_demo ../Demo/Matrix/mangle2.mtx > tmp/demo_mangle2.out
+ $(V) ./z_demo ../Demo/Matrix/mangle3.mtx > tmp/demo_mangle3.out
+ $(V) ./z_demo ../Demo/Matrix/mangle4.mtx > tmp/demo_mangle4.out
+ $(V) ./z_demo ../Demo/Matrix/pts5ldd03.mtx > tmp/demo_pts5ldd03.out
+ $(V) ./l_demo ../Demo/Matrix/bcsstk01.tri > tmp/ldemo_k1.out
+ $(V) ./l_demo ../Demo/Matrix/bcsstk02.tri > tmp/ldemo_k2.out
+ $(V) ./l_demo < ../Demo/Matrix/lp_afiro.tri > tmp/ldemo_afiro.out
+ $(V) ./l_demo < ../Demo/Matrix/can___24.mtx > tmp/ldemo_can24.out
+ $(V) ./l_demo < ../Demo/Matrix/c.tri > tmp/ldemo_c.out
+ $(V) ./l_demo < ../Demo/Matrix/d.tri > tmp/ldemo_d.out
+ $(V) ./l_demo < ../Demo/Matrix/up.tri > tmp/ldemo_up.out
+ $(V) ./l_demo < ../Demo/Matrix/c.mtx > tmp/ldemo_c_mtx.out
+ $(V) ./l_demo < ../Demo/Matrix/0.tri > tmp/ldemo_0.out
+ $(V) ./l_demo < Matrix/3_2 > tmp/ldemo_3_2.out
+ $(V) ./l_demo < Matrix/c5lo > tmp/ldemo_c5lo.out
+ $(V) ./l_demo < Matrix/c10 > tmp/ldemo_c10.out
+ $(V) ./l_demo no_such_file > tmp/ldemo_no_such_file.out
+ $(V) ./l_demo ../Demo/Matrix/mangle1.mtx > tmp/ldemo_mangle1.out
+ $(V) ./l_demo ../Demo/Matrix/mangle2.mtx > tmp/ldemo_mangle2.out
+ $(V) ./l_demo ../Demo/Matrix/mangle3.mtx > tmp/ldemo_mangle3.out
+ $(V) ./l_demo ../Demo/Matrix/mangle4.mtx > tmp/ldemo_mangle4.out
+ $(V) ./l_demo ../Demo/Matrix/pts5ldd03.mtx > tmp/ldemo_pts5ldd03.out
+ - grep resid tmp/demo*
+ $(V) ./cmread no_such_file > tmp/no_such_file.out
+ $(V) ./cmread Matrix/crud1 > tmp/crud1.out
+ $(V) ./cmread Matrix/crud2 > tmp/crud2.out
+ $(V) ./cmread Matrix/fullcrud.mtx > tmp/fullcrud.out
+ $(V) ./cmread Matrix/fullcrud1.mtx > tmp/fullcrud1.out
+ $(V) ./cmread Matrix/fullcrud2.mtx > tmp/fullcrud2.out
+ $(V) ./cmread Matrix/3by0.mtx > tmp/3by0.out
+ $(V) ./cmread Matrix/fullrza.mtx > tmp/fullrza.out
+ $(V) ./cmread Matrix/fullrsa.mtx > tmp/fullrsa.out
+ $(V) ./cmread Matrix/fullcsa.mtx > tmp/fullcsa.out
+ $(V) ./cmread Matrix/fullcza.mtx > tmp/fullcza.out
+ $(V) ./cmread Matrix/fullcha.mtx > tmp/fullcha.out
+ $(V) ./cmread Matrix/cha.mtx > tmp/cha.out
+ $(V) ./cmread Matrix/cza.mtx > tmp/cza.out
+ $(V) ./cmread Matrix/csa.mtx > tmp/csa.out
+ $(V) ./cmread Matrix/one > tmp/one.out
+ $(V) ./cmread Matrix/rza.mtx > tmp/rza.out
+ $(V) ./cmread ../Demo/Matrix/mangle5.tri > tmp/mangle5.out
+ $(V) ./cmread ../Demo/Matrix/mangle6.tri > tmp/mangle6.out
+ $(V) ./cmread ../Demo/Matrix/mangle7.tri > tmp/mangle6.out
+ $(V) ./cmread ../Demo/Matrix/mangle8.tri > tmp/mangle8.out
+ $(V) ./cmread ../Demo/Matrix/empty.tri > tmp/empty.out
+ $(V) ./cmread ../Demo/Matrix/one.tri > tmp/one.out
+ $(V) ./cmread Matrix/plskz362.mtx > tmp/plskz363.out
+ $(V) ./cmread Matrix/2diag.tri > tmp/2diag.out
+ $(V) ./cmread Matrix/r5lo > tmp/r5lo.out
+ $(V) ./cmread Matrix/r5lo2 > tmp/r5lo2.out
+ - diff tmp/r5lo.out tmp/r5lo2.out
+ $(V) ./cmread Matrix/cs.mtx > tmp/cs.out
+ $(V) ./cmread Matrix/2lo.tri > tmp/2lo.out
+ $(V) ./cmread Matrix/2.tri > tmp/2.out
+ $(V) ./cmread Matrix/2up.tri > tmp/2up.out
+ $(V) ./cmread Matrix/huge.tri > tmp/huge.out
+ $(V) ./cmread Matrix/1e99 > tmp/1e99.out
+ $(V) ./clread no_such_file > tmp/l_no_such_file.out
+ $(V) ./clread Matrix/crud1 > tmp/l_crud1.out
+ $(V) ./clread Matrix/crud2 > tmp/l_crud2.out
+ $(V) ./clread Matrix/fullcrud.mtx > tmp/l_fullcrud.out
+ $(V) ./clread Matrix/fullcrud1.mtx > tmp/l_fullcrud1.out
+ $(V) ./clread Matrix/fullcrud2.mtx > tmp/l_fullcrud2.out
+ $(V) ./clread Matrix/3by0.mtx > tmp/l_3by0.out
+ $(V) ./clread Matrix/fullrza.mtx > tmp/l_fullrza.out
+ $(V) ./clread Matrix/fullrsa.mtx > tmp/l_fullrsa.out
+ $(V) ./clread Matrix/fullcsa.mtx > tmp/l_fullcsa.out
+ $(V) ./clread Matrix/fullcza.mtx > tmp/l_fullcza.out
+ $(V) ./clread Matrix/fullcha.mtx > tmp/l_fullcha.out
+ $(V) ./clread Matrix/cha.mtx > tmp/l_cha.out
+ $(V) ./clread Matrix/cza.mtx > tmp/l_cza.out
+ $(V) ./clread Matrix/csa.mtx > tmp/l_csa.out
+ $(V) ./clread Matrix/one > tmp/l_one.out
+ $(V) ./clread Matrix/rza.mtx > tmp/l_rza.out
+ $(V) ./clread ../Demo/Matrix/mangle5.tri > tmp/l_mangle5.out
+ $(V) ./clread ../Demo/Matrix/mangle6.tri > tmp/l_mangle6.out
+ $(V) ./clread ../Demo/Matrix/mangle7.tri > tmp/l_mangle6.out
+ $(V) ./clread ../Demo/Matrix/mangle8.tri > tmp/l_mangle8.out
+ $(V) ./clread ../Demo/Matrix/empty.tri > tmp/l_empty.out
+ $(V) ./clread ../Demo/Matrix/one.tri > tmp/l_one.out
+ $(V) ./clread Matrix/plskz362.mtx > tmp/l_plskz363.out
+ $(V) ./clread Matrix/2diag.tri > tmp/l_2diag.out
+ $(V) ./clread Matrix/r5lo > tmp/l_r5lo.out
+ $(V) ./clread Matrix/r5lo2 > tmp/l_r5lo2.out
+ - diff tmp/r5lo.out tmp/r5lo2.out
+ $(V) ./clread Matrix/cs.mtx > tmp/l_cs.out
+ $(V) ./clread Matrix/2lo.tri > tmp/l_l_2lo.out
+ $(V) ./clread Matrix/2.tri > tmp/l_2.out
+ $(V) ./clread Matrix/2up.tri > tmp/l_2up.out
+ $(V) ./clread Matrix/huge.tri > tmp/l_huge.out
+ $(V) ./clread Matrix/1e99 > tmp/l_1e99.out
+ $(V) ./cm < Matrix/galenet > tmp/galenet.out
+ $(V) ./cl < Matrix/galenet > tmp/l_galenet.out
+ - $(COVER)
+ $(V) ./cm < Matrix/5by50 > tmp/5by50.out
+ $(V) ./cl < Matrix/5by50 > tmp/l_5by50.out
+ - $(COVER)
+ $(V) ./cm < Matrix/r5lo > tmp/r5lo.out
+ $(V) ./cl < Matrix/r5lo > tmp/l_r5lo.out
+ $(V) ./cm < Matrix/r5up > tmp/r5up.out
+ $(V) ./cl < Matrix/r5up > tmp/l_r5up.out
+ $(V) ./cm < Matrix/r5up2 > tmp/r5up2.out
+ $(V) ./cl < Matrix/r5up2 > tmp/l_r5up2.out
+ $(V) ./cm < Matrix/c5up2 > tmp/c5up2.out
+ $(V) ./cl < Matrix/c5up2 > tmp/l_c5up2.out
+ $(V) ./cm < Matrix/z5up2 > tmp/z5up2.out
+ $(V) ./cl < Matrix/z5up2 > tmp/l_z5up2.out
+ $(V) ./cm -m < Matrix/z5lo > tmp/z5lo.out
+ $(V) ./cl -m < Matrix/z5lo > tmp/l_z5lo.out
+ $(V) ./cm < Matrix/ibm32 > tmp/ibm.out
+ $(V) ./cl < Matrix/ibm32 > tmp/l_ibm.out
+ - $(COVER)
+ $(V) ./cm -m < Matrix/c5lo > tmp/c5lo.out
+ $(V) ./cl -m < Matrix/c5lo > tmp/l_c5lo.out
+ $(V) ./cm -m < Matrix/z10 > tmp/z10.out
+ $(V) ./cl -m < Matrix/z10 > tmp/l_z10.out
+ $(V) ./cm -m < Matrix/z5up > tmp/z5up.out
+ $(V) ./cl -m < Matrix/z5up > tmp/l_z5up.out
+ - $(COVER)
+ $(V) ./cm -s < Matrix/3singular > tmp/3singular.out
+ $(V) ./cl -s < Matrix/3singular > tmp/l_3singular.out
+ $(V) ./cm -s < Matrix/z3singular > tmp/z3singular.out
+ $(V) ./cl -s < Matrix/z3singular > tmp/l_z3singular.out
+ $(V) ./cm -s < Matrix/c3singular > tmp/c3singular.out
+ $(V) ./cl -s < Matrix/c3singular > tmp/l_c3singular.out
+ $(V) ./cm -m < Matrix/0 > tmp/0.out
+ $(V) ./cl -m < Matrix/0 > tmp/l_0.out
+ $(V) ./cm -m < Matrix/afiro > tmp/afiro.out
+ $(V) ./cl -m < Matrix/afiro > tmp/l_afiro.out
+ - $(COVER)
+ $(V) ./cm -m < Matrix/k01up > tmp/k01up.out
+ $(V) ./cl -m < Matrix/k01up > tmp/l_k01up.out
+ - $(COVER)
+ $(V) ./cm < Matrix/diag > tmp/diag.out
+ $(V) ./cl < Matrix/diag > tmp/l_diag.out
+ $(V) ./cm -m < Matrix/ex5lo > tmp/ex5lo.out
+ $(V) ./cl -m < Matrix/ex5lo > tmp/l_ex5lo.out
+ - $(COVER)
+ $(V) ./cm < Matrix/20lo > tmp/20lo.out
+ $(V) ./cl < Matrix/20lo > tmp/l_20lo.out
+ $(V) ./cm < Matrix/z30lo > tmp/z30lo.out
+ $(V) ./cl < Matrix/z30lo > tmp/l_z30lo.out
+ - $(COVER)
+ $(V) ./cm -m < Matrix/z30up > tmp/z30up.out
+ $(V) ./cl -m < Matrix/z30up > tmp/l_z30up.out
+ $(V) ./cm < Matrix/c10 > tmp/c10.out
+ $(V) ./cl < Matrix/c10 > tmp/l_c10.out
+ $(V) ./cm < Matrix/c30lo > tmp/c30lo.out
+ $(V) ./cl < Matrix/c30lo > tmp/l_c30lo.out
+ - $(COVER)
+ $(V) ./cm -m < Matrix/c30up > tmp/c30up.out
+ $(V) ./cl -m < Matrix/c30up > tmp/l_c30up.out
+ $(V) ./cm < Matrix/pi > tmp/pi.out
+ $(V) ./cl < Matrix/pi > tmp/l_pi.out
+ $(V) ./cm < Matrix/cpi > tmp/cpi.out
+ $(V) ./cl < Matrix/cpi > tmp/l_cpi.out
+ $(V) ./cm < Matrix/1_0 > tmp/1_0.out
+ $(V) ./cl < Matrix/1_0 > tmp/l_1_0.out
+ $(V) ./cm -s < Matrix/3b > tmp/3b.out
+ $(V) ./cl -s < Matrix/3b > tmp/l_3b.out
+ $(V) ./cm -s < Matrix/cza > tmp/cza2.out
+ $(V) ./cl -s < Matrix/cza > tmp/l_cza2.out
+ $(V) ./cm < Matrix/0_1 > tmp/0_1.out
+ $(V) ./cl < Matrix/0_1 > tmp/l_0_1.out
+ - $(COVER)
+ $(V) ./cm -n < Matrix/galenet > tmp/galenet_nan.out
+ - $(COVER)
+ $(V) ./cl -n < Matrix/galenet > tmp/l_galenet_nan.out
+ - $(COVER)
+ $(V) ./cm < Matrix/a1 > tmp/a1.out
+ - $(COVER)
+ $(V) ./cl < Matrix/a1 > tmp/l_a1.out
+ - $(COVER)
+ $(V) ./cm < Matrix/zero > tmp/zero.out
+ $(V) ./cl < Matrix/zero > tmp/zero.out
+ - $(COVER)
+
+cov:
+ - $(COVER)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) cm cl cmread clread *.c.gcov *.out tmp/*.out z_demo l_demo
+ - $(RM) leak zz_*.c z_*.c *.a l_*.c zl_*.c cov.sort yl_*.c yz_*.c
+ - $(RM) -r cm.profile cmread.profile z_demo.profile
+ - $(RM) -r cl.profile clread.profile l_demo.profile
+ - $(RM) *.gcda *.gcno
+ - $(RM) temp*.mtx
+
+clean:
+ - $(RM) $(CLEAN)
+
+
+$(AMDOBJ): $(AMDSRC)
+
+$(LAMDOBJ): $(AMDSRC)
+
+$(IOBJ): $(INC)
+
+$(LOBJ): $(INC)
+
+.c.o:
+ $(C) -c $(I) $*.c
+
+#-------------------------------------------------------------------------------
+# AMD
+#-------------------------------------------------------------------------------
+
+zz_amd_1.o: ../../AMD/Source/amd_1.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_1.c
+ $(C) -c $(I) zz_amd_1.c
+
+zz_amd_2.o: ../../AMD/Source/amd_2.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_2.c
+ $(C) -c $(I) zz_amd_2.c
+
+zz_amd_aat.o: ../../AMD/Source/amd_aat.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_aat.c
+ $(C) -c $(I) zz_amd_aat.c
+
+zz_amd_control.o: ../../AMD/Source/amd_control.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_control.c
+ $(C) -c $(I) zz_amd_control.c
+
+zz_amd_defaults.o: ../../AMD/Source/amd_defaults.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_defaults.c
+ $(C) -c $(I) zz_amd_defaults.c
+
+zz_amd_global.o: ../../AMD/Source/amd_global.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_global.c
+ $(C) -c $(I) zz_amd_global.c
+
+zz_amd_dump.o: ../../AMD/Source/amd_dump.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_dump.c
+ $(C) -c $(I) zz_amd_dump.c
+
+zz_amd_info.o: ../../AMD/Source/amd_info.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_info.c
+ $(C) -c $(I) zz_amd_info.c
+
+zz_amd_order.o: ../../AMD/Source/amd_order.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_order.c
+ $(C) -c $(I) zz_amd_order.c
+
+zz_amd_postorder.o: ../../AMD/Source/amd_postorder.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_postorder.c
+ $(C) -c $(I) zz_amd_postorder.c
+
+zz_amd_post_tree.o: ../../AMD/Source/amd_post_tree.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_post_tree.c
+ $(C) -c $(I) zz_amd_post_tree.c
+
+zz_amd_preprocess.o: ../../AMD/Source/amd_preprocess.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_preprocess.c
+ $(C) -c $(I) zz_amd_preprocess.c
+
+zz_amd_valid.o: ../../AMD/Source/amd_valid.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_amd_valid.c
+ $(C) -c $(I) zz_amd_valid.c
+
+#-------------------------------------------------------------------------------
+
+zl_amd_1.o: ../../AMD/Source/amd_1.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_1.c
+ $(C) -c $(I) zl_amd_1.c
+
+zl_amd_2.o: ../../AMD/Source/amd_2.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_2.c
+ $(C) -c $(I) zl_amd_2.c
+
+zl_amd_aat.o: ../../AMD/Source/amd_aat.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_aat.c
+ $(C) -c $(I) zl_amd_aat.c
+
+zl_amd_control.o: ../../AMD/Source/amd_control.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_control.c
+ $(C) -c $(I) zl_amd_control.c
+
+zl_amd_defaults.o: ../../AMD/Source/amd_defaults.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_defaults.c
+ $(C) -c $(I) zl_amd_defaults.c
+
+zl_amd_global.o: ../../AMD/Source/amd_global.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_global.c
+ $(C) -c $(I) zl_amd_global.c
+
+zl_amd_dump.o: ../../AMD/Source/amd_dump.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_dump.c
+ $(C) -c $(I) zl_amd_dump.c
+
+zl_amd_info.o: ../../AMD/Source/amd_info.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_info.c
+ $(C) -c $(I) zl_amd_info.c
+
+zl_amd_order.o: ../../AMD/Source/amd_order.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_order.c
+ $(C) -c $(I) zl_amd_order.c
+
+zl_amd_postorder.o: ../../AMD/Source/amd_postorder.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_postorder.c
+ $(C) -c $(I) zl_amd_postorder.c
+
+zl_amd_post_tree.o: ../../AMD/Source/amd_post_tree.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_post_tree.c
+ $(C) -c $(I) zl_amd_post_tree.c
+
+zl_amd_preprocess.o: ../../AMD/Source/amd_preprocess.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_preprocess.c
+ $(C) -c $(I) zl_amd_preprocess.c
+
+zl_amd_valid.o: ../../AMD/Source/amd_valid.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_amd_valid.c
+ $(C) -c $(I) zl_amd_valid.c
+
+#-------------------------------------------------------------------------------
+# CAMD
+#-------------------------------------------------------------------------------
+
+zz_camd_1.o: ../../CAMD/Source/camd_1.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_1.c
+ $(C) -c $(I) zz_camd_1.c
+
+zz_camd_2.o: ../../CAMD/Source/camd_2.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_2.c
+ $(C) -c $(I) zz_camd_2.c
+
+zz_camd_aat.o: ../../CAMD/Source/camd_aat.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_aat.c
+ $(C) -c $(I) zz_camd_aat.c
+
+zz_camd_control.o: ../../CAMD/Source/camd_control.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_control.c
+ $(C) -c $(I) zz_camd_control.c
+
+zz_camd_defaults.o: ../../CAMD/Source/camd_defaults.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_defaults.c
+ $(C) -c $(I) zz_camd_defaults.c
+
+zz_camd_global.o: ../../CAMD/Source/camd_global.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_global.c
+ $(C) -c $(I) zz_camd_global.c
+
+zz_camd_dump.o: ../../CAMD/Source/camd_dump.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_dump.c
+ $(C) -c $(I) zz_camd_dump.c
+
+zz_camd_info.o: ../../CAMD/Source/camd_info.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_info.c
+ $(C) -c $(I) zz_camd_info.c
+
+zz_camd_order.o: ../../CAMD/Source/camd_order.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_order.c
+ $(C) -c $(I) zz_camd_order.c
+
+zz_camd_postorder.o: ../../CAMD/Source/camd_postorder.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_postorder.c
+ $(C) -c $(I) zz_camd_postorder.c
+
+zz_camd_preprocess.o: ../../CAMD/Source/camd_preprocess.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_preprocess.c
+ $(C) -c $(I) zz_camd_preprocess.c
+
+zz_camd_valid.o: ../../CAMD/Source/camd_valid.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_camd_valid.c
+ $(C) -c $(I) zz_camd_valid.c
+
+#-------------------------------------------------------------------------------
+
+zl_camd_1.o: ../../CAMD/Source/camd_1.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_1.c
+ $(C) -c $(I) zl_camd_1.c
+
+zl_camd_2.o: ../../CAMD/Source/camd_2.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_2.c
+ $(C) -c $(I) zl_camd_2.c
+
+zl_camd_aat.o: ../../CAMD/Source/camd_aat.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_aat.c
+ $(C) -c $(I) zl_camd_aat.c
+
+zl_camd_control.o: ../../CAMD/Source/camd_control.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_control.c
+ $(C) -c $(I) zl_camd_control.c
+
+zl_camd_defaults.o: ../../CAMD/Source/camd_defaults.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_defaults.c
+ $(C) -c $(I) zl_camd_defaults.c
+
+zl_camd_global.o: ../../CAMD/Source/camd_global.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_global.c
+ $(C) -c $(I) zl_camd_global.c
+
+zl_camd_dump.o: ../../CAMD/Source/camd_dump.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_dump.c
+ $(C) -c $(I) zl_camd_dump.c
+
+zl_camd_info.o: ../../CAMD/Source/camd_info.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_info.c
+ $(C) -c $(I) zl_camd_info.c
+
+zl_camd_order.o: ../../CAMD/Source/camd_order.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_order.c
+ $(C) -c $(I) zl_camd_order.c
+
+zl_camd_postorder.o: ../../CAMD/Source/camd_postorder.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_postorder.c
+ $(C) -c $(I) zl_camd_postorder.c
+
+zl_camd_preprocess.o: ../../CAMD/Source/camd_preprocess.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_preprocess.c
+ $(C) -c $(I) zl_camd_preprocess.c
+
+zl_camd_valid.o: ../../CAMD/Source/camd_valid.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_camd_valid.c
+ $(C) -c $(I) zl_camd_valid.c
+
+#-------------------------------------------------------------------------------
+
+zz_colamd.o: ../../COLAMD/Source/colamd.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_colamd.c
+ $(C) -c $(I) zz_colamd.c
+
+yz_colamd_global.o: ../../COLAMD/Source/colamd_global.c
+ $(C) -E $(I) $< | $(PRETTY) > yz_colamd_global.c
+ $(C) -c $(I) yz_colamd_global.c
+
+zl_colamd.o: ../../COLAMD/Source/colamd.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_colamd.c
+ $(C) -c $(I) zl_colamd.c
+
+yl_colamd_global.o: ../../COLAMD/Source/colamd_global.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > yl_colamd_global.c
+ $(C) -c $(I) yl_colamd_global.c
+
+#-------------------------------------------------------------------------------
+
+zz_ccolamd.o: ../../CCOLAMD/Source/ccolamd.c
+ $(C) -E $(I) $< | $(PRETTY) > zz_ccolamd.c
+ $(C) -c $(I) zz_ccolamd.c
+
+yz_ccolamd_global.o: ../../CCOLAMD/Source/ccolamd_global.c
+ $(C) -E $(I) $< | $(PRETTY) > yz_ccolamd_global.c
+ $(C) -c $(I) yz_ccolamd_global.c
+
+zl_ccolamd.o: ../../CCOLAMD/Source/ccolamd.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > zl_ccolamd.c
+ $(C) -c $(I) zl_ccolamd.c
+
+yl_ccolamd_global.o: ../../CCOLAMD/Source/ccolamd_global.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > yl_ccolamd_global.c
+ $(C) -c $(I) yl_ccolamd_global.c
+
+#-------------------------------------------------------------------------------
+
+z_check.o: ../Check/cholmod_check.c
+ $(C) -E $(I) $< | $(PRETTY) > z_check.c
+ $(C) -c $(I) z_check.c
+
+z_read.o: ../Check/cholmod_read.c
+ $(C) -E $(I) $< | $(PRETTY) > z_read.c
+ $(C) -c $(I) z_read.c
+
+z_write.o: ../Check/cholmod_write.c
+ $(C) -E $(I) $< | $(PRETTY) > z_write.c
+ $(C) -c $(I) z_write.c
+
+#-------------------------------------------------------------------------------
+
+z_common.o: ../Core/cholmod_common.c
+ $(C) -E $(I) $< | $(PRETTY) > z_common.c
+ $(C) -c $(I) z_common.c
+
+z_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c
+ $(C) -E $(I) $< | $(PRETTY) > z_dense.c
+ $(C) -c $(I) z_dense.c
+
+z_factor.o: ../Core/cholmod_factor.c
+ $(C) -E $(I) $< | $(PRETTY) > z_factor.c
+ $(C) -c $(I) z_factor.c
+
+z_change_factor.o: ../Core/cholmod_change_factor.c \
+ ../Core/t_cholmod_change_factor.c
+ $(C) -E $(I) $< | $(PRETTY) > z_change_factor.c
+ $(C) -c $(I) z_change_factor.c
+
+z_memory.o: ../Core/cholmod_memory.c
+ $(C) -E $(I) $< | $(PRETTY) > z_memory.c
+ $(C) -c $(I) z_memory.c
+
+z_sparse.o: ../Core/cholmod_sparse.c
+ $(C) -E $(I) $< | $(PRETTY) > z_sparse.c
+ $(C) -c $(I) z_sparse.c
+
+z_complex.o: ../Core/cholmod_complex.c
+ $(C) -E $(I) $< | $(PRETTY) > z_complex.c
+ $(C) -c $(I) z_complex.c
+
+z_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c
+ $(C) -E $(I) $< | $(PRETTY) > z_transpose.c
+ $(C) -c $(I) z_transpose.c
+
+z_band.o: ../Core/cholmod_band.c
+ $(C) -E $(I) $< | $(PRETTY) > z_band.c
+ $(C) -c $(I) z_band.c
+
+z_copy.o: ../Core/cholmod_copy.c
+ $(C) -E $(I) $< | $(PRETTY) > z_copy.c
+ $(C) -c $(I) z_copy.c
+
+z_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c
+ $(C) -E $(I) $< | $(PRETTY) > z_triplet.c
+ $(C) -c $(I) z_triplet.c
+
+z_error.o: ../Core/cholmod_error.c
+ $(C) -E $(I) $< | $(PRETTY) > z_error.c
+ $(C) -c $(I) z_error.c
+
+z_aat.o: ../Core/cholmod_aat.c
+ $(C) -E $(I) $< | $(PRETTY) > z_aat.c
+ $(C) -c $(I) z_aat.c
+
+z_add.o: ../Core/cholmod_add.c
+ $(C) -E $(I) $< | $(PRETTY) > z_add.c
+ $(C) -c $(I) z_add.c
+
+#-------------------------------------------------------------------------------
+
+z_amd.o: ../Cholesky/cholmod_amd.c
+ $(C) -E $(I) $< | $(PRETTY) > z_amd.c
+ $(C) -c $(I) z_amd.c
+
+z_analyze.o: ../Cholesky/cholmod_analyze.c
+ $(C) -E $(I) $< | $(PRETTY) > z_analyze.c
+ $(C) -c $(I) z_analyze.c
+
+z_colamd.o: ../Cholesky/cholmod_colamd.c
+ $(C) -E $(I) $< | $(PRETTY) > z_colamd.c
+ $(C) -c $(I) z_colamd.c
+
+z_etree.o: ../Cholesky/cholmod_etree.c
+ $(C) -E $(I) $< | $(PRETTY) > z_etree.c
+ $(C) -c $(I) z_etree.c
+
+z_factorize.o: ../Cholesky/cholmod_factorize.c
+ $(C) -E $(I) $< | $(PRETTY) > z_factorize.c
+ $(C) -c $(I) z_factorize.c
+
+z_postorder.o: ../Cholesky/cholmod_postorder.c
+ $(C) -E $(I) $< | $(PRETTY) > z_postorder.c
+ $(C) -c $(I) z_postorder.c
+
+z_rcond.o: ../Cholesky/cholmod_rcond.c
+ $(C) -E $(I) $< | $(PRETTY) > z_rcond.c
+ $(C) -c $(I) z_rcond.c
+
+z_resymbol.o: ../Cholesky/cholmod_resymbol.c
+ $(C) -E $(I) $< | $(PRETTY) > z_resymbol.c
+ $(C) -c $(I) z_resymbol.c
+
+z_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c
+ $(C) -E $(I) $< | $(PRETTY) > z_rowcolcounts.c
+ $(C) -c $(I) z_rowcolcounts.c
+
+z_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \
+ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c
+ $(C) -E $(I) $< | $(PRETTY) > z_solve.c
+ $(C) -c $(I) z_solve.c
+
+z_spsolve.o: ../Cholesky/cholmod_spsolve.c
+ $(C) -E $(I) $< | $(PRETTY) > z_spsolve.c
+ $(C) -c $(I) z_spsolve.c
+
+z_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c
+ $(C) -E $(I) $< | $(PRETTY) > z_rowfac.c
+ $(C) -c $(I) z_rowfac.c
+
+#-------------------------------------------------------------------------------
+z_ccolamd.o: ../Partition/cholmod_ccolamd.c
+ $(C) -E $(I) $< | $(PRETTY) > z_ccolamd.c
+ $(C) -c $(I) z_ccolamd.c
+
+z_csymamd.o: ../Partition/cholmod_csymamd.c
+ $(C) -E $(I) $< | $(PRETTY) > z_csymamd.c
+ $(C) -c $(I) z_csymamd.c
+
+z_camd.o: ../Partition/cholmod_camd.c
+ $(C) -E $(I) $< | $(PRETTY) > z_camd.c
+ $(C) -c $(I) z_camd.c
+
+z_metis.o: ../Partition/cholmod_metis.c
+ $(C) -E $(I) $< | $(PRETTY) > z_metis.c
+ $(C) -c $(I) z_metis.c
+
+z_nesdis.o: ../Partition/cholmod_nesdis.c
+ $(C) -E $(I) $< | $(PRETTY) > z_nesdis.c
+ $(C) -c $(I) z_nesdis.c
+
+#-------------------------------------------------------------------------------
+
+z_horzcat.o: ../MatrixOps/cholmod_horzcat.c
+ $(C) -E $(I) $< | $(PRETTY) > z_horzcat.c
+ $(C) -c $(I) z_horzcat.c
+
+z_norm.o: ../MatrixOps/cholmod_norm.c
+ $(C) -E $(I) $< | $(PRETTY) > z_norm.c
+ $(C) -c $(I) z_norm.c
+
+z_scale.o: ../MatrixOps/cholmod_scale.c
+ $(C) -E $(I) $< | $(PRETTY) > z_scale.c
+ $(C) -c $(I) z_scale.c
+
+z_drop.o: ../MatrixOps/cholmod_drop.c
+ $(C) -E $(I) $< | $(PRETTY) > z_drop.c
+ $(C) -c $(I) z_drop.c
+
+z_sdmult.o: ../MatrixOps/cholmod_sdmult.c ../MatrixOps/t_cholmod_sdmult.c
+ $(C) -E $(I) $< | $(PRETTY) > z_sdmult.c
+ $(C) -c $(I) z_sdmult.c
+
+z_ssmult.o: ../MatrixOps/cholmod_ssmult.c
+ $(C) -E $(I) $< | $(PRETTY) > z_ssmult.c
+ $(C) -c $(I) z_ssmult.c
+
+z_submatrix.o: ../MatrixOps/cholmod_submatrix.c
+ $(C) -E $(I) $< | $(PRETTY) > z_submatrix.c
+ $(C) -c $(I) z_submatrix.c
+
+z_vertcat.o: ../MatrixOps/cholmod_vertcat.c
+ $(C) -E $(I) $< | $(PRETTY) > z_vertcat.c
+ $(C) -c $(I) z_vertcat.c
+
+z_symmetry.o: ../MatrixOps/cholmod_symmetry.c
+ $(C) -E $(I) $< | $(PRETTY) > z_symmetry.c
+ $(C) -c $(I) z_symmetry.c
+
+#-------------------------------------------------------------------------------
+
+z_rowadd.o: ../Modify/cholmod_rowadd.c
+ $(C) -E $(I) $< | $(PRETTY) > z_rowadd.c
+ $(C) -c $(I) z_rowadd.c
+
+z_rowdel.o: ../Modify/cholmod_rowdel.c
+ $(C) -E $(I) $< | $(PRETTY) > z_rowdel.c
+ $(C) -c $(I) z_rowdel.c
+
+z_updown.o: ../Modify/cholmod_updown.c \
+ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c
+ $(C) -E $(I) $< | $(PRETTY) > z_updown.c
+ $(C) -c $(I) z_updown.c
+
+#-------------------------------------------------------------------------------
+
+z_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \
+ ../Supernodal/t_cholmod_super_numeric.c
+ $(C) -E $(I) $< | $(PRETTY) > z_super_numeric.c
+ $(C) -c $(I) z_super_numeric.c
+
+z_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c
+ $(C) -E $(I) $< | $(PRETTY) > z_super_symbolic.c
+ $(C) -c $(I) z_super_symbolic.c
+
+z_super_solve.o: ../Supernodal/cholmod_super_solve.c
+ $(C) -E $(I) $< | $(PRETTY) > z_super_solve.c
+ $(C) -c $(I) z_super_solve.c
+
+#-------------------------------------------------------------------------------
+#-------------------------------------------------------------------------------
+
+l_check.o: ../Check/cholmod_check.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_check.c
+ $(C) -c $(I) l_check.c
+
+l_read.o: ../Check/cholmod_read.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_read.c
+ $(C) -c $(I) l_read.c
+
+l_write.o: ../Check/cholmod_write.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_write.c
+ $(C) -c $(I) l_write.c
+
+#-------------------------------------------------------------------------------
+
+l_common.o: ../Core/cholmod_common.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_common.c
+ $(C) -c $(I) l_common.c
+
+l_dense.o: ../Core/cholmod_dense.c ../Core/t_cholmod_dense.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_dense.c
+ $(C) -c $(I) l_dense.c
+
+l_factor.o: ../Core/cholmod_factor.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_factor.c
+ $(C) -c $(I) l_factor.c
+
+l_change_factor.o: ../Core/cholmod_change_factor.c \
+ ../Core/t_cholmod_change_factor.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_change_factor.c
+ $(C) -c $(I) l_change_factor.c
+
+l_memory.o: ../Core/cholmod_memory.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_memory.c
+ $(C) -c $(I) l_memory.c
+
+l_sparse.o: ../Core/cholmod_sparse.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_sparse.c
+ $(C) -c $(I) l_sparse.c
+
+l_complex.o: ../Core/cholmod_complex.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_complex.c
+ $(C) -c $(I) l_complex.c
+
+l_transpose.o: ../Core/cholmod_transpose.c ../Core/t_cholmod_transpose.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_transpose.c
+ $(C) -c $(I) l_transpose.c
+
+l_band.o: ../Core/cholmod_band.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_band.c
+ $(C) -c $(I) l_band.c
+
+l_copy.o: ../Core/cholmod_copy.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_copy.c
+ $(C) -c $(I) l_copy.c
+
+l_triplet.o: ../Core/cholmod_triplet.c ../Core/t_cholmod_triplet.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_triplet.c
+ $(C) -c $(I) l_triplet.c
+
+l_error.o: ../Core/cholmod_error.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_error.c
+ $(C) -c $(I) l_error.c
+
+l_aat.o: ../Core/cholmod_aat.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_aat.c
+ $(C) -c $(I) l_aat.c
+
+l_add.o: ../Core/cholmod_add.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_add.c
+ $(C) -c $(I) l_add.c
+
+#-------------------------------------------------------------------------------
+
+l_amd.o: ../Cholesky/cholmod_amd.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_amd.c
+ $(C) -c $(I) l_amd.c
+
+l_analyze.o: ../Cholesky/cholmod_analyze.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_analyze.c
+ $(C) -c $(I) l_analyze.c
+
+l_colamd.o: ../Cholesky/cholmod_colamd.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_colamd.c
+ $(C) -c $(I) l_colamd.c
+
+l_etree.o: ../Cholesky/cholmod_etree.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_etree.c
+ $(C) -c $(I) l_etree.c
+
+l_factorize.o: ../Cholesky/cholmod_factorize.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_factorize.c
+ $(C) -c $(I) l_factorize.c
+
+l_postorder.o: ../Cholesky/cholmod_postorder.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_postorder.c
+ $(C) -c $(I) l_postorder.c
+
+l_rcond.o: ../Cholesky/cholmod_rcond.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_rcond.c
+ $(C) -c $(I) l_rcond.c
+
+l_resymbol.o: ../Cholesky/cholmod_resymbol.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_resymbol.c
+ $(C) -c $(I) l_resymbol.c
+
+l_rowcolcounts.o: ../Cholesky/cholmod_rowcolcounts.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_rowcolcounts.c
+ $(C) -c $(I) l_rowcolcounts.c
+
+l_solve.o: ../Cholesky/cholmod_solve.c ../Cholesky/t_cholmod_lsolve.c \
+ ../Cholesky/t_cholmod_ltsolve.c ../Cholesky/t_cholmod_solve.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_solve.c
+ $(C) -c $(I) l_solve.c
+
+l_spsolve.o: ../Cholesky/cholmod_spsolve.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_spsolve.c
+ $(C) -c $(I) l_spsolve.c
+
+l_rowfac.o: ../Cholesky/cholmod_rowfac.c ../Cholesky/t_cholmod_rowfac.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_rowfac.c
+ $(C) -c $(I) l_rowfac.c
+
+#-------------------------------------------------------------------------------
+l_ccolamd.o: ../Partition/cholmod_ccolamd.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_ccolamd.c
+ $(C) -c $(I) l_ccolamd.c
+
+l_csymamd.o: ../Partition/cholmod_csymamd.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_csymamd.c
+ $(C) -c $(I) l_csymamd.c
+
+l_camd.o: ../Partition/cholmod_camd.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_camd.c
+ $(C) -c $(I) l_camd.c
+
+l_metis.o: ../Partition/cholmod_metis.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_metis.c
+ $(C) -c $(I) l_metis.c
+
+l_nesdis.o: ../Partition/cholmod_nesdis.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_nesdis.c
+ $(C) -c $(I) l_nesdis.c
+
+#-------------------------------------------------------------------------------
+
+l_horzcat.o: ../MatrixOps/cholmod_horzcat.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_horzcat.c
+ $(C) -c $(I) l_horzcat.c
+
+l_norm.o: ../MatrixOps/cholmod_norm.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_norm.c
+ $(C) -c $(I) l_norm.c
+
+l_scale.o: ../MatrixOps/cholmod_scale.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_scale.c
+ $(C) -c $(I) l_scale.c
+
+l_drop.o: ../MatrixOps/cholmod_drop.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_drop.c
+ $(C) -c $(I) l_drop.c
+
+l_sdmult.o: ../MatrixOps/cholmod_sdmult.c ../MatrixOps/t_cholmod_sdmult.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_sdmult.c
+ $(C) -c $(I) l_sdmult.c
+
+l_ssmult.o: ../MatrixOps/cholmod_ssmult.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_ssmult.c
+ $(C) -c $(I) l_ssmult.c
+
+l_submatrix.o: ../MatrixOps/cholmod_submatrix.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_submatrix.c
+ $(C) -c $(I) l_submatrix.c
+
+l_vertcat.o: ../MatrixOps/cholmod_vertcat.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_vertcat.c
+ $(C) -c $(I) l_vertcat.c
+
+l_symmetry.o: ../MatrixOps/cholmod_symmetry.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_symmetry.c
+ $(C) -c $(I) l_symmetry.c
+
+#-------------------------------------------------------------------------------
+
+l_rowadd.o: ../Modify/cholmod_rowadd.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_rowadd.c
+ $(C) -c $(I) l_rowadd.c
+
+l_rowdel.o: ../Modify/cholmod_rowdel.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_rowdel.c
+ $(C) -c $(I) l_rowdel.c
+
+l_updown.o: ../Modify/cholmod_updown.c \
+ ../Modify/t_cholmod_updown.c ../Modify/t_cholmod_updown_numkr.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_updown.c
+ $(C) -c $(I) l_updown.c
+
+#-------------------------------------------------------------------------------
+
+l_super_numeric.o: ../Supernodal/cholmod_super_numeric.c \
+ ../Supernodal/t_cholmod_super_numeric.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_super_numeric.c
+ $(C) -c $(I) l_super_numeric.c
+
+l_super_symbolic.o: ../Supernodal/cholmod_super_symbolic.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_super_symbolic.c
+ $(C) -c $(I) l_super_symbolic.c
+
+l_super_solve.o: ../Supernodal/cholmod_super_solve.c
+ $(C) -DDLONG -E $(I) $< | $(PRETTY) > l_super_solve.c
+ $(C) -c $(I) l_super_solve.c
+
+#-------------------------------------------------------------------------------
diff --git a/CHOLMOD/Tcov/Matrix/0 b/CHOLMOD/Tcov/Matrix/0
new file mode 100644
index 0000000..6a20ce4
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/0
@@ -0,0 +1 @@
+0 0 0 0
diff --git a/CHOLMOD/Tcov/Matrix/0_1 b/CHOLMOD/Tcov/Matrix/0_1
new file mode 100644
index 0000000..006db41
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/0_1
@@ -0,0 +1 @@
+0 1 0 0
diff --git a/CHOLMOD/Tcov/Matrix/1_0 b/CHOLMOD/Tcov/Matrix/1_0
new file mode 100644
index 0000000..0dea48b
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/1_0
@@ -0,0 +1 @@
+1 0 0 0
diff --git a/CHOLMOD/Tcov/Matrix/1e99 b/CHOLMOD/Tcov/Matrix/1e99
new file mode 100644
index 0000000..bda5c70
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/1e99
@@ -0,0 +1,4 @@
+%%MatrixMarket matrix coordinate real symmetric
+2 2 2
+1 1 1e99
+2 2 1e-99
diff --git a/CHOLMOD/Tcov/Matrix/2.tri b/CHOLMOD/Tcov/Matrix/2.tri
new file mode 100644
index 0000000..51fc412
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/2.tri
@@ -0,0 +1,5 @@
+2 2 4
+0 0 1
+0 1 2
+1 0 -2
+1 1 3
diff --git a/CHOLMOD/Tcov/Matrix/20lo b/CHOLMOD/Tcov/Matrix/20lo
new file mode 100644
index 0000000..9919a50
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/20lo
@@ -0,0 +1,211 @@
+20 20 210 -1
+0 0 1.0828864476260923e+01
+1 0 1.6627011669737349e-01
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diff --git a/CHOLMOD/Tcov/Matrix/2_3 b/CHOLMOD/Tcov/Matrix/2_3
new file mode 100644
index 0000000..b84a000
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/2_3
@@ -0,0 +1,7 @@
+2 3 6 0
+0 0 9.4423471389861624e-01
+1 0 8.3855545301913648e-01
+0 1 2.5842740296885991e-01
+1 1 4.2898125196177306e-02
+0 2 5.8847897639891693e-03
+1 2 5.7441796740690909e-01
diff --git a/CHOLMOD/Tcov/Matrix/2diag.tri b/CHOLMOD/Tcov/Matrix/2diag.tri
new file mode 100644
index 0000000..596dd10
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/2diag.tri
@@ -0,0 +1,3 @@
+2 2 2
+0 0 1
+1 1 3
diff --git a/CHOLMOD/Tcov/Matrix/2lo.tri b/CHOLMOD/Tcov/Matrix/2lo.tri
new file mode 100644
index 0000000..e428210
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/2lo.tri
@@ -0,0 +1,4 @@
+2 2 3
+0 0 1
+1 0 2
+1 1 3
diff --git a/CHOLMOD/Tcov/Matrix/2up.tri b/CHOLMOD/Tcov/Matrix/2up.tri
new file mode 100644
index 0000000..2a92ce5
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/2up.tri
@@ -0,0 +1,4 @@
+2 2 3
+0 0 1
+0 1 2
+1 1 3
diff --git a/CHOLMOD/Tcov/Matrix/3_2 b/CHOLMOD/Tcov/Matrix/3_2
new file mode 100644
index 0000000..b39f429
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/3_2
@@ -0,0 +1,7 @@
+3 2 6 0
+0 0 9.4423471389861624e-01
+1 0 2.5842740296885991e-01
+2 0 5.8847897639891693e-03
+0 1 8.3855545301913648e-01
+1 1 4.2898125196177306e-02
+2 1 5.7441796740690909e-01
diff --git a/CHOLMOD/Tcov/Matrix/3b b/CHOLMOD/Tcov/Matrix/3b
new file mode 100644
index 0000000..9ea6497
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/3b
@@ -0,0 +1,5 @@
+3 3 4
+0 0 1
+2 0 1
+0 1 1
+0 2 1
diff --git a/CHOLMOD/Tcov/Matrix/3by0.mtx b/CHOLMOD/Tcov/Matrix/3by0.mtx
new file mode 100644
index 0000000..1621a6f
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/3by0.mtx
@@ -0,0 +1,2 @@
+%%MatrixMarket matrix array real general
+3 0
diff --git a/CHOLMOD/Tcov/Matrix/3singular b/CHOLMOD/Tcov/Matrix/3singular
new file mode 100644
index 0000000..4d80e17
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/3singular
@@ -0,0 +1,5 @@
+3 3 4 1
+0 0 9.4423471389861624e-01
+0 1 8.3855545301913648e-01
+1 1 4.2898125196177306e-02
+1 2 5.7441796740690909e-01
diff --git a/CHOLMOD/Tcov/Matrix/4 b/CHOLMOD/Tcov/Matrix/4
new file mode 100644
index 0000000..d17570b
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/4
@@ -0,0 +1,17 @@
+4 4 16 0
+0 0 8.4472150190817474e-01
+1 0 3.6775288246828447e-01
+2 0 6.2080133182114383e-01
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+0 1 1.9389317998466821e-01
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+2 3 6.2731478808399666e-01
+3 3 6.9908013774533750e-01
diff --git a/CHOLMOD/Tcov/Matrix/4lo b/CHOLMOD/Tcov/Matrix/4lo
new file mode 100644
index 0000000..4177a39
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/4lo
@@ -0,0 +1,11 @@
+4 4 10 -1
+0 0 1.0828864476260923e+01
+1 0 1.6627011669737349e-01
+2 0 3.9390600531964565e-01
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diff --git a/CHOLMOD/Tcov/Matrix/5 b/CHOLMOD/Tcov/Matrix/5
new file mode 100644
index 0000000..8e58c54
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/5
@@ -0,0 +1,16 @@
+5 5 15 1
+0 0 2.3128893423956103e+00
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+1 1 2.3404148406122136e+00
+0 2 1.3087150593318868e+00
+1 2 1.0697105858626588e+00
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+0 3 1.8412759629133451e+00
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diff --git a/CHOLMOD/Tcov/Matrix/5by50 b/CHOLMOD/Tcov/Matrix/5by50
new file mode 100644
index 0000000..456110b
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/5by50
@@ -0,0 +1,69 @@
+5 50 68 0
+1 0 0.0157598
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+4 2 0.365078
+0 3 0.451425
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diff --git a/CHOLMOD/Tcov/Matrix/a1 b/CHOLMOD/Tcov/Matrix/a1
new file mode 100644
index 0000000..97afc3b
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/a1
@@ -0,0 +1 @@
+70000 70000 0 2
diff --git a/CHOLMOD/Tcov/Matrix/a2 b/CHOLMOD/Tcov/Matrix/a2
new file mode 100644
index 0000000..060e904
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diff --git a/CHOLMOD/Tcov/Matrix/c10 b/CHOLMOD/Tcov/Matrix/c10
new file mode 100644
index 0000000..e506746
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/c10
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diff --git a/CHOLMOD/Tcov/Matrix/c30lo b/CHOLMOD/Tcov/Matrix/c30lo
new file mode 100644
index 0000000..ddf7636
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/c30lo
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diff --git a/CHOLMOD/Tcov/Matrix/c30up b/CHOLMOD/Tcov/Matrix/c30up
new file mode 100644
index 0000000..0fba18a
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/c30up
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diff --git a/CHOLMOD/Tcov/Matrix/c3singular b/CHOLMOD/Tcov/Matrix/c3singular
new file mode 100644
index 0000000..f772d13
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/c3singular
@@ -0,0 +1,5 @@
+3 3 4 1 1
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diff --git a/CHOLMOD/Tcov/Matrix/c5lo b/CHOLMOD/Tcov/Matrix/c5lo
new file mode 100644
index 0000000..4046dc5
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/c5lo
@@ -0,0 +1,12 @@
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diff --git a/CHOLMOD/Tcov/Matrix/c5up b/CHOLMOD/Tcov/Matrix/c5up
new file mode 100644
index 0000000..7dfb288
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/c5up
@@ -0,0 +1,12 @@
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diff --git a/CHOLMOD/Tcov/Matrix/c5up2 b/CHOLMOD/Tcov/Matrix/c5up2
new file mode 100644
index 0000000..af15774
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/c5up2
@@ -0,0 +1,12 @@
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diff --git a/CHOLMOD/Tcov/Matrix/cha b/CHOLMOD/Tcov/Matrix/cha
new file mode 100644
index 0000000..c4e49e9
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/cha
@@ -0,0 +1,7 @@
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diff --git a/CHOLMOD/Tcov/Matrix/cha.mtx b/CHOLMOD/Tcov/Matrix/cha.mtx
new file mode 100644
index 0000000..52b8cd2
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/cha.mtx
@@ -0,0 +1,8 @@
+%%MatrixMarket matrix coordinate complex Hermitian
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diff --git a/CHOLMOD/Tcov/Matrix/cpi b/CHOLMOD/Tcov/Matrix/cpi
new file mode 100644
index 0000000..1c42281
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/cpi
@@ -0,0 +1,2 @@
+1 1 1 0 1
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diff --git a/CHOLMOD/Tcov/Matrix/crud1 b/CHOLMOD/Tcov/Matrix/crud1
new file mode 100644
index 0000000..d00491f
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/crud1
@@ -0,0 +1 @@
+1
diff --git a/CHOLMOD/Tcov/Matrix/crud2 b/CHOLMOD/Tcov/Matrix/crud2
new file mode 100644
index 0000000..ad59718
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/crud2
@@ -0,0 +1,2 @@
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diff --git a/CHOLMOD/Tcov/Matrix/cs.mtx b/CHOLMOD/Tcov/Matrix/cs.mtx
new file mode 100644
index 0000000..cacae9b
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/cs.mtx
@@ -0,0 +1,7 @@
+%%MatrixMarket matrix coordinate complex symmetric
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+2 2 1. 0.
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+3 3 42. 0.
diff --git a/CHOLMOD/Tcov/Matrix/csa.mtx b/CHOLMOD/Tcov/Matrix/csa.mtx
new file mode 100644
index 0000000..bb73a55
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/csa.mtx
@@ -0,0 +1,8 @@
+%%MatrixMarket matrix coordinate complex symmetric
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diff --git a/CHOLMOD/Tcov/Matrix/cza b/CHOLMOD/Tcov/Matrix/cza
new file mode 100644
index 0000000..f9b2f14
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/cza
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diff --git a/CHOLMOD/Tcov/Matrix/cza.mtx b/CHOLMOD/Tcov/Matrix/cza.mtx
new file mode 100644
index 0000000..6bb32d7
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/cza.mtx
@@ -0,0 +1,5 @@
+%%MatrixMarket matrix coordinate complex skew-symmetric
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diff --git a/CHOLMOD/Tcov/Matrix/diag b/CHOLMOD/Tcov/Matrix/diag
new file mode 100644
index 0000000..a8ecd13
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/diag
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new file mode 100644
index 0000000..cea660b
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/fullcha.mtx
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new file mode 100644
index 0000000..c2db3d8
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new file mode 100644
index 0000000..0e9436a
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new file mode 100644
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diff --git a/CHOLMOD/Tcov/Matrix/mega.tri b/CHOLMOD/Tcov/Matrix/mega.tri
new file mode 100644
index 0000000..8206f68
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/mega.tri
@@ -0,0 +1,2 @@
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diff --git a/CHOLMOD/Tcov/Matrix/one b/CHOLMOD/Tcov/Matrix/one
new file mode 100644
index 0000000..ca1c54c
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/one
@@ -0,0 +1,2 @@
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diff --git a/CHOLMOD/Tcov/Matrix/pi b/CHOLMOD/Tcov/Matrix/pi
new file mode 100644
index 0000000..1a1b09f
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/pi
@@ -0,0 +1,2 @@
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diff --git a/CHOLMOD/Tcov/Matrix/plskz362.mtx b/CHOLMOD/Tcov/Matrix/plskz362.mtx
new file mode 100644
index 0000000..64a267b
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/plskz362.mtx
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diff --git a/CHOLMOD/Tcov/Matrix/r5lo b/CHOLMOD/Tcov/Matrix/r5lo
new file mode 100644
index 0000000..c805e61
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/r5lo
@@ -0,0 +1,11 @@
+5 5 10 -1 0
+0 0 2.43872
+2 0 0.724062
+4 0 0.281634
+1 1 4.21742
+2 1 1.69463
+3 1 1.23492
+2 2 4.77818
+3 2 0.902819
+3 3 3.51267
+4 4 6.25922
diff --git a/CHOLMOD/Tcov/Matrix/r5lo2 b/CHOLMOD/Tcov/Matrix/r5lo2
new file mode 100644
index 0000000..36a5700
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/r5lo2
@@ -0,0 +1,15 @@
+% comments like this are ignored
+5 5 10 -1 0
+0 0 2.43872
+2 0 0.724062
+4 0 0.281634
+1 1 4.21742
+%
+% so are blank lines
+2 1 1.69463
+3 1 1.23492
+2 2 4.77818
+
+3 2 0.902819
+3 3 3.51267
+4 4 6.25922
diff --git a/CHOLMOD/Tcov/Matrix/r5up b/CHOLMOD/Tcov/Matrix/r5up
new file mode 100644
index 0000000..5de0efc
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/r5up
@@ -0,0 +1,11 @@
+5 5 10 1 0
+0 0 2.43872
+1 1 4.21742
+0 2 0.724062
+1 2 1.69463
+2 2 4.77818
+1 3 1.23492
+2 3 0.902819
+3 3 3.51267
+0 4 0.281634
+4 4 6.25922
diff --git a/CHOLMOD/Tcov/Matrix/r5up2 b/CHOLMOD/Tcov/Matrix/r5up2
new file mode 100644
index 0000000..c6250ce
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/r5up2
@@ -0,0 +1,11 @@
+5 5 10 1 0
+0 0 2.43872
+1 1 4.21742
+2 0 0.724062
+1 2 1.69463
+2 2 4.77818
+1 3 1.23492
+2 3 0.902819
+3 3 3.51267
+0 4 0.281634
+4 4 6.25922
diff --git a/CHOLMOD/Tcov/Matrix/rename.h b/CHOLMOD/Tcov/Matrix/rename.h
new file mode 100644
index 0000000..bd8aace
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/rename.h
@@ -0,0 +1,10 @@
+/* do not edit this file; generated by cholmod_make */
+#undef log2
+#include "../../metis-4.0/Lib/rename.h"
+#undef log2
+#define log2 METIS__log2
+#include "mex.h"
+#define malloc mxMalloc
+#define free mxFree
+#define calloc mxCalloc
+#define realloc mxRealloc
diff --git a/CHOLMOD/Tcov/Matrix/rza.mtx b/CHOLMOD/Tcov/Matrix/rza.mtx
new file mode 100644
index 0000000..35d78bf
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/rza.mtx
@@ -0,0 +1,5 @@
+%%MatrixMarket matrix coordinate integer skew-symmetric
+3 3 3
+2 1 -13
+3 1 -32
+3 2 -17
diff --git a/CHOLMOD/Tcov/Matrix/tri b/CHOLMOD/Tcov/Matrix/tri
new file mode 100644
index 0000000..7872038
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/tri
@@ -0,0 +1 @@
+10 10 44 3
diff --git a/CHOLMOD/Tcov/Matrix/tribig b/CHOLMOD/Tcov/Matrix/tribig
new file mode 100644
index 0000000..bae6846
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/tribig
@@ -0,0 +1 @@
+1000000 1000000 0 3
diff --git a/CHOLMOD/Tcov/Matrix/z10 b/CHOLMOD/Tcov/Matrix/z10
new file mode 100644
index 0000000..535fee1
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/z10
@@ -0,0 +1,61 @@
+10 15 60 0 2
+0 0 0.660427 0.980481
+2 0 0.673653 0.791832
+7 0 0.95733 0.152594
+1 1 0.191866 0.833027
+3 1 0.111216 0.191863
+4 1 0.565054 0.638987
+9 1 0.969166 0.669
+3 2 0.0237439 0.772088
+5 2 0.870216 0.379818
+7 2 0.0268766 0.441585
+8 2 0.519529 0.48306
+5 3 0.192291 0.608106
+6 3 0.715689 0.175996
+7 3 0.250673 0.00202556
+8 3 0.933865 0.790224
+9 3 0.137189 0.513609
+0 4 0.521622 0.213229
+1 4 0.895202 0.10345
+2 4 0.942387 0.157337
+3 4 0.335083 0.407515
+7 4 0.437364 0.407757
+6 5 0.471156 0.0526927
+8 5 0.14931 0.941815
+9 5 0.135864 0.149972
+2 6 0.532498 0.384374
+4 6 0.725789 0.311059
+5 6 0.398703 0.168534
+9 6 0.358419 0.896648
+0 7 0.285279 0.322724
+1 7 0.868635 0.733996
+2 7 0.626413 0.410904
+5 7 0.241172 0.399794
+6 7 0.978082 0.505522
+2 8 0.640501 0.169306
+8 8 0.229849 0.524745
+0 9 0.681335 0.641203
+1 9 0.665823 0.0161975
+2 9 0.134718 0.836852
+4 9 0.0224933 0.803462
+5 9 0.262199 0.697785
+7 9 0.116515 0.461888
+9 9 0.0693182 0.0826126
+0 10 0.85293 0.820717
+1 10 0.180331 0.19302
+8 10 0.0324186 0.445355
+9 10 0.733926 0.0129578
+0 11 0.536517 0.308742
+2 11 0.27603 0.875351
+8 11 0.368458 0.835259
+1 12 0.0128863 0.333095
+2 12 0.889206 0.880705
+8 12 0.866021 0.479687
+9 12 0.254247 0.560817
+0 13 0.569481 0.615909
+2 13 0.159265 0.661899
+3 13 0.594364 0.616633
+7 13 0.3311 0.68514
+9 13 0.658613 0.510153
+5 14 0.863634 0.713961
+8 14 0.567623 0.515208
diff --git a/CHOLMOD/Tcov/Matrix/z30lo b/CHOLMOD/Tcov/Matrix/z30lo
new file mode 100644
index 0000000..c4f7853
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/z30lo
@@ -0,0 +1,115 @@
+30 30 114 -1 2
+0 0 4.98585 0
+6 0 0.121047 0.335197
+9 0 0.450754 0.655531
+12 0 0.23788 -0.548513
+14 0 0.734908 -0.634266
+19 0 0.0491625 -0.680204
+20 0 0.982988 -0.498305
+24 0 0.715883 0.391904
+25 0 0.892842 0.627315
+27 0 0.273102 0.69908
+1 1 2.80724 0
+5 1 0.254769 0.397184
+6 1 0.170793 -0.700635
+10 1 0.865603 0.413629
+18 1 0.23235 0.655213
+21 1 0.804872 0.837585
+24 1 0.908398 0.371608
+26 1 0.231894 0.425253
+2 2 6.14737 0
+8 2 0.239313 0.594663
+23 2 0.0497545 0.565739
+3 3 6.78061 0
+4 4 5.13451 0
+5 4 0.640815 0.511311
+13 4 0.870381 -0.571057
+28 4 0.190887 0.776401
+5 5 2.14374 0
+12 5 0.645831 -0.26177
+14 5 0.843869 0.489345
+17 5 0.1739 0.185904
+20 5 0.552673 -0.434441
+23 5 0.919957 -0.273088
+28 5 0.569206 -0.474041
+6 6 6.06059 0
+12 6 0.994295 0.982709
+13 6 0.0099273 -0.700857
+17 6 0.422452 -0.253561
+20 6 0.439791 0.806638
+25 6 0.340048 0.703568
+7 7 5.05057 0
+21 7 0.375885 -0.754551
+8 8 5.50746 0
+12 8 0.314217 0.484964
+13 8 0.365078 0.114613
+18 8 0.457354 -0.96137
+20 8 0.400074 -0.562458
+26 8 0.39324 0.664856
+9 9 2.46098 0
+13 9 0.13701 -0.962288
+19 9 0.591525 0.365374
+20 9 0.119747 0.140044
+22 9 0.0381288 0.566773
+25 9 0.731277 -0.0889618
+10 10 4.12445 0
+11 10 0.934237 -0.999447
+20 10 0.198789 -0.616621
+22 10 0.458598 0.823008
+26 10 0.869867 0.673949
+11 11 3.87788 0
+16 11 0.264449 0.961636
+17 11 0.855976 -0.873451
+18 11 0.450689 -0.0720592
+19 11 0.1603 0.0588622
+25 11 0.872855 0.360311
+28 11 0.63179 -0.908989
+12 12 2.83077 0
+15 12 1.13292 -0.348118
+23 12 0.664931 0.049278
+29 12 0.234413 -0.596247
+13 13 6.16576 0
+14 13 0.818756 0.750518
+15 13 0.430166 0.739993
+18 13 0.412219 -0.553408
+23 13 0.844722 -0.626235
+26 13 0.193893 -0.271308
+28 13 0.890322 0.431873
+29 13 0.548782 -0.328955
+14 14 6.1932 0
+20 14 0.687324 0.803026
+26 14 0.346112 0.083881
+15 15 4.25807 0
+23 15 0.367753 -0.536852
+27 15 0.155613 0.915942
+16 16 6.78301 0
+18 16 0.90161 -0.291984
+22 16 0.191116 0.601987
+17 17 3.71627 0
+18 17 0.815935 0.732651
+28 17 0.46077 0.422227
+18 18 6.34966 0
+20 18 0.625201 -0.11334
+21 18 0.00558394 0.857964
+25 18 0.297406 0.335755
+26 18 0.904812 -0.409072
+19 19 5.84718 0
+22 19 0.69318 0.0534444
+26 19 0.650106 0.356656
+20 20 4.22081 0
+21 20 0.00987646 -0.791123
+29 20 0.733363 0.898252
+21 21 5.1031 0
+22 21 0.75367 -0.670004
+24 21 0.419858 0.814952
+22 22 6.75845 0
+27 22 0.793872 0.200876
+23 23 5.20005 0
+24 23 0.620801 0.0595041
+24 24 3.23664 0
+25 25 3.76351 0
+29 25 0.931583 -0.478194
+26 26 2.9393 0
+27 27 4.45322 0
+28 28 4.04637 0
+29 29 4.31763 0
diff --git a/CHOLMOD/Tcov/Matrix/z30up b/CHOLMOD/Tcov/Matrix/z30up
new file mode 100644
index 0000000..0a88cb9
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/z30up
@@ -0,0 +1,115 @@
+30 30 114 1 2
+0 0 4.98585 0
+1 1 2.80724 0
+2 2 6.14737 0
+3 3 6.78061 0
+4 4 5.13451 0
+1 5 0.254769 -0.397184
+4 5 0.640815 -0.511311
+5 5 2.14374 0
+0 6 0.121047 -0.335197
+1 6 0.170793 0.700635
+6 6 6.06059 0
+7 7 5.05057 0
+2 8 0.239313 -0.594663
+8 8 5.50746 0
+0 9 0.450754 -0.655531
+9 9 2.46098 0
+1 10 0.865603 -0.413629
+10 10 4.12445 0
+10 11 0.934237 0.999447
+11 11 3.87788 0
+0 12 0.23788 0.548513
+5 12 0.645831 0.26177
+6 12 0.994295 -0.982709
+8 12 0.314217 -0.484964
+12 12 2.83077 0
+4 13 0.870381 0.571057
+6 13 0.0099273 0.700857
+8 13 0.365078 -0.114613
+9 13 0.13701 0.962288
+13 13 6.16576 0
+0 14 0.734908 0.634266
+5 14 0.843869 -0.489345
+13 14 0.818756 -0.750518
+14 14 6.1932 0
+12 15 1.13292 0.348118
+13 15 0.430166 -0.739993
+15 15 4.25807 0
+11 16 0.264449 -0.961636
+16 16 6.78301 0
+5 17 0.1739 -0.185904
+6 17 0.422452 0.253561
+11 17 0.855976 0.873451
+17 17 3.71627 0
+1 18 0.23235 -0.655213
+8 18 0.457354 0.96137
+11 18 0.450689 0.0720592
+13 18 0.412219 0.553408
+16 18 0.90161 0.291984
+17 18 0.815935 -0.732651
+18 18 6.34966 0
+0 19 0.0491625 0.680204
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+11 19 0.1603 -0.0588622
+19 19 5.84718 0
+0 20 0.982988 0.498305
+5 20 0.552673 0.434441
+6 20 0.439791 -0.806638
+8 20 0.400074 0.562458
+9 20 0.119747 -0.140044
+10 20 0.198789 0.616621
+14 20 0.687324 -0.803026
+18 20 0.625201 0.11334
+20 20 4.22081 0
+1 21 0.804872 -0.837585
+7 21 0.375885 0.754551
+18 21 0.00558394 -0.857964
+20 21 0.00987646 0.791123
+21 21 5.1031 0
+9 22 0.0381288 -0.566773
+10 22 0.458598 -0.823008
+16 22 0.191116 -0.601987
+19 22 0.69318 -0.0534444
+21 22 0.75367 0.670004
+22 22 6.75845 0
+2 23 0.0497545 -0.565739
+5 23 0.919957 0.273088
+12 23 0.664931 -0.049278
+13 23 0.844722 0.626235
+15 23 0.367753 0.536852
+23 23 5.20005 0
+0 24 0.715883 -0.391904
+1 24 0.908398 -0.371608
+21 24 0.419858 -0.814952
+23 24 0.620801 -0.0595041
+24 24 3.23664 0
+0 25 0.892842 -0.627315
+6 25 0.340048 -0.703568
+9 25 0.731277 0.0889618
+11 25 0.872855 -0.360311
+18 25 0.297406 -0.335755
+25 25 3.76351 0
+1 26 0.231894 -0.425253
+8 26 0.39324 -0.664856
+10 26 0.869867 -0.673949
+13 26 0.193893 0.271308
+14 26 0.346112 -0.083881
+18 26 0.904812 0.409072
+19 26 0.650106 -0.356656
+26 26 2.9393 0
+0 27 0.273102 -0.69908
+15 27 0.155613 -0.915942
+22 27 0.793872 -0.200876
+27 27 4.45322 0
+4 28 0.190887 -0.776401
+5 28 0.569206 0.474041
+11 28 0.63179 0.908989
+13 28 0.890322 -0.431873
+17 28 0.46077 -0.422227
+28 28 4.04637 0
+12 29 0.234413 0.596247
+13 29 0.548782 0.328955
+20 29 0.733363 -0.898252
+25 29 0.931583 0.478194
+29 29 4.31763 0
diff --git a/CHOLMOD/Tcov/Matrix/z3singular b/CHOLMOD/Tcov/Matrix/z3singular
new file mode 100644
index 0000000..e06bcfd
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/z3singular
@@ -0,0 +1,5 @@
+3 3 4 1 2
+0 0 9.4423471389861624e-01 0.1
+0 1 8.3855545301913648e-01 0.2
+1 1 4.2898125196177306e-02 0.03
+1 2 5.7441796740690909e-01 0.04
diff --git a/CHOLMOD/Tcov/Matrix/z5lo b/CHOLMOD/Tcov/Matrix/z5lo
new file mode 100644
index 0000000..1dcfa83
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/z5lo
@@ -0,0 +1,12 @@
+5 5 11 -1 2
+0 0 2.43872 0
+1 0 0.261819 -0.16627
+2 0 0.724062 0.804517
+4 0 0.281634 0.828864
+1 1 4.21742 0
+2 1 1.69463 -0.324218
+3 1 1.23492 0.0754504
+2 2 4.77818 0
+3 2 0.902819 0.460806
+3 3 3.51267 0
+4 4 6.25922 0
diff --git a/CHOLMOD/Tcov/Matrix/z5up b/CHOLMOD/Tcov/Matrix/z5up
new file mode 100644
index 0000000..5ec7931
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/z5up
@@ -0,0 +1,12 @@
+5 5 11 1 2
+0 0 2.43872 0
+0 1 0.261819 0.16627
+1 1 4.21742 0
+0 2 0.724062 -0.804517
+1 2 1.69463 0.324218
+2 2 4.77818 0
+1 3 1.23492 -0.0754504
+2 3 0.902819 -0.460806
+3 3 3.51267 0
+0 4 0.281634 -0.828864
+4 4 6.25922 0
diff --git a/CHOLMOD/Tcov/Matrix/z5up2 b/CHOLMOD/Tcov/Matrix/z5up2
new file mode 100644
index 0000000..8900257
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/z5up2
@@ -0,0 +1,12 @@
+5 5 11 1 2
+0 0 2.43872 0
+0 1 0.261819 0.16627
+1 1 4.21742 0
+2 0 0.724062 -0.804517
+1 2 1.69463 0.324218
+2 2 4.77818 0
+1 3 1.23492 -0.0754504
+2 3 0.902819 -0.460806
+3 3 3.51267 0
+0 4 0.281634 -0.828864
+4 4 6.25922 0
diff --git a/CHOLMOD/Tcov/Matrix/zero b/CHOLMOD/Tcov/Matrix/zero
new file mode 100644
index 0000000..a05785f
--- /dev/null
+++ b/CHOLMOD/Tcov/Matrix/zero
@@ -0,0 +1 @@
+1100000000 1100000000 0 0
diff --git a/CHOLMOD/Tcov/README.txt b/CHOLMOD/Tcov/README.txt
new file mode 100644
index 0000000..5974f5c
--- /dev/null
+++ b/CHOLMOD/Tcov/README.txt
@@ -0,0 +1,46 @@
+Tcov directory: Torture test for CHOLMOD, with statement coverage.
+--------------------------------------------------------------------------------
+
+This test suite is not required to compile and use CHOLMOD. It is thus
+not ported to all architectures. Linux is assumed; see the Makefile for
+running on Solaris. Use tcov instead of gcov in the "covall" script. Edit
+the Makefile and change the definition of CC. You may need to change PRETTY
+as well. You will need to edit LIB to reflect the proper LAPACK and BLAS
+libraries.
+
+Requires all CHOLMOD modules except the Partition Module, which it can
+optionally use (and test). Also acts as a statement coverage test for
+AMD, COLAMD, and CCOLAMD.
+
+Type "make" in this directory to compile CHOLMOMD with statement coverage
+testing. Then type "make go" to run the tests.
+
+Note that about 500MB of disk space is required, mostly in the tmp/
+directory.
+
+Every line of AMD, CAMD, COLAMD, CCOLAMD, and CHOLMOD will be exercised,
+and their results checked. The line "All tests passed" should be
+printed for each test on stderr. Some matrices will report NaN as their
+maximum error; these are the four singular test matrices (Matrix/1_0,
+Matrix/3singular, Matrix/c3singluar, and Matrix/z3singular). These test
+results are expected. Nan's will also appear in tmp/galenet_nan.out and
+tmp/l_galenet_nan.out; these are generated intentionally, to test the code's
+NaN-handling features.
+
+The source code files are first preprocessed with cc -E, and the resulting
+file (z_*.c, zz_*.c, l_*.c, or zl_*.c) is then compiled. This is to ensure
+that all lines within macros and included *.c files are tested (take a look at
+z_updown.c and z_solve.c if you'd like to see how loop-unrolling and
+real/complex templates are done in CHOLMOD, and compare those files with their
+source files in ../Modify and ../Cholesky).
+
+Note that many, many error messages will appear in the test output itself
+(tmp/*.out), because all of CHOLMOD's error handling is checked as well.
+These errors are expected. Any unexpected error will cause the test to fail.
+The last line of each output file should be "All tests successful".
+
+To remove all but the original source files and output files from
+this directory, type "make clean". To remove all but the
+files in the original distribution, type "make distclean".
+
+The output of "make go" is in the "make_go.output" file.
diff --git a/CHOLMOD/Tcov/amdtest.c b/CHOLMOD/Tcov/amdtest.c
new file mode 100644
index 0000000..a11fa0d
--- /dev/null
+++ b/CHOLMOD/Tcov/amdtest.c
@@ -0,0 +1,377 @@
+/* ========================================================================== */
+/* === Tcov/amdtest ========================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Test for amd v2.0 */
+
+#include "cm.h"
+#include "amd.h"
+
+
+/* ========================================================================== */
+/* === amdtest ============================================================== */
+/* ========================================================================== */
+
+void amdtest (cholmod_sparse *A)
+{
+ double Control [AMD_CONTROL], Info [AMD_INFO], alpha ;
+ Int *P, *Cp, *Ci, *Sp, *Si, *Bp, *Bi, *Ep, *Ei, *Fp, *Fi,
+ *Len, *Nv, *Next, *Head, *Elen, *Deg, *Wi, *W, *Flag ;
+ cholmod_sparse *C, *B, *S, *E, *F ;
+ Int i, j, n, nrow, ncol, ok, cnz, bnz, p, trial, sorted ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nAMD test\n") ;
+
+ if (A == NULL)
+ {
+ return ;
+ }
+
+ if (A->stype)
+ {
+ B = CHOLMOD(copy) (A, 0, 0, cm) ;
+ }
+ else
+ {
+ B = CHOLMOD(aat) (A, NULL, 0, 0, cm) ;
+ }
+
+ if (A->nrow != A->ncol)
+ {
+ F = CHOLMOD(copy_sparse) (B, cm) ;
+ OK (F->nrow == F->ncol) ;
+ CHOLMOD(sort) (F, cm) ;
+ }
+ else
+ {
+ /* A is square and unsymmetric, and may have entries in A+A' that
+ * are not in A */
+ F = CHOLMOD(copy_sparse) (A, cm) ;
+ CHOLMOD(sort) (F, cm) ;
+ }
+
+ C = CHOLMOD(copy_sparse) (B, cm) ;
+
+ nrow = C->nrow ;
+ ncol = C->ncol ;
+ n = nrow ;
+ OK (nrow == ncol) ;
+
+ Cp = C->p ;
+ Ci = C->i ;
+
+ Bp = B->p ;
+ Bi = B->i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* S = sorted form of B, using AMD_preprocess */
+ /* ---------------------------------------------------------------------- */
+
+ cnz = CHOLMOD(nnz) (C, cm) ;
+ S = CHOLMOD(allocate_sparse) (n, n, cnz, TRUE, TRUE, 0, CHOLMOD_PATTERN,
+ cm);
+ Sp = S->p ;
+ Si = S->i ;
+
+ W = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Flag = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace for amd */
+ /* ---------------------------------------------------------------------- */
+
+ P = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ;
+
+ Len = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Nv = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Next = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Head = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ;
+ Elen = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Deg = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Wi = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+
+ /* ---------------------------------------------------------------------- */
+
+ for (sorted = 0 ; sorted <= 1 ; sorted++)
+ {
+
+ if (sorted) CHOLMOD(sort) (C, cm) ;
+
+ Cp = C->p ;
+ Ci = C->i ;
+
+ /* ------------------------------------------------------------------ */
+ /* order C with AMD_order */
+ /* ------------------------------------------------------------------ */
+
+ AMD_defaults (Control) ;
+ AMD_defaults (NULL) ;
+ AMD_control (Control) ;
+ AMD_control (NULL) ;
+ AMD_info (NULL) ;
+
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ printf ("amd return value: "ID"\n", ok) ;
+ AMD_info (Info) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation", cm)) ;
+
+ /* no dense rows/cols */
+ alpha = Control [AMD_DENSE] ;
+ Control [AMD_DENSE] = -1 ;
+ AMD_control (Control) ;
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ printf ("amd return value: "ID"\n", ok) ;
+ AMD_info (Info) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (alpha=-1)", cm)) ;
+
+ /* many dense rows/cols */
+ Control [AMD_DENSE] = 0 ;
+ AMD_control (Control) ;
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ printf ("amd return value: "ID"\n", ok) ;
+ AMD_info (Info) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (alpha=0)", cm)) ;
+ Control [AMD_DENSE] = alpha ;
+
+ /* no aggressive absorption */
+ Control [AMD_AGGRESSIVE] = FALSE ;
+ AMD_control (Control) ;
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ printf ("amd return value: "ID"\n", ok) ;
+ AMD_info (Info) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (no agg) ", cm)) ;
+ Control [AMD_AGGRESSIVE] = TRUE ;
+
+ /* ------------------------------------------------------------------ */
+ /* order F with AMD_order */
+ /* ------------------------------------------------------------------ */
+
+ Fp = F->p ;
+ Fi = F->i ;
+ ok = AMD_order (n, Fp, Fi, P, Control, Info) ;
+ printf ("amd return value: "ID"\n", ok) ;
+ AMD_info (Info) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "F: AMD permutation", cm)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* order S with AMD_order */
+ /* ------------------------------------------------------------------ */
+
+ ok = AMD_order (n, Sp, Si, P, Control, Info) ;
+ printf ("amd return value: "ID"\n", ok) ;
+ AMD_info (Info) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation", cm)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* order E with AMD_2, which destroys its contents */
+ /* ------------------------------------------------------------------ */
+
+ E = CHOLMOD(copy) (B, 0, -1, cm) ; /* remove diagonal entries */
+ bnz = CHOLMOD(nnz) (E, cm) ;
+
+ /* add the bare minimum extra space to E */
+ ok = CHOLMOD(reallocate_sparse) (bnz + n, E, cm) ;
+ OK (ok) ;
+ Ep = E->p ;
+ Ei = E->i ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ Len [j] = Ep [j+1] - Ep [j] ;
+ }
+
+ printf ("calling AMD_2:\n") ;
+ if (n > 0)
+ {
+ AMD_2 (n, Ep, Ei, Len, E->nzmax, Ep [n], Nv, Next, P, Head, Elen,
+ Deg, Wi, Control, Info) ;
+ AMD_info (Info) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "AMD2 permutation", cm)) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* error tests */
+ /* ------------------------------------------------------------------ */
+
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ ok = AMD_order (-1, Cp, Ci, P, Control, Info) ;
+ OK (ok == AMD_INVALID);
+ ok = AMD_order (0, Cp, Ci, P, Control, Info) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ ok = AMD_order (n, NULL, Ci, P, Control, Info) ;
+ OK (ok == AMD_INVALID);
+ ok = AMD_order (n, Cp, NULL, P, Control, Info) ;
+ OK (ok == AMD_INVALID);
+ ok = AMD_order (n, Cp, Ci, NULL, Control, Info) ;
+ OK (ok == AMD_INVALID);
+
+ if (n > 0)
+ {
+ printf ("AMD error tests:\n") ;
+
+ p = Cp [n] ;
+ Cp [n] = -1 ;
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ OK (ok == AMD_INVALID) ;
+
+ if (Size_max/2 == Int_max)
+ {
+ Cp [n] = Int_max ;
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ printf ("AMD status is %d\n", ok) ;
+ OK (ok == AMD_OUT_OF_MEMORY) ;
+ }
+
+ Cp [n] = p ;
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ if (Cp [n] > 0)
+ {
+ printf ("Mangle column zero:\n") ;
+ i = Ci [0] ;
+ Ci [0] = -1 ;
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ AMD_info (Info) ;
+ OK (ok == AMD_INVALID) ;
+ Ci [0] = i ;
+ }
+ }
+
+ ok = AMD_valid (n, n, Sp, Si) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ ok = AMD_valid (-1, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
+ ok = AMD_valid (n, -1, Sp, Si) ; OK (ok == AMD_INVALID) ;
+ ok = AMD_valid (n, n, NULL, Si) ; OK (ok == AMD_INVALID) ;
+ ok = AMD_valid (n, n, Sp, NULL) ; OK (ok == AMD_INVALID) ;
+
+ if (n > 0 && Sp [n] > 0)
+ {
+
+ p = Sp [n] ;
+ Sp [n] = -1 ;
+ ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
+ Sp [n] = p ;
+
+ p = Sp [0] ;
+ Sp [0] = -1 ;
+ ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
+ Sp [0] = p ;
+
+ p = Sp [1] ;
+ Sp [1] = -1 ;
+ ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
+ Sp [1] = p ;
+
+ i = Si [0] ;
+ Si [0] = -1 ;
+ ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
+ Si [0] = i ;
+
+ }
+
+ ok = AMD_valid (n, n, Sp, Si) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+ AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
+ ok = AMD_valid (n, n, Sp, Si) ;
+ OK (ok == AMD_OK) ;
+
+ if (n > 0 && Bp [n] > 0)
+ {
+
+ p = Bp [n] ;
+ Bp [n] = -1 ;
+ ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ;
+ Bp [n] = p ;
+
+
+ p = Bp [1] ;
+ Bp [1] = -1 ;
+ ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ;
+ Bp [1] = p ;
+
+ i = Bi [0] ;
+ Bi [0] = -1 ;
+ ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ;
+ Bi [0] = i ;
+ }
+
+ AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
+
+ Info [AMD_STATUS] = 777 ;
+ AMD_info (Info) ;
+
+ /* ------------------------------------------------------------------ */
+ /* memory tests */
+ /* ------------------------------------------------------------------ */
+
+ if (n > 0)
+ {
+ amd_malloc = cm->malloc_memory ;
+ amd_free = cm->free_memory ;
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
+
+ test_memory_handler ( ) ;
+ amd_malloc = cm->malloc_memory ;
+ amd_free = cm->free_memory ;
+ for (trial = 0 ; trial < 6 ; trial++)
+ {
+ my_tries = trial ;
+ printf ("AMD memory trial "ID"\n", trial) ;
+ ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
+ AMD_info (Info) ;
+ OK (ok == AMD_OUT_OF_MEMORY
+ || (sorted ? (ok == AMD_OK) : (ok >= AMD_OK))) ;
+ }
+ normal_memory_handler ( ) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "AMD2 permutation", cm)) ;
+
+ amd_malloc = cm->malloc_memory ;
+ amd_free = cm->free_memory ;
+ }
+
+ CHOLMOD(free_sparse) (&E, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free everything */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free) (n, sizeof (Int), Len, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Nv, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Next, cm) ;
+ CHOLMOD(free) (n+1, sizeof (Int), Head, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Elen, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Deg, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Wi, cm) ;
+
+ CHOLMOD(free) (n+1, sizeof (Int), P, cm) ;
+
+ CHOLMOD(free) (n, sizeof (Int), W, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Flag, cm) ;
+
+ CHOLMOD(free_sparse) (&S, cm) ;
+ CHOLMOD(free_sparse) (&B, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&F, cm) ;
+}
diff --git a/CHOLMOD/Tcov/aug.c b/CHOLMOD/Tcov/aug.c
new file mode 100644
index 0000000..2680e1a
--- /dev/null
+++ b/CHOLMOD/Tcov/aug.c
@@ -0,0 +1,242 @@
+/* ========================================================================== */
+/* === Tcov/aug ============================================================= */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Create the augmented system S = [-I A' ; A alpha*I], solve Sx=b, and return
+ * the residual. The system solved is (alpha*I + A*A')*x=b.
+ *
+ * r1 = norm (Sx-b)
+ * r2 = norm ((alpha*I+AA')x-b)
+ * alpha = norm(A)
+ */
+
+#include "cm.h"
+
+
+/* ========================================================================== */
+/* === aug ================================================================== */
+/* ========================================================================== */
+
+double aug (cholmod_sparse *A)
+{
+ double r, maxerr = 0, bnorm, anorm ;
+ cholmod_sparse *S, *Im, *In, *At, *A1, *A2, *Sup ;
+ cholmod_dense *Alpha, *B, *Baug, *X, *W1, *W2, *R, *X2, X2mat ;
+ cholmod_factor *L ;
+ double *b, *baug, *rx, *w, *x ;
+ Int nrow, ncol, nrhs, i, j, d, d2, save, save2, save3 ;
+
+ if (A == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cm: no A for aug") ;
+ return (1) ;
+ }
+
+ if (A->xtype != CHOLMOD_REAL)
+ {
+ return (0) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* A is m-by-n, B must be m-by-nrhs */
+ /* ---------------------------------------------------------------------- */
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ B = rhs (A, 5, A->nrow + 7) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create scalars */
+ /* ---------------------------------------------------------------------- */
+
+ bnorm = CHOLMOD(norm_dense) (B, 0, cm) ;
+ anorm = CHOLMOD(norm_sparse) (A, 1, cm) ;
+
+ Alpha = CHOLMOD(eye) (1, 1, CHOLMOD_REAL, cm) ;
+ if (Alpha != NULL)
+ {
+ ((double *) (Alpha->x)) [0] = anorm ;
+ }
+
+ CHOLMOD(print_dense) (M1, "MinusOne", cm) ;
+ CHOLMOD(print_dense) (Alpha, "Alpha = norm(A)", cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create augmented system, S = [-I A' ; A anorm*I] */
+ /* ---------------------------------------------------------------------- */
+
+ Im = CHOLMOD(speye) (nrow, nrow, CHOLMOD_REAL, cm) ;
+ In = CHOLMOD(speye) (ncol, ncol, CHOLMOD_REAL, cm) ;
+ CHOLMOD(scale) (Alpha, CHOLMOD_SCALAR, Im, cm) ;
+ CHOLMOD(scale) (M1, CHOLMOD_SCALAR, In, cm) ;
+ At = CHOLMOD(transpose) (A, 2, cm) ;
+
+ /* use one of two equivalent methods */
+ if (nrow % 2)
+ {
+ /* S = [[-In A'] ; [A alpha*Im]] */
+ A1 = CHOLMOD(horzcat) (In, At, TRUE, cm) ;
+ A2 = CHOLMOD(horzcat) (A, Im, TRUE, cm) ;
+ S = CHOLMOD(vertcat) (A1, A2, TRUE, cm) ;
+ }
+ else
+ {
+ /* S = [[-In ; A] [A' ; alpha*Im]] */
+ A1 = CHOLMOD(vertcat) (In, A, TRUE, cm) ;
+ A2 = CHOLMOD(vertcat) (At, Im, TRUE, cm) ;
+ S = CHOLMOD(horzcat) (A1, A2, TRUE, cm) ;
+ }
+
+ CHOLMOD(free_sparse) (&Im, cm) ;
+ CHOLMOD(free_sparse) (&In, cm) ;
+
+ CHOLMOD(print_sparse) (S, "S, augmented system", cm) ;
+
+ /* make a symmetric (upper) copy of S */
+ Sup = CHOLMOD(copy) (S, 1, 1, cm) ;
+
+ CHOLMOD(print_sparse) (S, "S, augmented system (upper)", cm) ;
+ CHOLMOD(print_sparse) (Sup, "Sup", cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create augmented right-hand-side, Baug = [ zeros(ncol,nrhs) ; B ] */
+ /* ---------------------------------------------------------------------- */
+
+ b = NULL ;
+ d = 0 ;
+ nrhs = 0 ;
+ d2 = 0 ;
+ if (B != NULL)
+ {
+ nrhs = B->ncol ;
+ d = B->d ;
+ b = B->x ;
+ Baug = CHOLMOD(zeros) (nrow+ncol, nrhs, CHOLMOD_REAL, cm) ;
+ if (Baug != NULL)
+ {
+ d2 = Baug->d ;
+ baug = Baug->x ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ baug [(i+ncol)+j*d2] = b [i+j*d] ;
+ }
+ }
+ }
+ }
+ else
+ {
+ Baug = NULL ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Sx=baug */
+ /* ---------------------------------------------------------------------- */
+
+ /* S is symmetric indefinite, so do not use a supernodal LL' */
+ save = cm->supernodal ;
+ save2 = cm->final_asis ;
+ cm->supernodal = CHOLMOD_SIMPLICIAL ;
+ cm->final_asis = TRUE ;
+ save3 = cm->metis_memory ;
+ cm->metis_memory = 2.0 ;
+ L = CHOLMOD(analyze) (Sup, cm) ;
+ CHOLMOD(factorize) (Sup, L, cm) ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L, Baug, cm) ;
+ cm->supernodal = save ;
+ cm->final_asis = save2 ;
+ cm->metis_memory = save3 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the residual */
+ /* ---------------------------------------------------------------------- */
+
+ r = resid (Sup, X, Baug) ;
+ MAXERR (maxerr, r, 1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create a shallow submatrix of X, X2 = X (ncol:end, :) */
+ /* ---------------------------------------------------------------------- */
+
+ if (X == NULL)
+ {
+ X2 = NULL ;
+ }
+ else
+ {
+ X2 = &X2mat ;
+ X2->nrow = nrow ;
+ X2->ncol = nrhs ;
+ X2->nzmax = X->nzmax ;
+ X2->d = X->d ;
+ X2->x = ((double *) X->x) + ncol ;
+ X2->z = NULL ;
+ X2->xtype = X->xtype ;
+ X2->dtype = X->dtype ;
+ }
+
+ CHOLMOD(print_dense) (X, "X", cm) ;
+ CHOLMOD(print_dense) (X2, "X2 = X (ncol:end,:)", cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute norm ((alpha*I + A*A')*x-b) */
+ /* ---------------------------------------------------------------------- */
+
+ /* W1 = A'*X2 */
+ W1 = CHOLMOD(zeros) (ncol, nrhs, CHOLMOD_REAL, cm) ;
+ CHOLMOD(sdmult) (A, TRUE, one, zero, X2, W1, cm) ;
+
+ /* W2 = A*W1 */
+ W2 = CHOLMOD(zeros) (nrow, nrhs, CHOLMOD_REAL, cm) ;
+ CHOLMOD(sdmult) (A, FALSE, one, zero, W1, W2, cm) ;
+
+ /* R = alpha*x + w2 - b */
+ R = CHOLMOD(zeros) (nrow, nrhs, CHOLMOD_REAL, cm) ;
+
+ if (R != NULL && W2 != NULL && X != NULL)
+ {
+ w = W2->x ;
+ rx = R->x ;
+ x = X2->x ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ rx [i+j*nrow] = anorm * x [i+j*d2] + w [i+j*nrow] - b [i+j*d] ;
+ }
+ }
+ }
+
+ r = CHOLMOD(norm_dense) (R, 1, cm) ;
+ MAXERR (maxerr, r, bnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free everything */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&At, cm) ;
+ CHOLMOD(free_sparse) (&A1, cm) ;
+ CHOLMOD(free_sparse) (&A2, cm) ;
+ CHOLMOD(free_sparse) (&S, cm) ;
+ CHOLMOD(free_sparse) (&Sup, cm) ;
+ CHOLMOD(free_factor) (&L, cm) ;
+ CHOLMOD(free_dense) (&R, cm) ;
+ CHOLMOD(free_dense) (&W1, cm) ;
+ CHOLMOD(free_dense) (&W2, cm) ;
+ CHOLMOD(free_dense) (&B, cm) ;
+ CHOLMOD(free_dense) (&Baug, cm) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ CHOLMOD(free_dense) (&Alpha, cm) ;
+
+ progress (0, '.') ;
+ return (maxerr) ;
+}
diff --git a/CHOLMOD/Tcov/camdtest.c b/CHOLMOD/Tcov/camdtest.c
new file mode 100644
index 0000000..ae9e1ef
--- /dev/null
+++ b/CHOLMOD/Tcov/camdtest.c
@@ -0,0 +1,415 @@
+/* ========================================================================== */
+/* === Tcov/camdtest ======================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Test for camd v2.0 */
+
+#include "cm.h"
+
+#ifndef NPARTITION
+#include "camd.h"
+
+/* ========================================================================== */
+/* === camdtest ============================================================= */
+/* ========================================================================== */
+
+void camdtest (cholmod_sparse *A)
+{
+ double Control [CAMD_CONTROL], Info [CAMD_INFO], alpha ;
+ Int *P, *Cp, *Ci, *Sp, *Si, *Bp, *Bi, *Ep, *Ei, *Fp, *Fi,
+ *Len, *Nv, *Next, *Head, *Elen, *Deg, *Wi, *W, *Flag, *BucketSet,
+ *Constraint ;
+ cholmod_sparse *C, *B, *S, *E, *F ;
+ Int i, j, n, nrow, ncol, ok, cnz, bnz, p, trial, sorted ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nCAMD test\n") ;
+
+ if (A == NULL)
+ {
+ return ;
+ }
+
+ if (A->stype)
+ {
+ B = CHOLMOD(copy) (A, 0, 0, cm) ;
+ }
+ else
+ {
+ B = CHOLMOD(aat) (A, NULL, 0, 0, cm) ;
+ }
+
+ if (A->nrow != A->ncol)
+ {
+ F = CHOLMOD(copy_sparse) (B, cm) ;
+ OK (F->nrow == F->ncol) ;
+ CHOLMOD(sort) (F, cm) ;
+ }
+ else
+ {
+ /* A is square and unsymmetric, and may have entries in A+A' that
+ * are not in A */
+ F = CHOLMOD(copy_sparse) (A, cm) ;
+ CHOLMOD(sort) (F, cm) ;
+ }
+
+ C = CHOLMOD(copy_sparse) (B, cm) ;
+
+ nrow = C->nrow ;
+ ncol = C->ncol ;
+ n = nrow ;
+ OK (nrow == ncol) ;
+
+ Cp = C->p ;
+ Ci = C->i ;
+
+ Bp = B->p ;
+ Bi = B->i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* S = sorted form of B, using CAMD_preprocess */
+ /* ---------------------------------------------------------------------- */
+
+ cnz = CHOLMOD(nnz) (C, cm) ;
+ S = CHOLMOD(allocate_sparse) (n, n, cnz, TRUE, TRUE, 0, CHOLMOD_PATTERN,
+ cm);
+ Sp = S->p ;
+ Si = S->i ;
+
+ W = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Flag = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ CAMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace for camd */
+ /* ---------------------------------------------------------------------- */
+
+ P = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ;
+ Constraint = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Constraint [i] = my_rand () % (MIN (n,6)) ;
+ }
+
+ ok = CAMD_cvalid (n, Constraint) ; OK (ok) ;
+ if (n > 0)
+ {
+ Constraint [0] = -1 ;
+ ok = CAMD_cvalid (n, Constraint) ; OK (!ok) ;
+ Constraint [0] = 0 ;
+ }
+ ok = CAMD_cvalid (n, Constraint) ; OK (ok) ;
+ ok = CAMD_cvalid (n, NULL) ; OK (ok) ;
+
+ Len = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Nv = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Next = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Head = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ;
+ Elen = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Deg = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Wi = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ;
+ BucketSet = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+
+ /* ---------------------------------------------------------------------- */
+
+ for (sorted = 0 ; sorted <= 1 ; sorted++)
+ {
+
+ if (sorted) CHOLMOD(sort) (C, cm) ;
+
+ Cp = C->p ;
+ Ci = C->i ;
+
+ /* ------------------------------------------------------------------ */
+ /* order C with CAMD_order */
+ /* ------------------------------------------------------------------ */
+
+ CAMD_defaults (Control) ;
+ CAMD_defaults (NULL) ;
+ CAMD_control (Control) ;
+ CAMD_control (NULL) ;
+ CAMD_info (NULL) ;
+
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, Constraint) ;
+ printf ("camd return value: "ID"\n", ok) ;
+ CAMD_info (Info) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation", cm)) ;
+
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ printf ("camd return value: "ID"\n", ok) ;
+ CAMD_info (Info) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation", cm)) ;
+
+ /* no dense rows/cols */
+ alpha = Control [CAMD_DENSE] ;
+ Control [CAMD_DENSE] = -1 ;
+ CAMD_control (Control) ;
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ printf ("camd return value: "ID"\n", ok) ;
+ CAMD_info (Info) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation (alpha=-1)", cm)) ;
+
+ /* many dense rows/cols */
+ Control [CAMD_DENSE] = 0 ;
+ CAMD_control (Control) ;
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ printf ("camd return value: "ID"\n", ok) ;
+ CAMD_info (Info) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation (alpha=0)", cm)) ;
+ Control [CAMD_DENSE] = alpha ;
+
+ /* no aggressive absorption */
+ Control [CAMD_AGGRESSIVE] = FALSE ;
+ CAMD_control (Control) ;
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ printf ("camd return value: "ID"\n", ok) ;
+ CAMD_info (Info) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation (no agg) ", cm)) ;
+ Control [CAMD_AGGRESSIVE] = TRUE ;
+
+ /* ------------------------------------------------------------------ */
+ /* order F with CAMD_order */
+ /* ------------------------------------------------------------------ */
+
+ Fp = F->p ;
+ Fi = F->i ;
+ ok = CAMD_order (n, Fp, Fi, P, Control, Info, NULL) ;
+ printf ("camd return value: "ID"\n", ok) ;
+ CAMD_info (Info) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "F: CAMD permutation", cm)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* order S with CAMD_order */
+ /* ------------------------------------------------------------------ */
+
+ ok = CAMD_order (n, Sp, Si, P, Control, Info, NULL) ;
+ printf ("camd return value: "ID"\n", ok) ;
+ CAMD_info (Info) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "CAMD permutation", cm)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* order E with CAMD_2, which destroys its contents */
+ /* ------------------------------------------------------------------ */
+
+ E = CHOLMOD(copy) (B, 0, -1, cm) ; /* remove diagonal entries */
+ bnz = CHOLMOD(nnz) (E, cm) ;
+
+ /* add the bare minimum extra space to E */
+ ok = CHOLMOD(reallocate_sparse) (bnz + n, E, cm) ;
+ OK (ok) ;
+ Ep = E->p ;
+ Ei = E->i ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ Len [j] = Ep [j+1] - Ep [j] ;
+ }
+
+ printf ("calling CAMD_2:\n") ;
+ if (n > 0)
+ {
+ CAMD_2 (n, Ep, Ei, Len, E->nzmax, Ep [n], Nv, Next, P, Head, Elen,
+ Deg, Wi, NULL, Info, NULL, BucketSet) ;
+ CAMD_info (Info) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "CAMD2 permutation", cm)) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* error tests */
+ /* ------------------------------------------------------------------ */
+
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ ok = CAMD_order (-1, Cp, Ci, P, Control, Info, NULL) ;
+ OK (ok == CAMD_INVALID);
+ ok = CAMD_order (0, Cp, Ci, P, Control, Info, NULL) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ ok = CAMD_order (n, NULL, Ci, P, Control, Info, NULL) ;
+ OK (ok == CAMD_INVALID);
+ ok = CAMD_order (n, Cp, NULL, P, Control, Info, NULL) ;
+ OK (ok == CAMD_INVALID);
+ ok = CAMD_order (n, Cp, Ci, NULL, Control, Info, NULL) ;
+ OK (ok == CAMD_INVALID);
+
+ if (n > 0)
+ {
+ printf ("CAMD error tests:\n") ;
+
+ p = Cp [n] ;
+ Cp [n] = -1 ;
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ OK (ok == CAMD_INVALID) ;
+
+ if (Size_max/2 == Int_max)
+ {
+ Cp [n] = Int_max ;
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ printf ("CAMD status is %d\n", ok) ;
+ OK (ok == CAMD_OUT_OF_MEMORY) ;
+ }
+
+ Cp [n] = p ;
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ if (Cp [n] > 0)
+ {
+ printf ("Mangle column zero:\n") ;
+ i = Ci [0] ;
+ Ci [0] = -1 ;
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ CAMD_info (Info) ;
+ OK (ok == CAMD_INVALID) ;
+ Ci [0] = i ;
+ }
+ }
+
+ ok = CAMD_valid (n, n, Sp, Si) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ ok = CAMD_valid (-1, n, Sp, Si) ; OK (ok == CAMD_INVALID) ;
+ ok = CAMD_valid (n, -1, Sp, Si) ; OK (ok == CAMD_INVALID) ;
+ ok = CAMD_valid (n, n, NULL, Si) ; OK (ok == CAMD_INVALID) ;
+ ok = CAMD_valid (n, n, Sp, NULL) ; OK (ok == CAMD_INVALID) ;
+
+ if (n > 0 && Sp [n] > 0)
+ {
+
+ p = Sp [n] ;
+ Sp [n] = -1 ;
+ ok = CAMD_valid (n, n, Sp, Si) ; OK (ok == CAMD_INVALID) ;
+ Sp [n] = p ;
+
+ p = Sp [0] ;
+ Sp [0] = -1 ;
+ ok = CAMD_valid (n, n, Sp, Si) ; OK (ok == CAMD_INVALID) ;
+ Sp [0] = p ;
+
+ p = Sp [1] ;
+ Sp [1] = -1 ;
+ ok = CAMD_valid (n, n, Sp, Si) ; OK (ok == CAMD_INVALID) ;
+ Sp [1] = p ;
+
+ i = Si [0] ;
+ Si [0] = -1 ;
+ ok = CAMD_valid (n, n, Sp, Si) ; OK (ok == CAMD_INVALID) ;
+ Si [0] = i ;
+
+ }
+
+ ok = CAMD_valid (n, n, Sp, Si) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+ CAMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
+ ok = CAMD_valid (n, n, Sp, Si) ;
+ OK (ok == CAMD_OK) ;
+
+ if (n > 0 && Bp [n] > 0)
+ {
+
+ p = Bp [n] ;
+ Bp [n] = -1 ;
+ ok = CAMD_valid (n, n, Bp, Bi) ; OK (ok == CAMD_INVALID) ;
+ Bp [n] = p ;
+
+
+ p = Bp [1] ;
+ Bp [1] = -1 ;
+ ok = CAMD_valid (n, n, Bp, Bi) ; OK (ok == CAMD_INVALID) ;
+ Bp [1] = p ;
+
+ i = Bi [0] ;
+ Bi [0] = -1 ;
+ ok = CAMD_valid (n, n, Bp, Bi) ; OK (ok == CAMD_INVALID) ;
+ Bi [0] = i ;
+ }
+
+ CAMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
+
+ Info [CAMD_STATUS] = 777 ;
+ CAMD_info (Info) ;
+
+ /* ------------------------------------------------------------------ */
+ /* memory tests */
+ /* ------------------------------------------------------------------ */
+
+ if (n > 0)
+ {
+ camd_malloc = cm->malloc_memory ;
+ camd_free = cm->free_memory ;
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ OK (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK)) ;
+
+ test_memory_handler ( ) ;
+ camd_malloc = cm->malloc_memory ;
+ camd_free = cm->free_memory ;
+ for (trial = 0 ; trial < 6 ; trial++)
+ {
+ my_tries = trial ;
+ printf ("CAMD memory trial "ID"\n", trial) ;
+ ok = CAMD_order (n, Cp, Ci, P, Control, Info, NULL) ;
+ CAMD_info (Info) ;
+ OK (ok == CAMD_OUT_OF_MEMORY
+ || (sorted ? (ok == CAMD_OK) : (ok >= CAMD_OK))) ;
+ }
+ normal_memory_handler ( ) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "CAMD2 permutation", cm)) ;
+
+ camd_malloc = cm->malloc_memory ;
+ camd_free = cm->free_memory ;
+ }
+
+ CHOLMOD(free_sparse) (&E, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free everything */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free) (n, sizeof (Int), Len, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Nv, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Next, cm) ;
+ CHOLMOD(free) (n+1, sizeof (Int), Head, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Elen, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Deg, cm) ;
+ CHOLMOD(free) (n+1, sizeof (Int), Wi, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), BucketSet, cm) ;
+
+ CHOLMOD(free) (n+1, sizeof (Int), P, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Constraint, cm) ;
+
+ CHOLMOD(free) (n, sizeof (Int), W, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Flag, cm) ;
+
+ CHOLMOD(free_sparse) (&S, cm) ;
+ CHOLMOD(free_sparse) (&B, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&F, cm) ;
+}
+
+#else
+
+void camdtest (cholmod_sparse *A)
+{
+ if (A == NULL)
+ {
+ return ;
+ }
+ cm->print = 1 ;
+}
+#endif
diff --git a/CHOLMOD/Tcov/cctest.c b/CHOLMOD/Tcov/cctest.c
new file mode 100644
index 0000000..9e02c92
--- /dev/null
+++ b/CHOLMOD/Tcov/cctest.c
@@ -0,0 +1,361 @@
+/* ========================================================================== */
+/* === Tcov/cctest ========================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Test for ccolamd v1.0. Not used if NPARTITION defined at compile time. */
+
+#include "cm.h"
+
+#ifndef NPARTITION
+#include "ccolamd.h"
+
+/* ========================================================================== */
+/* === check_constraints ==================================================== */
+/* ========================================================================== */
+
+/* Check to see if P obeys the constraints */
+Int check_constraints (Int *P, Int *Cmember, Int n)
+{
+ Int c, clast, k, i ;
+ if ((P == NULL) || !CHOLMOD(print_perm) (P, n, n, "ccolamd perm", cm))
+ {
+ printf ("cctest: Perm is bad\n") ;
+ return (FALSE) ;
+ }
+ clast = EMPTY ;
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P [k] ;
+ c = Cmember [i] ;
+ if (c < clast)
+ {
+ printf ("cctest: constraints are incorrect\n") ;
+ return (FALSE) ;
+ }
+ clast = c ;
+ }
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === cctest =============================================================== */
+/* ========================================================================== */
+
+void cctest (cholmod_sparse *A)
+{
+
+ double knobs [CCOLAMD_KNOBS], knobs2 [CCOLAMD_KNOBS] ;
+ Int *P, *Cmember, *Cp, *Ci, *Front_npivcol, *Front_nrows, *Front_ncols,
+ *Front_parent, *Front_cols, *InFront, *Si, *Sp ;
+ cholmod_sparse *C, *A2, *B, *S ;
+ Int nrow, ncol, alen, ok, stats [CCOLAMD_STATS], csets, i, nfr, c, p ;
+ size_t s ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ my_srand (42) ; /* RAND reset */
+
+ printf ("\nCCOLAMD test\n") ;
+
+ if (A == NULL)
+ {
+ return ;
+ }
+
+ if (A->stype)
+ {
+ A2 = CHOLMOD(copy) (A, 0, 0, cm) ;
+ B = A2 ;
+ }
+ else
+ {
+ A2 = NULL ;
+ B = A ;
+ }
+ S = CHOLMOD(copy_sparse) (A, cm) ;
+
+ nrow = B->nrow ;
+ ncol = B->ncol ;
+ Si = S->i ;
+ Sp = S->p ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace and Cmember for ccolamd */
+ /* ---------------------------------------------------------------------- */
+
+ P = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ;
+ Cmember = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+ Front_npivcol = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ;
+ Front_nrows = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ;
+ Front_ncols = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ;
+ Front_parent = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ;
+ Front_cols = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ;
+ InFront = CHOLMOD(malloc) (ncol, sizeof (Int), cm) ;
+
+ csets = MIN (6, nrow) ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Cmember [i] = nrand (csets) ;
+ }
+
+ CCOLAMD_set_defaults (knobs) ;
+ CCOLAMD_set_defaults (knobs2) ;
+ CCOLAMD_set_defaults (NULL) ;
+ CCOLAMD_report (NULL) ;
+ CSYMAMD_report (NULL) ;
+
+ alen = CCOLAMD_recommended (B->nzmax, ncol, nrow) ;
+ C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0,
+ CHOLMOD_PATTERN, cm) ;
+ Cp = C->p ;
+ Ci = C->i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order with ccolamd */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ CHOLMOD(print_sparse) (C, "C for ccolamd", cm) ;
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, NULL, stats, Cmember) ;
+ CCOLAMD_report (stats) ;
+ OK (ok) ;
+ ok = stats [CCOLAMD_STATUS] ;
+ ok = (ok == CCOLAMD_OK || ok == CCOLAMD_OK_BUT_JUMBLED) ;
+ OK (ok) ;
+
+ /* permutation returned in C->p, if the ordering succeeded */
+ /* make sure P obeys the constraints */
+ OK (check_constraints (Cp, Cmember, nrow)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order with ccolamd2 */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ ok = CCOLAMD_2 (ncol, nrow, alen, Ci, Cp, NULL, stats,
+ Front_npivcol, Front_nrows, Front_ncols, Front_parent,
+ Front_cols, &nfr, InFront, Cmember) ;
+ CCOLAMD_report (stats) ;
+ OK (check_constraints (Cp, Cmember, nrow)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* with a small dense-row threshold */
+ /* ---------------------------------------------------------------------- */
+
+ knobs2 [CCOLAMD_DENSE_ROW] = 0 ;
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats, Cmember) ;
+ CCOLAMD_report (stats) ;
+
+ knobs2 [CCOLAMD_DENSE_ROW] = 0.625 ;
+ knobs2 [CCOLAMD_DENSE_COL] = 0 ;
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats, Cmember) ;
+ CCOLAMD_report (stats) ;
+
+ knobs2 [CCOLAMD_DENSE_ROW] = 0.625 ;
+ knobs2 [CCOLAMD_DENSE_COL] = -1 ;
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats, Cmember) ;
+ CCOLAMD_report (stats) ;
+
+ knobs2 [CCOLAMD_DENSE_COL] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* duplicate entries */
+ /* ---------------------------------------------------------------------- */
+
+ if (ncol > 2 && nrow > 2)
+ {
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ;
+ OK (ok) ;
+ if (Cp [1] - Cp [0] > 2)
+ {
+ Ci [0] = Ci [1] ;
+ }
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats, Cmember) ;
+ CCOLAMD_report (stats) ;
+ OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "ccolamd perm", cm)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* csymamd */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow == ncol)
+ {
+ Int n = nrow ;
+
+ ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats,
+ cm->calloc_memory, cm->free_memory, Cmember, A->stype) ;
+ OK (ok) ;
+ OK (check_constraints (P, Cmember, n)) ;
+ CSYMAMD_report (stats) ;
+
+ /* ------------------------------------------------------------------ */
+ /* csymamd errors */
+ /* ------------------------------------------------------------------ */
+
+ ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, NULL, cm->calloc_memory,
+ cm->free_memory, Cmember, A->stype) ; NOT (ok);
+
+ ok = CSYMAMD_MAIN (n, NULL, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory, Cmember, A->stype) ; NOT (ok);
+ CSYMAMD_report (stats) ;
+
+ ok = CSYMAMD_MAIN (n, Si, NULL, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory, Cmember, A->stype) ; NOT (ok);
+ CSYMAMD_report (stats) ;
+
+ ok = CSYMAMD_MAIN (-1, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory, Cmember, A->stype) ; NOT (ok);
+ CSYMAMD_report (stats) ;
+
+ p = Sp [n] ;
+ Sp [n] = -1 ;
+ ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory, Cmember, A->stype) ; NOT (ok);
+ CSYMAMD_report (stats) ;
+ Sp [n] = p ;
+
+ Sp [0] = -1 ;
+ ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory, Cmember, A->stype) ; NOT (ok);
+ CSYMAMD_report (stats) ;
+ Sp [0] = 0 ;
+
+ if (n > 2 && Sp [n] > 3)
+ {
+ p = Sp [1] ;
+ Sp [1] = -1 ;
+ ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory, Cmember, A->stype) ; NOT (ok);
+ CSYMAMD_report (stats) ;
+ Sp [1] = p ;
+
+ i = Si [0] ;
+ Si [0] = -1 ;
+ ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory, Cmember, A->stype) ; NOT (ok);
+ CSYMAMD_report (stats) ;
+ Si [0] = i ;
+
+ /* ok, but jumbled */
+ i = Si [0] ;
+ Si [0] = Si [1] ;
+ Si [1] = i ;
+ ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory, Cmember, A->stype) ; OK (ok);
+ CSYMAMD_report (stats) ;
+ i = Si [0] ;
+ Si [0] = Si [1] ;
+ Si [1] = i ;
+
+ test_memory_handler ( ) ;
+ ok = CSYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory, Cmember, A->stype) ; NOT(ok);
+ CSYMAMD_report (stats) ;
+ normal_memory_handler ( ) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* error tests */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ ok = CCOLAMD_MAIN (ncol, nrow, 0, Ci, Cp, knobs, stats, Cmember) ; NOT (ok) ;
+ CCOLAMD_report (stats) ;
+
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, NULL, Cp, knobs, stats, Cmember); NOT (ok) ;
+ CCOLAMD_report (stats) ;
+
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, NULL, knobs, stats, Cmember); NOT (ok) ;
+ CCOLAMD_report (stats) ;
+
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, NULL, Cmember) ; NOT (ok) ;
+ CCOLAMD_report (stats) ;
+
+ ok = CCOLAMD_MAIN (-1, nrow, alen, Ci, Cp, knobs, stats, Cmember) ; NOT (ok) ;
+ CCOLAMD_report (stats) ;
+
+ ok = CCOLAMD_MAIN (ncol, -1, alen, Ci, Cp, knobs, stats, Cmember) ; NOT (ok) ;
+ CCOLAMD_report (stats) ;
+
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ Cp [nrow] = -1 ;
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats, Cmember) ; NOT (ok) ;
+ CCOLAMD_report (stats) ;
+
+ Cp [0] = 1 ;
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats, Cmember) ; NOT (ok) ;
+ CCOLAMD_report (stats) ;
+
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+
+ if (nrow > 0 && alen > 0 && Cp [1] > 0)
+ {
+ c = Cmember [0] ;
+ Cmember [0] = -1 ;
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats, Cmember) ;NOT(ok);
+ CCOLAMD_report (stats) ;
+ Cmember [0] = c ;
+
+ p = Cp [1] ;
+ Cp [1] = -1 ;
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats, Cmember) ;NOT(ok);
+ CCOLAMD_report (stats) ;
+ Cp [1] = p ;
+
+ i = Ci [0] ;
+ Ci [0] = -1 ;
+ ok = CCOLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats, Cmember) ;NOT(ok);
+ CCOLAMD_report (stats) ;
+ Ci [0] = i ;
+ }
+
+ s = CCOLAMD_recommended (-1, 0, 0) ;
+ OK (s == 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free) (nrow+1, sizeof (Int), Front_npivcol, cm) ;
+ CHOLMOD(free) (nrow+1, sizeof (Int), Front_nrows, cm) ;
+ CHOLMOD(free) (nrow+1, sizeof (Int), Front_ncols, cm) ;
+ CHOLMOD(free) (nrow+1, sizeof (Int), Front_parent, cm) ;
+ CHOLMOD(free) (nrow+1, sizeof (Int), Front_cols, cm) ;
+ CHOLMOD(free) (nrow+1, sizeof (Int), P, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), Cmember, cm) ;
+ CHOLMOD(free) (ncol, sizeof (Int), InFront, cm) ;
+
+ CHOLMOD(free_sparse) (&S, cm) ;
+ CHOLMOD(free_sparse) (&A2, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ cm->print = 1 ;
+}
+
+#else
+
+void cctest (cholmod_sparse *A)
+{
+ if (A == NULL)
+ {
+ return ;
+ }
+
+ cm->print = 1 ;
+}
+#endif
diff --git a/CHOLMOD/Tcov/cm.c b/CHOLMOD/Tcov/cm.c
new file mode 100644
index 0000000..4873349
--- /dev/null
+++ b/CHOLMOD/Tcov/cm.c
@@ -0,0 +1,1699 @@
+/* ========================================================================== */
+/* === Tcov/cm ============================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* A program for exhaustive statement-coverage for CHOLMOD, AMD, COLAMD, and
+ * CCOLAMD. It tests every line of code in all three packages.
+ *
+ * For a complete test, all CHOLMOD modules, AMD, COLAMD, CCOLAMD, METIS,
+ * LAPACK, and the BLAS are required. A partial test can be performed without
+ * the Supernodal and/or Partition modules. METIS is not required if the
+ * Partition module is not installed. LAPACK and the BLAS are not required
+ * if the Supernodal module is not installed.
+ *
+ * Usage:
+ *
+ * cm < input > output
+ *
+ * where "input" contains a sparse matrix in triplet form. The first line of
+ * the file contains four or five integers:
+ *
+ * nrow ncol nnz stype complex
+ *
+ * where the matrix is nrow-by-ncol. nnz is the number of (i,j,aij) triplets
+ * in the rest of the file, one triplet per line. stype is -1 (symmetric
+ * with entries in lower triangular part provided), 0 (unsymmetric), or 1
+ * (symmetric upper). If the 5th entry is missing, or 0, then the matrix is
+ * real; if 1 the matrix is complex, if 2 the matrix is zomplex. Each
+ * subsequent line contains
+ *
+ * i j aij
+ *
+ * for the row index, column index, and value of A(i,j). Duplicate entries
+ * are summed. If stype is 2 or 3, the rest of the file is ignored, and a
+ * special test matrix is constructed (2: arrowhead, 3: tridiagonal plus a
+ * dense row). Test matrices are located in the Matrix/ subdirectory.
+ *
+ * For complex matrices, each line consists of
+ *
+ * i j xij zij
+ *
+ * where xij is the real part of A(i,j) and zij is the imaginary part.
+ *
+ * cm takes one optional parameter. If present (it does not matter what the
+ * argument is, actually) then extension memory-failure tests are performed.
+ */
+
+#include "cm.h"
+
+/* ========================================================================== */
+/* === global variables ===================================================== */
+/* ========================================================================== */
+
+double zero [2], one [2], minusone [2] ;
+cholmod_common Common, *cm ;
+cholmod_dense *M1 ;
+Int dot = 0 ;
+double Zero [2] ;
+
+
+/* ========================================================================== */
+/* === my_rand ============================================================== */
+/* ========================================================================== */
+
+/* The POSIX example of rand, duplicated here so that the same sequence will
+ * be generated on different machines. */
+
+static unsigned long next = 1 ;
+
+/* RAND_MAX assumed to be 32767 */
+Int my_rand (void)
+{
+ next = next * 1103515245 + 12345 ;
+ return ((unsigned)(next/65536) % /* 32768 */ (MY_RAND_MAX + 1)) ;
+}
+
+void my_srand (unsigned seed)
+{
+ next = seed ;
+}
+
+unsigned long my_seed (void)
+{
+ return (next) ;
+}
+
+
+/* ========================================================================== */
+/* === progress ============================================================= */
+/* ========================================================================== */
+
+/* print a "." on stderr to indicate progress */
+
+#define LINEWIDTH 70
+#define COUNT 100
+
+void progress (Int force, char s)
+{
+ dot++ ;
+ if (force)
+ {
+ dot += (COUNT - (dot % COUNT)) ;
+ }
+ if (dot % COUNT == 0)
+ {
+ fprintf (stderr, "%c", s) ;
+ }
+ if (dot % (COUNT*LINEWIDTH) == 0)
+ {
+ fprintf (stderr, "\n") ;
+ }
+ fflush (stdout) ;
+ fflush (stderr) ;
+}
+
+
+/* ========================================================================== */
+/* === my_handler =========================================================== */
+/* ========================================================================== */
+
+/* An error occurred that should not have occurred */
+
+void my_handler (int status, char *file, int line, char *msg)
+{
+ printf ("Error handler: file %s line %d status %d: %s\n",
+ file, line, status, msg) ;
+ if (status < CHOLMOD_OK || status > CHOLMOD_DSMALL)
+ {
+ fprintf (stderr, "\n\n************************************************"
+ "********************************\n"
+ "*** Test failure: file: %s line: %d\n"
+ "*** status: %d message: %s\n"
+ "***********************************************************"
+ "*********************\n", file, line, status, msg);
+ fflush (stderr) ;
+ fflush (stdout) ;
+ abort ( ) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === Assert =============================================================== */
+/* ========================================================================== */
+
+void Assert (int truth, char *file, int line)
+{
+ if (!truth)
+ {
+ my_handler (-1, file, line, "") ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === nrand ================================================================ */
+/* ========================================================================== */
+
+/* return a random Int between 0 and n-1 */
+
+Int nrand (Int n)
+{
+ return ((n <= 0) ? (0) : (rand ( ) % n)) ;
+}
+
+/* ========================================================================== */
+/* === xrand ================================================================ */
+/* ========================================================================== */
+
+/* return a random double between 0 and x */
+
+double xrand (double range)
+{
+ return ((range * (double) (my_rand ( ))) / MY_RAND_MAX) ;
+}
+
+
+/* ========================================================================== */
+/* === prand ================================================================ */
+/* ========================================================================== */
+
+/* allocate and construct a random permutation of 0:n-1 */
+
+Int *prand (Int n)
+{
+ Int *P ;
+ Int t, j, k ;
+ P = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ if (P == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot create random perm") ;
+ return (NULL) ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = k ;
+ }
+ for (k = 0 ; k < n-1 ; k++)
+ {
+ j = k + nrand (n-k) ;
+ t = P [j] ;
+ P [j] = P [k] ;
+ P [k] = t ;
+ }
+ CHOLMOD(print_perm) (P, n, n, "Prandom", cm) ;
+ return (P) ;
+}
+
+
+/* ========================================================================== */
+/* === rand_set ============================================================= */
+/* ========================================================================== */
+
+/* allocate and construct a random set of 0:n-1, possibly with duplicates */
+
+Int *rand_set (Int len, Int n)
+{
+ Int *cset ;
+ Int k ;
+ cset = CHOLMOD(malloc) (len, sizeof (Int), cm) ;
+ if (cset == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot create random set") ;
+ return (NULL) ;
+ }
+ for (k = 0 ; k < len ; k++)
+ {
+ cset [k] = nrand (n) ;
+ }
+ CHOLMOD(print_subset) (cset, len, n, "random cset", cm) ;
+ return (cset) ;
+}
+
+
+/* ========================================================================== */
+/* === read_triplet ========================================================= */
+/* ========================================================================== */
+
+/* Read a triplet matrix from a file. */
+
+#define MAXLINE 1024
+
+cholmod_triplet *read_triplet
+(
+ FILE *f
+)
+{
+ cholmod_triplet *T ;
+ double *Tx, *Tz ;
+ long long x1, x2, x3, x4, x5 ;
+ Int *Ti, *Tj ;
+ Int n, j, k, nrow, ncol, nz, stype, arrowhead, tridiag_plus_denserow,
+ xtype, is_complex ;
+ char s [MAXLINE] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* read in a triplet matrix from a file */
+ /* ---------------------------------------------------------------------- */
+
+ dot = 0 ;
+ xtype = 0 ;
+ if (fgets (s, MAXLINE, f) == NULL)
+ {
+ return (NULL) ;
+ }
+
+ x1 = 0 ;
+ x2 = 0 ;
+ x3 = 0 ;
+ x4 = 0 ;
+ x5 = 0 ;
+ k = sscanf (s, "%lld %lld %lld %lld %lld\n", &x1, &x2, &x3, &x4, &x5) ;
+ nrow = x1 ;
+ ncol = x2 ;
+ nz = x3 ;
+ stype = x4 ;
+ xtype = x5 ;
+
+ xtype++ ;
+ is_complex = (xtype != CHOLMOD_REAL) ;
+
+ printf ("read_triplet: nrow "ID" ncol "ID" nz "ID" stype "ID" xtype "ID"\n",
+ nrow, ncol, nz, stype, xtype) ;
+
+ arrowhead = FALSE ;
+ tridiag_plus_denserow = FALSE ;
+
+ n = MAX (nrow, ncol) ;
+ if (stype == 2)
+ {
+ /* ignore nz and the rest of the file, and create an arrowhead matrix */
+ arrowhead = TRUE ;
+ nz = nrow + ncol + 1 ;
+ stype = (nrow == ncol) ? (1) : (0) ;
+ }
+ else if (stype == 3)
+ {
+ tridiag_plus_denserow = TRUE ;
+ nrow = n ;
+ ncol = n ;
+ nz = 4*n + 4 ;
+ stype = 0 ;
+ }
+
+ T = CHOLMOD(allocate_triplet) (nrow, ncol, nz, stype,
+ is_complex ? CHOLMOD_ZOMPLEX : CHOLMOD_REAL, cm) ;
+ if (T == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot create triplet matrix") ;
+ return (NULL) ;
+ }
+ Ti = T->i ;
+ Tj = T->j ;
+ Tx = T->x ;
+ Tz = T->z ;
+
+ if (arrowhead)
+ {
+ for (k = 0 ; k < MIN (nrow,ncol) ; k++)
+ {
+ Ti [k] = k ;
+ Tj [k] = k ;
+ Tx [k] = nrow + xrand (1) ; /* RAND */
+ if (is_complex)
+ {
+ Tz [k] = nrow + xrand (1) ; /* RAND */
+ }
+ }
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Ti [k] = 0 ;
+ Tj [k] = j ;
+ Tx [k] = - xrand (1) ; /* RAND */
+ if (is_complex)
+ {
+ Tz [k] = - xrand (1) ; /* RAND */
+ }
+ k++ ;
+ }
+ T->nnz = k ;
+ }
+ else if (tridiag_plus_denserow)
+ {
+ /* dense row, except for the last column */
+ for (k = 0 ; k < n-1 ; k++)
+ {
+ Ti [k] = 0 ;
+ Tj [k] = k ;
+ Tx [k] = xrand (1) ; /* RAND */
+ if (is_complex)
+ {
+ Tz [k] = xrand (1) ; /* RAND */
+ }
+ }
+
+ /* diagonal */
+ for (j = 0 ; j < n ; j++)
+ {
+ Ti [k] = j ;
+ Tj [k] = j ;
+ Tx [k] = nrow + xrand (1) ; /* RAND */
+ if (is_complex)
+ {
+ Tz [k] = nrow + xrand (1) ; /* RAND */
+ }
+ k++ ;
+ }
+
+ /* superdiagonal */
+ for (j = 1 ; j < n ; j++)
+ {
+ Ti [k] = j-1 ;
+ Tj [k] = j ;
+ Tx [k] = xrand (1) ; /* RAND */
+ if (is_complex)
+ {
+ Tz [k] = xrand (1) ; /* RAND */
+ }
+ k++ ;
+ }
+
+ /* subdiagonal */
+ for (j = 0 ; j < n-1 ; j++)
+ {
+ Ti [k] = j+1 ;
+ Tj [k] = j ;
+ Tx [k] = xrand (1) ; /* RAND */
+ if (is_complex)
+ {
+ Tz [k] = xrand (1) ; /* RAND */
+ }
+ k++ ;
+ }
+
+ /* a few extra terms in the last column */
+ Ti [k] = MAX (0, n-3) ;
+ Tj [k] = n-1 ;
+ Tx [k] = xrand (1) ; /* RAND */
+ if (is_complex)
+ {
+ Tz [k] = xrand (1) ; /* RAND */
+ }
+ k++ ;
+
+ Ti [k] = MAX (0, n-4) ;
+ Tj [k] = n-1 ;
+ Tx [k] = xrand (1) ; /* RAND */
+ if (is_complex)
+ {
+ Tz [k] = xrand (1) ; /* RAND */
+ }
+ k++ ;
+
+ Ti [k] = MAX (0, n-5) ;
+ Tj [k] = n-1 ;
+ Tx [k] = xrand (1) ; /* RAND */
+ if (is_complex)
+ {
+ Tz [k] = xrand (1) ; /* RAND */
+ }
+ k++ ;
+
+ T->nnz = k ;
+ }
+ else
+ {
+ if (is_complex)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ if (fscanf (f,""ID" "ID" %lg %lg\n", Ti+k, Tj+k, Tx+k, Tz+k)
+ == EOF)
+ {
+ ERROR (CHOLMOD_INVALID, "Error reading triplet matrix\n") ;
+ }
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ if (fscanf (f, ""ID" "ID" %lg\n", Ti+k, Tj+k, Tx+k) == EOF)
+ {
+ ERROR (CHOLMOD_INVALID, "Error reading triplet matrix\n") ;
+ }
+ }
+ }
+ T->nnz = nz ;
+ }
+
+ CHOLMOD(triplet_xtype) (xtype, T, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print the triplet matrix */
+ /* ---------------------------------------------------------------------- */
+
+ cm->print = 4 ;
+ CHOLMOD(print_triplet) (T, "T input", cm) ;
+ cm->print = 1 ;
+ fprintf (stderr, "Test matrix: "ID"-by-"ID" with "ID" entries, stype: "ID
+ "\n",
+ (Int) T->nrow, (Int) T->ncol, (Int) T->nnz, (Int) T->stype) ;
+ printf ("\n\n======================================================\n"
+ "Test matrix: "ID"-by-"ID" with "ID" entries, stype: "ID"\n",
+ (Int) T->nrow, (Int) T->ncol, (Int) T->nnz, (Int) T->stype) ;
+
+ if (MAX (nrow, ncol) > NLARGE)
+ {
+ fprintf (stderr, "Please wait, this will take a while ...") ;
+ dot = 39*LINEWIDTH ;
+ }
+ return (T) ;
+}
+
+
+/* ========================================================================== */
+/* === zeros ================================================================ */
+/* ========================================================================== */
+
+/* Same as cholmod_zeros or cholmod_l_zeros, except it allows for a leading
+ * dimension that is different than nrow */
+
+cholmod_dense *zeros (Int nrow, Int ncol, Int d, Int xtype)
+{
+ cholmod_dense *X ;
+ double *Xx, *Xz ;
+ Int i, nz ;
+ X = CHOLMOD(allocate_dense) (nrow, ncol, d, xtype, cm) ;
+ if (X == NULL)
+ {
+ return (NULL) ;
+ }
+ Xx = X->x ;
+ Xz = X->z ;
+ nz = MAX (1, X->nzmax) ;
+ switch (X->xtype)
+ {
+ case CHOLMOD_REAL:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [i] = 0 ;
+ }
+ break ;
+ case CHOLMOD_COMPLEX:
+ for (i = 0 ; i < 2*nz ; i++)
+ {
+ Xx [i] = 0 ;
+ }
+ break ;
+ case CHOLMOD_ZOMPLEX:
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xx [i] = 0 ;
+ }
+ for (i = 0 ; i < nz ; i++)
+ {
+ Xz [i] = 0 ;
+ }
+ break ;
+ }
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === xtrue ================================================================ */
+/* ========================================================================== */
+
+/* Allocate and construct a dense matrix, X(i,j) = i+j*d+1 */
+
+cholmod_dense *xtrue (Int nrow, Int ncol, Int d, Int xtype)
+{
+ double *x, *z ;
+ cholmod_dense *X ;
+ Int j, i ;
+ X = zeros (nrow, ncol, d, xtype) ;
+ if (X == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot create dense matrix") ;
+ return (NULL) ;
+ }
+ x = X->x ;
+ z = X->z ;
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ x [i+j*d] = i+j*d + 1 ;
+ }
+ }
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ x [2*(i+j*d) ] = i+j*d + 1 ;
+ x [2*(i+j*d)+1] = ((double) (j+i*d + 1))/10 ;
+ }
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ x [i+j*d] = i+j*d + 1 ;
+ z [i+j*d] = ((double) (j+i*d + 1))/10 ;
+ }
+ }
+ }
+ return (X) ;
+}
+
+
+/* ========================================================================== */
+/* === rhs ================================================================== */
+/* ========================================================================== */
+
+/* Create a right-hand-side, b = A*x, where x is a known solution */
+
+cholmod_dense *rhs (cholmod_sparse *A, Int nrhs, Int d)
+{
+ Int n ;
+ cholmod_dense *W, *Z, *B ;
+
+ if (A == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot compute rhs") ;
+ return (NULL) ;
+ }
+
+ n = A->nrow ;
+
+ /* B = zeros (n,rhs) but with leading dimension d */
+ B = zeros (n, nrhs, d, A->xtype) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create a known solution */
+ /* ---------------------------------------------------------------------- */
+
+ Z = xtrue (n, nrhs, d, A->xtype) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute B = A*Z or A*A'*Z */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0)
+ {
+ /* W = A'*Z */
+ W = CHOLMOD(zeros) (A->ncol, nrhs, A->xtype, cm) ;
+ CHOLMOD(sdmult) (A, TRUE, one, zero, Z, W, cm) ;
+ /* B = A*W */
+ CHOLMOD(sdmult) (A, FALSE, one, zero, W, B, cm) ;
+ CHOLMOD(free_dense) (&W, cm) ;
+ }
+ else
+ {
+ /* B = A*Z */
+ CHOLMOD(sdmult) (A, FALSE, one, zero, Z, B, cm) ;
+ }
+ CHOLMOD(free_dense) (&Z, cm) ;
+ return (B) ;
+}
+
+
+/* ========================================================================== */
+/* === resid ================================================================ */
+/* ========================================================================== */
+
+/* compute r = norm (A*x-b)/norm(b) or r = norm (A*A'*x-b)/norm(b) */
+
+double resid (cholmod_sparse *A, cholmod_dense *X, cholmod_dense *B)
+{
+ double r, bnorm ;
+ cholmod_dense *R, *X2, *B2 ;
+ cholmod_sparse *C, *A2 ;
+ Int d, n, nrhs, xtype ;
+
+ if (A == NULL || X == NULL || B == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot compute resid") ;
+ return (1) ;
+ }
+
+ cm->status = CHOLMOD_OK ;
+ n = B->nrow ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert all inputs to an identical xtype */
+ /* ---------------------------------------------------------------------- */
+
+ xtype = MAX (A->xtype, X->xtype) ;
+ xtype = MAX (xtype, B->xtype) ;
+ A2 = NULL ;
+ B2 = NULL ;
+ X2 = NULL ;
+ if (A->xtype != xtype)
+ {
+ A2 = CHOLMOD(copy_sparse) (A, cm) ;
+ CHOLMOD(sparse_xtype) (xtype, A2, cm) ;
+ A = A2 ;
+ }
+ if (X->xtype != xtype)
+ {
+ X2 = CHOLMOD(copy_dense) (X, cm) ;
+ CHOLMOD(dense_xtype) (xtype, X2, cm) ;
+ X = X2 ;
+ }
+ if (B->xtype != xtype)
+ {
+ B2 = CHOLMOD(copy_dense) (B, cm) ;
+ CHOLMOD(dense_xtype) (xtype, B2, cm) ;
+ B = B2 ;
+ }
+
+ if (cm->status < CHOLMOD_OK)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot compute resid") ;
+ CHOLMOD(free_sparse) (&A2, cm) ;
+ CHOLMOD(free_dense) (&B2, cm) ;
+ CHOLMOD(free_dense) (&X2, cm) ;
+ return (1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the right-hand-side, B, and its norm */
+ /* ---------------------------------------------------------------------- */
+
+ nrhs = B->ncol ;
+ d = B->d ;
+ if (nrhs == 1)
+ {
+ /* inf-norm, 1-norm, or 2-norm (random choice) */
+ bnorm = CHOLMOD(norm_dense) (B, nrand (2), cm) ;
+ }
+ else
+ {
+ /* inf-norm or 1-norm (random choice) */
+ bnorm = CHOLMOD(norm_dense) (B, nrand (1), cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the residual */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0)
+ {
+ if (n < 10 && A->xtype == CHOLMOD_REAL)
+ {
+ /* test cholmod_aat, C = A*A' */
+ C = CHOLMOD(aat) (A, NULL, 0, 1, cm) ;
+
+ /* R = B */
+ R = CHOLMOD(copy_dense) (B, cm) ;
+ /* R = C*X - R */
+ CHOLMOD(sdmult) (C, FALSE, one, minusone, X, R, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+
+ }
+ else
+ {
+ /* W = A'*X */
+ cholmod_dense *W ;
+ W = CHOLMOD(zeros) (A->ncol, nrhs, A->xtype, cm) ;
+ CHOLMOD(sdmult) (A, TRUE, one, zero, X, W, cm) ;
+ /* R = B */
+ R = CHOLMOD(copy_dense) (B, cm) ;
+ /* R = A*W - R */
+ CHOLMOD(sdmult) (A, FALSE, one, minusone, W, R, cm) ;
+ CHOLMOD(free_dense) (&W, cm) ;
+ }
+ }
+ else
+ {
+ /* R = B */
+ R = CHOLMOD(copy_dense) (B, cm) ;
+ /* R = A*X - R */
+ CHOLMOD(sdmult) (A, FALSE, one, minusone, X, R, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* r = norm (R) / norm (B) */
+ /* ---------------------------------------------------------------------- */
+
+ r = CHOLMOD(norm_dense) (R, 1, cm) ;
+
+ CHOLMOD(free_dense) (&R, cm) ;
+ CHOLMOD(free_sparse) (&A2, cm) ;
+ CHOLMOD(free_dense) (&B2, cm) ;
+ CHOLMOD(free_dense) (&X2, cm) ;
+
+ if (bnorm > 0)
+ {
+ r /= bnorm ;
+ }
+ return (r) ;
+}
+
+
+/* ========================================================================== */
+/* === resid_sparse ========================================================= */
+/* ========================================================================== */
+
+/* compute r = norm (A*x-b)/norm(b) or r = norm (A*A'*x-b)/norm(b) */
+
+double resid_sparse (cholmod_sparse *A, cholmod_sparse *X, cholmod_sparse *B)
+{
+ double r, bnorm ;
+ cholmod_sparse *R, *W, *AT, *W2 ;
+ cholmod_dense *X2, *B2 ;
+ Int n, nrhs, xtype ;
+
+ if (A == NULL || X == NULL || B == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot compute resid") ;
+ return (1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the residual */
+ /* ---------------------------------------------------------------------- */
+
+ xtype = MAX (A->xtype, X->xtype) ;
+ xtype = MAX (xtype, B->xtype) ;
+
+ if (xtype > CHOLMOD_REAL)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* convert X and B to dense if any is complex or zomplex */
+ /* ------------------------------------------------------------------ */
+
+ X2 = CHOLMOD(sparse_to_dense) (X, cm) ;
+ B2 = CHOLMOD(sparse_to_dense) (B, cm) ;
+ r = resid (A, X2, B2) ;
+ CHOLMOD(free_dense) (&X2, cm) ;
+ CHOLMOD(free_dense) (&B2, cm) ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* all inputs are real */
+ /* ------------------------------------------------------------------ */
+
+ n = B->nrow ;
+ nrhs = B->ncol ;
+ /* inf-norm or 1-norm (random choice) */
+ bnorm = CHOLMOD(norm_sparse) (B, nrand (1), cm) ;
+
+ if (A->stype == 0)
+ {
+ /* W = A'*X */
+ AT = CHOLMOD(transpose) (A, 1, cm) ;
+ W = CHOLMOD(ssmult) (AT, X, 0, TRUE, FALSE, cm) ;
+ CHOLMOD(free_sparse) (&AT, cm) ;
+ /* W2 = A*W */
+ W2 = CHOLMOD(ssmult) (A, W, 0, TRUE, FALSE, cm) ;
+ CHOLMOD(free_sparse) (&W, cm) ;
+ /* R = W2 - B */
+ R = CHOLMOD(add) (W2, B, one, minusone, TRUE, FALSE, cm) ;
+ CHOLMOD(free_sparse) (&W2, cm) ;
+ }
+ else
+ {
+ /* W = A*X */
+ W = CHOLMOD(ssmult) (A, X, 0, TRUE, FALSE, cm) ;
+ /* R = W - B */
+ R = CHOLMOD(add) (W, B, one, minusone, TRUE, FALSE, cm) ;
+ CHOLMOD(free_sparse) (&W, cm) ;
+ }
+
+ r = CHOLMOD(norm_sparse) (R, 1, cm) ;
+ CHOLMOD(free_sparse) (&R, cm) ;
+ if (bnorm > 0)
+ {
+ r /= bnorm ;
+ }
+ }
+
+ return (r) ;
+}
+
+
+/* ========================================================================== */
+/* === resid3 =============================================================== */
+/* ========================================================================== */
+
+/* r = norm (A1*A2*A3*x - b) / norm (b) */
+
+double resid3 (cholmod_sparse *A1, cholmod_sparse *A2, cholmod_sparse *A3,
+ cholmod_dense *X, cholmod_dense *B)
+{
+ double r, bnorm ;
+ cholmod_dense *R, *W1, *W2, *X2, *B2 ;
+ cholmod_sparse *C1, *C2, *C3 ;
+ Int n, nrhs, d, xtype ;
+
+ if (A1 == NULL || X == NULL || B == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot compute resid3") ;
+ return (1) ;
+ }
+
+ cm->status = CHOLMOD_OK ;
+
+ n = B->nrow ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert all inputs to an identical xtype */
+ /* ---------------------------------------------------------------------- */
+
+ xtype = MAX (A1->xtype, X->xtype) ;
+ xtype = MAX (xtype, B->xtype) ;
+ if (A2 != NULL)
+ {
+ xtype = MAX (xtype, A2->xtype) ;
+ }
+ if (A3 != NULL)
+ {
+ xtype = MAX (xtype, A3->xtype) ;
+ }
+
+ C1 = NULL ;
+ C2 = NULL ;
+ C3 = NULL ;
+ B2 = NULL ;
+ X2 = NULL ;
+
+ if (A1->xtype != xtype)
+ {
+ C1 = CHOLMOD(copy_sparse) (A1, cm) ;
+ CHOLMOD(sparse_xtype) (xtype, C1, cm) ;
+ A1 = C1 ;
+ }
+
+ if (A2 != NULL && A2->xtype != xtype)
+ {
+ C2 = CHOLMOD(copy_sparse) (A2, cm) ;
+ CHOLMOD(sparse_xtype) (xtype, C2, cm) ;
+ A2 = C2 ;
+ }
+
+ if (A3 != NULL && A3->xtype != xtype)
+ {
+ C3 = CHOLMOD(copy_sparse) (A3, cm) ;
+ CHOLMOD(sparse_xtype) (xtype, C3, cm) ;
+ A3 = C3 ;
+ }
+
+ if (X->xtype != xtype)
+ {
+ X2 = CHOLMOD(copy_dense) (X, cm) ;
+ CHOLMOD(dense_xtype) (xtype, X2, cm) ;
+ X = X2 ;
+ }
+
+ if (B->xtype != xtype)
+ {
+ B2 = CHOLMOD(copy_dense) (B, cm) ;
+ CHOLMOD(dense_xtype) (xtype, B2, cm) ;
+ B = B2 ;
+ }
+
+ if (cm->status < CHOLMOD_OK)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot compute resid3") ;
+ CHOLMOD(free_sparse) (&C1, cm) ;
+ CHOLMOD(free_sparse) (&C2, cm) ;
+ CHOLMOD(free_sparse) (&C3, cm) ;
+ CHOLMOD(free_dense) (&B2, cm) ;
+ CHOLMOD(free_dense) (&X2, cm) ;
+ return (1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get B and its norm */
+ /* ---------------------------------------------------------------------- */
+
+ nrhs = B->ncol ;
+ d = B->d ;
+ bnorm = CHOLMOD(norm_dense) (B, 1, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the residual */
+ /* ---------------------------------------------------------------------- */
+
+ if (A3 != NULL)
+ {
+ /* W1 = A3*X */
+ W1 = CHOLMOD(zeros) (n, nrhs, xtype, cm) ;
+ CHOLMOD(sdmult) (A3, FALSE, one, zero, X, W1, cm) ;
+ }
+ else
+ {
+ W1 = X ;
+ }
+
+ if (A2 != NULL)
+ {
+ /* W2 = A2*W1 */
+ W2 = CHOLMOD(eye) (n, nrhs, xtype, cm) ;
+ CHOLMOD(sdmult) (A2, FALSE, one, zero, W1, W2, cm) ;
+ }
+ else
+ {
+ W2 = W1 ;
+ }
+
+ /* R = B */
+ R = CHOLMOD(copy_dense) (B, cm) ;
+
+ /* R = A1*W2 - R */
+ CHOLMOD(sdmult) (A1, FALSE, one, minusone, W2, R, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* r = norm (R) / norm (B) */
+ /* ---------------------------------------------------------------------- */
+
+ r = CHOLMOD(norm_dense) (R, 1, cm) ;
+ CHOLMOD(free_dense) (&R, cm) ;
+
+ CHOLMOD(free_sparse) (&C1, cm) ;
+ CHOLMOD(free_sparse) (&C2, cm) ;
+ CHOLMOD(free_sparse) (&C3, cm) ;
+ CHOLMOD(free_dense) (&B2, cm) ;
+ CHOLMOD(free_dense) (&X2, cm) ;
+
+ if (A3 != NULL)
+ {
+ CHOLMOD(free_dense) (&W1, cm) ;
+ }
+ if (A2 != NULL)
+ {
+ CHOLMOD(free_dense) (&W2, cm) ;
+ }
+ if (bnorm > 0)
+ {
+ r /= bnorm ;
+ }
+ return (r) ;
+}
+
+
+/* ========================================================================== */
+/* === pnorm ================================================================ */
+/* ========================================================================== */
+
+/* r = norm (x-Pb) or r = norm(x-P'b). This is lengthy because CHOLMOD does
+ * not provide any operations on dense matrices, and because it used to test
+ * the sparse-to-dense conversion routine. Multiple methods are used to compute
+ * the same thing.
+ */
+
+double pnorm (cholmod_dense *X, Int *P, cholmod_dense *B, Int inv)
+{
+ cholmod_dense *R, *X2, *B2 ;
+ cholmod_factor *L ;
+ double *xx, *xz, *bx, *bz, *rx, *rz ;
+ Int *Pinv, *Perm ;
+ double rnorm, r ;
+ Int i, j, k, n, nrhs, xtype, ok, save, lxtype ;
+
+ if (X == NULL || P == NULL || B == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot compute pnorm") ;
+ return (1) ;
+ }
+
+ save = cm->prefer_zomplex ;
+ n = X->nrow ;
+ nrhs = X->ncol ;
+ rnorm = 0 ;
+
+ Pinv = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ if (Pinv != NULL)
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ Pinv [P [k]] = k ;
+ }
+ }
+
+ xtype = MAX (X->xtype, B->xtype) ;
+
+ R = CHOLMOD(zeros) (n, nrhs, CHOLMOD_ZOMPLEX, cm) ;
+ B2 = CHOLMOD(copy_dense) (B, cm) ;
+ ok = R != NULL && B2 != NULL ;
+ ok = ok && CHOLMOD(dense_xtype) (CHOLMOD_ZOMPLEX, B2, cm) ;
+
+ for (lxtype = CHOLMOD_REAL ; ok && lxtype <= CHOLMOD_ZOMPLEX ; lxtype++)
+ {
+ /* create a fake factor object */
+ L = CHOLMOD(allocate_factor) (n, cm) ;
+ CHOLMOD(change_factor) (lxtype, TRUE, FALSE, TRUE, TRUE, L, cm) ;
+ ok = ok && (L != NULL && L->Perm != NULL && Pinv != NULL) ;
+ if (ok)
+ {
+ L->ordering = CHOLMOD_GIVEN ;
+ Perm = L->Perm ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Perm [k] = Pinv [k] ;
+ }
+ }
+ for (k = 0 ; k <= 1 ; k++)
+ {
+ /* solve the inverse permutation system, X2 = P*X or X2 = P'*X */
+ cm->prefer_zomplex = k ;
+ X2 = CHOLMOD(solve) (inv ? CHOLMOD_Pt : CHOLMOD_P, L, X, cm) ;
+
+ ok = ok && CHOLMOD(dense_xtype) (CHOLMOD_ZOMPLEX, X2, cm) ;
+ if (ok && X2 != NULL)
+ {
+ rx = R->x ;
+ rz = R->z ;
+ xx = X2->x ;
+ xz = X2->z ;
+ bx = B2->x ;
+ bz = B2->z ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ rx [i+j*n] = xx [i+j*n] - bx [i+j*n] ;
+ rz [i+j*n] = xz [i+j*n] - bz [i+j*n] ;
+ }
+ }
+ }
+ r = CHOLMOD(norm_dense) (R, 0, cm) ;
+ rnorm = MAX (r, rnorm) ;
+ CHOLMOD(free_dense) (&X2, cm) ;
+ }
+ CHOLMOD(free_factor) (&L, cm) ;
+ }
+
+ CHOLMOD(free_dense) (&B2, cm) ;
+ CHOLMOD(free_dense) (&R, cm) ;
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ /* X and B are both real */
+ cholmod_sparse *Bs, *Pb ;
+ Bs = CHOLMOD(dense_to_sparse) (B, TRUE, cm) ;
+ Pb = CHOLMOD(submatrix) (Bs, inv ? Pinv : P, n, NULL, -1, TRUE, TRUE,cm);
+ X2 = CHOLMOD(sparse_to_dense) (Pb, cm) ;
+ R = CHOLMOD(zeros) (n, nrhs, CHOLMOD_REAL, cm) ;
+ if (R != NULL && X != NULL && X2 != NULL)
+ {
+ rx = R->x ;
+ xx = X->x ;
+ bx = X2->x ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ rx [i+j*n] = xx [i+j*n] - bx [i+j*n] ;
+ }
+ }
+ }
+ CHOLMOD(free_sparse) (&Bs, cm) ;
+ CHOLMOD(free_sparse) (&Pb, cm) ;
+ CHOLMOD(free_dense) (&X2, cm) ;
+ r = CHOLMOD(norm_dense) (R, 1, cm) ;
+ rnorm = MAX (rnorm, r) ;
+ CHOLMOD(free_dense) (&R, cm) ;
+ }
+
+ CHOLMOD(free) (n, sizeof (Int), Pinv, cm) ;
+ cm->prefer_zomplex = save ;
+ return (rnorm) ;
+}
+
+
+/* ========================================================================== */
+/* === prune_row ============================================================ */
+/* ========================================================================== */
+
+/* Set row k and column k of a packed matrix A to zero. Set A(k,k) to 1
+ * if space is available. */
+
+void prune_row (cholmod_sparse *A, Int k)
+{
+ double *Ax ;
+ Int *Ap, *Ai ;
+ Int ncol, p, i, j, nz ;
+
+ if (A == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "nothing to prune") ;
+ return ;
+ }
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ nz = 0 ;
+ ncol = A->ncol ;
+
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ Ap [j] = nz ;
+ if (j == k && nz < Ap [j+1])
+ {
+ Ai [nz] = k ;
+ Ax [nz] = 1 ;
+ nz++ ;
+ }
+ else
+ {
+ for ( ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ if (i != k)
+ {
+ Ai [nz] = i ;
+ Ax [nz] = Ax [p] ;
+ nz++ ;
+ }
+ }
+ }
+ }
+ Ap [ncol] = nz ;
+}
+
+
+/* ========================================================================== */
+/* === do_matrix =========================================================== */
+/* ========================================================================== */
+
+double do_matrix (cholmod_sparse *A)
+{
+ double err, maxerr = 0 ;
+ Int print, precise, maxprint, minprint, nmethods ;
+
+ if (A == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "no matrix") ;
+ return (1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine print level, based on matrix size */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->nrow <= 4)
+ {
+ minprint = 5 ;
+ maxprint = 5 ;
+ }
+ else if (A->nrow <= 8)
+ {
+ minprint = 4 ;
+ maxprint = 4 ;
+ }
+ else
+ {
+ minprint = 1 ;
+ maxprint = 1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* for all print levels and precisions, do: */
+ /* ---------------------------------------------------------------------- */
+
+ for (print = minprint ; print <= maxprint ; print++)
+ {
+ for (precise = 0 ; precise <= (print >= 4) ? 1 : 0 ; precise++)
+ {
+ Int save1, save2 ;
+
+ maxerr = 0 ;
+ my_srand (42) ; /* RAND reset */
+ cm->print = print ;
+ cm->precise = precise ;
+ printf ("\n----------Print level %d precise: %d\n",
+ cm->print, cm->precise) ;
+
+ save1 = cm->final_asis ;
+ save2 = cm->final_super ;
+ cm->final_asis = FALSE ;
+ cm->final_super = TRUE ;
+ OK (CHOLMOD(print_common) ("cm", cm)) ;
+ cm->final_asis = save1 ;
+ cm->final_super = save2 ;
+
+ /* -------------------------------------------------------------- */
+ /* test various matrix operations */
+ /* -------------------------------------------------------------- */
+
+ err = test_ops (A) ; /* RAND */
+ MAXERR (maxerr, err, 1) ;
+
+ /* -------------------------------------------------------------- */
+ /* solve the augmented system */
+ /* -------------------------------------------------------------- */
+
+ err = aug (A) ; /* no random number use */
+ MAXERR (maxerr, err, 1) ;
+
+ /* -------------------------------------------------------------- */
+ /* solve using different methods */
+ /* -------------------------------------------------------------- */
+
+ printf ("test_solver (1)\n") ;
+ cm->nmethods = 9 ;
+ cm->final_asis = TRUE ;
+ err = test_solver (A) ; /* RAND reset */
+ MAXERR (maxerr, err, 1) ;
+
+ printf ("test_solver (2)\n") ;
+ cm->final_asis = TRUE ;
+ cm->method [0].ordering = CHOLMOD_NATURAL ;
+ for (nmethods = 0 ; nmethods < 7 ; nmethods++)
+ {
+ cm->nmethods = nmethods ;
+ err = test_solver (A) ; /* RAND reset */
+ MAXERR (maxerr, err, 1) ;
+ }
+
+ printf ("test_solver (3)\n") ;
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NESDIS ;
+ err = test_solver (A) ; /* RAND reset */
+ MAXERR (maxerr, err, 1) ;
+
+ printf ("test_solver (3b)\n") ;
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NESDIS ;
+ cm->method [0].nd_camd = 2 ;
+ err = test_solver (A) ; /* RAND reset */
+ MAXERR (maxerr, err, 1) ;
+
+ printf ("test_solver (3c)\n") ;
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NATURAL ;
+ err = test_solver (A) ; /* RAND reset */
+ MAXERR (maxerr, err, 1) ;
+
+ printf ("test_solver (4)\n") ;
+ cm->nmethods = 1 ;
+ cm->method[0].ordering = CHOLMOD_METIS ;
+ err = test_solver (A) ; /* RAND reset */
+ MAXERR (maxerr, err, 1) ;
+
+ printf ("test_solver (5)\n") ;
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_AMD ;
+ CHOLMOD(free_work) (cm) ;
+ err = test_solver (A) ; /* RAND reset */
+ MAXERR (maxerr, err, 1) ;
+
+ printf ("test_solver (6)\n") ;
+ cm->nmethods = 1 ;
+ cm->method[0].ordering = CHOLMOD_COLAMD ;
+ err = test_solver (A) ; /* RAND reset */
+ MAXERR (maxerr, err, 1) ;
+
+ /* -------------------------------------------------------------- */
+ /* restore default control parameters */
+ /* -------------------------------------------------------------- */
+
+ OK (CHOLMOD(print_common) ("cm", cm)) ;
+ CHOLMOD(defaults) (cm) ;
+ }
+ }
+
+ printf ("do_matrix max error %.1g\n", maxerr) ;
+
+ return (maxerr) ;
+}
+
+
+/* ========================================================================== */
+/* === main ================================================================= */
+/* ========================================================================== */
+
+/* Usage:
+ * cm < matrix do not perform intensive memory-failure tests
+ * cm -m < matrix do perform memory tests
+ * cm -s < matrix matrix is singular, nan error expected
+ *
+ * (The memory tests are performed if any argument is given to cm).
+ */
+
+int main (int argc, char **argv)
+{
+ cholmod_triplet *T ;
+ cholmod_sparse *A, *C, *AT ;
+ char *s ;
+ double err = 0, maxerr = 0 ;
+ Int n = 0, nmin = 0, nrow = 0, ncol = 0, save ;
+ int singular, do_memory, i, do_nantests ;
+ double v = CHOLMOD_VERSION ;
+
+ printf ("Testing CHOLMOD (%g)\n", v) ;
+ printf ("%s: argc: %d\n", argv [0], argc) ;
+ my_srand (42) ; /* RAND */
+ fflush (stdout) ;
+
+ singular = FALSE ;
+ do_memory = FALSE ;
+ do_nantests = FALSE ;
+ for (i = 1 ; i < argc ; i++)
+ {
+ s = argv [i] ;
+ if (s [0] == '-' && s [1] == 'm') do_memory = TRUE ;
+ if (s [0] == '-' && s [1] == 's') singular = TRUE ;
+ if (s [0] == '-' && s [1] == 'n') do_nantests = TRUE ;
+ }
+
+ printf ("do_memory: %d singular: %d\n", do_memory, singular) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize CHOLMOD */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ OK (CHOLMOD(start) (cm)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test all methods with NULL common */
+ /* ---------------------------------------------------------------------- */
+
+ /* no user error handler, since lots of errors will be raised here */
+ cm->error_handler = NULL ;
+ null_test (NULL) ;
+ save = cm->itype ;
+ cm->itype = -999 ;
+ null_test (cm) ;
+ cm->itype = save ;
+ null_test2 ( ) ;
+ CHOLMOD(finish) (cm) ;
+ OK (cm->malloc_count == 0) ;
+ OK (CHOLMOD(start) (cm)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create basic scalars */
+ /* ---------------------------------------------------------------------- */
+
+ Zero [0] = 0 ;
+ Zero [1] = 0 ;
+
+ zero [0] = 0 ;
+ zero [1] = 0 ;
+ one [0] = 1 ;
+ one [1] = 0 ;
+ minusone [0] = -1 ;
+ minusone [1] = 0 ;
+ M1 = CHOLMOD(ones) (1, 1, CHOLMOD_REAL, cm) ;
+
+ if (M1 != NULL)
+ {
+ ((double *) (M1->x)) [0] = -1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read in a triplet matrix and use it to test CHOLMOD */
+ /* ---------------------------------------------------------------------- */
+
+ for ( ; (T = read_triplet (stdin)) != NULL ; ) /* RAND */
+ {
+
+ if (T->nrow > 1000000)
+ {
+ /* do huge-problem tests only */
+ huge ( ) ;
+ CHOLMOD(free_triplet) (&T, cm) ;
+ continue ;
+ }
+
+ maxerr = 0 ;
+ CHOLMOD(defaults) (cm) ;
+ cm->error_handler = my_handler ;
+ cm->print = 4 ;
+ cm->precise = FALSE ;
+ cm->nmethods = 8 ;
+
+ /* ------------------------------------------------------------------ */
+ /* convert triplet to sparse matrix */
+ /* ------------------------------------------------------------------ */
+
+ A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ;
+ AT = CHOLMOD(transpose) (A, 0, cm) ;
+ OK (CHOLMOD(print_sparse) (A, "Test matrix, A", cm)) ;
+ C = unpack (A) ; /* RAND */
+ OK (CHOLMOD(print_sparse) (C, "Unpacked/unsorted version of A", cm)) ;
+ cm->print = 1 ;
+
+ if (T != NULL)
+ {
+ nrow = T->nrow ;
+ ncol = T->ncol ;
+ n = MAX (nrow, ncol) ;
+ nmin = MIN (nrow, ncol) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* basic error tests */
+ /* ------------------------------------------------------------------ */
+
+ null2 (T, do_nantests) ; /* RAND */
+ printf ("Null2 OK : no error\n") ;
+ if (do_nantests)
+ {
+ maxerr = 0 ;
+ goto done ; /* yes, this is ugly */
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* raw factorization tests */
+ /* ------------------------------------------------------------------ */
+
+ cm->error_handler = NULL ;
+ err = raw_factor (A, 2) ; /* RAND */
+ cm->error_handler = my_handler ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("raw factorization error %.1g\n", err) ;
+
+ err = raw_factor2 (A, 0., 0) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("raw factorization error2 %.1g\n", err) ;
+
+ err = raw_factor2 (A, 1e-16, 0) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("raw factorization error3 %.1g\n", err) ;
+
+ if (n < 1000 && A && T && A->stype == 1)
+ {
+ /* factorize a symmetric matrix (upper part stored), possibly
+ * with ignored entries in lower triangular part. */
+ cholmod_sparse *F ;
+ int save = T->stype ;
+
+ T->stype = 0 ;
+ F = CHOLMOD(triplet_to_sparse) (T, 0, cm) ;
+ T->stype = save ;
+
+ /*
+ ET = CHOLMOD(transpose) (E, 2, cm) ;
+ if (E) E->stype = 0 ;
+ if (ET) ET->stype = 0 ;
+ F = CHOLMOD(add) (E, ET, one, one, 1, 1, cm) ;
+ */
+
+ if (F) F->stype = 1 ;
+
+ err = raw_factor2 (F, 0., 0) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("raw factorization error4 %.1g\n", err) ;
+
+ err = raw_factor2 (F, 1e-16, 0) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("raw factorization error5 %.1g\n", err) ;
+
+ cm->dbound = 1e-15 ;
+
+ err = raw_factor2 (F, 0., 0) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("raw factorization error6 %.1g\n", err) ;
+
+ err = raw_factor2 (F, 1e-16, 0) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("raw factorization error7 %.1g\n", err) ;
+
+ err = raw_factor2 (F, 1e-16, 1) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("raw factorization error8 %.1g\n", err) ;
+
+ cm->dbound = 0 ;
+
+ /*
+ CHOLMOD(free_sparse) (&E, cm) ;
+ CHOLMOD(free_sparse) (&ET, cm) ;
+ */
+
+ CHOLMOD(free_sparse) (&F, cm) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* matrix ops */
+ /* ------------------------------------------------------------------ */
+
+ err = test_ops (A) ; /* RAND */
+ MAXERR (maxerr, err, 1) ;
+ printf ("initial testops error %.1g\n", err) ;
+
+ /* ------------------------------------------------------------------ */
+ /* analyze, factorize, solve */
+ /* ------------------------------------------------------------------ */
+
+ err = solve (A) ; /* RAND */
+ MAXERR (maxerr, err, 1) ;
+ printf ("initial solve error %.1g\n", err) ;
+
+ /* ------------------------------------------------------------------ */
+ /* CCOLAMD tests */
+ /* ------------------------------------------------------------------ */
+
+ cctest (A) ; /* RAND reset */
+ cctest (AT) ; /* RAND reset */
+
+ /* ------------------------------------------------------------------ */
+ /* COLAMD tests */
+ /* ------------------------------------------------------------------ */
+
+ ctest (A) ;
+ ctest (AT) ;
+
+ /* ------------------------------------------------------------------ */
+ /* AMD tests */
+ /* ------------------------------------------------------------------ */
+
+ if (n < NLARGE || A->stype)
+ {
+ /* for unsymmetric matrices, this forms A*A' and A'*A, which can
+ * fail if A has a dense row or column. So it is only done for
+ * modest-sized unsymmetric matrices. */
+ amdtest (A) ;
+ amdtest (AT) ;
+ camdtest (A) ; /* RAND */
+ camdtest (AT) ; /* RAND */
+ }
+
+ if (n < NSMALL)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* do_matrix with an unpacked matrix */
+ /* -------------------------------------------------------------- */
+
+ /* try with an unpacked matrix, and a non-default dbound */
+ cm->dbound = 1e-15 ;
+ err = do_matrix (C) ; /* RAND reset */
+ MAXERR (maxerr, err, 1) ;
+ cm->dbound = 0 ;
+
+ /* -------------------------------------------------------------- */
+ /* do_matrix: analyze, factorize, and solve, with many options */
+ /* -------------------------------------------------------------- */
+
+ err = do_matrix (A) ; /* RAND reset */
+ MAXERR (maxerr, err, 1) ;
+
+ /* -------------------------------------------------------------- */
+ /* pretend to solve an LP */
+ /* -------------------------------------------------------------- */
+
+ if (nrow != ncol)
+ {
+ cm->print = 2 ;
+ err = lpdemo (T) ; /* RAND */
+ cm->print = 1 ;
+ MAXERR (maxerr, err, 1) ;
+ cm->print = 5; CHOLMOD(print_common) ("Common", cm);cm->print=1;
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_COLAMD ;
+ err = lpdemo (T) ; /* RAND */
+ MAXERR (maxerr, err, 1) ;
+ printf ("initial lp error %.1g, dbound %g\n", err, cm->dbound) ;
+ cm->nmethods = 0 ;
+ cm->method [0].ordering = CHOLMOD_GIVEN ;
+ }
+ }
+
+ progress (1, '|') ;
+
+ if (n < NSMALL && do_memory)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Exhaustive memory-error handling */
+ /* -------------------------------------------------------------- */
+
+ memory_tests (T) ; /* RAND */
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* free matrices and print results */
+ /* ------------------------------------------------------------------ */
+
+ done: /* an ugly "goto" target; added to minimize code changes
+ * when added "do_nantests", for version 1.0.2 */
+
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&AT, cm) ;
+ CHOLMOD(free_sparse) (&A, cm) ;
+ CHOLMOD(free_triplet) (&T, cm) ;
+
+ fprintf (stderr, "\n "
+ " Test OK") ;
+ if (nrow <= ncol && !singular)
+ {
+ /* maxerr should be NaN if nrow > ncol, so don't print it */
+ fprintf (stderr, ", maxerr %.1g", maxerr) ;
+ }
+ fprintf (stderr, "\n") ;
+ my_srand (42) ; /* RAND reset */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize CHOLMOD */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_dense) (&M1, cm) ;
+ CHOLMOD(finish) (cm) ;
+
+ cm->print = 5 ; OK (CHOLMOD(print_common) ("cm", cm)) ;
+ printf ("malloc count "ID" inuse "ID"\n",
+ (Int) cm->malloc_count,
+ (Int) cm->memory_inuse) ;
+ OK (cm->malloc_count == 0) ;
+ OK (cm->memory_inuse == 0) ;
+ if (nrow > ncol)
+ {
+ /* maxerr should be NaN, so don't print it */
+ printf ("All tests successful\n") ;
+ }
+ else
+ {
+ printf ("All tests successful: max error %.1g\n", maxerr) ;
+ }
+ return (0) ;
+}
diff --git a/CHOLMOD/Tcov/cm.h b/CHOLMOD/Tcov/cm.h
new file mode 100644
index 0000000..14e9da3
--- /dev/null
+++ b/CHOLMOD/Tcov/cm.h
@@ -0,0 +1,277 @@
+#include "cholmod.h"
+#include <stdlib.h>
+#include <stdio.h>
+#include <limits.h>
+#include <math.h>
+
+#define Size_max ((size_t) (-1))
+
+/* -------------------------------------------------------------------------- */
+/* double, UF_long */
+/* -------------------------------------------------------------------------- */
+
+#ifdef DLONG
+#define Real double
+#define Int UF_long
+#define Int_max UF_long_max
+#define CHOLMOD(name) cholmod_l_ ## name
+#define LONG
+#define DOUBLE
+#define ITYPE CHOLMOD_LONG
+#define DTYPE CHOLMOD_DOUBLE
+
+/* -------------------------------------------------------------------------- */
+/* double, int: this is the default */
+/* -------------------------------------------------------------------------- */
+
+#else
+
+#ifndef DINT
+#define DINT
+#endif
+#define INT
+#define DOUBLE
+
+#define Real double
+#define Int int
+#define Int_max INT_MAX
+#define CHOLMOD(name) cholmod_ ## name
+#define ITYPE CHOLMOD_INT
+#define DTYPE CHOLMOD_DOUBLE
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+
+#include "cholmod_blas.h"
+
+#define EMPTY (-1)
+#define TRUE 1
+#define FALSE 0
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+#define IMPLIES(p,q) (!(p) || (q))
+
+#if defined(WIN32) || defined(_WIN32)
+#define ISNAN(x) (((x) != (x)) || (((x) < (x))))
+#else
+#define ISNAN(x) ((x) != (x))
+#endif
+
+#define MY_RAND_MAX 32767
+
+#define MAXERR(maxerr,err,anorm) \
+{ \
+ if (ISNAN (maxerr)) \
+ { \
+ /* do nothing */ ; \
+ } \
+ else if (ISNAN (err)) \
+ { \
+ maxerr = err ; \
+ } \
+ else if (anorm > 0) \
+ { \
+ if ((err/anorm) > maxerr) maxerr = (err/anorm) ; \
+ } \
+ else \
+ { \
+ if (err > maxerr) maxerr = err ; \
+ } \
+ /* printf ("MAXERR: %7.2e %7.2e %7.2e in %d : %s\n", \
+ maxerr, err, (double) anorm, __LINE__, __FILE__ ) ; */ \
+}
+
+#define OKP(p) Assert ((p) != NULL, __FILE__, __LINE__)
+#define OK(truth) Assert (truth, __FILE__, __LINE__)
+#define NOT(truth) Assert (!(truth), __FILE__, __LINE__)
+#define NOP(p) Assert ((p) == NULL, __FILE__, __LINE__)
+
+#define NSMALL 200
+#define NLARGE 1000
+
+#define ERROR(status,message) \
+ CHOLMOD(error) (status, __FILE__, __LINE__, message, cm)
+
+/* -------------------------------------------------------------------------- */
+/* global variables */
+/* -------------------------------------------------------------------------- */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN double zero [2], one [2], minusone [2] ;
+EXTERN cholmod_common Common, *cm ;
+EXTERN cholmod_dense *M1 ;
+EXTERN Int my_tries ;
+EXTERN double Zero [2] ;
+
+/* -------------------------------------------------------------------------- */
+/* prototypes */
+/* -------------------------------------------------------------------------- */
+
+void null_test (cholmod_common *) ;
+void null_test2 (void) ;
+void Assert (int truth, char *file, int line) ;
+Int nrand (Int n) ;
+Int *prand (Int n) ;
+cholmod_triplet *read_triplet (FILE *f) ;
+double test_ops (cholmod_sparse *A) ;
+cholmod_dense *xtrue (Int nrow, Int ncol, Int d, Int xtype) ;
+double resid (cholmod_sparse *A, cholmod_dense *X, cholmod_dense *B) ;
+double solve (cholmod_sparse *A) ;
+double aug (cholmod_sparse *A) ;
+double do_matrix (cholmod_sparse *A) ;
+cholmod_dense *rhs (cholmod_sparse *A, Int nrhs, Int d) ;
+void prune_row (cholmod_sparse *A, Int k) ;
+double pnorm (cholmod_dense *X, Int *P, cholmod_dense *B, Int inv) ;
+double test_solver (cholmod_sparse *A) ;
+Int *rand_set (Int len, Int n) ;
+void my_handler (int status, char *file, int line, char *msg) ;
+void my_handler2 (int status, char *file, int line, char *msg) ;
+double resid3 (cholmod_sparse *A1, cholmod_sparse *A2, cholmod_sparse *A3,
+ cholmod_dense *X, cholmod_dense *B) ;
+double xrand (double range) ;
+double lp_resid (cholmod_sparse *A, Int *rflag, Int *fset, Int fsize,
+ double beta [2], cholmod_dense *X, cholmod_dense *B) ;
+double lpdemo (cholmod_triplet *T) ;
+cholmod_sparse *lp_prune ( cholmod_sparse *A, Int *rflag, Int *fset, Int fsize);
+void null2 (cholmod_triplet *Tok, int do_nantests) ;
+void *my_malloc2 (size_t size) ;
+void *my_calloc2 (size_t n, size_t size) ;
+void *my_realloc2 (void *p, size_t size) ;
+void my_free2 (void *p) ;
+void memory_tests (cholmod_triplet *T) ;
+void progress (Int force, char s) ;
+void test_memory_handler ( void ) ;
+void normal_memory_handler ( void ) ;
+cholmod_sparse *unpack (cholmod_sparse *A) ;
+Int nzdiag (cholmod_sparse *A) ;
+Int check_partition (cholmod_sparse *A, Int *Part) ;
+double raw_factor (cholmod_sparse *A, Int errors) ;
+double raw_factor2 (cholmod_sparse *A, double alpha, int domask) ;
+cholmod_sparse *get_row (cholmod_sparse *A, Int i, Int *rflag, Int *fset,
+ Int fsize, double beta [2]) ;
+Int my_rand (void) ;
+void my_srand (unsigned seed) ;
+unsigned long my_seed (void) ;
+void cctest (cholmod_sparse *A) ;
+Int check_constraints (Int *P, Int *Cmember, Int n) ;
+void ctest (cholmod_sparse *A) ;
+void amdtest (cholmod_sparse *A) ;
+double resid_sparse (cholmod_sparse *A, cholmod_sparse *X, cholmod_sparse *B) ;
+cholmod_dense *zeros (Int nrow, Int ncol, Int d, Int xtype) ;
+
+/* -------------------------------------------------------------------------- */
+/* AMD, COLAMD, and CCOLAMD */
+/* -------------------------------------------------------------------------- */
+
+#ifdef LONG
+
+#define ID "%ld"
+
+#define AMD_order amd_l_order
+#define AMD_defaults amd_l_defaults
+#define AMD_control amd_l_control
+#define AMD_info amd_l_info
+#define AMD_1 amd_l1
+#define AMD_2 amd_l2
+#define AMD_valid amd_l_valid
+#define AMD_aat amd_l_aat
+#define AMD_postorder amd_l_postorder
+#define AMD_post_tree amd_l_post_tree
+#define AMD_dump amd_l_dump
+#define AMD_debug amd_l_debug
+#define AMD_debug_init amd_l_debug_init
+#define AMD_preprocess amd_l_preprocess
+
+#define CAMD_order camd_l_order
+#define CAMD_defaults camd_l_defaults
+#define CAMD_control camd_l_control
+#define CAMD_info camd_l_info
+#define CAMD_1 camd_l1
+#define CAMD_2 camd_l2
+#define CAMD_valid camd_l_valid
+#define CAMD_cvalid camd_l_cvalid
+#define CAMD_aat camd_l_aat
+#define CAMD_postorder camd_l_postorder
+#define CAMD_dump camd_l_dump
+#define CAMD_debug camd_l_debug
+#define CAMD_debug_init camd_l_debug_init
+#define CAMD_preprocess camd_l_preprocess
+
+#define CCOLAMD_recommended ccolamd_l_recommended
+#define CCOLAMD_set_defaults ccolamd_l_set_defaults
+#define CCOLAMD_2 ccolamd2_l
+#define CCOLAMD_MAIN ccolamd_l
+#define CCOLAMD_apply_order ccolamd_l_apply_order
+#define CCOLAMD_postorder ccolamd_l_postorder
+#define CCOLAMD_post_tree ccolamd_l_post_tree
+#define CCOLAMD_fsize ccolamd_l_fsize
+#define CSYMAMD_MAIN csymamd_l
+#define CCOLAMD_report ccolamd_l_report
+#define CSYMAMD_report csymamd_l_report
+
+#define COLAMD_recommended colamd_l_recommended
+#define COLAMD_set_defaults colamd_l_set_defaults
+#define COLAMD_MAIN colamd_l
+#define SYMAMD_MAIN symamd_l
+#define COLAMD_report colamd_l_report
+#define SYMAMD_report symamd_l_report
+
+#else
+
+#define ID "%d"
+
+#define AMD_order amd_order
+#define AMD_defaults amd_defaults
+#define AMD_control amd_control
+#define AMD_info amd_info
+#define AMD_1 amd_1
+#define AMD_2 amd_2
+#define AMD_valid amd_valid
+#define AMD_aat amd_aat
+#define AMD_postorder amd_postorder
+#define AMD_post_tree amd_post_tree
+#define AMD_dump amd_dump
+#define AMD_debug amd_debug
+#define AMD_debug_init amd_debug_init
+#define AMD_preprocess amd_preprocess
+
+#define CAMD_order camd_order
+#define CAMD_defaults camd_defaults
+#define CAMD_control camd_control
+#define CAMD_info camd_info
+#define CAMD_1 camd_1
+#define CAMD_2 camd_2
+#define CAMD_valid camd_valid
+#define CAMD_cvalid camd_cvalid
+#define CAMD_aat camd_aat
+#define CAMD_postorder camd_postorder
+#define CAMD_dump camd_dump
+#define CAMD_debug camd_debug
+#define CAMD_debug_init camd_debug_init
+#define CAMD_preprocess camd_preprocess
+
+#define CCOLAMD_recommended ccolamd_recommended
+#define CCOLAMD_set_defaults ccolamd_set_defaults
+#define CCOLAMD_2 ccolamd2
+#define CCOLAMD_MAIN ccolamd
+#define CCOLAMD_apply_order ccolamd_apply_order
+#define CCOLAMD_postorder ccolamd_postorder
+#define CCOLAMD_post_tree ccolamd_post_tree
+#define CCOLAMD_fsize ccolamd_fsize
+#define CSYMAMD_MAIN csymamd
+#define CCOLAMD_report ccolamd_report
+#define CSYMAMD_report csymamd_report
+
+#define COLAMD_recommended colamd_recommended
+#define COLAMD_set_defaults colamd_set_defaults
+#define COLAMD_MAIN colamd
+#define SYMAMD_MAIN symamd
+#define COLAMD_report colamd_report
+#define SYMAMD_report symamd_report
+
+#endif
diff --git a/CHOLMOD/Tcov/cmread.c b/CHOLMOD/Tcov/cmread.c
new file mode 100644
index 0000000..6256fb6
--- /dev/null
+++ b/CHOLMOD/Tcov/cmread.c
@@ -0,0 +1,116 @@
+/* ========================================================================== */
+/* === Tcov/cmread ========================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Read in a matrix from a file and print it out.
+ *
+ * Usage:
+ * cmread matrixfile
+ * cmread < matrixfile
+ */
+
+#include "cholmod.h"
+
+#ifdef DLONG
+#define CHOLMOD(routine) cholmod_l_ ## routine
+#define Int UF_long
+#else
+#define CHOLMOD(routine) cholmod_ ## routine
+#define Int int
+#endif
+
+int main (int argc, char **argv)
+{
+ cholmod_sparse *A, *C, *Z ;
+ cholmod_dense *X ;
+ cholmod_triplet *T ;
+ void *V ;
+ FILE *f, *f2 ;
+ cholmod_common Common, *cm ;
+ int mtype, prefer, option ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the file containing the input matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (argc > 1)
+ {
+ if ((f = fopen (argv [1], "r")) == NULL)
+ {
+ printf ("cannot open file: %s\n", argv [1]) ;
+ return (0) ;
+ }
+ }
+ else
+ {
+ f = stdin ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* start CHOLMOD, read the matrix, print it, and free it */
+ /* ---------------------------------------------------------------------- */
+
+ cm = &Common ;
+ CHOLMOD (start) (cm) ;
+ cm->print = 5 ;
+ A = CHOLMOD (read_sparse) (f, cm) ;
+ if (argc > 1) fclose (f) ;
+ CHOLMOD (print_sparse) (A, "A", cm) ;
+
+ if (argc > 1)
+ {
+ for (prefer = 0 ; prefer <= 2 ; prefer++)
+ {
+ printf ("\n---------------------- Prefer: %d\n", prefer) ;
+ f = fopen (argv [1], "r") ;
+ V = CHOLMOD (read_matrix) (f, prefer, &mtype, cm) ;
+ if (V != NULL) switch (mtype)
+ {
+ case CHOLMOD_TRIPLET:
+ T = V ;
+ CHOLMOD (print_triplet) (T, "T", cm) ;
+ CHOLMOD (free_triplet) (&T, cm) ;
+ break ;
+ case CHOLMOD_SPARSE:
+ C = V ;
+ CHOLMOD (print_sparse) (C, "C", cm) ;
+ Z = CHOLMOD (speye) (C->nrow, C->ncol, CHOLMOD_PATTERN, cm);
+ for (option = 0 ; option <= 2 ; option++)
+ {
+ int asym ;
+ Int xmatch = 0, pmatch = 0, nzoff = 0, nzd = 0 ;
+ asym = CHOLMOD (symmetry) (C, option,
+ &xmatch, &pmatch, &nzoff, &nzd, cm) ;
+ f2 = fopen ("temp5.mtx", "w") ;
+ CHOLMOD (write_sparse) (f2, C, Z, NULL, cm) ;
+ fclose (f2) ;
+ printf ("asym %d\n", asym) ;
+ }
+ CHOLMOD (free_sparse) (&C, cm) ;
+ CHOLMOD (free_sparse) (&Z, cm) ;
+ break ;
+ case CHOLMOD_DENSE:
+ X = V ;
+ CHOLMOD (print_dense) (X, "X", cm) ;
+ f2 = fopen ("temp5.mtx", "w") ;
+ CHOLMOD (write_dense) (f2, X, NULL, cm) ;
+ fclose (f2) ;
+ CHOLMOD (free_dense) (&X, cm) ;
+ break ;
+ }
+ fclose (f) ;
+ }
+ }
+
+ CHOLMOD (free_sparse) (&A, cm) ;
+ CHOLMOD (finish) (cm) ;
+ return (0) ;
+}
diff --git a/CHOLMOD/Tcov/comments.txt b/CHOLMOD/Tcov/comments.txt
new file mode 100644
index 0000000..4b433a8
--- /dev/null
+++ b/CHOLMOD/Tcov/comments.txt
@@ -0,0 +1 @@
+ Comments for testing cholmod_read/write functions.
diff --git a/CHOLMOD/Tcov/cov.awk b/CHOLMOD/Tcov/cov.awk
new file mode 100644
index 0000000..5744b40
--- /dev/null
+++ b/CHOLMOD/Tcov/cov.awk
@@ -0,0 +1,17 @@
+/cannot/
+
+/function/ { f = $8 }
+
+/file/ { f = $8 }
+
+/lines/ {
+
+ k = match ($1, "%") ;
+ p = substr ($1, 1, k-1) ;
+
+ if ((p+0) != 100)
+ {
+ printf "%8s %s\n", p, f
+ }
+}
+
diff --git a/CHOLMOD/Tcov/covall b/CHOLMOD/Tcov/covall
new file mode 100755
index 0000000..08df13a
--- /dev/null
+++ b/CHOLMOD/Tcov/covall
@@ -0,0 +1,5 @@
+#!/bin/csh
+./gcovs z*.c l_*c
+./covs > covs.out
+echo -n "statments not yet tested: "
+grep -c "#####" covs.out
diff --git a/CHOLMOD/Tcov/covall.sol b/CHOLMOD/Tcov/covall.sol
new file mode 100755
index 0000000..aaa73dc
--- /dev/null
+++ b/CHOLMOD/Tcov/covall.sol
@@ -0,0 +1,5 @@
+#!/bin/csh
+ tcov -x cm.profile z*.c >& /dev/null
+ echo -n "statments not yet tested: "
+ ./covs > covs.out
+ grep "#####" *tcov | wc -l
diff --git a/CHOLMOD/Tcov/cover b/CHOLMOD/Tcov/cover
new file mode 100755
index 0000000..b3e685c
--- /dev/null
+++ b/CHOLMOD/Tcov/cover
@@ -0,0 +1,9 @@
+#!/bin/csh
+# usage: cover files
+echo '================================================================='
+foreach file ($argv[1-])
+ echo $file
+ echo '================================================================='
+ grep "#####" -A5 -B5 $file
+ echo '================================================================='
+ end
diff --git a/CHOLMOD/Tcov/covs b/CHOLMOD/Tcov/covs
new file mode 100755
index 0000000..46bcb9a
--- /dev/null
+++ b/CHOLMOD/Tcov/covs
@@ -0,0 +1,9 @@
+#!/bin/csh
+# usage: covs
+echo '================================================================='
+foreach file (*.?cov)
+ echo $file
+ grep "#####" $file | grep -v "__dev" | grep -v "__major" | \
+ grep -v "#####:[ ]*[0-9]*:[{}]"
+ echo '================================================================='
+ end
diff --git a/CHOLMOD/Tcov/ctest.c b/CHOLMOD/Tcov/ctest.c
new file mode 100644
index 0000000..0daeefe
--- /dev/null
+++ b/CHOLMOD/Tcov/ctest.c
@@ -0,0 +1,303 @@
+/* ========================================================================== */
+/* === Tcov/ctest =========================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Test for colamd v2.4 */
+
+#include "cm.h"
+#include "colamd.h"
+
+
+/* ========================================================================== */
+/* === ctest ================================================================ */
+/* ========================================================================== */
+
+void ctest (cholmod_sparse *A)
+{
+ double knobs [COLAMD_KNOBS], knobs2 [COLAMD_KNOBS] ;
+ Int *P, *Cp, *Ci, *Si, *Sp ;
+ cholmod_sparse *C, *A2, *B, *S, *BT ;
+ Int nrow, ncol, alen, ok, stats [COLAMD_STATS], i, p, trial ;
+ size_t s ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nCOLAMD test\n") ;
+
+ if (A == NULL)
+ {
+ return ;
+ }
+
+ if (A->stype)
+ {
+ A2 = CHOLMOD(copy) (A, 0, 0, cm) ;
+ B = A2 ;
+ }
+ else
+ {
+ A2 = NULL ;
+ B = A ;
+ }
+
+ nrow = B->nrow ;
+ ncol = B->ncol ;
+ S = NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace colamd */
+ /* ---------------------------------------------------------------------- */
+
+ P = CHOLMOD(malloc) (nrow+1, sizeof (Int), cm) ;
+
+ COLAMD_set_defaults (knobs) ;
+ COLAMD_set_defaults (knobs2) ;
+ COLAMD_set_defaults (NULL) ;
+ COLAMD_report (NULL) ;
+ SYMAMD_report (NULL) ;
+
+ alen = COLAMD_recommended (B->nzmax, ncol, nrow) ;
+ C = CHOLMOD(allocate_sparse) (ncol, nrow, alen, TRUE, TRUE, 0,
+ CHOLMOD_PATTERN, cm) ;
+ Cp = C->p ;
+ Ci = C->i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order with colamd */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ CHOLMOD(print_sparse) (C, "C for colamd", cm) ;
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, NULL, stats) ;
+ COLAMD_report (stats) ;
+ OK (ok) ;
+ ok = stats [COLAMD_STATUS] ;
+ ok = (ok == COLAMD_OK || ok == COLAMD_OK_BUT_JUMBLED) ;
+ OK (ok) ;
+
+ /* permutation returned in C->p, if the ordering succeeded */
+ /* make sure P obeys the constraints */
+ OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "colamd perm", cm)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* with different dense thresholds */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nall dense rows:\n") ;
+ knobs2 [COLAMD_DENSE_ROW] = 0 ;
+ knobs2 [COLAMD_DENSE_COL] = 0.5 ;
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats) ;
+ COLAMD_report (stats) ;
+ OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "colamd perm", cm)) ;
+
+ printf ("\nall dense cols:\n") ;
+ knobs2 [COLAMD_DENSE_ROW] = 0.5 ;
+ knobs2 [COLAMD_DENSE_COL] = 0 ;
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats) ;
+ COLAMD_report (stats) ;
+ OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "colamd perm", cm)) ;
+
+ printf ("\nno dense rows/cols:\n") ;
+ knobs2 [COLAMD_DENSE_ROW] = -1 ;
+ knobs2 [COLAMD_DENSE_COL] = -1 ;
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats) ;
+ COLAMD_report (stats) ;
+ OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "colamd perm", cm)) ;
+
+ knobs2 [COLAMD_DENSE_ROW] = 0.5 ;
+ knobs2 [COLAMD_DENSE_COL] = 0.5 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* duplicate entries */
+ /* ---------------------------------------------------------------------- */
+
+ if (ncol > 2 && nrow > 2)
+ {
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ;
+ OK (ok) ;
+ if (Cp [1] - Cp [0] > 2)
+ {
+ Ci [0] = Ci [1] ;
+ }
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs2, stats) ;
+ COLAMD_report (stats) ;
+ OK (CHOLMOD(print_perm) (Cp, nrow, nrow, "colamd perm", cm)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* symamd */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow == ncol)
+ {
+ Int n = nrow ;
+
+ BT = CHOLMOD(transpose) (B, 0, cm) ; OKP(BT);
+ S = CHOLMOD(add) (B, BT, one, one, FALSE, FALSE, cm) ;
+ CHOLMOD(free_sparse) (&BT, cm) ;
+ Si = S->i ;
+ Sp = S->p ;
+
+ ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats,
+ cm->calloc_memory, cm->free_memory) ;
+ OK (ok) ;
+ OK (CHOLMOD(print_perm) (P, n, n, "symamd perm", cm)) ;
+ SYMAMD_report (stats) ;
+
+ /* ------------------------------------------------------------------ */
+ /* symamd errors */
+ /* ------------------------------------------------------------------ */
+
+ test_memory_handler ( ) ;
+ for (trial = 0 ; trial < 3 ; trial++)
+ {
+ my_tries = trial ;
+ ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats,
+ cm->calloc_memory, cm->free_memory) ;
+ NOT (ok) ;
+ }
+ my_tries = 3 ;
+ ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats,
+ cm->calloc_memory, cm->free_memory) ;
+ OK (ok) ;
+ normal_memory_handler ( ) ;
+
+ ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, NULL, cm->calloc_memory,
+ cm->free_memory) ; NOT (ok);
+
+ ok = SYMAMD_MAIN (n, NULL, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory) ; NOT (ok);
+ SYMAMD_report (stats) ;
+
+ ok = SYMAMD_MAIN (n, Si, NULL, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory) ; NOT (ok);
+ SYMAMD_report (stats) ;
+
+ ok = SYMAMD_MAIN (-1, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory) ; NOT (ok);
+ SYMAMD_report (stats) ;
+
+ p = Sp [n] ;
+ Sp [n] = -1 ;
+ ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory) ; NOT (ok);
+ SYMAMD_report (stats) ;
+ Sp [n] = p ;
+
+ Sp [0] = -1 ;
+ ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory) ; NOT (ok);
+ SYMAMD_report (stats) ;
+ Sp [0] = 0 ;
+
+ if (n > 2 && Sp [n] > 3)
+ {
+ p = Sp [1] ;
+ Sp [1] = -1 ;
+ ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory) ; NOT (ok);
+ SYMAMD_report (stats) ;
+ Sp [1] = p ;
+
+ i = Si [0] ;
+ Si [0] = -1 ;
+ ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory) ; NOT (ok);
+ SYMAMD_report (stats) ;
+ Si [0] = i ;
+
+ /* ok, but jumbled */
+ i = Si [0] ;
+ Si [0] = Si [1] ;
+ Si [1] = i ;
+ ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory) ; OK (ok);
+ SYMAMD_report (stats) ;
+ OK (CHOLMOD(print_perm) (P, nrow, nrow, "symamd perm", cm)) ;
+ i = Si [0] ;
+ Si [0] = Si [1] ;
+ Si [1] = i ;
+
+ test_memory_handler ( ) ;
+ ok = SYMAMD_MAIN (n, Si, Sp, P, NULL, stats, cm->calloc_memory,
+ cm->free_memory) ; NOT (ok);
+ SYMAMD_report (stats) ;
+ normal_memory_handler ( ) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* error tests */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ ok = COLAMD_MAIN (ncol, nrow, 0, Ci, Cp, knobs, stats) ; NOT (ok) ;
+ COLAMD_report (stats) ;
+
+ ok = COLAMD_MAIN (ncol, nrow, alen, NULL, Cp, knobs, stats); NOT (ok) ;
+ COLAMD_report (stats) ;
+
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, NULL, knobs, stats); NOT (ok) ;
+ COLAMD_report (stats) ;
+
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, NULL) ; NOT (ok) ;
+ COLAMD_report (stats) ;
+
+ ok = COLAMD_MAIN (-1, nrow, alen, Ci, Cp, knobs, stats) ; NOT (ok) ;
+ COLAMD_report (stats) ;
+
+ ok = COLAMD_MAIN (ncol, -1, alen, Ci, Cp, knobs, stats) ; NOT (ok) ;
+ COLAMD_report (stats) ;
+
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+ Cp [nrow] = -1 ;
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats) ; NOT (ok) ;
+ COLAMD_report (stats) ;
+
+ Cp [0] = 1 ;
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats) ; NOT (ok) ;
+ COLAMD_report (stats) ;
+
+ ok = CHOLMOD(transpose_unsym) (B, 0, NULL, NULL, 0, C, cm) ; OK (ok) ;
+
+ if (nrow > 0 && alen > 0 && Cp [1] > 0)
+ {
+
+ p = Cp [1] ;
+ Cp [1] = -1 ;
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats) ; NOT(ok);
+ COLAMD_report (stats) ;
+ Cp [1] = p ;
+
+ i = Ci [0] ;
+ Ci [0] = -1 ;
+ ok = COLAMD_MAIN (ncol, nrow, alen, Ci, Cp, knobs, stats) ; NOT(ok);
+ COLAMD_report (stats) ;
+ Ci [0] = i ;
+ }
+
+ s = COLAMD_recommended (-1, 0, 0) ;
+ OK (s == 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free) (nrow+1, sizeof (Int), P, cm) ;
+ CHOLMOD(free_sparse) (&S, cm) ;
+ CHOLMOD(free_sparse) (&A2, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+}
diff --git a/CHOLMOD/Tcov/gcovs b/CHOLMOD/Tcov/gcovs
new file mode 100755
index 0000000..ddebc9e
--- /dev/null
+++ b/CHOLMOD/Tcov/gcovs
@@ -0,0 +1,4 @@
+# usage: gcovs files
+foreach file ($argv[1-])
+ gcov $file > /dev/null
+ end
diff --git a/CHOLMOD/Tcov/gpl.txt b/CHOLMOD/Tcov/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/CHOLMOD/Tcov/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it. (Some other Free Software Foundation software is covered by
+the GNU Library General Public License instead.) You can apply it to
+your programs, too.
+
+ When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+this service if you wish), that you receive source code or can get it
+if you want it, that you can change the software or use pieces of it
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+These restrictions translate to certain responsibilities for you if you
+distribute copies of the software, or if you modify it.
+
+ For example, if you distribute copies of such a program, whether
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+you have. You must make sure that they, too, receive or can get the
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+rights.
+
+ We protect your rights with two steps: (1) copyright the software, and
+(2) offer you this license which gives you legal permission to copy,
+distribute and/or modify the software.
+
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+that everyone understands that there is no warranty for this free
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+ Finally, any free program is threatened constantly by software
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+ The precise terms and conditions for copying, distribution and
+modification follow.
+
+ GNU GENERAL PUBLIC LICENSE
+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
+ 0. This License applies to any program or other work which contains
+a notice placed by the copyright holder saying it may be distributed
+under the terms of this General Public License. The "Program", below,
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+language. (Hereinafter, translation is included without limitation in
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+
+Activities other than copying, distribution and modification are not
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+running the Program is not restricted, and the output from the Program
+is covered only if its contents constitute a work based on the
+Program (independent of having been made by running the Program).
+Whether that is true depends on what the Program does.
+
+ 1. You may copy and distribute verbatim copies of the Program's
+source code as you receive it, in any medium, provided that you
+conspicuously and appropriately publish on each copy an appropriate
+copyright notice and disclaimer of warranty; keep intact all the
+notices that refer to this License and to the absence of any warranty;
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+along with the Program.
+
+You may charge a fee for the physical act of transferring a copy, and
+you may at your option offer warranty protection in exchange for a fee.
+
+ 2. You may modify your copy or copies of the Program or any portion
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+
+ a) You must cause the modified files to carry prominent notices
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+
+ b) You must cause any work that you distribute or publish, that in
+ whole or in part contains or is derived from the Program or any
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+
+ c) If the modified program normally reads commands interactively
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+ announcement including an appropriate copyright notice and a
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+
+These requirements apply to the modified work as a whole. If
+identifiable sections of that work are not derived from the Program,
+and can be reasonably considered independent and separate works in
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+sections when you distribute them as separate works. But when you
+distribute the same sections as part of a whole which is a work based
+on the Program, the distribution of the whole must be on the terms of
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+Thus, it is not the intent of this section to claim rights or contest
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+with the Program (or with a work based on the Program) on a volume of
+a storage or distribution medium does not bring the other work under
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+
+ 3. You may copy and distribute the Program (or a work based on it,
+under Section 2) in object code or executable form under the terms of
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+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ <signature of Ty Coon>, 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Library General
+Public License instead of this License.
diff --git a/CHOLMOD/Tcov/huge.c b/CHOLMOD/Tcov/huge.c
new file mode 100644
index 0000000..7021029
--- /dev/null
+++ b/CHOLMOD/Tcov/huge.c
@@ -0,0 +1,243 @@
+/* ========================================================================== */
+/* === Tcov/huge ============================================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Tests on huge matrices */
+
+#include "cm.h"
+#include "amd.h"
+#ifndef NPARTITION
+#include "camd.h"
+#endif
+
+
+/* ========================================================================== */
+/* === huge ================================================================= */
+/* ========================================================================== */
+
+void huge ( )
+{
+ cholmod_sparse *A, *C ;
+ cholmod_triplet *T ;
+ cholmod_factor *L ;
+ cholmod_dense *X ;
+ size_t n, nbig ;
+ int ok = TRUE, save ;
+ Int junk ;
+ FILE *f ;
+ double beta [2] ;
+
+ n = Size_max ;
+ CHOLMOD (free_work) (cm) ;
+ CHOLMOD (allocate_work) (n, 0, 0, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ n = CHOLMOD(add_size_t) (n, 1, &ok) ;
+ NOT (ok) ;
+
+ /* create a fake zero sparse matrix, with huge dimensions */
+ A = CHOLMOD (spzeros) (1, 1, 0, CHOLMOD_REAL, cm) ;
+ A->nrow = Size_max ;
+ A->ncol = Size_max ;
+ A->stype = 0 ;
+
+ /* create a fake factor, with huge dimensions. */
+ L = CHOLMOD (allocate_factor) (1, cm) ;
+ OKP (L) ;
+ L->n = Size_max ;
+ CHOLMOD (factorize) (A, L, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ /* free the fake factor */
+ L->n = 1 ;
+ CHOLMOD (free_factor) (&L, cm) ;
+
+ /* create a valid factor to test resymbol */
+ C = CHOLMOD (speye) (1, 1, CHOLMOD_REAL, cm) ;
+ C->stype = 1 ;
+ L = CHOLMOD (analyze) (C, cm) ;
+ OKP (L) ;
+ CHOLMOD (factorize) (C, L, cm) ;
+ ok = CHOLMOD (resymbol) (C, NULL, 0, 0, L, cm) ;
+ OK (ok) ;
+ C->nrow = Size_max ;
+ C->ncol = Size_max ;
+ L->n = Size_max ;
+
+ ok = CHOLMOD (resymbol) (C, NULL, 0, 0, L, cm) ;
+ NOT (ok) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ printf ("rowfac:\n") ;
+ beta [0] = 1 ;
+ beta [1] = 0 ;
+ C->xtype = CHOLMOD_COMPLEX ;
+ L->xtype = CHOLMOD_COMPLEX ;
+ ok = CHOLMOD (rowfac) (C, NULL, beta, 0, 0, L, cm) ;
+ printf ("rowfac %d\n", cm->status) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+ C->xtype = CHOLMOD_REAL ;
+ L->xtype = CHOLMOD_REAL ;
+ printf ("rowfac done:\n") ;
+
+ C->stype = -1 ;
+ ok = CHOLMOD (resymbol_noperm) (C, NULL, 0, 0, L, cm) ;
+ NOT (ok) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ C->ncol = 1 ;
+ CHOLMOD (rowadd) (0, C, L, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ CHOLMOD (rowdel) (0, C, L, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ C->ncol = 4 ;
+ CHOLMOD (updown) (1, C, L, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ C->nrow = 1 ;
+ C->ncol = 1 ;
+ L->n = 1 ;
+ CHOLMOD (free_sparse) (&C, cm) ;
+ CHOLMOD (free_factor) (&L, cm) ;
+
+ C = CHOLMOD (allocate_sparse) (Size_max, Size_max, Size_max, 0, 0, 0, 0, cm);
+ NOP (C) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ CHOLMOD (rowcolcounts) (A, NULL, 0,
+ &junk, &junk, &junk, &junk, &junk, &junk, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ C = CHOLMOD (submatrix) (A, &junk, Size_max/2, &junk, Size_max/2, 0, 0, cm) ;
+ NOP (C) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ ok = CHOLMOD (transpose_unsym) (A, 0, &junk, &junk, Size_max, A, cm) ;
+ NOT (ok) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ A->stype = 1 ;
+ ok = CHOLMOD (transpose_sym) (A, 0, &junk, A, cm) ;
+ NOT (ok) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ C = CHOLMOD (ptranspose) (A, 0, &junk, NULL, 0, cm) ;
+ NOP (C) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+ A->stype = 0 ;
+
+ CHOLMOD (amd) (A, NULL, 0, &junk, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ L = CHOLMOD (analyze) (A, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+ NOP (L) ;
+
+#ifndef NPARTITION
+ CHOLMOD (camd) (A, NULL, 0, &junk, NULL, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+#endif
+
+ printf ("calling colamd\n") ;
+ CHOLMOD (colamd) (A, NULL, 0, 0, &junk, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+#ifndef NPARTITION
+ printf ("calling ccolamd\n") ;
+ CHOLMOD (ccolamd) (A, NULL, 0, NULL, &junk, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+#endif
+
+ CHOLMOD (etree) (A, &junk, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ L = CHOLMOD (allocate_factor) (Size_max, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+ NOP (L) ;
+
+#ifndef NPARTITION
+ CHOLMOD (metis) (A, NULL, 0, 0, &junk, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ CHOLMOD (bisect) (A, NULL, 0, 0, &junk, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ CHOLMOD (nested_dissection) (A, NULL, 0, &junk, &junk, &junk, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+#endif
+
+ CHOLMOD (postorder) (&junk, Size_max, &junk, &junk, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ /* causes overflow in 32-bit version, but not 64-bit */
+ f = fopen ("../Tcov/Matrix/mega.tri", "r") ;
+ T = CHOLMOD (read_triplet) (f, cm) ;
+ if (sizeof (Int) == sizeof (int))
+ {
+ NOP (T) ;
+ OK (cm->status != CHOLMOD_OK) ;
+ }
+ CHOLMOD (free_triplet) (&T, cm) ;
+ fclose (f) ;
+
+ n = Size_max ;
+ X = CHOLMOD (allocate_dense) (n, 1, n, CHOLMOD_REAL, cm) ;
+ NOP (X) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+
+ /* supernodal symbolic test */
+ C = CHOLMOD (speye) (1, 1, CHOLMOD_REAL, cm) ;
+ C->stype = 1 ;
+ save = cm->supernodal ;
+ cm->supernodal = CHOLMOD_SIMPLICIAL ;
+ L = CHOLMOD (analyze) (C, cm) ;
+ OKP (L) ;
+ junk = 0 ;
+ C->nrow = Size_max ;
+ C->ncol = Size_max ;
+ L->n = Size_max ;
+ CHOLMOD (super_symbolic) (C, C, &junk, L, cm) ;
+ OK (cm->status == CHOLMOD_TOO_LARGE) ;
+ cm->supernodal = save ;
+ C->nrow = 1 ;
+ C->ncol = 1 ;
+ L->n = 1 ;
+ CHOLMOD (free_sparse) (&C, cm) ;
+ CHOLMOD (free_factor) (&L, cm) ;
+
+ /* supernodal numeric test */
+ C = CHOLMOD (speye) (1, 1, CHOLMOD_REAL, cm) ;
+ C->stype = -1 ;
+ save = cm->supernodal ;
+ cm->supernodal = CHOLMOD_SUPERNODAL ;
+ L = CHOLMOD (analyze) (C, cm) ;
+ OKP (L) ;
+ OK (cm->status == CHOLMOD_OK) ;
+ C->nrow = Size_max ;
+ C->ncol = Size_max ;
+ L->n = Size_max ;
+ CHOLMOD (super_numeric) (C, C, beta, L, cm) ;
+ cm->supernodal = save ;
+ C->nrow = 1 ;
+ C->ncol = 1 ;
+ L->n = 1 ;
+ CHOLMOD (free_sparse) (&C, cm) ;
+ CHOLMOD (free_factor) (&L, cm) ;
+
+ /* free the fake matrix */
+ A->nrow = 1 ;
+ A->ncol = 1 ;
+ CHOLMOD (free_sparse) (&A, cm) ;
+
+ fprintf (stderr, "\n") ;
+}
diff --git a/CHOLMOD/Tcov/leak.c b/CHOLMOD/Tcov/leak.c
new file mode 100644
index 0000000..4b5f29a
--- /dev/null
+++ b/CHOLMOD/Tcov/leak.c
@@ -0,0 +1,125 @@
+/* ========================================================================== */
+/* === Tcov/leak ============================================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Look for CHOLMOD memory leaks. Run cm with
+ * cholmod_dump >= cholmod_dump_malloc (see Check/cholmod_check.c),
+ * to get output file. Then grep "cnt:" output | leak
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#define LEN 2048
+char line [LEN] ;
+char operation [LEN] ;
+char s_cnt [LEN] ;
+char s_inuse [LEN] ;
+
+int block [LEN] ;
+int blocksize [LEN] ;
+
+#define FALSE 0
+#define TRUE 1
+
+int main (void)
+{
+ int p, size, cnt2, inuse2, nblocks, found, b, bfound, nlines ;
+
+ nblocks = 0 ;
+ nlines = 0 ;
+
+ while (fgets (line, LEN, stdin) != NULL)
+ {
+ sscanf (line, "%s %x %d %s %d %s %d\n",
+ operation, &p, &size, s_cnt, &cnt2, s_inuse, &inuse2) ;
+ nlines++ ;
+
+ printf ("%d:: %s %x %d %s %d %s %d\n",
+ nlines, operation, p, size, s_cnt, cnt2, s_inuse, inuse2) ;
+
+ /* determine operation */
+ if (strcmp (operation, "cholmod_malloc") == 0 ||
+ strcmp (operation, "cholmod_realloc_new:") == 0 ||
+ strcmp (operation, "cholmod_calloc") == 0)
+ {
+
+ /* p = malloc (size) */
+ for (b = 0 ; b < nblocks ; b++)
+ {
+ if (p == block [b])
+ {
+ printf ("duplicate!\n") ;
+ abort ( ) ;
+ }
+ }
+
+ if (nblocks >= LEN)
+ {
+ printf ("out of space!\n") ;
+ abort ( ) ;
+ }
+
+ /* add the new block to the list */
+ block [nblocks] = p ;
+ blocksize [nblocks] = size ;
+ nblocks++ ;
+
+ }
+
+ else if (strcmp (operation, "cholmod_free") == 0 ||
+ strcmp (operation, "cholmod_realloc_old:") == 0)
+ {
+
+ /* p = free (size) */
+ found = FALSE ;
+ for (b = 0 ; !found && b < nblocks ; b++)
+ {
+ if (p == block [b])
+ {
+ bfound = b ;
+ found = TRUE ;
+ }
+ }
+ if (!found)
+ {
+ printf ("not found!\n") ;
+ abort ( ) ;
+ }
+
+ if (size != blocksize [bfound])
+ {
+ printf ("wrong size! %x : %d vs %d\n",
+ p, size, blocksize[bfound]) ;
+ abort ( ) ;
+ }
+
+ /* remove the block from the list */
+ --nblocks ;
+ block [bfound] = block [nblocks] ;
+ blocksize [bfound] = blocksize [nblocks] ;
+
+ }
+ else
+ {
+ printf ("unrecognized!\n") ;
+ abort ( ) ;
+ }
+
+ if (cnt2 != nblocks)
+ {
+ printf ("nblocks wrong! %d %d\n", nblocks, cnt2) ;
+ }
+
+ }
+ return (0) ;
+}
diff --git a/CHOLMOD/Tcov/lpdemo.c b/CHOLMOD/Tcov/lpdemo.c
new file mode 100644
index 0000000..de3dde9
--- /dev/null
+++ b/CHOLMOD/Tcov/lpdemo.c
@@ -0,0 +1,932 @@
+/* ========================================================================== */
+/* === Tcov/lpdemo ========================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* A rectangular matrix is being tested (# nrows < # cols). This is a
+ * linear programming problem. Process the system using the same kind of
+ * operations that occur in an LP solver (the LP Dual Active Set Algorithm).
+ * This routine does not actually solve the LP. It simply mimics the kind
+ * of matrix operations that occur in LPDASA.
+ *
+ * The active set f is held in fset [0..fsize-1]. It is a subset of the columns
+ * of A. Columns not in the fset are in the list fnot [0..ncol-fsize-1].
+ *
+ * Rows can be added and deleted from A as well. A "dead" row is one that has
+ * been (temporarily) set to zero in A. If row i is dead, rflag [i] is 0,
+ * and 1 otherwise.
+ *
+ * The list r of "live" rows is kept in rset [0..rsize-1]. The list of "dead"
+ * rows is kept in rnot [0..nrow-rsize-1].
+ *
+ * The system to solve as r and/or f change is (beta*I + A(r,f)*A(r,f)') x = b.
+ * If a row i is deleted from A, it is set to zero. Row i of L and D are set
+ * to the ith row of the identity matrix.
+ */
+
+#include "cm.h"
+#define MAXCOLS 8
+
+
+/* ========================================================================== */
+/* === Lcheck =============================================================== */
+/* ========================================================================== */
+
+/* Testing only: make sure there are no dead rows in L (excluding diagonal) */
+
+static void Lcheck (cholmod_factor *L, Int *rflag)
+{
+ Int *Lp, *Li, *Lnz ;
+ Int i, n, j, p, pend ;
+ double *Lx ;
+
+ if (L == NULL)
+ {
+ return ;
+ }
+
+ Lp = L->p ;
+ Li = L->i ;
+ Lx = L->x ;
+ Lnz = L->nz ;
+ n = L->n ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Lp [j] ;
+ pend = p + Lnz [j] ;
+ for (p++ ; p < pend ; p++)
+ {
+ i = Li [p] ;
+ OK (IMPLIES (!rflag [i], Lx [p] == 0)) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === lp_prune ============================================================= */
+/* ========================================================================== */
+
+/* C = A (r,f), except that C and A have the same row dimension. Row i of C
+ * and A(:,f) are equal if row i is in the rset. Row i of C is zero
+ * otherwise. C has as many columns as the size of f. */
+
+cholmod_sparse *lp_prune
+(
+ cholmod_sparse *A,
+ Int *rflag,
+ Int *fset,
+ Int fsize
+)
+{
+ cholmod_sparse *C ;
+ double *Ax, *Cx ;
+ Int *Ai, *Ap, *Ci, *Cp ;
+ Int i, kk, j, p, nz, nf, ncol ;
+
+ if (A == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "nothing to prune") ;
+ return (NULL) ;
+ }
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ ncol = A->ncol ;
+ nf = (fset == NULL) ? ncol : fsize ;
+
+ OK (fsize >= 0) ;
+
+ C = CHOLMOD(allocate_sparse) (A->nrow, nf, A->nzmax, A->sorted,
+ TRUE, 0, CHOLMOD_REAL, cm) ;
+
+ if (C == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot create pruned C") ;
+ return (NULL) ;
+ }
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ nz = 0 ;
+
+ for (kk = 0 ; kk < nf ; kk++)
+ {
+ j = (fset == NULL) ? (kk) : (fset [kk]) ;
+ Cp [kk] = nz ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ if (rflag [i])
+ {
+ Ci [nz] = i ;
+ Cx [nz] = Ax [p] ;
+ nz++ ;
+ }
+ }
+ }
+ Cp [nf] = nz ;
+ return (C) ;
+}
+
+
+/* ========================================================================== */
+/* === lp_resid ============================================================= */
+/* ========================================================================== */
+
+/* Compute the 2-norm of the residual.
+ * norm ((beta*I + C*C')y(r) - b(r)), where C = A (r,f).
+ */
+
+double lp_resid
+(
+ cholmod_sparse *A,
+ Int *rflag,
+ Int *fset,
+ Int fsize,
+ double beta [2],
+ cholmod_dense *Y,
+ cholmod_dense *B
+)
+{
+ cholmod_dense *R ;
+ double *Rx, *Yx ;
+ double rnorm, bnorm, ynorm, norm ;
+ cholmod_sparse *C ;
+ cholmod_dense *W ;
+ Int i, nrow ;
+
+ if (A == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot compute LP resid") ;
+ return (1) ;
+ }
+
+ nrow = A->nrow ;
+ R = CHOLMOD(zeros) (nrow, 1, CHOLMOD_REAL, cm) ;
+
+ /* C = A(r,f). In LPDASA, we do this in place, without making a copy. */
+ C = lp_prune (A, rflag, fset, fsize) ;
+
+ /* W = C'*Y */
+ OK (fsize >= 0) ;
+ W = CHOLMOD(zeros) (fsize, 1, CHOLMOD_REAL, cm) ;
+ CHOLMOD(sdmult) (C, TRUE, one, zero, Y, W, cm) ;
+
+ /* R = B */
+ CHOLMOD(copy_dense2) (B, R, cm) ;
+
+ /* R = C*W - R */
+ CHOLMOD(sdmult) (C, FALSE, one, minusone, W, R, cm) ;
+
+ /* R = R + beta*Y, (beta = 1 for dropped rows) */
+ if (R != NULL && Y != NULL)
+ {
+ Rx = R->x ;
+ Yx = Y->x ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ if (rflag [i])
+ {
+ Rx [i] += beta [0] * Yx [i] ;
+ }
+ else
+ {
+ Rx [i] += Yx [i] ;
+ }
+ }
+ }
+
+ /* rnorm = norm (R) */
+ rnorm = CHOLMOD(norm_dense) (R, 2, cm) ;
+ bnorm = CHOLMOD(norm_dense) (B, 2, cm) ;
+ ynorm = CHOLMOD(norm_dense) (Y, 2, cm) ;
+ norm = MAX (bnorm, ynorm) ;
+ if (norm > 0)
+ {
+ rnorm /= norm ;
+ }
+
+ CHOLMOD(print_dense) (R, "R, resid", cm) ;
+
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_dense) (&W, cm) ;
+ CHOLMOD(free_dense) (&R, cm) ;
+
+ return (rnorm) ;
+}
+
+
+/* ========================================================================== */
+/* === get_row ============================================================== */
+/* ========================================================================== */
+
+/* S = column i of beta*I + A(r,f)*A(r,f)' */
+
+cholmod_sparse *get_row
+(
+ cholmod_sparse *A,
+ Int i,
+ Int *rflag,
+ Int *fset,
+ Int fsize,
+ double beta [2]
+)
+{
+ cholmod_sparse *Ri, *R, *C, *S ;
+ double *Sx ;
+ Int *Sp, *Si ;
+ Int p, ii, found ;
+
+ if (rflag [i] == 0)
+ {
+ S = CHOLMOD(speye) (A->nrow, A->nrow, CHOLMOD_REAL, cm) ;
+ CHOLMOD(print_sparse) (S, "S identity", cm) ;
+ return (S) ;
+ }
+ OK (fsize >= 0) ;
+
+ /* Getting row i of A is expensive. In LPDASA, we maintain
+ * a copy of A(r,f)', and extact row i as column i of that
+ * matrix. We compute S = A(r,f)*A(i,f)' and S(i) += beta
+ * in a single pass. This is a simpler but slower method. */
+
+ /* R = A (i,f)' */
+ Ri = CHOLMOD(submatrix) (A, &i, 1, fset, fsize, TRUE, FALSE, cm) ;
+ R = CHOLMOD(transpose) (Ri, 1, cm) ;
+ CHOLMOD(free_sparse) (&Ri, cm) ;
+
+ /* C = A (r,f) */
+ C = lp_prune (A, rflag, fset, fsize) ;
+
+ /* S = C*R */
+ S = CHOLMOD(ssmult) (C, R, 0, TRUE, TRUE, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&R, cm) ;
+
+ if (S == NULL)
+ {
+ return (NULL) ;
+ }
+
+ /* S (i) += beta */
+ found = FALSE ;
+ Sp = S->p ;
+ Si = S->i ;
+ Sx = S->x ;
+ for (p = Sp [0] ; p < Sp [1] ; p++)
+ {
+ ii = Si [p] ;
+ if (ii == i)
+ {
+ found = TRUE ;
+ Sx [p] += beta [0] ;
+ break ;
+ }
+ }
+ if (!found)
+ {
+ /* oops, row index i is not present in S. Add it. */
+ CHOLMOD(reallocate_sparse) (S->nzmax+1, S, cm) ;
+ OK (Sp [1] < (Int) (S->nzmax)) ;
+ Si = S->i ;
+ Sx = S->x ;
+ Si [Sp [1]] = i ;
+ Sx [Sp [1]] = beta [0] ;
+ Sp [1]++ ;
+ S->sorted = FALSE ;
+ }
+
+ CHOLMOD(print_sparse) (S, "S", cm) ;
+
+ return (S) ;
+}
+
+
+/* ========================================================================== */
+/* === lpdemo =============================================================== */
+/* ========================================================================== */
+
+double lpdemo (cholmod_triplet *T)
+{
+ double r, maxerr = 0, anorm, bnorm, norm, xnorm, ynorm ;
+ double *b = NULL, *Yx = NULL, *Xx = NULL, *Sx ;
+ cholmod_sparse *A, *AT, *Apermuted, *C, *S, *Row ;
+ cholmod_dense *X, *B, *Y, *DeltaB, *R ;
+ cholmod_factor *L ;
+ Int *init, *rset, *rnot, *fset, *fnot, *rflag, *P, *Pinv, *Lperm, *fflag,
+ *Sp, *Si, *StaticParent ;
+ Int i, j, k, nrow, ncol, fsize, cols [MAXCOLS+1], trial, rank, kk, rsize,
+ p, op, ok ;
+ double beta [2], bk [2], yk [2] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert T into a sparse matrix A */
+ /* ---------------------------------------------------------------------- */
+
+ if (T == NULL || T->ncol == 0)
+ {
+ /* nothing to do */
+ return (0) ;
+ }
+
+ if (T->xtype != CHOLMOD_REAL)
+ {
+ return (0) ;
+ }
+
+ A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ;
+
+ if (A == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "cannot continue LP demo") ;
+ return (1) ;
+ }
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+
+ anorm = CHOLMOD(norm_sparse) (A, 1, cm) ;
+
+ /* switch for afiro, but not galenet */
+ cm->supernodal_switch = 5 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* select a random initial row and column basis */
+ /* ---------------------------------------------------------------------- */
+
+ /* select an initial fset of size nrow */
+ init = prand (ncol) ; /* RAND */
+ fset = CHOLMOD(malloc) (ncol, sizeof (Int), cm) ;
+ fnot = CHOLMOD(malloc) (ncol, sizeof (Int), cm) ;
+ fflag = CHOLMOD(malloc) (ncol, sizeof (Int), cm) ;
+ fsize = MIN (nrow, ncol) ;
+
+ if (init != NULL && fset != NULL && fflag != NULL)
+ {
+ for (k = 0 ; k < fsize ; k++)
+ {
+ j = init [k] ;
+ fset [k] = j ;
+ fflag [j] = 1 ;
+ }
+ for ( ; k < ncol ; k++)
+ {
+ j = init [k] ;
+ fnot [k-fsize] = j ;
+ fflag [j] = 0 ;
+ }
+ }
+
+ CHOLMOD(free) (ncol, sizeof (Int), init, cm) ;
+
+ /* all rows are live */
+ rsize = nrow ;
+ rflag = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+ rset = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+ rnot = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+
+ if (rset != NULL && rflag != NULL)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ rflag [i] = 1 ;
+ rset [i] = i ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize the first matrix, beta*I + A(p,f)*A(p,f)' */
+ /* ---------------------------------------------------------------------- */
+
+ beta [0] = 1e-6 ;
+ beta [1] = 0 ;
+
+ /* Need to prune entries due to relaxed amalgamation, or else
+ * cholmod_row_subtree will not be able to find all the entries in row
+ * k of L. */
+ cm->final_resymbol = TRUE ;
+
+ cm->final_asis = FALSE ;
+ cm->final_super = FALSE ;
+ cm->final_ll = FALSE ;
+ cm->final_pack = FALSE ;
+ cm->final_monotonic = FALSE ;
+
+ L = CHOLMOD(analyze_p) (A, NULL, fset, fsize, cm) ;
+ CHOLMOD(factorize_p) (A, beta, fset, fsize, L, cm) ;
+
+ /* get a copy of the fill-reducing permutation P and compute its inverse */
+ Lperm = (L != NULL) ? (L->Perm) : NULL ;
+ P = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+ Pinv = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+
+ if (P != NULL && Pinv != NULL && Lperm != NULL)
+ {
+ for (k = 0 ; k < nrow ; k++)
+ {
+ P [k] = Lperm [k] ;
+ Pinv [P [k]] = k ;
+ }
+ }
+ else
+ {
+ P = CHOLMOD(free) (nrow, sizeof (Int), P, cm) ;
+ Pinv = CHOLMOD(free) (nrow, sizeof (Int), Pinv, cm) ;
+ }
+
+ if (cm->print > 1)
+ {
+ k = cm->print ;
+ cm->print = 5 ;
+ CHOLMOD(print_common) ("cm for lpdemo", cm) ;
+ cm->print = k ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* A=P*A: permute the rows of A according to P */
+ /* ---------------------------------------------------------------------- */
+
+ /* This is done just once, since the system will be solved and modified
+ * many times. It's faster, and easier, to work in the permuted ordering
+ * rather than the original ordering. */
+
+ /* A will become unsorted later on; don't bother to sort it here */
+ Apermuted = CHOLMOD(submatrix) (A, P, nrow, NULL, -1, TRUE, TRUE, cm) ;
+ CHOLMOD(free_sparse) (&A, cm) ;
+ A = Apermuted ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the etree of A*A' */
+ /* ---------------------------------------------------------------------- */
+
+ /* Since the fset is a subset of 0:ncol-1, and rset is a subset of 0:nrow-1,
+ * the nonzero pattern of the Cholesky factorization of A(r,f)*A(r,f)' is a
+ * subset of the Cholesky factorization of A*A'. After many updates/
+ * downdates/rowadds/rowdels, any given row i of L may have entries that
+ * are not in the factorization of A (r,f)*A(r,f)'. To drop a row using
+ * cholmod_rowdel, we either need to know the pattern of the ith row of L,
+ * we can pass NULL and have cholmod_rowdel look at each column 0 to i-1.
+ * The StaticParent array is the etree of A*A', and it suffices to compute
+ * the pattern of the ith row of L based on that etree, and A and A'
+ * (ignoring the fset and rset). This gives us an upper bound on the
+ * nonzero pattern of the ith row of the current L (the factorization
+ * of A(r,f)*A(r,f)'.
+ */
+
+ /* AT = nonzero pattern of A', used for row-subtree computations */
+ AT = CHOLMOD(transpose) (A, 0, cm) ;
+
+ /* Row = cholmod_row_subtree workspace (unsorted, packed, unsym, pattern) */
+ Row = CHOLMOD(allocate_sparse) (nrow, 1, nrow, FALSE, TRUE, 0,
+ CHOLMOD_PATTERN, cm) ;
+
+ /* Compute the "static" etree; the etree of A*A' */
+ StaticParent = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+ CHOLMOD(etree) (AT, StaticParent, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute initial right-hand-side */
+ /* ---------------------------------------------------------------------- */
+
+ /* If row i of the original A and B is row k of the permuted P*A and P*B,
+ * then P [k] = i and Pinv [i] = k. Row indices of A now refer to the
+ * permuted form of A, not the original A. Likewise, row k of B will
+ * refer to the permuted row k = Pinv [i], not the original row i. In a
+ * real program, this would affect how B is computed. This program just
+ * creates a random B anyway, so the order of B does not matter. It does
+ * use Pinv [i], just to show you how you would do it.
+ */
+
+ B = CHOLMOD(zeros) (nrow, 1, CHOLMOD_REAL, cm) ;
+
+ if (B != NULL && Pinv != NULL)
+ {
+ b = B->x ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ /* row i of the original B is row k of the permuted B */
+ k = Pinv [i] ;
+ b [k] = xrand (1.) ; /* RAND */
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve the system */
+ /* ---------------------------------------------------------------------- */
+
+ /* Solve the system (beta*I + A(:,f)*A(:,f)')y=b without using L->Perm,
+ * since A and B have already been permuted according to L->Perm. */
+
+ DeltaB = CHOLMOD(zeros) (nrow, 1, CHOLMOD_REAL, cm) ;
+
+ /* solve Lx=b */
+ X = CHOLMOD(solve) (CHOLMOD_L, L, B, cm) ;
+
+ /* solve DL'y=x */
+ Y = CHOLMOD(solve) (CHOLMOD_DLt, L, X, cm) ;
+
+ r = lp_resid (A, rflag, fset, fsize, beta, Y, B) ;
+ MAXERR (maxerr, r, 1) ;
+
+ bk [0] = 0 ;
+ bk [1] = 0 ;
+
+ yk [0] = 0 ;
+ yk [1] = 0 ;
+
+ bnorm = CHOLMOD(norm_dense) (B, 1, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify the system */
+ /* ---------------------------------------------------------------------- */
+
+ ok = (fset != NULL && fnot != NULL && fflag != NULL &&
+ rset != NULL && rnot != NULL && rflag != NULL &&
+ B != NULL && Y != NULL && X != NULL && Row != NULL && A != NULL &&
+ AT != NULL && StaticParent != NULL && DeltaB != NULL && L != NULL &&
+ L->xtype != CHOLMOD_PATTERN && !(L->is_ll) && !(L->is_super)) ;
+
+ for (trial = 1 ; ok && trial < MAX (64, 2*ncol) ; trial++)
+ {
+ /* select an operation at random */
+ op = nrand (6) ; /* RAND */
+
+ Xx = X->x ;
+ Yx = Y->x ;
+
+ switch (op)
+ {
+
+ /* -------------------------------------------------------------- */
+ case 0: /* update */
+ /* -------------------------------------------------------------- */
+
+ /* pick some columns at random, but not all columns */
+ rank = 1 + nrand (MAXCOLS+4) ; /* RAND */
+ rank = MIN (rank, MAXCOLS) ;
+
+ rank = MIN (rank, ncol-fsize-1) ;
+ if (rank <= 0)
+ {
+ continue ;
+ }
+
+ /* remove the columns from fnot and add them to fset */
+ for (k = 0 ; k < rank ; k++)
+ {
+ kk = nrand (ncol-fsize) ; /* RAND */
+ j = fnot [kk] ;
+ fnot [kk] = fnot [ncol-fsize-1] ;
+ fset [fsize++] = j ;
+ OK (fsize < ncol) ;
+ cols [k] = j ;
+ fflag [j] = 1 ;
+ }
+
+ /* update L, and the solution to Lx=b+deltaB */
+ C = lp_prune (A, rflag, cols, rank) ;
+ ok = CHOLMOD(updown_solve) (TRUE, C, L, X, DeltaB, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ break ;
+
+ /* -------------------------------------------------------------- */
+ case 1: /* downdate */
+ /* -------------------------------------------------------------- */
+
+ /* pick some columns at random, but not all columns */
+ rank = 1 + nrand (MAXCOLS+4) ; /* RAND */
+ rank = MIN (rank, MAXCOLS) ;
+
+ rank = MIN (rank, fsize-1) ;
+ if (rank <= 0)
+ {
+ continue ;
+ }
+
+ /* remove the columns from fset and add them to fnot */
+ for (k = 0 ; k < rank ; k++)
+ {
+ kk = nrand (fsize) ; /* RAND */
+ j = fset [kk] ;
+ fset [kk] = fset [fsize-1] ;
+ fnot [ncol-fsize] = j ;
+ fsize-- ;
+ OK (fsize > 0) ;
+ cols [k] = j ;
+ fflag [j] = 0 ;
+ }
+
+ /* downdate L, and the solution to Lx=b+deltaB */
+ C = lp_prune (A, rflag, cols, rank) ;
+ ok = CHOLMOD(updown_solve) (FALSE, C, L, X, DeltaB, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ break ;
+
+ /* -------------------------------------------------------------- */
+ case 2: /* resymbol (no change to numerical values) */
+ /* -------------------------------------------------------------- */
+
+ /* let resymbol handle the fset */
+ C = lp_prune (A, rflag, NULL, 0) ;
+ ok = CHOLMOD(resymbol_noperm) (C, fset, fsize, TRUE, L, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ break;
+
+ /* -------------------------------------------------------------- */
+ case 3: /* add row */
+ /* -------------------------------------------------------------- */
+
+ /* remove a row from rnot and add to rset */
+ if (nrow == rsize)
+ {
+ continue ;
+ }
+ kk = nrand (nrow-rsize) ; /* RAND */
+ i = rnot [kk] ;
+
+ OK (rflag [i] == 0) ;
+
+ rnot [kk] = rnot [nrow-rsize-1] ;
+ rset [rsize++] = i ;
+ rflag [i] = 1 ;
+
+ /* S = column i of beta*I + A(r,f)*A(r,f)' */
+ S = get_row (A, i, rflag, fset, fsize, beta) ;
+ ok = (S != NULL) ;
+
+ if (ok)
+ {
+ /* pick a random right-hand-side for this new row */
+ b [i] = 1 ; /* xrand (1) */ /* was RAND */
+ bk [0] = b [i] ;
+ bk [1] = 0 ;
+ ok = CHOLMOD(rowadd_solve) (i, S, bk, L, X, DeltaB, cm) ;
+ }
+
+ CHOLMOD(free_sparse) (&S, cm) ;
+ break ;
+
+ /* -------------------------------------------------------------- */
+ case 4: /* delete row */
+ /* -------------------------------------------------------------- */
+
+ /* remove a row from rset and add to rnot */
+ if (rsize == 0)
+ {
+ continue ;
+ }
+ kk = nrand (rsize) ; /* RAND */
+ i = rset [kk] ;
+
+ OK (rflag [i] == 1) ;
+ rset [kk] = rset [rsize-1] ;
+ rnot [nrow-rsize] = i ;
+ rsize-- ;
+
+ /* S = column i of beta*I + A(r,f)*A(r,f)' */
+ S = get_row (A, i, rflag, fset, fsize, beta) ;
+ ok = (S != NULL) ;
+
+ if (ok)
+ {
+ /* B = B - S * y(i) */
+ Sp = S->p ;
+ Si = S->i ;
+ Sx = S->x ;
+ for (p = 0 ; p < Sp [1] ; p++)
+ {
+ b [Si [p]] -= Sx [p] * Yx [i] ;
+ }
+ /* B(i) = y(i) */
+ b [i] = Yx [i] ;
+
+ yk [0] = Yx [i] ;
+ yk [1] = 0 ;
+
+ /* pick a method arbitrarily */
+ if (trial % 2)
+ {
+ /* get upper bound nonzero pattern of L(i,0:i-1) */
+ CHOLMOD(row_subtree) (A, AT, i, StaticParent, Row, cm) ;
+ ok = CHOLMOD(rowdel_solve) (i, Row, yk, L, X, DeltaB,
+ cm) ;
+ }
+ else
+ {
+ /* Look in all cols 0 to i-1 for entries in L(i,0:i-1).
+ * This is more costly, but requires no knowledge of
+ * an upper bound on the pattern of L. */
+ ok = CHOLMOD(rowdel_solve) (i, NULL, yk, L, X, DeltaB,
+ cm) ;
+ }
+
+ /* for testing only, to ensure cholmod_row_subtree worked */
+ if (ok)
+ {
+ rflag [i] = 0 ;
+ Lcheck (L, rflag) ;
+ }
+ }
+
+ if (ok)
+ {
+ /* let resymbol handle the fset */
+ C = lp_prune (A, rflag, NULL, 0) ;
+ ok = CHOLMOD(resymbol_noperm) (C, fset, fsize, TRUE, L, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ }
+
+ CHOLMOD(free_sparse) (&S, cm) ;
+ break ;
+
+ /* -------------------------------------------------------------- */
+ case 5: /* convert, just for testing */
+ /* -------------------------------------------------------------- */
+
+ /* convert to LDL', optionally packed */
+ if (trial % 2)
+ {
+ ok = CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE,
+ TRUE, TRUE, L, cm) ;
+ }
+ else
+ {
+ ok = CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE,
+ FALSE, TRUE, L, cm) ;
+ }
+ break ;
+
+ }
+
+ if (ok)
+ {
+
+ /* scale B and X if their norm is getting large */
+ ynorm = CHOLMOD(norm_dense) (Y, 1, cm) ;
+ bnorm = CHOLMOD(norm_dense) (B, 1, cm) ;
+ xnorm = CHOLMOD(norm_dense) (X, 1, cm) ;
+ norm = MAX (bnorm, xnorm) ;
+ norm = MAX (norm, ynorm) ;
+ if (norm > 1e10)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ Xx [i] /= norm ;
+ b [i] /= norm ;
+ }
+ }
+
+ CHOLMOD(free_dense) (&Y, cm) ;
+ Y = CHOLMOD(solve) (CHOLMOD_DLt, L, X, cm) ;
+
+ r = lp_resid (A, rflag, fset, fsize, beta, Y, B) ;
+ OK (!ISNAN (r)) ;
+ MAXERR (maxerr, r, 1) ;
+ if (r > 1e-6 && cm->print > 1)
+ {
+ printf ("lp err %.1g operation: "ID" ok "ID"\n", r, op, ok) ;
+ }
+ ok = (Y != NULL) ;
+ }
+ }
+
+ CHOLMOD(free_dense) (&Y, cm) ;
+ OK (CHOLMOD(print_common) ("cm in lpdemo", cm)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to LDL packed, LDL unpacked or LL packed and solve again */
+ /* ---------------------------------------------------------------------- */
+
+ /* solve the new system and check the residual */
+
+ CHOLMOD(print_factor) (L, "L final, for convert", cm) ;
+ if (ok)
+ {
+ switch (nrand (3)) /* RAND */
+ {
+ /* pick one at random */
+ case 0:
+ {
+ ok = CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, TRUE,
+ TRUE, L, cm) ;
+ Y = CHOLMOD(solve) (CHOLMOD_DLt, L, X, cm) ;
+ break ;
+ }
+ case 1:
+ {
+ ok = CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, FALSE,
+ TRUE, L, cm) ;
+ Y = CHOLMOD(solve) (CHOLMOD_DLt, L, X, cm) ;
+ break ;
+ }
+ case 2:
+ {
+ ok = CHOLMOD(change_factor) (CHOLMOD_REAL, TRUE, FALSE, TRUE,
+ TRUE, L, cm) ;
+ Y = CHOLMOD(solve) (CHOLMOD_LDLt, L, B, cm) ;
+ break ;
+ }
+ }
+ r = lp_resid (A, rflag, fset, fsize, beta, Y, B) ;
+ OK (!ISNAN (r)) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(print_factor) (L, "L after convert", cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* rank-1 update, but only partial Lx=b update */
+ /* ---------------------------------------------------------------------- */
+
+ if (ok && fsize < ncol && nrow > 3)
+ {
+ Int colmark [1] ;
+
+ j = fnot [0] ;
+ fnot [0] = fnot [ncol-fsize-1] ;
+ fset [fsize++] = j ;
+ OK (fsize <= ncol) ;
+ cols [0] = j ;
+ fflag [j] = 1 ;
+
+ for (colmark [0] = 0 ; colmark [0] <= nrow ; colmark [0]++)
+ {
+ cholmod_factor *L2 ;
+ cholmod_dense *X2 ;
+ double *X2x ;
+ L2 = CHOLMOD(copy_factor) (L, cm) ;
+ X2 = CHOLMOD(copy_dense) (X, cm) ;
+ X2x = (X2 == NULL) ? NULL : X2->x ;
+
+ /* fprintf (stderr, "check colmark "ID"\n", colmark [0]) ; */
+ printf ("check cholmark "ID"\n", colmark [0]) ;
+ /* colmark [0] = 3 ; */
+
+ /* update L, and the solution to Lx=b+deltaB,
+ * but only update solution in rows 0 to colmark[0] */
+ C = lp_prune (A, rflag, cols, 1) ;
+ ok = CHOLMOD(updown_mark) (TRUE, C, colmark, L2, X2, DeltaB, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+
+ /* compare with Lr=b+deltaB */
+ R = CHOLMOD(solve) (CHOLMOD_L, L2, B, cm) ;
+ r = -1 ;
+ if (ok && R != NULL)
+ {
+ double *Rx ;
+ Rx = R->x ;
+ r = 0 ;
+ for (i = 0 ; i < colmark [0] ; i++)
+ {
+ r = MAX (r, fabs (X2x [i] - Rx [i])) ;
+ }
+ MAXERR (maxerr, r, 1) ;
+ }
+ printf ("check cholmark resid %6.2e\n", r) ;
+ CHOLMOD(free_dense) (&R, cm) ;
+ CHOLMOD(free_dense) (&X2, cm) ;
+ CHOLMOD(free_factor) (&L2, cm) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free everything */
+ /* ---------------------------------------------------------------------- */
+
+ /* restore defaults */
+ cm->final_resymbol = FALSE ;
+ cm->final_asis = TRUE ;
+ cm->supernodal_switch = 40 ;
+
+ CHOLMOD(free) (nrow, sizeof (Int), StaticParent, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), Pinv, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), P, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), rflag, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), rset, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), rnot, cm) ;
+ CHOLMOD(free) (ncol, sizeof (Int), fset, cm) ;
+ CHOLMOD(free) (ncol, sizeof (Int), fnot, cm) ;
+ CHOLMOD(free) (ncol, sizeof (Int), fflag, cm) ;
+ CHOLMOD(free_factor) (&L, cm) ;
+ CHOLMOD(free_sparse) (&Row, cm) ;
+ CHOLMOD(free_sparse) (&AT, cm) ;
+ CHOLMOD(free_sparse) (&A, cm) ;
+ CHOLMOD(free_dense) (&B, cm) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ CHOLMOD(free_dense) (&Y, cm) ;
+ CHOLMOD(free_dense) (&DeltaB, cm) ;
+
+ progress (0, '.') ;
+ return (maxerr) ;
+}
diff --git a/CHOLMOD/Tcov/make_go.output b/CHOLMOD/Tcov/make_go.output
new file mode 100644
index 0000000..f38e569
--- /dev/null
+++ b/CHOLMOD/Tcov/make_go.output
@@ -0,0 +1,370 @@
+./z_demo ../Demo/Matrix/bcsstk01.tri > tmp/demo_k1.out
+./z_demo ../Demo/Matrix/bcsstk02.tri > tmp/demo_k2.out
+./z_demo < ../Demo/Matrix/lp_afiro.tri > tmp/demo_afiro.out
+./z_demo < ../Demo/Matrix/can___24.mtx > tmp/demo_can24.out
+./z_demo < ../Demo/Matrix/c.tri > tmp/demo_c.out
+./z_demo < ../Demo/Matrix/d.tri > tmp/demo_d.out
+./z_demo < ../Demo/Matrix/up.tri > tmp/demo_up.out
+./z_demo < ../Demo/Matrix/c.mtx > tmp/demo_c_mtx.out
+./z_demo < ../Demo/Matrix/0.tri > tmp/demo_0.out
+./z_demo < Matrix/3_2 > tmp/demo_3_2.out
+./z_demo < Matrix/c5lo > tmp/demo_c5lo.out
+./z_demo < Matrix/c10 > tmp/demo_c10.out
+./z_demo no_such_file > tmp/demo_no_such_file.out
+./z_demo ../Demo/Matrix/mangle1.mtx > tmp/demo_mangle1.out
+./z_demo ../Demo/Matrix/mangle2.mtx > tmp/demo_mangle2.out
+./z_demo ../Demo/Matrix/mangle3.mtx > tmp/demo_mangle3.out
+./z_demo ../Demo/Matrix/mangle4.mtx > tmp/demo_mangle4.out
+./z_demo ../Demo/Matrix/pts5ldd03.mtx > tmp/demo_pts5ldd03.out
+./l_demo ../Demo/Matrix/bcsstk01.tri > tmp/ldemo_k1.out
+./l_demo ../Demo/Matrix/bcsstk02.tri > tmp/ldemo_k2.out
+./l_demo < ../Demo/Matrix/lp_afiro.tri > tmp/ldemo_afiro.out
+./l_demo < ../Demo/Matrix/can___24.mtx > tmp/ldemo_can24.out
+./l_demo < ../Demo/Matrix/c.tri > tmp/ldemo_c.out
+./l_demo < ../Demo/Matrix/d.tri > tmp/ldemo_d.out
+./l_demo < ../Demo/Matrix/up.tri > tmp/ldemo_up.out
+./l_demo < ../Demo/Matrix/c.mtx > tmp/ldemo_c_mtx.out
+./l_demo < ../Demo/Matrix/0.tri > tmp/ldemo_0.out
+./l_demo < Matrix/3_2 > tmp/ldemo_3_2.out
+./l_demo < Matrix/c5lo > tmp/ldemo_c5lo.out
+./l_demo < Matrix/c10 > tmp/ldemo_c10.out
+./l_demo no_such_file > tmp/ldemo_no_such_file.out
+./l_demo ../Demo/Matrix/mangle1.mtx > tmp/ldemo_mangle1.out
+./l_demo ../Demo/Matrix/mangle2.mtx > tmp/ldemo_mangle2.out
+./l_demo ../Demo/Matrix/mangle3.mtx > tmp/ldemo_mangle3.out
+./l_demo ../Demo/Matrix/mangle4.mtx > tmp/ldemo_mangle4.out
+./l_demo ../Demo/Matrix/pts5ldd03.mtx > tmp/ldemo_pts5ldd03.out
+grep resid tmp/demo*
+tmp/demo_0.out:residual 0.0e+00 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_3_2.out:residual 9.4e-17 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_afiro.out:residual 6.5e-17 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_c10.out:residual 5.6e-17 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_c5lo.out:residual 6.3e-17 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_can24.out:residual 8.2e-17 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_can24.out:residual 1.0e-16 (|Ax-b|/(|A||x|+|b|)) after iterative refinement
+tmp/demo_c_mtx.out:residual 2.0e-17 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_c.out:residual 2.0e-17 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_d.out:residual 8.5e-18 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_k1.out:residual 1.5e-19 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_k1.out:residual 1.2e-19 (|Ax-b|/(|A||x|+|b|)) after iterative refinement
+tmp/demo_k2.out:residual 7.4e-17 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_k2.out:residual 4.0e-17 (|Ax-b|/(|A||x|+|b|)) after iterative refinement
+tmp/demo_pts5ldd03.out:residual 6.1e-14 (|Ax-b|/(|A||x|+|b|))
+tmp/demo_up.out:residual 1.1e-17 (|Ax-b|/(|A||x|+|b|))
+./cmread no_such_file > tmp/no_such_file.out
+./cmread ../Demo/Matrix/mangle5.tri > tmp/mangle5.out
+./cmread ../Demo/Matrix/mangle6.tri > tmp/mangle6.out
+./cmread ../Demo/Matrix/mangle7.tri > tmp/mangle6.out
+./cmread ../Demo/Matrix/mangle8.tri > tmp/mangle8.out
+./cmread ../Demo/Matrix/empty.tri > tmp/empty.out
+./cmread ../Demo/Matrix/one.tri > tmp/one.out
+./cmread Matrix/plskz362.mtx > tmp/plskz363.out
+./cmread Matrix/2diag.tri > tmp/2diag.out
+./cmread Matrix/r5lo > tmp/r5lo.out
+./cmread Matrix/r5lo2 > tmp/r5lo2.out
+diff tmp/r5lo.out tmp/r5lo2.out
+./cmread Matrix/cs.mtx > tmp/cs.out
+./cmread Matrix/2lo.tri > tmp/2lo.out
+./cmread Matrix/2.tri > tmp/2.out
+./cmread Matrix/2up.tri > tmp/2up.out
+./cmread Matrix/huge.tri > tmp/huge.out
+./clread no_such_file > tmp/l_no_such_file.out
+./clread ../Demo/Matrix/mangle5.tri > tmp/l_mangle5.out
+./clread ../Demo/Matrix/mangle6.tri > tmp/l_mangle6.out
+./clread ../Demo/Matrix/mangle7.tri > tmp/l_mangle6.out
+./clread ../Demo/Matrix/mangle8.tri > tmp/l_mangle8.out
+./clread ../Demo/Matrix/empty.tri > tmp/l_empty.out
+./clread ../Demo/Matrix/one.tri > tmp/l_one.out
+./clread Matrix/plskz362.mtx > tmp/l_plskz363.out
+./clread Matrix/2diag.tri > tmp/l_2diag.out
+./clread Matrix/r5lo > tmp/l_r5lo.out
+./clread Matrix/r5lo2 > tmp/l_r5lo2.out
+diff tmp/r5lo.out tmp/r5lo2.out
+./clread Matrix/cs.mtx > tmp/l_cs.out
+./clread Matrix/2lo.tri > tmp/l_l_2lo.out
+./clread Matrix/2.tri > tmp/l_2.out
+./clread Matrix/2up.tri > tmp/l_2up.out
+./clread Matrix/huge.tri > tmp/l_huge.out
+./cm < Matrix/galenet > tmp/galenet.out
+Test matrix: 8-by-14 with 22 entries, stype: 0
+........................................................|
+ Test OK, maxerr 1e-11
+./cl < Matrix/galenet > tmp/l_galenet.out ; ./covall
+Test matrix: 8-by-14 with 22 entries, stype: 0
+........................................................|
+ Test OK, maxerr 1e-11
+statments not yet tested: 10734
+./cm < Matrix/5by50 > tmp/5by50.out
+Test matrix: 5-by-50 with 68 entries, stype: 0
+........................................................|
+ Test OK, maxerr 4e-12
+./cl < Matrix/5by50 > tmp/l_5by50.out ; ./covall
+Test matrix: 5-by-50 with 68 entries, stype: 0
+........................................................|
+ Test OK, maxerr 4e-12
+statments not yet tested: 10358
+./cm < Matrix/r5lo > tmp/r5lo.out
+Test matrix: 5-by-5 with 10 entries, stype: -1
+........................................................|
+ Test OK, maxerr 2e-13
+./cl < Matrix/r5lo > tmp/l_r5lo.out
+Test matrix: 5-by-5 with 10 entries, stype: -1
+........................................................|
+ Test OK, maxerr 2e-13
+./cm < Matrix/r5up > tmp/r5up.out
+Test matrix: 5-by-5 with 10 entries, stype: 1
+........................................................|
+ Test OK, maxerr 2e-13
+./cl < Matrix/r5up > tmp/l_r5up.out
+Test matrix: 5-by-5 with 10 entries, stype: 1
+........................................................|
+ Test OK, maxerr 2e-13
+./cm < Matrix/r5up2 > tmp/r5up2.out
+Test matrix: 5-by-5 with 10 entries, stype: 1
+........................................................|
+ Test OK, maxerr 2e-13
+./cl < Matrix/r5up2 > tmp/l_r5up2.out
+Test matrix: 5-by-5 with 10 entries, stype: 1
+........................................................|
+ Test OK, maxerr 2e-13
+./cm < Matrix/c5up2 > tmp/c5up2.out
+Test matrix: 5-by-5 with 11 entries, stype: 1
+........................................................|
+ Test OK, maxerr 6e-16
+./cl < Matrix/c5up2 > tmp/l_c5up2.out
+Test matrix: 5-by-5 with 11 entries, stype: 1
+........................................................|
+ Test OK, maxerr 6e-16
+./cm < Matrix/z5up2 > tmp/z5up2.out
+Test matrix: 5-by-5 with 11 entries, stype: 1
+........................................................|
+ Test OK, maxerr 6e-16
+./cl < Matrix/z5up2 > tmp/l_z5up2.out
+Test matrix: 5-by-5 with 11 entries, stype: 1
+........................................................|
+ Test OK, maxerr 6e-16
+./cm -m < Matrix/z5lo > tmp/z5lo.out
+Test matrix: 5-by-5 with 11 entries, stype: -1
+........................................................|...........|
+ Test OK, maxerr 6e-16
+./cl -m < Matrix/z5lo > tmp/l_z5lo.out
+Test matrix: 5-by-5 with 11 entries, stype: -1
+........................................................|...........|
+ Test OK, maxerr 6e-16
+./cm < Matrix/ibm32 > tmp/ibm.out
+Test matrix: 32-by-32 with 126 entries, stype: 0
+............................|
+ Test OK, maxerr 9e-13
+./cl < Matrix/ibm32 > tmp/l_ibm.out ; ./covall
+Test matrix: 32-by-32 with 126 entries, stype: 0
+............................|
+ Test OK, maxerr 9e-13
+statments not yet tested: 1238
+./cm -m < Matrix/c5lo > tmp/c5lo.out
+Test matrix: 5-by-5 with 11 entries, stype: -1
+........................................................|...........|
+ Test OK, maxerr 6e-16
+./cl -m < Matrix/c5lo > tmp/l_c5lo.out
+Test matrix: 5-by-5 with 11 entries, stype: -1
+........................................................|...........|
+ Test OK, maxerr 6e-16
+./cm -m < Matrix/z10 > tmp/z10.out
+Test matrix: 10-by-15 with 60 entries, stype: 0
+............................|............|
+ Test OK, maxerr 3e-15
+./cl -m < Matrix/z10 > tmp/l_z10.out
+Test matrix: 10-by-15 with 60 entries, stype: 0
+............................|............|
+ Test OK, maxerr 3e-15
+./cm -m < Matrix/z5up > tmp/z5up.out
+Test matrix: 5-by-5 with 11 entries, stype: 1
+........................................................|.............
+...|
+ Test OK, maxerr 6e-16
+./cl -m < Matrix/z5up > tmp/l_z5up.out ; ./covall
+Test matrix: 5-by-5 with 11 entries, stype: 1
+........................................................|.............
+...|
+ Test OK, maxerr 6e-16
+statments not yet tested: 968
+./cm -s < Matrix/3singular > tmp/3singular.out
+Test matrix: 3-by-3 with 4 entries, stype: 1
+........................................................|
+ Test OK
+./cl -s < Matrix/3singular > tmp/l_3singular.out
+Test matrix: 3-by-3 with 4 entries, stype: 1
+........................................................|
+ Test OK
+./cm -s < Matrix/z3singular > tmp/z3singular.out
+Test matrix: 3-by-3 with 4 entries, stype: 1
+........................................................|
+ Test OK
+./cl -s < Matrix/z3singular > tmp/l_z3singular.out
+Test matrix: 3-by-3 with 4 entries, stype: 1
+........................................................|
+ Test OK
+./cm -s < Matrix/c3singular > tmp/c3singular.out
+Test matrix: 3-by-3 with 4 entries, stype: 1
+........................................................|
+ Test OK
+./cl -s < Matrix/c3singular > tmp/l_c3singular.out
+Test matrix: 3-by-3 with 4 entries, stype: 1
+........................................................|
+ Test OK
+./cm -m < Matrix/0 > tmp/0.out
+Test matrix: 0-by-0 with 0 entries, stype: 0
+........................................................|.............
+.|
+ Test OK, maxerr 0
+./cl -m < Matrix/0 > tmp/l_0.out
+Test matrix: 0-by-0 with 0 entries, stype: 0
+........................................................|.............
+.|
+ Test OK, maxerr 0
+./cm -m < Matrix/afiro > tmp/afiro.out
+Test matrix: 27-by-51 with 102 entries, stype: 0
+............................|.........................................
+...|
+ Test OK, maxerr 2e-10
+./cl -m < Matrix/afiro > tmp/l_afiro.out ; ./covall
+Test matrix: 27-by-51 with 102 entries, stype: 0
+............................|.........................................
+...|
+ Test OK, maxerr 2e-10
+statments not yet tested: 412
+./cm -m < Matrix/k01up > tmp/k01up.out
+Test matrix: 48-by-48 with 224 entries, stype: 1
+............................|........................|
+ Test OK, maxerr 8e-07
+./cl -m < Matrix/k01up > tmp/l_k01up.out ; ./covall
+Test matrix: 48-by-48 with 224 entries, stype: 1
+............................|........................|
+ Test OK, maxerr 8e-07
+statments not yet tested: 346
+./cm < Matrix/diag > tmp/diag.out
+Test matrix: 20-by-20 with 20 entries, stype: 1
+............................|
+ Test OK, maxerr 7e-13
+./cl < Matrix/diag > tmp/l_diag.out
+Test matrix: 20-by-20 with 20 entries, stype: 1
+............................|
+ Test OK, maxerr 7e-13
+./cm -m < Matrix/ex5lo > tmp/ex5lo.out
+Test matrix: 27-by-27 with 153 entries, stype: -1
+............................|.................|
+ Test OK, maxerr 4e-09
+./cl -m < Matrix/ex5lo > tmp/l_ex5lo.out ; ./covall
+Test matrix: 27-by-27 with 153 entries, stype: -1
+............................|.................|
+ Test OK, maxerr 4e-09
+statments not yet tested: 332
+./cm < Matrix/20lo > tmp/20lo.out
+Test matrix: 20-by-20 with 210 entries, stype: -1
+............................|
+ Test OK, maxerr 6e-14
+./cl < Matrix/20lo > tmp/l_20lo.out
+Test matrix: 20-by-20 with 210 entries, stype: -1
+............................|
+ Test OK, maxerr 6e-14
+./cm < Matrix/z30lo > tmp/z30lo.out
+Test matrix: 30-by-30 with 114 entries, stype: -1
+............................|
+ Test OK, maxerr 6e-15
+./cl < Matrix/z30lo > tmp/l_z30lo.out ; ./covall
+Test matrix: 30-by-30 with 114 entries, stype: -1
+............................|
+ Test OK, maxerr 6e-15
+statments not yet tested: 298
+./cm -m < Matrix/z30up > tmp/z30up.out
+Test matrix: 30-by-30 with 114 entries, stype: 1
+............................|..................|
+ Test OK, maxerr 6e-15
+./cl -m < Matrix/z30up > tmp/l_z30up.out
+Test matrix: 30-by-30 with 114 entries, stype: 1
+............................|..................|
+ Test OK, maxerr 6e-15
+./cm < Matrix/c10 > tmp/c10.out
+Test matrix: 10-by-15 with 60 entries, stype: 0
+............................|
+ Test OK, maxerr 3e-15
+./cl < Matrix/c10 > tmp/l_c10.out
+Test matrix: 10-by-15 with 60 entries, stype: 0
+............................|
+ Test OK, maxerr 3e-15
+./cm < Matrix/c30lo > tmp/c30lo.out
+Test matrix: 30-by-30 with 114 entries, stype: -1
+............................|
+ Test OK, maxerr 6e-15
+./cl < Matrix/c30lo > tmp/l_c30lo.out ; ./covall
+Test matrix: 30-by-30 with 114 entries, stype: -1
+............................|
+ Test OK, maxerr 6e-15
+statments not yet tested: 192
+./cm -m < Matrix/c30up > tmp/c30up.out
+Test matrix: 30-by-30 with 114 entries, stype: 1
+............................|................|
+ Test OK, maxerr 6e-15
+./cl -m < Matrix/c30up > tmp/l_c30up.out
+Test matrix: 30-by-30 with 114 entries, stype: 1
+............................|................|
+ Test OK, maxerr 6e-15
+./cm < Matrix/pi > tmp/pi.out
+Test matrix: 1-by-1 with 1 entries, stype: 0
+........................................................|
+ Test OK, maxerr 3e-13
+./cl < Matrix/pi > tmp/l_pi.out
+Test matrix: 1-by-1 with 1 entries, stype: 0
+........................................................|
+ Test OK, maxerr 3e-13
+./cm < Matrix/cpi > tmp/cpi.out
+Test matrix: 1-by-1 with 1 entries, stype: 0
+........................................................|
+ Test OK, maxerr 2e-15
+./cl < Matrix/cpi > tmp/l_cpi.out
+Test matrix: 1-by-1 with 1 entries, stype: 0
+........................................................|
+ Test OK, maxerr 2e-15
+./cm < Matrix/1_0 > tmp/1_0.out
+Test matrix: 1-by-0 with 0 entries, stype: 0
+........................................................|
+ Test OK
+./cl < Matrix/1_0 > tmp/l_1_0.out
+Test matrix: 1-by-0 with 0 entries, stype: 0
+........................................................|
+ Test OK
+./cm < Matrix/0_1 > tmp/0_1.out
+Test matrix: 0-by-1 with 0 entries, stype: 0
+........................................................|
+ Test OK, maxerr 0
+./cl < Matrix/0_1 > tmp/l_0_1.out ; ./covall
+Test matrix: 0-by-1 with 0 entries, stype: 0
+........................................................|
+ Test OK, maxerr 0
+statments not yet tested: 154
+./cm -n < Matrix/galenet > tmp/galenet_nan.out ; ./covall
+Test matrix: 8-by-14 with 22 entries, stype: 0
+
+ Test OK, maxerr 0
+statments not yet tested: 148
+./cl -n < Matrix/galenet > tmp/l_galenet_nan.out ; ./covall
+Test matrix: 8-by-14 with 22 entries, stype: 0
+
+ Test OK, maxerr 0
+statments not yet tested: 142
+./cm < Matrix/a1 > tmp/a1.out ; ./covall
+Test matrix: 70000-by-70000 with 140000 entries, stype: 1
+Please wait, this will take a while ................|
+ Test OK, maxerr 5e-12
+statments not yet tested: 124
+./cl < Matrix/a1 > tmp/l_a1.out ; ./covall
+Test matrix: 70000-by-70000 with 140000 entries, stype: 1
+Please wait, this will take a while ................|
+ Test OK, maxerr 5e-12
+statments not yet tested: 106
+./cm < Matrix/zero > tmp/zero.out
+Test matrix: 1100000000-by-1100000000 with 0 entries, stype: 0
+Please wait, this will take a while ...
+./cl < Matrix/zero > tmp/zero.out ; ./covall
+Test matrix: 1100000000-by-1100000000 with 0 entries, stype: 0
+Please wait, this will take a while ...
+statments not yet tested: 0
diff --git a/CHOLMOD/Tcov/memory.c b/CHOLMOD/Tcov/memory.c
new file mode 100644
index 0000000..0f468e6
--- /dev/null
+++ b/CHOLMOD/Tcov/memory.c
@@ -0,0 +1,358 @@
+/* ========================================================================== */
+/* === Tcov/memory ========================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Extensive memory-failure testing for CHOLMOD.
+ *
+ * my_malloc2, my_calloc2, and my_realloc2 pretend to fail if my_tries goes to
+ * zero, to test CHOLMOD's memory error handling. No failure occurs if
+ * my_tries is negative.
+ */
+
+#include "cm.h"
+
+
+/* ========================================================================== */
+/* === my_tries ============================================================= */
+/* ========================================================================== */
+
+Int my_tries = -1 ; /* a global variable */
+
+
+/* ========================================================================== */
+/* === my_malloc2 =========================================================== */
+/* ========================================================================== */
+
+void *my_malloc2 (size_t size)
+{
+ void *p ;
+ if (my_tries == 0)
+ {
+ /* pretend to fail */
+ /* printf ("p 0 (pretend to fail)\n") ; */
+ return (NULL) ;
+ }
+ if (my_tries > 0)
+ {
+ my_tries-- ;
+ }
+ p = malloc (size) ;
+ /* printf ("p %p\n", p) ; */
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === my_calloc2 =========================================================== */
+/* ========================================================================== */
+
+void *my_calloc2 (size_t n, size_t size)
+{
+ void *p ;
+ if (my_tries == 0)
+ {
+ /* pretend to fail */
+ /* printf ("p 0 (pretend to fail)\n") ; */
+ return (NULL) ;
+ }
+ if (my_tries > 0)
+ {
+ my_tries-- ;
+ }
+ p = calloc (n, size) ;
+ /* printf ("p %p\n", p) ; */
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === my_realloc2 ========================================================== */
+/* ========================================================================== */
+
+void *my_realloc2 (void *p, size_t size)
+{
+ void *p2 ;
+ if (my_tries == 0)
+ {
+ /* pretend to fail */
+ /* printf ("p2 0 (pretend to fail)\n") ; */
+ return (NULL) ;
+ }
+ if (my_tries > 0)
+ {
+ my_tries-- ;
+ }
+ p2 = realloc (p, size) ;
+ /* printf ("p2 %p\n", p2) ; */
+ return (p2) ;
+}
+
+
+/* ========================================================================== */
+/* === my_free2 ============================================================= */
+/* ========================================================================== */
+
+void my_free2 (void *p)
+{
+ free (p) ;
+}
+
+
+/* ========================================================================== */
+/* === normal_memory_handler ================================================ */
+/* ========================================================================== */
+
+void normal_memory_handler ( void )
+{
+ cm->malloc_memory = malloc ;
+ cm->calloc_memory = calloc ;
+ cm->realloc_memory = realloc ;
+ cm->free_memory = free ;
+ cm->error_handler = my_handler ;
+ CHOLMOD(free_work) (cm) ;
+}
+
+
+/* ========================================================================== */
+/* === test_memory_handler ================================================== */
+/* ========================================================================== */
+
+void test_memory_handler ( void )
+{
+ cm->malloc_memory = my_malloc2 ;
+ cm->calloc_memory = my_calloc2 ;
+ cm->realloc_memory = my_realloc2 ;
+ cm->free_memory = my_free2 ;
+ cm->error_handler = NULL ;
+ CHOLMOD(free_work) (cm) ;
+ my_tries = 0 ;
+}
+
+
+/* ========================================================================== */
+/* === memory tests ========================================================= */
+/* ========================================================================== */
+
+void memory_tests (cholmod_triplet *T)
+{
+ double err ;
+ cholmod_sparse *A ;
+ Int trial ;
+ size_t count, inuse ;
+
+ test_memory_handler ( ) ;
+ inuse = cm->memory_inuse ;
+
+ cm->nmethods = 8 ;
+ cm->print = 0 ;
+ cm->final_resymbol = TRUE ;
+
+ cm->final_asis = FALSE ;
+ cm->final_super = FALSE ;
+ cm->final_ll = FALSE ;
+ cm->final_pack = FALSE ;
+ cm->final_monotonic = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test raw factorizations */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("==================================== fac memory test\n") ;
+ count = cm->malloc_count ;
+ my_tries = -1 ;
+ for (trial = 0 ; my_tries <= 0 ; trial++)
+ {
+ cm->print = 0 ;
+ fflush (stdout) ;
+ my_tries = trial ;
+ A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ;
+ my_srand (trial+1) ; /* RAND reset */
+ err = raw_factor (A, FALSE) ; /* RAND */
+ CHOLMOD(free_sparse) (&A, cm) ;
+ OK (CHOLMOD(print_common) ("cm", cm)) ;
+ CHOLMOD(free_work) (cm) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+ }
+ CHOLMOD(free_work) (cm) ;
+ printf ("memory test: fac error %.1g trials "ID"\n", err, trial) ;
+ printf ("initial count: "ID" final count "ID"\n",
+ (Int) count, (Int) cm->malloc_count) ;
+ printf ("initial inuse: "ID" final inuse "ID"\n",
+ (Int) inuse, (Int) cm->memory_inuse) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test raw factorizations (rowfac_mask) */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("==================================== fac memory test2\n") ;
+ count = cm->malloc_count ;
+ my_tries = -1 ;
+ for (trial = 0 ; my_tries <= 0 ; trial++)
+ {
+ cm->print = 0 ;
+ fflush (stdout) ;
+ my_tries = trial ;
+ A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ;
+ my_srand (trial+1) ; /* RAND reset */
+ err = raw_factor2 (A, 0., 0) ; /* RAND */
+ CHOLMOD(free_sparse) (&A, cm) ;
+ OK (CHOLMOD(print_common) ("cm", cm)) ;
+ CHOLMOD(free_work) (cm) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+ }
+ CHOLMOD(free_work) (cm) ;
+ printf ("memory test: fac error %.1g trials "ID"\n", err, trial) ;
+ printf ("initial count: "ID" final count "ID"\n",
+ (Int) count, (Int) cm->malloc_count) ;
+ printf ("initial inuse: "ID" final inuse "ID"\n",
+ (Int) inuse, (Int) cm->memory_inuse) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test augmented system solver */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("==================================== aug memory test\n") ;
+ count = cm->malloc_count ;
+ my_tries = -1 ;
+ for (trial = 0 ; my_tries <= 0 ; trial++)
+ {
+ cm->print = 0 ;
+ fflush (stdout) ;
+ my_tries = trial ;
+ A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ;
+ err = aug (A) ; /* no random number use */
+ CHOLMOD(free_sparse) (&A, cm) ;
+ OK (CHOLMOD(print_common) ("cm", cm)) ;
+ CHOLMOD(free_work) (cm) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+ }
+ CHOLMOD(free_work) (cm) ;
+ printf ("memory test: aug error %.1g trials "ID"\n", err, trial) ;
+ printf ("initial count: "ID" final count "ID"\n",
+ (Int) count, (Int) cm->malloc_count) ;
+ printf ("initial inuse: "ID" final inuse "ID"\n",
+ (Int) inuse, (Int) cm->memory_inuse) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test ops */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("==================================== test_ops memory test\n") ;
+ count = cm->malloc_count ;
+ my_tries = -1 ;
+ for (trial = 0 ; my_tries <= 0 ; trial++)
+ {
+ cm->print = 0 ;
+ fflush (stdout) ;
+ my_tries = trial ;
+ A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ;
+ my_srand (trial+1) ; /* RAND reset */
+ err = test_ops (A) ; /* RAND */
+ CHOLMOD(free_sparse) (&A, cm) ;
+ OK (CHOLMOD(print_common) ("cm", cm)) ;
+ CHOLMOD(free_work) (cm) ;
+ printf ("inuse "ID" "ID"\n", inuse, cm->memory_inuse) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+ }
+ printf ("memory test: testops error %.1g trials "ID"\n", err, trial) ;
+ printf ("initial count: "ID" final count "ID"\n",
+ (Int) count, (Int) cm->malloc_count) ;
+ printf ("initial inuse: "ID" final inuse "ID"\n",
+ (Int) inuse, (Int) cm->memory_inuse) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test lpdemo */
+ /* ---------------------------------------------------------------------- */
+
+ if (T == NULL || T->nrow != T->ncol)
+ {
+ printf ("==================================== lpdemo memory test\n") ;
+ count = cm->malloc_count ;
+ my_tries = -1 ;
+ for (trial = 0 ; my_tries <= 0 ; trial++)
+ {
+ cm->print = 0 ;
+ fflush (stdout) ;
+ my_tries = trial ;
+ my_srand (trial+1) ; /* RAND reset */
+ err = lpdemo (T) ; /* RAND */
+ OK (CHOLMOD(print_common) ("cm", cm)) ;
+ CHOLMOD(free_work) (cm) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+ }
+ CHOLMOD(free_work) (cm) ;
+ printf ("memory test: lpdemo error %.1g trials "ID"\n", err, trial) ;
+ printf ("initial count: "ID" final count "ID"\n",
+ (Int) count, (Int) cm->malloc_count) ;
+ printf ("initial inuse: "ID" final inuse "ID"\n",
+ (Int) inuse, (Int) cm->memory_inuse) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* test solver */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("==================================== solve memory test\n") ;
+ count = cm->malloc_count ;
+ my_tries = -1 ;
+ for (trial = 0 ; my_tries <= 0 ; trial++)
+ {
+ CHOLMOD(defaults) (cm) ;
+ cm->supernodal = CHOLMOD_SUPERNODAL ;
+ cm->metis_memory = 2.0 ;
+ cm->nmethods = 4 ;
+ cm->print = 0 ;
+ fflush (stdout) ;
+ my_tries = trial ;
+ A = CHOLMOD(triplet_to_sparse) (T, 0, cm) ;
+ my_srand (trial+1) ; /* RAND reset */
+ err = solve (A) ; /* RAND */
+ CHOLMOD(free_sparse) (&A, cm) ;
+ OK (CHOLMOD(print_common) ("cm", cm)) ;
+ CHOLMOD(free_work) (cm) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+ }
+ CHOLMOD(free_work) (cm) ;
+ printf ("memory test: solve error %.1g trials "ID"\n", err, trial) ;
+ printf ("initial count: "ID" final count "ID"\n",
+ (Int) count, (Int) cm->malloc_count) ;
+ printf ("initial inuse: "ID" final inuse "ID"\n",
+ (Int) inuse, (Int) cm->memory_inuse) ;
+ OK (count == cm->malloc_count) ;
+ OK (inuse == cm->memory_inuse) ;
+ cm->supernodal = CHOLMOD_AUTO ;
+ progress (1, '|') ;
+
+ /* ---------------------------------------------------------------------- */
+ /* restore original memory handler */
+ /* ---------------------------------------------------------------------- */
+
+ normal_memory_handler ( ) ;
+ cm->print = 1 ;
+
+ printf ("All memory tests OK, no error\n") ;
+}
diff --git a/CHOLMOD/Tcov/null.c b/CHOLMOD/Tcov/null.c
new file mode 100644
index 0000000..943c549
--- /dev/null
+++ b/CHOLMOD/Tcov/null.c
@@ -0,0 +1,346 @@
+/* ========================================================================== */
+/* === Tcov/null ============================================================ */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Test CHOLMOD with NULL pointers, and other error cases. */
+
+#include "cm.h"
+
+
+/* ========================================================================== */
+/* === my_hander2 =========================================================== */
+/* ========================================================================== */
+
+void my_handler2 (int status, char *file, int line, char *msg)
+{
+ printf ("This ERROR is expected: file %s line %d\n%d: %s\n",
+ file, line, status, msg) ;
+}
+
+
+/* ========================================================================== */
+/* === null_test ============================================================ */
+/* ========================================================================== */
+
+/* This routine is not called during memory testing */
+
+void null_test (cholmod_common *cn)
+{
+ cholmod_sparse *A = NULL, *F = NULL, *C = NULL, *R = NULL, *B = NULL ;
+ cholmod_factor *L = NULL ;
+ cholmod_triplet *T = NULL ;
+ cholmod_dense *X = NULL, *DeltaB = NULL, *S = NULL, *Y = NULL, *E = NULL ;
+ void *p = NULL, *ii = NULL, *jj = NULL, *xx = NULL, *zz = NULL ;
+ Int *Perm = NULL, *fset = NULL, *Parent = NULL, *Post = NULL,
+ *RowCount = NULL, *ColCount = NULL, *First = NULL, *Level = NULL,
+ *UserPerm = NULL, *colmark = NULL, *Constraints = NULL,
+ *r = NULL, *c = NULL, *Set = NULL ;
+ char *name = NULL ;
+ double alpha [2], beta [2], bk [2], yk [2], rcond ;
+ double dj = 1, nm = 0, tol = 0 ;
+ int ok, stype = 0, xtype = 0, sorted = 0, packed = 0, nint = 0, update = 0,
+ postorder = 0, pack = 0, values = 0, mode = 0, sys = 0, norm = 0,
+ to_xtype = 0, to_ll = 0, to_super = 0, to_packed = 0, to_monotonic = 0,
+ scale = 0, transpose = 0, option = 0, ordering = 0, prefer = 0,
+ mtype = 0, asym = 0 ;
+ UF_long lr = 0, k1 = 0, k2 = 0 ;
+ size_t j = 0, need = 0, n = 0, mr = 0, nrow = 0, ncol = 0, iworksize = 0,
+ newsize = 0, fsize = 0, d = 0, nzmax = 0, nnew = 0, size = 0,
+ nold = 0, xwork = 0, kstart = 0, kend = 0, nr = 0, nc = 0, len = 0,
+ krow = 0, k = 0 ;
+
+#ifndef NPARTITION
+ Int *Anw = NULL, *Aew = NULL, *Partition = NULL,
+ *CParent = NULL, *Cmember = NULL ;
+ Int compress = 0 ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* Core */
+ /* ---------------------------------------------------------------------- */
+
+ if (cn == NULL)
+ {
+ ok = CHOLMOD(start)(cn) ; NOT (ok) ;
+ }
+ ok = CHOLMOD(finish)(cn) ; NOT (ok) ;
+ ok = CHOLMOD(defaults)(cn) ; NOT (ok) ;
+ mr = CHOLMOD(maxrank)(n, cn) ; NOT (mr>0) ;
+ ok = CHOLMOD(allocate_work)(nrow, iworksize, xwork, cn) ; NOT (ok) ;
+ ok = CHOLMOD(free_work)(cn) ; NOT (ok) ;
+ lr = CHOLMOD(clear_flag)(cn) ; NOT (lr>=0) ;
+
+ dj = CHOLMOD(dbound)(dj, cn) ; OK (dj==0) ;
+ ok = CHOLMOD(error)(CHOLMOD_INVALID, __FILE__, __LINE__, "oops", cn) ;
+ NOT (ok) ;
+ A = CHOLMOD(allocate_sparse)(nrow, ncol, nzmax, sorted,
+ packed, stype, xtype, cn) ; NOP (A) ;
+ ok = CHOLMOD(free_sparse)(&A, cn) ; NOT (ok) ;
+ ok = CHOLMOD(reallocate_sparse)(newsize, A, cn) ; NOT (ok) ;
+ lr = CHOLMOD(nnz)(A, cn) ; NOT (lr>=0) ;
+ A = CHOLMOD(speye)(nrow, ncol, xtype, cn) ; NOP (A) ;
+ A = CHOLMOD(spzeros)(nrow, ncol, 0, xtype, cn) ; NOP (A) ;
+ A = CHOLMOD(ptranspose)(A, values, Perm, fset, fsize, cn); NOP (A) ;
+ A = CHOLMOD(transpose)(A, values, cn) ; NOP (A) ;
+ ok = CHOLMOD(transpose_unsym)(A, values, Perm, fset, fsize, F, cn) ;
+ NOT (ok) ;
+ ok = CHOLMOD(transpose_sym)(A, values, Perm, F, cn) ; NOT (ok) ;
+ ok = CHOLMOD(sort)(A, cn) ; NOT (ok) ;
+ A = CHOLMOD(copy_sparse)(A, cn) ; NOP (A) ;
+ C = CHOLMOD(aat)(A, fset, fsize, mode, cn) ; NOP (C) ;
+
+ L = CHOLMOD(allocate_factor)(n, cn) ; NOP (L) ;
+ ok = CHOLMOD(free_factor)(&L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(reallocate_factor)(newsize, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(change_factor)(0, 0, 0, 0, 0, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(pack_factor)(L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(change_factor)(to_xtype, to_ll, to_super,
+ to_packed, to_monotonic, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(reallocate_column)(j, need, L, cn) ; NOT (ok) ;
+ A = CHOLMOD(factor_to_sparse)(L, cn) ; NOP (A) ;
+ L = CHOLMOD(copy_factor)(L, cn) ; NOP (L) ;
+
+ X = CHOLMOD(allocate_dense)(nrow, ncol, d, xtype, cn) ; NOP (X) ;
+ X = CHOLMOD(zeros)(nrow, ncol, xtype, cn) ; NOP (X) ;
+ X = CHOLMOD(ones)(nrow, ncol, xtype, cn) ; NOP (X) ;
+ X = CHOLMOD(eye)(nrow, ncol, xtype, cn) ; NOP (X) ;
+ ok = CHOLMOD(free_dense)(&X, cn) ; NOT (ok) ;
+ X = CHOLMOD(sparse_to_dense)(A, cn) ; NOP (X) ;
+ A = CHOLMOD(dense_to_sparse)(X, values, cn) ; NOP (A) ;
+ Y = CHOLMOD(copy_dense)(X, cn) ; NOP (X) ;
+ ok = CHOLMOD(copy_dense2)(X, Y, cn) ; NOT (ok) ;
+
+ T = CHOLMOD(allocate_triplet)(nrow, ncol, nzmax,
+ stype, xtype, cn) ; NOP (T) ;
+ ok = CHOLMOD(free_triplet)(&T, cn) ; NOT (ok) ;
+ T = CHOLMOD(sparse_to_triplet)(A, cn) ; NOP (T) ;
+ A = CHOLMOD(triplet_to_sparse)(T, 0, cn) ; NOP (A) ;
+ T = CHOLMOD(copy_triplet)(T, cn) ; NOP (T) ;
+ ok = CHOLMOD(reallocate_triplet)(nzmax, T, cn) ; NOT (ok) ;
+
+ lr = CHOLMOD(postorder)(Parent, nrow, NULL, Post, cn) ; NOT (lr>=0) ;
+ p = CHOLMOD(malloc)(n, size, cn) ; NOP (p) ;
+ p = CHOLMOD(calloc)(n, size, cn) ; NOP (p) ;
+ p = CHOLMOD(free)(n, size, p, cn) ; NOP (p) ;
+ p = CHOLMOD(realloc)(nnew, size, p, &n, cn) ; NOP (p) ;
+ ok = CHOLMOD(realloc_multiple)(nnew, nint, xtype,
+ &ii, &jj, &xx, &zz, &nold, cn) ; NOT (ok) ;
+
+ C = CHOLMOD(band)(A, k1, k2, mode, cn) ; NOP (C) ;
+ ok = CHOLMOD(band_inplace)(k1, k2, mode, A, cn) ; NOT (ok) ;
+
+ ok = CHOLMOD(factor_xtype)(CHOLMOD_REAL, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(sparse_xtype)(CHOLMOD_REAL, A, cn) ; NOT (ok) ;
+ ok = CHOLMOD(dense_xtype)(CHOLMOD_REAL, X, cn) ; NOT (ok) ;
+ ok = CHOLMOD(triplet_xtype)(CHOLMOD_REAL, T, cn) ; NOT (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Cholesky */
+ /* ---------------------------------------------------------------------- */
+
+ L = CHOLMOD(analyze)(A, cn) ; NOP (L) ;
+ L = CHOLMOD(analyze_p)(A, UserPerm, fset, fsize, cn) ; NOP (L) ;
+ ok = CHOLMOD(factorize)(A, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(factorize_p)(A, beta, fset, fsize, L, cn) ; NOT (ok) ;
+ rcond = CHOLMOD(rcond)(L, cn) ; NOT (rcond>=0) ;
+ X = CHOLMOD(solve)(sys, L, Y, cn) ; NOP (X) ;
+ C = CHOLMOD(spsolve)(sys, L, B, cn) ; NOP (C) ;
+ ok = CHOLMOD(etree)(A, Parent, cn) ; NOT (ok) ;
+ ok = CHOLMOD(rowcolcounts)(A, fset, fsize, Parent, Post,
+ RowCount, ColCount, First, Level, cn) ; NOT (ok) ;
+ ok = CHOLMOD(amd)(A, fset, fsize, Perm, cn) ; NOT (ok) ;
+ ok = CHOLMOD(camd)(A, fset, fsize, Constraints, Perm, cn) ; NOT (ok) ;
+ ok = CHOLMOD(colamd)(A, fset, fsize, postorder, Perm, cn) ; NOT (ok) ;
+ ok = CHOLMOD(rowfac)(A, F, beta, kstart, kend, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(row_subtree)(A, F, krow, Parent, R, cn) ; NOT (ok) ;
+ ok = CHOLMOD(row_lsubtree)(A, c, 0, krow, L, R, cn) ; NOT (ok) ;
+ ok = CHOLMOD(resymbol)(A, fset, fsize, pack, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(resymbol_noperm)(A, fset, fsize, pack, L, cn) ;NOT (ok) ;
+ ok = CHOLMOD(analyze_ordering)(A, ordering, Perm, fset,
+ fsize, Parent, Post, ColCount, First, Level, cn) ; NOT (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Modify */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(updown)(update, C, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(updown_solve)(update, C, L, X, DeltaB, cn) ; NOT (ok) ;
+ ok = CHOLMOD(updown_mark)(update, C, colmark, L, X, DeltaB,
+ cn) ; NOT (ok) ;
+ ok = CHOLMOD(rowadd)(k, R, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(rowadd_solve)(k, R, bk, L, X, DeltaB, cn) ; NOT (ok) ;
+ ok = CHOLMOD(rowadd_mark)(k, R, bk, colmark, L, X, DeltaB,
+ cn) ; NOT (ok) ;
+ ok = CHOLMOD(rowdel)(k, R, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(rowdel_solve)(k, R, yk, L, X, DeltaB, cn) ; NOT (ok) ;
+ ok = CHOLMOD(rowdel_mark)(k, R, yk, colmark, L, X, DeltaB,
+ cn) ; NOT (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* MatrixOps */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(add)(A, B, alpha, beta, values, sorted, cn) ; NOP (C) ;
+
+ C = CHOLMOD(copy)(A, stype, mode, cn) ; NOP (C) ;
+ ok = CHOLMOD(drop)(tol, A, cn) ; NOT (ok) ;
+ nm = CHOLMOD(norm_dense)(X, norm, cn) ; NOT (nm>=0) ;
+ nm = CHOLMOD(norm_sparse)(A, norm, cn) ; NOT (nm>=0) ;
+ C = CHOLMOD(horzcat)(A, B, values, cn) ; NOP (C) ;
+ ok = CHOLMOD(scale)(S, scale, A, cn) ; NOT (ok) ;
+ ok = CHOLMOD(sdmult)(A, transpose, alpha, beta, X, Y, cn) ; NOT (ok) ;
+ C = CHOLMOD(ssmult)(A, B, stype, values, sorted, cn) ; NOP (C) ;
+ C = CHOLMOD(submatrix)(A, r, nr, c, nc, values, sorted,
+ cn) ; NOP (C) ;
+ C = CHOLMOD(vertcat)(A, B, values, cn) ; NOP (C) ;
+ asym = CHOLMOD(symmetry)(A, option, NULL, NULL, NULL, NULL,
+ cn) ; NOT(asym>=0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Supernodal */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(super_symbolic)(A, F, Parent, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(super_numeric)(A, F, beta, L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(super_lsolve)(L, X, E, cn) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve)(L, X, E, cn) ; NOT (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Check */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(check_common)(cn) ; NOT (ok) ;
+ ok = CHOLMOD(print_common)(name, cn) ; NOT (ok) ;
+
+ ok = CHOLMOD(check_sparse)(A, cn) ; NOT (ok) ;
+ ok = CHOLMOD(print_sparse)(A, name, cn) ; NOT (ok) ;
+ ok = CHOLMOD(check_dense)(X, cn) ; NOT (ok) ;
+ ok = CHOLMOD(print_dense)(X, name, cn) ; NOT (ok) ;
+ ok = CHOLMOD(check_factor)(L, cn) ; NOT (ok) ;
+ ok = CHOLMOD(print_factor)(L, name, cn) ; NOT (ok) ;
+ ok = CHOLMOD(check_triplet)(T, cn) ; NOT (ok) ;
+ ok = CHOLMOD(print_triplet)(T, name, cn) ; NOT (ok) ;
+ ok = CHOLMOD(check_subset)(Set, len, n, cn) ; NOT (ok) ;
+ ok = CHOLMOD(print_subset)(Set, len, n, name, cn) ; NOT (ok) ;
+ ok = CHOLMOD(check_perm)(Perm, n, n, cn) ; NOT (ok) ;
+ ok = CHOLMOD(print_perm)(Perm, n, n, name, cn) ; NOT (ok) ;
+ ok = CHOLMOD(check_parent)(Parent, n, cn) ; NOT (ok) ;
+ ok = CHOLMOD(print_parent)(Parent, n, name, cn) ; NOT (ok) ;
+
+ A = CHOLMOD(read_sparse)(NULL, cn) ; NOP (A) ;
+ p = CHOLMOD(read_matrix)(NULL, prefer, &mtype, cn) ; NOP (p) ;
+ X = CHOLMOD(read_dense)(NULL, cn) ; NOP (X) ;
+ T = CHOLMOD(read_triplet)(NULL, cn) ; NOP (T) ;
+
+ asym = CHOLMOD(write_dense) (NULL, NULL, NULL, cn) ; NOT (asym>=0) ;
+ asym = CHOLMOD(write_dense) ((FILE *) 1, NULL, NULL, cn) ; NOT (asym>=0) ;
+
+ asym = CHOLMOD(write_sparse)(NULL, NULL, NULL, NULL, cn) ; NOT (asym>=0) ;
+ asym = CHOLMOD(write_sparse)((FILE *) 1, NULL, NULL, NULL,
+ cn) ; NOT (asym>=0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Partition */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NPARTITION
+ lr = CHOLMOD(nested_dissection)(A, fset, fsize, Perm,
+ CParent, Cmember, cn) ; NOT (lr >= 0) ;
+ lr = CHOLMOD(collapse_septree) (n, n, 1., 4,
+ CParent, Cmember, cn) ; NOT (lr >= 0) ;
+ ok = CHOLMOD(metis)(A, fset, fsize, postorder, Perm, cn) ; NOT (ok) ;
+ ok = CHOLMOD(ccolamd)(A, fset, fsize, Cmember, Perm, cn) ; NOT (ok) ;
+ ok = CHOLMOD(csymamd)(A, Cmember, Perm, cn) ; NOT (ok) ;
+ lr = CHOLMOD(bisect)(A, fset, fsize, compress,
+ Partition, cn) ; NOT (lr >= 0) ;
+ lr = CHOLMOD(metis_bisector)(A, Anw, Aew, Partition, cn) ; NOT (lr >= 0) ;
+#endif
+
+}
+
+/* ========================================================================== */
+/* === null_test2 =========================================================== */
+/* ========================================================================== */
+
+void null_test2 (void)
+{
+ cholmod_dense *X, *Xbad = NULL ;
+ cholmod_sparse *Sbad = NULL, *A ;
+ int ok ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Test Core Common */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(allocate_work)(Size_max, 1, 1, cm) ; NOT (ok) ;
+ ok = CHOLMOD(allocate_work)(1, Size_max, 1, cm) ; NOT (ok) ;
+ ok = CHOLMOD(allocate_work)(1, 1, Size_max, cm) ; NOT (ok) ;
+
+ /* free a NULL pointer */
+ CHOLMOD(free)(42, sizeof (char), NULL, cm) ;
+ cm->print = 5 ; CHOLMOD(print_common)("cm", cm) ; cm->print = 3 ;
+
+ cm->maxrank = 3 ;
+ cm->maxrank = CHOLMOD(maxrank)(5, cm) ; OK (cm->maxrank == 4) ;
+ cm->maxrank = 1 ;
+ cm->maxrank = CHOLMOD(maxrank)(5, cm) ; OK (cm->maxrank == 2) ;
+ cm->maxrank = 8 ;
+
+ /* test the error handler */
+ cm->error_handler = my_handler2 ;
+ CHOLMOD(drop)(0., NULL, cm) ;
+ cm->error_handler = NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* dense */
+ /* ---------------------------------------------------------------------- */
+
+ X = CHOLMOD(allocate_dense)(5, 4, 1, CHOLMOD_REAL, cm) ; NOP (X) ;
+ X = CHOLMOD(allocate_dense)(1, Int_max, 1, CHOLMOD_REAL, cm) ; NOP (X) ;
+ X = CHOLMOD(allocate_dense)(1, 1, 1, -1, cm) ; NOP (X) ;
+ CHOLMOD(free_dense)(&X, cm) ;
+
+ /* free a NULL dense matrix */
+ ok = CHOLMOD(free_dense)(&X, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_dense)(NULL, cm) ; OK (ok) ;
+
+ /* make an invalid sparse matrix */
+ Sbad = CHOLMOD(speye)(2, 3, CHOLMOD_REAL, cm) ; OKP (Sbad) ;
+ Sbad->stype = 1 ;
+ ok = CHOLMOD(check_sparse)(Sbad, cm) ; NOT (ok) ;
+ X = CHOLMOD(sparse_to_dense)(Sbad, cm) ; NOP (X) ;
+ ok = CHOLMOD(free_sparse)(&Sbad, cm) ; OK (ok) ;
+
+ /* make an invalid dense matrix */
+ Xbad = CHOLMOD(eye)(4, 4, CHOLMOD_REAL, cm) ; OKP (Xbad) ;
+ Xbad->d = 1 ;
+ ok = CHOLMOD(check_dense)(Xbad, cm) ; NOT (ok) ;
+ A = CHOLMOD(dense_to_sparse)(Xbad, TRUE, cm) ;
+ ok = CHOLMOD(free_dense)(&Xbad, cm) ; OK (ok) ;
+ CHOLMOD(print_common)("cm", cm) ;
+ cm->print = 5 ; CHOLMOD(print_sparse)(A, "Bad A", cm) ; cm->print = 3 ;
+ NOP (A) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* sparse */
+ /* ---------------------------------------------------------------------- */
+
+ /* free a NULL sparse matrix */
+ ok = CHOLMOD(free_sparse)(&A, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse)(NULL, cm) ; OK (ok) ;
+ A = CHOLMOD(copy_sparse)(NULL, cm) ; NOP (A) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* error tests done */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("------------------ null tests done\n") ;
+}
diff --git a/CHOLMOD/Tcov/null2.c b/CHOLMOD/Tcov/null2.c
new file mode 100644
index 0000000..692e323
--- /dev/null
+++ b/CHOLMOD/Tcov/null2.c
@@ -0,0 +1,3399 @@
+/* ========================================================================== */
+/* === Tcov/null2 =========================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Null and error tests, continued. */
+
+#include "cm.h"
+#include "amd.h"
+#ifndef NPARTITION
+#include "camd.h"
+#endif
+
+#define CSETSIZE 5
+
+
+/* ========================================================================== */
+/* === null2 ================================================================ */
+/* ========================================================================== */
+
+void null2 (cholmod_triplet *Tok, int do_nantests)
+{
+ double nm, gsave0, gsave1, r, anorm, beta [2], maxerr, xnan, rcond,
+ ax, az, bx, bz, cx, cz, dx, dz, ex, ez ;
+ cholmod_sparse *A, *C, *AT, *E, *F, *G, *Sok, *R0, *R1, *Aboth, *Axbad, *I1,
+ *Abad, *R, *Acopy, *R3, *Abad2, *I, *I3, *Abad3, *AA, *Rt, *AF, *AFT,
+ *I7, *C2, *R2, *Z ;
+ cholmod_dense *Xok, *Bok, *Two, *X, *W, *XX, *YY, *Xbad2, *B, *Scale,
+ *Y, *X1, *B1, *B2, *X7, *B7 ;
+ cholmod_factor *L, *L2, *L3, *L4, *L5, *L6, *Lcopy, *Lbad, *L7 ;
+ cholmod_triplet *T, *T2, *Tz, *T3 ;
+ Int *fsetok, *Pok, *Flag, *Head, *Cp, *Ci, *P2, *Parent, *Lperm,
+ *Lp, *Li, *Lnz, *Lprev, *Lnext, *Ls, *Lpi, *Lpx, *Super, *Tj, *Ti,
+ *Enz, *Ep, *Post, *Cmember, *CParent, *Partition, *Pinv, *ATi, *ATp,
+ *LColCount, *ColCount, *First, *Level, *fsetbad, *Pbad, *Lz,
+ *R2p, *R2i ;
+ double *Xwork, *Cx, *x, *Lx, *Tx, *Az, *R2x ;
+ size_t size, nznew, gsave2 ;
+ UF_long lr ;
+ void *pp, *ii, *jj, *xx ;
+ Int p, i, j, d, nrhs, nrow, ncol, stype, fsizeok, nz, ok, n2, trial, anz,
+ nzmax, cset [CSETSIZE], Axbad_type, isreal, xtype, enz, Lxtype, Cxtype,
+ Xxtype, Txtype, Abad2xtype, k, xtype2, Abad3xtype, save1, save2, save3,
+ save4, ok1, fnz ;
+ int option, asym ;
+ FILE *f ;
+
+ beta [0] = 1e-6 ;
+ beta [1] = 0 ;
+ xnan = 0 ;
+
+ xtype = Tok->xtype ;
+ isreal = (xtype == CHOLMOD_REAL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* hypot and divcomplex */
+ /* ---------------------------------------------------------------------- */
+
+ maxerr = 0 ;
+ ax = 4.3 ;
+ az = 9.2 ;
+ for (i = 0 ; i <= 1 ; i++)
+ {
+ if (i == 0)
+ {
+ bx = 3.14159 ;
+ bz = -1.2 ;
+ }
+ else
+ {
+ bx = 0.9 ;
+ bz = -1.2 ;
+ }
+ /* c = a/b */
+ CHOLMOD(divcomplex)(ax, az, bx, bz, &cx, &cz) ;
+ /* d = c*b */
+ dx = cx * bx - cz * bz ;
+ dz = cz * bx + cx * bz ;
+ /* e = d-a, which should be zero */
+ ex = dx - ax ;
+ ez = dz - az ;
+ r = CHOLMOD(hypot)(ex, ez) ;
+ MAXERR (maxerr, r, 1) ;
+ OK (r < 1e-14) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create objects to test */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\n------------------------null2 tests:\n") ;
+
+ cm->error_handler = my_handler ;
+
+ CHOLMOD(check_triplet)(Tok, cm) ;
+ nrhs = 5 ;
+ nrow = Tok->nrow ;
+ ncol = Tok->ncol ;
+ d = nrow + 2 ;
+
+ A = CHOLMOD(triplet_to_sparse)(Tok, 0, cm) ; /* [ */
+
+ anorm = CHOLMOD(norm_sparse)(A, 1, cm) ;
+ anz = A->nzmax ;
+
+ AT = CHOLMOD(transpose)(A, 2, cm) ; /* [ */
+
+ printf ("xtrue:\n") ;
+ Xok = xtrue (nrow, nrhs, d, xtype) ; /* [ */
+
+ printf ("rhs:\n") ;
+ Bok = rhs (A, nrhs, d) ; /* [ */
+ printf ("fset:\n") ;
+
+ fsetok = prand (ncol) ; /* [ */ /* RAND */
+ fsetbad = prand (ncol) ; /* [ */ /* RAND */
+
+ if (ncol > 0)
+ {
+ fsetbad [0] = -1 ;
+ }
+ Pbad = prand (nrow) ; /* [ */ /* RAND */
+
+ if (nrow > 0)
+ {
+ Pbad [0] = -1 ;
+ }
+ I1 = CHOLMOD(speye)(nrow+1, nrow+1, xtype, cm) ; /* [ */
+
+ fsizeok = (ncol < 2) ? ncol : (ncol/2) ;
+ Pok = prand (nrow) ; /* [ */ /* RAND */
+
+ R2 = CHOLMOD(allocate_sparse)(nrow, 1, nrow, FALSE, TRUE, 0, /* [ */
+ CHOLMOD_REAL, cm) ;
+ OKP (R2) ;
+
+ R2p = R2->p ;
+ R2i = R2->i ;
+ R2x = R2->x ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ R2i [i] = Pok [i] ;
+ R2x [i] = 1 ;
+ }
+ R2p [0] = 0 ;
+ R2p [1] = nrow ;
+
+ stype = A->stype ;
+ Two = CHOLMOD(zeros)(1, 1, xtype, cm) ; /* [ */
+ *((double *)(Two->x)) = 2 ;
+
+ Pinv = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ; /* [ */
+ Parent = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ;
+ Post = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ;
+ Cmember = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ;
+ CParent = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ;
+ Partition = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ;
+ ColCount = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ;
+ First = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ;
+ Level = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ;
+
+ printf ("etree:\n") ;
+
+ if (AT->stype >= 0)
+ {
+ /* AT is unsymmetric, or symmetric/upper */
+ CHOLMOD(etree)(AT, Parent, cm) ;
+ }
+ else
+ {
+ /* A is symmetric/upper */
+ CHOLMOD(etree)(A, Parent, cm) ;
+ }
+ CHOLMOD(check_parent)(Parent, nrow, cm) ;
+ for (cm->print = 0 ; cm->print <= ((nrow <= 30) ? 5 : 4) ; cm->print++)
+ {
+ CHOLMOD(print_parent)(Parent, nrow, "Parent", cm) ;
+ }
+ cm->print = 1 ;
+
+ /* get row 0 and row 1 of A */
+ R0 = NULL ;
+ R1 = NULL ;
+ Aboth = NULL ;
+ Sok = NULL ;
+
+ if (isreal)
+ {
+ Aboth = CHOLMOD(copy)(A, 0, 1, cm) ; /* [ */
+ Sok = CHOLMOD(copy)(A, 0, 0, cm) ;
+ Aboth->sorted = FALSE ;
+ }
+
+ if (isreal) /* [ */
+ {
+ if (nrow > 1)
+ {
+ cm->print = 4 ;
+ if (nrow < 10)
+ {
+ ok = CHOLMOD(print_sparse)(Aboth, "Aboth", cm) ; OK (ok) ;
+ }
+ i = 0 ;
+ R0 = CHOLMOD(submatrix)(Aboth, &i, 1, NULL, -1, TRUE, TRUE, cm) ;
+ ok = CHOLMOD(print_sparse)(R0, "Row zero", cm) ; OK (ok) ;
+ i = 1 ;
+ R1 = CHOLMOD(submatrix)(Aboth, &i, 1, NULL, -1, TRUE, TRUE, cm) ;
+ ok = CHOLMOD(print_sparse)(R1, "Row one", cm) ; OK (ok) ;
+ Rt = CHOLMOD(transpose)(R1, 1, cm) ;
+
+ C = CHOLMOD(ssmult)(R0, Rt, 0, TRUE, TRUE, cm) ; OKP (C) ;
+ ok = CHOLMOD(print_sparse)(C, "(Row zero)*(Row one)'", cm) ;OK (ok);
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse)(&Rt, cm) ; OK (ok) ;
+ cm->print = 1 ;
+ }
+ }
+
+ /* Abad: symmetric but not square, or null if A is square */
+ if (A->nrow != A->ncol)
+ {
+ Abad = CHOLMOD(copy_sparse)(A, cm) ; /* [ */
+ Abad->stype = 1 ;
+ }
+ else
+ {
+ Abad = NULL ;
+ }
+
+ /* Abad2: sparse matrix with invalid xtype */
+ printf ("allocate Abad2:\n") ;
+ Abad2 = CHOLMOD(copy_sparse)(A, cm) ; /* [ */
+ cm->print = 4 ;
+ CHOLMOD(print_sparse)(Abad2, "Abad2", cm) ;
+ cm->print = 1 ;
+ Abad2xtype = Abad2->xtype ;
+ Abad2->xtype = -999 ;
+
+ /* Xbad2: dense matrix with invalid xtype */
+ printf ("allocate Xbad2:\n") ;
+ Xbad2 = CHOLMOD(zeros)(2, 2, CHOLMOD_REAL, cm) ; /* [ */
+ Xbad2->xtype = -911 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* expect lots of errors */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\n------------------------null2 tests: ERRORs will occur\n") ;
+ cm->error_handler = NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* transpose */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(transpose)(Abad2, 1, cm) ; NOP (C) ;
+ ok = CHOLMOD(sort)(Abad2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(sort)(NULL, cm) ; NOT (ok) ;
+
+ if (nrow > 0)
+ {
+ C = CHOLMOD(ptranspose)(A, 1, Pbad, NULL, 0, cm) ; NOP (C) ;
+ }
+
+ C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, TRUE,
+ -(A->stype), xtype, cm) ; OKP (C) ;
+ ok = CHOLMOD(transpose_unsym)(A, 1, NULL, NULL, 0,
+ C, cm) ; OK (ok);
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, FALSE,
+ -(A->stype), xtype, cm) ; OKP (C) ;
+ ok = CHOLMOD(transpose_unsym)(A, 1, NULL, NULL, 0,
+ C, cm) ; OK (ok);
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, FALSE,
+ -(A->stype), xtype, cm) ; OKP (C) ;
+ ok = CHOLMOD(transpose_unsym)(A, 1, Pok, NULL, 0,
+ C, cm) ; OK (ok);
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, FALSE,
+ -(A->stype), xtype, cm) ; OKP (C) ;
+ ok = CHOLMOD(transpose_unsym)(A, 1, Pok, fsetok, fsizeok,
+ C, cm) ; OK (ok);
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, FALSE,
+ -(A->stype), xtype, cm) ; OKP (C) ;
+ ok = CHOLMOD(transpose_unsym)(A, 1, NULL, fsetok, fsizeok,
+ C, cm) ; OK (ok);
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ C = CHOLMOD(allocate_sparse)(ncol, nrow, anz, TRUE, FALSE,
+ -(A->stype), CHOLMOD_PATTERN, cm) ; OKP (C) ;
+ ok = CHOLMOD(transpose_unsym)(A, 1, NULL, fsetok, fsizeok,
+ C, cm) ; OK (ok);
+
+ E = CHOLMOD(allocate_sparse)(nrow, ncol, anz, TRUE, FALSE,
+ (A->stype), CHOLMOD_PATTERN, cm) ; OKP (C) ;
+ enz = CHOLMOD(nnz)(E, cm) ;
+ OK (enz == 0) ;
+ ok = CHOLMOD(transpose_unsym)(C, 1, NULL, Pok, nrow,
+ E, cm) ; OK (ok);
+ ok = CHOLMOD(free_sparse)(&E, cm) ; OK (ok) ;
+
+ if (A->nrow != A->ncol)
+ {
+ ok = CHOLMOD(transpose_sym)(A, 1, NULL, C, cm) ; NOT (ok) ;
+ }
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ /* Abad3: sparse matrix with invalid xtype [ */
+ printf ("allocate Abad3:\n") ;
+ C = CHOLMOD(copy_sparse)(A, cm) ;
+ Abad3 = CHOLMOD(transpose)(A, 1, cm) ; OKP (Abad3) ;
+ E = CHOLMOD(transpose)(A, 1, cm) ; OKP (E) ;
+ Abad3xtype = Abad3->xtype ;
+ Abad3->xtype = -999 ;
+
+ ok = CHOLMOD(transpose_sym)(C, 1, NULL, Abad3, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_sym)(Abad3, 1, NULL, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_unsym)(C, 1, NULL, NULL, 0, Abad3, cm) ;NOT (ok);
+ ok = CHOLMOD(transpose_unsym)(Abad3, 1, NULL, NULL, 0, C, cm) ;NOT (ok);
+
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ CHOLMOD(sparse_xtype)(CHOLMOD_COMPLEX, E, cm) ;
+ break ;
+ case CHOLMOD_COMPLEX:
+ CHOLMOD(sparse_xtype)(CHOLMOD_ZOMPLEX, E, cm) ;
+ break ;
+ case CHOLMOD_ZOMPLEX:
+ CHOLMOD(sparse_xtype)(CHOLMOD_COMPLEX, E, cm) ;
+ break ;
+ }
+
+ printf ("mismatch start [:\n") ;
+ ok = CHOLMOD(transpose_sym)(C, 1, NULL, E, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_sym)(E, 1, NULL, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_sym)(C, 2, NULL, E, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_sym)(E, 2, NULL, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_unsym)(C, 1, NULL, NULL, 0, E, cm) ; NOT (ok);
+ ok = CHOLMOD(transpose_unsym)(E, 1, NULL, NULL, 0, C, cm) ; NOT (ok);
+ ok = CHOLMOD(transpose_unsym)(C, 2, NULL, NULL, 0, E, cm) ; NOT (ok);
+ ok = CHOLMOD(transpose_unsym)(E, 2, NULL, NULL, 0, C, cm) ; NOT (ok);
+ printf ("mismatch done ]\n") ;
+
+ printf ("wrong dim [:\n") ;
+ ok = CHOLMOD(transpose_sym)(C, 1, NULL, I1, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_sym)(I1, 1, NULL, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_unsym)(C, 1, NULL, NULL, 0, I1, cm) ; NOT (ok);
+ ok = CHOLMOD(transpose_unsym)(I1, 1, NULL, NULL, 0, C, cm) ; NOT (ok);
+ ok = CHOLMOD(transpose_unsym)(C, 2, NULL, NULL, 0, I1, cm) ; NOT (ok);
+ ok = CHOLMOD(transpose_unsym)(I1, 2, NULL, NULL, 0, C, cm) ; NOT (ok);
+ printf ("wrong dim ]\n") ;
+
+ nz = CHOLMOD(nnz)(C, cm) ;
+ if (nz > 10)
+ {
+ printf ("F too small [:\n") ;
+ F = CHOLMOD(allocate_sparse)(C->ncol, C->nrow, C->nzmax-5, TRUE, TRUE,
+ -(C->stype), C->xtype, cm) ; OKP (F) ;
+ ok = CHOLMOD(transpose_sym)(C, 1, NULL, F, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_unsym)(C, 1, NULL, NULL, 0, F, cm) ; NOT (ok);
+ CHOLMOD(free_sparse)(&F, cm) ;
+ printf ("F too small ]\n") ;
+ }
+
+ ok = CHOLMOD(transpose_unsym)(C, 1, NULL, NULL, 0, NULL, cm) ; NOT (ok);
+ ok = CHOLMOD(transpose_unsym)(NULL, 1, NULL, NULL, 0, C, cm) ; NOT (ok);
+
+ ok = CHOLMOD(transpose_sym)(C, 1, NULL, NULL, cm) ; NOT (ok);
+ ok = CHOLMOD(transpose_sym)(NULL, 1, NULL, C, cm) ; NOT (ok);
+
+ CHOLMOD(free_sparse)(&C, cm) ;
+ CHOLMOD(free_sparse)(&E, cm) ;
+
+ Abad3->xtype = Abad3xtype ;
+ CHOLMOD(free_sparse)(&Abad3, cm) ; /* ] */
+
+ cm->status = CHOLMOD_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* aat */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(aat)(NULL, NULL, 0, 0, cm) ; NOP (C) ;
+ if (stype)
+ {
+ C = CHOLMOD(aat)(A, fsetok, fsizeok, 0, cm) ;
+ NOP (C) ;
+ }
+ else
+ {
+ C = CHOLMOD(aat)(A, fsetok, fsizeok, 0, cm) ; OKP (C) ;
+ CHOLMOD(free_sparse)(&C, cm) ;
+ C = CHOLMOD(aat)(Abad2, fsetok, fsizeok, 0, cm) ; NOP (C) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* add */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(add)(A, NULL, one, one, TRUE, TRUE, cm) ; NOP (C) ;
+ C = CHOLMOD(add)(NULL, AT, one, one, TRUE, TRUE, cm) ; NOP (C) ;
+
+ C = CHOLMOD(add)(A, AT, one, one, TRUE, TRUE, cm) ;
+ if (A->nrow == A->ncol && isreal)
+ {
+ OKP (C) ;
+ /* C should equal 2*A if A=A' */
+ if (stype)
+ {
+ double *s ;
+
+ E = CHOLMOD(copy_sparse)(A, cm) ;
+ CHOLMOD(scale)(Two, CHOLMOD_SCALAR, E, cm) ;
+ F = CHOLMOD(add)(C, E, one, minusone, TRUE, TRUE, cm) ;
+ CHOLMOD(drop)(0., F, cm) ;
+ nz = CHOLMOD(nnz)(F, cm) ;
+ OK (nz == 0) ;
+ CHOLMOD(free_sparse)(&E, cm) ;
+ CHOLMOD(free_sparse)(&F, cm) ;
+
+ Scale = CHOLMOD(zeros)(nrow, 1, CHOLMOD_REAL, cm) ;
+
+ s = Scale->x ;
+ for (i = 0 ; i < nrow ; i++)
+ {
+ s [i] = 2 ;
+ }
+ E = CHOLMOD(copy_sparse)(A, cm) ;
+ CHOLMOD(scale)(Scale, CHOLMOD_ROW, E, cm) ;
+ F = CHOLMOD(add)(C, E, one, minusone, TRUE, TRUE, cm) ;
+ CHOLMOD(drop)(0., F, cm) ;
+ nz = CHOLMOD(nnz)(F, cm) ;
+ r = CHOLMOD(norm_sparse)(F, 0, cm) ;
+ OK (nz == 0) ;
+ CHOLMOD(free_sparse)(&E, cm) ;
+ CHOLMOD(free_sparse)(&F, cm) ;
+
+ E = CHOLMOD(copy_sparse)(A, cm) ;
+ CHOLMOD(scale)(Scale, CHOLMOD_COL, E, cm) ;
+ F = CHOLMOD(add)(C, E, one, minusone, TRUE, TRUE, cm) ;
+ CHOLMOD(drop)(0., F, cm) ;
+ nz = CHOLMOD(nnz)(F, cm) ;
+ r = CHOLMOD(norm_sparse)(F, 0, cm) ;
+ OK (nz == 0) ;
+ CHOLMOD(free_sparse)(&E, cm) ;
+ CHOLMOD(free_sparse)(&F, cm) ;
+
+ for (i = 0 ; i < nrow ; i++)
+ {
+ s [i] = sqrt (2) ;
+ }
+ E = CHOLMOD(copy_sparse)(A, cm) ;
+ CHOLMOD(scale)(Scale, CHOLMOD_SYM, E, cm) ;
+ F = CHOLMOD(add)(C, E, one, minusone, TRUE, TRUE, cm) ;
+ CHOLMOD(drop)(0., F, cm) ;
+ nz = CHOLMOD(nnz)(F, cm) ;
+ r = CHOLMOD(norm_sparse)(F, 0, cm) ;
+ OK (r < 1e-12*anorm) ;
+
+ Scale->x = NULL ;
+ CHOLMOD(scale)(Scale, CHOLMOD_SYM, E, cm) ;
+ Scale->x = s ;
+
+ OKP (E) ;
+ OKP (cm) ;
+ ok = CHOLMOD(scale)(NULL, CHOLMOD_ROW, E, cm) ; NOT (ok) ;
+ ok = CHOLMOD(scale)(Scale, CHOLMOD_SYM, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(scale)(NULL, CHOLMOD_SYM, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(scale)(Scale, -1, E, cm) ; NOT (ok) ;
+
+ CHOLMOD(free_sparse)(&E, cm) ;
+ CHOLMOD(free_sparse)(&F, cm) ;
+ CHOLMOD(free_dense)(&Scale, cm) ;
+
+ }
+ CHOLMOD(free_sparse)(&C, cm) ;
+ }
+ else
+ {
+ NOP (C) ;
+ }
+
+ Axbad = CHOLMOD(copy_sparse)(A, cm) ; /* [ */
+ Axbad_type = Axbad->xtype ;
+ Axbad->xtype = CHOLMOD_COMPLEX ;
+ C = CHOLMOD(add)(A, Axbad, one, one, TRUE, TRUE, cm) ; NOP (C) ;
+
+ if (nrow > 1 && xtype == CHOLMOD_REAL)
+ {
+ /* C = A (0,:) + A (1,:) */
+ C = CHOLMOD(add)(R0, R1, one, one, TRUE, TRUE, cm) ; OKP (C) ;
+ OK (CHOLMOD(check_sparse)(C, cm)) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ }
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse)(NULL, cm) ; OK (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* sparse */
+ /* ---------------------------------------------------------------------- */
+
+ cm->print = 4 ;
+
+ ok = CHOLMOD(reallocate_sparse)(10, NULL, cm) ; NOT (ok) ;
+ C = CHOLMOD(allocate_sparse)(10, 10, 10, TRUE, TRUE, 0, -1, cm) ; NOP (C) ;
+ ok = CHOLMOD(reallocate_sparse)(Abad2->nzmax, Abad2, cm) ; NOT (ok) ;
+ C = CHOLMOD(copy_sparse)(Abad2, cm) ; NOP (C) ;
+ C = CHOLMOD(allocate_sparse)(2, 3, 6, TRUE, TRUE, 1, 0, cm) ; NOP (C) ;
+
+ C = CHOLMOD(copy)(A, 0, -1, cm) ; OKP (C) ;
+ E = unpack (C) ; OKP (E) ;
+ F = CHOLMOD(copy_sparse)(E, cm) ; OKP (F) ;
+ ok = CHOLMOD(sparse_xtype)(CHOLMOD_REAL, C, cm) ; OK (ok) ;
+ ok = CHOLMOD(sparse_xtype)(CHOLMOD_REAL, F, cm) ; OK (ok) ;
+ /* G = C-F */
+ G = CHOLMOD(add)(C, F, one, minusone, TRUE, FALSE, cm) ; OKP (G) ;
+ ok = CHOLMOD(drop)(0., G, cm) ; OK (ok) ;
+ nz = CHOLMOD(nnz)(G, cm) ;
+ CHOLMOD(print_sparse)(C, "C", cm) ;
+ CHOLMOD(print_sparse)(E, "E", cm) ;
+ CHOLMOD(print_sparse)(F, "F", cm) ;
+ CHOLMOD(print_sparse)(G, "G", cm) ;
+
+ OK (nz == 0) ;
+ CHOLMOD(free_sparse)(&C, cm) ;
+ CHOLMOD(free_sparse)(&E, cm) ;
+ CHOLMOD(free_sparse)(&F, cm) ;
+ CHOLMOD(free_sparse)(&G, cm) ;
+
+ cm->print = 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* scale */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(scale)(Two, -1, C, cm) ; NOT (ok) ;
+ if (nrow > 1)
+ {
+ E = CHOLMOD(copy_sparse)(A, cm) ; OKP (E) ;
+ CHOLMOD(scale)(Two, CHOLMOD_ROW, E, cm) ; NOT (ok) ;
+ ok = CHOLMOD(free_sparse)(&E, cm) ; OK (ok) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* amd */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(amd)(NULL, NULL, 0, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(amd)(A, NULL, 0, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(amd)(NULL, NULL, 0, Pok, cm) ; NOT (ok) ;
+ ok = CHOLMOD(amd)(A, NULL, 0, Pok, cm) ; OK (ok) ;
+ cm->current = -1 ;
+ ok = CHOLMOD(amd)(A, NULL, 0, Pok, cm) ; OK (ok) ;
+ cm->current = 0 ;
+ ok = CHOLMOD(print_perm)(Pok, nrow, nrow, "AMD perm", cm) ; OK (ok) ;
+ i = cm->print ;
+ cm->print = 4 ;
+ if (A->nrow < 1000 && isreal)
+ {
+ CHOLMOD(print_sparse)(Aboth, "Aboth", cm) ;
+ ok = CHOLMOD(amd)(Aboth, NULL, 0, Pok, cm) ; OK (ok) ;
+ }
+ cm->print = i ;
+ ok = CHOLMOD(amd)(Abad2, NULL, 0, Pok, cm) ; NOT (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* camd */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NPARTITION
+ ok = CHOLMOD(camd)(NULL, NULL, 0, NULL, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(camd)(A, NULL, 0, NULL, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(camd)(NULL, NULL, 0, NULL, Pok, cm) ; NOT (ok) ;
+ ok = CHOLMOD(camd)(A, NULL, 0, NULL, Pok, cm) ; OK (ok) ;
+ cm->current = -1 ;
+ ok = CHOLMOD(camd)(A, NULL, 0, NULL, Pok, cm) ; OK (ok) ;
+ cm->current = 0 ;
+ ok = CHOLMOD(print_perm)(Pok, nrow, nrow, "CAMD perm", cm) ; OK (ok) ;
+ i = cm->print ;
+ cm->print = 4 ;
+ if (A->nrow < 1000 && isreal)
+ {
+ CHOLMOD(print_sparse)(Aboth, "Aboth", cm) ;
+ ok = CHOLMOD(camd)(Aboth, NULL, 0, NULL, Pok, cm) ; OK (ok) ;
+ }
+ cm->print = i ;
+ ok = CHOLMOD(camd)(Abad2, NULL, 0, NULL, Pok, cm) ; NOT (ok) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* analyze */
+ /* ---------------------------------------------------------------------- */
+
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = -1 ;
+ ok = CHOLMOD(print_common)("Bad cm", cm) ; NOT (ok) ;
+ ok = CHOLMOD(analyze_ordering)(NULL, 0, NULL, NULL, 0,
+ NULL, NULL, NULL, NULL, NULL, cm) ; NOT (ok) ;
+ L = CHOLMOD(analyze)(NULL, cm) ; NOP (L) ;
+ L = CHOLMOD(analyze)(Abad2, cm) ; NOP (L) ;
+ L = CHOLMOD(analyze)(A, cm) ; OKP (L) ;
+ cm->nmethods = 0 ; /* restore defaults */
+ cm->method [0].ordering = CHOLMOD_GIVEN ;
+ cm->print = 4 ;
+ ok = CHOLMOD(print_common)("OKcm", cm) ; OK (ok) ;
+ ok = CHOLMOD(print_factor)(L, "L symbolic", cm) ; OK (ok) ;
+ cm->print = 1 ;
+ ok = CHOLMOD(free_factor)(&L, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_factor)(&L, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_factor)(NULL, cm) ; OK (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* band */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(band)(NULL, 0, 0, 0, cm) ; NOP (C) ;
+ C = CHOLMOD(band)(Abad2, 0, 0, 0, cm) ; NOP (C) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* ccolamd */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NPARTITION
+ ok = CHOLMOD(ccolamd)(NULL, fsetok, fsizeok, NULL, Pok, cm) ; NOT (ok) ;
+ ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, NULL, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, Pok, cm) ;
+ if (stype)
+ {
+ NOT (ok) ;
+ }
+ else
+ {
+ OK (ok) ;
+ }
+
+ cm->current = -1 ;
+ ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, Pok, cm) ;
+ cm->current = 0 ;
+ if (stype)
+ {
+ NOT (ok) ;
+ }
+ else
+ {
+ OK (ok) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* copy */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(print_sparse)(Abad, "Abad", cm) ;
+
+ C = CHOLMOD(copy)(Abad, 0, 1, cm) ;
+ CHOLMOD(print_sparse)(C, "copy of Abad", cm) ;
+ NOP (C) ;
+
+ C = CHOLMOD(copy_sparse)(Abad, cm) ;
+ CHOLMOD(print_sparse)(C, "another copy of Abad", cm) ;
+ NOP (C) ;
+
+ C = CHOLMOD(copy)(A, 0, -1, cm) ; OKP (C) ;
+ OK (nzdiag (C) == 0) ;
+
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* submatrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->nrow == A->ncol)
+ {
+ /* submatrix cannot operation on symmetric matrices */
+ C = CHOLMOD(copy)(A, 1, 0, cm) ; OKP (C) ;
+ E = CHOLMOD(submatrix)(C, NULL, -1, NULL, -1, TRUE, TRUE, cm); NOP (E) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ }
+
+ E = CHOLMOD(submatrix)(Abad2, NULL, -1, NULL, -1, TRUE, TRUE, cm) ; NOP(E) ;
+
+ if (A->stype == 0 && isreal)
+ {
+ /* E = A(:,:) */
+ E = CHOLMOD(submatrix)(NULL, NULL,-1, NULL,-1, TRUE, TRUE, cm) ; NOP(E);
+ E = CHOLMOD(submatrix)(A, NULL, -1, NULL, -1, TRUE, TRUE, cm) ; OKP(E) ;
+ /* C = A-E */
+ C = CHOLMOD(add)(A, E, one, minusone, TRUE, TRUE, cm) ; OKP (C) ;
+ ok = CHOLMOD(drop)(0., C, cm) ; OK (ok) ;
+ ok = CHOLMOD(drop)(0., Abad2, cm) ; NOT(ok) ;
+ nz = CHOLMOD(nnz)(C, cm) ;
+ OK (nz == 0) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse)(&E, cm) ; OK (ok) ;
+
+ i = -1 ;
+ E = CHOLMOD(submatrix)(A, &i, 1, NULL, -1, TRUE, TRUE, cm) ; NOP(E) ;
+ E = CHOLMOD(submatrix)(A, NULL, -1, &i, 1, TRUE, TRUE, cm) ; NOP(E) ;
+ E = CHOLMOD(submatrix)(A, &i, 1, &i, 1, TRUE, TRUE, cm) ; NOP(E) ;
+ i = 0 ;
+ j = -1 ;
+ E = CHOLMOD(submatrix)(A, &i, 1, &j, 1, TRUE, TRUE, cm) ; NOP(E) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(read_sparse)(NULL, cm) ; NOP (C) ;
+ X = CHOLMOD(read_dense)(NULL, cm) ; NOP (X) ;
+ pp = CHOLMOD(read_matrix)(NULL, 1, NULL, cm) ; NOP (pp) ;
+ pp = CHOLMOD(read_matrix)((FILE *) 1, 1, NULL, cm) ; NOP (pp) ;
+ T3 = CHOLMOD(read_triplet)(NULL, cm) ; NOP (T3) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* write */
+ /* ---------------------------------------------------------------------- */
+
+ asym = CHOLMOD(write_sparse) (NULL, NULL, NULL, NULL, cm) ; NOT (asym>=0);
+ asym = CHOLMOD(write_sparse) ((FILE *) 1, NULL, NULL, NULL, cm) ;
+ NOT (asym>=0);
+
+ asym = CHOLMOD(write_dense) (NULL, NULL, NULL, cm) ; NOT (asym>=0);
+ asym = CHOLMOD(write_dense) ((FILE *) 1, NULL, NULL, cm) ; NOT (asym>=0);
+
+ f = fopen ("temp4.mtx", "w") ;
+ asym = CHOLMOD(write_sparse) (f, A, NULL, "garbage.txt", cm) ;
+ fclose (f) ;
+ printf ("write_sparse, asym: %d\n", asym) ;
+ OK (asym == EMPTY) ;
+
+ if (A != NULL)
+ {
+ save1 = A->xtype ;
+ A->xtype = 999 ;
+ f = fopen ("temp4.mtx", "w") ;
+ asym = CHOLMOD(write_sparse) (f, A, NULL, NULL, cm) ;
+ fclose (f) ;
+ printf ("write_sparse, asym: %d\n", asym) ;
+ OK (asym == EMPTY) ;
+ A->xtype = save1 ;
+ }
+
+ Z = CHOLMOD(speye) (nrow+1, ncol+1, CHOLMOD_PATTERN, cm) ;
+ f = fopen ("temp4.mtx", "w") ;
+ asym = CHOLMOD(write_sparse) (f, A, Z, NULL, cm) ;
+ fclose (f) ;
+ printf ("write_sparse, asym: %d with Z\n", asym) ;
+ OK (asym == EMPTY) ;
+
+ Z->xtype = 999 ;
+ f = fopen ("temp4.mtx", "w") ;
+ asym = CHOLMOD(write_sparse) (f, A, Z, NULL, cm) ;
+ fclose (f) ;
+ printf ("write_sparse, asym: %d with Z2\n", asym) ;
+ OK (asym == EMPTY) ;
+ Z->xtype = CHOLMOD_PATTERN ;
+
+ CHOLMOD(free_sparse) (&Z, cm) ;
+
+ Z = CHOLMOD(speye) (0, ncol+1, CHOLMOD_PATTERN, cm) ;
+ f = fopen ("temp4.mtx", "w") ;
+ asym = CHOLMOD(write_sparse) (f, A, Z, NULL, cm) ;
+ fclose (f) ;
+ printf ("write_sparse, asym: %d with Z\n", asym) ;
+ if (A == NULL)
+ {
+ OK (asym == EMPTY) ;
+ }
+ else
+ {
+ OK (asym > EMPTY) ;
+ }
+ CHOLMOD(free_sparse) (&Z, cm) ;
+
+ X = CHOLMOD(ones) (4, 4, CHOLMOD_REAL, cm) ;
+ f = fopen ("temp6.mtx", "w") ;
+ asym = CHOLMOD(write_dense) (f, X, "garbage.txt", cm) ;
+ fclose (f) ;
+ OK (asym == EMPTY) ;
+
+ X->xtype = 999 ;
+ f = fopen ("temp6.mtx", "w") ;
+ asym = CHOLMOD(write_dense) (f, X, NULL, cm) ;
+ fclose (f) ;
+ OK (asym == EMPTY) ;
+ X->xtype = CHOLMOD_REAL ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print_common */
+ /* ---------------------------------------------------------------------- */
+
+ cm->print = 4 ;
+ ok = CHOLMOD(print_common)("Null", NULL) ; NOT (ok) ;
+ for (cm->status = CHOLMOD_INVALID ; cm->status <= CHOLMOD_DSMALL ;
+ cm->status++)
+ {
+ ok = CHOLMOD(print_common)("status", cm) ; OK (ok) ;
+ }
+ cm->status = 999 ;
+ ok = CHOLMOD(print_common)("bad status", cm) ; NOT (ok) ;
+ cm->status = CHOLMOD_OK ;
+
+ Flag = cm->Flag ;
+ cm->Flag = NULL ;
+ ok = CHOLMOD(print_common)("bad Flag", cm) ; NOT (ok) ;
+ cm->Flag = Flag ;
+ ok = CHOLMOD(print_common)("ok Flag", cm) ; OK (ok) ;
+
+ Flag [0] = Int_max ;
+ ok = CHOLMOD(print_common)("bad Flag", cm) ; NOT (ok) ;
+ Flag [0] = -1 ;
+ ok = CHOLMOD(print_common)("ok Flag", cm) ; OK (ok) ;
+
+ Head = cm->Head ;
+ cm->Head = NULL ;
+ ok = CHOLMOD(print_common)("bad Head", cm) ; NOT (ok) ;
+ cm->Head = Head ;
+ ok = CHOLMOD(print_common)("ok Head", cm) ; OK (ok) ;
+
+ Head [0] = Int_max ;
+ ok = CHOLMOD(print_common)("bad Head", cm) ; NOT (ok) ;
+ Head [0] = -1 ;
+ ok = CHOLMOD(print_common)("ok Head", cm) ; OK (ok) ;
+
+ Xwork = cm->Xwork ;
+ cm->Xwork = NULL ;
+ ok = CHOLMOD(print_common)("bad Xwork", cm) ; NOT (ok) ;
+ cm->Xwork = Xwork ;
+ ok = CHOLMOD(print_common)("ok Xwork", cm) ; OK (ok) ;
+
+ Xwork [0] = 1 ;
+ ok = CHOLMOD(print_common)("bad Xwork", cm) ; NOT (ok) ;
+ Xwork [0] = 0 ;
+ ok = CHOLMOD(print_common)("ok Xwork", cm) ; OK (ok) ;
+
+ p = cm->nmethods ;
+ i = cm->method [0].ordering ;
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = 999 ;
+ ok = CHOLMOD(print_common)("bad method", cm) ; NOT (ok) ;
+ cm->nmethods = p ;
+ cm->method [0].ordering = i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print_sparse */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(copy_sparse)(A, cm) ; OKP (C) ;
+
+ cm->print = 3 ;
+ C->itype = EMPTY ;
+ ok = CHOLMOD(print_sparse)(C, "CIbad", cm) ; NOT (ok) ;
+ C->itype = CHOLMOD_INTLONG ;
+ ok = CHOLMOD(print_sparse)(C, "Cibad", cm) ; NOT (ok) ;
+ C->itype = cm->itype ;
+ cm->print = 1 ;
+
+ cm->print = 4 ;
+#ifdef LONG
+ C->itype = CHOLMOD_INT ;
+#else
+ C->itype = CHOLMOD_LONG ;
+#endif
+ ok = CHOLMOD(print_sparse)(C, "Cibad2", cm) ; NOT (ok) ;
+ C->itype = cm->itype ;
+ cm->print = 1 ;
+
+ C->dtype = CHOLMOD_SINGLE ;
+ ok = CHOLMOD(print_sparse)(C, "Cdbad", cm) ; NOT (ok) ;
+ C->dtype = EMPTY ;
+ ok = CHOLMOD(print_sparse)(C, "CDbad", cm) ; NOT (ok) ;
+ C->dtype = CHOLMOD_DOUBLE ;
+
+ Cxtype = C->xtype ;
+ C->xtype = EMPTY ;
+ ok = CHOLMOD(print_sparse)(C, "CXbad", cm) ; NOT (ok) ;
+ C->xtype = Cxtype ;
+
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+
+ C->p = NULL ;
+ ok = CHOLMOD(print_sparse)(C, "Cp bad", cm) ; NOT (ok) ;
+ C->p = Cp ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+
+ C->i = NULL ;
+ ok = CHOLMOD(print_sparse)(C, "Ci bad", cm) ; NOT (ok) ;
+ C->i = Ci ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+
+ C->x = NULL ;
+ ok = CHOLMOD(print_sparse)(C, "Cx bad", cm) ; NOT (ok) ;
+ C->x = Cx ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+
+ Cp [0] = 42 ;
+ ok = CHOLMOD(print_sparse)(C, "Cp [0] bad", cm) ; NOT (ok) ;
+ Cp [0] = 0 ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+
+ p = Cp [ncol] ;
+ Cp [ncol] = C->nzmax + 10 ;
+ ok = CHOLMOD(print_sparse)(C, "Cp [ncol] bad", cm) ; NOT (ok) ;
+ Cp [ncol] = p ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+
+ p = Cp [ncol] ;
+ Cp [ncol] = -1 ;
+ ok = CHOLMOD(print_sparse)(C, "Cp [ncol] neg", cm) ; NOT (ok) ;
+ Cp [ncol] = p ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+
+ if (ncol > 0)
+ {
+ p = Cp [1] ;
+ Cp [1] = 2*nrow + 1 ;
+ ok = CHOLMOD(print_sparse)(C, "Cp [1] bad", cm) ; NOT (ok) ;
+ Cp [1] = p ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+ }
+
+ if (ncol > 2)
+ {
+ p = Cp [2] ;
+ Cp [2] = Cp [1] - 1 ;
+ ok = CHOLMOD(print_sparse)(C, "Cp [2] bad", cm) ; NOT (ok) ;
+ Cp [2] = p ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+ }
+
+ if (Cp [ncol] > 0)
+ {
+ i = Ci [0] ;
+ Ci [0] = -1 ;
+ ok = CHOLMOD(print_sparse)(C, "Ci [0] neg", cm) ; NOT (ok) ;
+ Ci [0] = i ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+ }
+
+ if (ncol > 0 && C->sorted && Cp [1] - Cp [0] > 2)
+ {
+ i = Ci [0] ;
+ Ci [0] = nrow-1 ;
+ ok = CHOLMOD(print_sparse)(C, "Ci [0] unsorted", cm) ; NOT (ok) ;
+ Ci [0] = i ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+ }
+
+ if (ncol > 0 && C->sorted && ncol > 2 && Cp [1] - Cp [0] > 2)
+ {
+ /* swap the first two entries */
+ p = Ci [0] ;
+ Ci [0] = Ci [1] ;
+ Ci [1] = p ;
+ ok = CHOLMOD(print_sparse)(C, "Ci [0] unsorted", cm) ; NOT (ok) ;
+ C->sorted = FALSE ;
+ ok = CHOLMOD(print_sparse)(C, "Ci [0] unsorted", cm) ; OK (ok) ;
+ Ci [1] = Ci [0] ;
+ ok = CHOLMOD(print_sparse)(C, "Ci [0] duplicate", cm) ; NOT (ok) ;
+ Ci [1] = p ;
+ ok = CHOLMOD(print_sparse)(C, "Ci [0] unsorted", cm) ; OK (ok) ;
+ p = Ci [0] ;
+ Ci [0] = Ci [1] ;
+ Ci [1] = p ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+ C->sorted = TRUE ;
+ ok = CHOLMOD(print_sparse)(C, "C ok", cm) ; OK (ok) ;
+ }
+
+ E = CHOLMOD(copy_sparse)(C, cm) ; OKP (E) ;
+ Enz = CHOLMOD(malloc)(ncol, sizeof (Int), cm) ; OKP (Enz) ;
+ E->nz = Enz ;
+ Ep = E->p ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ Enz [j] = Ep [j+1] - Ep [j] ;
+ }
+ E->packed = FALSE ;
+ ok = CHOLMOD(print_sparse)(E, "E unpacked ok", cm) ; OK (ok) ;
+
+ ok = CHOLMOD(band_inplace)(0, 0, 0, E, cm) ; NOT (ok) ;
+
+ E->nz = NULL ;
+ ok = CHOLMOD(print_sparse)(E, "E unpacked bad", cm) ; NOT (ok) ;
+ E->nz = Enz ;
+ ok = CHOLMOD(print_sparse)(E, "E unpacked ok", cm) ; OK (ok) ;
+
+ F = CHOLMOD(copy)(E, 0, 0, cm) ;
+ cm->print = 4 ;
+ ok = CHOLMOD(print_sparse)(F, "F pattern ok", cm) ; OK (ok) ;
+ cm->print = 1 ;
+
+ CHOLMOD(free_sparse)(&F, cm) ;
+ CHOLMOD(free_sparse)(&E, cm) ;
+ CHOLMOD(free_sparse)(&C, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print_dense */
+ /* ---------------------------------------------------------------------- */
+
+ X = CHOLMOD(sparse_to_dense)(NULL, cm) ; NOP (X) ;
+ X = CHOLMOD(sparse_to_dense)(Abad2, cm) ; NOP (X) ;
+ C = CHOLMOD(dense_to_sparse)(NULL, TRUE, cm) ; NOP (C) ;
+
+ X = CHOLMOD(copy_dense)(Xok, cm) ;
+
+ ok = CHOLMOD(print_dense)(NULL, "null", cm) ; NOT (ok) ;
+
+ x = X->x ;
+ X->x = NULL ;
+ ok = CHOLMOD(print_dense)(X, "Xnull", cm) ; NOT (ok) ;
+ X->x = x ;
+ ok = CHOLMOD(print_dense)(X, "X OK", cm) ; OK (ok) ;
+
+ X->nzmax = 1 ;
+ ok = CHOLMOD(print_dense)(X, "X nzmax too small", cm) ; NOT (ok) ;
+ X->nzmax = Xok->nzmax ;
+ ok = CHOLMOD(print_dense)(X, "X OK", cm) ; OK (ok) ;
+
+ X->d = -1 ;
+ ok = CHOLMOD(print_dense)(X, "X d too small", cm) ; NOT (ok) ;
+ X->d = Xok->d ;
+ ok = CHOLMOD(print_dense)(X, "X OK", cm) ; OK (ok) ;
+
+ Xxtype = X->xtype ;
+ X->xtype = CHOLMOD_PATTERN ;
+ ok = CHOLMOD(print_dense)(X, "X pattern", cm) ; NOT (ok) ;
+
+ X->xtype = -1 ;
+ ok = CHOLMOD(print_dense)(X, "X unknown", cm) ; NOT (ok) ;
+ X->xtype = Xxtype ;
+ ok = CHOLMOD(print_dense)(X, "X OK", cm) ; OK (ok) ;
+
+ X->dtype = CHOLMOD_SINGLE ;
+ ok = CHOLMOD(print_dense)(X, "X float", cm) ; NOT (ok) ;
+ X->dtype = -1 ;
+ ok = CHOLMOD(print_dense)(X, "X unknown", cm) ; NOT (ok) ;
+ X->dtype = CHOLMOD_DOUBLE ;
+ ok = CHOLMOD(print_dense)(X, "X OK", cm) ; OK (ok) ;
+
+ CHOLMOD(free_dense)(&X, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print_subset */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(check_subset)(NULL, 0, 0, cm) ; OK (ok) ;
+ ok = CHOLMOD(print_subset)(NULL, 0, 0, "null", cm) ; OK (ok) ;
+
+ for (i = 0 ; i < CSETSIZE ; i++)
+ {
+ cset [i] = i ;
+ }
+
+ for (cm->print = 0 ; cm->print <= 5 ; cm->print++)
+ {
+ ok = CHOLMOD(print_subset)(NULL, -1, 10, "[0:9]", cm) ;
+ OK (ok) ;
+ ok = CHOLMOD(print_subset)(cset, CSETSIZE, CSETSIZE, "cset OK", cm) ;
+ OK (ok) ;
+ cset [0] = -1 ;
+ ok = CHOLMOD(print_subset)(cset, CSETSIZE, CSETSIZE, "cset bad", cm) ;
+ NOT (ok) ;
+ cset [0] = CSETSIZE-1 ;
+ ok = CHOLMOD(print_subset)(cset, CSETSIZE, CSETSIZE, "cset OK", cm) ;
+ OK (ok) ;
+ }
+
+ cm->print = 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print_perm */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(check_perm)(NULL, 0, 0, cm) ; OK (ok) ;
+
+ for (cm->print = 3 ; cm->print <= 4 ; cm->print++)
+ {
+ ok = CHOLMOD(print_perm)(Pok, nrow, nrow, "P OK", cm) ;
+ OK (ok) ;
+ if (nrow > 0)
+ {
+ p = Pok [0] ;
+ Pok [0] = 2*ncol + 1 ;
+ ok = CHOLMOD(print_perm)(Pok, nrow, nrow, "P bad", cm) ;
+ NOT (ok) ;
+ Pok [0] = p ;
+ ok = CHOLMOD(print_perm)(Pok, nrow, nrow, "P OK", cm) ;
+ }
+ OK (ok) ;
+ }
+ cm->print = 1 ;
+
+ n2 = 2 * cm->nrow ;
+ P2 = prand (n2) ; /* RAND */
+
+ for (cm->print = 3 ; cm->print <= 4 ; cm->print++)
+ {
+ ok = CHOLMOD(print_perm)(P2, n2, n2, "P2 OK", cm) ;
+ OK (ok) ;
+ p = P2 [0] ;
+ P2 [0] = -1 ;
+ ok = CHOLMOD(print_perm)(P2, n2, n2, "P2 bad", cm) ;
+ NOT (ok) ;
+ P2 [0] = p ;
+ ok = CHOLMOD(print_perm)(P2, n2, n2, "P2 OK", cm) ;
+ OK (ok) ;
+ }
+ cm->print = 1 ;
+
+ CHOLMOD(free)(2 * (cm->nrow), sizeof (Int), P2, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print_parent */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(print_parent)(NULL, 0, "null", cm) ; NOT (ok) ;
+ if (nrow > 0)
+ {
+ i = Parent [0] ;
+ Parent [0] = -2 ;
+ ok = CHOLMOD(print_parent)(Parent, nrow, "bad Parent", cm) ; NOT (ok) ;
+ Parent [0] = i ;
+ ok = CHOLMOD(print_parent)(Parent, nrow, "OK Parent", cm) ; OK (ok) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print_factor */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0)
+ {
+ L = CHOLMOD(allocate_factor)(nrow, cm) ; OKP (L) ;
+ ok = CHOLMOD(super_symbolic)(A, NULL, Parent, L, cm) ; NOT (ok) ;
+ CHOLMOD(free_factor)(&L, cm) ;
+ }
+
+ ok = CHOLMOD(print_factor)(NULL, "L null", cm) ; NOT (ok) ;
+
+ /* create a valid symbolic supernodal L */
+ cm->supernodal = CHOLMOD_SUPERNODAL ;
+ cm->final_asis = TRUE ;
+ L = CHOLMOD(analyze)(A, cm) ; /* [ */ OKP (L) ;
+ ok = CHOLMOD(print_factor)(L, "L ok", cm) ; OK (ok) ;
+
+ ok = CHOLMOD(change_factor)(CHOLMOD_ZOMPLEX, TRUE, TRUE, TRUE, TRUE, L, cm);
+ NOT (ok) ;
+
+ OK (L->xtype == CHOLMOD_PATTERN) ;
+ OK (L->is_super) ;
+
+ L->itype = CHOLMOD_INTLONG ;
+ ok = CHOLMOD(print_factor)(L, "L int/UF_long", cm) ; NOT (ok) ;
+ L->itype = -1 ;
+ ok = CHOLMOD(print_factor)(L, "L int unknown", cm) ; NOT (ok) ;
+ L->itype = cm->itype ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ cm->print = 4 ;
+#ifdef LONG
+ L->itype = CHOLMOD_INT ;
+#else
+ L->itype = CHOLMOD_LONG ;
+#endif
+ ok = CHOLMOD(print_factor)(L, "L bad itype", cm) ; NOT (ok) ;
+ L->itype = cm->itype ;
+ cm->print = 1 ;
+
+ cm->print = 4 ;
+
+ i = L->ordering ;
+ L->ordering = -1 ;
+ ok = CHOLMOD(print_factor)(L, "L bad ordering", cm) ; NOT (ok) ;
+ L->ordering = CHOLMOD_GIVEN ;
+ ok = CHOLMOD(print_factor)(L, "L given ordering", cm) ; OK (ok) ;
+ L->ordering = i ;
+
+ Lxtype = L->xtype ;
+ L->xtype = CHOLMOD_REAL ;
+ ok = CHOLMOD(print_factor)(L, "L real", cm) ; NOT (ok) ;
+ L->xtype = CHOLMOD_COMPLEX ;
+ ok = CHOLMOD(print_factor)(L, "L complex", cm) ; NOT (ok) ;
+ L->xtype = CHOLMOD_ZOMPLEX ;
+ ok = CHOLMOD(print_factor)(L, "L zomplex", cm) ; NOT (ok) ;
+ L->xtype = -1 ;
+ ok = CHOLMOD(print_factor)(L, "L unknown", cm) ; NOT (ok) ;
+ L->xtype = CHOLMOD_PATTERN ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+ L->xtype = Lxtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal factor */
+ /* ---------------------------------------------------------------------- */
+
+ /* create a valid supernodal numeric L (simplicial if Supernodal
+ * module not installed) */
+ ok = CHOLMOD(factorize)(A, L, cm) ;
+ OK (ok || cm->status == CHOLMOD_NOT_POSDEF) ;
+
+ if (L->is_super)
+ {
+ /* there is no supernodal zomplex L */
+ ok = CHOLMOD(factor_xtype)(CHOLMOD_ZOMPLEX, L, cm) ; NOT (ok) ;
+ }
+
+ /* pack the simplicial factor, or return silently if supernodal */
+ ok = CHOLMOD(pack_factor)(L, cm) ; OK (ok) ;
+
+ Lbad = CHOLMOD(copy_factor)(L, cm) ; /* [ */
+ Lxtype = L->xtype ;
+ Lbad->xtype = -1 ;
+
+ OK (L->is_super && L->xtype != CHOLMOD_PATTERN && L->is_ll) ;
+
+ if (A->stype == 0)
+ {
+ ok = CHOLMOD(super_symbolic)(A, NULL, Parent, L, cm) ; NOT (ok) ;
+ }
+ ok = CHOLMOD(super_symbolic)(A, Abad2, Parent, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_symbolic)(Abad2, A, Parent, L, cm) ; NOT (ok) ;
+
+ W = CHOLMOD(zeros)(nrow, 1, L->xtype, cm) ; OKP (W) ;
+ X = CHOLMOD(ones)(nrow, 1, L->xtype, cm) ; OKP (X) ;
+ ok = CHOLMOD(super_lsolve)(L, X, W, cm) ; OK (ok) ;
+ ok = CHOLMOD(super_ltsolve)(L, X, W, cm) ; OK (ok) ;
+
+ ok = CHOLMOD(super_lsolve)(Lbad, X, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve)(Lbad, X, W, cm) ; NOT (ok) ;
+
+ XX = CHOLMOD(zeros)(nrow, 1,
+ L->xtype == CHOLMOD_REAL ? CHOLMOD_COMPLEX : CHOLMOD_REAL, cm) ;
+ ok = CHOLMOD(super_lsolve)(L, X, XX, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve)(L, X, XX, cm) ; NOT (ok) ;
+ CHOLMOD(free_dense)(&XX, cm) ;
+
+ ok = CHOLMOD(super_lsolve)(L, X, W, cm) ; OK (ok) ;
+ ok = CHOLMOD(super_ltsolve)(L, X, W, cm) ; OK (ok) ;
+
+ x = X->x ;
+ X->x = NULL ;
+ ok = CHOLMOD(super_lsolve)(L, X, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve)(L, X, W, cm) ; NOT (ok) ;
+ X->x = x ;
+
+ x = W->x ;
+ W->x = NULL ;
+ ok = CHOLMOD(super_lsolve)(L, X, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve)(L, X, W, cm) ; NOT (ok) ;
+ W->x = x ;
+ CHOLMOD(free_dense)(&X, cm) ;
+ CHOLMOD(free_dense)(&W, cm) ;
+
+ cm->precise = TRUE ;
+ ok = CHOLMOD(print_factor)(L, "L supernodal (precise)", cm) ; OK (ok) ;
+ cm->precise = FALSE ;
+ ok = CHOLMOD(print_factor)(L, "L supernodal", cm) ; OK (ok) ;
+ cm->print = 1 ;
+
+ /* cannot realloc a supernodal L */
+ ok = CHOLMOD(reallocate_factor)(10000, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(reallocate_factor)(10000, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(pack_factor)(NULL, cm) ; NOT (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print factor */
+ /* ---------------------------------------------------------------------- */
+
+ Lxtype = L->xtype ;
+
+ i = cm->print ;
+ cm->print = 4 ;
+ L->xtype = CHOLMOD_PATTERN ;
+ ok = CHOLMOD(print_factor)(L, "L pattern", cm) ; OK (ok) ;
+ C = CHOLMOD(factor_to_sparse)(L, cm) ; NOP (C) ;
+ L->xtype = Lxtype ;
+ cm->print = i ;
+
+ /* check with bad L factor */
+ ok = CHOLMOD(print_factor)(Lbad, "L unknown", cm) ; NOT (ok) ;
+ ok = CHOLMOD(reallocate_factor)(999, Lbad, cm) ; NOT (ok) ;
+ ok = CHOLMOD(pack_factor)(Lbad, cm) ; NOT (ok) ;
+ C = CHOLMOD(factor_to_sparse)(Lbad, cm) ; NOP (C) ;
+ L2 = CHOLMOD(copy_factor)(Lbad, cm) ; NOP (L2) ;
+ ok = CHOLMOD(factorize)(A, Lbad, cm) ; NOT (ok) ;
+ ok = CHOLMOD(resymbol)(A, NULL, 0, TRUE, Lbad, cm) ; NOT (ok) ;
+ ok = CHOLMOD(resymbol_noperm)(A, NULL, 0, TRUE, Lbad, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowadd)(nrow-2, A, Lbad, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowdel)(nrow-2, NULL, Lbad, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowfac)(A, AT, beta, 1, 2, Lbad, cm) ; NOT (ok) ;
+ ok = CHOLMOD(updown)(+1, A, Lbad, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ L->dtype = CHOLMOD_SINGLE ;
+ ok = CHOLMOD(print_factor)(L, "L float", cm) ; NOT (ok) ;
+ L->dtype = -1 ;
+ ok = CHOLMOD(print_factor)(L, "L unknown", cm) ; NOT (ok) ;
+ L->dtype = CHOLMOD_DOUBLE ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ if (nrow > 0)
+ {
+ Lperm = L->Perm ;
+ p = Lperm [0] ;
+ Lperm [0] = -1 ;
+ ok = CHOLMOD(print_factor)(L, "L perm invalid", cm) ; NOT (ok) ;
+ Lperm [0] = p ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+ }
+
+ LColCount = L->ColCount ;
+ L->ColCount = NULL ;
+ ok = CHOLMOD(print_factor)(L, "L no colcount", cm) ; NOT (ok) ;
+ L->ColCount = LColCount ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ if (nrow > 0)
+ {
+ LColCount = L->ColCount ;
+ p = LColCount [0] ;
+ LColCount [0] = -1 ;
+ ok = CHOLMOD(print_factor)(L, "L colcount vad", cm) ; NOT (ok) ;
+ LColCount [0] = p ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print simplicial factor */
+ /* ---------------------------------------------------------------------- */
+
+ /* check LDL' unpacked */
+ ok = CHOLMOD(print_factor)(L, "L OK for L2 copy", cm) ; OK (ok) ;
+ L2 = CHOLMOD(copy_factor)(L, cm) ; /* [ */ OKP (L2) ;
+ ok = CHOLMOD(change_factor)(L->xtype, FALSE, FALSE, FALSE,
+ TRUE, L2, cm) ;
+
+ /* check LDL' packed */
+ L3 = CHOLMOD(copy_factor)(L, cm) ; OKP (L3) ;
+ ok = CHOLMOD(change_factor)(L->xtype, FALSE, FALSE, TRUE,
+ TRUE, L3, cm) ;
+ ok = CHOLMOD(print_factor)(L3, "L3 OK", cm) ; OK (ok) ;
+ CHOLMOD(free_factor)(&L3, cm) ; OK (ok) ;
+ ok = CHOLMOD(print_factor)(L2, "L2 OK", cm) ; OK (ok) ;
+ ok = CHOLMOD(pack_factor)(L2, cm) ; OK (ok) ;
+ ok = CHOLMOD(print_factor)(L2, "L2 OK packed", cm) ; OK (ok) ;
+
+ /* create a simplicial factor from scratch */
+ cm->supernodal = CHOLMOD_SIMPLICIAL ;
+ cm->final_asis = TRUE ;
+ L6 = CHOLMOD(analyze)(A, cm) ; /* [ */ OKP (L6) ;
+ ok = CHOLMOD(factorize)(A, L6, cm) ;
+ OK (cm->status >= CHOLMOD_OK) ;
+ cm->supernodal = CHOLMOD_AUTO ;
+
+ ok = CHOLMOD(print_sparse)(A, "A OK", cm) ; OK (ok) ;
+ ok = CHOLMOD(print_factor)(L6, "L6 OK", cm) ; OK (ok) ;
+
+ Lz = L6->z ;
+ L6->z = NULL ;
+ ok = CHOLMOD(print_factor)(L6, "L6 no z", cm) ;
+ if (L6->xtype == CHOLMOD_ZOMPLEX)
+ {
+ NOT (ok) ;
+ }
+ else
+ {
+ OK (ok) ;
+ }
+ L6->z = Lz ;
+ CHOLMOD(free_factor)(&L6, cm) ; /* ] */
+
+ Az = A->z ;
+ A->z = NULL ;
+ ok = CHOLMOD(print_sparse)(A, "A no z", cm) ;
+ if (A->xtype == CHOLMOD_ZOMPLEX)
+ {
+ NOT (ok) ;
+ }
+ else
+ {
+ OK (ok) ;
+ }
+ A->z = Az ;
+
+ Lp = L2->p ;
+ Li = L2->i ;
+ Lx = L2->x ;
+ Lnz = L2->nz ;
+ Lnext = L2->next ;
+ Lprev = L2->prev ;
+
+ OK (Lp [0] == 0) ;
+
+ L2->p = NULL ;
+ ok = CHOLMOD(print_factor)(L2, "L no p", cm) ; NOT (ok) ;
+ L2->p = Lp ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ L2->i = NULL ;
+ ok = CHOLMOD(print_factor)(L2, "L no i", cm) ; NOT (ok) ;
+ L2->i = Li ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ L2->x = NULL ;
+ ok = CHOLMOD(print_factor)(L2, "L no x", cm) ; NOT (ok) ;
+ L2->x = Lx ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ L2->nz = NULL ;
+ ok = CHOLMOD(print_factor)(L2, "L no nz", cm) ; NOT (ok) ;
+ L2->nz = Lnz ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ L2->next = NULL ;
+ ok = CHOLMOD(print_factor)(L2, "L no next", cm) ; NOT (ok) ;
+ L2->next = Lnext ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ L2->prev = NULL ;
+ ok = CHOLMOD(print_factor)(L2, "L no prev", cm) ; NOT (ok) ;
+ L2->prev = Lprev ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ if (nrow > 0)
+ {
+ p = Lp [0] ;
+ Lp [0] = -1 ;
+ ok = CHOLMOD(print_factor)(L2, "Lp bad", cm) ; NOT (ok) ;
+ Lp [0] = p ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ p = Li [0] ;
+ Li [0] = -1 ;
+ ok = CHOLMOD(print_factor)(L2, "Li bad", cm) ; NOT (ok) ;
+ Li [0] = p ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ p = Lnz [0] ;
+ Lnz [0] = -1 ;
+ ok = CHOLMOD(print_factor)(L2, "Lnz bad", cm) ; NOT (ok) ;
+ Lnz [0] = p ;
+ }
+
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ OK (Lnz != NULL) ;
+
+ if (nrow > 0 && Lnz [0] > 3)
+ {
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+ p = Li [1] ;
+ Li [1] = nrow ;
+ ok = CHOLMOD(print_factor)(L2, "Li bad", cm) ; NOT (ok) ;
+ Li [1] = p ;
+ ok = CHOLMOD(print_factor)(L2, "L OK again", cm) ; OK (ok) ;
+
+ p = Li [2] ;
+ Li [2] = Li [1] ;
+ ok = CHOLMOD(print_factor)(L2, "Li bad", cm) ; NOT (ok) ;
+ Li [2] = p ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+ }
+
+ /* check LDL' dynamic link list */
+ ok = CHOLMOD(change_factor)(L->xtype, FALSE, FALSE, FALSE,
+ FALSE, L2, cm) ;
+ OK (ok) ;
+ ok = CHOLMOD(print_factor)(L2, "L2 OK", cm) ; OK (ok) ;
+ OK (L2->xtype != CHOLMOD_PATTERN && !(L2->is_ll) && !(L2->is_super)) ;
+
+ /* cannot do a supernodal factorization on a dynamic LDL' factor */
+ ok = CHOLMOD(super_numeric)(AT, NULL, Zero, L2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_numeric)(I1, NULL, Zero, L2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_numeric)(I1, I1, Zero, L2, cm) ; NOT (ok) ;
+
+ G = CHOLMOD(copy)(I1, 1, 0, cm) ; OKP (G) ;
+ ok = CHOLMOD(super_numeric)(G, NULL, Zero, L2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(free_sparse)(&G, cm) ; OK (ok) ;
+
+ G = CHOLMOD(copy)(I1, -1, 0, cm) ; OKP (G) ;
+ ok = CHOLMOD(super_numeric)(G, NULL, Zero, L2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(free_sparse)(&G, cm) ; OK (ok) ;
+
+ ok = CHOLMOD(super_numeric)(AT, I1, Zero, L2, cm) ; NOT (ok) ;
+ W = CHOLMOD(zeros)(nrow, 1, CHOLMOD_REAL, cm) ; OKP (W) ;
+ X = CHOLMOD(ones)(nrow, 1, CHOLMOD_REAL, cm) ; OKP (X) ;
+ ok = CHOLMOD(super_lsolve)(L2, X, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve)(L2, X, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(free_dense)(&W, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_dense)(&X, cm) ; OK (ok) ;
+
+ Lnext = L2->next ;
+ Lprev = L2->prev ;
+
+ if (nrow > 3)
+ {
+
+ p = Lnext [nrow+1] ;
+ Lnext [nrow+1] = -1 ;
+ ok = CHOLMOD(print_factor)(L2, "Lnext bad", cm) ; NOT (ok) ;
+ Lnext [nrow+1] = -p ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ p = Lnext [2] ;
+ Lnext [2] = 2 ;
+ ok = CHOLMOD(print_factor)(L2, "Lnext bad", cm) ; NOT (ok) ;
+ Lnext [2] = p ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ p = Lnext [2] ;
+ Lnext [2] = -1 ;
+ ok = CHOLMOD(print_factor)(L2, "Lnext bad", cm) ; NOT (ok) ;
+ Lnext [2] = p ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ p = Lprev [2] ;
+ Lprev [2] = -9 ;
+ ok = CHOLMOD(print_factor)(L2, "Lprev bad", cm) ; NOT (ok) ;
+ Lprev [2] = p ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ p = Lnext [nrow] ;
+ Lnext [nrow] = 0 ;
+ ok = CHOLMOD(print_factor)(L2, "Lnext/prev bad", cm) ; NOT (ok) ;
+ Lnext [nrow] = p ;
+ ok = CHOLMOD(print_factor)(L2, "L OK", cm) ; OK (ok) ;
+
+ /* make a non-monotonic copy of L2 and then mangle it */
+ L6 = CHOLMOD(copy_factor)(L2, cm) ;
+ ok = CHOLMOD(reallocate_column)(0, nrow, L6, cm) ;
+ if (ok && !(L6->is_monotonic))
+ {
+ ok = CHOLMOD(print_factor)(L6, "L6 monotonic OK ", cm) ; OK (ok) ;
+ L6->is_monotonic = TRUE ;
+ ok = CHOLMOD(print_factor)(L6, "L6 monotonic bad", cm) ; NOT (ok) ;
+ }
+ CHOLMOD(free_factor)(&L6, cm) ;
+ }
+
+
+ L6 = CHOLMOD(copy_factor)(L, cm) ; OKP (L6) ;
+ I = CHOLMOD(speye)(nrow, nrow, L->xtype, cm) ; OKP (I) ;
+ I3 = CHOLMOD(speye)(nrow, nrow, L->xtype-1, cm) ; OKP (I3) ;
+
+
+ ok = CHOLMOD(super_numeric)(I, I, beta, L6, cm) ; OK (ok) ;
+ ok = CHOLMOD(super_numeric)(I, I3, beta, L6, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_numeric)(I, Abad2, beta, L6, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_numeric)(I, I, beta, Lbad, cm) ; NOT (ok) ;
+ I->stype = -1 ;
+ ok = CHOLMOD(super_numeric)(I, I, beta, L6, cm) ; OK (ok) ;
+ ok = CHOLMOD(super_numeric)(I, NULL, beta, L6, cm) ; OK (ok) ;
+ I3->stype = -1 ;
+
+ cm->print = 4 ;
+ CHOLMOD(print_sparse)(I3, "I3", cm) ;
+ CHOLMOD(print_factor)(L6, "L6", cm) ;
+ cm->print = 1 ;
+
+ ok = CHOLMOD(super_numeric)(I3, NULL, beta, L6, cm) ; NOT (ok) ;
+ CHOLMOD(free_sparse)(&I, cm) ;
+ I = CHOLMOD(speye)(nrow+1, nrow+1, L->xtype, cm) ; OKP (I) ;
+ I->stype = -1 ;
+ ok = CHOLMOD(super_numeric)(I, I, beta, L6, cm) ; NOT (ok) ;
+
+
+ CHOLMOD(free_sparse)(&I, cm) ;
+ CHOLMOD(free_sparse)(&I3, cm) ;
+ ok = CHOLMOD(free_factor)(&L6, cm) ; OK (ok) ;
+
+ /* check the supernodal L */
+ Ls = L->s ;
+ Lpi = L->pi ;
+ Lpx = L->px ;
+ Super = L->super ;
+ Lx = L->x ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ L->s = NULL ;
+ ok = CHOLMOD(print_factor)(L, "L no s", cm) ; NOT (ok) ;
+ L->s = Ls ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ L->pi = NULL ;
+ ok = CHOLMOD(print_factor)(L, "L no pi", cm) ; NOT (ok) ;
+ L->pi = Lpi ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ L->px = NULL ;
+ ok = CHOLMOD(print_factor)(L, "L no px", cm) ; NOT (ok) ;
+ L->px = Lpx ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ L->super = NULL ;
+ ok = CHOLMOD(print_factor)(L, "L no super", cm) ; NOT (ok) ;
+ L->super = Super ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+
+ L->x = NULL ;
+ ok = CHOLMOD(print_factor)(L, "L no x", cm) ; NOT (ok) ;
+ L->x = Lx ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ p = Ls [0] ;
+ Ls [0] = -1 ;
+ ok = CHOLMOD(print_factor)(L, "L bad s", cm) ; NOT (ok) ;
+ Ls [0] = p ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ p = Lpi [0] ;
+ Lpi [0] = -1 ;
+ ok = CHOLMOD(print_factor)(L, "L bad pi", cm) ; NOT (ok) ;
+ Lpi [0] = p ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ p = Lpx [0] ;
+ Lpx [0] = -1 ;
+ ok = CHOLMOD(print_factor)(L, "L bad px", cm) ; NOT (ok) ;
+ Lpx [0] = p ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ if (nrow > 0)
+ {
+ p = Super [0] ;
+ Super [0] = -1 ;
+ ok = CHOLMOD(print_factor)(L, "L bad super", cm) ; NOT (ok) ;
+ Super [0] = p ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+
+ p = Ls [0] ;
+ Ls [0] = 42 ;
+ ok = CHOLMOD(print_factor)(L, "L bad s", cm) ; NOT (ok) ;
+ Ls [0] = p ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+ }
+
+ if (nrow > 0 && Lpi [1] - Lpi [0] > 3)
+ {
+ p = Ls [2] ;
+ Ls [2] = Ls [1] ;
+ ok = CHOLMOD(print_factor)(L, "L unsorted s", cm) ; NOT (ok) ;
+ Ls [2] = p ;
+ ok = CHOLMOD(print_factor)(L, "L OK", cm) ; OK (ok) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Cholesky */
+ /* ---------------------------------------------------------------------- */
+
+ /* test the supernodal symbolic L */
+ L3 = CHOLMOD(copy_factor)(L, cm) ; OKP (L3) ;
+ ok = CHOLMOD(change_factor)(CHOLMOD_PATTERN, TRUE, TRUE, TRUE, TRUE,
+ L3, cm) ;
+ OK (ok) ;
+
+ Ls = L3->s ;
+ Lpi = L3->pi ;
+ Super = L3->super ;
+
+ if (nrow > 0)
+ {
+ p = Ls [0] ;
+ Ls [0] = 42 ;
+ ok = CHOLMOD(print_factor)(L3, "Lsym bad s", cm) ; NOT (ok) ;
+ Ls [0] = p ;
+ ok = CHOLMOD(print_factor)(L3, "Lsym OK", cm) ; OK (ok) ;
+ }
+
+ if (nrow > 0 && Lpi [1] - Lpi [0] > 3)
+ {
+ p = Ls [2] ;
+ Ls [2] = Ls [1] ;
+ ok = CHOLMOD(print_factor)(L3, "Lsym unsorted s", cm) ; NOT (ok) ;
+ Ls [2] = p ;
+ ok = CHOLMOD(print_factor)(L3, "Lsym OK", cm) ; OK (ok) ;
+ }
+
+ if (nrow > 0 && L->nsuper > 0)
+ {
+ Int nscol = Super [1] ;
+ Int nsrow = Lpi [1] - Lpi [0] ;
+ if (nsrow > nscol + 1)
+ {
+ p = Ls [nscol] ;
+ Ls [nscol] = Ls [nscol+1] ;
+ ok = CHOLMOD(print_factor)(L3, "Lsym unsorted s2", cm) ; NOT (ok) ;
+ Ls [nscol] = p ;
+ ok = CHOLMOD(print_factor)(L3, "Lsym OK", cm) ; OK (ok) ;
+ }
+ }
+ CHOLMOD(free_factor)(&L3, cm) ;
+
+ /* (re)factorize as LL' */
+ L5 = CHOLMOD(copy_factor)(L, cm) ; /* [ */ OKP (L5) ;
+
+ ok = CHOLMOD(factor_xtype)(-1, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(factor_xtype)(CHOLMOD_REAL, NULL, cm) ; NOT (ok) ;
+
+ L3 = CHOLMOD(copy_factor)(L, cm) ; OKP (L3) ;
+ CHOLMOD(print_factor)(L3, "L3 before factorize", cm) ;
+ ok = CHOLMOD(change_factor)(L3->xtype, TRUE, FALSE, TRUE, TRUE, L3, cm) ;
+ OK (ok) ;
+
+ Acopy = CHOLMOD(copy_sparse)(A, cm) ; /* [ */
+ CHOLMOD(sparse_xtype)(L3->xtype, Acopy, cm) ;
+
+ CHOLMOD(print_sparse)(Acopy, "Acopy for factorize", cm) ;
+
+ ok = CHOLMOD(factorize)(Acopy, L3, cm) ;
+ OK (ok || cm->status >= CHOLMOD_OK) ;
+ ok = CHOLMOD(free_factor)(&L3, cm) ; OK (ok) ;
+
+ CHOLMOD(print_sparse)(A, "A for factorize", cm) ;
+ CHOLMOD(print_factor)(L3, "L3 for factorize", cm) ;
+
+ /* refactor, but with wrong-sized A */
+ ok = CHOLMOD(print_sparse)(I1, "I1", cm) ; OK (ok) ;
+ ok = CHOLMOD(factorize)(I1, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(factorize)(Abad2, L, cm) ; NOT (ok) ;
+ C = CHOLMOD(transpose)(I1, 0, cm) ; OKP (C) ;
+ ok = CHOLMOD(print_sparse)(C, "C = I1'", cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ ok = CHOLMOD(print_factor)(L, "L OK ", cm) ; OK (ok) ;
+
+ /* refactor, with invalid A (NULL, or symmetric but not square) */
+ ok = CHOLMOD(print_sparse)(Abad, "Abad", cm) ; NOT (ok) ;
+ ok = CHOLMOD(factorize)(Abad, L, cm) ; NOT (ok) ;
+
+ /* refactorize supernodal LL' */
+ printf ("refactorize here\n") ;
+ ok = CHOLMOD(print_sparse)(Acopy, "Acopy refactorize", cm) ; OK (ok) ;
+ ok = CHOLMOD(print_factor)(L, "L for refactorize", cm) ; OK (ok) ;
+
+ printf ("L->xtype for refactorize %d\n", L->xtype) ;
+ ok = CHOLMOD(factorize)(Acopy, L, cm) ;
+ OK (ok || cm->status == CHOLMOD_NOT_POSDEF) ;
+ ok = CHOLMOD(print_factor)(L, "L ok, here", cm) ; OK (ok) ;
+
+ ok = CHOLMOD(factorize)(Acopy, L, cm) ;
+ OK (ok || cm->status == CHOLMOD_NOT_POSDEF) ;
+ ok = CHOLMOD(print_factor)(L, "L ok, here2", cm) ; OK (ok) ;
+
+ /* solve */
+ B = CHOLMOD(ones)(nrow, 0, CHOLMOD_REAL, cm) ; OKP (B) ;
+ X = CHOLMOD(solve)(CHOLMOD_A, L, B, cm) ; OKP (X) ;
+ ok = CHOLMOD(free_dense)(&X, cm) ; OK (ok) ;
+
+ X = CHOLMOD(solve)(-1, L, B, cm) ; NOP (X) ;
+ ok = CHOLMOD(free_dense)(&B, cm) ; OK (ok) ;
+
+ B = CHOLMOD(zeros)(nrow+1, 0, CHOLMOD_REAL, cm) ; OKP (B) ;
+ X = CHOLMOD(solve)(CHOLMOD_A, L, B, cm) ; NOP (X) ;
+
+ B->xtype = 0 ;
+ X = CHOLMOD(solve)(CHOLMOD_A, L, B, cm) ; NOP (X) ;
+ B->xtype = CHOLMOD_REAL ;
+ ok = CHOLMOD(free_dense)(&B, cm) ; OK (ok) ;
+
+ /* sparse solve */
+ if (nrow < 100 && A->stype != 0)
+ {
+ /* solve A*C=I, so C should equal A inverse */
+ I = CHOLMOD(speye)(nrow, nrow, CHOLMOD_REAL, cm) ; OKP (I) ;
+ C = CHOLMOD(spsolve)(CHOLMOD_A, L, I, cm) ; OKP (C) ;
+ /* compute norm of A*C-I */
+ if (xtype == CHOLMOD_REAL)
+ {
+ E = CHOLMOD(ssmult)(A, C, 0, TRUE, FALSE, cm) ; OKP (E) ;
+ F = CHOLMOD(add)(E, I, minusone, one, TRUE, FALSE, cm) ;OKP (F) ;
+ cm->print = 4 ;
+ ok = CHOLMOD(print_sparse)(F, "A*inv(A)-I", cm) ; OK (ok) ;
+ cm->print = 1 ;
+ r = CHOLMOD(norm_sparse)(F, 1, cm) ;
+ OK (! (r < 0)) ;
+ MAXERR (maxerr, r, 1) ;
+ ok = CHOLMOD(free_sparse)(&E, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse)(&F, cm) ; OK (ok) ;
+ }
+ CHOLMOD(free_sparse)(&C, cm) ;
+
+ /* check error cases for sparse solve */
+ C = CHOLMOD(spsolve)(CHOLMOD_A, NULL, I, cm) ; NOP (C) ;
+ C = CHOLMOD(spsolve)(CHOLMOD_A, Lbad, I, cm) ; NOP (C) ;
+ C = CHOLMOD(spsolve)(CHOLMOD_A, L, NULL, cm) ; NOP (C) ;
+ I->xtype = 0 ;
+ C = CHOLMOD(spsolve)(CHOLMOD_A, L, I, cm) ; NOP (C) ;
+ I->xtype = CHOLMOD_REAL ;
+ I->stype = -1 ;
+ C = CHOLMOD(spsolve)(CHOLMOD_A, L, I, cm) ; NOP (C) ;
+ ok = CHOLMOD(free_sparse)(&I, cm) ; OK (ok) ;
+ I = CHOLMOD(speye)(nrow+1, nrow+1, CHOLMOD_REAL, cm) ; OKP (I) ;
+ C = CHOLMOD(spsolve)(CHOLMOD_A, L, I, cm) ; NOP (C) ;
+ ok = CHOLMOD(free_sparse)(&I, cm) ; OK (ok) ;
+ }
+
+ /* resymbol */
+ ok = CHOLMOD(resymbol)(I1, NULL, 0, TRUE, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(resymbol_noperm)(I1, NULL, 0, TRUE, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(change_factor)(L->xtype, FALSE, FALSE, FALSE, FALSE, L, cm) ;
+ OK (ok) ;
+ ok = CHOLMOD(resymbol)(I1, NULL, 0, TRUE, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(resymbol_noperm)(I1, NULL, 0, TRUE, L, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(change_factor)(-1, FALSE, FALSE, FALSE, FALSE, L, cm) ;
+ NOT (ok) ;
+
+ ok = CHOLMOD(change_factor)(L->xtype, FALSE, FALSE, FALSE, FALSE, Lbad, cm);
+ NOT (ok) ;
+
+ ok = CHOLMOD(resymbol_noperm)(Acopy, NULL, 0, TRUE, L2, cm) ;
+ if (Acopy->stype <= 0)
+ {
+ OK (ok) ;
+ }
+ else
+ {
+ NOT (ok) ;
+ }
+
+ ok = CHOLMOD(resymbol_noperm)(Abad2, NULL, 0, TRUE, L2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(resymbol)(Abad2, NULL, 0, TRUE, L2, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(resymbol_noperm)(Acopy, NULL, 0, TRUE, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(resymbol)(Acopy, NULL, 0, TRUE, L2, cm) ; OK (ok) ;
+
+ if (ncol > 0)
+ {
+ ok = CHOLMOD(print_perm)(fsetbad, ncol, ncol, "bad fset", cm) ;
+ NOT (ok) ;
+ }
+
+ if (ncol > 1)
+ {
+ ok = CHOLMOD(resymbol)(Acopy, fsetok, ncol/2, TRUE, L2, cm) ; OK (ok) ;
+ ok = CHOLMOD(resymbol)(Acopy, fsetbad, ncol/2, TRUE, L2, cm) ;
+ if (Acopy->stype)
+ {
+ /* fset is ignored */
+ OK (ok) ;
+ }
+ else
+ {
+ NOT (ok) ;
+ ok = CHOLMOD(resymbol_noperm)(Acopy, fsetbad, ncol/2, TRUE, L2, cm);
+ NOT (ok) ;
+ }
+ Acopy->sorted = FALSE ;
+ ok = CHOLMOD(resymbol)(Acopy, fsetok, ncol/2, TRUE, L2, cm) ;
+ OK (ok) ;
+ Acopy->sorted = TRUE ;
+ }
+
+ cm->print = 4 ;
+ gsave0 = cm->grow0 ;
+ gsave1 = cm->grow1 ;
+ gsave2 = cm->grow2 ;
+
+ /* reallocate column */
+ L4 = NULL ;
+ if (nrow > 0)
+ {
+ ok = CHOLMOD(print_factor)(L, "L ok, for colrealloc", cm) ; OK (ok) ;
+ L4 = CHOLMOD(copy_factor)(L, cm) ;
+ ok = CHOLMOD(print_factor)(L4, "L4 ok, for colrealloc", cm) ; OK (ok) ;
+ OK (nrow == (Int)(L->n)) ;
+ ok = CHOLMOD(reallocate_column)(nrow, 1, L4, cm) ; NOT (ok) ;
+ ok = CHOLMOD(reallocate_column)(nrow-1, 0, L4, cm) ; NOT (ok) ;
+ ok = CHOLMOD(reallocate_column)(nrow-1, 10, L4, cm) ; OK (ok) ;
+
+ cm->grow0 = 2e10 ;
+ cm->grow1 = 2 ;
+
+ /* this may or may not fail */
+ ok = CHOLMOD(reallocate_column)(0, 10, L4, cm) ;
+ CHOLMOD(print_common)("OK or too large", cm) ;
+ ok = CHOLMOD(free_factor)(&L4, cm) ; OK (ok) ;
+ }
+
+ cm->grow0 = gsave0 ;
+ cm->grow1 = gsave1 ;
+ cm->grow2 = gsave2 ;
+
+ if (ok && nrow > 2)
+ {
+ L4 = CHOLMOD(copy_factor)(L, cm) ;
+ ok = CHOLMOD(resymbol)(A, NULL, 0, TRUE, L4, cm) ; OK (ok) ;
+
+ /* make it non-monotonic and then monotonic (LDL' unpacked) */
+ ok = CHOLMOD(reallocate_column)(0, nrow-1, L4, cm) ; OK (ok) ;
+
+ /* this should be OK for small matrices, but fail for large ones */
+ cm->grow0 = nrow ;
+ cm->grow1 = nrow ;
+ cm->grow2 = nrow ;
+ ok = CHOLMOD(change_factor)(CHOLMOD_REAL, FALSE, FALSE, FALSE, TRUE,
+ L4, cm) ;
+
+ ok = CHOLMOD(free_factor)(&L4, cm) ; OK (ok) ;
+ L4 = CHOLMOD(copy_factor)(L, cm) ;
+ ok = CHOLMOD(resymbol)(A, NULL, 0, TRUE, L4, cm) ; OK (ok) ;
+ ok = CHOLMOD(pack_factor)(L4, cm) ; OK (ok) ;
+
+ /* now try to make L4 really huge */
+
+ /*
+ cm->print = 5 ;
+ CHOLMOD(print_sparse) (A, "A for huge", cm) ;
+ CHOLMOD(print_factor) (L4, "L4 for huge", cm) ;
+ */
+
+ if (ok && !(L->is_super) && L->xtype != CHOLMOD_PATTERN)
+ {
+
+ cm->grow0 = gsave0 ;
+ cm->grow1 = gsave1 ;
+ cm->grow2 = gsave2 ;
+
+ ok = CHOLMOD(reallocate_column)(0, nrow-1, L4, cm) ; OK (ok) ;
+
+ cm->grow0 = nrow ;
+ cm->grow1 = nrow ;
+ cm->grow2 = nrow ;
+
+ /*
+ CHOLMOD(print_factor) (L4, "L4 for huge, realloced", cm) ;
+ printf ("L4 for huge is monotonic: %d\n", L4->is_monotonic) ;
+ */
+
+ if (!(L4->is_monotonic))
+ {
+ /* printf ("Make L4 really huge: ") ; */
+ ok = CHOLMOD(change_factor)(CHOLMOD_REAL, TRUE, FALSE, FALSE,
+ TRUE, L4, cm) ;
+ printf ("L4 huge ok: "ID"\n", ok) ;
+ }
+ }
+ ok = CHOLMOD(free_factor)(&L4, cm) ; OK (ok) ;
+ }
+
+ cm->grow0 = gsave0 ;
+ cm->grow1 = gsave1 ;
+ cm->grow2 = gsave2 ;
+
+ cm->print = 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* more error tests */
+ /* ---------------------------------------------------------------------- */
+
+ cm->error_handler = NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify */
+ /* ---------------------------------------------------------------------- */
+
+ X = CHOLMOD(ones)(nrow, 1, CHOLMOD_REAL, cm) ; OKP (X) ;
+ R = CHOLMOD(dense_to_sparse)(X, TRUE, cm) ; /* [ */
+ OKP (R) ;
+
+ if (isreal)
+ {
+ C = CHOLMOD(speye)(nrow, 1, CHOLMOD_REAL, cm) ; OKP (C) ;
+ ok = CHOLMOD(updown)(+1, C, L, cm) ; OK (ok) ;
+ X1 = CHOLMOD(ones)(nrow, 1, CHOLMOD_REAL, cm) ;
+ B1 = CHOLMOD(eye)(nrow, 1, CHOLMOD_REAL, cm) ;
+ ok = CHOLMOD(updown_solve)(+1, C, L, X1, B1, cm) ; OK (ok) ;
+ B1->xtype = -999 ;
+ ok = CHOLMOD(updown_solve)(+1, C, L, X1, B1, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowadd_solve)(0, R, beta, L, X1, B1, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowdel_solve)(0, R, beta, L, X1, B1, cm) ; NOT (ok) ;
+ B1->xtype = CHOLMOD_REAL ;
+ CHOLMOD(free_dense)(&B1, cm) ;
+ B2 = CHOLMOD(ones)(nrow, 2, CHOLMOD_REAL, cm) ;
+ ok = CHOLMOD(updown_solve)(+1, C, L, X1, B2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowadd_solve)(0, R, beta, L, X1, B2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowdel_solve)(0, R, beta, L, X1, B2, cm) ; NOT (ok) ;
+
+ CHOLMOD(free_dense)(&B2, cm) ;
+ CHOLMOD(free_dense)(&X1, cm) ;
+ ok = CHOLMOD(updown)(+1, Abad2, L, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(updown)(+1, C, NULL, cm) ; NOT (ok) ;
+
+ C->sorted = FALSE ;
+ ok = CHOLMOD(updown)(+1, C, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ ok = CHOLMOD(updown)(+1, NULL, L, cm) ; NOT (ok) ;
+
+ if (nrow > 0)
+ {
+ C = CHOLMOD(speye)(nrow-1, 1, CHOLMOD_REAL, cm) ; OKP (C) ;
+ ok = CHOLMOD(updown)(+1, C, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ }
+
+ C = CHOLMOD(speye)(nrow, 0, CHOLMOD_REAL, cm) ; OKP (C) ;
+ ok = CHOLMOD(updown)(+1, C, L, cm) ; OK (ok) ;
+
+ ok = CHOLMOD(rowdel)(0, C, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* rowfac, rcond */
+ /* ---------------------------------------------------------------------- */
+
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NATURAL ;
+ cm->postorder = FALSE ;
+
+ cm->print = 5 ;
+ cm->final_ll = TRUE ;
+ for (xtype2 = CHOLMOD_REAL ; xtype2 <= CHOLMOD_ZOMPLEX ; xtype2++)
+ {
+ cm->supernodal = CHOLMOD_SIMPLICIAL ;
+
+ /* factor a singular matrix (C=LL') */
+ printf ("start singular LL'\n") ;
+ XX = CHOLMOD(ones)(4, 4, xtype2, cm) ; OKP (X) ;
+ C = CHOLMOD(dense_to_sparse)(XX, TRUE, cm) ; OKP (C) ;
+ CHOLMOD(free_dense)(&XX, cm) ;
+ C->stype = 1 ;
+ CHOLMOD(print_sparse)(C, "C ones", cm) ;
+ L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ;
+ ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ;
+ printf ("status %d\n", cm->status) ;
+ ok1 = (cm->status == CHOLMOD_NOT_POSDEF) ;
+ ok = CHOLMOD(print_factor)(L6, "L6 singular", cm) ; OK (ok) ;
+ OK (ok1) ;
+ rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ;
+
+ /* now make C positive definite */
+ CHOLMOD(free_sparse)(&C, cm) ;
+ XX = CHOLMOD(ones)(4, 4, xtype2, cm) ; OKP (X) ;
+ x = XX->x ;
+ for (i = 0 ; i < 4 ; i++)
+ {
+ if (xtype2 == CHOLMOD_REAL || xtype2 == CHOLMOD_ZOMPLEX)
+ {
+ x [i + 4*i] = 42 ;
+ }
+ else /* complex */
+ {
+ x [2*(i + 4*i)] = 42 ;
+ }
+ }
+ C = CHOLMOD(dense_to_sparse)(XX, TRUE, cm) ; OKP (C) ;
+ CHOLMOD(free_dense)(&XX, cm) ;
+ C->stype = 1 ;
+ CHOLMOD(print_sparse)(C, "C ok", cm) ;
+ ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ;
+ ok1 = (cm->status == CHOLMOD_OK) ;
+ ok = CHOLMOD(print_factor)(L6, "L6 ok", cm) ; OK (ok) ;
+ OK (ok1) ;
+ rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond > 0) ;
+
+/* generate intentional nan's, to test the nan-handling of cholmod_rcond */
+if (do_nantests)
+{
+
+ xnan = xnan/xnan ;
+
+ /* C(2,2) = nan */
+ x = C->x ;
+ i = 2 ;
+ if (xtype2 == CHOLMOD_REAL || xtype2 == CHOLMOD_ZOMPLEX)
+ {
+ x [i + 4*i] = xnan ;
+ }
+ else /* complex */
+ {
+ x [2*(i + 4*i)] = xnan ;
+ }
+ ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ;
+ ok1 = (cm->status == CHOLMOD_OK) ;
+ ok = CHOLMOD(print_factor)(L6, "L6 nan2", cm) ; OK (ok) ;
+ printf ("rcond %g\n", rcond) ;
+ OK (ok1) ;
+ rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ;
+ CHOLMOD(free_factor)(&L6, cm) ;
+
+ /* C(2,2) = nan, LDL' */
+ cm->supernodal = CHOLMOD_SIMPLICIAL ;
+ cm->final_ll = TRUE ;
+ L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ;
+ ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ;
+ ok1 = (cm->status == CHOLMOD_OK) ;
+ ok = CHOLMOD(print_factor)(L6, "LDL6 nan2", cm) ; OK (ok) ;
+ OK (ok1) ;
+ rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ;
+ CHOLMOD(free_factor)(&L6, cm) ;
+
+ /* C(2,2) = nan, supernodal */
+ cm->supernodal = CHOLMOD_SUPERNODAL ;
+ cm->final_ll = FALSE ;
+ L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ;
+ ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ;
+ ok1 = (cm->status == CHOLMOD_OK) ;
+ ok = CHOLMOD(print_factor)(L6, "L6 supernan2", cm) ; OK (ok) ;
+ OK (ok1) ;
+ rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ;
+ CHOLMOD(free_factor)(&L6, cm) ;
+
+ /* C(0,0) = nan */
+ cm->supernodal = CHOLMOD_SIMPLICIAL ;
+ cm->final_ll = FALSE ;
+ x [0] = xnan ;
+ L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ;
+ ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ;
+ ok1 = (cm->status == CHOLMOD_OK) ;
+ ok = CHOLMOD(print_factor)(L6, "L6 nan0", cm) ; OK (ok) ;
+ OK (ok1) ;
+ rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ;
+ CHOLMOD(free_factor)(&L6, cm) ;
+
+ /* C(0,0) = nan, LDL' */
+ cm->supernodal = CHOLMOD_SIMPLICIAL ;
+ cm->final_ll = TRUE ;
+ L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ;
+ ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ;
+ ok1 = (cm->status == CHOLMOD_OK) ;
+ ok = CHOLMOD(print_factor)(L6, "LDL6 nan0", cm) ; OK (ok) ;
+ OK (ok1) ;
+ rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ;
+ CHOLMOD(free_factor)(&L6, cm) ;
+
+ /* C(0,0) = nan, supernodal */
+ cm->supernodal = CHOLMOD_SUPERNODAL ;
+ cm->final_ll = FALSE ;
+ L6 = CHOLMOD(analyze)(C, cm) ; OKP (L6) ;
+ ok = CHOLMOD(factorize)(C, L6, cm) ; OK (ok) ;
+ ok1 = (cm->status == CHOLMOD_OK) ;
+ ok = CHOLMOD(print_factor)(L6, "L6 supernan0", cm) ; OK (ok) ;
+ OK (ok1) ;
+ rcond = CHOLMOD(rcond) (L6, cm) ; OK (rcond == 0) ;
+}
+
+ CHOLMOD(free_factor)(&L6, cm) ;
+ CHOLMOD(free_sparse)(&C, cm) ;
+ }
+ cm->supernodal = CHOLMOD_AUTO ;
+ cm->final_ll = FALSE ;
+ cm->print = 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* refactorize simplicial LDL' */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow < NLARGE)
+ {
+ L7 = CHOLMOD(analyze) (A, cm) ; OKP (L7) ;
+ ok = CHOLMOD(factorize) (A, L7, cm) ; OK (ok) ;
+ ok = CHOLMOD(factorize) (A, L7, cm) ; OK (ok) ;
+ B7 = CHOLMOD(ones) (nrow, 1, xtype, cm) ; OKP (B7) ;
+ X7 = CHOLMOD(solve) (CHOLMOD_A, L7, B7, cm) ; OKP (X7) ;
+ ok = CHOLMOD(free_dense) (&X7, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_dense) (&B7, cm) ; OK (ok) ;
+ if (A->stype > 0)
+ {
+ ok = CHOLMOD(rowfac) (A, NULL, zero, 0, nrow, L7, cm) ; OK (ok) ;
+ ok = CHOLMOD(rowfac) (A, NULL, zero, 0, nrow, L7, cm) ; OK (ok) ;
+ printf ("I7 :::\n") ;
+ I7 = CHOLMOD(speye) (nrow+1, 1, xtype, cm) ; OKP (I7) ;
+ I7->stype = 1 ;
+ ok = CHOLMOD(rowfac) (I7,NULL, zero, 0, nrow, L7, cm) ; NOT(ok) ;
+ printf ("I7 ::: done\n") ;
+ CHOLMOD(free_sparse) (&I7, cm) ;
+ }
+ ok = CHOLMOD(free_factor) (&L7, cm) ; OK (ok) ;
+ }
+
+ cm->nmethods = 0 ; /* restore defaults */
+ cm->method [0].ordering = CHOLMOD_GIVEN ;
+ cm->postorder = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* row subtree */
+ /* ---------------------------------------------------------------------- */
+
+ i = nrow / 2 ;
+
+ C = CHOLMOD(allocate_sparse)(nrow, 1, nrow, TRUE, TRUE, 0,
+ CHOLMOD_REAL, cm) ; OKP (C) ;
+ C2 = CHOLMOD(allocate_sparse)(nrow, 1, nrow, TRUE, TRUE, 0,
+ CHOLMOD_REAL, cm) ; OKP (C) ;
+ ok = CHOLMOD(row_subtree)(NULL, NULL, i, Parent, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_lsubtree)(NULL, NULL, 0, i, L, C2, cm) ; NOT (ok) ;
+
+ if (A->stype == 0 && nrow > 0 && AT != NULL)
+ {
+ ok = CHOLMOD(row_subtree)(A, AT, i, Parent, C, cm) ; OK (ok) ;
+
+ ATp = AT->p ;
+ ATi = AT->i ;
+ fnz = ATp [i+1] - ATp [i] ;
+ ok = CHOLMOD(row_lsubtree)(A, ATi, fnz, i, L, C2, cm) ; OK (ok) ;
+
+ ok = CHOLMOD(row_lsubtree)(Abad2, ATi, fnz, i, L, C2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_lsubtree)(A, NULL, fnz, i, L, C2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_lsubtree)(A, ATi, fnz, i, L, Abad2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_lsubtree)(A, ATi, fnz, i, NULL, C2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_lsubtree)(A, ATi, fnz, nrow+1, L, C2, cm) ;NOT (ok) ;
+
+ ok = CHOLMOD(row_subtree)(Abad2, AT, i, Parent, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_subtree)(A, Abad2, i, Parent, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_subtree)(A, AT, i, Parent, Abad2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_subtree)(A, NULL, i, Parent, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_subtree)(A, AT, nrow+1, Parent, C, cm) ; NOT (ok) ;
+ }
+ else if (A->stype == 1 && nrow > 0)
+ {
+ ok = CHOLMOD(row_subtree)(A, NULL, i, Parent, C, cm) ; OK (ok) ;
+ ok = CHOLMOD(row_lsubtree)(A, NULL, 0, i, L, C2, cm) ; OK (ok) ;
+ }
+ else
+ {
+ ok = CHOLMOD(row_subtree)(A, NULL, i, Parent, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_lsubtree)(A, NULL, 0, i, L, C2, cm) ; NOT (ok) ;
+ }
+ ok = CHOLMOD(row_subtree)(A, NULL, i, Parent, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_subtree)(A, NULL, i, NULL, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_lsubtree)(A, NULL, 0, i, L, NULL, cm) ; NOT (ok) ;
+
+ if (A->stype == 1 && nrow > 0)
+ {
+ /* add extra entries in the (ignored) lower triangular part to AA */
+ if (!(A->sorted))
+ {
+ ok = CHOLMOD(sort)(A, cm) ; OK (ok) ;
+ }
+ AA = CHOLMOD(copy)(A, 0, 0, cm) ;
+ OK (AA->sorted) ;
+ AA->stype = 1 ;
+ ok = CHOLMOD(row_subtree)(AA, NULL, i, Parent, C, cm) ; OK (ok) ;
+ ok = CHOLMOD(row_lsubtree)(AA, NULL, 0, i, L, C2, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse)(&AA, cm) ; OK (ok) ;
+ }
+
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse)(&C2, cm) ; OK (ok) ;
+
+ C = CHOLMOD(speye)(nrow, 0, CHOLMOD_REAL, cm) ; OKP (C) ;
+ if (A->stype == 0 && AT != NULL && nrow > 0)
+ {
+ ok = CHOLMOD(row_subtree)(A, AT, i, Parent, C, cm) ; NOT (ok) ;
+
+ ATp = AT->p ;
+ ATi = AT->i ;
+ fnz = ATp [i+1] - ATp [i] ;
+ ok = CHOLMOD(row_lsubtree)(A, ATi, fnz, i, L, C, cm) ; NOT (ok) ;
+ }
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ L6 = CHOLMOD(allocate_factor)(nrow, cm) ; OKP (L6) ;
+ if (A->stype == 0 && nrow > 2)
+ {
+ ok = CHOLMOD(rowfac)(A, AT, beta, 0, 1, L6, cm) ; OK (ok) ;
+ OK (cm->status == CHOLMOD_OK) ;
+ ok = CHOLMOD(rowfac)(A, NULL, beta, 1, 2, L6, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowfac)(A, AT, beta, 1, 2, L6, cm) ; OK (ok) ;
+ ok = CHOLMOD(rowfac)(Abad2, AT, beta, 1, 2, L6, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowfac)(A, Abad2, beta, 1, 2, L6, cm) ; NOT (ok) ;
+ }
+ ok = CHOLMOD(free_factor)(&L6, cm) ; OK (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* horzcat, vertcat */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->nrow != A->ncol)
+ {
+ C = CHOLMOD(horzcat)(A, AT, TRUE, cm) ; NOP (C) ;
+ C = CHOLMOD(vertcat)(A, AT, TRUE, cm) ; NOP (C) ;
+ }
+ C = CHOLMOD(horzcat)(A, Axbad, TRUE, cm) ; NOP (C) ;
+ C = CHOLMOD(vertcat)(A, Axbad, TRUE, cm) ; NOP (C) ;
+ C = CHOLMOD(vertcat)(A, NULL, TRUE, cm) ; NOP (C) ;
+ C = CHOLMOD(vertcat)(NULL, AT, TRUE, cm) ; NOP (C) ;
+ C = CHOLMOD(horzcat)(A, NULL, TRUE, cm) ; NOP (C) ;
+ C = CHOLMOD(horzcat)(NULL, AT, TRUE, cm) ; NOP (C) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print_triplet */
+ /* ---------------------------------------------------------------------- */
+
+ cm->print = 4 ;
+ ok = CHOLMOD(print_triplet)(Tok, "T ok", cm) ; OK (ok) ;
+ T = CHOLMOD(copy_triplet)(Tok, cm) ; /* [ */ OKP (T) ;
+
+ Tz = T->z ;
+ T->z = NULL ;
+ ok = CHOLMOD(print_triplet)(T, "T no z", cm) ;
+ if (T->xtype == CHOLMOD_ZOMPLEX)
+ {
+ NOT (ok) ;
+ }
+ else
+ {
+ OK (ok) ;
+ }
+ T->z = Tz ;
+ cm->print = 1 ;
+
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+
+ ok = CHOLMOD(print_triplet)(NULL, "null", cm) ; NOT (ok) ;
+
+ p = T->nzmax ;
+ T->nzmax = T->nnz - 1 ;
+ ok = CHOLMOD(print_triplet)(T, "T nzmax too small", cm) ; NOT (ok) ;
+ T->nzmax = p ;
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+
+ T->itype = -1 ;
+ ok = CHOLMOD(print_triplet)(T, "T itype bad", cm) ; NOT (ok) ;
+ T->itype = CHOLMOD_INTLONG ;
+ ok = CHOLMOD(print_triplet)(T, "T itype bad", cm) ; NOT (ok) ;
+ T->itype = cm->itype ;
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+
+ cm->print = 4 ;
+#ifdef LONG
+ T->itype = CHOLMOD_INT ;
+#else
+ T->itype = CHOLMOD_LONG ;
+#endif
+ ok = CHOLMOD(print_triplet)(T, "T bad itype", cm) ; NOT (ok) ;
+ T->itype = cm->itype ;
+ cm->print = 1 ;
+
+ Txtype = T->xtype ;
+ T->xtype = -1 ;
+ ok = CHOLMOD(print_triplet)(T, "T xtype bad", cm) ; NOT (ok) ;
+
+ T->xtype = Txtype ;
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+
+ T->dtype = -1 ;
+ ok = CHOLMOD(print_triplet)(T, "T dtype bad", cm) ; NOT (ok) ;
+ T->dtype = CHOLMOD_SINGLE ;
+ ok = CHOLMOD(print_triplet)(T, "T dtype bad", cm) ; NOT (ok) ;
+ T->dtype = CHOLMOD_DOUBLE ;
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+
+ Tj = T->j ;
+ Ti = T->i ;
+ Tx = T->x ;
+
+ T->j = NULL ;
+ ok = CHOLMOD(print_triplet)(T, "Tj null", cm) ; NOT (ok) ;
+ T->j = Tj ;
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+
+ T->i = NULL ;
+ ok = CHOLMOD(print_triplet)(T, "Ti null", cm) ; NOT (ok) ;
+ T->i = Ti ;
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+
+ T->x = NULL ;
+ ok = CHOLMOD(print_triplet)(T, "Tx null", cm) ; NOT (ok) ;
+ T->x = Tx ;
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+
+ if (T->nnz > 0)
+ {
+ p = Ti [0] ;
+ Ti [0] = -1 ;
+ ok = CHOLMOD(print_triplet)(T, "Ti bad", cm) ; NOT (ok) ;
+ C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; NOP (C) ;
+ Ti [0] = p ;
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+
+ p = Tj [0] ;
+ Tj [0] = -1 ;
+ ok = CHOLMOD(print_triplet)(T, "Tj bad", cm) ; NOT (ok) ;
+ C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; NOP (C) ;
+ Tj [0] = p ;
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+ }
+
+ cm->print = 4 ;
+ CHOLMOD(triplet_xtype)(CHOLMOD_PATTERN, T, cm) ;
+ ok = CHOLMOD(print_triplet)(T, "T pattern ok", cm) ; OK (ok) ;
+ cm->print = 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* triplet, realloc_multiple */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+ OK (cm->status == CHOLMOD_OK) ;
+
+ cm->print = 4 ;
+ if (T->nrow != T->ncol)
+ {
+ OK (T->stype == 0) ;
+
+ CHOLMOD(print_triplet)(T, "T ok", cm) ;
+
+ C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ;
+ CHOLMOD(print_sparse)(C, "C ok", cm) ;
+ OKP (C) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ Ti = T->i ;
+ T->i = NULL ;
+ C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; NOP (C) ;
+ T->i = Ti ;
+
+ Tj = T->j ;
+ T->j = NULL ;
+ C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; NOP (C) ;
+ T->j = Tj ;
+
+ T->stype = 1 ;
+ ok = CHOLMOD(print_triplet)(T, "T bad", cm) ; NOT (ok) ;
+ C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ; NOP (C) ;
+ T->stype = 0 ;
+ ok = CHOLMOD(print_triplet)(T, "T pattern ok", cm) ; OK (ok) ;
+ }
+ OK (cm->status == CHOLMOD_OK) ;
+ cm->print = 1 ;
+
+ ok = CHOLMOD(reallocate_triplet)(1, NULL, cm) ; NOT (ok) ;
+
+ CHOLMOD(print_triplet)(T, "T before realloc", cm) ;
+ ok = CHOLMOD(reallocate_triplet)(1+(T->nzmax), T, cm) ; OK (ok) ;
+ CHOLMOD(print_triplet)(T, "T after realloc", cm) ;
+
+ nznew = 10 + T->nzmax ;
+ pp = NULL ;
+
+ ok = CHOLMOD(realloc_multiple)(Size_max/2, 2, T->xtype, &(T->i),
+ &(T->j), &(T->x), &(T->z), &(T->nzmax), cm) ; NOT (ok) ;
+
+ size = 0 ;
+ ii = NULL ;
+ jj = NULL ;
+ xx = NULL ;
+ ok = CHOLMOD(realloc_multiple)(Size_max, 2, CHOLMOD_REAL, &ii, &jj, &xx,
+ NULL, &size, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(realloc_multiple)(0, 0, CHOLMOD_PATTERN, &ii, &jj, &xx, NULL,
+ &size, cm) ; OK (ok) ;
+
+ ok = CHOLMOD(realloc_multiple)(0, 0, -1, &ii, &jj, &xx, NULL,
+ &size, cm) ; NOT (ok) ;
+
+ /* change to pattern-only */
+ CHOLMOD(triplet_xtype)(CHOLMOD_PATTERN, T, cm) ;
+
+ ok = CHOLMOD(reallocate_triplet)(1+(T->nzmax), T, cm) ; OK (ok) ;
+
+ ok = CHOLMOD(free_triplet)(&T, cm) ; /* ] */ OK (ok) ;
+
+ T = CHOLMOD(allocate_triplet)(nrow, ncol, Size_max, 0, CHOLMOD_REAL, cm);
+ NOP (T) ;
+
+ T2 = CHOLMOD(allocate_triplet)(4, 4, 8, 0, CHOLMOD_REAL, cm); OKP (T2) ;
+ ok = CHOLMOD(reallocate_triplet)(12, T2, cm) ; OK (ok) ;
+ T = CHOLMOD(copy_triplet)(T2, cm) ; OKP (T) ;
+ CHOLMOD(free_triplet)(&T, cm) ;
+ T = CHOLMOD(sparse_to_triplet)(A, cm) ; OKP (T) ;
+ C = CHOLMOD(triplet_to_sparse)(T, 100, cm) ; OKP (C) ;
+ CHOLMOD(free_sparse)(&C, cm) ;
+ CHOLMOD(free_triplet)(&T, cm) ;
+
+ T2->xtype = -1 ;
+ ok = CHOLMOD(reallocate_triplet)(16, T2, cm) ; NOT (ok) ;
+ T = CHOLMOD(copy_triplet)(T2, cm) ; NOP (T) ;
+ C = CHOLMOD(triplet_to_sparse)(T2, 100, cm) ; NOP (C) ;
+ T2->xtype = CHOLMOD_REAL ;
+ CHOLMOD(free_triplet)(&T2, cm) ;
+
+ T = CHOLMOD(allocate_triplet)(4, 4, 16, 0, -1, cm); NOP (T) ;
+
+ T = CHOLMOD(sparse_to_triplet)(Abad2, cm) ; NOP (T) ;
+
+ for (stype = -1 ; stype <= 1 ; stype++)
+ {
+ T = CHOLMOD(allocate_triplet)(4, 4, 16, stype, CHOLMOD_PATTERN, cm) ;
+ OKP (T) ;
+ Ti = T->i ;
+ Tj = T->j ;
+ k = 0 ;
+ for (i = 0 ; i < 4 ; i++)
+ {
+ for (j = 0 ; j < 4 ; j++)
+ {
+ Ti [k] = i ;
+ Tj [k] = j ;
+ k++ ;
+ }
+ }
+ T->nnz = k ;
+ C = CHOLMOD(triplet_to_sparse)(T, 0, cm) ;
+ cm->print = 4 ;
+ printf ("stype "ID"\n", stype) ;
+ CHOLMOD(print_triplet)(T, "T from triplet", cm) ;
+ CHOLMOD(print_sparse)(C, "C from triplet", cm) ;
+ cm->print = 1 ;
+ OKP (C) ;
+ CHOLMOD(free_sparse)(&C, cm) ;
+ CHOLMOD(free_triplet)(&T, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* sparse_to_triplet */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->nrow != A->ncol)
+ {
+ OK (A->stype == 0) ;
+ T = CHOLMOD(sparse_to_triplet)(A, cm) ; OKP (T) ;
+ ok = CHOLMOD(print_triplet)(T, "T ok", cm) ; OK (ok) ;
+
+ T2 = CHOLMOD(copy_triplet)(NULL, cm) ; NOP (T2) ;
+
+ Ti = T->i ;
+ T->i = NULL ;
+ T2 = CHOLMOD(copy_triplet)(T, cm) ; NOP (T2) ;
+ T->i = Ti ;
+
+ Tj = T->j ;
+ T->j = NULL ;
+ T2 = CHOLMOD(copy_triplet)(T, cm) ; NOP (T2) ;
+ T->j = Tj ;
+
+ ok = CHOLMOD(free_triplet)(&T, cm) ; OK (ok) ;
+ A->stype = 1 ;
+ T = CHOLMOD(sparse_to_triplet)(A, cm) ; NOP (T) ;
+ A->stype = 0 ;
+ T = CHOLMOD(sparse_to_triplet)(NULL, cm) ; NOP (T) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* colamd */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(colamd)(A, fsetok, fsizeok, TRUE, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(colamd)(NULL, fsetok, fsizeok, TRUE, Pok, cm) ; NOT (ok) ;
+
+ cm->current = 0 ;
+
+ save1 = cm->method [0].prune_dense2 ;
+ save2 = cm->method [0].ordering ;
+ save4 = cm->nmethods ;
+
+ cm->method [0].prune_dense2 = 0.5 ;
+ cm->method [0].ordering = CHOLMOD_COLAMD ;
+ cm->nmethods = 1 ;
+
+ ok = CHOLMOD(colamd)(A, fsetok, fsizeok, TRUE, Pok, cm) ;
+ if (A->stype == 0)
+ {
+ save3 = cm->print ;
+ cm->print = 5 ;
+ ok = CHOLMOD(print_common) ("colamd dense2", cm) ; OK (ok) ;
+ cm->print = save3 ;
+ OK (ok) ;
+ }
+ else
+ {
+ NOT (ok) ;
+ }
+
+ cm->method [0].prune_dense2 = save1 ;
+ cm->method [0].ordering = save2 ;
+ cm->nmethods = save4 ;
+
+ cm->current = -1 ;
+ ok = CHOLMOD(colamd)(A, fsetok, fsizeok, TRUE, Pok, cm) ;
+ if (A->stype == 0)
+ {
+ OK (ok) ;
+ }
+ else
+ {
+ NOT (ok) ;
+ }
+ cm->current = 0 ;
+
+ ok = CHOLMOD(colamd)(Abad2, NULL, 0, TRUE, Pok, cm) ; NOT (ok) ;
+
+ if (ncol > 0)
+ {
+ ok = CHOLMOD(colamd)(A, fsetbad, ncol, TRUE, Pok, cm) ; NOT (ok) ;
+ }
+
+ /* mangle the matrix to test integer overflow in colamd */
+ if (A->stype == 0)
+ {
+ nzmax = A->nzmax ;
+ A->nzmax = Size_max/2 ;
+ ok = CHOLMOD(colamd)(A, fsetok, fsizeok, TRUE, Pok, cm) ; NOT (ok) ;
+ A->nzmax = nzmax ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* ccolamd/csymamd */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NPARTITION
+ ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, Pok, cm) ;
+ if (A->stype == 0)
+ {
+ OK (ok) ;
+ }
+ else
+ {
+ NOT (ok) ;
+ }
+ ok = CHOLMOD(ccolamd)(Abad2, NULL, 0, NULL, Pok, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(csymamd)(A, NULL, Pok, cm) ;
+ if (A->nrow == A->ncol)
+ {
+ OK (ok) ;
+ }
+ else
+ {
+ NOT (ok) ;
+ }
+ ok = CHOLMOD(csymamd)(Abad2, NULL, Pok, cm) ; NOT (ok) ;
+ ok = CHOLMOD(csymamd)(NULL, NULL, Pok, cm) ; NOT (ok) ;
+ ok = CHOLMOD(csymamd)(A, NULL, NULL, cm) ; NOT (ok) ;
+
+ /* mangle the matrix to test integer overflow in colamd */
+ if (A->stype == 0)
+ {
+ nzmax = A->nzmax ;
+ A->nzmax = Size_max/2 ;
+ ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, Pok, cm) ; NOT (ok) ;
+ A->nzmax = nzmax ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* amd */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(amd)(A, NULL, 0, Pok, cm) ; OK (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* metis */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NPARTITION
+ /* no METIS memory guard */
+ cm->metis_memory = 0 ;
+ if (A->stype)
+ {
+ E = CHOLMOD(copy)(A, 0, -1, cm) ;
+ }
+ else
+ {
+ E = CHOLMOD(aat)(A, NULL, 0, -1, cm) ;
+ }
+ enz = CHOLMOD(nnz)(E, cm) ;
+
+ CHOLMOD(print_sparse)(A, "A for metis", cm) ;
+
+ if (A != NULL && Pok != NULL)
+ {
+ ok = CHOLMOD(metis)(A, NULL, 0, TRUE, Pok, cm) ;
+
+ /* memory guard triggered */
+ if (nrow > 0)
+ {
+ double density ;
+
+ cm->metis_memory = Size_max ;
+ ok = CHOLMOD(metis)(A, NULL, 0, FALSE, Pok, cm) ;
+ OK (ok) ;
+ /* Pok should be identity */
+ for (j = 0 ; j < nrow ; j++)
+ {
+ OK (Pok [j] == j) ;
+ }
+
+ /* memory guard triggered */
+ cm->metis_memory = 2 ;
+ cm->metis_nswitch = 10 ;
+
+
+ ok = CHOLMOD(metis)(A, NULL, 0, FALSE, Pok, cm) ; OK (ok) ;
+ /* Pok should be identity if the matrix is dense */
+ density = ((double) enz) / (((double) nrow) * ((double) nrow)) ;
+ if (nrow > 10 && density > cm->metis_dswitch)
+ {
+ for (j = 0 ; j < nrow ; j++)
+ {
+ OK (Pok [j] == j) ;
+ }
+ }
+ }
+ }
+
+ /* restore METIS default memory guard */
+ cm->metis_memory = 2 ;
+ cm->metis_nswitch = 3000 ;
+
+ /* check metis bisector error handling */
+ if (E != NULL && enz > 0)
+ {
+ Int *Anw, *Aew ;
+ Anw = CHOLMOD(malloc)(nrow, sizeof (Int), cm) ;
+ Aew = CHOLMOD(malloc)(MAX (anz,enz), sizeof (Int), cm) ;
+ for (j = 0 ; j < nrow ; j++)
+ {
+ Anw [j] = 1 ;
+ }
+ for (j = 0 ; j < enz ; j++)
+ {
+ Aew [j] = 1 ;
+ }
+ lr = CHOLMOD(metis_bisector)(E, Anw, Aew, Pok, cm) ;
+ if (E->stype || E->nrow != E->ncol)
+ {
+ NOT (lr >= 0) ;
+ }
+ else
+ {
+ OK (lr >= 0) ;
+ }
+ lr = CHOLMOD(metis_bisector)(Abad2, Anw, Aew, Pok, cm) ;NOT (lr >= 0);
+ lr = CHOLMOD(metis_bisector)(NULL, Anw, Aew, Pok, cm) ; NOT (lr >= 0);
+ lr = CHOLMOD(metis_bisector)(A, NULL, Aew, Pok, cm) ; NOT (lr >= 0);
+ lr = CHOLMOD(metis_bisector)(A, Anw, NULL, Pok, cm) ; NOT (lr >= 0);
+ lr = CHOLMOD(metis_bisector)(A, Anw, Aew, NULL, cm) ; NOT (lr >= 0);
+
+ if (A->stype)
+ {
+ lr = CHOLMOD(metis_bisector)(A, Anw, Aew, Pok, cm) ; NOT (lr>=0) ;
+ }
+
+ CHOLMOD(free)(nrow, sizeof (Int), Anw, cm) ;
+ CHOLMOD(free)(MAX (anz,enz), sizeof (Int), Aew, cm) ;
+ }
+
+ CHOLMOD(free_sparse)(&E, cm) ;
+
+ CHOLMOD(print_sparse)(Abad, "Abad", cm) ;
+ lr = CHOLMOD(bisect)(Abad, NULL, 0, TRUE, Partition, cm) ;
+ if (Abad != NULL && Abad->nrow == 0)
+ {
+ OK (lr == 0) ;
+ }
+ else
+ {
+ NOT (lr >= 0) ;
+ }
+
+ lr = CHOLMOD(bisect)(A, NULL, 0, TRUE, NULL, cm) ; NOT (lr >= 0);
+ lr = CHOLMOD(bisect)(NULL, NULL, 0, TRUE, Partition, cm) ; NOT (lr >= 0);
+
+ lr = CHOLMOD(nested_dissection)(NULL, NULL, 0, Pok, CParent,
+ Cmember, cm) ; NOT (lr>=0) ;
+
+ lr = CHOLMOD(nested_dissection)(A, NULL, 0, NULL, CParent,
+ Cmember, cm) ; NOT (lr>=0) ;
+
+ lr = CHOLMOD(nested_dissection)(A, NULL, 0, Pok, NULL,
+ Cmember, cm) ; NOT (lr>=0) ;
+
+ lr = CHOLMOD(nested_dissection)(A, NULL, 0, Pok, CParent,
+ NULL, cm) ; NOT (lr>=0) ;
+
+ ok = CHOLMOD(metis)(NULL, NULL, 0, TRUE, Pok, cm) ; NOT (ok) ;
+ ok = CHOLMOD(metis)(A, NULL, 0, TRUE, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(metis)(Abad2, NULL, 0, FALSE, Pok, cm) ; NOT (ok) ;
+ lr = CHOLMOD(bisect)(Abad2, NULL, 0, TRUE, Partition, cm) ; NOT (lr >= 0);
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* etree */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype < 0)
+ {
+ ok = CHOLMOD(etree)(A, Parent, cm) ; NOT (ok) ;
+ }
+ ok = CHOLMOD(etree)(Abad2, Parent, cm) ; NOT (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* etree, postorder, rowcolcount */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0 && ncol > 0)
+ {
+ AFT = CHOLMOD(ptranspose)(A, 1, NULL, fsetok, fsizeok, cm) ; OKP(AFT);
+ AF = CHOLMOD(transpose)(AFT, 1, cm) ; OKP(AF);
+
+ ok = CHOLMOD(etree)(NULL, Parent, cm) ; NOT(ok);
+ ok = CHOLMOD(etree)(AFT, NULL, cm) ; NOT(ok);
+ ok = CHOLMOD(etree)(AFT, Parent, cm) ; OK (ok);
+
+ lr = CHOLMOD(postorder)(Parent, nrow, NULL, Post, cm) ; OK (lr>=0) ;
+ lr = CHOLMOD(postorder)(NULL, nrow, NULL, Post, cm) ; NOT (lr>=0) ;
+ lr = CHOLMOD(postorder)(Parent, nrow, NULL, NULL, cm) ; NOT (lr>=0) ;
+
+
+ ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent,
+ Post, NULL, ColCount, First, Level, cm) ; OK (ok);
+
+ ok = CHOLMOD(rowcolcounts)(Abad2, fsetok, fsizeok, Parent,
+ Post, NULL, ColCount, First, Level, cm) ; NOT(ok);
+
+ ok = CHOLMOD(rowcolcounts)(NULL, fsetok, fsizeok, Parent,
+ Post, NULL, ColCount, First, Level, cm) ; NOT(ok);
+ ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, NULL,
+ Post, NULL, ColCount, First, Level, cm) ; NOT(ok);
+ ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent,
+ NULL, NULL, ColCount, First, Level, cm) ; NOT(ok);
+ ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent,
+ Post, NULL, NULL, First, Level, cm) ; NOT(ok);
+ ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent,
+ Post, NULL, ColCount, NULL, Level, cm) ; NOT(ok);
+ ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent,
+ Post, NULL, ColCount, First, NULL, cm) ; NOT(ok);
+
+ ok = CHOLMOD(rowcolcounts)(A, fsetbad, ncol, Parent,
+ Post, NULL, ColCount, First, Level, cm) ; NOT(ok);
+ ok = CHOLMOD(rowcolcounts)(A, fsetok, fsizeok, Parent,
+ Post, NULL, ColCount, First, NULL, cm) ; NOT(ok);
+
+ CHOLMOD(free_sparse)(&AF, cm) ;
+ CHOLMOD(free_sparse)(&AFT, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* norm */
+ /* ---------------------------------------------------------------------- */
+
+ nm = CHOLMOD(norm_sparse)(A, 2, cm) ; NOT (nm>=0) ;
+ nm = CHOLMOD(norm_sparse)(Abad, 0, cm) ; NOT (nm>=0) ;
+ nm = CHOLMOD(norm_sparse)(Abad2, 2, cm) ; NOT (nm>=0) ;
+ nm = CHOLMOD(norm_dense)(Bok, 3, cm) ; NOT (nm>=0) ;
+ nm = CHOLMOD(norm_dense)(Bok, 2, cm) ; NOT (nm>=0) ;
+ nm = CHOLMOD(norm_dense)(Xbad2, 1, cm) ; NOT (nm>=0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy dense */
+ /* ---------------------------------------------------------------------- */
+
+ ok = CHOLMOD(copy_dense2)(NULL, Bok, cm) ; NOT (ok) ;
+ ok = CHOLMOD(copy_dense2)(Bok, NULL, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(copy_dense2)(Bok, Xbad2, cm) ; NOT (ok) ;
+ ok = CHOLMOD(copy_dense2)(Xbad2, Xbad2, cm) ; NOT (ok) ;
+
+ if (nrow > 1)
+ {
+
+ /* wrong dimensions */
+ ok = CHOLMOD(copy_dense2)(Two, Bok, cm) ; NOT (ok) ;
+
+ /* mangled matrix */
+ Y = CHOLMOD(copy_dense)(Bok, cm) ; OKP (Y) ;
+ Y->d = 0 ;
+ ok = CHOLMOD(copy_dense2)(Bok, Y, cm) ; NOT (ok) ;
+ CHOLMOD(free_dense)(&Y, cm) ;
+
+ Y = CHOLMOD(copy_dense)(Xbad2, cm) ; NOP (Y) ;
+ Y = CHOLMOD(copy_dense)(NULL, cm) ; NOP (Y) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* complex */
+ /* ---------------------------------------------------------------------- */
+
+ W = CHOLMOD(eye)(4, 4, CHOLMOD_COMPLEX, cm) ; OKP (W) ;
+ ok = CHOLMOD(dense_xtype)(0, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(dense_xtype)(CHOLMOD_REAL, W, cm) ; OK (ok) ;
+ ok = CHOLMOD(dense_xtype)(CHOLMOD_REAL, NULL, cm) ; NOT (ok) ;
+ k = W->xtype ;
+ W->xtype = -1 ;
+ ok = CHOLMOD(dense_xtype)(CHOLMOD_REAL, W, cm) ; NOT (ok) ;
+ W->xtype = k ;
+ ok = CHOLMOD(free_dense)(&W, cm) ; OK (ok) ;
+
+ C = CHOLMOD(speye)(4, 4, CHOLMOD_COMPLEX, cm) ; OKP (C) ;
+ ok = CHOLMOD(sparse_xtype)(-1, C, cm) ; NOT (ok) ;
+ ok = CHOLMOD(sparse_xtype)(CHOLMOD_ZOMPLEX, C, cm) ; OK (ok) ;
+ ok = CHOLMOD(sparse_xtype)(CHOLMOD_ZOMPLEX, NULL, cm) ; NOT (ok) ;
+ T = CHOLMOD(sparse_to_triplet)(C, cm) ; OKP (T) ;
+ ok = CHOLMOD(triplet_xtype)(-1, T, cm) ; NOT (ok) ;
+ ok = CHOLMOD(triplet_xtype)(CHOLMOD_ZOMPLEX, T, cm) ; OK (ok) ;
+ ok = CHOLMOD(triplet_xtype)(CHOLMOD_ZOMPLEX, NULL, cm) ; NOT (ok) ;
+
+ k = T->xtype ;
+ T->xtype = -1 ;
+ ok = CHOLMOD(triplet_xtype)(CHOLMOD_REAL, T, cm) ; NOT (ok) ;
+ T->xtype = k ;
+
+ k = C->xtype ;
+ C->xtype = -1 ;
+ ok = CHOLMOD(sparse_xtype)(CHOLMOD_REAL, C, cm) ; NOT (ok) ;
+ C->xtype = k ;
+
+ ok = CHOLMOD(free_triplet)(&T, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ ok = CHOLMOD(factor_xtype)(CHOLMOD_REAL, Lbad, cm) ; NOT (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* rowadd */
+ /* ---------------------------------------------------------------------- */
+
+ x = X->x ;
+ X->x = NULL ;
+ C = CHOLMOD(dense_to_sparse)(X, TRUE, cm) ; NOP (C) ;
+
+ if (nrow > 3 && isreal)
+ {
+ ok = CHOLMOD(rowadd)(1, I1, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowadd)(nrow+1, R, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowadd)(nrow+1, R, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowdel)(nrow+1, NULL, L5, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(rowdel)(nrow-2, NULL, L5, cm) ; OK (ok) ;
+ ok = CHOLMOD(rowdel)(nrow-2, NULL, L5, cm) ; OK (ok) ;
+ ok = CHOLMOD(rowdel)(nrow-2, Abad2, L5, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowdel)(nrow-1, R, L5, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(change_factor)(CHOLMOD_REAL, TRUE, FALSE, TRUE, TRUE, L5,
+ cm) ;
+ OK (ok) ;
+
+ ok = CHOLMOD(rowadd)(nrow-2, NULL, L5, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowadd)(nrow-2, R, NULL, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(rowadd)(nrow-2, R, L5, cm) ; OK (ok) ;
+
+ ok = CHOLMOD(rowadd)(nrow-2, Abad2, L5, cm) ; NOT (ok) ;
+
+/* ok = CHOLMOD(rowadd)(nrow-2, R, L5, cm) ; NOT (ok) ; */
+ ok = CHOLMOD(rowdel)(nrow-2, NULL, L5, cm) ; OK (ok) ;
+ ok = CHOLMOD(change_factor)(CHOLMOD_PATTERN, TRUE,
+ TRUE, TRUE, TRUE, L5, cm) ; NOT (ok) ;
+ ok = CHOLMOD(change_factor)(CHOLMOD_REAL, TRUE,
+ TRUE, TRUE, TRUE, L5, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(rowadd_solve)(nrow-2, R, beta, L5, X, X, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowdel_solve)(nrow-2, R, beta, L5, X, X, cm) ; NOT (ok) ;
+ ok = CHOLMOD(updown_solve)(TRUE, R, L5, X, X, cm) ; NOT (ok) ;
+
+ if (nrow < 200 && L5 != NULL && R2 != NULL)
+ {
+ cholmod_factor *L8 ;
+ Int *L8p, *L8i, *L8nz, rnz ;
+ double *L8x ;
+ L8 = CHOLMOD(copy_factor) (L5, cm) ;
+ ok = TRUE ;
+ for (k = nrow-1 ; ok && L8 != NULL
+ && L8->xtype == CHOLMOD_REAL && k >= 0 ; k--)
+ {
+ for (rnz = 0 ; rnz < nrow ; rnz++)
+ {
+ /* first, ensure row i is zero */
+ for (j = 0 ; j < nrow ; j++)
+ {
+ L8p = L8->p ;
+ L8i = L8->i ;
+ L8nz = L8->nz ;
+ L8x = L8->x ;
+ for (p = L8p [j] ; p < L8p [j] + L8nz [j] ; p++)
+ {
+ i = L8i [p] ;
+ if (i == k) L8x [p] = 0 ;
+ }
+ }
+ R2p [1] = rnz ;
+ ok = CHOLMOD(rowadd)(k, R2, L8, cm) ; OK (ok) ;
+ ok = CHOLMOD(rowdel)(k, NULL, L8, cm) ; OK (ok) ;
+ ok = CHOLMOD(rowadd)(k, R2, L8, cm) ; OK (ok) ;
+ }
+ }
+ CHOLMOD(free_factor) (&L8, cm) ;
+ }
+ }
+
+ X->x = x ;
+ ok = CHOLMOD(free_dense)(&X, cm) ; OK (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* ssmult */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow < 100)
+ {
+ C = CHOLMOD(ssmult)(A, A, 0, TRUE, TRUE, cm) ;
+ if (A->nrow != A->ncol || !isreal)
+ {
+ NOP (C) ;
+ }
+ else
+ {
+ OKP (C) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ }
+ C = CHOLMOD(ssmult)(NULL, A, 0, TRUE, TRUE, cm) ; NOP (C) ;
+ C = CHOLMOD(ssmult)(A, NULL, 0, TRUE, TRUE, cm) ; NOP (C) ;
+ C = CHOLMOD(ssmult)(A, Axbad, 0, TRUE, TRUE, cm) ; NOP (C) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* sdmult */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow > 1)
+ {
+ ok = CHOLMOD(sdmult)(A, FALSE, one, one, Two, Two, cm) ; NOT (ok) ;
+ }
+
+ YY = CHOLMOD(ones)(A->nrow, 1, xtype, cm) ; OKP (YY) ;
+ XX = CHOLMOD(ones)(A->ncol, 1, xtype, cm) ; OKP (XX) ;
+ cm->print = 4 ;
+ ok = CHOLMOD(print_dense)(XX, "XX", cm) ; OK (ok) ;
+ cm->print = 1 ;
+ ok = CHOLMOD(sdmult)(A, FALSE, one, one, XX, YY, cm) ; OK (ok) ;
+ ok = CHOLMOD(sdmult)(NULL, FALSE, one, one, XX, YY, cm) ; NOT (ok) ;
+ ok = CHOLMOD(sdmult)(A, FALSE, one, one, NULL, YY, cm) ; NOT (ok) ;
+ ok = CHOLMOD(sdmult)(A, FALSE, one, one, XX, NULL, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(sdmult)(Abad2, FALSE, one, one, XX, YY, cm) ; NOT (ok) ;
+
+ XX->xtype++ ;
+ ok = CHOLMOD(sdmult)(A, FALSE, one, one, XX, YY, cm) ; NOT (ok) ;
+ XX->xtype-- ;
+
+ YY->xtype++ ;
+ ok = CHOLMOD(sdmult)(A, FALSE, one, one, XX, YY, cm) ; NOT (ok) ;
+ YY->xtype-- ;
+
+ CHOLMOD(free_dense)(&YY, cm) ;
+ CHOLMOD(free_dense)(&XX, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symmetry */
+ /* ---------------------------------------------------------------------- */
+
+ for (option = 0 ; option <= 2 ; option++)
+ {
+ Int xmatched = 0, pmatched = 0, nzoffdiag = 0, nz_diag = 0 ;
+ int asym ;
+ printf ("test symmetry: option %d\n", option) ;
+ save1 = cm->print ;
+ cm->print = 5 ;
+ CHOLMOD(print_sparse) (A, "A", cm) ;
+ cm->print = save1 ;
+ asym = CHOLMOD(symmetry) (A, option, &xmatched, &pmatched,
+ &nzoffdiag, &nz_diag, cm) ;
+ printf ("asym: %d\n", asym) ;
+ OK (A->stype != 0 || asym >= 0) ;
+ save1 = A->xtype ;
+ A->xtype = CHOLMOD_PATTERN ;
+ asym = CHOLMOD(symmetry) (A, option, &xmatched, &pmatched,
+ &nzoffdiag, &nz_diag, cm) ;
+ printf ("asym: %d pattern\n", asym) ;
+ OK (A->stype != 0 || asym >= 0) ;
+ A->xtype = save1 ;
+ C = CHOLMOD(copy_sparse) (A, cm) ;
+ OKP (C) ;
+ ok = CHOLMOD(sparse_xtype) (CHOLMOD_ZOMPLEX, C, cm) ;
+ OK (ok) ;
+ asym = CHOLMOD(symmetry) (C, option, &xmatched, &pmatched,
+ &nzoffdiag, &nz_diag, cm) ;
+ OK (A->stype != 0 || asym >= 0) ;
+ printf ("asym: %d zomplex\n", asym) ;
+
+ asym = CHOLMOD(symmetry) (NULL, option, &xmatched, &pmatched,
+ &nzoffdiag, &nz_diag, cm) ;
+ NOT (asym >= 0) ;
+
+ C->xtype = 999 ;
+ asym = CHOLMOD(symmetry) (C, option, &xmatched, &pmatched,
+ &nzoffdiag, &nz_diag, cm) ;
+ NOT (asym >= 0) ;
+ C->xtype = CHOLMOD_ZOMPLEX ;
+
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+
+ C = CHOLMOD(copy) (A, 0, (A->xtype == CHOLMOD_REAL), cm) ;
+ OKP (C) ;
+ asym = CHOLMOD(symmetry) (C, option, &xmatched, &pmatched,
+ &nzoffdiag, &nz_diag, cm) ;
+ OK (asym >= 0) ;
+ ok = CHOLMOD(free_sparse)(&C, cm) ; OK (ok) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* memory tests */
+ /* ---------------------------------------------------------------------- */
+
+ R3 = CHOLMOD(speye)(nrow, 1, CHOLMOD_PATTERN, cm) ; /* [ */
+ OKP (R3) ;
+
+ test_memory_handler ( ) ;
+
+ ok = CHOLMOD(amd)(A, NULL, 0, Pok, cm) ;
+ if (A->nrow == 0)
+ {
+ OK (ok) ;
+ }
+ else
+ {
+ NOT (ok) ;
+ }
+
+#ifndef NPARTITION
+ ok = CHOLMOD(camd)(A, NULL, 0, NULL, Pok, cm) ;
+ if (A->nrow == 0)
+ {
+ OK (ok) ;
+ }
+ else
+ {
+ NOT (ok) ;
+ }
+#endif
+
+ C = CHOLMOD(aat)(A, NULL, 0, 0, cm) ; NOP (C) ;
+ A->sorted = FALSE ;
+ ok = CHOLMOD(check_sparse)(A, cm) ; NOT (ok) ;
+ A->sorted = TRUE ;
+
+ CHOLMOD(free_work)(cm) ;
+ if (A->stype == 0)
+ {
+ for (trial = 0 ; !ok && trial < 20 ; trial++)
+ {
+ my_tries = trial ;
+ printf ("--------------------- trial "ID"\n", my_tries) ;
+ ok = CHOLMOD(colamd)(A, NULL, 0, TRUE, Pok, cm) ;
+ }
+ OK (ok) ;
+ }
+
+
+#ifndef NPARTITION
+ test_memory_handler ( ) ;
+ ok = CHOLMOD(ccolamd)(A, fsetok, fsizeok, NULL, Pok, cm) ; NOT (ok) ;
+ ok = CHOLMOD(csymamd)(A, NULL, Pok, cm) ; NOT (ok) ;
+ for (trial = 0 ; trial < 7 ; trial++)
+ {
+ test_memory_handler ( ) ;
+ my_tries = trial ;
+ ok = CHOLMOD(csymamd)(A, NULL, Pok, cm) ; NOT (ok) ;
+ }
+
+ if (A->nrow == A->ncol && A->packed)
+ {
+ test_memory_handler ( ) ;
+ my_tries = 8 ;
+ ok = CHOLMOD(csymamd)(A, NULL, Pok, cm) ; OK (ok) ;
+ test_memory_handler ( ) ;
+ ok = CHOLMOD(csymamd)(A, NULL, Pok, cm) ; NOT (ok) ;
+ OK (cm->status == CHOLMOD_OUT_OF_MEMORY) ;
+ }
+
+ for (trial = 0 ; trial < 5 ; trial++)
+ {
+ test_memory_handler ( ) ;
+ my_tries = trial ;
+ ok = CHOLMOD(camd)(A, NULL, 0, NULL, Pok, cm) ;
+ if (A->nrow == 0)
+ {
+ OK (ok) ;
+ }
+ else
+ {
+ NOT (ok) ;
+ }
+ }
+#endif
+
+ test_memory_handler ( ) ;
+
+ ok = CHOLMOD(etree)(A, Parent, cm) ; NOT (ok) ;
+ ok = CHOLMOD(factorize)(A, L, cm) ; NOT (ok) ;
+
+ pp = CHOLMOD(malloc)(4, 0, cm) ; NOP (pp) ;
+ pp = CHOLMOD(calloc)(4, 0, cm) ; NOP (pp) ;
+ pp = CHOLMOD(calloc)(Size_max, 1, cm) ; NOP (pp) ;
+ pp = NULL ;
+ size = 0 ;
+ pp = CHOLMOD(realloc)(4, 0, pp, &size, cm) ; NOP (pp) ;
+ pp = CHOLMOD(realloc)(Size_max, 1, pp, &size, cm) ; NOP (pp) ;
+
+ normal_memory_handler ( ) ;
+ OK (CHOLMOD(print_sparse)(A, "A ok", cm)) ;
+ OK (CHOLMOD(print_factor)(L, "L ok", cm)) ;
+
+ /* test no_workspace_reallocate flag */
+ CHOLMOD (free_work) (cm) ;
+ CHOLMOD (allocate_work) (1, 1, 1, cm) ;
+ OK (cm->status == CHOLMOD_OK) ;
+ cm->no_workspace_reallocate = TRUE ;
+ ok = CHOLMOD (allocate_work) (2, 1, 1, cm) ;
+ NOT (ok) ;
+ ok = CHOLMOD (allocate_work) (1, 2, 1, cm) ;
+ NOT (ok) ;
+ ok = CHOLMOD (allocate_work) (1, 1, 2, cm) ;
+ NOT (ok) ;
+ cm->no_workspace_reallocate = FALSE ;
+ ok = CHOLMOD (allocate_work) (1, 1, 2, cm) ;
+ OK (ok) ;
+
+ cm->print = 4 ;
+ ok = CHOLMOD(print_factor)(L, "L for copy", cm) ;
+ OK (ok) ;
+ ok = FALSE ;
+ test_memory_handler ( ) ;
+ for (trial = 0 ; !ok && trial < 100 ; trial++)
+ {
+ my_tries = trial ;
+ Lcopy = CHOLMOD(copy_factor)(L, cm) ;
+ ok = (Lcopy != NULL) ;
+ }
+ normal_memory_handler ( ) ;
+ ok = CHOLMOD(print_factor)(Lcopy, "Lcopy", cm) ;
+ OK (ok) ;
+ CHOLMOD(free_factor)(&Lcopy, cm) ;
+ cm->print = 1 ;
+
+ test_memory_handler ( ) ;
+ ok = CHOLMOD(resymbol)(A, NULL, 0, TRUE, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(resymbol_noperm)(A, NULL, 0, TRUE, L, cm) ; NOT (ok) ;
+
+ lr = CHOLMOD(postorder)(Parent, nrow, NULL, Post, cm) ; NOT (lr>=0) ;
+
+ T = CHOLMOD(copy_triplet)(Tok, cm) ; NOT (ok) ;
+
+#ifndef NPARTITION
+ lr = CHOLMOD(nested_dissection)(A, NULL, 0, Pok, CParent,
+ Cmember, cm) ;
+ if (nrow == 0)
+ {
+ OK (lr >= 0) ;
+ }
+ else
+ {
+ NOT (lr >= 0) ;
+ }
+
+ lr = CHOLMOD(nested_dissection)(Abad2, NULL, 0, Pok, CParent,
+ Cmember, cm) ;
+ NOT (lr >= 0) ;
+
+ ok = CHOLMOD(metis)(A, NULL, 0, TRUE, Pok, cm) ;
+
+ if (nrow == 0)
+ {
+ OK (ok) ;
+ }
+ else
+ {
+ NOT (ok) ;
+ }
+ lr = CHOLMOD(bisect)(A, NULL, 0, TRUE, Partition, cm) ;
+
+ if (nrow == 0)
+ {
+ OK (lr == 0) ;
+ }
+ else
+ {
+ NOT (lr >= 0) ;
+ }
+
+ lr = CHOLMOD(bisect)(Abad2, NULL, 0, TRUE, Partition, cm) ; NOT (lr >= 0) ;
+
+#endif
+
+ if (nrow > 3)
+ {
+ ok = CHOLMOD(rowdel)(nrow-2, NULL, L5, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowadd)(nrow-2, R, L5, cm) ; NOT (ok) ;
+ ok = CHOLMOD(updown)(+1, A, L, cm) ; NOT (ok) ;
+ }
+
+ C = CHOLMOD(add)(A, A, one, one, TRUE, TRUE, cm) ; NOP (C) ;
+ C = CHOLMOD(ssmult)(A, A, 0, TRUE, TRUE, cm) ; NOP (C) ;
+
+ ok = CHOLMOD(rowcolcounts)(A, NULL, 0, Parent, Post,
+ NULL, ColCount, First, Level, cm) ; NOT (ok) ;
+
+ ok = CHOLMOD(rowfac)(A, NULL, beta, 0, 0, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_unsym)(A, 1, Pok, NULL, 0, R, cm) ; NOT (ok) ;
+ ok = CHOLMOD(transpose_sym)(A, 1, Pok, R, cm) ; NOT (ok) ;
+ if (nrow > 1)
+ {
+ ok = CHOLMOD(sort)(A, cm) ; NOT (ok) ;
+ }
+
+ ok = CHOLMOD(row_subtree)(A, AT, 0, Parent, R3, cm) ; NOT (ok) ;
+ ATi = (AT == NULL) ? NULL : AT->i ;
+ ok = CHOLMOD(row_lsubtree)(A, ATi, 0, 0, L, R3, cm) ; NOT (ok) ;
+
+ normal_memory_handler ( ) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the valid objects */
+ /* ---------------------------------------------------------------------- */
+
+ cm->status = CHOLMOD_OK ;
+
+ CHOLMOD(free_triplet)(NULL, cm) ;
+
+ CHOLMOD(free_sparse)(&R3, cm) ; /* ] */
+ CHOLMOD(free_sparse)(&R, cm) ; /* ] */
+ CHOLMOD(free_sparse)(&Acopy, cm) ; /* ] */
+ CHOLMOD(free_factor)(&L5, cm) ; /* ] */
+ CHOLMOD(free_factor)(&L2, cm) ; /* ] */
+
+ Lbad->xtype = Lxtype ;
+ CHOLMOD(free_factor)(&Lbad, cm) ; /* ] */
+
+ CHOLMOD(free_factor)(&L, cm) ; /* ] */
+
+ CHOLMOD(free_triplet)(&T, cm) ;
+
+ Axbad->xtype = Axbad_type ;
+ CHOLMOD(free_sparse)(&Axbad, cm) ; /* ] */
+
+ cm->error_handler = my_handler ;
+
+ Xbad2->xtype = CHOLMOD_REAL ;
+ CHOLMOD(free_dense)(&Xbad2, cm) ; /* ] */
+
+ Abad2->xtype = Abad2xtype ;
+ CHOLMOD(free_sparse)(&Abad2, cm) ; /* ] */
+
+ CHOLMOD(free_sparse)(&Abad, cm) ; /* ] */
+
+ CHOLMOD(free_sparse)(&R0, cm) ;
+ CHOLMOD(free_sparse)(&R1, cm) ; /* ] */
+
+ CHOLMOD(free_sparse)(&Aboth, cm) ; /* ] */
+ CHOLMOD(free_sparse)(&Sok, cm) ;
+
+
+ CHOLMOD(free)(nrow, sizeof (Int), Pinv, cm) ;
+ CHOLMOD(free)(nrow, sizeof (Int), Parent, cm) ;
+ CHOLMOD(free)(nrow, sizeof (Int), Post, cm) ;
+ CHOLMOD(free)(nrow, sizeof (Int), Cmember, cm) ;
+ CHOLMOD(free)(nrow, sizeof (Int), CParent, cm) ;
+ CHOLMOD(free)(nrow, sizeof (Int), Partition, cm) ;
+ CHOLMOD(free)(nrow, sizeof (Int), ColCount, cm) ;
+ CHOLMOD(free)(nrow, sizeof (Int), First, cm) ;
+ CHOLMOD(free)(nrow, sizeof (Int), Level, cm) ; /* ] */
+
+ CHOLMOD(free_dense)(&Two, cm) ; /* ] */
+
+ CHOLMOD(free_sparse)(&R2, cm) ; /* ] */
+ CHOLMOD(free)(nrow, sizeof (Int), Pok, cm) ; /* ] */
+
+ CHOLMOD(free_sparse)(&I1, cm) ; /* ] */
+
+ CHOLMOD(free)(nrow, sizeof (Int), Pbad, cm) ; /* ] */
+
+ CHOLMOD(free)(ncol, sizeof (Int), fsetbad, cm) ; /* ] */
+ CHOLMOD(free)(ncol, sizeof (Int), fsetok, cm) ; /* ] */
+
+ CHOLMOD(free_dense)(&Bok, cm) ; /* ] */
+
+ CHOLMOD(free_dense)(&Xok, cm) ; /* ] */
+
+ CHOLMOD(free_sparse)(&AT, cm) ; /* ] */
+
+ CHOLMOD(free_sparse)(&A, cm) ; /* ] */
+
+ OK (cm->status == CHOLMOD_OK) ;
+ printf ("\n------------------------null2 tests: All OK\n") ;
+}
diff --git a/CHOLMOD/Tcov/raw_factor.c b/CHOLMOD/Tcov/raw_factor.c
new file mode 100644
index 0000000..edf8203
--- /dev/null
+++ b/CHOLMOD/Tcov/raw_factor.c
@@ -0,0 +1,888 @@
+/* ========================================================================== */
+/* === Tcov/raw_factor ====================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Factorize A using cholmod_rowfac for the simplicial case, and the
+ * cholmod_super_* routines for the supernodal case, and test the solution to
+ * linear systems. */
+
+#include "cm.h"
+
+
+/* ========================================================================== */
+/* === icomp ================================================================ */
+/* ========================================================================== */
+
+/* for sorting by qsort */
+static int icomp (Int *i, Int *j)
+{
+ if (*i < *j)
+ {
+ return (-1) ;
+ }
+ else
+ {
+ return (1) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === add_gunk ============================================================= */
+/* ========================================================================== */
+
+static cholmod_sparse *add_gunk (cholmod_sparse *A)
+{
+ cholmod_sparse *S ;
+ double *Sx, *Sz ;
+ Int *Sp, *Si, nz, p, save3, j, n ;
+
+ if (A == NULL) return (NULL) ;
+
+ /* save3 = cm->print ; cm->print = 5 ; */
+
+ A->nzmax++ ;
+ S = CHOLMOD(copy_sparse) (A, cm) ;
+ A->nzmax-- ;
+
+ /* add a S(n,1)=1 entry to the matrix */
+ if (S != NULL)
+ {
+ S->sorted = FALSE ;
+ Sx = S->x ;
+ Si = S->i ;
+ Sp = S->p ;
+ Sz = S->z ;
+ n = S->ncol ;
+ nz = Sp [n] ;
+ for (j = 1 ; j <= n ; j++)
+ {
+ Sp [j]++ ;
+ }
+ if (S->xtype == CHOLMOD_REAL)
+ {
+ for (p = nz-1 ; p >= 0 ; p--)
+ {
+ Si [p+1] = Si [p] ;
+ Sx [p+1] = Sx [p] ;
+ }
+ Si [0] = n-1 ;
+ Sx [0] = 99999 ;
+ }
+ else if (S->xtype == CHOLMOD_COMPLEX)
+ {
+ for (p = nz-1 ; p >= 0 ; p--)
+ {
+ Si [p+1] = Si [p] ;
+ Sx [2*p+2] = Sx [2*p] ;
+ Sx [2*p+3] = Sx [2*p+1] ;
+ }
+ Si [0] = n-1 ;
+ Sx [0] = 99999 ;
+ Sx [1] = 0 ;
+ }
+ else if (S->xtype == CHOLMOD_ZOMPLEX)
+ {
+ for (p = nz-1 ; p >= 0 ; p--)
+ {
+ Si [p+1] = Si [p] ;
+ Sx [p+1] = Sx [p] ;
+ Sz [p+1] = Sz [p] ;
+ }
+ Si [0] = n-1 ;
+ Sx [0] = 99999 ;
+ Sz [0] = 0 ;
+ }
+ }
+
+ /* CHOLMOD(print_sparse) (A, "A for gunk", cm) ; */
+ /* CHOLMOD(print_sparse) (S, "S with gunk", cm) ; */
+ /* cm->print = save3 ; */
+
+ return (S) ;
+}
+
+
+/* ========================================================================== */
+/* === raw_factor =========================================================== */
+/* ========================================================================== */
+
+/* Factor A, without using any fill-reducing permutation. This may fail due
+ * to catastrophic fill-in (which is the desired test result for a large
+ * arrowhead matrix).
+ */
+
+double raw_factor (cholmod_sparse *A, Int check_errors)
+{
+ double maxerr = 0, r, anorm ;
+ cholmod_sparse *AT, *C, *LT, *Lsparse, *S, *ST, *R, *A1 ;
+ cholmod_factor *L, *Lcopy ;
+ cholmod_dense *X, *W, *B, *X2 ;
+ Int i, k, n, ok, ok1, ok2, trial, rnz, lnz, Lxtype, Axtype, posdef,
+ prefer_zomplex, Bxtype ;
+ Int *Parent, *Post, *First, *Level, *Ri, *Rp, *LTp = NULL, *LTi = NULL, *P,
+ *mask, *RLinkUp ;
+ UF_long lr ;
+ double beta [2] ;
+ unsigned UF_long save ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create the problem */
+ /* ---------------------------------------------------------------------- */
+
+ if (A == NULL || A->stype != 1)
+ {
+ return (0) ;
+ }
+
+ W = NULL ;
+ X2 = NULL ;
+ L = NULL ;
+ n = A->nrow ;
+ B = rhs (A, 1, n) ;
+ AT = CHOLMOD(transpose) (A, 2, cm) ;
+ Parent = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Post = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ First = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Level = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ beta [0] = 0 ;
+ beta [1] = 0 ;
+ anorm = CHOLMOD(norm_sparse) (A, 1, cm) ;
+
+ prefer_zomplex = (A->xtype == CHOLMOD_ZOMPLEX) ;
+ Bxtype = A->xtype ;
+
+ /* ---------------------------------------------------------------------- */
+ /* supernodal factorization */
+ /* ---------------------------------------------------------------------- */
+
+ L = CHOLMOD(allocate_factor) (n, cm) ;
+ ok1 = CHOLMOD(etree) (A, Parent, cm) ;
+ lr = CHOLMOD(postorder) (Parent, n, NULL, Post, cm) ;
+ ok2 = CHOLMOD(rowcolcounts) (AT, NULL, 0, Parent, Post,
+ NULL, (L != NULL) ? (L->ColCount) : NULL, First, Level, cm) ;
+
+ if (ok2)
+ {
+ printf ("raw_factor: cm->fl %g cm->lnz %g\n", cm->fl, cm->lnz) ;
+ }
+
+ if (check_errors)
+ {
+ OKP (AT) ;
+ OKP (Parent) ;
+ OKP (Post) ;
+ OKP (First) ;
+ OKP (Level) ;
+ OK (AT->stype == -1) ;
+ OKP (L) ;
+ OK (ok1) ;
+ OK (ok2) ;
+ OK (lr >= 0) ;
+
+ /* rowcolcounts requires A in symmetric lower form */
+ ok = CHOLMOD(rowcolcounts) (A, NULL, 0, Parent, Post,
+ NULL, L->ColCount, First, Level, cm) ; NOT (ok) ;
+ }
+
+ /* super_symbolic needs A in upper form, so this will succeed
+ * unless the problem is huge */
+ ok = CHOLMOD(super_symbolic) (A, NULL, Parent, L, cm) ;
+
+ /* super_symbolic should fail if lnz is too large */
+ if (cm->lnz > Size_max / 2)
+ {
+ printf ("raw_factor: problem is huge\n") ;
+ NOT (ok) ;
+ OK (L->xtype == CHOLMOD_PATTERN && !(L->is_super)) ;
+
+ /* try changing to LDL packed, which should also fail */
+ ok = CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, TRUE, TRUE,
+ L, cm) ;
+ NOT (ok) ;
+
+ CHOLMOD(free_factor) (&L, cm) ;
+ CHOLMOD(free_sparse) (&AT, cm) ;
+ CHOLMOD(free_dense) (&B, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), First, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Level, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Parent, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Post, cm) ;
+ return (0) ;
+ }
+
+ if (check_errors)
+ {
+
+ if (cm->status == CHOLMOD_OUT_OF_MEMORY
+ || cm->status == CHOLMOD_TOO_LARGE)
+ {
+ /* no test case will reach here, but check just to be safe */
+ printf ("raw_factor: out of memory for symbolic case %d\n",
+ cm->status) ;
+ CHOLMOD(free_factor) (&L, cm) ;
+ CHOLMOD(free_sparse) (&AT, cm) ;
+ CHOLMOD(free_dense) (&B, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), First, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Level, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Parent, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Post, cm) ;
+ return (0) ;
+ }
+
+ OK (ok) ;
+ ok = CHOLMOD(super_symbolic)(A, NULL, Parent, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_symbolic)(AT, NULL, Parent, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_symbolic)(NULL, NULL, Parent, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_symbolic)(A, NULL, NULL, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_symbolic)(A, NULL, Parent, NULL, cm) ; NOT (ok) ;
+ }
+
+ /* super_numeric needs A in lower form, so this will succeed unless
+ * the problem is huge */
+ ok = CHOLMOD(super_numeric) (AT, NULL, Zero, L, cm) ;
+
+ if (check_errors)
+ {
+
+ if (cm->status == CHOLMOD_OUT_OF_MEMORY)
+ {
+ /* For the 64-bit case, the Matrix/a1 problem will reach here */
+ printf ("raw_factor: out of memory for numeric case\n") ;
+ CHOLMOD(free_factor) (&L, cm) ;
+ CHOLMOD(free_sparse) (&AT, cm) ;
+ CHOLMOD(free_dense) (&B, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), First, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Level, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Parent, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Post, cm) ;
+ return (0) ;
+ }
+
+ OK (ok) ;
+ ok = CHOLMOD(super_numeric)(A, NULL, Zero, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_numeric)(NULL, NULL, Zero, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_numeric)(AT, NULL, Zero, NULL, cm) ; NOT (ok) ;
+ }
+
+ /* solve */
+ Lxtype = (L == NULL) ? CHOLMOD_REAL : L->xtype ;
+ W = CHOLMOD(zeros) (n, 1, Lxtype, cm) ;
+ X = CHOLMOD(copy_dense) (B, cm) ;
+ if (Bxtype == CHOLMOD_ZOMPLEX)
+ {
+ CHOLMOD(dense_xtype) (CHOLMOD_COMPLEX, X, cm) ;
+ }
+
+ CHOLMOD(print_factor) (L, "L for super l/ltsolve", cm) ;
+ CHOLMOD(print_dense) (W, "W", cm) ;
+ CHOLMOD(print_dense) (X, "X", cm) ;
+
+ ok1 = CHOLMOD(super_lsolve) (L, X, W, cm) ;
+ CHOLMOD(print_dense) (X, "X", cm) ;
+
+ ok2 = CHOLMOD(super_ltsolve) (L, X, W, cm) ;
+ CHOLMOD(print_dense) (X, "X", cm) ;
+
+ if (Bxtype == CHOLMOD_ZOMPLEX)
+ {
+ CHOLMOD(dense_xtype) (CHOLMOD_ZOMPLEX, X, cm) ;
+ }
+
+ r = resid (A, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+
+ if (Bxtype == CHOLMOD_ZOMPLEX)
+ {
+ CHOLMOD(dense_xtype) (CHOLMOD_COMPLEX, X, cm) ;
+ }
+
+ if (check_errors)
+ {
+ OKP (W) ;
+ OKP (X) ;
+ OK (ok1) ;
+ OK (ok2) ;
+ ok = CHOLMOD(super_lsolve) (NULL, X, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve) (NULL, X, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_lsolve) (L, NULL, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve) (L, NULL, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_lsolve) (L, X, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve) (L, X, NULL, cm) ; NOT (ok) ;
+
+ if (L != NULL && L->maxesize > 1)
+ {
+ /* W is too small */
+ ok = CHOLMOD(free_dense) (&W, cm) ; OK (ok) ;
+ W = CHOLMOD(zeros) (1, 1, Lxtype, cm) ; OKP (W) ;
+ ok = CHOLMOD(super_lsolve) (L, X, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve) (L, X, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(free_dense) (&W, cm) ; OK (ok) ;
+ W = CHOLMOD(zeros) (n, 1, Lxtype, cm) ; OKP (W) ;
+ }
+
+ /* X2 has the wrong dimensions */
+ X2 = CHOLMOD(zeros) (n+1, 1, Lxtype, cm) ; OKP (X2) ;
+ ok = CHOLMOD(super_lsolve) (L, X2, W, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_ltsolve) (L, X2, W, cm) ; NOT (ok) ;
+ CHOLMOD(free_dense) (&X2, cm) ;
+ }
+
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* X2 is n-by-0, which is OK */
+ X2 = CHOLMOD(zeros) (n, 0, Lxtype, cm) ;
+ ok1 = CHOLMOD(super_lsolve) (L, X2, W, cm) ;
+ ok2 = CHOLMOD(super_ltsolve) (L, X2, W, cm) ;
+ CHOLMOD(free_dense) (&W, cm) ;
+ CHOLMOD(free_dense) (&X2, cm) ;
+
+ if (check_errors)
+ {
+ OK (ok1) ;
+ OK (ok2) ;
+ test_memory_handler ( ) ;
+ my_tries = 0 ;
+ ok = CHOLMOD(super_symbolic) (A, NULL, Parent, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(super_numeric) (AT, NULL, Zero, L, cm) ; NOT (ok) ;
+ normal_memory_handler ( ) ;
+ cm->error_handler = NULL ;
+ }
+
+ /* R = space for result of row_subtree and row_lsubtree */
+ R = CHOLMOD(allocate_sparse)(n, 1, n, FALSE, TRUE, 0, CHOLMOD_PATTERN, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* erroneous factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* cannot use rowfac or row_lsubtree on a supernodal factorization */
+ if (check_errors && n > 0)
+ {
+ ok = CHOLMOD(rowfac) (A, NULL, beta, 0, 0, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(row_lsubtree) (A, &i, 0, n-1, L, R, cm) ; NOT (ok) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to simplicial LDL' */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(change_factor) (Lxtype, FALSE, FALSE, TRUE, TRUE, L, cm) ;
+
+ /* remove entries due to relaxed supernodal amalgamation */
+ CHOLMOD(resymbol) (A, NULL, 0, TRUE, L, cm) ;
+
+ /* refactorize a numeric factor */
+ posdef = 0 ; /* unknown */
+ if (A != NULL && A->stype >= 0)
+ {
+ if (A->stype > 0 && A->packed)
+ {
+ S = add_gunk (A) ;
+ CHOLMOD(rowfac) (S, NULL, beta, 0, n, L, cm) ;
+ if (S && S->xtype == CHOLMOD_COMPLEX)
+ {
+ CHOLMOD(sparse_xtype) (CHOLMOD_ZOMPLEX, S, cm) ;
+ }
+ ok = CHOLMOD(free_sparse) (&S, cm) ; OK (ok) ;
+ }
+ else
+ {
+ CHOLMOD(rowfac) (A, NULL, beta, 0, n, L, cm) ;
+ }
+ posdef = (cm->status == CHOLMOD_OK) ;
+ }
+
+ /* convert to a sparse matrix, and transpose L */
+ Lcopy = CHOLMOD(copy_factor)(L, cm) ;
+ Lsparse = CHOLMOD(factor_to_sparse) (L, cm) ;
+
+ LT = CHOLMOD(transpose) (Lsparse, 0, cm) ;
+ CHOLMOD(free_sparse) (&Lsparse, cm) ;
+
+ if (LT != NULL)
+ {
+ LTp = LT->p ;
+ LTi = LT->i ;
+ OK (LT->packed) ;
+ }
+
+ /* remove the unit diagonal of LT */
+ CHOLMOD(band_inplace) (1, n, -1, LT, cm) ;
+
+ /* ST = pattern of A(p,p)' */
+ P = (L == NULL) ? NULL : L->Perm ;
+ ST = CHOLMOD(ptranspose) (A, 0, P, NULL, 0, cm) ;
+
+ /* S = pattern of A(p,p) */
+ S = CHOLMOD(transpose) (ST, 0, cm) ;
+ ok = CHOLMOD(free_sparse) (&ST, cm) ;
+
+ if (R != NULL && LT != NULL && posdef && A != NULL && A->stype >= 0
+ && S != NULL && Lcopy != NULL)
+ {
+ LTp = LT->p ;
+ LTi = LT->i ;
+
+ Ri = R->i ;
+ Rp = R->p ;
+
+ save = my_seed ( ) ; /* RAND */
+ for (trial = 0 ; trial < 30 ; trial++)
+ {
+ /* pick a row at random */
+ i = nrand (n) ; /* RAND */
+
+ /* compute R = pattern of L(i,0:i-1), using row subtrees */
+ ok = CHOLMOD(row_subtree) (S, NULL, i, Parent, R, cm) ;
+ if (!ok)
+ {
+ break ;
+ }
+ rnz = Rp [1] ;
+
+ /* sort R */
+ qsort (Ri, rnz, sizeof (Int),
+ (int (*) (const void *, const void *)) icomp) ;
+
+ /* compare with ith column of L transpose */
+ lnz = LTp [i+1] - LTp [i] ;
+ ok = TRUE ;
+ for (k = 0 ; k < MIN (rnz,lnz) ; k++)
+ {
+ /* printf ("%d vs %d\n", Ri [k], LTi [LTp [i] + k]) ; */
+ ok = ok && (Ri [k] == LTi [LTp [i] + k]) ;
+ }
+ OK (ok) ;
+ OK (rnz == lnz) ;
+
+ /* compute R = pattern of L(i,0:i-1), using row lsubtrees */
+ ok = CHOLMOD(row_lsubtree) (S, NULL, 0, i, Lcopy, R, cm) ;
+ if (!ok)
+ {
+ break ;
+ }
+ rnz = Rp [1] ;
+
+ /* sort R */
+ qsort (Ri, rnz, sizeof (Int),
+ (int (*) (const void *, const void *)) icomp) ;
+
+ /* compare with ith column of L transpose */
+ lnz = LTp [i+1] - LTp [i] ;
+ ok = TRUE ;
+ for (k = 0 ; k < MIN (rnz,lnz) ; k++)
+ {
+ /* printf ("%d vs %d\n", Ri [k], LTi [LTp [i] + k]) ; */
+ ok = ok && (Ri [k] == LTi [LTp [i] + k]) ;
+ }
+ OK (ok) ;
+ OK (rnz == lnz) ;
+
+ /* L is symbolic, so cholmod_lsubtree will fail */
+ if (check_errors)
+ {
+ ok = CHOLMOD(row_lsubtree) (S, NULL, 0, i, L, R, cm) ;
+ NOT (ok) ;
+ }
+
+ }
+ my_srand (save) ; /* RAND */
+ }
+
+ ok = CHOLMOD(free_factor) (&L, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_factor) (&Lcopy, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse) (<, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse) (&R, cm) ; OK (ok) ;
+ ok = CHOLMOD(free_sparse) (&S, cm) ; OK (ok) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* simplicial LDL' or LL' factorization with no analysis */
+ /* ---------------------------------------------------------------------- */
+
+ for (trial = 0 ; trial <= check_errors ; trial++)
+ {
+
+ /* create a simplicial symbolic factor */
+ L = CHOLMOD(allocate_factor) (n, cm) ;
+ ok = TRUE ;
+ Axtype = (A == NULL) ? CHOLMOD_REAL : A->xtype ;
+
+ if (check_errors)
+ {
+ OKP (L) ;
+ if (trial == 0)
+ {
+ /* convert to packed LDL' first, then unpacked */
+ ok = CHOLMOD(change_factor) (Axtype, FALSE, FALSE, TRUE,
+ TRUE, L, cm) ;
+ OK (ok);
+ ok = CHOLMOD(change_factor) (Axtype, FALSE, FALSE, FALSE,
+ TRUE, L, cm) ;
+ OK (ok) ;
+ }
+ else if (trial == 1)
+ {
+ ok = CHOLMOD(rowfac)(NULL, NULL, beta, 0, 0, L, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowfac)(A, NULL, beta, 0, 0, NULL, cm) ; NOT (ok) ;
+ ok = CHOLMOD(rowfac)(AT, NULL, beta, 0, 0, L, cm) ; NOT (ok) ;
+ if (n > 1)
+ {
+ A1 = CHOLMOD(allocate_sparse)(1, 1, 1, TRUE, TRUE, 1,
+ CHOLMOD_PATTERN, cm) ; OKP (A1) ;
+ ok = CHOLMOD(rowfac)(A1, NULL, beta, 0, 0, L, cm); NOT (ok);
+ ok = CHOLMOD(free_sparse)(&A1, cm) ; OK (ok);
+ }
+ }
+ else
+ {
+ /* convert to symbolic LL' */
+ ok = CHOLMOD(change_factor) (CHOLMOD_PATTERN, TRUE, FALSE, TRUE,
+ TRUE, L, cm) ;
+ OK (ok) ;
+ OK (L->is_ll) ;
+ }
+ }
+
+ /* factor */
+ CHOLMOD(print_factor) (L, "L for rowfac", cm) ;
+ CHOLMOD(print_sparse) (A, "A for rowfac", cm) ;
+
+ cm->dbound = 1e-15 ;
+ for (k = 0 ; ok && k < n ; k++)
+ {
+ if (!CHOLMOD(rowfac) (A, NULL, beta, k, k+1, L, cm))
+ {
+ ok = FALSE ;
+ }
+ if (cm->status == CHOLMOD_NOT_POSDEF)
+ {
+ /* LL' factorization failed; subsequent rowfac's should fail */
+ k++ ;
+ ok = CHOLMOD(rowfac) (A, NULL, beta, k, k+1, L, cm) ;
+ NOT (ok) ;
+ ok = TRUE ;
+ }
+ }
+ cm->dbound = 0 ;
+
+ if (check_errors)
+ {
+ OK (ok) ;
+ ok = CHOLMOD(rowfac) (A, NULL, beta, n, n+1, L, cm) ; NOT (ok) ;
+ ok = TRUE ;
+ }
+
+ /* solve */
+ if (ok)
+ {
+
+/*
+int saveit = cm->print ;
+int saveit2 = cm->precise ;
+cm->print = 5 ;
+cm->precise = TRUE ;
+
+CHOLMOD (print_sparse) (A, "A here", cm) ;
+CHOLMOD (print_factor) (L, "L here", cm) ;
+CHOLMOD (print_dense) (B, "B here", cm) ;
+*/
+
+ cm->prefer_zomplex = prefer_zomplex ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+
+/*
+CHOLMOD (print_dense) (X, "X here", cm) ;
+*/
+
+ cm->prefer_zomplex = FALSE ;
+ r = resid (A, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+/*
+cm->print = saveit ;
+cm->precise = saveit2 ;
+fprintf (stderr, "solve %8.2e\n", r) ;
+*/
+ }
+
+ CHOLMOD(free_factor) (&L, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* factor again with entries in the (ignored) lower part A */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->packed)
+ {
+ L = CHOLMOD(allocate_factor) (n, cm) ;
+ C = add_gunk (A) ;
+
+/*
+ C = CHOLMOD(copy) (A, 0, 1, cm) ;
+ if (C != NULL)
+ {
+ C->stype = 1 ;
+ }
+*/
+
+ CHOLMOD(rowfac) (C, NULL, beta, 0, n, L, cm) ;
+
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+
+ r = resid (A, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_factor) (&L, cm) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* factor again using rowfac_mask (for LPDASA only) */
+ /* ---------------------------------------------------------------------- */
+
+ r = raw_factor2 (A, 0., 0) ;
+ MAXERR (maxerr, r, 1) ;
+
+ r = raw_factor2 (A, 1e-16, 0) ;
+ MAXERR (maxerr, r, 1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the problem */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_sparse) (&AT, cm) ;
+ CHOLMOD(free_dense) (&B, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), First, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Level, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Parent, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Post, cm) ;
+ progress (0, '.') ;
+ return (maxerr) ;
+}
+
+
+/* ========================================================================== */
+/* === raw_factor2 ========================================================== */
+/* ========================================================================== */
+
+/* A->stype can be 0 (lower), 1 (upper) or 0 (unsymmetric). In the first two
+ * cases, Ax=b is solved. In the third, A*A'x=b is solved. No analysis and no
+ * fill-reducing ordering is used. Both simplicial LL' and LDL' factorizations
+ * are used (testing rowfac_mask, for LPDASA only). */
+
+double raw_factor2 (cholmod_sparse *A, double alpha, int domask)
+{
+ Int n, i, prefer_zomplex, is_ll, xtype, sorted, axtype, stype ;
+ Int *mask = NULL, *RLinkUp = NULL, nz = 0 ;
+ Int *Cp = NULL, added_gunk ;
+ double maxerr = 0, r = 0 ;
+ cholmod_sparse *AT = NULL, *C = NULL, *CT = NULL, *CC = NULL, *C2 = NULL ;
+ cholmod_factor *L = NULL ;
+ cholmod_dense *B = NULL, *X = NULL ;
+ double beta [2] ;
+
+/*
+int saveit = cm->print ;
+int saveit2 = cm->precise ;
+cm->print = 5 ;
+cm->precise = TRUE ;
+*/
+
+ if (A == NULL)
+ {
+ return (0) ;
+ }
+ n = A->nrow ;
+ if (n > 1000)
+ {
+ printf ("\nSkipping rowfac, matrix too large\n") ;
+ return (0) ;
+ }
+ axtype = A->xtype ;
+ beta [0] = alpha ;
+ beta [1] = 0 ;
+
+ prefer_zomplex = (A->xtype == CHOLMOD_ZOMPLEX) ;
+ AT = CHOLMOD(transpose) (A, 2, cm) ;
+
+ /* ensure C has stype of 0 or 1. Do not prune any entries */
+ stype = A->stype ;
+ if (stype >= 0)
+ {
+ A->stype = 0 ;
+ C = CHOLMOD(copy_sparse) (A, cm) ;
+ A->stype = stype ;
+ if (C) C->stype = stype ;
+ /*
+ C = CHOLMOD(copy) (A, 0, 1, cm) ;
+ if (C) C->stype = A->stype ;
+ */
+ CT = AT ;
+
+ }
+ else
+ {
+ C = AT ;
+ /*
+ CT = CHOLMOD(copy_sparse) (A, cm) ;
+ */
+ /*
+ CT = CHOLMOD(copy) (A, 0, 1, cm) ;
+ if (CT) CT->stype = A->stype ;
+ */
+ A->stype = 0 ;
+ CT = CHOLMOD(copy_sparse) (A, cm) ;
+ A->stype = stype ;
+ if (CT) CT->stype = stype ;
+
+ /* only domask if C is symmetric and upper part stored */
+ domask = FALSE ;
+
+ }
+
+ mask = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ RLinkUp = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+
+ if (C && cm->status == CHOLMOD_OK)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ mask [i] = -1 ;
+ RLinkUp [i] = i+1 ;
+ }
+ }
+ else
+ {
+ domask = FALSE ;
+ }
+
+ if (C && !(C->packed) && !(C->sorted))
+ {
+ /* do not do the unpacked or unsorted cases */
+ domask = FALSE ;
+ }
+
+ /* make a copy of C and add some gunk if stype > 0 */
+ added_gunk = (C && C->stype > 0) ;
+ if (added_gunk)
+ {
+ C2 = add_gunk (C) ;
+ }
+ else
+ {
+ C2 = CHOLMOD(copy_sparse) (C, cm) ;
+ }
+
+ CC = CHOLMOD(copy_sparse) (C2, cm) ;
+
+ if (CC && domask)
+ {
+ Int *Cp, *Ci, p ;
+ double *Cx, *Cz ;
+
+ /* this implicitly sets the first row/col of C to zero, except diag. */
+ mask [0] = 1 ;
+
+ /* CC = C2, and then set the first row/col to zero, except diagonal */
+ Cp = CC->p ;
+ Ci = CC->i ;
+ Cx = CC->x ;
+ Cz = CC->z ;
+ nz = Cp [n] ;
+ switch (C->xtype)
+ {
+ case CHOLMOD_REAL:
+ for (p = 1 ; p < nz ; p++)
+ {
+ if (Ci [p] == 0) Cx [p] = 0 ;
+ }
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ for (p = 1 ; p < nz ; p++)
+ {
+ if (Ci [p] == 0)
+ {
+ Cx [2*p ] = 0 ;
+ Cx [2*p+1] = 0 ;
+ }
+ }
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ for (p = 1 ; p < nz ; p++)
+ {
+ if (Ci [p] == 0)
+ {
+ Cx [p] = 0 ;
+ Cz [p] = 0 ;
+ }
+ }
+ break ;
+ }
+ }
+
+ B = rhs (CC, 1, n) ;
+
+ for (sorted = 1 ; sorted >= 0 ; sorted--)
+ {
+
+ if (!sorted)
+ {
+ if (C2 && !added_gunk) C2->sorted = FALSE ;
+ if (C) C->sorted = FALSE ;
+ if (CT) CT->sorted = FALSE ;
+ }
+
+ for (is_ll = 0 ; is_ll <= 1 ; is_ll++)
+ {
+ for (xtype = 0 ; xtype <= 1 ; xtype++)
+ {
+
+ L = CHOLMOD(allocate_factor) (n, cm) ;
+ if (L) L->is_ll = is_ll ;
+
+ if (xtype)
+ {
+ CHOLMOD (change_factor) (axtype, is_ll, 0, 0, 1, L, cm) ;
+ }
+
+ CHOLMOD(rowfac_mask) (sorted ? C : C2,
+ CT, beta, 0, n, mask, RLinkUp, L, cm) ;
+
+ cm->prefer_zomplex = prefer_zomplex ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+ cm->prefer_zomplex = FALSE ;
+
+ r = resid (CC, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+
+ printf ("rowfac mask: resid is %g\n", r) ;
+
+ CHOLMOD(free_factor) (&L, cm) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ }
+ }
+ }
+
+ CHOLMOD(free) (n, sizeof (Int), mask, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), RLinkUp, cm) ;
+
+ CHOLMOD(free_sparse) (&C2, cm) ;
+ CHOLMOD(free_sparse) (&CC, cm) ;
+ CHOLMOD(free_sparse) (&CT, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_dense) (&B, cm) ;
+
+ return (maxerr) ;
+}
diff --git a/CHOLMOD/Tcov/solve.c b/CHOLMOD/Tcov/solve.c
new file mode 100644
index 0000000..380f304
--- /dev/null
+++ b/CHOLMOD/Tcov/solve.c
@@ -0,0 +1,1256 @@
+/* ========================================================================== */
+/* === Tcov/solve =========================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Test CHOLMOD for solving various systems of linear equations. */
+
+#include "cm.h"
+
+#define NFTYPES 17
+Int ll_types [NFTYPES] = { 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0 } ;
+Int pk_types [NFTYPES] = { 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0 } ;
+Int mn_types [NFTYPES] = { 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0 } ;
+Int co_types [NFTYPES] = { 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1 } ;
+
+#define NRHS 9
+
+#ifndef NDEBUG
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+EXTERN int cholmod_dump, cholmod_l_dump ;
+#endif
+
+/* ========================================================================== */
+/* === test_solver ========================================================== */
+/* ========================================================================== */
+
+/* Test solve(A) with various control parameters */
+
+double test_solver (cholmod_sparse *A)
+{
+ double err, maxerr = 0 ;
+ int save ;
+
+ for (cm->postorder = 0 ; cm->postorder <= 1 ; cm->postorder++)
+ {
+
+ my_srand (42) ; /* RAND reset */
+
+ /* simplicial, no extra memory */
+ printf ("test_solver: simplicial, no extra memory\n") ;
+ cm->supernodal = CHOLMOD_SIMPLICIAL ;
+ cm->grow2 = 0 ;
+ err = solve (A) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("test_solver err: %6.2e\n", err) ;
+
+ /* simplicial, extra space in columns of L */
+ printf ("test_solver: simplicial, extra space in columns of L\n") ;
+ cm->grow2 = 5 ;
+ err = solve (A) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("test_solver err: %6.2e\n", err) ;
+
+ /* supernodal */
+ printf ("test_solver: supernodal\n") ;
+ cm->supernodal = CHOLMOD_SUPERNODAL ;
+ err = solve (A) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("test_solver err: %6.2e\n", err) ;
+
+ /* supernodal, without final resymbol */
+ printf ("test_solver: supernodal, without final resymbol\n") ;
+ cm->final_resymbol = FALSE ;
+ err = solve (A) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("test_solver err: %6.2e\n", err) ;
+
+ /* supernodal, with resymbol, final_super false */
+ printf ("test_solver: supernodal, with resymbol\n") ;
+ cm->supernodal = CHOLMOD_SUPERNODAL ;
+ cm->final_asis = FALSE ;
+ cm->final_resymbol = TRUE ;
+ cm->final_super = FALSE ;
+ err = solve (A) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("test_solver err: %6.2e\n", err) ;
+
+ /* supernodal, with resymbol, final_super tree */
+ printf ("test_solver: supernodal, with resymbol\n") ;
+ cm->supernodal = CHOLMOD_SUPERNODAL ;
+ cm->final_asis = FALSE ;
+ cm->final_resymbol = TRUE ;
+ cm->final_super = TRUE ;
+ err = solve (A) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("test_solver err: %6.2e\n", err) ;
+
+ /* simplicial LL' */
+ printf ("test_solver: simplicial LL', try NESDIS instead of METIS\n") ;
+ cm->supernodal = CHOLMOD_SIMPLICIAL ;
+ cm->final_ll = TRUE ;
+cm->default_nesdis = TRUE ;
+ err = solve (A) ;
+cm->default_nesdis = FALSE ;
+ MAXERR (maxerr, err, 1) ;
+ cm->final_ll = FALSE ;
+ printf ("test_solver err: %6.2e\n", err) ;
+
+ /* supernodal, without final resymbol, and no relaxed supernodes */
+ printf (
+"test_solver: supernodal, without final resymbol, and no relaxed supernodes\n") ;
+ cm->supernodal = CHOLMOD_SUPERNODAL ;
+ cm->final_asis = TRUE ;
+ cm->nrelax [0] = 0 ;
+ cm->nrelax [1] = 0 ;
+ cm->nrelax [2] = 0 ;
+ cm->zrelax [0] = 0 ;
+ cm->zrelax [1] = 0 ;
+ cm->zrelax [2] = 0 ;
+ cm->grow0 = 1 ;
+ cm->grow1 = 1 ;
+ cm->grow2 = 0 ;
+ err = solve (A) ;
+ MAXERR (maxerr, err, 1) ;
+ printf ("test_solver err: %6.2e\n", err) ;
+
+ /* ------------------------------------------------------------------ */
+ /* restore defaults */
+ /* ------------------------------------------------------------------ */
+
+ cm->dbound = 0.0 ;
+
+ cm->grow0 = 1.2 ;
+ cm->grow1 = 1.2 ;
+ cm->grow2 = 5 ;
+
+ cm->final_asis = TRUE ;
+ cm->final_super = TRUE ;
+ cm->final_ll = FALSE ;
+ cm->final_pack = TRUE ;
+ cm->final_monotonic = TRUE ;
+ cm->final_resymbol = FALSE ;
+
+ cm->supernodal = CHOLMOD_AUTO ;
+ cm->nrelax [0] = 4 ;
+ cm->nrelax [1] = 16 ;
+ cm->nrelax [2] = 48 ;
+ cm->zrelax [0] = 0.8 ;
+ cm->zrelax [1] = 0.1 ;
+ cm->zrelax [2] = 0.05 ;
+
+ /* do not restore these defaults: */
+ /*
+ cm->maxrank = ...
+ cm->metis_memory = 2.0
+ cm->metis_nswitch = 3000
+ cm->metis_dswitch = 0.66
+ cm->print = 3
+ cm->precise = FALSE
+ */
+ }
+
+ progress (1, '.') ;
+ return (maxerr) ;
+}
+
+
+/* ========================================================================== */
+/* === solve ================================================================ */
+/* ========================================================================== */
+
+/* solve Ax=b or AA'x=b, systems involving just L, D, or L', and update/downdate
+ * the system. Returns the worst-case residual. This routine keeps going if
+ * it runs out of memory (unless the error handler terminates it), because
+ * it is used both normally and in the memory tests.
+ */
+
+double solve (cholmod_sparse *A)
+{
+ double r, enorm, snorm, maxerr = 0, gnorm, anorm, bnorm, xnorm, norm, rcond;
+ cholmod_factor *L, *Lcopy, *L2 ;
+ cholmod_sparse *Lmat, *Lo, *D, *Up, *S, *LD, *LDL, *E, *I, *C, *CC, *Ct,
+ *Ssym, *Cperm, *C2, *S2, *H, *F, *Lo1, *Aboth ;
+ cholmod_dense *X, *Cdense, *B, *Bcomplex, *Bzomplex, *Breal, *W, *R,
+ *A3, *C3, *E3 ;
+ cholmod_sparse *AFt, *AF, *G, *RowK, *Bsparse, *Xsparse ;
+ double *Cx ;
+ Int *P, *cset, *fset, *Parent, *Post, *RowCount, *ColCount,
+ *First, *Level, *rcount, *ccount, *Lp, *Li ;
+ Int p, i, j, k, n, nrhs, save, save2, csize, rank, nrow, ncol, is_ll,
+ xtype, isreal, prefer_zomplex, Lxtype, xtype2, save3 ;
+ int blas_ok = TRUE ;
+
+ if (cm->print > 1)
+ {
+ printf ("============================================== in solve:\n") ;
+ }
+
+ if (A == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "nothing to solve") ;
+ return (1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct right-hand-side (Ax=b if symmetric, AA'x=b otherwise) */
+ /* ---------------------------------------------------------------------- */
+
+ n = A->nrow ;
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ xtype = A->xtype ;
+ isreal = (xtype == CHOLMOD_REAL) ;
+ B = rhs (A, NRHS, n) ;
+ anorm = CHOLMOD(norm_sparse) (A, 1, cm) ;
+ save = cm->final_asis ;
+ cm->final_asis = TRUE ;
+
+ /* contents of these will be revised later */
+ Bzomplex = CHOLMOD(copy_dense) (B, cm) ;
+ Bcomplex = CHOLMOD(copy_dense) (Bzomplex, cm) ;
+ Breal = CHOLMOD(copy_dense) (Bzomplex, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* analyze */
+ /* ---------------------------------------------------------------------- */
+
+ if (n < 100 && cm->nmethods == 1 && cm->method[0].ordering == CHOLMOD_GIVEN)
+ {
+ Int *UserPerm = prand (nrow) ; /* RAND */
+ L = CHOLMOD(analyze_p) (A, UserPerm, NULL, 0, cm) ;
+ OK (CHOLMOD(print_common) ("with UserPerm", cm)) ;
+ CHOLMOD(free) (nrow, sizeof (Int), UserPerm, cm) ;
+ }
+ else
+ {
+ L = CHOLMOD(analyze) (A, cm) ;
+ }
+
+ /* test rowadd on a symbolic factor */
+ if (isreal)
+ {
+ RowK = CHOLMOD(spzeros) (n, 1, 0, CHOLMOD_REAL, cm) ;
+ Lcopy = CHOLMOD(copy_factor) (L, cm) ;
+ if (n > 0)
+ {
+ CHOLMOD(rowadd) (0, RowK, Lcopy, cm) ;
+ CHOLMOD(check_factor) (Lcopy, cm) ;
+ CHOLMOD(print_factor) (Lcopy, "Lcopy, now numeric", cm) ;
+ }
+ CHOLMOD(free_sparse) (&RowK, cm) ;
+ CHOLMOD(free_factor) (&Lcopy, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(factorize) (A, L, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* various solves */
+ /* ---------------------------------------------------------------------- */
+
+ if (B != NULL)
+ {
+ /* B->ncol = 1 ; */
+ prefer_zomplex = (B->xtype == CHOLMOD_ZOMPLEX) ;
+ }
+ else
+ {
+ prefer_zomplex = FALSE ;
+ }
+
+ for (k = 0 ; k <= 1 ; k++)
+ {
+ cm->prefer_zomplex = k ;
+
+ /* compute the residual, X complex if L or B not real */
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+ r = resid (A, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* zomplex right-hand-side */
+ CHOLMOD(dense_xtype) (CHOLMOD_ZOMPLEX, Bzomplex, cm) ;
+ if (Bzomplex != NULL && B != NULL && B->xtype == CHOLMOD_REAL
+ && Bzomplex->xtype == CHOLMOD_ZOMPLEX)
+ {
+ /* add an arbitrary imaginary part */
+ double *Bz = Bzomplex->z ;
+ for (j = 0 ; j < NRHS ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Bz [i+j*n] = (double) (i+j*n) ;
+ }
+ }
+ }
+ X = CHOLMOD(solve) (CHOLMOD_A, L, Bzomplex, cm) ;
+ r = resid (A, X, Bzomplex) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* complex right-hand-side */
+ CHOLMOD(dense_xtype) (CHOLMOD_COMPLEX, Bcomplex, cm) ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L, Bcomplex, cm) ;
+ r = resid (A, X, Bcomplex) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* real right-hand-side */
+ CHOLMOD(dense_xtype) (CHOLMOD_REAL, Breal, cm) ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L, Breal, cm) ;
+ r = resid (A, X, Breal) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* sparse solve of Ax=b, b real */
+ Bsparse = CHOLMOD(dense_to_sparse) (Breal, TRUE, cm) ;
+ Xsparse = CHOLMOD(spsolve) (CHOLMOD_A, L, Bsparse, cm) ;
+ r = resid_sparse (A, Xsparse, Bsparse) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_sparse) (&Bsparse, cm) ;
+ CHOLMOD(free_sparse) (&Xsparse, cm) ;
+
+ /* sparse solve of Ax=b, b complex */
+ Bsparse = CHOLMOD(dense_to_sparse) (Bcomplex, TRUE, cm) ;
+ Xsparse = CHOLMOD(spsolve) (CHOLMOD_A, L, Bsparse, cm) ;
+ r = resid_sparse (A, Xsparse, Bsparse) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_sparse) (&Bsparse, cm) ;
+ CHOLMOD(free_sparse) (&Xsparse, cm) ;
+
+ /* sparse solve of Ax=b, b zomplex */
+ Bsparse = CHOLMOD(dense_to_sparse) (Bzomplex, TRUE, cm) ;
+ Xsparse = CHOLMOD(spsolve) (CHOLMOD_A, L, Bsparse, cm) ;
+ r = resid_sparse (A, Xsparse, Bsparse) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_sparse) (&Bsparse, cm) ;
+ CHOLMOD(free_sparse) (&Xsparse, cm) ;
+ }
+
+ cm->prefer_zomplex = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* sparse solve to compute inv(A) */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(print_sparse) (A, "A", cm) ;
+ CHOLMOD(print_factor) (L, "L", cm) ;
+ rcond = CHOLMOD(rcond) (L, cm) ;
+ if (cm->print > 1)
+ {
+ printf ("rcond: %g\n", rcond) ;
+ }
+
+ if (n < 100 && A->stype != 0)
+ {
+ /* solve A*C=I, so C should equal A inverse */
+ I = CHOLMOD(speye) (n, n, CHOLMOD_REAL, cm) ;
+ C = CHOLMOD(spsolve) (CHOLMOD_A, L, I, cm) ;
+ /* compute norm of A*C-I */
+ if (isreal && n > 10)
+ {
+ /* A and C are large and real */
+ E = CHOLMOD(ssmult) (A, C, 0, TRUE, FALSE, cm) ;
+ F = CHOLMOD(add) (E, I, minusone, one, TRUE, FALSE, cm) ;
+ r = CHOLMOD(norm_sparse) (F, 1, cm) ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+ CHOLMOD(free_sparse) (&F, cm) ;
+ }
+ else
+ {
+ /* There is no complex ssmult or add, so use the BLAS.
+ * Also test sparse_to_dense for small symmetric matrices. */
+ A3 = CHOLMOD(sparse_to_dense) (A, cm) ;
+ C3 = CHOLMOD(sparse_to_dense) (C, cm) ;
+ xtype2 = isreal ? CHOLMOD_REAL : CHOLMOD_COMPLEX ;
+ CHOLMOD(dense_xtype) (xtype2, A3, cm) ;
+ CHOLMOD(dense_xtype) (xtype2, C3, cm) ;
+ E3 = CHOLMOD(eye) (n, n, xtype2, cm) ;
+ if (A3 != NULL && C3 != NULL && E3 != NULL)
+ {
+ /* E3 = A3*C3-I */
+ if (isreal)
+ {
+ BLAS_dgemm ("N", "N", n, n, n, one, A3->x, n, C3->x, n,
+ minusone, E3->x, n) ;
+ }
+ else
+ {
+ BLAS_zgemm ("N", "N", n, n, n, one, A3->x, n, C3->x, n,
+ minusone, E3->x, n) ;
+ }
+ OK (blas_ok) ;
+ }
+ r = CHOLMOD(norm_dense) (E3, 1, cm) ;
+ CHOLMOD(free_dense) (&A3, cm) ;
+ CHOLMOD(free_dense) (&C3, cm) ;
+ CHOLMOD(free_dense) (&E3, cm) ;
+ }
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_sparse) (&I, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* change complexity of L and solve again; test copy/change routines */
+ /* ---------------------------------------------------------------------- */
+
+ /* change to complex, otherwise leave as */
+ Lcopy = CHOLMOD(copy_factor) (L, cm) ;
+ CHOLMOD(factor_xtype) (CHOLMOD_COMPLEX, Lcopy, cm) ;
+ X = CHOLMOD(solve) (CHOLMOD_A, Lcopy, B, cm) ;
+ r = resid (A, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ CHOLMOD(free_factor) (&Lcopy, cm) ;
+
+ /* change to zomplex LDL' */
+ Lxtype = (L == NULL) ? CHOLMOD_REAL : (L->xtype) ;
+ Lcopy = CHOLMOD(copy_factor) (L, cm) ;
+ CHOLMOD(check_factor) (L, cm) ;
+ CHOLMOD(print_factor) (Lcopy, "Lcopy", cm) ;
+ CHOLMOD(change_factor) (Lxtype, FALSE, FALSE, TRUE, TRUE, Lcopy, cm) ;
+ CHOLMOD(factor_xtype) (CHOLMOD_ZOMPLEX, Lcopy, cm) ;
+ X = CHOLMOD(solve) (CHOLMOD_A, Lcopy, B, cm) ;
+ r = resid (A, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ CHOLMOD(free_factor) (&Lcopy, cm) ;
+
+ Lcopy = CHOLMOD(copy_factor) (L, cm) ;
+ CHOLMOD(change_factor) (Lxtype, TRUE, FALSE, FALSE, FALSE, Lcopy, cm) ;
+ CHOLMOD(check_factor) (L, cm) ;
+ CHOLMOD(print_factor) (Lcopy, "Lcopy LL unpacked", cm) ;
+ CHOLMOD(free_factor) (&Lcopy, cm) ;
+
+ CHOLMOD(free_factor) (&L, cm) ;
+ cm->final_asis = save ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve again, but use cm->final_asis as given */
+ /* ---------------------------------------------------------------------- */
+
+ if (n < 100 && cm->nmethods == 1 && cm->method[0].ordering == CHOLMOD_GIVEN)
+ {
+ Int *UserPerm = prand (nrow) ; /* RAND */
+ L = CHOLMOD(analyze_p) (A, UserPerm, NULL, 0, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), UserPerm, cm) ;
+ }
+ else
+ {
+ L = CHOLMOD(analyze) (A, cm) ;
+ }
+
+ CHOLMOD(print_factor) (L, "Lsymbolic", cm) ;
+ CHOLMOD(factorize) (A, L, cm) ;
+
+ /* turn off memory tests [ */
+ save3 = my_tries ;
+ my_tries = -1 ;
+
+ CHOLMOD(print_factor) (L, "Lnumeric for solver tests", cm) ;
+ CHOLMOD(print_dense) (B, "B for solver tests", cm) ;
+ CHOLMOD(print_dense) (Breal, "Breal for solver tests", cm) ;
+ CHOLMOD(print_dense) (Bcomplex, "Bcomplex for solver tests", cm) ;
+ CHOLMOD(print_dense) (Bzomplex, "Bzomplex for solver tests", cm) ;
+
+ if (B != NULL && Breal != NULL && Bcomplex != NULL && Bzomplex != NULL)
+ {
+ for (nrhs = 1 ; nrhs <= NRHS ; nrhs++)
+ {
+ for (cm->prefer_zomplex = 0 ; cm->prefer_zomplex <= 1 ;
+ cm->prefer_zomplex++)
+ {
+ B->ncol = nrhs ;
+ Breal->ncol = nrhs ;
+ Bcomplex->ncol = nrhs ;
+ Bzomplex->ncol = nrhs ;
+
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+ r = resid (A, X, B) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ MAXERR (maxerr, r, 1) ;
+
+ X = CHOLMOD(solve) (CHOLMOD_A, L, Breal, cm) ;
+ r = resid (A, X, Breal) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ MAXERR (maxerr, r, 1) ;
+
+ X = CHOLMOD(solve) (CHOLMOD_A, L, Bcomplex, cm) ;
+ r = resid (A, X, Bcomplex) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ MAXERR (maxerr, r, 1) ;
+
+ X = CHOLMOD(solve) (CHOLMOD_A, L, Bzomplex, cm) ;
+ r = resid (A, X, Bzomplex) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ MAXERR (maxerr, r, 1) ;
+ }
+ }
+ }
+ cm->prefer_zomplex = FALSE ;
+
+ /* turn memory tests back on, where we left off ] */
+ my_tries = save3 ;
+
+ Lcopy = CHOLMOD(copy_factor) (L, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to LDL' packed or LL packed */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("before change factor : %d\n", L ? L->is_super : -1) ;
+ is_ll = (L == NULL) ? FALSE : (L->is_ll) ;
+ Lxtype = (L == NULL) ? CHOLMOD_REAL : (L->xtype) ;
+ CHOLMOD(change_factor) (Lxtype, is_ll, FALSE, TRUE, TRUE, Lcopy, cm) ;
+ printf ("after change factor : %d\n", L ? L->is_super : -1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extract L, D, and L' as matrices from Lcopy */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(resymbol) (A, NULL, 0, TRUE, Lcopy, cm) ;
+
+ Lmat = CHOLMOD(factor_to_sparse) (Lcopy, cm) ;
+ CHOLMOD(check_sparse) (Lmat, cm) ;
+
+ I = CHOLMOD(speye) (n, n, CHOLMOD_REAL, cm) ;
+
+ Lo = NULL ;
+ D = NULL ;
+
+ Lxtype = (Lmat == NULL) ? CHOLMOD_REAL : (Lmat->xtype) ;
+
+ if (isreal)
+ {
+ /* use band and add */
+ if (!is_ll)
+ {
+ /* factorization is LDL' = Lo*D*Up */
+ Lo1 = CHOLMOD(band) (Lmat, -n, -1, 1, cm) ;
+ Lo = CHOLMOD(add) (Lo1, I, one, one, TRUE, TRUE, cm) ;
+ CHOLMOD(free_sparse) (&Lo1, cm) ;
+ D = CHOLMOD(band) (Lmat, 0, 0, 1, cm) ;
+ }
+ else
+ {
+ /* factorization is LL' = Lo*D*Up */
+ Lo = CHOLMOD(band) (Lmat, -n, 0, 1, cm) ;
+ D = CHOLMOD(speye) (n, n, Lxtype, cm) ;
+ }
+ }
+ else
+ {
+ /* band and add do not work for c/zomplex matrices*/
+ D = CHOLMOD(speye) (n, n, Lxtype, cm) ;
+ Lo = CHOLMOD(copy_sparse) (Lmat, cm) ;
+ if (!is_ll && D != NULL && Lo != NULL)
+ {
+ /* factorization is LDL' = Lo*D*Up */
+ double *Dx = D->x ;
+ double *Lx = Lo->x ;
+ Lp = Lo->p ;
+ for (k = 0 ; k < n ; k++)
+ {
+ p = Lp [k] ;
+ if (Lxtype == CHOLMOD_COMPLEX)
+ {
+ Dx [2*k] = Lx [2*p] ;
+ Lx [2*p] = 1 ;
+ }
+ else
+ {
+ Dx [k] = Lx [p] ;
+ Lx [p] = 1 ;
+ }
+ }
+ }
+ }
+
+ Up = CHOLMOD(transpose) (Lo, 2, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute 1-norm of (Lo*D*Up - PAP') or (Lo*D*Up - PAA'P') */
+ /* ---------------------------------------------------------------------- */
+
+ P = (L != NULL) ? (L->Perm) : NULL ;
+ S = NULL ;
+ G = NULL ;
+
+ if (isreal)
+ {
+
+ if (A->stype == 0)
+ {
+ /* G = A*A', try with fset = prand (ncol) */
+ fset = prand (ncol) ; /* RAND */
+ AFt = CHOLMOD(ptranspose) (A, 1, NULL, fset, ncol, cm) ;
+ AF = CHOLMOD(transpose) (AFt, 1, cm) ;
+ CHOLMOD(free) (ncol, sizeof (Int), fset, cm) ;
+ G = CHOLMOD(ssmult) (AF, AFt, 0, TRUE, TRUE, cm) ;
+
+ /* also try aat */
+ H = CHOLMOD(aat) (AF, NULL, 0, 1, cm) ;
+ E = CHOLMOD(add) (G, H, one, minusone, TRUE, FALSE, cm) ;
+ enorm = CHOLMOD(norm_sparse) (E, 0, cm) ;
+ gnorm = CHOLMOD(norm_sparse) (G, 0, cm) ;
+ MAXERR (maxerr, enorm, gnorm) ;
+ if (cm->print > 1)
+ {
+ printf ("enorm %g gnorm %g hnorm %g\n", enorm, gnorm,
+ CHOLMOD(norm_sparse) (H, 0, cm)) ;
+ }
+ if (gnorm > 0)
+ {
+ enorm /= gnorm ;
+ }
+ OK (enorm < 1e-8) ;
+ CHOLMOD(free_sparse) (&AFt, cm) ;
+ CHOLMOD(free_sparse) (&AF, cm) ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+ CHOLMOD(free_sparse) (&H, cm) ;
+ }
+ else
+ {
+ /* G = A */
+ G = CHOLMOD(copy) (A, 0, 1, cm) ;
+ }
+
+ if (A->stype == 0)
+ {
+ /* S = PAA'P' */
+ S = CHOLMOD(submatrix) (G, P, n, P, n, TRUE, FALSE, cm) ;
+ }
+ else
+ {
+ /* S = PAP' */
+ Aboth = CHOLMOD(copy) (A, 0, 1, cm) ;
+ S = CHOLMOD(submatrix) (Aboth, P, n, P, n, TRUE, FALSE, cm) ;
+ CHOLMOD(free_sparse) (&Aboth, cm) ;
+ }
+
+ if (n < NSMALL)
+ {
+ /* only do this for small test matrices, since L*D*L' can have many
+ * nonzero entries */
+
+ /* E = L*D*L' - S */
+ LD = CHOLMOD(ssmult) (Lo, D, 0, TRUE, FALSE, cm) ;
+ LDL = CHOLMOD(ssmult) (LD, Up, 0, TRUE, FALSE, cm) ;
+ CHOLMOD(free_sparse) (&LD, cm) ;
+ E = CHOLMOD(add) (LDL, S, one, minusone, TRUE, FALSE, cm) ;
+ CHOLMOD(free_sparse) (&LDL, cm) ;
+
+ /* e = norm (E) / norm (S) */
+ enorm = CHOLMOD(norm_sparse) (E, 1, cm) ;
+ snorm = CHOLMOD(norm_sparse) (S, 0, cm) ;
+ MAXERR (maxerr, enorm, snorm) ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+ }
+
+ /* check the row/col counts */
+ RowCount = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ ColCount = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Parent = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Post = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ First = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ Level = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
+ rcount = CHOLMOD(calloc) (n, sizeof (Int), cm) ;
+ ccount = CHOLMOD(calloc) (n, sizeof (Int), cm) ;
+
+ if (S != NULL && Lmat != NULL && RowCount != NULL && ColCount != NULL &&
+ Parent != NULL && Post != NULL && First != NULL && Level != NULL &&
+ rcount != NULL && ccount != NULL)
+ {
+ S->stype = 1 ;
+
+ CHOLMOD(etree) (S, Parent, cm) ;
+ CHOLMOD(print_parent) (Parent, n, "Parent", cm) ;
+ CHOLMOD(postorder) (Parent, n, NULL, Post, cm) ;
+ CHOLMOD(print_perm) (Post, n, n, "Post", cm) ;
+ S->stype = -1 ;
+ CHOLMOD(rowcolcounts) (S, NULL, 0, Parent, Post, RowCount, ColCount,
+ First, Level, cm) ;
+
+ Lp = Lmat->p ;
+ Li = Lmat->i ;
+ OK (Lmat->packed) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Lp [j] ; p < Lp [j+1] ; p++)
+ {
+ i = Li [p] ;
+ rcount [i]++ ;
+ ccount [j]++ ;
+ }
+ }
+ /* a singular matrix will only be partially factorized */
+ if (L->minor == (size_t) n)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ OK (ccount [j] == ColCount [j]) ;
+ }
+ }
+ for (i = 0 ; i < (Int) (L->minor) ; i++)
+ {
+ OK (rcount [i] == RowCount [i]) ;
+ }
+ }
+
+ CHOLMOD(free) (n, sizeof (Int), RowCount, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), ColCount, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Parent, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Post, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), First, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), Level, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), rcount, cm) ;
+ CHOLMOD(free) (n, sizeof (Int), ccount, cm) ;
+
+ CHOLMOD(free_sparse) (&S, cm) ;
+ }
+
+ CHOLMOD(free_factor) (&Lcopy, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve other systems */
+ /* ---------------------------------------------------------------------- */
+
+ /* turn off memory tests [ */
+ save3 = my_tries ;
+ my_tries = -1 ;
+
+ for (nrhs = 1 ; nrhs <= 4 ; nrhs++) /* reduced here (6 to 4) */
+ {
+ if (B == NULL)
+ {
+ break ;
+ }
+
+ B->ncol = nrhs ;
+
+ /* solve LDL'x=b */
+ X = CHOLMOD(solve) (CHOLMOD_LDLt, L, B, cm) ;
+ /* printf ("LDL'x=b %p %p %p\n", Lo, X, B) ; */
+ r = resid3 (Lo, D, Up, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* solve LDx=b */
+ X = CHOLMOD(solve) (CHOLMOD_LD, L, B, cm) ;
+ /* printf ("LDx=b %p %p %p\n", Lo, X, B) ; */
+ r = resid3 (Lo, D, NULL, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* solve DL'x=b */
+ X = CHOLMOD(solve) (CHOLMOD_DLt, L, B, cm) ;
+ /* printf ("DL'x=b %p %p %p\n", D, X, B) ; */
+ r = resid3 (D, Up, NULL, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* solve Lx=b */
+ X = CHOLMOD(solve) (CHOLMOD_L, L, B, cm) ;
+ /* printf ("Lx=b %p %p %p\n", Lo, X, B) ; */
+ r = resid3 (Lo, NULL, NULL, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* solve L'x=b */
+ X = CHOLMOD(solve) (CHOLMOD_Lt, L, B, cm) ;
+ /* printf ("L'x=b %p %p %p\n", Up, X, B) ; */
+ r = resid3 (Up, NULL, NULL, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* solve Dx=b */
+ X = CHOLMOD(solve) (CHOLMOD_D, L, B, cm) ;
+ /* printf ("Dx=b %p %p %p\n", D, X, B) ; */
+ r = resid3 (D, NULL, NULL, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ save2 = cm->prefer_zomplex ;
+ for (k = 0 ; k <= 1 ; k++)
+ {
+ cm->prefer_zomplex = k ;
+
+ /* x=Pb */
+ X = CHOLMOD(solve) (CHOLMOD_P, L, B, cm) ;
+ r = pnorm (X, P, B, FALSE) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* x=P'b */
+ X = CHOLMOD(solve) (CHOLMOD_Pt, L, B, cm) ;
+ r = pnorm (X, P, B, TRUE) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ }
+ cm->prefer_zomplex = save2 ;
+
+ }
+
+ /* turn memory tests back on, where we left off ] */
+ my_tries = save3 ;
+
+ CHOLMOD(free_dense) (&B, cm) ;
+ CHOLMOD(free_sparse) (&I, cm) ;
+ CHOLMOD(free_sparse) (&D, cm) ;
+ CHOLMOD(free_sparse) (&Lo, cm) ;
+ CHOLMOD(free_sparse) (&Up, cm) ;
+ CHOLMOD(free_sparse) (&Lmat, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* update the factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* turn off memory tests [ */
+ save3 = my_tries ;
+ my_tries = -1 ;
+
+ B = rhs (A, 1, n) ;
+
+ for (rank = 1 ; isreal && rank <= ((n < 100) ? 33 : 2) ; rank++)
+ {
+
+ /* pick a random C */
+ Cdense = CHOLMOD(zeros) (n, rank, CHOLMOD_REAL, cm) ;
+
+ if (Cdense != NULL)
+ {
+ Cx = Cdense->x ;
+ for (k = 0 ; k < 10*rank ; k++)
+ {
+ i = nrand (n) ; /* RAND */
+ j = nrand (rank) ; /* RAND */
+ Cx [i+j*n] += xrand (1.) ; /* RAND */
+ }
+ }
+
+ C = CHOLMOD(dense_to_sparse) (Cdense, TRUE, cm) ;
+ CHOLMOD(free_dense) (&Cdense, cm) ;
+
+ /* permute the rows according to L->Perm */
+ Cperm = CHOLMOD(submatrix) (C, P, n, NULL, -1, TRUE, TRUE, cm) ;
+
+ /* update */
+ CHOLMOD(updown) (TRUE, Cperm, L, cm) ;
+ CHOLMOD(free_sparse) (&Cperm, cm) ;
+
+ /* solve (G+C*C')x=b */
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+
+ /* an alternative method would be to compute (G*x + C*(C'*x) - b) */
+
+ /* compute S = G+C*C', with no sort */
+ Ct = CHOLMOD(transpose) (C, 1, cm) ;
+ CC = CHOLMOD(ssmult) (C, Ct, 0, TRUE, FALSE, cm) ;
+ S = CHOLMOD(add) (G, CC, one, one, TRUE, TRUE, cm) ;
+ Ssym = CHOLMOD(copy) (S, 1, 1, cm) ;
+ CHOLMOD(free_sparse) (&CC, cm) ;
+ CHOLMOD(free_sparse) (&Ct, cm) ;
+
+ /* compute norm (S*x-b) */
+ r = resid (Ssym, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* ------------------------------------------------------------------ */
+ /* factor A+CC' from scratch, using same permutation */
+ /* ------------------------------------------------------------------ */
+
+ if (rank == 1)
+ {
+ save = cm->nmethods ;
+ save2 = cm->method [0].ordering ;
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_GIVEN ;
+ L2 = CHOLMOD(analyze_p) (Ssym, P, NULL, 0, cm) ;
+ cm->nmethods = save ;
+ cm->method [0].ordering = save2 ;
+ CHOLMOD(factorize) (Ssym, L2, cm) ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L2, B, cm) ;
+ r = resid (Ssym, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ CHOLMOD(free_factor) (&L2, cm) ;
+ }
+
+ CHOLMOD(free_sparse) (&Ssym, cm) ;
+
+ /* ------------------------------------------------------------------ */
+ /* downdate, with just the first half of C */
+ /* ------------------------------------------------------------------ */
+
+ csize = MAX (1, rank / 2) ;
+ cset = CHOLMOD(malloc) (csize, sizeof (Int), cm) ;
+ if (cset != NULL)
+ {
+ for (i = 0 ; i < csize ; i++)
+ {
+ cset [i] = i ;
+ }
+ }
+ C2 = CHOLMOD(submatrix) (C, NULL, -1, cset, csize, TRUE, TRUE, cm) ;
+ Cperm = CHOLMOD(submatrix) (C2, P, n, NULL, -1, TRUE, TRUE, cm) ;
+ CHOLMOD(free) (csize, sizeof (Int), cset, cm) ;
+
+ CHOLMOD(updown) (FALSE, Cperm, L, cm) ;
+ CHOLMOD(free_sparse) (&Cperm, cm) ;
+
+ /* solve (G+C*C'-C2*C2')x=b */
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+
+ /* This is an expensive way to compute the residual. A better
+ * method would be to compute (G*x + C*(C'*x) - C2*(C2'*x) - b),
+ * using sdmult. It is done just to test the ssmult
+ * routine. */
+
+ /* compute S2 = G+C*C'-C2*C2', with no sort */
+ Ct = CHOLMOD(transpose) (C2, 1, cm) ;
+ CC = CHOLMOD(ssmult) (C2, Ct, 0, TRUE, FALSE, cm) ;
+ S2 = CHOLMOD(add) (S, CC, one, minusone, TRUE, FALSE, cm) ;
+ CHOLMOD(free_sparse) (&CC, cm) ;
+ CHOLMOD(free_sparse) (&Ct, cm) ;
+ CHOLMOD(free_sparse) (&C2, cm) ;
+
+ /* Ssym is a symmetric/upper copy of S2 */
+ Ssym = CHOLMOD(copy) (S2, 1, 1, cm) ;
+ CHOLMOD(free_sparse) (&S2, cm) ;
+
+ /* compute norm (S2*x-b) */
+ r = resid (Ssym, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* ------------------------------------------------------------------ */
+ /* factor S2 scratch, using same permutation */
+ /* ------------------------------------------------------------------ */
+
+ if (rank == 1)
+ {
+ save = cm->nmethods ;
+ save2 = cm->method [0].ordering ;
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_GIVEN ;
+ L2 = CHOLMOD(analyze_p) (Ssym, P, NULL, 0, cm) ;
+ cm->nmethods = save ;
+ cm->method [0].ordering = save2 ;
+ CHOLMOD(factorize) (Ssym, L2, cm) ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L2, B, cm) ;
+ r = resid (Ssym, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ CHOLMOD(free_factor) (&L2, cm) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* re-do the symbolic factorization on L */
+ /* ------------------------------------------------------------------ */
+
+ CHOLMOD(resymbol) (Ssym, NULL, 0, TRUE, L, cm) ;
+
+ /* solve (G+C*C'-C2*C2')x=b again */
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+
+ /* compute norm (S2*x-b) */
+ r = resid (Ssym, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ CHOLMOD(free_sparse) (&Ssym, cm) ;
+
+ /* ------------------------------------------------------------------ */
+ /* downdate, with the remaining part of C, to get original L */
+ /* ------------------------------------------------------------------ */
+
+ if (rank > csize)
+ {
+ cset = CHOLMOD(malloc) (rank-csize, sizeof (Int), cm) ;
+ if (cset != NULL)
+ {
+ for (i = csize ; i < rank ; i++)
+ {
+ cset [i-csize] = i ;
+ }
+ }
+ if (rank - csize == 4)
+ {
+ /* test the subset print/check routine */
+ CHOLMOD(print_subset) (cset, rank-csize, rank, "cset", cm) ;
+ }
+ C2 = CHOLMOD(submatrix) (C, NULL, -1, cset, rank-csize, TRUE, TRUE,
+ cm) ;
+ Cperm = CHOLMOD(submatrix) (C2, P, n, NULL, -1, TRUE, TRUE, cm) ;
+
+ CHOLMOD(free) (rank-csize, sizeof (Int), cset, cm) ;
+ CHOLMOD(updown) (FALSE, Cperm, L, cm) ;
+ CHOLMOD(free_sparse) (&Cperm, cm) ;
+ CHOLMOD(free_sparse) (&C2, cm) ;
+
+ /* solve the original system */
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+
+ /* compute the residual */
+ r = resid (A, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ }
+
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&S, cm) ;
+ }
+
+ /* turn memory tests back on, where we left off ] */
+ my_tries = save3 ;
+
+ CHOLMOD(free_dense) (&B, cm) ;
+ CHOLMOD(free_sparse) (&G, cm) ;
+ CHOLMOD(free_factor) (&L, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* factor again, then change the factor type many times */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(copy_sparse) (A, cm) ;
+ if (C != NULL)
+ {
+ C->sorted = FALSE ;
+ }
+ L = CHOLMOD(analyze) (C, cm) ;
+ CHOLMOD(factorize) (C, L, cm) ;
+
+ if (L != NULL && !(L->is_super))
+ {
+ CHOLMOD(resymbol) (C, NULL, 0, TRUE, L, cm) ;
+ }
+
+ B = rhs (C, 1, n) ;
+ cm->prefer_zomplex = prefer_zomplex ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+ cm->prefer_zomplex = FALSE ;
+ r = resid (C, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ for (k = 0 ; k < NFTYPES ; k++)
+ {
+
+ if (co_types [k] && n > 1)
+ {
+ /* reallocate column zero of L, to make it non-monotonic */
+ CHOLMOD(reallocate_column) (0, n, L, cm) ;
+ }
+ Lxtype = (L == NULL) ? CHOLMOD_REAL : (L->xtype) ;
+
+ CHOLMOD(change_factor) (Lxtype, ll_types [k], FALSE, pk_types [k],
+ mn_types [k], L, cm) ;
+
+ cm->prefer_zomplex = prefer_zomplex ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+ cm->prefer_zomplex = FALSE ;
+ r = resid (C, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ }
+
+ /* reallocate a column and solve again */
+ if (n > 3)
+ {
+ CHOLMOD(change_factor) (CHOLMOD_REAL, FALSE, FALSE, TRUE, TRUE, L, cm) ;
+ CHOLMOD(reallocate_column) (0, n, L, cm) ;
+ cm->prefer_zomplex = prefer_zomplex ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+ cm->prefer_zomplex = FALSE ;
+ r = resid (C, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ }
+
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_factor) (&L, cm) ;
+ CHOLMOD(free_dense) (&B, cm) ;
+ CHOLMOD(free_dense) (&Breal, cm) ;
+ CHOLMOD(free_dense) (&Bcomplex, cm) ;
+ CHOLMOD(free_dense) (&Bzomplex, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize and solve (A*A'+beta*I)x=b or A'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0)
+ {
+ double *Rx, *Rz, *Xx, *Xz ;
+ double beta [2] ;
+ beta [0] = 3.14159 ;
+ beta [1] = 0 ;
+ L = CHOLMOD(analyze) (A, cm) ;
+ CHOLMOD(factorize_p) (A, beta, NULL, 0, L, cm) ;
+ B = rhs (A, 1, n) ;
+ cm->prefer_zomplex = prefer_zomplex ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+ cm->prefer_zomplex = FALSE ;
+
+ /* compute the residual */
+
+ /* W = A'*X */
+ W = CHOLMOD(zeros) (ncol, 1, xtype, cm) ;
+ CHOLMOD(sdmult) (A, 2, one, zero, X, W, cm) ;
+
+ /* R = B */
+ R = CHOLMOD(copy_dense) (B, cm) ;
+
+ /* R = A*W - R */
+ CHOLMOD(sdmult) (A, 0, one, minusone, W, R, cm) ;
+
+ /* R = R + beta*X */
+ if (R != NULL && X != NULL)
+ {
+ Rx = R->x ;
+ Rz = R->z ;
+ Xx = X->x ;
+ Xz = X->z ;
+
+ for (i = 0 ; i < nrow ; i++)
+ {
+ switch (xtype)
+ {
+ case CHOLMOD_REAL:
+ Rx [i] += beta [0] * Xx [i] ;
+ break ;
+
+ case CHOLMOD_COMPLEX:
+ Rx [2*i ] += beta [0] * Xx [2*i ] ;
+ Rx [2*i+1] += beta [0] * Xx [2*i+1] ;
+ break ;
+
+ case CHOLMOD_ZOMPLEX:
+ Rx [i] += beta [0] * Xx [i] ;
+ Rz [i] += beta [0] * Xz [i] ;
+ break ;
+ }
+ }
+ }
+
+ r = CHOLMOD(norm_dense) (R, 2, cm) ;
+ bnorm = CHOLMOD(norm_dense) (B, 2, cm) ;
+ xnorm = CHOLMOD(norm_dense) (X, 2, cm) ;
+ norm = MAX (r, xnorm) ;
+ if (norm > 0)
+ {
+ r /= norm ;
+ }
+ MAXERR (maxerr, r, 1) ;
+
+ CHOLMOD(free_dense) (&X, cm) ;
+ CHOLMOD(free_dense) (&R, cm) ;
+ CHOLMOD(free_dense) (&W, cm) ;
+ CHOLMOD(free_factor) (&L, cm) ;
+ CHOLMOD(free_dense) (&B, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* test rowdel and updown */
+ /* ---------------------------------------------------------------------- */
+
+ if (isreal && A->stype == 1 && n > 0 && n < NLARGE)
+ {
+ Int save4, save5, save6 ;
+ save4 = cm->nmethods ;
+ save5 = cm->method [0].ordering ;
+ save6 = cm->supernodal ;
+
+ cm->nmethods = 1 ;
+ cm->method [0].ordering = CHOLMOD_NATURAL ;
+ cm->supernodal = CHOLMOD_SUPERNODAL ;
+
+ B = rhs (A, 1, n) ;
+ L = CHOLMOD(analyze) (A, cm) ;
+ CHOLMOD(factorize) (A, L, cm) ;
+
+ /* solve Ax=b */
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+ r = resid (A, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* determine the new system with row/column k missing */
+ k = n/2 ;
+ S = CHOLMOD(copy) (A, 0, 1, cm) ;
+ RowK = CHOLMOD(submatrix) (S, NULL, -1, &k, 1, TRUE, TRUE, cm) ;
+ CHOLMOD(print_sparse) (S, "S", cm) ;
+ CHOLMOD(print_sparse) (RowK, "RowK of S", cm) ;
+ CHOLMOD(free_sparse) (&RowK, cm) ;
+ prune_row (S, k) ;
+ if (S != NULL)
+ {
+ S->stype = 1 ;
+ }
+
+ /* delete row k of L (converts to LDL') */
+ /* printf ("rowdel here:\n") ; */
+ CHOLMOD(rowdel) (k, NULL, L, cm) ;
+ CHOLMOD(resymbol) (S, NULL, 0, TRUE, L, cm) ;
+
+ /* solve with row k missing */
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+ r = resid (S, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ CHOLMOD(free_sparse) (&S, cm) ;
+
+ /* factorize again */
+ CHOLMOD(free_factor) (&L, cm) ;
+ L = CHOLMOD(analyze) (A, cm) ;
+ CHOLMOD(factorize) (A, L, cm) ;
+
+ /* rank-3 update (converts to LDL') and solve */
+ C = CHOLMOD(speye) (n, 3, CHOLMOD_REAL, cm) ;
+ CC = CHOLMOD(aat) (C, NULL, 0, 1, cm) ;
+ S = CHOLMOD(add) (A, CC, one, one, TRUE, TRUE, cm) ;
+ if (S != NULL)
+ {
+ S->stype = 1 ;
+ }
+ CHOLMOD(updown) (TRUE, C, L, cm) ;
+ X = CHOLMOD(solve) (CHOLMOD_A, L, B, cm) ;
+ r = resid (S, X, B) ;
+ MAXERR (maxerr, r, 1) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* free everything */
+ CHOLMOD(free_sparse) (&S, cm) ;
+ CHOLMOD(free_sparse) (&CC, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&S, cm) ;
+ CHOLMOD(free_factor) (&L, cm) ;
+ CHOLMOD(free_dense) (&B, cm) ;
+
+ cm->nmethods = save4 ;
+ cm->method [0].ordering = save5 ;
+ cm->supernodal = save6 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free remaining workspace */
+ /* ---------------------------------------------------------------------- */
+
+ OK (CHOLMOD(print_common) ("cm", cm)) ;
+ progress (0, '.') ;
+ return (maxerr) ;
+}
diff --git a/CHOLMOD/Tcov/test_ops.c b/CHOLMOD/Tcov/test_ops.c
new file mode 100644
index 0000000..2f1ece1
--- /dev/null
+++ b/CHOLMOD/Tcov/test_ops.c
@@ -0,0 +1,1143 @@
+/* ========================================================================== */
+/* === Tcov/test_ops ======================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Test CHOLMOD matrix operators. */
+
+#include "cm.h"
+
+
+/* ========================================================================== */
+/* === nzdiag =============================================================== */
+/* ========================================================================== */
+
+/* Count the entries on the diagonal */
+
+Int nzdiag (cholmod_sparse *A)
+{
+ Int *Ap, *Ai, *Anz ;
+ Int nnzdiag, packed, j, p, i, pend, ncol ;
+ if (A == NULL)
+ {
+ return (EMPTY) ;
+ }
+ nnzdiag = 0 ;
+ ncol = A->ncol ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+ packed = A->packed ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i == j)
+ {
+ nnzdiag++ ;
+ }
+ }
+ }
+ return (nnzdiag) ;
+}
+
+
+/* ========================================================================== */
+/* === check_partition ====================================================== */
+/* ========================================================================== */
+
+/* Check a node separator, and return the # of nodes in the node separator or
+ * -1 if the separater is invalid. A node j is in the left part if
+ * Part [j] = 0, in the right part if Part [j] = 1, and in the separator if
+ * Part [j] = 2.
+ */
+
+Int check_partition (cholmod_sparse *A, Int *Part)
+{
+ Int *Ap, *Ai, *Anz ;
+ Int chek [3], which, i, j, p, n, pend, packed ;
+
+ if (A == NULL || Part == NULL || A->nrow != A->ncol)
+ {
+ return (EMPTY) ;
+ }
+ n = A->nrow ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Anz = A->nz ;
+ packed = A->packed ;
+
+ chek [0] = 0 ;
+ chek [1] = 0 ;
+ chek [2] = 0 ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ which = Part [j] ;
+ p = Ap [j] ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ for ( ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (which == 0)
+ {
+ if (Part [i] == 1)
+ {
+ return (EMPTY) ;
+ }
+ }
+ else if (which == 1)
+ {
+ if (Part [i] == 0)
+ {
+ return (EMPTY) ;
+ }
+ }
+ }
+ if (which < 0 || which > 2)
+ {
+ return (EMPTY) ;
+ }
+ chek [which]++ ;
+ }
+ return (chek [2]) ;
+}
+
+
+/* ========================================================================== */
+/* === check_equality ======================================================= */
+/* ========================================================================== */
+
+/* Ensure two sparse matrices are identical. */
+
+static void check_equality (cholmod_sparse *E, cholmod_sparse *D, Int xtype)
+{
+ double *Ex, *Ez, *Dx, *Dz ;
+ Int *Ep, *Ei, *Dp, *Di ;
+ Int j, nz, p, ncol ;
+
+ if (E == NULL || D == NULL || D->xtype != xtype || E->xtype != xtype)
+ {
+ return ;
+ }
+
+ Ep = E->p ;
+ Ei = E->i ;
+ Ex = E->x ;
+ Ez = E->z ;
+
+ Dp = D->p ;
+ Di = D->i ;
+ Dx = D->x ;
+ Dz = D->z ;
+
+ OK (E->ncol == D->ncol) ;
+ OK (E->nrow == D->nrow) ;
+
+ ncol = E->ncol ;
+
+ for (j = 0 ; j <= ncol ; j++)
+ {
+ OK (Ep [j] == Dp [j]) ;
+ }
+ nz = Ep [ncol] ;
+
+ for (p = 0 ; p < nz ; p++)
+ {
+ OK (Ei [p] == Di [p]) ;
+ }
+
+ if (xtype == CHOLMOD_REAL)
+ {
+ for (p = 0 ; p < nz ; p++)
+ {
+ OK (Ex [p] == Dx [p]) ;
+ }
+ }
+ else if (xtype == CHOLMOD_COMPLEX)
+ {
+ for (p = 0 ; p < 2*nz ; p++)
+ {
+ OK (Ex [p] == Dx [p]) ;
+ }
+ }
+ else if (xtype == CHOLMOD_ZOMPLEX)
+ {
+ for (p = 0 ; p < nz ; p++)
+ {
+ OK (Ex [p] == Dx [p]) ;
+ OK (Ez [p] == Dz [p]) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === test_ops ============================================================= */
+/* ========================================================================== */
+
+/* Test various matrix operations. */
+
+double test_ops (cholmod_sparse *A)
+{
+ double maxerr = 0, r, x, anorm, r1, rinf ;
+ double *Sx, *Sz ;
+ Int *Pinv, *P, *Si, *Sj, *Q, *Qinv, *fset, *Partition ;
+ cholmod_triplet *S ;
+ cholmod_sparse *C, *D, *E, *F, *G, *H, *AT, *Zs ;
+ cholmod_dense *X, *Y ;
+ Int n, kk, k, nrow, ncol, len, nz, ok, i, j, stype, nmin, mode, isreal,
+ xtype, xtype2, mtype, asym, xmatched, pmatched, nzoffdiag, nz_diag ;
+ size_t nz1, nz2 ;
+ void (*save) (int, char *, int, char *) ;
+ double alpha [2], beta [2], *Xx ;
+ FILE *f ;
+ int option, save3 ;
+
+ if (A == NULL)
+ {
+ ERROR (CHOLMOD_INVALID, "nothing for test_ops") ;
+ return (1) ;
+ }
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ H = NULL ;
+ n = MAX (nrow, ncol) ;
+ nmin = MIN (nrow, ncol) ;
+ xtype = A->xtype ;
+ isreal = (A->xtype == CHOLMOD_REAL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* norm */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(print_sparse) (A, "A for testops", cm) ;
+ r1 = CHOLMOD(norm_sparse) (A, 1, cm) ;
+ rinf = CHOLMOD(norm_sparse) (A, 0, cm) ;
+
+ anorm = r1 ;
+
+ /* E = pattern of A */
+ E = CHOLMOD(copy) (A, 0, 0, cm) ;
+ CHOLMOD(print_sparse) (E, "E = pattern of A", cm) ;
+ r1 = CHOLMOD(norm_sparse) (E, 1, cm) ;
+ rinf = CHOLMOD(norm_sparse) (E, 0, cm) ;
+ OK (r1 <= nrow) ;
+ OK (rinf <= ncol) ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+
+ /* E = pattern of A, but exclude the diagonal */
+ E = CHOLMOD(copy) (A, 0, -1, cm) ;
+ CHOLMOD(print_sparse) (E, "E = spones (A), excl diag", cm) ;
+ r1 = CHOLMOD(norm_sparse) (E, 1, cm) ;
+ rinf = CHOLMOD(norm_sparse) (E, 0, cm) ;
+ if (nrow < ncol)
+ {
+ OK (r1 <= nrow) ;
+ OK (rinf < MAX (1,ncol)) ;
+ }
+ else
+ {
+ OK (r1 < MAX (1,nrow)) ;
+ OK (rinf <= ncol) ;
+ }
+ CHOLMOD(free_sparse) (&E, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype)
+ {
+ /* E = tril (A), no diagonal */
+ E = CHOLMOD(copy) (A, -1, -1, cm) ;
+ CHOLMOD(print_sparse) (E, "E, lower and no diagonal", cm) ;
+ CHOLMOD(band_inplace) (0, n, 0, E, cm) ;
+ CHOLMOD(print_sparse) (E, "E Empty", cm) ;
+ nz = CHOLMOD(nnz) (E, cm) ;
+ if (E != NULL)
+ {
+ OK (nz == 0) ;
+ }
+ CHOLMOD(free_sparse) (&E, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read/write */
+ /* ---------------------------------------------------------------------- */
+
+/*
+ i = cm->print ;
+ cm->print = 4 ;
+ CHOLMOD(print_sparse) (A, "A for read/write", cm) ;
+ cm->print = i ;
+*/
+
+ /* delete the contents of the temp1.mtx and temp2.mtx file */
+ f = fopen ("temp1.mtx", "w") ;
+ fprintf (f, "temp1\n") ;
+ fclose (f) ;
+
+ f = fopen ("temp3.mtx", "w") ;
+ fprintf (f, "temp3\n") ;
+ fclose (f) ;
+
+ CHOLMOD(free_work) (cm) ;
+
+ f = fopen ("temp1.mtx", "w") ;
+ asym = CHOLMOD(write_sparse) (f, A, NULL, "comments.txt", cm) ;
+ fclose (f) ;
+ printf ("write_sparse, asym: %d\n", asym) ;
+ OK (IMPLIES (A != NULL, asym > EMPTY)) ;
+
+ f = fopen ("temp1.mtx", "r") ;
+ C = CHOLMOD(read_sparse) (f, cm) ;
+ fclose (f) ;
+ printf ("got_sparse\n") ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+
+ save3 = A->xtype ;
+ A->xtype = CHOLMOD_PATTERN ;
+ f = fopen ("temp3.mtx", "w") ;
+ asym = CHOLMOD(write_sparse) (f, A, NULL, "comments.txt", cm) ;
+ A->xtype = save3 ;
+ fclose (f) ;
+ printf ("write_sparse3, asym: %d\n", asym) ;
+
+ f = fopen ("temp3.mtx", "r") ;
+ C = CHOLMOD(read_sparse) (f, cm) ;
+ fclose (f) ;
+ printf ("got_sparse3\n") ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+
+ for (i = 0 ; i <= 1 ; i++)
+ {
+
+ f = fopen ("temp2.mtx", "w") ;
+ fprintf (f, "temp2\n") ;
+ fclose (f) ;
+
+ X = CHOLMOD(ones) (4, 4, CHOLMOD_REAL, cm) ;
+ if (X != NULL)
+ {
+ Xx = X->x ;
+ Xx [0] = (i == 0) ? 1.1e308 : -1.1e308 ;
+ }
+ f = fopen ("temp2.mtx", "w") ;
+ ok = CHOLMOD(write_dense) (f, X, "comments.txt", cm) ;
+ fclose (f) ;
+ printf ("wrote dense\n") ;
+
+ f = fopen ("temp2.mtx", "r") ;
+ Y = CHOLMOD(read_dense) (f, cm) ;
+ fclose (f) ;
+ printf ("got dense\n") ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ CHOLMOD(free_dense) (&Y, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* symmetry */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free_work) (cm) ;
+ xmatched = 0 ;
+ pmatched = 0 ;
+ nzoffdiag = 0 ;
+ nz_diag = 0 ;
+ for (option = 0 ; option <= 2 ; option++)
+ {
+ asym = CHOLMOD(symmetry) (A, option, &xmatched, &pmatched, &nzoffdiag,
+ &nz_diag, cm);
+ printf ("symmetry, asym: %d matched %d %d offdiag %d diag %d\n", asym,
+ xmatched, pmatched, nzoffdiag, nz_diag) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* transpose */
+ /* ---------------------------------------------------------------------- */
+
+ C = CHOLMOD(allocate_sparse) (A->ncol, A->nrow, A->nzmax, TRUE, TRUE,
+ -(A->stype), A->xtype, cm) ;
+ D = CHOLMOD(allocate_sparse) (A->nrow, A->ncol, A->nzmax, TRUE, TRUE,
+ A->stype, A->xtype, cm) ;
+ CHOLMOD(free_work) (cm) ;
+ ok = (C != NULL && D != NULL) ;
+
+ /* C = A' */
+ if (ok)
+ {
+ if (A->stype)
+ {
+ ok = CHOLMOD(transpose_sym) (A, 2, NULL, C, cm) ;
+ }
+ else
+ {
+ ok = CHOLMOD(transpose_unsym) (A, 2, NULL, NULL, 0, C, cm) ;
+ }
+ OK (ok || cm->status == CHOLMOD_OUT_OF_MEMORY) ;
+ }
+
+ /* D = C' */
+ if (ok)
+ {
+ if (A->stype)
+ {
+ ok = CHOLMOD(transpose_sym) (C, 2, NULL, D, cm) ;
+ }
+ else
+ {
+ ok = CHOLMOD(transpose_unsym) (C, 2, NULL, NULL, 0, D, cm) ;
+ }
+ OK (ok || cm->status == CHOLMOD_OUT_OF_MEMORY) ;
+ }
+
+ if (ok)
+ {
+ ok = CHOLMOD(check_sparse) (D, cm) ;
+ OK (ok || cm->status == CHOLMOD_OUT_OF_MEMORY) ;
+ }
+
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&D, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = A with jumbled triplets */
+ /* ---------------------------------------------------------------------- */
+
+ S = CHOLMOD(sparse_to_triplet) (A, cm) ; /* [ */
+
+ if (S != NULL && nmin > 0)
+ {
+
+ /* double the number of entries in S */
+ nz1 = S->nzmax ;
+ nz2 = 2*nz1 ;
+ ok = CHOLMOD(reallocate_triplet) (nz2, S, cm) ;
+
+ if (ok)
+ {
+ /* add duplicate entries, but keep the matrix the same */
+ OK (S->nzmax == nz2) ;
+ Si = S->i ;
+ Sj = S->j ;
+ Sx = S->x ;
+ Sz = S->z ;
+
+ for (k = nz1 ; k < ((Int) nz2) ; k++)
+ {
+ kk = nrand (k) ; /* RAND */
+ Si [k] = Si [kk] ;
+ Sj [k] = Sj [kk] ;
+
+ if (S->xtype == CHOLMOD_REAL)
+ {
+ x = Sx [kk] * (xrand (4.) - 2) ; /* RAND */
+ Sx [k] = x ;
+ Sx [kk] -= x ;
+ }
+ else if (S->xtype == CHOLMOD_COMPLEX)
+ {
+ x = Sx [2*kk] * (xrand (4.) - 2) ; /* RAND */
+ Sx [2*k] = x ;
+ Sx [2*kk] -= x ;
+
+ x = Sx [2*kk+1] * (xrand (4.) - 2) ; /* RAND */
+ Sx [2*k+1] = x ;
+ Sx [2*kk+1] -= x ;
+ }
+ else
+ {
+ x = Sx [kk] * (xrand (4.) - 2) ; /* RAND */
+ Sx [k] = x ;
+ Sx [kk] -= x ;
+
+ x = Sz [kk] * (xrand (4.) - 2) ; /* RAND */
+ Sz [k] = x ;
+ Sz [kk] -= x ;
+ }
+ }
+
+ /* randomly jumble the entries */
+ for (k = 0 ; k < ((Int) (nz2-1)) ; k++)
+ {
+ kk = k + nrand (nz2-k) ; /* RAND */
+ i = Si [k] ;
+ Si [k] = Si [kk] ;
+ Si [kk] = i ;
+ j = Sj [k] ;
+ Sj [k] = Sj [kk] ;
+ Sj [kk] = j ;
+
+ if (S->xtype == CHOLMOD_REAL)
+ {
+ x = Sx [k] ;
+ Sx [k] = Sx [kk] ;
+ Sx [kk] = x ;
+ }
+ else if (S->xtype == CHOLMOD_COMPLEX)
+ {
+ x = Sx [2*k] ;
+ Sx [2*k] = Sx [2*kk] ;
+ Sx [2*kk] = x ;
+ x = Sx [2*k+1] ;
+ Sx [2*k+1] = Sx [2*kk+1] ;
+ Sx [2*kk+1] = x ;
+ }
+ else
+ {
+ x = Sx [k] ;
+ Sx [k] = Sx [kk] ;
+ Sx [kk] = x ;
+ x = Sz [k] ;
+ Sz [k] = Sz [kk] ;
+ Sz [kk] = x ;
+ }
+ }
+ S->nnz = nz2 ;
+ }
+ else
+ {
+ OK (S->nzmax == nz1) ;
+ OK (S->nnz == nz1) ;
+ }
+ }
+
+ CHOLMOD(print_triplet) (S, "S jumbled", cm) ;
+
+ C = CHOLMOD(triplet_to_sparse) (S, 0, cm) ; /* [ */
+ CHOLMOD(print_sparse) (A, "A", cm) ;
+ CHOLMOD(print_sparse) (C, "C", cm) ;
+
+ Zs = CHOLMOD(spzeros) (nrow, ncol, 1, xtype, cm) ; /* [ */
+
+ G = NULL ;
+ F = NULL ;
+
+ if (isreal)
+ {
+
+ /* G=A+0 */
+ G = CHOLMOD(add) (A, Zs, one, one, TRUE, TRUE, cm) ; /* [ */
+
+ /* F = G-C */
+ F = CHOLMOD(add) (G, C, one, minusone, TRUE, TRUE, cm) ; /* [ */
+
+ CHOLMOD(print_sparse) (F, "F", cm) ;
+ r = CHOLMOD(norm_sparse) (F, 1, cm) ;
+ MAXERR (maxerr, r, anorm) ;
+ r = CHOLMOD(norm_sparse) (F, 0, cm) ;
+ CHOLMOD(drop) (0, F, cm) ;
+ rinf = CHOLMOD(norm_sparse) (F, 0, cm) ;
+ if (F != NULL)
+ {
+ OK (r == rinf) ;
+ }
+ MAXERR (maxerr, r, anorm) ;
+ MAXERR (maxerr, rinf, anorm) ;
+
+ /* E = F, with change of type and dropping small entries */
+ for (stype = -1 ; stype <= 1 ; stype++)
+ {
+ if (stype != 0 && (F != NULL && F->nrow != F->ncol))
+ {
+ continue ;
+ }
+ for (mode = 0 ; mode <= 1 ; mode++)
+ {
+ E = CHOLMOD(copy) (F, stype, mode, cm) ; /* [ */
+ CHOLMOD(drop) (1e-16, E, cm) ;
+ r1 = CHOLMOD(norm_sparse) (E, 1, cm) ;
+ rinf = CHOLMOD(norm_sparse) (E, 0, cm) ;
+ if (E != NULL)
+ {
+ if (mode == 0)
+ {
+ /* pattern only */
+ OK (r1 <= nrow) ;
+ OK (rinf <= ncol) ;
+ }
+ else
+ {
+ MAXERR (maxerr, r1, anorm) ;
+ MAXERR (maxerr, rinf, anorm) ;
+ }
+ }
+ CHOLMOD(free_sparse) (&E, cm) ; /* ] */
+ }
+ }
+
+ CHOLMOD(free_sparse) (&F, cm) ; /* ] */
+ CHOLMOD(free_sparse) (&G, cm) ; /* ] */
+ }
+
+ Y = CHOLMOD(ones) (nrow, 1, xtype, cm) ; /* [ */
+ X = CHOLMOD(ones) (ncol, 1, xtype, cm) ; /* [ */
+ alpha [0] = 0 ;
+ alpha [1] = 0 ;
+ beta [0] = 2 ;
+ beta [1] = 0 ;
+ /* Y = 0*A*X + 2*Y */
+ CHOLMOD(sdmult) (A, FALSE, alpha, beta, X, Y, cm) ;
+ r = CHOLMOD(norm_dense) (Y, 0, cm) ;
+ if (Y != NULL && X != NULL && A != NULL)
+ {
+ OK ((nrow == 0) ? (r == 0) : (r == 2)) ;
+ }
+
+ alpha [0] = 1 ;
+ /* Y = 1*(0)*X + 2*Y */
+ CHOLMOD(sdmult) (Zs, FALSE, alpha, beta, X, Y, cm) ;
+ r = CHOLMOD(norm_dense) (Y, 0, cm) ;
+ if (Y != NULL && X != NULL && A != NULL)
+ {
+ OK ((nrow == 0) ? (r == 0) : (r == 4)) ;
+ }
+
+ CHOLMOD(free_dense) (&X, cm) ; /* ] */
+ CHOLMOD(free_dense) (&Y, cm) ; /* ] */
+
+ CHOLMOD(free_sparse) (&Zs, cm) ; /* ] */
+ CHOLMOD(free_sparse) (&C, cm) ; /* ] */
+ CHOLMOD(free_triplet) (&S, cm) ; /* ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* C = P*A*Q in triplet form */
+ /* ---------------------------------------------------------------------- */
+
+ S = CHOLMOD(sparse_to_triplet) (A, cm) ;
+ P = prand (nrow) ; /* RAND */
+ if (A->stype == 0)
+ {
+ Q = prand (ncol) ; /* RAND */
+ }
+ else
+ {
+ /* if A is symmetric, and stored in either upper or lower form, then
+ * the following code only works if P = Q */
+ Q = P ;
+ }
+ Pinv = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+ Qinv = CHOLMOD(malloc) (ncol, sizeof (Int), cm) ;
+ Partition = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+
+ if (Pinv != NULL && Qinv != NULL && P != NULL && Q != NULL && S != NULL)
+ {
+ Si = S->i ;
+ Sj = S->j ;
+ nz = S->nnz ;
+ for (k = 0 ; k < nrow ; k++)
+ {
+ Pinv [P [k]] = k ;
+ }
+ for (k = 0 ; k < ncol ; k++)
+ {
+ Qinv [Q [k]] = k ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Si [k] = Pinv [Si [k]] ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Sj [k] = Qinv [Sj [k]] ;
+ }
+ }
+
+ C = CHOLMOD(triplet_to_sparse) (S, 0, cm) ;
+ D = NULL ;
+ E = NULL ;
+ F = NULL ;
+ G = NULL ;
+
+ if (isreal)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* E = P*A*Q in sparse form */
+ /* ------------------------------------------------------------------ */
+
+ D = CHOLMOD(copy) (A, 0, 1, cm) ;
+ E = CHOLMOD(submatrix) (D, P, nrow, Q, ncol, TRUE, FALSE, cm) ;
+ CHOLMOD(sort) (E, cm) ;
+
+ /* ------------------------------------------------------------------ */
+ /* F = E-G */
+ /* ------------------------------------------------------------------ */
+
+ G = CHOLMOD(copy) (C, 0, 1, cm) ;
+ F = CHOLMOD(add) (E, G, one, minusone, TRUE, TRUE, cm) ;
+ CHOLMOD(drop) (0, F, cm) ;
+ nz = CHOLMOD(nnz) (F, cm) ;
+ if (F != NULL)
+ {
+ OK (nz == 0) ;
+ }
+ }
+
+ CHOLMOD(free_sparse) (&F, cm) ;
+ CHOLMOD(free_sparse) (&G, cm) ;
+ CHOLMOD(free_sparse) (&D, cm) ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+ CHOLMOD(free_sparse) (&H, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_triplet) (&S, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* submatrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype == 0 && isreal)
+ {
+ /* E = A(:,:) */
+ E = CHOLMOD(submatrix) (A, NULL, -1, NULL, -1, TRUE, TRUE, cm) ;
+ /* C = A-E */
+ C = CHOLMOD(add) (A, E, one, minusone, TRUE, TRUE, cm) ;
+ ok = CHOLMOD(drop) (0., C, cm) ;
+ nz = CHOLMOD(nnz) (C, cm) ;
+ if (C != NULL)
+ {
+ OK (nz == 0) ;
+ }
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* test band and add, unsymmetric */
+ /* ---------------------------------------------------------------------- */
+
+ if (isreal)
+ {
+ CHOLMOD(print_sparse) (A, "A for do triplet", cm) ;
+
+ /* E = A */
+ E = CHOLMOD(copy) (A, 0, 1, cm) ;
+ CHOLMOD(print_sparse) (E, "E=triu(A)", cm) ;
+
+ /* E = triu (E) */
+ CHOLMOD(band_inplace) (0, ncol, 1, E, cm) ;
+
+ /* F = A */
+ F = CHOLMOD(copy) (A, 0, 1, cm) ;
+ CHOLMOD(print_sparse) (F, "F=tril(A)", cm) ;
+
+ /* F = tril(F,-1) */
+ CHOLMOD(band_inplace) (-nrow, -1, 1, F, cm) ;
+ CHOLMOD(print_sparse) (F, "Ftril", cm) ;
+
+ /* G = E+F */
+ G = CHOLMOD(add) (E, F, one, one, TRUE, TRUE, cm) ;
+ CHOLMOD(print_sparse) (G, "G=E+F", cm) ;
+
+ /* D = A-G, which should be empty */
+ D = CHOLMOD(add) (G, A, one, minusone, TRUE, TRUE, cm) ;
+ CHOLMOD(print_sparse) (D, "D=A-G", cm) ;
+
+ CHOLMOD(drop) (0, D, cm) ;
+ CHOLMOD(print_sparse) (D, "D drop", cm) ;
+ nz = CHOLMOD(nnz) (D, cm) ;
+ if (D != NULL)
+ {
+ OK (nz == 0) ;
+ }
+
+ CHOLMOD(free_sparse) (&F, cm) ;
+ CHOLMOD(free_sparse) (&D, cm) ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+ CHOLMOD(free_sparse) (&G, cm) ;
+
+ D = CHOLMOD(band) (A, 1, -1, 0, cm) ;
+ nz = CHOLMOD(nnz) (D, cm) ;
+ if (D != NULL)
+ {
+ OK (nz == 0) ;
+ }
+ CHOLMOD(free_sparse) (&D, cm) ;
+ D = CHOLMOD(band) (A, 0, 0, 0, cm) ;
+ nz = CHOLMOD(nnz) (D, cm) ;
+ if (D != NULL)
+ {
+ OK (nz == nzdiag (D)) ;
+ }
+ CHOLMOD(free_sparse) (&D, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* test band, add and copy_sparse (symmetric) */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype && isreal)
+ {
+
+ /* E = A, in symmetric/upper form */
+ E = CHOLMOD(copy) (A, 1, 1, cm) ;
+ CHOLMOD(print_sparse) (E, "E=A in sym/upper form", cm) ;
+
+ /* E = -E */
+ CHOLMOD(scale) (M1, CHOLMOD_SCALAR, E, cm) ;
+
+ /* F = A, in symmetric/lower form */
+ F = CHOLMOD(copy) (A, -1, 1, cm) ;
+ CHOLMOD(print_sparse) (F, "F=A in sym/lower form", cm) ;
+
+ /* C = F (exact copy) */
+ C = CHOLMOD(copy_sparse) (F, cm) ;
+
+ /* G = E+C */
+ G = CHOLMOD(add) (E, C, one, one, TRUE, FALSE, cm) ;
+ CHOLMOD(print_sparse) (G, "G=E+F", cm) ;
+ CHOLMOD(sort) (G, cm) ;
+
+ CHOLMOD(drop) (0, G, cm) ;
+ CHOLMOD(print_sparse) (G, "G drop", cm) ;
+ nz = CHOLMOD(nnz) (G, cm) ;
+ if (G != NULL)
+ {
+ OK (nz == 0) ;
+ }
+
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&F, cm) ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+ CHOLMOD(free_sparse) (&G, cm) ;
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* try a dense identity matrix */
+ /* ---------------------------------------------------------------------- */
+
+ X = CHOLMOD(eye) (3, 4, CHOLMOD_REAL, cm) ;
+ CHOLMOD(print_dense) (X, "Dense identity", cm) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* bisector and nested_dissection */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NPARTITION
+ if (A != NULL && A->nrow == A->ncol)
+ {
+ UF_long nc, nc_new ;
+ Int cnz, csep, save2 ;
+ Int *Cnw, *Cew, *Cmember, *CParent, *Perm ;
+ double save1 ;
+
+ /* try CHOLMOD's interface to METIS_NodeComputeSeparator */
+ cm->metis_memory = 2.0 ;
+ CHOLMOD(print_sparse) (A, "A for bisect", cm) ;
+ csep = CHOLMOD(bisect) (A, NULL, 0, TRUE, Partition, cm) ;
+ if (csep != EMPTY)
+ {
+ OK (csep == check_partition (A, Partition)) ;
+ }
+
+ /* try the raw interface to METIS_NodeComputeSeparator */
+ CHOLMOD(print_sparse) (A, "A for metis bisect", cm) ;
+
+ /* C = A+A', remove the diagonal */
+ AT = CHOLMOD(transpose) (A, 0, cm) ;
+ E = CHOLMOD(add) (A, AT, one, one, FALSE, TRUE, cm) ;
+ CHOLMOD(free_sparse) (&AT, cm) ;
+ C = CHOLMOD(copy) (E, 0, -1, cm) ;
+ CHOLMOD(print_sparse) (C, "C for metis bisect", cm) ;
+
+ cnz = (C != NULL) ? (C->nzmax) : 0 ;
+ Cew = CHOLMOD(malloc) (cnz, sizeof (Int), cm) ;
+ Cnw = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+ if (Cnw != NULL)
+ {
+ for (j = 0 ; j < (Int) (A->nrow) ; j++)
+ {
+ Cnw [j] = 1 ;
+ }
+ }
+ if (Cew != NULL)
+ {
+ for (j = 0 ; j < cnz ; j++)
+ {
+ Cew [j] = 1 ;
+ }
+ }
+ csep = CHOLMOD(metis_bisector) (C, Cnw, Cew, Partition, cm) ;
+ if (csep != EMPTY)
+ {
+ OK (csep == check_partition (C, Partition)) ;
+ }
+ CHOLMOD(free) (nrow, sizeof (Int), Cnw, cm) ;
+ CHOLMOD(free) (cnz, sizeof (Int), Cew, cm) ;
+
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+
+ Cmember = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+ CParent = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+ Perm = CHOLMOD(malloc) (nrow, sizeof (Int), cm) ;
+
+ save1 = cm->method [cm->current].nd_small ;
+ save2 = cm->method [cm->current].nd_oksep ;
+ cm->method [cm->current].nd_small = 1 ;
+ cm->method [cm->current].nd_oksep = 1.0 ;
+
+ nc = CHOLMOD(nested_dissection) (A, NULL, 0, Perm, CParent, Cmember,
+ cm);
+ if (nc > 0)
+ {
+ OK (CHOLMOD(check_perm) (Perm, n, n, cm)) ;
+ }
+
+ CHOLMOD(free_work) (cm) ;
+
+ /* collapse the septree */
+ if (nc > 0 && n > 0)
+ {
+ nc_new = CHOLMOD(collapse_septree) (n, nc, 0.1, 400,
+ CParent, Cmember, cm) ;
+
+ /* error checks */
+ save = cm->error_handler ;
+ cm->error_handler = NULL ;
+ nc_new = CHOLMOD(collapse_septree) (n, nc, 0.1, 400,
+ CParent, Cmember, NULL) ;
+ OK (nc_new == EMPTY) ;
+ nc_new = CHOLMOD(collapse_septree) (n, nc, 0.1, 400,
+ NULL, Cmember, cm) ;
+ OK (nc_new == EMPTY) ;
+ nc_new = CHOLMOD(collapse_septree) (n, nc, 0.1, 400,
+ CParent, NULL, cm) ;
+ OK (nc_new == EMPTY) ;
+ nc_new = CHOLMOD(collapse_septree) (0, 1, 0.1, 400,
+ CParent, Cmember, cm) ;
+ OK (nc_new == EMPTY) ;
+ nc_new = CHOLMOD(collapse_septree) (1, 1, 0.1, 400,
+ CParent, Cmember, cm) ;
+ OK (nc_new == 1 || nc_new == EMPTY) ;
+ nc_new = CHOLMOD(collapse_septree) (Int_max, Int_max,
+ 0.1, 400, CParent, Cmember, cm) ;
+ OK (nc_new == EMPTY) ;
+
+ cm->error_handler = save ;
+ }
+
+ CHOLMOD(free) (nrow, sizeof (Int), Cmember, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), CParent, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), Perm, cm) ;
+
+ cm->method [cm->current].nd_small = save1 ;
+ cm->method [cm->current].nd_oksep = save2 ;
+
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* dense to/from sparse conversions */
+ /* ---------------------------------------------------------------------- */
+
+ /* convert A to real, remove zero entries, and then convert to pattern */
+ if (MAX (nrow, ncol) < 1000)
+ {
+
+ C = CHOLMOD(copy_sparse) (A, cm) ;
+ CHOLMOD(sparse_xtype) (CHOLMOD_REAL, C, cm) ;
+ CHOLMOD(drop) (0., C, cm) ;
+ D = CHOLMOD(copy) (C, 0, 0, cm) ;
+ CHOLMOD(sort) (D, cm) ;
+
+ /* X = dense copy of C */
+ CHOLMOD(sparse_xtype) (CHOLMOD_PATTERN, C, cm) ;
+ X = CHOLMOD(sparse_to_dense) (C, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+
+ /* change X to sparse pattern and then real/complex/zomplex, it should
+ * equal D */
+ for (xtype2 = CHOLMOD_REAL ; xtype2 <= CHOLMOD_ZOMPLEX ; xtype2++)
+ {
+ E = CHOLMOD(dense_to_sparse) (X, FALSE, cm) ;
+ ok = CHOLMOD(sparse_xtype) (xtype2, E, cm) ;
+ ok = CHOLMOD(sparse_xtype) (xtype2, D, cm) ;
+ if (xtype2 == CHOLMOD_REAL)
+ {
+ F = CHOLMOD(add) (E, D, one, minusone, TRUE, TRUE, cm) ;
+ r = CHOLMOD(norm_sparse) (F, 0, cm) ;
+ if (F != NULL)
+ {
+ OK (r == 0) ;
+ }
+ CHOLMOD(free_sparse) (&F, cm) ;
+ }
+ else
+ {
+ check_equality (E, D, xtype2) ;
+ }
+ CHOLMOD(free_sparse) (&E, cm) ;
+ }
+
+ CHOLMOD(free_sparse) (&D, cm) ;
+ CHOLMOD(free_dense) (&X, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* unsymmetric transpose */
+ /* ---------------------------------------------------------------------- */
+
+ len = ncol/2 ;
+ fset = prand (ncol) ; /* RAND */
+ CHOLMOD(print_perm) (P, nrow, nrow, "P", cm) ;
+ CHOLMOD(print_subset) (fset, ncol, ncol, "fset", cm) ;
+
+ if (isreal)
+ {
+ C = CHOLMOD(copy) (A, 0, 1, cm) ;
+ D = CHOLMOD(ptranspose) (C, 1, P, fset, len, cm) ;
+ E = CHOLMOD(transpose) (D, 1, cm) ;
+ F = CHOLMOD(transpose) (E, 1, cm) ;
+ G = CHOLMOD(add) (D, F, one, minusone, TRUE, FALSE, cm) ;
+ r = CHOLMOD(norm_sparse) (G, 0, cm) ;
+ if (G != NULL)
+ {
+ OK (r == 0) ;
+ }
+ CHOLMOD(drop) (0, G, cm) ;
+ r = CHOLMOD(norm_sparse) (G, 0, cm) ;
+ nz = CHOLMOD(nnz) (G, cm) ;
+ if (G != NULL)
+ {
+ OK (r == 0) ;
+ OK (nz == 0) ;
+ }
+
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&D, cm) ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+ CHOLMOD(free_sparse) (&F, cm) ;
+ CHOLMOD(free_sparse) (&G, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* symmetric array transpose */
+ /* ---------------------------------------------------------------------- */
+
+ if (A->stype != 0)
+ {
+
+ /* C = A(p,p).' */
+ C = CHOLMOD(ptranspose) (A, 1, P, NULL, 0, cm) ;
+
+ /* D = C(pinv,pinv).' */
+ D = CHOLMOD(ptranspose) (C, 1, Pinv, NULL, 0, cm) ;
+ CHOLMOD(sort) (D, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+
+ /* C = A, sorted */
+ C = CHOLMOD(copy_sparse) (A, cm) ;
+ CHOLMOD(sort) (C, cm) ;
+
+ /* C and D should be equal */
+ check_equality (C, D, xtype) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&D, cm) ;
+
+ /* C = A.' */
+ C = CHOLMOD(transpose) (A, 1, cm) ;
+
+ /* D = C.' */
+ D = CHOLMOD(transpose) (C, 1, cm) ;
+ CHOLMOD(sort) (D, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+
+ /* C = A, sorted */
+ C = CHOLMOD(copy_sparse) (A, cm) ;
+ CHOLMOD(sort) (C, cm) ;
+
+ /* C and D should be equal */
+ check_equality (C, D, xtype) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&D, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* matrix multiply */
+ /* ---------------------------------------------------------------------- */
+
+ if (isreal)
+ {
+ /* this fails for a large arrowhead matrix, so turn off error hanlder */
+ save = cm->error_handler ;
+ cm->error_handler = NULL ;
+ AT = CHOLMOD(transpose) (A, 1, cm) ;
+ D = CHOLMOD(copy) (A, 0, 1, cm) ;
+ if (n > NLARGE) progress (1, '.') ;
+ C = CHOLMOD(aat) (D, NULL, 0, 1, cm) ;
+ if (n > NLARGE) progress (1, '.') ;
+ CHOLMOD(print_common) ("After A*A'", cm) ;
+
+ for (stype = -1 ; stype <= 1 ; stype++)
+ {
+ if (n > NLARGE) progress (1, '.') ;
+ E = CHOLMOD(ssmult) (A, AT, stype, TRUE, TRUE, cm) ;
+ if (n > NLARGE) progress (1, '.') ;
+ G = CHOLMOD(add) (C, E, one, minusone, TRUE, FALSE, cm) ;
+ if (n > NLARGE) progress (1, '.') ;
+ r = CHOLMOD(norm_sparse) (G, 0, cm) ;
+ if (G != NULL)
+ {
+ MAXERR (maxerr, r, anorm) ;
+ }
+ CHOLMOD(drop) (0, G, cm) ;
+ r = CHOLMOD(norm_sparse) (G, 0, cm) ;
+ if (G != NULL)
+ {
+ MAXERR (maxerr, r, anorm) ;
+ }
+ CHOLMOD(free_sparse) (&E, cm) ;
+ CHOLMOD(free_sparse) (&G, cm) ;
+ }
+
+ if (nrow == ncol)
+ {
+ /* E = pattern of A */
+ E = CHOLMOD(copy) (A, 0, 0, cm) ;
+ /* G = E*E */
+ if (n > NLARGE) progress (1, '.') ;
+ G = CHOLMOD(ssmult) (E, E, 0, FALSE, FALSE, cm) ;
+ if (n > NLARGE) progress (1, '.') ;
+ CHOLMOD(free_sparse) (&E, cm) ;
+ CHOLMOD(free_sparse) (&G, cm) ;
+ }
+
+ cm->error_handler = save ;
+
+ CHOLMOD(free_sparse) (&D, cm) ;
+ CHOLMOD(free_sparse) (&C, cm) ;
+ CHOLMOD(free_sparse) (&AT, cm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free P, Q, and their inverses */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD(free) (ncol, sizeof (Int), fset, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), P, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), Pinv, cm) ;
+ if (A->stype == 0)
+ {
+ CHOLMOD(free) (ncol, sizeof (Int), Q, cm) ;
+ }
+ CHOLMOD(free) (ncol, sizeof (Int), Qinv, cm) ;
+ CHOLMOD(free) (nrow, sizeof (Int), Partition, cm) ;
+
+ progress (0, '.') ;
+ return (maxerr) ;
+}
diff --git a/CHOLMOD/Tcov/unpack.c b/CHOLMOD/Tcov/unpack.c
new file mode 100644
index 0000000..4f91348
--- /dev/null
+++ b/CHOLMOD/Tcov/unpack.c
@@ -0,0 +1,185 @@
+/* ========================================================================== */
+/* === Tcov/unpack ========================================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Tcov Module. Copyright (C) 2005-2006, Timothy A. Davis
+ * The CHOLMOD/Tcov Module is licensed under Version 2.0 of the GNU
+ * General Public License. See gpl.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Create an unpacked, unsorted version of a matrix, with random-sized gaps in
+ * each column. */
+
+#include "cm.h"
+
+
+/* ========================================================================== */
+/* === unpack =============================================================== */
+/* ========================================================================== */
+
+cholmod_sparse *unpack (cholmod_sparse *A)
+{
+ double x ;
+ double *Ax, *Cx, *Az, *Cz ;
+ Int *Ap, *Ai, *Anz, *Cp, *Ci, *Cnz ;
+ cholmod_sparse *C ;
+ Int i, j, p, q, pdest, pend, nrow, ncol, nzmax, sorted, packed, stype,
+ extra ;
+
+ if (A == NULL)
+ {
+ return (NULL) ;
+ }
+
+ extra = 10 ;
+
+ nrow = A->nrow ;
+ ncol = A->ncol ;
+ nzmax = A->nzmax ;
+ sorted = A->sorted ;
+ packed = A->packed ;
+ stype = A->stype ;
+
+ C = CHOLMOD(allocate_sparse) (nrow, ncol, nzmax + extra*ncol, FALSE,
+ FALSE, stype, A->xtype, cm) ;
+
+ if (C == NULL)
+ {
+ return (NULL) ;
+ }
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ Az = A->z ;
+ Anz = A->nz ;
+
+ Cp = C->p ;
+ Ci = C->i ;
+ Cx = C->x ;
+ Cz = C->z ;
+ Cnz = C->nz ;
+ nzmax = C->nzmax ;
+ nzmax = MAX (1, nzmax) ;
+
+ for (p = 0 ; p < nzmax ; p++)
+ {
+ Ci [p] = 0 ;
+ }
+ if (A->xtype == CHOLMOD_REAL)
+ {
+ for (p = 0 ; p < nzmax ; p++)
+ {
+ Cx [p] = 0 ;
+ }
+ }
+ else if (A->xtype == CHOLMOD_COMPLEX)
+ {
+ for (p = 0 ; p < 2*nzmax ; p++)
+ {
+ Cx [p] = 0 ;
+ }
+ }
+ else if (A->xtype == CHOLMOD_ZOMPLEX)
+ {
+ for (p = 0 ; p < nzmax ; p++)
+ {
+ Cx [p] = 0 ;
+ Cz [p] = 0 ;
+ }
+ }
+
+ pdest = 0 ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ /* copy the column into C */
+ p = Ap [j] ;
+ Cp [j] = pdest ;
+ pend = (packed) ? (Ap [j+1]) : (p + Anz [j]) ;
+ Cnz [j] = pend - p ;
+ for ( ; p < pend ; p++)
+ {
+ Ci [pdest] = Ai [p] ;
+ if (A->xtype == CHOLMOD_REAL)
+ {
+ Cx [pdest] = Ax [p] ;
+ }
+ else if (A->xtype == CHOLMOD_COMPLEX)
+ {
+ Cx [2*pdest ] = Ax [2*p] ;
+ Cx [2*pdest+1] = Ax [2*p+1] ;
+ }
+ else if (A->xtype == CHOLMOD_ZOMPLEX)
+ {
+ Cx [pdest] = Ax [p] ;
+ Cz [pdest] = Az [p] ;
+ }
+ pdest++ ;
+ }
+
+ /* jumble the column */
+ p = Cp [j] ;
+ pend = p + Cnz [j] ;
+ for ( ; p < pend-1 ; p++)
+ {
+ q = p + nrand (pend-p) ; /* RAND */
+ i = Ci [p] ;
+ Ci [p] = Ci [q] ;
+ Ci [q] = i ;
+
+ if (A->xtype == CHOLMOD_REAL)
+ {
+ x = Cx [p] ;
+ Cx [p] = Cx [q] ;
+ Cx [q] = x ;
+ }
+ else if (A->xtype == CHOLMOD_COMPLEX)
+ {
+ x = Cx [2*p] ;
+ Cx [2*p] = Cx [2*q] ;
+ Cx [2*q] = x ;
+
+ x = Cx [2*p+1] ;
+ Cx [2*p+1] = Cx [2*q+1] ;
+ Cx [2*q+1] = x ;
+ }
+ else if (A->xtype == CHOLMOD_ZOMPLEX)
+ {
+ x = Cx [p] ;
+ Cx [p] = Cx [q] ;
+ Cx [q] = x ;
+
+ x = Cz [p] ;
+ Cz [p] = Cz [q] ;
+ Cz [q] = x ;
+ }
+ }
+
+ /* add some random blank space */
+ pdest += nrand (extra) ; /* RAND */
+ for (p = pend ; p < pdest ; p++)
+ {
+ Ci [p] = 0 ;
+ if (A->xtype == CHOLMOD_REAL)
+ {
+ Cx [p] = 0 ;
+ }
+ else if (A->xtype == CHOLMOD_COMPLEX)
+ {
+ Cx [2*p] = 0 ;
+ Cx [2*p+1] = 0 ;
+ }
+ else if (A->xtype == CHOLMOD_ZOMPLEX)
+ {
+ Cx [p] = 0 ;
+ Cz [p] = 0 ;
+ }
+ }
+ }
+ Cp [ncol] = pdest ;
+
+ return (C) ;
+}
diff --git a/CHOLMOD/Valgrind/License.txt b/CHOLMOD/Valgrind/License.txt
new file mode 100644
index 0000000..86ecced
--- /dev/null
+++ b/CHOLMOD/Valgrind/License.txt
@@ -0,0 +1,24 @@
+CHOLMOD/Valgrind Module. Copyright (C) 2005-2006, Timothy A. Davis.
+CHOLMOD is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Note that this license is for the CHOLMOD/Valgrind module only.
+All CHOLMOD modules are licensed separately.
+
+
+--------------------------------------------------------------------------------
+
+
+This Module is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
diff --git a/CHOLMOD/Valgrind/Make.inc b/CHOLMOD/Valgrind/Make.inc
new file mode 100644
index 0000000..9cd75c7
--- /dev/null
+++ b/CHOLMOD/Valgrind/Make.inc
@@ -0,0 +1,8 @@
+# valgrind options
+V = valgrind --suppressions=suppress --quiet
+
+# covall is not used
+COVER =
+
+# no test coverage needed
+CFLAGS = -O0 -g
diff --git a/CHOLMOD/Valgrind/Makefile b/CHOLMOD/Valgrind/Makefile
new file mode 100644
index 0000000..42080e3
--- /dev/null
+++ b/CHOLMOD/Valgrind/Makefile
@@ -0,0 +1,34 @@
+
+doall: links go
+
+links:
+ touch links
+ ln -s ../Tcov/amdtest.c
+ ln -s ../Tcov/aug.c
+ ln -s ../Tcov/camdtest.c
+ ln -s ../Tcov/cctest.c
+ ln -s ../Tcov/cm.c
+ ln -s ../Tcov/cm.h
+ ln -s ../Tcov/cmread.c
+ ln -s ../Tcov/ctest.c
+ ln -s ../Tcov/huge.c
+ ln -s ../Tcov/leak.c
+ ln -s ../Tcov/lpdemo.c
+ ln -s ../Tcov/memory.c
+ ln -s ../Tcov/null2.c
+ ln -s ../Tcov/null.c
+ ln -s ../Tcov/raw_factor.c
+ ln -s ../Tcov/solve.c
+ ln -s ../Tcov/test_ops.c
+ ln -s ../Tcov/unpack.c
+ ln -s ../Tcov/comments.txt
+ ln -s ../Tcov/Matrix
+
+include ../Tcov/Makefile
+
+dopurge: distclean
+ - $(RM) amdtest.c aug.c camdtest.c cctest.c cm.c cm.h cmread.c \
+ ctest.c huge.c leak.c lpdemo.c memory.c null2.c null.c \
+ raw_factor.c solve.c test_ops.c unpack.c comments.txt \
+ links Matrix
+
diff --git a/CHOLMOD/Valgrind/README.txt b/CHOLMOD/Valgrind/README.txt
new file mode 100644
index 0000000..574640a
--- /dev/null
+++ b/CHOLMOD/Valgrind/README.txt
@@ -0,0 +1,18 @@
+Torture test for CHOLMOD, using valgrind. Requires Linux.
+
+Type "make" to compile and run CHOLMOMD with valgrind.
+Every line of CHOLMOD will be exercised, and its results
+checked. The line "All tests passed" should appear in each
+output file (*.grind). Valgrind should report no errors,
+and no malloc'd blocks should be in use at exit.
+
+Note that many, many error messages will appear in the
+test output itself (tmp/*.out), because all of CHOLMOD's
+error handling is checked as well. These errors are
+expected.
+
+To remove all but the source files and output files from
+this directory, type "make clean". To remove all but the
+files in the original distribution and the symbolic links,
+type "make distclean". To remove all but the files in
+the original distribution, type "make dopurge".
diff --git a/CHOLMOD/Valgrind/gpl.txt b/CHOLMOD/Valgrind/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/CHOLMOD/Valgrind/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it. (Some other Free Software Foundation software is covered by
+the GNU Library General Public License instead.) You can apply it to
+your programs, too.
+
+ When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+this service if you wish), that you receive source code or can get it
+if you want it, that you can change the software or use pieces of it
+in new free programs; and that you know you can do these things.
+
+ To protect your rights, we need to make restrictions that forbid
+anyone to deny you these rights or to ask you to surrender the rights.
+These restrictions translate to certain responsibilities for you if you
+distribute copies of the software, or if you modify it.
+
+ For example, if you distribute copies of such a program, whether
+gratis or for a fee, you must give the recipients all the rights that
+you have. You must make sure that they, too, receive or can get the
+source code. And you must show them these terms so they know their
+rights.
+
+ We protect your rights with two steps: (1) copyright the software, and
+(2) offer you this license which gives you legal permission to copy,
+distribute and/or modify the software.
+
+ Also, for each author's protection and ours, we want to make certain
+that everyone understands that there is no warranty for this free
+software. If the software is modified by someone else and passed on, we
+want its recipients to know that what they have is not the original, so
+that any problems introduced by others will not reflect on the original
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+
+ Finally, any free program is threatened constantly by software
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+
+ The precise terms and conditions for copying, distribution and
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+
+ GNU GENERAL PUBLIC LICENSE
+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
+ 0. This License applies to any program or other work which contains
+a notice placed by the copyright holder saying it may be distributed
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+
+Activities other than copying, distribution and modification are not
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+is covered only if its contents constitute a work based on the
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+ 1. You may copy and distribute verbatim copies of the Program's
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+notices that refer to this License and to the absence of any warranty;
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+along with the Program.
+
+You may charge a fee for the physical act of transferring a copy, and
+you may at your option offer warranty protection in exchange for a fee.
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+ 2. You may modify your copy or copies of the Program or any portion
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+These requirements apply to the modified work as a whole. If
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+ You should have received a copy of the GNU General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+
+Also add information on how to contact you by electronic and paper mail.
+
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
+
+ Gnomovision version 69, Copyright (C) year name of author
+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ <signature of Ty Coon>, 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Library General
+Public License instead of this License.
diff --git a/CHOLMOD/Valgrind/suppress b/CHOLMOD/Valgrind/suppress
new file mode 100644
index 0000000..b57b278
--- /dev/null
+++ b/CHOLMOD/Valgrind/suppress
@@ -0,0 +1,5 @@
+{
+ complexity
+ Memcheck:Value8
+ fun:change_complexity
+}
diff --git a/COLAMD/Demo/Makefile b/COLAMD/Demo/Makefile
new file mode 100644
index 0000000..f08df2a
--- /dev/null
+++ b/COLAMD/Demo/Makefile
@@ -0,0 +1,43 @@
+#-----------------------------------------------------------------------------
+# compile the COLAMD demo
+#-----------------------------------------------------------------------------
+
+default: colamd_example colamd_l_example
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../Include -I../../UFconfig
+
+C = $(CC) $(CFLAGS) $(I)
+
+library:
+ ( cd ../Lib ; $(MAKE) )
+
+#------------------------------------------------------------------------------
+# Create the demo program, run it, and compare the output
+#------------------------------------------------------------------------------
+
+dist:
+
+colamd_example: colamd_example.c library
+ $(C) -o colamd_example colamd_example.c ../Lib/libcolamd.a -lm
+ - ./colamd_example > my_colamd_example.out
+ - diff colamd_example.out my_colamd_example.out
+
+colamd_l_example: colamd_l_example.c library
+ $(C) -o colamd_l_example colamd_l_example.c ../Lib/libcolamd.a -lm
+ - ./colamd_l_example > my_colamd_l_example.out
+ - diff colamd_example.out my_colamd_example.out
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) colamd_example colamd_l_example
+ - $(RM) my_colamd_example.out my_colamd_l_example.out
diff --git a/COLAMD/Demo/colamd_example.c b/COLAMD/Demo/colamd_example.c
new file mode 100644
index 0000000..fe824d8
--- /dev/null
+++ b/COLAMD/Demo/colamd_example.c
@@ -0,0 +1,181 @@
+/* ========================================================================== */
+/* === colamd and symamd example ============================================ */
+/* ========================================================================== */
+
+/* COLAMD / SYMAMD example
+
+ colamd example of use, to order the columns of a 5-by-4 matrix with
+ 11 nonzero entries in the following nonzero pattern, with default knobs.
+
+ x 0 x 0
+ x 0 x x
+ 0 x x 0
+ 0 0 x x
+ x x 0 0
+
+ symamd example of use, to order the rows and columns of a 5-by-5
+ matrix with 13 nonzero entries in the following nonzero pattern,
+ with default knobs.
+
+ x x 0 0 0
+ x x x x 0
+ 0 x x 0 0
+ 0 x 0 x x
+ 0 0 0 x x
+
+ (where x denotes a nonzero value).
+
+ See http://www.cise.ufl.edu/research/sparse/colamd/ (the colamd.c file)
+ for the routines this program calls, and for the License.
+*/
+
+/* ========================================================================== */
+
+#include <stdio.h>
+#include "colamd.h"
+
+#define A_NNZ 11
+#define A_NROW 5
+#define A_NCOL 4
+#define ALEN 150
+
+#define B_NNZ 4
+#define B_N 5
+
+int main (void)
+{
+
+ /* ====================================================================== */
+ /* input matrix A definition */
+ /* ====================================================================== */
+
+ int A [ALEN] = {
+
+ 0, 1, 4, /* row indices of nonzeros in column 0 */
+ 2, 4, /* row indices of nonzeros in column 1 */
+ 0, 1, 2, 3, /* row indices of nonzeros in column 2 */
+ 1, 3} ; /* row indices of nonzeros in column 3 */
+
+ int p [ ] = {
+
+ 0, /* column 0 is in A [0..2] */
+ 3, /* column 1 is in A [3..4] */
+ 5, /* column 2 is in A [5..8] */
+ 9, /* column 3 is in A [9..10] */
+ A_NNZ} ; /* number of nonzeros in A */
+
+ /* ====================================================================== */
+ /* input matrix B definition */
+ /* ====================================================================== */
+
+ int B [ ] = { /* Note: only strictly lower triangular part */
+ /* is included, since symamd ignores the */
+ /* diagonal and upper triangular part of B. */
+
+ 1, /* row indices of nonzeros in column 0 */
+ 2, 3, /* row indices of nonzeros in column 1 */
+ /* row indices of nonzeros in column 2 (none) */
+ 4 /* row indices of nonzeros in column 3 */
+ } ; /* row indices of nonzeros in column 4 (none) */
+
+ int q [ ] = {
+
+ 0, /* column 0 is in B [0] */
+ 1, /* column 1 is in B [1..2] */
+ 3, /* column 2 is empty */
+ 3, /* column 3 is in B [3] */
+ 4, /* column 4 is empty */
+ B_NNZ} ; /* number of nonzeros in strictly lower B */
+
+ /* ====================================================================== */
+ /* other variable definitions */
+ /* ====================================================================== */
+
+ int perm [B_N+1] ; /* note the size is N+1 */
+ int stats [COLAMD_STATS] ; /* for colamd and symamd output statistics */
+
+ int row, col, pp, length, ok ;
+
+ /* ====================================================================== */
+ /* dump the input matrix A */
+ /* ====================================================================== */
+
+ printf ("colamd %d-by-%d input matrix:\n", A_NROW, A_NCOL) ;
+ for (col = 0 ; col < A_NCOL ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ printf ("Column %d, with %d entries:\n", col, length) ;
+ for (pp = p [col] ; pp < p [col+1] ; pp++)
+ {
+ row = A [pp] ;
+ printf (" row %d\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix. Note that this destroys A and overwrites p */
+ /* ====================================================================== */
+
+ ok = colamd (A_NROW, A_NCOL, ALEN, A, p, (double *) NULL, stats) ;
+ colamd_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("colamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the column ordering */
+ /* ====================================================================== */
+
+ printf ("colamd column ordering:\n") ;
+ printf ("1st column: %d\n", p [0]) ;
+ printf ("2nd column: %d\n", p [1]) ;
+ printf ("3rd column: %d\n", p [2]) ;
+ printf ("4th column: %d\n", p [3]) ;
+
+ /* ====================================================================== */
+ /* dump the strictly lower triangular part of symmetric input matrix B */
+ /* ====================================================================== */
+
+ printf ("\n\nsymamd %d-by-%d input matrix:\n", B_N, B_N) ;
+ printf ("Entries in strictly lower triangular part:\n") ;
+ for (col = 0 ; col < B_N ; col++)
+ {
+ length = q [col+1] - q [col] ;
+ printf ("Column %d, with %d entries:\n", col, length) ;
+ for (pp = q [col] ; pp < q [col+1] ; pp++)
+ {
+ row = B [pp] ;
+ printf (" row %d\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix B. Note that this does not modify B or q. */
+ /* ====================================================================== */
+
+ ok = symamd (B_N, B, q, perm, (double *) NULL, stats, &calloc, &free) ;
+ symamd_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("symamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the symmetric ordering */
+ /* ====================================================================== */
+
+ printf ("symamd column ordering:\n") ;
+ printf ("1st row/column: %d\n", perm [0]) ;
+ printf ("2nd row/column: %d\n", perm [1]) ;
+ printf ("3rd row/column: %d\n", perm [2]) ;
+ printf ("4th row/column: %d\n", perm [3]) ;
+ printf ("5th row/column: %d\n", perm [4]) ;
+
+ exit (0) ;
+}
+
diff --git a/COLAMD/Demo/colamd_example.out b/COLAMD/Demo/colamd_example.out
new file mode 100644
index 0000000..93d121d
--- /dev/null
+++ b/COLAMD/Demo/colamd_example.out
@@ -0,0 +1,50 @@
+colamd 5-by-4 input matrix:
+Column 0, with 3 entries:
+ row 0
+ row 1
+ row 4
+Column 1, with 2 entries:
+ row 2
+ row 4
+Column 2, with 4 entries:
+ row 0
+ row 1
+ row 2
+ row 3
+Column 3, with 2 entries:
+ row 1
+ row 3
+
+colamd version 2.7, Nov 1, 2007: OK.
+colamd: number of dense or empty rows ignored: 0
+colamd: number of dense or empty columns ignored: 0
+colamd: number of garbage collections performed: 0
+colamd column ordering:
+1st column: 1
+2nd column: 0
+3rd column: 2
+4th column: 3
+
+
+symamd 5-by-5 input matrix:
+Entries in strictly lower triangular part:
+Column 0, with 1 entries:
+ row 1
+Column 1, with 2 entries:
+ row 2
+ row 3
+Column 2, with 0 entries:
+Column 3, with 1 entries:
+ row 4
+Column 4, with 0 entries:
+
+symamd version 2.7, Nov 1, 2007: OK.
+symamd: number of dense or empty rows ignored: 0
+symamd: number of dense or empty columns ignored: 0
+symamd: number of garbage collections performed: 0
+symamd column ordering:
+1st row/column: 0
+2nd row/column: 2
+3rd row/column: 1
+4th row/column: 3
+5th row/column: 4
diff --git a/COLAMD/Demo/colamd_l_example.c b/COLAMD/Demo/colamd_l_example.c
new file mode 100644
index 0000000..9ff9aeb
--- /dev/null
+++ b/COLAMD/Demo/colamd_l_example.c
@@ -0,0 +1,185 @@
+/* ========================================================================== */
+/* === colamd and symamd example ============================================ */
+/* ========================================================================== */
+
+/* COLAMD / SYMAMD example
+
+ colamd example of use, to order the columns of a 5-by-4 matrix with
+ 11 nonzero entries in the following nonzero pattern, with default knobs.
+
+ x 0 x 0
+ x 0 x x
+ 0 x x 0
+ 0 0 x x
+ x x 0 0
+
+ symamd example of use, to order the rows and columns of a 5-by-5
+ matrix with 13 nonzero entries in the following nonzero pattern,
+ with default knobs.
+
+ x x 0 0 0
+ x x x x 0
+ 0 x x 0 0
+ 0 x 0 x x
+ 0 0 0 x x
+
+ (where x denotes a nonzero value).
+
+
+ See http://www.cise.ufl.edu/research/sparse/colamd/ (the colamd.c file)
+ for the routines this program calls, and for the License.
+*/
+
+/* ========================================================================== */
+
+#include <stdio.h>
+#include "colamd.h"
+
+#define A_NNZ 11
+#define A_NROW 5
+#define A_NCOL 4
+#define ALEN 150
+
+#define B_NNZ 4
+#define B_N 5
+
+/* define UF_long */
+#include "UFconfig.h"
+
+int main (void)
+{
+
+ /* ====================================================================== */
+ /* input matrix A definition */
+ /* ====================================================================== */
+
+ UF_long A [ALEN] = {
+
+ 0, 1, 4, /* row indices of nonzeros in column 0 */
+ 2, 4, /* row indices of nonzeros in column 1 */
+ 0, 1, 2, 3, /* row indices of nonzeros in column 2 */
+ 1, 3} ; /* row indices of nonzeros in column 3 */
+
+ UF_long p [ ] = {
+
+ 0, /* column 0 is in A [0..2] */
+ 3, /* column 1 is in A [3..4] */
+ 5, /* column 2 is in A [5..8] */
+ 9, /* column 3 is in A [9..10] */
+ A_NNZ} ; /* number of nonzeros in A */
+
+ /* ====================================================================== */
+ /* input matrix B definition */
+ /* ====================================================================== */
+
+ UF_long B [ ] = { /* Note: only strictly lower triangular part */
+ /* is included, since symamd ignores the */
+ /* diagonal and upper triangular part of B. */
+
+ 1, /* row indices of nonzeros in column 0 */
+ 2, 3, /* row indices of nonzeros in column 1 */
+ /* row indices of nonzeros in column 2 (none) */
+ 4 /* row indices of nonzeros in column 3 */
+ } ; /* row indices of nonzeros in column 4 (none) */
+
+ UF_long q [ ] = {
+
+ 0, /* column 0 is in B [0] */
+ 1, /* column 1 is in B [1..2] */
+ 3, /* column 2 is empty */
+ 3, /* column 3 is in B [3] */
+ 4, /* column 4 is empty */
+ B_NNZ} ; /* number of nonzeros in strictly lower B */
+
+ /* ====================================================================== */
+ /* other variable definitions */
+ /* ====================================================================== */
+
+ UF_long perm [B_N+1] ; /* note the size is N+1 */
+ UF_long stats [COLAMD_STATS] ;/* for colamd and symamd output statistics */
+
+ UF_long row, col, pp, length, ok ;
+
+ /* ====================================================================== */
+ /* dump the input matrix A */
+ /* ====================================================================== */
+
+ printf ("colamd %d-by-%d input matrix:\n", A_NROW, A_NCOL) ;
+ for (col = 0 ; col < A_NCOL ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ printf ("Column %ld, with %ld entries:\n", col, length) ;
+ for (pp = p [col] ; pp < p [col+1] ; pp++)
+ {
+ row = A [pp] ;
+ printf (" row %ld\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix. Note that this destroys A and overwrites p */
+ /* ====================================================================== */
+
+ ok = colamd_l (A_NROW, A_NCOL, ALEN, A, p, (double *) NULL, stats) ;
+ colamd_l_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("colamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the column ordering */
+ /* ====================================================================== */
+
+ printf ("colamd_l column ordering:\n") ;
+ printf ("1st column: %ld\n", p [0]) ;
+ printf ("2nd column: %ld\n", p [1]) ;
+ printf ("3rd column: %ld\n", p [2]) ;
+ printf ("4th column: %ld\n", p [3]) ;
+
+ /* ====================================================================== */
+ /* dump the strictly lower triangular part of symmetric input matrix B */
+ /* ====================================================================== */
+
+ printf ("\n\nsymamd_l %d-by-%d input matrix:\n", B_N, B_N) ;
+ printf ("Entries in strictly lower triangular part:\n") ;
+ for (col = 0 ; col < B_N ; col++)
+ {
+ length = q [col+1] - q [col] ;
+ printf ("Column %ld, with %ld entries:\n", col, length) ;
+ for (pp = q [col] ; pp < q [col+1] ; pp++)
+ {
+ row = B [pp] ;
+ printf (" row %ld\n", row) ;
+ }
+ }
+
+ /* ====================================================================== */
+ /* order the matrix B. Note that this does not modify B or q. */
+ /* ====================================================================== */
+
+ ok = symamd_l (B_N, B, q, perm, (double *) NULL, stats, &calloc, &free) ;
+ symamd_l_report (stats) ;
+
+ if (!ok)
+ {
+ printf ("symamd error!\n") ;
+ exit (1) ;
+ }
+
+ /* ====================================================================== */
+ /* print the symmetric ordering */
+ /* ====================================================================== */
+
+ printf ("symamd_l column ordering:\n") ;
+ printf ("1st row/column: %ld\n", perm [0]) ;
+ printf ("2nd row/column: %ld\n", perm [1]) ;
+ printf ("3rd row/column: %ld\n", perm [2]) ;
+ printf ("4th row/column: %ld\n", perm [3]) ;
+ printf ("5th row/column: %ld\n", perm [4]) ;
+
+ exit (0) ;
+}
+
diff --git a/COLAMD/Demo/colamd_l_example.out b/COLAMD/Demo/colamd_l_example.out
new file mode 100644
index 0000000..3605229
--- /dev/null
+++ b/COLAMD/Demo/colamd_l_example.out
@@ -0,0 +1,50 @@
+colamd 5-by-4 input matrix:
+Column 0, with 3 entries:
+ row 0
+ row 1
+ row 4
+Column 1, with 2 entries:
+ row 2
+ row 4
+Column 2, with 4 entries:
+ row 0
+ row 1
+ row 2
+ row 3
+Column 3, with 2 entries:
+ row 1
+ row 3
+
+colamd version 2.7, Nov 1, 2007: OK.
+colamd: number of dense or empty rows ignored: 0
+colamd: number of dense or empty columns ignored: 0
+colamd: number of garbage collections performed: 0
+colamd_l column ordering:
+1st column: 1
+2nd column: 0
+3rd column: 2
+4th column: 3
+
+
+symamd_l 5-by-5 input matrix:
+Entries in strictly lower triangular part:
+Column 0, with 1 entries:
+ row 1
+Column 1, with 2 entries:
+ row 2
+ row 3
+Column 2, with 0 entries:
+Column 3, with 1 entries:
+ row 4
+Column 4, with 0 entries:
+
+symamd version 2.7, Nov 1, 2007: OK.
+symamd: number of dense or empty rows ignored: 0
+symamd: number of dense or empty columns ignored: 0
+symamd: number of garbage collections performed: 0
+symamd_l column ordering:
+1st row/column: 0
+2nd row/column: 2
+3rd row/column: 1
+4th row/column: 3
+5th row/column: 4
diff --git a/COLAMD/Doc/ChangeLog b/COLAMD/Doc/ChangeLog
new file mode 100644
index 0000000..29308e9
--- /dev/null
+++ b/COLAMD/Doc/ChangeLog
@@ -0,0 +1,129 @@
+May 31, 2007: version 2.7.0
+
+ * ported to 64-bit MATLAB
+
+ * subdirectories added (Source/, Include/, Lib/, Doc/, MATLAB/, Demo/)
+
+Dec 12, 2006, version 2.5.2
+
+ * minor MATLAB cleanup. MATLAB functions renamed colamd2 and symamd2,
+ so that they do not conflict with the built-in versions. Note that
+ the MATLAB built-in functions colamd and symamd are identical to
+ the colamd and symamd functions here.
+
+Aug 31, 2006: Version 2.5.1
+
+ * minor change to colamd.m and symamd.m, to use etree instead
+ of sparsfun.
+
+Apr. 30, 2006: Version 2.5
+
+ * colamd_recommended modified, to do more careful integer overflow
+ checking. It now returns size_t, not int. colamd_l_recommended
+ also returns size_t. A zero is returned if an error occurs. A
+ postive return value denotes success. In v2.4 and earlier,
+ -1 was returned on error (an int or long).
+
+ * long replaced with UF_long integer, which is long except on WIN64.
+
+Nov 15, 2005:
+
+ * minor editting of comments; version number (2.4) unchanged.
+
+Changes from Version 2.3 to 2.4 (Aug 30, 2005)
+
+ * Makefile now relies on ../UFconfig/UFconfig.mk
+
+ * changed the dense row/col detection. The meaning of the knobs
+ has thus changed.
+
+ * added an option to turn off aggressive absorption. It was
+ always on in versions 2.3 and earlier.
+
+ * added a #define'd version number
+
+ * added a function pointer (colamd_printf) for COLAMD's printing.
+
+ * added a -DNPRINT option, to turn off printing at compile-time.
+
+ * added a check for integer overflow in colamd_recommended
+
+ * minor changes to allow for more simpler 100% test coverage
+
+ * bug fix. If symamd v2.3 fails to allocate its copy of the input
+ matrix, then it erroneously frees a calloc'd workspace twice.
+ This bug has no effect on the MATLAB symamd mexFunction, since
+ mxCalloc terminates the mexFunction if it fails to allocate
+ memory. Similarly, UMFPACK is not affected because it does not
+ use symamd. The bug has no effect on the colamd ordering
+ routine in v2.3.
+
+Changes from Version 2.2 to 2.3 (Sept. 8, 2003)
+
+ * removed the call to the MATLAB spparms ('spumoni') function.
+ This can take a lot of time if you are ordering many small
+ matrices. Only affects the MATLAB interface (colamdmex.c,
+ symamdmex.c, colamdtestmex.c, and symamdtestmex.c). The
+ usage of the optional 2nd argument to the colamd and symamd
+ mexFunctions was changed accordingly.
+
+Changes from Version 2.1 to 2.2 (Sept. 23, 2002)
+
+ * extensive testing routines added (colamd_test.m, colamdtestmex.c,
+ and symamdtestmex.c), and the Makefile modified accordingly.
+
+ * a few typos in the comments corrected
+
+ * use of the MATLAB "flops" command removed from colamd_demo, and an
+ m-file routine luflops.m added.
+
+ * an explicit typecast from unsigned to int added, for COLAMD_C and
+ COLAMD_R in colamd.h.
+
+ * #include <stdio.h> added to colamd_example.c
+
+
+Changes from Version 2.0 to 2.1 (May 4, 2001)
+
+ * TRUE and FALSE are predefined on some systems, so they are defined
+ here only if not already defined.
+
+ * web site changed
+
+ * UNIX Makefile modified, to handle the case if "." is not in your path.
+
+
+Changes from Version 1.0 to 2.0 (January 31, 2000)
+
+ No bugs were found in version 1.1. These changes merely add new
+ functionality.
+
+ * added the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro.
+
+ * moved the output statistics, from A, to a separate output argument.
+ The arguments changed for the C-callable routines.
+
+ * added colamd_report and symamd_report.
+
+ * added a C-callable symamd routine. Formerly, symamd was only
+ available as a mexFunction from MATLAB.
+
+ * added error-checking to symamd. Formerly, it assumed its input
+ was error-free.
+
+ * added the optional stats and knobs arguments to the symamd mexFunction
+
+ * deleted colamd_help. A help message is still available from
+ "help colamd" and "help symamd" in MATLAB.
+
+ * deleted colamdtree.m and symamdtree.m. Now, colamd.m and symamd.m
+ also do the elimination tree post-ordering. The Version 1.1
+ colamd and symamd mexFunctions, which do not do the post-
+ ordering, are now visible as colamdmex and symamdmex from
+ MATLAB. Essentialy, the post-ordering is now the default
+ behavior of colamd.m and symamd.m, to match the behavior of
+ colmmd and symmmd. The post-ordering is only available in the
+ MATLAB interface, not the C-callable interface.
+
+ * made a slight change to the dense row/column detection in symamd,
+ to match the stated specifications.
diff --git a/COLAMD/Doc/lesser.txt b/COLAMD/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/COLAMD/Doc/lesser.txt
@@ -0,0 +1,504 @@
+ GNU LESSER GENERAL PUBLIC LICENSE
+ Version 2.1, February 1999
+
+ Copyright (C) 1991, 1999 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+[This is the first released version of the Lesser GPL. It also counts
+ as the successor of the GNU Library Public License, version 2, hence
+ the version number 2.1.]
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+Licenses are intended to guarantee your freedom to share and change
+free software--to make sure the software is free for all its users.
+
+ This license, the Lesser General Public License, applies to some
+specially designated software packages--typically libraries--of the
+Free Software Foundation and other authors who decide to use it. You
+can use it too, but we suggest you first think carefully about whether
+this license or the ordinary General Public License is the better
+strategy to use in any particular case, based on the explanations below.
+
+ When we speak of free software, we are referring to freedom of use,
+not price. Our General Public Licenses are designed to make sure that
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diff --git a/COLAMD/Include/colamd.h b/COLAMD/Include/colamd.h
new file mode 100644
index 0000000..26372d8
--- /dev/null
+++ b/COLAMD/Include/colamd.h
@@ -0,0 +1,255 @@
+/* ========================================================================== */
+/* === colamd/symamd prototypes and definitions ============================= */
+/* ========================================================================== */
+
+/* COLAMD / SYMAMD include file
+
+ You must include this file (colamd.h) in any routine that uses colamd,
+ symamd, or the related macros and definitions.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Notice:
+
+ Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved.
+
+ THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+
+ Permission is hereby granted to use, copy, modify, and/or distribute
+ this program, provided that the Copyright, this License, and the
+ Availability of the original version is retained on all copies and made
+ accessible to the end-user of any code or package that includes COLAMD
+ or any modified version of COLAMD.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the http://www.cise.ufl.edu/research/sparse/colamd/colamd.h
+ file. It is required by the colamd.c, colamdmex.c, and symamdmex.c
+ files, and by any C code that calls the routines whose prototypes are
+ listed below, or that uses the colamd/symamd definitions listed below.
+
+*/
+
+#ifndef COLAMD_H
+#define COLAMD_H
+
+/* make it easy for C++ programs to include COLAMD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include <stdlib.h>
+
+/* ========================================================================== */
+/* === COLAMD version ======================================================= */
+/* ========================================================================== */
+
+/* COLAMD Version 2.4 and later will include the following definitions.
+ * As an example, to test if the version you are using is 2.4 or later:
+ *
+ * #ifdef COLAMD_VERSION
+ * if (COLAMD_VERSION >= COLAMD_VERSION_CODE (2,4)) ...
+ * #endif
+ *
+ * This also works during compile-time:
+ *
+ * #if defined(COLAMD_VERSION) && (COLAMD_VERSION >= COLAMD_VERSION_CODE (2,4))
+ * printf ("This is version 2.4 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ *
+ * Versions 2.3 and earlier of COLAMD do not include a #define'd version number.
+ */
+
+#define COLAMD_DATE "Nov 1, 2007"
+#define COLAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define COLAMD_MAIN_VERSION 2
+#define COLAMD_SUB_VERSION 7
+#define COLAMD_SUBSUB_VERSION 1
+#define COLAMD_VERSION \
+ COLAMD_VERSION_CODE(COLAMD_MAIN_VERSION,COLAMD_SUB_VERSION)
+
+/* ========================================================================== */
+/* === Knob and statistics definitions ====================================== */
+/* ========================================================================== */
+
+/* size of the knobs [ ] array. Only knobs [0..1] are currently used. */
+#define COLAMD_KNOBS 20
+
+/* number of output statistics. Only stats [0..6] are currently used. */
+#define COLAMD_STATS 20
+
+/* knobs [0] and stats [0]: dense row knob and output statistic. */
+#define COLAMD_DENSE_ROW 0
+
+/* knobs [1] and stats [1]: dense column knob and output statistic. */
+#define COLAMD_DENSE_COL 1
+
+/* knobs [2]: aggressive absorption */
+#define COLAMD_AGGRESSIVE 2
+
+/* stats [2]: memory defragmentation count output statistic */
+#define COLAMD_DEFRAG_COUNT 2
+
+/* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */
+#define COLAMD_STATUS 3
+
+/* stats [4..6]: error info, or info on jumbled columns */
+#define COLAMD_INFO1 4
+#define COLAMD_INFO2 5
+#define COLAMD_INFO3 6
+
+/* error codes returned in stats [3]: */
+#define COLAMD_OK (0)
+#define COLAMD_OK_BUT_JUMBLED (1)
+#define COLAMD_ERROR_A_not_present (-1)
+#define COLAMD_ERROR_p_not_present (-2)
+#define COLAMD_ERROR_nrow_negative (-3)
+#define COLAMD_ERROR_ncol_negative (-4)
+#define COLAMD_ERROR_nnz_negative (-5)
+#define COLAMD_ERROR_p0_nonzero (-6)
+#define COLAMD_ERROR_A_too_small (-7)
+#define COLAMD_ERROR_col_length_negative (-8)
+#define COLAMD_ERROR_row_index_out_of_bounds (-9)
+#define COLAMD_ERROR_out_of_memory (-10)
+#define COLAMD_ERROR_internal_error (-999)
+
+
+/* ========================================================================== */
+/* === Prototypes of user-callable routines ================================= */
+/* ========================================================================== */
+
+/* define UF_long */
+#include "UFconfig.h"
+
+size_t colamd_recommended /* returns recommended value of Alen, */
+ /* or 0 if input arguments are erroneous */
+(
+ int nnz, /* nonzeros in A */
+ int n_row, /* number of rows in A */
+ int n_col /* number of columns in A */
+) ;
+
+size_t colamd_l_recommended /* returns recommended value of Alen, */
+ /* or 0 if input arguments are erroneous */
+(
+ UF_long nnz, /* nonzeros in A */
+ UF_long n_row, /* number of rows in A */
+ UF_long n_col /* number of columns in A */
+) ;
+
+void colamd_set_defaults /* sets default parameters */
+( /* knobs argument is modified on output */
+ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */
+) ;
+
+void colamd_l_set_defaults /* sets default parameters */
+( /* knobs argument is modified on output */
+ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */
+) ;
+
+int colamd /* returns (1) if successful, (0) otherwise*/
+( /* A and p arguments are modified on output */
+ int n_row, /* number of rows in A */
+ int n_col, /* number of columns in A */
+ int Alen, /* size of the array A */
+ int A [], /* row indices of A, of size Alen */
+ int p [], /* column pointers of A, of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */
+ int stats [COLAMD_STATS] /* colamd output statistics and error codes */
+) ;
+
+UF_long colamd_l /* returns (1) if successful, (0) otherwise*/
+( /* A and p arguments are modified on output */
+ UF_long n_row, /* number of rows in A */
+ UF_long n_col, /* number of columns in A */
+ UF_long Alen, /* size of the array A */
+ UF_long A [], /* row indices of A, of size Alen */
+ UF_long p [], /* column pointers of A, of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */
+ UF_long stats [COLAMD_STATS]/* colamd output statistics and error codes */
+) ;
+
+int symamd /* return (1) if OK, (0) otherwise */
+(
+ int n, /* number of rows and columns of A */
+ int A [], /* row indices of A */
+ int p [], /* column pointers of A */
+ int perm [], /* output permutation, size n_col+1 */
+ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */
+ int stats [COLAMD_STATS], /* output statistics and error codes */
+ void * (*allocate) (size_t, size_t),
+ /* pointer to calloc (ANSI C) or */
+ /* mxCalloc (for MATLAB mexFunction) */
+ void (*release) (void *)
+ /* pointer to free (ANSI C) or */
+ /* mxFree (for MATLAB mexFunction) */
+) ;
+
+UF_long symamd_l /* return (1) if OK, (0) otherwise */
+(
+ UF_long n, /* number of rows and columns of A */
+ UF_long A [], /* row indices of A */
+ UF_long p [], /* column pointers of A */
+ UF_long perm [], /* output permutation, size n_col+1 */
+ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */
+ UF_long stats [COLAMD_STATS], /* output statistics and error codes */
+ void * (*allocate) (size_t, size_t),
+ /* pointer to calloc (ANSI C) or */
+ /* mxCalloc (for MATLAB mexFunction) */
+ void (*release) (void *)
+ /* pointer to free (ANSI C) or */
+ /* mxFree (for MATLAB mexFunction) */
+) ;
+
+void colamd_report
+(
+ int stats [COLAMD_STATS]
+) ;
+
+void colamd_l_report
+(
+ UF_long stats [COLAMD_STATS]
+) ;
+
+void symamd_report
+(
+ int stats [COLAMD_STATS]
+) ;
+
+void symamd_l_report
+(
+ UF_long stats [COLAMD_STATS]
+) ;
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN int (*colamd_printf) (const char *, ...) ;
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* COLAMD_H */
diff --git a/COLAMD/Lib/Makefile b/COLAMD/Lib/Makefile
new file mode 100644
index 0000000..b1571ef
--- /dev/null
+++ b/COLAMD/Lib/Makefile
@@ -0,0 +1,32 @@
+#-------------------------------------------------------------------------------
+# COLAMD Makefile
+#-------------------------------------------------------------------------------
+
+default: libcolamd.a
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../Include -I../../UFconfig
+
+INC = ../Include/colamd.h ../../UFconfig/UFconfig.h
+
+SRC = ../Source/colamd.c ../Source/colamd_global.c
+
+# creates libcolamd.a, a C-callable COLAMD library
+libcolamd.a: $(SRC) $(INC)
+ $(CC) $(CFLAGS) $(I) -c ../Source/colamd_global.c
+ $(CC) $(CFLAGS) $(I) -c ../Source/colamd.c
+ $(CC) $(CFLAGS) $(I) -c ../Source/colamd.c -DDLONG -o colamd_l.o
+ $(AR) libcolamd.a colamd.o colamd_l.o colamd_global.o
+
+ccode: libcolamd.a
+
+library: libcolamd.a
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) libcolamd.a
diff --git a/COLAMD/MATLAB/Contents.m b/COLAMD/MATLAB/Contents.m
new file mode 100644
index 0000000..960fd14
--- /dev/null
+++ b/COLAMD/MATLAB/Contents.m
@@ -0,0 +1,19 @@
+% COLAMD, column approximate minimum degree ordering
+%
+% Primary:
+% colamd2 - Column approximate minimum degree permutation.
+% symamd2 - SYMAMD Symmetric approximate minimum degree permutation.
+%
+% helper and test functions:
+% colamd_demo - demo for colamd, column approx minimum degree ordering algorithm
+% colamd_make - compiles COLAMD2 and SYMAMD2 for MATLAB
+% colamd_make - compiles and installs COLAMD2 and SYMAMD2 for MATLAB
+% colamd_test - test colamd2 and symamd2
+% luflops - compute the flop count for sparse LU factorization
+%
+% Example:
+% p = colamd2 (A)
+%
+
+% Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore
+% Developed in collaboration with J. Gilbert and E. Ng.
diff --git a/COLAMD/MATLAB/Makefile b/COLAMD/MATLAB/Makefile
new file mode 100644
index 0000000..ee9415f
--- /dev/null
+++ b/COLAMD/MATLAB/Makefile
@@ -0,0 +1,35 @@
+# COLAMD Makefile for MATLAB mexFunctions
+
+default: colamd2 symamd2
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../../UFconfig -I../Include
+
+INC = ../Include/colamd.h ../../UFconfig/UFconfig.h
+
+SRC = ../Source/colamd.c ../Source/colamd_global.c
+
+MX = $(MEX) -DDLONG $(I)
+
+# Compiles the MATLAB-callable routines
+mex: colamd2 symamd2
+
+symamd2: symamdmex.c $(INC) $(SRC)
+ $(MX) -output symamd2mex symamdmex.c $(SRC)
+
+colamd2: colamdmex.c $(INC) $(SRC)
+ $(MX) -output colamd2mex colamdmex.c $(SRC)
+
+# Compiles the extensive test code
+test: mex colamdtestmex.c symamdtestmex.c $(INC) $(SRC)
+ $(MX) colamdtestmex.c $(SRC)
+ $(MX) symamdtestmex.c $(SRC)
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) *.mex* *.dll
diff --git a/COLAMD/MATLAB/colamd2.m b/COLAMD/MATLAB/colamd2.m
new file mode 100644
index 0000000..9916cc7
--- /dev/null
+++ b/COLAMD/MATLAB/colamd2.m
@@ -0,0 +1,87 @@
+function [p,stats] = colamd2 (S, knobs)
+%COLAMD2 Column approximate minimum degree permutation.
+% P = COLAMD2(S) returns the column approximate minimum degree permutation
+% vector for the sparse matrix S. For a non-symmetric matrix S, S(:,P)
+% tends to have sparser LU factors than S. The Cholesky factorization of
+% S(:,P)'*S(:,P) also tends to be sparser than that of S'*S. The ordering
+% is followed by a column elimination tree post-ordering.
+%
+% Note that this function is the source code for the built-in MATLAB colamd
+% function. It has been renamed here to colamd2 to avoid a filename clash.
+% colamd and colamd2 are identical.
+%
+% See also COLAMD, AMD, SYMAMD, SYMAMD2.
+%
+% Example:
+% P = colamd2 (S)
+% [P, stats] = colamd2 (S, knobs)
+%
+% knobs is an optional one- to three-element input vector. If S is m-by-n,
+% then rows with more than max(16,knobs(1)*sqrt(n)) entries are ignored.
+% Columns with more than max(16,knobs(2)*sqrt(min(m,n))) entries are
+% removed prior to ordering, and ordered last in the output permutation P.
+% Only completely dense rows or columns are removed if knobs(1) and knobs(2)
+% are < 0, respectively. If knobs(3) is nonzero, stats and knobs are
+% printed. The default is knobs = [10 10 0]. Note that knobs differs from
+% earlier versions of colamd.
+
+% Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore
+% Developed in collaboration with J. Gilbert and E. Ng.
+%
+% Acknowledgements: This work was supported by the National Science
+% Foundation, under grants DMS-9504974 and DMS-9803599.
+
+%-------------------------------------------------------------------------------
+% Perform the colamd ordering:
+%-------------------------------------------------------------------------------
+
+if (nargout <= 1 & nargin == 1) %#ok
+ p = colamd2mex (S) ;
+elseif (nargout <= 1 & nargin == 2) %#ok
+ p = colamd2mex (S, knobs) ;
+elseif (nargout == 2 & nargin == 1) %#ok
+ [p, stats] = colamd2mex (S) ;
+elseif (nargout == 2 & nargin == 2) %#ok
+ [p, stats] = colamd2mex (S, knobs) ;
+else
+ error ('colamd: incorrect number of input and/or output arguments') ;
+end
+
+%-------------------------------------------------------------------------------
+% column elimination tree post-ordering:
+%-------------------------------------------------------------------------------
+
+[ignore, q] = etree (S (:,p), 'col') ;
+p = p (q) ;
+
+% stats is an optional 20-element output vector that provides data about the
+% ordering and the validity of the input matrix S. Ordering statistics are
+% in stats (1:3). stats (1) and stats (2) are the number of dense or empty
+% rows and columns ignored by COLAMD and stats (3) is the number of
+% garbage collections performed on the internal data structure used by
+% COLAMD (roughly of size 2.2*nnz(S) + 4*m + 7*n integers).
+%
+% MATLAB built-in functions are intended to generate valid sparse matrices,
+% with no duplicate entries, with ascending row indices of the nonzeros
+% in each column, with a non-negative number of entries in each column (!)
+% and so on. If a matrix is invalid, then COLAMD may or may not be able
+% to continue. If there are duplicate entries (a row index appears two or
+% more times in the same column) or if the row indices in a column are out
+% of order, then COLAMD can correct these errors by ignoring the duplicate
+% entries and sorting each column of its internal copy of the matrix S (the
+% input matrix S is not repaired, however). If a matrix is invalid in other
+% ways then COLAMD cannot continue, an error message is printed, and no
+% output arguments (P or stats) are returned. COLAMD is thus a simple way
+% to check a sparse matrix to see if it's valid.
+%
+% stats (4:7) provide information if COLAMD was able to continue. The
+% matrix is OK if stats (4) is zero, or 1 if invalid. stats (5) is the
+% rightmost column index that is unsorted or contains duplicate entries,
+% or zero if no such column exists. stats (6) is the last seen duplicate
+% or out-of-order row index in the column index given by stats (5), or zero
+% if no such row index exists. stats (7) is the number of duplicate or
+% out-of-order row indices.
+%
+% stats (8:20) is always zero in the current version of COLAMD (reserved
+% for future use).
+
diff --git a/COLAMD/MATLAB/colamd_demo.m b/COLAMD/MATLAB/colamd_demo.m
new file mode 100644
index 0000000..f2fd442
--- /dev/null
+++ b/COLAMD/MATLAB/colamd_demo.m
@@ -0,0 +1,179 @@
+%COLAMD_DEMO demo for colamd, column approx minimum degree ordering algorithm
+%
+% Example:
+% colamd_demo
+%
+% The following m-files and mexFunctions provide alternative sparse matrix
+% ordering methods for MATLAB. They are typically faster (sometimes much
+% faster) and typically provide better orderings than their MATLAB counterparts:
+%
+% colamd a replacement for colmmd.
+%
+% Typical usage: p = colamd (A) ;
+%
+% symamd a replacement for symmmd. Based on colamd.
+%
+% Typical usage: p = symamd (A) ;
+%
+% For a description of the methods used, see the colamd.c file.
+%
+% http://www.cise.ufl.edu/research/sparse/colamd/
+%
+% See also colamd, symamd
+
+% Minor changes: in MATLAB 7, symmmd and colmmd are flagged as "obsolete".
+% This demo checks if they exist, so it should still work when they are removed.
+
+% Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+%-------------------------------------------------------------------------------
+% Print the introduction, the help info, and compile the mexFunctions
+%-------------------------------------------------------------------------------
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Colamd2/symamd2 demo.') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+help colamd_demo ;
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Colamd help information:') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+help colamd2 ;
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Symamd help information:') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+help symamd2 ;
+
+%-------------------------------------------------------------------------------
+% Solving Ax=b
+%-------------------------------------------------------------------------------
+
+n = 100 ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Solving Ax=b for a small %d-by-%d random matrix:', n, n) ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, '\nNote: Random sparse matrices are AWFUL test cases.\n') ;
+fprintf (1, 'They''re just easy to generate in a demo.\n') ;
+
+% set up the system
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+spparms ('default') ;
+A = sprandn (n, n, 5/n) + speye (n) ;
+b = (1:n)' ;
+
+fprintf (1, '\n\nSolving via lu (PAQ = LU), where Q is from colamd2:\n') ;
+q = colamd2 (A) ;
+I = speye (n) ;
+Q = I (:, q) ;
+[L,U,P] = lu (A*Q) ;
+fl = luflops (L, U) ;
+x = Q * (U \ (L \ (P * b))) ;
+fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ;
+fprintf (1, 'residual: %e\n', norm (A*x-b));
+
+try
+ fprintf (1, '\n\nSolving via lu (PAQ = LU), where Q is from colmmd:\n') ;
+ q = colmmd (A) ;
+ I = speye (n) ;
+ Q = I (:, q) ;
+ [L,U,P] = lu (A*Q) ;
+ fl = luflops (L, U) ;
+ x = Q * (U \ (L \ (P * b))) ;
+ fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ;
+ fprintf (1, 'residual: %e\n', ...
+ norm (A*x-b)) ;
+catch
+ fprintf (1, 'colmmd is obsolete; test skipped\n') ;
+end
+
+fprintf (1, '\n\nSolving via lu (PA = LU), without regard for sparsity:\n') ;
+[L,U,P] = lu (A) ;
+fl = luflops (L, U) ;
+x = U \ (L \ (P * b)) ;
+fprintf (1, '\nFlop count for [L,U,P] = lu (A*Q): %d\n', fl) ;
+fprintf (1, 'residual: %e\n', norm (A*x-b));
+
+%-------------------------------------------------------------------------------
+% Large demo for colamd2
+%-------------------------------------------------------------------------------
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Large demo for colamd2 (symbolic analysis only):') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+spparms ('default') ;
+n = 1000 ;
+fprintf (1, 'Generating a random %d-by-%d sparse matrix.\n', n, n) ;
+A = sprandn (n, n, 5/n) + speye (n) ;
+
+fprintf (1, '\n\nUnordered matrix:\n') ;
+lnz = symbfact (A, 'col') ;
+fprintf (1, 'nz in Cholesky factors of A''A: %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A''A: %d\n', sum (lnz.^2)) ;
+
+tic ;
+p = colamd2 (A) ;
+t = toc ;
+lnz = symbfact (A (:,p), 'col') ;
+fprintf (1, '\n\nColamd run time: %f\n', t) ;
+fprintf (1, 'colamd2 ordering quality: \n') ;
+fprintf (1, 'nz in Cholesky factors of A(:,p)''A(:,p): %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A(:,p)''A(:,p): %d\n', sum (lnz.^2)) ;
+
+try
+ tic ;
+ p = colmmd (A) ;
+ t = toc ;
+ lnz = symbfact (A (:,p), 'col') ;
+ fprintf (1, '\n\nColmmd run time: %f\n', t) ;
+ fprintf (1, 'colmmd ordering quality: \n') ;
+ fprintf (1, 'nz in Cholesky factors of A(:,p)''A(:,p): %d\n', sum (lnz)) ;
+ fprintf (1, 'flop count for Cholesky of A(:,p)''A(:,p): %d\n', ...
+ sum (lnz.^2)) ;
+catch
+ fprintf (1, 'colmmd is obsolete; test skipped\n') ;
+end
+
+%-------------------------------------------------------------------------------
+% Large demo for symamd2
+%-------------------------------------------------------------------------------
+
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+fprintf (1, 'Large demo for symamd2 (symbolic analysis only):') ;
+fprintf (1, '\n-----------------------------------------------------------\n') ;
+
+fprintf (1, 'Generating a random symmetric %d-by-%d sparse matrix.\n', n, n) ;
+A = A+A' ;
+
+fprintf (1, '\n\nUnordered matrix:\n') ;
+lnz = symbfact (A, 'sym') ;
+fprintf (1, 'nz in Cholesky factors of A: %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A: %d\n', sum (lnz.^2)) ;
+
+tic ;
+p = symamd2 (A) ;
+t = toc ;
+lnz = symbfact (A (p,p), 'sym') ;
+fprintf (1, '\n\nSymamd run time: %f\n', t) ;
+fprintf (1, 'symamd2 ordering quality: \n') ;
+fprintf (1, 'nz in Cholesky factors of A(p,p): %d\n', sum (lnz)) ;
+fprintf (1, 'flop count for Cholesky of A(p,p): %d\n', sum (lnz.^2)) ;
+
+try
+ tic ;
+ p = symmmd (A) ;
+ t = toc ;
+ lnz = symbfact (A (p,p), 'sym') ;
+ fprintf (1, '\n\nSymmmd run time: %f\n', t) ;
+ fprintf (1, 'symmmd ordering quality: \n') ;
+ fprintf (1, 'nz in Cholesky factors of A(p,p): %d\n', sum (lnz)) ;
+ fprintf (1, 'flop count for Cholesky of A(p,p): %d\n', sum (lnz.^2)) ;
+catch
+ fprintf (1, 'symmmd is obsolete\n') ;
+end
diff --git a/COLAMD/MATLAB/colamd_install.m b/COLAMD/MATLAB/colamd_install.m
new file mode 100644
index 0000000..7ac0110
--- /dev/null
+++ b/COLAMD/MATLAB/colamd_install.m
@@ -0,0 +1,18 @@
+function colamd_install
+%COLAMD_MAKE to compile and install the colamd2 and symamd2 mexFunction.
+% Your current directory must be COLAMD/MATLAB for this function to work.
+%
+% Example:
+% colamd_install
+%
+% See also colamd2, symamd2.
+
+% Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+colamd_make
+addpath (pwd)
+fprintf ('\nThe following path has been added. You may wish to add it\n') ;
+fprintf ('permanently, using the MATLAB pathtool command.\n') ;
+fprintf ('%s\n\n', pwd) ;
+colamd_demo
diff --git a/COLAMD/MATLAB/colamd_make.m b/COLAMD/MATLAB/colamd_make.m
new file mode 100644
index 0000000..1748f9d
--- /dev/null
+++ b/COLAMD/MATLAB/colamd_make.m
@@ -0,0 +1,29 @@
+function colamd_make
+%COLAMD_MAKE compiles COLAMD2 and SYMAMD2 for MATLAB
+%
+% Example:
+% colamd_make
+%
+% See also colamd, symamd
+
+% Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+details = 0 ; % 1 if details of each command are to be printed
+d = '' ;
+if (~isempty (strfind (computer, '64')))
+ d = '-largeArrayDims' ;
+end
+src = '../Source/colamd.c ../Source/colamd_global.c' ;
+cmd = sprintf ('mex -DDLONG -O %s -I../../UFconfig -I../Include -output ', d) ;
+s = [cmd 'colamd2mex colamdmex.c ' src] ;
+if (details)
+ fprintf ('%s\n', s) ;
+end
+eval (s) ;
+s = [cmd 'symamd2mex symamdmex.c ' src] ;
+if (details)
+ fprintf ('%s\n', s) ;
+end
+eval (s) ;
+fprintf ('COLAMD2 and SYMAMD2 successfully compiled.\n') ;
diff --git a/COLAMD/MATLAB/colamd_test.m b/COLAMD/MATLAB/colamd_test.m
new file mode 100644
index 0000000..8addcb0
--- /dev/null
+++ b/COLAMD/MATLAB/colamd_test.m
@@ -0,0 +1,505 @@
+function colamd_test
+%COLAMD_TEST test colamd2 and symamd2
+% Example:
+% colamd_test
+%
+% COLAMD and SYMAMD testing function. Here we try to give colamd2 and symamd2
+% every possible type of matrix and erroneous input that they may encounter.
+% We want either a valid permutation returned or we want them to fail
+% gracefully.
+%
+% You are prompted as to whether or not the colamd2 and symand routines and
+% the test mexFunctions are to be compiled.
+%
+% See also colamd2, symamd2
+
+% Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore
+% Developed in collaboration with J. Gilbert and E. Ng.
+
+
+help colamd_test
+
+
+ fprintf ('Compiling colamd2, symamd2, and test mexFunctions.\n') ;
+ colamd_make ;
+
+ d = '' ;
+ if (~isempty (strfind (computer, '64')))
+ d = '-largeArrayDims' ;
+ end
+ cmd = sprintf ('mex -DDLONG -O %s -I../../UFconfig -I../Include ', d) ;
+ src = '../Source/colamd.c ../Source/colamd_global.c' ;
+ eval ([cmd 'colamdtestmex.c ' src]) ;
+ eval ([cmd 'symamdtestmex.c ' src]) ;
+ fprintf ('Done compiling.\n') ;
+
+
+fprintf ('\nThe following codes will be tested:\n') ;
+which colamd2
+which symamd2
+which colamd2mex
+which symamd2mex
+which colamdtestmex
+which symamdtestmex
+
+fprintf ('\nStarting the tests. Please be patient.\n') ;
+
+h = waitbar (0, 'COLAMD test') ;
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+A = sprandn (500,500,0.4) ;
+
+p = colamd2 (A, [10 10 1]) ; check_perm (p, A) ;
+p = colamd2 (A, [2 7 1]) ; check_perm (p, A) ;
+p = symamd2 (A, [10 1]) ; check_perm (p, A) ;
+p = symamd2 (A, [7 1]) ; check_perm (p, A) ;
+p = symamd2 (A, [4 1]) ; check_perm (p, A) ;
+
+
+fprintf ('Null matrices') ;
+A = zeros (0,0) ;
+A = sparse (A) ;
+
+[p, stats] = colamd2 (A, [10 10 0]) ; %#ok
+check_perm (p, A) ;
+
+[p, stats] = symamd2 (A, [10 0]) ; %#ok
+check_perm (p, A) ;
+
+A = zeros (0, 100) ;
+A = sparse (A) ;
+[p, stats] = colamd2 (A, [10 10 0]) ; %#ok
+check_perm (p, A) ;
+
+A = zeros (100, 0) ;
+A = sparse (A) ;
+[p, stats] = colamd2 (A, [10 10 0]) ;
+check_perm (p, A) ;
+fprintf (' OK\n') ;
+
+
+fprintf ('Matrices with a few dense row/cols\n') ;
+
+for trial = 1:20
+
+ waitbar (trial/20, h, 'COLAMD: with dense rows/cols') ;
+
+ % random square unsymmetric matrix
+ A = rand_matrix (1000, 1000, 1, 10, 20) ;
+
+ for tol = [0:.1:2 3:20 1e6]
+
+ [p, stats] = colamd2 (A, [tol tol 0]) ; %#ok
+ check_perm (p, A) ;
+
+ B = A + A' ;
+ [p, stats] = symamd2 (B, [tol 0]) ; %#ok
+ check_perm (p, A) ;
+
+ [p, stats] = colamd2 (A, [tol 1 0]) ; %#ok
+ check_perm (p, A) ;
+
+ [p, stats] = colamd2 (A, [1 tol 0]) ; %#ok
+ check_perm (p, A) ;
+ end
+end
+fprintf (' OK\n') ;
+
+fprintf ('General matrices\n') ;
+for trial = 1:400
+
+ waitbar (trial/400, h, 'COLAMD: general') ;
+
+ % matrix of random mtype
+ mtype = irand (3) ;
+ A = rand_matrix (2000, 2000, mtype, 0, 0) ;
+ p = colamd2 (A) ;
+ check_perm (p, A) ;
+ if (mtype == 3)
+ p = symamd2 (A) ;
+ check_perm (p, A) ;
+ end
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('Test error handling with invalid inputs\n') ;
+
+% Check different erroneous input.
+for trial = 1:30
+
+ waitbar (trial/30, h, 'COLAMD: error handling') ;
+
+ A = rand_matrix (1000, 1000, 2, 0, 0) ;
+ [m n] = size (A) ;
+
+ for err = 1:13
+
+ p = Tcolamd (A, [n n 0 0 err]) ;
+ if (p ~= -1) %#ok
+ check_perm (p, A) ;
+ end
+
+ if (err == 1)
+ % check different (valid) input args to colamd2
+ p = Acolamd (A) ;
+
+ p2 = Acolamd (A, [10 10 0 0 0]) ;
+ if (any (p ~= p2))
+ error ('colamd2: mismatch 1!') ;
+ end
+ [p2 stats] = Acolamd (A) ; %#ok
+ if (any (p ~= p2))
+ error ('colamd2: mismatch 2!') ;
+ end
+ [p2 stats] = Acolamd (A, [10 10 0 0 0]) ;
+ if (any (p ~= p2))
+ error ('colamd2: mismatch 3!') ;
+ end
+ end
+
+ B = A'*A ;
+ p = Tsymamd (B, [n 0 err]) ;
+ if (p ~= -1) %#ok
+ check_perm (p, A) ;
+ end
+
+ if (err == 1)
+
+ % check different (valid) input args to symamd2
+ p = Asymamd (B) ;
+ check_perm (p, A) ;
+ p2 = Asymamd (B, [10 0 0]) ;
+ if (any (p ~= p2))
+ error ('symamd2: mismatch 1!') ;
+ end
+ [p2 stats] = Asymamd (B) ; %#ok
+ if (any (p ~= p2))
+ error ('symamd2: mismatch 2!') ;
+ end
+ [p2 stats] = Asymamd (B, [10 0 0]) ; %#ok
+ if (any (p ~= p2))
+ error ('symamd2: mismatch 3!') ;
+ end
+ end
+
+ end
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('Matrices with a few empty columns\n') ;
+
+for trial = 1:400
+
+ % some are square, some are rectangular
+ n = 0 ;
+ while (n < 5)
+ A = rand_matrix (1000, 1000, irand (2), 0, 0) ;
+ [m n] = size (A) ;
+ end
+
+ % Add 5 null columns at random locations.
+ null_col = randperm (n) ;
+ null_col = sort (null_col (1:5)) ;
+ A (:, null_col) = 0 ;
+
+ % Order the matrix and make sure that the null columns are ordered last.
+ [p, stats] = colamd2 (A, [1e6 1e6 0]) ;
+ check_perm (p, A) ;
+
+% if (stats (2) ~= 5)
+% stats (2)
+% error ('colamd2: wrong number of null columns') ;
+% end
+
+ % find all null columns in A
+ null_col = find (sum (spones (A), 1) == 0) ;
+ nnull = length (null_col) ; %#ok
+ if (any (null_col ~= p ((n-4):n)))
+ error ('colamd2: Null cols are not ordered last in natural order') ;
+ end
+
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('Matrices with a few empty rows and columns\n') ;
+
+for trial = 1:400
+
+ waitbar (trial/400, h, 'COLAMD: with empty rows/cols') ;
+
+ % symmetric matrices
+ n = 0 ;
+ while (n < 5)
+ A = rand_matrix (1000, 1000, 3, 0, 0) ;
+ [m n] = size (A) ;
+ end
+
+ % Add 5 null columns and rows at random locations.
+ null_col = randperm (n) ;
+ null_col = sort (null_col (1:5)) ;
+ A (:, null_col) = 0 ;
+ A (null_col, :) = 0 ;
+
+ % Order the matrix and make sure that the null rows/cols are ordered last.
+ [p,stats] = symamd2 (A, [10 0]) ;
+ check_perm (p, A) ;
+
+ % find actual number of null rows and columns
+ Alo = tril (A, -1) ;
+ nnull = length (find (sum (Alo') == 0 & sum (Alo) == 0)) ; %#ok
+
+ if (stats (2) ~= nnull | nnull < 5) %#ok
+ error ('symamd2: wrong number of null columns') ;
+ end
+ if (any (null_col ~= p ((n-4):n)))
+ error ('symamd2: Null cols are not ordered last in natural order') ;
+ end
+
+end
+fprintf (' OK\n') ;
+
+fprintf ('Matrices with a few empty rows\n') ;
+
+% Test matrices with null rows inserted.
+
+for trial = 1:400
+
+ waitbar (trial/400, h, 'COLAMD: with null rows') ;
+
+ m = 0 ;
+ while (m < 5)
+ A = rand_matrix (1000, 1000, 2, 0, 0) ;
+ [m n] = size (A) ; %#ok
+ end
+
+ % Add 5 null rows at random locations.
+ null_row = randperm (m) ;
+ null_row = sort (null_row (1:5)) ;
+ A (null_row, :) = 0 ;
+
+ p = colamd2 (A, [10 10 0]) ;
+ check_perm (p, A) ;
+ if (stats (1) ~= 5)
+ error ('colamd2: wrong number of null rows') ;
+ end
+
+end
+fprintf (' OK\n') ;
+
+
+fprintf ('\ncolamd2 and symamd2: all tests passed\n\n') ;
+close (h) ;
+
+%-------------------------------------------------------------------------------
+
+function [p,stats] = Acolamd (S, knobs)
+% Acolamd: compare colamd2 and Tcolamd results
+
+if (nargin < 3)
+ if (nargout == 1)
+ [p] = colamd2 (S) ;
+ [p1] = Tcolamd (S, [10 10 0 0 0]) ;
+ else
+ [p, stats] = colamd2 (S) ;
+ [p1, stats1] = Tcolamd (S, [10 10 0 0 0]) ; %#ok
+ end
+else
+ if (nargout == 1)
+ [p] = colamd2 (S, knobs (1:3)) ;
+ [p1] = Tcolamd (S, knobs) ;
+ else
+ [p, stats] = colamd2 (S, knobs (1:3)) ;
+ [p1, stats1] = Tcolamd (S, knobs) ; %#ok
+ end
+end
+
+check_perm (p, S) ;
+check_perm (p1, S) ;
+
+if (any (p1 ~= p))
+ error ('Acolamd mismatch!') ;
+end
+
+
+%-------------------------------------------------------------------------------
+
+function [p,stats] = Asymamd (S, knobs)
+% Asymamd: compare symamd2 and Tsymamd results
+
+if (nargin < 3)
+ if (nargout == 1)
+ [p] = symamd2 (S) ;
+ [p1] = Tsymamd (S, [10 0 0]) ;
+ else
+ [p, stats] = symamd2 (S) ;
+ [p1, stats1] = Tsymamd (S, [10 0 0]) ; %#ok
+ end
+else
+ if (nargout == 1)
+ [p] = symamd2 (S, knobs (1:2)) ;
+ [p1] = Tsymamd (S, knobs) ;
+ else
+ [p, stats] = symamd2 (S, knobs (1:2)) ;
+ [p1, stats1] = Tsymamd (S, knobs) ; %#ok
+ end
+end
+
+if (any (p1 ~= p))
+ error ('Asymamd mismatch!') ;
+end
+
+
+%-------------------------------------------------------------------------------
+
+function check_perm (p, A)
+% check_perm: check for a valid permutation vector
+
+if (isempty (A) & isempty (p)) %#ok
+ % empty permutation vectors of empty matrices are OK
+ return
+end
+
+if (isempty (p))
+ error ('bad permutation: cannot be empty') ;
+end
+
+[m n] = size (A) ;
+[pm pn] = size (p) ;
+if (pn == 1)
+ % force p to be a row vector
+ p = p' ;
+ [pm pn] = size (p) ;
+end
+
+if (n ~= pn)
+ error ('bad permutation: wrong size') ;
+end
+
+if (pm ~= 1) ;
+ % p must be a vector
+ error ('bad permutation: not a vector') ;
+else
+ if (any (sort (p) - (1:pn)))
+ error ('bad permutation') ;
+ end
+end
+
+%-------------------------------------------------------------------------------
+
+function i = irand (n)
+% irand: return a random integer between 1 and n
+i = min (n, 1 + floor (rand * n)) ;
+
+%-------------------------------------------------------------------------------
+
+function A = rand_matrix (nmax, mmax, mtype, drows, dcols)
+% rand_matrix: return a random sparse matrix
+%
+% A = rand_matrix (nmax, mmax, mtype, drows, dcols)
+%
+% A binary matrix of random size, at most nmax-by-mmax, with drows dense rows
+% and dcols dense columns.
+%
+% mtype 1: square unsymmetric (mmax is ignored)
+% mtype 2: rectangular
+% mtype 3: symmetric (mmax is ignored)
+
+n = irand (nmax) ;
+if (mtype ~= 2)
+ % square
+ m = n ;
+else
+ m = irand (mmax) ;
+end
+
+A = sprand (m, n, 10 / max (m,n)) ;
+
+if (drows > 0)
+ % add dense rows
+ for k = 1:drows
+ i = irand (m) ;
+ nz = irand (n) ;
+ p = randperm (n) ;
+ p = p (1:nz) ;
+ A (i,p) = 1 ;
+ end
+end
+
+if (dcols > 0)
+ % add dense cols
+ for k = 1:dcols
+ j = irand (n) ;
+ nz = irand (m) ;
+ p = randperm (m) ;
+ p = p (1:nz) ;
+ A (p,j) = 1 ;
+ end
+end
+
+A = spones (A) ;
+
+% ensure that there are no empty columns
+d = find (full (sum (A)) == 0) ; %#ok
+A (m,d) = 1 ; %#ok
+
+% ensure that there are no empty rows
+d = find (full (sum (A,2)) == 0) ; %#ok
+A (d,n) = 1 ; %#ok
+
+if (mtype == 3)
+ % symmetric
+ A = A + A' + speye (n) ;
+end
+
+A = spones (A) ;
+
+%-------------------------------------------------------------------------------
+
+function [p,stats] = Tcolamd (S, knobs)
+% Tcolamd: run colamd2 in a testing mode
+
+if (nargout <= 1 & nargin == 1) %#ok
+ p = colamdtestmex (S) ;
+elseif (nargout <= 1 & nargin == 2) %#ok
+ p = colamdtestmex (S, knobs) ;
+elseif (nargout == 2 & nargin == 1) %#ok
+ [p, stats] = colamdtestmex (S) ;
+elseif (nargout == 2 & nargin == 2) %#ok
+ [p, stats] = colamdtestmex (S, knobs) ;
+else
+ error ('colamd2: incorrect number of input and/or output arguments') ;
+end
+
+if (p (1) ~= -1)
+ [ignore, q] = etree (S (:,p), 'col') ;
+ p = p (q) ;
+ check_perm (p, S) ;
+end
+
+%-------------------------------------------------------------------------------
+
+function [p, stats] = Tsymamd (S, knobs)
+% Tsymamd: run symamd2 in a testing mode
+
+if (nargout <= 1 & nargin == 1) %#ok
+ p = symamdtestmex (S) ;
+elseif (nargout <= 1 & nargin == 2) %#ok
+ p = symamdtestmex (S, knobs) ;
+elseif (nargout == 2 & nargin == 1) %#ok
+ [p, stats] = symamdtestmex (S) ;
+elseif (nargout == 2 & nargin == 2) %#ok
+ [p, stats] = symamdtestmex (S, knobs) ;
+else
+ error ('symamd2: incorrect number of input and/or output arguments') ;
+end
+
+if (p (1) ~= -1)
+ [ignore, q] = etree (S (p,p)) ;
+ p = p (q) ;
+ check_perm (p, S) ;
+end
diff --git a/COLAMD/MATLAB/colamdmex.c b/COLAMD/MATLAB/colamdmex.c
new file mode 100644
index 0000000..93f16d5
--- /dev/null
+++ b/COLAMD/MATLAB/colamdmex.c
@@ -0,0 +1,220 @@
+/* ========================================================================== */
+/* === colamd mexFunction =================================================== */
+/* ========================================================================== */
+
+/* Usage:
+
+ P = colamd2 (A) ;
+ [ P, stats ] = colamd2 (A, knobs) ;
+
+ see colamd.m for a description.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Notice:
+
+ Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved.
+
+ See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+ file) for the License.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the http://www.cise.ufl.edu/research/sparse/colamd/colamdmex.c
+ file. It requires the colamd.c and colamd.h files.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "colamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include <string.h>
+#include "UFconfig.h"
+
+/* ========================================================================== */
+/* === colamd mexFunction =================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nlhs, /* number of left-hand sides */
+ mxArray *plhs [], /* left-hand side matrices */
+ int nrhs, /* number of right--hand sides */
+ const mxArray *prhs [] /* right-hand side matrices */
+)
+{
+ /* === Local variables ================================================== */
+
+ UF_long *A ; /* colamd's copy of the matrix, and workspace */
+ UF_long *p ; /* colamd's copy of the column pointers */
+ UF_long Alen ; /* size of A */
+ UF_long n_col ; /* number of columns of A */
+ UF_long n_row ; /* number of rows of A */
+ UF_long nnz ; /* number of entries in A */
+ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ UF_long i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ UF_long spumoni ; /* verbosity variable */
+ UF_long stats [COLAMD_STATS] ; /* stats for colamd */
+
+ colamd_printf = mexPrintf ; /* COLAMD printf routine */
+
+ /* === Check inputs ===================================================== */
+
+ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2)
+ {
+ mexErrMsgTxt (
+ "colamd: incorrect number of input and/or output arguments") ;
+ }
+
+ /* === Get knobs ======================================================== */
+
+ colamd_l_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ /* check for user-passed knobs */
+ if (nrhs == 2)
+ {
+ in_knobs = mxGetPr (prhs [1]) ;
+ i = mxGetNumberOfElements (prhs [1]) ;
+ if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ;
+ if (i > 1) knobs [COLAMD_DENSE_COL] = in_knobs [1] ;
+ if (i > 2) spumoni = (UF_long) (in_knobs [2] != 0) ;
+ }
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\ncolamd version %d.%d, %s:\n",
+ COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ;
+ if (knobs [COLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(1): %g, rows with > max(16,%g*sqrt(size(A,2)))"
+ " entries removed\n", in_knobs [0], knobs [COLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(1): %g, only completely dense rows removed\n",
+ in_knobs [0]) ;
+ }
+ if (knobs [COLAMD_DENSE_COL] >= 0)
+ {
+ mexPrintf ("knobs(2): %g, cols with > max(16,%g*sqrt(min(size(A)))"
+ " entries removed\n", in_knobs [1], knobs [COLAMD_DENSE_COL]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(2): %g, only completely dense columns removed\n",
+ in_knobs [1]) ;
+ }
+ mexPrintf ("knobs(3): %g, statistics and knobs printed\n",
+ in_knobs [2]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) prhs [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("colamd: input matrix must be 2-dimensional") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ;
+ }
+
+ /* === Allocate workspace for colamd ==================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+
+ /* get column pointer vector so we can find nnz */
+ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ;
+ (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ;
+ nnz = p [n_col] ;
+ Alen = (UF_long) colamd_l_recommended (nnz, n_row, n_col) ;
+ if (Alen == 0)
+ {
+ mexErrMsgTxt ("colamd: problem too large") ;
+ }
+
+ /* === Copy input matrix into workspace ================================= */
+
+ A = (UF_long *) mxCalloc (Alen, sizeof (UF_long)) ;
+ (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ;
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+ /* === Order the columns (destroys A) =================================== */
+
+ if (!colamd_l (n_row, n_col, Alen, A, p, knobs, stats))
+ {
+ colamd_l_report (stats) ;
+ mexErrMsgTxt ("colamd error!") ;
+ }
+ mxFree (A) ;
+
+ /* === Return the permutation vector ==================================== */
+
+ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* colamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = p [i] + 1 ;
+ }
+ mxFree (p) ;
+
+ /* === Return the stats vector ========================================== */
+
+ /* print stats if spumoni is set */
+ if (spumoni)
+ {
+ colamd_l_report (stats) ;
+ }
+
+ if (nlhs == 2)
+ {
+ plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (plhs [1]) ;
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ out_stats [i] = stats [i] ;
+ }
+
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if symamd returns FALSE */
+ out_stats [COLAMD_INFO1] ++ ;
+ out_stats [COLAMD_INFO2] ++ ;
+ }
+}
diff --git a/COLAMD/MATLAB/colamdtestmex.c b/COLAMD/MATLAB/colamdtestmex.c
new file mode 100644
index 0000000..9b90a46
--- /dev/null
+++ b/COLAMD/MATLAB/colamdtestmex.c
@@ -0,0 +1,577 @@
+/* ========================================================================== */
+/* === colamdtest mexFunction =============================================== */
+/* ========================================================================== */
+
+/* COLAMD test function
+
+ This MATLAB mexFunction is for testing only. It is not meant for
+ production use. See colamdmex.c instead.
+
+ Usage:
+
+ [ P, stats ] = colamdtest (A, knobs) ;
+
+ See colamd.m for a description. knobs is required.
+
+ knobs (1) dense row control
+ knobs (2) dense column control
+ knobs (3) spumoni
+ knobs (4) for testing only. Controls the workspace used by
+ colamd.
+
+ knobs (5) for testing only. Controls how the input matrix is
+ jumbled prior to calling colamd, to test its error
+ handling capability.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Notice:
+
+ Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved.
+
+ See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+ file) for the License.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the
+ http://www.cise.ufl.edu/research/sparse/colamd/colamdtestmex.c
+ file. It requires the colamd.c and colamd.h files.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "colamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include <string.h>
+#include "UFconfig.h"
+
+static void dump_matrix
+(
+ UF_long A [ ],
+ UF_long p [ ],
+ UF_long n_row,
+ UF_long n_col,
+ UF_long Alen,
+ UF_long limit
+) ;
+
+/* ========================================================================== */
+/* === colamd mexFunction =================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nlhs, /* number of left-hand sides */
+ mxArray *plhs [], /* left-hand side matrices */
+ int nrhs, /* number of right--hand sides */
+ const mxArray *prhs [] /* right-hand side matrices */
+)
+{
+ /* === Local variables ================================================== */
+
+ UF_long *A ; /* colamd's copy of the matrix, and workspace */
+ UF_long *p ; /* colamd's copy of the column pointers */
+ UF_long Alen ; /* size of A */
+ UF_long n_col ; /* number of columns of A */
+ UF_long n_row ; /* number of rows of A */
+ UF_long nnz ; /* number of entries in A */
+ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ UF_long i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ UF_long spumoni ; /* verbosity variable */
+ UF_long stats2 [COLAMD_STATS] ; /* stats for colamd */
+
+ UF_long *cp, *cp_end, result, col, length ;
+ UF_long *stats ;
+ stats = stats2 ;
+
+ colamd_printf = mexPrintf ; /* COLAMD printf routine */
+
+ /* === Check inputs ===================================================== */
+
+ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2)
+ {
+ mexErrMsgTxt (
+ "colamd: incorrect number of input and/or output arguments") ;
+ }
+
+ if (nrhs != 2)
+ {
+ mexErrMsgTxt ("colamdtest: knobs are required") ;
+ }
+ /* for testing we require all 5 knobs */
+ if (mxGetNumberOfElements (prhs [1]) != 5)
+ {
+ mexErrMsgTxt ("colamd: must have all 5 knobs for testing") ;
+ }
+
+ /* === Get knobs ======================================================== */
+
+ colamd_l_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ /* check for user-passed knobs */
+ if (nrhs == 2)
+ {
+ in_knobs = mxGetPr (prhs [1]) ;
+ i = mxGetNumberOfElements (prhs [1]) ;
+ if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ;
+ if (i > 1) knobs [COLAMD_DENSE_COL] = in_knobs [1] ;
+ if (i > 2) spumoni = (UF_long) in_knobs [2] ;
+ }
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\ncolamd version %d.%d, %s:\n",
+ COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ;
+ if (knobs [COLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(1): %g, rows with > max(16,%g*sqrt(size(A,2)))"
+ " entries removed\n", in_knobs [0], knobs [COLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(1): %g, only completely dense rows removed\n",
+ in_knobs [0]) ;
+ }
+ if (knobs [COLAMD_DENSE_COL] >= 0)
+ {
+ mexPrintf ("knobs(2): %g, cols with > max(16,%g*sqrt(min(size(A)))"
+ " entries removed\n", in_knobs [1], knobs [COLAMD_DENSE_COL]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(2): %g, only completely dense columns removed\n",
+ in_knobs [1]) ;
+ }
+ mexPrintf ("knobs(3): %g, statistics and knobs printed\n",
+ in_knobs [2]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) prhs [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("colamd: input matrix must be 2-dimensional") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ;
+ }
+
+ /* === Allocate workspace for colamd ==================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+
+ /* get column pointer vector so we can find nnz */
+ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ;
+ (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ;
+ nnz = p [n_col] ;
+ Alen = (UF_long) colamd_l_recommended (nnz, n_row, n_col) ;
+ if (Alen == 0)
+ {
+ mexErrMsgTxt ("colamd: problem too large") ;
+ }
+
+
+/* === Modify size of Alen if testing ======================================= */
+
+/*
+ knobs [3] amount of workspace given to colamd.
+ < 0 : TIGHT memory
+ > 0 : MIN + knob [3] - 1
+ == 0 : RECOMMENDED memory
+*/
+
+/* Here only for testing */
+/* size of the Col and Row structures */
+#define COLAMD_C(n_col) (((n_col) + 1) * 24 / sizeof (UF_long))
+#define COLAMD_R(n_row) (((n_row) + 1) * 16 / sizeof (UF_long))
+#ifdef MIN
+#undef MIN
+#endif
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+#define COLAMD_MIN_MEMORY(nnz,n_row,n_col) \
+ (2 * (nnz) + COLAMD_C (n_col) + COLAMD_R (n_row))
+
+ /* get knob [3], if negative */
+ if (in_knobs [3] < 0)
+ {
+ Alen = COLAMD_MIN_MEMORY (nnz, n_row, n_col) + n_col ;
+ }
+ else if (in_knobs [3] > 0)
+ {
+ Alen = COLAMD_MIN_MEMORY (nnz, n_row, n_col) + in_knobs [3] - 1 ;
+ }
+
+ /* otherwise, we use the recommended amount set above */
+
+ /* === Copy input matrix into workspace ================================= */
+
+ A = (UF_long *) mxCalloc (Alen, sizeof (UF_long)) ;
+ (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ;
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+
+/* === Jumble matrix ======================================================== */
+
+/*
+ knobs [4] FOR TESTING ONLY: Specifies how to jumble matrix
+ 0 : No jumbling
+ 1 : Make n_row less than zero
+ 2 : Make first pointer non-zero
+ 3 : Make column pointers not non-decreasing
+ 4 : Make a column pointer greater or equal to Alen
+ 5 : Make row indices not strictly increasing
+ 6 : Make a row index greater or equal to n_row
+ 7 : Set A = NULL
+ 8 : Set p = NULL
+ 9 : Repeat row index
+ 10: make row indices not sorted
+ 11: jumble columns massively (note this changes
+ the pattern of the matrix A.)
+ 12: Set stats = NULL
+ 13: Make n_col less than zero
+*/
+
+ /* jumble appropriately */
+ switch ((UF_long) in_knobs [4])
+ {
+
+ case 0 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: no errors expected\n") ;
+ }
+ result = 1 ; /* no errors */
+ break ;
+
+ case 1 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: nrow out of range\n") ;
+ }
+ result = 0 ; /* nrow out of range */
+ n_row = -1 ;
+ break ;
+
+ case 2 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: p [0] nonzero\n") ;
+ }
+ result = 0 ; /* p [0] must be zero */
+ p [0] = 1 ;
+ break ;
+
+ case 3 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: negative length last column\n") ;
+ }
+ result = (n_col == 0) ; /* p must be monotonically inc. */
+ p [n_col] = p [0] ;
+ break ;
+
+ case 4 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: Alen too small\n") ;
+ }
+ result = 0 ; /* out of memory */
+ p [n_col] = Alen ;
+ break ;
+
+ case 5 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: row index out of range (-1)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ result = 0 ;
+ A [nnz-1] = -1 ;
+ }
+ else
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 6 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: row index out of range (n_row)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf ("Changing A[nnz-1] from %d to %d\n",
+ A [nnz-1], n_row) ;
+ }
+ result = 0 ;
+ A [nnz-1] = n_row ;
+ }
+ else
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 7 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: A not present\n") ;
+ }
+ result = 0 ; /* A not present */
+ A = (UF_long *) NULL ;
+ break ;
+
+ case 8 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: p not present\n") ;
+ }
+ result = 0 ; /* p not present */
+ p = (UF_long *) NULL ;
+ break ;
+
+ case 9 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: duplicate row index\n") ;
+ }
+ result = 1 ; /* duplicate row index */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ A [p [col]] = A [p [col] + 1] ;
+ if (spumoni > 0)
+ {
+ mexPrintf ("Made duplicate row %d in col %d\n",
+ A [p [col] + 1], col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, Alen, col+2) ;
+ }
+ break ;
+
+ case 10 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: unsorted column\n") ;
+ }
+ result = 1 ; /* jumbled columns */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ i = A[p [col]] ;
+ A [p [col]] = A[p [col] + 1] ;
+ A [p [col] + 1] = i ;
+ if (spumoni > 0)
+ {
+ mexPrintf ("Unsorted column %d \n", col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, Alen, col+2) ;
+ }
+ break ;
+
+ case 11 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: massive jumbling\n") ;
+ }
+ result = 1 ; /* massive jumbling, but no errors */
+ srand (1) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ cp = &A [p [i]] ;
+ cp_end = &A [p [i+1]] ;
+ while (cp < cp_end)
+ {
+ *cp++ = rand() % n_row ;
+ }
+ }
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, Alen, n_col) ;
+ }
+ break ;
+
+ case 12 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: stats not present\n") ;
+ }
+ result = 0 ; /* stats not present */
+ stats = (UF_long *) NULL ;
+ break ;
+
+ case 13 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("colamdtest: ncol out of range\n") ;
+ }
+ result = 0 ; /* ncol out of range */
+ n_col = -1 ;
+ break ;
+
+ }
+
+
+ /* === Order the columns (destroys A) =================================== */
+
+ if (!colamd_l (n_row, n_col, Alen, A, p, knobs, stats))
+ {
+
+ /* return p = -1 if colamd failed */
+ plhs [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ out_perm [0] = -1 ;
+ mxFree (p) ;
+ mxFree (A) ;
+
+ if (spumoni > 0 || result)
+ {
+ colamd_l_report (stats) ;
+ }
+
+ if (result)
+ {
+ mexErrMsgTxt ("colamd should have returned TRUE\n") ;
+ }
+
+ return ;
+ /* mexErrMsgTxt ("colamd error!") ; */
+ }
+
+ if (!result)
+ {
+ colamd_l_report (stats) ;
+ mexErrMsgTxt ("colamd should have returned FALSE\n") ;
+ }
+ mxFree (A) ;
+
+ /* === Return the permutation vector ==================================== */
+
+ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* colamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = p [i] + 1 ;
+ }
+ mxFree (p) ;
+
+ /* === Return the stats vector ========================================== */
+
+ /* print stats if spumoni > 0 */
+ if (spumoni > 0)
+ {
+ colamd_l_report (stats) ;
+ }
+
+ if (nlhs == 2)
+ {
+ plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (plhs [1]) ;
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ out_stats [i] = stats [i] ;
+ }
+
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if symamd returns FALSE */
+ out_stats [COLAMD_INFO1] ++ ;
+ out_stats [COLAMD_INFO2] ++ ;
+ }
+}
+
+
+static void dump_matrix
+(
+ UF_long A [ ],
+ UF_long p [ ],
+ UF_long n_row,
+ UF_long n_col,
+ UF_long Alen,
+ UF_long limit
+)
+{
+ UF_long col, k, row ;
+
+ mexPrintf ("dump matrix: nrow %d ncol %d Alen %d\n", n_row, n_col, Alen) ;
+
+ for (col = 0 ; col < MIN (n_col, limit) ; col++)
+ {
+ mexPrintf ("column %d, p[col] %d, p [col+1] %d, length %d\n",
+ col, p [col], p [col+1], p [col+1] - p [col]) ;
+ for (k = p [col] ; k < p [col+1] ; k++)
+ {
+ row = A [k] ;
+ mexPrintf (" %d", row) ;
+ }
+ mexPrintf ("\n") ;
+ }
+}
diff --git a/COLAMD/MATLAB/luflops.m b/COLAMD/MATLAB/luflops.m
new file mode 100644
index 0000000..f3c9e45
--- /dev/null
+++ b/COLAMD/MATLAB/luflops.m
@@ -0,0 +1,34 @@
+function fl = luflops (L, U)
+%LUFLOPS compute the flop count for sparse LU factorization
+%
+% Example:
+% fl = luflops (L,U)
+%
+% Given a sparse LU factorization (L and U), return the flop count required
+% by a conventional LU factorization algorithm to compute it. L and U can
+% be either sparse or full matrices. L must be lower triangular and U must
+% be upper triangular. Do not attempt to use this on the permuted L from
+% [L,U] = lu (A). Instead, use [L,U,P] = lu (A) or [L,U,P,Q] = lu (A).
+%
+% Note that there is a subtle undercount in this estimate. Suppose A is
+% completely dense, but during LU factorization exact cancellation occurs,
+% causing some of the entries in L and U to become identically zero. The
+% flop count returned by this routine is an undercount. There is a simple
+% way to fix this (L = spones (L) + spones (tril (A))), but the fix is partial.
+% It can also occur that some entry in L is a "symbolic" fill-in (zero in
+% A, but a fill-in entry and thus must be computed), but numerically
+% zero. The only way to get a reliable LU factorization would be to do a
+% purely symbolic factorization of A. This cannot be done with
+% symbfact (A, 'col').
+%
+% See NA Digest, Vol 00, #50, Tuesday, Dec. 5, 2000
+%
+% See also symbfact
+
+% Copyright 1998-2007, Timothy A. Davis
+
+
+Lnz = full (sum (spones (L))) - 1 ; % off diagonal nz in cols of L
+Unz = full (sum (spones (U')))' - 1 ; % off diagonal nz in rows of U
+fl = 2*Lnz*Unz + sum (Lnz) ;
+
diff --git a/COLAMD/MATLAB/symamd2.m b/COLAMD/MATLAB/symamd2.m
new file mode 100644
index 0000000..ecae450
--- /dev/null
+++ b/COLAMD/MATLAB/symamd2.m
@@ -0,0 +1,86 @@
+function [p, stats] = symamd2 (S, knobs)
+%SYMAMD Symmetric approximate minimum degree permutation.
+% P = SYMAMD2(S) for a symmetric positive definite matrix S, returns the
+% permutation vector p such that S(p,p) tends to have a sparser Cholesky
+% factor than S. Sometimes SYMAMD works well for symmetric indefinite
+% matrices too. The matrix S is assumed to be symmetric; only the
+% strictly lower triangular part is referenced. S must be square.
+% Note that p = amd(S) is much faster and generates comparable orderings.
+% The ordering is followed by an elimination tree post-ordering.
+%
+% Note that this function is source code for the built-in MATLAB symamd
+% function. It has been renamed here to symamd2 to avoid a filename clash.
+% symamd and symamd2 are identical.
+%
+% See also SYMAMD, AMD, COLAMD, COLAMD2.
+%
+% Example:
+% P = symamd2 (S)
+% [P, stats] = symamd2 (S, knobs)
+%
+% knobs is an optional one- to two-element input vector. If S is n-by-n,
+% then rows and columns with more than max(16,knobs(1)*sqrt(n)) entries are
+% removed prior to ordering, and ordered last in the output permutation P.
+% No rows/columns are removed if knobs(1)<0. If knobs(2) is nonzero, stats
+% and knobs are printed. The default is knobs = [10 0]. Note that knobs
+% differs from earlier versions of symamd.
+
+% Copyright 1998-2007, Timothy A. Davis, and Stefan Larimore
+% Developed in collaboration with J. Gilbert and E. Ng.
+% Acknowledgements: This work was supported by the National Science
+% Foundation, under grants DMS-9504974 and DMS-9803599.
+
+%-------------------------------------------------------------------------------
+% perform the symamd ordering:
+%-------------------------------------------------------------------------------
+
+if (nargout <= 1 & nargin == 1) %#ok
+ p = symamd2mex (S) ;
+elseif (nargout <= 1 & nargin == 2) %#ok
+ p = symamd2mex (S, knobs) ;
+elseif (nargout == 2 & nargin == 1) %#ok
+ [p, stats] = symamd2mex (S) ;
+elseif (nargout == 2 & nargin == 2) %#ok
+ [p, stats] = symamd2mex (S, knobs) ;
+else
+ error('symamd: incorrect number of input and/or output arguments.') ;
+end
+
+%-------------------------------------------------------------------------------
+% symmetric elimination tree post-ordering:
+%-------------------------------------------------------------------------------
+
+[ignore, q] = etree (S (p,p)) ;
+p = p (q) ;
+
+
+% stats is an optional 20-element output vector that provides data about the
+% ordering and the validity of the input matrix S. Ordering statistics are
+% in stats (1:3). stats (1) = stats (2) is the number of dense or empty
+% rows and columns ignored by SYMAMD and stats (3) is the number of
+% garbage collections performed on the internal data structure used by
+% SYMAMD (roughly of size 8.4*nnz(tril(S,-1)) + 9*n integers).
+%
+% MATLAB built-in functions are intended to generate valid sparse matrices,
+% with no duplicate entries, with ascending row indices of the nonzeros
+% in each column, with a non-negative number of entries in each column (!)
+% and so on. If a matrix is invalid, then SYMAMD may or may not be able
+% to continue. If there are duplicate entries (a row index appears two or
+% more times in the same column) or if the row indices in a column are out
+% of order, then SYMAMD can correct these errors by ignoring the duplicate
+% entries and sorting each column of its internal copy of the matrix S (the
+% input matrix S is not repaired, however). If a matrix is invalid in other
+% ways then SYMAMD cannot continue, an error message is printed, and no
+% output arguments (P or stats) are returned. SYMAMD is thus a simple way
+% to check a sparse matrix to see if it's valid.
+%
+% stats (4:7) provide information if SYMAMD was able to continue. The
+% matrix is OK if stats (4) is zero, or 1 if invalid. stats (5) is the
+% rightmost column index that is unsorted or contains duplicate entries,
+% or zero if no such column exists. stats (6) is the last seen duplicate
+% or out-of-order row index in the column index given by stats (5), or zero
+% if no such row index exists. stats (7) is the number of duplicate or
+% out-of-order row indices.
+%
+% stats (8:20) is always zero in the current version of SYMAMD (reserved
+% for future use).
diff --git a/COLAMD/MATLAB/symamdmex.c b/COLAMD/MATLAB/symamdmex.c
new file mode 100644
index 0000000..253366d
--- /dev/null
+++ b/COLAMD/MATLAB/symamdmex.c
@@ -0,0 +1,201 @@
+/* ========================================================================== */
+/* === symamd mexFunction =================================================== */
+/* ========================================================================== */
+
+/* SYMAMD mexFunction
+
+ Usage:
+
+ P = symamd2 (A) ;
+ [ P, stats ] = symamd2 (A, knobs) ;
+
+ See symamd.m for a description.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Notice:
+
+ Copyright (c) 1998-2007, Timothy A. Davis. All Rights Reserved.
+
+ See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+ file) for the License.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the http://www.cise.ufl.edu/research/sparse/colamd/symamdmex.c
+ file. It requires the colamd.c and colamd.h files.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "colamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include "UFconfig.h"
+
+/* ========================================================================== */
+/* === symamd mexFunction =================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nlhs, /* number of left-hand sides */
+ mxArray *plhs [], /* left-hand side matrices */
+ int nrhs, /* number of right--hand sides */
+ const mxArray *prhs [] /* right-hand side matrices */
+)
+{
+ /* === Local variables ================================================== */
+
+ UF_long *perm ; /* column ordering of M and ordering of A */
+ UF_long *A ; /* row indices of input matrix A */
+ UF_long *p ; /* column pointers of input matrix A */
+ UF_long n_col ; /* number of columns of A */
+ UF_long n_row ; /* number of rows of A */
+ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ UF_long i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ UF_long spumoni ; /* verbosity variable */
+ UF_long stats [COLAMD_STATS] ; /* stats for symamd */
+
+ colamd_printf = mexPrintf ; /* COLAMD printf routine */
+
+ /* === Check inputs ===================================================== */
+
+ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2)
+ {
+ mexErrMsgTxt (
+ "symamd: incorrect number of input and/or output arguments.") ;
+ }
+
+ /* === Get knobs ======================================================== */
+
+ colamd_l_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ /* check for user-passed knobs */
+ if (nrhs == 2)
+ {
+ in_knobs = mxGetPr (prhs [1]) ;
+ i = mxGetNumberOfElements (prhs [1]) ;
+ if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ;
+ if (i > 1) spumoni = (UF_long) (in_knobs [1] != 0) ;
+ }
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\nsymamd version %d.%d, %s:\n",
+ COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ;
+ if (knobs [COLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(1): %g, rows/cols with > "
+ "max(16,%g*sqrt(size(A,2))) entries removed\n",
+ in_knobs [0], knobs [COLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(1): %g, no dense rows removed\n", in_knobs [0]) ;
+ }
+ mexPrintf ("knobs(2): %g, statistics and knobs printed\n",
+ in_knobs [1]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) prhs [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("symamd: input matrix must be 2-dimensional.") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ;
+ }
+
+ /* === Allocate workspace for symamd ==================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+ if (n_col != n_row)
+ {
+ mexErrMsgTxt ("symamd: matrix must be square.") ;
+ }
+
+ A = (UF_long *) mxGetIr (Ainput) ;
+ p = (UF_long *) mxGetJc (Ainput) ;
+ perm = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ;
+
+ /* === Order the rows and columns of A (does not destroy A) ============= */
+
+ if (!symamd_l (n_col, A, p, perm, knobs, stats, &mxCalloc, &mxFree))
+ {
+ symamd_l_report (stats) ;
+ mexErrMsgTxt ("symamd error!") ;
+ }
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+ /* === Return the permutation vector ==================================== */
+
+ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* symamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = perm [i] + 1 ;
+ }
+ mxFree (perm) ;
+
+ /* === Return the stats vector ========================================== */
+
+ /* print stats if spumoni is set */
+ if (spumoni)
+ {
+ symamd_l_report (stats) ;
+ }
+
+ if (nlhs == 2)
+ {
+ plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (plhs [1]) ;
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ out_stats [i] = stats [i] ;
+ }
+
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if symamd returns FALSE */
+ out_stats [COLAMD_INFO1] ++ ;
+ out_stats [COLAMD_INFO2] ++ ;
+ }
+}
diff --git a/COLAMD/MATLAB/symamdtestmex.c b/COLAMD/MATLAB/symamdtestmex.c
new file mode 100644
index 0000000..c41101f
--- /dev/null
+++ b/COLAMD/MATLAB/symamdtestmex.c
@@ -0,0 +1,543 @@
+/* ========================================================================== */
+/* === symamdtest mexFunction =============================================== */
+/* ========================================================================== */
+
+/* SYMAMD test function
+
+ This MATLAB mexFunction is for testing only. It is not meant for
+ production use. See symamdmex.c instead.
+
+ Usage:
+
+ [ P, stats ] = symamdtest (A, knobs) ;
+
+ See symamd.m for a description. knobs is required.
+
+ knobs (1) dense row control
+ knobs (2) spumoni
+ knobs (3) for testing only. Controls how the input matrix is
+ jumbled prior to calling symamd, to test its error
+ handling capability.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Notice:
+
+ Copyright (c) 1998-2007, Timothy A. Davis. All Rights Reserved.
+
+ See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+ file) for the License.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the
+ http://www.cise.ufl.edu/research/sparse/colamd/symamdtestmex.c
+ file. It requires the colamd.c and colamd.h files.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "colamd.h"
+#include "mex.h"
+#include "matrix.h"
+#include <stdlib.h>
+#include <string.h>
+#include "UFconfig.h"
+
+static void dump_matrix
+(
+ UF_long A [ ],
+ UF_long p [ ],
+ UF_long n_row,
+ UF_long n_col,
+ UF_long Alen,
+ UF_long limit
+) ;
+
+/* ========================================================================== */
+/* === symamd mexFunction =================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ /* === Parameters ======================================================= */
+
+ int nlhs, /* number of left-hand sides */
+ mxArray *plhs [], /* left-hand side matrices */
+ int nrhs, /* number of right--hand sides */
+ const mxArray *prhs [] /* right-hand side matrices */
+)
+{
+ /* === Local variables ================================================== */
+
+ UF_long *perm ; /* column ordering of M and ordering of A */
+ UF_long *A ; /* row indices of input matrix A */
+ UF_long *p ; /* column pointers of input matrix A */
+ UF_long n_col ; /* number of columns of A */
+ UF_long n_row ; /* number of rows of A */
+ UF_long full ; /* TRUE if input matrix full, FALSE if sparse */
+ double knobs [COLAMD_KNOBS] ; /* colamd user-controllable parameters */
+ double *out_perm ; /* output permutation vector */
+ double *out_stats ; /* output stats vector */
+ double *in_knobs ; /* input knobs vector */
+ UF_long i ; /* loop counter */
+ mxArray *Ainput ; /* input matrix handle */
+ UF_long spumoni ; /* verbosity variable */
+ UF_long stats2 [COLAMD_STATS] ; /* stats for symamd */
+
+ UF_long *cp, *cp_end, result, nnz, col, length ;
+ UF_long *stats ;
+ stats = stats2 ;
+
+ colamd_printf = mexPrintf ; /* COLAMD printf routine */
+
+ /* === Check inputs ===================================================== */
+
+ if (nrhs < 1 || nrhs > 2 || nlhs < 0 || nlhs > 2)
+ {
+ mexErrMsgTxt (
+ "symamd: incorrect number of input and/or output arguments.") ;
+ }
+
+ if (nrhs != 2)
+ {
+ mexErrMsgTxt ("symamdtest: knobs are required") ;
+ }
+ /* for testing we require all 3 knobs */
+ if (mxGetNumberOfElements (prhs [1]) != 3)
+ {
+ mexErrMsgTxt ("symamdtest: must have all 3 knobs for testing") ;
+ }
+
+ /* === Get knobs ======================================================== */
+
+ colamd_l_set_defaults (knobs) ;
+ spumoni = 0 ;
+
+ /* check for user-passed knobs */
+ if (nrhs == 2)
+ {
+ in_knobs = mxGetPr (prhs [1]) ;
+ i = mxGetNumberOfElements (prhs [1]) ;
+ if (i > 0) knobs [COLAMD_DENSE_ROW] = in_knobs [0] ;
+ if (i > 1) spumoni = (UF_long) in_knobs [1] ;
+ }
+
+ /* print knob settings if spumoni is set */
+ if (spumoni)
+ {
+ mexPrintf ("\nsymamd version %d.%d, %s:\n",
+ COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE) ;
+ if (knobs [COLAMD_DENSE_ROW] >= 0)
+ {
+ mexPrintf ("knobs(1): %g, rows/cols with > "
+ "max(16,%g*sqrt(size(A,2))) entries removed\n",
+ in_knobs [0], knobs [COLAMD_DENSE_ROW]) ;
+ }
+ else
+ {
+ mexPrintf ("knobs(1): %g, no dense rows removed\n", in_knobs [0]) ;
+ }
+ mexPrintf ("knobs(2): %g, statistics and knobs printed\n",
+ in_knobs [1]) ;
+ mexPrintf ("Testing %d\n", in_knobs [2]) ;
+ }
+
+ /* === If A is full, convert to a sparse matrix ========================= */
+
+ Ainput = (mxArray *) prhs [0] ;
+ if (mxGetNumberOfDimensions (Ainput) != 2)
+ {
+ mexErrMsgTxt ("symamd: input matrix must be 2-dimensional.") ;
+ }
+ full = !mxIsSparse (Ainput) ;
+ if (full)
+ {
+ mexCallMATLAB (1, &Ainput, 1, (mxArray **) prhs, "sparse") ;
+ }
+
+ /* === Allocate workspace for symamd ==================================== */
+
+ /* get size of matrix */
+ n_row = mxGetM (Ainput) ;
+ n_col = mxGetN (Ainput) ;
+ if (n_col != n_row)
+ {
+ mexErrMsgTxt ("symamd: matrix must be square.") ;
+ }
+
+ /* p = mxGetJc (Ainput) ; */
+ p = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ;
+ (void) memcpy (p, mxGetJc (Ainput), (n_col+1)*sizeof (UF_long)) ;
+
+ nnz = p [n_col] ;
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: nnz %d\n", nnz) ;
+ }
+
+ /* A = mxGetIr (Ainput) ; */
+ A = (UF_long *) mxCalloc (nnz+1, sizeof (UF_long)) ;
+ (void) memcpy (A, mxGetIr (Ainput), nnz*sizeof (UF_long)) ;
+
+ perm = (UF_long *) mxCalloc (n_col+1, sizeof (UF_long)) ;
+
+/* === Jumble matrix ======================================================== */
+
+
+/*
+ knobs [2] FOR TESTING ONLY: Specifies how to jumble matrix
+ 0 : No jumbling
+ 1 : (no errors)
+ 2 : Make first pointer non-zero
+ 3 : Make column pointers not non-decreasing
+ 4 : (no errors)
+ 5 : Make row indices not strictly increasing
+ 6 : Make a row index greater or equal to n_row
+ 7 : Set A = NULL
+ 8 : Set p = NULL
+ 9 : Repeat row index
+ 10: make row indices not sorted
+ 11: jumble columns massively (note this changes
+ the pattern of the matrix A.)
+ 12: Set stats = NULL
+ 13: Make n_col less than zero
+*/
+
+ /* jumble appropriately */
+ switch ((UF_long) in_knobs [2])
+ {
+
+ case 0 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: no errors expected\n") ;
+ }
+ result = 1 ; /* no errors */
+ break ;
+
+ case 1 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: no errors expected (1)\n") ;
+ }
+ result = 1 ;
+ break ;
+
+ case 2 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: p [0] nonzero\n") ;
+ }
+ result = 0 ; /* p [0] must be zero */
+ p [0] = 1 ;
+ break ;
+
+ case 3 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: negative length last column\n") ;
+ }
+ result = (n_col == 0) ; /* p must be monotonically inc. */
+ p [n_col] = p [0] ;
+ break ;
+
+ case 4 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: no errors expected (4)\n") ;
+ }
+ result = 1 ;
+ break ;
+
+ case 5 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: row index out of range (-1)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ result = 0 ;
+ A [nnz-1] = -1 ;
+ }
+ else
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 6 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: row index out of range (ncol)\n") ;
+ }
+ if (nnz > 0) /* row index out of range */
+ {
+ result = 0 ;
+ A [nnz-1] = n_col ;
+ }
+ else
+ {
+ if (spumoni > 0)
+ {
+ mexPrintf ("Note: no row indices to put out of range\n") ;
+ }
+ result = 1 ;
+ }
+ break ;
+
+ case 7 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: A not present\n") ;
+ }
+ result = 0 ; /* A not present */
+ A = (UF_long *) NULL ;
+ break ;
+
+ case 8 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: p not present\n") ;
+ }
+ result = 0 ; /* p not present */
+ p = (UF_long *) NULL ;
+ break ;
+
+ case 9 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: duplicate row index\n") ;
+ }
+ result = 1 ; /* duplicate row index */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ A [p [col+1]-2] = A [p [col+1] - 1] ;
+ if (spumoni > 0)
+ {
+ mexPrintf ("Made duplicate row %d in col %d\n",
+ A [p [col+1] - 1], col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, nnz, col+2) ;
+ }
+ break ;
+
+ case 10 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: unsorted column\n") ;
+ }
+ result = 1 ; /* jumbled columns */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ length = p [col+1] - p [col] ;
+ if (length > 1)
+ {
+ i = A[p [col]] ;
+ A [p [col]] = A[p [col] + 1] ;
+ A [p [col] + 1] = i ;
+ if (spumoni > 0)
+ {
+ mexPrintf ("Unsorted column %d \n", col) ;
+ }
+ break ;
+ }
+ }
+
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, nnz, col+2) ;
+ }
+ break ;
+
+ case 11 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: massive jumbling\n") ;
+ }
+ result = 1 ; /* massive jumbling, but no errors */
+ srand (1) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ cp = &A [p [i]] ;
+ cp_end = &A [p [i+1]] ;
+ while (cp < cp_end)
+ {
+ *cp++ = rand() % n_row ;
+ }
+ }
+ if (spumoni > 1)
+ {
+ dump_matrix (A, p, n_row, n_col, nnz, n_col) ;
+ }
+ break ;
+
+ case 12 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: stats not present\n") ;
+ }
+ result = 0 ; /* stats not present */
+ stats = (UF_long *) NULL ;
+ break ;
+
+ case 13 :
+ if (spumoni > 0)
+ {
+ mexPrintf ("symamdtest: ncol out of range\n") ;
+ }
+ result = 0 ; /* ncol out of range */
+ n_col = -1 ;
+ break ;
+
+ }
+
+ /* === Order the rows and columns of A (does not destroy A) ============= */
+
+ if (!symamd_l (n_col, A, p, perm, knobs, stats, &mxCalloc, &mxFree))
+ {
+
+ /* return p = -1 if colamd failed */
+ plhs [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ out_perm [0] = -1 ;
+ mxFree (p) ;
+ mxFree (A) ;
+
+ if (spumoni > 0 || result)
+ {
+ symamd_l_report (stats) ;
+ }
+
+ if (result)
+ {
+ mexErrMsgTxt ("symamd should have returned TRUE\n") ;
+ }
+
+ return ;
+ /* mexErrMsgTxt ("symamd error!") ; */
+ }
+
+ if (!result)
+ {
+ symamd_l_report (stats) ;
+ mexErrMsgTxt ("symamd should have returned FALSE\n") ;
+ }
+
+ if (full)
+ {
+ mxDestroyArray (Ainput) ;
+ }
+
+ /* === Return the permutation vector ==================================== */
+
+ plhs [0] = mxCreateDoubleMatrix (1, n_col, mxREAL) ;
+ out_perm = mxGetPr (plhs [0]) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* symamd is 0-based, but MATLAB expects this to be 1-based */
+ out_perm [i] = perm [i] + 1 ;
+ }
+ mxFree (perm) ;
+
+ /* === Return the stats vector ========================================== */
+
+ /* print stats if spumoni > 0 */
+ if (spumoni > 0)
+ {
+ symamd_l_report (stats) ;
+ }
+
+ if (nlhs == 2)
+ {
+ plhs [1] = mxCreateDoubleMatrix (1, COLAMD_STATS, mxREAL) ;
+ out_stats = mxGetPr (plhs [1]) ;
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ out_stats [i] = stats [i] ;
+ }
+
+ /* fix stats (5) and (6), for 1-based information on jumbled matrix. */
+ /* note that this correction doesn't occur if symamd returns FALSE */
+ out_stats [COLAMD_INFO1] ++ ;
+ out_stats [COLAMD_INFO2] ++ ;
+ }
+}
+
+
+#ifdef MIN
+#undef MIN
+#endif
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+
+static void dump_matrix
+(
+ UF_long A [ ],
+ UF_long p [ ],
+ UF_long n_row,
+ UF_long n_col,
+ UF_long Alen,
+ UF_long limit
+)
+{
+ UF_long col, k, row ;
+
+ mexPrintf ("dump matrix: nrow %d ncol %d Alen %d\n", n_row, n_col, Alen) ;
+
+ if (!A)
+ {
+ mexPrintf ("A not present\n") ;
+ return ;
+ }
+
+ if (!p)
+ {
+ mexPrintf ("p not present\n") ;
+ return ;
+ }
+
+ for (col = 0 ; col < MIN (n_col, limit) ; col++)
+ {
+ mexPrintf ("column %d, p[col] %d, p [col+1] %d, length %d\n",
+ col, p [col], p [col+1], p [col+1] - p [col]) ;
+ for (k = p [col] ; k < p [col+1] ; k++)
+ {
+ row = A [k] ;
+ mexPrintf (" %d", row) ;
+ }
+ mexPrintf ("\n") ;
+ }
+}
diff --git a/COLAMD/Makefile b/COLAMD/Makefile
new file mode 100644
index 0000000..fd1397b
--- /dev/null
+++ b/COLAMD/Makefile
@@ -0,0 +1,49 @@
+#------------------------------------------------------------------------------
+# COLAMD Makefile
+#------------------------------------------------------------------------------
+
+default: demo
+
+include ../UFconfig/UFconfig.mk
+
+# Compile all C code, including the C-callable routine and the mexFunctions.
+# Do not the MATLAB interface.
+demo:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+# Compile all C code, including the C-callable routine and the mexFunctions.
+all:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+ ( cd MATLAB ; $(MAKE) )
+
+# compile just the C-callable libraries (not mexFunctions or Demos)
+library:
+ ( cd Lib ; $(MAKE) )
+
+# remove object files, but keep the compiled programs and library archives
+clean:
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+ ( cd MATLAB ; $(MAKE) clean )
+
+# clean, and then remove compiled programs and library archives
+purge:
+ ( cd Lib ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd MATLAB ; $(MAKE) purge )
+
+distclean: purge
+
+# get ready for distribution
+dist: purge
+ ( cd Demo ; $(MAKE) dist )
+
+ccode: library
+
+lib: library
+
+# compile the MATLAB mexFunction
+mex:
+ ( cd MATLAB ; $(MAKE) )
diff --git a/COLAMD/README.txt b/COLAMD/README.txt
new file mode 100644
index 0000000..5ed81c7
--- /dev/null
+++ b/COLAMD/README.txt
@@ -0,0 +1,127 @@
+The COLAMD ordering method - Version 2.7
+-------------------------------------------------------------------------------
+
+The COLAMD column approximate minimum degree ordering algorithm computes
+a permutation vector P such that the LU factorization of A (:,P)
+tends to be sparser than that of A. The Cholesky factorization of
+(A (:,P))'*(A (:,P)) will also tend to be sparser than that of A'*A.
+SYMAMD is a symmetric minimum degree ordering method based on COLAMD,
+available as a MATLAB-callable function. It constructs a matrix M such
+that M'*M has the same pattern as A, and then uses COLAMD to compute a column
+ordering of M. Colamd and symamd tend to be faster and generate better
+orderings than their MATLAB counterparts, colmmd and symmmd.
+
+To compile and test the colamd m-files and mexFunctions, just unpack the
+COLAMD/ directory from the COLAMD.tar.gz file, and run MATLAB from
+within that directory. Next, type colamd_test to compile and test colamd
+and symamd. This will work on any computer with MATLAB (Unix, PC, or Mac).
+Alternatively, type "make" (in Unix) to compile and run a simple example C
+code, without using MATLAB.
+
+To compile and install the colamd m-files and mexFunctions, just cd to
+COLAMD/MATLAB and type colamd_install in the MATLAB command window.
+A short demo will run. Optionally, type colamd_test to run an extensive tests.
+Type "make" in Unix in the COLAMD directory to compile the C-callable
+library and to run a short demo.
+
+If you have MATLAB 7.2 or earlier, you must first edit UFconfig/UFconfig.h to
+remove the "-largeArrayDims" option from the MEX command (or just use
+colamd_make.m inside MATLAB).
+
+Colamd is a built-in routine in MATLAB, available from The
+Mathworks, Inc. Under most cases, the compiled COLAMD from Versions 2.0 to the
+current version do not differ. Colamd Versions 2.2 and 2.3 differ only in their
+mexFunction interaces to MATLAB. v2.4 fixes a bug in the symamd routine in
+v2.3. The bug (in v2.3 and earlier) has no effect on the MATLAB symamd
+mexFunction. v2.5 adds additional checks for integer overflow, so that
+the "int" version can be safely used with 64-bit pointers. Refer to the
+ChangeLog for more details.
+
+To use colamd and symamd within an application written in C, all you need are
+colamd.c, colamd_global.c, and colamd.h, which are the C-callable
+colamd/symamd codes. See colamd.c for more information on how to call
+colamd from a C program.
+
+Requires UFconfig, in the ../UFconfig directory relative to this directory.
+
+ Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved.
+
+ See http://www.cise.ufl.edu/research/sparse/colamd (the colamd.c
+ file) for the License.
+
+
+Related papers:
+
+ T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate column
+ minimum degree ordering algorithm, ACM Transactions on Mathematical
+ Software, vol. 30, no. 3., pp. 353-376, 2004.
+
+ T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD,
+ an approximate column minimum degree ordering algorithm, ACM
+ Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380,
+ 2004.
+
+ "An approximate minimum degree column ordering algorithm",
+ S. I. Larimore, MS Thesis, Dept. of Computer and Information
+ Science and Engineering, University of Florida, Gainesville, FL,
+ 1998. CISE Tech Report TR-98-016. Available at
+ ftp://ftp.cise.ufl.edu/cis/tech-reports/tr98/tr98-016.ps
+ via anonymous ftp.
+
+ Approximate Deficiency for Ordering the Columns of a Matrix,
+ J. L. Kern, Senior Thesis, Dept. of Computer and Information
+ Science and Engineering, University of Florida, Gainesville, FL,
+ 1999. Available at http://www.cise.ufl.edu/~davis/Kern/kern.ps
+
+
+Authors: Stefan I. Larimore and Timothy A. Davis, University of Florida,
+in collaboration with John Gilbert, Xerox PARC (now at UC Santa Barbara),
+and Esmong Ng, Lawrence Berkeley National Laboratory (much of this work
+he did while at Oak Ridge National Laboratory).
+
+COLAMD files:
+
+ Demo simple demo
+ Doc additional documentation (see colamd.c for more)
+ Include include file
+ Lib compiled C-callable library
+ Makefile primary Unix Makefile
+ MATLAB MATLAB functions
+ README.txt this file
+ Source C source code
+
+ ./Demo:
+ colamd_example.c simple example
+ colamd_example.out output of colamd_example.c
+ colamd_l_example.c simple example, long integers
+ colamd_l_example.out output of colamd_l_example.c
+ Makefile Makefile for C demos
+
+ ./Doc:
+ ChangeLog change log
+ lesser.txt license
+
+ ./Include:
+ colamd.h include file
+
+ ./Lib:
+ Makefile Makefile for C-callable library
+
+ ./MATLAB:
+ colamd2.m MATLAB interface for colamd2
+ colamd_demo.m simple demo
+ colamd_install.m compile and install colamd2 and symamd2
+ colamd_make.m compile colamd2 and symamd2
+ colamdmex.ca MATLAB mexFunction for colamd2
+ colamd_test.m extensive test
+ colamdtestmex.c test function for colamd
+ Contents.m contents of the MATLAB directory
+ luflops.m test code
+ Makefile Makefile for MATLAB functions
+ symamd2.m MATLAB interface for symamd2
+ symamdmex.c MATLAB mexFunction for symamd2
+ symamdtestmex.c test function for symamd
+
+ ./Source:
+ colamd.c primary source code
+ colamd_global.c globally defined function pointers (malloc, free, ...)
diff --git a/COLAMD/Source/colamd.c b/COLAMD/Source/colamd.c
new file mode 100644
index 0000000..5fe20d6
--- /dev/null
+++ b/COLAMD/Source/colamd.c
@@ -0,0 +1,3611 @@
+/* ========================================================================== */
+/* === colamd/symamd - a sparse matrix column ordering algorithm ============ */
+/* ========================================================================== */
+
+/* COLAMD / SYMAMD
+
+ colamd: an approximate minimum degree column ordering algorithm,
+ for LU factorization of symmetric or unsymmetric matrices,
+ QR factorization, least squares, interior point methods for
+ linear programming problems, and other related problems.
+
+ symamd: an approximate minimum degree ordering algorithm for Cholesky
+ factorization of symmetric matrices.
+
+ Purpose:
+
+ Colamd computes a permutation Q such that the Cholesky factorization of
+ (AQ)'(AQ) has less fill-in and requires fewer floating point operations
+ than A'A. This also provides a good ordering for sparse partial
+ pivoting methods, P(AQ) = LU, where Q is computed prior to numerical
+ factorization, and P is computed during numerical factorization via
+ conventional partial pivoting with row interchanges. Colamd is the
+ column ordering method used in SuperLU, part of the ScaLAPACK library.
+ It is also available as built-in function in MATLAB Version 6,
+ available from MathWorks, Inc. (http://www.mathworks.com). This
+ routine can be used in place of colmmd in MATLAB.
+
+ Symamd computes a permutation P of a symmetric matrix A such that the
+ Cholesky factorization of PAP' has less fill-in and requires fewer
+ floating point operations than A. Symamd constructs a matrix M such
+ that M'M has the same nonzero pattern of A, and then orders the columns
+ of M using colmmd. The column ordering of M is then returned as the
+ row and column ordering P of A.
+
+ Authors:
+
+ The authors of the code itself are Stefan I. Larimore and Timothy A.
+ Davis (davis at cise.ufl.edu), University of Florida. The algorithm was
+ developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+ Ng, Oak Ridge National Laboratory.
+
+ Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974 and DMS-9803599.
+
+ Copyright and License:
+
+ Copyright (c) 1998-2007, Timothy A. Davis, All Rights Reserved.
+ COLAMD is also available under alternate licenses, contact T. Davis
+ for details.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+ Availability:
+
+ The colamd/symamd library is available at
+
+ http://www.cise.ufl.edu/research/sparse/colamd/
+
+ This is the http://www.cise.ufl.edu/research/sparse/colamd/colamd.c
+ file. It requires the colamd.h file. It is required by the colamdmex.c
+ and symamdmex.c files, for the MATLAB interface to colamd and symamd.
+ Appears as ACM Algorithm 836.
+
+ See the ChangeLog file for changes since Version 1.0.
+
+ References:
+
+ T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate column
+ minimum degree ordering algorithm, ACM Transactions on Mathematical
+ Software, vol. 30, no. 3., pp. 353-376, 2004.
+
+ T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836: COLAMD,
+ an approximate column minimum degree ordering algorithm, ACM
+ Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380,
+ 2004.
+
+*/
+
+/* ========================================================================== */
+/* === Description of user-callable routines ================================ */
+/* ========================================================================== */
+
+/* COLAMD includes both int and UF_long versions of all its routines. The
+ * description below is for the int version. For UF_long, all int arguments
+ * become UF_long. UF_long is normally defined as long, except for WIN64.
+
+ ----------------------------------------------------------------------------
+ colamd_recommended:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ size_t colamd_recommended (int nnz, int n_row, int n_col) ;
+ size_t colamd_l_recommended (UF_long nnz, UF_long n_row,
+ UF_long n_col) ;
+
+ Purpose:
+
+ Returns recommended value of Alen for use by colamd. Returns 0
+ if any input argument is negative. The use of this routine
+ is optional. Not needed for symamd, which dynamically allocates
+ its own memory.
+
+ Note that in v2.4 and earlier, these routines returned int or long.
+ They now return a value of type size_t.
+
+ Arguments (all input arguments):
+
+ int nnz ; Number of nonzeros in the matrix A. This must
+ be the same value as p [n_col] in the call to
+ colamd - otherwise you will get a wrong value
+ of the recommended memory to use.
+
+ int n_row ; Number of rows in the matrix A.
+
+ int n_col ; Number of columns in the matrix A.
+
+ ----------------------------------------------------------------------------
+ colamd_set_defaults:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ colamd_set_defaults (double knobs [COLAMD_KNOBS]) ;
+ colamd_l_set_defaults (double knobs [COLAMD_KNOBS]) ;
+
+ Purpose:
+
+ Sets the default parameters. The use of this routine is optional.
+
+ Arguments:
+
+ double knobs [COLAMD_KNOBS] ; Output only.
+
+ NOTE: the meaning of the dense row/col knobs has changed in v2.4
+
+ knobs [0] and knobs [1] control dense row and col detection:
+
+ Colamd: rows with more than
+ max (16, knobs [COLAMD_DENSE_ROW] * sqrt (n_col))
+ entries are removed prior to ordering. Columns with more than
+ max (16, knobs [COLAMD_DENSE_COL] * sqrt (MIN (n_row,n_col)))
+ entries are removed prior to
+ ordering, and placed last in the output column ordering.
+
+ Symamd: uses only knobs [COLAMD_DENSE_ROW], which is knobs [0].
+ Rows and columns with more than
+ max (16, knobs [COLAMD_DENSE_ROW] * sqrt (n))
+ entries are removed prior to ordering, and placed last in the
+ output ordering.
+
+ COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1,
+ respectively, in colamd.h. Default values of these two knobs
+ are both 10. Currently, only knobs [0] and knobs [1] are
+ used, but future versions may use more knobs. If so, they will
+ be properly set to their defaults by the future version of
+ colamd_set_defaults, so that the code that calls colamd will
+ not need to change, assuming that you either use
+ colamd_set_defaults, or pass a (double *) NULL pointer as the
+ knobs array to colamd or symamd.
+
+ knobs [2]: aggressive absorption
+
+ knobs [COLAMD_AGGRESSIVE] controls whether or not to do
+ aggressive absorption during the ordering. Default is TRUE.
+
+
+ ----------------------------------------------------------------------------
+ colamd:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ int colamd (int n_row, int n_col, int Alen, int *A, int *p,
+ double knobs [COLAMD_KNOBS], int stats [COLAMD_STATS]) ;
+ UF_long colamd_l (UF_long n_row, UF_long n_col, UF_long Alen,
+ UF_long *A, UF_long *p, double knobs [COLAMD_KNOBS],
+ UF_long stats [COLAMD_STATS]) ;
+
+ Purpose:
+
+ Computes a column ordering (Q) of A such that P(AQ)=LU or
+ (AQ)'AQ=LL' have less fill-in and require fewer floating point
+ operations than factorizing the unpermuted matrix A or A'A,
+ respectively.
+
+ Returns:
+
+ TRUE (1) if successful, FALSE (0) otherwise.
+
+ Arguments:
+
+ int n_row ; Input argument.
+
+ Number of rows in the matrix A.
+ Restriction: n_row >= 0.
+ Colamd returns FALSE if n_row is negative.
+
+ int n_col ; Input argument.
+
+ Number of columns in the matrix A.
+ Restriction: n_col >= 0.
+ Colamd returns FALSE if n_col is negative.
+
+ int Alen ; Input argument.
+
+ Restriction (see note):
+ Alen >= 2*nnz + 6*(n_col+1) + 4*(n_row+1) + n_col
+ Colamd returns FALSE if these conditions are not met.
+
+ Note: this restriction makes an modest assumption regarding
+ the size of the two typedef's structures in colamd.h.
+ We do, however, guarantee that
+
+ Alen >= colamd_recommended (nnz, n_row, n_col)
+
+ will be sufficient. Note: the macro version does not check
+ for integer overflow, and thus is not recommended. Use
+ the colamd_recommended routine instead.
+
+ int A [Alen] ; Input argument, undefined on output.
+
+ A is an integer array of size Alen. Alen must be at least as
+ large as the bare minimum value given above, but this is very
+ low, and can result in excessive run time. For best
+ performance, we recommend that Alen be greater than or equal to
+ colamd_recommended (nnz, n_row, n_col), which adds
+ nnz/5 to the bare minimum value given above.
+
+ On input, the row indices of the entries in column c of the
+ matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices
+ in a given column c need not be in ascending order, and
+ duplicate row indices may be be present. However, colamd will
+ work a little faster if both of these conditions are met
+ (Colamd puts the matrix into this format, if it finds that the
+ the conditions are not met).
+
+ The matrix is 0-based. That is, rows are in the range 0 to
+ n_row-1, and columns are in the range 0 to n_col-1. Colamd
+ returns FALSE if any row index is out of range.
+
+ The contents of A are modified during ordering, and are
+ undefined on output.
+
+ int p [n_col+1] ; Both input and output argument.
+
+ p is an integer array of size n_col+1. On input, it holds the
+ "pointers" for the column form of the matrix A. Column c of
+ the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first
+ entry, p [0], must be zero, and p [c] <= p [c+1] must hold
+ for all c in the range 0 to n_col-1. The value p [n_col] is
+ thus the total number of entries in the pattern of the matrix A.
+ Colamd returns FALSE if these conditions are not met.
+
+ On output, if colamd returns TRUE, the array p holds the column
+ permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is
+ the first column index in the new ordering, and p [n_col-1] is
+ the last. That is, p [k] = j means that column j of A is the
+ kth pivot column, in AQ, where k is in the range 0 to n_col-1
+ (p [0] = j means that column j of A is the first column in AQ).
+
+ If colamd returns FALSE, then no permutation is returned, and
+ p is undefined on output.
+
+ double knobs [COLAMD_KNOBS] ; Input argument.
+
+ See colamd_set_defaults for a description.
+
+ int stats [COLAMD_STATS] ; Output argument.
+
+ Statistics on the ordering, and error status.
+ See colamd.h for related definitions.
+ Colamd returns FALSE if stats is not present.
+
+ stats [0]: number of dense or empty rows ignored.
+
+ stats [1]: number of dense or empty columns ignored (and
+ ordered last in the output permutation p)
+ Note that a row can become "empty" if it
+ contains only "dense" and/or "empty" columns,
+ and similarly a column can become "empty" if it
+ only contains "dense" and/or "empty" rows.
+
+ stats [2]: number of garbage collections performed.
+ This can be excessively high if Alen is close
+ to the minimum required value.
+
+ stats [3]: status code. < 0 is an error code.
+ > 1 is a warning or notice.
+
+ 0 OK. Each column of the input matrix contained
+ row indices in increasing order, with no
+ duplicates.
+
+ 1 OK, but columns of input matrix were jumbled
+ (unsorted columns or duplicate entries). Colamd
+ had to do some extra work to sort the matrix
+ first and remove duplicate entries, but it
+ still was able to return a valid permutation
+ (return value of colamd was TRUE).
+
+ stats [4]: highest numbered column that
+ is unsorted or has duplicate
+ entries.
+ stats [5]: last seen duplicate or
+ unsorted row index.
+ stats [6]: number of duplicate or
+ unsorted row indices.
+
+ -1 A is a null pointer
+
+ -2 p is a null pointer
+
+ -3 n_row is negative
+
+ stats [4]: n_row
+
+ -4 n_col is negative
+
+ stats [4]: n_col
+
+ -5 number of nonzeros in matrix is negative
+
+ stats [4]: number of nonzeros, p [n_col]
+
+ -6 p [0] is nonzero
+
+ stats [4]: p [0]
+
+ -7 A is too small
+
+ stats [4]: required size
+ stats [5]: actual size (Alen)
+
+ -8 a column has a negative number of entries
+
+ stats [4]: column with < 0 entries
+ stats [5]: number of entries in col
+
+ -9 a row index is out of bounds
+
+ stats [4]: column with bad row index
+ stats [5]: bad row index
+ stats [6]: n_row, # of rows of matrx
+
+ -10 (unused; see symamd.c)
+
+ -999 (unused; see symamd.c)
+
+ Future versions may return more statistics in the stats array.
+
+ Example:
+
+ See http://www.cise.ufl.edu/research/sparse/colamd/example.c
+ for a complete example.
+
+ To order the columns of a 5-by-4 matrix with 11 nonzero entries in
+ the following nonzero pattern
+
+ x 0 x 0
+ x 0 x x
+ 0 x x 0
+ 0 0 x x
+ x x 0 0
+
+ with default knobs and no output statistics, do the following:
+
+ #include "colamd.h"
+ #define ALEN 100
+ int A [ALEN] = {0, 1, 4, 2, 4, 0, 1, 2, 3, 1, 3} ;
+ int p [ ] = {0, 3, 5, 9, 11} ;
+ int stats [COLAMD_STATS] ;
+ colamd (5, 4, ALEN, A, p, (double *) NULL, stats) ;
+
+ The permutation is returned in the array p, and A is destroyed.
+
+ ----------------------------------------------------------------------------
+ symamd:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ int symamd (int n, int *A, int *p, int *perm,
+ double knobs [COLAMD_KNOBS], int stats [COLAMD_STATS],
+ void (*allocate) (size_t, size_t), void (*release) (void *)) ;
+ UF_long symamd_l (UF_long n, UF_long *A, UF_long *p, UF_long *perm,
+ double knobs [COLAMD_KNOBS], UF_long stats [COLAMD_STATS],
+ void (*allocate) (size_t, size_t), void (*release) (void *)) ;
+
+ Purpose:
+
+ The symamd routine computes an ordering P of a symmetric sparse
+ matrix A such that the Cholesky factorization PAP' = LL' remains
+ sparse. It is based on a column ordering of a matrix M constructed
+ so that the nonzero pattern of M'M is the same as A. The matrix A
+ is assumed to be symmetric; only the strictly lower triangular part
+ is accessed. You must pass your selected memory allocator (usually
+ calloc/free or mxCalloc/mxFree) to symamd, for it to allocate
+ memory for the temporary matrix M.
+
+ Returns:
+
+ TRUE (1) if successful, FALSE (0) otherwise.
+
+ Arguments:
+
+ int n ; Input argument.
+
+ Number of rows and columns in the symmetrix matrix A.
+ Restriction: n >= 0.
+ Symamd returns FALSE if n is negative.
+
+ int A [nnz] ; Input argument.
+
+ A is an integer array of size nnz, where nnz = p [n].
+
+ The row indices of the entries in column c of the matrix are
+ held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a
+ given column c need not be in ascending order, and duplicate
+ row indices may be present. However, symamd will run faster
+ if the columns are in sorted order with no duplicate entries.
+
+ The matrix is 0-based. That is, rows are in the range 0 to
+ n-1, and columns are in the range 0 to n-1. Symamd
+ returns FALSE if any row index is out of range.
+
+ The contents of A are not modified.
+
+ int p [n+1] ; Input argument.
+
+ p is an integer array of size n+1. On input, it holds the
+ "pointers" for the column form of the matrix A. Column c of
+ the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first
+ entry, p [0], must be zero, and p [c] <= p [c+1] must hold
+ for all c in the range 0 to n-1. The value p [n] is
+ thus the total number of entries in the pattern of the matrix A.
+ Symamd returns FALSE if these conditions are not met.
+
+ The contents of p are not modified.
+
+ int perm [n+1] ; Output argument.
+
+ On output, if symamd returns TRUE, the array perm holds the
+ permutation P, where perm [0] is the first index in the new
+ ordering, and perm [n-1] is the last. That is, perm [k] = j
+ means that row and column j of A is the kth column in PAP',
+ where k is in the range 0 to n-1 (perm [0] = j means
+ that row and column j of A are the first row and column in
+ PAP'). The array is used as a workspace during the ordering,
+ which is why it must be of length n+1, not just n.
+
+ double knobs [COLAMD_KNOBS] ; Input argument.
+
+ See colamd_set_defaults for a description.
+
+ int stats [COLAMD_STATS] ; Output argument.
+
+ Statistics on the ordering, and error status.
+ See colamd.h for related definitions.
+ Symamd returns FALSE if stats is not present.
+
+ stats [0]: number of dense or empty row and columns ignored
+ (and ordered last in the output permutation
+ perm). Note that a row/column can become
+ "empty" if it contains only "dense" and/or
+ "empty" columns/rows.
+
+ stats [1]: (same as stats [0])
+
+ stats [2]: number of garbage collections performed.
+
+ stats [3]: status code. < 0 is an error code.
+ > 1 is a warning or notice.
+
+ 0 OK. Each column of the input matrix contained
+ row indices in increasing order, with no
+ duplicates.
+
+ 1 OK, but columns of input matrix were jumbled
+ (unsorted columns or duplicate entries). Symamd
+ had to do some extra work to sort the matrix
+ first and remove duplicate entries, but it
+ still was able to return a valid permutation
+ (return value of symamd was TRUE).
+
+ stats [4]: highest numbered column that
+ is unsorted or has duplicate
+ entries.
+ stats [5]: last seen duplicate or
+ unsorted row index.
+ stats [6]: number of duplicate or
+ unsorted row indices.
+
+ -1 A is a null pointer
+
+ -2 p is a null pointer
+
+ -3 (unused, see colamd.c)
+
+ -4 n is negative
+
+ stats [4]: n
+
+ -5 number of nonzeros in matrix is negative
+
+ stats [4]: # of nonzeros (p [n]).
+
+ -6 p [0] is nonzero
+
+ stats [4]: p [0]
+
+ -7 (unused)
+
+ -8 a column has a negative number of entries
+
+ stats [4]: column with < 0 entries
+ stats [5]: number of entries in col
+
+ -9 a row index is out of bounds
+
+ stats [4]: column with bad row index
+ stats [5]: bad row index
+ stats [6]: n_row, # of rows of matrx
+
+ -10 out of memory (unable to allocate temporary
+ workspace for M or count arrays using the
+ "allocate" routine passed into symamd).
+
+ Future versions may return more statistics in the stats array.
+
+ void * (*allocate) (size_t, size_t)
+
+ A pointer to a function providing memory allocation. The
+ allocated memory must be returned initialized to zero. For a
+ C application, this argument should normally be a pointer to
+ calloc. For a MATLAB mexFunction, the routine mxCalloc is
+ passed instead.
+
+ void (*release) (size_t, size_t)
+
+ A pointer to a function that frees memory allocated by the
+ memory allocation routine above. For a C application, this
+ argument should normally be a pointer to free. For a MATLAB
+ mexFunction, the routine mxFree is passed instead.
+
+
+ ----------------------------------------------------------------------------
+ colamd_report:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ colamd_report (int stats [COLAMD_STATS]) ;
+ colamd_l_report (UF_long stats [COLAMD_STATS]) ;
+
+ Purpose:
+
+ Prints the error status and statistics recorded in the stats
+ array on the standard error output (for a standard C routine)
+ or on the MATLAB output (for a mexFunction).
+
+ Arguments:
+
+ int stats [COLAMD_STATS] ; Input only. Statistics from colamd.
+
+
+ ----------------------------------------------------------------------------
+ symamd_report:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ symamd_report (int stats [COLAMD_STATS]) ;
+ symamd_l_report (UF_long stats [COLAMD_STATS]) ;
+
+ Purpose:
+
+ Prints the error status and statistics recorded in the stats
+ array on the standard error output (for a standard C routine)
+ or on the MATLAB output (for a mexFunction).
+
+ Arguments:
+
+ int stats [COLAMD_STATS] ; Input only. Statistics from symamd.
+
+
+*/
+
+/* ========================================================================== */
+/* === Scaffolding code definitions ======================================== */
+/* ========================================================================== */
+
+/* Ensure that debugging is turned off: */
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+
+/* turn on debugging by uncommenting the following line
+ #undef NDEBUG
+*/
+
+/*
+ Our "scaffolding code" philosophy: In our opinion, well-written library
+ code should keep its "debugging" code, and just normally have it turned off
+ by the compiler so as not to interfere with performance. This serves
+ several purposes:
+
+ (1) assertions act as comments to the reader, telling you what the code
+ expects at that point. All assertions will always be true (unless
+ there really is a bug, of course).
+
+ (2) leaving in the scaffolding code assists anyone who would like to modify
+ the code, or understand the algorithm (by reading the debugging output,
+ one can get a glimpse into what the code is doing).
+
+ (3) (gasp!) for actually finding bugs. This code has been heavily tested
+ and "should" be fully functional and bug-free ... but you never know...
+
+ The code will become outrageously slow when debugging is
+ enabled. To control the level of debugging output, set an environment
+ variable D to 0 (little), 1 (some), 2, 3, or 4 (lots). When debugging,
+ you should see the following message on the standard output:
+
+ colamd: debug version, D = 1 (THIS WILL BE SLOW!)
+
+ or a similar message for symamd. If you don't, then debugging has not
+ been enabled.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include "colamd.h"
+#include <limits.h>
+#include <math.h>
+
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#include "matrix.h"
+#endif /* MATLAB_MEX_FILE */
+
+#if !defined (NPRINT) || !defined (NDEBUG)
+#include <stdio.h>
+#endif
+
+#ifndef NULL
+#define NULL ((void *) 0)
+#endif
+
+/* ========================================================================== */
+/* === int or UF_long ======================================================= */
+/* ========================================================================== */
+
+/* define UF_long */
+#include "UFconfig.h"
+
+#ifdef DLONG
+
+#define Int UF_long
+#define ID UF_long_id
+#define Int_MAX UF_long_max
+
+#define COLAMD_recommended colamd_l_recommended
+#define COLAMD_set_defaults colamd_l_set_defaults
+#define COLAMD_MAIN colamd_l
+#define SYMAMD_MAIN symamd_l
+#define COLAMD_report colamd_l_report
+#define SYMAMD_report symamd_l_report
+
+#else
+
+#define Int int
+#define ID "%d"
+#define Int_MAX INT_MAX
+
+#define COLAMD_recommended colamd_recommended
+#define COLAMD_set_defaults colamd_set_defaults
+#define COLAMD_MAIN colamd
+#define SYMAMD_MAIN symamd
+#define COLAMD_report colamd_report
+#define SYMAMD_report symamd_report
+
+#endif
+
+/* ========================================================================== */
+/* === Row and Column structures ============================================ */
+/* ========================================================================== */
+
+/* User code that makes use of the colamd/symamd routines need not directly */
+/* reference these structures. They are used only for colamd_recommended. */
+
+typedef struct Colamd_Col_struct
+{
+ Int start ; /* index for A of first row in this column, or DEAD */
+ /* if column is dead */
+ Int length ; /* number of rows in this column */
+ union
+ {
+ Int thickness ; /* number of original columns represented by this */
+ /* col, if the column is alive */
+ Int parent ; /* parent in parent tree super-column structure, if */
+ /* the column is dead */
+ } shared1 ;
+ union
+ {
+ Int score ; /* the score used to maintain heap, if col is alive */
+ Int order ; /* pivot ordering of this column, if col is dead */
+ } shared2 ;
+ union
+ {
+ Int headhash ; /* head of a hash bucket, if col is at the head of */
+ /* a degree list */
+ Int hash ; /* hash value, if col is not in a degree list */
+ Int prev ; /* previous column in degree list, if col is in a */
+ /* degree list (but not at the head of a degree list) */
+ } shared3 ;
+ union
+ {
+ Int degree_next ; /* next column, if col is in a degree list */
+ Int hash_next ; /* next column, if col is in a hash list */
+ } shared4 ;
+
+} Colamd_Col ;
+
+typedef struct Colamd_Row_struct
+{
+ Int start ; /* index for A of first col in this row */
+ Int length ; /* number of principal columns in this row */
+ union
+ {
+ Int degree ; /* number of principal & non-principal columns in row */
+ Int p ; /* used as a row pointer in init_rows_cols () */
+ } shared1 ;
+ union
+ {
+ Int mark ; /* for computing set differences and marking dead rows*/
+ Int first_column ;/* first column in row (used in garbage collection) */
+ } shared2 ;
+
+} Colamd_Row ;
+
+/* ========================================================================== */
+/* === Definitions ========================================================== */
+/* ========================================================================== */
+
+/* Routines are either PUBLIC (user-callable) or PRIVATE (not user-callable) */
+#define PUBLIC
+#define PRIVATE static
+
+#define DENSE_DEGREE(alpha,n) \
+ ((Int) MAX (16.0, (alpha) * sqrt ((double) (n))))
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+#define ONES_COMPLEMENT(r) (-(r)-1)
+
+/* -------------------------------------------------------------------------- */
+/* Change for version 2.1: define TRUE and FALSE only if not yet defined */
+/* -------------------------------------------------------------------------- */
+
+#ifndef TRUE
+#define TRUE (1)
+#endif
+
+#ifndef FALSE
+#define FALSE (0)
+#endif
+
+/* -------------------------------------------------------------------------- */
+
+#define EMPTY (-1)
+
+/* Row and column status */
+#define ALIVE (0)
+#define DEAD (-1)
+
+/* Column status */
+#define DEAD_PRINCIPAL (-1)
+#define DEAD_NON_PRINCIPAL (-2)
+
+/* Macros for row and column status update and checking. */
+#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark)
+#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE)
+#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE)
+#define COL_IS_DEAD(c) (Col [c].start < ALIVE)
+#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE)
+#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL)
+#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; }
+#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; }
+#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }
+
+/* ========================================================================== */
+/* === Colamd reporting mechanism =========================================== */
+/* ========================================================================== */
+
+#if defined (MATLAB_MEX_FILE) || defined (MATHWORKS)
+/* In MATLAB, matrices are 1-based to the user, but 0-based internally */
+#define INDEX(i) ((i)+1)
+#else
+/* In C, matrices are 0-based and indices are reported as such in *_report */
+#define INDEX(i) (i)
+#endif
+
+/* All output goes through the PRINTF macro. */
+#define PRINTF(params) { if (colamd_printf != NULL) (void) colamd_printf params ; }
+
+/* ========================================================================== */
+/* === Prototypes of PRIVATE routines ======================================= */
+/* ========================================================================== */
+
+PRIVATE Int init_rows_cols
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int p [],
+ Int stats [COLAMD_STATS]
+) ;
+
+PRIVATE void init_scoring
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ double knobs [COLAMD_KNOBS],
+ Int *p_n_row2,
+ Int *p_n_col2,
+ Int *p_max_deg
+) ;
+
+PRIVATE Int find_ordering
+(
+ Int n_row,
+ Int n_col,
+ Int Alen,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ Int n_col2,
+ Int max_deg,
+ Int pfree,
+ Int aggressive
+) ;
+
+PRIVATE void order_children
+(
+ Int n_col,
+ Colamd_Col Col [],
+ Int p []
+) ;
+
+PRIVATE void detect_super_cols
+(
+
+#ifndef NDEBUG
+ Int n_col,
+ Colamd_Row Row [],
+#endif /* NDEBUG */
+
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ Int row_start,
+ Int row_length
+) ;
+
+PRIVATE Int garbage_collection
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int *pfree
+) ;
+
+PRIVATE Int clear_mark
+(
+ Int tag_mark,
+ Int max_mark,
+ Int n_row,
+ Colamd_Row Row []
+) ;
+
+PRIVATE void print_report
+(
+ char *method,
+ Int stats [COLAMD_STATS]
+) ;
+
+/* ========================================================================== */
+/* === Debugging prototypes and definitions ================================= */
+/* ========================================================================== */
+
+#ifndef NDEBUG
+
+#include <assert.h>
+
+/* colamd_debug is the *ONLY* global variable, and is only */
+/* present when debugging */
+
+PRIVATE Int colamd_debug = 0 ; /* debug print level */
+
+#define DEBUG0(params) { PRINTF (params) ; }
+#define DEBUG1(params) { if (colamd_debug >= 1) PRINTF (params) ; }
+#define DEBUG2(params) { if (colamd_debug >= 2) PRINTF (params) ; }
+#define DEBUG3(params) { if (colamd_debug >= 3) PRINTF (params) ; }
+#define DEBUG4(params) { if (colamd_debug >= 4) PRINTF (params) ; }
+
+#ifdef MATLAB_MEX_FILE
+#define ASSERT(expression) (mxAssert ((expression), ""))
+#else
+#define ASSERT(expression) (assert (expression))
+#endif /* MATLAB_MEX_FILE */
+
+PRIVATE void colamd_get_debug /* gets the debug print level from getenv */
+(
+ char *method
+) ;
+
+PRIVATE void debug_deg_lists
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int head [],
+ Int min_score,
+ Int should,
+ Int max_deg
+) ;
+
+PRIVATE void debug_mark
+(
+ Int n_row,
+ Colamd_Row Row [],
+ Int tag_mark,
+ Int max_mark
+) ;
+
+PRIVATE void debug_matrix
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A []
+) ;
+
+PRIVATE void debug_structures
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int n_col2
+) ;
+
+#else /* NDEBUG */
+
+/* === No debugging ========================================================= */
+
+#define DEBUG0(params) ;
+#define DEBUG1(params) ;
+#define DEBUG2(params) ;
+#define DEBUG3(params) ;
+#define DEBUG4(params) ;
+
+#define ASSERT(expression)
+
+#endif /* NDEBUG */
+
+/* ========================================================================== */
+/* === USER-CALLABLE ROUTINES: ============================================== */
+/* ========================================================================== */
+
+/* ========================================================================== */
+/* === colamd_recommended =================================================== */
+/* ========================================================================== */
+
+/*
+ The colamd_recommended routine returns the suggested size for Alen. This
+ value has been determined to provide good balance between the number of
+ garbage collections and the memory requirements for colamd. If any
+ argument is negative, or if integer overflow occurs, a 0 is returned as an
+ error condition. 2*nnz space is required for the row and column
+ indices of the matrix. COLAMD_C (n_col) + COLAMD_R (n_row) space is
+ required for the Col and Row arrays, respectively, which are internal to
+ colamd (roughly 6*n_col + 4*n_row). An additional n_col space is the
+ minimal amount of "elbow room", and nnz/5 more space is recommended for
+ run time efficiency.
+
+ Alen is approximately 2.2*nnz + 7*n_col + 4*n_row + 10.
+
+ This function is not needed when using symamd.
+*/
+
+/* add two values of type size_t, and check for integer overflow */
+static size_t t_add (size_t a, size_t b, int *ok)
+{
+ (*ok) = (*ok) && ((a + b) >= MAX (a,b)) ;
+ return ((*ok) ? (a + b) : 0) ;
+}
+
+/* compute a*k where k is a small integer, and check for integer overflow */
+static size_t t_mult (size_t a, size_t k, int *ok)
+{
+ size_t i, s = 0 ;
+ for (i = 0 ; i < k ; i++)
+ {
+ s = t_add (s, a, ok) ;
+ }
+ return (s) ;
+}
+
+/* size of the Col and Row structures */
+#define COLAMD_C(n_col,ok) \
+ ((t_mult (t_add (n_col, 1, ok), sizeof (Colamd_Col), ok) / sizeof (Int)))
+
+#define COLAMD_R(n_row,ok) \
+ ((t_mult (t_add (n_row, 1, ok), sizeof (Colamd_Row), ok) / sizeof (Int)))
+
+
+PUBLIC size_t COLAMD_recommended /* returns recommended value of Alen. */
+(
+ /* === Parameters ======================================================= */
+
+ Int nnz, /* number of nonzeros in A */
+ Int n_row, /* number of rows in A */
+ Int n_col /* number of columns in A */
+)
+{
+ size_t s, c, r ;
+ int ok = TRUE ;
+ if (nnz < 0 || n_row < 0 || n_col < 0)
+ {
+ return (0) ;
+ }
+ s = t_mult (nnz, 2, &ok) ; /* 2*nnz */
+ c = COLAMD_C (n_col, &ok) ; /* size of column structures */
+ r = COLAMD_R (n_row, &ok) ; /* size of row structures */
+ s = t_add (s, c, &ok) ;
+ s = t_add (s, r, &ok) ;
+ s = t_add (s, n_col, &ok) ; /* elbow room */
+ s = t_add (s, nnz/5, &ok) ; /* elbow room */
+ ok = ok && (s < Int_MAX) ;
+ return (ok ? s : 0) ;
+}
+
+
+/* ========================================================================== */
+/* === colamd_set_defaults ================================================== */
+/* ========================================================================== */
+
+/*
+ The colamd_set_defaults routine sets the default values of the user-
+ controllable parameters for colamd and symamd:
+
+ Colamd: rows with more than max (16, knobs [0] * sqrt (n_col))
+ entries are removed prior to ordering. Columns with more than
+ max (16, knobs [1] * sqrt (MIN (n_row,n_col))) entries are removed
+ prior to ordering, and placed last in the output column ordering.
+
+ Symamd: Rows and columns with more than max (16, knobs [0] * sqrt (n))
+ entries are removed prior to ordering, and placed last in the
+ output ordering.
+
+ knobs [0] dense row control
+
+ knobs [1] dense column control
+
+ knobs [2] if nonzero, do aggresive absorption
+
+ knobs [3..19] unused, but future versions might use this
+
+*/
+
+PUBLIC void COLAMD_set_defaults
+(
+ /* === Parameters ======================================================= */
+
+ double knobs [COLAMD_KNOBS] /* knob array */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ;
+
+ if (!knobs)
+ {
+ return ; /* no knobs to initialize */
+ }
+ for (i = 0 ; i < COLAMD_KNOBS ; i++)
+ {
+ knobs [i] = 0 ;
+ }
+ knobs [COLAMD_DENSE_ROW] = 10 ;
+ knobs [COLAMD_DENSE_COL] = 10 ;
+ knobs [COLAMD_AGGRESSIVE] = TRUE ; /* default: do aggressive absorption*/
+}
+
+
+/* ========================================================================== */
+/* === symamd =============================================================== */
+/* ========================================================================== */
+
+PUBLIC Int SYMAMD_MAIN /* return TRUE if OK, FALSE otherwise */
+(
+ /* === Parameters ======================================================= */
+
+ Int n, /* number of rows and columns of A */
+ Int A [], /* row indices of A */
+ Int p [], /* column pointers of A */
+ Int perm [], /* output permutation, size n+1 */
+ double knobs [COLAMD_KNOBS], /* parameters (uses defaults if NULL) */
+ Int stats [COLAMD_STATS], /* output statistics and error codes */
+ void * (*allocate) (size_t, size_t),
+ /* pointer to calloc (ANSI C) or */
+ /* mxCalloc (for MATLAB mexFunction) */
+ void (*release) (void *)
+ /* pointer to free (ANSI C) or */
+ /* mxFree (for MATLAB mexFunction) */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int *count ; /* length of each column of M, and col pointer*/
+ Int *mark ; /* mark array for finding duplicate entries */
+ Int *M ; /* row indices of matrix M */
+ size_t Mlen ; /* length of M */
+ Int n_row ; /* number of rows in M */
+ Int nnz ; /* number of entries in A */
+ Int i ; /* row index of A */
+ Int j ; /* column index of A */
+ Int k ; /* row index of M */
+ Int mnz ; /* number of nonzeros in M */
+ Int pp ; /* index into a column of A */
+ Int last_row ; /* last row seen in the current column */
+ Int length ; /* number of nonzeros in a column */
+
+ double cknobs [COLAMD_KNOBS] ; /* knobs for colamd */
+ double default_knobs [COLAMD_KNOBS] ; /* default knobs for colamd */
+
+#ifndef NDEBUG
+ colamd_get_debug ("symamd") ;
+#endif /* NDEBUG */
+
+ /* === Check the input arguments ======================================== */
+
+ if (!stats)
+ {
+ DEBUG0 (("symamd: stats not present\n")) ;
+ return (FALSE) ;
+ }
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ stats [i] = 0 ;
+ }
+ stats [COLAMD_STATUS] = COLAMD_OK ;
+ stats [COLAMD_INFO1] = -1 ;
+ stats [COLAMD_INFO2] = -1 ;
+
+ if (!A)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;
+ DEBUG0 (("symamd: A not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (!p) /* p is not present */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;
+ DEBUG0 (("symamd: p not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (n < 0) /* n must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;
+ stats [COLAMD_INFO1] = n ;
+ DEBUG0 (("symamd: n negative %d\n", n)) ;
+ return (FALSE) ;
+ }
+
+ nnz = p [n] ;
+ if (nnz < 0) /* nnz must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;
+ stats [COLAMD_INFO1] = nnz ;
+ DEBUG0 (("symamd: number of entries negative %d\n", nnz)) ;
+ return (FALSE) ;
+ }
+
+ if (p [0] != 0)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;
+ stats [COLAMD_INFO1] = p [0] ;
+ DEBUG0 (("symamd: p[0] not zero %d\n", p [0])) ;
+ return (FALSE) ;
+ }
+
+ /* === If no knobs, set default knobs =================================== */
+
+ if (!knobs)
+ {
+ COLAMD_set_defaults (default_knobs) ;
+ knobs = default_knobs ;
+ }
+
+ /* === Allocate count and mark ========================================== */
+
+ count = (Int *) ((*allocate) (n+1, sizeof (Int))) ;
+ if (!count)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ;
+ DEBUG0 (("symamd: allocate count (size %d) failed\n", n+1)) ;
+ return (FALSE) ;
+ }
+
+ mark = (Int *) ((*allocate) (n+1, sizeof (Int))) ;
+ if (!mark)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ;
+ (*release) ((void *) count) ;
+ DEBUG0 (("symamd: allocate mark (size %d) failed\n", n+1)) ;
+ return (FALSE) ;
+ }
+
+ /* === Compute column counts of M, check if A is valid ================== */
+
+ stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/
+
+ for (i = 0 ; i < n ; i++)
+ {
+ mark [i] = -1 ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ last_row = -1 ;
+
+ length = p [j+1] - p [j] ;
+ if (length < 0)
+ {
+ /* column pointers must be non-decreasing */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;
+ stats [COLAMD_INFO1] = j ;
+ stats [COLAMD_INFO2] = length ;
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ;
+ DEBUG0 (("symamd: col %d negative length %d\n", j, length)) ;
+ return (FALSE) ;
+ }
+
+ for (pp = p [j] ; pp < p [j+1] ; pp++)
+ {
+ i = A [pp] ;
+ if (i < 0 || i >= n)
+ {
+ /* row index i, in column j, is out of bounds */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;
+ stats [COLAMD_INFO1] = j ;
+ stats [COLAMD_INFO2] = i ;
+ stats [COLAMD_INFO3] = n ;
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ;
+ DEBUG0 (("symamd: row %d col %d out of bounds\n", i, j)) ;
+ return (FALSE) ;
+ }
+
+ if (i <= last_row || mark [i] == j)
+ {
+ /* row index is unsorted or repeated (or both), thus col */
+ /* is jumbled. This is a notice, not an error condition. */
+ stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ;
+ stats [COLAMD_INFO1] = j ;
+ stats [COLAMD_INFO2] = i ;
+ (stats [COLAMD_INFO3]) ++ ;
+ DEBUG1 (("symamd: row %d col %d unsorted/duplicate\n", i, j)) ;
+ }
+
+ if (i > j && mark [i] != j)
+ {
+ /* row k of M will contain column indices i and j */
+ count [i]++ ;
+ count [j]++ ;
+ }
+
+ /* mark the row as having been seen in this column */
+ mark [i] = j ;
+
+ last_row = i ;
+ }
+ }
+
+ /* v2.4: removed free(mark) */
+
+ /* === Compute column pointers of M ===================================== */
+
+ /* use output permutation, perm, for column pointers of M */
+ perm [0] = 0 ;
+ for (j = 1 ; j <= n ; j++)
+ {
+ perm [j] = perm [j-1] + count [j-1] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ count [j] = perm [j] ;
+ }
+
+ /* === Construct M ====================================================== */
+
+ mnz = perm [n] ;
+ n_row = mnz / 2 ;
+ Mlen = COLAMD_recommended (mnz, n_row, n) ;
+ M = (Int *) ((*allocate) (Mlen, sizeof (Int))) ;
+ DEBUG0 (("symamd: M is %d-by-%d with %d entries, Mlen = %g\n",
+ n_row, n, mnz, (double) Mlen)) ;
+
+ if (!M)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_out_of_memory ;
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ;
+ DEBUG0 (("symamd: allocate M (size %g) failed\n", (double) Mlen)) ;
+ return (FALSE) ;
+ }
+
+ k = 0 ;
+
+ if (stats [COLAMD_STATUS] == COLAMD_OK)
+ {
+ /* Matrix is OK */
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (p [j+1] - p [j] >= 0) ;
+ for (pp = p [j] ; pp < p [j+1] ; pp++)
+ {
+ i = A [pp] ;
+ ASSERT (i >= 0 && i < n) ;
+ if (i > j)
+ {
+ /* row k of M contains column indices i and j */
+ M [count [i]++] = k ;
+ M [count [j]++] = k ;
+ k++ ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* Matrix is jumbled. Do not add duplicates to M. Unsorted cols OK. */
+ DEBUG0 (("symamd: Duplicates in A.\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ mark [i] = -1 ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSERT (p [j+1] - p [j] >= 0) ;
+ for (pp = p [j] ; pp < p [j+1] ; pp++)
+ {
+ i = A [pp] ;
+ ASSERT (i >= 0 && i < n) ;
+ if (i > j && mark [i] != j)
+ {
+ /* row k of M contains column indices i and j */
+ M [count [i]++] = k ;
+ M [count [j]++] = k ;
+ k++ ;
+ mark [i] = j ;
+ }
+ }
+ }
+ /* v2.4: free(mark) moved below */
+ }
+
+ /* count and mark no longer needed */
+ (*release) ((void *) count) ;
+ (*release) ((void *) mark) ; /* v2.4: free (mark) moved here */
+ ASSERT (k == n_row) ;
+
+ /* === Adjust the knobs for M =========================================== */
+
+ for (i = 0 ; i < COLAMD_KNOBS ; i++)
+ {
+ cknobs [i] = knobs [i] ;
+ }
+
+ /* there are no dense rows in M */
+ cknobs [COLAMD_DENSE_ROW] = -1 ;
+ cknobs [COLAMD_DENSE_COL] = knobs [COLAMD_DENSE_ROW] ;
+
+ /* === Order the columns of M =========================================== */
+
+ /* v2.4: colamd cannot fail here, so the error check is removed */
+ (void) COLAMD_MAIN (n_row, n, (Int) Mlen, M, perm, cknobs, stats) ;
+
+ /* Note that the output permutation is now in perm */
+
+ /* === get the statistics for symamd from colamd ======================== */
+
+ /* a dense column in colamd means a dense row and col in symamd */
+ stats [COLAMD_DENSE_ROW] = stats [COLAMD_DENSE_COL] ;
+
+ /* === Free M =========================================================== */
+
+ (*release) ((void *) M) ;
+ DEBUG0 (("symamd: done.\n")) ;
+ return (TRUE) ;
+
+}
+
+/* ========================================================================== */
+/* === colamd =============================================================== */
+/* ========================================================================== */
+
+/*
+ The colamd routine computes a column ordering Q of a sparse matrix
+ A such that the LU factorization P(AQ) = LU remains sparse, where P is
+ selected via partial pivoting. The routine can also be viewed as
+ providing a permutation Q such that the Cholesky factorization
+ (AQ)'(AQ) = LL' remains sparse.
+*/
+
+PUBLIC Int COLAMD_MAIN /* returns TRUE if successful, FALSE otherwise*/
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows in A */
+ Int n_col, /* number of columns in A */
+ Int Alen, /* length of A */
+ Int A [], /* row indices of A */
+ Int p [], /* pointers to columns in A */
+ double knobs [COLAMD_KNOBS],/* parameters (uses defaults if NULL) */
+ Int stats [COLAMD_STATS] /* output statistics and error codes */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ; /* loop index */
+ Int nnz ; /* nonzeros in A */
+ size_t Row_size ; /* size of Row [], in integers */
+ size_t Col_size ; /* size of Col [], in integers */
+ size_t need ; /* minimum required length of A */
+ Colamd_Row *Row ; /* pointer into A of Row [0..n_row] array */
+ Colamd_Col *Col ; /* pointer into A of Col [0..n_col] array */
+ Int n_col2 ; /* number of non-dense, non-empty columns */
+ Int n_row2 ; /* number of non-dense, non-empty rows */
+ Int ngarbage ; /* number of garbage collections performed */
+ Int max_deg ; /* maximum row degree */
+ double default_knobs [COLAMD_KNOBS] ; /* default knobs array */
+ Int aggressive ; /* do aggressive absorption */
+ int ok ;
+
+#ifndef NDEBUG
+ colamd_get_debug ("colamd") ;
+#endif /* NDEBUG */
+
+ /* === Check the input arguments ======================================== */
+
+ if (!stats)
+ {
+ DEBUG0 (("colamd: stats not present\n")) ;
+ return (FALSE) ;
+ }
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ stats [i] = 0 ;
+ }
+ stats [COLAMD_STATUS] = COLAMD_OK ;
+ stats [COLAMD_INFO1] = -1 ;
+ stats [COLAMD_INFO2] = -1 ;
+
+ if (!A) /* A is not present */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;
+ DEBUG0 (("colamd: A not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (!p) /* p is not present */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;
+ DEBUG0 (("colamd: p not present\n")) ;
+ return (FALSE) ;
+ }
+
+ if (n_row < 0) /* n_row must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ;
+ stats [COLAMD_INFO1] = n_row ;
+ DEBUG0 (("colamd: nrow negative %d\n", n_row)) ;
+ return (FALSE) ;
+ }
+
+ if (n_col < 0) /* n_col must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;
+ stats [COLAMD_INFO1] = n_col ;
+ DEBUG0 (("colamd: ncol negative %d\n", n_col)) ;
+ return (FALSE) ;
+ }
+
+ nnz = p [n_col] ;
+ if (nnz < 0) /* nnz must be >= 0 */
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;
+ stats [COLAMD_INFO1] = nnz ;
+ DEBUG0 (("colamd: number of entries negative %d\n", nnz)) ;
+ return (FALSE) ;
+ }
+
+ if (p [0] != 0)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;
+ stats [COLAMD_INFO1] = p [0] ;
+ DEBUG0 (("colamd: p[0] not zero %d\n", p [0])) ;
+ return (FALSE) ;
+ }
+
+ /* === If no knobs, set default knobs =================================== */
+
+ if (!knobs)
+ {
+ COLAMD_set_defaults (default_knobs) ;
+ knobs = default_knobs ;
+ }
+
+ aggressive = (knobs [COLAMD_AGGRESSIVE] != FALSE) ;
+
+ /* === Allocate the Row and Col arrays from array A ===================== */
+
+ ok = TRUE ;
+ Col_size = COLAMD_C (n_col, &ok) ; /* size of Col array of structs */
+ Row_size = COLAMD_R (n_row, &ok) ; /* size of Row array of structs */
+
+ /* need = 2*nnz + n_col + Col_size + Row_size ; */
+ need = t_mult (nnz, 2, &ok) ;
+ need = t_add (need, n_col, &ok) ;
+ need = t_add (need, Col_size, &ok) ;
+ need = t_add (need, Row_size, &ok) ;
+
+ if (!ok || need > (size_t) Alen || need > Int_MAX)
+ {
+ /* not enough space in array A to perform the ordering */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ;
+ stats [COLAMD_INFO1] = need ;
+ stats [COLAMD_INFO2] = Alen ;
+ DEBUG0 (("colamd: Need Alen >= %d, given only Alen = %d\n", need,Alen));
+ return (FALSE) ;
+ }
+
+ Alen -= Col_size + Row_size ;
+ Col = (Colamd_Col *) &A [Alen] ;
+ Row = (Colamd_Row *) &A [Alen + Col_size] ;
+
+ /* === Construct the row and column data structures ===================== */
+
+ if (!init_rows_cols (n_row, n_col, Row, Col, A, p, stats))
+ {
+ /* input matrix is invalid */
+ DEBUG0 (("colamd: Matrix invalid\n")) ;
+ return (FALSE) ;
+ }
+
+ /* === Initialize scores, kill dense rows/columns ======================= */
+
+ init_scoring (n_row, n_col, Row, Col, A, p, knobs,
+ &n_row2, &n_col2, &max_deg) ;
+
+ /* === Order the supercolumns =========================================== */
+
+ ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p,
+ n_col2, max_deg, 2*nnz, aggressive) ;
+
+ /* === Order the non-principal columns ================================== */
+
+ order_children (n_col, Col, p) ;
+
+ /* === Return statistics in stats ======================================= */
+
+ stats [COLAMD_DENSE_ROW] = n_row - n_row2 ;
+ stats [COLAMD_DENSE_COL] = n_col - n_col2 ;
+ stats [COLAMD_DEFRAG_COUNT] = ngarbage ;
+ DEBUG0 (("colamd: done.\n")) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === colamd_report ======================================================== */
+/* ========================================================================== */
+
+PUBLIC void COLAMD_report
+(
+ Int stats [COLAMD_STATS]
+)
+{
+ print_report ("colamd", stats) ;
+}
+
+
+/* ========================================================================== */
+/* === symamd_report ======================================================== */
+/* ========================================================================== */
+
+PUBLIC void SYMAMD_report
+(
+ Int stats [COLAMD_STATS]
+)
+{
+ print_report ("symamd", stats) ;
+}
+
+
+
+/* ========================================================================== */
+/* === NON-USER-CALLABLE ROUTINES: ========================================== */
+/* ========================================================================== */
+
+/* There are no user-callable routines beyond this point in the file */
+
+
+/* ========================================================================== */
+/* === init_rows_cols ======================================================= */
+/* ========================================================================== */
+
+/*
+ Takes the column form of the matrix in A and creates the row form of the
+ matrix. Also, row and column attributes are stored in the Col and Row
+ structs. If the columns are un-sorted or contain duplicate row indices,
+ this routine will also sort and remove duplicate row indices from the
+ column form of the matrix. Returns FALSE if the matrix is invalid,
+ TRUE otherwise. Not user-callable.
+*/
+
+PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* row indices of A, of size Alen */
+ Int p [], /* pointers to columns in A, of size n_col+1 */
+ Int stats [COLAMD_STATS] /* colamd statistics */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int col ; /* a column index */
+ Int row ; /* a row index */
+ Int *cp ; /* a column pointer */
+ Int *cp_end ; /* a pointer to the end of a column */
+ Int *rp ; /* a row pointer */
+ Int *rp_end ; /* a pointer to the end of a row */
+ Int last_row ; /* previous row */
+
+ /* === Initialize columns, and check column pointers ==================== */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Col [col].start = p [col] ;
+ Col [col].length = p [col+1] - p [col] ;
+
+ if (Col [col].length < 0)
+ {
+ /* column pointers must be non-decreasing */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = Col [col].length ;
+ DEBUG0 (("colamd: col %d length %d < 0\n", col, Col [col].length)) ;
+ return (FALSE) ;
+ }
+
+ Col [col].shared1.thickness = 1 ;
+ Col [col].shared2.score = 0 ;
+ Col [col].shared3.prev = EMPTY ;
+ Col [col].shared4.degree_next = EMPTY ;
+ }
+
+ /* p [0..n_col] no longer needed, used as "head" in subsequent routines */
+
+ /* === Scan columns, compute row degrees, and check row indices ========= */
+
+ stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].length = 0 ;
+ Row [row].shared2.mark = -1 ;
+ }
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ last_row = -1 ;
+
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+
+ /* make sure row indices within range */
+ if (row < 0 || row >= n_row)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = row ;
+ stats [COLAMD_INFO3] = n_row ;
+ DEBUG0 (("colamd: row %d col %d out of bounds\n", row, col)) ;
+ return (FALSE) ;
+ }
+
+ if (row <= last_row || Row [row].shared2.mark == col)
+ {
+ /* row index are unsorted or repeated (or both), thus col */
+ /* is jumbled. This is a notice, not an error condition. */
+ stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = row ;
+ (stats [COLAMD_INFO3]) ++ ;
+ DEBUG1 (("colamd: row %d col %d unsorted/duplicate\n",row,col));
+ }
+
+ if (Row [row].shared2.mark != col)
+ {
+ Row [row].length++ ;
+ }
+ else
+ {
+ /* this is a repeated entry in the column, */
+ /* it will be removed */
+ Col [col].length-- ;
+ }
+
+ /* mark the row as having been seen in this column */
+ Row [row].shared2.mark = col ;
+
+ last_row = row ;
+ }
+ }
+
+ /* === Compute row pointers ============================================= */
+
+ /* row form of the matrix starts directly after the column */
+ /* form of matrix in A */
+ Row [0].start = p [n_col] ;
+ Row [0].shared1.p = Row [0].start ;
+ Row [0].shared2.mark = -1 ;
+ for (row = 1 ; row < n_row ; row++)
+ {
+ Row [row].start = Row [row-1].start + Row [row-1].length ;
+ Row [row].shared1.p = Row [row].start ;
+ Row [row].shared2.mark = -1 ;
+ }
+
+ /* === Create row form ================================================== */
+
+ if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)
+ {
+ /* if cols jumbled, watch for repeated row indices */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+ if (Row [row].shared2.mark != col)
+ {
+ A [(Row [row].shared1.p)++] = col ;
+ Row [row].shared2.mark = col ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* if cols not jumbled, we don't need the mark (this is faster) */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ A [(Row [*cp++].shared1.p)++] = col ;
+ }
+ }
+ }
+
+ /* === Clear the row marks and set row degrees ========================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].shared2.mark = 0 ;
+ Row [row].shared1.degree = Row [row].length ;
+ }
+
+ /* === See if we need to re-create columns ============================== */
+
+ if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)
+ {
+ DEBUG0 (("colamd: reconstructing column form, matrix jumbled\n")) ;
+
+#ifndef NDEBUG
+ /* make sure column lengths are correct */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ p [col] = Col [col].length ;
+ }
+ for (row = 0 ; row < n_row ; row++)
+ {
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ p [*rp++]-- ;
+ }
+ }
+ for (col = 0 ; col < n_col ; col++)
+ {
+ ASSERT (p [col] == 0) ;
+ }
+ /* now p is all zero (different than when debugging is turned off) */
+#endif /* NDEBUG */
+
+ /* === Compute col pointers ========================================= */
+
+ /* col form of the matrix starts at A [0]. */
+ /* Note, we may have a gap between the col form and the row */
+ /* form if there were duplicate entries, if so, it will be */
+ /* removed upon the first garbage collection */
+ Col [0].start = 0 ;
+ p [0] = Col [0].start ;
+ for (col = 1 ; col < n_col ; col++)
+ {
+ /* note that the lengths here are for pruned columns, i.e. */
+ /* no duplicate row indices will exist for these columns */
+ Col [col].start = Col [col-1].start + Col [col-1].length ;
+ p [col] = Col [col].start ;
+ }
+
+ /* === Re-create col form =========================================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ A [(p [*rp++])++] = row ;
+ }
+ }
+ }
+
+ /* === Done. Matrix is not (or no longer) jumbled ====================== */
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === init_scoring ========================================================= */
+/* ========================================================================== */
+
+/*
+ Kills dense or empty columns and rows, calculates an initial score for
+ each column, and places all columns in the degree lists. Not user-callable.
+*/
+
+PRIVATE void init_scoring
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* column form and row form of A */
+ Int head [], /* of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameters */
+ Int *p_n_row2, /* number of non-dense, non-empty rows */
+ Int *p_n_col2, /* number of non-dense, non-empty columns */
+ Int *p_max_deg /* maximum row degree */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int c ; /* a column index */
+ Int r, row ; /* a row index */
+ Int *cp ; /* a column pointer */
+ Int deg ; /* degree of a row or column */
+ Int *cp_end ; /* a pointer to the end of a column */
+ Int *new_cp ; /* new column pointer */
+ Int col_length ; /* length of pruned column */
+ Int score ; /* current column score */
+ Int n_col2 ; /* number of non-dense, non-empty columns */
+ Int n_row2 ; /* number of non-dense, non-empty rows */
+ Int dense_row_count ; /* remove rows with more entries than this */
+ Int dense_col_count ; /* remove cols with more entries than this */
+ Int min_score ; /* smallest column score */
+ Int max_deg ; /* maximum row degree */
+ Int next_col ; /* Used to add to degree list.*/
+
+#ifndef NDEBUG
+ Int debug_count ; /* debug only. */
+#endif /* NDEBUG */
+
+ /* === Extract knobs ==================================================== */
+
+ /* Note: if knobs contains a NaN, this is undefined: */
+ if (knobs [COLAMD_DENSE_ROW] < 0)
+ {
+ /* only remove completely dense rows */
+ dense_row_count = n_col-1 ;
+ }
+ else
+ {
+ dense_row_count = DENSE_DEGREE (knobs [COLAMD_DENSE_ROW], n_col) ;
+ }
+ if (knobs [COLAMD_DENSE_COL] < 0)
+ {
+ /* only remove completely dense columns */
+ dense_col_count = n_row-1 ;
+ }
+ else
+ {
+ dense_col_count =
+ DENSE_DEGREE (knobs [COLAMD_DENSE_COL], MIN (n_row, n_col)) ;
+ }
+
+ DEBUG1 (("colamd: densecount: %d %d\n", dense_row_count, dense_col_count)) ;
+ max_deg = 0 ;
+ n_col2 = n_col ;
+ n_row2 = n_row ;
+
+ /* === Kill empty columns =============================================== */
+
+ /* Put the empty columns at the end in their natural order, so that LU */
+ /* factorization can proceed as far as possible. */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ deg = Col [c].length ;
+ if (deg == 0)
+ {
+ /* this is a empty column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ }
+ DEBUG1 (("colamd: null columns killed: %d\n", n_col - n_col2)) ;
+
+ /* === Kill dense columns =============================================== */
+
+ /* Put the dense columns at the end, in their natural order */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip any dead columns */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ deg = Col [c].length ;
+ if (deg > dense_col_count)
+ {
+ /* this is a dense column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ /* decrement the row degrees */
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ Row [*cp++].shared1.degree-- ;
+ }
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ }
+ DEBUG1 (("colamd: Dense and null columns killed: %d\n", n_col - n_col2)) ;
+
+ /* === Kill dense and empty rows ======================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ deg = Row [r].shared1.degree ;
+ ASSERT (deg >= 0 && deg <= n_col) ;
+ if (deg > dense_row_count || deg == 0)
+ {
+ /* kill a dense or empty row */
+ KILL_ROW (r) ;
+ --n_row2 ;
+ }
+ else
+ {
+ /* keep track of max degree of remaining rows */
+ max_deg = MAX (max_deg, deg) ;
+ }
+ }
+ DEBUG1 (("colamd: Dense and null rows killed: %d\n", n_row - n_row2)) ;
+
+ /* === Compute initial column scores ==================================== */
+
+ /* At this point the row degrees are accurate. They reflect the number */
+ /* of "live" (non-dense) columns in each row. No empty rows exist. */
+ /* Some "live" columns may contain only dead rows, however. These are */
+ /* pruned in the code below. */
+
+ /* now find the initial matlab score for each column */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip dead column */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ score = 0 ;
+ cp = &A [Col [c].start] ;
+ new_cp = cp ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ /* skip if dead */
+ if (ROW_IS_DEAD (row))
+ {
+ continue ;
+ }
+ /* compact the column */
+ *new_cp++ = row ;
+ /* add row's external degree */
+ score += Row [row].shared1.degree - 1 ;
+ /* guard against integer overflow */
+ score = MIN (score, n_col) ;
+ }
+ /* determine pruned column length */
+ col_length = (Int) (new_cp - &A [Col [c].start]) ;
+ if (col_length == 0)
+ {
+ /* a newly-made null column (all rows in this col are "dense" */
+ /* and have already been killed) */
+ DEBUG2 (("Newly null killed: %d\n", c)) ;
+ Col [c].shared2.order = --n_col2 ;
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ else
+ {
+ /* set column length and set score */
+ ASSERT (score >= 0) ;
+ ASSERT (score <= n_col) ;
+ Col [c].length = col_length ;
+ Col [c].shared2.score = score ;
+ }
+ }
+ DEBUG1 (("colamd: Dense, null, and newly-null columns killed: %d\n",
+ n_col-n_col2)) ;
+
+ /* At this point, all empty rows and columns are dead. All live columns */
+ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */
+ /* yet). Rows may contain dead columns, but all live rows contain at */
+ /* least one live column. */
+
+#ifndef NDEBUG
+ debug_structures (n_row, n_col, Row, Col, A, n_col2) ;
+#endif /* NDEBUG */
+
+ /* === Initialize degree lists ========================================== */
+
+#ifndef NDEBUG
+ debug_count = 0 ;
+#endif /* NDEBUG */
+
+ /* clear the hash buckets */
+ for (c = 0 ; c <= n_col ; c++)
+ {
+ head [c] = EMPTY ;
+ }
+ min_score = n_col ;
+ /* place in reverse order, so low column indices are at the front */
+ /* of the lists. This is to encourage natural tie-breaking */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* only add principal columns to degree lists */
+ if (COL_IS_ALIVE (c))
+ {
+ DEBUG4 (("place %d score %d minscore %d ncol %d\n",
+ c, Col [c].shared2.score, min_score, n_col)) ;
+
+ /* === Add columns score to DList =============================== */
+
+ score = Col [c].shared2.score ;
+
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (score >= 0) ;
+ ASSERT (score <= n_col) ;
+ ASSERT (head [score] >= EMPTY) ;
+
+ /* now add this column to dList at proper score location */
+ next_col = head [score] ;
+ Col [c].shared3.prev = EMPTY ;
+ Col [c].shared4.degree_next = next_col ;
+
+ /* if there already was a column with the same score, set its */
+ /* previous pointer to this new column */
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = c ;
+ }
+ head [score] = c ;
+
+ /* see if this score is less than current min */
+ min_score = MIN (min_score, score) ;
+
+#ifndef NDEBUG
+ debug_count++ ;
+#endif /* NDEBUG */
+
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("colamd: Live cols %d out of %d, non-princ: %d\n",
+ debug_count, n_col, n_col-debug_count)) ;
+ ASSERT (debug_count == n_col2) ;
+ debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2, max_deg) ;
+#endif /* NDEBUG */
+
+ /* === Return number of remaining columns, and max row degree =========== */
+
+ *p_n_col2 = n_col2 ;
+ *p_n_row2 = n_row2 ;
+ *p_max_deg = max_deg ;
+}
+
+
+/* ========================================================================== */
+/* === find_ordering ======================================================== */
+/* ========================================================================== */
+
+/*
+ Order the principal columns of the supercolumn form of the matrix
+ (no supercolumns on input). Uses a minimum approximate column minimum
+ degree ordering method. Not user-callable.
+*/
+
+PRIVATE Int find_ordering /* return the number of garbage collections */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Int Alen, /* size of A, 2*nnz + n_col or larger */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* column form and row form of A */
+ Int head [], /* of size n_col+1 */
+ Int n_col2, /* Remaining columns to order */
+ Int max_deg, /* Maximum row degree */
+ Int pfree, /* index of first free slot (2*nnz on entry) */
+ Int aggressive
+)
+{
+ /* === Local variables ================================================== */
+
+ Int k ; /* current pivot ordering step */
+ Int pivot_col ; /* current pivot column */
+ Int *cp ; /* a column pointer */
+ Int *rp ; /* a row pointer */
+ Int pivot_row ; /* current pivot row */
+ Int *new_cp ; /* modified column pointer */
+ Int *new_rp ; /* modified row pointer */
+ Int pivot_row_start ; /* pointer to start of pivot row */
+ Int pivot_row_degree ; /* number of columns in pivot row */
+ Int pivot_row_length ; /* number of supercolumns in pivot row */
+ Int pivot_col_score ; /* score of pivot column */
+ Int needed_memory ; /* free space needed for pivot row */
+ Int *cp_end ; /* pointer to the end of a column */
+ Int *rp_end ; /* pointer to the end of a row */
+ Int row ; /* a row index */
+ Int col ; /* a column index */
+ Int max_score ; /* maximum possible score */
+ Int cur_score ; /* score of current column */
+ unsigned Int hash ; /* hash value for supernode detection */
+ Int head_column ; /* head of hash bucket */
+ Int first_col ; /* first column in hash bucket */
+ Int tag_mark ; /* marker value for mark array */
+ Int row_mark ; /* Row [row].shared2.mark */
+ Int set_difference ; /* set difference size of row with pivot row */
+ Int min_score ; /* smallest column score */
+ Int col_thickness ; /* "thickness" (no. of columns in a supercol) */
+ Int max_mark ; /* maximum value of tag_mark */
+ Int pivot_col_thickness ; /* number of columns represented by pivot col */
+ Int prev_col ; /* Used by Dlist operations. */
+ Int next_col ; /* Used by Dlist operations. */
+ Int ngarbage ; /* number of garbage collections performed */
+
+#ifndef NDEBUG
+ Int debug_d ; /* debug loop counter */
+ Int debug_step = 0 ; /* debug loop counter */
+#endif /* NDEBUG */
+
+ /* === Initialization and clear mark ==================================== */
+
+ max_mark = INT_MAX - n_col ; /* INT_MAX defined in <limits.h> */
+ tag_mark = clear_mark (0, max_mark, n_row, Row) ;
+ min_score = 0 ;
+ ngarbage = 0 ;
+ DEBUG1 (("colamd: Ordering, n_col2=%d\n", n_col2)) ;
+
+ /* === Order the columns ================================================ */
+
+ for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */)
+ {
+
+#ifndef NDEBUG
+ if (debug_step % 100 == 0)
+ {
+ DEBUG2 (("\n... Step k: %d out of n_col2: %d\n", k, n_col2)) ;
+ }
+ else
+ {
+ DEBUG3 (("\n----------Step k: %d out of n_col2: %d\n", k, n_col2)) ;
+ }
+ debug_step++ ;
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k, max_deg) ;
+ debug_matrix (n_row, n_col, Row, Col, A) ;
+#endif /* NDEBUG */
+
+ /* === Select pivot column, and order it ============================ */
+
+ /* make sure degree list isn't empty */
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (head [min_score] >= EMPTY) ;
+
+#ifndef NDEBUG
+ for (debug_d = 0 ; debug_d < min_score ; debug_d++)
+ {
+ ASSERT (head [debug_d] == EMPTY) ;
+ }
+#endif /* NDEBUG */
+
+ /* get pivot column from head of minimum degree list */
+ while (head [min_score] == EMPTY && min_score < n_col)
+ {
+ min_score++ ;
+ }
+ pivot_col = head [min_score] ;
+ ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;
+ next_col = Col [pivot_col].shared4.degree_next ;
+ head [min_score] = next_col ;
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = EMPTY ;
+ }
+
+ ASSERT (COL_IS_ALIVE (pivot_col)) ;
+
+ /* remember score for defrag check */
+ pivot_col_score = Col [pivot_col].shared2.score ;
+
+ /* the pivot column is the kth column in the pivot order */
+ Col [pivot_col].shared2.order = k ;
+
+ /* increment order count by column thickness */
+ pivot_col_thickness = Col [pivot_col].shared1.thickness ;
+ k += pivot_col_thickness ;
+ ASSERT (pivot_col_thickness > 0) ;
+ DEBUG3 (("Pivot col: %d thick %d\n", pivot_col, pivot_col_thickness)) ;
+
+ /* === Garbage_collection, if necessary ============================= */
+
+ needed_memory = MIN (pivot_col_score, n_col - k) ;
+ if (pfree + needed_memory >= Alen)
+ {
+ pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;
+ ngarbage++ ;
+ /* after garbage collection we will have enough */
+ ASSERT (pfree + needed_memory < Alen) ;
+ /* garbage collection has wiped out the Row[].shared2.mark array */
+ tag_mark = clear_mark (0, max_mark, n_row, Row) ;
+
+#ifndef NDEBUG
+ debug_matrix (n_row, n_col, Row, Col, A) ;
+#endif /* NDEBUG */
+ }
+
+ /* === Compute pivot row pattern ==================================== */
+
+ /* get starting location for this new merged row */
+ pivot_row_start = pfree ;
+
+ /* initialize new row counts to zero */
+ pivot_row_degree = 0 ;
+
+ /* tag pivot column as having been visited so it isn't included */
+ /* in merged pivot row */
+ Col [pivot_col].shared1.thickness = -pivot_col_thickness ;
+
+ /* pivot row is the union of all rows in the pivot column pattern */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ DEBUG4 (("Pivot col pattern %d %d\n", ROW_IS_ALIVE (row), row)) ;
+ /* skip if row is dead */
+ if (ROW_IS_ALIVE (row))
+ {
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ /* add the column, if alive and untagged */
+ col_thickness = Col [col].shared1.thickness ;
+ if (col_thickness > 0 && COL_IS_ALIVE (col))
+ {
+ /* tag column in pivot row */
+ Col [col].shared1.thickness = -col_thickness ;
+ ASSERT (pfree < Alen) ;
+ /* place column in pivot row */
+ A [pfree++] = col ;
+ pivot_row_degree += col_thickness ;
+ }
+ }
+ }
+ }
+
+ /* clear tag on pivot column */
+ Col [pivot_col].shared1.thickness = pivot_col_thickness ;
+ max_deg = MAX (max_deg, pivot_row_degree) ;
+
+#ifndef NDEBUG
+ DEBUG3 (("check2\n")) ;
+ debug_mark (n_row, Row, tag_mark, max_mark) ;
+#endif /* NDEBUG */
+
+ /* === Kill all rows used to construct pivot row ==================== */
+
+ /* also kill pivot row, temporarily */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* may be killing an already dead row */
+ row = *cp++ ;
+ DEBUG3 (("Kill row in pivot col: %d\n", row)) ;
+ KILL_ROW (row) ;
+ }
+
+ /* === Select a row index to use as the new pivot row =============== */
+
+ pivot_row_length = pfree - pivot_row_start ;
+ if (pivot_row_length > 0)
+ {
+ /* pick the "pivot" row arbitrarily (first row in col) */
+ pivot_row = A [Col [pivot_col].start] ;
+ DEBUG3 (("Pivotal row is %d\n", pivot_row)) ;
+ }
+ else
+ {
+ /* there is no pivot row, since it is of zero length */
+ pivot_row = EMPTY ;
+ ASSERT (pivot_row_length == 0) ;
+ }
+ ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;
+
+ /* === Approximate degree computation =============================== */
+
+ /* Here begins the computation of the approximate degree. The column */
+ /* score is the sum of the pivot row "length", plus the size of the */
+ /* set differences of each row in the column minus the pattern of the */
+ /* pivot row itself. The column ("thickness") itself is also */
+ /* excluded from the column score (we thus use an approximate */
+ /* external degree). */
+
+ /* The time taken by the following code (compute set differences, and */
+ /* add them up) is proportional to the size of the data structure */
+ /* being scanned - that is, the sum of the sizes of each column in */
+ /* the pivot row. Thus, the amortized time to compute a column score */
+ /* is proportional to the size of that column (where size, in this */
+ /* context, is the column "length", or the number of row indices */
+ /* in that column). The number of row indices in a column is */
+ /* monotonically non-decreasing, from the length of the original */
+ /* column on input to colamd. */
+
+ /* === Compute set differences ====================================== */
+
+ DEBUG3 (("** Computing set differences phase. **\n")) ;
+
+ /* pivot row is currently dead - it will be revived later. */
+
+ DEBUG3 (("Pivot row: ")) ;
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ DEBUG3 (("Col: %d\n", col)) ;
+
+ /* clear tags used to construct pivot row pattern */
+ col_thickness = -Col [col].shared1.thickness ;
+ ASSERT (col_thickness > 0) ;
+ Col [col].shared1.thickness = col_thickness ;
+
+ /* === Remove column from degree list =========================== */
+
+ cur_score = Col [col].shared2.score ;
+ prev_col = Col [col].shared3.prev ;
+ next_col = Col [col].shared4.degree_next ;
+ ASSERT (cur_score >= 0) ;
+ ASSERT (cur_score <= n_col) ;
+ ASSERT (cur_score >= EMPTY) ;
+ if (prev_col == EMPTY)
+ {
+ head [cur_score] = next_col ;
+ }
+ else
+ {
+ Col [prev_col].shared4.degree_next = next_col ;
+ }
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = prev_col ;
+ }
+
+ /* === Scan the column ========================================== */
+
+ cp = &A [Col [col].start] ;
+ cp_end = cp + Col [col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ continue ;
+ }
+ ASSERT (row != pivot_row) ;
+ set_difference = row_mark - tag_mark ;
+ /* check if the row has been seen yet */
+ if (set_difference < 0)
+ {
+ ASSERT (Row [row].shared1.degree <= max_deg) ;
+ set_difference = Row [row].shared1.degree ;
+ }
+ /* subtract column thickness from this row's set difference */
+ set_difference -= col_thickness ;
+ ASSERT (set_difference >= 0) ;
+ /* absorb this row if the set difference becomes zero */
+ if (set_difference == 0 && aggressive)
+ {
+ DEBUG3 (("aggressive absorption. Row: %d\n", row)) ;
+ KILL_ROW (row) ;
+ }
+ else
+ {
+ /* save the new mark */
+ Row [row].shared2.mark = set_difference + tag_mark ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k-pivot_row_degree, max_deg) ;
+#endif /* NDEBUG */
+
+ /* === Add up set differences for each column ======================= */
+
+ DEBUG3 (("** Adding set differences phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ hash = 0 ;
+ cur_score = 0 ;
+ cp = &A [Col [col].start] ;
+ /* compact the column */
+ new_cp = cp ;
+ cp_end = cp + Col [col].length ;
+
+ DEBUG4 (("Adding set diffs for Col: %d.\n", col)) ;
+
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ ASSERT(row >= 0 && row < n_row) ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ DEBUG4 ((" Row %d, dead\n", row)) ;
+ continue ;
+ }
+ DEBUG4 ((" Row %d, set diff %d\n", row, row_mark-tag_mark));
+ ASSERT (row_mark >= tag_mark) ;
+ /* compact the column */
+ *new_cp++ = row ;
+ /* compute hash function */
+ hash += row ;
+ /* add set difference */
+ cur_score += row_mark - tag_mark ;
+ /* integer overflow... */
+ cur_score = MIN (cur_score, n_col) ;
+ }
+
+ /* recompute the column's length */
+ Col [col].length = (Int) (new_cp - &A [Col [col].start]) ;
+
+ /* === Further mass elimination ================================= */
+
+ if (Col [col].length == 0)
+ {
+ DEBUG4 (("further mass elimination. Col: %d\n", col)) ;
+ /* nothing left but the pivot row in this column */
+ KILL_PRINCIPAL_COL (col) ;
+ pivot_row_degree -= Col [col].shared1.thickness ;
+ ASSERT (pivot_row_degree >= 0) ;
+ /* order it */
+ Col [col].shared2.order = k ;
+ /* increment order count by column thickness */
+ k += Col [col].shared1.thickness ;
+ }
+ else
+ {
+ /* === Prepare for supercolumn detection ==================== */
+
+ DEBUG4 (("Preparing supercol detection for Col: %d.\n", col)) ;
+
+ /* save score so far */
+ Col [col].shared2.score = cur_score ;
+
+ /* add column to hash table, for supercolumn detection */
+ hash %= n_col + 1 ;
+
+ DEBUG4 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ;
+ ASSERT (((Int) hash) <= n_col) ;
+
+ head_column = head [hash] ;
+ if (head_column > EMPTY)
+ {
+ /* degree list "hash" is non-empty, use prev (shared3) of */
+ /* first column in degree list as head of hash bucket */
+ first_col = Col [head_column].shared3.headhash ;
+ Col [head_column].shared3.headhash = col ;
+ }
+ else
+ {
+ /* degree list "hash" is empty, use head as hash bucket */
+ first_col = - (head_column + 2) ;
+ head [hash] = - (col + 2) ;
+ }
+ Col [col].shared4.hash_next = first_col ;
+
+ /* save hash function in Col [col].shared3.hash */
+ Col [col].shared3.hash = (Int) hash ;
+ ASSERT (COL_IS_ALIVE (col)) ;
+ }
+ }
+
+ /* The approximate external column degree is now computed. */
+
+ /* === Supercolumn detection ======================================== */
+
+ DEBUG3 (("** Supercolumn detection phase. **\n")) ;
+
+ detect_super_cols (
+
+#ifndef NDEBUG
+ n_col, Row,
+#endif /* NDEBUG */
+
+ Col, A, head, pivot_row_start, pivot_row_length) ;
+
+ /* === Kill the pivotal column ====================================== */
+
+ KILL_PRINCIPAL_COL (pivot_col) ;
+
+ /* === Clear mark =================================================== */
+
+ tag_mark = clear_mark (tag_mark+max_deg+1, max_mark, n_row, Row) ;
+
+#ifndef NDEBUG
+ DEBUG3 (("check3\n")) ;
+ debug_mark (n_row, Row, tag_mark, max_mark) ;
+#endif /* NDEBUG */
+
+ /* === Finalize the new pivot row, and column scores ================ */
+
+ DEBUG3 (("** Finalize scores phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ /* compact the pivot row */
+ new_rp = rp ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ /* skip dead columns */
+ if (COL_IS_DEAD (col))
+ {
+ continue ;
+ }
+ *new_rp++ = col ;
+ /* add new pivot row to column */
+ A [Col [col].start + (Col [col].length++)] = pivot_row ;
+
+ /* retrieve score so far and add on pivot row's degree. */
+ /* (we wait until here for this in case the pivot */
+ /* row's degree was reduced due to mass elimination). */
+ cur_score = Col [col].shared2.score + pivot_row_degree ;
+
+ /* calculate the max possible score as the number of */
+ /* external columns minus the 'k' value minus the */
+ /* columns thickness */
+ max_score = n_col - k - Col [col].shared1.thickness ;
+
+ /* make the score the external degree of the union-of-rows */
+ cur_score -= Col [col].shared1.thickness ;
+
+ /* make sure score is less or equal than the max score */
+ cur_score = MIN (cur_score, max_score) ;
+ ASSERT (cur_score >= 0) ;
+
+ /* store updated score */
+ Col [col].shared2.score = cur_score ;
+
+ /* === Place column back in degree list ========================= */
+
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (cur_score >= 0) ;
+ ASSERT (cur_score <= n_col) ;
+ ASSERT (head [cur_score] >= EMPTY) ;
+ next_col = head [cur_score] ;
+ Col [col].shared4.degree_next = next_col ;
+ Col [col].shared3.prev = EMPTY ;
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = col ;
+ }
+ head [cur_score] = col ;
+
+ /* see if this score is less than current min */
+ min_score = MIN (min_score, cur_score) ;
+
+ }
+
+#ifndef NDEBUG
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k, max_deg) ;
+#endif /* NDEBUG */
+
+ /* === Resurrect the new pivot row ================================== */
+
+ if (pivot_row_degree > 0)
+ {
+ /* update pivot row length to reflect any cols that were killed */
+ /* during super-col detection and mass elimination */
+ Row [pivot_row].start = pivot_row_start ;
+ Row [pivot_row].length = (Int) (new_rp - &A[pivot_row_start]) ;
+ ASSERT (Row [pivot_row].length > 0) ;
+ Row [pivot_row].shared1.degree = pivot_row_degree ;
+ Row [pivot_row].shared2.mark = 0 ;
+ /* pivot row is no longer dead */
+
+ DEBUG1 (("Resurrect Pivot_row %d deg: %d\n",
+ pivot_row, pivot_row_degree)) ;
+ }
+ }
+
+ /* === All principal columns have now been ordered ====================== */
+
+ return (ngarbage) ;
+}
+
+
+/* ========================================================================== */
+/* === order_children ======================================================= */
+/* ========================================================================== */
+
+/*
+ The find_ordering routine has ordered all of the principal columns (the
+ representatives of the supercolumns). The non-principal columns have not
+ yet been ordered. This routine orders those columns by walking up the
+ parent tree (a column is a child of the column which absorbed it). The
+ final permutation vector is then placed in p [0 ... n_col-1], with p [0]
+ being the first column, and p [n_col-1] being the last. It doesn't look
+ like it at first glance, but be assured that this routine takes time linear
+ in the number of columns. Although not immediately obvious, the time
+ taken by this routine is O (n_col), that is, linear in the number of
+ columns. Not user-callable.
+*/
+
+PRIVATE void order_children
+(
+ /* === Parameters ======================================================= */
+
+ Int n_col, /* number of columns of A */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int p [] /* p [0 ... n_col-1] is the column permutation*/
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ; /* loop counter for all columns */
+ Int c ; /* column index */
+ Int parent ; /* index of column's parent */
+ Int order ; /* column's order */
+
+ /* === Order each non-principal column ================================== */
+
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* find an un-ordered non-principal column */
+ ASSERT (COL_IS_DEAD (i)) ;
+ if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == EMPTY)
+ {
+ parent = i ;
+ /* once found, find its principal parent */
+ do
+ {
+ parent = Col [parent].shared1.parent ;
+ } while (!COL_IS_DEAD_PRINCIPAL (parent)) ;
+
+ /* now, order all un-ordered non-principal columns along path */
+ /* to this parent. collapse tree at the same time */
+ c = i ;
+ /* get order of parent */
+ order = Col [parent].shared2.order ;
+
+ do
+ {
+ ASSERT (Col [c].shared2.order == EMPTY) ;
+
+ /* order this column */
+ Col [c].shared2.order = order++ ;
+ /* collaps tree */
+ Col [c].shared1.parent = parent ;
+
+ /* get immediate parent of this column */
+ c = Col [c].shared1.parent ;
+
+ /* continue until we hit an ordered column. There are */
+ /* guarranteed not to be anymore unordered columns */
+ /* above an ordered column */
+ } while (Col [c].shared2.order == EMPTY) ;
+
+ /* re-order the super_col parent to largest order for this group */
+ Col [parent].shared2.order = order ;
+ }
+ }
+
+ /* === Generate the permutation ========================================= */
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ p [Col [c].shared2.order] = c ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === detect_super_cols ==================================================== */
+/* ========================================================================== */
+
+/*
+ Detects supercolumns by finding matches between columns in the hash buckets.
+ Check amongst columns in the set A [row_start ... row_start + row_length-1].
+ The columns under consideration are currently *not* in the degree lists,
+ and have already been placed in the hash buckets.
+
+ The hash bucket for columns whose hash function is equal to h is stored
+ as follows:
+
+ if head [h] is >= 0, then head [h] contains a degree list, so:
+
+ head [h] is the first column in degree bucket h.
+ Col [head [h]].headhash gives the first column in hash bucket h.
+
+ otherwise, the degree list is empty, and:
+
+ -(head [h] + 2) is the first column in hash bucket h.
+
+ For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous
+ column" pointer. Col [c].shared3.hash is used instead as the hash number
+ for that column. The value of Col [c].shared4.hash_next is the next column
+ in the same hash bucket.
+
+ Assuming no, or "few" hash collisions, the time taken by this routine is
+ linear in the sum of the sizes (lengths) of each column whose score has
+ just been computed in the approximate degree computation.
+ Not user-callable.
+*/
+
+PRIVATE void detect_super_cols
+(
+ /* === Parameters ======================================================= */
+
+#ifndef NDEBUG
+ /* these two parameters are only needed when debugging is enabled: */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+#endif /* NDEBUG */
+
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* row indices of A */
+ Int head [], /* head of degree lists and hash buckets */
+ Int row_start, /* pointer to set of columns to check */
+ Int row_length /* number of columns to check */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int hash ; /* hash value for a column */
+ Int *rp ; /* pointer to a row */
+ Int c ; /* a column index */
+ Int super_c ; /* column index of the column to absorb into */
+ Int *cp1 ; /* column pointer for column super_c */
+ Int *cp2 ; /* column pointer for column c */
+ Int length ; /* length of column super_c */
+ Int prev_c ; /* column preceding c in hash bucket */
+ Int i ; /* loop counter */
+ Int *rp_end ; /* pointer to the end of the row */
+ Int col ; /* a column index in the row to check */
+ Int head_column ; /* first column in hash bucket or degree list */
+ Int first_col ; /* first column in hash bucket */
+
+ /* === Consider each column in the row ================================== */
+
+ rp = &A [row_start] ;
+ rp_end = rp + row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ if (COL_IS_DEAD (col))
+ {
+ continue ;
+ }
+
+ /* get hash number for this column */
+ hash = Col [col].shared3.hash ;
+ ASSERT (hash <= n_col) ;
+
+ /* === Get the first column in this hash bucket ===================== */
+
+ head_column = head [hash] ;
+ if (head_column > EMPTY)
+ {
+ first_col = Col [head_column].shared3.headhash ;
+ }
+ else
+ {
+ first_col = - (head_column + 2) ;
+ }
+
+ /* === Consider each column in the hash bucket ====================== */
+
+ for (super_c = first_col ; super_c != EMPTY ;
+ super_c = Col [super_c].shared4.hash_next)
+ {
+ ASSERT (COL_IS_ALIVE (super_c)) ;
+ ASSERT (Col [super_c].shared3.hash == hash) ;
+ length = Col [super_c].length ;
+
+ /* prev_c is the column preceding column c in the hash bucket */
+ prev_c = super_c ;
+
+ /* === Compare super_c with all columns after it ================ */
+
+ for (c = Col [super_c].shared4.hash_next ;
+ c != EMPTY ; c = Col [c].shared4.hash_next)
+ {
+ ASSERT (c != super_c) ;
+ ASSERT (COL_IS_ALIVE (c)) ;
+ ASSERT (Col [c].shared3.hash == hash) ;
+
+ /* not identical if lengths or scores are different */
+ if (Col [c].length != length ||
+ Col [c].shared2.score != Col [super_c].shared2.score)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* compare the two columns */
+ cp1 = &A [Col [super_c].start] ;
+ cp2 = &A [Col [c].start] ;
+
+ for (i = 0 ; i < length ; i++)
+ {
+ /* the columns are "clean" (no dead rows) */
+ ASSERT (ROW_IS_ALIVE (*cp1)) ;
+ ASSERT (ROW_IS_ALIVE (*cp2)) ;
+ /* row indices will same order for both supercols, */
+ /* no gather scatter nessasary */
+ if (*cp1++ != *cp2++)
+ {
+ break ;
+ }
+ }
+
+ /* the two columns are different if the for-loop "broke" */
+ if (i != length)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* === Got it! two columns are identical =================== */
+
+ ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;
+
+ Col [super_c].shared1.thickness += Col [c].shared1.thickness ;
+ Col [c].shared1.parent = super_c ;
+ KILL_NON_PRINCIPAL_COL (c) ;
+ /* order c later, in order_children() */
+ Col [c].shared2.order = EMPTY ;
+ /* remove c from hash bucket */
+ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;
+ }
+ }
+
+ /* === Empty this hash bucket ======================================= */
+
+ if (head_column > EMPTY)
+ {
+ /* corresponding degree list "hash" is not empty */
+ Col [head_column].shared3.headhash = EMPTY ;
+ }
+ else
+ {
+ /* corresponding degree list "hash" is empty */
+ head [hash] = EMPTY ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === garbage_collection =================================================== */
+/* ========================================================================== */
+
+/*
+ Defragments and compacts columns and rows in the workspace A. Used when
+ all avaliable memory has been used while performing row merging. Returns
+ the index of the first free position in A, after garbage collection. The
+ time taken by this routine is linear is the size of the array A, which is
+ itself linear in the number of nonzeros in the input matrix.
+ Not user-callable.
+*/
+
+PRIVATE Int garbage_collection /* returns the new value of pfree */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows */
+ Int n_col, /* number of columns */
+ Colamd_Row Row [], /* row info */
+ Colamd_Col Col [], /* column info */
+ Int A [], /* A [0 ... Alen-1] holds the matrix */
+ Int *pfree /* &A [0] ... pfree is in use */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int *psrc ; /* source pointer */
+ Int *pdest ; /* destination pointer */
+ Int j ; /* counter */
+ Int r ; /* a row index */
+ Int c ; /* a column index */
+ Int length ; /* length of a row or column */
+
+#ifndef NDEBUG
+ Int debug_rows ;
+ DEBUG2 (("Defrag..\n")) ;
+ for (psrc = &A[0] ; psrc < pfree ; psrc++) ASSERT (*psrc >= 0) ;
+ debug_rows = 0 ;
+#endif /* NDEBUG */
+
+ /* === Defragment the columns =========================================== */
+
+ pdest = &A[0] ;
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ psrc = &A [Col [c].start] ;
+
+ /* move and compact the column */
+ ASSERT (pdest <= psrc) ;
+ Col [c].start = (Int) (pdest - &A [0]) ;
+ length = Col [c].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ r = *psrc++ ;
+ if (ROW_IS_ALIVE (r))
+ {
+ *pdest++ = r ;
+ }
+ }
+ Col [c].length = (Int) (pdest - &A [Col [c].start]) ;
+ }
+ }
+
+ /* === Prepare to defragment the rows =================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_DEAD (r) || (Row [r].length == 0))
+ {
+ /* This row is already dead, or is of zero length. Cannot compact
+ * a row of zero length, so kill it. NOTE: in the current version,
+ * there are no zero-length live rows. Kill the row (for the first
+ * time, or again) just to be safe. */
+ KILL_ROW (r) ;
+ }
+ else
+ {
+ /* save first column index in Row [r].shared2.first_column */
+ psrc = &A [Row [r].start] ;
+ Row [r].shared2.first_column = *psrc ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ /* flag the start of the row with the one's complement of row */
+ *psrc = ONES_COMPLEMENT (r) ;
+#ifndef NDEBUG
+ debug_rows++ ;
+#endif /* NDEBUG */
+ }
+ }
+
+ /* === Defragment the rows ============================================== */
+
+ psrc = pdest ;
+ while (psrc < pfree)
+ {
+ /* find a negative number ... the start of a row */
+ if (*psrc++ < 0)
+ {
+ psrc-- ;
+ /* get the row index */
+ r = ONES_COMPLEMENT (*psrc) ;
+ ASSERT (r >= 0 && r < n_row) ;
+ /* restore first column index */
+ *psrc = Row [r].shared2.first_column ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ ASSERT (Row [r].length > 0) ;
+ /* move and compact the row */
+ ASSERT (pdest <= psrc) ;
+ Row [r].start = (Int) (pdest - &A [0]) ;
+ length = Row [r].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ c = *psrc++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ *pdest++ = c ;
+ }
+ }
+ Row [r].length = (Int) (pdest - &A [Row [r].start]) ;
+ ASSERT (Row [r].length > 0) ;
+#ifndef NDEBUG
+ debug_rows-- ;
+#endif /* NDEBUG */
+ }
+ }
+ /* ensure we found all the rows */
+ ASSERT (debug_rows == 0) ;
+
+ /* === Return the new value of pfree ==================================== */
+
+ return ((Int) (pdest - &A [0])) ;
+}
+
+
+/* ========================================================================== */
+/* === clear_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ Clears the Row [].shared2.mark array, and returns the new tag_mark.
+ Return value is the new tag_mark. Not user-callable.
+*/
+
+PRIVATE Int clear_mark /* return the new value for tag_mark */
+(
+ /* === Parameters ======================================================= */
+
+ Int tag_mark, /* new value of tag_mark */
+ Int max_mark, /* max allowed value of tag_mark */
+
+ Int n_row, /* number of rows in A */
+ Colamd_Row Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+
+ if (tag_mark <= 0 || tag_mark >= max_mark)
+ {
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ Row [r].shared2.mark = 0 ;
+ }
+ }
+ tag_mark = 1 ;
+ }
+
+ return (tag_mark) ;
+}
+
+
+/* ========================================================================== */
+/* === print_report ========================================================= */
+/* ========================================================================== */
+
+PRIVATE void print_report
+(
+ char *method,
+ Int stats [COLAMD_STATS]
+)
+{
+
+ Int i1, i2, i3 ;
+
+ PRINTF (("\n%s version %d.%d, %s: ", method,
+ COLAMD_MAIN_VERSION, COLAMD_SUB_VERSION, COLAMD_DATE)) ;
+
+ if (!stats)
+ {
+ PRINTF (("No statistics available.\n")) ;
+ return ;
+ }
+
+ i1 = stats [COLAMD_INFO1] ;
+ i2 = stats [COLAMD_INFO2] ;
+ i3 = stats [COLAMD_INFO3] ;
+
+ if (stats [COLAMD_STATUS] >= 0)
+ {
+ PRINTF (("OK. ")) ;
+ }
+ else
+ {
+ PRINTF (("ERROR. ")) ;
+ }
+
+ switch (stats [COLAMD_STATUS])
+ {
+
+ case COLAMD_OK_BUT_JUMBLED:
+
+ PRINTF(("Matrix has unsorted or duplicate row indices.\n")) ;
+
+ PRINTF(("%s: number of duplicate or out-of-order row indices: %d\n",
+ method, i3)) ;
+
+ PRINTF(("%s: last seen duplicate or out-of-order row index: %d\n",
+ method, INDEX (i2))) ;
+
+ PRINTF(("%s: last seen in column: %d",
+ method, INDEX (i1))) ;
+
+ /* no break - fall through to next case instead */
+
+ case COLAMD_OK:
+
+ PRINTF(("\n")) ;
+
+ PRINTF(("%s: number of dense or empty rows ignored: %d\n",
+ method, stats [COLAMD_DENSE_ROW])) ;
+
+ PRINTF(("%s: number of dense or empty columns ignored: %d\n",
+ method, stats [COLAMD_DENSE_COL])) ;
+
+ PRINTF(("%s: number of garbage collections performed: %d\n",
+ method, stats [COLAMD_DEFRAG_COUNT])) ;
+ break ;
+
+ case COLAMD_ERROR_A_not_present:
+
+ PRINTF(("Array A (row indices of matrix) not present.\n")) ;
+ break ;
+
+ case COLAMD_ERROR_p_not_present:
+
+ PRINTF(("Array p (column pointers for matrix) not present.\n")) ;
+ break ;
+
+ case COLAMD_ERROR_nrow_negative:
+
+ PRINTF(("Invalid number of rows (%d).\n", i1)) ;
+ break ;
+
+ case COLAMD_ERROR_ncol_negative:
+
+ PRINTF(("Invalid number of columns (%d).\n", i1)) ;
+ break ;
+
+ case COLAMD_ERROR_nnz_negative:
+
+ PRINTF(("Invalid number of nonzero entries (%d).\n", i1)) ;
+ break ;
+
+ case COLAMD_ERROR_p0_nonzero:
+
+ PRINTF(("Invalid column pointer, p [0] = %d, must be zero.\n", i1));
+ break ;
+
+ case COLAMD_ERROR_A_too_small:
+
+ PRINTF(("Array A too small.\n")) ;
+ PRINTF((" Need Alen >= %d, but given only Alen = %d.\n",
+ i1, i2)) ;
+ break ;
+
+ case COLAMD_ERROR_col_length_negative:
+
+ PRINTF
+ (("Column %d has a negative number of nonzero entries (%d).\n",
+ INDEX (i1), i2)) ;
+ break ;
+
+ case COLAMD_ERROR_row_index_out_of_bounds:
+
+ PRINTF
+ (("Row index (row %d) out of bounds (%d to %d) in column %d.\n",
+ INDEX (i2), INDEX (0), INDEX (i3-1), INDEX (i1))) ;
+ break ;
+
+ case COLAMD_ERROR_out_of_memory:
+
+ PRINTF(("Out of memory.\n")) ;
+ break ;
+
+ /* v2.4: internal-error case deleted */
+ }
+}
+
+
+
+
+/* ========================================================================== */
+/* === colamd debugging routines ============================================ */
+/* ========================================================================== */
+
+/* When debugging is disabled, the remainder of this file is ignored. */
+
+#ifndef NDEBUG
+
+
+/* ========================================================================== */
+/* === debug_structures ===================================================== */
+/* ========================================================================== */
+
+/*
+ At this point, all empty rows and columns are dead. All live columns
+ are "clean" (containing no dead rows) and simplicial (no supercolumns
+ yet). Rows may contain dead columns, but all live rows contain at
+ least one live column.
+*/
+
+PRIVATE void debug_structures
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int n_col2
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ;
+ Int c ;
+ Int *cp ;
+ Int *cp_end ;
+ Int len ;
+ Int score ;
+ Int r ;
+ Int *rp ;
+ Int *rp_end ;
+ Int deg ;
+
+ /* === Check A, Row, and Col ============================================ */
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ len = Col [c].length ;
+ score = Col [c].shared2.score ;
+ DEBUG4 (("initial live col %5d %5d %5d\n", c, len, score)) ;
+ ASSERT (len > 0) ;
+ ASSERT (score >= 0) ;
+ ASSERT (Col [c].shared1.thickness == 1) ;
+ cp = &A [Col [c].start] ;
+ cp_end = cp + len ;
+ while (cp < cp_end)
+ {
+ r = *cp++ ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ }
+ }
+ else
+ {
+ i = Col [c].shared2.order ;
+ ASSERT (i >= n_col2 && i < n_col) ;
+ }
+ }
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ i = 0 ;
+ len = Row [r].length ;
+ deg = Row [r].shared1.degree ;
+ ASSERT (len > 0) ;
+ ASSERT (deg > 0) ;
+ rp = &A [Row [r].start] ;
+ rp_end = rp + len ;
+ while (rp < rp_end)
+ {
+ c = *rp++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ i++ ;
+ }
+ }
+ ASSERT (i > 0) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_deg_lists ====================================================== */
+/* ========================================================================== */
+
+/*
+ Prints the contents of the degree lists. Counts the number of columns
+ in the degree list and compares it to the total it should have. Also
+ checks the row degrees.
+*/
+
+PRIVATE void debug_deg_lists
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int head [],
+ Int min_score,
+ Int should,
+ Int max_deg
+)
+{
+ /* === Local variables ================================================== */
+
+ Int deg ;
+ Int col ;
+ Int have ;
+ Int row ;
+
+ /* === Check the degree lists =========================================== */
+
+ if (n_col > 10000 && colamd_debug <= 0)
+ {
+ return ;
+ }
+ have = 0 ;
+ DEBUG4 (("Degree lists: %d\n", min_score)) ;
+ for (deg = 0 ; deg <= n_col ; deg++)
+ {
+ col = head [deg] ;
+ if (col == EMPTY)
+ {
+ continue ;
+ }
+ DEBUG4 (("%d:", deg)) ;
+ while (col != EMPTY)
+ {
+ DEBUG4 ((" %d", col)) ;
+ have += Col [col].shared1.thickness ;
+ ASSERT (COL_IS_ALIVE (col)) ;
+ col = Col [col].shared4.degree_next ;
+ }
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("should %d have %d\n", should, have)) ;
+ ASSERT (should == have) ;
+
+ /* === Check the row degrees ============================================ */
+
+ if (n_row > 10000 && colamd_debug <= 0)
+ {
+ return ;
+ }
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (ROW_IS_ALIVE (row))
+ {
+ ASSERT (Row [row].shared1.degree <= max_deg) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ Ensures that the tag_mark is less that the maximum and also ensures that
+ each entry in the mark array is less than the tag mark.
+*/
+
+PRIVATE void debug_mark
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Colamd_Row Row [],
+ Int tag_mark,
+ Int max_mark
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+
+ /* === Check the Row marks ============================================== */
+
+ ASSERT (tag_mark > 0 && tag_mark <= max_mark) ;
+ if (n_row > 10000 && colamd_debug <= 0)
+ {
+ return ;
+ }
+ for (r = 0 ; r < n_row ; r++)
+ {
+ ASSERT (Row [r].shared2.mark < tag_mark) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_matrix ========================================================= */
+/* ========================================================================== */
+
+/*
+ Prints out the contents of the columns and the rows.
+*/
+
+PRIVATE void debug_matrix
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A []
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+ Int c ;
+ Int *rp ;
+ Int *rp_end ;
+ Int *cp ;
+ Int *cp_end ;
+
+ /* === Dump the rows and columns of the matrix ========================== */
+
+ if (colamd_debug < 3)
+ {
+ return ;
+ }
+ DEBUG3 (("DUMP MATRIX:\n")) ;
+ for (r = 0 ; r < n_row ; r++)
+ {
+ DEBUG3 (("Row %d alive? %d\n", r, ROW_IS_ALIVE (r))) ;
+ if (ROW_IS_DEAD (r))
+ {
+ continue ;
+ }
+ DEBUG3 (("start %d length %d degree %d\n",
+ Row [r].start, Row [r].length, Row [r].shared1.degree)) ;
+ rp = &A [Row [r].start] ;
+ rp_end = rp + Row [r].length ;
+ while (rp < rp_end)
+ {
+ c = *rp++ ;
+ DEBUG4 ((" %d col %d\n", COL_IS_ALIVE (c), c)) ;
+ }
+ }
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ DEBUG3 (("Col %d alive? %d\n", c, COL_IS_ALIVE (c))) ;
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ DEBUG3 (("start %d length %d shared1 %d shared2 %d\n",
+ Col [c].start, Col [c].length,
+ Col [c].shared1.thickness, Col [c].shared2.score)) ;
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ r = *cp++ ;
+ DEBUG4 ((" %d row %d\n", ROW_IS_ALIVE (r), r)) ;
+ }
+ }
+}
+
+PRIVATE void colamd_get_debug
+(
+ char *method
+)
+{
+ FILE *f ;
+ colamd_debug = 0 ; /* no debug printing */
+ f = fopen ("debug", "r") ;
+ if (f == (FILE *) NULL)
+ {
+ colamd_debug = 0 ;
+ }
+ else
+ {
+ fscanf (f, "%d", &colamd_debug) ;
+ fclose (f) ;
+ }
+ DEBUG0 (("%s: debug version, D = %d (THIS WILL BE SLOW!)\n",
+ method, colamd_debug)) ;
+}
+
+#endif /* NDEBUG */
diff --git a/COLAMD/Source/colamd_global.c b/COLAMD/Source/colamd_global.c
new file mode 100644
index 0000000..4d1ae22
--- /dev/null
+++ b/COLAMD/Source/colamd_global.c
@@ -0,0 +1,24 @@
+/* ========================================================================== */
+/* === colamd_global.c ====================================================== */
+/* ========================================================================== */
+
+/* ----------------------------------------------------------------------------
+ * COLAMD, Copyright (C) 2007, Timothy A. Davis.
+ * See License.txt for the Version 2.1 of the GNU Lesser General Public License
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* Global variables for COLAMD */
+
+#ifndef NPRINT
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+int (*colamd_printf) (const char *, ...) = mexPrintf ;
+#else
+#include <stdio.h>
+int (*colamd_printf) (const char *, ...) = printf ;
+#endif
+#else
+int (*colamd_printf) (const char *, ...) = ((void *) 0) ;
+#endif
+
diff --git a/CSparse/Demo/Makefile b/CSparse/Demo/Makefile
new file mode 100644
index 0000000..742ed8a
--- /dev/null
+++ b/CSparse/Demo/Makefile
@@ -0,0 +1,39 @@
+CC = cc
+CFLAGS = -O
+
+I = -I../Include
+
+CS = ../Lib/libcsparse.a
+
+all: lib cs_demo1 cs_demo2 cs_demo3
+ - ./cs_demo1 < ../Matrix/t1
+ - ./cs_demo2 < ../Matrix/t1
+ - ./cs_demo2 < ../Matrix/ash219
+ - ./cs_demo2 < ../Matrix/bcsstk01
+ - ./cs_demo2 < ../Matrix/fs_183_1
+ - ./cs_demo2 < ../Matrix/mbeacxc
+ - ./cs_demo2 < ../Matrix/west0067
+ - ./cs_demo2 < ../Matrix/lp_afiro
+ - ./cs_demo2 < ../Matrix/bcsstk16
+ - ./cs_demo3 < ../Matrix/bcsstk01
+ - ./cs_demo3 < ../Matrix/bcsstk16
+
+lib:
+ ( cd ../Lib ; $(MAKE) )
+
+cs_demo1: lib cs_demo1.c Makefile
+ $(CC) $(CFLAGS) $(I) -o cs_demo1 cs_demo1.c $(CS) -lm
+
+cs_demo2: lib cs_demo2.c cs_demo.c cs_demo.h Makefile
+ $(CC) $(CFLAGS) $(I) -o cs_demo2 cs_demo2.c cs_demo.c $(CS) -lm
+
+cs_demo3: lib cs_demo3.c cs_demo.c cs_demo.h Makefile
+ $(CC) $(CFLAGS) $(I) -o cs_demo3 cs_demo3.c cs_demo.c $(CS) -lm
+
+clean:
+ rm -f *.o
+
+purge: distclean
+
+distclean: clean
+ rm -f cs_demo1 cs_demo2 cs_demo3 *.a
diff --git a/CSparse/Demo/README.txt b/CSparse/Demo/README.txt
new file mode 100644
index 0000000..ea7385f
--- /dev/null
+++ b/CSparse/Demo/README.txt
@@ -0,0 +1,4 @@
+CSparse/Demo: to compile a run the demos, just type "make" in this directory.
+The printed residuals should all be small, except for the mbeacxc matrix
+(which is numerically and structurally singular), and ash219 (which is a
+least-squares problem). See cs_demo.out for the proper output of "make".
diff --git a/CSparse/Demo/cs_demo.c b/CSparse/Demo/cs_demo.c
new file mode 100644
index 0000000..4e85757
--- /dev/null
+++ b/CSparse/Demo/cs_demo.c
@@ -0,0 +1,286 @@
+#include "cs_demo.h"
+#include <time.h>
+/* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */
+static int is_sym (cs *A)
+{
+ int is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ;
+ if (m != n) return (0) ;
+ is_upper = 1 ;
+ is_lower = 1 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ if (Ai [p] > j) is_upper = 0 ;
+ if (Ai [p] < j) is_lower = 0 ;
+ }
+ }
+ return (is_upper ? 1 : (is_lower ? -1 : 0)) ;
+}
+
+/* true for off-diagonal entries */
+static int dropdiag (int i, int j, double aij, void *other) { return (i != j) ;}
+
+/* C = A + triu(A,1)' */
+static cs *make_sym (cs *A)
+{
+ cs *AT, *C ;
+ AT = cs_transpose (A, 1) ; /* AT = A' */
+ cs_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */
+ C = cs_add (A, AT, 1, 1) ; /* C = A+AT */
+ cs_spfree (AT) ;
+ return (C) ;
+}
+
+/* create a right-hand side */
+static void rhs (double *x, double *b, int m)
+{
+ int i ;
+ for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ;
+ for (i = 0 ; i < m ; i++) x [i] = b [i] ;
+}
+
+/* infinity-norm of x */
+static double norm (double *x, int n)
+{
+ int i ;
+ double normx = 0 ;
+ for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, fabs (x [i])) ;
+ return (normx) ;
+}
+
+/* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */
+static void print_resid (int ok, cs *A, double *x, double *b, double *resid)
+{
+ int i, m, n ;
+ if (!ok) { printf (" (failed)\n") ; return ; }
+ m = A->m ; n = A->n ;
+ for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */
+ cs_gaxpy (A, x, resid) ; /* resid = resid + A*x */
+ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 :
+ (cs_norm (A) * norm (x,n) + norm (b,m)))) ;
+}
+
+static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; }
+static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; }
+
+static void print_order (int order)
+{
+ switch (order)
+ {
+ case 0: printf ("natural ") ; break ;
+ case 1: printf ("amd(A+A') ") ; break ;
+ case 2: printf ("amd(S'*S) ") ; break ;
+ case 3: printf ("amd(A'*A) ") ; break ;
+ }
+}
+
+/* read a problem from a file */
+problem *get_problem (FILE *f, double tol)
+{
+ cs *T, *A, *C ;
+ int sym, m, n, mn, nz1, nz2 ;
+ problem *Prob ;
+ Prob = cs_calloc (1, sizeof (problem)) ;
+ if (!Prob) return (NULL) ;
+ T = cs_load (f) ; /* load triplet matrix T from a file */
+ Prob->A = A = cs_compress (T) ; /* A = compressed-column form of T */
+ cs_spfree (T) ; /* clear T */
+ if (!cs_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */
+ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */
+ m = A->m ; n = A->n ;
+ mn = CS_MAX (m,n) ;
+ nz1 = A->p [n] ;
+ cs_dropzeros (A) ; /* drop zero entries */
+ nz2 = A->p [n] ;
+ if (tol > 0) cs_droptol (A, tol) ; /* drop tiny entries (just to test) */
+ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */
+ if (!C) return (free_problem (Prob)) ;
+ printf ("\n--- Matrix: %d-by-%d, nnz: %d (sym: %d: nnz %d), norm: %8.2e\n",
+ m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_norm (C)) ;
+ if (nz1 != nz2) printf ("zero entries dropped: %d\n", nz1 - nz2) ;
+ if (nz2 != A->p [n]) printf ("tiny entries dropped: %d\n", nz2 - A->p [n]) ;
+ Prob->b = cs_malloc (mn, sizeof (double)) ;
+ Prob->x = cs_malloc (mn, sizeof (double)) ;
+ Prob->resid = cs_malloc (mn, sizeof (double)) ;
+ return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ;
+}
+
+/* free a problem */
+problem *free_problem (problem *Prob)
+{
+ if (!Prob) return (NULL) ;
+ cs_spfree (Prob->A) ;
+ if (Prob->sym) cs_spfree (Prob->C) ;
+ cs_free (Prob->b) ;
+ cs_free (Prob->x) ;
+ cs_free (Prob->resid) ;
+ return (cs_free (Prob)) ;
+}
+
+/* solve a linear system using Cholesky, LU, and QR, with various orderings */
+int demo2 (problem *Prob)
+{
+ cs *A, *C ;
+ double *b, *x, *resid, t, tol ;
+ int k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ;
+ csd *D ;
+ if (!Prob) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ m = A->m ; n = A->n ;
+ tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */
+ D = cs_dmperm (C, 1) ; /* randomized dmperm analysis */
+ if (!D) return (0) ;
+ nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ;
+ sprank = rr [3] ;
+ for (ns = 0, k = 0 ; k < nb ; k++)
+ {
+ ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ;
+ }
+ printf ("blocks: %d singletons: %d structural rank: %d\n", nb, ns, sprank) ;
+ cs_dfree (D) ;
+ for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("QR ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/
+ for (order = 0 ; order <= 3 ; order++) /* try all orderings */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("LU ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_lusol (order, C, x, tol) ; /* solve Ax=b with LU */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (!Prob->sym) return (1) ;
+ for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("Chol ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ return (1) ;
+}
+
+/* free workspace for demo3 */
+static int done3 (int ok, css *S, csn *N, double *y, cs *W, cs *E, int *p)
+{
+ cs_sfree (S) ;
+ cs_nfree (N) ;
+ cs_free (y) ;
+ cs_spfree (W) ;
+ cs_spfree (E) ;
+ cs_free (p) ;
+ return (ok) ;
+}
+
+/* Cholesky update/downdate */
+int demo3 (problem *Prob)
+{
+ cs *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ;
+ int n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ;
+ double *b, *x, *resid, *y = NULL, *Lx, *Wx, s, t, t1 ;
+ css *S = NULL ;
+ csn *N = NULL ;
+ if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ n = A->n ;
+ if (!Prob->sym || n == 0) return (1) ;
+ rhs (x, b, n) ; /* compute right-hand side */
+ printf ("\nchol then update/downdate ") ;
+ print_order (1) ;
+ y = cs_malloc (n, sizeof (double)) ;
+ t = tic () ;
+ S = cs_schol (1, C) ; /* symbolic Chol, amd(A+A') */
+ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ;
+ t = tic () ;
+ N = cs_chol (C, S) ; /* numeric Cholesky */
+ printf ("numeric chol time %8.2f\n", toc (t)) ;
+ if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_lsolve (N->L, y) ; /* y = L\y */
+ cs_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ printf ("solve chol time %8.2f\n", toc (t)) ;
+ printf ("original: ") ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ k = n/2 ; /* construct W */
+ W = cs_spalloc (n, 1, n, 1, 0) ;
+ if (!W) return (done3 (0, S, N, y, W, E, p)) ;
+ Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ;
+ Wp = W->p ; Wi = W->i ; Wx = W->x ;
+ Wp [0] = 0 ;
+ p1 = Lp [k] ;
+ Wp [1] = Lp [k+1] - p1 ;
+ s = Lx [p1] ;
+ srand (1) ;
+ for ( ; p1 < Lp [k+1] ; p1++)
+ {
+ p2 = p1 - Lp [k] ;
+ Wi [p2] = Li [p1] ;
+ Wx [p2] = s * rand () / ((double) RAND_MAX) ;
+ }
+ t = tic () ;
+ ok = cs_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */
+ t1 = toc (t) ;
+ printf ("update: time: %8.2f\n", t1) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_lsolve (N->L, y) ; /* y = L\y */
+ cs_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ p = cs_pinv (S->pinv, n) ;
+ W2 = cs_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */
+ WT = cs_transpose (W2,1) ;
+ WW = cs_multiply (W2, WT) ;
+ cs_spfree (WT) ;
+ cs_spfree (W2) ;
+ E = cs_add (C, WW, 1, 1) ;
+ cs_spfree (WW) ;
+ if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("update: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ cs_nfree (N) ; /* clear N */
+ t = tic () ;
+ N = cs_chol (E, S) ; /* numeric Cholesky */
+ if (!N) return (done3 (0, S, N, y, W, E, p)) ;
+ cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_lsolve (N->L, y) ; /* y = L\y */
+ cs_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("rechol: time: %8.2f (incl solve) ", t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ t = tic () ;
+ ok = cs_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */
+ t1 = toc (t) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("downdate: time: %8.2f\n", t1) ;
+ t = tic () ;
+ cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_lsolve (N->L, y) ; /* y = L\y */
+ cs_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("downdate: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ return (done3 (1, S, N, y, W, E, p)) ;
+}
diff --git a/CSparse/Demo/cs_demo.h b/CSparse/Demo/cs_demo.h
new file mode 100644
index 0000000..a0e9e72
--- /dev/null
+++ b/CSparse/Demo/cs_demo.h
@@ -0,0 +1,15 @@
+#include "cs.h"
+typedef struct problem_struct
+{
+ cs *A ;
+ cs *C ;
+ int sym ;
+ double *x ;
+ double *b ;
+ double *resid ;
+} problem ;
+
+problem *get_problem (FILE *f, double tol) ;
+int demo2 (problem *Prob) ;
+int demo3 (problem *Prob) ;
+problem *free_problem (problem *Prob) ;
diff --git a/CSparse/Demo/cs_demo.out b/CSparse/Demo/cs_demo.out
new file mode 100644
index 0000000..c5771b4
--- /dev/null
+++ b/CSparse/Demo/cs_demo.out
@@ -0,0 +1,170 @@
+./cs_demo1 < ../Matrix/t1
+T:
+CSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : 3
+ 1 0 : 3.1
+ 3 3 : 1
+ 0 2 : 3.2
+ 1 1 : 2.9
+ 3 0 : 3.5
+ 3 1 : 0.4
+ 1 3 : 0.9
+ 0 0 : 4.5
+ 2 1 : 1.7
+A:
+CSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1
+ col 0 : locations 0 to 2
+ 1 : 3.1
+ 3 : 3.5
+ 0 : 4.5
+ col 1 : locations 3 to 5
+ 1 : 2.9
+ 3 : 0.4
+ 2 : 1.7
+ col 2 : locations 6 to 7
+ 2 : 3
+ 0 : 3.2
+ col 3 : locations 8 to 9
+ 3 : 1
+ 1 : 0.9
+AT:
+CSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 7.7
+ col 0 : locations 0 to 1
+ 0 : 4.5
+ 2 : 3.2
+ col 1 : locations 2 to 4
+ 0 : 3.1
+ 1 : 2.9
+ 3 : 0.9
+ col 2 : locations 5 to 6
+ 1 : 1.7
+ 2 : 3
+ col 3 : locations 7 to 9
+ 0 : 3.5
+ 1 : 0.4
+ 3 : 1
+D:
+CSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 16 nnz: 16, 1-norm: 139.58
+ col 0 : locations 0 to 3
+ 1 : 13.95
+ 3 : 15.75
+ 0 : 100.28
+ 2 : 9.6
+ col 1 : locations 4 to 7
+ 1 : 88.62
+ 3 : 12.91
+ 0 : 13.95
+ 2 : 4.93
+ col 2 : locations 8 to 11
+ 1 : 4.93
+ 3 : 0.68
+ 2 : 81.68
+ 0 : 9.6
+ col 3 : locations 12 to 15
+ 1 : 12.91
+ 3 : 83.2
+ 0 : 15.75
+ 2 : 0.68
+./cs_demo2 < ../Matrix/t1
+
+--- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.11e+01
+blocks: 1 singletons: 0 structural rank: 4
+QR natural time: 0.00 resid: 3.06e-17
+QR amd(A'*A) time: 0.00 resid: 3.06e-17
+LU natural time: 0.00 resid: 1.53e-17
+LU amd(A+A') time: 0.00 resid: 1.53e-17
+LU amd(S'*S) time: 0.00 resid: 0.00e+00
+LU amd(A'*A) time: 0.00 resid: 1.53e-17
+./cs_demo2 < ../Matrix/ash219
+
+--- Matrix: 219-by-85, nnz: 438 (sym: 0: nnz 0), norm: 9.00e+00
+blocks: 1 singletons: 0 structural rank: 85
+QR natural time: 0.00 resid: 1.61e-02
+QR amd(A'*A) time: 0.00 resid: 1.61e-02
+./cs_demo2 < ../Matrix/bcsstk01
+
+--- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09
+blocks: 1 singletons: 0 structural rank: 48
+QR natural time: 0.00 resid: 2.62e-19
+QR amd(A'*A) time: 0.00 resid: 5.27e-19
+LU natural time: 0.00 resid: 2.17e-19
+LU amd(A+A') time: 0.00 resid: 1.87e-19
+LU amd(S'*S) time: 0.00 resid: 2.38e-19
+LU amd(A'*A) time: 0.00 resid: 2.38e-19
+Chol natural time: 0.00 resid: 2.64e-19
+Chol amd(A+A') time: 0.00 resid: 2.55e-19
+./cs_demo2 < ../Matrix/fs_183_1
+
+--- Matrix: 183-by-183, nnz: 988 (sym: 0: nnz 0), norm: 1.70e+09
+zero entries dropped: 71
+tiny entries dropped: 10
+blocks: 38 singletons: 37 structural rank: 183
+QR natural time: 0.01 resid: 6.84e-28
+QR amd(A'*A) time: 0.00 resid: 9.38e-28
+LU natural time: 0.00 resid: 6.20e-28
+LU amd(A+A') time: 0.00 resid: 1.55e-27
+LU amd(S'*S) time: 0.01 resid: 6.98e-28
+LU amd(A'*A) time: 0.00 resid: 6.98e-28
+./cs_demo2 < ../Matrix/mbeacxc
+
+--- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01
+blocks: 10 singletons: 8 structural rank: 448
+QR natural time: 0.14 resid: nan
+QR amd(A'*A) time: 0.18 resid: nan
+./cs_demo2 < ../Matrix/west0067
+
+--- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.14e+00
+blocks: 2 singletons: 1 structural rank: 67
+QR natural time: 0.00 resid: 7.14e-17
+QR amd(A'*A) time: 0.00 resid: 3.10e-17
+LU natural time: 0.00 resid: 3.89e-17
+LU amd(A+A') time: 0.00 resid: 2.27e-17
+LU amd(S'*S) time: 0.00 resid: 1.95e-17
+LU amd(A'*A) time: 0.00 resid: 2.60e-17
+./cs_demo2 < ../Matrix/lp_afiro
+
+--- Matrix: 27-by-51, nnz: 102 (sym: 0: nnz 0), norm: 3.43e+00
+blocks: 1 singletons: 0 structural rank: 27
+QR natural time: 0.00 resid: 3.96e-16
+QR amd(A'*A) time: 0.00 resid: 2.25e-16
+./cs_demo2 < ../Matrix/bcsstk16
+
+--- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09
+blocks: 75 singletons: 74 structural rank: 4884
+QR amd(A'*A) time: 1.88 resid: 1.39e-22
+LU amd(A+A') time: 1.16 resid: 1.10e-22
+LU amd(S'*S) time: 1.15 resid: 1.28e-22
+LU amd(A'*A) time: 1.20 resid: 1.78e-22
+Chol amd(A+A') time: 0.37 resid: 1.19e-22
+./cs_demo3 < ../Matrix/bcsstk01
+
+--- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.00
+numeric chol time 0.00
+solve chol time 0.00
+original: resid: 2.55e-19
+update: time: 0.00
+update: time: 0.00 (incl solve) resid: 9.66e-19
+rechol: time: 0.00 (incl solve) resid: 1.55e-18
+downdate: time: 0.00
+downdate: time: 0.00 (incl solve) resid: 3.74e-17
+./cs_demo3 < ../Matrix/bcsstk16
+
+--- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.02
+numeric chol time 0.34
+solve chol time 0.00
+original: resid: 1.19e-22
+update: time: 0.00
+update: time: 0.01 (incl solve) resid: 1.12e-23
+rechol: time: 0.34 (incl solve) resid: 1.17e-23
+downdate: time: 0.00
+downdate: time: 0.00 (incl solve) resid: 4.09e-22
diff --git a/CSparse/Demo/cs_demo1.c b/CSparse/Demo/cs_demo1.c
new file mode 100644
index 0000000..ea1a059
--- /dev/null
+++ b/CSparse/Demo/cs_demo1.c
@@ -0,0 +1,27 @@
+#include "cs.h"
+int main (void)
+{
+ cs *T, *A, *Eye, *AT, *C, *D ;
+ int i, m ;
+ T = cs_load (stdin) ; /* load triplet matrix T from stdin */
+ printf ("T:\n") ; cs_print (T, 0) ; /* print T */
+ A = cs_compress (T) ; /* A = compressed-column form of T */
+ printf ("A:\n") ; cs_print (A, 0) ; /* print A */
+ cs_spfree (T) ; /* clear T */
+ AT = cs_transpose (A, 1) ; /* AT = A' */
+ printf ("AT:\n") ; cs_print (AT, 0) ; /* print AT */
+ m = A ? A->m : 0 ; /* m = # of rows of A */
+ T = cs_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */
+ for (i = 0 ; i < m ; i++) cs_entry (T, i, i, 1) ;
+ Eye = cs_compress (T) ; /* Eye = speye (m) */
+ cs_spfree (T) ;
+ C = cs_multiply (A, AT) ; /* C = A*A' */
+ D = cs_add (C, Eye, 1, cs_norm (C)) ; /* D = C + Eye*norm (C,1) */
+ printf ("D:\n") ; cs_print (D, 0) ; /* print D */
+ cs_spfree (A) ; /* clear A AT C D Eye */
+ cs_spfree (AT) ;
+ cs_spfree (C) ;
+ cs_spfree (D) ;
+ cs_spfree (Eye) ;
+ return (0) ;
+}
diff --git a/CSparse/Demo/cs_demo2.c b/CSparse/Demo/cs_demo2.c
new file mode 100644
index 0000000..71e7ad0
--- /dev/null
+++ b/CSparse/Demo/cs_demo2.c
@@ -0,0 +1,9 @@
+#include "cs_demo.h"
+/* cs_demo2: read a matrix and solve a linear system */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 1e-14) ;
+ demo2 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CSparse/Demo/cs_demo3.c b/CSparse/Demo/cs_demo3.c
new file mode 100644
index 0000000..726fc39
--- /dev/null
+++ b/CSparse/Demo/cs_demo3.c
@@ -0,0 +1,9 @@
+#include "cs_demo.h"
+/* cs_demo3: read a matrix and test Cholesky update/downdate */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 0) ;
+ demo3 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CSparse/Doc/ChangeLog b/CSparse/Doc/ChangeLog
new file mode 100644
index 0000000..ea1e3d0
--- /dev/null
+++ b/CSparse/Doc/ChangeLog
@@ -0,0 +1,258 @@
+Nov 1, 2007, v2.2.1
+
+ * very minor change to Include/cs.h: Changed name of 2nd argument of
+ cs_permute, to match the code. This has no affect on the code itself,
+ since the type ("int *") is unchanged. It's just a documentation issue.
+
+ * minor lint cleanup in mexFunctions
+
+Mar 31, 2007, v2.2.0
+
+ * few changes to primary Source/ files. Changes mostly affect MATLAB
+ interface.
+
+ * Source/cs_house.c: correction to comment
+
+ * Souce/cs_updown.c: whitespace changed to reflect change in CXSparse,
+ no impact at all on CSparse itself.
+
+ * Doc/, Lib/ and Include/ directories created.
+
+ * Source/cs.h moved to Include/cs.h, version number changed to 2.2.0.
+
+ * modification to Makefiles, cs_make.m
+
+ * correction to help comments in cs_dmperm.m, cs_qr.m, cs_scc2.m, cs_scc.m
+
+ * if complex matrix passed to CSparse in MATLAB, error message
+ suggests using CXSparse instead
+
+ * minor performance fix to cs_sparse_mex.c
+
+ * cs_randperm added to MATLAB/Makefile; already appeared in cs_make.m
+
+ * minor improvements to MATLAB/ demos.
+
+Mar 1, 2007, v2.1.0
+
+ * Source/cs_add.c: added test for matrix dimensions
+
+ * Source/cs_multiply.c: added test for matrix dimensions
+
+ * correction to MATLAB demo3 (no error in C code version of the demo)
+
+ * minor corrections to MATLAB m-file help comments.
+
+Dec 12, 2006, v2.0.7
+
+ * minor MATLAB cleanup
+
+Dec 6, 2006, v2.0.6
+
+ * Update to UFget. Now relies on the MATLAB urlwrite function instead of
+ my own Java code.
+
+Nov 2006, v2.0.5
+
+ * Added UFgrep to UFget toolbox.
+
+ * No changes to C Source code, except for version number and date.
+
+ * Added two test matrices: ibm32a and ibm32b. ibm32a is the Harwell/
+ Boeing matrix ibm32, but with the last column removed. ibm32b
+ is the transpose of ibm32a. With optimization enabled (-O),
+ 2 lines in cs_maxtrans.c are not tested; these matrices correct
+ that problem.
+
+ * Fixed UFget. Earlier version could not download matrices larger than
+ 32MB.
+
+ * Modified UFget/UFweb, to reflect changes in the UF Sparse Matrix
+ Collection.
+
+ * Added ccspy.m and cs_scc2.m MATLAB functions
+
+ * Added examples to help info in each *.m MATLAB file
+
+ * modified cs_dmspy to speed up the plotting of large matrices with many
+ singletons
+
+ * minor change to cspy: now draws a box around the matrix.
+
+ * minor changes to MATLAB demos and tests.
+
+Oct 13, 2006, v2.0.4
+
+ * minor modification to cs_updown.c. "n" was incorrectly declared "double".
+ It should be "int". This was safe, just a little confusing (n was only
+ used in an argument to cs_malloc, and is thus typecast).
+
+Sept 28, 2006, v2.0.3
+
+ * minor modifications to MATLAB interface, to allow CSparse to be used
+ in MATLAB 6.5.
+
+ * added examples to m-files, other minor m-file cleanup.
+
+ * bug fix to cspy, to handle NaN's properly.
+
+Aug 23, 2006: v2.0.2
+
+ * change to cs_updown mexFunction, to handle multiple rank updates
+
+ * symbolic links removed from Tcov/ directory in the distribution.
+ They are now created by Tcov/Makefile as needed. This makes the
+ zip files cleaner. Tcov/*test.c test files renamed.
+
+July 19, 2006:
+
+ * minor fix to cs_must_compile.m and cs_make.m, to allow CSparse to be
+ compiled in MATLAB 6.5 with cs_make.
+
+ * minor fix to cspy for complex matrices (imaginary part was ignored).
+
+ * no change to version number or date, since there are no changes that
+ affect the appearance of CSparse in the book ("Direct Methods for
+ Sparse Linear Systems", SIAM, 2006).
+
+June 24, 2006:
+
+ * minor typos in comments corrected. No change in code itself,
+ and no change in version number or date.
+
+May 27, 2006, v2.0.1: (this version is printed in the book)
+
+ * minor bug fix. cs_util.c modified, so that cs_sprealloc (T,0) works
+ properly for a triplet matrix T (setting T->nzmax equal to T->nz).
+ The line in v2.0.0:
+
+ nzmax = (nzmax <= 0) ? (A->p [A->n]) : nzmax ;
+
+ changes to the following in v2.0.1:
+
+ if (nzmax <= 0) nzmax = (CS_CSC (A)) ? (A->p [A->n]) : A->nz ;
+
+ * minor typographical changes arising from the editting of the book.
+
+Apr 12, 2006, v2.0.0:
+
+ * random permutation option added to cs_maxtrans and cs_dmperm, to help
+ avoid rare cases where the O(|A|n) time complexity is reached in
+ practice (GHS_indef/boyd2 in the UF sparse matrix collection, for
+ example). New cs_randperm function added.
+
+Apr 10, 2006:
+
+ * stylistic changes for the book (except for the bug fix):
+
+ * "int order" parameter of cs_amd, cs_lusol, cs_cholsol, cs_qrsol, cs_sqr,
+ cs_schol changed. Now 0 means no ordering, 1 is A+A', 2 is S*S', and
+ 3 is A*A'. In v1.2 and earlier, "order" took on a value ranging from
+ -1 to 2. "int n" parameter rearranged for cs_ipvec, cs_pvec, cs_post
+ (int n moved to the end). cs_triplet renamed cs_compress.
+
+ To ensure that these changes are propagated into user code that calls
+ CSparse, the "order" parameter has been placed as the first parameter
+ in all these routines. Your compiler will complain (gcc will halt) if
+ you upgrade from v1.2 to v2.0 without changing your code. This is much
+ better than a silent error in which you get the wrong ordering by
+ mistake (with a huge penalty in run-time performance and no compiler
+ warnings).
+
+ New syntax (v2.0 and later):
+ ----------------------------
+
+ order = 0: natural ordering
+ order = 1: amd (A+A')
+ order = 2: amd (S'*S), where S=A except dense rows dropped
+ order = 3: amd (A'*A)
+
+ int cs_cholsol (int order, const cs *A, double *b) ;
+ int cs_lusol (int order, const cs *A, double *b, double tol) ;
+ int cs_qrsol (int order, const cs *A, double *b) ;
+ int *cs_amd (int order, const cs *A) ;
+ css *cs_schol (int order, const cs *A) ;
+ css *cs_sqr (int order, const cs *A, int qr) ;
+
+ int *cs_post (const int *parent, int n) ;
+ int cs_ipvec (const int *p, const double *b, double *x, int n) ;
+ int cs_pvec (const int *p, const double *b, double *x, int n) ;
+
+ cs *cs_compress (const cs *T) ;
+
+ Old syntax (v1.2 and earlier):
+ ------------------------------
+
+ order = -1: natural ordering
+ order = 0: amd (A+A')
+ order = 1: amd (S'*S), where S=A except dense rows dropped
+ order = 2: amd (A'*A)
+
+ int cs_cholsol (const cs *A, double *b, int order) ;
+ int cs_lusol (const cs *A, double *b, int order, double tol) ;
+ int cs_qrsol (const cs *A, double *b, int order) ;
+ int *cs_amd (const cs *A, int order) ;
+ css *cs_schol (const cs *A, int order) ;
+ css *cs_sqr (const cs *A, int order, int qr) ;
+
+ int *cs_post (int n, const int *parent) ;
+ int cs_ipvec (int n, const int *p, const double *b, double *x) ;
+ int cs_pvec (int n, const int *p, const double *b, double *x) ;
+
+ cs *cs_triplet (const cs *T) ;
+
+ * CS_OVERFLOW macro removed (removed from cs_malloc.c; not needed).
+
+ * S->leftmost added to css (it was tacked onto S->pinv before).
+
+ * P,Q,R,S components of csd struct changed to p,q,r,s.
+
+ * Pinv and Q components of css struct changed to pinv and q.
+
+ * CS_CSC and CS_TRIPLET macros added, to clarify which CSparse functions
+ accept cs matrices in compressed column form, triplet form, or both.
+
+ * check for negative row/column indices added to cs_entry.
+
+ * cs_ereach and cs_leaf functions added.
+
+ * call to cs_sprealloc added to cs_fkeep.
+
+ * bug fixes in cs_counts and cs_amd (memory leak under rare out-of-memory
+ conditions).
+
+Mar 15, 2006:
+
+ * cs_scc modified so that the row and columns of each component are put in
+ their natural order. cs_dmperm modified so that columns of each block
+ (instead of rows) are placed in their natural order.
+
+ * cs_splsolve renamed cs_spsolve, generalized to handle both Lx=b and
+ Ux=b, and non-unit diagonal, and placed in its own file (cs_spsolve.c;
+ it was a static function in cs_lu.c). cs_lsolve_mex.c and
+ cs_splsolve_mex.c merged (the latter was removed). cs_spsolve.c file
+ added
+
+ * cs_dmspy changed, so that block borders line up better with the matrix.
+
+Mar 6, 2006:
+
+ * Makefile modified so that the Tcov tests (which may not be portable)
+ are not compiled and run by the default "make" in the CSparse directory.
+ To compile everything, including the Tcov tests, use "make all".
+ Trivial change to cs.h.
+
+Feb 27, 2006:
+
+ * cs_reach, cs_dfs, cs_splsolve, cs_lu, and cs_scc changed to remove O(n)
+ initialized workspace.
+ * cs_reach and cs_splsolve now user-callable (were static in cs_lu.c).
+
+Feb 20, 2006:
+
+ * various changes to simplify the construction of CXSparse
+
+Feb 7, 2006:
+
+ * changed prototypes, adding "const" where appropriate.
+
diff --git a/CSparse/Doc/License.txt b/CSparse/Doc/License.txt
new file mode 100644
index 0000000..55ff722
--- /dev/null
+++ b/CSparse/Doc/License.txt
@@ -0,0 +1,19 @@
+CSparse: a Concise Sparse matrix package.
+Copyright (c) 2006, Timothy A. Davis.
+http://www.cise.ufl.edu/research/sparse/CSparse
+
+--------------------------------------------------------------------------------
+
+CSparse is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+CSparse is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
diff --git a/CSparse/Doc/lesser.txt b/CSparse/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/CSparse/Doc/lesser.txt
@@ -0,0 +1,504 @@
+ GNU LESSER GENERAL PUBLIC LICENSE
+ Version 2.1, February 1999
+
+ Copyright (C) 1991, 1999 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+[This is the first released version of the Lesser GPL. It also counts
+ as the successor of the GNU Library Public License, version 2, hence
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diff --git a/CSparse/Include/cs.h b/CSparse/Include/cs.h
new file mode 100644
index 0000000..39b2a89
--- /dev/null
+++ b/CSparse/Include/cs.h
@@ -0,0 +1,143 @@
+#ifndef _CS_H
+#define _CS_H
+#include <stdlib.h>
+#include <limits.h>
+#include <math.h>
+#include <stdio.h>
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#endif
+#define CS_VER 2 /* CSparse Version 2.2.1 */
+#define CS_SUBVER 2
+#define CS_SUBSUB 1
+#define CS_DATE "Nov 1, 2007" /* CSparse release date */
+#define CS_COPYRIGHT "Copyright (c) Timothy A. Davis, 2006-2007"
+
+/* --- primary CSparse routines and data structures ------------------------- */
+typedef struct cs_sparse /* matrix in compressed-column or triplet form */
+{
+ int nzmax ; /* maximum number of entries */
+ int m ; /* number of rows */
+ int n ; /* number of columns */
+ int *p ; /* column pointers (size n+1) or col indices (size nzmax) */
+ int *i ; /* row indices, size nzmax */
+ double *x ; /* numerical values, size nzmax */
+ int nz ; /* # of entries in triplet matrix, -1 for compressed-col */
+} cs ;
+
+cs *cs_add (const cs *A, const cs *B, double alpha, double beta) ;
+int cs_cholsol (int order, const cs *A, double *b) ;
+cs *cs_compress (const cs *T) ;
+int cs_dupl (cs *A) ;
+int cs_entry (cs *T, int i, int j, double x) ;
+int cs_gaxpy (const cs *A, const double *x, double *y) ;
+cs *cs_load (FILE *f) ;
+int cs_lusol (int order, const cs *A, double *b, double tol) ;
+cs *cs_multiply (const cs *A, const cs *B) ;
+double cs_norm (const cs *A) ;
+int cs_print (const cs *A, int brief) ;
+int cs_qrsol (int order, const cs *A, double *b) ;
+cs *cs_transpose (const cs *A, int values) ;
+/* utilities */
+void *cs_calloc (int n, size_t size) ;
+void *cs_free (void *p) ;
+void *cs_realloc (void *p, int n, size_t size, int *ok) ;
+cs *cs_spalloc (int m, int n, int nzmax, int values, int triplet) ;
+cs *cs_spfree (cs *A) ;
+int cs_sprealloc (cs *A, int nzmax) ;
+void *cs_malloc (int n, size_t size) ;
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+typedef struct cs_symbolic /* symbolic Cholesky, LU, or QR analysis */
+{
+ int *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */
+ int *q ; /* fill-reducing column permutation for LU and QR */
+ int *parent ; /* elimination tree for Cholesky and QR */
+ int *cp ; /* column pointers for Cholesky, row counts for QR */
+ int *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */
+ int m2 ; /* # of rows for QR, after adding fictitious rows */
+ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */
+ double unz ; /* # entries in U for LU; in R for QR */
+} css ;
+
+typedef struct cs_numeric /* numeric Cholesky, LU, or QR factorization */
+{
+ cs *L ; /* L for LU and Cholesky, V for QR */
+ cs *U ; /* U for LU, R for QR, not used for Cholesky */
+ int *pinv ; /* partial pivoting for LU */
+ double *B ; /* beta [0..n-1] for QR */
+} csn ;
+
+typedef struct cs_dmperm_results /* cs_dmperm or cs_scc output */
+{
+ int *p ; /* size m, row permutation */
+ int *q ; /* size n, column permutation */
+ int *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */
+ int *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */
+ int nb ; /* # of blocks in fine dmperm decomposition */
+ int rr [5] ; /* coarse row decomposition */
+ int cc [5] ; /* coarse column decomposition */
+} csd ;
+
+int *cs_amd (int order, const cs *A) ;
+csn *cs_chol (const cs *A, const css *S) ;
+csd *cs_dmperm (const cs *A, int seed) ;
+int cs_droptol (cs *A, double tol) ;
+int cs_dropzeros (cs *A) ;
+int cs_happly (const cs *V, int i, double beta, double *x) ;
+int cs_ipvec (const int *p, const double *b, double *x, int n) ;
+int cs_lsolve (const cs *L, double *x) ;
+int cs_ltsolve (const cs *L, double *x) ;
+csn *cs_lu (const cs *A, const css *S, double tol) ;
+cs *cs_permute (const cs *A, const int *pinv, const int *q, int values) ;
+int *cs_pinv (const int *p, int n) ;
+int cs_pvec (const int *p, const double *b, double *x, int n) ;
+csn *cs_qr (const cs *A, const css *S) ;
+css *cs_schol (int order, const cs *A) ;
+css *cs_sqr (int order, const cs *A, int qr) ;
+cs *cs_symperm (const cs *A, const int *pinv, int values) ;
+int cs_updown (cs *L, int sigma, const cs *C, const int *parent) ;
+int cs_usolve (const cs *U, double *x) ;
+int cs_utsolve (const cs *U, double *x) ;
+/* utilities */
+css *cs_sfree (css *S) ;
+csn *cs_nfree (csn *N) ;
+csd *cs_dfree (csd *D) ;
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+int *cs_counts (const cs *A, const int *parent, const int *post, int ata) ;
+double cs_cumsum (int *p, int *c, int n) ;
+int cs_dfs (int j, cs *G, int top, int *xi, int *pstack, const int *pinv) ;
+int cs_ereach (const cs *A, int k, const int *parent, int *s, int *w) ;
+int *cs_etree (const cs *A, int ata) ;
+int cs_fkeep (cs *A, int (*fkeep) (int, int, double, void *), void *other) ;
+double cs_house (double *x, double *beta, int n) ;
+int cs_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf,
+ int *ancestor, int *jleaf) ;
+int *cs_maxtrans (const cs *A, int seed) ;
+int *cs_post (const int *parent, int n) ;
+int *cs_randperm (int n, int seed) ;
+int cs_reach (cs *G, const cs *B, int k, int *xi, const int *pinv) ;
+int cs_scatter (const cs *A, int j, double beta, int *w, double *x, int mark,
+ cs *C, int nz) ;
+csd *cs_scc (cs *A) ;
+int cs_spsolve (cs *G, const cs *B, int k, int *xi, double *x,
+ const int *pinv, int lo) ;
+int cs_tdfs (int j, int k, int *head, const int *next, int *post,
+ int *stack) ;
+/* utilities */
+csd *cs_dalloc (int m, int n) ;
+csd *cs_ddone (csd *D, cs *C, void *w, int ok) ;
+cs *cs_done (cs *C, void *w, void *x, int ok) ;
+int *cs_idone (int *p, cs *C, void *w, int ok) ;
+csn *cs_ndone (csn *N, cs *C, void *w, void *x, int ok) ;
+
+#define CS_MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define CS_MIN(a,b) (((a) < (b)) ? (a) : (b))
+#define CS_FLIP(i) (-(i)-2)
+#define CS_UNFLIP(i) (((i) < 0) ? CS_FLIP(i) : (i))
+#define CS_MARKED(w,j) (w [j] < 0)
+#define CS_MARK(w,j) { w [j] = CS_FLIP (w [j]) ; }
+#define CS_CSC(A) (A && (A->nz == -1))
+#define CS_TRIPLET(A) (A && (A->nz >= 0))
+#endif
diff --git a/CSparse/Lib/Makefile b/CSparse/Lib/Makefile
new file mode 100644
index 0000000..435e15f
--- /dev/null
+++ b/CSparse/Lib/Makefile
@@ -0,0 +1,35 @@
+# Modify the "-O" optimization option for best performance (-O3 on Linux):
+CC = cc
+CFLAGS = -O -I../Include
+
+AR = ar cr
+RANLIB = ranlib
+
+all: libcsparse.a
+
+CS = cs_add.o cs_amd.o cs_chol.o cs_cholsol.o cs_counts.o cs_cumsum.o \
+ cs_droptol.o cs_dropzeros.o cs_dupl.o cs_entry.o \
+ cs_etree.o cs_fkeep.o cs_gaxpy.o cs_happly.o cs_house.o cs_ipvec.o \
+ cs_lsolve.o cs_ltsolve.o cs_lu.o cs_lusol.o cs_util.o cs_multiply.o \
+ cs_permute.o cs_pinv.o cs_post.o cs_pvec.o cs_qr.o cs_qrsol.o \
+ cs_scatter.o cs_schol.o cs_sqr.o cs_symperm.o cs_tdfs.o cs_malloc.o \
+ cs_transpose.o cs_compress.o cs_usolve.o cs_utsolve.o cs_scc.o \
+ cs_maxtrans.o cs_dmperm.o cs_updown.o cs_print.o cs_norm.o cs_load.o \
+ cs_dfs.o cs_reach.o cs_spsolve.o cs_ereach.o cs_leaf.o cs_randperm.o
+
+$(CS): ../Include/cs.h Makefile
+
+%.o: ../Source/%.c ../Include/cs.h
+ $(CC) $(CFLAGS) -c $<
+
+libcsparse.a: $(CS)
+ $(AR) libcsparse.a $(CS)
+ $(RANLIB) libcsparse.a
+
+clean:
+ rm -f *.o
+
+purge: distclean
+
+distclean: clean
+ rm -f *.a
diff --git a/CSparse/MATLAB/CSparse/Contents.m b/CSparse/MATLAB/CSparse/Contents.m
new file mode 100644
index 0000000..e2d0b0e
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/Contents.m
@@ -0,0 +1,53 @@
+% CSparse: a Concise Sparse matrix Package.
+%
+% Matrices used in CSparse must in general be either sparse and real,
+% or dense vectors. Ordering methods can accept any sparse matrix.
+%
+% cs_add - sparse matrix addition.
+% cs_amd - approximate minimum degree ordering.
+% cs_chol - sparse Cholesky factorization.
+% cs_cholsol - solve A*x=b using a sparse Cholesky factorization.
+% cs_counts - column counts for sparse Cholesky factor L.
+% cs_dmperm - maximum matching or Dulmage-Mendelsohn permutation.
+% cs_dmsol - x=A\b using the coarse Dulmage-Mendelsohn decomposition.
+% cs_dmspy - plot the Dulmage-Mendelsohn decomposition of a matrix.
+% cs_droptol - remove small entries from a sparse matrix.
+% cs_esep - find an edge separator of a symmetric matrix A
+% cs_etree - elimination tree of A or A'*A.
+% cs_gaxpy - sparse matrix times vector.
+% cs_lsolve - solve a sparse lower triangular system L*x=b.
+% cs_ltsolve - solve a sparse upper triangular system L'*x=b.
+% cs_lu - sparse LU factorization, with fill-reducing ordering.
+% cs_lusol - solve Ax=b using LU factorization.
+% cs_make - compiles CSparse for use in MATLAB.
+% cs_multiply - sparse matrix multiply.
+% cs_nd - generalized nested dissection ordering.
+% cs_nsep - find a node separator of a symmetric matrix A.
+% cs_permute - permute a sparse matrix.
+% cs_print - print the contents of a sparse matrix.
+% cs_qr - sparse QR factorization.
+% cs_qleft - apply Householder vectors on the left.
+% cs_qright - apply Householder vectors on the right.
+% cs_qrsol - solve a sparse least-squares problem.
+% cs_randperm - random permutation.
+% cs_sep - convert an edge separator into a node separator.
+% cs_scc - strongly-connected components of a square sparse matrix.
+% cs_scc2 - cs_scc, or connected components of a bipartite graph.
+% cs_sparse - convert a triplet form into a sparse matrix.
+% cs_sqr - symbolic sparse QR factorization.
+% cs_symperm - symmetric permutation of a symmetric matrix.
+% cs_transpose - transpose a real sparse matrix.
+% cs_updown - rank-1 update/downdate of a sparse Cholesky factorization.
+% cs_usolve - solve a sparse upper triangular system U*x=b.
+% cs_utsolve - solve a sparse lower triangular system U'*x=b.
+% cspy - plot a matrix in color.
+% ccspy - plot the connected components of a matrix.
+
+% Example:
+% help cs_add
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+% helper function:
+% cs_must_compile - return 1 if source code f must be compiled, 0 otherwise
diff --git a/CSparse/MATLAB/CSparse/Makefile b/CSparse/MATLAB/CSparse/Makefile
new file mode 100644
index 0000000..34c8301
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/Makefile
@@ -0,0 +1,259 @@
+MEX = mex -O
+AR = ar cr
+RANLIB = ranlib
+
+I = -I../../Include
+
+all: mexcsparse.a cs_mex.h
+ $(MEX) cs_thumb_mex.c $(I) mexcsparse.a -output cs_thumb
+ $(MEX) cs_print_mex.c $(I) mexcsparse.a -output cs_print
+ $(MEX) cs_updown_mex.c $(I) mexcsparse.a -output cs_updown
+ $(MEX) cs_gaxpy_mex.c $(I) mexcsparse.a -output cs_gaxpy
+ $(MEX) cs_transpose_mex.c $(I) mexcsparse.a -output cs_transpose
+ $(MEX) cs_sparse_mex.c $(I) mexcsparse.a -output cs_sparse
+ $(MEX) cs_multiply_mex.c $(I) mexcsparse.a -output cs_multiply
+ $(MEX) cs_add_mex.c $(I) mexcsparse.a -output cs_add
+ $(MEX) cs_permute_mex.c $(I) mexcsparse.a -output cs_permute
+ $(MEX) cs_symperm_mex.c $(I) mexcsparse.a -output cs_symperm
+ $(MEX) cs_lsolve_mex.c $(I) mexcsparse.a -output cs_lsolve
+ $(MEX) cs_ltsolve_mex.c $(I) mexcsparse.a -output cs_ltsolve
+ $(MEX) cs_usolve_mex.c $(I) mexcsparse.a -output cs_usolve
+ $(MEX) cs_utsolve_mex.c $(I) mexcsparse.a -output cs_utsolve
+ $(MEX) cs_chol_mex.c $(I) mexcsparse.a -output cs_chol
+ $(MEX) cs_etree_mex.c $(I) mexcsparse.a -output cs_etree
+ $(MEX) cs_counts_mex.c $(I) mexcsparse.a -output cs_counts
+ $(MEX) cs_qr_mex.c $(I) mexcsparse.a -output cs_qr
+ $(MEX) cs_amd_mex.c $(I) mexcsparse.a -output cs_amd
+ $(MEX) cs_lu_mex.c $(I) mexcsparse.a -output cs_lu
+ $(MEX) cs_cholsol_mex.c $(I) mexcsparse.a -output cs_cholsol
+ $(MEX) cs_lusol_mex.c $(I) mexcsparse.a -output cs_lusol
+ $(MEX) cs_droptol_mex.c $(I) mexcsparse.a -output cs_droptol
+ $(MEX) cs_qrsol_mex.c $(I) mexcsparse.a -output cs_qrsol
+ $(MEX) cs_dmperm_mex.c $(I) mexcsparse.a -output cs_dmperm
+ $(MEX) cs_scc_mex.c $(I) mexcsparse.a -output cs_scc
+ $(MEX) cs_sqr_mex.c $(I) mexcsparse.a -output cs_sqr
+ $(MEX) cs_randperm_mex.c $(I) mexcsparse.a -output cs_randperm
+
+CS = cs_mex.o \
+ cs_amd.o \
+ cs_chol.o \
+ cs_counts.o \
+ cs_cumsum.o \
+ cs_fkeep.o \
+ cs_dfs.o \
+ cs_dmperm.o \
+ cs_droptol.o \
+ cs_dropzeros.o \
+ cs_dupl.o \
+ cs_entry.o \
+ cs_etree.o \
+ cs_gaxpy.o \
+ cs_ipvec.o \
+ cs_lsolve.o \
+ cs_ltsolve.o \
+ cs_lu.o \
+ cs_maxtrans.o \
+ cs_util.o \
+ cs_malloc.o \
+ cs_multiply.o \
+ cs_add.o \
+ cs_scatter.o \
+ cs_permute.o \
+ cs_pinv.o \
+ cs_post.o \
+ cs_tdfs.o \
+ cs_pvec.o \
+ cs_qr.o \
+ cs_happly.o \
+ cs_house.o \
+ cs_schol.o \
+ cs_scc.o \
+ cs_sqr.o \
+ cs_symperm.o \
+ cs_transpose.o \
+ cs_compress.o \
+ cs_usolve.o \
+ cs_utsolve.o \
+ cs_cholsol.o \
+ cs_lusol.o \
+ cs_qrsol.o \
+ cs_updown.o \
+ cs_norm.o \
+ cs_print.o \
+ cs_load.o \
+ cs_spsolve.o \
+ cs_reach.o \
+ cs_ereach.o \
+ cs_leaf.o \
+ cs_randperm.o
+
+mexcsparse.a: $(CS)
+ $(AR) mexcsparse.a $(CS)
+ $(RANLIB) mexcsparse.a
+
+$(CS): ../../Include/cs.h
+
+
+cs_mex.o: cs_mex.c cs_mex.h
+ $(MEX) -c $(I) $<
+
+cs_amd.o: ../../Source/cs_amd.c
+ $(MEX) -c $(I) $<
+
+cs_chol.o: ../../Source/cs_chol.c
+ $(MEX) -c $(I) $<
+
+cs_ereach.o: ../../Source/cs_ereach.c
+ $(MEX) -c $(I) $<
+
+cs_cholsol.o: ../../Source/cs_cholsol.c
+ $(MEX) -c $(I) $<
+
+cs_lusol.o: ../../Source/cs_lusol.c
+ $(MEX) -c $(I) $<
+
+cs_qrsol.o: ../../Source/cs_qrsol.c
+ $(MEX) -c $(I) $<
+
+cs_counts.o: ../../Source/cs_counts.c
+ $(MEX) -c $(I) $<
+
+cs_leaf.o: ../../Source/cs_leaf.c
+ $(MEX) -c $(I) $<
+
+cs_cumsum.o: ../../Source/cs_cumsum.c
+ $(MEX) -c $(I) $<
+
+cs_fkeep.o: ../../Source/cs_fkeep.c
+ $(MEX) -c $(I) $<
+
+cs_dfs.o: ../../Source/cs_dfs.c
+ $(MEX) -c $(I) $<
+
+cs_droptol.o: ../../Source/cs_droptol.c
+ $(MEX) -c $(I) $<
+
+cs_dropzeros.o: ../../Source/cs_dropzeros.c
+ $(MEX) -c $(I) $<
+
+cs_dupl.o: ../../Source/cs_dupl.c
+ $(MEX) -c $(I) $<
+
+cs_entry.o: ../../Source/cs_entry.c
+ $(MEX) -c $(I) $<
+
+cs_etree.o: ../../Source/cs_etree.c
+ $(MEX) -c $(I) $<
+
+cs_gaxpy.o: ../../Source/cs_gaxpy.c
+ $(MEX) -c $(I) $<
+
+cs_ipvec.o: ../../Source/cs_ipvec.c
+ $(MEX) -c $(I) $<
+
+cs_lsolve.o: ../../Source/cs_lsolve.c
+ $(MEX) -c $(I) $<
+
+cs_ltsolve.o: ../../Source/cs_ltsolve.c
+ $(MEX) -c $(I) $<
+
+cs_lu.o: ../../Source/cs_lu.c
+ $(MEX) -c $(I) $<
+
+cs_util.o: ../../Source/cs_util.c
+ $(MEX) -c $(I) $<
+
+cs_malloc.o: ../../Source/cs_malloc.c
+ $(MEX) -c $(I) $<
+
+cs_multiply.o: ../../Source/cs_multiply.c
+ $(MEX) -c $(I) $<
+
+cs_add.o: ../../Source/cs_add.c
+ $(MEX) -c $(I) $<
+
+cs_scatter.o: ../../Source/cs_scatter.c
+ $(MEX) -c $(I) $<
+
+cs_permute.o: ../../Source/cs_permute.c
+ $(MEX) -c $(I) $<
+
+cs_pinv.o: ../../Source/cs_pinv.c
+ $(MEX) -c $(I) $<
+
+cs_post.o: ../../Source/cs_post.c
+ $(MEX) -c $(I) $<
+
+cs_tdfs.o: ../../Source/cs_tdfs.c
+ $(MEX) -c $(I) $<
+
+cs_pvec.o: ../../Source/cs_pvec.c
+ $(MEX) -c $(I) $<
+
+cs_qr.o: ../../Source/cs_qr.c
+ $(MEX) -c $(I) $<
+
+cs_happly.o: ../../Source/cs_happly.c
+ $(MEX) -c $(I) $<
+
+cs_house.o: ../../Source/cs_house.c
+ $(MEX) -c $(I) $<
+
+cs_schol.o: ../../Source/cs_schol.c
+ $(MEX) -c $(I) $<
+
+cs_spsolve.o: ../../Source/cs_spsolve.c
+ $(MEX) -c $(I) $<
+
+cs_reach.o: ../../Source/cs_reach.c
+ $(MEX) -c $(I) $<
+
+cs_sqr.o: ../../Source/cs_sqr.c
+ $(MEX) -c $(I) $<
+
+cs_symperm.o: ../../Source/cs_symperm.c
+ $(MEX) -c $(I) $<
+
+cs_transpose.o: ../../Source/cs_transpose.c
+ $(MEX) -c $(I) $<
+
+cs_compress.o: ../../Source/cs_compress.c
+ $(MEX) -c $(I) $<
+
+cs_usolve.o: ../../Source/cs_usolve.c
+ $(MEX) -c $(I) $<
+
+cs_utsolve.o: ../../Source/cs_utsolve.c
+ $(MEX) -c $(I) $<
+
+cs_dmperm.o: ../../Source/cs_dmperm.c
+ $(MEX) -c $(I) $<
+
+cs_randperm.o: ../../Source/cs_randperm.c
+ $(MEX) -c $(I) $<
+
+cs_maxtrans.o: ../../Source/cs_maxtrans.c
+ $(MEX) -c $(I) $<
+
+cs_scc.o: ../../Source/cs_scc.c
+ $(MEX) -c $(I) $<
+
+cs_updown.o: ../../Source/cs_updown.c
+ $(MEX) -c $(I) $<
+
+cs_print.o: ../../Source/cs_print.c
+ $(MEX) -c $(I) $<
+
+cs_norm.o: ../../Source/cs_norm.c
+ $(MEX) -c $(I) $<
+
+cs_load.o: ../../Source/cs_load.c
+ $(MEX) -c $(I) $<
+
+clean:
+ rm -f *.o
+
+distclean: clean
+ rm -f *.mex* *.dll *.a
+
+purge: distclean
diff --git a/CSparse/MATLAB/CSparse/README.txt b/CSparse/MATLAB/CSparse/README.txt
new file mode 100644
index 0000000..7c97060
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/README.txt
@@ -0,0 +1 @@
+MATLAB interface for CSparse. See Contents.m for details.
diff --git a/CSparse/MATLAB/CSparse/ccspy.m b/CSparse/MATLAB/CSparse/ccspy.m
new file mode 100644
index 0000000..787eada
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/ccspy.m
@@ -0,0 +1,67 @@
+function [p, q, r, s] = ccspy (A, bipartite, res)
+%CCSPY plot the connected components of a matrix.
+%
+% Example:
+% [p, q, r, s] = ccspy (A, bipartite, res)
+%
+% If A is square, [p,q,r,s] = ccspy(A) finds a permutation p so that A(p,q)
+% is permuted into block upper triangular form. In this case, r=s, p=q and
+% the kth diagonal block is given by A (t,t) where t = r(k):r(k+1)-1.
+% The diagonal of A is ignored.
+%
+% If A is not square (or for [p,q,r,s] = ccspy(A,1)), then the connected
+% components of the bipartite graph of A are found. A(p,q) is permuted into
+% block diagonal form, where the diagonal blocks are rectangular. The kth
+% block is given by A(r(k):r(k+1)-1,s(k):s(k+1)-1). A can be rectangular.
+%
+% It then plots the result via cspy, drawing a greenbox around each component.
+% A 3rd input argument (res) controls the resolution (see cspy for a
+% description of the res parameter).
+%
+% See also CSPY, CS_DMPERM, DMPERM, CS_SCC, CS_SCC2, CS_DMSPY.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (~issparse (A))
+ A = sparse (A) ;
+end
+[m n] = size (A) ;
+if (nargin < 3)
+ res = 256 ;
+end
+if (nargin < 2)
+ bipartite = [ ] ;
+end
+if (isempty (bipartite))
+ bipartite = (m ~= n) ;
+end
+
+% find the strongly connected components
+[p1 q r s] = cs_scc2 (A, bipartite) ;
+if (nargout > 0)
+ p = p1 ;
+end
+
+nb = length (r)-1 ;
+
+% plot the result
+S = A (p1,q) ;
+if (res == 0)
+ spy (S) ;
+ e = 1 ;
+else
+ e = cspy (S,res) ;
+end
+hold on
+
+title (sprintf ('%d-by-%d, strongly connected commponents: %d\n', m, n, nb)) ;
+
+if (~bipartite)
+ plot ([.5 .5 n+.5 n+.5], [.5 .5 n+.5 n+.5], 'r') ;
+end
+
+drawboxes (nb, e, r, s) ;
+
+drawbox (1,m+1,1,n+1,'k',1,e) ;
+hold off
diff --git a/CSparse/MATLAB/CSparse/cs_add.m b/CSparse/MATLAB/CSparse/cs_add.m
new file mode 100644
index 0000000..f85c562
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_add.m
@@ -0,0 +1,17 @@
+function C = cs_add (A,B,alpha,beta) %#ok
+%CS_ADD sparse matrix addition.
+% C = cs_add(A,B,alpha,beta) computes C = alpha*A+beta*B,
+% where alpha and beta default to 1 if not present.
+%
+% Example:
+% Prob1 = UFget ('HB/ibm32') ; A = Prob1.A ;
+% Prob2 = UFget ('Hamrle/Hamrle1') ; B = Prob2.A ;
+% C = cs_add (A,B) ;
+% D = A+B ; % same as C
+%
+% See also CS_MULTIPLY, CS_GAXPY, PLUS, MINUS.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_add mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_add_mex.c b/CSparse/MATLAB/CSparse/cs_add_mex.c
new file mode 100644
index 0000000..4bb778a
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_add_mex.c
@@ -0,0 +1,28 @@
+#include "cs_mex.h"
+/* cs_add: sparse matrix addition */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double alpha, beta ;
+ cs Amatrix, Bmatrix, *A, *B, *C, *D ;
+ if (nargout > 1 || nargin < 2 || nargin > 4)
+ {
+ mexErrMsgTxt ("Usage: C = cs_add(A,B,alpha,beta)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */
+ alpha = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; /* get alpha */
+ beta = (nargin < 4) ? 1 : mxGetScalar (pargin [3]) ; /* get beta */
+ C = cs_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */
+ cs_dropzeros (C) ; /* drop zeros */
+ D = cs_transpose (C, 1) ; /* sort result via double transpose */
+ cs_spfree (C) ;
+ C = cs_transpose (D, 1) ;
+ cs_spfree (D) ;
+ pargout [0] = cs_mex_put_sparse (&C) ; /* return C */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_amd.m b/CSparse/MATLAB/CSparse/cs_amd.m
new file mode 100644
index 0000000..b8a3ec9
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_amd.m
@@ -0,0 +1,25 @@
+function p = cs_amd (A,order) %#ok
+%CS_AMD approximate minimum degree ordering.
+% p = cs_amd(A) finds a minimum degree ordering of A+A'
+% p = cs_amd(A,order):
+% order = 1: same as cs_amd(A)
+% order = 2: minimum degree ordering of S'*S where S = A except that
+% "dense" rows of A are removed from S (a dense row has
+% 10*sqrt(n) or more entries where n = size(A,2)). Similar
+% to p = colamd(A), except that colamd does not form A'*A
+% explicitly.
+% order = 3: minimum degree ordering of A'*A. Similar to colamd(A,[n m])
+% where [m n] = size(A), except that colamd does not form A'*A
+% explicitly.
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ;
+% p = cs_amd (A) ;
+% nnz (chol (A))
+% nnz (chol (A (p,p)))
+%
+% See also AMD, COLAMD, SYMAMD.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_amd mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_amd_mex.c b/CSparse/MATLAB/CSparse/cs_amd_mex.c
new file mode 100644
index 0000000..896a4ca
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_amd_mex.c
@@ -0,0 +1,23 @@
+#include "cs_mex.h"
+/* cs_amd: approximate minimum degree ordering */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *A ;
+ int *P, order ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: p = cs_amd(A,order)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */
+ order = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; /* get ordering */
+ order = CS_MAX (order, 1) ;
+ order = CS_MIN (order, 3) ;
+ P = cs_amd (order, A) ; /* min. degree ordering */
+ pargout [0] = cs_mex_put_int (P, A->n, 1, 1) ; /* return P */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_chol.m b/CSparse/MATLAB/CSparse/cs_chol.m
new file mode 100644
index 0000000..b31c003
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_chol.m
@@ -0,0 +1,19 @@
+function [L,p] = cs_chol (A,drop) %#ok
+%CS_CHOL sparse Cholesky factorization.
+% L = cs_chol(A) is the same as L = chol(A)', using triu(A).
+% [L,p] = cs_chol(A) first orders A with p=cs_amd(A), so that L*L' = A(p,p).
+% A second optional input argument controls whether or not numerically zero
+% entries are removed from L. cs_chol(A) and cs_chol(A,1) drop them;
+% cs_chol(A,0) keeps them. They must be kept for cs_updown to work properly.
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; [L,p] = cs_chol (A) ;
+% cspy (A (p,p)) ;
+% cspy (L) ;
+%
+% See also CS_AMD, CS_UPDOWN, CHOL, AMD, SYMAMD.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_chol mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_chol_mex.c b/CSparse/MATLAB/CSparse/cs_chol_mex.c
new file mode 100644
index 0000000..9f3d61c
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_chol_mex.c
@@ -0,0 +1,28 @@
+#include "cs_mex.h"
+/* cs_chol: sparse Cholesky factorization */
+void mexFunction (int nargout, mxArray *pargout [ ], int nargin,
+ const mxArray *pargin [ ])
+{
+ cs Amatrix, *A ;
+ int order, n, drop, *p ;
+ css *S ;
+ csn *N ;
+ if (nargout > 2 || nargin < 1 || nargin > 2)
+ mexErrMsgTxt ("Usage: [L,p] = cs_chol(A,drop)") ;
+ A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ n = A->n ;
+ order = (nargout > 1) ? 1 : 0 ; /* determine ordering */
+ S = cs_schol (order, A) ; /* symbolic Cholesky */
+ N = cs_chol (A, S) ; /* numeric Cholesky */
+ if (!N) mexErrMsgTxt ("cs_chol failed: not positive definite\n") ;
+ drop = (nargin == 1) ? 1 : mxGetScalar (pargin [1]) ;
+ if (drop) cs_dropzeros (N->L) ; /* drop zeros if requested*/
+ pargout [0] = cs_mex_put_sparse (&(N->L)) ; /* return L */
+ if (nargout > 1)
+ {
+ p = cs_pinv (S->pinv, n) ; /* p=pinv' */
+ pargout [1] = cs_mex_put_int (p, n, 1, 1) ; /* return p */
+ }
+ cs_nfree (N) ;
+ cs_sfree (S) ;
+}
diff --git a/CSparse/MATLAB/CSparse/cs_cholsol.m b/CSparse/MATLAB/CSparse/cs_cholsol.m
new file mode 100644
index 0000000..7717222
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_cholsol.m
@@ -0,0 +1,17 @@
+function x = cs_cholsol (A,b,order) %#ok
+%CS_CHOLSOL solve A*x=b using a sparse Cholesky factorization.
+% x = cs_cholsol(A,b) computes x = A\b, where A sparse symmetric positive
+% definite, and b is a full vector. A 3rd input parameter allows the
+% ordering to be modified: 0: natural, 1:amd(A), 2: amd(S'*S) where S=A except
+% with no dense rows, 3:amd(A'*A). The default ordering option is 1.
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; b = rand (size (A,1),1) ;
+% x = cs_cholsol (A,b) ; norm (A*x-b)
+%
+% See also CS_CHOL, CS_AMD, CS_LUSOL, CS_QRSOL, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_cholsol mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_cholsol_mex.c b/CSparse/MATLAB/CSparse/cs_cholsol_mex.c
new file mode 100644
index 0000000..a5360ef
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_cholsol_mex.c
@@ -0,0 +1,28 @@
+#include "cs_mex.h"
+/* cs_cholsol: solve A*x=b using a sparse Cholesky factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs *A, Amatrix ;
+ double *x, *b ;
+ int order ;
+ if (nargout > 1 || nargin < 2 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: x = cs_cholsol(A,b,order)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ b = cs_mex_get_double (A->n, pargin [1]) ; /* get b */
+ x = cs_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */
+ order = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ;
+ order = CS_MAX (order, 0) ;
+ order = CS_MIN (order, 3) ;
+ if (!cs_cholsol (order, A, x)) /* x = A\x */
+ {
+ mexErrMsgTxt ("A not positive definite") ;
+ }
+}
diff --git a/CSparse/MATLAB/CSparse/cs_counts.m b/CSparse/MATLAB/CSparse/cs_counts.m
new file mode 100644
index 0000000..6d6a879
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_counts.m
@@ -0,0 +1,19 @@
+function c = cs_counts (A,mode) %#ok
+%CS_COUNTS column counts for sparse Cholesky factor L.
+% c = cs_counts(A) returns a vector of the column counts of L, for the
+% Cholesky factorization L*L' = A. That is, c = sum(spones(chol(A)')),
+% except the Cholesky factorization is not computed.
+% c = cs_counts(A), returns counts for cs_chol(A).
+% c = cs_counts(A,'col'), returns counts for cs_chol(A'*A).
+% c = cs_counts(A,'sym'), same as cs_counts(A).
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; c = cs_counts (A)
+% full (sum (spones (chol (A)')))
+%
+% See also SYMBFACT.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_counts mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_counts_mex.c b/CSparse/MATLAB/CSparse/cs_counts_mex.c
new file mode 100644
index 0000000..3dcef2c
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_counts_mex.c
@@ -0,0 +1,32 @@
+#include "cs_mex.h"
+/* cs_counts: column counts for sparse Cholesky factor L. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *A ;
+ int n, ata, *parent, *post, *c ;
+ char mode [20] ;
+ if (nargout > 2 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: c = cs_counts(A,mode)") ;
+ }
+ ata = 0 ; /* get mode */
+ if (nargin > 1 && mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], mode, 8) ;
+ ata = (mode [0] == 'c') ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */
+ n = A->n ;
+ parent = cs_etree (A, ata) ; /* compute etree */
+ post = cs_post (parent, n) ; /* postorder the etree*/
+ c = cs_counts (A, parent, post, ata) ; /* get column counts */
+ pargout [0] = cs_mex_put_int (c, n, 0, 1) ; /* return counts */
+ cs_free (parent) ;
+ cs_free (post) ;
+}
diff --git a/CSparse/MATLAB/CSparse/cs_dmperm.m b/CSparse/MATLAB/CSparse/cs_dmperm.m
new file mode 100644
index 0000000..e281ec9
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_dmperm.m
@@ -0,0 +1,64 @@
+function [p,q,r,s,cc,rr] = cs_dmperm (A,seed) %#ok
+%CS_DMPERM maximum matching or Dulmage-Mendelsohn permutation.
+% p = cs_dmperm(A) finds a maximum matching p such that p(j) = i if column j
+% is matched to row i, or 0 if column j is unmatched. If A is square and
+% full structural rank, p is a row permutation and A(p,:) has a zero-free
+% diagonal. The structural rank of A is sprank(A) = sum(p>0).
+%
+% [p,q,r,s,cc,rr] = cs_dmperm(A) finds the Dulmage-Mendelsohn decomposition
+% of A. p and q are permutation vectors. cc and rr are vectors of length 5.
+% C = A(p,q) is split into a 4-by-4 set of coarse blocks:
+%
+% A11 A12 A13 A14
+% 0 0 A23 A24
+% 0 0 0 A34
+% 0 0 0 A44
+%
+% where A12, A23, and A34 are square with zero-free diagonals. The columns of
+% A11 are the unmatched columns, and the rows of A44 are the unmatched rows.
+% Any of these blocks can be empty. In the "coarse" decomposition, the
+% (i,j)th block is C(rr(i):rr(i+1)-1,cc(j):cc(j+1)-1). In terms of a linear
+% system, [A11 A12] is the underdetermined part of the system (it is always
+% rectangular and with more columns and rows, or 0-by-0), A23 is the well-
+% determined part of the system (it is always square), and [A34 ; A44] is
+% the over-determined part of the system (it is always rectangular with more
+% rows than columns, or 0-by-0).
+%
+% The structural rank of A is sprank(A) = rr(4)-1, which is an upper bound on
+% the numerical rank of A. sprank(A) = rank(full(sprand(A))) with probability
+% 1 in exact arithmetic.
+%
+% The A23 submatrix is further subdivided into block upper triangular form
+% via the "fine" decomposition (the strongly-connected components of A23).
+% If A is square and structurally non-singular, A23 is the entire matrix.
+%
+% C(r(i):r(i+1)-1,s(j):s(j+1)-1) is the (i,j)th block of the fine
+% decomposition. The (1,1) block is the rectangular block [A11 A12], unless
+% this block is 0-by-0. The (b,b) block is the rectangular block [A34 ; A44],
+% unless this block is 0-by-0, where b = length(r)-1. All other blocks of the
+% form C(r(i):r(i+1)-1,s(i):s(i+1)-1) are diagonal blocks of A23, and are
+% square with a zero-free diagonal.
+%
+% The matching algorithm used in cs_dmperm can take a very long time
+% in rare cases. This can be avoided by exploiting a randomized algorithm,
+% with cs_dmperm(A,seed). If seed=0, the non-randomized algorithm is used
+% (columns are considered in order 1:n). If seed=-1, columns are considered
+% in reverse order. Otherwise, the columns are considered in a random order,
+% using seed as the random number generator seed. Try cs_dmpmerm(A,1) or
+% cs_dmperm(A,rand), for a randomized order, for example. Seed defaults to 0.
+%
+%
+% Example:
+% Prob = UFget ('HB/west0479') ; A = Prob.A ; cspy (A) ;
+% p = cs_dmperm (A) ;
+% cspy (A (p,:)) ;
+% [p q r s cc rr] = cs_dmperm (A) ;
+% cspy (A (p,q)) ;
+% cs_dmspy (A) ;
+%
+% See also CS_DMSPY, CS_DMSOL, DMPERM, SPRANK, CS_RANDPERM, RAND
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_dmperm mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_dmperm_mex.c b/CSparse/MATLAB/CSparse/cs_dmperm_mex.c
new file mode 100644
index 0000000..2719aec
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_dmperm_mex.c
@@ -0,0 +1,41 @@
+#include "cs_mex.h"
+/* cs_dmperm: maximum matching or Dulmage-Mendelsohn permutation. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double seed ;
+ cs *A, Amatrix ;
+ csd *D ;
+ int m, n, *jmatch, iseed ;
+ if (nargin < 1 || nargin > 2 || nargout > 6)
+ {
+ mexErrMsgTxt ("Usage: [p,q,r,s,cc,rr] = cs_dmperm (A,seed)") ;
+ }
+ seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 0 ; /* get seed */
+ iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ;
+ A = cs_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */
+ n = A->n ;
+ m = A->m ;
+ if (nargout <= 1)
+ {
+ jmatch = cs_maxtrans (A, iseed) ; /* max. matching */
+ pargout [0] = cs_mex_put_int (jmatch+m, n, 1, 0) ; /* return imatch */
+ cs_free (jmatch) ;
+ }
+ else
+ {
+ D = cs_dmperm (A, iseed) ; /* Dulmage-Mendelsohn decomposition */
+ pargout [0] = cs_mex_put_int (D->p, m, 1, 0) ;
+ pargout [1] = cs_mex_put_int (D->q, n, 1, 0) ;
+ pargout [2] = cs_mex_put_int (D->r, D->nb+1, 1, 0) ;
+ pargout [3] = cs_mex_put_int (D->s, D->nb+1, 1, 0) ;
+ pargout [4] = cs_mex_put_int (D->cc, 5, 1, 0) ;
+ pargout [5] = cs_mex_put_int (D->rr, 5, 1, 0) ;
+ cs_dfree (D) ;
+ }
+}
diff --git a/CSparse/MATLAB/CSparse/cs_dmsol.m b/CSparse/MATLAB/CSparse/cs_dmsol.m
new file mode 100644
index 0000000..32b4b63
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_dmsol.m
@@ -0,0 +1,33 @@
+function x = cs_dmsol (A,b)
+%CS_DMSOL x=A\b using the coarse Dulmage-Mendelsohn decomposition.
+% x = cs_dmsol(A,b) computes x=A\b where A may be rectangular and/or
+% structurally rank deficient, and b is a full vector.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; b = rand (size (A,1),1) ;
+% x = cs_dmsol (A,b) ; norm (A*x-b)
+%
+% See also CS_QRSOL, CS_LUSOL, CS_DMPERM, SPRANK, RANK.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+[p q r s cc rr] = cs_dmperm (A) ;
+C = A (p,q) ;
+b = b (p) ;
+x = zeros (n,1) ;
+if (rr(3) <= m & cc(4) <= n) %#ok
+ x (cc(4):n) = cs_qrsol (C (rr(3):m, cc(4):n), b (rr(3):m)) ;
+ b (1:rr(3)-1) = b (1:rr(3)-1) - C (1:rr(3)-1, cc(4):n) * x (cc(4):n) ;
+end
+if (rr(2) < rr (3) & cc(3) < cc(4)) %#ok
+ x (cc(3):cc(4)-1) = ...
+ cs_lusol (C (rr(2):rr(3)-1, cc(3):cc(4)-1), b (rr(2):rr(3)-1)) ;
+ b (1:rr(2)-1) = ...
+ b (1:rr(2)-1) - C (1:rr(2)-1, cc(3):cc(4)-1) * x (cc(3):cc(4)-1) ;
+end
+if (rr(2) > 1 & cc(3) > 1) %#ok
+ x (1:cc(3)-1) = cs_qrsol (C (1:rr(2)-1, 1:cc(3)-1), b (1:rr(2)-1)) ;
+end
+x (q) = x ;
diff --git a/CSparse/MATLAB/CSparse/cs_dmspy.m b/CSparse/MATLAB/CSparse/cs_dmspy.m
new file mode 100644
index 0000000..5539cca
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_dmspy.m
@@ -0,0 +1,66 @@
+function [p,q,r,s,cc,rr] = cs_dmspy (A,res,seed)
+%CS_DMSPY plot the Dulmage-Mendelsohn decomposition of a matrix.
+% [p,q,r,s,cc,rr] = cs_dmspy(A) computes [p,q,r,s,cc,rr] = cs_dmperm(A),
+% does spy(A(p,q)), and then draws boxes around the coarse and fine
+% decompositions. A 2nd input argument (cs_dmspy(A,res)) changes the
+% resolution of the image to res-by-res (default resolution is 256).
+% If res is zero, spy is used instead of cspy. If the resolution is low, the
+% picture of the blocks in the figure can overlap. They do not actually
+% overlap in the matrix. With 3 arguments, cs_dmspy(A,res,seed),
+% cs_dmperm(A,seed) is used, where seed controls the randomized algorithm
+% used by cs_dmperm.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; cs_dmspy (Prob.A) ;
+%
+% See also CS_DMPERM, CS_DMSOL, DMPERM, SPRANK, SPY.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (~issparse (A))
+ A = sparse (A) ;
+end
+if (nargin < 2)
+ res = 256 ;
+end
+if (nargin < 3)
+ seed = 0 ;
+end
+
+% Dulmage-Mendelsohn permutation
+[p1,q,r,s,cc,rr] = cs_dmperm (A,seed) ;
+if (nargout > 0)
+ p = p1 ;
+end
+
+nb = length (r)-1 ;
+
+% plot the result
+S = A (p1,q) ;
+if (res == 0)
+ spy (S) ;
+ e = 1 ;
+else
+ e = cspy (S,res) ;
+end
+hold on
+
+title (sprintf ( ...
+ '%d-by-%d, sprank: %d, fine blocks: %d, coarse blocks: %d-by-%d\n', ...
+ size (A), rr(4)-1, nb, length (find (diff (rr))), ...
+ length (find (diff (cc))))) ;
+
+drawboxes (nb, e, r, s) ;
+
+[m n] = size (A) ;
+drawbox (1,m+1,1,n+1,'k',1,e) ;
+
+drawbox (rr(1), rr(2), cc(1), cc (2), 'r', 2, e) ;
+drawbox (rr(1), rr(2), cc(2), cc (3), 'r', 2, e) ;
+drawbox (rr(2), rr(3), cc(3), cc (4), 'k', 2, e) ;
+drawbox (rr(3), rr(4), cc(4), cc (5), 'r', 2, e) ;
+drawbox (rr(4), rr(5), cc(4), cc (5), 'r', 2, e) ;
+
+hold off
+
diff --git a/CSparse/MATLAB/CSparse/cs_droptol.m b/CSparse/MATLAB/CSparse/cs_droptol.m
new file mode 100644
index 0000000..83a97ab
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_droptol.m
@@ -0,0 +1,18 @@
+function C = cs_droptol (A, tol) %#ok
+%CS_DROPTOL remove small entries from a sparse matrix.
+% C = cs_droptol(A,tol) removes entries from A of magnitude less than or
+% equal to tol. Same as A = A .* (abs (A) >= tol).
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ;
+% cspy (abs (A) >= 1e-10) ;
+% C = cs_droptol (A, 1e-10) ;
+% cspy (C) ;
+%
+% See also: RELOP, ABS
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_droptol mexFunction not found') ;
+
diff --git a/CSparse/MATLAB/CSparse/cs_droptol_mex.c b/CSparse/MATLAB/CSparse/cs_droptol_mex.c
new file mode 100644
index 0000000..580d47e
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_droptol_mex.c
@@ -0,0 +1,26 @@
+#include "cs_mex.h"
+/* cs_droptol: remove small entries from A */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *C, *A ;
+ int j, k ;
+ double tol ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_droptol(A,tol)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ tol = mxGetScalar (pargin [1]) ; /* get tol */
+ C = cs_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */
+ for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ;
+ for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ;
+ for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ;
+ cs_droptol (C, tol) ; /* drop from C */
+ pargout [0] = cs_mex_put_sparse (&C) ; /* return C */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_esep.m b/CSparse/MATLAB/CSparse/cs_esep.m
new file mode 100644
index 0000000..db51fc1
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_esep.m
@@ -0,0 +1,20 @@
+function [a,b] = cs_esep (A)
+%CS_ESEP find an edge separator of a symmetric matrix A
+% [a,b] = cs_esep(A) finds a edge separator s that splits the graph of A
+% into two parts a and b of roughly equal size. The edge separator is the
+% set of entries in A(a,b).
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ;
+% [a,b] = cs_esep (A) ;
+% cspy (A (a,b)) ;
+%
+% See also CS_NSEP, CS_SEP, CS_ND, SYMRCM.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+p = symrcm (A) ;
+n2 = fix (size(A,1)/2) ;
+a = p (1:n2) ;
+b = p (n2+1:end) ;
diff --git a/CSparse/MATLAB/CSparse/cs_etree.m b/CSparse/MATLAB/CSparse/cs_etree.m
new file mode 100644
index 0000000..545e54c
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_etree.m
@@ -0,0 +1,19 @@
+function [parent, post] = cs_etree (A, mode) %#ok
+%CS_ETREE elimination tree of A or A'*A.
+% parent = cs_etree (A) returns the elimination tree of A.
+% parent = cs_etree (A,'col') returns the elimination tree of A'*A.
+% parent = cs_etree (A,'sym') is the same as cs_etree(A).
+% For the symmetric case (cs_etree(A)), only triu(A) is used.
+%
+% [parent,post] = cs_etree(...) also returns a postorder of the tree.
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ;
+% parent = cs_etree (A) ; treeplot (parent) ;
+%
+% See also ETREE, TREEPLOT.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_etree mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_etree_mex.c b/CSparse/MATLAB/CSparse/cs_etree_mex.c
new file mode 100644
index 0000000..d002ceb
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_etree_mex.c
@@ -0,0 +1,33 @@
+#include "cs_mex.h"
+/* cs_etree: elimination tree of A or A'*A */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *A ;
+ int n, ata, *parent, *post ;
+ char mode [20] ;
+ if (nargout > 2 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: [parent,post] = cs_etree(A,mode)") ;
+ }
+ ata = 0 ; /* get mode */
+ if (nargin > 1 && mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], mode, 8) ;
+ ata = (mode [0] == 'c') ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */
+ n = A->n ;
+ parent = cs_etree (A, ata) ; /* compute etree */
+ if (nargout > 1)
+ {
+ post = cs_post (parent, n) ; /* postorder the etree*/
+ pargout [1] = cs_mex_put_int (post, n, 1, 1) ; /* return post */
+ }
+ pargout [0] = cs_mex_put_int (parent, n, 1, 1) ; /* return parent */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_gaxpy.m b/CSparse/MATLAB/CSparse/cs_gaxpy.m
new file mode 100644
index 0000000..173223c
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_gaxpy.m
@@ -0,0 +1,15 @@
+function z = cs_gaxpy (A,x,y) %#ok
+%CS_GAXPY sparse matrix times vector.
+% z = cs_gaxpy(A,x,y) computes z = A*x+y where x and y are full vectors.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; [m n] = size (A) ;
+% x = rand (m,1) ; y = rand (n,1) ;
+% z = cs_gaxpy (A, x, y) ;
+%
+% See also PLUS, MTIMES.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_gaxpy mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_gaxpy_mex.c b/CSparse/MATLAB/CSparse/cs_gaxpy_mex.c
new file mode 100644
index 0000000..24c78b5
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_gaxpy_mex.c
@@ -0,0 +1,22 @@
+#include "cs_mex.h"
+/* z = cs_gaxpy (A,x,y) computes z = A*x+y */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *A ;
+ double *x, *y, *z ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: z = cs_gaxpy(A,x,y)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ x = cs_mex_get_double (A->n, pargin [1]) ; /* get x */
+ y = cs_mex_get_double (A->m, pargin [2]) ; /* get y */
+ z = cs_mex_put_double (A->m, y, &(pargout [0])) ; /* z = y */
+ cs_gaxpy (A, x, z) ; /* z = z + A*x */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_lsolve.m b/CSparse/MATLAB/CSparse/cs_lsolve.m
new file mode 100644
index 0000000..1e37600
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_lsolve.m
@@ -0,0 +1,17 @@
+function x = cs_lsolve (L,b) %#ok
+%CS_LSOLVE solve a sparse lower triangular system L*x=b.
+% x = cs_lsolve(L,b) computes x = L\b, L must be lower triangular with a
+% zero-free diagonal. b must be a column vector. x is full if b is full.
+% If b is sparse, x is sparse but the nonzero pattern of x is NOT sorted (it
+% is returned in topological order).
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; L = cs_chol (Prob.A) ; n = size (L,1) ;
+% b = rand (n,1) ; x = cs_lsolve (L,b) ; norm (L*x-b)
+%
+% See also CS_LTSOLVE, CS_USOLVE, CS_UTSOLVE, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_lsolve mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_lsolve_mex.c b/CSparse/MATLAB/CSparse/cs_lsolve_mex.c
new file mode 100644
index 0000000..1f50c1c
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_lsolve_mex.c
@@ -0,0 +1,59 @@
+#include "cs_mex.h"
+/* cs_lsolve: x=L\b. L must be sparse, real, and lower triangular. b must be a
+ * real full or sparse vector. x is full or sparse, depending on b.
+ *
+ * Time taken is O(flop count), which may be less than n if b is sparse,
+ * depending on L and b.
+ *
+ * This function works with MATLAB 7.2, but is not perfectly compatible with
+ * the requirements of a MATLAB mexFunction when b is sparse. X is returned
+ * as an unsorted sparse vector. Also, this mexFunction temporarily modifies
+ * its input, L, by modifying L->p (in the cs_dfs function) and then restoring
+ * it. This could be corrected by creating a copy of L->p
+ * (see cs_dmperm_mex.c), but this would take O(n) time, destroying the
+ * O(flop count) time complexity of this function.
+ */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Lmatrix, Bmatrix, *L, *B, *X ;
+ double *x, *b ;
+ int top, nz, p, *xi ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_lsolve(L,b)") ;
+ }
+ L = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */
+ if (mxIsSparse (pargin [1]))
+ {
+ B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b */
+ cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ;
+ xi = cs_malloc (2*L->n, sizeof (int)) ; /* get workspace */
+ x = cs_malloc (L->n, sizeof (double)) ;
+ top = cs_spsolve (L, B, 0, xi, x, NULL, 1) ; /* x = L\b */
+ X = cs_spalloc (L->n, 1, L->n-top, 1, 0) ; /* create sparse x*/
+ X->p [0] = 0 ;
+ nz = 0 ;
+ for (p = top ; p < L->n ; p++)
+ {
+ X->i [nz] = xi [p] ;
+ X->x [nz++] = x [xi [p]] ;
+ }
+ X->p [1] = nz ;
+ pargout [0] = cs_mex_put_sparse (&X) ;
+ cs_free (x) ;
+ cs_free (xi) ;
+ }
+ else
+ {
+ b = cs_mex_get_double (L->n, pargin [1]) ; /* get full b */
+ x = cs_mex_put_double (L->n, b, &(pargout [0])) ; /* x = b */
+ cs_lsolve (L, x) ; /* x = L\x */
+ }
+}
diff --git a/CSparse/MATLAB/CSparse/cs_ltsolve.m b/CSparse/MATLAB/CSparse/cs_ltsolve.m
new file mode 100644
index 0000000..4e902b6
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_ltsolve.m
@@ -0,0 +1,15 @@
+function x = cs_ltsolve (L,b) %#ok
+%CS_LTSOLVE solve a sparse upper triangular system L'*x=b.
+% x = cs_ltsolve(L,b) computes x = L'\b, L must be lower triangular with a
+% zero-free diagonal. b must be a full vector.
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; L = cs_chol (Prob.A) ; n = size (L,1) ;
+% b = rand (n,1) ; x = cs_ltsolve (L,b) ; norm (L'*x-b)
+%
+% See also CS_LSOLVE, CS_USOLVE, CS_UTSOLVE, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_ltsolve mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_ltsolve_mex.c b/CSparse/MATLAB/CSparse/cs_ltsolve_mex.c
new file mode 100644
index 0000000..aa10918
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_ltsolve_mex.c
@@ -0,0 +1,21 @@
+#include "cs_mex.h"
+/* cs_ltsolve: solve an upper triangular system L'*x=b */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Lmatrix, *L ;
+ double *x, *b ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_ltsolve(L,b)") ;
+ }
+ L = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */
+ b = cs_mex_get_double (L->n, pargin [1]) ; /* get b */
+ x = cs_mex_put_double (L->n, b, &(pargout [0])) ; /* x = b */
+ cs_ltsolve (L, x) ; /* x = L'\x */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_lu.m b/CSparse/MATLAB/CSparse/cs_lu.m
new file mode 100644
index 0000000..4ff80fc
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_lu.m
@@ -0,0 +1,29 @@
+function [L,U,p,q] = cs_lu (A,tol) %#ok
+%CS_LU sparse LU factorization, with fill-reducing ordering.
+% [L,U,p] = cs_lu(A) factorizes A(p,:) into L*U using no fill-reducing
+% ordering.
+%
+% [L,U,p] = cs_lu(A,tol) factorizes A(p,:) into L*U using no fill-reducing
+% ordering. Entries on the diagonal are given preference in partial pivoting.
+%
+% [L,U,p,q] = cs_lu(A) factorizes A(p,q) into L*U using a fill-reducing
+% ordering q = cs_amd(A,2). Normal partial pivoting is used.
+%
+% [L,U,p,q] = cs_lu(A,tol) factorizes A(p,q) into L*U, using a fill-reducing
+% ordering q = cs_amd(A,1). Entries on the diagonal are given preference in
+% partial pivoting. With a pivot tolerance tol, the entries in L have
+% magnitude 1/tol or less. tol = 1 is normal partial pivoting (with
+% q = cs_amd(A)). tol = 0 ensures p = q. 0<tol<1 is relaxed partial
+% pivoting; the diagonal is selected if it is >= tol * max(abs(A(:,k))).
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; [L,U,p,q] = cs_lu (A) ;
+% cspy (A (p,q)) ; cspy (L+U) ;
+% norm (L*U - A(p,q), 1)
+%
+% See also CS_AMD, LU, UMFPACK, AMD, COLAMD.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_lu mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_lu_mex.c b/CSparse/MATLAB/CSparse/cs_lu_mex.c
new file mode 100644
index 0000000..c17650d
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_lu_mex.c
@@ -0,0 +1,53 @@
+#include "cs_mex.h"
+/* cs_lu: sparse LU factorization, with optional fill-reducing ordering */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ css *S ;
+ csn *N ;
+ cs Amatrix, *A, *D ;
+ int n, order, *p ;
+ double tol ;
+ if (nargout > 4 || nargin > 3 || nargin < 1)
+ {
+ mexErrMsgTxt ("Usage: [L,U,p,q] = cs_lu (A,tol)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ n = A->n ;
+ if (nargin == 2) /* determine tol and ordering */
+ {
+ tol = mxGetScalar (pargin [1]) ;
+ order = (nargout == 4) ? 1 : 0 ; /* amd (A+A'), or natural */
+ }
+ else
+ {
+ tol = 1 ;
+ order = (nargout == 4) ? 2 : 0 ; /* amd(S'*S) w/dense rows or I */
+ }
+ S = cs_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */
+ N = cs_lu (A, S, tol) ; /* numeric factorization */
+ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ;
+ cs_dropzeros (N->L) ; /* drop zeros from L and sort it */
+ D = cs_transpose (N->L, 1) ;
+ cs_spfree (N->L) ;
+ N->L = cs_transpose (D, 1) ;
+ cs_spfree (D) ;
+ cs_dropzeros (N->U) ; /* drop zeros from U and sort it */
+ D = cs_transpose (N->U, 1) ;
+ cs_spfree (N->U) ;
+ N->U = cs_transpose (D, 1) ;
+ cs_spfree (D) ;
+ p = cs_pinv (N->pinv, n) ; /* p=pinv' */
+ pargout [0] = cs_mex_put_sparse (&(N->L)) ; /* return L */
+ pargout [1] = cs_mex_put_sparse (&(N->U)) ; /* return U */
+ pargout [2] = cs_mex_put_int (p, n, 1, 1) ; /* return p */
+ /* return Q */
+ if (nargout == 4) pargout [3] = cs_mex_put_int (S->q, n, 1, 0) ;
+ cs_nfree (N) ;
+ cs_sfree (S) ;
+}
diff --git a/CSparse/MATLAB/CSparse/cs_lusol.m b/CSparse/MATLAB/CSparse/cs_lusol.m
new file mode 100644
index 0000000..ff00f7a
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_lusol.m
@@ -0,0 +1,23 @@
+function x = cs_lusol (A,b,order,tol) %#ok
+%CS_LUSOL solve Ax=b using LU factorization.
+% x = cs_lusol(A,b) computes x = A\b, where A is sparse and square, and b is a
+% full vector. The ordering cs_amd(A,2) is used.
+%
+% x = cs_lusol(A,b,1) also computes x = A\b, but uses the cs_amd(A) ordering
+% with diagonal preference (tol=0.001).
+%
+% x = cs_lusol(A,b,order,tol) allows both the ordering and tolerance to be
+% defined. The ordering defaults to 1, and tol defaults to 1.
+% ordering: 0: natural, 1: amd(A+A'), 2: amd(S'*S) where S=A except with no
+% dense rows, 3: amd(A'*A).
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size(A,1) ;
+% b = rand (n,1) ; x = cs_lusol (A,b) ; norm (A*x-b)
+%
+% See also CS_LU, CS_AMD, CS_CHOLSOL, CS_QRSOL, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_lusol mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_lusol_mex.c b/CSparse/MATLAB/CSparse/cs_lusol_mex.c
new file mode 100644
index 0000000..c17778f
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_lusol_mex.c
@@ -0,0 +1,40 @@
+#include "cs_mex.h"
+/* cs_lusol: solve A*x=b using a sparse LU factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs *A, Amatrix ;
+ int order ;
+ double *x, *b, tol ;
+ if (nargout > 1 || nargin < 2 || nargin > 4)
+ {
+ mexErrMsgTxt ("Usage: x = cs_lusol(A,b,order,tol)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ b = cs_mex_get_double (A->n, pargin [1]) ; /* get b */
+ x = cs_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */
+ order = (nargin < 3) ? 2 : mxGetScalar (pargin [2]) ;
+ order = CS_MAX (order, 0) ;
+ order = CS_MIN (order, 3) ;
+ if (nargin == 2)
+ {
+ tol = 1 ; /* normal partial pivoting */
+ }
+ else if (nargin == 3)
+ {
+ tol = (order == 1) ? 0.001 : 1 ; /* tol = 0.001 for amd(A+A') */
+ }
+ else
+ {
+ tol = mxGetScalar (pargin [3]) ;
+ }
+ if (!cs_lusol (order, A, x, tol)) /* x = A\x */
+ {
+ mexErrMsgTxt ("LU factorization failed (singular or out of memory)") ;
+ }
+}
diff --git a/CSparse/MATLAB/CSparse/cs_make.m b/CSparse/MATLAB/CSparse/cs_make.m
new file mode 100644
index 0000000..0291919
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_make.m
@@ -0,0 +1,169 @@
+function [objfiles, timestamp_out] = cs_make (f)
+%CS_MAKE compiles CSparse for use in MATLAB.
+% Usage:
+% cs_make
+% [objfiles, timestamp] = cs_make (f)
+%
+% With no input arguments, or with f=0, only those files needing to be
+% compiled are compiled (like the Unix/Linux/GNU "make" command, but not
+% requiring "make"). If f is a nonzero number, all files are compiled.
+% If f is a string, only that mexFunction is compiled. For example,
+% cs_make ('cs_add') just compiles the cs_add mexFunction. This option is
+% useful when developing a single new mexFunction. This function can only be
+% used if the current directory is CSparse/MATLAB/CSparse. Returns a list of
+% the object files in CSparse, and the latest modification time of any source
+% codes.
+%
+% To add a new function and its MATLAB mexFunction to CSparse:
+%
+% (1) Create a source code file CSparse/Source/cs_mynewfunc.c.
+% (2) Create a help file, CSparse/MATLAB/CSparse/cs_mynewfunc.m.
+% This is very useful, but not strictly required.
+% (3) Add the prototype of cs_mynewfunc to CSparse/Include/cs.h.
+% (4) Create its MATLAB mexFunction, CSparse/MATLAB/cs_mynewfunc_mex.c.
+% (5) Edit cs_make.m, and add 'cs_mynewfunc' to the 'cs' and 'csm' lists.
+% (6) Type 'cs_make' in the CSparse/MATLAB/CSparse directory.
+% If all goes well, your new function is ready for use in MATLAB.
+%
+% (7) Optionally add 'cs_mynewfunc' to CSparse/Source/Makefile
+% and CSparse/MATLAB/CSparse/Makefile, if you want to use the
+% Unix/Linux/GNU make command instead of cs_make.m. See where
+% 'cs_add' and 'cs_add_mex' appear in those files, and add
+% 'cs_mynewfunc' accordingly.
+% (8) Optionally add 'cs_mynewfunc' to Tcov/Makefile, and add additional
+% test code to cs_test.c, and add MATLAB test code to MATLAB/Test/*.
+%
+% Example:
+% cs_make % compile everything
+% cs_make ('cs_chol') ; % just compile cs_chol mexFunction
+%
+% See also MEX.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('Compiling CSparse\n') ;
+
+% CSparse source files, in ../../Source, such as ../../Source/cs_add.c.
+% Note that not all CSparse source files have their own mexFunction.
+cs = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ...
+ 'cs_cumsum', 'cs_dfs', 'cs_dmperm', 'cs_droptol', 'cs_dropzeros', ...
+ 'cs_dupl', 'cs_entry', 'cs_etree', 'cs_fkeep', 'cs_gaxpy', 'cs_happly', ...
+ 'cs_house', 'cs_ipvec', 'cs_load', 'cs_lsolve', 'cs_ltsolve', 'cs_lu', ...
+ 'cs_lusol', 'cs_malloc', 'cs_maxtrans', 'cs_multiply', 'cs_norm', ...
+ 'cs_permute', 'cs_pinv', 'cs_post', 'cs_print', 'cs_pvec', 'cs_qr', ...
+ 'cs_qrsol', 'cs_scatter', 'cs_scc', 'cs_schol', 'cs_sqr', 'cs_symperm', ...
+ 'cs_tdfs', 'cs_transpose', 'cs_compress', 'cs_updown', 'cs_usolve', ...
+ 'cs_utsolve', 'cs_util', 'cs_reach', 'cs_spsolve', 'cs_ereach', ...
+ 'cs_leaf', 'cs_randperm' } ;
+ % add cs_mynewfunc to the above list
+
+details = 1 ;
+kk = 0 ;
+csm = { } ;
+if (nargin == 0)
+ force = 0 ;
+elseif (ischar (f))
+ fprintf ('cs_make: compiling ../../Source files and %s_mex.c\n', f) ;
+ force = 0 ;
+ csm = {f} ;
+else
+ force = f ;
+ details = details | (force > 1) ; %#ok
+ if (force & details) %#ok
+ fprintf ('cs_make: re-compiling everything\n') ;
+ end
+end
+if (force)
+ fprintf ('Compiling CSparse\n') ;
+end
+
+if (isempty (csm))
+ % mexFunctions, of the form cs_add_mex.c, etc, in this directory
+ csm = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ...
+ 'cs_dmperm', 'cs_droptol', 'cs_etree', 'cs_gaxpy', 'cs_lsolve', ...
+ 'cs_ltsolve', 'cs_lu', 'cs_lusol', 'cs_multiply', 'cs_permute', ...
+ 'cs_print', 'cs_qr', 'cs_qrsol', 'cs_scc', 'cs_symperm', 'cs_thumb', ...
+ 'cs_transpose', 'cs_sparse', 'cs_updown', 'cs_usolve', ...
+ 'cs_utsolve', 'cs_randperm', 'cs_sqr' } ;
+ % add cs_mynewfunc to the above list
+end
+
+try
+ % ispc does not appear in MATLAB 5.3
+ pc = ispc ;
+catch
+ % if ispc fails, assume we are on a Windows PC if it's not unix
+ pc = ~isunix ;
+end
+
+if (pc)
+ obj = '.obj' ;
+else
+ obj = '.o' ;
+end
+
+srcdir = '../../Source/' ;
+hfile = '../../Include/cs.h' ;
+
+% compile each CSparse source file
+[anysrc timestamp kk] = compile_source ('', 'cs_mex', obj, hfile, force, ...
+ kk, details) ;
+CS = ['cs_mex' obj] ;
+if (nargout > 0)
+ objfiles = ['..' filesep 'CSparse' filesep 'cs_mex' obj] ;
+end
+for i = 1:length (cs)
+ [s t kk] = compile_source (srcdir, cs {i}, obj, hfile, force, kk, details) ;
+ timestamp = max (timestamp, t) ;
+ anysrc = anysrc | s ; %#ok
+ CS = [CS ' ' cs{i} obj] ; %#ok
+ if (nargout > 0)
+ objfiles = [objfiles ' ..' filesep 'CSparse' filesep cs{i} obj] ; %#ok
+ end
+end
+
+% compile each CSparse mexFunction
+obj = ['.' mexext] ;
+for i = 1:length (csm)
+ [s t] = cs_must_compile ('', csm{i}, '_mex', obj, hfile, force) ;
+ timestamp = max (timestamp, t) ;
+ if (anysrc | s) %#ok
+ cmd = sprintf ('mex -O -I../../Include %s_mex.c %s -output %s', ...
+ csm{i}, CS, csm{i}) ;
+ kk = do_cmd (cmd, kk, details) ;
+ end
+end
+
+fprintf ('\n') ;
+if (nargout > 1)
+ timestamp_out = timestamp ;
+end
+
+if (force)
+ fprintf ('CSparse successfully compiled.\n') ;
+end
+
+%-------------------------------------------------------------------------------
+function [s,t,kk] = compile_source (srcdir, f, obj, hfile, force, kk, details)
+% compile a source code file in ../../Source, leaving object file in
+% this directory.
+[s t] = cs_must_compile (srcdir, f, '', obj, hfile, force) ;
+if (s)
+ cmd = sprintf ('mex -O -c -I../../Include %s%s.c', srcdir, f) ;
+ kk = do_cmd (cmd, kk, details) ;
+end
+
+%-------------------------------------------------------------------------------
+function kk = do_cmd (s, kk, details)
+%DO_CMD: evaluate a command, and either print it or print a "."
+if (details)
+ fprintf ('%s\n', s) ;
+else
+ if (mod (kk, 60) == 0)
+ fprintf ('\n') ;
+ end
+ kk = kk + 1 ;
+ fprintf ('.') ;
+end
+eval (s) ;
diff --git a/CSparse/MATLAB/CSparse/cs_mex.c b/CSparse/MATLAB/CSparse/cs_mex.c
new file mode 100644
index 0000000..a88b529
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_mex.c
@@ -0,0 +1,118 @@
+#include "cs_mex.h"
+/* check MATLAB input argument */
+void cs_mex_check (int nel, int m, int n, int square, int sparse, int values,
+ const mxArray *A)
+{
+ int nnel, mm = mxGetM (A), nn = mxGetN (A) ;
+ if (values)
+ {
+ if (mxIsComplex (A))
+ {
+ mexErrMsgTxt ("matrix must be real; try CXSparse instead") ;
+ }
+ }
+ if (sparse && !mxIsSparse (A)) mexErrMsgTxt ("matrix must be sparse") ;
+ if (!sparse)
+ {
+ if (mxIsSparse (A)) mexErrMsgTxt ("matrix must be full") ;
+ if (values && !mxIsDouble (A)) mexErrMsgTxt ("matrix must be double") ;
+ }
+ if (nel)
+ {
+ /* check number of elements */
+ nnel = mxGetNumberOfElements (A) ;
+ if (m >= 0 && n >= 0 && m*n != nnel) mexErrMsgTxt ("wrong length") ;
+ }
+ else
+ {
+ /* check row and/or column dimensions */
+ if (m >= 0 && m != mm) mexErrMsgTxt ("wrong dimension") ;
+ if (n >= 0 && n != nn) mexErrMsgTxt ("wrong dimension") ;
+ }
+ if (square && mm != nn) mexErrMsgTxt ("matrix must be square") ;
+}
+
+/* get a MATLAB sparse matrix and convert to cs */
+cs *cs_mex_get_sparse (cs *A, int square, int values, const mxArray *Amatlab)
+{
+ cs_mex_check (0, -1, -1, square, 1, values, Amatlab) ;
+ A->m = mxGetM (Amatlab) ;
+ A->n = mxGetN (Amatlab) ;
+ A->p = mxGetJc (Amatlab) ;
+ A->i = mxGetIr (Amatlab) ;
+ A->x = values ? mxGetPr (Amatlab) : NULL ;
+ A->nzmax = mxGetNzmax (Amatlab) ;
+ A->nz = -1 ; /* denotes a compressed-col matrix, instead of triplet */
+ return (A) ;
+}
+
+/* return a sparse matrix to MATLAB */
+mxArray *cs_mex_put_sparse (cs **Ahandle)
+{
+ cs *A ;
+ mxArray *Amatlab ;
+ A = *Ahandle ;
+ Amatlab = mxCreateSparse (0, 0, 0, mxREAL) ;
+ mxSetM (Amatlab, A->m) ;
+ mxSetN (Amatlab, A->n) ;
+ mxSetNzmax (Amatlab, A->nzmax) ;
+ cs_free (mxGetJc (Amatlab)) ;
+ cs_free (mxGetIr (Amatlab)) ;
+ cs_free (mxGetPr (Amatlab)) ;
+ mxSetJc (Amatlab, A->p) ; /* assign A->p pointer to MATLAB A */
+ mxSetIr (Amatlab, A->i) ;
+ mxSetPr (Amatlab, A->x) ;
+ mexMakeMemoryPersistent (A->p) ; /* ensure MATLAB does not free A->p */
+ mexMakeMemoryPersistent (A->i) ;
+ mexMakeMemoryPersistent (A->x) ;
+ cs_free (A) ; /* frees A struct only, not A->p, etc */
+ *Ahandle = NULL ;
+ return (Amatlab) ;
+}
+
+/* get a MATLAB dense column vector */
+double *cs_mex_get_double (int n, const mxArray *X)
+{
+ cs_mex_check (0, n, 1, 0, 0, 1, X) ;
+ return (mxGetPr (X)) ;
+}
+
+/* return a double vector to MATLAB */
+double *cs_mex_put_double (int n, const double *b, mxArray **X)
+{
+ double *x ;
+ int k ;
+ *X = mxCreateDoubleMatrix (n, 1, mxREAL) ; /* create x */
+ x = mxGetPr (*X) ;
+ for (k = 0 ; k < n ; k++) x [k] = b [k] ; /* copy x = b */
+ return (x) ;
+}
+
+/* get a MATLAB flint array and convert to int */
+int *cs_mex_get_int (int n, const mxArray *Imatlab, int *imax, int lo)
+{
+ double *p ;
+ int i, k, *C = cs_malloc (n, sizeof (int)) ;
+ cs_mex_check (1, n, 1, 0, 0, 1, Imatlab) ;
+ p = mxGetPr (Imatlab) ;
+ *imax = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ i = p [k] ;
+ C [k] = i - 1 ;
+ if (i < lo) mexErrMsgTxt ("index out of bounds") ;
+ *imax = CS_MAX (*imax, i) ;
+ }
+ return (C) ;
+}
+
+/* return an int array to MATLAB as a flint row vector */
+mxArray *cs_mex_put_int (int *p, int n, int offset, int do_free)
+{
+ mxArray *X = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ double *x = mxGetPr (X) ;
+ int k ;
+ for (k = 0 ; k < n ; k++) x [k] = (p ? p [k] : k) + offset ;
+ if (do_free) cs_free (p) ;
+ return (X) ;
+}
diff --git a/CSparse/MATLAB/CSparse/cs_mex.h b/CSparse/MATLAB/CSparse/cs_mex.h
new file mode 100644
index 0000000..e238bdc
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_mex.h
@@ -0,0 +1,10 @@
+#include "cs.h"
+#include "mex.h"
+cs *cs_mex_get_sparse (cs *A, int square, int values, const mxArray *Amatlab) ;
+mxArray *cs_mex_put_sparse (cs **A) ;
+void cs_mex_check (int nel, int m, int n, int square, int sparse, int values,
+ const mxArray *A) ;
+int *cs_mex_get_int (int n, const mxArray *Imatlab, int *imax, int lo) ;
+mxArray *cs_mex_put_int (int *p, int n, int offset, int do_free) ;
+double *cs_mex_get_double (int n, const mxArray *X) ;
+double *cs_mex_put_double (int n, const double *b, mxArray **X) ;
diff --git a/CSparse/MATLAB/CSparse/cs_multiply.m b/CSparse/MATLAB/CSparse/cs_multiply.m
new file mode 100644
index 0000000..071b60e
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_multiply.m
@@ -0,0 +1,16 @@
+function C = cs_multiply (A,B) %#ok
+%CS_MULTIPLY sparse matrix multiply.
+% C = cs_multiply(A,B) computes C = A*B.
+%
+% Example:
+% Prob1 = UFget ('HB/ibm32') ; A = Prob1.A ;
+% Prob2 = UFget ('Hamrle/Hamrle1') ; B = Prob2.A ;
+% C = cs_multiply (A,B) ;
+% D = A*B ; % same as C
+%
+% See also CS_GAXPY, CS_ADD, MTIMES.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_mult mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_multiply_mex.c b/CSparse/MATLAB/CSparse/cs_multiply_mex.c
new file mode 100644
index 0000000..8b61dbc
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_multiply_mex.c
@@ -0,0 +1,25 @@
+#include "cs_mex.h"
+/* cs_multiply: sparse matrix multiply */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, Bmatrix, *A, *B, *C, *D ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_multiply(A,B)") ;
+ }
+ A = cs_transpose (cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]), 1) ;
+ B = cs_transpose (cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]), 1) ;
+ D = cs_multiply (B,A) ; /* D = B'*A' */
+ cs_spfree (A) ;
+ cs_spfree (B) ;
+ cs_dropzeros (D) ; /* drop zeros from D */
+ C = cs_transpose (D, 1) ; /* C = D', so that C is sorted */
+ cs_spfree (D) ;
+ pargout [0] = cs_mex_put_sparse (&C) ; /* return C */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_must_compile.m b/CSparse/MATLAB/CSparse/cs_must_compile.m
new file mode 100644
index 0000000..1810a57
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_must_compile.m
@@ -0,0 +1,23 @@
+function [s, t, tobj] = cs_must_compile (srcdir, f, suffix, obj, hfile, force)
+%CS_MUST_COMPILE return 1 if source code f must be compiled, 0 otherwise
+% Used by cs_make, and MATLAB/Test/cs_test_make.m.
+%
+% Example:
+% none, not meant for end users.
+% See also: CS_MAKE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+dobj = dir ([f obj]) ;
+if (force | isempty (dobj)) %#ok
+ s = 1 ;
+ t = Inf ;
+ tobj = -1 ;
+ return
+end
+dsrc = dir ([srcdir f suffix '.c']) ;
+dh = dir (hfile) ;
+t = max (datenum (dsrc.date), datenum (dh.date)) ;
+tobj = datenum (dobj.date) ;
+s = (tobj < t) ;
diff --git a/CSparse/MATLAB/CSparse/cs_nd.m b/CSparse/MATLAB/CSparse/cs_nd.m
new file mode 100644
index 0000000..1afcbfc
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_nd.m
@@ -0,0 +1,27 @@
+function p = cs_nd (A)
+%CS_ND generalized nested dissection ordering.
+% p = cs_nd(A) computes the nested dissection ordering of a matrix. Small
+% submatrices (order 500 or less) are ordered via cs_amd. A must be sparse
+% and symmetric (use p = cs_nd(A|A') if it is not symmetric).
+%
+% Example:
+% A = delsq (numgrid ('L', 300)) ; % matrix used in 'bench'
+% p = cs_nd (A) ;
+% cspy (A (p,p)) ;
+%
+% See also CS_AMD, CS_SEP, CS_ESEP, CS_NSEP, AMD.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+if (n == 1)
+ p = 1 ;
+elseif (n < 500)
+ p = cs_amd (A) ; % use cs_amd on small graphs
+else
+ [s a b] = cs_nsep (A) ; % find a node separator
+ a = a (cs_nd (A (a,a))) ; % order A(a,a) recursively
+ b = b (cs_nd (A (b,b))) ; % order A(b,b) recursively
+ p = [a b s] ; % concatenate to obtain the final ordering
+end
diff --git a/CSparse/MATLAB/CSparse/cs_nsep.m b/CSparse/MATLAB/CSparse/cs_nsep.m
new file mode 100644
index 0000000..b7a22fc
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_nsep.m
@@ -0,0 +1,18 @@
+function [s,a,b] = cs_nsep (A)
+%CS_NSEP find a node separator of a symmetric matrix A.
+% [s,a,b] = cs_nsep(A) finds a node separator s that splits the graph of A
+% into two parts a and b of roughly equal size. If A is unsymmetric, use
+% cs_nsep(A|A'). The permutation p = [a b s] is a one-level dissection of A.
+%
+% Example:
+% A = delsq (numgrid ('L', 10)) ; % smaller version as used in 'bench'
+% [s a b] = cs_nsep (A) ; p = [a b s] ;
+% cspy (A (p,p)) ;
+%
+% See also CS_SEP, CS_ESEP, CS_ND.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[a b] = cs_esep (A) ;
+[s a b] = cs_sep (A, a, b) ;
diff --git a/CSparse/MATLAB/CSparse/cs_permute.m b/CSparse/MATLAB/CSparse/cs_permute.m
new file mode 100644
index 0000000..ac138b1
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_permute.m
@@ -0,0 +1,15 @@
+function C = cs_permute (A,p,q) %#ok
+%CS_PERMUTE permute a sparse matrix.
+% C = cs_permute(A,p,q) computes C = A(p,q)
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; [m n] = size (A) ;
+% p = randperm (m) ; q = randperm (n) ;
+% C = cs_permute (A,p,q) ; % C = A(p,q)
+%
+% See also CS_SYMPERM, SUBSREF.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_permute mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_permute_mex.c b/CSparse/MATLAB/CSparse/cs_permute_mex.c
new file mode 100644
index 0000000..3358442
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_permute_mex.c
@@ -0,0 +1,30 @@
+#include "cs_mex.h"
+/* cs_permute: permute a sparse matrix */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *A, *C, *D ;
+ int ignore, *P, *Q, *Pinv ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: C = cs_permute(A,p,q)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ P = cs_mex_get_int (A->m, pargin [1], &ignore, 1) ; /* get P */
+ Q = cs_mex_get_int (A->n, pargin [2], &ignore, 1) ; /* get Q */
+ Pinv = cs_pinv (P, A->m) ; /* P = Pinv' */
+ C = cs_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */
+ D = cs_transpose (C, 1) ; /* sort C via double transpose */
+ cs_spfree (C) ;
+ C = cs_transpose (D, 1) ;
+ cs_spfree (D) ;
+ pargout [0] = cs_mex_put_sparse (&C) ; /* return C */
+ cs_free (Pinv) ;
+ cs_free (P) ;
+ cs_free (Q) ;
+}
diff --git a/CSparse/MATLAB/CSparse/cs_print.m b/CSparse/MATLAB/CSparse/cs_print.m
new file mode 100644
index 0000000..90d4ed0
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_print.m
@@ -0,0 +1,14 @@
+function cs_print (A,brief) %#ok
+%CS_PRINT print the contents of a sparse matrix.
+% cs_print(A) prints a sparse matrix. cs_print(A,1) prints just a few entries.
+%
+% Example:
+% Prob = UFget ('vanHeukelum/cage3') ; A = Prob.A
+% cs_print (A) ;
+%
+% See also: DISPLAY.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_print mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_print_mex.c b/CSparse/MATLAB/CSparse/cs_print_mex.c
new file mode 100644
index 0000000..e66f71f
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_print_mex.c
@@ -0,0 +1,20 @@
+#include "cs_mex.h"
+/* cs_print: print the contents of a sparse matrix. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *A ;
+ int brief ;
+ if (nargout > 0 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: cs_print(A,brief)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ brief = (nargin < 2) ? 0 : mxGetScalar (pargin [1]) ; /* get brief */
+ cs_print (A, brief) ; /* print A */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_qleft.m b/CSparse/MATLAB/CSparse/cs_qleft.m
new file mode 100644
index 0000000..0762562
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_qleft.m
@@ -0,0 +1,36 @@
+function X = cs_qleft (V, Beta, p, Y)
+%CS_QLEFT apply Householder vectors on the left.
+% X = cs_qleft(V,Beta,p,Y) computes X = Hn*...*H2*H1*P*Y = Q'*Y where Q is
+% represented by the Householder vectors V, coefficients Beta, and
+% permutation p. p can be [], which denotes the identity permutation.
+%
+% Example:
+% Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ;
+% b = rand (m,1) ;
+% [V,beta,p,R] = cs_qr (A) ; % QR factorization of A(p,:)
+% b1 = cs_qleft (V, beta, p, b) ;
+% x1 = R (1:n,1:n) \ b1 (1:n) ;
+% x2 = A\b ;
+% norm (x1-x2)
+%
+% See also CS_QR, CS_QRIGHT.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m2 n] = size (V) ;
+[m ny] = size (Y) ;
+X = Y ;
+if (m2 > m)
+ if (issparse (Y))
+ X = [X ; sparse(m2-m,ny)] ;
+ else
+ X = [X ; zeros(m2-m,ny)] ;
+ end
+end
+if (~isempty (p))
+ X = X (p,:) ;
+end
+for k = 1:n
+ X = X - V (:,k) * (Beta (k) * (V (:,k)' * X)) ;
+end
diff --git a/CSparse/MATLAB/CSparse/cs_qr.m b/CSparse/MATLAB/CSparse/cs_qr.m
new file mode 100644
index 0000000..7c4767c
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_qr.m
@@ -0,0 +1,33 @@
+function [V,beta,p,R,q] = cs_qr (A) %#ok
+%CS_QR sparse QR factorization (Householder-based).
+% [V,beta,p,R] = cs_qr(A) computes the QR factorization of A(p,:).
+% [V,beta,p,R,q] = cs_qr(A) computes the QR factorization of A(p,q).
+% The V, beta, and p terms represent the Householder vectors and coefficients.
+% The fill-reducing ordering q is found via q = cs_amd(A,3).
+% The orthogonal factor Q can be obtained via
+% Q = cs_qright(V,beta,p,speye(size(V,1))), in which case Q*R=A(:,q) is the
+% resulting factorization (the permutation p is folded into Q). A must be
+% m-by-n with m >= n. If A is structurally rank deficient, additional empty
+% rows may have been added to V and R. Note that V is typically much sparser
+% than Q.
+%
+% Example:
+%
+% Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ;
+% b = rand (m,1) ;
+% [V,beta,p,R,q] = cs_qr (A) ; % QR factorization of A(p,q)
+% b1 = cs_qleft (V, beta, p, b) ;
+% x1 = R (1:n,1:n) \ b1 (1:n) ;
+% x1 (q) = x1 ;
+% x2 = A\b ;
+% norm (x1-x2)
+% Q = cs_qright(V,beta,p,speye(size(V,1))) ; % Note: p accounted for in Q
+% norm (Q*R-A(:,q),1)
+% fprintf ('nnz(R) %d, nnz(V) %d, nnz(Q) %d\n', nnz(R), nnz(V), nnz(Q)) ;
+%
+% See also CS_AMD, CS_QRIGHT, CS_QR, CS_DMPERM, QR, COLAMD.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_qr mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_qr_mex.c b/CSparse/MATLAB/CSparse/cs_qr_mex.c
new file mode 100644
index 0000000..57cd8da
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_qr_mex.c
@@ -0,0 +1,46 @@
+#include "cs_mex.h"
+/* cs_qr: sparse QR factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ css *S ;
+ csn *N ;
+ cs Amatrix, *A, *D ;
+ int m, n, order, *p ;
+ if (nargout > 5 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: [V,beta,p,R,q] = cs_qr(A)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ m = A->m ;
+ n = A->n ;
+ if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ;
+ order = (nargout == 5) ? 3 : 0 ; /* determine ordering */
+ S = cs_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
+ N = cs_qr (A, S) ; /* numeric QR factorization */
+ if (!N) mexErrMsgTxt ("qr failed") ;
+ cs_dropzeros (N->L) ; /* drop zeros from V and sort */
+ D = cs_transpose (N->L, 1) ;
+ cs_spfree (N->L) ;
+ N->L = cs_transpose (D, 1) ;
+ cs_spfree (D) ;
+ cs_dropzeros (N->U) ; /* drop zeros from R and sort */
+ D = cs_transpose (N->U, 1) ;
+ cs_spfree (N->U) ;
+ N->U = cs_transpose (D, 1) ;
+ cs_spfree (D) ;
+ m = N->L->m ; /* m may be larger now */
+ p = cs_pinv (S->pinv, m) ; /* p = pinv' */
+ pargout [0] = cs_mex_put_sparse (&(N->L)) ; /* return V */
+ cs_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */
+ pargout [2] = cs_mex_put_int (p, m, 1, 1) ; /* return p */
+ pargout [3] = cs_mex_put_sparse (&(N->U)) ; /* return R */
+ pargout [4] = cs_mex_put_int (S->q, n, 1, 0) ; /* return q */
+ cs_nfree (N) ;
+ cs_sfree (S) ;
+}
diff --git a/CSparse/MATLAB/CSparse/cs_qright.m b/CSparse/MATLAB/CSparse/cs_qright.m
new file mode 100644
index 0000000..951c60a
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_qright.m
@@ -0,0 +1,26 @@
+function X = cs_qright (V, Beta, p, Y)
+%CS_QRIGHT apply Householder vectors on the right.
+% X = cs_qright(V,Beta,p,Y) computes X = Y*P'*H1*H2*...*Hn = Y*Q where Q is
+% represented by the Householder vectors V, coefficients Beta, and
+% permutation p. p can be [], which denotes the identity permutation.
+% To obtain Q itself, use Q = cs_qright(V,Beta,p,speye(size(V,1))).
+%
+% Example:
+% load west0479 ; q = colamd (west0479) ; A = west0479 (:,q) ;
+% [Q,R] = qr (A) ; norm (Q*R-A, 1)
+% [V,beta,p,R2] = cs_qr (A) ;
+% Q2 = cs_qright (V, beta, p, speye(size(V,1))) ; norm (Q2*R2-A, 1)
+%
+% See also CS_QR, CS_QLEFT.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (V) ;
+X = Y ;
+if (~isempty (p))
+ X = X (:,p) ;
+end
+for k = 1:n
+ X = X - (X * (Beta (k) * V (:,k))) * V (:,k)' ;
+end
diff --git a/CSparse/MATLAB/CSparse/cs_qrsol.m b/CSparse/MATLAB/CSparse/cs_qrsol.m
new file mode 100644
index 0000000..3c49456
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_qrsol.m
@@ -0,0 +1,23 @@
+function x = cs_qrsol (A,b,order) %#ok
+%CS_QRSOL solve a sparse least-squares problem.
+% x = cs_qrsol(A,b) solves the over-determined least squares problem to
+% find x that minimizes norm(A*x-b), where b is a full vector and
+% A is m-by-n with m >= n. If m < n, it solves the underdetermined system
+% Ax=b. A 3rd input argument specifies the ordering method to use
+% (0: natural, 3: amd(A'*A)). The default ordering is 3.
+%
+% Example:
+% Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ;
+% b = rand (m,1) ;
+% x1 = cs_qrsol (A,b) ;
+% x2 = A\b ;
+% norm (x1-x2)
+%
+% For this example, cs_qrsol is about 3 times faster than A\b in MATLAB 7.3.
+%
+% See also CS_QR, CS_AMD, CS_LUSOL, CS_CHOLSOL, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_qrsol mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_qrsol_mex.c b/CSparse/MATLAB/CSparse/cs_qrsol_mex.c
new file mode 100644
index 0000000..74222ee
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_qrsol_mex.c
@@ -0,0 +1,31 @@
+#include "cs_mex.h"
+/* cs_qrsol: solve least squares or underdetermined problem */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs *A, Amatrix ;
+ double *x, *b ;
+ int k, order ;
+ if (nargout > 1 || nargin < 2 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: x = cs_qrsol(A,b,order)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ b = cs_mex_get_double (A->m, pargin [1]) ; /* get b */
+ x = cs_calloc (CS_MAX (A->m, A->n), sizeof (double)) ; /* x = b */
+ for (k = 0 ; k < A->m ; k++) x [k] = b [k] ;
+ order = (nargin < 3) ? 3 : mxGetScalar (pargin [2]) ;
+ order = CS_MAX (order, 0) ;
+ order = CS_MIN (order, 3) ;
+ if (!cs_qrsol (order, A, x)) /* x = A\x */
+ {
+ mexErrMsgTxt ("QR solve failed") ;
+ }
+ cs_mex_put_double (A->n, x, &(pargout [0])) ; /* return x */
+ cs_free (x) ;
+}
diff --git a/CSparse/MATLAB/CSparse/cs_randperm.m b/CSparse/MATLAB/CSparse/cs_randperm.m
new file mode 100644
index 0000000..845cce8
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_randperm.m
@@ -0,0 +1,18 @@
+function p = cs_randperm (n, seed) %#ok
+%CS_RANDPERM random permutation.
+% p = cs_randperm (n) returns a repeatable random permutation of 1:n.
+% p = cs_randperm (n,seed) returns the random permutation using the given
+% seed for the random number generator (try cs_randperm (n,rand)), where
+% seed is not 0 or -1. Two special cases are not random permutations at all:
+% p=cs_randperm (n,0) is 1:n, and p=cs_randperm (n,-1) is n:-1:1.
+% This function does not change RAND's state.
+%
+% Example:
+% p = cs_randperm (10)
+%
+% See also CS_DMPERM, RAND, RANDPERM
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_randperm mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_randperm_mex.c b/CSparse/MATLAB/CSparse/cs_randperm_mex.c
new file mode 100644
index 0000000..9df7b6a
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_randperm_mex.c
@@ -0,0 +1,28 @@
+#include "cs_mex.h"
+/* cs_randperm: random permutation. p=cs_randperm(n,0) is 1:n,
+ * p=cs_randperm(n,-1) is n:-1:1. p = cs_randperm (n,seed) is a random
+ * permutation using the given seed (where seed is not 0 or -1).
+ * seed defaults to 1. A single seed always gives a repeatable permutation.
+ * Use p = cs_randperm(n,rand) to get a permutation that varies with each use.
+ */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double seed ;
+ int iseed, n, *p ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: p = cs_randperm(n,seed)") ;
+ }
+ seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ;
+ iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ;
+ n = mxGetScalar (pargin [0]) ;
+ n = CS_MAX (n, 0) ;
+ p = cs_randperm (n, iseed) ;
+ pargout [0] = cs_mex_put_int (p, n, 1, 1) ; /* return p */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_scc.m b/CSparse/MATLAB/CSparse/cs_scc.m
new file mode 100644
index 0000000..787b24f
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_scc.m
@@ -0,0 +1,17 @@
+function [p,r] = cs_scc (A) %#ok
+%CS_SCC strongly-connected components of a square sparse matrix.
+% [p,r] = cs_scc(A) finds a permutation p so that A(p,p) is permuted into
+% block upper triangular form. The diagonal of A is ignored. The kth block
+% is given by A (s,s) where s = r(k):r(k+1)-1. A must be square.
+% For bipartite or rectangular graphs, use cs_scc2.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; [p r] = cs_scc (A) ;
+% cspy (A (p,p)) ;
+%
+% See also CS_DMPERM, DMPERM, CS_SCC2.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_scc mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_scc2.m b/CSparse/MATLAB/CSparse/cs_scc2.m
new file mode 100644
index 0000000..a511235
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_scc2.m
@@ -0,0 +1,61 @@
+function [p, q, r, s] = cs_scc2 (A, bipartite)
+%CS_SCC2 cs_scc, or connected components of a bipartite graph.
+% [p,q,r,s] = cs_scc2(A) finds a permutation p so that A(p,q) is permuted into
+% block upper triangular form (if A is square). In this case, r=s, p=q and
+% the kth diagonal block is given by A (t,t) where t = r(k):r(k)+1.
+% The diagonal of A is ignored. Each block is one strongly connected
+% component of A.
+%
+% If A is not square (or for [p,q,r,s] = cs_scc2(A,1)), then the connected
+% components of the bipartite graph of A are found. A(p,q) is permuted into
+% block diagonal form, where the diagonal blocks are rectangular. The kth
+% block is given by A(r(k):r(k+1)-1,s(k):s(k+1)-1). A can be rectangular.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; [p q r s] = cs_scc2 (A) ;
+% cspy (A (p,q)) ;
+% Prob = UFget ('HB/wm1') ; A = Prob.A ; [p q r s] = cs_scc2 (A) ;
+% cspy (A (p,q)) ;
+%
+% See also CS_DMPERM, DMPERM, CS_SCC, CCSPY.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+if (nargin < 2)
+ bipartite = 0 ;
+end
+
+if (m ~= n | bipartite) %#ok
+
+ % find the connected components of [I A ; A' 0]
+ S = spaugment (A) ;
+ [psym,rsym] = cs_scc (S) ;
+ p = psym (find (psym <= m)) ; %#ok
+ q = psym (find (psym > m)) - m ; %#ok
+ nb = length (rsym) - 1 ;
+ r = zeros (1,nb+1) ;
+ s = zeros (1,nb+1) ;
+ krow = 1 ;
+ kcol = 1 ;
+ for k = 1:nb
+ % find the rows and columns in the kth component
+ r (k) = krow ;
+ s (k) = kcol ;
+ ksym = psym (rsym (k):rsym (k+1)-1) ;
+ krow = krow + length (find (ksym <= m)) ;
+ kcol = kcol + length (find (ksym > m)) ;
+ end
+ r (nb+1) = m+1 ;
+ s (nb+1) = n+1 ;
+
+else
+
+ % find the strongly connected components of A
+ [p,r] = cs_scc (A) ;
+ q = p ;
+ s = r ;
+
+end
+
diff --git a/CSparse/MATLAB/CSparse/cs_scc_mex.c b/CSparse/MATLAB/CSparse/cs_scc_mex.c
new file mode 100644
index 0000000..21da4e6
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_scc_mex.c
@@ -0,0 +1,32 @@
+#include "cs_mex.h"
+/* [p,r] = cs_scc (A) finds the strongly connected components of A */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *A ;
+ csd *D ;
+ int n, j, *Ap2 ;
+ if (nargout > 2 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: [p,r] = cs_scc(A)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ; /* get A */
+ /* cs_scc modifies A->p and then restores it (in cs_dfs). Avoid the issue
+ * of a mexFunction modifying its input (even temporarily) by making a copy
+ * of A->p. This issue does not arise in cs_dmperm, because that function
+ * applies cs_scc to a submatrix C, not to A directly. */
+ n = A->n ;
+ Ap2 = cs_malloc (n+1, sizeof (int)) ;
+ for (j = 0 ; j <= n ; j++) Ap2 [j] = A->p [j] ;
+ A->p = Ap2 ;
+ D = cs_scc (A) ; /* find conn. comp. */
+ pargout [0] = cs_mex_put_int (D->p, n, 1, 0) ; /* return p */
+ pargout [1] = cs_mex_put_int (D->r, D->nb+1, 1, 0) ; /* return r */
+ cs_dfree (D) ;
+ cs_free (Ap2) ; /* free the copy of A->p */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_sep.m b/CSparse/MATLAB/CSparse/cs_sep.m
new file mode 100644
index 0000000..88ba1bb
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_sep.m
@@ -0,0 +1,21 @@
+function [s,as,bs] = cs_sep (A,a,b)
+%CS_SEP convert an edge separator into a node separator.
+% [s,as,bs] = cs_sep (A,a,b) converts an edge separator into a node separator.
+% [a b] is a partition of 1:n, thus the edges in A(a,b) are an edge separator
+% of A. s is the node separator, consisting of a node cover of the edges of
+% A(a,b). as and bs are the sets a and b with s removed.
+%
+% Example:
+% type cs_nsep ; % to see a simple example of use in cs_nsep.m
+%
+% See also CS_DMPERM, CS_NSEP, CS_ESEP, CS_ND.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[p q r s cc rr] = cs_dmperm (A (a,b)) ;
+s = [(a (p (1:rr(2)-1))) (b (q (cc(3):(cc(5)-1))))] ;
+w = ones (1, size (A,1)) ;
+w (s) = 0 ;
+as = a (find (w (a))) ; %#ok
+bs = b (find (w (b))) ; %#ok
diff --git a/CSparse/MATLAB/CSparse/cs_sparse.m b/CSparse/MATLAB/CSparse/cs_sparse.m
new file mode 100644
index 0000000..cad6e30
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_sparse.m
@@ -0,0 +1,17 @@
+function A = cs_sparse (i,j,x) %#ok
+%CS_SPARSE convert a triplet form into a sparse matrix.
+% A = cs_sparse(i,j,x) is identical to A = sparse(i,j,x), except that x must
+% be real, and the length of i, j, and x must be the same.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; S = Prob.A ;
+% [i j x] = find (S) ;
+% A = cs_sparse (i,j,x) ;
+% S-A
+%
+% See also FIND, SPARSE, SPCONVERT.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_sparse mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_sparse_mex.c b/CSparse/MATLAB/CSparse/cs_sparse_mex.c
new file mode 100644
index 0000000..36652ef
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_sparse_mex.c
@@ -0,0 +1,31 @@
+#include "cs_mex.h"
+/* cs_sparse: convert triplet form into compress-column form sparse matrix */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs *A, *C, *T, Tmatrix ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: A = cs_sparse(i,j,x)") ;
+ }
+ T = &Tmatrix ; /* get i,j,x and copy to triplet form */
+ T->nz = mxGetM (pargin [0]) ;
+ T->p = cs_mex_get_int (T->nz, pargin [0], &(T->n), 1) ;
+ T->i = cs_mex_get_int (T->nz, pargin [1], &(T->m), 1) ;
+ cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ;
+ T->x = mxGetPr (pargin [2]) ;
+ T->nzmax = T->nz ;
+ C = cs_compress (T) ; /* create sparse matrix C */
+ cs_dupl (C) ; /* remove duplicates from C */
+ cs_dropzeros (C) ; /* remove zeros from C */
+ A = cs_transpose (C, 1) ; /* A=C' */
+ cs_spfree (C) ;
+ pargout [0] = cs_mex_put_sparse (&A) ; /* return A */
+ cs_free (T->p) ;
+ cs_free (T->i) ;
+}
diff --git a/CSparse/MATLAB/CSparse/cs_sqr.m b/CSparse/MATLAB/CSparse/cs_sqr.m
new file mode 100644
index 0000000..cdb7d8c
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_sqr.m
@@ -0,0 +1,25 @@
+function [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr (A) %#ok
+%CS_SQR symbolic sparse QR factorization.
+% [vnz,rnz,parent,c,leftmost,p] = cs_sqr(A): symbolic QR of A(p,:).
+% [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A) computes the symbolic QR
+% factorization of A(p,q). The fill-reducing ordering q is found via
+% q = cs_amd(A,3).
+%
+% vnz is the number of entries in the matrix of Householder vectors, V.
+% rnz is the number of entries in R. parent is elimination tree.
+% c(i) is the number of entries in R(i,:). leftmost(i) = min(find(A(i,q))).
+% p is the row permutation used to ensure R has a symbolically zero-free
+% diagonal (it can be larger than m if A is structurally rank deficient).
+% q is the fill-reducing ordering, if requested.
+%
+% Example:
+% Prob = UFget ('HB/ibm32') ; A = Prob.A ;
+% [vnz, rnz, parent, c, leftmost, p, q] = cs_sqr (A) ;
+% cspy (A (p,q)) ;
+%
+% See also CS_AMD, CS_QR.
+%
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_sqr mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_sqr_mex.c b/CSparse/MATLAB/CSparse/cs_sqr_mex.c
new file mode 100644
index 0000000..ba06174
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_sqr_mex.c
@@ -0,0 +1,40 @@
+#include "cs_mex.h"
+/* cs_sqr: symbolic sparse QR factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double s ;
+ css *S ;
+ cs Amatrix, *A ;
+ int m, n, order, *p ;
+ if (nargout > 7 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ m = A->m ;
+ n = A->n ;
+ if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ;
+ order = (nargout == 7) ? 3 : 0 ; /* determine ordering */
+ S = cs_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
+ if (!S) mexErrMsgTxt ("cs_sqr failed") ;
+ s = S->lnz ;
+ cs_mex_put_double (1, &s, &(pargout [0])) ; /* return nnz(V) */
+ s = S->unz ;
+ cs_mex_put_double (1, &s, &(pargout [1])) ; /* return nnz(R) */
+ pargout [2] = cs_mex_put_int (S->parent, n, 1, 0) ; /* return parent */
+ pargout [3] = cs_mex_put_int (S->cp, n, 0, 0) ; /* return c */
+ pargout [4] = cs_mex_put_int (S->leftmost, m, 1, 0) ; /* return leftmost*/
+ p = cs_pinv (S->pinv, S->m2) ; /* p = pinv' */
+ pargout [5] = cs_mex_put_int (p, S->m2, 1, 1) ; /* return p */
+ if (nargout > 6)
+ {
+ pargout [6] = cs_mex_put_int (S->q, n, 1, 0) ; /* return q */
+ }
+ cs_sfree (S) ;
+}
diff --git a/CSparse/MATLAB/CSparse/cs_symperm.m b/CSparse/MATLAB/CSparse/cs_symperm.m
new file mode 100644
index 0000000..a913553
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_symperm.m
@@ -0,0 +1,20 @@
+function C = cs_symperm (A,p) %#ok
+%CS_SYMPERM symmetric permutation of a symmetric matrix.
+% C = cs_symperm(A,p) computes C = A(p,p), but accesses only the
+% upper triangular part of A, and returns C upper triangular (A and C are
+% symmetric with just their upper triangular parts stored). A must be square.
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ;
+% p = cs_amd (A) ;
+% C = cs_symperm (A, p) ;
+% cspy (A (p,p)) ;
+% cspy (C) ;
+% C - triu (A (p,p))
+%
+% See also CS_PERMUTE, SUBSREF, TRIU.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_symperm mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_symperm_mex.c b/CSparse/MATLAB/CSparse/cs_symperm_mex.c
new file mode 100644
index 0000000..c263eda
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_symperm_mex.c
@@ -0,0 +1,29 @@
+#include "cs_mex.h"
+/* cs_symperm: symmetric permutation of a symmetric sparse matrix. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *A, *C, *D ;
+ int ignore, n, *P, *Pinv ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_symperm(A,p)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ;
+ n = A->n ;
+ P = cs_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */
+ Pinv = cs_pinv (P, n) ; /* P=Pinv' */
+ C = cs_symperm (A, Pinv, 1) ; /* C = A(p,p) */
+ D = cs_transpose (C, 1) ; /* sort C */
+ cs_spfree (C) ;
+ C = cs_transpose (D, 1) ;
+ cs_spfree (D) ;
+ pargout [0] = cs_mex_put_sparse (&C) ; /* return C */
+ cs_free (P) ;
+ cs_free (Pinv) ;
+}
diff --git a/CSparse/MATLAB/CSparse/cs_thumb_mex.c b/CSparse/MATLAB/CSparse/cs_thumb_mex.c
new file mode 100644
index 0000000..8a1b1d8
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_thumb_mex.c
@@ -0,0 +1,56 @@
+#include "cs_mex.h"
+/* cs_thumb: convert a sparse matrix to a dense 2D thumbnail matrix of size
+ * at most k-by-k. k defaults to 256. A helper mexFunction for cspy. */
+
+#define INDEX(i,j,lda) ((i)+(j)*(lda))
+#define ISNAN(x) ((x) != (x))
+#ifdef DBL_MAX
+#define BIG_VALUE DBL_MAX
+#else
+#define BIG_VALUE 1.7e308
+#endif
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *A ;
+ int m, n, mn, m2, n2, k, s, j, ij, sj, si, p, *Ap, *Ai ;
+ double aij, *S, *Ax ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: S = cs_thumb(A,k)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ m = A->m ;
+ n = A->n ;
+ mn = CS_MAX (m,n) ;
+ k = (nargin == 1) ? 256 : mxGetScalar (pargin [1]) ; /* get k */
+ /* s = size of each submatrix; A(1:s,1:s) maps to S(1,1) */
+ s = (mn < k) ? 1 : (int) ceil ((double) mn / (double) k) ;
+ m2 = (int) ceil ((double) m / (double) s) ;
+ n2 = (int) ceil ((double) n / (double) s) ;
+ /* create S */
+ pargout [0] = mxCreateDoubleMatrix (m2, n2, mxREAL) ;
+ S = mxGetPr (pargout [0]) ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ sj = j/s ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ si = Ai [p] / s ;
+ ij = INDEX (si,sj,m2) ;
+ aij = fabs (Ax [p]) ;
+ if (ISNAN (aij)) aij = BIG_VALUE ;
+ aij = CS_MIN (BIG_VALUE, aij) ;
+ S [ij] = CS_MAX (S [ij], aij) ;
+ }
+ }
+}
diff --git a/CSparse/MATLAB/CSparse/cs_transpose.m b/CSparse/MATLAB/CSparse/cs_transpose.m
new file mode 100644
index 0000000..8cdb65f
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_transpose.m
@@ -0,0 +1,17 @@
+function C = cs_transpose (A) %#ok
+%CS_TRANSPOSE transpose a real sparse matrix.
+% C = cs_transpose(A), computes C = A' where A must be sparse and real.
+%
+% Example:
+% Prob = UFget ('HB/ibm32') ; A = Prob.A ;
+% C = cs_transpose (A) ;
+% C-A'
+%
+% See also TRANSPOSE, CTRANSPOSE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_transpose mexFunction not found') ;
+
+
diff --git a/CSparse/MATLAB/CSparse/cs_transpose_mex.c b/CSparse/MATLAB/CSparse/cs_transpose_mex.c
new file mode 100644
index 0000000..af6a88a
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_transpose_mex.c
@@ -0,0 +1,19 @@
+#include "cs_mex.h"
+/* C = cs_transpose (A), computes C=A', where A must be sparse and real */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Amatrix, *A, *C ;
+ if (nargout > 1 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: C = cs_transpose(A)") ;
+ }
+ A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ C = cs_transpose (A, 1) ; /* C = A' */
+ pargout [0] = cs_mex_put_sparse (&C) ; /* return C */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_updown.m b/CSparse/MATLAB/CSparse/cs_updown.m
new file mode 100644
index 0000000..f4fa3cc
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_updown.m
@@ -0,0 +1,26 @@
+function L = cs_updown (L, c, parent, sigma) %#ok
+%CS_UPDOWN rank-1 update/downdate of a sparse Cholesky factorization.
+% L = cs_updown(L,c,parent) computes the rank-1 update L = chol(L*L'+c*c')',
+% where parent is the elimination tree of L. c must be a sparse column
+% vector, and find(c) must be a subset of find(L(:,k)) where k = min(find(c)).
+% L = cs_updown(L,c,parent,'-') is the downdate L = chol(L*L'-c*c').
+% L = cs_updown(L,c,parent,'+') is the update L = chol(L*L'+c*c').
+% Updating/downdating is much faster than refactorizing the matrix with
+% cs_chol or chol. L must not have an entries dropped due to numerical
+% cancellation (use cs_chol(A,0)).
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; n = size (A,1) ;
+% L = cs_chol (A,0) ;
+% parent = cs_etree (A) ;
+% c = sprand (L (:, floor(n/2))) ;
+% L1 = cs_updown (L, c, parent) ;
+% L2 = cs_chol (A + c*c', 0) ;
+% norm (L1-L2, 1)
+%
+% See also CS_ETREE, CS_CHOL, ETREE, CHOLUPDATE, CHOL.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_updown mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_updown_mex.c b/CSparse/MATLAB/CSparse/cs_updown_mex.c
new file mode 100644
index 0000000..c9d9b3a
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_updown_mex.c
@@ -0,0 +1,53 @@
+#include "cs_mex.h"
+/* cs_updown: sparse Cholesky update/downdate (rank-1 or multiple rank) */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
+ int ignore, j, k, n, lnz, *parent, sigma = 1, cp [2] ;
+ char sigma_string [20] ;
+
+ if (nargout > 1 || nargin < 3 || nargin > 4)
+ {
+ mexErrMsgTxt ("Usage: L = cs_updown(L,C,parent,sigma)") ;
+ }
+ Lin = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get input L */
+ n = Lin->n ;
+ if (nargin > 3 && mxIsChar (pargin [3]))
+ {
+ mxGetString (pargin [3], sigma_string, 8) ;
+ sigma = (sigma_string [0] == '-') ? (-1) : 1 ;
+ }
+ /* make a copy of L (this can take more work than updating L itself) */
+ lnz = Lin->p [n] ;
+ L = cs_spalloc (n, n, lnz, 1, 0) ;
+ for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
+ for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
+ for (k = 0 ; k < lnz ; k++) L->x [k] = Lin->x [k] ;
+ cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
+ C = cs_mex_get_sparse (&Cmatrix, 0, 1, pargin [1]) ;
+ parent = cs_mex_get_int (n, pargin [2], &ignore, 0) ; /* get parent */
+
+ /* do the update one column at a time */
+ Cvec = &Cvector ;
+ Cvec->m = n ;
+ Cvec->n = 1 ;
+ Cvec->p = cp ;
+ Cvec->nz = -1 ;
+ cp [0] = 0 ;
+ for (k = 0 ; k < C->n ; k++)
+ {
+ /* extract C(:,k) */
+ cp [1] = C->p [k+1] - C->p [k] ;
+ Cvec->nzmax = cp [1] ;
+ Cvec->i = C->i + C->p [k] ;
+ Cvec->x = C->x + C->p [k] ;
+ cs_updown (L, sigma, Cvec, parent) ; /* update/downdate */
+ }
+ pargout [0] = cs_mex_put_sparse (&L) ; /* return new L */
+}
diff --git a/CSparse/MATLAB/CSparse/cs_usolve.m b/CSparse/MATLAB/CSparse/cs_usolve.m
new file mode 100644
index 0000000..842dcfa
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_usolve.m
@@ -0,0 +1,21 @@
+function x = cs_usolve (U,b) %#ok
+%CS_USOLVE solve a sparse upper triangular system U*x=b.
+% x = cs_usolve(U,b) computes x = U\b, U must be lower triangular with a
+% zero-free diagonal. b must be a column vector. x is full if b is full.
+% If b is sparse, x is sparse but nonzero pattern of x is NOT sorted (it is
+% returned in topological order).
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size (A,1) ;
+% b = rand (n,1);
+% [L U p q] = cs_lu (A) ;
+% x = cs_usolve (U, cs_lsolve (L, b(p))) ; % x = U \ (L \ b(p)) ;
+% x (q) = x ;
+% norm (A*x-b)
+%
+% See also CS_LSOLVE, CS_LTSOLVE, CS_UTSOLVE, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_usolve mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_usolve_mex.c b/CSparse/MATLAB/CSparse/cs_usolve_mex.c
new file mode 100644
index 0000000..7aad1ed
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_usolve_mex.c
@@ -0,0 +1,59 @@
+#include "cs_mex.h"
+/* cs_usolve: x=U\b. U must be sparse, real, and upper triangular. b must be a
+ * real full or sparse vector. x is full or sparse, depending on b.
+ *
+ * Time taken is O(flop count), which may be less than n if b is sparse,
+ * depending on U and b.
+ *
+ * This function works with MATLAB 7.2, but is not perfectly compatible with
+ * the requirements of a MATLAB mexFunction when b is sparse. X is returned
+ * as an unsorted sparse vector. Also, this mexFunction temporarily modifies
+ * its input, U, by modifying U->p (in the cs_dfs function) and then restoring
+ * it. This could be corrected by creating a copy of U->p (see
+ * cs_dmperm_mex.c), but this would take O(n) time, destroying the
+ * O(flop count) time complexity of this function.
+ */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Umatrix, Bmatrix, *U, *B, *X ;
+ double *x, *b ;
+ int top, nz, p, *xi ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_usolve(U,b)") ;
+ }
+ U = cs_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */
+ if (mxIsSparse (pargin [1]))
+ {
+ B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b */
+ cs_mex_check (0, U->n, 1, 0, 1, 1, pargin [1]) ;
+ xi = cs_malloc (2*U->n, sizeof (int)) ; /* get workspace */
+ x = cs_malloc (U->n, sizeof (double)) ;
+ top = cs_spsolve (U, B, 0, xi, x, NULL, 0) ; /* x = U\b */
+ X = cs_spalloc (U->n, 1, U->n-top, 1, 0) ; /* create sparse x*/
+ X->p [0] = 0 ;
+ nz = 0 ;
+ for (p = top ; p < U->n ; p++)
+ {
+ X->i [nz] = xi [p] ;
+ X->x [nz++] = x [xi [p]] ;
+ }
+ X->p [1] = nz ;
+ pargout [0] = cs_mex_put_sparse (&X) ;
+ cs_free (x) ;
+ cs_free (xi) ;
+ }
+ else
+ {
+ b = cs_mex_get_double (U->n, pargin [1]) ; /* get full b */
+ x = cs_mex_put_double (U->n, b, &(pargout [0])) ; /* x = b */
+ cs_usolve (U, x) ; /* x = U\x */
+ }
+}
diff --git a/CSparse/MATLAB/CSparse/cs_utsolve.m b/CSparse/MATLAB/CSparse/cs_utsolve.m
new file mode 100644
index 0000000..05c8037
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_utsolve.m
@@ -0,0 +1,19 @@
+function x = cs_utsolve (U,b) %#ok
+%CS_UTSOLVE solve a sparse lower triangular system U'*x=b.
+% x = cs_utsolve(U,b) computes x = U'\b, U must be upper triangular with a
+% zero-free diagonal. b must be a full vector.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size (A,1) ;
+% b = rand (n,1);
+% [L U p q] = cs_lu (A) ;
+% x = cs_ltsolve (L, cs_utsolve (U, b(q))) ; % x = L' \ (U' \ b(q)) ;
+% x (p) = x ;
+% norm (A'*x-b)
+%
+% See also CS_LSOLVE, CS_LTSOLVE, CS_USOLVE, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_utsolve mexFunction not found') ;
diff --git a/CSparse/MATLAB/CSparse/cs_utsolve_mex.c b/CSparse/MATLAB/CSparse/cs_utsolve_mex.c
new file mode 100644
index 0000000..37fc147
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cs_utsolve_mex.c
@@ -0,0 +1,21 @@
+#include "cs_mex.h"
+/* cs_utsolve: solve a lower triangular system U'*x=b */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Umatrix, *U ;
+ double *x, *b ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_utsolve(U,b)") ;
+ }
+ U = cs_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */
+ b = cs_mex_get_double (U->n, pargin [1]) ; /* get b */
+ x = cs_mex_put_double (U->n, b, &(pargout [0])) ; /* x = b */
+ cs_utsolve (U, x) ; /* x = U'\x */
+}
diff --git a/CSparse/MATLAB/CSparse/cspy.m b/CSparse/MATLAB/CSparse/cspy.m
new file mode 100644
index 0000000..a86f01c
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/cspy.m
@@ -0,0 +1,100 @@
+function [s,M,H] = cspy (A,res)
+%CSPY plot a matrix in color.
+% cspy(A) plots a matrix, in color, with a default resolution of
+% 256-by-256. cspy(A,res) changes the resolution to res. Zero entries are
+% white. Entries with tiny absolute value are light orange. Entries with
+% large magnitude are black. Entries in the midrange (the median of the
+% log10 of the nonzero values, +/- one standard deviation) range from light
+% green to deep blue. With no inputs, the color legend of cspy is plotted.
+% [s,M,H] = cspy(A) returns the scale factor s, the image M, and colormap H.
+%
+% The matrix A can be full or sparse, and either numeric (double, single,
+% integer) or character type, and either complex or real.
+%
+% Example
+% A = delsq (numgrid ('L', 10)) ;
+% cspy (A) ;
+%
+% See also CS_DMSPY, SPY.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if nargin < 2
+ res = 256 ;
+end
+
+h = jet (64) ;
+h = h (64:-1:1,:) ;
+h = h (30:end,:) ;
+hmax = size (h,1) ;
+
+h (1,:) = [1 1 1] ; % white for zero
+h (2,:) = [1 .9 .5] ; % light orange for tiny entries
+h (hmax,:) = [0 0 0] ; % black for very large entries
+colormap (h) ;
+
+if (nargin == 0)
+ image (1:hmax) ;
+ title ('cspy color map') ;
+ return
+end
+
+% convert complex, integers, and strings to real double
+if (~isreal (A) | ~isa (A, 'double') | ~issparse (A)) %#ok
+ A = sparse (abs (double (A))) ;
+end
+
+[m1 n1] = size (A) ;
+if (m1 == 0 | n1 == 0) %#ok
+ A (1,1) = 0 ;
+end
+[m1 n1] = size (A) ;
+
+S = cs_thumb (A,res) ; % get the thumbnail of the matrix
+[m n] = size (S) ;
+[i j x] = find (S) ;
+x = log10 (x) ;
+
+if (isempty (x))
+ S = zeros (size (S)) ;
+else
+ med = median (x) ;
+ sdev = std (x) ;
+ big = med + sdev ;
+ tiny = med - sdev ;
+ imid = find (x > tiny & x < big) ;
+ itiny = find (x <= tiny) ;
+ ibig = find (x >= big) ;
+ x (imid) = 1 + ceil ((hmax-2) * (x (imid) - tiny) / (big - tiny)) ;
+ x (itiny) = 1 ; %#ok
+ x (ibig) = hmax-1 ; %#ok
+ S = full (1 + sparse (i,j,x,m,n)) ;
+
+% title (sprintf ('tiny: %-8.2g median: %-8.2g big: %-8.2g\n', ...
+% 10^tiny, 10^med, 10^big)) ;
+end
+
+% draw the matrix
+image (S) ;
+axis equal ;
+axis ([-1 n+1 -1 m+1]) ;
+axis off
+
+% draw a box around the whole matrix
+e = ceil (max (m1,n1) / max (m,n)) ; % scale factor
+hold on
+drawbox (1,m1+1,1,n1+1,'k',1,e) ;
+hold off
+
+% return results
+if (nargout > 0)
+ s = e ;
+end
+if (nargout > 1)
+ M = S ; % image
+end
+if (nargout > 2)
+ H = h ; % colormap
+end
+
diff --git a/CSparse/MATLAB/CSparse/private/drawbox.m b/CSparse/MATLAB/CSparse/private/drawbox.m
new file mode 100644
index 0000000..d46d5d7
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/private/drawbox.m
@@ -0,0 +1,29 @@
+function drawbox (r1,r2,c1,c2,color,w,e)
+%DRAWBOX draw a box around a submatrix in the figure.
+% Used by cspy, cs_dmspy, and ccspy.
+% Example:
+% drawbox (r1,r2,c1,c2,color,w,e)
+% See also drawboxes, plot
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (r1 == r2 | c1 == c2) %#ok
+ return
+end
+
+if (e == 1)
+ r1 = r1 - .5 ;
+ r2 = r2 - .5 ;
+ c1 = c1 - .5 ;
+ c2 = c2 - .5 ;
+else
+ r1 = ceil (r1 / e) - .5 ;
+ r2 = ceil ((r2 - 1) / e) + .5 ;
+ c1 = ceil (c1 / e) - .5 ;
+ c2 = ceil ((c2 - 1) / e) + .5 ;
+end
+
+if (c2 > c1 | r2 > r1) %#ok
+ plot ([c1 c2 c2 c1 c1], [r1 r1 r2 r2 r1], color, 'LineWidth', w) ;
+end
diff --git a/CSparse/MATLAB/CSparse/private/drawboxes.m b/CSparse/MATLAB/CSparse/private/drawboxes.m
new file mode 100644
index 0000000..86e3bb5
--- /dev/null
+++ b/CSparse/MATLAB/CSparse/private/drawboxes.m
@@ -0,0 +1,29 @@
+function drawboxes (nb, e, r, s)
+%DRAWBOXES: helper function for cs_dmpsy and ccspy
+% Example:
+% drawboxes (nb, e, r, s)
+% See also drawbox, plot
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nb > 1)
+ if (e == 1)
+ r1 = r (1:nb) - .5 ;
+ r2 = r (2:nb+1) - .5 ;
+ c1 = s (1:nb) - .5 ;
+ c2 = s (2:nb+1) - .5 ;
+ else
+ r1 = ceil (r (1:nb) / e) - .5 ;
+ r2 = ceil ((r (2:nb+1) - 1) / e) + .5 ;
+ c1 = ceil (s (1:nb) / e) - .5 ;
+ c2 = ceil ((s (2:nb+1) - 1) / e) + .5 ;
+ end
+ kk = find (diff (c1) > 0 | diff (c2) > 0 | diff (r1) > 0 | diff (r2) > 0) ;
+ kk = [1 kk+1] ;
+ for k = kk
+ plot ([c1(k) c2(k) c2(k) c1(k) c1(k)], ...
+ [r1(k) r1(k) r2(k) r2(k) r1(k)], 'k', 'LineWidth', 1) ;
+ end
+end
+
diff --git a/CSparse/MATLAB/Demo/Contents.m b/CSparse/MATLAB/Demo/Contents.m
new file mode 100644
index 0000000..1a3bda9
--- /dev/null
+++ b/CSparse/MATLAB/Demo/Contents.m
@@ -0,0 +1,11 @@
+% CSparse MATLAB demos.
+%
+% cs_demo - run all CSparse demos.
+% cs_demo1 - MATLAB version of the CSparse/Demo/cs_demo1.c program.
+% cs_demo2 - MATLAB version of the CSparse/Demo/cs_demo2.c program.
+% cs_demo3 - MATLAB version of the CSparse/Demo/cs_demo3.c program.
+
+% Example:
+% help cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis
diff --git a/CSparse/MATLAB/Demo/README.txt b/CSparse/MATLAB/Demo/README.txt
new file mode 100644
index 0000000..bcc9eec
--- /dev/null
+++ b/CSparse/MATLAB/Demo/README.txt
@@ -0,0 +1 @@
+Demo for MATLAB interface for CSparse. See Contents.m for details.
diff --git a/CSparse/MATLAB/Demo/cs_demo.m b/CSparse/MATLAB/Demo/cs_demo.m
new file mode 100644
index 0000000..a9cee29
--- /dev/null
+++ b/CSparse/MATLAB/Demo/cs_demo.m
@@ -0,0 +1,47 @@
+function cs_demo (do_pause, matrixpath)
+%CS_DEMO run all CSparse demos.
+% cs_demo(0) will run all demos without pausing.
+%
+% Example:
+% cs_demo
+% See also: cs_demo1, cs_demo2, cs_demo3
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+help cs_demo
+if (nargin < 1)
+ do_pause = 1 ;
+end
+if (nargin < 2)
+ matrixpath = [] ;
+end
+
+figure (1)
+clf
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help cs_demo1 ;
+cs_demo1 (matrixpath) ;
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help cs_demo2
+cs_demo2 (do_pause, matrixpath) ;
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help cs_demo3
+cs_demo3 (do_pause, matrixpath) ;
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help ex_1
+ex_1
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help ex2
+ex2
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help ex3
+ex3
+
+fprintf ('\nAll CSparse demos finished.\n') ;
diff --git a/CSparse/MATLAB/Demo/cs_demo1.m b/CSparse/MATLAB/Demo/cs_demo1.m
new file mode 100644
index 0000000..cd023cd
--- /dev/null
+++ b/CSparse/MATLAB/Demo/cs_demo1.m
@@ -0,0 +1,56 @@
+function cs_demo1 (matrixpath)
+%CS_DEMO1 MATLAB version of the CSparse/Demo/cs_demo1.c program.
+% Uses both MATLAB functions and CSparse mexFunctions, and compares the two
+% results. This demo also plots the results, which the C version does not do.
+%
+% Example:
+% cs_demo1
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 1)
+ matrixpath = [] ;
+end
+
+if (isempty (matrixpath))
+ try
+ % older versions of MATLAB do not have an input argument to mfilename
+ p = mfilename ('fullpath') ;
+ t = strfind (p, filesep) ;
+ matrixpath = [ p(1:t(end)) '../../Matrix' ] ;
+ catch
+ % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory
+ matrixpath = '../../Matrix' ;
+ end
+end
+
+t1 = load ([matrixpath '/t1']) ;
+
+T = t1 %#ok
+A = sparse (T(:,1)+1, T(:,2)+1, T(:,3)) %#ok
+A2 = cs_sparse (T(:,1)+1, T(:,2)+1, T(:,3)) %#ok
+fprintf ('A difference: %g\n', norm (A-A2,1)) ;
+% CSparse/Demo/cs_demo1.c also clears the triplet matrix T at this point:
+% clear T
+clf
+subplot (2,2,1) ; cspy (A) ; title ('A', 'FontSize', 16) ;
+AT = A' %#ok
+AT2 = cs_transpose (A) %#ok
+fprintf ('AT difference: %g\n', norm (AT-AT2,1)) ;
+subplot (2,2,2) ; cspy (AT) ; title ('A''', 'FontSize', 16) ;
+n = size (A,2) ;
+I = speye (n) ;
+C = A*AT ;
+C2 = cs_multiply (A, AT) %#ok
+fprintf ('C difference: %g\n', norm (C-C2,1)) ;
+subplot (2,2,3) ; cspy (C) ; title ('C=A*A''', 'FontSize', 16) ;
+cnorm = norm (C,1) ;
+D = C + I*cnorm %#ok
+D2 = cs_add (C, I, 1, cnorm) %#ok
+fprintf ('D difference: %g\n', norm (D-D2,1)) ;
+subplot (2,2,4) ; cspy (D) ; title ('D=C+I*norm(C,1)', 'FontSize', 16) ;
+% CSparse/Demo/cs_demo1.c clears all matrices at this point:
+% clear A AT C D I
+% clear A2 AT2 C2 D2
diff --git a/CSparse/MATLAB/Demo/cs_demo2.m b/CSparse/MATLAB/Demo/cs_demo2.m
new file mode 100644
index 0000000..98486fa
--- /dev/null
+++ b/CSparse/MATLAB/Demo/cs_demo2.m
@@ -0,0 +1,42 @@
+function cs_demo2 (do_pause, matrixpath)
+%CS_DEMO2 MATLAB version of the CSparse/Demo/cs_demo2.c program.
+% Solves a linear system using Cholesky, LU, and QR, with various orderings.
+%
+% Example:
+% cs_demo2
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 2)
+ matrixpath = [] ;
+end
+
+if (isempty (matrixpath))
+ try
+ % older versions of MATLAB do not have an input argument to mfilename
+ p = mfilename ('fullpath') ;
+ t = strfind (p, filesep) ;
+ matrixpath = [ p(1:t(end)) '../../Matrix' ] ;
+ catch
+ % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory
+ matrixpath = '../../Matrix' ;
+ end
+end
+
+matrices = { 't1', 'HB/fs_183_1', 'HB/west0067', 'LPnetlib/lp_afiro', ...
+'HB/ash219', 'HB/mbeacxc', 'HB/bcsstk01', 'HB/bcsstk16' } ;
+
+if (nargin < 1)
+ do_pause = 1 ;
+end
+
+for i = 1:length(matrices)
+ name = matrices {i} ;
+ [C sym] = get_problem (matrixpath, name, 1e-14) ;
+ demo2 (C, sym, name) ;
+ if (do_pause)
+ input ('Hit enter to continue: ') ;
+ end
+end
diff --git a/CSparse/MATLAB/Demo/cs_demo3.m b/CSparse/MATLAB/Demo/cs_demo3.m
new file mode 100644
index 0000000..2527884
--- /dev/null
+++ b/CSparse/MATLAB/Demo/cs_demo3.m
@@ -0,0 +1,41 @@
+function cs_demo3 (do_pause, matrixpath)
+%CS_DEMO3 MATLAB version of the CSparse/Demo/cs_demo3.c program.
+% Cholesky update/downdate.
+%
+% Example:
+% cs_demo3
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 2)
+ matrixpath = [] ;
+end
+
+if (isempty (matrixpath))
+ try
+ % older versions of MATLAB do not have an input argument to mfilename
+ p = mfilename ('fullpath') ;
+ t = strfind (p, filesep) ;
+ matrixpath = [ p(1:t(end)) '../../Matrix' ] ;
+ catch
+ % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory
+ matrixpath = '../../Matrix' ;
+ end
+end
+
+matrices = { 'HB/bcsstk01', 'HB/bcsstk16' } ;
+
+if (nargin < 1)
+ do_pause = 1 ;
+end
+
+for i = 1:length(matrices)
+ name = matrices {i} ;
+ [C sym] = get_problem (matrixpath, name, 1e-14) ;
+ demo3 (C, sym, name) ;
+ if (do_pause)
+ input ('Hit enter to continue: ') ;
+ end
+end
diff --git a/CSparse/MATLAB/Demo/private/demo2.m b/CSparse/MATLAB/Demo/private/demo2.m
new file mode 100644
index 0000000..5b8e805
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/demo2.m
@@ -0,0 +1,109 @@
+function demo2 (C, sym, name)
+%DEMO2: solve a linear system using Cholesky, LU, and QR, with various orderings
+%
+% Example:
+% demo2 (C, 1, 'name of system')
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clf
+subplot (2,2,1) ; cspy (C) ;
+title (name, 'FontSize', 16, 'Interpreter', 'none') ;
+[m n] = size (C) ;
+[p,q,r,s,cc,rr] = cs_dmperm (C) ;
+subplot (2,2,3) ; cs_dmspy (C) ;
+subplot (2,2,2) ; ccspy (C) ;
+drawnow
+
+sprnk = rr (4) - 1 ;
+nb = length (r) - 1 ;
+ns = sum ((r (2:nb+1) == r (1:nb)+1) & (s (2:nb+1) == s (1:nb)+1)) ;
+fprintf ('blocks: %d singletons %d structural rank %d\n', nb, ns, sprnk) ;
+
+if (sprnk ~= sprank (C))
+ error ('sprank mismatch!') ;
+end
+
+if (sprnk < min (m,n))
+ return ; % return if structurally singular
+end
+
+
+% the following code is not in the C version of this demo:
+if (m == n)
+ if (sym)
+ try
+ [L,p] = cs_chol (C) ; %#ok
+ subplot (2,2,4) ;
+ cspy (L+triu(L',1)) ; title ('L+L''') ;
+ catch
+ % tol = 0.001 ;
+ [L,U,p,q] = cs_lu (C,0.001) ; %#ok
+ subplot (2,2,4) ;
+ cspy (L+U-speye(n)) ; title ('L+U') ;
+ end
+ else
+ [L,U,p,q] = cs_lu (C) ; %#ok
+ subplot (2,2,4) ;
+ cspy (L+U-speye(n)) ; title ('L+U') ;
+ end
+else
+ if (m < n)
+ [V,beta,p,R,q] = cs_qr (C') ; %#ok
+ else
+ [V,beta,p,R,q] = cs_qr (C) ; %#ok
+ end
+ subplot (2,2,4) ;
+ cspy (V+R) ; title ('V+R') ;
+end
+drawnow
+
+% continue with the MATLAB equivalent of the C cs_demo2 program
+for order = [0 3]
+ if (order == 0 & m > 1000) %#ok
+ continue ;
+ end
+ fprintf ('QR ') ;
+ print_order (order) ;
+ b = rhs (m) ; % compute right-hand-side
+ tic ;
+ x = cs_qrsol (C, b, order) ;
+ fprintf ('time %8.2f ', toc) ;
+ print_resid (C, x, b) ;
+end
+
+if (m ~= n)
+ return ;
+end
+
+for order = 0:3
+ if (order == 0 & m > 1000) %#ok
+ continue ;
+ end
+ fprintf ('LU ') ;
+ print_order (order) ;
+ b = rhs (m) ; % compute right-hand-side
+ tic ;
+ x = cs_lusol (C, b, order) ;
+ fprintf ('time %8.2f ', toc) ;
+ print_resid (C, x, b) ;
+end
+
+if (sym == 0)
+ return ;
+end
+
+for order = 0:1
+ if (order == 0 & m > 1000) %#ok
+ continue ;
+ end
+ fprintf ('Chol ') ;
+ print_order (order) ;
+ b = rhs (m) ; % compute right-hand-side
+ tic ;
+ x = cs_cholsol (C, b, order) ;
+ fprintf ('time %8.2f ', toc) ;
+ print_resid (C, x, b) ;
+end
diff --git a/CSparse/MATLAB/Demo/private/demo3.m b/CSparse/MATLAB/Demo/private/demo3.m
new file mode 100644
index 0000000..3d627f8
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/demo3.m
@@ -0,0 +1,97 @@
+function demo3 (C, sym, name)
+%DEMO3: Cholesky update/downdate
+%
+% Example:
+% demo3 (C, 1, 'name of system')
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clf
+subplot (2,2,1) ; cspy (C) ;
+title (name, 'FontSize', 16, 'Interpreter', 'none') ;
+drawnow
+
+[m n] = size (C) ;
+if (m ~= n | ~sym) %#ok
+ return ;
+end
+
+b = rhs (n) ;
+fprintf ('chol then update/downdate ') ;
+print_order (0) ;
+
+tic ;
+[L,p] = cs_chol (C) ;
+t = toc ;
+fprintf ('\nchol time: %8.2f\n', t) ;
+
+subplot (2,2,2) ; cspy (L) ; title ('L') ;
+drawnow
+
+tic ;
+x = b (p) ;
+x = cs_lsolve (L,x) ;
+x = cs_ltsolve (L,x) ;
+x (p) = x ;
+t = toc ;
+fprintf ('solve time: %8.2f\n', t) ;
+
+fprintf ('original: ') ;
+print_resid (C, x, b) ;
+
+k = fix (n/2) ;
+w = L(k,k) * sprand (L (:,k)) ;
+
+parent = cs_etree (C (p,p)) ;
+
+tic ;
+L2 = cs_updown (L, w, parent, '+') ;
+t1 = toc ;
+fprintf ('update: time: %8.2f\n', t1) ;
+
+subplot (2,2,3) ; cspy (L2) ; title ('updated L') ;
+subplot (2,2,4) ; cspy (L-L2) ; title ('L - updated L') ;
+drawnow
+
+tic ;
+x = b (p) ;
+x = cs_lsolve (L2,x) ;
+x = cs_ltsolve (L2,x) ;
+x (p) = x ;
+t = toc ;
+
+w2 = sparse (n,1) ;
+w2 (p) = w ; % w2 = P'*w
+wt = cs_transpose (w2) ;
+ww = cs_multiply (w2,wt) ;
+E = cs_add (C, ww, 1, 1) ; % E = C + w2*w2' ;
+
+fprintf ('update: time: %8.2f (incl solve) ', t1+t) ;
+print_resid (E, x, b) ;
+
+tic
+[L,p2] = cs_chol (E) ;
+x = b (p2) ;
+x = cs_lsolve (L,x) ;
+x = cs_ltsolve (L,x) ;
+x (p2) = x ;
+t = toc ;
+fprintf ('rechol: time: %8.2f (incl solve) ', t) ;
+print_resid (E, x, b) ;
+
+tic ;
+L3 = cs_updown (L2, w, parent, '-') ;
+t1 = toc ;
+fprintf ('downdate: time: %8.2f\n', t1) ;
+
+tic ;
+x = b (p) ;
+x = cs_lsolve (L3,x) ;
+x = cs_ltsolve (L3,x) ;
+x (p) = x ;
+t = toc ;
+fprintf ('downdate: time: %8.2f (incl solve) ', t1+t) ;
+print_resid (C, x, b) ;
diff --git a/CSparse/MATLAB/Demo/private/ex2.m b/CSparse/MATLAB/Demo/private/ex2.m
new file mode 100644
index 0000000..2b814c9
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/ex2.m
@@ -0,0 +1,91 @@
+function ex2 (n)
+%EX2: create an n-by-n 2D mesh, four different ways
+
+% Example:
+% ex2
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 1)
+ n = 30 ;
+end
+
+subplot (1,2,1) ;
+
+% method 1: create an n-by-n 2D mesh for the 2nd difference operator
+tic
+ii = zeros (5*n^2, 1) ;
+jj = zeros (5*n^2, 1) ;
+xx = zeros (5*n^2, 1) ;
+k = 1 ;
+for j = 0:n-1
+ for i = 0:n-1
+ s = j*n+i + 1 ;
+ ii (k:k+4) = [(j-1)*n+i j*n+(i-1) j*n+i j*n+(i+1) (j+1)*n+i ] + 1 ;
+ jj (k:k+4) = [s s s s s] ;
+ xx (k:k+4) = [-1 -1 4 -1 -1] ;
+ k = k + 5 ;
+ end
+end
+
+% remove entries beyond the boundary
+keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ;
+ii = ii (keep) ;
+jj = jj (keep) ;
+xx = xx (keep) ;
+A = sparse (ii,jj,xx) ;
+t1 = toc ; disp (t1) ;
+% subplot (2,2,1) ;
+spy (A)
+title (sprintf ('%d-by-%d 2D mesh\n', n, n)) ;
+
+% method 2, using no for loops
+tic
+nn = 1:n^2 ;
+i2 = [nn-n ; nn-1 ; nn ; nn+1 ; nn+n] ;
+j2 = repmat (nn, 5, 1) ;
+x2 = repmat ([-1 -1 4 -1 -1]', 1, n^2) ;
+keep = find (i2 >= 1 & i2 <= n^2 & j2 >= 1 & j2 <= n^2) ;
+i2 = i2 (keep) ;
+j2 = j2 (keep) ;
+x2 = x2 (keep) ;
+C = sparse (i2,j2,x2) ;
+t2 = toc ; disp (t2) ;
+
+% subplot (2,2,2) ; plot (j2) ;
+% title ('2D fast j2') ;
+disp (A-C) ;
+
+any (ii-i2)
+any (jj-jj)
+
+% method 3: create an n-by-n-by-n 3D mesh for the 2nd difference operator
+tic
+[A, keep, ii, jj, xx] = mesh3d1 (n) ;
+ii = ii (keep) ;
+jj = jj (keep) ;
+xx = xx (keep) ;
+t3 = toc ; disp (t3) ;
+tic
+E = sparse (ii,jj,xx) ;
+t3b = toc ; disp (t3b) ;
+subplot (1,2,2) ; spy (E) ;
+title (sprintf ('%d-by-%d-by-%d 3D mesh\n', n, n, n)) ;
+
+% method 4, using no for loops
+tic
+nn = 1:n^3 ;
+i2 = [nn-n^2 ; nn-n ; nn-1 ; nn ; nn+1 ; nn+n ; nn+n^2] ;
+j2 = repmat (nn, 7, 1) ;
+x2 = repmat ([-1 -1 -1 6 -1 -1 -1]', 1, n^3) ;
+keep = find (i2 >= 1 & i2 <= n^3 & j2 >= 1 & j2 <= n^3) ;
+i2 = i2 (keep) ;
+j2 = j2 (keep) ;
+x2 = x2 (keep) ;
+t4 = toc ; disp (t4) ;
+tic
+F = sparse (i2,j2,x2) ;
+t4b = toc ; disp (t4b) ;
+disp (E-F) ;
diff --git a/CSparse/MATLAB/Demo/private/ex3.m b/CSparse/MATLAB/Demo/private/ex3.m
new file mode 100644
index 0000000..b425900
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/ex3.m
@@ -0,0 +1,42 @@
+function ex3
+%EX3: create 2D and 3D meshes using mesh2d1, mesh2d2, mesh3d1, mesh3d2.
+
+% Example:
+% ex3
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+t1 = zeros (50,1) ;
+t2 = zeros (50,1) ;
+t3 = zeros (50,1) ;
+t4 = zeros (50,1) ;
+
+fprintf ('run times for each method, given n:\n') ;
+for n = 2:50
+
+ tic ;
+ A = mesh2d1 (n) ;
+ t1 (n) = toc ;
+
+ tic
+ B = mesh2d2 (n) ;
+ t2 (n) = toc ;
+
+ tic
+ C = mesh3d1 (n) ;
+ t3 (n) = toc ;
+
+ tic
+ D = mesh3d2 (n) ;
+ t4 (n) = toc ;
+
+ fprintf ('%3d: %8.3f %8.3f %8.3f %8.3f\n', n, t1(n), t2(n), t3(n), t4(n)) ;
+
+ subplot (2,2,1) ; spy (A) ; title ('2D mesh, method 1') ;
+ subplot (2,2,2) ; spy (B) ; title ('2D mesh, method 2') ;
+ subplot (2,2,3) ; spy (C) ; title ('3D mesh, method 1') ;
+ subplot (2,2,4) ; spy (D) ; title ('3D mesh, method 2') ;
+ drawnow
+end
diff --git a/CSparse/MATLAB/Demo/private/ex_1.m b/CSparse/MATLAB/Demo/private/ex_1.m
new file mode 100644
index 0000000..6a14818
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/ex_1.m
@@ -0,0 +1,86 @@
+function ex_1
+%EX_1: four methods for creating the same matrix.
+% (please wait, this can take a while...)
+
+% Example:
+% ex_1
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = 1000 ;
+nz = 1e5 ;
+
+tic
+% method 1: A(i,j) = ...
+rand ('state', 0) ;
+A = sparse (n,n) ;
+for k = 1:nz
+ % compute some arbitrary entry and add it into the matrix
+ i = 1 + fix (n * rand (1)) ;
+ j = 1 + fix (n * rand (1)) ;
+ x = rand (1) ;
+ A (i,j) = A (i,j) + x ; % VERY slow, esp. if A(i,j) not already nonzero!
+end
+fprintf ('Method 1: ') ;
+toc
+A1 = A ;
+
+tic
+% method 2: triplet form, one entry at a time
+rand ('state', 0) ;
+ii = zeros (nz, 1) ; % preallocate ii, jj, and xx
+jj = zeros (nz, 1) ;
+xx = zeros (nz, 1) ;
+for k = 1:nz
+ % compute some arbitrary entry and add it into the matrix
+ ii (k) = 1 + fix (n * rand (1)) ;
+ jj (k) = 1 + fix (n * rand (1)) ;
+ xx (k) = rand (1) ;
+end
+A = sparse (ii,jj,xx) ;
+fprintf ('Method 2: ') ;
+toc
+A2 = A ;
+disp (A1-A2) ;
+
+tic
+% method 3: triplet form, one entry at a time, pretend nz is unknown
+rand ('state', 0) ;
+len = 16 ;
+ii = zeros (len, 1) ;
+jj = zeros (len, 1) ;
+xx = zeros (len, 1) ;
+for k = 1:nz
+ % compute some arbitrary entry and add it into the matrix
+ if (k > len)
+ % double the size of ii,jj,xx
+ len = 2*len ;
+ ii (len) = 0 ;
+ jj (len) = 0 ;
+ xx (len) = 0 ;
+ end
+ ii (k) = 1 + fix (n * rand (1)) ;
+ jj (k) = 1 + fix (n * rand (1)) ;
+ xx (k) = rand (1) ;
+end
+A = sparse (ii (1:k), jj (1:k), xx (1:k)) ;
+fprintf ('Method 3: ') ;
+toc
+
+A3 = A ;
+disp (A1-A3) ;
+
+tic
+% method 4: avoid the for loop
+rand ('state', 0) ;
+e = rand (3, nz) ;
+e (1,:) = 1 + fix (n * e (1,:)) ;
+e (2,:) = 1 + fix (n * e (2,:)) ;
+A = sparse (e (1,:), e (2,:), e (3,:)) ;
+fprintf ('Method 4: ') ;
+toc
+
+A4 = A ;
+disp (A1-A4) ;
diff --git a/CSparse/MATLAB/Demo/private/frand.m b/CSparse/MATLAB/Demo/private/frand.m
new file mode 100644
index 0000000..4d3b16a
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/frand.m
@@ -0,0 +1,28 @@
+function A = frand (n,nel,s)
+% A = frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel finite
+% elements, each of which are of size s-by-s with random symmetric nonzero
+% pattern, plus the identity matrix.
+%
+% Example:
+% A = frand (100, 100, 4) ; cspy (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+ss = s^2 ;
+nz = nel*ss ;
+ii = zeros (nz,1) ;
+jj = zeros (nz,1) ;
+xx = zeros (nz,1) ;
+k = 1 ;
+for e = 1:nel
+ i = 1 + fix (n * rand (s,1)) ;
+ i = repmat (i, 1, s) ;
+ j = i' ;
+ x = rand (s,s) ;
+ ii (k:k+ss-1) = i (:) ;
+ jj (k:k+ss-1) = j (:) ;
+ xx (k:k+ss-1) = x (:) ;
+ k = k + ss ;
+end
+A = sparse (ii,jj,xx,n,n) + speye (n) ;
diff --git a/CSparse/MATLAB/Demo/private/get_problem.m b/CSparse/MATLAB/Demo/private/get_problem.m
new file mode 100644
index 0000000..a2dc3d6
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/get_problem.m
@@ -0,0 +1,57 @@
+function [C, sym] = get_problem (prefix, name, tol)
+% [C, sym] = get_problem(prefix, name,tol)
+% read a problem from a file, drop entries with abs value < tol
+% tol defaults to zero if not present
+%
+% Example:
+% [C, sym] = get_problem ('', 'west0067') ;
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('\n------------------- Matrix: %s\n', name) ;
+
+if (nargin < 2)
+ tol = 0 ;
+end
+
+s = find (name == '/') ;
+if (isempty (s))
+ s = 0 ;
+end
+% f = sprintf ('%s..%s..%sMatrix%s%s', ...
+% prefix, filesep, filesep, filesep, name (s+1:end)) ;
+
+% load the triplet version of the matrix
+T = load ([ prefix '/' name(s+1:end) ]) ;
+
+% convert into a sparse matrix and compare with cs_sparse
+A = sparse (T (:,1)+1, T (:,2)+1, T (:,3)) ;
+A2 = cs_sparse (T (:,1)+1, T (:,2)+1, T (:,3)) ;
+err = norm (A-A2,1) ;
+if (err > 0)
+ fprintf ('A difference: %g\n', err) ;
+end
+
+[m n] = size (A) ;
+nz2 = nnz (A) ;
+
+if (tol > 0)
+ A = cs_droptol (A, tol) ;
+end
+
+% assume A is symmetric if it is upper or lower triangular
+sym = is_sym (A) ;
+if (sym)
+ C = A + (A' - diag (diag (A))) ;
+else
+ C = A ;
+end
+
+fprintf ('--- Matrix: %d-by-%d, nnz: %d (sym: %d nnz %d), norm: %8.2e\n', ...
+ m, n, nnz(A), sym, abs(sym)*nnz(C), norm (C,1)) ;
+
+if (nz2 ~= nnz(A))
+ fprintf ('tiny entries dropped: %d\n', nz2 - nnz(A))
+end
diff --git a/CSparse/MATLAB/Demo/private/is_sym.m b/CSparse/MATLAB/Demo/private/is_sym.m
new file mode 100644
index 0000000..6a84215
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/is_sym.m
@@ -0,0 +1,23 @@
+function sym = is_sym (A)
+% sym = is_sym(A)
+% 1 if A is square and upper tri., -1 if square and lower tri., 0 otherwise
+%
+% Example:
+% sym = is_sym (A) ;
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+sym = 0 ;
+if (m == n)
+ is_upper = nnz (tril (A,-1)) == 0 ;
+ is_lower = nnz (triu (A,1)) == 0 ;
+ if (is_upper)
+ sym = 1 ;
+ elseif (is_lower)
+ sym = -1 ;
+ end
+end
+
diff --git a/CSparse/MATLAB/Demo/private/mesh2d1.m b/CSparse/MATLAB/Demo/private/mesh2d1.m
new file mode 100644
index 0000000..39ca45f
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/mesh2d1.m
@@ -0,0 +1,25 @@
+function A = mesh2d1 (n)
+% create an n-by-n 2D mesh for the 2nd difference operator
+% Example:
+% A = mesh2d1 (30) ; % a 30-by-30 mesh
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+ii = zeros (5*n^2, 1) ; % preallocate ii, jj, and xx
+jj = zeros (5*n^2, 1) ;
+xx = zeros (5*n^2, 1) ;
+k = 1 ;
+for j = 0:n-1
+ for i = 0:n-1
+ s = j*n+i + 1 ;
+ ii (k:k+4) = [(j-1)*n+i j*n+(i-1) j*n+i j*n+(i+1) (j+1)*n+i ] + 1 ;
+ jj (k:k+4) = [s s s s s] ;
+ xx (k:k+4) = [-1 -1 4 -1 -1] ;
+ k = k + 5 ;
+ end
+end
+% remove entries beyond the boundary
+keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ;
+A = sparse (ii (keep), jj (keep), xx (keep)) ;
diff --git a/CSparse/MATLAB/Demo/private/mesh2d2.m b/CSparse/MATLAB/Demo/private/mesh2d2.m
new file mode 100644
index 0000000..f3133bf
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/mesh2d2.m
@@ -0,0 +1,15 @@
+function A = mesh2d2 (n)
+% create an n-by-n 2D mesh for the 2nd difference operator
+% Example:
+% A = mesh2d2 (30) ; % a 30-by-30 mesh
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+nn = 1:n^2 ;
+ii = [nn-n ; nn-1 ; nn ; nn+1 ; nn+n] ;
+jj = repmat (nn, 5, 1) ;
+xx = repmat ([-1 -1 4 -1 -1]', 1, n^2) ;
+keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ;
+A = sparse (ii (keep), jj (keep), xx (keep)) ;
diff --git a/CSparse/MATLAB/Demo/private/mesh3d1.m b/CSparse/MATLAB/Demo/private/mesh3d1.m
new file mode 100644
index 0000000..2c431d9
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/mesh3d1.m
@@ -0,0 +1,33 @@
+function [A, keep, ii, jj, xx] = mesh3d1 (n)
+% create an n-by-n-by-n 3D mesh for the 2nd difference operator
+% Example:
+% A = mesh3d1 (10) ; % a 10-by-10-by-10 mesh
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+ii = zeros (7*n^3, 1) ;
+jj = zeros (7*n^3, 1) ;
+xx = zeros (7*n^3, 1) ;
+t = 1 ;
+for k = 0:n-1
+ for j = 0:n-1
+ for i = 0:n-1
+ s = k*n^2 + j*n+i + 1 ;
+ ii (t:t+6) = [
+ (k-1)*n^2 + j*n+i
+ k*n^2 + (j-1)*n+i
+ k*n^2 + j*n+(i-1)
+ k*n^2 + j*n+i
+ k*n^2 + j*n+(i+1)
+ k*n^2 + (j+1)*n+i
+ (k+1)*n^2 + j*n+i ]' + 1 ;
+ jj (t:t+6) = [s s s s s s s] ;
+ xx (t:t+6) = [-1 -1 -1 6 -1 -1 -1] ;
+ t = t + 7 ;
+ end
+ end
+end
+keep = find (ii >= 1 & ii <= n^3 & jj >= 1 & jj <= n^3) ;
+A = sparse (ii (keep), jj (keep), xx (keep)) ;
diff --git a/CSparse/MATLAB/Demo/private/mesh3d2.m b/CSparse/MATLAB/Demo/private/mesh3d2.m
new file mode 100644
index 0000000..4a644f3
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/mesh3d2.m
@@ -0,0 +1,15 @@
+function A = mesh3d2 (n)
+% create an n-by-n-by-n 3D mesh for the 2nd difference operator
+% Example:
+% A = mesh3d2 (10) ; % a 10-by-10-by-10 mesh
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+nn = 1:n^3 ;
+ii = [nn-n^2 ; nn-n ; nn-1 ; nn ; nn+1 ; nn+n ; nn+n^2] ;
+jj = repmat (nn, 7, 1) ;
+xx = repmat ([-1 -1 -1 6 -1 -1 -1]', 1, n^3) ;
+keep = find (ii >= 1 & ii <= n^3 & jj >= 1 & jj <= n^3) ;
+A = sparse (ii (keep), jj (keep), xx (keep)) ;
diff --git a/CSparse/MATLAB/Demo/private/print_order.m b/CSparse/MATLAB/Demo/private/print_order.m
new file mode 100644
index 0000000..4f65d4b
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/print_order.m
@@ -0,0 +1,21 @@
+function print_order (order)
+% print_order(order) prints the ordering determined by the order parameter
+% Example:
+% print_order (0)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+switch (fix (order))
+ case 0
+ fprintf ('natural ') ;
+ case 1
+ fprintf ('amd(A+A'') ') ;
+ case 2
+ fprintf ('amd(S''*S) ') ;
+ case 3
+ fprintf ('amd(A''*A) ') ;
+ otherwise
+ fprintf ('undefined ') ;
+end
diff --git a/CSparse/MATLAB/Demo/private/print_resid.m b/CSparse/MATLAB/Demo/private/print_resid.m
new file mode 100644
index 0000000..4b22047
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/print_resid.m
@@ -0,0 +1,12 @@
+function print_resid (A, x, b)
+% print_resid (A, x, b), print the relative residual,
+% norm (A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf))
+% Example:
+% print_resid (A, x, b) ;
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('resid: %8.2e\n', ...
+ norm (A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf))) ;
diff --git a/CSparse/MATLAB/Demo/private/rhs.m b/CSparse/MATLAB/Demo/private/rhs.m
new file mode 100644
index 0000000..f7bc531
--- /dev/null
+++ b/CSparse/MATLAB/Demo/private/rhs.m
@@ -0,0 +1,10 @@
+function b = rhs (m)
+% b = rhs (m), compute a right-hand-side
+% Example:
+% b = rhs (30) ;
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+b = ones (m,1) + (0:m-1)'/m ;
diff --git a/CSparse/MATLAB/Makefile b/CSparse/MATLAB/Makefile
new file mode 100644
index 0000000..4636246
--- /dev/null
+++ b/CSparse/MATLAB/Makefile
@@ -0,0 +1,14 @@
+all:
+ ( cd CSparse ; $(MAKE) )
+ ( cd Test ; $(MAKE) )
+
+clean:
+ ( cd CSparse ; $(MAKE) clean )
+ ( cd Test ; $(MAKE) clean )
+
+purge:
+ ( cd CSparse ; $(MAKE) purge )
+ ( cd Test ; $(MAKE) purge )
+
+distclean: purge
+
diff --git a/CSparse/MATLAB/README.txt b/CSparse/MATLAB/README.txt
new file mode 100644
index 0000000..6153439
--- /dev/null
+++ b/CSparse/MATLAB/README.txt
@@ -0,0 +1,18 @@
+CSparse/MATLAB directory, which contains the MATLAB mexFunction interfaces
+for CSparse, demos, and tests. It includes various "textbook" files
+that are printed in the book, but not a proper part of CSparse itself.
+It also includes "UFget", a MATLAB interface for the UF Sparse Matrix
+Collection.
+
+Type the command "cs_install" while in this directory. It will compile
+CSparse, and add the directories:
+
+ CSparse/MATLAB/CSparse
+ CSparse/MATLAB/Demo
+ CSparse/MATLAB/UFget
+
+to your MATLAB path (see the "pathtool" command to add these to your path
+permanently, for future MATLAB sessions).
+
+To run the MATLAB demo programs, run cs_demo in the Demo directory.
+To run the MATLAB test programs, run testall in the Test directory.
diff --git a/CSparse/MATLAB/Test/Contents.m b/CSparse/MATLAB/Test/Contents.m
new file mode 100644
index 0000000..54d0d83
--- /dev/null
+++ b/CSparse/MATLAB/Test/Contents.m
@@ -0,0 +1,102 @@
+% CSparse "textbook" MATLAB M-files and mexFunctions, related to CSparse but
+% not a part of CSparse itself.
+%
+% M-files:
+%
+% chol_downdate - downdate a Cholesky factorization.
+% chol_left - left-looking Cholesky factorization.
+% chol_left2 - left-looking Cholesky factorization, more details.
+% chol_right - right-looking Cholesky factorization.
+% chol_super - left-looking "supernodal" Cholesky factorization.
+% chol_up - up-looking Cholesky factorization.
+% chol_update - update a Cholesky factorization.
+% chol_updown - update or downdate a Cholesky factorization.
+% cond1est - 1-norm condition estimate.
+% cs_fiedler - the Fiedler vector of a connected graph.
+% givens2 - find a Givens rotation.
+% house - find a Householder reflection.
+% lu_left - left-looking LU factorization.
+% lu_right - right-looking LU factorization.
+% lu_rightp - right-looking LU factorization, with partial pivoting.
+% lu_rightpr - recursive right-looking LU, with partial pivoting.
+% lu_rightr - recursive right-looking LU.
+% norm1est - 1-norm estimate.
+% qr_givens - Givens-rotation QR factorization.
+% qr_givens_full - Givens-rotation QR factorization, for full matrices.
+% qr_left - left-looking Householder QR factorization.
+% qr_right - right-looking Householder QR factorization.
+%
+% mexFunctions:
+%
+% cs_frand - generate a random finite-element matrix
+% cs_ipvec - x(p)=b
+% cs_maxtransr - recursive maximum matching algorithm
+% cs_pvec - x=b(p)
+% cs_reach - non-recursive reach (interface to CSparse cs_reach)
+% cs_reachr - recursive reach (interface to CSparse cs_reachr)
+% cs_rowcnt - row counts for sparse Cholesky
+% cs_sparse2 - same as cs_sparse, to test cs_entry function
+%
+% Extensive test functions, not for normal usage:
+%
+% check_if_same - check if two inputs are identical or not
+% choldn - Cholesky downdate
+% cholup - Cholesky update, using Given's rotations
+% cholupdown - Cholesky update/downdate (Bischof, Pan, and Tang method)
+% cs_q1 - construct Q from Householder vectors
+% cs_test_make - compiles the CSparse, Demo, and Test mexFunctions.
+% dmperm_test - test cs_dmperm
+% chol_example - simple Cholesky factorization example
+% etree_sample - construct a sample etree and symbolic factorization
+% gqr3 - QR factorization, based on Givens rotations
+% happly - apply Householder reflection to a vector
+% hmake1 - construct a Householder reflection
+% mynormest1 - estimate norm(A,1), using LU factorization (L*U = P*A*Q).
+% myqr - QR factorization using Householder reflections
+% another_colormap - try another color map
+% cspy_test - test cspy and cs_dmspy
+% qr2 - QR factorization based on Householder reflections
+% sample_colormap - try a colormap for use in cspy
+% signum - compute and display the sign of a column vector x
+% sqr_example - test cs_sqr
+% dmspy_test - test cspy, cs_dmspy, and cs_dmperm
+% test_qr - test various QR factorization methods
+% test_randperms - test random permutations
+% testh - test Householder reflections
+% test_qr1 - test QR factorizations
+% test_qrsol - test cs_qrsol
+% test_sep - test cs_sep, and compare with Gilbert's meshpart vtxsep
+% testall - test all CSparse functions (run tests 1 to 28 below)
+% test1 - test cs_transpose
+% test2 - test cs_sparse
+% test3 - test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol
+% test4 - test cs_multiply
+% test5 - test cs_add
+% test6 - test cs_reach, cs_reachr, cs_lsolve, cs_usolve
+% test7 - test cs_lu
+% test8 - test cs_cholsol, cs_lusol
+% test9 - test cs_qr
+% test10 - test cs_qr
+% test11 - test cs_rowcnt
+% test12 - test cs_qr and compare with svd
+% test13 - test cs_counts, cs_etree
+% test14 - test cs_droptol
+% test15 - test cs_amd
+% test16 - test cs_amd
+% test17 - test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol
+% test18 - test iterative refinement after backslash
+% test19 - test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc
+% test20 - test cholupdown
+% test21 - test cs_updown
+% test22 - test cond1est
+% test23 - test cs_dmspy
+% test24 - test cs_fielder
+% test25 - test cs_nd
+% test26 - test cs_dmsol and cs_dmspy
+% test27 - test cs_qr, cs_utsolve, cs_qrsol
+% test28 - test cs_randperm, cs_dmperm
+
+% Example:
+% help chol_update
+
+% Copyright 2006-2007, Timothy A. Davis
diff --git a/CSparse/MATLAB/Test/Makefile b/CSparse/MATLAB/Test/Makefile
new file mode 100644
index 0000000..94f345d
--- /dev/null
+++ b/CSparse/MATLAB/Test/Makefile
@@ -0,0 +1,51 @@
+MEX = mex -O
+AR = ar cr
+RANLIB = ranlib
+
+all: cs_sparse2.mexglx \
+ cs_ipvec.mexglx \
+ cs_pvec.mexglx \
+ cs_reach.mexglx \
+ cs_maxtransr.mexglx \
+ cs_reachr.mexglx \
+ cs_rowcnt.mexglx \
+ cs_frand.mexglx
+
+mexcsparse:
+ ( cd ../CSparse ; make mexcsparse.a )
+
+I = -I../../Include -I../CSparse
+
+cs_ipvec.mexglx: cs_ipvec_mex.c mexcsparse
+ $(MEX) -output cs_ipvec $< $(I) ../CSparse/mexcsparse.a
+
+cs_pvec.mexglx: cs_pvec_mex.c mexcsparse
+ $(MEX) -output cs_pvec $< $(I) ../CSparse/mexcsparse.a
+
+cs_reach.mexglx: cs_reach_mex.c mexcsparse
+ $(MEX) -output cs_reach $< $(I) ../CSparse/mexcsparse.a
+
+cs_sparse2.mexglx: cs_sparse2_mex.c mexcsparse
+ $(MEX) -output cs_sparse2 $< $(I) ../CSparse/mexcsparse.a
+
+cs_maxtransr.mexglx: cs_maxtransr_mex.c mexcsparse
+ $(MEX) -output cs_maxtransr $< $(I) ../CSparse/mexcsparse.a
+
+cs_reachr.mexglx: cs_reachr_mex.c mexcsparse
+ $(MEX) -output cs_reachr $< $(I) ../CSparse/mexcsparse.a
+
+cs_rowcnt.mexglx: cs_rowcnt_mex.c mexcsparse
+ $(MEX) -output cs_rowcnt $< $(I) ../CSparse/mexcsparse.a
+
+cs_frand.mexglx: cs_frand_mex.c mexcsparse
+ $(MEX) -output cs_frand $< $(I) ../CSparse/mexcsparse.a
+
+
+
+clean:
+ rm -f *.o
+
+distclean: clean
+ rm -f *.mex* *.dll *.a
+
+purge: distclean
diff --git a/CSparse/MATLAB/Test/README.txt b/CSparse/MATLAB/Test/README.txt
new file mode 100644
index 0000000..d42da19
--- /dev/null
+++ b/CSparse/MATLAB/Test/README.txt
@@ -0,0 +1,4 @@
+Test for MATLAB interface for CSparse. Type "testall" to run all the tests.
+
+Also includes "textbook" codes for the book "Direct Methods for Sparse Linear
+Systems", which are not part of CSparse proper, but are used in the tests.
diff --git a/CSparse/MATLAB/Test/another_colormap.m b/CSparse/MATLAB/Test/another_colormap.m
new file mode 100644
index 0000000..50342e9
--- /dev/null
+++ b/CSparse/MATLAB/Test/another_colormap.m
@@ -0,0 +1,30 @@
+function another_colormap
+%ANOTHER_COLORMAP try another color map
+%
+% Example:
+% another_colormap
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+j = jet (128) ;
+j = j (48:112, :) ;
+
+% jj = linspace (0,1,64)' ./ sum (jet,2) ;
+% j (:,1) = j (:,1) .* jj ;
+% j (:,2) = j (:,2) .* jj ;
+% j (:,3) = j (:,3) .* jj ;
+
+
+% white = [1 1 1] ;
+% gray = [.5 .5 .5] ; %#ok
+
+% j = [white ; purple ; j ] ;
+disp ('j = ') ;
+disp (j)
+
+
+image (1:size(j,1)) ;
+colormap (j) ;
diff --git a/CSparse/MATLAB/Test/check_if_same.m b/CSparse/MATLAB/Test/check_if_same.m
new file mode 100644
index 0000000..9a81e92
--- /dev/null
+++ b/CSparse/MATLAB/Test/check_if_same.m
@@ -0,0 +1,22 @@
+function check_if_same (p1,p2)
+%CHECK_IF_SAME check if two inputs are identical or not
+%
+% Example:
+% check_if_same (1:5, 2:6)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+ if (isempty (p1))
+ if (~isempty (p2))
+ p1 %#ok
+ p2 %#ok
+ error ('empty!') ;
+ end
+ elseif (any (p1 ~= p2))
+ p1 %#ok
+ p2 %#ok
+ error ('!') ;
+ end
+
diff --git a/CSparse/MATLAB/Test/chol_downdate.m b/CSparse/MATLAB/Test/chol_downdate.m
new file mode 100644
index 0000000..8cf9794
--- /dev/null
+++ b/CSparse/MATLAB/Test/chol_downdate.m
@@ -0,0 +1,28 @@
+function [L, w] = chol_downdate (L, w)
+%CHOL_DOWNDATE downdate a Cholesky factorization.
+% Example
+% [L, w] = chol_downdate (L, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+beta = 1 ;
+n = size (L,1) ;
+for j = 1:n
+ alpha = w (j) / L (j,j) ;
+ beta2 = sqrt (beta^2 - alpha^2) ;
+ if (~isreal (beta2))
+ error ('not positive definite') ;
+ end
+ gamma = alpha / (beta2 * beta) ;
+ delta = beta2 / beta ;
+ L (j,j) = delta * L (j,j) ;
+ w (j) = alpha ;
+ beta = beta2 ;
+ if (j == n)
+ return
+ end
+ w (j+1:n) = w (j+1:n) - alpha * L (j+1:n,j) ;
+ L (j+1:n,j) = delta * L (j+1:n,j) - gamma * w (j+1:n) ;
+end
diff --git a/CSparse/MATLAB/Test/chol_example.m b/CSparse/MATLAB/Test/chol_example.m
new file mode 100644
index 0000000..f488f7d
--- /dev/null
+++ b/CSparse/MATLAB/Test/chol_example.m
@@ -0,0 +1,35 @@
+function chol_example
+%CHOL_EXAMPLE simple Cholesky factorization example
+% Example
+% chol_example
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+D = 10 ;
+X = 1 ;
+o = 0 ;
+
+A = sparse ([
+D o X o o o o X o o
+o D o o X o o o o X
+X o D o o o X o o o
+o o o D o o o o X X
+o X o o D o o o X X
+o o o o o D X X o o
+o o X o o X D o o o
+X o o o o X o D X X
+o o o X X o o X D o
+o X o X X o o X o D ]) ;
+
+disp ('A = ') ; disp (A) ;
+
+L = chol(A)' ;
+
+disp ('L = ') ; disp (L) ;
+
+clf
+subplot (1,2,1) ; spy (A) ;
+subplot (1,2,2) ; spy (L+L') ;
diff --git a/CSparse/MATLAB/Test/chol_left.m b/CSparse/MATLAB/Test/chol_left.m
new file mode 100644
index 0000000..ec75416
--- /dev/null
+++ b/CSparse/MATLAB/Test/chol_left.m
@@ -0,0 +1,15 @@
+function L = chol_left (A)
+%CHOL_LEFT left-looking Cholesky factorization.
+% Example
+% L = chol_left (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+L = zeros (n) ;
+for k = 1:n
+ L (k,k) = sqrt (A (k,k) - L (k,1:k-1) * L (k,1:k-1)') ;
+ L (k+1:n,k) = (A (k+1:n,k) - L (k+1:n,1:k-1) * L (k,1:k-1)') / L (k,k) ;
+end
diff --git a/CSparse/MATLAB/Test/chol_left2.m b/CSparse/MATLAB/Test/chol_left2.m
new file mode 100644
index 0000000..c809b9e
--- /dev/null
+++ b/CSparse/MATLAB/Test/chol_left2.m
@@ -0,0 +1,20 @@
+function L = chol_left2 (A)
+%CHOL_LEFT2 left-looking Cholesky factorization, more details.
+% Example
+% L = chol_left2 (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+L = sparse (n,n) ;
+a = sparse (n,1) ;
+for k = 1:n
+ a (k:n) = A (k:n,k) ;
+ for j = find (L (k,:))
+ a (k:n) = a (k:n) - L (k:n,j) * L (k,j) ;
+ end
+ L (k,k) = sqrt (a (k)) ;
+ L (k+1:n,k) = a (k+1:n) / L (k,k) ;
+end
diff --git a/CSparse/MATLAB/Test/chol_right.m b/CSparse/MATLAB/Test/chol_right.m
new file mode 100644
index 0000000..7aa60e1
--- /dev/null
+++ b/CSparse/MATLAB/Test/chol_right.m
@@ -0,0 +1,16 @@
+function L = chol_right (A)
+%CHOL_RIGHT right-looking Cholesky factorization.
+% Example
+% L = chol_right (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A) ;
+L = zeros (n) ;
+for k = 1:n
+ L (k,k) = sqrt (A (k,k)) ;
+ L (k+1:n,k) = A (k+1:n,k) / L (k,k) ;
+ A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - L (k+1:n,k) * L (k+1:n,k)' ;
+end
diff --git a/CSparse/MATLAB/Test/chol_super.m b/CSparse/MATLAB/Test/chol_super.m
new file mode 100644
index 0000000..1744130
--- /dev/null
+++ b/CSparse/MATLAB/Test/chol_super.m
@@ -0,0 +1,19 @@
+function L = chol_super (A,s)
+%CHOL_SUPER left-looking "supernodal" Cholesky factorization.
+% Example:
+% L = chol_super (A,s)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A) ;
+L = zeros (n) ;
+ss = cumsum ([1 s]) ;
+for j = 1:length (s)
+ k1 = ss (j) ;
+ k2 = ss (j+1) ;
+ k = k1:(k2-1) ;
+ L (k,k) = chol (A (k,k) - L (k,1:k1-1) * L (k,1:k1-1)')' ;
+ L (k2:n,k) = (A (k2:n,k) - L (k2:n,1:k1-1) * L (k,1:k1-1)') / L (k,k)' ;
+end
diff --git a/CSparse/MATLAB/Test/chol_up.m b/CSparse/MATLAB/Test/chol_up.m
new file mode 100644
index 0000000..09d0218
--- /dev/null
+++ b/CSparse/MATLAB/Test/chol_up.m
@@ -0,0 +1,15 @@
+function L = chol_up (A)
+%CHOL_UP up-looking Cholesky factorization.
+% Example:
+% L = chol_up (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A) ;
+L = zeros (n) ;
+for k = 1:n
+ L (k,1:k-1) = (L (1:k-1,1:k-1) \ A (1:k-1,k))' ;
+ L (k,k) = sqrt (A (k,k) - L (k,1:k-1) * L (k,1:k-1)') ;
+end
diff --git a/CSparse/MATLAB/Test/chol_update.m b/CSparse/MATLAB/Test/chol_update.m
new file mode 100644
index 0000000..5d95152
--- /dev/null
+++ b/CSparse/MATLAB/Test/chol_update.m
@@ -0,0 +1,26 @@
+function [L, w] = chol_update (L, w)
+%CHOL_UPDATE update a Cholesky factorization.
+% Example:
+% [L, w] = chol_update (L, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+beta = 1 ;
+n = size (L,1) ;
+for j = 1:n
+ alpha = w (j) / L (j,j) ;
+ beta2 = sqrt (beta^2 + alpha^2) ;
+ gamma = alpha / (beta2 * beta) ;
+ delta = beta / beta2 ;
+ L (j,j) = delta * L (j,j) + gamma * w (j) ;
+ w (j) = alpha ;
+ beta = beta2 ;
+ if (j == n)
+ return
+ end
+ w1 = w (j+1:n) ;
+ w (j+1:n) = w (j+1:n) - alpha * L (j+1:n,j) ;
+ L (j+1:n,j) = delta * L (j+1:n,j) + gamma * w1 ;
+end
diff --git a/CSparse/MATLAB/Test/chol_updown.m b/CSparse/MATLAB/Test/chol_updown.m
new file mode 100644
index 0000000..2f286c9
--- /dev/null
+++ b/CSparse/MATLAB/Test/chol_updown.m
@@ -0,0 +1,36 @@
+function [L, w] = chol_updown (L, sigma, w)
+%CHOL_UPDOWN update or downdate a Cholesky factorization.
+% Example:
+% [L, w] = chol_updown (L, sigma, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+beta = 1 ;
+n = size (L,1) ;
+if (n == 1)
+ L = sqrt (L*L'+sigma*w*w') ;
+ return ;
+end
+for k = 1:n
+ alpha = w(k) / L(k,k) ;
+ beta2 = sqrt (beta^2 + sigma*alpha^2) ;
+ gamma = sigma * alpha / (beta2 * beta) ;
+ if (sigma > 0)
+ % update
+ delta = beta / beta2 ;
+ L (k,k) = delta * L (k,k) + gamma * w (k) ;
+ w1 = w (k+1:n) ;
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k+1:n,k) = delta * L (k+1:n,k) + gamma * w1 ;
+ else
+ % downdate
+ delta = beta2 / beta ;
+ L (k,k) = delta * L (k,k) ;
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k+1:n,k) = delta * L (k+1:n,k) + gamma * w (k+1:n) ;
+ end
+ w (k) = alpha ;
+ beta = beta2 ;
+end
diff --git a/CSparse/MATLAB/Test/choldn.m b/CSparse/MATLAB/Test/choldn.m
new file mode 100644
index 0000000..10ea9d9
--- /dev/null
+++ b/CSparse/MATLAB/Test/choldn.m
@@ -0,0 +1,46 @@
+function L = choldn (Lold,w)
+%CHOLDN Cholesky downdate
+% given Lold and w, compute L so that L*L' = Lold*Lold' - w*w'
+%
+% Example:
+% L = cholnd (Lold,w)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (Lold,1) ;
+L = Lold ;
+
+alpha = 1 ;
+beta = 1 ;
+
+wold = w ;
+wnew = zeros (n,1) ;
+
+for i = 1:n
+
+ a = w (i) / L(i,i) ;
+ alpha = alpha - a^2 ;
+ if (alpha <= 0)
+ error ('not pos def') ;
+ end
+ beta_new = sqrt (alpha) ;
+ b = beta_new / beta ;
+ c = (a / (beta*beta_new)) ;
+ beta = beta_new ;
+
+ % L (i,i) = b * L (i,i) ;
+
+ wnew (i) = a ;
+
+ for k = i:n
+ w (k) = w (k) - a * L (k,i) ;
+ L (k,i) = b * L (k,i) - c * w(k) ;
+ end
+
+end
+
+% w
+% wnew
+disp (wnew - Lold\wold)
diff --git a/CSparse/MATLAB/Test/cholup.m b/CSparse/MATLAB/Test/cholup.m
new file mode 100644
index 0000000..e8f196c
--- /dev/null
+++ b/CSparse/MATLAB/Test/cholup.m
@@ -0,0 +1,26 @@
+function L = cholup (Lold,w)
+%CHOLUP Cholesky update, using Given's rotations
+% given Lold and w, compute L so that L*L' = Lold*Lold' + w*w'
+% Example:
+% L = cholup (Lold,w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (Lold,1) ;
+L = [Lold w] ;
+
+for k = 1:n
+
+ g = givens (L(k,k), L(k,n+1)) ;
+
+ L (:, [k n+1]) = L (:, [k n+1]) * g' ;
+
+ disp ('L:') ;
+ disp (L)
+ pause
+end
+
+L = L (:,1:n) ;
+disp (L) ;
diff --git a/CSparse/MATLAB/Test/cholupdown.m b/CSparse/MATLAB/Test/cholupdown.m
new file mode 100644
index 0000000..fe2eb0e
--- /dev/null
+++ b/CSparse/MATLAB/Test/cholupdown.m
@@ -0,0 +1,58 @@
+function L = cholupdown (Lold, sigma, w)
+%CHOLUPDOWN Cholesky update/downdate (Bischof, Pan, and Tang method)
+% Example:
+% L = cholupdown (Lold, sigma, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+beta = 1 ;
+n = size (Lold,1) ;
+L = Lold ;
+% x = weros (n,1) ;
+worig = w ;
+
+for k = 1:n
+
+ alpha = w(k) / L(k,k) ;
+ beta_new = sqrt (beta^2 + sigma*alpha^2) ;
+ gamma = alpha / (beta_new * beta) ;
+
+ if (sigma < 0)
+
+ % downdate
+ bratio = beta_new / beta ;
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k,k) = bratio * L (k,k) ;
+ L (k+1:n,k) = bratio * L (k+1:n,k) - gamma*w(k+1:n) ;
+
+ else
+
+ % update
+ bratio = beta / beta_new ;
+
+% wold = w (k+1:n) ;
+% w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+% L (k ,k) = bratio * L (k ,k) + gamma*w(k) ;
+% L (k+1:n,k) = bratio * L (k+1:n,k) + gamma*wold ;
+
+ L (k,k) = bratio * L (k,k) + gamma*w(k) ;
+ for i = k+1:n
+
+ wold = w (i) ;
+ w (i) = w (i) - alpha * L (i,k) ;
+ L (i,k) = bratio * L (i,k) + gamma*wold ;
+
+ end
+
+ end
+
+ w (k) = alpha ;
+
+ beta = beta_new ;
+
+end
+
+norm (w-(Lold\worig))
diff --git a/CSparse/MATLAB/Test/cond1est.m b/CSparse/MATLAB/Test/cond1est.m
new file mode 100644
index 0000000..e634168
--- /dev/null
+++ b/CSparse/MATLAB/Test/cond1est.m
@@ -0,0 +1,23 @@
+function c = cond1est (A)
+%COND1EST 1-norm condition estimate.
+% Example:
+% c = cond1est(A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+if (m ~= n | ~isreal (A)) %#ok
+ error ('A must be square and real') ;
+end
+if isempty(A)
+ c = 0 ;
+ return ;
+end
+[L,U,P,Q] = lu (A) ;
+if (~isempty (find (abs (diag (U)) == 0))) %#ok
+ c = Inf ;
+else
+ c = norm (A,1) * norm1est (L,U,P,Q) ;
+end
diff --git a/CSparse/MATLAB/Test/cs_fiedler.m b/CSparse/MATLAB/Test/cs_fiedler.m
new file mode 100644
index 0000000..75c2b6a
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_fiedler.m
@@ -0,0 +1,27 @@
+function [p,v,d] = cs_fiedler (A)
+%CS_FIEDLER the Fiedler vector of a connected graph.
+% [p,v,d] = cs_fiedler(A) computes the Fiedler vector v (the eigenvector
+% corresponding to the 2nd smallest eigenvalue d of the Laplacian of the graph
+% of A+A'). p is the permutation obtained when v is sorted. A should be a
+% connected graph.
+%
+% Example:
+% [p,v,d] = cs_fiedler (A) ;
+%
+% See also CS_SCC, EIGS, SYMRCM, UNMESH.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+if (n < 2)
+ p = 1 ; v = 1 ; d = 0 ; return ;
+end
+opt.disp = 0 ; % turn off printing in eigs
+opt.tol = sqrt (eps) ;
+S = A | A' | speye (n) ; % compute the Laplacian of A
+S = diag (sum (S)) - S ;
+[v,d] = eigs (S, 2, 'SA', opt) ; % find the Fiedler vector v
+v = v (:,2) ;
+d = d (2,2) ;
+[ignore p] = sort (v) ; % sort it to get p
diff --git a/CSparse/MATLAB/Test/cs_frand.m b/CSparse/MATLAB/Test/cs_frand.m
new file mode 100644
index 0000000..c75069f
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_frand.m
@@ -0,0 +1,15 @@
+function A = cs_frand (n,nel,s) %#ok
+%CS_FRAND generate a random finite-element matrix
+% A = cs_frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel
+% finite elements, each of which are of size s-by-s with random symmetric
+% nonzero pattern, plus the identity matrix.
+%
+% Example
+% A = cs_frand (100, 100, 3) ;
+% See also cs_demo.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_frand mexFunction not found') ;
+
diff --git a/CSparse/MATLAB/Test/cs_frand_mex.c b/CSparse/MATLAB/Test/cs_frand_mex.c
new file mode 100644
index 0000000..a801322
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_frand_mex.c
@@ -0,0 +1,60 @@
+#include "cs_mex.h"
+/* A = cs_frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel
+ * finite elements, each of which are of size s-by-s with random symmetric
+ * nonzero pattern, plus the identity matrix.
+ * See also MATLAB/Demo/private/frand.m */
+
+static
+cs *cs_frand (int n, int nel, int s)
+{
+ int ss = s*s, nz = nel*ss, e, i, j, *P ;
+ cs *A, *T = cs_spalloc (n, n, nz, 1, 1) ;
+ if (!T) return (NULL) ;
+ P = cs_malloc (s, sizeof (int)) ;
+ if (!P) return (cs_spfree (T)) ;
+ for (e = 0 ; e < nel ; e++)
+ {
+ for (i = 0 ; i < s ; i++) P [i] = rand () % n ;
+ for (j = 0 ; j < s ; j++)
+ {
+ for (i = 0 ; i < s ; i++)
+ {
+ cs_entry (T, P [i], P [j], rand () / (double) RAND_MAX) ;
+ }
+ }
+ }
+ for (i = 0 ; i < n ; i++) cs_entry (T, i, i, 1) ;
+ A = cs_compress (T) ;
+ cs_spfree (T) ;
+ return (cs_dupl (A) ? A : cs_spfree (A)) ;
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ int n, nel, s ;
+ cs *A, *AT ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: C = cs_frand(n,nel,s)") ;
+ }
+ n = mxGetScalar (pargin [0]) ;
+ nel = mxGetScalar (pargin [1]) ;
+ s = mxGetScalar (pargin [2]) ;
+
+ n = CS_MAX (1,n) ;
+ nel = CS_MAX (1,nel) ;
+ s = CS_MAX (1,s) ;
+
+ AT = cs_frand (n, nel, s) ;
+ A = cs_transpose (AT, 1) ;
+ cs_spfree (AT) ;
+ cs_dropzeros (A) ;
+
+ pargout [0] = cs_mex_put_sparse (&A) ;
+}
diff --git a/CSparse/MATLAB/Test/cs_ipvec.m b/CSparse/MATLAB/Test/cs_ipvec.m
new file mode 100644
index 0000000..f86bab6
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_ipvec.m
@@ -0,0 +1,12 @@
+function x = cs_ipvec (b,p) %#ok
+%CS_IPVEC x(p)=b
+%
+% Example:
+% x = cs_ipvec (b,p)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_ipvec mexFunction not found') ;
+
diff --git a/CSparse/MATLAB/Test/cs_ipvec_mex.c b/CSparse/MATLAB/Test/cs_ipvec_mex.c
new file mode 100644
index 0000000..880972d
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_ipvec_mex.c
@@ -0,0 +1,37 @@
+#include "cs_mex.h"
+/* x(p) = b */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ int n, k, *p ;
+ double *x, *b, *xx ;
+
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_ipvec(b,p)") ;
+ }
+
+ b = mxGetPr (pargin [0]) ;
+ n = mxGetNumberOfElements (pargin [0]) ;
+
+ if (n != mxGetNumberOfElements (pargin [1]))
+ {
+ mexErrMsgTxt ("b or p wrong size") ;
+ }
+
+ pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ;
+
+ xx = mxGetPr (pargin [1]) ;
+ p = cs_malloc (n, sizeof (int)) ;
+ for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ;
+
+ x = mxGetPr (pargout [0]) ;
+ cs_ipvec (p, b, x, n) ;
+
+ cs_free (p) ;
+}
diff --git a/CSparse/MATLAB/Test/cs_maxtransr.m b/CSparse/MATLAB/Test/cs_maxtransr.m
new file mode 100644
index 0000000..df9bca9
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_maxtransr.m
@@ -0,0 +1,12 @@
+function p = cs_maxtransr(A) %#ok
+%CS_MAXTRANSR recursive maximum matching algorithm
+% Example:
+% p = cs_maxtransr(A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_maxtransr mexFunction not found') ;
+
+
diff --git a/CSparse/MATLAB/Test/cs_maxtransr_mex.c b/CSparse/MATLAB/Test/cs_maxtransr_mex.c
new file mode 100644
index 0000000..7aaef50
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_maxtransr_mex.c
@@ -0,0 +1,87 @@
+#include "cs_mex.h"
+/* find an augmenting path starting at column j and extend the match if found */
+static
+int augment (int k, cs *A, int *jmatch, int *cheap, int *w, int j)
+{
+ int found = 0, p, i = -1, *Ap = A->p, *Ai = A->i ;
+ /* --- Start depth-first-search at node j ------------------------------- */
+ w [j] = k ; /* mark j as visited for kth path */
+ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++)
+ {
+ i = Ai [p] ; /* try a cheap assignment (i,j) */
+ found = (jmatch [i] == -1) ;
+ }
+ cheap [j] = p ; /* start here next time for j */
+ /* --- Depth-first-search of neighbors of j ----------------------------- */
+ for (p = Ap [j] ; p < Ap [j+1] && !found ; p++)
+ {
+ i = Ai [p] ; /* consider row i */
+ if (w [jmatch [i]] == k) continue ; /* skip col jmatch [i] if marked */
+ found = augment (k, A, jmatch, cheap, w, jmatch [i]) ;
+ }
+ if (found) jmatch [i] = j ; /* augment jmatch if path found */
+ return (found) ;
+}
+
+/* find a maximum transveral */
+static
+int *maxtrans (cs *A) /* returns jmatch [0..m-1] */
+{
+ int i, j, k, n, m, *Ap, *jmatch, *w, *cheap ;
+ if (!A) return (NULL) ; /* check inputs */
+ n = A->n ; m = A->m ; Ap = A->p ;
+ jmatch = cs_malloc (m, sizeof (int)) ; /* allocate result */
+ w = cs_malloc (2*n, sizeof (int)) ; /* allocate workspace */
+ if (!w || !jmatch) return (cs_idone (jmatch, NULL, w, 0)) ;
+ cheap = w + n ;
+ for (j = 0 ; j < n ; j++) cheap [j] = Ap [j] ; /* for cheap assignment */
+ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */
+ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* no rows matched yet */
+ for (k = 0 ; k < n ; k++) augment (k, A, jmatch, cheap, w, k) ;
+ return (cs_idone (jmatch, NULL, w, 1)) ;
+}
+
+/* invert a maximum matching */
+static int *invmatch (int *jmatch, int m, int n)
+{
+ int i, j, *imatch ;
+ if (!jmatch) return (NULL) ;
+ imatch = cs_malloc (n, sizeof (int)) ;
+ if (!imatch) return (NULL) ;
+ for (j = 0 ; j < n ; j++) imatch [j] = -1 ;
+ for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ;
+ return (imatch) ;
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs *A, Amatrix ;
+ double *x ;
+ int i, m, n, *imatch, *jmatch ;
+
+ if (nargout > 1 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: p = cr_maxtransr(A)") ;
+ }
+
+ /* get inputs */
+ A = cs_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ;
+ m = A->m ;
+ n = A->n ;
+
+ jmatch = maxtrans (A) ;
+ imatch = invmatch (jmatch, m, n) ; /* imatch = inverse of jmatch */
+
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n ; i++) x [i] = imatch [i] + 1 ;
+
+ cs_free (jmatch) ;
+ cs_free (imatch) ;
+}
diff --git a/CSparse/MATLAB/Test/cs_pvec.m b/CSparse/MATLAB/Test/cs_pvec.m
new file mode 100644
index 0000000..bbd3a87
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_pvec.m
@@ -0,0 +1,12 @@
+function x = cs_pvec (b,p) %#ok
+%CS_PVEC x=b(p)
+%
+% Example:
+% x = cs_pvec (b,p)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_pvec mexFunction not found') ;
+
diff --git a/CSparse/MATLAB/Test/cs_pvec_mex.c b/CSparse/MATLAB/Test/cs_pvec_mex.c
new file mode 100644
index 0000000..d72065b
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_pvec_mex.c
@@ -0,0 +1,37 @@
+#include "cs_mex.h"
+/* x = b(p) */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ int n, k, *p ;
+ double *x, *b, *xx ;
+
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_pvec(b,p)") ;
+ }
+
+ b = mxGetPr (pargin [0]) ;
+ n = mxGetNumberOfElements (pargin [0]) ;
+
+ if (n != mxGetNumberOfElements (pargin [1]))
+ {
+ mexErrMsgTxt ("b or p wrong size") ;
+ }
+
+ pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ;
+
+ xx = mxGetPr (pargin [1]) ;
+ p = cs_malloc (n, sizeof (int)) ;
+ for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ;
+
+ x = mxGetPr (pargout [0]) ;
+ cs_pvec (p, b, x, n) ;
+
+ cs_free (p) ;
+}
diff --git a/CSparse/MATLAB/Test/cs_q1.m b/CSparse/MATLAB/Test/cs_q1.m
new file mode 100644
index 0000000..45a51ec
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_q1.m
@@ -0,0 +1,19 @@
+function Q = cs_q1 (V, Beta, p)
+%CS_Q1 construct Q from Householder vectors
+% Example:
+% Q = cs_q1 (V, beta, p)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (V) ;
+Q = speye (m) ;
+if (nargin > 2)
+ Q = Q (:,p) ;
+end
+for i = 1:m
+ for k = 1:n
+ Q (i,:) = Q (i,:) - ((Q(i,:) * V(:,k)) * Beta(k)) * V(:,k)' ;
+ end
+end
diff --git a/CSparse/MATLAB/Test/cs_reach.m b/CSparse/MATLAB/Test/cs_reach.m
new file mode 100644
index 0000000..2e68e7a
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_reach.m
@@ -0,0 +1,14 @@
+function x = cs_reach(L,b) %#ok
+%CS_REACH non-recursive reach (interface to CSparse cs_reach)
+% find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower
+% triangular. b must be a real sparse vector.
+%
+% Example:
+% x = cs_reach(L,b)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_reach mexFunction not found') ;
+
diff --git a/CSparse/MATLAB/Test/cs_reach_mex.c b/CSparse/MATLAB/Test/cs_reach_mex.c
new file mode 100644
index 0000000..f180637
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_reach_mex.c
@@ -0,0 +1,39 @@
+#include "cs_mex.h"
+/* find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower
+ * triangular. b must be a real sparse vector. */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Lmatrix, Bmatrix, *L, *B ;
+ double *x ;
+ int k, i, j, top, *xi, *perm ;
+
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_reach(L,b)") ;
+ }
+
+ /* get inputs */
+ L = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
+ B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;
+ cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ;
+ perm = cs_malloc (L->n, sizeof (int)) ;
+ for (k = 0 ; k < L->n ; k++) perm [k] = k ;
+
+ xi = cs_calloc (3*L->n, sizeof (int)) ;
+
+ top = cs_reach (L, B, 0, xi, perm) ;
+
+ pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ;
+
+ cs_free (xi) ;
+ cs_free (perm) ;
+}
diff --git a/CSparse/MATLAB/Test/cs_reachr.m b/CSparse/MATLAB/Test/cs_reachr.m
new file mode 100644
index 0000000..d6bbfc7
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_reachr.m
@@ -0,0 +1,15 @@
+function x = cs_reachr(L,b) %#ok
+%CS_REACHR recursive reach (interface to CSparse cs_reachr)
+% find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower
+% triangular. b must be a real sparse vector.
+%
+% Example:
+% x = cs_reachr(L,b)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+error ('cs_reach mexFunction not found') ;
+
diff --git a/CSparse/MATLAB/Test/cs_reachr_mex.c b/CSparse/MATLAB/Test/cs_reachr_mex.c
new file mode 100644
index 0000000..f5af2aa
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_reachr_mex.c
@@ -0,0 +1,67 @@
+#include "cs_mex.h"
+/* find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower
+ * triangular. b must be a real sparse vector. */
+
+static
+void dfsr (int j, const cs *L, int *top, int *xi, int *w)
+{
+ int p ;
+ w [j] = 1 ; /* mark node j */
+ for (p = L->p [j] ; p < L->p [j+1] ; p++) /* for each i in L(:,j) */
+ {
+ if (w [L->i [p]] != 1) /* if i is unmarked */
+ {
+ dfsr (L->i [p], L, top, xi, w) ; /* start a dfs at i */
+ }
+ }
+ xi [--(*top)] = j ; /* push j onto the stack */
+}
+
+/* w [0..n-1] == 0 on input, <= 1 on output. size n */
+static
+int reachr (const cs *L, const cs *B, int *xi, int *w)
+{
+ int p, n = L->n ;
+ int top = n ; /* stack is empty */
+ for (p = B->p [0] ; p < B->p [1] ; p++) /* for each i in pattern of b */
+ {
+ if (w [B->i [p]] != 1) /* if i is unmarked */
+ {
+ dfsr (B->i [p], L, &top, xi, w) ; /* start a dfs at i */
+ }
+ }
+ return (top) ; /* return top of stack */
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Lmatrix, Bmatrix, *L, *B ;
+ double *x ;
+ int i, j, top, *xi ;
+
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_reachr(L,b)") ;
+ }
+
+ /* get inputs */
+ L = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
+ B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;
+ cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ;
+
+ xi = cs_calloc (2*L->n, sizeof (int)) ;
+
+ top = reachr (L, B, xi, xi + L->n) ;
+
+ pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ;
+
+ cs_free (xi) ;
+}
diff --git a/CSparse/MATLAB/Test/cs_rowcnt.m b/CSparse/MATLAB/Test/cs_rowcnt.m
new file mode 100644
index 0000000..d57d661
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_rowcnt.m
@@ -0,0 +1,15 @@
+function r = cs_rowcnt(A,parent,post) %#ok
+%CS_ROWCNT row counts for sparse Cholesky
+% Compute the row counts of the Cholesky factor L of the matrix A. Uses
+% the lower triangular part of A.
+%
+% Example:
+% r = cs_rowcnt(A,parent,post)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+error ('cs_rowcnt mexFunction not found') ;
+
diff --git a/CSparse/MATLAB/Test/cs_rowcnt_mex.c b/CSparse/MATLAB/Test/cs_rowcnt_mex.c
new file mode 100644
index 0000000..9c1e710
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_rowcnt_mex.c
@@ -0,0 +1,86 @@
+/* Compute the row counts of the Cholesky factor L of the matrix A. Uses
+ * the lower triangular part of A. */
+
+#include "cs_mex.h"
+
+static
+void firstdesc (int n, int *parent, int *post, int *first, int *level)
+{
+ int len, i, k, r, s ;
+ for (i = 0 ; i < n ; i++) first [i] = -1 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ i = post [k] ; /* node i of etree is kth postordered node */
+ len = 0 ; /* traverse from i towards the root */
+ for (r = i ; r != -1 && first [r] == -1 ; r = parent [r], len++)
+ first [r] = k ;
+ len += (r == -1) ? (-1) : level [r] ; /* root node or end of path */
+ for (s = i ; s != r ; s = parent [s]) level [s] = len-- ;
+ }
+}
+
+static
+int *rowcnt (cs *A, int *parent, int *post) /* return rowcount [0..n-1] */
+{
+ int i, j, k, p, q, n, jleaf, *Ap, *Ai, *maxfirst,
+ *ancestor, *prevleaf, *w, *first, *level, *rowcount ;
+ n = A->n ; Ap = A->p ; Ai = A->i ; /* get A */
+ w = cs_malloc (5*n, sizeof (int)) ; /* get workspace */
+ ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ;
+ level = w+4*n ;
+ rowcount = cs_malloc (n, sizeof (int)) ; /* allocate result */
+ firstdesc (n, parent, post, first, level) ; /* find first and level */
+ for (i = 0 ; i < n ; i++)
+ {
+ rowcount [i] = 1 ; /* count the diagonal of L */
+ prevleaf [i] = -1 ; /* no previous leaf of the ith row subtree */
+ maxfirst [i] = -1 ; /* max first[j] for node j in ith subtree */
+ ancestor [i] = i ; /* every node is in its own set, by itself */
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ j = post [k] ; /* j is the kth node in the postordered etree */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ q = cs_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf) ;
+ if (jleaf) rowcount [i] += (level [j] - level [q]) ;
+ }
+ if (parent [j] != -1) ancestor [j] = parent [j] ;
+ }
+ cs_free (w) ;
+ return (rowcount) ;
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs *A, Amatrix ;
+ double *x ;
+ int i, n, *parent, *post, *rowcount ;
+
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: r = rowcnt(A,parent,post)") ;
+ }
+
+ /* get inputs */
+ A = cs_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ;
+ n = A->n ;
+
+ parent = cs_mex_get_int (n, pargin [1], &i, 0) ;
+ post = cs_mex_get_int (n, pargin [2], &i, 1) ;
+
+ rowcount = rowcnt (A, parent, post) ;
+
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n ; i++) x [i] = rowcount [i] ;
+
+ cs_free (rowcount) ;
+}
diff --git a/CSparse/MATLAB/Test/cs_sparse2.m b/CSparse/MATLAB/Test/cs_sparse2.m
new file mode 100644
index 0000000..32d9319
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_sparse2.m
@@ -0,0 +1,15 @@
+function A = cs_sparse2 (i,j,x) %#ok
+%CS_SPARSE2 same as cs_sparse, to test cs_entry function
+% A = cs_sparse2 (i,j,x), removing duplicates and numerically zero entries,
+% and returning A sorted (test cs_entry)
+%
+% Example:
+% A = cs_sparse2 (i,j,x)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+error ('cs_sparse2 mexFunction not found') ;
+
diff --git a/CSparse/MATLAB/Test/cs_sparse2_mex.c b/CSparse/MATLAB/Test/cs_sparse2_mex.c
new file mode 100644
index 0000000..005102a
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_sparse2_mex.c
@@ -0,0 +1,41 @@
+#include "cs_mex.h"
+/* A = cs_sparse2 (i,j,x), removing duplicates and numerically zero entries,
+ * and returning A sorted (test cs_entry) */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double *Tx ;
+ cs *A, *C, *T ;
+ int k, m, n, nz, *Ti, *Tj ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: A = cs_sparse2(i,j,x)") ;
+ }
+ nz = mxGetM (pargin [0]) ;
+ Ti = cs_mex_get_int (nz, pargin [0], &m, 1) ;
+ Tj = cs_mex_get_int (nz, pargin [1], &n, 1) ;
+ cs_mex_check (1, nz, 1, 0, 0, 1, pargin [2]) ;
+ Tx = mxGetPr (pargin [2]) ;
+
+ T = cs_spalloc (n, m, 1, 1, 1) ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ cs_entry (T, Tj [k], Ti [k], Tx [k]) ;
+ }
+
+ C = cs_compress (T) ;
+ cs_spfree (T) ;
+
+ cs_dupl (C) ;
+ cs_dropzeros (C) ;
+ A = cs_transpose (C, 1) ;
+ cs_spfree (C) ;
+ pargout [0] = cs_mex_put_sparse (&A) ;
+ cs_free (Ti) ;
+ cs_free (Tj) ;
+}
diff --git a/CSparse/MATLAB/Test/cs_test_make.m b/CSparse/MATLAB/Test/cs_test_make.m
new file mode 100644
index 0000000..4908fcb
--- /dev/null
+++ b/CSparse/MATLAB/Test/cs_test_make.m
@@ -0,0 +1,33 @@
+function cs_test_make (force)
+%CS_TEST_MAKE compiles the CSparse, Demo, and Test mexFunctions.
+% The current directory must be CSparse/MATLAB/Test to use this function.
+%
+% Example:
+% cs_test_make
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 1)
+ force = 0 ;
+end
+
+cd ('../CSparse') ;
+[object_files timestamp] = cs_make ;
+cd ('../Test') ;
+
+mexfunc = { 'cs_ipvec', 'cs_pvec', 'cs_sparse2', ...
+ 'cs_reach', 'cs_maxtransr', 'cs_reachr', 'cs_rowcnt', 'cs_frand' } ;
+
+for i = 1:length(mexfunc)
+ [s t tobj] = cs_must_compile ('', mexfunc{i}, '_mex', ...
+ ['.' mexext], 'cs_test_make.m', force) ;
+ if (s | tobj < timestamp) %#ok
+ cmd = ['mex -O -output ' mexfunc{i} ' ' mexfunc{i} '_mex.c -I..' ...
+ filesep '..' filesep 'Include -I..' ...
+ filesep 'CSparse ' object_files] ;
+ fprintf ('%s\n', cmd) ;
+ eval (cmd) ;
+ end
+end
diff --git a/CSparse/MATLAB/Test/cspy_test.m b/CSparse/MATLAB/Test/cspy_test.m
new file mode 100644
index 0000000..1312ca3
--- /dev/null
+++ b/CSparse/MATLAB/Test/cspy_test.m
@@ -0,0 +1,50 @@
+function cspy_test
+%CSPY_TEST test cspy and cs_dmspy
+% Example
+% cspy_test
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+
+clf
+
+% f = f (523:end) ;
+% f = f ((find (f == 938)):end) ;
+
+for i = f
+
+ Prob = UFget (i,index) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ try
+ subplot (1,4,1) ; cspy (A) ;
+ drawnow
+ subplot (1,4,2) ; cspy (A,64) ;
+ drawnow
+ subplot (1,4,3) ; cs_dmspy (A) ;
+ drawnow
+ subplot (1,4,4) ; cs_dmspy (A,0) ;
+ drawnow
+ catch
+ fprintf ('failed...\n') ;
+ end
+
+ [m n] = size (A) ;
+ if (m == n & nnz (diag (A)) == n) %#ok
+ p = cs_dmperm (A) ;
+ if (any (p ~= 1:n))
+ error ('!') ;
+ end
+ [p q r s cc rr] = cs_dmperm (A) ; %#ok
+ if (any (p ~= q))
+ error ('not sym!') ;
+ end
+ end
+
+ drawnow
+end
diff --git a/CSparse/MATLAB/Test/dmperm_test.m b/CSparse/MATLAB/Test/dmperm_test.m
new file mode 100644
index 0000000..2f1fd38
--- /dev/null
+++ b/CSparse/MATLAB/Test/dmperm_test.m
@@ -0,0 +1,126 @@
+function dmperm_test
+%DMPERM_TEST test cs_dmperm
+%
+% Example:
+% dmperm_test
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+
+f = find (index.nrows ~= index.ncols) ;
+[ignore i] = sort (index.nrows(f) ./ index.ncols(f)) ;
+f = [209:211 f(i)] ;
+
+nmat = length(f) ;
+
+tt1 = zeros (1,nmat) ;
+tt2 = zeros (1,nmat) ;
+tt3 = zeros (1,nmat) ;
+tt4 = zeros (1,nmat) ;
+mm = zeros (1,nmat) ;
+nn = zeros (1,nmat) ;
+ss = zeros (1,nmat) ;
+me = zeros (1,nmat) ;
+ne = zeros (1,nmat) ;
+
+p = cs_dmperm (sparse (1)) ;
+
+for k = 1:length(f)
+
+ i = f(k) ;
+
+ Prob = UFget (i) %#ok
+
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m > n)
+ % make sure A is short and fat
+ A = A' ;
+ end
+ % C is tall and thin
+ C = A' ;
+ [m n] = size (A) ;
+
+ k1 = 0 ;
+ t1 = 0 ;
+ while (t1 < 1)
+ tic
+ p = cs_dmperm (A) ;
+ t = toc ;
+ t1 = t1 + t ;
+ k1 = k1 + 1 ;
+ end
+ t1 = t1 / k1 ;
+ s1 = sum (p > 0) ;
+
+ k2 = 0 ;
+ t2 = 0 ;
+ while (t2 < 1)
+ tic
+ p = cs_dmperm (C) ;
+ t = toc ;
+ t2 = t2 + t ;
+ k2 = k2 + 1 ;
+ end
+ t2 = t2 / k2 ;
+ s2 = sum (p > 0) ;
+
+ k3 = 0 ;
+ t3 = 0 ;
+ while (t3 < 1)
+ tic
+ p = cs_dmperm_orig (A) ;
+ t = toc ;
+ t3 = t3 + t ;
+ k3 = k3 + 1 ;
+ end
+ t3 = t3 / k3 ;
+
+ k4 = 0 ;
+ t4 = 0 ;
+ while (t4 < 1)
+ tic
+ p = cs_dmperm_orig (A') ;
+ t = toc ;
+ t4 = t4 + t ;
+ k4 = k4 + 1 ;
+ end
+ t4 = t4 / k4 ;
+
+ sprnk = sum (p > 0) ;
+ nempty = full (sum (sum (spones (A)) == 0)) ;
+ mempty = full (sum (sum (spones (C)) == 0)) ;
+
+ fprintf ('[m %d:%d n %d:%d (%d)]:\n', m, mempty, n, nempty, sprnk) ;
+ fprintf (' A: t1 %10.6f (%6d) C: t2 %10.6f (%6d) new\n', ...
+ t1, k1, t2, k2) ;
+ fprintf (' A: t3 %10.6f (%6d) C: t4 %10.6f (%6d) orig\n', ...
+ t3, k3, t4, k4) ;
+
+ if (s1 ~= sprnk | s2 ~= sprnk) %#ok
+ s1 %#ok
+ s2 %#ok
+ sprnk %#ok
+ error ('!') ;
+ end
+
+ tt1 (k) = t1 ;
+ tt2 (k) = t2 ;
+ tt3 (k) = t3 ;
+ tt4 (k) = t4 ;
+ mm (k) = m ;
+ nn (k) = n ;
+ ss (k) = sprnk ;
+ me (k) = mempty ;
+ ne (k) = nempty ;
+
+ clear A C
+
+ semilogy (ss(1:k) ./ nn(1:k), tt1(1:k) ./ tt3(1:k), 'o', ...
+ [0 1], [1 1], 'r-') ;
+ drawnow
+
+end
diff --git a/CSparse/MATLAB/Test/dmspy_test.m b/CSparse/MATLAB/Test/dmspy_test.m
new file mode 100644
index 0000000..fff2057
--- /dev/null
+++ b/CSparse/MATLAB/Test/dmspy_test.m
@@ -0,0 +1,28 @@
+function dmspy_test
+%DMSPY_TEST test cspy, cs_dmspy, and cs_dmperm
+% Example:
+% dmspy_test
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+f = find (index.nblocks > 1) ;
+% f = find (index.nblocks > 1 & index.nrows == index.ncols & ...
+% index.nnzdiag == index.nrows) ;
+[ignore i] = sort (index.nnz (f)) ;
+f = f (i) ;
+
+for i = f
+ Prob = UFget (i,index) ;
+ disp (Prob) ;
+ clf
+ subplot (2,2,1) ; cspy (Prob.A) ;
+ subplot (2,2,2) ; cs_dmspy (Prob.A) ;
+ [p,q,r,s,cc,rr] = cs_dmperm (Prob.A) ; %#ok
+ subplot (2,2,3) ; plot (p) ;
+ subplot (2,2,4) ; plot (q) ;
+ drawnow
+end
diff --git a/CSparse/MATLAB/Test/etree_sample.m b/CSparse/MATLAB/Test/etree_sample.m
new file mode 100644
index 0000000..9a38f0a
--- /dev/null
+++ b/CSparse/MATLAB/Test/etree_sample.m
@@ -0,0 +1,71 @@
+function etree_sample
+% ETREE_SAMPLE construct a sample etree and symbolic factorization
+%
+% Example
+% etree_sample
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clf
+
+% desired etree:
+% 1 2 3 4 5 6 7 8 9 10 11
+goal = [6 3 8 6 8 7 9 10 10 11 0] ;
+
+o = 0 ;
+X = 1 ;
+x = 0 ;
+
+A = [
+1 o o o o o o o o o o
+o 2 o o o o o o o o o
+o X 3 o o o o o o o o
+o o o 4 o o o o o o o
+o o o o 5 o o o o o o
+X o o X o 6 o o o o o
+X o o x o x 7 o o o o
+o X x o X o o 8 o o o
+x o o x o X x o 9 o o
+x x X X x X x X x 10 o
+x x X x X x X X x X 11 ] ;
+
+A = A + tril(A,-1)' ;
+disp ('A = ') ;
+disp (A)
+
+[count,h,parent,post,R] = symbfact (A) ;
+L = R' ;
+
+subplot (2,3,1) ;
+spy (A)
+title ('A') ;
+
+subplot (2,3,2) ;
+etreeplot (A)
+title ('etree') ;
+
+% [parent, post] = etree (A) ;
+
+subplot (2,3,3) ;
+spy (L)
+title ('L, not postordered') ;
+
+n = size (A,1) ;
+for k = 1:n
+ fprintf ('parent (%d) = %d goal: %d ok: %d\n', ...
+ k, parent (k), goal (k), goal (k) == parent(k)) ;
+end
+
+
+[count,h,parent2,post2,R] = symbfact (A (post,post)) ;
+L = R' ;
+
+subplot (2,3,5) ;
+spy (A (post,post))
+title ('A postordered') ;
+
+subplot (2,3,6) ;
+spy (L)
+title ('L postordered') ;
diff --git a/CSparse/MATLAB/Test/givens2.m b/CSparse/MATLAB/Test/givens2.m
new file mode 100644
index 0000000..5420101
--- /dev/null
+++ b/CSparse/MATLAB/Test/givens2.m
@@ -0,0 +1,17 @@
+function g = givens2(a,b)
+%GIVENS2 find a Givens rotation.
+% Example:
+% g = givens2(a,b)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (b == 0)
+ c = 1 ; s = 0 ;
+elseif (abs (b) > abs (a))
+ tau = -a/b ; s = 1 / sqrt (1+tau^2) ; c = s*tau ;
+else
+ tau = -b/a ; c = 1 / sqrt (1+tau^2) ; s = c*tau ;
+end
+g = [c -s ; s c] ;
diff --git a/CSparse/MATLAB/Test/gqr3.m b/CSparse/MATLAB/Test/gqr3.m
new file mode 100644
index 0000000..9f31d09
--- /dev/null
+++ b/CSparse/MATLAB/Test/gqr3.m
@@ -0,0 +1,30 @@
+function R = gqr3 (A)
+%GQR3 QR factorization, based on Givens rotations
+%
+% Example:
+% R = gqr3 (A)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+[m n] = size (A) ;
+
+% parent = cs_etree (sparse (A), 'col') ;
+
+for i = 2:m
+ % i
+ for k = 1:min(i-1,n)
+ % k
+ % Givens rotation to zero out A(i,k) using A(k,k)
+ G = givens2 (A(k,k), A(i,k)) ;
+ A ([k i],k:n) = G * A ([k i],k:n) ;
+ A (i,k) = 0 ;
+ % fprintf ('A(21,25)=%g\n', A(21,25)) ;
+ % if (A(21,25) ~= 0)
+ % pause
+ % end
+ end
+end
+R = A ;
diff --git a/CSparse/MATLAB/Test/happly.m b/CSparse/MATLAB/Test/happly.m
new file mode 100644
index 0000000..770c5d9
--- /dev/null
+++ b/CSparse/MATLAB/Test/happly.m
@@ -0,0 +1,11 @@
+function hx = happly (v, beta, x)
+%HAPPLY apply Householder reflection to a vector
+% Example:
+% hx = happly (v,beta,x) ; % computes hx = x - v * (beta * (v' *x)) ;
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+hx = x - v * (beta * (v' *x)) ;
diff --git a/CSparse/MATLAB/Test/hmake1.m b/CSparse/MATLAB/Test/hmake1.m
new file mode 100644
index 0000000..52f8c6c
--- /dev/null
+++ b/CSparse/MATLAB/Test/hmake1.m
@@ -0,0 +1,39 @@
+function [v,beta,xnorm] = hmake1 (x)
+%HMAKE1 construct a Householder reflection
+% Example:
+% [v,beta,xnorm] = hmake1 (x)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = length (x) ;
+if (n == 1)
+ v = 1 ;
+ xnorm = norm (x) ;
+ if (x (1) < 0)
+ beta = 2 ;
+ else
+ beta = 0 ;
+ end
+ return
+end
+sigma = x (2:n)'*x(2:n) ;
+xnorm = sqrt (x (1)^2 + sigma) ;
+v = x ;
+if (sigma == 0)
+ v (1) = 1 ;
+ if (x (1) < 0)
+ beta = 2 ;
+ else
+ beta = 0 ;
+ end
+else
+ if (x (1) <= 0)
+ v (1) = x(1) - xnorm ;
+ else
+ v (1) = -sigma / (x(1) + xnorm) ;
+ end
+ beta = (2*v(1)^2) / (sigma + v(1)^2) ;
+ v = v / v(1) ;
+end
diff --git a/CSparse/MATLAB/Test/house.m b/CSparse/MATLAB/Test/house.m
new file mode 100644
index 0000000..42f3e4c
--- /dev/null
+++ b/CSparse/MATLAB/Test/house.m
@@ -0,0 +1,29 @@
+function [v,beta,s] = house (x)
+%HOUSE find a Householder reflection.
+% Example:
+% [v,beta,s] = house (x)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = length (x) ;
+if (n == 1)
+ sigma = 0 ;
+else
+ sigma = x (2:n)' * x (2:n) ;
+end
+v = x ;
+if (sigma == 0)
+ s = x (1) ;
+ v (1) = 0 ;
+ beta = 0 ;
+else
+ s = sqrt (x(1)^2 + sigma) ;
+ if (x (1) <= 0)
+ v (1) = x (1) - s ;
+ else
+ v (1) = -sigma / (x (1) + s) ;
+ end
+ beta = -1 / (s * v(1)) ;
+end
diff --git a/CSparse/MATLAB/Test/lu_left.m b/CSparse/MATLAB/Test/lu_left.m
new file mode 100644
index 0000000..73723f6
--- /dev/null
+++ b/CSparse/MATLAB/Test/lu_left.m
@@ -0,0 +1,25 @@
+function [L,U,P] = lu_left (A)
+%LU_LEFT left-looking LU factorization.
+% Example:
+% [L,U,P] = lu_left (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+P = eye (n) ;
+L = zeros (n) ;
+U = zeros (n) ;
+for k = 1:n
+ x = [ L(:,1:k-1) [ zeros(k-1,n-k+1) ; eye(n-k+1) ]] \ (P * A (:,k)) ;
+ U (1:k-1,k) = x (1:k-1) ; % the column of U
+ [a i] = max (abs (x (k:n))) ; % find the pivot row i
+ i = i + k - 1 ;
+ L ([i k],:) = L ([k i], :) ; % swap rows i and k of L, P, and x
+ P ([i k],:) = P ([k i], :) ;
+ x ([i k]) = x ([k i]) ;
+ U (k,k) = x (k) ;
+ L (k,k) = 1 ;
+ L (k+1:n,k) = x (k+1:n) / x (k) ; % divide the pivot column by U(k,k)
+end
diff --git a/CSparse/MATLAB/Test/lu_right.m b/CSparse/MATLAB/Test/lu_right.m
new file mode 100644
index 0000000..39b5ceb
--- /dev/null
+++ b/CSparse/MATLAB/Test/lu_right.m
@@ -0,0 +1,17 @@
+function [L,U] = lu_right (A)
+%LU_RIGHT right-looking LU factorization.
+% Example:
+% [L,U] = lu_right (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+L = eye (n) ;
+U = zeros (n) ;
+for k = 1:n
+ U (k,k:n) = A (k,k:n) ; % (6.4) and (6.5)
+ L (k+1:n,k) = A (k+1:n,k) / U (k,k) ; % (6.6)
+ A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - L (k+1:n,k) * U (k,k+1:n) ; % (6.7)
+end
diff --git a/CSparse/MATLAB/Test/lu_rightp.m b/CSparse/MATLAB/Test/lu_rightp.m
new file mode 100644
index 0000000..84bfbbb
--- /dev/null
+++ b/CSparse/MATLAB/Test/lu_rightp.m
@@ -0,0 +1,22 @@
+function [L,U,P] = lu_rightp (A)
+%LU_RIGHTP right-looking LU factorization, with partial pivoting.
+%
+% Example:
+% [L,U,P] = lu_rightp (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+P = eye (n) ;
+for k = 1:n
+ [x,i] = max (abs (A (k:n,k))) ; % partial pivoting
+ i = i+k-1 ;
+ P ([k i],:) = P ([i k], :) ;
+ A ([k i],:) = A ([i k], :) ; % (6.10), (6.11)
+ A (k+1:n,k) = A (k+1:n,k) / A (k,k) ; % (6.12)
+ A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - A (k+1:n,k) * A (k,k+1:n) ; % (6.9)
+end
+L = tril (A,-1) + eye (n) ;
+U = triu (A) ;
diff --git a/CSparse/MATLAB/Test/lu_rightpr.m b/CSparse/MATLAB/Test/lu_rightpr.m
new file mode 100644
index 0000000..ee5ba84
--- /dev/null
+++ b/CSparse/MATLAB/Test/lu_rightpr.m
@@ -0,0 +1,29 @@
+function [L,U,P] = lu_rightpr (A)
+%LU_RIGHTPR recursive right-looking LU, with partial pivoting.
+%
+% Example:
+% [L,U,P] = lu_rightpr (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+if (n == 1)
+ P = 1 ;
+ L = 1 ;
+ U = A ;
+else
+ [x,i] = max (abs (A (1:n,1))) ; % partial pivoting
+ P1 = eye (n) ;
+ P1 ([1 i],:) = P1 ([i 1], :) ;
+ A = P1*A ;
+ u11 = A (1,1) ; % (6.10)
+ u12 = A (1,2:n) ; % (6.11)
+ l21 = A (2:n,1) / u11 ; % (6.12)
+ [L22,U22,P2] = lu_rightpr (A (2:n,2:n) - l21*u12) ; % (6.9) or (6.13)
+ o = zeros(1,n-1) ;
+ L = [ 1 o ; P2*l21 L22 ] ; % (6.14)
+ U = [ u11 u12 ; o' U22 ] ;
+ P = [ 1 o ; o' P2] * P1 ;
+end
diff --git a/CSparse/MATLAB/Test/lu_rightr.m b/CSparse/MATLAB/Test/lu_rightr.m
new file mode 100644
index 0000000..8f1e74a
--- /dev/null
+++ b/CSparse/MATLAB/Test/lu_rightr.m
@@ -0,0 +1,21 @@
+function [L,U] = lu_rightr (A)
+%LU_RIGHTR recursive right-looking LU.
+% Example:
+% [L,U] = lu_rightr (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+if (n == 1)
+ L = 1 ;
+ U = A ;
+else
+ u11 = A (1,1) ; % (6.4)
+ u12 = A (1,2:n) ; % (6.5)
+ l21 = A (2:n,1) / u11 ; % (6.6)
+ [L22,U22] = lu_rightr (A (2:n,2:n) - l21*u12) ; % (6.7)
+ L = [ 1 zeros(1,n-1) ; l21 L22 ] ;
+ U = [ u11 u12 ; zeros(n-1,1) U22 ] ;
+end
diff --git a/CSparse/MATLAB/Test/mynormest1.m b/CSparse/MATLAB/Test/mynormest1.m
new file mode 100644
index 0000000..414f21b
--- /dev/null
+++ b/CSparse/MATLAB/Test/mynormest1.m
@@ -0,0 +1,92 @@
+function est = mynormest1 (L, U, P, Q)
+%MYNORMEST1 estimate norm(A,1), using LU factorization (L*U = P*A*Q).
+%
+% Example:
+% est = mynormest1 (L, U, P, Q)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+n = size (L,1) ;
+est = 0 ;
+S = zeros (n,1) ;
+
+for k = 1:5
+
+ if k == 1
+ x = ones (n,1) / n ;
+ else
+
+ j = find (abs (x) == max (abs (x))) ;
+ j = j (1) ;
+ x = zeros (n,1) ;
+ x (j) = 1 ;
+
+ % fprintf ('eka: k %d j %d est %g\n', k, j, est) ;
+ end
+
+
+ % x=A\x, but use the existing P*A*Q=L*U factorization
+
+ x = Q * (U \ (L \ (P*x))) ;
+
+ est_old = est ;
+ est = sum (abs (x)) ;
+
+ unchanged = 1 ;
+ for i = 1:n
+ if (x (i) >= 0)
+ s = 1 ;
+ else
+ s = -1 ;
+ end
+ if (s ~= S (i))
+ S (i) = s ;
+ unchanged = 0 ;
+ end
+ end
+
+ if (any (S ~= signum (x)))
+ S' %#ok
+ signum(x)' %#ok
+ error ('Hey!') ;
+ end
+
+ if k > 1 & (est <= est_old | unchanged) %#ok
+ break ;
+ end
+ x = S ;
+
+ % x=A'\x, but use the existing P*A*Q=L*U factorization
+ x = P' * (L' \ (U' \ (Q'*x))) ;
+
+ if k > 1
+ jnew = find (abs (x) == max (abs (x))) ;
+ if (jnew == j)
+ break ;
+ end
+ end
+
+end
+
+for k = 1:n
+ x (k) = power (-1, k+1) * (1 + ((k-1)/(n-1))) ;
+end
+
+% x=A\x, but use the existing P*A*Q=L*U factorization
+x = Q * (U \ (L \ (P*x))) ;
+
+est_new = 2 * sum (abs (x)) / (3 * n) ;
+if (est_new > est)
+ est = est_new ;
+end
+
+
+
+
+function s = signum (x)
+%SIGNUM compute sign of x
+s = ones (length (x),1) ;
+s (find (x < 0)) = -1 ; %#ok
diff --git a/CSparse/MATLAB/Test/myqr.m b/CSparse/MATLAB/Test/myqr.m
new file mode 100644
index 0000000..451518a
--- /dev/null
+++ b/CSparse/MATLAB/Test/myqr.m
@@ -0,0 +1,56 @@
+function [H,R] = myqr (A)
+%MYQR QR factorization using Householder reflections
+% uses function [v,beta,xnorm] = hmake1 (x)
+% and function hx = happly (v, beta, x)
+%
+% Example
+% [H,R] = myqr (A)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+[m n] = size (A) ;
+
+H = zeros (m,n) ;
+R = zeros (m,n) ;
+
+for k = 1:n
+
+ % apply prior H's
+ % fprintf ('\n-----------------init %d\n', k) ;
+ x = A (:,k) ;
+ for i = 1:k-1
+ v = H(((i+1):m),i) ;
+ v = [1 ; v] ; %#ok
+ beta = H (i,i) ;
+ % n1 = norm (x (i:m)) ;
+ x (i:m) = happly (v, beta, x (i:m)) ;
+ % n2 = norm (x (i:m)) ;
+ % fprintf ('=============== i %d %g %g\n', i, n1, n2) ;
+ % beta
+ % v'
+ % X = x'
+ % pause
+ % i
+ % x
+ end
+ % k
+ % x
+
+ % make Hk
+ % fprintf ('x(k:m) = ') ; x (k:m)
+ [v,beta,xnorm] = hmake1 (x (k:m)) ;
+
+ H (k,k) = beta ;
+ H (k+1:m, k) = v (2:end) ;
+
+ R (1:(k-1),k) = x (1:(k-1)) ;
+ R (k,k) = xnorm ;
+ % full (R)
+ % pause
+end
+
+% s2 = svd (full (R)) ;
+% [s1 s2 s1-s2]
diff --git a/CSparse/MATLAB/Test/norm1est.m b/CSparse/MATLAB/Test/norm1est.m
new file mode 100644
index 0000000..d1e7704
--- /dev/null
+++ b/CSparse/MATLAB/Test/norm1est.m
@@ -0,0 +1,34 @@
+function est = norm1est (L,U,P,Q)
+%NORM1EST 1-norm estimate.
+% Example:
+% est = norm1est (L,U,P,Q)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (L,1) ;
+for k = 1:5
+ if (k == 1)
+ est = 0 ;
+ x = ones (n,1) / n ;
+ jold = -1 ;
+ else
+ j = min (find (abs (x) == norm (x,inf))) ; %#ok
+ if (j == jold)
+ break
+ end ;
+ x = zeros (n,1) ;
+ x (j) = 1 ;
+ jold = j ;
+ end
+ x = Q * (U \ (L \ (P*x))) ;
+ est_old = est ;
+ est = norm (x,1) ;
+ if (k > 1 & est <= est_old) %#ok
+ break
+ end ;
+ s = ones (n,1) ;
+ s (find (x < 0)) = -1 ; %#ok
+ x = P' * (L' \ (U' \ (Q'*s))) ;
+end
diff --git a/CSparse/MATLAB/Test/qr2.m b/CSparse/MATLAB/Test/qr2.m
new file mode 100644
index 0000000..d9b19a5
--- /dev/null
+++ b/CSparse/MATLAB/Test/qr2.m
@@ -0,0 +1,21 @@
+function [V,Beta,R] = qr2 (A)
+%QR2 QR factorization based on Householder reflections
+%
+% Example:
+% [V,beta,R] = qr2 (A)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+V = zeros (m,n) ;
+Beta = zeros (1,n) ;
+for k = 1:n
+ % [v,beta,s] = gallery ('house', A (k:m,k), 2) ;
+ [v,beta] = house (A (k:m,k)) ;
+ V (k:m,k) = v ;
+ Beta (k) = beta ;
+ A (k:m,k:n) = A (k:m,k:n) - v * (beta * (v' * A (k:m,k:n))) ;
+end
+R = triu (A) ;
diff --git a/CSparse/MATLAB/Test/qr_givens.m b/CSparse/MATLAB/Test/qr_givens.m
new file mode 100644
index 0000000..1a59736
--- /dev/null
+++ b/CSparse/MATLAB/Test/qr_givens.m
@@ -0,0 +1,24 @@
+function R = qr_givens (A)
+%QR_GIVENS Givens-rotation QR factorization.
+% Example:
+% R = qr_givens (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+parent = cs_etree (sparse (A), 'col') ;
+A = full (A) ;
+for i = 2:m
+ k = min (find (A (i,:))) ; %#ok
+ if (isempty (k))
+ continue ;
+ end
+ while (k > 0 & k <= min (i-1,n)) %#ok
+ A ([k i],k:n) = givens2 (A(k,k), A(i,k)) * A ([k i],k:n) ;
+ A (i,k) = 0 ;
+ k = parent (k) ;
+ end
+end
+R = sparse (A) ;
diff --git a/CSparse/MATLAB/Test/qr_givens_full.m b/CSparse/MATLAB/Test/qr_givens_full.m
new file mode 100644
index 0000000..5a57cb7
--- /dev/null
+++ b/CSparse/MATLAB/Test/qr_givens_full.m
@@ -0,0 +1,17 @@
+function R = qr_givens_full (A)
+%QR_GIVENS_FULL Givens-rotation QR factorization, for full matrices.
+% Example:
+% R = qr_givens_full (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+for i = 2:m
+ for k = 1:min(i-1,n)
+ A ([k i],k:n) = givens2 (A(k,k), A(i,k)) * A ([k i],k:n) ;
+ A (i,k) = 0 ;
+ end
+end
+R = A ;
diff --git a/CSparse/MATLAB/Test/qr_left.m b/CSparse/MATLAB/Test/qr_left.m
new file mode 100644
index 0000000..8b2a5d5
--- /dev/null
+++ b/CSparse/MATLAB/Test/qr_left.m
@@ -0,0 +1,26 @@
+function [V,Beta,R] = qr_left (A)
+%QR_LEFT left-looking Householder QR factorization.
+% Example:
+% [V,Beta,R] = qr_left (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+V = zeros (m,n) ;
+Beta = zeros (1,n) ;
+R = zeros (m,n) ;
+for k = 1:n
+ x = A (:,k) ;
+ for i = 1:k-1
+ v = V (i:m,i) ;
+ beta = Beta (i) ;
+ x (i:m) = x (i:m) - v * (beta * (v' * x (i:m))) ;
+ end
+ [v,beta,s] = gallery ('house', x (k:m), 2) ;
+ V (k:m,k) = v ;
+ Beta (k) = beta ;
+ R (1:(k-1),k) = x (1:(k-1)) ;
+ R (k,k) = s ;
+end
diff --git a/CSparse/MATLAB/Test/qr_right.m b/CSparse/MATLAB/Test/qr_right.m
new file mode 100644
index 0000000..24de54c
--- /dev/null
+++ b/CSparse/MATLAB/Test/qr_right.m
@@ -0,0 +1,19 @@
+function [V,Beta,R] = qr_right (A)
+%QR_RIGHT right-looking Householder QR factorization.
+% Example:
+% [V,Beta,R] = qr_right (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+V = zeros (m,n) ;
+Beta = zeros (1,n) ;
+for k = 1:n
+ [v,beta] = gallery ('house', A (k:m,k), 2) ;
+ V (k:m,k) = v ;
+ Beta (k) = beta ;
+ A (k:m,k:n) = A (k:m,k:n) - v * (beta * (v' * A (k:m,k:n))) ;
+end
+R = A ;
diff --git a/CSparse/MATLAB/Test/sample_colormap.m b/CSparse/MATLAB/Test/sample_colormap.m
new file mode 100644
index 0000000..50ef089
--- /dev/null
+++ b/CSparse/MATLAB/Test/sample_colormap.m
@@ -0,0 +1,41 @@
+function sample_colormap
+%SAMPLE_COLORMAP try a colormap for use in cspy
+%
+% Example:
+% sample_colormap
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+h = jet (64) ;
+h = h (64:-1:1,:) ;
+h = h (20:end,:) ;
+
+% h = h (17:128,:) ;
+
+% s = sum (jet,2) ;
+% h (:,1) = h (:,1) ./ s ;
+% h (:,2) = h (:,2) ./ s ;
+% h (:,3) = h (:,3) ./ s ;
+
+h (1,:) = [1 1 1] ; % white
+h (2,:) = [1 1 .8] ; % light yellow
+
+% h
+colormap (h) ;
+
+clf
+subplot (5,1,1) ;
+image (1:size(h,1)) ;
+
+h = rgb2hsv (h) ;
+% h (:,3) = linspace (1,0,64) ;
+% h= hsv2rgb (h) ;
+
+subplot (5,1,2) ; plot (h(:,1)) ; axis ([1 64 0 1]) ; ylabel ('red') ;
+subplot (5,1,3) ; plot (h(:,2)) ; axis ([1 64 0 1]) ; ylabel ('green') ;
+subplot (5,1,4) ; plot (h(:,3)) ; axis ([1 64 0 1]) ; ylabel ('blue') ;
+subplot (5,1,5) ; plot (sum(h,2)) ; axis ([1 64 0 3]) ; ylabel ('sum') ;
+
diff --git a/CSparse/MATLAB/Test/signum.m b/CSparse/MATLAB/Test/signum.m
new file mode 100644
index 0000000..ec806bc
--- /dev/null
+++ b/CSparse/MATLAB/Test/signum.m
@@ -0,0 +1,13 @@
+function s = signum (x)
+%SIGNUM compute and display the sign of a column vector x
+% Example
+% s = signum(x)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+s = ones (length (x),1) ;
+s (find (x < 0)) = -1 ; %#ok
+disp ('s =') ;
+disp (s) ;
diff --git a/CSparse/MATLAB/Test/sqr_example.m b/CSparse/MATLAB/Test/sqr_example.m
new file mode 100644
index 0000000..9c07379
--- /dev/null
+++ b/CSparse/MATLAB/Test/sqr_example.m
@@ -0,0 +1,29 @@
+function sqr_example
+%SQR_EXAMPLE test cs_sqr
+% Example:
+% sqr_example
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+Prob = UFget (706) ;
+
+A = Prob.A' ;
+q = colamd (A) ;
+A = A (:,q) ;
+A = sprandn (A) ;
+[m n] = size (A) ;
+
+[vnz, rnz, parent, c, leftmost, p] = cs_sqr(A) ;
+
+m2 = length (p) ;
+B = [A ; sparse(m2-m,n)] ;
+B = B (p,q) ;
+
+R1 = gqr3 (B) ;
+
+clf
+subplot (2,2,1) ; spy(A)
+subplot (2,2,3) ; spy (chol (A'*A + 100*speye(n))) ;
+subplot (2,2,4) ; spy (R1) ;
diff --git a/CSparse/MATLAB/Test/test1.m b/CSparse/MATLAB/Test/test1.m
new file mode 100644
index 0000000..bbe7346
--- /dev/null
+++ b/CSparse/MATLAB/Test/test1.m
@@ -0,0 +1,64 @@
+function test1
+%TEST1 test cs_transpose
+%
+% Example:
+% test1
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+for ii = f
+ Prob = UFget (ii) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ if (~isreal (A))
+ continue
+ end
+ B = A' ;
+
+ C = cs_transpose (A) ;
+ if (nnz (B-C) ~= 0)
+ error ('!')
+ end
+
+ [m n] = size (A) ;
+ % if (m == n)
+ x = rand (n,1) ;
+ y = rand (m,1) ;
+ z = y+A*x ;
+ q = cs_gaxpy (A,x,y) ;
+ err = norm (z-q,1) / norm (z,1) ;
+ disp (err) ;
+ if (err > 1e-14)
+ error ('!')
+ end
+ % end
+
+
+ [i j x] = find (A) ;
+ p = randperm (length (i)) ;
+ i = i (p) ;
+ j = j (p) ;
+ x = x (p) ;
+ D = sparse (i,j,x) ;
+ E = cs_sparse (i,j,x) ;
+ % [i j x]
+ F = cs_sparse2 (i,j,x) ;
+ if (nnz (D-E) ~= 0)
+ error ('!')
+ end
+ if (nnz (F-E) ~= 0)
+ error ('!')
+ end
+
+ clear A B C D E F
+ % pause
+
+end
+
diff --git a/CSparse/MATLAB/Test/test10.m b/CSparse/MATLAB/Test/test10.m
new file mode 100644
index 0000000..3a07778
--- /dev/null
+++ b/CSparse/MATLAB/Test/test10.m
@@ -0,0 +1,96 @@
+function test10
+%TEST10 test cs_qr
+%
+% Example:
+% test10
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+
+% f = 185 ;
+% f = 449 ;
+clf
+
+for trials = 1:100
+
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = 0.1 * rand (1) ;
+ A = sprandn (m, n, d) ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ sp = sprank (A) ;
+ % if (sp < n)
+ % continue ;
+ % end
+
+ Aorig = A ;
+
+ % A = A (:, colamd (A)) ;
+
+ tic ;
+ R = qr (A) ;
+ t1 = toc ;
+
+ % tic ;
+ % [Q,R] = qr (A) ;
+ % t1 = toc ;
+
+ [c,h,parent] = symbfact (A, 'col') ; %#ok
+ rnz = sum (c) ; %#ok
+ tic ;
+ [V2,Beta2,p,R2] = cs_qr (sparse(A)) ;
+ t2 = toc ;
+
+ C = A ;
+ m2 = size (V2,1) ;
+ if (m2 > m)
+ C = [A ; sparse(m2-m, n)] ;
+ end
+ C = C (p,:) ;
+
+ [H1,R1] = myqr (C) ;
+ err1 = norm (R1-R2,1) / norm (R1) ;
+ disp ('err1 = ') ;
+ disp (err1) ;
+ % [svd(A) svd(R1) svd(full(R2))]
+ s1 = svd (full (A)) ;
+ s2 = svd (full (R2)) ;
+ if (n > 0)
+ err2 = norm (s1 - s2) / s1 (1) ;
+ disp ('err2 = ') ;
+ disp (err2) ;
+ else
+ err2 = 0 ;
+ end
+ fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d vs %d\n', t1, t2, t1/t2, sp, n) ;
+
+ % H2 = full (H2)
+ % R2 = full (R2)
+
+ subplot (2,4,1) ; spy (A) ; title ('A colamd') ;
+ subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ;
+ subplot (2,4,2) ; spy (C) ; title ('A rperm') ;
+ subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ;
+ subplot (2,4,6) ; spy (R) ; title ('matlab R') ;
+ subplot (2,4,7) ; spy (R2) ; title ('spqr R') ;
+ subplot (2,4,8) ; spy (V2) ; title ('spqr H') ;
+ drawnow
+
+ if (err2 > 1e-9)
+ error ('!') ;
+ end
+
+ if (m2 > m)
+ fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ;
+ end
+end
+
diff --git a/CSparse/MATLAB/Test/test11.m b/CSparse/MATLAB/Test/test11.m
new file mode 100644
index 0000000..6c5c419
--- /dev/null
+++ b/CSparse/MATLAB/Test/test11.m
@@ -0,0 +1,50 @@
+function test11
+%TEST11 test cs_rowcnt
+%
+% Example:
+% test11
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clear functions
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+
+for i = f
+ Prob = UFget (i, index) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (~isreal (A) | m ~= n) %#ok
+ continue
+ end
+
+ A = spones (A) ;
+ A = A+A' + speye(n) ;
+
+ [cc h pa po R] = symbfact (A) ;
+ rc1 = full (sum (R)) ;
+ rc2 = cs_rowcnt (A, pa, po) ;
+ if (any (rc1 ~= rc2))
+ error ('!') ;
+ end
+
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ A = A (p,p) ;
+
+ [cc h pa po R] = symbfact (A) ;
+ rc1 = full (sum (R)) ;
+ rc2 = cs_rowcnt (A, pa, po) ;
+ if (any (rc1 ~= rc2))
+ error ('!') ;
+ end
+
+end
+
diff --git a/CSparse/MATLAB/Test/test12.m b/CSparse/MATLAB/Test/test12.m
new file mode 100644
index 0000000..ef7e388
--- /dev/null
+++ b/CSparse/MATLAB/Test/test12.m
@@ -0,0 +1,44 @@
+function test12
+%TEST12 test cs_qr and compare with svd
+%
+% Example:
+% test12
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('test 12\n') ;
+rand ('state',0) ;
+% A = rand (3,4)
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = .1 * rand (1) ;
+ A = sprandn (m,n,d) ;
+ fprintf ('m %d n %d nnz %d\n', m, n, nnz(A)) ;
+ if (m < n)
+ continue ;
+ end
+ if (m == 0 | n == 0) %#ok
+ continue ;
+ end
+ % save A A
+ fprintf ('[ ') ;
+ [V,Beta,p,R] = cs_qr (A) ;
+ % [Q,R] = svd (full(A)) ;
+ fprintf (']\n') ;
+
+ s1 = svd (full (A)) ;
+ s2 = svd (full (R)) ;
+ s2 = s2 (1:length(s1)) ;
+ err = norm (s1-s2) ;
+ if (length (s1) > 1)
+ err = err / s1 (1) ;
+ end
+ fprintf ('err %g\n', err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+end
diff --git a/CSparse/MATLAB/Test/test13.m b/CSparse/MATLAB/Test/test13.m
new file mode 100644
index 0000000..f6d0196
--- /dev/null
+++ b/CSparse/MATLAB/Test/test13.m
@@ -0,0 +1,82 @@
+function test13
+%TEST13 test cs_counts, cs_etree
+%
+% Example:
+% test13
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+randn ('state',0) ;
+rand ('state',0) ;
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = .1 * rand (1) ;
+ A = sprandn (n,n,d) ;
+ C = sprandn (m,n,d) ;
+ A = A+A' ;
+ fprintf ('m %4d n %4d nnz(A) %6d nnz(C) %6d\n', m, n, nnz(A), nnz(C)) ;
+
+ [p1,po1] = etree (A) ;
+
+ [p2,po2] = cs_etree (A) ;
+ [p3,po3] = cs_etree (A, 'sym') ;
+ % po2 = cs_post (p2) ;
+
+ check_if_same (p1,p2) ;
+ check_if_same (po1,po2) ;
+
+ check_if_same (p1,p3) ;
+ check_if_same (po1,po3) ;
+
+ c1 = symbfact (A) ;
+ c2 = cs_counts (A) ;
+
+ % A-A'
+
+ check_if_same (c1,c2) ;
+
+ c2 = cs_counts (triu (A)) ;
+ check_if_same (c1,c2) ;
+ % pause
+
+ p0 = etree (A, 'col') ;
+ % p1 = etree2 (A, 'col') ; % CHOLMOD
+ p2 = cs_etree (A, 'col') ;
+
+ if (~isempty (A))
+ check_if_same (p0,p2) ;
+ end
+
+ p0 = etree (C, 'col') ;
+ % p1 = etree2 (C, 'col') ; % CHOLMOD
+ p2 = cs_etree (C, 'col') ;
+
+ if (~isempty (C))
+ check_if_same (p0,p2) ;
+ end
+
+ % find etree of A'A, and postorder it
+ [m n] = size (A) ; %#ok
+ % full (A)
+
+ [cp0 cpo0] = etree (A, 'col') ;
+ % [cp1 cpo1] = etree2 (A, 'col') ; % CHOLMOD
+ [cp2 cpo2] = cs_etree (A, 'col') ;
+ % cpo2 = cs_post (cp2) ;
+
+ check_if_same (cp0, cp2) ;
+ check_if_same (cpo0, cpo2) ;
+
+ c0 = symbfact (A, 'col') ;
+ % c1 = symbfact2 (A, 'col') ; % CHOLMOD
+ c2 = cs_counts (A, 'col') ;
+
+ check_if_same (c0, c2) ;
+
+end
diff --git a/CSparse/MATLAB/Test/test14.m b/CSparse/MATLAB/Test/test14.m
new file mode 100644
index 0000000..35d49e8
--- /dev/null
+++ b/CSparse/MATLAB/Test/test14.m
@@ -0,0 +1,38 @@
+function test14
+%TEST14 test cs_droptol
+%
+% Example:
+% test14
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = 0.1*rand (1) ;
+ A = sprandn (m,n,d) ;
+ [i j x] = find (A) ;
+ A = sparse (i,j,2*x-1) ;
+ fprintf ('test14 m %3d n %3d nz %d\n', m, n, nnz (A)) ;
+
+ % using CSparse
+ tol = 0.5 ;
+ B = cs_droptol (A, tol) ;
+
+ % using MATLAB
+ A = A .* (abs (A) > tol) ;
+% [m n] = size (A) ;
+% s = abs (A) > tol ;
+% [i j] = find (s) ;
+% x = A (find (s)) ;
+% A = sparse (i, j, x, m, n) ;
+
+ if (norm (A-B,1) > 0)
+ error ('!') ;
+ end
+end
diff --git a/CSparse/MATLAB/Test/test15.m b/CSparse/MATLAB/Test/test15.m
new file mode 100644
index 0000000..2214dd8
--- /dev/null
+++ b/CSparse/MATLAB/Test/test15.m
@@ -0,0 +1,48 @@
+function test15
+%TEST15 test cs_amd
+%
+% Example:
+% test15
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+clf
+
+for trials = 1:100
+ n = fix (200 * rand (1)) ;
+ d = 0.05 * rand (1) ;
+ A = sprandn (n, n, d) ;
+
+ % add a randomly placed dense column
+ k = fix (n * rand (1)) ;
+ k = max (1, k) ;
+ k = min (n, k) ;
+ A (:,k) = 1 ;
+
+ try
+ p0 = amd (A) ;
+ catch
+ p0 = symamd (A) ;
+ end
+ p1 = cs_amd (A) ;
+
+ if (any (sort (p1) ~= 1:n))
+ error ('not perm!') ;
+ end
+
+ C = A+A' + speye (n) ;
+ lnz0 = sum (symbfact (C (p0,p0))) ;
+ lnz1 = sum (symbfact (C (p1,p1))) ;
+ subplot (1,3,1) ; spy (C)
+ subplot (1,3,2) ; spy (C (p0,p0))
+ subplot (1,3,3) ; spy (C (p1,p1))
+ fprintf ('n %4d nz %6d lnz %6d %6d\n', n, nnz(A), lnz0, lnz1) ;
+ drawnow
+
+end
+
diff --git a/CSparse/MATLAB/Test/test16.m b/CSparse/MATLAB/Test/test16.m
new file mode 100644
index 0000000..a57eee0
--- /dev/null
+++ b/CSparse/MATLAB/Test/test16.m
@@ -0,0 +1,90 @@
+function test16
+%TEST16 test cs_amd
+%
+% Example:
+% test16
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+clf
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+skip = 811 ;
+
+% f = 719
+
+for i = f
+ if (any (i == skip))
+ continue
+ end
+ Prob = UFget (i) ;
+ A = spones (Prob.A) ;
+ Aorig = A ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ if (m ~= n)
+ A = A'*A ;
+ end
+
+ fprintf ('n %4d nz %d\n', n, nnz (A)) ;
+
+ try
+ p0 = amd (A) ;
+ catch
+ p0 = symamd (A) ;
+ end
+ fprintf ('symmetric case:\n') ;
+ p1 = cs_amd (A) ;
+
+ if (any (sort (p1) ~= 1:n))
+ error ('not perm!') ;
+ end
+
+ C = A+A' + speye (n) ;
+ lnz0 = sum (symbfact (C (p0,p0))) ;
+ lnz1 = sum (symbfact (C (p1,p1))) ;
+ subplot (2,3,1) ; spy (C)
+ subplot (2,3,2) ; spy (C (p0,p0)) ; title ('amd') ;
+ subplot (2,3,3) ; spy (C (p1,p1)) ; title ('csamd') ;
+ drawnow
+
+ if (lnz0 ~= lnz1)
+ fprintf ('----------------- lnz %d %d %9.4f\n', ...
+ lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ;
+ end
+
+ if (1)
+
+ p0 = colamd (Aorig) ;
+ [m n] = size (Aorig) ;
+ fprintf ('m %d n %d\n', m, n) ;
+
+ fprintf ('A''A case, no dense rows (for QR):\n') ;
+ p1 = cs_amd (Aorig, 3) ;
+ if (any (sort (p1) ~= 1:n))
+ error ('not perm!') ;
+ end
+
+ subplot (2,3,4) ; spy (Aorig)
+ subplot (2,3,5) ; spy (Aorig (:,p0)) ; title ('colamd') ;
+ subplot (2,3,6) ; spy (Aorig (:,p1)) ; title ('cs amd(A''A)') ;
+ lnz0 = sum (symbfact (Aorig (:,p0), 'col')) ;
+ lnz1 = sum (symbfact (Aorig (:,p1), 'col')) ;
+ fprintf (' A''A: %7d %7d %9.4f\n', ...
+ lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ;
+ drawnow
+
+ % pause
+
+ end
+end
+
diff --git a/CSparse/MATLAB/Test/test17.m b/CSparse/MATLAB/Test/test17.m
new file mode 100644
index 0000000..ef2ff6c
--- /dev/null
+++ b/CSparse/MATLAB/Test/test17.m
@@ -0,0 +1,108 @@
+function test17
+%TEST17 test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol
+%
+% Example:
+% test17
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+clf
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+for trials = 1:100
+
+ m = 1 + fix (10 * rand (1)) ;
+ n = 1 + fix (10 * rand (1)) ;
+ d = rand (1) ;
+% n = m ;
+
+ A = sprandn (m, n, d) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+
+ subplot (3,4,1) ; spy (A) ;
+
+ [V1, Beta1, p1, R1, q1] = cs_qr (A) ;
+ Q1 = cs_qright (V1, Beta1, p1, speye (size (V1,1))) ;
+ Q1b = cs_q1 (V1, Beta1, p1) ;
+
+ err = norm (Q1-Q1b,1) ;
+ disp ('err = ') ;
+ disp (err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+ m2 = size (Q1,1) ;
+ A1 = [A ; sparse(m2-m,n)] ;
+
+ subplot (3,4,5) ; spy (A1 (p1,q1)) ;
+ subplot (3,4,6) ; spy (V1) ;
+ subplot (3,4,7) ; spy (R1) ;
+ subplot (3,4,8) ; spy (Q1) ;
+
+ [V3, Beta3, R3] = qr2 (A) ;
+ % Q3 = cs_qmake (V3, Beta3) ;
+ Q3 = cs_q1 (V3, Beta3) ;
+ subplot (3,4,9) ; spy (A) ;
+ subplot (3,4,10) ; spy (V3) ;
+ subplot (3,4,11) ; spy (R3) ;
+ subplot (3,4,12) ; spy (Q3) ;
+
+ err1 = norm (Q1*R1 - A1(:,q1), 1) ;
+% err2 = norm (Q2*R2 - A (:,q2), 1) ;
+ err3 = norm (Q3*R3 - A, 1) ;
+
+ fprintf ('m %3d m2 %3d n %3d ::: %3d %6.2e %6.2e\n', ...
+ m, m2, n, m2-m, err1, err3) ;
+
+ if (err1 > 1e-12)
+ error ('!') ;
+ end
+
+% if (err2 > 1e-12)
+% error ('!') ;
+% end
+
+ if (err3 > 1e-12)
+ error ('!') ;
+ end
+
+try
+
+ b = rand (m,1) ;
+ [Q,R] = qr (A (:,q1)) ;
+ x = R\(Q'*b) ;
+ x (q1) = x ;
+ r1 = norm (A*x-b) ;
+
+ x2 = cs_qrsol (A,b) ;
+ r2 = norm (A*x2(1:n)-b) ;
+
+ qt = cs_qleft (V1, Beta1, p1, speye(size(V1,1))) ;
+ fprintf ('Q''*A-R: %6.2e\n', norm (qt*A1(:,q1)-R1,1)) ;
+
+ qtb = cs_qleft (V1, Beta1, p1, b) ;
+ % [V1, Beta1, p1, R1, q1] = cs_qr (A) ;
+ x3 = R1 \ qtb ;
+ r3 = norm (A(:,q1)*x3(1:n)-b) ;
+
+ fprintf ('least sq: %6.2e %6.2e %6.2e diff %6.2e %6.2e\n', ...
+ r1, r2, r3, r1-r2, r1-r3) ;
+
+catch
+end
+
+ drawnow
+
+ % pause
+
+end
diff --git a/CSparse/MATLAB/Test/test18.m b/CSparse/MATLAB/Test/test18.m
new file mode 100644
index 0000000..b2d9339
--- /dev/null
+++ b/CSparse/MATLAB/Test/test18.m
@@ -0,0 +1,34 @@
+function test18
+%TEST18 test iterative refinement after backslash
+%
+% Example:
+% test18
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+clf
+% f = f(1)
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (~isreal (A) | m ~= n) %#ok
+ continue
+ end
+
+ b = rand (n,1) ;
+ x = A\b ;
+ r = b - A*x ;
+ x = x + A\r ;
+
+ fprintf ('\n%6.2e to %6.2e\n', norm (r), norm (b-A*x)) ;
+end
diff --git a/CSparse/MATLAB/Test/test19.m b/CSparse/MATLAB/Test/test19.m
new file mode 100644
index 0000000..6644a7b
--- /dev/null
+++ b/CSparse/MATLAB/Test/test19.m
@@ -0,0 +1,200 @@
+function test19
+%TEST19 test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc
+%
+% Example:
+% test19
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+clf
+
+for trials = 1:1000
+
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ % d = 0.1 * rand (1) ;
+ d = rand (1) * 4 * max (m,n) / max (m*n,1) ;
+ A = sprandn (m,n,d) ;
+ S = sprandn (m,m,d) + speye (m) ;
+
+ subplot (2,3,1) ;
+ cspy (A) ;
+
+ pp = dmperm (A) ;
+
+ sprnk = sum (pp > 0) ;
+
+ pp2 = cs_dmperm (A) ;
+ spr2 = sum (pp2 > 0) ;
+ if (spr2 ~= sprnk)
+ error ('!')
+ end
+
+ pp2 = cs_maxtransr (A) ;
+ spr2 = sum (pp2 > 0) ;
+ if (spr2 ~= sprnk)
+ error ('!')
+ end
+
+ [p,q,r,s] = dmperm (A) ;
+ C = A (p,q) ;
+ % r
+ % s
+
+ nk = length (r) - 1 ;
+
+ fprintf ('sprnk: %d m %d n %d nb: %d\n', sprnk, m, n, nk) ;
+
+ subplot (2,3,2) ;
+ hold off
+ spy (C)
+ hold on
+
+ for k = 1:nk
+ r1 = r(k) ;
+ r2 = r(k+1) ;
+ c1 = s(k) ;
+ c2 = s(k+1) ;
+ plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+ end
+
+ [p2,q2,rr2,ss2,cp,rp] = cs_dmperm (A) ;
+
+ if (min (m,n) > 0)
+ if (length (rr2) ~= length (r))
+ error ('# fine blocks!') ;
+ end
+ end
+
+ if (rp (4) - 1 ~= sprnk)
+ rp %#ok
+ sprnk %#ok
+ error ('!') ;
+ end
+
+ if (any (sort (p2) ~= 1:m))
+ error ('p2!') ;
+ end
+
+ if (any (sort (q2) ~= 1:n))
+ error ('q2!') ;
+ end
+
+ if (cp (5) ~= n+1)
+ error ('cp!') ;
+ end
+
+ if (rp (5) ~= m+1)
+ error ('rp!') ;
+ end
+
+ C = A (p2,q2) ;
+
+ subplot (2,3,3) ; cs_dmspy (A,0) ;
+
+ % hold off
+ % spy (C) ;
+ % hold on
+
+ % r1 = rp(1) ;
+ % r2 = rp(2) ;
+ % c1 = cp(1) ;
+ % c2 = cp(2) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ r1 = rp(1) ;
+ r2 = rp(2) ;
+ c1 = cp(2) ;
+ c2 = cp(3) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ B = C (r1:r2-1, c1:c2-1) ;
+ if (nnz (diag (B)) ~= size (B,1))
+ error ('C1 diag!') ;
+ end
+
+ r1 = rp(2) ;
+ r2 = rp(3) ;
+ c1 = cp(3) ;
+ c2 = cp(4) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'r') ;
+
+ B = C (r1:r2-1, c1:c2-1) ;
+ if (nnz (diag (B)) ~= size (B,1))
+ error ('C2 diag!') ;
+ end
+
+ r1 = rp(3) ;
+ r2 = rp(4) ;
+ c1 = cp(4) ;
+ c2 = cp(5) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ B = C (r1:r2-1, c1:c2-1) ;
+ if (nnz (diag (B)) ~= size (B,1))
+ error ('C3 diag!') ;
+ end
+
+ r1 = rp(4) ; %#ok
+ r2 = rp(5) ; %#ok
+ c1 = cp(4) ; %#ok
+ c2 = cp(5) ; %#ok
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ if (~isempty (S))
+
+ [p1,q1,r0,s0] = dmperm (S) ;
+ [p3,r3] = cs_scc (S) ;
+ if (length (r3) ~= length (r0))
+ error ('scc size!') ;
+ end
+
+ if (any (sort (p3) ~= 1:m))
+ error ('scc perm!') ;
+ end
+
+ nk = length (r0)-1 ;
+
+ subplot (2,3,4) ;
+ hold off
+ spy (S (p1,q1)) ;
+ hold on
+ for k = 1:nk
+ r1 = r0(k) ;
+ r2 = r0(k+1) ;
+ c1 = s0(k) ;
+ c2 = s0(k+1) ;
+ plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+ end
+
+ subplot (2,3,5) ;
+ hold off
+ spy (S (p3,p3)) ;
+ hold on
+ for k = 1:nk
+ r1 = r3(k) ;
+ r2 = r3(k+1) ;
+ c1 = r3(k) ;
+ c2 = r3(k+1) ;
+ plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+ end
+
+ end
+
+ subplot (2,3,6) ;
+ cs_dmspy (A) ;
+ drawnow
+ % pause
+
+
+
+
+end
diff --git a/CSparse/MATLAB/Test/test2.m b/CSparse/MATLAB/Test/test2.m
new file mode 100644
index 0000000..264bd2c
--- /dev/null
+++ b/CSparse/MATLAB/Test/test2.m
@@ -0,0 +1,102 @@
+function test2
+%TEST2 test cs_sparse
+%
+% Example:
+% test2
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0)
+% clf
+
+for trial = 1:100
+ m = fix (10 * rand (1)) ;
+ n = fix (10 * rand (1)) ;
+ nz = fix (100 * rand (1)) ;
+
+ i = 1 + fix (m * rand (nz,1)) ;
+ j = 1 + fix (n * rand (nz,1)) ;
+ x = rand (nz,1) ;
+
+ A = sparse (i,j,x) ;
+ B = cs_sparse (i,j,x) ;
+ D = cs_sparse2 (i,j,x) ;
+ fprintf ('%3d %3d %6d : %6d %6d : %d\n', ...
+ m, n, nz, nnz (A), nnz(B), nz-nnz(A)) ;
+
+ err = norm (A-B,1) / norm (A,1) ;
+ if (err > 0)
+ disp ('err = ') ;
+ disp (err) ;
+ end
+ if (err > 1e-14)
+ error ('!') ;
+ end
+
+ if (nnz (B-D) > 0)
+ error ('!') ;
+ end
+
+ if (nnz (A) ~= nnz (B))
+ error ('nz!') ;
+ end
+
+ if (max (1,nnz (B)) ~= max (1,nzmax (B)))
+ nnz (B)
+ nzmax (B)
+ error ('nzmax!') ;
+ end
+ % pack
+
+
+ [m n] = size (A) ;
+ p = randperm (m) ;
+ q = randperm (n) ;
+ C1 = A (p,q) ;
+ C2 = cs_permute (A,p,q) ;
+ err = norm (C1-C2,1) ;
+ if (err > 0)
+ error ('!') ;
+ end
+
+% subplot (1,2,1) ; spy (A)
+% subplot (1,2,2) ; spy (C2)
+% drawnow
+
+ x = rand (m,1) ;
+ x1 = x (p) ;
+ x2 = cs_pvec (x, p) ;
+
+ err = norm (x1-x2,1) ;
+ if (err > 0)
+ error ('!') ;
+ end
+
+ x1 = zeros (m,1) ;
+ x1 (p) = x ; %#ok
+ x2 = cs_ipvec (x, p) ; %#ok
+
+ n = min (m,n) ;
+ B = A (1:n, 1:n) ;
+ p = randperm (n) ;
+ B = B+B' ;
+
+ C1 = triu (B (p,p)) ;
+ C2 = cs_symperm (B,p) ;
+
+ try
+ pp = amd (C2) ; %#ok
+ catch
+ pp = symamd (C2) ; %#ok
+ end
+
+ err = norm (C1-C2,1) ;
+ if (err > 0)
+ error ('!') ;
+ end
+
+
+
+end
diff --git a/CSparse/MATLAB/Test/test20.m b/CSparse/MATLAB/Test/test20.m
new file mode 100644
index 0000000..2fd8f58
--- /dev/null
+++ b/CSparse/MATLAB/Test/test20.m
@@ -0,0 +1,47 @@
+function test20
+%TEST20 test cholupdown
+%
+% Example:
+% test20
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+rand ('state', 0) ;
+
+for trials = 1:10
+
+ n = fix (100 * rand (1)) ;
+ A = rand (n) ;
+ A1 = A*A' + n*eye (n) ;
+
+ try
+ L1 = chol (A1)' ;
+ catch
+ continue ;
+ end
+ err1 = norm (L1*L1'-A1) ;
+
+ w = rand (n,1) ;
+
+ A2 = A1 + w*w' ;
+
+ L2 = chol (A2)' ;
+ err2 = norm (L2*L2'-A2) ;
+
+ % try an update
+ L2b = cholupdown (L1, +1, w) ;
+ err2b = norm (L2b*L2b'-A2) ;
+
+ % try a downdate
+ L1b = cholupdown (L2, -1, w) ; %#ok
+ err1b = norm (L2b*L2b'-A2) ;
+
+
+ fprintf ('%3d: %6.2e %6.2e : %6.2e %6.2e\n', n, err1, err2, err2b, err1b) ;
+ % pause
+end
diff --git a/CSparse/MATLAB/Test/test21.m b/CSparse/MATLAB/Test/test21.m
new file mode 100644
index 0000000..a6158fb
--- /dev/null
+++ b/CSparse/MATLAB/Test/test21.m
@@ -0,0 +1,118 @@
+function test21
+%TEST21 test cs_updown
+%
+% Example:
+% test21
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+clf
+
+for trials = 1:10
+ if (trials <= 1)
+ n = trials ;
+ else
+ n = 1+fix (100 * rand (1)) ;
+ end
+ fprintf ('n: %d\n', n) ;
+ d = 0.1 * rand (1) ;
+ A = sprandn (n,n,d) ;
+ A = A+A' + 100 * speye (n) ;
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ A = sparse (A (p,p)) ;
+
+ try
+ L = chol (A)' ;
+ catch
+ continue ;
+ end
+
+ parent = etree (A) ;
+
+ subplot (1,3,1) ;
+ spy (A) ;
+
+ if (n > 0)
+ subplot (1,3,2) ;
+ treeplot (parent) ;
+ end
+
+ subplot (1,3,3) ;
+ spy (L) ;
+
+ drawnow
+
+ for trials2 = 1:10
+
+ k = 1+fix (n * rand (1)) ;
+ if (k <= 0 | k > n) %#ok
+ k = 1 ;
+ end
+
+ w = sprandn (L (:,k)) ;
+ Anew = A + w*w' ;
+
+ % Lnew = cs_update (L, w, parent) ;
+ % err1 = norm (Lnew*Lnew' - Anew, 1) ;
+
+ Lnew = cs_updown (L, w, parent) ;
+ err6 = norm (Lnew*Lnew' - Anew, 1) ;
+
+ Lnew = cs_updown (L, w, parent, '+') ;
+ err7 = norm (Lnew*Lnew' - Anew, 1) ;
+
+ [Lnew, wnew] = chol_update (L, w) ;
+ err2 = norm (Lnew*Lnew' - Anew, 1) ;
+ err10 = norm (wnew - (L\w)) ;
+
+ L3 = chol_updown (L, +1, w) ;
+ err9 = norm (L3*L3' - Anew, 1) ;
+
+
+
+ [L2, wnew] = chol_downdate (Lnew, w) ;
+ err3 = norm (L2*L2' - A, 1) ;
+ err11 = norm (wnew - (Lnew\w)) ;
+
+ % L2 = cs_downdate (Lnew, w, parent) ;
+ % err4 = norm (L2*L2' - A, 1) ;
+
+ L2 = cs_updown (Lnew, w, parent, '-') ;
+ err5 = norm (L2*L2' - A, 1) ;
+
+ L2 = chol_updown (Lnew, -1, w) ;
+ err8 = norm (L2*L2' - A, 1) ;
+
+ err = max ([err2 err3 err5 err6 err7 err9 err8 err10 err11]) ;
+
+ fprintf (' k %3d %6.2e\n', k, err) ;
+
+ if (err > 1e-11)
+ err2 %#ok
+ err3 %#ok
+ err5 %#ok
+ err6 %#ok
+ err7 %#ok
+ err8 %#ok
+ err9 %#ok
+ err10 %#ok
+ err11 %#ok
+ pause
+ end
+
+
+ end
+ % pause
+
+end
diff --git a/CSparse/MATLAB/Test/test22.m b/CSparse/MATLAB/Test/test22.m
new file mode 100644
index 0000000..334dddf
--- /dev/null
+++ b/CSparse/MATLAB/Test/test22.m
@@ -0,0 +1,71 @@
+function test22
+%TEST22 test cond1est
+%
+% Example:
+% test22
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+
+clf
+% f = f(1)
+
+nprob = length (f) ;
+C1 = zeros (nprob,1) ;
+C2 = zeros (nprob,1) ;
+C3 = zeros (nprob,1) ;
+
+
+for k = 1:length (f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (~isreal (A) | m ~= n) %#ok
+ continue
+ end
+
+ c1 = condest (A) ;
+ c2 = cond1est (A) ;
+ if (c1 == c2)
+ err = 0 ;
+ else
+ err = (c1-c2)/max(1,c1) ;
+ end
+
+ c3 = cond (full (A), 1) ;
+
+ fprintf ('%10.4e %10.4e (%10.4e) : %10.4e\n', c1, c2, c3, err) ;
+
+ if (err ~= 0)
+ % pause
+ end
+
+ C1 (k) = c1 ;
+ C2 (k) = c2 ;
+ C3 (k) = c3 ;
+
+ subplot (1,2,1) ;
+ loglog (C1, C2, 'x', [1 1e20], [1 1e20], 'r') ;
+ subplot (1,2,2) ;
+ loglog (C3, C2, 'x', [1 1e20], [1 1e20], 'r') ;
+ drawnow
+
+ % pause
+
+% if (c3 < c2)
+% c3
+% c2
+% c2-c3
+% pause
+% end
+
+end
diff --git a/CSparse/MATLAB/Test/test23.m b/CSparse/MATLAB/Test/test23.m
new file mode 100644
index 0000000..e27f90c
--- /dev/null
+++ b/CSparse/MATLAB/Test/test23.m
@@ -0,0 +1,32 @@
+function test23
+%TEST23 test cs_dmspy
+%
+% Example:
+% test23
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clear functions
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+clf
+
+for trials = 1:1000
+
+ % m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ m = n ;
+ % d = 0.1 * rand (1) ;
+ d = rand (1) * 4 * max (m,n) / max (m*n,1) ;
+ A = sprandn (m,n,d) ;
+ % S = sprandn (m,m,d) + speye (m) ;
+
+ cs_dmspy (A) ;
+ drawnow
+
+ % pause
+end
diff --git a/CSparse/MATLAB/Test/test24.m b/CSparse/MATLAB/Test/test24.m
new file mode 100644
index 0000000..638816f
--- /dev/null
+++ b/CSparse/MATLAB/Test/test24.m
@@ -0,0 +1,55 @@
+function test24
+%TEST24 test cs_fielder
+%
+% Example:
+% test24
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+
+clf
+% f = f(1)
+
+for k = 1:length (f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = real (Prob.A) ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ tic
+ p1 = symrcm (A) ;
+ t1 = toc ;
+
+ tic
+ p2 = cs_fiedler (A) ;
+ t2 = toc ;
+
+ rel = t2 / max (t1,1e-6) ;
+
+ fprintf ('time: symrcm %8.3f fiedler %8.3f rel %8.2f\n', t1, t2, rel) ;
+
+ A = A|A' ;
+
+ subplot (1,3,1) ; spy (A) ;
+ subplot (1,3,2) ; spy (A (p1,p1)) ;
+ subplot (1,3,3) ; spy (A (p2,p2)) ;
+
+ % evaluate the profile ...
+
+
+ drawnow
+ % pause
+end
diff --git a/CSparse/MATLAB/Test/test25.m b/CSparse/MATLAB/Test/test25.m
new file mode 100644
index 0000000..ce1e919
--- /dev/null
+++ b/CSparse/MATLAB/Test/test25.m
@@ -0,0 +1,66 @@
+function test25
+%TEST25 test cs_nd
+%
+% Example:
+% test25
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+clf
+% f = f(1)
+
+for k = 1:length (f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = real (Prob.A) ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ A = A|A' ;
+
+ tic ;
+ p1 = symrcm (A) ;
+ t1 = toc ;
+
+ tic ;
+ p2 = cs_nd (sparse (1)) ;
+ toc ;
+ if (p2 ~= 1)
+ error ('!') ;
+ end
+
+ tic ;
+ p2 = cs_nd (A) ;
+ t2 = toc ;
+
+ if (any (sort (p2) ~= 1:n))
+ error ('!') ;
+ end
+
+ rel = t2 / max (t1,1e-6) ;
+
+ fprintf ('time: symrcm %8.3f nd %8.3f rel %8.2f\n', t1, t2, rel) ;
+
+ subplot (1,3,1) ; spy (A) ;
+ subplot (1,3,2) ; spy (A (p1,p1)) ;
+ subplot (1,3,3) ; spy (A (p2,p2)) ;
+
+ % evaluate the profile ...
+
+
+ drawnow
+ % pause
+end
diff --git a/CSparse/MATLAB/Test/test26.m b/CSparse/MATLAB/Test/test26.m
new file mode 100644
index 0000000..b48aae9
--- /dev/null
+++ b/CSparse/MATLAB/Test/test26.m
@@ -0,0 +1,70 @@
+function test26
+%TEST26 test cs_dmsol and cs_dmspy
+%
+% Example:
+% test26
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+clf
+
+ntrials = 1000 ;
+e1 = zeros (ntrials,1) ;
+e2 = zeros (ntrials,1) ;
+
+for trials = 1:ntrials
+
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ % d = 0.1 * rand (1) ;
+ d = rand (1) * 4 * max (m,n) / max (m*n,1) ;
+ A = sprandn (m,n,d) ;
+ % S = sprandn (m,m,d) + speye (m) ;
+
+ subplot (1,3,2) ; spy (A) ;
+ subplot (1,3,3) ; cs_dmspy (A) ;
+
+ b = rand (m,1) ;
+
+ x1 = A\b ;
+ x2 = cs_dmsol (A,b) ;
+
+ err1 = norm (A*x1-b) ;
+ err2 = norm (A*x2-b) ;
+
+ lerr1 = log10 (max (err1, eps)) ;
+ lerr2 = log10 (max (err2, eps)) ;
+
+ fprintf ('rank: %3d %3d err %6.2e %6.2e : %6.1f\n', ...
+ sprank(A), rank(full(A)), err1, err2, lerr1 - lerr2) ;
+
+ if (isnan (err1))
+ lerr1 = 10 ;
+ end
+ if (isnan (err2))
+ lerr2 = 10 ;
+ end
+
+ if (lerr2 > lerr1 + 5)
+ % pause
+ end
+
+ e1 (trials) = lerr1 ;
+ e2 (trials) = lerr2 ;
+
+ subplot (1,3,1) ; plot (e1, e2, 'o', [-16 10], [-16 10], 'r') ;
+ xlabel ('MATLAB error') ;
+ ylabel ('dmsol error') ;
+
+
+ drawnow
+ % pause
+end
diff --git a/CSparse/MATLAB/Test/test27.m b/CSparse/MATLAB/Test/test27.m
new file mode 100644
index 0000000..3c1418c
--- /dev/null
+++ b/CSparse/MATLAB/Test/test27.m
@@ -0,0 +1,47 @@
+function test27
+%TEST27 test cs_qr, cs_utsolve, cs_qrsol
+%
+% Example:
+% test27
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+
+clear functions
+rand ('state', 0) ;
+
+Prob = UFget ('HB/ibm32') ;
+A = Prob.A ;
+A = A (1:10,:) ;
+[m n] = size (A) ;
+
+[V,Beta,p,R,q] = cs_qr (A') ;
+
+b = rand (m,1) ;
+
+Rm = R (1:m,1:m) ;
+
+bq = b (q) ;
+rtbq = Rm' \ bq ;
+
+rt2 = cs_utsolve (Rm, bq) ;
+
+norm (rtbq - rt2)
+
+x = [rt2 ; zeros(n-m,1)] ;
+
+for k = m:-1:1
+ x = x - V(:,k) * (Beta (k) * (V (:,k)' * x)) ;
+end
+
+x (p) = x ;
+
+norm (A*x-b)
+
+x2 = cs_qrsol (A,b) ;
+
+norm (A*x2-b)
+norm (x-x2)
diff --git a/CSparse/MATLAB/Test/test28.m b/CSparse/MATLAB/Test/test28.m
new file mode 100644
index 0000000..1e27270
--- /dev/null
+++ b/CSparse/MATLAB/Test/test28.m
@@ -0,0 +1,113 @@
+function test28
+%TEST28 test cs_randperm, cs_dmperm
+%
+% Example:
+% test28
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clear functions
+
+rand ('state', 0) ;
+for n = 1:100
+ for trials = 1:1000
+ p = cs_randperm (n, rand) ;
+ if (any (sort (p) ~= 1:n))
+ n %#ok
+ p %#ok
+ error ('!')
+ end
+ end
+end
+
+index = UFget ;
+[ignore f] = sort (index.nnz) ;
+
+fprintf ('p=dmperm (std, rand, rev) [p,q,r,s]=dmperm (std, rand, rev)\n') ;
+
+nmat = min (100, length (f)) ;
+T1 = zeros (nmat,1) ;
+T2 = zeros (nmat,1) ;
+T3 = zeros (nmat,1) ;
+D1 = zeros (nmat,1) ;
+D2 = zeros (nmat,1) ;
+D3 = zeros (nmat,1) ;
+
+
+for k = 1:nmat
+
+ i = f (k) ;
+ Prob = UFget (i,index) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ fprintf ('%35s: ', Prob.name) ;
+
+ tic
+ p = cs_dmperm (A) ;
+ t1 = toc ;
+ sprank1 = sum (p > 0) ;
+ fprintf (' %8.2f', t1) ;
+ T1 (k) = t1 ;
+
+ tic
+ p = cs_dmperm (A,1) ;
+ t2 = toc ;
+ sprank2 = sum (p > 0) ;
+ fprintf (' %8.2f', t2) ;
+ T2 (k) = t2 ;
+
+ tic
+ p = cs_dmperm (A,-1) ;
+ t3 = toc ;
+ sprank3 = sum (p > 0) ;
+ fprintf (' %8.2f', t3) ;
+ T3 (k) = t3 ;
+
+ if (sprank1 ~= sprank2 | sprank1 ~= sprank3) %#ok
+ error ('!') ;
+ end
+
+ tic
+ [p1,q1,r1,s1,cc1,rr1] = cs_dmperm (A) ; %#ok
+ d1 = toc ;
+ fprintf (' %8.2f', d1) ;
+ D1 (k) = d1 ;
+
+ tic
+ [p2,q2,r2,s2,cc2,rr2] = cs_dmperm (A,1) ; %#ok
+ d2 = toc ;
+ fprintf (' %8.2f', d2) ;
+ D2 (k) = d2 ;
+
+ tic
+ [p3,q3,r3,s3,cc3,rr3] = cs_dmperm (A,-1) ; %#ok
+ d3 = toc ;
+ fprintf (' %8.2f\n', d3) ;
+ D3 (k) = d3 ;
+
+ if (sprank1 == max (m,n))
+ nz1 = nnz (diag (A (p1,q1))) ;
+ nz2 = nnz (diag (A (p2,q2))) ;
+ nz3 = nnz (diag (A (p3,q3))) ;
+
+ if (nz1 ~= sprank1 | nz2 ~= sprank2 | nz3 ~= sprank3) %#ok
+ error ('!')
+ end
+ end
+
+ subplot (1,2,1)
+ loglog (T1 (1:k), T2 (1:k), 'x', ...
+ T1 (1:k), T3 (1:k), 'go', ...
+ [1e-5 1e3], [1e-5 1e3], 'r-') ;
+ axis equal
+
+ subplot (1,2,2)
+ loglog (D1 (1:k), D2 (1:k), 'x', ...
+ D1 (1:k), D3 (1:k), 'go', ...
+ [1e-5 1e3], [1e-5 1e3], 'r-') ;
+ axis equal
+
+ drawnow
+end
diff --git a/CSparse/MATLAB/Test/test3.m b/CSparse/MATLAB/Test/test3.m
new file mode 100644
index 0000000..fd32454
--- /dev/null
+++ b/CSparse/MATLAB/Test/test3.m
@@ -0,0 +1,97 @@
+function test3
+%TEST3 test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol
+%
+% Example:
+% test3
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+clf
+% f = f(1)
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (~isreal (A) | m ~= n) %#ok
+ continue
+ end
+
+ A = A*A' + 2*n*speye (n) ;
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ try
+ L0 = chol (A)' ;
+ catch
+ continue
+ end
+ b = rand (n,1) ;
+
+ C = A(p,p) ;
+ c = condest (C) ;
+ fprintf ('condest: %g\n', c) ;
+
+ x1 = L0\b ;
+ x2 = cs_lsolve (L0,b) ;
+ err = norm (x1-x2,1) ;
+ if (err > 1e-12 * c)
+ error ('!') ;
+ end
+
+ x1 = L0'\b ;
+ x2 = cs_ltsolve (L0,b) ;
+ err = norm (x1-x2,1) ;
+ if (err > 1e-10 * c)
+ error ('!') ;
+ end
+
+ U = L0' ;
+
+ x1 = U\b ;
+ x2 = cs_usolve (U,b) ;
+ err = norm (x1-x2,1) ;
+ if (err > 1e-10 * c)
+ error ('!') ;
+ end
+
+ L2 = cs_chol (A) ;
+ subplot (2,3,1) ; spy (L0) ;
+ subplot (2,3,4) ; spy (L2) ;
+ err = norm (L0-L2,1) ;
+ if (err > 1e-8 * c)
+ error ('!') ;
+ end
+
+ L1 = chol (C)' ;
+ L2 = cs_chol (C) ;
+ subplot (2,3,2) ; spy (L1) ;
+ subplot (2,3,5) ; spy (L2) ;
+ err = norm (L1-L2,1) ;
+ if (err > 1e-8 * c)
+ error ('!') ;
+ end
+
+ [L3,p] = cs_chol (A) ;
+ C = A(p,p) ;
+ L4 = chol (C)' ;
+ subplot (2,3,3) ; spy (L4) ;
+ subplot (2,3,6) ; spy (L3) ;
+ err = norm (L4-L3,1) ;
+ if (err > 1e-8 * c)
+ error ('!') ;
+ end
+
+ drawnow
+
+end
+
diff --git a/CSparse/MATLAB/Test/test4.m b/CSparse/MATLAB/Test/test4.m
new file mode 100644
index 0000000..da207b5
--- /dev/null
+++ b/CSparse/MATLAB/Test/test4.m
@@ -0,0 +1,33 @@
+function test4
+%TEST4 test cs_multiply
+%
+% Example:
+% test4
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ k = fix (100 * rand (1)) ;
+ d = rand (1) ;
+ A = sprandn (m,n,d) ;
+ B = sprandn (n,k,d) ;
+ C = A*B ;
+ D = cs_multiply (A,B) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d k %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, k, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+end
diff --git a/CSparse/MATLAB/Test/test5.m b/CSparse/MATLAB/Test/test5.m
new file mode 100644
index 0000000..5be775e
--- /dev/null
+++ b/CSparse/MATLAB/Test/test5.m
@@ -0,0 +1,60 @@
+function test5
+%TEST5 test cs_add
+%
+% Example:
+% test5
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = rand (1) ;
+ A = sprandn (m,n,d) ;
+ B = sprandn (m,n,d) ;
+
+ C = A+B ;
+ D = cs_add (A,B) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+ C = pi*A+B ;
+ D = cs_add (A,B,pi) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+ C = pi*A+3*B ;
+ D = cs_add (A,B,pi,3) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+end
diff --git a/CSparse/MATLAB/Test/test6.m b/CSparse/MATLAB/Test/test6.m
new file mode 100644
index 0000000..97b1cc8
--- /dev/null
+++ b/CSparse/MATLAB/Test/test6.m
@@ -0,0 +1,93 @@
+function test6
+%TEST6 test cs_reach, cs_reachr, cs_lsolve, cs_usolve
+%
+% Example:
+% test6
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0)
+maxerr = 0 ;
+clf
+for trial = 1:201
+ n = fix (100 * rand (1)) ;
+ d = 0.1 * rand (1) ;
+ L = tril (sprandn (n,n,d),-1) + sprand (speye (n)) ;
+ b = sprandn (n,1,d) ;
+
+ for uplo = 0:1
+
+ if (uplo == 1)
+ % solve Ux=b instead ;
+ L = L' ;
+ end
+
+ x = L\b ;
+ sr = 1 + cs_reachr (L,b) ;
+ sz = 1 + cs_reachr (L,b) ;
+
+ check_if_same (sr,sz) ;
+
+ s2 = 1 + cs_reach (L,b) ;
+
+ if (uplo == 0)
+ x3 = cs_lsolve (L,b) ;
+ else
+ x3 = cs_usolve (L,b) ;
+ end
+
+ spy ([L b x x3])
+ drawnow
+
+ s = sort (sr) ;
+ [i j xx] = find (x) ; %#ok
+ [i3 j3 xx3] = find (x3) ; %#ok
+
+ if (isempty (i))
+ if (~isempty (s))
+ i %#ok
+ s %#ok
+ error ('!') ;
+ end
+ elseif (any (s ~= i))
+ i %#ok
+ s %#ok
+ error ('!') ;
+ end
+
+ if (isempty (i3))
+ if (~isempty (s))
+ i3 %#ok
+ s %#ok
+ error ('!') ;
+ end
+ elseif (any (s ~= sort (i3)))
+ s %#ok
+ i3 %#ok
+ error ('!') ;
+ end
+
+ if (any (s2 ~= sr))
+ s2 %#ok
+ sr %#ok
+ error ('!') ;
+ end
+
+ err = norm (x-x3,1) ;
+ if (err > 1e-12)
+ x %#ok
+ x3 %#ok
+ uplo %#ok
+ err %#ok
+ error ('!')
+ end
+
+ maxerr = max (maxerr, err) ;
+
+ end
+
+ drawnow
+end
+fprintf ('maxerr = %g\n', maxerr) ;
diff --git a/CSparse/MATLAB/Test/test7.m b/CSparse/MATLAB/Test/test7.m
new file mode 100644
index 0000000..24fd0d5
--- /dev/null
+++ b/CSparse/MATLAB/Test/test7.m
@@ -0,0 +1,107 @@
+function test7
+%TEST7 test cs_lu
+%
+% Example:
+% test7
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+clf
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ if (~isreal (A))
+ continue
+ end
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ [L,U,P] = lu (A) ;
+
+ udiag = full (diag (U)) ;
+ umin = min (abs (udiag)) ;
+ fprintf ('umin %g\n', umin) ;
+
+ if (umin > 1e-14)
+
+ [L2,U2,p] = cs_lu (A) ;
+
+ subplot (3,4,1) ; spy (A) ;
+ subplot (3,4,2) ; spy (A(p,:)) ;
+ subplot (3,4,3) ; spy (L2) ;
+ subplot (3,4,4) ; spy (U2) ;
+
+ err1 = norm (L*U-P*A,1) ;
+ err2 = norm (L2*U2-A(p,:),1) ;
+ fprintf ('err %g %g\n', err1, err2) ;
+ end
+
+ q = colamd (A) ;
+
+ [L,U,P] = lu (A (:,q)) ;
+
+ udiag = full (diag (U)) ;
+ umin = min (abs (udiag)) ;
+ fprintf ('umin %g with q\n', umin) ;
+
+ if (umin > 1e-14)
+
+ [L2,U2,p,q2] = cs_lu (A) ;
+
+ subplot (3,4,5) ; spy (A) ;
+ subplot (3,4,6) ; spy (A(p,q2)) ;
+ subplot (3,4,7) ; spy (L2) ;
+ subplot (3,4,8) ; spy (U2) ;
+
+ err1 = norm (L*U-P*A(:,q),1) ;
+ err2 = norm (L2*U2-A(p,q2),1) ;
+ fprintf ('err %g %g\n', err1, err2) ;
+ end
+
+
+ try
+ q = amd (A) ;
+ catch
+ q = symamd (A) ;
+ end
+
+ tol = 0.01 ;
+
+ [L,U,P] = lu (A (q,q), tol) ;
+
+ udiag = full (diag (U)) ;
+ umin = min (abs (udiag)) ;
+ fprintf ('umin %g with amd q\n', umin) ;
+
+ if (umin > 1e-14)
+
+ [L2,U2,p,q2] = cs_lu (A,tol) ;
+
+ subplot (3,4,9) ; spy (A) ;
+ subplot (3,4,10) ; spy (A(p,q2)) ;
+ subplot (3,4,11) ; spy (L2) ;
+ subplot (3,4,12) ; spy (U2) ;
+
+ err1 = norm (L*U-P*A(q,q),1) ;
+ err2 = norm (L2*U2-A(p,q2),1) ;
+ lbig = full (max (max (abs (L2)))) ;
+ fprintf ('err %g %g lbig %g\n', err1, err2, lbig) ;
+ if (lbig > 1/tol)
+ error ('L!') ;
+ end
+ end
+
+ drawnow
+ % pause
+
+end
diff --git a/CSparse/MATLAB/Test/test8.m b/CSparse/MATLAB/Test/test8.m
new file mode 100644
index 0000000..7922fc3
--- /dev/null
+++ b/CSparse/MATLAB/Test/test8.m
@@ -0,0 +1,85 @@
+%TEST8 test cs_cholsol, cs_lusol
+%
+% Example:
+% test8
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+% f = f(1)
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (~isreal (A) | m ~= n) %#ok
+ continue
+ end
+
+ spd = 0 ;
+ if (m == n)
+ if (nnz (A-A') == 0)
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ [R,p] = chol (A (p,p)) ;
+ spd = (p == 0) ;
+ end
+ end
+
+ if (spd)
+ C = A ;
+ else
+ C = A*A' + n*speye (n) ;
+ try
+ p = amd (C) ;
+ catch
+ p = symamd (C) ;
+ end
+ try
+ R = chol (C (p,p)) ;
+ catch
+ continue
+ end
+ end
+
+ b = rand (n,1) ;
+
+ x1 = C\b ;
+ x2 = cs_cholsol (C,b) ;
+ r1 = norm (C*x1-b,1) / norm (C,1) ;
+ r2 = norm (C*x2-b,1) / norm (C,1) ;
+ err = abs (r1-r2) ;
+ fprintf ('err %g\n', err) ;
+ if (err > 1e-10)
+ error ('!') ;
+ end
+
+ x2 = cs_lusol (C,b, 1, 0.001) ;
+ r2 = norm (C*x2-b,1) / norm (C,1) ;
+ err = abs (r1-r2) ;
+ fprintf ('err %g (lu with amd(A+A'')\n', err) ;
+ if (err > 1e-10)
+ error ('!') ;
+ end
+
+ if (m ~= n)
+ continue ;
+ end
+
+ x1 = A\b ;
+ r1 = norm (A*x1-b,1) / norm (A,1) ;
+ if (r1 < 1e-6)
+ x2 = cs_lusol (A,b) ;
+ r2 = norm (A*x2-b,1) / norm (A,1) ;
+ fprintf ('lu resid %g %g\n', r1, r2) ;
+ end
+end
diff --git a/CSparse/MATLAB/Test/test9.m b/CSparse/MATLAB/Test/test9.m
new file mode 100644
index 0000000..17cecc7
--- /dev/null
+++ b/CSparse/MATLAB/Test/test9.m
@@ -0,0 +1,114 @@
+function test9
+%TEST9 test cs_qr
+%
+% Example:
+% test9
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0) ;
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+clf
+
+% f = 185 ;
+% f = 449 ;
+% f = 186
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ sp = sprank (A) ;
+% if (sprank (A) < min (m,n))
+% continue
+% end
+ Aorig = A ;
+
+ A = A (:, colamd (A)) ;
+ s1 = svd (full (A)) ;
+
+ tic ;
+ R = qr (A) ;
+ t1 = toc ; %#ok
+
+ % tic ;
+ % [Q,R] = qr (A) ;
+ % t1 = toc ;
+
+ [c,h,parent] = symbfact (A, 'col') ;
+ rnz = sum (c) ; %#ok
+ tic ;
+ [V2,Beta2,p,R2] = cs_qr (sparse(A)) ;
+ t2 = toc ; %#ok
+
+ v2 = full (V2) ;
+ if (any (spones (v2) ~= spones (V2)))
+ error ('got zeros!') ;
+ end
+
+ C = A ;
+ m2 = size (V2,1) ;
+ if (m2 > m)
+ C = [A ; sparse(m2-m, n)] ;
+ end
+ C = C (p,:) ;
+
+% [H1,R1] = myqr (C) ;
+% err1 = norm (R1-R2,1) / norm (R1)
+% % [svd(A) svd(R1) svd(full(R2))]
+% s2 = svd (full (R2)) ;
+% err2 = norm (s1 - s2) / s1 (1)
+% fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d n %d\n', ...
+% t1, t2, t1/t2, sp, n) ;
+% err2
+
+ % left-looking:
+ [V,Beta3,R3] = qr_left (C) ; %#ok
+ s3 = svd (full (R2)) ;
+ err3 = norm (s1 - s3) / s1 (1) ;
+ disp ('err3 = ') ; disp (err3) ;
+ if (err3 > 1e-12)
+ error ('!') ;
+ end
+
+ % right-looking:
+ [V,Beta4,R4] = qr_right (C) ; %#ok
+ s4 = svd (full (R2)) ;
+ err4 = norm (s1 - s4) / s1 (1) ;
+ disp ('err4 = ') ; disp (err4) ;
+ if (err4 > 1e-12)
+ error ('!') ;
+ end
+
+ % H2 = full (H2)
+ % R2 = full (R2)
+
+ subplot (2,4,1) ; spy (A) ; title ('A colamd') ;
+ subplot (2,4,2) ; spy (C) ; title ('A rperm') ;
+ subplot (2,4,3) ; treeplot (parent) ;
+ subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ;
+ subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ;
+ subplot (2,4,6) ; spy (R) ; title ('matlab R') ;
+ subplot (2,4,7) ; spy (R2) ; title ('spqr R') ;
+ subplot (2,4,8) ; spy (V2) ; title ('spqr V') ;
+ drawnow
+
+% if (err2 > 1e-9)
+% error ('!') ;
+% end
+ if (m2 > m)
+ fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ;
+ end
+ % pause
+end
+
diff --git a/CSparse/MATLAB/Test/test_qr.m b/CSparse/MATLAB/Test/test_qr.m
new file mode 100644
index 0000000..349960c
--- /dev/null
+++ b/CSparse/MATLAB/Test/test_qr.m
@@ -0,0 +1,55 @@
+function test_qr
+%TEST_QR test various QR factorization methods
+%
+% Example:
+% test_qr
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows,index.ncols)) ;
+
+% f = 276
+% f = 706
+f = f (1:100) ;
+
+for i = f
+
+ % Prob = UFget (i,index)
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ if (sprank (A) < n | ~isreal (A)) %#ok
+ continue ;
+ end
+
+ [V,beta,p,R1,q] = cs_qr(A) ;
+ A = A (p,q) ;
+ parent = etree (A, 'col') ; %#ok
+
+ R0 = qr (A) ;
+ R2 = qr_givens (full (A)) ;
+ R3 = qr_givens_full (full (A)) ;
+
+ subplot (2,2,1) ; cspy (R0) ; title ('matlab') ;
+ subplot (2,2,2) ; cspy (R3) ; title ('qr-full') ;
+ subplot (2,2,3) ; cspy (R2) ; title ('qr-givens') ;
+ subplot (2,2,4) ; cspy (R1) ; title ('cs-qr') ;
+
+ e0 = norm (A'*A-R0'*R0,1) / norm (A,1) ;
+ e1 = norm (A'*A-R1'*R1,1) / norm (A,1) ;
+ e2 = norm (A'*A-R2'*R2,1) / norm (A,1) ;
+ e3 = norm (A'*A-R3'*R3,1) / norm (A,1) ;
+ fprintf ('error %6.2e %6.2e %6.2e %6.2e\n', e0, e1, e2, e3) ;
+ drawnow
+ if (e1 > e0*1e3 | e2 > e0*1e3) %#ok
+ pause
+ end
+end
diff --git a/CSparse/MATLAB/Test/test_qr1.m b/CSparse/MATLAB/Test/test_qr1.m
new file mode 100644
index 0000000..b2143a5
--- /dev/null
+++ b/CSparse/MATLAB/Test/test_qr1.m
@@ -0,0 +1,58 @@
+function test_qr1
+%TEST_QR1 test QR factorizations
+%
+% Example:
+% test_qr1
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+
+for i = f
+ Prob = UFget (i,index) ;
+ A = Prob.A ;
+ if (~isreal (A))
+ continue ;
+ end
+
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+
+ t0 = 0 ;
+ k0 = 0 ;
+ while (t0 < 0.1)
+ tic
+ q = colamd (A, [-1 10]) ;
+ % [Q,R] = qr (A (:,q)) ;
+ R = qr (A (:,q)) ; %#ok
+ t = toc ;
+ t0 = t0 + t ;
+ k0 = k0 + 1 ;
+ end
+ t0 = t0 / k0 ;
+
+ t1 = 0 ;
+ k1 = 0 ;
+ while (t1 < 0.1)
+ tic
+ [V,beta, p, R,q] = cs_qr (A) ; %#ok
+ t = toc ;
+ t1 = t1 + t ;
+ k1 = k1 + 1 ;
+ end
+ t1 = t1 / k1 ;
+
+ fprintf (...
+ '%25s MATLAB: %10.4f (%8d) CS: %10.4f (%8d) speedup: %8.2f\n', ...
+ Prob.name, t0, k0, t1, k1, t0/t1) ;
+
+
+
+end
+
diff --git a/CSparse/MATLAB/Test/test_qrsol.m b/CSparse/MATLAB/Test/test_qrsol.m
new file mode 100644
index 0000000..22c4ade
--- /dev/null
+++ b/CSparse/MATLAB/Test/test_qrsol.m
@@ -0,0 +1,50 @@
+function test_qrsol
+%TEST_QRSOL test cs_qrsol
+%
+% Example:
+% test_qrsol
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+
+k = 0 ;
+rs1 = zeros (1,0) ;
+rs2 = zeros (1,0) ;
+
+for i = f
+ Prob = UFget (i,index) ;
+ A = Prob.A ;
+ if (~isreal (A))
+ continue ;
+ end
+
+ [m n] = size (A) ; %#ok
+ b = rand (m,1) ;
+
+ x1 = A\b ;
+ x2 = cs_qrsol (A,b) ;
+
+ x1 (~isfinite (x1)) = 0 ;
+ x2 (~isfinite (x2)) = 0 ;
+
+ r1 = norm (A*x1-b) ;
+ r2 = norm (A*x2-b) ;
+
+ k = k + 1 ;
+ rs1 (k) = r1 ;
+ rs2 (k) = r2 ;
+
+ fprintf ('%30s MATLAB: %6.2e CS: %6.2e\n', Prob.name, r1, r2) ;
+
+ loglog (rs1, rs2, 'o') ;
+ drawnow
+
+ clear A b x1 x2
+ % pack
+
+end
+
diff --git a/CSparse/MATLAB/Test/test_randperms.m b/CSparse/MATLAB/Test/test_randperms.m
new file mode 100644
index 0000000..193cf9c
--- /dev/null
+++ b/CSparse/MATLAB/Test/test_randperms.m
@@ -0,0 +1,60 @@
+function test_randperms
+%TEST_RANDPERMS test random permutations
+% Example:
+% test_randperms
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0)
+
+for trial = 1:100
+ m = fix (30 * rand (1)) ;
+ n = fix (30 * rand (1)) ;
+ d = rand (1) ;
+ A = sprandn (m,n,d) ;
+
+ if (m == 0)
+ p = [] ;
+ else
+ p = randperm (m) ;
+ end
+ if (n == 0)
+ q = [] ;
+ else
+ q = randperm (n) ;
+ end
+
+ C = A(p,q) ;
+
+ Im = speye (m) ;
+ In = speye (n) ;
+ P = Im (p,:) ;
+ Q = In (:,q) ;
+
+ q2 = find (Q) ;
+ if (any (q ~= q2'))
+ error ('!')
+ end
+
+ p2 = find (P') ;
+ if (any (p ~= p2'))
+ error ('!')
+ end
+
+ E = P*A*Q ;
+ if (norm (C-E,1) ~= 0)
+ error ('!')
+ end
+
+ P = sparse (1:m, p, 1) ;
+ Q = sparse (q, 1:n, 1) ;
+
+ E = P*A*Q ;
+ if (norm (C-E,1) ~= 0)
+ error ('2!')
+ end
+
+end
+
diff --git a/CSparse/MATLAB/Test/test_sep.m b/CSparse/MATLAB/Test/test_sep.m
new file mode 100644
index 0000000..59213d2
--- /dev/null
+++ b/CSparse/MATLAB/Test/test_sep.m
@@ -0,0 +1,102 @@
+function test_sep
+%TEST_SEP test cs_sep, and compare with Gilbert's meshpart vtxsep
+% (requires MESHPART).
+%
+% Example:
+% test_sep
+%
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+
+clf
+
+for k = 1:length(f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = spones (Prob.A) ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ A = A'*A ;
+ end
+
+ A = A|A' ;
+
+ p = symrcm (A) ;
+
+ n = size (A,1) ;
+ n2 = fix (n/2) ;
+ a = p (1:n2) ;
+ b = p ((n2+1):n) ;
+
+ clf
+
+ subplot (2,3,1) ; spy (A) ;
+ subplot (2,3,2) ; spy (A (p,p)) ;
+
+ hold on
+ plot ([.5 n2+.5 n2+.5 .5 .5], [.5 .5 n2+.5 n2+.5 .5], 'r', 'LineWidth', 2) ;
+ hold off
+
+ subplot (2,3,3) ; spy (A (a,b)) ; title ('edge sep') ;
+ subplot (2,3,6) ; cs_dmspy (A (a,b)) ; title ('node sep') ;
+
+ [s as bs] = vtxsep (A,a,b) ; %#ok
+ [s2 a2 b2] = cs_sep (A,a,b) ;
+
+ p2 = [a2 b2 s2] ;
+ B = A (p2,p2) ;
+ subplot (2,3,5) ; spy (B) ;
+ hold on
+
+ px = [s2 a2 b2] ;
+ if (any (sort (px) ~= 1:n))
+ px %#ok
+ n %#ok
+ error ('!') ;
+ end
+
+ na = length (a2) ;
+ nb = length (b2) ;
+ ns = length (s2) ; %#ok
+
+ nab = na + nb ;
+
+ plot ([.5 na+.5 na+.5 .5 .5], [.5 .5 na+.5 na+.5 .5], 'r', 'LineWidth', 2) ;
+
+ plot ([na nab nab na na]+0.5, [na na nab nab na]+0.5, 'r', 'LineWidth', 2) ;
+
+ plot ([.5 nab+.5 nab+.5 .5 .5], [.5 .5 nab+.5 nab+.5 .5], 'g', 'LineWidth', 1) ;
+
+ hold off
+
+ nz1 = nnz (A (a2,b2)) ;
+ if (nz1 ~= 0)
+ nz1 %#ok
+ error ('!') ;
+ end
+
+ nz2 = nnz (A (a2,b2)) ;
+ if (nz2 ~= 0)
+ nz2 %#ok
+ error ('!') ;
+ end
+
+ if (length (s) ~= length (s2))
+ fprintf ('lengths differ: %d %d\n', length (s), length (s2)) ;
+ end
+
+ drawnow
+ % pause
+
+
+end
diff --git a/CSparse/MATLAB/Test/testall.m b/CSparse/MATLAB/Test/testall.m
new file mode 100644
index 0000000..5fb720c
--- /dev/null
+++ b/CSparse/MATLAB/Test/testall.m
@@ -0,0 +1,51 @@
+function testall
+%TESTALL test all CSparse functions (run tests 1 to 28 below)
+%
+% Example:
+% testall
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+h = waitbar (0, 'CSparse') ;
+
+cs_test_make % compile all CSparse, Demo, Text, and Test mexFunctions
+
+ntests = 28 ;
+
+testwait (1, ntests, h) ; test1 ;
+testwait (2, ntests, h) ; test2 ;
+testwait (3, ntests, h) ; test3 ;
+testwait (4, ntests, h) ; test4 ;
+testwait (5, ntests, h) ; test5 ;
+testwait (6, ntests, h) ; test6 ;
+testwait (7, ntests, h) ; test7 ;
+testwait (8, ntests, h) ; test8 ;
+testwait (9, ntests, h) ; test9 ;
+testwait (10, ntests, h) ; test10 ;
+testwait (11, ntests, h) ; test11 ;
+testwait (12, ntests, h) ; test12 ;
+testwait (13, ntests, h) ; test13 ;
+testwait (14, ntests, h) ; test14 ;
+testwait (15, ntests, h) ; test15 ;
+testwait (16, ntests, h) ; test16 ;
+testwait (17, ntests, h) ; test17 ;
+testwait (18, ntests, h) ; test18 ;
+testwait (19, ntests, h) ; test19 ;
+testwait (20, ntests, h) ; test20 ;
+testwait (21, ntests, h) ; test21 ;
+testwait (22, ntests, h) ; test22 ;
+testwait (23, ntests, h) ; test23 ;
+testwait (24, ntests, h) ; test24 ;
+testwait (25, ntests, h) ; test25 ;
+testwait (26, ntests, h) ; test26 ;
+testwait (27, ntests, h) ; test27 ;
+testwait (28, ntests, h) ; test28 ;
+
+close (h)
+
+function testwait (n,ntests,h)
+fprintf ('\n------------------------ test%d\n', n) ;
+waitbar (n/(ntests+1), h, sprintf ('CSparse test %d of %d\n', n, ntests)) ;
+
diff --git a/CSparse/MATLAB/Test/testh.m b/CSparse/MATLAB/Test/testh.m
new file mode 100644
index 0000000..9f32f27
--- /dev/null
+++ b/CSparse/MATLAB/Test/testh.m
@@ -0,0 +1,85 @@
+function testh
+%TESTH test Householder reflections
+%
+% Example:
+% testh
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+format long e
+fprintf ('-------------------------------------------------\n') ;
+x = [-3 4 5]' ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+
+x = [3 4 5]' ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = [1 eps]' ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = pi ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = -pi ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = [1 0 0]' ;
+disp (x) ;
+[v, beta, s] = house (x) ; %#ok
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
diff --git a/CSparse/MATLAB/UFget/Contents.m b/CSparse/MATLAB/UFget/Contents.m
new file mode 100644
index 0000000..398226a
--- /dev/null
+++ b/CSparse/MATLAB/UFget/Contents.m
@@ -0,0 +1,16 @@
+% UFget: MATLAB interface for the UF Sparse Matrix Collection.
+%
+% UFget - loads a matrix from the UF Sparse Matrix Collection.
+% UFweb - opens the URL for a matrix.
+% UFgrep - search for matrices in the UF Sparse Matrix Collection.
+%
+% Helper functions:
+%
+% UFget_defaults - returns default parameter settings for UFget.
+% UFget_example - a demo for UFget.
+% UFget_lookup - gets the group, name, and id of a matrix.
+%
+% Example:
+% help UFget
+
+% Copyright 2007, Timothy A. Davis
diff --git a/CSparse/MATLAB/UFget/README.txt b/CSparse/MATLAB/UFget/README.txt
new file mode 100644
index 0000000..0353409
--- /dev/null
+++ b/CSparse/MATLAB/UFget/README.txt
@@ -0,0 +1,67 @@
+UFget: a MATLAB interface to the UF sparse matrix collection.
+MATLAB 7.0 or later is required.
+
+Date: May 31, 2007.
+
+Copyright 2005-2007, Tim Davis, University of Florida.
+Authors: Tim Davis and Erich Mirable.
+Availability: http://www.cise.ufl.edu/research/sparse/mat/UFget
+
+See http://www.cise.ufl.edu/research/sparse/mat/UFget.tar.gz
+for a single archive file with all the files listed below.
+
+ UFget/Contents.m help for UFget
+ UFget/README.txt this file
+
+ UFget/UFget_defaults.m default parameter settings for UFget
+ UFget/UFget_example.m demo for UFget
+ UFget/UFget_lookup.m get the group, name, and id of a matrix
+ UFget/UFget.m primary user interface
+
+ UFget/UFweb.m opens the URL for a matrix or collection
+
+ UFget/mat default download directory (can be changed)
+ UFget/mat/UF_Index.mat index to the UF sparse matrix collection
+
+To install the package, just add the path containing the UFget directory
+to your MATLAB path. Type "pathtool" in MATLAB for more details.
+
+For a simple example of use, type this command in MATLAB:
+
+ UFget_example
+
+The MATLAB statement
+
+ Problem = UFget ('HB/arc130')
+
+(for example), will download a sparse matrix called HB/arc130 (a laser
+simulation problem) and load it into MATLAB. You don't need to use your
+web browser to load the matrix. The statement
+
+ Problem = UFget (6)
+
+will also load same the HB/arc130 matrix. Each matrix in the collection has
+a unique identifier, in the range 1 to the number of matrices. As new
+matrices are added, the id's of existing matrices will not change.
+
+To view an index of the entire collection, just type
+
+ UFget
+
+in MATLAB. To modify your download directory, edit the UFget_defaults.m file.
+
+To open a URL of the entire collection, just type
+
+ UFweb
+
+To open the URL of a group of matrices in the collection:
+
+ UFweb ('HB')
+
+To open the web page for one matrix, use either of these formats:
+
+ UFweb ('HB/arc130')
+ UFweb (6)
+
+For more information on how the index entries were created, see
+http://www.cise.ufl.edu/research/sparse/SuiteSparse.
diff --git a/CSparse/MATLAB/UFget/UFget.m b/CSparse/MATLAB/UFget/UFget.m
new file mode 100644
index 0000000..2ef17ed
--- /dev/null
+++ b/CSparse/MATLAB/UFget/UFget.m
@@ -0,0 +1,142 @@
+function Problem = UFget (matrix, UF_Index)
+%UFGET loads a matrix from the UF Sparse Matrix Collection.
+%
+% Problem = UFget(matrix) loads a matrix from the UF sparse matrix collection,
+% specified as either a number (1 to the # of matrices in the collection) or
+% as a string (the name of the matrix). With no input parameters, index=UFget
+% returns an index of matrices in the collection. A local copy of the matrix
+% is saved (be aware that as of May 2007 the entire collection is over 8GB
+% in size). If no input or output arguments are provided, the index is
+% printed. With a 2nd parameter (Problem = UFget (matrix, index)), the index
+% file is not loaded. This is faster if you are loading lots of matrices.
+%
+% Examples:
+% index = UFget ;
+% Problem = UFget (6)
+% Problem = UFget ('HB/arc130')
+% Problem = UFget (6, index)
+% Problem = UFget ('HB/arc130', index)
+%
+% See also UFgrep, UFweb, UFget_example, UFget_defaults, urlwrite.
+
+% Copyright 2007, Tim Davis, University of Florida.
+
+%-------------------------------------------------------------------------------
+% get the parameter settings
+%-------------------------------------------------------------------------------
+
+params = UFget_defaults ;
+indexfile = sprintf ('%sUF_Index.mat', params.dir) ;
+indexurl = sprintf ('%s/UF_Index.mat', params.url) ;
+
+%-------------------------------------------------------------------------------
+% get the index file (download a new one if necessary)
+%-------------------------------------------------------------------------------
+
+try
+ % load the existing index file
+ if (nargin < 2)
+ load (indexfile) ;
+ end
+ % see if the index file is old; if so, download a fresh copy
+ refresh = (UF_Index.DownloadTimeStamp + params.refresh < now) ;
+catch
+ % oops, no index file. download it.
+ refresh = 1 ;
+end
+
+if (refresh)
+ % a new UF_Index.mat file to get access to new matrices (if any)
+ fprintf ('downloading %s\n', indexurl) ;
+ fprintf ('to %s\n', indexfile) ;
+ urlwrite (indexurl, indexfile) ;
+ load (indexfile) ;
+ UF_Index.DownloadTimeStamp = now ;
+ save (indexfile, 'UF_Index') ;
+end
+
+%-------------------------------------------------------------------------------
+% return the index file if requested
+%-------------------------------------------------------------------------------
+
+% if the user passed in a zero or no argument at all, return the index file
+if nargin == 0
+ matrix = 0 ;
+end
+
+if (matrix == 0)
+ if (nargout == 0)
+ % no output arguments have been passed, so print the index file
+ fprintf ('\nUF sparse matrix collection index: %s\n', ...
+ UF_Index.LastRevisionDate) ;
+ fprintf ('\nLegend:\n') ;
+ fprintf ('(p,n)sym: symmetry of the pattern and values\n') ;
+ fprintf (' (0 = unsymmetric, 1 = symmetric, - = not computed)\n') ;
+ fprintf ('type: real\n') ;
+ fprintf (' complex\n') ;
+ fprintf (' binary: all entries are 0 or 1\n') ;
+ nmat = length (UF_Index.nrows) ;
+ for j = 1:nmat
+ if (mod (j, 25) == 1)
+ fprintf ('\n') ;
+ fprintf ('ID Group/Name nrows-by- ncols nonzeros (p,n)sym type\n') ;
+ end
+ s = sprintf ('%s/%s', UF_Index.Group {j}, UF_Index.Name {j}) ;
+ fprintf ('%4d %-30s %7d-by-%7d %9d ', ...
+ j, s, UF_Index.nrows (j), UF_Index.ncols (j), UF_Index.nnz (j)) ;
+ psym = UF_Index.pattern_symmetry (j) ;
+ nsym = UF_Index.numerical_symmetry (j) ;
+ if (psym < 0)
+ fprintf (' - ') ;
+ else
+ fprintf (' %4.2f', psym) ;
+ end
+ if (nsym < 0)
+ fprintf (' - ') ;
+ else
+ fprintf (' %4.2f', nsym) ;
+ end
+ if (UF_Index.isBinary (j))
+ fprintf (' binary\n') ;
+ elseif (~UF_Index.isReal (j))
+ fprintf (' complex\n') ;
+ else
+ fprintf (' real\n') ;
+ end
+ end
+ else
+ Problem = UF_Index ;
+ end
+ return ;
+end
+
+%-------------------------------------------------------------------------------
+% determine if the matrix parameter is a matrix index or name
+%-------------------------------------------------------------------------------
+
+[group matrix id] = UFget_lookup (matrix, UF_Index) ;
+
+if (id == 0)
+ error ('invalid matrix') ;
+end
+
+%-------------------------------------------------------------------------------
+% download the matrix (if needed) and load it into MATLAB
+
+matdir = sprintf ('%s%s%s%s.mat', params.dir, group) ;
+matfile = sprintf ('%s%s%s.mat', matdir, filesep, matrix) ;
+maturl = sprintf ('%s/%s/%s.mat', params.url, group, matrix) ;
+
+if (~exist (matdir, 'dir'))
+ mkdir (matdir) ;
+end
+
+if (exist (matfile, 'file'))
+ load (matfile)
+else
+ fprintf ('downloading %s\n', maturl) ;
+ fprintf ('to %s\n', matfile) ;
+ urlwrite (maturl, matfile) ;
+ load (matfile)
+ save (matfile, 'Problem') ;
+end
diff --git a/CSparse/MATLAB/UFget/UFget_defaults.m b/CSparse/MATLAB/UFget/UFget_defaults.m
new file mode 100644
index 0000000..31425c4
--- /dev/null
+++ b/CSparse/MATLAB/UFget/UFget_defaults.m
@@ -0,0 +1,43 @@
+function params = UFget_defaults
+%UFGET_DEFAULTS returns default parameter settings for UFget.
+% Usage: params = UFget_defaults ; Returns the default parameter settings for
+% UFget. This file may be editted to change these settings:
+%
+% params.url: UF sparse matrix web site
+% params.dir: your local directory for downloaded sparse matrices.
+% params.refresh: how many days should elapse before re-downloading the
+% index file (for obtaining access to new matrices in the collection).
+%
+% Example:
+% params = UFget_defaults ;
+%
+% See also UFget.
+
+% Copyright 2007, Tim Davis, University of Florida.
+
+%-------------------------------------------------------------------------------
+% location of the UF sparse matrix collection
+params.url = 'http://www.cise.ufl.edu/research/sparse/mat' ;
+
+%-------------------------------------------------------------------------------
+% decode the current directory for this M-file
+s = which (mfilename) ;
+i = find (s == filesep) ;
+s = s (1:i(end)) ;
+
+%-------------------------------------------------------------------------------
+% define the directory to download into. Should end in file separator.
+% Some examples include:
+% params.dir = '/cise/research/sparse/public_html/mat/' ; % if at UF
+% params.dir = 'your directory here/' ;
+% params.dir = 'c:\matlab\work\UFget\mat\' ;
+
+% Default: the directory containing this UFget_defaults function
+params.dir = sprintf ('%smat%s', s, filesep) ;
+
+%-------------------------------------------------------------------------------
+% define how often to check for a new index file (in # of days)
+% inf will force the program to ignore the need to refresh
+
+% params.refresh = Inf ; % if at UF
+params.refresh = 90 ;
diff --git a/CSparse/MATLAB/UFget/UFget_example.m b/CSparse/MATLAB/UFget/UFget_example.m
new file mode 100644
index 0000000..7381c1a
--- /dev/null
+++ b/CSparse/MATLAB/UFget/UFget_example.m
@@ -0,0 +1,30 @@
+%UFGET_EXAMPLE a demo for UFget.
+% This example script gets the index file of the UF sparse matrix collection,
+% and then loads in all symmetric non-binary matrices, in increasing order of
+% number of rows in the matrix.
+%
+% Example:
+% type UFget_example ; % to see an example of how to use UFget
+%
+% See also UFget, UFweb, UFgrep.
+
+% Copyright 2007, Tim Davis, University of Florida.
+
+type UFget_example ;
+
+index = UFget ;
+f = find (index.numerical_symmetry == 1 & ~index.isBinary) ;
+[y, j] = sort (index.nrows (f)) ;
+f = f (j) ;
+
+for i = f
+ fprintf ('Loading %s%s%s, please wait ...\n', ...
+ index.Group {i}, filesep, index.Name {i}) ;
+ Problem = UFget (i,index) ;
+ disp (Problem) ;
+ spy (Problem.A) ;
+ title (sprintf ('%s:%s', Problem.name, Problem.title')) ;
+ UFweb (i) ;
+ input ('hit enter to continue:') ;
+end
+
diff --git a/CSparse/MATLAB/UFget/UFget_lookup.m b/CSparse/MATLAB/UFget/UFget_lookup.m
new file mode 100644
index 0000000..bbc9055
--- /dev/null
+++ b/CSparse/MATLAB/UFget/UFget_lookup.m
@@ -0,0 +1,77 @@
+function [group, name, id] = UFget_lookup (matrix, UF_Index)
+%UFGET_LOOKUP gets the group, name, and id of a matrix.
+%
+% Example:
+% [group name id] = UFget_lookup (matrix, UF_Index)
+%
+% See also UFget.
+
+% Copyright 2007, Tim Davis, University of Florida.
+
+if (isnumeric (matrix))
+
+ % make sure that the matrix parameter is only one integer value
+ % this means that if we get an array, just use the first value
+ id = fix (full (matrix (1))) ;
+
+ % if the index is less than one or bigger than the length of the array,
+ % then no particular matrix is accessed
+ if (id > length (UF_Index.nrows) | id < 1) %#ok
+ id = 0 ;
+ group = '' ;
+ name = '' ;
+ else
+ % assign the group and name for the given id
+ group = UF_Index.Group {matrix} ;
+ name = UF_Index.Name {matrix} ;
+ end
+
+elseif (ischar (matrix))
+
+ % the group and matrix name are in the string as in GroupName\MatrixName
+
+ % find the group index for the file separator
+ % check both types of slashes, and a colon
+ gi = find (matrix == '/') ;
+ if (length (gi) == 0) %#ok
+ gi = find (matrix == '\') ;
+ end
+ if (length (gi) == 0) %#ok
+ gi = find (matrix == ':') ;
+ end
+
+ % if no name divider is in the string, a whole group is specified
+ if (length (gi) == 0) %#ok
+
+ id = 0 ;
+ group = matrix ;
+ name = '' ;
+
+ else
+
+ % group equals the first part of the string up to the character before
+ % the last file separator
+ group = matrix (1:gi(end)-1) ;
+
+ % group equals the last section of the string after the last file
+ % separator
+ name = matrix (gi(end)+1:end) ;
+
+ % validate the given name and group by checking the index for a match
+ refName = strmatch (name, UF_Index.Name) ;
+ refGroup = strmatch (group, UF_Index.Group) ;
+ id = intersect (refName, refGroup) ;
+ if (length (id) >= 1)
+ id = id (1) ;
+ else
+ % the given group/matrix does not exist in the index file
+ id = 0 ;
+ end
+ end
+
+else
+
+ % there is an error in the argument types passed into the function
+ error ('invalid input') ;
+
+end
diff --git a/CSparse/MATLAB/UFget/UFgrep.m b/CSparse/MATLAB/UFget/UFgrep.m
new file mode 100644
index 0000000..be7beff
--- /dev/null
+++ b/CSparse/MATLAB/UFget/UFgrep.m
@@ -0,0 +1,53 @@
+function list = UFgrep (expression, index)
+%UFGREP search for matrices in the UF Sparse Matrix Collection.
+% UFgrep returns a list of Problem id's whose Problem.name string matches an
+% expression. With no output arguments, the list is displayed. Otherwise, it
+% is returned as a list of integer id's.
+%
+% Example:
+% UFgrep ('HB') ; % all matrices in the HB group
+% UFgrep ('\<B*') ; % all matrices in groups starting with the letter B
+% UFgrep ('bp') ; % all bp matrices (in the HB group)
+% UFgrep ('[0-9]') ; % all matrices with a digit in their name
+% UFgrep ('c-') ; % all c-* optimization matrices (in 2 groups)
+%
+% An optional 2nd input argument is the UF index, which is a little faster if
+% UFgrep is used multiple times. With no input arguments, all Problems are
+% listed.
+%
+% index = UFget ;
+% UFgrep ('HB/*', index) ;
+%
+% See also regexp, UFget.
+
+% Copyright 2007, Timothy A. Davis
+
+if (nargin < 2)
+ index = UFget ;
+end
+
+if (nargin < 1)
+ expression = '.' ;
+end
+
+nmat = length (index.nrows) ;
+list1 = zeros (1, nmat) ;
+matched = 0 ;
+
+for id = 1:nmat
+ name = [index.Group{id} '/' index.Name{id}] ;
+ if (~isempty (regexp (name, expression, 'once')))
+ matched = matched + 1 ;
+ list1 (matched) = id ;
+ end
+end
+
+list1 = list1 (1,1:matched) ;
+
+if (nargout == 0)
+ for id = list1
+ fprintf ('%4d: %s/%s\n', id, index.Group {id}, index.Name {id}) ;
+ end
+else
+ list = list1 ;
+end
diff --git a/CSparse/MATLAB/UFget/UFweb.m b/CSparse/MATLAB/UFget/UFweb.m
new file mode 100644
index 0000000..d91ea8a
--- /dev/null
+++ b/CSparse/MATLAB/UFget/UFweb.m
@@ -0,0 +1,135 @@
+function stats = UFweb (matrix, opts)
+%UFWEB opens the URL for a matrix.
+%
+% UFweb(matrix) opens the URL for a matrix. This parameter can be a string,
+% or an integer. If it is a string with no "/" character, the web page for a
+% matrix group is displayed. With no arguments, a list of all the matrix
+% groups is displayed.
+%
+% Example:
+%
+% If Problem = UFget ('HB/arc130'), the first four examples display
+% the same thing, the web page for the HB/arc130 matrix:
+%
+% UFweb (6)
+% UFweb ('HB/arc130')
+% stats = UFweb (6)
+%
+% The latter also returns statistics about the matrix or matrix group.
+% To display the web page for the HB (Harwell-Boeing) group:
+%
+% UFweb ('HB')
+%
+% To display the home page for the UF sparse matrix collection:
+%
+% UFweb
+% UFweb (0)
+% UFweb ('')
+%
+% The latter two are useful if a second optional parameter is specified.
+% The second optional argument is a string passed as additional parameters to
+% the MATLAB web command. To use the system web browser instead of the MATLAB
+% browser, for example, use UFweb ('HB/arc130', '-browser').
+%
+% See also web, UFget, UFget_defaults.
+
+% Copyright 2007, Tim Davis, University of Florida.
+
+params = UFget_defaults ;
+UF_Index = UFget ;
+
+if (nargin < 1)
+ matrix = '' ;
+end
+if (nargin < 2)
+ opts = '' ;
+end
+
+% get the matrix group, name, and id
+[group name id] = UFget_lookup (matrix, UF_Index) ;
+
+url = params.url ;
+len = length (url) ;
+if (strcmp (url ((len-3):len), '/mat'))
+ % remove the trailing '/mat'
+ url = url (1:(len-4)) ;
+end
+
+% open the web page for the matrix, group, or whole collection
+if (id == 0)
+ if (isempty (group))
+ eval (['web ' url '/matrices/index.html ' opts])
+ else
+ eval (['web ' url '/matrices/' group '/index.html ' opts])
+ end
+else
+ eval (['web ' url '/matrices/' group '/' name '.html ' opts])
+end
+
+% return stats
+if (nargout > 0)
+
+ if (id == 0)
+
+ if (isempty (group))
+
+ % return stats about the whole collection
+ stats.nmatrices = length (UF_Index.nrows) ;
+ stats.LastRevisionDate = UF_Index.LastRevisionDate ;
+ stats.DownloadTime = datestr (UF_Index.DownloadTimeStamp) ;
+
+ else
+
+ % return stats about one matrix group
+ nmat = length (UF_Index.nrows) ;
+ ngroup = 0 ;
+ for i = 1:nmat
+ if (strcmp (group, UF_Index.Group {i}))
+ ngroup = ngroup + 1 ;
+ end
+ end
+ stats.nmatrices = ngroup ;
+ stats.LastRevisionDate = UF_Index.LastRevisionDate ;
+ stats.DownloadTime = datestr (UF_Index.DownloadTimeStamp) ;
+
+ end
+ else
+
+ % look up the matrix statistics
+ stats.Group = group ;
+ stats.Name = name ;
+ stats.nrows = UF_Index.nrows (id) ;
+ stats.ncols = UF_Index.ncols (id) ;
+ stats.nnz = UF_Index.nnz (id) ;
+ stats.nzero = UF_Index.nzero (id) ;
+ stats.pattern_symmetry = UF_Index.pattern_symmetry (id) ;
+ stats.numerical_symmetry = UF_Index.numerical_symmetry (id) ;
+ stats.isBinary = UF_Index.isBinary (id) ;
+ stats.isReal = UF_Index.isReal (id) ;
+
+ stats.nnzdiag = UF_Index.nnzdiag (id) ;
+ stats.posdef = UF_Index.posdef (id) ;
+
+ stats.amd_lnz = UF_Index.amd_lnz (id) ;
+ stats.amd_flops = UF_Index.amd_flops (id) ;
+ stats.amd_vnz = UF_Index.amd_vnz (id) ;
+ stats.amd_rnz = UF_Index.amd_rnz (id) ;
+ stats.metis_lnz = UF_Index.metis_lnz (id) ;
+ stats.metis_flops = UF_Index.metis_flops (id) ;
+ stats.metis_vnz = UF_Index.metis_vnz (id) ;
+ stats.metis_rnz = UF_Index.metis_rnz (id) ;
+ stats.nblocks = UF_Index.nblocks (id) ;
+ stats.sprank = UF_Index.sprank (id) ;
+ stats.nzoff = UF_Index.nzoff (id) ;
+ stats.dmperm_lnz = UF_Index.dmperm_lnz (id) ;
+ stats.dmperm_unz = UF_Index.dmperm_unz (id) ;
+ stats.dmperm_flops = UF_Index.dmperm_flops (id) ;
+ stats.dmperm_vnz = UF_Index.dmperm_vnz (id) ;
+ stats.dmperm_rnz = UF_Index.dmperm_rnz (id) ;
+
+ stats.RBtype = UF_Index.RBtype (id,:) ;
+ stats.cholcand = UF_Index.cholcand (id) ;
+ stats.ncc = UF_Index.ncc (id) ;
+
+ end
+end
diff --git a/CSparse/MATLAB/UFget/mat/UF_Index.mat b/CSparse/MATLAB/UFget/mat/UF_Index.mat
new file mode 100644
index 0000000..d17778e
Binary files /dev/null and b/CSparse/MATLAB/UFget/mat/UF_Index.mat differ
diff --git a/CSparse/MATLAB/cs_install.m b/CSparse/MATLAB/cs_install.m
new file mode 100644
index 0000000..b8f387e
--- /dev/null
+++ b/CSparse/MATLAB/cs_install.m
@@ -0,0 +1,60 @@
+function cs_install (do_pause)
+%CS_INSTALL: compile and install CSparse for use in MATLAB.
+% Your current working directory must be CSparse/MATLAB in order to use this
+% function.
+%
+% The directories
+%
+% CSparse/MATLAB/CSparse
+% CSparse/MATLAB/Demo
+% CSparse/MATLAB/UFget
+%
+% are added to your MATLAB path (see the "pathtool" command to add these to
+% your path permanently, for future MATLAB sessions).
+%
+% Next, the MATLAB CSparse demo program, CSparse/MATLAB/cs_demo is executed.
+% To run the demo with pauses so you can see the results, use cs_install(1).
+% To run the full MATLAB test programs for CSparse, run testall in the
+% Test directory.
+%
+% Example:
+% cs_install % install and run demo with no pauses
+% cs_install(1) % install and run demo with pauses
+%
+% See also: cs_demo
+%
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('Compiling and installing CSparse\n') ;
+if (nargin < 1)
+ do_pause = 0 ;
+end
+
+if (~isempty (strfind (computer, '64')))
+ error ('64-bit version not supported; use CXSparse instead') ;
+end
+
+if (do_pause)
+ input ('Hit enter to continue: ') ;
+end
+addpath ([pwd filesep 'CSparse']) ;
+addpath ([pwd filesep 'Demo']) ;
+
+v = getversion ;
+if (v >= 7.0)
+ addpath ([pwd filesep 'UFget']) ;
+else
+ fprintf ('UFget not installed (MATLAB 7.0 or later required)\n') ;
+end
+
+cd ('CSparse') ;
+cs_make (1) ;
+cd ('../Demo') ;
+cs_demo (do_pause)
+
+%-------------------------------------------------------------------------------
+function v = getversion
+% determine the MATLAB version, and return it as a double.
+v = sscanf (version, '%d.%d.%d') ;
+v = 10.^(0:-1:-(length(v)-1)) * v ;
diff --git a/CSparse/Makefile b/CSparse/Makefile
new file mode 100644
index 0000000..5700dcb
--- /dev/null
+++ b/CSparse/Makefile
@@ -0,0 +1,30 @@
+# CSparse Makefile
+
+C:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+all: C cov
+
+library:
+ ( cd Lib ; $(MAKE) )
+
+cov:
+ ( cd Tcov ; $(MAKE) )
+
+mex:
+ ( cd MATLAB ; $(MAKE) )
+
+clean:
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+ ( cd Tcov ; $(MAKE) clean )
+ ( cd MATLAB ; $(MAKE) clean )
+
+purge:
+ ( cd Lib ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd Tcov ; $(MAKE) purge )
+ ( cd MATLAB ; $(MAKE) purge )
+
+distclean: purge
diff --git a/CSparse/Matrix/ash219 b/CSparse/Matrix/ash219
new file mode 100644
index 0000000..b092930
--- /dev/null
+++ b/CSparse/Matrix/ash219
@@ -0,0 +1,438 @@
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diff --git a/CSparse/Matrix/bcsstk01 b/CSparse/Matrix/bcsstk01
new file mode 100644
index 0000000..b529e93
--- /dev/null
+++ b/CSparse/Matrix/bcsstk01
@@ -0,0 +1,224 @@
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diff --git a/CSparse/Matrix/bcsstk16 b/CSparse/Matrix/bcsstk16
new file mode 100644
index 0000000..8dd72b3
--- /dev/null
+++ b/CSparse/Matrix/bcsstk16
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diff --git a/CSparse/Matrix/fs_183_1 b/CSparse/Matrix/fs_183_1
new file mode 100644
index 0000000..7797188
--- /dev/null
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diff --git a/CSparse/Matrix/ibm32a b/CSparse/Matrix/ibm32a
new file mode 100644
index 0000000..d474d02
--- /dev/null
+++ b/CSparse/Matrix/ibm32a
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diff --git a/CSparse/Matrix/ibm32b b/CSparse/Matrix/ibm32b
new file mode 100644
index 0000000..9a70e18
--- /dev/null
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diff --git a/CSparse/Matrix/lp_afiro b/CSparse/Matrix/lp_afiro
new file mode 100644
index 0000000..0e2c5ae
--- /dev/null
+++ b/CSparse/Matrix/lp_afiro
@@ -0,0 +1,102 @@
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diff --git a/CSparse/Matrix/mbeacxc b/CSparse/Matrix/mbeacxc
new file mode 100644
index 0000000..f9b4c06
--- /dev/null
+++ b/CSparse/Matrix/mbeacxc
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diff --git a/CSparse/Matrix/t1 b/CSparse/Matrix/t1
new file mode 100644
index 0000000..3fbb980
--- /dev/null
+++ b/CSparse/Matrix/t1
@@ -0,0 +1,10 @@
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diff --git a/CSparse/Matrix/west0067 b/CSparse/Matrix/west0067
new file mode 100644
index 0000000..09e42cb
--- /dev/null
+++ b/CSparse/Matrix/west0067
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diff --git a/CSparse/README.txt b/CSparse/README.txt
new file mode 100644
index 0000000..ee99f19
--- /dev/null
+++ b/CSparse/README.txt
@@ -0,0 +1,428 @@
+CSparse: a Concise Sparse Matrix package.
+Version 2.2.0, Copyright (c) 2006-2007, Timothy A. Davis, Mar 31, 2007.
+
+Refer to "Direct Methods for Sparse Linear Systems," Timothy A. Davis,
+SIAM, Philadelphia, 2006. No detailed user guide is included in this
+package; the user guide is the book itself.
+
+The algorithms contained in CSparse have been chosen with five goals in mind:
+(1) they must embody much of the theory behind sparse matrix algorithms,
+(2) they must be either asymptotically optimal in their run time and memory
+ usage or be fast in practice,
+(3) they must be concise so as to be easily understood and short enough to
+ print in the book,
+(4) they must cover a wide spectrum of matrix operations, and
+(5) they must be accurate and robust.
+The focus is on direct methods; iterative methods and solvers for
+eigenvalue problems are beyond the scope of this package.
+
+No detailed user guide is included in this package; the user guide is the
+book itself. Some indication of how to call the CSparse C routines is given
+by the M-files in the MATLAB/CSparse directory.
+
+Complex matrices are not supported, except for methods that operate only
+on the nonzero pattern of a matrix. A complex version of CSparse appears
+as a separate package, CXSparse ("Concise Extended Sparse matrix package").
+
+The performance of the sparse factorization methods in CSparse will not be
+competitive with UMFPACK or CHOLMOD, but the codes are much more concise and
+easy to understand (see the above goals). Other methods are competitive.
+
+Some of the MATLAB tests require the AMD package.
+See http://www.cise.ufl.edu/research/sparse for CSparse and the AMD ordering
+package. See the Doc/License.txt file for the license (GNU LGPL).
+
+To compile the C-library (./Source) and C demo programs (./Demo) just type
+"make" in this directory. This should work on any system with the "make"
+command. To run the exhaustive tests, type "make" in the Tcov directory
+(Linux is assumed). To compile the MATLAB mexFunctions type "make mex" in
+this directory, or just "make" in the MATLAB directory. To remove all files
+not in the original distribution, type "make distclean". I recommend that you
+use a different level of optimization than "cc -O", which was chosen so that
+the Makefile is portable. See Source/Makefile.
+
+You can simply type "cs_install" while in the CSparse/MATLAB directory to
+compile and install CSparse for use in MATLAB. This is especially useful for
+a typical Microsoft Windows system, which does not include "make". For more
+details, see CSparse/MATLAB/README.txt.
+
+--------------------------------------------------------------------------------
+Contents:
+--------------------------------------------------------------------------------
+
+Demo/ demo C programs that use CSparse
+Doc/ license and change log
+Makefile Makefile for the whole package
+MATLAB/ MATLAB interface, demos, and tests for CSparse
+Matrix/ sample matrices
+README.txt this file
+Source/ primary CSparse source files (C only, no MATLAB)
+Tcov/ CSparse tests
+
+--------------------------------------------------------------------------------
+./Doc: license and change log
+--------------------------------------------------------------------------------
+
+ChangeLog changes in CSparse since first release
+lesser.txt the GNU LGPL
+License.txt license (GNU LGPL)
+
+--------------------------------------------------------------------------------
+./Source: Primary source code for CSparse
+--------------------------------------------------------------------------------
+
+cs_add.c add sparse matrices
+cs_amd.c approximate minimum degree
+cs_chol.c sparse Cholesky
+cs_cholsol.c x=A\b using sparse Cholesky
+cs_compress.c convert a triplet form to compressed-column form
+cs_counts.c column counts for Cholesky and QR
+cs_cumsum.c cumulative sum
+cs_dfs.c depth-first-search
+cs_dmperm.c Dulmage-Mendelsohn permutation
+cs_droptol.c drop small entries from a sparse matrix
+cs_dropzeros.c drop zeros from a sparse matrix
+cs_dupl.c remove (and sum) duplicates
+cs_entry.c add an entry to a triplet matrix
+cs_ereach.c nonzero pattern of Cholesky L(k,:) from etree and triu(A(:,k))
+cs_etree.c find elimination tree
+cs_fkeep.c drop entries from a sparse matrix
+cs_gaxpy.c sparse matrix times dense matrix
+cs.h include file for CSparse
+cs_happly.c apply Householder reflection
+cs_house.c compute Householder reflection
+cs_ipvec.c x(p)=b
+cs_leaf.c determine if j is a leaf of the skeleton matrix and find lca
+cs_load.c load a sparse matrix from a file
+cs_lsolve.c x=L\b
+cs_ltsolve.c x=L'\b
+cs_lu.c sparse LU factorization
+cs_lusol.c x=A\b using sparse LU factorization
+cs_malloc.c memory manager
+cs_maxtrans.c maximum transveral (permutation for zero-free diagonal)
+cs_multiply.c sparse matrix multiply
+cs_norm.c sparse matrix norm
+cs_permute.c permute a sparse matrix
+cs_pinv.c invert a permutation vector
+cs_post.c postorder an elimination tree
+cs_print.c print a sparse matrix
+cs_pvec.c x=b(p)
+cs_qr.c sparse QR
+cs_qrsol.c solve a least-squares problem
+cs_randperm.c random permutation
+cs_reach.c find nonzero pattern of x=L\b for sparse L and b
+cs_scatter.c scatter a sparse vector
+cs_scc.c strongly-connected components
+cs_schol.c symbolic Cholesky
+cs_spsolve.c x=G\b where G, x, and b are sparse, and G upper/lower triangular
+cs_sqr.c symbolic QR (also can be used for LU)
+cs_symperm.c symmetric permutation of a sparse matrix
+cs_tdfs.c depth-first-search of a tree
+cs_transpose.c transpose a sparse matrix
+cs_updown.c sparse rank-1 Cholesky update/downate
+cs_usolve.c x=U\b
+cs_util.c various utilities (allocate/free matrices, workspace, etc)
+cs_utsolve.c x=U'\b
+Makefile Makefile for CSparse
+README.txt README file for CSparse
+
+
+--------------------------------------------------------------------------------
+./Demo: C program demos
+--------------------------------------------------------------------------------
+
+cs_demo1.c read a matrix from a file and perform basic matrix operations
+cs_demo2.c read a matrix from a file and solve a linear system
+cs_demo3.c read a matrix, solve a linear system, update/downdate
+cs_demo.c support routines for cs_demo*.c
+cs_demo.h include file for demo programs
+cs_demo.out output of "make", which runs the demos on some matrices
+Makefile Makefile for Demo programs
+readhb.f read a Rutherford-Boeing matrix
+README.txt Demo README file
+
+
+--------------------------------------------------------------------------------
+./MATLAB: MATLAB interface, demos, and tests
+--------------------------------------------------------------------------------
+
+cs_install.m MATLAB function for compiling and installing CSparse for MATLAB
+CSparse/ MATLAB interface for CSparse
+Demo/ MATLAB demos for CSparse
+Makefile MATLAB interface Makefile
+README.txt MATLAB README file
+Test/ MATLAB test for CSparse, and "textbook" routines
+UFget/ MATLAB interface to UF Sparse Matrix Collection
+
+
+--------------------------------------------------------------------------------
+./MATLAB/CSparse: MATLAB interface for CSparse
+--------------------------------------------------------------------------------
+
+Contents.m Contents of MATLAB interface to CSparse
+cs_add.m add two sparse matrices
+cs_add_mex.c
+cs_amd.m approximate minimum degree
+cs_amd_mex.c
+cs_chol.m sparse Cholesky
+cs_chol_mex.c
+cs_cholsol.m x=A\b using a sparse Cholesky
+cs_cholsol_mex.c
+cs_counts.m column counts for Cholesky or QR (like "symbfact" in MATLAB)
+cs_counts_mex.c
+cs_dmperm.m Dulmage-Mendelsohn permutation
+cs_dmperm_mex.c
+cs_dmsol.m x=A\b using dmperm
+cs_dmspy.m plot a picture of a dmperm-permuted matrix
+cs_droptol.m drop small entries
+cs_droptol_mex.c
+cs_esep.m find edge separator
+cs_etree.m compute elimination tree
+cs_etree_mex.c
+cs_gaxpy.m sparse matrix times dense vector
+cs_gaxpy_mex.c
+cs_lsolve.m x=L\b where L is lower triangular
+cs_lsolve_mex.c
+cs_ltsolve.m x=L'\b where L is lower triangular
+cs_ltsolve_mex.c
+cs_lu.m sparse LU factorization
+cs_lu_mex.c
+cs_lusol.m x=A\b using sparse LU factorization
+cs_lusol_mex.c
+cs_make.m compiles CSparse for use in MATLAB
+cs_mex.c support routines for CSparse mexFunctions
+cs_mex.h
+cs_multiply.m sparse matrix multiply
+cs_multiply_mex.c
+cs_must_compile.m determine if a source file needs to be compiled with mex
+cs_nd.m nested dissection
+cs_nsep.m find node separator
+cs_permute.m permute a sparse matrix
+cs_permute_mex.c
+cs_print.m print a sparse matrix
+cs_print_mex.c
+cs_qleft.m apply Householder vectors to the left
+cs_qright.m apply Householder vectors to the right
+cs_qr.m sparse QR factorization
+cs_qr_mex.c
+cs_qrsol.m solve a sparse least squares problem
+cs_qrsol_mex.c
+cs_randperm.m randdom permutation
+cs_randperm_mex.c
+cs_scc.m strongly-connected components
+cs_scc_mex.c
+cs_sep.m convert an edge separator into a node separator
+cs_sparse.m convert a triplet form matrix to a compress-column form
+cs_sparse_mex.c
+cs_symperm.m symmetric permutation of a sparse matrix
+cs_symperm_mex.c
+cs_sqr.m symbolic QR ordering and analysis
+cs_sqr_mex.c
+cs_thumb_mex.c compute small "thumbnail" of a sparse matrix (for cspy).
+cs_transpose.m transpose a sparse matrix
+cs_transpose_mex.c
+cs_updown.m sparse Cholesky update/downdate
+cs_updown_mex.c
+cs_usolve.m x=U\b where U is upper triangular
+cs_usolve_mex.c
+cs_utsolve.m x=U'\b where U is upper triangular
+cs_utsolve_mex.c
+cspy.m a color "spy"
+Makefile Makefile for CSparse MATLAB interface
+README.txt README file for CSparse MATLAB interface
+
+
+--------------------------------------------------------------------------------
+./MATLAB/Demo: MATLAB demos for CSparse
+--------------------------------------------------------------------------------
+
+Contents.m Contents of MATLAB demo for CSparse
+cs_demo.m run all MATLAB demos for CSparse
+cs_demo1.m MATLAB version of Demo/cs_demo1.c
+cs_demo2.m MATLAB version of Demo/cs_demo2.c
+cs_demo3.m MATLAB version of Demo/cs_demo3.c
+private/ private functions for MATLAB demos
+README.txt README file for CSparse MATLAB demo
+
+
+--------------------------------------------------------------------------------
+./MATLAB/Demo/private: private functions for MATLAB demos
+--------------------------------------------------------------------------------
+
+demo2.m demo 2
+demo3.m demo 3
+ex_1.m example 1
+ex2.m example 2
+ex3.m example 3
+frand.m generate a random finite-element matrix
+get_problem.m get a matrix
+is_sym.m determine if a matrix is symmetric
+mesh2d1.m construct a 2D mesh (method 1)
+mesh2d2.m construct a 2D mesh (method 2)
+mesh3d1.m construct a 3D mesh (method 1)
+mesh3d2.m construct a 3D mesh (method 2)
+print_order.m print the ordering method used
+resid.m compute residual
+rhs.m create right-hand-side
+
+
+--------------------------------------------------------------------------------
+./MATLAB/Test: Extensive test of CSparse, in MATLAB
+--------------------------------------------------------------------------------
+
+Makefile Makefile for MATLAB Test directory
+README.txt README file for MATLAB/Test
+Contents.m Contents of MATLAB/Test, "textbook" files only
+
+chol_downdate.m downdate a Cholesky factorization.
+chol_left.m left-looking Cholesky factorization.
+chol_left2.m left-looking Cholesky factorization, more details.
+chol_right.m right-looking Cholesky factorization.
+chol_super.m left-looking "supernodal" Cholesky factorization.
+chol_up.m up-looking Cholesky factorization.
+chol_update.m update a Cholesky factorization.
+chol_updown.m update or downdate a Cholesky factorization.
+cond1est.m 1-norm condition estimate.
+cs_fiedler.m the Fiedler vector of a connected graph.
+givens2.m find a Givens rotation.
+house.m find a Householder reflection.
+lu_left.m left-looking LU factorization.
+lu_right.m right-looking LU factorization.
+lu_rightp.m right-looking LU factorization, with partial pivoting.
+lu_rightpr.m recursive right-looking LU, with partial pivoting.
+lu_rightr.m recursive right-looking LU.
+norm1est.m 1-norm estimate.
+qr_givens.m Givens-rotation QR factorization.
+qr_givens_full.m Givens-rotation QR factorization, for full matrices.
+qr_left.m left-looking Householder QR factorization.
+qr_right.m right-looking Householder QR factorization.
+cs_fiedler.m Fiedler vector
+
+cs_frand.m generate a random finite-element matrix
+cs_frand_mex.c
+cs_ipvec.m x(p)=b
+cs_ipvec_mex.c
+cs_maxtransr.m recursive maximum matching algorithm
+cs_maxtransr_mex.c
+cs_pvec.m x=b(p)
+cs_pvec_mex.c interface for cs_pvec
+cs_reach.m non-recursive reach (interface to CSparse cs_reach)
+cs_reach_mex.c non-recursive x=spones(L\sparse(b))
+cs_reachr.m recursive reach (interface to CSparse cs_reachr)
+cs_reachr_mex.c
+cs_rowcnt.m row counts for sparse Cholesky
+cs_rowcnt_mex.c row counts for sparse Cholesky
+cs_sparse2.m same as cs_sparse, to test cs_entry function
+cs_sparse2_mex.c like cs_sparse, but for testing cs_entry
+
+cs_test_make.m compiles MATLAB tests
+
+check_if_same.m check if two inputs are identical or not
+choldn.m Cholesky downdate
+cholup.m Cholesky update, using Given's rotations
+cholupdown.m Cholesky update/downdate (Bischof, Pan, and Tang method)
+cs_q1.m construct Q from Householder vectors
+cs_test_make.m compiles the CSparse, Demo, and Test mexFunctions.
+dmperm_test.m test cs_dmperm
+chol_example.m simple Cholesky factorization example
+etree_sample.m construct a sample etree and symbolic factorization
+gqr3.m QR factorization, based on Givens rotations
+happly.m apply Householder reflection to a vector
+hmake1.m construct a Householder reflection
+mynormest1.m estimate norm(A,1), using LU factorization (L*U = P*A*Q).
+myqr.m QR factorization using Householder reflections
+another_colormap.m try another color map
+cspy_test.m test cspy and cs_dmspy
+qr2.m QR factorization based on Householder reflections
+sample_colormap.m try a colormap for use in cspy
+signum.m compute and display the sign of a column vector x
+sqr_example.m test cs_sqr
+dmspy_test.m test cspy, cs_dmspy, and cs_dmperm
+test_qr.m test various QR factorization methods
+test_randperms.m test random permutations
+testh.m test Householder reflections
+test_qr1.m test QR factorizations
+test_qrsol.m test cs_qrsol
+test_sep.m test cs_sep, and compare with Gilbert's meshpart vtxsep
+testall.m test all CSparse functions (run tests 1 to 28 below)
+test1.m test cs_transpose
+test2.m test cs_sparse
+test3.m test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol
+test4.m test cs_multiply
+test5.m test cs_add
+test6.m test cs_reach, cs_reachr, cs_lsolve, cs_usolve
+test7.m test cs_lu
+test8.m test cs_cholsol, cs_lusol
+test9.m test cs_qr
+test10.m test cs_qr
+test11.m test cs_rowcnt
+test12.m test cs_qr and compare with svd
+test13.m test cs_counts, cs_etree
+test14.m test cs_droptol
+test15.m test cs_amd
+test16.m test cs_amd
+test17.m test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol
+test18.m test iterative refinement after backslash
+test19.m test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc
+test20.m test cholupdown
+test21.m test cs_updown
+test22.m test cond1est
+test23.m test cs_dmspy
+test24.m test cs_fielder
+test25.m test cs_nd
+test26.m test cs_dmsol and cs_dmspy
+test27.m test cs_qr, cs_utsolve, cs_qrsol
+test28.m test cs_randperm, cs_dmperm
+
+
+--------------------------------------------------------------------------------
+./MATLAB/UFget: MATLAB interface for the UF Sparse Matrix Collection
+--------------------------------------------------------------------------------
+
+Contents.m Contents of UFget
+mat/ default directory where downloaded matrices will be put
+README.txt README file for UFget
+UFget_defaults.m default parameter settings
+UFget_example.m example of use
+UFget_install.m installs UFget temporarily (for current session)
+UFget_java.class read a url and load it in into MATLAB (compiled Java code)
+UFget_java.java read a url and load it in into MATLAB (Java source code)
+UFget_lookup.m look up a matrix in the index
+UFget.m UFget itself (primary user interface)
+UFweb.m open url for a matrix or collection
+mat/UF_Index.mat index of matrices in UF Sparse Matrix Collection
+
+
+--------------------------------------------------------------------------------
+./Matrix: Sample matrices, most from Rutherford/Boeing collection
+--------------------------------------------------------------------------------
+
+ash219 overdetermined pattern of Holland survey. Ashkenazi, 1974.
+bcsstk01 stiffness matrix for small generalized eigenvalue problem
+bcsstk16 stiffness matrix, Corp of Engineers dam
+fs_183_1 unsymmetric facsimile convergence matrix
+lp_afiro NETLIB afiro linear programming problem
+mbeacxc US economy, 1972. Dan Szyld, while at NYU
+t1 small example used in Chapter 2
+west0067 Cavett problem with 5 components (chemical eng., Westerberg)
+
+
+--------------------------------------------------------------------------------
+./Tcov: Exhaustive test coverage of CSparse
+--------------------------------------------------------------------------------
+
+covall same as covall.linux
+covall.linux find coverage (Linux)
+covall.sol find coverage (Solaris)
+cov.awk coverage summary
+cover print uncovered lines
+covs print uncovered lines
+cstcov_malloc_test.c malloc test
+cstcov_malloc_test.h
+cstcov_test.c main program for Tcov tests
+gcovs run gcov (Linux)
+Makefile Makefile for Tcov tests
+nil an empty matrix
+zero a 1-by-1 zero matrix
+README.txt README file for Tcov directory
+
diff --git a/CSparse/Source/README.txt b/CSparse/Source/README.txt
new file mode 100644
index 0000000..9507521
--- /dev/null
+++ b/CSparse/Source/README.txt
@@ -0,0 +1,3 @@
+CSparse/Source directory: primary ANSI C source code files for CSparse.
+All of these files are printed verbatim in the book. To compile the
+libcsparse.a C-callable library, just type "make" in this directory.
diff --git a/CSparse/Source/cs_add.c b/CSparse/Source/cs_add.c
new file mode 100644
index 0000000..2c3c146
--- /dev/null
+++ b/CSparse/Source/cs_add.c
@@ -0,0 +1,28 @@
+#include "cs.h"
+/* C = alpha*A + beta*B */
+cs *cs_add (const cs *A, const cs *B, double alpha, double beta)
+{
+ int p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values ;
+ double *x, *Bx, *Cx ;
+ cs *C ;
+ if (!CS_CSC (A) || !CS_CSC (B)) return (NULL) ; /* check inputs */
+ if (A->m != B->m || A->n != B->n) return (NULL) ;
+ m = A->m ; anz = A->p [A->n] ;
+ n = B->n ; Bp = B->p ; Bx = B->x ; bnz = Bp [n] ;
+ w = cs_calloc (m, sizeof (int)) ; /* get workspace */
+ values = (A->x != NULL) && (Bx != NULL) ;
+ x = values ? cs_malloc (m, sizeof (double)) : NULL ; /* get workspace */
+ C = cs_spalloc (m, n, anz + bnz, values, 0) ; /* allocate result*/
+ if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Cp [j] = nz ; /* column j of C starts here */
+ nz = cs_scatter (A, j, alpha, w, x, j+1, C, nz) ; /* alpha*A(:,j)*/
+ nz = cs_scatter (B, j, beta, w, x, j+1, C, nz) ; /* beta*B(:,j) */
+ if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ;
+ }
+ Cp [n] = nz ; /* finalize the last column of C */
+ cs_sprealloc (C, 0) ; /* remove extra space from C */
+ return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */
+}
diff --git a/CSparse/Source/cs_amd.c b/CSparse/Source/cs_amd.c
new file mode 100644
index 0000000..58b5d0e
--- /dev/null
+++ b/CSparse/Source/cs_amd.c
@@ -0,0 +1,364 @@
+#include "cs.h"
+/* clear w */
+static int cs_wclear (int mark, int lemax, int *w, int n)
+{
+ int k ;
+ if (mark < 2 || (mark + lemax < 0))
+ {
+ for (k = 0 ; k < n ; k++) if (w [k] != 0) w [k] = 1 ;
+ mark = 2 ;
+ }
+ return (mark) ; /* at this point, w [0..n-1] < mark holds */
+}
+
+/* keep off-diagonal entries; drop diagonal entries */
+static int cs_diag (int i, int j, double aij, void *other) { return (i != j) ; }
+
+/* p = amd(A+A') if symmetric is true, or amd(A'A) otherwise */
+int *cs_amd (int order, const cs *A) /* order 0:natural, 1:Chol, 2:LU, 3:QR */
+{
+ cs *C, *A2, *AT ;
+ int *Cp, *Ci, *last, *W, *len, *nv, *next, *P, *head, *elen, *degree, *w,
+ *hhead, *ATp, *ATi, d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1,
+ k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi,
+ ok, cnz, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, n, m, t ;
+ unsigned int h ;
+ /* --- Construct matrix C ----------------------------------------------- */
+ if (!CS_CSC (A) || order <= 0 || order > 3) return (NULL) ; /* check */
+ AT = cs_transpose (A, 0) ; /* compute A' */
+ if (!AT) return (NULL) ;
+ m = A->m ; n = A->n ;
+ dense = CS_MAX (16, 10 * sqrt ((double) n)) ; /* find dense threshold */
+ dense = CS_MIN (n-2, dense) ;
+ if (order == 1 && n == m)
+ {
+ C = cs_add (A, AT, 0, 0) ; /* C = A+A' */
+ }
+ else if (order == 2)
+ {
+ ATp = AT->p ; /* drop dense columns from AT */
+ ATi = AT->i ;
+ for (p2 = 0, j = 0 ; j < m ; j++)
+ {
+ p = ATp [j] ; /* column j of AT starts here */
+ ATp [j] = p2 ; /* new column j starts here */
+ if (ATp [j+1] - p > dense) continue ; /* skip dense col j */
+ for ( ; p < ATp [j+1] ; p++) ATi [p2++] = ATi [p] ;
+ }
+ ATp [m] = p2 ; /* finalize AT */
+ A2 = cs_transpose (AT, 0) ; /* A2 = AT' */
+ C = A2 ? cs_multiply (AT, A2) : NULL ; /* C=A'*A with no dense rows */
+ cs_spfree (A2) ;
+ }
+ else
+ {
+ C = cs_multiply (AT, A) ; /* C=A'*A */
+ }
+ cs_spfree (AT) ;
+ if (!C) return (NULL) ;
+ cs_fkeep (C, &cs_diag, NULL) ; /* drop diagonal entries */
+ Cp = C->p ;
+ cnz = Cp [n] ;
+ P = cs_malloc (n+1, sizeof (int)) ; /* allocate result */
+ W = cs_malloc (8*(n+1), sizeof (int)) ; /* get workspace */
+ t = cnz + cnz/5 + 2*n ; /* add elbow room to C */
+ if (!P || !W || !cs_sprealloc (C, t)) return (cs_idone (P, C, W, 0)) ;
+ len = W ; nv = W + (n+1) ; next = W + 2*(n+1) ;
+ head = W + 3*(n+1) ; elen = W + 4*(n+1) ; degree = W + 5*(n+1) ;
+ w = W + 6*(n+1) ; hhead = W + 7*(n+1) ;
+ last = P ; /* use P as workspace for last */
+ /* --- Initialize quotient graph ---------------------------------------- */
+ for (k = 0 ; k < n ; k++) len [k] = Cp [k+1] - Cp [k] ;
+ len [n] = 0 ;
+ nzmax = C->nzmax ;
+ Ci = C->i ;
+ for (i = 0 ; i <= n ; i++)
+ {
+ head [i] = -1 ; /* degree list i is empty */
+ last [i] = -1 ;
+ next [i] = -1 ;
+ hhead [i] = -1 ; /* hash list i is empty */
+ nv [i] = 1 ; /* node i is just one node */
+ w [i] = 1 ; /* node i is alive */
+ elen [i] = 0 ; /* Ek of node i is empty */
+ degree [i] = len [i] ; /* degree of node i */
+ }
+ mark = cs_wclear (0, 0, w, n) ; /* clear w */
+ elen [n] = -2 ; /* n is a dead element */
+ Cp [n] = -1 ; /* n is a root of assembly tree */
+ w [n] = 0 ; /* n is a dead element */
+ /* --- Initialize degree lists ------------------------------------------ */
+ for (i = 0 ; i < n ; i++)
+ {
+ d = degree [i] ;
+ if (d == 0) /* node i is empty */
+ {
+ elen [i] = -2 ; /* element i is dead */
+ nel++ ;
+ Cp [i] = -1 ; /* i is a root of assembly tree */
+ w [i] = 0 ;
+ }
+ else if (d > dense) /* node i is dense */
+ {
+ nv [i] = 0 ; /* absorb i into element n */
+ elen [i] = -1 ; /* node i is dead */
+ nel++ ;
+ Cp [i] = CS_FLIP (n) ;
+ nv [n]++ ;
+ }
+ else
+ {
+ if (head [d] != -1) last [head [d]] = i ;
+ next [i] = head [d] ; /* put node i in degree list d */
+ head [d] = i ;
+ }
+ }
+ while (nel < n) /* while (selecting pivots) do */
+ {
+ /* --- Select node of minimum approximate degree -------------------- */
+ for (k = -1 ; mindeg < n && (k = head [mindeg]) == -1 ; mindeg++) ;
+ if (next [k] != -1) last [next [k]] = -1 ;
+ head [mindeg] = next [k] ; /* remove k from degree list */
+ elenk = elen [k] ; /* elenk = |Ek| */
+ nvk = nv [k] ; /* # of nodes k represents */
+ nel += nvk ; /* nv[k] nodes of A eliminated */
+ /* --- Garbage collection ------------------------------------------- */
+ if (elenk > 0 && cnz + mindeg >= nzmax)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ if ((p = Cp [j]) >= 0) /* j is a live node or element */
+ {
+ Cp [j] = Ci [p] ; /* save first entry of object */
+ Ci [p] = CS_FLIP (j) ; /* first entry is now CS_FLIP(j) */
+ }
+ }
+ for (q = 0, p = 0 ; p < cnz ; ) /* scan all of memory */
+ {
+ if ((j = CS_FLIP (Ci [p++])) >= 0) /* found object j */
+ {
+ Ci [q] = Cp [j] ; /* restore first entry of object */
+ Cp [j] = q++ ; /* new pointer to object j */
+ for (k3 = 0 ; k3 < len [j]-1 ; k3++) Ci [q++] = Ci [p++] ;
+ }
+ }
+ cnz = q ; /* Ci [cnz...nzmax-1] now free */
+ }
+ /* --- Construct new element ---------------------------------------- */
+ dk = 0 ;
+ nv [k] = -nvk ; /* flag k as in Lk */
+ p = Cp [k] ;
+ pk1 = (elenk == 0) ? p : cnz ; /* do in place if elen[k] == 0 */
+ pk2 = pk1 ;
+ for (k1 = 1 ; k1 <= elenk + 1 ; k1++)
+ {
+ if (k1 > elenk)
+ {
+ e = k ; /* search the nodes in k */
+ pj = p ; /* list of nodes starts at Ci[pj]*/
+ ln = len [k] - elenk ; /* length of list of nodes in k */
+ }
+ else
+ {
+ e = Ci [p++] ; /* search the nodes in e */
+ pj = Cp [e] ;
+ ln = len [e] ; /* length of list of nodes in e */
+ }
+ for (k2 = 1 ; k2 <= ln ; k2++)
+ {
+ i = Ci [pj++] ;
+ if ((nvi = nv [i]) <= 0) continue ; /* node i dead, or seen */
+ dk += nvi ; /* degree[Lk] += size of node i */
+ nv [i] = -nvi ; /* negate nv[i] to denote i in Lk*/
+ Ci [pk2++] = i ; /* place i in Lk */
+ if (next [i] != -1) last [next [i]] = last [i] ;
+ if (last [i] != -1) /* remove i from degree list */
+ {
+ next [last [i]] = next [i] ;
+ }
+ else
+ {
+ head [degree [i]] = next [i] ;
+ }
+ }
+ if (e != k)
+ {
+ Cp [e] = CS_FLIP (k) ; /* absorb e into k */
+ w [e] = 0 ; /* e is now a dead element */
+ }
+ }
+ if (elenk != 0) cnz = pk2 ; /* Ci [cnz...nzmax] is free */
+ degree [k] = dk ; /* external degree of k - |Lk\i| */
+ Cp [k] = pk1 ; /* element k is in Ci[pk1..pk2-1] */
+ len [k] = pk2 - pk1 ;
+ elen [k] = -2 ; /* k is now an element */
+ /* --- Find set differences ----------------------------------------- */
+ mark = cs_wclear (mark, lemax, w, n) ; /* clear w if necessary */
+ for (pk = pk1 ; pk < pk2 ; pk++) /* scan 1: find |Le\Lk| */
+ {
+ i = Ci [pk] ;
+ if ((eln = elen [i]) <= 0) continue ;/* skip if elen[i] empty */
+ nvi = -nv [i] ; /* nv [i] was negated */
+ wnvi = mark - nvi ;
+ for (p = Cp [i] ; p <= Cp [i] + eln - 1 ; p++) /* scan Ei */
+ {
+ e = Ci [p] ;
+ if (w [e] >= mark)
+ {
+ w [e] -= nvi ; /* decrement |Le\Lk| */
+ }
+ else if (w [e] != 0) /* ensure e is a live element */
+ {
+ w [e] = degree [e] + wnvi ; /* 1st time e seen in scan 1 */
+ }
+ }
+ }
+ /* --- Degree update ------------------------------------------------ */
+ for (pk = pk1 ; pk < pk2 ; pk++) /* scan2: degree update */
+ {
+ i = Ci [pk] ; /* consider node i in Lk */
+ p1 = Cp [i] ;
+ p2 = p1 + elen [i] - 1 ;
+ pn = p1 ;
+ for (h = 0, d = 0, p = p1 ; p <= p2 ; p++) /* scan Ei */
+ {
+ e = Ci [p] ;
+ if (w [e] != 0) /* e is an unabsorbed element */
+ {
+ dext = w [e] - mark ; /* dext = |Le\Lk| */
+ if (dext > 0)
+ {
+ d += dext ; /* sum up the set differences */
+ Ci [pn++] = e ; /* keep e in Ei */
+ h += e ; /* compute the hash of node i */
+ }
+ else
+ {
+ Cp [e] = CS_FLIP (k) ; /* aggressive absorb. e->k */
+ w [e] = 0 ; /* e is a dead element */
+ }
+ }
+ }
+ elen [i] = pn - p1 + 1 ; /* elen[i] = |Ei| */
+ p3 = pn ;
+ p4 = p1 + len [i] ;
+ for (p = p2 + 1 ; p < p4 ; p++) /* prune edges in Ai */
+ {
+ j = Ci [p] ;
+ if ((nvj = nv [j]) <= 0) continue ; /* node j dead or in Lk */
+ d += nvj ; /* degree(i) += |j| */
+ Ci [pn++] = j ; /* place j in node list of i */
+ h += j ; /* compute hash for node i */
+ }
+ if (d == 0) /* check for mass elimination */
+ {
+ Cp [i] = CS_FLIP (k) ; /* absorb i into k */
+ nvi = -nv [i] ;
+ dk -= nvi ; /* |Lk| -= |i| */
+ nvk += nvi ; /* |k| += nv[i] */
+ nel += nvi ;
+ nv [i] = 0 ;
+ elen [i] = -1 ; /* node i is dead */
+ }
+ else
+ {
+ degree [i] = CS_MIN (degree [i], d) ; /* update degree(i) */
+ Ci [pn] = Ci [p3] ; /* move first node to end */
+ Ci [p3] = Ci [p1] ; /* move 1st el. to end of Ei */
+ Ci [p1] = k ; /* add k as 1st element in of Ei */
+ len [i] = pn - p1 + 1 ; /* new len of adj. list of node i */
+ h %= n ; /* finalize hash of i */
+ next [i] = hhead [h] ; /* place i in hash bucket */
+ hhead [h] = i ;
+ last [i] = h ; /* save hash of i in last[i] */
+ }
+ } /* scan2 is done */
+ degree [k] = dk ; /* finalize |Lk| */
+ lemax = CS_MAX (lemax, dk) ;
+ mark = cs_wclear (mark+lemax, lemax, w, n) ; /* clear w */
+ /* --- Supernode detection ------------------------------------------ */
+ for (pk = pk1 ; pk < pk2 ; pk++)
+ {
+ i = Ci [pk] ;
+ if (nv [i] >= 0) continue ; /* skip if i is dead */
+ h = last [i] ; /* scan hash bucket of node i */
+ i = hhead [h] ;
+ hhead [h] = -1 ; /* hash bucket will be empty */
+ for ( ; i != -1 && next [i] != -1 ; i = next [i], mark++)
+ {
+ ln = len [i] ;
+ eln = elen [i] ;
+ for (p = Cp [i]+1 ; p <= Cp [i] + ln-1 ; p++) w [Ci [p]] = mark;
+ jlast = i ;
+ for (j = next [i] ; j != -1 ; ) /* compare i with all j */
+ {
+ ok = (len [j] == ln) && (elen [j] == eln) ;
+ for (p = Cp [j] + 1 ; ok && p <= Cp [j] + ln - 1 ; p++)
+ {
+ if (w [Ci [p]] != mark) ok = 0 ; /* compare i and j*/
+ }
+ if (ok) /* i and j are identical */
+ {
+ Cp [j] = CS_FLIP (i) ; /* absorb j into i */
+ nv [i] += nv [j] ;
+ nv [j] = 0 ;
+ elen [j] = -1 ; /* node j is dead */
+ j = next [j] ; /* delete j from hash bucket */
+ next [jlast] = j ;
+ }
+ else
+ {
+ jlast = j ; /* j and i are different */
+ j = next [j] ;
+ }
+ }
+ }
+ }
+ /* --- Finalize new element------------------------------------------ */
+ for (p = pk1, pk = pk1 ; pk < pk2 ; pk++) /* finalize Lk */
+ {
+ i = Ci [pk] ;
+ if ((nvi = -nv [i]) <= 0) continue ;/* skip if i is dead */
+ nv [i] = nvi ; /* restore nv[i] */
+ d = degree [i] + dk - nvi ; /* compute external degree(i) */
+ d = CS_MIN (d, n - nel - nvi) ;
+ if (head [d] != -1) last [head [d]] = i ;
+ next [i] = head [d] ; /* put i back in degree list */
+ last [i] = -1 ;
+ head [d] = i ;
+ mindeg = CS_MIN (mindeg, d) ; /* find new minimum degree */
+ degree [i] = d ;
+ Ci [p++] = i ; /* place i in Lk */
+ }
+ nv [k] = nvk ; /* # nodes absorbed into k */
+ if ((len [k] = p-pk1) == 0) /* length of adj list of element k*/
+ {
+ Cp [k] = -1 ; /* k is a root of the tree */
+ w [k] = 0 ; /* k is now a dead element */
+ }
+ if (elenk != 0) cnz = p ; /* free unused space in Lk */
+ }
+ /* --- Postordering ----------------------------------------------------- */
+ for (i = 0 ; i < n ; i++) Cp [i] = CS_FLIP (Cp [i]) ;/* fix assembly tree */
+ for (j = 0 ; j <= n ; j++) head [j] = -1 ;
+ for (j = n ; j >= 0 ; j--) /* place unordered nodes in lists */
+ {
+ if (nv [j] > 0) continue ; /* skip if j is an element */
+ next [j] = head [Cp [j]] ; /* place j in list of its parent */
+ head [Cp [j]] = j ;
+ }
+ for (e = n ; e >= 0 ; e--) /* place elements in lists */
+ {
+ if (nv [e] <= 0) continue ; /* skip unless e is an element */
+ if (Cp [e] != -1)
+ {
+ next [e] = head [Cp [e]] ; /* place e in list of its parent */
+ head [Cp [e]] = e ;
+ }
+ }
+ for (k = 0, i = 0 ; i <= n ; i++) /* postorder the assembly tree */
+ {
+ if (Cp [i] == -1) k = cs_tdfs (i, k, head, next, P, w) ;
+ }
+ return (cs_idone (P, C, W, 1)) ;
+}
diff --git a/CSparse/Source/cs_chol.c b/CSparse/Source/cs_chol.c
new file mode 100644
index 0000000..5eb12b3
--- /dev/null
+++ b/CSparse/Source/cs_chol.c
@@ -0,0 +1,58 @@
+#include "cs.h"
+/* L = chol (A, [pinv parent cp]), pinv is optional */
+csn *cs_chol (const cs *A, const css *S)
+{
+ double d, lki, *Lx, *x, *Cx ;
+ int top, i, p, k, n, *Li, *Lp, *cp, *pinv, *s, *c, *parent, *Cp, *Ci ;
+ cs *L, *C, *E ;
+ csn *N ;
+ if (!CS_CSC (A) || !S || !S->cp || !S->parent) return (NULL) ;
+ n = A->n ;
+ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */
+ c = cs_malloc (2*n, sizeof (int)) ; /* get int workspace */
+ x = cs_malloc (n, sizeof (double)) ; /* get double workspace */
+ cp = S->cp ; pinv = S->pinv ; parent = S->parent ;
+ C = pinv ? cs_symperm (A, pinv, 1) : ((cs *) A) ;
+ E = pinv ? C : NULL ; /* E is alias for A, or a copy E=A(p,p) */
+ if (!N || !c || !x || !C) return (cs_ndone (N, E, c, x, 0)) ;
+ s = c + n ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ N->L = L = cs_spalloc (n, n, cp [n], 1, 0) ; /* allocate result */
+ if (!L) return (cs_ndone (N, E, c, x, 0)) ;
+ Lp = L->p ; Li = L->i ; Lx = L->x ;
+ for (k = 0 ; k < n ; k++) Lp [k] = c [k] = cp [k] ;
+ for (k = 0 ; k < n ; k++) /* compute L(:,k) for L*L' = C */
+ {
+ /* --- Nonzero pattern of L(k,:) ------------------------------------ */
+ top = cs_ereach (C, k, parent, s, c) ; /* find pattern of L(k,:) */
+ x [k] = 0 ; /* x (0:k) is now zero */
+ for (p = Cp [k] ; p < Cp [k+1] ; p++) /* x = full(triu(C(:,k))) */
+ {
+ if (Ci [p] <= k) x [Ci [p]] = Cx [p] ;
+ }
+ d = x [k] ; /* d = C(k,k) */
+ x [k] = 0 ; /* clear x for k+1st iteration */
+ /* --- Triangular solve --------------------------------------------- */
+ for ( ; top < n ; top++) /* solve L(0:k-1,0:k-1) * x = C(:,k) */
+ {
+ i = s [top] ; /* s [top..n-1] is pattern of L(k,:) */
+ lki = x [i] / Lx [Lp [i]] ; /* L(k,i) = x (i) / L(i,i) */
+ x [i] = 0 ; /* clear x for k+1st iteration */
+ for (p = Lp [i] + 1 ; p < c [i] ; p++)
+ {
+ x [Li [p]] -= Lx [p] * lki ;
+ }
+ d -= lki * lki ; /* d = d - L(k,i)*L(k,i) */
+ p = c [i]++ ;
+ Li [p] = k ; /* store L(k,i) in column i */
+ Lx [p] = lki ;
+ }
+ /* --- Compute L(k,k) ----------------------------------------------- */
+ if (d <= 0) return (cs_ndone (N, E, c, x, 0)) ; /* not pos def */
+ p = c [k]++ ;
+ Li [p] = k ; /* store L(k,k) = sqrt (d) in column k */
+ Lx [p] = sqrt (d) ;
+ }
+ Lp [n] = cp [n] ; /* finalize L */
+ return (cs_ndone (N, E, c, x, 1)) ; /* success: free E,s,x; return N */
+}
diff --git a/CSparse/Source/cs_cholsol.c b/CSparse/Source/cs_cholsol.c
new file mode 100644
index 0000000..f3cf414
--- /dev/null
+++ b/CSparse/Source/cs_cholsol.c
@@ -0,0 +1,26 @@
+#include "cs.h"
+/* x=A\b where A is symmetric positive definite; b overwritten with solution */
+int cs_cholsol (int order, const cs *A, double *b)
+{
+ double *x ;
+ css *S ;
+ csn *N ;
+ int n, ok ;
+ if (!CS_CSC (A) || !b) return (0) ; /* check inputs */
+ n = A->n ;
+ S = cs_schol (order, A) ; /* ordering and symbolic analysis */
+ N = cs_chol (A, S) ; /* numeric Cholesky factorization */
+ x = cs_malloc (n, sizeof (double)) ; /* get workspace */
+ ok = (S && N && x) ;
+ if (ok)
+ {
+ cs_ipvec (S->pinv, b, x, n) ; /* x = P*b */
+ cs_lsolve (N->L, x) ; /* x = L\x */
+ cs_ltsolve (N->L, x) ; /* x = L'\x */
+ cs_pvec (S->pinv, x, b, n) ; /* b = P'*x */
+ }
+ cs_free (x) ;
+ cs_sfree (S) ;
+ cs_nfree (N) ;
+ return (ok) ;
+}
diff --git a/CSparse/Source/cs_compress.c b/CSparse/Source/cs_compress.c
new file mode 100644
index 0000000..d18e840
--- /dev/null
+++ b/CSparse/Source/cs_compress.c
@@ -0,0 +1,22 @@
+#include "cs.h"
+/* C = compressed-column form of a triplet matrix T */
+cs *cs_compress (const cs *T)
+{
+ int m, n, nz, p, k, *Cp, *Ci, *w, *Ti, *Tj ;
+ double *Cx, *Tx ;
+ cs *C ;
+ if (!CS_TRIPLET (T)) return (NULL) ; /* check inputs */
+ m = T->m ; n = T->n ; Ti = T->i ; Tj = T->p ; Tx = T->x ; nz = T->nz ;
+ C = cs_spalloc (m, n, nz, Tx != NULL, 0) ; /* allocate result */
+ w = cs_calloc (n, sizeof (int)) ; /* get workspace */
+ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ for (k = 0 ; k < nz ; k++) w [Tj [k]]++ ; /* column counts */
+ cs_cumsum (Cp, w, n) ; /* column pointers */
+ for (k = 0 ; k < nz ; k++)
+ {
+ Ci [p = w [Tj [k]]++] = Ti [k] ; /* A(i,j) is the pth entry in C */
+ if (Cx) Cx [p] = Tx [k] ;
+ }
+ return (cs_done (C, w, NULL, 1)) ; /* success; free w and return C */
+}
diff --git a/CSparse/Source/cs_counts.c b/CSparse/Source/cs_counts.c
new file mode 100644
index 0000000..ff32b6f
--- /dev/null
+++ b/CSparse/Source/cs_counts.c
@@ -0,0 +1,61 @@
+#include "cs.h"
+/* column counts of LL'=A or LL'=A'A, given parent & post ordering */
+#define HEAD(k,j) (ata ? head [k] : j)
+#define NEXT(J) (ata ? next [J] : -1)
+static void init_ata (cs *AT, const int *post, int *w, int **head, int **next)
+{
+ int i, k, p, m = AT->n, n = AT->m, *ATp = AT->p, *ATi = AT->i ;
+ *head = w+4*n, *next = w+5*n+1 ;
+ for (k = 0 ; k < n ; k++) w [post [k]] = k ; /* invert post */
+ for (i = 0 ; i < m ; i++)
+ {
+ for (k = n, p = ATp[i] ; p < ATp[i+1] ; p++) k = CS_MIN (k, w [ATi[p]]);
+ (*next) [i] = (*head) [k] ; /* place row i in linked list k */
+ (*head) [k] = i ;
+ }
+}
+int *cs_counts (const cs *A, const int *parent, const int *post, int ata)
+{
+ int i, j, k, n, m, J, s, p, q, jleaf, *ATp, *ATi, *maxfirst, *prevleaf,
+ *ancestor, *head = NULL, *next = NULL, *colcount, *w, *first, *delta ;
+ cs *AT ;
+ if (!CS_CSC (A) || !parent || !post) return (NULL) ; /* check inputs */
+ m = A->m ; n = A->n ;
+ s = 4*n + (ata ? (n+m+1) : 0) ;
+ delta = colcount = cs_malloc (n, sizeof (int)) ; /* allocate result */
+ w = cs_malloc (s, sizeof (int)) ; /* get workspace */
+ AT = cs_transpose (A, 0) ; /* AT = A' */
+ if (!AT || !colcount || !w) return (cs_idone (colcount, AT, w, 0)) ;
+ ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ;
+ for (k = 0 ; k < s ; k++) w [k] = -1 ; /* clear workspace w [0..s-1] */
+ for (k = 0 ; k < n ; k++) /* find first [j] */
+ {
+ j = post [k] ;
+ delta [j] = (first [j] == -1) ? 1 : 0 ; /* delta[j]=1 if j is a leaf */
+ for ( ; j != -1 && first [j] == -1 ; j = parent [j]) first [j] = k ;
+ }
+ ATp = AT->p ; ATi = AT->i ;
+ if (ata) init_ata (AT, post, w, &head, &next) ;
+ for (i = 0 ; i < n ; i++) ancestor [i] = i ; /* each node in its own set */
+ for (k = 0 ; k < n ; k++)
+ {
+ j = post [k] ; /* j is the kth node in postordered etree */
+ if (parent [j] != -1) delta [parent [j]]-- ; /* j is not a root */
+ for (J = HEAD (k,j) ; J != -1 ; J = NEXT (J)) /* J=j for LL'=A case */
+ {
+ for (p = ATp [J] ; p < ATp [J+1] ; p++)
+ {
+ i = ATi [p] ;
+ q = cs_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf);
+ if (jleaf >= 1) delta [j]++ ; /* A(i,j) is in skeleton */
+ if (jleaf == 2) delta [q]-- ; /* account for overlap in q */
+ }
+ }
+ if (parent [j] != -1) ancestor [j] = parent [j] ;
+ }
+ for (j = 0 ; j < n ; j++) /* sum up delta's of each child */
+ {
+ if (parent [j] != -1) colcount [parent [j]] += colcount [j] ;
+ }
+ return (cs_idone (colcount, AT, w, 1)) ; /* success: free workspace */
+}
diff --git a/CSparse/Source/cs_cumsum.c b/CSparse/Source/cs_cumsum.c
new file mode 100644
index 0000000..b8b7778
--- /dev/null
+++ b/CSparse/Source/cs_cumsum.c
@@ -0,0 +1,17 @@
+#include "cs.h"
+/* p [0..n] = cumulative sum of c [0..n-1], and then copy p [0..n-1] into c */
+double cs_cumsum (int *p, int *c, int n)
+{
+ int i, nz = 0 ;
+ double nz2 = 0 ;
+ if (!p || !c) return (-1) ; /* check inputs */
+ for (i = 0 ; i < n ; i++)
+ {
+ p [i] = nz ;
+ nz += c [i] ;
+ nz2 += c [i] ; /* also in double to avoid int overflow */
+ c [i] = p [i] ; /* also copy p[0..n-1] back into c[0..n-1]*/
+ }
+ p [n] = nz ;
+ return (nz2) ; /* return sum (c [0..n-1]) */
+}
diff --git a/CSparse/Source/cs_dfs.c b/CSparse/Source/cs_dfs.c
new file mode 100644
index 0000000..250dcf3
--- /dev/null
+++ b/CSparse/Source/cs_dfs.c
@@ -0,0 +1,36 @@
+#include "cs.h"
+/* depth-first-search of the graph of a matrix, starting at node j */
+int cs_dfs (int j, cs *G, int top, int *xi, int *pstack, const int *pinv)
+{
+ int i, p, p2, done, jnew, head = 0, *Gp, *Gi ;
+ if (!CS_CSC (G) || !xi || !pstack) return (-1) ; /* check inputs */
+ Gp = G->p ; Gi = G->i ;
+ xi [0] = j ; /* initialize the recursion stack */
+ while (head >= 0)
+ {
+ j = xi [head] ; /* get j from the top of the recursion stack */
+ jnew = pinv ? (pinv [j]) : j ;
+ if (!CS_MARKED (Gp, j))
+ {
+ CS_MARK (Gp, j) ; /* mark node j as visited */
+ pstack [head] = (jnew < 0) ? 0 : CS_UNFLIP (Gp [jnew]) ;
+ }
+ done = 1 ; /* node j done if no unvisited neighbors */
+ p2 = (jnew < 0) ? 0 : CS_UNFLIP (Gp [jnew+1]) ;
+ for (p = pstack [head] ; p < p2 ; p++) /* examine all neighbors of j */
+ {
+ i = Gi [p] ; /* consider neighbor node i */
+ if (CS_MARKED (Gp, i)) continue ; /* skip visited node i */
+ pstack [head] = p ; /* pause depth-first search of node j */
+ xi [++head] = i ; /* start dfs at node i */
+ done = 0 ; /* node j is not done */
+ break ; /* break, to start dfs (i) */
+ }
+ if (done) /* depth-first search at node j is done */
+ {
+ head-- ; /* remove j from the recursion stack */
+ xi [--top] = j ; /* and place in the output stack */
+ }
+ }
+ return (top) ;
+}
diff --git a/CSparse/Source/cs_dmperm.c b/CSparse/Source/cs_dmperm.c
new file mode 100644
index 0000000..29f72f6
--- /dev/null
+++ b/CSparse/Source/cs_dmperm.c
@@ -0,0 +1,144 @@
+#include "cs.h"
+/* breadth-first search for coarse decomposition (C0,C1,R1 or R0,R3,C3) */
+static int cs_bfs (const cs *A, int n, int *wi, int *wj, int *queue,
+ const int *imatch, const int *jmatch, int mark)
+{
+ int *Ap, *Ai, head = 0, tail = 0, j, i, p, j2 ;
+ cs *C ;
+ for (j = 0 ; j < n ; j++) /* place all unmatched nodes in queue */
+ {
+ if (imatch [j] >= 0) continue ; /* skip j if matched */
+ wj [j] = 0 ; /* j in set C0 (R0 if transpose) */
+ queue [tail++] = j ; /* place unmatched col j in queue */
+ }
+ if (tail == 0) return (1) ; /* quick return if no unmatched nodes */
+ C = (mark == 1) ? ((cs *) A) : cs_transpose (A, 0) ;
+ if (!C) return (0) ; /* bfs of C=A' to find R3,C3 from R0 */
+ Ap = C->p ; Ai = C->i ;
+ while (head < tail) /* while queue is not empty */
+ {
+ j = queue [head++] ; /* get the head of the queue */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ if (wi [i] >= 0) continue ; /* skip if i is marked */
+ wi [i] = mark ; /* i in set R1 (C3 if transpose) */
+ j2 = jmatch [i] ; /* traverse alternating path to j2 */
+ if (wj [j2] >= 0) continue ;/* skip j2 if it is marked */
+ wj [j2] = mark ; /* j2 in set C1 (R3 if transpose) */
+ queue [tail++] = j2 ; /* add j2 to queue */
+ }
+ }
+ if (mark != 1) cs_spfree (C) ; /* free A' if it was created */
+ return (1) ;
+}
+
+/* collect matched rows and columns into p and q */
+static void cs_matched (int n, const int *wj, const int *imatch, int *p, int *q,
+ int *cc, int *rr, int set, int mark)
+{
+ int kc = cc [set], j ;
+ int kr = rr [set-1] ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (wj [j] != mark) continue ; /* skip if j is not in C set */
+ p [kr++] = imatch [j] ;
+ q [kc++] = j ;
+ }
+ cc [set+1] = kc ;
+ rr [set] = kr ;
+}
+
+/* collect unmatched rows into the permutation vector p */
+static void cs_unmatched (int m, const int *wi, int *p, int *rr, int set)
+{
+ int i, kr = rr [set] ;
+ for (i = 0 ; i < m ; i++) if (wi [i] == 0) p [kr++] = i ;
+ rr [set+1] = kr ;
+}
+
+/* return 1 if row i is in R2 */
+static int cs_rprune (int i, int j, double aij, void *other)
+{
+ int *rr = (int *) other ;
+ return (i >= rr [1] && i < rr [2]) ;
+}
+
+/* Given A, compute coarse and then fine dmperm */
+csd *cs_dmperm (const cs *A, int seed)
+{
+ int m, n, i, j, k, cnz, nc, *jmatch, *imatch, *wi, *wj, *pinv, *Cp, *Ci,
+ *ps, *rs, nb1, nb2, *p, *q, *cc, *rr, *r, *s, ok ;
+ cs *C ;
+ csd *D, *scc ;
+ /* --- Maximum matching ------------------------------------------------- */
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ m = A->m ; n = A->n ;
+ D = cs_dalloc (m, n) ; /* allocate result */
+ if (!D) return (NULL) ;
+ p = D->p ; q = D->q ; r = D->r ; s = D->s ; cc = D->cc ; rr = D->rr ;
+ jmatch = cs_maxtrans (A, seed) ; /* max transversal */
+ imatch = jmatch + m ; /* imatch = inverse of jmatch */
+ if (!jmatch) return (cs_ddone (D, NULL, jmatch, 0)) ;
+ /* --- Coarse decomposition --------------------------------------------- */
+ wi = r ; wj = s ; /* use r and s as workspace */
+ for (j = 0 ; j < n ; j++) wj [j] = -1 ; /* unmark all cols for bfs */
+ for (i = 0 ; i < m ; i++) wi [i] = -1 ; /* unmark all rows for bfs */
+ cs_bfs (A, n, wi, wj, q, imatch, jmatch, 1) ; /* find C1, R1 from C0*/
+ ok = cs_bfs (A, m, wj, wi, p, jmatch, imatch, 3) ; /* find R3, C3 from R0*/
+ if (!ok) return (cs_ddone (D, NULL, jmatch, 0)) ;
+ cs_unmatched (n, wj, q, cc, 0) ; /* unmatched set C0 */
+ cs_matched (n, wj, imatch, p, q, cc, rr, 1, 1) ; /* set R1 and C1 */
+ cs_matched (n, wj, imatch, p, q, cc, rr, 2, -1) ; /* set R2 and C2 */
+ cs_matched (n, wj, imatch, p, q, cc, rr, 3, 3) ; /* set R3 and C3 */
+ cs_unmatched (m, wi, p, rr, 3) ; /* unmatched set R0 */
+ cs_free (jmatch) ;
+ /* --- Fine decomposition ----------------------------------------------- */
+ pinv = cs_pinv (p, m) ; /* pinv=p' */
+ if (!pinv) return (cs_ddone (D, NULL, NULL, 0)) ;
+ C = cs_permute (A, pinv, q, 0) ;/* C=A(p,q) (it will hold A(R2,C2)) */
+ cs_free (pinv) ;
+ if (!C) return (cs_ddone (D, NULL, NULL, 0)) ;
+ Cp = C->p ;
+ nc = cc [3] - cc [2] ; /* delete cols C0, C1, and C3 from C */
+ if (cc [2] > 0) for (j = cc [2] ; j <= cc [3] ; j++) Cp [j-cc[2]] = Cp [j] ;
+ C->n = nc ;
+ if (rr [2] - rr [1] < m) /* delete rows R0, R1, and R3 from C */
+ {
+ cs_fkeep (C, cs_rprune, rr) ;
+ cnz = Cp [nc] ;
+ Ci = C->i ;
+ if (rr [1] > 0) for (k = 0 ; k < cnz ; k++) Ci [k] -= rr [1] ;
+ }
+ C->m = nc ;
+ scc = cs_scc (C) ; /* find strongly connected components of C*/
+ if (!scc) return (cs_ddone (D, C, NULL, 0)) ;
+ /* --- Combine coarse and fine decompositions --------------------------- */
+ ps = scc->p ; /* C(ps,ps) is the permuted matrix */
+ rs = scc->r ; /* kth block is rs[k]..rs[k+1]-1 */
+ nb1 = scc->nb ; /* # of blocks of A(R2,C2) */
+ for (k = 0 ; k < nc ; k++) wj [k] = q [ps [k] + cc [2]] ;
+ for (k = 0 ; k < nc ; k++) q [k + cc [2]] = wj [k] ;
+ for (k = 0 ; k < nc ; k++) wi [k] = p [ps [k] + rr [1]] ;
+ for (k = 0 ; k < nc ; k++) p [k + rr [1]] = wi [k] ;
+ nb2 = 0 ; /* create the fine block partitions */
+ r [0] = s [0] = 0 ;
+ if (cc [2] > 0) nb2++ ; /* leading coarse block A (R1, [C0 C1]) */
+ for (k = 0 ; k < nb1 ; k++) /* coarse block A (R2,C2) */
+ {
+ r [nb2] = rs [k] + rr [1] ; /* A (R2,C2) splits into nb1 fine blocks */
+ s [nb2] = rs [k] + cc [2] ;
+ nb2++ ;
+ }
+ if (rr [2] < m)
+ {
+ r [nb2] = rr [2] ; /* trailing coarse block A ([R3 R0], C3) */
+ s [nb2] = cc [3] ;
+ nb2++ ;
+ }
+ r [nb2] = m ;
+ s [nb2] = n ;
+ D->nb = nb2 ;
+ cs_dfree (scc) ;
+ return (cs_ddone (D, C, NULL, 1)) ;
+}
diff --git a/CSparse/Source/cs_droptol.c b/CSparse/Source/cs_droptol.c
new file mode 100644
index 0000000..2afb660
--- /dev/null
+++ b/CSparse/Source/cs_droptol.c
@@ -0,0 +1,9 @@
+#include "cs.h"
+static int cs_tol (int i, int j, double aij, void *tol)
+{
+ return (fabs (aij) > *((double *) tol)) ;
+}
+int cs_droptol (cs *A, double tol)
+{
+ return (cs_fkeep (A, &cs_tol, &tol)) ; /* keep all large entries */
+}
diff --git a/CSparse/Source/cs_dropzeros.c b/CSparse/Source/cs_dropzeros.c
new file mode 100644
index 0000000..441e54d
--- /dev/null
+++ b/CSparse/Source/cs_dropzeros.c
@@ -0,0 +1,9 @@
+#include "cs.h"
+static int cs_nonzero (int i, int j, double aij, void *other)
+{
+ return (aij != 0) ;
+}
+int cs_dropzeros (cs *A)
+{
+ return (cs_fkeep (A, &cs_nonzero, NULL)) ; /* keep all nonzero entries */
+}
diff --git a/CSparse/Source/cs_dupl.c b/CSparse/Source/cs_dupl.c
new file mode 100644
index 0000000..7a60d63
--- /dev/null
+++ b/CSparse/Source/cs_dupl.c
@@ -0,0 +1,34 @@
+#include "cs.h"
+/* remove duplicate entries from A */
+int cs_dupl (cs *A)
+{
+ int i, j, p, q, nz = 0, n, m, *Ap, *Ai, *w ;
+ double *Ax ;
+ if (!CS_CSC (A)) return (0) ; /* check inputs */
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ w = cs_malloc (m, sizeof (int)) ; /* get workspace */
+ if (!w) return (0) ; /* out of memory */
+ for (i = 0 ; i < m ; i++) w [i] = -1 ; /* row i not yet seen */
+ for (j = 0 ; j < n ; j++)
+ {
+ q = nz ; /* column j will start at q */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ; /* A(i,j) is nonzero */
+ if (w [i] >= q)
+ {
+ Ax [w [i]] += Ax [p] ; /* A(i,j) is a duplicate */
+ }
+ else
+ {
+ w [i] = nz ; /* record where row i occurs */
+ Ai [nz] = i ; /* keep A(i,j) */
+ Ax [nz++] = Ax [p] ;
+ }
+ }
+ Ap [j] = q ; /* record start of column j */
+ }
+ Ap [n] = nz ; /* finalize A */
+ cs_free (w) ; /* free workspace */
+ return (cs_sprealloc (A, 0)) ; /* remove extra space from A */
+}
diff --git a/CSparse/Source/cs_entry.c b/CSparse/Source/cs_entry.c
new file mode 100644
index 0000000..98f6788
--- /dev/null
+++ b/CSparse/Source/cs_entry.c
@@ -0,0 +1,13 @@
+#include "cs.h"
+/* add an entry to a triplet matrix; return 1 if ok, 0 otherwise */
+int cs_entry (cs *T, int i, int j, double x)
+{
+ if (!CS_TRIPLET (T) || i < 0 || j < 0) return (0) ; /* check inputs */
+ if (T->nz >= T->nzmax && !cs_sprealloc (T,2*(T->nzmax))) return (0) ;
+ if (T->x) T->x [T->nz] = x ;
+ T->i [T->nz] = i ;
+ T->p [T->nz++] = j ;
+ T->m = CS_MAX (T->m, i+1) ;
+ T->n = CS_MAX (T->n, j+1) ;
+ return (1) ;
+}
diff --git a/CSparse/Source/cs_ereach.c b/CSparse/Source/cs_ereach.c
new file mode 100644
index 0000000..c54213b
--- /dev/null
+++ b/CSparse/Source/cs_ereach.c
@@ -0,0 +1,23 @@
+#include "cs.h"
+/* find nonzero pattern of Cholesky L(k,1:k-1) using etree and triu(A(:,k)) */
+int cs_ereach (const cs *A, int k, const int *parent, int *s, int *w)
+{
+ int i, p, n, len, top, *Ap, *Ai ;
+ if (!CS_CSC (A) || !parent || !s || !w) return (-1) ; /* check inputs */
+ top = n = A->n ; Ap = A->p ; Ai = A->i ;
+ CS_MARK (w, k) ; /* mark node k as visited */
+ for (p = Ap [k] ; p < Ap [k+1] ; p++)
+ {
+ i = Ai [p] ; /* A(i,k) is nonzero */
+ if (i > k) continue ; /* only use upper triangular part of A */
+ for (len = 0 ; !CS_MARKED (w,i) ; i = parent [i]) /* traverse up etree*/
+ {
+ s [len++] = i ; /* L(k,i) is nonzero */
+ CS_MARK (w, i) ; /* mark i as visited */
+ }
+ while (len > 0) s [--top] = s [--len] ; /* push path onto stack */
+ }
+ for (p = top ; p < n ; p++) CS_MARK (w, s [p]) ; /* unmark all nodes */
+ CS_MARK (w, k) ; /* unmark node k */
+ return (top) ; /* s [top..n-1] contains pattern of L(k,:)*/
+}
diff --git a/CSparse/Source/cs_etree.c b/CSparse/Source/cs_etree.c
new file mode 100644
index 0000000..30712bc
--- /dev/null
+++ b/CSparse/Source/cs_etree.c
@@ -0,0 +1,30 @@
+#include "cs.h"
+/* compute the etree of A (using triu(A), or A'A without forming A'A */
+int *cs_etree (const cs *A, int ata)
+{
+ int i, k, p, m, n, inext, *Ap, *Ai, *w, *parent, *ancestor, *prev ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ;
+ parent = cs_malloc (n, sizeof (int)) ; /* allocate result */
+ w = cs_malloc (n + (ata ? m : 0), sizeof (int)) ; /* get workspace */
+ if (!w || !parent) return (cs_idone (parent, NULL, w, 0)) ;
+ ancestor = w ; prev = w + n ;
+ if (ata) for (i = 0 ; i < m ; i++) prev [i] = -1 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ parent [k] = -1 ; /* node k has no parent yet */
+ ancestor [k] = -1 ; /* nor does k have an ancestor */
+ for (p = Ap [k] ; p < Ap [k+1] ; p++)
+ {
+ i = ata ? (prev [Ai [p]]) : (Ai [p]) ;
+ for ( ; i != -1 && i < k ; i = inext) /* traverse from i to k */
+ {
+ inext = ancestor [i] ; /* inext = ancestor of i */
+ ancestor [i] = k ; /* path compression */
+ if (inext == -1) parent [i] = k ; /* no anc., parent is k */
+ }
+ if (ata) prev [Ai [p]] = k ;
+ }
+ }
+ return (cs_idone (parent, NULL, w, 1)) ;
+}
diff --git a/CSparse/Source/cs_fkeep.c b/CSparse/Source/cs_fkeep.c
new file mode 100644
index 0000000..0e32051
--- /dev/null
+++ b/CSparse/Source/cs_fkeep.c
@@ -0,0 +1,25 @@
+#include "cs.h"
+/* drop entries for which fkeep(A(i,j)) is false; return nz if OK, else -1 */
+int cs_fkeep (cs *A, int (*fkeep) (int, int, double, void *), void *other)
+{
+ int j, p, nz = 0, n, *Ap, *Ai ;
+ double *Ax ;
+ if (!CS_CSC (A) || !fkeep) return (-1) ; /* check inputs */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Ap [j] ; /* get current location of col j */
+ Ap [j] = nz ; /* record new location of col j */
+ for ( ; p < Ap [j+1] ; p++)
+ {
+ if (fkeep (Ai [p], j, Ax ? Ax [p] : 1, other))
+ {
+ if (Ax) Ax [nz] = Ax [p] ; /* keep A(i,j) */
+ Ai [nz++] = Ai [p] ;
+ }
+ }
+ }
+ Ap [n] = nz ; /* finalize A */
+ cs_sprealloc (A, 0) ; /* remove extra space from A */
+ return (nz) ;
+}
diff --git a/CSparse/Source/cs_gaxpy.c b/CSparse/Source/cs_gaxpy.c
new file mode 100644
index 0000000..580f600
--- /dev/null
+++ b/CSparse/Source/cs_gaxpy.c
@@ -0,0 +1,17 @@
+#include "cs.h"
+/* y = A*x+y */
+int cs_gaxpy (const cs *A, const double *x, double *y)
+{
+ int p, j, n, *Ap, *Ai ;
+ double *Ax ;
+ if (!CS_CSC (A) || !x || !y) return (0) ; /* check inputs */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ y [Ai [p]] += Ax [p] * x [j] ;
+ }
+ }
+ return (1) ;
+}
diff --git a/CSparse/Source/cs_happly.c b/CSparse/Source/cs_happly.c
new file mode 100644
index 0000000..b2d4346
--- /dev/null
+++ b/CSparse/Source/cs_happly.c
@@ -0,0 +1,19 @@
+#include "cs.h"
+/* apply the ith Householder vector to x */
+int cs_happly (const cs *V, int i, double beta, double *x)
+{
+ int p, *Vp, *Vi ;
+ double *Vx, tau = 0 ;
+ if (!CS_CSC (V) || !x) return (0) ; /* check inputs */
+ Vp = V->p ; Vi = V->i ; Vx = V->x ;
+ for (p = Vp [i] ; p < Vp [i+1] ; p++) /* tau = v'*x */
+ {
+ tau += Vx [p] * x [Vi [p]] ;
+ }
+ tau *= beta ; /* tau = beta*(v'*x) */
+ for (p = Vp [i] ; p < Vp [i+1] ; p++) /* x = x - v*tau */
+ {
+ x [Vi [p]] -= Vx [p] * tau ;
+ }
+ return (1) ;
+}
diff --git a/CSparse/Source/cs_house.c b/CSparse/Source/cs_house.c
new file mode 100644
index 0000000..5935f4c
--- /dev/null
+++ b/CSparse/Source/cs_house.c
@@ -0,0 +1,23 @@
+#include "cs.h"
+/* create a Householder reflection [v,beta,s]=house(x), overwrite x with v,
+ * where (I-beta*v*v')*x = s*e1. See Algo 5.1.1, Golub & Van Loan, 3rd ed. */
+double cs_house (double *x, double *beta, int n)
+{
+ double s, sigma = 0 ;
+ int i ;
+ if (!x || !beta) return (-1) ; /* check inputs */
+ for (i = 1 ; i < n ; i++) sigma += x [i] * x [i] ;
+ if (sigma == 0)
+ {
+ s = fabs (x [0]) ; /* s = |x(0)| */
+ (*beta) = (x [0] <= 0) ? 2 : 0 ;
+ x [0] = 1 ;
+ }
+ else
+ {
+ s = sqrt (x [0] * x [0] + sigma) ; /* s = norm (x) */
+ x [0] = (x [0] <= 0) ? (x [0] - s) : (-sigma / (x [0] + s)) ;
+ (*beta) = -1. / (s * x [0]) ;
+ }
+ return (s) ;
+}
diff --git a/CSparse/Source/cs_ipvec.c b/CSparse/Source/cs_ipvec.c
new file mode 100644
index 0000000..cb1e9a9
--- /dev/null
+++ b/CSparse/Source/cs_ipvec.c
@@ -0,0 +1,9 @@
+#include "cs.h"
+/* x(p) = b, for dense vectors x and b; p=NULL denotes identity */
+int cs_ipvec (const int *p, const double *b, double *x, int n)
+{
+ int k ;
+ if (!x || !b) return (0) ; /* check inputs */
+ for (k = 0 ; k < n ; k++) x [p ? p [k] : k] = b [k] ;
+ return (1) ;
+}
diff --git a/CSparse/Source/cs_leaf.c b/CSparse/Source/cs_leaf.c
new file mode 100644
index 0000000..1601cb9
--- /dev/null
+++ b/CSparse/Source/cs_leaf.c
@@ -0,0 +1,22 @@
+#include "cs.h"
+/* consider A(i,j), node j in ith row subtree and return lca(jprev,j) */
+int cs_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf,
+ int *ancestor, int *jleaf)
+{
+ int q, s, sparent, jprev ;
+ if (!first || !maxfirst || !prevleaf || !ancestor || !jleaf) return (-1) ;
+ *jleaf = 0 ;
+ if (i <= j || first [j] <= maxfirst [i]) return (-1) ; /* j not a leaf */
+ maxfirst [i] = first [j] ; /* update max first[j] seen so far */
+ jprev = prevleaf [i] ; /* jprev = previous leaf of ith subtree */
+ prevleaf [i] = j ;
+ *jleaf = (jprev == -1) ? 1: 2 ; /* j is first or subsequent leaf */
+ if (*jleaf == 1) return (i) ; /* if 1st leaf, q = root of ith subtree */
+ for (q = jprev ; q != ancestor [q] ; q = ancestor [q]) ;
+ for (s = jprev ; s != q ; s = sparent)
+ {
+ sparent = ancestor [s] ; /* path compression */
+ ancestor [s] = q ;
+ }
+ return (q) ; /* q = least common ancester (jprev,j) */
+}
diff --git a/CSparse/Source/cs_load.c b/CSparse/Source/cs_load.c
new file mode 100644
index 0000000..e1e8719
--- /dev/null
+++ b/CSparse/Source/cs_load.c
@@ -0,0 +1,15 @@
+#include "cs.h"
+/* load a triplet matrix from a file */
+cs *cs_load (FILE *f)
+{
+ int i, j ;
+ double x ;
+ cs *T ;
+ if (!f) return (NULL) ; /* check inputs */
+ T = cs_spalloc (0, 0, 1, 1, 1) ; /* allocate result */
+ while (fscanf (f, "%d %d %lg\n", &i, &j, &x) == 3)
+ {
+ if (!cs_entry (T, i, j, x)) return (cs_spfree (T)) ;
+ }
+ return (T) ;
+}
diff --git a/CSparse/Source/cs_lsolve.c b/CSparse/Source/cs_lsolve.c
new file mode 100644
index 0000000..69376ac
--- /dev/null
+++ b/CSparse/Source/cs_lsolve.c
@@ -0,0 +1,18 @@
+#include "cs.h"
+/* solve Lx=b where x and b are dense. x=b on input, solution on output. */
+int cs_lsolve (const cs *L, double *x)
+{
+ int p, j, n, *Lp, *Li ;
+ double *Lx ;
+ if (!CS_CSC (L) || !x) return (0) ; /* check inputs */
+ n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ x [j] /= Lx [Lp [j]] ;
+ for (p = Lp [j]+1 ; p < Lp [j+1] ; p++)
+ {
+ x [Li [p]] -= Lx [p] * x [j] ;
+ }
+ }
+ return (1) ;
+}
diff --git a/CSparse/Source/cs_ltsolve.c b/CSparse/Source/cs_ltsolve.c
new file mode 100644
index 0000000..fc2ee4f
--- /dev/null
+++ b/CSparse/Source/cs_ltsolve.c
@@ -0,0 +1,18 @@
+#include "cs.h"
+/* solve L'x=b where x and b are dense. x=b on input, solution on output. */
+int cs_ltsolve (const cs *L, double *x)
+{
+ int p, j, n, *Lp, *Li ;
+ double *Lx ;
+ if (!CS_CSC (L) || !x) return (0) ; /* check inputs */
+ n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ;
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ for (p = Lp [j]+1 ; p < Lp [j+1] ; p++)
+ {
+ x [j] -= Lx [p] * x [Li [p]] ;
+ }
+ x [j] /= Lx [Lp [j]] ;
+ }
+ return (1) ;
+}
diff --git a/CSparse/Source/cs_lu.c b/CSparse/Source/cs_lu.c
new file mode 100644
index 0000000..c8883c6
--- /dev/null
+++ b/CSparse/Source/cs_lu.c
@@ -0,0 +1,86 @@
+#include "cs.h"
+/* [L,U,pinv]=lu(A, [q lnz unz]). lnz and unz can be guess */
+csn *cs_lu (const cs *A, const css *S, double tol)
+{
+ cs *L, *U ;
+ csn *N ;
+ double pivot, *Lx, *Ux, *x, a, t ;
+ int *Lp, *Li, *Up, *Ui, *pinv, *xi, *q, n, ipiv, k, top, p, i, col, lnz,unz;
+ if (!CS_CSC (A) || !S) return (NULL) ; /* check inputs */
+ n = A->n ;
+ q = S->q ; lnz = S->lnz ; unz = S->unz ;
+ x = cs_malloc (n, sizeof (double)) ; /* get double workspace */
+ xi = cs_malloc (2*n, sizeof (int)) ; /* get int workspace */
+ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */
+ if (!x || !xi || !N) return (cs_ndone (N, NULL, xi, x, 0)) ;
+ N->L = L = cs_spalloc (n, n, lnz, 1, 0) ; /* allocate result L */
+ N->U = U = cs_spalloc (n, n, unz, 1, 0) ; /* allocate result U */
+ N->pinv = pinv = cs_malloc (n, sizeof (int)) ; /* allocate result pinv */
+ if (!L || !U || !pinv) return (cs_ndone (N, NULL, xi, x, 0)) ;
+ Lp = L->p ; Up = U->p ;
+ for (i = 0 ; i < n ; i++) x [i] = 0 ; /* clear workspace */
+ for (i = 0 ; i < n ; i++) pinv [i] = -1 ; /* no rows pivotal yet */
+ for (k = 0 ; k <= n ; k++) Lp [k] = 0 ; /* no cols of L yet */
+ lnz = unz = 0 ;
+ for (k = 0 ; k < n ; k++) /* compute L(:,k) and U(:,k) */
+ {
+ /* --- Triangular solve --------------------------------------------- */
+ Lp [k] = lnz ; /* L(:,k) starts here */
+ Up [k] = unz ; /* U(:,k) starts here */
+ if ((lnz + n > L->nzmax && !cs_sprealloc (L, 2*L->nzmax + n)) ||
+ (unz + n > U->nzmax && !cs_sprealloc (U, 2*U->nzmax + n)))
+ {
+ return (cs_ndone (N, NULL, xi, x, 0)) ;
+ }
+ Li = L->i ; Lx = L->x ; Ui = U->i ; Ux = U->x ;
+ col = q ? (q [k]) : k ;
+ top = cs_spsolve (L, A, col, xi, x, pinv, 1) ; /* x = L\A(:,col) */
+ /* --- Find pivot --------------------------------------------------- */
+ ipiv = -1 ;
+ a = -1 ;
+ for (p = top ; p < n ; p++)
+ {
+ i = xi [p] ; /* x(i) is nonzero */
+ if (pinv [i] < 0) /* row i is not yet pivotal */
+ {
+ if ((t = fabs (x [i])) > a)
+ {
+ a = t ; /* largest pivot candidate so far */
+ ipiv = i ;
+ }
+ }
+ else /* x(i) is the entry U(pinv[i],k) */
+ {
+ Ui [unz] = pinv [i] ;
+ Ux [unz++] = x [i] ;
+ }
+ }
+ if (ipiv == -1 || a <= 0) return (cs_ndone (N, NULL, xi, x, 0)) ;
+ if (pinv [col] < 0 && fabs (x [col]) >= a*tol) ipiv = col ;
+ /* --- Divide by pivot ---------------------------------------------- */
+ pivot = x [ipiv] ; /* the chosen pivot */
+ Ui [unz] = k ; /* last entry in U(:,k) is U(k,k) */
+ Ux [unz++] = pivot ;
+ pinv [ipiv] = k ; /* ipiv is the kth pivot row */
+ Li [lnz] = ipiv ; /* first entry in L(:,k) is L(k,k) = 1 */
+ Lx [lnz++] = 1 ;
+ for (p = top ; p < n ; p++) /* L(k+1:n,k) = x / pivot */
+ {
+ i = xi [p] ;
+ if (pinv [i] < 0) /* x(i) is an entry in L(:,k) */
+ {
+ Li [lnz] = i ; /* save unpermuted row in L */
+ Lx [lnz++] = x [i] / pivot ; /* scale pivot column */
+ }
+ x [i] = 0 ; /* x [0..n-1] = 0 for next k */
+ }
+ }
+ /* --- Finalize L and U ------------------------------------------------- */
+ Lp [n] = lnz ;
+ Up [n] = unz ;
+ Li = L->i ; /* fix row indices of L for final pinv */
+ for (p = 0 ; p < lnz ; p++) Li [p] = pinv [Li [p]] ;
+ cs_sprealloc (L, 0) ; /* remove extra space from L and U */
+ cs_sprealloc (U, 0) ;
+ return (cs_ndone (N, NULL, xi, x, 1)) ; /* success */
+}
diff --git a/CSparse/Source/cs_lusol.c b/CSparse/Source/cs_lusol.c
new file mode 100644
index 0000000..e7d79a1
--- /dev/null
+++ b/CSparse/Source/cs_lusol.c
@@ -0,0 +1,26 @@
+#include "cs.h"
+/* x=A\b where A is unsymmetric; b overwritten with solution */
+int cs_lusol (int order, const cs *A, double *b, double tol)
+{
+ double *x ;
+ css *S ;
+ csn *N ;
+ int n, ok ;
+ if (!CS_CSC (A) || !b) return (0) ; /* check inputs */
+ n = A->n ;
+ S = cs_sqr (order, A, 0) ; /* ordering and symbolic analysis */
+ N = cs_lu (A, S, tol) ; /* numeric LU factorization */
+ x = cs_malloc (n, sizeof (double)) ; /* get workspace */
+ ok = (S && N && x) ;
+ if (ok)
+ {
+ cs_ipvec (N->pinv, b, x, n) ; /* x = b(p) */
+ cs_lsolve (N->L, x) ; /* x = L\x */
+ cs_usolve (N->U, x) ; /* x = U\x */
+ cs_ipvec (S->q, x, b, n) ; /* b(q) = x */
+ }
+ cs_free (x) ;
+ cs_sfree (S) ;
+ cs_nfree (N) ;
+ return (ok) ;
+}
diff --git a/CSparse/Source/cs_malloc.c b/CSparse/Source/cs_malloc.c
new file mode 100644
index 0000000..4d8e2e1
--- /dev/null
+++ b/CSparse/Source/cs_malloc.c
@@ -0,0 +1,35 @@
+#include "cs.h"
+#ifdef MATLAB_MEX_FILE
+#define malloc mxMalloc
+#define free mxFree
+#define realloc mxRealloc
+#define calloc mxCalloc
+#endif
+
+/* wrapper for malloc */
+void *cs_malloc (int n, size_t size)
+{
+ return (malloc (CS_MAX (n,1) * size)) ;
+}
+
+/* wrapper for calloc */
+void *cs_calloc (int n, size_t size)
+{
+ return (calloc (CS_MAX (n,1), size)) ;
+}
+
+/* wrapper for free */
+void *cs_free (void *p)
+{
+ if (p) free (p) ; /* free p if it is not already NULL */
+ return (NULL) ; /* return NULL to simplify the use of cs_free */
+}
+
+/* wrapper for realloc */
+void *cs_realloc (void *p, int n, size_t size, int *ok)
+{
+ void *pnew ;
+ pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */
+ *ok = (pnew != NULL) ; /* realloc fails if pnew is NULL */
+ return ((*ok) ? pnew : p) ; /* return original p if failure */
+}
diff --git a/CSparse/Source/cs_maxtrans.c b/CSparse/Source/cs_maxtrans.c
new file mode 100644
index 0000000..7c8ea65
--- /dev/null
+++ b/CSparse/Source/cs_maxtrans.c
@@ -0,0 +1,92 @@
+#include "cs.h"
+/* find an augmenting path starting at column k and extend the match if found */
+static void cs_augment (int k, const cs *A, int *jmatch, int *cheap, int *w,
+ int *js, int *is, int *ps)
+{
+ int found = 0, p, i = -1, *Ap = A->p, *Ai = A->i, head = 0, j ;
+ js [0] = k ; /* start with just node k in jstack */
+ while (head >= 0)
+ {
+ /* --- Start (or continue) depth-first-search at node j ------------- */
+ j = js [head] ; /* get j from top of jstack */
+ if (w [j] != k) /* 1st time j visited for kth path */
+ {
+ w [j] = k ; /* mark j as visited for kth path */
+ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++)
+ {
+ i = Ai [p] ; /* try a cheap assignment (i,j) */
+ found = (jmatch [i] == -1) ;
+ }
+ cheap [j] = p ; /* start here next time j is traversed*/
+ if (found)
+ {
+ is [head] = i ; /* column j matched with row i */
+ break ; /* end of augmenting path */
+ }
+ ps [head] = Ap [j] ; /* no cheap match: start dfs for j */
+ }
+ /* --- Depth-first-search of neighbors of j ------------------------- */
+ for (p = ps [head] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ; /* consider row i */
+ if (w [jmatch [i]] == k) continue ; /* skip jmatch [i] if marked */
+ ps [head] = p + 1 ; /* pause dfs of node j */
+ is [head] = i ; /* i will be matched with j if found */
+ js [++head] = jmatch [i] ; /* start dfs at column jmatch [i] */
+ break ;
+ }
+ if (p == Ap [j+1]) head-- ; /* node j is done; pop from stack */
+ } /* augment the match if path found: */
+ if (found) for (p = head ; p >= 0 ; p--) jmatch [is [p]] = js [p] ;
+}
+
+/* find a maximum transveral */
+int *cs_maxtrans (const cs *A, int seed) /*[jmatch [0..m-1]; imatch [0..n-1]]*/
+{
+ int i, j, k, n, m, p, n2 = 0, m2 = 0, *Ap, *jimatch, *w, *cheap, *js, *is,
+ *ps, *Ai, *Cp, *jmatch, *imatch, *q ;
+ cs *C ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ n = A->n ; m = A->m ; Ap = A->p ; Ai = A->i ;
+ w = jimatch = cs_calloc (m+n, sizeof (int)) ; /* allocate result */
+ if (!jimatch) return (NULL) ;
+ for (k = 0, j = 0 ; j < n ; j++) /* count nonempty rows and columns */
+ {
+ n2 += (Ap [j] < Ap [j+1]) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ w [Ai [p]] = 1 ;
+ k += (j == Ai [p]) ; /* count entries already on diagonal */
+ }
+ }
+ if (k == CS_MIN (m,n)) /* quick return if diagonal zero-free */
+ {
+ jmatch = jimatch ; imatch = jimatch + m ;
+ for (i = 0 ; i < k ; i++) jmatch [i] = i ;
+ for ( ; i < m ; i++) jmatch [i] = -1 ;
+ for (j = 0 ; j < k ; j++) imatch [j] = j ;
+ for ( ; j < n ; j++) imatch [j] = -1 ;
+ return (cs_idone (jimatch, NULL, NULL, 1)) ;
+ }
+ for (i = 0 ; i < m ; i++) m2 += w [i] ;
+ C = (m2 < n2) ? cs_transpose (A,0) : ((cs *) A) ; /* transpose if needed */
+ if (!C) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, NULL, 0)) ;
+ n = C->n ; m = C->m ; Cp = C->p ;
+ jmatch = (m2 < n2) ? jimatch + n : jimatch ;
+ imatch = (m2 < n2) ? jimatch : jimatch + m ;
+ w = cs_malloc (5*n, sizeof (int)) ; /* get workspace */
+ if (!w) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 0)) ;
+ cheap = w + n ; js = w + 2*n ; is = w + 3*n ; ps = w + 4*n ;
+ for (j = 0 ; j < n ; j++) cheap [j] = Cp [j] ; /* for cheap assignment */
+ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */
+ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* nothing matched yet */
+ q = cs_randperm (n, seed) ; /* q = random permutation */
+ for (k = 0 ; k < n ; k++) /* augment, starting at column q[k] */
+ {
+ cs_augment (q ? q [k]: k, C, jmatch, cheap, w, js, is, ps) ;
+ }
+ cs_free (q) ;
+ for (j = 0 ; j < n ; j++) imatch [j] = -1 ; /* find row match */
+ for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ;
+ return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 1)) ;
+}
diff --git a/CSparse/Source/cs_multiply.c b/CSparse/Source/cs_multiply.c
new file mode 100644
index 0000000..c52ebea
--- /dev/null
+++ b/CSparse/Source/cs_multiply.c
@@ -0,0 +1,35 @@
+#include "cs.h"
+/* C = A*B */
+cs *cs_multiply (const cs *A, const cs *B)
+{
+ int p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values, *Bi ;
+ double *x, *Bx, *Cx ;
+ cs *C ;
+ if (!CS_CSC (A) || !CS_CSC (B)) return (NULL) ; /* check inputs */
+ if (A->n != B->m) return (NULL) ;
+ m = A->m ; anz = A->p [A->n] ;
+ n = B->n ; Bp = B->p ; Bi = B->i ; Bx = B->x ; bnz = Bp [n] ;
+ w = cs_calloc (m, sizeof (int)) ; /* get workspace */
+ values = (A->x != NULL) && (Bx != NULL) ;
+ x = values ? cs_malloc (m, sizeof (double)) : NULL ; /* get workspace */
+ C = cs_spalloc (m, n, anz + bnz, values, 0) ; /* allocate result */
+ if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ;
+ Cp = C->p ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (nz + m > C->nzmax && !cs_sprealloc (C, 2*(C->nzmax)+m))
+ {
+ return (cs_done (C, w, x, 0)) ; /* out of memory */
+ }
+ Ci = C->i ; Cx = C->x ; /* C->i and C->x may be reallocated */
+ Cp [j] = nz ; /* column j of C starts here */
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ nz = cs_scatter (A, Bi [p], Bx ? Bx [p] : 1, w, x, j+1, C, nz) ;
+ }
+ if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ;
+ }
+ Cp [n] = nz ; /* finalize the last column of C */
+ cs_sprealloc (C, 0) ; /* remove extra space from C */
+ return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */
+}
diff --git a/CSparse/Source/cs_norm.c b/CSparse/Source/cs_norm.c
new file mode 100644
index 0000000..24f8a2e
--- /dev/null
+++ b/CSparse/Source/cs_norm.c
@@ -0,0 +1,15 @@
+#include "cs.h"
+/* 1-norm of a sparse matrix = max (sum (abs (A))), largest column sum */
+double cs_norm (const cs *A)
+{
+ int p, j, n, *Ap ;
+ double *Ax, norm = 0, s ;
+ if (!CS_CSC (A) || !A->x) return (-1) ; /* check inputs */
+ n = A->n ; Ap = A->p ; Ax = A->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (s = 0, p = Ap [j] ; p < Ap [j+1] ; p++) s += fabs (Ax [p]) ;
+ norm = CS_MAX (norm, s) ;
+ }
+ return (norm) ;
+}
diff --git a/CSparse/Source/cs_permute.c b/CSparse/Source/cs_permute.c
new file mode 100644
index 0000000..f08e4d1
--- /dev/null
+++ b/CSparse/Source/cs_permute.c
@@ -0,0 +1,25 @@
+#include "cs.h"
+/* C = A(p,q) where p and q are permutations of 0..m-1 and 0..n-1. */
+cs *cs_permute (const cs *A, const int *pinv, const int *q, int values)
+{
+ int t, j, k, nz = 0, m, n, *Ap, *Ai, *Cp, *Ci ;
+ double *Cx, *Ax ;
+ cs *C ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ C = cs_spalloc (m, n, Ap [n], values && Ax != NULL, 0) ; /* alloc result */
+ if (!C) return (cs_done (C, NULL, NULL, 0)) ; /* out of memory */
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Cp [k] = nz ; /* column k of C is column q[k] of A */
+ j = q ? (q [k]) : k ;
+ for (t = Ap [j] ; t < Ap [j+1] ; t++)
+ {
+ if (Cx) Cx [nz] = Ax [t] ; /* row i of A is row pinv[i] of C */
+ Ci [nz++] = pinv ? (pinv [Ai [t]]) : Ai [t] ;
+ }
+ }
+ Cp [n] = nz ; /* finalize the last column of C */
+ return (cs_done (C, NULL, NULL, 1)) ;
+}
diff --git a/CSparse/Source/cs_pinv.c b/CSparse/Source/cs_pinv.c
new file mode 100644
index 0000000..0583e77
--- /dev/null
+++ b/CSparse/Source/cs_pinv.c
@@ -0,0 +1,11 @@
+#include "cs.h"
+/* pinv = p', or p = pinv' */
+int *cs_pinv (int const *p, int n)
+{
+ int k, *pinv ;
+ if (!p) return (NULL) ; /* p = NULL denotes identity */
+ pinv = cs_malloc (n, sizeof (int)) ; /* allocate result */
+ if (!pinv) return (NULL) ; /* out of memory */
+ for (k = 0 ; k < n ; k++) pinv [p [k]] = k ;/* invert the permutation */
+ return (pinv) ; /* return result */
+}
diff --git a/CSparse/Source/cs_post.c b/CSparse/Source/cs_post.c
new file mode 100644
index 0000000..80e66e6
--- /dev/null
+++ b/CSparse/Source/cs_post.c
@@ -0,0 +1,24 @@
+#include "cs.h"
+/* post order a forest */
+int *cs_post (const int *parent, int n)
+{
+ int j, k = 0, *post, *w, *head, *next, *stack ;
+ if (!parent) return (NULL) ; /* check inputs */
+ post = cs_malloc (n, sizeof (int)) ; /* allocate result */
+ w = cs_malloc (3*n, sizeof (int)) ; /* get workspace */
+ if (!w || !post) return (cs_idone (post, NULL, w, 0)) ;
+ head = w ; next = w + n ; stack = w + 2*n ;
+ for (j = 0 ; j < n ; j++) head [j] = -1 ; /* empty linked lists */
+ for (j = n-1 ; j >= 0 ; j--) /* traverse nodes in reverse order*/
+ {
+ if (parent [j] == -1) continue ; /* j is a root */
+ next [j] = head [parent [j]] ; /* add j to list of its parent */
+ head [parent [j]] = j ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ if (parent [j] != -1) continue ; /* skip j if it is not a root */
+ k = cs_tdfs (j, k, head, next, post, stack) ;
+ }
+ return (cs_idone (post, NULL, w, 1)) ; /* success; free w, return post */
+}
diff --git a/CSparse/Source/cs_print.c b/CSparse/Source/cs_print.c
new file mode 100644
index 0000000..8e3f33e
--- /dev/null
+++ b/CSparse/Source/cs_print.c
@@ -0,0 +1,36 @@
+#include "cs.h"
+/* print a sparse matrix */
+int cs_print (const cs *A, int brief)
+{
+ int p, j, m, n, nzmax, nz, *Ap, *Ai ;
+ double *Ax ;
+ if (!A) { printf ("(null)\n") ; return (0) ; }
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ nzmax = A->nzmax ; nz = A->nz ;
+ printf ("CSparse Version %d.%d.%d, %s. %s\n", CS_VER, CS_SUBVER,
+ CS_SUBSUB, CS_DATE, CS_COPYRIGHT) ;
+ if (nz < 0)
+ {
+ printf ("%d-by-%d, nzmax: %d nnz: %d, 1-norm: %g\n", m, n, nzmax,
+ Ap [n], cs_norm (A)) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" col %d : locations %d to %d\n", j, Ap [j], Ap [j+1]-1);
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ printf (" %d : %g\n", Ai [p], Ax ? Ax [p] : 1) ;
+ if (brief && p > 20) { printf (" ...\n") ; return (1) ; }
+ }
+ }
+ }
+ else
+ {
+ printf ("triplet: %d-by-%d, nzmax: %d nnz: %d\n", m, n, nzmax, nz) ;
+ for (p = 0 ; p < nz ; p++)
+ {
+ printf (" %d %d : %g\n", Ai [p], Ap [p], Ax ? Ax [p] : 1) ;
+ if (brief && p > 20) { printf (" ...\n") ; return (1) ; }
+ }
+ }
+ return (1) ;
+}
diff --git a/CSparse/Source/cs_pvec.c b/CSparse/Source/cs_pvec.c
new file mode 100644
index 0000000..03c3cc6
--- /dev/null
+++ b/CSparse/Source/cs_pvec.c
@@ -0,0 +1,9 @@
+#include "cs.h"
+/* x = b(p), for dense vectors x and b; p=NULL denotes identity */
+int cs_pvec (const int *p, const double *b, double *x, int n)
+{
+ int k ;
+ if (!x || !b) return (0) ; /* check inputs */
+ for (k = 0 ; k < n ; k++) x [k] = b [p ? p [k] : k] ;
+ return (1) ;
+}
diff --git a/CSparse/Source/cs_qr.c b/CSparse/Source/cs_qr.c
new file mode 100644
index 0000000..eb1774d
--- /dev/null
+++ b/CSparse/Source/cs_qr.c
@@ -0,0 +1,73 @@
+#include "cs.h"
+/* sparse QR factorization [V,beta,pinv,R] = qr (A) */
+csn *cs_qr (const cs *A, const css *S)
+{
+ double *Rx, *Vx, *Ax, *x, *Beta ;
+ int i, k, p, m, n, vnz, p1, top, m2, len, col, rnz, *s, *leftmost, *Ap, *Ai,
+ *parent, *Rp, *Ri, *Vp, *Vi, *w, *pinv, *q ;
+ cs *R, *V ;
+ csn *N ;
+ if (!CS_CSC (A) || !S) return (NULL) ;
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ q = S->q ; parent = S->parent ; pinv = S->pinv ; m2 = S->m2 ;
+ vnz = S->lnz ; rnz = S->unz ; leftmost = S->leftmost ;
+ w = cs_malloc (m2+n, sizeof (int)) ; /* get int workspace */
+ x = cs_malloc (m2, sizeof (double)) ; /* get double workspace */
+ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */
+ if (!w || !x || !N) return (cs_ndone (N, NULL, w, x, 0)) ;
+ s = w + m2 ; /* s is size n */
+ for (k = 0 ; k < m2 ; k++) x [k] = 0 ; /* clear workspace x */
+ N->L = V = cs_spalloc (m2, n, vnz, 1, 0) ; /* allocate result V */
+ N->U = R = cs_spalloc (m2, n, rnz, 1, 0) ; /* allocate result R */
+ N->B = Beta = cs_malloc (n, sizeof (double)) ; /* allocate result Beta */
+ if (!R || !V || !Beta) return (cs_ndone (N, NULL, w, x, 0)) ;
+ Rp = R->p ; Ri = R->i ; Rx = R->x ;
+ Vp = V->p ; Vi = V->i ; Vx = V->x ;
+ for (i = 0 ; i < m2 ; i++) w [i] = -1 ; /* clear w, to mark nodes */
+ rnz = 0 ; vnz = 0 ;
+ for (k = 0 ; k < n ; k++) /* compute V and R */
+ {
+ Rp [k] = rnz ; /* R(:,k) starts here */
+ Vp [k] = p1 = vnz ; /* V(:,k) starts here */
+ w [k] = k ; /* add V(k,k) to pattern of V */
+ Vi [vnz++] = k ;
+ top = n ;
+ col = q ? q [k] : k ;
+ for (p = Ap [col] ; p < Ap [col+1] ; p++) /* find R(:,k) pattern */
+ {
+ i = leftmost [Ai [p]] ; /* i = min(find(A(i,q))) */
+ for (len = 0 ; w [i] != k ; i = parent [i]) /* traverse up to k */
+ {
+ s [len++] = i ;
+ w [i] = k ;
+ }
+ while (len > 0) s [--top] = s [--len] ; /* push path on stack */
+ i = pinv [Ai [p]] ; /* i = permuted row of A(:,col) */
+ x [i] = Ax [p] ; /* x (i) = A(:,col) */
+ if (i > k && w [i] < k) /* pattern of V(:,k) = x (k+1:m) */
+ {
+ Vi [vnz++] = i ; /* add i to pattern of V(:,k) */
+ w [i] = k ;
+ }
+ }
+ for (p = top ; p < n ; p++) /* for each i in pattern of R(:,k) */
+ {
+ i = s [p] ; /* R(i,k) is nonzero */
+ cs_happly (V, i, Beta [i], x) ; /* apply (V(i),Beta(i)) to x */
+ Ri [rnz] = i ; /* R(i,k) = x(i) */
+ Rx [rnz++] = x [i] ;
+ x [i] = 0 ;
+ if (parent [i] == k) vnz = cs_scatter (V, i, 0, w, NULL, k, V, vnz);
+ }
+ for (p = p1 ; p < vnz ; p++) /* gather V(:,k) = x */
+ {
+ Vx [p] = x [Vi [p]] ;
+ x [Vi [p]] = 0 ;
+ }
+ Ri [rnz] = k ; /* R(k,k) = norm (x) */
+ Rx [rnz++] = cs_house (Vx+p1, Beta+k, vnz-p1) ; /* [v,beta]=house(x) */
+ }
+ Rp [n] = rnz ; /* finalize R */
+ Vp [n] = vnz ; /* finalize V */
+ return (cs_ndone (N, NULL, w, x, 1)) ; /* success */
+}
diff --git a/CSparse/Source/cs_qrsol.c b/CSparse/Source/cs_qrsol.c
new file mode 100644
index 0000000..7d07966
--- /dev/null
+++ b/CSparse/Source/cs_qrsol.c
@@ -0,0 +1,53 @@
+#include "cs.h"
+/* x=A\b where A can be rectangular; b overwritten with solution */
+int cs_qrsol (int order, const cs *A, double *b)
+{
+ double *x ;
+ css *S ;
+ csn *N ;
+ cs *AT = NULL ;
+ int k, m, n, ok ;
+ if (!CS_CSC (A) || !b) return (0) ; /* check inputs */
+ n = A->n ;
+ m = A->m ;
+ if (m >= n)
+ {
+ S = cs_sqr (order, A, 1) ; /* ordering and symbolic analysis */
+ N = cs_qr (A, S) ; /* numeric QR factorization */
+ x = cs_calloc (S ? S->m2 : 1, sizeof (double)) ; /* get workspace */
+ ok = (S && N && x) ;
+ if (ok)
+ {
+ cs_ipvec (S->pinv, b, x, m) ; /* x(0:m-1) = b(p(0:m-1) */
+ for (k = 0 ; k < n ; k++) /* apply Householder refl. to x */
+ {
+ cs_happly (N->L, k, N->B [k], x) ;
+ }
+ cs_usolve (N->U, x) ; /* x = R\x */
+ cs_ipvec (S->q, x, b, n) ; /* b(q(0:n-1)) = x(0:n-1) */
+ }
+ }
+ else
+ {
+ AT = cs_transpose (A, 1) ; /* Ax=b is underdetermined */
+ S = cs_sqr (order, AT, 1) ; /* ordering and symbolic analysis */
+ N = cs_qr (AT, S) ; /* numeric QR factorization of A' */
+ x = cs_calloc (S ? S->m2 : 1, sizeof (double)) ; /* get workspace */
+ ok = (AT && S && N && x) ;
+ if (ok)
+ {
+ cs_pvec (S->q, b, x, m) ; /* x(q(0:m-1)) = b(0:m-1) */
+ cs_utsolve (N->U, x) ; /* x = R'\x */
+ for (k = m-1 ; k >= 0 ; k--) /* apply Householder refl. to x */
+ {
+ cs_happly (N->L, k, N->B [k], x) ;
+ }
+ cs_pvec (S->pinv, x, b, n) ; /* b(0:n-1) = x(p(0:n-1)) */
+ }
+ }
+ cs_free (x) ;
+ cs_sfree (S) ;
+ cs_nfree (N) ;
+ cs_spfree (AT) ;
+ return (ok) ;
+}
diff --git a/CSparse/Source/cs_randperm.c b/CSparse/Source/cs_randperm.c
new file mode 100644
index 0000000..de6b007
--- /dev/null
+++ b/CSparse/Source/cs_randperm.c
@@ -0,0 +1,22 @@
+#include "cs.h"
+/* return a random permutation vector, the identity perm, or p = n-1:-1:0.
+ * seed = -1 means p = n-1:-1:0. seed = 0 means p = identity. otherwise
+ * p = random permutation. */
+int *cs_randperm (int n, int seed)
+{
+ int *p, k, j, t ;
+ if (seed == 0) return (NULL) ; /* return p = NULL (identity) */
+ p = cs_malloc (n, sizeof (int)) ; /* allocate result */
+ if (!p) return (NULL) ; /* out of memory */
+ for (k = 0 ; k < n ; k++) p [k] = n-k-1 ;
+ if (seed == -1) return (p) ; /* return reverse permutation */
+ srand (seed) ; /* get new random number seed */
+ for (k = 0 ; k < n ; k++)
+ {
+ j = k + (rand ( ) % (n-k)) ; /* j = rand int in range k to n-1 */
+ t = p [j] ; /* swap p[k] and p[j] */
+ p [j] = p [k] ;
+ p [k] = t ;
+ }
+ return (p) ;
+}
diff --git a/CSparse/Source/cs_reach.c b/CSparse/Source/cs_reach.c
new file mode 100644
index 0000000..29e8ca5
--- /dev/null
+++ b/CSparse/Source/cs_reach.c
@@ -0,0 +1,19 @@
+#include "cs.h"
+/* xi [top...n-1] = nodes reachable from graph of G*P' via nodes in B(:,k).
+ * xi [n...2n-1] used as workspace */
+int cs_reach (cs *G, const cs *B, int k, int *xi, const int *pinv)
+{
+ int p, n, top, *Bp, *Bi, *Gp ;
+ if (!CS_CSC (G) || !CS_CSC (B) || !xi) return (-1) ; /* check inputs */
+ n = G->n ; Bp = B->p ; Bi = B->i ; Gp = G->p ;
+ top = n ;
+ for (p = Bp [k] ; p < Bp [k+1] ; p++)
+ {
+ if (!CS_MARKED (Gp, Bi [p])) /* start a dfs at unmarked node i */
+ {
+ top = cs_dfs (Bi [p], G, top, xi, xi+n, pinv) ;
+ }
+ }
+ for (p = top ; p < n ; p++) CS_MARK (Gp, xi [p]) ; /* restore G */
+ return (top) ;
+}
diff --git a/CSparse/Source/cs_scatter.c b/CSparse/Source/cs_scatter.c
new file mode 100644
index 0000000..0077826
--- /dev/null
+++ b/CSparse/Source/cs_scatter.c
@@ -0,0 +1,22 @@
+#include "cs.h"
+/* x = x + beta * A(:,j), where x is a dense vector and A(:,j) is sparse */
+int cs_scatter (const cs *A, int j, double beta, int *w, double *x, int mark,
+ cs *C, int nz)
+{
+ int i, p, *Ap, *Ai, *Ci ;
+ double *Ax ;
+ if (!CS_CSC (A) || !w || !CS_CSC (C)) return (-1) ; /* check inputs */
+ Ap = A->p ; Ai = A->i ; Ax = A->x ; Ci = C->i ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ; /* A(i,j) is nonzero */
+ if (w [i] < mark)
+ {
+ w [i] = mark ; /* i is new entry in column j */
+ Ci [nz++] = i ; /* add i to pattern of C(:,j) */
+ if (x) x [i] = beta * Ax [p] ; /* x(i) = beta*A(i,j) */
+ }
+ else if (x) x [i] += beta * Ax [p] ; /* i exists in C(:,j) already */
+ }
+ return (nz) ;
+}
diff --git a/CSparse/Source/cs_scc.c b/CSparse/Source/cs_scc.c
new file mode 100644
index 0000000..e56d086
--- /dev/null
+++ b/CSparse/Source/cs_scc.c
@@ -0,0 +1,41 @@
+#include "cs.h"
+/* find the strongly connected components of a square matrix */
+csd *cs_scc (cs *A) /* matrix A temporarily modified, then restored */
+{
+ int n, i, k, b, nb = 0, top, *xi, *pstack, *p, *r, *Ap, *ATp, *rcopy, *Blk ;
+ cs *AT ;
+ csd *D ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ n = A->n ; Ap = A->p ;
+ D = cs_dalloc (n, 0) ; /* allocate result */
+ AT = cs_transpose (A, 0) ; /* AT = A' */
+ xi = cs_malloc (2*n+1, sizeof (int)) ; /* get workspace */
+ if (!D || !AT || !xi) return (cs_ddone (D, AT, xi, 0)) ;
+ Blk = xi ; rcopy = pstack = xi + n ;
+ p = D->p ; r = D->r ; ATp = AT->p ;
+ top = n ;
+ for (i = 0 ; i < n ; i++) /* first dfs(A) to find finish times (xi) */
+ {
+ if (!CS_MARKED (Ap, i)) top = cs_dfs (i, A, top, xi, pstack, NULL) ;
+ }
+ for (i = 0 ; i < n ; i++) CS_MARK (Ap, i) ; /* restore A; unmark all nodes*/
+ top = n ;
+ nb = n ;
+ for (k = 0 ; k < n ; k++) /* dfs(A') to find strongly connnected comp */
+ {
+ i = xi [k] ; /* get i in reverse order of finish times */
+ if (CS_MARKED (ATp, i)) continue ; /* skip node i if already ordered */
+ r [nb--] = top ; /* node i is the start of a component in p */
+ top = cs_dfs (i, AT, top, p, pstack, NULL) ;
+ }
+ r [nb] = 0 ; /* first block starts at zero; shift r up */
+ for (k = nb ; k <= n ; k++) r [k-nb] = r [k] ;
+ D->nb = nb = n-nb ; /* nb = # of strongly connected components */
+ for (b = 0 ; b < nb ; b++) /* sort each block in natural order */
+ {
+ for (k = r [b] ; k < r [b+1] ; k++) Blk [p [k]] = b ;
+ }
+ for (b = 0 ; b <= nb ; b++) rcopy [b] = r [b] ;
+ for (i = 0 ; i < n ; i++) p [rcopy [Blk [i]]++] = i ;
+ return (cs_ddone (D, AT, xi, 1)) ;
+}
diff --git a/CSparse/Source/cs_schol.c b/CSparse/Source/cs_schol.c
new file mode 100644
index 0000000..32c6734
--- /dev/null
+++ b/CSparse/Source/cs_schol.c
@@ -0,0 +1,26 @@
+#include "cs.h"
+/* ordering and symbolic analysis for a Cholesky factorization */
+css *cs_schol (int order, const cs *A)
+{
+ int n, *c, *post, *P ;
+ cs *C ;
+ css *S ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ n = A->n ;
+ S = cs_calloc (1, sizeof (css)) ; /* allocate result S */
+ if (!S) return (NULL) ; /* out of memory */
+ P = cs_amd (order, A) ; /* P = amd(A+A'), or natural */
+ S->pinv = cs_pinv (P, n) ; /* find inverse permutation */
+ cs_free (P) ;
+ if (order && !S->pinv) return (cs_sfree (S)) ;
+ C = cs_symperm (A, S->pinv, 0) ; /* C = spones(triu(A(P,P))) */
+ S->parent = cs_etree (C, 0) ; /* find etree of C */
+ post = cs_post (S->parent, n) ; /* postorder the etree */
+ c = cs_counts (C, S->parent, post, 0) ; /* find column counts of chol(C) */
+ cs_free (post) ;
+ cs_spfree (C) ;
+ S->cp = cs_malloc (n+1, sizeof (int)) ; /* allocate result S->cp */
+ S->unz = S->lnz = cs_cumsum (S->cp, c, n) ; /* find column pointers for L */
+ cs_free (c) ;
+ return ((S->lnz >= 0) ? S : cs_sfree (S)) ;
+}
diff --git a/CSparse/Source/cs_spsolve.c b/CSparse/Source/cs_spsolve.c
new file mode 100644
index 0000000..d004f9c
--- /dev/null
+++ b/CSparse/Source/cs_spsolve.c
@@ -0,0 +1,28 @@
+#include "cs.h"
+/* solve Gx=b(:,k), where G is either upper (lo=0) or lower (lo=1) triangular */
+int cs_spsolve (cs *G, const cs *B, int k, int *xi, double *x, const int *pinv,
+ int lo)
+{
+ int j, J, p, q, px, top, n, *Gp, *Gi, *Bp, *Bi ;
+ double *Gx, *Bx ;
+ if (!CS_CSC (G) || !CS_CSC (B) || !xi || !x) return (-1) ;
+ Gp = G->p ; Gi = G->i ; Gx = G->x ; n = G->n ;
+ Bp = B->p ; Bi = B->i ; Bx = B->x ;
+ top = cs_reach (G, B, k, xi, pinv) ; /* xi[top..n-1]=Reach(B(:,k)) */
+ for (p = top ; p < n ; p++) x [xi [p]] = 0 ; /* clear x */
+ for (p = Bp [k] ; p < Bp [k+1] ; p++) x [Bi [p]] = Bx [p] ; /* scatter B */
+ for (px = top ; px < n ; px++)
+ {
+ j = xi [px] ; /* x(j) is nonzero */
+ J = pinv ? (pinv [j]) : j ; /* j maps to col J of G */
+ if (J < 0) continue ; /* column J is empty */
+ x [j] /= Gx [lo ? (Gp [J]) : (Gp [J+1]-1)] ;/* x(j) /= G(j,j) */
+ p = lo ? (Gp [J]+1) : (Gp [J]) ; /* lo: L(j,j) 1st entry */
+ q = lo ? (Gp [J+1]) : (Gp [J+1]-1) ; /* up: U(j,j) last entry */
+ for ( ; p < q ; p++)
+ {
+ x [Gi [p]] -= Gx [p] * x [j] ; /* x(i) -= G(i,j) * x(j) */
+ }
+ }
+ return (top) ; /* return top of stack */
+}
diff --git a/CSparse/Source/cs_sqr.c b/CSparse/Source/cs_sqr.c
new file mode 100644
index 0000000..ad39bd2
--- /dev/null
+++ b/CSparse/Source/cs_sqr.c
@@ -0,0 +1,88 @@
+#include "cs.h"
+/* compute nnz(V) = S->lnz, S->pinv, S->leftmost, S->m2 from A and S->parent */
+static int cs_vcount (const cs *A, css *S)
+{
+ int i, k, p, pa, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i, *next, *head,
+ *tail, *nque, *pinv, *leftmost, *w, *parent = S->parent ;
+ S->pinv = pinv = cs_malloc (m+n, sizeof (int)) ; /* allocate pinv, */
+ S->leftmost = leftmost = cs_malloc (m, sizeof (int)) ; /* and leftmost */
+ w = cs_malloc (m+3*n, sizeof (int)) ; /* get workspace */
+ if (!pinv || !w || !leftmost)
+ {
+ cs_free (w) ; /* pinv and leftmost freed later */
+ return (0) ; /* out of memory */
+ }
+ next = w ; head = w + m ; tail = w + m + n ; nque = w + m + 2*n ;
+ for (k = 0 ; k < n ; k++) head [k] = -1 ; /* queue k is empty */
+ for (k = 0 ; k < n ; k++) tail [k] = -1 ;
+ for (k = 0 ; k < n ; k++) nque [k] = 0 ;
+ for (i = 0 ; i < m ; i++) leftmost [i] = -1 ;
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ for (p = Ap [k] ; p < Ap [k+1] ; p++)
+ {
+ leftmost [Ai [p]] = k ; /* leftmost[i] = min(find(A(i,:)))*/
+ }
+ }
+ for (i = m-1 ; i >= 0 ; i--) /* scan rows in reverse order */
+ {
+ pinv [i] = -1 ; /* row i is not yet ordered */
+ k = leftmost [i] ;
+ if (k == -1) continue ; /* row i is empty */
+ if (nque [k]++ == 0) tail [k] = i ; /* first row in queue k */
+ next [i] = head [k] ; /* put i at head of queue k */
+ head [k] = i ;
+ }
+ S->lnz = 0 ;
+ S->m2 = m ;
+ for (k = 0 ; k < n ; k++) /* find row permutation and nnz(V)*/
+ {
+ i = head [k] ; /* remove row i from queue k */
+ S->lnz++ ; /* count V(k,k) as nonzero */
+ if (i < 0) i = S->m2++ ; /* add a fictitious row */
+ pinv [i] = k ; /* associate row i with V(:,k) */
+ if (--nque [k] <= 0) continue ; /* skip if V(k+1:m,k) is empty */
+ S->lnz += nque [k] ; /* nque [k] is nnz (V(k+1:m,k)) */
+ if ((pa = parent [k]) != -1) /* move all rows to parent of k */
+ {
+ if (nque [pa] == 0) tail [pa] = tail [k] ;
+ next [tail [k]] = head [pa] ;
+ head [pa] = next [i] ;
+ nque [pa] += nque [k] ;
+ }
+ }
+ for (i = 0 ; i < m ; i++) if (pinv [i] < 0) pinv [i] = k++ ;
+ cs_free (w) ;
+ return (1) ;
+}
+
+/* symbolic ordering and analysis for QR or LU */
+css *cs_sqr (int order, const cs *A, int qr)
+{
+ int n, k, ok = 1, *post ;
+ css *S ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ n = A->n ;
+ S = cs_calloc (1, sizeof (css)) ; /* allocate result S */
+ if (!S) return (NULL) ; /* out of memory */
+ S->q = cs_amd (order, A) ; /* fill-reducing ordering */
+ if (order && !S->q) return (cs_sfree (S)) ;
+ if (qr) /* QR symbolic analysis */
+ {
+ cs *C = order ? cs_permute (A, NULL, S->q, 0) : ((cs *) A) ;
+ S->parent = cs_etree (C, 1) ; /* etree of C'*C, where C=A(:,q) */
+ post = cs_post (S->parent, n) ;
+ S->cp = cs_counts (C, S->parent, post, 1) ; /* col counts chol(C'*C) */
+ cs_free (post) ;
+ ok = C && S->parent && S->cp && cs_vcount (C, S) ;
+ if (ok) for (S->unz = 0, k = 0 ; k < n ; k++) S->unz += S->cp [k] ;
+ ok = ok && S->lnz >= 0 && S->unz >= 0 ; /* int overflow guard */
+ if (order) cs_spfree (C) ;
+ }
+ else
+ {
+ S->unz = 4*(A->p [n]) + n ; /* for LU factorization only, */
+ S->lnz = S->unz ; /* guess nnz(L) and nnz(U) */
+ }
+ return (ok ? S : cs_sfree (S)) ; /* return result S */
+}
diff --git a/CSparse/Source/cs_symperm.c b/CSparse/Source/cs_symperm.c
new file mode 100644
index 0000000..668526d
--- /dev/null
+++ b/CSparse/Source/cs_symperm.c
@@ -0,0 +1,39 @@
+#include "cs.h"
+/* C = A(p,p) where A and C are symmetric the upper part stored; pinv not p */
+cs *cs_symperm (const cs *A, const int *pinv, int values)
+{
+ int i, j, p, q, i2, j2, n, *Ap, *Ai, *Cp, *Ci, *w ;
+ double *Cx, *Ax ;
+ cs *C ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ C = cs_spalloc (n, n, Ap [n], values && (Ax != NULL), 0) ; /* alloc result*/
+ w = cs_calloc (n, sizeof (int)) ; /* get workspace */
+ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ for (j = 0 ; j < n ; j++) /* count entries in each column of C */
+ {
+ j2 = pinv ? pinv [j] : j ; /* column j of A is column j2 of C */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ if (i > j) continue ; /* skip lower triangular part of A */
+ i2 = pinv ? pinv [i] : i ; /* row i of A is row i2 of C */
+ w [CS_MAX (i2, j2)]++ ; /* column count of C */
+ }
+ }
+ cs_cumsum (Cp, w, n) ; /* compute column pointers of C */
+ for (j = 0 ; j < n ; j++)
+ {
+ j2 = pinv ? pinv [j] : j ; /* column j of A is column j2 of C */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ if (i > j) continue ; /* skip lower triangular part of A*/
+ i2 = pinv ? pinv [i] : i ; /* row i of A is row i2 of C */
+ Ci [q = w [CS_MAX (i2, j2)]++] = CS_MIN (i2, j2) ;
+ if (Cx) Cx [q] = Ax [p] ;
+ }
+ }
+ return (cs_done (C, w, NULL, 1)) ; /* success; free workspace, return C */
+}
diff --git a/CSparse/Source/cs_tdfs.c b/CSparse/Source/cs_tdfs.c
new file mode 100644
index 0000000..ad19890
--- /dev/null
+++ b/CSparse/Source/cs_tdfs.c
@@ -0,0 +1,24 @@
+#include "cs.h"
+/* depth-first search and postorder of a tree rooted at node j */
+int cs_tdfs (int j, int k, int *head, const int *next, int *post, int *stack)
+{
+ int i, p, top = 0 ;
+ if (!head || !next || !post || !stack) return (-1) ; /* check inputs */
+ stack [0] = j ; /* place j on the stack */
+ while (top >= 0) /* while (stack is not empty) */
+ {
+ p = stack [top] ; /* p = top of stack */
+ i = head [p] ; /* i = youngest child of p */
+ if (i == -1)
+ {
+ top-- ; /* p has no unordered children left */
+ post [k++] = p ; /* node p is the kth postordered node */
+ }
+ else
+ {
+ head [p] = next [i] ; /* remove i from children of p */
+ stack [++top] = i ; /* start dfs on child node i */
+ }
+ }
+ return (k) ;
+}
diff --git a/CSparse/Source/cs_transpose.c b/CSparse/Source/cs_transpose.c
new file mode 100644
index 0000000..9daa84d
--- /dev/null
+++ b/CSparse/Source/cs_transpose.c
@@ -0,0 +1,25 @@
+#include "cs.h"
+/* C = A' */
+cs *cs_transpose (const cs *A, int values)
+{
+ int p, q, j, *Cp, *Ci, n, m, *Ap, *Ai, *w ;
+ double *Cx, *Ax ;
+ cs *C ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ C = cs_spalloc (n, m, Ap [n], values && Ax, 0) ; /* allocate result */
+ w = cs_calloc (m, sizeof (int)) ; /* get workspace */
+ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ for (p = 0 ; p < Ap [n] ; p++) w [Ai [p]]++ ; /* row counts */
+ cs_cumsum (Cp, w, m) ; /* row pointers */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ Ci [q = w [Ai [p]]++] = j ; /* place A(i,j) as entry C(j,i) */
+ if (Cx) Cx [q] = Ax [p] ;
+ }
+ }
+ return (cs_done (C, w, NULL, 1)) ; /* success; free w and return C */
+}
diff --git a/CSparse/Source/cs_updown.c b/CSparse/Source/cs_updown.c
new file mode 100644
index 0000000..90dc4cc
--- /dev/null
+++ b/CSparse/Source/cs_updown.c
@@ -0,0 +1,37 @@
+#include "cs.h"
+/* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */
+int cs_updown (cs *L, int sigma, const cs *C, const int *parent)
+{
+ int n, p, f, j, *Lp, *Li, *Cp, *Ci ;
+ double *Lx, *Cx, alpha, beta = 1, delta, gamma, w1, w2, *w, beta2 = 1 ;
+ if (!CS_CSC (L) || !CS_CSC (C) || !parent) return (0) ; /* check inputs */
+ Lp = L->p ; Li = L->i ; Lx = L->x ; n = L->n ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ if ((p = Cp [0]) >= Cp [1]) return (1) ; /* return if C empty */
+ w = cs_malloc (n, sizeof (double)) ; /* get workspace */
+ if (!w) return (0) ; /* out of memory */
+ f = Ci [p] ;
+ for ( ; p < Cp [1] ; p++) f = CS_MIN (f, Ci [p]) ; /* f = min (find (C)) */
+ for (j = f ; j != -1 ; j = parent [j]) w [j] = 0 ; /* clear workspace w */
+ for (p = Cp [0] ; p < Cp [1] ; p++) w [Ci [p]] = Cx [p] ; /* w = C */
+ for (j = f ; j != -1 ; j = parent [j]) /* walk path f up to root */
+ {
+ p = Lp [j] ;
+ alpha = w [j] / Lx [p] ; /* alpha = w(j) / L(j,j) */
+ beta2 = beta*beta + sigma*alpha*alpha ;
+ if (beta2 <= 0) break ; /* not positive definite */
+ beta2 = sqrt (beta2) ;
+ delta = (sigma > 0) ? (beta / beta2) : (beta2 / beta) ;
+ gamma = sigma * alpha / (beta2 * beta) ;
+ Lx [p] = delta * Lx [p] + ((sigma > 0) ? (gamma * w [j]) : 0) ;
+ beta = beta2 ;
+ for (p++ ; p < Lp [j+1] ; p++)
+ {
+ w1 = w [Li [p]] ;
+ w [Li [p]] = w2 = w1 - alpha * Lx [p] ;
+ Lx [p] = delta * Lx [p] + gamma * ((sigma > 0) ? w1 : w2) ;
+ }
+ }
+ cs_free (w) ;
+ return (beta2 > 0) ;
+}
diff --git a/CSparse/Source/cs_usolve.c b/CSparse/Source/cs_usolve.c
new file mode 100644
index 0000000..40e0892
--- /dev/null
+++ b/CSparse/Source/cs_usolve.c
@@ -0,0 +1,18 @@
+#include "cs.h"
+/* solve Ux=b where x and b are dense. x=b on input, solution on output. */
+int cs_usolve (const cs *U, double *x)
+{
+ int p, j, n, *Up, *Ui ;
+ double *Ux ;
+ if (!CS_CSC (U) || !x) return (0) ; /* check inputs */
+ n = U->n ; Up = U->p ; Ui = U->i ; Ux = U->x ;
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ x [j] /= Ux [Up [j+1]-1] ;
+ for (p = Up [j] ; p < Up [j+1]-1 ; p++)
+ {
+ x [Ui [p]] -= Ux [p] * x [j] ;
+ }
+ }
+ return (1) ;
+}
diff --git a/CSparse/Source/cs_util.c b/CSparse/Source/cs_util.c
new file mode 100644
index 0000000..5684cd2
--- /dev/null
+++ b/CSparse/Source/cs_util.c
@@ -0,0 +1,119 @@
+#include "cs.h"
+/* allocate a sparse matrix (triplet form or compressed-column form) */
+cs *cs_spalloc (int m, int n, int nzmax, int values, int triplet)
+{
+ cs *A = cs_calloc (1, sizeof (cs)) ; /* allocate the cs struct */
+ if (!A) return (NULL) ; /* out of memory */
+ A->m = m ; /* define dimensions and nzmax */
+ A->n = n ;
+ A->nzmax = nzmax = CS_MAX (nzmax, 1) ;
+ A->nz = triplet ? 0 : -1 ; /* allocate triplet or comp.col */
+ A->p = cs_malloc (triplet ? nzmax : n+1, sizeof (int)) ;
+ A->i = cs_malloc (nzmax, sizeof (int)) ;
+ A->x = values ? cs_malloc (nzmax, sizeof (double)) : NULL ;
+ return ((!A->p || !A->i || (values && !A->x)) ? cs_spfree (A) : A) ;
+}
+
+/* change the max # of entries sparse matrix */
+int cs_sprealloc (cs *A, int nzmax)
+{
+ int ok, oki, okj = 1, okx = 1 ;
+ if (!A) return (0) ;
+ if (nzmax <= 0) nzmax = (CS_CSC (A)) ? (A->p [A->n]) : A->nz ;
+ A->i = cs_realloc (A->i, nzmax, sizeof (int), &oki) ;
+ if (CS_TRIPLET (A)) A->p = cs_realloc (A->p, nzmax, sizeof (int), &okj) ;
+ if (A->x) A->x = cs_realloc (A->x, nzmax, sizeof (double), &okx) ;
+ ok = (oki && okj && okx) ;
+ if (ok) A->nzmax = nzmax ;
+ return (ok) ;
+}
+
+/* free a sparse matrix */
+cs *cs_spfree (cs *A)
+{
+ if (!A) return (NULL) ; /* do nothing if A already NULL */
+ cs_free (A->p) ;
+ cs_free (A->i) ;
+ cs_free (A->x) ;
+ return (cs_free (A)) ; /* free the cs struct and return NULL */
+}
+
+/* free a numeric factorization */
+csn *cs_nfree (csn *N)
+{
+ if (!N) return (NULL) ; /* do nothing if N already NULL */
+ cs_spfree (N->L) ;
+ cs_spfree (N->U) ;
+ cs_free (N->pinv) ;
+ cs_free (N->B) ;
+ return (cs_free (N)) ; /* free the csn struct and return NULL */
+}
+
+/* free a symbolic factorization */
+css *cs_sfree (css *S)
+{
+ if (!S) return (NULL) ; /* do nothing if S already NULL */
+ cs_free (S->pinv) ;
+ cs_free (S->q) ;
+ cs_free (S->parent) ;
+ cs_free (S->cp) ;
+ cs_free (S->leftmost) ;
+ return (cs_free (S)) ; /* free the css struct and return NULL */
+}
+
+/* allocate a cs_dmperm or cs_scc result */
+csd *cs_dalloc (int m, int n)
+{
+ csd *D ;
+ D = cs_calloc (1, sizeof (csd)) ;
+ if (!D) return (NULL) ;
+ D->p = cs_malloc (m, sizeof (int)) ;
+ D->r = cs_malloc (m+6, sizeof (int)) ;
+ D->q = cs_malloc (n, sizeof (int)) ;
+ D->s = cs_malloc (n+6, sizeof (int)) ;
+ return ((!D->p || !D->r || !D->q || !D->s) ? cs_dfree (D) : D) ;
+}
+
+/* free a cs_dmperm or cs_scc result */
+csd *cs_dfree (csd *D)
+{
+ if (!D) return (NULL) ; /* do nothing if D already NULL */
+ cs_free (D->p) ;
+ cs_free (D->q) ;
+ cs_free (D->r) ;
+ cs_free (D->s) ;
+ return (cs_free (D)) ;
+}
+
+/* free workspace and return a sparse matrix result */
+cs *cs_done (cs *C, void *w, void *x, int ok)
+{
+ cs_free (w) ; /* free workspace */
+ cs_free (x) ;
+ return (ok ? C : cs_spfree (C)) ; /* return result if OK, else free it */
+}
+
+/* free workspace and return int array result */
+int *cs_idone (int *p, cs *C, void *w, int ok)
+{
+ cs_spfree (C) ; /* free temporary matrix */
+ cs_free (w) ; /* free workspace */
+ return (ok ? p : cs_free (p)) ; /* return result if OK, else free it */
+}
+
+/* free workspace and return a numeric factorization (Cholesky, LU, or QR) */
+csn *cs_ndone (csn *N, cs *C, void *w, void *x, int ok)
+{
+ cs_spfree (C) ; /* free temporary matrix */
+ cs_free (w) ; /* free workspace */
+ cs_free (x) ;
+ return (ok ? N : cs_nfree (N)) ; /* return result if OK, else free it */
+}
+
+/* free workspace and return a csd result */
+csd *cs_ddone (csd *D, cs *C, void *w, int ok)
+{
+ cs_spfree (C) ; /* free temporary matrix */
+ cs_free (w) ; /* free workspace */
+ return (ok ? D : cs_dfree (D)) ; /* return result if OK, else free it */
+}
diff --git a/CSparse/Source/cs_utsolve.c b/CSparse/Source/cs_utsolve.c
new file mode 100644
index 0000000..9d6bf63
--- /dev/null
+++ b/CSparse/Source/cs_utsolve.c
@@ -0,0 +1,18 @@
+#include "cs.h"
+/* solve U'x=b where x and b are dense. x=b on input, solution on output. */
+int cs_utsolve (const cs *U, double *x)
+{
+ int p, j, n, *Up, *Ui ;
+ double *Ux ;
+ if (!CS_CSC (U) || !x) return (0) ; /* check inputs */
+ n = U->n ; Up = U->p ; Ui = U->i ; Ux = U->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Up [j] ; p < Up [j+1]-1 ; p++)
+ {
+ x [j] -= Ux [p] * x [Ui [p]] ;
+ }
+ x [j] /= Ux [Up [j+1]-1] ;
+ }
+ return (1) ;
+}
diff --git a/CSparse/Tcov/Makefile b/CSparse/Tcov/Makefile
new file mode 100644
index 0000000..57ce844
--- /dev/null
+++ b/CSparse/Tcov/Makefile
@@ -0,0 +1,102 @@
+# To run with valgrind:
+V =
+# V = valgrind -q
+
+# Linux test coverage
+CC = gcc
+CFLAGS = -O -g -fprofile-arcs -ftest-coverage \
+ -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \
+ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi \
+ -Wno-unused-parameter -Werror -I../Include -I../Demo
+
+run: all run1 runbook run3 runtest
+ ./covall
+
+all: cs_demo1 cs_demo2 cs_demo3 cstcov_test
+
+CS = cs_add.o cs_amd.o cs_chol.o cs_cholsol.o cs_counts.o cs_cumsum.o \
+ cs_droptol.o cs_dropzeros.o cs_dupl.o cs_entry.o \
+ cs_etree.o cs_fkeep.o cs_gaxpy.o cs_happly.o cs_house.o cs_ipvec.o \
+ cs_lsolve.o cs_ltsolve.o cs_lu.o cs_lusol.o cs_util.o cs_multiply.o \
+ cs_permute.o cs_pinv.o cs_post.o cs_pvec.o cs_qr.o cs_qrsol.o \
+ cs_scatter.o cs_schol.o cs_sqr.o cs_symperm.o cs_tdfs.o \
+ cs_transpose.o cs_compress.o cs_usolve.o cs_scc.o cs_maxtrans.o \
+ cs_dmperm.o cs_updown.o cs_print.o cs_norm.o cs_load.o cs_dfs.o \
+ cstcov_malloc_test.o cs_utsolve.o cs_reach.o cs_spsolve.o cs_ereach.o \
+ cs_leaf.o cs_randperm.o
+
+$(CS): ../Include/cs.h cstcov_malloc_test.h
+
+.PRECIOUS: cs_%.c cs_dem%.c
+
+cs_dem%.c:
+ - ln -s ../Demo/$@
+
+cs_%.c:
+ - ln -s ../Source/$@
+
+cs_demo1: $(CS) cs_demo1.c
+ $(CC) $(CFLAGS) -o cs_demo1 cs_demo1.c $(CS) -lm
+
+cs_demo2: $(CS) cs_demo2.c cs_demo.c
+ $(CC) $(CFLAGS) -o cs_demo2 cs_demo2.c cs_demo.c $(CS) -lm
+
+cs_demo3: $(CS) cs_demo3.c cs_demo.c
+ $(CC) $(CFLAGS) -o cs_demo3 cs_demo3.c cs_demo.c $(CS) -lm
+
+cstcov_test: $(CS) cstcov_test.c cs_demo.c
+ $(CC) $(CFLAGS) -o cstcov_test cstcov_test.c cs_demo.c $(CS) -lm
+
+# tiny tests
+run1: all
+ - $(V) ./cs_demo1 < nil
+ - $(V) ./cs_demo1 < zero
+ - $(V) ./cs_demo2 < nil
+ - $(V) ./cs_demo2 < zero
+ - $(V) ./cs_demo3 < nil
+
+# test coverage for book:
+runbook: all
+ - $(V) ./cs_demo1 < ../Matrix/t1
+ - $(V) ./cs_demo2 < ../Matrix/bcsstk01
+ - $(V) ./cs_demo2 < ../Matrix/fs_183_1
+ - $(V) ./cs_demo2 < ../Matrix/mbeacxc
+ - $(V) ./cs_demo2 < ../Matrix/west0067
+ - $(V) ./cs_demo2 < ../Matrix/lp_afiro
+ - $(V) ./cs_demo3 < ../Matrix/bcsstk16
+
+# other tests
+run3: all
+ - $(V) ./cs_demo2 < ../Matrix/t1
+ - $(V) ./cs_demo2 < ../Matrix/ash219
+ - $(V) ./cs_demo3 < ../Matrix/bcsstk01
+ - $(V) ./cs_demo2 < ../Matrix/bcsstk16
+ - $(V) ./cs_demo2 < ../Matrix/ibm32a
+ - $(V) ./cs_demo2 < ../Matrix/ibm32b
+
+# exhaustive memory tests
+runtest: all
+ - $(V) ./cstcov_test nil > test_nil.out
+ - $(V) ./cstcov_test zero > test_zero.out
+ - $(V) ./cstcov_test ../Matrix/t1 > test_t1.out
+ - $(V) ./cstcov_test ../Matrix/bcsstk01 > test_k1.out
+ - $(V) ./cstcov_test ../Matrix/fs_183_1 > test_fs.out
+ - $(V) ./cstcov_test ../Matrix/west0067 > test_we.out
+ - $(V) ./cstcov_test ../Matrix/ash219 > test_ash.out
+ - $(V) ./cstcov_test ../Matrix/lp_afiro > test_afiro.out
+
+readhb: readhb.f
+ f77 -o readhb readhb.f
+
+readhb.f:
+ - ln -s readhb.f
+
+clean:
+ rm -f *.o *.bbg *.da *.gcov *.gcda *.gcno
+
+purge: distclean
+
+# remove everything for distribution, including all symbolic links
+distclean: clean
+ rm -f cs_demo1 cs_demo2 readhb *.out *.a cs_demo3 cstcov_test cov.sort
+ rm -f cs_*.c
diff --git a/CSparse/Tcov/README.txt b/CSparse/Tcov/README.txt
new file mode 100644
index 0000000..74df39d
--- /dev/null
+++ b/CSparse/Tcov/README.txt
@@ -0,0 +1,13 @@
+CSparse/Tcov: comprehensive test coverage for CSparse. Requires Linux.
+Type "make" to compile, and then "make run" to run the tests.
+The test coverage is in cover.out. The test output is
+printed on stdout, except for cs_test (which prints its output in various
+*.out files).
+
+If the test is successful, the last line printed should be
+"statements not yet tested: 0", and all printed residuals should be small.
+
+Note that you will get warnings about unused parameters for some functions.
+These warnings can be safely ignored. They are parameters for functions that
+are passed to cs_fkeep, and all functions used in this manner must have the
+same calling sequence, even if some of the parameters are not used.
diff --git a/CSparse/Tcov/cov.awk b/CSparse/Tcov/cov.awk
new file mode 100644
index 0000000..5744b40
--- /dev/null
+++ b/CSparse/Tcov/cov.awk
@@ -0,0 +1,17 @@
+/cannot/
+
+/function/ { f = $8 }
+
+/file/ { f = $8 }
+
+/lines/ {
+
+ k = match ($1, "%") ;
+ p = substr ($1, 1, k-1) ;
+
+ if ((p+0) != 100)
+ {
+ printf "%8s %s\n", p, f
+ }
+}
+
diff --git a/CSparse/Tcov/covall b/CSparse/Tcov/covall
new file mode 100755
index 0000000..1751690
--- /dev/null
+++ b/CSparse/Tcov/covall
@@ -0,0 +1,7 @@
+#!/bin/csh
+ ./gcovs cs*.c |& awk -f cov.awk | sort -n > cov.out
+ sort -n cov.out > cov.sort
+ ./covs > covs.out
+ echo -n "statments not yet tested: "
+ grep "#####" *gcov | wc -l
+ ./cover *v > cover.out
diff --git a/CSparse/Tcov/covall.linux b/CSparse/Tcov/covall.linux
new file mode 100755
index 0000000..1751690
--- /dev/null
+++ b/CSparse/Tcov/covall.linux
@@ -0,0 +1,7 @@
+#!/bin/csh
+ ./gcovs cs*.c |& awk -f cov.awk | sort -n > cov.out
+ sort -n cov.out > cov.sort
+ ./covs > covs.out
+ echo -n "statments not yet tested: "
+ grep "#####" *gcov | wc -l
+ ./cover *v > cover.out
diff --git a/CSparse/Tcov/covall.sol b/CSparse/Tcov/covall.sol
new file mode 100755
index 0000000..457ad63
--- /dev/null
+++ b/CSparse/Tcov/covall.sol
@@ -0,0 +1,5 @@
+#!/bin/csh
+ tcov -x cm.profile cs*.c >& /dev/null
+ echo -n "statments not yet tested: "
+ ./covs > covs.out
+ grep "#####" *tcov | wc -l
diff --git a/CSparse/Tcov/cover b/CSparse/Tcov/cover
new file mode 100755
index 0000000..b3e685c
--- /dev/null
+++ b/CSparse/Tcov/cover
@@ -0,0 +1,9 @@
+#!/bin/csh
+# usage: cover files
+echo '================================================================='
+foreach file ($argv[1-])
+ echo $file
+ echo '================================================================='
+ grep "#####" -A5 -B5 $file
+ echo '================================================================='
+ end
diff --git a/CSparse/Tcov/covs b/CSparse/Tcov/covs
new file mode 100755
index 0000000..4171380
--- /dev/null
+++ b/CSparse/Tcov/covs
@@ -0,0 +1,7 @@
+#!/bin/csh
+echo '================================================================='
+foreach file (*.?cov)
+ echo $file
+ grep "#####" $file
+ echo '================================================================='
+ end
diff --git a/CSparse/Tcov/cstcov_malloc_test.c b/CSparse/Tcov/cstcov_malloc_test.c
new file mode 100644
index 0000000..28269f9
--- /dev/null
+++ b/CSparse/Tcov/cstcov_malloc_test.c
@@ -0,0 +1,34 @@
+#include "cstcov_malloc_test.h"
+int malloc_count = INT_MAX ;
+
+/* wrapper for malloc */
+void *cs_malloc (int n, size_t size)
+{
+ if (--malloc_count < 0) return (NULL) ; /* pretend to fail */
+ return (malloc (CS_MAX (n,1) * size)) ;
+}
+
+/* wrapper for calloc */
+void *cs_calloc (int n, size_t size)
+{
+ if (--malloc_count < 0) return (NULL) ; /* pretend to fail */
+ return (calloc (CS_MAX (n,1), size)) ;
+}
+
+/* wrapper for free */
+void *cs_free (void *p)
+{
+ if (p) free (p) ; /* free p if it is not already NULL */
+ return (NULL) ; /* return NULL to simplify the use of cs_free */
+}
+
+/* wrapper for realloc */
+void *cs_realloc (void *p, int n, size_t size, int *ok)
+{
+ void *pnew ;
+ *ok = 0 ;
+ if (--malloc_count < 0) return (p) ; /* pretend to fail */
+ pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */
+ *ok = (pnew != NULL) ;
+ return ((*ok) ? pnew : p) ; /* return original p if failure */
+}
diff --git a/CSparse/Tcov/cstcov_malloc_test.h b/CSparse/Tcov/cstcov_malloc_test.h
new file mode 100644
index 0000000..5bf6d75
--- /dev/null
+++ b/CSparse/Tcov/cstcov_malloc_test.h
@@ -0,0 +1,5 @@
+#include "cs.h"
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+EXTERN int malloc_count ;
diff --git a/CSparse/Tcov/cstcov_test.c b/CSparse/Tcov/cstcov_test.c
new file mode 100644
index 0000000..1626904
--- /dev/null
+++ b/CSparse/Tcov/cstcov_test.c
@@ -0,0 +1,30 @@
+#include "cs_demo.h"
+/* cs_test: read a matrix and run cs_demo2 and cs_demo3, using malloc tests. */
+
+#include "cstcov_malloc_test.h"
+
+int main (int argc, char **argv)
+{
+ FILE *f ;
+ problem *Prob ;
+ int trials, ok, demo ;
+ if (argc < 2) return (-1) ;
+ printf ("cs_test, file: %s\n", argv [1]) ;
+ for (demo = 2 ; demo <= 3 ; demo++)
+ {
+ printf ("demo: %d\n", demo) ;
+ for (trials = 0 ; trials < 4000 ; trials++)
+ {
+ malloc_count = trials ;
+ f = fopen (argv [1], "r") ;
+ if (!f) return (-1) ;
+ Prob = get_problem (f, (demo == 2) ? 1e-14 : 0) ;
+ fclose (f) ;
+ if (Prob) ok = (demo == 2) ? demo2 (Prob) : demo3 (Prob) ;
+ free_problem (Prob) ;
+ if (malloc_count > 0) break ;
+ }
+ printf ("demo %d # trials: %d\n", demo, trials) ;
+ }
+ return (0) ;
+}
diff --git a/CSparse/Tcov/gcovs b/CSparse/Tcov/gcovs
new file mode 100755
index 0000000..9fddaf1
--- /dev/null
+++ b/CSparse/Tcov/gcovs
@@ -0,0 +1,6 @@
+# usage: gcovs files
+echo '================================================================='
+foreach file ($argv[1-])
+ gcov -f $file
+ echo '================================================================='
+ end
diff --git a/CSparse/Tcov/nil b/CSparse/Tcov/nil
new file mode 100644
index 0000000..e69de29
diff --git a/CSparse/Tcov/zero b/CSparse/Tcov/zero
new file mode 100644
index 0000000..a5c7b77
--- /dev/null
+++ b/CSparse/Tcov/zero
@@ -0,0 +1 @@
+0 0 0
diff --git a/CSparse_to_CXSparse b/CSparse_to_CXSparse
new file mode 100755
index 0000000..b3f45d6
--- /dev/null
+++ b/CSparse_to_CXSparse
@@ -0,0 +1,341 @@
+#! /usr/bin/perl
+# Constructs the CXSparse package from CSparse, adding four different sets of
+# functions (int/UF_long, and double/complex). Backward compatible with
+# CSparse. No MATLAB interface is provided for CXSparse, however.
+#
+# To create CXSparse from CSparse, the ./CXSparse directory should not (yet)
+# exist. Use the following commands, where CSparse is the CSparse directory:
+#
+# ./CSparse_to_CXSparse CSparse CXSparse CXSparse_newfiles.tar.gz
+# cd CXSparse/Demo
+# make > cs_demo.out
+#
+# Alternatively, use "make cx", using the UFsparse/Makefile, while in the
+# UFsparse directory.
+#
+# Created by David Bateman, Feb. 2006, David dot Bateman atsign motorola
+# dot com. Modified by Tim Davis, Aug 23, 2006.
+
+use strict;
+use Cwd;
+use File::Find;
+use File::Basename;
+use Text::Wrap;
+use FileHandle;
+use IPC::Open3;
+
+my $in_dir = @ARGV[0];
+my $out_dir = @ARGV[1];
+my $tar_file = @ARGV[2];
+
+#-------------------------------------------------------------------------------
+# copy all files from CSparse to CXSparse
+#-------------------------------------------------------------------------------
+
+system ("cp -pr $in_dir $out_dir") ;
+
+#-------------------------------------------------------------------------------
+# Add the new files from the tar file given by the third argument
+#-------------------------------------------------------------------------------
+
+my $old_pwd = cwd();
+chdir($out_dir);
+system ("tar xpBvzf $old_pwd/$tar_file");
+chdir($old_pwd);
+
+#-------------------------------------------------------------------------------
+# Convert Demo/* files
+#-------------------------------------------------------------------------------
+
+# convert demo *.[ch] files into the four different versions (di, dl, ci, cl)
+my @demo_files = ('demo1.c', 'demo2.c', 'demo3.c', 'demo.c', 'demo.h') ;
+
+foreach my $fff ( @demo_files )
+{
+ my $infile = sprintf ("%s/Demo/cs_%s", $out_dir, $fff) ;
+
+ # create di version
+ my $outfile = sprintf ("%s/Demo/cs_di_%s", $out_dir, $fff) ;
+ if (open (OUT, ">$outfile"))
+ {
+ if (open (IN, $infile))
+ {
+ while (<IN>)
+ {
+ # change all "cs*" names to "cs_di*", except #include "cs.h"
+ s/\bcs/cs_di/g ;
+ s/cs_di\.h/cs.h/ ;
+ print OUT $_;
+ }
+ close (IN);
+ }
+ close (OUT);
+ }
+
+ # create dl version
+ my $outfile = sprintf ("%s/Demo/cs_dl_%s", $out_dir, $fff) ;
+ if (open (OUT, ">$outfile"))
+ {
+ if (open (IN, $infile))
+ {
+ while (<IN>)
+ {
+ # change all "cs*" names to "cs_dl*", except #include "cs.h"
+ s/\bcs/cs_dl/g ;
+ s/cs_dl\.h/cs.h/ ;
+ # change int to UF_long, except for "int main"
+ s/\bint\b/UF_long/g;
+ s/UF_long main/int main/;
+ # change %d to %ld in printf and scanf
+ s/\%d/\%ld/g;
+ print OUT $_;
+ }
+ close (IN);
+ }
+ close (OUT);
+ }
+
+ # create ci version
+ my $outfile = sprintf ("%s/Demo/cs_ci_%s", $out_dir, $fff) ;
+ if (open (OUT, ">$outfile"))
+ {
+ if (open (IN, $infile))
+ {
+ while (<IN>)
+ {
+ # change all "cs*" names to "cs_ci*", except #include "cs.h"
+ s/\bcs/cs_ci/g ;
+ s/cs_ci\.h/cs.h/ ;
+ # fabs becomes cabs
+ s/fabs/cabs/g;
+ # change double to cs_complex_t
+ s/\bdouble\b/cs_complex_t/g;
+ # (double) typecasts stay double
+ s/\(cs_complex_t\) /(double) /g;
+ # tic, toc, tol, and norm are double, not cs_complex_t
+ s/cs_complex_t norm/double norm/;
+ s/cs_complex_t tic/double tic/;
+ s/cs_complex_t toc \(cs_complex_t/double toc (double/;
+ s/cs_complex_t s = tic/double s = tic/;
+ s/cs_complex_t tol/double tol/;
+ # cumsum, S->lnz, S->unz are double
+ s/cs_complex_t lnz/double lnz/;
+ s/cs_complex_t unz/double unz/;
+ s/cs_complex_t cs_cumsum/double cs_cumsum/;
+ # local variable declarations that stay double
+ s/, / ;\n double / ;
+ print OUT $_;
+ }
+ close (IN);
+ }
+ close (OUT);
+ }
+
+ # create cl version
+ my $outfile = sprintf ("%s/Demo/cs_cl_%s", $out_dir, $fff) ;
+ if (open (OUT, ">$outfile"))
+ {
+ if (open (IN, $infile))
+ {
+ while (<IN>)
+ {
+ # change all "cs*" names to "cs_cl*", except #include "cs.h"
+ s/\bcs/cs_cl/g ;
+ s/cs_cl\.h/cs.h/ ;
+ # change int to UF_long, except for "int main"
+ s/\bint\b/UF_long/g;
+ s/UF_long main/int main/;
+ # change %d to %ld in printf and scanf
+ s/\%d/\%ld/g;
+ # fabs becomes cabs
+ s/fabs/cabs/g;
+ # change double to cs_complex_t
+ s/\bdouble\b/cs_complex_t/g;
+ # (double) typecasts stay double
+ s/\(cs_complex_t\) /(double) /g;
+ # tic, toc, tol, and norm are double, not cs_complex_t
+ s/cs_complex_t norm/double norm/;
+ s/cs_complex_t tic/double tic/;
+ s/cs_complex_t toc \(cs_complex_t/double toc (double/;
+ s/cs_complex_t s = tic/double s = tic/;
+ s/cs_complex_t tol/double tol/;
+ # cumsum, S->lnz, S->unz are double
+ s/cs_complex_t lnz/double lnz/;
+ s/cs_complex_t unz/double unz/;
+ s/cs_complex_t cs_cumsum/double cs_cumsum/;
+ # local variable declarations that stay double
+ s/, / ;\n double / ;
+ print OUT $_;
+ }
+ close (IN);
+ }
+ close (OUT);
+ }
+}
+
+#-------------------------------------------------------------------------------
+# Convert Source/*.c files (except cs_house.c)
+#-------------------------------------------------------------------------------
+
+# note that cs.h, cs_house.c, cs_updown.c, ...
+# are not included in this list
+my @src_files = ('Source/cs_add.c', 'Source/cs_amd.c', 'Source/cs_chol.c',
+ 'Source/cs_cholsol.c', 'Source/cs_counts.c', 'Source/cs_cumsum.c',
+ 'Source/cs_dfs.c', 'Source/cs_dmperm.c', 'Source/cs_droptol.c',
+ 'Source/cs_dropzeros.c', 'Source/cs_dupl.c', 'Source/cs_entry.c',
+ 'Source/cs_etree.c', 'Source/cs_fkeep.c', 'Source/cs_gaxpy.c',
+ 'Source/cs_happly.c', 'Source/cs_ipvec.c', 'Source/cs_load.c',
+ 'Source/cs_lsolve.c', 'Source/cs_ltsolve.c', 'Source/cs_lu.c',
+ 'Source/cs_lusol.c', 'Source/cs_malloc.c', 'Source/cs_maxtrans.c',
+ 'Source/cs_multiply.c', 'Source/cs_norm.c', 'Source/cs_permute.c',
+ 'Source/cs_pinv.c', 'Source/cs_post.c', 'Source/cs_print.c',
+ 'Source/cs_pvec.c', 'Source/cs_qr.c', 'Source/cs_qrsol.c',
+ 'Source/cs_scatter.c', 'Source/cs_scc.c', 'Source/cs_schol.c',
+ 'Source/cs_sqr.c', 'Source/cs_symperm.c', 'Source/cs_tdfs.c',
+ 'Source/cs_transpose.c', 'Source/cs_compress.c',
+ 'Source/cs_usolve.c', 'Source/cs_util.c', 'Source/cs_utsolve.c',
+ 'Source/cs_reach.c', 'Source/cs_spsolve.c', 'Source/cs_leaf.c',
+ 'Source/cs_ereach.c', 'Source/cs_randperm.c' ) ;
+
+foreach my $file ( @src_files )
+{
+ my $infile = sprintf ("%s/%s", $in_dir, $file) ;
+ my $outfile = sprintf ("%s/%s", $out_dir, $file) ;
+ my $fbase = basename($file,('.c'));
+
+ if (open(OUT,">$outfile"))
+ {
+ if (open(IN,$infile))
+ {
+ # my $qrsol_beta_seen = 0;
+ while (<IN>)
+ {
+
+ # change the name of the package (for cs_print.c)
+ s/CSparse/CXSparse/g;
+
+ # fabs becomes CS_ABS
+ s/fabs/CS_ABS/g;
+
+ # change int to CS_INT
+ s/\bint\b/CS_INT/g;
+
+ # change %d to "CS_ID" in printf and scanf (except version #'s)
+ s/\%d/"CS_ID"/g;
+ s/"CS_ID"\."CS_ID"\."CS_ID"/%d.%d.%d/;
+
+ # change double to CS_ENTRY
+ s/\bdouble\b/CS_ENTRY/g;
+
+ # (double) and (double *) typecasts stay double,
+ # tol and vnz for cs_vcount stays double
+ s/\(CS_ENTRY\) /(double) /g;
+ s/\(CS_ENTRY \*\) /(double \*) /;
+ s/CS_ENTRY tol/double tol/;
+ s/CS_ENTRY \*vnz/double \*vnz/;
+
+ # local variable declarations that stay double
+ s/, / ;\n double / ;
+
+ # nargin and nargout stay "int" for MATLAB mexFunctions
+ s/CS_INT nargin/int nargin/;
+ s/CS_INT nargout/int nargout/;
+
+ #---------------------------------------------------------------
+ # Special cases. Some undo changes made above.
+ #---------------------------------------------------------------
+
+ # cs_mex.c
+ if ($fbase =~ /cs_mex/)
+ {
+ s/matrix must be CS_ENTRY/matrix must be double/;
+ s/A->p =/A->p = (CS_INT *)/;
+ s/A->i =/A->i = (CS_INT *)/;
+ s/, A->p/, (mwIndex *) A->p/;
+ s/, A->i/, (mwIndex *) A->i/;
+ }
+
+ # fix comments in cs_add_mex.c and cs_permute_mex.c
+ if ($fbase =~ /cs_add_mex/ || $fbase =~ /cs_permute_mex/)
+ {
+ s/via CS_ENTRY transpose/via double transpose/;
+ }
+
+ # cs_chol
+ if ($fbase =~ /cs_chol/)
+ {
+ s/\(d <= 0\)/(CS_REAL (d) <= 0 || CS_IMAG (d) != 0)\n\t /;
+ s/lki \* lki/lki * CS_CONJ (lki)/;
+ s/ = lki/ = CS_CONJ (lki)/;
+ }
+
+ # cs_norm
+ if ($fbase =~ /cs_norm/)
+ {
+ s/^CS_ENTRY cs_norm/double cs_norm/;
+ }
+
+ # cs_cumsum
+ if ($fbase =~ /cs_cumsum/)
+ {
+ s/CS_ENTRY/double/;
+ }
+
+ # cs_transpose
+ if ($fbase =~ /cs_transpose/)
+ {
+ s/Ax \[p\]/(values > 0) ? CS_CONJ (Ax [p]) : Ax [p]/;
+ }
+
+ # cs_symperm
+ if ($fbase =~ /cs_symperm/)
+ {
+ s/Ax \[p\]/(i2 <= j2) ? Ax [p] : CS_CONJ (Ax [p])/;
+ }
+
+ # cs_qr
+ if ($fbase =~ /cs_qr/)
+ {
+ s/n, sizeof \(CS_ENTRY\)/n, sizeof (double)/;
+ }
+
+ # cs_happly
+ if ($fbase =~ /cs_happly/)
+ {
+ s/^(.*tau.*)(Vx\s*\[p\])/$1CS_CONJ ($2)/;
+ s/CS_ENTRY beta/double beta/;
+ }
+
+ # cs_ltsolve
+ if ($fbase =~ /cs_ltsolve/)
+ {
+ s/(Lx \[.*?\])(\s+[\*;])/CS_CONJ ($1)$2/;
+ }
+
+ # cs_utsolve
+ if ($fbase =~ /cs_utsolve/)
+ {
+ s/(Ux \[.*?\])(\s+[\*;])/CS_CONJ ($1)$2/;
+ }
+
+ # cs_load
+ if ($fbase =~ /cs_load/)
+ {
+ s/CS_ENTRY x ;/double x ;\n#ifdef CS_COMPLEX\n double xi ;\n#endif/ ;
+ s/^(\s*while.*)%lg(.*)&x\) == 3(.*)$/#ifdef CS_COMPLEX\n$1%lg %lg$2&x, &xi) == 4$3\n#else\n$1%lg$2&x) == 3$3\n#endif/;
+ s/(.*cs_entry.*), x(.*)$/#ifdef CS_COMPLEX\n$1, x + xi*I$2\n#else\n$1, x$2\n#endif/
+ }
+
+ # cs_print
+ if ($fbase =~ /cs_print/)
+ {
+ s/^(.*)%g(.*)Ax\s*\?\s*Ax\s*\[p\]\s*:\s*1(.*)/#ifdef CS_COMPLEX\n$1(%g, %g)$2\n\t\t Ax ? CS_REAL (Ax [p]) : 1, Ax ? CS_IMAG (Ax [p]) : 0$3\n#else\n$1%g$2Ax ? Ax [p] : 1$3\n#endif/;
+ }
+
+ print OUT $_;
+ }
+ close (IN);
+ }
+ close (OUT);
+ }
+}
diff --git a/CXSparse/Demo/Makefile b/CXSparse/Demo/Makefile
new file mode 100644
index 0000000..c1352f0
--- /dev/null
+++ b/CXSparse/Demo/Makefile
@@ -0,0 +1,168 @@
+CC = cc
+CFLAGS = -O
+
+I = -I../Include -I../../UFconfig
+
+CS = ../Lib/libcxsparse.a
+
+all: $(CS) cs_demo1 cs_demo2 cs_demo3 \
+ cs_di_demo1 cs_di_demo2 cs_di_demo3 \
+ cs_dl_demo1 cs_dl_demo2 cs_dl_demo3 \
+ cs_ci_demo1 cs_ci_demo2 cs_ci_demo3 \
+ cs_cl_demo1 cs_cl_demo2 cs_cl_demo3 \
+ tests cs_idemo
+
+tests: test_convert test test_di test_dl test_ci test_cl
+
+test: cs_demo1 cs_demo2 cs_demo3
+ - ./cs_demo1 < ../Matrix/t1
+ - ./cs_demo2 < ../Matrix/t1
+ - ./cs_demo2 < ../Matrix/fs_183_1
+ - ./cs_demo2 < ../Matrix/west0067
+ - ./cs_demo2 < ../Matrix/lp_afiro
+ - ./cs_demo2 < ../Matrix/ash219
+ - ./cs_demo2 < ../Matrix/mbeacxc
+ - ./cs_demo2 < ../Matrix/bcsstk01
+ - ./cs_demo3 < ../Matrix/bcsstk01
+ - ./cs_demo2 < ../Matrix/bcsstk16
+ - ./cs_demo3 < ../Matrix/bcsstk16
+
+test_di: cs_di_demo1 cs_di_demo2 cs_di_demo3
+ - ./cs_di_demo1 < ../Matrix/t1
+ - ./cs_di_demo2 < ../Matrix/t1
+ - ./cs_di_demo2 < ../Matrix/fs_183_1
+ - ./cs_di_demo2 < ../Matrix/west0067
+ - ./cs_di_demo2 < ../Matrix/lp_afiro
+ - ./cs_di_demo2 < ../Matrix/ash219
+ - ./cs_di_demo2 < ../Matrix/mbeacxc
+ - ./cs_di_demo2 < ../Matrix/bcsstk01
+ - ./cs_di_demo3 < ../Matrix/bcsstk01
+ - ./cs_di_demo2 < ../Matrix/bcsstk16
+ - ./cs_di_demo3 < ../Matrix/bcsstk16
+
+test_dl: cs_dl_demo1 cs_dl_demo2 cs_dl_demo3
+ - ./cs_dl_demo1 < ../Matrix/t1
+ - ./cs_dl_demo2 < ../Matrix/t1
+ - ./cs_dl_demo2 < ../Matrix/fs_183_1
+ - ./cs_dl_demo2 < ../Matrix/west0067
+ - ./cs_dl_demo2 < ../Matrix/lp_afiro
+ - ./cs_dl_demo2 < ../Matrix/ash219
+ - ./cs_dl_demo2 < ../Matrix/mbeacxc
+ - ./cs_dl_demo2 < ../Matrix/bcsstk01
+ - ./cs_dl_demo3 < ../Matrix/bcsstk01
+ - ./cs_dl_demo2 < ../Matrix/bcsstk16
+ - ./cs_dl_demo3 < ../Matrix/bcsstk16
+
+test_ci: cs_ci_demo1 cs_ci_demo2 cs_ci_demo3
+ - ./cs_ci_demo1 < ../Matrix/t2
+ - ./cs_ci_demo2 < ../Matrix/t2
+ - ./cs_ci_demo2 < ../Matrix/t3
+ - ./cs_ci_demo2 < ../Matrix/t4
+ - ./cs_ci_demo2 < ../Matrix/c_west0067
+ - ./cs_ci_demo2 < ../Matrix/c_mbeacxc
+ - ./cs_ci_demo2 < ../Matrix/young1c
+ - ./cs_ci_demo2 < ../Matrix/qc324
+ - ./cs_ci_demo2 < ../Matrix/neumann
+ - ./cs_ci_demo2 < ../Matrix/c4
+ - ./cs_ci_demo3 < ../Matrix/c4
+ - ./cs_ci_demo2 < ../Matrix/mhd1280b
+ - ./cs_ci_demo3 < ../Matrix/mhd1280b
+
+test_cl: cs_cl_demo1 cs_cl_demo2 cs_cl_demo3
+ - ./cs_cl_demo1 < ../Matrix/t2
+ - ./cs_cl_demo2 < ../Matrix/t2
+ - ./cs_cl_demo2 < ../Matrix/t3
+ - ./cs_cl_demo2 < ../Matrix/t4
+ - ./cs_cl_demo2 < ../Matrix/c_west0067
+ - ./cs_cl_demo2 < ../Matrix/c_mbeacxc
+ - ./cs_cl_demo2 < ../Matrix/young1c
+ - ./cs_cl_demo2 < ../Matrix/qc324
+ - ./cs_cl_demo2 < ../Matrix/neumann
+ - ./cs_cl_demo2 < ../Matrix/c4
+ - ./cs_cl_demo3 < ../Matrix/c4
+ - ./cs_cl_demo2 < ../Matrix/mhd1280b
+ - ./cs_cl_demo3 < ../Matrix/mhd1280b
+
+test_convert: cs_idemo cs_ldemo
+ - ./cs_idemo < ../Matrix/t2
+ - ./cs_ldemo < ../Matrix/t2
+
+$(CS):
+ ( cd ../Lib ; $(MAKE) )
+
+cs_demo1: $(CS) cs_demo1.c Makefile $(CS)
+ $(CC) $(I) -o cs_demo1 cs_demo1.c $(CS) -lm
+
+cs_demo2: $(CS) cs_demo2.c cs_demo.c cs_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_demo2 cs_demo2.c cs_demo.c $(CS) -lm
+
+cs_demo3: $(CS) cs_demo3.c cs_demo.c cs_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_demo3 cs_demo3.c cs_demo.c $(CS) -lm
+
+
+
+
+cs_di_demo1: $(CS) cs_di_demo1.c Makefile $(CS)
+ $(CC) $(I) -o cs_di_demo1 cs_di_demo1.c $(CS) -lm
+
+cs_di_demo2: $(CS) cs_di_demo2.c cs_di_demo.c cs_di_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_di_demo2 cs_di_demo2.c cs_di_demo.c $(CS) -lm
+
+cs_di_demo3: $(CS) cs_di_demo3.c cs_di_demo.c cs_di_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_di_demo3 cs_di_demo3.c cs_di_demo.c $(CS) -lm
+
+
+
+
+cs_ci_demo1: $(CS) cs_ci_demo1.c Makefile $(CS)
+ $(CC) $(I) -o cs_ci_demo1 cs_ci_demo1.c $(CS) -lm
+
+cs_ci_demo2: $(CS) cs_ci_demo2.c cs_ci_demo.c cs_ci_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_ci_demo2 cs_ci_demo2.c cs_ci_demo.c $(CS) -lm
+
+cs_ci_demo3: $(CS) cs_ci_demo3.c cs_ci_demo.c cs_ci_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_ci_demo3 cs_ci_demo3.c cs_ci_demo.c $(CS) -lm
+
+
+
+cs_dl_demo1: $(CS) cs_dl_demo1.c Makefile $(CS)
+ $(CC) $(I) -o cs_dl_demo1 cs_dl_demo1.c $(CS) -lm
+
+cs_dl_demo2: $(CS) cs_dl_demo2.c cs_dl_demo.c cs_dl_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_dl_demo2 cs_dl_demo2.c cs_dl_demo.c $(CS) -lm
+
+cs_dl_demo3: $(CS) cs_dl_demo3.c cs_dl_demo.c cs_dl_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_dl_demo3 cs_dl_demo3.c cs_dl_demo.c $(CS) -lm
+
+
+cs_cl_demo1: $(CS) cs_cl_demo1.c Makefile $(CS)
+ $(CC) $(I) -o cs_cl_demo1 cs_cl_demo1.c $(CS) -lm
+
+cs_cl_demo2: $(CS) cs_cl_demo2.c cs_cl_demo.c cs_cl_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_cl_demo2 cs_cl_demo2.c cs_cl_demo.c $(CS) -lm
+
+cs_cl_demo3: $(CS) cs_cl_demo3.c cs_cl_demo.c cs_cl_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_cl_demo3 cs_cl_demo3.c cs_cl_demo.c $(CS) -lm
+
+
+
+
+cs_idemo: $(CS) cs_idemo.c Makefile $(CS)
+ $(CC) $(I) -o cs_idemo cs_idemo.c $(CS) -lm
+
+cs_ldemo: $(CS) cs_ldemo.c Makefile $(CS)
+ $(CC) $(I) -DCS_LONG -o cs_ldemo cs_ldemo.c $(CS) -lm
+
+
+clean:
+ rm -f *.o
+
+purge: distclean
+
+distclean: clean
+ rm -f cs_demo1 cs_demo2 cs_demo3 *.a
+ rm -f cs_di_demo1 cs_di_demo2 cs_di_demo3
+ rm -f cs_dl_demo1 cs_dl_demo2 cs_dl_demo3
+ rm -f cs_ci_demo1 cs_ci_demo2 cs_ci_demo3
+ rm -f cs_cl_demo1 cs_cl_demo2 cs_cl_demo3
+ rm -f cs_idemo cs_ldemo
diff --git a/CXSparse/Demo/README.txt b/CXSparse/Demo/README.txt
new file mode 100644
index 0000000..93eeb3a
--- /dev/null
+++ b/CXSparse/Demo/README.txt
@@ -0,0 +1,4 @@
+CXSparse/Demo: to compile a run the demos, just type "make" in this directory.
+The printed residuals should all be small, except for the mbeacxc matrix
+(which is numerically and structurally singular), and ash219 (which is a
+least-squares problem). See cs_demo.out for the proper output of "make".
diff --git a/CXSparse/Demo/cs_ci_demo.c b/CXSparse/Demo/cs_ci_demo.c
new file mode 100644
index 0000000..96b22a2
--- /dev/null
+++ b/CXSparse/Demo/cs_ci_demo.c
@@ -0,0 +1,288 @@
+#include "cs_ci_demo.h"
+#include <time.h>
+/* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */
+static int is_sym (cs_ci *A)
+{
+ int is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ;
+ if (m != n) return (0) ;
+ is_upper = 1 ;
+ is_lower = 1 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ if (Ai [p] > j) is_upper = 0 ;
+ if (Ai [p] < j) is_lower = 0 ;
+ }
+ }
+ return (is_upper ? 1 : (is_lower ? -1 : 0)) ;
+}
+
+/* true for off-diagonal entries */
+static int dropdiag (int i, int j, cs_complex_t aij, void *other) { return (i != j) ;}
+
+/* C = A + triu(A,1)' */
+static cs_ci *make_sym (cs_ci *A)
+{
+ cs_ci *AT, *C ;
+ AT = cs_ci_transpose (A, 1) ; /* AT = A' */
+ cs_ci_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */
+ C = cs_ci_add (A, AT, 1, 1) ; /* C = A+AT */
+ cs_ci_spfree (AT) ;
+ return (C) ;
+}
+
+/* create a right-hand side */
+static void rhs (cs_complex_t *x, cs_complex_t *b, int m)
+{
+ int i ;
+ for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ;
+ for (i = 0 ; i < m ; i++) x [i] = b [i] ;
+}
+
+/* infinity-norm of x */
+static double norm (cs_complex_t *x, int n)
+{
+ int i ;
+ double normx = 0 ;
+ for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, cabs (x [i])) ;
+ return (normx) ;
+}
+
+/* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */
+static void print_resid (int ok, cs_ci *A, cs_complex_t *x, cs_complex_t *b, cs_complex_t *resid)
+{
+ int i, m, n ;
+ if (!ok) { printf (" (failed)\n") ; return ; }
+ m = A->m ; n = A->n ;
+ for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */
+ cs_ci_gaxpy (A, x, resid) ; /* resid = resid + A*x */
+ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 :
+ (cs_ci_norm (A) * norm (x,n) + norm (b,m)))) ;
+}
+
+static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; }
+static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; }
+
+static void print_order (int order)
+{
+ switch (order)
+ {
+ case 0: printf ("natural ") ; break ;
+ case 1: printf ("amd(A+A') ") ; break ;
+ case 2: printf ("amd(S'*S) ") ; break ;
+ case 3: printf ("amd(A'*A) ") ; break ;
+ }
+}
+
+/* read a problem from a file */
+problem *get_problem (FILE *f, double tol)
+{
+ cs_ci *T, *A, *C ;
+ int sym, m, n, mn, nz1, nz2 ;
+ problem *Prob ;
+ Prob = cs_ci_calloc (1, sizeof (problem)) ;
+ if (!Prob) return (NULL) ;
+ T = cs_ci_load (f) ; /* load triplet matrix T from a file */
+ Prob->A = A = cs_ci_compress (T) ; /* A = compressed-column form of T */
+ cs_ci_spfree (T) ; /* clear T */
+ if (!cs_ci_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */
+ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */
+ m = A->m ; n = A->n ;
+ mn = CS_MAX (m,n) ;
+ nz1 = A->p [n] ;
+ cs_ci_dropzeros (A) ; /* drop zero entries */
+ nz2 = A->p [n] ;
+ if (tol > 0) cs_ci_droptol (A, tol) ; /* drop tiny entries (just to test) */
+ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */
+ if (!C) return (free_problem (Prob)) ;
+ printf ("\n--- Matrix: %d-by-%d, nnz: %d (sym: %d: nnz %d), norm: %8.2e\n",
+ m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_ci_norm (C)) ;
+ if (nz1 != nz2) printf ("zero entries dropped: %d\n", nz1 - nz2) ;
+ if (nz2 != A->p [n]) printf ("tiny entries dropped: %d\n", nz2 - A->p [n]) ;
+ Prob->b = cs_ci_malloc (mn, sizeof (cs_complex_t)) ;
+ Prob->x = cs_ci_malloc (mn, sizeof (cs_complex_t)) ;
+ Prob->resid = cs_ci_malloc (mn, sizeof (cs_complex_t)) ;
+ return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ;
+}
+
+/* free a problem */
+problem *free_problem (problem *Prob)
+{
+ if (!Prob) return (NULL) ;
+ cs_ci_spfree (Prob->A) ;
+ if (Prob->sym) cs_ci_spfree (Prob->C) ;
+ cs_ci_free (Prob->b) ;
+ cs_ci_free (Prob->x) ;
+ cs_ci_free (Prob->resid) ;
+ return (cs_ci_free (Prob)) ;
+}
+
+/* solve a linear system using Cholesky, LU, and QR, with various orderings */
+int demo2 (problem *Prob)
+{
+ cs_ci *A, *C ;
+ cs_complex_t *b, *x, *resid ;
+ double t, tol ;
+ int k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ;
+ cs_cid *D ;
+ if (!Prob) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ m = A->m ; n = A->n ;
+ tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */
+ D = cs_ci_dmperm (C, 1) ; /* randomized dmperm analysis */
+ if (!D) return (0) ;
+ nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ;
+ sprank = rr [3] ;
+ for (ns = 0, k = 0 ; k < nb ; k++)
+ {
+ ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ;
+ }
+ printf ("blocks: %d singletons: %d structural rank: %d\n", nb, ns, sprank) ;
+ cs_ci_dfree (D) ;
+ for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("QR ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_ci_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/
+ for (order = 0 ; order <= 3 ; order++) /* try all orderings */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("LU ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_ci_lusol (order, C, x, tol) ; /* solve Ax=b with LU */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (!Prob->sym) return (1) ;
+ for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("Chol ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_ci_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ return (1) ;
+}
+
+/* free workspace for demo3 */
+static int done3 (int ok, cs_cis *S, cs_cin *N, cs_complex_t *y, cs_ci *W, cs_ci *E, int *p)
+{
+ cs_ci_sfree (S) ;
+ cs_ci_nfree (N) ;
+ cs_ci_free (y) ;
+ cs_ci_spfree (W) ;
+ cs_ci_spfree (E) ;
+ cs_ci_free (p) ;
+ return (ok) ;
+}
+
+/* Cholesky update/downdate */
+int demo3 (problem *Prob)
+{
+ cs_ci *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ;
+ int n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ;
+ cs_complex_t *b, *x, *resid, *y = NULL, *Lx, *Wx, s ;
+ double t, t1 ;
+ cs_cis *S = NULL ;
+ cs_cin *N = NULL ;
+ if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ n = A->n ;
+ if (!Prob->sym || n == 0) return (1) ;
+ rhs (x, b, n) ; /* compute right-hand side */
+ printf ("\nchol then update/downdate ") ;
+ print_order (1) ;
+ y = cs_ci_malloc (n, sizeof (cs_complex_t)) ;
+ t = tic () ;
+ S = cs_ci_schol (1, C) ; /* symbolic Chol, amd(A+A') */
+ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ;
+ t = tic () ;
+ N = cs_ci_chol (C, S) ; /* numeric Cholesky */
+ printf ("numeric chol time %8.2f\n", toc (t)) ;
+ if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_ci_lsolve (N->L, y) ; /* y = L\y */
+ cs_ci_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ printf ("solve chol time %8.2f\n", toc (t)) ;
+ printf ("original: ") ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ k = n/2 ; /* construct W */
+ W = cs_ci_spalloc (n, 1, n, 1, 0) ;
+ if (!W) return (done3 (0, S, N, y, W, E, p)) ;
+ Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ;
+ Wp = W->p ; Wi = W->i ; Wx = W->x ;
+ Wp [0] = 0 ;
+ p1 = Lp [k] ;
+ Wp [1] = Lp [k+1] - p1 ;
+ s = Lx [p1] ;
+ srand (1) ;
+ for ( ; p1 < Lp [k+1] ; p1++)
+ {
+ p2 = p1 - Lp [k] ;
+ Wi [p2] = Li [p1] ;
+ Wx [p2] = s * rand () / ((double) RAND_MAX) ;
+ }
+ t = tic () ;
+ ok = cs_ci_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */
+ t1 = toc (t) ;
+ printf ("update: time: %8.2f\n", t1) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_ci_lsolve (N->L, y) ; /* y = L\y */
+ cs_ci_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ p = cs_ci_pinv (S->pinv, n) ;
+ W2 = cs_ci_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */
+ WT = cs_ci_transpose (W2,1) ;
+ WW = cs_ci_multiply (W2, WT) ;
+ cs_ci_spfree (WT) ;
+ cs_ci_spfree (W2) ;
+ E = cs_ci_add (C, WW, 1, 1) ;
+ cs_ci_spfree (WW) ;
+ if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("update: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ cs_ci_nfree (N) ; /* clear N */
+ t = tic () ;
+ N = cs_ci_chol (E, S) ; /* numeric Cholesky */
+ if (!N) return (done3 (0, S, N, y, W, E, p)) ;
+ cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_ci_lsolve (N->L, y) ; /* y = L\y */
+ cs_ci_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("rechol: time: %8.2f (incl solve) ", t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ t = tic () ;
+ ok = cs_ci_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */
+ t1 = toc (t) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("downdate: time: %8.2f\n", t1) ;
+ t = tic () ;
+ cs_ci_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_ci_lsolve (N->L, y) ; /* y = L\y */
+ cs_ci_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_ci_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("downdate: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ return (done3 (1, S, N, y, W, E, p)) ;
+}
diff --git a/CXSparse/Demo/cs_ci_demo.h b/CXSparse/Demo/cs_ci_demo.h
new file mode 100644
index 0000000..8b74ef3
--- /dev/null
+++ b/CXSparse/Demo/cs_ci_demo.h
@@ -0,0 +1,15 @@
+#include "cs.h"
+typedef struct problem_struct
+{
+ cs_ci *A ;
+ cs_ci *C ;
+ int sym ;
+ cs_complex_t *x ;
+ cs_complex_t *b ;
+ cs_complex_t *resid ;
+} problem ;
+
+problem *get_problem (FILE *f, double tol) ;
+int demo2 (problem *Prob) ;
+int demo3 (problem *Prob) ;
+problem *free_problem (problem *Prob) ;
diff --git a/CXSparse/Demo/cs_ci_demo1.c b/CXSparse/Demo/cs_ci_demo1.c
new file mode 100644
index 0000000..7a0950a
--- /dev/null
+++ b/CXSparse/Demo/cs_ci_demo1.c
@@ -0,0 +1,27 @@
+#include "cs.h"
+int main (void)
+{
+ cs_ci *T, *A, *Eye, *AT, *C, *D ;
+ int i, m ;
+ T = cs_ci_load (stdin) ; /* load triplet matrix T from stdin */
+ printf ("T:\n") ; cs_ci_print (T, 0) ; /* print T */
+ A = cs_ci_compress (T) ; /* A = compressed-column form of T */
+ printf ("A:\n") ; cs_ci_print (A, 0) ; /* print A */
+ cs_ci_spfree (T) ; /* clear T */
+ AT = cs_ci_transpose (A, 1) ; /* AT = A' */
+ printf ("AT:\n") ; cs_ci_print (AT, 0) ; /* print AT */
+ m = A ? A->m : 0 ; /* m = # of rows of A */
+ T = cs_ci_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */
+ for (i = 0 ; i < m ; i++) cs_ci_entry (T, i, i, 1) ;
+ Eye = cs_ci_compress (T) ; /* Eye = speye (m) */
+ cs_ci_spfree (T) ;
+ C = cs_ci_multiply (A, AT) ; /* C = A*A' */
+ D = cs_ci_add (C, Eye, 1, cs_ci_norm (C)) ; /* D = C + Eye*norm (C,1) */
+ printf ("D:\n") ; cs_ci_print (D, 0) ; /* print D */
+ cs_ci_spfree (A) ; /* clear A AT C D Eye */
+ cs_ci_spfree (AT) ;
+ cs_ci_spfree (C) ;
+ cs_ci_spfree (D) ;
+ cs_ci_spfree (Eye) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_ci_demo2.c b/CXSparse/Demo/cs_ci_demo2.c
new file mode 100644
index 0000000..900571a
--- /dev/null
+++ b/CXSparse/Demo/cs_ci_demo2.c
@@ -0,0 +1,9 @@
+#include "cs_ci_demo.h"
+/* cs_ci_demo2: read a matrix and solve a linear system */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 1e-14) ;
+ demo2 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_ci_demo3.c b/CXSparse/Demo/cs_ci_demo3.c
new file mode 100644
index 0000000..e05379d
--- /dev/null
+++ b/CXSparse/Demo/cs_ci_demo3.c
@@ -0,0 +1,9 @@
+#include "cs_ci_demo.h"
+/* cs_ci_demo3: read a matrix and test Cholesky update/downdate */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 0) ;
+ demo3 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_cl_demo.c b/CXSparse/Demo/cs_cl_demo.c
new file mode 100644
index 0000000..e294ef5
--- /dev/null
+++ b/CXSparse/Demo/cs_cl_demo.c
@@ -0,0 +1,288 @@
+#include "cs_cl_demo.h"
+#include <time.h>
+/* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */
+static UF_long is_sym (cs_cl *A)
+{
+ UF_long is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ;
+ if (m != n) return (0) ;
+ is_upper = 1 ;
+ is_lower = 1 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ if (Ai [p] > j) is_upper = 0 ;
+ if (Ai [p] < j) is_lower = 0 ;
+ }
+ }
+ return (is_upper ? 1 : (is_lower ? -1 : 0)) ;
+}
+
+/* true for off-diagonal entries */
+static UF_long dropdiag (UF_long i, UF_long j, cs_complex_t aij, void *other) { return (i != j) ;}
+
+/* C = A + triu(A,1)' */
+static cs_cl *make_sym (cs_cl *A)
+{
+ cs_cl *AT, *C ;
+ AT = cs_cl_transpose (A, 1) ; /* AT = A' */
+ cs_cl_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */
+ C = cs_cl_add (A, AT, 1, 1) ; /* C = A+AT */
+ cs_cl_spfree (AT) ;
+ return (C) ;
+}
+
+/* create a right-hand side */
+static void rhs (cs_complex_t *x, cs_complex_t *b, UF_long m)
+{
+ UF_long i ;
+ for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ;
+ for (i = 0 ; i < m ; i++) x [i] = b [i] ;
+}
+
+/* infinity-norm of x */
+static double norm (cs_complex_t *x, UF_long n)
+{
+ UF_long i ;
+ double normx = 0 ;
+ for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, cabs (x [i])) ;
+ return (normx) ;
+}
+
+/* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */
+static void print_resid (UF_long ok, cs_cl *A, cs_complex_t *x, cs_complex_t *b, cs_complex_t *resid)
+{
+ UF_long i, m, n ;
+ if (!ok) { printf (" (failed)\n") ; return ; }
+ m = A->m ; n = A->n ;
+ for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */
+ cs_cl_gaxpy (A, x, resid) ; /* resid = resid + A*x */
+ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 :
+ (cs_cl_norm (A) * norm (x,n) + norm (b,m)))) ;
+}
+
+static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; }
+static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; }
+
+static void print_order (UF_long order)
+{
+ switch (order)
+ {
+ case 0: printf ("natural ") ; break ;
+ case 1: printf ("amd(A+A') ") ; break ;
+ case 2: printf ("amd(S'*S) ") ; break ;
+ case 3: printf ("amd(A'*A) ") ; break ;
+ }
+}
+
+/* read a problem from a file */
+problem *get_problem (FILE *f, double tol)
+{
+ cs_cl *T, *A, *C ;
+ UF_long sym, m, n, mn, nz1, nz2 ;
+ problem *Prob ;
+ Prob = cs_cl_calloc (1, sizeof (problem)) ;
+ if (!Prob) return (NULL) ;
+ T = cs_cl_load (f) ; /* load triplet matrix T from a file */
+ Prob->A = A = cs_cl_compress (T) ; /* A = compressed-column form of T */
+ cs_cl_spfree (T) ; /* clear T */
+ if (!cs_cl_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */
+ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */
+ m = A->m ; n = A->n ;
+ mn = CS_MAX (m,n) ;
+ nz1 = A->p [n] ;
+ cs_cl_dropzeros (A) ; /* drop zero entries */
+ nz2 = A->p [n] ;
+ if (tol > 0) cs_cl_droptol (A, tol) ; /* drop tiny entries (just to test) */
+ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */
+ if (!C) return (free_problem (Prob)) ;
+ printf ("\n--- Matrix: %ld-by-%ld, nnz: %ld (sym: %ld: nnz %ld), norm: %8.2e\n",
+ m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_cl_norm (C)) ;
+ if (nz1 != nz2) printf ("zero entries dropped: %ld\n", nz1 - nz2) ;
+ if (nz2 != A->p [n]) printf ("tiny entries dropped: %ld\n", nz2 - A->p [n]) ;
+ Prob->b = cs_cl_malloc (mn, sizeof (cs_complex_t)) ;
+ Prob->x = cs_cl_malloc (mn, sizeof (cs_complex_t)) ;
+ Prob->resid = cs_cl_malloc (mn, sizeof (cs_complex_t)) ;
+ return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ;
+}
+
+/* free a problem */
+problem *free_problem (problem *Prob)
+{
+ if (!Prob) return (NULL) ;
+ cs_cl_spfree (Prob->A) ;
+ if (Prob->sym) cs_cl_spfree (Prob->C) ;
+ cs_cl_free (Prob->b) ;
+ cs_cl_free (Prob->x) ;
+ cs_cl_free (Prob->resid) ;
+ return (cs_cl_free (Prob)) ;
+}
+
+/* solve a linear system using Cholesky, LU, and QR, with various orderings */
+UF_long demo2 (problem *Prob)
+{
+ cs_cl *A, *C ;
+ cs_complex_t *b, *x, *resid ;
+ double t, tol ;
+ UF_long k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ;
+ cs_cld *D ;
+ if (!Prob) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ m = A->m ; n = A->n ;
+ tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */
+ D = cs_cl_dmperm (C, 1) ; /* randomized dmperm analysis */
+ if (!D) return (0) ;
+ nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ;
+ sprank = rr [3] ;
+ for (ns = 0, k = 0 ; k < nb ; k++)
+ {
+ ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ;
+ }
+ printf ("blocks: %ld singletons: %ld structural rank: %ld\n", nb, ns, sprank) ;
+ cs_cl_dfree (D) ;
+ for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("QR ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_cl_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/
+ for (order = 0 ; order <= 3 ; order++) /* try all orderings */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("LU ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_cl_lusol (order, C, x, tol) ; /* solve Ax=b with LU */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (!Prob->sym) return (1) ;
+ for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("Chol ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_cl_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ return (1) ;
+}
+
+/* free workspace for demo3 */
+static UF_long done3 (UF_long ok, cs_cls *S, cs_cln *N, cs_complex_t *y, cs_cl *W, cs_cl *E, UF_long *p)
+{
+ cs_cl_sfree (S) ;
+ cs_cl_nfree (N) ;
+ cs_cl_free (y) ;
+ cs_cl_spfree (W) ;
+ cs_cl_spfree (E) ;
+ cs_cl_free (p) ;
+ return (ok) ;
+}
+
+/* Cholesky update/downdate */
+UF_long demo3 (problem *Prob)
+{
+ cs_cl *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ;
+ UF_long n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ;
+ cs_complex_t *b, *x, *resid, *y = NULL, *Lx, *Wx, s ;
+ double t, t1 ;
+ cs_cls *S = NULL ;
+ cs_cln *N = NULL ;
+ if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ n = A->n ;
+ if (!Prob->sym || n == 0) return (1) ;
+ rhs (x, b, n) ; /* compute right-hand side */
+ printf ("\nchol then update/downdate ") ;
+ print_order (1) ;
+ y = cs_cl_malloc (n, sizeof (cs_complex_t)) ;
+ t = tic () ;
+ S = cs_cl_schol (1, C) ; /* symbolic Chol, amd(A+A') */
+ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ;
+ t = tic () ;
+ N = cs_cl_chol (C, S) ; /* numeric Cholesky */
+ printf ("numeric chol time %8.2f\n", toc (t)) ;
+ if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_cl_lsolve (N->L, y) ; /* y = L\y */
+ cs_cl_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ printf ("solve chol time %8.2f\n", toc (t)) ;
+ printf ("original: ") ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ k = n/2 ; /* construct W */
+ W = cs_cl_spalloc (n, 1, n, 1, 0) ;
+ if (!W) return (done3 (0, S, N, y, W, E, p)) ;
+ Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ;
+ Wp = W->p ; Wi = W->i ; Wx = W->x ;
+ Wp [0] = 0 ;
+ p1 = Lp [k] ;
+ Wp [1] = Lp [k+1] - p1 ;
+ s = Lx [p1] ;
+ srand (1) ;
+ for ( ; p1 < Lp [k+1] ; p1++)
+ {
+ p2 = p1 - Lp [k] ;
+ Wi [p2] = Li [p1] ;
+ Wx [p2] = s * rand () / ((double) RAND_MAX) ;
+ }
+ t = tic () ;
+ ok = cs_cl_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */
+ t1 = toc (t) ;
+ printf ("update: time: %8.2f\n", t1) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_cl_lsolve (N->L, y) ; /* y = L\y */
+ cs_cl_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ p = cs_cl_pinv (S->pinv, n) ;
+ W2 = cs_cl_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */
+ WT = cs_cl_transpose (W2,1) ;
+ WW = cs_cl_multiply (W2, WT) ;
+ cs_cl_spfree (WT) ;
+ cs_cl_spfree (W2) ;
+ E = cs_cl_add (C, WW, 1, 1) ;
+ cs_cl_spfree (WW) ;
+ if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("update: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ cs_cl_nfree (N) ; /* clear N */
+ t = tic () ;
+ N = cs_cl_chol (E, S) ; /* numeric Cholesky */
+ if (!N) return (done3 (0, S, N, y, W, E, p)) ;
+ cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_cl_lsolve (N->L, y) ; /* y = L\y */
+ cs_cl_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("rechol: time: %8.2f (incl solve) ", t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ t = tic () ;
+ ok = cs_cl_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */
+ t1 = toc (t) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("downdate: time: %8.2f\n", t1) ;
+ t = tic () ;
+ cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_cl_lsolve (N->L, y) ; /* y = L\y */
+ cs_cl_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("downdate: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ return (done3 (1, S, N, y, W, E, p)) ;
+}
diff --git a/CXSparse/Demo/cs_cl_demo.h b/CXSparse/Demo/cs_cl_demo.h
new file mode 100644
index 0000000..2ae9f82
--- /dev/null
+++ b/CXSparse/Demo/cs_cl_demo.h
@@ -0,0 +1,15 @@
+#include "cs.h"
+typedef struct problem_struct
+{
+ cs_cl *A ;
+ cs_cl *C ;
+ UF_long sym ;
+ cs_complex_t *x ;
+ cs_complex_t *b ;
+ cs_complex_t *resid ;
+} problem ;
+
+problem *get_problem (FILE *f, double tol) ;
+UF_long demo2 (problem *Prob) ;
+UF_long demo3 (problem *Prob) ;
+problem *free_problem (problem *Prob) ;
diff --git a/CXSparse/Demo/cs_cl_demo1.c b/CXSparse/Demo/cs_cl_demo1.c
new file mode 100644
index 0000000..d0aaceb
--- /dev/null
+++ b/CXSparse/Demo/cs_cl_demo1.c
@@ -0,0 +1,27 @@
+#include "cs.h"
+int main (void)
+{
+ cs_cl *T, *A, *Eye, *AT, *C, *D ;
+ UF_long i, m ;
+ T = cs_cl_load (stdin) ; /* load triplet matrix T from stdin */
+ printf ("T:\n") ; cs_cl_print (T, 0) ; /* print T */
+ A = cs_cl_compress (T) ; /* A = compressed-column form of T */
+ printf ("A:\n") ; cs_cl_print (A, 0) ; /* print A */
+ cs_cl_spfree (T) ; /* clear T */
+ AT = cs_cl_transpose (A, 1) ; /* AT = A' */
+ printf ("AT:\n") ; cs_cl_print (AT, 0) ; /* print AT */
+ m = A ? A->m : 0 ; /* m = # of rows of A */
+ T = cs_cl_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */
+ for (i = 0 ; i < m ; i++) cs_cl_entry (T, i, i, 1) ;
+ Eye = cs_cl_compress (T) ; /* Eye = speye (m) */
+ cs_cl_spfree (T) ;
+ C = cs_cl_multiply (A, AT) ; /* C = A*A' */
+ D = cs_cl_add (C, Eye, 1, cs_cl_norm (C)) ; /* D = C + Eye*norm (C,1) */
+ printf ("D:\n") ; cs_cl_print (D, 0) ; /* print D */
+ cs_cl_spfree (A) ; /* clear A AT C D Eye */
+ cs_cl_spfree (AT) ;
+ cs_cl_spfree (C) ;
+ cs_cl_spfree (D) ;
+ cs_cl_spfree (Eye) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_cl_demo2.c b/CXSparse/Demo/cs_cl_demo2.c
new file mode 100644
index 0000000..a630f83
--- /dev/null
+++ b/CXSparse/Demo/cs_cl_demo2.c
@@ -0,0 +1,9 @@
+#include "cs_cl_demo.h"
+/* cs_cl_demo2: read a matrix and solve a linear system */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 1e-14) ;
+ demo2 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_cl_demo3.c b/CXSparse/Demo/cs_cl_demo3.c
new file mode 100644
index 0000000..d0c5970
--- /dev/null
+++ b/CXSparse/Demo/cs_cl_demo3.c
@@ -0,0 +1,9 @@
+#include "cs_cl_demo.h"
+/* cs_cl_demo3: read a matrix and test Cholesky update/downdate */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 0) ;
+ demo3 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_demo.c b/CXSparse/Demo/cs_demo.c
new file mode 100644
index 0000000..4e85757
--- /dev/null
+++ b/CXSparse/Demo/cs_demo.c
@@ -0,0 +1,286 @@
+#include "cs_demo.h"
+#include <time.h>
+/* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */
+static int is_sym (cs *A)
+{
+ int is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ;
+ if (m != n) return (0) ;
+ is_upper = 1 ;
+ is_lower = 1 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ if (Ai [p] > j) is_upper = 0 ;
+ if (Ai [p] < j) is_lower = 0 ;
+ }
+ }
+ return (is_upper ? 1 : (is_lower ? -1 : 0)) ;
+}
+
+/* true for off-diagonal entries */
+static int dropdiag (int i, int j, double aij, void *other) { return (i != j) ;}
+
+/* C = A + triu(A,1)' */
+static cs *make_sym (cs *A)
+{
+ cs *AT, *C ;
+ AT = cs_transpose (A, 1) ; /* AT = A' */
+ cs_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */
+ C = cs_add (A, AT, 1, 1) ; /* C = A+AT */
+ cs_spfree (AT) ;
+ return (C) ;
+}
+
+/* create a right-hand side */
+static void rhs (double *x, double *b, int m)
+{
+ int i ;
+ for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ;
+ for (i = 0 ; i < m ; i++) x [i] = b [i] ;
+}
+
+/* infinity-norm of x */
+static double norm (double *x, int n)
+{
+ int i ;
+ double normx = 0 ;
+ for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, fabs (x [i])) ;
+ return (normx) ;
+}
+
+/* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */
+static void print_resid (int ok, cs *A, double *x, double *b, double *resid)
+{
+ int i, m, n ;
+ if (!ok) { printf (" (failed)\n") ; return ; }
+ m = A->m ; n = A->n ;
+ for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */
+ cs_gaxpy (A, x, resid) ; /* resid = resid + A*x */
+ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 :
+ (cs_norm (A) * norm (x,n) + norm (b,m)))) ;
+}
+
+static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; }
+static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; }
+
+static void print_order (int order)
+{
+ switch (order)
+ {
+ case 0: printf ("natural ") ; break ;
+ case 1: printf ("amd(A+A') ") ; break ;
+ case 2: printf ("amd(S'*S) ") ; break ;
+ case 3: printf ("amd(A'*A) ") ; break ;
+ }
+}
+
+/* read a problem from a file */
+problem *get_problem (FILE *f, double tol)
+{
+ cs *T, *A, *C ;
+ int sym, m, n, mn, nz1, nz2 ;
+ problem *Prob ;
+ Prob = cs_calloc (1, sizeof (problem)) ;
+ if (!Prob) return (NULL) ;
+ T = cs_load (f) ; /* load triplet matrix T from a file */
+ Prob->A = A = cs_compress (T) ; /* A = compressed-column form of T */
+ cs_spfree (T) ; /* clear T */
+ if (!cs_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */
+ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */
+ m = A->m ; n = A->n ;
+ mn = CS_MAX (m,n) ;
+ nz1 = A->p [n] ;
+ cs_dropzeros (A) ; /* drop zero entries */
+ nz2 = A->p [n] ;
+ if (tol > 0) cs_droptol (A, tol) ; /* drop tiny entries (just to test) */
+ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */
+ if (!C) return (free_problem (Prob)) ;
+ printf ("\n--- Matrix: %d-by-%d, nnz: %d (sym: %d: nnz %d), norm: %8.2e\n",
+ m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_norm (C)) ;
+ if (nz1 != nz2) printf ("zero entries dropped: %d\n", nz1 - nz2) ;
+ if (nz2 != A->p [n]) printf ("tiny entries dropped: %d\n", nz2 - A->p [n]) ;
+ Prob->b = cs_malloc (mn, sizeof (double)) ;
+ Prob->x = cs_malloc (mn, sizeof (double)) ;
+ Prob->resid = cs_malloc (mn, sizeof (double)) ;
+ return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ;
+}
+
+/* free a problem */
+problem *free_problem (problem *Prob)
+{
+ if (!Prob) return (NULL) ;
+ cs_spfree (Prob->A) ;
+ if (Prob->sym) cs_spfree (Prob->C) ;
+ cs_free (Prob->b) ;
+ cs_free (Prob->x) ;
+ cs_free (Prob->resid) ;
+ return (cs_free (Prob)) ;
+}
+
+/* solve a linear system using Cholesky, LU, and QR, with various orderings */
+int demo2 (problem *Prob)
+{
+ cs *A, *C ;
+ double *b, *x, *resid, t, tol ;
+ int k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ;
+ csd *D ;
+ if (!Prob) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ m = A->m ; n = A->n ;
+ tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */
+ D = cs_dmperm (C, 1) ; /* randomized dmperm analysis */
+ if (!D) return (0) ;
+ nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ;
+ sprank = rr [3] ;
+ for (ns = 0, k = 0 ; k < nb ; k++)
+ {
+ ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ;
+ }
+ printf ("blocks: %d singletons: %d structural rank: %d\n", nb, ns, sprank) ;
+ cs_dfree (D) ;
+ for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("QR ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/
+ for (order = 0 ; order <= 3 ; order++) /* try all orderings */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("LU ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_lusol (order, C, x, tol) ; /* solve Ax=b with LU */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (!Prob->sym) return (1) ;
+ for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("Chol ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ return (1) ;
+}
+
+/* free workspace for demo3 */
+static int done3 (int ok, css *S, csn *N, double *y, cs *W, cs *E, int *p)
+{
+ cs_sfree (S) ;
+ cs_nfree (N) ;
+ cs_free (y) ;
+ cs_spfree (W) ;
+ cs_spfree (E) ;
+ cs_free (p) ;
+ return (ok) ;
+}
+
+/* Cholesky update/downdate */
+int demo3 (problem *Prob)
+{
+ cs *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ;
+ int n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ;
+ double *b, *x, *resid, *y = NULL, *Lx, *Wx, s, t, t1 ;
+ css *S = NULL ;
+ csn *N = NULL ;
+ if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ n = A->n ;
+ if (!Prob->sym || n == 0) return (1) ;
+ rhs (x, b, n) ; /* compute right-hand side */
+ printf ("\nchol then update/downdate ") ;
+ print_order (1) ;
+ y = cs_malloc (n, sizeof (double)) ;
+ t = tic () ;
+ S = cs_schol (1, C) ; /* symbolic Chol, amd(A+A') */
+ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ;
+ t = tic () ;
+ N = cs_chol (C, S) ; /* numeric Cholesky */
+ printf ("numeric chol time %8.2f\n", toc (t)) ;
+ if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_lsolve (N->L, y) ; /* y = L\y */
+ cs_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ printf ("solve chol time %8.2f\n", toc (t)) ;
+ printf ("original: ") ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ k = n/2 ; /* construct W */
+ W = cs_spalloc (n, 1, n, 1, 0) ;
+ if (!W) return (done3 (0, S, N, y, W, E, p)) ;
+ Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ;
+ Wp = W->p ; Wi = W->i ; Wx = W->x ;
+ Wp [0] = 0 ;
+ p1 = Lp [k] ;
+ Wp [1] = Lp [k+1] - p1 ;
+ s = Lx [p1] ;
+ srand (1) ;
+ for ( ; p1 < Lp [k+1] ; p1++)
+ {
+ p2 = p1 - Lp [k] ;
+ Wi [p2] = Li [p1] ;
+ Wx [p2] = s * rand () / ((double) RAND_MAX) ;
+ }
+ t = tic () ;
+ ok = cs_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */
+ t1 = toc (t) ;
+ printf ("update: time: %8.2f\n", t1) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_lsolve (N->L, y) ; /* y = L\y */
+ cs_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ p = cs_pinv (S->pinv, n) ;
+ W2 = cs_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */
+ WT = cs_transpose (W2,1) ;
+ WW = cs_multiply (W2, WT) ;
+ cs_spfree (WT) ;
+ cs_spfree (W2) ;
+ E = cs_add (C, WW, 1, 1) ;
+ cs_spfree (WW) ;
+ if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("update: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ cs_nfree (N) ; /* clear N */
+ t = tic () ;
+ N = cs_chol (E, S) ; /* numeric Cholesky */
+ if (!N) return (done3 (0, S, N, y, W, E, p)) ;
+ cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_lsolve (N->L, y) ; /* y = L\y */
+ cs_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("rechol: time: %8.2f (incl solve) ", t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ t = tic () ;
+ ok = cs_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */
+ t1 = toc (t) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("downdate: time: %8.2f\n", t1) ;
+ t = tic () ;
+ cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_lsolve (N->L, y) ; /* y = L\y */
+ cs_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("downdate: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ return (done3 (1, S, N, y, W, E, p)) ;
+}
diff --git a/CXSparse/Demo/cs_demo.h b/CXSparse/Demo/cs_demo.h
new file mode 100644
index 0000000..a0e9e72
--- /dev/null
+++ b/CXSparse/Demo/cs_demo.h
@@ -0,0 +1,15 @@
+#include "cs.h"
+typedef struct problem_struct
+{
+ cs *A ;
+ cs *C ;
+ int sym ;
+ double *x ;
+ double *b ;
+ double *resid ;
+} problem ;
+
+problem *get_problem (FILE *f, double tol) ;
+int demo2 (problem *Prob) ;
+int demo3 (problem *Prob) ;
+problem *free_problem (problem *Prob) ;
diff --git a/CXSparse/Demo/cs_demo.out b/CXSparse/Demo/cs_demo.out
new file mode 100644
index 0000000..7924f07
--- /dev/null
+++ b/CXSparse/Demo/cs_demo.out
@@ -0,0 +1,1204 @@
+make[1]: Entering directory `/amd/netapp3/vol/research0a/research18/sparse2/SuiteSparse/CXSparse/Demo'
+./cs_idemo < ../Matrix/t2
+
+--- cs_idemo, size of CS_INT: 4
+
+T:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : (3, 3.14159)
+ 1 0 : (3.1, 42)
+ 3 3 : (1, 7)
+ 0 2 : (3.2, 0.1)
+ 1 1 : (2.9, 1.3)
+ 3 0 : (3.5, 0)
+ 3 1 : (0.4, 2.71828)
+ 1 3 : (0.9, 99)
+ 0 0 : (4.5, 6)
+ 2 1 : (1.7, 1)
+
+Treal:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : 3
+ 1 0 : 3.1
+ 3 3 : 1
+ 0 2 : 3.2
+ 1 1 : 2.9
+ 3 0 : 3.5
+ 3 1 : 0.4
+ 1 3 : 0.9
+ 0 0 : 4.5
+ 2 1 : 1.7
+
+Timag:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : 3.14159
+ 1 0 : 42
+ 3 3 : 7
+ 0 2 : 0.1
+ 1 1 : 1.3
+ 3 0 : 0
+ 3 1 : 2.71828
+ 1 3 : 99
+ 0 0 : 6
+ 2 1 : 1
+
+A:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075
+ col 0 : locations 0 to 2
+ 1 : (3.1, 42)
+ 3 : (3.5, 0)
+ 0 : (4.5, 6)
+ col 1 : locations 3 to 5
+ 1 : (2.9, 1.3)
+ 3 : (0.4, 2.71828)
+ 2 : (1.7, 1)
+ col 2 : locations 6 to 7
+ 2 : (3, 3.14159)
+ 0 : (3.2, 0.1)
+ col 3 : locations 8 to 9
+ 3 : (1, 7)
+ 1 : (0.9, 99)
+
+C1 = real(A):
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1
+ col 0 : locations 0 to 2
+ 1 : 3.1
+ 3 : 3.5
+ 0 : 4.5
+ col 1 : locations 3 to 5
+ 1 : 2.9
+ 3 : 0.4
+ 2 : 1.7
+ col 2 : locations 6 to 7
+ 2 : 3
+ 0 : 3.2
+ col 3 : locations 8 to 9
+ 3 : 1
+ 1 : 0.9
+
+C2 = imag(A):
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 106
+ col 0 : locations 0 to 2
+ 1 : 42
+ 3 : 0
+ 0 : 6
+ col 1 : locations 3 to 5
+ 1 : 1.3
+ 3 : 2.71828
+ 2 : 1
+ col 2 : locations 6 to 7
+ 2 : 3.14159
+ 0 : 0.1
+ col 3 : locations 8 to 9
+ 3 : 7
+ 1 : 99
+
+A1:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1
+ col 0 : locations 0 to 2
+ 1 : (3.1, 0)
+ 3 : (3.5, 0)
+ 0 : (4.5, 0)
+ col 1 : locations 3 to 5
+ 1 : (2.9, 0)
+ 3 : (0.4, 0)
+ 2 : (1.7, 0)
+ col 2 : locations 6 to 7
+ 2 : (3, 0)
+ 0 : (3.2, 0)
+ col 3 : locations 8 to 9
+ 3 : (1, 0)
+ 1 : (0.9, 0)
+
+A2:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 106
+ col 0 : locations 0 to 2
+ 1 : (0, 42)
+ 3 : (0, 0)
+ 0 : (0, 6)
+ col 1 : locations 3 to 5
+ 1 : (0, 1.3)
+ 3 : (0, 2.71828)
+ 2 : (0, 1)
+ col 2 : locations 6 to 7
+ 2 : (0, 3.14159)
+ 0 : (0, 0.1)
+ col 3 : locations 8 to 9
+ 3 : (0, 7)
+ 1 : (0, 99)
+
+B = conj(A):
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075
+ col 0 : locations 0 to 2
+ 1 : (3.1, -42)
+ 3 : (3.5, 0)
+ 0 : (4.5, -6)
+ col 1 : locations 3 to 5
+ 1 : (2.9, -1.3)
+ 3 : (0.4, -2.71828)
+ 2 : (1.7, -1)
+ col 2 : locations 6 to 7
+ 2 : (3, -3.14159)
+ 0 : (3.2, -0.1)
+ col 3 : locations 8 to 9
+ 3 : (1, -7)
+ 1 : (0.9, -99)
+./cs_ldemo < ../Matrix/t2
+
+--- cs_ldemo, size of CS_INT: 8
+
+T:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : (3, 3.14159)
+ 1 0 : (3.1, 42)
+ 3 3 : (1, 7)
+ 0 2 : (3.2, 0.1)
+ 1 1 : (2.9, 1.3)
+ 3 0 : (3.5, 0)
+ 3 1 : (0.4, 2.71828)
+ 1 3 : (0.9, 99)
+ 0 0 : (4.5, 6)
+ 2 1 : (1.7, 1)
+
+Treal:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : 3
+ 1 0 : 3.1
+ 3 3 : 1
+ 0 2 : 3.2
+ 1 1 : 2.9
+ 3 0 : 3.5
+ 3 1 : 0.4
+ 1 3 : 0.9
+ 0 0 : 4.5
+ 2 1 : 1.7
+
+Timag:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : 3.14159
+ 1 0 : 42
+ 3 3 : 7
+ 0 2 : 0.1
+ 1 1 : 1.3
+ 3 0 : 0
+ 3 1 : 2.71828
+ 1 3 : 99
+ 0 0 : 6
+ 2 1 : 1
+
+A:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075
+ col 0 : locations 0 to 2
+ 1 : (3.1, 42)
+ 3 : (3.5, 0)
+ 0 : (4.5, 6)
+ col 1 : locations 3 to 5
+ 1 : (2.9, 1.3)
+ 3 : (0.4, 2.71828)
+ 2 : (1.7, 1)
+ col 2 : locations 6 to 7
+ 2 : (3, 3.14159)
+ 0 : (3.2, 0.1)
+ col 3 : locations 8 to 9
+ 3 : (1, 7)
+ 1 : (0.9, 99)
+
+C1 = real(A):
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1
+ col 0 : locations 0 to 2
+ 1 : 3.1
+ 3 : 3.5
+ 0 : 4.5
+ col 1 : locations 3 to 5
+ 1 : 2.9
+ 3 : 0.4
+ 2 : 1.7
+ col 2 : locations 6 to 7
+ 2 : 3
+ 0 : 3.2
+ col 3 : locations 8 to 9
+ 3 : 1
+ 1 : 0.9
+
+C2 = imag(A):
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 106
+ col 0 : locations 0 to 2
+ 1 : 42
+ 3 : 0
+ 0 : 6
+ col 1 : locations 3 to 5
+ 1 : 1.3
+ 3 : 2.71828
+ 2 : 1
+ col 2 : locations 6 to 7
+ 2 : 3.14159
+ 0 : 0.1
+ col 3 : locations 8 to 9
+ 3 : 7
+ 1 : 99
+
+A1:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1
+ col 0 : locations 0 to 2
+ 1 : (3.1, 0)
+ 3 : (3.5, 0)
+ 0 : (4.5, 0)
+ col 1 : locations 3 to 5
+ 1 : (2.9, 0)
+ 3 : (0.4, 0)
+ 2 : (1.7, 0)
+ col 2 : locations 6 to 7
+ 2 : (3, 0)
+ 0 : (3.2, 0)
+ col 3 : locations 8 to 9
+ 3 : (1, 0)
+ 1 : (0.9, 0)
+
+A2:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 106
+ col 0 : locations 0 to 2
+ 1 : (0, 42)
+ 3 : (0, 0)
+ 0 : (0, 6)
+ col 1 : locations 3 to 5
+ 1 : (0, 1.3)
+ 3 : (0, 2.71828)
+ 2 : (0, 1)
+ col 2 : locations 6 to 7
+ 2 : (0, 3.14159)
+ 0 : (0, 0.1)
+ col 3 : locations 8 to 9
+ 3 : (0, 7)
+ 1 : (0, 99)
+
+B = conj(A):
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075
+ col 0 : locations 0 to 2
+ 1 : (3.1, -42)
+ 3 : (3.5, 0)
+ 0 : (4.5, -6)
+ col 1 : locations 3 to 5
+ 1 : (2.9, -1.3)
+ 3 : (0.4, -2.71828)
+ 2 : (1.7, -1)
+ col 2 : locations 6 to 7
+ 2 : (3, -3.14159)
+ 0 : (3.2, -0.1)
+ col 3 : locations 8 to 9
+ 3 : (1, -7)
+ 1 : (0.9, -99)
+./cs_demo1 < ../Matrix/t1
+T:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : 3
+ 1 0 : 3.1
+ 3 3 : 1
+ 0 2 : 3.2
+ 1 1 : 2.9
+ 3 0 : 3.5
+ 3 1 : 0.4
+ 1 3 : 0.9
+ 0 0 : 4.5
+ 2 1 : 1.7
+A:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1
+ col 0 : locations 0 to 2
+ 1 : 3.1
+ 3 : 3.5
+ 0 : 4.5
+ col 1 : locations 3 to 5
+ 1 : 2.9
+ 3 : 0.4
+ 2 : 1.7
+ col 2 : locations 6 to 7
+ 2 : 3
+ 0 : 3.2
+ col 3 : locations 8 to 9
+ 3 : 1
+ 1 : 0.9
+AT:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 7.7
+ col 0 : locations 0 to 1
+ 0 : 4.5
+ 2 : 3.2
+ col 1 : locations 2 to 4
+ 0 : 3.1
+ 1 : 2.9
+ 3 : 0.9
+ col 2 : locations 5 to 6
+ 1 : 1.7
+ 2 : 3
+ col 3 : locations 7 to 9
+ 0 : 3.5
+ 1 : 0.4
+ 3 : 1
+D:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 16 nnz: 16, 1-norm: 139.58
+ col 0 : locations 0 to 3
+ 1 : 13.95
+ 3 : 15.75
+ 0 : 100.28
+ 2 : 9.6
+ col 1 : locations 4 to 7
+ 1 : 88.62
+ 3 : 12.91
+ 0 : 13.95
+ 2 : 4.93
+ col 2 : locations 8 to 11
+ 1 : 4.93
+ 3 : 0.68
+ 2 : 81.68
+ 0 : 9.6
+ col 3 : locations 12 to 15
+ 1 : 12.91
+ 3 : 83.2
+ 0 : 15.75
+ 2 : 0.68
+./cs_demo2 < ../Matrix/t1
+
+--- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.11e+01
+blocks: 1 singletons: 0 structural rank: 4
+QR natural time: 0.00 resid: 3.06e-17
+QR amd(A'*A) time: 0.00 resid: 2.30e-17
+LU natural time: 0.00 resid: 1.53e-17
+LU amd(A+A') time: 0.00 resid: 1.53e-17
+LU amd(S'*S) time: 0.00 resid: 0.00e+00
+LU amd(A'*A) time: 0.00 resid: 1.53e-17
+./cs_demo2 < ../Matrix/fs_183_1
+
+--- Matrix: 183-by-183, nnz: 988 (sym: 0: nnz 0), norm: 1.70e+09
+zero entries dropped: 71
+tiny entries dropped: 10
+blocks: 38 singletons: 37 structural rank: 183
+QR natural time: 0.01 resid: 1.42e-27
+QR amd(A'*A) time: 0.00 resid: 3.35e-28
+LU natural time: 0.01 resid: 6.20e-28
+LU amd(A+A') time: 0.00 resid: 1.55e-27
+LU amd(S'*S) time: 0.00 resid: 6.98e-28
+LU amd(A'*A) time: 0.00 resid: 6.98e-28
+./cs_demo2 < ../Matrix/west0067
+
+--- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.14e+00
+blocks: 2 singletons: 1 structural rank: 67
+QR natural time: 0.00 resid: 5.19e-17
+QR amd(A'*A) time: 0.00 resid: 3.25e-17
+LU natural time: 0.00 resid: 3.89e-17
+LU amd(A+A') time: 0.00 resid: 2.27e-17
+LU amd(S'*S) time: 0.00 resid: 1.95e-17
+LU amd(A'*A) time: 0.00 resid: 2.60e-17
+./cs_demo2 < ../Matrix/lp_afiro
+
+--- Matrix: 27-by-51, nnz: 102 (sym: 0: nnz 0), norm: 3.43e+00
+blocks: 1 singletons: 0 structural rank: 27
+QR natural time: 0.00 resid: 3.85e-16
+QR amd(A'*A) time: 0.00 resid: 1.50e-16
+./cs_demo2 < ../Matrix/ash219
+
+--- Matrix: 219-by-85, nnz: 438 (sym: 0: nnz 0), norm: 9.00e+00
+blocks: 1 singletons: 0 structural rank: 85
+QR natural time: 0.00 resid: 1.61e-02
+QR amd(A'*A) time: 0.00 resid: 1.61e-02
+./cs_demo2 < ../Matrix/mbeacxc
+
+--- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01
+blocks: 10 singletons: 8 structural rank: 448
+QR natural time: 0.13 resid: nan
+QR amd(A'*A) time: 0.19 resid: nan
+./cs_demo2 < ../Matrix/bcsstk01
+
+--- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09
+blocks: 1 singletons: 0 structural rank: 48
+QR natural time: 0.00 resid: 3.65e-19
+QR amd(A'*A) time: 0.00 resid: 4.02e-19
+LU natural time: 0.00 resid: 2.17e-19
+LU amd(A+A') time: 0.00 resid: 1.87e-19
+LU amd(S'*S) time: 0.00 resid: 2.38e-19
+LU amd(A'*A) time: 0.00 resid: 2.38e-19
+Chol natural time: 0.00 resid: 2.64e-19
+Chol amd(A+A') time: 0.00 resid: 2.55e-19
+./cs_demo3 < ../Matrix/bcsstk01
+
+--- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.00
+numeric chol time 0.00
+solve chol time 0.00
+original: resid: 2.55e-19
+update: time: 0.00
+update: time: 0.00 (incl solve) resid: 9.66e-19
+rechol: time: 0.00 (incl solve) resid: 1.55e-18
+downdate: time: 0.00
+downdate: time: 0.00 (incl solve) resid: 3.74e-17
+./cs_demo2 < ../Matrix/bcsstk16
+
+--- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09
+blocks: 75 singletons: 74 structural rank: 4884
+QR amd(A'*A) time: 2.13 resid: 2.01e-22
+LU amd(A+A') time: 1.19 resid: 1.10e-22
+LU amd(S'*S) time: 1.15 resid: 1.28e-22
+LU amd(A'*A) time: 1.22 resid: 1.78e-22
+Chol amd(A+A') time: 0.37 resid: 1.19e-22
+./cs_demo3 < ../Matrix/bcsstk16
+
+--- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.02
+numeric chol time 0.35
+solve chol time 0.00
+original: resid: 1.19e-22
+update: time: 0.00
+update: time: 0.01 (incl solve) resid: 1.12e-23
+rechol: time: 0.34 (incl solve) resid: 1.17e-23
+downdate: time: 0.00
+downdate: time: 0.01 (incl solve) resid: 4.09e-22
+./cs_di_demo1 < ../Matrix/t1
+T:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : 3
+ 1 0 : 3.1
+ 3 3 : 1
+ 0 2 : 3.2
+ 1 1 : 2.9
+ 3 0 : 3.5
+ 3 1 : 0.4
+ 1 3 : 0.9
+ 0 0 : 4.5
+ 2 1 : 1.7
+A:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1
+ col 0 : locations 0 to 2
+ 1 : 3.1
+ 3 : 3.5
+ 0 : 4.5
+ col 1 : locations 3 to 5
+ 1 : 2.9
+ 3 : 0.4
+ 2 : 1.7
+ col 2 : locations 6 to 7
+ 2 : 3
+ 0 : 3.2
+ col 3 : locations 8 to 9
+ 3 : 1
+ 1 : 0.9
+AT:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 7.7
+ col 0 : locations 0 to 1
+ 0 : 4.5
+ 2 : 3.2
+ col 1 : locations 2 to 4
+ 0 : 3.1
+ 1 : 2.9
+ 3 : 0.9
+ col 2 : locations 5 to 6
+ 1 : 1.7
+ 2 : 3
+ col 3 : locations 7 to 9
+ 0 : 3.5
+ 1 : 0.4
+ 3 : 1
+D:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 16 nnz: 16, 1-norm: 139.58
+ col 0 : locations 0 to 3
+ 1 : 13.95
+ 3 : 15.75
+ 0 : 100.28
+ 2 : 9.6
+ col 1 : locations 4 to 7
+ 1 : 88.62
+ 3 : 12.91
+ 0 : 13.95
+ 2 : 4.93
+ col 2 : locations 8 to 11
+ 1 : 4.93
+ 3 : 0.68
+ 2 : 81.68
+ 0 : 9.6
+ col 3 : locations 12 to 15
+ 1 : 12.91
+ 3 : 83.2
+ 0 : 15.75
+ 2 : 0.68
+./cs_di_demo2 < ../Matrix/t1
+
+--- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.11e+01
+blocks: 1 singletons: 0 structural rank: 4
+QR natural time: 0.00 resid: 3.06e-17
+QR amd(A'*A) time: 0.00 resid: 2.30e-17
+LU natural time: 0.00 resid: 1.53e-17
+LU amd(A+A') time: 0.00 resid: 1.53e-17
+LU amd(S'*S) time: 0.00 resid: 0.00e+00
+LU amd(A'*A) time: 0.00 resid: 1.53e-17
+./cs_di_demo2 < ../Matrix/fs_183_1
+
+--- Matrix: 183-by-183, nnz: 988 (sym: 0: nnz 0), norm: 1.70e+09
+zero entries dropped: 71
+tiny entries dropped: 10
+blocks: 38 singletons: 37 structural rank: 183
+QR natural time: 0.00 resid: 1.42e-27
+QR amd(A'*A) time: 0.00 resid: 3.35e-28
+LU natural time: 0.01 resid: 6.20e-28
+LU amd(A+A') time: 0.00 resid: 1.55e-27
+LU amd(S'*S) time: 0.00 resid: 6.98e-28
+LU amd(A'*A) time: 0.00 resid: 6.98e-28
+./cs_di_demo2 < ../Matrix/west0067
+
+--- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.14e+00
+blocks: 2 singletons: 1 structural rank: 67
+QR natural time: 0.00 resid: 5.19e-17
+QR amd(A'*A) time: 0.00 resid: 3.25e-17
+LU natural time: 0.00 resid: 3.89e-17
+LU amd(A+A') time: 0.00 resid: 2.27e-17
+LU amd(S'*S) time: 0.00 resid: 1.95e-17
+LU amd(A'*A) time: 0.00 resid: 2.60e-17
+./cs_di_demo2 < ../Matrix/lp_afiro
+
+--- Matrix: 27-by-51, nnz: 102 (sym: 0: nnz 0), norm: 3.43e+00
+blocks: 1 singletons: 0 structural rank: 27
+QR natural time: 0.00 resid: 3.85e-16
+QR amd(A'*A) time: 0.00 resid: 1.50e-16
+./cs_di_demo2 < ../Matrix/ash219
+
+--- Matrix: 219-by-85, nnz: 438 (sym: 0: nnz 0), norm: 9.00e+00
+blocks: 1 singletons: 0 structural rank: 85
+QR natural time: 0.00 resid: 1.61e-02
+QR amd(A'*A) time: 0.00 resid: 1.61e-02
+./cs_di_demo2 < ../Matrix/mbeacxc
+
+--- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01
+blocks: 10 singletons: 8 structural rank: 448
+QR natural time: 0.13 resid: nan
+QR amd(A'*A) time: 0.19 resid: nan
+./cs_di_demo2 < ../Matrix/bcsstk01
+
+--- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09
+blocks: 1 singletons: 0 structural rank: 48
+QR natural time: 0.00 resid: 3.65e-19
+QR amd(A'*A) time: 0.00 resid: 4.02e-19
+LU natural time: 0.00 resid: 2.17e-19
+LU amd(A+A') time: 0.00 resid: 1.87e-19
+LU amd(S'*S) time: 0.00 resid: 2.38e-19
+LU amd(A'*A) time: 0.00 resid: 2.38e-19
+Chol natural time: 0.00 resid: 2.64e-19
+Chol amd(A+A') time: 0.00 resid: 2.55e-19
+./cs_di_demo3 < ../Matrix/bcsstk01
+
+--- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.00
+numeric chol time 0.00
+solve chol time 0.00
+original: resid: 2.55e-19
+update: time: 0.00
+update: time: 0.00 (incl solve) resid: 9.66e-19
+rechol: time: 0.00 (incl solve) resid: 1.55e-18
+downdate: time: 0.00
+downdate: time: 0.00 (incl solve) resid: 3.74e-17
+./cs_di_demo2 < ../Matrix/bcsstk16
+
+--- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09
+blocks: 75 singletons: 74 structural rank: 4884
+QR amd(A'*A) time: 2.17 resid: 2.01e-22
+LU amd(A+A') time: 1.23 resid: 1.10e-22
+LU amd(S'*S) time: 1.18 resid: 1.28e-22
+LU amd(A'*A) time: 1.23 resid: 1.78e-22
+Chol amd(A+A') time: 0.39 resid: 1.19e-22
+./cs_di_demo3 < ../Matrix/bcsstk16
+
+--- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.03
+numeric chol time 0.33
+solve chol time 0.00
+original: resid: 1.19e-22
+update: time: 0.00
+update: time: 0.01 (incl solve) resid: 1.12e-23
+rechol: time: 0.34 (incl solve) resid: 1.17e-23
+downdate: time: 0.00
+downdate: time: 0.01 (incl solve) resid: 4.09e-22
+./cs_dl_demo1 < ../Matrix/t1
+T:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : 3
+ 1 0 : 3.1
+ 3 3 : 1
+ 0 2 : 3.2
+ 1 1 : 2.9
+ 3 0 : 3.5
+ 3 1 : 0.4
+ 1 3 : 0.9
+ 0 0 : 4.5
+ 2 1 : 1.7
+A:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 11.1
+ col 0 : locations 0 to 2
+ 1 : 3.1
+ 3 : 3.5
+ 0 : 4.5
+ col 1 : locations 3 to 5
+ 1 : 2.9
+ 3 : 0.4
+ 2 : 1.7
+ col 2 : locations 6 to 7
+ 2 : 3
+ 0 : 3.2
+ col 3 : locations 8 to 9
+ 3 : 1
+ 1 : 0.9
+AT:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 7.7
+ col 0 : locations 0 to 1
+ 0 : 4.5
+ 2 : 3.2
+ col 1 : locations 2 to 4
+ 0 : 3.1
+ 1 : 2.9
+ 3 : 0.9
+ col 2 : locations 5 to 6
+ 1 : 1.7
+ 2 : 3
+ col 3 : locations 7 to 9
+ 0 : 3.5
+ 1 : 0.4
+ 3 : 1
+D:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 16 nnz: 16, 1-norm: 139.58
+ col 0 : locations 0 to 3
+ 1 : 13.95
+ 3 : 15.75
+ 0 : 100.28
+ 2 : 9.6
+ col 1 : locations 4 to 7
+ 1 : 88.62
+ 3 : 12.91
+ 0 : 13.95
+ 2 : 4.93
+ col 2 : locations 8 to 11
+ 1 : 4.93
+ 3 : 0.68
+ 2 : 81.68
+ 0 : 9.6
+ col 3 : locations 12 to 15
+ 1 : 12.91
+ 3 : 83.2
+ 0 : 15.75
+ 2 : 0.68
+./cs_dl_demo2 < ../Matrix/t1
+
+--- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.11e+01
+blocks: 1 singletons: 0 structural rank: 4
+QR natural time: 0.00 resid: 3.06e-17
+QR amd(A'*A) time: 0.00 resid: 2.30e-17
+LU natural time: 0.00 resid: 1.53e-17
+LU amd(A+A') time: 0.00 resid: 1.53e-17
+LU amd(S'*S) time: 0.00 resid: 0.00e+00
+LU amd(A'*A) time: 0.00 resid: 1.53e-17
+./cs_dl_demo2 < ../Matrix/fs_183_1
+
+--- Matrix: 183-by-183, nnz: 988 (sym: 0: nnz 0), norm: 1.70e+09
+zero entries dropped: 71
+tiny entries dropped: 10
+blocks: 38 singletons: 37 structural rank: 183
+QR natural time: 0.01 resid: 1.42e-27
+QR amd(A'*A) time: 0.00 resid: 3.35e-28
+LU natural time: 0.00 resid: 6.20e-28
+LU amd(A+A') time: 0.00 resid: 1.55e-27
+LU amd(S'*S) time: 0.00 resid: 6.98e-28
+LU amd(A'*A) time: 0.01 resid: 6.98e-28
+./cs_dl_demo2 < ../Matrix/west0067
+
+--- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.14e+00
+blocks: 2 singletons: 1 structural rank: 67
+QR natural time: 0.00 resid: 5.19e-17
+QR amd(A'*A) time: 0.00 resid: 3.25e-17
+LU natural time: 0.00 resid: 3.89e-17
+LU amd(A+A') time: 0.00 resid: 2.27e-17
+LU amd(S'*S) time: 0.00 resid: 1.95e-17
+LU amd(A'*A) time: 0.00 resid: 2.60e-17
+./cs_dl_demo2 < ../Matrix/lp_afiro
+
+--- Matrix: 27-by-51, nnz: 102 (sym: 0: nnz 0), norm: 3.43e+00
+blocks: 1 singletons: 0 structural rank: 27
+QR natural time: 0.00 resid: 3.85e-16
+QR amd(A'*A) time: 0.00 resid: 1.50e-16
+./cs_dl_demo2 < ../Matrix/ash219
+
+--- Matrix: 219-by-85, nnz: 438 (sym: 0: nnz 0), norm: 9.00e+00
+blocks: 1 singletons: 0 structural rank: 85
+QR natural time: 0.00 resid: 1.61e-02
+QR amd(A'*A) time: 0.00 resid: 1.61e-02
+./cs_dl_demo2 < ../Matrix/mbeacxc
+
+--- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01
+blocks: 10 singletons: 8 structural rank: 448
+QR natural time: 0.15 resid: nan
+QR amd(A'*A) time: 0.20 resid: nan
+./cs_dl_demo2 < ../Matrix/bcsstk01
+
+--- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09
+blocks: 1 singletons: 0 structural rank: 48
+QR natural time: 0.00 resid: 3.65e-19
+QR amd(A'*A) time: 0.00 resid: 4.02e-19
+LU natural time: 0.00 resid: 2.17e-19
+LU amd(A+A') time: 0.00 resid: 1.87e-19
+LU amd(S'*S) time: 0.00 resid: 2.38e-19
+LU amd(A'*A) time: 0.00 resid: 2.38e-19
+Chol natural time: 0.00 resid: 2.64e-19
+Chol amd(A+A') time: 0.00 resid: 2.55e-19
+./cs_dl_demo3 < ../Matrix/bcsstk01
+
+--- Matrix: 48-by-48, nnz: 224 (sym: -1: nnz 400), norm: 3.57e+09
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.00
+numeric chol time 0.00
+solve chol time 0.00
+original: resid: 2.55e-19
+update: time: 0.00
+update: time: 0.00 (incl solve) resid: 9.66e-19
+rechol: time: 0.00 (incl solve) resid: 1.55e-18
+downdate: time: 0.00
+downdate: time: 0.00 (incl solve) resid: 3.74e-17
+./cs_dl_demo2 < ../Matrix/bcsstk16
+
+--- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09
+blocks: 75 singletons: 74 structural rank: 4884
+QR amd(A'*A) time: 2.62 resid: 2.01e-22
+LU amd(A+A') time: 1.43 resid: 1.10e-22
+LU amd(S'*S) time: 1.28 resid: 1.28e-22
+LU amd(A'*A) time: 1.35 resid: 1.78e-22
+Chol amd(A+A') time: 0.49 resid: 1.19e-22
+./cs_dl_demo3 < ../Matrix/bcsstk16
+
+--- Matrix: 4884-by-4884, nnz: 147631 (sym: -1: nnz 290378), norm: 7.01e+09
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.02
+numeric chol time 0.46
+solve chol time 0.02
+original: resid: 1.19e-22
+update: time: 0.00
+update: time: 0.01 (incl solve) resid: 1.12e-23
+rechol: time: 0.52 (incl solve) resid: 1.17e-23
+downdate: time: 0.00
+downdate: time: 0.01 (incl solve) resid: 4.09e-22
+./cs_ci_demo1 < ../Matrix/t2
+T:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : (3, 3.14159)
+ 1 0 : (3.1, 42)
+ 3 3 : (1, 7)
+ 0 2 : (3.2, 0.1)
+ 1 1 : (2.9, 1.3)
+ 3 0 : (3.5, 0)
+ 3 1 : (0.4, 2.71828)
+ 1 3 : (0.9, 99)
+ 0 0 : (4.5, 6)
+ 2 1 : (1.7, 1)
+A:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075
+ col 0 : locations 0 to 2
+ 1 : (3.1, 42)
+ 3 : (3.5, 0)
+ 0 : (4.5, 6)
+ col 1 : locations 3 to 5
+ 1 : (2.9, 1.3)
+ 3 : (0.4, 2.71828)
+ 2 : (1.7, 1)
+ col 2 : locations 6 to 7
+ 2 : (3, 3.14159)
+ 0 : (3.2, 0.1)
+ col 3 : locations 8 to 9
+ 3 : (1, 7)
+ 1 : (0.9, 99)
+AT:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 144.296
+ col 0 : locations 0 to 1
+ 0 : (4.5, -6)
+ 2 : (3.2, -0.1)
+ col 1 : locations 2 to 4
+ 0 : (3.1, -42)
+ 1 : (2.9, -1.3)
+ 3 : (0.9, -99)
+ col 2 : locations 5 to 6
+ 1 : (1.7, -1)
+ 2 : (3, -3.14159)
+ col 3 : locations 7 to 9
+ 0 : (3.5, -0)
+ 1 : (0.4, -2.71828)
+ 3 : (1, -7)
+D:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 16 nnz: 16, 1-norm: 25308.3
+ col 0 : locations 0 to 3
+ 1 : (265.95, 170.4)
+ 3 : (15.75, -21)
+ 0 : (12720.7, 0)
+ 2 : (9.91416, 9.7531)
+ col 1 : locations 4 to 7
+ 1 : (24239.7, 0)
+ 3 : (709.444, -232.337)
+ 0 : (265.95, -170.4)
+ 2 : (6.23, 0.69)
+ col 2 : locations 8 to 11
+ 1 : (6.23, -0.69)
+ 3 : (3.39828, 4.22108)
+ 2 : (12676.9, 0)
+ 0 : (9.91416, -9.7531)
+ col 3 : locations 12 to 15
+ 1 : (709.444, 232.337)
+ 3 : (12724, 0)
+ 0 : (15.75, 21)
+ 2 : (3.39828, -4.22108)
+./cs_ci_demo2 < ../Matrix/t2
+
+--- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.06e+02
+blocks: 1 singletons: 0 structural rank: 4
+QR natural time: 0.00 resid: 2.06e-17
+QR amd(A'*A) time: 0.00 resid: 6.36e-18
+LU natural time: 0.00 resid: 4.88e-18
+LU amd(A+A') time: 0.00 resid: 2.11e-18
+LU amd(S'*S) time: 0.00 resid: 6.36e-18
+LU amd(A'*A) time: 0.00 resid: 2.11e-18
+./cs_ci_demo2 < ../Matrix/t3
+
+--- Matrix: 3-by-4, nnz: 12 (sym: 0: nnz 0), norm: 3.06e+00
+blocks: 1 singletons: 0 structural rank: 3
+QR natural time: 0.00 resid: 1.05e-16
+QR amd(A'*A) time: 0.00 resid: 1.05e-16
+./cs_ci_demo2 < ../Matrix/t4
+
+--- Matrix: 2-by-2, nnz: 3 (sym: 1: nnz 4), norm: 2.83e+00
+blocks: 1 singletons: 0 structural rank: 2
+QR natural time: 0.00 resid: 5.65e-17
+QR amd(A'*A) time: 0.00 resid: 5.65e-17
+LU natural time: 0.00 resid: 0.00e+00
+LU amd(A+A') time: 0.00 resid: 0.00e+00
+LU amd(S'*S) time: 0.00 resid: 0.00e+00
+LU amd(A'*A) time: 0.00 resid: 0.00e+00
+Chol natural time: 0.00 (failed)
+Chol amd(A+A') time: 0.00 (failed)
+./cs_ci_demo2 < ../Matrix/c_west0067
+
+--- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.17e+00
+blocks: 2 singletons: 1 structural rank: 67
+QR natural time: 0.00 resid: 8.16e-17
+QR amd(A'*A) time: 0.00 resid: 5.34e-17
+LU natural time: 0.00 resid: 4.54e-17
+LU amd(A+A') time: 0.00 resid: 5.90e-17
+LU amd(S'*S) time: 0.00 resid: 5.28e-17
+LU amd(A'*A) time: 0.00 resid: 4.76e-17
+./cs_ci_demo2 < ../Matrix/c_mbeacxc
+
+--- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01
+blocks: 10 singletons: 8 structural rank: 448
+QR natural time: 0.32 resid: nan
+QR amd(A'*A) time: 0.37 resid: nan
+./cs_ci_demo2 < ../Matrix/young1c
+
+--- Matrix: 841-by-841, nnz: 4089 (sym: 0: nnz 0), norm: 7.30e+02
+blocks: 1 singletons: 0 structural rank: 841
+QR natural time: 0.02 resid: 1.51e-16
+QR amd(A'*A) time: 0.00 resid: 1.53e-16
+LU natural time: 0.01 resid: 1.39e-16
+LU amd(A+A') time: 0.01 resid: 2.95e-16
+LU amd(S'*S) time: 0.01 resid: 3.37e-16
+LU amd(A'*A) time: 0.00 resid: 3.37e-16
+./cs_ci_demo2 < ../Matrix/qc324
+
+--- Matrix: 324-by-324, nnz: 26730 (sym: 0: nnz 0), norm: 1.71e+00
+blocks: 1 singletons: 0 structural rank: 324
+QR natural time: 0.04 resid: 9.08e-17
+QR amd(A'*A) time: 0.05 resid: 8.71e-17
+LU natural time: 0.02 resid: 6.01e-17
+LU amd(A+A') time: 0.02 resid: 4.05e-17
+LU amd(S'*S) time: 0.04 resid: 4.71e-17
+LU amd(A'*A) time: 0.03 resid: 4.71e-17
+./cs_ci_demo2 < ../Matrix/neumann
+
+--- Matrix: 1600-by-1600, nnz: 7840 (sym: 0: nnz 0), norm: 1.41e+01
+blocks: 1 singletons: 0 structural rank: 1600
+QR amd(A'*A) time: 0.03 resid: 1.04e-15
+LU amd(A+A') time: 0.00 resid: 3.55e-16
+LU amd(S'*S) time: 0.02 resid: 4.03e-16
+LU amd(A'*A) time: 0.02 resid: 4.03e-16
+./cs_ci_demo2 < ../Matrix/c4
+
+--- Matrix: 4-by-4, nnz: 10 (sym: -1: nnz 16), norm: 7.37e+01
+blocks: 1 singletons: 0 structural rank: 4
+QR natural time: 0.00 resid: 5.85e-17
+QR amd(A'*A) time: 0.00 resid: 5.85e-17
+LU natural time: 0.00 resid: 2.29e-17
+LU amd(A+A') time: 0.00 resid: 2.29e-17
+LU amd(S'*S) time: 0.00 resid: 2.29e-17
+LU amd(A'*A) time: 0.00 resid: 2.29e-17
+Chol natural time: 0.00 resid: 6.88e-17
+Chol amd(A+A') time: 0.00 resid: 6.88e-17
+./cs_ci_demo3 < ../Matrix/c4
+
+--- Matrix: 4-by-4, nnz: 10 (sym: -1: nnz 16), norm: 7.37e+01
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.00
+numeric chol time 0.00
+solve chol time 0.00
+original: resid: 6.88e-17
+update: time: 0.00
+update: time: 0.00 (incl solve) resid: 6.49e-17
+rechol: time: 0.00 (incl solve) resid: 6.49e-17
+downdate: time: 0.00
+downdate: time: 0.00 (incl solve) resid: 5.85e-17
+./cs_ci_demo2 < ../Matrix/mhd1280b
+
+--- Matrix: 1280-by-1280, nnz: 11963 (sym: -1: nnz 22646), norm: 8.00e+01
+tiny entries dropped: 66
+blocks: 20 singletons: 14 structural rank: 1280
+QR amd(A'*A) time: 0.01 resid: 6.15e-25
+LU amd(A+A') time: 0.01 resid: 2.33e-25
+LU amd(S'*S) time: 0.01 resid: 3.96e-25
+LU amd(A'*A) time: 0.01 resid: 3.96e-25
+Chol amd(A+A') time: 0.00 resid: 1.58e-25
+./cs_ci_demo3 < ../Matrix/mhd1280b
+
+--- Matrix: 1280-by-1280, nnz: 12029 (sym: -1: nnz 22778), norm: 8.00e+01
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.01
+numeric chol time 0.00
+solve chol time 0.00
+original: resid: 1.51e-25
+update: time: 0.00
+update: time: 0.00 (incl solve) resid: 1.75e-25
+rechol: time: 0.00 (incl solve) resid: 1.71e-25
+downdate: time: 0.00
+downdate: time: 0.00 (incl solve) resid: 5.85e-25
+./cs_cl_demo1 < ../Matrix/t2
+T:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+triplet: 4-by-4, nzmax: 16 nnz: 10
+ 2 2 : (3, 3.14159)
+ 1 0 : (3.1, 42)
+ 3 3 : (1, 7)
+ 0 2 : (3.2, 0.1)
+ 1 1 : (2.9, 1.3)
+ 3 0 : (3.5, 0)
+ 3 1 : (0.4, 2.71828)
+ 1 3 : (0.9, 99)
+ 0 0 : (4.5, 6)
+ 2 1 : (1.7, 1)
+A:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 106.075
+ col 0 : locations 0 to 2
+ 1 : (3.1, 42)
+ 3 : (3.5, 0)
+ 0 : (4.5, 6)
+ col 1 : locations 3 to 5
+ 1 : (2.9, 1.3)
+ 3 : (0.4, 2.71828)
+ 2 : (1.7, 1)
+ col 2 : locations 6 to 7
+ 2 : (3, 3.14159)
+ 0 : (3.2, 0.1)
+ col 3 : locations 8 to 9
+ 3 : (1, 7)
+ 1 : (0.9, 99)
+AT:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 10 nnz: 10, 1-norm: 144.296
+ col 0 : locations 0 to 1
+ 0 : (4.5, -6)
+ 2 : (3.2, -0.1)
+ col 1 : locations 2 to 4
+ 0 : (3.1, -42)
+ 1 : (2.9, -1.3)
+ 3 : (0.9, -99)
+ col 2 : locations 5 to 6
+ 1 : (1.7, -1)
+ 2 : (3, -3.14159)
+ col 3 : locations 7 to 9
+ 0 : (3.5, -0)
+ 1 : (0.4, -2.71828)
+ 3 : (1, -7)
+D:
+CXSparse Version 2.2.1, Nov 1, 2007. Copyright (c) Timothy A. Davis, 2006-2007
+4-by-4, nzmax: 16 nnz: 16, 1-norm: 25308.3
+ col 0 : locations 0 to 3
+ 1 : (265.95, 170.4)
+ 3 : (15.75, -21)
+ 0 : (12720.7, 0)
+ 2 : (9.91416, 9.7531)
+ col 1 : locations 4 to 7
+ 1 : (24239.7, 0)
+ 3 : (709.444, -232.337)
+ 0 : (265.95, -170.4)
+ 2 : (6.23, 0.69)
+ col 2 : locations 8 to 11
+ 1 : (6.23, -0.69)
+ 3 : (3.39828, 4.22108)
+ 2 : (12676.9, 0)
+ 0 : (9.91416, -9.7531)
+ col 3 : locations 12 to 15
+ 1 : (709.444, 232.337)
+ 3 : (12724, 0)
+ 0 : (15.75, 21)
+ 2 : (3.39828, -4.22108)
+./cs_cl_demo2 < ../Matrix/t2
+
+--- Matrix: 4-by-4, nnz: 10 (sym: 0: nnz 0), norm: 1.06e+02
+blocks: 1 singletons: 0 structural rank: 4
+QR natural time: 0.00 resid: 2.06e-17
+QR amd(A'*A) time: 0.00 resid: 6.36e-18
+LU natural time: 0.00 resid: 4.88e-18
+LU amd(A+A') time: 0.00 resid: 2.11e-18
+LU amd(S'*S) time: 0.00 resid: 6.36e-18
+LU amd(A'*A) time: 0.00 resid: 2.11e-18
+./cs_cl_demo2 < ../Matrix/t3
+
+--- Matrix: 3-by-4, nnz: 12 (sym: 0: nnz 0), norm: 3.06e+00
+blocks: 1 singletons: 0 structural rank: 3
+QR natural time: 0.00 resid: 1.05e-16
+QR amd(A'*A) time: 0.00 resid: 1.05e-16
+./cs_cl_demo2 < ../Matrix/t4
+
+--- Matrix: 2-by-2, nnz: 3 (sym: 1: nnz 4), norm: 2.83e+00
+blocks: 1 singletons: 0 structural rank: 2
+QR natural time: 0.00 resid: 5.65e-17
+QR amd(A'*A) time: 0.00 resid: 5.65e-17
+LU natural time: 0.00 resid: 0.00e+00
+LU amd(A+A') time: 0.00 resid: 0.00e+00
+LU amd(S'*S) time: 0.00 resid: 0.00e+00
+LU amd(A'*A) time: 0.00 resid: 0.00e+00
+Chol natural time: 0.00 (failed)
+Chol amd(A+A') time: 0.00 (failed)
+./cs_cl_demo2 < ../Matrix/c_west0067
+
+--- Matrix: 67-by-67, nnz: 294 (sym: 0: nnz 0), norm: 6.17e+00
+blocks: 2 singletons: 1 structural rank: 67
+QR natural time: 0.00 resid: 8.16e-17
+QR amd(A'*A) time: 0.00 resid: 5.34e-17
+LU natural time: 0.00 resid: 4.54e-17
+LU amd(A+A') time: 0.00 resid: 5.90e-17
+LU amd(S'*S) time: 0.00 resid: 5.28e-17
+LU amd(A'*A) time: 0.00 resid: 4.76e-17
+./cs_cl_demo2 < ../Matrix/c_mbeacxc
+
+--- Matrix: 492-by-490, nnz: 49920 (sym: 0: nnz 0), norm: 9.29e-01
+blocks: 10 singletons: 8 structural rank: 448
+QR natural time: 0.29 resid: nan
+QR amd(A'*A) time: 0.35 resid: nan
+./cs_cl_demo2 < ../Matrix/young1c
+
+--- Matrix: 841-by-841, nnz: 4089 (sym: 0: nnz 0), norm: 7.30e+02
+blocks: 1 singletons: 0 structural rank: 841
+QR natural time: 0.02 resid: 1.51e-16
+QR amd(A'*A) time: 0.01 resid: 1.53e-16
+LU natural time: 0.01 resid: 1.39e-16
+LU amd(A+A') time: 0.01 resid: 2.95e-16
+LU amd(S'*S) time: 0.01 resid: 3.37e-16
+LU amd(A'*A) time: 0.00 resid: 3.37e-16
+./cs_cl_demo2 < ../Matrix/qc324
+
+--- Matrix: 324-by-324, nnz: 26730 (sym: 0: nnz 0), norm: 1.71e+00
+blocks: 1 singletons: 0 structural rank: 324
+QR natural time: 0.04 resid: 9.08e-17
+QR amd(A'*A) time: 0.06 resid: 8.71e-17
+LU natural time: 0.02 resid: 6.01e-17
+LU amd(A+A') time: 0.03 resid: 4.05e-17
+LU amd(S'*S) time: 0.03 resid: 4.71e-17
+LU amd(A'*A) time: 0.03 resid: 4.71e-17
+./cs_cl_demo2 < ../Matrix/neumann
+
+--- Matrix: 1600-by-1600, nnz: 7840 (sym: 0: nnz 0), norm: 1.41e+01
+blocks: 1 singletons: 0 structural rank: 1600
+QR amd(A'*A) time: 0.03 resid: 1.04e-15
+LU amd(A+A') time: 0.01 resid: 3.55e-16
+LU amd(S'*S) time: 0.03 resid: 4.03e-16
+LU amd(A'*A) time: 0.01 resid: 4.03e-16
+./cs_cl_demo2 < ../Matrix/c4
+
+--- Matrix: 4-by-4, nnz: 10 (sym: -1: nnz 16), norm: 7.37e+01
+blocks: 1 singletons: 0 structural rank: 4
+QR natural time: 0.00 resid: 5.85e-17
+QR amd(A'*A) time: 0.00 resid: 5.85e-17
+LU natural time: 0.00 resid: 2.29e-17
+LU amd(A+A') time: 0.00 resid: 2.29e-17
+LU amd(S'*S) time: 0.00 resid: 2.29e-17
+LU amd(A'*A) time: 0.00 resid: 2.29e-17
+Chol natural time: 0.00 resid: 6.88e-17
+Chol amd(A+A') time: 0.00 resid: 6.88e-17
+./cs_cl_demo3 < ../Matrix/c4
+
+--- Matrix: 4-by-4, nnz: 10 (sym: -1: nnz 16), norm: 7.37e+01
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.00
+numeric chol time 0.00
+solve chol time 0.00
+original: resid: 6.88e-17
+update: time: 0.00
+update: time: 0.00 (incl solve) resid: 6.49e-17
+rechol: time: 0.00 (incl solve) resid: 6.49e-17
+downdate: time: 0.00
+downdate: time: 0.00 (incl solve) resid: 5.85e-17
+./cs_cl_demo2 < ../Matrix/mhd1280b
+
+--- Matrix: 1280-by-1280, nnz: 11963 (sym: -1: nnz 22646), norm: 8.00e+01
+tiny entries dropped: 66
+blocks: 20 singletons: 14 structural rank: 1280
+QR amd(A'*A) time: 0.01 resid: 6.15e-25
+LU amd(A+A') time: 0.00 resid: 2.33e-25
+LU amd(S'*S) time: 0.01 resid: 3.96e-25
+LU amd(A'*A) time: 0.00 resid: 3.96e-25
+Chol amd(A+A') time: 0.01 resid: 1.58e-25
+./cs_cl_demo3 < ../Matrix/mhd1280b
+
+--- Matrix: 1280-by-1280, nnz: 12029 (sym: -1: nnz 22778), norm: 8.00e+01
+
+chol then update/downdate amd(A+A')
+symbolic chol time 0.01
+numeric chol time 0.00
+solve chol time 0.00
+original: resid: 1.51e-25
+update: time: 0.00
+update: time: 0.00 (incl solve) resid: 1.75e-25
+rechol: time: 0.00 (incl solve) resid: 1.71e-25
+downdate: time: 0.00
+downdate: time: 0.00 (incl solve) resid: 5.85e-25
+make[1]: Leaving directory `/amd/netapp3/vol/research0a/research18/sparse2/SuiteSparse/CXSparse/Demo'
diff --git a/CXSparse/Demo/cs_demo1.c b/CXSparse/Demo/cs_demo1.c
new file mode 100644
index 0000000..ea1a059
--- /dev/null
+++ b/CXSparse/Demo/cs_demo1.c
@@ -0,0 +1,27 @@
+#include "cs.h"
+int main (void)
+{
+ cs *T, *A, *Eye, *AT, *C, *D ;
+ int i, m ;
+ T = cs_load (stdin) ; /* load triplet matrix T from stdin */
+ printf ("T:\n") ; cs_print (T, 0) ; /* print T */
+ A = cs_compress (T) ; /* A = compressed-column form of T */
+ printf ("A:\n") ; cs_print (A, 0) ; /* print A */
+ cs_spfree (T) ; /* clear T */
+ AT = cs_transpose (A, 1) ; /* AT = A' */
+ printf ("AT:\n") ; cs_print (AT, 0) ; /* print AT */
+ m = A ? A->m : 0 ; /* m = # of rows of A */
+ T = cs_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */
+ for (i = 0 ; i < m ; i++) cs_entry (T, i, i, 1) ;
+ Eye = cs_compress (T) ; /* Eye = speye (m) */
+ cs_spfree (T) ;
+ C = cs_multiply (A, AT) ; /* C = A*A' */
+ D = cs_add (C, Eye, 1, cs_norm (C)) ; /* D = C + Eye*norm (C,1) */
+ printf ("D:\n") ; cs_print (D, 0) ; /* print D */
+ cs_spfree (A) ; /* clear A AT C D Eye */
+ cs_spfree (AT) ;
+ cs_spfree (C) ;
+ cs_spfree (D) ;
+ cs_spfree (Eye) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_demo2.c b/CXSparse/Demo/cs_demo2.c
new file mode 100644
index 0000000..71e7ad0
--- /dev/null
+++ b/CXSparse/Demo/cs_demo2.c
@@ -0,0 +1,9 @@
+#include "cs_demo.h"
+/* cs_demo2: read a matrix and solve a linear system */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 1e-14) ;
+ demo2 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_demo3.c b/CXSparse/Demo/cs_demo3.c
new file mode 100644
index 0000000..726fc39
--- /dev/null
+++ b/CXSparse/Demo/cs_demo3.c
@@ -0,0 +1,9 @@
+#include "cs_demo.h"
+/* cs_demo3: read a matrix and test Cholesky update/downdate */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 0) ;
+ demo3 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_di_demo.c b/CXSparse/Demo/cs_di_demo.c
new file mode 100644
index 0000000..78fa22a
--- /dev/null
+++ b/CXSparse/Demo/cs_di_demo.c
@@ -0,0 +1,286 @@
+#include "cs_di_demo.h"
+#include <time.h>
+/* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */
+static int is_sym (cs_di *A)
+{
+ int is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ;
+ if (m != n) return (0) ;
+ is_upper = 1 ;
+ is_lower = 1 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ if (Ai [p] > j) is_upper = 0 ;
+ if (Ai [p] < j) is_lower = 0 ;
+ }
+ }
+ return (is_upper ? 1 : (is_lower ? -1 : 0)) ;
+}
+
+/* true for off-diagonal entries */
+static int dropdiag (int i, int j, double aij, void *other) { return (i != j) ;}
+
+/* C = A + triu(A,1)' */
+static cs_di *make_sym (cs_di *A)
+{
+ cs_di *AT, *C ;
+ AT = cs_di_transpose (A, 1) ; /* AT = A' */
+ cs_di_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */
+ C = cs_di_add (A, AT, 1, 1) ; /* C = A+AT */
+ cs_di_spfree (AT) ;
+ return (C) ;
+}
+
+/* create a right-hand side */
+static void rhs (double *x, double *b, int m)
+{
+ int i ;
+ for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ;
+ for (i = 0 ; i < m ; i++) x [i] = b [i] ;
+}
+
+/* infinity-norm of x */
+static double norm (double *x, int n)
+{
+ int i ;
+ double normx = 0 ;
+ for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, fabs (x [i])) ;
+ return (normx) ;
+}
+
+/* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */
+static void print_resid (int ok, cs_di *A, double *x, double *b, double *resid)
+{
+ int i, m, n ;
+ if (!ok) { printf (" (failed)\n") ; return ; }
+ m = A->m ; n = A->n ;
+ for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */
+ cs_di_gaxpy (A, x, resid) ; /* resid = resid + A*x */
+ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 :
+ (cs_di_norm (A) * norm (x,n) + norm (b,m)))) ;
+}
+
+static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; }
+static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; }
+
+static void print_order (int order)
+{
+ switch (order)
+ {
+ case 0: printf ("natural ") ; break ;
+ case 1: printf ("amd(A+A') ") ; break ;
+ case 2: printf ("amd(S'*S) ") ; break ;
+ case 3: printf ("amd(A'*A) ") ; break ;
+ }
+}
+
+/* read a problem from a file */
+problem *get_problem (FILE *f, double tol)
+{
+ cs_di *T, *A, *C ;
+ int sym, m, n, mn, nz1, nz2 ;
+ problem *Prob ;
+ Prob = cs_di_calloc (1, sizeof (problem)) ;
+ if (!Prob) return (NULL) ;
+ T = cs_di_load (f) ; /* load triplet matrix T from a file */
+ Prob->A = A = cs_di_compress (T) ; /* A = compressed-column form of T */
+ cs_di_spfree (T) ; /* clear T */
+ if (!cs_di_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */
+ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */
+ m = A->m ; n = A->n ;
+ mn = CS_MAX (m,n) ;
+ nz1 = A->p [n] ;
+ cs_di_dropzeros (A) ; /* drop zero entries */
+ nz2 = A->p [n] ;
+ if (tol > 0) cs_di_droptol (A, tol) ; /* drop tiny entries (just to test) */
+ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */
+ if (!C) return (free_problem (Prob)) ;
+ printf ("\n--- Matrix: %d-by-%d, nnz: %d (sym: %d: nnz %d), norm: %8.2e\n",
+ m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_di_norm (C)) ;
+ if (nz1 != nz2) printf ("zero entries dropped: %d\n", nz1 - nz2) ;
+ if (nz2 != A->p [n]) printf ("tiny entries dropped: %d\n", nz2 - A->p [n]) ;
+ Prob->b = cs_di_malloc (mn, sizeof (double)) ;
+ Prob->x = cs_di_malloc (mn, sizeof (double)) ;
+ Prob->resid = cs_di_malloc (mn, sizeof (double)) ;
+ return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ;
+}
+
+/* free a problem */
+problem *free_problem (problem *Prob)
+{
+ if (!Prob) return (NULL) ;
+ cs_di_spfree (Prob->A) ;
+ if (Prob->sym) cs_di_spfree (Prob->C) ;
+ cs_di_free (Prob->b) ;
+ cs_di_free (Prob->x) ;
+ cs_di_free (Prob->resid) ;
+ return (cs_di_free (Prob)) ;
+}
+
+/* solve a linear system using Cholesky, LU, and QR, with various orderings */
+int demo2 (problem *Prob)
+{
+ cs_di *A, *C ;
+ double *b, *x, *resid, t, tol ;
+ int k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ;
+ cs_did *D ;
+ if (!Prob) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ m = A->m ; n = A->n ;
+ tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */
+ D = cs_di_dmperm (C, 1) ; /* randomized dmperm analysis */
+ if (!D) return (0) ;
+ nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ;
+ sprank = rr [3] ;
+ for (ns = 0, k = 0 ; k < nb ; k++)
+ {
+ ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ;
+ }
+ printf ("blocks: %d singletons: %d structural rank: %d\n", nb, ns, sprank) ;
+ cs_di_dfree (D) ;
+ for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("QR ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_di_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/
+ for (order = 0 ; order <= 3 ; order++) /* try all orderings */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("LU ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_di_lusol (order, C, x, tol) ; /* solve Ax=b with LU */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (!Prob->sym) return (1) ;
+ for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("Chol ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_di_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ return (1) ;
+}
+
+/* free workspace for demo3 */
+static int done3 (int ok, cs_dis *S, cs_din *N, double *y, cs_di *W, cs_di *E, int *p)
+{
+ cs_di_sfree (S) ;
+ cs_di_nfree (N) ;
+ cs_di_free (y) ;
+ cs_di_spfree (W) ;
+ cs_di_spfree (E) ;
+ cs_di_free (p) ;
+ return (ok) ;
+}
+
+/* Cholesky update/downdate */
+int demo3 (problem *Prob)
+{
+ cs_di *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ;
+ int n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ;
+ double *b, *x, *resid, *y = NULL, *Lx, *Wx, s, t, t1 ;
+ cs_dis *S = NULL ;
+ cs_din *N = NULL ;
+ if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ n = A->n ;
+ if (!Prob->sym || n == 0) return (1) ;
+ rhs (x, b, n) ; /* compute right-hand side */
+ printf ("\nchol then update/downdate ") ;
+ print_order (1) ;
+ y = cs_di_malloc (n, sizeof (double)) ;
+ t = tic () ;
+ S = cs_di_schol (1, C) ; /* symbolic Chol, amd(A+A') */
+ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ;
+ t = tic () ;
+ N = cs_di_chol (C, S) ; /* numeric Cholesky */
+ printf ("numeric chol time %8.2f\n", toc (t)) ;
+ if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_di_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_di_lsolve (N->L, y) ; /* y = L\y */
+ cs_di_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_di_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ printf ("solve chol time %8.2f\n", toc (t)) ;
+ printf ("original: ") ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ k = n/2 ; /* construct W */
+ W = cs_di_spalloc (n, 1, n, 1, 0) ;
+ if (!W) return (done3 (0, S, N, y, W, E, p)) ;
+ Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ;
+ Wp = W->p ; Wi = W->i ; Wx = W->x ;
+ Wp [0] = 0 ;
+ p1 = Lp [k] ;
+ Wp [1] = Lp [k+1] - p1 ;
+ s = Lx [p1] ;
+ srand (1) ;
+ for ( ; p1 < Lp [k+1] ; p1++)
+ {
+ p2 = p1 - Lp [k] ;
+ Wi [p2] = Li [p1] ;
+ Wx [p2] = s * rand () / ((double) RAND_MAX) ;
+ }
+ t = tic () ;
+ ok = cs_di_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */
+ t1 = toc (t) ;
+ printf ("update: time: %8.2f\n", t1) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_di_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_di_lsolve (N->L, y) ; /* y = L\y */
+ cs_di_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_di_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ p = cs_di_pinv (S->pinv, n) ;
+ W2 = cs_di_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */
+ WT = cs_di_transpose (W2,1) ;
+ WW = cs_di_multiply (W2, WT) ;
+ cs_di_spfree (WT) ;
+ cs_di_spfree (W2) ;
+ E = cs_di_add (C, WW, 1, 1) ;
+ cs_di_spfree (WW) ;
+ if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("update: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ cs_di_nfree (N) ; /* clear N */
+ t = tic () ;
+ N = cs_di_chol (E, S) ; /* numeric Cholesky */
+ if (!N) return (done3 (0, S, N, y, W, E, p)) ;
+ cs_di_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_di_lsolve (N->L, y) ; /* y = L\y */
+ cs_di_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_di_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("rechol: time: %8.2f (incl solve) ", t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ t = tic () ;
+ ok = cs_di_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */
+ t1 = toc (t) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("downdate: time: %8.2f\n", t1) ;
+ t = tic () ;
+ cs_di_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_di_lsolve (N->L, y) ; /* y = L\y */
+ cs_di_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_di_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("downdate: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ return (done3 (1, S, N, y, W, E, p)) ;
+}
diff --git a/CXSparse/Demo/cs_di_demo.h b/CXSparse/Demo/cs_di_demo.h
new file mode 100644
index 0000000..097561d
--- /dev/null
+++ b/CXSparse/Demo/cs_di_demo.h
@@ -0,0 +1,15 @@
+#include "cs.h"
+typedef struct problem_struct
+{
+ cs_di *A ;
+ cs_di *C ;
+ int sym ;
+ double *x ;
+ double *b ;
+ double *resid ;
+} problem ;
+
+problem *get_problem (FILE *f, double tol) ;
+int demo2 (problem *Prob) ;
+int demo3 (problem *Prob) ;
+problem *free_problem (problem *Prob) ;
diff --git a/CXSparse/Demo/cs_di_demo1.c b/CXSparse/Demo/cs_di_demo1.c
new file mode 100644
index 0000000..ad9d641
--- /dev/null
+++ b/CXSparse/Demo/cs_di_demo1.c
@@ -0,0 +1,27 @@
+#include "cs.h"
+int main (void)
+{
+ cs_di *T, *A, *Eye, *AT, *C, *D ;
+ int i, m ;
+ T = cs_di_load (stdin) ; /* load triplet matrix T from stdin */
+ printf ("T:\n") ; cs_di_print (T, 0) ; /* print T */
+ A = cs_di_compress (T) ; /* A = compressed-column form of T */
+ printf ("A:\n") ; cs_di_print (A, 0) ; /* print A */
+ cs_di_spfree (T) ; /* clear T */
+ AT = cs_di_transpose (A, 1) ; /* AT = A' */
+ printf ("AT:\n") ; cs_di_print (AT, 0) ; /* print AT */
+ m = A ? A->m : 0 ; /* m = # of rows of A */
+ T = cs_di_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */
+ for (i = 0 ; i < m ; i++) cs_di_entry (T, i, i, 1) ;
+ Eye = cs_di_compress (T) ; /* Eye = speye (m) */
+ cs_di_spfree (T) ;
+ C = cs_di_multiply (A, AT) ; /* C = A*A' */
+ D = cs_di_add (C, Eye, 1, cs_di_norm (C)) ; /* D = C + Eye*norm (C,1) */
+ printf ("D:\n") ; cs_di_print (D, 0) ; /* print D */
+ cs_di_spfree (A) ; /* clear A AT C D Eye */
+ cs_di_spfree (AT) ;
+ cs_di_spfree (C) ;
+ cs_di_spfree (D) ;
+ cs_di_spfree (Eye) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_di_demo2.c b/CXSparse/Demo/cs_di_demo2.c
new file mode 100644
index 0000000..e5f8200
--- /dev/null
+++ b/CXSparse/Demo/cs_di_demo2.c
@@ -0,0 +1,9 @@
+#include "cs_di_demo.h"
+/* cs_di_demo2: read a matrix and solve a linear system */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 1e-14) ;
+ demo2 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_di_demo3.c b/CXSparse/Demo/cs_di_demo3.c
new file mode 100644
index 0000000..a75b215
--- /dev/null
+++ b/CXSparse/Demo/cs_di_demo3.c
@@ -0,0 +1,9 @@
+#include "cs_di_demo.h"
+/* cs_di_demo3: read a matrix and test Cholesky update/downdate */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 0) ;
+ demo3 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_dl_demo.c b/CXSparse/Demo/cs_dl_demo.c
new file mode 100644
index 0000000..3037366
--- /dev/null
+++ b/CXSparse/Demo/cs_dl_demo.c
@@ -0,0 +1,286 @@
+#include "cs_dl_demo.h"
+#include <time.h>
+/* 1 if A is square & upper tri., -1 if square & lower tri., 0 otherwise */
+static UF_long is_sym (cs_dl *A)
+{
+ UF_long is_upper, is_lower, j, p, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i ;
+ if (m != n) return (0) ;
+ is_upper = 1 ;
+ is_lower = 1 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ if (Ai [p] > j) is_upper = 0 ;
+ if (Ai [p] < j) is_lower = 0 ;
+ }
+ }
+ return (is_upper ? 1 : (is_lower ? -1 : 0)) ;
+}
+
+/* true for off-diagonal entries */
+static UF_long dropdiag (UF_long i, UF_long j, double aij, void *other) { return (i != j) ;}
+
+/* C = A + triu(A,1)' */
+static cs_dl *make_sym (cs_dl *A)
+{
+ cs_dl *AT, *C ;
+ AT = cs_dl_transpose (A, 1) ; /* AT = A' */
+ cs_dl_fkeep (AT, &dropdiag, NULL) ; /* drop diagonal entries from AT */
+ C = cs_dl_add (A, AT, 1, 1) ; /* C = A+AT */
+ cs_dl_spfree (AT) ;
+ return (C) ;
+}
+
+/* create a right-hand side */
+static void rhs (double *x, double *b, UF_long m)
+{
+ UF_long i ;
+ for (i = 0 ; i < m ; i++) b [i] = 1 + ((double) i) / m ;
+ for (i = 0 ; i < m ; i++) x [i] = b [i] ;
+}
+
+/* infinity-norm of x */
+static double norm (double *x, UF_long n)
+{
+ UF_long i ;
+ double normx = 0 ;
+ for (i = 0 ; i < n ; i++) normx = CS_MAX (normx, fabs (x [i])) ;
+ return (normx) ;
+}
+
+/* compute residual, norm(A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf)) */
+static void print_resid (UF_long ok, cs_dl *A, double *x, double *b, double *resid)
+{
+ UF_long i, m, n ;
+ if (!ok) { printf (" (failed)\n") ; return ; }
+ m = A->m ; n = A->n ;
+ for (i = 0 ; i < m ; i++) resid [i] = -b [i] ; /* resid = -b */
+ cs_dl_gaxpy (A, x, resid) ; /* resid = resid + A*x */
+ printf ("resid: %8.2e\n", norm (resid,m) / ((n == 0) ? 1 :
+ (cs_dl_norm (A) * norm (x,n) + norm (b,m)))) ;
+}
+
+static double tic (void) { return (clock () / (double) CLOCKS_PER_SEC) ; }
+static double toc (double t) { double s = tic () ; return (CS_MAX (0, s-t)) ; }
+
+static void print_order (UF_long order)
+{
+ switch (order)
+ {
+ case 0: printf ("natural ") ; break ;
+ case 1: printf ("amd(A+A') ") ; break ;
+ case 2: printf ("amd(S'*S) ") ; break ;
+ case 3: printf ("amd(A'*A) ") ; break ;
+ }
+}
+
+/* read a problem from a file */
+problem *get_problem (FILE *f, double tol)
+{
+ cs_dl *T, *A, *C ;
+ UF_long sym, m, n, mn, nz1, nz2 ;
+ problem *Prob ;
+ Prob = cs_dl_calloc (1, sizeof (problem)) ;
+ if (!Prob) return (NULL) ;
+ T = cs_dl_load (f) ; /* load triplet matrix T from a file */
+ Prob->A = A = cs_dl_compress (T) ; /* A = compressed-column form of T */
+ cs_dl_spfree (T) ; /* clear T */
+ if (!cs_dl_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */
+ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */
+ m = A->m ; n = A->n ;
+ mn = CS_MAX (m,n) ;
+ nz1 = A->p [n] ;
+ cs_dl_dropzeros (A) ; /* drop zero entries */
+ nz2 = A->p [n] ;
+ if (tol > 0) cs_dl_droptol (A, tol) ; /* drop tiny entries (just to test) */
+ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */
+ if (!C) return (free_problem (Prob)) ;
+ printf ("\n--- Matrix: %ld-by-%ld, nnz: %ld (sym: %ld: nnz %ld), norm: %8.2e\n",
+ m, n, A->p [n], sym, sym ? C->p [n] : 0, cs_dl_norm (C)) ;
+ if (nz1 != nz2) printf ("zero entries dropped: %ld\n", nz1 - nz2) ;
+ if (nz2 != A->p [n]) printf ("tiny entries dropped: %ld\n", nz2 - A->p [n]) ;
+ Prob->b = cs_dl_malloc (mn, sizeof (double)) ;
+ Prob->x = cs_dl_malloc (mn, sizeof (double)) ;
+ Prob->resid = cs_dl_malloc (mn, sizeof (double)) ;
+ return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ;
+}
+
+/* free a problem */
+problem *free_problem (problem *Prob)
+{
+ if (!Prob) return (NULL) ;
+ cs_dl_spfree (Prob->A) ;
+ if (Prob->sym) cs_dl_spfree (Prob->C) ;
+ cs_dl_free (Prob->b) ;
+ cs_dl_free (Prob->x) ;
+ cs_dl_free (Prob->resid) ;
+ return (cs_dl_free (Prob)) ;
+}
+
+/* solve a linear system using Cholesky, LU, and QR, with various orderings */
+UF_long demo2 (problem *Prob)
+{
+ cs_dl *A, *C ;
+ double *b, *x, *resid, t, tol ;
+ UF_long k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ;
+ cs_dld *D ;
+ if (!Prob) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ m = A->m ; n = A->n ;
+ tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */
+ D = cs_dl_dmperm (C, 1) ; /* randomized dmperm analysis */
+ if (!D) return (0) ;
+ nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ;
+ sprank = rr [3] ;
+ for (ns = 0, k = 0 ; k < nb ; k++)
+ {
+ ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ;
+ }
+ printf ("blocks: %ld singletons: %ld structural rank: %ld\n", nb, ns, sprank) ;
+ cs_dl_dfree (D) ;
+ for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("QR ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_dl_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/
+ for (order = 0 ; order <= 3 ; order++) /* try all orderings */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("LU ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_dl_lusol (order, C, x, tol) ; /* solve Ax=b with LU */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ if (!Prob->sym) return (1) ;
+ for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */
+ {
+ if (!order && m > 1000) continue ;
+ printf ("Chol ") ;
+ print_order (order) ;
+ rhs (x, b, m) ; /* compute right-hand side */
+ t = tic () ;
+ ok = cs_dl_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */
+ printf ("time: %8.2f ", toc (t)) ;
+ print_resid (ok, C, x, b, resid) ; /* print residual */
+ }
+ return (1) ;
+}
+
+/* free workspace for demo3 */
+static UF_long done3 (UF_long ok, cs_dls *S, cs_dln *N, double *y, cs_dl *W, cs_dl *E, UF_long *p)
+{
+ cs_dl_sfree (S) ;
+ cs_dl_nfree (N) ;
+ cs_dl_free (y) ;
+ cs_dl_spfree (W) ;
+ cs_dl_spfree (E) ;
+ cs_dl_free (p) ;
+ return (ok) ;
+}
+
+/* Cholesky update/downdate */
+UF_long demo3 (problem *Prob)
+{
+ cs_dl *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ;
+ UF_long n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ;
+ double *b, *x, *resid, *y = NULL, *Lx, *Wx, s, t, t1 ;
+ cs_dls *S = NULL ;
+ cs_dln *N = NULL ;
+ if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ;
+ A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
+ n = A->n ;
+ if (!Prob->sym || n == 0) return (1) ;
+ rhs (x, b, n) ; /* compute right-hand side */
+ printf ("\nchol then update/downdate ") ;
+ print_order (1) ;
+ y = cs_dl_malloc (n, sizeof (double)) ;
+ t = tic () ;
+ S = cs_dl_schol (1, C) ; /* symbolic Chol, amd(A+A') */
+ printf ("\nsymbolic chol time %8.2f\n", toc (t)) ;
+ t = tic () ;
+ N = cs_dl_chol (C, S) ; /* numeric Cholesky */
+ printf ("numeric chol time %8.2f\n", toc (t)) ;
+ if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_dl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_dl_lsolve (N->L, y) ; /* y = L\y */
+ cs_dl_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_dl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ printf ("solve chol time %8.2f\n", toc (t)) ;
+ printf ("original: ") ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ k = n/2 ; /* construct W */
+ W = cs_dl_spalloc (n, 1, n, 1, 0) ;
+ if (!W) return (done3 (0, S, N, y, W, E, p)) ;
+ Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ;
+ Wp = W->p ; Wi = W->i ; Wx = W->x ;
+ Wp [0] = 0 ;
+ p1 = Lp [k] ;
+ Wp [1] = Lp [k+1] - p1 ;
+ s = Lx [p1] ;
+ srand (1) ;
+ for ( ; p1 < Lp [k+1] ; p1++)
+ {
+ p2 = p1 - Lp [k] ;
+ Wi [p2] = Li [p1] ;
+ Wx [p2] = s * rand () / ((double) RAND_MAX) ;
+ }
+ t = tic () ;
+ ok = cs_dl_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */
+ t1 = toc (t) ;
+ printf ("update: time: %8.2f\n", t1) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ t = tic () ;
+ cs_dl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_dl_lsolve (N->L, y) ; /* y = L\y */
+ cs_dl_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_dl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ p = cs_dl_pinv (S->pinv, n) ;
+ W2 = cs_dl_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */
+ WT = cs_dl_transpose (W2,1) ;
+ WW = cs_dl_multiply (W2, WT) ;
+ cs_dl_spfree (WT) ;
+ cs_dl_spfree (W2) ;
+ E = cs_dl_add (C, WW, 1, 1) ;
+ cs_dl_spfree (WW) ;
+ if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("update: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ cs_dl_nfree (N) ; /* clear N */
+ t = tic () ;
+ N = cs_dl_chol (E, S) ; /* numeric Cholesky */
+ if (!N) return (done3 (0, S, N, y, W, E, p)) ;
+ cs_dl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_dl_lsolve (N->L, y) ; /* y = L\y */
+ cs_dl_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_dl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("rechol: time: %8.2f (incl solve) ", t) ;
+ print_resid (1, E, x, b, resid) ; /* print residual */
+ t = tic () ;
+ ok = cs_dl_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */
+ t1 = toc (t) ;
+ if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
+ printf ("downdate: time: %8.2f\n", t1) ;
+ t = tic () ;
+ cs_dl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
+ cs_dl_lsolve (N->L, y) ; /* y = L\y */
+ cs_dl_ltsolve (N->L, y) ; /* y = L'\y */
+ cs_dl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
+ t = toc (t) ;
+ printf ("downdate: time: %8.2f (incl solve) ", t1+t) ;
+ print_resid (1, C, x, b, resid) ; /* print residual */
+ return (done3 (1, S, N, y, W, E, p)) ;
+}
diff --git a/CXSparse/Demo/cs_dl_demo.h b/CXSparse/Demo/cs_dl_demo.h
new file mode 100644
index 0000000..9539f63
--- /dev/null
+++ b/CXSparse/Demo/cs_dl_demo.h
@@ -0,0 +1,15 @@
+#include "cs.h"
+typedef struct problem_struct
+{
+ cs_dl *A ;
+ cs_dl *C ;
+ UF_long sym ;
+ double *x ;
+ double *b ;
+ double *resid ;
+} problem ;
+
+problem *get_problem (FILE *f, double tol) ;
+UF_long demo2 (problem *Prob) ;
+UF_long demo3 (problem *Prob) ;
+problem *free_problem (problem *Prob) ;
diff --git a/CXSparse/Demo/cs_dl_demo1.c b/CXSparse/Demo/cs_dl_demo1.c
new file mode 100644
index 0000000..8a55e45
--- /dev/null
+++ b/CXSparse/Demo/cs_dl_demo1.c
@@ -0,0 +1,27 @@
+#include "cs.h"
+int main (void)
+{
+ cs_dl *T, *A, *Eye, *AT, *C, *D ;
+ UF_long i, m ;
+ T = cs_dl_load (stdin) ; /* load triplet matrix T from stdin */
+ printf ("T:\n") ; cs_dl_print (T, 0) ; /* print T */
+ A = cs_dl_compress (T) ; /* A = compressed-column form of T */
+ printf ("A:\n") ; cs_dl_print (A, 0) ; /* print A */
+ cs_dl_spfree (T) ; /* clear T */
+ AT = cs_dl_transpose (A, 1) ; /* AT = A' */
+ printf ("AT:\n") ; cs_dl_print (AT, 0) ; /* print AT */
+ m = A ? A->m : 0 ; /* m = # of rows of A */
+ T = cs_dl_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */
+ for (i = 0 ; i < m ; i++) cs_dl_entry (T, i, i, 1) ;
+ Eye = cs_dl_compress (T) ; /* Eye = speye (m) */
+ cs_dl_spfree (T) ;
+ C = cs_dl_multiply (A, AT) ; /* C = A*A' */
+ D = cs_dl_add (C, Eye, 1, cs_dl_norm (C)) ; /* D = C + Eye*norm (C,1) */
+ printf ("D:\n") ; cs_dl_print (D, 0) ; /* print D */
+ cs_dl_spfree (A) ; /* clear A AT C D Eye */
+ cs_dl_spfree (AT) ;
+ cs_dl_spfree (C) ;
+ cs_dl_spfree (D) ;
+ cs_dl_spfree (Eye) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_dl_demo2.c b/CXSparse/Demo/cs_dl_demo2.c
new file mode 100644
index 0000000..1ce473c
--- /dev/null
+++ b/CXSparse/Demo/cs_dl_demo2.c
@@ -0,0 +1,9 @@
+#include "cs_dl_demo.h"
+/* cs_dl_demo2: read a matrix and solve a linear system */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 1e-14) ;
+ demo2 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_dl_demo3.c b/CXSparse/Demo/cs_dl_demo3.c
new file mode 100644
index 0000000..06df0c8
--- /dev/null
+++ b/CXSparse/Demo/cs_dl_demo3.c
@@ -0,0 +1,9 @@
+#include "cs_dl_demo.h"
+/* cs_dl_demo3: read a matrix and test Cholesky update/downdate */
+int main (void)
+{
+ problem *Prob = get_problem (stdin, 0) ;
+ demo3 (Prob) ;
+ free_problem (Prob) ;
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_idemo.c b/CXSparse/Demo/cs_idemo.c
new file mode 100644
index 0000000..d2f962b
--- /dev/null
+++ b/CXSparse/Demo/cs_idemo.c
@@ -0,0 +1,57 @@
+#include "cs.h"
+/* test real/complex conversion routines (int version) */
+int main (void)
+{
+ cs_ci *T, *A, *A1, *A2, *B ;
+ cs_di *C1, *C2, *Treal, *Timag ;
+
+ printf ("\n--- cs_idemo, size of CS_INT: %d\n", (int) sizeof (CS_INT)) ;
+
+ T = cs_ci_load (stdin) ; /* load a complex triplet matrix, T */
+ printf ("\nT:\n") ;
+ cs_ci_print (T, 0) ;
+
+ Treal = cs_i_real (T, 1) ; /* Treal = real part of T */
+ printf ("\nTreal:\n") ;
+ cs_di_print (Treal, 0) ;
+
+ Timag = cs_i_real (T, 0) ; /* Treal = imaginary part of T */
+ printf ("\nTimag:\n") ;
+ cs_di_print (Timag, 0) ;
+
+ A = cs_ci_compress (T) ; /* A = compressed-column form of T */
+ printf ("\nA:\n") ;
+ cs_ci_print (A, 0) ;
+
+ C1 = cs_i_real (A, 1) ; /* C1 = real (A) */
+ printf ("\nC1 = real(A):\n") ;
+ cs_di_print (C1, 0) ;
+
+ C2 = cs_i_real (A, 0) ; /* C2 = imag (A) */
+ printf ("\nC2 = imag(A):\n") ;
+ cs_di_print (C2, 0) ;
+
+ A1 = cs_i_complex (C1, 1) ; /* A1 = complex version of C1 */
+ printf ("\nA1:\n") ;
+ cs_ci_print (A1, 0) ;
+
+ A2 = cs_i_complex (C2, 0) ; /* A2 = complex version of C2 (imag.) */
+ printf ("\nA2:\n") ;
+ cs_ci_print (A2, 0) ;
+
+ B = cs_ci_add (A1, A2, 1., -1.) ; /* B = A1 - A2 */
+ printf ("\nB = conj(A):\n") ;
+ cs_ci_print (B, 0) ;
+
+ cs_ci_spfree (T) ;
+ cs_ci_spfree (A) ;
+ cs_ci_spfree (A1) ;
+ cs_ci_spfree (A2) ;
+ cs_ci_spfree (B) ;
+ cs_di_spfree (C1) ;
+ cs_di_spfree (C2) ;
+ cs_di_spfree (Treal) ;
+ cs_di_spfree (Timag) ;
+
+ return (0) ;
+}
diff --git a/CXSparse/Demo/cs_ldemo.c b/CXSparse/Demo/cs_ldemo.c
new file mode 100644
index 0000000..5c09795
--- /dev/null
+++ b/CXSparse/Demo/cs_ldemo.c
@@ -0,0 +1,57 @@
+#include "cs.h"
+/* test real/complex conversion routines (int version) */
+int main (void)
+{
+ cs_cl *T, *A, *A1, *A2, *B ;
+ cs_dl *C1, *C2, *Treal, *Timag ;
+
+ printf ("\n--- cs_ldemo, size of CS_INT: %d\n", (int) sizeof (CS_INT)) ;
+
+ T = cs_cl_load (stdin) ; /* load a complex triplet matrix, T */
+ printf ("\nT:\n") ;
+ cs_cl_print (T, 0) ;
+
+ Treal = cs_l_real (T, 1) ; /* Treal = real part of T */
+ printf ("\nTreal:\n") ;
+ cs_dl_print (Treal, 0) ;
+
+ Timag = cs_l_real (T, 0) ; /* Treal = imaginary part of T */
+ printf ("\nTimag:\n") ;
+ cs_dl_print (Timag, 0) ;
+
+ A = cs_cl_compress (T) ; /* A = compressed-column form of T */
+ printf ("\nA:\n") ;
+ cs_cl_print (A, 0) ;
+
+ C1 = cs_l_real (A, 1) ; /* C1 = real (A) */
+ printf ("\nC1 = real(A):\n") ;
+ cs_dl_print (C1, 0) ;
+
+ C2 = cs_l_real (A, 0) ; /* C2 = imag (A) */
+ printf ("\nC2 = imag(A):\n") ;
+ cs_dl_print (C2, 0) ;
+
+ A1 = cs_l_complex (C1, 1) ; /* A1 = complex version of C1 */
+ printf ("\nA1:\n") ;
+ cs_cl_print (A1, 0) ;
+
+ A2 = cs_l_complex (C2, 0) ; /* A2 = complex version of C2 (imag.) */
+ printf ("\nA2:\n") ;
+ cs_cl_print (A2, 0) ;
+
+ B = cs_cl_add (A1, A2, 1., -1.) ; /* B = A1 - A2 */
+ printf ("\nB = conj(A):\n") ;
+ cs_cl_print (B, 0) ;
+
+ cs_cl_spfree (T) ;
+ cs_cl_spfree (A) ;
+ cs_cl_spfree (A1) ;
+ cs_cl_spfree (A2) ;
+ cs_cl_spfree (B) ;
+ cs_dl_spfree (C1) ;
+ cs_dl_spfree (C2) ;
+ cs_dl_spfree (Treal) ;
+ cs_dl_spfree (Timag) ;
+
+ return (0) ;
+}
diff --git a/CXSparse/Doc/ChangeLog b/CXSparse/Doc/ChangeLog
new file mode 100644
index 0000000..ea1e3d0
--- /dev/null
+++ b/CXSparse/Doc/ChangeLog
@@ -0,0 +1,258 @@
+Nov 1, 2007, v2.2.1
+
+ * very minor change to Include/cs.h: Changed name of 2nd argument of
+ cs_permute, to match the code. This has no affect on the code itself,
+ since the type ("int *") is unchanged. It's just a documentation issue.
+
+ * minor lint cleanup in mexFunctions
+
+Mar 31, 2007, v2.2.0
+
+ * few changes to primary Source/ files. Changes mostly affect MATLAB
+ interface.
+
+ * Source/cs_house.c: correction to comment
+
+ * Souce/cs_updown.c: whitespace changed to reflect change in CXSparse,
+ no impact at all on CSparse itself.
+
+ * Doc/, Lib/ and Include/ directories created.
+
+ * Source/cs.h moved to Include/cs.h, version number changed to 2.2.0.
+
+ * modification to Makefiles, cs_make.m
+
+ * correction to help comments in cs_dmperm.m, cs_qr.m, cs_scc2.m, cs_scc.m
+
+ * if complex matrix passed to CSparse in MATLAB, error message
+ suggests using CXSparse instead
+
+ * minor performance fix to cs_sparse_mex.c
+
+ * cs_randperm added to MATLAB/Makefile; already appeared in cs_make.m
+
+ * minor improvements to MATLAB/ demos.
+
+Mar 1, 2007, v2.1.0
+
+ * Source/cs_add.c: added test for matrix dimensions
+
+ * Source/cs_multiply.c: added test for matrix dimensions
+
+ * correction to MATLAB demo3 (no error in C code version of the demo)
+
+ * minor corrections to MATLAB m-file help comments.
+
+Dec 12, 2006, v2.0.7
+
+ * minor MATLAB cleanup
+
+Dec 6, 2006, v2.0.6
+
+ * Update to UFget. Now relies on the MATLAB urlwrite function instead of
+ my own Java code.
+
+Nov 2006, v2.0.5
+
+ * Added UFgrep to UFget toolbox.
+
+ * No changes to C Source code, except for version number and date.
+
+ * Added two test matrices: ibm32a and ibm32b. ibm32a is the Harwell/
+ Boeing matrix ibm32, but with the last column removed. ibm32b
+ is the transpose of ibm32a. With optimization enabled (-O),
+ 2 lines in cs_maxtrans.c are not tested; these matrices correct
+ that problem.
+
+ * Fixed UFget. Earlier version could not download matrices larger than
+ 32MB.
+
+ * Modified UFget/UFweb, to reflect changes in the UF Sparse Matrix
+ Collection.
+
+ * Added ccspy.m and cs_scc2.m MATLAB functions
+
+ * Added examples to help info in each *.m MATLAB file
+
+ * modified cs_dmspy to speed up the plotting of large matrices with many
+ singletons
+
+ * minor change to cspy: now draws a box around the matrix.
+
+ * minor changes to MATLAB demos and tests.
+
+Oct 13, 2006, v2.0.4
+
+ * minor modification to cs_updown.c. "n" was incorrectly declared "double".
+ It should be "int". This was safe, just a little confusing (n was only
+ used in an argument to cs_malloc, and is thus typecast).
+
+Sept 28, 2006, v2.0.3
+
+ * minor modifications to MATLAB interface, to allow CSparse to be used
+ in MATLAB 6.5.
+
+ * added examples to m-files, other minor m-file cleanup.
+
+ * bug fix to cspy, to handle NaN's properly.
+
+Aug 23, 2006: v2.0.2
+
+ * change to cs_updown mexFunction, to handle multiple rank updates
+
+ * symbolic links removed from Tcov/ directory in the distribution.
+ They are now created by Tcov/Makefile as needed. This makes the
+ zip files cleaner. Tcov/*test.c test files renamed.
+
+July 19, 2006:
+
+ * minor fix to cs_must_compile.m and cs_make.m, to allow CSparse to be
+ compiled in MATLAB 6.5 with cs_make.
+
+ * minor fix to cspy for complex matrices (imaginary part was ignored).
+
+ * no change to version number or date, since there are no changes that
+ affect the appearance of CSparse in the book ("Direct Methods for
+ Sparse Linear Systems", SIAM, 2006).
+
+June 24, 2006:
+
+ * minor typos in comments corrected. No change in code itself,
+ and no change in version number or date.
+
+May 27, 2006, v2.0.1: (this version is printed in the book)
+
+ * minor bug fix. cs_util.c modified, so that cs_sprealloc (T,0) works
+ properly for a triplet matrix T (setting T->nzmax equal to T->nz).
+ The line in v2.0.0:
+
+ nzmax = (nzmax <= 0) ? (A->p [A->n]) : nzmax ;
+
+ changes to the following in v2.0.1:
+
+ if (nzmax <= 0) nzmax = (CS_CSC (A)) ? (A->p [A->n]) : A->nz ;
+
+ * minor typographical changes arising from the editting of the book.
+
+Apr 12, 2006, v2.0.0:
+
+ * random permutation option added to cs_maxtrans and cs_dmperm, to help
+ avoid rare cases where the O(|A|n) time complexity is reached in
+ practice (GHS_indef/boyd2 in the UF sparse matrix collection, for
+ example). New cs_randperm function added.
+
+Apr 10, 2006:
+
+ * stylistic changes for the book (except for the bug fix):
+
+ * "int order" parameter of cs_amd, cs_lusol, cs_cholsol, cs_qrsol, cs_sqr,
+ cs_schol changed. Now 0 means no ordering, 1 is A+A', 2 is S*S', and
+ 3 is A*A'. In v1.2 and earlier, "order" took on a value ranging from
+ -1 to 2. "int n" parameter rearranged for cs_ipvec, cs_pvec, cs_post
+ (int n moved to the end). cs_triplet renamed cs_compress.
+
+ To ensure that these changes are propagated into user code that calls
+ CSparse, the "order" parameter has been placed as the first parameter
+ in all these routines. Your compiler will complain (gcc will halt) if
+ you upgrade from v1.2 to v2.0 without changing your code. This is much
+ better than a silent error in which you get the wrong ordering by
+ mistake (with a huge penalty in run-time performance and no compiler
+ warnings).
+
+ New syntax (v2.0 and later):
+ ----------------------------
+
+ order = 0: natural ordering
+ order = 1: amd (A+A')
+ order = 2: amd (S'*S), where S=A except dense rows dropped
+ order = 3: amd (A'*A)
+
+ int cs_cholsol (int order, const cs *A, double *b) ;
+ int cs_lusol (int order, const cs *A, double *b, double tol) ;
+ int cs_qrsol (int order, const cs *A, double *b) ;
+ int *cs_amd (int order, const cs *A) ;
+ css *cs_schol (int order, const cs *A) ;
+ css *cs_sqr (int order, const cs *A, int qr) ;
+
+ int *cs_post (const int *parent, int n) ;
+ int cs_ipvec (const int *p, const double *b, double *x, int n) ;
+ int cs_pvec (const int *p, const double *b, double *x, int n) ;
+
+ cs *cs_compress (const cs *T) ;
+
+ Old syntax (v1.2 and earlier):
+ ------------------------------
+
+ order = -1: natural ordering
+ order = 0: amd (A+A')
+ order = 1: amd (S'*S), where S=A except dense rows dropped
+ order = 2: amd (A'*A)
+
+ int cs_cholsol (const cs *A, double *b, int order) ;
+ int cs_lusol (const cs *A, double *b, int order, double tol) ;
+ int cs_qrsol (const cs *A, double *b, int order) ;
+ int *cs_amd (const cs *A, int order) ;
+ css *cs_schol (const cs *A, int order) ;
+ css *cs_sqr (const cs *A, int order, int qr) ;
+
+ int *cs_post (int n, const int *parent) ;
+ int cs_ipvec (int n, const int *p, const double *b, double *x) ;
+ int cs_pvec (int n, const int *p, const double *b, double *x) ;
+
+ cs *cs_triplet (const cs *T) ;
+
+ * CS_OVERFLOW macro removed (removed from cs_malloc.c; not needed).
+
+ * S->leftmost added to css (it was tacked onto S->pinv before).
+
+ * P,Q,R,S components of csd struct changed to p,q,r,s.
+
+ * Pinv and Q components of css struct changed to pinv and q.
+
+ * CS_CSC and CS_TRIPLET macros added, to clarify which CSparse functions
+ accept cs matrices in compressed column form, triplet form, or both.
+
+ * check for negative row/column indices added to cs_entry.
+
+ * cs_ereach and cs_leaf functions added.
+
+ * call to cs_sprealloc added to cs_fkeep.
+
+ * bug fixes in cs_counts and cs_amd (memory leak under rare out-of-memory
+ conditions).
+
+Mar 15, 2006:
+
+ * cs_scc modified so that the row and columns of each component are put in
+ their natural order. cs_dmperm modified so that columns of each block
+ (instead of rows) are placed in their natural order.
+
+ * cs_splsolve renamed cs_spsolve, generalized to handle both Lx=b and
+ Ux=b, and non-unit diagonal, and placed in its own file (cs_spsolve.c;
+ it was a static function in cs_lu.c). cs_lsolve_mex.c and
+ cs_splsolve_mex.c merged (the latter was removed). cs_spsolve.c file
+ added
+
+ * cs_dmspy changed, so that block borders line up better with the matrix.
+
+Mar 6, 2006:
+
+ * Makefile modified so that the Tcov tests (which may not be portable)
+ are not compiled and run by the default "make" in the CSparse directory.
+ To compile everything, including the Tcov tests, use "make all".
+ Trivial change to cs.h.
+
+Feb 27, 2006:
+
+ * cs_reach, cs_dfs, cs_splsolve, cs_lu, and cs_scc changed to remove O(n)
+ initialized workspace.
+ * cs_reach and cs_splsolve now user-callable (were static in cs_lu.c).
+
+Feb 20, 2006:
+
+ * various changes to simplify the construction of CXSparse
+
+Feb 7, 2006:
+
+ * changed prototypes, adding "const" where appropriate.
+
diff --git a/CXSparse/Doc/License.txt b/CXSparse/Doc/License.txt
new file mode 100644
index 0000000..9fbb144
--- /dev/null
+++ b/CXSparse/Doc/License.txt
@@ -0,0 +1,19 @@
+CXSparse: a Concise Sparse matrix package - Extended.
+Copyright (c) 2006, Timothy A. Davis.
+http://www.cise.ufl.edu/research/sparse/CSparse
+
+--------------------------------------------------------------------------------
+
+CXSparse is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+CXSparse is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
diff --git a/CXSparse/Doc/lesser.txt b/CXSparse/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/CXSparse/Doc/lesser.txt
@@ -0,0 +1,504 @@
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diff --git a/CXSparse/Include/cs.h b/CXSparse/Include/cs.h
new file mode 100644
index 0000000..a511d35
--- /dev/null
+++ b/CXSparse/Include/cs.h
@@ -0,0 +1,736 @@
+#ifndef _CXS_H
+#define _CXS_H
+#include <stdlib.h>
+#include <limits.h>
+#include <math.h>
+#include <stdio.h>
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#endif
+
+
+#ifdef __cplusplus
+#ifndef NCOMPLEX
+#include <complex>
+typedef std::complex<double> cs_complex_t ;
+#endif
+extern "C" {
+#else
+#ifndef NCOMPLEX
+#include <complex.h>
+#define cs_complex_t double _Complex
+#endif
+#endif
+
+#define CS_VER 2 /* CXSparse Version 2.2.1 */
+#define CS_SUBVER 2
+#define CS_SUBSUB 1
+#define CS_DATE "Nov 1, 2007" /* CXSparse release date */
+#define CS_COPYRIGHT "Copyright (c) Timothy A. Davis, 2006-2007"
+#define CXSPARSE
+
+/* define UF_long */
+#include "UFconfig.h"
+
+/* -------------------------------------------------------------------------- */
+/* double/int version of CXSparse */
+/* -------------------------------------------------------------------------- */
+
+/* --- primary CSparse routines and data structures ------------------------- */
+
+typedef struct cs_di_sparse /* matrix in compressed-column or triplet form */
+{
+ int nzmax ; /* maximum number of entries */
+ int m ; /* number of rows */
+ int n ; /* number of columns */
+ int *p ; /* column pointers (size n+1) or col indices (size nzmax) */
+ int *i ; /* row indices, size nzmax */
+ double *x ; /* numerical values, size nzmax */
+ int nz ; /* # of entries in triplet matrix, -1 for compressed-col */
+} cs_di ;
+
+cs_di *cs_di_add (const cs_di *A, const cs_di *B, double alpha, double beta) ;
+int cs_di_cholsol (int order, const cs_di *A, double *b) ;
+int cs_di_dupl (cs_di *A) ;
+int cs_di_entry (cs_di *T, int i, int j, double x) ;
+int cs_di_lusol (int order, const cs_di *A, double *b, double tol) ;
+int cs_di_gaxpy (const cs_di *A, const double *x, double *y) ;
+cs_di *cs_di_multiply (const cs_di *A, const cs_di *B) ;
+int cs_di_qrsol (int order, const cs_di *A, double *b) ;
+cs_di *cs_di_transpose (const cs_di *A, int values) ;
+cs_di *cs_di_compress (const cs_di *T) ;
+double cs_di_norm (const cs_di *A) ;
+int cs_di_print (const cs_di *A, int brief) ;
+cs_di *cs_di_load (FILE *f) ;
+
+/* utilities */
+void *cs_di_calloc (int n, size_t size) ;
+void *cs_di_free (void *p) ;
+void *cs_di_realloc (void *p, int n, size_t size, int *ok) ;
+cs_di *cs_di_spalloc (int m, int n, int nzmax, int values, int t) ;
+cs_di *cs_di_spfree (cs_di *A) ;
+int cs_di_sprealloc (cs_di *A, int nzmax) ;
+void *cs_di_malloc (int n, size_t size) ;
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+
+typedef struct cs_di_symbolic /* symbolic Cholesky, LU, or QR analysis */
+{
+ int *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */
+ int *q ; /* fill-reducing column permutation for LU and QR */
+ int *parent ; /* elimination tree for Cholesky and QR */
+ int *cp ; /* column pointers for Cholesky, row counts for QR */
+ int *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */
+ int m2 ; /* # of rows for QR, after adding fictitious rows */
+ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */
+ double unz ; /* # entries in U for LU; in R for QR */
+} cs_dis ;
+
+typedef struct cs_di_numeric /* numeric Cholesky, LU, or QR factorization */
+{
+ cs_di *L ; /* L for LU and Cholesky, V for QR */
+ cs_di *U ; /* U for LU, r for QR, not used for Cholesky */
+ int *pinv ; /* partial pivoting for LU */
+ double *B ; /* beta [0..n-1] for QR */
+} cs_din ;
+
+typedef struct cs_di_dmperm_results /* cs_di_dmperm or cs_di_scc output */
+{
+ int *p ; /* size m, row permutation */
+ int *q ; /* size n, column permutation */
+ int *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */
+ int *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */
+ int nb ; /* # of blocks in fine dmperm decomposition */
+ int rr [5] ; /* coarse row decomposition */
+ int cc [5] ; /* coarse column decomposition */
+} cs_did ;
+
+int *cs_di_amd (int order, const cs_di *A) ;
+cs_din *cs_di_chol (const cs_di *A, const cs_dis *S) ;
+cs_did *cs_di_dmperm (const cs_di *A, int seed) ;
+int cs_di_droptol (cs_di *A, double tol) ;
+int cs_di_dropzeros (cs_di *A) ;
+int cs_di_happly (const cs_di *V, int i, double beta, double *x) ;
+int cs_di_ipvec (const int *p, const double *b, double *x, int n) ;
+int cs_di_lsolve (const cs_di *L, double *x) ;
+int cs_di_ltsolve (const cs_di *L, double *x) ;
+cs_din *cs_di_lu (const cs_di *A, const cs_dis *S, double tol) ;
+cs_di *cs_di_permute (const cs_di *A, const int *pinv, const int *q,
+ int values) ;
+int *cs_di_pinv (const int *p, int n) ;
+int cs_di_pvec (const int *p, const double *b, double *x, int n) ;
+cs_din *cs_di_qr (const cs_di *A, const cs_dis *S) ;
+cs_dis *cs_di_schol (int order, const cs_di *A) ;
+cs_dis *cs_di_sqr (int order, const cs_di *A, int qr) ;
+cs_di *cs_di_symperm (const cs_di *A, const int *pinv, int values) ;
+int cs_di_usolve (const cs_di *U, double *x) ;
+int cs_di_utsolve (const cs_di *U, double *x) ;
+int cs_di_updown (cs_di *L, int sigma, const cs_di *C, const int *parent) ;
+
+/* utilities */
+cs_dis *cs_di_sfree (cs_dis *S) ;
+cs_din *cs_di_nfree (cs_din *N) ;
+cs_did *cs_di_dfree (cs_did *D) ;
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+
+int *cs_di_counts (const cs_di *A, const int *parent, const int *post,
+ int ata) ;
+double cs_di_cumsum (int *p, int *c, int n) ;
+int cs_di_dfs (int j, cs_di *G, int top, int *xi, int *pstack,
+ const int *pinv) ;
+int *cs_di_etree (const cs_di *A, int ata) ;
+int cs_di_fkeep (cs_di *A, int (*fkeep) (int, int, double, void *),
+ void *other) ;
+double cs_di_house (double *x, double *beta, int n) ;
+int *cs_di_maxtrans (const cs_di *A, int seed) ;
+int *cs_di_post (const int *parent, int n) ;
+cs_did *cs_di_scc (cs_di *A) ;
+int cs_di_scatter (const cs_di *A, int j, double beta, int *w, double *x,
+ int mark, cs_di *C, int nz) ;
+int cs_di_tdfs (int j, int k, int *head, const int *next, int *post,
+ int *stack) ;
+int cs_di_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf,
+ int *ancestor, int *jleaf) ;
+int cs_di_reach (cs_di *G, const cs_di *B, int k, int *xi, const int *pinv) ;
+int cs_di_spsolve (cs_di *L, const cs_di *B, int k, int *xi, double *x,
+ const int *pinv, int lo) ;
+int cs_di_ereach (const cs_di *A, int k, const int *parent, int *s, int *w) ;
+int *cs_di_randperm (int n, int seed) ;
+
+/* utilities */
+cs_did *cs_di_dalloc (int m, int n) ;
+cs_di *cs_di_done (cs_di *C, void *w, void *x, int ok) ;
+int *cs_di_idone (int *p, cs_di *C, void *w, int ok) ;
+cs_din *cs_di_ndone (cs_din *N, cs_di *C, void *w, void *x, int ok) ;
+cs_did *cs_di_ddone (cs_did *D, cs_di *C, void *w, int ok) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* double/UF_long version of CXSparse */
+/* -------------------------------------------------------------------------- */
+
+/* --- primary CSparse routines and data structures ------------------------- */
+
+typedef struct cs_dl_sparse /* matrix in compressed-column or triplet form */
+{
+ UF_long nzmax ; /* maximum number of entries */
+ UF_long m ; /* number of rows */
+ UF_long n ; /* number of columns */
+ UF_long *p ; /* column pointers (size n+1) or col indlces (size nzmax) */
+ UF_long *i ; /* row indices, size nzmax */
+ double *x ; /* numerical values, size nzmax */
+ UF_long nz ; /* # of entries in triplet matrix, -1 for compressed-col */
+} cs_dl ;
+
+cs_dl *cs_dl_add (const cs_dl *A, const cs_dl *B, double alpha, double beta) ;
+UF_long cs_dl_cholsol (UF_long order, const cs_dl *A, double *b) ;
+UF_long cs_dl_dupl (cs_dl *A) ;
+UF_long cs_dl_entry (cs_dl *T, UF_long i, UF_long j, double x) ;
+UF_long cs_dl_lusol (UF_long order, const cs_dl *A, double *b, double tol) ;
+UF_long cs_dl_gaxpy (const cs_dl *A, const double *x, double *y) ;
+cs_dl *cs_dl_multiply (const cs_dl *A, const cs_dl *B) ;
+UF_long cs_dl_qrsol (UF_long order, const cs_dl *A, double *b) ;
+cs_dl *cs_dl_transpose (const cs_dl *A, UF_long values) ;
+cs_dl *cs_dl_compress (const cs_dl *T) ;
+double cs_dl_norm (const cs_dl *A) ;
+UF_long cs_dl_print (const cs_dl *A, UF_long brief) ;
+cs_dl *cs_dl_load (FILE *f) ;
+
+/* utilities */
+void *cs_dl_calloc (UF_long n, size_t size) ;
+void *cs_dl_free (void *p) ;
+void *cs_dl_realloc (void *p, UF_long n, size_t size, UF_long *ok) ;
+cs_dl *cs_dl_spalloc (UF_long m, UF_long n, UF_long nzmax, UF_long values,
+ UF_long t) ;
+cs_dl *cs_dl_spfree (cs_dl *A) ;
+UF_long cs_dl_sprealloc (cs_dl *A, UF_long nzmax) ;
+void *cs_dl_malloc (UF_long n, size_t size) ;
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+
+typedef struct cs_dl_symbolic /* symbolic Cholesky, LU, or QR analysis */
+{
+ UF_long *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */
+ UF_long *q ; /* fill-reducing column permutation for LU and QR */
+ UF_long *parent ; /* elimination tree for Cholesky and QR */
+ UF_long *cp ; /* column pointers for Cholesky, row counts for QR */
+ UF_long *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */
+ UF_long m2 ; /* # of rows for QR, after adding fictitious rows */
+ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */
+ double unz ; /* # entries in U for LU; in R for QR */
+} cs_dls ;
+
+typedef struct cs_dl_numeric /* numeric Cholesky, LU, or QR factorization */
+{
+ cs_dl *L ; /* L for LU and Cholesky, V for QR */
+ cs_dl *U ; /* U for LU, r for QR, not used for Cholesky */
+ UF_long *pinv ; /* partial pivoting for LU */
+ double *B ; /* beta [0..n-1] for QR */
+} cs_dln ;
+
+typedef struct cs_dl_dmperm_results /* cs_dl_dmperm or cs_dl_scc output */
+{
+ UF_long *p ; /* size m, row permutation */
+ UF_long *q ; /* size n, column permutation */
+ UF_long *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */
+ UF_long *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */
+ UF_long nb ; /* # of blocks in fine dmperm decomposition */
+ UF_long rr [5] ; /* coarse row decomposition */
+ UF_long cc [5] ; /* coarse column decomposition */
+} cs_dld ;
+
+UF_long *cs_dl_amd (UF_long order, const cs_dl *A) ;
+cs_dln *cs_dl_chol (const cs_dl *A, const cs_dls *S) ;
+cs_dld *cs_dl_dmperm (const cs_dl *A, UF_long seed) ;
+UF_long cs_dl_droptol (cs_dl *A, double tol) ;
+UF_long cs_dl_dropzeros (cs_dl *A) ;
+UF_long cs_dl_happly (const cs_dl *V, UF_long i, double beta, double *x) ;
+UF_long cs_dl_ipvec (const UF_long *p, const double *b, double *x, UF_long n) ;
+UF_long cs_dl_lsolve (const cs_dl *L, double *x) ;
+UF_long cs_dl_ltsolve (const cs_dl *L, double *x) ;
+cs_dln *cs_dl_lu (const cs_dl *A, const cs_dls *S, double tol) ;
+cs_dl *cs_dl_permute (const cs_dl *A, const UF_long *pinv, const UF_long *q,
+ UF_long values) ;
+UF_long *cs_dl_pinv (const UF_long *p, UF_long n) ;
+UF_long cs_dl_pvec (const UF_long *p, const double *b, double *x, UF_long n) ;
+cs_dln *cs_dl_qr (const cs_dl *A, const cs_dls *S) ;
+cs_dls *cs_dl_schol (UF_long order, const cs_dl *A) ;
+cs_dls *cs_dl_sqr (UF_long order, const cs_dl *A, UF_long qr) ;
+cs_dl *cs_dl_symperm (const cs_dl *A, const UF_long *pinv, UF_long values) ;
+UF_long cs_dl_usolve (const cs_dl *U, double *x) ;
+UF_long cs_dl_utsolve (const cs_dl *U, double *x) ;
+UF_long cs_dl_updown (cs_dl *L, UF_long sigma, const cs_dl *C,
+ const UF_long *parent) ;
+
+/* utilities */
+cs_dls *cs_dl_sfree (cs_dls *S) ;
+cs_dln *cs_dl_nfree (cs_dln *N) ;
+cs_dld *cs_dl_dfree (cs_dld *D) ;
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+
+UF_long *cs_dl_counts (const cs_dl *A, const UF_long *parent,
+ const UF_long *post, UF_long ata) ;
+double cs_dl_cumsum (UF_long *p, UF_long *c, UF_long n) ;
+UF_long cs_dl_dfs (UF_long j, cs_dl *G, UF_long top, UF_long *xi,
+ UF_long *pstack, const UF_long *pinv) ;
+UF_long *cs_dl_etree (const cs_dl *A, UF_long ata) ;
+UF_long cs_dl_fkeep (cs_dl *A,
+ UF_long (*fkeep) (UF_long, UF_long, double, void *), void *other) ;
+double cs_dl_house (double *x, double *beta, UF_long n) ;
+UF_long *cs_dl_maxtrans (const cs_dl *A, UF_long seed) ;
+UF_long *cs_dl_post (const UF_long *parent, UF_long n) ;
+cs_dld *cs_dl_scc (cs_dl *A) ;
+UF_long cs_dl_scatter (const cs_dl *A, UF_long j, double beta, UF_long *w,
+ double *x, UF_long mark,cs_dl *C, UF_long nz) ;
+UF_long cs_dl_tdfs (UF_long j, UF_long k, UF_long *head, const UF_long *next,
+ UF_long *post, UF_long *stack) ;
+UF_long cs_dl_leaf (UF_long i, UF_long j, const UF_long *first,
+ UF_long *maxfirst, UF_long *prevleaf, UF_long *ancestor, UF_long *jleaf) ;
+UF_long cs_dl_reach (cs_dl *G, const cs_dl *B, UF_long k, UF_long *xi,
+ const UF_long *pinv) ;
+UF_long cs_dl_spsolve (cs_dl *L, const cs_dl *B, UF_long k, UF_long *xi,
+ double *x, const UF_long *pinv, UF_long lo) ;
+UF_long cs_dl_ereach (const cs_dl *A, UF_long k, const UF_long *parent,
+ UF_long *s, UF_long *w) ;
+UF_long *cs_dl_randperm (UF_long n, UF_long seed) ;
+
+/* utilities */
+cs_dld *cs_dl_dalloc (UF_long m, UF_long n) ;
+cs_dl *cs_dl_done (cs_dl *C, void *w, void *x, UF_long ok) ;
+UF_long *cs_dl_idone (UF_long *p, cs_dl *C, void *w, UF_long ok) ;
+cs_dln *cs_dl_ndone (cs_dln *N, cs_dl *C, void *w, void *x, UF_long ok) ;
+cs_dld *cs_dl_ddone (cs_dld *D, cs_dl *C, void *w, UF_long ok) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* complex/int version of CXSparse */
+/* -------------------------------------------------------------------------- */
+
+#ifndef NCOMPLEX
+
+/* --- primary CSparse routines and data structures ------------------------- */
+
+typedef struct cs_ci_sparse /* matrix in compressed-column or triplet form */
+{
+ int nzmax ; /* maximum number of entries */
+ int m ; /* number of rows */
+ int n ; /* number of columns */
+ int *p ; /* column pointers (size n+1) or col indices (size nzmax) */
+ int *i ; /* row indices, size nzmax */
+ cs_complex_t *x ; /* numerical values, size nzmax */
+ int nz ; /* # of entries in triplet matrix, -1 for compressed-col */
+} cs_ci ;
+
+cs_ci *cs_ci_add (const cs_ci *A, const cs_ci *B, cs_complex_t alpha,
+ cs_complex_t beta) ;
+int cs_ci_cholsol (int order, const cs_ci *A, cs_complex_t *b) ;
+int cs_ci_dupl (cs_ci *A) ;
+int cs_ci_entry (cs_ci *T, int i, int j, cs_complex_t x) ;
+int cs_ci_lusol (int order, const cs_ci *A, cs_complex_t *b, double tol) ;
+int cs_ci_gaxpy (const cs_ci *A, const cs_complex_t *x, cs_complex_t *y) ;
+cs_ci *cs_ci_multiply (const cs_ci *A, const cs_ci *B) ;
+int cs_ci_qrsol (int order, const cs_ci *A, cs_complex_t *b) ;
+cs_ci *cs_ci_transpose (const cs_ci *A, int values) ;
+cs_ci *cs_ci_compress (const cs_ci *T) ;
+double cs_ci_norm (const cs_ci *A) ;
+int cs_ci_print (const cs_ci *A, int brief) ;
+cs_ci *cs_ci_load (FILE *f) ;
+
+/* utilities */
+void *cs_ci_calloc (int n, size_t size) ;
+void *cs_ci_free (void *p) ;
+void *cs_ci_realloc (void *p, int n, size_t size, int *ok) ;
+cs_ci *cs_ci_spalloc (int m, int n, int nzmax, int values, int t) ;
+cs_ci *cs_ci_spfree (cs_ci *A) ;
+int cs_ci_sprealloc (cs_ci *A, int nzmax) ;
+void *cs_ci_malloc (int n, size_t size) ;
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+
+typedef struct cs_ci_symbolic /* symbolic Cholesky, LU, or QR analysis */
+{
+ int *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */
+ int *q ; /* fill-reducing column permutation for LU and QR */
+ int *parent ; /* elimination tree for Cholesky and QR */
+ int *cp ; /* column pointers for Cholesky, row counts for QR */
+ int *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */
+ int m2 ; /* # of rows for QR, after adding fictitious rows */
+ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */
+ double unz ; /* # entries in U for LU; in R for QR */
+} cs_cis ;
+
+typedef struct cs_ci_numeric /* numeric Cholesky, LU, or QR factorization */
+{
+ cs_ci *L ; /* L for LU and Cholesky, V for QR */
+ cs_ci *U ; /* U for LU, r for QR, not used for Cholesky */
+ int *pinv ; /* partial pivoting for LU */
+ double *B ; /* beta [0..n-1] for QR */
+} cs_cin ;
+
+typedef struct cs_ci_dmperm_results /* cs_ci_dmperm or cs_ci_scc output */
+{
+ int *p ; /* size m, row permutation */
+ int *q ; /* size n, column permutation */
+ int *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */
+ int *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */
+ int nb ; /* # of blocks in fine dmperm decomposition */
+ int rr [5] ; /* coarse row decomposition */
+ int cc [5] ; /* coarse column decomposition */
+} cs_cid ;
+
+int *cs_ci_amd (int order, const cs_ci *A) ;
+cs_cin *cs_ci_chol (const cs_ci *A, const cs_cis *S) ;
+cs_cid *cs_ci_dmperm (const cs_ci *A, int seed) ;
+int cs_ci_droptol (cs_ci *A, double tol) ;
+int cs_ci_dropzeros (cs_ci *A) ;
+int cs_ci_happly (const cs_ci *V, int i, double beta, cs_complex_t *x) ;
+int cs_ci_ipvec (const int *p, const cs_complex_t *b, cs_complex_t *x, int n) ;
+int cs_ci_lsolve (const cs_ci *L, cs_complex_t *x) ;
+int cs_ci_ltsolve (const cs_ci *L, cs_complex_t *x) ;
+cs_cin *cs_ci_lu (const cs_ci *A, const cs_cis *S, double tol) ;
+cs_ci *cs_ci_permute (const cs_ci *A, const int *pinv, const int *q,
+ int values) ;
+int *cs_ci_pinv (const int *p, int n) ;
+int cs_ci_pvec (const int *p, const cs_complex_t *b, cs_complex_t *x, int n) ;
+cs_cin *cs_ci_qr (const cs_ci *A, const cs_cis *S) ;
+cs_cis *cs_ci_schol (int order, const cs_ci *A) ;
+cs_cis *cs_ci_sqr (int order, const cs_ci *A, int qr) ;
+cs_ci *cs_ci_symperm (const cs_ci *A, const int *pinv, int values) ;
+int cs_ci_usolve (const cs_ci *U, cs_complex_t *x) ;
+int cs_ci_utsolve (const cs_ci *U, cs_complex_t *x) ;
+int cs_ci_updown (cs_ci *L, int sigma, const cs_ci *C, const int *parent) ;
+
+/* utilities */
+cs_cis *cs_ci_sfree (cs_cis *S) ;
+cs_cin *cs_ci_nfree (cs_cin *N) ;
+cs_cid *cs_ci_dfree (cs_cid *D) ;
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+
+int *cs_ci_counts (const cs_ci *A, const int *parent, const int *post,
+ int ata) ;
+double cs_ci_cumsum (int *p, int *c, int n) ;
+int cs_ci_dfs (int j, cs_ci *G, int top, int *xi, int *pstack,
+ const int *pinv) ;
+int *cs_ci_etree (const cs_ci *A, int ata) ;
+int cs_ci_fkeep (cs_ci *A, int (*fkeep) (int, int, cs_complex_t, void *),
+ void *other) ;
+cs_complex_t cs_ci_house (cs_complex_t *x, double *beta, int n) ;
+int *cs_ci_maxtrans (const cs_ci *A, int seed) ;
+int *cs_ci_post (const int *parent, int n) ;
+cs_cid *cs_ci_scc (cs_ci *A) ;
+int cs_ci_scatter (const cs_ci *A, int j, cs_complex_t beta, int *w,
+ cs_complex_t *x, int mark,cs_ci *C, int nz) ;
+int cs_ci_tdfs (int j, int k, int *head, const int *next, int *post,
+ int *stack) ;
+int cs_ci_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf,
+ int *ancestor, int *jleaf) ;
+int cs_ci_reach (cs_ci *G, const cs_ci *B, int k, int *xi, const int *pinv) ;
+int cs_ci_spsolve (cs_ci *L, const cs_ci *B, int k, int *xi,
+ cs_complex_t *x, const int *pinv, int lo) ;
+int cs_ci_ereach (const cs_ci *A, int k, const int *parent, int *s, int *w) ;
+int *cs_ci_randperm (int n, int seed) ;
+
+/* utilities */
+cs_cid *cs_ci_dalloc (int m, int n) ;
+cs_ci *cs_ci_done (cs_ci *C, void *w, void *x, int ok) ;
+int *cs_ci_idone (int *p, cs_ci *C, void *w, int ok) ;
+cs_cin *cs_ci_ndone (cs_cin *N, cs_ci *C, void *w, void *x, int ok) ;
+cs_cid *cs_ci_ddone (cs_cid *D, cs_ci *C, void *w, int ok) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* complex/UF_long version of CXSparse */
+/* -------------------------------------------------------------------------- */
+
+/* --- primary CSparse routines and data structures ------------------------- */
+
+typedef struct cs_cl_sparse /* matrix in compressed-column or triplet form */
+{
+ UF_long nzmax ; /* maximum number of entries */
+ UF_long m ; /* number of rows */
+ UF_long n ; /* number of columns */
+ UF_long *p ; /* column pointers (size n+1) or col indlces (size nzmax) */
+ UF_long *i ; /* row indices, size nzmax */
+ cs_complex_t *x ; /* numerical values, size nzmax */
+ UF_long nz ; /* # of entries in triplet matrix, -1 for compressed-col */
+} cs_cl ;
+
+cs_cl *cs_cl_add (const cs_cl *A, const cs_cl *B, cs_complex_t alpha,
+ cs_complex_t beta) ;
+UF_long cs_cl_cholsol (UF_long order, const cs_cl *A, cs_complex_t *b) ;
+UF_long cs_cl_dupl (cs_cl *A) ;
+UF_long cs_cl_entry (cs_cl *T, UF_long i, UF_long j, cs_complex_t x) ;
+UF_long cs_cl_lusol (UF_long order, const cs_cl *A, cs_complex_t *b,
+ double tol) ;
+UF_long cs_cl_gaxpy (const cs_cl *A, const cs_complex_t *x, cs_complex_t *y) ;
+cs_cl *cs_cl_multiply (const cs_cl *A, const cs_cl *B) ;
+UF_long cs_cl_qrsol (UF_long order, const cs_cl *A, cs_complex_t *b) ;
+cs_cl *cs_cl_transpose (const cs_cl *A, UF_long values) ;
+cs_cl *cs_cl_compress (const cs_cl *T) ;
+double cs_cl_norm (const cs_cl *A) ;
+UF_long cs_cl_print (const cs_cl *A, UF_long brief) ;
+cs_cl *cs_cl_load (FILE *f) ;
+
+/* utilities */
+void *cs_cl_calloc (UF_long n, size_t size) ;
+void *cs_cl_free (void *p) ;
+void *cs_cl_realloc (void *p, UF_long n, size_t size, UF_long *ok) ;
+cs_cl *cs_cl_spalloc (UF_long m, UF_long n, UF_long nzmax, UF_long values,
+ UF_long t) ;
+cs_cl *cs_cl_spfree (cs_cl *A) ;
+UF_long cs_cl_sprealloc (cs_cl *A, UF_long nzmax) ;
+void *cs_cl_malloc (UF_long n, size_t size) ;
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+
+typedef struct cs_cl_symbolic /* symbolic Cholesky, LU, or QR analysis */
+{
+ UF_long *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */
+ UF_long *q ; /* fill-reducing column permutation for LU and QR */
+ UF_long *parent ; /* elimination tree for Cholesky and QR */
+ UF_long *cp ; /* column pointers for Cholesky, row counts for QR */
+ UF_long *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */
+ UF_long m2 ; /* # of rows for QR, after adding fictitious rows */
+ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */
+ double unz ; /* # entries in U for LU; in R for QR */
+} cs_cls ;
+
+typedef struct cs_cl_numeric /* numeric Cholesky, LU, or QR factorization */
+{
+ cs_cl *L ; /* L for LU and Cholesky, V for QR */
+ cs_cl *U ; /* U for LU, r for QR, not used for Cholesky */
+ UF_long *pinv ; /* partial pivoting for LU */
+ double *B ; /* beta [0..n-1] for QR */
+} cs_cln ;
+
+typedef struct cs_cl_dmperm_results /* cs_cl_dmperm or cs_cl_scc output */
+{
+ UF_long *p ; /* size m, row permutation */
+ UF_long *q ; /* size n, column permutation */
+ UF_long *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */
+ UF_long *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */
+ UF_long nb ; /* # of blocks in fine dmperm decomposition */
+ UF_long rr [5] ; /* coarse row decomposition */
+ UF_long cc [5] ; /* coarse column decomposition */
+} cs_cld ;
+
+UF_long *cs_cl_amd (UF_long order, const cs_cl *A) ;
+cs_cln *cs_cl_chol (const cs_cl *A, const cs_cls *S) ;
+cs_cld *cs_cl_dmperm (const cs_cl *A, UF_long seed) ;
+UF_long cs_cl_droptol (cs_cl *A, double tol) ;
+UF_long cs_cl_dropzeros (cs_cl *A) ;
+UF_long cs_cl_happly (const cs_cl *V, UF_long i, double beta, cs_complex_t *x) ;
+UF_long cs_cl_ipvec (const UF_long *p, const cs_complex_t *b,
+ cs_complex_t *x, UF_long n) ;
+UF_long cs_cl_lsolve (const cs_cl *L, cs_complex_t *x) ;
+UF_long cs_cl_ltsolve (const cs_cl *L, cs_complex_t *x) ;
+cs_cln *cs_cl_lu (const cs_cl *A, const cs_cls *S, double tol) ;
+cs_cl *cs_cl_permute (const cs_cl *A, const UF_long *pinv, const UF_long *q,
+ UF_long values) ;
+UF_long *cs_cl_pinv (const UF_long *p, UF_long n) ;
+UF_long cs_cl_pvec (const UF_long *p, const cs_complex_t *b,
+ cs_complex_t *x, UF_long n) ;
+cs_cln *cs_cl_qr (const cs_cl *A, const cs_cls *S) ;
+cs_cls *cs_cl_schol (UF_long order, const cs_cl *A) ;
+cs_cls *cs_cl_sqr (UF_long order, const cs_cl *A, UF_long qr) ;
+cs_cl *cs_cl_symperm (const cs_cl *A, const UF_long *pinv, UF_long values) ;
+UF_long cs_cl_usolve (const cs_cl *U, cs_complex_t *x) ;
+UF_long cs_cl_utsolve (const cs_cl *U, cs_complex_t *x) ;
+UF_long cs_cl_updown (cs_cl *L, UF_long sigma, const cs_cl *C,
+ const UF_long *parent) ;
+
+/* utilities */
+cs_cls *cs_cl_sfree (cs_cls *S) ;
+cs_cln *cs_cl_nfree (cs_cln *N) ;
+cs_cld *cs_cl_dfree (cs_cld *D) ;
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+
+UF_long *cs_cl_counts (const cs_cl *A, const UF_long *parent,
+ const UF_long *post, UF_long ata) ;
+double cs_cl_cumsum (UF_long *p, UF_long *c, UF_long n) ;
+UF_long cs_cl_dfs (UF_long j, cs_cl *G, UF_long top, UF_long *xi,
+ UF_long *pstack, const UF_long *pinv) ;
+UF_long *cs_cl_etree (const cs_cl *A, UF_long ata) ;
+UF_long cs_cl_fkeep (cs_cl *A,
+ UF_long (*fkeep) (UF_long, UF_long, cs_complex_t, void *), void *other) ;
+cs_complex_t cs_cl_house (cs_complex_t *x, double *beta, UF_long n) ;
+UF_long *cs_cl_maxtrans (const cs_cl *A, UF_long seed) ;
+UF_long *cs_cl_post (const UF_long *parent, UF_long n) ;
+cs_cld *cs_cl_scc (cs_cl *A) ;
+UF_long cs_cl_scatter (const cs_cl *A, UF_long j, cs_complex_t beta,
+ UF_long *w, cs_complex_t *x, UF_long mark,cs_cl *C, UF_long nz) ;
+UF_long cs_cl_tdfs (UF_long j, UF_long k, UF_long *head, const UF_long *next,
+ UF_long *post, UF_long *stack) ;
+UF_long cs_cl_leaf (UF_long i, UF_long j, const UF_long *first,
+ UF_long *maxfirst, UF_long *prevleaf, UF_long *ancestor, UF_long *jleaf) ;
+UF_long cs_cl_reach (cs_cl *G, const cs_cl *B, UF_long k, UF_long *xi,
+ const UF_long *pinv) ;
+UF_long cs_cl_spsolve (cs_cl *L, const cs_cl *B, UF_long k, UF_long *xi,
+ cs_complex_t *x, const UF_long *pinv, UF_long lo) ;
+UF_long cs_cl_ereach (const cs_cl *A, UF_long k, const UF_long *parent,
+ UF_long *s, UF_long *w) ;
+UF_long *cs_cl_randperm (UF_long n, UF_long seed) ;
+
+/* utilities */
+cs_cld *cs_cl_dalloc (UF_long m, UF_long n) ;
+cs_cl *cs_cl_done (cs_cl *C, void *w, void *x, UF_long ok) ;
+UF_long *cs_cl_idone (UF_long *p, cs_cl *C, void *w, UF_long ok) ;
+cs_cln *cs_cl_ndone (cs_cln *N, cs_cl *C, void *w, void *x, UF_long ok) ;
+cs_cld *cs_cl_ddone (cs_cld *D, cs_cl *C, void *w, UF_long ok) ;
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Macros for constructing each version of CSparse */
+/* -------------------------------------------------------------------------- */
+
+#ifdef CS_LONG
+#define CS_INT UF_long
+#define CS_INT_MAX UF_long_max
+#define CS_ID UF_long_id
+#ifdef CS_COMPLEX
+#define CS_ENTRY cs_complex_t
+#define CS_NAME(nm) cs_cl ## nm
+#define cs cs_cl
+#else
+#define CS_ENTRY double
+#define CS_NAME(nm) cs_dl ## nm
+#define cs cs_dl
+#endif
+#else
+#define CS_INT int
+#define CS_INT_MAX INT_MAX
+#define CS_ID "%d"
+#ifdef CS_COMPLEX
+#define CS_ENTRY cs_complex_t
+#define CS_NAME(nm) cs_ci ## nm
+#define cs cs_ci
+#else
+#define CS_ENTRY double
+#define CS_NAME(nm) cs_di ## nm
+#define cs cs_di
+#endif
+#endif
+
+#ifdef CS_COMPLEX
+#define CS_REAL(x) creal(x)
+#define CS_IMAG(x) cimag(x)
+#define CS_CONJ(x) conj(x)
+#define CS_ABS(x) cabs(x)
+#else
+#define CS_REAL(x) (x)
+#define CS_IMAG(x) (0.)
+#define CS_CONJ(x) (x)
+#define CS_ABS(x) fabs(x)
+#endif
+
+#define CS_MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define CS_MIN(a,b) (((a) < (b)) ? (a) : (b))
+#define CS_FLIP(i) (-(i)-2)
+#define CS_UNFLIP(i) (((i) < 0) ? CS_FLIP(i) : (i))
+#define CS_MARKED(w,j) (w [j] < 0)
+#define CS_MARK(w,j) { w [j] = CS_FLIP (w [j]) ; }
+#define CS_CSC(A) (A && (A->nz == -1))
+#define CS_TRIPLET(A) (A && (A->nz >= 0))
+
+/* --- primary CSparse routines and data structures ------------------------- */
+
+#define cs_add CS_NAME (_add)
+#define cs_cholsol CS_NAME (_cholsol)
+#define cs_dupl CS_NAME (_dupl)
+#define cs_entry CS_NAME (_entry)
+#define cs_lusol CS_NAME (_lusol)
+#define cs_gaxpy CS_NAME (_gaxpy)
+#define cs_multiply CS_NAME (_multiply)
+#define cs_qrsol CS_NAME (_qrsol)
+#define cs_transpose CS_NAME (_transpose)
+#define cs_compress CS_NAME (_compress)
+#define cs_norm CS_NAME (_norm)
+#define cs_print CS_NAME (_print)
+#define cs_load CS_NAME (_load)
+
+/* utilities */
+#define cs_calloc CS_NAME (_calloc)
+#define cs_free CS_NAME (_free)
+#define cs_realloc CS_NAME (_realloc)
+#define cs_spalloc CS_NAME (_spalloc)
+#define cs_spfree CS_NAME (_spfree)
+#define cs_sprealloc CS_NAME (_sprealloc)
+#define cs_malloc CS_NAME (_malloc)
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+#define css CS_NAME (s)
+#define csn CS_NAME (n)
+#define csd CS_NAME (d)
+
+#define cs_amd CS_NAME (_amd)
+#define cs_chol CS_NAME (_chol)
+#define cs_dmperm CS_NAME (_dmperm)
+#define cs_droptol CS_NAME (_droptol)
+#define cs_dropzeros CS_NAME (_dropzeros)
+#define cs_happly CS_NAME (_happly)
+#define cs_ipvec CS_NAME (_ipvec)
+#define cs_lsolve CS_NAME (_lsolve)
+#define cs_ltsolve CS_NAME (_ltsolve)
+#define cs_lu CS_NAME (_lu)
+#define cs_permute CS_NAME (_permute)
+#define cs_pinv CS_NAME (_pinv)
+#define cs_pvec CS_NAME (_pvec)
+#define cs_qr CS_NAME (_qr)
+#define cs_schol CS_NAME (_schol)
+#define cs_sqr CS_NAME (_sqr)
+#define cs_symperm CS_NAME (_symperm)
+#define cs_usolve CS_NAME (_usolve)
+#define cs_utsolve CS_NAME (_utsolve)
+#define cs_updown CS_NAME (_updown)
+
+/* utilities */
+#define cs_sfree CS_NAME (_sfree)
+#define cs_nfree CS_NAME (_nfree)
+#define cs_dfree CS_NAME (_dfree)
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+#define cs_counts CS_NAME (_counts)
+#define cs_cumsum CS_NAME (_cumsum)
+#define cs_dfs CS_NAME (_dfs)
+#define cs_etree CS_NAME (_etree)
+#define cs_fkeep CS_NAME (_fkeep)
+#define cs_house CS_NAME (_house)
+#define cs_invmatch CS_NAME (_invmatch)
+#define cs_maxtrans CS_NAME (_maxtrans)
+#define cs_post CS_NAME (_post)
+#define cs_scc CS_NAME (_scc)
+#define cs_scatter CS_NAME (_scatter)
+#define cs_tdfs CS_NAME (_tdfs)
+#define cs_reach CS_NAME (_reach)
+#define cs_spsolve CS_NAME (_spsolve)
+#define cs_ereach CS_NAME (_ereach)
+#define cs_randperm CS_NAME (_randperm)
+#define cs_leaf CS_NAME (_leaf)
+
+/* utilities */
+#define cs_dalloc CS_NAME (_dalloc)
+#define cs_done CS_NAME (_done)
+#define cs_idone CS_NAME (_idone)
+#define cs_ndone CS_NAME (_ndone)
+#define cs_ddone CS_NAME (_ddone)
+
+/* -------------------------------------------------------------------------- */
+/* Conversion routines */
+/* -------------------------------------------------------------------------- */
+
+#ifndef NCOMPLEX
+cs_di *cs_i_real (cs_ci *A, int real) ;
+cs_ci *cs_i_complex (cs_di *A, int real) ;
+cs_dl *cs_l_real (cs_cl *A, UF_long real) ;
+cs_cl *cs_l_complex (cs_dl *A, UF_long real) ;
+#endif
+
+#ifdef __cplusplus
+}
+#endif
+#endif
diff --git a/CXSparse/Lib/Makefile b/CXSparse/Lib/Makefile
new file mode 100644
index 0000000..c937956
--- /dev/null
+++ b/CXSparse/Lib/Makefile
@@ -0,0 +1,98 @@
+# Modify the "-O" optimization option for best performance (-O3 on Linux):
+CC = cc
+CFLAGS = -O
+I = -I../../UFconfig -I../Include
+
+AR = ar cr
+RANLIB = ranlib
+
+all: libcxsparse.a
+
+CS_SOURCE = cs_add.c cs_amd.c cs_chol.c cs_cholsol.c cs_counts.c cs_cumsum.c \
+ cs_droptol.c cs_dropzeros.c cs_dupl.c cs_entry.c \
+ cs_etree.c cs_fkeep.c cs_gaxpy.c cs_happly.c cs_house.c cs_ipvec.c \
+ cs_lsolve.c cs_ltsolve.c cs_lu.c cs_lusol.c cs_util.c cs_multiply.c \
+ cs_permute.c cs_pinv.c cs_post.c cs_pvec.c cs_qr.c cs_qrsol.c \
+ cs_scatter.c cs_schol.c cs_sqr.c cs_symperm.c cs_tdfs.c cs_malloc.c \
+ cs_transpose.c cs_compress.c cs_usolve.c cs_utsolve.c cs_scc.c \
+ cs_maxtrans.c cs_dmperm.c cs_updown.c cs_print.c cs_norm.c cs_load.c \
+ cs_dfs.c cs_reach.c cs_spsolve.c cs_leaf.c cs_ereach.c cs_randperm.c
+
+CS_DI_OBJ = cs_add_di.o cs_amd_di.o cs_chol_di.o cs_cholsol_di.o cs_counts_di.o \
+ cs_cumsum_di.o cs_droptol_di.o cs_dropzeros_di.o cs_dupl_di.o \
+ cs_entry_di.o cs_etree_di.o cs_fkeep_di.o cs_gaxpy_di.o cs_happly_di.o \
+ cs_house_di.o cs_ipvec_di.o cs_lsolve_di.o cs_ltsolve_di.o cs_lu_di.o \
+ cs_lusol_di.o cs_util_di.o cs_multiply_di.o cs_permute_di.o cs_pinv_di.o \
+ cs_post_di.o cs_pvec_di.o cs_qr_di.o cs_qrsol_di.o cs_scatter_di.o \
+ cs_schol_di.o cs_sqr_di.o cs_symperm_di.o cs_tdfs_di.o cs_malloc_di.o \
+ cs_transpose_di.o cs_compress_di.o cs_usolve_di.o cs_utsolve_di.o \
+ cs_scc_di.o cs_maxtrans_di.o cs_dmperm_di.o cs_updown_di.o cs_print_di.o \
+ cs_norm_di.o cs_load_di.o cs_dfs_di.o cs_reach_di.o cs_spsolve_di.o \
+ cs_leaf_di.o cs_ereach_di.o cs_randperm_di.o
+
+CS_DL_OBJ = cs_add_dl.o cs_amd_dl.o cs_chol_dl.o cs_cholsol_dl.o cs_counts_dl.o \
+ cs_cumsum_dl.o cs_droptol_dl.o cs_dropzeros_dl.o cs_dupl_dl.o \
+ cs_entry_dl.o cs_etree_dl.o cs_fkeep_dl.o cs_gaxpy_dl.o cs_happly_dl.o \
+ cs_house_dl.o cs_ipvec_dl.o cs_lsolve_dl.o cs_ltsolve_dl.o cs_lu_dl.o \
+ cs_lusol_dl.o cs_util_dl.o cs_multiply_dl.o cs_permute_dl.o cs_pinv_dl.o \
+ cs_post_dl.o cs_pvec_dl.o cs_qr_dl.o cs_qrsol_dl.o cs_scatter_dl.o \
+ cs_schol_dl.o cs_sqr_dl.o cs_symperm_dl.o cs_tdfs_dl.o cs_malloc_dl.o \
+ cs_transpose_dl.o cs_compress_dl.o cs_usolve_dl.o cs_utsolve_dl.o \
+ cs_scc_dl.o cs_maxtrans_dl.o cs_dmperm_dl.o cs_updown_dl.o cs_print_dl.o \
+ cs_norm_dl.o cs_load_dl.o cs_dfs_dl.o cs_reach_dl.o cs_spsolve_dl.o \
+ cs_leaf_dl.o cs_ereach_dl.o cs_randperm_dl.o
+
+CS_CI_OBJ = cs_add_ci.o cs_amd_ci.o cs_chol_ci.o cs_cholsol_ci.o cs_counts_ci.o \
+ cs_cumsum_ci.o cs_droptol_ci.o cs_dropzeros_ci.o cs_dupl_ci.o \
+ cs_entry_ci.o cs_etree_ci.o cs_fkeep_ci.o cs_gaxpy_ci.o cs_happly_ci.o \
+ cs_house_ci.o cs_ipvec_ci.o cs_lsolve_ci.o cs_ltsolve_ci.o cs_lu_ci.o \
+ cs_lusol_ci.o cs_util_ci.o cs_multiply_ci.o cs_permute_ci.o cs_pinv_ci.o \
+ cs_post_ci.o cs_pvec_ci.o cs_qr_ci.o cs_qrsol_ci.o cs_scatter_ci.o \
+ cs_schol_ci.o cs_sqr_ci.o cs_symperm_ci.o cs_tdfs_ci.o cs_malloc_ci.o \
+ cs_transpose_ci.o cs_compress_ci.o cs_usolve_ci.o cs_utsolve_ci.o \
+ cs_scc_ci.o cs_maxtrans_ci.o cs_dmperm_ci.o cs_updown_ci.o cs_print_ci.o \
+ cs_norm_ci.o cs_load_ci.o cs_dfs_ci.o cs_reach_ci.o cs_spsolve_ci.o \
+ cs_leaf_ci.o cs_ereach_ci.o cs_randperm_ci.o
+
+CS_CL_OBJ = cs_add_cl.o cs_amd_cl.o cs_chol_cl.o cs_cholsol_cl.o cs_counts_cl.o \
+ cs_cumsum_cl.o cs_droptol_cl.o cs_dropzeros_cl.o cs_dupl_cl.o \
+ cs_entry_cl.o cs_etree_cl.o cs_fkeep_cl.o cs_gaxpy_cl.o cs_happly_cl.o \
+ cs_house_cl.o cs_ipvec_cl.o cs_lsolve_cl.o cs_ltsolve_cl.o cs_lu_cl.o \
+ cs_lusol_cl.o cs_util_cl.o cs_multiply_cl.o cs_permute_cl.o cs_pinv_cl.o \
+ cs_post_cl.o cs_pvec_cl.o cs_qr_cl.o cs_qrsol_cl.o cs_scatter_cl.o \
+ cs_schol_cl.o cs_sqr_cl.o cs_symperm_cl.o cs_tdfs_cl.o cs_malloc_cl.o \
+ cs_transpose_cl.o cs_compress_cl.o cs_usolve_cl.o cs_utsolve_cl.o \
+ cs_scc_cl.o cs_maxtrans_cl.o cs_dmperm_cl.o cs_updown_cl.o cs_print_cl.o \
+ cs_norm_cl.o cs_load_cl.o cs_dfs_cl.o cs_reach_cl.o cs_spsolve_cl.o \
+ cs_leaf_cl.o cs_ereach_cl.o cs_randperm_cl.o
+
+CS = cs_convert.o $(CS_DI_OBJ) $(CS_DL_OBJ) $(CS_CI_OBJ) $(CS_CL_OBJ)
+
+$(CS): ../Include/cs.h Makefile
+
+cs_convert.o: ../Source/cs_convert.c
+ $(CC) $(CFLAGS) $(I) -c $< -o $@
+
+%_di.o : ../Source/%.c
+ $(CC) $(CFLAGS) $(I) -c $< -o $@
+
+%_dl.o : ../Source/%.c
+ $(CC) $(CFLAGS) $(I) -DCS_LONG -c $< -o $@
+
+%_ci.o : ../Source/%.c
+ $(CC) $(CFLAGS) $(I) -DCS_COMPLEX -c $< -o $@
+
+%_cl.o : ../Source/%.c
+ $(CC) $(CFLAGS) $(I) -DCS_LONG -DCS_COMPLEX -c $< -o $@
+
+libcxsparse.a: $(CS)
+ $(AR) libcxsparse.a $(CS)
+ $(RANLIB) libcxsparse.a
+
+clean:
+ rm -f *.o
+
+purge: distclean
+
+distclean: clean
+ rm -f *.a
diff --git a/CXSparse/MATLAB/CSparse/Contents.m b/CXSparse/MATLAB/CSparse/Contents.m
new file mode 100644
index 0000000..4af6293
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/Contents.m
@@ -0,0 +1,54 @@
+% CXSparse: a Concise Sparse matrix Package.
+%
+% Matrices used in CXSparse must in general be either sparse matrices
+% or dense vectors. Ordering methods can accept any sparse matrix.
+% CXsparse allows for complex matrices (CSparse does not).
+%
+% cs_add - sparse matrix addition.
+% cs_amd - approximate minimum degree ordering.
+% cs_chol - sparse Cholesky factorization.
+% cs_cholsol - solve A*x=b using a sparse Cholesky factorization.
+% cs_counts - column counts for sparse Cholesky factor L.
+% cs_dmperm - maximum matching or Dulmage-Mendelsohn permutation.
+% cs_dmsol - x=A\b using the coarse Dulmage-Mendelsohn decomposition.
+% cs_dmspy - plot the Dulmage-Mendelsohn decomposition of a matrix.
+% cs_droptol - remove small entries from a sparse matrix.
+% cs_esep - find an edge separator of a symmetric matrix A
+% cs_etree - elimination tree of A or A'*A.
+% cs_gaxpy - sparse matrix times vector.
+% cs_lsolve - solve a sparse lower triangular system L*x=b.
+% cs_ltsolve - solve a sparse upper triangular system L'*x=b.
+% cs_lu - sparse LU factorization, with fill-reducing ordering.
+% cs_lusol - solve Ax=b using LU factorization.
+% cs_make - compiles CXSparse for use in MATLAB.
+% cs_multiply - sparse matrix multiply.
+% cs_nd - generalized nested dissection ordering.
+% cs_nsep - find a node separator of a symmetric matrix A.
+% cs_permute - permute a sparse matrix.
+% cs_print - print the contents of a sparse matrix.
+% cs_qr - sparse QR factorization (Householder-based).
+% cs_qleft - apply Householder vectors on the left.
+% cs_qright - apply Householder vectors on the right.
+% cs_qrsol - solve a sparse least-squares problem.
+% cs_randperm - random permutation.
+% cs_sep - convert an edge separator into a node separator.
+% cs_scc - strongly-connected components of a square sparse matrix.
+% cs_scc2 - cs_scc, or connected components of a bipartite graph.
+% cs_sparse - convert a triplet form into a sparse matrix.
+% cs_sqr - symbolic sparse QR factorization.
+% cs_symperm - symmetric permutation of a symmetric matrix.
+% cs_transpose - transpose a sparse matrix.
+% cs_updown - rank-1 update/downdate of a sparse Cholesky factorization.
+% cs_usolve - solve a sparse upper triangular system U*x=b.
+% cs_utsolve - solve a sparse lower triangular system U'*x=b.
+% cspy - plot a matrix in color.
+% ccspy - plot the connected components of a matrix.
+
+% Example:
+% help cs_add
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+% helper function:
+% cs_must_compile - return 1 if source code f must be compiled, 0 otherwise
diff --git a/CXSparse/MATLAB/CSparse/Makefile b/CXSparse/MATLAB/CSparse/Makefile
new file mode 100644
index 0000000..830e630
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/Makefile
@@ -0,0 +1,171 @@
+include ../../../UFconfig/UFconfig.mk
+
+MX = $(MEX) -DCS_LONG
+AR = ar cr
+RANLIB = ranlib
+
+I = -I../../Include -I../../../UFconfig
+
+all: mexcsparse.a cs_mex.h
+ $(MX) cs_thumb_mex.c $(I) mexcsparse.a -output cs_thumb
+ $(MX) cs_print_mex.c $(I) mexcsparse.a -output cs_print
+ $(MX) cs_updown_mex.c $(I) mexcsparse.a -output cs_updown
+ $(MX) cs_gaxpy_mex.c $(I) mexcsparse.a -output cs_gaxpy
+ $(MX) cs_transpose_mex.c $(I) mexcsparse.a -output cs_transpose
+ $(MX) cs_sparse_mex.c $(I) mexcsparse.a -output cs_sparse
+ $(MX) cs_multiply_mex.c $(I) mexcsparse.a -output cs_multiply
+ $(MX) cs_add_mex.c $(I) mexcsparse.a -output cs_add
+ $(MX) cs_permute_mex.c $(I) mexcsparse.a -output cs_permute
+ $(MX) cs_symperm_mex.c $(I) mexcsparse.a -output cs_symperm
+ $(MX) cs_lsolve_mex.c $(I) mexcsparse.a -output cs_lsolve
+ $(MX) cs_ltsolve_mex.c $(I) mexcsparse.a -output cs_ltsolve
+ $(MX) cs_usolve_mex.c $(I) mexcsparse.a -output cs_usolve
+ $(MX) cs_utsolve_mex.c $(I) mexcsparse.a -output cs_utsolve
+ $(MX) cs_chol_mex.c $(I) mexcsparse.a -output cs_chol
+ $(MX) cs_etree_mex.c $(I) mexcsparse.a -output cs_etree
+ $(MX) cs_counts_mex.c $(I) mexcsparse.a -output cs_counts
+ $(MX) cs_qr_mex.c $(I) mexcsparse.a -output cs_qr
+ $(MX) cs_amd_mex.c $(I) mexcsparse.a -output cs_amd
+ $(MX) cs_lu_mex.c $(I) mexcsparse.a -output cs_lu
+ $(MX) cs_cholsol_mex.c $(I) mexcsparse.a -output cs_cholsol
+ $(MX) cs_lusol_mex.c $(I) mexcsparse.a -output cs_lusol
+ $(MX) cs_droptol_mex.c $(I) mexcsparse.a -output cs_droptol
+ $(MX) cs_qrsol_mex.c $(I) mexcsparse.a -output cs_qrsol
+ $(MX) cs_dmperm_mex.c $(I) mexcsparse.a -output cs_dmperm
+ $(MX) cs_scc_mex.c $(I) mexcsparse.a -output cs_scc
+ $(MX) cs_sqr_mex.c $(I) mexcsparse.a -output cs_sqr
+ $(MX) cs_randperm_mex.c $(I) mexcsparse.a -output cs_randperm
+
+CSD = cs_mex.o \
+ cs_amd.o \
+ cs_chol.o \
+ cs_counts.o \
+ cs_cumsum.o \
+ cs_fkeep.o \
+ cs_dfs.o \
+ cs_dmperm.o \
+ cs_droptol.o \
+ cs_dropzeros.o \
+ cs_dupl.o \
+ cs_entry.o \
+ cs_etree.o \
+ cs_gaxpy.o \
+ cs_ipvec.o \
+ cs_lsolve.o \
+ cs_ltsolve.o \
+ cs_lu.o \
+ cs_maxtrans.o \
+ cs_util.o \
+ cs_malloc.o \
+ cs_multiply.o \
+ cs_add.o \
+ cs_scatter.o \
+ cs_permute.o \
+ cs_pinv.o \
+ cs_post.o \
+ cs_tdfs.o \
+ cs_pvec.o \
+ cs_qr.o \
+ cs_happly.o \
+ cs_house.o \
+ cs_schol.o \
+ cs_scc.o \
+ cs_sqr.o \
+ cs_symperm.o \
+ cs_transpose.o \
+ cs_compress.o \
+ cs_usolve.o \
+ cs_utsolve.o \
+ cs_cholsol.o \
+ cs_lusol.o \
+ cs_qrsol.o \
+ cs_updown.o \
+ cs_norm.o \
+ cs_print.o \
+ cs_load.o \
+ cs_spsolve.o \
+ cs_reach.o \
+ cs_ereach.o \
+ cs_leaf.o \
+ cs_randperm.o
+
+CSC = \
+ cs_cl_amd.o \
+ cs_cl_chol.o \
+ cs_cl_counts.o \
+ cs_cl_cumsum.o \
+ cs_cl_fkeep.o \
+ cs_cl_dfs.o \
+ cs_cl_dmperm.o \
+ cs_cl_droptol.o \
+ cs_cl_dropzeros.o \
+ cs_cl_dupl.o \
+ cs_cl_entry.o \
+ cs_cl_etree.o \
+ cs_cl_gaxpy.o \
+ cs_cl_ipvec.o \
+ cs_cl_lsolve.o \
+ cs_cl_ltsolve.o \
+ cs_cl_lu.o \
+ cs_cl_maxtrans.o \
+ cs_cl_util.o \
+ cs_cl_malloc.o \
+ cs_cl_multiply.o \
+ cs_cl_add.o \
+ cs_cl_scatter.o \
+ cs_cl_permute.o \
+ cs_cl_pinv.o \
+ cs_cl_post.o \
+ cs_cl_tdfs.o \
+ cs_cl_pvec.o \
+ cs_cl_qr.o \
+ cs_cl_happly.o \
+ cs_cl_house.o \
+ cs_cl_schol.o \
+ cs_cl_scc.o \
+ cs_cl_sqr.o \
+ cs_cl_symperm.o \
+ cs_cl_transpose.o \
+ cs_cl_compress.o \
+ cs_cl_usolve.o \
+ cs_cl_utsolve.o \
+ cs_cl_cholsol.o \
+ cs_cl_lusol.o \
+ cs_cl_qrsol.o \
+ cs_cl_updown.o \
+ cs_cl_norm.o \
+ cs_cl_print.o \
+ cs_cl_load.o \
+ cs_cl_spsolve.o \
+ cs_cl_reach.o \
+ cs_cl_ereach.o \
+ cs_cl_leaf.o \
+ cs_cl_randperm.o
+
+CS = $(CSD) $(CSC)
+
+mexcsparse.a: $(CS)
+ $(AR) mexcsparse.a $(CS)
+ $(RANLIB) mexcsparse.a
+
+$(CS): ../../Include/cs.h
+
+
+cs_mex.o: cs_mex.c cs_mex.h
+ $(MX) -c $(I) $<
+
+cs_cl_%.o: ../../Source/cs_%.c
+ cp -f $< cs_cl_$*.c
+ $(MX) -DCS_COMPLEX -c $(I) cs_cl_$*.c
+
+cs_%.o: ../../Source/cs_%.c
+ $(MX) -c $(I) $<
+
+
+clean:
+ - rm -f *.o
+
+distclean: clean
+ - rm -f *.mex* *.dll *.a cs_cl_*.c
+
+purge: distclean
diff --git a/CXSparse/MATLAB/CSparse/README.txt b/CXSparse/MATLAB/CSparse/README.txt
new file mode 100644
index 0000000..e3a5aa1
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/README.txt
@@ -0,0 +1 @@
+MATLAB interface for CXSparse. See Contents.m for details.
diff --git a/CXSparse/MATLAB/CSparse/ccspy.m b/CXSparse/MATLAB/CSparse/ccspy.m
new file mode 100644
index 0000000..787eada
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/ccspy.m
@@ -0,0 +1,67 @@
+function [p, q, r, s] = ccspy (A, bipartite, res)
+%CCSPY plot the connected components of a matrix.
+%
+% Example:
+% [p, q, r, s] = ccspy (A, bipartite, res)
+%
+% If A is square, [p,q,r,s] = ccspy(A) finds a permutation p so that A(p,q)
+% is permuted into block upper triangular form. In this case, r=s, p=q and
+% the kth diagonal block is given by A (t,t) where t = r(k):r(k+1)-1.
+% The diagonal of A is ignored.
+%
+% If A is not square (or for [p,q,r,s] = ccspy(A,1)), then the connected
+% components of the bipartite graph of A are found. A(p,q) is permuted into
+% block diagonal form, where the diagonal blocks are rectangular. The kth
+% block is given by A(r(k):r(k+1)-1,s(k):s(k+1)-1). A can be rectangular.
+%
+% It then plots the result via cspy, drawing a greenbox around each component.
+% A 3rd input argument (res) controls the resolution (see cspy for a
+% description of the res parameter).
+%
+% See also CSPY, CS_DMPERM, DMPERM, CS_SCC, CS_SCC2, CS_DMSPY.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (~issparse (A))
+ A = sparse (A) ;
+end
+[m n] = size (A) ;
+if (nargin < 3)
+ res = 256 ;
+end
+if (nargin < 2)
+ bipartite = [ ] ;
+end
+if (isempty (bipartite))
+ bipartite = (m ~= n) ;
+end
+
+% find the strongly connected components
+[p1 q r s] = cs_scc2 (A, bipartite) ;
+if (nargout > 0)
+ p = p1 ;
+end
+
+nb = length (r)-1 ;
+
+% plot the result
+S = A (p1,q) ;
+if (res == 0)
+ spy (S) ;
+ e = 1 ;
+else
+ e = cspy (S,res) ;
+end
+hold on
+
+title (sprintf ('%d-by-%d, strongly connected commponents: %d\n', m, n, nb)) ;
+
+if (~bipartite)
+ plot ([.5 .5 n+.5 n+.5], [.5 .5 n+.5 n+.5], 'r') ;
+end
+
+drawboxes (nb, e, r, s) ;
+
+drawbox (1,m+1,1,n+1,'k',1,e) ;
+hold off
diff --git a/CXSparse/MATLAB/CSparse/cs_add.m b/CXSparse/MATLAB/CSparse/cs_add.m
new file mode 100644
index 0000000..f85c562
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_add.m
@@ -0,0 +1,17 @@
+function C = cs_add (A,B,alpha,beta) %#ok
+%CS_ADD sparse matrix addition.
+% C = cs_add(A,B,alpha,beta) computes C = alpha*A+beta*B,
+% where alpha and beta default to 1 if not present.
+%
+% Example:
+% Prob1 = UFget ('HB/ibm32') ; A = Prob1.A ;
+% Prob2 = UFget ('Hamrle/Hamrle1') ; B = Prob2.A ;
+% C = cs_add (A,B) ;
+% D = A+B ; % same as C
+%
+% See also CS_MULTIPLY, CS_GAXPY, PLUS, MINUS.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_add mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_add_mex.c b/CXSparse/MATLAB/CSparse/cs_add_mex.c
new file mode 100644
index 0000000..b8f4e70
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_add_mex.c
@@ -0,0 +1,67 @@
+#include "cs_mex.h"
+/* cs_add: sparse matrix addition */
+
+#ifndef NCOMPLEX
+static cs_complex_t get_complex (const mxArray *a)
+{
+ cs_complex_t s = mxGetScalar (a) ;
+ if (mxIsComplex (a))
+ {
+ double *z = mxGetPi (a) ;
+ s += I * z [0] ;
+ }
+ return (s) ;
+}
+#endif
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin < 2 || nargin > 4)
+ {
+ mexErrMsgTxt ("Usage: C = cs_add(A,B,alpha,beta)") ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])
+ || (nargin > 2 && mxIsComplex (pargin [2]))
+ || (nargin > 3 && mxIsComplex (pargin [3])))
+ {
+#ifndef NCOMPLEX
+ cs_complex_t alpha, beta ;
+ cs_cl Amatrix, Bmatrix, *A, *B, *C, *D ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ B = cs_cl_mex_get_sparse (&Bmatrix, 0, pargin [1]) ; /* get B */
+ alpha = (nargin < 3) ? 1 : get_complex (pargin [2]) ; /* get alpha */
+ beta = (nargin < 4) ? 1 : get_complex (pargin [3]) ; /* get beta */
+ C = cs_cl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */
+ cs_cl_dropzeros (C) ; /* drop zeros */
+ D = cs_cl_transpose (C, 1) ; /* sort result via double transpose */
+ cs_cl_spfree (C) ;
+ C = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ double alpha, beta ;
+ cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */
+ alpha = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; /* get alpha */
+ beta = (nargin < 4) ? 1 : mxGetScalar (pargin [3]) ; /* get beta */
+ C = cs_dl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */
+ cs_dl_dropzeros (C) ; /* drop zeros */
+ D = cs_dl_transpose (C, 1) ; /* sort result via double transpose */
+ cs_dl_spfree (C) ;
+ C = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_amd.m b/CXSparse/MATLAB/CSparse/cs_amd.m
new file mode 100644
index 0000000..b8a3ec9
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_amd.m
@@ -0,0 +1,25 @@
+function p = cs_amd (A,order) %#ok
+%CS_AMD approximate minimum degree ordering.
+% p = cs_amd(A) finds a minimum degree ordering of A+A'
+% p = cs_amd(A,order):
+% order = 1: same as cs_amd(A)
+% order = 2: minimum degree ordering of S'*S where S = A except that
+% "dense" rows of A are removed from S (a dense row has
+% 10*sqrt(n) or more entries where n = size(A,2)). Similar
+% to p = colamd(A), except that colamd does not form A'*A
+% explicitly.
+% order = 3: minimum degree ordering of A'*A. Similar to colamd(A,[n m])
+% where [m n] = size(A), except that colamd does not form A'*A
+% explicitly.
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ;
+% p = cs_amd (A) ;
+% nnz (chol (A))
+% nnz (chol (A (p,p)))
+%
+% See also AMD, COLAMD, SYMAMD.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_amd mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_amd_mex.c b/CXSparse/MATLAB/CSparse/cs_amd_mex.c
new file mode 100644
index 0000000..7d8ff09
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_amd_mex.c
@@ -0,0 +1,23 @@
+#include "cs_mex.h"
+/* cs_amd: approximate minimum degree ordering */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl Amatrix, *A ;
+ CS_INT *P, order ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: p = cs_amd(A,order)") ;
+ }
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */
+ order = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; /* get ordering */
+ order = CS_MAX (order, 1) ;
+ order = CS_MIN (order, 3) ;
+ P = cs_dl_amd (order, A) ; /* min. degree ordering */
+ pargout [0] = cs_dl_mex_put_int (P, A->n, 1, 1) ; /* return P */
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_chol.m b/CXSparse/MATLAB/CSparse/cs_chol.m
new file mode 100644
index 0000000..b31c003
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_chol.m
@@ -0,0 +1,19 @@
+function [L,p] = cs_chol (A,drop) %#ok
+%CS_CHOL sparse Cholesky factorization.
+% L = cs_chol(A) is the same as L = chol(A)', using triu(A).
+% [L,p] = cs_chol(A) first orders A with p=cs_amd(A), so that L*L' = A(p,p).
+% A second optional input argument controls whether or not numerically zero
+% entries are removed from L. cs_chol(A) and cs_chol(A,1) drop them;
+% cs_chol(A,0) keeps them. They must be kept for cs_updown to work properly.
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; [L,p] = cs_chol (A) ;
+% cspy (A (p,p)) ;
+% cspy (L) ;
+%
+% See also CS_AMD, CS_UPDOWN, CHOL, AMD, SYMAMD.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_chol mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_chol_mex.c b/CXSparse/MATLAB/CSparse/cs_chol_mex.c
new file mode 100644
index 0000000..e3b1c5e
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_chol_mex.c
@@ -0,0 +1,58 @@
+#include "cs_mex.h"
+/* cs_chol: sparse Cholesky factorization */
+void mexFunction (int nargout, mxArray *pargout [ ], int nargin,
+ const mxArray *pargin [ ])
+{
+ CS_INT order, n, drop, *p ;
+ if (nargout > 2 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: [L,p] = cs_chol(A,drop)") ;
+ }
+ drop = (nargin == 1) ? 1 : mxGetScalar (pargin [1]) ;
+ order = (nargout > 1) ? 1 : 0 ; /* determine ordering */
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A ;
+ cs_cls *S ;
+ cs_cln *N ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */
+ n = A->n ;
+ S = cs_cl_schol (order, A) ; /* symbolic Cholesky */
+ N = cs_cl_chol (A, S) ; /* numeric Cholesky */
+ if (!N) mexErrMsgTxt ("cs_chol failed: not positive definite\n") ;
+ cs_free (A->x) ;
+ if (drop) cs_cl_dropzeros (N->L) ; /* drop zeros if requested*/
+ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return L */
+ if (nargout > 1)
+ {
+ p = cs_cl_pinv (S->pinv, n) ; /* p=pinv' */
+ pargout [1] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
+ }
+ cs_cl_nfree (N) ;
+ cs_cl_sfree (S) ;
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A ;
+ cs_dls *S ;
+ cs_dln *N ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ n = A->n ;
+ S = cs_dl_schol (order, A) ; /* symbolic Cholesky */
+ N = cs_dl_chol (A, S) ; /* numeric Cholesky */
+ if (!N) mexErrMsgTxt ("cs_chol failed: not positive definite\n") ;
+ if (drop) cs_dl_dropzeros (N->L) ; /* drop zeros if requested*/
+ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return L */
+ if (nargout > 1)
+ {
+ p = cs_dl_pinv (S->pinv, n) ; /* p=pinv' */
+ pargout [1] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
+ }
+ cs_dl_nfree (N) ;
+ cs_dl_sfree (S) ;
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_cholsol.m b/CXSparse/MATLAB/CSparse/cs_cholsol.m
new file mode 100644
index 0000000..7717222
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_cholsol.m
@@ -0,0 +1,17 @@
+function x = cs_cholsol (A,b,order) %#ok
+%CS_CHOLSOL solve A*x=b using a sparse Cholesky factorization.
+% x = cs_cholsol(A,b) computes x = A\b, where A sparse symmetric positive
+% definite, and b is a full vector. A 3rd input parameter allows the
+% ordering to be modified: 0: natural, 1:amd(A), 2: amd(S'*S) where S=A except
+% with no dense rows, 3:amd(A'*A). The default ordering option is 1.
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; b = rand (size (A,1),1) ;
+% x = cs_cholsol (A,b) ; norm (A*x-b)
+%
+% See also CS_CHOL, CS_AMD, CS_LUSOL, CS_QRSOL, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_cholsol mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_cholsol_mex.c b/CXSparse/MATLAB/CSparse/cs_cholsol_mex.c
new file mode 100644
index 0000000..08b9f40
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_cholsol_mex.c
@@ -0,0 +1,48 @@
+#include "cs_mex.h"
+/* cs_cholsol: solve A*x=b using a sparse Cholesky factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT order ;
+ if (nargout > 1 || nargin < 2 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: x = cs_cholsol(A,b,order)") ;
+ }
+ order = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ;
+ order = CS_MAX (order, 0) ;
+ order = CS_MIN (order, 3) ;
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl *A, Amatrix ;
+ cs_complex_t *x ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */
+ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* x = b */
+ if (!cs_cl_cholsol (order, A, x)) /* x = A\x */
+ {
+ mexErrMsgTxt ("A not positive definite") ;
+ }
+ cs_free (A->x) ;
+ pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl *A, Amatrix ;
+ double *x, *b ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ b = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */
+ if (!cs_dl_cholsol (order, A, x)) /* x = A\x */
+ {
+ mexErrMsgTxt ("A not positive definite") ;
+ }
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_counts.m b/CXSparse/MATLAB/CSparse/cs_counts.m
new file mode 100644
index 0000000..6d6a879
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_counts.m
@@ -0,0 +1,19 @@
+function c = cs_counts (A,mode) %#ok
+%CS_COUNTS column counts for sparse Cholesky factor L.
+% c = cs_counts(A) returns a vector of the column counts of L, for the
+% Cholesky factorization L*L' = A. That is, c = sum(spones(chol(A)')),
+% except the Cholesky factorization is not computed.
+% c = cs_counts(A), returns counts for cs_chol(A).
+% c = cs_counts(A,'col'), returns counts for cs_chol(A'*A).
+% c = cs_counts(A,'sym'), same as cs_counts(A).
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; c = cs_counts (A)
+% full (sum (spones (chol (A)')))
+%
+% See also SYMBFACT.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_counts mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_counts_mex.c b/CXSparse/MATLAB/CSparse/cs_counts_mex.c
new file mode 100644
index 0000000..60e680b
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_counts_mex.c
@@ -0,0 +1,32 @@
+#include "cs_mex.h"
+/* cs_counts: column counts for sparse Cholesky factor L. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl Amatrix, *A ;
+ CS_INT n, ata, *parent, *post, *c ;
+ char mode [20] ;
+ if (nargout > 2 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: c = cs_counts(A,mode)") ;
+ }
+ ata = 0 ; /* get mode */
+ if (nargin > 1 && mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], mode, 8) ;
+ ata = (mode [0] == 'c') ;
+ }
+ A = cs_dl_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */
+ n = A->n ;
+ parent = cs_dl_etree (A, ata) ; /* compute etree */
+ post = cs_dl_post (parent, n) ; /* postorder the etree*/
+ c = cs_dl_counts (A, parent, post, ata) ; /* get column counts */
+ pargout [0] = cs_dl_mex_put_int (c, n, 0, 1) ; /* return counts */
+ cs_free (parent) ;
+ cs_free (post) ;
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_dmperm.m b/CXSparse/MATLAB/CSparse/cs_dmperm.m
new file mode 100644
index 0000000..e281ec9
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_dmperm.m
@@ -0,0 +1,64 @@
+function [p,q,r,s,cc,rr] = cs_dmperm (A,seed) %#ok
+%CS_DMPERM maximum matching or Dulmage-Mendelsohn permutation.
+% p = cs_dmperm(A) finds a maximum matching p such that p(j) = i if column j
+% is matched to row i, or 0 if column j is unmatched. If A is square and
+% full structural rank, p is a row permutation and A(p,:) has a zero-free
+% diagonal. The structural rank of A is sprank(A) = sum(p>0).
+%
+% [p,q,r,s,cc,rr] = cs_dmperm(A) finds the Dulmage-Mendelsohn decomposition
+% of A. p and q are permutation vectors. cc and rr are vectors of length 5.
+% C = A(p,q) is split into a 4-by-4 set of coarse blocks:
+%
+% A11 A12 A13 A14
+% 0 0 A23 A24
+% 0 0 0 A34
+% 0 0 0 A44
+%
+% where A12, A23, and A34 are square with zero-free diagonals. The columns of
+% A11 are the unmatched columns, and the rows of A44 are the unmatched rows.
+% Any of these blocks can be empty. In the "coarse" decomposition, the
+% (i,j)th block is C(rr(i):rr(i+1)-1,cc(j):cc(j+1)-1). In terms of a linear
+% system, [A11 A12] is the underdetermined part of the system (it is always
+% rectangular and with more columns and rows, or 0-by-0), A23 is the well-
+% determined part of the system (it is always square), and [A34 ; A44] is
+% the over-determined part of the system (it is always rectangular with more
+% rows than columns, or 0-by-0).
+%
+% The structural rank of A is sprank(A) = rr(4)-1, which is an upper bound on
+% the numerical rank of A. sprank(A) = rank(full(sprand(A))) with probability
+% 1 in exact arithmetic.
+%
+% The A23 submatrix is further subdivided into block upper triangular form
+% via the "fine" decomposition (the strongly-connected components of A23).
+% If A is square and structurally non-singular, A23 is the entire matrix.
+%
+% C(r(i):r(i+1)-1,s(j):s(j+1)-1) is the (i,j)th block of the fine
+% decomposition. The (1,1) block is the rectangular block [A11 A12], unless
+% this block is 0-by-0. The (b,b) block is the rectangular block [A34 ; A44],
+% unless this block is 0-by-0, where b = length(r)-1. All other blocks of the
+% form C(r(i):r(i+1)-1,s(i):s(i+1)-1) are diagonal blocks of A23, and are
+% square with a zero-free diagonal.
+%
+% The matching algorithm used in cs_dmperm can take a very long time
+% in rare cases. This can be avoided by exploiting a randomized algorithm,
+% with cs_dmperm(A,seed). If seed=0, the non-randomized algorithm is used
+% (columns are considered in order 1:n). If seed=-1, columns are considered
+% in reverse order. Otherwise, the columns are considered in a random order,
+% using seed as the random number generator seed. Try cs_dmpmerm(A,1) or
+% cs_dmperm(A,rand), for a randomized order, for example. Seed defaults to 0.
+%
+%
+% Example:
+% Prob = UFget ('HB/west0479') ; A = Prob.A ; cspy (A) ;
+% p = cs_dmperm (A) ;
+% cspy (A (p,:)) ;
+% [p q r s cc rr] = cs_dmperm (A) ;
+% cspy (A (p,q)) ;
+% cs_dmspy (A) ;
+%
+% See also CS_DMSPY, CS_DMSOL, DMPERM, SPRANK, CS_RANDPERM, RAND
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_dmperm mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_dmperm_mex.c b/CXSparse/MATLAB/CSparse/cs_dmperm_mex.c
new file mode 100644
index 0000000..7575493
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_dmperm_mex.c
@@ -0,0 +1,41 @@
+#include "cs_mex.h"
+/* cs_dmperm: maximum matching or Dulmage-Mendelsohn permutation. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double seed ;
+ cs_dl *A, Amatrix ;
+ cs_dld *D ;
+ CS_INT m, n, *jmatch, iseed ;
+ if (nargin < 1 || nargin > 2 || nargout > 6)
+ {
+ mexErrMsgTxt ("Usage: [p,q,r,s,cc,rr] = cs_dmperm (A,seed)") ;
+ }
+ seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 0 ; /* get seed */
+ iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */
+ n = A->n ;
+ m = A->m ;
+ if (nargout <= 1)
+ {
+ jmatch = cs_dl_maxtrans (A, iseed) ; /* max. matching */
+ pargout [0] = cs_dl_mex_put_int (jmatch+m, n, 1, 0) ; /* return imatch */
+ cs_free (jmatch) ;
+ }
+ else
+ {
+ D = cs_dl_dmperm (A, iseed) ; /* Dulmage-Mendelsohn decomposition */
+ pargout [0] = cs_dl_mex_put_int (D->p, m, 1, 0) ;
+ pargout [1] = cs_dl_mex_put_int (D->q, n, 1, 0) ;
+ pargout [2] = cs_dl_mex_put_int (D->r, D->nb+1, 1, 0) ;
+ pargout [3] = cs_dl_mex_put_int (D->s, D->nb+1, 1, 0) ;
+ pargout [4] = cs_dl_mex_put_int (D->cc, 5, 1, 0) ;
+ pargout [5] = cs_dl_mex_put_int (D->rr, 5, 1, 0) ;
+ cs_dl_dfree (D) ;
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_dmsol.m b/CXSparse/MATLAB/CSparse/cs_dmsol.m
new file mode 100644
index 0000000..32b4b63
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_dmsol.m
@@ -0,0 +1,33 @@
+function x = cs_dmsol (A,b)
+%CS_DMSOL x=A\b using the coarse Dulmage-Mendelsohn decomposition.
+% x = cs_dmsol(A,b) computes x=A\b where A may be rectangular and/or
+% structurally rank deficient, and b is a full vector.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; b = rand (size (A,1),1) ;
+% x = cs_dmsol (A,b) ; norm (A*x-b)
+%
+% See also CS_QRSOL, CS_LUSOL, CS_DMPERM, SPRANK, RANK.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+[p q r s cc rr] = cs_dmperm (A) ;
+C = A (p,q) ;
+b = b (p) ;
+x = zeros (n,1) ;
+if (rr(3) <= m & cc(4) <= n) %#ok
+ x (cc(4):n) = cs_qrsol (C (rr(3):m, cc(4):n), b (rr(3):m)) ;
+ b (1:rr(3)-1) = b (1:rr(3)-1) - C (1:rr(3)-1, cc(4):n) * x (cc(4):n) ;
+end
+if (rr(2) < rr (3) & cc(3) < cc(4)) %#ok
+ x (cc(3):cc(4)-1) = ...
+ cs_lusol (C (rr(2):rr(3)-1, cc(3):cc(4)-1), b (rr(2):rr(3)-1)) ;
+ b (1:rr(2)-1) = ...
+ b (1:rr(2)-1) - C (1:rr(2)-1, cc(3):cc(4)-1) * x (cc(3):cc(4)-1) ;
+end
+if (rr(2) > 1 & cc(3) > 1) %#ok
+ x (1:cc(3)-1) = cs_qrsol (C (1:rr(2)-1, 1:cc(3)-1), b (1:rr(2)-1)) ;
+end
+x (q) = x ;
diff --git a/CXSparse/MATLAB/CSparse/cs_dmspy.m b/CXSparse/MATLAB/CSparse/cs_dmspy.m
new file mode 100644
index 0000000..5539cca
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_dmspy.m
@@ -0,0 +1,66 @@
+function [p,q,r,s,cc,rr] = cs_dmspy (A,res,seed)
+%CS_DMSPY plot the Dulmage-Mendelsohn decomposition of a matrix.
+% [p,q,r,s,cc,rr] = cs_dmspy(A) computes [p,q,r,s,cc,rr] = cs_dmperm(A),
+% does spy(A(p,q)), and then draws boxes around the coarse and fine
+% decompositions. A 2nd input argument (cs_dmspy(A,res)) changes the
+% resolution of the image to res-by-res (default resolution is 256).
+% If res is zero, spy is used instead of cspy. If the resolution is low, the
+% picture of the blocks in the figure can overlap. They do not actually
+% overlap in the matrix. With 3 arguments, cs_dmspy(A,res,seed),
+% cs_dmperm(A,seed) is used, where seed controls the randomized algorithm
+% used by cs_dmperm.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; cs_dmspy (Prob.A) ;
+%
+% See also CS_DMPERM, CS_DMSOL, DMPERM, SPRANK, SPY.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (~issparse (A))
+ A = sparse (A) ;
+end
+if (nargin < 2)
+ res = 256 ;
+end
+if (nargin < 3)
+ seed = 0 ;
+end
+
+% Dulmage-Mendelsohn permutation
+[p1,q,r,s,cc,rr] = cs_dmperm (A,seed) ;
+if (nargout > 0)
+ p = p1 ;
+end
+
+nb = length (r)-1 ;
+
+% plot the result
+S = A (p1,q) ;
+if (res == 0)
+ spy (S) ;
+ e = 1 ;
+else
+ e = cspy (S,res) ;
+end
+hold on
+
+title (sprintf ( ...
+ '%d-by-%d, sprank: %d, fine blocks: %d, coarse blocks: %d-by-%d\n', ...
+ size (A), rr(4)-1, nb, length (find (diff (rr))), ...
+ length (find (diff (cc))))) ;
+
+drawboxes (nb, e, r, s) ;
+
+[m n] = size (A) ;
+drawbox (1,m+1,1,n+1,'k',1,e) ;
+
+drawbox (rr(1), rr(2), cc(1), cc (2), 'r', 2, e) ;
+drawbox (rr(1), rr(2), cc(2), cc (3), 'r', 2, e) ;
+drawbox (rr(2), rr(3), cc(3), cc (4), 'k', 2, e) ;
+drawbox (rr(3), rr(4), cc(4), cc (5), 'r', 2, e) ;
+drawbox (rr(4), rr(5), cc(4), cc (5), 'r', 2, e) ;
+
+hold off
+
diff --git a/CXSparse/MATLAB/CSparse/cs_droptol.m b/CXSparse/MATLAB/CSparse/cs_droptol.m
new file mode 100644
index 0000000..83a97ab
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_droptol.m
@@ -0,0 +1,18 @@
+function C = cs_droptol (A, tol) %#ok
+%CS_DROPTOL remove small entries from a sparse matrix.
+% C = cs_droptol(A,tol) removes entries from A of magnitude less than or
+% equal to tol. Same as A = A .* (abs (A) >= tol).
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ;
+% cspy (abs (A) >= 1e-10) ;
+% C = cs_droptol (A, 1e-10) ;
+% cspy (C) ;
+%
+% See also: RELOP, ABS
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_droptol mexFunction not found') ;
+
diff --git a/CXSparse/MATLAB/CSparse/cs_droptol_mex.c b/CXSparse/MATLAB/CSparse/cs_droptol_mex.c
new file mode 100644
index 0000000..29117f0
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_droptol_mex.c
@@ -0,0 +1,45 @@
+#include "cs_mex.h"
+/* cs_droptol: remove small entries from A */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT j, k ;
+ double tol ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_droptol(A,tol)") ;
+ }
+ tol = mxGetScalar (pargin [1]) ; /* get tol */
+
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *C, *A ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ C = cs_cl_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */
+ for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ;
+ for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ;
+ for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ;
+ cs_cl_droptol (C, tol) ; /* drop from C */
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *C, *A ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ C = cs_dl_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */
+ for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ;
+ for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ;
+ for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ;
+ cs_dl_droptol (C, tol) ; /* drop from C */
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_esep.m b/CXSparse/MATLAB/CSparse/cs_esep.m
new file mode 100644
index 0000000..8bb7d32
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_esep.m
@@ -0,0 +1,23 @@
+function [a,b] = cs_esep (A)
+%CS_ESEP find an edge separator of a symmetric matrix A
+% [a,b] = cs_esep(A) finds a edge separator s that splits the graph of A
+% into two parts a and b of roughly equal size. The edge separator is the
+% set of entries in A(a,b).
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ;
+% [a,b] = cs_esep (A) ;
+% cspy (A (a,b)) ;
+%
+% See also CS_NSEP, CS_SEP, CS_ND, SYMRCM.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (~isreal (A))
+ A = spones (A) ;
+end
+p = symrcm (A) ;
+n2 = fix (size(A,1)/2) ;
+a = p (1:n2) ;
+b = p (n2+1:end) ;
diff --git a/CXSparse/MATLAB/CSparse/cs_etree.m b/CXSparse/MATLAB/CSparse/cs_etree.m
new file mode 100644
index 0000000..545e54c
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_etree.m
@@ -0,0 +1,19 @@
+function [parent, post] = cs_etree (A, mode) %#ok
+%CS_ETREE elimination tree of A or A'*A.
+% parent = cs_etree (A) returns the elimination tree of A.
+% parent = cs_etree (A,'col') returns the elimination tree of A'*A.
+% parent = cs_etree (A,'sym') is the same as cs_etree(A).
+% For the symmetric case (cs_etree(A)), only triu(A) is used.
+%
+% [parent,post] = cs_etree(...) also returns a postorder of the tree.
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ;
+% parent = cs_etree (A) ; treeplot (parent) ;
+%
+% See also ETREE, TREEPLOT.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_etree mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_etree_mex.c b/CXSparse/MATLAB/CSparse/cs_etree_mex.c
new file mode 100644
index 0000000..99753fd
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_etree_mex.c
@@ -0,0 +1,34 @@
+#include "cs_mex.h"
+/* cs_etree: elimination tree of A or A'*A */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl Amatrix, *A ;
+ CS_INT n, *parent, *post ;
+ int ata ;
+ char mode [20] ;
+ if (nargout > 2 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: [parent,post] = cs_etree(A,mode)") ;
+ }
+ ata = 0 ; /* get mode */
+ if (nargin > 1 && mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], mode, 8) ;
+ ata = (mode [0] == 'c') ;
+ }
+ A = cs_dl_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */
+ n = A->n ;
+ parent = cs_dl_etree (A, ata) ; /* compute etree */
+ if (nargout > 1)
+ {
+ post = cs_dl_post (parent, n) ; /* postorder the etree*/
+ pargout [1] = cs_dl_mex_put_int (post, n, 1, 1) ; /* return post */
+ }
+ pargout [0] = cs_dl_mex_put_int (parent, n, 1, 1) ; /* return parent */
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_gaxpy.m b/CXSparse/MATLAB/CSparse/cs_gaxpy.m
new file mode 100644
index 0000000..173223c
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_gaxpy.m
@@ -0,0 +1,15 @@
+function z = cs_gaxpy (A,x,y) %#ok
+%CS_GAXPY sparse matrix times vector.
+% z = cs_gaxpy(A,x,y) computes z = A*x+y where x and y are full vectors.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; [m n] = size (A) ;
+% x = rand (m,1) ; y = rand (n,1) ;
+% z = cs_gaxpy (A, x, y) ;
+%
+% See also PLUS, MTIMES.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_gaxpy mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_gaxpy_mex.c b/CXSparse/MATLAB/CSparse/cs_gaxpy_mex.c
new file mode 100644
index 0000000..13dc30a
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_gaxpy_mex.c
@@ -0,0 +1,42 @@
+#include "cs_mex.h"
+/* z = cs_gaxpy (A,x,y) computes z = A*x+y */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: z = cs_gaxpy(A,x,y)") ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])
+ || mxIsComplex (pargin [2]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A ;
+ cs_complex_t *x, *z ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ;/* get A */
+ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* get x */
+ z = cs_cl_mex_get_double (A->m, pargin [2]) ; /* z = y */
+ cs_cl_gaxpy (A, x, z) ; /* z = z + A*x */
+ cs_free (x) ;
+ cs_free (A->x) ;
+ pargout [0] = cs_cl_mex_put_double (A->m, z) ; /* return z */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A ;
+ double *x, *y, *z ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ;/* get A */
+ x = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get x */
+ y = cs_dl_mex_get_double (A->m, pargin [2]) ; /* get y */
+ z = cs_dl_mex_put_double (A->m, y, &(pargout [0])) ; /* z = y */
+ cs_dl_gaxpy (A, x, z) ; /* z = z + A*x */
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_lsolve.m b/CXSparse/MATLAB/CSparse/cs_lsolve.m
new file mode 100644
index 0000000..1e37600
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_lsolve.m
@@ -0,0 +1,17 @@
+function x = cs_lsolve (L,b) %#ok
+%CS_LSOLVE solve a sparse lower triangular system L*x=b.
+% x = cs_lsolve(L,b) computes x = L\b, L must be lower triangular with a
+% zero-free diagonal. b must be a column vector. x is full if b is full.
+% If b is sparse, x is sparse but the nonzero pattern of x is NOT sorted (it
+% is returned in topological order).
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; L = cs_chol (Prob.A) ; n = size (L,1) ;
+% b = rand (n,1) ; x = cs_lsolve (L,b) ; norm (L*x-b)
+%
+% See also CS_LTSOLVE, CS_USOLVE, CS_UTSOLVE, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_lsolve mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_lsolve_mex.c b/CXSparse/MATLAB/CSparse/cs_lsolve_mex.c
new file mode 100644
index 0000000..0153d6a
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_lsolve_mex.c
@@ -0,0 +1,92 @@
+#include "cs_mex.h"
+/* cs_lsolve: x=L\b. L must be sparse and lower triangular. b must be a
+ * full or sparse vector. x is full or sparse, depending on b.
+ *
+ * Time taken is O(flop count), which may be less than n if b is sparse,
+ * depending on L and b.
+ *
+ * This function works with MATLAB 7.2, but is not perfectly compatible with
+ * the requirements of a MATLAB mexFunction when b is sparse. X is returned
+ * as an unsorted sparse vector. Also, this mexFunction temporarily modifies
+ * its input, L, by modifying L->p (in the cs_dfs function) and then restoring
+ * it. This could be corrected by creating a copy of L->p
+ * (see cs_dmperm_mex.c), but this would take O(n) time, destroying the
+ * O(flop count) time complexity of this function.
+ *
+ * Note that b cannot be sparse complex. This function does not support
+ * sparse complex L and b because the sparse x=L\b only accesses part of the
+ * matrix L. Converting L from a MATLAB complex matrix to a CXSparse complex
+ * matrix requires all of L to be accessed, defeating the purpose of this
+ * function.
+ *
+ * L can be sparse complex, but in that case b must be full real or complex,
+ * not sparse.
+ */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT top, nz, p, *xi, n ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_lsolve(L,b)") ;
+ }
+ if (mxIsSparse (pargin [1]))
+ {
+ cs_dl Lmatrix, Bmatrix, *L, *B, *X ;
+ double *x ;
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+ mexErrMsgTxt ("sparse complex case not supported") ;
+ }
+ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;/* get L */
+ n = L->n ;
+ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b*/
+ cs_mex_check (0, n, 1, 0, 1, 1, pargin [1]) ;
+ xi = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* get workspace */
+ x = cs_dl_malloc (n, sizeof (double)) ;
+ top = cs_dl_spsolve (L, B, 0, xi, x, NULL, 1) ; /* x = L\b */
+ X = cs_dl_spalloc (n, 1, n-top, 1, 0) ; /* create sparse x*/
+ X->p [0] = 0 ;
+ nz = 0 ;
+ for (p = top ; p < n ; p++)
+ {
+ X->i [nz] = xi [p] ;
+ X->x [nz++] = x [xi [p]] ;
+ }
+ X->p [1] = nz ;
+ pargout [0] = cs_dl_mex_put_sparse (&X) ;
+ cs_free (x) ;
+ cs_free (xi) ;
+ }
+ else if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Lmatrix, *L ;
+ cs_complex_t *x ;
+ L = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ; /* get L */
+ n = L->n ;
+ x = cs_cl_mex_get_double (n, pargin [1]) ; /* x = b */
+ cs_cl_lsolve (L, x) ; /* x = L\x */
+ cs_free (L->x) ;
+ pargout [0] = cs_cl_mex_put_double (n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Lmatrix, *L ;
+ double *x, *b ;
+ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */
+ n = L->n ;
+ b = cs_dl_mex_get_double (n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (n, b, &(pargout [0])) ; /* x = b */
+ cs_dl_lsolve (L, x) ; /* x = L\x */
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_ltsolve.m b/CXSparse/MATLAB/CSparse/cs_ltsolve.m
new file mode 100644
index 0000000..4e902b6
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_ltsolve.m
@@ -0,0 +1,15 @@
+function x = cs_ltsolve (L,b) %#ok
+%CS_LTSOLVE solve a sparse upper triangular system L'*x=b.
+% x = cs_ltsolve(L,b) computes x = L'\b, L must be lower triangular with a
+% zero-free diagonal. b must be a full vector.
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; L = cs_chol (Prob.A) ; n = size (L,1) ;
+% b = rand (n,1) ; x = cs_ltsolve (L,b) ; norm (L'*x-b)
+%
+% See also CS_LSOLVE, CS_USOLVE, CS_UTSOLVE, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_ltsolve mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_ltsolve_mex.c b/CXSparse/MATLAB/CSparse/cs_ltsolve_mex.c
new file mode 100644
index 0000000..63d4141
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_ltsolve_mex.c
@@ -0,0 +1,38 @@
+#include "cs_mex.h"
+/* cs_ltsolve: solve an upper triangular system L'*x=b */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_ltsolve(L,b)") ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Lmatrix, *L ;
+ cs_complex_t *x ;
+ L = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ; /* get L */
+ x = cs_cl_mex_get_double (L->n, pargin [1]) ; /* x = b */
+ cs_cl_ltsolve (L, x) ; /* x = L'\x */
+ cs_free (L->x) ;
+ pargout [0] = cs_cl_mex_put_double (L->n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Lmatrix, *L ;
+ double *x, *b ;
+ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */
+ b = cs_dl_mex_get_double (L->n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (L->n, b, &(pargout [0])) ; /* x = b */
+ cs_dl_ltsolve (L, x) ; /* x = L'\x */
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_lu.m b/CXSparse/MATLAB/CSparse/cs_lu.m
new file mode 100644
index 0000000..4ff80fc
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_lu.m
@@ -0,0 +1,29 @@
+function [L,U,p,q] = cs_lu (A,tol) %#ok
+%CS_LU sparse LU factorization, with fill-reducing ordering.
+% [L,U,p] = cs_lu(A) factorizes A(p,:) into L*U using no fill-reducing
+% ordering.
+%
+% [L,U,p] = cs_lu(A,tol) factorizes A(p,:) into L*U using no fill-reducing
+% ordering. Entries on the diagonal are given preference in partial pivoting.
+%
+% [L,U,p,q] = cs_lu(A) factorizes A(p,q) into L*U using a fill-reducing
+% ordering q = cs_amd(A,2). Normal partial pivoting is used.
+%
+% [L,U,p,q] = cs_lu(A,tol) factorizes A(p,q) into L*U, using a fill-reducing
+% ordering q = cs_amd(A,1). Entries on the diagonal are given preference in
+% partial pivoting. With a pivot tolerance tol, the entries in L have
+% magnitude 1/tol or less. tol = 1 is normal partial pivoting (with
+% q = cs_amd(A)). tol = 0 ensures p = q. 0<tol<1 is relaxed partial
+% pivoting; the diagonal is selected if it is >= tol * max(abs(A(:,k))).
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; [L,U,p,q] = cs_lu (A) ;
+% cspy (A (p,q)) ; cspy (L+U) ;
+% norm (L*U - A(p,q), 1)
+%
+% See also CS_AMD, LU, UMFPACK, AMD, COLAMD.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_lu mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_lu_mex.c b/CXSparse/MATLAB/CSparse/cs_lu_mex.c
new file mode 100644
index 0000000..31a5a59
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_lu_mex.c
@@ -0,0 +1,90 @@
+#include "cs_mex.h"
+/* cs_lu: sparse LU factorization, with optional fill-reducing ordering */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT n, order, *p ;
+ double tol ;
+ if (nargout > 4 || nargin > 3 || nargin < 1)
+ {
+ mexErrMsgTxt ("Usage: [L,U,p,q] = cs_lu (A,tol)") ;
+ }
+ if (nargin == 2) /* determine tol and ordering */
+ {
+ tol = mxGetScalar (pargin [1]) ;
+ order = (nargout == 4) ? 1 : 0 ; /* amd (A+A'), or natural */
+ }
+ else
+ {
+ tol = 1 ;
+ order = (nargout == 4) ? 2 : 0 ; /* amd(S'*S) w/dense rows or I */
+ }
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cls *S ;
+ cs_cln *N ;
+ cs_cl Amatrix, *A, *D ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */
+ n = A->n ;
+ S = cs_cl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */
+ N = cs_cl_lu (A, S, tol) ; /* numeric factorization */
+ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ;
+ cs_cl_free (A->x) ; /* complex copy no longer needed */
+ cs_cl_dropzeros (N->L) ; /* drop zeros from L and sort it */
+ D = cs_cl_transpose (N->L, 1) ;
+ cs_cl_spfree (N->L) ;
+ N->L = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ cs_cl_dropzeros (N->U) ; /* drop zeros from U and sort it */
+ D = cs_cl_transpose (N->U, 1) ;
+ cs_cl_spfree (N->U) ;
+ N->U = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ p = cs_cl_pinv (N->pinv, n) ; /* p=pinv' */
+ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return L */
+ pargout [1] = cs_cl_mex_put_sparse (&(N->U)) ; /* return U */
+ pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
+ /* return Q */
+ if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ;
+ cs_cl_nfree (N) ;
+ cs_cl_sfree (S) ;
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dls *S ;
+ cs_dln *N ;
+ cs_dl Amatrix, *A, *D ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ n = A->n ;
+ S = cs_dl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */
+ N = cs_dl_lu (A, S, tol) ; /* numeric factorization */
+ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ;
+ cs_dl_dropzeros (N->L) ; /* drop zeros from L and sort it */
+ D = cs_dl_transpose (N->L, 1) ;
+ cs_dl_spfree (N->L) ;
+ N->L = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ cs_dl_dropzeros (N->U) ; /* drop zeros from U and sort it */
+ D = cs_dl_transpose (N->U, 1) ;
+ cs_dl_spfree (N->U) ;
+ N->U = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ p = cs_dl_pinv (N->pinv, n) ; /* p=pinv' */
+ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return L */
+ pargout [1] = cs_dl_mex_put_sparse (&(N->U)) ; /* return U */
+ pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
+ /* return Q */
+ if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ;
+ cs_dl_nfree (N) ;
+ cs_dl_sfree (S) ;
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_lusol.m b/CXSparse/MATLAB/CSparse/cs_lusol.m
new file mode 100644
index 0000000..ff00f7a
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_lusol.m
@@ -0,0 +1,23 @@
+function x = cs_lusol (A,b,order,tol) %#ok
+%CS_LUSOL solve Ax=b using LU factorization.
+% x = cs_lusol(A,b) computes x = A\b, where A is sparse and square, and b is a
+% full vector. The ordering cs_amd(A,2) is used.
+%
+% x = cs_lusol(A,b,1) also computes x = A\b, but uses the cs_amd(A) ordering
+% with diagonal preference (tol=0.001).
+%
+% x = cs_lusol(A,b,order,tol) allows both the ordering and tolerance to be
+% defined. The ordering defaults to 1, and tol defaults to 1.
+% ordering: 0: natural, 1: amd(A+A'), 2: amd(S'*S) where S=A except with no
+% dense rows, 3: amd(A'*A).
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size(A,1) ;
+% b = rand (n,1) ; x = cs_lusol (A,b) ; norm (A*x-b)
+%
+% See also CS_LU, CS_AMD, CS_CHOLSOL, CS_QRSOL, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_lusol mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_lusol_mex.c b/CXSparse/MATLAB/CSparse/cs_lusol_mex.c
new file mode 100644
index 0000000..be34770
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_lusol_mex.c
@@ -0,0 +1,61 @@
+#include "cs_mex.h"
+/* cs_lusol: solve A*x=b using a sparse LU factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double tol ;
+ CS_INT order ;
+ if (nargout > 1 || nargin < 2 || nargin > 4)
+ {
+ mexErrMsgTxt ("Usage: x = cs_lusol(A,b,order,tol)") ;
+ }
+ order = (nargin < 3) ? 2 : mxGetScalar (pargin [2]) ;
+ order = CS_MAX (order, 0) ;
+ order = CS_MIN (order, 3) ;
+ if (nargin == 2)
+ {
+ tol = 1 ; /* normal partial pivoting */
+ }
+ else if (nargin == 3)
+ {
+ tol = (order == 1) ? 0.001 : 1 ; /* tol = 0.001 for amd(A+A') */
+ }
+ else
+ {
+ tol = mxGetScalar (pargin [3]) ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl *A, Amatrix ;
+ cs_complex_t *x ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */
+ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* x = b */
+ if (!cs_cl_lusol (order, A, x, tol)) /* x = A\x */
+ {
+ mexErrMsgTxt ("failed (singular or out of memory)") ;
+ }
+ cs_cl_free (A->x) ; /* complex copy no longer needed */
+ pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl *A, Amatrix ;
+ double *x, *b ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ b = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */
+ if (!cs_dl_lusol (order, A, x, tol)) /* x = A\x */
+ {
+ mexErrMsgTxt ("failed (singular or out of memory)") ;
+ }
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_make.m b/CXSparse/MATLAB/CSparse/cs_make.m
new file mode 100644
index 0000000..982403a
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_make.m
@@ -0,0 +1,86 @@
+function [objfiles, timestamp] = cs_make (f, docomplex)
+%CS_MAKE compiles CXSparse for use in MATLAB.
+% Usage:
+% cs_make
+% [objfiles, timestamp] = cs_make (f, docomplex)
+%
+% With no input arguments, or with f=0, only those files needing to be
+% compiled are compiled (like the Unix/Linux/GNU "make" command, but not
+% requiring "make"). If f is a nonzero number, all files are compiled.
+% If f is a string, only that mexFunction is compiled. For example,
+% cs_make ('cs_add') just compiles the cs_add mexFunction. This option is
+% useful when developing a single new mexFunction. This function can only be
+% used if the current directory is CXSparse/MATLAB/CSparse. Returns a list of
+% the object files in CXSparse, and the latest modification time of any source
+% codes.
+%
+% NOTE: if your compiler does not support the ANSI C99 complex type (most
+% notably Microsoft Windows), the CXSparse mexFunctions will not support
+% complex sparse matrices. The complex case is not attempted if docomplex is
+% zero.
+%
+% To add a new function and its MATLAB mexFunction to CXSparse:
+%
+% (1) Create a source code file CXSparse/Source/cs_mynewfunc.c.
+% (2) Create a help file, CXSparse/MATLAB/CSparse/cs_mynewfunc.m.
+% This is very useful, but not strictly required.
+% (3) Add the prototype of cs_mynewfunc to CXSparse/Include/cs.h.
+% (4) Create its MATLAB mexFunction, CXSparse/MATLAB/cs_mynewfunc_mex.c.
+% (5) Edit cs_make.m, and add 'cs_mynewfunc' to the 'cs' and 'csm' lists.
+% (6) Type 'cs_make' in the CXSparse/MATLAB/CSparse directory.
+% If all goes well, your new function is ready for use in MATLAB.
+%
+% (7) Optionally add 'cs_mynewfunc' to CXSparse/Source/Makefile
+% and CXSparse/MATLAB/CSparse/Makefile, if you want to use the
+% Unix/Linux/GNU make command instead of cs_make.m. See where
+% 'cs_add' and 'cs_add_mex' appear in those files, and add
+% 'cs_mynewfunc' accordingly.
+% (8) Optionally add 'cs_mynewfunc' to Tcov/Makefile, and add additional
+% test code to cs_test.c, and add MATLAB test code to MATLAB/Test/*.
+%
+% Example:
+% cs_make % compile everything
+% cs_make ('cs_chol') ; % just compile cs_chol mexFunction
+%
+% See also MEX.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 1)
+ f = 0 ;
+end
+if (nargin < 2)
+ docomplex = 1 ;
+end
+
+try
+ % ispc does not appear in MATLAB 5.3
+ pc = ispc ;
+catch
+ % if ispc fails, assume we are on a Windows PC if it's not unix
+ pc = ~isunix ;
+end
+
+if (pc)
+ docomplex = 0 ;
+end
+
+if (docomplex == 0)
+ % do not attempt to compile with complex matrices
+ [objfiles, timestamp] = cs_make_helper (f, 0) ;
+else
+ try
+ % try with complex support
+ [objfiles, timestamp] = cs_make_helper (f, 1) ;
+ catch
+ % oops - that failed, try without complex support
+ fprintf ('retrying without complex matrix support\n') ;
+ [objfiles, timestamp] = cs_make_helper (f, 0) ;
+ end
+end
+
+if (f > 0)
+ fprintf ('CXSparse successfully installed.\n') ;
+end
+
diff --git a/CXSparse/MATLAB/CSparse/cs_mex.c b/CXSparse/MATLAB/CSparse/cs_mex.c
new file mode 100644
index 0000000..6b09a5f
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_mex.c
@@ -0,0 +1,216 @@
+#include "cs_mex.h"
+/* check MATLAB input argument */
+void cs_mex_check (CS_INT nel, CS_INT m, CS_INT n, int square, int sparse,
+ int values, const mxArray *A)
+{
+ CS_INT nnel, mm = mxGetM (A), nn = mxGetN (A) ;
+#ifdef NCOMPLEX
+ if (values)
+ {
+ if (mxIsComplex (A)) mexErrMsgTxt ("complex matrices not supported") ;
+ }
+#endif
+ if (sparse && !mxIsSparse (A)) mexErrMsgTxt ("matrix must be sparse") ;
+ if (!sparse)
+ {
+ if (mxIsSparse (A)) mexErrMsgTxt ("matrix must be full") ;
+ if (values && !mxIsDouble (A)) mexErrMsgTxt ("matrix must be double") ;
+ }
+ if (nel)
+ {
+ /* check number of elements */
+ nnel = mxGetNumberOfElements (A) ;
+ if (m >= 0 && n >= 0 && m*n != nnel) mexErrMsgTxt ("wrong length") ;
+ }
+ else
+ {
+ /* check row and/or column dimensions */
+ if (m >= 0 && m != mm) mexErrMsgTxt ("wrong dimension") ;
+ if (n >= 0 && n != nn) mexErrMsgTxt ("wrong dimension") ;
+ }
+ if (square && mm != nn) mexErrMsgTxt ("matrix must be square") ;
+}
+
+/* get a real (or pattern) MATLAB sparse matrix and convert to cs_dl */
+cs_dl *cs_dl_mex_get_sparse (cs_dl *A, int square, int values,
+ const mxArray *Amatlab)
+{
+ cs_mex_check (0, -1, -1, square, 1, values, Amatlab) ;
+ A->m = mxGetM (Amatlab) ;
+ A->n = mxGetN (Amatlab) ;
+ A->p = (CS_INT *) mxGetJc (Amatlab) ;
+ A->i = (CS_INT *) mxGetIr (Amatlab) ;
+ A->x = values ? mxGetPr (Amatlab) : NULL ;
+ A->nzmax = mxGetNzmax (Amatlab) ;
+ A->nz = -1 ; /* denotes a compressed-col matrix, instead of triplet */
+ return (A) ;
+}
+
+
+/* return a real sparse matrix to MATLAB */
+mxArray *cs_dl_mex_put_sparse (cs_dl **Ahandle)
+{
+ cs_dl *A ;
+ mxArray *Amatlab ;
+ A = *Ahandle ;
+ if (!A) mexErrMsgTxt ("failed") ;
+ Amatlab = mxCreateSparse (0, 0, 0, mxREAL) ;
+ mxSetM (Amatlab, A->m) ;
+ mxSetN (Amatlab, A->n) ;
+ mxSetNzmax (Amatlab, A->nzmax) ;
+ cs_free (mxGetJc (Amatlab)) ;
+ cs_free (mxGetIr (Amatlab)) ;
+ cs_free (mxGetPr (Amatlab)) ;
+ mxSetJc (Amatlab, (void *) (A->p)) ; /* assign A->p pointer to MATLAB A */
+ mxSetIr (Amatlab, (void *) (A->i)) ;
+ mxSetPr (Amatlab, A->x) ;
+ cs_free (A) ; /* frees A struct only, not A->p, etc */
+ *Ahandle = NULL ;
+ return (Amatlab) ;
+}
+
+/* get a real MATLAB dense column vector */
+double *cs_dl_mex_get_double (CS_INT n, const mxArray *X)
+{
+ cs_mex_check (0, n, 1, 0, 0, 1, X) ;
+ return (mxGetPr (X)) ;
+}
+
+/* return a double vector to MATLAB */
+double *cs_dl_mex_put_double (CS_INT n, const double *b, mxArray **X)
+{
+ double *x ;
+ CS_INT k ;
+ *X = mxCreateDoubleMatrix (n, 1, mxREAL) ; /* create x */
+ x = mxGetPr (*X) ;
+ for (k = 0 ; k < n ; k++) x [k] = b [k] ; /* copy x = b */
+ return (x) ;
+}
+
+/* get a MATLAB flint array and convert to CS_INT */
+CS_INT *cs_dl_mex_get_int (CS_INT n, const mxArray *Imatlab, CS_INT *imax,
+ int lo)
+{
+ double *p ;
+ CS_INT i, k, *C = cs_dl_malloc (n, sizeof (CS_INT)) ;
+ cs_mex_check (1, n, 1, 0, 0, 1, Imatlab) ;
+ if (mxIsComplex (Imatlab))
+ {
+ mexErrMsgTxt ("integer input cannot be complex") ;
+ }
+ p = mxGetPr (Imatlab) ;
+ *imax = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ i = p [k] ;
+ C [k] = i - 1 ;
+ if (i < lo) mexErrMsgTxt ("index out of bounds") ;
+ *imax = CS_MAX (*imax, i) ;
+ }
+ return (C) ;
+}
+
+/* return an CS_INT array to MATLAB as a flint row vector */
+mxArray *cs_dl_mex_put_int (CS_INT *p, CS_INT n, CS_INT offset, int do_free)
+{
+ mxArray *X = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ double *x = mxGetPr (X) ;
+ CS_INT k ;
+ for (k = 0 ; k < n ; k++) x [k] = (p ? p [k] : k) + offset ;
+ if (do_free) cs_free (p) ;
+ return (X) ;
+}
+
+#ifndef NCOMPLEX
+
+/* copy a MATLAB real or complex vector into a cs_cl complex vector */
+static cs_complex_t *cs_cl_get_vector (CS_INT n, CS_INT size,
+ const mxArray *Xmatlab)
+{
+ CS_INT p ;
+ double *X, *Z ;
+ cs_complex_t *Y ;
+ X = mxGetPr (Xmatlab) ;
+ Z = (mxIsComplex (Xmatlab)) ? mxGetPi (Xmatlab) : NULL ;
+ Y = cs_dl_malloc (size, sizeof (cs_complex_t)) ;
+ for (p = 0 ; p < n ; p++)
+ {
+ Y [p] = X [p] + I * (Z ? Z [p] : 0) ;
+ }
+ return (Y) ;
+}
+
+/* get a real or complex MATLAB sparse matrix and convert to cs_cl */
+cs_cl *cs_cl_mex_get_sparse (cs_cl *A, int square, const mxArray *Amatlab)
+{
+ cs_mex_check (0, -1, -1, square, 1, 1, Amatlab) ;
+ A->m = mxGetM (Amatlab) ;
+ A->n = mxGetN (Amatlab) ;
+ A->p = (CS_INT *) mxGetJc (Amatlab) ;
+ A->i = (CS_INT *) mxGetIr (Amatlab) ;
+ A->nzmax = mxGetNzmax (Amatlab) ;
+ A->x = cs_cl_get_vector (A->p [A->n], A->nzmax, Amatlab) ;
+ A->nz = -1 ; /* denotes a compressed-col matrix, instead of triplet */
+ return (A) ;
+}
+
+/* return a complex sparse matrix to MATLAB */
+mxArray *cs_cl_mex_put_sparse (cs_cl **Ahandle)
+{
+ cs_cl *A ;
+ double *x, *z ;
+ mxArray *Amatlab ;
+ CS_INT k ;
+
+ A = *Ahandle ;
+ if (!A) mexErrMsgTxt ("failed") ;
+ Amatlab = mxCreateSparse (0, 0, 0, mxCOMPLEX) ;
+ mxSetM (Amatlab, A->m) ;
+ mxSetN (Amatlab, A->n) ;
+ mxSetNzmax (Amatlab, A->nzmax) ;
+ cs_cl_free (mxGetJc (Amatlab)) ;
+ cs_cl_free (mxGetIr (Amatlab)) ;
+ cs_cl_free (mxGetPr (Amatlab)) ;
+ cs_cl_free (mxGetPi (Amatlab)) ;
+ mxSetJc (Amatlab, (void *) (A->p)) ; /* assign A->p pointer to MATLAB A */
+ mxSetIr (Amatlab, (void *) (A->i)) ;
+ x = cs_dl_malloc (A->nzmax, sizeof (double)) ;
+ z = cs_dl_malloc (A->nzmax, sizeof (double)) ;
+ for (k = 0 ; k < A->nzmax ; k++)
+ {
+ x [k] = creal (A->x [k]) ; /* copy and split numerical values */
+ z [k] = cimag (A->x [k]) ;
+ }
+ cs_cl_free (A->x) ; /* free copy of complex values */
+ mxSetPr (Amatlab, x) ;
+ mxSetPi (Amatlab, z) ;
+ cs_cl_free (A) ; /* frees A struct only, not A->p, etc */
+ *Ahandle = NULL ;
+ return (Amatlab) ;
+}
+
+/* get a real or complex MATLAB dense column vector, and copy to cs_complex_t */
+cs_complex_t *cs_cl_mex_get_double (CS_INT n, const mxArray *X)
+{
+ cs_mex_check (0, n, 1, 0, 0, 1, X) ;
+ return (cs_cl_get_vector (n, n, X)) ;
+}
+
+/* copy a complex vector back to MATLAB and free it */
+mxArray *cs_cl_mex_put_double (CS_INT n, cs_complex_t *b)
+{
+ double *x, *z ;
+ mxArray *X ;
+ CS_INT k ;
+ X = mxCreateDoubleMatrix (n, 1, mxCOMPLEX) ; /* create x */
+ x = mxGetPr (X) ;
+ z = mxGetPi (X) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ x [k] = creal (b [k]) ; /* copy x = b */
+ z [k] = cimag (b [k]) ;
+ }
+ cs_cl_free (b) ;
+ return (X) ;
+}
+#endif
diff --git a/CXSparse/MATLAB/CSparse/cs_mex.h b/CXSparse/MATLAB/CSparse/cs_mex.h
new file mode 100644
index 0000000..153a099
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_mex.h
@@ -0,0 +1,22 @@
+#include "cs.h"
+#include "mex.h"
+
+void cs_mex_check (CS_INT nel, CS_INT m, CS_INT n, int square,
+ int sparse, int values, const mxArray *A) ;
+
+CS_INT *cs_dl_mex_get_int (CS_INT n, const mxArray *Imatlab, CS_INT *imax,
+ int lo);
+mxArray *cs_dl_mex_put_int (CS_INT *p, CS_INT n, CS_INT offset, int do_free) ;
+
+double *cs_dl_mex_get_double (CS_INT n, const mxArray *X) ;
+cs_dl *cs_dl_mex_get_sparse (cs_dl *A, int square, int values,
+ const mxArray *Amatlab) ;
+double *cs_dl_mex_put_double (CS_INT n, const double *b, mxArray **X) ;
+mxArray *cs_dl_mex_put_sparse (cs_dl **A) ;
+
+#ifndef NCOMPLEX
+cs_complex_t *cs_cl_mex_get_double (CS_INT n, const mxArray *X) ;
+cs_cl *cs_cl_mex_get_sparse (cs_cl *A, int square, const mxArray *Amatlab) ;
+mxArray *cs_cl_mex_put_double (CS_INT n, cs_complex_t *b) ;
+mxArray *cs_cl_mex_put_sparse (cs_cl **Ahandle) ;
+#endif
diff --git a/CXSparse/MATLAB/CSparse/cs_multiply.m b/CXSparse/MATLAB/CSparse/cs_multiply.m
new file mode 100644
index 0000000..071b60e
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_multiply.m
@@ -0,0 +1,16 @@
+function C = cs_multiply (A,B) %#ok
+%CS_MULTIPLY sparse matrix multiply.
+% C = cs_multiply(A,B) computes C = A*B.
+%
+% Example:
+% Prob1 = UFget ('HB/ibm32') ; A = Prob1.A ;
+% Prob2 = UFget ('Hamrle/Hamrle1') ; B = Prob2.A ;
+% C = cs_multiply (A,B) ;
+% D = A*B ; % same as C
+%
+% See also CS_GAXPY, CS_ADD, MTIMES.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_mult mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_multiply_mex.c b/CXSparse/MATLAB/CSparse/cs_multiply_mex.c
new file mode 100644
index 0000000..63b712e
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_multiply_mex.c
@@ -0,0 +1,49 @@
+#include "cs_mex.h"
+/* cs_multiply: sparse matrix multiply */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_multiply(A,B)") ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl A1matrix, B1matrix, *A, *B, *C, *D, *A1, *B1 ;
+ A1 = cs_cl_mex_get_sparse (&A1matrix, 0, pargin [0]) ;
+ A = cs_cl_transpose (A1, 1) ;
+ cs_cl_free (A1->x) ; /* complex copy no longer needed */
+ B1 = cs_cl_mex_get_sparse (&B1matrix, 0, pargin [1]) ;
+ B = cs_cl_transpose (B1, 1) ;
+ cs_cl_free (B1->x) ; /* complex copy no longer needed */
+ D = cs_cl_multiply (B,A) ; /* D = B'*A' */
+ cs_cl_spfree (A) ;
+ cs_cl_spfree (B) ;
+ cs_cl_dropzeros (D) ; /* drop zeros from D */
+ C = cs_cl_transpose (D, 1) ; /* C = D', so C is sorted */
+ cs_cl_spfree (D) ;
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ;
+ A = cs_dl_transpose (cs_dl_mex_get_sparse (&Amatrix, 0,1, pargin[0]),1);
+ B = cs_dl_transpose (cs_dl_mex_get_sparse (&Bmatrix, 0,1, pargin[1]),1);
+ D = cs_dl_multiply (B,A) ; /* D = B'*A' */
+ cs_dl_spfree (A) ;
+ cs_dl_spfree (B) ;
+ cs_dl_dropzeros (D) ; /* drop zeros from D */
+ C = cs_dl_transpose (D, 1) ; /* C = D', so C is sorted */
+ cs_dl_spfree (D) ;
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_must_compile.m b/CXSparse/MATLAB/CSparse/cs_must_compile.m
new file mode 100644
index 0000000..1810a57
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_must_compile.m
@@ -0,0 +1,23 @@
+function [s, t, tobj] = cs_must_compile (srcdir, f, suffix, obj, hfile, force)
+%CS_MUST_COMPILE return 1 if source code f must be compiled, 0 otherwise
+% Used by cs_make, and MATLAB/Test/cs_test_make.m.
+%
+% Example:
+% none, not meant for end users.
+% See also: CS_MAKE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+dobj = dir ([f obj]) ;
+if (force | isempty (dobj)) %#ok
+ s = 1 ;
+ t = Inf ;
+ tobj = -1 ;
+ return
+end
+dsrc = dir ([srcdir f suffix '.c']) ;
+dh = dir (hfile) ;
+t = max (datenum (dsrc.date), datenum (dh.date)) ;
+tobj = datenum (dobj.date) ;
+s = (tobj < t) ;
diff --git a/CXSparse/MATLAB/CSparse/cs_nd.m b/CXSparse/MATLAB/CSparse/cs_nd.m
new file mode 100644
index 0000000..1afcbfc
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_nd.m
@@ -0,0 +1,27 @@
+function p = cs_nd (A)
+%CS_ND generalized nested dissection ordering.
+% p = cs_nd(A) computes the nested dissection ordering of a matrix. Small
+% submatrices (order 500 or less) are ordered via cs_amd. A must be sparse
+% and symmetric (use p = cs_nd(A|A') if it is not symmetric).
+%
+% Example:
+% A = delsq (numgrid ('L', 300)) ; % matrix used in 'bench'
+% p = cs_nd (A) ;
+% cspy (A (p,p)) ;
+%
+% See also CS_AMD, CS_SEP, CS_ESEP, CS_NSEP, AMD.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+if (n == 1)
+ p = 1 ;
+elseif (n < 500)
+ p = cs_amd (A) ; % use cs_amd on small graphs
+else
+ [s a b] = cs_nsep (A) ; % find a node separator
+ a = a (cs_nd (A (a,a))) ; % order A(a,a) recursively
+ b = b (cs_nd (A (b,b))) ; % order A(b,b) recursively
+ p = [a b s] ; % concatenate to obtain the final ordering
+end
diff --git a/CXSparse/MATLAB/CSparse/cs_nsep.m b/CXSparse/MATLAB/CSparse/cs_nsep.m
new file mode 100644
index 0000000..b7a22fc
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_nsep.m
@@ -0,0 +1,18 @@
+function [s,a,b] = cs_nsep (A)
+%CS_NSEP find a node separator of a symmetric matrix A.
+% [s,a,b] = cs_nsep(A) finds a node separator s that splits the graph of A
+% into two parts a and b of roughly equal size. If A is unsymmetric, use
+% cs_nsep(A|A'). The permutation p = [a b s] is a one-level dissection of A.
+%
+% Example:
+% A = delsq (numgrid ('L', 10)) ; % smaller version as used in 'bench'
+% [s a b] = cs_nsep (A) ; p = [a b s] ;
+% cspy (A (p,p)) ;
+%
+% See also CS_SEP, CS_ESEP, CS_ND.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[a b] = cs_esep (A) ;
+[s a b] = cs_sep (A, a, b) ;
diff --git a/CXSparse/MATLAB/CSparse/cs_permute.m b/CXSparse/MATLAB/CSparse/cs_permute.m
new file mode 100644
index 0000000..ac138b1
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_permute.m
@@ -0,0 +1,15 @@
+function C = cs_permute (A,p,q) %#ok
+%CS_PERMUTE permute a sparse matrix.
+% C = cs_permute(A,p,q) computes C = A(p,q)
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; [m n] = size (A) ;
+% p = randperm (m) ; q = randperm (n) ;
+% C = cs_permute (A,p,q) ; % C = A(p,q)
+%
+% See also CS_SYMPERM, SUBSREF.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_permute mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_permute_mex.c b/CXSparse/MATLAB/CSparse/cs_permute_mex.c
new file mode 100644
index 0000000..1e6ad11
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_permute_mex.c
@@ -0,0 +1,51 @@
+#include "cs_mex.h"
+/* cs_permute: permute a sparse matrix */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT ignore, *P, *Q, *Pinv, m, n ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: C = cs_permute(A,p,q)") ;
+ }
+ m = mxGetM (pargin [0]) ;
+ n = mxGetN (pargin [0]) ;
+ P = cs_dl_mex_get_int (m, pargin [1], &ignore, 1) ; /* get P */
+ Q = cs_dl_mex_get_int (n, pargin [2], &ignore, 1) ; /* get Q */
+ Pinv = cs_pinv (P, m) ; /* P = Pinv' */
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A, *C, *D ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ C = cs_cl_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */
+ cs_cl_free (A->x) ;
+ D = cs_cl_transpose (C, 1) ; /* sort C via double transpose */
+ cs_cl_spfree (C) ;
+ C = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A, *C, *D ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ C = cs_dl_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */
+ D = cs_dl_transpose (C, 1) ; /* sort C via double transpose */
+ cs_dl_spfree (C) ;
+ C = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ }
+ cs_free (Pinv) ;
+ cs_free (P) ;
+ cs_free (Q) ;
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_print.m b/CXSparse/MATLAB/CSparse/cs_print.m
new file mode 100644
index 0000000..90d4ed0
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_print.m
@@ -0,0 +1,14 @@
+function cs_print (A,brief) %#ok
+%CS_PRINT print the contents of a sparse matrix.
+% cs_print(A) prints a sparse matrix. cs_print(A,1) prints just a few entries.
+%
+% Example:
+% Prob = UFget ('vanHeukelum/cage3') ; A = Prob.A
+% cs_print (A) ;
+%
+% See also: DISPLAY.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_print mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_print_mex.c b/CXSparse/MATLAB/CSparse/cs_print_mex.c
new file mode 100644
index 0000000..58864c2
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_print_mex.c
@@ -0,0 +1,34 @@
+#include "cs_mex.h"
+/* cs_print: print the contents of a sparse matrix. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT brief ;
+ if (nargout > 0 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: cs_print(A,brief)") ;
+ }
+ brief = (nargin < 2) ? 0 : mxGetScalar (pargin [1]) ; /* get brief */
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ cs_cl_print (A, brief) ; /* print A */
+ cs_free (A->x) ;
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ;/* get A */
+ cs_print (A, brief) ; /* print A */
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_qleft.m b/CXSparse/MATLAB/CSparse/cs_qleft.m
new file mode 100644
index 0000000..0762562
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_qleft.m
@@ -0,0 +1,36 @@
+function X = cs_qleft (V, Beta, p, Y)
+%CS_QLEFT apply Householder vectors on the left.
+% X = cs_qleft(V,Beta,p,Y) computes X = Hn*...*H2*H1*P*Y = Q'*Y where Q is
+% represented by the Householder vectors V, coefficients Beta, and
+% permutation p. p can be [], which denotes the identity permutation.
+%
+% Example:
+% Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ;
+% b = rand (m,1) ;
+% [V,beta,p,R] = cs_qr (A) ; % QR factorization of A(p,:)
+% b1 = cs_qleft (V, beta, p, b) ;
+% x1 = R (1:n,1:n) \ b1 (1:n) ;
+% x2 = A\b ;
+% norm (x1-x2)
+%
+% See also CS_QR, CS_QRIGHT.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m2 n] = size (V) ;
+[m ny] = size (Y) ;
+X = Y ;
+if (m2 > m)
+ if (issparse (Y))
+ X = [X ; sparse(m2-m,ny)] ;
+ else
+ X = [X ; zeros(m2-m,ny)] ;
+ end
+end
+if (~isempty (p))
+ X = X (p,:) ;
+end
+for k = 1:n
+ X = X - V (:,k) * (Beta (k) * (V (:,k)' * X)) ;
+end
diff --git a/CXSparse/MATLAB/CSparse/cs_qr.m b/CXSparse/MATLAB/CSparse/cs_qr.m
new file mode 100644
index 0000000..7c4767c
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_qr.m
@@ -0,0 +1,33 @@
+function [V,beta,p,R,q] = cs_qr (A) %#ok
+%CS_QR sparse QR factorization (Householder-based).
+% [V,beta,p,R] = cs_qr(A) computes the QR factorization of A(p,:).
+% [V,beta,p,R,q] = cs_qr(A) computes the QR factorization of A(p,q).
+% The V, beta, and p terms represent the Householder vectors and coefficients.
+% The fill-reducing ordering q is found via q = cs_amd(A,3).
+% The orthogonal factor Q can be obtained via
+% Q = cs_qright(V,beta,p,speye(size(V,1))), in which case Q*R=A(:,q) is the
+% resulting factorization (the permutation p is folded into Q). A must be
+% m-by-n with m >= n. If A is structurally rank deficient, additional empty
+% rows may have been added to V and R. Note that V is typically much sparser
+% than Q.
+%
+% Example:
+%
+% Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ;
+% b = rand (m,1) ;
+% [V,beta,p,R,q] = cs_qr (A) ; % QR factorization of A(p,q)
+% b1 = cs_qleft (V, beta, p, b) ;
+% x1 = R (1:n,1:n) \ b1 (1:n) ;
+% x1 (q) = x1 ;
+% x2 = A\b ;
+% norm (x1-x2)
+% Q = cs_qright(V,beta,p,speye(size(V,1))) ; % Note: p accounted for in Q
+% norm (Q*R-A(:,q),1)
+% fprintf ('nnz(R) %d, nnz(V) %d, nnz(Q) %d\n', nnz(R), nnz(V), nnz(Q)) ;
+%
+% See also CS_AMD, CS_QRIGHT, CS_QR, CS_DMPERM, QR, COLAMD.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_qr mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_qr_mex.c b/CXSparse/MATLAB/CSparse/cs_qr_mex.c
new file mode 100644
index 0000000..9d31207
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_qr_mex.c
@@ -0,0 +1,83 @@
+#include "cs_mex.h"
+/* cs_qr: sparse QR factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT m, n, order, *p ;
+ if (nargout > 5 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: [V,beta,p,R,q] = cs_qr(A)") ;
+ }
+ order = (nargout == 5) ? 3 : 0 ; /* determine ordering */
+ m = mxGetM (pargin [0]) ;
+ n = mxGetN (pargin [0]) ;
+ if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ;
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cls *S ;
+ cs_cln *N ;
+ cs_cl Amatrix, *A, *D ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ S = cs_cl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
+ N = cs_cl_qr (A, S) ; /* numeric QR factorization */
+ cs_free (A->x) ;
+ if (!N) mexErrMsgTxt ("qr failed") ;
+ cs_cl_dropzeros (N->L) ; /* drop zeros from V and sort */
+ D = cs_cl_transpose (N->L, 1) ;
+ cs_cl_spfree (N->L) ;
+ N->L = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ cs_cl_dropzeros (N->U) ; /* drop zeros from R and sort */
+ D = cs_cl_transpose (N->U, 1) ;
+ cs_cl_spfree (N->U) ;
+ N->U = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ m = N->L->m ; /* m may be larger now */
+ p = cs_cl_pinv (S->pinv, m) ; /* p = pinv' */
+ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return V */
+ cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */
+ pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */
+ pargout [3] = cs_cl_mex_put_sparse (&(N->U)) ; /* return R */
+ pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
+ cs_cl_nfree (N) ;
+ cs_cl_sfree (S) ;
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dls *S ;
+ cs_dln *N ;
+ cs_dl Amatrix, *A, *D ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
+ N = cs_dl_qr (A, S) ; /* numeric QR factorization */
+ if (!N) mexErrMsgTxt ("qr failed") ;
+ cs_dl_dropzeros (N->L) ; /* drop zeros from V and sort */
+ D = cs_dl_transpose (N->L, 1) ;
+ cs_dl_spfree (N->L) ;
+ N->L = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ cs_dl_dropzeros (N->U) ; /* drop zeros from R and sort */
+ D = cs_dl_transpose (N->U, 1) ;
+ cs_dl_spfree (N->U) ;
+ N->U = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ m = N->L->m ; /* m may be larger now */
+ p = cs_dl_pinv (S->pinv, m) ; /* p = pinv' */
+ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return V */
+ cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */
+ pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */
+ pargout [3] = cs_dl_mex_put_sparse (&(N->U)) ; /* return R */
+ pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
+ cs_dl_nfree (N) ;
+ cs_dl_sfree (S) ;
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_qright.m b/CXSparse/MATLAB/CSparse/cs_qright.m
new file mode 100644
index 0000000..951c60a
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_qright.m
@@ -0,0 +1,26 @@
+function X = cs_qright (V, Beta, p, Y)
+%CS_QRIGHT apply Householder vectors on the right.
+% X = cs_qright(V,Beta,p,Y) computes X = Y*P'*H1*H2*...*Hn = Y*Q where Q is
+% represented by the Householder vectors V, coefficients Beta, and
+% permutation p. p can be [], which denotes the identity permutation.
+% To obtain Q itself, use Q = cs_qright(V,Beta,p,speye(size(V,1))).
+%
+% Example:
+% load west0479 ; q = colamd (west0479) ; A = west0479 (:,q) ;
+% [Q,R] = qr (A) ; norm (Q*R-A, 1)
+% [V,beta,p,R2] = cs_qr (A) ;
+% Q2 = cs_qright (V, beta, p, speye(size(V,1))) ; norm (Q2*R2-A, 1)
+%
+% See also CS_QR, CS_QLEFT.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (V) ;
+X = Y ;
+if (~isempty (p))
+ X = X (:,p) ;
+end
+for k = 1:n
+ X = X - (X * (Beta (k) * V (:,k))) * V (:,k)' ;
+end
diff --git a/CXSparse/MATLAB/CSparse/cs_qrsol.m b/CXSparse/MATLAB/CSparse/cs_qrsol.m
new file mode 100644
index 0000000..3c49456
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_qrsol.m
@@ -0,0 +1,23 @@
+function x = cs_qrsol (A,b,order) %#ok
+%CS_QRSOL solve a sparse least-squares problem.
+% x = cs_qrsol(A,b) solves the over-determined least squares problem to
+% find x that minimizes norm(A*x-b), where b is a full vector and
+% A is m-by-n with m >= n. If m < n, it solves the underdetermined system
+% Ax=b. A 3rd input argument specifies the ordering method to use
+% (0: natural, 3: amd(A'*A)). The default ordering is 3.
+%
+% Example:
+% Prob = UFget ('HB/well1033') ; A = Prob.A ; [m n] = size (A) ;
+% b = rand (m,1) ;
+% x1 = cs_qrsol (A,b) ;
+% x2 = A\b ;
+% norm (x1-x2)
+%
+% For this example, cs_qrsol is about 3 times faster than A\b in MATLAB 7.3.
+%
+% See also CS_QR, CS_AMD, CS_LUSOL, CS_CHOLSOL, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_qrsol mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_qrsol_mex.c b/CXSparse/MATLAB/CSparse/cs_qrsol_mex.c
new file mode 100644
index 0000000..18af03d
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_qrsol_mex.c
@@ -0,0 +1,54 @@
+#include "cs_mex.h"
+/* cs_qrsol: solve least squares or underdetermined problem */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT k, order ;
+ if (nargout > 1 || nargin < 2 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: x = cs_qrsol(A,b,order)") ;
+ }
+ order = (nargin < 3) ? 3 : mxGetScalar (pargin [2]) ;
+ order = CS_MAX (order, 0) ;
+ order = CS_MIN (order, 3) ;
+
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl *A, Amatrix ;
+ cs_complex_t *x, *b ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ b = cs_cl_mex_get_double (A->m, pargin [1]) ; /* get b */
+ x = cs_dl_calloc (CS_MAX (A->m, A->n), sizeof (cs_complex_t)) ;
+ for (k = 0 ; k < A->m ; k++) x [k] = b [k] ; /* x = b */
+ cs_free (b) ;
+ if (!cs_cl_qrsol (order, A, x)) /* x = A\x */
+ {
+ mexErrMsgTxt ("QR solve failed") ;
+ }
+ pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl *A, Amatrix ;
+ double *x, *b ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ b = cs_dl_mex_get_double (A->m, pargin [1]) ; /* get b */
+ x = cs_dl_calloc (CS_MAX (A->m, A->n), sizeof (double)) ; /* x = b */
+ for (k = 0 ; k < A->m ; k++) x [k] = b [k] ;
+ if (!cs_dl_qrsol (order, A, x)) /* x = A\x */
+ {
+ mexErrMsgTxt ("QR solve failed") ;
+ }
+ cs_dl_mex_put_double (A->n, x, &(pargout [0])) ; /* return x */
+ cs_free (x) ;
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_randperm.m b/CXSparse/MATLAB/CSparse/cs_randperm.m
new file mode 100644
index 0000000..845cce8
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_randperm.m
@@ -0,0 +1,18 @@
+function p = cs_randperm (n, seed) %#ok
+%CS_RANDPERM random permutation.
+% p = cs_randperm (n) returns a repeatable random permutation of 1:n.
+% p = cs_randperm (n,seed) returns the random permutation using the given
+% seed for the random number generator (try cs_randperm (n,rand)), where
+% seed is not 0 or -1. Two special cases are not random permutations at all:
+% p=cs_randperm (n,0) is 1:n, and p=cs_randperm (n,-1) is n:-1:1.
+% This function does not change RAND's state.
+%
+% Example:
+% p = cs_randperm (10)
+%
+% See also CS_DMPERM, RAND, RANDPERM
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_randperm mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_randperm_mex.c b/CXSparse/MATLAB/CSparse/cs_randperm_mex.c
new file mode 100644
index 0000000..0398ede
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_randperm_mex.c
@@ -0,0 +1,28 @@
+#include "cs_mex.h"
+/* cs_randperm: random permutation. p=cs_randperm(n,0) is 1:n,
+ * p=cs_randperm(n,-1) is n:-1:1. p = cs_randperm (n,seed) is a random
+ * permutation using the given seed (where seed is not 0 or -1).
+ * seed defaults to 1. A single seed always gives a repeatable permutation.
+ * Use p = cs_randperm(n,rand) to get a permutation that varies with each use.
+ */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double seed ;
+ CS_INT iseed, n, *p ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: p = cs_randperm(n,seed)") ;
+ }
+ seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ;
+ iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ;
+ n = mxGetScalar (pargin [0]) ;
+ n = CS_MAX (n, 0) ;
+ p = cs_dl_randperm (n, iseed) ;
+ pargout [0] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_scc.m b/CXSparse/MATLAB/CSparse/cs_scc.m
new file mode 100644
index 0000000..787b24f
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_scc.m
@@ -0,0 +1,17 @@
+function [p,r] = cs_scc (A) %#ok
+%CS_SCC strongly-connected components of a square sparse matrix.
+% [p,r] = cs_scc(A) finds a permutation p so that A(p,p) is permuted into
+% block upper triangular form. The diagonal of A is ignored. The kth block
+% is given by A (s,s) where s = r(k):r(k+1)-1. A must be square.
+% For bipartite or rectangular graphs, use cs_scc2.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; [p r] = cs_scc (A) ;
+% cspy (A (p,p)) ;
+%
+% See also CS_DMPERM, DMPERM, CS_SCC2.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_scc mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_scc2.m b/CXSparse/MATLAB/CSparse/cs_scc2.m
new file mode 100644
index 0000000..a511235
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_scc2.m
@@ -0,0 +1,61 @@
+function [p, q, r, s] = cs_scc2 (A, bipartite)
+%CS_SCC2 cs_scc, or connected components of a bipartite graph.
+% [p,q,r,s] = cs_scc2(A) finds a permutation p so that A(p,q) is permuted into
+% block upper triangular form (if A is square). In this case, r=s, p=q and
+% the kth diagonal block is given by A (t,t) where t = r(k):r(k)+1.
+% The diagonal of A is ignored. Each block is one strongly connected
+% component of A.
+%
+% If A is not square (or for [p,q,r,s] = cs_scc2(A,1)), then the connected
+% components of the bipartite graph of A are found. A(p,q) is permuted into
+% block diagonal form, where the diagonal blocks are rectangular. The kth
+% block is given by A(r(k):r(k+1)-1,s(k):s(k+1)-1). A can be rectangular.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; [p q r s] = cs_scc2 (A) ;
+% cspy (A (p,q)) ;
+% Prob = UFget ('HB/wm1') ; A = Prob.A ; [p q r s] = cs_scc2 (A) ;
+% cspy (A (p,q)) ;
+%
+% See also CS_DMPERM, DMPERM, CS_SCC, CCSPY.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+if (nargin < 2)
+ bipartite = 0 ;
+end
+
+if (m ~= n | bipartite) %#ok
+
+ % find the connected components of [I A ; A' 0]
+ S = spaugment (A) ;
+ [psym,rsym] = cs_scc (S) ;
+ p = psym (find (psym <= m)) ; %#ok
+ q = psym (find (psym > m)) - m ; %#ok
+ nb = length (rsym) - 1 ;
+ r = zeros (1,nb+1) ;
+ s = zeros (1,nb+1) ;
+ krow = 1 ;
+ kcol = 1 ;
+ for k = 1:nb
+ % find the rows and columns in the kth component
+ r (k) = krow ;
+ s (k) = kcol ;
+ ksym = psym (rsym (k):rsym (k+1)-1) ;
+ krow = krow + length (find (ksym <= m)) ;
+ kcol = kcol + length (find (ksym > m)) ;
+ end
+ r (nb+1) = m+1 ;
+ s (nb+1) = n+1 ;
+
+else
+
+ % find the strongly connected components of A
+ [p,r] = cs_scc (A) ;
+ q = p ;
+ s = r ;
+
+end
+
diff --git a/CXSparse/MATLAB/CSparse/cs_scc_mex.c b/CXSparse/MATLAB/CSparse/cs_scc_mex.c
new file mode 100644
index 0000000..28ad3f2
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_scc_mex.c
@@ -0,0 +1,32 @@
+#include "cs_mex.h"
+/* [p,r] = cs_scc (A) finds the strongly connected components of A */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl Amatrix, *A ;
+ cs_dld *D ;
+ CS_INT n, j, *Ap2 ;
+ if (nargout > 2 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: [p,r] = cs_scc(A)") ;
+ }
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ; /* get A */
+ /* cs_scc modifies A->p and then restores it (in cs_dfs). Avoid the issue
+ * of a mexFunction modifying its input (even temporarily) by making a copy
+ * of A->p. This issue does not arise in cs_dmperm, because that function
+ * applies cs_scc to a submatrix C, not to A directly. */
+ n = A->n ;
+ Ap2 = cs_dl_malloc (n+1, sizeof (CS_INT)) ;
+ for (j = 0 ; j <= n ; j++) Ap2 [j] = A->p [j] ;
+ A->p = Ap2 ;
+ D = cs_dl_scc (A) ; /* find conn. comp. */
+ pargout [0] = cs_dl_mex_put_int (D->p, n, 1, 0) ; /* return p */
+ pargout [1] = cs_dl_mex_put_int (D->r, D->nb+1, 1, 0) ; /* return r */
+ cs_dl_dfree (D) ;
+ cs_free (Ap2) ; /* free the copy of A->p */
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_sep.m b/CXSparse/MATLAB/CSparse/cs_sep.m
new file mode 100644
index 0000000..88ba1bb
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_sep.m
@@ -0,0 +1,21 @@
+function [s,as,bs] = cs_sep (A,a,b)
+%CS_SEP convert an edge separator into a node separator.
+% [s,as,bs] = cs_sep (A,a,b) converts an edge separator into a node separator.
+% [a b] is a partition of 1:n, thus the edges in A(a,b) are an edge separator
+% of A. s is the node separator, consisting of a node cover of the edges of
+% A(a,b). as and bs are the sets a and b with s removed.
+%
+% Example:
+% type cs_nsep ; % to see a simple example of use in cs_nsep.m
+%
+% See also CS_DMPERM, CS_NSEP, CS_ESEP, CS_ND.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[p q r s cc rr] = cs_dmperm (A (a,b)) ;
+s = [(a (p (1:rr(2)-1))) (b (q (cc(3):(cc(5)-1))))] ;
+w = ones (1, size (A,1)) ;
+w (s) = 0 ;
+as = a (find (w (a))) ; %#ok
+bs = b (find (w (b))) ; %#ok
diff --git a/CXSparse/MATLAB/CSparse/cs_sparse.m b/CXSparse/MATLAB/CSparse/cs_sparse.m
new file mode 100644
index 0000000..cad6e30
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_sparse.m
@@ -0,0 +1,17 @@
+function A = cs_sparse (i,j,x) %#ok
+%CS_SPARSE convert a triplet form into a sparse matrix.
+% A = cs_sparse(i,j,x) is identical to A = sparse(i,j,x), except that x must
+% be real, and the length of i, j, and x must be the same.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; S = Prob.A ;
+% [i j x] = find (S) ;
+% A = cs_sparse (i,j,x) ;
+% S-A
+%
+% See also FIND, SPARSE, SPCONVERT.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_sparse mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_sparse_mex.c b/CXSparse/MATLAB/CSparse/cs_sparse_mex.c
new file mode 100644
index 0000000..4c22b71
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_sparse_mex.c
@@ -0,0 +1,58 @@
+#include "cs_mex.h"
+/* cs_sparse: convert triplet form into compress-column form sparse matrix */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: A = cs_sparse(i,j,x)") ;
+ }
+ if (mxIsComplex (pargin [2]))
+ {
+#ifndef NCOMPLEX
+ cs_cl *A, *C, *T, Tmatrix ;
+ T = &Tmatrix ; /* get i,j,x and copy to triplet form */
+ T->nz = mxGetM (pargin [0]) ;
+ T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ;
+ T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ;
+ cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ;
+ T->x = cs_cl_mex_get_double (T->nz, pargin [2]) ;
+ T->nzmax = T->nz ;
+ C = cs_cl_compress (T) ; /* create sparse matrix C */
+ cs_cl_dupl (C) ; /* remove duplicates from C */
+ cs_cl_dropzeros (C) ; /* remove zeros from C */
+ A = cs_cl_transpose (C, -1) ; /* A=C.' */
+ cs_cl_spfree (C) ;
+ pargout [0] = cs_cl_mex_put_sparse (&A) ; /* return A */
+ cs_free (T->p) ;
+ cs_free (T->i) ;
+ cs_free (T->x) ; /* free copy of complex values*/
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl *A, *C, *T, Tmatrix ;
+ T = &Tmatrix ; /* get i,j,x and copy to triplet form */
+ T->nz = mxGetM (pargin [0]) ;
+ T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ;
+ T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ;
+ cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ;
+ T->x = mxGetPr (pargin [2]) ;
+ T->nzmax = T->nz ;
+ C = cs_dl_compress (T) ; /* create sparse matrix C */
+ cs_dl_dupl (C) ; /* remove duplicates from C */
+ cs_dl_dropzeros (C) ; /* remove zeros from C */
+ A = cs_dl_transpose (C, 1) ; /* A=C' */
+ cs_dl_spfree (C) ;
+ pargout [0] = cs_dl_mex_put_sparse (&A) ; /* return A */
+ cs_free (T->p) ;
+ cs_free (T->i) ;
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_sqr.m b/CXSparse/MATLAB/CSparse/cs_sqr.m
new file mode 100644
index 0000000..cdb7d8c
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_sqr.m
@@ -0,0 +1,25 @@
+function [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr (A) %#ok
+%CS_SQR symbolic sparse QR factorization.
+% [vnz,rnz,parent,c,leftmost,p] = cs_sqr(A): symbolic QR of A(p,:).
+% [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A) computes the symbolic QR
+% factorization of A(p,q). The fill-reducing ordering q is found via
+% q = cs_amd(A,3).
+%
+% vnz is the number of entries in the matrix of Householder vectors, V.
+% rnz is the number of entries in R. parent is elimination tree.
+% c(i) is the number of entries in R(i,:). leftmost(i) = min(find(A(i,q))).
+% p is the row permutation used to ensure R has a symbolically zero-free
+% diagonal (it can be larger than m if A is structurally rank deficient).
+% q is the fill-reducing ordering, if requested.
+%
+% Example:
+% Prob = UFget ('HB/ibm32') ; A = Prob.A ;
+% [vnz, rnz, parent, c, leftmost, p, q] = cs_sqr (A) ;
+% cspy (A (p,q)) ;
+%
+% See also CS_AMD, CS_QR.
+%
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_sqr mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_sqr_mex.c b/CXSparse/MATLAB/CSparse/cs_sqr_mex.c
new file mode 100644
index 0000000..6c6f75f
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_sqr_mex.c
@@ -0,0 +1,40 @@
+#include "cs_mex.h"
+/* cs_sqr: symbolic sparse QR factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double s ;
+ cs_dls *S ;
+ cs_dl Amatrix, *A ;
+ CS_INT m, n, order, *p ;
+ if (nargout > 7 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A)") ;
+ }
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ m = A->m ;
+ n = A->n ;
+ if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ;
+ order = (nargout == 7) ? 3 : 0 ; /* determine ordering */
+ S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
+ if (!S) mexErrMsgTxt ("cs_sqr failed") ;
+ s = S->lnz ;
+ cs_dl_mex_put_double (1, &s, &(pargout [0])) ; /* return nnz(V) */
+ s = S->unz ;
+ cs_dl_mex_put_double (1, &s, &(pargout [1])) ; /* return nnz(R) */
+ pargout [2] = cs_dl_mex_put_int (S->parent, n, 1, 0) ; /* return parent */
+ pargout [3] = cs_dl_mex_put_int (S->cp, n, 0, 0) ; /* return c */
+ pargout [4] = cs_dl_mex_put_int (S->leftmost, m, 1, 0) ;/* return leftmost*/
+ p = cs_dl_pinv (S->pinv, S->m2) ; /* p = pinv' */
+ pargout [5] = cs_dl_mex_put_int (p, S->m2, 1, 1) ; /* return p */
+ if (nargout > 6)
+ {
+ pargout [6] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
+ }
+ cs_dl_sfree (S) ;
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_symperm.m b/CXSparse/MATLAB/CSparse/cs_symperm.m
new file mode 100644
index 0000000..a913553
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_symperm.m
@@ -0,0 +1,20 @@
+function C = cs_symperm (A,p) %#ok
+%CS_SYMPERM symmetric permutation of a symmetric matrix.
+% C = cs_symperm(A,p) computes C = A(p,p), but accesses only the
+% upper triangular part of A, and returns C upper triangular (A and C are
+% symmetric with just their upper triangular parts stored). A must be square.
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ;
+% p = cs_amd (A) ;
+% C = cs_symperm (A, p) ;
+% cspy (A (p,p)) ;
+% cspy (C) ;
+% C - triu (A (p,p))
+%
+% See also CS_PERMUTE, SUBSREF, TRIU.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_symperm mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_symperm_mex.c b/CXSparse/MATLAB/CSparse/cs_symperm_mex.c
new file mode 100644
index 0000000..d6c90b5
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_symperm_mex.c
@@ -0,0 +1,52 @@
+#include "cs_mex.h"
+/* cs_symperm: symmetric permutation of a symmetric sparse matrix. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT ignore, n, *P, *Pinv ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_symperm(A,p)") ;
+ }
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A, *C, *D ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ;
+ n = A->n ;
+ P = cs_dl_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */
+ Pinv = cs_cl_pinv (P, n) ; /* P=Pinv' */
+ C = cs_cl_symperm (A, Pinv, 1) ; /* C = A(p,p) */
+ D = cs_cl_transpose (C, 1) ; /* sort C */
+ cs_cl_spfree (C) ;
+ C = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+ cs_free (P) ;
+ cs_free (Pinv) ;
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A, *C, *D ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ;
+ n = A->n ;
+ P = cs_dl_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */
+ Pinv = cs_dl_pinv (P, n) ; /* P=Pinv' */
+ C = cs_dl_symperm (A, Pinv, 1) ; /* C = A(p,p) */
+ D = cs_dl_transpose (C, 1) ; /* sort C */
+ cs_dl_spfree (C) ;
+ C = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ cs_free (P) ;
+ cs_free (Pinv) ;
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_thumb_mex.c b/CXSparse/MATLAB/CSparse/cs_thumb_mex.c
new file mode 100644
index 0000000..f1ce68b
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_thumb_mex.c
@@ -0,0 +1,65 @@
+#include "cs_mex.h"
+/* cs_thumb: convert a sparse matrix to a dense 2D thumbnail matrix of size
+ * at most k-by-k. k defaults to 256. A helper mexFunction for cspy. */
+
+#define INDEX(i,j,lda) ((i)+(j)*(lda))
+#define ISNAN(x) ((x) != (x))
+#ifdef DBL_MAX
+#define BIG_VALUE DBL_MAX
+#else
+#define BIG_VALUE 1.7e308
+#endif
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT m, n, mn, m2, n2, k, s, j, ij, sj, si, p, *Ap, *Ai ;
+ double aij, ax, az, *S, *Ax, *Az ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: S = cs_thumb(A,k)") ;
+ }
+ cs_mex_check (0, -1, -1, 0, 1, 1, pargin [0]) ;
+ m = mxGetM (pargin [0]) ;
+ n = mxGetN (pargin [0]) ;
+ mn = CS_MAX (m,n) ;
+ k = (nargin == 1) ? 256 : mxGetScalar (pargin [1]) ; /* get k */
+ /* s = size of each submatrix; A(1:s,1:s) maps to S(1,1) */
+ s = (mn < k) ? 1 : (CS_INT) ceil ((double) mn / (double) k) ;
+ m2 = (CS_INT) ceil ((double) m / (double) s) ;
+ n2 = (CS_INT) ceil ((double) n / (double) s) ;
+ /* create S */
+ pargout [0] = mxCreateDoubleMatrix (m2, n2, mxREAL) ;
+ S = mxGetPr (pargout [0]) ;
+ Ap = (CS_INT *) mxGetJc (pargin [0]) ;
+ Ai = (CS_INT *) mxGetIr (pargin [0]) ;
+ Ax = mxGetPr (pargin [0]) ;
+ Az = (mxIsComplex (pargin [0])) ? mxGetPi (pargin [0]) : NULL ;
+ for (j = 0 ; j < n ; j++)
+ {
+ sj = j/s ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ si = Ai [p] / s ;
+ ij = INDEX (si,sj,m2) ;
+ ax = Ax [p] ;
+ az = Az ? Az [p] : 0 ;
+ if (az == 0)
+ {
+ aij = fabs (ax) ;
+ }
+ else
+ {
+ aij = sqrt (ax*ax + az*az) ;
+ }
+ if (ISNAN (aij)) aij = BIG_VALUE ;
+ aij = CS_MIN (BIG_VALUE, aij) ;
+ S [ij] = CS_MAX (S [ij], aij) ;
+ }
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_transpose.m b/CXSparse/MATLAB/CSparse/cs_transpose.m
new file mode 100644
index 0000000..d94ae6c
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_transpose.m
@@ -0,0 +1,19 @@
+function C = cs_transpose (A) %#ok
+%CS_TRANSPOSE transpose a sparse matrix.
+% C = cs_transpose(A), computes C = A'
+% C = cs_transpose(A,-1) computes C=A.'
+% C = cs_transpose(A,1) computes C=A'
+%
+% Example:
+% Prob = UFget ('HB/ibm32') ; A = Prob.A ;
+% C = cs_transpose (A) ;
+% C-A'
+%
+% See also TRANSPOSE, CTRANSPOSE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_transpose mexFunction not found') ;
+
+
diff --git a/CXSparse/MATLAB/CSparse/cs_transpose_mex.c b/CXSparse/MATLAB/CSparse/cs_transpose_mex.c
new file mode 100644
index 0000000..c36803a
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_transpose_mex.c
@@ -0,0 +1,37 @@
+#include "cs_mex.h"
+/* C = cs_transpose (A), computes C=A', where A must be sparse.
+ C = cs_transpose (A,kind) computes C=A.' if kind <= 0, C=A' if kind > 0 */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT values ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_transpose(A,kind)") ;
+ }
+ values = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ;
+ values = (values <= 0) ? -1 : 1 ;
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A, *C ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ C = cs_cl_transpose (A, values) ; /* C = A' */
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A, *C ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ C = cs_dl_transpose (A, values) ; /* C = A' */
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_updown.m b/CXSparse/MATLAB/CSparse/cs_updown.m
new file mode 100644
index 0000000..f4fa3cc
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_updown.m
@@ -0,0 +1,26 @@
+function L = cs_updown (L, c, parent, sigma) %#ok
+%CS_UPDOWN rank-1 update/downdate of a sparse Cholesky factorization.
+% L = cs_updown(L,c,parent) computes the rank-1 update L = chol(L*L'+c*c')',
+% where parent is the elimination tree of L. c must be a sparse column
+% vector, and find(c) must be a subset of find(L(:,k)) where k = min(find(c)).
+% L = cs_updown(L,c,parent,'-') is the downdate L = chol(L*L'-c*c').
+% L = cs_updown(L,c,parent,'+') is the update L = chol(L*L'+c*c').
+% Updating/downdating is much faster than refactorizing the matrix with
+% cs_chol or chol. L must not have an entries dropped due to numerical
+% cancellation (use cs_chol(A,0)).
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ; n = size (A,1) ;
+% L = cs_chol (A,0) ;
+% parent = cs_etree (A) ;
+% c = sprand (L (:, floor(n/2))) ;
+% L1 = cs_updown (L, c, parent) ;
+% L2 = cs_chol (A + c*c', 0) ;
+% norm (L1-L2, 1)
+%
+% See also CS_ETREE, CS_CHOL, ETREE, CHOLUPDATE, CHOL.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_updown mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_updown_mex.c b/CXSparse/MATLAB/CSparse/cs_updown_mex.c
new file mode 100644
index 0000000..c42769b
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_updown_mex.c
@@ -0,0 +1,108 @@
+#include "cs_mex.h"
+/* cs_updown: sparse Cholesky update/downdate (rank-1 or multiple rank) */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT ignore, j, k, n, lnz, *parent, sigma = 1, cp [2], ok ;
+ char sigma_string [20] ;
+ if (nargout > 1 || nargin < 3 || nargin > 4)
+ {
+ mexErrMsgTxt ("Usage: L = cs_updown(L,C,parent,sigma)") ;
+ }
+ if (nargin > 3 && mxIsChar (pargin [3]))
+ {
+ mxGetString (pargin [3], sigma_string, 8) ;
+ sigma = (sigma_string [0] == '-') ? (-1) : 1 ;
+ }
+ n = mxGetN (pargin [0]) ;
+ parent = cs_dl_mex_get_int (n, pargin [2], &ignore, 0) ; /* get parent*/
+
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+
+#ifndef NCOMPLEX
+ cs_cl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
+ /* get input L, and copy MATLAB complex to C complex type */
+ Lin = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ;
+
+ /* make a copy of L (this can take more work than updating L itself) */
+ lnz = Lin->p [n] ;
+ L = cs_cl_spalloc (n, n, lnz, 0, 0) ;
+ for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
+ for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
+
+ /* complex values already copied into Lin->x, use shallow copy for L */
+ L->x = Lin->x ;
+
+ cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
+ C = cs_cl_mex_get_sparse (&Cmatrix, 0, pargin [1]) ;
+
+ /* do the update one column at a time */
+ Cvec = &Cvector ;
+ Cvec->m = n ;
+ Cvec->n = 1 ;
+ Cvec->p = cp ;
+ Cvec->nz = -1 ;
+ cp [0] = 0 ;
+ for (k = 0 ; k < C->n ; k++)
+ {
+ /* extract C(:,k) */
+ cp [1] = C->p [k+1] - C->p [k] ;
+ Cvec->nzmax = cp [1] ;
+ Cvec->i = C->i + C->p [k] ;
+ Cvec->x = C->x + C->p [k] ;
+ /* update/downdate */
+ ok = cs_cl_updown (L, sigma, Cvec, parent) ;
+ if (!ok) mexErrMsgTxt ("matrix is not positive definite") ;
+ }
+ /* return new L */
+ pargout [0] = cs_cl_mex_put_sparse (&L) ;
+
+ cs_free (C->x) ; /* free complex copy of C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+
+ }
+ else
+ {
+
+ cs_dl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
+ /* get input L */
+ Lin = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
+ /* make a copy of L (this can take more work than updating L itself) */
+ lnz = Lin->p [n] ;
+ L = cs_dl_spalloc (n, n, lnz, 1, 0) ;
+ for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
+ for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
+ for (k = 0 ; k < lnz ; k++) L->x [k] = Lin->x [k] ;
+ cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
+ C = cs_dl_mex_get_sparse (&Cmatrix, 0, 1, pargin [1]) ;
+
+ /* do the update one column at a time */
+ Cvec = &Cvector ;
+ Cvec->m = n ;
+ Cvec->n = 1 ;
+ Cvec->p = cp ;
+ Cvec->nz = -1 ;
+ cp [0] = 0 ;
+ for (k = 0 ; k < C->n ; k++)
+ {
+ /* extract C(:,k) */
+ cp [1] = C->p [k+1] - C->p [k] ;
+ Cvec->nzmax = cp [1] ;
+ Cvec->i = C->i + C->p [k] ;
+ Cvec->x = C->x + C->p [k] ;
+ /* update/downdate */
+ ok = cs_dl_updown (L, sigma, Cvec, parent) ;
+ if (!ok) mexErrMsgTxt ("matrix is not positive definite") ;
+ }
+ /* return new L */
+ pargout [0] = cs_dl_mex_put_sparse (&L) ;
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_usolve.m b/CXSparse/MATLAB/CSparse/cs_usolve.m
new file mode 100644
index 0000000..842dcfa
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_usolve.m
@@ -0,0 +1,21 @@
+function x = cs_usolve (U,b) %#ok
+%CS_USOLVE solve a sparse upper triangular system U*x=b.
+% x = cs_usolve(U,b) computes x = U\b, U must be lower triangular with a
+% zero-free diagonal. b must be a column vector. x is full if b is full.
+% If b is sparse, x is sparse but nonzero pattern of x is NOT sorted (it is
+% returned in topological order).
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size (A,1) ;
+% b = rand (n,1);
+% [L U p q] = cs_lu (A) ;
+% x = cs_usolve (U, cs_lsolve (L, b(p))) ; % x = U \ (L \ b(p)) ;
+% x (q) = x ;
+% norm (A*x-b)
+%
+% See also CS_LSOLVE, CS_LTSOLVE, CS_UTSOLVE, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_usolve mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_usolve_mex.c b/CXSparse/MATLAB/CSparse/cs_usolve_mex.c
new file mode 100644
index 0000000..b1bb32c
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_usolve_mex.c
@@ -0,0 +1,92 @@
+#include "cs_mex.h"
+/* cs_usolve: x=U\b. U must be sparse and upper triangular. b must be a
+ * full or sparse vector. x is full or sparse, depending on b.
+ *
+ * Time taken is O(flop count), which may be less than n if b is sparse,
+ * depending on U and b.
+ *
+ * This function works with MATLAB 7.2, but is not perfectly compatible with
+ * the requirements of a MATLAB mexFunction when b is sparse. X is returned
+ * as an unsorted sparse vector. Also, this mexFunction temporarily modifies
+ * its input, U, by modifying U->p (in the cs_dfs function) and then restoring
+ * it. This could be corrected by creating a copy of U->p
+ * (see cs_dmperm_mex.c), but this would take O(n) time, destroying the
+ * O(flop count) time complexity of this function.
+ *
+ * Note that b cannot be sparse complex. This function does not support
+ * sparse complex U and b because the sparse x=U\b only accesses part of the
+ * matrix U. Converting U from a MATLAB complex matrix to a CXSparse complex
+ * matrix requires all of U to be accessed, defeating the purpose of this
+ * function.
+ *
+ * U can be sparse complex, but in that case b must be full real or complex,
+ * not sparse.
+ */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT top, nz, p, *xi, n ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_usolve(U,b)") ;
+ }
+ if (mxIsSparse (pargin [1]))
+ {
+ cs_dl Umatrix, Bmatrix, *U, *B, *X ;
+ double *x ;
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+ mexErrMsgTxt ("sparse complex case not supported") ;
+ }
+ U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ;/* get U */
+ n = U->n ;
+ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b*/
+ cs_mex_check (0, n, 1, 0, 1, 1, pargin [1]) ;
+ xi = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* get workspace */
+ x = cs_dl_malloc (n, sizeof (double)) ;
+ top = cs_dl_spsolve (U, B, 0, xi, x, NULL, 0) ; /* x = U\b */
+ X = cs_dl_spalloc (n, 1, n-top, 1, 0) ; /* create sparse x*/
+ X->p [0] = 0 ;
+ nz = 0 ;
+ for (p = top ; p < n ; p++)
+ {
+ X->i [nz] = xi [p] ;
+ X->x [nz++] = x [xi [p]] ;
+ }
+ X->p [1] = nz ;
+ pargout [0] = cs_dl_mex_put_sparse (&X) ;
+ cs_free (x) ;
+ cs_free (xi) ;
+ }
+ else if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Umatrix, *U ;
+ cs_complex_t *x ;
+ U = cs_cl_mex_get_sparse (&Umatrix, 1, pargin [0]) ; /* get U */
+ n = U->n ;
+ x = cs_cl_mex_get_double (n, pargin [1]) ; /* x = b */
+ cs_cl_usolve (U, x) ; /* x = U\x */
+ cs_free (U->x) ;
+ pargout [0] = cs_cl_mex_put_double (n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Umatrix, *U ;
+ double *x, *b ;
+ U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */
+ n = U->n ;
+ b = cs_dl_mex_get_double (n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (n, b, &(pargout [0])) ; /* x = b */
+ cs_dl_usolve (U, x) ; /* x = U\x */
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cs_utsolve.m b/CXSparse/MATLAB/CSparse/cs_utsolve.m
new file mode 100644
index 0000000..05c8037
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_utsolve.m
@@ -0,0 +1,19 @@
+function x = cs_utsolve (U,b) %#ok
+%CS_UTSOLVE solve a sparse lower triangular system U'*x=b.
+% x = cs_utsolve(U,b) computes x = U'\b, U must be upper triangular with a
+% zero-free diagonal. b must be a full vector.
+%
+% Example:
+% Prob = UFget ('HB/arc130') ; A = Prob.A ; n = size (A,1) ;
+% b = rand (n,1);
+% [L U p q] = cs_lu (A) ;
+% x = cs_ltsolve (L, cs_utsolve (U, b(q))) ; % x = L' \ (U' \ b(q)) ;
+% x (p) = x ;
+% norm (A'*x-b)
+%
+% See also CS_LSOLVE, CS_LTSOLVE, CS_USOLVE, MLDIVIDE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_utsolve mexFunction not found') ;
diff --git a/CXSparse/MATLAB/CSparse/cs_utsolve_mex.c b/CXSparse/MATLAB/CSparse/cs_utsolve_mex.c
new file mode 100644
index 0000000..f4913bd
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cs_utsolve_mex.c
@@ -0,0 +1,38 @@
+#include "cs_mex.h"
+/* cs_utsolve: solve a lower triangular system U'*x=b */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_utsolve(U,b)") ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Umatrix, *U ;
+ cs_complex_t *x ;
+ U = cs_cl_mex_get_sparse (&Umatrix, 1, pargin [0]) ; /* get U */
+ x = cs_cl_mex_get_double (U->n, pargin [1]) ; /* x = b */
+ cs_cl_utsolve (U, x) ; /* x = U'\x */
+ cs_free (U->x) ;
+ pargout [0] = cs_cl_mex_put_double (U->n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Umatrix, *U ;
+ double *x, *b ;
+ U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */
+ b = cs_dl_mex_get_double (U->n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (U->n, b, &(pargout [0])) ; /* x = b */
+ cs_dl_utsolve (U, x) ; /* x = U'\x */
+ }
+}
diff --git a/CXSparse/MATLAB/CSparse/cspy.m b/CXSparse/MATLAB/CSparse/cspy.m
new file mode 100644
index 0000000..a86f01c
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/cspy.m
@@ -0,0 +1,100 @@
+function [s,M,H] = cspy (A,res)
+%CSPY plot a matrix in color.
+% cspy(A) plots a matrix, in color, with a default resolution of
+% 256-by-256. cspy(A,res) changes the resolution to res. Zero entries are
+% white. Entries with tiny absolute value are light orange. Entries with
+% large magnitude are black. Entries in the midrange (the median of the
+% log10 of the nonzero values, +/- one standard deviation) range from light
+% green to deep blue. With no inputs, the color legend of cspy is plotted.
+% [s,M,H] = cspy(A) returns the scale factor s, the image M, and colormap H.
+%
+% The matrix A can be full or sparse, and either numeric (double, single,
+% integer) or character type, and either complex or real.
+%
+% Example
+% A = delsq (numgrid ('L', 10)) ;
+% cspy (A) ;
+%
+% See also CS_DMSPY, SPY.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if nargin < 2
+ res = 256 ;
+end
+
+h = jet (64) ;
+h = h (64:-1:1,:) ;
+h = h (30:end,:) ;
+hmax = size (h,1) ;
+
+h (1,:) = [1 1 1] ; % white for zero
+h (2,:) = [1 .9 .5] ; % light orange for tiny entries
+h (hmax,:) = [0 0 0] ; % black for very large entries
+colormap (h) ;
+
+if (nargin == 0)
+ image (1:hmax) ;
+ title ('cspy color map') ;
+ return
+end
+
+% convert complex, integers, and strings to real double
+if (~isreal (A) | ~isa (A, 'double') | ~issparse (A)) %#ok
+ A = sparse (abs (double (A))) ;
+end
+
+[m1 n1] = size (A) ;
+if (m1 == 0 | n1 == 0) %#ok
+ A (1,1) = 0 ;
+end
+[m1 n1] = size (A) ;
+
+S = cs_thumb (A,res) ; % get the thumbnail of the matrix
+[m n] = size (S) ;
+[i j x] = find (S) ;
+x = log10 (x) ;
+
+if (isempty (x))
+ S = zeros (size (S)) ;
+else
+ med = median (x) ;
+ sdev = std (x) ;
+ big = med + sdev ;
+ tiny = med - sdev ;
+ imid = find (x > tiny & x < big) ;
+ itiny = find (x <= tiny) ;
+ ibig = find (x >= big) ;
+ x (imid) = 1 + ceil ((hmax-2) * (x (imid) - tiny) / (big - tiny)) ;
+ x (itiny) = 1 ; %#ok
+ x (ibig) = hmax-1 ; %#ok
+ S = full (1 + sparse (i,j,x,m,n)) ;
+
+% title (sprintf ('tiny: %-8.2g median: %-8.2g big: %-8.2g\n', ...
+% 10^tiny, 10^med, 10^big)) ;
+end
+
+% draw the matrix
+image (S) ;
+axis equal ;
+axis ([-1 n+1 -1 m+1]) ;
+axis off
+
+% draw a box around the whole matrix
+e = ceil (max (m1,n1) / max (m,n)) ; % scale factor
+hold on
+drawbox (1,m1+1,1,n1+1,'k',1,e) ;
+hold off
+
+% return results
+if (nargout > 0)
+ s = e ;
+end
+if (nargout > 1)
+ M = S ; % image
+end
+if (nargout > 2)
+ H = h ; % colormap
+end
+
diff --git a/CXSparse/MATLAB/CSparse/private/cs_make_helper.m b/CXSparse/MATLAB/CSparse/private/cs_make_helper.m
new file mode 100644
index 0000000..99a9c35
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/private/cs_make_helper.m
@@ -0,0 +1,200 @@
+function [objfiles, timestamp_out] = cs_make_helper (f, docomplex)
+%CS_MAKE_HELPER compiles CXSparse for use in MATLAB.
+% Usage:
+% [objfiles, timestamp] = cs_make (f, docomplex)
+%
+% With f=0, only those files needing to be
+% compiled are compiled (like the Unix/Linux/GNU "make" command, but not
+% requiring "make"). If f is a nonzero number, all files are compiled.
+% If f is a string, only that mexFunction is compiled. For example,
+% cs_make ('cs_add') just compiles the cs_add mexFunction. This option is
+% useful when developing a single new mexFunction. This function can only be
+% used if the current directory is CXSparse/MATLAB/CSparse. Returns a list of
+% the object files in CXSparse, and the latest modification time of any source
+% codes.
+%
+% NOTE: if your compiler does not support the ANSI C99 complex type, the
+% CXSparse mexFunctions will not support complex sparse matrices.
+%
+% To add a new function and its MATLAB mexFunction to CXSparse:
+%
+% (1) Create a source code file CXSparse/Source/cs_mynewfunc.c.
+% (2) Create a help file, CXSparse/MATLAB/CSparse/cs_mynewfunc.m.
+% This is very useful, but not strictly required.
+% (3) Add the prototype of cs_mynewfunc to CXSparse/Include/cs.h.
+% (4) Create its MATLAB mexFunction, CXSparse/MATLAB/cs_mynewfunc_mex.c.
+% (5) Edit cs_make.m, and add 'cs_mynewfunc' to the 'cs' and 'csm' lists.
+% (6) Type 'cs_make' in the CXSparse/MATLAB/CSparse directory.
+% If all goes well, your new function is ready for use in MATLAB.
+%
+% (7) Optionally add 'cs_mynewfunc' to CXSparse/Source/Makefile
+% and CXSparse/MATLAB/CSparse/Makefile, if you want to use the
+% Unix/Linux/GNU make command instead of cs_make.m. See where
+% 'cs_add' and 'cs_add_mex' appear in those files, and add
+% 'cs_mynewfunc' accordingly.
+% (8) Optionally add 'cs_mynewfunc' to Tcov/Makefile, and add additional
+% test code to cs_test.c, and add MATLAB test code to MATLAB/Test/*.
+%
+% Example:
+% cs_make_helper (1,1) ; % compile everything
+% cs_make ('cs_chol', 1) ; % just compile cs_chol mexFunction
+%
+% See also MEX.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+mexcmd = 'mex -DCS_LONG -I../../../UFconfig' ;
+if (~isempty (strfind (computer, '64')))
+ mexcmd = [mexcmd ' -largeArrayDims'] ;
+end
+
+if (nargin < 2)
+ docomplex = 1 ;
+end
+
+if (~docomplex)
+ mexcmd = [mexcmd ' -DNCOMPLEX'] ;
+end
+
+% CSparse source files, in ../../Source, such as ../../Source/cs_add.c.
+% Note that not all CSparse source files have their own mexFunction.
+cs = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ...
+ 'cs_cumsum', 'cs_dfs', 'cs_dmperm', 'cs_droptol', 'cs_dropzeros', ...
+ 'cs_dupl', 'cs_entry', 'cs_etree', 'cs_fkeep', 'cs_gaxpy', 'cs_happly', ...
+ 'cs_house', 'cs_ipvec', 'cs_load', 'cs_lsolve', 'cs_ltsolve', 'cs_lu', ...
+ 'cs_lusol', 'cs_malloc', 'cs_maxtrans', 'cs_multiply', 'cs_norm', ...
+ 'cs_permute', 'cs_pinv', 'cs_post', 'cs_print', 'cs_pvec', 'cs_qr', ...
+ 'cs_qrsol', 'cs_scatter', 'cs_scc', 'cs_schol', 'cs_sqr', 'cs_symperm', ...
+ 'cs_tdfs', 'cs_transpose', 'cs_compress', 'cs_updown', 'cs_usolve', ...
+ 'cs_utsolve', 'cs_util', 'cs_reach', 'cs_spsolve', 'cs_ereach', ...
+ 'cs_leaf', 'cs_randperm' } ;
+ % add cs_mynewfunc to the above list
+
+details = 1 ;
+kk = 0 ;
+csm = { } ;
+if (nargin == 0)
+ force = 0 ;
+elseif (ischar (f))
+ fprintf ('cs_make: compiling ../../Source files and %s_mex.c\n', f) ;
+ force = 0 ;
+ csm = {f} ;
+else
+ force = f ;
+ details = details | (force > 1) ; %#ok
+ if (force & details) %#ok
+ fprintf ('cs_make: re-compiling everything\n') ;
+ end
+end
+
+if (isempty (csm))
+ % mexFunctions, of the form cs_add_mex.c, etc, in this directory
+ csm = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ...
+ 'cs_dmperm', 'cs_droptol', 'cs_etree', 'cs_gaxpy', 'cs_lsolve', ...
+ 'cs_ltsolve', 'cs_lu', 'cs_lusol', 'cs_multiply', 'cs_permute', ...
+ 'cs_print', 'cs_qr', 'cs_qrsol', 'cs_scc', 'cs_symperm', 'cs_thumb', ...
+ 'cs_transpose', 'cs_sparse', 'cs_updown', 'cs_usolve', ...
+ 'cs_utsolve', 'cs_randperm', 'cs_sqr' } ;
+ % add cs_mynewfunc to the above list
+end
+
+
+try
+ % ispc does not appear in MATLAB 5.3
+ pc = ispc ;
+catch
+ % if ispc fails, assume we are on a Windows PC if it's not unix
+ pc = ~isunix ;
+end
+
+if (pc)
+ obj = '.obj' ;
+else
+ obj = '.o' ;
+end
+
+srcdir = '../../Source/' ;
+hfile = '../../Include/cs.h' ;
+
+% compile each CSparse source file
+[anysrc timestamp kk] = compile_source ('', 'cs_mex', obj, hfile, force, ...
+ mexcmd, kk, details) ;
+CS = ['cs_mex' obj] ;
+if (nargout > 0)
+ objfiles = ['..' filesep 'CSparse' filesep 'cs_mex' obj] ;
+end
+for i = 1:length (cs)
+
+ [s t kk] = compile_source (srcdir, cs{i}, obj, hfile, force, mexcmd, ...
+ kk, details) ;
+ timestamp = max (timestamp, t) ;
+ anysrc = anysrc | s ; %#ok
+ CS = [CS ' ' cs{i} obj] ; %#ok
+ if (nargout > 0)
+ objfiles = [objfiles ' ..' filesep 'CSparse' filesep cs{i} obj] ; %#ok
+ end
+
+ % complex version:
+ if (docomplex)
+ csrc = cs {i} ;
+ csrc = [ 'cs_cl_' csrc(4:end) ] ;
+ CS = [CS ' ' csrc obj] ; %#ok
+ if (nargout > 0)
+ objfiles = [objfiles ' ..' filesep 'CSparse' filesep csrc obj] ;%#ok
+ end
+ if (s)
+ copyfile (['../../Source/' cs{i} '.c'], [csrc '.c'], 'f') ;
+ if (details)
+ fprintf ('%s\n', ['cp -f ../../Source/' cs{i} '.c ' csrc '.c']);
+ end
+ cmd = sprintf ('%s -DCS_COMPLEX -O -c -I../../Include %s.c\n', ...
+ mexcmd, csrc) ;
+ kk = do_cmd (cmd, kk, details) ;
+ end
+ end
+
+end
+
+% compile each CSparse mexFunction
+obj = ['.' mexext] ;
+for i = 1:length (csm)
+ [s t] = cs_must_compile ('', csm{i}, '_mex', obj, hfile, force) ;
+ timestamp = max (timestamp, t) ;
+ if (anysrc | s) %#ok
+ cmd = sprintf ('%s -O -I../../Include %s_mex.c %s -output %s\n', ...
+ mexcmd, csm{i}, CS, csm{i}) ;
+ kk = do_cmd (cmd, kk, details) ;
+ end
+end
+
+if (nargout > 1)
+ timestamp_out = timestamp ;
+end
+
+fprintf ('\n') ;
+
+%-------------------------------------------------------------------------------
+function [s,t,kk] = compile_source (srcdir, f, obj, hfile, force, mexcmd, ...
+ kk, details)
+% compile a source code file in ../../Source, leaving object file in
+% this directory.
+[s t] = cs_must_compile (srcdir, f, '', obj, hfile, force) ;
+if (s)
+ cmd = sprintf ('%s -O -c -I../../Include %s%s.c\n', mexcmd, srcdir, f) ;
+ kk = do_cmd (cmd, kk, details) ;
+end
+
+%-------------------------------------------------------------------------------
+function kk = do_cmd (s, kk, details)
+%DO_CMD: evaluate a command, and either print it or print a "."
+if (details)
+ fprintf ('%s', s) ;
+else
+ if (mod (kk, 60) == 0)
+ fprintf ('\n') ;
+ end
+ kk = kk + 1 ;
+ fprintf ('.') ;
+end
+eval (s) ;
diff --git a/CXSparse/MATLAB/CSparse/private/drawbox.m b/CXSparse/MATLAB/CSparse/private/drawbox.m
new file mode 100644
index 0000000..d46d5d7
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/private/drawbox.m
@@ -0,0 +1,29 @@
+function drawbox (r1,r2,c1,c2,color,w,e)
+%DRAWBOX draw a box around a submatrix in the figure.
+% Used by cspy, cs_dmspy, and ccspy.
+% Example:
+% drawbox (r1,r2,c1,c2,color,w,e)
+% See also drawboxes, plot
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (r1 == r2 | c1 == c2) %#ok
+ return
+end
+
+if (e == 1)
+ r1 = r1 - .5 ;
+ r2 = r2 - .5 ;
+ c1 = c1 - .5 ;
+ c2 = c2 - .5 ;
+else
+ r1 = ceil (r1 / e) - .5 ;
+ r2 = ceil ((r2 - 1) / e) + .5 ;
+ c1 = ceil (c1 / e) - .5 ;
+ c2 = ceil ((c2 - 1) / e) + .5 ;
+end
+
+if (c2 > c1 | r2 > r1) %#ok
+ plot ([c1 c2 c2 c1 c1], [r1 r1 r2 r2 r1], color, 'LineWidth', w) ;
+end
diff --git a/CXSparse/MATLAB/CSparse/private/drawboxes.m b/CXSparse/MATLAB/CSparse/private/drawboxes.m
new file mode 100644
index 0000000..86e3bb5
--- /dev/null
+++ b/CXSparse/MATLAB/CSparse/private/drawboxes.m
@@ -0,0 +1,29 @@
+function drawboxes (nb, e, r, s)
+%DRAWBOXES: helper function for cs_dmpsy and ccspy
+% Example:
+% drawboxes (nb, e, r, s)
+% See also drawbox, plot
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nb > 1)
+ if (e == 1)
+ r1 = r (1:nb) - .5 ;
+ r2 = r (2:nb+1) - .5 ;
+ c1 = s (1:nb) - .5 ;
+ c2 = s (2:nb+1) - .5 ;
+ else
+ r1 = ceil (r (1:nb) / e) - .5 ;
+ r2 = ceil ((r (2:nb+1) - 1) / e) + .5 ;
+ c1 = ceil (s (1:nb) / e) - .5 ;
+ c2 = ceil ((s (2:nb+1) - 1) / e) + .5 ;
+ end
+ kk = find (diff (c1) > 0 | diff (c2) > 0 | diff (r1) > 0 | diff (r2) > 0) ;
+ kk = [1 kk+1] ;
+ for k = kk
+ plot ([c1(k) c2(k) c2(k) c1(k) c1(k)], ...
+ [r1(k) r1(k) r2(k) r2(k) r1(k)], 'k', 'LineWidth', 1) ;
+ end
+end
+
diff --git a/CXSparse/MATLAB/Demo/Contents.m b/CXSparse/MATLAB/Demo/Contents.m
new file mode 100644
index 0000000..b8398dc
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/Contents.m
@@ -0,0 +1,11 @@
+% CXSparse MATLAB demos.
+%
+% cs_demo - run all CXSparse demos.
+% cs_demo1 - MATLAB version of the CSparse/Demo/cs_demo1.c program.
+% cs_demo2 - MATLAB version of the CSparse/Demo/cs_demo2.c program.
+% cs_demo3 - MATLAB version of the CSparse/Demo/cs_demo3.c program.
+
+% Example:
+% help cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis
diff --git a/CXSparse/MATLAB/Demo/README.txt b/CXSparse/MATLAB/Demo/README.txt
new file mode 100644
index 0000000..36b4e08
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/README.txt
@@ -0,0 +1 @@
+Demo for MATLAB interface for CXSparse. See Contents.m for details.
diff --git a/CXSparse/MATLAB/Demo/cs_demo.m b/CXSparse/MATLAB/Demo/cs_demo.m
new file mode 100644
index 0000000..d01135d
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/cs_demo.m
@@ -0,0 +1,47 @@
+function cs_demo (do_pause, matrixpath)
+%CS_DEMO run all CXSparse demos.
+% cs_demo(0) will run all demos without pausing.
+%
+% Example:
+% cs_demo
+% See also: cs_demo1, cs_demo2, cs_demo3
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+help cs_demo
+if (nargin < 1)
+ do_pause = 1 ;
+end
+if (nargin < 2)
+ matrixpath = [] ;
+end
+
+figure (1)
+clf
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help cs_demo1 ;
+cs_demo1 (matrixpath) ;
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help cs_demo2
+cs_demo2 (do_pause, matrixpath) ;
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help cs_demo3
+cs_demo3 (do_pause, matrixpath) ;
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help ex_1
+ex_1
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help ex2
+ex2
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help ex3
+ex3
+
+fprintf ('\nAll CXSparse demos finished.\n') ;
diff --git a/CXSparse/MATLAB/Demo/cs_demo1.m b/CXSparse/MATLAB/Demo/cs_demo1.m
new file mode 100644
index 0000000..cd023cd
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/cs_demo1.m
@@ -0,0 +1,56 @@
+function cs_demo1 (matrixpath)
+%CS_DEMO1 MATLAB version of the CSparse/Demo/cs_demo1.c program.
+% Uses both MATLAB functions and CSparse mexFunctions, and compares the two
+% results. This demo also plots the results, which the C version does not do.
+%
+% Example:
+% cs_demo1
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 1)
+ matrixpath = [] ;
+end
+
+if (isempty (matrixpath))
+ try
+ % older versions of MATLAB do not have an input argument to mfilename
+ p = mfilename ('fullpath') ;
+ t = strfind (p, filesep) ;
+ matrixpath = [ p(1:t(end)) '../../Matrix' ] ;
+ catch
+ % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory
+ matrixpath = '../../Matrix' ;
+ end
+end
+
+t1 = load ([matrixpath '/t1']) ;
+
+T = t1 %#ok
+A = sparse (T(:,1)+1, T(:,2)+1, T(:,3)) %#ok
+A2 = cs_sparse (T(:,1)+1, T(:,2)+1, T(:,3)) %#ok
+fprintf ('A difference: %g\n', norm (A-A2,1)) ;
+% CSparse/Demo/cs_demo1.c also clears the triplet matrix T at this point:
+% clear T
+clf
+subplot (2,2,1) ; cspy (A) ; title ('A', 'FontSize', 16) ;
+AT = A' %#ok
+AT2 = cs_transpose (A) %#ok
+fprintf ('AT difference: %g\n', norm (AT-AT2,1)) ;
+subplot (2,2,2) ; cspy (AT) ; title ('A''', 'FontSize', 16) ;
+n = size (A,2) ;
+I = speye (n) ;
+C = A*AT ;
+C2 = cs_multiply (A, AT) %#ok
+fprintf ('C difference: %g\n', norm (C-C2,1)) ;
+subplot (2,2,3) ; cspy (C) ; title ('C=A*A''', 'FontSize', 16) ;
+cnorm = norm (C,1) ;
+D = C + I*cnorm %#ok
+D2 = cs_add (C, I, 1, cnorm) %#ok
+fprintf ('D difference: %g\n', norm (D-D2,1)) ;
+subplot (2,2,4) ; cspy (D) ; title ('D=C+I*norm(C,1)', 'FontSize', 16) ;
+% CSparse/Demo/cs_demo1.c clears all matrices at this point:
+% clear A AT C D I
+% clear A2 AT2 C2 D2
diff --git a/CXSparse/MATLAB/Demo/cs_demo2.m b/CXSparse/MATLAB/Demo/cs_demo2.m
new file mode 100644
index 0000000..98486fa
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/cs_demo2.m
@@ -0,0 +1,42 @@
+function cs_demo2 (do_pause, matrixpath)
+%CS_DEMO2 MATLAB version of the CSparse/Demo/cs_demo2.c program.
+% Solves a linear system using Cholesky, LU, and QR, with various orderings.
+%
+% Example:
+% cs_demo2
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 2)
+ matrixpath = [] ;
+end
+
+if (isempty (matrixpath))
+ try
+ % older versions of MATLAB do not have an input argument to mfilename
+ p = mfilename ('fullpath') ;
+ t = strfind (p, filesep) ;
+ matrixpath = [ p(1:t(end)) '../../Matrix' ] ;
+ catch
+ % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory
+ matrixpath = '../../Matrix' ;
+ end
+end
+
+matrices = { 't1', 'HB/fs_183_1', 'HB/west0067', 'LPnetlib/lp_afiro', ...
+'HB/ash219', 'HB/mbeacxc', 'HB/bcsstk01', 'HB/bcsstk16' } ;
+
+if (nargin < 1)
+ do_pause = 1 ;
+end
+
+for i = 1:length(matrices)
+ name = matrices {i} ;
+ [C sym] = get_problem (matrixpath, name, 1e-14) ;
+ demo2 (C, sym, name) ;
+ if (do_pause)
+ input ('Hit enter to continue: ') ;
+ end
+end
diff --git a/CXSparse/MATLAB/Demo/cs_demo3.m b/CXSparse/MATLAB/Demo/cs_demo3.m
new file mode 100644
index 0000000..2527884
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/cs_demo3.m
@@ -0,0 +1,41 @@
+function cs_demo3 (do_pause, matrixpath)
+%CS_DEMO3 MATLAB version of the CSparse/Demo/cs_demo3.c program.
+% Cholesky update/downdate.
+%
+% Example:
+% cs_demo3
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 2)
+ matrixpath = [] ;
+end
+
+if (isempty (matrixpath))
+ try
+ % older versions of MATLAB do not have an input argument to mfilename
+ p = mfilename ('fullpath') ;
+ t = strfind (p, filesep) ;
+ matrixpath = [ p(1:t(end)) '../../Matrix' ] ;
+ catch
+ % assume we are in the C*Sparse/MATLAB/CSparse/Demo directory
+ matrixpath = '../../Matrix' ;
+ end
+end
+
+matrices = { 'HB/bcsstk01', 'HB/bcsstk16' } ;
+
+if (nargin < 1)
+ do_pause = 1 ;
+end
+
+for i = 1:length(matrices)
+ name = matrices {i} ;
+ [C sym] = get_problem (matrixpath, name, 1e-14) ;
+ demo3 (C, sym, name) ;
+ if (do_pause)
+ input ('Hit enter to continue: ') ;
+ end
+end
diff --git a/CXSparse/MATLAB/Demo/private/demo2.m b/CXSparse/MATLAB/Demo/private/demo2.m
new file mode 100644
index 0000000..5b8e805
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/demo2.m
@@ -0,0 +1,109 @@
+function demo2 (C, sym, name)
+%DEMO2: solve a linear system using Cholesky, LU, and QR, with various orderings
+%
+% Example:
+% demo2 (C, 1, 'name of system')
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clf
+subplot (2,2,1) ; cspy (C) ;
+title (name, 'FontSize', 16, 'Interpreter', 'none') ;
+[m n] = size (C) ;
+[p,q,r,s,cc,rr] = cs_dmperm (C) ;
+subplot (2,2,3) ; cs_dmspy (C) ;
+subplot (2,2,2) ; ccspy (C) ;
+drawnow
+
+sprnk = rr (4) - 1 ;
+nb = length (r) - 1 ;
+ns = sum ((r (2:nb+1) == r (1:nb)+1) & (s (2:nb+1) == s (1:nb)+1)) ;
+fprintf ('blocks: %d singletons %d structural rank %d\n', nb, ns, sprnk) ;
+
+if (sprnk ~= sprank (C))
+ error ('sprank mismatch!') ;
+end
+
+if (sprnk < min (m,n))
+ return ; % return if structurally singular
+end
+
+
+% the following code is not in the C version of this demo:
+if (m == n)
+ if (sym)
+ try
+ [L,p] = cs_chol (C) ; %#ok
+ subplot (2,2,4) ;
+ cspy (L+triu(L',1)) ; title ('L+L''') ;
+ catch
+ % tol = 0.001 ;
+ [L,U,p,q] = cs_lu (C,0.001) ; %#ok
+ subplot (2,2,4) ;
+ cspy (L+U-speye(n)) ; title ('L+U') ;
+ end
+ else
+ [L,U,p,q] = cs_lu (C) ; %#ok
+ subplot (2,2,4) ;
+ cspy (L+U-speye(n)) ; title ('L+U') ;
+ end
+else
+ if (m < n)
+ [V,beta,p,R,q] = cs_qr (C') ; %#ok
+ else
+ [V,beta,p,R,q] = cs_qr (C) ; %#ok
+ end
+ subplot (2,2,4) ;
+ cspy (V+R) ; title ('V+R') ;
+end
+drawnow
+
+% continue with the MATLAB equivalent of the C cs_demo2 program
+for order = [0 3]
+ if (order == 0 & m > 1000) %#ok
+ continue ;
+ end
+ fprintf ('QR ') ;
+ print_order (order) ;
+ b = rhs (m) ; % compute right-hand-side
+ tic ;
+ x = cs_qrsol (C, b, order) ;
+ fprintf ('time %8.2f ', toc) ;
+ print_resid (C, x, b) ;
+end
+
+if (m ~= n)
+ return ;
+end
+
+for order = 0:3
+ if (order == 0 & m > 1000) %#ok
+ continue ;
+ end
+ fprintf ('LU ') ;
+ print_order (order) ;
+ b = rhs (m) ; % compute right-hand-side
+ tic ;
+ x = cs_lusol (C, b, order) ;
+ fprintf ('time %8.2f ', toc) ;
+ print_resid (C, x, b) ;
+end
+
+if (sym == 0)
+ return ;
+end
+
+for order = 0:1
+ if (order == 0 & m > 1000) %#ok
+ continue ;
+ end
+ fprintf ('Chol ') ;
+ print_order (order) ;
+ b = rhs (m) ; % compute right-hand-side
+ tic ;
+ x = cs_cholsol (C, b, order) ;
+ fprintf ('time %8.2f ', toc) ;
+ print_resid (C, x, b) ;
+end
diff --git a/CXSparse/MATLAB/Demo/private/demo3.m b/CXSparse/MATLAB/Demo/private/demo3.m
new file mode 100644
index 0000000..3d627f8
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/demo3.m
@@ -0,0 +1,97 @@
+function demo3 (C, sym, name)
+%DEMO3: Cholesky update/downdate
+%
+% Example:
+% demo3 (C, 1, 'name of system')
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clf
+subplot (2,2,1) ; cspy (C) ;
+title (name, 'FontSize', 16, 'Interpreter', 'none') ;
+drawnow
+
+[m n] = size (C) ;
+if (m ~= n | ~sym) %#ok
+ return ;
+end
+
+b = rhs (n) ;
+fprintf ('chol then update/downdate ') ;
+print_order (0) ;
+
+tic ;
+[L,p] = cs_chol (C) ;
+t = toc ;
+fprintf ('\nchol time: %8.2f\n', t) ;
+
+subplot (2,2,2) ; cspy (L) ; title ('L') ;
+drawnow
+
+tic ;
+x = b (p) ;
+x = cs_lsolve (L,x) ;
+x = cs_ltsolve (L,x) ;
+x (p) = x ;
+t = toc ;
+fprintf ('solve time: %8.2f\n', t) ;
+
+fprintf ('original: ') ;
+print_resid (C, x, b) ;
+
+k = fix (n/2) ;
+w = L(k,k) * sprand (L (:,k)) ;
+
+parent = cs_etree (C (p,p)) ;
+
+tic ;
+L2 = cs_updown (L, w, parent, '+') ;
+t1 = toc ;
+fprintf ('update: time: %8.2f\n', t1) ;
+
+subplot (2,2,3) ; cspy (L2) ; title ('updated L') ;
+subplot (2,2,4) ; cspy (L-L2) ; title ('L - updated L') ;
+drawnow
+
+tic ;
+x = b (p) ;
+x = cs_lsolve (L2,x) ;
+x = cs_ltsolve (L2,x) ;
+x (p) = x ;
+t = toc ;
+
+w2 = sparse (n,1) ;
+w2 (p) = w ; % w2 = P'*w
+wt = cs_transpose (w2) ;
+ww = cs_multiply (w2,wt) ;
+E = cs_add (C, ww, 1, 1) ; % E = C + w2*w2' ;
+
+fprintf ('update: time: %8.2f (incl solve) ', t1+t) ;
+print_resid (E, x, b) ;
+
+tic
+[L,p2] = cs_chol (E) ;
+x = b (p2) ;
+x = cs_lsolve (L,x) ;
+x = cs_ltsolve (L,x) ;
+x (p2) = x ;
+t = toc ;
+fprintf ('rechol: time: %8.2f (incl solve) ', t) ;
+print_resid (E, x, b) ;
+
+tic ;
+L3 = cs_updown (L2, w, parent, '-') ;
+t1 = toc ;
+fprintf ('downdate: time: %8.2f\n', t1) ;
+
+tic ;
+x = b (p) ;
+x = cs_lsolve (L3,x) ;
+x = cs_ltsolve (L3,x) ;
+x (p) = x ;
+t = toc ;
+fprintf ('downdate: time: %8.2f (incl solve) ', t1+t) ;
+print_resid (C, x, b) ;
diff --git a/CXSparse/MATLAB/Demo/private/ex2.m b/CXSparse/MATLAB/Demo/private/ex2.m
new file mode 100644
index 0000000..2b814c9
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/ex2.m
@@ -0,0 +1,91 @@
+function ex2 (n)
+%EX2: create an n-by-n 2D mesh, four different ways
+
+% Example:
+% ex2
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 1)
+ n = 30 ;
+end
+
+subplot (1,2,1) ;
+
+% method 1: create an n-by-n 2D mesh for the 2nd difference operator
+tic
+ii = zeros (5*n^2, 1) ;
+jj = zeros (5*n^2, 1) ;
+xx = zeros (5*n^2, 1) ;
+k = 1 ;
+for j = 0:n-1
+ for i = 0:n-1
+ s = j*n+i + 1 ;
+ ii (k:k+4) = [(j-1)*n+i j*n+(i-1) j*n+i j*n+(i+1) (j+1)*n+i ] + 1 ;
+ jj (k:k+4) = [s s s s s] ;
+ xx (k:k+4) = [-1 -1 4 -1 -1] ;
+ k = k + 5 ;
+ end
+end
+
+% remove entries beyond the boundary
+keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ;
+ii = ii (keep) ;
+jj = jj (keep) ;
+xx = xx (keep) ;
+A = sparse (ii,jj,xx) ;
+t1 = toc ; disp (t1) ;
+% subplot (2,2,1) ;
+spy (A)
+title (sprintf ('%d-by-%d 2D mesh\n', n, n)) ;
+
+% method 2, using no for loops
+tic
+nn = 1:n^2 ;
+i2 = [nn-n ; nn-1 ; nn ; nn+1 ; nn+n] ;
+j2 = repmat (nn, 5, 1) ;
+x2 = repmat ([-1 -1 4 -1 -1]', 1, n^2) ;
+keep = find (i2 >= 1 & i2 <= n^2 & j2 >= 1 & j2 <= n^2) ;
+i2 = i2 (keep) ;
+j2 = j2 (keep) ;
+x2 = x2 (keep) ;
+C = sparse (i2,j2,x2) ;
+t2 = toc ; disp (t2) ;
+
+% subplot (2,2,2) ; plot (j2) ;
+% title ('2D fast j2') ;
+disp (A-C) ;
+
+any (ii-i2)
+any (jj-jj)
+
+% method 3: create an n-by-n-by-n 3D mesh for the 2nd difference operator
+tic
+[A, keep, ii, jj, xx] = mesh3d1 (n) ;
+ii = ii (keep) ;
+jj = jj (keep) ;
+xx = xx (keep) ;
+t3 = toc ; disp (t3) ;
+tic
+E = sparse (ii,jj,xx) ;
+t3b = toc ; disp (t3b) ;
+subplot (1,2,2) ; spy (E) ;
+title (sprintf ('%d-by-%d-by-%d 3D mesh\n', n, n, n)) ;
+
+% method 4, using no for loops
+tic
+nn = 1:n^3 ;
+i2 = [nn-n^2 ; nn-n ; nn-1 ; nn ; nn+1 ; nn+n ; nn+n^2] ;
+j2 = repmat (nn, 7, 1) ;
+x2 = repmat ([-1 -1 -1 6 -1 -1 -1]', 1, n^3) ;
+keep = find (i2 >= 1 & i2 <= n^3 & j2 >= 1 & j2 <= n^3) ;
+i2 = i2 (keep) ;
+j2 = j2 (keep) ;
+x2 = x2 (keep) ;
+t4 = toc ; disp (t4) ;
+tic
+F = sparse (i2,j2,x2) ;
+t4b = toc ; disp (t4b) ;
+disp (E-F) ;
diff --git a/CXSparse/MATLAB/Demo/private/ex3.m b/CXSparse/MATLAB/Demo/private/ex3.m
new file mode 100644
index 0000000..b425900
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/ex3.m
@@ -0,0 +1,42 @@
+function ex3
+%EX3: create 2D and 3D meshes using mesh2d1, mesh2d2, mesh3d1, mesh3d2.
+
+% Example:
+% ex3
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+t1 = zeros (50,1) ;
+t2 = zeros (50,1) ;
+t3 = zeros (50,1) ;
+t4 = zeros (50,1) ;
+
+fprintf ('run times for each method, given n:\n') ;
+for n = 2:50
+
+ tic ;
+ A = mesh2d1 (n) ;
+ t1 (n) = toc ;
+
+ tic
+ B = mesh2d2 (n) ;
+ t2 (n) = toc ;
+
+ tic
+ C = mesh3d1 (n) ;
+ t3 (n) = toc ;
+
+ tic
+ D = mesh3d2 (n) ;
+ t4 (n) = toc ;
+
+ fprintf ('%3d: %8.3f %8.3f %8.3f %8.3f\n', n, t1(n), t2(n), t3(n), t4(n)) ;
+
+ subplot (2,2,1) ; spy (A) ; title ('2D mesh, method 1') ;
+ subplot (2,2,2) ; spy (B) ; title ('2D mesh, method 2') ;
+ subplot (2,2,3) ; spy (C) ; title ('3D mesh, method 1') ;
+ subplot (2,2,4) ; spy (D) ; title ('3D mesh, method 2') ;
+ drawnow
+end
diff --git a/CXSparse/MATLAB/Demo/private/ex_1.m b/CXSparse/MATLAB/Demo/private/ex_1.m
new file mode 100644
index 0000000..6a14818
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/ex_1.m
@@ -0,0 +1,86 @@
+function ex_1
+%EX_1: four methods for creating the same matrix.
+% (please wait, this can take a while...)
+
+% Example:
+% ex_1
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = 1000 ;
+nz = 1e5 ;
+
+tic
+% method 1: A(i,j) = ...
+rand ('state', 0) ;
+A = sparse (n,n) ;
+for k = 1:nz
+ % compute some arbitrary entry and add it into the matrix
+ i = 1 + fix (n * rand (1)) ;
+ j = 1 + fix (n * rand (1)) ;
+ x = rand (1) ;
+ A (i,j) = A (i,j) + x ; % VERY slow, esp. if A(i,j) not already nonzero!
+end
+fprintf ('Method 1: ') ;
+toc
+A1 = A ;
+
+tic
+% method 2: triplet form, one entry at a time
+rand ('state', 0) ;
+ii = zeros (nz, 1) ; % preallocate ii, jj, and xx
+jj = zeros (nz, 1) ;
+xx = zeros (nz, 1) ;
+for k = 1:nz
+ % compute some arbitrary entry and add it into the matrix
+ ii (k) = 1 + fix (n * rand (1)) ;
+ jj (k) = 1 + fix (n * rand (1)) ;
+ xx (k) = rand (1) ;
+end
+A = sparse (ii,jj,xx) ;
+fprintf ('Method 2: ') ;
+toc
+A2 = A ;
+disp (A1-A2) ;
+
+tic
+% method 3: triplet form, one entry at a time, pretend nz is unknown
+rand ('state', 0) ;
+len = 16 ;
+ii = zeros (len, 1) ;
+jj = zeros (len, 1) ;
+xx = zeros (len, 1) ;
+for k = 1:nz
+ % compute some arbitrary entry and add it into the matrix
+ if (k > len)
+ % double the size of ii,jj,xx
+ len = 2*len ;
+ ii (len) = 0 ;
+ jj (len) = 0 ;
+ xx (len) = 0 ;
+ end
+ ii (k) = 1 + fix (n * rand (1)) ;
+ jj (k) = 1 + fix (n * rand (1)) ;
+ xx (k) = rand (1) ;
+end
+A = sparse (ii (1:k), jj (1:k), xx (1:k)) ;
+fprintf ('Method 3: ') ;
+toc
+
+A3 = A ;
+disp (A1-A3) ;
+
+tic
+% method 4: avoid the for loop
+rand ('state', 0) ;
+e = rand (3, nz) ;
+e (1,:) = 1 + fix (n * e (1,:)) ;
+e (2,:) = 1 + fix (n * e (2,:)) ;
+A = sparse (e (1,:), e (2,:), e (3,:)) ;
+fprintf ('Method 4: ') ;
+toc
+
+A4 = A ;
+disp (A1-A4) ;
diff --git a/CXSparse/MATLAB/Demo/private/frand.m b/CXSparse/MATLAB/Demo/private/frand.m
new file mode 100644
index 0000000..4d3b16a
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/frand.m
@@ -0,0 +1,28 @@
+function A = frand (n,nel,s)
+% A = frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel finite
+% elements, each of which are of size s-by-s with random symmetric nonzero
+% pattern, plus the identity matrix.
+%
+% Example:
+% A = frand (100, 100, 4) ; cspy (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+ss = s^2 ;
+nz = nel*ss ;
+ii = zeros (nz,1) ;
+jj = zeros (nz,1) ;
+xx = zeros (nz,1) ;
+k = 1 ;
+for e = 1:nel
+ i = 1 + fix (n * rand (s,1)) ;
+ i = repmat (i, 1, s) ;
+ j = i' ;
+ x = rand (s,s) ;
+ ii (k:k+ss-1) = i (:) ;
+ jj (k:k+ss-1) = j (:) ;
+ xx (k:k+ss-1) = x (:) ;
+ k = k + ss ;
+end
+A = sparse (ii,jj,xx,n,n) + speye (n) ;
diff --git a/CXSparse/MATLAB/Demo/private/get_problem.m b/CXSparse/MATLAB/Demo/private/get_problem.m
new file mode 100644
index 0000000..a2dc3d6
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/get_problem.m
@@ -0,0 +1,57 @@
+function [C, sym] = get_problem (prefix, name, tol)
+% [C, sym] = get_problem(prefix, name,tol)
+% read a problem from a file, drop entries with abs value < tol
+% tol defaults to zero if not present
+%
+% Example:
+% [C, sym] = get_problem ('', 'west0067') ;
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('\n------------------- Matrix: %s\n', name) ;
+
+if (nargin < 2)
+ tol = 0 ;
+end
+
+s = find (name == '/') ;
+if (isempty (s))
+ s = 0 ;
+end
+% f = sprintf ('%s..%s..%sMatrix%s%s', ...
+% prefix, filesep, filesep, filesep, name (s+1:end)) ;
+
+% load the triplet version of the matrix
+T = load ([ prefix '/' name(s+1:end) ]) ;
+
+% convert into a sparse matrix and compare with cs_sparse
+A = sparse (T (:,1)+1, T (:,2)+1, T (:,3)) ;
+A2 = cs_sparse (T (:,1)+1, T (:,2)+1, T (:,3)) ;
+err = norm (A-A2,1) ;
+if (err > 0)
+ fprintf ('A difference: %g\n', err) ;
+end
+
+[m n] = size (A) ;
+nz2 = nnz (A) ;
+
+if (tol > 0)
+ A = cs_droptol (A, tol) ;
+end
+
+% assume A is symmetric if it is upper or lower triangular
+sym = is_sym (A) ;
+if (sym)
+ C = A + (A' - diag (diag (A))) ;
+else
+ C = A ;
+end
+
+fprintf ('--- Matrix: %d-by-%d, nnz: %d (sym: %d nnz %d), norm: %8.2e\n', ...
+ m, n, nnz(A), sym, abs(sym)*nnz(C), norm (C,1)) ;
+
+if (nz2 ~= nnz(A))
+ fprintf ('tiny entries dropped: %d\n', nz2 - nnz(A))
+end
diff --git a/CXSparse/MATLAB/Demo/private/is_sym.m b/CXSparse/MATLAB/Demo/private/is_sym.m
new file mode 100644
index 0000000..6a84215
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/is_sym.m
@@ -0,0 +1,23 @@
+function sym = is_sym (A)
+% sym = is_sym(A)
+% 1 if A is square and upper tri., -1 if square and lower tri., 0 otherwise
+%
+% Example:
+% sym = is_sym (A) ;
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+sym = 0 ;
+if (m == n)
+ is_upper = nnz (tril (A,-1)) == 0 ;
+ is_lower = nnz (triu (A,1)) == 0 ;
+ if (is_upper)
+ sym = 1 ;
+ elseif (is_lower)
+ sym = -1 ;
+ end
+end
+
diff --git a/CXSparse/MATLAB/Demo/private/mesh2d1.m b/CXSparse/MATLAB/Demo/private/mesh2d1.m
new file mode 100644
index 0000000..39ca45f
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/mesh2d1.m
@@ -0,0 +1,25 @@
+function A = mesh2d1 (n)
+% create an n-by-n 2D mesh for the 2nd difference operator
+% Example:
+% A = mesh2d1 (30) ; % a 30-by-30 mesh
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+ii = zeros (5*n^2, 1) ; % preallocate ii, jj, and xx
+jj = zeros (5*n^2, 1) ;
+xx = zeros (5*n^2, 1) ;
+k = 1 ;
+for j = 0:n-1
+ for i = 0:n-1
+ s = j*n+i + 1 ;
+ ii (k:k+4) = [(j-1)*n+i j*n+(i-1) j*n+i j*n+(i+1) (j+1)*n+i ] + 1 ;
+ jj (k:k+4) = [s s s s s] ;
+ xx (k:k+4) = [-1 -1 4 -1 -1] ;
+ k = k + 5 ;
+ end
+end
+% remove entries beyond the boundary
+keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ;
+A = sparse (ii (keep), jj (keep), xx (keep)) ;
diff --git a/CXSparse/MATLAB/Demo/private/mesh2d2.m b/CXSparse/MATLAB/Demo/private/mesh2d2.m
new file mode 100644
index 0000000..f3133bf
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/mesh2d2.m
@@ -0,0 +1,15 @@
+function A = mesh2d2 (n)
+% create an n-by-n 2D mesh for the 2nd difference operator
+% Example:
+% A = mesh2d2 (30) ; % a 30-by-30 mesh
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+nn = 1:n^2 ;
+ii = [nn-n ; nn-1 ; nn ; nn+1 ; nn+n] ;
+jj = repmat (nn, 5, 1) ;
+xx = repmat ([-1 -1 4 -1 -1]', 1, n^2) ;
+keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ;
+A = sparse (ii (keep), jj (keep), xx (keep)) ;
diff --git a/CXSparse/MATLAB/Demo/private/mesh3d1.m b/CXSparse/MATLAB/Demo/private/mesh3d1.m
new file mode 100644
index 0000000..2c431d9
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/mesh3d1.m
@@ -0,0 +1,33 @@
+function [A, keep, ii, jj, xx] = mesh3d1 (n)
+% create an n-by-n-by-n 3D mesh for the 2nd difference operator
+% Example:
+% A = mesh3d1 (10) ; % a 10-by-10-by-10 mesh
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+ii = zeros (7*n^3, 1) ;
+jj = zeros (7*n^3, 1) ;
+xx = zeros (7*n^3, 1) ;
+t = 1 ;
+for k = 0:n-1
+ for j = 0:n-1
+ for i = 0:n-1
+ s = k*n^2 + j*n+i + 1 ;
+ ii (t:t+6) = [
+ (k-1)*n^2 + j*n+i
+ k*n^2 + (j-1)*n+i
+ k*n^2 + j*n+(i-1)
+ k*n^2 + j*n+i
+ k*n^2 + j*n+(i+1)
+ k*n^2 + (j+1)*n+i
+ (k+1)*n^2 + j*n+i ]' + 1 ;
+ jj (t:t+6) = [s s s s s s s] ;
+ xx (t:t+6) = [-1 -1 -1 6 -1 -1 -1] ;
+ t = t + 7 ;
+ end
+ end
+end
+keep = find (ii >= 1 & ii <= n^3 & jj >= 1 & jj <= n^3) ;
+A = sparse (ii (keep), jj (keep), xx (keep)) ;
diff --git a/CXSparse/MATLAB/Demo/private/mesh3d2.m b/CXSparse/MATLAB/Demo/private/mesh3d2.m
new file mode 100644
index 0000000..4a644f3
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/mesh3d2.m
@@ -0,0 +1,15 @@
+function A = mesh3d2 (n)
+% create an n-by-n-by-n 3D mesh for the 2nd difference operator
+% Example:
+% A = mesh3d2 (10) ; % a 10-by-10-by-10 mesh
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+nn = 1:n^3 ;
+ii = [nn-n^2 ; nn-n ; nn-1 ; nn ; nn+1 ; nn+n ; nn+n^2] ;
+jj = repmat (nn, 7, 1) ;
+xx = repmat ([-1 -1 -1 6 -1 -1 -1]', 1, n^3) ;
+keep = find (ii >= 1 & ii <= n^3 & jj >= 1 & jj <= n^3) ;
+A = sparse (ii (keep), jj (keep), xx (keep)) ;
diff --git a/CXSparse/MATLAB/Demo/private/print_order.m b/CXSparse/MATLAB/Demo/private/print_order.m
new file mode 100644
index 0000000..4f65d4b
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/print_order.m
@@ -0,0 +1,21 @@
+function print_order (order)
+% print_order(order) prints the ordering determined by the order parameter
+% Example:
+% print_order (0)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+switch (fix (order))
+ case 0
+ fprintf ('natural ') ;
+ case 1
+ fprintf ('amd(A+A'') ') ;
+ case 2
+ fprintf ('amd(S''*S) ') ;
+ case 3
+ fprintf ('amd(A''*A) ') ;
+ otherwise
+ fprintf ('undefined ') ;
+end
diff --git a/CXSparse/MATLAB/Demo/private/print_resid.m b/CXSparse/MATLAB/Demo/private/print_resid.m
new file mode 100644
index 0000000..4b22047
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/print_resid.m
@@ -0,0 +1,12 @@
+function print_resid (A, x, b)
+% print_resid (A, x, b), print the relative residual,
+% norm (A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf))
+% Example:
+% print_resid (A, x, b) ;
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('resid: %8.2e\n', ...
+ norm (A*x-b,inf) / (norm(A,1)*norm(x,inf) + norm(b,inf))) ;
diff --git a/CXSparse/MATLAB/Demo/private/rhs.m b/CXSparse/MATLAB/Demo/private/rhs.m
new file mode 100644
index 0000000..f7bc531
--- /dev/null
+++ b/CXSparse/MATLAB/Demo/private/rhs.m
@@ -0,0 +1,10 @@
+function b = rhs (m)
+% b = rhs (m), compute a right-hand-side
+% Example:
+% b = rhs (30) ;
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+b = ones (m,1) + (0:m-1)'/m ;
diff --git a/CXSparse/MATLAB/Makefile b/CXSparse/MATLAB/Makefile
new file mode 100644
index 0000000..4636246
--- /dev/null
+++ b/CXSparse/MATLAB/Makefile
@@ -0,0 +1,14 @@
+all:
+ ( cd CSparse ; $(MAKE) )
+ ( cd Test ; $(MAKE) )
+
+clean:
+ ( cd CSparse ; $(MAKE) clean )
+ ( cd Test ; $(MAKE) clean )
+
+purge:
+ ( cd CSparse ; $(MAKE) purge )
+ ( cd Test ; $(MAKE) purge )
+
+distclean: purge
+
diff --git a/CXSparse/MATLAB/README.txt b/CXSparse/MATLAB/README.txt
new file mode 100644
index 0000000..8ece299
--- /dev/null
+++ b/CXSparse/MATLAB/README.txt
@@ -0,0 +1,24 @@
+CXSparse/MATLAB directory, which contains the MATLAB mexFunction interfaces
+for CXSparse, demos, and tests. It includes various "textbook" files
+that are printed in the book, but not a proper part of CSparse itself.
+It also includes "UFget", a MATLAB interface for the UF Sparse Matrix
+Collection.
+
+Type the command "cs_install" while in this directory. It will compile
+CSparse, and add the directories:
+
+ CXSparse/MATLAB/CSparse
+ CXSparse/MATLAB/Demo
+ CXSparse/MATLAB/UFget
+
+to your MATLAB path (see the "pathtool" command to add these to your path
+permanently, for future MATLAB sessions).
+
+To run the MATLAB demo programs, run cs_demo in the Demo directory.
+This demo will work whether or not your compiler supports the complex type.
+
+To run the MATLAB test programs, run testall in the Test directory.
+However, you may run the tests in the Test directory only if your compiler
+supports the ANSI C99 complex type. If it does not support the ANSI C99
+complex type, the tests in the Test directory will fail, since the codes there
+test both the real and complex cases in CXSparse.
diff --git a/CXSparse/MATLAB/Test/Contents.m b/CXSparse/MATLAB/Test/Contents.m
new file mode 100644
index 0000000..08dadeb
--- /dev/null
+++ b/CXSparse/MATLAB/Test/Contents.m
@@ -0,0 +1,103 @@
+% CXSparse testing and "textbook" MATLAB M-files and mexFunctions, related to
+% CXSparse but not a part of CXSparse itself.
+%
+% M-files:
+%
+% chol_downdate - downdate a Cholesky factorization.
+% chol_left - left-looking Cholesky factorization.
+% chol_left2 - left-looking Cholesky factorization, more details.
+% chol_right - right-looking Cholesky factorization.
+% chol_super - left-looking "supernodal" Cholesky factorization.
+% chol_up - up-looking Cholesky factorization.
+% chol_update - update a Cholesky factorization.
+% chol_updown - update or downdate a Cholesky factorization.
+% chol_updown2 - Cholesky update/downdate (real and complex)
+% cond1est - 1-norm condition estimate.
+% cs_fiedler - the Fiedler vector of a connected graph.
+% givens2 - find a Givens rotation.
+% house - find a Householder reflection.
+% lu_left - left-looking LU factorization.
+% lu_right - right-looking LU factorization.
+% lu_rightp - right-looking LU factorization, with partial pivoting.
+% lu_rightpr - recursive right-looking LU, with partial pivoting.
+% lu_rightr - recursive right-looking LU.
+% norm1est - 1-norm estimate.
+% qr_givens - Givens-rotation QR factorization.
+% qr_givens_full - Givens-rotation QR factorization, for full matrices.
+% qr_left - left-looking Householder QR factorization.
+% qr_right - right-looking Householder QR factorization.
+%
+% mexFunctions:
+%
+% cs_frand - generate a random finite-element matrix
+% cs_ipvec - x(p)=b
+% cs_maxtransr - recursive maximum matching algorithm
+% cs_pvec - x=b(p)
+% cs_reach - non-recursive reach (interface to CSparse cs_reach)
+% cs_reachr - recursive reach (interface to CSparse cs_reachr)
+% cs_rowcnt - row counts for sparse Cholesky
+% cs_sparse2 - same as cs_sparse, to test cs_entry function
+%
+% Extensive test functions, not for normal usage:
+%
+% check_if_same - check if two inputs are identical or not
+% choldn - Cholesky downdate
+% cholup - Cholesky update, using Given's rotations
+% cholupdown - Cholesky update/downdate (Bischof, Pan, and Tang method)
+% cs_q1 - construct Q from Householder vectors
+% cs_test_make - compiles the CSparse, Demo, and Test mexFunctions.
+% dmperm_test - test cs_dmperm
+% chol_example - simple Cholesky factorization example
+% etree_sample - construct a sample etree and symbolic factorization
+% gqr3 - QR factorization, based on Givens rotations
+% happly - apply Householder reflection to a vector
+% hmake1 - construct a Householder reflection
+% mynormest1 - estimate norm(A,1), using LU factorization (L*U = P*A*Q).
+% myqr - QR factorization using Householder reflections
+% another_colormap - try another color map
+% cspy_test - test cspy and cs_dmspy
+% qr2 - QR factorization based on Householder reflections
+% sample_colormap - try a colormap for use in cspy
+% signum - compute and display the sign of a column vector x
+% sqr_example - test cs_sqr
+% dmspy_test - test cspy, cs_dmspy, and cs_dmperm
+% test_qr - test various QR factorization methods
+% test_randperms - test random permutations
+% testh - test Householder reflections
+% test_qr1 - test QR factorizations
+% test_qrsol - test cs_qrsol
+% test_sep - test cs_sep, and compare with Gilbert's meshpart vtxsep
+% testall - test all CSparse functions (run tests 1 to 28 below)
+% test1 - test cs_transpose, cs_gaxpy, cs_sparse, cs_sparse2
+% test2 - test cs_sparse, cs_permute, cs_pvec, cs_ipvec, cs_symperm
+% test3 - test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol
+% test4 - test cs_multiply
+% test5 - test cs_add
+% test6 - test cs_reach, cs_reachr, cs_lsolve, cs_usolve
+% test7 - test cs_lu
+% test8 - test cs_cholsol, cs_lusol
+% test9 - test cs_qr
+% test10 - test cs_qr
+% test11 - test cs_rowcnt
+% test12 - test cs_qr and compare with svd
+% test13 - test cs_counts, cs_etree
+% test14 - test cs_droptol
+% test15 - test cs_amd
+% test16 - test cs_amd
+% test17 - test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol
+% test18 - test iterative refinement after backslash
+% test19 - test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc, cspy
+% test20 - test chol_updown2
+% test21 - test cs_updown, chol_updown2
+% test22 - test cond1est
+% test23 - test cs_dmspy
+% test24 - test cs_fielder
+% test25 - test cs_nd
+% test26 - test cs_dmsol and cs_dmspy
+% test27 - test cs_qr, cs_utsolve, cs_qrsol
+% test28 - test cs_randperm, cs_dmperm
+
+% Example:
+% help chol_update
+
+% Copyright 2006-2007, Timothy A. Davis
diff --git a/CXSparse/MATLAB/Test/Makefile b/CXSparse/MATLAB/Test/Makefile
new file mode 100644
index 0000000..3b4e4ef
--- /dev/null
+++ b/CXSparse/MATLAB/Test/Makefile
@@ -0,0 +1,53 @@
+include ../../../UFconfig/UFconfig.mk
+
+MX = $(MEX) -DCS_LONG
+AR = ar cr
+RANLIB = ranlib
+
+I = -I../../Include -I../../../UFconfig -I../CSparse
+
+all: cs_sparse2.mexglx \
+ cs_ipvec.mexglx \
+ cs_pvec.mexglx \
+ cs_reach.mexglx \
+ cs_maxtransr.mexglx \
+ cs_reachr.mexglx \
+ cs_rowcnt.mexglx \
+ cs_frand.mexglx
+
+mexcsparse:
+ ( cd ../CSparse ; make mexcsparse.a )
+
+cs_ipvec.mexglx: cs_ipvec_mex.c mexcsparse
+ $(MX) -output cs_ipvec $< $(I) ../CSparse/mexcsparse.a
+
+cs_pvec.mexglx: cs_pvec_mex.c mexcsparse
+ $(MX) -output cs_pvec $< $(I) ../CSparse/mexcsparse.a
+
+cs_reach.mexglx: cs_reach_mex.c mexcsparse
+ $(MX) -output cs_reach $< $(I) ../CSparse/mexcsparse.a
+
+cs_sparse2.mexglx: cs_sparse2_mex.c mexcsparse
+ $(MX) -output cs_sparse2 $< $(I) ../CSparse/mexcsparse.a
+
+cs_maxtransr.mexglx: cs_maxtransr_mex.c mexcsparse
+ $(MX) -output cs_maxtransr $< $(I) ../CSparse/mexcsparse.a
+
+cs_reachr.mexglx: cs_reachr_mex.c mexcsparse
+ $(MX) -output cs_reachr $< $(I) ../CSparse/mexcsparse.a
+
+cs_rowcnt.mexglx: cs_rowcnt_mex.c mexcsparse
+ $(MX) -output cs_rowcnt $< $(I) ../CSparse/mexcsparse.a
+
+cs_frand.mexglx: cs_frand_mex.c mexcsparse
+ $(MX) -output cs_frand $< $(I) ../CSparse/mexcsparse.a
+
+
+
+clean:
+ rm -f *.o
+
+distclean: clean
+ rm -f *.mex* *.a cs_cl_*.c
+
+purge: distclean
diff --git a/CXSparse/MATLAB/Test/README.txt b/CXSparse/MATLAB/Test/README.txt
new file mode 100644
index 0000000..e075bac
--- /dev/null
+++ b/CXSparse/MATLAB/Test/README.txt
@@ -0,0 +1,4 @@
+Test for MATLAB interface for CXSparse. Type "testall" to run all the tests.
+
+Also includes "textbook" codes for the book "Direct Methods for Sparse Linear
+Systems", which are not part of CXSparse proper, but are used in the tests.
diff --git a/CXSparse/MATLAB/Test/another_colormap.m b/CXSparse/MATLAB/Test/another_colormap.m
new file mode 100644
index 0000000..50342e9
--- /dev/null
+++ b/CXSparse/MATLAB/Test/another_colormap.m
@@ -0,0 +1,30 @@
+function another_colormap
+%ANOTHER_COLORMAP try another color map
+%
+% Example:
+% another_colormap
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+j = jet (128) ;
+j = j (48:112, :) ;
+
+% jj = linspace (0,1,64)' ./ sum (jet,2) ;
+% j (:,1) = j (:,1) .* jj ;
+% j (:,2) = j (:,2) .* jj ;
+% j (:,3) = j (:,3) .* jj ;
+
+
+% white = [1 1 1] ;
+% gray = [.5 .5 .5] ; %#ok
+
+% j = [white ; purple ; j ] ;
+disp ('j = ') ;
+disp (j)
+
+
+image (1:size(j,1)) ;
+colormap (j) ;
diff --git a/CXSparse/MATLAB/Test/check_if_same.m b/CXSparse/MATLAB/Test/check_if_same.m
new file mode 100644
index 0000000..9a81e92
--- /dev/null
+++ b/CXSparse/MATLAB/Test/check_if_same.m
@@ -0,0 +1,22 @@
+function check_if_same (p1,p2)
+%CHECK_IF_SAME check if two inputs are identical or not
+%
+% Example:
+% check_if_same (1:5, 2:6)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+ if (isempty (p1))
+ if (~isempty (p2))
+ p1 %#ok
+ p2 %#ok
+ error ('empty!') ;
+ end
+ elseif (any (p1 ~= p2))
+ p1 %#ok
+ p2 %#ok
+ error ('!') ;
+ end
+
diff --git a/CXSparse/MATLAB/Test/chol_downdate.m b/CXSparse/MATLAB/Test/chol_downdate.m
new file mode 100644
index 0000000..8cf9794
--- /dev/null
+++ b/CXSparse/MATLAB/Test/chol_downdate.m
@@ -0,0 +1,28 @@
+function [L, w] = chol_downdate (L, w)
+%CHOL_DOWNDATE downdate a Cholesky factorization.
+% Example
+% [L, w] = chol_downdate (L, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+beta = 1 ;
+n = size (L,1) ;
+for j = 1:n
+ alpha = w (j) / L (j,j) ;
+ beta2 = sqrt (beta^2 - alpha^2) ;
+ if (~isreal (beta2))
+ error ('not positive definite') ;
+ end
+ gamma = alpha / (beta2 * beta) ;
+ delta = beta2 / beta ;
+ L (j,j) = delta * L (j,j) ;
+ w (j) = alpha ;
+ beta = beta2 ;
+ if (j == n)
+ return
+ end
+ w (j+1:n) = w (j+1:n) - alpha * L (j+1:n,j) ;
+ L (j+1:n,j) = delta * L (j+1:n,j) - gamma * w (j+1:n) ;
+end
diff --git a/CXSparse/MATLAB/Test/chol_example.m b/CXSparse/MATLAB/Test/chol_example.m
new file mode 100644
index 0000000..f488f7d
--- /dev/null
+++ b/CXSparse/MATLAB/Test/chol_example.m
@@ -0,0 +1,35 @@
+function chol_example
+%CHOL_EXAMPLE simple Cholesky factorization example
+% Example
+% chol_example
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+D = 10 ;
+X = 1 ;
+o = 0 ;
+
+A = sparse ([
+D o X o o o o X o o
+o D o o X o o o o X
+X o D o o o X o o o
+o o o D o o o o X X
+o X o o D o o o X X
+o o o o o D X X o o
+o o X o o X D o o o
+X o o o o X o D X X
+o o o X X o o X D o
+o X o X X o o X o D ]) ;
+
+disp ('A = ') ; disp (A) ;
+
+L = chol(A)' ;
+
+disp ('L = ') ; disp (L) ;
+
+clf
+subplot (1,2,1) ; spy (A) ;
+subplot (1,2,2) ; spy (L+L') ;
diff --git a/CXSparse/MATLAB/Test/chol_left.m b/CXSparse/MATLAB/Test/chol_left.m
new file mode 100644
index 0000000..ec75416
--- /dev/null
+++ b/CXSparse/MATLAB/Test/chol_left.m
@@ -0,0 +1,15 @@
+function L = chol_left (A)
+%CHOL_LEFT left-looking Cholesky factorization.
+% Example
+% L = chol_left (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+L = zeros (n) ;
+for k = 1:n
+ L (k,k) = sqrt (A (k,k) - L (k,1:k-1) * L (k,1:k-1)') ;
+ L (k+1:n,k) = (A (k+1:n,k) - L (k+1:n,1:k-1) * L (k,1:k-1)') / L (k,k) ;
+end
diff --git a/CXSparse/MATLAB/Test/chol_left2.m b/CXSparse/MATLAB/Test/chol_left2.m
new file mode 100644
index 0000000..c809b9e
--- /dev/null
+++ b/CXSparse/MATLAB/Test/chol_left2.m
@@ -0,0 +1,20 @@
+function L = chol_left2 (A)
+%CHOL_LEFT2 left-looking Cholesky factorization, more details.
+% Example
+% L = chol_left2 (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+L = sparse (n,n) ;
+a = sparse (n,1) ;
+for k = 1:n
+ a (k:n) = A (k:n,k) ;
+ for j = find (L (k,:))
+ a (k:n) = a (k:n) - L (k:n,j) * L (k,j) ;
+ end
+ L (k,k) = sqrt (a (k)) ;
+ L (k+1:n,k) = a (k+1:n) / L (k,k) ;
+end
diff --git a/CXSparse/MATLAB/Test/chol_right.m b/CXSparse/MATLAB/Test/chol_right.m
new file mode 100644
index 0000000..7aa60e1
--- /dev/null
+++ b/CXSparse/MATLAB/Test/chol_right.m
@@ -0,0 +1,16 @@
+function L = chol_right (A)
+%CHOL_RIGHT right-looking Cholesky factorization.
+% Example
+% L = chol_right (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A) ;
+L = zeros (n) ;
+for k = 1:n
+ L (k,k) = sqrt (A (k,k)) ;
+ L (k+1:n,k) = A (k+1:n,k) / L (k,k) ;
+ A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - L (k+1:n,k) * L (k+1:n,k)' ;
+end
diff --git a/CXSparse/MATLAB/Test/chol_super.m b/CXSparse/MATLAB/Test/chol_super.m
new file mode 100644
index 0000000..1744130
--- /dev/null
+++ b/CXSparse/MATLAB/Test/chol_super.m
@@ -0,0 +1,19 @@
+function L = chol_super (A,s)
+%CHOL_SUPER left-looking "supernodal" Cholesky factorization.
+% Example:
+% L = chol_super (A,s)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A) ;
+L = zeros (n) ;
+ss = cumsum ([1 s]) ;
+for j = 1:length (s)
+ k1 = ss (j) ;
+ k2 = ss (j+1) ;
+ k = k1:(k2-1) ;
+ L (k,k) = chol (A (k,k) - L (k,1:k1-1) * L (k,1:k1-1)')' ;
+ L (k2:n,k) = (A (k2:n,k) - L (k2:n,1:k1-1) * L (k,1:k1-1)') / L (k,k)' ;
+end
diff --git a/CXSparse/MATLAB/Test/chol_up.m b/CXSparse/MATLAB/Test/chol_up.m
new file mode 100644
index 0000000..09d0218
--- /dev/null
+++ b/CXSparse/MATLAB/Test/chol_up.m
@@ -0,0 +1,15 @@
+function L = chol_up (A)
+%CHOL_UP up-looking Cholesky factorization.
+% Example:
+% L = chol_up (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A) ;
+L = zeros (n) ;
+for k = 1:n
+ L (k,1:k-1) = (L (1:k-1,1:k-1) \ A (1:k-1,k))' ;
+ L (k,k) = sqrt (A (k,k) - L (k,1:k-1) * L (k,1:k-1)') ;
+end
diff --git a/CXSparse/MATLAB/Test/chol_update.m b/CXSparse/MATLAB/Test/chol_update.m
new file mode 100644
index 0000000..5d95152
--- /dev/null
+++ b/CXSparse/MATLAB/Test/chol_update.m
@@ -0,0 +1,26 @@
+function [L, w] = chol_update (L, w)
+%CHOL_UPDATE update a Cholesky factorization.
+% Example:
+% [L, w] = chol_update (L, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+beta = 1 ;
+n = size (L,1) ;
+for j = 1:n
+ alpha = w (j) / L (j,j) ;
+ beta2 = sqrt (beta^2 + alpha^2) ;
+ gamma = alpha / (beta2 * beta) ;
+ delta = beta / beta2 ;
+ L (j,j) = delta * L (j,j) + gamma * w (j) ;
+ w (j) = alpha ;
+ beta = beta2 ;
+ if (j == n)
+ return
+ end
+ w1 = w (j+1:n) ;
+ w (j+1:n) = w (j+1:n) - alpha * L (j+1:n,j) ;
+ L (j+1:n,j) = delta * L (j+1:n,j) + gamma * w1 ;
+end
diff --git a/CXSparse/MATLAB/Test/chol_updown.m b/CXSparse/MATLAB/Test/chol_updown.m
new file mode 100644
index 0000000..2f286c9
--- /dev/null
+++ b/CXSparse/MATLAB/Test/chol_updown.m
@@ -0,0 +1,36 @@
+function [L, w] = chol_updown (L, sigma, w)
+%CHOL_UPDOWN update or downdate a Cholesky factorization.
+% Example:
+% [L, w] = chol_updown (L, sigma, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+beta = 1 ;
+n = size (L,1) ;
+if (n == 1)
+ L = sqrt (L*L'+sigma*w*w') ;
+ return ;
+end
+for k = 1:n
+ alpha = w(k) / L(k,k) ;
+ beta2 = sqrt (beta^2 + sigma*alpha^2) ;
+ gamma = sigma * alpha / (beta2 * beta) ;
+ if (sigma > 0)
+ % update
+ delta = beta / beta2 ;
+ L (k,k) = delta * L (k,k) + gamma * w (k) ;
+ w1 = w (k+1:n) ;
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k+1:n,k) = delta * L (k+1:n,k) + gamma * w1 ;
+ else
+ % downdate
+ delta = beta2 / beta ;
+ L (k,k) = delta * L (k,k) ;
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k+1:n,k) = delta * L (k+1:n,k) + gamma * w (k+1:n) ;
+ end
+ w (k) = alpha ;
+ beta = beta2 ;
+end
diff --git a/CXSparse/MATLAB/Test/chol_updown2.m b/CXSparse/MATLAB/Test/chol_updown2.m
new file mode 100644
index 0000000..5cc844e
--- /dev/null
+++ b/CXSparse/MATLAB/Test/chol_updown2.m
@@ -0,0 +1,47 @@
+function [L, w] = chol_updown2 (L, sigma, w)
+%CHOL_UPDOWN2 Cholesky update/downdate (real and complex)
+% (real or complex)
+% Example:
+% [L, w] = chol_updown2 (L, sigma, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis, William W. Hager
+% http://www.cise.ufl.edu/research/sparse
+
+beta = 1 ;
+n = size (L,1) ;
+if (n == 1)
+ wnew = L\w ;
+ L = sqrt (L*L'+sigma*w*w') ;
+ w = wnew ;
+ return ;
+end
+for k = 1:n
+ alpha = w(k) / L(k,k) ;
+ beta2 = sqrt (beta*beta + sigma*alpha*conj(alpha)) ;
+ gamma = sigma * conj(alpha) / (beta2 * beta) ;
+ if (sigma > 0)
+ % update
+ delta = beta / beta2 ;
+ L (k,k) = delta * L (k,k) + gamma * w (k) ;
+ phase = abs (L (k, k))/L (k, k) ;
+ L (k, k) = phase*L (k, k) ;
+
+ w1 = w (k+1:n) ;
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k+1:n,k) = phase * (delta * L (k+1:n,k) + gamma * w1) ;
+
+ else
+ % downdate
+ delta = beta2 / beta ;
+ L (k,k) = delta * L (k,k) ;
+ phase = abs (L (k, k))/L (k, k) ;
+ L (k, k) = phase*L (k, k) ;
+
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k+1:n,k) = phase * (delta * L (k+1:n,k) + gamma * w (k+1:n)) ;
+
+ end
+ w (k) = alpha ;
+ beta = beta2 ;
+end
diff --git a/CXSparse/MATLAB/Test/choldn.m b/CXSparse/MATLAB/Test/choldn.m
new file mode 100644
index 0000000..10ea9d9
--- /dev/null
+++ b/CXSparse/MATLAB/Test/choldn.m
@@ -0,0 +1,46 @@
+function L = choldn (Lold,w)
+%CHOLDN Cholesky downdate
+% given Lold and w, compute L so that L*L' = Lold*Lold' - w*w'
+%
+% Example:
+% L = cholnd (Lold,w)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (Lold,1) ;
+L = Lold ;
+
+alpha = 1 ;
+beta = 1 ;
+
+wold = w ;
+wnew = zeros (n,1) ;
+
+for i = 1:n
+
+ a = w (i) / L(i,i) ;
+ alpha = alpha - a^2 ;
+ if (alpha <= 0)
+ error ('not pos def') ;
+ end
+ beta_new = sqrt (alpha) ;
+ b = beta_new / beta ;
+ c = (a / (beta*beta_new)) ;
+ beta = beta_new ;
+
+ % L (i,i) = b * L (i,i) ;
+
+ wnew (i) = a ;
+
+ for k = i:n
+ w (k) = w (k) - a * L (k,i) ;
+ L (k,i) = b * L (k,i) - c * w(k) ;
+ end
+
+end
+
+% w
+% wnew
+disp (wnew - Lold\wold)
diff --git a/CXSparse/MATLAB/Test/cholup.m b/CXSparse/MATLAB/Test/cholup.m
new file mode 100644
index 0000000..e8f196c
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cholup.m
@@ -0,0 +1,26 @@
+function L = cholup (Lold,w)
+%CHOLUP Cholesky update, using Given's rotations
+% given Lold and w, compute L so that L*L' = Lold*Lold' + w*w'
+% Example:
+% L = cholup (Lold,w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (Lold,1) ;
+L = [Lold w] ;
+
+for k = 1:n
+
+ g = givens (L(k,k), L(k,n+1)) ;
+
+ L (:, [k n+1]) = L (:, [k n+1]) * g' ;
+
+ disp ('L:') ;
+ disp (L)
+ pause
+end
+
+L = L (:,1:n) ;
+disp (L) ;
diff --git a/CXSparse/MATLAB/Test/cholupdown.m b/CXSparse/MATLAB/Test/cholupdown.m
new file mode 100644
index 0000000..e450347
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cholupdown.m
@@ -0,0 +1,60 @@
+function L = cholupdown (Lold, sigma, w)
+%CHOLUPDOWN Cholesky update/downdate (Bischof, Pan, and Tang method)
+% This version only works for the real case. See chol_updown2 for
+% a code that handles both the real and complex cases.
+% Example:
+% L = cholupdown (Lold, sigma, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+beta = 1 ;
+n = size (Lold,1) ;
+L = Lold ;
+% x = weros (n,1) ;
+% worig = w ;
+
+for k = 1:n
+
+ alpha = w(k) / L(k,k) ;
+ beta_new = sqrt (beta^2 + sigma*alpha^2) ;
+ gamma = alpha / (beta_new * beta) ;
+
+ if (sigma < 0)
+
+ % downdate
+ bratio = beta_new / beta ;
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k,k) = bratio * L (k,k) ;
+ L (k+1:n,k) = bratio * L (k+1:n,k) - gamma*w(k+1:n) ;
+
+ else
+
+ % update
+ bratio = beta / beta_new ;
+
+% wold = w (k+1:n) ;
+% w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+% L (k ,k) = bratio * L (k ,k) + gamma*w(k) ;
+% L (k+1:n,k) = bratio * L (k+1:n,k) + gamma*wold ;
+
+ L (k,k) = bratio * L (k,k) + gamma*w(k) ;
+ for i = k+1:n
+
+ wold = w (i) ;
+ w (i) = w (i) - alpha * L (i,k) ;
+ L (i,k) = bratio * L (i,k) + gamma*wold ;
+
+ end
+
+ end
+
+ w (k) = alpha ;
+
+ beta = beta_new ;
+
+end
+
+% norm (w-(Lold\worig))
diff --git a/CXSparse/MATLAB/Test/cond1est.m b/CXSparse/MATLAB/Test/cond1est.m
new file mode 100644
index 0000000..e634168
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cond1est.m
@@ -0,0 +1,23 @@
+function c = cond1est (A)
+%COND1EST 1-norm condition estimate.
+% Example:
+% c = cond1est(A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+if (m ~= n | ~isreal (A)) %#ok
+ error ('A must be square and real') ;
+end
+if isempty(A)
+ c = 0 ;
+ return ;
+end
+[L,U,P,Q] = lu (A) ;
+if (~isempty (find (abs (diag (U)) == 0))) %#ok
+ c = Inf ;
+else
+ c = norm (A,1) * norm1est (L,U,P,Q) ;
+end
diff --git a/CXSparse/MATLAB/Test/cs_fiedler.m b/CXSparse/MATLAB/Test/cs_fiedler.m
new file mode 100644
index 0000000..35db8dc
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_fiedler.m
@@ -0,0 +1,30 @@
+function [p,v,d] = cs_fiedler (A)
+%CS_FIEDLER the Fiedler vector of a connected graph.
+% [p,v,d] = cs_fiedler(A) computes the Fiedler vector v (the eigenvector
+% corresponding to the 2nd smallest eigenvalue d of the Laplacian of the graph
+% of A+A'). p is the permutation obtained when v is sorted. A should be a
+% connected graph.
+%
+% Example:
+% [p,v,d] = cs_fiedler (A) ;
+%
+% See also CS_SCC, EIGS, SYMRCM, UNMESH.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+if (n < 2)
+ p = 1 ; v = 1 ; d = 0 ; return ;
+end
+opt.disp = 0 ; % turn off printing in eigs
+opt.tol = sqrt (eps) ;
+if (~isreal (A))
+ A = spones (A) ;
+end
+S = A | A' | speye (n) ; % compute the Laplacian of A
+S = diag (sum (S)) - S ;
+[v,d] = eigs (S, 2, 'SA', opt) ; % find the Fiedler vector v
+v = v (:,2) ;
+d = d (2,2) ;
+[ignore p] = sort (v) ; % sort it to get p
diff --git a/CXSparse/MATLAB/Test/cs_frand.m b/CXSparse/MATLAB/Test/cs_frand.m
new file mode 100644
index 0000000..c75069f
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_frand.m
@@ -0,0 +1,15 @@
+function A = cs_frand (n,nel,s) %#ok
+%CS_FRAND generate a random finite-element matrix
+% A = cs_frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel
+% finite elements, each of which are of size s-by-s with random symmetric
+% nonzero pattern, plus the identity matrix.
+%
+% Example
+% A = cs_frand (100, 100, 3) ;
+% See also cs_demo.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_frand mexFunction not found') ;
+
diff --git a/CXSparse/MATLAB/Test/cs_frand_mex.c b/CXSparse/MATLAB/Test/cs_frand_mex.c
new file mode 100644
index 0000000..9768797
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_frand_mex.c
@@ -0,0 +1,59 @@
+#include "cs_mex.h"
+/* A = cs_frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel
+ * finite elements, each of which are of size s-by-s with random symmetric
+ * nonzero pattern, plus the identity matrix.
+ * See also MATLAB/Demo/private/frand.m */
+
+cs_dl *cs_dl_frand (CS_INT n, CS_INT nel, CS_INT s)
+{
+ CS_INT ss = s*s, nz = nel*ss, e, i, j, *P ;
+ cs *A, *T = cs_dl_spalloc (n, n, nz, 1, 1) ;
+ if (!T) return (NULL) ;
+ P = cs_dl_malloc (s, sizeof (CS_INT)) ;
+ if (!P) return (cs_dl_spfree (T)) ;
+ for (e = 0 ; e < nel ; e++)
+ {
+ for (i = 0 ; i < s ; i++) P [i] = rand () % n ;
+ for (j = 0 ; j < s ; j++)
+ {
+ for (i = 0 ; i < s ; i++)
+ {
+ cs_dl_entry (T, P [i], P [j], rand () / (double) RAND_MAX) ;
+ }
+ }
+ }
+ for (i = 0 ; i < n ; i++) cs_dl_entry (T, i, i, 1) ;
+ A = cs_dl_compress (T) ;
+ cs_dl_spfree (T) ;
+ return (cs_dl_dupl (A) ? A : cs_dl_spfree (A)) ;
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT n, nel, s ;
+ cs *A, *AT ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: C = cs_frand(n,nel,s)") ;
+ }
+ n = mxGetScalar (pargin [0]) ;
+ nel = mxGetScalar (pargin [1]) ;
+ s = mxGetScalar (pargin [2]) ;
+
+ n = CS_MAX (1,n) ;
+ nel = CS_MAX (1,nel) ;
+ s = CS_MAX (1,s) ;
+
+ AT = cs_dl_frand (n, nel, s) ;
+ A = cs_dl_transpose (AT, 1) ;
+ cs_dl_spfree (AT) ;
+ cs_dl_dropzeros (A) ;
+
+ pargout [0] = cs_dl_mex_put_sparse (&A) ;
+}
diff --git a/CXSparse/MATLAB/Test/cs_ipvec.m b/CXSparse/MATLAB/Test/cs_ipvec.m
new file mode 100644
index 0000000..f86bab6
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_ipvec.m
@@ -0,0 +1,12 @@
+function x = cs_ipvec (b,p) %#ok
+%CS_IPVEC x(p)=b
+%
+% Example:
+% x = cs_ipvec (b,p)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_ipvec mexFunction not found') ;
+
diff --git a/CXSparse/MATLAB/Test/cs_ipvec_mex.c b/CXSparse/MATLAB/Test/cs_ipvec_mex.c
new file mode 100644
index 0000000..974af01
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_ipvec_mex.c
@@ -0,0 +1,49 @@
+#include "cs_mex.h"
+/* x(p) = b */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT n, k, *p ;
+ double *xx ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_ipvec(b,p)") ;
+ }
+ n = mxGetNumberOfElements (pargin [0]) ;
+ if (n != mxGetNumberOfElements (pargin [1]))
+ {
+ mexErrMsgTxt ("b or p wrong size") ;
+ }
+
+ xx = mxGetPr (pargin [1]) ;
+ p = cs_dl_malloc (n, sizeof (CS_INT)) ;
+ for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ;
+
+ if (mxIsComplex (pargin [0]))
+ {
+#ifdef NCOMPLEX
+ mexErrMsgTxt ("complex case not supported") ;
+#else
+ cs_complex_t *x, *b ;
+ b = cs_cl_mex_get_double (n, pargin [0]) ;
+ x = cs_dl_malloc (n, sizeof (cs_complex_t)) ;
+ cs_cl_ipvec (p, b, x, n) ;
+ pargout [0] = cs_cl_mex_put_double (n, x) ;
+ cs_free (b) ; /* free copy of complex values */
+#endif
+ }
+ else
+ {
+ double *x, *b ;
+ b = cs_dl_mex_get_double (n, pargin [0]) ;
+ pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ cs_dl_ipvec (p, b, x, n) ;
+ }
+ cs_free (p) ;
+}
diff --git a/CXSparse/MATLAB/Test/cs_maxtransr.m b/CXSparse/MATLAB/Test/cs_maxtransr.m
new file mode 100644
index 0000000..df9bca9
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_maxtransr.m
@@ -0,0 +1,12 @@
+function p = cs_maxtransr(A) %#ok
+%CS_MAXTRANSR recursive maximum matching algorithm
+% Example:
+% p = cs_maxtransr(A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_maxtransr mexFunction not found') ;
+
+
diff --git a/CXSparse/MATLAB/Test/cs_maxtransr_mex.c b/CXSparse/MATLAB/Test/cs_maxtransr_mex.c
new file mode 100644
index 0000000..e97cec6
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_maxtransr_mex.c
@@ -0,0 +1,88 @@
+#include "cs_mex.h"
+/* find an augmenting path starting at column j and extend the match if found */
+static
+CS_INT augment (CS_INT k, cs_dl *A, CS_INT *jmatch, CS_INT *cheap, CS_INT *w,
+ CS_INT j)
+{
+ CS_INT found = 0, p, i = -1, *Ap = A->p, *Ai = A->i ;
+ /* --- Start depth-first-search at node j ------------------------------- */
+ w [j] = k ; /* mark j as visited for kth path */
+ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++)
+ {
+ i = Ai [p] ; /* try a cheap assignment (i,j) */
+ found = (jmatch [i] == -1) ;
+ }
+ cheap [j] = p ; /* start here next time for j */
+ /* --- Depth-first-search of neighbors of j ----------------------------- */
+ for (p = Ap [j] ; p < Ap [j+1] && !found ; p++)
+ {
+ i = Ai [p] ; /* consider row i */
+ if (w [jmatch [i]] == k) continue ; /* skip col jmatch [i] if marked */
+ found = augment (k, A, jmatch, cheap, w, jmatch [i]) ;
+ }
+ if (found) jmatch [i] = j ; /* augment jmatch if path found */
+ return (found) ;
+}
+
+/* find a maximum transveral */
+static
+CS_INT *maxtrans (cs_dl *A) /* returns jmatch [0..m-1] */
+{
+ CS_INT i, j, k, n, m, *Ap, *jmatch, *w, *cheap ;
+ if (!A) return (NULL) ; /* check inputs */
+ n = A->n ; m = A->m ; Ap = A->p ;
+ jmatch = cs_dl_malloc (m, sizeof (CS_INT)) ; /* allocate result */
+ w = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* allocate workspace */
+ if (!w || !jmatch) return (cs_dl_idone (jmatch, NULL, w, 0)) ;
+ cheap = w + n ;
+ for (j = 0 ; j < n ; j++) cheap [j] = Ap [j] ; /* for cheap assignment */
+ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */
+ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* no rows matched yet */
+ for (k = 0 ; k < n ; k++) augment (k, A, jmatch, cheap, w, k) ;
+ return (cs_dl_idone (jmatch, NULL, w, 1)) ;
+}
+
+/* invert a maximum matching */
+static CS_INT *invmatch (CS_INT *jmatch, CS_INT m, CS_INT n)
+{
+ CS_INT i, j, *imatch ;
+ if (!jmatch) return (NULL) ;
+ imatch = cs_dl_malloc (n, sizeof (CS_INT)) ;
+ if (!imatch) return (NULL) ;
+ for (j = 0 ; j < n ; j++) imatch [j] = -1 ;
+ for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ;
+ return (imatch) ;
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl *A, Amatrix ;
+ double *x ;
+ CS_INT i, m, n, *imatch, *jmatch ;
+
+ if (nargout > 1 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: p = cr_maxtransr(A)") ;
+ }
+
+ /* get inputs */
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ;
+ m = A->m ;
+ n = A->n ;
+
+ jmatch = maxtrans (A) ;
+ imatch = invmatch (jmatch, m, n) ; /* imatch = inverse of jmatch */
+
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n ; i++) x [i] = imatch [i] + 1 ;
+
+ cs_free (jmatch) ;
+ cs_free (imatch) ;
+}
diff --git a/CXSparse/MATLAB/Test/cs_pvec.m b/CXSparse/MATLAB/Test/cs_pvec.m
new file mode 100644
index 0000000..bbd3a87
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_pvec.m
@@ -0,0 +1,12 @@
+function x = cs_pvec (b,p) %#ok
+%CS_PVEC x=b(p)
+%
+% Example:
+% x = cs_pvec (b,p)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_pvec mexFunction not found') ;
+
diff --git a/CXSparse/MATLAB/Test/cs_pvec_mex.c b/CXSparse/MATLAB/Test/cs_pvec_mex.c
new file mode 100644
index 0000000..d8505fa
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_pvec_mex.c
@@ -0,0 +1,49 @@
+#include "cs_mex.h"
+/* x = b(p) */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT n, k, *p ;
+ double *xx ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_pvec(b,p)") ;
+ }
+ n = mxGetNumberOfElements (pargin [0]) ;
+ if (n != mxGetNumberOfElements (pargin [1]))
+ {
+ mexErrMsgTxt ("b or p wrong size") ;
+ }
+
+ xx = mxGetPr (pargin [1]) ;
+ p = cs_dl_malloc (n, sizeof (CS_INT)) ;
+ for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ;
+
+ if (mxIsComplex (pargin [0]))
+ {
+#ifdef NCOMPLEX
+ mexErrMsgTxt ("complex case not supported") ;
+#else
+ cs_complex_t *x, *b ;
+ b = cs_cl_mex_get_double (n, pargin [0]) ;
+ x = cs_dl_malloc (n, sizeof (cs_complex_t)) ;
+ cs_cl_pvec (p, b, x, n) ;
+ pargout [0] = cs_cl_mex_put_double (n, x) ;
+ cs_free (b) ; /* free copy of complex values */
+#endif
+ }
+ else
+ {
+ double *x, *b ;
+ b = cs_dl_mex_get_double (n, pargin [0]) ;
+ pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ cs_dl_pvec (p, b, x, n) ;
+ }
+ cs_free (p) ;
+}
diff --git a/CXSparse/MATLAB/Test/cs_q1.m b/CXSparse/MATLAB/Test/cs_q1.m
new file mode 100644
index 0000000..45a51ec
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_q1.m
@@ -0,0 +1,19 @@
+function Q = cs_q1 (V, Beta, p)
+%CS_Q1 construct Q from Householder vectors
+% Example:
+% Q = cs_q1 (V, beta, p)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (V) ;
+Q = speye (m) ;
+if (nargin > 2)
+ Q = Q (:,p) ;
+end
+for i = 1:m
+ for k = 1:n
+ Q (i,:) = Q (i,:) - ((Q(i,:) * V(:,k)) * Beta(k)) * V(:,k)' ;
+ end
+end
diff --git a/CXSparse/MATLAB/Test/cs_reach.m b/CXSparse/MATLAB/Test/cs_reach.m
new file mode 100644
index 0000000..2e68e7a
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_reach.m
@@ -0,0 +1,14 @@
+function x = cs_reach(L,b) %#ok
+%CS_REACH non-recursive reach (interface to CSparse cs_reach)
+% find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower
+% triangular. b must be a real sparse vector.
+%
+% Example:
+% x = cs_reach(L,b)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_reach mexFunction not found') ;
+
diff --git a/CXSparse/MATLAB/Test/cs_reach_mex.c b/CXSparse/MATLAB/Test/cs_reach_mex.c
new file mode 100644
index 0000000..ec72443
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_reach_mex.c
@@ -0,0 +1,39 @@
+#include "cs_mex.h"
+/* find nonzero pattern of x=L\sparse(b). L must be sparse and lower
+ * triangular. b must be a sparse vector. */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Lmatrix, Bmatrix, *L, *B ;
+ double *x ;
+ CS_INT k, i, j, top, *xi, *perm ;
+
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_reach(L,b)") ;
+ }
+
+ /* get inputs */
+ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
+ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;
+ cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ;
+ perm = cs_dl_malloc (L->n, sizeof (CS_INT)) ;
+ for (k = 0 ; k < L->n ; k++) perm [k] = k ;
+
+ xi = cs_dl_calloc (3*L->n, sizeof (CS_INT)) ;
+
+ top = cs_dl_reach (L, B, 0, xi, perm) ;
+
+ pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ;
+
+ cs_free (xi) ;
+ cs_free (perm) ;
+}
diff --git a/CXSparse/MATLAB/Test/cs_reachr.m b/CXSparse/MATLAB/Test/cs_reachr.m
new file mode 100644
index 0000000..d6bbfc7
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_reachr.m
@@ -0,0 +1,15 @@
+function x = cs_reachr(L,b) %#ok
+%CS_REACHR recursive reach (interface to CSparse cs_reachr)
+% find nonzero pattern of x=L\sparse(b). L must be sparse, real, and lower
+% triangular. b must be a real sparse vector.
+%
+% Example:
+% x = cs_reachr(L,b)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+error ('cs_reach mexFunction not found') ;
+
diff --git a/CXSparse/MATLAB/Test/cs_reachr_mex.c b/CXSparse/MATLAB/Test/cs_reachr_mex.c
new file mode 100644
index 0000000..ca7e009
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_reachr_mex.c
@@ -0,0 +1,67 @@
+#include "cs_mex.h"
+/* find nonzero pattern of x=L\sparse(b). L must be sparse and lower
+ * triangular. b must be a sparse vector. */
+
+static
+void dfsr (CS_INT j, const cs *L, CS_INT *top, CS_INT *xi, CS_INT *w)
+{
+ CS_INT p ;
+ w [j] = 1 ; /* mark node j */
+ for (p = L->p [j] ; p < L->p [j+1] ; p++) /* for each i in L(:,j) */
+ {
+ if (w [L->i [p]] != 1) /* if i is unmarked */
+ {
+ dfsr (L->i [p], L, top, xi, w) ; /* start a dfs at i */
+ }
+ }
+ xi [--(*top)] = j ; /* push j onto the stack */
+}
+
+/* w [0..n-1] == 0 on input, <= 1 on output. size n */
+static
+CS_INT reachr (const cs *L, const cs *B, CS_INT *xi, CS_INT *w)
+{
+ CS_INT p, n = L->n ;
+ CS_INT top = n ; /* stack is empty */
+ for (p = B->p [0] ; p < B->p [1] ; p++) /* for each i in pattern of b */
+ {
+ if (w [B->i [p]] != 1) /* if i is unmarked */
+ {
+ dfsr (B->i [p], L, &top, xi, w) ; /* start a dfs at i */
+ }
+ }
+ return (top) ; /* return top of stack */
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl Lmatrix, Bmatrix, *L, *B ;
+ double *x ;
+ CS_INT i, j, top, *xi ;
+
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_reachr(L,b)") ;
+ }
+
+ /* get inputs */
+ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
+ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;
+ cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ;
+
+ xi = cs_dl_calloc (2*L->n, sizeof (CS_INT)) ;
+
+ top = reachr (L, B, xi, xi + L->n) ;
+
+ pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ;
+
+ cs_free (xi) ;
+}
diff --git a/CXSparse/MATLAB/Test/cs_rowcnt.m b/CXSparse/MATLAB/Test/cs_rowcnt.m
new file mode 100644
index 0000000..d57d661
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_rowcnt.m
@@ -0,0 +1,15 @@
+function r = cs_rowcnt(A,parent,post) %#ok
+%CS_ROWCNT row counts for sparse Cholesky
+% Compute the row counts of the Cholesky factor L of the matrix A. Uses
+% the lower triangular part of A.
+%
+% Example:
+% r = cs_rowcnt(A,parent,post)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+error ('cs_rowcnt mexFunction not found') ;
+
diff --git a/CXSparse/MATLAB/Test/cs_rowcnt_mex.c b/CXSparse/MATLAB/Test/cs_rowcnt_mex.c
new file mode 100644
index 0000000..7ba9a30
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_rowcnt_mex.c
@@ -0,0 +1,88 @@
+/* Compute the row counts of the Cholesky factor L of the matrix A. Uses
+ * the lower triangular part of A. */
+
+#include "cs_mex.h"
+
+static
+void firstdesc (CS_INT n, CS_INT *parent, CS_INT *post, CS_INT *first,
+ CS_INT *level)
+{
+ CS_INT len, i, k, r, s ;
+ for (i = 0 ; i < n ; i++) first [i] = -1 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ i = post [k] ; /* node i of etree is kth postordered node */
+ len = 0 ; /* traverse from i towards the root */
+ for (r = i ; r != -1 && first [r] == -1 ; r = parent [r], len++)
+ first [r] = k ;
+ len += (r == -1) ? (-1) : level [r] ; /* root node or end of path */
+ for (s = i ; s != r ; s = parent [s]) level [s] = len-- ;
+ }
+}
+
+/* return rowcount [0..n-1] */
+static
+CS_INT *rowcnt (cs_dl *A, CS_INT *parent, CS_INT *post)
+{
+ CS_INT i, j, k, len, s, p, jprev, q, n, sparent, jleaf, *Ap, *Ai, *maxfirst,
+ *ancestor, *prevleaf, *w, *first, *level, *rowcount ;
+ n = A->n ; Ap = A->p ; Ai = A->i ; /* get A */
+ w = cs_dl_malloc (5*n, sizeof (CS_INT)) ; /* get workspace */
+ ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ;
+ level = w+4*n ;
+ rowcount = cs_dl_malloc (n, sizeof (CS_INT)) ; /* allocate result */
+ firstdesc (n, parent, post, first, level) ; /* find first and level */
+ for (i = 0 ; i < n ; i++)
+ {
+ rowcount [i] = 1 ; /* count the diagonal of L */
+ prevleaf [i] = -1 ; /* no previous leaf of the ith row subtree */
+ maxfirst [i] = -1 ; /* max first[j] for node j in ith subtree */
+ ancestor [i] = i ; /* every node is in its own set, by itself */
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ j = post [k] ; /* j is the kth node in the postordered etree */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ q = cs_dl_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf) ;
+ if (jleaf) rowcount [i] += (level [j] - level [q]) ;
+ }
+ if (parent [j] != -1) ancestor [j] = parent [j] ;
+ }
+ cs_dl_free (w) ;
+ return (rowcount) ;
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl *A, Amatrix ;
+ double *x ;
+ CS_INT i, m, n, *parent, *post, *rowcount ;
+
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: r = cs_rowcnt(A,parent,post)") ;
+ }
+
+ /* get inputs */
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ;
+ n = A->n ;
+
+ parent = cs_dl_mex_get_int (n, pargin [1], &i, 0) ;
+ post = cs_dl_mex_get_int (n, pargin [2], &i, 1) ;
+
+ rowcount = rowcnt (A, parent, post) ;
+
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n ; i++) x [i] = rowcount [i] ;
+
+ cs_dl_free (rowcount) ;
+}
diff --git a/CXSparse/MATLAB/Test/cs_sparse2.m b/CXSparse/MATLAB/Test/cs_sparse2.m
new file mode 100644
index 0000000..32d9319
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_sparse2.m
@@ -0,0 +1,15 @@
+function A = cs_sparse2 (i,j,x) %#ok
+%CS_SPARSE2 same as cs_sparse, to test cs_entry function
+% A = cs_sparse2 (i,j,x), removing duplicates and numerically zero entries,
+% and returning A sorted (test cs_entry)
+%
+% Example:
+% A = cs_sparse2 (i,j,x)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+error ('cs_sparse2 mexFunction not found') ;
+
diff --git a/CXSparse/MATLAB/Test/cs_sparse2_mex.c b/CXSparse/MATLAB/Test/cs_sparse2_mex.c
new file mode 100644
index 0000000..dddcad9
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_sparse2_mex.c
@@ -0,0 +1,64 @@
+#include "cs_mex.h"
+/* A = cs_sparse2 (i,j,x), removing duplicates and numerically zero entries,
+ * and returning A sorted (test cs_entry) */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT k, m, n, nz, *Ti, *Tj ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: A = cs_sparse2(i,j,x)") ;
+ }
+ nz = mxGetM (pargin [0]) ;
+ Ti = cs_dl_mex_get_int (nz, pargin [0], &m, 1) ;
+ Tj = cs_dl_mex_get_int (nz, pargin [1], &n, 1) ;
+ cs_mex_check (1, nz, 1, 0, 0, 1, pargin [2]) ;
+ if (mxIsComplex (pargin [2]))
+ {
+#ifdef NCOMPLEX
+ mexErrMsgTxt ("complex case not supported") ;
+#else
+ cs_complex_t *Tx ;
+ cs_cl *A, *C, *T ;
+ Tx = cs_cl_mex_get_double (nz, pargin [2]) ;
+ T = cs_cl_spalloc (n, m, 1, 1, 1) ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ cs_cl_entry (T, Tj [k], Ti [k], Tx [k]) ;
+ }
+ C = cs_cl_compress (T) ;
+ cs_cl_spfree (T) ;
+ cs_cl_dupl (C) ;
+ cs_cl_dropzeros (C) ;
+ A = cs_cl_transpose (C, -1) ;
+ cs_cl_spfree (C) ;
+ pargout [0] = cs_cl_mex_put_sparse (&A) ;
+ cs_free (Tx) ;
+#endif
+ }
+ else
+ {
+ double *Tx ;
+ cs_dl *A, *C, *T ;
+ Tx = mxGetPr (pargin [2]) ;
+ T = cs_dl_spalloc (n, m, 1, 1, 1) ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ cs_dl_entry (T, Tj [k], Ti [k], Tx [k]) ;
+ }
+ C = cs_dl_compress (T) ;
+ cs_dl_spfree (T) ;
+ cs_dl_dupl (C) ;
+ cs_dl_dropzeros (C) ;
+ A = cs_dl_transpose (C, 1) ;
+ cs_dl_spfree (C) ;
+ pargout [0] = cs_dl_mex_put_sparse (&A) ;
+ }
+ cs_free (Ti) ;
+ cs_free (Tj) ;
+}
diff --git a/CXSparse/MATLAB/Test/cs_test_make.m b/CXSparse/MATLAB/Test/cs_test_make.m
new file mode 100644
index 0000000..60303b6
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cs_test_make.m
@@ -0,0 +1,43 @@
+function cs_test_make (force)
+%CS_TEST_MAKE compiles the CSparse, Demo, and Test mexFunctions.
+% The current directory must be CSparse/MATLAB/Test to use this function.
+%
+% Example:
+% cs_test_make
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+mexcmd = 'mex -DCS_LONG -I../../../UFconfig' ;
+if (~isempty (strfind (computer, '64')))
+ mexcmd = [mexcmd ' -largeArrayDims'] ;
+end
+
+if (nargin < 1)
+ force = 0 ;
+end
+
+cd ('../CSparse') ;
+[object_files timestamp] = cs_make ;
+cd ('../Test') ;
+
+mexfunc = { 'cs_ipvec', 'cs_pvec', 'cs_sparse2', ...
+ 'cs_reach', 'cs_maxtransr', 'cs_reachr', 'cs_rowcnt', 'cs_frand' } ;
+
+if (ispc)
+ % Windows does not support ANSI C99
+ mexcmd = [mexcmd ' -DNCOMPLEX'] ;
+end
+
+for i = 1:length(mexfunc)
+ [s t tobj] = cs_must_compile ('', mexfunc{i}, '_mex', ...
+ ['.' mexext], 'cs_test_make.m', force) ;
+ if (s | tobj < timestamp) %#ok
+ cmd = [mexcmd ' -O -output ' mexfunc{i} ' ' mexfunc{i} '_mex.c -I..' ...
+ filesep '..' filesep 'Include -I..' ...
+ filesep 'CSparse ' object_files] ;
+ fprintf ('%s\n', cmd) ;
+ eval (cmd) ;
+ end
+end
diff --git a/CXSparse/MATLAB/Test/cspy_test.m b/CXSparse/MATLAB/Test/cspy_test.m
new file mode 100644
index 0000000..1312ca3
--- /dev/null
+++ b/CXSparse/MATLAB/Test/cspy_test.m
@@ -0,0 +1,50 @@
+function cspy_test
+%CSPY_TEST test cspy and cs_dmspy
+% Example
+% cspy_test
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+
+clf
+
+% f = f (523:end) ;
+% f = f ((find (f == 938)):end) ;
+
+for i = f
+
+ Prob = UFget (i,index) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ try
+ subplot (1,4,1) ; cspy (A) ;
+ drawnow
+ subplot (1,4,2) ; cspy (A,64) ;
+ drawnow
+ subplot (1,4,3) ; cs_dmspy (A) ;
+ drawnow
+ subplot (1,4,4) ; cs_dmspy (A,0) ;
+ drawnow
+ catch
+ fprintf ('failed...\n') ;
+ end
+
+ [m n] = size (A) ;
+ if (m == n & nnz (diag (A)) == n) %#ok
+ p = cs_dmperm (A) ;
+ if (any (p ~= 1:n))
+ error ('!') ;
+ end
+ [p q r s cc rr] = cs_dmperm (A) ; %#ok
+ if (any (p ~= q))
+ error ('not sym!') ;
+ end
+ end
+
+ drawnow
+end
diff --git a/CXSparse/MATLAB/Test/dmperm_test.m b/CXSparse/MATLAB/Test/dmperm_test.m
new file mode 100644
index 0000000..2f1fd38
--- /dev/null
+++ b/CXSparse/MATLAB/Test/dmperm_test.m
@@ -0,0 +1,126 @@
+function dmperm_test
+%DMPERM_TEST test cs_dmperm
+%
+% Example:
+% dmperm_test
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+
+f = find (index.nrows ~= index.ncols) ;
+[ignore i] = sort (index.nrows(f) ./ index.ncols(f)) ;
+f = [209:211 f(i)] ;
+
+nmat = length(f) ;
+
+tt1 = zeros (1,nmat) ;
+tt2 = zeros (1,nmat) ;
+tt3 = zeros (1,nmat) ;
+tt4 = zeros (1,nmat) ;
+mm = zeros (1,nmat) ;
+nn = zeros (1,nmat) ;
+ss = zeros (1,nmat) ;
+me = zeros (1,nmat) ;
+ne = zeros (1,nmat) ;
+
+p = cs_dmperm (sparse (1)) ;
+
+for k = 1:length(f)
+
+ i = f(k) ;
+
+ Prob = UFget (i) %#ok
+
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m > n)
+ % make sure A is short and fat
+ A = A' ;
+ end
+ % C is tall and thin
+ C = A' ;
+ [m n] = size (A) ;
+
+ k1 = 0 ;
+ t1 = 0 ;
+ while (t1 < 1)
+ tic
+ p = cs_dmperm (A) ;
+ t = toc ;
+ t1 = t1 + t ;
+ k1 = k1 + 1 ;
+ end
+ t1 = t1 / k1 ;
+ s1 = sum (p > 0) ;
+
+ k2 = 0 ;
+ t2 = 0 ;
+ while (t2 < 1)
+ tic
+ p = cs_dmperm (C) ;
+ t = toc ;
+ t2 = t2 + t ;
+ k2 = k2 + 1 ;
+ end
+ t2 = t2 / k2 ;
+ s2 = sum (p > 0) ;
+
+ k3 = 0 ;
+ t3 = 0 ;
+ while (t3 < 1)
+ tic
+ p = cs_dmperm_orig (A) ;
+ t = toc ;
+ t3 = t3 + t ;
+ k3 = k3 + 1 ;
+ end
+ t3 = t3 / k3 ;
+
+ k4 = 0 ;
+ t4 = 0 ;
+ while (t4 < 1)
+ tic
+ p = cs_dmperm_orig (A') ;
+ t = toc ;
+ t4 = t4 + t ;
+ k4 = k4 + 1 ;
+ end
+ t4 = t4 / k4 ;
+
+ sprnk = sum (p > 0) ;
+ nempty = full (sum (sum (spones (A)) == 0)) ;
+ mempty = full (sum (sum (spones (C)) == 0)) ;
+
+ fprintf ('[m %d:%d n %d:%d (%d)]:\n', m, mempty, n, nempty, sprnk) ;
+ fprintf (' A: t1 %10.6f (%6d) C: t2 %10.6f (%6d) new\n', ...
+ t1, k1, t2, k2) ;
+ fprintf (' A: t3 %10.6f (%6d) C: t4 %10.6f (%6d) orig\n', ...
+ t3, k3, t4, k4) ;
+
+ if (s1 ~= sprnk | s2 ~= sprnk) %#ok
+ s1 %#ok
+ s2 %#ok
+ sprnk %#ok
+ error ('!') ;
+ end
+
+ tt1 (k) = t1 ;
+ tt2 (k) = t2 ;
+ tt3 (k) = t3 ;
+ tt4 (k) = t4 ;
+ mm (k) = m ;
+ nn (k) = n ;
+ ss (k) = sprnk ;
+ me (k) = mempty ;
+ ne (k) = nempty ;
+
+ clear A C
+
+ semilogy (ss(1:k) ./ nn(1:k), tt1(1:k) ./ tt3(1:k), 'o', ...
+ [0 1], [1 1], 'r-') ;
+ drawnow
+
+end
diff --git a/CXSparse/MATLAB/Test/dmspy_test.m b/CXSparse/MATLAB/Test/dmspy_test.m
new file mode 100644
index 0000000..fff2057
--- /dev/null
+++ b/CXSparse/MATLAB/Test/dmspy_test.m
@@ -0,0 +1,28 @@
+function dmspy_test
+%DMSPY_TEST test cspy, cs_dmspy, and cs_dmperm
+% Example:
+% dmspy_test
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+f = find (index.nblocks > 1) ;
+% f = find (index.nblocks > 1 & index.nrows == index.ncols & ...
+% index.nnzdiag == index.nrows) ;
+[ignore i] = sort (index.nnz (f)) ;
+f = f (i) ;
+
+for i = f
+ Prob = UFget (i,index) ;
+ disp (Prob) ;
+ clf
+ subplot (2,2,1) ; cspy (Prob.A) ;
+ subplot (2,2,2) ; cs_dmspy (Prob.A) ;
+ [p,q,r,s,cc,rr] = cs_dmperm (Prob.A) ; %#ok
+ subplot (2,2,3) ; plot (p) ;
+ subplot (2,2,4) ; plot (q) ;
+ drawnow
+end
diff --git a/CXSparse/MATLAB/Test/etree_sample.m b/CXSparse/MATLAB/Test/etree_sample.m
new file mode 100644
index 0000000..9a38f0a
--- /dev/null
+++ b/CXSparse/MATLAB/Test/etree_sample.m
@@ -0,0 +1,71 @@
+function etree_sample
+% ETREE_SAMPLE construct a sample etree and symbolic factorization
+%
+% Example
+% etree_sample
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clf
+
+% desired etree:
+% 1 2 3 4 5 6 7 8 9 10 11
+goal = [6 3 8 6 8 7 9 10 10 11 0] ;
+
+o = 0 ;
+X = 1 ;
+x = 0 ;
+
+A = [
+1 o o o o o o o o o o
+o 2 o o o o o o o o o
+o X 3 o o o o o o o o
+o o o 4 o o o o o o o
+o o o o 5 o o o o o o
+X o o X o 6 o o o o o
+X o o x o x 7 o o o o
+o X x o X o o 8 o o o
+x o o x o X x o 9 o o
+x x X X x X x X x 10 o
+x x X x X x X X x X 11 ] ;
+
+A = A + tril(A,-1)' ;
+disp ('A = ') ;
+disp (A)
+
+[count,h,parent,post,R] = symbfact (A) ;
+L = R' ;
+
+subplot (2,3,1) ;
+spy (A)
+title ('A') ;
+
+subplot (2,3,2) ;
+etreeplot (A)
+title ('etree') ;
+
+% [parent, post] = etree (A) ;
+
+subplot (2,3,3) ;
+spy (L)
+title ('L, not postordered') ;
+
+n = size (A,1) ;
+for k = 1:n
+ fprintf ('parent (%d) = %d goal: %d ok: %d\n', ...
+ k, parent (k), goal (k), goal (k) == parent(k)) ;
+end
+
+
+[count,h,parent2,post2,R] = symbfact (A (post,post)) ;
+L = R' ;
+
+subplot (2,3,5) ;
+spy (A (post,post))
+title ('A postordered') ;
+
+subplot (2,3,6) ;
+spy (L)
+title ('L postordered') ;
diff --git a/CXSparse/MATLAB/Test/givens2.m b/CXSparse/MATLAB/Test/givens2.m
new file mode 100644
index 0000000..5420101
--- /dev/null
+++ b/CXSparse/MATLAB/Test/givens2.m
@@ -0,0 +1,17 @@
+function g = givens2(a,b)
+%GIVENS2 find a Givens rotation.
+% Example:
+% g = givens2(a,b)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (b == 0)
+ c = 1 ; s = 0 ;
+elseif (abs (b) > abs (a))
+ tau = -a/b ; s = 1 / sqrt (1+tau^2) ; c = s*tau ;
+else
+ tau = -b/a ; c = 1 / sqrt (1+tau^2) ; s = c*tau ;
+end
+g = [c -s ; s c] ;
diff --git a/CXSparse/MATLAB/Test/gqr3.m b/CXSparse/MATLAB/Test/gqr3.m
new file mode 100644
index 0000000..9f31d09
--- /dev/null
+++ b/CXSparse/MATLAB/Test/gqr3.m
@@ -0,0 +1,30 @@
+function R = gqr3 (A)
+%GQR3 QR factorization, based on Givens rotations
+%
+% Example:
+% R = gqr3 (A)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+[m n] = size (A) ;
+
+% parent = cs_etree (sparse (A), 'col') ;
+
+for i = 2:m
+ % i
+ for k = 1:min(i-1,n)
+ % k
+ % Givens rotation to zero out A(i,k) using A(k,k)
+ G = givens2 (A(k,k), A(i,k)) ;
+ A ([k i],k:n) = G * A ([k i],k:n) ;
+ A (i,k) = 0 ;
+ % fprintf ('A(21,25)=%g\n', A(21,25)) ;
+ % if (A(21,25) ~= 0)
+ % pause
+ % end
+ end
+end
+R = A ;
diff --git a/CXSparse/MATLAB/Test/happly.m b/CXSparse/MATLAB/Test/happly.m
new file mode 100644
index 0000000..770c5d9
--- /dev/null
+++ b/CXSparse/MATLAB/Test/happly.m
@@ -0,0 +1,11 @@
+function hx = happly (v, beta, x)
+%HAPPLY apply Householder reflection to a vector
+% Example:
+% hx = happly (v,beta,x) ; % computes hx = x - v * (beta * (v' *x)) ;
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+hx = x - v * (beta * (v' *x)) ;
diff --git a/CXSparse/MATLAB/Test/hmake1.m b/CXSparse/MATLAB/Test/hmake1.m
new file mode 100644
index 0000000..52f8c6c
--- /dev/null
+++ b/CXSparse/MATLAB/Test/hmake1.m
@@ -0,0 +1,39 @@
+function [v,beta,xnorm] = hmake1 (x)
+%HMAKE1 construct a Householder reflection
+% Example:
+% [v,beta,xnorm] = hmake1 (x)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = length (x) ;
+if (n == 1)
+ v = 1 ;
+ xnorm = norm (x) ;
+ if (x (1) < 0)
+ beta = 2 ;
+ else
+ beta = 0 ;
+ end
+ return
+end
+sigma = x (2:n)'*x(2:n) ;
+xnorm = sqrt (x (1)^2 + sigma) ;
+v = x ;
+if (sigma == 0)
+ v (1) = 1 ;
+ if (x (1) < 0)
+ beta = 2 ;
+ else
+ beta = 0 ;
+ end
+else
+ if (x (1) <= 0)
+ v (1) = x(1) - xnorm ;
+ else
+ v (1) = -sigma / (x(1) + xnorm) ;
+ end
+ beta = (2*v(1)^2) / (sigma + v(1)^2) ;
+ v = v / v(1) ;
+end
diff --git a/CXSparse/MATLAB/Test/house.m b/CXSparse/MATLAB/Test/house.m
new file mode 100644
index 0000000..6c6c589
--- /dev/null
+++ b/CXSparse/MATLAB/Test/house.m
@@ -0,0 +1,24 @@
+function [v,beta,s] = house (x)
+%HOUSE find a Householder reflection.
+% real or complex case.
+% Example:
+% [v,beta,s] = house (x)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+v = x ;
+s = norm (x) ;
+if (s == 0)
+ beta = 0 ;
+ v (1) = 1 ;
+else
+ if (x (1) ~= 0)
+ s = sign (x (1)) * s ;
+ end
+ v (1) = v (1) + s ;
+ beta = 1 / real (conj (s) * v (1)) ;
+end
+s = - s ;
+
diff --git a/CXSparse/MATLAB/Test/lu_left.m b/CXSparse/MATLAB/Test/lu_left.m
new file mode 100644
index 0000000..73723f6
--- /dev/null
+++ b/CXSparse/MATLAB/Test/lu_left.m
@@ -0,0 +1,25 @@
+function [L,U,P] = lu_left (A)
+%LU_LEFT left-looking LU factorization.
+% Example:
+% [L,U,P] = lu_left (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+P = eye (n) ;
+L = zeros (n) ;
+U = zeros (n) ;
+for k = 1:n
+ x = [ L(:,1:k-1) [ zeros(k-1,n-k+1) ; eye(n-k+1) ]] \ (P * A (:,k)) ;
+ U (1:k-1,k) = x (1:k-1) ; % the column of U
+ [a i] = max (abs (x (k:n))) ; % find the pivot row i
+ i = i + k - 1 ;
+ L ([i k],:) = L ([k i], :) ; % swap rows i and k of L, P, and x
+ P ([i k],:) = P ([k i], :) ;
+ x ([i k]) = x ([k i]) ;
+ U (k,k) = x (k) ;
+ L (k,k) = 1 ;
+ L (k+1:n,k) = x (k+1:n) / x (k) ; % divide the pivot column by U(k,k)
+end
diff --git a/CXSparse/MATLAB/Test/lu_right.m b/CXSparse/MATLAB/Test/lu_right.m
new file mode 100644
index 0000000..39b5ceb
--- /dev/null
+++ b/CXSparse/MATLAB/Test/lu_right.m
@@ -0,0 +1,17 @@
+function [L,U] = lu_right (A)
+%LU_RIGHT right-looking LU factorization.
+% Example:
+% [L,U] = lu_right (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+L = eye (n) ;
+U = zeros (n) ;
+for k = 1:n
+ U (k,k:n) = A (k,k:n) ; % (6.4) and (6.5)
+ L (k+1:n,k) = A (k+1:n,k) / U (k,k) ; % (6.6)
+ A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - L (k+1:n,k) * U (k,k+1:n) ; % (6.7)
+end
diff --git a/CXSparse/MATLAB/Test/lu_rightp.m b/CXSparse/MATLAB/Test/lu_rightp.m
new file mode 100644
index 0000000..84bfbbb
--- /dev/null
+++ b/CXSparse/MATLAB/Test/lu_rightp.m
@@ -0,0 +1,22 @@
+function [L,U,P] = lu_rightp (A)
+%LU_RIGHTP right-looking LU factorization, with partial pivoting.
+%
+% Example:
+% [L,U,P] = lu_rightp (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+P = eye (n) ;
+for k = 1:n
+ [x,i] = max (abs (A (k:n,k))) ; % partial pivoting
+ i = i+k-1 ;
+ P ([k i],:) = P ([i k], :) ;
+ A ([k i],:) = A ([i k], :) ; % (6.10), (6.11)
+ A (k+1:n,k) = A (k+1:n,k) / A (k,k) ; % (6.12)
+ A (k+1:n,k+1:n) = A (k+1:n,k+1:n) - A (k+1:n,k) * A (k,k+1:n) ; % (6.9)
+end
+L = tril (A,-1) + eye (n) ;
+U = triu (A) ;
diff --git a/CXSparse/MATLAB/Test/lu_rightpr.m b/CXSparse/MATLAB/Test/lu_rightpr.m
new file mode 100644
index 0000000..ee5ba84
--- /dev/null
+++ b/CXSparse/MATLAB/Test/lu_rightpr.m
@@ -0,0 +1,29 @@
+function [L,U,P] = lu_rightpr (A)
+%LU_RIGHTPR recursive right-looking LU, with partial pivoting.
+%
+% Example:
+% [L,U,P] = lu_rightpr (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+if (n == 1)
+ P = 1 ;
+ L = 1 ;
+ U = A ;
+else
+ [x,i] = max (abs (A (1:n,1))) ; % partial pivoting
+ P1 = eye (n) ;
+ P1 ([1 i],:) = P1 ([i 1], :) ;
+ A = P1*A ;
+ u11 = A (1,1) ; % (6.10)
+ u12 = A (1,2:n) ; % (6.11)
+ l21 = A (2:n,1) / u11 ; % (6.12)
+ [L22,U22,P2] = lu_rightpr (A (2:n,2:n) - l21*u12) ; % (6.9) or (6.13)
+ o = zeros(1,n-1) ;
+ L = [ 1 o ; P2*l21 L22 ] ; % (6.14)
+ U = [ u11 u12 ; o' U22 ] ;
+ P = [ 1 o ; o' P2] * P1 ;
+end
diff --git a/CXSparse/MATLAB/Test/lu_rightr.m b/CXSparse/MATLAB/Test/lu_rightr.m
new file mode 100644
index 0000000..8f1e74a
--- /dev/null
+++ b/CXSparse/MATLAB/Test/lu_rightr.m
@@ -0,0 +1,21 @@
+function [L,U] = lu_rightr (A)
+%LU_RIGHTR recursive right-looking LU.
+% Example:
+% [L,U] = lu_rightr (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+if (n == 1)
+ L = 1 ;
+ U = A ;
+else
+ u11 = A (1,1) ; % (6.4)
+ u12 = A (1,2:n) ; % (6.5)
+ l21 = A (2:n,1) / u11 ; % (6.6)
+ [L22,U22] = lu_rightr (A (2:n,2:n) - l21*u12) ; % (6.7)
+ L = [ 1 zeros(1,n-1) ; l21 L22 ] ;
+ U = [ u11 u12 ; zeros(n-1,1) U22 ] ;
+end
diff --git a/CXSparse/MATLAB/Test/mynormest1.m b/CXSparse/MATLAB/Test/mynormest1.m
new file mode 100644
index 0000000..414f21b
--- /dev/null
+++ b/CXSparse/MATLAB/Test/mynormest1.m
@@ -0,0 +1,92 @@
+function est = mynormest1 (L, U, P, Q)
+%MYNORMEST1 estimate norm(A,1), using LU factorization (L*U = P*A*Q).
+%
+% Example:
+% est = mynormest1 (L, U, P, Q)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+n = size (L,1) ;
+est = 0 ;
+S = zeros (n,1) ;
+
+for k = 1:5
+
+ if k == 1
+ x = ones (n,1) / n ;
+ else
+
+ j = find (abs (x) == max (abs (x))) ;
+ j = j (1) ;
+ x = zeros (n,1) ;
+ x (j) = 1 ;
+
+ % fprintf ('eka: k %d j %d est %g\n', k, j, est) ;
+ end
+
+
+ % x=A\x, but use the existing P*A*Q=L*U factorization
+
+ x = Q * (U \ (L \ (P*x))) ;
+
+ est_old = est ;
+ est = sum (abs (x)) ;
+
+ unchanged = 1 ;
+ for i = 1:n
+ if (x (i) >= 0)
+ s = 1 ;
+ else
+ s = -1 ;
+ end
+ if (s ~= S (i))
+ S (i) = s ;
+ unchanged = 0 ;
+ end
+ end
+
+ if (any (S ~= signum (x)))
+ S' %#ok
+ signum(x)' %#ok
+ error ('Hey!') ;
+ end
+
+ if k > 1 & (est <= est_old | unchanged) %#ok
+ break ;
+ end
+ x = S ;
+
+ % x=A'\x, but use the existing P*A*Q=L*U factorization
+ x = P' * (L' \ (U' \ (Q'*x))) ;
+
+ if k > 1
+ jnew = find (abs (x) == max (abs (x))) ;
+ if (jnew == j)
+ break ;
+ end
+ end
+
+end
+
+for k = 1:n
+ x (k) = power (-1, k+1) * (1 + ((k-1)/(n-1))) ;
+end
+
+% x=A\x, but use the existing P*A*Q=L*U factorization
+x = Q * (U \ (L \ (P*x))) ;
+
+est_new = 2 * sum (abs (x)) / (3 * n) ;
+if (est_new > est)
+ est = est_new ;
+end
+
+
+
+
+function s = signum (x)
+%SIGNUM compute sign of x
+s = ones (length (x),1) ;
+s (find (x < 0)) = -1 ; %#ok
diff --git a/CXSparse/MATLAB/Test/myqr.m b/CXSparse/MATLAB/Test/myqr.m
new file mode 100644
index 0000000..451518a
--- /dev/null
+++ b/CXSparse/MATLAB/Test/myqr.m
@@ -0,0 +1,56 @@
+function [H,R] = myqr (A)
+%MYQR QR factorization using Householder reflections
+% uses function [v,beta,xnorm] = hmake1 (x)
+% and function hx = happly (v, beta, x)
+%
+% Example
+% [H,R] = myqr (A)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+[m n] = size (A) ;
+
+H = zeros (m,n) ;
+R = zeros (m,n) ;
+
+for k = 1:n
+
+ % apply prior H's
+ % fprintf ('\n-----------------init %d\n', k) ;
+ x = A (:,k) ;
+ for i = 1:k-1
+ v = H(((i+1):m),i) ;
+ v = [1 ; v] ; %#ok
+ beta = H (i,i) ;
+ % n1 = norm (x (i:m)) ;
+ x (i:m) = happly (v, beta, x (i:m)) ;
+ % n2 = norm (x (i:m)) ;
+ % fprintf ('=============== i %d %g %g\n', i, n1, n2) ;
+ % beta
+ % v'
+ % X = x'
+ % pause
+ % i
+ % x
+ end
+ % k
+ % x
+
+ % make Hk
+ % fprintf ('x(k:m) = ') ; x (k:m)
+ [v,beta,xnorm] = hmake1 (x (k:m)) ;
+
+ H (k,k) = beta ;
+ H (k+1:m, k) = v (2:end) ;
+
+ R (1:(k-1),k) = x (1:(k-1)) ;
+ R (k,k) = xnorm ;
+ % full (R)
+ % pause
+end
+
+% s2 = svd (full (R)) ;
+% [s1 s2 s1-s2]
diff --git a/CXSparse/MATLAB/Test/norm1est.m b/CXSparse/MATLAB/Test/norm1est.m
new file mode 100644
index 0000000..edd5d09
--- /dev/null
+++ b/CXSparse/MATLAB/Test/norm1est.m
@@ -0,0 +1,35 @@
+function est = norm1est (L,U,P,Q)
+%NORM1EST 1-norm estimate.
+% L and U must be real.
+% Example:
+% est = norm1est (L,U,P,Q)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (L,1) ;
+for k = 1:5
+ if (k == 1)
+ est = 0 ;
+ x = ones (n,1) / n ;
+ jold = -1 ;
+ else
+ j = min (find (abs (x) == norm (x,inf))) ; %#ok
+ if (j == jold)
+ break
+ end ;
+ x = zeros (n,1) ;
+ x (j) = 1 ;
+ jold = j ;
+ end
+ x = Q * (U \ (L \ (P*x))) ;
+ est_old = est ;
+ est = norm (x,1) ;
+ if (k > 1 & est <= est_old) %#ok
+ break
+ end ;
+ s = ones (n,1) ;
+ s (find (x < 0)) = -1 ; %#ok
+ x = P' * (L' \ (U' \ (Q'*s))) ;
+end
diff --git a/CXSparse/MATLAB/Test/qr2.m b/CXSparse/MATLAB/Test/qr2.m
new file mode 100644
index 0000000..d9b19a5
--- /dev/null
+++ b/CXSparse/MATLAB/Test/qr2.m
@@ -0,0 +1,21 @@
+function [V,Beta,R] = qr2 (A)
+%QR2 QR factorization based on Householder reflections
+%
+% Example:
+% [V,beta,R] = qr2 (A)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+V = zeros (m,n) ;
+Beta = zeros (1,n) ;
+for k = 1:n
+ % [v,beta,s] = gallery ('house', A (k:m,k), 2) ;
+ [v,beta] = house (A (k:m,k)) ;
+ V (k:m,k) = v ;
+ Beta (k) = beta ;
+ A (k:m,k:n) = A (k:m,k:n) - v * (beta * (v' * A (k:m,k:n))) ;
+end
+R = triu (A) ;
diff --git a/CXSparse/MATLAB/Test/qr_givens.m b/CXSparse/MATLAB/Test/qr_givens.m
new file mode 100644
index 0000000..1a59736
--- /dev/null
+++ b/CXSparse/MATLAB/Test/qr_givens.m
@@ -0,0 +1,24 @@
+function R = qr_givens (A)
+%QR_GIVENS Givens-rotation QR factorization.
+% Example:
+% R = qr_givens (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+parent = cs_etree (sparse (A), 'col') ;
+A = full (A) ;
+for i = 2:m
+ k = min (find (A (i,:))) ; %#ok
+ if (isempty (k))
+ continue ;
+ end
+ while (k > 0 & k <= min (i-1,n)) %#ok
+ A ([k i],k:n) = givens2 (A(k,k), A(i,k)) * A ([k i],k:n) ;
+ A (i,k) = 0 ;
+ k = parent (k) ;
+ end
+end
+R = sparse (A) ;
diff --git a/CXSparse/MATLAB/Test/qr_givens_full.m b/CXSparse/MATLAB/Test/qr_givens_full.m
new file mode 100644
index 0000000..5a57cb7
--- /dev/null
+++ b/CXSparse/MATLAB/Test/qr_givens_full.m
@@ -0,0 +1,17 @@
+function R = qr_givens_full (A)
+%QR_GIVENS_FULL Givens-rotation QR factorization, for full matrices.
+% Example:
+% R = qr_givens_full (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+for i = 2:m
+ for k = 1:min(i-1,n)
+ A ([k i],k:n) = givens2 (A(k,k), A(i,k)) * A ([k i],k:n) ;
+ A (i,k) = 0 ;
+ end
+end
+R = A ;
diff --git a/CXSparse/MATLAB/Test/qr_left.m b/CXSparse/MATLAB/Test/qr_left.m
new file mode 100644
index 0000000..8b2a5d5
--- /dev/null
+++ b/CXSparse/MATLAB/Test/qr_left.m
@@ -0,0 +1,26 @@
+function [V,Beta,R] = qr_left (A)
+%QR_LEFT left-looking Householder QR factorization.
+% Example:
+% [V,Beta,R] = qr_left (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+V = zeros (m,n) ;
+Beta = zeros (1,n) ;
+R = zeros (m,n) ;
+for k = 1:n
+ x = A (:,k) ;
+ for i = 1:k-1
+ v = V (i:m,i) ;
+ beta = Beta (i) ;
+ x (i:m) = x (i:m) - v * (beta * (v' * x (i:m))) ;
+ end
+ [v,beta,s] = gallery ('house', x (k:m), 2) ;
+ V (k:m,k) = v ;
+ Beta (k) = beta ;
+ R (1:(k-1),k) = x (1:(k-1)) ;
+ R (k,k) = s ;
+end
diff --git a/CXSparse/MATLAB/Test/qr_right.m b/CXSparse/MATLAB/Test/qr_right.m
new file mode 100644
index 0000000..24de54c
--- /dev/null
+++ b/CXSparse/MATLAB/Test/qr_right.m
@@ -0,0 +1,19 @@
+function [V,Beta,R] = qr_right (A)
+%QR_RIGHT right-looking Householder QR factorization.
+% Example:
+% [V,Beta,R] = qr_right (A)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+[m n] = size (A) ;
+V = zeros (m,n) ;
+Beta = zeros (1,n) ;
+for k = 1:n
+ [v,beta] = gallery ('house', A (k:m,k), 2) ;
+ V (k:m,k) = v ;
+ Beta (k) = beta ;
+ A (k:m,k:n) = A (k:m,k:n) - v * (beta * (v' * A (k:m,k:n))) ;
+end
+R = A ;
diff --git a/CXSparse/MATLAB/Test/sample_colormap.m b/CXSparse/MATLAB/Test/sample_colormap.m
new file mode 100644
index 0000000..50ef089
--- /dev/null
+++ b/CXSparse/MATLAB/Test/sample_colormap.m
@@ -0,0 +1,41 @@
+function sample_colormap
+%SAMPLE_COLORMAP try a colormap for use in cspy
+%
+% Example:
+% sample_colormap
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+h = jet (64) ;
+h = h (64:-1:1,:) ;
+h = h (20:end,:) ;
+
+% h = h (17:128,:) ;
+
+% s = sum (jet,2) ;
+% h (:,1) = h (:,1) ./ s ;
+% h (:,2) = h (:,2) ./ s ;
+% h (:,3) = h (:,3) ./ s ;
+
+h (1,:) = [1 1 1] ; % white
+h (2,:) = [1 1 .8] ; % light yellow
+
+% h
+colormap (h) ;
+
+clf
+subplot (5,1,1) ;
+image (1:size(h,1)) ;
+
+h = rgb2hsv (h) ;
+% h (:,3) = linspace (1,0,64) ;
+% h= hsv2rgb (h) ;
+
+subplot (5,1,2) ; plot (h(:,1)) ; axis ([1 64 0 1]) ; ylabel ('red') ;
+subplot (5,1,3) ; plot (h(:,2)) ; axis ([1 64 0 1]) ; ylabel ('green') ;
+subplot (5,1,4) ; plot (h(:,3)) ; axis ([1 64 0 1]) ; ylabel ('blue') ;
+subplot (5,1,5) ; plot (sum(h,2)) ; axis ([1 64 0 3]) ; ylabel ('sum') ;
+
diff --git a/CXSparse/MATLAB/Test/signum.m b/CXSparse/MATLAB/Test/signum.m
new file mode 100644
index 0000000..ec806bc
--- /dev/null
+++ b/CXSparse/MATLAB/Test/signum.m
@@ -0,0 +1,13 @@
+function s = signum (x)
+%SIGNUM compute and display the sign of a column vector x
+% Example
+% s = signum(x)
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+s = ones (length (x),1) ;
+s (find (x < 0)) = -1 ; %#ok
+disp ('s =') ;
+disp (s) ;
diff --git a/CXSparse/MATLAB/Test/sqr_example.m b/CXSparse/MATLAB/Test/sqr_example.m
new file mode 100644
index 0000000..9c07379
--- /dev/null
+++ b/CXSparse/MATLAB/Test/sqr_example.m
@@ -0,0 +1,29 @@
+function sqr_example
+%SQR_EXAMPLE test cs_sqr
+% Example:
+% sqr_example
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+Prob = UFget (706) ;
+
+A = Prob.A' ;
+q = colamd (A) ;
+A = A (:,q) ;
+A = sprandn (A) ;
+[m n] = size (A) ;
+
+[vnz, rnz, parent, c, leftmost, p] = cs_sqr(A) ;
+
+m2 = length (p) ;
+B = [A ; sparse(m2-m,n)] ;
+B = B (p,q) ;
+
+R1 = gqr3 (B) ;
+
+clf
+subplot (2,2,1) ; spy(A)
+subplot (2,2,3) ; spy (chol (A'*A + 100*speye(n))) ;
+subplot (2,2,4) ; spy (R1) ;
diff --git a/CXSparse/MATLAB/Test/test1.m b/CXSparse/MATLAB/Test/test1.m
new file mode 100644
index 0000000..d5c2196
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test1.m
@@ -0,0 +1,88 @@
+function test1
+%TEST1 test cs_transpose, cs_gaxpy, cs_sparse, cs_sparse2
+%
+% Example:
+% test1
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+for ii = f
+
+ Prob = UFget (ii) ;
+ disp (Prob) ;
+ for cmplex = 0:double(~ispc)
+
+ A = Prob.A ;
+ if (cmplex)
+ A = A + 1i*sprand(A) ;
+ end
+
+ B = A' ;
+ C = cs_transpose (A) ;
+ if (nnz (B-C) ~= 0)
+ error ('!')
+ end
+
+ C = cs_transpose (A,0) ;
+ if (nnz (A.'-C) ~= 0)
+ error ('!')
+ end
+
+ C = cs_transpose (A,1) ;
+ if (nnz (A'-C) ~= 0)
+ error ('!')
+ end
+
+ [m n] = size (A) ;
+ % if (m == n)
+ x = rand (n,1) ;
+ y = rand (m,1) ;
+ z = y+A*x ;
+ q = cs_gaxpy (A,x,y) ;
+ err = norm (z-q,1) / norm (z,1) ;
+ disp (err) ;
+ if (err > 1e-14)
+ error ('!')
+ end
+ % end
+
+ if (~ispc)
+ x = x + 1i*rand (n,1) ;
+ y = y + 1i*rand (m,1) ;
+ z = y+A*x ;
+ q = cs_gaxpy (A,x,y) ;
+ err = norm (z-q,1) / norm (z,1) ;
+ disp (err) ;
+ if (err > 1e-14)
+ error ('!')
+ end
+ end
+
+ [i j x] = find (A) ;
+ p = randperm (length (i)) ;
+ i = i (p) ;
+ j = j (p) ;
+ x = x (p) ;
+ D = sparse (i,j,x) ;
+ E = cs_sparse (i,j,x) ;
+ % [i j x]
+ F = cs_sparse2 (i,j,x) ;
+ if (nnz (D-E) ~= 0)
+ error ('!')
+ end
+ if (nnz (F-E) ~= 0)
+ error ('!')
+ end
+
+ clear A B C D E F
+ % pause
+
+ end
+end
diff --git a/CXSparse/MATLAB/Test/test10.m b/CXSparse/MATLAB/Test/test10.m
new file mode 100644
index 0000000..f33fe9e
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test10.m
@@ -0,0 +1,108 @@
+function test10
+%TEST10 test cs_qr
+%
+% Example:
+% test10
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+
+% f = 185 ;
+% f = 449 ;
+clf
+
+for trials = 1:100
+
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = 0.1 * rand (1) ;
+ A = sprandn (m, n, d) ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ sp = sprank (A) ;
+ % if (sp < n)
+ % continue ;
+ % end
+
+ for cmplex = 0:double(~ispc)
+
+ if (cmplex)
+ A = A + 1i * sprand (A) * norm (A,1) / 10 ;
+ end
+
+ Aorig = A ;
+
+ % A = A (:, colamd (A)) ;
+
+ if (cmplex)
+ tic ;
+ R = chol (A'*A + speye (n)) ;
+ t1 = toc ;
+ else
+ tic ;
+ R = qr (A) ;
+ t1 = toc ;
+ end
+
+ % tic ;
+ % [Q,R] = qr (A) ;
+ % t1 = toc ;
+
+ [c,h,parent] = symbfact (A, 'col') ; %#ok
+ rnz = sum (c) ; %#ok
+ tic ;
+ [V2,Beta2,p,R2] = cs_qr (sparse(A)) ;
+ t2 = toc ;
+
+ C = A ;
+ m2 = size (V2,1) ;
+ if (m2 > m)
+ C = [A ; sparse(m2-m, n)] ;
+ end
+ C = C (p,:) ;
+
+ [H1,R1] = myqr (C) ;
+ err1 = norm (R1-R2,1) / norm (R1) ;
+ disp ('err1 = ') ;
+ disp (err1) ;
+ % [svd(A) svd(R1) svd(full(R2))]
+ s1 = svd (full (A)) ;
+ s2 = svd (full (R2)) ;
+ if (n > 0)
+ err2 = norm (s1 - s2) / s1 (1) ;
+ disp ('err2 = ') ;
+ disp (err2) ;
+ else
+ err2 = 0 ;
+ end
+ fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d vs %d\n', t1, t2, t1/t2, sp, n) ;
+
+ % H2 = full (H2)
+ % R2 = full (R2)
+
+ subplot (2,4,1) ; spy (A) ; title ('A colamd') ;
+ subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ;
+ subplot (2,4,2) ; spy (C) ; title ('A rperm') ;
+ subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ;
+ subplot (2,4,6) ; spy (R) ; title ('matlab R') ;
+ subplot (2,4,7) ; spy (R2) ; title ('spqr R') ;
+ subplot (2,4,8) ; spy (V2) ; title ('spqr H') ;
+ drawnow
+
+ if (err2 > 1e-9)
+ error ('!') ;
+ end
+
+ if (m2 > m)
+ fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ;
+ end
+ end
+end
diff --git a/CXSparse/MATLAB/Test/test11.m b/CXSparse/MATLAB/Test/test11.m
new file mode 100644
index 0000000..2e86baa
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test11.m
@@ -0,0 +1,55 @@
+function test11
+%TEST11 test cs_rowcnt
+%
+% Example:
+% test11
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+
+for i = f
+ Prob = UFget (i, index) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ A = spones (A) ;
+ A = A+A' + speye(n) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ [cc h pa po R] = symbfact (A) ;
+ rc1 = full (sum (R)) ;
+ rc2 = cs_rowcnt (A, pa, po) ;
+ if (any (rc1 ~= rc2))
+ error ('!') ;
+ end
+
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ A = A (p,p) ;
+
+ [cc h pa po R] = symbfact (A) ;
+ rc1 = full (sum (R)) ;
+ rc2 = cs_rowcnt (A, pa, po) ;
+ if (any (rc1 ~= rc2))
+ error ('!') ;
+ end
+
+end
+
diff --git a/CXSparse/MATLAB/Test/test12.m b/CXSparse/MATLAB/Test/test12.m
new file mode 100644
index 0000000..e4c3b49
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test12.m
@@ -0,0 +1,47 @@
+function test12
+%TEST12 test cs_qr and compare with svd
+%
+% Example:
+% test12
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('test 12\n') ;
+rand ('state',0) ;
+% A = rand (3,4)
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = .1 * rand (1) ;
+ A = sprandn (m,n,d) ;
+ if (m < n)
+ continue ;
+ end
+ if (m == 0 | n == 0) %#ok
+ continue ;
+ end
+
+ for cmplex = 0:double(~ispc)
+ if (cmplex)
+ A = A + 1i * sprand (A) ;
+ end
+
+ fprintf ('m %d n %d nnz %d\n', m, n, nnz(A)) ;
+ [V,Beta,p,R] = cs_qr (A) ;
+
+ s1 = svd (full (A)) ;
+ s2 = svd (full (R)) ;
+ s2 = s2 (1:length(s1)) ;
+ err = norm (s1-s2) ;
+ if (length (s1) > 1)
+ err = err / s1 (1) ;
+ end
+ fprintf ('err %g\n', err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+ end
+end
diff --git a/CXSparse/MATLAB/Test/test13.m b/CXSparse/MATLAB/Test/test13.m
new file mode 100644
index 0000000..fd3b2e5
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test13.m
@@ -0,0 +1,88 @@
+function test13
+%TEST13 test cs_counts, cs_etree
+%
+% Example:
+% test13
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+randn ('state',0) ;
+rand ('state',0) ;
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = .1 * rand (1) ;
+ A = sprandn (n,n,d) ;
+ C = sprandn (m,n,d) ;
+ A = A+A' ;
+ fprintf ('m %4d n %4d nnz(A) %6d nnz(C) %6d\n', m, n, nnz(A), nnz(C)) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ [p1,po1] = etree (A) ;
+
+ [p2,po2] = cs_etree (A) ;
+ [p3,po3] = cs_etree (A, 'sym') ;
+ % po2 = cs_post (p2) ;
+
+ check_if_same (p1,p2) ;
+ check_if_same (po1,po2) ;
+
+ check_if_same (p1,p3) ;
+ check_if_same (po1,po3) ;
+
+ c1 = symbfact (A) ;
+ c2 = cs_counts (A) ;
+
+ % A-A'
+
+ check_if_same (c1,c2) ;
+
+ c2 = cs_counts (triu (A)) ;
+ check_if_same (c1,c2) ;
+ % pause
+
+ p0 = etree (A, 'col') ;
+ % p1 = etree2 (A, 'col') ; % CHOLMOD
+ p2 = cs_etree (A, 'col') ;
+
+ if (~isempty (A))
+ check_if_same (p0,p2) ;
+ end
+
+ p0 = etree (C, 'col') ;
+ % p1 = etree2 (C, 'col') ; % CHOLMOD
+ p2 = cs_etree (C, 'col') ;
+
+ if (~isempty (C))
+ check_if_same (p0,p2) ;
+ end
+
+ % find etree of A'A, and postorder it
+ [m n] = size (A) ; %#ok
+ % full (A)
+
+ [cp0 cpo0] = etree (A, 'col') ;
+ % [cp1 cpo1] = etree2 (A, 'col') ; % CHOLMOD
+ [cp2 cpo2] = cs_etree (A, 'col') ;
+ % cpo2 = cs_post (cp2) ;
+
+ check_if_same (cp0, cp2) ;
+ check_if_same (cpo0, cpo2) ;
+
+ c0 = symbfact (A, 'col') ;
+ % c1 = symbfact2 (A, 'col') ; % CHOLMOD
+ c2 = cs_counts (A, 'col') ;
+
+ check_if_same (c0, c2) ;
+
+end
diff --git a/CXSparse/MATLAB/Test/test14.m b/CXSparse/MATLAB/Test/test14.m
new file mode 100644
index 0000000..4de44a1
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test14.m
@@ -0,0 +1,45 @@
+function test14
+%TEST14 test cs_droptol
+%
+% Example:
+% test14
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = 0.1*rand (1) ;
+ A = sprandn (m,n,d) ;
+ [i j x] = find (A) ;
+ A = sparse (i,j,2*x-1) ;
+ fprintf ('test14 m %3d n %3d nz %d\n', m, n, nnz (A)) ;
+
+ for cmplex = 0:double(~ispc)
+
+ if (cmplex)
+ A = A + 1i * sparse (i,j,2*rand(size(x))-1) ;
+ end
+
+ % using CSparse
+ tol = 0.5 ;
+ B = cs_droptol (A, tol) ;
+
+ % using MATLAB
+ C = A .* (abs (A) > tol) ;
+ % [m n] = size (A) ;
+ % s = abs (A) > tol ;
+ % [i j] = find (s) ;
+ % x = A (find (s)) ;
+ % A = sparse (i, j, x, m, n) ;
+
+ if (norm (C-B,1) > 0)
+ error ('!') ;
+ end
+ end
+end
diff --git a/CXSparse/MATLAB/Test/test15.m b/CXSparse/MATLAB/Test/test15.m
new file mode 100644
index 0000000..9269d36
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test15.m
@@ -0,0 +1,56 @@
+function test15
+%TEST15 test cs_amd
+%
+% Example:
+% test15
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+clf
+
+for trials = 1:100
+ n = fix (200 * rand (1)) ;
+ d = 0.05 * rand (1) ;
+ A = sprandn (n, n, d) ;
+
+ % add a randomly placed dense column
+ k = fix (n * rand (1)) ;
+ k = max (1, k) ;
+ k = min (n, k) ;
+ if (n > 0)
+ A (:,k) = 1 ;
+ end
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ try
+ p0 = amd (A) ;
+ catch
+ p0 = symamd (A) ;
+ end
+ p1 = cs_amd (A) ;
+
+ if (any (sort (p1) ~= 1:n))
+ error ('not perm!') ;
+ end
+
+ C = A+A' + speye (n) ;
+ lnz0 = sum (symbfact (C (p0,p0))) ;
+ lnz1 = sum (symbfact (C (p1,p1))) ;
+ subplot (1,3,1) ; spy (C)
+ subplot (1,3,2) ; spy (C (p0,p0))
+ subplot (1,3,3) ; spy (C (p1,p1))
+ fprintf ('n %4d nz %6d lnz %6d %6d\n', n, nnz(A), lnz0, lnz1) ;
+ drawnow
+
+end
+
diff --git a/CXSparse/MATLAB/Test/test16.m b/CXSparse/MATLAB/Test/test16.m
new file mode 100644
index 0000000..fe7529c
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test16.m
@@ -0,0 +1,96 @@
+function test16
+%TEST16 test cs_amd
+%
+% Example:
+% test16
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+clf
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+skip = 811 ;
+
+% f = 719
+
+for i = f
+ if (any (i == skip))
+ continue
+ end
+ Prob = UFget (i) ;
+ A = spones (Prob.A) ;
+ Aorig = A ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ if (m ~= n)
+ A = A'*A ;
+ end
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ fprintf ('n %4d nz %d\n', n, nnz (A)) ;
+
+ try
+ p0 = amd (A) ;
+ catch
+ p0 = symamd (A) ;
+ end
+ fprintf ('symmetric case:\n') ;
+ p1 = cs_amd (A) ;
+
+ if (any (sort (p1) ~= 1:n))
+ error ('not perm!') ;
+ end
+
+ C = A+A' + speye (n) ;
+ lnz0 = sum (symbfact (C (p0,p0))) ;
+ lnz1 = sum (symbfact (C (p1,p1))) ;
+ subplot (2,3,1) ; spy (C)
+ subplot (2,3,2) ; spy (C (p0,p0)) ; title ('amd') ;
+ subplot (2,3,3) ; spy (C (p1,p1)) ; title ('csamd') ;
+ drawnow
+
+ if (lnz0 ~= lnz1)
+ fprintf ('----------------- lnz %d %d %9.4f\n', ...
+ lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ;
+ end
+
+ if (1)
+
+ p0 = colamd (Aorig) ;
+ [m n] = size (Aorig) ;
+ fprintf ('m %d n %d\n', m, n) ;
+
+ fprintf ('A''A case, no dense rows (for QR):\n') ;
+ p1 = cs_amd (Aorig, 3) ;
+ if (any (sort (p1) ~= 1:n))
+ error ('not perm!') ;
+ end
+
+ subplot (2,3,4) ; spy (Aorig)
+ subplot (2,3,5) ; spy (Aorig (:,p0)) ; title ('colamd') ;
+ subplot (2,3,6) ; spy (Aorig (:,p1)) ; title ('cs amd(A''A)') ;
+ lnz0 = sum (symbfact (Aorig (:,p0), 'col')) ;
+ lnz1 = sum (symbfact (Aorig (:,p1), 'col')) ;
+ fprintf (' A''A: %7d %7d %9.4f\n', ...
+ lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ;
+ drawnow
+
+ % pause
+
+ end
+end
+
diff --git a/CXSparse/MATLAB/Test/test17.m b/CXSparse/MATLAB/Test/test17.m
new file mode 100644
index 0000000..1ab9406
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test17.m
@@ -0,0 +1,115 @@
+function test17
+%TEST17 test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol
+%
+% Example:
+% test17
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+clf
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+for trials = 1:100
+
+ m = 1 + fix (10 * rand (1)) ;
+ n = 1 + fix (10 * rand (1)) ;
+ d = rand (1) ;
+% n = m ;
+
+ A = sprandn (m, n, d) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ subplot (3,4,1) ; spy (A) ;
+
+ [V1, Beta1, p1, R1, q1] = cs_qr (A) ;
+ Q1 = cs_qright (V1, Beta1, p1, speye (size (V1,1))) ;
+ Q1b = cs_q1 (V1, Beta1, p1) ;
+
+ err = norm (Q1-Q1b,1) ;
+ disp ('err = ') ;
+ disp (err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+ m2 = size (Q1,1) ;
+ A1 = [A ; sparse(m2-m,n)] ;
+
+ subplot (3,4,5) ; spy (A1 (p1,q1)) ;
+ subplot (3,4,6) ; spy (V1) ;
+ subplot (3,4,7) ; spy (R1) ;
+ subplot (3,4,8) ; spy (Q1) ;
+
+ [V3, Beta3, R3] = qr2 (A) ;
+ % Q3 = cs_qmake (V3, Beta3) ;
+ Q3 = cs_q1 (V3, Beta3) ;
+ subplot (3,4,9) ; spy (A) ;
+ subplot (3,4,10) ; spy (V3) ;
+ subplot (3,4,11) ; spy (R3) ;
+ subplot (3,4,12) ; spy (Q3) ;
+
+ err1 = norm (Q1*R1 - A1(:,q1), 1) ;
+% err2 = norm (Q2*R2 - A (:,q2), 1) ;
+ err3 = norm (Q3*R3 - A, 1) ;
+
+ fprintf ('m %3d m2 %3d n %3d ::: %3d %6.2e %6.2e\n', ...
+ m, m2, n, m2-m, err1, err3) ;
+
+ if (err1 > 1e-12)
+ error ('2!') ;
+ end
+
+% if (err2 > 1e-12)
+% error ('!') ;
+% end
+
+ if (err3 > 1e-12)
+ error ('3!') ;
+ end
+
+try
+
+ % this fails if A is complex
+ b = rand (m,1) ;
+ [Q,R] = qr (A (:,q1)) ;
+ x = R\(Q'*b) ;
+ x (q1) = x ;
+ r1 = norm (A*x-b) ;
+
+ x2 = cs_qrsol (A,b) ;
+ r2 = norm (A*x2(1:n)-b) ;
+
+ qt = cs_qleft (V1, Beta1, p1, speye(size(V1,1))) ;
+ fprintf ('Q''*A-R: %6.2e\n', norm (qt*A1(:,q1)-R1,1)) ;
+
+ qtb = cs_qleft (V1, Beta1, p1, b) ;
+ % [V1, Beta1, p1, R1, q1] = cs_qr (A) ;
+ x3 = R1 \ qtb ;
+ r3 = norm (A(:,q1)*x3(1:n)-b) ;
+
+ fprintf ('least sq: %6.2e %6.2e %6.2e diff %6.2e %6.2e\n', ...
+ r1, r2, r3, r1-r2, r1-r3) ;
+
+catch
+end
+
+ drawnow
+
+ % pause
+
+end
diff --git a/CXSparse/MATLAB/Test/test18.m b/CXSparse/MATLAB/Test/test18.m
new file mode 100644
index 0000000..b2d9339
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test18.m
@@ -0,0 +1,34 @@
+function test18
+%TEST18 test iterative refinement after backslash
+%
+% Example:
+% test18
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+clf
+% f = f(1)
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (~isreal (A) | m ~= n) %#ok
+ continue
+ end
+
+ b = rand (n,1) ;
+ x = A\b ;
+ r = b - A*x ;
+ x = x + A\r ;
+
+ fprintf ('\n%6.2e to %6.2e\n', norm (r), norm (b-A*x)) ;
+end
diff --git a/CXSparse/MATLAB/Test/test19.m b/CXSparse/MATLAB/Test/test19.m
new file mode 100644
index 0000000..6143241
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test19.m
@@ -0,0 +1,209 @@
+function test19
+%TEST19 test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc, cspy
+%
+% Example:
+% test19
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+clf
+
+for trials = 1:100
+
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ % d = 0.1 * rand (1) ;
+ d = rand (1) * 4 * max (m,n) / max (m*n,1) ;
+ A = sprandn (m,n,d) ;
+ S = sprandn (m,m,d) + speye (m) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ if (rand ( ) > .5)
+ S = S + 1i * sprand (S) ;
+ end
+ end
+
+ subplot (2,3,1) ;
+ cspy (A) ;
+
+ pp = dmperm (A) ;
+
+ sprnk = sum (pp > 0) ;
+
+ pp2 = cs_dmperm (A) ;
+ spr2 = sum (pp2 > 0) ;
+ if (spr2 ~= sprnk)
+ error ('!')
+ end
+
+ pp2 = cs_maxtransr (A) ;
+ spr2 = sum (pp2 > 0) ;
+ if (spr2 ~= sprnk)
+ error ('!')
+ end
+
+ [p,q,r,s] = dmperm (A) ;
+ C = A (p,q) ;
+ % r
+ % s
+
+ nk = length (r) - 1 ;
+
+ fprintf ('sprnk: %d m %d n %d nb: %d\n', sprnk, m, n, nk) ;
+
+ subplot (2,3,2) ;
+ hold off
+ spy (C)
+ hold on
+
+ for k = 1:nk
+ r1 = r(k) ;
+ r2 = r(k+1) ;
+ c1 = s(k) ;
+ c2 = s(k+1) ;
+ plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+ end
+
+ [p2,q2,rr2,ss2,cp,rp] = cs_dmperm (A) ;
+
+ if (min (m,n) > 0)
+ if (length (rr2) ~= length (r))
+ error ('# fine blocks!') ;
+ end
+ end
+
+ if (rp (4) - 1 ~= sprnk)
+ rp %#ok
+ sprnk %#ok
+ error ('!') ;
+ end
+
+ if (any (sort (p2) ~= 1:m))
+ error ('p2!') ;
+ end
+
+ if (any (sort (q2) ~= 1:n))
+ error ('q2!') ;
+ end
+
+ if (cp (5) ~= n+1)
+ error ('cp!') ;
+ end
+
+ if (rp (5) ~= m+1)
+ error ('rp!') ;
+ end
+
+ C = A (p2,q2) ;
+
+ subplot (2,3,3) ; cs_dmspy (A,0) ;
+
+ % hold off
+ % spy (C) ;
+ % hold on
+
+ % r1 = rp(1) ;
+ % r2 = rp(2) ;
+ % c1 = cp(1) ;
+ % c2 = cp(2) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ r1 = rp(1) ;
+ r2 = rp(2) ;
+ c1 = cp(2) ;
+ c2 = cp(3) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ B = C (r1:r2-1, c1:c2-1) ;
+ if (nnz (diag (B)) ~= size (B,1))
+ error ('C1 diag!') ;
+ end
+
+ r1 = rp(2) ;
+ r2 = rp(3) ;
+ c1 = cp(3) ;
+ c2 = cp(4) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'r') ;
+
+ B = C (r1:r2-1, c1:c2-1) ;
+ if (nnz (diag (B)) ~= size (B,1))
+ error ('C2 diag!') ;
+ end
+
+ r1 = rp(3) ;
+ r2 = rp(4) ;
+ c1 = cp(4) ;
+ c2 = cp(5) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ B = C (r1:r2-1, c1:c2-1) ;
+ if (nnz (diag (B)) ~= size (B,1))
+ error ('C3 diag!') ;
+ end
+
+ r1 = rp(4) ; %#ok
+ r2 = rp(5) ; %#ok
+ c1 = cp(4) ; %#ok
+ c2 = cp(5) ; %#ok
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ if (~isempty (S))
+
+ [p1,q1,r0,s0] = dmperm (S) ;
+ [p3,r3] = cs_scc (S) ;
+ if (length (r3) ~= length (r0))
+ error ('scc size!') ;
+ end
+
+ if (any (sort (p3) ~= 1:m))
+ error ('scc perm!') ;
+ end
+
+ nk = length (r0)-1 ;
+
+ subplot (2,3,4) ;
+ hold off
+ spy (S (p1,q1)) ;
+ hold on
+ for k = 1:nk
+ r1 = r0(k) ;
+ r2 = r0(k+1) ;
+ c1 = s0(k) ;
+ c2 = s0(k+1) ;
+ plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+ end
+
+ subplot (2,3,5) ;
+ hold off
+ spy (S (p3,p3)) ;
+ hold on
+ for k = 1:nk
+ r1 = r3(k) ;
+ r2 = r3(k+1) ;
+ c1 = r3(k) ;
+ c2 = r3(k+1) ;
+ plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+ end
+
+ end
+
+ subplot (2,3,6) ;
+ cs_dmspy (A) ;
+ drawnow
+ % pause
+
+
+
+
+end
diff --git a/CXSparse/MATLAB/Test/test2.m b/CXSparse/MATLAB/Test/test2.m
new file mode 100644
index 0000000..6d603fa
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test2.m
@@ -0,0 +1,113 @@
+function test2
+%TEST2 test cs_sparse, cs_permute, cs_pvec, cs_ipvec, cs_symperm
+%
+% Example:
+% test2
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0)
+% clf
+
+for trial = 1:100
+ m = fix (10 * rand (1)) ;
+ n = fix (10 * rand (1)) ;
+ nz = fix (100 * rand (1)) ;
+
+ i = 1 + fix (m * rand (nz,1)) ;
+ j = 1 + fix (n * rand (nz,1)) ;
+ x = rand (nz,1) ;
+
+ if (~ispc)
+ if (mod (trial, 2) == 1)
+ x = x + 1i * (2*rand(nz,1)-1) ;
+ end
+ end
+
+ A = sparse (i,j,x) ;
+ B = cs_sparse (i,j,x) ;
+ D = cs_sparse2 (i,j,x) ;
+ fprintf ('%3d %3d %6d : %6d %6d : %d\n', ...
+ m, n, nz, nnz (A), nnz(B), nz-nnz(A)) ;
+
+ err = norm (A-B,1) / max (1, norm (A,1)) ;
+ if (err > 0)
+ disp ('err = ') ;
+ disp (err) ;
+ end
+ if (err > 1e-14)
+ error ('!') ;
+ end
+
+ if (nnz (B-D) > 0)
+ error ('!') ;
+ end
+
+ if (nnz (A) ~= nnz (B))
+ error ('nz!') ;
+ end
+
+ if (max (1,nnz (B)) ~= max (1,nzmax (B)))
+ nnz (B)
+ nzmax (B)
+ error ('nzmax!') ;
+ end
+ % pack
+
+
+ [m n] = size (A) ;
+ p = randperm (m) ;
+ q = randperm (n) ;
+ C1 = A (p,q) ;
+ C2 = cs_permute (A,p,q) ;
+ err = norm (C1-C2,1) ;
+ if (err > 0)
+ error ('!') ;
+ end
+
+% subplot (1,2,1) ; spy (A)
+% subplot (1,2,2) ; spy (C2)
+% drawnow
+
+ x = rand (m,1) ;
+
+ if (~ispc)
+ if (mod (trial, 2) == 1)
+ x = x + 1i * (2*rand(m,1)-1) ;
+ end
+ end
+
+ x1 = x (p) ;
+ x2 = cs_pvec (x, p) ;
+
+ err = norm (x1-x2,1) ;
+ if (err > 0)
+ error ('!') ;
+ end
+
+ x1 = zeros (m,1) ;
+ x1 (p) = x ; %#ok
+ x2 = cs_ipvec (x, p) ; %#ok
+
+ n = min (m,n) ;
+ B = A (1:n, 1:n) ;
+ p = randperm (n) ;
+ B = B+B' ;
+
+ C1 = triu (B (p,p)) ;
+ C2 = cs_symperm (B,p) ;
+
+ try
+ pp = amd (C2) ; %#ok
+ catch
+ pp = symamd (C2) ; %#ok
+ end
+
+ err = norm (C1-C2,1) ;
+ if (err > 0)
+ error ('!') ;
+ end
+
+end
diff --git a/CXSparse/MATLAB/Test/test20.m b/CXSparse/MATLAB/Test/test20.m
new file mode 100644
index 0000000..d2264ae
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test20.m
@@ -0,0 +1,59 @@
+function test20
+%TEST20 test chol_updown2
+%
+% Example:
+% test20
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+rand ('state', 0) ;
+maxerr = [0 0 0 0] ;
+
+for trials = 1:100
+
+ n = fix (100 * rand (1)) ;
+ A = rand (n) ;
+
+ if (~ispc)
+ if (mod (trials, 2) == 0)
+ A = A + 1i*rand(n) ;
+ end
+ end
+
+ A1 = A*A' + n*eye (n) ;
+
+ try
+ L1 = chol (A1)' ;
+ catch
+ continue ;
+ end
+ err1 = norm (L1*L1'-A1) ;
+
+ w = rand (n,1) ;
+
+ A2 = A1 + w*w' ;
+
+ L2 = chol (A2)' ;
+ err2 = norm (L2*L2'-A2) ;
+
+ % try an update
+ L2b = chol_updown2 (L1, +1, w) ;
+ err2b = norm (L2b*L2b'-A2) ;
+
+ % try a downdate
+ L1b = chol_updown2 (L2, -1, w) ; %#ok
+ err1b = norm (L1b*L1b'-A1) ;
+
+
+ fprintf ('%3d: %6.2e %6.2e : %6.2e %6.2e\n', n, err1, err2, err2b, err1b) ;
+ % pause
+
+ maxerr = max (maxerr, [err1 err2 err2b err1b]) ;
+end
+
+fprintf ('maxerr: %g\n', maxerr) ;
diff --git a/CXSparse/MATLAB/Test/test21.m b/CXSparse/MATLAB/Test/test21.m
new file mode 100644
index 0000000..37ce99b
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test21.m
@@ -0,0 +1,119 @@
+function test21
+%TEST21 test cs_updown, chol_updown2
+%
+% Example:
+% test21
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+clf
+
+for trials = 1:100
+ if (trials <= 1)
+ n = trials ;
+ else
+ n = 1+fix (100 * rand (1)) ;
+ end
+ fprintf ('n: %d\n', n) ;
+ d = 0.1 * rand (1) ;
+ A = sprandn (n,n,d) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ A = A+A' + 100 * speye (n) ;
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ A = sparse (A (p,p)) ;
+
+ try
+ L = chol (A)' ;
+ catch
+ continue ;
+ end
+
+ parent = etree (A) ;
+
+ subplot (1,3,1) ;
+ spy (A) ;
+
+ if (n > 0)
+ subplot (1,3,2) ;
+ treeplot (parent) ;
+ end
+
+ subplot (1,3,3) ;
+ spy (L) ;
+
+ drawnow
+
+ for trials2 = 1:10
+
+ k = 1+fix (n * rand (1)) ;
+ if (k <= 0 | k > n) %#ok
+ k = 1 ;
+ end
+
+ w = sprandn (L (:,k)) ;
+ Anew = A + w*w' ;
+
+ Lnew = cs_updown (L, w, parent) ;
+ err6 = norm (Lnew*Lnew' - Anew, 1) ;
+
+ Lnew = cs_updown (L, w, parent, '+') ;
+ err7 = norm (Lnew*Lnew' - Anew, 1) ;
+
+ [Lnew, wnew] = chol_updown2 (L, 1, w) ;
+ err2 = norm (Lnew*Lnew' - Anew, 1) ;
+ err10 = norm (wnew - (L\w)) ;
+
+ L3 = chol_updown2 (L, +1, w) ;
+ err9 = norm (L3*L3' - Anew, 1) ;
+
+
+
+ [L2, wnew] = chol_updown2 (Lnew, -1, w) ;
+ err3 = norm (L2*L2' - A, 1) ;
+ err11 = norm (wnew - (Lnew\w)) ;
+
+ L2 = cs_updown (Lnew, w, parent, '-') ;
+ err5 = norm (L2*L2' - A, 1) ;
+
+ L2 = chol_updown2 (Lnew, -1, w) ;
+ err8 = norm (L2*L2' - A, 1) ;
+
+ err = max ([err2 err3 err5 err6 err7 err9 err8 err10 err11]) ;
+
+ fprintf (' k %3d %6.2e\n', k, err) ;
+
+ if (err > 1e-11)
+ err2 %#ok
+ err3 %#ok
+ err5 %#ok
+ err6 %#ok
+ err7 %#ok
+ err8 %#ok
+ err9 %#ok
+ err10 %#ok
+ err11 %#ok
+ pause
+ end
+
+
+ end
+ % pause
+
+end
diff --git a/CXSparse/MATLAB/Test/test22.m b/CXSparse/MATLAB/Test/test22.m
new file mode 100644
index 0000000..ab32370
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test22.m
@@ -0,0 +1,58 @@
+function test22
+%TEST22 test cond1est
+%
+% Example:
+% test22
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+
+clf
+% f = f(1)
+
+nprob = length (f) ;
+C1 = zeros (nprob,1) ;
+C2 = zeros (nprob,1) ;
+C3 = zeros (nprob,1) ;
+
+
+for k = 1:length (f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (~isreal (A) | m ~= n) %#ok
+ continue
+ end
+
+ c1 = condest (A) ;
+ c2 = cond1est (A) ;
+ if (c1 == c2)
+ err = 0 ;
+ else
+ err = (c1-c2)/max(1,c1) ;
+ end
+
+ c3 = cond (full (A), 1) ;
+
+ fprintf ('%10.4e %10.4e (%10.4e) : %10.4e\n', c1, c2, c3, err) ;
+
+ C1 (k) = c1 ;
+ C2 (k) = c2 ;
+ C3 (k) = c3 ;
+
+ subplot (1,2,1) ;
+ loglog (C1, C2, 'x', [1 1e20], [1 1e20], 'r') ;
+ subplot (1,2,2) ;
+ loglog (C3, C2, 'x', [1 1e20], [1 1e20], 'r') ;
+ drawnow
+
+end
diff --git a/CXSparse/MATLAB/Test/test23.m b/CXSparse/MATLAB/Test/test23.m
new file mode 100644
index 0000000..d4c12e6
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test23.m
@@ -0,0 +1,38 @@
+function test23
+%TEST23 test cs_dmspy
+%
+% Example:
+% test23
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clear functions
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+clf
+
+for trials = 1:1000
+
+ % m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ m = n ;
+ % d = 0.1 * rand (1) ;
+ d = rand (1) * 4 * max (m,n) / max (m*n,1) ;
+ A = sprandn (m,n,d) ;
+ % S = sprandn (m,m,d) + speye (m) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ cs_dmspy (A) ;
+ drawnow
+
+ % pause
+end
diff --git a/CXSparse/MATLAB/Test/test24.m b/CXSparse/MATLAB/Test/test24.m
new file mode 100644
index 0000000..0134224
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test24.m
@@ -0,0 +1,63 @@
+function test24
+%TEST24 test cs_fielder
+%
+% Example:
+% test24
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+
+clf
+% f = f(1)
+
+for k = 1:length (f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = real (Prob.A) ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ S = A ;
+
+ if (~ispc)
+ if (mod (k,2) == 0)
+ S = S + 1i * sprand (A) ;
+ end
+ end
+
+ tic
+ p1 = symrcm (A) ;
+ t1 = toc ;
+
+ tic
+ p2 = cs_fiedler (S) ;
+ t2 = toc ;
+
+ rel = t2 / max (t1,1e-6) ;
+
+ fprintf ('time: symrcm %8.3f fiedler %8.3f rel %8.2f\n', t1, t2, rel) ;
+
+ A = A|A' ;
+
+ subplot (1,3,1) ; spy (A) ;
+ subplot (1,3,2) ; spy (A (p1,p1)) ;
+ subplot (1,3,3) ; spy (A (p2,p2)) ;
+
+ % evaluate the profile ...
+
+
+ drawnow
+ % pause
+end
diff --git a/CXSparse/MATLAB/Test/test25.m b/CXSparse/MATLAB/Test/test25.m
new file mode 100644
index 0000000..26c488d
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test25.m
@@ -0,0 +1,73 @@
+function test25
+%TEST25 test cs_nd
+%
+% Example:
+% test25
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:400) ;
+
+clf
+% f = f(1)
+
+for k = 1:length (f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = real (Prob.A) ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ A = A|A' ;
+
+ S = A ;
+ if (~ispc)
+ if (mod (k,2) == 0)
+ S = S + 1i * sprand (A) ;
+ end
+ end
+
+ tic ;
+ p1 = symrcm (A) ;
+ t1 = toc ;
+
+ tic ;
+ p2 = cs_nd (sparse (1)) ;
+ toc ;
+ if (p2 ~= 1)
+ error ('!') ;
+ end
+
+ tic ;
+ p2 = cs_nd (S) ;
+ t2 = toc ;
+
+ if (any (sort (p2) ~= 1:n))
+ error ('!') ;
+ end
+
+ rel = t2 / max (t1,1e-6) ;
+
+ fprintf ('time: symrcm %8.3f nd %8.3f rel %8.2f\n', t1, t2, rel) ;
+
+ subplot (1,3,1) ; spy (A) ;
+ subplot (1,3,2) ; spy (A (p1,p1)) ;
+ subplot (1,3,3) ; spy (A (p2,p2)) ;
+
+ % evaluate the profile ...
+
+
+ drawnow
+ % pause
+end
diff --git a/CXSparse/MATLAB/Test/test26.m b/CXSparse/MATLAB/Test/test26.m
new file mode 100644
index 0000000..7e3ddb2
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test26.m
@@ -0,0 +1,91 @@
+function test26
+%TEST26 test cs_dmsol and cs_dmspy
+%
+% Example:
+% test26
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+clf
+
+ntrials = 1000 ;
+e1 = zeros (ntrials,1) ;
+e2 = zeros (ntrials,1) ;
+
+for trials = 1:ntrials
+
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ % d = 0.1 * rand (1) ;
+ d = rand (1) * 4 * max (m,n) / max (m*n,1) ;
+ A = sprandn (m,n,d) ;
+ % S = sprandn (m,m,d) + speye (m) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ subplot (1,3,2) ; spy (A) ;
+ subplot (1,3,3) ; cs_dmspy (A) ;
+
+ b = rand (m,1) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ b = b + 1i * rand (size (b)) ;
+ end
+ end
+ % MATLAB cannot do A\b when A is sparse and rectangular and either
+ % A or b are complex
+ if (m ~= n & isreal (A) & ~isreal (b)) %#ok
+ x1 = (A\real(b)) + 1i * (A\imag(b)) ;
+ err1 = norm (A*x1-b) ;
+ elseif ((m ~= n) & ~isreal (A)) %#ok
+ err1 = 1 ;
+ else
+ x1 = A\b ;
+ err1 = norm (A*x1-b) ;
+ end
+
+ x2 = cs_dmsol (A,b) ;
+
+ err2 = norm (A*x2-b) ;
+
+ lerr1 = log10 (max (err1, eps)) ;
+ lerr2 = log10 (max (err2, eps)) ;
+
+ fprintf ('rank: %3d %3d err %6.2e %6.2e : %6.1f\n', ...
+ sprank(A), rank(full(A)), err1, err2, lerr1 - lerr2) ;
+
+ if (isnan (err1))
+ lerr1 = 10 ;
+ end
+ if (isnan (err2))
+ lerr2 = 10 ;
+ end
+
+ if (lerr2 > lerr1 + 5)
+ % pause
+ end
+
+ e1 (trials) = lerr1 ;
+ e2 (trials) = lerr2 ;
+
+ subplot (1,3,1) ; plot (e1, e2, 'o', [-16 10], [-16 10], 'r') ;
+ xlabel ('MATLAB error') ;
+ ylabel ('dmsol error') ;
+
+
+ drawnow
+ % pause
+end
diff --git a/CXSparse/MATLAB/Test/test27.m b/CXSparse/MATLAB/Test/test27.m
new file mode 100644
index 0000000..3c1418c
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test27.m
@@ -0,0 +1,47 @@
+function test27
+%TEST27 test cs_qr, cs_utsolve, cs_qrsol
+%
+% Example:
+% test27
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+
+clear functions
+rand ('state', 0) ;
+
+Prob = UFget ('HB/ibm32') ;
+A = Prob.A ;
+A = A (1:10,:) ;
+[m n] = size (A) ;
+
+[V,Beta,p,R,q] = cs_qr (A') ;
+
+b = rand (m,1) ;
+
+Rm = R (1:m,1:m) ;
+
+bq = b (q) ;
+rtbq = Rm' \ bq ;
+
+rt2 = cs_utsolve (Rm, bq) ;
+
+norm (rtbq - rt2)
+
+x = [rt2 ; zeros(n-m,1)] ;
+
+for k = m:-1:1
+ x = x - V(:,k) * (Beta (k) * (V (:,k)' * x)) ;
+end
+
+x (p) = x ;
+
+norm (A*x-b)
+
+x2 = cs_qrsol (A,b) ;
+
+norm (A*x2-b)
+norm (x-x2)
diff --git a/CXSparse/MATLAB/Test/test28.m b/CXSparse/MATLAB/Test/test28.m
new file mode 100644
index 0000000..a64c5ce
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test28.m
@@ -0,0 +1,120 @@
+function test28
+%TEST28 test cs_randperm, cs_dmperm
+%
+% Example:
+% test28
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clear functions
+
+rand ('state', 0) ;
+for n = 1:100
+ for trials = 1:1000
+ p = cs_randperm (n, rand) ;
+ if (any (sort (p) ~= 1:n))
+ n %#ok
+ p %#ok
+ error ('!')
+ end
+ end
+end
+
+index = UFget ;
+[ignore f] = sort (index.nnz) ;
+
+fprintf ('p=dmperm (std, rand, rev) [p,q,r,s]=dmperm (std, rand, rev)\n') ;
+
+nmat = length (f) ;
+nmat = min (100, nmat) ;
+T1 = zeros (nmat,1) ;
+T2 = zeros (nmat,1) ;
+T3 = zeros (nmat,1) ;
+D1 = zeros (nmat,1) ;
+D2 = zeros (nmat,1) ;
+D3 = zeros (nmat,1) ;
+
+
+for k = 1:nmat
+
+ i = f (k) ;
+ Prob = UFget (i,index) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ fprintf ('%35s: ', Prob.name) ;
+
+ if (~ispc)
+ if (rand () > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ tic
+ p = cs_dmperm (A) ;
+ t1 = toc ;
+ sprank1 = sum (p > 0) ;
+ fprintf (' %8.2f', t1) ;
+ T1 (k) = t1 ;
+
+ tic
+ p = cs_dmperm (A,1) ;
+ t2 = toc ;
+ sprank2 = sum (p > 0) ;
+ fprintf (' %8.2f', t2) ;
+ T2 (k) = t2 ;
+
+ tic
+ p = cs_dmperm (A,-1) ;
+ t3 = toc ;
+ sprank3 = sum (p > 0) ;
+ fprintf (' %8.2f', t3) ;
+ T3 (k) = t3 ;
+
+ if (sprank1 ~= sprank2 | sprank1 ~= sprank3) %#ok
+ error ('!') ;
+ end
+
+ tic
+ [p1,q1,r1,s1,cc1,rr1] = cs_dmperm (A) ; %#ok
+ d1 = toc ;
+ fprintf (' %8.2f', d1) ;
+ D1 (k) = d1 ;
+
+ tic
+ [p2,q2,r2,s2,cc2,rr2] = cs_dmperm (A,1) ; %#ok
+ d2 = toc ;
+ fprintf (' %8.2f', d2) ;
+ D2 (k) = d2 ;
+
+ tic
+ [p3,q3,r3,s3,cc3,rr3] = cs_dmperm (A,-1) ; %#ok
+ d3 = toc ;
+ fprintf (' %8.2f\n', d3) ;
+ D3 (k) = d3 ;
+
+ if (sprank1 == max (m,n))
+ nz1 = nnz (diag (A (p1,q1))) ;
+ nz2 = nnz (diag (A (p2,q2))) ;
+ nz3 = nnz (diag (A (p3,q3))) ;
+
+ if (nz1 ~= sprank1 | nz2 ~= sprank2 | nz3 ~= sprank3) %#ok
+ error ('!')
+ end
+ end
+
+ subplot (1,2,1)
+ loglog (T1 (1:k), T2 (1:k), 'x', ...
+ T1 (1:k), T3 (1:k), 'go', ...
+ [1e-5 1e3], [1e-5 1e3], 'r-') ;
+ axis equal
+
+ subplot (1,2,2)
+ loglog (D1 (1:k), D2 (1:k), 'x', ...
+ D1 (1:k), D3 (1:k), 'go', ...
+ [1e-5 1e3], [1e-5 1e3], 'r-') ;
+ axis equal
+
+ drawnow
+end
diff --git a/CXSparse/MATLAB/Test/test3.m b/CXSparse/MATLAB/Test/test3.m
new file mode 100644
index 0000000..de3037d
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test3.m
@@ -0,0 +1,112 @@
+function test3
+%TEST3 test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol
+%
+% Example:
+% test3
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clear
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+clf
+% f = f(1)
+
+for i = f
+
+ Prob = UFget (i) ;
+ disp (Prob) ;
+
+ for cmplex = 0:double(~ispc)
+
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ if (cmplex)
+ A = A + 1i*sprand(A) ;
+ end
+
+ A = A*A' + 2*n*speye (n) ;
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ try
+ L0 = chol (A)' ;
+ catch
+ continue
+ end
+ b = rand (n,1) ;
+
+ if (~ispc)
+ if (mod (i,2) == 1)
+ b = b + 1i*rand(n,1) ;
+ end
+ end
+
+ C = A(p,p) ;
+ c = condest (C) ;
+ fprintf ('condest: %g\n', c) ;
+
+ x1 = L0\b ;
+ x2 = cs_lsolve (L0,b) ;
+ err = norm (x1-x2,1) ;
+ if (err > 1e-12 * c)
+ error ('!') ;
+ end
+
+ x1 = L0'\b ;
+ x2 = cs_ltsolve (L0,b) ;
+ err = norm (x1-x2,1) ;
+ if (err > 1e-10 * c)
+ error ('!') ;
+ end
+
+ U = L0' ;
+
+ x1 = U\b ;
+ x2 = cs_usolve (U,b) ;
+ err = norm (x1-x2,1) ;
+ if (err > 1e-10 * c)
+ error ('!') ;
+ end
+
+ L2 = cs_chol (A) ;
+ subplot (2,3,1) ; spy (L0) ;
+ subplot (2,3,4) ; spy (L2) ;
+ err = norm (L0-L2,1) ;
+ if (err > 1e-8 * c)
+ error ('!') ;
+ end
+
+ L1 = chol (C)' ;
+ L2 = cs_chol (C) ;
+ subplot (2,3,2) ; spy (L1) ;
+ subplot (2,3,5) ; spy (L2) ;
+ err = norm (L1-L2,1) ;
+ if (err > 1e-8 * c)
+ error ('!') ;
+ end
+
+ [L3,p] = cs_chol (A) ;
+ C = A(p,p) ;
+ L4 = chol (C)' ;
+ subplot (2,3,3) ; spy (L4) ;
+ subplot (2,3,6) ; spy (L3) ;
+ err = norm (L4-L3,1) ;
+ if (err > 1e-8 * c)
+ error ('!') ;
+ end
+
+ drawnow
+
+ end
+end
diff --git a/CXSparse/MATLAB/Test/test4.m b/CXSparse/MATLAB/Test/test4.m
new file mode 100644
index 0000000..7e884bc
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test4.m
@@ -0,0 +1,43 @@
+function test4
+%TEST4 test cs_multiply
+%
+% Example:
+% test4
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+for trial = 1:100
+ m = fix (10 * rand (1)) ;
+ n = fix (10 * rand (1)) ;
+ k = fix (10 * rand (1)) ;
+ d = rand (1) ;
+ A = sprandn (m,n,d) ;
+ B = sprandn (n,k,d) ;
+
+ if (~ispc)
+ if (mod (trial, 4) == 0)
+ A = A + 1i * sprandn (A) ;
+ end
+ if (mod (trial, 2) == 0)
+ B = B + 1i * sprandn (B) ;
+ end
+ end
+
+ C = A*B ;
+ D = cs_multiply (A,B) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d k %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, k, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+end
diff --git a/CXSparse/MATLAB/Test/test5.m b/CXSparse/MATLAB/Test/test5.m
new file mode 100644
index 0000000..60f0081
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test5.m
@@ -0,0 +1,81 @@
+function test5
+%TEST5 test cs_add
+%
+% Example:
+% test5
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+for trial = 1:200
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = rand (1) ;
+ A = sprandn (m,n,d) ;
+ B = sprandn (m,n,d) ;
+
+ if (~ispc)
+ if (mod (trial, 4) == 0)
+ A = A + 1i*sprand(A) ;
+ end
+ if (mod (trial, 2) == 0)
+ B = B + 1i*sprand(B) ;
+ end
+ end
+
+ C = A+B ;
+ D = cs_add (A,B) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+ alpha = pi ;
+ beta = 3 ;
+
+ if (~ispc)
+ if (rand () > .5)
+ alpha = alpha + rand ( ) * 1i ;
+ end
+ if (rand () > .5)
+ beta = beta + rand ( ) * 1i ;
+ end
+ end
+
+ C = alpha*A+B ;
+ D = cs_add (A,B,alpha) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+ C = alpha*A + beta*B ;
+ D = cs_add (A,B,alpha,beta) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+end
diff --git a/CXSparse/MATLAB/Test/test6.m b/CXSparse/MATLAB/Test/test6.m
new file mode 100644
index 0000000..9c89a74
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test6.m
@@ -0,0 +1,111 @@
+function test6
+%TEST6 test cs_reach, cs_reachr, cs_lsolve, cs_usolve
+%
+% Example:
+% test6
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0)
+maxerr = 0 ;
+clf
+for trial = 1:201
+ n = fix (100 * rand (1)) ;
+ d = 0.1 * rand (1) ;
+ L = tril (sprandn (n,n,d),-1) + sprand (speye (n)) ;
+ b = sprandn (n,1,d) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ L = L + 1i*sprand(L) ;
+ end
+ if (rand ( ) > .5)
+ b = b + 1i*sprand(b) ;
+ end
+ end
+
+ for uplo = 0:1
+
+ if (uplo == 1)
+ % solve Ux=b instead ;
+ L = L' ;
+ end
+
+ x = L\b ;
+ sr = 1 + cs_reachr (L,b) ;
+ sz = 1 + cs_reachr (L,b) ;
+
+ check_if_same (sr,sz) ;
+
+ s2 = 1 + cs_reach (L,b) ;
+
+ try
+ if (uplo == 0)
+ x3 = cs_lsolve (L,b) ;
+ else
+ x3 = cs_usolve (L,b) ;
+ end
+ catch
+ if (isreal (L) & isreal (b)) %#ok
+ lasterr
+ error ('!') ;
+ end
+ % punt: sparse(L)\sparse(b) not handled by cs_lsolve or cs_usolve
+ x3 = L\b ;
+ end
+
+ spy ([L b x x3])
+ drawnow
+
+ s = sort (sr) ;
+ [i j xx] = find (x) ; %#ok
+ [i3 j3 xx3] = find (x3) ; %#ok
+
+ if (isempty (i))
+ if (~isempty (s))
+ i %#ok
+ s %#ok
+ error ('!') ;
+ end
+ elseif (any (s ~= i))
+ i %#ok
+ s %#ok
+ error ('!') ;
+ end
+
+ if (isempty (i3))
+ if (~isempty (s))
+ i3 %#ok
+ s %#ok
+ error ('!') ;
+ end
+ elseif (any (s ~= sort (i3)))
+ s %#ok
+ i3 %#ok
+ error ('!') ;
+ end
+
+ if (any (s2 ~= sr))
+ s2 %#ok
+ sr %#ok
+ error ('!') ;
+ end
+
+ err = norm (x-x3,1) ;
+ if (err > 1e-12)
+ x %#ok
+ x3 %#ok
+ uplo %#ok
+ err %#ok
+ error ('!')
+ end
+
+ maxerr = max (maxerr, err) ;
+
+ end
+
+ drawnow
+end
+fprintf ('maxerr = %g\n', maxerr) ;
diff --git a/CXSparse/MATLAB/Test/test7.m b/CXSparse/MATLAB/Test/test7.m
new file mode 100644
index 0000000..219ed21
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test7.m
@@ -0,0 +1,136 @@
+function test7
+%TEST7 test cs_lu
+%
+% Example:
+% test7
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+clf
+
+maxerr1 = 0 ;
+maxerr2 = 0 ;
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ for cmplex = 0:1
+
+ if (cmplex)
+ A = A + norm(A,1) * sprand (A) / 3 ;
+ end
+
+ [L,U,P] = lu (A) ;
+
+ udiag = full (diag (U)) ;
+ umin = min (abs (udiag)) ;
+ fprintf ('umin %g\n', umin) ;
+
+ if (umin > 1e-14)
+
+ [L2,U2,p] = cs_lu (A) ;
+
+ subplot (3,4,1) ; spy (A) ;
+ subplot (3,4,2) ; spy (A(p,:)) ;
+ subplot (3,4,3) ; spy (L2) ;
+ subplot (3,4,4) ; spy (U2) ;
+
+ err1 = norm (L*U-P*A,1) / norm (A,1) ;
+ err2 = norm (L2*U2-A(p,:),1) / norm (A,1) ;
+ fprintf ('err %g %g\n', err1, err2) ;
+
+ if (err1 > 1e-10 | err2 > 1e-10) %#ok
+ error ('!') ;
+ end
+ maxerr1 = max (maxerr1, err1) ;
+ maxerr2 = max (maxerr2, err2) ;
+
+ end
+
+ q = colamd (A) ;
+
+ [L,U,P] = lu (A (:,q)) ;
+
+ udiag = full (diag (U)) ;
+ umin = min (abs (udiag)) ;
+ fprintf ('umin %g with q\n', umin) ;
+
+ if (umin > 1e-14)
+
+ [L2,U2,p,q2] = cs_lu (A) ;
+
+ subplot (3,4,5) ; spy (A) ;
+ subplot (3,4,6) ; spy (A(p,q2)) ;
+ subplot (3,4,7) ; spy (L2) ;
+ subplot (3,4,8) ; spy (U2) ;
+
+ err1 = norm (L*U-P*A(:,q),1) / norm (A,1) ;
+ err2 = norm (L2*U2-A(p,q2),1) / norm (A,1) ;
+ fprintf ('err %g %g\n', err1, err2) ;
+
+ if (err1 > 1e-10 | err2 > 1e-10) %#ok
+ error ('!') ;
+ end
+ maxerr1 = max (maxerr1, err1) ;
+ maxerr2 = max (maxerr2, err2) ;
+ end
+
+
+ try
+ q = amd (A) ;
+ catch
+ q = symamd (A) ;
+ end
+
+ tol = 0.01 ;
+
+ [L,U,P] = lu (A (q,q), tol) ;
+
+ udiag = full (diag (U)) ;
+ umin = min (abs (udiag)) ;
+ fprintf ('umin %g with amd q\n', umin) ;
+
+ if (umin > 1e-14)
+
+ [L2,U2,p,q2] = cs_lu (A,tol) ;
+
+ subplot (3,4,9) ; spy (A) ;
+ subplot (3,4,10) ; spy (A(p,q2)) ;
+ subplot (3,4,11) ; spy (L2) ;
+ subplot (3,4,12) ; spy (U2) ;
+
+ err1 = norm (L*U-P*A(q,q),1) / norm (A,1) ;
+ err2 = norm (L2*U2-A(p,q2),1) / norm (A,1) ;
+ lbig = full (max (max (abs (L2)))) ;
+ fprintf ('err %g %g lbig %g\n', err1, err2, lbig) ;
+ if (lbig > 1/tol)
+ error ('L!') ;
+ end
+
+ if (err1 > 1e-10 | err2 > 1e-10) %#ok
+ error ('!') ;
+ end
+ maxerr1 = max (maxerr1, err1) ;
+ maxerr2 = max (maxerr2, err2) ;
+ end
+
+ drawnow
+ % pause
+
+ end
+end
+
+fprintf ('maxerr %g %g\n', maxerr1, maxerr2) ;
diff --git a/CXSparse/MATLAB/Test/test8.m b/CXSparse/MATLAB/Test/test8.m
new file mode 100644
index 0000000..42806ed
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test8.m
@@ -0,0 +1,93 @@
+function test8
+%TEST8 test cs_cholsol, cs_lusol
+%
+% Example:
+% test8
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+% f = f(1)
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ for cmplex = 0:double(~ispc)
+
+ if (cmplex)
+ A = A + 0.1i * (sprand (tril (A,-1) + triu (A,1))) ;
+ end
+
+ spd = 0 ;
+ if (m == n)
+ if (nnz (A-A') == 0)
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ [R,p] = chol (A (p,p)) ;
+ spd = (p == 0) ;
+ end
+ end
+
+ if (spd)
+ C = A ;
+ else
+ C = A*A' + n*speye (n) ;
+ try
+ p = amd (C) ;
+ catch
+ p = symamd (C) ;
+ end
+ try
+ R = chol (C (p,p)) ; %#ok
+ catch
+ continue
+ end
+ end
+
+ b = rand (n,1) ;
+
+ x1 = C\b ;
+ x2 = cs_cholsol (C,b) ;
+ r1 = norm (C*x1-b,1) / norm (C,1) ;
+ r2 = norm (C*x2-b,1) / norm (C,1) ;
+ err = abs (r1-r2) ;
+ fprintf ('err %g\n', err) ;
+ if (err > 1e-10)
+ error ('!') ;
+ end
+
+ x2 = cs_lusol (C,b, 1, 0.001) ;
+ r2 = norm (C*x2-b,1) / norm (C,1) ;
+ err = abs (r1-r2) ;
+ fprintf ('err %g (lu with amd(A+A'')\n', err) ;
+ if (err > 1e-10)
+ error ('!') ;
+ end
+
+ if (m ~= n)
+ continue ;
+ end
+
+ x1 = A\b ;
+ r1 = norm (A*x1-b,1) / norm (A,1) ;
+ if (r1 < 1e-6)
+ x2 = cs_lusol (A,b) ;
+ r2 = norm (A*x2-b,1) / norm (A,1) ;
+ fprintf ('lu resid %g %g\n', r1, r2) ;
+ end
+ end
+end
diff --git a/CXSparse/MATLAB/Test/test9.m b/CXSparse/MATLAB/Test/test9.m
new file mode 100644
index 0000000..2b0293a
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test9.m
@@ -0,0 +1,134 @@
+function test9
+%TEST9 test cs_qr
+%
+% Example:
+% test9
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0) ;
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+clf
+
+% f = 185 ;
+% f = 449 ;
+% f = 186
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ sp = sprank (A) ;
+% if (sprank (A) < min (m,n))
+% continue
+% end
+
+
+ for cmplex = 0:double(~ispc)
+
+ if (cmplex)
+ A = A + 1i * sprand (A) ;
+ end
+
+ Aorig = A ;
+
+ A = A (:, colamd (A)) ;
+ s1 = svd (full (A)) ;
+
+ if (cmplex)
+ try
+ tic ;
+ R = chol (A'*A) ;
+ t1 = toc ; %#ok
+ catch
+ fprintf ('chol (A''*A) failed\n') ;
+ R = [ ] ;
+ end
+ else
+ tic ;
+ R = qr (A) ;
+ t1 = toc ; %#ok
+ end
+
+ % tic ;
+ % [Q,R] = qr (A) ;
+ % t1 = toc ;
+
+ [c,h,parent] = symbfact (A, 'col') ;
+ rnz = sum (c) ; %#ok
+ tic ;
+ [V2,Beta2,p,R2] = cs_qr (sparse(A)) ;
+ t2 = toc ; %#ok
+
+ v2 = full (V2) ;
+ if (any (spones (v2) ~= spones (V2)))
+ error ('got zeros!') ;
+ end
+
+ C = A ;
+ m2 = size (V2,1) ;
+ if (m2 > m)
+ C = [A ; sparse(m2-m, n)] ;
+ end
+ C = C (p,:) ;
+
+ % [H1,R1] = myqr (C) ;
+ % err1 = norm (R1-R2,1) / norm (R1)
+ % % [svd(A) svd(R1) svd(full(R2))]
+ % s2 = svd (full (R2)) ;
+ % err2 = norm (s1 - s2) / s1 (1)
+ % fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d n %d\n', ...
+ % t1, t2, t1/t2, sp, n) ;
+ % err2
+
+ % left-looking:
+ [V,Beta3,R3] = qr_left (C) ; %#ok
+ s3 = svd (full (R2)) ;
+ err3 = norm (s1 - s3) / s1 (1) ;
+ disp ('err3 = ') ; disp (err3) ;
+ if (err3 > 1e-12)
+ error ('!') ;
+ end
+
+ % right-looking:
+ [V,Beta4,R4] = qr_right (C) ; %#ok
+ s4 = svd (full (R2)) ;
+ err4 = norm (s1 - s4) / s1 (1) ;
+ disp ('err4 = ') ; disp (err4) ;
+ if (err4 > 1e-12)
+ error ('!') ;
+ end
+
+ % H2 = full (H2)
+ % R2 = full (R2)
+
+ subplot (2,4,1) ; spy (A) ; title ('A colamd') ;
+ subplot (2,4,2) ; spy (C) ; title ('A rperm') ;
+ subplot (2,4,3) ; treeplot (parent) ;
+ subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ;
+ subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ;
+ subplot (2,4,6) ; spy (R) ; title ('matlab R') ;
+ subplot (2,4,7) ; spy (R2) ; title ('spqr R') ;
+ subplot (2,4,8) ; spy (V2) ; title ('spqr V') ;
+ drawnow
+
+ % if (err2 > 1e-9)
+ % error ('!') ;
+ % end
+ if (m2 > m)
+ fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ;
+ end
+ % pause
+ end
+
+end
diff --git a/CXSparse/MATLAB/Test/test_qr.m b/CXSparse/MATLAB/Test/test_qr.m
new file mode 100644
index 0000000..349960c
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test_qr.m
@@ -0,0 +1,55 @@
+function test_qr
+%TEST_QR test various QR factorization methods
+%
+% Example:
+% test_qr
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows,index.ncols)) ;
+
+% f = 276
+% f = 706
+f = f (1:100) ;
+
+for i = f
+
+ % Prob = UFget (i,index)
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ if (sprank (A) < n | ~isreal (A)) %#ok
+ continue ;
+ end
+
+ [V,beta,p,R1,q] = cs_qr(A) ;
+ A = A (p,q) ;
+ parent = etree (A, 'col') ; %#ok
+
+ R0 = qr (A) ;
+ R2 = qr_givens (full (A)) ;
+ R3 = qr_givens_full (full (A)) ;
+
+ subplot (2,2,1) ; cspy (R0) ; title ('matlab') ;
+ subplot (2,2,2) ; cspy (R3) ; title ('qr-full') ;
+ subplot (2,2,3) ; cspy (R2) ; title ('qr-givens') ;
+ subplot (2,2,4) ; cspy (R1) ; title ('cs-qr') ;
+
+ e0 = norm (A'*A-R0'*R0,1) / norm (A,1) ;
+ e1 = norm (A'*A-R1'*R1,1) / norm (A,1) ;
+ e2 = norm (A'*A-R2'*R2,1) / norm (A,1) ;
+ e3 = norm (A'*A-R3'*R3,1) / norm (A,1) ;
+ fprintf ('error %6.2e %6.2e %6.2e %6.2e\n', e0, e1, e2, e3) ;
+ drawnow
+ if (e1 > e0*1e3 | e2 > e0*1e3) %#ok
+ pause
+ end
+end
diff --git a/CXSparse/MATLAB/Test/test_qr1.m b/CXSparse/MATLAB/Test/test_qr1.m
new file mode 100644
index 0000000..b2143a5
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test_qr1.m
@@ -0,0 +1,58 @@
+function test_qr1
+%TEST_QR1 test QR factorizations
+%
+% Example:
+% test_qr1
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+
+for i = f
+ Prob = UFget (i,index) ;
+ A = Prob.A ;
+ if (~isreal (A))
+ continue ;
+ end
+
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+
+ t0 = 0 ;
+ k0 = 0 ;
+ while (t0 < 0.1)
+ tic
+ q = colamd (A, [-1 10]) ;
+ % [Q,R] = qr (A (:,q)) ;
+ R = qr (A (:,q)) ; %#ok
+ t = toc ;
+ t0 = t0 + t ;
+ k0 = k0 + 1 ;
+ end
+ t0 = t0 / k0 ;
+
+ t1 = 0 ;
+ k1 = 0 ;
+ while (t1 < 0.1)
+ tic
+ [V,beta, p, R,q] = cs_qr (A) ; %#ok
+ t = toc ;
+ t1 = t1 + t ;
+ k1 = k1 + 1 ;
+ end
+ t1 = t1 / k1 ;
+
+ fprintf (...
+ '%25s MATLAB: %10.4f (%8d) CS: %10.4f (%8d) speedup: %8.2f\n', ...
+ Prob.name, t0, k0, t1, k1, t0/t1) ;
+
+
+
+end
+
diff --git a/CXSparse/MATLAB/Test/test_qrsol.m b/CXSparse/MATLAB/Test/test_qrsol.m
new file mode 100644
index 0000000..22c4ade
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test_qrsol.m
@@ -0,0 +1,50 @@
+function test_qrsol
+%TEST_QRSOL test cs_qrsol
+%
+% Example:
+% test_qrsol
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+
+k = 0 ;
+rs1 = zeros (1,0) ;
+rs2 = zeros (1,0) ;
+
+for i = f
+ Prob = UFget (i,index) ;
+ A = Prob.A ;
+ if (~isreal (A))
+ continue ;
+ end
+
+ [m n] = size (A) ; %#ok
+ b = rand (m,1) ;
+
+ x1 = A\b ;
+ x2 = cs_qrsol (A,b) ;
+
+ x1 (~isfinite (x1)) = 0 ;
+ x2 (~isfinite (x2)) = 0 ;
+
+ r1 = norm (A*x1-b) ;
+ r2 = norm (A*x2-b) ;
+
+ k = k + 1 ;
+ rs1 (k) = r1 ;
+ rs2 (k) = r2 ;
+
+ fprintf ('%30s MATLAB: %6.2e CS: %6.2e\n', Prob.name, r1, r2) ;
+
+ loglog (rs1, rs2, 'o') ;
+ drawnow
+
+ clear A b x1 x2
+ % pack
+
+end
+
diff --git a/CXSparse/MATLAB/Test/test_randperms.m b/CXSparse/MATLAB/Test/test_randperms.m
new file mode 100644
index 0000000..193cf9c
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test_randperms.m
@@ -0,0 +1,60 @@
+function test_randperms
+%TEST_RANDPERMS test random permutations
+% Example:
+% test_randperms
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0)
+
+for trial = 1:100
+ m = fix (30 * rand (1)) ;
+ n = fix (30 * rand (1)) ;
+ d = rand (1) ;
+ A = sprandn (m,n,d) ;
+
+ if (m == 0)
+ p = [] ;
+ else
+ p = randperm (m) ;
+ end
+ if (n == 0)
+ q = [] ;
+ else
+ q = randperm (n) ;
+ end
+
+ C = A(p,q) ;
+
+ Im = speye (m) ;
+ In = speye (n) ;
+ P = Im (p,:) ;
+ Q = In (:,q) ;
+
+ q2 = find (Q) ;
+ if (any (q ~= q2'))
+ error ('!')
+ end
+
+ p2 = find (P') ;
+ if (any (p ~= p2'))
+ error ('!')
+ end
+
+ E = P*A*Q ;
+ if (norm (C-E,1) ~= 0)
+ error ('!')
+ end
+
+ P = sparse (1:m, p, 1) ;
+ Q = sparse (q, 1:n, 1) ;
+
+ E = P*A*Q ;
+ if (norm (C-E,1) ~= 0)
+ error ('2!')
+ end
+
+end
+
diff --git a/CXSparse/MATLAB/Test/test_sep.m b/CXSparse/MATLAB/Test/test_sep.m
new file mode 100644
index 0000000..59213d2
--- /dev/null
+++ b/CXSparse/MATLAB/Test/test_sep.m
@@ -0,0 +1,102 @@
+function test_sep
+%TEST_SEP test cs_sep, and compare with Gilbert's meshpart vtxsep
+% (requires MESHPART).
+%
+% Example:
+% test_sep
+%
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+
+clf
+
+for k = 1:length(f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = spones (Prob.A) ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ A = A'*A ;
+ end
+
+ A = A|A' ;
+
+ p = symrcm (A) ;
+
+ n = size (A,1) ;
+ n2 = fix (n/2) ;
+ a = p (1:n2) ;
+ b = p ((n2+1):n) ;
+
+ clf
+
+ subplot (2,3,1) ; spy (A) ;
+ subplot (2,3,2) ; spy (A (p,p)) ;
+
+ hold on
+ plot ([.5 n2+.5 n2+.5 .5 .5], [.5 .5 n2+.5 n2+.5 .5], 'r', 'LineWidth', 2) ;
+ hold off
+
+ subplot (2,3,3) ; spy (A (a,b)) ; title ('edge sep') ;
+ subplot (2,3,6) ; cs_dmspy (A (a,b)) ; title ('node sep') ;
+
+ [s as bs] = vtxsep (A,a,b) ; %#ok
+ [s2 a2 b2] = cs_sep (A,a,b) ;
+
+ p2 = [a2 b2 s2] ;
+ B = A (p2,p2) ;
+ subplot (2,3,5) ; spy (B) ;
+ hold on
+
+ px = [s2 a2 b2] ;
+ if (any (sort (px) ~= 1:n))
+ px %#ok
+ n %#ok
+ error ('!') ;
+ end
+
+ na = length (a2) ;
+ nb = length (b2) ;
+ ns = length (s2) ; %#ok
+
+ nab = na + nb ;
+
+ plot ([.5 na+.5 na+.5 .5 .5], [.5 .5 na+.5 na+.5 .5], 'r', 'LineWidth', 2) ;
+
+ plot ([na nab nab na na]+0.5, [na na nab nab na]+0.5, 'r', 'LineWidth', 2) ;
+
+ plot ([.5 nab+.5 nab+.5 .5 .5], [.5 .5 nab+.5 nab+.5 .5], 'g', 'LineWidth', 1) ;
+
+ hold off
+
+ nz1 = nnz (A (a2,b2)) ;
+ if (nz1 ~= 0)
+ nz1 %#ok
+ error ('!') ;
+ end
+
+ nz2 = nnz (A (a2,b2)) ;
+ if (nz2 ~= 0)
+ nz2 %#ok
+ error ('!') ;
+ end
+
+ if (length (s) ~= length (s2))
+ fprintf ('lengths differ: %d %d\n', length (s), length (s2)) ;
+ end
+
+ drawnow
+ % pause
+
+
+end
diff --git a/CXSparse/MATLAB/Test/testall.m b/CXSparse/MATLAB/Test/testall.m
new file mode 100644
index 0000000..a3d3534
--- /dev/null
+++ b/CXSparse/MATLAB/Test/testall.m
@@ -0,0 +1,52 @@
+function testall
+%TESTALL test all CSparse functions (run tests 1 to 28 below)
+%
+% Example:
+% testall
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+h = waitbar (0, 'CXSparse') ;
+
+cs_test_make % compile all CSparse, Demo, Text, and Test mexFunctions
+
+ntests = 29 ;
+
+testwait (1, ntests, h) ; test1 ;
+testwait (2, ntests, h) ; test2 ;
+testwait (3, ntests, h) ; test3 ;
+testwait (4, ntests, h) ; test4 ;
+testwait (5, ntests, h) ; test5 ;
+testwait (6, ntests, h) ; test6 ;
+testwait (7, ntests, h) ; test7 ;
+testwait (8, ntests, h) ; test8 ;
+testwait (9, ntests, h) ; test9 ;
+testwait (10, ntests, h) ; test10 ;
+testwait (11, ntests, h) ; test11 ;
+testwait (12, ntests, h) ; test12 ;
+testwait (13, ntests, h) ; test13 ;
+testwait (14, ntests, h) ; test14 ;
+testwait (15, ntests, h) ; test15 ;
+testwait (16, ntests, h) ; test16 ;
+testwait (17, ntests, h) ; test17 ;
+testwait (18, ntests, h) ; test18 ;
+testwait (19, ntests, h) ; test19 ;
+testwait (20, ntests, h) ; test20 ;
+testwait (21, ntests, h) ; test21 ;
+testwait (22, ntests, h) ; test22 ;
+testwait (23, ntests, h) ; test23 ;
+testwait (24, ntests, h) ; test24 ;
+testwait (25, ntests, h) ; test25 ;
+testwait (26, ntests, h) ; test26 ;
+testwait (27, ntests, h) ; test27 ;
+testwait (28, ntests, h) ; test28 ;
+testwait (29, ntests, h) ; test_qr ;
+
+close (h)
+
+function testwait (n,ntests,h)
+fprintf ('\n------------------------ test%d\n', n) ;
+waitbar (n/(ntests+1), h, sprintf ('CXSparse test %d of %d\n', n, ntests)) ;
+
diff --git a/CXSparse/MATLAB/Test/testh.m b/CXSparse/MATLAB/Test/testh.m
new file mode 100644
index 0000000..9f32f27
--- /dev/null
+++ b/CXSparse/MATLAB/Test/testh.m
@@ -0,0 +1,85 @@
+function testh
+%TESTH test Householder reflections
+%
+% Example:
+% testh
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+format long e
+fprintf ('-------------------------------------------------\n') ;
+x = [-3 4 5]' ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+
+x = [3 4 5]' ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = [1 eps]' ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = pi ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = -pi ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = [1 0 0]' ;
+disp (x) ;
+[v, beta, s] = house (x) ; %#ok
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
diff --git a/CXSparse/MATLAB/UFget/Contents.m b/CXSparse/MATLAB/UFget/Contents.m
new file mode 100644
index 0000000..398226a
--- /dev/null
+++ b/CXSparse/MATLAB/UFget/Contents.m
@@ -0,0 +1,16 @@
+% UFget: MATLAB interface for the UF Sparse Matrix Collection.
+%
+% UFget - loads a matrix from the UF Sparse Matrix Collection.
+% UFweb - opens the URL for a matrix.
+% UFgrep - search for matrices in the UF Sparse Matrix Collection.
+%
+% Helper functions:
+%
+% UFget_defaults - returns default parameter settings for UFget.
+% UFget_example - a demo for UFget.
+% UFget_lookup - gets the group, name, and id of a matrix.
+%
+% Example:
+% help UFget
+
+% Copyright 2007, Timothy A. Davis
diff --git a/CXSparse/MATLAB/UFget/README.txt b/CXSparse/MATLAB/UFget/README.txt
new file mode 100644
index 0000000..0353409
--- /dev/null
+++ b/CXSparse/MATLAB/UFget/README.txt
@@ -0,0 +1,67 @@
+UFget: a MATLAB interface to the UF sparse matrix collection.
+MATLAB 7.0 or later is required.
+
+Date: May 31, 2007.
+
+Copyright 2005-2007, Tim Davis, University of Florida.
+Authors: Tim Davis and Erich Mirable.
+Availability: http://www.cise.ufl.edu/research/sparse/mat/UFget
+
+See http://www.cise.ufl.edu/research/sparse/mat/UFget.tar.gz
+for a single archive file with all the files listed below.
+
+ UFget/Contents.m help for UFget
+ UFget/README.txt this file
+
+ UFget/UFget_defaults.m default parameter settings for UFget
+ UFget/UFget_example.m demo for UFget
+ UFget/UFget_lookup.m get the group, name, and id of a matrix
+ UFget/UFget.m primary user interface
+
+ UFget/UFweb.m opens the URL for a matrix or collection
+
+ UFget/mat default download directory (can be changed)
+ UFget/mat/UF_Index.mat index to the UF sparse matrix collection
+
+To install the package, just add the path containing the UFget directory
+to your MATLAB path. Type "pathtool" in MATLAB for more details.
+
+For a simple example of use, type this command in MATLAB:
+
+ UFget_example
+
+The MATLAB statement
+
+ Problem = UFget ('HB/arc130')
+
+(for example), will download a sparse matrix called HB/arc130 (a laser
+simulation problem) and load it into MATLAB. You don't need to use your
+web browser to load the matrix. The statement
+
+ Problem = UFget (6)
+
+will also load same the HB/arc130 matrix. Each matrix in the collection has
+a unique identifier, in the range 1 to the number of matrices. As new
+matrices are added, the id's of existing matrices will not change.
+
+To view an index of the entire collection, just type
+
+ UFget
+
+in MATLAB. To modify your download directory, edit the UFget_defaults.m file.
+
+To open a URL of the entire collection, just type
+
+ UFweb
+
+To open the URL of a group of matrices in the collection:
+
+ UFweb ('HB')
+
+To open the web page for one matrix, use either of these formats:
+
+ UFweb ('HB/arc130')
+ UFweb (6)
+
+For more information on how the index entries were created, see
+http://www.cise.ufl.edu/research/sparse/SuiteSparse.
diff --git a/CXSparse/MATLAB/UFget/UFget.m b/CXSparse/MATLAB/UFget/UFget.m
new file mode 100644
index 0000000..2ef17ed
--- /dev/null
+++ b/CXSparse/MATLAB/UFget/UFget.m
@@ -0,0 +1,142 @@
+function Problem = UFget (matrix, UF_Index)
+%UFGET loads a matrix from the UF Sparse Matrix Collection.
+%
+% Problem = UFget(matrix) loads a matrix from the UF sparse matrix collection,
+% specified as either a number (1 to the # of matrices in the collection) or
+% as a string (the name of the matrix). With no input parameters, index=UFget
+% returns an index of matrices in the collection. A local copy of the matrix
+% is saved (be aware that as of May 2007 the entire collection is over 8GB
+% in size). If no input or output arguments are provided, the index is
+% printed. With a 2nd parameter (Problem = UFget (matrix, index)), the index
+% file is not loaded. This is faster if you are loading lots of matrices.
+%
+% Examples:
+% index = UFget ;
+% Problem = UFget (6)
+% Problem = UFget ('HB/arc130')
+% Problem = UFget (6, index)
+% Problem = UFget ('HB/arc130', index)
+%
+% See also UFgrep, UFweb, UFget_example, UFget_defaults, urlwrite.
+
+% Copyright 2007, Tim Davis, University of Florida.
+
+%-------------------------------------------------------------------------------
+% get the parameter settings
+%-------------------------------------------------------------------------------
+
+params = UFget_defaults ;
+indexfile = sprintf ('%sUF_Index.mat', params.dir) ;
+indexurl = sprintf ('%s/UF_Index.mat', params.url) ;
+
+%-------------------------------------------------------------------------------
+% get the index file (download a new one if necessary)
+%-------------------------------------------------------------------------------
+
+try
+ % load the existing index file
+ if (nargin < 2)
+ load (indexfile) ;
+ end
+ % see if the index file is old; if so, download a fresh copy
+ refresh = (UF_Index.DownloadTimeStamp + params.refresh < now) ;
+catch
+ % oops, no index file. download it.
+ refresh = 1 ;
+end
+
+if (refresh)
+ % a new UF_Index.mat file to get access to new matrices (if any)
+ fprintf ('downloading %s\n', indexurl) ;
+ fprintf ('to %s\n', indexfile) ;
+ urlwrite (indexurl, indexfile) ;
+ load (indexfile) ;
+ UF_Index.DownloadTimeStamp = now ;
+ save (indexfile, 'UF_Index') ;
+end
+
+%-------------------------------------------------------------------------------
+% return the index file if requested
+%-------------------------------------------------------------------------------
+
+% if the user passed in a zero or no argument at all, return the index file
+if nargin == 0
+ matrix = 0 ;
+end
+
+if (matrix == 0)
+ if (nargout == 0)
+ % no output arguments have been passed, so print the index file
+ fprintf ('\nUF sparse matrix collection index: %s\n', ...
+ UF_Index.LastRevisionDate) ;
+ fprintf ('\nLegend:\n') ;
+ fprintf ('(p,n)sym: symmetry of the pattern and values\n') ;
+ fprintf (' (0 = unsymmetric, 1 = symmetric, - = not computed)\n') ;
+ fprintf ('type: real\n') ;
+ fprintf (' complex\n') ;
+ fprintf (' binary: all entries are 0 or 1\n') ;
+ nmat = length (UF_Index.nrows) ;
+ for j = 1:nmat
+ if (mod (j, 25) == 1)
+ fprintf ('\n') ;
+ fprintf ('ID Group/Name nrows-by- ncols nonzeros (p,n)sym type\n') ;
+ end
+ s = sprintf ('%s/%s', UF_Index.Group {j}, UF_Index.Name {j}) ;
+ fprintf ('%4d %-30s %7d-by-%7d %9d ', ...
+ j, s, UF_Index.nrows (j), UF_Index.ncols (j), UF_Index.nnz (j)) ;
+ psym = UF_Index.pattern_symmetry (j) ;
+ nsym = UF_Index.numerical_symmetry (j) ;
+ if (psym < 0)
+ fprintf (' - ') ;
+ else
+ fprintf (' %4.2f', psym) ;
+ end
+ if (nsym < 0)
+ fprintf (' - ') ;
+ else
+ fprintf (' %4.2f', nsym) ;
+ end
+ if (UF_Index.isBinary (j))
+ fprintf (' binary\n') ;
+ elseif (~UF_Index.isReal (j))
+ fprintf (' complex\n') ;
+ else
+ fprintf (' real\n') ;
+ end
+ end
+ else
+ Problem = UF_Index ;
+ end
+ return ;
+end
+
+%-------------------------------------------------------------------------------
+% determine if the matrix parameter is a matrix index or name
+%-------------------------------------------------------------------------------
+
+[group matrix id] = UFget_lookup (matrix, UF_Index) ;
+
+if (id == 0)
+ error ('invalid matrix') ;
+end
+
+%-------------------------------------------------------------------------------
+% download the matrix (if needed) and load it into MATLAB
+
+matdir = sprintf ('%s%s%s%s.mat', params.dir, group) ;
+matfile = sprintf ('%s%s%s.mat', matdir, filesep, matrix) ;
+maturl = sprintf ('%s/%s/%s.mat', params.url, group, matrix) ;
+
+if (~exist (matdir, 'dir'))
+ mkdir (matdir) ;
+end
+
+if (exist (matfile, 'file'))
+ load (matfile)
+else
+ fprintf ('downloading %s\n', maturl) ;
+ fprintf ('to %s\n', matfile) ;
+ urlwrite (maturl, matfile) ;
+ load (matfile)
+ save (matfile, 'Problem') ;
+end
diff --git a/CXSparse/MATLAB/UFget/UFget_defaults.m b/CXSparse/MATLAB/UFget/UFget_defaults.m
new file mode 100644
index 0000000..31425c4
--- /dev/null
+++ b/CXSparse/MATLAB/UFget/UFget_defaults.m
@@ -0,0 +1,43 @@
+function params = UFget_defaults
+%UFGET_DEFAULTS returns default parameter settings for UFget.
+% Usage: params = UFget_defaults ; Returns the default parameter settings for
+% UFget. This file may be editted to change these settings:
+%
+% params.url: UF sparse matrix web site
+% params.dir: your local directory for downloaded sparse matrices.
+% params.refresh: how many days should elapse before re-downloading the
+% index file (for obtaining access to new matrices in the collection).
+%
+% Example:
+% params = UFget_defaults ;
+%
+% See also UFget.
+
+% Copyright 2007, Tim Davis, University of Florida.
+
+%-------------------------------------------------------------------------------
+% location of the UF sparse matrix collection
+params.url = 'http://www.cise.ufl.edu/research/sparse/mat' ;
+
+%-------------------------------------------------------------------------------
+% decode the current directory for this M-file
+s = which (mfilename) ;
+i = find (s == filesep) ;
+s = s (1:i(end)) ;
+
+%-------------------------------------------------------------------------------
+% define the directory to download into. Should end in file separator.
+% Some examples include:
+% params.dir = '/cise/research/sparse/public_html/mat/' ; % if at UF
+% params.dir = 'your directory here/' ;
+% params.dir = 'c:\matlab\work\UFget\mat\' ;
+
+% Default: the directory containing this UFget_defaults function
+params.dir = sprintf ('%smat%s', s, filesep) ;
+
+%-------------------------------------------------------------------------------
+% define how often to check for a new index file (in # of days)
+% inf will force the program to ignore the need to refresh
+
+% params.refresh = Inf ; % if at UF
+params.refresh = 90 ;
diff --git a/CXSparse/MATLAB/UFget/UFget_example.m b/CXSparse/MATLAB/UFget/UFget_example.m
new file mode 100644
index 0000000..7381c1a
--- /dev/null
+++ b/CXSparse/MATLAB/UFget/UFget_example.m
@@ -0,0 +1,30 @@
+%UFGET_EXAMPLE a demo for UFget.
+% This example script gets the index file of the UF sparse matrix collection,
+% and then loads in all symmetric non-binary matrices, in increasing order of
+% number of rows in the matrix.
+%
+% Example:
+% type UFget_example ; % to see an example of how to use UFget
+%
+% See also UFget, UFweb, UFgrep.
+
+% Copyright 2007, Tim Davis, University of Florida.
+
+type UFget_example ;
+
+index = UFget ;
+f = find (index.numerical_symmetry == 1 & ~index.isBinary) ;
+[y, j] = sort (index.nrows (f)) ;
+f = f (j) ;
+
+for i = f
+ fprintf ('Loading %s%s%s, please wait ...\n', ...
+ index.Group {i}, filesep, index.Name {i}) ;
+ Problem = UFget (i,index) ;
+ disp (Problem) ;
+ spy (Problem.A) ;
+ title (sprintf ('%s:%s', Problem.name, Problem.title')) ;
+ UFweb (i) ;
+ input ('hit enter to continue:') ;
+end
+
diff --git a/CXSparse/MATLAB/UFget/UFget_lookup.m b/CXSparse/MATLAB/UFget/UFget_lookup.m
new file mode 100644
index 0000000..bbc9055
--- /dev/null
+++ b/CXSparse/MATLAB/UFget/UFget_lookup.m
@@ -0,0 +1,77 @@
+function [group, name, id] = UFget_lookup (matrix, UF_Index)
+%UFGET_LOOKUP gets the group, name, and id of a matrix.
+%
+% Example:
+% [group name id] = UFget_lookup (matrix, UF_Index)
+%
+% See also UFget.
+
+% Copyright 2007, Tim Davis, University of Florida.
+
+if (isnumeric (matrix))
+
+ % make sure that the matrix parameter is only one integer value
+ % this means that if we get an array, just use the first value
+ id = fix (full (matrix (1))) ;
+
+ % if the index is less than one or bigger than the length of the array,
+ % then no particular matrix is accessed
+ if (id > length (UF_Index.nrows) | id < 1) %#ok
+ id = 0 ;
+ group = '' ;
+ name = '' ;
+ else
+ % assign the group and name for the given id
+ group = UF_Index.Group {matrix} ;
+ name = UF_Index.Name {matrix} ;
+ end
+
+elseif (ischar (matrix))
+
+ % the group and matrix name are in the string as in GroupName\MatrixName
+
+ % find the group index for the file separator
+ % check both types of slashes, and a colon
+ gi = find (matrix == '/') ;
+ if (length (gi) == 0) %#ok
+ gi = find (matrix == '\') ;
+ end
+ if (length (gi) == 0) %#ok
+ gi = find (matrix == ':') ;
+ end
+
+ % if no name divider is in the string, a whole group is specified
+ if (length (gi) == 0) %#ok
+
+ id = 0 ;
+ group = matrix ;
+ name = '' ;
+
+ else
+
+ % group equals the first part of the string up to the character before
+ % the last file separator
+ group = matrix (1:gi(end)-1) ;
+
+ % group equals the last section of the string after the last file
+ % separator
+ name = matrix (gi(end)+1:end) ;
+
+ % validate the given name and group by checking the index for a match
+ refName = strmatch (name, UF_Index.Name) ;
+ refGroup = strmatch (group, UF_Index.Group) ;
+ id = intersect (refName, refGroup) ;
+ if (length (id) >= 1)
+ id = id (1) ;
+ else
+ % the given group/matrix does not exist in the index file
+ id = 0 ;
+ end
+ end
+
+else
+
+ % there is an error in the argument types passed into the function
+ error ('invalid input') ;
+
+end
diff --git a/CXSparse/MATLAB/UFget/UFgrep.m b/CXSparse/MATLAB/UFget/UFgrep.m
new file mode 100644
index 0000000..be7beff
--- /dev/null
+++ b/CXSparse/MATLAB/UFget/UFgrep.m
@@ -0,0 +1,53 @@
+function list = UFgrep (expression, index)
+%UFGREP search for matrices in the UF Sparse Matrix Collection.
+% UFgrep returns a list of Problem id's whose Problem.name string matches an
+% expression. With no output arguments, the list is displayed. Otherwise, it
+% is returned as a list of integer id's.
+%
+% Example:
+% UFgrep ('HB') ; % all matrices in the HB group
+% UFgrep ('\<B*') ; % all matrices in groups starting with the letter B
+% UFgrep ('bp') ; % all bp matrices (in the HB group)
+% UFgrep ('[0-9]') ; % all matrices with a digit in their name
+% UFgrep ('c-') ; % all c-* optimization matrices (in 2 groups)
+%
+% An optional 2nd input argument is the UF index, which is a little faster if
+% UFgrep is used multiple times. With no input arguments, all Problems are
+% listed.
+%
+% index = UFget ;
+% UFgrep ('HB/*', index) ;
+%
+% See also regexp, UFget.
+
+% Copyright 2007, Timothy A. Davis
+
+if (nargin < 2)
+ index = UFget ;
+end
+
+if (nargin < 1)
+ expression = '.' ;
+end
+
+nmat = length (index.nrows) ;
+list1 = zeros (1, nmat) ;
+matched = 0 ;
+
+for id = 1:nmat
+ name = [index.Group{id} '/' index.Name{id}] ;
+ if (~isempty (regexp (name, expression, 'once')))
+ matched = matched + 1 ;
+ list1 (matched) = id ;
+ end
+end
+
+list1 = list1 (1,1:matched) ;
+
+if (nargout == 0)
+ for id = list1
+ fprintf ('%4d: %s/%s\n', id, index.Group {id}, index.Name {id}) ;
+ end
+else
+ list = list1 ;
+end
diff --git a/CXSparse/MATLAB/UFget/UFweb.m b/CXSparse/MATLAB/UFget/UFweb.m
new file mode 100644
index 0000000..d91ea8a
--- /dev/null
+++ b/CXSparse/MATLAB/UFget/UFweb.m
@@ -0,0 +1,135 @@
+function stats = UFweb (matrix, opts)
+%UFWEB opens the URL for a matrix.
+%
+% UFweb(matrix) opens the URL for a matrix. This parameter can be a string,
+% or an integer. If it is a string with no "/" character, the web page for a
+% matrix group is displayed. With no arguments, a list of all the matrix
+% groups is displayed.
+%
+% Example:
+%
+% If Problem = UFget ('HB/arc130'), the first four examples display
+% the same thing, the web page for the HB/arc130 matrix:
+%
+% UFweb (6)
+% UFweb ('HB/arc130')
+% stats = UFweb (6)
+%
+% The latter also returns statistics about the matrix or matrix group.
+% To display the web page for the HB (Harwell-Boeing) group:
+%
+% UFweb ('HB')
+%
+% To display the home page for the UF sparse matrix collection:
+%
+% UFweb
+% UFweb (0)
+% UFweb ('')
+%
+% The latter two are useful if a second optional parameter is specified.
+% The second optional argument is a string passed as additional parameters to
+% the MATLAB web command. To use the system web browser instead of the MATLAB
+% browser, for example, use UFweb ('HB/arc130', '-browser').
+%
+% See also web, UFget, UFget_defaults.
+
+% Copyright 2007, Tim Davis, University of Florida.
+
+params = UFget_defaults ;
+UF_Index = UFget ;
+
+if (nargin < 1)
+ matrix = '' ;
+end
+if (nargin < 2)
+ opts = '' ;
+end
+
+% get the matrix group, name, and id
+[group name id] = UFget_lookup (matrix, UF_Index) ;
+
+url = params.url ;
+len = length (url) ;
+if (strcmp (url ((len-3):len), '/mat'))
+ % remove the trailing '/mat'
+ url = url (1:(len-4)) ;
+end
+
+% open the web page for the matrix, group, or whole collection
+if (id == 0)
+ if (isempty (group))
+ eval (['web ' url '/matrices/index.html ' opts])
+ else
+ eval (['web ' url '/matrices/' group '/index.html ' opts])
+ end
+else
+ eval (['web ' url '/matrices/' group '/' name '.html ' opts])
+end
+
+% return stats
+if (nargout > 0)
+
+ if (id == 0)
+
+ if (isempty (group))
+
+ % return stats about the whole collection
+ stats.nmatrices = length (UF_Index.nrows) ;
+ stats.LastRevisionDate = UF_Index.LastRevisionDate ;
+ stats.DownloadTime = datestr (UF_Index.DownloadTimeStamp) ;
+
+ else
+
+ % return stats about one matrix group
+ nmat = length (UF_Index.nrows) ;
+ ngroup = 0 ;
+ for i = 1:nmat
+ if (strcmp (group, UF_Index.Group {i}))
+ ngroup = ngroup + 1 ;
+ end
+ end
+ stats.nmatrices = ngroup ;
+ stats.LastRevisionDate = UF_Index.LastRevisionDate ;
+ stats.DownloadTime = datestr (UF_Index.DownloadTimeStamp) ;
+
+ end
+ else
+
+ % look up the matrix statistics
+ stats.Group = group ;
+ stats.Name = name ;
+ stats.nrows = UF_Index.nrows (id) ;
+ stats.ncols = UF_Index.ncols (id) ;
+ stats.nnz = UF_Index.nnz (id) ;
+ stats.nzero = UF_Index.nzero (id) ;
+ stats.pattern_symmetry = UF_Index.pattern_symmetry (id) ;
+ stats.numerical_symmetry = UF_Index.numerical_symmetry (id) ;
+ stats.isBinary = UF_Index.isBinary (id) ;
+ stats.isReal = UF_Index.isReal (id) ;
+
+ stats.nnzdiag = UF_Index.nnzdiag (id) ;
+ stats.posdef = UF_Index.posdef (id) ;
+
+ stats.amd_lnz = UF_Index.amd_lnz (id) ;
+ stats.amd_flops = UF_Index.amd_flops (id) ;
+ stats.amd_vnz = UF_Index.amd_vnz (id) ;
+ stats.amd_rnz = UF_Index.amd_rnz (id) ;
+ stats.metis_lnz = UF_Index.metis_lnz (id) ;
+ stats.metis_flops = UF_Index.metis_flops (id) ;
+ stats.metis_vnz = UF_Index.metis_vnz (id) ;
+ stats.metis_rnz = UF_Index.metis_rnz (id) ;
+ stats.nblocks = UF_Index.nblocks (id) ;
+ stats.sprank = UF_Index.sprank (id) ;
+ stats.nzoff = UF_Index.nzoff (id) ;
+ stats.dmperm_lnz = UF_Index.dmperm_lnz (id) ;
+ stats.dmperm_unz = UF_Index.dmperm_unz (id) ;
+ stats.dmperm_flops = UF_Index.dmperm_flops (id) ;
+ stats.dmperm_vnz = UF_Index.dmperm_vnz (id) ;
+ stats.dmperm_rnz = UF_Index.dmperm_rnz (id) ;
+
+ stats.RBtype = UF_Index.RBtype (id,:) ;
+ stats.cholcand = UF_Index.cholcand (id) ;
+ stats.ncc = UF_Index.ncc (id) ;
+
+ end
+end
diff --git a/CXSparse/MATLAB/UFget/mat/UF_Index.mat b/CXSparse/MATLAB/UFget/mat/UF_Index.mat
new file mode 100644
index 0000000..d17778e
Binary files /dev/null and b/CXSparse/MATLAB/UFget/mat/UF_Index.mat differ
diff --git a/CXSparse/MATLAB/cs_install.m b/CXSparse/MATLAB/cs_install.m
new file mode 100644
index 0000000..526821b
--- /dev/null
+++ b/CXSparse/MATLAB/cs_install.m
@@ -0,0 +1,56 @@
+function cs_install (do_pause)
+%CS_INSTALL: compile and install CXSparse for use in MATLAB.
+% Your current working directory must be CXSparse/MATLAB in order to use this
+% function.
+%
+% The directories
+%
+% CXSparse/MATLAB/CSparse
+% CXSparse/MATLAB/Demo
+% CXSparse/MATLAB/UFget
+%
+% are added to your MATLAB path (see the "pathtool" command to add these to
+% your path permanently, for future MATLAB sessions).
+%
+% Next, the MATLAB CXSparse demo program, CXSparse/MATLAB/cs_demo is executed.
+% To run the demo with pauses so you can see the results, use cs_install(1).
+% To run the full MATLAB test programs for CXSparse, run testall in the
+% Test directory.
+%
+% Example:
+% cs_install % install and run demo with no pauses
+% cs_install(1) % install and run demo with pauses
+%
+% See also: cs_demo
+%
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('Compiling and installing CXSparse\n') ;
+if (nargin < 1)
+ do_pause = 0 ;
+end
+
+if (do_pause)
+ input ('Hit enter to continue: ') ;
+end
+addpath ([pwd filesep 'CSparse']) ;
+addpath ([pwd filesep 'Demo']) ;
+
+v = getversion ;
+if (v >= 7.0)
+ addpath ([pwd filesep 'UFget']) ;
+else
+ fprintf ('UFget not installed (MATLAB 7.0 or later required)\n') ;
+end
+
+cd ('CSparse') ;
+cs_make (1) ;
+cd ('../Demo') ;
+cs_demo (do_pause)
+
+%-------------------------------------------------------------------------------
+function v = getversion
+% determine the MATLAB version, and return it as a double.
+v = sscanf (version, '%d.%d.%d') ;
+v = 10.^(0:-1:-(length(v)-1)) * v ;
diff --git a/CXSparse/Makefile b/CXSparse/Makefile
new file mode 100644
index 0000000..5700dcb
--- /dev/null
+++ b/CXSparse/Makefile
@@ -0,0 +1,30 @@
+# CSparse Makefile
+
+C:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+all: C cov
+
+library:
+ ( cd Lib ; $(MAKE) )
+
+cov:
+ ( cd Tcov ; $(MAKE) )
+
+mex:
+ ( cd MATLAB ; $(MAKE) )
+
+clean:
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+ ( cd Tcov ; $(MAKE) clean )
+ ( cd MATLAB ; $(MAKE) clean )
+
+purge:
+ ( cd Lib ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd Tcov ; $(MAKE) purge )
+ ( cd MATLAB ; $(MAKE) purge )
+
+distclean: purge
diff --git a/CXSparse/Matrix/ash219 b/CXSparse/Matrix/ash219
new file mode 100644
index 0000000..b092930
--- /dev/null
+++ b/CXSparse/Matrix/ash219
@@ -0,0 +1,438 @@
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diff --git a/CXSparse/Matrix/bcsstk01 b/CXSparse/Matrix/bcsstk01
new file mode 100644
index 0000000..b529e93
--- /dev/null
+++ b/CXSparse/Matrix/bcsstk01
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diff --git a/CXSparse/Matrix/bcsstk16 b/CXSparse/Matrix/bcsstk16
new file mode 100644
index 0000000..8dd72b3
--- /dev/null
+++ b/CXSparse/Matrix/bcsstk16
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diff --git a/CXSparse/Matrix/c4 b/CXSparse/Matrix/c4
new file mode 100644
index 0000000..eb6e600
--- /dev/null
+++ b/CXSparse/Matrix/c4
@@ -0,0 +1,10 @@
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diff --git a/CXSparse/Matrix/c_ibm32a b/CXSparse/Matrix/c_ibm32a
new file mode 100644
index 0000000..d33de73
--- /dev/null
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new file mode 100644
index 0000000..5fe0e62
--- /dev/null
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diff --git a/CXSparse/Matrix/c_mbeacxc b/CXSparse/Matrix/c_mbeacxc
new file mode 100644
index 0000000..08cd8c0
--- /dev/null
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diff --git a/CXSparse/Matrix/c_west0067 b/CXSparse/Matrix/c_west0067
new file mode 100644
index 0000000..309378c
--- /dev/null
+++ b/CXSparse/Matrix/c_west0067
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diff --git a/CXSparse/Matrix/fs_183_1 b/CXSparse/Matrix/fs_183_1
new file mode 100644
index 0000000..7797188
--- /dev/null
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diff --git a/CXSparse/Matrix/ibm32a b/CXSparse/Matrix/ibm32a
new file mode 100644
index 0000000..d474d02
--- /dev/null
+++ b/CXSparse/Matrix/ibm32a
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diff --git a/CXSparse/Matrix/ibm32b b/CXSparse/Matrix/ibm32b
new file mode 100644
index 0000000..9a70e18
--- /dev/null
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diff --git a/CXSparse/Matrix/lp_afiro b/CXSparse/Matrix/lp_afiro
new file mode 100644
index 0000000..0e2c5ae
--- /dev/null
+++ b/CXSparse/Matrix/lp_afiro
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diff --git a/CXSparse/Matrix/mbeacxc b/CXSparse/Matrix/mbeacxc
new file mode 100644
index 0000000..f9b4c06
--- /dev/null
+++ b/CXSparse/Matrix/mbeacxc
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diff --git a/CXSparse/Matrix/mhd1280b b/CXSparse/Matrix/mhd1280b
new file mode 100644
index 0000000..27e5412
--- /dev/null
+++ b/CXSparse/Matrix/mhd1280b
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diff --git a/CXSparse/Matrix/neumann b/CXSparse/Matrix/neumann
new file mode 100644
index 0000000..60f431b
--- /dev/null
+++ b/CXSparse/Matrix/neumann
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diff --git a/CXSparse/Matrix/qc324 b/CXSparse/Matrix/qc324
new file mode 100644
index 0000000..bc4fa4b
--- /dev/null
+++ b/CXSparse/Matrix/qc324
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diff --git a/CXSparse/Matrix/t1 b/CXSparse/Matrix/t1
new file mode 100644
index 0000000..3fbb980
--- /dev/null
+++ b/CXSparse/Matrix/t1
@@ -0,0 +1,10 @@
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diff --git a/CXSparse/Matrix/t2 b/CXSparse/Matrix/t2
new file mode 100644
index 0000000..5e47066
--- /dev/null
+++ b/CXSparse/Matrix/t2
@@ -0,0 +1,10 @@
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diff --git a/CXSparse/Matrix/t3 b/CXSparse/Matrix/t3
new file mode 100644
index 0000000..87239c5
--- /dev/null
+++ b/CXSparse/Matrix/t3
@@ -0,0 +1,12 @@
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diff --git a/CXSparse/Matrix/t4 b/CXSparse/Matrix/t4
new file mode 100644
index 0000000..2dbf71a
--- /dev/null
+++ b/CXSparse/Matrix/t4
@@ -0,0 +1,3 @@
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diff --git a/CXSparse/Matrix/west0067 b/CXSparse/Matrix/west0067
new file mode 100644
index 0000000..09e42cb
--- /dev/null
+++ b/CXSparse/Matrix/west0067
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diff --git a/CXSparse/Matrix/young1c b/CXSparse/Matrix/young1c
new file mode 100644
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diff --git a/CXSparse/README.txt b/CXSparse/README.txt
new file mode 100644
index 0000000..b108f66
--- /dev/null
+++ b/CXSparse/README.txt
@@ -0,0 +1,572 @@
+CXSparse: a Concise Sparse Matrix package - Extended.
+Version 2.2.0, Copyright (c) 2006-2007, Timothy A. Davis.
+Derived from CSparse. Conversion originally by David Bateman, Motorola,
+and then modified by Tim Davis. ANSI C99 is required, with support for
+the _Complex data type.
+(if you use a C++ compiler, the C++ complex type is used instead).
+
+CXSparse is a version of CSparse that operates on both real and complex
+matrices, using either int or UF_long integers. A UF_long is normally
+just a long on most platforms, but becomes __int64 on WIN64.
+It now includes a MATLAB interface, enabling the use of CXSparse functions on
+both 32-bit and 64-bit platforms.
+
+To install for use in MATLAB, simply type "cs_install" in the MATLAB Command
+Window, while in the CXSparse/MATLAB directory. (NOTE: Windows users cannot
+use the "lcc" command; run "mex -setup" first, and select a different
+compiler). If you use the Unix "make" command in that directory instead and
+are using a 64-bit platform, then you must edit the CXSparse/MATLAB/Makefile
+first. Refer to the instructions in that file.
+
+Refer to "Direct Methods for Sparse Linear Systems," Timothy A. Davis,
+SIAM, Philadelphia, 2006. No detailed user guide is included in this
+package; the user guide is the book itself.
+
+To compile the C-library (./Source), C demo programs (./Demo) just type "make"
+in this directory. To run the exhaustive statement coverage tests, type
+"make" in the Tcov directory; the Tcov tests assume you are using Linux. To
+remove all files not in the original distribution, type "make distclean".
+I recommend that you use a different level of
+optimization than "cc -O", which was chosen so that the Makefile is portable.
+See Source/Makefile.
+
+If your C compiler does not support the ANSI C99 complex type, the
+#include <complex.h> statement will fail. If this happens, compile the
+code with the -DNCOMPLEX flag (the MATLAB cs_install will do this for you).
+
+This package is backward compatible with CSparse. That is, user code that
+uses CSparse may switch to using CXSparse without any changes to the user code.
+Each CXSparse function has a generic version with the same name as the CSparse
+function, and four type-specific versions. For example:
+
+ cs_add same as cs_add_di by default, but can be changed to use UF_long
+ integers if user code is compiled with -DCS_LONG, and/or can
+ be changed to operate on complex matrices with -DCS_COMPLEX.
+
+ cs_di_add double/int version of cs_add
+ cs_dl_add double/UF_long version of cs_add
+ cs_ci_add complex/int version of cs_add
+ cs_cl_add complex/UF_long version of cs_add
+
+The sparse matrix data structures are treated in the same way: cs, css,
+csn, and csd become cs_di, cs_dis, cs_din, and cs_did for the double/int case,
+cs_cl, cs_cls, cs_cln, and cs_cld for the complex/UF_long case, and so on.
+
+See cs_demo.c for a type-generic user program, and cs_cl_demo.c for a
+type-specific version of the same program (complex/UF_long).
+
+Several macros are available in CXSparse (but not in CSparse) to allow user
+code to be written in a type-generic manner:
+
+ CS_INT int by default, UF_long if -DCS_LONG compiler flag is used
+ CS_ENTRY double by default, double complex if -DCS_COMPLEX flag is used.
+ CS_ID "%d" or "%ld", for printf and scanf of the CS_INT type.
+ CS_INT_MAX INT_MAX or LONG_MAX, the largest possible value of CS_INT.
+ CS_REAL(x) x or creal(x)
+ CS_IMAG(x) 0 or cimag(x)
+ CS_CONJ(x) x or conj(x)
+ CS_ABS(x) fabs(x) or cabs(x)
+
+Even the name of the include file (cs.h) is the same. To use CXSparse instead
+of CSparse, simply compile with -ICXSparse/Source instead of -ICSparse/Source,
+and link against libcxsparse.a instead of the CSparse libcsparse.a library.
+
+To determine at compile time if CXSparse or CSparse is being used:
+
+ #ifdef CXSPARSE
+ CXSparse is in use. The generic functions equivalent to CSparse may
+ be used (cs_add, etc). These generic functions can use different
+ types, depending on the -DCS_LONG and -DCS_COMPLEX compile flags, with
+ the default being double/int. The type-specific functions and data
+ types (cs_di_add, cs_di, CS_INT, etc.) can be used.
+ #else
+ CSparse is in use. Only the generic functions "cs_add", etc., are
+ available, and they are of type double/int.
+ #endif
+
+See cs.h for the prototypes of each function, and the book "Direct Methods
+for Sparse Linear Systems" for full documentation of CSparse and CXSparse.
+
+Other changes from CSparse: cs_transpose performs the complex conjugate
+transpose if values>0 (C=A'), the pattern-only transpose if values=0
+(C=spones(A') in MATLAB), and the array transpose if values<0 (C=A.' in
+MATLAB notation). A set of four conversion routines are included in CXSparse,
+to convert real matrices to/from complex matrices.
+The Householder reflection constructed by cs_house.c also differs slightly, to
+accomodate both the real and complex cases properly.
+
+CXSparse is generated automatically from CSparse. Refer to
+http://www.cise.ufl.edu/research/sparse/CSparse for details.
+
+--------------------------------------------------------------------------------
+Contents:
+--------------------------------------------------------------------------------
+
+Demo/ demo C programs that use CXSparse
+Doc/ license and change log
+Makefile Makefile for the whole package
+MATLAB/ MATLAB interface, demos, and tests for CXSparse
+Matrix/ sample matrices (with extra complex matrices for CXSparse)
+README.txt this file
+Source/ primary CXSparse source files
+Tcov/ CXSparse tests
+
+--------------------------------------------------------------------------------
+./Doc: license and change log
+--------------------------------------------------------------------------------
+
+ChangeLog changes in CSparse since first release
+lesser.txt the GNU LGPL
+License.txt license (GNU LGPL)
+
+--------------------------------------------------------------------------------
+./Source: Primary source code for CXSparse
+--------------------------------------------------------------------------------
+
+cs_add.c add sparse matrices
+cs_amd.c approximate minimum degree
+cs_chol.c sparse Cholesky
+cs_cholsol.c x=A\b using sparse Cholesky
+cs_compress.c convert a compress form to compressed-column form
+cs_counts.c column counts for Cholesky and QR
+cs_convert.c convert real to complex and complex to real (not in CSparse)
+cs_cumsum.c cumulative sum
+cs_dfs.c depth-first-search
+cs_dmperm.c Dulmage-Mendelsohn permutation
+cs_droptol.c drop small entries from a sparse matrix
+cs_dropzeros.c drop zeros from a sparse matrix
+cs_dupl.c remove (and sum) duplicates
+cs_entry.c add an entry to a triplet matrix
+cs_ereach.c nonzero pattern of Cholesky L(k,:) from etree and triu(A(:,k))
+cs_etree.c find elimination tree
+cs_fkeep.c drop entries from a sparse matrix
+cs_gaxpy.c sparse matrix times dense matrix
+cs.h include file for CXSparse
+cs_happly.c apply Householder reflection
+cs_house.c Householder reflection (*** NOTE: different algo. from CSparse)
+cs_ipvec.c x(p)=b
+cs_leaf.c determine if j is a leaf of the skeleton matrix and find lca
+cs_load.c load a sparse matrix from a file
+cs_lsolve.c x=L\b
+cs_ltsolve.c x=L'\b
+cs_lu.c sparse LU factorization
+cs_lusol.c x=A\b using sparse LU factorization
+cs_malloc.c memory manager
+cs_maxtrans.c maximum transveral (permutation for zero-free diagonal)
+cs_multiply.c sparse matrix multiply
+cs_norm.c sparse matrix norm
+cs_permute.c permute a sparse matrix
+cs_pinv.c invert a permutation vector
+cs_post.c postorder an elimination tree
+cs_print.c print a sparse matrix
+cs_pvec.c x=b(p)
+cs_qr.c sparse QR
+cs_qrsol.c solve a least-squares problem
+cs_randperm.c random permutation
+cs_reach.c find nonzero pattern of x=L\b for sparse L and b
+cs_scatter.c scatter a sparse vector
+cs_scc.c strongly-connected components
+cs_schol.c symbolic Cholesky
+cs_spsolve.c x=Z\b where Z, x, and b are sparse, and Z upper/lower triangular
+cs_sqr.c symbolic QR (also can be used for LU)
+cs_symperm.c symmetric permutation of a sparse matrix
+cs_tdfs.c depth-first-search of a tree
+cs_transpose.c transpose a sparse matrix
+cs_updown.c sparse rank-1 Cholesky update/downate
+cs_usolve.c x=U\b
+cs_util.c various utilities (allocate/free matrices, workspace, etc)
+cs_utsolve.c x=U'\b
+Makefile Makefile for CXSparse
+README.txt README file for CXSparse
+
+--------------------------------------------------------------------------------
+./Demo: C program demos
+--------------------------------------------------------------------------------
+
+cs_ci_demo1.c complex/int version of cs_demo1.c
+cs_ci_demo2.c complex/int version of cs_demo2.c
+cs_ci_demo3.c complex/int version of cs_demo3.c
+cs_ci_demo.c complex/int version of cs_demo.c
+cs_ci_demo.h complex/int version of cs_demo.h
+
+cs_cl_demo1.c complex/UF_long version of cs_demo1.c
+cs_cl_demo2.c complex/UF_long version of cs_demo2.c
+cs_cl_demo3.c complex/UF_long version of cs_demo3.c
+cs_cl_demo.c complex/UF_long version of cs_demo.c
+cs_cl_demo.h complex/UF_long version of cs_demo.h
+
+cs_demo1.c read a matrix from a file and perform basic matrix operations
+cs_demo2.c read a matrix from a file and solve a linear system
+cs_demo3.c read a matrix, solve a linear system, update/downdate
+cs_demo.c support routines for cs_demo*.c
+cs_demo.h include file for demo programs
+
+cs_demo.out output of "make", which runs the demos on some matrices
+
+cs_di_demo1.c double/int version of cs_demo1.c
+cs_di_demo2.c double/int version of cs_demo2.c
+cs_di_demo3.c double/int version of cs_demo3.c
+cs_di_demo.c double/int version of cs_demo.c
+cs_di_demo.h double/int version of cs_demo.h
+
+cs_dl_demo1.c double/UF_long version of cs_demo1.c
+cs_dl_demo2.c double/UF_long version of cs_demo2.c
+cs_dl_demo3.c double/UF_long version of cs_demo3.c
+cs_dl_demo.c double/UF_long version of cs_demo.c
+cs_dl_demo.h double/UF_long version of cs_demo.h
+
+cs_idemo.c convert real matrices to/from complex (int version)
+cs_ldemo.c convert real matrices to/from complex (UF_long version)
+
+Makefile Makefile for Demo programs
+readhb.f read a Rutherford-Boeing matrix (real matrices only)
+README.txt Demo README file
+
+--------------------------------------------------------------------------------
+./MATLAB: MATLAB interface, demos, and tests
+--------------------------------------------------------------------------------
+
+cs_install.m MATLAB function for compiling and installing CSparse for MATLAB
+CSparse/ MATLAB interface for CSparse
+Demo/ MATLAB demos for CSparse
+Makefile MATLAB interface Makefile
+README.txt MATLAB README file
+Test/ MATLAB test for CSparse, and "textbook" routines
+UFget/ MATLAB interface to UF Sparse Matrix Collection
+
+
+--------------------------------------------------------------------------------
+./MATLAB/CSparse: MATLAB interface for CSparse
+--------------------------------------------------------------------------------
+
+Contents.m Contents of MATLAB interface to CSparse
+cs_add.m add two sparse matrices
+cs_add_mex.c
+cs_amd.m approximate minimum degree
+cs_amd_mex.c
+cs_chol.m sparse Cholesky
+cs_chol_mex.c
+cs_cholsol.m x=A\b using a sparse Cholesky
+cs_cholsol_mex.c
+cs_counts.m column counts for Cholesky or QR (like "symbfact" in MATLAB)
+cs_counts_mex.c
+cs_dmperm.m Dulmage-Mendelsohn permutation
+cs_dmperm_mex.c
+cs_dmsol.m x=A\b using dmperm
+cs_dmspy.m plot a picture of a dmperm-permuted matrix
+cs_droptol.m drop small entries
+cs_droptol_mex.c
+cs_esep.m find edge separator
+cs_etree.m compute elimination tree
+cs_etree_mex.c
+cs_gaxpy.m sparse matrix times dense vector
+cs_gaxpy_mex.c
+cs_lsolve.m x=L\b where L is lower triangular
+cs_lsolve_mex.c
+cs_ltsolve.m x=L'\b where L is lower triangular
+cs_ltsolve_mex.c
+cs_lu.m sparse LU factorization
+cs_lu_mex.c
+cs_lusol.m x=A\b using sparse LU factorization
+cs_lusol_mex.c
+cs_make.m compiles CSparse for use in MATLAB
+cs_mex.c support routines for CSparse mexFunctions
+cs_mex.h
+cs_multiply.m sparse matrix multiply
+cs_multiply_mex.c
+cs_must_compile.m determine if a source file needs to be compiled with mex
+cs_nd.m nested dissection
+cs_nsep.m find node separator
+cs_permute.m permute a sparse matrix
+cs_permute_mex.c
+cs_print.m print a sparse matrix
+cs_print_mex.c
+cs_qleft.m apply Householder vectors to the left
+cs_qright.m apply Householder vectors to the right
+cs_qr.m sparse QR factorization
+cs_qr_mex.c
+cs_qrsol.m solve a sparse least squares problem
+cs_qrsol_mex.c
+cs_randperm.m randdom permutation
+cs_randperm_mex.c
+cs_scc.m strongly-connected components
+cs_scc_mex.c
+cs_sep.m convert an edge separator into a node separator
+cs_sparse.m convert a triplet form matrix to a compress-column form
+cs_sparse_mex.c
+cs_symperm.m symmetric permutation of a sparse matrix
+cs_symperm_mex.c
+cs_sqr.m symbolic QR ordering and analysis
+cs_sqr_mex.c
+cs_thumb_mex.c compute small "thumbnail" of a sparse matrix (for cspy).
+cs_transpose.m transpose a sparse matrix
+cs_transpose_mex.c
+cs_updown.m sparse Cholesky update/downdate
+cs_updown_mex.c
+cs_usolve.m x=U\b where U is upper triangular
+cs_usolve_mex.c
+cs_utsolve.m x=U'\b where U is upper triangular
+cs_utsolve_mex.c
+cspy.m a color "spy"
+Makefile Makefile for CSparse MATLAB interface
+README.txt README file for CSparse MATLAB interface
+
+
+--------------------------------------------------------------------------------
+./MATLAB/Demo: MATLAB demos for CSparse
+--------------------------------------------------------------------------------
+
+Contents.m Contents of MATLAB demo for CSparse
+cs_demo.m run all MATLAB demos for CSparse
+cs_demo1.m MATLAB version of Demo/cs_demo1.c
+cs_demo2.m MATLAB version of Demo/cs_demo2.c
+cs_demo3.m MATLAB version of Demo/cs_demo3.c
+private/ private functions for MATLAB demos
+README.txt README file for CSparse MATLAB demo
+
+
+--------------------------------------------------------------------------------
+./MATLAB/Demo/private: private functions for MATLAB demos
+--------------------------------------------------------------------------------
+
+demo2.m demo 2
+demo3.m demo 3
+ex_1.m example 1
+ex2.m example 2
+ex3.m example 3
+frand.m generate a random finite-element matrix
+get_problem.m get a matrix
+is_sym.m determine if a matrix is symmetric
+mesh2d1.m construct a 2D mesh (method 1)
+mesh2d2.m construct a 2D mesh (method 2)
+mesh3d1.m construct a 3D mesh (method 1)
+mesh3d2.m construct a 3D mesh (method 2)
+print_order.m print the ordering method used
+resid.m compute residual
+rhs.m create right-hand-side
+
+
+--------------------------------------------------------------------------------
+./MATLAB/Test: Extensive test of CSparse, in MATLAB
+--------------------------------------------------------------------------------
+
+Makefile Makefile for MATLAB Test directory
+README.txt README file for MATLAB/Test
+Contents.m Contents of MATLAB/Test, "textbook" files only
+
+chol_downdate.m downdate a Cholesky factorization.
+chol_left.m left-looking Cholesky factorization.
+chol_left2.m left-looking Cholesky factorization, more details.
+chol_right.m right-looking Cholesky factorization.
+chol_super.m left-looking "supernodal" Cholesky factorization.
+chol_up.m up-looking Cholesky factorization.
+chol_update.m update a Cholesky factorization.
+chol_updown.m update or downdate a Cholesky factorization.
+cond1est.m 1-norm condition estimate.
+cs_fiedler.m the Fiedler vector of a connected graph.
+givens2.m find a Givens rotation.
+house.m find a Householder reflection.
+lu_left.m left-looking LU factorization.
+lu_right.m right-looking LU factorization.
+lu_rightp.m right-looking LU factorization, with partial pivoting.
+lu_rightpr.m recursive right-looking LU, with partial pivoting.
+lu_rightr.m recursive right-looking LU.
+norm1est.m 1-norm estimate.
+qr_givens.m Givens-rotation QR factorization.
+qr_givens_full.m Givens-rotation QR factorization, for full matrices.
+qr_left.m left-looking Householder QR factorization.
+qr_right.m right-looking Householder QR factorization.
+cs_fiedler.m Fiedler vector
+
+cs_frand.m generate a random finite-element matrix
+cs_frand_mex.c
+cs_ipvec.m x(p)=b
+cs_ipvec_mex.c
+cs_maxtransr.m recursive maximum matching algorithm
+cs_maxtransr_mex.c
+cs_pvec.m x=b(p)
+cs_pvec_mex.c interface for cs_pvec
+cs_reach.m non-recursive reach (interface to CSparse cs_reach)
+cs_reach_mex.c non-recursive x=spones(L\sparse(b))
+cs_reachr.m recursive reach (interface to CSparse cs_reachr)
+cs_reachr_mex.c
+cs_rowcnt.m row counts for sparse Cholesky
+cs_rowcnt_mex.c row counts for sparse Cholesky
+cs_sparse2.m same as cs_sparse, to test cs_entry function
+cs_sparse2_mex.c like cs_sparse, but for testing cs_entry
+
+cs_test_make.m compiles MATLAB tests
+
+check_if_same.m check if two inputs are identical or not
+choldn.m Cholesky downdate
+cholup.m Cholesky update, using Given's rotations
+cholupdown.m Cholesky update/downdate (Bischof, Pan, and Tang method)
+cs_q1.m construct Q from Householder vectors
+cs_test_make.m compiles the CSparse, Demo, and Test mexFunctions.
+dmperm_test.m test cs_dmperm
+chol_example.m simple Cholesky factorization example
+etree_sample.m construct a sample etree and symbolic factorization
+gqr3.m QR factorization, based on Givens rotations
+happly.m apply Householder reflection to a vector
+hmake1.m construct a Householder reflection
+mynormest1.m estimate norm(A,1), using LU factorization (L*U = P*A*Q).
+myqr.m QR factorization using Householder reflections
+another_colormap.m try another color map
+cspy_test.m test cspy and cs_dmspy
+qr2.m QR factorization based on Householder reflections
+sample_colormap.m try a colormap for use in cspy
+signum.m compute and display the sign of a column vector x
+sqr_example.m test cs_sqr
+dmspy_test.m test cspy, cs_dmspy, and cs_dmperm
+test_qr.m test various QR factorization methods
+test_randperms.m test random permutations
+testh.m test Householder reflections
+test_qr1.m test QR factorizations
+test_qrsol.m test cs_qrsol
+test_sep.m test cs_sep, and compare with Gilbert's meshpart vtxsep
+testall.m test all CSparse functions (run tests 1 to 28 below)
+test1.m test cs_transpose
+test2.m test cs_sparse
+test3.m test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol
+test4.m test cs_multiply
+test5.m test cs_add
+test6.m test cs_reach, cs_reachr, cs_lsolve, cs_usolve
+test7.m test cs_lu
+test8.m test cs_cholsol, cs_lusol
+test9.m test cs_qr
+test10.m test cs_qr
+test11.m test cs_rowcnt
+test12.m test cs_qr and compare with svd
+test13.m test cs_counts, cs_etree
+test14.m test cs_droptol
+test15.m test cs_amd
+test16.m test cs_amd
+test17.m test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol
+test18.m test iterative refinement after backslash
+test19.m test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc
+test20.m test cholupdown
+test21.m test cs_updown
+test22.m test cond1est
+test23.m test cs_dmspy
+test24.m test cs_fielder
+test25.m test cs_nd
+test26.m test cs_dmsol and cs_dmspy
+test27.m test cs_qr, cs_utsolve, cs_qrsol
+test28.m test cs_randperm, cs_dmperm
+
+
+--------------------------------------------------------------------------------
+./MATLAB/UFget: MATLAB interface for the UF Sparse Matrix Collection
+--------------------------------------------------------------------------------
+
+Contents.m Contents of UFget
+mat/ default directory where downloaded matrices will be put
+README.txt README file for UFget
+UFget_defaults.m default parameter settings
+UFget_example.m example of use
+UFget_install.m installs UFget temporarily (for current session)
+UFget_java.class read a url and load it in into MATLAB (compiled Java code)
+UFget_java.java read a url and load it in into MATLAB (Java source code)
+UFget_lookup.m look up a matrix in the index
+UFget.m UFget itself (primary user interface)
+UFweb.m open url for a matrix or collection
+mat/UF_Index.mat index of matrices in UF Sparse Matrix Collection
+
+
+--------------------------------------------------------------------------------
+./Matrix: Sample matrices, most from Rutherford/Boeing collection
+--------------------------------------------------------------------------------
+
+ash219 overdetermined pattern of Holland survey. Ashkenazi, 1974.
+bcsstk01 stiffness matrix for small generalized eigenvalue problem
+bcsstk16 stiffness matrix, Corp of Engineers dam
+fs_183_1 unsymmetric facsimile convergence matrix
+lp_afiro NETLIB afiro linear programming problem
+mbeacxc US economy, 1972. Dan Szyld, while at NYU
+t1 small example used in Chapter 2
+west0067 Cavett problem with 5 components (chemical eng., Westerberg)
+
+c_mbeacxc complex version of mbeacxc
+c_west0067 complex version of west0067
+mhd1280b Alfven spectra in magnetohydrodynamics (complex)
+neumann complex matrix
+qc324 model of H+ in an electromagnetic field (complex)
+t2 small complex matrix
+t3 small complex matrix
+t4 small complex matrix
+c4 small complex matrix
+young1c aeronautical problem (complex matrix)
+
+--------------------------------------------------------------------------------
+./Tcov: Exhaustive test coverage of CXSparse
+--------------------------------------------------------------------------------
+
+covall same as covall.linux
+covall.linux find coverage (Linux)
+covall.sol find coverage (Solaris)
+cov.awk coverage summary
+cover print uncovered lines
+covs print uncovered lines
+cstcov_malloc_test.c malloc test
+cstcov_malloc_test.h
+cstcov_test.c main program for Tcov tests
+gcovs run gcov (Linux)
+Makefile Makefile for Tcov tests
+nil an empty matrix
+zero a 1-by-1 zero matrix
+czero a 1-by-1 complex zero matrix
+README.txt README file for Tcov directory
+
+
+--------------------------------------------------------------------------------
+Change Log:
+--------------------------------------------------------------------------------
+
+Refer to CSparse for changes in CSparse, which are immediately propagated
+into CXSparse (those Change Log entries are not repeated here).
+
+Nov 1, 2007. version 2.2.1
+
+ CXSparse/MATLAB/Test ported to Windows
+
+
+May 31, 2007. version 2.2.0
+
+ * back-port to MATLAB 7.2 and earlier (which does not have mwIndex).
+
+ * more graceful failure in cs_make when attempting complex matrix support
+ (Windows, in particular)
+
+ * correction to CXSparse/Demo/Makefile
+
+ * added sizeof(CS_INT) printout to cs_idemo.c, cs_ldemo.c
+
+Mar 14, 2007. Version 2.1.0.
+
+ * MATLAB interface added for CXSparse.
+
+ * cs_complex_t type added (a #define for "double _Complex", which is the
+ complex type used in CXSparse 2.0.x). When compiling with a C++
+ compiler, the std::compex<double> type is used for the complex case.
+
+ * bug fix in complex sparse Cholesky (cs_chol.c).
+
+ * bug fix in complex sparse Cholesky update/downdate (cs_updown.c).
+
+ * bug fix in cs_symperm for the complex case.
+
+ * "beta" changed from complex to real, in sparse QR (cs_house.c,
+ cs_happly.c, cs_qr.c), (a performance/memory improvement, not a
+ bug fix). Similar change to "nz2" in cs_cumsum.c.
+
+May 5, 2006. Version 2.0.1 released.
+
+ * long changed to UF_long, dependency in ../UFconfig/UFconfig.h added.
+ "UF_long" is a #define'd term in UFconfig.h. It is normally defined
+ as "long", but can be redefined as something else if desired.
+ On Windows-64, it becomes __int64.
+
+Mar 6, 2006
+
+ "double complex" changed to "double _Complex", to avoid conflicts when
+ CXSparse is compiled with a C++ compiler. Other minor changes to cs.h.
diff --git a/CXSparse/Source/README.txt b/CXSparse/Source/README.txt
new file mode 100644
index 0000000..5f39716
--- /dev/null
+++ b/CXSparse/Source/README.txt
@@ -0,0 +1,3 @@
+CXSparse/Source directory: primary ANSI C source code files for CXSparse.
+To compile the libcxsparse.a C-callable library, just type "make" in this
+directory.
diff --git a/CXSparse/Source/cs_add.c b/CXSparse/Source/cs_add.c
new file mode 100644
index 0000000..134fee5
--- /dev/null
+++ b/CXSparse/Source/cs_add.c
@@ -0,0 +1,28 @@
+#include "cs.h"
+/* C = alpha*A + beta*B */
+cs *cs_add (const cs *A, const cs *B, CS_ENTRY alpha, CS_ENTRY beta)
+{
+ CS_INT p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values ;
+ CS_ENTRY *x, *Bx, *Cx ;
+ cs *C ;
+ if (!CS_CSC (A) || !CS_CSC (B)) return (NULL) ; /* check inputs */
+ if (A->m != B->m || A->n != B->n) return (NULL) ;
+ m = A->m ; anz = A->p [A->n] ;
+ n = B->n ; Bp = B->p ; Bx = B->x ; bnz = Bp [n] ;
+ w = cs_calloc (m, sizeof (CS_INT)) ; /* get workspace */
+ values = (A->x != NULL) && (Bx != NULL) ;
+ x = values ? cs_malloc (m, sizeof (CS_ENTRY)) : NULL ; /* get workspace */
+ C = cs_spalloc (m, n, anz + bnz, values, 0) ; /* allocate result*/
+ if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Cp [j] = nz ; /* column j of C starts here */
+ nz = cs_scatter (A, j, alpha, w, x, j+1, C, nz) ; /* alpha*A(:,j)*/
+ nz = cs_scatter (B, j, beta, w, x, j+1, C, nz) ; /* beta*B(:,j) */
+ if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ;
+ }
+ Cp [n] = nz ; /* finalize the last column of C */
+ cs_sprealloc (C, 0) ; /* remove extra space from C */
+ return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */
+}
diff --git a/CXSparse/Source/cs_amd.c b/CXSparse/Source/cs_amd.c
new file mode 100644
index 0000000..ec430ee
--- /dev/null
+++ b/CXSparse/Source/cs_amd.c
@@ -0,0 +1,364 @@
+#include "cs.h"
+/* clear w */
+static CS_INT cs_wclear (CS_INT mark, CS_INT lemax, CS_INT *w, CS_INT n)
+{
+ CS_INT k ;
+ if (mark < 2 || (mark + lemax < 0))
+ {
+ for (k = 0 ; k < n ; k++) if (w [k] != 0) w [k] = 1 ;
+ mark = 2 ;
+ }
+ return (mark) ; /* at this point, w [0..n-1] < mark holds */
+}
+
+/* keep off-diagonal entries; drop diagonal entries */
+static CS_INT cs_diag (CS_INT i, CS_INT j, CS_ENTRY aij, void *other) { return (i != j) ; }
+
+/* p = amd(A+A') if symmetric is true, or amd(A'A) otherwise */
+CS_INT *cs_amd (CS_INT order, const cs *A) /* order 0:natural, 1:Chol, 2:LU, 3:QR */
+{
+ cs *C, *A2, *AT ;
+ CS_INT *Cp, *Ci, *last, *W, *len, *nv, *next, *P, *head, *elen, *degree, *w,
+ *hhead, *ATp, *ATi, d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1,
+ k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi,
+ ok, cnz, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, n, m, t ;
+ unsigned CS_INT h ;
+ /* --- Construct matrix C ----------------------------------------------- */
+ if (!CS_CSC (A) || order <= 0 || order > 3) return (NULL) ; /* check */
+ AT = cs_transpose (A, 0) ; /* compute A' */
+ if (!AT) return (NULL) ;
+ m = A->m ; n = A->n ;
+ dense = CS_MAX (16, 10 * sqrt ((double) n)) ; /* find dense threshold */
+ dense = CS_MIN (n-2, dense) ;
+ if (order == 1 && n == m)
+ {
+ C = cs_add (A, AT, 0, 0) ; /* C = A+A' */
+ }
+ else if (order == 2)
+ {
+ ATp = AT->p ; /* drop dense columns from AT */
+ ATi = AT->i ;
+ for (p2 = 0, j = 0 ; j < m ; j++)
+ {
+ p = ATp [j] ; /* column j of AT starts here */
+ ATp [j] = p2 ; /* new column j starts here */
+ if (ATp [j+1] - p > dense) continue ; /* skip dense col j */
+ for ( ; p < ATp [j+1] ; p++) ATi [p2++] = ATi [p] ;
+ }
+ ATp [m] = p2 ; /* finalize AT */
+ A2 = cs_transpose (AT, 0) ; /* A2 = AT' */
+ C = A2 ? cs_multiply (AT, A2) : NULL ; /* C=A'*A with no dense rows */
+ cs_spfree (A2) ;
+ }
+ else
+ {
+ C = cs_multiply (AT, A) ; /* C=A'*A */
+ }
+ cs_spfree (AT) ;
+ if (!C) return (NULL) ;
+ cs_fkeep (C, &cs_diag, NULL) ; /* drop diagonal entries */
+ Cp = C->p ;
+ cnz = Cp [n] ;
+ P = cs_malloc (n+1, sizeof (CS_INT)) ; /* allocate result */
+ W = cs_malloc (8*(n+1), sizeof (CS_INT)) ; /* get workspace */
+ t = cnz + cnz/5 + 2*n ; /* add elbow room to C */
+ if (!P || !W || !cs_sprealloc (C, t)) return (cs_idone (P, C, W, 0)) ;
+ len = W ; nv = W + (n+1) ; next = W + 2*(n+1) ;
+ head = W + 3*(n+1) ; elen = W + 4*(n+1) ; degree = W + 5*(n+1) ;
+ w = W + 6*(n+1) ; hhead = W + 7*(n+1) ;
+ last = P ; /* use P as workspace for last */
+ /* --- Initialize quotient graph ---------------------------------------- */
+ for (k = 0 ; k < n ; k++) len [k] = Cp [k+1] - Cp [k] ;
+ len [n] = 0 ;
+ nzmax = C->nzmax ;
+ Ci = C->i ;
+ for (i = 0 ; i <= n ; i++)
+ {
+ head [i] = -1 ; /* degree list i is empty */
+ last [i] = -1 ;
+ next [i] = -1 ;
+ hhead [i] = -1 ; /* hash list i is empty */
+ nv [i] = 1 ; /* node i is just one node */
+ w [i] = 1 ; /* node i is alive */
+ elen [i] = 0 ; /* Ek of node i is empty */
+ degree [i] = len [i] ; /* degree of node i */
+ }
+ mark = cs_wclear (0, 0, w, n) ; /* clear w */
+ elen [n] = -2 ; /* n is a dead element */
+ Cp [n] = -1 ; /* n is a root of assembly tree */
+ w [n] = 0 ; /* n is a dead element */
+ /* --- Initialize degree lists ------------------------------------------ */
+ for (i = 0 ; i < n ; i++)
+ {
+ d = degree [i] ;
+ if (d == 0) /* node i is empty */
+ {
+ elen [i] = -2 ; /* element i is dead */
+ nel++ ;
+ Cp [i] = -1 ; /* i is a root of assembly tree */
+ w [i] = 0 ;
+ }
+ else if (d > dense) /* node i is dense */
+ {
+ nv [i] = 0 ; /* absorb i into element n */
+ elen [i] = -1 ; /* node i is dead */
+ nel++ ;
+ Cp [i] = CS_FLIP (n) ;
+ nv [n]++ ;
+ }
+ else
+ {
+ if (head [d] != -1) last [head [d]] = i ;
+ next [i] = head [d] ; /* put node i in degree list d */
+ head [d] = i ;
+ }
+ }
+ while (nel < n) /* while (selecting pivots) do */
+ {
+ /* --- Select node of minimum approximate degree -------------------- */
+ for (k = -1 ; mindeg < n && (k = head [mindeg]) == -1 ; mindeg++) ;
+ if (next [k] != -1) last [next [k]] = -1 ;
+ head [mindeg] = next [k] ; /* remove k from degree list */
+ elenk = elen [k] ; /* elenk = |Ek| */
+ nvk = nv [k] ; /* # of nodes k represents */
+ nel += nvk ; /* nv[k] nodes of A eliminated */
+ /* --- Garbage collection ------------------------------------------- */
+ if (elenk > 0 && cnz + mindeg >= nzmax)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ if ((p = Cp [j]) >= 0) /* j is a live node or element */
+ {
+ Cp [j] = Ci [p] ; /* save first entry of object */
+ Ci [p] = CS_FLIP (j) ; /* first entry is now CS_FLIP(j) */
+ }
+ }
+ for (q = 0, p = 0 ; p < cnz ; ) /* scan all of memory */
+ {
+ if ((j = CS_FLIP (Ci [p++])) >= 0) /* found object j */
+ {
+ Ci [q] = Cp [j] ; /* restore first entry of object */
+ Cp [j] = q++ ; /* new pointer to object j */
+ for (k3 = 0 ; k3 < len [j]-1 ; k3++) Ci [q++] = Ci [p++] ;
+ }
+ }
+ cnz = q ; /* Ci [cnz...nzmax-1] now free */
+ }
+ /* --- Construct new element ---------------------------------------- */
+ dk = 0 ;
+ nv [k] = -nvk ; /* flag k as in Lk */
+ p = Cp [k] ;
+ pk1 = (elenk == 0) ? p : cnz ; /* do in place if elen[k] == 0 */
+ pk2 = pk1 ;
+ for (k1 = 1 ; k1 <= elenk + 1 ; k1++)
+ {
+ if (k1 > elenk)
+ {
+ e = k ; /* search the nodes in k */
+ pj = p ; /* list of nodes starts at Ci[pj]*/
+ ln = len [k] - elenk ; /* length of list of nodes in k */
+ }
+ else
+ {
+ e = Ci [p++] ; /* search the nodes in e */
+ pj = Cp [e] ;
+ ln = len [e] ; /* length of list of nodes in e */
+ }
+ for (k2 = 1 ; k2 <= ln ; k2++)
+ {
+ i = Ci [pj++] ;
+ if ((nvi = nv [i]) <= 0) continue ; /* node i dead, or seen */
+ dk += nvi ; /* degree[Lk] += size of node i */
+ nv [i] = -nvi ; /* negate nv[i] to denote i in Lk*/
+ Ci [pk2++] = i ; /* place i in Lk */
+ if (next [i] != -1) last [next [i]] = last [i] ;
+ if (last [i] != -1) /* remove i from degree list */
+ {
+ next [last [i]] = next [i] ;
+ }
+ else
+ {
+ head [degree [i]] = next [i] ;
+ }
+ }
+ if (e != k)
+ {
+ Cp [e] = CS_FLIP (k) ; /* absorb e into k */
+ w [e] = 0 ; /* e is now a dead element */
+ }
+ }
+ if (elenk != 0) cnz = pk2 ; /* Ci [cnz...nzmax] is free */
+ degree [k] = dk ; /* external degree of k - |Lk\i| */
+ Cp [k] = pk1 ; /* element k is in Ci[pk1..pk2-1] */
+ len [k] = pk2 - pk1 ;
+ elen [k] = -2 ; /* k is now an element */
+ /* --- Find set differences ----------------------------------------- */
+ mark = cs_wclear (mark, lemax, w, n) ; /* clear w if necessary */
+ for (pk = pk1 ; pk < pk2 ; pk++) /* scan 1: find |Le\Lk| */
+ {
+ i = Ci [pk] ;
+ if ((eln = elen [i]) <= 0) continue ;/* skip if elen[i] empty */
+ nvi = -nv [i] ; /* nv [i] was negated */
+ wnvi = mark - nvi ;
+ for (p = Cp [i] ; p <= Cp [i] + eln - 1 ; p++) /* scan Ei */
+ {
+ e = Ci [p] ;
+ if (w [e] >= mark)
+ {
+ w [e] -= nvi ; /* decrement |Le\Lk| */
+ }
+ else if (w [e] != 0) /* ensure e is a live element */
+ {
+ w [e] = degree [e] + wnvi ; /* 1st time e seen in scan 1 */
+ }
+ }
+ }
+ /* --- Degree update ------------------------------------------------ */
+ for (pk = pk1 ; pk < pk2 ; pk++) /* scan2: degree update */
+ {
+ i = Ci [pk] ; /* consider node i in Lk */
+ p1 = Cp [i] ;
+ p2 = p1 + elen [i] - 1 ;
+ pn = p1 ;
+ for (h = 0, d = 0, p = p1 ; p <= p2 ; p++) /* scan Ei */
+ {
+ e = Ci [p] ;
+ if (w [e] != 0) /* e is an unabsorbed element */
+ {
+ dext = w [e] - mark ; /* dext = |Le\Lk| */
+ if (dext > 0)
+ {
+ d += dext ; /* sum up the set differences */
+ Ci [pn++] = e ; /* keep e in Ei */
+ h += e ; /* compute the hash of node i */
+ }
+ else
+ {
+ Cp [e] = CS_FLIP (k) ; /* aggressive absorb. e->k */
+ w [e] = 0 ; /* e is a dead element */
+ }
+ }
+ }
+ elen [i] = pn - p1 + 1 ; /* elen[i] = |Ei| */
+ p3 = pn ;
+ p4 = p1 + len [i] ;
+ for (p = p2 + 1 ; p < p4 ; p++) /* prune edges in Ai */
+ {
+ j = Ci [p] ;
+ if ((nvj = nv [j]) <= 0) continue ; /* node j dead or in Lk */
+ d += nvj ; /* degree(i) += |j| */
+ Ci [pn++] = j ; /* place j in node list of i */
+ h += j ; /* compute hash for node i */
+ }
+ if (d == 0) /* check for mass elimination */
+ {
+ Cp [i] = CS_FLIP (k) ; /* absorb i into k */
+ nvi = -nv [i] ;
+ dk -= nvi ; /* |Lk| -= |i| */
+ nvk += nvi ; /* |k| += nv[i] */
+ nel += nvi ;
+ nv [i] = 0 ;
+ elen [i] = -1 ; /* node i is dead */
+ }
+ else
+ {
+ degree [i] = CS_MIN (degree [i], d) ; /* update degree(i) */
+ Ci [pn] = Ci [p3] ; /* move first node to end */
+ Ci [p3] = Ci [p1] ; /* move 1st el. to end of Ei */
+ Ci [p1] = k ; /* add k as 1st element in of Ei */
+ len [i] = pn - p1 + 1 ; /* new len of adj. list of node i */
+ h %= n ; /* finalize hash of i */
+ next [i] = hhead [h] ; /* place i in hash bucket */
+ hhead [h] = i ;
+ last [i] = h ; /* save hash of i in last[i] */
+ }
+ } /* scan2 is done */
+ degree [k] = dk ; /* finalize |Lk| */
+ lemax = CS_MAX (lemax, dk) ;
+ mark = cs_wclear (mark+lemax, lemax, w, n) ; /* clear w */
+ /* --- Supernode detection ------------------------------------------ */
+ for (pk = pk1 ; pk < pk2 ; pk++)
+ {
+ i = Ci [pk] ;
+ if (nv [i] >= 0) continue ; /* skip if i is dead */
+ h = last [i] ; /* scan hash bucket of node i */
+ i = hhead [h] ;
+ hhead [h] = -1 ; /* hash bucket will be empty */
+ for ( ; i != -1 && next [i] != -1 ; i = next [i], mark++)
+ {
+ ln = len [i] ;
+ eln = elen [i] ;
+ for (p = Cp [i]+1 ; p <= Cp [i] + ln-1 ; p++) w [Ci [p]] = mark;
+ jlast = i ;
+ for (j = next [i] ; j != -1 ; ) /* compare i with all j */
+ {
+ ok = (len [j] == ln) && (elen [j] == eln) ;
+ for (p = Cp [j] + 1 ; ok && p <= Cp [j] + ln - 1 ; p++)
+ {
+ if (w [Ci [p]] != mark) ok = 0 ; /* compare i and j*/
+ }
+ if (ok) /* i and j are identical */
+ {
+ Cp [j] = CS_FLIP (i) ; /* absorb j into i */
+ nv [i] += nv [j] ;
+ nv [j] = 0 ;
+ elen [j] = -1 ; /* node j is dead */
+ j = next [j] ; /* delete j from hash bucket */
+ next [jlast] = j ;
+ }
+ else
+ {
+ jlast = j ; /* j and i are different */
+ j = next [j] ;
+ }
+ }
+ }
+ }
+ /* --- Finalize new element------------------------------------------ */
+ for (p = pk1, pk = pk1 ; pk < pk2 ; pk++) /* finalize Lk */
+ {
+ i = Ci [pk] ;
+ if ((nvi = -nv [i]) <= 0) continue ;/* skip if i is dead */
+ nv [i] = nvi ; /* restore nv[i] */
+ d = degree [i] + dk - nvi ; /* compute external degree(i) */
+ d = CS_MIN (d, n - nel - nvi) ;
+ if (head [d] != -1) last [head [d]] = i ;
+ next [i] = head [d] ; /* put i back in degree list */
+ last [i] = -1 ;
+ head [d] = i ;
+ mindeg = CS_MIN (mindeg, d) ; /* find new minimum degree */
+ degree [i] = d ;
+ Ci [p++] = i ; /* place i in Lk */
+ }
+ nv [k] = nvk ; /* # nodes absorbed into k */
+ if ((len [k] = p-pk1) == 0) /* length of adj list of element k*/
+ {
+ Cp [k] = -1 ; /* k is a root of the tree */
+ w [k] = 0 ; /* k is now a dead element */
+ }
+ if (elenk != 0) cnz = p ; /* free unused space in Lk */
+ }
+ /* --- Postordering ----------------------------------------------------- */
+ for (i = 0 ; i < n ; i++) Cp [i] = CS_FLIP (Cp [i]) ;/* fix assembly tree */
+ for (j = 0 ; j <= n ; j++) head [j] = -1 ;
+ for (j = n ; j >= 0 ; j--) /* place unordered nodes in lists */
+ {
+ if (nv [j] > 0) continue ; /* skip if j is an element */
+ next [j] = head [Cp [j]] ; /* place j in list of its parent */
+ head [Cp [j]] = j ;
+ }
+ for (e = n ; e >= 0 ; e--) /* place elements in lists */
+ {
+ if (nv [e] <= 0) continue ; /* skip unless e is an element */
+ if (Cp [e] != -1)
+ {
+ next [e] = head [Cp [e]] ; /* place e in list of its parent */
+ head [Cp [e]] = e ;
+ }
+ }
+ for (k = 0, i = 0 ; i <= n ; i++) /* postorder the assembly tree */
+ {
+ if (Cp [i] == -1) k = cs_tdfs (i, k, head, next, P, w) ;
+ }
+ return (cs_idone (P, C, W, 1)) ;
+}
diff --git a/CXSparse/Source/cs_chol.c b/CXSparse/Source/cs_chol.c
new file mode 100644
index 0000000..a5e2912
--- /dev/null
+++ b/CXSparse/Source/cs_chol.c
@@ -0,0 +1,59 @@
+#include "cs.h"
+/* L = chol (A, [pinv parent cp]), pinv is optional */
+csn *cs_chol (const cs *A, const css *S)
+{
+ CS_ENTRY d, lki, *Lx, *x, *Cx ;
+ CS_INT top, i, p, k, n, *Li, *Lp, *cp, *pinv, *s, *c, *parent, *Cp, *Ci ;
+ cs *L, *C, *E ;
+ csn *N ;
+ if (!CS_CSC (A) || !S || !S->cp || !S->parent) return (NULL) ;
+ n = A->n ;
+ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */
+ c = cs_malloc (2*n, sizeof (CS_INT)) ; /* get CS_INT workspace */
+ x = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get CS_ENTRY workspace */
+ cp = S->cp ; pinv = S->pinv ; parent = S->parent ;
+ C = pinv ? cs_symperm (A, pinv, 1) : ((cs *) A) ;
+ E = pinv ? C : NULL ; /* E is alias for A, or a copy E=A(p,p) */
+ if (!N || !c || !x || !C) return (cs_ndone (N, E, c, x, 0)) ;
+ s = c + n ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ N->L = L = cs_spalloc (n, n, cp [n], 1, 0) ; /* allocate result */
+ if (!L) return (cs_ndone (N, E, c, x, 0)) ;
+ Lp = L->p ; Li = L->i ; Lx = L->x ;
+ for (k = 0 ; k < n ; k++) Lp [k] = c [k] = cp [k] ;
+ for (k = 0 ; k < n ; k++) /* compute L(:,k) for L*L' = C */
+ {
+ /* --- Nonzero pattern of L(k,:) ------------------------------------ */
+ top = cs_ereach (C, k, parent, s, c) ; /* find pattern of L(k,:) */
+ x [k] = 0 ; /* x (0:k) is now zero */
+ for (p = Cp [k] ; p < Cp [k+1] ; p++) /* x = full(triu(C(:,k))) */
+ {
+ if (Ci [p] <= k) x [Ci [p]] = Cx [p] ;
+ }
+ d = x [k] ; /* d = C(k,k) */
+ x [k] = 0 ; /* clear x for k+1st iteration */
+ /* --- Triangular solve --------------------------------------------- */
+ for ( ; top < n ; top++) /* solve L(0:k-1,0:k-1) * x = C(:,k) */
+ {
+ i = s [top] ; /* s [top..n-1] is pattern of L(k,:) */
+ lki = x [i] / Lx [Lp [i]] ; /* L(k,i) = x (i) / L(i,i) */
+ x [i] = 0 ; /* clear x for k+1st iteration */
+ for (p = Lp [i] + 1 ; p < c [i] ; p++)
+ {
+ x [Li [p]] -= Lx [p] * lki ;
+ }
+ d -= lki * CS_CONJ (lki) ; /* d = d - L(k,i)*L(k,i) */
+ p = c [i]++ ;
+ Li [p] = k ; /* store L(k,i) in column i */
+ Lx [p] = CS_CONJ (lki) ;
+ }
+ /* --- Compute L(k,k) ----------------------------------------------- */
+ if (CS_REAL (d) <= 0 || CS_IMAG (d) != 0)
+ return (cs_ndone (N, E, c, x, 0)) ; /* not pos def */
+ p = c [k]++ ;
+ Li [p] = k ; /* store L(k,k) = sqrt (d) in column k */
+ Lx [p] = sqrt (d) ;
+ }
+ Lp [n] = cp [n] ; /* finalize L */
+ return (cs_ndone (N, E, c, x, 1)) ; /* success: free E,s,x; return N */
+}
diff --git a/CXSparse/Source/cs_cholsol.c b/CXSparse/Source/cs_cholsol.c
new file mode 100644
index 0000000..3646981
--- /dev/null
+++ b/CXSparse/Source/cs_cholsol.c
@@ -0,0 +1,26 @@
+#include "cs.h"
+/* x=A\b where A is symmetric positive definite; b overwritten with solution */
+CS_INT cs_cholsol (CS_INT order, const cs *A, CS_ENTRY *b)
+{
+ CS_ENTRY *x ;
+ css *S ;
+ csn *N ;
+ CS_INT n, ok ;
+ if (!CS_CSC (A) || !b) return (0) ; /* check inputs */
+ n = A->n ;
+ S = cs_schol (order, A) ; /* ordering and symbolic analysis */
+ N = cs_chol (A, S) ; /* numeric Cholesky factorization */
+ x = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get workspace */
+ ok = (S && N && x) ;
+ if (ok)
+ {
+ cs_ipvec (S->pinv, b, x, n) ; /* x = P*b */
+ cs_lsolve (N->L, x) ; /* x = L\x */
+ cs_ltsolve (N->L, x) ; /* x = L'\x */
+ cs_pvec (S->pinv, x, b, n) ; /* b = P'*x */
+ }
+ cs_free (x) ;
+ cs_sfree (S) ;
+ cs_nfree (N) ;
+ return (ok) ;
+}
diff --git a/CXSparse/Source/cs_compress.c b/CXSparse/Source/cs_compress.c
new file mode 100644
index 0000000..4162bd9
--- /dev/null
+++ b/CXSparse/Source/cs_compress.c
@@ -0,0 +1,22 @@
+#include "cs.h"
+/* C = compressed-column form of a triplet matrix T */
+cs *cs_compress (const cs *T)
+{
+ CS_INT m, n, nz, p, k, *Cp, *Ci, *w, *Ti, *Tj ;
+ CS_ENTRY *Cx, *Tx ;
+ cs *C ;
+ if (!CS_TRIPLET (T)) return (NULL) ; /* check inputs */
+ m = T->m ; n = T->n ; Ti = T->i ; Tj = T->p ; Tx = T->x ; nz = T->nz ;
+ C = cs_spalloc (m, n, nz, Tx != NULL, 0) ; /* allocate result */
+ w = cs_calloc (n, sizeof (CS_INT)) ; /* get workspace */
+ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ for (k = 0 ; k < nz ; k++) w [Tj [k]]++ ; /* column counts */
+ cs_cumsum (Cp, w, n) ; /* column pointers */
+ for (k = 0 ; k < nz ; k++)
+ {
+ Ci [p = w [Tj [k]]++] = Ti [k] ; /* A(i,j) is the pth entry in C */
+ if (Cx) Cx [p] = Tx [k] ;
+ }
+ return (cs_done (C, w, NULL, 1)) ; /* success; free w and return C */
+}
diff --git a/CXSparse/Source/cs_convert.c b/CXSparse/Source/cs_convert.c
new file mode 100644
index 0000000..2d6607f
--- /dev/null
+++ b/CXSparse/Source/cs_convert.c
@@ -0,0 +1,93 @@
+#include "cs.h"
+
+/* convert from complex to real (int version) */
+/* C = real(A) if real is true, imag(A) otherwise */
+cs_di *cs_i_real (cs_ci *A, int real)
+{
+ cs_di *C ;
+ int n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ;
+ cs_complex_t *Ax ;
+ double *Cx ;
+ if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */
+ nz = triplet ? A->nz : Ap [n] ;
+ C = cs_di_spalloc (A->m, n, A->nzmax, 1, triplet) ;
+ if (!C) return (NULL) ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ nn = triplet ? nz : (n+1) ;
+ for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ;
+ for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ;
+ for (p = 0 ; p < nz ; p++) Cx [p] = real ? creal (Ax [p]) : cimag (Ax [p]) ;
+ if (triplet) C->nz = nz ;
+ return (C) ;
+}
+
+/* convert from real to complex (int version) */
+/* C = A if real is true, or C = i*A otherwise */
+cs_ci *cs_i_complex (cs_di *A, int real)
+{
+ cs_ci *C ;
+ int n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ;
+ double *Ax ;
+ cs_complex_t *Cx ;
+ if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */
+ nz = triplet ? A->nz : Ap [n] ;
+ C = cs_ci_spalloc (A->m, n, A->nzmax, 1, triplet) ;
+ if (!C) return (NULL) ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ nn = triplet ? nz : (n+1) ;
+ for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ;
+ for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ;
+ for (p = 0 ; p < nz ; p++) Cx [p] = real ? Ax [p] : (I * Ax [p]) ;
+ if (triplet) C->nz = nz ;
+ return (C) ;
+}
+
+/* convert from complex to real (UF_long version) */
+/* C = real(A) if real is true, imag(A) otherwise */
+cs_dl *cs_l_real (cs_cl *A, UF_long real)
+{
+ cs_dl *C ;
+ UF_long n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ;
+ cs_complex_t *Ax ;
+ double *Cx ;
+ if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */
+ nz = triplet ? A->nz : Ap [n] ;
+ C = cs_dl_spalloc (A->m, n, A->nzmax, 1, triplet) ;
+ if (!C) return (NULL) ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ nn = triplet ? nz : (n+1) ;
+ for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ;
+ for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ;
+ for (p = 0 ; p < nz ; p++) Cx [p] = real ? creal (Ax [p]) : cimag (Ax [p]) ;
+ if (triplet) C->nz = nz ;
+ return (C) ;
+}
+
+/* convert from real to complex (UF_long version) */
+/* C = A if real is true, or C = i*A otherwise */
+cs_cl *cs_l_complex (cs_dl *A, UF_long real)
+{
+ cs_cl *C ;
+ UF_long n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ;
+ double *Ax ;
+ cs_complex_t *Cx ;
+ if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */
+ nz = triplet ? A->nz : Ap [n] ;
+ C = cs_cl_spalloc (A->m, n, A->nzmax, 1, triplet) ;
+ if (!C) return (NULL) ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ nn = triplet ? nz : (n+1) ;
+ for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ;
+ for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ;
+ for (p = 0 ; p < nz ; p++) Cx [p] = real ? Ax [p] : (I * Ax [p]) ;
+ if (triplet) C->nz = nz ;
+ return (C) ;
+}
diff --git a/CXSparse/Source/cs_counts.c b/CXSparse/Source/cs_counts.c
new file mode 100644
index 0000000..de97b96
--- /dev/null
+++ b/CXSparse/Source/cs_counts.c
@@ -0,0 +1,61 @@
+#include "cs.h"
+/* column counts of LL'=A or LL'=A'A, given parent & post ordering */
+#define HEAD(k,j) (ata ? head [k] : j)
+#define NEXT(J) (ata ? next [J] : -1)
+static void init_ata (cs *AT, const CS_INT *post, CS_INT *w, CS_INT **head, CS_INT **next)
+{
+ CS_INT i, k, p, m = AT->n, n = AT->m, *ATp = AT->p, *ATi = AT->i ;
+ *head = w+4*n, *next = w+5*n+1 ;
+ for (k = 0 ; k < n ; k++) w [post [k]] = k ; /* invert post */
+ for (i = 0 ; i < m ; i++)
+ {
+ for (k = n, p = ATp[i] ; p < ATp[i+1] ; p++) k = CS_MIN (k, w [ATi[p]]);
+ (*next) [i] = (*head) [k] ; /* place row i in linked list k */
+ (*head) [k] = i ;
+ }
+}
+CS_INT *cs_counts (const cs *A, const CS_INT *parent, const CS_INT *post, CS_INT ata)
+{
+ CS_INT i, j, k, n, m, J, s, p, q, jleaf, *ATp, *ATi, *maxfirst, *prevleaf,
+ *ancestor, *head = NULL, *next = NULL, *colcount, *w, *first, *delta ;
+ cs *AT ;
+ if (!CS_CSC (A) || !parent || !post) return (NULL) ; /* check inputs */
+ m = A->m ; n = A->n ;
+ s = 4*n + (ata ? (n+m+1) : 0) ;
+ delta = colcount = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */
+ w = cs_malloc (s, sizeof (CS_INT)) ; /* get workspace */
+ AT = cs_transpose (A, 0) ; /* AT = A' */
+ if (!AT || !colcount || !w) return (cs_idone (colcount, AT, w, 0)) ;
+ ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ;
+ for (k = 0 ; k < s ; k++) w [k] = -1 ; /* clear workspace w [0..s-1] */
+ for (k = 0 ; k < n ; k++) /* find first [j] */
+ {
+ j = post [k] ;
+ delta [j] = (first [j] == -1) ? 1 : 0 ; /* delta[j]=1 if j is a leaf */
+ for ( ; j != -1 && first [j] == -1 ; j = parent [j]) first [j] = k ;
+ }
+ ATp = AT->p ; ATi = AT->i ;
+ if (ata) init_ata (AT, post, w, &head, &next) ;
+ for (i = 0 ; i < n ; i++) ancestor [i] = i ; /* each node in its own set */
+ for (k = 0 ; k < n ; k++)
+ {
+ j = post [k] ; /* j is the kth node in postordered etree */
+ if (parent [j] != -1) delta [parent [j]]-- ; /* j is not a root */
+ for (J = HEAD (k,j) ; J != -1 ; J = NEXT (J)) /* J=j for LL'=A case */
+ {
+ for (p = ATp [J] ; p < ATp [J+1] ; p++)
+ {
+ i = ATi [p] ;
+ q = cs_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf);
+ if (jleaf >= 1) delta [j]++ ; /* A(i,j) is in skeleton */
+ if (jleaf == 2) delta [q]-- ; /* account for overlap in q */
+ }
+ }
+ if (parent [j] != -1) ancestor [j] = parent [j] ;
+ }
+ for (j = 0 ; j < n ; j++) /* sum up delta's of each child */
+ {
+ if (parent [j] != -1) colcount [parent [j]] += colcount [j] ;
+ }
+ return (cs_idone (colcount, AT, w, 1)) ; /* success: free workspace */
+}
diff --git a/CXSparse/Source/cs_cumsum.c b/CXSparse/Source/cs_cumsum.c
new file mode 100644
index 0000000..780dde6
--- /dev/null
+++ b/CXSparse/Source/cs_cumsum.c
@@ -0,0 +1,17 @@
+#include "cs.h"
+/* p [0..n] = cumulative sum of c [0..n-1], and then copy p [0..n-1] into c */
+double cs_cumsum (CS_INT *p, CS_INT *c, CS_INT n)
+{
+ CS_INT i, nz = 0 ;
+ double nz2 = 0 ;
+ if (!p || !c) return (-1) ; /* check inputs */
+ for (i = 0 ; i < n ; i++)
+ {
+ p [i] = nz ;
+ nz += c [i] ;
+ nz2 += c [i] ; /* also in double to avoid CS_INT overflow */
+ c [i] = p [i] ; /* also copy p[0..n-1] back into c[0..n-1]*/
+ }
+ p [n] = nz ;
+ return (nz2) ; /* return sum (c [0..n-1]) */
+}
diff --git a/CXSparse/Source/cs_dfs.c b/CXSparse/Source/cs_dfs.c
new file mode 100644
index 0000000..6886b10
--- /dev/null
+++ b/CXSparse/Source/cs_dfs.c
@@ -0,0 +1,36 @@
+#include "cs.h"
+/* depth-first-search of the graph of a matrix, starting at node j */
+CS_INT cs_dfs (CS_INT j, cs *G, CS_INT top, CS_INT *xi, CS_INT *pstack, const CS_INT *pinv)
+{
+ CS_INT i, p, p2, done, jnew, head = 0, *Gp, *Gi ;
+ if (!CS_CSC (G) || !xi || !pstack) return (-1) ; /* check inputs */
+ Gp = G->p ; Gi = G->i ;
+ xi [0] = j ; /* initialize the recursion stack */
+ while (head >= 0)
+ {
+ j = xi [head] ; /* get j from the top of the recursion stack */
+ jnew = pinv ? (pinv [j]) : j ;
+ if (!CS_MARKED (Gp, j))
+ {
+ CS_MARK (Gp, j) ; /* mark node j as visited */
+ pstack [head] = (jnew < 0) ? 0 : CS_UNFLIP (Gp [jnew]) ;
+ }
+ done = 1 ; /* node j done if no unvisited neighbors */
+ p2 = (jnew < 0) ? 0 : CS_UNFLIP (Gp [jnew+1]) ;
+ for (p = pstack [head] ; p < p2 ; p++) /* examine all neighbors of j */
+ {
+ i = Gi [p] ; /* consider neighbor node i */
+ if (CS_MARKED (Gp, i)) continue ; /* skip visited node i */
+ pstack [head] = p ; /* pause depth-first search of node j */
+ xi [++head] = i ; /* start dfs at node i */
+ done = 0 ; /* node j is not done */
+ break ; /* break, to start dfs (i) */
+ }
+ if (done) /* depth-first search at node j is done */
+ {
+ head-- ; /* remove j from the recursion stack */
+ xi [--top] = j ; /* and place in the output stack */
+ }
+ }
+ return (top) ;
+}
diff --git a/CXSparse/Source/cs_dmperm.c b/CXSparse/Source/cs_dmperm.c
new file mode 100644
index 0000000..c9807d8
--- /dev/null
+++ b/CXSparse/Source/cs_dmperm.c
@@ -0,0 +1,144 @@
+#include "cs.h"
+/* breadth-first search for coarse decomposition (C0,C1,R1 or R0,R3,C3) */
+static CS_INT cs_bfs (const cs *A, CS_INT n, CS_INT *wi, CS_INT *wj, CS_INT *queue,
+ const CS_INT *imatch, const CS_INT *jmatch, CS_INT mark)
+{
+ CS_INT *Ap, *Ai, head = 0, tail = 0, j, i, p, j2 ;
+ cs *C ;
+ for (j = 0 ; j < n ; j++) /* place all unmatched nodes in queue */
+ {
+ if (imatch [j] >= 0) continue ; /* skip j if matched */
+ wj [j] = 0 ; /* j in set C0 (R0 if transpose) */
+ queue [tail++] = j ; /* place unmatched col j in queue */
+ }
+ if (tail == 0) return (1) ; /* quick return if no unmatched nodes */
+ C = (mark == 1) ? ((cs *) A) : cs_transpose (A, 0) ;
+ if (!C) return (0) ; /* bfs of C=A' to find R3,C3 from R0 */
+ Ap = C->p ; Ai = C->i ;
+ while (head < tail) /* while queue is not empty */
+ {
+ j = queue [head++] ; /* get the head of the queue */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ if (wi [i] >= 0) continue ; /* skip if i is marked */
+ wi [i] = mark ; /* i in set R1 (C3 if transpose) */
+ j2 = jmatch [i] ; /* traverse alternating path to j2 */
+ if (wj [j2] >= 0) continue ;/* skip j2 if it is marked */
+ wj [j2] = mark ; /* j2 in set C1 (R3 if transpose) */
+ queue [tail++] = j2 ; /* add j2 to queue */
+ }
+ }
+ if (mark != 1) cs_spfree (C) ; /* free A' if it was created */
+ return (1) ;
+}
+
+/* collect matched rows and columns into p and q */
+static void cs_matched (CS_INT n, const CS_INT *wj, const CS_INT *imatch, CS_INT *p, CS_INT *q,
+ CS_INT *cc, CS_INT *rr, CS_INT set, CS_INT mark)
+{
+ CS_INT kc = cc [set], j ;
+ CS_INT kr = rr [set-1] ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (wj [j] != mark) continue ; /* skip if j is not in C set */
+ p [kr++] = imatch [j] ;
+ q [kc++] = j ;
+ }
+ cc [set+1] = kc ;
+ rr [set] = kr ;
+}
+
+/* collect unmatched rows into the permutation vector p */
+static void cs_unmatched (CS_INT m, const CS_INT *wi, CS_INT *p, CS_INT *rr, CS_INT set)
+{
+ CS_INT i, kr = rr [set] ;
+ for (i = 0 ; i < m ; i++) if (wi [i] == 0) p [kr++] = i ;
+ rr [set+1] = kr ;
+}
+
+/* return 1 if row i is in R2 */
+static CS_INT cs_rprune (CS_INT i, CS_INT j, CS_ENTRY aij, void *other)
+{
+ CS_INT *rr = (CS_INT *) other ;
+ return (i >= rr [1] && i < rr [2]) ;
+}
+
+/* Given A, compute coarse and then fine dmperm */
+csd *cs_dmperm (const cs *A, CS_INT seed)
+{
+ CS_INT m, n, i, j, k, cnz, nc, *jmatch, *imatch, *wi, *wj, *pinv, *Cp, *Ci,
+ *ps, *rs, nb1, nb2, *p, *q, *cc, *rr, *r, *s, ok ;
+ cs *C ;
+ csd *D, *scc ;
+ /* --- Maximum matching ------------------------------------------------- */
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ m = A->m ; n = A->n ;
+ D = cs_dalloc (m, n) ; /* allocate result */
+ if (!D) return (NULL) ;
+ p = D->p ; q = D->q ; r = D->r ; s = D->s ; cc = D->cc ; rr = D->rr ;
+ jmatch = cs_maxtrans (A, seed) ; /* max transversal */
+ imatch = jmatch + m ; /* imatch = inverse of jmatch */
+ if (!jmatch) return (cs_ddone (D, NULL, jmatch, 0)) ;
+ /* --- Coarse decomposition --------------------------------------------- */
+ wi = r ; wj = s ; /* use r and s as workspace */
+ for (j = 0 ; j < n ; j++) wj [j] = -1 ; /* unmark all cols for bfs */
+ for (i = 0 ; i < m ; i++) wi [i] = -1 ; /* unmark all rows for bfs */
+ cs_bfs (A, n, wi, wj, q, imatch, jmatch, 1) ; /* find C1, R1 from C0*/
+ ok = cs_bfs (A, m, wj, wi, p, jmatch, imatch, 3) ; /* find R3, C3 from R0*/
+ if (!ok) return (cs_ddone (D, NULL, jmatch, 0)) ;
+ cs_unmatched (n, wj, q, cc, 0) ; /* unmatched set C0 */
+ cs_matched (n, wj, imatch, p, q, cc, rr, 1, 1) ; /* set R1 and C1 */
+ cs_matched (n, wj, imatch, p, q, cc, rr, 2, -1) ; /* set R2 and C2 */
+ cs_matched (n, wj, imatch, p, q, cc, rr, 3, 3) ; /* set R3 and C3 */
+ cs_unmatched (m, wi, p, rr, 3) ; /* unmatched set R0 */
+ cs_free (jmatch) ;
+ /* --- Fine decomposition ----------------------------------------------- */
+ pinv = cs_pinv (p, m) ; /* pinv=p' */
+ if (!pinv) return (cs_ddone (D, NULL, NULL, 0)) ;
+ C = cs_permute (A, pinv, q, 0) ;/* C=A(p,q) (it will hold A(R2,C2)) */
+ cs_free (pinv) ;
+ if (!C) return (cs_ddone (D, NULL, NULL, 0)) ;
+ Cp = C->p ;
+ nc = cc [3] - cc [2] ; /* delete cols C0, C1, and C3 from C */
+ if (cc [2] > 0) for (j = cc [2] ; j <= cc [3] ; j++) Cp [j-cc[2]] = Cp [j] ;
+ C->n = nc ;
+ if (rr [2] - rr [1] < m) /* delete rows R0, R1, and R3 from C */
+ {
+ cs_fkeep (C, cs_rprune, rr) ;
+ cnz = Cp [nc] ;
+ Ci = C->i ;
+ if (rr [1] > 0) for (k = 0 ; k < cnz ; k++) Ci [k] -= rr [1] ;
+ }
+ C->m = nc ;
+ scc = cs_scc (C) ; /* find strongly connected components of C*/
+ if (!scc) return (cs_ddone (D, C, NULL, 0)) ;
+ /* --- Combine coarse and fine decompositions --------------------------- */
+ ps = scc->p ; /* C(ps,ps) is the permuted matrix */
+ rs = scc->r ; /* kth block is rs[k]..rs[k+1]-1 */
+ nb1 = scc->nb ; /* # of blocks of A(R2,C2) */
+ for (k = 0 ; k < nc ; k++) wj [k] = q [ps [k] + cc [2]] ;
+ for (k = 0 ; k < nc ; k++) q [k + cc [2]] = wj [k] ;
+ for (k = 0 ; k < nc ; k++) wi [k] = p [ps [k] + rr [1]] ;
+ for (k = 0 ; k < nc ; k++) p [k + rr [1]] = wi [k] ;
+ nb2 = 0 ; /* create the fine block partitions */
+ r [0] = s [0] = 0 ;
+ if (cc [2] > 0) nb2++ ; /* leading coarse block A (R1, [C0 C1]) */
+ for (k = 0 ; k < nb1 ; k++) /* coarse block A (R2,C2) */
+ {
+ r [nb2] = rs [k] + rr [1] ; /* A (R2,C2) splits into nb1 fine blocks */
+ s [nb2] = rs [k] + cc [2] ;
+ nb2++ ;
+ }
+ if (rr [2] < m)
+ {
+ r [nb2] = rr [2] ; /* trailing coarse block A ([R3 R0], C3) */
+ s [nb2] = cc [3] ;
+ nb2++ ;
+ }
+ r [nb2] = m ;
+ s [nb2] = n ;
+ D->nb = nb2 ;
+ cs_dfree (scc) ;
+ return (cs_ddone (D, C, NULL, 1)) ;
+}
diff --git a/CXSparse/Source/cs_droptol.c b/CXSparse/Source/cs_droptol.c
new file mode 100644
index 0000000..59b8df2
--- /dev/null
+++ b/CXSparse/Source/cs_droptol.c
@@ -0,0 +1,9 @@
+#include "cs.h"
+static CS_INT cs_tol (CS_INT i, CS_INT j, CS_ENTRY aij, void *tol)
+{
+ return (CS_ABS (aij) > *((double *) tol)) ;
+}
+CS_INT cs_droptol (cs *A, double tol)
+{
+ return (cs_fkeep (A, &cs_tol, &tol)) ; /* keep all large entries */
+}
diff --git a/CXSparse/Source/cs_dropzeros.c b/CXSparse/Source/cs_dropzeros.c
new file mode 100644
index 0000000..0e77aad
--- /dev/null
+++ b/CXSparse/Source/cs_dropzeros.c
@@ -0,0 +1,9 @@
+#include "cs.h"
+static CS_INT cs_nonzero (CS_INT i, CS_INT j, CS_ENTRY aij, void *other)
+{
+ return (aij != 0) ;
+}
+CS_INT cs_dropzeros (cs *A)
+{
+ return (cs_fkeep (A, &cs_nonzero, NULL)) ; /* keep all nonzero entries */
+}
diff --git a/CXSparse/Source/cs_dupl.c b/CXSparse/Source/cs_dupl.c
new file mode 100644
index 0000000..f5aec44
--- /dev/null
+++ b/CXSparse/Source/cs_dupl.c
@@ -0,0 +1,34 @@
+#include "cs.h"
+/* remove duplicate entries from A */
+CS_INT cs_dupl (cs *A)
+{
+ CS_INT i, j, p, q, nz = 0, n, m, *Ap, *Ai, *w ;
+ CS_ENTRY *Ax ;
+ if (!CS_CSC (A)) return (0) ; /* check inputs */
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ w = cs_malloc (m, sizeof (CS_INT)) ; /* get workspace */
+ if (!w) return (0) ; /* out of memory */
+ for (i = 0 ; i < m ; i++) w [i] = -1 ; /* row i not yet seen */
+ for (j = 0 ; j < n ; j++)
+ {
+ q = nz ; /* column j will start at q */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ; /* A(i,j) is nonzero */
+ if (w [i] >= q)
+ {
+ Ax [w [i]] += Ax [p] ; /* A(i,j) is a duplicate */
+ }
+ else
+ {
+ w [i] = nz ; /* record where row i occurs */
+ Ai [nz] = i ; /* keep A(i,j) */
+ Ax [nz++] = Ax [p] ;
+ }
+ }
+ Ap [j] = q ; /* record start of column j */
+ }
+ Ap [n] = nz ; /* finalize A */
+ cs_free (w) ; /* free workspace */
+ return (cs_sprealloc (A, 0)) ; /* remove extra space from A */
+}
diff --git a/CXSparse/Source/cs_entry.c b/CXSparse/Source/cs_entry.c
new file mode 100644
index 0000000..0b1b94a
--- /dev/null
+++ b/CXSparse/Source/cs_entry.c
@@ -0,0 +1,13 @@
+#include "cs.h"
+/* add an entry to a triplet matrix; return 1 if ok, 0 otherwise */
+CS_INT cs_entry (cs *T, CS_INT i, CS_INT j, CS_ENTRY x)
+{
+ if (!CS_TRIPLET (T) || i < 0 || j < 0) return (0) ; /* check inputs */
+ if (T->nz >= T->nzmax && !cs_sprealloc (T,2*(T->nzmax))) return (0) ;
+ if (T->x) T->x [T->nz] = x ;
+ T->i [T->nz] = i ;
+ T->p [T->nz++] = j ;
+ T->m = CS_MAX (T->m, i+1) ;
+ T->n = CS_MAX (T->n, j+1) ;
+ return (1) ;
+}
diff --git a/CXSparse/Source/cs_ereach.c b/CXSparse/Source/cs_ereach.c
new file mode 100644
index 0000000..14d68e0
--- /dev/null
+++ b/CXSparse/Source/cs_ereach.c
@@ -0,0 +1,23 @@
+#include "cs.h"
+/* find nonzero pattern of Cholesky L(k,1:k-1) using etree and triu(A(:,k)) */
+CS_INT cs_ereach (const cs *A, CS_INT k, const CS_INT *parent, CS_INT *s, CS_INT *w)
+{
+ CS_INT i, p, n, len, top, *Ap, *Ai ;
+ if (!CS_CSC (A) || !parent || !s || !w) return (-1) ; /* check inputs */
+ top = n = A->n ; Ap = A->p ; Ai = A->i ;
+ CS_MARK (w, k) ; /* mark node k as visited */
+ for (p = Ap [k] ; p < Ap [k+1] ; p++)
+ {
+ i = Ai [p] ; /* A(i,k) is nonzero */
+ if (i > k) continue ; /* only use upper triangular part of A */
+ for (len = 0 ; !CS_MARKED (w,i) ; i = parent [i]) /* traverse up etree*/
+ {
+ s [len++] = i ; /* L(k,i) is nonzero */
+ CS_MARK (w, i) ; /* mark i as visited */
+ }
+ while (len > 0) s [--top] = s [--len] ; /* push path onto stack */
+ }
+ for (p = top ; p < n ; p++) CS_MARK (w, s [p]) ; /* unmark all nodes */
+ CS_MARK (w, k) ; /* unmark node k */
+ return (top) ; /* s [top..n-1] contains pattern of L(k,:)*/
+}
diff --git a/CXSparse/Source/cs_etree.c b/CXSparse/Source/cs_etree.c
new file mode 100644
index 0000000..6f275d2
--- /dev/null
+++ b/CXSparse/Source/cs_etree.c
@@ -0,0 +1,30 @@
+#include "cs.h"
+/* compute the etree of A (using triu(A), or A'A without forming A'A */
+CS_INT *cs_etree (const cs *A, CS_INT ata)
+{
+ CS_INT i, k, p, m, n, inext, *Ap, *Ai, *w, *parent, *ancestor, *prev ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ;
+ parent = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */
+ w = cs_malloc (n + (ata ? m : 0), sizeof (CS_INT)) ; /* get workspace */
+ if (!w || !parent) return (cs_idone (parent, NULL, w, 0)) ;
+ ancestor = w ; prev = w + n ;
+ if (ata) for (i = 0 ; i < m ; i++) prev [i] = -1 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ parent [k] = -1 ; /* node k has no parent yet */
+ ancestor [k] = -1 ; /* nor does k have an ancestor */
+ for (p = Ap [k] ; p < Ap [k+1] ; p++)
+ {
+ i = ata ? (prev [Ai [p]]) : (Ai [p]) ;
+ for ( ; i != -1 && i < k ; i = inext) /* traverse from i to k */
+ {
+ inext = ancestor [i] ; /* inext = ancestor of i */
+ ancestor [i] = k ; /* path compression */
+ if (inext == -1) parent [i] = k ; /* no anc., parent is k */
+ }
+ if (ata) prev [Ai [p]] = k ;
+ }
+ }
+ return (cs_idone (parent, NULL, w, 1)) ;
+}
diff --git a/CXSparse/Source/cs_fkeep.c b/CXSparse/Source/cs_fkeep.c
new file mode 100644
index 0000000..c1b05d0
--- /dev/null
+++ b/CXSparse/Source/cs_fkeep.c
@@ -0,0 +1,25 @@
+#include "cs.h"
+/* drop entries for which fkeep(A(i,j)) is false; return nz if OK, else -1 */
+CS_INT cs_fkeep (cs *A, CS_INT (*fkeep) (CS_INT, CS_INT, CS_ENTRY, void *), void *other)
+{
+ CS_INT j, p, nz = 0, n, *Ap, *Ai ;
+ CS_ENTRY *Ax ;
+ if (!CS_CSC (A) || !fkeep) return (-1) ; /* check inputs */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ p = Ap [j] ; /* get current location of col j */
+ Ap [j] = nz ; /* record new location of col j */
+ for ( ; p < Ap [j+1] ; p++)
+ {
+ if (fkeep (Ai [p], j, Ax ? Ax [p] : 1, other))
+ {
+ if (Ax) Ax [nz] = Ax [p] ; /* keep A(i,j) */
+ Ai [nz++] = Ai [p] ;
+ }
+ }
+ }
+ Ap [n] = nz ; /* finalize A */
+ cs_sprealloc (A, 0) ; /* remove extra space from A */
+ return (nz) ;
+}
diff --git a/CXSparse/Source/cs_gaxpy.c b/CXSparse/Source/cs_gaxpy.c
new file mode 100644
index 0000000..93944de
--- /dev/null
+++ b/CXSparse/Source/cs_gaxpy.c
@@ -0,0 +1,17 @@
+#include "cs.h"
+/* y = A*x+y */
+CS_INT cs_gaxpy (const cs *A, const CS_ENTRY *x, CS_ENTRY *y)
+{
+ CS_INT p, j, n, *Ap, *Ai ;
+ CS_ENTRY *Ax ;
+ if (!CS_CSC (A) || !x || !y) return (0) ; /* check inputs */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ y [Ai [p]] += Ax [p] * x [j] ;
+ }
+ }
+ return (1) ;
+}
diff --git a/CXSparse/Source/cs_happly.c b/CXSparse/Source/cs_happly.c
new file mode 100644
index 0000000..6793645
--- /dev/null
+++ b/CXSparse/Source/cs_happly.c
@@ -0,0 +1,19 @@
+#include "cs.h"
+/* apply the ith Householder vector to x */
+CS_INT cs_happly (const cs *V, CS_INT i, double beta, CS_ENTRY *x)
+{
+ CS_INT p, *Vp, *Vi ;
+ CS_ENTRY *Vx, tau = 0 ;
+ if (!CS_CSC (V) || !x) return (0) ; /* check inputs */
+ Vp = V->p ; Vi = V->i ; Vx = V->x ;
+ for (p = Vp [i] ; p < Vp [i+1] ; p++) /* tau = v'*x */
+ {
+ tau += CS_CONJ (Vx [p]) * x [Vi [p]] ;
+ }
+ tau *= beta ; /* tau = beta*(v'*x) */
+ for (p = Vp [i] ; p < Vp [i+1] ; p++) /* x = x - v*tau */
+ {
+ x [Vi [p]] -= Vx [p] * tau ;
+ }
+ return (1) ;
+}
diff --git a/CXSparse/Source/cs_house.c b/CXSparse/Source/cs_house.c
new file mode 100644
index 0000000..baf4082
--- /dev/null
+++ b/CXSparse/Source/cs_house.c
@@ -0,0 +1,30 @@
+#include "cs.h"
+/* create a Householder reflection [v,beta,s]=house(x), overwrite x with v,
+ * where (I-beta*v*v')*x = s*e1 and e1 = [1 0 ... 0]'.
+ * Note that this CXSparse version is different than CSparse. See Higham,
+ * Accuracy & Stability of Num Algorithms, 2nd ed, 2002, page 357. */
+CS_ENTRY cs_house (CS_ENTRY *x, double *beta, CS_INT n)
+{
+ CS_ENTRY s = 0 ;
+ CS_INT i ;
+ if (!x || !beta) return (-1) ; /* check inputs */
+ /* s = norm(x) */
+ for (i = 0 ; i < n ; i++) s += x [i] * CS_CONJ (x [i]) ;
+ s = sqrt (s) ;
+ if (s == 0)
+ {
+ (*beta) = 0 ;
+ x [0] = 1 ;
+ }
+ else
+ {
+ /* s = sign(x[0]) * norm (x) ; */
+ if (x [0] != 0)
+ {
+ s *= x [0] / CS_ABS (x [0]) ;
+ }
+ x [0] += s ;
+ (*beta) = 1. / CS_REAL (CS_CONJ (s) * x [0]) ;
+ }
+ return (-s) ;
+}
diff --git a/CXSparse/Source/cs_ipvec.c b/CXSparse/Source/cs_ipvec.c
new file mode 100644
index 0000000..d87fe29
--- /dev/null
+++ b/CXSparse/Source/cs_ipvec.c
@@ -0,0 +1,9 @@
+#include "cs.h"
+/* x(p) = b, for dense vectors x and b; p=NULL denotes identity */
+CS_INT cs_ipvec (const CS_INT *p, const CS_ENTRY *b, CS_ENTRY *x, CS_INT n)
+{
+ CS_INT k ;
+ if (!x || !b) return (0) ; /* check inputs */
+ for (k = 0 ; k < n ; k++) x [p ? p [k] : k] = b [k] ;
+ return (1) ;
+}
diff --git a/CXSparse/Source/cs_leaf.c b/CXSparse/Source/cs_leaf.c
new file mode 100644
index 0000000..57307a4
--- /dev/null
+++ b/CXSparse/Source/cs_leaf.c
@@ -0,0 +1,22 @@
+#include "cs.h"
+/* consider A(i,j), node j in ith row subtree and return lca(jprev,j) */
+CS_INT cs_leaf (CS_INT i, CS_INT j, const CS_INT *first, CS_INT *maxfirst, CS_INT *prevleaf,
+ CS_INT *ancestor, CS_INT *jleaf)
+{
+ CS_INT q, s, sparent, jprev ;
+ if (!first || !maxfirst || !prevleaf || !ancestor || !jleaf) return (-1) ;
+ *jleaf = 0 ;
+ if (i <= j || first [j] <= maxfirst [i]) return (-1) ; /* j not a leaf */
+ maxfirst [i] = first [j] ; /* update max first[j] seen so far */
+ jprev = prevleaf [i] ; /* jprev = previous leaf of ith subtree */
+ prevleaf [i] = j ;
+ *jleaf = (jprev == -1) ? 1: 2 ; /* j is first or subsequent leaf */
+ if (*jleaf == 1) return (i) ; /* if 1st leaf, q = root of ith subtree */
+ for (q = jprev ; q != ancestor [q] ; q = ancestor [q]) ;
+ for (s = jprev ; s != q ; s = sparent)
+ {
+ sparent = ancestor [s] ; /* path compression */
+ ancestor [s] = q ;
+ }
+ return (q) ; /* q = least common ancester (jprev,j) */
+}
diff --git a/CXSparse/Source/cs_load.c b/CXSparse/Source/cs_load.c
new file mode 100644
index 0000000..16c94cb
--- /dev/null
+++ b/CXSparse/Source/cs_load.c
@@ -0,0 +1,26 @@
+#include "cs.h"
+/* load a triplet matrix from a file */
+cs *cs_load (FILE *f)
+{
+ CS_INT i, j ;
+ double x ;
+#ifdef CS_COMPLEX
+ double xi ;
+#endif
+ cs *T ;
+ if (!f) return (NULL) ; /* check inputs */
+ T = cs_spalloc (0, 0, 1, 1, 1) ; /* allocate result */
+#ifdef CS_COMPLEX
+ while (fscanf (f, ""CS_ID" "CS_ID" %lg %lg\n", &i, &j, &x, &xi) == 4)
+#else
+ while (fscanf (f, ""CS_ID" "CS_ID" %lg\n", &i, &j, &x) == 3)
+#endif
+ {
+#ifdef CS_COMPLEX
+ if (!cs_entry (T, i, j, x + xi*I)) return (cs_spfree (T)) ;
+#else
+ if (!cs_entry (T, i, j, x)) return (cs_spfree (T)) ;
+#endif
+ }
+ return (T) ;
+}
diff --git a/CXSparse/Source/cs_lsolve.c b/CXSparse/Source/cs_lsolve.c
new file mode 100644
index 0000000..1daa028
--- /dev/null
+++ b/CXSparse/Source/cs_lsolve.c
@@ -0,0 +1,18 @@
+#include "cs.h"
+/* solve Lx=b where x and b are dense. x=b on input, solution on output. */
+CS_INT cs_lsolve (const cs *L, CS_ENTRY *x)
+{
+ CS_INT p, j, n, *Lp, *Li ;
+ CS_ENTRY *Lx ;
+ if (!CS_CSC (L) || !x) return (0) ; /* check inputs */
+ n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ x [j] /= Lx [Lp [j]] ;
+ for (p = Lp [j]+1 ; p < Lp [j+1] ; p++)
+ {
+ x [Li [p]] -= Lx [p] * x [j] ;
+ }
+ }
+ return (1) ;
+}
diff --git a/CXSparse/Source/cs_ltsolve.c b/CXSparse/Source/cs_ltsolve.c
new file mode 100644
index 0000000..a818b07
--- /dev/null
+++ b/CXSparse/Source/cs_ltsolve.c
@@ -0,0 +1,18 @@
+#include "cs.h"
+/* solve L'x=b where x and b are dense. x=b on input, solution on output. */
+CS_INT cs_ltsolve (const cs *L, CS_ENTRY *x)
+{
+ CS_INT p, j, n, *Lp, *Li ;
+ CS_ENTRY *Lx ;
+ if (!CS_CSC (L) || !x) return (0) ; /* check inputs */
+ n = L->n ; Lp = L->p ; Li = L->i ; Lx = L->x ;
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ for (p = Lp [j]+1 ; p < Lp [j+1] ; p++)
+ {
+ x [j] -= CS_CONJ (Lx [p]) * x [Li [p]] ;
+ }
+ x [j] /= CS_CONJ (Lx [Lp [j]]) ;
+ }
+ return (1) ;
+}
diff --git a/CXSparse/Source/cs_lu.c b/CXSparse/Source/cs_lu.c
new file mode 100644
index 0000000..f53f804
--- /dev/null
+++ b/CXSparse/Source/cs_lu.c
@@ -0,0 +1,87 @@
+#include "cs.h"
+/* [L,U,pinv]=lu(A, [q lnz unz]). lnz and unz can be guess */
+csn *cs_lu (const cs *A, const css *S, double tol)
+{
+ cs *L, *U ;
+ csn *N ;
+ CS_ENTRY pivot, *Lx, *Ux, *x ;
+ double a, t ;
+ CS_INT *Lp, *Li, *Up, *Ui, *pinv, *xi, *q, n, ipiv, k, top, p, i, col, lnz,unz;
+ if (!CS_CSC (A) || !S) return (NULL) ; /* check inputs */
+ n = A->n ;
+ q = S->q ; lnz = S->lnz ; unz = S->unz ;
+ x = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get CS_ENTRY workspace */
+ xi = cs_malloc (2*n, sizeof (CS_INT)) ; /* get CS_INT workspace */
+ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */
+ if (!x || !xi || !N) return (cs_ndone (N, NULL, xi, x, 0)) ;
+ N->L = L = cs_spalloc (n, n, lnz, 1, 0) ; /* allocate result L */
+ N->U = U = cs_spalloc (n, n, unz, 1, 0) ; /* allocate result U */
+ N->pinv = pinv = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result pinv */
+ if (!L || !U || !pinv) return (cs_ndone (N, NULL, xi, x, 0)) ;
+ Lp = L->p ; Up = U->p ;
+ for (i = 0 ; i < n ; i++) x [i] = 0 ; /* clear workspace */
+ for (i = 0 ; i < n ; i++) pinv [i] = -1 ; /* no rows pivotal yet */
+ for (k = 0 ; k <= n ; k++) Lp [k] = 0 ; /* no cols of L yet */
+ lnz = unz = 0 ;
+ for (k = 0 ; k < n ; k++) /* compute L(:,k) and U(:,k) */
+ {
+ /* --- Triangular solve --------------------------------------------- */
+ Lp [k] = lnz ; /* L(:,k) starts here */
+ Up [k] = unz ; /* U(:,k) starts here */
+ if ((lnz + n > L->nzmax && !cs_sprealloc (L, 2*L->nzmax + n)) ||
+ (unz + n > U->nzmax && !cs_sprealloc (U, 2*U->nzmax + n)))
+ {
+ return (cs_ndone (N, NULL, xi, x, 0)) ;
+ }
+ Li = L->i ; Lx = L->x ; Ui = U->i ; Ux = U->x ;
+ col = q ? (q [k]) : k ;
+ top = cs_spsolve (L, A, col, xi, x, pinv, 1) ; /* x = L\A(:,col) */
+ /* --- Find pivot --------------------------------------------------- */
+ ipiv = -1 ;
+ a = -1 ;
+ for (p = top ; p < n ; p++)
+ {
+ i = xi [p] ; /* x(i) is nonzero */
+ if (pinv [i] < 0) /* row i is not yet pivotal */
+ {
+ if ((t = CS_ABS (x [i])) > a)
+ {
+ a = t ; /* largest pivot candidate so far */
+ ipiv = i ;
+ }
+ }
+ else /* x(i) is the entry U(pinv[i],k) */
+ {
+ Ui [unz] = pinv [i] ;
+ Ux [unz++] = x [i] ;
+ }
+ }
+ if (ipiv == -1 || a <= 0) return (cs_ndone (N, NULL, xi, x, 0)) ;
+ if (pinv [col] < 0 && CS_ABS (x [col]) >= a*tol) ipiv = col ;
+ /* --- Divide by pivot ---------------------------------------------- */
+ pivot = x [ipiv] ; /* the chosen pivot */
+ Ui [unz] = k ; /* last entry in U(:,k) is U(k,k) */
+ Ux [unz++] = pivot ;
+ pinv [ipiv] = k ; /* ipiv is the kth pivot row */
+ Li [lnz] = ipiv ; /* first entry in L(:,k) is L(k,k) = 1 */
+ Lx [lnz++] = 1 ;
+ for (p = top ; p < n ; p++) /* L(k+1:n,k) = x / pivot */
+ {
+ i = xi [p] ;
+ if (pinv [i] < 0) /* x(i) is an entry in L(:,k) */
+ {
+ Li [lnz] = i ; /* save unpermuted row in L */
+ Lx [lnz++] = x [i] / pivot ; /* scale pivot column */
+ }
+ x [i] = 0 ; /* x [0..n-1] = 0 for next k */
+ }
+ }
+ /* --- Finalize L and U ------------------------------------------------- */
+ Lp [n] = lnz ;
+ Up [n] = unz ;
+ Li = L->i ; /* fix row indices of L for final pinv */
+ for (p = 0 ; p < lnz ; p++) Li [p] = pinv [Li [p]] ;
+ cs_sprealloc (L, 0) ; /* remove extra space from L and U */
+ cs_sprealloc (U, 0) ;
+ return (cs_ndone (N, NULL, xi, x, 1)) ; /* success */
+}
diff --git a/CXSparse/Source/cs_lusol.c b/CXSparse/Source/cs_lusol.c
new file mode 100644
index 0000000..affe754
--- /dev/null
+++ b/CXSparse/Source/cs_lusol.c
@@ -0,0 +1,26 @@
+#include "cs.h"
+/* x=A\b where A is unsymmetric; b overwritten with solution */
+CS_INT cs_lusol (CS_INT order, const cs *A, CS_ENTRY *b, double tol)
+{
+ CS_ENTRY *x ;
+ css *S ;
+ csn *N ;
+ CS_INT n, ok ;
+ if (!CS_CSC (A) || !b) return (0) ; /* check inputs */
+ n = A->n ;
+ S = cs_sqr (order, A, 0) ; /* ordering and symbolic analysis */
+ N = cs_lu (A, S, tol) ; /* numeric LU factorization */
+ x = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get workspace */
+ ok = (S && N && x) ;
+ if (ok)
+ {
+ cs_ipvec (N->pinv, b, x, n) ; /* x = b(p) */
+ cs_lsolve (N->L, x) ; /* x = L\x */
+ cs_usolve (N->U, x) ; /* x = U\x */
+ cs_ipvec (S->q, x, b, n) ; /* b(q) = x */
+ }
+ cs_free (x) ;
+ cs_sfree (S) ;
+ cs_nfree (N) ;
+ return (ok) ;
+}
diff --git a/CXSparse/Source/cs_malloc.c b/CXSparse/Source/cs_malloc.c
new file mode 100644
index 0000000..c442ab7
--- /dev/null
+++ b/CXSparse/Source/cs_malloc.c
@@ -0,0 +1,35 @@
+#include "cs.h"
+#ifdef MATLAB_MEX_FILE
+#define malloc mxMalloc
+#define free mxFree
+#define realloc mxRealloc
+#define calloc mxCalloc
+#endif
+
+/* wrapper for malloc */
+void *cs_malloc (CS_INT n, size_t size)
+{
+ return (malloc (CS_MAX (n,1) * size)) ;
+}
+
+/* wrapper for calloc */
+void *cs_calloc (CS_INT n, size_t size)
+{
+ return (calloc (CS_MAX (n,1), size)) ;
+}
+
+/* wrapper for free */
+void *cs_free (void *p)
+{
+ if (p) free (p) ; /* free p if it is not already NULL */
+ return (NULL) ; /* return NULL to simplify the use of cs_free */
+}
+
+/* wrapper for realloc */
+void *cs_realloc (void *p, CS_INT n, size_t size, CS_INT *ok)
+{
+ void *pnew ;
+ pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */
+ *ok = (pnew != NULL) ; /* realloc fails if pnew is NULL */
+ return ((*ok) ? pnew : p) ; /* return original p if failure */
+}
diff --git a/CXSparse/Source/cs_maxtrans.c b/CXSparse/Source/cs_maxtrans.c
new file mode 100644
index 0000000..bf4421e
--- /dev/null
+++ b/CXSparse/Source/cs_maxtrans.c
@@ -0,0 +1,92 @@
+#include "cs.h"
+/* find an augmenting path starting at column k and extend the match if found */
+static void cs_augment (CS_INT k, const cs *A, CS_INT *jmatch, CS_INT *cheap, CS_INT *w,
+ CS_INT *js, CS_INT *is, CS_INT *ps)
+{
+ CS_INT found = 0, p, i = -1, *Ap = A->p, *Ai = A->i, head = 0, j ;
+ js [0] = k ; /* start with just node k in jstack */
+ while (head >= 0)
+ {
+ /* --- Start (or continue) depth-first-search at node j ------------- */
+ j = js [head] ; /* get j from top of jstack */
+ if (w [j] != k) /* 1st time j visited for kth path */
+ {
+ w [j] = k ; /* mark j as visited for kth path */
+ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++)
+ {
+ i = Ai [p] ; /* try a cheap assignment (i,j) */
+ found = (jmatch [i] == -1) ;
+ }
+ cheap [j] = p ; /* start here next time j is traversed*/
+ if (found)
+ {
+ is [head] = i ; /* column j matched with row i */
+ break ; /* end of augmenting path */
+ }
+ ps [head] = Ap [j] ; /* no cheap match: start dfs for j */
+ }
+ /* --- Depth-first-search of neighbors of j ------------------------- */
+ for (p = ps [head] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ; /* consider row i */
+ if (w [jmatch [i]] == k) continue ; /* skip jmatch [i] if marked */
+ ps [head] = p + 1 ; /* pause dfs of node j */
+ is [head] = i ; /* i will be matched with j if found */
+ js [++head] = jmatch [i] ; /* start dfs at column jmatch [i] */
+ break ;
+ }
+ if (p == Ap [j+1]) head-- ; /* node j is done; pop from stack */
+ } /* augment the match if path found: */
+ if (found) for (p = head ; p >= 0 ; p--) jmatch [is [p]] = js [p] ;
+}
+
+/* find a maximum transveral */
+CS_INT *cs_maxtrans (const cs *A, CS_INT seed) /*[jmatch [0..m-1]; imatch [0..n-1]]*/
+{
+ CS_INT i, j, k, n, m, p, n2 = 0, m2 = 0, *Ap, *jimatch, *w, *cheap, *js, *is,
+ *ps, *Ai, *Cp, *jmatch, *imatch, *q ;
+ cs *C ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ n = A->n ; m = A->m ; Ap = A->p ; Ai = A->i ;
+ w = jimatch = cs_calloc (m+n, sizeof (CS_INT)) ; /* allocate result */
+ if (!jimatch) return (NULL) ;
+ for (k = 0, j = 0 ; j < n ; j++) /* count nonempty rows and columns */
+ {
+ n2 += (Ap [j] < Ap [j+1]) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ w [Ai [p]] = 1 ;
+ k += (j == Ai [p]) ; /* count entries already on diagonal */
+ }
+ }
+ if (k == CS_MIN (m,n)) /* quick return if diagonal zero-free */
+ {
+ jmatch = jimatch ; imatch = jimatch + m ;
+ for (i = 0 ; i < k ; i++) jmatch [i] = i ;
+ for ( ; i < m ; i++) jmatch [i] = -1 ;
+ for (j = 0 ; j < k ; j++) imatch [j] = j ;
+ for ( ; j < n ; j++) imatch [j] = -1 ;
+ return (cs_idone (jimatch, NULL, NULL, 1)) ;
+ }
+ for (i = 0 ; i < m ; i++) m2 += w [i] ;
+ C = (m2 < n2) ? cs_transpose (A,0) : ((cs *) A) ; /* transpose if needed */
+ if (!C) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, NULL, 0)) ;
+ n = C->n ; m = C->m ; Cp = C->p ;
+ jmatch = (m2 < n2) ? jimatch + n : jimatch ;
+ imatch = (m2 < n2) ? jimatch : jimatch + m ;
+ w = cs_malloc (5*n, sizeof (CS_INT)) ; /* get workspace */
+ if (!w) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 0)) ;
+ cheap = w + n ; js = w + 2*n ; is = w + 3*n ; ps = w + 4*n ;
+ for (j = 0 ; j < n ; j++) cheap [j] = Cp [j] ; /* for cheap assignment */
+ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */
+ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* nothing matched yet */
+ q = cs_randperm (n, seed) ; /* q = random permutation */
+ for (k = 0 ; k < n ; k++) /* augment, starting at column q[k] */
+ {
+ cs_augment (q ? q [k]: k, C, jmatch, cheap, w, js, is, ps) ;
+ }
+ cs_free (q) ;
+ for (j = 0 ; j < n ; j++) imatch [j] = -1 ; /* find row match */
+ for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ;
+ return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 1)) ;
+}
diff --git a/CXSparse/Source/cs_multiply.c b/CXSparse/Source/cs_multiply.c
new file mode 100644
index 0000000..74255e1
--- /dev/null
+++ b/CXSparse/Source/cs_multiply.c
@@ -0,0 +1,35 @@
+#include "cs.h"
+/* C = A*B */
+cs *cs_multiply (const cs *A, const cs *B)
+{
+ CS_INT p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values, *Bi ;
+ CS_ENTRY *x, *Bx, *Cx ;
+ cs *C ;
+ if (!CS_CSC (A) || !CS_CSC (B)) return (NULL) ; /* check inputs */
+ if (A->n != B->m) return (NULL) ;
+ m = A->m ; anz = A->p [A->n] ;
+ n = B->n ; Bp = B->p ; Bi = B->i ; Bx = B->x ; bnz = Bp [n] ;
+ w = cs_calloc (m, sizeof (CS_INT)) ; /* get workspace */
+ values = (A->x != NULL) && (Bx != NULL) ;
+ x = values ? cs_malloc (m, sizeof (CS_ENTRY)) : NULL ; /* get workspace */
+ C = cs_spalloc (m, n, anz + bnz, values, 0) ; /* allocate result */
+ if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ;
+ Cp = C->p ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (nz + m > C->nzmax && !cs_sprealloc (C, 2*(C->nzmax)+m))
+ {
+ return (cs_done (C, w, x, 0)) ; /* out of memory */
+ }
+ Ci = C->i ; Cx = C->x ; /* C->i and C->x may be reallocated */
+ Cp [j] = nz ; /* column j of C starts here */
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ nz = cs_scatter (A, Bi [p], Bx ? Bx [p] : 1, w, x, j+1, C, nz) ;
+ }
+ if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ;
+ }
+ Cp [n] = nz ; /* finalize the last column of C */
+ cs_sprealloc (C, 0) ; /* remove extra space from C */
+ return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */
+}
diff --git a/CXSparse/Source/cs_norm.c b/CXSparse/Source/cs_norm.c
new file mode 100644
index 0000000..115c15a
--- /dev/null
+++ b/CXSparse/Source/cs_norm.c
@@ -0,0 +1,16 @@
+#include "cs.h"
+/* 1-norm of a sparse matrix = max (sum (abs (A))), largest column sum */
+double cs_norm (const cs *A)
+{
+ CS_INT p, j, n, *Ap ;
+ CS_ENTRY *Ax ;
+ double norm = 0, s ;
+ if (!CS_CSC (A) || !A->x) return (-1) ; /* check inputs */
+ n = A->n ; Ap = A->p ; Ax = A->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (s = 0, p = Ap [j] ; p < Ap [j+1] ; p++) s += CS_ABS (Ax [p]) ;
+ norm = CS_MAX (norm, s) ;
+ }
+ return (norm) ;
+}
diff --git a/CXSparse/Source/cs_permute.c b/CXSparse/Source/cs_permute.c
new file mode 100644
index 0000000..8ab5966
--- /dev/null
+++ b/CXSparse/Source/cs_permute.c
@@ -0,0 +1,25 @@
+#include "cs.h"
+/* C = A(p,q) where p and q are permutations of 0..m-1 and 0..n-1. */
+cs *cs_permute (const cs *A, const CS_INT *pinv, const CS_INT *q, CS_INT values)
+{
+ CS_INT t, j, k, nz = 0, m, n, *Ap, *Ai, *Cp, *Ci ;
+ CS_ENTRY *Cx, *Ax ;
+ cs *C ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ C = cs_spalloc (m, n, Ap [n], values && Ax != NULL, 0) ; /* alloc result */
+ if (!C) return (cs_done (C, NULL, NULL, 0)) ; /* out of memory */
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Cp [k] = nz ; /* column k of C is column q[k] of A */
+ j = q ? (q [k]) : k ;
+ for (t = Ap [j] ; t < Ap [j+1] ; t++)
+ {
+ if (Cx) Cx [nz] = Ax [t] ; /* row i of A is row pinv[i] of C */
+ Ci [nz++] = pinv ? (pinv [Ai [t]]) : Ai [t] ;
+ }
+ }
+ Cp [n] = nz ; /* finalize the last column of C */
+ return (cs_done (C, NULL, NULL, 1)) ;
+}
diff --git a/CXSparse/Source/cs_pinv.c b/CXSparse/Source/cs_pinv.c
new file mode 100644
index 0000000..4bcd0f0
--- /dev/null
+++ b/CXSparse/Source/cs_pinv.c
@@ -0,0 +1,11 @@
+#include "cs.h"
+/* pinv = p', or p = pinv' */
+CS_INT *cs_pinv (CS_INT const *p, CS_INT n)
+{
+ CS_INT k, *pinv ;
+ if (!p) return (NULL) ; /* p = NULL denotes identity */
+ pinv = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */
+ if (!pinv) return (NULL) ; /* out of memory */
+ for (k = 0 ; k < n ; k++) pinv [p [k]] = k ;/* invert the permutation */
+ return (pinv) ; /* return result */
+}
diff --git a/CXSparse/Source/cs_post.c b/CXSparse/Source/cs_post.c
new file mode 100644
index 0000000..bf3a69c
--- /dev/null
+++ b/CXSparse/Source/cs_post.c
@@ -0,0 +1,24 @@
+#include "cs.h"
+/* post order a forest */
+CS_INT *cs_post (const CS_INT *parent, CS_INT n)
+{
+ CS_INT j, k = 0, *post, *w, *head, *next, *stack ;
+ if (!parent) return (NULL) ; /* check inputs */
+ post = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */
+ w = cs_malloc (3*n, sizeof (CS_INT)) ; /* get workspace */
+ if (!w || !post) return (cs_idone (post, NULL, w, 0)) ;
+ head = w ; next = w + n ; stack = w + 2*n ;
+ for (j = 0 ; j < n ; j++) head [j] = -1 ; /* empty linked lists */
+ for (j = n-1 ; j >= 0 ; j--) /* traverse nodes in reverse order*/
+ {
+ if (parent [j] == -1) continue ; /* j is a root */
+ next [j] = head [parent [j]] ; /* add j to list of its parent */
+ head [parent [j]] = j ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ if (parent [j] != -1) continue ; /* skip j if it is not a root */
+ k = cs_tdfs (j, k, head, next, post, stack) ;
+ }
+ return (cs_idone (post, NULL, w, 1)) ; /* success; free w, return post */
+}
diff --git a/CXSparse/Source/cs_print.c b/CXSparse/Source/cs_print.c
new file mode 100644
index 0000000..aa4830c
--- /dev/null
+++ b/CXSparse/Source/cs_print.c
@@ -0,0 +1,46 @@
+#include "cs.h"
+/* print a sparse matrix */
+CS_INT cs_print (const cs *A, CS_INT brief)
+{
+ CS_INT p, j, m, n, nzmax, nz, *Ap, *Ai ;
+ CS_ENTRY *Ax ;
+ if (!A) { printf ("(null)\n") ; return (0) ; }
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ nzmax = A->nzmax ; nz = A->nz ;
+ printf ("CXSparse Version %d.%d.%d, %s. %s\n", CS_VER, CS_SUBVER,
+ CS_SUBSUB, CS_DATE, CS_COPYRIGHT) ;
+ if (nz < 0)
+ {
+ printf (""CS_ID"-by-"CS_ID", nzmax: "CS_ID" nnz: "CS_ID", 1-norm: %g\n", m, n, nzmax,
+ Ap [n], cs_norm (A)) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" col "CS_ID" : locations "CS_ID" to "CS_ID"\n", j, Ap [j], Ap [j+1]-1);
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+#ifdef CS_COMPLEX
+ printf (" "CS_ID" : (%g, %g)\n", Ai [p],
+ Ax ? CS_REAL (Ax [p]) : 1, Ax ? CS_IMAG (Ax [p]) : 0) ;
+#else
+ printf (" "CS_ID" : %g\n", Ai [p], Ax ? Ax [p] : 1) ;
+#endif
+ if (brief && p > 20) { printf (" ...\n") ; return (1) ; }
+ }
+ }
+ }
+ else
+ {
+ printf ("triplet: "CS_ID"-by-"CS_ID", nzmax: "CS_ID" nnz: "CS_ID"\n", m, n, nzmax, nz) ;
+ for (p = 0 ; p < nz ; p++)
+ {
+#ifdef CS_COMPLEX
+ printf (" "CS_ID" "CS_ID" : (%g, %g)\n", Ai [p], Ap [p],
+ Ax ? CS_REAL (Ax [p]) : 1, Ax ? CS_IMAG (Ax [p]) : 0) ;
+#else
+ printf (" "CS_ID" "CS_ID" : %g\n", Ai [p], Ap [p], Ax ? Ax [p] : 1) ;
+#endif
+ if (brief && p > 20) { printf (" ...\n") ; return (1) ; }
+ }
+ }
+ return (1) ;
+}
diff --git a/CXSparse/Source/cs_pvec.c b/CXSparse/Source/cs_pvec.c
new file mode 100644
index 0000000..3d8da3e
--- /dev/null
+++ b/CXSparse/Source/cs_pvec.c
@@ -0,0 +1,9 @@
+#include "cs.h"
+/* x = b(p), for dense vectors x and b; p=NULL denotes identity */
+CS_INT cs_pvec (const CS_INT *p, const CS_ENTRY *b, CS_ENTRY *x, CS_INT n)
+{
+ CS_INT k ;
+ if (!x || !b) return (0) ; /* check inputs */
+ for (k = 0 ; k < n ; k++) x [k] = b [p ? p [k] : k] ;
+ return (1) ;
+}
diff --git a/CXSparse/Source/cs_qr.c b/CXSparse/Source/cs_qr.c
new file mode 100644
index 0000000..609b471
--- /dev/null
+++ b/CXSparse/Source/cs_qr.c
@@ -0,0 +1,74 @@
+#include "cs.h"
+/* sparse QR factorization [V,beta,pinv,R] = qr (A) */
+csn *cs_qr (const cs *A, const css *S)
+{
+ CS_ENTRY *Rx, *Vx, *Ax, *x ;
+ double *Beta ;
+ CS_INT i, k, p, m, n, vnz, p1, top, m2, len, col, rnz, *s, *leftmost, *Ap, *Ai,
+ *parent, *Rp, *Ri, *Vp, *Vi, *w, *pinv, *q ;
+ cs *R, *V ;
+ csn *N ;
+ if (!CS_CSC (A) || !S) return (NULL) ;
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ q = S->q ; parent = S->parent ; pinv = S->pinv ; m2 = S->m2 ;
+ vnz = S->lnz ; rnz = S->unz ; leftmost = S->leftmost ;
+ w = cs_malloc (m2+n, sizeof (CS_INT)) ; /* get CS_INT workspace */
+ x = cs_malloc (m2, sizeof (CS_ENTRY)) ; /* get CS_ENTRY workspace */
+ N = cs_calloc (1, sizeof (csn)) ; /* allocate result */
+ if (!w || !x || !N) return (cs_ndone (N, NULL, w, x, 0)) ;
+ s = w + m2 ; /* s is size n */
+ for (k = 0 ; k < m2 ; k++) x [k] = 0 ; /* clear workspace x */
+ N->L = V = cs_spalloc (m2, n, vnz, 1, 0) ; /* allocate result V */
+ N->U = R = cs_spalloc (m2, n, rnz, 1, 0) ; /* allocate result R */
+ N->B = Beta = cs_malloc (n, sizeof (double)) ; /* allocate result Beta */
+ if (!R || !V || !Beta) return (cs_ndone (N, NULL, w, x, 0)) ;
+ Rp = R->p ; Ri = R->i ; Rx = R->x ;
+ Vp = V->p ; Vi = V->i ; Vx = V->x ;
+ for (i = 0 ; i < m2 ; i++) w [i] = -1 ; /* clear w, to mark nodes */
+ rnz = 0 ; vnz = 0 ;
+ for (k = 0 ; k < n ; k++) /* compute V and R */
+ {
+ Rp [k] = rnz ; /* R(:,k) starts here */
+ Vp [k] = p1 = vnz ; /* V(:,k) starts here */
+ w [k] = k ; /* add V(k,k) to pattern of V */
+ Vi [vnz++] = k ;
+ top = n ;
+ col = q ? q [k] : k ;
+ for (p = Ap [col] ; p < Ap [col+1] ; p++) /* find R(:,k) pattern */
+ {
+ i = leftmost [Ai [p]] ; /* i = min(find(A(i,q))) */
+ for (len = 0 ; w [i] != k ; i = parent [i]) /* traverse up to k */
+ {
+ s [len++] = i ;
+ w [i] = k ;
+ }
+ while (len > 0) s [--top] = s [--len] ; /* push path on stack */
+ i = pinv [Ai [p]] ; /* i = permuted row of A(:,col) */
+ x [i] = Ax [p] ; /* x (i) = A(:,col) */
+ if (i > k && w [i] < k) /* pattern of V(:,k) = x (k+1:m) */
+ {
+ Vi [vnz++] = i ; /* add i to pattern of V(:,k) */
+ w [i] = k ;
+ }
+ }
+ for (p = top ; p < n ; p++) /* for each i in pattern of R(:,k) */
+ {
+ i = s [p] ; /* R(i,k) is nonzero */
+ cs_happly (V, i, Beta [i], x) ; /* apply (V(i),Beta(i)) to x */
+ Ri [rnz] = i ; /* R(i,k) = x(i) */
+ Rx [rnz++] = x [i] ;
+ x [i] = 0 ;
+ if (parent [i] == k) vnz = cs_scatter (V, i, 0, w, NULL, k, V, vnz);
+ }
+ for (p = p1 ; p < vnz ; p++) /* gather V(:,k) = x */
+ {
+ Vx [p] = x [Vi [p]] ;
+ x [Vi [p]] = 0 ;
+ }
+ Ri [rnz] = k ; /* R(k,k) = norm (x) */
+ Rx [rnz++] = cs_house (Vx+p1, Beta+k, vnz-p1) ; /* [v,beta]=house(x) */
+ }
+ Rp [n] = rnz ; /* finalize R */
+ Vp [n] = vnz ; /* finalize V */
+ return (cs_ndone (N, NULL, w, x, 1)) ; /* success */
+}
diff --git a/CXSparse/Source/cs_qrsol.c b/CXSparse/Source/cs_qrsol.c
new file mode 100644
index 0000000..b759178
--- /dev/null
+++ b/CXSparse/Source/cs_qrsol.c
@@ -0,0 +1,53 @@
+#include "cs.h"
+/* x=A\b where A can be rectangular; b overwritten with solution */
+CS_INT cs_qrsol (CS_INT order, const cs *A, CS_ENTRY *b)
+{
+ CS_ENTRY *x ;
+ css *S ;
+ csn *N ;
+ cs *AT = NULL ;
+ CS_INT k, m, n, ok ;
+ if (!CS_CSC (A) || !b) return (0) ; /* check inputs */
+ n = A->n ;
+ m = A->m ;
+ if (m >= n)
+ {
+ S = cs_sqr (order, A, 1) ; /* ordering and symbolic analysis */
+ N = cs_qr (A, S) ; /* numeric QR factorization */
+ x = cs_calloc (S ? S->m2 : 1, sizeof (CS_ENTRY)) ; /* get workspace */
+ ok = (S && N && x) ;
+ if (ok)
+ {
+ cs_ipvec (S->pinv, b, x, m) ; /* x(0:m-1) = b(p(0:m-1) */
+ for (k = 0 ; k < n ; k++) /* apply Householder refl. to x */
+ {
+ cs_happly (N->L, k, N->B [k], x) ;
+ }
+ cs_usolve (N->U, x) ; /* x = R\x */
+ cs_ipvec (S->q, x, b, n) ; /* b(q(0:n-1)) = x(0:n-1) */
+ }
+ }
+ else
+ {
+ AT = cs_transpose (A, 1) ; /* Ax=b is underdetermined */
+ S = cs_sqr (order, AT, 1) ; /* ordering and symbolic analysis */
+ N = cs_qr (AT, S) ; /* numeric QR factorization of A' */
+ x = cs_calloc (S ? S->m2 : 1, sizeof (CS_ENTRY)) ; /* get workspace */
+ ok = (AT && S && N && x) ;
+ if (ok)
+ {
+ cs_pvec (S->q, b, x, m) ; /* x(q(0:m-1)) = b(0:m-1) */
+ cs_utsolve (N->U, x) ; /* x = R'\x */
+ for (k = m-1 ; k >= 0 ; k--) /* apply Householder refl. to x */
+ {
+ cs_happly (N->L, k, N->B [k], x) ;
+ }
+ cs_pvec (S->pinv, x, b, n) ; /* b(0:n-1) = x(p(0:n-1)) */
+ }
+ }
+ cs_free (x) ;
+ cs_sfree (S) ;
+ cs_nfree (N) ;
+ cs_spfree (AT) ;
+ return (ok) ;
+}
diff --git a/CXSparse/Source/cs_randperm.c b/CXSparse/Source/cs_randperm.c
new file mode 100644
index 0000000..fe5110a
--- /dev/null
+++ b/CXSparse/Source/cs_randperm.c
@@ -0,0 +1,22 @@
+#include "cs.h"
+/* return a random permutation vector, the identity perm, or p = n-1:-1:0.
+ * seed = -1 means p = n-1:-1:0. seed = 0 means p = identity. otherwise
+ * p = random permutation. */
+CS_INT *cs_randperm (CS_INT n, CS_INT seed)
+{
+ CS_INT *p, k, j, t ;
+ if (seed == 0) return (NULL) ; /* return p = NULL (identity) */
+ p = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */
+ if (!p) return (NULL) ; /* out of memory */
+ for (k = 0 ; k < n ; k++) p [k] = n-k-1 ;
+ if (seed == -1) return (p) ; /* return reverse permutation */
+ srand (seed) ; /* get new random number seed */
+ for (k = 0 ; k < n ; k++)
+ {
+ j = k + (rand ( ) % (n-k)) ; /* j = rand CS_INT in range k to n-1 */
+ t = p [j] ; /* swap p[k] and p[j] */
+ p [j] = p [k] ;
+ p [k] = t ;
+ }
+ return (p) ;
+}
diff --git a/CXSparse/Source/cs_reach.c b/CXSparse/Source/cs_reach.c
new file mode 100644
index 0000000..d6c7f21
--- /dev/null
+++ b/CXSparse/Source/cs_reach.c
@@ -0,0 +1,19 @@
+#include "cs.h"
+/* xi [top...n-1] = nodes reachable from graph of G*P' via nodes in B(:,k).
+ * xi [n...2n-1] used as workspace */
+CS_INT cs_reach (cs *G, const cs *B, CS_INT k, CS_INT *xi, const CS_INT *pinv)
+{
+ CS_INT p, n, top, *Bp, *Bi, *Gp ;
+ if (!CS_CSC (G) || !CS_CSC (B) || !xi) return (-1) ; /* check inputs */
+ n = G->n ; Bp = B->p ; Bi = B->i ; Gp = G->p ;
+ top = n ;
+ for (p = Bp [k] ; p < Bp [k+1] ; p++)
+ {
+ if (!CS_MARKED (Gp, Bi [p])) /* start a dfs at unmarked node i */
+ {
+ top = cs_dfs (Bi [p], G, top, xi, xi+n, pinv) ;
+ }
+ }
+ for (p = top ; p < n ; p++) CS_MARK (Gp, xi [p]) ; /* restore G */
+ return (top) ;
+}
diff --git a/CXSparse/Source/cs_scatter.c b/CXSparse/Source/cs_scatter.c
new file mode 100644
index 0000000..fd499f3
--- /dev/null
+++ b/CXSparse/Source/cs_scatter.c
@@ -0,0 +1,22 @@
+#include "cs.h"
+/* x = x + beta * A(:,j), where x is a dense vector and A(:,j) is sparse */
+CS_INT cs_scatter (const cs *A, CS_INT j, CS_ENTRY beta, CS_INT *w, CS_ENTRY *x, CS_INT mark,
+ cs *C, CS_INT nz)
+{
+ CS_INT i, p, *Ap, *Ai, *Ci ;
+ CS_ENTRY *Ax ;
+ if (!CS_CSC (A) || !w || !CS_CSC (C)) return (-1) ; /* check inputs */
+ Ap = A->p ; Ai = A->i ; Ax = A->x ; Ci = C->i ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ; /* A(i,j) is nonzero */
+ if (w [i] < mark)
+ {
+ w [i] = mark ; /* i is new entry in column j */
+ Ci [nz++] = i ; /* add i to pattern of C(:,j) */
+ if (x) x [i] = beta * Ax [p] ; /* x(i) = beta*A(i,j) */
+ }
+ else if (x) x [i] += beta * Ax [p] ; /* i exists in C(:,j) already */
+ }
+ return (nz) ;
+}
diff --git a/CXSparse/Source/cs_scc.c b/CXSparse/Source/cs_scc.c
new file mode 100644
index 0000000..c090736
--- /dev/null
+++ b/CXSparse/Source/cs_scc.c
@@ -0,0 +1,41 @@
+#include "cs.h"
+/* find the strongly connected components of a square matrix */
+csd *cs_scc (cs *A) /* matrix A temporarily modified, then restored */
+{
+ CS_INT n, i, k, b, nb = 0, top, *xi, *pstack, *p, *r, *Ap, *ATp, *rcopy, *Blk ;
+ cs *AT ;
+ csd *D ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ n = A->n ; Ap = A->p ;
+ D = cs_dalloc (n, 0) ; /* allocate result */
+ AT = cs_transpose (A, 0) ; /* AT = A' */
+ xi = cs_malloc (2*n+1, sizeof (CS_INT)) ; /* get workspace */
+ if (!D || !AT || !xi) return (cs_ddone (D, AT, xi, 0)) ;
+ Blk = xi ; rcopy = pstack = xi + n ;
+ p = D->p ; r = D->r ; ATp = AT->p ;
+ top = n ;
+ for (i = 0 ; i < n ; i++) /* first dfs(A) to find finish times (xi) */
+ {
+ if (!CS_MARKED (Ap, i)) top = cs_dfs (i, A, top, xi, pstack, NULL) ;
+ }
+ for (i = 0 ; i < n ; i++) CS_MARK (Ap, i) ; /* restore A; unmark all nodes*/
+ top = n ;
+ nb = n ;
+ for (k = 0 ; k < n ; k++) /* dfs(A') to find strongly connnected comp */
+ {
+ i = xi [k] ; /* get i in reverse order of finish times */
+ if (CS_MARKED (ATp, i)) continue ; /* skip node i if already ordered */
+ r [nb--] = top ; /* node i is the start of a component in p */
+ top = cs_dfs (i, AT, top, p, pstack, NULL) ;
+ }
+ r [nb] = 0 ; /* first block starts at zero; shift r up */
+ for (k = nb ; k <= n ; k++) r [k-nb] = r [k] ;
+ D->nb = nb = n-nb ; /* nb = # of strongly connected components */
+ for (b = 0 ; b < nb ; b++) /* sort each block in natural order */
+ {
+ for (k = r [b] ; k < r [b+1] ; k++) Blk [p [k]] = b ;
+ }
+ for (b = 0 ; b <= nb ; b++) rcopy [b] = r [b] ;
+ for (i = 0 ; i < n ; i++) p [rcopy [Blk [i]]++] = i ;
+ return (cs_ddone (D, AT, xi, 1)) ;
+}
diff --git a/CXSparse/Source/cs_schol.c b/CXSparse/Source/cs_schol.c
new file mode 100644
index 0000000..4179b8f
--- /dev/null
+++ b/CXSparse/Source/cs_schol.c
@@ -0,0 +1,26 @@
+#include "cs.h"
+/* ordering and symbolic analysis for a Cholesky factorization */
+css *cs_schol (CS_INT order, const cs *A)
+{
+ CS_INT n, *c, *post, *P ;
+ cs *C ;
+ css *S ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ n = A->n ;
+ S = cs_calloc (1, sizeof (css)) ; /* allocate result S */
+ if (!S) return (NULL) ; /* out of memory */
+ P = cs_amd (order, A) ; /* P = amd(A+A'), or natural */
+ S->pinv = cs_pinv (P, n) ; /* find inverse permutation */
+ cs_free (P) ;
+ if (order && !S->pinv) return (cs_sfree (S)) ;
+ C = cs_symperm (A, S->pinv, 0) ; /* C = spones(triu(A(P,P))) */
+ S->parent = cs_etree (C, 0) ; /* find etree of C */
+ post = cs_post (S->parent, n) ; /* postorder the etree */
+ c = cs_counts (C, S->parent, post, 0) ; /* find column counts of chol(C) */
+ cs_free (post) ;
+ cs_spfree (C) ;
+ S->cp = cs_malloc (n+1, sizeof (CS_INT)) ; /* allocate result S->cp */
+ S->unz = S->lnz = cs_cumsum (S->cp, c, n) ; /* find column pointers for L */
+ cs_free (c) ;
+ return ((S->lnz >= 0) ? S : cs_sfree (S)) ;
+}
diff --git a/CXSparse/Source/cs_spsolve.c b/CXSparse/Source/cs_spsolve.c
new file mode 100644
index 0000000..91594cb
--- /dev/null
+++ b/CXSparse/Source/cs_spsolve.c
@@ -0,0 +1,28 @@
+#include "cs.h"
+/* solve Gx=b(:,k), where G is either upper (lo=0) or lower (lo=1) triangular */
+CS_INT cs_spsolve (cs *G, const cs *B, CS_INT k, CS_INT *xi, CS_ENTRY *x, const CS_INT *pinv,
+ CS_INT lo)
+{
+ CS_INT j, J, p, q, px, top, n, *Gp, *Gi, *Bp, *Bi ;
+ CS_ENTRY *Gx, *Bx ;
+ if (!CS_CSC (G) || !CS_CSC (B) || !xi || !x) return (-1) ;
+ Gp = G->p ; Gi = G->i ; Gx = G->x ; n = G->n ;
+ Bp = B->p ; Bi = B->i ; Bx = B->x ;
+ top = cs_reach (G, B, k, xi, pinv) ; /* xi[top..n-1]=Reach(B(:,k)) */
+ for (p = top ; p < n ; p++) x [xi [p]] = 0 ; /* clear x */
+ for (p = Bp [k] ; p < Bp [k+1] ; p++) x [Bi [p]] = Bx [p] ; /* scatter B */
+ for (px = top ; px < n ; px++)
+ {
+ j = xi [px] ; /* x(j) is nonzero */
+ J = pinv ? (pinv [j]) : j ; /* j maps to col J of G */
+ if (J < 0) continue ; /* column J is empty */
+ x [j] /= Gx [lo ? (Gp [J]) : (Gp [J+1]-1)] ;/* x(j) /= G(j,j) */
+ p = lo ? (Gp [J]+1) : (Gp [J]) ; /* lo: L(j,j) 1st entry */
+ q = lo ? (Gp [J+1]) : (Gp [J+1]-1) ; /* up: U(j,j) last entry */
+ for ( ; p < q ; p++)
+ {
+ x [Gi [p]] -= Gx [p] * x [j] ; /* x(i) -= G(i,j) * x(j) */
+ }
+ }
+ return (top) ; /* return top of stack */
+}
diff --git a/CXSparse/Source/cs_sqr.c b/CXSparse/Source/cs_sqr.c
new file mode 100644
index 0000000..f0bfb08
--- /dev/null
+++ b/CXSparse/Source/cs_sqr.c
@@ -0,0 +1,88 @@
+#include "cs.h"
+/* compute nnz(V) = S->lnz, S->pinv, S->leftmost, S->m2 from A and S->parent */
+static CS_INT cs_vcount (const cs *A, css *S)
+{
+ CS_INT i, k, p, pa, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i, *next, *head,
+ *tail, *nque, *pinv, *leftmost, *w, *parent = S->parent ;
+ S->pinv = pinv = cs_malloc (m+n, sizeof (CS_INT)) ; /* allocate pinv, */
+ S->leftmost = leftmost = cs_malloc (m, sizeof (CS_INT)) ; /* and leftmost */
+ w = cs_malloc (m+3*n, sizeof (CS_INT)) ; /* get workspace */
+ if (!pinv || !w || !leftmost)
+ {
+ cs_free (w) ; /* pinv and leftmost freed later */
+ return (0) ; /* out of memory */
+ }
+ next = w ; head = w + m ; tail = w + m + n ; nque = w + m + 2*n ;
+ for (k = 0 ; k < n ; k++) head [k] = -1 ; /* queue k is empty */
+ for (k = 0 ; k < n ; k++) tail [k] = -1 ;
+ for (k = 0 ; k < n ; k++) nque [k] = 0 ;
+ for (i = 0 ; i < m ; i++) leftmost [i] = -1 ;
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ for (p = Ap [k] ; p < Ap [k+1] ; p++)
+ {
+ leftmost [Ai [p]] = k ; /* leftmost[i] = min(find(A(i,:)))*/
+ }
+ }
+ for (i = m-1 ; i >= 0 ; i--) /* scan rows in reverse order */
+ {
+ pinv [i] = -1 ; /* row i is not yet ordered */
+ k = leftmost [i] ;
+ if (k == -1) continue ; /* row i is empty */
+ if (nque [k]++ == 0) tail [k] = i ; /* first row in queue k */
+ next [i] = head [k] ; /* put i at head of queue k */
+ head [k] = i ;
+ }
+ S->lnz = 0 ;
+ S->m2 = m ;
+ for (k = 0 ; k < n ; k++) /* find row permutation and nnz(V)*/
+ {
+ i = head [k] ; /* remove row i from queue k */
+ S->lnz++ ; /* count V(k,k) as nonzero */
+ if (i < 0) i = S->m2++ ; /* add a fictitious row */
+ pinv [i] = k ; /* associate row i with V(:,k) */
+ if (--nque [k] <= 0) continue ; /* skip if V(k+1:m,k) is empty */
+ S->lnz += nque [k] ; /* nque [k] is nnz (V(k+1:m,k)) */
+ if ((pa = parent [k]) != -1) /* move all rows to parent of k */
+ {
+ if (nque [pa] == 0) tail [pa] = tail [k] ;
+ next [tail [k]] = head [pa] ;
+ head [pa] = next [i] ;
+ nque [pa] += nque [k] ;
+ }
+ }
+ for (i = 0 ; i < m ; i++) if (pinv [i] < 0) pinv [i] = k++ ;
+ cs_free (w) ;
+ return (1) ;
+}
+
+/* symbolic ordering and analysis for QR or LU */
+css *cs_sqr (CS_INT order, const cs *A, CS_INT qr)
+{
+ CS_INT n, k, ok = 1, *post ;
+ css *S ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ n = A->n ;
+ S = cs_calloc (1, sizeof (css)) ; /* allocate result S */
+ if (!S) return (NULL) ; /* out of memory */
+ S->q = cs_amd (order, A) ; /* fill-reducing ordering */
+ if (order && !S->q) return (cs_sfree (S)) ;
+ if (qr) /* QR symbolic analysis */
+ {
+ cs *C = order ? cs_permute (A, NULL, S->q, 0) : ((cs *) A) ;
+ S->parent = cs_etree (C, 1) ; /* etree of C'*C, where C=A(:,q) */
+ post = cs_post (S->parent, n) ;
+ S->cp = cs_counts (C, S->parent, post, 1) ; /* col counts chol(C'*C) */
+ cs_free (post) ;
+ ok = C && S->parent && S->cp && cs_vcount (C, S) ;
+ if (ok) for (S->unz = 0, k = 0 ; k < n ; k++) S->unz += S->cp [k] ;
+ ok = ok && S->lnz >= 0 && S->unz >= 0 ; /* CS_INT overflow guard */
+ if (order) cs_spfree (C) ;
+ }
+ else
+ {
+ S->unz = 4*(A->p [n]) + n ; /* for LU factorization only, */
+ S->lnz = S->unz ; /* guess nnz(L) and nnz(U) */
+ }
+ return (ok ? S : cs_sfree (S)) ; /* return result S */
+}
diff --git a/CXSparse/Source/cs_symperm.c b/CXSparse/Source/cs_symperm.c
new file mode 100644
index 0000000..79fa121
--- /dev/null
+++ b/CXSparse/Source/cs_symperm.c
@@ -0,0 +1,39 @@
+#include "cs.h"
+/* C = A(p,p) where A and C are symmetric the upper part stored; pinv not p */
+cs *cs_symperm (const cs *A, const CS_INT *pinv, CS_INT values)
+{
+ CS_INT i, j, p, q, i2, j2, n, *Ap, *Ai, *Cp, *Ci, *w ;
+ CS_ENTRY *Cx, *Ax ;
+ cs *C ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ C = cs_spalloc (n, n, Ap [n], values && (Ax != NULL), 0) ; /* alloc result*/
+ w = cs_calloc (n, sizeof (CS_INT)) ; /* get workspace */
+ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ for (j = 0 ; j < n ; j++) /* count entries in each column of C */
+ {
+ j2 = pinv ? pinv [j] : j ; /* column j of A is column j2 of C */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ if (i > j) continue ; /* skip lower triangular part of A */
+ i2 = pinv ? pinv [i] : i ; /* row i of A is row i2 of C */
+ w [CS_MAX (i2, j2)]++ ; /* column count of C */
+ }
+ }
+ cs_cumsum (Cp, w, n) ; /* compute column pointers of C */
+ for (j = 0 ; j < n ; j++)
+ {
+ j2 = pinv ? pinv [j] : j ; /* column j of A is column j2 of C */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ if (i > j) continue ; /* skip lower triangular part of A*/
+ i2 = pinv ? pinv [i] : i ; /* row i of A is row i2 of C */
+ Ci [q = w [CS_MAX (i2, j2)]++] = CS_MIN (i2, j2) ;
+ if (Cx) Cx [q] = (i2 <= j2) ? Ax [p] : CS_CONJ (Ax [p]) ;
+ }
+ }
+ return (cs_done (C, w, NULL, 1)) ; /* success; free workspace, return C */
+}
diff --git a/CXSparse/Source/cs_tdfs.c b/CXSparse/Source/cs_tdfs.c
new file mode 100644
index 0000000..3d48e6e
--- /dev/null
+++ b/CXSparse/Source/cs_tdfs.c
@@ -0,0 +1,24 @@
+#include "cs.h"
+/* depth-first search and postorder of a tree rooted at node j */
+CS_INT cs_tdfs (CS_INT j, CS_INT k, CS_INT *head, const CS_INT *next, CS_INT *post, CS_INT *stack)
+{
+ CS_INT i, p, top = 0 ;
+ if (!head || !next || !post || !stack) return (-1) ; /* check inputs */
+ stack [0] = j ; /* place j on the stack */
+ while (top >= 0) /* while (stack is not empty) */
+ {
+ p = stack [top] ; /* p = top of stack */
+ i = head [p] ; /* i = youngest child of p */
+ if (i == -1)
+ {
+ top-- ; /* p has no unordered children left */
+ post [k++] = p ; /* node p is the kth postordered node */
+ }
+ else
+ {
+ head [p] = next [i] ; /* remove i from children of p */
+ stack [++top] = i ; /* start dfs on child node i */
+ }
+ }
+ return (k) ;
+}
diff --git a/CXSparse/Source/cs_transpose.c b/CXSparse/Source/cs_transpose.c
new file mode 100644
index 0000000..0f10c12
--- /dev/null
+++ b/CXSparse/Source/cs_transpose.c
@@ -0,0 +1,25 @@
+#include "cs.h"
+/* C = A' */
+cs *cs_transpose (const cs *A, CS_INT values)
+{
+ CS_INT p, q, j, *Cp, *Ci, n, m, *Ap, *Ai, *w ;
+ CS_ENTRY *Cx, *Ax ;
+ cs *C ;
+ if (!CS_CSC (A)) return (NULL) ; /* check inputs */
+ m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ C = cs_spalloc (n, m, Ap [n], values && Ax, 0) ; /* allocate result */
+ w = cs_calloc (m, sizeof (CS_INT)) ; /* get workspace */
+ if (!C || !w) return (cs_done (C, w, NULL, 0)) ; /* out of memory */
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ for (p = 0 ; p < Ap [n] ; p++) w [Ai [p]]++ ; /* row counts */
+ cs_cumsum (Cp, w, m) ; /* row pointers */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ Ci [q = w [Ai [p]]++] = j ; /* place A(i,j) as entry C(j,i) */
+ if (Cx) Cx [q] = (values > 0) ? CS_CONJ (Ax [p]) : Ax [p] ;
+ }
+ }
+ return (cs_done (C, w, NULL, 1)) ; /* success; free w and return C */
+}
diff --git a/CXSparse/Source/cs_updown.c b/CXSparse/Source/cs_updown.c
new file mode 100644
index 0000000..1584dff
--- /dev/null
+++ b/CXSparse/Source/cs_updown.c
@@ -0,0 +1,48 @@
+#include "cs.h"
+/* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */
+CS_INT cs_updown (cs *L, CS_INT sigma, const cs *C, const CS_INT *parent)
+{
+ CS_INT n, p, f, j, *Lp, *Li, *Cp, *Ci ;
+ CS_ENTRY *Lx, *Cx, alpha, gamma, w1, w2, *w ;
+ double beta = 1, beta2 = 1, delta ;
+#ifdef CS_COMPLEX
+ cs_complex_t phase ;
+#endif
+ if (!CS_CSC (L) || !CS_CSC (C) || !parent) return (0) ; /* check inputs */
+ Lp = L->p ; Li = L->i ; Lx = L->x ; n = L->n ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ if ((p = Cp [0]) >= Cp [1]) return (1) ; /* return if C empty */
+ w = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get workspace */
+ if (!w) return (0) ; /* out of memory */
+ f = Ci [p] ;
+ for ( ; p < Cp [1] ; p++) f = CS_MIN (f, Ci [p]) ; /* f = min (find (C)) */
+ for (j = f ; j != -1 ; j = parent [j]) w [j] = 0 ; /* clear workspace w */
+ for (p = Cp [0] ; p < Cp [1] ; p++) w [Ci [p]] = Cx [p] ; /* w = C */
+ for (j = f ; j != -1 ; j = parent [j]) /* walk path f up to root */
+ {
+ p = Lp [j] ;
+ alpha = w [j] / Lx [p] ; /* alpha = w(j) / L(j,j) */
+ beta2 = beta*beta + sigma*alpha*CS_CONJ(alpha) ;
+ if (beta2 <= 0) break ; /* not positive definite */
+ beta2 = sqrt (beta2) ;
+ delta = (sigma > 0) ? (beta / beta2) : (beta2 / beta) ;
+ gamma = sigma * CS_CONJ(alpha) / (beta2 * beta) ;
+ Lx [p] = delta * Lx [p] + ((sigma > 0) ? (gamma * w [j]) : 0) ;
+ beta = beta2 ;
+#ifdef CS_COMPLEX
+ phase = CS_ABS (Lx [p]) / Lx [p] ; /* phase = abs(L(j,j))/L(j,j)*/
+ Lx [p] *= phase ; /* L(j,j) = L(j,j) * phase */
+#endif
+ for (p++ ; p < Lp [j+1] ; p++)
+ {
+ w1 = w [Li [p]] ;
+ w [Li [p]] = w2 = w1 - alpha * Lx [p] ;
+ Lx [p] = delta * Lx [p] + gamma * ((sigma > 0) ? w1 : w2) ;
+#ifdef CS_COMPLEX
+ Lx [p] *= phase ; /* L(i,j) = L(i,j) * phase */
+#endif
+ }
+ }
+ cs_free (w) ;
+ return (beta2 > 0) ;
+}
diff --git a/CXSparse/Source/cs_usolve.c b/CXSparse/Source/cs_usolve.c
new file mode 100644
index 0000000..58bc3a8
--- /dev/null
+++ b/CXSparse/Source/cs_usolve.c
@@ -0,0 +1,18 @@
+#include "cs.h"
+/* solve Ux=b where x and b are dense. x=b on input, solution on output. */
+CS_INT cs_usolve (const cs *U, CS_ENTRY *x)
+{
+ CS_INT p, j, n, *Up, *Ui ;
+ CS_ENTRY *Ux ;
+ if (!CS_CSC (U) || !x) return (0) ; /* check inputs */
+ n = U->n ; Up = U->p ; Ui = U->i ; Ux = U->x ;
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ x [j] /= Ux [Up [j+1]-1] ;
+ for (p = Up [j] ; p < Up [j+1]-1 ; p++)
+ {
+ x [Ui [p]] -= Ux [p] * x [j] ;
+ }
+ }
+ return (1) ;
+}
diff --git a/CXSparse/Source/cs_util.c b/CXSparse/Source/cs_util.c
new file mode 100644
index 0000000..800b7dc
--- /dev/null
+++ b/CXSparse/Source/cs_util.c
@@ -0,0 +1,119 @@
+#include "cs.h"
+/* allocate a sparse matrix (triplet form or compressed-column form) */
+cs *cs_spalloc (CS_INT m, CS_INT n, CS_INT nzmax, CS_INT values, CS_INT triplet)
+{
+ cs *A = cs_calloc (1, sizeof (cs)) ; /* allocate the cs struct */
+ if (!A) return (NULL) ; /* out of memory */
+ A->m = m ; /* define dimensions and nzmax */
+ A->n = n ;
+ A->nzmax = nzmax = CS_MAX (nzmax, 1) ;
+ A->nz = triplet ? 0 : -1 ; /* allocate triplet or comp.col */
+ A->p = cs_malloc (triplet ? nzmax : n+1, sizeof (CS_INT)) ;
+ A->i = cs_malloc (nzmax, sizeof (CS_INT)) ;
+ A->x = values ? cs_malloc (nzmax, sizeof (CS_ENTRY)) : NULL ;
+ return ((!A->p || !A->i || (values && !A->x)) ? cs_spfree (A) : A) ;
+}
+
+/* change the max # of entries sparse matrix */
+CS_INT cs_sprealloc (cs *A, CS_INT nzmax)
+{
+ CS_INT ok, oki, okj = 1, okx = 1 ;
+ if (!A) return (0) ;
+ if (nzmax <= 0) nzmax = (CS_CSC (A)) ? (A->p [A->n]) : A->nz ;
+ A->i = cs_realloc (A->i, nzmax, sizeof (CS_INT), &oki) ;
+ if (CS_TRIPLET (A)) A->p = cs_realloc (A->p, nzmax, sizeof (CS_INT), &okj) ;
+ if (A->x) A->x = cs_realloc (A->x, nzmax, sizeof (CS_ENTRY), &okx) ;
+ ok = (oki && okj && okx) ;
+ if (ok) A->nzmax = nzmax ;
+ return (ok) ;
+}
+
+/* free a sparse matrix */
+cs *cs_spfree (cs *A)
+{
+ if (!A) return (NULL) ; /* do nothing if A already NULL */
+ cs_free (A->p) ;
+ cs_free (A->i) ;
+ cs_free (A->x) ;
+ return (cs_free (A)) ; /* free the cs struct and return NULL */
+}
+
+/* free a numeric factorization */
+csn *cs_nfree (csn *N)
+{
+ if (!N) return (NULL) ; /* do nothing if N already NULL */
+ cs_spfree (N->L) ;
+ cs_spfree (N->U) ;
+ cs_free (N->pinv) ;
+ cs_free (N->B) ;
+ return (cs_free (N)) ; /* free the csn struct and return NULL */
+}
+
+/* free a symbolic factorization */
+css *cs_sfree (css *S)
+{
+ if (!S) return (NULL) ; /* do nothing if S already NULL */
+ cs_free (S->pinv) ;
+ cs_free (S->q) ;
+ cs_free (S->parent) ;
+ cs_free (S->cp) ;
+ cs_free (S->leftmost) ;
+ return (cs_free (S)) ; /* free the css struct and return NULL */
+}
+
+/* allocate a cs_dmperm or cs_scc result */
+csd *cs_dalloc (CS_INT m, CS_INT n)
+{
+ csd *D ;
+ D = cs_calloc (1, sizeof (csd)) ;
+ if (!D) return (NULL) ;
+ D->p = cs_malloc (m, sizeof (CS_INT)) ;
+ D->r = cs_malloc (m+6, sizeof (CS_INT)) ;
+ D->q = cs_malloc (n, sizeof (CS_INT)) ;
+ D->s = cs_malloc (n+6, sizeof (CS_INT)) ;
+ return ((!D->p || !D->r || !D->q || !D->s) ? cs_dfree (D) : D) ;
+}
+
+/* free a cs_dmperm or cs_scc result */
+csd *cs_dfree (csd *D)
+{
+ if (!D) return (NULL) ; /* do nothing if D already NULL */
+ cs_free (D->p) ;
+ cs_free (D->q) ;
+ cs_free (D->r) ;
+ cs_free (D->s) ;
+ return (cs_free (D)) ;
+}
+
+/* free workspace and return a sparse matrix result */
+cs *cs_done (cs *C, void *w, void *x, CS_INT ok)
+{
+ cs_free (w) ; /* free workspace */
+ cs_free (x) ;
+ return (ok ? C : cs_spfree (C)) ; /* return result if OK, else free it */
+}
+
+/* free workspace and return CS_INT array result */
+CS_INT *cs_idone (CS_INT *p, cs *C, void *w, CS_INT ok)
+{
+ cs_spfree (C) ; /* free temporary matrix */
+ cs_free (w) ; /* free workspace */
+ return (ok ? p : cs_free (p)) ; /* return result if OK, else free it */
+}
+
+/* free workspace and return a numeric factorization (Cholesky, LU, or QR) */
+csn *cs_ndone (csn *N, cs *C, void *w, void *x, CS_INT ok)
+{
+ cs_spfree (C) ; /* free temporary matrix */
+ cs_free (w) ; /* free workspace */
+ cs_free (x) ;
+ return (ok ? N : cs_nfree (N)) ; /* return result if OK, else free it */
+}
+
+/* free workspace and return a csd result */
+csd *cs_ddone (csd *D, cs *C, void *w, CS_INT ok)
+{
+ cs_spfree (C) ; /* free temporary matrix */
+ cs_free (w) ; /* free workspace */
+ return (ok ? D : cs_dfree (D)) ; /* return result if OK, else free it */
+}
diff --git a/CXSparse/Source/cs_utsolve.c b/CXSparse/Source/cs_utsolve.c
new file mode 100644
index 0000000..bcfc3f1
--- /dev/null
+++ b/CXSparse/Source/cs_utsolve.c
@@ -0,0 +1,18 @@
+#include "cs.h"
+/* solve U'x=b where x and b are dense. x=b on input, solution on output. */
+CS_INT cs_utsolve (const cs *U, CS_ENTRY *x)
+{
+ CS_INT p, j, n, *Up, *Ui ;
+ CS_ENTRY *Ux ;
+ if (!CS_CSC (U) || !x) return (0) ; /* check inputs */
+ n = U->n ; Up = U->p ; Ui = U->i ; Ux = U->x ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Up [j] ; p < Up [j+1]-1 ; p++)
+ {
+ x [j] -= CS_CONJ (Ux [p]) * x [Ui [p]] ;
+ }
+ x [j] /= CS_CONJ (Ux [Up [j+1]-1]) ;
+ }
+ return (1) ;
+}
diff --git a/CXSparse/Tcov/Makefile b/CXSparse/Tcov/Makefile
new file mode 100644
index 0000000..04609af
--- /dev/null
+++ b/CXSparse/Tcov/Makefile
@@ -0,0 +1,318 @@
+
+# To run with valgrind:
+V =
+# V = valgrind -q
+
+# Linux test coverage
+CC = gcc
+CFLAGS = -O -g -fprofile-arcs -ftest-coverage \
+ -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \
+ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi \
+ -Wno-unused-parameter -Werror -I../Include -I../Demo -I../../UFconfig
+
+run: all run_convert run_di run_dl run_ci run_cl
+ ./covall
+
+all: cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di \
+ cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl \
+ cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci \
+ cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl \
+ cs_idemo cs_ldemo
+
+CS_DI = cs_add_di.o cs_amd_di.o cs_chol_di.o cs_cholsol_di.o cs_counts_di.o \
+ cs_cumsum_di.o cs_droptol_di.o cs_dropzeros_di.o cs_dupl_di.o \
+ cs_entry_di.o cs_etree_di.o cs_fkeep_di.o cs_gaxpy_di.o cs_happly_di.o \
+ cs_house_di.o cs_ipvec_di.o cs_lsolve_di.o cs_ltsolve_di.o cs_lu_di.o \
+ cs_lusol_di.o cs_util_di.o cs_multiply_di.o cs_permute_di.o \
+ cs_pinv_di.o cs_post_di.o cs_pvec_di.o cs_qr_di.o cs_qrsol_di.o \
+ cs_scatter_di.o cs_schol_di.o cs_sqr_di.o cs_symperm_di.o cs_tdfs_di.o \
+ cs_transpose_di.o cs_compress_di.o cs_usolve_di.o cs_scc_di.o \
+ cs_maxtrans_di.o cs_dmperm_di.o cs_updown_di.o cs_print_di.o \
+ cs_norm_di.o cs_load_di.o cs_dfs_di.o cstcov_malloc_test_di.o \
+ cs_utsolve_di.o cs_reach_di.o cs_spsolve_di.o \
+ cs_leaf_di.o cs_ereach_di.o cs_randperm_di.o
+
+CS_DL = cs_add_dl.o cs_amd_dl.o cs_chol_dl.o cs_cholsol_dl.o cs_counts_dl.o \
+ cs_cumsum_dl.o cs_droptol_dl.o cs_dropzeros_dl.o cs_dupl_dl.o \
+ cs_entry_dl.o cs_etree_dl.o cs_fkeep_dl.o cs_gaxpy_dl.o cs_happly_dl.o \
+ cs_house_dl.o cs_ipvec_dl.o cs_lsolve_dl.o cs_ltsolve_dl.o cs_lu_dl.o \
+ cs_lusol_dl.o cs_util_dl.o cs_multiply_dl.o cs_permute_dl.o \
+ cs_pinv_dl.o cs_post_dl.o cs_pvec_dl.o cs_qr_dl.o cs_qrsol_dl.o \
+ cs_scatter_dl.o cs_schol_dl.o cs_sqr_dl.o cs_symperm_dl.o cs_tdfs_dl.o \
+ cs_transpose_dl.o cs_compress_dl.o cs_usolve_dl.o cs_scc_dl.o \
+ cs_maxtrans_dl.o cs_dmperm_dl.o cs_updown_dl.o cs_print_dl.o \
+ cs_norm_dl.o cs_load_dl.o cs_dfs_dl.o cstcov_malloc_test_dl.o \
+ cs_utsolve_dl.o cs_reach_dl.o cs_spsolve_dl.o \
+ cs_leaf_dl.o cs_ereach_dl.o cs_randperm_dl.o
+
+CS_CI = cs_add_ci.o cs_amd_ci.o cs_chol_ci.o cs_cholsol_ci.o cs_counts_ci.o \
+ cs_cumsum_ci.o cs_droptol_ci.o cs_dropzeros_ci.o cs_dupl_ci.o \
+ cs_entry_ci.o cs_etree_ci.o cs_fkeep_ci.o cs_gaxpy_ci.o cs_happly_ci.o \
+ cs_house_ci.o cs_ipvec_ci.o cs_lsolve_ci.o cs_ltsolve_ci.o cs_lu_ci.o \
+ cs_lusol_ci.o cs_util_ci.o cs_multiply_ci.o cs_permute_ci.o \
+ cs_pinv_ci.o cs_post_ci.o cs_pvec_ci.o cs_qr_ci.o cs_qrsol_ci.o \
+ cs_scatter_ci.o cs_schol_ci.o cs_sqr_ci.o cs_symperm_ci.o cs_tdfs_ci.o \
+ cs_transpose_ci.o cs_compress_ci.o cs_usolve_ci.o cs_scc_ci.o \
+ cs_maxtrans_ci.o cs_dmperm_ci.o cs_updown_ci.o cs_print_ci.o \
+ cs_norm_ci.o cs_load_ci.o cs_dfs_ci.o cstcov_malloc_test_ci.o \
+ cs_utsolve_ci.o cs_reach_ci.o cs_spsolve_ci.o \
+ cs_leaf_ci.o cs_ereach_ci.o cs_randperm_ci.o
+
+CS_CL = cs_add_cl.o cs_amd_cl.o cs_chol_cl.o cs_cholsol_cl.o cs_counts_cl.o \
+ cs_cumsum_cl.o cs_droptol_cl.o cs_dropzeros_cl.o cs_dupl_cl.o \
+ cs_entry_cl.o cs_etree_cl.o cs_fkeep_cl.o cs_gaxpy_cl.o cs_happly_cl.o \
+ cs_house_cl.o cs_ipvec_cl.o cs_lsolve_cl.o cs_ltsolve_cl.o cs_lu_cl.o \
+ cs_lusol_cl.o cs_util_cl.o cs_multiply_cl.o cs_permute_cl.o \
+ cs_pinv_cl.o cs_post_cl.o cs_pvec_cl.o cs_qr_cl.o cs_qrsol_cl.o \
+ cs_scatter_cl.o cs_schol_cl.o cs_sqr_cl.o cs_symperm_cl.o cs_tdfs_cl.o \
+ cs_transpose_cl.o cs_compress_cl.o cs_usolve_cl.o cs_scc_cl.o \
+ cs_maxtrans_cl.o cs_dmperm_cl.o cs_updown_cl.o cs_print_cl.o \
+ cs_norm_cl.o cs_load_cl.o cs_dfs_cl.o cstcov_malloc_test_cl.o \
+ cs_utsolve_cl.o cs_reach_cl.o cs_spsolve_cl.o \
+ cs_leaf_cl.o cs_ereach_cl.o cs_randperm_cl.o
+
+OBJ = $(CS_DI) $(CS_DL) $(CS_CI) $(CS_CL) cs_convert.o
+
+$(OBJ): ../Include/cs.h cstcov_malloc_test.h Makefile
+
+
+.PRECIOUS: %demo.c %demo1.c %demo2.c %demo3.c cs_%.c cs_%_ci.c cs_%_cl.c cs_%_di.c cs_%_dl.c cstcov_%.c
+
+
+%demo.c:
+ - ln -s ../Demo/$*demo.c
+
+%demo1.c:
+ - ln -s ../Demo/$*demo1.c
+
+%demo2.c:
+ - ln -s ../Demo/$*demo2.c
+
+%demo3.c:
+ - ln -s ../Demo/$*demo3.c
+
+
+cstcov_%.c:
+ - ln -s cstcov_malloc_test.c cstcov_$*.c
+
+cs_convert.c:
+ - ln -s ../Source/cs_convert.c
+
+cs_%_ci.c:
+ - ln -s ../Source/cs_$*.c cs_$*_ci.c
+
+cs_%_di.c:
+ - ln -s ../Source/cs_$*.c cs_$*_di.c
+
+cs_%_dl.c:
+ - ln -s ../Source/cs_$*.c cs_$*_dl.c
+
+cs_%_cl.c:
+ - ln -s ../Source/cs_$*.c cs_$*_cl.c
+
+
+%_di.o: %_di.c
+ $(CC) $(CFLAGS) -c $<
+
+%_dl.o: %_dl.c
+ $(CC) $(CFLAGS) -DCS_LONG -c $<
+
+%_ci.o: %_ci.c
+ $(CC) $(CFLAGS) -DCS_COMPLEX -c $<
+
+%_cl.o: %_cl.c
+ $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -c $<
+
+
+cs_idemo: $(OBJ) cs_idemo.c
+ $(CC) $(CFLAGS) -o cs_idemo cs_idemo.c $(OBJ) -lm
+
+cs_ldemo: $(OBJ) cs_ldemo.c
+ $(CC) $(CFLAGS) -o cs_ldemo cs_ldemo.c $(OBJ) -lm
+
+
+cs_demo1_di: $(CS_DI) cs_di_demo1.c
+ $(CC) $(CFLAGS) -o cs_demo1_di cs_di_demo1.c $(CS_DI) -lm
+
+cs_demo2_di: $(CS_DI) cs_di_demo2.c cs_di_demo.c
+ $(CC) $(CFLAGS) -o cs_demo2_di cs_di_demo2.c cs_di_demo.c $(CS_DI) -lm
+
+cs_demo3_di: $(CS_DI) cs_di_demo3.c cs_di_demo.c
+ $(CC) $(CFLAGS) -o cs_demo3_di cs_di_demo3.c cs_di_demo.c $(CS_DI) -lm
+
+cstcov_test_di: $(CS_DI) cstcov_test.c cs_di_demo.c
+ $(CC) $(CFLAGS) -o cstcov_test_di cstcov_test.c cs_di_demo.c $(CS_DI) -lm
+
+
+cs_demo1_dl: $(CS_DL) cs_dl_demo1.c
+ $(CC) $(CFLAGS) -DCS_LONG -o cs_demo1_dl cs_dl_demo1.c $(CS_DL) -lm
+
+cs_demo2_dl: $(CS_DL) cs_dl_demo2.c cs_dl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -o cs_demo2_dl cs_dl_demo2.c cs_dl_demo.c $(CS_DL) -lm
+
+cs_demo3_dl: $(CS_DL) cs_dl_demo3.c cs_dl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -o cs_demo3_dl cs_dl_demo3.c cs_dl_demo.c $(CS_DL) -lm
+
+cstcov_test_dl: $(CS_DL) cstcov_test.c cs_dl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -o cstcov_test_dl cstcov_test.c cs_dl_demo.c $(CS_DL) -lm
+
+
+cs_demo1_ci: $(CS_CI) cs_ci_demo1.c
+ $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo1_ci cs_ci_demo1.c $(CS_CI) -lm
+
+cs_demo2_ci: $(CS_CI) cs_ci_demo2.c cs_ci_demo.c
+ $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo2_ci cs_ci_demo2.c cs_ci_demo.c $(CS_CI) -lm
+
+cs_demo3_ci: $(CS_CI) cs_ci_demo3.c cs_ci_demo.c
+ $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo3_ci cs_ci_demo3.c cs_ci_demo.c $(CS_CI) -lm
+
+cstcov_test_ci: $(CS_CI) cstcov_test.c cs_ci_demo.c
+ $(CC) $(CFLAGS) -DCS_COMPLEX -o cstcov_test_ci cstcov_test.c cs_ci_demo.c $(CS_CI) -lm
+
+
+cs_demo1_cl: $(CS_CL) cs_cl_demo1.c
+ $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo1_cl cs_cl_demo1.c $(CS_CL) -lm
+
+cs_demo2_cl: $(CS_CL) cs_cl_demo2.c cs_cl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo2_cl cs_cl_demo2.c cs_cl_demo.c $(CS_CL) -lm
+
+cs_demo3_cl: $(CS_CL) cs_cl_demo3.c cs_cl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo3_cl cs_cl_demo3.c cs_cl_demo.c $(CS_CL) -lm
+
+cstcov_test_cl: $(CS_CL) cstcov_test.c cs_cl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cstcov_test_cl cstcov_test.c cs_cl_demo.c $(CS_CL) -lm
+
+
+run_convert: cs_idemo cs_ldemo
+ - $(V) ./cs_idemo < ../Matrix/t2
+ - $(V) ./cs_ldemo < ../Matrix/t2
+
+run_di: cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di
+ - $(V) ./cs_demo1_di < ../Matrix/t1
+ - $(V) ./cs_demo1_di < nil
+ - $(V) ./cs_demo1_di < zero
+ - $(V) ./cs_demo2_di < nil
+ - $(V) ./cs_demo2_di < zero
+ - $(V) ./cs_demo2_di < ../Matrix/t1
+ - $(V) ./cs_demo2_di < ../Matrix/bcsstk01
+ - $(V) ./cs_demo2_di < ../Matrix/fs_183_1
+ - $(V) ./cs_demo2_di < ../Matrix/west0067
+ - $(V) ./cs_demo2_di < ../Matrix/lp_afiro
+ - $(V) ./cs_demo2_di < ../Matrix/ash219
+ - $(V) ./cs_demo2_di < ../Matrix/mbeacxc
+ - $(V) ./cs_demo2_di < ../Matrix/bcsstk16
+ - $(V) ./cs_demo2_di < ../Matrix/ibm32a
+ - $(V) ./cs_demo2_di < ../Matrix/ibm32b
+ - $(V) ./cs_demo3_di < nil
+ - $(V) ./cs_demo3_di < ../Matrix/bcsstk01
+ - $(V) ./cs_demo3_di < ../Matrix/bcsstk16
+ - $(V) ./cstcov_test_di nil > test_di_nil.out
+ - $(V) ./cstcov_test_di zero > test_di_zero.out
+ - $(V) ./cstcov_test_di ../Matrix/t1 > test_di_t1.out
+ - $(V) ./cstcov_test_di ../Matrix/bcsstk01 > test_di_k1.out
+ - $(V) ./cstcov_test_di ../Matrix/fs_183_1 > test_di_fs.out
+ - $(V) ./cstcov_test_di ../Matrix/west0067 > test_di_we.out
+ - $(V) ./cstcov_test_di ../Matrix/ash219 > test_di_ash.out
+ - $(V) ./cstcov_test_di ../Matrix/lp_afiro > test_di_afiro.out
+
+run_dl: cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl
+ - $(V) ./cs_demo1_dl < ../Matrix/t1
+ - $(V) ./cs_demo1_dl < nil
+ - $(V) ./cs_demo1_dl < zero
+ - $(V) ./cs_demo2_dl < nil
+ - $(V) ./cs_demo2_dl < zero
+ - $(V) ./cs_demo2_dl < ../Matrix/t1
+ - $(V) ./cs_demo2_dl < ../Matrix/bcsstk01
+ - $(V) ./cs_demo2_dl < ../Matrix/fs_183_1
+ - $(V) ./cs_demo2_dl < ../Matrix/west0067
+ - $(V) ./cs_demo2_dl < ../Matrix/lp_afiro
+ - $(V) ./cs_demo2_dl < ../Matrix/ash219
+ - $(V) ./cs_demo2_dl < ../Matrix/mbeacxc
+ - $(V) ./cs_demo2_dl < ../Matrix/bcsstk16
+ - $(V) ./cs_demo2_dl < ../Matrix/ibm32a
+ - $(V) ./cs_demo2_dl < ../Matrix/ibm32b
+ - $(V) ./cs_demo3_dl < nil
+ - $(V) ./cs_demo3_dl < ../Matrix/bcsstk01
+ - $(V) ./cs_demo3_dl < ../Matrix/bcsstk16
+ - $(V) ./cstcov_test_dl nil > test_dl_nil.out
+ - $(V) ./cstcov_test_dl zero > test_dl_zero.out
+ - $(V) ./cstcov_test_dl ../Matrix/t1 > test_dl_t1.out
+ - $(V) ./cstcov_test_dl ../Matrix/bcsstk01 > test_dl_k1.out
+ - $(V) ./cstcov_test_dl ../Matrix/fs_183_1 > test_dl_fs.out
+ - $(V) ./cstcov_test_dl ../Matrix/west0067 > test_dl_we.out
+ - $(V) ./cstcov_test_dl ../Matrix/ash219 > test_dl_ash.out
+ - $(V) ./cstcov_test_dl ../Matrix/lp_afiro > test_dl_afiro.out
+
+run_ci: cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci
+ - $(V) ./cs_demo1_ci < ../Matrix/t2
+ - $(V) ./cs_demo2_ci < ../Matrix/t2
+ - $(V) ./cs_demo1_ci < czero
+ - $(V) ./cs_demo2_ci < czero
+ - $(V) ./cs_demo1_ci < ../Matrix/t3
+ - $(V) ./cs_demo2_ci < ../Matrix/t3
+ - $(V) ./cs_demo1_ci < ../Matrix/t4
+ - $(V) ./cs_demo2_ci < ../Matrix/t4
+ - $(V) ./cs_demo2_ci < ../Matrix/c_west0067
+ - $(V) ./cs_demo2_ci < ../Matrix/c_mbeacxc
+ - $(V) ./cs_demo2_ci < ../Matrix/c_ibm32a
+ - $(V) ./cs_demo2_ci < ../Matrix/c_ibm32b
+ - $(V) ./cs_demo2_ci < ../Matrix/young1c
+ - $(V) ./cs_demo2_ci < ../Matrix/qc324
+ - $(V) ./cs_demo2_ci < ../Matrix/neumann
+ - $(V) ./cs_demo2_ci < ../Matrix/c4
+ - $(V) ./cs_demo3_ci < ../Matrix/c4
+ - $(V) ./cs_demo2_ci < ../Matrix/mhd1280b
+ - $(V) ./cs_demo3_ci < ../Matrix/mhd1280b
+ - $(V) ./cstcov_test_ci ../Matrix/t2 > test_ci_t2.out
+ - $(V) ./cstcov_test_ci ../Matrix/young1c > test_ci_young1c.out
+ - $(V) ./cstcov_test_ci ../Matrix/qc324 > test_ci_qc324.out
+ - $(V) ./cstcov_test_ci ../Matrix/neumann > test_ci_neumann.out
+ - $(V) ./cstcov_test_ci ../Matrix/mhd1280b > test_ci_mhd1280b.out
+
+run_cl: cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl
+ - $(V) ./cs_demo1_cl < ../Matrix/t2
+ - $(V) ./cs_demo2_cl < ../Matrix/t2
+ - $(V) ./cs_demo1_cl < czero
+ - $(V) ./cs_demo2_cl < czero
+ - $(V) ./cs_demo1_cl < ../Matrix/t3
+ - $(V) ./cs_demo2_cl < ../Matrix/t3
+ - $(V) ./cs_demo1_cl < ../Matrix/t4
+ - $(V) ./cs_demo2_cl < ../Matrix/t4
+ - $(V) ./cs_demo2_cl < ../Matrix/c_west0067
+ - $(V) ./cs_demo2_cl < ../Matrix/c_mbeacxc
+ - $(V) ./cs_demo2_cl < ../Matrix/c_ibm32a
+ - $(V) ./cs_demo2_cl < ../Matrix/c_ibm32b
+ - $(V) ./cs_demo2_cl < ../Matrix/young1c
+ - $(V) ./cs_demo2_cl < ../Matrix/qc324
+ - $(V) ./cs_demo2_cl < ../Matrix/neumann
+ - $(V) ./cs_demo2_cl < ../Matrix/c4
+ - $(V) ./cs_demo3_cl < ../Matrix/c4
+ - $(V) ./cs_demo2_cl < ../Matrix/mhd1280b
+ - $(V) ./cs_demo3_cl < ../Matrix/mhd1280b
+ - $(V) ./cstcov_test_cl ../Matrix/t2 > test_cl_t2.out
+ - $(V) ./cstcov_test_cl ../Matrix/young1c > test_cl_young1c.out
+ - $(V) ./cstcov_test_cl ../Matrix/qc324 > test_cl_qc324.out
+ - $(V) ./cstcov_test_cl ../Matrix/neumann > test_cl_neumann.out
+ - $(V) ./cstcov_test_cl ../Matrix/mhd1280b > test_cl_mhd1280b.out
+
+
+readhb: readhb.f
+ f77 -o readhb readhb.f
+
+readhb.f:
+ - ln -s ../Demo/readhb.f
+
+clean:
+ rm -f *.o *.bbg *.da *.gcov *.gcda *.gcno
+
+purge: distclean
+
+distclean: clean
+ rm -f readhb *.out *.a cov.sort
+ rm -f cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di
+ rm -f cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl
+ rm -f cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci
+ rm -f cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl
+ rm -f cs_idemo cs_ldemo
+ rm -f cs_*.c
+ rm -f cs*_di.c cs*_dl.c cs*_ci.c cs*_cl.c
diff --git a/CXSparse/Tcov/README.txt b/CXSparse/Tcov/README.txt
new file mode 100644
index 0000000..caae525
--- /dev/null
+++ b/CXSparse/Tcov/README.txt
@@ -0,0 +1,13 @@
+CXSparse/Tcov: comprehensive test coverage for CXSparse. Requires Linux.
+Type "make" to compile, and then "make run" to run the tests.
+The test coverage is in cover.out. The test output is
+printed on stdout, except for cs_test (which prints its output in various
+*.out files).
+
+If the test is successful, the last line printed should be
+"statements not yet tested: 0", and all printed residuals should be small.
+
+Note that you will get warnings about unused parameters for some functions.
+These warnings can be safely ignored. They are parameters for functions that
+are passed to cs_fkeep, and all functions used in this manner must have the
+same calling sequence, even if some of the parameters are not used.
diff --git a/CXSparse/Tcov/cov.awk b/CXSparse/Tcov/cov.awk
new file mode 100644
index 0000000..5744b40
--- /dev/null
+++ b/CXSparse/Tcov/cov.awk
@@ -0,0 +1,17 @@
+/cannot/
+
+/function/ { f = $8 }
+
+/file/ { f = $8 }
+
+/lines/ {
+
+ k = match ($1, "%") ;
+ p = substr ($1, 1, k-1) ;
+
+ if ((p+0) != 100)
+ {
+ printf "%8s %s\n", p, f
+ }
+}
+
diff --git a/CXSparse/Tcov/covall b/CXSparse/Tcov/covall
new file mode 100755
index 0000000..1751690
--- /dev/null
+++ b/CXSparse/Tcov/covall
@@ -0,0 +1,7 @@
+#!/bin/csh
+ ./gcovs cs*.c |& awk -f cov.awk | sort -n > cov.out
+ sort -n cov.out > cov.sort
+ ./covs > covs.out
+ echo -n "statments not yet tested: "
+ grep "#####" *gcov | wc -l
+ ./cover *v > cover.out
diff --git a/CXSparse/Tcov/covall.linux b/CXSparse/Tcov/covall.linux
new file mode 100755
index 0000000..1751690
--- /dev/null
+++ b/CXSparse/Tcov/covall.linux
@@ -0,0 +1,7 @@
+#!/bin/csh
+ ./gcovs cs*.c |& awk -f cov.awk | sort -n > cov.out
+ sort -n cov.out > cov.sort
+ ./covs > covs.out
+ echo -n "statments not yet tested: "
+ grep "#####" *gcov | wc -l
+ ./cover *v > cover.out
diff --git a/CXSparse/Tcov/covall.sol b/CXSparse/Tcov/covall.sol
new file mode 100755
index 0000000..457ad63
--- /dev/null
+++ b/CXSparse/Tcov/covall.sol
@@ -0,0 +1,5 @@
+#!/bin/csh
+ tcov -x cm.profile cs*.c >& /dev/null
+ echo -n "statments not yet tested: "
+ ./covs > covs.out
+ grep "#####" *tcov | wc -l
diff --git a/CXSparse/Tcov/cover b/CXSparse/Tcov/cover
new file mode 100755
index 0000000..b3e685c
--- /dev/null
+++ b/CXSparse/Tcov/cover
@@ -0,0 +1,9 @@
+#!/bin/csh
+# usage: cover files
+echo '================================================================='
+foreach file ($argv[1-])
+ echo $file
+ echo '================================================================='
+ grep "#####" -A5 -B5 $file
+ echo '================================================================='
+ end
diff --git a/CXSparse/Tcov/covs b/CXSparse/Tcov/covs
new file mode 100755
index 0000000..4171380
--- /dev/null
+++ b/CXSparse/Tcov/covs
@@ -0,0 +1,7 @@
+#!/bin/csh
+echo '================================================================='
+foreach file (*.?cov)
+ echo $file
+ grep "#####" $file
+ echo '================================================================='
+ end
diff --git a/CXSparse/Tcov/cstcov_malloc_test.c b/CXSparse/Tcov/cstcov_malloc_test.c
new file mode 100644
index 0000000..e72878d
--- /dev/null
+++ b/CXSparse/Tcov/cstcov_malloc_test.c
@@ -0,0 +1,34 @@
+#include "cstcov_malloc_test.h"
+int malloc_count = INT_MAX ;
+
+/* wrapper for malloc */
+void *cs_malloc (CS_INT n, size_t size)
+{
+ if (--malloc_count < 0) return (NULL) ; /* pretend to fail */
+ return (malloc (CS_MAX (n,1) * size)) ;
+}
+
+/* wrapper for calloc */
+void *cs_calloc (CS_INT n, size_t size)
+{
+ if (--malloc_count < 0) return (NULL) ; /* pretend to fail */
+ return (calloc (CS_MAX (n,1), size)) ;
+}
+
+/* wrapper for free */
+void *cs_free (void *p)
+{
+ if (p) free (p) ; /* free p if it is not already NULL */
+ return (NULL) ; /* return NULL to simplify the use of cs_free */
+}
+
+/* wrapper for realloc */
+void *cs_realloc (void *p, CS_INT n, size_t size, CS_INT *ok)
+{
+ void *pnew ;
+ *ok = 0 ;
+ if (--malloc_count < 0) return (p) ; /* pretend to fail */
+ pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */
+ *ok = (pnew != NULL) ;
+ return ((*ok) ? pnew : p) ; /* return original p if failure */
+}
diff --git a/CXSparse/Tcov/cstcov_malloc_test.h b/CXSparse/Tcov/cstcov_malloc_test.h
new file mode 100644
index 0000000..f235ad9
--- /dev/null
+++ b/CXSparse/Tcov/cstcov_malloc_test.h
@@ -0,0 +1,7 @@
+#include "cs.h"
+#define malloc_count CS_NAME (_malloc_count)
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+EXTERN int malloc_count ;
+
diff --git a/CXSparse/Tcov/cstcov_test.c b/CXSparse/Tcov/cstcov_test.c
new file mode 100644
index 0000000..1626904
--- /dev/null
+++ b/CXSparse/Tcov/cstcov_test.c
@@ -0,0 +1,30 @@
+#include "cs_demo.h"
+/* cs_test: read a matrix and run cs_demo2 and cs_demo3, using malloc tests. */
+
+#include "cstcov_malloc_test.h"
+
+int main (int argc, char **argv)
+{
+ FILE *f ;
+ problem *Prob ;
+ int trials, ok, demo ;
+ if (argc < 2) return (-1) ;
+ printf ("cs_test, file: %s\n", argv [1]) ;
+ for (demo = 2 ; demo <= 3 ; demo++)
+ {
+ printf ("demo: %d\n", demo) ;
+ for (trials = 0 ; trials < 4000 ; trials++)
+ {
+ malloc_count = trials ;
+ f = fopen (argv [1], "r") ;
+ if (!f) return (-1) ;
+ Prob = get_problem (f, (demo == 2) ? 1e-14 : 0) ;
+ fclose (f) ;
+ if (Prob) ok = (demo == 2) ? demo2 (Prob) : demo3 (Prob) ;
+ free_problem (Prob) ;
+ if (malloc_count > 0) break ;
+ }
+ printf ("demo %d # trials: %d\n", demo, trials) ;
+ }
+ return (0) ;
+}
diff --git a/CXSparse/Tcov/czero b/CXSparse/Tcov/czero
new file mode 100644
index 0000000..6a20ce4
--- /dev/null
+++ b/CXSparse/Tcov/czero
@@ -0,0 +1 @@
+0 0 0 0
diff --git a/CXSparse/Tcov/gcovs b/CXSparse/Tcov/gcovs
new file mode 100755
index 0000000..9fddaf1
--- /dev/null
+++ b/CXSparse/Tcov/gcovs
@@ -0,0 +1,6 @@
+# usage: gcovs files
+echo '================================================================='
+foreach file ($argv[1-])
+ gcov -f $file
+ echo '================================================================='
+ end
diff --git a/CXSparse/Tcov/nil b/CXSparse/Tcov/nil
new file mode 100644
index 0000000..e69de29
diff --git a/CXSparse/Tcov/zero b/CXSparse/Tcov/zero
new file mode 100644
index 0000000..a5c7b77
--- /dev/null
+++ b/CXSparse/Tcov/zero
@@ -0,0 +1 @@
+0 0 0
diff --git a/CXSparse_newfiles.tar.gz b/CXSparse_newfiles.tar.gz
new file mode 100644
index 0000000..9704691
Binary files /dev/null and b/CXSparse_newfiles.tar.gz differ
diff --git a/CXSparse_newfiles/Demo/Makefile b/CXSparse_newfiles/Demo/Makefile
new file mode 100644
index 0000000..c1352f0
--- /dev/null
+++ b/CXSparse_newfiles/Demo/Makefile
@@ -0,0 +1,168 @@
+CC = cc
+CFLAGS = -O
+
+I = -I../Include -I../../UFconfig
+
+CS = ../Lib/libcxsparse.a
+
+all: $(CS) cs_demo1 cs_demo2 cs_demo3 \
+ cs_di_demo1 cs_di_demo2 cs_di_demo3 \
+ cs_dl_demo1 cs_dl_demo2 cs_dl_demo3 \
+ cs_ci_demo1 cs_ci_demo2 cs_ci_demo3 \
+ cs_cl_demo1 cs_cl_demo2 cs_cl_demo3 \
+ tests cs_idemo
+
+tests: test_convert test test_di test_dl test_ci test_cl
+
+test: cs_demo1 cs_demo2 cs_demo3
+ - ./cs_demo1 < ../Matrix/t1
+ - ./cs_demo2 < ../Matrix/t1
+ - ./cs_demo2 < ../Matrix/fs_183_1
+ - ./cs_demo2 < ../Matrix/west0067
+ - ./cs_demo2 < ../Matrix/lp_afiro
+ - ./cs_demo2 < ../Matrix/ash219
+ - ./cs_demo2 < ../Matrix/mbeacxc
+ - ./cs_demo2 < ../Matrix/bcsstk01
+ - ./cs_demo3 < ../Matrix/bcsstk01
+ - ./cs_demo2 < ../Matrix/bcsstk16
+ - ./cs_demo3 < ../Matrix/bcsstk16
+
+test_di: cs_di_demo1 cs_di_demo2 cs_di_demo3
+ - ./cs_di_demo1 < ../Matrix/t1
+ - ./cs_di_demo2 < ../Matrix/t1
+ - ./cs_di_demo2 < ../Matrix/fs_183_1
+ - ./cs_di_demo2 < ../Matrix/west0067
+ - ./cs_di_demo2 < ../Matrix/lp_afiro
+ - ./cs_di_demo2 < ../Matrix/ash219
+ - ./cs_di_demo2 < ../Matrix/mbeacxc
+ - ./cs_di_demo2 < ../Matrix/bcsstk01
+ - ./cs_di_demo3 < ../Matrix/bcsstk01
+ - ./cs_di_demo2 < ../Matrix/bcsstk16
+ - ./cs_di_demo3 < ../Matrix/bcsstk16
+
+test_dl: cs_dl_demo1 cs_dl_demo2 cs_dl_demo3
+ - ./cs_dl_demo1 < ../Matrix/t1
+ - ./cs_dl_demo2 < ../Matrix/t1
+ - ./cs_dl_demo2 < ../Matrix/fs_183_1
+ - ./cs_dl_demo2 < ../Matrix/west0067
+ - ./cs_dl_demo2 < ../Matrix/lp_afiro
+ - ./cs_dl_demo2 < ../Matrix/ash219
+ - ./cs_dl_demo2 < ../Matrix/mbeacxc
+ - ./cs_dl_demo2 < ../Matrix/bcsstk01
+ - ./cs_dl_demo3 < ../Matrix/bcsstk01
+ - ./cs_dl_demo2 < ../Matrix/bcsstk16
+ - ./cs_dl_demo3 < ../Matrix/bcsstk16
+
+test_ci: cs_ci_demo1 cs_ci_demo2 cs_ci_demo3
+ - ./cs_ci_demo1 < ../Matrix/t2
+ - ./cs_ci_demo2 < ../Matrix/t2
+ - ./cs_ci_demo2 < ../Matrix/t3
+ - ./cs_ci_demo2 < ../Matrix/t4
+ - ./cs_ci_demo2 < ../Matrix/c_west0067
+ - ./cs_ci_demo2 < ../Matrix/c_mbeacxc
+ - ./cs_ci_demo2 < ../Matrix/young1c
+ - ./cs_ci_demo2 < ../Matrix/qc324
+ - ./cs_ci_demo2 < ../Matrix/neumann
+ - ./cs_ci_demo2 < ../Matrix/c4
+ - ./cs_ci_demo3 < ../Matrix/c4
+ - ./cs_ci_demo2 < ../Matrix/mhd1280b
+ - ./cs_ci_demo3 < ../Matrix/mhd1280b
+
+test_cl: cs_cl_demo1 cs_cl_demo2 cs_cl_demo3
+ - ./cs_cl_demo1 < ../Matrix/t2
+ - ./cs_cl_demo2 < ../Matrix/t2
+ - ./cs_cl_demo2 < ../Matrix/t3
+ - ./cs_cl_demo2 < ../Matrix/t4
+ - ./cs_cl_demo2 < ../Matrix/c_west0067
+ - ./cs_cl_demo2 < ../Matrix/c_mbeacxc
+ - ./cs_cl_demo2 < ../Matrix/young1c
+ - ./cs_cl_demo2 < ../Matrix/qc324
+ - ./cs_cl_demo2 < ../Matrix/neumann
+ - ./cs_cl_demo2 < ../Matrix/c4
+ - ./cs_cl_demo3 < ../Matrix/c4
+ - ./cs_cl_demo2 < ../Matrix/mhd1280b
+ - ./cs_cl_demo3 < ../Matrix/mhd1280b
+
+test_convert: cs_idemo cs_ldemo
+ - ./cs_idemo < ../Matrix/t2
+ - ./cs_ldemo < ../Matrix/t2
+
+$(CS):
+ ( cd ../Lib ; $(MAKE) )
+
+cs_demo1: $(CS) cs_demo1.c Makefile $(CS)
+ $(CC) $(I) -o cs_demo1 cs_demo1.c $(CS) -lm
+
+cs_demo2: $(CS) cs_demo2.c cs_demo.c cs_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_demo2 cs_demo2.c cs_demo.c $(CS) -lm
+
+cs_demo3: $(CS) cs_demo3.c cs_demo.c cs_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_demo3 cs_demo3.c cs_demo.c $(CS) -lm
+
+
+
+
+cs_di_demo1: $(CS) cs_di_demo1.c Makefile $(CS)
+ $(CC) $(I) -o cs_di_demo1 cs_di_demo1.c $(CS) -lm
+
+cs_di_demo2: $(CS) cs_di_demo2.c cs_di_demo.c cs_di_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_di_demo2 cs_di_demo2.c cs_di_demo.c $(CS) -lm
+
+cs_di_demo3: $(CS) cs_di_demo3.c cs_di_demo.c cs_di_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_di_demo3 cs_di_demo3.c cs_di_demo.c $(CS) -lm
+
+
+
+
+cs_ci_demo1: $(CS) cs_ci_demo1.c Makefile $(CS)
+ $(CC) $(I) -o cs_ci_demo1 cs_ci_demo1.c $(CS) -lm
+
+cs_ci_demo2: $(CS) cs_ci_demo2.c cs_ci_demo.c cs_ci_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_ci_demo2 cs_ci_demo2.c cs_ci_demo.c $(CS) -lm
+
+cs_ci_demo3: $(CS) cs_ci_demo3.c cs_ci_demo.c cs_ci_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_ci_demo3 cs_ci_demo3.c cs_ci_demo.c $(CS) -lm
+
+
+
+cs_dl_demo1: $(CS) cs_dl_demo1.c Makefile $(CS)
+ $(CC) $(I) -o cs_dl_demo1 cs_dl_demo1.c $(CS) -lm
+
+cs_dl_demo2: $(CS) cs_dl_demo2.c cs_dl_demo.c cs_dl_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_dl_demo2 cs_dl_demo2.c cs_dl_demo.c $(CS) -lm
+
+cs_dl_demo3: $(CS) cs_dl_demo3.c cs_dl_demo.c cs_dl_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_dl_demo3 cs_dl_demo3.c cs_dl_demo.c $(CS) -lm
+
+
+cs_cl_demo1: $(CS) cs_cl_demo1.c Makefile $(CS)
+ $(CC) $(I) -o cs_cl_demo1 cs_cl_demo1.c $(CS) -lm
+
+cs_cl_demo2: $(CS) cs_cl_demo2.c cs_cl_demo.c cs_cl_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_cl_demo2 cs_cl_demo2.c cs_cl_demo.c $(CS) -lm
+
+cs_cl_demo3: $(CS) cs_cl_demo3.c cs_cl_demo.c cs_cl_demo.h Makefile $(CS)
+ $(CC) $(I) -o cs_cl_demo3 cs_cl_demo3.c cs_cl_demo.c $(CS) -lm
+
+
+
+
+cs_idemo: $(CS) cs_idemo.c Makefile $(CS)
+ $(CC) $(I) -o cs_idemo cs_idemo.c $(CS) -lm
+
+cs_ldemo: $(CS) cs_ldemo.c Makefile $(CS)
+ $(CC) $(I) -DCS_LONG -o cs_ldemo cs_ldemo.c $(CS) -lm
+
+
+clean:
+ rm -f *.o
+
+purge: distclean
+
+distclean: clean
+ rm -f cs_demo1 cs_demo2 cs_demo3 *.a
+ rm -f cs_di_demo1 cs_di_demo2 cs_di_demo3
+ rm -f cs_dl_demo1 cs_dl_demo2 cs_dl_demo3
+ rm -f cs_ci_demo1 cs_ci_demo2 cs_ci_demo3
+ rm -f cs_cl_demo1 cs_cl_demo2 cs_cl_demo3
+ rm -f cs_idemo cs_ldemo
diff --git a/CXSparse_newfiles/Demo/README.txt b/CXSparse_newfiles/Demo/README.txt
new file mode 100644
index 0000000..93eeb3a
--- /dev/null
+++ b/CXSparse_newfiles/Demo/README.txt
@@ -0,0 +1,4 @@
+CXSparse/Demo: to compile a run the demos, just type "make" in this directory.
+The printed residuals should all be small, except for the mbeacxc matrix
+(which is numerically and structurally singular), and ash219 (which is a
+least-squares problem). See cs_demo.out for the proper output of "make".
diff --git a/CXSparse_newfiles/Demo/cs_idemo.c b/CXSparse_newfiles/Demo/cs_idemo.c
new file mode 100644
index 0000000..d2f962b
--- /dev/null
+++ b/CXSparse_newfiles/Demo/cs_idemo.c
@@ -0,0 +1,57 @@
+#include "cs.h"
+/* test real/complex conversion routines (int version) */
+int main (void)
+{
+ cs_ci *T, *A, *A1, *A2, *B ;
+ cs_di *C1, *C2, *Treal, *Timag ;
+
+ printf ("\n--- cs_idemo, size of CS_INT: %d\n", (int) sizeof (CS_INT)) ;
+
+ T = cs_ci_load (stdin) ; /* load a complex triplet matrix, T */
+ printf ("\nT:\n") ;
+ cs_ci_print (T, 0) ;
+
+ Treal = cs_i_real (T, 1) ; /* Treal = real part of T */
+ printf ("\nTreal:\n") ;
+ cs_di_print (Treal, 0) ;
+
+ Timag = cs_i_real (T, 0) ; /* Treal = imaginary part of T */
+ printf ("\nTimag:\n") ;
+ cs_di_print (Timag, 0) ;
+
+ A = cs_ci_compress (T) ; /* A = compressed-column form of T */
+ printf ("\nA:\n") ;
+ cs_ci_print (A, 0) ;
+
+ C1 = cs_i_real (A, 1) ; /* C1 = real (A) */
+ printf ("\nC1 = real(A):\n") ;
+ cs_di_print (C1, 0) ;
+
+ C2 = cs_i_real (A, 0) ; /* C2 = imag (A) */
+ printf ("\nC2 = imag(A):\n") ;
+ cs_di_print (C2, 0) ;
+
+ A1 = cs_i_complex (C1, 1) ; /* A1 = complex version of C1 */
+ printf ("\nA1:\n") ;
+ cs_ci_print (A1, 0) ;
+
+ A2 = cs_i_complex (C2, 0) ; /* A2 = complex version of C2 (imag.) */
+ printf ("\nA2:\n") ;
+ cs_ci_print (A2, 0) ;
+
+ B = cs_ci_add (A1, A2, 1., -1.) ; /* B = A1 - A2 */
+ printf ("\nB = conj(A):\n") ;
+ cs_ci_print (B, 0) ;
+
+ cs_ci_spfree (T) ;
+ cs_ci_spfree (A) ;
+ cs_ci_spfree (A1) ;
+ cs_ci_spfree (A2) ;
+ cs_ci_spfree (B) ;
+ cs_di_spfree (C1) ;
+ cs_di_spfree (C2) ;
+ cs_di_spfree (Treal) ;
+ cs_di_spfree (Timag) ;
+
+ return (0) ;
+}
diff --git a/CXSparse_newfiles/Demo/cs_ldemo.c b/CXSparse_newfiles/Demo/cs_ldemo.c
new file mode 100644
index 0000000..5c09795
--- /dev/null
+++ b/CXSparse_newfiles/Demo/cs_ldemo.c
@@ -0,0 +1,57 @@
+#include "cs.h"
+/* test real/complex conversion routines (int version) */
+int main (void)
+{
+ cs_cl *T, *A, *A1, *A2, *B ;
+ cs_dl *C1, *C2, *Treal, *Timag ;
+
+ printf ("\n--- cs_ldemo, size of CS_INT: %d\n", (int) sizeof (CS_INT)) ;
+
+ T = cs_cl_load (stdin) ; /* load a complex triplet matrix, T */
+ printf ("\nT:\n") ;
+ cs_cl_print (T, 0) ;
+
+ Treal = cs_l_real (T, 1) ; /* Treal = real part of T */
+ printf ("\nTreal:\n") ;
+ cs_dl_print (Treal, 0) ;
+
+ Timag = cs_l_real (T, 0) ; /* Treal = imaginary part of T */
+ printf ("\nTimag:\n") ;
+ cs_dl_print (Timag, 0) ;
+
+ A = cs_cl_compress (T) ; /* A = compressed-column form of T */
+ printf ("\nA:\n") ;
+ cs_cl_print (A, 0) ;
+
+ C1 = cs_l_real (A, 1) ; /* C1 = real (A) */
+ printf ("\nC1 = real(A):\n") ;
+ cs_dl_print (C1, 0) ;
+
+ C2 = cs_l_real (A, 0) ; /* C2 = imag (A) */
+ printf ("\nC2 = imag(A):\n") ;
+ cs_dl_print (C2, 0) ;
+
+ A1 = cs_l_complex (C1, 1) ; /* A1 = complex version of C1 */
+ printf ("\nA1:\n") ;
+ cs_cl_print (A1, 0) ;
+
+ A2 = cs_l_complex (C2, 0) ; /* A2 = complex version of C2 (imag.) */
+ printf ("\nA2:\n") ;
+ cs_cl_print (A2, 0) ;
+
+ B = cs_cl_add (A1, A2, 1., -1.) ; /* B = A1 - A2 */
+ printf ("\nB = conj(A):\n") ;
+ cs_cl_print (B, 0) ;
+
+ cs_cl_spfree (T) ;
+ cs_cl_spfree (A) ;
+ cs_cl_spfree (A1) ;
+ cs_cl_spfree (A2) ;
+ cs_cl_spfree (B) ;
+ cs_dl_spfree (C1) ;
+ cs_dl_spfree (C2) ;
+ cs_dl_spfree (Treal) ;
+ cs_dl_spfree (Timag) ;
+
+ return (0) ;
+}
diff --git a/CXSparse_newfiles/Doc/License.txt b/CXSparse_newfiles/Doc/License.txt
new file mode 100644
index 0000000..9fbb144
--- /dev/null
+++ b/CXSparse_newfiles/Doc/License.txt
@@ -0,0 +1,19 @@
+CXSparse: a Concise Sparse matrix package - Extended.
+Copyright (c) 2006, Timothy A. Davis.
+http://www.cise.ufl.edu/research/sparse/CSparse
+
+--------------------------------------------------------------------------------
+
+CXSparse is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+CXSparse is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
diff --git a/CXSparse_newfiles/Include/cs.h b/CXSparse_newfiles/Include/cs.h
new file mode 100644
index 0000000..a511d35
--- /dev/null
+++ b/CXSparse_newfiles/Include/cs.h
@@ -0,0 +1,736 @@
+#ifndef _CXS_H
+#define _CXS_H
+#include <stdlib.h>
+#include <limits.h>
+#include <math.h>
+#include <stdio.h>
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#endif
+
+
+#ifdef __cplusplus
+#ifndef NCOMPLEX
+#include <complex>
+typedef std::complex<double> cs_complex_t ;
+#endif
+extern "C" {
+#else
+#ifndef NCOMPLEX
+#include <complex.h>
+#define cs_complex_t double _Complex
+#endif
+#endif
+
+#define CS_VER 2 /* CXSparse Version 2.2.1 */
+#define CS_SUBVER 2
+#define CS_SUBSUB 1
+#define CS_DATE "Nov 1, 2007" /* CXSparse release date */
+#define CS_COPYRIGHT "Copyright (c) Timothy A. Davis, 2006-2007"
+#define CXSPARSE
+
+/* define UF_long */
+#include "UFconfig.h"
+
+/* -------------------------------------------------------------------------- */
+/* double/int version of CXSparse */
+/* -------------------------------------------------------------------------- */
+
+/* --- primary CSparse routines and data structures ------------------------- */
+
+typedef struct cs_di_sparse /* matrix in compressed-column or triplet form */
+{
+ int nzmax ; /* maximum number of entries */
+ int m ; /* number of rows */
+ int n ; /* number of columns */
+ int *p ; /* column pointers (size n+1) or col indices (size nzmax) */
+ int *i ; /* row indices, size nzmax */
+ double *x ; /* numerical values, size nzmax */
+ int nz ; /* # of entries in triplet matrix, -1 for compressed-col */
+} cs_di ;
+
+cs_di *cs_di_add (const cs_di *A, const cs_di *B, double alpha, double beta) ;
+int cs_di_cholsol (int order, const cs_di *A, double *b) ;
+int cs_di_dupl (cs_di *A) ;
+int cs_di_entry (cs_di *T, int i, int j, double x) ;
+int cs_di_lusol (int order, const cs_di *A, double *b, double tol) ;
+int cs_di_gaxpy (const cs_di *A, const double *x, double *y) ;
+cs_di *cs_di_multiply (const cs_di *A, const cs_di *B) ;
+int cs_di_qrsol (int order, const cs_di *A, double *b) ;
+cs_di *cs_di_transpose (const cs_di *A, int values) ;
+cs_di *cs_di_compress (const cs_di *T) ;
+double cs_di_norm (const cs_di *A) ;
+int cs_di_print (const cs_di *A, int brief) ;
+cs_di *cs_di_load (FILE *f) ;
+
+/* utilities */
+void *cs_di_calloc (int n, size_t size) ;
+void *cs_di_free (void *p) ;
+void *cs_di_realloc (void *p, int n, size_t size, int *ok) ;
+cs_di *cs_di_spalloc (int m, int n, int nzmax, int values, int t) ;
+cs_di *cs_di_spfree (cs_di *A) ;
+int cs_di_sprealloc (cs_di *A, int nzmax) ;
+void *cs_di_malloc (int n, size_t size) ;
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+
+typedef struct cs_di_symbolic /* symbolic Cholesky, LU, or QR analysis */
+{
+ int *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */
+ int *q ; /* fill-reducing column permutation for LU and QR */
+ int *parent ; /* elimination tree for Cholesky and QR */
+ int *cp ; /* column pointers for Cholesky, row counts for QR */
+ int *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */
+ int m2 ; /* # of rows for QR, after adding fictitious rows */
+ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */
+ double unz ; /* # entries in U for LU; in R for QR */
+} cs_dis ;
+
+typedef struct cs_di_numeric /* numeric Cholesky, LU, or QR factorization */
+{
+ cs_di *L ; /* L for LU and Cholesky, V for QR */
+ cs_di *U ; /* U for LU, r for QR, not used for Cholesky */
+ int *pinv ; /* partial pivoting for LU */
+ double *B ; /* beta [0..n-1] for QR */
+} cs_din ;
+
+typedef struct cs_di_dmperm_results /* cs_di_dmperm or cs_di_scc output */
+{
+ int *p ; /* size m, row permutation */
+ int *q ; /* size n, column permutation */
+ int *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */
+ int *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */
+ int nb ; /* # of blocks in fine dmperm decomposition */
+ int rr [5] ; /* coarse row decomposition */
+ int cc [5] ; /* coarse column decomposition */
+} cs_did ;
+
+int *cs_di_amd (int order, const cs_di *A) ;
+cs_din *cs_di_chol (const cs_di *A, const cs_dis *S) ;
+cs_did *cs_di_dmperm (const cs_di *A, int seed) ;
+int cs_di_droptol (cs_di *A, double tol) ;
+int cs_di_dropzeros (cs_di *A) ;
+int cs_di_happly (const cs_di *V, int i, double beta, double *x) ;
+int cs_di_ipvec (const int *p, const double *b, double *x, int n) ;
+int cs_di_lsolve (const cs_di *L, double *x) ;
+int cs_di_ltsolve (const cs_di *L, double *x) ;
+cs_din *cs_di_lu (const cs_di *A, const cs_dis *S, double tol) ;
+cs_di *cs_di_permute (const cs_di *A, const int *pinv, const int *q,
+ int values) ;
+int *cs_di_pinv (const int *p, int n) ;
+int cs_di_pvec (const int *p, const double *b, double *x, int n) ;
+cs_din *cs_di_qr (const cs_di *A, const cs_dis *S) ;
+cs_dis *cs_di_schol (int order, const cs_di *A) ;
+cs_dis *cs_di_sqr (int order, const cs_di *A, int qr) ;
+cs_di *cs_di_symperm (const cs_di *A, const int *pinv, int values) ;
+int cs_di_usolve (const cs_di *U, double *x) ;
+int cs_di_utsolve (const cs_di *U, double *x) ;
+int cs_di_updown (cs_di *L, int sigma, const cs_di *C, const int *parent) ;
+
+/* utilities */
+cs_dis *cs_di_sfree (cs_dis *S) ;
+cs_din *cs_di_nfree (cs_din *N) ;
+cs_did *cs_di_dfree (cs_did *D) ;
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+
+int *cs_di_counts (const cs_di *A, const int *parent, const int *post,
+ int ata) ;
+double cs_di_cumsum (int *p, int *c, int n) ;
+int cs_di_dfs (int j, cs_di *G, int top, int *xi, int *pstack,
+ const int *pinv) ;
+int *cs_di_etree (const cs_di *A, int ata) ;
+int cs_di_fkeep (cs_di *A, int (*fkeep) (int, int, double, void *),
+ void *other) ;
+double cs_di_house (double *x, double *beta, int n) ;
+int *cs_di_maxtrans (const cs_di *A, int seed) ;
+int *cs_di_post (const int *parent, int n) ;
+cs_did *cs_di_scc (cs_di *A) ;
+int cs_di_scatter (const cs_di *A, int j, double beta, int *w, double *x,
+ int mark, cs_di *C, int nz) ;
+int cs_di_tdfs (int j, int k, int *head, const int *next, int *post,
+ int *stack) ;
+int cs_di_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf,
+ int *ancestor, int *jleaf) ;
+int cs_di_reach (cs_di *G, const cs_di *B, int k, int *xi, const int *pinv) ;
+int cs_di_spsolve (cs_di *L, const cs_di *B, int k, int *xi, double *x,
+ const int *pinv, int lo) ;
+int cs_di_ereach (const cs_di *A, int k, const int *parent, int *s, int *w) ;
+int *cs_di_randperm (int n, int seed) ;
+
+/* utilities */
+cs_did *cs_di_dalloc (int m, int n) ;
+cs_di *cs_di_done (cs_di *C, void *w, void *x, int ok) ;
+int *cs_di_idone (int *p, cs_di *C, void *w, int ok) ;
+cs_din *cs_di_ndone (cs_din *N, cs_di *C, void *w, void *x, int ok) ;
+cs_did *cs_di_ddone (cs_did *D, cs_di *C, void *w, int ok) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* double/UF_long version of CXSparse */
+/* -------------------------------------------------------------------------- */
+
+/* --- primary CSparse routines and data structures ------------------------- */
+
+typedef struct cs_dl_sparse /* matrix in compressed-column or triplet form */
+{
+ UF_long nzmax ; /* maximum number of entries */
+ UF_long m ; /* number of rows */
+ UF_long n ; /* number of columns */
+ UF_long *p ; /* column pointers (size n+1) or col indlces (size nzmax) */
+ UF_long *i ; /* row indices, size nzmax */
+ double *x ; /* numerical values, size nzmax */
+ UF_long nz ; /* # of entries in triplet matrix, -1 for compressed-col */
+} cs_dl ;
+
+cs_dl *cs_dl_add (const cs_dl *A, const cs_dl *B, double alpha, double beta) ;
+UF_long cs_dl_cholsol (UF_long order, const cs_dl *A, double *b) ;
+UF_long cs_dl_dupl (cs_dl *A) ;
+UF_long cs_dl_entry (cs_dl *T, UF_long i, UF_long j, double x) ;
+UF_long cs_dl_lusol (UF_long order, const cs_dl *A, double *b, double tol) ;
+UF_long cs_dl_gaxpy (const cs_dl *A, const double *x, double *y) ;
+cs_dl *cs_dl_multiply (const cs_dl *A, const cs_dl *B) ;
+UF_long cs_dl_qrsol (UF_long order, const cs_dl *A, double *b) ;
+cs_dl *cs_dl_transpose (const cs_dl *A, UF_long values) ;
+cs_dl *cs_dl_compress (const cs_dl *T) ;
+double cs_dl_norm (const cs_dl *A) ;
+UF_long cs_dl_print (const cs_dl *A, UF_long brief) ;
+cs_dl *cs_dl_load (FILE *f) ;
+
+/* utilities */
+void *cs_dl_calloc (UF_long n, size_t size) ;
+void *cs_dl_free (void *p) ;
+void *cs_dl_realloc (void *p, UF_long n, size_t size, UF_long *ok) ;
+cs_dl *cs_dl_spalloc (UF_long m, UF_long n, UF_long nzmax, UF_long values,
+ UF_long t) ;
+cs_dl *cs_dl_spfree (cs_dl *A) ;
+UF_long cs_dl_sprealloc (cs_dl *A, UF_long nzmax) ;
+void *cs_dl_malloc (UF_long n, size_t size) ;
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+
+typedef struct cs_dl_symbolic /* symbolic Cholesky, LU, or QR analysis */
+{
+ UF_long *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */
+ UF_long *q ; /* fill-reducing column permutation for LU and QR */
+ UF_long *parent ; /* elimination tree for Cholesky and QR */
+ UF_long *cp ; /* column pointers for Cholesky, row counts for QR */
+ UF_long *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */
+ UF_long m2 ; /* # of rows for QR, after adding fictitious rows */
+ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */
+ double unz ; /* # entries in U for LU; in R for QR */
+} cs_dls ;
+
+typedef struct cs_dl_numeric /* numeric Cholesky, LU, or QR factorization */
+{
+ cs_dl *L ; /* L for LU and Cholesky, V for QR */
+ cs_dl *U ; /* U for LU, r for QR, not used for Cholesky */
+ UF_long *pinv ; /* partial pivoting for LU */
+ double *B ; /* beta [0..n-1] for QR */
+} cs_dln ;
+
+typedef struct cs_dl_dmperm_results /* cs_dl_dmperm or cs_dl_scc output */
+{
+ UF_long *p ; /* size m, row permutation */
+ UF_long *q ; /* size n, column permutation */
+ UF_long *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */
+ UF_long *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */
+ UF_long nb ; /* # of blocks in fine dmperm decomposition */
+ UF_long rr [5] ; /* coarse row decomposition */
+ UF_long cc [5] ; /* coarse column decomposition */
+} cs_dld ;
+
+UF_long *cs_dl_amd (UF_long order, const cs_dl *A) ;
+cs_dln *cs_dl_chol (const cs_dl *A, const cs_dls *S) ;
+cs_dld *cs_dl_dmperm (const cs_dl *A, UF_long seed) ;
+UF_long cs_dl_droptol (cs_dl *A, double tol) ;
+UF_long cs_dl_dropzeros (cs_dl *A) ;
+UF_long cs_dl_happly (const cs_dl *V, UF_long i, double beta, double *x) ;
+UF_long cs_dl_ipvec (const UF_long *p, const double *b, double *x, UF_long n) ;
+UF_long cs_dl_lsolve (const cs_dl *L, double *x) ;
+UF_long cs_dl_ltsolve (const cs_dl *L, double *x) ;
+cs_dln *cs_dl_lu (const cs_dl *A, const cs_dls *S, double tol) ;
+cs_dl *cs_dl_permute (const cs_dl *A, const UF_long *pinv, const UF_long *q,
+ UF_long values) ;
+UF_long *cs_dl_pinv (const UF_long *p, UF_long n) ;
+UF_long cs_dl_pvec (const UF_long *p, const double *b, double *x, UF_long n) ;
+cs_dln *cs_dl_qr (const cs_dl *A, const cs_dls *S) ;
+cs_dls *cs_dl_schol (UF_long order, const cs_dl *A) ;
+cs_dls *cs_dl_sqr (UF_long order, const cs_dl *A, UF_long qr) ;
+cs_dl *cs_dl_symperm (const cs_dl *A, const UF_long *pinv, UF_long values) ;
+UF_long cs_dl_usolve (const cs_dl *U, double *x) ;
+UF_long cs_dl_utsolve (const cs_dl *U, double *x) ;
+UF_long cs_dl_updown (cs_dl *L, UF_long sigma, const cs_dl *C,
+ const UF_long *parent) ;
+
+/* utilities */
+cs_dls *cs_dl_sfree (cs_dls *S) ;
+cs_dln *cs_dl_nfree (cs_dln *N) ;
+cs_dld *cs_dl_dfree (cs_dld *D) ;
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+
+UF_long *cs_dl_counts (const cs_dl *A, const UF_long *parent,
+ const UF_long *post, UF_long ata) ;
+double cs_dl_cumsum (UF_long *p, UF_long *c, UF_long n) ;
+UF_long cs_dl_dfs (UF_long j, cs_dl *G, UF_long top, UF_long *xi,
+ UF_long *pstack, const UF_long *pinv) ;
+UF_long *cs_dl_etree (const cs_dl *A, UF_long ata) ;
+UF_long cs_dl_fkeep (cs_dl *A,
+ UF_long (*fkeep) (UF_long, UF_long, double, void *), void *other) ;
+double cs_dl_house (double *x, double *beta, UF_long n) ;
+UF_long *cs_dl_maxtrans (const cs_dl *A, UF_long seed) ;
+UF_long *cs_dl_post (const UF_long *parent, UF_long n) ;
+cs_dld *cs_dl_scc (cs_dl *A) ;
+UF_long cs_dl_scatter (const cs_dl *A, UF_long j, double beta, UF_long *w,
+ double *x, UF_long mark,cs_dl *C, UF_long nz) ;
+UF_long cs_dl_tdfs (UF_long j, UF_long k, UF_long *head, const UF_long *next,
+ UF_long *post, UF_long *stack) ;
+UF_long cs_dl_leaf (UF_long i, UF_long j, const UF_long *first,
+ UF_long *maxfirst, UF_long *prevleaf, UF_long *ancestor, UF_long *jleaf) ;
+UF_long cs_dl_reach (cs_dl *G, const cs_dl *B, UF_long k, UF_long *xi,
+ const UF_long *pinv) ;
+UF_long cs_dl_spsolve (cs_dl *L, const cs_dl *B, UF_long k, UF_long *xi,
+ double *x, const UF_long *pinv, UF_long lo) ;
+UF_long cs_dl_ereach (const cs_dl *A, UF_long k, const UF_long *parent,
+ UF_long *s, UF_long *w) ;
+UF_long *cs_dl_randperm (UF_long n, UF_long seed) ;
+
+/* utilities */
+cs_dld *cs_dl_dalloc (UF_long m, UF_long n) ;
+cs_dl *cs_dl_done (cs_dl *C, void *w, void *x, UF_long ok) ;
+UF_long *cs_dl_idone (UF_long *p, cs_dl *C, void *w, UF_long ok) ;
+cs_dln *cs_dl_ndone (cs_dln *N, cs_dl *C, void *w, void *x, UF_long ok) ;
+cs_dld *cs_dl_ddone (cs_dld *D, cs_dl *C, void *w, UF_long ok) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* complex/int version of CXSparse */
+/* -------------------------------------------------------------------------- */
+
+#ifndef NCOMPLEX
+
+/* --- primary CSparse routines and data structures ------------------------- */
+
+typedef struct cs_ci_sparse /* matrix in compressed-column or triplet form */
+{
+ int nzmax ; /* maximum number of entries */
+ int m ; /* number of rows */
+ int n ; /* number of columns */
+ int *p ; /* column pointers (size n+1) or col indices (size nzmax) */
+ int *i ; /* row indices, size nzmax */
+ cs_complex_t *x ; /* numerical values, size nzmax */
+ int nz ; /* # of entries in triplet matrix, -1 for compressed-col */
+} cs_ci ;
+
+cs_ci *cs_ci_add (const cs_ci *A, const cs_ci *B, cs_complex_t alpha,
+ cs_complex_t beta) ;
+int cs_ci_cholsol (int order, const cs_ci *A, cs_complex_t *b) ;
+int cs_ci_dupl (cs_ci *A) ;
+int cs_ci_entry (cs_ci *T, int i, int j, cs_complex_t x) ;
+int cs_ci_lusol (int order, const cs_ci *A, cs_complex_t *b, double tol) ;
+int cs_ci_gaxpy (const cs_ci *A, const cs_complex_t *x, cs_complex_t *y) ;
+cs_ci *cs_ci_multiply (const cs_ci *A, const cs_ci *B) ;
+int cs_ci_qrsol (int order, const cs_ci *A, cs_complex_t *b) ;
+cs_ci *cs_ci_transpose (const cs_ci *A, int values) ;
+cs_ci *cs_ci_compress (const cs_ci *T) ;
+double cs_ci_norm (const cs_ci *A) ;
+int cs_ci_print (const cs_ci *A, int brief) ;
+cs_ci *cs_ci_load (FILE *f) ;
+
+/* utilities */
+void *cs_ci_calloc (int n, size_t size) ;
+void *cs_ci_free (void *p) ;
+void *cs_ci_realloc (void *p, int n, size_t size, int *ok) ;
+cs_ci *cs_ci_spalloc (int m, int n, int nzmax, int values, int t) ;
+cs_ci *cs_ci_spfree (cs_ci *A) ;
+int cs_ci_sprealloc (cs_ci *A, int nzmax) ;
+void *cs_ci_malloc (int n, size_t size) ;
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+
+typedef struct cs_ci_symbolic /* symbolic Cholesky, LU, or QR analysis */
+{
+ int *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */
+ int *q ; /* fill-reducing column permutation for LU and QR */
+ int *parent ; /* elimination tree for Cholesky and QR */
+ int *cp ; /* column pointers for Cholesky, row counts for QR */
+ int *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */
+ int m2 ; /* # of rows for QR, after adding fictitious rows */
+ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */
+ double unz ; /* # entries in U for LU; in R for QR */
+} cs_cis ;
+
+typedef struct cs_ci_numeric /* numeric Cholesky, LU, or QR factorization */
+{
+ cs_ci *L ; /* L for LU and Cholesky, V for QR */
+ cs_ci *U ; /* U for LU, r for QR, not used for Cholesky */
+ int *pinv ; /* partial pivoting for LU */
+ double *B ; /* beta [0..n-1] for QR */
+} cs_cin ;
+
+typedef struct cs_ci_dmperm_results /* cs_ci_dmperm or cs_ci_scc output */
+{
+ int *p ; /* size m, row permutation */
+ int *q ; /* size n, column permutation */
+ int *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */
+ int *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */
+ int nb ; /* # of blocks in fine dmperm decomposition */
+ int rr [5] ; /* coarse row decomposition */
+ int cc [5] ; /* coarse column decomposition */
+} cs_cid ;
+
+int *cs_ci_amd (int order, const cs_ci *A) ;
+cs_cin *cs_ci_chol (const cs_ci *A, const cs_cis *S) ;
+cs_cid *cs_ci_dmperm (const cs_ci *A, int seed) ;
+int cs_ci_droptol (cs_ci *A, double tol) ;
+int cs_ci_dropzeros (cs_ci *A) ;
+int cs_ci_happly (const cs_ci *V, int i, double beta, cs_complex_t *x) ;
+int cs_ci_ipvec (const int *p, const cs_complex_t *b, cs_complex_t *x, int n) ;
+int cs_ci_lsolve (const cs_ci *L, cs_complex_t *x) ;
+int cs_ci_ltsolve (const cs_ci *L, cs_complex_t *x) ;
+cs_cin *cs_ci_lu (const cs_ci *A, const cs_cis *S, double tol) ;
+cs_ci *cs_ci_permute (const cs_ci *A, const int *pinv, const int *q,
+ int values) ;
+int *cs_ci_pinv (const int *p, int n) ;
+int cs_ci_pvec (const int *p, const cs_complex_t *b, cs_complex_t *x, int n) ;
+cs_cin *cs_ci_qr (const cs_ci *A, const cs_cis *S) ;
+cs_cis *cs_ci_schol (int order, const cs_ci *A) ;
+cs_cis *cs_ci_sqr (int order, const cs_ci *A, int qr) ;
+cs_ci *cs_ci_symperm (const cs_ci *A, const int *pinv, int values) ;
+int cs_ci_usolve (const cs_ci *U, cs_complex_t *x) ;
+int cs_ci_utsolve (const cs_ci *U, cs_complex_t *x) ;
+int cs_ci_updown (cs_ci *L, int sigma, const cs_ci *C, const int *parent) ;
+
+/* utilities */
+cs_cis *cs_ci_sfree (cs_cis *S) ;
+cs_cin *cs_ci_nfree (cs_cin *N) ;
+cs_cid *cs_ci_dfree (cs_cid *D) ;
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+
+int *cs_ci_counts (const cs_ci *A, const int *parent, const int *post,
+ int ata) ;
+double cs_ci_cumsum (int *p, int *c, int n) ;
+int cs_ci_dfs (int j, cs_ci *G, int top, int *xi, int *pstack,
+ const int *pinv) ;
+int *cs_ci_etree (const cs_ci *A, int ata) ;
+int cs_ci_fkeep (cs_ci *A, int (*fkeep) (int, int, cs_complex_t, void *),
+ void *other) ;
+cs_complex_t cs_ci_house (cs_complex_t *x, double *beta, int n) ;
+int *cs_ci_maxtrans (const cs_ci *A, int seed) ;
+int *cs_ci_post (const int *parent, int n) ;
+cs_cid *cs_ci_scc (cs_ci *A) ;
+int cs_ci_scatter (const cs_ci *A, int j, cs_complex_t beta, int *w,
+ cs_complex_t *x, int mark,cs_ci *C, int nz) ;
+int cs_ci_tdfs (int j, int k, int *head, const int *next, int *post,
+ int *stack) ;
+int cs_ci_leaf (int i, int j, const int *first, int *maxfirst, int *prevleaf,
+ int *ancestor, int *jleaf) ;
+int cs_ci_reach (cs_ci *G, const cs_ci *B, int k, int *xi, const int *pinv) ;
+int cs_ci_spsolve (cs_ci *L, const cs_ci *B, int k, int *xi,
+ cs_complex_t *x, const int *pinv, int lo) ;
+int cs_ci_ereach (const cs_ci *A, int k, const int *parent, int *s, int *w) ;
+int *cs_ci_randperm (int n, int seed) ;
+
+/* utilities */
+cs_cid *cs_ci_dalloc (int m, int n) ;
+cs_ci *cs_ci_done (cs_ci *C, void *w, void *x, int ok) ;
+int *cs_ci_idone (int *p, cs_ci *C, void *w, int ok) ;
+cs_cin *cs_ci_ndone (cs_cin *N, cs_ci *C, void *w, void *x, int ok) ;
+cs_cid *cs_ci_ddone (cs_cid *D, cs_ci *C, void *w, int ok) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* complex/UF_long version of CXSparse */
+/* -------------------------------------------------------------------------- */
+
+/* --- primary CSparse routines and data structures ------------------------- */
+
+typedef struct cs_cl_sparse /* matrix in compressed-column or triplet form */
+{
+ UF_long nzmax ; /* maximum number of entries */
+ UF_long m ; /* number of rows */
+ UF_long n ; /* number of columns */
+ UF_long *p ; /* column pointers (size n+1) or col indlces (size nzmax) */
+ UF_long *i ; /* row indices, size nzmax */
+ cs_complex_t *x ; /* numerical values, size nzmax */
+ UF_long nz ; /* # of entries in triplet matrix, -1 for compressed-col */
+} cs_cl ;
+
+cs_cl *cs_cl_add (const cs_cl *A, const cs_cl *B, cs_complex_t alpha,
+ cs_complex_t beta) ;
+UF_long cs_cl_cholsol (UF_long order, const cs_cl *A, cs_complex_t *b) ;
+UF_long cs_cl_dupl (cs_cl *A) ;
+UF_long cs_cl_entry (cs_cl *T, UF_long i, UF_long j, cs_complex_t x) ;
+UF_long cs_cl_lusol (UF_long order, const cs_cl *A, cs_complex_t *b,
+ double tol) ;
+UF_long cs_cl_gaxpy (const cs_cl *A, const cs_complex_t *x, cs_complex_t *y) ;
+cs_cl *cs_cl_multiply (const cs_cl *A, const cs_cl *B) ;
+UF_long cs_cl_qrsol (UF_long order, const cs_cl *A, cs_complex_t *b) ;
+cs_cl *cs_cl_transpose (const cs_cl *A, UF_long values) ;
+cs_cl *cs_cl_compress (const cs_cl *T) ;
+double cs_cl_norm (const cs_cl *A) ;
+UF_long cs_cl_print (const cs_cl *A, UF_long brief) ;
+cs_cl *cs_cl_load (FILE *f) ;
+
+/* utilities */
+void *cs_cl_calloc (UF_long n, size_t size) ;
+void *cs_cl_free (void *p) ;
+void *cs_cl_realloc (void *p, UF_long n, size_t size, UF_long *ok) ;
+cs_cl *cs_cl_spalloc (UF_long m, UF_long n, UF_long nzmax, UF_long values,
+ UF_long t) ;
+cs_cl *cs_cl_spfree (cs_cl *A) ;
+UF_long cs_cl_sprealloc (cs_cl *A, UF_long nzmax) ;
+void *cs_cl_malloc (UF_long n, size_t size) ;
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+
+typedef struct cs_cl_symbolic /* symbolic Cholesky, LU, or QR analysis */
+{
+ UF_long *pinv ; /* inverse row perm. for QR, fill red. perm for Chol */
+ UF_long *q ; /* fill-reducing column permutation for LU and QR */
+ UF_long *parent ; /* elimination tree for Cholesky and QR */
+ UF_long *cp ; /* column pointers for Cholesky, row counts for QR */
+ UF_long *leftmost ; /* leftmost[i] = min(find(A(i,:))), for QR */
+ UF_long m2 ; /* # of rows for QR, after adding fictitious rows */
+ double lnz ; /* # entries in L for LU or Cholesky; in V for QR */
+ double unz ; /* # entries in U for LU; in R for QR */
+} cs_cls ;
+
+typedef struct cs_cl_numeric /* numeric Cholesky, LU, or QR factorization */
+{
+ cs_cl *L ; /* L for LU and Cholesky, V for QR */
+ cs_cl *U ; /* U for LU, r for QR, not used for Cholesky */
+ UF_long *pinv ; /* partial pivoting for LU */
+ double *B ; /* beta [0..n-1] for QR */
+} cs_cln ;
+
+typedef struct cs_cl_dmperm_results /* cs_cl_dmperm or cs_cl_scc output */
+{
+ UF_long *p ; /* size m, row permutation */
+ UF_long *q ; /* size n, column permutation */
+ UF_long *r ; /* size nb+1, block k is rows r[k] to r[k+1]-1 in A(p,q) */
+ UF_long *s ; /* size nb+1, block k is cols s[k] to s[k+1]-1 in A(p,q) */
+ UF_long nb ; /* # of blocks in fine dmperm decomposition */
+ UF_long rr [5] ; /* coarse row decomposition */
+ UF_long cc [5] ; /* coarse column decomposition */
+} cs_cld ;
+
+UF_long *cs_cl_amd (UF_long order, const cs_cl *A) ;
+cs_cln *cs_cl_chol (const cs_cl *A, const cs_cls *S) ;
+cs_cld *cs_cl_dmperm (const cs_cl *A, UF_long seed) ;
+UF_long cs_cl_droptol (cs_cl *A, double tol) ;
+UF_long cs_cl_dropzeros (cs_cl *A) ;
+UF_long cs_cl_happly (const cs_cl *V, UF_long i, double beta, cs_complex_t *x) ;
+UF_long cs_cl_ipvec (const UF_long *p, const cs_complex_t *b,
+ cs_complex_t *x, UF_long n) ;
+UF_long cs_cl_lsolve (const cs_cl *L, cs_complex_t *x) ;
+UF_long cs_cl_ltsolve (const cs_cl *L, cs_complex_t *x) ;
+cs_cln *cs_cl_lu (const cs_cl *A, const cs_cls *S, double tol) ;
+cs_cl *cs_cl_permute (const cs_cl *A, const UF_long *pinv, const UF_long *q,
+ UF_long values) ;
+UF_long *cs_cl_pinv (const UF_long *p, UF_long n) ;
+UF_long cs_cl_pvec (const UF_long *p, const cs_complex_t *b,
+ cs_complex_t *x, UF_long n) ;
+cs_cln *cs_cl_qr (const cs_cl *A, const cs_cls *S) ;
+cs_cls *cs_cl_schol (UF_long order, const cs_cl *A) ;
+cs_cls *cs_cl_sqr (UF_long order, const cs_cl *A, UF_long qr) ;
+cs_cl *cs_cl_symperm (const cs_cl *A, const UF_long *pinv, UF_long values) ;
+UF_long cs_cl_usolve (const cs_cl *U, cs_complex_t *x) ;
+UF_long cs_cl_utsolve (const cs_cl *U, cs_complex_t *x) ;
+UF_long cs_cl_updown (cs_cl *L, UF_long sigma, const cs_cl *C,
+ const UF_long *parent) ;
+
+/* utilities */
+cs_cls *cs_cl_sfree (cs_cls *S) ;
+cs_cln *cs_cl_nfree (cs_cln *N) ;
+cs_cld *cs_cl_dfree (cs_cld *D) ;
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+
+UF_long *cs_cl_counts (const cs_cl *A, const UF_long *parent,
+ const UF_long *post, UF_long ata) ;
+double cs_cl_cumsum (UF_long *p, UF_long *c, UF_long n) ;
+UF_long cs_cl_dfs (UF_long j, cs_cl *G, UF_long top, UF_long *xi,
+ UF_long *pstack, const UF_long *pinv) ;
+UF_long *cs_cl_etree (const cs_cl *A, UF_long ata) ;
+UF_long cs_cl_fkeep (cs_cl *A,
+ UF_long (*fkeep) (UF_long, UF_long, cs_complex_t, void *), void *other) ;
+cs_complex_t cs_cl_house (cs_complex_t *x, double *beta, UF_long n) ;
+UF_long *cs_cl_maxtrans (const cs_cl *A, UF_long seed) ;
+UF_long *cs_cl_post (const UF_long *parent, UF_long n) ;
+cs_cld *cs_cl_scc (cs_cl *A) ;
+UF_long cs_cl_scatter (const cs_cl *A, UF_long j, cs_complex_t beta,
+ UF_long *w, cs_complex_t *x, UF_long mark,cs_cl *C, UF_long nz) ;
+UF_long cs_cl_tdfs (UF_long j, UF_long k, UF_long *head, const UF_long *next,
+ UF_long *post, UF_long *stack) ;
+UF_long cs_cl_leaf (UF_long i, UF_long j, const UF_long *first,
+ UF_long *maxfirst, UF_long *prevleaf, UF_long *ancestor, UF_long *jleaf) ;
+UF_long cs_cl_reach (cs_cl *G, const cs_cl *B, UF_long k, UF_long *xi,
+ const UF_long *pinv) ;
+UF_long cs_cl_spsolve (cs_cl *L, const cs_cl *B, UF_long k, UF_long *xi,
+ cs_complex_t *x, const UF_long *pinv, UF_long lo) ;
+UF_long cs_cl_ereach (const cs_cl *A, UF_long k, const UF_long *parent,
+ UF_long *s, UF_long *w) ;
+UF_long *cs_cl_randperm (UF_long n, UF_long seed) ;
+
+/* utilities */
+cs_cld *cs_cl_dalloc (UF_long m, UF_long n) ;
+cs_cl *cs_cl_done (cs_cl *C, void *w, void *x, UF_long ok) ;
+UF_long *cs_cl_idone (UF_long *p, cs_cl *C, void *w, UF_long ok) ;
+cs_cln *cs_cl_ndone (cs_cln *N, cs_cl *C, void *w, void *x, UF_long ok) ;
+cs_cld *cs_cl_ddone (cs_cld *D, cs_cl *C, void *w, UF_long ok) ;
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Macros for constructing each version of CSparse */
+/* -------------------------------------------------------------------------- */
+
+#ifdef CS_LONG
+#define CS_INT UF_long
+#define CS_INT_MAX UF_long_max
+#define CS_ID UF_long_id
+#ifdef CS_COMPLEX
+#define CS_ENTRY cs_complex_t
+#define CS_NAME(nm) cs_cl ## nm
+#define cs cs_cl
+#else
+#define CS_ENTRY double
+#define CS_NAME(nm) cs_dl ## nm
+#define cs cs_dl
+#endif
+#else
+#define CS_INT int
+#define CS_INT_MAX INT_MAX
+#define CS_ID "%d"
+#ifdef CS_COMPLEX
+#define CS_ENTRY cs_complex_t
+#define CS_NAME(nm) cs_ci ## nm
+#define cs cs_ci
+#else
+#define CS_ENTRY double
+#define CS_NAME(nm) cs_di ## nm
+#define cs cs_di
+#endif
+#endif
+
+#ifdef CS_COMPLEX
+#define CS_REAL(x) creal(x)
+#define CS_IMAG(x) cimag(x)
+#define CS_CONJ(x) conj(x)
+#define CS_ABS(x) cabs(x)
+#else
+#define CS_REAL(x) (x)
+#define CS_IMAG(x) (0.)
+#define CS_CONJ(x) (x)
+#define CS_ABS(x) fabs(x)
+#endif
+
+#define CS_MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define CS_MIN(a,b) (((a) < (b)) ? (a) : (b))
+#define CS_FLIP(i) (-(i)-2)
+#define CS_UNFLIP(i) (((i) < 0) ? CS_FLIP(i) : (i))
+#define CS_MARKED(w,j) (w [j] < 0)
+#define CS_MARK(w,j) { w [j] = CS_FLIP (w [j]) ; }
+#define CS_CSC(A) (A && (A->nz == -1))
+#define CS_TRIPLET(A) (A && (A->nz >= 0))
+
+/* --- primary CSparse routines and data structures ------------------------- */
+
+#define cs_add CS_NAME (_add)
+#define cs_cholsol CS_NAME (_cholsol)
+#define cs_dupl CS_NAME (_dupl)
+#define cs_entry CS_NAME (_entry)
+#define cs_lusol CS_NAME (_lusol)
+#define cs_gaxpy CS_NAME (_gaxpy)
+#define cs_multiply CS_NAME (_multiply)
+#define cs_qrsol CS_NAME (_qrsol)
+#define cs_transpose CS_NAME (_transpose)
+#define cs_compress CS_NAME (_compress)
+#define cs_norm CS_NAME (_norm)
+#define cs_print CS_NAME (_print)
+#define cs_load CS_NAME (_load)
+
+/* utilities */
+#define cs_calloc CS_NAME (_calloc)
+#define cs_free CS_NAME (_free)
+#define cs_realloc CS_NAME (_realloc)
+#define cs_spalloc CS_NAME (_spalloc)
+#define cs_spfree CS_NAME (_spfree)
+#define cs_sprealloc CS_NAME (_sprealloc)
+#define cs_malloc CS_NAME (_malloc)
+
+/* --- secondary CSparse routines and data structures ----------------------- */
+#define css CS_NAME (s)
+#define csn CS_NAME (n)
+#define csd CS_NAME (d)
+
+#define cs_amd CS_NAME (_amd)
+#define cs_chol CS_NAME (_chol)
+#define cs_dmperm CS_NAME (_dmperm)
+#define cs_droptol CS_NAME (_droptol)
+#define cs_dropzeros CS_NAME (_dropzeros)
+#define cs_happly CS_NAME (_happly)
+#define cs_ipvec CS_NAME (_ipvec)
+#define cs_lsolve CS_NAME (_lsolve)
+#define cs_ltsolve CS_NAME (_ltsolve)
+#define cs_lu CS_NAME (_lu)
+#define cs_permute CS_NAME (_permute)
+#define cs_pinv CS_NAME (_pinv)
+#define cs_pvec CS_NAME (_pvec)
+#define cs_qr CS_NAME (_qr)
+#define cs_schol CS_NAME (_schol)
+#define cs_sqr CS_NAME (_sqr)
+#define cs_symperm CS_NAME (_symperm)
+#define cs_usolve CS_NAME (_usolve)
+#define cs_utsolve CS_NAME (_utsolve)
+#define cs_updown CS_NAME (_updown)
+
+/* utilities */
+#define cs_sfree CS_NAME (_sfree)
+#define cs_nfree CS_NAME (_nfree)
+#define cs_dfree CS_NAME (_dfree)
+
+/* --- tertiary CSparse routines -------------------------------------------- */
+#define cs_counts CS_NAME (_counts)
+#define cs_cumsum CS_NAME (_cumsum)
+#define cs_dfs CS_NAME (_dfs)
+#define cs_etree CS_NAME (_etree)
+#define cs_fkeep CS_NAME (_fkeep)
+#define cs_house CS_NAME (_house)
+#define cs_invmatch CS_NAME (_invmatch)
+#define cs_maxtrans CS_NAME (_maxtrans)
+#define cs_post CS_NAME (_post)
+#define cs_scc CS_NAME (_scc)
+#define cs_scatter CS_NAME (_scatter)
+#define cs_tdfs CS_NAME (_tdfs)
+#define cs_reach CS_NAME (_reach)
+#define cs_spsolve CS_NAME (_spsolve)
+#define cs_ereach CS_NAME (_ereach)
+#define cs_randperm CS_NAME (_randperm)
+#define cs_leaf CS_NAME (_leaf)
+
+/* utilities */
+#define cs_dalloc CS_NAME (_dalloc)
+#define cs_done CS_NAME (_done)
+#define cs_idone CS_NAME (_idone)
+#define cs_ndone CS_NAME (_ndone)
+#define cs_ddone CS_NAME (_ddone)
+
+/* -------------------------------------------------------------------------- */
+/* Conversion routines */
+/* -------------------------------------------------------------------------- */
+
+#ifndef NCOMPLEX
+cs_di *cs_i_real (cs_ci *A, int real) ;
+cs_ci *cs_i_complex (cs_di *A, int real) ;
+cs_dl *cs_l_real (cs_cl *A, UF_long real) ;
+cs_cl *cs_l_complex (cs_dl *A, UF_long real) ;
+#endif
+
+#ifdef __cplusplus
+}
+#endif
+#endif
diff --git a/CXSparse_newfiles/Lib/Makefile b/CXSparse_newfiles/Lib/Makefile
new file mode 100644
index 0000000..c937956
--- /dev/null
+++ b/CXSparse_newfiles/Lib/Makefile
@@ -0,0 +1,98 @@
+# Modify the "-O" optimization option for best performance (-O3 on Linux):
+CC = cc
+CFLAGS = -O
+I = -I../../UFconfig -I../Include
+
+AR = ar cr
+RANLIB = ranlib
+
+all: libcxsparse.a
+
+CS_SOURCE = cs_add.c cs_amd.c cs_chol.c cs_cholsol.c cs_counts.c cs_cumsum.c \
+ cs_droptol.c cs_dropzeros.c cs_dupl.c cs_entry.c \
+ cs_etree.c cs_fkeep.c cs_gaxpy.c cs_happly.c cs_house.c cs_ipvec.c \
+ cs_lsolve.c cs_ltsolve.c cs_lu.c cs_lusol.c cs_util.c cs_multiply.c \
+ cs_permute.c cs_pinv.c cs_post.c cs_pvec.c cs_qr.c cs_qrsol.c \
+ cs_scatter.c cs_schol.c cs_sqr.c cs_symperm.c cs_tdfs.c cs_malloc.c \
+ cs_transpose.c cs_compress.c cs_usolve.c cs_utsolve.c cs_scc.c \
+ cs_maxtrans.c cs_dmperm.c cs_updown.c cs_print.c cs_norm.c cs_load.c \
+ cs_dfs.c cs_reach.c cs_spsolve.c cs_leaf.c cs_ereach.c cs_randperm.c
+
+CS_DI_OBJ = cs_add_di.o cs_amd_di.o cs_chol_di.o cs_cholsol_di.o cs_counts_di.o \
+ cs_cumsum_di.o cs_droptol_di.o cs_dropzeros_di.o cs_dupl_di.o \
+ cs_entry_di.o cs_etree_di.o cs_fkeep_di.o cs_gaxpy_di.o cs_happly_di.o \
+ cs_house_di.o cs_ipvec_di.o cs_lsolve_di.o cs_ltsolve_di.o cs_lu_di.o \
+ cs_lusol_di.o cs_util_di.o cs_multiply_di.o cs_permute_di.o cs_pinv_di.o \
+ cs_post_di.o cs_pvec_di.o cs_qr_di.o cs_qrsol_di.o cs_scatter_di.o \
+ cs_schol_di.o cs_sqr_di.o cs_symperm_di.o cs_tdfs_di.o cs_malloc_di.o \
+ cs_transpose_di.o cs_compress_di.o cs_usolve_di.o cs_utsolve_di.o \
+ cs_scc_di.o cs_maxtrans_di.o cs_dmperm_di.o cs_updown_di.o cs_print_di.o \
+ cs_norm_di.o cs_load_di.o cs_dfs_di.o cs_reach_di.o cs_spsolve_di.o \
+ cs_leaf_di.o cs_ereach_di.o cs_randperm_di.o
+
+CS_DL_OBJ = cs_add_dl.o cs_amd_dl.o cs_chol_dl.o cs_cholsol_dl.o cs_counts_dl.o \
+ cs_cumsum_dl.o cs_droptol_dl.o cs_dropzeros_dl.o cs_dupl_dl.o \
+ cs_entry_dl.o cs_etree_dl.o cs_fkeep_dl.o cs_gaxpy_dl.o cs_happly_dl.o \
+ cs_house_dl.o cs_ipvec_dl.o cs_lsolve_dl.o cs_ltsolve_dl.o cs_lu_dl.o \
+ cs_lusol_dl.o cs_util_dl.o cs_multiply_dl.o cs_permute_dl.o cs_pinv_dl.o \
+ cs_post_dl.o cs_pvec_dl.o cs_qr_dl.o cs_qrsol_dl.o cs_scatter_dl.o \
+ cs_schol_dl.o cs_sqr_dl.o cs_symperm_dl.o cs_tdfs_dl.o cs_malloc_dl.o \
+ cs_transpose_dl.o cs_compress_dl.o cs_usolve_dl.o cs_utsolve_dl.o \
+ cs_scc_dl.o cs_maxtrans_dl.o cs_dmperm_dl.o cs_updown_dl.o cs_print_dl.o \
+ cs_norm_dl.o cs_load_dl.o cs_dfs_dl.o cs_reach_dl.o cs_spsolve_dl.o \
+ cs_leaf_dl.o cs_ereach_dl.o cs_randperm_dl.o
+
+CS_CI_OBJ = cs_add_ci.o cs_amd_ci.o cs_chol_ci.o cs_cholsol_ci.o cs_counts_ci.o \
+ cs_cumsum_ci.o cs_droptol_ci.o cs_dropzeros_ci.o cs_dupl_ci.o \
+ cs_entry_ci.o cs_etree_ci.o cs_fkeep_ci.o cs_gaxpy_ci.o cs_happly_ci.o \
+ cs_house_ci.o cs_ipvec_ci.o cs_lsolve_ci.o cs_ltsolve_ci.o cs_lu_ci.o \
+ cs_lusol_ci.o cs_util_ci.o cs_multiply_ci.o cs_permute_ci.o cs_pinv_ci.o \
+ cs_post_ci.o cs_pvec_ci.o cs_qr_ci.o cs_qrsol_ci.o cs_scatter_ci.o \
+ cs_schol_ci.o cs_sqr_ci.o cs_symperm_ci.o cs_tdfs_ci.o cs_malloc_ci.o \
+ cs_transpose_ci.o cs_compress_ci.o cs_usolve_ci.o cs_utsolve_ci.o \
+ cs_scc_ci.o cs_maxtrans_ci.o cs_dmperm_ci.o cs_updown_ci.o cs_print_ci.o \
+ cs_norm_ci.o cs_load_ci.o cs_dfs_ci.o cs_reach_ci.o cs_spsolve_ci.o \
+ cs_leaf_ci.o cs_ereach_ci.o cs_randperm_ci.o
+
+CS_CL_OBJ = cs_add_cl.o cs_amd_cl.o cs_chol_cl.o cs_cholsol_cl.o cs_counts_cl.o \
+ cs_cumsum_cl.o cs_droptol_cl.o cs_dropzeros_cl.o cs_dupl_cl.o \
+ cs_entry_cl.o cs_etree_cl.o cs_fkeep_cl.o cs_gaxpy_cl.o cs_happly_cl.o \
+ cs_house_cl.o cs_ipvec_cl.o cs_lsolve_cl.o cs_ltsolve_cl.o cs_lu_cl.o \
+ cs_lusol_cl.o cs_util_cl.o cs_multiply_cl.o cs_permute_cl.o cs_pinv_cl.o \
+ cs_post_cl.o cs_pvec_cl.o cs_qr_cl.o cs_qrsol_cl.o cs_scatter_cl.o \
+ cs_schol_cl.o cs_sqr_cl.o cs_symperm_cl.o cs_tdfs_cl.o cs_malloc_cl.o \
+ cs_transpose_cl.o cs_compress_cl.o cs_usolve_cl.o cs_utsolve_cl.o \
+ cs_scc_cl.o cs_maxtrans_cl.o cs_dmperm_cl.o cs_updown_cl.o cs_print_cl.o \
+ cs_norm_cl.o cs_load_cl.o cs_dfs_cl.o cs_reach_cl.o cs_spsolve_cl.o \
+ cs_leaf_cl.o cs_ereach_cl.o cs_randperm_cl.o
+
+CS = cs_convert.o $(CS_DI_OBJ) $(CS_DL_OBJ) $(CS_CI_OBJ) $(CS_CL_OBJ)
+
+$(CS): ../Include/cs.h Makefile
+
+cs_convert.o: ../Source/cs_convert.c
+ $(CC) $(CFLAGS) $(I) -c $< -o $@
+
+%_di.o : ../Source/%.c
+ $(CC) $(CFLAGS) $(I) -c $< -o $@
+
+%_dl.o : ../Source/%.c
+ $(CC) $(CFLAGS) $(I) -DCS_LONG -c $< -o $@
+
+%_ci.o : ../Source/%.c
+ $(CC) $(CFLAGS) $(I) -DCS_COMPLEX -c $< -o $@
+
+%_cl.o : ../Source/%.c
+ $(CC) $(CFLAGS) $(I) -DCS_LONG -DCS_COMPLEX -c $< -o $@
+
+libcxsparse.a: $(CS)
+ $(AR) libcxsparse.a $(CS)
+ $(RANLIB) libcxsparse.a
+
+clean:
+ rm -f *.o
+
+purge: distclean
+
+distclean: clean
+ rm -f *.a
diff --git a/CXSparse_newfiles/MATLAB/CSparse/Contents.m b/CXSparse_newfiles/MATLAB/CSparse/Contents.m
new file mode 100644
index 0000000..4af6293
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/Contents.m
@@ -0,0 +1,54 @@
+% CXSparse: a Concise Sparse matrix Package.
+%
+% Matrices used in CXSparse must in general be either sparse matrices
+% or dense vectors. Ordering methods can accept any sparse matrix.
+% CXsparse allows for complex matrices (CSparse does not).
+%
+% cs_add - sparse matrix addition.
+% cs_amd - approximate minimum degree ordering.
+% cs_chol - sparse Cholesky factorization.
+% cs_cholsol - solve A*x=b using a sparse Cholesky factorization.
+% cs_counts - column counts for sparse Cholesky factor L.
+% cs_dmperm - maximum matching or Dulmage-Mendelsohn permutation.
+% cs_dmsol - x=A\b using the coarse Dulmage-Mendelsohn decomposition.
+% cs_dmspy - plot the Dulmage-Mendelsohn decomposition of a matrix.
+% cs_droptol - remove small entries from a sparse matrix.
+% cs_esep - find an edge separator of a symmetric matrix A
+% cs_etree - elimination tree of A or A'*A.
+% cs_gaxpy - sparse matrix times vector.
+% cs_lsolve - solve a sparse lower triangular system L*x=b.
+% cs_ltsolve - solve a sparse upper triangular system L'*x=b.
+% cs_lu - sparse LU factorization, with fill-reducing ordering.
+% cs_lusol - solve Ax=b using LU factorization.
+% cs_make - compiles CXSparse for use in MATLAB.
+% cs_multiply - sparse matrix multiply.
+% cs_nd - generalized nested dissection ordering.
+% cs_nsep - find a node separator of a symmetric matrix A.
+% cs_permute - permute a sparse matrix.
+% cs_print - print the contents of a sparse matrix.
+% cs_qr - sparse QR factorization (Householder-based).
+% cs_qleft - apply Householder vectors on the left.
+% cs_qright - apply Householder vectors on the right.
+% cs_qrsol - solve a sparse least-squares problem.
+% cs_randperm - random permutation.
+% cs_sep - convert an edge separator into a node separator.
+% cs_scc - strongly-connected components of a square sparse matrix.
+% cs_scc2 - cs_scc, or connected components of a bipartite graph.
+% cs_sparse - convert a triplet form into a sparse matrix.
+% cs_sqr - symbolic sparse QR factorization.
+% cs_symperm - symmetric permutation of a symmetric matrix.
+% cs_transpose - transpose a sparse matrix.
+% cs_updown - rank-1 update/downdate of a sparse Cholesky factorization.
+% cs_usolve - solve a sparse upper triangular system U*x=b.
+% cs_utsolve - solve a sparse lower triangular system U'*x=b.
+% cspy - plot a matrix in color.
+% ccspy - plot the connected components of a matrix.
+
+% Example:
+% help cs_add
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+% helper function:
+% cs_must_compile - return 1 if source code f must be compiled, 0 otherwise
diff --git a/CXSparse_newfiles/MATLAB/CSparse/Makefile b/CXSparse_newfiles/MATLAB/CSparse/Makefile
new file mode 100644
index 0000000..830e630
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/Makefile
@@ -0,0 +1,171 @@
+include ../../../UFconfig/UFconfig.mk
+
+MX = $(MEX) -DCS_LONG
+AR = ar cr
+RANLIB = ranlib
+
+I = -I../../Include -I../../../UFconfig
+
+all: mexcsparse.a cs_mex.h
+ $(MX) cs_thumb_mex.c $(I) mexcsparse.a -output cs_thumb
+ $(MX) cs_print_mex.c $(I) mexcsparse.a -output cs_print
+ $(MX) cs_updown_mex.c $(I) mexcsparse.a -output cs_updown
+ $(MX) cs_gaxpy_mex.c $(I) mexcsparse.a -output cs_gaxpy
+ $(MX) cs_transpose_mex.c $(I) mexcsparse.a -output cs_transpose
+ $(MX) cs_sparse_mex.c $(I) mexcsparse.a -output cs_sparse
+ $(MX) cs_multiply_mex.c $(I) mexcsparse.a -output cs_multiply
+ $(MX) cs_add_mex.c $(I) mexcsparse.a -output cs_add
+ $(MX) cs_permute_mex.c $(I) mexcsparse.a -output cs_permute
+ $(MX) cs_symperm_mex.c $(I) mexcsparse.a -output cs_symperm
+ $(MX) cs_lsolve_mex.c $(I) mexcsparse.a -output cs_lsolve
+ $(MX) cs_ltsolve_mex.c $(I) mexcsparse.a -output cs_ltsolve
+ $(MX) cs_usolve_mex.c $(I) mexcsparse.a -output cs_usolve
+ $(MX) cs_utsolve_mex.c $(I) mexcsparse.a -output cs_utsolve
+ $(MX) cs_chol_mex.c $(I) mexcsparse.a -output cs_chol
+ $(MX) cs_etree_mex.c $(I) mexcsparse.a -output cs_etree
+ $(MX) cs_counts_mex.c $(I) mexcsparse.a -output cs_counts
+ $(MX) cs_qr_mex.c $(I) mexcsparse.a -output cs_qr
+ $(MX) cs_amd_mex.c $(I) mexcsparse.a -output cs_amd
+ $(MX) cs_lu_mex.c $(I) mexcsparse.a -output cs_lu
+ $(MX) cs_cholsol_mex.c $(I) mexcsparse.a -output cs_cholsol
+ $(MX) cs_lusol_mex.c $(I) mexcsparse.a -output cs_lusol
+ $(MX) cs_droptol_mex.c $(I) mexcsparse.a -output cs_droptol
+ $(MX) cs_qrsol_mex.c $(I) mexcsparse.a -output cs_qrsol
+ $(MX) cs_dmperm_mex.c $(I) mexcsparse.a -output cs_dmperm
+ $(MX) cs_scc_mex.c $(I) mexcsparse.a -output cs_scc
+ $(MX) cs_sqr_mex.c $(I) mexcsparse.a -output cs_sqr
+ $(MX) cs_randperm_mex.c $(I) mexcsparse.a -output cs_randperm
+
+CSD = cs_mex.o \
+ cs_amd.o \
+ cs_chol.o \
+ cs_counts.o \
+ cs_cumsum.o \
+ cs_fkeep.o \
+ cs_dfs.o \
+ cs_dmperm.o \
+ cs_droptol.o \
+ cs_dropzeros.o \
+ cs_dupl.o \
+ cs_entry.o \
+ cs_etree.o \
+ cs_gaxpy.o \
+ cs_ipvec.o \
+ cs_lsolve.o \
+ cs_ltsolve.o \
+ cs_lu.o \
+ cs_maxtrans.o \
+ cs_util.o \
+ cs_malloc.o \
+ cs_multiply.o \
+ cs_add.o \
+ cs_scatter.o \
+ cs_permute.o \
+ cs_pinv.o \
+ cs_post.o \
+ cs_tdfs.o \
+ cs_pvec.o \
+ cs_qr.o \
+ cs_happly.o \
+ cs_house.o \
+ cs_schol.o \
+ cs_scc.o \
+ cs_sqr.o \
+ cs_symperm.o \
+ cs_transpose.o \
+ cs_compress.o \
+ cs_usolve.o \
+ cs_utsolve.o \
+ cs_cholsol.o \
+ cs_lusol.o \
+ cs_qrsol.o \
+ cs_updown.o \
+ cs_norm.o \
+ cs_print.o \
+ cs_load.o \
+ cs_spsolve.o \
+ cs_reach.o \
+ cs_ereach.o \
+ cs_leaf.o \
+ cs_randperm.o
+
+CSC = \
+ cs_cl_amd.o \
+ cs_cl_chol.o \
+ cs_cl_counts.o \
+ cs_cl_cumsum.o \
+ cs_cl_fkeep.o \
+ cs_cl_dfs.o \
+ cs_cl_dmperm.o \
+ cs_cl_droptol.o \
+ cs_cl_dropzeros.o \
+ cs_cl_dupl.o \
+ cs_cl_entry.o \
+ cs_cl_etree.o \
+ cs_cl_gaxpy.o \
+ cs_cl_ipvec.o \
+ cs_cl_lsolve.o \
+ cs_cl_ltsolve.o \
+ cs_cl_lu.o \
+ cs_cl_maxtrans.o \
+ cs_cl_util.o \
+ cs_cl_malloc.o \
+ cs_cl_multiply.o \
+ cs_cl_add.o \
+ cs_cl_scatter.o \
+ cs_cl_permute.o \
+ cs_cl_pinv.o \
+ cs_cl_post.o \
+ cs_cl_tdfs.o \
+ cs_cl_pvec.o \
+ cs_cl_qr.o \
+ cs_cl_happly.o \
+ cs_cl_house.o \
+ cs_cl_schol.o \
+ cs_cl_scc.o \
+ cs_cl_sqr.o \
+ cs_cl_symperm.o \
+ cs_cl_transpose.o \
+ cs_cl_compress.o \
+ cs_cl_usolve.o \
+ cs_cl_utsolve.o \
+ cs_cl_cholsol.o \
+ cs_cl_lusol.o \
+ cs_cl_qrsol.o \
+ cs_cl_updown.o \
+ cs_cl_norm.o \
+ cs_cl_print.o \
+ cs_cl_load.o \
+ cs_cl_spsolve.o \
+ cs_cl_reach.o \
+ cs_cl_ereach.o \
+ cs_cl_leaf.o \
+ cs_cl_randperm.o
+
+CS = $(CSD) $(CSC)
+
+mexcsparse.a: $(CS)
+ $(AR) mexcsparse.a $(CS)
+ $(RANLIB) mexcsparse.a
+
+$(CS): ../../Include/cs.h
+
+
+cs_mex.o: cs_mex.c cs_mex.h
+ $(MX) -c $(I) $<
+
+cs_cl_%.o: ../../Source/cs_%.c
+ cp -f $< cs_cl_$*.c
+ $(MX) -DCS_COMPLEX -c $(I) cs_cl_$*.c
+
+cs_%.o: ../../Source/cs_%.c
+ $(MX) -c $(I) $<
+
+
+clean:
+ - rm -f *.o
+
+distclean: clean
+ - rm -f *.mex* *.dll *.a cs_cl_*.c
+
+purge: distclean
diff --git a/CXSparse_newfiles/MATLAB/CSparse/README.txt b/CXSparse_newfiles/MATLAB/CSparse/README.txt
new file mode 100644
index 0000000..e3a5aa1
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/README.txt
@@ -0,0 +1 @@
+MATLAB interface for CXSparse. See Contents.m for details.
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_add_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_add_mex.c
new file mode 100644
index 0000000..b8f4e70
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_add_mex.c
@@ -0,0 +1,67 @@
+#include "cs_mex.h"
+/* cs_add: sparse matrix addition */
+
+#ifndef NCOMPLEX
+static cs_complex_t get_complex (const mxArray *a)
+{
+ cs_complex_t s = mxGetScalar (a) ;
+ if (mxIsComplex (a))
+ {
+ double *z = mxGetPi (a) ;
+ s += I * z [0] ;
+ }
+ return (s) ;
+}
+#endif
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin < 2 || nargin > 4)
+ {
+ mexErrMsgTxt ("Usage: C = cs_add(A,B,alpha,beta)") ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])
+ || (nargin > 2 && mxIsComplex (pargin [2]))
+ || (nargin > 3 && mxIsComplex (pargin [3])))
+ {
+#ifndef NCOMPLEX
+ cs_complex_t alpha, beta ;
+ cs_cl Amatrix, Bmatrix, *A, *B, *C, *D ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ B = cs_cl_mex_get_sparse (&Bmatrix, 0, pargin [1]) ; /* get B */
+ alpha = (nargin < 3) ? 1 : get_complex (pargin [2]) ; /* get alpha */
+ beta = (nargin < 4) ? 1 : get_complex (pargin [3]) ; /* get beta */
+ C = cs_cl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */
+ cs_cl_dropzeros (C) ; /* drop zeros */
+ D = cs_cl_transpose (C, 1) ; /* sort result via double transpose */
+ cs_cl_spfree (C) ;
+ C = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ double alpha, beta ;
+ cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */
+ alpha = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; /* get alpha */
+ beta = (nargin < 4) ? 1 : mxGetScalar (pargin [3]) ; /* get beta */
+ C = cs_dl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */
+ cs_dl_dropzeros (C) ; /* drop zeros */
+ D = cs_dl_transpose (C, 1) ; /* sort result via double transpose */
+ cs_dl_spfree (C) ;
+ C = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_amd_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_amd_mex.c
new file mode 100644
index 0000000..7d8ff09
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_amd_mex.c
@@ -0,0 +1,23 @@
+#include "cs_mex.h"
+/* cs_amd: approximate minimum degree ordering */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl Amatrix, *A ;
+ CS_INT *P, order ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: p = cs_amd(A,order)") ;
+ }
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */
+ order = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; /* get ordering */
+ order = CS_MAX (order, 1) ;
+ order = CS_MIN (order, 3) ;
+ P = cs_dl_amd (order, A) ; /* min. degree ordering */
+ pargout [0] = cs_dl_mex_put_int (P, A->n, 1, 1) ; /* return P */
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_chol_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_chol_mex.c
new file mode 100644
index 0000000..e3b1c5e
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_chol_mex.c
@@ -0,0 +1,58 @@
+#include "cs_mex.h"
+/* cs_chol: sparse Cholesky factorization */
+void mexFunction (int nargout, mxArray *pargout [ ], int nargin,
+ const mxArray *pargin [ ])
+{
+ CS_INT order, n, drop, *p ;
+ if (nargout > 2 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: [L,p] = cs_chol(A,drop)") ;
+ }
+ drop = (nargin == 1) ? 1 : mxGetScalar (pargin [1]) ;
+ order = (nargout > 1) ? 1 : 0 ; /* determine ordering */
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A ;
+ cs_cls *S ;
+ cs_cln *N ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */
+ n = A->n ;
+ S = cs_cl_schol (order, A) ; /* symbolic Cholesky */
+ N = cs_cl_chol (A, S) ; /* numeric Cholesky */
+ if (!N) mexErrMsgTxt ("cs_chol failed: not positive definite\n") ;
+ cs_free (A->x) ;
+ if (drop) cs_cl_dropzeros (N->L) ; /* drop zeros if requested*/
+ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return L */
+ if (nargout > 1)
+ {
+ p = cs_cl_pinv (S->pinv, n) ; /* p=pinv' */
+ pargout [1] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
+ }
+ cs_cl_nfree (N) ;
+ cs_cl_sfree (S) ;
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A ;
+ cs_dls *S ;
+ cs_dln *N ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ n = A->n ;
+ S = cs_dl_schol (order, A) ; /* symbolic Cholesky */
+ N = cs_dl_chol (A, S) ; /* numeric Cholesky */
+ if (!N) mexErrMsgTxt ("cs_chol failed: not positive definite\n") ;
+ if (drop) cs_dl_dropzeros (N->L) ; /* drop zeros if requested*/
+ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return L */
+ if (nargout > 1)
+ {
+ p = cs_dl_pinv (S->pinv, n) ; /* p=pinv' */
+ pargout [1] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
+ }
+ cs_dl_nfree (N) ;
+ cs_dl_sfree (S) ;
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_cholsol_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_cholsol_mex.c
new file mode 100644
index 0000000..08b9f40
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_cholsol_mex.c
@@ -0,0 +1,48 @@
+#include "cs_mex.h"
+/* cs_cholsol: solve A*x=b using a sparse Cholesky factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT order ;
+ if (nargout > 1 || nargin < 2 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: x = cs_cholsol(A,b,order)") ;
+ }
+ order = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ;
+ order = CS_MAX (order, 0) ;
+ order = CS_MIN (order, 3) ;
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl *A, Amatrix ;
+ cs_complex_t *x ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */
+ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* x = b */
+ if (!cs_cl_cholsol (order, A, x)) /* x = A\x */
+ {
+ mexErrMsgTxt ("A not positive definite") ;
+ }
+ cs_free (A->x) ;
+ pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl *A, Amatrix ;
+ double *x, *b ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ b = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */
+ if (!cs_dl_cholsol (order, A, x)) /* x = A\x */
+ {
+ mexErrMsgTxt ("A not positive definite") ;
+ }
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_counts_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_counts_mex.c
new file mode 100644
index 0000000..60e680b
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_counts_mex.c
@@ -0,0 +1,32 @@
+#include "cs_mex.h"
+/* cs_counts: column counts for sparse Cholesky factor L. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl Amatrix, *A ;
+ CS_INT n, ata, *parent, *post, *c ;
+ char mode [20] ;
+ if (nargout > 2 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: c = cs_counts(A,mode)") ;
+ }
+ ata = 0 ; /* get mode */
+ if (nargin > 1 && mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], mode, 8) ;
+ ata = (mode [0] == 'c') ;
+ }
+ A = cs_dl_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */
+ n = A->n ;
+ parent = cs_dl_etree (A, ata) ; /* compute etree */
+ post = cs_dl_post (parent, n) ; /* postorder the etree*/
+ c = cs_dl_counts (A, parent, post, ata) ; /* get column counts */
+ pargout [0] = cs_dl_mex_put_int (c, n, 0, 1) ; /* return counts */
+ cs_free (parent) ;
+ cs_free (post) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_dmperm_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_dmperm_mex.c
new file mode 100644
index 0000000..7575493
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_dmperm_mex.c
@@ -0,0 +1,41 @@
+#include "cs_mex.h"
+/* cs_dmperm: maximum matching or Dulmage-Mendelsohn permutation. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double seed ;
+ cs_dl *A, Amatrix ;
+ cs_dld *D ;
+ CS_INT m, n, *jmatch, iseed ;
+ if (nargin < 1 || nargin > 2 || nargout > 6)
+ {
+ mexErrMsgTxt ("Usage: [p,q,r,s,cc,rr] = cs_dmperm (A,seed)") ;
+ }
+ seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 0 ; /* get seed */
+ iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */
+ n = A->n ;
+ m = A->m ;
+ if (nargout <= 1)
+ {
+ jmatch = cs_dl_maxtrans (A, iseed) ; /* max. matching */
+ pargout [0] = cs_dl_mex_put_int (jmatch+m, n, 1, 0) ; /* return imatch */
+ cs_free (jmatch) ;
+ }
+ else
+ {
+ D = cs_dl_dmperm (A, iseed) ; /* Dulmage-Mendelsohn decomposition */
+ pargout [0] = cs_dl_mex_put_int (D->p, m, 1, 0) ;
+ pargout [1] = cs_dl_mex_put_int (D->q, n, 1, 0) ;
+ pargout [2] = cs_dl_mex_put_int (D->r, D->nb+1, 1, 0) ;
+ pargout [3] = cs_dl_mex_put_int (D->s, D->nb+1, 1, 0) ;
+ pargout [4] = cs_dl_mex_put_int (D->cc, 5, 1, 0) ;
+ pargout [5] = cs_dl_mex_put_int (D->rr, 5, 1, 0) ;
+ cs_dl_dfree (D) ;
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_droptol_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_droptol_mex.c
new file mode 100644
index 0000000..29117f0
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_droptol_mex.c
@@ -0,0 +1,45 @@
+#include "cs_mex.h"
+/* cs_droptol: remove small entries from A */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT j, k ;
+ double tol ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_droptol(A,tol)") ;
+ }
+ tol = mxGetScalar (pargin [1]) ; /* get tol */
+
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *C, *A ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ C = cs_cl_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */
+ for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ;
+ for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ;
+ for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ;
+ cs_cl_droptol (C, tol) ; /* drop from C */
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *C, *A ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ C = cs_dl_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */
+ for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ;
+ for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ;
+ for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ;
+ cs_dl_droptol (C, tol) ; /* drop from C */
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_esep.m b/CXSparse_newfiles/MATLAB/CSparse/cs_esep.m
new file mode 100644
index 0000000..8bb7d32
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_esep.m
@@ -0,0 +1,23 @@
+function [a,b] = cs_esep (A)
+%CS_ESEP find an edge separator of a symmetric matrix A
+% [a,b] = cs_esep(A) finds a edge separator s that splits the graph of A
+% into two parts a and b of roughly equal size. The edge separator is the
+% set of entries in A(a,b).
+%
+% Example:
+% Prob = UFget ('HB/bcsstk01') ; A = Prob.A ;
+% [a,b] = cs_esep (A) ;
+% cspy (A (a,b)) ;
+%
+% See also CS_NSEP, CS_SEP, CS_ND, SYMRCM.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (~isreal (A))
+ A = spones (A) ;
+end
+p = symrcm (A) ;
+n2 = fix (size(A,1)/2) ;
+a = p (1:n2) ;
+b = p (n2+1:end) ;
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_etree_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_etree_mex.c
new file mode 100644
index 0000000..99753fd
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_etree_mex.c
@@ -0,0 +1,34 @@
+#include "cs_mex.h"
+/* cs_etree: elimination tree of A or A'*A */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl Amatrix, *A ;
+ CS_INT n, *parent, *post ;
+ int ata ;
+ char mode [20] ;
+ if (nargout > 2 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: [parent,post] = cs_etree(A,mode)") ;
+ }
+ ata = 0 ; /* get mode */
+ if (nargin > 1 && mxIsChar (pargin [1]))
+ {
+ mxGetString (pargin [1], mode, 8) ;
+ ata = (mode [0] == 'c') ;
+ }
+ A = cs_dl_mex_get_sparse (&Amatrix, !ata, 0, pargin [0]) ; /* get A */
+ n = A->n ;
+ parent = cs_dl_etree (A, ata) ; /* compute etree */
+ if (nargout > 1)
+ {
+ post = cs_dl_post (parent, n) ; /* postorder the etree*/
+ pargout [1] = cs_dl_mex_put_int (post, n, 1, 1) ; /* return post */
+ }
+ pargout [0] = cs_dl_mex_put_int (parent, n, 1, 1) ; /* return parent */
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_gaxpy_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_gaxpy_mex.c
new file mode 100644
index 0000000..13dc30a
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_gaxpy_mex.c
@@ -0,0 +1,42 @@
+#include "cs_mex.h"
+/* z = cs_gaxpy (A,x,y) computes z = A*x+y */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: z = cs_gaxpy(A,x,y)") ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])
+ || mxIsComplex (pargin [2]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A ;
+ cs_complex_t *x, *z ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ;/* get A */
+ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* get x */
+ z = cs_cl_mex_get_double (A->m, pargin [2]) ; /* z = y */
+ cs_cl_gaxpy (A, x, z) ; /* z = z + A*x */
+ cs_free (x) ;
+ cs_free (A->x) ;
+ pargout [0] = cs_cl_mex_put_double (A->m, z) ; /* return z */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A ;
+ double *x, *y, *z ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ;/* get A */
+ x = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get x */
+ y = cs_dl_mex_get_double (A->m, pargin [2]) ; /* get y */
+ z = cs_dl_mex_put_double (A->m, y, &(pargout [0])) ; /* z = y */
+ cs_dl_gaxpy (A, x, z) ; /* z = z + A*x */
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_lsolve_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_lsolve_mex.c
new file mode 100644
index 0000000..0153d6a
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_lsolve_mex.c
@@ -0,0 +1,92 @@
+#include "cs_mex.h"
+/* cs_lsolve: x=L\b. L must be sparse and lower triangular. b must be a
+ * full or sparse vector. x is full or sparse, depending on b.
+ *
+ * Time taken is O(flop count), which may be less than n if b is sparse,
+ * depending on L and b.
+ *
+ * This function works with MATLAB 7.2, but is not perfectly compatible with
+ * the requirements of a MATLAB mexFunction when b is sparse. X is returned
+ * as an unsorted sparse vector. Also, this mexFunction temporarily modifies
+ * its input, L, by modifying L->p (in the cs_dfs function) and then restoring
+ * it. This could be corrected by creating a copy of L->p
+ * (see cs_dmperm_mex.c), but this would take O(n) time, destroying the
+ * O(flop count) time complexity of this function.
+ *
+ * Note that b cannot be sparse complex. This function does not support
+ * sparse complex L and b because the sparse x=L\b only accesses part of the
+ * matrix L. Converting L from a MATLAB complex matrix to a CXSparse complex
+ * matrix requires all of L to be accessed, defeating the purpose of this
+ * function.
+ *
+ * L can be sparse complex, but in that case b must be full real or complex,
+ * not sparse.
+ */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT top, nz, p, *xi, n ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_lsolve(L,b)") ;
+ }
+ if (mxIsSparse (pargin [1]))
+ {
+ cs_dl Lmatrix, Bmatrix, *L, *B, *X ;
+ double *x ;
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+ mexErrMsgTxt ("sparse complex case not supported") ;
+ }
+ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;/* get L */
+ n = L->n ;
+ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b*/
+ cs_mex_check (0, n, 1, 0, 1, 1, pargin [1]) ;
+ xi = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* get workspace */
+ x = cs_dl_malloc (n, sizeof (double)) ;
+ top = cs_dl_spsolve (L, B, 0, xi, x, NULL, 1) ; /* x = L\b */
+ X = cs_dl_spalloc (n, 1, n-top, 1, 0) ; /* create sparse x*/
+ X->p [0] = 0 ;
+ nz = 0 ;
+ for (p = top ; p < n ; p++)
+ {
+ X->i [nz] = xi [p] ;
+ X->x [nz++] = x [xi [p]] ;
+ }
+ X->p [1] = nz ;
+ pargout [0] = cs_dl_mex_put_sparse (&X) ;
+ cs_free (x) ;
+ cs_free (xi) ;
+ }
+ else if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Lmatrix, *L ;
+ cs_complex_t *x ;
+ L = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ; /* get L */
+ n = L->n ;
+ x = cs_cl_mex_get_double (n, pargin [1]) ; /* x = b */
+ cs_cl_lsolve (L, x) ; /* x = L\x */
+ cs_free (L->x) ;
+ pargout [0] = cs_cl_mex_put_double (n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Lmatrix, *L ;
+ double *x, *b ;
+ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */
+ n = L->n ;
+ b = cs_dl_mex_get_double (n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (n, b, &(pargout [0])) ; /* x = b */
+ cs_dl_lsolve (L, x) ; /* x = L\x */
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_ltsolve_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_ltsolve_mex.c
new file mode 100644
index 0000000..63d4141
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_ltsolve_mex.c
@@ -0,0 +1,38 @@
+#include "cs_mex.h"
+/* cs_ltsolve: solve an upper triangular system L'*x=b */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_ltsolve(L,b)") ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Lmatrix, *L ;
+ cs_complex_t *x ;
+ L = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ; /* get L */
+ x = cs_cl_mex_get_double (L->n, pargin [1]) ; /* x = b */
+ cs_cl_ltsolve (L, x) ; /* x = L'\x */
+ cs_free (L->x) ;
+ pargout [0] = cs_cl_mex_put_double (L->n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Lmatrix, *L ;
+ double *x, *b ;
+ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */
+ b = cs_dl_mex_get_double (L->n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (L->n, b, &(pargout [0])) ; /* x = b */
+ cs_dl_ltsolve (L, x) ; /* x = L'\x */
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_lu_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_lu_mex.c
new file mode 100644
index 0000000..31a5a59
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_lu_mex.c
@@ -0,0 +1,90 @@
+#include "cs_mex.h"
+/* cs_lu: sparse LU factorization, with optional fill-reducing ordering */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT n, order, *p ;
+ double tol ;
+ if (nargout > 4 || nargin > 3 || nargin < 1)
+ {
+ mexErrMsgTxt ("Usage: [L,U,p,q] = cs_lu (A,tol)") ;
+ }
+ if (nargin == 2) /* determine tol and ordering */
+ {
+ tol = mxGetScalar (pargin [1]) ;
+ order = (nargout == 4) ? 1 : 0 ; /* amd (A+A'), or natural */
+ }
+ else
+ {
+ tol = 1 ;
+ order = (nargout == 4) ? 2 : 0 ; /* amd(S'*S) w/dense rows or I */
+ }
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cls *S ;
+ cs_cln *N ;
+ cs_cl Amatrix, *A, *D ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */
+ n = A->n ;
+ S = cs_cl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */
+ N = cs_cl_lu (A, S, tol) ; /* numeric factorization */
+ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ;
+ cs_cl_free (A->x) ; /* complex copy no longer needed */
+ cs_cl_dropzeros (N->L) ; /* drop zeros from L and sort it */
+ D = cs_cl_transpose (N->L, 1) ;
+ cs_cl_spfree (N->L) ;
+ N->L = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ cs_cl_dropzeros (N->U) ; /* drop zeros from U and sort it */
+ D = cs_cl_transpose (N->U, 1) ;
+ cs_cl_spfree (N->U) ;
+ N->U = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ p = cs_cl_pinv (N->pinv, n) ; /* p=pinv' */
+ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return L */
+ pargout [1] = cs_cl_mex_put_sparse (&(N->U)) ; /* return U */
+ pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
+ /* return Q */
+ if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ;
+ cs_cl_nfree (N) ;
+ cs_cl_sfree (S) ;
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dls *S ;
+ cs_dln *N ;
+ cs_dl Amatrix, *A, *D ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ n = A->n ;
+ S = cs_dl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */
+ N = cs_dl_lu (A, S, tol) ; /* numeric factorization */
+ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ;
+ cs_dl_dropzeros (N->L) ; /* drop zeros from L and sort it */
+ D = cs_dl_transpose (N->L, 1) ;
+ cs_dl_spfree (N->L) ;
+ N->L = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ cs_dl_dropzeros (N->U) ; /* drop zeros from U and sort it */
+ D = cs_dl_transpose (N->U, 1) ;
+ cs_dl_spfree (N->U) ;
+ N->U = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ p = cs_dl_pinv (N->pinv, n) ; /* p=pinv' */
+ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return L */
+ pargout [1] = cs_dl_mex_put_sparse (&(N->U)) ; /* return U */
+ pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
+ /* return Q */
+ if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ;
+ cs_dl_nfree (N) ;
+ cs_dl_sfree (S) ;
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_lusol_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_lusol_mex.c
new file mode 100644
index 0000000..be34770
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_lusol_mex.c
@@ -0,0 +1,61 @@
+#include "cs_mex.h"
+/* cs_lusol: solve A*x=b using a sparse LU factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double tol ;
+ CS_INT order ;
+ if (nargout > 1 || nargin < 2 || nargin > 4)
+ {
+ mexErrMsgTxt ("Usage: x = cs_lusol(A,b,order,tol)") ;
+ }
+ order = (nargin < 3) ? 2 : mxGetScalar (pargin [2]) ;
+ order = CS_MAX (order, 0) ;
+ order = CS_MIN (order, 3) ;
+ if (nargin == 2)
+ {
+ tol = 1 ; /* normal partial pivoting */
+ }
+ else if (nargin == 3)
+ {
+ tol = (order == 1) ? 0.001 : 1 ; /* tol = 0.001 for amd(A+A') */
+ }
+ else
+ {
+ tol = mxGetScalar (pargin [3]) ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl *A, Amatrix ;
+ cs_complex_t *x ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */
+ x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* x = b */
+ if (!cs_cl_lusol (order, A, x, tol)) /* x = A\x */
+ {
+ mexErrMsgTxt ("failed (singular or out of memory)") ;
+ }
+ cs_cl_free (A->x) ; /* complex copy no longer needed */
+ pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl *A, Amatrix ;
+ double *x, *b ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
+ b = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */
+ if (!cs_dl_lusol (order, A, x, tol)) /* x = A\x */
+ {
+ mexErrMsgTxt ("failed (singular or out of memory)") ;
+ }
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_make.m b/CXSparse_newfiles/MATLAB/CSparse/cs_make.m
new file mode 100644
index 0000000..982403a
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_make.m
@@ -0,0 +1,86 @@
+function [objfiles, timestamp] = cs_make (f, docomplex)
+%CS_MAKE compiles CXSparse for use in MATLAB.
+% Usage:
+% cs_make
+% [objfiles, timestamp] = cs_make (f, docomplex)
+%
+% With no input arguments, or with f=0, only those files needing to be
+% compiled are compiled (like the Unix/Linux/GNU "make" command, but not
+% requiring "make"). If f is a nonzero number, all files are compiled.
+% If f is a string, only that mexFunction is compiled. For example,
+% cs_make ('cs_add') just compiles the cs_add mexFunction. This option is
+% useful when developing a single new mexFunction. This function can only be
+% used if the current directory is CXSparse/MATLAB/CSparse. Returns a list of
+% the object files in CXSparse, and the latest modification time of any source
+% codes.
+%
+% NOTE: if your compiler does not support the ANSI C99 complex type (most
+% notably Microsoft Windows), the CXSparse mexFunctions will not support
+% complex sparse matrices. The complex case is not attempted if docomplex is
+% zero.
+%
+% To add a new function and its MATLAB mexFunction to CXSparse:
+%
+% (1) Create a source code file CXSparse/Source/cs_mynewfunc.c.
+% (2) Create a help file, CXSparse/MATLAB/CSparse/cs_mynewfunc.m.
+% This is very useful, but not strictly required.
+% (3) Add the prototype of cs_mynewfunc to CXSparse/Include/cs.h.
+% (4) Create its MATLAB mexFunction, CXSparse/MATLAB/cs_mynewfunc_mex.c.
+% (5) Edit cs_make.m, and add 'cs_mynewfunc' to the 'cs' and 'csm' lists.
+% (6) Type 'cs_make' in the CXSparse/MATLAB/CSparse directory.
+% If all goes well, your new function is ready for use in MATLAB.
+%
+% (7) Optionally add 'cs_mynewfunc' to CXSparse/Source/Makefile
+% and CXSparse/MATLAB/CSparse/Makefile, if you want to use the
+% Unix/Linux/GNU make command instead of cs_make.m. See where
+% 'cs_add' and 'cs_add_mex' appear in those files, and add
+% 'cs_mynewfunc' accordingly.
+% (8) Optionally add 'cs_mynewfunc' to Tcov/Makefile, and add additional
+% test code to cs_test.c, and add MATLAB test code to MATLAB/Test/*.
+%
+% Example:
+% cs_make % compile everything
+% cs_make ('cs_chol') ; % just compile cs_chol mexFunction
+%
+% See also MEX.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 1)
+ f = 0 ;
+end
+if (nargin < 2)
+ docomplex = 1 ;
+end
+
+try
+ % ispc does not appear in MATLAB 5.3
+ pc = ispc ;
+catch
+ % if ispc fails, assume we are on a Windows PC if it's not unix
+ pc = ~isunix ;
+end
+
+if (pc)
+ docomplex = 0 ;
+end
+
+if (docomplex == 0)
+ % do not attempt to compile with complex matrices
+ [objfiles, timestamp] = cs_make_helper (f, 0) ;
+else
+ try
+ % try with complex support
+ [objfiles, timestamp] = cs_make_helper (f, 1) ;
+ catch
+ % oops - that failed, try without complex support
+ fprintf ('retrying without complex matrix support\n') ;
+ [objfiles, timestamp] = cs_make_helper (f, 0) ;
+ end
+end
+
+if (f > 0)
+ fprintf ('CXSparse successfully installed.\n') ;
+end
+
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_mex.c
new file mode 100644
index 0000000..6b09a5f
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_mex.c
@@ -0,0 +1,216 @@
+#include "cs_mex.h"
+/* check MATLAB input argument */
+void cs_mex_check (CS_INT nel, CS_INT m, CS_INT n, int square, int sparse,
+ int values, const mxArray *A)
+{
+ CS_INT nnel, mm = mxGetM (A), nn = mxGetN (A) ;
+#ifdef NCOMPLEX
+ if (values)
+ {
+ if (mxIsComplex (A)) mexErrMsgTxt ("complex matrices not supported") ;
+ }
+#endif
+ if (sparse && !mxIsSparse (A)) mexErrMsgTxt ("matrix must be sparse") ;
+ if (!sparse)
+ {
+ if (mxIsSparse (A)) mexErrMsgTxt ("matrix must be full") ;
+ if (values && !mxIsDouble (A)) mexErrMsgTxt ("matrix must be double") ;
+ }
+ if (nel)
+ {
+ /* check number of elements */
+ nnel = mxGetNumberOfElements (A) ;
+ if (m >= 0 && n >= 0 && m*n != nnel) mexErrMsgTxt ("wrong length") ;
+ }
+ else
+ {
+ /* check row and/or column dimensions */
+ if (m >= 0 && m != mm) mexErrMsgTxt ("wrong dimension") ;
+ if (n >= 0 && n != nn) mexErrMsgTxt ("wrong dimension") ;
+ }
+ if (square && mm != nn) mexErrMsgTxt ("matrix must be square") ;
+}
+
+/* get a real (or pattern) MATLAB sparse matrix and convert to cs_dl */
+cs_dl *cs_dl_mex_get_sparse (cs_dl *A, int square, int values,
+ const mxArray *Amatlab)
+{
+ cs_mex_check (0, -1, -1, square, 1, values, Amatlab) ;
+ A->m = mxGetM (Amatlab) ;
+ A->n = mxGetN (Amatlab) ;
+ A->p = (CS_INT *) mxGetJc (Amatlab) ;
+ A->i = (CS_INT *) mxGetIr (Amatlab) ;
+ A->x = values ? mxGetPr (Amatlab) : NULL ;
+ A->nzmax = mxGetNzmax (Amatlab) ;
+ A->nz = -1 ; /* denotes a compressed-col matrix, instead of triplet */
+ return (A) ;
+}
+
+
+/* return a real sparse matrix to MATLAB */
+mxArray *cs_dl_mex_put_sparse (cs_dl **Ahandle)
+{
+ cs_dl *A ;
+ mxArray *Amatlab ;
+ A = *Ahandle ;
+ if (!A) mexErrMsgTxt ("failed") ;
+ Amatlab = mxCreateSparse (0, 0, 0, mxREAL) ;
+ mxSetM (Amatlab, A->m) ;
+ mxSetN (Amatlab, A->n) ;
+ mxSetNzmax (Amatlab, A->nzmax) ;
+ cs_free (mxGetJc (Amatlab)) ;
+ cs_free (mxGetIr (Amatlab)) ;
+ cs_free (mxGetPr (Amatlab)) ;
+ mxSetJc (Amatlab, (void *) (A->p)) ; /* assign A->p pointer to MATLAB A */
+ mxSetIr (Amatlab, (void *) (A->i)) ;
+ mxSetPr (Amatlab, A->x) ;
+ cs_free (A) ; /* frees A struct only, not A->p, etc */
+ *Ahandle = NULL ;
+ return (Amatlab) ;
+}
+
+/* get a real MATLAB dense column vector */
+double *cs_dl_mex_get_double (CS_INT n, const mxArray *X)
+{
+ cs_mex_check (0, n, 1, 0, 0, 1, X) ;
+ return (mxGetPr (X)) ;
+}
+
+/* return a double vector to MATLAB */
+double *cs_dl_mex_put_double (CS_INT n, const double *b, mxArray **X)
+{
+ double *x ;
+ CS_INT k ;
+ *X = mxCreateDoubleMatrix (n, 1, mxREAL) ; /* create x */
+ x = mxGetPr (*X) ;
+ for (k = 0 ; k < n ; k++) x [k] = b [k] ; /* copy x = b */
+ return (x) ;
+}
+
+/* get a MATLAB flint array and convert to CS_INT */
+CS_INT *cs_dl_mex_get_int (CS_INT n, const mxArray *Imatlab, CS_INT *imax,
+ int lo)
+{
+ double *p ;
+ CS_INT i, k, *C = cs_dl_malloc (n, sizeof (CS_INT)) ;
+ cs_mex_check (1, n, 1, 0, 0, 1, Imatlab) ;
+ if (mxIsComplex (Imatlab))
+ {
+ mexErrMsgTxt ("integer input cannot be complex") ;
+ }
+ p = mxGetPr (Imatlab) ;
+ *imax = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ i = p [k] ;
+ C [k] = i - 1 ;
+ if (i < lo) mexErrMsgTxt ("index out of bounds") ;
+ *imax = CS_MAX (*imax, i) ;
+ }
+ return (C) ;
+}
+
+/* return an CS_INT array to MATLAB as a flint row vector */
+mxArray *cs_dl_mex_put_int (CS_INT *p, CS_INT n, CS_INT offset, int do_free)
+{
+ mxArray *X = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ double *x = mxGetPr (X) ;
+ CS_INT k ;
+ for (k = 0 ; k < n ; k++) x [k] = (p ? p [k] : k) + offset ;
+ if (do_free) cs_free (p) ;
+ return (X) ;
+}
+
+#ifndef NCOMPLEX
+
+/* copy a MATLAB real or complex vector into a cs_cl complex vector */
+static cs_complex_t *cs_cl_get_vector (CS_INT n, CS_INT size,
+ const mxArray *Xmatlab)
+{
+ CS_INT p ;
+ double *X, *Z ;
+ cs_complex_t *Y ;
+ X = mxGetPr (Xmatlab) ;
+ Z = (mxIsComplex (Xmatlab)) ? mxGetPi (Xmatlab) : NULL ;
+ Y = cs_dl_malloc (size, sizeof (cs_complex_t)) ;
+ for (p = 0 ; p < n ; p++)
+ {
+ Y [p] = X [p] + I * (Z ? Z [p] : 0) ;
+ }
+ return (Y) ;
+}
+
+/* get a real or complex MATLAB sparse matrix and convert to cs_cl */
+cs_cl *cs_cl_mex_get_sparse (cs_cl *A, int square, const mxArray *Amatlab)
+{
+ cs_mex_check (0, -1, -1, square, 1, 1, Amatlab) ;
+ A->m = mxGetM (Amatlab) ;
+ A->n = mxGetN (Amatlab) ;
+ A->p = (CS_INT *) mxGetJc (Amatlab) ;
+ A->i = (CS_INT *) mxGetIr (Amatlab) ;
+ A->nzmax = mxGetNzmax (Amatlab) ;
+ A->x = cs_cl_get_vector (A->p [A->n], A->nzmax, Amatlab) ;
+ A->nz = -1 ; /* denotes a compressed-col matrix, instead of triplet */
+ return (A) ;
+}
+
+/* return a complex sparse matrix to MATLAB */
+mxArray *cs_cl_mex_put_sparse (cs_cl **Ahandle)
+{
+ cs_cl *A ;
+ double *x, *z ;
+ mxArray *Amatlab ;
+ CS_INT k ;
+
+ A = *Ahandle ;
+ if (!A) mexErrMsgTxt ("failed") ;
+ Amatlab = mxCreateSparse (0, 0, 0, mxCOMPLEX) ;
+ mxSetM (Amatlab, A->m) ;
+ mxSetN (Amatlab, A->n) ;
+ mxSetNzmax (Amatlab, A->nzmax) ;
+ cs_cl_free (mxGetJc (Amatlab)) ;
+ cs_cl_free (mxGetIr (Amatlab)) ;
+ cs_cl_free (mxGetPr (Amatlab)) ;
+ cs_cl_free (mxGetPi (Amatlab)) ;
+ mxSetJc (Amatlab, (void *) (A->p)) ; /* assign A->p pointer to MATLAB A */
+ mxSetIr (Amatlab, (void *) (A->i)) ;
+ x = cs_dl_malloc (A->nzmax, sizeof (double)) ;
+ z = cs_dl_malloc (A->nzmax, sizeof (double)) ;
+ for (k = 0 ; k < A->nzmax ; k++)
+ {
+ x [k] = creal (A->x [k]) ; /* copy and split numerical values */
+ z [k] = cimag (A->x [k]) ;
+ }
+ cs_cl_free (A->x) ; /* free copy of complex values */
+ mxSetPr (Amatlab, x) ;
+ mxSetPi (Amatlab, z) ;
+ cs_cl_free (A) ; /* frees A struct only, not A->p, etc */
+ *Ahandle = NULL ;
+ return (Amatlab) ;
+}
+
+/* get a real or complex MATLAB dense column vector, and copy to cs_complex_t */
+cs_complex_t *cs_cl_mex_get_double (CS_INT n, const mxArray *X)
+{
+ cs_mex_check (0, n, 1, 0, 0, 1, X) ;
+ return (cs_cl_get_vector (n, n, X)) ;
+}
+
+/* copy a complex vector back to MATLAB and free it */
+mxArray *cs_cl_mex_put_double (CS_INT n, cs_complex_t *b)
+{
+ double *x, *z ;
+ mxArray *X ;
+ CS_INT k ;
+ X = mxCreateDoubleMatrix (n, 1, mxCOMPLEX) ; /* create x */
+ x = mxGetPr (X) ;
+ z = mxGetPi (X) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ x [k] = creal (b [k]) ; /* copy x = b */
+ z [k] = cimag (b [k]) ;
+ }
+ cs_cl_free (b) ;
+ return (X) ;
+}
+#endif
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_mex.h b/CXSparse_newfiles/MATLAB/CSparse/cs_mex.h
new file mode 100644
index 0000000..153a099
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_mex.h
@@ -0,0 +1,22 @@
+#include "cs.h"
+#include "mex.h"
+
+void cs_mex_check (CS_INT nel, CS_INT m, CS_INT n, int square,
+ int sparse, int values, const mxArray *A) ;
+
+CS_INT *cs_dl_mex_get_int (CS_INT n, const mxArray *Imatlab, CS_INT *imax,
+ int lo);
+mxArray *cs_dl_mex_put_int (CS_INT *p, CS_INT n, CS_INT offset, int do_free) ;
+
+double *cs_dl_mex_get_double (CS_INT n, const mxArray *X) ;
+cs_dl *cs_dl_mex_get_sparse (cs_dl *A, int square, int values,
+ const mxArray *Amatlab) ;
+double *cs_dl_mex_put_double (CS_INT n, const double *b, mxArray **X) ;
+mxArray *cs_dl_mex_put_sparse (cs_dl **A) ;
+
+#ifndef NCOMPLEX
+cs_complex_t *cs_cl_mex_get_double (CS_INT n, const mxArray *X) ;
+cs_cl *cs_cl_mex_get_sparse (cs_cl *A, int square, const mxArray *Amatlab) ;
+mxArray *cs_cl_mex_put_double (CS_INT n, cs_complex_t *b) ;
+mxArray *cs_cl_mex_put_sparse (cs_cl **Ahandle) ;
+#endif
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_multiply_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_multiply_mex.c
new file mode 100644
index 0000000..63b712e
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_multiply_mex.c
@@ -0,0 +1,49 @@
+#include "cs_mex.h"
+/* cs_multiply: sparse matrix multiply */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_multiply(A,B)") ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl A1matrix, B1matrix, *A, *B, *C, *D, *A1, *B1 ;
+ A1 = cs_cl_mex_get_sparse (&A1matrix, 0, pargin [0]) ;
+ A = cs_cl_transpose (A1, 1) ;
+ cs_cl_free (A1->x) ; /* complex copy no longer needed */
+ B1 = cs_cl_mex_get_sparse (&B1matrix, 0, pargin [1]) ;
+ B = cs_cl_transpose (B1, 1) ;
+ cs_cl_free (B1->x) ; /* complex copy no longer needed */
+ D = cs_cl_multiply (B,A) ; /* D = B'*A' */
+ cs_cl_spfree (A) ;
+ cs_cl_spfree (B) ;
+ cs_cl_dropzeros (D) ; /* drop zeros from D */
+ C = cs_cl_transpose (D, 1) ; /* C = D', so C is sorted */
+ cs_cl_spfree (D) ;
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ;
+ A = cs_dl_transpose (cs_dl_mex_get_sparse (&Amatrix, 0,1, pargin[0]),1);
+ B = cs_dl_transpose (cs_dl_mex_get_sparse (&Bmatrix, 0,1, pargin[1]),1);
+ D = cs_dl_multiply (B,A) ; /* D = B'*A' */
+ cs_dl_spfree (A) ;
+ cs_dl_spfree (B) ;
+ cs_dl_dropzeros (D) ; /* drop zeros from D */
+ C = cs_dl_transpose (D, 1) ; /* C = D', so C is sorted */
+ cs_dl_spfree (D) ;
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_permute_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_permute_mex.c
new file mode 100644
index 0000000..1e6ad11
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_permute_mex.c
@@ -0,0 +1,51 @@
+#include "cs_mex.h"
+/* cs_permute: permute a sparse matrix */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT ignore, *P, *Q, *Pinv, m, n ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: C = cs_permute(A,p,q)") ;
+ }
+ m = mxGetM (pargin [0]) ;
+ n = mxGetN (pargin [0]) ;
+ P = cs_dl_mex_get_int (m, pargin [1], &ignore, 1) ; /* get P */
+ Q = cs_dl_mex_get_int (n, pargin [2], &ignore, 1) ; /* get Q */
+ Pinv = cs_pinv (P, m) ; /* P = Pinv' */
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A, *C, *D ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ C = cs_cl_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */
+ cs_cl_free (A->x) ;
+ D = cs_cl_transpose (C, 1) ; /* sort C via double transpose */
+ cs_cl_spfree (C) ;
+ C = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A, *C, *D ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ C = cs_dl_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */
+ D = cs_dl_transpose (C, 1) ; /* sort C via double transpose */
+ cs_dl_spfree (C) ;
+ C = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ }
+ cs_free (Pinv) ;
+ cs_free (P) ;
+ cs_free (Q) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_print_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_print_mex.c
new file mode 100644
index 0000000..58864c2
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_print_mex.c
@@ -0,0 +1,34 @@
+#include "cs_mex.h"
+/* cs_print: print the contents of a sparse matrix. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT brief ;
+ if (nargout > 0 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: cs_print(A,brief)") ;
+ }
+ brief = (nargin < 2) ? 0 : mxGetScalar (pargin [1]) ; /* get brief */
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ cs_cl_print (A, brief) ; /* print A */
+ cs_free (A->x) ;
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ;/* get A */
+ cs_print (A, brief) ; /* print A */
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_qr_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_qr_mex.c
new file mode 100644
index 0000000..9d31207
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_qr_mex.c
@@ -0,0 +1,83 @@
+#include "cs_mex.h"
+/* cs_qr: sparse QR factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT m, n, order, *p ;
+ if (nargout > 5 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: [V,beta,p,R,q] = cs_qr(A)") ;
+ }
+ order = (nargout == 5) ? 3 : 0 ; /* determine ordering */
+ m = mxGetM (pargin [0]) ;
+ n = mxGetN (pargin [0]) ;
+ if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ;
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cls *S ;
+ cs_cln *N ;
+ cs_cl Amatrix, *A, *D ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ S = cs_cl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
+ N = cs_cl_qr (A, S) ; /* numeric QR factorization */
+ cs_free (A->x) ;
+ if (!N) mexErrMsgTxt ("qr failed") ;
+ cs_cl_dropzeros (N->L) ; /* drop zeros from V and sort */
+ D = cs_cl_transpose (N->L, 1) ;
+ cs_cl_spfree (N->L) ;
+ N->L = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ cs_cl_dropzeros (N->U) ; /* drop zeros from R and sort */
+ D = cs_cl_transpose (N->U, 1) ;
+ cs_cl_spfree (N->U) ;
+ N->U = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ m = N->L->m ; /* m may be larger now */
+ p = cs_cl_pinv (S->pinv, m) ; /* p = pinv' */
+ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return V */
+ cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */
+ pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */
+ pargout [3] = cs_cl_mex_put_sparse (&(N->U)) ; /* return R */
+ pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
+ cs_cl_nfree (N) ;
+ cs_cl_sfree (S) ;
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dls *S ;
+ cs_dln *N ;
+ cs_dl Amatrix, *A, *D ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
+ N = cs_dl_qr (A, S) ; /* numeric QR factorization */
+ if (!N) mexErrMsgTxt ("qr failed") ;
+ cs_dl_dropzeros (N->L) ; /* drop zeros from V and sort */
+ D = cs_dl_transpose (N->L, 1) ;
+ cs_dl_spfree (N->L) ;
+ N->L = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ cs_dl_dropzeros (N->U) ; /* drop zeros from R and sort */
+ D = cs_dl_transpose (N->U, 1) ;
+ cs_dl_spfree (N->U) ;
+ N->U = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ m = N->L->m ; /* m may be larger now */
+ p = cs_dl_pinv (S->pinv, m) ; /* p = pinv' */
+ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return V */
+ cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */
+ pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */
+ pargout [3] = cs_dl_mex_put_sparse (&(N->U)) ; /* return R */
+ pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
+ cs_dl_nfree (N) ;
+ cs_dl_sfree (S) ;
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_qrsol_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_qrsol_mex.c
new file mode 100644
index 0000000..18af03d
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_qrsol_mex.c
@@ -0,0 +1,54 @@
+#include "cs_mex.h"
+/* cs_qrsol: solve least squares or underdetermined problem */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT k, order ;
+ if (nargout > 1 || nargin < 2 || nargin > 3)
+ {
+ mexErrMsgTxt ("Usage: x = cs_qrsol(A,b,order)") ;
+ }
+ order = (nargin < 3) ? 3 : mxGetScalar (pargin [2]) ;
+ order = CS_MAX (order, 0) ;
+ order = CS_MIN (order, 3) ;
+
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl *A, Amatrix ;
+ cs_complex_t *x, *b ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ b = cs_cl_mex_get_double (A->m, pargin [1]) ; /* get b */
+ x = cs_dl_calloc (CS_MAX (A->m, A->n), sizeof (cs_complex_t)) ;
+ for (k = 0 ; k < A->m ; k++) x [k] = b [k] ; /* x = b */
+ cs_free (b) ;
+ if (!cs_cl_qrsol (order, A, x)) /* x = A\x */
+ {
+ mexErrMsgTxt ("QR solve failed") ;
+ }
+ pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl *A, Amatrix ;
+ double *x, *b ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ b = cs_dl_mex_get_double (A->m, pargin [1]) ; /* get b */
+ x = cs_dl_calloc (CS_MAX (A->m, A->n), sizeof (double)) ; /* x = b */
+ for (k = 0 ; k < A->m ; k++) x [k] = b [k] ;
+ if (!cs_dl_qrsol (order, A, x)) /* x = A\x */
+ {
+ mexErrMsgTxt ("QR solve failed") ;
+ }
+ cs_dl_mex_put_double (A->n, x, &(pargout [0])) ; /* return x */
+ cs_free (x) ;
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_randperm_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_randperm_mex.c
new file mode 100644
index 0000000..0398ede
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_randperm_mex.c
@@ -0,0 +1,28 @@
+#include "cs_mex.h"
+/* cs_randperm: random permutation. p=cs_randperm(n,0) is 1:n,
+ * p=cs_randperm(n,-1) is n:-1:1. p = cs_randperm (n,seed) is a random
+ * permutation using the given seed (where seed is not 0 or -1).
+ * seed defaults to 1. A single seed always gives a repeatable permutation.
+ * Use p = cs_randperm(n,rand) to get a permutation that varies with each use.
+ */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double seed ;
+ CS_INT iseed, n, *p ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: p = cs_randperm(n,seed)") ;
+ }
+ seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ;
+ iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ;
+ n = mxGetScalar (pargin [0]) ;
+ n = CS_MAX (n, 0) ;
+ p = cs_dl_randperm (n, iseed) ;
+ pargout [0] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_scc_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_scc_mex.c
new file mode 100644
index 0000000..28ad3f2
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_scc_mex.c
@@ -0,0 +1,32 @@
+#include "cs_mex.h"
+/* [p,r] = cs_scc (A) finds the strongly connected components of A */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl Amatrix, *A ;
+ cs_dld *D ;
+ CS_INT n, j, *Ap2 ;
+ if (nargout > 2 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: [p,r] = cs_scc(A)") ;
+ }
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ; /* get A */
+ /* cs_scc modifies A->p and then restores it (in cs_dfs). Avoid the issue
+ * of a mexFunction modifying its input (even temporarily) by making a copy
+ * of A->p. This issue does not arise in cs_dmperm, because that function
+ * applies cs_scc to a submatrix C, not to A directly. */
+ n = A->n ;
+ Ap2 = cs_dl_malloc (n+1, sizeof (CS_INT)) ;
+ for (j = 0 ; j <= n ; j++) Ap2 [j] = A->p [j] ;
+ A->p = Ap2 ;
+ D = cs_dl_scc (A) ; /* find conn. comp. */
+ pargout [0] = cs_dl_mex_put_int (D->p, n, 1, 0) ; /* return p */
+ pargout [1] = cs_dl_mex_put_int (D->r, D->nb+1, 1, 0) ; /* return r */
+ cs_dl_dfree (D) ;
+ cs_free (Ap2) ; /* free the copy of A->p */
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_sparse_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_sparse_mex.c
new file mode 100644
index 0000000..4c22b71
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_sparse_mex.c
@@ -0,0 +1,58 @@
+#include "cs_mex.h"
+/* cs_sparse: convert triplet form into compress-column form sparse matrix */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: A = cs_sparse(i,j,x)") ;
+ }
+ if (mxIsComplex (pargin [2]))
+ {
+#ifndef NCOMPLEX
+ cs_cl *A, *C, *T, Tmatrix ;
+ T = &Tmatrix ; /* get i,j,x and copy to triplet form */
+ T->nz = mxGetM (pargin [0]) ;
+ T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ;
+ T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ;
+ cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ;
+ T->x = cs_cl_mex_get_double (T->nz, pargin [2]) ;
+ T->nzmax = T->nz ;
+ C = cs_cl_compress (T) ; /* create sparse matrix C */
+ cs_cl_dupl (C) ; /* remove duplicates from C */
+ cs_cl_dropzeros (C) ; /* remove zeros from C */
+ A = cs_cl_transpose (C, -1) ; /* A=C.' */
+ cs_cl_spfree (C) ;
+ pargout [0] = cs_cl_mex_put_sparse (&A) ; /* return A */
+ cs_free (T->p) ;
+ cs_free (T->i) ;
+ cs_free (T->x) ; /* free copy of complex values*/
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl *A, *C, *T, Tmatrix ;
+ T = &Tmatrix ; /* get i,j,x and copy to triplet form */
+ T->nz = mxGetM (pargin [0]) ;
+ T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ;
+ T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ;
+ cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ;
+ T->x = mxGetPr (pargin [2]) ;
+ T->nzmax = T->nz ;
+ C = cs_dl_compress (T) ; /* create sparse matrix C */
+ cs_dl_dupl (C) ; /* remove duplicates from C */
+ cs_dl_dropzeros (C) ; /* remove zeros from C */
+ A = cs_dl_transpose (C, 1) ; /* A=C' */
+ cs_dl_spfree (C) ;
+ pargout [0] = cs_dl_mex_put_sparse (&A) ; /* return A */
+ cs_free (T->p) ;
+ cs_free (T->i) ;
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_sqr_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_sqr_mex.c
new file mode 100644
index 0000000..6c6f75f
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_sqr_mex.c
@@ -0,0 +1,40 @@
+#include "cs_mex.h"
+/* cs_sqr: symbolic sparse QR factorization */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double s ;
+ cs_dls *S ;
+ cs_dl Amatrix, *A ;
+ CS_INT m, n, order, *p ;
+ if (nargout > 7 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A)") ;
+ }
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ m = A->m ;
+ n = A->n ;
+ if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ;
+ order = (nargout == 7) ? 3 : 0 ; /* determine ordering */
+ S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
+ if (!S) mexErrMsgTxt ("cs_sqr failed") ;
+ s = S->lnz ;
+ cs_dl_mex_put_double (1, &s, &(pargout [0])) ; /* return nnz(V) */
+ s = S->unz ;
+ cs_dl_mex_put_double (1, &s, &(pargout [1])) ; /* return nnz(R) */
+ pargout [2] = cs_dl_mex_put_int (S->parent, n, 1, 0) ; /* return parent */
+ pargout [3] = cs_dl_mex_put_int (S->cp, n, 0, 0) ; /* return c */
+ pargout [4] = cs_dl_mex_put_int (S->leftmost, m, 1, 0) ;/* return leftmost*/
+ p = cs_dl_pinv (S->pinv, S->m2) ; /* p = pinv' */
+ pargout [5] = cs_dl_mex_put_int (p, S->m2, 1, 1) ; /* return p */
+ if (nargout > 6)
+ {
+ pargout [6] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
+ }
+ cs_dl_sfree (S) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_symperm_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_symperm_mex.c
new file mode 100644
index 0000000..d6c90b5
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_symperm_mex.c
@@ -0,0 +1,52 @@
+#include "cs_mex.h"
+/* cs_symperm: symmetric permutation of a symmetric sparse matrix. */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT ignore, n, *P, *Pinv ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_symperm(A,p)") ;
+ }
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A, *C, *D ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ;
+ n = A->n ;
+ P = cs_dl_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */
+ Pinv = cs_cl_pinv (P, n) ; /* P=Pinv' */
+ C = cs_cl_symperm (A, Pinv, 1) ; /* C = A(p,p) */
+ D = cs_cl_transpose (C, 1) ; /* sort C */
+ cs_cl_spfree (C) ;
+ C = cs_cl_transpose (D, 1) ;
+ cs_cl_spfree (D) ;
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+ cs_free (P) ;
+ cs_free (Pinv) ;
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A, *C, *D ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ;
+ n = A->n ;
+ P = cs_dl_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */
+ Pinv = cs_dl_pinv (P, n) ; /* P=Pinv' */
+ C = cs_dl_symperm (A, Pinv, 1) ; /* C = A(p,p) */
+ D = cs_dl_transpose (C, 1) ; /* sort C */
+ cs_dl_spfree (C) ;
+ C = cs_dl_transpose (D, 1) ;
+ cs_dl_spfree (D) ;
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ cs_free (P) ;
+ cs_free (Pinv) ;
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_thumb_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_thumb_mex.c
new file mode 100644
index 0000000..f1ce68b
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_thumb_mex.c
@@ -0,0 +1,65 @@
+#include "cs_mex.h"
+/* cs_thumb: convert a sparse matrix to a dense 2D thumbnail matrix of size
+ * at most k-by-k. k defaults to 256. A helper mexFunction for cspy. */
+
+#define INDEX(i,j,lda) ((i)+(j)*(lda))
+#define ISNAN(x) ((x) != (x))
+#ifdef DBL_MAX
+#define BIG_VALUE DBL_MAX
+#else
+#define BIG_VALUE 1.7e308
+#endif
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT m, n, mn, m2, n2, k, s, j, ij, sj, si, p, *Ap, *Ai ;
+ double aij, ax, az, *S, *Ax, *Az ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: S = cs_thumb(A,k)") ;
+ }
+ cs_mex_check (0, -1, -1, 0, 1, 1, pargin [0]) ;
+ m = mxGetM (pargin [0]) ;
+ n = mxGetN (pargin [0]) ;
+ mn = CS_MAX (m,n) ;
+ k = (nargin == 1) ? 256 : mxGetScalar (pargin [1]) ; /* get k */
+ /* s = size of each submatrix; A(1:s,1:s) maps to S(1,1) */
+ s = (mn < k) ? 1 : (CS_INT) ceil ((double) mn / (double) k) ;
+ m2 = (CS_INT) ceil ((double) m / (double) s) ;
+ n2 = (CS_INT) ceil ((double) n / (double) s) ;
+ /* create S */
+ pargout [0] = mxCreateDoubleMatrix (m2, n2, mxREAL) ;
+ S = mxGetPr (pargout [0]) ;
+ Ap = (CS_INT *) mxGetJc (pargin [0]) ;
+ Ai = (CS_INT *) mxGetIr (pargin [0]) ;
+ Ax = mxGetPr (pargin [0]) ;
+ Az = (mxIsComplex (pargin [0])) ? mxGetPi (pargin [0]) : NULL ;
+ for (j = 0 ; j < n ; j++)
+ {
+ sj = j/s ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ si = Ai [p] / s ;
+ ij = INDEX (si,sj,m2) ;
+ ax = Ax [p] ;
+ az = Az ? Az [p] : 0 ;
+ if (az == 0)
+ {
+ aij = fabs (ax) ;
+ }
+ else
+ {
+ aij = sqrt (ax*ax + az*az) ;
+ }
+ if (ISNAN (aij)) aij = BIG_VALUE ;
+ aij = CS_MIN (BIG_VALUE, aij) ;
+ S [ij] = CS_MAX (S [ij], aij) ;
+ }
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_transpose.m b/CXSparse_newfiles/MATLAB/CSparse/cs_transpose.m
new file mode 100644
index 0000000..d94ae6c
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_transpose.m
@@ -0,0 +1,19 @@
+function C = cs_transpose (A) %#ok
+%CS_TRANSPOSE transpose a sparse matrix.
+% C = cs_transpose(A), computes C = A'
+% C = cs_transpose(A,-1) computes C=A.'
+% C = cs_transpose(A,1) computes C=A'
+%
+% Example:
+% Prob = UFget ('HB/ibm32') ; A = Prob.A ;
+% C = cs_transpose (A) ;
+% C-A'
+%
+% See also TRANSPOSE, CTRANSPOSE.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+error ('cs_transpose mexFunction not found') ;
+
+
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_transpose_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_transpose_mex.c
new file mode 100644
index 0000000..c36803a
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_transpose_mex.c
@@ -0,0 +1,37 @@
+#include "cs_mex.h"
+/* C = cs_transpose (A), computes C=A', where A must be sparse.
+ C = cs_transpose (A,kind) computes C=A.' if kind <= 0, C=A' if kind > 0 */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT values ;
+ if (nargout > 1 || nargin < 1 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage: C = cs_transpose(A,kind)") ;
+ }
+ values = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ;
+ values = (values <= 0) ? -1 : 1 ;
+ if (mxIsComplex (pargin [0]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Amatrix, *A, *C ;
+ A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
+ C = cs_cl_transpose (A, values) ; /* C = A' */
+ pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Amatrix, *A, *C ;
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
+ C = cs_dl_transpose (A, values) ; /* C = A' */
+ pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_updown_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_updown_mex.c
new file mode 100644
index 0000000..c42769b
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_updown_mex.c
@@ -0,0 +1,108 @@
+#include "cs_mex.h"
+/* cs_updown: sparse Cholesky update/downdate (rank-1 or multiple rank) */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT ignore, j, k, n, lnz, *parent, sigma = 1, cp [2], ok ;
+ char sigma_string [20] ;
+ if (nargout > 1 || nargin < 3 || nargin > 4)
+ {
+ mexErrMsgTxt ("Usage: L = cs_updown(L,C,parent,sigma)") ;
+ }
+ if (nargin > 3 && mxIsChar (pargin [3]))
+ {
+ mxGetString (pargin [3], sigma_string, 8) ;
+ sigma = (sigma_string [0] == '-') ? (-1) : 1 ;
+ }
+ n = mxGetN (pargin [0]) ;
+ parent = cs_dl_mex_get_int (n, pargin [2], &ignore, 0) ; /* get parent*/
+
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+
+#ifndef NCOMPLEX
+ cs_cl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
+ /* get input L, and copy MATLAB complex to C complex type */
+ Lin = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ;
+
+ /* make a copy of L (this can take more work than updating L itself) */
+ lnz = Lin->p [n] ;
+ L = cs_cl_spalloc (n, n, lnz, 0, 0) ;
+ for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
+ for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
+
+ /* complex values already copied into Lin->x, use shallow copy for L */
+ L->x = Lin->x ;
+
+ cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
+ C = cs_cl_mex_get_sparse (&Cmatrix, 0, pargin [1]) ;
+
+ /* do the update one column at a time */
+ Cvec = &Cvector ;
+ Cvec->m = n ;
+ Cvec->n = 1 ;
+ Cvec->p = cp ;
+ Cvec->nz = -1 ;
+ cp [0] = 0 ;
+ for (k = 0 ; k < C->n ; k++)
+ {
+ /* extract C(:,k) */
+ cp [1] = C->p [k+1] - C->p [k] ;
+ Cvec->nzmax = cp [1] ;
+ Cvec->i = C->i + C->p [k] ;
+ Cvec->x = C->x + C->p [k] ;
+ /* update/downdate */
+ ok = cs_cl_updown (L, sigma, Cvec, parent) ;
+ if (!ok) mexErrMsgTxt ("matrix is not positive definite") ;
+ }
+ /* return new L */
+ pargout [0] = cs_cl_mex_put_sparse (&L) ;
+
+ cs_free (C->x) ; /* free complex copy of C */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+
+ }
+ else
+ {
+
+ cs_dl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
+ /* get input L */
+ Lin = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
+ /* make a copy of L (this can take more work than updating L itself) */
+ lnz = Lin->p [n] ;
+ L = cs_dl_spalloc (n, n, lnz, 1, 0) ;
+ for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
+ for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
+ for (k = 0 ; k < lnz ; k++) L->x [k] = Lin->x [k] ;
+ cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
+ C = cs_dl_mex_get_sparse (&Cmatrix, 0, 1, pargin [1]) ;
+
+ /* do the update one column at a time */
+ Cvec = &Cvector ;
+ Cvec->m = n ;
+ Cvec->n = 1 ;
+ Cvec->p = cp ;
+ Cvec->nz = -1 ;
+ cp [0] = 0 ;
+ for (k = 0 ; k < C->n ; k++)
+ {
+ /* extract C(:,k) */
+ cp [1] = C->p [k+1] - C->p [k] ;
+ Cvec->nzmax = cp [1] ;
+ Cvec->i = C->i + C->p [k] ;
+ Cvec->x = C->x + C->p [k] ;
+ /* update/downdate */
+ ok = cs_dl_updown (L, sigma, Cvec, parent) ;
+ if (!ok) mexErrMsgTxt ("matrix is not positive definite") ;
+ }
+ /* return new L */
+ pargout [0] = cs_dl_mex_put_sparse (&L) ;
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_usolve_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_usolve_mex.c
new file mode 100644
index 0000000..b1bb32c
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_usolve_mex.c
@@ -0,0 +1,92 @@
+#include "cs_mex.h"
+/* cs_usolve: x=U\b. U must be sparse and upper triangular. b must be a
+ * full or sparse vector. x is full or sparse, depending on b.
+ *
+ * Time taken is O(flop count), which may be less than n if b is sparse,
+ * depending on U and b.
+ *
+ * This function works with MATLAB 7.2, but is not perfectly compatible with
+ * the requirements of a MATLAB mexFunction when b is sparse. X is returned
+ * as an unsorted sparse vector. Also, this mexFunction temporarily modifies
+ * its input, U, by modifying U->p (in the cs_dfs function) and then restoring
+ * it. This could be corrected by creating a copy of U->p
+ * (see cs_dmperm_mex.c), but this would take O(n) time, destroying the
+ * O(flop count) time complexity of this function.
+ *
+ * Note that b cannot be sparse complex. This function does not support
+ * sparse complex U and b because the sparse x=U\b only accesses part of the
+ * matrix U. Converting U from a MATLAB complex matrix to a CXSparse complex
+ * matrix requires all of U to be accessed, defeating the purpose of this
+ * function.
+ *
+ * U can be sparse complex, but in that case b must be full real or complex,
+ * not sparse.
+ */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT top, nz, p, *xi, n ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_usolve(U,b)") ;
+ }
+ if (mxIsSparse (pargin [1]))
+ {
+ cs_dl Umatrix, Bmatrix, *U, *B, *X ;
+ double *x ;
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+ mexErrMsgTxt ("sparse complex case not supported") ;
+ }
+ U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ;/* get U */
+ n = U->n ;
+ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b*/
+ cs_mex_check (0, n, 1, 0, 1, 1, pargin [1]) ;
+ xi = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* get workspace */
+ x = cs_dl_malloc (n, sizeof (double)) ;
+ top = cs_dl_spsolve (U, B, 0, xi, x, NULL, 0) ; /* x = U\b */
+ X = cs_dl_spalloc (n, 1, n-top, 1, 0) ; /* create sparse x*/
+ X->p [0] = 0 ;
+ nz = 0 ;
+ for (p = top ; p < n ; p++)
+ {
+ X->i [nz] = xi [p] ;
+ X->x [nz++] = x [xi [p]] ;
+ }
+ X->p [1] = nz ;
+ pargout [0] = cs_dl_mex_put_sparse (&X) ;
+ cs_free (x) ;
+ cs_free (xi) ;
+ }
+ else if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Umatrix, *U ;
+ cs_complex_t *x ;
+ U = cs_cl_mex_get_sparse (&Umatrix, 1, pargin [0]) ; /* get U */
+ n = U->n ;
+ x = cs_cl_mex_get_double (n, pargin [1]) ; /* x = b */
+ cs_cl_usolve (U, x) ; /* x = U\x */
+ cs_free (U->x) ;
+ pargout [0] = cs_cl_mex_put_double (n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Umatrix, *U ;
+ double *x, *b ;
+ U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */
+ n = U->n ;
+ b = cs_dl_mex_get_double (n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (n, b, &(pargout [0])) ; /* x = b */
+ cs_dl_usolve (U, x) ; /* x = U\x */
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/cs_utsolve_mex.c b/CXSparse_newfiles/MATLAB/CSparse/cs_utsolve_mex.c
new file mode 100644
index 0000000..f4913bd
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/cs_utsolve_mex.c
@@ -0,0 +1,38 @@
+#include "cs_mex.h"
+/* cs_utsolve: solve a lower triangular system U'*x=b */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_utsolve(U,b)") ;
+ }
+ if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
+ {
+#ifndef NCOMPLEX
+ cs_cl Umatrix, *U ;
+ cs_complex_t *x ;
+ U = cs_cl_mex_get_sparse (&Umatrix, 1, pargin [0]) ; /* get U */
+ x = cs_cl_mex_get_double (U->n, pargin [1]) ; /* x = b */
+ cs_cl_utsolve (U, x) ; /* x = U'\x */
+ cs_free (U->x) ;
+ pargout [0] = cs_cl_mex_put_double (U->n, x) ; /* return x */
+#else
+ mexErrMsgTxt ("complex matrices not supported") ;
+#endif
+ }
+ else
+ {
+ cs_dl Umatrix, *U ;
+ double *x, *b ;
+ U = cs_dl_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */
+ b = cs_dl_mex_get_double (U->n, pargin [1]) ; /* get b */
+ x = cs_dl_mex_put_double (U->n, b, &(pargout [0])) ; /* x = b */
+ cs_dl_utsolve (U, x) ; /* x = U'\x */
+ }
+}
diff --git a/CXSparse_newfiles/MATLAB/CSparse/private/cs_make_helper.m b/CXSparse_newfiles/MATLAB/CSparse/private/cs_make_helper.m
new file mode 100644
index 0000000..99a9c35
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/CSparse/private/cs_make_helper.m
@@ -0,0 +1,200 @@
+function [objfiles, timestamp_out] = cs_make_helper (f, docomplex)
+%CS_MAKE_HELPER compiles CXSparse for use in MATLAB.
+% Usage:
+% [objfiles, timestamp] = cs_make (f, docomplex)
+%
+% With f=0, only those files needing to be
+% compiled are compiled (like the Unix/Linux/GNU "make" command, but not
+% requiring "make"). If f is a nonzero number, all files are compiled.
+% If f is a string, only that mexFunction is compiled. For example,
+% cs_make ('cs_add') just compiles the cs_add mexFunction. This option is
+% useful when developing a single new mexFunction. This function can only be
+% used if the current directory is CXSparse/MATLAB/CSparse. Returns a list of
+% the object files in CXSparse, and the latest modification time of any source
+% codes.
+%
+% NOTE: if your compiler does not support the ANSI C99 complex type, the
+% CXSparse mexFunctions will not support complex sparse matrices.
+%
+% To add a new function and its MATLAB mexFunction to CXSparse:
+%
+% (1) Create a source code file CXSparse/Source/cs_mynewfunc.c.
+% (2) Create a help file, CXSparse/MATLAB/CSparse/cs_mynewfunc.m.
+% This is very useful, but not strictly required.
+% (3) Add the prototype of cs_mynewfunc to CXSparse/Include/cs.h.
+% (4) Create its MATLAB mexFunction, CXSparse/MATLAB/cs_mynewfunc_mex.c.
+% (5) Edit cs_make.m, and add 'cs_mynewfunc' to the 'cs' and 'csm' lists.
+% (6) Type 'cs_make' in the CXSparse/MATLAB/CSparse directory.
+% If all goes well, your new function is ready for use in MATLAB.
+%
+% (7) Optionally add 'cs_mynewfunc' to CXSparse/Source/Makefile
+% and CXSparse/MATLAB/CSparse/Makefile, if you want to use the
+% Unix/Linux/GNU make command instead of cs_make.m. See where
+% 'cs_add' and 'cs_add_mex' appear in those files, and add
+% 'cs_mynewfunc' accordingly.
+% (8) Optionally add 'cs_mynewfunc' to Tcov/Makefile, and add additional
+% test code to cs_test.c, and add MATLAB test code to MATLAB/Test/*.
+%
+% Example:
+% cs_make_helper (1,1) ; % compile everything
+% cs_make ('cs_chol', 1) ; % just compile cs_chol mexFunction
+%
+% See also MEX.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+mexcmd = 'mex -DCS_LONG -I../../../UFconfig' ;
+if (~isempty (strfind (computer, '64')))
+ mexcmd = [mexcmd ' -largeArrayDims'] ;
+end
+
+if (nargin < 2)
+ docomplex = 1 ;
+end
+
+if (~docomplex)
+ mexcmd = [mexcmd ' -DNCOMPLEX'] ;
+end
+
+% CSparse source files, in ../../Source, such as ../../Source/cs_add.c.
+% Note that not all CSparse source files have their own mexFunction.
+cs = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ...
+ 'cs_cumsum', 'cs_dfs', 'cs_dmperm', 'cs_droptol', 'cs_dropzeros', ...
+ 'cs_dupl', 'cs_entry', 'cs_etree', 'cs_fkeep', 'cs_gaxpy', 'cs_happly', ...
+ 'cs_house', 'cs_ipvec', 'cs_load', 'cs_lsolve', 'cs_ltsolve', 'cs_lu', ...
+ 'cs_lusol', 'cs_malloc', 'cs_maxtrans', 'cs_multiply', 'cs_norm', ...
+ 'cs_permute', 'cs_pinv', 'cs_post', 'cs_print', 'cs_pvec', 'cs_qr', ...
+ 'cs_qrsol', 'cs_scatter', 'cs_scc', 'cs_schol', 'cs_sqr', 'cs_symperm', ...
+ 'cs_tdfs', 'cs_transpose', 'cs_compress', 'cs_updown', 'cs_usolve', ...
+ 'cs_utsolve', 'cs_util', 'cs_reach', 'cs_spsolve', 'cs_ereach', ...
+ 'cs_leaf', 'cs_randperm' } ;
+ % add cs_mynewfunc to the above list
+
+details = 1 ;
+kk = 0 ;
+csm = { } ;
+if (nargin == 0)
+ force = 0 ;
+elseif (ischar (f))
+ fprintf ('cs_make: compiling ../../Source files and %s_mex.c\n', f) ;
+ force = 0 ;
+ csm = {f} ;
+else
+ force = f ;
+ details = details | (force > 1) ; %#ok
+ if (force & details) %#ok
+ fprintf ('cs_make: re-compiling everything\n') ;
+ end
+end
+
+if (isempty (csm))
+ % mexFunctions, of the form cs_add_mex.c, etc, in this directory
+ csm = { 'cs_add', 'cs_amd', 'cs_chol', 'cs_cholsol', 'cs_counts', ...
+ 'cs_dmperm', 'cs_droptol', 'cs_etree', 'cs_gaxpy', 'cs_lsolve', ...
+ 'cs_ltsolve', 'cs_lu', 'cs_lusol', 'cs_multiply', 'cs_permute', ...
+ 'cs_print', 'cs_qr', 'cs_qrsol', 'cs_scc', 'cs_symperm', 'cs_thumb', ...
+ 'cs_transpose', 'cs_sparse', 'cs_updown', 'cs_usolve', ...
+ 'cs_utsolve', 'cs_randperm', 'cs_sqr' } ;
+ % add cs_mynewfunc to the above list
+end
+
+
+try
+ % ispc does not appear in MATLAB 5.3
+ pc = ispc ;
+catch
+ % if ispc fails, assume we are on a Windows PC if it's not unix
+ pc = ~isunix ;
+end
+
+if (pc)
+ obj = '.obj' ;
+else
+ obj = '.o' ;
+end
+
+srcdir = '../../Source/' ;
+hfile = '../../Include/cs.h' ;
+
+% compile each CSparse source file
+[anysrc timestamp kk] = compile_source ('', 'cs_mex', obj, hfile, force, ...
+ mexcmd, kk, details) ;
+CS = ['cs_mex' obj] ;
+if (nargout > 0)
+ objfiles = ['..' filesep 'CSparse' filesep 'cs_mex' obj] ;
+end
+for i = 1:length (cs)
+
+ [s t kk] = compile_source (srcdir, cs{i}, obj, hfile, force, mexcmd, ...
+ kk, details) ;
+ timestamp = max (timestamp, t) ;
+ anysrc = anysrc | s ; %#ok
+ CS = [CS ' ' cs{i} obj] ; %#ok
+ if (nargout > 0)
+ objfiles = [objfiles ' ..' filesep 'CSparse' filesep cs{i} obj] ; %#ok
+ end
+
+ % complex version:
+ if (docomplex)
+ csrc = cs {i} ;
+ csrc = [ 'cs_cl_' csrc(4:end) ] ;
+ CS = [CS ' ' csrc obj] ; %#ok
+ if (nargout > 0)
+ objfiles = [objfiles ' ..' filesep 'CSparse' filesep csrc obj] ;%#ok
+ end
+ if (s)
+ copyfile (['../../Source/' cs{i} '.c'], [csrc '.c'], 'f') ;
+ if (details)
+ fprintf ('%s\n', ['cp -f ../../Source/' cs{i} '.c ' csrc '.c']);
+ end
+ cmd = sprintf ('%s -DCS_COMPLEX -O -c -I../../Include %s.c\n', ...
+ mexcmd, csrc) ;
+ kk = do_cmd (cmd, kk, details) ;
+ end
+ end
+
+end
+
+% compile each CSparse mexFunction
+obj = ['.' mexext] ;
+for i = 1:length (csm)
+ [s t] = cs_must_compile ('', csm{i}, '_mex', obj, hfile, force) ;
+ timestamp = max (timestamp, t) ;
+ if (anysrc | s) %#ok
+ cmd = sprintf ('%s -O -I../../Include %s_mex.c %s -output %s\n', ...
+ mexcmd, csm{i}, CS, csm{i}) ;
+ kk = do_cmd (cmd, kk, details) ;
+ end
+end
+
+if (nargout > 1)
+ timestamp_out = timestamp ;
+end
+
+fprintf ('\n') ;
+
+%-------------------------------------------------------------------------------
+function [s,t,kk] = compile_source (srcdir, f, obj, hfile, force, mexcmd, ...
+ kk, details)
+% compile a source code file in ../../Source, leaving object file in
+% this directory.
+[s t] = cs_must_compile (srcdir, f, '', obj, hfile, force) ;
+if (s)
+ cmd = sprintf ('%s -O -c -I../../Include %s%s.c\n', mexcmd, srcdir, f) ;
+ kk = do_cmd (cmd, kk, details) ;
+end
+
+%-------------------------------------------------------------------------------
+function kk = do_cmd (s, kk, details)
+%DO_CMD: evaluate a command, and either print it or print a "."
+if (details)
+ fprintf ('%s', s) ;
+else
+ if (mod (kk, 60) == 0)
+ fprintf ('\n') ;
+ end
+ kk = kk + 1 ;
+ fprintf ('.') ;
+end
+eval (s) ;
diff --git a/CXSparse_newfiles/MATLAB/Demo/Contents.m b/CXSparse_newfiles/MATLAB/Demo/Contents.m
new file mode 100644
index 0000000..b8398dc
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Demo/Contents.m
@@ -0,0 +1,11 @@
+% CXSparse MATLAB demos.
+%
+% cs_demo - run all CXSparse demos.
+% cs_demo1 - MATLAB version of the CSparse/Demo/cs_demo1.c program.
+% cs_demo2 - MATLAB version of the CSparse/Demo/cs_demo2.c program.
+% cs_demo3 - MATLAB version of the CSparse/Demo/cs_demo3.c program.
+
+% Example:
+% help cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis
diff --git a/CXSparse_newfiles/MATLAB/Demo/README.txt b/CXSparse_newfiles/MATLAB/Demo/README.txt
new file mode 100644
index 0000000..36b4e08
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Demo/README.txt
@@ -0,0 +1 @@
+Demo for MATLAB interface for CXSparse. See Contents.m for details.
diff --git a/CXSparse_newfiles/MATLAB/Demo/cs_demo.m b/CXSparse_newfiles/MATLAB/Demo/cs_demo.m
new file mode 100644
index 0000000..d01135d
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Demo/cs_demo.m
@@ -0,0 +1,47 @@
+function cs_demo (do_pause, matrixpath)
+%CS_DEMO run all CXSparse demos.
+% cs_demo(0) will run all demos without pausing.
+%
+% Example:
+% cs_demo
+% See also: cs_demo1, cs_demo2, cs_demo3
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+help cs_demo
+if (nargin < 1)
+ do_pause = 1 ;
+end
+if (nargin < 2)
+ matrixpath = [] ;
+end
+
+figure (1)
+clf
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help cs_demo1 ;
+cs_demo1 (matrixpath) ;
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help cs_demo2
+cs_demo2 (do_pause, matrixpath) ;
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help cs_demo3
+cs_demo3 (do_pause, matrixpath) ;
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help ex_1
+ex_1
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help ex2
+ex2
+
+fprintf ('\n\n-------------------------------------------------------\n') ;
+help ex3
+ex3
+
+fprintf ('\nAll CXSparse demos finished.\n') ;
diff --git a/CXSparse_newfiles/MATLAB/README.txt b/CXSparse_newfiles/MATLAB/README.txt
new file mode 100644
index 0000000..8ece299
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/README.txt
@@ -0,0 +1,24 @@
+CXSparse/MATLAB directory, which contains the MATLAB mexFunction interfaces
+for CXSparse, demos, and tests. It includes various "textbook" files
+that are printed in the book, but not a proper part of CSparse itself.
+It also includes "UFget", a MATLAB interface for the UF Sparse Matrix
+Collection.
+
+Type the command "cs_install" while in this directory. It will compile
+CSparse, and add the directories:
+
+ CXSparse/MATLAB/CSparse
+ CXSparse/MATLAB/Demo
+ CXSparse/MATLAB/UFget
+
+to your MATLAB path (see the "pathtool" command to add these to your path
+permanently, for future MATLAB sessions).
+
+To run the MATLAB demo programs, run cs_demo in the Demo directory.
+This demo will work whether or not your compiler supports the complex type.
+
+To run the MATLAB test programs, run testall in the Test directory.
+However, you may run the tests in the Test directory only if your compiler
+supports the ANSI C99 complex type. If it does not support the ANSI C99
+complex type, the tests in the Test directory will fail, since the codes there
+test both the real and complex cases in CXSparse.
diff --git a/CXSparse_newfiles/MATLAB/Test/Contents.m b/CXSparse_newfiles/MATLAB/Test/Contents.m
new file mode 100644
index 0000000..08dadeb
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/Contents.m
@@ -0,0 +1,103 @@
+% CXSparse testing and "textbook" MATLAB M-files and mexFunctions, related to
+% CXSparse but not a part of CXSparse itself.
+%
+% M-files:
+%
+% chol_downdate - downdate a Cholesky factorization.
+% chol_left - left-looking Cholesky factorization.
+% chol_left2 - left-looking Cholesky factorization, more details.
+% chol_right - right-looking Cholesky factorization.
+% chol_super - left-looking "supernodal" Cholesky factorization.
+% chol_up - up-looking Cholesky factorization.
+% chol_update - update a Cholesky factorization.
+% chol_updown - update or downdate a Cholesky factorization.
+% chol_updown2 - Cholesky update/downdate (real and complex)
+% cond1est - 1-norm condition estimate.
+% cs_fiedler - the Fiedler vector of a connected graph.
+% givens2 - find a Givens rotation.
+% house - find a Householder reflection.
+% lu_left - left-looking LU factorization.
+% lu_right - right-looking LU factorization.
+% lu_rightp - right-looking LU factorization, with partial pivoting.
+% lu_rightpr - recursive right-looking LU, with partial pivoting.
+% lu_rightr - recursive right-looking LU.
+% norm1est - 1-norm estimate.
+% qr_givens - Givens-rotation QR factorization.
+% qr_givens_full - Givens-rotation QR factorization, for full matrices.
+% qr_left - left-looking Householder QR factorization.
+% qr_right - right-looking Householder QR factorization.
+%
+% mexFunctions:
+%
+% cs_frand - generate a random finite-element matrix
+% cs_ipvec - x(p)=b
+% cs_maxtransr - recursive maximum matching algorithm
+% cs_pvec - x=b(p)
+% cs_reach - non-recursive reach (interface to CSparse cs_reach)
+% cs_reachr - recursive reach (interface to CSparse cs_reachr)
+% cs_rowcnt - row counts for sparse Cholesky
+% cs_sparse2 - same as cs_sparse, to test cs_entry function
+%
+% Extensive test functions, not for normal usage:
+%
+% check_if_same - check if two inputs are identical or not
+% choldn - Cholesky downdate
+% cholup - Cholesky update, using Given's rotations
+% cholupdown - Cholesky update/downdate (Bischof, Pan, and Tang method)
+% cs_q1 - construct Q from Householder vectors
+% cs_test_make - compiles the CSparse, Demo, and Test mexFunctions.
+% dmperm_test - test cs_dmperm
+% chol_example - simple Cholesky factorization example
+% etree_sample - construct a sample etree and symbolic factorization
+% gqr3 - QR factorization, based on Givens rotations
+% happly - apply Householder reflection to a vector
+% hmake1 - construct a Householder reflection
+% mynormest1 - estimate norm(A,1), using LU factorization (L*U = P*A*Q).
+% myqr - QR factorization using Householder reflections
+% another_colormap - try another color map
+% cspy_test - test cspy and cs_dmspy
+% qr2 - QR factorization based on Householder reflections
+% sample_colormap - try a colormap for use in cspy
+% signum - compute and display the sign of a column vector x
+% sqr_example - test cs_sqr
+% dmspy_test - test cspy, cs_dmspy, and cs_dmperm
+% test_qr - test various QR factorization methods
+% test_randperms - test random permutations
+% testh - test Householder reflections
+% test_qr1 - test QR factorizations
+% test_qrsol - test cs_qrsol
+% test_sep - test cs_sep, and compare with Gilbert's meshpart vtxsep
+% testall - test all CSparse functions (run tests 1 to 28 below)
+% test1 - test cs_transpose, cs_gaxpy, cs_sparse, cs_sparse2
+% test2 - test cs_sparse, cs_permute, cs_pvec, cs_ipvec, cs_symperm
+% test3 - test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol
+% test4 - test cs_multiply
+% test5 - test cs_add
+% test6 - test cs_reach, cs_reachr, cs_lsolve, cs_usolve
+% test7 - test cs_lu
+% test8 - test cs_cholsol, cs_lusol
+% test9 - test cs_qr
+% test10 - test cs_qr
+% test11 - test cs_rowcnt
+% test12 - test cs_qr and compare with svd
+% test13 - test cs_counts, cs_etree
+% test14 - test cs_droptol
+% test15 - test cs_amd
+% test16 - test cs_amd
+% test17 - test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol
+% test18 - test iterative refinement after backslash
+% test19 - test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc, cspy
+% test20 - test chol_updown2
+% test21 - test cs_updown, chol_updown2
+% test22 - test cond1est
+% test23 - test cs_dmspy
+% test24 - test cs_fielder
+% test25 - test cs_nd
+% test26 - test cs_dmsol and cs_dmspy
+% test27 - test cs_qr, cs_utsolve, cs_qrsol
+% test28 - test cs_randperm, cs_dmperm
+
+% Example:
+% help chol_update
+
+% Copyright 2006-2007, Timothy A. Davis
diff --git a/CXSparse_newfiles/MATLAB/Test/Makefile b/CXSparse_newfiles/MATLAB/Test/Makefile
new file mode 100644
index 0000000..3b4e4ef
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/Makefile
@@ -0,0 +1,53 @@
+include ../../../UFconfig/UFconfig.mk
+
+MX = $(MEX) -DCS_LONG
+AR = ar cr
+RANLIB = ranlib
+
+I = -I../../Include -I../../../UFconfig -I../CSparse
+
+all: cs_sparse2.mexglx \
+ cs_ipvec.mexglx \
+ cs_pvec.mexglx \
+ cs_reach.mexglx \
+ cs_maxtransr.mexglx \
+ cs_reachr.mexglx \
+ cs_rowcnt.mexglx \
+ cs_frand.mexglx
+
+mexcsparse:
+ ( cd ../CSparse ; make mexcsparse.a )
+
+cs_ipvec.mexglx: cs_ipvec_mex.c mexcsparse
+ $(MX) -output cs_ipvec $< $(I) ../CSparse/mexcsparse.a
+
+cs_pvec.mexglx: cs_pvec_mex.c mexcsparse
+ $(MX) -output cs_pvec $< $(I) ../CSparse/mexcsparse.a
+
+cs_reach.mexglx: cs_reach_mex.c mexcsparse
+ $(MX) -output cs_reach $< $(I) ../CSparse/mexcsparse.a
+
+cs_sparse2.mexglx: cs_sparse2_mex.c mexcsparse
+ $(MX) -output cs_sparse2 $< $(I) ../CSparse/mexcsparse.a
+
+cs_maxtransr.mexglx: cs_maxtransr_mex.c mexcsparse
+ $(MX) -output cs_maxtransr $< $(I) ../CSparse/mexcsparse.a
+
+cs_reachr.mexglx: cs_reachr_mex.c mexcsparse
+ $(MX) -output cs_reachr $< $(I) ../CSparse/mexcsparse.a
+
+cs_rowcnt.mexglx: cs_rowcnt_mex.c mexcsparse
+ $(MX) -output cs_rowcnt $< $(I) ../CSparse/mexcsparse.a
+
+cs_frand.mexglx: cs_frand_mex.c mexcsparse
+ $(MX) -output cs_frand $< $(I) ../CSparse/mexcsparse.a
+
+
+
+clean:
+ rm -f *.o
+
+distclean: clean
+ rm -f *.mex* *.a cs_cl_*.c
+
+purge: distclean
diff --git a/CXSparse_newfiles/MATLAB/Test/README.txt b/CXSparse_newfiles/MATLAB/Test/README.txt
new file mode 100644
index 0000000..e075bac
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/README.txt
@@ -0,0 +1,4 @@
+Test for MATLAB interface for CXSparse. Type "testall" to run all the tests.
+
+Also includes "textbook" codes for the book "Direct Methods for Sparse Linear
+Systems", which are not part of CXSparse proper, but are used in the tests.
diff --git a/CXSparse_newfiles/MATLAB/Test/chol_updown2.m b/CXSparse_newfiles/MATLAB/Test/chol_updown2.m
new file mode 100644
index 0000000..5cc844e
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/chol_updown2.m
@@ -0,0 +1,47 @@
+function [L, w] = chol_updown2 (L, sigma, w)
+%CHOL_UPDOWN2 Cholesky update/downdate (real and complex)
+% (real or complex)
+% Example:
+% [L, w] = chol_updown2 (L, sigma, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis, William W. Hager
+% http://www.cise.ufl.edu/research/sparse
+
+beta = 1 ;
+n = size (L,1) ;
+if (n == 1)
+ wnew = L\w ;
+ L = sqrt (L*L'+sigma*w*w') ;
+ w = wnew ;
+ return ;
+end
+for k = 1:n
+ alpha = w(k) / L(k,k) ;
+ beta2 = sqrt (beta*beta + sigma*alpha*conj(alpha)) ;
+ gamma = sigma * conj(alpha) / (beta2 * beta) ;
+ if (sigma > 0)
+ % update
+ delta = beta / beta2 ;
+ L (k,k) = delta * L (k,k) + gamma * w (k) ;
+ phase = abs (L (k, k))/L (k, k) ;
+ L (k, k) = phase*L (k, k) ;
+
+ w1 = w (k+1:n) ;
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k+1:n,k) = phase * (delta * L (k+1:n,k) + gamma * w1) ;
+
+ else
+ % downdate
+ delta = beta2 / beta ;
+ L (k,k) = delta * L (k,k) ;
+ phase = abs (L (k, k))/L (k, k) ;
+ L (k, k) = phase*L (k, k) ;
+
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k+1:n,k) = phase * (delta * L (k+1:n,k) + gamma * w (k+1:n)) ;
+
+ end
+ w (k) = alpha ;
+ beta = beta2 ;
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/cholupdown.m b/CXSparse_newfiles/MATLAB/Test/cholupdown.m
new file mode 100644
index 0000000..e450347
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cholupdown.m
@@ -0,0 +1,60 @@
+function L = cholupdown (Lold, sigma, w)
+%CHOLUPDOWN Cholesky update/downdate (Bischof, Pan, and Tang method)
+% This version only works for the real case. See chol_updown2 for
+% a code that handles both the real and complex cases.
+% Example:
+% L = cholupdown (Lold, sigma, w)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+beta = 1 ;
+n = size (Lold,1) ;
+L = Lold ;
+% x = weros (n,1) ;
+% worig = w ;
+
+for k = 1:n
+
+ alpha = w(k) / L(k,k) ;
+ beta_new = sqrt (beta^2 + sigma*alpha^2) ;
+ gamma = alpha / (beta_new * beta) ;
+
+ if (sigma < 0)
+
+ % downdate
+ bratio = beta_new / beta ;
+ w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+ L (k,k) = bratio * L (k,k) ;
+ L (k+1:n,k) = bratio * L (k+1:n,k) - gamma*w(k+1:n) ;
+
+ else
+
+ % update
+ bratio = beta / beta_new ;
+
+% wold = w (k+1:n) ;
+% w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
+% L (k ,k) = bratio * L (k ,k) + gamma*w(k) ;
+% L (k+1:n,k) = bratio * L (k+1:n,k) + gamma*wold ;
+
+ L (k,k) = bratio * L (k,k) + gamma*w(k) ;
+ for i = k+1:n
+
+ wold = w (i) ;
+ w (i) = w (i) - alpha * L (i,k) ;
+ L (i,k) = bratio * L (i,k) + gamma*wold ;
+
+ end
+
+ end
+
+ w (k) = alpha ;
+
+ beta = beta_new ;
+
+end
+
+% norm (w-(Lold\worig))
diff --git a/CXSparse_newfiles/MATLAB/Test/cs_fiedler.m b/CXSparse_newfiles/MATLAB/Test/cs_fiedler.m
new file mode 100644
index 0000000..35db8dc
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cs_fiedler.m
@@ -0,0 +1,30 @@
+function [p,v,d] = cs_fiedler (A)
+%CS_FIEDLER the Fiedler vector of a connected graph.
+% [p,v,d] = cs_fiedler(A) computes the Fiedler vector v (the eigenvector
+% corresponding to the 2nd smallest eigenvalue d of the Laplacian of the graph
+% of A+A'). p is the permutation obtained when v is sorted. A should be a
+% connected graph.
+%
+% Example:
+% [p,v,d] = cs_fiedler (A) ;
+%
+% See also CS_SCC, EIGS, SYMRCM, UNMESH.
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (A,1) ;
+if (n < 2)
+ p = 1 ; v = 1 ; d = 0 ; return ;
+end
+opt.disp = 0 ; % turn off printing in eigs
+opt.tol = sqrt (eps) ;
+if (~isreal (A))
+ A = spones (A) ;
+end
+S = A | A' | speye (n) ; % compute the Laplacian of A
+S = diag (sum (S)) - S ;
+[v,d] = eigs (S, 2, 'SA', opt) ; % find the Fiedler vector v
+v = v (:,2) ;
+d = d (2,2) ;
+[ignore p] = sort (v) ; % sort it to get p
diff --git a/CXSparse_newfiles/MATLAB/Test/cs_frand_mex.c b/CXSparse_newfiles/MATLAB/Test/cs_frand_mex.c
new file mode 100644
index 0000000..9768797
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cs_frand_mex.c
@@ -0,0 +1,59 @@
+#include "cs_mex.h"
+/* A = cs_frand (n,nel,s) creates an n-by-n sparse matrix consisting of nel
+ * finite elements, each of which are of size s-by-s with random symmetric
+ * nonzero pattern, plus the identity matrix.
+ * See also MATLAB/Demo/private/frand.m */
+
+cs_dl *cs_dl_frand (CS_INT n, CS_INT nel, CS_INT s)
+{
+ CS_INT ss = s*s, nz = nel*ss, e, i, j, *P ;
+ cs *A, *T = cs_dl_spalloc (n, n, nz, 1, 1) ;
+ if (!T) return (NULL) ;
+ P = cs_dl_malloc (s, sizeof (CS_INT)) ;
+ if (!P) return (cs_dl_spfree (T)) ;
+ for (e = 0 ; e < nel ; e++)
+ {
+ for (i = 0 ; i < s ; i++) P [i] = rand () % n ;
+ for (j = 0 ; j < s ; j++)
+ {
+ for (i = 0 ; i < s ; i++)
+ {
+ cs_dl_entry (T, P [i], P [j], rand () / (double) RAND_MAX) ;
+ }
+ }
+ }
+ for (i = 0 ; i < n ; i++) cs_dl_entry (T, i, i, 1) ;
+ A = cs_dl_compress (T) ;
+ cs_dl_spfree (T) ;
+ return (cs_dl_dupl (A) ? A : cs_dl_spfree (A)) ;
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT n, nel, s ;
+ cs *A, *AT ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: C = cs_frand(n,nel,s)") ;
+ }
+ n = mxGetScalar (pargin [0]) ;
+ nel = mxGetScalar (pargin [1]) ;
+ s = mxGetScalar (pargin [2]) ;
+
+ n = CS_MAX (1,n) ;
+ nel = CS_MAX (1,nel) ;
+ s = CS_MAX (1,s) ;
+
+ AT = cs_dl_frand (n, nel, s) ;
+ A = cs_dl_transpose (AT, 1) ;
+ cs_dl_spfree (AT) ;
+ cs_dl_dropzeros (A) ;
+
+ pargout [0] = cs_dl_mex_put_sparse (&A) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/Test/cs_ipvec_mex.c b/CXSparse_newfiles/MATLAB/Test/cs_ipvec_mex.c
new file mode 100644
index 0000000..974af01
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cs_ipvec_mex.c
@@ -0,0 +1,49 @@
+#include "cs_mex.h"
+/* x(p) = b */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT n, k, *p ;
+ double *xx ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_ipvec(b,p)") ;
+ }
+ n = mxGetNumberOfElements (pargin [0]) ;
+ if (n != mxGetNumberOfElements (pargin [1]))
+ {
+ mexErrMsgTxt ("b or p wrong size") ;
+ }
+
+ xx = mxGetPr (pargin [1]) ;
+ p = cs_dl_malloc (n, sizeof (CS_INT)) ;
+ for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ;
+
+ if (mxIsComplex (pargin [0]))
+ {
+#ifdef NCOMPLEX
+ mexErrMsgTxt ("complex case not supported") ;
+#else
+ cs_complex_t *x, *b ;
+ b = cs_cl_mex_get_double (n, pargin [0]) ;
+ x = cs_dl_malloc (n, sizeof (cs_complex_t)) ;
+ cs_cl_ipvec (p, b, x, n) ;
+ pargout [0] = cs_cl_mex_put_double (n, x) ;
+ cs_free (b) ; /* free copy of complex values */
+#endif
+ }
+ else
+ {
+ double *x, *b ;
+ b = cs_dl_mex_get_double (n, pargin [0]) ;
+ pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ cs_dl_ipvec (p, b, x, n) ;
+ }
+ cs_free (p) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/Test/cs_maxtransr_mex.c b/CXSparse_newfiles/MATLAB/Test/cs_maxtransr_mex.c
new file mode 100644
index 0000000..e97cec6
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cs_maxtransr_mex.c
@@ -0,0 +1,88 @@
+#include "cs_mex.h"
+/* find an augmenting path starting at column j and extend the match if found */
+static
+CS_INT augment (CS_INT k, cs_dl *A, CS_INT *jmatch, CS_INT *cheap, CS_INT *w,
+ CS_INT j)
+{
+ CS_INT found = 0, p, i = -1, *Ap = A->p, *Ai = A->i ;
+ /* --- Start depth-first-search at node j ------------------------------- */
+ w [j] = k ; /* mark j as visited for kth path */
+ for (p = cheap [j] ; p < Ap [j+1] && !found ; p++)
+ {
+ i = Ai [p] ; /* try a cheap assignment (i,j) */
+ found = (jmatch [i] == -1) ;
+ }
+ cheap [j] = p ; /* start here next time for j */
+ /* --- Depth-first-search of neighbors of j ----------------------------- */
+ for (p = Ap [j] ; p < Ap [j+1] && !found ; p++)
+ {
+ i = Ai [p] ; /* consider row i */
+ if (w [jmatch [i]] == k) continue ; /* skip col jmatch [i] if marked */
+ found = augment (k, A, jmatch, cheap, w, jmatch [i]) ;
+ }
+ if (found) jmatch [i] = j ; /* augment jmatch if path found */
+ return (found) ;
+}
+
+/* find a maximum transveral */
+static
+CS_INT *maxtrans (cs_dl *A) /* returns jmatch [0..m-1] */
+{
+ CS_INT i, j, k, n, m, *Ap, *jmatch, *w, *cheap ;
+ if (!A) return (NULL) ; /* check inputs */
+ n = A->n ; m = A->m ; Ap = A->p ;
+ jmatch = cs_dl_malloc (m, sizeof (CS_INT)) ; /* allocate result */
+ w = cs_dl_malloc (2*n, sizeof (CS_INT)) ; /* allocate workspace */
+ if (!w || !jmatch) return (cs_dl_idone (jmatch, NULL, w, 0)) ;
+ cheap = w + n ;
+ for (j = 0 ; j < n ; j++) cheap [j] = Ap [j] ; /* for cheap assignment */
+ for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */
+ for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* no rows matched yet */
+ for (k = 0 ; k < n ; k++) augment (k, A, jmatch, cheap, w, k) ;
+ return (cs_dl_idone (jmatch, NULL, w, 1)) ;
+}
+
+/* invert a maximum matching */
+static CS_INT *invmatch (CS_INT *jmatch, CS_INT m, CS_INT n)
+{
+ CS_INT i, j, *imatch ;
+ if (!jmatch) return (NULL) ;
+ imatch = cs_dl_malloc (n, sizeof (CS_INT)) ;
+ if (!imatch) return (NULL) ;
+ for (j = 0 ; j < n ; j++) imatch [j] = -1 ;
+ for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ;
+ return (imatch) ;
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl *A, Amatrix ;
+ double *x ;
+ CS_INT i, m, n, *imatch, *jmatch ;
+
+ if (nargout > 1 || nargin != 1)
+ {
+ mexErrMsgTxt ("Usage: p = cr_maxtransr(A)") ;
+ }
+
+ /* get inputs */
+ A = cs_dl_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ;
+ m = A->m ;
+ n = A->n ;
+
+ jmatch = maxtrans (A) ;
+ imatch = invmatch (jmatch, m, n) ; /* imatch = inverse of jmatch */
+
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n ; i++) x [i] = imatch [i] + 1 ;
+
+ cs_free (jmatch) ;
+ cs_free (imatch) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/Test/cs_pvec_mex.c b/CXSparse_newfiles/MATLAB/Test/cs_pvec_mex.c
new file mode 100644
index 0000000..d8505fa
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cs_pvec_mex.c
@@ -0,0 +1,49 @@
+#include "cs_mex.h"
+/* x = b(p) */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT n, k, *p ;
+ double *xx ;
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_pvec(b,p)") ;
+ }
+ n = mxGetNumberOfElements (pargin [0]) ;
+ if (n != mxGetNumberOfElements (pargin [1]))
+ {
+ mexErrMsgTxt ("b or p wrong size") ;
+ }
+
+ xx = mxGetPr (pargin [1]) ;
+ p = cs_dl_malloc (n, sizeof (CS_INT)) ;
+ for (k = 0 ; k < n ; k++) p [k] = xx [k] - 1 ;
+
+ if (mxIsComplex (pargin [0]))
+ {
+#ifdef NCOMPLEX
+ mexErrMsgTxt ("complex case not supported") ;
+#else
+ cs_complex_t *x, *b ;
+ b = cs_cl_mex_get_double (n, pargin [0]) ;
+ x = cs_dl_malloc (n, sizeof (cs_complex_t)) ;
+ cs_cl_pvec (p, b, x, n) ;
+ pargout [0] = cs_cl_mex_put_double (n, x) ;
+ cs_free (b) ; /* free copy of complex values */
+#endif
+ }
+ else
+ {
+ double *x, *b ;
+ b = cs_dl_mex_get_double (n, pargin [0]) ;
+ pargout [0] = mxCreateDoubleMatrix (n, 1, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ cs_dl_pvec (p, b, x, n) ;
+ }
+ cs_free (p) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/Test/cs_reach_mex.c b/CXSparse_newfiles/MATLAB/Test/cs_reach_mex.c
new file mode 100644
index 0000000..ec72443
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cs_reach_mex.c
@@ -0,0 +1,39 @@
+#include "cs_mex.h"
+/* find nonzero pattern of x=L\sparse(b). L must be sparse and lower
+ * triangular. b must be a sparse vector. */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs Lmatrix, Bmatrix, *L, *B ;
+ double *x ;
+ CS_INT k, i, j, top, *xi, *perm ;
+
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_reach(L,b)") ;
+ }
+
+ /* get inputs */
+ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
+ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;
+ cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ;
+ perm = cs_dl_malloc (L->n, sizeof (CS_INT)) ;
+ for (k = 0 ; k < L->n ; k++) perm [k] = k ;
+
+ xi = cs_dl_calloc (3*L->n, sizeof (CS_INT)) ;
+
+ top = cs_dl_reach (L, B, 0, xi, perm) ;
+
+ pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ;
+
+ cs_free (xi) ;
+ cs_free (perm) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/Test/cs_reachr_mex.c b/CXSparse_newfiles/MATLAB/Test/cs_reachr_mex.c
new file mode 100644
index 0000000..ca7e009
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cs_reachr_mex.c
@@ -0,0 +1,67 @@
+#include "cs_mex.h"
+/* find nonzero pattern of x=L\sparse(b). L must be sparse and lower
+ * triangular. b must be a sparse vector. */
+
+static
+void dfsr (CS_INT j, const cs *L, CS_INT *top, CS_INT *xi, CS_INT *w)
+{
+ CS_INT p ;
+ w [j] = 1 ; /* mark node j */
+ for (p = L->p [j] ; p < L->p [j+1] ; p++) /* for each i in L(:,j) */
+ {
+ if (w [L->i [p]] != 1) /* if i is unmarked */
+ {
+ dfsr (L->i [p], L, top, xi, w) ; /* start a dfs at i */
+ }
+ }
+ xi [--(*top)] = j ; /* push j onto the stack */
+}
+
+/* w [0..n-1] == 0 on input, <= 1 on output. size n */
+static
+CS_INT reachr (const cs *L, const cs *B, CS_INT *xi, CS_INT *w)
+{
+ CS_INT p, n = L->n ;
+ CS_INT top = n ; /* stack is empty */
+ for (p = B->p [0] ; p < B->p [1] ; p++) /* for each i in pattern of b */
+ {
+ if (w [B->i [p]] != 1) /* if i is unmarked */
+ {
+ dfsr (B->i [p], L, &top, xi, w) ; /* start a dfs at i */
+ }
+ }
+ return (top) ; /* return top of stack */
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl Lmatrix, Bmatrix, *L, *B ;
+ double *x ;
+ CS_INT i, j, top, *xi ;
+
+ if (nargout > 1 || nargin != 2)
+ {
+ mexErrMsgTxt ("Usage: x = cs_reachr(L,b)") ;
+ }
+
+ /* get inputs */
+ L = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
+ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;
+ cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ;
+
+ xi = cs_dl_calloc (2*L->n, sizeof (CS_INT)) ;
+
+ top = reachr (L, B, xi, xi + L->n) ;
+
+ pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ;
+
+ cs_free (xi) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/Test/cs_rowcnt_mex.c b/CXSparse_newfiles/MATLAB/Test/cs_rowcnt_mex.c
new file mode 100644
index 0000000..7ba9a30
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cs_rowcnt_mex.c
@@ -0,0 +1,88 @@
+/* Compute the row counts of the Cholesky factor L of the matrix A. Uses
+ * the lower triangular part of A. */
+
+#include "cs_mex.h"
+
+static
+void firstdesc (CS_INT n, CS_INT *parent, CS_INT *post, CS_INT *first,
+ CS_INT *level)
+{
+ CS_INT len, i, k, r, s ;
+ for (i = 0 ; i < n ; i++) first [i] = -1 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ i = post [k] ; /* node i of etree is kth postordered node */
+ len = 0 ; /* traverse from i towards the root */
+ for (r = i ; r != -1 && first [r] == -1 ; r = parent [r], len++)
+ first [r] = k ;
+ len += (r == -1) ? (-1) : level [r] ; /* root node or end of path */
+ for (s = i ; s != r ; s = parent [s]) level [s] = len-- ;
+ }
+}
+
+/* return rowcount [0..n-1] */
+static
+CS_INT *rowcnt (cs_dl *A, CS_INT *parent, CS_INT *post)
+{
+ CS_INT i, j, k, len, s, p, jprev, q, n, sparent, jleaf, *Ap, *Ai, *maxfirst,
+ *ancestor, *prevleaf, *w, *first, *level, *rowcount ;
+ n = A->n ; Ap = A->p ; Ai = A->i ; /* get A */
+ w = cs_dl_malloc (5*n, sizeof (CS_INT)) ; /* get workspace */
+ ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ;
+ level = w+4*n ;
+ rowcount = cs_dl_malloc (n, sizeof (CS_INT)) ; /* allocate result */
+ firstdesc (n, parent, post, first, level) ; /* find first and level */
+ for (i = 0 ; i < n ; i++)
+ {
+ rowcount [i] = 1 ; /* count the diagonal of L */
+ prevleaf [i] = -1 ; /* no previous leaf of the ith row subtree */
+ maxfirst [i] = -1 ; /* max first[j] for node j in ith subtree */
+ ancestor [i] = i ; /* every node is in its own set, by itself */
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ j = post [k] ; /* j is the kth node in the postordered etree */
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ q = cs_dl_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf) ;
+ if (jleaf) rowcount [i] += (level [j] - level [q]) ;
+ }
+ if (parent [j] != -1) ancestor [j] = parent [j] ;
+ }
+ cs_dl_free (w) ;
+ return (rowcount) ;
+}
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ cs_dl *A, Amatrix ;
+ double *x ;
+ CS_INT i, m, n, *parent, *post, *rowcount ;
+
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: r = cs_rowcnt(A,parent,post)") ;
+ }
+
+ /* get inputs */
+ A = cs_dl_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ;
+ n = A->n ;
+
+ parent = cs_dl_mex_get_int (n, pargin [1], &i, 0) ;
+ post = cs_dl_mex_get_int (n, pargin [2], &i, 1) ;
+
+ rowcount = rowcnt (A, parent, post) ;
+
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ x = mxGetPr (pargout [0]) ;
+ for (i = 0 ; i < n ; i++) x [i] = rowcount [i] ;
+
+ cs_dl_free (rowcount) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/Test/cs_sparse2_mex.c b/CXSparse_newfiles/MATLAB/Test/cs_sparse2_mex.c
new file mode 100644
index 0000000..dddcad9
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cs_sparse2_mex.c
@@ -0,0 +1,64 @@
+#include "cs_mex.h"
+/* A = cs_sparse2 (i,j,x), removing duplicates and numerically zero entries,
+ * and returning A sorted (test cs_entry) */
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ CS_INT k, m, n, nz, *Ti, *Tj ;
+ if (nargout > 1 || nargin != 3)
+ {
+ mexErrMsgTxt ("Usage: A = cs_sparse2(i,j,x)") ;
+ }
+ nz = mxGetM (pargin [0]) ;
+ Ti = cs_dl_mex_get_int (nz, pargin [0], &m, 1) ;
+ Tj = cs_dl_mex_get_int (nz, pargin [1], &n, 1) ;
+ cs_mex_check (1, nz, 1, 0, 0, 1, pargin [2]) ;
+ if (mxIsComplex (pargin [2]))
+ {
+#ifdef NCOMPLEX
+ mexErrMsgTxt ("complex case not supported") ;
+#else
+ cs_complex_t *Tx ;
+ cs_cl *A, *C, *T ;
+ Tx = cs_cl_mex_get_double (nz, pargin [2]) ;
+ T = cs_cl_spalloc (n, m, 1, 1, 1) ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ cs_cl_entry (T, Tj [k], Ti [k], Tx [k]) ;
+ }
+ C = cs_cl_compress (T) ;
+ cs_cl_spfree (T) ;
+ cs_cl_dupl (C) ;
+ cs_cl_dropzeros (C) ;
+ A = cs_cl_transpose (C, -1) ;
+ cs_cl_spfree (C) ;
+ pargout [0] = cs_cl_mex_put_sparse (&A) ;
+ cs_free (Tx) ;
+#endif
+ }
+ else
+ {
+ double *Tx ;
+ cs_dl *A, *C, *T ;
+ Tx = mxGetPr (pargin [2]) ;
+ T = cs_dl_spalloc (n, m, 1, 1, 1) ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ cs_dl_entry (T, Tj [k], Ti [k], Tx [k]) ;
+ }
+ C = cs_dl_compress (T) ;
+ cs_dl_spfree (T) ;
+ cs_dl_dupl (C) ;
+ cs_dl_dropzeros (C) ;
+ A = cs_dl_transpose (C, 1) ;
+ cs_dl_spfree (C) ;
+ pargout [0] = cs_dl_mex_put_sparse (&A) ;
+ }
+ cs_free (Ti) ;
+ cs_free (Tj) ;
+}
diff --git a/CXSparse_newfiles/MATLAB/Test/cs_test_make.m b/CXSparse_newfiles/MATLAB/Test/cs_test_make.m
new file mode 100644
index 0000000..60303b6
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/cs_test_make.m
@@ -0,0 +1,43 @@
+function cs_test_make (force)
+%CS_TEST_MAKE compiles the CSparse, Demo, and Test mexFunctions.
+% The current directory must be CSparse/MATLAB/Test to use this function.
+%
+% Example:
+% cs_test_make
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+mexcmd = 'mex -DCS_LONG -I../../../UFconfig' ;
+if (~isempty (strfind (computer, '64')))
+ mexcmd = [mexcmd ' -largeArrayDims'] ;
+end
+
+if (nargin < 1)
+ force = 0 ;
+end
+
+cd ('../CSparse') ;
+[object_files timestamp] = cs_make ;
+cd ('../Test') ;
+
+mexfunc = { 'cs_ipvec', 'cs_pvec', 'cs_sparse2', ...
+ 'cs_reach', 'cs_maxtransr', 'cs_reachr', 'cs_rowcnt', 'cs_frand' } ;
+
+if (ispc)
+ % Windows does not support ANSI C99
+ mexcmd = [mexcmd ' -DNCOMPLEX'] ;
+end
+
+for i = 1:length(mexfunc)
+ [s t tobj] = cs_must_compile ('', mexfunc{i}, '_mex', ...
+ ['.' mexext], 'cs_test_make.m', force) ;
+ if (s | tobj < timestamp) %#ok
+ cmd = [mexcmd ' -O -output ' mexfunc{i} ' ' mexfunc{i} '_mex.c -I..' ...
+ filesep '..' filesep 'Include -I..' ...
+ filesep 'CSparse ' object_files] ;
+ fprintf ('%s\n', cmd) ;
+ eval (cmd) ;
+ end
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/house.m b/CXSparse_newfiles/MATLAB/Test/house.m
new file mode 100644
index 0000000..6c6c589
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/house.m
@@ -0,0 +1,24 @@
+function [v,beta,s] = house (x)
+%HOUSE find a Householder reflection.
+% real or complex case.
+% Example:
+% [v,beta,s] = house (x)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+v = x ;
+s = norm (x) ;
+if (s == 0)
+ beta = 0 ;
+ v (1) = 1 ;
+else
+ if (x (1) ~= 0)
+ s = sign (x (1)) * s ;
+ end
+ v (1) = v (1) + s ;
+ beta = 1 / real (conj (s) * v (1)) ;
+end
+s = - s ;
+
diff --git a/CXSparse_newfiles/MATLAB/Test/norm1est.m b/CXSparse_newfiles/MATLAB/Test/norm1est.m
new file mode 100644
index 0000000..edd5d09
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/norm1est.m
@@ -0,0 +1,35 @@
+function est = norm1est (L,U,P,Q)
+%NORM1EST 1-norm estimate.
+% L and U must be real.
+% Example:
+% est = norm1est (L,U,P,Q)
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+n = size (L,1) ;
+for k = 1:5
+ if (k == 1)
+ est = 0 ;
+ x = ones (n,1) / n ;
+ jold = -1 ;
+ else
+ j = min (find (abs (x) == norm (x,inf))) ; %#ok
+ if (j == jold)
+ break
+ end ;
+ x = zeros (n,1) ;
+ x (j) = 1 ;
+ jold = j ;
+ end
+ x = Q * (U \ (L \ (P*x))) ;
+ est_old = est ;
+ est = norm (x,1) ;
+ if (k > 1 & est <= est_old) %#ok
+ break
+ end ;
+ s = ones (n,1) ;
+ s (find (x < 0)) = -1 ; %#ok
+ x = P' * (L' \ (U' \ (Q'*s))) ;
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test1.m b/CXSparse_newfiles/MATLAB/Test/test1.m
new file mode 100644
index 0000000..d5c2196
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test1.m
@@ -0,0 +1,88 @@
+function test1
+%TEST1 test cs_transpose, cs_gaxpy, cs_sparse, cs_sparse2
+%
+% Example:
+% test1
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+for ii = f
+
+ Prob = UFget (ii) ;
+ disp (Prob) ;
+ for cmplex = 0:double(~ispc)
+
+ A = Prob.A ;
+ if (cmplex)
+ A = A + 1i*sprand(A) ;
+ end
+
+ B = A' ;
+ C = cs_transpose (A) ;
+ if (nnz (B-C) ~= 0)
+ error ('!')
+ end
+
+ C = cs_transpose (A,0) ;
+ if (nnz (A.'-C) ~= 0)
+ error ('!')
+ end
+
+ C = cs_transpose (A,1) ;
+ if (nnz (A'-C) ~= 0)
+ error ('!')
+ end
+
+ [m n] = size (A) ;
+ % if (m == n)
+ x = rand (n,1) ;
+ y = rand (m,1) ;
+ z = y+A*x ;
+ q = cs_gaxpy (A,x,y) ;
+ err = norm (z-q,1) / norm (z,1) ;
+ disp (err) ;
+ if (err > 1e-14)
+ error ('!')
+ end
+ % end
+
+ if (~ispc)
+ x = x + 1i*rand (n,1) ;
+ y = y + 1i*rand (m,1) ;
+ z = y+A*x ;
+ q = cs_gaxpy (A,x,y) ;
+ err = norm (z-q,1) / norm (z,1) ;
+ disp (err) ;
+ if (err > 1e-14)
+ error ('!')
+ end
+ end
+
+ [i j x] = find (A) ;
+ p = randperm (length (i)) ;
+ i = i (p) ;
+ j = j (p) ;
+ x = x (p) ;
+ D = sparse (i,j,x) ;
+ E = cs_sparse (i,j,x) ;
+ % [i j x]
+ F = cs_sparse2 (i,j,x) ;
+ if (nnz (D-E) ~= 0)
+ error ('!')
+ end
+ if (nnz (F-E) ~= 0)
+ error ('!')
+ end
+
+ clear A B C D E F
+ % pause
+
+ end
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test10.m b/CXSparse_newfiles/MATLAB/Test/test10.m
new file mode 100644
index 0000000..f33fe9e
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test10.m
@@ -0,0 +1,108 @@
+function test10
+%TEST10 test cs_qr
+%
+% Example:
+% test10
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+
+% f = 185 ;
+% f = 449 ;
+clf
+
+for trials = 1:100
+
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = 0.1 * rand (1) ;
+ A = sprandn (m, n, d) ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ sp = sprank (A) ;
+ % if (sp < n)
+ % continue ;
+ % end
+
+ for cmplex = 0:double(~ispc)
+
+ if (cmplex)
+ A = A + 1i * sprand (A) * norm (A,1) / 10 ;
+ end
+
+ Aorig = A ;
+
+ % A = A (:, colamd (A)) ;
+
+ if (cmplex)
+ tic ;
+ R = chol (A'*A + speye (n)) ;
+ t1 = toc ;
+ else
+ tic ;
+ R = qr (A) ;
+ t1 = toc ;
+ end
+
+ % tic ;
+ % [Q,R] = qr (A) ;
+ % t1 = toc ;
+
+ [c,h,parent] = symbfact (A, 'col') ; %#ok
+ rnz = sum (c) ; %#ok
+ tic ;
+ [V2,Beta2,p,R2] = cs_qr (sparse(A)) ;
+ t2 = toc ;
+
+ C = A ;
+ m2 = size (V2,1) ;
+ if (m2 > m)
+ C = [A ; sparse(m2-m, n)] ;
+ end
+ C = C (p,:) ;
+
+ [H1,R1] = myqr (C) ;
+ err1 = norm (R1-R2,1) / norm (R1) ;
+ disp ('err1 = ') ;
+ disp (err1) ;
+ % [svd(A) svd(R1) svd(full(R2))]
+ s1 = svd (full (A)) ;
+ s2 = svd (full (R2)) ;
+ if (n > 0)
+ err2 = norm (s1 - s2) / s1 (1) ;
+ disp ('err2 = ') ;
+ disp (err2) ;
+ else
+ err2 = 0 ;
+ end
+ fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d vs %d\n', t1, t2, t1/t2, sp, n) ;
+
+ % H2 = full (H2)
+ % R2 = full (R2)
+
+ subplot (2,4,1) ; spy (A) ; title ('A colamd') ;
+ subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ;
+ subplot (2,4,2) ; spy (C) ; title ('A rperm') ;
+ subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ;
+ subplot (2,4,6) ; spy (R) ; title ('matlab R') ;
+ subplot (2,4,7) ; spy (R2) ; title ('spqr R') ;
+ subplot (2,4,8) ; spy (V2) ; title ('spqr H') ;
+ drawnow
+
+ if (err2 > 1e-9)
+ error ('!') ;
+ end
+
+ if (m2 > m)
+ fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ;
+ end
+ end
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test11.m b/CXSparse_newfiles/MATLAB/Test/test11.m
new file mode 100644
index 0000000..2e86baa
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test11.m
@@ -0,0 +1,55 @@
+function test11
+%TEST11 test cs_rowcnt
+%
+% Example:
+% test11
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+
+for i = f
+ Prob = UFget (i, index) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ A = spones (A) ;
+ A = A+A' + speye(n) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ [cc h pa po R] = symbfact (A) ;
+ rc1 = full (sum (R)) ;
+ rc2 = cs_rowcnt (A, pa, po) ;
+ if (any (rc1 ~= rc2))
+ error ('!') ;
+ end
+
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ A = A (p,p) ;
+
+ [cc h pa po R] = symbfact (A) ;
+ rc1 = full (sum (R)) ;
+ rc2 = cs_rowcnt (A, pa, po) ;
+ if (any (rc1 ~= rc2))
+ error ('!') ;
+ end
+
+end
+
diff --git a/CXSparse_newfiles/MATLAB/Test/test12.m b/CXSparse_newfiles/MATLAB/Test/test12.m
new file mode 100644
index 0000000..e4c3b49
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test12.m
@@ -0,0 +1,47 @@
+function test12
+%TEST12 test cs_qr and compare with svd
+%
+% Example:
+% test12
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('test 12\n') ;
+rand ('state',0) ;
+% A = rand (3,4)
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = .1 * rand (1) ;
+ A = sprandn (m,n,d) ;
+ if (m < n)
+ continue ;
+ end
+ if (m == 0 | n == 0) %#ok
+ continue ;
+ end
+
+ for cmplex = 0:double(~ispc)
+ if (cmplex)
+ A = A + 1i * sprand (A) ;
+ end
+
+ fprintf ('m %d n %d nnz %d\n', m, n, nnz(A)) ;
+ [V,Beta,p,R] = cs_qr (A) ;
+
+ s1 = svd (full (A)) ;
+ s2 = svd (full (R)) ;
+ s2 = s2 (1:length(s1)) ;
+ err = norm (s1-s2) ;
+ if (length (s1) > 1)
+ err = err / s1 (1) ;
+ end
+ fprintf ('err %g\n', err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+ end
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test13.m b/CXSparse_newfiles/MATLAB/Test/test13.m
new file mode 100644
index 0000000..fd3b2e5
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test13.m
@@ -0,0 +1,88 @@
+function test13
+%TEST13 test cs_counts, cs_etree
+%
+% Example:
+% test13
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+randn ('state',0) ;
+rand ('state',0) ;
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = .1 * rand (1) ;
+ A = sprandn (n,n,d) ;
+ C = sprandn (m,n,d) ;
+ A = A+A' ;
+ fprintf ('m %4d n %4d nnz(A) %6d nnz(C) %6d\n', m, n, nnz(A), nnz(C)) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ [p1,po1] = etree (A) ;
+
+ [p2,po2] = cs_etree (A) ;
+ [p3,po3] = cs_etree (A, 'sym') ;
+ % po2 = cs_post (p2) ;
+
+ check_if_same (p1,p2) ;
+ check_if_same (po1,po2) ;
+
+ check_if_same (p1,p3) ;
+ check_if_same (po1,po3) ;
+
+ c1 = symbfact (A) ;
+ c2 = cs_counts (A) ;
+
+ % A-A'
+
+ check_if_same (c1,c2) ;
+
+ c2 = cs_counts (triu (A)) ;
+ check_if_same (c1,c2) ;
+ % pause
+
+ p0 = etree (A, 'col') ;
+ % p1 = etree2 (A, 'col') ; % CHOLMOD
+ p2 = cs_etree (A, 'col') ;
+
+ if (~isempty (A))
+ check_if_same (p0,p2) ;
+ end
+
+ p0 = etree (C, 'col') ;
+ % p1 = etree2 (C, 'col') ; % CHOLMOD
+ p2 = cs_etree (C, 'col') ;
+
+ if (~isempty (C))
+ check_if_same (p0,p2) ;
+ end
+
+ % find etree of A'A, and postorder it
+ [m n] = size (A) ; %#ok
+ % full (A)
+
+ [cp0 cpo0] = etree (A, 'col') ;
+ % [cp1 cpo1] = etree2 (A, 'col') ; % CHOLMOD
+ [cp2 cpo2] = cs_etree (A, 'col') ;
+ % cpo2 = cs_post (cp2) ;
+
+ check_if_same (cp0, cp2) ;
+ check_if_same (cpo0, cpo2) ;
+
+ c0 = symbfact (A, 'col') ;
+ % c1 = symbfact2 (A, 'col') ; % CHOLMOD
+ c2 = cs_counts (A, 'col') ;
+
+ check_if_same (c0, c2) ;
+
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test14.m b/CXSparse_newfiles/MATLAB/Test/test14.m
new file mode 100644
index 0000000..4de44a1
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test14.m
@@ -0,0 +1,45 @@
+function test14
+%TEST14 test cs_droptol
+%
+% Example:
+% test14
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+for trial = 1:100
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = 0.1*rand (1) ;
+ A = sprandn (m,n,d) ;
+ [i j x] = find (A) ;
+ A = sparse (i,j,2*x-1) ;
+ fprintf ('test14 m %3d n %3d nz %d\n', m, n, nnz (A)) ;
+
+ for cmplex = 0:double(~ispc)
+
+ if (cmplex)
+ A = A + 1i * sparse (i,j,2*rand(size(x))-1) ;
+ end
+
+ % using CSparse
+ tol = 0.5 ;
+ B = cs_droptol (A, tol) ;
+
+ % using MATLAB
+ C = A .* (abs (A) > tol) ;
+ % [m n] = size (A) ;
+ % s = abs (A) > tol ;
+ % [i j] = find (s) ;
+ % x = A (find (s)) ;
+ % A = sparse (i, j, x, m, n) ;
+
+ if (norm (C-B,1) > 0)
+ error ('!') ;
+ end
+ end
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test15.m b/CXSparse_newfiles/MATLAB/Test/test15.m
new file mode 100644
index 0000000..9269d36
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test15.m
@@ -0,0 +1,56 @@
+function test15
+%TEST15 test cs_amd
+%
+% Example:
+% test15
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+clf
+
+for trials = 1:100
+ n = fix (200 * rand (1)) ;
+ d = 0.05 * rand (1) ;
+ A = sprandn (n, n, d) ;
+
+ % add a randomly placed dense column
+ k = fix (n * rand (1)) ;
+ k = max (1, k) ;
+ k = min (n, k) ;
+ if (n > 0)
+ A (:,k) = 1 ;
+ end
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ try
+ p0 = amd (A) ;
+ catch
+ p0 = symamd (A) ;
+ end
+ p1 = cs_amd (A) ;
+
+ if (any (sort (p1) ~= 1:n))
+ error ('not perm!') ;
+ end
+
+ C = A+A' + speye (n) ;
+ lnz0 = sum (symbfact (C (p0,p0))) ;
+ lnz1 = sum (symbfact (C (p1,p1))) ;
+ subplot (1,3,1) ; spy (C)
+ subplot (1,3,2) ; spy (C (p0,p0))
+ subplot (1,3,3) ; spy (C (p1,p1))
+ fprintf ('n %4d nz %6d lnz %6d %6d\n', n, nnz(A), lnz0, lnz1) ;
+ drawnow
+
+end
+
diff --git a/CXSparse_newfiles/MATLAB/Test/test16.m b/CXSparse_newfiles/MATLAB/Test/test16.m
new file mode 100644
index 0000000..fe7529c
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test16.m
@@ -0,0 +1,96 @@
+function test16
+%TEST16 test cs_amd
+%
+% Example:
+% test16
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+clf
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+skip = 811 ;
+
+% f = 719
+
+for i = f
+ if (any (i == skip))
+ continue
+ end
+ Prob = UFget (i) ;
+ A = spones (Prob.A) ;
+ Aorig = A ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ if (m ~= n)
+ A = A'*A ;
+ end
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ fprintf ('n %4d nz %d\n', n, nnz (A)) ;
+
+ try
+ p0 = amd (A) ;
+ catch
+ p0 = symamd (A) ;
+ end
+ fprintf ('symmetric case:\n') ;
+ p1 = cs_amd (A) ;
+
+ if (any (sort (p1) ~= 1:n))
+ error ('not perm!') ;
+ end
+
+ C = A+A' + speye (n) ;
+ lnz0 = sum (symbfact (C (p0,p0))) ;
+ lnz1 = sum (symbfact (C (p1,p1))) ;
+ subplot (2,3,1) ; spy (C)
+ subplot (2,3,2) ; spy (C (p0,p0)) ; title ('amd') ;
+ subplot (2,3,3) ; spy (C (p1,p1)) ; title ('csamd') ;
+ drawnow
+
+ if (lnz0 ~= lnz1)
+ fprintf ('----------------- lnz %d %d %9.4f\n', ...
+ lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ;
+ end
+
+ if (1)
+
+ p0 = colamd (Aorig) ;
+ [m n] = size (Aorig) ;
+ fprintf ('m %d n %d\n', m, n) ;
+
+ fprintf ('A''A case, no dense rows (for QR):\n') ;
+ p1 = cs_amd (Aorig, 3) ;
+ if (any (sort (p1) ~= 1:n))
+ error ('not perm!') ;
+ end
+
+ subplot (2,3,4) ; spy (Aorig)
+ subplot (2,3,5) ; spy (Aorig (:,p0)) ; title ('colamd') ;
+ subplot (2,3,6) ; spy (Aorig (:,p1)) ; title ('cs amd(A''A)') ;
+ lnz0 = sum (symbfact (Aorig (:,p0), 'col')) ;
+ lnz1 = sum (symbfact (Aorig (:,p1), 'col')) ;
+ fprintf (' A''A: %7d %7d %9.4f\n', ...
+ lnz0, lnz1, 100*(lnz0-lnz1)/max([1 lnz0])) ;
+ drawnow
+
+ % pause
+
+ end
+end
+
diff --git a/CXSparse_newfiles/MATLAB/Test/test17.m b/CXSparse_newfiles/MATLAB/Test/test17.m
new file mode 100644
index 0000000..1ab9406
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test17.m
@@ -0,0 +1,115 @@
+function test17
+%TEST17 test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol
+%
+% Example:
+% test17
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+clf
+
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+for trials = 1:100
+
+ m = 1 + fix (10 * rand (1)) ;
+ n = 1 + fix (10 * rand (1)) ;
+ d = rand (1) ;
+% n = m ;
+
+ A = sprandn (m, n, d) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ subplot (3,4,1) ; spy (A) ;
+
+ [V1, Beta1, p1, R1, q1] = cs_qr (A) ;
+ Q1 = cs_qright (V1, Beta1, p1, speye (size (V1,1))) ;
+ Q1b = cs_q1 (V1, Beta1, p1) ;
+
+ err = norm (Q1-Q1b,1) ;
+ disp ('err = ') ;
+ disp (err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+ m2 = size (Q1,1) ;
+ A1 = [A ; sparse(m2-m,n)] ;
+
+ subplot (3,4,5) ; spy (A1 (p1,q1)) ;
+ subplot (3,4,6) ; spy (V1) ;
+ subplot (3,4,7) ; spy (R1) ;
+ subplot (3,4,8) ; spy (Q1) ;
+
+ [V3, Beta3, R3] = qr2 (A) ;
+ % Q3 = cs_qmake (V3, Beta3) ;
+ Q3 = cs_q1 (V3, Beta3) ;
+ subplot (3,4,9) ; spy (A) ;
+ subplot (3,4,10) ; spy (V3) ;
+ subplot (3,4,11) ; spy (R3) ;
+ subplot (3,4,12) ; spy (Q3) ;
+
+ err1 = norm (Q1*R1 - A1(:,q1), 1) ;
+% err2 = norm (Q2*R2 - A (:,q2), 1) ;
+ err3 = norm (Q3*R3 - A, 1) ;
+
+ fprintf ('m %3d m2 %3d n %3d ::: %3d %6.2e %6.2e\n', ...
+ m, m2, n, m2-m, err1, err3) ;
+
+ if (err1 > 1e-12)
+ error ('2!') ;
+ end
+
+% if (err2 > 1e-12)
+% error ('!') ;
+% end
+
+ if (err3 > 1e-12)
+ error ('3!') ;
+ end
+
+try
+
+ % this fails if A is complex
+ b = rand (m,1) ;
+ [Q,R] = qr (A (:,q1)) ;
+ x = R\(Q'*b) ;
+ x (q1) = x ;
+ r1 = norm (A*x-b) ;
+
+ x2 = cs_qrsol (A,b) ;
+ r2 = norm (A*x2(1:n)-b) ;
+
+ qt = cs_qleft (V1, Beta1, p1, speye(size(V1,1))) ;
+ fprintf ('Q''*A-R: %6.2e\n', norm (qt*A1(:,q1)-R1,1)) ;
+
+ qtb = cs_qleft (V1, Beta1, p1, b) ;
+ % [V1, Beta1, p1, R1, q1] = cs_qr (A) ;
+ x3 = R1 \ qtb ;
+ r3 = norm (A(:,q1)*x3(1:n)-b) ;
+
+ fprintf ('least sq: %6.2e %6.2e %6.2e diff %6.2e %6.2e\n', ...
+ r1, r2, r3, r1-r2, r1-r3) ;
+
+catch
+end
+
+ drawnow
+
+ % pause
+
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test18.m b/CXSparse_newfiles/MATLAB/Test/test18.m
new file mode 100644
index 0000000..b2d9339
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test18.m
@@ -0,0 +1,34 @@
+function test18
+%TEST18 test iterative refinement after backslash
+%
+% Example:
+% test18
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+clf
+% f = f(1)
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (~isreal (A) | m ~= n) %#ok
+ continue
+ end
+
+ b = rand (n,1) ;
+ x = A\b ;
+ r = b - A*x ;
+ x = x + A\r ;
+
+ fprintf ('\n%6.2e to %6.2e\n', norm (r), norm (b-A*x)) ;
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test19.m b/CXSparse_newfiles/MATLAB/Test/test19.m
new file mode 100644
index 0000000..6143241
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test19.m
@@ -0,0 +1,209 @@
+function test19
+%TEST19 test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc, cspy
+%
+% Example:
+% test19
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+clf
+
+for trials = 1:100
+
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ % d = 0.1 * rand (1) ;
+ d = rand (1) * 4 * max (m,n) / max (m*n,1) ;
+ A = sprandn (m,n,d) ;
+ S = sprandn (m,m,d) + speye (m) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ if (rand ( ) > .5)
+ S = S + 1i * sprand (S) ;
+ end
+ end
+
+ subplot (2,3,1) ;
+ cspy (A) ;
+
+ pp = dmperm (A) ;
+
+ sprnk = sum (pp > 0) ;
+
+ pp2 = cs_dmperm (A) ;
+ spr2 = sum (pp2 > 0) ;
+ if (spr2 ~= sprnk)
+ error ('!')
+ end
+
+ pp2 = cs_maxtransr (A) ;
+ spr2 = sum (pp2 > 0) ;
+ if (spr2 ~= sprnk)
+ error ('!')
+ end
+
+ [p,q,r,s] = dmperm (A) ;
+ C = A (p,q) ;
+ % r
+ % s
+
+ nk = length (r) - 1 ;
+
+ fprintf ('sprnk: %d m %d n %d nb: %d\n', sprnk, m, n, nk) ;
+
+ subplot (2,3,2) ;
+ hold off
+ spy (C)
+ hold on
+
+ for k = 1:nk
+ r1 = r(k) ;
+ r2 = r(k+1) ;
+ c1 = s(k) ;
+ c2 = s(k+1) ;
+ plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+ end
+
+ [p2,q2,rr2,ss2,cp,rp] = cs_dmperm (A) ;
+
+ if (min (m,n) > 0)
+ if (length (rr2) ~= length (r))
+ error ('# fine blocks!') ;
+ end
+ end
+
+ if (rp (4) - 1 ~= sprnk)
+ rp %#ok
+ sprnk %#ok
+ error ('!') ;
+ end
+
+ if (any (sort (p2) ~= 1:m))
+ error ('p2!') ;
+ end
+
+ if (any (sort (q2) ~= 1:n))
+ error ('q2!') ;
+ end
+
+ if (cp (5) ~= n+1)
+ error ('cp!') ;
+ end
+
+ if (rp (5) ~= m+1)
+ error ('rp!') ;
+ end
+
+ C = A (p2,q2) ;
+
+ subplot (2,3,3) ; cs_dmspy (A,0) ;
+
+ % hold off
+ % spy (C) ;
+ % hold on
+
+ % r1 = rp(1) ;
+ % r2 = rp(2) ;
+ % c1 = cp(1) ;
+ % c2 = cp(2) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ r1 = rp(1) ;
+ r2 = rp(2) ;
+ c1 = cp(2) ;
+ c2 = cp(3) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ B = C (r1:r2-1, c1:c2-1) ;
+ if (nnz (diag (B)) ~= size (B,1))
+ error ('C1 diag!') ;
+ end
+
+ r1 = rp(2) ;
+ r2 = rp(3) ;
+ c1 = cp(3) ;
+ c2 = cp(4) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'r') ;
+
+ B = C (r1:r2-1, c1:c2-1) ;
+ if (nnz (diag (B)) ~= size (B,1))
+ error ('C2 diag!') ;
+ end
+
+ r1 = rp(3) ;
+ r2 = rp(4) ;
+ c1 = cp(4) ;
+ c2 = cp(5) ;
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ B = C (r1:r2-1, c1:c2-1) ;
+ if (nnz (diag (B)) ~= size (B,1))
+ error ('C3 diag!') ;
+ end
+
+ r1 = rp(4) ; %#ok
+ r2 = rp(5) ; %#ok
+ c1 = cp(4) ; %#ok
+ c2 = cp(5) ; %#ok
+ % plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+
+ if (~isempty (S))
+
+ [p1,q1,r0,s0] = dmperm (S) ;
+ [p3,r3] = cs_scc (S) ;
+ if (length (r3) ~= length (r0))
+ error ('scc size!') ;
+ end
+
+ if (any (sort (p3) ~= 1:m))
+ error ('scc perm!') ;
+ end
+
+ nk = length (r0)-1 ;
+
+ subplot (2,3,4) ;
+ hold off
+ spy (S (p1,q1)) ;
+ hold on
+ for k = 1:nk
+ r1 = r0(k) ;
+ r2 = r0(k+1) ;
+ c1 = s0(k) ;
+ c2 = s0(k+1) ;
+ plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+ end
+
+ subplot (2,3,5) ;
+ hold off
+ spy (S (p3,p3)) ;
+ hold on
+ for k = 1:nk
+ r1 = r3(k) ;
+ r2 = r3(k+1) ;
+ c1 = r3(k) ;
+ c2 = r3(k+1) ;
+ plot ([c1 c2 c2 c1 c1]-.5, [r1 r1 r2 r2 r1]-.5, 'g') ;
+ end
+
+ end
+
+ subplot (2,3,6) ;
+ cs_dmspy (A) ;
+ drawnow
+ % pause
+
+
+
+
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test2.m b/CXSparse_newfiles/MATLAB/Test/test2.m
new file mode 100644
index 0000000..6d603fa
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test2.m
@@ -0,0 +1,113 @@
+function test2
+%TEST2 test cs_sparse, cs_permute, cs_pvec, cs_ipvec, cs_symperm
+%
+% Example:
+% test2
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0)
+% clf
+
+for trial = 1:100
+ m = fix (10 * rand (1)) ;
+ n = fix (10 * rand (1)) ;
+ nz = fix (100 * rand (1)) ;
+
+ i = 1 + fix (m * rand (nz,1)) ;
+ j = 1 + fix (n * rand (nz,1)) ;
+ x = rand (nz,1) ;
+
+ if (~ispc)
+ if (mod (trial, 2) == 1)
+ x = x + 1i * (2*rand(nz,1)-1) ;
+ end
+ end
+
+ A = sparse (i,j,x) ;
+ B = cs_sparse (i,j,x) ;
+ D = cs_sparse2 (i,j,x) ;
+ fprintf ('%3d %3d %6d : %6d %6d : %d\n', ...
+ m, n, nz, nnz (A), nnz(B), nz-nnz(A)) ;
+
+ err = norm (A-B,1) / max (1, norm (A,1)) ;
+ if (err > 0)
+ disp ('err = ') ;
+ disp (err) ;
+ end
+ if (err > 1e-14)
+ error ('!') ;
+ end
+
+ if (nnz (B-D) > 0)
+ error ('!') ;
+ end
+
+ if (nnz (A) ~= nnz (B))
+ error ('nz!') ;
+ end
+
+ if (max (1,nnz (B)) ~= max (1,nzmax (B)))
+ nnz (B)
+ nzmax (B)
+ error ('nzmax!') ;
+ end
+ % pack
+
+
+ [m n] = size (A) ;
+ p = randperm (m) ;
+ q = randperm (n) ;
+ C1 = A (p,q) ;
+ C2 = cs_permute (A,p,q) ;
+ err = norm (C1-C2,1) ;
+ if (err > 0)
+ error ('!') ;
+ end
+
+% subplot (1,2,1) ; spy (A)
+% subplot (1,2,2) ; spy (C2)
+% drawnow
+
+ x = rand (m,1) ;
+
+ if (~ispc)
+ if (mod (trial, 2) == 1)
+ x = x + 1i * (2*rand(m,1)-1) ;
+ end
+ end
+
+ x1 = x (p) ;
+ x2 = cs_pvec (x, p) ;
+
+ err = norm (x1-x2,1) ;
+ if (err > 0)
+ error ('!') ;
+ end
+
+ x1 = zeros (m,1) ;
+ x1 (p) = x ; %#ok
+ x2 = cs_ipvec (x, p) ; %#ok
+
+ n = min (m,n) ;
+ B = A (1:n, 1:n) ;
+ p = randperm (n) ;
+ B = B+B' ;
+
+ C1 = triu (B (p,p)) ;
+ C2 = cs_symperm (B,p) ;
+
+ try
+ pp = amd (C2) ; %#ok
+ catch
+ pp = symamd (C2) ; %#ok
+ end
+
+ err = norm (C1-C2,1) ;
+ if (err > 0)
+ error ('!') ;
+ end
+
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test20.m b/CXSparse_newfiles/MATLAB/Test/test20.m
new file mode 100644
index 0000000..d2264ae
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test20.m
@@ -0,0 +1,59 @@
+function test20
+%TEST20 test chol_updown2
+%
+% Example:
+% test20
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+rand ('state', 0) ;
+maxerr = [0 0 0 0] ;
+
+for trials = 1:100
+
+ n = fix (100 * rand (1)) ;
+ A = rand (n) ;
+
+ if (~ispc)
+ if (mod (trials, 2) == 0)
+ A = A + 1i*rand(n) ;
+ end
+ end
+
+ A1 = A*A' + n*eye (n) ;
+
+ try
+ L1 = chol (A1)' ;
+ catch
+ continue ;
+ end
+ err1 = norm (L1*L1'-A1) ;
+
+ w = rand (n,1) ;
+
+ A2 = A1 + w*w' ;
+
+ L2 = chol (A2)' ;
+ err2 = norm (L2*L2'-A2) ;
+
+ % try an update
+ L2b = chol_updown2 (L1, +1, w) ;
+ err2b = norm (L2b*L2b'-A2) ;
+
+ % try a downdate
+ L1b = chol_updown2 (L2, -1, w) ; %#ok
+ err1b = norm (L1b*L1b'-A1) ;
+
+
+ fprintf ('%3d: %6.2e %6.2e : %6.2e %6.2e\n', n, err1, err2, err2b, err1b) ;
+ % pause
+
+ maxerr = max (maxerr, [err1 err2 err2b err1b]) ;
+end
+
+fprintf ('maxerr: %g\n', maxerr) ;
diff --git a/CXSparse_newfiles/MATLAB/Test/test21.m b/CXSparse_newfiles/MATLAB/Test/test21.m
new file mode 100644
index 0000000..37ce99b
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test21.m
@@ -0,0 +1,119 @@
+function test21
+%TEST21 test cs_updown, chol_updown2
+%
+% Example:
+% test21
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+rand ('state', 0) ;
+randn ('state', 0) ;
+
+clf
+
+for trials = 1:100
+ if (trials <= 1)
+ n = trials ;
+ else
+ n = 1+fix (100 * rand (1)) ;
+ end
+ fprintf ('n: %d\n', n) ;
+ d = 0.1 * rand (1) ;
+ A = sprandn (n,n,d) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ A = A+A' + 100 * speye (n) ;
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ A = sparse (A (p,p)) ;
+
+ try
+ L = chol (A)' ;
+ catch
+ continue ;
+ end
+
+ parent = etree (A) ;
+
+ subplot (1,3,1) ;
+ spy (A) ;
+
+ if (n > 0)
+ subplot (1,3,2) ;
+ treeplot (parent) ;
+ end
+
+ subplot (1,3,3) ;
+ spy (L) ;
+
+ drawnow
+
+ for trials2 = 1:10
+
+ k = 1+fix (n * rand (1)) ;
+ if (k <= 0 | k > n) %#ok
+ k = 1 ;
+ end
+
+ w = sprandn (L (:,k)) ;
+ Anew = A + w*w' ;
+
+ Lnew = cs_updown (L, w, parent) ;
+ err6 = norm (Lnew*Lnew' - Anew, 1) ;
+
+ Lnew = cs_updown (L, w, parent, '+') ;
+ err7 = norm (Lnew*Lnew' - Anew, 1) ;
+
+ [Lnew, wnew] = chol_updown2 (L, 1, w) ;
+ err2 = norm (Lnew*Lnew' - Anew, 1) ;
+ err10 = norm (wnew - (L\w)) ;
+
+ L3 = chol_updown2 (L, +1, w) ;
+ err9 = norm (L3*L3' - Anew, 1) ;
+
+
+
+ [L2, wnew] = chol_updown2 (Lnew, -1, w) ;
+ err3 = norm (L2*L2' - A, 1) ;
+ err11 = norm (wnew - (Lnew\w)) ;
+
+ L2 = cs_updown (Lnew, w, parent, '-') ;
+ err5 = norm (L2*L2' - A, 1) ;
+
+ L2 = chol_updown2 (Lnew, -1, w) ;
+ err8 = norm (L2*L2' - A, 1) ;
+
+ err = max ([err2 err3 err5 err6 err7 err9 err8 err10 err11]) ;
+
+ fprintf (' k %3d %6.2e\n', k, err) ;
+
+ if (err > 1e-11)
+ err2 %#ok
+ err3 %#ok
+ err5 %#ok
+ err6 %#ok
+ err7 %#ok
+ err8 %#ok
+ err9 %#ok
+ err10 %#ok
+ err11 %#ok
+ pause
+ end
+
+
+ end
+ % pause
+
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test22.m b/CXSparse_newfiles/MATLAB/Test/test22.m
new file mode 100644
index 0000000..ab32370
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test22.m
@@ -0,0 +1,58 @@
+function test22
+%TEST22 test cond1est
+%
+% Example:
+% test22
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+
+clf
+% f = f(1)
+
+nprob = length (f) ;
+C1 = zeros (nprob,1) ;
+C2 = zeros (nprob,1) ;
+C3 = zeros (nprob,1) ;
+
+
+for k = 1:length (f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (~isreal (A) | m ~= n) %#ok
+ continue
+ end
+
+ c1 = condest (A) ;
+ c2 = cond1est (A) ;
+ if (c1 == c2)
+ err = 0 ;
+ else
+ err = (c1-c2)/max(1,c1) ;
+ end
+
+ c3 = cond (full (A), 1) ;
+
+ fprintf ('%10.4e %10.4e (%10.4e) : %10.4e\n', c1, c2, c3, err) ;
+
+ C1 (k) = c1 ;
+ C2 (k) = c2 ;
+ C3 (k) = c3 ;
+
+ subplot (1,2,1) ;
+ loglog (C1, C2, 'x', [1 1e20], [1 1e20], 'r') ;
+ subplot (1,2,2) ;
+ loglog (C3, C2, 'x', [1 1e20], [1 1e20], 'r') ;
+ drawnow
+
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test23.m b/CXSparse_newfiles/MATLAB/Test/test23.m
new file mode 100644
index 0000000..d4c12e6
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test23.m
@@ -0,0 +1,38 @@
+function test23
+%TEST23 test cs_dmspy
+%
+% Example:
+% test23
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clear functions
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+clf
+
+for trials = 1:1000
+
+ % m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ m = n ;
+ % d = 0.1 * rand (1) ;
+ d = rand (1) * 4 * max (m,n) / max (m*n,1) ;
+ A = sprandn (m,n,d) ;
+ % S = sprandn (m,m,d) + speye (m) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ cs_dmspy (A) ;
+ drawnow
+
+ % pause
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test24.m b/CXSparse_newfiles/MATLAB/Test/test24.m
new file mode 100644
index 0000000..0134224
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test24.m
@@ -0,0 +1,63 @@
+function test24
+%TEST24 test cs_fielder
+%
+% Example:
+% test24
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:200) ;
+
+clf
+% f = f(1)
+
+for k = 1:length (f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = real (Prob.A) ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ S = A ;
+
+ if (~ispc)
+ if (mod (k,2) == 0)
+ S = S + 1i * sprand (A) ;
+ end
+ end
+
+ tic
+ p1 = symrcm (A) ;
+ t1 = toc ;
+
+ tic
+ p2 = cs_fiedler (S) ;
+ t2 = toc ;
+
+ rel = t2 / max (t1,1e-6) ;
+
+ fprintf ('time: symrcm %8.3f fiedler %8.3f rel %8.2f\n', t1, t2, rel) ;
+
+ A = A|A' ;
+
+ subplot (1,3,1) ; spy (A) ;
+ subplot (1,3,2) ; spy (A (p1,p1)) ;
+ subplot (1,3,3) ; spy (A (p2,p2)) ;
+
+ % evaluate the profile ...
+
+
+ drawnow
+ % pause
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test25.m b/CXSparse_newfiles/MATLAB/Test/test25.m
new file mode 100644
index 0000000..26c488d
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test25.m
@@ -0,0 +1,73 @@
+function test25
+%TEST25 test cs_nd
+%
+% Example:
+% test25
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:400) ;
+
+clf
+% f = f(1)
+
+for k = 1:length (f)
+
+ i = f (k) ;
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = real (Prob.A) ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ A = A|A' ;
+
+ S = A ;
+ if (~ispc)
+ if (mod (k,2) == 0)
+ S = S + 1i * sprand (A) ;
+ end
+ end
+
+ tic ;
+ p1 = symrcm (A) ;
+ t1 = toc ;
+
+ tic ;
+ p2 = cs_nd (sparse (1)) ;
+ toc ;
+ if (p2 ~= 1)
+ error ('!') ;
+ end
+
+ tic ;
+ p2 = cs_nd (S) ;
+ t2 = toc ;
+
+ if (any (sort (p2) ~= 1:n))
+ error ('!') ;
+ end
+
+ rel = t2 / max (t1,1e-6) ;
+
+ fprintf ('time: symrcm %8.3f nd %8.3f rel %8.2f\n', t1, t2, rel) ;
+
+ subplot (1,3,1) ; spy (A) ;
+ subplot (1,3,2) ; spy (A (p1,p1)) ;
+ subplot (1,3,3) ; spy (A (p2,p2)) ;
+
+ % evaluate the profile ...
+
+
+ drawnow
+ % pause
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test26.m b/CXSparse_newfiles/MATLAB/Test/test26.m
new file mode 100644
index 0000000..7e3ddb2
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test26.m
@@ -0,0 +1,91 @@
+function test26
+%TEST26 test cs_dmsol and cs_dmspy
+%
+% Example:
+% test26
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+clear functions
+
+randn ('state', 0) ;
+rand ('state', 0) ;
+
+clf
+
+ntrials = 1000 ;
+e1 = zeros (ntrials,1) ;
+e2 = zeros (ntrials,1) ;
+
+for trials = 1:ntrials
+
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ % d = 0.1 * rand (1) ;
+ d = rand (1) * 4 * max (m,n) / max (m*n,1) ;
+ A = sprandn (m,n,d) ;
+ % S = sprandn (m,m,d) + speye (m) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ subplot (1,3,2) ; spy (A) ;
+ subplot (1,3,3) ; cs_dmspy (A) ;
+
+ b = rand (m,1) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ b = b + 1i * rand (size (b)) ;
+ end
+ end
+ % MATLAB cannot do A\b when A is sparse and rectangular and either
+ % A or b are complex
+ if (m ~= n & isreal (A) & ~isreal (b)) %#ok
+ x1 = (A\real(b)) + 1i * (A\imag(b)) ;
+ err1 = norm (A*x1-b) ;
+ elseif ((m ~= n) & ~isreal (A)) %#ok
+ err1 = 1 ;
+ else
+ x1 = A\b ;
+ err1 = norm (A*x1-b) ;
+ end
+
+ x2 = cs_dmsol (A,b) ;
+
+ err2 = norm (A*x2-b) ;
+
+ lerr1 = log10 (max (err1, eps)) ;
+ lerr2 = log10 (max (err2, eps)) ;
+
+ fprintf ('rank: %3d %3d err %6.2e %6.2e : %6.1f\n', ...
+ sprank(A), rank(full(A)), err1, err2, lerr1 - lerr2) ;
+
+ if (isnan (err1))
+ lerr1 = 10 ;
+ end
+ if (isnan (err2))
+ lerr2 = 10 ;
+ end
+
+ if (lerr2 > lerr1 + 5)
+ % pause
+ end
+
+ e1 (trials) = lerr1 ;
+ e2 (trials) = lerr2 ;
+
+ subplot (1,3,1) ; plot (e1, e2, 'o', [-16 10], [-16 10], 'r') ;
+ xlabel ('MATLAB error') ;
+ ylabel ('dmsol error') ;
+
+
+ drawnow
+ % pause
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test27.m b/CXSparse_newfiles/MATLAB/Test/test27.m
new file mode 100644
index 0000000..3c1418c
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test27.m
@@ -0,0 +1,47 @@
+function test27
+%TEST27 test cs_qr, cs_utsolve, cs_qrsol
+%
+% Example:
+% test27
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+
+clear functions
+rand ('state', 0) ;
+
+Prob = UFget ('HB/ibm32') ;
+A = Prob.A ;
+A = A (1:10,:) ;
+[m n] = size (A) ;
+
+[V,Beta,p,R,q] = cs_qr (A') ;
+
+b = rand (m,1) ;
+
+Rm = R (1:m,1:m) ;
+
+bq = b (q) ;
+rtbq = Rm' \ bq ;
+
+rt2 = cs_utsolve (Rm, bq) ;
+
+norm (rtbq - rt2)
+
+x = [rt2 ; zeros(n-m,1)] ;
+
+for k = m:-1:1
+ x = x - V(:,k) * (Beta (k) * (V (:,k)' * x)) ;
+end
+
+x (p) = x ;
+
+norm (A*x-b)
+
+x2 = cs_qrsol (A,b) ;
+
+norm (A*x2-b)
+norm (x-x2)
diff --git a/CXSparse_newfiles/MATLAB/Test/test28.m b/CXSparse_newfiles/MATLAB/Test/test28.m
new file mode 100644
index 0000000..a64c5ce
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test28.m
@@ -0,0 +1,120 @@
+function test28
+%TEST28 test cs_randperm, cs_dmperm
+%
+% Example:
+% test28
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clear functions
+
+rand ('state', 0) ;
+for n = 1:100
+ for trials = 1:1000
+ p = cs_randperm (n, rand) ;
+ if (any (sort (p) ~= 1:n))
+ n %#ok
+ p %#ok
+ error ('!')
+ end
+ end
+end
+
+index = UFget ;
+[ignore f] = sort (index.nnz) ;
+
+fprintf ('p=dmperm (std, rand, rev) [p,q,r,s]=dmperm (std, rand, rev)\n') ;
+
+nmat = length (f) ;
+nmat = min (100, nmat) ;
+T1 = zeros (nmat,1) ;
+T2 = zeros (nmat,1) ;
+T3 = zeros (nmat,1) ;
+D1 = zeros (nmat,1) ;
+D2 = zeros (nmat,1) ;
+D3 = zeros (nmat,1) ;
+
+
+for k = 1:nmat
+
+ i = f (k) ;
+ Prob = UFget (i,index) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ fprintf ('%35s: ', Prob.name) ;
+
+ if (~ispc)
+ if (rand () > .5)
+ A = A + 1i * sprand (A) ;
+ end
+ end
+
+ tic
+ p = cs_dmperm (A) ;
+ t1 = toc ;
+ sprank1 = sum (p > 0) ;
+ fprintf (' %8.2f', t1) ;
+ T1 (k) = t1 ;
+
+ tic
+ p = cs_dmperm (A,1) ;
+ t2 = toc ;
+ sprank2 = sum (p > 0) ;
+ fprintf (' %8.2f', t2) ;
+ T2 (k) = t2 ;
+
+ tic
+ p = cs_dmperm (A,-1) ;
+ t3 = toc ;
+ sprank3 = sum (p > 0) ;
+ fprintf (' %8.2f', t3) ;
+ T3 (k) = t3 ;
+
+ if (sprank1 ~= sprank2 | sprank1 ~= sprank3) %#ok
+ error ('!') ;
+ end
+
+ tic
+ [p1,q1,r1,s1,cc1,rr1] = cs_dmperm (A) ; %#ok
+ d1 = toc ;
+ fprintf (' %8.2f', d1) ;
+ D1 (k) = d1 ;
+
+ tic
+ [p2,q2,r2,s2,cc2,rr2] = cs_dmperm (A,1) ; %#ok
+ d2 = toc ;
+ fprintf (' %8.2f', d2) ;
+ D2 (k) = d2 ;
+
+ tic
+ [p3,q3,r3,s3,cc3,rr3] = cs_dmperm (A,-1) ; %#ok
+ d3 = toc ;
+ fprintf (' %8.2f\n', d3) ;
+ D3 (k) = d3 ;
+
+ if (sprank1 == max (m,n))
+ nz1 = nnz (diag (A (p1,q1))) ;
+ nz2 = nnz (diag (A (p2,q2))) ;
+ nz3 = nnz (diag (A (p3,q3))) ;
+
+ if (nz1 ~= sprank1 | nz2 ~= sprank2 | nz3 ~= sprank3) %#ok
+ error ('!')
+ end
+ end
+
+ subplot (1,2,1)
+ loglog (T1 (1:k), T2 (1:k), 'x', ...
+ T1 (1:k), T3 (1:k), 'go', ...
+ [1e-5 1e3], [1e-5 1e3], 'r-') ;
+ axis equal
+
+ subplot (1,2,2)
+ loglog (D1 (1:k), D2 (1:k), 'x', ...
+ D1 (1:k), D3 (1:k), 'go', ...
+ [1e-5 1e3], [1e-5 1e3], 'r-') ;
+ axis equal
+
+ drawnow
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test3.m b/CXSparse_newfiles/MATLAB/Test/test3.m
new file mode 100644
index 0000000..de3037d
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test3.m
@@ -0,0 +1,112 @@
+function test3
+%TEST3 test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol
+%
+% Example:
+% test3
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+clear
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+clf
+% f = f(1)
+
+for i = f
+
+ Prob = UFget (i) ;
+ disp (Prob) ;
+
+ for cmplex = 0:double(~ispc)
+
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ if (cmplex)
+ A = A + 1i*sprand(A) ;
+ end
+
+ A = A*A' + 2*n*speye (n) ;
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ try
+ L0 = chol (A)' ;
+ catch
+ continue
+ end
+ b = rand (n,1) ;
+
+ if (~ispc)
+ if (mod (i,2) == 1)
+ b = b + 1i*rand(n,1) ;
+ end
+ end
+
+ C = A(p,p) ;
+ c = condest (C) ;
+ fprintf ('condest: %g\n', c) ;
+
+ x1 = L0\b ;
+ x2 = cs_lsolve (L0,b) ;
+ err = norm (x1-x2,1) ;
+ if (err > 1e-12 * c)
+ error ('!') ;
+ end
+
+ x1 = L0'\b ;
+ x2 = cs_ltsolve (L0,b) ;
+ err = norm (x1-x2,1) ;
+ if (err > 1e-10 * c)
+ error ('!') ;
+ end
+
+ U = L0' ;
+
+ x1 = U\b ;
+ x2 = cs_usolve (U,b) ;
+ err = norm (x1-x2,1) ;
+ if (err > 1e-10 * c)
+ error ('!') ;
+ end
+
+ L2 = cs_chol (A) ;
+ subplot (2,3,1) ; spy (L0) ;
+ subplot (2,3,4) ; spy (L2) ;
+ err = norm (L0-L2,1) ;
+ if (err > 1e-8 * c)
+ error ('!') ;
+ end
+
+ L1 = chol (C)' ;
+ L2 = cs_chol (C) ;
+ subplot (2,3,2) ; spy (L1) ;
+ subplot (2,3,5) ; spy (L2) ;
+ err = norm (L1-L2,1) ;
+ if (err > 1e-8 * c)
+ error ('!') ;
+ end
+
+ [L3,p] = cs_chol (A) ;
+ C = A(p,p) ;
+ L4 = chol (C)' ;
+ subplot (2,3,3) ; spy (L4) ;
+ subplot (2,3,6) ; spy (L3) ;
+ err = norm (L4-L3,1) ;
+ if (err > 1e-8 * c)
+ error ('!') ;
+ end
+
+ drawnow
+
+ end
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test4.m b/CXSparse_newfiles/MATLAB/Test/test4.m
new file mode 100644
index 0000000..7e884bc
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test4.m
@@ -0,0 +1,43 @@
+function test4
+%TEST4 test cs_multiply
+%
+% Example:
+% test4
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+for trial = 1:100
+ m = fix (10 * rand (1)) ;
+ n = fix (10 * rand (1)) ;
+ k = fix (10 * rand (1)) ;
+ d = rand (1) ;
+ A = sprandn (m,n,d) ;
+ B = sprandn (n,k,d) ;
+
+ if (~ispc)
+ if (mod (trial, 4) == 0)
+ A = A + 1i * sprandn (A) ;
+ end
+ if (mod (trial, 2) == 0)
+ B = B + 1i * sprandn (B) ;
+ end
+ end
+
+ C = A*B ;
+ D = cs_multiply (A,B) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d k %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, k, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test5.m b/CXSparse_newfiles/MATLAB/Test/test5.m
new file mode 100644
index 0000000..60f0081
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test5.m
@@ -0,0 +1,81 @@
+function test5
+%TEST5 test cs_add
+%
+% Example:
+% test5
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+rand ('state', 0) ;
+
+for trial = 1:200
+ m = fix (100 * rand (1)) ;
+ n = fix (100 * rand (1)) ;
+ d = rand (1) ;
+ A = sprandn (m,n,d) ;
+ B = sprandn (m,n,d) ;
+
+ if (~ispc)
+ if (mod (trial, 4) == 0)
+ A = A + 1i*sprand(A) ;
+ end
+ if (mod (trial, 2) == 0)
+ B = B + 1i*sprand(B) ;
+ end
+ end
+
+ C = A+B ;
+ D = cs_add (A,B) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+ alpha = pi ;
+ beta = 3 ;
+
+ if (~ispc)
+ if (rand () > .5)
+ alpha = alpha + rand ( ) * 1i ;
+ end
+ if (rand () > .5)
+ beta = beta + rand ( ) * 1i ;
+ end
+ end
+
+ C = alpha*A+B ;
+ D = cs_add (A,B,alpha) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+ C = alpha*A + beta*B ;
+ D = cs_add (A,B,alpha,beta) ;
+ err = nnz (spones (C) - spones (D)) ;
+ if (err > 0)
+ error ('nz!') ;
+ end
+ err = norm (C-D,1) ;
+ fprintf ('m %3d n %3d nnz(A) %6d nnz(B) %6d nnz(C) %6d err %g\n', ...
+ m, n, nnz(A), nnz(B), nnz(C), err) ;
+ if (err > 1e-12)
+ error ('!') ;
+ end
+
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test6.m b/CXSparse_newfiles/MATLAB/Test/test6.m
new file mode 100644
index 0000000..9c89a74
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test6.m
@@ -0,0 +1,111 @@
+function test6
+%TEST6 test cs_reach, cs_reachr, cs_lsolve, cs_usolve
+%
+% Example:
+% test6
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0)
+maxerr = 0 ;
+clf
+for trial = 1:201
+ n = fix (100 * rand (1)) ;
+ d = 0.1 * rand (1) ;
+ L = tril (sprandn (n,n,d),-1) + sprand (speye (n)) ;
+ b = sprandn (n,1,d) ;
+
+ if (~ispc)
+ if (rand ( ) > .5)
+ L = L + 1i*sprand(L) ;
+ end
+ if (rand ( ) > .5)
+ b = b + 1i*sprand(b) ;
+ end
+ end
+
+ for uplo = 0:1
+
+ if (uplo == 1)
+ % solve Ux=b instead ;
+ L = L' ;
+ end
+
+ x = L\b ;
+ sr = 1 + cs_reachr (L,b) ;
+ sz = 1 + cs_reachr (L,b) ;
+
+ check_if_same (sr,sz) ;
+
+ s2 = 1 + cs_reach (L,b) ;
+
+ try
+ if (uplo == 0)
+ x3 = cs_lsolve (L,b) ;
+ else
+ x3 = cs_usolve (L,b) ;
+ end
+ catch
+ if (isreal (L) & isreal (b)) %#ok
+ lasterr
+ error ('!') ;
+ end
+ % punt: sparse(L)\sparse(b) not handled by cs_lsolve or cs_usolve
+ x3 = L\b ;
+ end
+
+ spy ([L b x x3])
+ drawnow
+
+ s = sort (sr) ;
+ [i j xx] = find (x) ; %#ok
+ [i3 j3 xx3] = find (x3) ; %#ok
+
+ if (isempty (i))
+ if (~isempty (s))
+ i %#ok
+ s %#ok
+ error ('!') ;
+ end
+ elseif (any (s ~= i))
+ i %#ok
+ s %#ok
+ error ('!') ;
+ end
+
+ if (isempty (i3))
+ if (~isempty (s))
+ i3 %#ok
+ s %#ok
+ error ('!') ;
+ end
+ elseif (any (s ~= sort (i3)))
+ s %#ok
+ i3 %#ok
+ error ('!') ;
+ end
+
+ if (any (s2 ~= sr))
+ s2 %#ok
+ sr %#ok
+ error ('!') ;
+ end
+
+ err = norm (x-x3,1) ;
+ if (err > 1e-12)
+ x %#ok
+ x3 %#ok
+ uplo %#ok
+ err %#ok
+ error ('!')
+ end
+
+ maxerr = max (maxerr, err) ;
+
+ end
+
+ drawnow
+end
+fprintf ('maxerr = %g\n', maxerr) ;
diff --git a/CXSparse_newfiles/MATLAB/Test/test7.m b/CXSparse_newfiles/MATLAB/Test/test7.m
new file mode 100644
index 0000000..219ed21
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test7.m
@@ -0,0 +1,136 @@
+function test7
+%TEST7 test cs_lu
+%
+% Example:
+% test7
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+clf
+
+maxerr1 = 0 ;
+maxerr2 = 0 ;
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ for cmplex = 0:1
+
+ if (cmplex)
+ A = A + norm(A,1) * sprand (A) / 3 ;
+ end
+
+ [L,U,P] = lu (A) ;
+
+ udiag = full (diag (U)) ;
+ umin = min (abs (udiag)) ;
+ fprintf ('umin %g\n', umin) ;
+
+ if (umin > 1e-14)
+
+ [L2,U2,p] = cs_lu (A) ;
+
+ subplot (3,4,1) ; spy (A) ;
+ subplot (3,4,2) ; spy (A(p,:)) ;
+ subplot (3,4,3) ; spy (L2) ;
+ subplot (3,4,4) ; spy (U2) ;
+
+ err1 = norm (L*U-P*A,1) / norm (A,1) ;
+ err2 = norm (L2*U2-A(p,:),1) / norm (A,1) ;
+ fprintf ('err %g %g\n', err1, err2) ;
+
+ if (err1 > 1e-10 | err2 > 1e-10) %#ok
+ error ('!') ;
+ end
+ maxerr1 = max (maxerr1, err1) ;
+ maxerr2 = max (maxerr2, err2) ;
+
+ end
+
+ q = colamd (A) ;
+
+ [L,U,P] = lu (A (:,q)) ;
+
+ udiag = full (diag (U)) ;
+ umin = min (abs (udiag)) ;
+ fprintf ('umin %g with q\n', umin) ;
+
+ if (umin > 1e-14)
+
+ [L2,U2,p,q2] = cs_lu (A) ;
+
+ subplot (3,4,5) ; spy (A) ;
+ subplot (3,4,6) ; spy (A(p,q2)) ;
+ subplot (3,4,7) ; spy (L2) ;
+ subplot (3,4,8) ; spy (U2) ;
+
+ err1 = norm (L*U-P*A(:,q),1) / norm (A,1) ;
+ err2 = norm (L2*U2-A(p,q2),1) / norm (A,1) ;
+ fprintf ('err %g %g\n', err1, err2) ;
+
+ if (err1 > 1e-10 | err2 > 1e-10) %#ok
+ error ('!') ;
+ end
+ maxerr1 = max (maxerr1, err1) ;
+ maxerr2 = max (maxerr2, err2) ;
+ end
+
+
+ try
+ q = amd (A) ;
+ catch
+ q = symamd (A) ;
+ end
+
+ tol = 0.01 ;
+
+ [L,U,P] = lu (A (q,q), tol) ;
+
+ udiag = full (diag (U)) ;
+ umin = min (abs (udiag)) ;
+ fprintf ('umin %g with amd q\n', umin) ;
+
+ if (umin > 1e-14)
+
+ [L2,U2,p,q2] = cs_lu (A,tol) ;
+
+ subplot (3,4,9) ; spy (A) ;
+ subplot (3,4,10) ; spy (A(p,q2)) ;
+ subplot (3,4,11) ; spy (L2) ;
+ subplot (3,4,12) ; spy (U2) ;
+
+ err1 = norm (L*U-P*A(q,q),1) / norm (A,1) ;
+ err2 = norm (L2*U2-A(p,q2),1) / norm (A,1) ;
+ lbig = full (max (max (abs (L2)))) ;
+ fprintf ('err %g %g lbig %g\n', err1, err2, lbig) ;
+ if (lbig > 1/tol)
+ error ('L!') ;
+ end
+
+ if (err1 > 1e-10 | err2 > 1e-10) %#ok
+ error ('!') ;
+ end
+ maxerr1 = max (maxerr1, err1) ;
+ maxerr2 = max (maxerr2, err2) ;
+ end
+
+ drawnow
+ % pause
+
+ end
+end
+
+fprintf ('maxerr %g %g\n', maxerr1, maxerr2) ;
diff --git a/CXSparse_newfiles/MATLAB/Test/test8.m b/CXSparse_newfiles/MATLAB/Test/test8.m
new file mode 100644
index 0000000..42806ed
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test8.m
@@ -0,0 +1,93 @@
+function test8
+%TEST8 test cs_cholsol, cs_lusol
+%
+% Example:
+% test8
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+
+% f = f(1)
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ continue
+ end
+
+ for cmplex = 0:double(~ispc)
+
+ if (cmplex)
+ A = A + 0.1i * (sprand (tril (A,-1) + triu (A,1))) ;
+ end
+
+ spd = 0 ;
+ if (m == n)
+ if (nnz (A-A') == 0)
+ try
+ p = amd (A) ;
+ catch
+ p = symamd (A) ;
+ end
+ [R,p] = chol (A (p,p)) ;
+ spd = (p == 0) ;
+ end
+ end
+
+ if (spd)
+ C = A ;
+ else
+ C = A*A' + n*speye (n) ;
+ try
+ p = amd (C) ;
+ catch
+ p = symamd (C) ;
+ end
+ try
+ R = chol (C (p,p)) ; %#ok
+ catch
+ continue
+ end
+ end
+
+ b = rand (n,1) ;
+
+ x1 = C\b ;
+ x2 = cs_cholsol (C,b) ;
+ r1 = norm (C*x1-b,1) / norm (C,1) ;
+ r2 = norm (C*x2-b,1) / norm (C,1) ;
+ err = abs (r1-r2) ;
+ fprintf ('err %g\n', err) ;
+ if (err > 1e-10)
+ error ('!') ;
+ end
+
+ x2 = cs_lusol (C,b, 1, 0.001) ;
+ r2 = norm (C*x2-b,1) / norm (C,1) ;
+ err = abs (r1-r2) ;
+ fprintf ('err %g (lu with amd(A+A'')\n', err) ;
+ if (err > 1e-10)
+ error ('!') ;
+ end
+
+ if (m ~= n)
+ continue ;
+ end
+
+ x1 = A\b ;
+ r1 = norm (A*x1-b,1) / norm (A,1) ;
+ if (r1 < 1e-6)
+ x2 = cs_lusol (A,b) ;
+ r2 = norm (A*x2-b,1) / norm (A,1) ;
+ fprintf ('lu resid %g %g\n', r1, r2) ;
+ end
+ end
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/test9.m b/CXSparse_newfiles/MATLAB/Test/test9.m
new file mode 100644
index 0000000..2b0293a
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/test9.m
@@ -0,0 +1,134 @@
+function test9
+%TEST9 test cs_qr
+%
+% Example:
+% test9
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+rand ('state', 0) ;
+
+index = UFget ;
+[ignore f] = sort (max (index.nrows, index.ncols)) ;
+f = f (1:100) ;
+clf
+
+% f = 185 ;
+% f = 449 ;
+% f = 186
+
+for i = f
+ Prob = UFget (i) ;
+ disp (Prob) ;
+ A = Prob.A ;
+ [m n] = size (A) ;
+ if (m < n)
+ A = A' ;
+ end
+ [m n] = size (A) ;
+ sp = sprank (A) ;
+% if (sprank (A) < min (m,n))
+% continue
+% end
+
+
+ for cmplex = 0:double(~ispc)
+
+ if (cmplex)
+ A = A + 1i * sprand (A) ;
+ end
+
+ Aorig = A ;
+
+ A = A (:, colamd (A)) ;
+ s1 = svd (full (A)) ;
+
+ if (cmplex)
+ try
+ tic ;
+ R = chol (A'*A) ;
+ t1 = toc ; %#ok
+ catch
+ fprintf ('chol (A''*A) failed\n') ;
+ R = [ ] ;
+ end
+ else
+ tic ;
+ R = qr (A) ;
+ t1 = toc ; %#ok
+ end
+
+ % tic ;
+ % [Q,R] = qr (A) ;
+ % t1 = toc ;
+
+ [c,h,parent] = symbfact (A, 'col') ;
+ rnz = sum (c) ; %#ok
+ tic ;
+ [V2,Beta2,p,R2] = cs_qr (sparse(A)) ;
+ t2 = toc ; %#ok
+
+ v2 = full (V2) ;
+ if (any (spones (v2) ~= spones (V2)))
+ error ('got zeros!') ;
+ end
+
+ C = A ;
+ m2 = size (V2,1) ;
+ if (m2 > m)
+ C = [A ; sparse(m2-m, n)] ;
+ end
+ C = C (p,:) ;
+
+ % [H1,R1] = myqr (C) ;
+ % err1 = norm (R1-R2,1) / norm (R1)
+ % % [svd(A) svd(R1) svd(full(R2))]
+ % s2 = svd (full (R2)) ;
+ % err2 = norm (s1 - s2) / s1 (1)
+ % fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d n %d\n', ...
+ % t1, t2, t1/t2, sp, n) ;
+ % err2
+
+ % left-looking:
+ [V,Beta3,R3] = qr_left (C) ; %#ok
+ s3 = svd (full (R2)) ;
+ err3 = norm (s1 - s3) / s1 (1) ;
+ disp ('err3 = ') ; disp (err3) ;
+ if (err3 > 1e-12)
+ error ('!') ;
+ end
+
+ % right-looking:
+ [V,Beta4,R4] = qr_right (C) ; %#ok
+ s4 = svd (full (R2)) ;
+ err4 = norm (s1 - s4) / s1 (1) ;
+ disp ('err4 = ') ; disp (err4) ;
+ if (err4 > 1e-12)
+ error ('!') ;
+ end
+
+ % H2 = full (H2)
+ % R2 = full (R2)
+
+ subplot (2,4,1) ; spy (A) ; title ('A colamd') ;
+ subplot (2,4,2) ; spy (C) ; title ('A rperm') ;
+ subplot (2,4,3) ; treeplot (parent) ;
+ subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ;
+ subplot (2,4,5) ; spy (abs(R2)>0) ; title ('spqr R, no zeros') ;
+ subplot (2,4,6) ; spy (R) ; title ('matlab R') ;
+ subplot (2,4,7) ; spy (R2) ; title ('spqr R') ;
+ subplot (2,4,8) ; spy (V2) ; title ('spqr V') ;
+ drawnow
+
+ % if (err2 > 1e-9)
+ % error ('!') ;
+ % end
+ if (m2 > m)
+ fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ;
+ end
+ % pause
+ end
+
+end
diff --git a/CXSparse_newfiles/MATLAB/Test/testall.m b/CXSparse_newfiles/MATLAB/Test/testall.m
new file mode 100644
index 0000000..a3d3534
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/testall.m
@@ -0,0 +1,52 @@
+function testall
+%TESTALL test all CSparse functions (run tests 1 to 28 below)
+%
+% Example:
+% testall
+% See also: cs_demo
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+h = waitbar (0, 'CXSparse') ;
+
+cs_test_make % compile all CSparse, Demo, Text, and Test mexFunctions
+
+ntests = 29 ;
+
+testwait (1, ntests, h) ; test1 ;
+testwait (2, ntests, h) ; test2 ;
+testwait (3, ntests, h) ; test3 ;
+testwait (4, ntests, h) ; test4 ;
+testwait (5, ntests, h) ; test5 ;
+testwait (6, ntests, h) ; test6 ;
+testwait (7, ntests, h) ; test7 ;
+testwait (8, ntests, h) ; test8 ;
+testwait (9, ntests, h) ; test9 ;
+testwait (10, ntests, h) ; test10 ;
+testwait (11, ntests, h) ; test11 ;
+testwait (12, ntests, h) ; test12 ;
+testwait (13, ntests, h) ; test13 ;
+testwait (14, ntests, h) ; test14 ;
+testwait (15, ntests, h) ; test15 ;
+testwait (16, ntests, h) ; test16 ;
+testwait (17, ntests, h) ; test17 ;
+testwait (18, ntests, h) ; test18 ;
+testwait (19, ntests, h) ; test19 ;
+testwait (20, ntests, h) ; test20 ;
+testwait (21, ntests, h) ; test21 ;
+testwait (22, ntests, h) ; test22 ;
+testwait (23, ntests, h) ; test23 ;
+testwait (24, ntests, h) ; test24 ;
+testwait (25, ntests, h) ; test25 ;
+testwait (26, ntests, h) ; test26 ;
+testwait (27, ntests, h) ; test27 ;
+testwait (28, ntests, h) ; test28 ;
+testwait (29, ntests, h) ; test_qr ;
+
+close (h)
+
+function testwait (n,ntests,h)
+fprintf ('\n------------------------ test%d\n', n) ;
+waitbar (n/(ntests+1), h, sprintf ('CXSparse test %d of %d\n', n, ntests)) ;
+
diff --git a/CXSparse_newfiles/MATLAB/Test/testh.m b/CXSparse_newfiles/MATLAB/Test/testh.m
new file mode 100644
index 0000000..9f32f27
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/Test/testh.m
@@ -0,0 +1,85 @@
+function testh
+%TESTH test Householder reflections
+%
+% Example:
+% testh
+% See also: testall
+
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+
+format long e
+fprintf ('-------------------------------------------------\n') ;
+x = [-3 4 5]' ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+
+x = [3 4 5]' ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = [1 eps]' ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = pi ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = -pi ;
+disp (x) ;
+[v, beta, s] = house (x) ;
+disp ('v = ') ;
+disp (v) ;
+disp ('beta = ') ;
+disp (beta) ;
+disp ('s = ') ;
+disp (s) ;
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
+
+x = [1 0 0]' ;
+disp (x) ;
+[v, beta, s] = house (x) ; %#ok
+x = x - v*(beta*(v'*x)) ;
+disp (x) ;
+fprintf ('-------------------------------------------------\n') ;
diff --git a/CXSparse_newfiles/MATLAB/cs_install.m b/CXSparse_newfiles/MATLAB/cs_install.m
new file mode 100644
index 0000000..526821b
--- /dev/null
+++ b/CXSparse_newfiles/MATLAB/cs_install.m
@@ -0,0 +1,56 @@
+function cs_install (do_pause)
+%CS_INSTALL: compile and install CXSparse for use in MATLAB.
+% Your current working directory must be CXSparse/MATLAB in order to use this
+% function.
+%
+% The directories
+%
+% CXSparse/MATLAB/CSparse
+% CXSparse/MATLAB/Demo
+% CXSparse/MATLAB/UFget
+%
+% are added to your MATLAB path (see the "pathtool" command to add these to
+% your path permanently, for future MATLAB sessions).
+%
+% Next, the MATLAB CXSparse demo program, CXSparse/MATLAB/cs_demo is executed.
+% To run the demo with pauses so you can see the results, use cs_install(1).
+% To run the full MATLAB test programs for CXSparse, run testall in the
+% Test directory.
+%
+% Example:
+% cs_install % install and run demo with no pauses
+% cs_install(1) % install and run demo with pauses
+%
+% See also: cs_demo
+%
+% Copyright 2006-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+
+fprintf ('Compiling and installing CXSparse\n') ;
+if (nargin < 1)
+ do_pause = 0 ;
+end
+
+if (do_pause)
+ input ('Hit enter to continue: ') ;
+end
+addpath ([pwd filesep 'CSparse']) ;
+addpath ([pwd filesep 'Demo']) ;
+
+v = getversion ;
+if (v >= 7.0)
+ addpath ([pwd filesep 'UFget']) ;
+else
+ fprintf ('UFget not installed (MATLAB 7.0 or later required)\n') ;
+end
+
+cd ('CSparse') ;
+cs_make (1) ;
+cd ('../Demo') ;
+cs_demo (do_pause)
+
+%-------------------------------------------------------------------------------
+function v = getversion
+% determine the MATLAB version, and return it as a double.
+v = sscanf (version, '%d.%d.%d') ;
+v = 10.^(0:-1:-(length(v)-1)) * v ;
diff --git a/CXSparse_newfiles/Matrix/c4 b/CXSparse_newfiles/Matrix/c4
new file mode 100644
index 0000000..eb6e600
--- /dev/null
+++ b/CXSparse_newfiles/Matrix/c4
@@ -0,0 +1,10 @@
+0 0 9.27539 0
+1 0 14.7693 -1.04429
+2 0 7.96934 2.8854
+3 0 13.0094 -2.32583
+1 1 23.8338 0
+2 1 12.4165 5.57382
+3 1 21.3387 -2.14682
+2 2 8.10265 0
+3 2 10.755 -6.1787
+3 3 19.8115 0
diff --git a/CXSparse_newfiles/Matrix/c_ibm32a b/CXSparse_newfiles/Matrix/c_ibm32a
new file mode 100644
index 0000000..d33de73
--- /dev/null
+++ b/CXSparse_newfiles/Matrix/c_ibm32a
@@ -0,0 +1,123 @@
+0 0 1 1
+1 0 1 1
+2 0 1 1
+3 0 1 1
+6 0 1 1
+25 0 1 1
+0 1 1 1
+1 1 1 1
+8 1 1 1
+20 1 1 1
+27 1 1 1
+1 2 1 1
+2 2 1 1
+5 2 1 1
+7 2 1 1
+8 2 1 1
+28 2 1 1
+2 3 1 1
+3 3 1 1
+4 3 1 1
+11 3 1 1
+2 4 1 1
+4 4 1 1
+22 4 1 1
+26 4 1 1
+0 5 1 1
+5 5 1 1
+15 5 1 1
+2 6 1 1
+6 6 1 1
+13 6 1 1
+20 6 1 1
+30 6 1 1
+0 7 1 1
+7 7 1 1
+11 7 1 1
+16 7 1 1
+26 7 1 1
+6 8 1 1
+8 8 1 1
+9 8 1 1
+12 8 1 1
+18 8 1 1
+22 8 1 1
+26 8 1 1
+0 9 1 1
+9 9 1 1
+10 9 1 1
+20 9 1 1
+22 9 1 1
+24 9 1 1
+26 9 1 1
+1 10 1 1
+10 10 1 1
+14 10 1 1
+17 10 1 1
+28 10 1 1
+5 11 1 1
+11 11 1 1
+23 11 1 1
+10 12 1 1
+12 12 1 1
+2 13 1 1
+13 13 1 1
+1 14 1 1
+14 14 1 1
+19 14 1 1
+3 15 1 1
+15 15 1 1
+21 15 1 1
+3 16 1 1
+15 16 1 1
+16 16 1 1
+5 17 1 1
+9 17 1 1
+17 17 1 1
+19 17 1 1
+29 17 1 1
+0 18 1 1
+18 18 1 1
+25 18 1 1
+7 19 1 1
+15 19 1 1
+19 19 1 1
+2 20 1 1
+20 20 1 1
+31 20 1 1
+10 21 1 1
+21 21 1 1
+1 22 1 1
+16 22 1 1
+20 22 1 1
+22 22 1 1
+11 23 1 1
+23 23 1 1
+25 23 1 1
+5 24 1 1
+14 24 1 1
+17 24 1 1
+23 24 1 1
+24 24 1 1
+12 25 1 1
+17 25 1 1
+21 25 1 1
+25 25 1 1
+4 26 1 1
+23 26 1 1
+25 26 1 1
+26 26 1 1
+8 27 1 1
+27 27 1 1
+2 28 1 1
+4 28 1 1
+26 28 1 1
+28 28 1 1
+31 28 1 1
+11 29 1 1
+16 29 1 1
+22 29 1 1
+29 29 1 1
+12 30 1 1
+13 30 1 1
+30 30 1 1
diff --git a/CXSparse_newfiles/Matrix/c_ibm32b b/CXSparse_newfiles/Matrix/c_ibm32b
new file mode 100644
index 0000000..5fe0e62
--- /dev/null
+++ b/CXSparse_newfiles/Matrix/c_ibm32b
@@ -0,0 +1,123 @@
+0 0 1 1
+1 0 1 1
+5 0 1 1
+7 0 1 1
+9 0 1 1
+18 0 1 1
+0 1 1 1
+1 1 1 1
+2 1 1 1
+10 1 1 1
+14 1 1 1
+22 1 1 1
+0 2 1 1
+2 2 1 1
+3 2 1 1
+4 2 1 1
+6 2 1 1
+13 2 1 1
+20 2 1 1
+28 2 1 1
+0 3 1 1
+3 3 1 1
+15 3 1 1
+16 3 1 1
+3 4 1 1
+4 4 1 1
+26 4 1 1
+28 4 1 1
+2 5 1 1
+5 5 1 1
+11 5 1 1
+17 5 1 1
+24 5 1 1
+0 6 1 1
+6 6 1 1
+8 6 1 1
+2 7 1 1
+7 7 1 1
+19 7 1 1
+1 8 1 1
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diff --git a/CXSparse_newfiles/Matrix/c_mbeacxc b/CXSparse_newfiles/Matrix/c_mbeacxc
new file mode 100644
index 0000000..08cd8c0
--- /dev/null
+++ b/CXSparse_newfiles/Matrix/c_mbeacxc
@@ -0,0 +1,49920 @@
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diff --git a/CXSparse_newfiles/Matrix/c_west0067 b/CXSparse_newfiles/Matrix/c_west0067
new file mode 100644
index 0000000..309378c
--- /dev/null
+++ b/CXSparse_newfiles/Matrix/c_west0067
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diff --git a/CXSparse_newfiles/Matrix/mhd1280b b/CXSparse_newfiles/Matrix/mhd1280b
new file mode 100644
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diff --git a/CXSparse_newfiles/Matrix/neumann b/CXSparse_newfiles/Matrix/neumann
new file mode 100644
index 0000000..60f431b
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diff --git a/CXSparse_newfiles/Matrix/qc324 b/CXSparse_newfiles/Matrix/qc324
new file mode 100644
index 0000000..bc4fa4b
--- /dev/null
+++ b/CXSparse_newfiles/Matrix/qc324
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diff --git a/CXSparse_newfiles/README.txt b/CXSparse_newfiles/README.txt
new file mode 100644
index 0000000..b108f66
--- /dev/null
+++ b/CXSparse_newfiles/README.txt
@@ -0,0 +1,572 @@
+CXSparse: a Concise Sparse Matrix package - Extended.
+Version 2.2.0, Copyright (c) 2006-2007, Timothy A. Davis.
+Derived from CSparse. Conversion originally by David Bateman, Motorola,
+and then modified by Tim Davis. ANSI C99 is required, with support for
+the _Complex data type.
+(if you use a C++ compiler, the C++ complex type is used instead).
+
+CXSparse is a version of CSparse that operates on both real and complex
+matrices, using either int or UF_long integers. A UF_long is normally
+just a long on most platforms, but becomes __int64 on WIN64.
+It now includes a MATLAB interface, enabling the use of CXSparse functions on
+both 32-bit and 64-bit platforms.
+
+To install for use in MATLAB, simply type "cs_install" in the MATLAB Command
+Window, while in the CXSparse/MATLAB directory. (NOTE: Windows users cannot
+use the "lcc" command; run "mex -setup" first, and select a different
+compiler). If you use the Unix "make" command in that directory instead and
+are using a 64-bit platform, then you must edit the CXSparse/MATLAB/Makefile
+first. Refer to the instructions in that file.
+
+Refer to "Direct Methods for Sparse Linear Systems," Timothy A. Davis,
+SIAM, Philadelphia, 2006. No detailed user guide is included in this
+package; the user guide is the book itself.
+
+To compile the C-library (./Source), C demo programs (./Demo) just type "make"
+in this directory. To run the exhaustive statement coverage tests, type
+"make" in the Tcov directory; the Tcov tests assume you are using Linux. To
+remove all files not in the original distribution, type "make distclean".
+I recommend that you use a different level of
+optimization than "cc -O", which was chosen so that the Makefile is portable.
+See Source/Makefile.
+
+If your C compiler does not support the ANSI C99 complex type, the
+#include <complex.h> statement will fail. If this happens, compile the
+code with the -DNCOMPLEX flag (the MATLAB cs_install will do this for you).
+
+This package is backward compatible with CSparse. That is, user code that
+uses CSparse may switch to using CXSparse without any changes to the user code.
+Each CXSparse function has a generic version with the same name as the CSparse
+function, and four type-specific versions. For example:
+
+ cs_add same as cs_add_di by default, but can be changed to use UF_long
+ integers if user code is compiled with -DCS_LONG, and/or can
+ be changed to operate on complex matrices with -DCS_COMPLEX.
+
+ cs_di_add double/int version of cs_add
+ cs_dl_add double/UF_long version of cs_add
+ cs_ci_add complex/int version of cs_add
+ cs_cl_add complex/UF_long version of cs_add
+
+The sparse matrix data structures are treated in the same way: cs, css,
+csn, and csd become cs_di, cs_dis, cs_din, and cs_did for the double/int case,
+cs_cl, cs_cls, cs_cln, and cs_cld for the complex/UF_long case, and so on.
+
+See cs_demo.c for a type-generic user program, and cs_cl_demo.c for a
+type-specific version of the same program (complex/UF_long).
+
+Several macros are available in CXSparse (but not in CSparse) to allow user
+code to be written in a type-generic manner:
+
+ CS_INT int by default, UF_long if -DCS_LONG compiler flag is used
+ CS_ENTRY double by default, double complex if -DCS_COMPLEX flag is used.
+ CS_ID "%d" or "%ld", for printf and scanf of the CS_INT type.
+ CS_INT_MAX INT_MAX or LONG_MAX, the largest possible value of CS_INT.
+ CS_REAL(x) x or creal(x)
+ CS_IMAG(x) 0 or cimag(x)
+ CS_CONJ(x) x or conj(x)
+ CS_ABS(x) fabs(x) or cabs(x)
+
+Even the name of the include file (cs.h) is the same. To use CXSparse instead
+of CSparse, simply compile with -ICXSparse/Source instead of -ICSparse/Source,
+and link against libcxsparse.a instead of the CSparse libcsparse.a library.
+
+To determine at compile time if CXSparse or CSparse is being used:
+
+ #ifdef CXSPARSE
+ CXSparse is in use. The generic functions equivalent to CSparse may
+ be used (cs_add, etc). These generic functions can use different
+ types, depending on the -DCS_LONG and -DCS_COMPLEX compile flags, with
+ the default being double/int. The type-specific functions and data
+ types (cs_di_add, cs_di, CS_INT, etc.) can be used.
+ #else
+ CSparse is in use. Only the generic functions "cs_add", etc., are
+ available, and they are of type double/int.
+ #endif
+
+See cs.h for the prototypes of each function, and the book "Direct Methods
+for Sparse Linear Systems" for full documentation of CSparse and CXSparse.
+
+Other changes from CSparse: cs_transpose performs the complex conjugate
+transpose if values>0 (C=A'), the pattern-only transpose if values=0
+(C=spones(A') in MATLAB), and the array transpose if values<0 (C=A.' in
+MATLAB notation). A set of four conversion routines are included in CXSparse,
+to convert real matrices to/from complex matrices.
+The Householder reflection constructed by cs_house.c also differs slightly, to
+accomodate both the real and complex cases properly.
+
+CXSparse is generated automatically from CSparse. Refer to
+http://www.cise.ufl.edu/research/sparse/CSparse for details.
+
+--------------------------------------------------------------------------------
+Contents:
+--------------------------------------------------------------------------------
+
+Demo/ demo C programs that use CXSparse
+Doc/ license and change log
+Makefile Makefile for the whole package
+MATLAB/ MATLAB interface, demos, and tests for CXSparse
+Matrix/ sample matrices (with extra complex matrices for CXSparse)
+README.txt this file
+Source/ primary CXSparse source files
+Tcov/ CXSparse tests
+
+--------------------------------------------------------------------------------
+./Doc: license and change log
+--------------------------------------------------------------------------------
+
+ChangeLog changes in CSparse since first release
+lesser.txt the GNU LGPL
+License.txt license (GNU LGPL)
+
+--------------------------------------------------------------------------------
+./Source: Primary source code for CXSparse
+--------------------------------------------------------------------------------
+
+cs_add.c add sparse matrices
+cs_amd.c approximate minimum degree
+cs_chol.c sparse Cholesky
+cs_cholsol.c x=A\b using sparse Cholesky
+cs_compress.c convert a compress form to compressed-column form
+cs_counts.c column counts for Cholesky and QR
+cs_convert.c convert real to complex and complex to real (not in CSparse)
+cs_cumsum.c cumulative sum
+cs_dfs.c depth-first-search
+cs_dmperm.c Dulmage-Mendelsohn permutation
+cs_droptol.c drop small entries from a sparse matrix
+cs_dropzeros.c drop zeros from a sparse matrix
+cs_dupl.c remove (and sum) duplicates
+cs_entry.c add an entry to a triplet matrix
+cs_ereach.c nonzero pattern of Cholesky L(k,:) from etree and triu(A(:,k))
+cs_etree.c find elimination tree
+cs_fkeep.c drop entries from a sparse matrix
+cs_gaxpy.c sparse matrix times dense matrix
+cs.h include file for CXSparse
+cs_happly.c apply Householder reflection
+cs_house.c Householder reflection (*** NOTE: different algo. from CSparse)
+cs_ipvec.c x(p)=b
+cs_leaf.c determine if j is a leaf of the skeleton matrix and find lca
+cs_load.c load a sparse matrix from a file
+cs_lsolve.c x=L\b
+cs_ltsolve.c x=L'\b
+cs_lu.c sparse LU factorization
+cs_lusol.c x=A\b using sparse LU factorization
+cs_malloc.c memory manager
+cs_maxtrans.c maximum transveral (permutation for zero-free diagonal)
+cs_multiply.c sparse matrix multiply
+cs_norm.c sparse matrix norm
+cs_permute.c permute a sparse matrix
+cs_pinv.c invert a permutation vector
+cs_post.c postorder an elimination tree
+cs_print.c print a sparse matrix
+cs_pvec.c x=b(p)
+cs_qr.c sparse QR
+cs_qrsol.c solve a least-squares problem
+cs_randperm.c random permutation
+cs_reach.c find nonzero pattern of x=L\b for sparse L and b
+cs_scatter.c scatter a sparse vector
+cs_scc.c strongly-connected components
+cs_schol.c symbolic Cholesky
+cs_spsolve.c x=Z\b where Z, x, and b are sparse, and Z upper/lower triangular
+cs_sqr.c symbolic QR (also can be used for LU)
+cs_symperm.c symmetric permutation of a sparse matrix
+cs_tdfs.c depth-first-search of a tree
+cs_transpose.c transpose a sparse matrix
+cs_updown.c sparse rank-1 Cholesky update/downate
+cs_usolve.c x=U\b
+cs_util.c various utilities (allocate/free matrices, workspace, etc)
+cs_utsolve.c x=U'\b
+Makefile Makefile for CXSparse
+README.txt README file for CXSparse
+
+--------------------------------------------------------------------------------
+./Demo: C program demos
+--------------------------------------------------------------------------------
+
+cs_ci_demo1.c complex/int version of cs_demo1.c
+cs_ci_demo2.c complex/int version of cs_demo2.c
+cs_ci_demo3.c complex/int version of cs_demo3.c
+cs_ci_demo.c complex/int version of cs_demo.c
+cs_ci_demo.h complex/int version of cs_demo.h
+
+cs_cl_demo1.c complex/UF_long version of cs_demo1.c
+cs_cl_demo2.c complex/UF_long version of cs_demo2.c
+cs_cl_demo3.c complex/UF_long version of cs_demo3.c
+cs_cl_demo.c complex/UF_long version of cs_demo.c
+cs_cl_demo.h complex/UF_long version of cs_demo.h
+
+cs_demo1.c read a matrix from a file and perform basic matrix operations
+cs_demo2.c read a matrix from a file and solve a linear system
+cs_demo3.c read a matrix, solve a linear system, update/downdate
+cs_demo.c support routines for cs_demo*.c
+cs_demo.h include file for demo programs
+
+cs_demo.out output of "make", which runs the demos on some matrices
+
+cs_di_demo1.c double/int version of cs_demo1.c
+cs_di_demo2.c double/int version of cs_demo2.c
+cs_di_demo3.c double/int version of cs_demo3.c
+cs_di_demo.c double/int version of cs_demo.c
+cs_di_demo.h double/int version of cs_demo.h
+
+cs_dl_demo1.c double/UF_long version of cs_demo1.c
+cs_dl_demo2.c double/UF_long version of cs_demo2.c
+cs_dl_demo3.c double/UF_long version of cs_demo3.c
+cs_dl_demo.c double/UF_long version of cs_demo.c
+cs_dl_demo.h double/UF_long version of cs_demo.h
+
+cs_idemo.c convert real matrices to/from complex (int version)
+cs_ldemo.c convert real matrices to/from complex (UF_long version)
+
+Makefile Makefile for Demo programs
+readhb.f read a Rutherford-Boeing matrix (real matrices only)
+README.txt Demo README file
+
+--------------------------------------------------------------------------------
+./MATLAB: MATLAB interface, demos, and tests
+--------------------------------------------------------------------------------
+
+cs_install.m MATLAB function for compiling and installing CSparse for MATLAB
+CSparse/ MATLAB interface for CSparse
+Demo/ MATLAB demos for CSparse
+Makefile MATLAB interface Makefile
+README.txt MATLAB README file
+Test/ MATLAB test for CSparse, and "textbook" routines
+UFget/ MATLAB interface to UF Sparse Matrix Collection
+
+
+--------------------------------------------------------------------------------
+./MATLAB/CSparse: MATLAB interface for CSparse
+--------------------------------------------------------------------------------
+
+Contents.m Contents of MATLAB interface to CSparse
+cs_add.m add two sparse matrices
+cs_add_mex.c
+cs_amd.m approximate minimum degree
+cs_amd_mex.c
+cs_chol.m sparse Cholesky
+cs_chol_mex.c
+cs_cholsol.m x=A\b using a sparse Cholesky
+cs_cholsol_mex.c
+cs_counts.m column counts for Cholesky or QR (like "symbfact" in MATLAB)
+cs_counts_mex.c
+cs_dmperm.m Dulmage-Mendelsohn permutation
+cs_dmperm_mex.c
+cs_dmsol.m x=A\b using dmperm
+cs_dmspy.m plot a picture of a dmperm-permuted matrix
+cs_droptol.m drop small entries
+cs_droptol_mex.c
+cs_esep.m find edge separator
+cs_etree.m compute elimination tree
+cs_etree_mex.c
+cs_gaxpy.m sparse matrix times dense vector
+cs_gaxpy_mex.c
+cs_lsolve.m x=L\b where L is lower triangular
+cs_lsolve_mex.c
+cs_ltsolve.m x=L'\b where L is lower triangular
+cs_ltsolve_mex.c
+cs_lu.m sparse LU factorization
+cs_lu_mex.c
+cs_lusol.m x=A\b using sparse LU factorization
+cs_lusol_mex.c
+cs_make.m compiles CSparse for use in MATLAB
+cs_mex.c support routines for CSparse mexFunctions
+cs_mex.h
+cs_multiply.m sparse matrix multiply
+cs_multiply_mex.c
+cs_must_compile.m determine if a source file needs to be compiled with mex
+cs_nd.m nested dissection
+cs_nsep.m find node separator
+cs_permute.m permute a sparse matrix
+cs_permute_mex.c
+cs_print.m print a sparse matrix
+cs_print_mex.c
+cs_qleft.m apply Householder vectors to the left
+cs_qright.m apply Householder vectors to the right
+cs_qr.m sparse QR factorization
+cs_qr_mex.c
+cs_qrsol.m solve a sparse least squares problem
+cs_qrsol_mex.c
+cs_randperm.m randdom permutation
+cs_randperm_mex.c
+cs_scc.m strongly-connected components
+cs_scc_mex.c
+cs_sep.m convert an edge separator into a node separator
+cs_sparse.m convert a triplet form matrix to a compress-column form
+cs_sparse_mex.c
+cs_symperm.m symmetric permutation of a sparse matrix
+cs_symperm_mex.c
+cs_sqr.m symbolic QR ordering and analysis
+cs_sqr_mex.c
+cs_thumb_mex.c compute small "thumbnail" of a sparse matrix (for cspy).
+cs_transpose.m transpose a sparse matrix
+cs_transpose_mex.c
+cs_updown.m sparse Cholesky update/downdate
+cs_updown_mex.c
+cs_usolve.m x=U\b where U is upper triangular
+cs_usolve_mex.c
+cs_utsolve.m x=U'\b where U is upper triangular
+cs_utsolve_mex.c
+cspy.m a color "spy"
+Makefile Makefile for CSparse MATLAB interface
+README.txt README file for CSparse MATLAB interface
+
+
+--------------------------------------------------------------------------------
+./MATLAB/Demo: MATLAB demos for CSparse
+--------------------------------------------------------------------------------
+
+Contents.m Contents of MATLAB demo for CSparse
+cs_demo.m run all MATLAB demos for CSparse
+cs_demo1.m MATLAB version of Demo/cs_demo1.c
+cs_demo2.m MATLAB version of Demo/cs_demo2.c
+cs_demo3.m MATLAB version of Demo/cs_demo3.c
+private/ private functions for MATLAB demos
+README.txt README file for CSparse MATLAB demo
+
+
+--------------------------------------------------------------------------------
+./MATLAB/Demo/private: private functions for MATLAB demos
+--------------------------------------------------------------------------------
+
+demo2.m demo 2
+demo3.m demo 3
+ex_1.m example 1
+ex2.m example 2
+ex3.m example 3
+frand.m generate a random finite-element matrix
+get_problem.m get a matrix
+is_sym.m determine if a matrix is symmetric
+mesh2d1.m construct a 2D mesh (method 1)
+mesh2d2.m construct a 2D mesh (method 2)
+mesh3d1.m construct a 3D mesh (method 1)
+mesh3d2.m construct a 3D mesh (method 2)
+print_order.m print the ordering method used
+resid.m compute residual
+rhs.m create right-hand-side
+
+
+--------------------------------------------------------------------------------
+./MATLAB/Test: Extensive test of CSparse, in MATLAB
+--------------------------------------------------------------------------------
+
+Makefile Makefile for MATLAB Test directory
+README.txt README file for MATLAB/Test
+Contents.m Contents of MATLAB/Test, "textbook" files only
+
+chol_downdate.m downdate a Cholesky factorization.
+chol_left.m left-looking Cholesky factorization.
+chol_left2.m left-looking Cholesky factorization, more details.
+chol_right.m right-looking Cholesky factorization.
+chol_super.m left-looking "supernodal" Cholesky factorization.
+chol_up.m up-looking Cholesky factorization.
+chol_update.m update a Cholesky factorization.
+chol_updown.m update or downdate a Cholesky factorization.
+cond1est.m 1-norm condition estimate.
+cs_fiedler.m the Fiedler vector of a connected graph.
+givens2.m find a Givens rotation.
+house.m find a Householder reflection.
+lu_left.m left-looking LU factorization.
+lu_right.m right-looking LU factorization.
+lu_rightp.m right-looking LU factorization, with partial pivoting.
+lu_rightpr.m recursive right-looking LU, with partial pivoting.
+lu_rightr.m recursive right-looking LU.
+norm1est.m 1-norm estimate.
+qr_givens.m Givens-rotation QR factorization.
+qr_givens_full.m Givens-rotation QR factorization, for full matrices.
+qr_left.m left-looking Householder QR factorization.
+qr_right.m right-looking Householder QR factorization.
+cs_fiedler.m Fiedler vector
+
+cs_frand.m generate a random finite-element matrix
+cs_frand_mex.c
+cs_ipvec.m x(p)=b
+cs_ipvec_mex.c
+cs_maxtransr.m recursive maximum matching algorithm
+cs_maxtransr_mex.c
+cs_pvec.m x=b(p)
+cs_pvec_mex.c interface for cs_pvec
+cs_reach.m non-recursive reach (interface to CSparse cs_reach)
+cs_reach_mex.c non-recursive x=spones(L\sparse(b))
+cs_reachr.m recursive reach (interface to CSparse cs_reachr)
+cs_reachr_mex.c
+cs_rowcnt.m row counts for sparse Cholesky
+cs_rowcnt_mex.c row counts for sparse Cholesky
+cs_sparse2.m same as cs_sparse, to test cs_entry function
+cs_sparse2_mex.c like cs_sparse, but for testing cs_entry
+
+cs_test_make.m compiles MATLAB tests
+
+check_if_same.m check if two inputs are identical or not
+choldn.m Cholesky downdate
+cholup.m Cholesky update, using Given's rotations
+cholupdown.m Cholesky update/downdate (Bischof, Pan, and Tang method)
+cs_q1.m construct Q from Householder vectors
+cs_test_make.m compiles the CSparse, Demo, and Test mexFunctions.
+dmperm_test.m test cs_dmperm
+chol_example.m simple Cholesky factorization example
+etree_sample.m construct a sample etree and symbolic factorization
+gqr3.m QR factorization, based on Givens rotations
+happly.m apply Householder reflection to a vector
+hmake1.m construct a Householder reflection
+mynormest1.m estimate norm(A,1), using LU factorization (L*U = P*A*Q).
+myqr.m QR factorization using Householder reflections
+another_colormap.m try another color map
+cspy_test.m test cspy and cs_dmspy
+qr2.m QR factorization based on Householder reflections
+sample_colormap.m try a colormap for use in cspy
+signum.m compute and display the sign of a column vector x
+sqr_example.m test cs_sqr
+dmspy_test.m test cspy, cs_dmspy, and cs_dmperm
+test_qr.m test various QR factorization methods
+test_randperms.m test random permutations
+testh.m test Householder reflections
+test_qr1.m test QR factorizations
+test_qrsol.m test cs_qrsol
+test_sep.m test cs_sep, and compare with Gilbert's meshpart vtxsep
+testall.m test all CSparse functions (run tests 1 to 28 below)
+test1.m test cs_transpose
+test2.m test cs_sparse
+test3.m test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol
+test4.m test cs_multiply
+test5.m test cs_add
+test6.m test cs_reach, cs_reachr, cs_lsolve, cs_usolve
+test7.m test cs_lu
+test8.m test cs_cholsol, cs_lusol
+test9.m test cs_qr
+test10.m test cs_qr
+test11.m test cs_rowcnt
+test12.m test cs_qr and compare with svd
+test13.m test cs_counts, cs_etree
+test14.m test cs_droptol
+test15.m test cs_amd
+test16.m test cs_amd
+test17.m test cs_qr, cs_qright, cs_q1, cs_qrleft, cs_qrsol
+test18.m test iterative refinement after backslash
+test19.m test cs_dmperm, cs_maxtransr, cs_dmspy, cs_scc
+test20.m test cholupdown
+test21.m test cs_updown
+test22.m test cond1est
+test23.m test cs_dmspy
+test24.m test cs_fielder
+test25.m test cs_nd
+test26.m test cs_dmsol and cs_dmspy
+test27.m test cs_qr, cs_utsolve, cs_qrsol
+test28.m test cs_randperm, cs_dmperm
+
+
+--------------------------------------------------------------------------------
+./MATLAB/UFget: MATLAB interface for the UF Sparse Matrix Collection
+--------------------------------------------------------------------------------
+
+Contents.m Contents of UFget
+mat/ default directory where downloaded matrices will be put
+README.txt README file for UFget
+UFget_defaults.m default parameter settings
+UFget_example.m example of use
+UFget_install.m installs UFget temporarily (for current session)
+UFget_java.class read a url and load it in into MATLAB (compiled Java code)
+UFget_java.java read a url and load it in into MATLAB (Java source code)
+UFget_lookup.m look up a matrix in the index
+UFget.m UFget itself (primary user interface)
+UFweb.m open url for a matrix or collection
+mat/UF_Index.mat index of matrices in UF Sparse Matrix Collection
+
+
+--------------------------------------------------------------------------------
+./Matrix: Sample matrices, most from Rutherford/Boeing collection
+--------------------------------------------------------------------------------
+
+ash219 overdetermined pattern of Holland survey. Ashkenazi, 1974.
+bcsstk01 stiffness matrix for small generalized eigenvalue problem
+bcsstk16 stiffness matrix, Corp of Engineers dam
+fs_183_1 unsymmetric facsimile convergence matrix
+lp_afiro NETLIB afiro linear programming problem
+mbeacxc US economy, 1972. Dan Szyld, while at NYU
+t1 small example used in Chapter 2
+west0067 Cavett problem with 5 components (chemical eng., Westerberg)
+
+c_mbeacxc complex version of mbeacxc
+c_west0067 complex version of west0067
+mhd1280b Alfven spectra in magnetohydrodynamics (complex)
+neumann complex matrix
+qc324 model of H+ in an electromagnetic field (complex)
+t2 small complex matrix
+t3 small complex matrix
+t4 small complex matrix
+c4 small complex matrix
+young1c aeronautical problem (complex matrix)
+
+--------------------------------------------------------------------------------
+./Tcov: Exhaustive test coverage of CXSparse
+--------------------------------------------------------------------------------
+
+covall same as covall.linux
+covall.linux find coverage (Linux)
+covall.sol find coverage (Solaris)
+cov.awk coverage summary
+cover print uncovered lines
+covs print uncovered lines
+cstcov_malloc_test.c malloc test
+cstcov_malloc_test.h
+cstcov_test.c main program for Tcov tests
+gcovs run gcov (Linux)
+Makefile Makefile for Tcov tests
+nil an empty matrix
+zero a 1-by-1 zero matrix
+czero a 1-by-1 complex zero matrix
+README.txt README file for Tcov directory
+
+
+--------------------------------------------------------------------------------
+Change Log:
+--------------------------------------------------------------------------------
+
+Refer to CSparse for changes in CSparse, which are immediately propagated
+into CXSparse (those Change Log entries are not repeated here).
+
+Nov 1, 2007. version 2.2.1
+
+ CXSparse/MATLAB/Test ported to Windows
+
+
+May 31, 2007. version 2.2.0
+
+ * back-port to MATLAB 7.2 and earlier (which does not have mwIndex).
+
+ * more graceful failure in cs_make when attempting complex matrix support
+ (Windows, in particular)
+
+ * correction to CXSparse/Demo/Makefile
+
+ * added sizeof(CS_INT) printout to cs_idemo.c, cs_ldemo.c
+
+Mar 14, 2007. Version 2.1.0.
+
+ * MATLAB interface added for CXSparse.
+
+ * cs_complex_t type added (a #define for "double _Complex", which is the
+ complex type used in CXSparse 2.0.x). When compiling with a C++
+ compiler, the std::compex<double> type is used for the complex case.
+
+ * bug fix in complex sparse Cholesky (cs_chol.c).
+
+ * bug fix in complex sparse Cholesky update/downdate (cs_updown.c).
+
+ * bug fix in cs_symperm for the complex case.
+
+ * "beta" changed from complex to real, in sparse QR (cs_house.c,
+ cs_happly.c, cs_qr.c), (a performance/memory improvement, not a
+ bug fix). Similar change to "nz2" in cs_cumsum.c.
+
+May 5, 2006. Version 2.0.1 released.
+
+ * long changed to UF_long, dependency in ../UFconfig/UFconfig.h added.
+ "UF_long" is a #define'd term in UFconfig.h. It is normally defined
+ as "long", but can be redefined as something else if desired.
+ On Windows-64, it becomes __int64.
+
+Mar 6, 2006
+
+ "double complex" changed to "double _Complex", to avoid conflicts when
+ CXSparse is compiled with a C++ compiler. Other minor changes to cs.h.
diff --git a/CXSparse_newfiles/Source/README.txt b/CXSparse_newfiles/Source/README.txt
new file mode 100644
index 0000000..5f39716
--- /dev/null
+++ b/CXSparse_newfiles/Source/README.txt
@@ -0,0 +1,3 @@
+CXSparse/Source directory: primary ANSI C source code files for CXSparse.
+To compile the libcxsparse.a C-callable library, just type "make" in this
+directory.
diff --git a/CXSparse_newfiles/Source/cs_convert.c b/CXSparse_newfiles/Source/cs_convert.c
new file mode 100644
index 0000000..2d6607f
--- /dev/null
+++ b/CXSparse_newfiles/Source/cs_convert.c
@@ -0,0 +1,93 @@
+#include "cs.h"
+
+/* convert from complex to real (int version) */
+/* C = real(A) if real is true, imag(A) otherwise */
+cs_di *cs_i_real (cs_ci *A, int real)
+{
+ cs_di *C ;
+ int n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ;
+ cs_complex_t *Ax ;
+ double *Cx ;
+ if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */
+ nz = triplet ? A->nz : Ap [n] ;
+ C = cs_di_spalloc (A->m, n, A->nzmax, 1, triplet) ;
+ if (!C) return (NULL) ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ nn = triplet ? nz : (n+1) ;
+ for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ;
+ for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ;
+ for (p = 0 ; p < nz ; p++) Cx [p] = real ? creal (Ax [p]) : cimag (Ax [p]) ;
+ if (triplet) C->nz = nz ;
+ return (C) ;
+}
+
+/* convert from real to complex (int version) */
+/* C = A if real is true, or C = i*A otherwise */
+cs_ci *cs_i_complex (cs_di *A, int real)
+{
+ cs_ci *C ;
+ int n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ;
+ double *Ax ;
+ cs_complex_t *Cx ;
+ if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */
+ nz = triplet ? A->nz : Ap [n] ;
+ C = cs_ci_spalloc (A->m, n, A->nzmax, 1, triplet) ;
+ if (!C) return (NULL) ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ nn = triplet ? nz : (n+1) ;
+ for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ;
+ for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ;
+ for (p = 0 ; p < nz ; p++) Cx [p] = real ? Ax [p] : (I * Ax [p]) ;
+ if (triplet) C->nz = nz ;
+ return (C) ;
+}
+
+/* convert from complex to real (UF_long version) */
+/* C = real(A) if real is true, imag(A) otherwise */
+cs_dl *cs_l_real (cs_cl *A, UF_long real)
+{
+ cs_dl *C ;
+ UF_long n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ;
+ cs_complex_t *Ax ;
+ double *Cx ;
+ if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */
+ nz = triplet ? A->nz : Ap [n] ;
+ C = cs_dl_spalloc (A->m, n, A->nzmax, 1, triplet) ;
+ if (!C) return (NULL) ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ nn = triplet ? nz : (n+1) ;
+ for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ;
+ for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ;
+ for (p = 0 ; p < nz ; p++) Cx [p] = real ? creal (Ax [p]) : cimag (Ax [p]) ;
+ if (triplet) C->nz = nz ;
+ return (C) ;
+}
+
+/* convert from real to complex (UF_long version) */
+/* C = A if real is true, or C = i*A otherwise */
+cs_cl *cs_l_complex (cs_dl *A, UF_long real)
+{
+ cs_cl *C ;
+ UF_long n, triplet, nn, p, nz, *Ap, *Ai, *Cp, *Ci ;
+ double *Ax ;
+ cs_complex_t *Cx ;
+ if (!A || !A->x) return (NULL) ; /* return if A NULL or pattern-only */
+ n = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ;
+ triplet = (A->nz >= 0) ; /* true if A is a triplet matrix */
+ nz = triplet ? A->nz : Ap [n] ;
+ C = cs_cl_spalloc (A->m, n, A->nzmax, 1, triplet) ;
+ if (!C) return (NULL) ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ nn = triplet ? nz : (n+1) ;
+ for (p = 0 ; p < nz ; p++) Ci [p] = Ai [p] ;
+ for (p = 0 ; p < nn ; p++) Cp [p] = Ap [p] ;
+ for (p = 0 ; p < nz ; p++) Cx [p] = real ? Ax [p] : (I * Ax [p]) ;
+ if (triplet) C->nz = nz ;
+ return (C) ;
+}
diff --git a/CXSparse_newfiles/Source/cs_house.c b/CXSparse_newfiles/Source/cs_house.c
new file mode 100644
index 0000000..baf4082
--- /dev/null
+++ b/CXSparse_newfiles/Source/cs_house.c
@@ -0,0 +1,30 @@
+#include "cs.h"
+/* create a Householder reflection [v,beta,s]=house(x), overwrite x with v,
+ * where (I-beta*v*v')*x = s*e1 and e1 = [1 0 ... 0]'.
+ * Note that this CXSparse version is different than CSparse. See Higham,
+ * Accuracy & Stability of Num Algorithms, 2nd ed, 2002, page 357. */
+CS_ENTRY cs_house (CS_ENTRY *x, double *beta, CS_INT n)
+{
+ CS_ENTRY s = 0 ;
+ CS_INT i ;
+ if (!x || !beta) return (-1) ; /* check inputs */
+ /* s = norm(x) */
+ for (i = 0 ; i < n ; i++) s += x [i] * CS_CONJ (x [i]) ;
+ s = sqrt (s) ;
+ if (s == 0)
+ {
+ (*beta) = 0 ;
+ x [0] = 1 ;
+ }
+ else
+ {
+ /* s = sign(x[0]) * norm (x) ; */
+ if (x [0] != 0)
+ {
+ s *= x [0] / CS_ABS (x [0]) ;
+ }
+ x [0] += s ;
+ (*beta) = 1. / CS_REAL (CS_CONJ (s) * x [0]) ;
+ }
+ return (-s) ;
+}
diff --git a/CXSparse_newfiles/Source/cs_updown.c b/CXSparse_newfiles/Source/cs_updown.c
new file mode 100644
index 0000000..1584dff
--- /dev/null
+++ b/CXSparse_newfiles/Source/cs_updown.c
@@ -0,0 +1,48 @@
+#include "cs.h"
+/* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */
+CS_INT cs_updown (cs *L, CS_INT sigma, const cs *C, const CS_INT *parent)
+{
+ CS_INT n, p, f, j, *Lp, *Li, *Cp, *Ci ;
+ CS_ENTRY *Lx, *Cx, alpha, gamma, w1, w2, *w ;
+ double beta = 1, beta2 = 1, delta ;
+#ifdef CS_COMPLEX
+ cs_complex_t phase ;
+#endif
+ if (!CS_CSC (L) || !CS_CSC (C) || !parent) return (0) ; /* check inputs */
+ Lp = L->p ; Li = L->i ; Lx = L->x ; n = L->n ;
+ Cp = C->p ; Ci = C->i ; Cx = C->x ;
+ if ((p = Cp [0]) >= Cp [1]) return (1) ; /* return if C empty */
+ w = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get workspace */
+ if (!w) return (0) ; /* out of memory */
+ f = Ci [p] ;
+ for ( ; p < Cp [1] ; p++) f = CS_MIN (f, Ci [p]) ; /* f = min (find (C)) */
+ for (j = f ; j != -1 ; j = parent [j]) w [j] = 0 ; /* clear workspace w */
+ for (p = Cp [0] ; p < Cp [1] ; p++) w [Ci [p]] = Cx [p] ; /* w = C */
+ for (j = f ; j != -1 ; j = parent [j]) /* walk path f up to root */
+ {
+ p = Lp [j] ;
+ alpha = w [j] / Lx [p] ; /* alpha = w(j) / L(j,j) */
+ beta2 = beta*beta + sigma*alpha*CS_CONJ(alpha) ;
+ if (beta2 <= 0) break ; /* not positive definite */
+ beta2 = sqrt (beta2) ;
+ delta = (sigma > 0) ? (beta / beta2) : (beta2 / beta) ;
+ gamma = sigma * CS_CONJ(alpha) / (beta2 * beta) ;
+ Lx [p] = delta * Lx [p] + ((sigma > 0) ? (gamma * w [j]) : 0) ;
+ beta = beta2 ;
+#ifdef CS_COMPLEX
+ phase = CS_ABS (Lx [p]) / Lx [p] ; /* phase = abs(L(j,j))/L(j,j)*/
+ Lx [p] *= phase ; /* L(j,j) = L(j,j) * phase */
+#endif
+ for (p++ ; p < Lp [j+1] ; p++)
+ {
+ w1 = w [Li [p]] ;
+ w [Li [p]] = w2 = w1 - alpha * Lx [p] ;
+ Lx [p] = delta * Lx [p] + gamma * ((sigma > 0) ? w1 : w2) ;
+#ifdef CS_COMPLEX
+ Lx [p] *= phase ; /* L(i,j) = L(i,j) * phase */
+#endif
+ }
+ }
+ cs_free (w) ;
+ return (beta2 > 0) ;
+}
diff --git a/CXSparse_newfiles/Tcov/Makefile b/CXSparse_newfiles/Tcov/Makefile
new file mode 100644
index 0000000..04609af
--- /dev/null
+++ b/CXSparse_newfiles/Tcov/Makefile
@@ -0,0 +1,318 @@
+
+# To run with valgrind:
+V =
+# V = valgrind -q
+
+# Linux test coverage
+CC = gcc
+CFLAGS = -O -g -fprofile-arcs -ftest-coverage \
+ -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \
+ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi \
+ -Wno-unused-parameter -Werror -I../Include -I../Demo -I../../UFconfig
+
+run: all run_convert run_di run_dl run_ci run_cl
+ ./covall
+
+all: cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di \
+ cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl \
+ cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci \
+ cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl \
+ cs_idemo cs_ldemo
+
+CS_DI = cs_add_di.o cs_amd_di.o cs_chol_di.o cs_cholsol_di.o cs_counts_di.o \
+ cs_cumsum_di.o cs_droptol_di.o cs_dropzeros_di.o cs_dupl_di.o \
+ cs_entry_di.o cs_etree_di.o cs_fkeep_di.o cs_gaxpy_di.o cs_happly_di.o \
+ cs_house_di.o cs_ipvec_di.o cs_lsolve_di.o cs_ltsolve_di.o cs_lu_di.o \
+ cs_lusol_di.o cs_util_di.o cs_multiply_di.o cs_permute_di.o \
+ cs_pinv_di.o cs_post_di.o cs_pvec_di.o cs_qr_di.o cs_qrsol_di.o \
+ cs_scatter_di.o cs_schol_di.o cs_sqr_di.o cs_symperm_di.o cs_tdfs_di.o \
+ cs_transpose_di.o cs_compress_di.o cs_usolve_di.o cs_scc_di.o \
+ cs_maxtrans_di.o cs_dmperm_di.o cs_updown_di.o cs_print_di.o \
+ cs_norm_di.o cs_load_di.o cs_dfs_di.o cstcov_malloc_test_di.o \
+ cs_utsolve_di.o cs_reach_di.o cs_spsolve_di.o \
+ cs_leaf_di.o cs_ereach_di.o cs_randperm_di.o
+
+CS_DL = cs_add_dl.o cs_amd_dl.o cs_chol_dl.o cs_cholsol_dl.o cs_counts_dl.o \
+ cs_cumsum_dl.o cs_droptol_dl.o cs_dropzeros_dl.o cs_dupl_dl.o \
+ cs_entry_dl.o cs_etree_dl.o cs_fkeep_dl.o cs_gaxpy_dl.o cs_happly_dl.o \
+ cs_house_dl.o cs_ipvec_dl.o cs_lsolve_dl.o cs_ltsolve_dl.o cs_lu_dl.o \
+ cs_lusol_dl.o cs_util_dl.o cs_multiply_dl.o cs_permute_dl.o \
+ cs_pinv_dl.o cs_post_dl.o cs_pvec_dl.o cs_qr_dl.o cs_qrsol_dl.o \
+ cs_scatter_dl.o cs_schol_dl.o cs_sqr_dl.o cs_symperm_dl.o cs_tdfs_dl.o \
+ cs_transpose_dl.o cs_compress_dl.o cs_usolve_dl.o cs_scc_dl.o \
+ cs_maxtrans_dl.o cs_dmperm_dl.o cs_updown_dl.o cs_print_dl.o \
+ cs_norm_dl.o cs_load_dl.o cs_dfs_dl.o cstcov_malloc_test_dl.o \
+ cs_utsolve_dl.o cs_reach_dl.o cs_spsolve_dl.o \
+ cs_leaf_dl.o cs_ereach_dl.o cs_randperm_dl.o
+
+CS_CI = cs_add_ci.o cs_amd_ci.o cs_chol_ci.o cs_cholsol_ci.o cs_counts_ci.o \
+ cs_cumsum_ci.o cs_droptol_ci.o cs_dropzeros_ci.o cs_dupl_ci.o \
+ cs_entry_ci.o cs_etree_ci.o cs_fkeep_ci.o cs_gaxpy_ci.o cs_happly_ci.o \
+ cs_house_ci.o cs_ipvec_ci.o cs_lsolve_ci.o cs_ltsolve_ci.o cs_lu_ci.o \
+ cs_lusol_ci.o cs_util_ci.o cs_multiply_ci.o cs_permute_ci.o \
+ cs_pinv_ci.o cs_post_ci.o cs_pvec_ci.o cs_qr_ci.o cs_qrsol_ci.o \
+ cs_scatter_ci.o cs_schol_ci.o cs_sqr_ci.o cs_symperm_ci.o cs_tdfs_ci.o \
+ cs_transpose_ci.o cs_compress_ci.o cs_usolve_ci.o cs_scc_ci.o \
+ cs_maxtrans_ci.o cs_dmperm_ci.o cs_updown_ci.o cs_print_ci.o \
+ cs_norm_ci.o cs_load_ci.o cs_dfs_ci.o cstcov_malloc_test_ci.o \
+ cs_utsolve_ci.o cs_reach_ci.o cs_spsolve_ci.o \
+ cs_leaf_ci.o cs_ereach_ci.o cs_randperm_ci.o
+
+CS_CL = cs_add_cl.o cs_amd_cl.o cs_chol_cl.o cs_cholsol_cl.o cs_counts_cl.o \
+ cs_cumsum_cl.o cs_droptol_cl.o cs_dropzeros_cl.o cs_dupl_cl.o \
+ cs_entry_cl.o cs_etree_cl.o cs_fkeep_cl.o cs_gaxpy_cl.o cs_happly_cl.o \
+ cs_house_cl.o cs_ipvec_cl.o cs_lsolve_cl.o cs_ltsolve_cl.o cs_lu_cl.o \
+ cs_lusol_cl.o cs_util_cl.o cs_multiply_cl.o cs_permute_cl.o \
+ cs_pinv_cl.o cs_post_cl.o cs_pvec_cl.o cs_qr_cl.o cs_qrsol_cl.o \
+ cs_scatter_cl.o cs_schol_cl.o cs_sqr_cl.o cs_symperm_cl.o cs_tdfs_cl.o \
+ cs_transpose_cl.o cs_compress_cl.o cs_usolve_cl.o cs_scc_cl.o \
+ cs_maxtrans_cl.o cs_dmperm_cl.o cs_updown_cl.o cs_print_cl.o \
+ cs_norm_cl.o cs_load_cl.o cs_dfs_cl.o cstcov_malloc_test_cl.o \
+ cs_utsolve_cl.o cs_reach_cl.o cs_spsolve_cl.o \
+ cs_leaf_cl.o cs_ereach_cl.o cs_randperm_cl.o
+
+OBJ = $(CS_DI) $(CS_DL) $(CS_CI) $(CS_CL) cs_convert.o
+
+$(OBJ): ../Include/cs.h cstcov_malloc_test.h Makefile
+
+
+.PRECIOUS: %demo.c %demo1.c %demo2.c %demo3.c cs_%.c cs_%_ci.c cs_%_cl.c cs_%_di.c cs_%_dl.c cstcov_%.c
+
+
+%demo.c:
+ - ln -s ../Demo/$*demo.c
+
+%demo1.c:
+ - ln -s ../Demo/$*demo1.c
+
+%demo2.c:
+ - ln -s ../Demo/$*demo2.c
+
+%demo3.c:
+ - ln -s ../Demo/$*demo3.c
+
+
+cstcov_%.c:
+ - ln -s cstcov_malloc_test.c cstcov_$*.c
+
+cs_convert.c:
+ - ln -s ../Source/cs_convert.c
+
+cs_%_ci.c:
+ - ln -s ../Source/cs_$*.c cs_$*_ci.c
+
+cs_%_di.c:
+ - ln -s ../Source/cs_$*.c cs_$*_di.c
+
+cs_%_dl.c:
+ - ln -s ../Source/cs_$*.c cs_$*_dl.c
+
+cs_%_cl.c:
+ - ln -s ../Source/cs_$*.c cs_$*_cl.c
+
+
+%_di.o: %_di.c
+ $(CC) $(CFLAGS) -c $<
+
+%_dl.o: %_dl.c
+ $(CC) $(CFLAGS) -DCS_LONG -c $<
+
+%_ci.o: %_ci.c
+ $(CC) $(CFLAGS) -DCS_COMPLEX -c $<
+
+%_cl.o: %_cl.c
+ $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -c $<
+
+
+cs_idemo: $(OBJ) cs_idemo.c
+ $(CC) $(CFLAGS) -o cs_idemo cs_idemo.c $(OBJ) -lm
+
+cs_ldemo: $(OBJ) cs_ldemo.c
+ $(CC) $(CFLAGS) -o cs_ldemo cs_ldemo.c $(OBJ) -lm
+
+
+cs_demo1_di: $(CS_DI) cs_di_demo1.c
+ $(CC) $(CFLAGS) -o cs_demo1_di cs_di_demo1.c $(CS_DI) -lm
+
+cs_demo2_di: $(CS_DI) cs_di_demo2.c cs_di_demo.c
+ $(CC) $(CFLAGS) -o cs_demo2_di cs_di_demo2.c cs_di_demo.c $(CS_DI) -lm
+
+cs_demo3_di: $(CS_DI) cs_di_demo3.c cs_di_demo.c
+ $(CC) $(CFLAGS) -o cs_demo3_di cs_di_demo3.c cs_di_demo.c $(CS_DI) -lm
+
+cstcov_test_di: $(CS_DI) cstcov_test.c cs_di_demo.c
+ $(CC) $(CFLAGS) -o cstcov_test_di cstcov_test.c cs_di_demo.c $(CS_DI) -lm
+
+
+cs_demo1_dl: $(CS_DL) cs_dl_demo1.c
+ $(CC) $(CFLAGS) -DCS_LONG -o cs_demo1_dl cs_dl_demo1.c $(CS_DL) -lm
+
+cs_demo2_dl: $(CS_DL) cs_dl_demo2.c cs_dl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -o cs_demo2_dl cs_dl_demo2.c cs_dl_demo.c $(CS_DL) -lm
+
+cs_demo3_dl: $(CS_DL) cs_dl_demo3.c cs_dl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -o cs_demo3_dl cs_dl_demo3.c cs_dl_demo.c $(CS_DL) -lm
+
+cstcov_test_dl: $(CS_DL) cstcov_test.c cs_dl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -o cstcov_test_dl cstcov_test.c cs_dl_demo.c $(CS_DL) -lm
+
+
+cs_demo1_ci: $(CS_CI) cs_ci_demo1.c
+ $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo1_ci cs_ci_demo1.c $(CS_CI) -lm
+
+cs_demo2_ci: $(CS_CI) cs_ci_demo2.c cs_ci_demo.c
+ $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo2_ci cs_ci_demo2.c cs_ci_demo.c $(CS_CI) -lm
+
+cs_demo3_ci: $(CS_CI) cs_ci_demo3.c cs_ci_demo.c
+ $(CC) $(CFLAGS) -DCS_COMPLEX -o cs_demo3_ci cs_ci_demo3.c cs_ci_demo.c $(CS_CI) -lm
+
+cstcov_test_ci: $(CS_CI) cstcov_test.c cs_ci_demo.c
+ $(CC) $(CFLAGS) -DCS_COMPLEX -o cstcov_test_ci cstcov_test.c cs_ci_demo.c $(CS_CI) -lm
+
+
+cs_demo1_cl: $(CS_CL) cs_cl_demo1.c
+ $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo1_cl cs_cl_demo1.c $(CS_CL) -lm
+
+cs_demo2_cl: $(CS_CL) cs_cl_demo2.c cs_cl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo2_cl cs_cl_demo2.c cs_cl_demo.c $(CS_CL) -lm
+
+cs_demo3_cl: $(CS_CL) cs_cl_demo3.c cs_cl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cs_demo3_cl cs_cl_demo3.c cs_cl_demo.c $(CS_CL) -lm
+
+cstcov_test_cl: $(CS_CL) cstcov_test.c cs_cl_demo.c
+ $(CC) $(CFLAGS) -DCS_LONG -DCS_COMPLEX -o cstcov_test_cl cstcov_test.c cs_cl_demo.c $(CS_CL) -lm
+
+
+run_convert: cs_idemo cs_ldemo
+ - $(V) ./cs_idemo < ../Matrix/t2
+ - $(V) ./cs_ldemo < ../Matrix/t2
+
+run_di: cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di
+ - $(V) ./cs_demo1_di < ../Matrix/t1
+ - $(V) ./cs_demo1_di < nil
+ - $(V) ./cs_demo1_di < zero
+ - $(V) ./cs_demo2_di < nil
+ - $(V) ./cs_demo2_di < zero
+ - $(V) ./cs_demo2_di < ../Matrix/t1
+ - $(V) ./cs_demo2_di < ../Matrix/bcsstk01
+ - $(V) ./cs_demo2_di < ../Matrix/fs_183_1
+ - $(V) ./cs_demo2_di < ../Matrix/west0067
+ - $(V) ./cs_demo2_di < ../Matrix/lp_afiro
+ - $(V) ./cs_demo2_di < ../Matrix/ash219
+ - $(V) ./cs_demo2_di < ../Matrix/mbeacxc
+ - $(V) ./cs_demo2_di < ../Matrix/bcsstk16
+ - $(V) ./cs_demo2_di < ../Matrix/ibm32a
+ - $(V) ./cs_demo2_di < ../Matrix/ibm32b
+ - $(V) ./cs_demo3_di < nil
+ - $(V) ./cs_demo3_di < ../Matrix/bcsstk01
+ - $(V) ./cs_demo3_di < ../Matrix/bcsstk16
+ - $(V) ./cstcov_test_di nil > test_di_nil.out
+ - $(V) ./cstcov_test_di zero > test_di_zero.out
+ - $(V) ./cstcov_test_di ../Matrix/t1 > test_di_t1.out
+ - $(V) ./cstcov_test_di ../Matrix/bcsstk01 > test_di_k1.out
+ - $(V) ./cstcov_test_di ../Matrix/fs_183_1 > test_di_fs.out
+ - $(V) ./cstcov_test_di ../Matrix/west0067 > test_di_we.out
+ - $(V) ./cstcov_test_di ../Matrix/ash219 > test_di_ash.out
+ - $(V) ./cstcov_test_di ../Matrix/lp_afiro > test_di_afiro.out
+
+run_dl: cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl
+ - $(V) ./cs_demo1_dl < ../Matrix/t1
+ - $(V) ./cs_demo1_dl < nil
+ - $(V) ./cs_demo1_dl < zero
+ - $(V) ./cs_demo2_dl < nil
+ - $(V) ./cs_demo2_dl < zero
+ - $(V) ./cs_demo2_dl < ../Matrix/t1
+ - $(V) ./cs_demo2_dl < ../Matrix/bcsstk01
+ - $(V) ./cs_demo2_dl < ../Matrix/fs_183_1
+ - $(V) ./cs_demo2_dl < ../Matrix/west0067
+ - $(V) ./cs_demo2_dl < ../Matrix/lp_afiro
+ - $(V) ./cs_demo2_dl < ../Matrix/ash219
+ - $(V) ./cs_demo2_dl < ../Matrix/mbeacxc
+ - $(V) ./cs_demo2_dl < ../Matrix/bcsstk16
+ - $(V) ./cs_demo2_dl < ../Matrix/ibm32a
+ - $(V) ./cs_demo2_dl < ../Matrix/ibm32b
+ - $(V) ./cs_demo3_dl < nil
+ - $(V) ./cs_demo3_dl < ../Matrix/bcsstk01
+ - $(V) ./cs_demo3_dl < ../Matrix/bcsstk16
+ - $(V) ./cstcov_test_dl nil > test_dl_nil.out
+ - $(V) ./cstcov_test_dl zero > test_dl_zero.out
+ - $(V) ./cstcov_test_dl ../Matrix/t1 > test_dl_t1.out
+ - $(V) ./cstcov_test_dl ../Matrix/bcsstk01 > test_dl_k1.out
+ - $(V) ./cstcov_test_dl ../Matrix/fs_183_1 > test_dl_fs.out
+ - $(V) ./cstcov_test_dl ../Matrix/west0067 > test_dl_we.out
+ - $(V) ./cstcov_test_dl ../Matrix/ash219 > test_dl_ash.out
+ - $(V) ./cstcov_test_dl ../Matrix/lp_afiro > test_dl_afiro.out
+
+run_ci: cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci
+ - $(V) ./cs_demo1_ci < ../Matrix/t2
+ - $(V) ./cs_demo2_ci < ../Matrix/t2
+ - $(V) ./cs_demo1_ci < czero
+ - $(V) ./cs_demo2_ci < czero
+ - $(V) ./cs_demo1_ci < ../Matrix/t3
+ - $(V) ./cs_demo2_ci < ../Matrix/t3
+ - $(V) ./cs_demo1_ci < ../Matrix/t4
+ - $(V) ./cs_demo2_ci < ../Matrix/t4
+ - $(V) ./cs_demo2_ci < ../Matrix/c_west0067
+ - $(V) ./cs_demo2_ci < ../Matrix/c_mbeacxc
+ - $(V) ./cs_demo2_ci < ../Matrix/c_ibm32a
+ - $(V) ./cs_demo2_ci < ../Matrix/c_ibm32b
+ - $(V) ./cs_demo2_ci < ../Matrix/young1c
+ - $(V) ./cs_demo2_ci < ../Matrix/qc324
+ - $(V) ./cs_demo2_ci < ../Matrix/neumann
+ - $(V) ./cs_demo2_ci < ../Matrix/c4
+ - $(V) ./cs_demo3_ci < ../Matrix/c4
+ - $(V) ./cs_demo2_ci < ../Matrix/mhd1280b
+ - $(V) ./cs_demo3_ci < ../Matrix/mhd1280b
+ - $(V) ./cstcov_test_ci ../Matrix/t2 > test_ci_t2.out
+ - $(V) ./cstcov_test_ci ../Matrix/young1c > test_ci_young1c.out
+ - $(V) ./cstcov_test_ci ../Matrix/qc324 > test_ci_qc324.out
+ - $(V) ./cstcov_test_ci ../Matrix/neumann > test_ci_neumann.out
+ - $(V) ./cstcov_test_ci ../Matrix/mhd1280b > test_ci_mhd1280b.out
+
+run_cl: cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl
+ - $(V) ./cs_demo1_cl < ../Matrix/t2
+ - $(V) ./cs_demo2_cl < ../Matrix/t2
+ - $(V) ./cs_demo1_cl < czero
+ - $(V) ./cs_demo2_cl < czero
+ - $(V) ./cs_demo1_cl < ../Matrix/t3
+ - $(V) ./cs_demo2_cl < ../Matrix/t3
+ - $(V) ./cs_demo1_cl < ../Matrix/t4
+ - $(V) ./cs_demo2_cl < ../Matrix/t4
+ - $(V) ./cs_demo2_cl < ../Matrix/c_west0067
+ - $(V) ./cs_demo2_cl < ../Matrix/c_mbeacxc
+ - $(V) ./cs_demo2_cl < ../Matrix/c_ibm32a
+ - $(V) ./cs_demo2_cl < ../Matrix/c_ibm32b
+ - $(V) ./cs_demo2_cl < ../Matrix/young1c
+ - $(V) ./cs_demo2_cl < ../Matrix/qc324
+ - $(V) ./cs_demo2_cl < ../Matrix/neumann
+ - $(V) ./cs_demo2_cl < ../Matrix/c4
+ - $(V) ./cs_demo3_cl < ../Matrix/c4
+ - $(V) ./cs_demo2_cl < ../Matrix/mhd1280b
+ - $(V) ./cs_demo3_cl < ../Matrix/mhd1280b
+ - $(V) ./cstcov_test_cl ../Matrix/t2 > test_cl_t2.out
+ - $(V) ./cstcov_test_cl ../Matrix/young1c > test_cl_young1c.out
+ - $(V) ./cstcov_test_cl ../Matrix/qc324 > test_cl_qc324.out
+ - $(V) ./cstcov_test_cl ../Matrix/neumann > test_cl_neumann.out
+ - $(V) ./cstcov_test_cl ../Matrix/mhd1280b > test_cl_mhd1280b.out
+
+
+readhb: readhb.f
+ f77 -o readhb readhb.f
+
+readhb.f:
+ - ln -s ../Demo/readhb.f
+
+clean:
+ rm -f *.o *.bbg *.da *.gcov *.gcda *.gcno
+
+purge: distclean
+
+distclean: clean
+ rm -f readhb *.out *.a cov.sort
+ rm -f cs_demo1_di cs_demo2_di cs_demo3_di cstcov_test_di
+ rm -f cs_demo1_dl cs_demo2_dl cs_demo3_dl cstcov_test_dl
+ rm -f cs_demo1_ci cs_demo2_ci cs_demo3_ci cstcov_test_ci
+ rm -f cs_demo1_cl cs_demo2_cl cs_demo3_cl cstcov_test_cl
+ rm -f cs_idemo cs_ldemo
+ rm -f cs_*.c
+ rm -f cs*_di.c cs*_dl.c cs*_ci.c cs*_cl.c
diff --git a/CXSparse_newfiles/Tcov/README.txt b/CXSparse_newfiles/Tcov/README.txt
new file mode 100644
index 0000000..caae525
--- /dev/null
+++ b/CXSparse_newfiles/Tcov/README.txt
@@ -0,0 +1,13 @@
+CXSparse/Tcov: comprehensive test coverage for CXSparse. Requires Linux.
+Type "make" to compile, and then "make run" to run the tests.
+The test coverage is in cover.out. The test output is
+printed on stdout, except for cs_test (which prints its output in various
+*.out files).
+
+If the test is successful, the last line printed should be
+"statements not yet tested: 0", and all printed residuals should be small.
+
+Note that you will get warnings about unused parameters for some functions.
+These warnings can be safely ignored. They are parameters for functions that
+are passed to cs_fkeep, and all functions used in this manner must have the
+same calling sequence, even if some of the parameters are not used.
diff --git a/CXSparse_newfiles/Tcov/cstcov_malloc_test.c b/CXSparse_newfiles/Tcov/cstcov_malloc_test.c
new file mode 100644
index 0000000..e72878d
--- /dev/null
+++ b/CXSparse_newfiles/Tcov/cstcov_malloc_test.c
@@ -0,0 +1,34 @@
+#include "cstcov_malloc_test.h"
+int malloc_count = INT_MAX ;
+
+/* wrapper for malloc */
+void *cs_malloc (CS_INT n, size_t size)
+{
+ if (--malloc_count < 0) return (NULL) ; /* pretend to fail */
+ return (malloc (CS_MAX (n,1) * size)) ;
+}
+
+/* wrapper for calloc */
+void *cs_calloc (CS_INT n, size_t size)
+{
+ if (--malloc_count < 0) return (NULL) ; /* pretend to fail */
+ return (calloc (CS_MAX (n,1), size)) ;
+}
+
+/* wrapper for free */
+void *cs_free (void *p)
+{
+ if (p) free (p) ; /* free p if it is not already NULL */
+ return (NULL) ; /* return NULL to simplify the use of cs_free */
+}
+
+/* wrapper for realloc */
+void *cs_realloc (void *p, CS_INT n, size_t size, CS_INT *ok)
+{
+ void *pnew ;
+ *ok = 0 ;
+ if (--malloc_count < 0) return (p) ; /* pretend to fail */
+ pnew = realloc (p, CS_MAX (n,1) * size) ; /* realloc the block */
+ *ok = (pnew != NULL) ;
+ return ((*ok) ? pnew : p) ; /* return original p if failure */
+}
diff --git a/CXSparse_newfiles/Tcov/cstcov_malloc_test.h b/CXSparse_newfiles/Tcov/cstcov_malloc_test.h
new file mode 100644
index 0000000..f235ad9
--- /dev/null
+++ b/CXSparse_newfiles/Tcov/cstcov_malloc_test.h
@@ -0,0 +1,7 @@
+#include "cs.h"
+#define malloc_count CS_NAME (_malloc_count)
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+EXTERN int malloc_count ;
+
diff --git a/CXSparse_newfiles/Tcov/czero b/CXSparse_newfiles/Tcov/czero
new file mode 100644
index 0000000..6a20ce4
--- /dev/null
+++ b/CXSparse_newfiles/Tcov/czero
@@ -0,0 +1 @@
+0 0 0 0
diff --git a/Contents.m b/Contents.m
new file mode 100644
index 0000000..5f6f306
--- /dev/null
+++ b/Contents.m
@@ -0,0 +1,134 @@
+% Welcome to SuiteSparse : a Suite of Sparse matrix packages, containing a
+% collection of sparse matrix packages authored or co-authored by Tim Davis.
+% Only the primary MATLAB functions are listed below.
+%
+% Example:
+% SuiteSparse_install
+% compiles and installs all of SuiteSparse, and runs several demos and tests.
+%
+%-------------------------------------------------------------------------------
+% Ordering methods:
+%-------------------------------------------------------------------------------
+%
+% amd2 - approximate minimum degree ordering.
+% colamd2 - column approximate minimum degree ordering.
+% symamd2 - symmetrix approximate min degree ordering based on colamd.
+% camd - constrained amd.
+% ccolamd - constrained colamd.
+% csymamd - constrained symamd.
+% meshnd - nested dissection of regular 2D and 3D meshes
+%
+%-------------------------------------------------------------------------------
+% CHOLMOD: a sparse supernodal Cholesky update/downdate package:
+%-------------------------------------------------------------------------------
+%
+% cholmod2 - computes x=A\b when A is symmetric and positive definite.
+% chol2 - same as MATLAB chol(sparse(A)), just faster.
+% lchol - computes an LL' factorization.
+% ldlchol - computes an LDL' factorization.
+% ldlupdate - updates an LDL' factorization.
+% resymbol - recomputes symbolic LL or LDL' factorization.
+% ldlsolve - solves Ax=b using an LDL' factorization.
+% ldlsplit - splits LD into L and D.
+% metis - interface to METIS node-nested-dissection.
+% nesdis - interface to CHOLMOD's nested-dissection (based on METIS).
+% septree - prune a separator tree.
+% bisect - interface to METIS' node bisector.
+% analyze - order and analyze using CHOLMOD.
+% etree2 - same as MATLAB "etree", just faster and more reliable.
+% sparse2 - same as MATLAB "sparse", just faster.
+% symbfact2 - same as MATLAB "symbfact", just faster and more reliable.
+% sdmult - same as MATLAB S*F or S'*F (S sparse, F full), just faster.
+% ldl_normest - compute error in LDL' factorization.
+% lu_normest - compute error in LU factorization.
+% mread - read a sparse matrix in Matrix Market format
+% mwrite - write a sparse matrix in Matrix Market format
+% spsym - determine the symmetry of a sparse matrix
+%
+%-------------------------------------------------------------------------------
+% CSPARSE / CXSPARSE: a Concise Sparse matrix package:
+%-------------------------------------------------------------------------------
+%
+% Matrices used in CSparse must in general be either sparse and real, or
+% dense vectors. Ordering methods can accept any sparse matrix. CXSparse
+% supports complex matrices and 64-bit MATLAB; it is installed by default.
+%
+% cs_add - sparse matrix addition.
+% cs_amd - approximate minimum degree ordering.
+% cs_chol - sparse Cholesky factorization.
+% cs_cholsol - solve A*x=b using a sparse Cholesky factorization.
+% cs_counts - column counts for sparse Cholesky factor L.
+% cs_dmperm - maximum matching or Dulmage-Mendelsohn permutation.
+% cs_dmsol - x=A\b using the coarse Dulmage-Mendelsohn decomposition.
+% cs_dmspy - plot the Dulmage-Mendelsohn decomposition of a matrix.
+% cs_droptol - remove small entries from a sparse matrix.
+% cs_esep - find an edge separator of a symmetric matrix A
+% cs_etree - elimination tree of A or A'*A.
+% cs_gaxpy - sparse matrix times vector.
+% cs_lsolve - solve a sparse lower triangular system L*x=b.
+% cs_ltsolve - solve a sparse upper triangular system L'*x=b.
+% cs_lu - sparse LU factorization, with fill-reducing ordering.
+% cs_lusol - solve Ax=b using LU factorization.
+% cs_make - compiles CSparse for use in MATLAB.
+% cs_multiply - sparse matrix multiply.
+% cs_nd - generalized nested dissection ordering.
+% cs_nsep - find a node separator of a symmetric matrix A.
+% cs_permute - permute a sparse matrix.
+% cs_print - print the contents of a sparse matrix.
+% cs_qr - sparse QR factorization.
+% cs_qleft - apply Householder vectors on the left.
+% cs_qright - apply Householder vectors on the right.
+% cs_qrsol - solve a sparse least-squares problem.
+% cs_randperm - random permutation.
+% cs_sep - convert an edge separator into a node separator.
+% cs_scc - strongly-connected components of a square sparse matrix.
+% cs_scc2 - cs_scc, or connected components of a bipartite graph.
+% cs_sparse - convert a triplet form into a sparse matrix.
+% cs_sqr - symbolic sparse QR factorization.
+% cs_symperm - symmetric permutation of a symmetric matrix.
+% cs_transpose - transpose a sparse matrix.
+% cs_updown - rank-1 update/downdate of a sparse Cholesky factorization.
+% cs_usolve - solve a sparse upper triangular system U*x=b.
+% cs_utsolve - solve a sparse lower triangular system U'*x=b.
+% cspy - plot a sparse matrix in color.
+% ccspy - plot the connected components of a matrix.
+%
+%-------------------------------------------------------------------------------
+% LDL: Sparse LDL factorization:
+%-------------------------------------------------------------------------------
+%
+% ldlsparse - LDL' factorization of a real, sparse, symmetric matrix.
+% ldlrow - an m-file description of the algorithm used by LDL.
+%
+%-------------------------------------------------------------------------------
+% UMFPACK: the Unsymmetric MultiFrontal Package:
+%-------------------------------------------------------------------------------
+%
+% umfpack2 - computes x=A\b, x=A/b, or lu (A) for a sparse matrix A
+% umfpack_details - details on all the options for using umfpack in MATLAB
+% umfpack_report - prints optional control settings and statistics
+% umfpack_btf - factorize A using a block triangular form
+% umfpack_solve - x = A\b or x = b/A
+% lu_normest - estimates norm (L*U-A,1) without forming L*U-A
+% (duplicate of CHOLMOD/lu_normest, for completeness)
+% luflop - given L and U, computes # of flops required
+%
+%-------------------------------------------------------------------------------
+% Other packages:
+%-------------------------------------------------------------------------------
+%
+% UFGET MATLAB interface to the UF Sparse Matrix Collection
+% MATLAB_Tools various simple m-files
+% SSMULT sparse matrix times sparse matrix
+% LINFACTOR solve Ax=b using LU or CHOL
+%
+%-------------------------------------------------------------------------------
+%
+% For help on compiling SuiteSparse or the demos, testing functions, etc.,
+% please see the help for each individual package. UFcollection and RBio
+% are two additional toolboxes, for managing the UF Sparse Matrix Collection.
+%
+% Copyright 2007, Timothy A. Davis
+% http://www.cise.ufl.edu/research/sparse
+
+help SuiteSparse
diff --git a/KLU/Demo/Makefile b/KLU/Demo/Makefile
new file mode 100644
index 0000000..734be48
--- /dev/null
+++ b/KLU/Demo/Makefile
@@ -0,0 +1,65 @@
+# KLU Demo Makefile. The klu_simple demo is stand-alone. The other demos
+# require CHOLMOD.
+
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+LIB = ../Lib/libklu.a ../../BTF/Lib/libbtf.a \
+ ../../AMD/Lib/libamd.a ../../COLAMD/Lib/libcolamd.a
+
+CHOLMOD = ../../CHOLMOD/Lib/libcholmod.a
+
+I = -I../../UFconfig -I../../AMD/Include -I../../COLAMD/Include \
+ -I../../BTF/Include -I../Include -I../../CHOLMOD/Include
+
+all: $(LIB) klu_simple $(CHOLMOD) kludemo kluldemo
+ - ./klu_simple
+ - ./kludemo < ../Matrix/1c.mtx
+ - ./kludemo < ../Matrix/arrowc.mtx
+ - ./kludemo < ../Matrix/arrow.mtx
+ - ./kludemo < ../Matrix/impcol_a.mtx
+ - ./kludemo < ../Matrix/w156.mtx
+ - ./kludemo < ../Matrix/ctina.mtx
+ - ./kluldemo < ../Matrix/1c.mtx
+ - ./kluldemo < ../Matrix/arrowc.mtx
+ - ./kluldemo < ../Matrix/arrow.mtx
+ - ./kluldemo < ../Matrix/impcol_a.mtx
+ - ./kluldemo < ../Matrix/w156.mtx
+ - ./kluldemo < ../Matrix/ctina.mtx
+
+../Lib/libklu.a:
+ ( cd ../Lib ; $(MAKE) )
+
+../../BTF/Lib/libbtf.a:
+ ( cd ../../BTF ; $(MAKE) library )
+
+../../AMD/Lib/libamd.a:
+ ( cd ../../AMD ; $(MAKE) library )
+
+../../COLAMD/Lib/libcolamd.a:
+ ( cd ../../COLAMD ; $(MAKE) library )
+
+../../CHOLMOD/Lib/libcholmod.a:
+ ( cd ../../CHOLMOD ; $(MAKE) library )
+# ( cd ../../CAMD ; $(MAKE) )
+# ( cd ../../CCOLAMD ; $(MAKE) )
+# ( cd ../../metis-4.0 ; $(MAKE) )
+
+purge: distclean
+
+distclean: clean
+ - $(RM) kludemo kluldemo klu_simple
+
+clean:
+ - $(RM) $(CLEAN)
+
+kludemo: kludemo.c Makefile $(LIB)
+ $(CC) $(CFLAGS) $(I) kludemo.c -o kludemo $(LIB) $(CHOLMOD) -lm
+
+kluldemo: kludemo.c Makefile $(LIB)
+ $(CC) $(CFLAGS) $(I) kluldemo.c -o kluldemo $(LIB) $(CHOLMOD) -lm
+
+klu_simple: klu_simple.c Makefile $(LIB)
+ $(CC) $(CFLAGS) $(I) klu_simple.c -o klu_simple $(LIB) -lm
+ - ./klu_simple
diff --git a/KLU/Demo/klu_simple.c b/KLU/Demo/klu_simple.c
new file mode 100644
index 0000000..72c4379
--- /dev/null
+++ b/KLU/Demo/klu_simple.c
@@ -0,0 +1,27 @@
+/* klu_simple: a simple KLU demo */
+
+#include <stdio.h>
+#include "klu.h"
+
+int n = 5 ;
+int Ap [ ] = {0, 2, 5, 9, 10, 12} ;
+int Ai [ ] = { 0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4} ;
+double Ax [ ] = {2., 3., 3., -1., 4., 4., -3., 1., 2., 2., 6., 1.} ;
+double b [ ] = {8., 45., -3., 3., 19.} ;
+
+int main (void)
+{
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ int i ;
+ klu_defaults (&Common) ;
+ Symbolic = klu_analyze (n, Ap, Ai, &Common) ;
+ Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ;
+ klu_solve (Symbolic, Numeric, 5, 1, b, &Common) ;
+ klu_free_symbolic (&Symbolic, &Common) ;
+ klu_free_numeric (&Numeric, &Common) ;
+ for (i = 0 ; i < n ; i++) printf ("x [%d] = %g\n", i, b [i]) ;
+ return (0) ;
+}
+
diff --git a/KLU/Demo/kludemo.c b/KLU/Demo/kludemo.c
new file mode 100644
index 0000000..1efa47d
--- /dev/null
+++ b/KLU/Demo/kludemo.c
@@ -0,0 +1,326 @@
+/* ========================================================================== */
+/* === KLU DEMO ============================================================= */
+/* ========================================================================== */
+
+/* Read in a Matrix Market matrix (using CHOLMOD) and solve a linear system. */
+
+#include <math.h>
+#include <stdio.h>
+#include "klu.h"
+
+/* for handling complex matrices */
+#define REAL(X,i) (X [2*(i)])
+#define IMAG(X,i) (X [2*(i)+1])
+#define CABS(X,i) (sqrt (REAL (X,i) * REAL (X,i) + IMAG (X,i) * IMAG (X,i)))
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+
+/* ========================================================================== */
+/* === klu_backslash ======================================================== */
+/* ========================================================================== */
+
+static int klu_backslash /* return 1 if successful, 0 otherwise */
+(
+ /* --- input ---- */
+ int n, /* A is n-by-n */
+ int *Ap, /* size n+1, column pointers */
+ int *Ai, /* size nz = Ap [n], row indices */
+ double *Ax, /* size nz, numerical values */
+ int isreal, /* nonzero if A is real, 0 otherwise */
+ double *B, /* size n, right-hand-side */
+
+ /* --- output ---- */
+ double *X, /* size n, solution to Ax=b */
+ double *R, /* size n, residual r = b-A*x */
+
+ /* --- scalar output --- */
+ int *lunz, /* nnz (L+U+F) */
+ double *rnorm, /* norm (b-A*x,1) / norm (A,1) */
+
+ /* --- workspace - */
+
+ klu_common *Common /* default parameters and statistics */
+)
+{
+ double anorm = 0, asum ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ int i, j, p ;
+
+ if (!Ap || !Ai || !Ax || !B || !X || !B) return (0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic ordering and analysis */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic = klu_analyze (n, Ap, Ai, Common) ;
+ if (!Symbolic) return (0) ;
+
+ if (isreal)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* factorization */
+ /* ------------------------------------------------------------------ */
+
+ Numeric = klu_factor (Ap, Ai, Ax, Symbolic, Common) ;
+ if (!Numeric)
+ {
+ klu_free_symbolic (&Symbolic, Common) ;
+ return (0) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* statistics (not required to solve Ax=b) */
+ /* ------------------------------------------------------------------ */
+
+ klu_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, Common) ;
+ klu_condest (Ap, Ax, Symbolic, Numeric, Common) ;
+ klu_rcond (Symbolic, Numeric, Common) ;
+ klu_flops (Symbolic, Numeric, Common) ;
+ *lunz = Numeric->lnz + Numeric->unz - n +
+ ((Numeric->Offp) ? (Numeric->Offp [n]) : 0) ;
+
+ /* ------------------------------------------------------------------ */
+ /* solve Ax=b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ X [i] = B [i] ;
+ }
+ klu_solve (Symbolic, Numeric, n, 1, X, Common) ;
+
+ /* ------------------------------------------------------------------ */
+ /* compute residual, rnorm = norm(b-Ax,1) / norm(A,1) */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ R [i] = B [i] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ asum = 0 ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ /* R (i) -= A (i,j) * X (j) */
+ R [Ai [p]] -= Ax [p] * X [j] ;
+ asum += fabs (Ax [p]) ;
+ }
+ anorm = MAX (anorm, asum) ;
+ }
+ *rnorm = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ *rnorm = MAX (*rnorm, fabs (R [i])) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* free numeric factorization */
+ /* ------------------------------------------------------------------ */
+
+ klu_free_numeric (&Numeric, Common) ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* statistics (not required to solve Ax=b) */
+ /* ------------------------------------------------------------------ */
+
+ Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, Common) ;
+ if (!Numeric)
+ {
+ klu_free_symbolic (&Symbolic, Common) ;
+ return (0) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* statistics */
+ /* ------------------------------------------------------------------ */
+
+ klu_z_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, Common) ;
+ klu_z_condest (Ap, Ax, Symbolic, Numeric, Common) ;
+ klu_z_rcond (Symbolic, Numeric, Common) ;
+ klu_z_flops (Symbolic, Numeric, Common) ;
+ *lunz = Numeric->lnz + Numeric->unz - n +
+ ((Numeric->Offp) ? (Numeric->Offp [n]) : 0) ;
+
+ /* ------------------------------------------------------------------ */
+ /* solve Ax=b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < 2*n ; i++)
+ {
+ X [i] = B [i] ;
+ }
+ klu_z_solve (Symbolic, Numeric, n, 1, X, Common) ;
+
+ /* ------------------------------------------------------------------ */
+ /* compute residual, rnorm = norm(b-Ax,1) / norm(A,1) */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < 2*n ; i++)
+ {
+ R [i] = B [i] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ asum = 0 ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ /* R (i) -= A (i,j) * X (j) */
+ i = Ai [p] ;
+ REAL (R,i) -= REAL(Ax,p) * REAL(X,j) - IMAG(Ax,p) * IMAG(X,j) ;
+ IMAG (R,i) -= IMAG(Ax,p) * REAL(X,j) + REAL(Ax,p) * IMAG(X,j) ;
+ asum += CABS (Ax, p) ;
+ }
+ anorm = MAX (anorm, asum) ;
+ }
+ *rnorm = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ *rnorm = MAX (*rnorm, CABS (R, i)) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* free numeric factorization */
+ /* ------------------------------------------------------------------ */
+
+ klu_z_free_numeric (&Numeric, Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free symbolic analysis, and residual */
+ /* ---------------------------------------------------------------------- */
+
+ klu_free_symbolic (&Symbolic, Common) ;
+ return (1) ;
+}
+
+
+/* ========================================================================== */
+/* === klu_demo ============================================================= */
+/* ========================================================================== */
+
+/* Given a sparse matrix A, set up a right-hand-side and solve X = A\b */
+
+static void klu_demo (int n, int *Ap, int *Ai, double *Ax, int isreal)
+{
+ double rnorm ;
+ klu_common Common ;
+ double *B, *X, *R ;
+ int i, lunz ;
+
+ printf ("KLU: %s, version: %d.%d.%d\n", KLU_DATE, KLU_MAIN_VERSION,
+ KLU_SUB_VERSION, KLU_SUBSUB_VERSION) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* set defaults */
+ /* ---------------------------------------------------------------------- */
+
+ klu_defaults (&Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create a right-hand-side */
+ /* ---------------------------------------------------------------------- */
+
+ if (isreal)
+ {
+ /* B = 1 + (1:n)/n */
+ B = klu_malloc (n, sizeof (double), &Common) ;
+ X = klu_malloc (n, sizeof (double), &Common) ;
+ R = klu_malloc (n, sizeof (double), &Common) ;
+ if (B)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ B [i] = 1 + ((double) i+1) / ((double) n) ;
+ }
+ }
+ }
+ else
+ {
+ /* real (B) = 1 + (1:n)/n, imag(B) = (n:-1:1)/n */
+ B = klu_malloc (n, 2 * sizeof (double), &Common) ;
+ X = klu_malloc (n, 2 * sizeof (double), &Common) ;
+ R = klu_malloc (n, 2 * sizeof (double), &Common) ;
+ if (B)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ REAL (B, i) = 1 + ((double) i+1) / ((double) n) ;
+ IMAG (B, i) = ((double) n-i) / ((double) n) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* X = A\b using KLU and print statistics */
+ /* ---------------------------------------------------------------------- */
+
+ if (!klu_backslash (n, Ap, Ai, Ax, isreal, B, X, R, &lunz, &rnorm, &Common))
+ {
+ printf ("KLU failed\n") ;
+ }
+ else
+ {
+ printf ("n %d nnz(A) %d nnz(L+U+F) %d resid %g\n"
+ "recip growth %g condest %g rcond %g flops %g\n",
+ n, Ap [n], lunz, rnorm, Common.rgrowth, Common.condest,
+ Common.rcond, Common.flops) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the problem */
+ /* ---------------------------------------------------------------------- */
+
+ if (isreal)
+ {
+ klu_free (B, n, sizeof (double), &Common) ;
+ klu_free (X, n, sizeof (double), &Common) ;
+ klu_free (R, n, sizeof (double), &Common) ;
+ }
+ else
+ {
+ klu_free (B, 2*n, sizeof (double), &Common) ;
+ klu_free (X, 2*n, sizeof (double), &Common) ;
+ klu_free (R, 2*n, sizeof (double), &Common) ;
+ }
+ printf ("peak memory usage: %g bytes\n\n", (double) (Common.mempeak)) ;
+}
+
+
+/* ========================================================================== */
+/* === main ================================================================= */
+/* ========================================================================== */
+
+/* Read in a sparse matrix in Matrix Market format using CHOLMOD, and then
+ * solve Ax=b with KLU. Note that CHOLMOD is only used to read the matrix. */
+
+#include "cholmod.h"
+
+int main (void)
+{
+ cholmod_sparse *A ;
+ cholmod_common ch ;
+ cholmod_start (&ch) ;
+ A = cholmod_read_sparse (stdin, &ch) ;
+ if (A)
+ {
+ if (A->nrow != A->ncol || A->stype != 0
+ || (!(A->xtype == CHOLMOD_REAL || A->xtype == CHOLMOD_COMPLEX)))
+ {
+ printf ("invalid matrix\n") ;
+ }
+ else
+ {
+ klu_demo (A->nrow, A->p, A->i, A->x, A->xtype == CHOLMOD_REAL) ;
+ }
+ cholmod_free_sparse (&A, &ch) ;
+ }
+ cholmod_finish (&ch) ;
+ return (0) ;
+}
diff --git a/KLU/Demo/kludemo.out b/KLU/Demo/kludemo.out
new file mode 100644
index 0000000..c619e86
--- /dev/null
+++ b/KLU/Demo/kludemo.out
@@ -0,0 +1,78 @@
+./klu_simple
+x [0] = 1
+x [1] = 2
+x [2] = 3
+x [3] = 4
+x [4] = 5
+./kludemo < ../Matrix/1c.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 1 nnz(A) 1 nnz(L+U+F) 1 resid 0
+recip growth 1 condest 1 rcond 1 flops 0
+peak memory usage: 492 bytes
+
+./kludemo < ../Matrix/arrowc.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 100 nnz(A) 298 nnz(L+U+F) 298 resid 1.68007e-14
+recip growth 0.019999 condest 295.99 rcond 0.019999 flops 297
+peak memory usage: 32244 bytes
+
+./kludemo < ../Matrix/arrow.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 100 nnz(A) 298 nnz(L+U+F) 298 resid 1.77636e-15
+recip growth 0.0204082 condest 303 rcond 0.0204082 flops 297
+peak memory usage: 20412 bytes
+
+./kludemo < ../Matrix/impcol_a.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 207 nnz(A) 572 nnz(L+U+F) 615 resid 6.98492e-10
+recip growth 0.00957447 condest 4.35093e+07 rcond 4.5277e-05 flops 259
+peak memory usage: 34276 bytes
+
+./kludemo < ../Matrix/w156.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 156 nnz(A) 362 nnz(L+U+F) 396 resid 6.23816e-08
+recip growth 0.00889922 condest 1.79787e+09 rcond 0.000124785 flops 175
+peak memory usage: 39516 bytes
+
+./kludemo < ../Matrix/ctina.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 11 nnz(A) 36 nnz(L+U+F) 45 resid 4.44089e-16
+recip growth 1 condest 56 rcond 1 flops 73
+peak memory usage: 4268 bytes
+
+./kluldemo < ../Matrix/1c.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 1 nnz(A) 1 nnz(L+U+F) 1 resid 0
+recip growth 1 condest 1 rcond 1 flops 0
+peak memory usage: 600 bytes
+
+./kluldemo < ../Matrix/arrowc.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 100 nnz(A) 298 nnz(L+U+F) 298 resid 1.68007e-14
+recip growth 0.019999 condest 295.99 rcond 0.019999 flops 297
+peak memory usage: 39000 bytes
+
+./kluldemo < ../Matrix/arrow.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 100 nnz(A) 298 nnz(L+U+F) 298 resid 1.77636e-15
+recip growth 0.0204082 condest 303 rcond 0.0204082 flops 297
+peak memory usage: 29584 bytes
+
+./kluldemo < ../Matrix/impcol_a.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 207 nnz(A) 572 nnz(L+U+F) 615 resid 6.98492e-10
+recip growth 0.00957447 condest 4.35093e+07 rcond 4.5277e-05 flops 259
+peak memory usage: 44800 bytes
+
+./kluldemo < ../Matrix/w156.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 156 nnz(A) 362 nnz(L+U+F) 396 resid 6.23816e-08
+recip growth 0.00889922 condest 1.79787e+09 rcond 0.000124785 flops 175
+peak memory usage: 47480 bytes
+
+./kluldemo < ../Matrix/ctina.mtx
+KLU: Nov 1, 2007, version: 1.0.1
+n 11 nnz(A) 36 nnz(L+U+F) 45 resid 4.44089e-16
+recip growth 1 condest 56 rcond 1 flops 73
+peak memory usage: 5144 bytes
+
diff --git a/KLU/Demo/kluldemo.c b/KLU/Demo/kluldemo.c
new file mode 100644
index 0000000..69d9ebb
--- /dev/null
+++ b/KLU/Demo/kluldemo.c
@@ -0,0 +1,329 @@
+/* ========================================================================== */
+/* === KLU DEMO (long integer version) ====================================== */
+/* ========================================================================== */
+
+/* Read in a Matrix Market matrix (using CHOLMOD) and solve a linear system.
+ * UF_long is normally a "long", but it becomes "_int64" on Windows 64. */
+
+#include <math.h>
+#include <stdio.h>
+#include "klu.h"
+
+/* for handling complex matrices */
+#define REAL(X,i) (X [2*(i)])
+#define IMAG(X,i) (X [2*(i)+1])
+#define CABS(X,i) (sqrt (REAL (X,i) * REAL (X,i) + IMAG (X,i) * IMAG (X,i)))
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+
+/* ========================================================================== */
+/* === klu_l_backslash ====================================================== */
+/* ========================================================================== */
+
+static UF_long klu_l_backslash /* return 1 if successful, 0 otherwise */
+(
+ /* --- input ---- */
+ UF_long n, /* A is n-by-n */
+ UF_long *Ap, /* size n+1, column pointers */
+ UF_long *Ai, /* size nz = Ap [n], row indices */
+ double *Ax, /* size nz, numerical values */
+ UF_long isreal, /* nonzero if A is real, 0 otherwise */
+ double *B, /* size n, right-hand-side */
+
+ /* --- output ---- */
+ double *X, /* size n, solution to Ax=b */
+ double *R, /* size n, residual r = b-A*x */
+
+ /* --- scalar output --- */
+ UF_long *lunz, /* nnz (L+U+F) */
+ double *rnorm, /* norm (b-A*x,1) / norm (A,1) */
+
+ /* --- workspace - */
+
+ klu_l_common *Common /* default parameters and statistics */
+)
+{
+ double anorm = 0, asum ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_numeric *Numeric ;
+ UF_long i, j, p ;
+
+ if (!Ap || !Ai || !Ax || !B || !X || !B) return (0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic ordering and analysis */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic = klu_l_analyze (n, Ap, Ai, Common) ;
+ if (!Symbolic) return (0) ;
+
+ if (isreal)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* factorization */
+ /* ------------------------------------------------------------------ */
+
+ Numeric = klu_l_factor (Ap, Ai, Ax, Symbolic, Common) ;
+ if (!Numeric)
+ {
+ klu_l_free_symbolic (&Symbolic, Common) ;
+ return (0) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* statistics (not required to solve Ax=b) */
+ /* ------------------------------------------------------------------ */
+
+ klu_l_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, Common) ;
+ klu_l_condest (Ap, Ax, Symbolic, Numeric, Common) ;
+ klu_l_rcond (Symbolic, Numeric, Common) ;
+ klu_l_flops (Symbolic, Numeric, Common) ;
+ *lunz = Numeric->lnz + Numeric->unz - n +
+ ((Numeric->Offp) ? (Numeric->Offp [n]) : 0) ;
+
+ /* ------------------------------------------------------------------ */
+ /* solve Ax=b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ X [i] = B [i] ;
+ }
+ klu_l_solve (Symbolic, Numeric, n, 1, X, Common) ;
+
+ /* ------------------------------------------------------------------ */
+ /* compute residual, rnorm = norm(b-Ax,1) / norm(A,1) */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ R [i] = B [i] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ asum = 0 ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ /* R (i) -= A (i,j) * X (j) */
+ R [Ai [p]] -= Ax [p] * X [j] ;
+ asum += fabs (Ax [p]) ;
+ }
+ anorm = MAX (anorm, asum) ;
+ }
+ *rnorm = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ *rnorm = MAX (*rnorm, fabs (R [i])) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* free numeric factorization */
+ /* ------------------------------------------------------------------ */
+
+ klu_l_free_numeric (&Numeric, Common) ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* statistics (not required to solve Ax=b) */
+ /* ------------------------------------------------------------------ */
+
+ Numeric = klu_zl_factor (Ap, Ai, Ax, Symbolic, Common) ;
+ if (!Numeric)
+ {
+ klu_l_free_symbolic (&Symbolic, Common) ;
+ return (0) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* statistics */
+ /* ------------------------------------------------------------------ */
+
+ klu_zl_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, Common) ;
+ klu_zl_condest (Ap, Ax, Symbolic, Numeric, Common) ;
+ klu_zl_rcond (Symbolic, Numeric, Common) ;
+ klu_zl_flops (Symbolic, Numeric, Common) ;
+ *lunz = Numeric->lnz + Numeric->unz - n +
+ ((Numeric->Offp) ? (Numeric->Offp [n]) : 0) ;
+
+ /* ------------------------------------------------------------------ */
+ /* solve Ax=b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < 2*n ; i++)
+ {
+ X [i] = B [i] ;
+ }
+ klu_zl_solve (Symbolic, Numeric, n, 1, X, Common) ;
+
+ /* ------------------------------------------------------------------ */
+ /* compute residual, rnorm = norm(b-Ax,1) / norm(A,1) */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < 2*n ; i++)
+ {
+ R [i] = B [i] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ asum = 0 ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ /* R (i) -= A (i,j) * X (j) */
+ i = Ai [p] ;
+ REAL (R,i) -= REAL(Ax,p) * REAL(X,j) - IMAG(Ax,p) * IMAG(X,j) ;
+ IMAG (R,i) -= IMAG(Ax,p) * REAL(X,j) + REAL(Ax,p) * IMAG(X,j) ;
+ asum += CABS (Ax, p) ;
+ }
+ anorm = MAX (anorm, asum) ;
+ }
+ *rnorm = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ *rnorm = MAX (*rnorm, CABS (R, i)) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* free numeric factorization */
+ /* ------------------------------------------------------------------ */
+
+ klu_zl_free_numeric (&Numeric, Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free symbolic analysis, and residual */
+ /* ---------------------------------------------------------------------- */
+
+ klu_l_free_symbolic (&Symbolic, Common) ;
+ return (1) ;
+}
+
+
+/* ========================================================================== */
+/* === klu_l_demo =========================================================== */
+/* ========================================================================== */
+
+/* Given a sparse matrix A, set up a right-hand-side and solve X = A\b */
+
+static void klu_l_demo (UF_long n, UF_long *Ap, UF_long *Ai, double *Ax,
+ UF_long isreal)
+{
+ double rnorm ;
+ klu_l_common Common ;
+ double *B, *X, *R ;
+ UF_long i, lunz ;
+
+ printf ("KLU: %s, version: %d.%d.%d\n", KLU_DATE, KLU_MAIN_VERSION,
+ KLU_SUB_VERSION, KLU_SUBSUB_VERSION) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* set defaults */
+ /* ---------------------------------------------------------------------- */
+
+ klu_l_defaults (&Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create a right-hand-side */
+ /* ---------------------------------------------------------------------- */
+
+ if (isreal)
+ {
+ /* B = 1 + (1:n)/n */
+ B = klu_l_malloc (n, sizeof (double), &Common) ;
+ X = klu_l_malloc (n, sizeof (double), &Common) ;
+ R = klu_l_malloc (n, sizeof (double), &Common) ;
+ if (B)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ B [i] = 1 + ((double) i+1) / ((double) n) ;
+ }
+ }
+ }
+ else
+ {
+ /* real (B) = 1 + (1:n)/n, imag(B) = (n:-1:1)/n */
+ B = klu_l_malloc (n, 2 * sizeof (double), &Common) ;
+ X = klu_l_malloc (n, 2 * sizeof (double), &Common) ;
+ R = klu_l_malloc (n, 2 * sizeof (double), &Common) ;
+ if (B)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ REAL (B, i) = 1 + ((double) i+1) / ((double) n) ;
+ IMAG (B, i) = ((double) n-i) / ((double) n) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* X = A\b using KLU and print statistics */
+ /* ---------------------------------------------------------------------- */
+
+ if (!klu_l_backslash (n, Ap, Ai, Ax, isreal, B, X, R, &lunz, &rnorm,
+ &Common))
+ {
+ printf ("KLU failed\n") ;
+ }
+ else
+ {
+ printf ("n %d nnz(A) %d nnz(L+U+F) %d resid %g\n"
+ "recip growth %g condest %g rcond %g flops %g\n",
+ n, Ap [n], lunz, rnorm, Common.rgrowth, Common.condest,
+ Common.rcond, Common.flops) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the problem */
+ /* ---------------------------------------------------------------------- */
+
+ if (isreal)
+ {
+ klu_l_free (B, n, sizeof (double), &Common) ;
+ klu_l_free (X, n, sizeof (double), &Common) ;
+ klu_l_free (R, n, sizeof (double), &Common) ;
+ }
+ else
+ {
+ klu_l_free (B, 2*n, sizeof (double), &Common) ;
+ klu_l_free (X, 2*n, sizeof (double), &Common) ;
+ klu_l_free (R, 2*n, sizeof (double), &Common) ;
+ }
+ printf ("peak memory usage: %g bytes\n\n", (double) (Common.mempeak)) ;
+}
+
+
+/* ========================================================================== */
+/* === main ================================================================= */
+/* ========================================================================== */
+
+/* Read in a sparse matrix in Matrix Market format using CHOLMOD, and then
+ * solve Ax=b with KLU. Note that CHOLMOD is only used to read the matrix. */
+
+#include "cholmod.h"
+
+int main (void)
+{
+ cholmod_sparse *A ;
+ cholmod_common ch ;
+ cholmod_l_start (&ch) ;
+ A = cholmod_l_read_sparse (stdin, &ch) ;
+ if (A)
+ {
+ if (A->nrow != A->ncol || A->stype != 0
+ || (!(A->xtype == CHOLMOD_REAL || A->xtype == CHOLMOD_COMPLEX)))
+ {
+ printf ("invalid matrix\n") ;
+ }
+ else
+ {
+ klu_l_demo (A->nrow, A->p, A->i, A->x, A->xtype == CHOLMOD_REAL) ;
+ }
+ cholmod_l_free_sparse (&A, &ch) ;
+ }
+ cholmod_l_finish (&ch) ;
+ return (0) ;
+}
diff --git a/KLU/Doc/ChangeLog b/KLU/Doc/ChangeLog
new file mode 100644
index 0000000..26ab332
--- /dev/null
+++ b/KLU/Doc/ChangeLog
@@ -0,0 +1,51 @@
+Nov 1, 2007, version 1.0.1
+
+ * minor lint cleanup
+
+May 31, 2007, version 1.0
+
+ * Overview: this is the first clean release of KLU. Only one bug was
+ fixed since in the last pre-1.0 version (see below). This release adds
+ a 64-bit version, a better Demo, a 100% statement coverage test, new
+ parameters and statistics in the KLU Common object, reduced memory
+ usage, a method for limiting worst-case work in the BTF ordering, and a
+ completely redesigned MATLAB interface.
+
+ * scaling default changed from no scaling, to max row scaling
+
+ * C-callable API modified for klu_malloc, klu_free, klu_realloc, klu_rcond,
+ klu_rgrowth, klu_condest. API of other user-callable KLU functions not
+ modified.
+
+ * user ordering function prototype modified (final argument is now
+ klu_common, not Common->user_data)
+
+ * User Guide added.
+
+ * KLU Demo completely rewritten. Now depends on CHOLMOD to read in its
+ matrices, in Matrix Market format.
+
+ * port to 64-bit version
+
+ * reduction in memory usage, particularly when the BTF form results in
+ many small diagonal blocks
+
+ * new Common parameter (maxwork) and statistics (work, memusage, mempeak)
+
+ * Makefile and object files (*.o) now placed in KLU/Lib, not KLU/Source
+
+ * added klu_install.m, klu_demo.m, klu_make.m to KLU/MATLAB.
+
+ * klu mexFunction now returns a struct for LU, not a lengthy list of
+ matrices. MATLAB interface completely rewritten.
+
+ * Tcov tests completely rewritten
+
+ * bug fix in complex klu_z_refactor, when both btf and scaling are in use
+
+ * bug fix in klu_rgrowth, when the matrix is scaled
+
+Dec 12, 2006: version 0.11
+
+ * minor MATLAB cleanup
+
diff --git a/KLU/Doc/KLU_UserGuide.bib b/KLU/Doc/KLU_UserGuide.bib
new file mode 100644
index 0000000..e69f199
--- /dev/null
+++ b/KLU/Doc/KLU_UserGuide.bib
@@ -0,0 +1,132 @@
+%-------------------------------------------------------------------------------
+
+ at string{TOMS = "{ACM} Trans. Math. Software"}
+ at string{SIAMJSSC = "{SIAM} J. Sci. Statist. Comput."}
+ at string{SIMAX = "{SIAM} J. Matrix Anal. Appl."}
+ at string{SICOMP= "{SIAM} J. Comput."}
+ at string{SIAMJSC = "{SIAM} J. Sci. Comput."}
+
+ at techreport{NagelPederson,
+ author={Nagel, L. W and Pederson, D. O.},
+ title={{SPICE} (Simulation Program with Integrated Circuit Emphasis)},
+ number={Memorandum No. ERL-M382},
+ address={University of California, Berkeley}, year={1973}}
+
+ at incollection{Kundert86,
+ author={Kundert, K. S.},
+ year={1986},
+ title={Sparse Matrix Techniques and Their Applications to Circuit Simulation},
+ editor={Ruehli, A. E.},
+ booktitle={Circuit Analysis, Simulation and Design},
+ publisher={New York: North-Holland}}
+
+ at techreport{KundertSangiovanniVincentelli85,
+ author={Kundert, K. S. and Sangiovanni-Vincentelli, A.},
+ month={Oct.},
+ year={1985},
+ title={User's Guide: Sparse1.2},
+ institution={Dept.~of EE and CS, UC Berkeley},
+ keywords={ 31 Sparse1.2 software package direct methods}}
+
+ at phdthesis{Quarles:M89/42,
+ Author = {Thomas L. Quarles},
+ Title = {Analysis of Performance and Convergence Issues for Circuit Simulation},
+ School = {EECS Department, University of California, Berkeley},
+ Year = {1989},
+ URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1989/1216.html},
+ Number = {UCB/ERL M89/42}}
+
+ at book{Davis06book,
+ author={T. A. Davis},
+ title={Direct Methods for Sparse Linear Systems},
+ publisher={SIAM}, year={2006}, address={Philadelphia, PA}}
+
+ at article{GilbertPeierls88,
+ author={Gilbert, J. R. and Peierls, T.},
+ year={1988},
+ title={Sparse Partial Pivoting in Time Proportional to Arithmetic Operations},
+ journal=SIAMJSSC, volume={9}, pages={862-874}}
+
+ at article{Duff78a,
+ author={Duff, I. S. and Reid, J. K.},
+ year={1978},
+ title={An Implementation of {Tarjan}'s Algorithm for the Block Triangularization of a Matrix},
+ journal=TOMS, volume={4}, pages={137-147}}
+
+ at article{Duff81,
+ author={Duff, I. S.},
+ year={1981},
+ title={On Algorithms for Obtaining a Maximum Transversal},
+ journal=TOMS, volume={7}, pages={315-330}}
+
+ at article{AmestoyDavisDuff96,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={An approximate minimum degree ordering algorithm},
+ journal=SIMAX, year={1996}, volume={17}, pages={886--905}}
+
+ at article{AmestoyDavisDuff03,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm},
+ journal=TOMS, year={2004}, volume={30}, pages={381-388}}
+
+ at article{Tarjan72,
+ author={Tarjan, R. E.},
+ title={Depth first search and linear graph algorithms},
+ journal=SICOMP, year={1972}, volume={1}, pages={146--160}}
+
+ at article{DavisGilbertLarimoreNg00,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={A column approximate minimum degree ordering algorithm},
+ journal=TOMS, year={2004}, volume={30}, pages={353-376}}
+
+ at article{DavisGilbertLarimoreNg00_algo,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={Algorithm 836: {COLAMD}, a column approximate minimum degree ordering algorithm},
+ journal=TOMS, year={2004}, volume={30}, pages={377-380}}
+
+ at article{ChenDavisHagerRajamanickam06,
+ author={Chen, Y. and Davis, T. A. and Hager, W. W. and Rajamanickam, S.},
+ title={Algorithm 8xx: {CHOLMOD}, supernodal sparse {Cholesky} factorization and update/downdate},
+ journal=TOMS, note={(submitted)}, year={2006}}
+
+ at article{KarypisKumar98e,
+ author={Karypis, G. and Kumar, V.},
+ title={A fast and high quality multilevel scheme for partitioning irregular graphs},
+ journal=SIAMJSC, year={1998}, volume={20}}
+
+ at article{ACM679a,
+ author={Dongarra, J. J. and {Du Croz}, J. and Duff, I. S. and Hammarling, S.},
+ title={A set of level-3 basic linear algebra subprograms},
+ journal=TOMS, year={1990}, volume={16}, pages={1--17}}
+
+ at article{SuperLU99,
+ author={Demmel, J. W. and Eisenstat, S. C. and Gilbert, J. R. and Li, X. S. and Liu, J. W. H.},
+ title={A supernodal approach to sparse partial pivoting},
+ journal=SIMAX, year={1999}, volume={20}, pages={720-755} }
+
+ at article{Davis03,
+ author={Davis, T. A.},
+ title={A column pre-ordering strategy for the unsymmetric-pattern multifrontal method},
+ journal=TOMS, year={2004}, volume={30}, pages={165--195}}
+
+ at article{Davis03_algo,
+ author={Davis, T. A.},
+ title={Algorithm 832: {UMFPACK V4.3}, an unsymmetric-pattern multifrontal method},
+ journal=TOMS, year={2002}, volume={30}, pages={196--199}}
+
+ at article{Hager84,
+ author={Hager, W. W.},
+ title={Condition estimates},
+ journal=SIAMJSSC, year={1984},volume={5}, pages={311-316}}
+
+ at article{HighamTisseur00,
+ author={Higham, N. J. and Tisseur, F.},
+ title={A block algorithm for matrix 1-norm estimation with an application to 1-norm pseudospectra},
+ journal=SIMAX, year={2000},volume={21},pages={1185--1201} }
+
+ at techreport{Palamadai05,
+ author={Palamadai, E.},
+ title={{KLU} - a high performance sparse linear system solver for
+ circuit simulation problems},
+ note={M.S. Thesis},
+ address={CISE Department, Univ. of Florida}}
diff --git a/KLU/Doc/KLU_UserGuide.pdf b/KLU/Doc/KLU_UserGuide.pdf
new file mode 100644
index 0000000..8d98c23
Binary files /dev/null and b/KLU/Doc/KLU_UserGuide.pdf differ
diff --git a/KLU/Doc/KLU_UserGuide.tex b/KLU/Doc/KLU_UserGuide.tex
new file mode 100644
index 0000000..9a70a8c
--- /dev/null
+++ b/KLU/Doc/KLU_UserGuide.tex
@@ -0,0 +1,1329 @@
+\documentclass[11pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+%------------------------------------------------------------------------------
+\begin{document}
+%------------------------------------------------------------------------------
+
+\title{User Guide for KLU Version 1.0.1 and BTF Version 1.0.1}
+\author{
+Timothy A. Davis\thanks{
+Dept.~of Computer and Information Science and Engineering,
+Univ.~of Florida, Gainesville, FL, USA.
+email: davis at cise.ufl.edu.
+http://www.cise.ufl.edu/$\sim$davis.
+This work was supported by Sandia National Labs, and the National
+Science Foundation.
+Portions of the work were done while on sabbatical at Stanford University
+and Lawrence Berkeley National Laboratory (with funding from Stanford
+University and the SciDAC program).
+}
+\and Eka Palamadai}
+
+\date{Nov 1, 2007}
+\maketitle
+
+%------------------------------------------------------------------------------
+\begin{abstract}
+KLU is a set of routines for solving sparse linear systems of equations.
+It is particularly well-suited to matrices arising in SPICE-like circuit
+simulation applications.
+It relies on a permutation to block triangular form (BTF), several methods
+for finding a fill-reducing ordering (variants of approximate minimum degree,
+and nested dissection), and a sparse left-looking LU factorization method
+to factorize each block. A MATLAB interface is included.
+\end{abstract}
+%------------------------------------------------------------------------------
+
+\newpage
+\tableofcontents
+\newpage
+
+%------------------------------------------------------------------------------
+\section{License and Copyright}
+%------------------------------------------------------------------------------
+
+KLU Version 1.0.1, Copyright\copyright 2007 University of Florida.
+All Rights Reserved.
+KLU is available under alternate licenses; contact T. Davis for details.
+
+{\bf KLU License:}
+ Your use or distribution of KLU or any modified version of
+ KLU implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+{\bf Availability:}
+
+ {\tt http://www.cise.ufl.edu/research/sparse/klu}
+
+ {\tt http://www.cise.ufl.edu/research/sparse/btf}
+
+{\bf Acknowledgments:}
+
+ This work was supported by Sandia National Laboratories (Mike Heroux)
+ and the National Science Foundation under grants 0203270 and 0620286.
+
+
+%------------------------------------------------------------------------------
+\newpage
+\section{Overview}
+%------------------------------------------------------------------------------
+
+KLU is a set of routines for solving sparse linear systems of equations. It
+first permutes the matrix into upper block triangular form, via the BTF
+package. This is done by first finding a permutation for a zero-free diagonal
+(a maximum transversal) \cite{Duff81}. If there is no such permutation, then
+the matrix is structurally rank-deficient, and is numerically singular. Next,
+Tarjan's method \cite{Duff78a,Tarjan72} is used to find the strongly-connected
+components of the graph. The block triangular form is essentially unique; any
+method will lead to the same number and sizes of blocks, although the ordering
+of the blocks may vary (consider a diagonal matrix, for example). Assuming the
+matrix has full structural rank, the permuted matrix has the following form:
+\[
+PAQ =
+\left[
+\begin{array}{ccc}
+A_{11} & \cdots & A_{1k} \\
+ & \ddots & \vdots \\
+ & & A_{kk} \\
+\end{array}
+\right],
+\]
+where each diagonal block is square with a zero-free diagonal.
+
+Next, each diagonal block is factorized with a sparse left-looking method
+\cite{GilbertPeierls88}. The kernel of this factorization method is an
+efficient method for solving $Lx=b$ when $L$, $x$, and $b$ are all sparse.
+This kernel is used to compute each column of $L$ and $U$, one column at a time.
+The total work performed by this method is always proportional to the number of
+floating-point operations, something that is not true of any other sparse LU
+factorization method.
+
+Prior to factorizing each diagonal block, the blocks are ordered to reduce
+fill-in. By default, the symmetric approximate minimum degree (AMD) ordering
+is used on $A_{ii}+A_{ii}^T$ \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}.
+Another ordering option is to find a column ordering via COLAMD
+\cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00}.
+Alternatively, a permutation can be provided by the user, or a pointer to
+a user-provided ordering function can be passed, which is then used to order
+each block.
+
+Only the diagonal blocks need to be factorized. Consider a linear system where
+the matrix is permuted into three blocks, for example:
+\[
+\left[
+\begin{array}{ccc}
+A_{11} & A_{12} & A_{13} \\
+ & A_{22} & A_{23} \\
+ & & A_{33} \\
+\end{array}
+\right]
+\left[
+\begin{array}{c}
+x_{1} \\
+x_{2} \\
+x_{3} \\
+\end{array}
+\right]
+=
+\left[
+\begin{array}{c}
+b_{1} \\
+b_{2} \\
+b_{3} \\
+\end{array}
+\right].
+\]
+
+The non-singular system $A_{33} x_{3} = b_{3}$ can first be solved for $x_{3}$.
+After a block back substitution, the resulting system becomes
+\[
+\left[
+\begin{array}{cc}
+A_{11} & A_{12} \\
+ & A_{22} \\
+\end{array}
+\right]
+\left[
+\begin{array}{c}
+x_{1} \\
+x_{2} \\
+\end{array}
+\right]
+=
+\left[
+\begin{array}{c}
+b_{1} - A_{13} x_{3}\\
+b_{2} - A_{23} x_{3}\\
+\end{array}
+\right]
+=
+\left[
+\begin{array}{c}
+b'_{1} \\
+b'_{2} \\
+\end{array}
+\right]
+\]
+and the $A_{22} x_{2} = b'_{2}$ system can be solved for $x_{2}$. The primary
+advantage of this method is that no fill-in occurs in the off-diagonal blocks
+($A_{12}$, $A_{13}$, and $A_{23}$). This is particular critical for sparse
+linear systems arising in SPICE-like circuit simulation
+\cite{Kundert86,KundertSangiovanniVincentelli85,NagelPederson,Quarles:M89/42}.
+Circuit matrices are typically permutable into block triangular form, with many
+singletons (1-by-1 blocks). They also often have a handful of rows and columns
+with many nonzero entries, due to voltage and current sources. These rows and
+columns are pushed into the upper block triangular form, and related to the
+singleton blocks (for example, $A_{33}$ in the above system is 1-by-1, and the
+column in $A_{13}$ and $A_{23}$ has many nonzero entries). Since these
+nearly-dense rows and columns do not appear in the LU factorization of the
+diagonal blocks, they cause no fill-in.
+
+The structural rank of a matrix is based solely on the pattern of its entries,
+not their numerical values. With random entries, the two ranks are equal with
+probability one. The structural rank of any matrix is an upper bound on the
+numerical rank. The maximum transversal algorithm in the BTF package is useful
+in determining if a matrix is structurally rank deficient, and if so, it
+reveals a (non-unique) set of rows and columns that contribute to that rank
+deficiency. This is useful in determining what parts of a circuit are poorly
+formulated (such as dangling components).
+
+When ordered and factorized with KLU, very little fill-in occurs in the
+resulting LU factors, which means that there is little scope for use of the
+BLAS \cite{ACM679a}. Sparse LU factorization methods that use the BLAS (such
+as SuperLU \cite{SuperLU99} amd UMFPACK \cite{Davis03_algo,Davis03}) are slower
+than KLU when applied to sparse matrices arising in circuit simulation. Both
+KLU and SuperLU are based on Gilbert and Peierl's left-looking method
+\cite{GilbertPeierls88}. SuperLU uses supernodes, but KLU does not; thus the
+name {\em KLU} refers to a ``Clark Kent'' LU factorization algorithm (what
+SuperLU was before it became Super).
+
+For details of the permutation to block triangular form, left-looking sparse
+LU factorization, and approximate minimum degree, refer to \cite{Davis06book}.
+Concise versions of these methods can be found in the CSparse package. KLU is
+also the topic of a Master's thesis by Palamadai \cite{Palamadai05}; a copy of
+the thesis can be found in the {\tt KLU/Doc} directory. It includes a
+description of an earlier version of KLU; some of the function names and
+parameter lists have changed in this version. The descriptions of the methods
+used still applies to the current version of KLU, however.
+
+%------------------------------------------------------------------------------
+\section{Availability}
+%------------------------------------------------------------------------------
+
+KLU and its required ordering packages (BTF, COLAMD, AMD, and UFconfig) are
+available at \newline {\tt http://www.cise.ufl.edu/research/sparse.} In
+addition, KLU can make use of any user-provided ordering function. One such
+function is included, which provides KLU with an interface to the ordering
+methods used in CHOLMOD \cite{ChenDavisHagerRajamanickam06}, such as METIS, a
+nested dissection method \cite{KarypisKumar98e}. After permutation to block
+triangular form, circuit matrices have very good node separators, and are thus
+excellent candidates for nested dissection. The METIS ordering takes much more
+time to compute than the AMD ordering, but if the ordering is reused many times
+(typical in circuit simulation) the better-quality ordering can pay off in
+lower total simulation time.
+
+To use KLU, you must obtain the KLU, BTF, UFconfig, AMD, and COLAMD packages
+in the SuiteSparse suite of sparse matrix libraries. See
+{\tt http://www.cise.ufl.edu/research/sparse} for each of these packages.
+They are also all contained within the single {\tt SuiteSparse.zip} or
+{\tt SuiteSparse.tar.gz} distribution.
+
+%------------------------------------------------------------------------------
+\section{Using KLU and BTF in MATLAB}
+%------------------------------------------------------------------------------
+
+KLU has a single MATLAB interface which provides several options for factorizing
+a matrix and/or using the factors to solve a linear system. The following is
+a synopsis of its use. For more details, type {\tt help klu} in MATLAB.
+
+{\footnotesize
+\begin{verbatim}
+ LU = klu (A) factorizes R\A(p,q) into L*U+F, returning a struct
+ x = klu (A,'\',b) x = A\b
+ x = klu (b,'/',A) x = b/A
+ x = klu (LU,'\',b) x = A\b, where LU = klu(A)
+ x = klu (b,'/',LU) x = b/A, where LU = klu(A)
+\end{verbatim}
+}
+
+With a single input {\tt klu(A)} returns a MATLAB struct containing the LU
+factors. The factorization is in the form \verb'L*U + F = R \ A(p,q)'
+where {\tt L*U} is the LU factorization of just the diagonal blocks of the
+block triangular form, {\tt F} is a sparse matrix containing the entries in
+the off-diagonal blocks, {\tt R} is a diagonal matrix containing the row
+scale factors, and {\tt p} and {\tt q} are permutation vectors. The {\tt LU}
+struct also contains a vector {\tt r} which describes the block boundaries
+(the same as the third output parameter of {\tt dmperm}). The {\tt k}th
+block consists of rows and columns {\tt r(k)} to {\tt r(k+1)-1} in the
+permuted matrix {\tt A(p,q)} and the factors {\tt L} and {\tt U}.
+
+An optional final input argument ({\tt klu(A,opts)} for example) provides a
+way of modifying KLU's user-definable parameters, including a partial pivoting
+tolerance and ordering options. A second output argument
+({\tt [LU,info] = klu ( ... )}) provides statistics on the factorization.
+
+The BTF package includes three user-callable MATLAB functions which replicate
+most of features of the MATLAB built-in {\tt dmperm} function, and provide an
+additional option which can significantly limit the worst-case time taken by
+{\tt dmperm}. For more details, type {\tt help btf}, {\tt help maxtrans},
+and {\tt help strongcomp} in MATLAB. Additional information about how
+these functions work can be found in \cite{Davis06book}.
+
+{\footnotesize
+\begin{verbatim}
+ [p,q,r] = btf (A) similar to [p,q,r] = dmperm (A)
+ q = maxtrans (A) similar to q = dmperm (A')
+ [p,r] = strongcomp (A) similar to [p,q,r] = dmperm (A + speye(n))
+\end{verbatim}
+}
+
+Both {\tt btf} and {\tt maxtrans} include a second option input, {\tt maxwork},
+which limits the total work performed in the maximum transversal to
+{\tt maxwork * nnz(A)}. The worst-case time taken by the algorithm is
+$O$ ({\tt n * nnz(A)}), where the matrix {\tt A} is {\tt n}-by-{\tt n}, but
+this worst-case time is rarely reached in practice.
+
+To use the KLU and BTF functions in MATLAB, you must first compile and install
+them. In the {\tt BTF/MATLAB} directory, type {\tt btf\_install}, and then
+type {\tt klu\_install} in the {\tt KLU/MATLAB} directory. Alternatively, if
+you have the entire SuiteSparse, simply run the {\tt SuiteSparse\_install}
+function in the {\tt SuiteSparse} directory. To use METIS 4.0.1 with KLU (and
+CHOLMOD, another part of SuiteSparse) you must first download it from {\tt
+http://glaros.dtc.umn.edu/gkhome/views/metis} and place the {\tt metis-4.0}
+directory in the {\tt SuiteSparse} directory, alongside the {\tt KLU} and {\tt
+BTF} directories.
+
+After running the installation scripts, type {\tt pathtool} and save your path
+for future MATLAB sessions. If you cannot save your path because of file
+permissions, edit your {\tt startup.m} by adding {\tt addpath} commands (type
+{\tt doc startup} and {\tt doc addpath} for more information).
+
+%------------------------------------------------------------------------------
+\section{Using KLU and BTF in a C program}
+\label{Cversion}
+%------------------------------------------------------------------------------
+
+KLU and BTF include the following C-callable functions. Each function is
+available in two or four versions: with {\tt int} or {\tt long} integers, and
+(for functions that deal with numerical values), with {\tt double} or complex
+{\tt double} values. The {\tt long} integer is actually a {\tt UF\_long},
+which is typically a {\tt long}, defined with a {\tt \#define} statement. It
+becomes an {\tt \_\_int64} on Microsoft Windows 64, however.
+
+The usage of real and complex, and {\tt int} and {\tt UF\_long}, must not be
+mixed, except that some functions can be used for both real and complex cases.
+
+%------------------------------------------------------------------------------
+\subsection{KLU Common object}
+%------------------------------------------------------------------------------
+
+The {\tt klu\_common} object ({\tt klu\_l\_common} for the {\tt UF\_long}
+version) contains user-definable parameters and statistics returned from
+KLU functions. This object appears in every KLU function as the last
+parameter. Details are given in the {\tt klu.h} include file, which also
+appears below in Section~\ref{klu_include}. Primary parameters and statistics
+are summarized below. The defaults are chosen specifically for circuit
+simulation matrices.
+
+\begin{itemize}
+\item {\tt tol}: partial pivoting tolerance. If the diagonal entry has a
+magnitude greater than or equal to {\tt tol} times the largest magnitude
+of entries in the pivot column, then the diagonal entry is chosen.
+Default value: 0.001.
+
+\item {\tt ordering}: which fill-reducing ordering to use: 0 for AMD,
+1 for COLAMD, 2 for a user-provided permutation {\tt P} and {\tt Q}
+(or a natural ordering if {\tt P} and {\tt Q} are NULL), or 3 for
+the {\tt user\_order} function. Default: 0 (AMD).
+
+\item {\tt scale}: whether or not the matrix should be scaled.
+If {\tt scale < 0}, then no scaling is performed and the input matrix
+is not checked for errors. If {\tt scale >= 0}, the input matrix is
+check for errors.
+If {\tt scale=0}, then no scaling is performed.
+If {\tt scale=1}, then each row of {\tt A} is divided by the sum of
+the absolute values in that row.
+If {\tt scale=2}, then each row of {\tt A} is divided by the maximum
+absolute value in that row. Default: 2.
+
+\item {\tt btf}: if nonzero, then BTF is used to permute the input matrix
+into block upper triangular form. This step is skipped if {\tt Common.btf}
+is zero. Default: 1.
+
+\item {\tt maxwork}: sets an upper limit on the amount of work performed in
+{\tt btf\_maxtrans} to \newline {\tt maxwork*nnz(A)}. If the limit is reached,
+a partial zero-free diagonal might be found. This has no effect on whether or
+not the matrix can be factorized, since the matrix can be factorized with no
+BTF pre-ordering at all. This option provides a tradeoff between the
+effectiveness of the BTF ordering and the cost to compute it. A partial result
+can result in fewer, and larger, blocks in the BTF form, resulting to more work
+required to factorize the matrix. No limit is enforced if {\tt maxwork <= 0}.
+Default: 0.
+
+\item {\tt user\_order}: a pointer to a function that can be provided by the
+application that uses KLU, to redefine the fill-reducing ordering used by KLU
+for each diagonal block. The {\tt int} and {\tt UF\_long} prototypes must be
+as follows:
+
+{\footnotesize
+\begin{verbatim}
+int my_ordering_function (int n, int Ap [ ], int Ai [ ], int Perm [ ], klu_common *Common) ;
+
+
+UF_long my_long_ordering_function (UF_long n, UF_long Ap [ ], UF_long Ai [ ],
+ UF_long Perm [ ], klu_l_common *Common);
+\end{verbatim}
+}
+
+The function should return 0 if an error occurred, and either -1 or a positive
+(nonzero) value if no error occurred. If greater than zero, then the return
+value is interpreted by KLU as an estimate of the number of nonzeros in $L$ or
+$U$ (whichever is greater), when the permuted matrix is factorized. Only an
+estimate is possible, since partial pivoting with row interchanges is performed
+during numerical factorization. The input matrix is provided to the function
+in the parameters {\tt n}, {\tt Ap}, and {\tt Ai}, in compressed-column form.
+The matrix {\tt A} is {\tt n}-by-{\tt n}. The {\tt Ap} array is of size {\tt
+n+1}; the {\tt j}th column of {\tt A} has row indices {\tt Ai[Ap[j] ...
+Ap[j+1]-1]}. The {\tt Ai} array is of size {\tt Ap[n]}. The first column
+pointer {\tt Ap[0]} is zero. The row indices might not appear sorted in each
+column, but no duplicates will appear.
+
+The output permutation is to be passed back in the {\tt Perm} array, where
+{\tt Perm[k]=j} means that row and column {\tt j} of {\tt A} will appear as
+the {\tt k}th row and column of the permuted matrix factorized by KLU. The
+{\tt Perm} array is already allocated when it is passed to the user function.
+
+The user function may use, and optionally modify, the contents of the {\tt
+klu\_common Common} object. In particular, prior to calling KLU, the user
+application can set both {\tt Common.user\_order} and {\tt Common.user\_data}.
+The latter is a {\tt void *} pointer that KLU does not use, except to pass to
+the user ordering function pointed to by {\tt Common.user\_order}. This is a
+mechanism for passing additional arguments to the user function.
+
+An example user function is provided in the {\tt KLU/User} directory, which
+provides an interface to the ordering method in CHOLMOD.
+
+\end{itemize}
+
+%------------------------------------------------------------------------------
+\subsection{KLU Symbolic object}
+%------------------------------------------------------------------------------
+
+KLU performs its sparse LU factorization in two steps. The first is purely
+symbolic, and does not depend on the numerical values. This analysis returns a
+{\tt klu\_symbolic} object ({\tt klu\_l\_symbolic} in the {\tt UF\_long}
+version). The {\tt Symbolic} object contains a pre-ordering which combines the
+block triangular form with the fill-reducing ordering, and an estimate of the
+number of nonzeros in the factors of each block. Its size is thus modest, only
+proportional to {\tt n}, the dimension of {\tt A}. It can be reused multiple
+times for the factorization of a sequence of matrices with identical nonzero
+pattern. Note: a {\em nonzero} in this sense is an entry present in the data
+structure of {\tt A}; such entries may in fact be numerically zero.
+
+%------------------------------------------------------------------------------
+\subsection{KLU Numeric object}
+%------------------------------------------------------------------------------
+
+The {\tt Numeric} object contains the numeric sparse LU factorization, including
+the final pivot permutations. To solve a linear system, both the {\tt Symbolic}
+and {\tt Numeric} objects are required.
+
+%------------------------------------------------------------------------------
+\subsection{A sparse matrix in KLU}
+%------------------------------------------------------------------------------
+
+% From here on, only the {\tt int} version is described. In the {\tt UF\_long}
+% version, the function names change slightly ({\tt klu\_factor} becomes
+% {\tt klu\_l\_factor}, and the {\tt int}/complex version {\tt klu\_z\_factor}
+% becomes {\tt klu\_zl\_factor}, for example). For more details on the
+% {\tt UF\_long} version, refer to Section~\ref{klu_include}.
+
+The input matrix provided to KLU is in sparse compressed-column form, which is
+the same data structure used internally in MATLAB, except that the version used
+here allows for the row indices to appear in any ordering, and this version
+also allows explicit zero entries to appear in the data structure. The same
+data structure is used in CSparse, which is fully documented in
+\cite{Davis06book}. If you wish to use a simpler input data structure,
+consider creating a triplet matrix in CSparse (or CXSparse if you use the long
+and/or complex versions of KLU), and then convert this data structure into a
+sparse compressed-column data structure, using the CSparse {\tt cs\_compress}
+and {\tt cs\_dupl} functions. Similar functions are available in CHOLMOD
+{\tt cholmod\_triplet\_to\_sparse}.
+
+The matrix is described with four parameters:
+
+\begin{itemize}
+\item {\tt n}: an integer scalar. The matrix is {\tt n}-by-{\tt n}. Note that
+KLU only operates on square matrices.
+
+\item {\tt Ap}: an integer array of size {\tt n+1}. The first entry is {\tt
+Ap[0]=0}, and the last entry {\tt nz=Ap[n]} is equal to the number of entries
+in the matrix.
+
+\item {\tt Ai}: an integer array of size {\tt nz = Ap[n]}.
+The row indices of entries in column {\tt j} of {\tt A} are located in
+{\tt Ai [Ap [j] ... Ap [j+1]-1]}. The matrix is zero-based; row and column
+indices are in the range 0 to {\tt n-1}.
+
+\item {\tt Ax}: a {\tt double} array of size {\tt nz} for the real case, or
+{\tt 2*nz} for the complex case. For the complex case, the real and imaginary
+parts are interleaved, compatible with Fortran and the ANSI C99 Complex data
+type. KLU does not rely on the ANSI C99 data type, however, for portability
+reasons. The numerical values in column {\tt j} of a real matrix are located
+in {\tt Ax [Ap [j] ... Ap [j+1]-1]}. For a complex matrix, they appear in {\tt
+Ax [2*Ap [j] ... 2*Ap [j+1]-1]}, as real/imaginary pairs (the real part appears
+first, followed by the imaginary part).
+
+\end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_defaults}: set default parameters}
+%-------------------------------------------------------------------------------
+
+This function sets the default parameters for KLU and clears the statistics.
+It may be used for either the real or complex cases. A value of 0 is returned
+if an error occurs, 1 otherwise. This function {\bf must} be called before
+any other KLU function can be called.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int ok ;
+ klu_common Common ;
+ ok = klu_defaults (&Common) ; /* real or complex */
+
+
+ #include "klu.h"
+ UF_long ok ;
+ klu_l_common Common ;
+ ok = klu_l_defaults (&Common) ; /* real or complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_analyze}: order and analyze a matrix}
+%-------------------------------------------------------------------------------
+
+The following usage returns a {\tt Symbolic} object that contains the
+fill-reducing ordering needed to factorize the matrix {\tt A}. A NULL pointer
+is returned if a failure occurs. The error status for this function, and all
+others, is returned in {\tt Common.status}. These functions may be used for
+both real and complex cases. The AMD ordering is used if {\tt Common.ordering
+= 0}, COLAMD is used if it is 1, the natural ordering is used if it is 2, and
+the user-provided {\tt Common.user\_ordering} is used if it is 3.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int n, Ap [n+1], Ai [nz] ;
+ klu_symbolic *Symbolic ;
+ klu_common Common ;
+ Symbolic = klu_analyze (n, Ap, Ai, &Common) ; /* real or complex */
+
+
+ #include "klu.h"
+ UF_long n, Ap [n+1], Ai [nz] ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_common Common ;
+ Symbolic = klu_l_analyze (n, Ap, Ai, &Common) ; /* real or complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_analyze\_given}: order and analyze a matrix}
+%-------------------------------------------------------------------------------
+
+In this routine, the fill-reducing ordering is provided by the user ({\tt
+Common.ordering} is ignored). Instead, the row permutation {\tt P} and column
+permutation {\tt Q} are used. These are integer arrays of size {\tt n}. If
+NULL, a natural ordering is used (so to provide just a column ordering, pass
+{\tt Q} as non-NULL and {\tt P} as NULL). A NULL pointer is returned if an
+error occurs. These functions may be used for both real and complex cases.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int n, Ap [n+1], Ai [nz], P [n], Q [n] ;
+ klu_symbolic *Symbolic ;
+ klu_common Common ;
+ Symbolic = klu_analyze_given (n, Ap, Ai, P, Q, &Common) ; /* real or complex */
+
+
+ #include "klu.h"
+ UF_long n, Ap [n+1], Ai [nz], P [n], Q [n] ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_common Common ;
+ Symbolic = klu_l_analyze_given (n, Ap, Ai, P, Q, &Common) ; /* real or complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_factor}: numerical factorization}
+%-------------------------------------------------------------------------------
+
+The {\tt klu\_factor} function factorizes a matrix, using a sparse left-looking
+method with threshold partial pivoting. The inputs {\tt Ap} and {\tt Ai} must
+be unchanged from the previous call to {\tt klu\_analyze} that created the {\tt
+Symbolic} object. A NULL pointer is returned if an error occurs.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int Ap [n+1], Ai [nz] ;
+ double Ax [nz], Az [2*nz] ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ; /* real */
+ Numeric = klu_z_factor (Ap, Ai, Az, Symbolic, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long Ap [n+1], Ai [nz] ;
+ double Ax [nz], Az [2*nz] ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_numeric *Numeric ;
+ klu_l_common Common ;
+ Numeric = klu_l_factor (Ap, Ai, Ax, Symbolic, &Common) ; /* real */
+ Numeric = klu_zl_factor (Ap, Ai, Az, Symbolic, &Common) ; /* complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_solve}: solve a linear system}
+%-------------------------------------------------------------------------------
+
+Solves the linear system $Ax=b$, using the {\tt Symbolic} and {\tt Numeric}
+objects. The right-hand side {\tt B} is overwritten with the solution on
+output. The array {\tt B} is stored in column major order, with a leading
+dimension of {\tt ldim}, and {\tt nrhs} columns. Thus, the real entry $b_{ij}$
+is stored in {\tt B [i+j*ldim]}, where {\tt ldim >= n} must hold. A complex
+entry $b_{ij}$ is stored in {\tt B [2*(i+j*ldim)]} and {\tt B [2*(i+j*ldim)+1]}
+(for the real and imaginary parts, respectively). Returns 1 if successful,
+0 if an error occurs.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int ldim, nrhs, ok ;
+ double B [ldim*nrhs], Bz [2*ldim*nrhs] ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_solve (Symbolic, Numeric, ldim, nrhs, B, &Common) ; /* real */
+ ok = klu_z_solve (Symbolic, Numeric, ldim, nrhs, Bz, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long ldim, nrhs, ok ;
+ double B [ldim*nrhs], Bz [2*ldim*nrhs] ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_l_solve (Symbolic, Numeric, ldim, nrhs, B, &Common) ; /* real */
+ ok = klu_zl_solve (Symbolic, Numeric, ldim, nrhs, Bz, &Common) ; /* complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_tsolve}: solve a transposed linear system}
+%-------------------------------------------------------------------------------
+
+Solves the linear system $A^Tx=b$ or $A^Hx=b$. The {\tt conj\_solve} input
+is 0 for $A^Tx=b$, or nonzero for $A^Hx=b$. Otherwise, the function is
+identical to {\tt klu\_solve}.
+
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int ldim, nrhs, ok ;
+ double B [ldim*nrhs], Bz [2*ldim*nrhs] ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_tsolve (Symbolic, Numeric, ldim, nrhs, B, &Common) ; /* real */
+ ok = klu_z_tsolve (Symbolic, Numeric, ldim, nrhs, Bz, conj_solve, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long ldim, nrhs, ok ;
+ double B [ldim*nrhs], Bz [2*ldim*nrhs] ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_l_tsolve (Symbolic, Numeric, ldim, nrhs, B, &Common) ; /* real */
+ ok = klu_zl_tsolve (Symbolic, Numeric, ldim, nrhs, Bz, conj_solve, &Common) ; /* complex */
+\end{verbatim}
+}
+
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_refactor}: numerical refactorization}
+%-------------------------------------------------------------------------------
+
+The {\tt klu\_refactor} function takes as input the {\tt Numeric} object
+created by {\tt klu\_factor} (or as modified by a previous call to {\tt
+klu\_refactor}). It factorizes a new matrix with the same nonzero pattern as
+that given to the call to {\tt klu\_factor} which created it. The same pivot
+order is used. Since this can lead to numeric instability, the use of {\tt
+klu\_rcond}, {\tt klu\_rgrowth}, or {\tt klu\_condest} is recommended to check
+the accuracy of the resulting factorization. The inputs {\tt Ap} and {\tt Ai}
+must be unmodified since the call to {\tt klu\_factor} that first created the
+{\tt Numeric} object. This is function is much faster than {\tt klu\_factor},
+and requires no dynamic memory allocation.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int ok, Ap [n+1], Ai [nz] ;
+ double Ax [nz], Az [2*nz] ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_refactor (Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_z_refactor (Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long ok, Ap [n+1], Ai [nz] ;
+ double Ax [nz], Az [2*nz] ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_numeric *Numeric ;
+ klu_l_common Common ;
+ ok = klu_l_refactor (Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_zl_refactor (Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_free\_symbolic}: destroy the {\tt Symbolic} object}
+%-------------------------------------------------------------------------------
+
+It is the user's responsibility to destroy the {\tt Symbolic} object when it is
+no longer needed, or else a memory leak will occur. It is safe to pass a NULL
+{\tt Symbolic} pointer. These functions may be used for both real and complex
+cases.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ klu_symbolic *Symbolic ;
+ klu_common Common ;
+ klu_free_symbolic (&Symbolic, &Common) ; /* real or complex */
+
+
+ #include "klu.h"
+ klu_l_symbolic *Symbolic ;
+ klu_l_common Common ;
+ klu_l_free_symbolic (&Symbolic, &Common) ; /* real or complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_free\_numeric}: destroy the {\tt Numeric} object}
+%-------------------------------------------------------------------------------
+
+It is the user's responsibility to destroy the {\tt Numeric} object when it is
+no longer needed, or else a memory leak will occur. It is safe to pass a NULL
+{\tt Numeric} pointer.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ klu_free_numeric (&Numeric, &Common) ; /* real */
+ klu_z_free_numeric (&Numeric, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ klu_l_numeric *Numeric ;
+ klu_l_common Common ;
+ klu_l_free_numeric (&Numeric, &Common) ; /* real */
+ klu_zl_free_numeric (&Numeric, &Common) ; /* complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_sort}: sort the columns of L and U}
+%-------------------------------------------------------------------------------
+
+The {\tt klu\_factor} function creates a {\tt Numeric} object with factors
+{\tt L} and {\tt U} stored in a compressed-column form (not the same data
+structure as {\tt A}, but similar). The columns typically contain lists of
+row indices in unsorted order. This function sorts these indices, for two
+purposes: (1) to return {\tt L} and {\tt U} to MATLAB, which expects its
+sparse matrices to have sorted columns, and (2) to slightly improve the
+performance of subsequent calls to {\tt klu\_solve} and {\tt klu\_tsolve}.
+Except within a MATLAB mexFunction (see {\tt KLU/MATLAB/klu\_mex.c}, the use
+of this function is optional.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int ok ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_sort (Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_z_sort (Symbolic, Numeric, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long ok ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_numeric *Numeric ;
+ klu_l_common Common ;
+ ok = klu_l_sort (Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_zl_sort (Symbolic, Numeric, &Common) ; /* complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_flops}: determine the flop count}
+%-------------------------------------------------------------------------------
+
+This function determines the number of floating-point operations performed
+when the matrix was factorized by {\tt klu\_factor} or {\tt klu\_refactor}.
+The result is returned in {\tt Common.flops}.
+
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int ok ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_flops (Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_z_flops (Symbolic, Numeric, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long ok ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_numeric *Numeric ;
+ klu_l_common Common ;
+ ok = klu_l_flops (Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_zl_flops (Symbolic, Numeric, &Common) ; /* complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_rgrowth}: determine the pivot growth}
+%-------------------------------------------------------------------------------
+
+Computes the reciprocal pivot growth,
+$\mbox{\em rgrowth} = \min_j (( \max_i |c_{ij}| ) / ( \max_i |u_{ij}| ))$,
+where $c_{ij}$ is a scaled entry in a diagonal block of the block triangular
+form. In MATLAB notation:
+\begin{verbatim}
+ rgrowth = min (max (abs (R\A(p,q) - F)) ./ max (abs (U)))
+\end{verbatim}
+where the factorization is \verb'L*U + F = R \ A(p,q)'.
+This function returns 0 if an error occurred, 1 otherwise. If {\tt rgrowth} is
+very small, an inaccurate factorization may have been performed. The inputs
+{\tt Ap}, {\tt Ai}, and {\tt Ax} ({\tt Az} in the complex case) must be
+unchanged since the last call to {\tt klu\_factor} or {\tt klu\_refactor}. The
+result is returned in {\tt Common.rgrowth}.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int ok, Ap [n+1], Ai [nz] ;
+ double Ax [nz], Az [2*nz] ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_z_rgrowth (Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long ok, Ap [n+1], Ai [nz] ;
+ double Ax [nz], Az [2*nz] ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_numeric *Numeric ;
+ klu_l_common Common ;
+ ok = klu_l_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_zl_rgrowth (Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_condest}: accurate condition number estimation}
+%-------------------------------------------------------------------------------
+
+This function is essentially the same as the MATLAB {\tt condest} function. It
+computes an estimate of the 1-norm condition number, using Hager's method
+\cite{Hager84} and the generalization by Higham and Tisseur
+\cite{HighamTisseur00}. The inputs {\tt Ap}, and {\tt Ax} ({\tt Az} in the
+complex case) must be unchanged since the last call to {\tt klu\_factor} or
+{\tt klu\_refactor}. The result is returned in {\tt Common.condest}.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int ok, Ap [n+1] ;
+ double Ax [nz], Az [2*nz] ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_condest (Ap, Ax, Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_z_condest (Ap, Az, Symbolic, Numeric, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long ok, Ap [n+1] ;
+ double Ax [nz], Az [2*nz] ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_numeric *Numeric ;
+ klu_l_common Common ;
+ ok = klu_l_condest (Ap, Ax, Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_zl_condest (Ap, Az, Symbolic, Numeric, &Common) ; /* complex */
+\end{verbatim}
+}
+
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_rcond}: cheap reciprocal condition number estimation}
+%-------------------------------------------------------------------------------
+
+This function returns the smallest diagonal entry of {\tt U} divided by the
+largest, which is a very crude estimate of the reciprocal of the condition
+number of the matrix {\tt A}. It is very cheap to compute, however.
+In MATLAB notation, {\tt rcond = min(abs(diag(U))) / max(abs(diag(U)))}.
+If the matrix is singular, {\tt rcond} will be zero. The result is returned
+in {\tt Common.rcond}.
+
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int ok ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_rcond (Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_z_rcond (Symbolic, Numeric, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long ok ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_numeric *Numeric ;
+ klu_l_common Common ;
+ ok = klu_l_rcond (Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_zl_rcond (Symbolic, Numeric, &Common) ; /* complex */
+\end{verbatim}
+}
+
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_scale}: scale and check a sparse matrix}
+%-------------------------------------------------------------------------------
+
+This function computes the row scaling factors of a matrix and checks to see if
+it is a valid sparse matrix. It can perform two kinds of scaling, computing
+either the largest magnitude in each row, or the sum of the magnitudes of the
+entries each row. KLU calls this function itself, depending upon the {\tt
+Common.scale} parameter, where {\tt scale < 0} means no scaling, {\tt scale=1}
+means the sum, and {\tt scale=2} means the maximum. That is, in MATLAB
+notation, {\tt Rs = sum(abs(A'))} or {\tt Rs = max(abs(A'))}. KLU then divides
+each row of {\tt A} by its corresponding scale factor. The function returns 0
+if the matrix is invalid, or 1 otherwise. A valid sparse matrix must meet the
+following conditions:
+
+\begin{enumerate}
+\item {\tt n > 0}. Note that KLU does not handle empty (0-by-0) matrices.
+\item {\tt Ap}, {\tt Ai}, and {\tt Ax} ({\tt Az} for the complex case) must not be NULL.
+\item {\tt Ap[0]=0}, and {\tt Ap [j] <= Ap [j+1]} for all {\tt j} in the range 0 to {\tt n-1}.
+\item The row indices in each column, {\tt Ai [Ap [j] ... Ap [j+1]-1]}, must be in
+the range 0 to {\tt n-1}, and no duplicates can appear. If the workspace {\tt W} is
+NULL on input, the check for duplicate entries is skipped.
+\end{enumerate}
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int scale, ok, n, Ap [n+1], Ai [nz], W [n] ;
+ double Ax [nz], Az [2*nz], Rs [n] ;
+ klu_common Common ;
+ ok = klu_scale (scale, n, Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_z_scale (scale, n, Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long scale, ok, n, Ap [n+1], Ai [nz], W [n] ;
+ double Ax [nz], Az [2*nz], Rs [n] ;
+ klu_l_common Common ;
+ ok = klu_l_scale (scale, n, Ap, Ai, Ax, Symbolic, Numeric, &Common) ; /* real */
+ ok = klu_zl_scale (scale, n, Ap, Ai, Az, Symbolic, Numeric, &Common) ; /* complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_extract}: extract the LU factorization}
+%-------------------------------------------------------------------------------
+
+This function extracts the LU factorization into a set of data structures
+suitable for passing back to MATLAB, with matrices in conventional
+compressed-column form. The {\tt klu\_sort} function should be called first if
+the row indices should be returned sorted. The factorization is returned in
+caller-provided arrays; if any of them are NULL, that part of the factorization
+is not extracted (this is not an error). Returns 1 if successful, 0 otherwise.
+
+The sizes of {\tt Li}, {\tt Lx}, and {\tt Lz} are {\tt Numeric->lnz},
+{\tt Ui}, {\tt Ux}, and {\tt Uz} are of size {\tt Numeric->unz}, and
+{\tt Fi}, {\tt Fx}, and {\tt Fz} are of size {\tt Numeric->nzoff}.
+Note that in the complex versions, the real and imaginary parts are returned
+in separate arrays, to be compatible with how MATLAB stores complex matrices.
+
+This function is not required to solve a linear system with KLU. KLU does not
+itself make use of the extracted LU factorization returned by this function.
+It is only provided to simplify the MATLAB interface to KLU, and it may be of
+use to the end user who wishes to examine the contents of the LU factors.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ int ok, Lp [n+1], Li [lnz], Up [n+1], Ui [unz], Fp [n+1], Fi [nzoff], P [n], Q [n], R [n] ;
+ double Lx [lnz], Lz [lnz], Ux [unz], Uz [unz], Fx [nzoff], Fz [nzoff], Rs [n] ;
+ klu_symbolic *Symbolic ;
+ klu_numeric *Numeric ;
+ klu_common Common ;
+ ok = klu_extract (Numeric, Symbolic,
+ Lp, Li, Lx, Up, Ui, Ux, Fp, Fi, Fx, P, Q, Rs, R, &Common) ; /* real */
+ ok = klu_z_extract (Numeric, Symbolic,
+ Lp, Li, Lx, Lz, Up, Ui, Ux, Uz, Fp, Fi, Fx, Fz, P, Q, Rs, R, &Common) ; /* complex */
+
+
+ #include "klu.h"
+ UF_long ok, Lp [n+1], Li [lnz], Up [n+1], Ui [unz], Fp [n+1], Fi [nzoff], P [n], Q [n], R [n] ;
+ double Lx [lnz], Lz [lnz], Ux [unz], Uz [unz], Fx [nzoff], Fz [nzoff], Rs [n] ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_numeric *Numeric ;
+ klu_l_common Common ;
+ ok = klu_l_extract (Numeric, Symbolic,
+ Lp, Li, Lx, Up, Ui, Ux, Fp, Fi, Fx, P, Q, Rs, R, &Common) ; /* real */
+ ok = klu_zl_extract (Numeric, Symbolic,
+ Lp, Li, Lx, Lz, Up, Ui, Ux, Uz, Fp, Fi, Fx, Fz, P, Q, Rs, R, &Common) ; /* complex */
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt klu\_malloc}, {\tt klu\_free}, {\tt klu\_realloc}:
+memory management}
+%-------------------------------------------------------------------------------
+
+KLU uses a set of wrapper routines for {\tt malloc}, {\tt free}, and {\tt
+realloc}. By default, these wrapper routines call the ANSI C versions of these
+functions. However, pointers to functions in {\tt Common} can be modified
+after calling {\tt klu\_defaults} to allow the use of other memory management
+functions (such as the MATLAB {\tt mxMalloc}, {\tt mxFree}, and {\tt
+mxRealloc}. These wrapper functions keep track of the current and peak memory
+usage of KLU. They can be called by the user.
+
+{\tt klu\_malloc} is essentially the same as {\tt p = malloc (n * sizeof
+(size))}, {\tt klu\_free} is essentially the same as {\tt free(p)} except that
+{\tt klu\_free} returns NULL which can then be assigned to {\tt p}. {\tt
+klu\_realloc} is similar to {\tt realloc}, except that if the reallocation
+fails, {\tt p} is returned unchanged. Failure conditions are returned in {\tt
+Common.status}.
+
+{\footnotesize
+\begin{verbatim}
+ #include "klu.h"
+ size_t n, nnew, nold, size ;
+ void *p ;
+ klu_common Common ;
+ p = klu_malloc (n, size, &Common) ;
+ p = klu_free (p, n, size, &Common) ;
+ p = klu_realloc (nnew, nold, size, p, &Common) ;
+
+
+ #include "klu.h"
+ size_t n, nnew, nold, size ;
+ void *p ;
+ klu_l_common Common ;
+ p = klu_l_malloc (n, size, &Common) ;
+ p = klu_l_free (p, n, size, &Common) ;
+ p = klu_l_realloc (nnew, nold, size, p, &Common) ;
+ \end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt btf\_maxtrans}: maximum transversal}
+%-------------------------------------------------------------------------------
+
+The BTF package includes three user-callable functions (each with {\tt int}
+and {\tt UF\_long} versions). They do not need to be called directly by an
+application that uses KLU. KLU will call these functions to perform the
+permutation into upper block triangular form.
+
+The {\tt btf\_maxtrans} function finds a column permutation {\tt Q} that gives
+{\tt A*Q} a zero-free diagonal, if one exists. If row {\tt i} is matched to
+column {\tt j}, then {\tt Match[i]=j}. If the matrix is structurally singular,
+there will be some unmatched rows. If row {\tt i} is unmatched, then {\tt
+Match[i]=-1}. If the matrix is square and structurally non-singular, then {\tt
+Q=Match} is the column permutation. The {\tt btf\_maxtrans} function can
+accept as input a rectangular matrix; it operates on the bipartite graph of
+{\tt A}. It returns the number of columns matched. Unlike the KLU
+user-callable functions, the BTF functions do not check its inputs at all; a
+segmentation fault will occur if any input pointers are NULL, for example.
+
+The function can require up to $O$({\tt n*nnz(A)}) time (excluding the {\em
+cheap match} phase, which takes another $O$({\tt nnz(A)}) time. If {\tt
+maxwork > 0} on input, the work is limited to $O$({\tt maxwork*nnz(A)})
+(excluding the cheap match), but the maximum transversal might not be found if
+the limit is reached.
+
+The {\tt Work} array is workspace required by the methods; its contents
+are undefined on input and output.
+
+{\footnotesize
+\begin{verbatim}
+ int nrow, ncol, Ap [ncol+1], Ai [nz], Match [nrow], Work [5*ncol], nmatch ;
+ double maxwork, work ;
+ nmatch = btf_maxtrans (nrow, ncol, Ap, Ai, maxwork, &work, Match, Work) ;
+
+
+ UF_long nrow, ncol, Ap [ncol+1], Ai [nz], Match [nrow], Work [5*ncol], nmatch ;
+ double maxwork, work ;
+ nmatch = btf_l_maxtrans (nrow, ncol, Ap, Ai, maxwork, &work, Match, Work) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt btf\_strongcomp}: strongly connected components}
+%-------------------------------------------------------------------------------
+
+The {\tt btf\_strongcomp} function finds the strongly connected components of a
+directed graph, returning a symmetric permutation {\tt P}. The matrix {\tt A}
+must be square. The diagonal of {\tt A} (or {\tt A*Q} if a column permutation
+is given on input) is ignored. If {\tt Q} is NULL on input, the matrix
+{\tt P*A*P'} is in upper block triangular form. Otherwise, {\tt Q} is modified
+on output so that {\tt P*A*Q} is in upper block triangular form. The vector
+{\tt R} gives the block boundaries, where the {\tt k}th block consists of
+rows and columns {\tt R[k]} through {\tt R[k+1]-1} in the permuted matrix.
+The function returns the number of strongly connected components found
+(the diagonal blocks in the block triangular form).
+
+{\footnotesize
+\begin{verbatim}
+ int n, Ap [n+1], Ai [nz], Q [n], P [n], R [n+1], Work [4*n], ncomp ;
+ ncomp = btf_strongcomp (n, Ap, Ai, Q, P, R, Work) ;
+
+
+ UF_long n, Ap [n+1], Ai [nz], Q [n], P [n], R [n+1], Work [4*n], ncomp ;
+ ncomp = btf_l_strongcomp (n, Ap, Ai, Q, P, R, Work) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{{\tt btf\_order}: permutation to block triangular form}
+%-------------------------------------------------------------------------------
+
+
+The {\tt btf\_order} function combines the above two functions, first finding a
+maximum transversal and then permuting the resulting matrix into upper block
+triangular form. Unlike {\tt dmperm} in MATLAB, it always reveals the maximum
+matching along the diagonal, even if the matrix is structurally singular.
+
+On output, {\tt P} and {\tt Q} are the row and column permutations, where
+{\tt i = P[k]} if row {\tt i} of {\tt A} is the {\tt k}th row of {\tt P*A*Q},
+and {\tt j = BTF\_UNFLIP(Q[k])} if column {\tt j} of {\tt A} is the {\tt k}th
+column of {\tt P*A*Q}. If {\tt Q[k] < 0}, then the {\tt (k,k)}th entry in
+{\tt P*A*Q} is structurally zero. The vector {\tt R}, and the return value,
+are the same as {\tt btf\_strongcomp}.
+
+{\footnotesize
+\begin{verbatim}
+ int n, Ap [n+1], Ai [nz], P [n], Q [n], R [n+1], nfound, Work [5*n], ncomp, nfound ;
+ double maxwork, work ;
+ ncomp = btf_order (n, Ap, Ai, maxwork, &work, P, Q, R, &nfound, Work) ;
+
+
+ UF_long n, Ap [n+1], Ai [nz], P [n], Q [n], R [n+1], nfound, Work [5*n], ncomp, nfound ;
+ double maxwork, work ;
+ ncomp = btf_l_order (n, Ap, Ai, maxwork, &work, P, Q, R, &nfound, Work) ;
+\end{verbatim}
+}
+
+%------------------------------------------------------------------------------
+\subsection{Sample C programs that use KLU}
+%------------------------------------------------------------------------------
+
+Here is a simple main program, {\tt klu\_simple.c}, that illustrates the basic
+usage of KLU. It uses KLU, and indirectly makes use of BTF and AMD. COLAMD is
+required to compile the demo, but it is not called by this example. It uses
+statically defined global variables for the sparse matrix {\tt A}, which would
+not be typical of a complete application. It just makes for a simpler example.
+
+{\footnotesize
+\input{klu_simple_c.tex}
+}
+
+The {\tt Ap}, {\tt Ai}, and {\tt Ax} arrays represent the matrix
+\[
+A = \left[
+\begin{array}{ccccc}
+ 2 & 3 & 0 & 0 & 0 \\
+ 3 & 0 & 4 & 0 & 6 \\
+ 0 & -1 & -3 & 2 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 4 & 2 & 0 & 1 \\
+\end{array}
+\right].
+\]
+The solution to $Ax=b$ is $x = [1 \, 2 \, 3 \, 4 \, 5]^T$. The program
+uses default control settings (no scaling, permutation to block triangular
+form, and the AMD ordering). It ignores the error codes in the return values
+and {\tt Common.status}.
+
+The block triangular form found by {\tt btf\_order} for this matrix is
+given below
+\[
+PAQ = \left[
+\begin{array}{c|ccc|c}
+2 & 0 & 0 & -1 & -3 \\
+\hline
+ & 2 & 0 & 3 & 0 \\
+ & 3 & 6 & 0 & 4 \\
+ & 0 & 1 & 4 & 1 \\
+\hline
+ & & & & 1 \\
+\end{array}
+\right].
+\]
+This ordering is not modified by the AMD ordering because the 3-by-3 matrix
+$A_{22} + A_{22}^T$ happens to be a dense matrix. No partial pivoting happens
+to occur during LU factorization; all pivots are selected along the diagonal of
+each block. The matrix contains two singletons, which are the original entries
+$a_{34}=2$ and $a_{43}=1$, and one 3-by-3 diagonal block (in which a single
+fill-in entry occurs during factorization: the $u_{23}$ entry of this 3-by-3
+matrix).
+
+For a more complete program that uses KLU, see {\tt KLU/Demo/kludemo.c} for an
+{\tt int} version, and {\tt KLU/Demo/kluldemo.c} for a version that uses {\tt
+UF\_long} instead. The top-level main routine uses CHOLMOD to read in a
+compressed-column sparse matrix from a Matrix Market file, because KLU does not
+include such a function. Otherwise, no CHOLMOD functions are used. Unlike
+{\tt klu\_simple.c}, CHOLMOD is required to run the {\tt kludemo.c} and {\tt
+kluldemo.c} programs.
+
+%------------------------------------------------------------------------------
+\section{Installation}
+\label{Install}
+%------------------------------------------------------------------------------
+
+Installation of the C-callable interface requires the {\tt make} utility, in
+Linux/Unix. Alternatively, you can use the Cygwin {\tt make} in Windows.
+The MATLAB installation in any platform, including Windows is simple; just
+type {\tt klu\_install} to compile and install KLU, BTF, AMD, and COLAMD.
+
+For {\tt make}, system-dependent configurations are in the {\tt
+../UFconfig/UFconfig.mk} file. You can edit that file to customize the
+compilation. The default settings will work on most systems. Sample
+configuration files are provided for Linux, Sun Solaris, SGI IRIX, IBM AIX, and
+the DEC/Compaq Alpha.
+
+To compile and install the C-callable KLU, BTF, AMD, and COLAMD libraries, go
+to the {\tt KLU} directory and type {\tt make}. The KLU and BTF libraries are
+placed in {\tt KLU/Lib/libklu.a} and {\tt BTF/Lib/libbtf.a}. Two KLU demo
+programs will be compiled and tested in the {\tt KLU/Demo} directory. You can
+compare the output of {\tt make} with the results in the KLU distribution, {\tt
+kludemo.out}.
+
+Typing {\tt make clean} will remove all but the final compiled libraries and
+demo programs. Typing {\tt make purge} or {\tt make distclean} removes all
+files not in the original distribution. If you compile KLU or BTF and then
+later change the {\tt ../UFconfig/UFconfig.mk} file then you should type {\tt
+make purge} and then {\tt make} to recompile.
+
+When you compile your program that uses the C-callable KLU library, you need to
+add the {\tt KLU/Lib/libklu.a}, {\tt BTF/Lib/libbtf.a}, {\tt AMD/Lib/libamd.a},
+and {\tt COLAMD/Lib/libamd.a} libraries, a nd you need to tell your compiler to
+look in the {\tt KLU/Include} and {\tt BTF/Include} directory for include
+files.
+
+If all you want to use is the KLU mexFunction in MATLAB, you can skip the use
+of the {\tt make} command entirely. Simply type {\tt klu\_install} in the
+MATLAB command window while in the {\tt KLU/MATLAB} directory. This works on
+any system with MATLAB, including Windows. Alternately, type {\tt make} in the
+{\tt KLU/MATLAB} directory.
+
+If you have MATLAB 7.2 or earlier, you must first edit UFconfig/UFconfig.h to
+remove the {\tt -largeArrayDims} option from the {\tt MEX} command, prior to
+{\tt make mex} or {\tt make} in the MATLAB directory (or just use {\tt
+klu\_install.m} inside MATLAB, which handles this case).
+
+%------------------------------------------------------------------------------
+\newpage
+\section{The KLU routines}
+\label{klu_include}
+%------------------------------------------------------------------------------
+
+The file {\tt KLU/Include/klu.h} listed below describes each user-callable
+routine in the C version of KLU, and gives details on their use.
+
+{\footnotesize
+\input{klu_h.tex}
+}
+
+%------------------------------------------------------------------------------
+\newpage
+\section{The BTF routines}
+\label{btf_include}
+%------------------------------------------------------------------------------
+
+The file {\tt BTF/Include/btf.h} listed below describes each user-callable
+routine in the C version of BTF, and gives details on their use.
+
+{\footnotesize
+\input{btf_h.tex}
+}
+
+%------------------------------------------------------------------------------
+\newpage
+% References
+%------------------------------------------------------------------------------
+
+\bibliographystyle{plain}
+\bibliography{KLU_UserGuide}
+
+\end{document}
diff --git a/KLU/Doc/Makefile b/KLU/Doc/Makefile
new file mode 100644
index 0000000..daa0c1e
--- /dev/null
+++ b/KLU/Doc/Makefile
@@ -0,0 +1,44 @@
+#------------------------------------------------------------------------------
+# KLU Makefile for creating the user guide
+#------------------------------------------------------------------------------
+
+default: dist
+
+include ../../UFconfig/UFconfig.mk
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+
+#------------------------------------------------------------------------------
+# Create the User Guide and Quick Start Guide
+#------------------------------------------------------------------------------
+
+KLU_UserGuide.pdf: KLU_UserGuide.tex KLU_UserGuide.bib \
+ ../Include/klu.h ../../BTF/Include/btf.h
+ echo '\begin{verbatim}' > klu_h.tex
+ expand -8 ../Include/klu.h >> klu_h.tex
+ echo '\end{verbatim}' >> klu_h.tex
+ echo '\begin{verbatim}' > btf_h.tex
+ expand -8 ../../BTF/Include/btf.h >> btf_h.tex
+ echo '\end{verbatim}' >> btf_h.tex
+ echo '\begin{verbatim}' > klu_simple_c.tex
+ expand -8 ../Demo/klu_simple.c >> klu_simple_c.tex
+ echo '\end{verbatim}' >> klu_simple_c.tex
+ pdflatex KLU_UserGuide
+ bibtex KLU_UserGuide
+ pdflatex KLU_UserGuide
+ pdflatex KLU_UserGuide
+
+dist: KLU_UserGuide.pdf
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+ - $(RM) klu_simple_c.tex klu_h.tex btf_h.tex
+
diff --git a/KLU/Doc/lesser.txt b/KLU/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/KLU/Doc/lesser.txt
@@ -0,0 +1,504 @@
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+SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
+DAMAGES.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Libraries
+
+ If you develop a new library, and you want it to be of the greatest
+possible use to the public, we recommend making it free software that
+everyone can redistribute and change. You can do so by permitting
+redistribution under these terms (or, alternatively, under the terms of the
+ordinary General Public License).
+
+ To apply these terms, attach the following notices to the library. It is
+safest to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least the
+"copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the library's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+Also add information on how to contact you by electronic and paper mail.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the library, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the
+ library `Frob' (a library for tweaking knobs) written by James Random Hacker.
+
+ <signature of Ty Coon>, 1 April 1990
+ Ty Coon, President of Vice
+
+That's all there is to it!
+
+
diff --git a/KLU/Doc/palamadai_e.pdf b/KLU/Doc/palamadai_e.pdf
new file mode 100644
index 0000000..6896e0e
Binary files /dev/null and b/KLU/Doc/palamadai_e.pdf differ
diff --git a/KLU/Include/klu.h b/KLU/Include/klu.h
new file mode 100644
index 0000000..867ed42
--- /dev/null
+++ b/KLU/Include/klu.h
@@ -0,0 +1,831 @@
+/* ========================================================================== */
+/* === klu include file ===================================================== */
+/* ========================================================================== */
+
+/* Include file for user programs that call klu_* routines */
+
+#ifndef _KLU_H
+#define _KLU_H
+
+/* make it easy for C++ programs to include KLU */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include "amd.h"
+#include "colamd.h"
+#include "btf.h"
+
+/* -------------------------------------------------------------------------- */
+/* Symbolic object - contains the pre-ordering computed by klu_analyze */
+/* -------------------------------------------------------------------------- */
+
+typedef struct
+{
+ /* A (P,Q) is in upper block triangular form. The kth block goes from
+ * row/col index R [k] to R [k+1]-1. The estimated number of nonzeros
+ * in the L factor of the kth block is Lnz [k].
+ */
+
+ /* only computed if the AMD ordering is chosen: */
+ double symmetry ; /* symmetry of largest block */
+ double est_flops ; /* est. factorization flop count */
+ double lnz, unz ; /* estimated nz in L and U, including diagonals */
+ double *Lnz ; /* size n, but only Lnz [0..nblocks-1] is used */
+
+ /* computed for all orderings: */
+ int
+ n, /* input matrix A is n-by-n */
+ nz, /* # entries in input matrix */
+ *P, /* size n */
+ *Q, /* size n */
+ *R, /* size n+1, but only R [0..nblocks] is used */
+ nzoff, /* nz in off-diagonal blocks */
+ nblocks, /* number of blocks */
+ maxblock, /* size of largest block */
+ ordering, /* ordering used (AMD, COLAMD, or GIVEN) */
+ do_btf ; /* whether or not BTF preordering was requested */
+
+ /* only computed if BTF preordering requested */
+ int structural_rank ; /* 0 to n-1 if the matrix is structurally rank
+ * deficient. -1 if not computed. n if the matrix has
+ * full structural rank */
+
+} klu_symbolic ;
+
+typedef struct /* 64-bit version (otherwise same as above) */
+{
+ double symmetry, est_flops, lnz, unz ;
+ double *Lnz ;
+ UF_long n, nz, *P, *Q, *R, nzoff, nblocks, maxblock, ordering, do_btf,
+ structural_rank ;
+
+} klu_l_symbolic ;
+
+/* -------------------------------------------------------------------------- */
+/* Numeric object - contains the factors computed by klu_factor */
+/* -------------------------------------------------------------------------- */
+
+typedef struct
+{
+ /* LU factors of each block, the pivot row permutation, and the
+ * entries in the off-diagonal blocks */
+
+ int n ; /* A is n-by-n */
+ int nblocks ; /* number of diagonal blocks */
+ int lnz ; /* actual nz in L, including diagonal */
+ int unz ; /* actual nz in U, including diagonal */
+ int max_lnz_block ; /* max actual nz in L in any one block, incl. diag */
+ int max_unz_block ; /* max actual nz in U in any one block, incl. diag */
+ int *Pnum ; /* size n. final pivot permutation */
+ int *Pinv ; /* size n. inverse of final pivot permutation */
+
+ /* LU factors of each block */
+ int *Lip ; /* size n. pointers into LUbx[block] for L */
+ int *Uip ; /* size n. pointers into LUbx[block] for U */
+ int *Llen ; /* size n. Llen [k] = # of entries in kth column of L */
+ int *Ulen ; /* size n. Ulen [k] = # of entries in kth column of U */
+ void **LUbx ; /* L and U indices and entries (excl. diagonal of U) */
+ size_t *LUsize ; /* size of each LUbx [block], in sizeof (Unit) */
+ void *Udiag ; /* diagonal of U */
+
+ /* scale factors; can be NULL if no scaling */
+ double *Rs ; /* size n. Rs [i] is scale factor for row i */
+
+ /* permanent workspace for factorization and solve */
+ size_t worksize ; /* size (in bytes) of Work */
+ void *Work ; /* workspace */
+ void *Xwork ; /* alias into Numeric->Work */
+ int *Iwork ; /* alias into Numeric->Work */
+
+ /* off-diagonal entries in a conventional compressed-column sparse matrix */
+ int *Offp ; /* size n+1, column pointers */
+ int *Offi ; /* size nzoff, row indices */
+ void *Offx ; /* size nzoff, numerical values */
+ int nzoff ;
+
+} klu_numeric ;
+
+typedef struct /* 64-bit version (otherwise same as above) */
+{
+ UF_long n, nblocks, lnz, unz, max_lnz_block, max_unz_block, *Pnum, *Pinv,
+ *Lip, *Uip, *Llen, *Ulen ;
+ void **LUbx ;
+ size_t *LUsize ;
+ void *Udiag ;
+ double *Rs ;
+ size_t worksize ;
+ void *Work, *Xwork ;
+ UF_long *Iwork ;
+ UF_long *Offp, *Offi ;
+ void *Offx ;
+ UF_long nzoff ;
+
+} klu_l_numeric ;
+
+/* -------------------------------------------------------------------------- */
+/* KLU control parameters and statistics */
+/* -------------------------------------------------------------------------- */
+
+/* Common->status values */
+#define KLU_OK 0
+#define KLU_SINGULAR (1) /* status > 0 is a warning, not an error */
+#define KLU_OUT_OF_MEMORY (-2)
+#define KLU_INVALID (-3)
+#define KLU_TOO_LARGE (-4) /* integer overflow has occured */
+
+typedef struct klu_common_struct
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* parameters */
+ /* ---------------------------------------------------------------------- */
+
+ double tol ; /* pivot tolerance for diagonal preference */
+ double memgrow ; /* realloc memory growth size for LU factors */
+ double initmem_amd ; /* init. memory size with AMD: c*nnz(L) + n */
+ double initmem ; /* init. memory size: c*nnz(A) + n */
+ double maxwork ; /* maxwork for BTF, <= 0 if no limit */
+
+ int btf ; /* use BTF pre-ordering, or not */
+ int ordering ; /* 0: AMD, 1: COLAMD, 2: user P and Q,
+ * 3: user function */
+ int scale ; /* row scaling: -1: none (and no error check),
+ * 0: none, 1: sum, 2: max */
+
+ /* memory management routines */
+ void *(*malloc_memory) (size_t) ; /* pointer to malloc */
+ void *(*realloc_memory) (void *, size_t) ; /* pointer to realloc */
+ void (*free_memory) (void *) ; /* pointer to free */
+ void *(*calloc_memory) (size_t, size_t) ; /* pointer to calloc */
+
+ /* pointer to user ordering function */
+ int (*user_order) (int, int *, int *, int *, struct klu_common_struct *) ;
+
+ /* pointer to user data, passed unchanged as the last parameter to the
+ * user ordering function (optional, the user function need not use this
+ * information). */
+ void *user_data ;
+
+ int halt_if_singular ; /* how to handle a singular matrix:
+ * FALSE: keep going. Return a Numeric object with a zero U(k,k). A
+ * divide-by-zero may occur when computing L(:,k). The Numeric object
+ * can be passed to klu_solve (a divide-by-zero will occur). It can
+ * also be safely passed to klu_refactor.
+ * TRUE: stop quickly. klu_factor will free the partially-constructed
+ * Numeric object. klu_refactor will not free it, but will leave the
+ * numerical values only partially defined. This is the default. */
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics */
+ /* ---------------------------------------------------------------------- */
+
+ int status ; /* KLU_OK if OK, < 0 if error */
+ int nrealloc ; /* # of reallocations of L and U */
+
+ int structural_rank ; /* 0 to n-1 if the matrix is structurally rank
+ * deficient (as determined by maxtrans). -1 if not computed. n if the
+ * matrix has full structural rank. This is computed by klu_analyze
+ * if a BTF preordering is requested. */
+
+ int numerical_rank ; /* First k for which a zero U(k,k) was found,
+ * if the matrix was singular (in the range 0 to n-1). n if the matrix
+ * has full rank. This is not a true rank-estimation. It just reports
+ * where the first zero pivot was found. -1 if not computed.
+ * Computed by klu_factor and klu_refactor. */
+
+ int singular_col ; /* n if the matrix is not singular. If in the
+ * range 0 to n-1, this is the column index of the original matrix A that
+ * corresponds to the column of U that contains a zero diagonal entry.
+ * -1 if not computed. Computed by klu_factor and klu_refactor. */
+
+ int noffdiag ; /* # of off-diagonal pivots, -1 if not computed */
+
+ double flops ; /* actual factorization flop count, from klu_flops */
+ double rcond ; /* crude reciprocal condition est., from klu_rcond */
+ double condest ; /* accurate condition est., from klu_condest */
+ double rgrowth ; /* reciprocal pivot rgrowth, from klu_rgrowth */
+ double work ; /* actual work done in BTF, in klu_analyze */
+
+ size_t memusage ; /* current memory usage, in bytes */
+ size_t mempeak ; /* peak memory usage, in bytes */
+
+} klu_common ;
+
+typedef struct klu_l_common_struct /* 64-bit version (otherwise same as above)*/
+{
+
+ double tol, memgrow, initmem_amd, initmem, maxwork ;
+ UF_long btf, ordering, scale ;
+ void *(*malloc_memory) (size_t) ;
+ void *(*realloc_memory) (void *, size_t) ;
+ void (*free_memory) (void *) ;
+ void *(*calloc_memory) (size_t, size_t) ;
+ UF_long (*user_order) (UF_long, UF_long *, UF_long *, UF_long *,
+ struct klu_l_common_struct *) ;
+ void *user_data ;
+ UF_long halt_if_singular ;
+ UF_long status, nrealloc, structural_rank, numerical_rank, singular_col,
+ noffdiag ;
+ double flops, rcond, condest, rgrowth, work ;
+ size_t memusage, mempeak ;
+
+} klu_l_common ;
+
+/* -------------------------------------------------------------------------- */
+/* klu_defaults: sets default control parameters */
+/* -------------------------------------------------------------------------- */
+
+int klu_defaults
+(
+ klu_common *Common
+) ;
+
+UF_long klu_l_defaults (klu_l_common *Common) ;
+
+/* -------------------------------------------------------------------------- */
+/* klu_analyze: orders and analyzes a matrix */
+/* -------------------------------------------------------------------------- */
+
+/* Order the matrix with BTF (or not), then order each block with AMD, COLAMD,
+ * a natural ordering, or with a user-provided ordering function */
+
+klu_symbolic *klu_analyze
+(
+ /* inputs, not modified */
+ int n, /* A is n-by-n */
+ int Ap [ ], /* size n+1, column pointers */
+ int Ai [ ], /* size nz, row indices */
+ klu_common *Common
+) ;
+
+klu_l_symbolic *klu_l_analyze (UF_long, UF_long *, UF_long *,
+ klu_l_common *Common) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_analyze_given: analyzes a matrix using given P and Q */
+/* -------------------------------------------------------------------------- */
+
+/* Order the matrix with BTF (or not), then use natural or given ordering
+ * P and Q on the blocks. P and Q are interpretted as identity
+ * if NULL. */
+
+klu_symbolic *klu_analyze_given
+(
+ /* inputs, not modified */
+ int n, /* A is n-by-n */
+ int Ap [ ], /* size n+1, column pointers */
+ int Ai [ ], /* size nz, row indices */
+ int P [ ], /* size n, user's row permutation (may be NULL) */
+ int Q [ ], /* size n, user's column permutation (may be NULL) */
+ klu_common *Common
+) ;
+
+klu_l_symbolic *klu_l_analyze_given (UF_long, UF_long *, UF_long *, UF_long *,
+ UF_long *, klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_factor: factors a matrix using the klu_analyze results */
+/* -------------------------------------------------------------------------- */
+
+klu_numeric *klu_factor /* returns KLU_OK if OK, < 0 if error */
+(
+ /* inputs, not modified */
+ int Ap [ ], /* size n+1, column pointers */
+ int Ai [ ], /* size nz, row indices */
+ double Ax [ ], /* size nz, numerical values */
+ klu_symbolic *Symbolic,
+ klu_common *Common
+) ;
+
+klu_numeric *klu_z_factor /* returns KLU_OK if OK, < 0 if error */
+(
+ /* inputs, not modified */
+ int Ap [ ], /* size n+1, column pointers */
+ int Ai [ ], /* size nz, row indices */
+ double Ax [ ], /* size 2*nz, numerical values (real,imag pairs) */
+ klu_symbolic *Symbolic,
+ klu_common *Common
+) ;
+
+/* long / real version */
+klu_l_numeric *klu_l_factor (UF_long *, UF_long *, double *, klu_l_symbolic *,
+ klu_l_common *) ;
+
+/* long / complex version */
+klu_l_numeric *klu_zl_factor (UF_long *, UF_long *, double *, klu_l_symbolic *,
+ klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_solve: solves Ax=b using the Symbolic and Numeric objects */
+/* -------------------------------------------------------------------------- */
+
+int klu_solve
+(
+ /* inputs, not modified */
+ klu_symbolic *Symbolic,
+ klu_numeric *Numeric,
+ int ldim, /* leading dimension of B */
+ int nrhs, /* number of right-hand-sides */
+
+ /* right-hand-side on input, overwritten with solution to Ax=b on output */
+ double B [ ], /* size ldim*nrhs */
+ klu_common *Common
+) ;
+
+int klu_z_solve
+(
+ /* inputs, not modified */
+ klu_symbolic *Symbolic,
+ klu_numeric *Numeric,
+ int ldim, /* leading dimension of B */
+ int nrhs, /* number of right-hand-sides */
+
+ /* right-hand-side on input, overwritten with solution to Ax=b on output */
+ double B [ ], /* size 2*ldim*nrhs */
+ klu_common *Common
+) ;
+
+UF_long klu_l_solve (klu_l_symbolic *, klu_l_numeric *, UF_long, UF_long,
+ double *, klu_l_common *) ;
+
+UF_long klu_zl_solve (klu_l_symbolic *, klu_l_numeric *, UF_long, UF_long,
+ double *, klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_tsolve: solves A'x=b using the Symbolic and Numeric objects */
+/* -------------------------------------------------------------------------- */
+
+int klu_tsolve
+(
+ /* inputs, not modified */
+ klu_symbolic *Symbolic,
+ klu_numeric *Numeric,
+ int ldim, /* leading dimension of B */
+ int nrhs, /* number of right-hand-sides */
+
+ /* right-hand-side on input, overwritten with solution to Ax=b on output */
+ double B [ ], /* size ldim*nrhs */
+ klu_common *Common
+) ;
+
+int klu_z_tsolve
+(
+ /* inputs, not modified */
+ klu_symbolic *Symbolic,
+ klu_numeric *Numeric,
+ int ldim, /* leading dimension of B */
+ int nrhs, /* number of right-hand-sides */
+
+ /* right-hand-side on input, overwritten with solution to Ax=b on output */
+ double B [ ], /* size 2*ldim*nrhs */
+ int conj_solve, /* TRUE: conjugate solve, FALSE: solve A.'x=b */
+ klu_common *Common
+
+) ;
+
+UF_long klu_l_tsolve (klu_l_symbolic *, klu_l_numeric *, UF_long, UF_long,
+ double *, klu_l_common *) ;
+
+UF_long klu_zl_tsolve (klu_l_symbolic *, klu_l_numeric *, UF_long, UF_long,
+ double *, UF_long, klu_l_common * ) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_refactor: refactorizes matrix with same ordering as klu_factor */
+/* -------------------------------------------------------------------------- */
+
+int klu_refactor /* return TRUE if successful, FALSE otherwise */
+(
+ /* inputs, not modified */
+ int Ap [ ], /* size n+1, column pointers */
+ int Ai [ ], /* size nz, row indices */
+ double Ax [ ], /* size nz, numerical values */
+ klu_symbolic *Symbolic,
+ /* input, and numerical values modified on output */
+ klu_numeric *Numeric,
+ klu_common *Common
+) ;
+
+int klu_z_refactor /* return TRUE if successful, FALSE otherwise */
+(
+ /* inputs, not modified */
+ int Ap [ ], /* size n+1, column pointers */
+ int Ai [ ], /* size nz, row indices */
+ double Ax [ ], /* size 2*nz, numerical values */
+ klu_symbolic *Symbolic,
+ /* input, and numerical values modified on output */
+ klu_numeric *Numeric,
+ klu_common *Common
+) ;
+
+UF_long klu_l_refactor (UF_long *, UF_long *, double *, klu_l_symbolic *,
+ klu_l_numeric *, klu_l_common *) ;
+
+UF_long klu_zl_refactor (UF_long *, UF_long *, double *, klu_l_symbolic *,
+ klu_l_numeric *, klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_free_symbolic: destroys the Symbolic object */
+/* -------------------------------------------------------------------------- */
+
+int klu_free_symbolic
+(
+ klu_symbolic **Symbolic,
+ klu_common *Common
+) ;
+
+UF_long klu_l_free_symbolic (klu_l_symbolic **, klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_free_numeric: destroys the Numeric object */
+/* -------------------------------------------------------------------------- */
+
+/* Note that klu_free_numeric and klu_z_free_numeric are identical; each can
+ * free both kinds of Numeric objects (real and complex) */
+
+int klu_free_numeric
+(
+ klu_numeric **Numeric,
+ klu_common *Common
+) ;
+
+int klu_z_free_numeric
+(
+ klu_numeric **Numeric,
+ klu_common *Common
+) ;
+
+UF_long klu_l_free_numeric (klu_l_numeric **, klu_l_common *) ;
+UF_long klu_zl_free_numeric (klu_l_numeric **, klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_sort: sorts the columns of the LU factorization */
+/* -------------------------------------------------------------------------- */
+
+/* this is not needed except for the MATLAB interface */
+
+int klu_sort
+(
+ /* inputs, not modified */
+ klu_symbolic *Symbolic,
+ /* input/output */
+ klu_numeric *Numeric,
+ klu_common *Common
+) ;
+
+int klu_z_sort
+(
+ /* inputs, not modified */
+ klu_symbolic *Symbolic,
+ /* input/output */
+ klu_numeric *Numeric,
+ klu_common *Common
+) ;
+
+UF_long klu_l_sort (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ;
+UF_long klu_zl_sort (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_flops: determines # of flops performed in numeric factorzation */
+/* -------------------------------------------------------------------------- */
+
+int klu_flops
+(
+ /* inputs, not modified */
+ klu_symbolic *Symbolic,
+ klu_numeric *Numeric,
+ /* input/output */
+ klu_common *Common
+) ;
+
+int klu_z_flops
+(
+ /* inputs, not modified */
+ klu_symbolic *Symbolic,
+ klu_numeric *Numeric,
+ /* input/output */
+ klu_common *Common
+) ;
+
+UF_long klu_l_flops (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ;
+UF_long klu_zl_flops (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ;
+
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_rgrowth : compute the reciprocal pivot growth */
+/* -------------------------------------------------------------------------- */
+
+/* Pivot growth is computed after the input matrix is permuted, scaled, and
+ * off-diagonal entries pruned. This is because the LU factorization of each
+ * block takes as input the scaled diagonal blocks of the BTF form. The
+ * reciprocal pivot growth in column j of an LU factorization of a matrix C
+ * is the largest entry in C divided by the largest entry in U; then the overall
+ * reciprocal pivot growth is the smallest such value for all columns j. Note
+ * that the off-diagonal entries are not scaled, since they do not take part in
+ * the LU factorization of the diagonal blocks.
+ *
+ * In MATLAB notation:
+ *
+ * rgrowth = min (max (abs ((R \ A(p,q)) - F)) ./ max (abs (U))) */
+
+int klu_rgrowth
+(
+ int Ap [ ],
+ int Ai [ ],
+ double Ax [ ],
+ klu_symbolic *Symbolic,
+ klu_numeric *Numeric,
+ klu_common *Common /* Common->rgrowth = reciprocal pivot growth */
+) ;
+
+int klu_z_rgrowth
+(
+ int Ap [ ],
+ int Ai [ ],
+ double Ax [ ],
+ klu_symbolic *Symbolic,
+ klu_numeric *Numeric,
+ klu_common *Common /* Common->rgrowth = reciprocal pivot growth */
+) ;
+
+UF_long klu_l_rgrowth (UF_long *, UF_long *, double *, klu_l_symbolic *,
+ klu_l_numeric *, klu_l_common *) ;
+
+UF_long klu_zl_rgrowth (UF_long *, UF_long *, double *, klu_l_symbolic *,
+ klu_l_numeric *, klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_condest */
+/* -------------------------------------------------------------------------- */
+
+/* Computes a reasonably accurate estimate of the 1-norm condition number, using
+ * Hager's method, as modified by Higham and Tisseur (same method as used in
+ * MATLAB's condest */
+
+int klu_condest
+(
+ int Ap [ ], /* size n+1, column pointers, not modified */
+ double Ax [ ], /* size nz = Ap[n], numerical values, not modified*/
+ klu_symbolic *Symbolic, /* symbolic analysis, not modified */
+ klu_numeric *Numeric, /* numeric factorization, not modified */
+ klu_common *Common /* result returned in Common->condest */
+) ;
+
+int klu_z_condest
+(
+ int Ap [ ],
+ double Ax [ ], /* size 2*nz */
+ klu_symbolic *Symbolic,
+ klu_numeric *Numeric,
+ klu_common *Common /* result returned in Common->condest */
+) ;
+
+UF_long klu_l_condest (UF_long *, double *, klu_l_symbolic *, klu_l_numeric *,
+ klu_l_common *) ;
+
+UF_long klu_zl_condest (UF_long *, double *, klu_l_symbolic *, klu_l_numeric *,
+ klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_rcond: compute min(abs(diag(U))) / max(abs(diag(U))) */
+/* -------------------------------------------------------------------------- */
+
+int klu_rcond
+(
+ klu_symbolic *Symbolic, /* input, not modified */
+ klu_numeric *Numeric, /* input, not modified */
+ klu_common *Common /* result in Common->rcond */
+) ;
+
+int klu_z_rcond
+(
+ klu_symbolic *Symbolic, /* input, not modified */
+ klu_numeric *Numeric, /* input, not modified */
+ klu_common *Common /* result in Common->rcond */
+) ;
+
+UF_long klu_l_rcond (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ;
+
+UF_long klu_zl_rcond (klu_l_symbolic *, klu_l_numeric *, klu_l_common *) ;
+
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_scale */
+/* -------------------------------------------------------------------------- */
+
+int klu_scale /* return TRUE if successful, FALSE otherwise */
+(
+ /* inputs, not modified */
+ int scale, /* <0: none, no error check; 0: none, 1: sum, 2: max */
+ int n,
+ int Ap [ ], /* size n+1, column pointers */
+ int Ai [ ], /* size nz, row indices */
+ double Ax [ ],
+ /* outputs, not defined on input */
+ double Rs [ ],
+ /* workspace, not defined on input or output */
+ int W [ ], /* size n, can be NULL */
+ klu_common *Common
+) ;
+
+int klu_z_scale /* return TRUE if successful, FALSE otherwise */
+(
+ /* inputs, not modified */
+ int scale, /* <0: none, no error check; 0: none, 1: sum, 2: max */
+ int n,
+ int Ap [ ], /* size n+1, column pointers */
+ int Ai [ ], /* size nz, row indices */
+ double Ax [ ],
+ /* outputs, not defined on input */
+ double Rs [ ],
+ /* workspace, not defined on input or output */
+ int W [ ], /* size n, can be NULL */
+ klu_common *Common
+) ;
+
+UF_long klu_l_scale (UF_long, UF_long, UF_long *, UF_long *, double *,
+ double *, UF_long *, klu_l_common *) ;
+
+UF_long klu_zl_scale (UF_long, UF_long, UF_long *, UF_long *, double *,
+ double *, UF_long *, klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* klu_extract */
+/* -------------------------------------------------------------------------- */
+
+int klu_extract /* returns TRUE if successful, FALSE otherwise */
+(
+ /* inputs: */
+ klu_numeric *Numeric,
+ klu_symbolic *Symbolic,
+
+ /* outputs, either allocated on input, or ignored otherwise */
+
+ /* L */
+ int *Lp, /* size n+1 */
+ int *Li, /* size Numeric->lnz */
+ double *Lx, /* size Numeric->lnz */
+
+ /* U */
+ int *Up, /* size n+1 */
+ int *Ui, /* size Numeric->unz */
+ double *Ux, /* size Numeric->unz */
+
+ /* F */
+ int *Fp, /* size n+1 */
+ int *Fi, /* size Numeric->nzoff */
+ double *Fx, /* size Numeric->nzoff */
+
+ /* P, row permutation */
+ int *P, /* size n */
+
+ /* Q, column permutation */
+ int *Q, /* size n */
+
+ /* Rs, scale factors */
+ double *Rs, /* size n */
+
+ /* R, block boundaries */
+ int *R, /* size Symbolic->nblocks+1 (nblocks is at most n) */
+
+ klu_common *Common
+) ;
+
+
+int klu_z_extract /* returns TRUE if successful, FALSE otherwise */
+(
+ /* inputs: */
+ klu_numeric *Numeric,
+ klu_symbolic *Symbolic,
+
+ /* outputs, all of which must be allocated on input */
+
+ /* L */
+ int *Lp, /* size n+1 */
+ int *Li, /* size nnz(L) */
+ double *Lx, /* size nnz(L) */
+ double *Lz, /* size nnz(L) for the complex case, ignored if real */
+
+ /* U */
+ int *Up, /* size n+1 */
+ int *Ui, /* size nnz(U) */
+ double *Ux, /* size nnz(U) */
+ double *Uz, /* size nnz(U) for the complex case, ignored if real */
+
+ /* F */
+ int *Fp, /* size n+1 */
+ int *Fi, /* size nnz(F) */
+ double *Fx, /* size nnz(F) */
+ double *Fz, /* size nnz(F) for the complex case, ignored if real */
+
+ /* P, row permutation */
+ int *P, /* size n */
+
+ /* Q, column permutation */
+ int *Q, /* size n */
+
+ /* Rs, scale factors */
+ double *Rs, /* size n */
+
+ /* R, block boundaries */
+ int *R, /* size Symbolic->nblocks+1 (nblocks is at most n) */
+
+ klu_common *Common
+) ;
+
+UF_long klu_l_extract (klu_l_numeric *, klu_l_symbolic *,
+ UF_long *, UF_long *, double *,
+ UF_long *, UF_long *, double *,
+ UF_long *, UF_long *, double *,
+ UF_long *, UF_long *, double *, UF_long *, klu_l_common *) ;
+
+UF_long klu_zl_extract (klu_l_numeric *, klu_l_symbolic *,
+ UF_long *, UF_long *, double *, double *,
+ UF_long *, UF_long *, double *, double *,
+ UF_long *, UF_long *, double *, double *,
+ UF_long *, UF_long *, double *, UF_long *, klu_l_common *) ;
+
+
+/* -------------------------------------------------------------------------- */
+/* KLU memory management routines */
+/* -------------------------------------------------------------------------- */
+
+void *klu_malloc /* returns pointer to the newly malloc'd block */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ klu_common *Common
+) ;
+
+void *klu_free /* always returns NULL */
+(
+ /* ---- in/out --- */
+ void *p, /* block of memory to free */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ klu_common *Common
+) ;
+
+void *klu_realloc /* returns pointer to reallocated block */
+(
+ /* ---- input ---- */
+ size_t nnew, /* requested # of items in reallocated block */
+ size_t nold, /* current size of block, in # of items */
+ size_t size, /* size of each item */
+ /* ---- in/out --- */
+ void *p, /* block of memory to realloc */
+ /* --------------- */
+ klu_common *Common
+) ;
+
+void *klu_l_malloc (size_t, size_t, klu_l_common *) ;
+void *klu_l_free (void *, size_t, size_t, klu_l_common *) ;
+void *klu_l_realloc (size_t, size_t, size_t, void *, klu_l_common *) ;
+
+
+/* ========================================================================== */
+/* === KLU version ========================================================== */
+/* ========================================================================== */
+
+/* All versions of KLU include these definitions.
+ * As an example, to test if the version you are using is 1.2 or later:
+ *
+ * if (KLU_VERSION >= KLU_VERSION_CODE (1,2)) ...
+ *
+ * This also works during compile-time:
+ *
+ * #if (KLU >= KLU_VERSION_CODE (1,2))
+ * printf ("This is version 1.2 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ */
+
+#define KLU_DATE "Nov 1, 2007"
+#define KLU_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define KLU_MAIN_VERSION 1
+#define KLU_SUB_VERSION 0
+#define KLU_SUBSUB_VERSION 1
+#define KLU_VERSION KLU_VERSION_CODE(KLU_MAIN_VERSION,KLU_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+#endif
diff --git a/KLU/Include/klu_internal.h b/KLU/Include/klu_internal.h
new file mode 100644
index 0000000..da73bc4
--- /dev/null
+++ b/KLU/Include/klu_internal.h
@@ -0,0 +1,243 @@
+/* ========================================================================== */
+/* === KLU/Include/klu_internal.h =========================================== */
+/* ========================================================================== */
+
+/* For internal use in KLU routines only, not for user programs */
+
+#ifndef _KLU_INTERNAL_H
+#define _KLU_INTERNAL_H
+
+#include "klu.h"
+#include "btf.h"
+#include "klu_version.h"
+
+/* ========================================================================== */
+/* make sure debugging and printing is turned off */
+
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+#ifndef NPRINT
+#define NPRINT
+#endif
+
+/* To enable debugging and assertions, uncomment this line:
+ #undef NDEBUG
+ */
+
+/* To enable diagnostic printing, uncomment this line:
+ #undef NPRINT
+ */
+
+/* ========================================================================== */
+
+#include <stdio.h>
+#include <assert.h>
+#include <limits.h>
+#include <stdlib.h>
+#include <math.h>
+
+#undef ASSERT
+#ifndef NDEBUG
+#define ASSERT(a) assert(a)
+#else
+#define ASSERT(a)
+#endif
+
+#define SCALAR_IS_NAN(x) ((x) != (x))
+
+/* true if an integer (stored in double x) would overflow (or if x is NaN) */
+#define INT_OVERFLOW(x) ((!((x) * (1.0+1e-8) <= (double) INT_MAX)) \
+ || SCALAR_IS_NAN (x))
+
+#undef TRUE
+#undef FALSE
+#undef MAX
+#undef MIN
+#undef PRINTF
+#undef FLIP
+
+#ifndef NPRINT
+#define PRINTF(s) { printf s ; } ;
+#else
+#define PRINTF(s)
+#endif
+
+#define TRUE 1
+#define FALSE 0
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+
+/* FLIP is a "negation about -1", and is used to mark an integer i that is
+ * normally non-negative. FLIP (EMPTY) is EMPTY. FLIP of a number > EMPTY
+ * is negative, and FLIP of a number < EMTPY is positive. FLIP (FLIP (i)) = i
+ * for all integers i. UNFLIP (i) is >= EMPTY. */
+#define EMPTY (-1)
+#define FLIP(i) (-(i)-2)
+#define UNFLIP(i) (((i) < EMPTY) ? FLIP (i) : (i))
+
+
+size_t KLU_kernel /* final size of LU on output */
+(
+ /* input, not modified */
+ Int n, /* A is n-by-n */
+ Int Ap [ ], /* size n+1, column pointers for A */
+ Int Ai [ ], /* size nz = Ap [n], row indices for A */
+ Entry Ax [ ], /* size nz, values of A */
+ Int Q [ ], /* size n, optional input permutation */
+ size_t lusize, /* initial size of LU */
+
+ /* output, not defined on input */
+ Int Pinv [ ], /* size n */
+ Int P [ ], /* size n */
+ Unit **p_LU, /* size lusize on input, size Uxp[n] on output*/
+ Entry Udiag [ ], /* size n, diagonal of U */
+ Int Llen [ ], /* size n, column length of L */
+ Int Ulen [ ], /* size n, column length of U */
+ Int Lip [ ], /* size n+1 */
+ Int Uip [ ], /* size n+1 */
+ Int *lnz, /* size of L */
+ Int *unz, /* size of U */
+
+ /* workspace, not defined on input */
+ Entry X [ ], /* size n, zero on output */
+
+ /* workspace, not defined on input or output */
+ Int Stack [ ], /* size n */
+ Int Flag [ ], /* size n */
+ Int adj_pos [ ], /* size n */
+
+ /* workspace for pruning only */
+ Int Lpend [ ], /* size n workspace */
+
+ /* inputs, not modified on output */
+ Int k1, /* the block of A is from k1 to k2-1 */
+ Int PSinv [ ], /* inverse of P from symbolic factorization */
+ double Rs [ ], /* scale factors for A */
+
+ /* inputs, modified on output */
+ Int Offp [ ], /* off-diagonal matrix (modified by this routine) */
+ Int Offi [ ],
+ Entry Offx [ ],
+ KLU_common *Common /* the control input/output structure */
+) ;
+
+
+size_t KLU_kernel_factor /* 0 if failure, size of LU if OK */
+(
+ /* inputs, not modified */
+ Int n, /* A is n-by-n. n must be > 0. */
+ Int Ap [ ], /* size n+1, column pointers for A */
+ Int Ai [ ], /* size nz = Ap [n], row indices for A */
+ Entry Ax [ ], /* size nz, values of A */
+ Int Q [ ], /* size n, optional column permutation */
+ double Lsize, /* initial size of L and U */
+
+ /* outputs, not defined on input */
+ Unit **p_LU, /* row indices and values of L and U */
+ Entry Udiag [ ], /* size n, diagonal of U */
+ Int Llen [ ], /* size n, column length of L */
+ Int Ulen [ ], /* size n, column length of U */
+ Int Lip [ ], /* size n+1, column pointers of L */
+ Int Uip [ ], /* size n+1, column pointers of U */
+ Int P [ ], /* row permutation, size n */
+ Int *lnz, /* size of L */
+ Int *unz, /* size of U */
+
+ /* workspace, undefined on input */
+ Entry *X, /* size n entries. Zero on output */
+ Int *Work, /* size 5n Int's */
+
+ /* inputs, not modified on output */
+ Int k1, /* the block of A is from k1 to k2-1 */
+ Int PSinv [ ], /* inverse of P from symbolic factorization */
+ double Rs [ ], /* scale factors for A */
+
+ /* inputs, modified on output */
+ Int Offp [ ], /* off-diagonal matrix (modified by this routine) */
+ Int Offi [ ],
+ Entry Offx [ ],
+ KLU_common *Common /* the control input/output structure */
+) ;
+
+void KLU_lsolve
+(
+ /* inputs, not modified: */
+ Int n,
+ Int Lp [ ],
+ Int Li [ ],
+ Unit LU [ ],
+ Int nrhs,
+ /* right-hand-side on input, solution to Lx=b on output */
+ Entry X [ ]
+) ;
+
+void KLU_ltsolve
+(
+ /* inputs, not modified: */
+ Int n,
+ Int Lp [ ],
+ Int Li [ ],
+ Unit LU [ ],
+ Int nrhs,
+#ifdef COMPLEX
+ Int conj_solve,
+#endif
+ /* right-hand-side on input, solution to L'x=b on output */
+ Entry X [ ]
+) ;
+
+
+void KLU_usolve
+(
+ /* inputs, not modified: */
+ Int n,
+ Int Up [ ],
+ Int Ui [ ],
+ Unit LU [ ],
+ Entry Udiag [ ],
+ Int nrhs,
+ /* right-hand-side on input, solution to Ux=b on output */
+ Entry X [ ]
+) ;
+
+void KLU_utsolve
+(
+ /* inputs, not modified: */
+ Int n,
+ Int Up [ ],
+ Int Ui [ ],
+ Unit LU [ ],
+ Entry Udiag [ ],
+ Int nrhs,
+#ifdef COMPLEX
+ Int conj_solve,
+#endif
+ /* right-hand-side on input, solution to U'x=b on output */
+ Entry X [ ]
+) ;
+
+Int KLU_valid
+(
+ Int n,
+ Int Ap [ ],
+ Int Ai [ ],
+ Entry Ax [ ]
+) ;
+
+Int KLU_valid_LU
+(
+ Int n,
+ Int flag_test_start_ptr,
+ Int Xip [ ],
+ Int Xlen [ ],
+ Unit LU [ ]
+);
+
+size_t KLU_add_size_t (size_t a, size_t b, Int *ok) ;
+
+size_t KLU_mult_size_t (size_t a, size_t k, Int *ok) ;
+
+KLU_symbolic *KLU_alloc_symbolic (Int n, Int *Ap, Int *Ai, KLU_common *Common) ;
+
+#endif
diff --git a/KLU/Include/klu_version.h b/KLU/Include/klu_version.h
new file mode 100644
index 0000000..13fde51
--- /dev/null
+++ b/KLU/Include/klu_version.h
@@ -0,0 +1,694 @@
+#ifndef _KLU_VERSION_H
+#define _KLU_VERSION_H
+
+#ifdef DLONG
+#define Int UF_long
+#define Int_id UF_long_id
+#define Int_MAX UF_long_max
+#else
+#define Int int
+#define Int_id "%d"
+#define Int_MAX INT_MAX
+#endif
+
+#define NPRINT
+
+#define BYTES(type,n) (sizeof (type) * (n))
+#define CEILING(b,u) (((b)+(u)-1) / (u))
+#define UNITS(type,n) (CEILING (BYTES (type,n), sizeof (Unit)))
+#define DUNITS(type,n) (ceil (BYTES (type, (double) n) / sizeof (Unit)))
+
+#define GET_I_POINTER(LU, Xip, Xi, k) \
+{ \
+ Xi = (Int *) (LU + Xip [k]) ; \
+}
+
+#define GET_X_POINTER(LU, Xip, Xlen, Xx, k) \
+{ \
+ Xx = (Entry *) (LU + Xip [k] + UNITS (Int, Xlen [k])) ; \
+}
+
+#define GET_POINTER(LU, Xip, Xlen, Xi, Xx, k, xlen) \
+{ \
+ Unit *xp = LU + Xip [k] ; \
+ xlen = Xlen [k] ; \
+ Xi = (Int *) xp ; \
+ Xx = (Entry *) (xp + UNITS (Int, xlen)) ; \
+}
+
+/* function names */
+#ifdef COMPLEX
+
+#ifdef DLONG
+
+#define KLU_scale klu_zl_scale
+#define KLU_solve klu_zl_solve
+#define KLU_tsolve klu_zl_tsolve
+#define KLU_free_numeric klu_zl_free_numeric
+#define KLU_factor klu_zl_factor
+#define KLU_refactor klu_zl_refactor
+#define KLU_kernel_factor klu_zl_kernel_factor
+#define KLU_lsolve klu_zl_lsolve
+#define KLU_ltsolve klu_zl_ltsolve
+#define KLU_usolve klu_zl_usolve
+#define KLU_utsolve klu_zl_utsolve
+#define KLU_kernel klu_zl_kernel
+#define KLU_valid klu_zl_valid
+#define KLU_valid_LU klu_zl_valid_LU
+#define KLU_sort klu_zl_sort
+#define KLU_rgrowth klu_zl_rgrowth
+#define KLU_rcond klu_zl_rcond
+#define KLU_extract klu_zl_extract
+#define KLU_condest klu_zl_condest
+#define KLU_flops klu_zl_flops
+
+#else
+
+#define KLU_scale klu_z_scale
+#define KLU_solve klu_z_solve
+#define KLU_tsolve klu_z_tsolve
+#define KLU_free_numeric klu_z_free_numeric
+#define KLU_factor klu_z_factor
+#define KLU_refactor klu_z_refactor
+#define KLU_kernel_factor klu_z_kernel_factor
+#define KLU_lsolve klu_z_lsolve
+#define KLU_ltsolve klu_z_ltsolve
+#define KLU_usolve klu_z_usolve
+#define KLU_utsolve klu_z_utsolve
+#define KLU_kernel klu_z_kernel
+#define KLU_valid klu_z_valid
+#define KLU_valid_LU klu_z_valid_LU
+#define KLU_sort klu_z_sort
+#define KLU_rgrowth klu_z_rgrowth
+#define KLU_rcond klu_z_rcond
+#define KLU_extract klu_z_extract
+#define KLU_condest klu_z_condest
+#define KLU_flops klu_z_flops
+
+#endif
+
+#else
+
+#ifdef DLONG
+
+#define KLU_scale klu_l_scale
+#define KLU_solve klu_l_solve
+#define KLU_tsolve klu_l_tsolve
+#define KLU_free_numeric klu_l_free_numeric
+#define KLU_factor klu_l_factor
+#define KLU_refactor klu_l_refactor
+#define KLU_kernel_factor klu_l_kernel_factor
+#define KLU_lsolve klu_l_lsolve
+#define KLU_ltsolve klu_l_ltsolve
+#define KLU_usolve klu_l_usolve
+#define KLU_utsolve klu_l_utsolve
+#define KLU_kernel klu_l_kernel
+#define KLU_valid klu_l_valid
+#define KLU_valid_LU klu_l_valid_LU
+#define KLU_sort klu_l_sort
+#define KLU_rgrowth klu_l_rgrowth
+#define KLU_rcond klu_l_rcond
+#define KLU_extract klu_l_extract
+#define KLU_condest klu_l_condest
+#define KLU_flops klu_l_flops
+
+#else
+
+#define KLU_scale klu_scale
+#define KLU_solve klu_solve
+#define KLU_tsolve klu_tsolve
+#define KLU_free_numeric klu_free_numeric
+#define KLU_factor klu_factor
+#define KLU_refactor klu_refactor
+#define KLU_kernel_factor klu_kernel_factor
+#define KLU_lsolve klu_lsolve
+#define KLU_ltsolve klu_ltsolve
+#define KLU_usolve klu_usolve
+#define KLU_utsolve klu_utsolve
+#define KLU_kernel klu_kernel
+#define KLU_valid klu_valid
+#define KLU_valid_LU klu_valid_LU
+#define KLU_sort klu_sort
+#define KLU_rgrowth klu_rgrowth
+#define KLU_rcond klu_rcond
+#define KLU_extract klu_extract
+#define KLU_condest klu_condest
+#define KLU_flops klu_flops
+
+#endif
+
+#endif
+
+
+#ifdef DLONG
+
+#define KLU_analyze klu_l_analyze
+#define KLU_analyze_given klu_l_analyze_given
+#define KLU_alloc_symbolic klu_l_alloc_symbolic
+#define KLU_free_symbolic klu_l_free_symbolic
+#define KLU_defaults klu_l_defaults
+#define KLU_free klu_l_free
+#define KLU_malloc klu_l_malloc
+#define KLU_realloc klu_l_realloc
+#define KLU_add_size_t klu_l_add_size_t
+#define KLU_mult_size_t klu_l_mult_size_t
+
+#define KLU_symbolic klu_l_symbolic
+#define KLU_numeric klu_l_numeric
+#define KLU_common klu_l_common
+
+#define BTF_order btf_l_order
+#define BTF_strongcomp btf_l_strongcomp
+
+#define AMD_order amd_l_order
+#define COLAMD colamd_l
+#define COLAMD_recommended colamd_l_recommended
+
+#else
+
+#define KLU_analyze klu_analyze
+#define KLU_analyze_given klu_analyze_given
+#define KLU_alloc_symbolic klu_alloc_symbolic
+#define KLU_free_symbolic klu_free_symbolic
+#define KLU_defaults klu_defaults
+#define KLU_free klu_free
+#define KLU_malloc klu_malloc
+#define KLU_realloc klu_realloc
+#define KLU_add_size_t klu_add_size_t
+#define KLU_mult_size_t klu_mult_size_t
+
+#define KLU_symbolic klu_symbolic
+#define KLU_numeric klu_numeric
+#define KLU_common klu_common
+
+#define BTF_order btf_order
+#define BTF_strongcomp btf_strongcomp
+
+#define AMD_order amd_order
+#define COLAMD colamd
+#define COLAMD_recommended colamd_recommended
+
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* Numerical relop macros for correctly handling the NaN case */
+/* -------------------------------------------------------------------------- */
+
+/*
+SCALAR_IS_NAN(x):
+ True if x is NaN. False otherwise. The commonly-existing isnan(x)
+ function could be used, but it's not in Kernighan & Ritchie 2nd edition
+ (ANSI C). It may appear in <math.h>, but I'm not certain about
+ portability. The expression x != x is true if and only if x is NaN,
+ according to the IEEE 754 floating-point standard.
+
+SCALAR_IS_ZERO(x):
+ True if x is zero. False if x is nonzero, NaN, or +/- Inf.
+ This is (x == 0) if the compiler is IEEE 754 compliant.
+
+SCALAR_IS_NONZERO(x):
+ True if x is nonzero, NaN, or +/- Inf. False if x zero.
+ This is (x != 0) if the compiler is IEEE 754 compliant.
+
+SCALAR_IS_LTZERO(x):
+ True if x is < zero or -Inf. False if x is >= 0, NaN, or +Inf.
+ This is (x < 0) if the compiler is IEEE 754 compliant.
+*/
+
+/* These all work properly, according to the IEEE 754 standard ... except on */
+/* a PC with windows. Works fine in Linux on the same PC... */
+#define SCALAR_IS_NAN(x) ((x) != (x))
+#define SCALAR_IS_ZERO(x) ((x) == 0.)
+#define SCALAR_IS_NONZERO(x) ((x) != 0.)
+#define SCALAR_IS_LTZERO(x) ((x) < 0.)
+
+
+/* scalar absolute value macro. If x is NaN, the result is NaN: */
+#define SCALAR_ABS(x) ((SCALAR_IS_LTZERO (x)) ? -(x) : (x))
+
+/* print a scalar (avoid printing "-0" for negative zero). */
+#ifdef NPRINT
+#define PRINT_SCALAR(a)
+#else
+#define PRINT_SCALAR(a) \
+{ \
+ if (SCALAR_IS_NONZERO (a)) \
+ { \
+ PRINTF ((" (%g)", (a))) ; \
+ } \
+ else \
+ { \
+ PRINTF ((" (0)")) ; \
+ } \
+}
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Real floating-point arithmetic */
+/* -------------------------------------------------------------------------- */
+
+#ifndef COMPLEX
+
+typedef double Unit ;
+#define Entry double
+
+#define SPLIT(s) (1)
+#define REAL(c) (c)
+#define IMAG(c) (0.)
+#define ASSIGN(c,s1,s2,p,split) { (c) = (s1)[p] ; }
+#define CLEAR(c) { (c) = 0. ; }
+#define CLEAR_AND_INCREMENT(p) { *p++ = 0. ; }
+#define IS_NAN(a) SCALAR_IS_NAN (a)
+#define IS_ZERO(a) SCALAR_IS_ZERO (a)
+#define IS_NONZERO(a) SCALAR_IS_NONZERO (a)
+#define SCALE_DIV(c,s) { (c) /= (s) ; }
+#define SCALE_DIV_ASSIGN(a,c,s) { a = c / s ; }
+#define SCALE(c,s) { (c) *= (s) ; }
+#define ASSEMBLE(c,a) { (c) += (a) ; }
+#define ASSEMBLE_AND_INCREMENT(c,p) { (c) += *p++ ; }
+#define DECREMENT(c,a) { (c) -= (a) ; }
+#define MULT(c,a,b) { (c) = (a) * (b) ; }
+#define MULT_CONJ(c,a,b) { (c) = (a) * (b) ; }
+#define MULT_SUB(c,a,b) { (c) -= (a) * (b) ; }
+#define MULT_SUB_CONJ(c,a,b) { (c) -= (a) * (b) ; }
+#define DIV(c,a,b) { (c) = (a) / (b) ; }
+#define RECIPROCAL(c) { (c) = 1.0 / (c) ; }
+#define DIV_CONJ(c,a,b) { (c) = (a) / (b) ; }
+#define APPROX_ABS(s,a) { (s) = SCALAR_ABS (a) ; }
+#define ABS(s,a) { (s) = SCALAR_ABS (a) ; }
+#define PRINT_ENTRY(a) PRINT_SCALAR (a)
+#define CONJ(a,x) a = x
+
+/* for flop counts */
+#define MULTSUB_FLOPS 2. /* c -= a*b */
+#define DIV_FLOPS 1. /* c = a/b */
+#define ABS_FLOPS 0. /* c = abs (a) */
+#define ASSEMBLE_FLOPS 1. /* c += a */
+#define DECREMENT_FLOPS 1. /* c -= a */
+#define MULT_FLOPS 1. /* c = a*b */
+#define SCALE_FLOPS 1. /* c = a/s */
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* Complex floating-point arithmetic */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Note: An alternative to this Double_Complex type would be to use a
+ struct { double r ; double i ; }. The problem with that method
+ (used by the Sun Performance Library, for example) is that ANSI C provides
+ no guarantee about the layout of a struct. It is possible that the sizeof
+ the struct above would be greater than 2 * sizeof (double). This would
+ mean that the complex BLAS could not be used. The method used here avoids
+ that possibility. ANSI C *does* guarantee that an array of structs has
+ the same size as n times the size of one struct.
+
+ The ANSI C99 version of the C language includes a "double _Complex" type.
+ It should be possible in that case to do the following:
+
+ #define Entry double _Complex
+
+ and remove the Double_Complex struct. The macros, below, could then be
+ replaced with instrinsic operators. Note that the #define Real and
+ #define Imag should also be removed (they only appear in this file).
+
+ For the MULT, MULT_SUB, MULT_SUB_CONJ, and MULT_CONJ macros,
+ the output argument c cannot be the same as any input argument.
+
+*/
+
+typedef struct
+{
+ double component [2] ; /* real and imaginary parts */
+
+} Double_Complex ;
+
+typedef Double_Complex Unit ;
+#define Entry Double_Complex
+#define Real component [0]
+#define Imag component [1]
+
+/* for flop counts */
+#define MULTSUB_FLOPS 8. /* c -= a*b */
+#define DIV_FLOPS 9. /* c = a/b */
+#define ABS_FLOPS 6. /* c = abs (a), count sqrt as one flop */
+#define ASSEMBLE_FLOPS 2. /* c += a */
+#define DECREMENT_FLOPS 2. /* c -= a */
+#define MULT_FLOPS 6. /* c = a*b */
+#define SCALE_FLOPS 2. /* c = a/s or c = a*s */
+
+/* -------------------------------------------------------------------------- */
+
+/* real part of c */
+#define REAL(c) ((c).Real)
+
+/* -------------------------------------------------------------------------- */
+
+/* imag part of c */
+#define IMAG(c) ((c).Imag)
+
+/* -------------------------------------------------------------------------- */
+
+/* Return TRUE if a complex number is in split form, FALSE if in packed form */
+#define SPLIT(sz) ((sz) != (double *) NULL)
+
+/* c = (s1) + (s2)*i, if s2 is null, then X is in "packed" format (compatible
+ * with Entry and ANSI C99 double _Complex type). */
+/*#define ASSIGN(c,s1,s2,p,split) \
+{ \
+ if (split) \
+ { \
+ (c).Real = (s1)[p] ; \
+ (c).Imag = (s2)[p] ; \
+ } \
+ else \
+ { \
+ (c) = ((Entry *)(s1))[p] ; \
+ } \
+}*/
+
+/* -------------------------------------------------------------------------- */
+#define CONJ(a, x) \
+{ \
+ a.Real = x.Real ; \
+ a.Imag = -x.Imag ; \
+}
+
+/* c = 0 */
+#define CLEAR(c) \
+{ \
+ (c).Real = 0. ; \
+ (c).Imag = 0. ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* *p++ = 0 */
+#define CLEAR_AND_INCREMENT(p) \
+{ \
+ p->Real = 0. ; \
+ p->Imag = 0. ; \
+ p++ ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* True if a == 0 */
+#define IS_ZERO(a) \
+ (SCALAR_IS_ZERO ((a).Real) && SCALAR_IS_ZERO ((a).Imag))
+
+/* -------------------------------------------------------------------------- */
+
+/* True if a is NaN */
+#define IS_NAN(a) \
+ (SCALAR_IS_NAN ((a).Real) || SCALAR_IS_NAN ((a).Imag))
+
+/* -------------------------------------------------------------------------- */
+
+/* True if a != 0 */
+#define IS_NONZERO(a) \
+ (SCALAR_IS_NONZERO ((a).Real) || SCALAR_IS_NONZERO ((a).Imag))
+
+/* -------------------------------------------------------------------------- */
+
+/* a = c/s */
+#define SCALE_DIV_ASSIGN(a,c,s) \
+{ \
+ a.Real = c.Real / s ; \
+ a.Imag = c.Imag / s ; \
+}
+
+/* c /= s */
+#define SCALE_DIV(c,s) \
+{ \
+ (c).Real /= (s) ; \
+ (c).Imag /= (s) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c *= s */
+#define SCALE(c,s) \
+{ \
+ (c).Real *= (s) ; \
+ (c).Imag *= (s) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c += a */
+#define ASSEMBLE(c,a) \
+{ \
+ (c).Real += (a).Real ; \
+ (c).Imag += (a).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c += *p++ */
+#define ASSEMBLE_AND_INCREMENT(c,p) \
+{ \
+ (c).Real += p->Real ; \
+ (c).Imag += p->Imag ; \
+ p++ ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c -= a */
+#define DECREMENT(c,a) \
+{ \
+ (c).Real -= (a).Real ; \
+ (c).Imag -= (a).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a*b, assert because c cannot be the same as a or b */
+#define MULT(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real = (a).Real * (b).Real - (a).Imag * (b).Imag ; \
+ (c).Imag = (a).Imag * (b).Real + (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a*conjugate(b), assert because c cannot be the same as a or b */
+#define MULT_CONJ(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real = (a).Real * (b).Real + (a).Imag * (b).Imag ; \
+ (c).Imag = (a).Imag * (b).Real - (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c -= a*b, assert because c cannot be the same as a or b */
+#define MULT_SUB(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real -= (a).Real * (b).Real - (a).Imag * (b).Imag ; \
+ (c).Imag -= (a).Imag * (b).Real + (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c -= a*conjugate(b), assert because c cannot be the same as a or b */
+#define MULT_SUB_CONJ(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real -= (a).Real * (b).Real + (a).Imag * (b).Imag ; \
+ (c).Imag -= (a).Imag * (b).Real - (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a/b, be careful to avoid underflow and overflow */
+#ifdef MATHWORKS
+#define DIV(c,a,b) \
+{ \
+ (void) utDivideComplex ((a).Real, (a).Imag, (b).Real, (b).Imag, \
+ &((c).Real), &((c).Imag)) ; \
+}
+#else
+/* This uses ACM Algo 116, by R. L. Smith, 1962. */
+/* c can be the same variable as a or b. */
+/* Ignore NaN case for double relop br>=bi. */
+#define DIV(c,a,b) \
+{ \
+ double r, den, ar, ai, br, bi ; \
+ br = (b).Real ; \
+ bi = (b).Imag ; \
+ ar = (a).Real ; \
+ ai = (a).Imag ; \
+ if (SCALAR_ABS (br) >= SCALAR_ABS (bi)) \
+ { \
+ r = bi / br ; \
+ den = br + r * bi ; \
+ (c).Real = (ar + ai * r) / den ; \
+ (c).Imag = (ai - ar * r) / den ; \
+ } \
+ else \
+ { \
+ r = br / bi ; \
+ den = r * br + bi ; \
+ (c).Real = (ar * r + ai) / den ; \
+ (c).Imag = (ai * r - ar) / den ; \
+ } \
+}
+#endif
+
+/* -------------------------------------------------------------------------- */
+
+/* c = 1/c, be careful to avoid underflow and overflow */
+/* Not used if MATHWORKS is defined. */
+/* This uses ACM Algo 116, by R. L. Smith, 1962. */
+/* Ignore NaN case for double relop cr>=ci. */
+#define RECIPROCAL(c) \
+{ \
+ double r, den, cr, ci ; \
+ cr = (c).Real ; \
+ ci = (c).Imag ; \
+ if (SCALAR_ABS (cr) >= SCALAR_ABS (ci)) \
+ { \
+ r = ci / cr ; \
+ den = cr + r * ci ; \
+ (c).Real = 1.0 / den ; \
+ (c).Imag = - r / den ; \
+ } \
+ else \
+ { \
+ r = cr / ci ; \
+ den = r * cr + ci ; \
+ (c).Real = r / den ; \
+ (c).Imag = - 1.0 / den ; \
+ } \
+}
+
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a/conjugate(b), be careful to avoid underflow and overflow */
+#ifdef MATHWORKS
+#define DIV_CONJ(c,a,b) \
+{ \
+ (void) utDivideComplex ((a).Real, (a).Imag, (b).Real, (-(b).Imag), \
+ &((c).Real), &((c).Imag)) ; \
+}
+#else
+/* This uses ACM Algo 116, by R. L. Smith, 1962. */
+/* c can be the same variable as a or b. */
+/* Ignore NaN case for double relop br>=bi. */
+#define DIV_CONJ(c,a,b) \
+{ \
+ double r, den, ar, ai, br, bi ; \
+ br = (b).Real ; \
+ bi = (b).Imag ; \
+ ar = (a).Real ; \
+ ai = (a).Imag ; \
+ if (SCALAR_ABS (br) >= SCALAR_ABS (bi)) \
+ { \
+ r = (-bi) / br ; \
+ den = br - r * bi ; \
+ (c).Real = (ar + ai * r) / den ; \
+ (c).Imag = (ai - ar * r) / den ; \
+ } \
+ else \
+ { \
+ r = br / (-bi) ; \
+ den = r * br - bi; \
+ (c).Real = (ar * r + ai) / den ; \
+ (c).Imag = (ai * r - ar) / den ; \
+ } \
+}
+#endif
+
+/* -------------------------------------------------------------------------- */
+
+/* approximate absolute value, s = |r|+|i| */
+#define APPROX_ABS(s,a) \
+{ \
+ (s) = SCALAR_ABS ((a).Real) + SCALAR_ABS ((a).Imag) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* exact absolute value, s = sqrt (a.real^2 + amag^2) */
+#ifdef MATHWORKS
+#define ABS(s,a) \
+{ \
+ (s) = utFdlibm_hypot ((a).Real, (a).Imag) ; \
+}
+#else
+/* Ignore NaN case for the double relops ar>=ai and ar+ai==ar. */
+#define ABS(s,a) \
+{ \
+ double r, ar, ai ; \
+ ar = SCALAR_ABS ((a).Real) ; \
+ ai = SCALAR_ABS ((a).Imag) ; \
+ if (ar >= ai) \
+ { \
+ if (ar + ai == ar) \
+ { \
+ (s) = ar ; \
+ } \
+ else \
+ { \
+ r = ai / ar ; \
+ (s) = ar * sqrt (1.0 + r*r) ; \
+ } \
+ } \
+ else \
+ { \
+ if (ai + ar == ai) \
+ { \
+ (s) = ai ; \
+ } \
+ else \
+ { \
+ r = ar / ai ; \
+ (s) = ai * sqrt (1.0 + r*r) ; \
+ } \
+ } \
+}
+#endif
+
+/* -------------------------------------------------------------------------- */
+
+/* print an entry (avoid printing "-0" for negative zero). */
+#ifdef NPRINT
+#define PRINT_ENTRY(a)
+#else
+#define PRINT_ENTRY(a) \
+{ \
+ if (SCALAR_IS_NONZERO ((a).Real)) \
+ { \
+ PRINTF ((" (%g", (a).Real)) ; \
+ } \
+ else \
+ { \
+ PRINTF ((" (0")) ; \
+ } \
+ if (SCALAR_IS_LTZERO ((a).Imag)) \
+ { \
+ PRINTF ((" - %gi)", -(a).Imag)) ; \
+ } \
+ else if (SCALAR_IS_ZERO ((a).Imag)) \
+ { \
+ PRINTF ((" + 0i)")) ; \
+ } \
+ else \
+ { \
+ PRINTF ((" + %gi)", (a).Imag)) ; \
+ } \
+}
+#endif
+
+/* -------------------------------------------------------------------------- */
+
+#endif /* #ifndef COMPLEX */
+
+#endif
diff --git a/KLU/Lib/Makefile b/KLU/Lib/Makefile
new file mode 100644
index 0000000..8b0fdfc
--- /dev/null
+++ b/KLU/Lib/Makefile
@@ -0,0 +1,248 @@
+default: all
+
+ccode: all
+
+include ../../UFconfig/UFconfig.mk
+
+# for testing only:
+# TEST = -DTESTING
+
+C = $(CC) $(CFLAGS)
+
+INC = ../Include/klu.h ../Include/klu_internal.h ../Include/klu_version.h \
+ ../../UFconfig/UFconfig.h Makefile
+
+I = -I../../AMD/Include -I../../COLAMD/Include -I../../BTF/Include \
+ -I../Include -I../../UFconfig
+
+all: library
+
+library: libklu.a
+
+KLU_D = klu_d.o klu_d_kernel.o klu_d_dump.o \
+ klu_d_factor.o klu_d_free_numeric.o klu_d_solve.o \
+ klu_d_scale.o klu_d_refactor.o \
+ klu_d_tsolve.o klu_d_diagnostics.o klu_d_sort.o klu_d_extract.o
+
+KLU_Z = klu_z.o klu_z_kernel.o klu_z_dump.o \
+ klu_z_factor.o klu_z_free_numeric.o klu_z_solve.o \
+ klu_z_scale.o klu_z_refactor.o \
+ klu_z_tsolve.o klu_z_diagnostics.o klu_z_sort.o klu_z_extract.o
+
+KLU_L = klu_l.o klu_l_kernel.o klu_l_dump.o \
+ klu_l_factor.o klu_l_free_numeric.o klu_l_solve.o \
+ klu_l_scale.o klu_l_refactor.o \
+ klu_l_tsolve.o klu_l_diagnostics.o klu_l_sort.o klu_l_extract.o
+
+KLU_ZL = klu_zl.o klu_zl_kernel.o klu_zl_dump.o \
+ klu_zl_factor.o klu_zl_free_numeric.o klu_zl_solve.o \
+ klu_zl_scale.o klu_zl_refactor.o \
+ klu_zl_tsolve.o klu_zl_diagnostics.o klu_zl_sort.o klu_zl_extract.o
+
+COMMON = \
+ klu_free_symbolic.o klu_defaults.o klu_analyze_given.o \
+ klu_analyze.o klu_memory.o \
+ klu_l_free_symbolic.o klu_l_defaults.o klu_l_analyze_given.o \
+ klu_l_analyze.o klu_l_memory.o
+
+OBJ = $(COMMON) $(KLU_D) $(KLU_Z) $(KLU_L) $(KLU_ZL)
+
+libklu.a: $(OBJ)
+ $(AR) libklu.a $(OBJ)
+ $(RANLIB) libklu.a
+
+$(OBJ): $(INC)
+
+#-------------------------------------------------------------------------------
+
+klu_d.o: ../Source/klu.c
+ $(C) -c $(I) $< -o $@
+
+klu_z.o: ../Source/klu.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_kernel.o: ../Source/klu_kernel.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_kernel.o: ../Source/klu_kernel.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_sort.o: ../Source/klu_sort.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_sort.o: ../Source/klu_sort.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_diagnostics.o: ../Source/klu_diagnostics.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_diagnostics.o: ../Source/klu_diagnostics.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_dump.o: ../Source/klu_dump.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_dump.o: ../Source/klu_dump.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_factor.o: ../Source/klu_factor.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_factor.o: ../Source/klu_factor.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_free_numeric.o: ../Source/klu_free_numeric.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_free_numeric.o: ../Source/klu_free_numeric.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_extract.o: ../Source/klu_extract.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_extract.o: ../Source/klu_extract.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_refactor.o: ../Source/klu_refactor.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_refactor.o: ../Source/klu_refactor.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_scale.o: ../Source/klu_scale.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_scale.o: ../Source/klu_scale.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_solve.o: ../Source/klu_solve.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_solve.o: ../Source/klu_solve.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+klu_d_tsolve.o: ../Source/klu_tsolve.c
+ $(C) -c $(I) $< -o $@
+
+klu_z_tsolve.o: ../Source/klu_tsolve.c
+ $(C) -c -DCOMPLEX $(I) $< -o $@
+
+#-------------------------------------------------------------------------------
+
+klu_analyze.o: ../Source/klu_analyze.c
+ $(C) -c $(I) $< -o $@
+
+klu_analyze_given.o: ../Source/klu_analyze_given.c
+ $(C) -c $(I) $< -o $@
+
+klu_defaults.o: ../Source/klu_defaults.c
+ $(C) -c $(I) $< -o $@
+
+klu_free_symbolic.o: ../Source/klu_free_symbolic.c
+ $(C) -c $(I) $< -o $@
+
+klu_memory.o: ../Source/klu_memory.c
+ $(C) -c $(I) $< -o $@
+
+#-------------------------------------------------------------------------------
+
+purge: distclean
+
+distclean: clean
+ - $(RM) libklu.a
+
+clean:
+ - $(RM) $(CLEAN)
+
+#-------------------------------------------------------------------------------
+
+klu_l.o: ../Source/klu.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl.o: ../Source/klu.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_kernel.o: ../Source/klu_kernel.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_kernel.o: ../Source/klu_kernel.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_sort.o: ../Source/klu_sort.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_sort.o: ../Source/klu_sort.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_diagnostics.o: ../Source/klu_diagnostics.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_diagnostics.o: ../Source/klu_diagnostics.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_dump.o: ../Source/klu_dump.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_dump.o: ../Source/klu_dump.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_factor.o: ../Source/klu_factor.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_factor.o: ../Source/klu_factor.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_free_numeric.o: ../Source/klu_free_numeric.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_free_numeric.o: ../Source/klu_free_numeric.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_extract.o: ../Source/klu_extract.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_extract.o: ../Source/klu_extract.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_refactor.o: ../Source/klu_refactor.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_refactor.o: ../Source/klu_refactor.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_scale.o: ../Source/klu_scale.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_scale.o: ../Source/klu_scale.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_solve.o: ../Source/klu_solve.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_solve.o: ../Source/klu_solve.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+klu_l_tsolve.o: ../Source/klu_tsolve.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_zl_tsolve.o: ../Source/klu_tsolve.c
+ $(C) -c -DCOMPLEX -DDLONG $(I) $< -o $@
+
+#-------------------------------------------------------------------------------
+
+klu_l_analyze.o: ../Source/klu_analyze.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_l_analyze_given.o: ../Source/klu_analyze_given.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_l_defaults.o: ../Source/klu_defaults.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_l_free_symbolic.o: ../Source/klu_free_symbolic.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+klu_l_memory.o: ../Source/klu_memory.c
+ $(C) -c -DDLONG $(I) $< -o $@
+
+#-------------------------------------------------------------------------------
diff --git a/KLU/MATLAB/Contents.m b/KLU/MATLAB/Contents.m
new file mode 100644
index 0000000..e8dcfd9
--- /dev/null
+++ b/KLU/MATLAB/Contents.m
@@ -0,0 +1,16 @@
+% KLU: a "Clark Kent" LU factorization algorithm
+%
+% klu - sparse left-looking LU factorization, using a block triangular form.
+% klu_install - compiles and installs the KLU, BTF, AMD, and COLAMD mexFunctions
+% klu_demo - KLU demo
+% klu_make - compiles the KLU mexFunctions
+%
+% Example:
+%
+% LU = klu (A) ;
+% x = klu (A, '\', b) ;
+% x = klu (LU, '\', b) ;
+%
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+% KLU Version 1.0.
+
diff --git a/KLU/MATLAB/Makefile b/KLU/MATLAB/Makefile
new file mode 100644
index 0000000..0be69ca
--- /dev/null
+++ b/KLU/MATLAB/Makefile
@@ -0,0 +1,699 @@
+#===============================================================================
+# KLU/MATLAB/Makefile
+#===============================================================================
+
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+# with CHOLMOD and supporting functions (CAMD, CCOLAMD, METIS)
+I = -I. -I../../AMD/Include -I../../COLAMD/Include \
+ -I../Include -I../../UFconfig -I../../BTF/Include -I../User \
+ -I../../CCOLAMD/Include -I../../CAMD/Include \
+ -I$(METIS_PATH)/Lib -I../../CHOLMOD/Include
+
+all: klu
+
+MX = $(MEX) -DDLONG -DNLARGEFILE $(I)
+
+distclean: purge
+
+purge: clean
+ - $(RM) *.mex* rename.h
+
+clean:
+ - $(RM) $(CLEAN)
+
+#===============================================================================
+
+AMD_INC = ../../AMD/Include/amd.h ../../AMD/Include/amd_internal.h
+
+AMD = \
+ amd_1.o \
+ amd_2.o \
+ amd_aat.o \
+ amd_control.o \
+ amd_defaults.o \
+ amd_dump.o \
+ amd_global.o \
+ amd_info.o \
+ amd_order.o \
+ amd_postorder.o \
+ amd_post_tree.o \
+ amd_preprocess.o \
+ amd_valid.o
+
+$(AMD): $(AMD_INC)
+amd_1.o: ../../AMD/Source/amd_1.c
+ $(MX) -c $<
+
+amd_2.o: ../../AMD/Source/amd_2.c
+ $(MX) -c $<
+
+amd_aat.o: ../../AMD/Source/amd_aat.c
+ $(MX) -c $<
+
+amd_control.o: ../../AMD/Source/amd_control.c
+ $(MX) -c $<
+
+amd_defaults.o: ../../AMD/Source/amd_defaults.c
+ $(MX) -c $<
+
+amd_dump.o: ../../AMD/Source/amd_dump.c
+ $(MX) -c $<
+
+amd_global.o: ../../AMD/Source/amd_global.c
+ $(MX) -c $<
+
+amd_info.o: ../../AMD/Source/amd_info.c
+ $(MX) -c $<
+
+amd_order.o: ../../AMD/Source/amd_order.c
+ $(MX) -c $<
+
+amd_postorder.o: ../../AMD/Source/amd_postorder.c
+ $(MX) -c $<
+
+amd_post_tree.o: ../../AMD/Source/amd_post_tree.c
+ $(MX) -c $<
+
+amd_preprocess.o: ../../AMD/Source/amd_preprocess.c
+ $(MX) -c $<
+
+amd_valid.o: ../../AMD/Source/amd_valid.c
+ $(MX) -c $<
+
+#===============================================================================
+
+CAMD_INC = ../../CAMD/Include/camd.h ../../CAMD/Include/camd_internal.h
+
+CAMD = \
+ camd_1.o \
+ camd_2.o \
+ camd_aat.o \
+ camd_control.o \
+ camd_defaults.o \
+ camd_dump.o \
+ camd_global.o \
+ camd_info.o \
+ camd_order.o \
+ camd_postorder.o \
+ camd_preprocess.o \
+ camd_valid.o
+
+$(CAMD): $(CAMD_INC)
+
+camd_1.o: ../../CAMD/Source/camd_1.c
+ $(MX) -c $<
+
+camd_2.o: ../../CAMD/Source/camd_2.c
+ $(MX) -c $<
+
+camd_aat.o: ../../CAMD/Source/camd_aat.c
+ $(MX) -c $<
+
+camd_control.o: ../../CAMD/Source/camd_control.c
+ $(MX) -c $<
+
+camd_defaults.o: ../../CAMD/Source/camd_defaults.c
+ $(MX) -c $<
+
+camd_dump.o: ../../CAMD/Source/camd_dump.c
+ $(MX) -c $<
+
+camd_global.o: ../../CAMD/Source/camd_global.c
+ $(MX) -c $<
+
+camd_info.o: ../../CAMD/Source/camd_info.c
+ $(MX) -c $<
+
+camd_order.o: ../../CAMD/Source/camd_order.c
+ $(MX) -c $<
+
+camd_postorder.o: ../../CAMD/Source/camd_postorder.c
+ $(MX) -c $<
+
+camd_post_tree.o: ../../CAMD/Source/camd_post_tree.c
+ $(MX) -c $<
+
+camd_preprocess.o: ../../CAMD/Source/camd_preprocess.c
+ $(MX) -c $<
+
+camd_valid.o: ../../CAMD/Source/camd_valid.c
+ $(MX) -c $<
+
+#===============================================================================
+
+COLAMD_INC = ../../COLAMD/Include/colamd.h
+
+COLAMD = colamd.o colamd_global.o
+
+$(COLAMD): $(COLAMD_INC)
+
+colamd.o: ../../COLAMD/Source/colamd.c
+ $(MX) -c $<
+
+colamd_global.o: ../../COLAMD/Source/colamd_global.c
+ $(MX) -c $<
+
+#===============================================================================
+
+CCOLAMD_INC = ../../CCOLAMD/Include/ccolamd.h
+
+CCOLAMD = ccolamd.o ccolamd_global.o
+
+$(CCOLAMD): $(CCOLAMD_INC)
+
+ccolamd.o: ../../CCOLAMD/Source/ccolamd.c
+ $(MX) -c $<
+
+ccolamd_global.o: ../../CCOLAMD/Source/ccolamd_global.c
+ $(MX) -c $<
+
+#===============================================================================
+
+# patch METIS 4.0.1
+rename.h: $(METIS_PATH)/Lib/rename.h
+ echo '/* do not edit this file; generated by KLU/MATLAB/Makefile */' > rename.h
+ echo '#undef log2' >> rename.h
+ echo '#include "$(METIS_PATH)/Lib/rename.h"' >> rename.h
+ echo '#undef log2' >> rename.h
+ echo '#define log2 METIS__log2' >> rename.h
+ echo '#include "mex.h"' >> rename.h
+ echo '#define malloc mxMalloc' >> rename.h
+ echo '#define free mxFree' >> rename.h
+ echo '#define calloc mxCalloc' >> rename.h
+ echo '#define realloc mxRealloc' >> rename.h
+
+METIS_INC = rename.h \
+ $(METIS_PATH)/Lib/defs.h \
+ $(METIS_PATH)/Lib/macros.h \
+ $(METIS_PATH)/Lib/metis.h \
+ $(METIS_PATH)/Lib/proto.h \
+ $(METIS_PATH)/Lib/rename.h \
+ $(METIS_PATH)/Lib/struct.h
+
+METIS = \
+ balance.o \
+ bucketsort.o \
+ ccgraph.o \
+ coarsen.o \
+ compress.o \
+ debug.o \
+ estmem.o \
+ fm.o \
+ fortran.o \
+ frename.o \
+ graph.o \
+ initpart.o \
+ kmetis.o \
+ kvmetis.o \
+ kwayfm.o \
+ kwayrefine.o \
+ kwayvolfm.o \
+ kwayvolrefine.o \
+ match.o \
+ mbalance2.o \
+ mbalance.o \
+ mcoarsen.o \
+ memory.o \
+ mesh.o \
+ meshpart.o \
+ mfm2.o \
+ mfm.o \
+ mincover.o \
+ minitpart2.o \
+ minitpart.o \
+ mkmetis.o \
+ mkwayfmh.o \
+ mkwayrefine.o \
+ mmatch.o \
+ mmd.o \
+ mpmetis.o \
+ mrefine2.o \
+ mrefine.o \
+ mutil.o \
+ myqsort.o \
+ ometis.o \
+ parmetis.o \
+ pmetis.o \
+ pqueue.o \
+ refine.o \
+ separator.o \
+ sfm.o \
+ srefine.o \
+ stat.o \
+ subdomains.o \
+ timing.o \
+ util.o
+
+$(METIS): $(METIS_INC)
+
+balance.o: $(METIS_PATH)/Lib/balance.c
+ $(MX) -c $<
+
+bucketsort.o: $(METIS_PATH)/Lib/bucketsort.c
+ $(MX) -c $<
+
+ccgraph.o: $(METIS_PATH)/Lib/ccgraph.c
+ $(MX) -c $<
+
+coarsen.o: $(METIS_PATH)/Lib/coarsen.c
+ $(MX) -c $<
+
+compress.o: $(METIS_PATH)/Lib/compress.c
+ $(MX) -c $<
+
+debug.o: $(METIS_PATH)/Lib/debug.c
+ $(MX) -c $<
+
+estmem.o: $(METIS_PATH)/Lib/estmem.c
+ $(MX) -c $<
+
+fm.o: $(METIS_PATH)/Lib/fm.c
+ $(MX) -c $<
+
+fortran.o: $(METIS_PATH)/Lib/fortran.c
+ $(MX) -c $<
+
+frename.o: $(METIS_PATH)/Lib/frename.c
+ $(MX) -c $<
+
+graph.o: $(METIS_PATH)/Lib/graph.c
+ $(MX) -c $<
+
+initpart.o: $(METIS_PATH)/Lib/initpart.c
+ $(MX) -c $<
+
+kmetis.o: $(METIS_PATH)/Lib/kmetis.c
+ $(MX) -c $<
+
+kvmetis.o: $(METIS_PATH)/Lib/kvmetis.c
+ $(MX) -c $<
+
+kwayfm.o: $(METIS_PATH)/Lib/kwayfm.c
+ $(MX) -c $<
+
+kwayrefine.o: $(METIS_PATH)/Lib/kwayrefine.c
+ $(MX) -c $<
+
+kwayvolfm.o: $(METIS_PATH)/Lib/kwayvolfm.c
+ $(MX) -c $<
+
+kwayvolrefine.o: $(METIS_PATH)/Lib/kwayvolrefine.c
+ $(MX) -c $<
+
+match.o: $(METIS_PATH)/Lib/match.c
+ $(MX) -c $<
+
+mbalance2.o: $(METIS_PATH)/Lib/mbalance2.c
+ $(MX) -c $<
+
+mbalance.o: $(METIS_PATH)/Lib/mbalance.c
+ $(MX) -c $<
+
+mcoarsen.o: $(METIS_PATH)/Lib/mcoarsen.c
+ $(MX) -c $<
+
+memory.o: $(METIS_PATH)/Lib/memory.c
+ $(MX) -c $<
+
+mesh.o: $(METIS_PATH)/Lib/mesh.c
+ $(MX) -c $<
+
+meshpart.o: $(METIS_PATH)/Lib/meshpart.c
+ $(MX) -c $<
+
+mfm2.o: $(METIS_PATH)/Lib/mfm2.c
+ $(MX) -c $<
+
+mfm.o: $(METIS_PATH)/Lib/mfm.c
+ $(MX) -c $<
+
+mincover.o: $(METIS_PATH)/Lib/mincover.c
+ $(MX) -c $<
+
+minitpart2.o: $(METIS_PATH)/Lib/minitpart2.c
+ $(MX) -c $<
+
+minitpart.o: $(METIS_PATH)/Lib/minitpart.c
+ $(MX) -c $<
+
+mkmetis.o: $(METIS_PATH)/Lib/mkmetis.c
+ $(MX) -c $<
+
+mkwayfmh.o: $(METIS_PATH)/Lib/mkwayfmh.c
+ $(MX) -c $<
+
+mkwayrefine.o: $(METIS_PATH)/Lib/mkwayrefine.c
+ $(MX) -c $<
+
+mmatch.o: $(METIS_PATH)/Lib/mmatch.c
+ $(MX) -c $<
+
+mmd.o: $(METIS_PATH)/Lib/mmd.c
+ $(MX) -c $<
+
+mpmetis.o: $(METIS_PATH)/Lib/mpmetis.c
+ $(MX) -c $<
+
+mrefine2.o: $(METIS_PATH)/Lib/mrefine2.c
+ $(MX) -c $<
+
+mrefine.o: $(METIS_PATH)/Lib/mrefine.c
+ $(MX) -c $<
+
+mutil.o: $(METIS_PATH)/Lib/mutil.c
+ $(MX) -c $<
+
+myqsort.o: $(METIS_PATH)/Lib/myqsort.c
+ $(MX) -c $<
+
+ometis.o: $(METIS_PATH)/Lib/ometis.c
+ $(MX) -c $<
+
+parmetis.o: $(METIS_PATH)/Lib/parmetis.c
+ $(MX) -c $<
+
+pmetis.o: $(METIS_PATH)/Lib/pmetis.c
+ $(MX) -c $<
+
+pqueue.o: $(METIS_PATH)/Lib/pqueue.c
+ $(MX) -c $<
+
+refine.o: $(METIS_PATH)/Lib/refine.c
+ $(MX) -c $<
+
+separator.o: $(METIS_PATH)/Lib/separator.c
+ $(MX) -c $<
+
+sfm.o: $(METIS_PATH)/Lib/sfm.c
+ $(MX) -c $<
+
+srefine.o: $(METIS_PATH)/Lib/srefine.c
+ $(MX) -c $<
+
+stat.o: $(METIS_PATH)/Lib/stat.c
+ $(MX) -c $<
+
+subdomains.o: $(METIS_PATH)/Lib/subdomains.c
+ $(MX) -c $<
+
+timing.o: $(METIS_PATH)/Lib/timing.c
+ $(MX) -c $<
+
+util.o: $(METIS_PATH)/Lib/util.c
+ $(MX) -c $<
+
+#===============================================================================
+
+CHOLMOD_INC = \
+ ../../CHOLMOD/Include/cholmod_blas.h \
+ ../../CHOLMOD/Include/cholmod_cholesky.h \
+ ../../CHOLMOD/Include/cholmod_complexity.h \
+ ../../CHOLMOD/Include/cholmod_config.h \
+ ../../CHOLMOD/Include/cholmod_core.h \
+ ../../CHOLMOD/Include/cholmod.h \
+ ../../CHOLMOD/Include/cholmod_internal.h \
+ ../../CHOLMOD/Include/cholmod_io64.h \
+ ../../CHOLMOD/Include/cholmod_partition.h \
+ ../../CHOLMOD/Include/cholmod_template.h
+
+CHOLMOD = \
+ cholmod_amd.o \
+ cholmod_analyze.o \
+ cholmod_colamd.o \
+ cholmod_etree.o \
+ cholmod_postorder.o \
+ cholmod_rowcolcounts.o \
+ cholmod_aat.o \
+ cholmod_add.o \
+ cholmod_band.o \
+ cholmod_change_factor.o \
+ cholmod_common.o \
+ cholmod_complex.o \
+ cholmod_copy.o \
+ cholmod_dense.o \
+ cholmod_error.o \
+ cholmod_factor.o \
+ cholmod_memory.o \
+ cholmod_sparse.o \
+ cholmod_transpose.o \
+ cholmod_triplet.o \
+ cholmod_camd.o \
+ cholmod_ccolamd.o \
+ cholmod_csymamd.o \
+ cholmod_metis.o \
+ cholmod_nesdis.o
+
+$(CHOLMOD): $(CHOLMOD_INC)
+
+CH = -DNSUPERNODAL -DNMODIFY -DNMATRIXOPS -DNCHECK
+
+cholmod_amd.o: ../../CHOLMOD/Cholesky/cholmod_amd.c
+ $(MX) $(CH) -c $<
+
+cholmod_analyze.o: ../../CHOLMOD/Cholesky/cholmod_analyze.c
+ $(MX) $(CH) -c $<
+
+cholmod_colamd.o: ../../CHOLMOD/Cholesky/cholmod_colamd.c
+ $(MX) $(CH) -c $<
+
+cholmod_etree.o: ../../CHOLMOD/Cholesky/cholmod_etree.c
+ $(MX) $(CH) -c $<
+
+cholmod_postorder.o: ../../CHOLMOD/Cholesky/cholmod_postorder.c
+ $(MX) $(CH) -c $<
+
+cholmod_rowcolcounts.o: ../../CHOLMOD/Cholesky/cholmod_rowcolcounts.c
+ $(MX) $(CH) -c $<
+
+cholmod_aat.o: ../../CHOLMOD/Core/cholmod_aat.c
+ $(MX) $(CH) -c $<
+
+cholmod_add.o: ../../CHOLMOD/Core/cholmod_add.c
+ $(MX) $(CH) -c $<
+
+cholmod_band.o: ../../CHOLMOD/Core/cholmod_band.c
+ $(MX) $(CH) -c $<
+
+cholmod_change_factor.o: ../../CHOLMOD/Core/cholmod_change_factor.c \
+ ../../CHOLMOD/Core/t_cholmod_change_factor.c
+ $(MX) $(CH) -c $<
+
+cholmod_common.o: ../../CHOLMOD/Core/cholmod_common.c
+ $(MX) $(CH) -c $<
+
+cholmod_complex.o: ../../CHOLMOD/Core/cholmod_complex.c
+ $(MX) $(CH) -c $<
+
+cholmod_copy.o: ../../CHOLMOD/Core/cholmod_copy.c
+ $(MX) $(CH) -c $<
+
+cholmod_dense.o: ../../CHOLMOD/Core/cholmod_dense.c \
+ ../../CHOLMOD/Core/t_cholmod_dense.c
+ $(MX) $(CH) -c $<
+
+cholmod_error.o: ../../CHOLMOD/Core/cholmod_error.c
+ $(MX) $(CH) -c $<
+
+cholmod_factor.o: ../../CHOLMOD/Core/cholmod_factor.c
+ $(MX) $(CH) -c $<
+
+cholmod_memory.o: ../../CHOLMOD/Core/cholmod_memory.c
+ $(MX) $(CH) -c $<
+
+cholmod_sparse.o: ../../CHOLMOD/Core/cholmod_sparse.c
+ $(MX) $(CH) -c $<
+
+cholmod_transpose.o: ../../CHOLMOD/Core/cholmod_transpose.c \
+ ../../CHOLMOD/Core/t_cholmod_transpose.c
+ $(MX) $(CH) -c $<
+
+cholmod_triplet.o: ../../CHOLMOD/Core/cholmod_triplet.c \
+ ../../CHOLMOD/Core/t_cholmod_triplet.c
+ $(MX) $(CH) -c $<
+
+cholmod_camd.o: ../../CHOLMOD/Partition/cholmod_camd.c
+ $(MX) $(CH) -c $<
+
+cholmod_ccolamd.o: ../../CHOLMOD/Partition/cholmod_ccolamd.c
+ $(MX) $(CH) -c $<
+
+cholmod_csymamd.o: ../../CHOLMOD/Partition/cholmod_csymamd.c
+ $(MX) $(CH) -c $<
+
+cholmod_metis.o: ../../CHOLMOD/Partition/cholmod_metis.c
+ $(MX) $(CH) -c $<
+
+cholmod_nesdis.o: ../../CHOLMOD/Partition/cholmod_nesdis.c
+ $(MX) $(CH) -c $<
+
+#===============================================================================
+
+BTF_INC = ../../BTF/Include/btf.h ../../BTF/Include/btf_internal.h
+
+BTF = btf_maxtrans.o btf_order.o btf_strongcomp.o
+
+$(BTF): $(BTF_INC)
+
+btf_maxtrans.o: ../../BTF/Source/btf_maxtrans.c
+ $(MX) -c $<
+
+btf_order.o: ../../BTF/Source/btf_order.c
+ $(MX) -c $<
+
+btf_strongcomp.o: ../../BTF/Source/btf_strongcomp.c
+ $(MX) -c $<
+
+#===============================================================================
+
+KLU_INC = ../Include/klu.h ../Include/klu_internal.h ../Include/klu_version.h \
+ ../User/klu_cholmod.h
+
+KLU_L = klu_l.o klu_l_kernel.o klu_l_dump.o \
+ klu_l_factor.o klu_l_free_numeric.o klu_l_solve.o \
+ klu_l_scale.o klu_l_refactor.o \
+ klu_l_tsolve.o klu_l_diagnostics.o klu_l_sort.o klu_l_extract.o
+
+KLU_ZL = klu_zl.o klu_zl_kernel.o klu_zl_dump.o \
+ klu_zl_factor.o klu_zl_free_numeric.o klu_zl_solve.o \
+ klu_zl_scale.o klu_zl_refactor.o \
+ klu_zl_tsolve.o klu_zl_diagnostics.o klu_zl_sort.o klu_zl_extract.o
+
+COMMON = klu_free_symbolic.o klu_defaults.o klu_analyze_given.o \
+ klu_analyze.o klu_memory.o
+
+USER = klu_l_cholmod.o
+
+KLU = $(COMMON) $(KLU_L) $(KLU_ZL) $(USER)
+
+$(KLU): $(KLU_INC)
+
+#-------------------------------------------------------------------------------
+
+klu_l.o: ../Source/klu.c
+ $(MX) -c $<
+ $(MV) klu.o $@
+
+klu_zl.o: ../Source/klu.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu.o $@
+
+klu_l_kernel.o: ../Source/klu_kernel.c
+ $(MX) -c $<
+ $(MV) klu_kernel.o $@
+
+klu_zl_kernel.o: ../Source/klu_kernel.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_kernel.o $@
+
+klu_l_sort.o: ../Source/klu_sort.c
+ $(MX) -c $<
+ $(MV) klu_sort.o $@
+
+klu_zl_sort.o: ../Source/klu_sort.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_sort.o $@
+
+klu_l_diagnostics.o: ../Source/klu_diagnostics.c
+ $(MX) -c $<
+ $(MV) klu_diagnostics.o $@
+
+klu_zl_diagnostics.o: ../Source/klu_diagnostics.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_diagnostics.o $@
+
+klu_l_dump.o: ../Source/klu_dump.c
+ $(MX) -c $<
+ $(MV) klu_dump.o $@
+
+klu_zl_dump.o: ../Source/klu_dump.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_dump.o $@
+
+klu_l_factor.o: ../Source/klu_factor.c
+ $(MX) -c $<
+ $(MV) klu_factor.o $@
+
+klu_zl_factor.o: ../Source/klu_factor.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_factor.o $@
+
+klu_l_free_numeric.o: ../Source/klu_free_numeric.c
+ $(MX) -c $<
+ $(MV) klu_free_numeric.o $@
+
+klu_zl_free_numeric.o: ../Source/klu_free_numeric.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_free_numeric.o $@
+
+klu_l_extract.o: ../Source/klu_extract.c
+ $(MX) -c $<
+ $(MV) klu_extract.o $@
+
+klu_zl_extract.o: ../Source/klu_extract.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_extract.o $@
+
+klu_l_refactor.o: ../Source/klu_refactor.c
+ $(MX) -c $<
+ $(MV) klu_refactor.o $@
+
+klu_zl_refactor.o: ../Source/klu_refactor.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_refactor.o $@
+
+klu_l_scale.o: ../Source/klu_scale.c
+ $(MX) -c $<
+ $(MV) klu_scale.o $@
+
+klu_zl_scale.o: ../Source/klu_scale.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_scale.o $@
+
+klu_l_solve.o: ../Source/klu_solve.c
+ $(MX) -c $<
+ $(MV) klu_solve.o $@
+
+klu_zl_solve.o: ../Source/klu_solve.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_solve.o $@
+
+klu_l_tsolve.o: ../Source/klu_tsolve.c
+ $(MX) -c $<
+ $(MV) klu_tsolve.o $@
+
+klu_zl_tsolve.o: ../Source/klu_tsolve.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_tsolve.o $@
+
+#-------------------------------------------------------------------------------
+
+klu_analyze.o: ../Source/klu_analyze.c
+ $(MX) -c $<
+
+klu_analyze_given.o: ../Source/klu_analyze_given.c
+ $(MX) -c $<
+
+klu_defaults.o: ../Source/klu_defaults.c
+ $(MX) -c $<
+
+klu_free_symbolic.o: ../Source/klu_free_symbolic.c
+ $(MX) -c $<
+
+klu_memory.o: ../Source/klu_memory.c
+ $(MX) -c $<
+
+#-------------------------------------------------------------------------------
+
+klu_l_cholmod.o: ../User/klu_l_cholmod.c
+ $(MX) $(CH) -c $<
+
+#===============================================================================
+
+OBJ = $(AMD) $(CAMD) $(COLAMD) $(CCOLAMD) $(METIS) $(CHOLMOD) $(KLU) $(BTF)
+
+klu: klu_mex.c $(OBJ)
+ $(MX) -output klu klu_mex.c $(OBJ)
+
diff --git a/KLU/MATLAB/Makefile_no_CHOLMOD b/KLU/MATLAB/Makefile_no_CHOLMOD
new file mode 100644
index 0000000..9e30248
--- /dev/null
+++ b/KLU/MATLAB/Makefile_no_CHOLMOD
@@ -0,0 +1,263 @@
+#===============================================================================
+# KLU/MATLAB/Makefile_no_CHOLMOD
+#===============================================================================
+
+# Makefile for klu mexFunction, without the use of CHOLMOD. Ordering options
+# 3 and 4 for klu will not be available. See "help klu" in MATLAB for more
+# details. Usage:
+#
+# make -f Makefile_no_CHOLMOD
+
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+# without CHOLMOD
+I = -I. -I../../AMD/Include -I../../AMD/Source -I../../COLAMD/Include \
+ -I../Include -I../../UFconfig -I../../BTF/Include
+
+all: klu
+
+MX = $(MEX) -DDLONG -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE $(I)
+
+distclean: purge
+
+purge: clean
+ - $(RM) *.mex* rename.h
+
+clean:
+ - $(RM) $(CLEAN)
+
+#===============================================================================
+
+AMD_INC = ../../AMD/Include/amd.h ../../AMD/Include/amd_internal.h
+
+AMD = \
+ amd_1.o \
+ amd_2.o \
+ amd_aat.o \
+ amd_control.o \
+ amd_defaults.o \
+ amd_dump.o \
+ amd_global.o \
+ amd_info.o \
+ amd_order.o \
+ amd_postorder.o \
+ amd_post_tree.o \
+ amd_preprocess.o \
+ amd_valid.o
+
+$(AMD): $(AMD_INC)
+amd_1.o: ../../AMD/Source/amd_1.c
+ $(MX) -c $<
+
+amd_2.o: ../../AMD/Source/amd_2.c
+ $(MX) -c $<
+
+amd_aat.o: ../../AMD/Source/amd_aat.c
+ $(MX) -c $<
+
+amd_control.o: ../../AMD/Source/amd_control.c
+ $(MX) -c $<
+
+amd_defaults.o: ../../AMD/Source/amd_defaults.c
+ $(MX) -c $<
+
+amd_dump.o: ../../AMD/Source/amd_dump.c
+ $(MX) -c $<
+
+amd_global.o: ../../AMD/Source/amd_global.c
+ $(MX) -c $<
+
+amd_info.o: ../../AMD/Source/amd_info.c
+ $(MX) -c $<
+
+amd_order.o: ../../AMD/Source/amd_order.c
+ $(MX) -c $<
+
+amd_postorder.o: ../../AMD/Source/amd_postorder.c
+ $(MX) -c $<
+
+amd_post_tree.o: ../../AMD/Source/amd_post_tree.c
+ $(MX) -c $<
+
+amd_preprocess.o: ../../AMD/Source/amd_preprocess.c
+ $(MX) -c $<
+
+amd_valid.o: ../../AMD/Source/amd_valid.c
+ $(MX) -c $<
+
+#===============================================================================
+
+COLAMD_INC = ../../COLAMD/Include/colamd.h
+
+COLAMD = colamd.o colamd_global.o
+
+$(COLAMD): $(COLAMD_INC)
+
+colamd.o: ../../COLAMD/Source/colamd.c
+ $(MX) -c $<
+
+colamd_global.o: ../../COLAMD/Source/colamd_global.c
+ $(MX) -c $<
+
+#===============================================================================
+
+BTF_INC = ../../BTF/Include/btf.h ../../BTF/Include/btf_internal.h
+
+BTF = btf_maxtrans.o btf_order.o btf_strongcomp.o
+
+$(BTF): $(BTF_INC)
+
+btf_maxtrans.o: ../../BTF/Source/btf_maxtrans.c
+ $(MX) -c $<
+
+btf_order.o: ../../BTF/Source/btf_order.c
+ $(MX) -c $<
+
+btf_strongcomp.o: ../../BTF/Source/btf_strongcomp.c
+ $(MX) -c $<
+
+#===============================================================================
+
+KLU_INC = ../Include/klu.h ../Include/klu_internal.h ../Include/klu_version.h
+
+KLU_L = klu_l.o klu_l_kernel.o klu_l_dump.o \
+ klu_l_factor.o klu_l_free_numeric.o klu_l_solve.o \
+ klu_l_scale.o klu_l_refactor.o \
+ klu_l_tsolve.o klu_l_diagnostics.o klu_l_sort.o klu_l_extract.o
+
+KLU_ZL = klu_zl.o klu_zl_kernel.o klu_zl_dump.o \
+ klu_zl_factor.o klu_zl_free_numeric.o klu_zl_solve.o \
+ klu_zl_scale.o klu_zl_refactor.o \
+ klu_zl_tsolve.o klu_zl_diagnostics.o klu_zl_sort.o klu_zl_extract.o
+
+COMMON = klu_free_symbolic.o klu_defaults.o klu_analyze_given.o \
+ klu_analyze.o klu_memory.o
+
+KLU = $(COMMON) $(KLU_L) $(KLU_ZL)
+
+$(KLU): $(KLU_INC)
+
+#-------------------------------------------------------------------------------
+
+klu_l.o: ../Source/klu.c
+ $(MX) -c $<
+ $(MV) klu.o $@
+
+klu_zl.o: ../Source/klu.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu.o $@
+
+klu_l_kernel.o: ../Source/klu_kernel.c
+ $(MX) -c $<
+ $(MV) klu_kernel.o $@
+
+klu_zl_kernel.o: ../Source/klu_kernel.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_kernel.o $@
+
+klu_l_sort.o: ../Source/klu_sort.c
+ $(MX) -c $<
+ $(MV) klu_sort.o $@
+
+klu_zl_sort.o: ../Source/klu_sort.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_sort.o $@
+
+klu_l_diagnostics.o: ../Source/klu_diagnostics.c
+ $(MX) -c $<
+ $(MV) klu_diagnostics.o $@
+
+klu_zl_diagnostics.o: ../Source/klu_diagnostics.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_diagnostics.o $@
+
+klu_l_dump.o: ../Source/klu_dump.c
+ $(MX) -c $<
+ $(MV) klu_dump.o $@
+
+klu_zl_dump.o: ../Source/klu_dump.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_dump.o $@
+
+klu_l_factor.o: ../Source/klu_factor.c
+ $(MX) -c $<
+ $(MV) klu_factor.o $@
+
+klu_zl_factor.o: ../Source/klu_factor.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_factor.o $@
+
+klu_l_free_numeric.o: ../Source/klu_free_numeric.c
+ $(MX) -c $<
+ $(MV) klu_free_numeric.o $@
+
+klu_zl_free_numeric.o: ../Source/klu_free_numeric.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_free_numeric.o $@
+
+klu_l_extract.o: ../Source/klu_extract.c
+ $(MX) -c $<
+ $(MV) klu_extract.o $@
+
+klu_zl_extract.o: ../Source/klu_extract.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_extract.o $@
+
+klu_l_refactor.o: ../Source/klu_refactor.c
+ $(MX) -c $<
+ $(MV) klu_refactor.o $@
+
+klu_zl_refactor.o: ../Source/klu_refactor.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_refactor.o $@
+
+klu_l_scale.o: ../Source/klu_scale.c
+ $(MX) -c $<
+ $(MV) klu_scale.o $@
+
+klu_zl_scale.o: ../Source/klu_scale.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_scale.o $@
+
+klu_l_solve.o: ../Source/klu_solve.c
+ $(MX) -c $<
+ $(MV) klu_solve.o $@
+
+klu_zl_solve.o: ../Source/klu_solve.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_solve.o $@
+
+klu_l_tsolve.o: ../Source/klu_tsolve.c
+ $(MX) -c $<
+ $(MV) klu_tsolve.o $@
+
+klu_zl_tsolve.o: ../Source/klu_tsolve.c
+ $(MX) -c -DCOMPLEX $<
+ $(MV) klu_tsolve.o $@
+
+#-------------------------------------------------------------------------------
+
+klu_analyze.o: ../Source/klu_analyze.c
+ $(MX) -c $<
+
+klu_analyze_given.o: ../Source/klu_analyze_given.c
+ $(MX) -c $<
+
+klu_defaults.o: ../Source/klu_defaults.c
+ $(MX) -c $<
+
+klu_free_symbolic.o: ../Source/klu_free_symbolic.c
+ $(MX) -c $<
+
+klu_memory.o: ../Source/klu_memory.c
+ $(MX) -c $<
+
+#===============================================================================
+
+OBJ = $(AMD) $(COLAMD) $(KLU) $(BTF)
+
+klu: klu_mex.c $(OBJ)
+ $(MX) -DNCHOLMOD -output klu klu_mex.c $(OBJ)
+
diff --git a/KLU/MATLAB/Test/klu_test.m b/KLU/MATLAB/Test/klu_test.m
new file mode 100644
index 0000000..0574ed5
--- /dev/null
+++ b/KLU/MATLAB/Test/klu_test.m
@@ -0,0 +1,19 @@
+function klu_test (nmat)
+%klu_test KLU test
+% Example:
+% klu_test
+%
+% See also klu
+
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 1)
+ nmat = 500 ;
+end
+
+test1 (nmat) ;
+test2 (nmat) ;
+test3 ;
+test4 (nmat) ;
+test5 ;
diff --git a/KLU/MATLAB/Test/test1.m b/KLU/MATLAB/Test/test1.m
new file mode 100644
index 0000000..ce3cf1b
--- /dev/null
+++ b/KLU/MATLAB/Test/test1.m
@@ -0,0 +1,117 @@
+function test1 (nmat)
+%test1: KLU test
+% Example:
+% test1
+%
+% See also klu
+
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+% http://www.cise.ufl.edu/research/sparse
+
+clear functions
+rand ('state', 0) ;
+
+index = UFget ;
+f = find (index.nrows == index.ncols & index.isReal) ;
+[ignore i] = sort (index.nnz (f)) ;
+f = f (i) ;
+
+h = waitbar (0, 'KLU test 1 of 5') ;
+
+if (nargin < 1)
+ nmat = 500 ;
+end
+nmat = min (nmat, length (f)) ;
+
+% just use the first 100 matrices
+nmat = min (nmat, 100) ;
+
+f = f (1:nmat) ;
+
+% f = 274
+% f = 101 ; % MATLAB condest is poor
+
+nmat = length (f) ;
+
+conds_klu = ones (1,nmat) ;
+conds_matlab = ones (1,nmat) ;
+
+figure (1)
+clf
+
+try
+
+ for k = 1:nmat
+
+ waitbar (k/nmat, h) ;
+
+ i = f (k) ;
+ try
+ c = -1 ;
+ blocks = 0 ;
+ rho = 0 ;
+ c2 = 0 ;
+ r1 = 0 ;
+ r2 = 0 ;
+ err = 0 ;
+
+ Prob = UFget (i,index) ;
+ A = Prob.A ;
+ c = condest (A) ;
+ % klu (A)
+ % [L,U,p,q,R,F,r,info] = klu (A) ;
+
+ [LU, info, c2] = klu (A) ;
+
+ L = LU.L ;
+ U = LU.U ;
+ p = LU.p ;
+ q = LU.q ;
+ R = LU.R ;
+ F = LU.F ;
+ r = LU.r ;
+ blocks = length (r) - 1 ;
+
+ n = size (A,1) ;
+ b = rand (n,1) ;
+ x = klu (LU,'\',b) ;
+ err = norm (A*x-b,1) / norm (A,1) ;
+
+ % info
+ rho = lu_normest (R\A(p,q) - F, L, U) ;
+ r1 = info.rcond ;
+ r2 = full (min (abs (diag (U))) / max (abs (diag (U)))) ;
+
+ if (r1 ~= r2)
+ fprintf ('!\n') ;
+ pause
+ end
+
+ conds_klu (k) = c2 ;
+ conds_matlab (k) = c ;
+
+ catch
+ disp (lasterr) ;
+ end
+
+ fprintf (...
+ 'blocks %6d err %8.2e condest %8.2e %8.2e rcond %8.2e %8.2e err %8.2e\n', ...
+ blocks, rho, c2, c, r1, r2, err) ;
+
+ end
+
+ k = nmat ;
+ plot (1:k, log10 (conds_klu (1:k) ./ conds_matlab (1:k)), 'o') ;
+ drawnow
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
diff --git a/KLU/MATLAB/Test/test2.m b/KLU/MATLAB/Test/test2.m
new file mode 100644
index 0000000..83cdd54
--- /dev/null
+++ b/KLU/MATLAB/Test/test2.m
@@ -0,0 +1,184 @@
+function test2 (nmat)
+%test2: KLU test
+% Example:
+% test2
+% See also klu
+
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+% http://www.cise.ufl.edu/research/sparse
+
+clear functions
+rand ('state', 0) ;
+% warning ('off', 'MATLAB:singularMatrix') ;
+% warning ('off', 'MATLAB:nearlySingularMatrix') ;
+% warning ('off', 'MATLAB:divideByZero') ;
+
+index = UFget ;
+f = find (index.nrows == index.ncols) ;
+[ignore i] = sort (index.nnz (f)) ;
+f = f (i) ;
+
+if (nargin < 1)
+ nmat = 500 ;
+end
+nmat = min (nmat, length (f)) ;
+f = f (1:nmat) ;
+
+if (~isempty (strfind (computer, '64')))
+ is64 = 1 ;
+else
+ is64 = 0 ;
+end
+
+Tklu = 1e-6 * ones (2*nmat,1) ;
+Tmatlab = zeros (2*nmat,1) ;
+Tcsparse = zeros (2*nmat,1) ;
+LUnz = zeros (2*nmat, 1) ;
+k = 0 ;
+
+h = waitbar (0, 'KLU test 2 of 5') ;
+
+figure (1)
+clf
+
+try
+
+ for kk = 1:nmat
+
+ Prob = UFget (f (kk), index) ;
+
+ waitbar (kk/nmat, h) ;
+
+ disp (Prob) ;
+ if (isfield (Prob, 'kind'))
+ if (~isempty (strfind (Prob.kind, 'subsequent')))
+ fprintf ('skip ...\n') ;
+ continue
+ end
+ end
+ A = Prob.A ;
+
+ for do_complex = 0:1
+
+ k = k + 1 ;
+ if (do_complex)
+ A = sprand (A) + 1i * sprand (A) ;
+ end
+
+ try
+ [L,U,p,q] = lu (A, 'vector') ;
+ catch
+ % older version of MATLAB, which doesn't have 'vector' option
+ [L,U,P,Q] = lu (A) ;
+ [p ignore1 ignore2] = find (P') ;
+ [q ignore1 ignore2] = find (Q) ;
+ clear ignore1 ignore2 P Q
+ end
+
+ LU.L = L ;
+ LU.U = U ;
+ if (is64)
+ LU.p = int64 (p) ;
+ LU.q = int64 (q) ;
+ else
+ LU.p = int32 (p) ;
+ LU.q = int32 (q) ;
+ end
+ C = A (p,q) ;
+ LUnz (k) = nnz (L) + nnz (U) ;
+
+ n = size (A,1) ;
+
+ do_klu = (nnz (diag (U)) == n) ;
+ if (do_klu)
+
+ fprintf ('klu...\n') ;
+ err = 0 ;
+ erc = 0 ;
+ er2 = 0 ;
+ for nrhs = 10:-1:1
+
+ b = rand (n,nrhs) ;
+
+ tic ;
+ x = klu (LU,'\',b) ;
+ Tklu (k) = max (1e-6, toc) ;
+
+ tic ;
+ y = U \ (L \ b (p,:)) ;
+ y (q,:) = y ;
+ Tmatlab (k) = max (1e-6, toc) ;
+
+ if (nrhs == 1 & isreal (U) & isreal (L) & isreal (b)) %#ok
+ tic ;
+ z = cs_usolve (U, cs_lsolve (L, b (p))) ;
+ z (q) = z ;
+ Tcsparse (k) = max (1e-6, toc) ;
+ erc = norm (A*z-b,1) / norm (A,1) ;
+ end
+
+ err = max (err, norm (A*x-b,1) / norm (A,1)) ;
+ er2 = max (er2, norm (A*y-b,1) / norm (A,1)) ;
+ if (err > 100*er2)
+ fprintf ('error %g %g\n', err, er2) ;
+ error ('?') ;
+ end
+ end
+
+ fprintf ('klu... with randomized scaling for L\n') ;
+ er3 = 0 ;
+ er4 = 0 ;
+ D = spdiags (rand (n,1), 0, n, n) ;
+ LU.L = D * L ;
+ A2 = D * A (p,q) ;
+ if (is64)
+ LU.p = int64 (1:n) ;
+ LU.q = int64 (1:n) ;
+ else
+ LU.p = int32 (1:n) ;
+ LU.q = int32 (1:n) ;
+ end
+ for nrhs = 1:10
+ b = rand (n,nrhs) ;
+ x = klu (LU,'\',b) ;
+ y = U \ (LU.L \ b) ;
+ er3 = max (er3, norm (A2*x-b,1) / norm (A,1)) ;
+ er4 = max (er4, norm (A2*y-b,1) / norm (A,1)) ;
+ if (er3 > 1e3*er4)
+ fprintf ('error %g %g\n', er3, er4) ;
+ error ('?') ;
+ end
+ end
+
+
+ else
+ err = Inf ;
+ er2 = Inf ;
+ er3 = Inf ;
+ er4 = Inf ;
+ erc = Inf ;
+ end
+
+ lumax = max (LUnz (1:k)) ;
+ loglog (...
+ LUnz (1:k), Tmatlab (1:k) ./ Tklu (1:k), 'o', ...
+ LUnz (1:k), Tcsparse (1:k) ./ Tklu (1:k), 'x', ...
+ [20 lumax], [1 1], 'r-') ;
+ axis ([20 lumax .1 20]) ;
+ drawnow
+
+ fprintf ('err %g %g %g\n', err, er2, erc) ;
+ end
+ end
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
diff --git a/KLU/MATLAB/Test/test3.m b/KLU/MATLAB/Test/test3.m
new file mode 100644
index 0000000..a8edbbb
--- /dev/null
+++ b/KLU/MATLAB/Test/test3.m
@@ -0,0 +1,61 @@
+function test3
+%test3: KLU test
+% Example:
+% test3
+% See also klu
+
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+% http://www.cise.ufl.edu/research/sparse
+
+h = waitbar (1/12, 'KLU test 3 of 5') ;
+
+rand ('state', 0) ;
+
+load west0479
+A = west0479 ;
+% A = sparse (rand (4)) ;
+% A (3:4, 1:2) = 0 ;
+
+n = size (A,1) ;
+b = rand (n,1) ;
+spparms ('spumoni',2)
+x = A\b ;
+spparms ('spumoni',0)
+fprintf ('MATLAB resid %g\n', norm (A*x-b,1)) ;
+
+[LU,info,cond_estimate] = klu (A) ;
+fprintf ('\nLU = \n') ; disp (LU) ;
+fprintf ('\ninfo = \n') ; disp (info) ;
+fprintf ('KLU condest %g\n', cond_estimate) ;
+matlab_condest = condest (A) ;
+matlab_cond = cond (full (A)) ;
+fprintf ('MATLAB condest %g cond %g\n', matlab_condest, matlab_cond) ;
+
+for nrhs = 1:10
+ waitbar (nrhs/12, h) ;
+ b = rand (n,nrhs) ;
+ x = klu (LU,'\',b) ;
+ fprintf ('nrhs: %d resid: %g\n', ...
+ nrhs, norm (A*x-b,1) / norm (A,1)) ;
+end
+
+[x,info,cond_estimate] = klu (A, '\', b) ;
+fprintf ('\ninfo = \n') ; disp (info) ;
+fprintf ('KLU cond_estimate %g\n', cond_estimate) ;
+
+waitbar (11/12, h) ;
+
+[x,info] = klu (A, '\', b, struct ('ordering',1)) ;
+fprintf ('\ninfo = \n') ; disp (info) ;
+[x,info,cond_estimate] = klu (A, '\', b, struct ('ordering',2)) ;
+fprintf ('\ninfo = \n') ; disp (info) ;
+try
+ [x,info,cond_estimate] = klu (A, '\', b, struct ('ordering',3)) ;
+ fprintf ('\ninfo = \n') ; disp (info) ;
+ [x,info,cond_estimate] = klu (A, '\', b, struct ('ordering',4)) ;
+ fprintf ('\ninfo = \n') ; disp (info) ;
+catch
+ fprintf ('KLU test with CHOLMOD skipped (CHOLMOD not installed)\n') ;
+end
+
+close (h) ;
diff --git a/KLU/MATLAB/Test/test4.m b/KLU/MATLAB/Test/test4.m
new file mode 100644
index 0000000..9ae5388
--- /dev/null
+++ b/KLU/MATLAB/Test/test4.m
@@ -0,0 +1,221 @@
+function test4 (nmat)
+%test4: KLU test
+% Example:
+% test4
+% See also klu
+
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+% http://www.cise.ufl.edu/research/sparse
+
+% rand ('state', 0) ;
+% warning ('off', 'MATLAB:singularMatrix') ;
+% warning ('off', 'MATLAB:nearlySingularMatrix') ;
+% warning ('off', 'KLU:rcond') ;
+% warning ('off', 'MATLAB:Axes:NegativeDataInLogAxis') ;
+
+index = UFget ;
+f = find (index.nrows == index.ncols & index.isReal & index.amd_lnz > 0) ;
+[ignore i] = sort (index.amd_lnz (f)) ;
+f = f (i) ;
+% f = f (1:100) ;
+
+if (nargin < 1)
+ nmat = 500 ;
+end
+nmat = min (nmat, length (f)) ;
+f = f (1:nmat) ;
+
+if (1)
+ Tlu = -ones (nmat,1) ;
+ Tklu = -ones (nmat,1) ;
+ Tklu2 = -ones (nmat,1) ;
+ LUnz = -ones (nmat,1) ;
+ k = 0 ;
+end
+
+if (~isempty (strfind (computer, '64')))
+ is64 = 1 ;
+else
+ is64 = 0 ;
+end
+
+% 589: Sieber
+
+h = waitbar (0, 'KLU test 4 of 5') ;
+
+figure (1)
+clf
+
+try
+
+ for kk = 1:nmat
+
+ Prob = UFget (f (kk), index) ;
+
+ waitbar (kk/nmat, h) ;
+
+ disp (Prob) ;
+ if (isfield (Prob, 'kind'))
+ if (~isempty (strfind (Prob.kind, 'subsequent')))
+ fprintf ('skip ...\n') ;
+ continue
+ end
+ if (~isempty (strfind (Prob.kind, 'random')))
+ fprintf ('skip ...\n') ;
+ continue
+ end
+ end
+ k = k + 1 ;
+ A = Prob.A ;
+ n = size (A,1) ;
+ err1 = 0 ;
+ err2 = 0 ;
+ err4 = 0 ;
+ terr1 = 0 ;
+ terr2 = 0 ;
+ terr4 = 0 ;
+
+
+ for do_imag = 0:1
+ if (do_imag)
+ A = sprand (A) + 1i * sprand (A) ;
+ end
+
+ % compare with UMFPACK
+ try
+ tic
+ [L,U,p,q,R1] = lu (A, 'vector') ;
+ t1 = max (1e-6, toc) ;
+ catch
+ % older version of MATLAB, which doesn't have 'vector' option
+ tic
+ [L,U,P,Q] = lu (A) ;
+ t1 = max (1e-6, toc) ;
+ [p ignore1 ignore2] = find (P') ;
+ [q ignore1 ignore2] = find (Q) ;
+ clear ignore1 ignore2 P Q
+ R1 = speye (n) ;
+ end
+
+ if (Tlu (k) == -1)
+ Tlu (k) = t1 ;
+ LUnz (k) = nnz (L) + nnz (U) ;
+ end
+
+ % note that the scaling R1 and R2 are different with KLU and UMFPACK
+ % UMFPACK: L*U-P*(R1\A)*Q
+ % KLU: L*U-R2\(P*A*Q)
+ %
+ % R1 and R2 are related, via P, where R2 = P*R*P', or equivalently
+ % R2 = R1 (p,p).
+
+ rcond = min (abs (diag (U))) / max (abs (diag (U))) ;
+ if (rcond < 1e-15)
+ fprintf ('skip...\n') ;
+ break ;
+ end
+
+ F.L = L ;
+ F.U = U ;
+ if (is64)
+ F.p = int64(p) ;
+ F.q = int64(q) ;
+ else
+ F.p = int32(p) ;
+ F.q = int32(q) ;
+ end
+
+ F.R = R1(p,p) ;
+ b = rand (n,1) ;
+ x = klu (F, '\', b) ;
+ y = klu (b', '/', F) ;
+
+ fprintf ('solve with klu %g\n', ...
+ norm (A*x-b,1)/norm(A,1)) ;
+ fprintf ('solve with klu %g transpose\n', ...
+ norm (y*A-b',1)/norm(A,1)) ;
+
+
+ for nrhs = 1:10
+ for do_b_imag = 0:1
+ b = rand (n, nrhs) ;
+ if (do_b_imag)
+ b = b + 1i * rand (n, nrhs) ;
+ end
+
+ % KLU backslash
+ tic ;
+ x = klu (A,'\',b) ;
+ t2 = max (1e-6, toc) ;
+
+ % KLU slash
+ xt = klu (b','/',A) ;
+
+ % KLU backslash with precomputed LU
+ tic
+ LU = klu (A) ;
+ z = klu (LU,'\',b) ;
+ t4 = max (1e-6, toc) ;
+
+ % KLU slash with precomputed LU
+ zt = klu (b','/',LU) ;
+
+ % UMFPACK
+ tic
+ rb = R1 \ b ;
+ y = U \ (L \ rb (p,:)) ;
+ y (q,:) = y ;
+ t3 = max (1e-6, toc) ;
+
+ yt = (L' \ (U' \ b (q,:))) ;
+ yt (p,:) = yt ;
+ yt = R1 \ yt ;
+ yt = yt' ;
+
+ if (Tklu (k) == -1)
+ Tlu (k) = Tlu (k) + t3 ;
+ Tklu (k) = t2 ;
+ Tklu2 (k) = t4 ;
+ end
+
+ err1 = max (err1, norm (A*x-b,1) / norm (A,1)) ;
+ err2 = max (err2, norm (A*y-b,1) / norm (A,1)) ;
+ err4 = max (err4, norm (A*z-b,1) / norm (A,1)) ;
+
+ terr1 = max (terr1, norm (xt*A-b',1) / norm (A,1)) ;
+ terr2 = max (terr2, norm (yt*A-b',1) / norm (A,1)) ;
+ terr4 = max (terr4, norm (zt*A-b',1) / norm (A,1)) ;
+ end
+ end
+ end
+
+ fprintf ('err %g %g %g\n', err1, err2, err4) ;
+ if (err1 > 1e4*err2 | err4 > 1e4*err2) %#ok
+ fprintf ('warning: KLU inaccurate!\n')
+ end
+
+ fprintf ('terr %g %g %g\n', terr1, terr2, terr4) ;
+ if (terr1 > 1e4*terr2 | terr4 > 1e4*terr2) %#ok
+ fprintf ('warning: KLU T inaccurate!\n')
+ end
+
+ lunzmax = max (LUnz (1:k)) ;
+ loglog ( ...
+ LUnz (1:k), Tklu (1:k) ./ Tlu (1:k), 'o', ...
+ LUnz (1:k), Tklu2 (1:k) ./ Tlu (1:k), 'x', ...
+ [10 lunzmax], [1 1], 'r-') ;
+ drawnow
+
+ end
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
diff --git a/KLU/MATLAB/Test/test5.m b/KLU/MATLAB/Test/test5.m
new file mode 100644
index 0000000..e6aa618
--- /dev/null
+++ b/KLU/MATLAB/Test/test5.m
@@ -0,0 +1,180 @@
+function test5
+%test5: KLU test
+% Example:
+% test5
+%
+% test circuit matrices in the UF sparse matrix collection.
+%
+% See also klu
+
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+% http://www.cise.ufl.edu/research/sparse
+
+do_diary = 0 ;
+
+if (do_diary)
+ diary off
+ s = date ;
+ t = clock ;
+ s = sprintf ('diary test5_%s_%d-%d-%d.txt\n', s, t (4), t(5), fix(t(6)));
+ eval (s) ;
+end
+
+% ATandT frequency-domain circuits, exclude these:
+freq = [ 283 284 285 286 ] ;
+
+% sorted in order of MATLAB 7.3 x=A\b time on storm
+% (AMD Opteron, 64-bit, 8GB mem, 2 cores)
+circ = [
+1195 % Rajat/rajat11 n: 135 nz 665
+1198 % Rajat/rajat14 n: 180 nz 1475
+1189 % Rajat/rajat05 n: 301 nz 1250
+1169 % Sandia/oscil_trans_01 n: 430 nz 1614
+1112 % Sandia/oscil_dcop_01 n: 430 nz 1544
+1346 % Rajat/rajat19 n: 1157 nz 3699
+1199 % Hamrle/Hamrle1 n: 32 nz 98
+1106 % Sandia/fpga_trans_01 n: 1220 nz 7382
+1188 % Rajat/rajat04 n: 1041 nz 8725
+1055 % Sandia/fpga_dcop_01 n: 1220 nz 5892
+1108 % Sandia/init_adder1 n: 1813 nz 11156
+1196 % Rajat/rajat12 n: 1879 nz 12818
+1053 % Sandia/adder_trans_01 n: 1814 nz 14579
+539 % Hamm/add20 n: 2395 nz 13151
+371 % Bomhof/circuit_2 n: 4510 nz 21199
+540 % Hamm/add32 n: 4960 nz 19848
+1186 % Rajat/rajat02 n: 1960 nz 11187
+466 % Grund/meg4 n: 5860 nz 25258
+465 % Grund/meg1 n: 2904 nz 58142
+370 % Bomhof/circuit_1 n: 2624 nz 35823
+1200 % Hamrle/Hamrle2 n: 5952 nz 22162
+1197 % Rajat/rajat13 n: 7598 nz 48762
+1187 % Rajat/rajat03 n: 7602 nz 32653
+372 % Bomhof/circuit_3 n: 12127 nz 48137
+1185 % Rajat/rajat01 n: 6833 nz 43250
+1183 % IBM_Austin/coupled n: 11341 nz 97193
+1376 % Rajat/rajat27 n: 20640 nz 97353
+543 % Hamm/memplus n: 17758 nz 99147
+1109 % Sandia/mult_dcop_01 n: 25187 nz 193276
+1371 % Rajat/rajat22 n: 39899 nz 195429
+1375 % Rajat/rajat26 n: 51032 nz 247528
+1414 % IBM_EDA/ckt11752_tr_0 n: 49702 nz 332807
+541 % Hamm/bcircuit n: 68902 nz 375558
+1413 % IBM_EDA/ckt11752_dc_1 n: 49702 nz 333029
+542 % Hamm/hcircuit n: 105676 nz 513072
+1316 % Rajat/rajat15 n: 37261 nz 443573
+1190 % Rajat/rajat06 n: 10922 nz 46983
+1191 % Rajat/rajat07 n: 14842 nz 63913
+1372 % Rajat/rajat23 n: 110355 nz 555441
+373 % Bomhof/circuit_4 n: 80209 nz 307604
+544 % Hamm/scircuit n: 170998 nz 958936
+1412 % AMD/G2_circuit n: 150102 nz 726674 is this solid state device?
+1415 % Sandia/ASIC_100k n: 99340 nz 940621
+1416 % Sandia/ASIC_100ks n: 99190 nz 578890
+1420 % Sandia/ASIC_680ks n: 682712 nz 1693767
+1192 % Rajat/rajat08 n: 19362 nz 83443
+1193 % Rajat/rajat09 n: 24482 nz 105573
+1323 % IBM_EDA/trans4 n: 116835 nz 749800
+1320 % IBM_EDA/dc1 n: 116835 nz 766396
+1194 % Rajat/rajat10 n: 30202 nz 130303
+1418 % Sandia/ASIC_320ks n: 321671 nz 1316085
+1417 % Sandia/ASIC_320k n: 321821 nz 1931828
+1343 % Rajat/rajat16 n: 94294 nz 476766
+1345 % Rajat/rajat18 n: 94294 nz 479151
+1344 % Rajat/rajat17 n: 94294 nz 479246
+1377 % Rajat/rajat28 n: 87190 nz 606489
+1369 % Rajat/rajat20 n: 86916 nz 604299
+1374 % Rajat/rajat25 n: 87190 nz 606489
+1370 % Rajat/rajat21 n: 411676 nz 1876011
+1419
+1396
+1201
+1397
+1421
+1398
+1373 % Rajat/rajat24 n: 358172 nz 1946979
+]' ;
+
+fprintf ('Running KLU on %d circuits.\n', length (circ)) ;
+
+index = UFget ;
+
+opts_noscale.scale = -1 ;
+opts_sum.scale = 1 ;
+opts_max.scale = 2 ; % default scaling
+
+h = waitbar (0, 'KLU test 5 of 5') ;
+nmat = length (circ) ;
+
+try
+
+ for kk = 1:nmat
+
+ k = circ (kk) ;
+ Prob = UFget (k, index) ;
+
+ waitbar (kk/nmat, h) ;
+
+ A = Prob.A ;
+ n = size (A,1) ;
+ b = rand (n,1) ;
+ fprintf ('\n%d : %s n: %d nz %d\n', k, Prob.name, n, nnz (A)) ;
+
+ try
+ tic ;
+ x2 = klu (A, '\', b, opts_noscale) ;
+ t2 = toc ;
+ e2 = norm (A*x2-b) ;
+ catch
+ t2 = 0 ;
+ e2 = 0 ;
+ end
+ fprintf ('KLU no scale: err %8.2e t: %8.4f\n', e2, t2) ;
+
+ try
+ tic ;
+ x4 = klu (A, '\', b, opts_max) ;
+ t4 = toc ;
+ e4 = norm (A*x4-b) ;
+ catch
+ t4 = 0 ;
+ e4 = 0 ;
+ end
+ fprintf ('KLU max scale: err %8.2e t: %8.4f\n', e4, t4) ;
+
+ try
+ tic ;
+ x3 = klu (A, '\', b, opts_sum) ;
+ t3 = toc ;
+ e3 = norm (A*x3-b) ;
+ catch
+ t3 = 0 ;
+ e3 = 0 ;
+ end
+ fprintf ('KLU sum scale: err %8.2e t: %8.4f\n', e3, t3) ;
+
+ tic
+ x1 = A\b ;
+ t1 = toc ;
+ e1 = norm (A*x1-b) ;
+ fprintf ('matlab: err %8.2e t: %8.4f\n', e1, t1) ;
+
+ fprintf (' speedup %8.2f\n', t1 / t4) ;
+ clear Prob
+
+ if (do_diary)
+ diary off
+ diary on
+ end
+ end
+
+catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+end
+
+close (h) ;
diff --git a/KLU/MATLAB/klu.m b/KLU/MATLAB/klu.m
new file mode 100644
index 0000000..547c2bf
--- /dev/null
+++ b/KLU/MATLAB/klu.m
@@ -0,0 +1,71 @@
+function [LU_or_x,info,c] = klu (A,operation,b,opts) %#ok
+%KLU sparse left-looking LU factorization, using a block triangular form.
+%
+% Example:
+% LU = klu (A) factorizes R\A(p,q) into L*U+F, returning a struct
+% x = klu (A,'\',b) x = A\b, using KLU
+% x = klu (b,'/',A) x = b/A, using KLU
+% x = klu (LU,'\',b) x = A\b, where LU = klu(A)
+% x = klu (b,'/',LU) x = b/A, where LU = klu(A)
+%
+% KLU(A) factorizes a square sparse matrix, L*U+F = R\A(p,q), where L and U
+% are the factors of the diagonal blocks of the block, F are the entries
+% above the diagonal blocks. r corresponds to the 3rd output of dmperm; it
+% specifies where the block boundaries are. The kth block consists of
+% rows/columns r(k) to r(k+1)-1 of A(p,q).
+%
+% Note that the use of the scale factor R differs between KLU and UMFPACK
+% (and the LU function, which is based on UMFPACK). In LU, the factorization
+% is L*U = P*(R1\A)*Q; in KLU it is L*U+F = R2\(P*A*Q). R1 and R2 are related
+% via R2 = P*R1*P', or equivalently R2 = R1(p,p).
+%
+% The LU output is a struct containing members L, U, p, q, R, F, and r.
+%
+% opts is an optional input struct which appears as the last input argument.
+% Entries not present are set to their defaults:
+%
+% opts.tol 0.001 partial pivoting tolerance; valid range 0 to 1.
+% opts.btf 1 use block triangular form (BTF) if nonzero
+% opts.ordering 0 how each block is ordered:
+% 0: AMD, 1: COLAMD, 2: natural,
+% 3: CHOLMOD's ordering of (A'*A),
+% 4: CHOLMOD's ordering of (A+A')
+% opts.scale -1 1: R = diag(sum(abs(A)')), row-sum
+% 2: R = diag(max(abs(A)')), max in each row
+% otherwise: none (R=I)
+% opts.maxwork 0 if > 0, limit work in BTF ordering to
+% opts.maxwork*nnz(A); no limit if <= 0.
+%
+% The CHOLMOD ordering is to try AMD (for A+A') or COLAMD (for A'*A)
+% first. If the fill-in with AMD or COLAMD is high, METIS is tried (on
+% A+A' or A'*A), and the best ordering found is selected. CHOLMOD, METIS,
+% CAMD, and CCOLAMD are required. If not available, only ordering options
+% 0, 1, and 2 may be used (AMD and COLAMD are always required by KLU).
+%
+% Two optional outputs, [LU,info,c] = klu (A) or [x,info,c] = klu (A,'\',b)
+% provide statistics about the factorization:
+%
+% info.noffdiag number of off-diagonal pivots chosen (after preordering)
+% info.nrealloc number of memory reallocations of L and U
+% info.rcond a very cheap estimate of 1/(condition number)
+% info.rgrowth reciprocal pivot growth
+% info.flops flop count
+% info.nblocks # of blocks in BTF form (1 if not computed)
+% info.ordering AMD, COLAMD, natural, cholmod(AA'), cholmod(A+A')
+% info.scale scaling (<=0: none, 1: sum, 2: max)
+% info.lnz nnz(L), including diagonal
+% info.unz nnz(U), including diagonal
+% info.offnz nnz(F)
+% info.tol pivot tolerance used
+% info.memory peak memory usage in bytes
+% c the same as MATLAB's condest
+%
+% info and c are relevant only if the matrix is factorized (LU = klu (A),
+% x = klu (A,'/',b), or x = klu (b,'/',A) usages).
+%
+% See also BTF, LU, DMPERM, CONDEST, CHOLMOD, AMD, COLAMD, CAMD, CCOLAMD.
+
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+% http://www.cise.ufl.edu/research/sparse
+
+error ('klu mexFunction not found') ;
diff --git a/KLU/MATLAB/klu_demo.m b/KLU/MATLAB/klu_demo.m
new file mode 100644
index 0000000..6fdce1e
--- /dev/null
+++ b/KLU/MATLAB/klu_demo.m
@@ -0,0 +1,79 @@
+function klu_demo
+% KLU demo
+%
+% Example:
+% klu_demo
+%
+% See also klu, btf
+
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+
+load west0479
+A = west0479 ;
+
+n = size (A,1) ;
+b = rand (n,1) ;
+
+clf
+subplot (2,2,1) ;
+spy (A)
+title ('west0479') ;
+
+subplot (2,2,2) ;
+[p, q, r] = btf (A) ;
+drawbtf (A, p, q, r) ;
+title ('BTF form') ;
+
+[x,info,c] = klu (A, '\', b) ;
+matlab_condest = condest (A) ;
+matlab_cond = cond (full (A)) ;
+fprintf ('MATLAB condest: %g KLU condest: %g cond: %g\n', ...
+ matlab_condest, c, matlab_cond) ;
+
+fprintf ('\nKLU with scaling, AMD ordering and condition number estimate:\n') ;
+[LU,info] = klu (A, struct ('ordering',0, 'scale', 1)) ;
+x = klu (LU, '\', b) ;
+resid = norm (A*x-b,1) / norm (A,1) ;
+rgrowth = full (min (max (abs ((LU.R \ A (LU.p,LU.q)) - LU.F)) ./ ...
+ max (abs (LU.U)))) ;
+fprintf ('resid: %g KLU condest: %g rgrowth: %g\n', resid, c, rgrowth) ;
+disp (info) ;
+
+subplot (2,2,3) ;
+spy (LU.L + LU.U + LU.F) ;
+title ('KLU+AMD factors') ;
+
+fprintf ('\nKLU with COLAMD ordering\n') ;
+[LU,info] = klu (A, struct ('ordering',1)) ;
+x = klu (LU, '\', b) ;
+resid = norm (A*x-b,1) / norm (A,1) ;
+fprintf ('resid: %g\n', resid) ;
+disp (info) ;
+
+subplot (2,2,4) ;
+spy (LU.L + LU.U + LU.F) ;
+title ('KLU+COLAMD factors') ;
+
+fprintf ('\nKLU with natural ordering (lots of fillin)\n') ;
+[x,info] = klu (A, '\', b, struct ('ordering',2)) ;
+resid = norm (A*x-b,1) / norm (A,1) ;
+fprintf ('resid: %g\n', resid) ;
+disp (info) ;
+
+try
+
+ fprintf ('\nKLU with CHOLMOD(A''*A) ordering\n') ;
+ [x,info] = klu (A, '\', b, struct ('ordering',3)) ;
+ resid = norm (A*x-b,1) / norm (A,1) ;
+ fprintf ('resid: %g\n', resid) ;
+ disp (info) ;
+
+ fprintf ('\nKLU with CHOLMOD(A+A'') ordering\n') ;
+ [x,info] = klu (A, '\', b, struct ('ordering',4)) ;
+ resid = norm (A*x-b,1) / norm (A,1) ;
+ fprintf ('resid: %g\n', resid) ;
+ disp (info) ;
+
+catch
+ fprintf ('KLU test with CHOLMOD skipped (CHOLMOD not installed)\n') ;
+end
diff --git a/KLU/MATLAB/klu_demo.m.out b/KLU/MATLAB/klu_demo.m.out
new file mode 100644
index 0000000..c591adf
--- /dev/null
+++ b/KLU/MATLAB/klu_demo.m.out
@@ -0,0 +1,88 @@
+klu_demo
+MATLAB condest: 1.42443e+12 KLU condest: 1.42443e+12 cond: 3.25816e+11
+
+KLU with scaling, AMD ordering and condition number estimate:
+resid: 3.88932e-13 KLU condest: 1.42443e+12 rgrowth: 1.85769e-05
+ noffdiag: 12
+ nrealloc: 0
+ rcond: 7.1253e-09
+ rgrowth: 1.8577e-05
+ flops: 31592
+ nblocks: 166
+ ordering: 0
+ scale: 1
+ lnz: 1923
+ unz: 1892
+ offnz: 450
+ tol: 1.0000e-03
+ memory: 136748
+
+
+KLU with COLAMD ordering
+resid: 1.00707e-11
+ noffdiag: 14
+ nrealloc: 0
+ rcond: 9.1888e-10
+ rgrowth: 4.3963e-08
+ flops: 42513
+ nblocks: 166
+ ordering: 1
+ scale: 2
+ lnz: 1956
+ unz: 2490
+ offnz: 450
+ tol: 1.0000e-03
+ memory: 397692
+
+
+KLU with natural ordering (lots of fillin)
+resid: 3.13025e-13
+ noffdiag: 437
+ nrealloc: 0
+ rcond: 6.4525e-08
+ rgrowth: 1.7654e-04
+ flops: 328911
+ nblocks: 2
+ ordering: 2
+ scale: 2
+ lnz: 7846
+ unz: 7332
+ offnz: 40
+ tol: 1.0000e-03
+ memory: 453556
+
+
+KLU with CHOLMOD(A'*A) ordering
+resid: 1.7568e-13
+ noffdiag: 24
+ nrealloc: 0
+ rcond: 4.1814e-09
+ rgrowth: 1.0676e-04
+ flops: 36747
+ nblocks: 166
+ ordering: 3
+ scale: 2
+ lnz: 2020
+ unz: 2227
+ offnz: 450
+ tol: 1.0000e-03
+ memory: 191132
+
+
+KLU with CHOLMOD(A+A') ordering
+resid: 5.1045e-13
+ noffdiag: 13
+ nrealloc: 0
+ rcond: 3.9046e-11
+ rgrowth: 2.4378e-06
+ flops: 31925
+ nblocks: 166
+ ordering: 4
+ scale: 2
+ lnz: 2000
+ unz: 1878
+ offnz: 450
+ tol: 1.0000e-03
+ memory: 136044
+
+diary off
diff --git a/KLU/MATLAB/klu_install.m b/KLU/MATLAB/klu_install.m
new file mode 100644
index 0000000..779c36d
--- /dev/null
+++ b/KLU/MATLAB/klu_install.m
@@ -0,0 +1,59 @@
+function klu_install (with_cholmod)
+%KLU_INSTALL compiles and installs the KLU, BTF, AMD, and COLAMD mexFunctions
+%
+% Example:
+% klu_install % compiles KLU without CHOLMOD
+% klu_install (1) % with CHOLMOD, CCAMD, CCOLAMD, and METIS
+%
+% KLU relies on AMD, COLAMD, and BTF for its ordering options, and can
+% optionally use CHOLMOD, CCOLAMD, CAMD, and METIS as well. By default,
+% CHOLMOD, CCOLAMD, CAMD, and METIS are not used.
+%
+% See http://www-users.cs.umn.edu/~karypis/metis for a copy of METIS 4.0.1.
+%
+% You must type the klu_install command while in the KLU/MATLAB directory.
+%
+% See also klu, btf
+
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+
+if (nargin < 1)
+ with_cholmod = 0 ;
+end
+
+% compile KLU and add to the path
+klu_make (with_cholmod) ;
+klu_path = pwd ;
+addpath (klu_path)
+
+fprintf ('\nNow compiling the AMD, COLAMD, and BTF mexFunctions:\n') ;
+
+% compile BTF and add to the path
+cd ../../BTF/MATLAB
+btf_make
+btf_path = pwd ;
+addpath (btf_path)
+
+% compile AMD and add to the path
+cd ../../AMD/MATLAB
+amd_make
+amd_path = pwd ;
+addpath (amd_path)
+
+% compile COLAMD and add to the path
+cd ../../COLAMD/MATLAB
+colamd_make
+colamd_path = pwd ;
+addpath (colamd_path)
+
+cd (klu_path)
+
+fprintf ('\nThe following paths have been added. You may wish to add them\n') ;
+fprintf ('permanently, using the MATLAB pathtool command.\n') ;
+fprintf ('%s\n', klu_path) ;
+fprintf ('%s\n', amd_path) ;
+fprintf ('%s\n', colamd_path) ;
+fprintf ('%s\n', btf_path) ;
+
+fprintf ('\nTo try your new mexFunctions, cut-and-paste this command:\n') ;
+fprintf ('klu_demo, btf_demo, amd_demo, colamd_demo\n') ;
diff --git a/KLU/MATLAB/klu_make.m b/KLU/MATLAB/klu_make.m
new file mode 100644
index 0000000..1afd42c
--- /dev/null
+++ b/KLU/MATLAB/klu_make.m
@@ -0,0 +1,368 @@
+function klu_make (with_cholmod)
+%KLU_MAKE compiles the KLU mexFunctions
+%
+% Example:
+% klu_make % compiles KLU without CHOLMOD
+% klu_make (1) % with CHOLMOD, CCAMD, CCOLAMD, and METIS
+%
+% KLU relies on AMD, COLAMD, and BTF for its ordering options, and can
+% optionally use CHOLMOD, CCOLAMD, CAMD, and METIS as well. By default,
+% CHOLMOD, CCOLAMD, CAMD, and METIS are not used.
+%
+% See http://www-users.cs.umn.edu/~karypis/metis for a copy of METIS 4.0.1.
+%
+% You must type the klu_make command while in the KLU/MATLAB directory.
+%
+% See also klu
+
+% Copyright 2004-2007 Timothy A. Davis, Univ. of Florida
+% http://www.cise.ufl.edu/research/sparse
+
+if (nargin < 1)
+ with_cholmod = 0 ;
+end
+
+details = 0 ; % if 1, print details of each command
+
+% modify this if your copy of METIS is not in SuiteSparse/metis-4.0:
+metis_path = '../../metis-4.0' ;
+
+d = '' ;
+if (~isempty (strfind (computer, '64')))
+ % 64-bit MATLAB
+ d = '-largeArrayDims' ;
+end
+
+fprintf ('Compiling KLU ') ;
+kk = 0 ;
+
+include = '-I. -I../../AMD/Include -I../../COLAMD/Include -I../Include -I../../UFconfig -I../../BTF/Include' ;
+
+if (with_cholmod)
+ include = [include ' -I../../CCOLAMD/Include -I../../CAMD/Include -I../../CHOLMOD/Include -I../../UFconfig -I' metis_path '/Lib -I../User'] ;
+end
+
+% do not attempt to compile CHOLMOD with large file support (not needed)
+include = [include ' -DNLARGEFILE'] ;
+
+% fix the METIS 4.0.1 rename.h file
+if (with_cholmod)
+ fprintf ('with CHOLMOD, CCAMD, CCOLAMD, and METIS\n') ;
+ f = fopen ('rename.h', 'w') ;
+ if (f == -1)
+ error ('unable to create rename.h in current directory') ;
+ end
+ fprintf (f, '/* do not edit this file; generated by klu_make */\n') ;
+ fprintf (f, '#undef log2\n') ;
+ fprintf (f, '#include "%s/Lib/rename.h"\n', metis_path) ;
+ fprintf (f, '#undef log2\n') ;
+ fprintf (f, '#define log2 METIS__log2\n') ;
+ fprintf (f, '#include "mex.h"\n') ;
+ fprintf (f, '#define malloc mxMalloc\n') ;
+ fprintf (f, '#define free mxFree\n') ;
+ fprintf (f, '#define calloc mxCalloc\n') ;
+ fprintf (f, '#define realloc mxRealloc\n') ;
+ fclose (f) ;
+ include = ['-DNSUPERNODAL -DNMODIFY -DNMATRIXOPS -DNCHECK ' include] ;
+else
+ fprintf ('without CHOLMOD, CCAMD, CCOLAMD, and METIS\n') ;
+ include = ['-DNCHOLMOD ' include] ;
+end
+
+include = strrep (include, '/', filesep) ;
+
+amd_src = { ...
+ '../../AMD/Source/amd_1', ...
+ '../../AMD/Source/amd_2', ...
+ '../../AMD/Source/amd_aat', ...
+ '../../AMD/Source/amd_control', ...
+ '../../AMD/Source/amd_defaults', ...
+ '../../AMD/Source/amd_dump', ...
+ '../../AMD/Source/amd_global', ...
+ '../../AMD/Source/amd_info', ...
+ '../../AMD/Source/amd_order', ...
+ '../../AMD/Source/amd_postorder', ...
+ '../../AMD/Source/amd_post_tree', ...
+ '../../AMD/Source/amd_preprocess', ...
+ '../../AMD/Source/amd_valid' } ;
+
+camd_src = { ...
+ '../../CAMD/Source/camd_1', ...
+ '../../CAMD/Source/camd_2', ...
+ '../../CAMD/Source/camd_aat', ...
+ '../../CAMD/Source/camd_control', ...
+ '../../CAMD/Source/camd_defaults', ...
+ '../../CAMD/Source/camd_dump', ...
+ '../../CAMD/Source/camd_global', ...
+ '../../CAMD/Source/camd_info', ...
+ '../../CAMD/Source/camd_order', ...
+ '../../CAMD/Source/camd_postorder', ...
+ '../../CAMD/Source/camd_preprocess', ...
+ '../../CAMD/Source/camd_valid' } ;
+
+colamd_src = {
+ '../../COLAMD/Source/colamd', ...
+ '../../COLAMD/Source/colamd_global' } ;
+
+ccolamd_src = {
+ '../../CCOLAMD/Source/ccolamd', ...
+ '../../CCOLAMD/Source/ccolamd_global' } ;
+
+metis_src = {
+ 'Lib/balance', ...
+ 'Lib/bucketsort', ...
+ 'Lib/ccgraph', ...
+ 'Lib/coarsen', ...
+ 'Lib/compress', ...
+ 'Lib/debug', ...
+ 'Lib/estmem', ...
+ 'Lib/fm', ...
+ 'Lib/fortran', ...
+ 'Lib/frename', ...
+ 'Lib/graph', ...
+ 'Lib/initpart', ...
+ 'Lib/kmetis', ...
+ 'Lib/kvmetis', ...
+ 'Lib/kwayfm', ...
+ 'Lib/kwayrefine', ...
+ 'Lib/kwayvolfm', ...
+ 'Lib/kwayvolrefine', ...
+ 'Lib/match', ...
+ 'Lib/mbalance2', ...
+ 'Lib/mbalance', ...
+ 'Lib/mcoarsen', ...
+ 'Lib/memory', ...
+ 'Lib/mesh', ...
+ 'Lib/meshpart', ...
+ 'Lib/mfm2', ...
+ 'Lib/mfm', ...
+ 'Lib/mincover', ...
+ 'Lib/minitpart2', ...
+ 'Lib/minitpart', ...
+ 'Lib/mkmetis', ...
+ 'Lib/mkwayfmh', ...
+ 'Lib/mkwayrefine', ...
+ 'Lib/mmatch', ...
+ 'Lib/mmd', ...
+ 'Lib/mpmetis', ...
+ 'Lib/mrefine2', ...
+ 'Lib/mrefine', ...
+ 'Lib/mutil', ...
+ 'Lib/myqsort', ...
+ 'Lib/ometis', ...
+ 'Lib/parmetis', ...
+ 'Lib/pmetis', ...
+ 'Lib/pqueue', ...
+ 'Lib/refine', ...
+ 'Lib/separator', ...
+ 'Lib/sfm', ...
+ 'Lib/srefine', ...
+ 'Lib/stat', ...
+ 'Lib/subdomains', ...
+ 'Lib/timing', ...
+ 'Lib/util' } ;
+
+for i = 1:length (metis_src)
+ metis_src {i} = [metis_path '/' metis_src{i}] ;
+end
+
+cholmod_src = {
+ '../../CHOLMOD/Core/cholmod_aat', ...
+ '../../CHOLMOD/Core/cholmod_add', ...
+ '../../CHOLMOD/Core/cholmod_band', ...
+ '../../CHOLMOD/Core/cholmod_change_factor', ...
+ '../../CHOLMOD/Core/cholmod_common', ...
+ '../../CHOLMOD/Core/cholmod_complex', ...
+ '../../CHOLMOD/Core/cholmod_copy', ...
+ '../../CHOLMOD/Core/cholmod_dense', ...
+ '../../CHOLMOD/Core/cholmod_error', ...
+ '../../CHOLMOD/Core/cholmod_factor', ...
+ '../../CHOLMOD/Core/cholmod_memory', ...
+ '../../CHOLMOD/Core/cholmod_sparse', ...
+ '../../CHOLMOD/Core/cholmod_transpose', ...
+ '../../CHOLMOD/Core/cholmod_triplet', ...
+ '../../CHOLMOD/Cholesky/cholmod_amd', ...
+ '../../CHOLMOD/Cholesky/cholmod_analyze', ...
+ '../../CHOLMOD/Cholesky/cholmod_colamd', ...
+ '../../CHOLMOD/Cholesky/cholmod_etree', ...
+ '../../CHOLMOD/Cholesky/cholmod_postorder', ...
+ '../../CHOLMOD/Cholesky/cholmod_rowcolcounts', ...
+ '../../CHOLMOD/Partition/cholmod_ccolamd', ...
+ '../../CHOLMOD/Partition/cholmod_csymamd', ...
+ '../../CHOLMOD/Partition/cholmod_camd', ...
+ '../../CHOLMOD/Partition/cholmod_metis', ...
+ '../../CHOLMOD/Partition/cholmod_nesdis' } ;
+
+btf_src = {
+ '../../BTF/Source/btf_maxtrans', ...
+ '../../BTF/Source/btf_order', ...
+ '../../BTF/Source/btf_strongcomp' } ;
+
+klu_src = {
+ '../Source/klu_free_symbolic', ...
+ '../Source/klu_defaults', ...
+ '../Source/klu_analyze_given', ...
+ '../Source/klu_analyze', ...
+ '../Source/klu_memory' } ;
+
+if (with_cholmod)
+ klu_src = [klu_src { '../User/klu_l_cholmod' }] ; %#ok
+end
+
+klu_zlsrc = {
+ '../Source/klu', ...
+ '../Source/klu_kernel', ...
+ '../Source/klu_dump', ...
+ '../Source/klu_factor', ...
+ '../Source/klu_free_numeric', ...
+ '../Source/klu_solve', ...
+ '../Source/klu_scale', ...
+ '../Source/klu_refactor', ...
+ '../Source/klu_tsolve', ...
+ '../Source/klu_diagnostics', ...
+ '../Source/klu_sort', ...
+ '../Source/klu_extract', ...
+ } ;
+
+klu_lobj = {
+ 'klu_l', ...
+ 'klu_l_kernel', ...
+ 'klu_l_dump', ...
+ 'klu_l_factor', ...
+ 'klu_l_free_numeric', ...
+ 'klu_l_solve', ...
+ 'klu_l_scale', ...
+ 'klu_l_refactor', ...
+ 'klu_l_tsolve', ...
+ 'klu_l_diagnostics', ...
+ 'klu_l_sort', ...
+ 'klu_l_extract', ...
+ } ;
+
+klu_zlobj = {
+ 'klu_zl', ...
+ 'klu_zl_kernel', ...
+ 'klu_zl_dump', ...
+ 'klu_zl_factor', ...
+ 'klu_zl_free_numeric', ...
+ 'klu_zl_solve', ...
+ 'klu_zl_scale', ...
+ 'klu_zl_refactor', ...
+ 'klu_zl_tsolve', ...
+ 'klu_zl_diagnostics', ...
+ 'klu_zl_sort', ...
+ 'klu_zl_extract', ...
+ } ;
+
+try
+ % ispc does not appear in MATLAB 5.3
+ pc = ispc ;
+catch
+ % if ispc fails, assume we are on a Windows PC if it's not unix
+ pc = ~isunix ;
+end
+
+if (pc)
+ % Windows does not have drand48 and srand48, required by METIS. Use
+ % drand48 and srand48 in CHOLMOD/MATLAB/Windows/rand48.c instead.
+ obj_extension = '.obj' ;
+ cholmod_src = [cholmod_src {'../../CHOLMOD/MATLAB/Windows/rand48'}] ;
+ include = [include ' -I../../CHOLMOD/MATLAB/Windows'] ;
+else
+ obj_extension = '.o' ;
+end
+
+% compile each library source file
+obj = ' ' ;
+
+source = [amd_src btf_src klu_src colamd_src] ;
+if (with_cholmod)
+ source = [metis_src ccolamd_src camd_src cholmod_src source] ;
+end
+
+for f = source
+ fs = strrep (f {1}, '/', filesep) ;
+ slash = strfind (fs, filesep) ;
+ if (isempty (slash))
+ slash = 1 ;
+ else
+ slash = slash (end) + 1 ;
+ end
+ o = fs (slash:end) ;
+ obj = [obj ' ' o obj_extension] ; %#ok
+ s = sprintf ('mex %s -DDLONG -O %s -c %s.c', d, include, fs) ;
+ kk = do_cmd (s, kk, details) ;
+end
+
+for k = 1:length(klu_zlsrc)
+ ff = strrep (klu_zlsrc {k}, '/', filesep) ;
+ slash = strfind (ff, filesep) ;
+ if (isempty (slash))
+ slash = 1 ;
+ else
+ slash = slash (end) + 1 ;
+ end
+ o = ff (slash:end) ;
+ s = sprintf ('mex %s -DDLONG -O %s -c %s.c', d, include, ff) ;
+ kk = do_cmd (s, kk, details) ;
+ lobj = klu_lobj {k} ;
+ obj = [obj ' ' lobj obj_extension] ; %#ok
+ mvfile ([o obj_extension], [lobj obj_extension]) ;
+ s = sprintf ('mex %s -DDLONG -DCOMPLEX -O %s -c %s.c', d, include, ff) ;
+ kk = do_cmd (s, kk, details) ;
+ zlobj = klu_zlobj {k} ;
+ obj = [obj ' ' zlobj obj_extension] ; %#ok
+ mvfile ([o obj_extension], [zlobj obj_extension]) ;
+end
+
+% compile the KLU mexFunction
+s = sprintf ('mex %s -DDLONG -O %s -output klu klu_mex.c', d, include) ;
+s = [s obj] ; %#ok
+kk = do_cmd (s, kk, details) ;
+
+% clean up
+s = ['delete ' obj] ;
+do_cmd (s, kk, details) ;
+
+fprintf ('\nKLU successfully compiled\n') ;
+
+%-------------------------------------------------------------------------------
+
+function rmfile (file)
+% rmfile: delete a file, but only if it exists
+if (length (dir (file)) > 0) %#ok
+ delete (file) ;
+end
+
+%-------------------------------------------------------------------------------
+
+function cpfile (src, dst)
+% cpfile: copy the src file to the filename dst, overwriting dst if it exists
+rmfile (dst)
+if (length (dir (src)) == 0) %#ok
+ fprintf ('File does not exist: %s\n', src) ;
+ error ('File does not exist') ;
+end
+copyfile (src, dst) ;
+
+%-------------------------------------------------------------------------------
+
+function mvfile (src, dst)
+% mvfile: move the src file to the filename dst, overwriting dst if it exists
+cpfile (src, dst) ;
+rmfile (src) ;
+
+%-------------------------------------------------------------------------------
+function kk = do_cmd (s, kk, details)
+%DO_CMD: evaluate a command, and either print it or print a "."
+if (details)
+ fprintf ('%s\n', s) ;
+else
+ if (mod (kk, 60) == 0)
+ fprintf ('\n') ;
+ end
+ kk = kk + 1 ;
+ fprintf ('.') ;
+end
+eval (s) ;
+
diff --git a/KLU/MATLAB/klu_mex.c b/KLU/MATLAB/klu_mex.c
new file mode 100644
index 0000000..89864ac
--- /dev/null
+++ b/KLU/MATLAB/klu_mex.c
@@ -0,0 +1,1979 @@
+/* ========================================================================== */
+/* === klu mexFunction ====================================================== */
+/* ========================================================================== */
+
+/* KLU: a MATLAB interface to a "Clark Kent" sparse LU factorization algorithm.
+
+ 3 or 4 input arguments: factorize and solve, returning the solution:
+
+ x = klu (A, '\', b)
+ x = klu (A, '\', b, opts)
+ x = klu (b, '/', A)
+ x = klu (b, '/', A, opts)
+
+ A can be the LU struct, instead:
+
+ x = klu (LU, '\', b)
+ x = klu (LU, '\', b, opts)
+ x = klu (b, '/', LU)
+ x = klu (b, '/', LU, opts)
+
+ where LU is a struct containing members: L, U, p, q, R, F, and r. Only L
+ and U are required. The factorization is L*U+F = R\A(p,q), where r defines
+ the block boundaries of the BTF form, and F contains the entries in the
+ upper block triangular part.
+
+ with 1 or 2 input arguments: factorize, returning the LU struct:
+
+ LU = klu (A)
+ LU = klu (A, opts)
+
+ 2nd optional output: info, which is only meaningful if A was factorized.
+
+ A must be square. b can be a matrix, but it cannot be sparse.
+
+ Obscure options, mainly for testing:
+
+ opts.memgrow 1.2 when L and U need to grow, inc. by this ratio.
+ valid range: 1 or more.
+ opts.imemamd 1.2 initial size of L and U with AMD or other
+ symmetric ordering is 1.2*nnz(L)+n;
+ valid range 1 or more.
+ opts.imem 10 initial size of L and U is 10*nnz(A)+n if a
+ symmetric ordering not used; valid range 1 or
+ more
+*/
+
+/* ========================================================================== */
+
+#include "klu.h"
+#include <string.h>
+
+#ifndef NCHOLMOD
+#include "klu_cholmod.h"
+#endif
+
+#include "mex.h"
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+#define ABS(x) (((x) < 0) ? -(x) : (x))
+#define STRING_MATCH(s1,s2) (strcmp ((s1), (s2)) == 0)
+
+/* Complex division. This uses ACM Algo 116, by R. L. Smith, 1962. */
+/* Note that c cannot be the same variable as a or b */
+#define DIV(cx,cz,ax,az,bx,bz) \
+{ \
+ double r, den ; \
+ if (ABS (bx) >= ABS (bz)) \
+ { \
+ r = bz / bx ; \
+ den = bx + r * bz ; \
+ cx = (ax + az * r) / den ; \
+ cz = (az - ax * r) / den ; \
+ } \
+ else \
+ { \
+ r = bx / bz ; \
+ den = r * bx + bz ; \
+ cx = (ax * r + az) / den ; \
+ cz = (az * r - ax) / den ; \
+ } \
+}
+
+/* complex multiply/subtract, c -= a*b */
+/* Note that c cannot be the same variable as a or b */
+#define MULT_SUB(cx,cz,ax,az,bx,bz) \
+{ \
+ cx -= ax * bx - az * bz ; \
+ cz -= az * bx + ax * bz ; \
+}
+
+/* complex multiply/subtract, c -= a*conj(b) */
+/* Note that c cannot be the same variable as a or b */
+#define MULT_SUB_CONJ(cx,cz,ax,az,bx,bz) \
+{ \
+ cx -= ax * bx + az * bz ; \
+ cz -= az * bx - ax * bz ; \
+}
+
+/* ========================================================================== */
+/* === klu mexFunction ====================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double ukk, lkk, rs, s, lik, uik, x [4], offik, z, ukkz, lkkz, sz, wx, wz ;
+ double *X, *B, *Xz, *Xx, *Bx, *Bz, *A, *Ax, *Az, *Lx, *Ux, *Rs, *Offx, *Wx,
+ *Uz, *Lz, *Offz, *Wz, *W, *Xi, *Bi ;
+ UF_long *Ap, *Ai, *Lp, *Li, *Up, *Ui, *P, *Q, *R, *Rp, *Ri, *Offp, *Offi ;
+ char *operator ;
+ mxArray *L_matlab, *U_matlab, *p_matlab, *q_matlab, *R_matlab, *F_matlab,
+ *r_matlab, *field ;
+ const mxArray *A_matlab = NULL, *LU_matlab, *B_matlab = NULL, *opts_matlab ;
+ klu_l_symbolic *Symbolic ;
+ klu_l_numeric *Numeric ;
+ klu_l_common Common ;
+ UF_long n = 0, k, nrhs = 0, do_solve, do_factorize, symmetric,
+ A_complex = 0, B_complex, nz, do_transpose = 0, p, pend, nblocks,
+ R1 [2], chunk, nr, i, j, block, k1, k2, nk, bn = 0, ordering ;
+ int mx_int ;
+ static const char *fnames [ ] = {
+ "noffdiag", /* # of off-diagonal pivots */
+ "nrealloc", /* # of memory reallocations */
+ "rcond", /* cheap reciprocal number estimate */
+ "rgrowth", /* reciprocal pivot growth */
+ "flops", /* flop count */
+ "nblocks", /* # of blocks in BTF form (1 if not computed) */
+ "ordering", /* AMD, COLAMD, natural, cholmod(AA'), cholmod(A+A') */
+ "scale", /* scaling (<=0: none, 1: sum, 2: max */
+ "lnz", /* nnz(L), including diagonal */
+ "unz", /* nnz(U), including diagonal */
+ "offnz", /* nnz(F), including diagonal */
+ "tol", /* pivot tolerance used */
+ "memory" /* peak memory usage */
+ },
+ *LUnames [ ] = { "L", "U", "p", "q", "R", "F", "r" } ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin < 1 || nargin > 4 || nargout > 3)
+ {
+ mexErrMsgTxt (
+ "Usage: x = klu(A,'\',b), x = klu(A,'/',b) or LU = klu(A)") ;
+ }
+
+ /* return the solution x, or just do LU factorization */
+ do_solve = (nargin > 2) ;
+
+ /* determine size of the MATLAB integer */
+ if (sizeof (UF_long) == sizeof (INT32_T))
+ {
+ mx_int = mxINT32_CLASS ;
+ }
+ else
+ {
+ mx_int = mxINT64_CLASS ;
+ }
+
+ if (do_solve)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* slash or backslash */
+ /* ------------------------------------------------------------------ */
+
+ /* usage, where opts is the optional 4th input argument:
+ x = klu (A, '\', b)
+ x = klu (LU, '\', b)
+ x = klu (b, '/', A)
+ x = klu (b, '/', LU)
+ */
+
+ /* determine the operator, slash (/) or backslash (\) */
+ if (!mxIsChar (pargin [1]))
+ {
+ mexErrMsgTxt ("invalid operator") ;
+ }
+ operator = mxArrayToString (pargin [1]) ;
+ if (STRING_MATCH (operator, "\\"))
+ {
+ do_transpose = 0 ;
+ A_matlab = pargin [0] ;
+ B_matlab = pargin [2] ;
+ nrhs = mxGetN (B_matlab) ;
+ bn = mxGetM (B_matlab) ;
+ }
+ else if (STRING_MATCH (operator, "/"))
+ {
+ do_transpose = 1 ;
+ A_matlab = pargin [2] ;
+ B_matlab = pargin [0] ;
+ nrhs = mxGetM (B_matlab) ;
+ bn = mxGetN (B_matlab) ;
+ }
+ else
+ {
+ mexErrMsgTxt ("invalid operator") ;
+ }
+
+ if (mxIsSparse (B_matlab))
+ {
+ mexErrMsgTxt ("B cannot be sparse") ;
+ }
+
+ opts_matlab = (nargin > 3) ? pargin [3] : NULL ;
+
+ /* determine if the factorization needs to be performed */
+ do_factorize = !mxIsStruct (A_matlab) ;
+ if (do_factorize)
+ {
+ LU_matlab = NULL ;
+ }
+ else
+ {
+ LU_matlab = A_matlab ;
+ A_matlab = NULL ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* factorize A and return LU factorization */
+ /* ------------------------------------------------------------------ */
+
+ /* usage, where opts in the optional 2nd input argument:
+ LU = klu (A)
+ */
+
+ LU_matlab = NULL ;
+ A_matlab = pargin [0] ;
+ B_matlab = NULL ;
+ opts_matlab = (nargin > 1) ? pargin [1] : NULL ;
+ do_factorize = 1 ;
+ if (mxIsStruct (A_matlab))
+ {
+ mexErrMsgTxt ("invalid input, A must be a sparse matrix") ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get options and set Common defaults */
+ /* ---------------------------------------------------------------------- */
+
+ klu_l_defaults (&Common) ;
+
+ /* memory management routines */
+ Common.malloc_memory = mxMalloc ;
+ Common.calloc_memory = mxCalloc ;
+ Common.free_memory = mxFree ;
+ Common.realloc_memory = mxRealloc ;
+
+ /* factorization options */
+ if (opts_matlab != NULL && mxIsStruct (opts_matlab))
+ {
+ if ((field = mxGetField (opts_matlab, 0, "tol")) != NULL)
+ {
+ Common.tol = mxGetScalar (field) ;
+ }
+ if ((field = mxGetField (opts_matlab, 0, "memgrow")) != NULL)
+ {
+ Common.memgrow = mxGetScalar (field) ;
+ }
+ if ((field = mxGetField (opts_matlab, 0, "imemamd")) != NULL)
+ {
+ Common.initmem_amd = mxGetScalar (field) ;
+ }
+ if ((field = mxGetField (opts_matlab, 0, "imem")) != NULL)
+ {
+ Common.initmem = mxGetScalar (field) ;
+ }
+ if ((field = mxGetField (opts_matlab, 0, "btf")) != NULL)
+ {
+ Common.btf = mxGetScalar (field) ;
+ }
+ if ((field = mxGetField (opts_matlab, 0, "ordering")) != NULL)
+ {
+ Common.ordering = mxGetScalar (field) ;
+ }
+ if ((field = mxGetField (opts_matlab, 0, "scale")) != NULL)
+ {
+ Common.scale = mxGetScalar (field) ;
+ }
+ if ((field = mxGetField (opts_matlab, 0, "maxwork")) != NULL)
+ {
+ Common.maxwork = mxGetScalar (field) ;
+ }
+ }
+
+ if (Common.ordering < 0 || Common.ordering > 4)
+ {
+ mexErrMsgTxt ("invalid ordering option") ;
+ }
+ ordering = Common.ordering ;
+
+#ifndef NCHOLMOD
+ /* ordering option 3,4 becomes KLU option 3, with symmetric 0 or 1 */
+ symmetric = (Common.ordering == 4) ;
+ if (symmetric) Common.ordering = 3 ;
+ Common.user_order = klu_l_cholmod ;
+ Common.user_data = &symmetric ;
+#else
+ /* CHOLMOD, METIS, CAMD, CCOLAMD, not available */
+ if (Common.ordering > 2)
+ {
+ mexErrMsgTxt ("invalid ordering option") ;
+ }
+#endif
+
+ if (Common.scale < 1 || Common.scale > 2)
+ {
+ Common.scale = -1 ; /* no scaling, and no error checking either */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize, if needed */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_factorize)
+ {
+
+ /* get input matrix A to factorize */
+ n = mxGetN (A_matlab) ;
+ if (!mxIsSparse (A_matlab) || n != mxGetM (A_matlab) || n == 0)
+ {
+ mexErrMsgTxt ("A must be sparse, square, and non-empty") ;
+ }
+
+ Ap = (UF_long *) mxGetJc (A_matlab) ;
+ Ai = (UF_long *) mxGetIr (A_matlab) ;
+ Ax = mxGetPr (A_matlab) ;
+ Az = mxGetPi (A_matlab) ;
+ nz = Ap [n] ;
+ A_complex = mxIsComplex (A_matlab) ;
+
+ if (do_solve && (n != bn || nrhs == 0))
+ {
+ mexErrMsgTxt ("B must be non-empty with same number of rows as A") ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* analyze */
+ /* ------------------------------------------------------------------ */
+
+ Symbolic = klu_l_analyze (n, Ap, Ai, &Common) ;
+ if (Symbolic == (klu_l_symbolic *) NULL)
+ {
+ mexErrMsgTxt ("klu symbolic analysis failed") ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* factorize */
+ /* ------------------------------------------------------------------ */
+
+ if (A_complex)
+ {
+ /* A is complex */
+ A = mxMalloc (nz * 2 * sizeof (double)) ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ A [2*k ] = Ax [k] ; /* real part */
+ A [2*k+1] = Az [k] ; /* imaginary part */
+ }
+ Numeric = klu_zl_factor (Ap, Ai, A, Symbolic, &Common) ;
+ if (nargout > 1)
+ {
+ /* flops and rgrowth, if requested */
+ klu_zl_flops (Symbolic, Numeric, &Common) ;
+ klu_zl_rgrowth (Ap, Ai, A, Symbolic, Numeric, &Common) ;
+ }
+ mxFree (A) ;
+ }
+ else
+ {
+ /* A is real */
+ Numeric = klu_l_factor (Ap, Ai, Ax, Symbolic, &Common) ;
+ if (nargout > 1)
+ {
+ /* flops, if requested */
+ klu_l_flops (Symbolic, Numeric, &Common) ;
+ klu_l_rgrowth (Ap, Ai, Ax, Symbolic, Numeric, &Common) ;
+ }
+ }
+ if (Common.status != KLU_OK)
+ {
+ mexErrMsgTxt ("klu numeric factorization failed") ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* compute cheap condition number estimate */
+ /* ------------------------------------------------------------------ */
+
+ if (A_complex)
+ {
+ klu_zl_rcond (Symbolic, Numeric, &Common) ;
+ }
+ else
+ {
+ klu_l_rcond (Symbolic, Numeric, &Common) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* return info, if requested */
+ /* ------------------------------------------------------------------ */
+
+#define INFO(i,x) \
+ mxSetFieldByNumber (pargout [1], 0, i, mxCreateScalarDouble (x))
+
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateStructMatrix (1, 1, 13, fnames) ;
+ INFO (0, Common.noffdiag) ;
+ INFO (1, Common.nrealloc) ;
+ INFO (2, Common.rcond) ;
+ INFO (3, Common.rgrowth) ;
+ INFO (4, Common.flops) ;
+ INFO (5, Symbolic->nblocks) ;
+ INFO (6, ordering) ;
+ INFO (7, Common.scale) ;
+ INFO (8, Numeric->lnz) ;
+ INFO (9, Numeric->unz) ;
+ INFO (10, Numeric->nzoff) ;
+ INFO (11, Common.tol) ;
+ INFO (12, Common.mempeak) ;
+ }
+ if (nargout > 2)
+ {
+ /* this is done separately, since it's costly */
+ klu_l_condest (Ap, Ax, Symbolic, Numeric, &Common) ;
+ pargout [2] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ Wx = mxGetPr (pargout [2]) ;
+ Wx [0] = Common.condest ;
+ }
+
+ }
+ else
+ {
+ /* create an empty "info" and "condest" output */
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (0, 0, mxREAL) ;
+ }
+ if (nargout > 2)
+ {
+ pargout [2] = mxCreateDoubleMatrix (0, 0, mxREAL) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve, or return LU factorization */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_solve)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve, x = klu ( ... ) usage */
+ /* ------------------------------------------------------------------ */
+
+ B_complex = mxIsComplex (B_matlab) ;
+
+ if (do_factorize)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve using KLU factors computed above */
+ /* -------------------------------------------------------------- */
+
+ /* klu (A,'\',b) or klu (b,'/',A) usage */
+
+ /* create X */
+ if (do_transpose)
+ {
+ pargout [0] = mxCreateDoubleMatrix (nrhs, n,
+ (A_complex || B_complex) ? mxCOMPLEX : mxREAL) ;
+ }
+ else
+ {
+ pargout [0] = mxCreateDoubleMatrix (n, nrhs,
+ (A_complex || B_complex) ? mxCOMPLEX : mxREAL) ;
+ }
+
+ if (A_complex)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* A is complex, but B might be real */
+ /* ---------------------------------------------------------- */
+
+ X = mxMalloc (n * nrhs * 2 * sizeof (double)) ;
+ Bx = mxGetPr (B_matlab) ;
+ Bz = mxGetPi (B_matlab) ;
+
+ if (do_transpose)
+ {
+
+ /* X = B', merge and transpose B */
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ X [2*(i+j*n) ] = Bx [j+i*nrhs] ; /* real */
+ X [2*(i+j*n)+1] = Bz ? (-Bz [j+i*nrhs]) : 0 ;
+ }
+ }
+
+ /* solve A'x=b (complex conjugate) */
+ klu_zl_tsolve (Symbolic, Numeric, n, nrhs, X, 1, &Common) ;
+
+ /* split and transpose the solution */
+ Xx = mxGetPr (pargout [0]) ;
+ Xz = mxGetPi (pargout [0]) ;
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [j+i*nrhs] = X [2*(i+j*n) ] ; /* real part */
+ Xz [j+i*nrhs] = -X [2*(i+j*n)+1] ; /* imag part */
+ }
+ }
+
+ }
+ else
+ {
+
+ /* X = B, but create merged X from a split B */
+ for (k = 0 ; k < n*nrhs ; k++)
+ {
+ X [2*k ] = Bx [k] ; /* real part */
+ X [2*k+1] = Bz ? (Bz [k]) : 0 ; /* imaginary part */
+ }
+
+ /* solve Ax=b */
+ klu_zl_solve (Symbolic, Numeric, n, nrhs, X, &Common) ;
+
+ /* split the solution into real and imaginary parts */
+ Xx = mxGetPr (pargout [0]) ;
+ Xz = mxGetPi (pargout [0]) ;
+ for (k = 0 ; k < n*nrhs ; k++)
+ {
+ Xx [k] = X [2*k ] ; /* real part */
+ Xz [k] = X [2*k+1] ; /* imaginary part */
+ }
+ }
+
+ mxFree (X) ;
+ }
+ else
+ {
+
+ if (do_transpose)
+ {
+
+ /* solve in chunks of 4 columns at a time */
+ W = mxMalloc (n * MAX (nrhs,4) * sizeof (double)) ;
+ X = mxGetPr (pargout [0]) ;
+ B = mxGetPr (B_matlab) ;
+ Xi = mxGetPi (pargout [0]) ;
+ Bi = mxGetPi (B_matlab) ;
+
+ for (chunk = 0 ; chunk < nrhs ; chunk += 4)
+ {
+
+ /* A is real: real(X) = real(b) / real(A) */
+ UF_long chunksize = MIN (nrhs - chunk, 4) ;
+ for (j = 0 ; j < chunksize ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i+j*n] = B [i*nrhs+j] ;
+ }
+ }
+ klu_l_tsolve (Symbolic, Numeric, n, chunksize, W,
+ &Common) ;
+ for (j = 0 ; j < chunksize ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ X [i*nrhs+j] = W [i+j*n] ;
+ }
+ }
+ X += 4 ;
+ B += 4 ;
+
+ if (B_complex)
+ {
+ /* B is complex: imag(X) = imag(B) / real(A) */
+
+ for (j = 0 ; j < chunksize ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i+j*n] = Bi [i*nrhs+j] ;
+ }
+ }
+ klu_l_tsolve (Symbolic, Numeric, n, chunksize, W,
+ &Common) ;
+ for (j = 0 ; j < chunksize ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xi [i*nrhs+j] = W [i+j*n] ;
+ }
+ }
+ Xi += 4 ;
+ Bi += 4 ;
+ }
+
+ }
+ mxFree (W) ;
+
+ }
+ else
+ {
+
+ /* A is real: real(X) = real(A) \ real(b) */
+ X = mxGetPr (pargout [0]) ;
+ B = mxGetPr (B_matlab) ;
+ for (k = 0 ; k < n*nrhs ; k++)
+ {
+ X [k] = B [k] ;
+ }
+ klu_l_solve (Symbolic, Numeric, n, nrhs, X, &Common) ;
+ if (B_complex)
+ {
+ /* B is complex: imag(X) = real(A) \ imag(B) */
+ X = mxGetPi (pargout [0]) ;
+ B = mxGetPi (B_matlab) ;
+ for (k = 0 ; k < n*nrhs ; k++)
+ {
+ X [k] = B [k] ;
+ }
+ klu_l_solve (Symbolic, Numeric, n, nrhs, X, &Common) ;
+ }
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* free Symbolic and Numeric objects */
+ /* -------------------------------------------------------------- */
+
+ klu_l_free_symbolic (&Symbolic, &Common) ;
+ if (A_complex)
+ {
+ klu_zl_free_numeric (&Numeric, &Common) ;
+ }
+ else
+ {
+ klu_l_free_numeric (&Numeric, &Common) ;
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* solve using LU struct given on input */
+ /* -------------------------------------------------------------- */
+
+ /* the factorization is L*U+F = R\A(p,q), where L*U is block
+ diagonal, and F contains the entries in the upper block
+ triangular part */
+
+ L_matlab = mxGetField (LU_matlab, 0, "L") ;
+ U_matlab = mxGetField (LU_matlab, 0, "U") ;
+ p_matlab = mxGetField (LU_matlab, 0, "p") ;
+ q_matlab = mxGetField (LU_matlab, 0, "q") ;
+ R_matlab = mxGetField (LU_matlab, 0, "R") ;
+ F_matlab = mxGetField (LU_matlab, 0, "F") ;
+ r_matlab = mxGetField (LU_matlab, 0, "r") ;
+
+ if (!L_matlab || !U_matlab || !mxIsSparse (L_matlab) ||
+ !mxIsSparse (U_matlab))
+ {
+ mexErrMsgTxt ("invalid LU struct") ;
+ }
+
+ n = mxGetM (L_matlab) ;
+ if (n != mxGetN (L_matlab) ||
+ n != mxGetM (U_matlab) || n != mxGetN (U_matlab)
+ /* ... */
+ )
+ {
+ mexErrMsgTxt ("invalid LU struct") ;
+ }
+
+ if (n != bn || nrhs == 0)
+ {
+ mexErrMsgTxt (
+ "B must be non-empty with same number of rows as L and U") ;
+ }
+
+ /* get L */
+ if (!mxIsSparse (L_matlab) ||
+ n != mxGetM (L_matlab) || n != mxGetN (L_matlab))
+ {
+ mexErrMsgTxt ("LU.L must be sparse and same size as A") ;
+ }
+
+ Lp = (UF_long *) mxGetJc (L_matlab) ;
+ Li = (UF_long *) mxGetIr (L_matlab) ;
+ Lx = mxGetPr (L_matlab) ;
+ Lz = mxGetPi (L_matlab) ;
+
+ /* get U */
+ if (!mxIsSparse (U_matlab) ||
+ n != mxGetM (U_matlab) || n != mxGetN (U_matlab))
+ {
+ mexErrMsgTxt ("LU.U must be sparse and same size as A") ;
+ }
+ Up = (UF_long *) mxGetJc (U_matlab) ;
+ Ui = (UF_long *) mxGetIr (U_matlab) ;
+ Ux = mxGetPr (U_matlab) ;
+ Uz = mxGetPi (U_matlab) ;
+
+ /* get p */
+ if (p_matlab)
+ {
+ if (mxGetNumberOfElements (p_matlab) != n
+ || mxIsSparse (p_matlab)
+ || mxGetClassID (p_matlab) != mx_int)
+ {
+ mexErrMsgTxt ("P invalid") ;
+ }
+ P = (UF_long *) mxGetData (p_matlab) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ if (P [k] < 1 || P [k] > n) mexErrMsgTxt ("P invalid") ;
+ }
+ }
+ else
+ {
+ /* no P, use identity instead */
+ P = NULL ;
+ }
+
+ /* get q */
+ if (q_matlab)
+ {
+ if (mxGetNumberOfElements (q_matlab) != n
+ || mxIsSparse (q_matlab)
+ || mxGetClassID (q_matlab) != mx_int)
+ {
+ mexErrMsgTxt ("Q invalid") ;
+ }
+ Q = (UF_long *) mxGetData (q_matlab) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ if (Q [k] < 1 || Q [k] > n) mexErrMsgTxt ("Q invalid.") ;
+ }
+ }
+ else
+ {
+ /* no Q, use identity instead */
+ Q = NULL ;
+ }
+
+ /* get r */
+ R1 [0] = 1 ;
+ R1 [1] = n+1 ;
+ if (r_matlab)
+ {
+ nblocks = mxGetNumberOfElements (r_matlab) - 1 ;
+ if (nblocks < 1 || nblocks > n || mxIsSparse (r_matlab)
+ || mxGetClassID (r_matlab) != mx_int)
+ {
+ mexErrMsgTxt ("r invalid") ;
+ }
+ R = (UF_long *) mxGetData (r_matlab) ;
+ if (R [0] != 1) mexErrMsgTxt ("r invalid") ;
+ for (k = 1 ; k <= nblocks ; k++)
+ {
+ if (R [k] <= R [k-1] || R [k] > n+1)
+ {
+ mexErrMsgTxt ("rinvalid") ;
+ }
+ }
+ if (R [nblocks] != n+1) mexErrMsgTxt ("r invalid") ;
+ }
+ else
+ {
+ /* no r */
+ nblocks = 1 ;
+ R = R1 ;
+ }
+
+ /* get R, scale factors */
+ if (R_matlab)
+ {
+ /* ensure R is sparse, real, and has the right size */
+ if (!mxIsSparse (R_matlab) ||
+ n != mxGetM (R_matlab) || n != mxGetN (R_matlab))
+ {
+ mexErrMsgTxt ("LU.R must be sparse and same size as A") ;
+ }
+ Rp = (UF_long *) mxGetJc (R_matlab) ;
+ Rs = mxGetPr (R_matlab) ;
+ if (Rp [n] != n)
+ {
+ mexErrMsgTxt ("LU.R invalid, must be diagonal") ;
+ }
+ }
+ else
+ {
+ /* no scale factors */
+ Rs = NULL ;
+ }
+
+ /* get F, off diagonal entries */
+ if (F_matlab)
+ {
+ if (!mxIsSparse (F_matlab) ||
+ n != mxGetM (F_matlab) || n != mxGetN (F_matlab))
+ {
+ mexErrMsgTxt ("LU.F must be sparse and same size as A") ;
+ }
+ Offp = (UF_long *) mxGetJc (F_matlab) ;
+ Offi = (UF_long *) mxGetIr (F_matlab) ;
+ Offx = mxGetPr (F_matlab) ;
+ Offz = mxGetPi (F_matlab) ;
+ }
+ else
+ {
+ /* no off-diagonal entries */
+ Offp = NULL ;
+ Offi = NULL ;
+ Offx = NULL ;
+ Offz = NULL ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* solve */
+ /* -------------------------------------------------------------- */
+
+ if (mxIsComplex (L_matlab) || mxIsComplex (U_matlab) ||
+ (F_matlab && mxIsComplex (F_matlab)) || B_complex)
+ {
+
+ /* ========================================================== */
+ /* === complex case ========================================= */
+ /* ========================================================== */
+
+ /* create X */
+ if (do_transpose)
+ {
+ pargout [0] = mxCreateDoubleMatrix (nrhs, n, mxCOMPLEX) ;
+ }
+ else
+ {
+ pargout [0] = mxCreateDoubleMatrix (n, nrhs, mxCOMPLEX) ;
+ }
+ Xx = mxGetPr (pargout [0]) ;
+ Xz = mxGetPi (pargout [0]) ;
+
+ Bx = mxGetPr (B_matlab) ;
+ Bz = mxGetPi (B_matlab) ;
+
+ /* get workspace */
+ Wx = mxMalloc (n * sizeof (double)) ;
+ Wz = mxMalloc (n * sizeof (double)) ;
+
+ /* ---------------------------------------------------------- */
+ /* do just one row/column of the right-hand-side at a time */
+ /* ---------------------------------------------------------- */
+
+ if (do_transpose)
+ {
+
+ for (chunk = 0 ; chunk < nrhs ; chunk++)
+ {
+
+ /* -------------------------------------------------- */
+ /* transpose and permute right hand side, W = Q'*B' */
+ /* -------------------------------------------------- */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q ? (Q [k] - 1) : k ;
+ Wx [k] = Bx [i*nrhs] ;
+ Wz [k] = Bz ? (-Bz [i*nrhs]) : 0 ;
+ }
+
+ /* -------------------------------------------------- */
+ /* solve W = (L*U + Off)'\W */
+ /* -------------------------------------------------- */
+
+ for (block = 0 ; block < nblocks ; block++)
+ {
+
+ /* ---------------------------------------------- */
+ /* block of size nk, rows/columns k1 to k2-1 */
+ /* ---------------------------------------------- */
+
+ k1 = R [block] - 1 ; /* R is 1-based */
+ k2 = R [block+1] - 1 ;
+ nk = k2 - k1 ;
+
+ /* ---------------------------------------------- */
+ /* block back-substitution for off-diagonal-block */
+ /* ---------------------------------------------- */
+
+ if (block > 0 && Offp != NULL)
+ {
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+ /* W [k] -= W [i] * conj(Off [p]) ; */
+ z = Offz ? Offz [p] : 0 ;
+ MULT_SUB_CONJ (Wx [k], Wz [k],
+ Wx [i], Wz [i], Offx [p], z) ;
+ }
+ }
+ }
+
+
+ /* solve the block system */
+ if (nk == 1)
+ {
+
+ /* W [k1] /= conj (L(k1,k1)) ; */
+ p = Lp [k1] ;
+ s = Lx [p] ;
+ sz = Lz ? (-Lz [p]) : 0 ;
+ DIV (wx, wz, Wx [k1], Wz [k1], s, sz) ;
+ Wx [k1] = wx ;
+ Wz [k1] = wz ;
+
+ /* W [k1] /= conj (U(k1,k1)) ; */
+ p = Up [k1] ;
+ s = Ux [p] ;
+ sz = Uz ? (-Uz [p]) : 0 ;
+ DIV (wx, wz, Wx [k1], Wz [k1], s, sz) ;
+ Wx [k1] = wx ;
+ Wz [k1] = wz ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------ */
+ /* W = U'\W and then W=L'\W */
+ /* ------------------------------------------ */
+
+ /* W = U'\W */
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Up [k+1] - 1 ;
+ /* w = W [k] */
+ wx = Wx [k] ;
+ wz = Wz [k] ;
+ for (p = Up [k] ; p < pend ; p++)
+ {
+ i = Ui [p] ;
+ /* w -= W [i] * conj(U [p]) */
+ z = Uz ? Uz [p] : 0 ;
+ MULT_SUB_CONJ (wx, wz,
+ Wx [i], Wz [i], Ux [p], z) ;
+ }
+ /* W [k] = w / conj(ukk) ; */
+ ukk = Ux [pend] ;
+ ukkz = Uz ? (-Uz [pend]) : 0 ;
+ DIV (Wx [k], Wz [k], wx, wz, ukk, ukkz) ;
+ }
+
+ /* W = L'\W */
+ for (k = k2-1 ; k >= k1 ; k--)
+ {
+ p = Lp [k] ;
+ pend = Lp [k+1] ;
+ /* w = W [k] */
+ wx = Wx [k] ;
+ wz = Wz [k] ;
+ lkk = Lx [p] ;
+ lkkz = Lz ? (-Lz [p]) : 0 ;
+ for (p++ ; p < pend ; p++)
+ {
+ i = Li [p] ;
+ /* w -= W [i] * conj (Lx [p]) ; */
+ z = Lz ? Lz [p] : 0 ;
+ MULT_SUB_CONJ (wx, wz,
+ Wx [i], Wz [i], Lx [p], z) ;
+ }
+ /* W [k] = w / conj(lkk) ; */
+ DIV (Wx [k], Wz [k], wx, wz, lkk, lkkz) ;
+ }
+ }
+ }
+
+ /* -------------------------------------------------- */
+ /* scale, permute, and tranpose: X = (P*(R\W))' */
+ /* -------------------------------------------------- */
+
+ if (Rs == NULL)
+ {
+ /* no scaling */
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ Xx [i*nrhs] = Wx [k] ;
+ Xz [i*nrhs] = Wz ? (-Wz [k]) : 0 ;
+ }
+ }
+ else
+ {
+ /* with scaling */
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ rs = Rs [k] ;
+ Xx [i*nrhs] = Wx [k] / rs ;
+ Xz [i*nrhs] = Wz ? (-Wz [k] / rs) : 0 ;
+ }
+ }
+
+ /* -------------------------------------------------- */
+ /* go to the next row of B and X */
+ /* -------------------------------------------------- */
+
+ Xx++ ;
+ Xz++ ;
+ Bx++ ;
+ if (Bz) Bz++ ;
+ }
+
+ }
+ else
+ {
+
+ for (chunk = 0 ; chunk < nrhs ; chunk++)
+ {
+
+ /* -------------------------------------------------- */
+ /* scale and permute the right hand side, W = P*(R\B) */
+ /* -------------------------------------------------- */
+
+ if (Rs == NULL)
+ {
+ /* no scaling */
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ Wx [k] = Bx [i] ;
+ Wz [k] = Bz ? Bz [i] : 0 ;
+ }
+ }
+ else
+ {
+ /* with scaling */
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ rs = Rs [k] ;
+ Wx [k] = Bx [i] / rs ;
+ Wz [k] = Bz ? (Bz [i] / rs) : 0 ;
+ }
+ }
+
+ /* -------------------------------------------------- */
+ /* solve W = (L*U + Off)\W */
+ /* -------------------------------------------------- */
+
+ for (block = nblocks-1 ; block >= 0 ; block--)
+ {
+
+ /* ---------------------------------------------- */
+ /* block of size nk, rows/columns k1 to k2-1 */
+ /* ---------------------------------------------- */
+
+ k1 = R [block] - 1 ; /* R is 1-based */
+ k2 = R [block+1] - 1 ;
+ nk = k2 - k1 ;
+
+ /* solve the block system */
+ if (nk == 1)
+ {
+
+ /* W [k1] /= L(k1,k1) ; */
+ p = Lp [k1] ;
+ s = Lx [p] ;
+ sz = Lz ? Lz [p] : 0 ;
+ DIV (wx, wz, Wx [k1], Wz [k1], s, sz) ;
+ Wx [k1] = wx ;
+ Wz [k1] = wz ;
+
+ /* W [k1] /= U(k1,k1) ; */
+ p = Up [k1] ;
+ s = Ux [p] ;
+ sz = Uz ? Uz [p] : 0 ;
+ DIV (wx, wz, Wx [k1], Wz [k1], s, sz) ;
+ Wx [k1] = wx ;
+ Wz [k1] = wz ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------ */
+ /* W = L\W and then W=U\W */
+ /* ------------------------------------------ */
+
+ /* W = L\W */
+ for (k = k1 ; k < k2 ; k++)
+ {
+ p = Lp [k] ;
+ pend = Lp [k+1] ;
+ lkk = Lx [p] ;
+ lkkz = Lz ? Lz [p] : 0 ;
+ /* w = W [k] / lkk ; */
+ DIV (wx, wz, Wx [k], Wz [k], lkk, lkkz) ;
+ Wx [k] = wx ;
+ Wz [k] = wz ;
+ for (p++ ; p < pend ; p++)
+ {
+ i = Li [p] ;
+ /* W [i] -= Lx [p] * w ; */
+ z = Lz ? Lz [p] : 0 ;
+ MULT_SUB (Wx [i], Wz [i], Lx [p], z,
+ wx, wz) ;
+ }
+ }
+
+ /* W = U\W */
+ for (k = k2-1 ; k >= k1 ; k--)
+ {
+ pend = Up [k+1] - 1 ;
+ ukk = Ux [pend] ;
+ ukkz = Uz ? Uz [pend] : 0 ;
+ /* w = W [k] / ukk ; */
+ DIV (wx, wz, Wx [k], Wz [k], ukk, ukkz) ;
+ Wx [k] = wx ;
+ Wz [k] = wz ;
+ for (p = Up [k] ; p < pend ; p++)
+ {
+ i = Ui [p] ;
+ /* W [i] -= U [p] * w ; */
+ z = Uz ? Uz [p] : 0 ;
+ MULT_SUB (Wx [i], Wz [i], Ux [p], z,
+ wx, wz) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------- */
+ /* block back-substitution for off-diagonal-block */
+ /* ---------------------------------------------- */
+
+ if (block > 0 && Offp != NULL)
+ {
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ wx = Wx [k] ;
+ wz = Wz [k] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+ /* W [Offi [p]] -= Offx [p] * w ; */
+ z = Offz ? Offz [p] : 0 ;
+ MULT_SUB (Wx [i], Wz [i], Offx [p], z,
+ wx, wz) ;
+ }
+ }
+ }
+ }
+
+ /* -------------------------------------------------- */
+ /* permute the result, X = Q*W */
+ /* -------------------------------------------------- */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q ? (Q [k] - 1) : k ;
+ Xx [i] = Wx [k] ;
+ Xz [i] = Wz [k] ;
+ }
+
+ /* -------------------------------------------------- */
+ /* go to the next column of B and X */
+ /* -------------------------------------------------- */
+
+ Xx += n ;
+ Xz += n ;
+ Bx += n ;
+ if (Bz) Bz += n ;
+ }
+ }
+
+ /* free workspace */
+ mxFree (Wx) ;
+ mxFree (Wz) ;
+
+ }
+ else
+ {
+
+ /* ========================================================== */
+ /* === real case ============================================ */
+ /* ========================================================== */
+
+ /* create X */
+ if (do_transpose)
+ {
+ pargout [0] = mxCreateDoubleMatrix (nrhs, n, mxREAL) ;
+ }
+ else
+ {
+ pargout [0] = mxCreateDoubleMatrix (n, nrhs, mxREAL) ;
+ }
+
+ Xx = mxGetPr (pargout [0]) ;
+ Bx = mxGetPr (B_matlab) ;
+
+ if (do_transpose)
+ {
+
+ /* ------------------------------------------------------ */
+ /* solve in chunks of one row at a time */
+ /* ------------------------------------------------------ */
+
+ /* get workspace */
+ Wx = mxMalloc (n * sizeof (double)) ;
+
+ for (chunk = 0 ; chunk < nrhs ; chunk++)
+ {
+
+ /* -------------------------------------------------- */
+ /* transpose and permute right hand side, W = Q'*B' */
+ /* -------------------------------------------------- */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q ? (Q [k] - 1) : k ;
+ Wx [k] = Bx [i*nrhs] ;
+ }
+
+ /* -------------------------------------------------- */
+ /* solve W = (L*U + Off)'\W */
+ /* -------------------------------------------------- */
+
+ for (block = 0 ; block < nblocks ; block++)
+ {
+
+ /* ---------------------------------------------- */
+ /* block of size nk, rows/columns k1 to k2-1 */
+ /* ---------------------------------------------- */
+
+ k1 = R [block] - 1 ; /* R is 1-based */
+ k2 = R [block+1] - 1 ;
+ nk = k2 - k1 ;
+
+ /* ---------------------------------------------- */
+ /* block back-substitution for off-diagonal-block */
+ /* ---------------------------------------------- */
+
+ if (block > 0 && Offp != NULL)
+ {
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ Wx [k] -= Wx [Offi [p]] * Offx [p] ;
+ }
+ }
+ }
+
+ /* solve the block system */
+ if (nk == 1)
+ {
+ Wx [k1] /= Lx [Lp [k1]] ;
+ Wx [k1] /= Ux [Up [k1]] ;
+ }
+ else
+ {
+
+ /* ------------------------------------------ */
+ /* W = U'\W and then W=L'\W */
+ /* ------------------------------------------ */
+
+ /* W = U'\W */
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Up [k+1] - 1 ;
+ for (p = Up [k] ; p < pend ; p++)
+ {
+ Wx [k] -= Wx [Ui [p]] * Ux [p] ;
+ }
+ Wx [k] /= Ux [pend] ;
+ }
+
+ /* W = L'\W */
+ for (k = k2-1 ; k >= k1 ; k--)
+ {
+ p = Lp [k] ;
+ pend = Lp [k+1] ;
+ lkk = Lx [p] ;
+ for (p++ ; p < pend ; p++)
+ {
+ Wx [k] -= Wx [Li [p]] * Lx [p] ;
+ }
+ Wx [k] /= lkk ;
+ }
+ }
+ }
+
+ /* -------------------------------------------------- */
+ /* scale, permute, and tranpose: X = (P*(R\W))' */
+ /* -------------------------------------------------- */
+
+ if (Rs == NULL)
+ {
+ /* no scaling */
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ Xx [i*nrhs] = Wx [k] ;
+ }
+ }
+ else
+ {
+ /* with scaling */
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ rs = Rs [k] ;
+ Xx [i*nrhs] = Wx [k] / rs ;
+ }
+ }
+
+ /* -------------------------------------------------- */
+ /* go to the next row of B and X */
+ /* -------------------------------------------------- */
+
+ Xx++ ;
+ Bx++ ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------ */
+ /* solve in chunks of 4 columns at a time */
+ /* ------------------------------------------------------ */
+
+ /* get workspace */
+ Wx = mxMalloc (n * MAX (4, nrhs) * sizeof (double)) ;
+
+ for (chunk = 0 ; chunk < nrhs ; chunk += 4)
+ {
+ /* -------------------------------------------------- */
+ /* get the size of the current chunk */
+ /* -------------------------------------------------- */
+
+ nr = MIN (nrhs - chunk, 4) ;
+
+ /* -------------------------------------------------- */
+ /* scale and permute the right hand side, W = P*(R\B) */
+ /* -------------------------------------------------- */
+
+ if (Rs == NULL)
+ {
+
+ /* no scaling */
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ Wx [k] = Bx [i] ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ Wx [2*k ] = Bx [i ] ;
+ Wx [2*k + 1] = Bx [i + n ] ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ Wx [3*k ] = Bx [i ] ;
+ Wx [3*k + 1] = Bx [i + n ] ;
+ Wx [3*k + 2] = Bx [i + n*2] ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ Wx [4*k ] = Bx [i ] ;
+ Wx [4*k + 1] = Bx [i + n ] ;
+ Wx [4*k + 2] = Bx [i + n*2] ;
+ Wx [4*k + 3] = Bx [i + n*3] ;
+ }
+ break ;
+ }
+
+ }
+ else
+ {
+
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ rs = Rs [k] ;
+ Wx [k] = Bx [i] / rs ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ rs = Rs [k] ;
+ Wx [2*k ] = Bx [i ] / rs ;
+ Wx [2*k + 1] = Bx [i + n ] / rs ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ rs = Rs [k] ;
+ Wx [3*k ] = Bx [i ] / rs ;
+ Wx [3*k + 1] = Bx [i + n ] / rs ;
+ Wx [3*k + 2] = Bx [i + n*2] / rs ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P ? (P [k] - 1) : k ;
+ rs = Rs [k] ;
+ Wx [4*k ] = Bx [i ] / rs ;
+ Wx [4*k + 1] = Bx [i + n ] / rs ;
+ Wx [4*k + 2] = Bx [i + n*2] / rs ;
+ Wx [4*k + 3] = Bx [i + n*3] / rs ;
+ }
+ break ;
+ }
+ }
+
+ /* -------------------------------------------------- */
+ /* solve W = (L*U + Off)\W */
+ /* -------------------------------------------------- */
+
+ for (block = nblocks-1 ; block >= 0 ; block--)
+ {
+
+ /* ---------------------------------------------- */
+ /* block of size nk is rows/columns k1 to k2-1 */
+ /* ---------------------------------------------- */
+
+ k1 = R [block] - 1 ; /* R is 1-based */
+ k2 = R [block+1] - 1 ;
+ nk = k2 - k1 ;
+
+ /* solve the block system */
+ if (nk == 1)
+ {
+
+ /* this is not done if L comes from KLU, since
+ in that case, L is unit lower triangular */
+ s = Lx [Lp [k1]] ;
+ if (s != 1.0) switch (nr)
+ {
+ case 1:
+ Wx [k1] /= s ;
+ break ;
+ case 2:
+ Wx [2*k1] /= s ;
+ Wx [2*k1 + 1] /= s ;
+ break ;
+ case 3:
+ Wx [3*k1] /= s ;
+ Wx [3*k1 + 1] /= s ;
+ Wx [3*k1 + 2] /= s ;
+ break ;
+ case 4:
+ Wx [4*k1] /= s ;
+ Wx [4*k1 + 1] /= s ;
+ Wx [4*k1 + 2] /= s ;
+ Wx [4*k1 + 3] /= s ;
+ break ;
+ }
+
+ s = Ux [Up [k1]] ;
+ if (s != 1.0) switch (nr)
+ {
+ case 1:
+ Wx [k1] /= s ;
+ break ;
+ case 2:
+ Wx [2*k1] /= s ;
+ Wx [2*k1 + 1] /= s ;
+ break ;
+ case 3:
+ Wx [3*k1] /= s ;
+ Wx [3*k1 + 1] /= s ;
+ Wx [3*k1 + 2] /= s ;
+ break ;
+ case 4:
+ Wx [4*k1] /= s ;
+ Wx [4*k1 + 1] /= s ;
+ Wx [4*k1 + 2] /= s ;
+ Wx [4*k1 + 3] /= s ;
+ break ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------ */
+ /* W = L\W and then W=U\W */
+ /* ------------------------------------------ */
+
+ switch (nr)
+ {
+
+ case 1:
+ /* W = L\W */
+ for (k = k1 ; k < k2 ; k++)
+ {
+ p = Lp [k] ;
+ pend = Lp [k+1] ;
+ lkk = Lx [p++] ;
+ x [0] = Wx [k] / lkk ;
+ Wx [k] = x [0] ;
+ for ( ; p < pend ; p++)
+ {
+ Wx [Li [p]] -= Lx [p] * x [0] ;
+ }
+ }
+
+ /* W = U\W */
+ for (k = k2-1 ; k >= k1 ; k--)
+ {
+ pend = Up [k+1] - 1 ;
+ ukk = Ux [pend] ;
+ x [0] = Wx [k] / ukk ;
+ Wx [k] = x [0] ;
+ for (p = Up [k] ; p < pend ; p++)
+ {
+ Wx [Ui [p]] -= Ux [p] * x [0] ;
+ }
+ }
+ break ;
+
+ case 2:
+
+ /* W = L\W */
+ for (k = k1 ; k < k2 ; k++)
+ {
+ p = Lp [k] ;
+ pend = Lp [k+1] ;
+ lkk = Lx [p++] ;
+ x [0] = Wx [2*k ] / lkk ;
+ x [1] = Wx [2*k + 1] / lkk ;
+ Wx [2*k ] = x [0] ;
+ Wx [2*k + 1] = x [1] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Li [p] ;
+ lik = Lx [p] ;
+ Wx [2*i ] -= lik * x [0] ;
+ Wx [2*i + 1] -= lik * x [1] ;
+ }
+ }
+
+ /* W = U\W */
+ for (k = k2-1 ; k >= k1 ; k--)
+ {
+ pend = Up [k+1] - 1 ;
+ ukk = Ux [pend] ;
+ x [0] = Wx [2*k ] / ukk ;
+ x [1] = Wx [2*k + 1] / ukk ;
+ Wx [2*k ] = x [0] ;
+ Wx [2*k + 1] = x [1] ;
+ for (p = Up [k] ; p < pend ; p++)
+ {
+ i = Ui [p] ;
+ uik = Ux [p] ;
+ Wx [2*i ] -= uik * x [0] ;
+ Wx [2*i + 1] -= uik * x [1] ;
+ }
+ }
+ break ;
+
+ case 3:
+
+ /* W = L\W */
+ for (k = k1 ; k < k2 ; k++)
+ {
+ p = Lp [k] ;
+ pend = Lp [k+1] ;
+ lkk = Lx [p++] ;
+ x [0] = Wx [3*k ] / lkk ;
+ x [1] = Wx [3*k + 1] / lkk ;
+ x [2] = Wx [3*k + 2] / lkk ;
+ Wx [3*k ] = x [0] ;
+ Wx [3*k + 1] = x [1] ;
+ Wx [3*k + 2] = x [2] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Li [p] ;
+ lik = Lx [p] ;
+ Wx [3*i ] -= lik * x [0] ;
+ Wx [3*i + 1] -= lik * x [1] ;
+ Wx [3*i + 2] -= lik * x [2] ;
+ }
+ }
+
+ /* W = U\W */
+ for (k = k2-1 ; k >= k1 ; k--)
+ {
+ pend = Up [k+1] - 1 ;
+ ukk = Ux [pend] ;
+ x [0] = Wx [3*k ] / ukk ;
+ x [1] = Wx [3*k + 1] / ukk ;
+ x [2] = Wx [3*k + 2] / ukk ;
+ Wx [3*k ] = x [0] ;
+ Wx [3*k + 1] = x [1] ;
+ Wx [3*k + 2] = x [2] ;
+ for (p = Up [k] ; p < pend ; p++)
+ {
+ i = Ui [p] ;
+ uik = Ux [p] ;
+ Wx [3*i ] -= uik * x [0] ;
+ Wx [3*i + 1] -= uik * x [1] ;
+ Wx [3*i + 2] -= uik * x [2] ;
+ }
+ }
+ break ;
+
+ case 4:
+
+ /* W = L\W */
+ for (k = k1 ; k < k2 ; k++)
+ {
+ p = Lp [k] ;
+ pend = Lp [k+1] ;
+ lkk = Lx [p++] ;
+ x [0] = Wx [4*k ] / lkk ;
+ x [1] = Wx [4*k + 1] / lkk ;
+ x [2] = Wx [4*k + 2] / lkk ;
+ x [3] = Wx [4*k + 3] / lkk ;
+ Wx [4*k ] = x [0] ;
+ Wx [4*k + 1] = x [1] ;
+ Wx [4*k + 2] = x [2] ;
+ Wx [4*k + 3] = x [3] ;
+ for ( ; p < pend ; p++)
+ {
+ i = Li [p] ;
+ lik = Lx [p] ;
+ Wx [4*i ] -= lik * x [0] ;
+ Wx [4*i + 1] -= lik * x [1] ;
+ Wx [4*i + 2] -= lik * x [2] ;
+ Wx [4*i + 3] -= lik * x [3] ;
+ }
+ }
+
+ /* Wx = U\Wx */
+ for (k = k2-1 ; k >= k1 ; k--)
+ {
+ pend = Up [k+1] - 1 ;
+ ukk = Ux [pend] ;
+ x [0] = Wx [4*k ] / ukk ;
+ x [1] = Wx [4*k + 1] / ukk ;
+ x [2] = Wx [4*k + 2] / ukk ;
+ x [3] = Wx [4*k + 3] / ukk ;
+ Wx [4*k ] = x [0] ;
+ Wx [4*k + 1] = x [1] ;
+ Wx [4*k + 2] = x [2] ;
+ Wx [4*k + 3] = x [3] ;
+ for (p = Up [k] ; p < pend ; p++)
+ {
+ i = Ui [p] ;
+ uik = Ux [p] ;
+ Wx [4*i ] -= uik * x [0] ;
+ Wx [4*i + 1] -= uik * x [1] ;
+ Wx [4*i + 2] -= uik * x [2] ;
+ Wx [4*i + 3] -= uik * x [3] ;
+ }
+ }
+ break ;
+ }
+ }
+
+ /* ---------------------------------------------- */
+ /* block back-substitution for off-diagonal-block */
+ /* ---------------------------------------------- */
+
+ if (block > 0 && Offp != NULL)
+ {
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = Wx [k] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ Wx [Offi [p]] -= Offx[p] * x[0];
+ }
+ }
+ break ;
+
+ case 2:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = Wx [2*k ] ;
+ x [1] = Wx [2*k + 1] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+ offik = Offx [p] ;
+ Wx [2*i ] -= offik * x [0] ;
+ Wx [2*i + 1] -= offik * x [1] ;
+ }
+ }
+ break ;
+
+ case 3:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = Wx [3*k ] ;
+ x [1] = Wx [3*k + 1] ;
+ x [2] = Wx [3*k + 2] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+ offik = Offx [p] ;
+ Wx [3*i ] -= offik * x [0] ;
+ Wx [3*i + 1] -= offik * x [1] ;
+ Wx [3*i + 2] -= offik * x [2] ;
+ }
+ }
+ break ;
+
+ case 4:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = Wx [4*k ] ;
+ x [1] = Wx [4*k + 1] ;
+ x [2] = Wx [4*k + 2] ;
+ x [3] = Wx [4*k + 3] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+ offik = Offx [p] ;
+ Wx [4*i ] -= offik * x [0] ;
+ Wx [4*i + 1] -= offik * x [1] ;
+ Wx [4*i + 2] -= offik * x [2] ;
+ Wx [4*i + 3] -= offik * x [3] ;
+ }
+ }
+ break ;
+ }
+ }
+ }
+
+ /* -------------------------------------------------- */
+ /* permute the result, X = Q*W */
+ /* -------------------------------------------------- */
+
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q ? (Q [k] - 1) : k ;
+ Xx [i] = Wx [k] ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q ? (Q [k] - 1) : k ;
+ Xx [i ] = Wx [2*k ] ;
+ Xx [i + n ] = Wx [2*k + 1] ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q ? (Q [k] - 1) : k ;
+ Xx [i ] = Wx [3*k ] ;
+ Xx [i + n ] = Wx [3*k + 1] ;
+ Xx [i + n*2] = Wx [3*k + 2] ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q ? (Q [k] - 1) : k ;
+ Xx [i ] = Wx [4*k ] ;
+ Xx [i + n ] = Wx [4*k + 1] ;
+ Xx [i + n*2] = Wx [4*k + 2] ;
+ Xx [i + n*3] = Wx [4*k + 3] ;
+ }
+ break ;
+ }
+
+ /* -------------------------------------------------- */
+ /* go to the next chunk of B and X */
+ /* -------------------------------------------------- */
+
+ Xx += n*4 ;
+ Bx += n*4 ;
+ }
+ }
+
+ /* free workspace */
+ mxFree (Wx) ;
+ }
+
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* LU = klu (A) usage; extract factorization */
+ /* ------------------------------------------------------------------ */
+
+ /* sort the row indices in each column of L and U */
+ if (A_complex)
+ {
+ klu_zl_sort (Symbolic, Numeric, &Common) ;
+ }
+ else
+ {
+ klu_l_sort (Symbolic, Numeric, &Common) ;
+ }
+
+ /* L */
+ L_matlab = mxCreateSparse (n, n, Numeric->lnz,
+ A_complex ? mxCOMPLEX: mxREAL) ;
+ Lp = (UF_long *) mxGetJc (L_matlab) ;
+ Li = (UF_long *) mxGetIr (L_matlab) ;
+ Lx = mxGetPr (L_matlab) ;
+ Lz = mxGetPi (L_matlab) ;
+
+ /* U */
+ U_matlab = mxCreateSparse (n, n, Numeric->unz,
+ A_complex ? mxCOMPLEX: mxREAL) ;
+ Up = (UF_long *) mxGetJc (U_matlab) ;
+ Ui = (UF_long *) mxGetIr (U_matlab) ;
+ Ux = mxGetPr (U_matlab) ;
+ Uz = mxGetPi (U_matlab) ;
+
+ /* p */
+ p_matlab = mxCreateNumericMatrix (1, n, mx_int, mxREAL) ;
+ P = (UF_long *) mxGetData (p_matlab) ;
+
+ /* q */
+ q_matlab = mxCreateNumericMatrix (1, n, mx_int, mxREAL) ;
+ Q = (UF_long *) mxGetData (q_matlab) ;
+
+ /* R, as a sparse diagonal matrix */
+ R_matlab = mxCreateSparse (n, n, n+1, mxREAL) ;
+ Rp = (UF_long *) mxGetJc (R_matlab) ;
+ Ri = (UF_long *) mxGetIr (R_matlab) ;
+ Rs = mxGetPr (R_matlab) ;
+ for (k = 0 ; k <= n ; k++)
+ {
+ Rp [k] = k ;
+ Ri [k] = k ;
+ }
+
+ /* F, off diagonal blocks */
+ F_matlab = mxCreateSparse (n, n, Numeric->nzoff,
+ A_complex ? mxCOMPLEX: mxREAL) ;
+ Offp = (UF_long *) mxGetJc (F_matlab) ;
+ Offi = (UF_long *) mxGetIr (F_matlab) ;
+ Offx = mxGetPr (F_matlab) ;
+ Offz = mxGetPi (F_matlab) ;
+
+ /* r, block boundaries */
+ nblocks = Symbolic->nblocks ;
+ r_matlab = mxCreateNumericMatrix (1, nblocks+1, mx_int, mxREAL) ;
+ R = (UF_long *) mxGetData (r_matlab) ;
+
+ /* extract the LU factorization from KLU Numeric and Symbolic objects */
+ if (A_complex)
+ {
+ klu_zl_extract (Numeric, Symbolic, Lp, Li, Lx, Lz, Up, Ui, Ux, Uz,
+ Offp, Offi, Offx, Offz, P, Q, Rs, R, &Common) ;
+ }
+ else
+ {
+ klu_l_extract (Numeric, Symbolic, Lp, Li, Lx, Up, Ui, Ux,
+ Offp, Offi, Offx, P, Q, Rs, R, &Common) ;
+ }
+
+ /* fix p and q for 1-based indexing */
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k]++ ;
+ Q [k]++ ;
+ }
+
+ /* fix r for 1-based indexing */
+ for (k = 0 ; k <= nblocks ; k++)
+ {
+ R [k]++ ;
+ }
+
+ /* create output LU struct */
+ pargout [0] = mxCreateStructMatrix (1, 1, 7, LUnames) ;
+ mxSetFieldByNumber (pargout [0], 0, 0, L_matlab) ;
+ mxSetFieldByNumber (pargout [0], 0, 1, U_matlab) ;
+ mxSetFieldByNumber (pargout [0], 0, 2, p_matlab) ;
+ mxSetFieldByNumber (pargout [0], 0, 3, q_matlab) ;
+ mxSetFieldByNumber (pargout [0], 0, 4, R_matlab) ;
+ mxSetFieldByNumber (pargout [0], 0, 5, F_matlab) ;
+ mxSetFieldByNumber (pargout [0], 0, 6, r_matlab) ;
+
+ /* ------------------------------------------------------------------ */
+ /* free Symbolic and Numeric objects */
+ /* ------------------------------------------------------------------ */
+
+ klu_l_free_symbolic (&Symbolic, &Common) ;
+ klu_l_free_numeric (&Numeric, &Common) ;
+ }
+}
diff --git a/KLU/Makefile b/KLU/Makefile
new file mode 100644
index 0000000..7f5a62e
--- /dev/null
+++ b/KLU/Makefile
@@ -0,0 +1,27 @@
+default: library
+
+include ../UFconfig/UFconfig.mk
+
+library:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+clean:
+ ( cd Demo ; $(MAKE) clean )
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Tcov ; $(MAKE) clean )
+
+distclean:
+ ( cd Demo ; $(MAKE) distclean )
+ ( cd Lib ; $(MAKE) distclean )
+ ( cd Tcov ; $(MAKE) distclean )
+ ( cd User ; $(MAKE) distclean )
+ ( cd MATLAB ; $(MAKE) distclean )
+
+mex:
+ ( cd MATLAB ; $(MAKE) )
+
+purge: distclean
+
+cov: library
+ ( cd Tcov ; $(MAKE) )
diff --git a/KLU/Matrix/1c.mtx b/KLU/Matrix/1c.mtx
new file mode 100644
index 0000000..b9da424
--- /dev/null
+++ b/KLU/Matrix/1c.mtx
@@ -0,0 +1,3 @@
+%%MatrixMarket matrix coordinate complex general
+1 1 1
+1 1 1 1
diff --git a/KLU/Matrix/GD99_cc.mtx b/KLU/Matrix/GD99_cc.mtx
new file mode 100644
index 0000000..4f5baec
--- /dev/null
+++ b/KLU/Matrix/GD99_cc.mtx
@@ -0,0 +1,152 @@
+%%MatrixMarket matrix coordinate complex general
+% imaginary part is Pajek/GD99_c, real part is zero
+105 105 149
+6 1 0 1
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diff --git a/KLU/Matrix/arrow.mtx b/KLU/Matrix/arrow.mtx
new file mode 100644
index 0000000..27419e4
--- /dev/null
+++ b/KLU/Matrix/arrow.mtx
@@ -0,0 +1,300 @@
+%%MatrixMarket matrix coordinate integer general
+100 100 298
+1 1 2
+2 1 1
+3 1 1
+4 1 1
+5 1 1
+6 1 1
+7 1 1
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+9 1 1
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diff --git a/KLU/Matrix/arrowc.mtx b/KLU/Matrix/arrowc.mtx
new file mode 100644
index 0000000..bf4d3c5
--- /dev/null
+++ b/KLU/Matrix/arrowc.mtx
@@ -0,0 +1,300 @@
+%%MatrixMarket matrix coordinate complex general
+100 100 298
+1 1 0 1
+2 1 1 0
+3 1 1 0
+4 1 1 0
+5 1 1 0
+6 1 1 0
+7 1 1 0
+8 1 1 0
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diff --git a/KLU/Matrix/ctina.mtx b/KLU/Matrix/ctina.mtx
new file mode 100644
index 0000000..3773ee1
--- /dev/null
+++ b/KLU/Matrix/ctina.mtx
@@ -0,0 +1,39 @@
+%%MatrixMarket matrix coordinate complex general
+% complex matrix with same nonzero pattern as Pajek/Tina_AskCog
+11 11 36
+3 1 0 1
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diff --git a/KLU/Matrix/impcol_a.mtx b/KLU/Matrix/impcol_a.mtx
new file mode 100644
index 0000000..49952a6
--- /dev/null
+++ b/KLU/Matrix/impcol_a.mtx
@@ -0,0 +1,586 @@
+%%MatrixMarket matrix coordinate real general
+%-------------------------------------------------------------------------------
+% UF Sparse Matrix Collection, Tim Davis
+% http://www.cise.ufl.edu/research/sparse/matrices/HB/impcol_a
+% name: HB/impcol_a
+% [UNSYMMETRIC MATRIX - HEAT EXCHANGER NETWORK (CHEM ENG) ,1982]
+% id: 171
+% date: 1982
+% author: D. Bogle
+% ed: I. Duff, R. Grimes, J. Lewis
+% fields: title A name id date author ed kind
+% kind: chemical process simulation problem
+%-------------------------------------------------------------------------------
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diff --git a/KLU/Matrix/one.mtx b/KLU/Matrix/one.mtx
new file mode 100644
index 0000000..ef09891
--- /dev/null
+++ b/KLU/Matrix/one.mtx
@@ -0,0 +1,6 @@
+%%MatrixMarket matrix coordinate real general
+2 2 4
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diff --git a/KLU/Matrix/onec.mtx b/KLU/Matrix/onec.mtx
new file mode 100644
index 0000000..59c8534
--- /dev/null
+++ b/KLU/Matrix/onec.mtx
@@ -0,0 +1,6 @@
+%%MatrixMarket matrix coordinate complex general
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diff --git a/KLU/Matrix/two.mtx b/KLU/Matrix/two.mtx
new file mode 100644
index 0000000..7457e81
--- /dev/null
+++ b/KLU/Matrix/two.mtx
@@ -0,0 +1,3 @@
+%%MatrixMarket matrix coordinate real general
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diff --git a/KLU/Matrix/w156.mtx b/KLU/Matrix/w156.mtx
new file mode 100644
index 0000000..658309c
--- /dev/null
+++ b/KLU/Matrix/w156.mtx
@@ -0,0 +1,365 @@
+%%MatrixMarket matrix coordinate complex general
+% complex matrix with the same real part, and same pattern, as HB/west0156
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diff --git a/KLU/README.txt b/KLU/README.txt
new file mode 100644
index 0000000..510a439
--- /dev/null
+++ b/KLU/README.txt
@@ -0,0 +1,139 @@
+KLU Version 1.0, May 31, 2007, by Timothy A. Davis and Ekanathan Palamadai.
+Copyright (C) 2004-2007, University of Florida
+KLU is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+Requires the AMD, COLAMD, and BTF libraries, in ../AMD, ../COLAMD, and ../BTF,
+respectively. Requires the ../UFconfig/UFconfig.mk configuration file.
+Optionally uses CHOLMOD (KLU/User example ordering). The Tcov tests and
+the Demo both require CHOLMOD.
+
+To compile the libklu.a library, type "make". The compiled library is located
+in KLU/Lib/libklu.a. Compile code that uses KLU with -IKLU/Include.
+
+Type "make clean" to remove all but the compiled library, and "make distclean"
+to remove all files not in the original distribution.
+
+--------------------------------------------------------------------------------
+
+KLU is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This Module is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+--------------------------------------------------------------------------------
+
+A full text of the license is in Doc/lesser.txt.
+
+Files in this distribution:
+
+ Demo example programs that use KLU (requires CHOLMOD)
+ Doc documentation
+ Include include files
+ Lib compiled library
+ Makefile top-level Makefile
+ MATLAB MATLAB interface
+ Matrix test matrices
+ README.txt this file
+ Source source code
+ Tcov exhaustive test of KLU and BTF
+ User example user ordering function (interface to CHOLMOD)
+
+./Demo:
+ kludemo.c KLU demo (int version)
+ kludemo.out output of "make" in this directory
+ kluldemo.c KLU demo (UF_long version)
+ Makefile Makefile for compiling the demo
+
+./Doc:
+ ChangeLog
+ KLU_UserGuide.bib Bibiography
+ KLU_UserGuide.pdf PDF version of KLU User Guide
+ KLU_UserGuide.tex TEX source of KLU User Guide
+ lesser.txt license (LGPL)
+ Makefile Makefile for creating the User Guide
+ palamadai_e.pdf Eka Palamadai's MS thesis
+
+./Include:
+ klu.h user include file
+ klu_internal.h internal include file, not needed by the user
+ klu_version.h internal include file, not needed by the user
+
+./Lib:
+ Makefile Makefile for compiling the KLU C-callable library
+
+./MATLAB:
+ Contents.m list of MATLAB functions in KLU
+ klu_demo.m MATLAB demo
+ klu_demo.m.out output of MATLAB demo
+ klu_install.m compiles and installs KLU for use in MATLAB, runs demo
+ klu.m MATLAB help for KLU
+ klu_make.m compiles KLU for use in MATLAB
+ klu_mex.c MATLAB mexFunction interface for KLU
+ Makefile Makefile for KLU mexFunction, with CHOLMOD
+ Makefile_no_CHOLMOD Makefile for KLU mexFunction, without CHOLMOD
+ Test MATLAB tests
+
+./MATLAB/Test: KLU tests, requires UFget
+ test1.m
+ test2.m
+ test3.m
+ test4.m
+ test5.m
+
+./Matrix: test matrices for programs in ./Demo and ./Tcov
+ 1c.mtx
+ arrowc.mtx
+ arrow.mtx
+ ctina.mtx
+ GD99_cc.mtx
+ impcol_a.mtx
+ onec.mtx
+ one.mtx
+ two.mtx
+ w156.mtx
+
+./Source:
+ klu_analyze.c klu_analyze and supporting functions
+ klu_analyze_given.c klu_analyze_given and supporting functions
+ klu.c kernel factor/solve functions, not user-callable
+ klu_defaults.c klu_defaults function
+ klu_diagnostics.c klu_rcond, klu_condest, klu_rgrowth, kluflops
+ klu_dump.c debugging functions
+ klu_extract.c klu_extract
+ klu_factor.c klu_factor and supporting functions
+ klu_free_numeric.c klu_free_numeric function
+ klu_free_symbolic.c klu_free_symbolic function
+ klu_kernel.c kernel factor functions, not user-callable
+ klu_memory.c klu_malloc, klu_free, klu_realloc, and supporing func.
+ klu_refactor.c klu_refactor function
+ klu_scale.c klu_scale function
+ klu_solve.c klu_solve function
+ klu_sort.c klu_sort and supporting functions
+ klu_tsolve.c klu_tsovle function
+
+./Tcov: exhaustive test suite; requires Linux/Unix
+ coverage determine statement coverage
+ klultests KLU UF_long tests
+ klutest.c KLU test program
+ klutests KLU int tests
+ Makefile Makefile for compiling and running the tests
+ README.txt README file for Tcov
+ vklutests KLU int tests, using valgrind
+ vklultests KLU UF_long tests, using valgrind
+
+./User:
+ klu_cholmod.c sample KLU user ordering function (int version)
+ klu_cholmod.h include file for klu_cholmod and klu_l_cholmod
+ klu_l_cholmod.c sample KLU user ordering function (UF_long version)
+ Makefile Makefile for compiling the user ordering functions
+ README.txt README for User directory
diff --git a/KLU/Source/klu.c b/KLU/Source/klu.c
new file mode 100644
index 0000000..8b58008
--- /dev/null
+++ b/KLU/Source/klu.c
@@ -0,0 +1,773 @@
+/* ========================================================================== */
+/* === klu ================================================================== */
+/* ========================================================================== */
+
+/* KLU: factorizes P*A into L*U, using the Gilbert-Peierls algorithm [1], with
+ * optional symmetric pruning by Eisenstat and Liu [2]. The code is by Tim
+ * Davis. This algorithm is what appears as the default sparse LU routine in
+ * MATLAB version 6.0, and still appears in MATLAB 6.5 as [L,U,P] = lu (A).
+ * Note that no column ordering is provided (see COLAMD or AMD for suitable
+ * orderings). SuperLU is based on this algorithm, except that it adds the
+ * use of dense matrix operations on "supernodes" (adjacent columns with
+ * identical). This code doesn't use supernodes, thus its name ("Kent" LU,
+ * as in "Clark Kent", in contrast with Super-LU...). This algorithm is slower
+ * than SuperLU and UMFPACK for large matrices with lots of nonzeros in their
+ * factors (such as for most finite-element problems). However, for matrices
+ * with very sparse LU factors, this algorithm is typically faster than both
+ * SuperLU and UMFPACK, since in this case there is little chance to exploit
+ * dense matrix kernels (the BLAS).
+ *
+ * Only one block of A is factorized, in the BTF form. The input n is the
+ * size of the block; k1 is the first row and column in the block.
+ *
+ * NOTE: no error checking is done on the inputs. This version is not meant to
+ * be called directly by the user. Use klu_factor instead.
+ *
+ * No fill-reducing ordering is provided. The ordering quality of
+ * klu_kernel_factor is the responsibility of the caller. The input A must
+ * pre-permuted to reduce fill-in, or fill-reducing input permutation Q must
+ * be provided.
+ *
+ * The input matrix A must be in compressed-column form, with either sorted
+ * or unsorted row indices. Row indices for column j of A is in
+ * Ai [Ap [j] ... Ap [j+1]-1] and the same range of indices in Ax holds the
+ * numerical values. No duplicate entries are allowed.
+ *
+ * Copyright 2004-2007, Tim Davis. All rights reserved. See the README
+ * file for details on permitted use. Note that no code from The MathWorks,
+ * Inc, or from SuperLU, or from any other source appears here. The code is
+ * written from scratch, from the algorithmic description in Gilbert & Peierls'
+ * and Eisenstat & Liu's journal papers [1,2].
+ *
+ * If an input permutation Q is provided, the factorization L*U = A (P,Q)
+ * is computed, where P is determined by partial pivoting, and Q is the input
+ * ordering. If the pivot tolerance is less than 1, the "diagonal" entry that
+ * KLU attempts to choose is the diagonal of A (Q,Q). In other words, the
+ * input permutation is applied symmetrically to the input matrix. The output
+ * permutation P includes both the partial pivoting ordering and the input
+ * permutation. If Q is NULL, then it is assumed to be the identity
+ * permutation. Q is not modified.
+ *
+ * [1] Gilbert, J. R. and Peierls, T., "Sparse Partial Pivoting in Time
+ * Proportional to Arithmetic Operations," SIAM J. Sci. Stat. Comp.,
+ * vol 9, pp. 862-874, 1988.
+ * [2] Eisenstat, S. C. and Liu, J. W. H., "Exploiting Structural Symmetry in
+ * Unsymmetric Sparse Symbolic Factorization," SIAM J. Matrix Analysis &
+ * Applic., vol 13, pp. 202-211, 1992.
+ */
+
+/* ========================================================================== */
+
+#include "klu_internal.h"
+
+size_t KLU_kernel_factor /* 0 if failure, size of LU if OK */
+(
+ /* inputs, not modified */
+ Int n, /* A is n-by-n. n must be > 0. */
+ Int Ap [ ], /* size n+1, column pointers for A */
+ Int Ai [ ], /* size nz = Ap [n], row indices for A */
+ Entry Ax [ ], /* size nz, values of A */
+ Int Q [ ], /* size n, optional column permutation */
+ double Lsize, /* estimate of number of nonzeros in L */
+
+ /* outputs, not defined on input */
+ Unit **p_LU, /* row indices and values of L and U */
+ Entry Udiag [ ], /* size n, diagonal of U */
+ Int Llen [ ], /* size n, column length of L */
+ Int Ulen [ ], /* size n, column length of U */
+ Int Lip [ ], /* size n, column pointers for L */
+ Int Uip [ ], /* size n, column pointers for U */
+ Int P [ ], /* row permutation, size n */
+ Int *lnz, /* size of L */
+ Int *unz, /* size of U */
+
+ /* workspace, undefined on input */
+ Entry *X, /* size n double's, zero on output */
+ Int *Work, /* size 5n Int's */
+
+ /* inputs, not modified on output */
+ Int k1, /* the block of A is from k1 to k2-1 */
+ Int PSinv [ ], /* inverse of P from symbolic factorization */
+ double Rs [ ], /* scale factors for A */
+
+ /* inputs, modified on output */
+ Int Offp [ ], /* off-diagonal matrix (modified by this routine) */
+ Int Offi [ ],
+ Entry Offx [ ],
+ /* --------------- */
+ KLU_common *Common
+)
+{
+ double maxlnz, dunits ;
+ Unit *LU ;
+ Int *Pinv, *Lpend, *Stack, *Flag, *Ap_pos, *W ;
+ Int lsize, usize, anz, ok ;
+ size_t lusize ;
+ ASSERT (Common != NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get control parameters, or use defaults */
+ /* ---------------------------------------------------------------------- */
+
+ n = MAX (1, n) ;
+ anz = Ap [n+k1] - Ap [k1] ;
+
+ if (Lsize <= 0)
+ {
+ Lsize = -Lsize ;
+ Lsize = MAX (Lsize, 1.0) ;
+ lsize = Lsize * anz + n ;
+ }
+ else
+ {
+ lsize = Lsize ;
+ }
+
+ usize = lsize ;
+
+ lsize = MAX (n+1, lsize) ;
+ usize = MAX (n+1, usize) ;
+
+ maxlnz = (((double) n) * ((double) n) + ((double) n)) / 2. ;
+ maxlnz = MIN (maxlnz, ((double) INT_MAX)) ;
+ lsize = MIN (maxlnz, lsize) ;
+ usize = MIN (maxlnz, usize) ;
+
+ PRINTF (("Welcome to klu: n %d anz %d k1 %d lsize %d usize %d maxlnz %g\n",
+ n, anz, k1, lsize, usize, maxlnz)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace and outputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* return arguments are not yet assigned */
+ *p_LU = (Unit *) NULL ;
+
+ /* these computations are safe from size_t overflow */
+ W = Work ;
+ Pinv = (Int *) W ; W += n ;
+ Stack = (Int *) W ; W += n ;
+ Flag = (Int *) W ; W += n ;
+ Lpend = (Int *) W ; W += n ;
+ Ap_pos = (Int *) W ; W += n ;
+
+ dunits = DUNITS (Int, lsize) + DUNITS (Entry, lsize) +
+ DUNITS (Int, usize) + DUNITS (Entry, usize) ;
+ lusize = (size_t) dunits ;
+ ok = !INT_OVERFLOW (dunits) ;
+ LU = ok ? KLU_malloc (lusize, sizeof (Unit), Common) : NULL ;
+ if (LU == NULL)
+ {
+ /* out of memory, or problem too large */
+ Common->status = KLU_OUT_OF_MEMORY ;
+ lusize = 0 ;
+ return (lusize) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize */
+ /* ---------------------------------------------------------------------- */
+
+ /* with pruning, and non-recursive depth-first-search */
+ lusize = KLU_kernel (n, Ap, Ai, Ax, Q, lusize,
+ Pinv, P, &LU, Udiag, Llen, Ulen, Lip, Uip, lnz, unz,
+ X, Stack, Flag, Ap_pos, Lpend,
+ k1, PSinv, Rs, Offp, Offi, Offx, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return LU factors, or return nothing if an error occurred */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->status < KLU_OK)
+ {
+ LU = KLU_free (LU, lusize, sizeof (Unit), Common) ;
+ lusize = 0 ;
+ }
+ *p_LU = LU ;
+ PRINTF ((" in klu noffdiag %d\n", Common->noffdiag)) ;
+ return (lusize) ;
+}
+
+
+/* ========================================================================== */
+/* === KLU_lsolve =========================================================== */
+/* ========================================================================== */
+
+/* Solve Lx=b. Assumes L is unit lower triangular and where the unit diagonal
+ * entry is NOT stored. Overwrites B with the solution X. B is n-by-nrhs
+ * and is stored in ROW form with row dimension nrhs. nrhs must be in the
+ * range 1 to 4. */
+
+void KLU_lsolve
+(
+ /* inputs, not modified: */
+ Int n,
+ Int Lip [ ],
+ Int Llen [ ],
+ Unit LU [ ],
+ Int nrhs,
+ /* right-hand-side on input, solution to Lx=b on output */
+ Entry X [ ]
+)
+{
+ Entry x [4], lik ;
+ Int *Li ;
+ Entry *Lx ;
+ Int k, p, len, i ;
+
+ switch (nrhs)
+ {
+
+ case 1:
+ for (k = 0 ; k < n ; k++)
+ {
+ x [0] = X [k] ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+ /* unit diagonal of L is not stored*/
+ for (p = 0 ; p < len ; p++)
+ {
+ /* X [Li [p]] -= Lx [p] * x [0] ; */
+ MULT_SUB (X [Li [p]], Lx [p], x [0]) ;
+ }
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ x [0] = X [2*k ] ;
+ x [1] = X [2*k + 1] ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Li [p] ;
+ lik = Lx [p] ;
+ MULT_SUB (X [2*i], lik, x [0]) ;
+ MULT_SUB (X [2*i + 1], lik, x [1]) ;
+ }
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ x [0] = X [3*k ] ;
+ x [1] = X [3*k + 1] ;
+ x [2] = X [3*k + 2] ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Li [p] ;
+ lik = Lx [p] ;
+ MULT_SUB (X [3*i], lik, x [0]) ;
+ MULT_SUB (X [3*i + 1], lik, x [1]) ;
+ MULT_SUB (X [3*i + 2], lik, x [2]) ;
+ }
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ x [0] = X [4*k ] ;
+ x [1] = X [4*k + 1] ;
+ x [2] = X [4*k + 2] ;
+ x [3] = X [4*k + 3] ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Li [p] ;
+ lik = Lx [p] ;
+ MULT_SUB (X [4*i], lik, x [0]) ;
+ MULT_SUB (X [4*i + 1], lik, x [1]) ;
+ MULT_SUB (X [4*i + 2], lik, x [2]) ;
+ MULT_SUB (X [4*i + 3], lik, x [3]) ;
+ }
+ }
+ break ;
+
+ }
+}
+
+/* ========================================================================== */
+/* === KLU_usolve =========================================================== */
+/* ========================================================================== */
+
+/* Solve Ux=b. Assumes U is non-unit upper triangular and where the diagonal
+ * entry is NOT stored. Overwrites B with the solution X. B is n-by-nrhs
+ * and is stored in ROW form with row dimension nrhs. nrhs must be in the
+ * range 1 to 4. */
+
+void KLU_usolve
+(
+ /* inputs, not modified: */
+ Int n,
+ Int Uip [ ],
+ Int Ulen [ ],
+ Unit LU [ ],
+ Entry Udiag [ ],
+ Int nrhs,
+ /* right-hand-side on input, solution to Ux=b on output */
+ Entry X [ ]
+)
+{
+ Entry x [4], uik, ukk ;
+ Int *Ui ;
+ Entry *Ux ;
+ Int k, p, len, i ;
+
+ switch (nrhs)
+ {
+
+ case 1:
+
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
+ /* x [0] = X [k] / Udiag [k] ; */
+ DIV (x [0], X [k], Udiag [k]) ;
+ X [k] = x [0] ;
+ for (p = 0 ; p < len ; p++)
+ {
+ /* X [Ui [p]] -= Ux [p] * x [0] ; */
+ MULT_SUB (X [Ui [p]], Ux [p], x [0]) ;
+
+ }
+ }
+
+ break ;
+
+ case 2:
+
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
+ ukk = Udiag [k] ;
+ /* x [0] = X [2*k ] / ukk ;
+ x [1] = X [2*k + 1] / ukk ; */
+ DIV (x [0], X [2*k], ukk) ;
+ DIV (x [1], X [2*k + 1], ukk) ;
+
+ X [2*k ] = x [0] ;
+ X [2*k + 1] = x [1] ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Ui [p] ;
+ uik = Ux [p] ;
+ /* X [2*i ] -= uik * x [0] ;
+ X [2*i + 1] -= uik * x [1] ; */
+ MULT_SUB (X [2*i], uik, x [0]) ;
+ MULT_SUB (X [2*i + 1], uik, x [1]) ;
+ }
+ }
+
+ break ;
+
+ case 3:
+
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
+ ukk = Udiag [k] ;
+
+ DIV (x [0], X [3*k], ukk) ;
+ DIV (x [1], X [3*k + 1], ukk) ;
+ DIV (x [2], X [3*k + 2], ukk) ;
+
+ X [3*k ] = x [0] ;
+ X [3*k + 1] = x [1] ;
+ X [3*k + 2] = x [2] ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Ui [p] ;
+ uik = Ux [p] ;
+ MULT_SUB (X [3*i], uik, x [0]) ;
+ MULT_SUB (X [3*i + 1], uik, x [1]) ;
+ MULT_SUB (X [3*i + 2], uik, x [2]) ;
+ }
+ }
+
+ break ;
+
+ case 4:
+
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
+ ukk = Udiag [k] ;
+
+ DIV (x [0], X [4*k], ukk) ;
+ DIV (x [1], X [4*k + 1], ukk) ;
+ DIV (x [2], X [4*k + 2], ukk) ;
+ DIV (x [3], X [4*k + 3], ukk) ;
+
+ X [4*k ] = x [0] ;
+ X [4*k + 1] = x [1] ;
+ X [4*k + 2] = x [2] ;
+ X [4*k + 3] = x [3] ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Ui [p] ;
+ uik = Ux [p] ;
+
+ MULT_SUB (X [4*i], uik, x [0]) ;
+ MULT_SUB (X [4*i + 1], uik, x [1]) ;
+ MULT_SUB (X [4*i + 2], uik, x [2]) ;
+ MULT_SUB (X [4*i + 3], uik, x [3]) ;
+ }
+ }
+
+ break ;
+
+ }
+}
+
+
+/* ========================================================================== */
+/* === KLU_ltsolve ========================================================== */
+/* ========================================================================== */
+
+/* Solve L'x=b. Assumes L is unit lower triangular and where the unit diagonal
+ * entry is NOT stored. Overwrites B with the solution X. B is n-by-nrhs
+ * and is stored in ROW form with row dimension nrhs. nrhs must in the
+ * range 1 to 4. */
+
+void KLU_ltsolve
+(
+ /* inputs, not modified: */
+ Int n,
+ Int Lip [ ],
+ Int Llen [ ],
+ Unit LU [ ],
+ Int nrhs,
+#ifdef COMPLEX
+ Int conj_solve,
+#endif
+ /* right-hand-side on input, solution to L'x=b on output */
+ Entry X [ ]
+)
+{
+ Entry x [4], lik ;
+ Int *Li ;
+ Entry *Lx ;
+ Int k, p, len, i ;
+
+ switch (nrhs)
+ {
+
+ case 1:
+
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+ x [0] = X [k] ;
+ for (p = 0 ; p < len ; p++)
+ {
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ /* x [0] -= CONJ (Lx [p]) * X [Li [p]] ; */
+ MULT_SUB_CONJ (x [0], X [Li [p]], Lx [p]) ;
+ }
+ else
+#endif
+ {
+ /*x [0] -= Lx [p] * X [Li [p]] ;*/
+ MULT_SUB (x [0], Lx [p], X [Li [p]]) ;
+ }
+ }
+ X [k] = x [0] ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ x [0] = X [2*k ] ;
+ x [1] = X [2*k + 1] ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Li [p] ;
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (lik, Lx [p]) ;
+ }
+ else
+#endif
+ {
+ lik = Lx [p] ;
+ }
+ MULT_SUB (x [0], lik, X [2*i]) ;
+ MULT_SUB (x [1], lik, X [2*i + 1]) ;
+ }
+ X [2*k ] = x [0] ;
+ X [2*k + 1] = x [1] ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ x [0] = X [3*k ] ;
+ x [1] = X [3*k + 1] ;
+ x [2] = X [3*k + 2] ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Li [p] ;
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (lik, Lx [p]) ;
+ }
+ else
+#endif
+ {
+ lik = Lx [p] ;
+ }
+ MULT_SUB (x [0], lik, X [3*i]) ;
+ MULT_SUB (x [1], lik, X [3*i + 1]) ;
+ MULT_SUB (x [2], lik, X [3*i + 2]) ;
+ }
+ X [3*k ] = x [0] ;
+ X [3*k + 1] = x [1] ;
+ X [3*k + 2] = x [2] ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ x [0] = X [4*k ] ;
+ x [1] = X [4*k + 1] ;
+ x [2] = X [4*k + 2] ;
+ x [3] = X [4*k + 3] ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Li [p] ;
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (lik, Lx [p]) ;
+ }
+ else
+#endif
+ {
+ lik = Lx [p] ;
+ }
+ MULT_SUB (x [0], lik, X [4*i]) ;
+ MULT_SUB (x [1], lik, X [4*i + 1]) ;
+ MULT_SUB (x [2], lik, X [4*i + 2]) ;
+ MULT_SUB (x [3], lik, X [4*i + 3]) ;
+ }
+ X [4*k ] = x [0] ;
+ X [4*k + 1] = x [1] ;
+ X [4*k + 2] = x [2] ;
+ X [4*k + 3] = x [3] ;
+ }
+ break ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === KLU_utsolve ========================================================== */
+/* ========================================================================== */
+
+/* Solve U'x=b. Assumes U is non-unit upper triangular and where the diagonal
+ * entry is stored (and appears last in each column of U). Overwrites B
+ * with the solution X. B is n-by-nrhs and is stored in ROW form with row
+ * dimension nrhs. nrhs must be in the range 1 to 4. */
+
+void KLU_utsolve
+(
+ /* inputs, not modified: */
+ Int n,
+ Int Uip [ ],
+ Int Ulen [ ],
+ Unit LU [ ],
+ Entry Udiag [ ],
+ Int nrhs,
+#ifdef COMPLEX
+ Int conj_solve,
+#endif
+ /* right-hand-side on input, solution to Ux=b on output */
+ Entry X [ ]
+)
+{
+ Entry x [4], uik, ukk ;
+ Int k, p, len, i ;
+ Int *Ui ;
+ Entry *Ux ;
+
+ switch (nrhs)
+ {
+
+ case 1:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
+ x [0] = X [k] ;
+ for (p = 0 ; p < len ; p++)
+ {
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ /* x [0] -= CONJ (Ux [p]) * X [Ui [p]] ; */
+ MULT_SUB_CONJ (x [0], X [Ui [p]], Ux [p]) ;
+ }
+ else
+#endif
+ {
+ /* x [0] -= Ux [p] * X [Ui [p]] ; */
+ MULT_SUB (x [0], Ux [p], X [Ui [p]]) ;
+ }
+ }
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (ukk, Udiag [k]) ;
+ }
+ else
+#endif
+ {
+ ukk = Udiag [k] ;
+ }
+ DIV (X [k], x [0], ukk) ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
+ x [0] = X [2*k ] ;
+ x [1] = X [2*k + 1] ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Ui [p] ;
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (uik, Ux [p]) ;
+ }
+ else
+#endif
+ {
+ uik = Ux [p] ;
+ }
+ MULT_SUB (x [0], uik, X [2*i]) ;
+ MULT_SUB (x [1], uik, X [2*i + 1]) ;
+ }
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (ukk, Udiag [k]) ;
+ }
+ else
+#endif
+ {
+ ukk = Udiag [k] ;
+ }
+ DIV (X [2*k], x [0], ukk) ;
+ DIV (X [2*k + 1], x [1], ukk) ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
+ x [0] = X [3*k ] ;
+ x [1] = X [3*k + 1] ;
+ x [2] = X [3*k + 2] ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Ui [p] ;
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (uik, Ux [p]) ;
+ }
+ else
+#endif
+ {
+ uik = Ux [p] ;
+ }
+ MULT_SUB (x [0], uik, X [3*i]) ;
+ MULT_SUB (x [1], uik, X [3*i + 1]) ;
+ MULT_SUB (x [2], uik, X [3*i + 2]) ;
+ }
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (ukk, Udiag [k]) ;
+ }
+ else
+#endif
+ {
+ ukk = Udiag [k] ;
+ }
+ DIV (X [3*k], x [0], ukk) ;
+ DIV (X [3*k + 1], x [1], ukk) ;
+ DIV (X [3*k + 2], x [2], ukk) ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
+ x [0] = X [4*k ] ;
+ x [1] = X [4*k + 1] ;
+ x [2] = X [4*k + 2] ;
+ x [3] = X [4*k + 3] ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Ui [p] ;
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (uik, Ux [p]) ;
+ }
+ else
+#endif
+ {
+ uik = Ux [p] ;
+ }
+ MULT_SUB (x [0], uik, X [4*i]) ;
+ MULT_SUB (x [1], uik, X [4*i + 1]) ;
+ MULT_SUB (x [2], uik, X [4*i + 2]) ;
+ MULT_SUB (x [3], uik, X [4*i + 3]) ;
+ }
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (ukk, Udiag [k]) ;
+ }
+ else
+#endif
+ {
+ ukk = Udiag [k] ;
+ }
+ DIV (X [4*k], x [0], ukk) ;
+ DIV (X [4*k + 1], x [1], ukk) ;
+ DIV (X [4*k + 2], x [2], ukk) ;
+ DIV (X [4*k + 3], x [3], ukk) ;
+ }
+ break ;
+ }
+}
diff --git a/KLU/Source/klu_analyze.c b/KLU/Source/klu_analyze.c
new file mode 100644
index 0000000..ecc715b
--- /dev/null
+++ b/KLU/Source/klu_analyze.c
@@ -0,0 +1,488 @@
+/* ========================================================================== */
+/* === klu_analyze ========================================================== */
+/* ========================================================================== */
+
+/* Order the matrix using BTF (or not), and then AMD, COLAMD, the natural
+ * ordering, or the user-provided-function on the blocks. Does not support
+ * using a given ordering (use klu_analyze_given for that case). */
+
+#include "klu_internal.h"
+
+/* ========================================================================== */
+/* === analyze_worker ======================================================= */
+/* ========================================================================== */
+
+static Int analyze_worker /* returns KLU_OK or < 0 if error */
+(
+ /* inputs, not modified */
+ Int n, /* A is n-by-n */
+ Int Ap [ ], /* size n+1, column pointers */
+ Int Ai [ ], /* size nz, row indices */
+ Int nblocks, /* # of blocks */
+ Int Pbtf [ ], /* BTF row permutation */
+ Int Qbtf [ ], /* BTF col permutation */
+ Int R [ ], /* size n+1, but only Rbtf [0..nblocks] is used */
+ Int ordering, /* what ordering to use (0, 1, or 3 for this routine) */
+
+ /* output only, not defined on input */
+ Int P [ ], /* size n */
+ Int Q [ ], /* size n */
+ double Lnz [ ], /* size n, but only Lnz [0..nblocks-1] is used */
+
+ /* workspace, not defined on input or output */
+ Int Pblk [ ], /* size maxblock */
+ Int Cp [ ], /* size maxblock+1 */
+ Int Ci [ ], /* size MAX (nz+1, Cilen) */
+ Int Cilen, /* nz+1, or COLAMD_recommend(nz,n,n) for COLAMD */
+ Int Pinv [ ], /* size maxblock */
+
+ /* input/output */
+ KLU_symbolic *Symbolic,
+ KLU_common *Common
+)
+{
+ double amd_Info [AMD_INFO], lnz, lnz1, flops, flops1 ;
+ Int k1, k2, nk, k, block, oldcol, pend, newcol, result, pc, p, newrow,
+ maxnz, nzoff, cstats [COLAMD_STATS], ok, err = KLU_INVALID ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+ /* compute the inverse of Pbtf */
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = EMPTY ;
+ Q [k] = EMPTY ;
+ Pinv [k] = EMPTY ;
+ }
+#endif
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSERT (Pbtf [k] >= 0 && Pbtf [k] < n) ;
+ Pinv [Pbtf [k]] = k ;
+ }
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++) ASSERT (Pinv [k] != EMPTY) ;
+#endif
+ nzoff = 0 ;
+ lnz = 0 ;
+ maxnz = 0 ;
+ flops = 0 ;
+ Symbolic->symmetry = EMPTY ; /* only computed by AMD */
+
+ /* ---------------------------------------------------------------------- */
+ /* order each block */
+ /* ---------------------------------------------------------------------- */
+
+ for (block = 0 ; block < nblocks ; block++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* the block is from rows/columns k1 to k2-1 */
+ /* ------------------------------------------------------------------ */
+
+ k1 = R [block] ;
+ k2 = R [block+1] ;
+ nk = k2 - k1 ;
+ PRINTF (("BLOCK %d, k1 %d k2-1 %d nk %d\n", block, k1, k2-1, nk)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* construct the kth block, C */
+ /* ------------------------------------------------------------------ */
+
+ Lnz [block] = EMPTY ;
+ pc = 0 ;
+ for (k = k1 ; k < k2 ; k++)
+ {
+ newcol = k-k1 ;
+ Cp [newcol] = pc ;
+ oldcol = Qbtf [k] ;
+ pend = Ap [oldcol+1] ;
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ newrow = Pinv [Ai [p]] ;
+ if (newrow < k1)
+ {
+ nzoff++ ;
+ }
+ else
+ {
+ /* (newrow,newcol) is an entry in the block */
+ ASSERT (newrow < k2) ;
+ newrow -= k1 ;
+ Ci [pc++] = newrow ;
+ }
+ }
+ }
+ Cp [nk] = pc ;
+ maxnz = MAX (maxnz, pc) ;
+ ASSERT (KLU_valid (nk, Cp, Ci, NULL)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* order the block C */
+ /* ------------------------------------------------------------------ */
+
+ if (nk <= 3)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* use natural ordering for tiny blocks (3-by-3 or less) */
+ /* -------------------------------------------------------------- */
+
+ for (k = 0 ; k < nk ; k++)
+ {
+ Pblk [k] = k ;
+ }
+ lnz1 = nk * (nk + 1) / 2 ;
+ flops1 = nk * (nk - 1) / 2 + (nk-1)*nk*(2*nk-1) / 6 ;
+ ok = TRUE ;
+
+ }
+ else if (ordering == 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* order the block with AMD (C+C') */
+ /* -------------------------------------------------------------- */
+
+ result = AMD_order (nk, Cp, Ci, Pblk, NULL, amd_Info) ;
+ ok = (result >= AMD_OK) ;
+ if (result == AMD_OUT_OF_MEMORY)
+ {
+ err = KLU_OUT_OF_MEMORY ;
+ }
+
+ /* account for memory usage in AMD */
+ Common->mempeak = MAX (Common->mempeak,
+ Common->memusage + amd_Info [AMD_MEMORY]) ;
+
+ /* get the ordering statistics from AMD */
+ lnz1 = (Int) (amd_Info [AMD_LNZ]) + nk ;
+ flops1 = 2 * amd_Info [AMD_NMULTSUBS_LU] + amd_Info [AMD_NDIV] ;
+ if (pc == maxnz)
+ {
+ /* get the symmetry of the biggest block */
+ Symbolic->symmetry = amd_Info [AMD_SYMMETRY] ;
+ }
+
+ }
+ else if (ordering == 1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* order the block with COLAMD (C) */
+ /* -------------------------------------------------------------- */
+
+ /* order (and destroy) Ci, returning column permutation in Cp.
+ * COLAMD "cannot" fail since the matrix has already been checked,
+ * and Ci allocated. */
+
+ ok = COLAMD (nk, nk, Cilen, Ci, Cp, NULL, cstats) ;
+ lnz1 = EMPTY ;
+ flops1 = EMPTY ;
+
+ /* copy the permutation from Cp to Pblk */
+ for (k = 0 ; k < nk ; k++)
+ {
+ Pblk [k] = Cp [k] ;
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* pass the block to the user-provided ordering function */
+ /* -------------------------------------------------------------- */
+
+ lnz1 = (Common->user_order) (nk, Cp, Ci, Pblk, Common) ;
+ flops1 = EMPTY ;
+ ok = (lnz1 != 0) ;
+ }
+
+ if (!ok)
+ {
+ return (err) ; /* ordering method failed */
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* keep track of nnz(L) and flops statistics */
+ /* ------------------------------------------------------------------ */
+
+ Lnz [block] = lnz1 ;
+ lnz = (lnz == EMPTY || lnz1 == EMPTY) ? EMPTY : (lnz + lnz1) ;
+ flops = (flops == EMPTY || flops1 == EMPTY) ? EMPTY : (flops + flops1) ;
+
+ /* ------------------------------------------------------------------ */
+ /* combine the preordering with the BTF ordering */
+ /* ------------------------------------------------------------------ */
+
+ PRINTF (("Pblk, 1-based:\n")) ;
+ for (k = 0 ; k < nk ; k++)
+ {
+ ASSERT (k + k1 < n) ;
+ ASSERT (Pblk [k] + k1 < n) ;
+ Q [k + k1] = Qbtf [Pblk [k] + k1] ;
+ }
+ for (k = 0 ; k < nk ; k++)
+ {
+ ASSERT (k + k1 < n) ;
+ ASSERT (Pblk [k] + k1 < n) ;
+ P [k + k1] = Pbtf [Pblk [k] + k1] ;
+ }
+ }
+
+ PRINTF (("nzoff %d Ap[n] %d\n", nzoff, Ap [n])) ;
+ ASSERT (nzoff >= 0 && nzoff <= Ap [n]) ;
+
+ /* return estimates of # of nonzeros in L including diagonal */
+ Symbolic->lnz = lnz ; /* EMPTY if COLAMD used */
+ Symbolic->unz = lnz ;
+ Symbolic->nzoff = nzoff ;
+ Symbolic->est_flops = flops ; /* EMPTY if COLAMD or user-ordering used */
+ return (KLU_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === order_and_analyze ==================================================== */
+/* ========================================================================== */
+
+/* Orders the matrix with or with BTF, then orders each block with AMD, COLAMD,
+ * or the user ordering function. Does not handle the natural or given
+ * ordering cases. */
+
+static KLU_symbolic *order_and_analyze /* returns NULL if error, or a valid
+ KLU_symbolic object if successful */
+(
+ /* inputs, not modified */
+ Int n, /* A is n-by-n */
+ Int Ap [ ], /* size n+1, column pointers */
+ Int Ai [ ], /* size nz, row indices */
+ /* --------------------- */
+ KLU_common *Common
+)
+{
+ double work ;
+ KLU_symbolic *Symbolic ;
+ double *Lnz ;
+ Int *Qbtf, *Cp, *Ci, *Pinv, *Pblk, *Pbtf, *P, *Q, *R ;
+ Int nblocks, nz, block, maxblock, k1, k2, nk, do_btf, ordering, k, Cilen,
+ *Work ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the Symbolic object, and check input matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic = KLU_alloc_symbolic (n, Ap, Ai, Common) ;
+ if (Symbolic == NULL)
+ {
+ return (NULL) ;
+ }
+ P = Symbolic->P ;
+ Q = Symbolic->Q ;
+ R = Symbolic->R ;
+ Lnz = Symbolic->Lnz ;
+ nz = Symbolic->nz ;
+
+ ordering = Common->ordering ;
+ if (ordering == 1)
+ {
+ /* COLAMD */
+ Cilen = COLAMD_recommended (nz, n, n) ;
+ }
+ else if (ordering == 0 || (ordering == 3 && Common->user_order != NULL))
+ {
+ /* AMD or user ordering function */
+ Cilen = nz+1 ;
+ }
+ else
+ {
+ /* invalid ordering */
+ Common->status = KLU_INVALID ;
+ KLU_free_symbolic (&Symbolic, Common) ;
+ return (NULL) ;
+ }
+
+ /* AMD memory management routines */
+ amd_malloc = Common->malloc_memory ;
+ amd_free = Common->free_memory ;
+ amd_calloc = Common->calloc_memory ;
+ amd_realloc = Common->realloc_memory ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace for BTF permutation */
+ /* ---------------------------------------------------------------------- */
+
+ Pbtf = KLU_malloc (n, sizeof (Int), Common) ;
+ Qbtf = KLU_malloc (n, sizeof (Int), Common) ;
+ if (Common->status < KLU_OK)
+ {
+ KLU_free (Pbtf, n, sizeof (Int), Common) ;
+ KLU_free (Qbtf, n, sizeof (Int), Common) ;
+ KLU_free_symbolic (&Symbolic, Common) ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the common parameters for BTF and ordering method */
+ /* ---------------------------------------------------------------------- */
+
+ do_btf = Common->btf ;
+ do_btf = (do_btf) ? TRUE : FALSE ;
+ Symbolic->ordering = ordering ;
+ Symbolic->do_btf = do_btf ;
+ Symbolic->structural_rank = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the block triangular form (if requested) */
+ /* ---------------------------------------------------------------------- */
+
+ Common->work = 0 ;
+
+ if (do_btf)
+ {
+ Work = KLU_malloc (5*n, sizeof (Int), Common) ;
+ if (Common->status < KLU_OK)
+ {
+ /* out of memory */
+ KLU_free (Pbtf, n, sizeof (Int), Common) ;
+ KLU_free (Qbtf, n, sizeof (Int), Common) ;
+ KLU_free_symbolic (&Symbolic, Common) ;
+ return (NULL) ;
+ }
+
+ nblocks = BTF_order (n, Ap, Ai, Common->maxwork, &work, Pbtf, Qbtf, R,
+ &(Symbolic->structural_rank), Work) ;
+ Common->structural_rank = Symbolic->structural_rank ;
+ Common->work += work ;
+
+ KLU_free (Work, 5*n, sizeof (Int), Common) ;
+
+ /* unflip Qbtf if the matrix does not have full structural rank */
+ if (Symbolic->structural_rank < n)
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ Qbtf [k] = BTF_UNFLIP (Qbtf [k]) ;
+ }
+ }
+
+ /* find the size of the largest block */
+ maxblock = 1 ;
+ for (block = 0 ; block < nblocks ; block++)
+ {
+ k1 = R [block] ;
+ k2 = R [block+1] ;
+ nk = k2 - k1 ;
+ PRINTF (("block %d size %d\n", block, nk)) ;
+ maxblock = MAX (maxblock, nk) ;
+ }
+ }
+ else
+ {
+ /* BTF not requested */
+ nblocks = 1 ;
+ maxblock = n ;
+ R [0] = 0 ;
+ R [1] = n ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Pbtf [k] = k ;
+ Qbtf [k] = k ;
+ }
+ }
+
+ Symbolic->nblocks = nblocks ;
+
+ PRINTF (("maxblock size %d\n", maxblock)) ;
+ Symbolic->maxblock = maxblock ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate more workspace, for analyze_worker */
+ /* ---------------------------------------------------------------------- */
+
+ Pblk = KLU_malloc (maxblock, sizeof (Int), Common) ;
+ Cp = KLU_malloc (maxblock + 1, sizeof (Int), Common) ;
+ Ci = KLU_malloc (MAX (Cilen, nz+1), sizeof (Int), Common) ;
+ Pinv = KLU_malloc (n, sizeof (Int), Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order each block of the BTF ordering, and a fill-reducing ordering */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->status == KLU_OK)
+ {
+ PRINTF (("calling analyze_worker\n")) ;
+ Common->status = analyze_worker (n, Ap, Ai, nblocks, Pbtf, Qbtf, R,
+ ordering, P, Q, Lnz, Pblk, Cp, Ci, Cilen, Pinv, Symbolic, Common) ;
+ PRINTF (("analyze_worker done\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free all workspace */
+ /* ---------------------------------------------------------------------- */
+
+ KLU_free (Pblk, maxblock, sizeof (Int), Common) ;
+ KLU_free (Cp, maxblock+1, sizeof (Int), Common) ;
+ KLU_free (Ci, MAX (Cilen, nz+1), sizeof (Int), Common) ;
+ KLU_free (Pinv, n, sizeof (Int), Common) ;
+ KLU_free (Pbtf, n, sizeof (Int), Common) ;
+ KLU_free (Qbtf, n, sizeof (Int), Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return the symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->status < KLU_OK)
+ {
+ KLU_free_symbolic (&Symbolic, Common) ;
+ }
+ return (Symbolic) ;
+}
+
+
+/* ========================================================================== */
+/* === KLU_analyze ========================================================== */
+/* ========================================================================== */
+
+KLU_symbolic *KLU_analyze /* returns NULL if error, or a valid
+ KLU_symbolic object if successful */
+(
+ /* inputs, not modified */
+ Int n, /* A is n-by-n */
+ Int Ap [ ], /* size n+1, column pointers */
+ Int Ai [ ], /* size nz, row indices */
+ /* -------------------- */
+ KLU_common *Common
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* get the control parameters for BTF and ordering method */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common == NULL)
+ {
+ return (NULL) ;
+ }
+ Common->status = KLU_OK ;
+ Common->structural_rank = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* order and analyze */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->ordering == 2)
+ {
+ /* natural ordering */
+ return (KLU_analyze_given (n, Ap, Ai, NULL, NULL, Common)) ;
+ }
+ else
+ {
+ /* order with P and Q */
+ return (order_and_analyze (n, Ap, Ai, Common)) ;
+ }
+}
diff --git a/KLU/Source/klu_analyze_given.c b/KLU/Source/klu_analyze_given.c
new file mode 100644
index 0000000..002b1cb
--- /dev/null
+++ b/KLU/Source/klu_analyze_given.c
@@ -0,0 +1,369 @@
+/* ========================================================================== */
+/* === klu_analyze_given ==================================================== */
+/* ========================================================================== */
+
+/* Given an input permutation P and Q, create the Symbolic object. BTF can
+ * be done to modify the user's P and Q (does not perform the max transversal;
+ * just finds the strongly-connected components). */
+
+#include "klu_internal.h"
+
+/* ========================================================================== */
+/* === klu_alloc_symbolic =================================================== */
+/* ========================================================================== */
+
+/* Allocate Symbolic object, and check input matrix. Not user callable. */
+
+KLU_symbolic *KLU_alloc_symbolic
+(
+ Int n,
+ Int *Ap,
+ Int *Ai,
+ KLU_common *Common
+)
+{
+ KLU_symbolic *Symbolic ;
+ Int *P, *Q, *R ;
+ double *Lnz ;
+ Int nz, i, j, p, pend ;
+
+ if (Common == NULL)
+ {
+ return (NULL) ;
+ }
+ Common->status = KLU_OK ;
+
+ /* A is n-by-n, with n > 0. Ap [0] = 0 and nz = Ap [n] >= 0 required.
+ * Ap [j] <= Ap [j+1] must hold for all j = 0 to n-1. Row indices in Ai
+ * must be in the range 0 to n-1, and no duplicate entries can be present.
+ * The list of row indices in each column of A need not be sorted.
+ */
+
+ if (n <= 0 || Ap == NULL || Ai == NULL)
+ {
+ /* Ap and Ai must be present, and n must be > 0 */
+ Common->status = KLU_INVALID ;
+ return (NULL) ;
+ }
+
+ nz = Ap [n] ;
+ if (Ap [0] != 0 || nz < 0)
+ {
+ /* nz must be >= 0 and Ap [0] must equal zero */
+ Common->status = KLU_INVALID ;
+ return (NULL) ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Ap [j] > Ap [j+1])
+ {
+ /* column pointers must be non-decreasing */
+ Common->status = KLU_INVALID ;
+ return (NULL) ;
+ }
+ }
+ P = KLU_malloc (n, sizeof (Int), Common) ;
+ if (Common->status < KLU_OK)
+ {
+ /* out of memory */
+ Common->status = KLU_OUT_OF_MEMORY ;
+ return (NULL) ;
+ }
+ for (i = 0 ; i < n ; i++)
+ {
+ P [i] = EMPTY ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ pend = Ap [j+1] ;
+ for (p = Ap [j] ; p < pend ; p++)
+ {
+ i = Ai [p] ;
+ if (i < 0 || i >= n || P [i] == j)
+ {
+ /* row index out of range, or duplicate entry */
+ KLU_free (P, n, sizeof (Int), Common) ;
+ Common->status = KLU_INVALID ;
+ return (NULL) ;
+ }
+ /* flag row i as appearing in column j */
+ P [i] = j ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic = KLU_malloc (sizeof (KLU_symbolic), 1, Common) ;
+ if (Common->status < KLU_OK)
+ {
+ /* out of memory */
+ KLU_free (P, n, sizeof (Int), Common) ;
+ Common->status = KLU_OUT_OF_MEMORY ;
+ return (NULL) ;
+ }
+
+ Q = KLU_malloc (n, sizeof (Int), Common) ;
+ R = KLU_malloc (n+1, sizeof (Int), Common) ;
+ Lnz = KLU_malloc (n, sizeof (double), Common) ;
+
+ Symbolic->n = n ;
+ Symbolic->nz = nz ;
+ Symbolic->P = P ;
+ Symbolic->Q = Q ;
+ Symbolic->R = R ;
+ Symbolic->Lnz = Lnz ;
+
+ if (Common->status < KLU_OK)
+ {
+ /* out of memory */
+ KLU_free_symbolic (&Symbolic, Common) ;
+ Common->status = KLU_OUT_OF_MEMORY ;
+ return (NULL) ;
+ }
+
+ return (Symbolic) ;
+}
+
+
+/* ========================================================================== */
+/* === KLU_analyze_given ==================================================== */
+/* ========================================================================== */
+
+KLU_symbolic *KLU_analyze_given /* returns NULL if error, or a valid
+ KLU_symbolic object if successful */
+(
+ /* inputs, not modified */
+ Int n, /* A is n-by-n */
+ Int Ap [ ], /* size n+1, column pointers */
+ Int Ai [ ], /* size nz, row indices */
+ Int Puser [ ], /* size n, user's row permutation (may be NULL) */
+ Int Quser [ ], /* size n, user's column permutation (may be NULL) */
+ /* -------------------- */
+ KLU_common *Common
+)
+{
+ KLU_symbolic *Symbolic ;
+ double *Lnz ;
+ Int nblocks, nz, block, maxblock, *P, *Q, *R, nzoff, p, pend, do_btf, k ;
+
+ /* ---------------------------------------------------------------------- */
+ /* determine if input matrix is valid, and get # of nonzeros */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic = KLU_alloc_symbolic (n, Ap, Ai, Common) ;
+ if (Symbolic == NULL)
+ {
+ return (NULL) ;
+ }
+ P = Symbolic->P ;
+ Q = Symbolic->Q ;
+ R = Symbolic->R ;
+ Lnz = Symbolic->Lnz ;
+ nz = Symbolic->nz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Q = Quser, or identity if Quser is NULL */
+ /* ---------------------------------------------------------------------- */
+
+ if (Quser == (Int *) NULL)
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ Q [k] = k ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ Q [k] = Quser [k] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the control parameters for BTF and ordering method */
+ /* ---------------------------------------------------------------------- */
+
+ do_btf = Common->btf ;
+ do_btf = (do_btf) ? TRUE : FALSE ;
+ Symbolic->ordering = 2 ;
+ Symbolic->do_btf = do_btf ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the block triangular form, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_btf)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get workspace for BTF_strongcomp */
+ /* ------------------------------------------------------------------ */
+
+ Int *Pinv, *Work, *Bi, k1, k2, nk, oldcol ;
+
+ Work = KLU_malloc (4*n, sizeof (Int), Common) ;
+ Pinv = KLU_malloc (n, sizeof (Int), Common) ;
+ if (Puser != (Int *) NULL)
+ {
+ Bi = KLU_malloc (nz+1, sizeof (Int), Common) ;
+ }
+ else
+ {
+ Bi = Ai ;
+ }
+
+ if (Common->status < KLU_OK)
+ {
+ /* out of memory */
+ KLU_free (Work, 4*n, sizeof (Int), Common) ;
+ KLU_free (Pinv, n, sizeof (Int), Common) ;
+ if (Puser != (Int *) NULL)
+ {
+ KLU_free (Bi, nz+1, sizeof (Int), Common) ;
+ }
+ KLU_free_symbolic (&Symbolic, Common) ;
+ Common->status = KLU_OUT_OF_MEMORY ;
+ return (NULL) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* B = Puser * A */
+ /* ------------------------------------------------------------------ */
+
+ if (Puser != (Int *) NULL)
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ Pinv [Puser [k]] = k ;
+ }
+ for (p = 0 ; p < nz ; p++)
+ {
+ Bi [p] = Pinv [Ai [p]] ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* find the strongly-connected components */
+ /* ------------------------------------------------------------------ */
+
+ /* modifies Q, and determines P and R */
+ nblocks = BTF_strongcomp (n, Ap, Bi, Q, P, R, Work) ;
+
+ /* ------------------------------------------------------------------ */
+ /* P = P * Puser */
+ /* ------------------------------------------------------------------ */
+
+ if (Puser != (Int *) NULL)
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ Work [k] = Puser [P [k]] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = Work [k] ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* Pinv = inverse of P */
+ /* ------------------------------------------------------------------ */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Pinv [P [k]] = k ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* analyze each block */
+ /* ------------------------------------------------------------------ */
+
+ nzoff = 0 ; /* nz in off-diagonal part */
+ maxblock = 1 ; /* size of the largest block */
+
+ for (block = 0 ; block < nblocks ; block++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* the block is from rows/columns k1 to k2-1 */
+ /* -------------------------------------------------------------- */
+
+ k1 = R [block] ;
+ k2 = R [block+1] ;
+ nk = k2 - k1 ;
+ PRINTF (("BLOCK %d, k1 %d k2-1 %d nk %d\n", block, k1, k2-1, nk)) ;
+ maxblock = MAX (maxblock, nk) ;
+
+ /* -------------------------------------------------------------- */
+ /* scan the kth block, C */
+ /* -------------------------------------------------------------- */
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ oldcol = Q [k] ;
+ pend = Ap [oldcol+1] ;
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ if (Pinv [Ai [p]] < k1)
+ {
+ nzoff++ ;
+ }
+ }
+ }
+
+ /* fill-in not estimated */
+ Lnz [block] = EMPTY ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* free all workspace */
+ /* ------------------------------------------------------------------ */
+
+ KLU_free (Work, 4*n, sizeof (Int), Common) ;
+ KLU_free (Pinv, n, sizeof (Int), Common) ;
+ if (Puser != (Int *) NULL)
+ {
+ KLU_free (Bi, nz+1, sizeof (Int), Common) ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* BTF not requested */
+ /* ------------------------------------------------------------------ */
+
+ nzoff = 0 ;
+ nblocks = 1 ;
+ maxblock = n ;
+ R [0] = 0 ;
+ R [1] = n ;
+ Lnz [0] = EMPTY ;
+
+ /* ------------------------------------------------------------------ */
+ /* P = Puser, or identity if Puser is NULL */
+ /* ------------------------------------------------------------------ */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = (Puser == NULL) ? k : Puser [k] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic->nblocks = nblocks ;
+ Symbolic->maxblock = maxblock ;
+ Symbolic->lnz = EMPTY ;
+ Symbolic->unz = EMPTY ;
+ Symbolic->nzoff = nzoff ;
+
+ return (Symbolic) ;
+}
diff --git a/KLU/Source/klu_defaults.c b/KLU/Source/klu_defaults.c
new file mode 100644
index 0000000..8f4ce6d
--- /dev/null
+++ b/KLU/Source/klu_defaults.c
@@ -0,0 +1,60 @@
+/* ========================================================================== */
+/* === KLU_defaults ========================================================= */
+/* ========================================================================== */
+
+/* Sets default parameters for KLU */
+
+#include "klu_internal.h"
+
+Int KLU_defaults
+(
+ KLU_common *Common
+)
+{
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+
+ /* parameters */
+ Common->tol = 0.001 ; /* pivot tolerance for diagonal */
+ Common->memgrow = 1.2; /* realloc size ratio increase for LU factors */
+ Common->initmem_amd = 1.2 ; /* init. mem with AMD: c*nnz(L) + n */
+ Common->initmem = 10 ; /* init. mem otherwise: c*nnz(A) + n */
+ Common->btf = TRUE ; /* use BTF pre-ordering, or not */
+ Common->maxwork = 0 ; /* no limit to work done by btf_order */
+ Common->ordering = 0 ; /* 0: AMD, 1: COLAMD, 2: user-provided P and Q,
+ * 3: user-provided function */
+ Common->scale = 2 ; /* scale: -1: none, and do not check for errors
+ * in the input matrix in KLU_refactor.
+ * 0: none, but check for errors,
+ * 1: sum, 2: max */
+ Common->halt_if_singular = TRUE ; /* quick halt if matrix is singular */
+
+ /* memory management routines */
+ Common->malloc_memory = malloc ;
+ Common->calloc_memory = calloc ;
+ Common->free_memory = free ;
+ Common->realloc_memory = realloc ;
+
+ /* user ordering function and optional argument */
+ Common->user_order = NULL ;
+ Common->user_data = NULL ;
+
+ /* statistics */
+ Common->status = KLU_OK ;
+ Common->nrealloc = 0 ;
+ Common->structural_rank = EMPTY ;
+ Common->numerical_rank = EMPTY ;
+ Common->noffdiag = EMPTY ;
+ Common->flops = EMPTY ;
+ Common->rcond = EMPTY ;
+ Common->condest = EMPTY ;
+ Common->rgrowth = EMPTY ;
+ Common->work = 0 ; /* work done by btf_order */
+
+ Common->memusage = 0 ;
+ Common->mempeak = 0 ;
+
+ return (TRUE) ;
+}
diff --git a/KLU/Source/klu_diagnostics.c b/KLU/Source/klu_diagnostics.c
new file mode 100644
index 0000000..a65442f
--- /dev/null
+++ b/KLU/Source/klu_diagnostics.c
@@ -0,0 +1,570 @@
+/* ========================================================================== */
+/* === KLU_diagnostics ====================================================== */
+/* ========================================================================== */
+
+/* Linear algebraic diagnostics:
+ * KLU_rgrowth: reciprocal pivot growth, takes O(|A|+|U|) time
+ * KLU_condest: condition number estimator, takes about O(|A|+5*(|L|+|U|)) time
+ * KLU_flops: compute # flops required to factorize A into L*U
+ * KLU_rcond: compute a really cheap estimate of the reciprocal of the
+ * condition number, min(abs(diag(U))) / max(abs(diag(U))).
+ * Takes O(n) time.
+ */
+
+#include "klu_internal.h"
+
+/* ========================================================================== */
+/* === KLU_rgrowth ========================================================== */
+/* ========================================================================== */
+
+/* Compute the reciprocal pivot growth factor. In MATLAB notation:
+ *
+ * rgrowth = min (max (abs ((R \ A (p,q)) - F))) ./ max (abs (U)))
+ */
+
+Int KLU_rgrowth /* return TRUE if successful, FALSE otherwise */
+(
+ Int *Ap,
+ Int *Ai,
+ double *Ax,
+ KLU_symbolic *Symbolic,
+ KLU_numeric *Numeric,
+ KLU_common *Common
+)
+{
+ double temp, max_ai, max_ui, min_block_rgrowth ;
+ Entry aik ;
+ Int *Q, *Ui, *Uip, *Ulen, *Pinv ;
+ Unit *LU ;
+ Entry *Aentry, *Ux, *Ukk ;
+ double *Rs ;
+ Int i, newrow, oldrow, k1, k2, nk, j, oldcol, k, pend, len ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+
+ if (Symbolic == NULL || Ap == NULL || Ai == NULL || Ax == NULL)
+ {
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+
+ if (Numeric == NULL)
+ {
+ /* treat this as a singular matrix */
+ Common->rgrowth = 0 ;
+ Common->status = KLU_SINGULAR ;
+ return (TRUE) ;
+ }
+ Common->status = KLU_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the reciprocal pivot growth */
+ /* ---------------------------------------------------------------------- */
+
+ Aentry = (Entry *) Ax ;
+ Pinv = Numeric->Pinv ;
+ Rs = Numeric->Rs ;
+ Q = Symbolic->Q ;
+ Common->rgrowth = 1 ;
+
+ for (i = 0 ; i < Symbolic->nblocks ; i++)
+ {
+ k1 = Symbolic->R[i] ;
+ k2 = Symbolic->R[i+1] ;
+ nk = k2 - k1 ;
+ if (nk == 1)
+ {
+ continue ; /* skip singleton blocks */
+ }
+ LU = (Unit *) Numeric->LUbx[i] ;
+ Uip = Numeric->Uip + k1 ;
+ Ulen = Numeric->Ulen + k1 ;
+ Ukk = ((Entry *) Numeric->Udiag) + k1 ;
+ min_block_rgrowth = 1 ;
+ for (j = 0 ; j < nk ; j++)
+ {
+ max_ai = 0 ;
+ max_ui = 0 ;
+ oldcol = Q[j + k1] ;
+ pend = Ap [oldcol + 1] ;
+ for (k = Ap [oldcol] ; k < pend ; k++)
+ {
+ oldrow = Ai [k] ;
+ newrow = Pinv [oldrow] ;
+ if (newrow < k1)
+ {
+ continue ; /* skip entry outside the block */
+ }
+ ASSERT (newrow < k2) ;
+ if (Rs != NULL)
+ {
+ /* aik = Aentry [k] / Rs [oldrow] */
+ SCALE_DIV_ASSIGN (aik, Aentry [k], Rs [newrow]) ;
+ }
+ else
+ {
+ aik = Aentry [k] ;
+ }
+ /* temp = ABS (aik) */
+ ABS (temp, aik) ;
+ if (temp > max_ai)
+ {
+ max_ai = temp ;
+ }
+ }
+
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, j, len) ;
+ for (k = 0 ; k < len ; k++)
+ {
+ /* temp = ABS (Ux [k]) */
+ ABS (temp, Ux [k]) ;
+ if (temp > max_ui)
+ {
+ max_ui = temp ;
+ }
+ }
+ /* consider the diagonal element */
+ ABS (temp, Ukk [j]) ;
+ if (temp > max_ui)
+ {
+ max_ui = temp ;
+ }
+
+ /* if max_ui is 0, skip the column */
+ if (SCALAR_IS_ZERO (max_ui))
+ {
+ continue ;
+ }
+ temp = max_ai / max_ui ;
+ if (temp < min_block_rgrowth)
+ {
+ min_block_rgrowth = temp ;
+ }
+ }
+
+ if (min_block_rgrowth < Common->rgrowth)
+ {
+ Common->rgrowth = min_block_rgrowth ;
+ }
+ }
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === KLU_condest ========================================================== */
+/* ========================================================================== */
+
+/* Estimate the condition number. Uses Higham and Tisseur's algorithm
+ * (A block algorithm for matrix 1-norm estimation, with applications to
+ * 1-norm pseudospectra, SIAM J. Matrix Anal. Appl., 21(4):1185-1201, 2000.
+ */
+
+Int KLU_condest /* return TRUE if successful, FALSE otherwise */
+(
+ Int Ap [ ],
+ double Ax [ ],
+ KLU_symbolic *Symbolic,
+ KLU_numeric *Numeric,
+ KLU_common *Common
+)
+{
+ double xj, Xmax, csum, anorm, ainv_norm, est_old, est_new, abs_value ;
+ Entry *Udiag, *Aentry, *X, *S ;
+ Int *R ;
+ Int nblocks, i, j, jmax, jnew, pend, n ;
+#ifndef COMPLEX
+ Int unchanged ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+ if (Symbolic == NULL || Ap == NULL || Ax == NULL)
+ {
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+ abs_value = 0 ;
+ if (Numeric == NULL)
+ {
+ /* treat this as a singular matrix */
+ Common->condest = 1 / abs_value ;
+ Common->status = KLU_SINGULAR ;
+ return (TRUE) ;
+ }
+ Common->status = KLU_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs */
+ /* ---------------------------------------------------------------------- */
+
+ n = Symbolic->n ;
+ nblocks = Symbolic->nblocks ;
+ R = Symbolic->R ;
+ Udiag = Numeric->Udiag ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check if diagonal of U has a zero on it */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ ABS (abs_value, Udiag [i]) ;
+ if (SCALAR_IS_ZERO (abs_value))
+ {
+ Common->condest = 1 / abs_value ;
+ Common->status = KLU_SINGULAR ;
+ return (TRUE) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute 1-norm (maximum column sum) of the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ anorm = 0.0 ;
+ Aentry = (Entry *) Ax ;
+ for (i = 0 ; i < n ; i++)
+ {
+ pend = Ap [i + 1] ;
+ csum = 0.0 ;
+ for (j = Ap [i] ; j < pend ; j++)
+ {
+ ABS (abs_value, Aentry [j]) ;
+ csum += abs_value ;
+ }
+ if (csum > anorm)
+ {
+ anorm = csum ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute estimate of 1-norm of inv (A) */
+ /* ---------------------------------------------------------------------- */
+
+ /* get workspace (size 2*n Entry's) */
+ X = Numeric->Xwork ; /* size n space used in KLU_solve, tsolve */
+ X += n ; /* X is size n */
+ S = X + n ; /* S is size n */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ CLEAR (S [i]) ;
+ CLEAR (X [i]) ;
+ REAL (X [i]) = 1.0 / ((double) n) ;
+ }
+ jmax = 0 ;
+
+ ainv_norm = 0.0 ;
+ for (i = 0 ; i < 5 ; i++)
+ {
+ if (i > 0)
+ {
+ /* X [jmax] is the largest entry in X */
+ for (j = 0 ; j < n ; j++)
+ {
+ /* X [j] = 0 ;*/
+ CLEAR (X [j]) ;
+ }
+ REAL (X [jmax]) = 1 ;
+ }
+
+ KLU_solve (Symbolic, Numeric, n, 1, (double *) X, Common) ;
+ est_old = ainv_norm ;
+ ainv_norm = 0.0 ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ /* ainv_norm += ABS (X [j]) ;*/
+ ABS (abs_value, X [j]) ;
+ ainv_norm += abs_value ;
+ }
+
+#ifndef COMPLEX
+ unchanged = TRUE ;
+
+ for (j = 0 ; j < n ; j++)
+ {
+ double s = (X [j] >= 0) ? 1 : -1 ;
+ if (s != (Int) REAL (S [j]))
+ {
+ S [j] = s ;
+ unchanged = FALSE ;
+ }
+ }
+
+ if (i > 0 && (ainv_norm <= est_old || unchanged))
+ {
+ break ;
+ }
+#else
+ for (j = 0 ; j < n ; j++)
+ {
+ if (IS_NONZERO (X [j]))
+ {
+ ABS (abs_value, X [j]) ;
+ SCALE_DIV_ASSIGN (S [j], X [j], abs_value) ;
+ }
+ else
+ {
+ CLEAR (S [j]) ;
+ REAL (S [j]) = 1 ;
+ }
+ }
+
+ if (i > 0 && ainv_norm <= est_old)
+ {
+ break ;
+ }
+#endif
+
+ for (j = 0 ; j < n ; j++)
+ {
+ X [j] = S [j] ;
+ }
+
+#ifndef COMPLEX
+ /* do a transpose solve */
+ KLU_tsolve (Symbolic, Numeric, n, 1, X, Common) ;
+#else
+ /* do a conjugate transpose solve */
+ KLU_tsolve (Symbolic, Numeric, n, 1, (double *) X, 1, Common) ;
+#endif
+
+ /* jnew = the position of the largest entry in X */
+ jnew = 0 ;
+ Xmax = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ /* xj = ABS (X [j]) ;*/
+ ABS (xj, X [j]) ;
+ if (xj > Xmax)
+ {
+ Xmax = xj ;
+ jnew = j ;
+ }
+ }
+ if (i > 0 && jnew == jmax)
+ {
+ /* the position of the largest entry did not change
+ * from the previous iteration */
+ break ;
+ }
+ jmax = jnew ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute another estimate of norm(inv(A),1), and take the largest one */
+ /* ---------------------------------------------------------------------- */
+
+ for (j = 0 ; j < n ; j++)
+ {
+ CLEAR (X [j]) ;
+ if (j % 2)
+ {
+ REAL (X [j]) = 1 + ((double) j) / ((double) (n-1)) ;
+ }
+ else
+ {
+ REAL (X [j]) = -1 - ((double) j) / ((double) (n-1)) ;
+ }
+ }
+
+ KLU_solve (Symbolic, Numeric, n, 1, (double *) X, Common) ;
+
+ est_new = 0.0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ /* est_new += ABS (X [j]) ;*/
+ ABS (abs_value, X [j]) ;
+ est_new += abs_value ;
+ }
+ est_new = 2 * est_new / (3 * n) ;
+ ainv_norm = MAX (est_new, ainv_norm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute estimate of condition number */
+ /* ---------------------------------------------------------------------- */
+
+ Common->condest = ainv_norm * anorm ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === KLU_flops ============================================================ */
+/* ========================================================================== */
+
+/* Compute the flop count for the LU factorization (in Common->flops) */
+
+Int KLU_flops /* return TRUE if successful, FALSE otherwise */
+(
+ KLU_symbolic *Symbolic,
+ KLU_numeric *Numeric,
+ KLU_common *Common
+)
+{
+ double flops = 0 ;
+ Int *R, *Ui, *Uip, *Llen, *Ulen ;
+ Unit **LUbx ;
+ Unit *LU ;
+ Int k, ulen, p, n, nk, block, nblocks, k1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+ Common->flops = EMPTY ;
+ if (Numeric == NULL || Symbolic == NULL)
+ {
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+ Common->status = KLU_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the contents of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ n = Symbolic->n ;
+ R = Symbolic->R ;
+ nblocks = Symbolic->nblocks ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the contents of the Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ LUbx = (Unit **) Numeric->LUbx ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the flop count */
+ /* ---------------------------------------------------------------------- */
+
+ for (block = 0 ; block < nblocks ; block++)
+ {
+ k1 = R [block] ;
+ nk = R [block+1] - k1 ;
+ if (nk > 1)
+ {
+ Llen = Numeric->Llen + k1 ;
+ Uip = Numeric->Uip + k1 ;
+ Ulen = Numeric->Ulen + k1 ;
+ LU = LUbx [block] ;
+ for (k = 0 ; k < nk ; k++)
+ {
+ /* compute kth column of U, and update kth column of A */
+ GET_I_POINTER (LU, Uip, Ui, k) ;
+ ulen = Ulen [k] ;
+ for (p = 0 ; p < ulen ; p++)
+ {
+ flops += 2 * Llen [Ui [p]] ;
+ }
+ /* gather and divide by pivot to get kth column of L */
+ flops += Llen [k] ;
+ }
+ }
+ }
+ Common->flops = flops ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === KLU_rcond ============================================================ */
+/* ========================================================================== */
+
+/* Compute a really cheap estimate of the reciprocal of the condition number,
+ * condition number, min(abs(diag(U))) / max(abs(diag(U))). If U has a zero
+ * pivot, or a NaN pivot, rcond will be zero. Takes O(n) time.
+ */
+
+Int KLU_rcond /* return TRUE if successful, FALSE otherwise */
+(
+ KLU_symbolic *Symbolic, /* input, not modified */
+ KLU_numeric *Numeric, /* input, not modified */
+ KLU_common *Common /* result in Common->rcond */
+)
+{
+ double ukk, umin = 0, umax = 0 ;
+ Entry *Udiag ;
+ Int j, n ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+ if (Symbolic == NULL)
+ {
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+ if (Numeric == NULL)
+ {
+ Common->rcond = 0 ;
+ Common->status = KLU_SINGULAR ;
+ return (TRUE) ;
+ }
+ Common->status = KLU_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute rcond */
+ /* ---------------------------------------------------------------------- */
+
+ n = Symbolic->n ;
+ Udiag = Numeric->Udiag ;
+ for (j = 0 ; j < n ; j++)
+ {
+ /* get the magnitude of the pivot */
+ ABS (ukk, Udiag [j]) ;
+ if (SCALAR_IS_NAN (ukk) || SCALAR_IS_ZERO (ukk))
+ {
+ /* if NaN, or zero, the rcond is zero */
+ Common->rcond = 0 ;
+ Common->status = KLU_SINGULAR ;
+ return (TRUE) ;
+ }
+ if (j == 0)
+ {
+ /* first pivot entry */
+ umin = ukk ;
+ umax = ukk ;
+ }
+ else
+ {
+ /* subsequent pivots */
+ umin = MIN (umin, ukk) ;
+ umax = MAX (umax, ukk) ;
+ }
+ }
+
+ Common->rcond = umin / umax ;
+ if (SCALAR_IS_NAN (Common->rcond) || SCALAR_IS_ZERO (Common->rcond))
+ {
+ /* this can occur if umin or umax are Inf or NaN */
+ Common->rcond = 0 ;
+ Common->status = KLU_SINGULAR ;
+ }
+ return (TRUE) ;
+}
diff --git a/KLU/Source/klu_dump.c b/KLU/Source/klu_dump.c
new file mode 100644
index 0000000..b625fda
--- /dev/null
+++ b/KLU/Source/klu_dump.c
@@ -0,0 +1,142 @@
+/* ========================================================================== */
+/* === KLU_dump ============================================================= */
+/* ========================================================================== */
+
+/* Debug routines for klu. Only used when NDEBUG is not defined at
+ * compile-time.
+ */
+
+#include "klu_internal.h"
+
+#ifndef NDEBUG
+
+/* ========================================================================== */
+/* === KLU_valid ============================================================ */
+/* ========================================================================== */
+
+/* Check if a column-form matrix is valid or not. The matrix A is
+ * n-by-n. The row indices of entries in column j are in
+ * Ai [Ap [j] ... Ap [j+1]-1]. Required conditions are:
+ *
+ * n >= 0
+ * nz = Ap [n_col] >= 0 number of entries in the matrix
+ * Ap [0] == 0
+ * Ap [j] <= Ap [j+1] for all j in the range 0 to n_col.
+ * row indices in Ai [Ap [j] ... Ap [j+1]-1]
+ * must be in the range 0 to n_row-1,
+ * and no duplicate entries can exist (duplicates not checked here).
+ *
+ * Not user-callable. Only used when debugging.
+ */
+
+Int KLU_valid (Int n, Int Ap [ ], Int Ai [ ], Entry Ax [ ])
+{
+ Int nz, j, p1, p2, i, p ;
+ PRINTF (("\ncolumn oriented matrix, n = %d\n", n)) ;
+ if (n <= 0)
+ {
+ PRINTF (("n must be >= 0: %d\n", n)) ;
+ return (FALSE) ;
+ }
+ nz = Ap [n] ;
+ if (Ap [0] != 0 || nz < 0)
+ {
+ /* column pointers must start at Ap [0] = 0, and Ap [n] must be >= 0 */
+ PRINTF (("column 0 pointer bad or nz < 0\n")) ;
+ return (FALSE) ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ p1 = Ap [j] ;
+ p2 = Ap [j+1] ;
+ PRINTF (("\nColumn: %d p1: %d p2: %d\n", j, p1, p2)) ;
+ if (p1 > p2)
+ {
+ /* column pointers must be ascending */
+ PRINTF (("column %d pointer bad\n", j)) ;
+ return (FALSE) ;
+ }
+ for (p = p1 ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ PRINTF (("row: %d", i)) ;
+ if (i < 0 || i >= n)
+ {
+ /* row index out of range */
+ PRINTF (("index out of range, col %d row %d\n", j, i)) ;
+ return (FALSE) ;
+ }
+ if (Ax != (Entry *) NULL)
+ {
+ PRINT_ENTRY (Ax [p]) ;
+ }
+ PRINTF (("\n")) ;
+ }
+ }
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === KLU_valid_LU ========================================================= */
+/* ========================================================================== */
+
+/* This function does the same validity tests as KLU_valid but for the
+ * LU factor storage format. The flag flag_test_start_ptr is used to
+ * test if Xip [0] = 0. This is not applicable for U. So when calling this
+ * function for U, the flag should be set to false. Only used when debugging.
+ */
+
+Int KLU_valid_LU (Int n, Int flag_test_start_ptr, Int Xip [ ],
+ Int Xlen [ ], Unit LU [ ])
+{
+ Int *Xi ;
+ Entry *Xx ;
+ Int j, p1, p2, i, p, len ;
+
+ PRINTF (("\ncolumn oriented matrix, n = %d\n", n)) ;
+ if (n <= 0)
+ {
+ PRINTF (("n must be >= 0: %d\n", n)) ;
+ return (FALSE) ;
+ }
+ if (flag_test_start_ptr && Xip [0] != 0)
+ {
+ /* column pointers must start at Xip [0] = 0*/
+ PRINTF (("column 0 pointer bad\n")) ;
+ return (FALSE) ;
+ }
+
+ for (j = 0 ; j < n ; j++)
+ {
+ p1 = Xip [j] ;
+ p2 = Xip [j+1] ;
+ PRINTF (("\nColumn: %d p1: %d p2: %d\n", j, p1, p2)) ;
+ if (p1 > p2)
+ {
+ /* column pointers must be ascending */
+ PRINTF (("column %d pointer bad\n", j)) ;
+ return (FALSE) ;
+ }
+ GET_POINTER (LU, Xip, Xlen, Xi, Xx, j, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Xi [p] ;
+ PRINTF (("row: %d", i)) ;
+ if (i < 0 || i >= n)
+ {
+ /* row index out of range */
+ PRINTF (("index out of range, col %d row %d\n", j, i)) ;
+ return (FALSE) ;
+ }
+ if (Xx != (Entry *) NULL)
+ {
+ PRINT_ENTRY (Xx [p]) ;
+ }
+ PRINTF (("\n")) ;
+ }
+ }
+
+ return (TRUE) ;
+}
+#endif
diff --git a/KLU/Source/klu_extract.c b/KLU/Source/klu_extract.c
new file mode 100644
index 0000000..5a44aa0
--- /dev/null
+++ b/KLU/Source/klu_extract.c
@@ -0,0 +1,290 @@
+/* ========================================================================== */
+/* === KLU_extract ========================================================== */
+/* ========================================================================== */
+
+/* Extract KLU factorization into conventional compressed-column matrices.
+ * If any output array is NULL, that part of the LU factorization is not
+ * extracted (this is not an error condition).
+ *
+ * nnz(L) = Numeric->lnz, nnz(U) = Numeric->unz, and nnz(F) = Numeric->Offp [n]
+ */
+
+#include "klu_internal.h"
+
+Int KLU_extract /* returns TRUE if successful, FALSE otherwise */
+(
+ /* inputs: */
+ KLU_numeric *Numeric,
+ KLU_symbolic *Symbolic,
+
+ /* outputs, all of which must be allocated on input */
+
+ /* L */
+ Int *Lp, /* size n+1 */
+ Int *Li, /* size nnz(L) */
+ double *Lx, /* size nnz(L) */
+#ifdef COMPLEX
+ double *Lz, /* size nnz(L) for the complex case, ignored if real */
+#endif
+
+ /* U */
+ Int *Up, /* size n+1 */
+ Int *Ui, /* size nnz(U) */
+ double *Ux, /* size nnz(U) */
+#ifdef COMPLEX
+ double *Uz, /* size nnz(U) for the complex case, ignored if real */
+#endif
+
+ /* F */
+ Int *Fp, /* size n+1 */
+ Int *Fi, /* size nnz(F) */
+ double *Fx, /* size nnz(F) */
+#ifdef COMPLEX
+ double *Fz, /* size nnz(F) for the complex case, ignored if real */
+#endif
+
+ /* P, row permutation */
+ Int *P, /* size n */
+
+ /* Q, column permutation */
+ Int *Q, /* size n */
+
+ /* Rs, scale factors */
+ double *Rs, /* size n */
+
+ /* R, block boundaries */
+ Int *R, /* size nblocks+1 */
+
+ KLU_common *Common
+)
+{
+ Int *Lip, *Llen, *Uip, *Ulen, *Li2, *Ui2 ;
+ Unit *LU ;
+ Entry *Lx2, *Ux2, *Ukk ;
+ Int i, k, block, nblocks, n, nz, k1, k2, nk, len, kk, p ;
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+
+ if (Symbolic == NULL || Numeric == NULL)
+ {
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+
+ Common->status = KLU_OK ;
+ n = Symbolic->n ;
+ nblocks = Symbolic->nblocks ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extract scale factors */
+ /* ---------------------------------------------------------------------- */
+
+ if (Rs != NULL)
+ {
+ if (Numeric->Rs != NULL)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Rs [i] = Numeric->Rs [i] ;
+ }
+ }
+ else
+ {
+ /* no scaling */
+ for (i = 0 ; i < n ; i++)
+ {
+ Rs [i] = 1 ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* extract block boundaries */
+ /* ---------------------------------------------------------------------- */
+
+ if (R != NULL)
+ {
+ for (block = 0 ; block <= nblocks ; block++)
+ {
+ R [block] = Symbolic->R [block] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* extract final row permutation */
+ /* ---------------------------------------------------------------------- */
+
+ if (P != NULL)
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = Numeric->Pnum [k] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* extract column permutation */
+ /* ---------------------------------------------------------------------- */
+
+ if (Q != NULL)
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ Q [k] = Symbolic->Q [k] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* extract each block of L */
+ /* ---------------------------------------------------------------------- */
+
+ if (Lp != NULL && Li != NULL && Lx != NULL
+#ifdef COMPLEX
+ && Lz != NULL
+#endif
+ )
+ {
+ nz = 0 ;
+ for (block = 0 ; block < nblocks ; block++)
+ {
+ k1 = Symbolic->R [block] ;
+ k2 = Symbolic->R [block+1] ;
+ nk = k2 - k1 ;
+ if (nk == 1)
+ {
+ /* singleton block */
+ Lp [k1] = nz ;
+ Li [nz] = k1 ;
+ Lx [nz] = 1 ;
+#ifdef COMPLEX
+ Lz [nz] = 0 ;
+#endif
+ nz++ ;
+ }
+ else
+ {
+ /* non-singleton block */
+ LU = Numeric->LUbx [block] ;
+ Lip = Numeric->Lip + k1 ;
+ Llen = Numeric->Llen + k1 ;
+ for (kk = 0 ; kk < nk ; kk++)
+ {
+ Lp [k1+kk] = nz ;
+ /* add the unit diagonal entry */
+ Li [nz] = k1 + kk ;
+ Lx [nz] = 1 ;
+#ifdef COMPLEX
+ Lz [nz] = 0 ;
+#endif
+ nz++ ;
+ GET_POINTER (LU, Lip, Llen, Li2, Lx2, kk, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ Li [nz] = k1 + Li2 [p] ;
+ Lx [nz] = REAL (Lx2 [p]) ;
+#ifdef COMPLEX
+ Lz [nz] = IMAG (Lx2 [p]) ;
+#endif
+ nz++ ;
+ }
+ }
+ }
+ }
+ Lp [n] = nz ;
+ ASSERT (nz == Numeric->lnz) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* extract each block of U */
+ /* ---------------------------------------------------------------------- */
+
+ if (Up != NULL && Ui != NULL && Ux != NULL
+#ifdef COMPLEX
+ && Uz != NULL
+#endif
+ )
+ {
+ nz = 0 ;
+ for (block = 0 ; block < nblocks ; block++)
+ {
+ k1 = Symbolic->R [block] ;
+ k2 = Symbolic->R [block+1] ;
+ nk = k2 - k1 ;
+ Ukk = ((Entry *) Numeric->Udiag) + k1 ;
+ if (nk == 1)
+ {
+ /* singleton block */
+ Up [k1] = nz ;
+ Ui [nz] = k1 ;
+ Ux [nz] = REAL (Ukk [0]) ;
+#ifdef COMPLEX
+ Uz [nz] = IMAG (Ukk [0]) ;
+#endif
+ nz++ ;
+ }
+ else
+ {
+ /* non-singleton block */
+ LU = Numeric->LUbx [block] ;
+ Uip = Numeric->Uip + k1 ;
+ Ulen = Numeric->Ulen + k1 ;
+ for (kk = 0 ; kk < nk ; kk++)
+ {
+ Up [k1+kk] = nz ;
+ GET_POINTER (LU, Uip, Ulen, Ui2, Ux2, kk, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ Ui [nz] = k1 + Ui2 [p] ;
+ Ux [nz] = REAL (Ux2 [p]) ;
+#ifdef COMPLEX
+ Uz [nz] = IMAG (Ux2 [p]) ;
+#endif
+ nz++ ;
+ }
+ /* add the diagonal entry */
+ Ui [nz] = k1 + kk ;
+ Ux [nz] = REAL (Ukk [kk]) ;
+#ifdef COMPLEX
+ Uz [nz] = IMAG (Ukk [kk]) ;
+#endif
+ nz++ ;
+ }
+ }
+ }
+ Up [n] = nz ;
+ ASSERT (nz == Numeric->unz) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* extract the off-diagonal blocks, F */
+ /* ---------------------------------------------------------------------- */
+
+ if (Fp != NULL && Fi != NULL && Fx != NULL
+#ifdef COMPLEX
+ && Fz != NULL
+#endif
+ )
+ {
+ for (k = 0 ; k <= n ; k++)
+ {
+ Fp [k] = Numeric->Offp [k] ;
+ }
+ nz = Fp [n] ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ Fi [k] = Numeric->Offi [k] ;
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ Fx [k] = REAL (((Entry *) Numeric->Offx) [k]) ;
+#ifdef COMPLEX
+ Fz [k] = IMAG (((Entry *) Numeric->Offx) [k]) ;
+#endif
+ }
+ }
+
+ return (TRUE) ;
+}
diff --git a/KLU/Source/klu_factor.c b/KLU/Source/klu_factor.c
new file mode 100644
index 0000000..84af42c
--- /dev/null
+++ b/KLU/Source/klu_factor.c
@@ -0,0 +1,545 @@
+/* ========================================================================== */
+/* === KLU_factor =========================================================== */
+/* ========================================================================== */
+
+/* Factor the matrix, after ordering and analyzing it with KLU_analyze
+ * or KLU_analyze_given.
+ */
+
+#include "klu_internal.h"
+
+/* ========================================================================== */
+/* === KLU_factor2 ========================================================== */
+/* ========================================================================== */
+
+static void factor2
+(
+ /* inputs, not modified */
+ Int Ap [ ], /* size n+1, column pointers */
+ Int Ai [ ], /* size nz, row indices */
+ Entry Ax [ ],
+ KLU_symbolic *Symbolic,
+
+ /* inputs, modified on output: */
+ KLU_numeric *Numeric,
+ KLU_common *Common
+)
+{
+ double lsize ;
+ double *Lnz, *Rs ;
+ Int *P, *Q, *R, *Pnum, *Offp, *Offi, *Pblock, *Pinv, *Iwork,
+ *Lip, *Uip, *Llen, *Ulen ;
+ Entry *Offx, *X, s, *Udiag ;
+ Unit **LUbx ;
+ Int k1, k2, nk, k, block, oldcol, pend, oldrow, n, lnz, unz, p, newrow,
+ nblocks, poff, nzoff, lnz_block, unz_block, scale, max_lnz_block,
+ max_unz_block ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+ /* get the contents of the Symbolic object */
+ n = Symbolic->n ;
+ P = Symbolic->P ;
+ Q = Symbolic->Q ;
+ R = Symbolic->R ;
+ Lnz = Symbolic->Lnz ;
+ nblocks = Symbolic->nblocks ;
+ nzoff = Symbolic->nzoff ;
+
+ Pnum = Numeric->Pnum ;
+ Offp = Numeric->Offp ;
+ Offi = Numeric->Offi ;
+ Offx = (Entry *) Numeric->Offx ;
+
+ Lip = Numeric->Lip ;
+ Uip = Numeric->Uip ;
+ Llen = Numeric->Llen ;
+ Ulen = Numeric->Ulen ;
+ LUbx = (Unit **) Numeric->LUbx ;
+ Udiag = Numeric->Udiag ;
+
+ Rs = Numeric->Rs ;
+ Pinv = Numeric->Pinv ;
+ X = (Entry *) Numeric->Xwork ; /* X is of size n */
+ Iwork = Numeric->Iwork ; /* 5*maxblock for KLU_factor */
+ /* 1*maxblock for Pblock */
+ Pblock = Iwork + 5*((size_t) Symbolic->maxblock) ;
+ Common->nrealloc = 0 ;
+ scale = Common->scale ;
+ max_lnz_block = 1 ;
+ max_unz_block = 1 ;
+
+ /* compute the inverse of P from symbolic analysis. Will be updated to
+ * become the inverse of the numerical factorization when the factorization
+ * is done, for use in KLU_refactor */
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++)
+ {
+ Pinv [k] = EMPTY ;
+ }
+#endif
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSERT (P [k] >= 0 && P [k] < n) ;
+ Pinv [P [k]] = k ;
+ }
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++) ASSERT (Pinv [k] != EMPTY) ;
+#endif
+
+ lnz = 0 ;
+ unz = 0 ;
+ Common->noffdiag = 0 ;
+ Offp [0] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* optionally check input matrix and compute scale factors */
+ /* ---------------------------------------------------------------------- */
+
+ if (scale >= 0)
+ {
+ /* use Pnum as workspace. NOTE: scale factors are not yet permuted
+ * according to the final pivot row ordering, so Rs [oldrow] is the
+ * scale factor for A (oldrow,:), for the user's matrix A. Pnum is
+ * used as workspace in KLU_scale. When the factorization is done,
+ * the scale factors are permuted according to the final pivot row
+ * permutation, so that Rs [k] is the scale factor for the kth row of
+ * A(p,q) where p and q are the final row and column permutations. */
+ KLU_scale (scale, n, Ap, Ai, (double *) Ax, Rs, Pnum, Common) ;
+ if (Common->status < KLU_OK)
+ {
+ /* matrix is invalid */
+ return ;
+ }
+ }
+
+#ifndef NDEBUG
+ if (scale > 0)
+ {
+ for (k = 0 ; k < n ; k++) PRINTF (("Rs [%d] %g\n", k, Rs [k])) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* factor each block using klu */
+ /* ---------------------------------------------------------------------- */
+
+ for (block = 0 ; block < nblocks ; block++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* the block is from rows/columns k1 to k2-1 */
+ /* ------------------------------------------------------------------ */
+
+ k1 = R [block] ;
+ k2 = R [block+1] ;
+ nk = k2 - k1 ;
+ PRINTF (("FACTOR BLOCK %d, k1 %d k2-1 %d nk %d\n", block, k1,k2-1,nk)) ;
+
+ if (nk == 1)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* singleton case */
+ /* -------------------------------------------------------------- */
+
+ poff = Offp [k1] ;
+ oldcol = Q [k1] ;
+ pend = Ap [oldcol+1] ;
+ CLEAR (s) ;
+
+ if (scale <= 0)
+ {
+ /* no scaling */
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = Pinv [oldrow] ;
+ if (newrow < k1)
+ {
+ Offi [poff] = oldrow ;
+ Offx [poff] = Ax [p] ;
+ poff++ ;
+ }
+ else
+ {
+ ASSERT (newrow == k1) ;
+ PRINTF (("singleton block %d", block)) ;
+ PRINT_ENTRY (Ax [p]) ;
+ s = Ax [p] ;
+ }
+ }
+ }
+ else
+ {
+ /* row scaling. NOTE: scale factors are not yet permuted
+ * according to the pivot row permutation, so Rs [oldrow] is
+ * used below. When the factorization is done, the scale
+ * factors are permuted, so that Rs [newrow] will be used in
+ * klu_solve, klu_tsolve, and klu_rgrowth */
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = Pinv [oldrow] ;
+ if (newrow < k1)
+ {
+ Offi [poff] = oldrow ;
+ /* Offx [poff] = Ax [p] / Rs [oldrow] ; */
+ SCALE_DIV_ASSIGN (Offx [poff], Ax [p], Rs [oldrow]) ;
+ poff++ ;
+ }
+ else
+ {
+ ASSERT (newrow == k1) ;
+ PRINTF (("singleton block %d ", block)) ;
+ PRINT_ENTRY (Ax[p]) ;
+ SCALE_DIV_ASSIGN (s, Ax [p], Rs [oldrow]) ;
+ }
+ }
+ }
+
+ Udiag [k1] = s ;
+
+ if (IS_ZERO (s))
+ {
+ /* singular singleton */
+ Common->status = KLU_SINGULAR ;
+ Common->numerical_rank = k1 ;
+ Common->singular_col = oldcol ;
+ if (Common->halt_if_singular)
+ {
+ return ;
+ }
+ }
+
+ Offp [k1+1] = poff ;
+ Pnum [k1] = P [k1] ;
+ lnz++ ;
+ unz++ ;
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* construct and factorize the kth block */
+ /* -------------------------------------------------------------- */
+
+ if (Lnz [block] < 0)
+ {
+ /* COLAMD was used - no estimate of fill-in */
+ /* use 10 times the nnz in A, plus n */
+ lsize = -(Common->initmem) ;
+ }
+ else
+ {
+ lsize = Common->initmem_amd * Lnz [block] + nk ;
+ }
+
+ /* allocates 1 arrays: LUbx [block] */
+ Numeric->LUsize [block] = KLU_kernel_factor (nk, Ap, Ai, Ax, Q,
+ lsize, &LUbx [block], Udiag + k1, Llen + k1, Ulen + k1,
+ Lip + k1, Uip + k1, Pblock, &lnz_block, &unz_block,
+ X, Iwork, k1, Pinv, Rs, Offp, Offi, Offx, Common) ;
+
+ if (Common->status < KLU_OK ||
+ (Common->status == KLU_SINGULAR && Common->halt_if_singular))
+ {
+ /* out of memory, invalid inputs, or singular */
+ return ;
+ }
+
+ PRINTF (("\n----------------------- L %d:\n", block)) ;
+ ASSERT (KLU_valid_LU (nk, TRUE, Lip+k1, Llen+k1, LUbx [block])) ;
+ PRINTF (("\n----------------------- U %d:\n", block)) ;
+ ASSERT (KLU_valid_LU (nk, FALSE, Uip+k1, Ulen+k1, LUbx [block])) ;
+
+ /* -------------------------------------------------------------- */
+ /* get statistics */
+ /* -------------------------------------------------------------- */
+
+ lnz += lnz_block ;
+ unz += unz_block ;
+ max_lnz_block = MAX (max_lnz_block, lnz_block) ;
+ max_unz_block = MAX (max_unz_block, unz_block) ;
+
+ if (Lnz [block] == EMPTY)
+ {
+ /* revise estimate for subsequent factorization */
+ Lnz [block] = MAX (lnz_block, unz_block) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* combine the klu row ordering with the symbolic pre-ordering */
+ /* -------------------------------------------------------------- */
+
+ PRINTF (("Pnum, 1-based:\n")) ;
+ for (k = 0 ; k < nk ; k++)
+ {
+ ASSERT (k + k1 < n) ;
+ ASSERT (Pblock [k] + k1 < n) ;
+ Pnum [k + k1] = P [Pblock [k] + k1] ;
+ PRINTF (("Pnum (%d + %d + 1 = %d) = %d + 1 = %d\n",
+ k, k1, k+k1+1, Pnum [k+k1], Pnum [k+k1]+1)) ;
+ }
+
+ /* the local pivot row permutation Pblock is no longer needed */
+ }
+ }
+ ASSERT (nzoff == Offp [n]) ;
+ PRINTF (("\n------------------- Off diagonal entries:\n")) ;
+ ASSERT (KLU_valid (n, Offp, Offi, Offx)) ;
+
+ Numeric->lnz = lnz ;
+ Numeric->unz = unz ;
+ Numeric->max_lnz_block = max_lnz_block ;
+ Numeric->max_unz_block = max_unz_block ;
+
+ /* compute the inverse of Pnum */
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++)
+ {
+ Pinv [k] = EMPTY ;
+ }
+#endif
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSERT (Pnum [k] >= 0 && Pnum [k] < n) ;
+ Pinv [Pnum [k]] = k ;
+ }
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++) ASSERT (Pinv [k] != EMPTY) ;
+#endif
+
+ /* permute scale factors Rs according to pivotal row order */
+ if (scale > 0)
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ REAL (X [k]) = Rs [Pnum [k]] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ Rs [k] = REAL (X [k]) ;
+ }
+ }
+
+ PRINTF (("\n------------------- Off diagonal entries, old:\n")) ;
+ ASSERT (KLU_valid (n, Offp, Offi, Offx)) ;
+
+ /* apply the pivot row permutations to the off-diagonal entries */
+ for (p = 0 ; p < nzoff ; p++)
+ {
+ ASSERT (Offi [p] >= 0 && Offi [p] < n) ;
+ Offi [p] = Pinv [Offi [p]] ;
+ }
+
+ PRINTF (("\n------------------- Off diagonal entries, new:\n")) ;
+ ASSERT (KLU_valid (n, Offp, Offi, Offx)) ;
+
+#ifndef NDEBUG
+ {
+ PRINTF (("\n ############# KLU_BTF_FACTOR done, nblocks %d\n",nblocks));
+ Entry ss, *Udiag = Numeric->Udiag ;
+ for (block = 0 ; block < nblocks && Common->status == KLU_OK ; block++)
+ {
+ k1 = R [block] ;
+ k2 = R [block+1] ;
+ nk = k2 - k1 ;
+ PRINTF (("\n======================KLU_factor output: k1 %d k2 %d nk %d\n",k1,k2,nk)) ;
+ if (nk == 1)
+ {
+ PRINTF (("singleton ")) ;
+ /* ENTRY_PRINT (singleton [block]) ; */
+ ss = Udiag [k1] ;
+ PRINT_ENTRY (ss) ;
+ }
+ else
+ {
+ Int *Lip, *Uip, *Llen, *Ulen ;
+ Unit *LU ;
+ Lip = Numeric->Lip + k1 ;
+ Llen = Numeric->Llen + k1 ;
+ LU = (Unit *) Numeric->LUbx [block] ;
+ PRINTF (("\n---- L block %d\n", block));
+ ASSERT (KLU_valid_LU (nk, TRUE, Lip, Llen, LU)) ;
+ Uip = Numeric->Uip + k1 ;
+ Ulen = Numeric->Ulen + k1 ;
+ PRINTF (("\n---- U block %d\n", block)) ;
+ ASSERT (KLU_valid_LU (nk, FALSE, Uip, Ulen, LU)) ;
+ }
+ }
+ }
+#endif
+}
+
+
+
+/* ========================================================================== */
+/* === KLU_factor =========================================================== */
+/* ========================================================================== */
+
+KLU_numeric *KLU_factor /* returns NULL if error, or a valid
+ KLU_numeric object if successful */
+(
+ /* --- inputs --- */
+ Int Ap [ ], /* size n+1, column pointers */
+ Int Ai [ ], /* size nz, row indices */
+ double Ax [ ],
+ KLU_symbolic *Symbolic,
+ /* -------------- */
+ KLU_common *Common
+)
+{
+ Int n, nzoff, nblocks, maxblock, k, ok = TRUE ;
+ Int *R ;
+ KLU_numeric *Numeric ;
+ size_t n1, nzoff1, s, b6, n3 ;
+
+ if (Common == NULL)
+ {
+ return (NULL) ;
+ }
+ Common->status = KLU_OK ;
+ Common->numerical_rank = EMPTY ;
+ Common->singular_col = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the contents of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ /* check for a valid Symbolic object */
+ if (Symbolic == NULL)
+ {
+ Common->status = KLU_INVALID ;
+ return (NULL) ;
+ }
+
+ n = Symbolic->n ;
+ nzoff = Symbolic->nzoff ;
+ nblocks = Symbolic->nblocks ;
+ maxblock = Symbolic->maxblock ;
+ R = Symbolic->R ;
+ PRINTF (("KLU_factor: n %d nzoff %d nblocks %d maxblock %d\n",
+ n, nzoff, nblocks, maxblock)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get control parameters and make sure they are in the proper range */
+ /* ---------------------------------------------------------------------- */
+
+ Common->initmem_amd = MAX (1.0, Common->initmem_amd) ;
+ Common->initmem = MAX (1.0, Common->initmem) ;
+ Common->tol = MIN (Common->tol, 1.0) ;
+ Common->tol = MAX (0.0, Common->tol) ;
+ Common->memgrow = MAX (1.0, Common->memgrow) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ /* this will not cause size_t overflow (already checked by KLU_symbolic) */
+ n1 = ((size_t) n) + 1 ;
+ nzoff1 = ((size_t) nzoff) + 1 ;
+
+ Numeric = KLU_malloc (sizeof (KLU_numeric), 1, Common) ;
+ if (Common->status < KLU_OK)
+ {
+ /* out of memory */
+ Common->status = KLU_OUT_OF_MEMORY ;
+ return (NULL) ;
+ }
+ Numeric->n = n ;
+ Numeric->nblocks = nblocks ;
+ Numeric->nzoff = nzoff ;
+ Numeric->Pnum = KLU_malloc (n, sizeof (Int), Common) ;
+ Numeric->Offp = KLU_malloc (n1, sizeof (Int), Common) ;
+ Numeric->Offi = KLU_malloc (nzoff1, sizeof (Int), Common) ;
+ Numeric->Offx = KLU_malloc (nzoff1, sizeof (Entry), Common) ;
+
+ Numeric->Lip = KLU_malloc (n, sizeof (Int), Common) ;
+ Numeric->Uip = KLU_malloc (n, sizeof (Int), Common) ;
+ Numeric->Llen = KLU_malloc (n, sizeof (Int), Common) ;
+ Numeric->Ulen = KLU_malloc (n, sizeof (Int), Common) ;
+
+ Numeric->LUsize = KLU_malloc (nblocks, sizeof (size_t), Common) ;
+
+ Numeric->LUbx = KLU_malloc (nblocks, sizeof (Unit *), Common) ;
+ if (Numeric->LUbx != NULL)
+ {
+ for (k = 0 ; k < nblocks ; k++)
+ {
+ Numeric->LUbx [k] = NULL ;
+ }
+ }
+
+ Numeric->Udiag = KLU_malloc (n, sizeof (Entry), Common) ;
+
+ if (Common->scale > 0)
+ {
+ Numeric->Rs = KLU_malloc (n, sizeof (double), Common) ;
+ }
+ else
+ {
+ /* no scaling */
+ Numeric->Rs = NULL ;
+ }
+
+ Numeric->Pinv = KLU_malloc (n, sizeof (Int), Common) ;
+
+ /* allocate permanent workspace for factorization and solve. Note that the
+ * solver will use an Xwork of size 4n, whereas the factorization codes use
+ * an Xwork of size n and integer space (Iwork) of size 6n. KLU_condest
+ * uses an Xwork of size 2n. Total size is:
+ *
+ * n*sizeof(Entry) + max (6*maxblock*sizeof(Int), 3*n*sizeof(Entry))
+ */
+ s = KLU_mult_size_t (n, sizeof (Entry), &ok) ;
+ n3 = KLU_mult_size_t (n, 3 * sizeof (Entry), &ok) ;
+ b6 = KLU_mult_size_t (maxblock, 6 * sizeof (Int), &ok) ;
+ Numeric->worksize = KLU_add_size_t (s, MAX (n3, b6), &ok) ;
+ Numeric->Work = KLU_malloc (Numeric->worksize, 1, Common) ;
+ Numeric->Xwork = Numeric->Work ;
+ Numeric->Iwork = (Int *) ((Entry *) Numeric->Xwork + n) ;
+ if (!ok || Common->status < KLU_OK)
+ {
+ /* out of memory or problem too large */
+ Common->status = ok ? KLU_OUT_OF_MEMORY : KLU_TOO_LARGE ;
+ KLU_free_numeric (&Numeric, Common) ;
+ return (NULL) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize the blocks */
+ /* ---------------------------------------------------------------------- */
+
+ factor2 (Ap, Ai, (Entry *) Ax, Symbolic, Numeric, Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return or free the Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common->status < KLU_OK)
+ {
+ /* out of memory or inputs invalid */
+ KLU_free_numeric (&Numeric, Common) ;
+ }
+ else if (Common->status == KLU_SINGULAR)
+ {
+ if (Common->halt_if_singular)
+ {
+ /* Matrix is singular, and the Numeric object is only partially
+ * defined because we halted early. This is the default case for
+ * a singular matrix. */
+ KLU_free_numeric (&Numeric, Common) ;
+ }
+ }
+ else if (Common->status == KLU_OK)
+ {
+ /* successful non-singular factorization */
+ Common->numerical_rank = n ;
+ Common->singular_col = n ;
+ }
+ return (Numeric) ;
+}
diff --git a/KLU/Source/klu_free_numeric.c b/KLU/Source/klu_free_numeric.c
new file mode 100644
index 0000000..304da61
--- /dev/null
+++ b/KLU/Source/klu_free_numeric.c
@@ -0,0 +1,71 @@
+/* ========================================================================== */
+/* === KLU_free_numeric ===================================================== */
+/* ========================================================================== */
+
+/* Free the KLU Numeric object. */
+
+#include "klu_internal.h"
+
+Int KLU_free_numeric
+(
+ KLU_numeric **NumericHandle,
+ KLU_common *Common
+)
+{
+ KLU_numeric *Numeric ;
+ Unit **LUbx ;
+ size_t *LUsize ;
+ Int block, n, nzoff, nblocks ;
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+ if (NumericHandle == NULL || *NumericHandle == NULL)
+ {
+ return (TRUE) ;
+ }
+
+ Numeric = *NumericHandle ;
+
+ n = Numeric->n ;
+ nzoff = Numeric->nzoff ;
+ nblocks = Numeric->nblocks ;
+ LUsize = Numeric->LUsize ;
+
+ LUbx = (Unit **) Numeric->LUbx ;
+ if (LUbx != NULL)
+ {
+ for (block = 0 ; block < nblocks ; block++)
+ {
+ KLU_free (LUbx [block], LUsize ? LUsize [block] : 0,
+ sizeof (Unit), Common) ;
+ }
+ }
+
+ KLU_free (Numeric->Pnum, n, sizeof (Int), Common) ;
+ KLU_free (Numeric->Offp, n+1, sizeof (Int), Common) ;
+ KLU_free (Numeric->Offi, nzoff+1, sizeof (Int), Common) ;
+ KLU_free (Numeric->Offx, nzoff+1, sizeof (Entry), Common) ;
+
+ KLU_free (Numeric->Lip, n, sizeof (Int), Common) ;
+ KLU_free (Numeric->Llen, n, sizeof (Int), Common) ;
+ KLU_free (Numeric->Uip, n, sizeof (Int), Common) ;
+ KLU_free (Numeric->Ulen, n, sizeof (Int), Common) ;
+
+ KLU_free (Numeric->LUsize, nblocks, sizeof (size_t), Common) ;
+
+ KLU_free (Numeric->LUbx, nblocks, sizeof (Unit *), Common) ;
+
+ KLU_free (Numeric->Udiag, n, sizeof (Entry), Common) ;
+
+ KLU_free (Numeric->Rs, n, sizeof (double), Common) ;
+ KLU_free (Numeric->Pinv, n, sizeof (Int), Common) ;
+
+ KLU_free (Numeric->Work, Numeric->worksize, 1, Common) ;
+
+ KLU_free (Numeric, 1, sizeof (KLU_numeric), Common) ;
+
+ *NumericHandle = NULL ;
+ return (TRUE) ;
+}
diff --git a/KLU/Source/klu_free_symbolic.c b/KLU/Source/klu_free_symbolic.c
new file mode 100644
index 0000000..5dad960
--- /dev/null
+++ b/KLU/Source/klu_free_symbolic.c
@@ -0,0 +1,34 @@
+/* ========================================================================== */
+/* === KLU_free_symbolic ==================================================== */
+/* ========================================================================== */
+
+/* Free the KLU Symbolic object. */
+
+#include "klu_internal.h"
+
+Int KLU_free_symbolic
+(
+ KLU_symbolic **SymbolicHandle,
+ KLU_common *Common
+)
+{
+ KLU_symbolic *Symbolic ;
+ Int n ;
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+ if (SymbolicHandle == NULL || *SymbolicHandle == NULL)
+ {
+ return (TRUE) ;
+ }
+ Symbolic = *SymbolicHandle ;
+ n = Symbolic->n ;
+ KLU_free (Symbolic->P, n, sizeof (Int), Common) ;
+ KLU_free (Symbolic->Q, n, sizeof (Int), Common) ;
+ KLU_free (Symbolic->R, n+1, sizeof (Int), Common) ;
+ KLU_free (Symbolic->Lnz, n, sizeof (double), Common) ;
+ KLU_free (Symbolic, 1, sizeof (KLU_symbolic), Common) ;
+ *SymbolicHandle = NULL ;
+ return (TRUE) ;
+}
diff --git a/KLU/Source/klu_kernel.c b/KLU/Source/klu_kernel.c
new file mode 100644
index 0000000..88611ee
--- /dev/null
+++ b/KLU/Source/klu_kernel.c
@@ -0,0 +1,1009 @@
+/* ========================================================================== */
+/* === KLU_kernel =========================================================== */
+/* ========================================================================== */
+
+/* Sparse left-looking LU factorization, with partial pivoting. Based on
+ * Gilbert & Peierl's method, with a non-recursive DFS and with Eisenstat &
+ * Liu's symmetric pruning. No user-callable routines are in this file.
+ */
+
+#include "klu_internal.h"
+
+/* ========================================================================== */
+/* === dfs ================================================================== */
+/* ========================================================================== */
+
+/* Does a depth-first-search, starting at node j. */
+
+static Int dfs
+(
+ /* input, not modified on output: */
+ Int j, /* node at which to start the DFS */
+ Int k, /* mark value, for the Flag array */
+ Int Pinv [ ], /* Pinv [i] = k if row i is kth pivot row, or EMPTY if
+ * row i is not yet pivotal. */
+ Int Llen [ ], /* size n, Llen [k] = # nonzeros in column k of L */
+ Int Lip [ ], /* size n, Lip [k] is position in LU of column k of L */
+
+ /* workspace, not defined on input or output */
+ Int Stack [ ], /* size n */
+
+ /* input/output: */
+ Int Flag [ ], /* Flag [i] == k means i is marked */
+ Int Lpend [ ], /* for symmetric pruning */
+ Int top, /* top of stack on input*/
+ Unit LU [],
+ Int *Lik, /* Li row index array of the kth column */
+ Int *plength,
+
+ /* other, not defined on input or output */
+ Int Ap_pos [ ] /* keeps track of position in adj list during DFS */
+)
+{
+ Int i, pos, jnew, head, l_length ;
+ Int *Li ;
+
+ l_length = *plength ;
+
+ head = 0 ;
+ Stack [0] = j ;
+ ASSERT (Flag [j] != k) ;
+
+ while (head >= 0)
+ {
+ j = Stack [head] ;
+ jnew = Pinv [j] ;
+ ASSERT (jnew >= 0 && jnew < k) ; /* j is pivotal */
+
+ if (Flag [j] != k) /* a node is not yet visited */
+ {
+ /* first time that j has been visited */
+ Flag [j] = k ;
+ PRINTF (("[ start dfs at %d : new %d\n", j, jnew)) ;
+ /* set Ap_pos [head] to one past the last entry in col j to scan */
+ Ap_pos [head] =
+ (Lpend [jnew] == EMPTY) ? Llen [jnew] : Lpend [jnew] ;
+ }
+
+ /* add the adjacent nodes to the recursive stack by iterating through
+ * until finding another non-visited pivotal node */
+ Li = (Int *) (LU + Lip [jnew]) ;
+ for (pos = --Ap_pos [head] ; pos >= 0 ; --pos)
+ {
+ i = Li [pos] ;
+ if (Flag [i] != k)
+ {
+ /* node i is not yet visited */
+ if (Pinv [i] >= 0)
+ {
+ /* keep track of where we left off in the scan of the
+ * adjacency list of node j so we can restart j where we
+ * left off. */
+ Ap_pos [head] = pos ;
+
+ /* node i is pivotal; push it onto the recursive stack
+ * and immediately break so we can recurse on node i. */
+ Stack [++head] = i ;
+ break ;
+ }
+ else
+ {
+ /* node i is not pivotal (no outgoing edges). */
+ /* Flag as visited and store directly into L,
+ * and continue with current node j. */
+ Flag [i] = k ;
+ Lik [l_length] = i ;
+ l_length++ ;
+ }
+ }
+ }
+
+ if (pos == -1)
+ {
+ /* if all adjacent nodes of j are already visited, pop j from
+ * recursive stack and push j onto output stack */
+ head-- ;
+ Stack[--top] = j ;
+ PRINTF ((" end dfs at %d ] head : %d\n", j, head)) ;
+ }
+ }
+
+ *plength = l_length ;
+ return (top) ;
+}
+
+
+/* ========================================================================== */
+/* === lsolve_symbolic ====================================================== */
+/* ========================================================================== */
+
+/* Finds the pattern of x, for the solution of Lx=b */
+
+static Int lsolve_symbolic
+(
+ /* input, not modified on output: */
+ Int n, /* L is n-by-n, where n >= 0 */
+ Int k, /* also used as the mark value, for the Flag array */
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Q [ ],
+ Int Pinv [ ], /* Pinv [i] = k if i is kth pivot row, or EMPTY if row i
+ * is not yet pivotal. */
+
+ /* workspace, not defined on input or output */
+ Int Stack [ ], /* size n */
+
+ /* workspace, defined on input and output */
+ Int Flag [ ], /* size n. Initially, all of Flag [0..n-1] < k. After
+ * lsolve_symbolic is done, Flag [i] == k if i is in
+ * the pattern of the output, and Flag [0..n-1] <= k. */
+
+ /* other */
+ Int Lpend [ ], /* for symmetric pruning */
+ Int Ap_pos [ ], /* workspace used in dfs */
+
+ Unit LU [ ], /* LU factors (pattern and values) */
+ Int lup, /* pointer to free space in LU */
+ Int Llen [ ], /* size n, Llen [k] = # nonzeros in column k of L */
+ Int Lip [ ], /* size n, Lip [k] is position in LU of column k of L */
+
+ /* ---- the following are only used in the BTF case --- */
+
+ Int k1, /* the block of A is from k1 to k2-1 */
+ Int PSinv [ ] /* inverse of P from symbolic factorization */
+)
+{
+ Int *Lik ;
+ Int i, p, pend, oldcol, kglobal, top, l_length ;
+
+ top = n ;
+ l_length = 0 ;
+ Lik = (Int *) (LU + lup);
+
+ /* ---------------------------------------------------------------------- */
+ /* BTF factorization of A (k1:k2-1, k1:k2-1) */
+ /* ---------------------------------------------------------------------- */
+
+ kglobal = k + k1 ; /* column k of the block is col kglobal of A */
+ oldcol = Q [kglobal] ; /* Q must be present for BTF case */
+ pend = Ap [oldcol+1] ;
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ i = PSinv [Ai [p]] - k1 ;
+ if (i < 0) continue ; /* skip entry outside the block */
+
+ /* (i,k) is an entry in the block. start a DFS at node i */
+ PRINTF (("\n ===== DFS at node %d in b, inew: %d\n", i, Pinv [i])) ;
+ if (Flag [i] != k)
+ {
+ if (Pinv [i] >= 0)
+ {
+ top = dfs (i, k, Pinv, Llen, Lip, Stack, Flag,
+ Lpend, top, LU, Lik, &l_length, Ap_pos) ;
+ }
+ else
+ {
+ /* i is not pivotal, and not flagged. Flag and put in L */
+ Flag [i] = k ;
+ Lik [l_length] = i ;
+ l_length++;
+ }
+ }
+ }
+
+ /* If Llen [k] is zero, the matrix is structurally singular */
+ Llen [k] = l_length ;
+ return (top) ;
+}
+
+
+/* ========================================================================== */
+/* === construct_column ===================================================== */
+/* ========================================================================== */
+
+/* Construct the kth column of A, and the off-diagonal part, if requested.
+ * Scatter the numerical values into the workspace X, and construct the
+ * corresponding column of the off-diagonal matrix. */
+
+static void construct_column
+(
+ /* inputs, not modified on output */
+ Int k, /* the column of A (or the column of the block) to get */
+ Int Ap [ ],
+ Int Ai [ ],
+ Entry Ax [ ],
+ Int Q [ ], /* column pre-ordering */
+
+ /* zero on input, modified on output */
+ Entry X [ ],
+
+ /* ---- the following are only used in the BTF case --- */
+
+ /* inputs, not modified on output */
+ Int k1, /* the block of A is from k1 to k2-1 */
+ Int PSinv [ ], /* inverse of P from symbolic factorization */
+ double Rs [ ], /* scale factors for A */
+ Int scale, /* 0: no scaling, nonzero: scale the rows with Rs */
+
+ /* inputs, modified on output */
+ Int Offp [ ], /* off-diagonal matrix (modified by this routine) */
+ Int Offi [ ],
+ Entry Offx [ ]
+)
+{
+ Entry aik ;
+ Int i, p, pend, oldcol, kglobal, poff, oldrow ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Scale and scatter the column into X. */
+ /* ---------------------------------------------------------------------- */
+
+ kglobal = k + k1 ; /* column k of the block is col kglobal of A */
+ poff = Offp [kglobal] ; /* start of off-diagonal column */
+ oldcol = Q [kglobal] ;
+ pend = Ap [oldcol+1] ;
+
+ if (scale <= 0)
+ {
+ /* no scaling */
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ oldrow = Ai [p] ;
+ i = PSinv [oldrow] - k1 ;
+ aik = Ax [p] ;
+ if (i < 0)
+ {
+ /* this is an entry in the off-diagonal part */
+ Offi [poff] = oldrow ;
+ Offx [poff] = aik ;
+ poff++ ;
+ }
+ else
+ {
+ /* (i,k) is an entry in the block. scatter into X */
+ X [i] = aik ;
+ }
+ }
+ }
+ else
+ {
+ /* row scaling */
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ oldrow = Ai [p] ;
+ i = PSinv [oldrow] - k1 ;
+ aik = Ax [p] ;
+ SCALE_DIV (aik, Rs [oldrow]) ;
+ if (i < 0)
+ {
+ /* this is an entry in the off-diagonal part */
+ Offi [poff] = oldrow ;
+ Offx [poff] = aik ;
+ poff++ ;
+ }
+ else
+ {
+ /* (i,k) is an entry in the block. scatter into X */
+ X [i] = aik ;
+ }
+ }
+ }
+
+ Offp [kglobal+1] = poff ; /* start of the next col of off-diag part */
+}
+
+
+/* ========================================================================== */
+/* === lsolve_numeric ======================================================= */
+/* ========================================================================== */
+
+/* Computes the numerical values of x, for the solution of Lx=b. Note that x
+ * may include explicit zeros if numerical cancelation occurs. L is assumed
+ * to be unit-diagonal, with possibly unsorted columns (but the first entry in
+ * the column must always be the diagonal entry). */
+
+static void lsolve_numeric
+(
+ /* input, not modified on output: */
+ Int Pinv [ ], /* Pinv [i] = k if i is kth pivot row, or EMPTY if row i
+ * is not yet pivotal. */
+ Unit *LU, /* LU factors (pattern and values) */
+ Int Stack [ ], /* stack for dfs */
+ Int Lip [ ], /* size n, Lip [k] is position in LU of column k of L */
+ Int top, /* top of stack on input */
+ Int n, /* A is n-by-n */
+ Int Llen [ ], /* size n, Llen [k] = # nonzeros in column k of L */
+
+ /* output, must be zero on input: */
+ Entry X [ ] /* size n, initially zero. On output,
+ * X [Ui [up1..up-1]] and X [Li [lp1..lp-1]]
+ * contains the solution. */
+
+)
+{
+ Entry xj ;
+ Entry *Lx ;
+ Int *Li ;
+ Int p, s, j, jnew, len ;
+
+ /* solve Lx=b */
+ for (s = top ; s < n ; s++)
+ {
+ /* forward solve with column j of L */
+ j = Stack [s] ;
+ jnew = Pinv [j] ;
+ ASSERT (jnew >= 0) ;
+ xj = X [j] ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, jnew, len) ;
+ ASSERT (Lip [jnew] <= Lip [jnew+1]) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ /*X [Li [p]] -= Lx [p] * xj ; */
+ MULT_SUB (X [Li [p]], Lx [p], xj) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === lpivot =============================================================== */
+/* ========================================================================== */
+
+/* Find a pivot via partial pivoting, and scale the column of L. */
+
+static Int lpivot
+(
+ Int diagrow,
+ Int *p_pivrow,
+ Entry *p_pivot,
+ double *p_abs_pivot,
+ double tol,
+ Entry X [ ],
+ Unit *LU, /* LU factors (pattern and values) */
+ Int Lip [ ],
+ Int Llen [ ],
+ Int k,
+ Int n,
+
+ Int Pinv [ ], /* Pinv [i] = k if row i is kth pivot row, or EMPTY if
+ * row i is not yet pivotal. */
+
+ Int *p_firstrow,
+ KLU_common *Common
+)
+{
+ Entry x, pivot, *Lx ;
+ double abs_pivot, xabs ;
+ Int p, i, ppivrow, pdiag, pivrow, *Li, last_row_index, firstrow, len ;
+
+ pivrow = EMPTY ;
+ if (Llen [k] == 0)
+ {
+ /* matrix is structurally singular */
+ if (Common->halt_if_singular)
+ {
+ return (FALSE) ;
+ }
+ for (firstrow = *p_firstrow ; firstrow < n ; firstrow++)
+ {
+ PRINTF (("check %d\n", firstrow)) ;
+ if (Pinv [firstrow] < 0)
+ {
+ /* found the lowest-numbered non-pivotal row. Pick it. */
+ pivrow = firstrow ;
+ PRINTF (("Got pivotal row: %d\n", pivrow)) ;
+ break ;
+ }
+ }
+ ASSERT (pivrow >= 0 && pivrow < n) ;
+ CLEAR (pivot) ;
+ *p_pivrow = pivrow ;
+ *p_pivot = pivot ;
+ *p_abs_pivot = 0 ;
+ *p_firstrow = firstrow ;
+ return (FALSE) ;
+ }
+
+ pdiag = EMPTY ;
+ ppivrow = EMPTY ;
+ abs_pivot = EMPTY ;
+ i = Llen [k] - 1 ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+ last_row_index = Li [i] ;
+
+ /* decrement the length by 1 */
+ Llen [k] = i ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+
+ /* look in Li [0 ..Llen [k] - 1 ] for a pivot row */
+ for (p = 0 ; p < len ; p++)
+ {
+ /* gather the entry from X and store in L */
+ i = Li [p] ;
+ x = X [i] ;
+ CLEAR (X [i]) ;
+
+ Lx [p] = x ;
+ /* xabs = ABS (x) ; */
+ ABS (xabs, x) ;
+
+ /* find the diagonal */
+ if (i == diagrow)
+ {
+ pdiag = p ;
+ }
+
+ /* find the partial-pivoting choice */
+ if (xabs > abs_pivot)
+ {
+ abs_pivot = xabs ;
+ ppivrow = p ;
+ }
+ }
+
+ /* xabs = ABS (X [last_row_index]) ;*/
+ ABS (xabs, X [last_row_index]) ;
+ if (xabs > abs_pivot)
+ {
+ abs_pivot = xabs ;
+ ppivrow = EMPTY ;
+ }
+
+ /* compare the diagonal with the largest entry */
+ if (last_row_index == diagrow)
+ {
+ if (xabs >= tol * abs_pivot)
+ {
+ abs_pivot = xabs ;
+ ppivrow = EMPTY ;
+ }
+ }
+ else if (pdiag != EMPTY)
+ {
+ /* xabs = ABS (Lx [pdiag]) ;*/
+ ABS (xabs, Lx [pdiag]) ;
+ if (xabs >= tol * abs_pivot)
+ {
+ /* the diagonal is large enough */
+ abs_pivot = xabs ;
+ ppivrow = pdiag ;
+ }
+ }
+
+ if (ppivrow != EMPTY)
+ {
+ pivrow = Li [ppivrow] ;
+ pivot = Lx [ppivrow] ;
+ /* overwrite the ppivrow values with last index values */
+ Li [ppivrow] = last_row_index ;
+ Lx [ppivrow] = X [last_row_index] ;
+ }
+ else
+ {
+ pivrow = last_row_index ;
+ pivot = X [last_row_index] ;
+ }
+ CLEAR (X [last_row_index]) ;
+
+ *p_pivrow = pivrow ;
+ *p_pivot = pivot ;
+ *p_abs_pivot = abs_pivot ;
+ ASSERT (pivrow >= 0 && pivrow < n) ;
+
+ if (IS_ZERO (pivot) && Common->halt_if_singular)
+ {
+ /* numerically singular case */
+ return (FALSE) ;
+ }
+
+ /* divide L by the pivot value */
+ for (p = 0 ; p < Llen [k] ; p++)
+ {
+ /* Lx [p] /= pivot ; */
+ DIV (Lx [p], Lx [p], pivot) ;
+ }
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === prune ================================================================ */
+/* ========================================================================== */
+
+/* Prune the columns of L to reduce work in subsequent depth-first searches */
+static void prune
+(
+ /* input/output: */
+ Int Lpend [ ], /* Lpend [j] marks symmetric pruning point for L(:,j) */
+
+ /* input: */
+ Int Pinv [ ], /* Pinv [i] = k if row i is kth pivot row, or EMPTY if
+ * row i is not yet pivotal. */
+ Int k, /* prune using column k of U */
+ Int pivrow, /* current pivot row */
+
+ /* input/output: */
+ Unit *LU, /* LU factors (pattern and values) */
+
+ /* input */
+ Int Uip [ ], /* size n, column pointers for U */
+ Int Lip [ ], /* size n, column pointers for L */
+ Int Ulen [ ], /* size n, column length of U */
+ Int Llen [ ] /* size n, column length of L */
+)
+{
+ Entry x ;
+ Entry *Lx, *Ux ;
+ Int *Li, *Ui ;
+ Int p, i, j, p2, phead, ptail, llen, ulen ;
+
+ /* check to see if any column of L can be pruned */
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, ulen) ;
+ for (p = 0 ; p < ulen ; p++)
+ {
+ j = Ui [p] ;
+ ASSERT (j < k) ;
+ PRINTF (("%d is pruned: %d. Lpend[j] %d Lip[j+1] %d\n",
+ j, Lpend [j] != EMPTY, Lpend [j], Lip [j+1])) ;
+ if (Lpend [j] == EMPTY)
+ {
+ /* scan column j of L for the pivot row */
+ GET_POINTER (LU, Lip, Llen, Li, Lx, j, llen) ;
+ for (p2 = 0 ; p2 < llen ; p2++)
+ {
+ if (pivrow == Li [p2])
+ {
+ /* found it! This column can be pruned */
+#ifndef NDEBUG
+ PRINTF (("==== PRUNE: col j %d of L\n", j)) ;
+ {
+ Int p3 ;
+ for (p3 = 0 ; p3 < Llen [j] ; p3++)
+ {
+ PRINTF (("before: %i pivotal: %d\n", Li [p3],
+ Pinv [Li [p3]] >= 0)) ;
+ }
+ }
+#endif
+
+ /* partition column j of L. The unit diagonal of L
+ * is not stored in the column of L. */
+ phead = 0 ;
+ ptail = Llen [j] ;
+ while (phead < ptail)
+ {
+ i = Li [phead] ;
+ if (Pinv [i] >= 0)
+ {
+ /* leave at the head */
+ phead++ ;
+ }
+ else
+ {
+ /* swap with the tail */
+ ptail-- ;
+ Li [phead] = Li [ptail] ;
+ Li [ptail] = i ;
+ x = Lx [phead] ;
+ Lx [phead] = Lx [ptail] ;
+ Lx [ptail] = x ;
+ }
+ }
+
+ /* set Lpend to one past the last entry in the
+ * first part of the column of L. Entries in
+ * Li [0 ... Lpend [j]-1] are the only part of
+ * column j of L that needs to be scanned in the DFS.
+ * Lpend [j] was EMPTY; setting it >= 0 also flags
+ * column j as pruned. */
+ Lpend [j] = ptail ;
+
+#ifndef NDEBUG
+ {
+ Int p3 ;
+ for (p3 = 0 ; p3 < Llen [j] ; p3++)
+ {
+ if (p3 == Lpend [j]) PRINTF (("----\n")) ;
+ PRINTF (("after: %i pivotal: %d\n", Li [p3],
+ Pinv [Li [p3]] >= 0)) ;
+ }
+ }
+#endif
+
+ break ;
+ }
+ }
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === KLU_kernel =========================================================== */
+/* ========================================================================== */
+
+size_t KLU_kernel /* final size of LU on output */
+(
+ /* input, not modified */
+ Int n, /* A is n-by-n */
+ Int Ap [ ], /* size n+1, column pointers for A */
+ Int Ai [ ], /* size nz = Ap [n], row indices for A */
+ Entry Ax [ ], /* size nz, values of A */
+ Int Q [ ], /* size n, optional input permutation */
+ size_t lusize, /* initial size of LU on input */
+
+ /* output, not defined on input */
+ Int Pinv [ ], /* size n, inverse row permutation, where Pinv [i] = k if
+ * row i is the kth pivot row */
+ Int P [ ], /* size n, row permutation, where P [k] = i if row i is the
+ * kth pivot row. */
+ Unit **p_LU, /* LU array, size lusize on input */
+ Entry Udiag [ ], /* size n, diagonal of U */
+ Int Llen [ ], /* size n, column length of L */
+ Int Ulen [ ], /* size n, column length of U */
+ Int Lip [ ], /* size n, column pointers for L */
+ Int Uip [ ], /* size n, column pointers for U */
+ Int *lnz, /* size of L*/
+ Int *unz, /* size of U*/
+ /* workspace, not defined on input */
+ Entry X [ ], /* size n, undefined on input, zero on output */
+
+ /* workspace, not defined on input or output */
+ Int Stack [ ], /* size n */
+ Int Flag [ ], /* size n */
+ Int Ap_pos [ ], /* size n */
+
+ /* other workspace: */
+ Int Lpend [ ], /* size n workspace, for pruning only */
+
+ /* inputs, not modified on output */
+ Int k1, /* the block of A is from k1 to k2-1 */
+ Int PSinv [ ], /* inverse of P from symbolic factorization */
+ double Rs [ ], /* scale factors for A */
+
+ /* inputs, modified on output */
+ Int Offp [ ], /* off-diagonal matrix (modified by this routine) */
+ Int Offi [ ],
+ Entry Offx [ ],
+ /* --------------- */
+ KLU_common *Common
+)
+{
+ Entry pivot ;
+ double abs_pivot, xsize, nunits, tol, memgrow ;
+ Entry *Ux ;
+ Int *Li, *Ui ;
+ Unit *LU ; /* LU factors (pattern and values) */
+ Int k, p, i, j, pivrow = 0, kbar, diagrow, firstrow, lup, top, scale, len ;
+ size_t newlusize ;
+
+#ifndef NDEBUG
+ Entry *Lx ;
+#endif
+
+ ASSERT (Common != NULL) ;
+ scale = Common->scale ;
+ tol = Common->tol ;
+ memgrow = Common->memgrow ;
+ *lnz = 0 ;
+ *unz = 0 ;
+ CLEAR (pivot) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get initial Li, Lx, Ui, and Ux */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF (("input: lusize %d \n", lusize)) ;
+ ASSERT (lusize > 0) ;
+ LU = *p_LU ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+ firstrow = 0 ;
+ lup = 0 ;
+
+ for (k = 0 ; k < n ; k++)
+ {
+ /* X [k] = 0 ; */
+ CLEAR (X [k]) ;
+ Flag [k] = EMPTY ;
+ Lpend [k] = EMPTY ; /* flag k as not pruned */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* mark all rows as non-pivotal and determine initial diagonal mapping */
+ /* ---------------------------------------------------------------------- */
+
+ /* PSinv does the symmetric permutation, so don't do it here */
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = k ;
+ Pinv [k] = FLIP (k) ; /* mark all rows as non-pivotal */
+ }
+ /* initialize the construction of the off-diagonal matrix */
+ Offp [0] = 0 ;
+
+ /* P [k] = row means that UNFLIP (Pinv [row]) = k, and visa versa.
+ * If row is pivotal, then Pinv [row] >= 0. A row is initially "flipped"
+ * (Pinv [k] < EMPTY), and then marked "unflipped" when it becomes
+ * pivotal. */
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++)
+ {
+ PRINTF (("Initial P [%d] = %d\n", k, P [k])) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n ; k++)
+ {
+
+ PRINTF (("\n\n==================================== k: %d\n", k)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* determine if LU factors have grown too big */
+ /* ------------------------------------------------------------------ */
+
+ /* (n - k) entries for L and k entries for U */
+ nunits = DUNITS (Int, n - k) + DUNITS (Int, k) +
+ DUNITS (Entry, n - k) + DUNITS (Entry, k) ;
+
+ /* LU can grow by at most 'nunits' entries if the column is dense */
+ PRINTF (("lup %d lusize %g lup+nunits: %g\n", lup, (double) lusize,
+ lup+nunits));
+ xsize = ((double) lup) + nunits ;
+ if (xsize > (double) lusize)
+ {
+ /* check here how much to grow */
+ xsize = (memgrow * ((double) lusize) + 4*n + 1) ;
+ if (INT_OVERFLOW (xsize))
+ {
+ PRINTF (("Matrix is too large (Int overflow)\n")) ;
+ Common->status = KLU_TOO_LARGE ;
+ return (lusize) ;
+ }
+ newlusize = memgrow * lusize + 2*n + 1 ;
+ /* Future work: retry mechanism in case of malloc failure */
+ LU = KLU_realloc (newlusize, lusize, sizeof (Unit), LU, Common) ;
+ Common->nrealloc++ ;
+ *p_LU = LU ;
+ if (Common->status == KLU_OUT_OF_MEMORY)
+ {
+ PRINTF (("Matrix is too large (LU)\n")) ;
+ return (lusize) ;
+ }
+ lusize = newlusize ;
+ PRINTF (("inc LU to %d done\n", lusize)) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* start the kth column of L and U */
+ /* ------------------------------------------------------------------ */
+
+ Lip [k] = lup ;
+
+ /* ------------------------------------------------------------------ */
+ /* compute the nonzero pattern of the kth column of L and U */
+ /* ------------------------------------------------------------------ */
+
+#ifndef NDEBUG
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSERT (Flag [i] < k) ;
+ /* ASSERT (X [i] == 0) ; */
+ ASSERT (IS_ZERO (X [i])) ;
+ }
+#endif
+
+ top = lsolve_symbolic (n, k, Ap, Ai, Q, Pinv, Stack, Flag,
+ Lpend, Ap_pos, LU, lup, Llen, Lip, k1, PSinv) ;
+
+#ifndef NDEBUG
+ PRINTF (("--- in U:\n")) ;
+ for (p = top ; p < n ; p++)
+ {
+ PRINTF (("pattern of X for U: %d : %d pivot row: %d\n",
+ p, Stack [p], Pinv [Stack [p]])) ;
+ ASSERT (Flag [Stack [p]] == k) ;
+ }
+ PRINTF (("--- in L:\n")) ;
+ Li = (Int *) (LU + Lip [k]);
+ for (p = 0 ; p < Llen [k] ; p++)
+ {
+ PRINTF (("pattern of X in L: %d : %d pivot row: %d\n",
+ p, Li [p], Pinv [Li [p]])) ;
+ ASSERT (Flag [Li [p]] == k) ;
+ }
+ p = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSERT (Flag [i] <= k) ;
+ if (Flag [i] == k) p++ ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* get the column of the matrix to factorize and scatter into X */
+ /* ------------------------------------------------------------------ */
+
+ construct_column (k, Ap, Ai, Ax, Q, X,
+ k1, PSinv, Rs, scale, Offp, Offi, Offx) ;
+
+ /* ------------------------------------------------------------------ */
+ /* compute the numerical values of the kth column (s = L \ A (:,k)) */
+ /* ------------------------------------------------------------------ */
+
+ lsolve_numeric (Pinv, LU, Stack, Lip, top, n, Llen, X) ;
+
+#ifndef NDEBUG
+ for (p = top ; p < n ; p++)
+ {
+ PRINTF (("X for U %d : ", Stack [p])) ;
+ PRINT_ENTRY (X [Stack [p]]) ;
+ }
+ Li = (Int *) (LU + Lip [k]) ;
+ for (p = 0 ; p < Llen [k] ; p++)
+ {
+ PRINTF (("X for L %d : ", Li [p])) ;
+ PRINT_ENTRY (X [Li [p]]) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* partial pivoting with diagonal preference */
+ /* ------------------------------------------------------------------ */
+
+ /* determine what the "diagonal" is */
+ diagrow = P [k] ; /* might already be pivotal */
+ PRINTF (("k %d, diagrow = %d, UNFLIP (diagrow) = %d\n",
+ k, diagrow, UNFLIP (diagrow))) ;
+
+ /* find a pivot and scale the pivot column */
+ if (!lpivot (diagrow, &pivrow, &pivot, &abs_pivot, tol, X, LU, Lip,
+ Llen, k, n, Pinv, &firstrow, Common))
+ {
+ /* matrix is structurally or numerically singular */
+ Common->status = KLU_SINGULAR ;
+ if (Common->numerical_rank == EMPTY)
+ {
+ Common->numerical_rank = k+k1 ;
+ Common->singular_col = Q [k+k1] ;
+ }
+ if (Common->halt_if_singular)
+ {
+ /* do not continue the factorization */
+ return (lusize) ;
+ }
+ }
+
+ /* we now have a valid pivot row, even if the column has NaN's or
+ * has no entries on or below the diagonal at all. */
+ PRINTF (("\nk %d : Pivot row %d : ", k, pivrow)) ;
+ PRINT_ENTRY (pivot) ;
+ ASSERT (pivrow >= 0 && pivrow < n) ;
+ ASSERT (Pinv [pivrow] < 0) ;
+
+ /* set the Uip pointer */
+ Uip [k] = Lip [k] + UNITS (Int, Llen [k]) + UNITS (Entry, Llen [k]) ;
+
+ /* move the lup pointer to the position where indices of U
+ * should be stored */
+ lup += UNITS (Int, Llen [k]) + UNITS (Entry, Llen [k]) ;
+
+ Ulen [k] = n - top ;
+
+ /* extract Stack [top..n-1] to Ui and the values to Ux and clear X */
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
+ for (p = top, i = 0 ; p < n ; p++, i++)
+ {
+ j = Stack [p] ;
+ Ui [i] = Pinv [j] ;
+ Ux [i] = X [j] ;
+ CLEAR (X [j]) ;
+ }
+
+ /* position the lu index at the starting point for next column */
+ lup += UNITS (Int, Ulen [k]) + UNITS (Entry, Ulen [k]) ;
+
+ /* U(k,k) = pivot */
+ Udiag [k] = pivot ;
+
+ /* ------------------------------------------------------------------ */
+ /* log the pivot permutation */
+ /* ------------------------------------------------------------------ */
+
+ ASSERT (UNFLIP (Pinv [diagrow]) < n) ;
+ ASSERT (P [UNFLIP (Pinv [diagrow])] == diagrow) ;
+
+ if (pivrow != diagrow)
+ {
+ /* an off-diagonal pivot has been chosen */
+ Common->noffdiag++ ;
+ PRINTF ((">>>>>>>>>>>>>>>>> pivrow %d k %d off-diagonal\n",
+ pivrow, k)) ;
+ if (Pinv [diagrow] < 0)
+ {
+ /* the former diagonal row index, diagrow, has not yet been
+ * chosen as a pivot row. Log this diagrow as the "diagonal"
+ * entry in the column kbar for which the chosen pivot row,
+ * pivrow, was originally logged as the "diagonal" */
+ kbar = FLIP (Pinv [pivrow]) ;
+ P [kbar] = diagrow ;
+ Pinv [diagrow] = FLIP (kbar) ;
+ }
+ }
+ P [k] = pivrow ;
+ Pinv [pivrow] = k ;
+
+#ifndef NDEBUG
+ for (i = 0 ; i < n ; i++) { ASSERT (IS_ZERO (X [i])) ;}
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ PRINTF (("Column %d of U: %d : ", k, Ui [p])) ;
+ PRINT_ENTRY (Ux [p]) ;
+ }
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ PRINTF (("Column %d of L: %d : ", k, Li [p])) ;
+ PRINT_ENTRY (Lx [p]) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* symmetric pruning */
+ /* ------------------------------------------------------------------ */
+
+ prune (Lpend, Pinv, k, pivrow, LU, Uip, Lip, Ulen, Llen) ;
+
+ *lnz += Llen [k] + 1 ; /* 1 added to lnz for diagonal */
+ *unz += Ulen [k] + 1 ; /* 1 added to unz for diagonal */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize column pointers for L and U, and put L in the pivotal order */
+ /* ---------------------------------------------------------------------- */
+
+ for (p = 0 ; p < n ; p++)
+ {
+ Li = (Int *) (LU + Lip [p]) ;
+ for (i = 0 ; i < Llen [p] ; i++)
+ {
+ Li [i] = Pinv [Li [i]] ;
+ }
+ }
+
+#ifndef NDEBUG
+ for (i = 0 ; i < n ; i++)
+ {
+ PRINTF (("P [%d] = %d Pinv [%d] = %d\n", i, P [i], i, Pinv [i])) ;
+ }
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSERT (Pinv [i] >= 0 && Pinv [i] < n) ;
+ ASSERT (P [i] >= 0 && P [i] < n) ;
+ ASSERT (P [Pinv [i]] == i) ;
+ ASSERT (IS_ZERO (X [i])) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* shrink the LU factors to just the required size */
+ /* ---------------------------------------------------------------------- */
+
+ newlusize = lup ;
+ ASSERT ((size_t) newlusize <= lusize) ;
+
+ /* this cannot fail, since the block is descreasing in size */
+ LU = KLU_realloc (newlusize, lusize, sizeof (Unit), LU, Common) ;
+ *p_LU = LU ;
+ return (newlusize) ;
+}
diff --git a/KLU/Source/klu_memory.c b/KLU/Source/klu_memory.c
new file mode 100644
index 0000000..a4fa3b8
--- /dev/null
+++ b/KLU/Source/klu_memory.c
@@ -0,0 +1,225 @@
+/* ========================================================================== */
+/* === KLU_memory =========================================================== */
+/* ========================================================================== */
+
+/* KLU memory management routines:
+ *
+ * KLU_malloc malloc wrapper
+ * KLU_free free wrapper
+ * KLU_realloc realloc wrapper
+ */
+
+#include "klu_internal.h"
+
+/* ========================================================================== */
+/* === KLU_add_size_t ======================================================= */
+/* ========================================================================== */
+
+/* Safely compute a+b, and check for size_t overflow */
+
+size_t KLU_add_size_t (size_t a, size_t b, Int *ok)
+{
+ (*ok) = (*ok) && ((a + b) >= MAX (a,b)) ;
+ return ((*ok) ? (a + b) : ((size_t) -1)) ;
+}
+
+/* ========================================================================== */
+/* === KLU_mult_size_t ====================================================== */
+/* ========================================================================== */
+
+/* Safely compute a*k, where k should be small, and check for size_t overflow */
+
+size_t KLU_mult_size_t (size_t a, size_t k, Int *ok)
+{
+ size_t i, s = 0 ;
+ for (i = 0 ; i < k ; i++)
+ {
+ s = KLU_add_size_t (s, a, ok) ;
+ }
+ return ((*ok) ? s : ((size_t) -1)) ;
+}
+
+/* ========================================================================== */
+/* === KLU_malloc =========================================================== */
+/* ========================================================================== */
+
+/* Wrapper around malloc routine (mxMalloc for a mexFunction). Allocates
+ * space of size MAX(1,n)*size, where size is normally a sizeof (...).
+ *
+ * This routine and KLU_realloc do not set Common->status to KLU_OK on success,
+ * so that a sequence of KLU_malloc's or KLU_realloc's can be used. If any of
+ * them fails, the Common->status will hold the most recent error status.
+ *
+ * Usage, for a pointer to Int:
+ *
+ * p = KLU_malloc (n, sizeof (Int), Common)
+ *
+ * Uses a pointer to the malloc routine (or its equivalent) defined in Common.
+ */
+
+void *KLU_malloc /* returns pointer to the newly malloc'd block */
+(
+ /* ---- input ---- */
+ size_t n, /* number of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ KLU_common *Common
+)
+{
+ void *p ;
+ size_t s ;
+ Int ok = TRUE ;
+
+ if (Common == NULL)
+ {
+ p = NULL ;
+ }
+ else if (size == 0)
+ {
+ /* size must be > 0 */
+ Common->status = KLU_INVALID ;
+ p = NULL ;
+ }
+ else if (n >= INT_MAX)
+ {
+ /* object is too big to allocate; p[i] where i is an Int will not
+ * be enough. */
+ Common->status = KLU_TOO_LARGE ;
+ p = NULL ;
+ }
+ else
+ {
+ /* call malloc, or its equivalent */
+ s = KLU_mult_size_t (MAX (1,n), size, &ok) ;
+ p = ok ? ((Common->malloc_memory) (s)) : NULL ;
+ if (p == NULL)
+ {
+ /* failure: out of memory */
+ Common->status = KLU_OUT_OF_MEMORY ;
+ }
+ else
+ {
+ Common->memusage += s ;
+ Common->mempeak = MAX (Common->mempeak, Common->memusage) ;
+ }
+ }
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === KLU_free ============================================================= */
+/* ========================================================================== */
+
+/* Wrapper around free routine (mxFree for a mexFunction). Returns NULL,
+ * which can be assigned to the pointer being freed, as in:
+ *
+ * p = KLU_free (p, n, sizeof (int), Common) ;
+ */
+
+void *KLU_free /* always returns NULL */
+(
+ /* ---- in/out --- */
+ void *p, /* block of memory to free */
+ /* ---- input --- */
+ size_t n, /* size of block to free, in # of items */
+ size_t size, /* size of each item */
+ /* --------------- */
+ KLU_common *Common
+)
+{
+ size_t s ;
+ Int ok = TRUE ;
+ if (p != NULL && Common != NULL)
+ {
+ /* only free the object if the pointer is not NULL */
+ /* call free, or its equivalent */
+ (Common->free_memory) (p) ;
+ s = KLU_mult_size_t (MAX (1,n), size, &ok) ;
+ Common->memusage -= s ;
+ }
+ /* return NULL, and the caller should assign this to p. This avoids
+ * freeing the same pointer twice. */
+ return (NULL) ;
+}
+
+
+/* ========================================================================== */
+/* === KLU_realloc ========================================================== */
+/* ========================================================================== */
+
+/* Wrapper around realloc routine (mxRealloc for a mexFunction). Given a
+ * pointer p to a block allocated by KLU_malloc, it changes the size of the
+ * block pointed to by p to be MAX(1,nnew)*size in size. It may return a
+ * pointer different than p. This should be used as (for a pointer to Int):
+ *
+ * p = KLU_realloc (nnew, nold, sizeof (Int), p, Common) ;
+ *
+ * If p is NULL, this is the same as p = KLU_malloc (...).
+ * A size of nnew=0 is treated as nnew=1.
+ *
+ * If the realloc fails, p is returned unchanged and Common->status is set
+ * to KLU_OUT_OF_MEMORY. If successful, Common->status is not modified,
+ * and p is returned (possibly changed) and pointing to a large block of memory.
+ *
+ * Uses a pointer to the realloc routine (or its equivalent) defined in Common.
+ */
+
+void *KLU_realloc /* returns pointer to reallocated block */
+(
+ /* ---- input ---- */
+ size_t nnew, /* requested # of items in reallocated block */
+ size_t nold, /* old # of items */
+ size_t size, /* size of each item */
+ /* ---- in/out --- */
+ void *p, /* block of memory to realloc */
+ /* --------------- */
+ KLU_common *Common
+)
+{
+ void *pnew ;
+ size_t snew, sold ;
+ Int ok = TRUE ;
+
+ if (Common == NULL)
+ {
+ p = NULL ;
+ }
+ else if (size == 0)
+ {
+ /* size must be > 0 */
+ Common->status = KLU_INVALID ;
+ p = NULL ;
+ }
+ else if (p == NULL)
+ {
+ /* A fresh object is being allocated. */
+ p = KLU_malloc (nnew, size, Common) ;
+ }
+ else if (nnew >= INT_MAX)
+ {
+ /* failure: nnew is too big. Do not change p */
+ Common->status = KLU_TOO_LARGE ;
+ }
+ else
+ {
+ /* The object exists, and is changing to some other nonzero size. */
+ /* call realloc, or its equivalent */
+ snew = KLU_mult_size_t (MAX (1,nnew), size, &ok) ;
+ sold = KLU_mult_size_t (MAX (1,nold), size, &ok) ;
+ pnew = ok ? ((Common->realloc_memory) (p, snew)) : NULL ;
+ if (pnew == NULL)
+ {
+ /* Do not change p, since it still points to allocated memory */
+ Common->status = KLU_OUT_OF_MEMORY ;
+ }
+ else
+ {
+ /* success: return the new p and change the size of the block */
+ Common->memusage += (snew - sold) ;
+ Common->mempeak = MAX (Common->mempeak, Common->memusage) ;
+ p = pnew ;
+ }
+ }
+ return (p) ;
+}
diff --git a/KLU/Source/klu_refactor.c b/KLU/Source/klu_refactor.c
new file mode 100644
index 0000000..1415788
--- /dev/null
+++ b/KLU/Source/klu_refactor.c
@@ -0,0 +1,478 @@
+/* ========================================================================== */
+/* === KLU_refactor ========================================================= */
+/* ========================================================================== */
+
+/* Factor the matrix, after ordering and analyzing it with KLU_analyze, and
+ * factoring it once with KLU_factor. This routine cannot do any numerical
+ * pivoting. The pattern of the input matrix (Ap, Ai) must be identical to
+ * the pattern given to KLU_factor.
+ */
+
+#include "klu_internal.h"
+
+
+/* ========================================================================== */
+/* === KLU_refactor ========================================================= */
+/* ========================================================================== */
+
+Int KLU_refactor /* returns TRUE if successful, FALSE otherwise */
+(
+ /* inputs, not modified */
+ Int Ap [ ], /* size n+1, column pointers */
+ Int Ai [ ], /* size nz, row indices */
+ double Ax [ ],
+ KLU_symbolic *Symbolic,
+
+ /* input/output */
+ KLU_numeric *Numeric,
+ KLU_common *Common
+)
+{
+ Entry ukk, ujk, s ;
+ Entry *Offx, *Lx, *Ux, *X, *Az, *Udiag ;
+ double *Rs ;
+ Int *P, *Q, *R, *Pnum, *Offp, *Offi, *Ui, *Li, *Pinv, *Lip, *Uip, *Llen,
+ *Ulen ;
+ Unit **LUbx ;
+ Unit *LU ;
+ Int k1, k2, nk, k, block, oldcol, pend, oldrow, n, p, newrow, scale,
+ nblocks, poff, i, j, up, ulen, llen, maxblock, nzoff ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+ Common->status = KLU_OK ;
+
+ if (Numeric == NULL)
+ {
+ /* invalid Numeric object */
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+
+ Common->numerical_rank = EMPTY ;
+ Common->singular_col = EMPTY ;
+
+ Az = (Entry *) Ax ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the contents of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ n = Symbolic->n ;
+ P = Symbolic->P ;
+ Q = Symbolic->Q ;
+ R = Symbolic->R ;
+ nblocks = Symbolic->nblocks ;
+ maxblock = Symbolic->maxblock ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the contents of the Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ Pnum = Numeric->Pnum ;
+ Offp = Numeric->Offp ;
+ Offi = Numeric->Offi ;
+ Offx = (Entry *) Numeric->Offx ;
+
+ LUbx = (Unit **) Numeric->LUbx ;
+
+ scale = Common->scale ;
+ if (scale > 0)
+ {
+ /* factorization was not scaled, but refactorization is scaled */
+ if (Numeric->Rs == NULL)
+ {
+ Numeric->Rs = KLU_malloc (n, sizeof (double), Common) ;
+ if (Common->status < KLU_OK)
+ {
+ Common->status = KLU_OUT_OF_MEMORY ;
+ return (FALSE) ;
+ }
+ }
+ }
+ else
+ {
+ /* no scaling for refactorization; ensure Numeric->Rs is freed. This
+ * does nothing if Numeric->Rs is already NULL. */
+ Numeric->Rs = KLU_free (Numeric->Rs, n, sizeof (double), Common) ;
+ }
+ Rs = Numeric->Rs ;
+
+ Pinv = Numeric->Pinv ;
+ X = (Entry *) Numeric->Xwork ;
+ Common->nrealloc = 0 ;
+ Udiag = Numeric->Udiag ;
+ nzoff = Symbolic->nzoff ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check the input matrix compute the row scale factors, Rs */
+ /* ---------------------------------------------------------------------- */
+
+ /* do no scale, or check the input matrix, if scale < 0 */
+ if (scale >= 0)
+ {
+ /* check for out-of-range indices, but do not check for duplicates */
+ if (!KLU_scale (scale, n, Ap, Ai, Ax, Rs, NULL, Common))
+ {
+ return (FALSE) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* clear workspace X */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < maxblock ; k++)
+ {
+ /* X [k] = 0 */
+ CLEAR (X [k]) ;
+ }
+
+ poff = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* factor each block */
+ /* ---------------------------------------------------------------------- */
+
+ if (scale <= 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* no scaling */
+ /* ------------------------------------------------------------------ */
+
+ for (block = 0 ; block < nblocks ; block++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* the block is from rows/columns k1 to k2-1 */
+ /* -------------------------------------------------------------- */
+
+ k1 = R [block] ;
+ k2 = R [block+1] ;
+ nk = k2 - k1 ;
+
+ if (nk == 1)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* singleton case */
+ /* ---------------------------------------------------------- */
+
+ oldcol = Q [k1] ;
+ pend = Ap [oldcol+1] ;
+ CLEAR (s) ;
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ newrow = Pinv [Ai [p]] - k1 ;
+ if (newrow < 0 && poff < nzoff)
+ {
+ /* entry in off-diagonal block */
+ Offx [poff] = Az [p] ;
+ poff++ ;
+ }
+ else
+ {
+ /* singleton */
+ s = Az [p] ;
+ }
+ }
+ Udiag [k1] = s ;
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* construct and factor the kth block */
+ /* ---------------------------------------------------------- */
+
+ Lip = Numeric->Lip + k1 ;
+ Llen = Numeric->Llen + k1 ;
+ Uip = Numeric->Uip + k1 ;
+ Ulen = Numeric->Ulen + k1 ;
+ LU = LUbx [block] ;
+
+ for (k = 0 ; k < nk ; k++)
+ {
+
+ /* ------------------------------------------------------ */
+ /* scatter kth column of the block into workspace X */
+ /* ------------------------------------------------------ */
+
+ oldcol = Q [k+k1] ;
+ pend = Ap [oldcol+1] ;
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ newrow = Pinv [Ai [p]] - k1 ;
+ if (newrow < 0 && poff < nzoff)
+ {
+ /* entry in off-diagonal block */
+ Offx [poff] = Az [p] ;
+ poff++ ;
+ }
+ else
+ {
+ /* (newrow,k) is an entry in the block */
+ X [newrow] = Az [p] ;
+ }
+ }
+
+ /* ------------------------------------------------------ */
+ /* compute kth column of U, and update kth column of A */
+ /* ------------------------------------------------------ */
+
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, ulen) ;
+ for (up = 0 ; up < ulen ; up++)
+ {
+ j = Ui [up] ;
+ ujk = X [j] ;
+ /* X [j] = 0 */
+ CLEAR (X [j]) ;
+ Ux [up] = ujk ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, j, llen) ;
+ for (p = 0 ; p < llen ; p++)
+ {
+ /* X [Li [p]] -= Lx [p] * ujk */
+ MULT_SUB (X [Li [p]], Lx [p], ujk) ;
+ }
+ }
+ /* get the diagonal entry of U */
+ ukk = X [k] ;
+ /* X [k] = 0 */
+ CLEAR (X [k]) ;
+ /* singular case */
+ if (IS_ZERO (ukk))
+ {
+ /* matrix is numerically singular */
+ Common->status = KLU_SINGULAR ;
+ if (Common->numerical_rank == EMPTY)
+ {
+ Common->numerical_rank = k+k1 ;
+ Common->singular_col = Q [k+k1] ;
+ }
+ if (Common->halt_if_singular)
+ {
+ /* do not continue the factorization */
+ return (FALSE) ;
+ }
+ }
+ Udiag [k+k1] = ukk ;
+ /* gather and divide by pivot to get kth column of L */
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, llen) ;
+ for (p = 0 ; p < llen ; p++)
+ {
+ i = Li [p] ;
+ DIV (Lx [p], X [i], ukk) ;
+ CLEAR (X [i]) ;
+ }
+
+ }
+ }
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* scaling */
+ /* ------------------------------------------------------------------ */
+
+ for (block = 0 ; block < nblocks ; block++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* the block is from rows/columns k1 to k2-1 */
+ /* -------------------------------------------------------------- */
+
+ k1 = R [block] ;
+ k2 = R [block+1] ;
+ nk = k2 - k1 ;
+
+ if (nk == 1)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* singleton case */
+ /* ---------------------------------------------------------- */
+
+ oldcol = Q [k1] ;
+ pend = Ap [oldcol+1] ;
+ CLEAR (s) ;
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = Pinv [oldrow] - k1 ;
+ if (newrow < 0 && poff < nzoff)
+ {
+ /* entry in off-diagonal block */
+ /* Offx [poff] = Az [p] / Rs [oldrow] */
+ SCALE_DIV_ASSIGN (Offx [poff], Az [p], Rs [oldrow]) ;
+ poff++ ;
+ }
+ else
+ {
+ /* singleton */
+ /* s = Az [p] / Rs [oldrow] */
+ SCALE_DIV_ASSIGN (s, Az [p], Rs [oldrow]) ;
+ }
+ }
+ Udiag [k1] = s ;
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* construct and factor the kth block */
+ /* ---------------------------------------------------------- */
+
+ Lip = Numeric->Lip + k1 ;
+ Llen = Numeric->Llen + k1 ;
+ Uip = Numeric->Uip + k1 ;
+ Ulen = Numeric->Ulen + k1 ;
+ LU = LUbx [block] ;
+
+ for (k = 0 ; k < nk ; k++)
+ {
+
+ /* ------------------------------------------------------ */
+ /* scatter kth column of the block into workspace X */
+ /* ------------------------------------------------------ */
+
+ oldcol = Q [k+k1] ;
+ pend = Ap [oldcol+1] ;
+ for (p = Ap [oldcol] ; p < pend ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = Pinv [oldrow] - k1 ;
+ if (newrow < 0 && poff < nzoff)
+ {
+ /* entry in off-diagonal part */
+ /* Offx [poff] = Az [p] / Rs [oldrow] */
+ SCALE_DIV_ASSIGN (Offx [poff], Az [p], Rs [oldrow]);
+ poff++ ;
+ }
+ else
+ {
+ /* (newrow,k) is an entry in the block */
+ /* X [newrow] = Az [p] / Rs [oldrow] */
+ SCALE_DIV_ASSIGN (X [newrow], Az [p], Rs [oldrow]) ;
+ }
+ }
+
+ /* ------------------------------------------------------ */
+ /* compute kth column of U, and update kth column of A */
+ /* ------------------------------------------------------ */
+
+ GET_POINTER (LU, Uip, Ulen, Ui, Ux, k, ulen) ;
+ for (up = 0 ; up < ulen ; up++)
+ {
+ j = Ui [up] ;
+ ujk = X [j] ;
+ /* X [j] = 0 */
+ CLEAR (X [j]) ;
+ Ux [up] = ujk ;
+ GET_POINTER (LU, Lip, Llen, Li, Lx, j, llen) ;
+ for (p = 0 ; p < llen ; p++)
+ {
+ /* X [Li [p]] -= Lx [p] * ujk */
+ MULT_SUB (X [Li [p]], Lx [p], ujk) ;
+ }
+ }
+ /* get the diagonal entry of U */
+ ukk = X [k] ;
+ /* X [k] = 0 */
+ CLEAR (X [k]) ;
+ /* singular case */
+ if (IS_ZERO (ukk))
+ {
+ /* matrix is numerically singular */
+ Common->status = KLU_SINGULAR ;
+ if (Common->numerical_rank == EMPTY)
+ {
+ Common->numerical_rank = k+k1 ;
+ Common->singular_col = Q [k+k1] ;
+ }
+ if (Common->halt_if_singular)
+ {
+ /* do not continue the factorization */
+ return (FALSE) ;
+ }
+ }
+ Udiag [k+k1] = ukk ;
+ /* gather and divide by pivot to get kth column of L */
+ GET_POINTER (LU, Lip, Llen, Li, Lx, k, llen) ;
+ for (p = 0 ; p < llen ; p++)
+ {
+ i = Li [p] ;
+ DIV (Lx [p], X [i], ukk) ;
+ CLEAR (X [i]) ;
+ }
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* permute scale factors Rs according to pivotal row order */
+ /* ---------------------------------------------------------------------- */
+
+ if (scale > 0)
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ REAL (X [k]) = Rs [Pnum [k]] ;
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ Rs [k] = REAL (X [k]) ;
+ }
+ }
+
+#ifndef NDEBUG
+ ASSERT (Offp [n] == poff) ;
+ ASSERT (Symbolic->nzoff == poff) ;
+ PRINTF (("\n------------------- Off diagonal entries, new:\n")) ;
+ ASSERT (KLU_valid (n, Offp, Offi, Offx)) ;
+ if (Common->status == KLU_OK)
+ {
+ PRINTF (("\n ########### KLU_BTF_REFACTOR done, nblocks %d\n",nblocks));
+ for (block = 0 ; block < nblocks ; block++)
+ {
+ k1 = R [block] ;
+ k2 = R [block+1] ;
+ nk = k2 - k1 ;
+ PRINTF ((
+ "\n================KLU_refactor output: k1 %d k2 %d nk %d\n",
+ k1, k2, nk)) ;
+ if (nk == 1)
+ {
+ PRINTF (("singleton ")) ;
+ PRINT_ENTRY (Udiag [k1]) ;
+ }
+ else
+ {
+ Lip = Numeric->Lip + k1 ;
+ Llen = Numeric->Llen + k1 ;
+ LU = (Unit *) Numeric->LUbx [block] ;
+ PRINTF (("\n---- L block %d\n", block)) ;
+ ASSERT (KLU_valid_LU (nk, TRUE, Lip, Llen, LU)) ;
+ Uip = Numeric->Uip + k1 ;
+ Ulen = Numeric->Ulen + k1 ;
+ PRINTF (("\n---- U block %d\n", block)) ;
+ ASSERT (KLU_valid_LU (nk, FALSE, Uip, Ulen, LU)) ;
+ }
+ }
+ }
+#endif
+
+ return (TRUE) ;
+}
diff --git a/KLU/Source/klu_scale.c b/KLU/Source/klu_scale.c
new file mode 100644
index 0000000..8a65ce0
--- /dev/null
+++ b/KLU/Source/klu_scale.c
@@ -0,0 +1,159 @@
+/* ========================================================================== */
+/* === KLU_scale ============================================================ */
+/* ========================================================================== */
+
+/* Scale a matrix and check to see if it is valid. Can be called by the user.
+ * This is called by KLU_factor and KLU_refactor. Returns TRUE if the input
+ * matrix is valid, FALSE otherwise. If the W input argument is non-NULL,
+ * then the input matrix is checked for duplicate entries.
+ *
+ * scaling methods:
+ * <0: no scaling, do not compute Rs, and do not check input matrix.
+ * 0: no scaling
+ * 1: the scale factor for row i is sum (abs (A (i,:)))
+ * 2 or more: the scale factor for row i is max (abs (A (i,:)))
+ */
+
+#include "klu_internal.h"
+
+Int KLU_scale /* return TRUE if successful, FALSE otherwise */
+(
+ /* inputs, not modified */
+ Int scale, /* 0: none, 1: sum, 2: max */
+ Int n,
+ Int Ap [ ], /* size n+1, column pointers */
+ Int Ai [ ], /* size nz, row indices */
+ double Ax [ ],
+ /* outputs, not defined on input */
+ double Rs [ ], /* size n, can be NULL if scale <= 0 */
+ /* workspace, not defined on input or output */
+ Int W [ ], /* size n, can be NULL */
+ /* --------------- */
+ KLU_common *Common
+)
+{
+ double a ;
+ Entry *Az ;
+ Int row, col, p, pend, check_duplicates ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+ Common->status = KLU_OK ;
+
+ if (scale < 0)
+ {
+ /* return without checking anything and without computing the
+ * scale factors */
+ return (TRUE) ;
+ }
+
+ Az = (Entry *) Ax ;
+
+ if (n <= 0 || Ap == NULL || Ai == NULL || Az == NULL ||
+ (scale > 0 && Rs == NULL))
+ {
+ /* Ap, Ai, Ax and Rs must be present, and n must be > 0 */
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+ if (Ap [0] != 0 || Ap [n] < 0)
+ {
+ /* nz = Ap [n] must be >= 0 and Ap [0] must equal zero */
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+ for (col = 0 ; col < n ; col++)
+ {
+ if (Ap [col] > Ap [col+1])
+ {
+ /* column pointers must be non-decreasing */
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* scale */
+ /* ---------------------------------------------------------------------- */
+
+ if (scale > 0)
+ {
+ /* initialize row sum or row max */
+ for (row = 0 ; row < n ; row++)
+ {
+ Rs [row] = 0 ;
+ }
+ }
+
+ /* check for duplicates only if W is present */
+ check_duplicates = (W != (Int *) NULL) ;
+ if (check_duplicates)
+ {
+ for (row = 0 ; row < n ; row++)
+ {
+ W [row] = EMPTY ;
+ }
+ }
+
+ for (col = 0 ; col < n ; col++)
+ {
+ pend = Ap [col+1] ;
+ for (p = Ap [col] ; p < pend ; p++)
+ {
+ row = Ai [p] ;
+ if (row < 0 || row >= n)
+ {
+ /* row index out of range, or duplicate entry */
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+ if (check_duplicates)
+ {
+ if (W [row] == col)
+ {
+ /* duplicate entry */
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+ /* flag row i as appearing in column col */
+ W [row] = col ;
+ }
+ /* a = ABS (Az [p]) ;*/
+ ABS (a, Az [p]) ;
+ if (scale == 1)
+ {
+ /* accumulate the abs. row sum */
+ Rs [row] += a ;
+ }
+ else if (scale > 1)
+ {
+ /* find the max abs. value in the row */
+ Rs [row] = MAX (Rs [row], a) ;
+ }
+ }
+ }
+
+ if (scale > 0)
+ {
+ /* do not scale empty rows */
+ for (row = 0 ; row < n ; row++)
+ {
+ /* matrix is singular */
+ PRINTF (("Rs [%d] = %g\n", row, Rs [row])) ;
+
+ if (Rs [row] == 0.0)
+ {
+ PRINTF (("Row %d of A is all zero\n", row)) ;
+ Rs [row] = 1.0 ;
+ }
+ }
+ }
+
+ return (TRUE) ;
+}
diff --git a/KLU/Source/klu_solve.c b/KLU/Source/klu_solve.c
new file mode 100644
index 0000000..d725152
--- /dev/null
+++ b/KLU/Source/klu_solve.c
@@ -0,0 +1,396 @@
+/* ========================================================================== */
+/* === KLU_solve ============================================================ */
+/* ========================================================================== */
+
+/* Solve Ax=b using the symbolic and numeric objects from KLU_analyze
+ * (or KLU_analyze_given) and KLU_factor. Note that no iterative refinement is
+ * performed. Uses Numeric->Xwork as workspace (undefined on input and output),
+ * of size 4n Entry's (note that columns 2 to 4 of Xwork overlap with
+ * Numeric->Iwork).
+ */
+
+#include "klu_internal.h"
+
+Int KLU_solve
+(
+ /* inputs, not modified */
+ KLU_symbolic *Symbolic,
+ KLU_numeric *Numeric,
+ Int d, /* leading dimension of B */
+ Int nrhs, /* number of right-hand-sides */
+
+ /* right-hand-side on input, overwritten with solution to Ax=b on output */
+ double B [ ], /* size n*nrhs, in column-oriented form, with
+ * leading dimension d. */
+ /* --------------- */
+ KLU_common *Common
+)
+{
+ Entry x [4], offik, s ;
+ double rs, *Rs ;
+ Entry *Offx, *X, *Bz, *Udiag ;
+ Int *Q, *R, *Pnum, *Offp, *Offi, *Lip, *Uip, *Llen, *Ulen ;
+ Unit **LUbx ;
+ Int k1, k2, nk, k, block, pend, n, p, nblocks, chunk, nr, i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+ if (Numeric == NULL || Symbolic == NULL || d < Symbolic->n || nrhs < 0 ||
+ B == NULL)
+ {
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+ Common->status = KLU_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the contents of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ Bz = (Entry *) B ;
+ n = Symbolic->n ;
+ nblocks = Symbolic->nblocks ;
+ Q = Symbolic->Q ;
+ R = Symbolic->R ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the contents of the Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (nblocks == Numeric->nblocks) ;
+ Pnum = Numeric->Pnum ;
+ Offp = Numeric->Offp ;
+ Offi = Numeric->Offi ;
+ Offx = (Entry *) Numeric->Offx ;
+
+ Lip = Numeric->Lip ;
+ Llen = Numeric->Llen ;
+ Uip = Numeric->Uip ;
+ Ulen = Numeric->Ulen ;
+ LUbx = (Unit **) Numeric->LUbx ;
+ Udiag = Numeric->Udiag ;
+
+ Rs = Numeric->Rs ;
+ X = (Entry *) Numeric->Xwork ;
+
+ ASSERT (KLU_valid (n, Offp, Offi, Offx)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve in chunks of 4 columns at a time */
+ /* ---------------------------------------------------------------------- */
+
+ for (chunk = 0 ; chunk < nrhs ; chunk += 4)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the size of the current chunk */
+ /* ------------------------------------------------------------------ */
+
+ nr = MIN (nrhs - chunk, 4) ;
+
+ /* ------------------------------------------------------------------ */
+ /* scale and permute the right hand side, X = P*(R\B) */
+ /* ------------------------------------------------------------------ */
+
+ if (Rs == NULL)
+ {
+
+ /* no scaling */
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ X [k] = Bz [Pnum [k]] ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ X [2*k ] = Bz [i ] ;
+ X [2*k + 1] = Bz [i + d ] ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ X [3*k ] = Bz [i ] ;
+ X [3*k + 1] = Bz [i + d ] ;
+ X [3*k + 2] = Bz [i + d*2] ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ X [4*k ] = Bz [i ] ;
+ X [4*k + 1] = Bz [i + d ] ;
+ X [4*k + 2] = Bz [i + d*2] ;
+ X [4*k + 3] = Bz [i + d*3] ;
+ }
+ break ;
+ }
+
+ }
+ else
+ {
+
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ SCALE_DIV_ASSIGN (X [k], Bz [Pnum [k]], Rs [k]) ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ rs = Rs [k] ;
+ SCALE_DIV_ASSIGN (X [2*k], Bz [i], rs) ;
+ SCALE_DIV_ASSIGN (X [2*k + 1], Bz [i + d], rs) ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ rs = Rs [k] ;
+ SCALE_DIV_ASSIGN (X [3*k], Bz [i], rs) ;
+ SCALE_DIV_ASSIGN (X [3*k + 1], Bz [i + d], rs) ;
+ SCALE_DIV_ASSIGN (X [3*k + 2], Bz [i + d*2], rs) ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ rs = Rs [k] ;
+ SCALE_DIV_ASSIGN (X [4*k], Bz [i], rs) ;
+ SCALE_DIV_ASSIGN (X [4*k + 1], Bz [i + d], rs) ;
+ SCALE_DIV_ASSIGN (X [4*k + 2], Bz [i + d*2], rs) ;
+ SCALE_DIV_ASSIGN (X [4*k + 3], Bz [i + d*3], rs) ;
+ }
+ break ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* solve X = (L*U + Off)\X */
+ /* ------------------------------------------------------------------ */
+
+ for (block = nblocks-1 ; block >= 0 ; block--)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* the block of size nk is from rows/columns k1 to k2-1 */
+ /* -------------------------------------------------------------- */
+
+ k1 = R [block] ;
+ k2 = R [block+1] ;
+ nk = k2 - k1 ;
+ PRINTF (("solve %d, k1 %d k2-1 %d nk %d\n", block, k1,k2-1,nk)) ;
+
+ /* solve the block system */
+ if (nk == 1)
+ {
+ s = Udiag [k1] ;
+ switch (nr)
+ {
+
+ case 1:
+ DIV (X [k1], X [k1], s) ;
+ break ;
+
+ case 2:
+ DIV (X [2*k1], X [2*k1], s) ;
+ DIV (X [2*k1 + 1], X [2*k1 + 1], s) ;
+ break ;
+
+ case 3:
+ DIV (X [3*k1], X [3*k1], s) ;
+ DIV (X [3*k1 + 1], X [3*k1 + 1], s) ;
+ DIV (X [3*k1 + 2], X [3*k1 + 2], s) ;
+ break ;
+
+ case 4:
+ DIV (X [4*k1], X [4*k1], s) ;
+ DIV (X [4*k1 + 1], X [4*k1 + 1], s) ;
+ DIV (X [4*k1 + 2], X [4*k1 + 2], s) ;
+ DIV (X [4*k1 + 3], X [4*k1 + 3], s) ;
+ break ;
+
+ }
+ }
+ else
+ {
+ KLU_lsolve (nk, Lip + k1, Llen + k1, LUbx [block], nr,
+ X + nr*k1) ;
+ KLU_usolve (nk, Uip + k1, Ulen + k1, LUbx [block],
+ Udiag + k1, nr, X + nr*k1) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* block back-substitution for the off-diagonal-block entries */
+ /* -------------------------------------------------------------- */
+
+ if (block > 0)
+ {
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = X [k] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ MULT_SUB (X [Offi [p]], Offx [p], x [0]) ;
+ }
+ }
+ break ;
+
+ case 2:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = X [2*k ] ;
+ x [1] = X [2*k + 1] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+ offik = Offx [p] ;
+ MULT_SUB (X [2*i], offik, x [0]) ;
+ MULT_SUB (X [2*i + 1], offik, x [1]) ;
+ }
+ }
+ break ;
+
+ case 3:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = X [3*k ] ;
+ x [1] = X [3*k + 1] ;
+ x [2] = X [3*k + 2] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+ offik = Offx [p] ;
+ MULT_SUB (X [3*i], offik, x [0]) ;
+ MULT_SUB (X [3*i + 1], offik, x [1]) ;
+ MULT_SUB (X [3*i + 2], offik, x [2]) ;
+ }
+ }
+ break ;
+
+ case 4:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = X [4*k ] ;
+ x [1] = X [4*k + 1] ;
+ x [2] = X [4*k + 2] ;
+ x [3] = X [4*k + 3] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+ offik = Offx [p] ;
+ MULT_SUB (X [4*i], offik, x [0]) ;
+ MULT_SUB (X [4*i + 1], offik, x [1]) ;
+ MULT_SUB (X [4*i + 2], offik, x [2]) ;
+ MULT_SUB (X [4*i + 3], offik, x [3]) ;
+ }
+ }
+ break ;
+ }
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* permute the result, Bz = Q*X */
+ /* ------------------------------------------------------------------ */
+
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Bz [Q [k]] = X [k] ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q [k] ;
+ Bz [i ] = X [2*k ] ;
+ Bz [i + d ] = X [2*k + 1] ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q [k] ;
+ Bz [i ] = X [3*k ] ;
+ Bz [i + d ] = X [3*k + 1] ;
+ Bz [i + d*2] = X [3*k + 2] ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q [k] ;
+ Bz [i ] = X [4*k ] ;
+ Bz [i + d ] = X [4*k + 1] ;
+ Bz [i + d*2] = X [4*k + 2] ;
+ Bz [i + d*3] = X [4*k + 3] ;
+ }
+ break ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* go to the next chunk of B */
+ /* ------------------------------------------------------------------ */
+
+ Bz += d*4 ;
+ }
+ return (TRUE) ;
+}
diff --git a/KLU/Source/klu_sort.c b/KLU/Source/klu_sort.c
new file mode 100644
index 0000000..5405b4f
--- /dev/null
+++ b/KLU/Source/klu_sort.c
@@ -0,0 +1,156 @@
+/* ========================================================================== */
+/* === KLU_sort ============================================================= */
+/* ========================================================================== */
+
+/* sorts the columns of L and U so that the row indices appear in strictly
+ * increasing order.
+ */
+
+#include "klu_internal.h"
+
+/* ========================================================================== */
+/* === sort ================================================================= */
+/* ========================================================================== */
+
+/* Sort L or U using a double-transpose */
+
+static void sort (Int n, Int *Xip, Int *Xlen, Unit *LU, Int *Tp, Int *Tj,
+ Entry *Tx, Int *W)
+{
+ Int *Xi ;
+ Entry *Xx ;
+ Int p, i, j, len, nz, tp, xlen, pend ;
+
+ ASSERT (KLU_valid_LU (n, FALSE, Xip, Xlen, LU)) ;
+
+ /* count the number of entries in each row of L or U */
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = 0 ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ GET_POINTER (LU, Xip, Xlen, Xi, Xx, j, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ W [Xi [p]]++ ;
+ }
+ }
+
+ /* construct the row pointers for T */
+ nz = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Tp [i] = nz ;
+ nz += W [i] ;
+ }
+ Tp [n] = nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = Tp [i] ;
+ }
+
+ /* transpose the matrix into Tp, Ti, Tx */
+ for (j = 0 ; j < n ; j++)
+ {
+ GET_POINTER (LU, Xip, Xlen, Xi, Xx, j, len) ;
+ for (p = 0 ; p < len ; p++)
+ {
+ tp = W [Xi [p]]++ ;
+ Tj [tp] = j ;
+ Tx [tp] = Xx [p] ;
+ }
+ }
+
+ /* transpose the matrix back into Xip, Xlen, Xi, Xx */
+ for (j = 0 ; j < n ; j++)
+ {
+ W [j] = 0 ;
+ }
+ for (i = 0 ; i < n ; i++)
+ {
+ pend = Tp [i+1] ;
+ for (p = Tp [i] ; p < pend ; p++)
+ {
+ j = Tj [p] ;
+ GET_POINTER (LU, Xip, Xlen, Xi, Xx, j, len) ;
+ xlen = W [j]++ ;
+ Xi [xlen] = i ;
+ Xx [xlen] = Tx [p] ;
+ }
+ }
+
+ ASSERT (KLU_valid_LU (n, FALSE, Xip, Xlen, LU)) ;
+}
+
+
+/* ========================================================================== */
+/* === KLU_sort ============================================================= */
+/* ========================================================================== */
+
+Int KLU_sort
+(
+ KLU_symbolic *Symbolic,
+ KLU_numeric *Numeric,
+ KLU_common *Common
+)
+{
+ Int *R, *W, *Tp, *Ti, *Lip, *Uip, *Llen, *Ulen ;
+ Entry *Tx ;
+ Unit **LUbx ;
+ Int n, nk, nz, block, nblocks, maxblock, k1 ;
+ size_t m1 ;
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+ Common->status = KLU_OK ;
+
+ n = Symbolic->n ;
+ R = Symbolic->R ;
+ nblocks = Symbolic->nblocks ;
+ maxblock = Symbolic->maxblock ;
+
+ Lip = Numeric->Lip ;
+ Llen = Numeric->Llen ;
+ Uip = Numeric->Uip ;
+ Ulen = Numeric->Ulen ;
+ LUbx = (Unit **) Numeric->LUbx ;
+
+ m1 = ((size_t) maxblock) + 1 ;
+
+ /* allocate workspace */
+ nz = MAX (Numeric->max_lnz_block, Numeric->max_unz_block) ;
+ W = KLU_malloc (maxblock, sizeof (Int), Common) ;
+ Tp = KLU_malloc (m1, sizeof (Int), Common) ;
+ Ti = KLU_malloc (nz, sizeof (Int), Common) ;
+ Tx = KLU_malloc (nz, sizeof (Entry), Common) ;
+
+ PRINTF (("\n======================= Start sort:\n")) ;
+
+ if (Common->status == KLU_OK)
+ {
+ /* sort each block of L and U */
+ for (block = 0 ; block < nblocks ; block++)
+ {
+ k1 = R [block] ;
+ nk = R [block+1] - k1 ;
+ if (nk > 1)
+ {
+ PRINTF (("\n-------------------block: %d nk %d\n", block, nk)) ;
+ sort (nk, Lip + k1, Llen + k1, LUbx [block], Tp, Ti, Tx, W) ;
+ sort (nk, Uip + k1, Ulen + k1, LUbx [block], Tp, Ti, Tx, W) ;
+ }
+ }
+ }
+
+ PRINTF (("\n======================= sort done.\n")) ;
+
+ /* free workspace */
+ KLU_free (W, maxblock, sizeof (Int), Common) ;
+ KLU_free (Tp, m1, sizeof (Int), Common) ;
+ KLU_free (Ti, nz, sizeof (Int), Common) ;
+ KLU_free (Tx, nz, sizeof (Entry), Common) ;
+ return (Common->status == KLU_OK) ;
+}
diff --git a/KLU/Source/klu_tsolve.c b/KLU/Source/klu_tsolve.c
new file mode 100644
index 0000000..c06b5b2
--- /dev/null
+++ b/KLU/Source/klu_tsolve.c
@@ -0,0 +1,465 @@
+/* ========================================================================== */
+/* === KLU_tsolve =========================================================== */
+/* ========================================================================== */
+
+/* Solve A'x=b using the symbolic and numeric objects from KLU_analyze
+ * (or KLU_analyze_given) and KLU_factor. Note that no iterative refinement is
+ * performed. Uses Numeric->Xwork as workspace (undefined on input and output),
+ * of size 4n Entry's (note that columns 2 to 4 of Xwork overlap with
+ * Numeric->Iwork).
+ */
+
+#include "klu_internal.h"
+
+Int KLU_tsolve
+(
+ /* inputs, not modified */
+ KLU_symbolic *Symbolic,
+ KLU_numeric *Numeric,
+ Int d, /* leading dimension of B */
+ Int nrhs, /* number of right-hand-sides */
+
+ /* right-hand-side on input, overwritten with solution to Ax=b on output */
+ double B [ ], /* size n*nrhs, in column-oriented form, with
+ * leading dimension d. */
+#ifdef COMPLEX
+ Int conj_solve, /* TRUE for conjugate transpose solve, FALSE for
+ * array transpose solve. Used for the complex
+ * case only. */
+#endif
+ /* --------------- */
+ KLU_common *Common
+)
+{
+ Entry x [4], offik, s ;
+ double rs, *Rs ;
+ Entry *Offx, *X, *Bz, *Udiag ;
+ Int *Q, *R, *Pnum, *Offp, *Offi, *Lip, *Uip, *Llen, *Ulen ;
+ Unit **LUbx ;
+ Int k1, k2, nk, k, block, pend, n, p, nblocks, chunk, nr, i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (Common == NULL)
+ {
+ return (FALSE) ;
+ }
+ if (Numeric == NULL || Symbolic == NULL || d < Symbolic->n || nrhs < 0 ||
+ B == NULL)
+ {
+ Common->status = KLU_INVALID ;
+ return (FALSE) ;
+ }
+ Common->status = KLU_OK ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the contents of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ Bz = (Entry *) B ;
+ n = Symbolic->n ;
+ nblocks = Symbolic->nblocks ;
+ Q = Symbolic->Q ;
+ R = Symbolic->R ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the contents of the Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (nblocks == Numeric->nblocks) ;
+ Pnum = Numeric->Pnum ;
+ Offp = Numeric->Offp ;
+ Offi = Numeric->Offi ;
+ Offx = (Entry *) Numeric->Offx ;
+
+ Lip = Numeric->Lip ;
+ Llen = Numeric->Llen ;
+ Uip = Numeric->Uip ;
+ Ulen = Numeric->Ulen ;
+ LUbx = (Unit **) Numeric->LUbx ;
+ Udiag = Numeric->Udiag ;
+
+ Rs = Numeric->Rs ;
+ X = (Entry *) Numeric->Xwork ;
+ ASSERT (KLU_valid (n, Offp, Offi, Offx)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve in chunks of 4 columns at a time */
+ /* ---------------------------------------------------------------------- */
+
+ for (chunk = 0 ; chunk < nrhs ; chunk += 4)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* get the size of the current chunk */
+ /* ------------------------------------------------------------------ */
+
+ nr = MIN (nrhs - chunk, 4) ;
+
+ /* ------------------------------------------------------------------ */
+ /* permute the right hand side, X = Q'*B */
+ /* ------------------------------------------------------------------ */
+
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ X [k] = Bz [Q [k]] ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q [k] ;
+ X [2*k ] = Bz [i ] ;
+ X [2*k + 1] = Bz [i + d ] ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q [k] ;
+ X [3*k ] = Bz [i ] ;
+ X [3*k + 1] = Bz [i + d ] ;
+ X [3*k + 2] = Bz [i + d*2] ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Q [k] ;
+ X [4*k ] = Bz [i ] ;
+ X [4*k + 1] = Bz [i + d ] ;
+ X [4*k + 2] = Bz [i + d*2] ;
+ X [4*k + 3] = Bz [i + d*3] ;
+ }
+ break ;
+
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* solve X = (L*U + Off)'\X */
+ /* ------------------------------------------------------------------ */
+
+ for (block = 0 ; block < nblocks ; block++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* the block of size nk is from rows/columns k1 to k2-1 */
+ /* -------------------------------------------------------------- */
+
+ k1 = R [block] ;
+ k2 = R [block+1] ;
+ nk = k2 - k1 ;
+ PRINTF (("tsolve %d, k1 %d k2-1 %d nk %d\n", block, k1,k2-1,nk)) ;
+
+ /* -------------------------------------------------------------- */
+ /* block back-substitution for the off-diagonal-block entries */
+ /* -------------------------------------------------------------- */
+
+ if (block > 0)
+ {
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ MULT_SUB_CONJ (X [k], X [Offi [p]],
+ Offx [p]) ;
+ }
+ else
+#endif
+ {
+ MULT_SUB (X [k], Offx [p], X [Offi [p]]) ;
+ }
+ }
+ }
+ break ;
+
+ case 2:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = X [2*k ] ;
+ x [1] = X [2*k + 1] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (offik, Offx [p]) ;
+ }
+ else
+#endif
+ {
+ offik = Offx [p] ;
+ }
+ MULT_SUB (x [0], offik, X [2*i]) ;
+ MULT_SUB (x [1], offik, X [2*i + 1]) ;
+ }
+ X [2*k ] = x [0] ;
+ X [2*k + 1] = x [1] ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = X [3*k ] ;
+ x [1] = X [3*k + 1] ;
+ x [2] = X [3*k + 2] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (offik, Offx [p]) ;
+ }
+ else
+#endif
+ {
+ offik = Offx [p] ;
+ }
+ MULT_SUB (x [0], offik, X [3*i]) ;
+ MULT_SUB (x [1], offik, X [3*i + 1]) ;
+ MULT_SUB (x [2], offik, X [3*i + 2]) ;
+ }
+ X [3*k ] = x [0] ;
+ X [3*k + 1] = x [1] ;
+ X [3*k + 2] = x [2] ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = k1 ; k < k2 ; k++)
+ {
+ pend = Offp [k+1] ;
+ x [0] = X [4*k ] ;
+ x [1] = X [4*k + 1] ;
+ x [2] = X [4*k + 2] ;
+ x [3] = X [4*k + 3] ;
+ for (p = Offp [k] ; p < pend ; p++)
+ {
+ i = Offi [p] ;
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ(offik, Offx [p]) ;
+ }
+ else
+#endif
+ {
+ offik = Offx [p] ;
+ }
+ MULT_SUB (x [0], offik, X [4*i]) ;
+ MULT_SUB (x [1], offik, X [4*i + 1]) ;
+ MULT_SUB (x [2], offik, X [4*i + 2]) ;
+ MULT_SUB (x [3], offik, X [4*i + 3]) ;
+ }
+ X [4*k ] = x [0] ;
+ X [4*k + 1] = x [1] ;
+ X [4*k + 2] = x [2] ;
+ X [4*k + 3] = x [3] ;
+ }
+ break ;
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* solve the block system */
+ /* -------------------------------------------------------------- */
+
+ if (nk == 1)
+ {
+#ifdef COMPLEX
+ if (conj_solve)
+ {
+ CONJ (s, Udiag [k1]) ;
+ }
+ else
+#endif
+ {
+ s = Udiag [k1] ;
+ }
+ switch (nr)
+ {
+
+ case 1:
+ DIV (X [k1], X [k1], s) ;
+ break ;
+
+ case 2:
+ DIV (X [2*k1], X [2*k1], s) ;
+ DIV (X [2*k1 + 1], X [2*k1 + 1], s) ;
+ break ;
+
+ case 3:
+ DIV (X [3*k1], X [3*k1], s) ;
+ DIV (X [3*k1 + 1], X [3*k1 + 1], s) ;
+ DIV (X [3*k1 + 2], X [3*k1 + 2], s) ;
+ break ;
+
+ case 4:
+ DIV (X [4*k1], X [4*k1], s) ;
+ DIV (X [4*k1 + 1], X [4*k1 + 1], s) ;
+ DIV (X [4*k1 + 2], X [4*k1 + 2], s) ;
+ DIV (X [4*k1 + 3], X [4*k1 + 3], s) ;
+ break ;
+
+ }
+ }
+ else
+ {
+ KLU_utsolve (nk, Uip + k1, Ulen + k1, LUbx [block],
+ Udiag + k1, nr,
+#ifdef COMPLEX
+ conj_solve,
+#endif
+ X + nr*k1) ;
+ KLU_ltsolve (nk, Lip + k1, Llen + k1, LUbx [block], nr,
+#ifdef COMPLEX
+ conj_solve,
+#endif
+ X + nr*k1) ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* scale and permute the result, Bz = P'(R\X) */
+ /* ------------------------------------------------------------------ */
+
+ if (Rs == NULL)
+ {
+
+ /* no scaling */
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ Bz [Pnum [k]] = X [k] ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ Bz [i ] = X [2*k ] ;
+ Bz [i + d ] = X [2*k + 1] ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ Bz [i ] = X [3*k ] ;
+ Bz [i + d ] = X [3*k + 1] ;
+ Bz [i + d*2] = X [3*k + 2] ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ Bz [i ] = X [4*k ] ;
+ Bz [i + d ] = X [4*k + 1] ;
+ Bz [i + d*2] = X [4*k + 2] ;
+ Bz [i + d*3] = X [4*k + 3] ;
+ }
+ break ;
+ }
+
+ }
+ else
+ {
+
+ switch (nr)
+ {
+
+ case 1:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ SCALE_DIV_ASSIGN (Bz [Pnum [k]], X [k], Rs [k]) ;
+ }
+ break ;
+
+ case 2:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ rs = Rs [k] ;
+ SCALE_DIV_ASSIGN (Bz [i], X [2*k], rs) ;
+ SCALE_DIV_ASSIGN (Bz [i + d], X [2*k + 1], rs) ;
+ }
+ break ;
+
+ case 3:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ rs = Rs [k] ;
+ SCALE_DIV_ASSIGN (Bz [i], X [3*k], rs) ;
+ SCALE_DIV_ASSIGN (Bz [i + d], X [3*k + 1], rs) ;
+ SCALE_DIV_ASSIGN (Bz [i + d*2], X [3*k + 2], rs) ;
+ }
+ break ;
+
+ case 4:
+
+ for (k = 0 ; k < n ; k++)
+ {
+ i = Pnum [k] ;
+ rs = Rs [k] ;
+ SCALE_DIV_ASSIGN (Bz [i], X [4*k], rs) ;
+ SCALE_DIV_ASSIGN (Bz [i + d], X [4*k + 1], rs) ;
+ SCALE_DIV_ASSIGN (Bz [i + d*2], X [4*k + 2], rs) ;
+ SCALE_DIV_ASSIGN (Bz [i + d*3], X [4*k + 3], rs) ;
+ }
+ break ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* go to the next chunk of B */
+ /* ------------------------------------------------------------------ */
+
+ Bz += d*4 ;
+ }
+ return (TRUE) ;
+}
diff --git a/KLU/Tcov/Makefile b/KLU/Tcov/Makefile
new file mode 100644
index 0000000..a4fc665
--- /dev/null
+++ b/KLU/Tcov/Makefile
@@ -0,0 +1,420 @@
+# If the libraries (AMD, COLAMD, CAMD, CCOLAMD, metis, and CHOLMOD) are not
+# yet built, use "make libs" first. Then "make" to compile and run all tests.
+
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+# CFLAGS = -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \
+# -Wredundant-decls -Wnested-externs -Wdisabled-optimization \
+# -pedantic -ansi -O3 -pg
+
+# for statement coverage, picky tests
+CFLAGS = -Wall -W -Werror -Wshadow -Wmissing-prototypes -Wstrict-prototypes \
+ -Wredundant-decls -Wnested-externs -Wdisabled-optimization \
+ -ansi -g -ftest-coverage -fprofile-arcs -fexceptions
+
+C = $(CC) $(CFLAGS)
+
+LIB = ../../AMD/Lib/libamd.a ../../COLAMD/Lib/libcolamd.a \
+ ../../CHOLMOD/Lib/libcholmod.a \
+ ../../CAMD/Lib/libcamd.a ../../CCOLAMD/Lib/libccolamd.a \
+ ../../metis-4.0/libmetis.a \
+ -lm
+
+I = -I../../UFconfig -I../../AMD/Include -I../../COLAMD/Include \
+ -I../../BTF/Include -I../../CHOLMOD/Include -I../../CAMD/Include \
+ -I../../CCOLAMD/Include -I../../metis-4.0/Lib -I../Include -I../User
+
+PRETTY = grep -v "^\#" | indent -bl -nce -ss -bli0 -i4 -sob
+
+all: purge libs klutest klultest
+ - ./klultests > klultests.out
+ - ./klutests > klutests.out
+ - ./coverage
+
+valgrind: purge klutest klultest
+ - ./vklutests > klutests.out
+ - ./vklultests > klultests.out
+ - ./coverage
+
+libs:
+ ( cd ../../AMD ; $(MAKE) library )
+ ( cd ../../COLAMD ; $(MAKE) library )
+ ( cd ../../CAMD ; $(MAKE) library )
+ ( cd ../../CCOLAMD ; $(MAKE) library )
+ ( cd ../../metis-4.0 ; $(MAKE) )
+ ( cd ../../CHOLMOD ; $(MAKE) library )
+
+purge: distclean
+
+distclean: clean
+ - $(RM) klutest klultest *.c.gcov *.out *.a cov_*.c *.gcda *.gcno
+
+clean:
+ - $(RM) $(CLEAN)
+
+INC = \
+ ../Include/klu.h \
+ ../Include/klu_internal.h \
+ ../Include/klu_version.h
+
+BTFOBJ = \
+ cov_btf_order.o \
+ cov_btf_maxtrans.o \
+ cov_btf_strongcomp.o \
+
+BTFLOBJ = \
+ cov_btf_l_order.o \
+ cov_btf_l_maxtrans.o \
+ cov_btf_l_strongcomp.o
+
+KLUOBJ = \
+ cov_klu_analyze.o \
+ cov_klu_analyze_given.o \
+ cov_klu_defaults.o \
+ cov_klu_free_symbolic.o \
+ cov_klu_memory.o \
+ cov_klu_d.o \
+ cov_klu_d_diagnostics.o \
+ cov_klu_d_dump.o \
+ cov_klu_d_factor.o \
+ cov_klu_d_free_numeric.o \
+ cov_klu_d_kernel.o \
+ cov_klu_d_extract.o \
+ cov_klu_d_refactor.o \
+ cov_klu_d_scale.o \
+ cov_klu_d_solve.o \
+ cov_klu_d_tsolve.o \
+ cov_klu_z.o \
+ cov_klu_z_diagnostics.o \
+ cov_klu_z_dump.o \
+ cov_klu_z_factor.o \
+ cov_klu_z_free_numeric.o \
+ cov_klu_z_kernel.o \
+ cov_klu_z_extract.o \
+ cov_klu_z_refactor.o \
+ cov_klu_z_scale.o \
+ cov_klu_z_solve.o \
+ cov_klu_z_tsolve.o
+
+KLULOBJ = \
+ cov_klu_l_analyze.o \
+ cov_klu_l_analyze_given.o \
+ cov_klu_l_defaults.o \
+ cov_klu_l_free_symbolic.o \
+ cov_klu_l_memory.o \
+ cov_klu_l.o \
+ cov_klu_l_diagnostics.o \
+ cov_klu_l_dump.o \
+ cov_klu_l_factor.o \
+ cov_klu_l_free_numeric.o \
+ cov_klu_l_kernel.o \
+ cov_klu_l_extract.o \
+ cov_klu_l_refactor.o \
+ cov_klu_l_scale.o \
+ cov_klu_l_solve.o \
+ cov_klu_l_tsolve.o \
+ cov_klu_zl.o \
+ cov_klu_zl_diagnostics.o \
+ cov_klu_zl_dump.o \
+ cov_klu_zl_factor.o \
+ cov_klu_zl_free_numeric.o \
+ cov_klu_zl_kernel.o \
+ cov_klu_zl_extract.o \
+ cov_klu_zl_refactor.o \
+ cov_klu_zl_scale.o \
+ cov_klu_zl_solve.o \
+ cov_klu_zl_tsolve.o
+
+KLUCHOLMODOBJ = cov_klu_cholmod.o
+
+KLUCHOLMODLOBJ = cov_klu_l_cholmod.o
+
+OBJ = $(BTFOBJ) $(KLUOBJ) $(KLUCHOLMODOBJ)
+
+LOBJ = $(BTFLOBJ) $(KLULOBJ) $(KLUCHOLMODLOBJ)
+
+$(OBJ): $(INC)
+
+$(LOBJ): $(INC)
+
+klutest: $(OBJ) klutest.c
+ $(C) $(I) klutest.c -o klutest $(OBJ) $(LIB)
+
+klultest: $(LOBJ) klutest.c
+ $(C) -DDLONG $(I) klutest.c -o klultest $(LOBJ) $(LIB)
+
+.c.o:
+ $(C) -c $(I) $*.c
+
+#-------------------------------------------------------------------------------
+
+cov_klu_d.o: ../Source/klu.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d.c
+ $(C) -c $(I) cov_klu_d.c
+
+cov_klu_z.o: ../Source/klu.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z.c
+ $(C) -c $(I) cov_klu_z.c
+
+cov_klu_d_kernel.o: ../Source/klu_kernel.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_kernel.c
+ $(C) -c $(I) cov_klu_d_kernel.c
+
+cov_klu_z_kernel.o: ../Source/klu_kernel.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_kernel.c
+ $(C) -c $(I) cov_klu_z_kernel.c
+
+cov_klu_d_diagnostics.o: ../Source/klu_diagnostics.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_diagnostics.c
+ $(C) -c $(I) cov_klu_d_diagnostics.c
+
+cov_klu_z_diagnostics.o: ../Source/klu_diagnostics.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_diagnostics.c
+ $(C) -c $(I) cov_klu_z_diagnostics.c
+
+cov_klu_d_dump.o: ../Source/klu_dump.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_dump.c
+ $(C) -c $(I) cov_klu_d_dump.c
+
+cov_klu_z_dump.o: ../Source/klu_dump.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_dump.c
+ $(C) -c $(I) cov_klu_z_dump.c
+
+cov_klu_d_factor.o: ../Source/klu_factor.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_factor.c
+ $(C) -c $(I) cov_klu_d_factor.c
+
+cov_klu_z_factor.o: ../Source/klu_factor.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_factor.c
+ $(C) -c $(I) cov_klu_z_factor.c
+
+cov_klu_d_free_numeric.o: ../Source/klu_free_numeric.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_free_numeric.c
+ $(C) -c $(I) cov_klu_d_free_numeric.c
+
+cov_klu_z_free_numeric.o: ../Source/klu_free_numeric.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_free_numeric.c
+ $(C) -c $(I) cov_klu_z_free_numeric.c
+
+cov_klu_d_extract.o: ../Source/klu_extract.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_extract.c
+ $(C) -c $(I) cov_klu_d_extract.c
+
+cov_klu_z_extract.o: ../Source/klu_extract.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_extract.c
+ $(C) -c $(I) cov_klu_z_extract.c
+
+cov_klu_d_refactor.o: ../Source/klu_refactor.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_refactor.c
+ $(C) -c $(I) cov_klu_d_refactor.c
+
+cov_klu_z_refactor.o: ../Source/klu_refactor.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_refactor.c
+ $(C) -c $(I) cov_klu_z_refactor.c
+
+cov_klu_d_scale.o: ../Source/klu_scale.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_scale.c
+ $(C) -c $(I) cov_klu_d_scale.c
+
+cov_klu_z_scale.o: ../Source/klu_scale.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_scale.c
+ $(C) -c $(I) cov_klu_z_scale.c
+
+cov_klu_d_solve.o: ../Source/klu_solve.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_solve.c
+ $(C) -c $(I) cov_klu_d_solve.c
+
+cov_klu_z_solve.o: ../Source/klu_solve.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_solve.c
+ $(C) -c $(I) cov_klu_z_solve.c
+
+cov_klu_d_tsolve.o: ../Source/klu_tsolve.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_d_tsolve.c
+ $(C) -c $(I) cov_klu_d_tsolve.c
+
+cov_klu_z_tsolve.o: ../Source/klu_tsolve.c
+ $(C) -E $(I) -DCOMPLEX $< | $(PRETTY) > cov_klu_z_tsolve.c
+ $(C) -c $(I) cov_klu_z_tsolve.c
+
+#-------------------------------------------------------------------------------
+
+cov_klu_analyze.o: ../Source/klu_analyze.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_analyze.c
+ $(C) -c $(I) cov_klu_analyze.c
+
+cov_klu_analyze_given.o: ../Source/klu_analyze_given.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_analyze_given.c
+ $(C) -c $(I) cov_klu_analyze_given.c
+
+cov_klu_defaults.o: ../Source/klu_defaults.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_defaults.c
+ $(C) -c $(I) cov_klu_defaults.c
+
+cov_klu_free_symbolic.o: ../Source/klu_free_symbolic.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_free_symbolic.c
+ $(C) -c $(I) cov_klu_free_symbolic.c
+
+cov_klu_memory.o: ../Source/klu_memory.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_memory.c
+ $(C) -c $(I) cov_klu_memory.c
+
+#-------------------------------------------------------------------------------
+
+cov_btf_order.o: ../../BTF/Source/btf_order.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_btf_order.c
+ $(C) -c $(I) cov_btf_order.c
+
+cov_btf_maxtrans.o: ../../BTF/Source/btf_maxtrans.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_btf_maxtrans.c
+ $(C) -c $(I) cov_btf_maxtrans.c
+
+cov_btf_strongcomp.o: ../../BTF/Source/btf_strongcomp.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_btf_strongcomp.c
+ $(C) -c $(I) cov_btf_strongcomp.c
+
+#-------------------------------------------------------------------------------
+
+cov_klu_cholmod.o: ../User/klu_cholmod.c
+ $(C) -E $(I) $< | $(PRETTY) > cov_klu_cholmod.c
+ $(C) -c $(I) cov_klu_cholmod.c
+
+
+
+
+
+
+
+#-------------------------------------------------------------------------------
+
+cov_klu_l.o: ../Source/klu.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l.c
+ $(C) -c $(I) cov_klu_l.c
+
+cov_klu_zl.o: ../Source/klu.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl.c
+ $(C) -c $(I) cov_klu_zl.c
+
+cov_klu_l_kernel.o: ../Source/klu_kernel.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_kernel.c
+ $(C) -c $(I) cov_klu_l_kernel.c
+
+cov_klu_zl_kernel.o: ../Source/klu_kernel.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_kernel.c
+ $(C) -c $(I) cov_klu_zl_kernel.c
+
+cov_klu_l_diagnostics.o: ../Source/klu_diagnostics.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_diagnostics.c
+ $(C) -c $(I) cov_klu_l_diagnostics.c
+
+cov_klu_zl_diagnostics.o: ../Source/klu_diagnostics.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_diagnostics.c
+ $(C) -c $(I) cov_klu_zl_diagnostics.c
+
+cov_klu_l_dump.o: ../Source/klu_dump.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_dump.c
+ $(C) -c $(I) cov_klu_l_dump.c
+
+cov_klu_zl_dump.o: ../Source/klu_dump.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_dump.c
+ $(C) -c $(I) cov_klu_zl_dump.c
+
+cov_klu_l_factor.o: ../Source/klu_factor.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_factor.c
+ $(C) -c $(I) cov_klu_l_factor.c
+
+cov_klu_zl_factor.o: ../Source/klu_factor.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_factor.c
+ $(C) -c $(I) cov_klu_zl_factor.c
+
+cov_klu_l_free_numeric.o: ../Source/klu_free_numeric.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_free_numeric.c
+ $(C) -c $(I) cov_klu_l_free_numeric.c
+
+cov_klu_zl_free_numeric.o: ../Source/klu_free_numeric.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_free_numeric.c
+ $(C) -c $(I) cov_klu_zl_free_numeric.c
+
+cov_klu_l_extract.o: ../Source/klu_extract.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_extract.c
+ $(C) -c $(I) cov_klu_l_extract.c
+
+cov_klu_zl_extract.o: ../Source/klu_extract.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_extract.c
+ $(C) -c $(I) cov_klu_zl_extract.c
+
+cov_klu_l_refactor.o: ../Source/klu_refactor.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_refactor.c
+ $(C) -c $(I) cov_klu_l_refactor.c
+
+cov_klu_zl_refactor.o: ../Source/klu_refactor.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_refactor.c
+ $(C) -c $(I) cov_klu_zl_refactor.c
+
+cov_klu_l_scale.o: ../Source/klu_scale.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_scale.c
+ $(C) -c $(I) cov_klu_l_scale.c
+
+cov_klu_zl_scale.o: ../Source/klu_scale.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_scale.c
+ $(C) -c $(I) cov_klu_zl_scale.c
+
+cov_klu_l_solve.o: ../Source/klu_solve.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_solve.c
+ $(C) -c $(I) cov_klu_l_solve.c
+
+cov_klu_zl_solve.o: ../Source/klu_solve.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_solve.c
+ $(C) -c $(I) cov_klu_zl_solve.c
+
+cov_klu_l_tsolve.o: ../Source/klu_tsolve.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_tsolve.c
+ $(C) -c $(I) cov_klu_l_tsolve.c
+
+cov_klu_zl_tsolve.o: ../Source/klu_tsolve.c
+ $(C) -E $(I) -DDLONG -DCOMPLEX $< | $(PRETTY) > cov_klu_zl_tsolve.c
+ $(C) -c $(I) cov_klu_zl_tsolve.c
+
+#-------------------------------------------------------------------------------
+
+cov_klu_l_analyze.o: ../Source/klu_analyze.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_analyze.c
+ $(C) -c $(I) cov_klu_l_analyze.c
+
+cov_klu_l_analyze_given.o: ../Source/klu_analyze_given.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_analyze_given.c
+ $(C) -c $(I) cov_klu_l_analyze_given.c
+
+cov_klu_l_defaults.o: ../Source/klu_defaults.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_defaults.c
+ $(C) -c $(I) cov_klu_l_defaults.c
+
+cov_klu_l_free_symbolic.o: ../Source/klu_free_symbolic.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_free_symbolic.c
+ $(C) -c $(I) cov_klu_l_free_symbolic.c
+
+cov_klu_l_memory.o: ../Source/klu_memory.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_memory.c
+ $(C) -c $(I) cov_klu_l_memory.c
+
+#-------------------------------------------------------------------------------
+
+cov_btf_l_order.o: ../../BTF/Source/btf_order.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_btf_l_order.c
+ $(C) -c $(I) cov_btf_l_order.c
+
+cov_btf_l_maxtrans.o: ../../BTF/Source/btf_maxtrans.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_btf_l_maxtrans.c
+ $(C) -c $(I) cov_btf_l_maxtrans.c
+
+cov_btf_l_strongcomp.o: ../../BTF/Source/btf_strongcomp.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_btf_l_strongcomp.c
+ $(C) -c $(I) cov_btf_l_strongcomp.c
+
+#-------------------------------------------------------------------------------
+
+cov_klu_l_cholmod.o: ../User/klu_l_cholmod.c
+ $(C) -E $(I) -DDLONG $< | $(PRETTY) > cov_klu_l_cholmod.c
+ $(C) -c $(I) cov_klu_l_cholmod.c
+
diff --git a/KLU/Tcov/README.txt b/KLU/Tcov/README.txt
new file mode 100644
index 0000000..8ecec0a
--- /dev/null
+++ b/KLU/Tcov/README.txt
@@ -0,0 +1,5 @@
+Test suite for KLU
+
+To compile and run the test suite, first type "make" in the Linux/Unix shell.
+The libraries must be compiled first (if they aren't use "make libs").
+"make clean" or "make distclean" will remove all unnecessary files.
diff --git a/KLU/Tcov/coverage b/KLU/Tcov/coverage
new file mode 100755
index 0000000..c081588
--- /dev/null
+++ b/KLU/Tcov/coverage
@@ -0,0 +1,4 @@
+#!/bin/csh
+gcov cov*.c >& /dev/null
+echo -n 'statements not covered: '
+grep "#####" *.c.gcov | wc -l
diff --git a/KLU/Tcov/klultests b/KLU/Tcov/klultests
new file mode 100755
index 0000000..98f2734
--- /dev/null
+++ b/KLU/Tcov/klultests
@@ -0,0 +1,31 @@
+#!/bin/csh
+
+# 57 unique statements:
+./klultest < ../Matrix/impcol_a.mtx
+
+# 20:
+./klultest < ../Matrix/GD99_cc.mtx
+
+# 17:
+./klultest < ../Matrix/two.mtx
+
+# 10:
+./klultest < ../Matrix/w156.mtx
+
+# 3, xsize memgrow in klu_kernel
+./klultest < ../Matrix/arrow.mtx
+
+# 3, xsize memgrow in klu_kernel, 1 in klu_z_condest,
+./klultest < ../Matrix/arrowc.mtx
+
+# 2 in klu_z_kernel (if pivot == 0 and halt_if_singular, and in complex divide)
+./klultest < ../Matrix/onec.mtx
+
+# 1 in klu_kernel (if pivot == 0 and halt if singular)
+./klultest < ../Matrix/one.mtx
+
+# 1 in klu_z_condest:
+./klultest < ../Matrix/1c.mtx
+
+# 1 in klu_z_condest:
+./klultest < ../Matrix/ctina.mtx
diff --git a/KLU/Tcov/klutest.c b/KLU/Tcov/klutest.c
new file mode 100644
index 0000000..ea8b491
--- /dev/null
+++ b/KLU/Tcov/klutest.c
@@ -0,0 +1,1377 @@
+/* ========================================================================== */
+/* === KLU test ============================================================= */
+/* ========================================================================== */
+
+/* Exhaustive test for KLU and BTF (int, long, real, and complex versions) */
+
+#include <string.h>
+#include "cholmod.h"
+#include "klu_cholmod.h"
+#include "klu_internal.h"
+
+#define ID Int_id
+
+#define NRHS 6
+
+#define HALT { fprintf (stderr, "Test failure: %d\n", __LINE__) ; abort () ; }
+#define OK(a) { if (!(a)) HALT ; }
+#define FAIL(a) { if (a) HALT ; }
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+
+
+#ifdef DLONG
+
+#define klu_z_scale klu_zl_scale
+#define klu_z_solve klu_zl_solve
+#define klu_z_tsolve klu_zl_tsolve
+#define klu_z_free_numeric klu_zl_free_numeric
+#define klu_z_factor klu_zl_factor
+#define klu_z_refactor klu_zl_refactor
+#define klu_z_lsolve klu_zl_lsolve
+#define klu_z_ltsolve klu_zl_ltsolve
+#define klu_z_usolve klu_zl_usolve
+#define klu_z_utsolve klu_zl_utsolve
+#define klu_z_defaults klu_zl_defaults
+#define klu_z_rgrowth klu_zl_rgrowth
+#define klu_z_rcond klu_zl_rcond
+#define klu_z_extract klu_zl_extract
+#define klu_z_condest klu_zl_condest
+#define klu_z_flops klu_zl_flops
+
+#define klu_scale klu_l_scale
+#define klu_solve klu_l_solve
+#define klu_tsolve klu_l_tsolve
+#define klu_free_numeric klu_l_free_numeric
+#define klu_factor klu_l_factor
+#define klu_refactor klu_l_refactor
+#define klu_lsolve klu_l_lsolve
+#define klu_ltsolve klu_l_ltsolve
+#define klu_usolve klu_l_usolve
+#define klu_utsolve klu_l_utsolve
+#define klu_defaults klu_l_defaults
+#define klu_rgrowth klu_l_rgrowth
+#define klu_rcond klu_l_rcond
+#define klu_extract klu_l_extract
+#define klu_condest klu_l_condest
+#define klu_flops klu_l_flops
+
+#define klu_analyze klu_l_analyze
+#define klu_analyze_given klu_l_analyze_given
+#define klu_malloc klu_l_malloc
+#define klu_free klu_l_free
+#define klu_realloc klu_l_realloc
+#define klu_free_symbolic klu_l_free_symbolic
+#define klu_free_numeric klu_l_free_numeric
+#define klu_defaults klu_l_defaults
+
+#define klu_cholmod klu_l_cholmod
+
+#endif
+
+
+#ifdef DLONG
+
+#define CHOLMOD_print_sparse cholmod_l_print_sparse
+#define CHOLMOD_print_dense cholmod_l_print_dense
+#define CHOLMOD_copy_sparse cholmod_l_copy_sparse
+#define CHOLMOD_copy_dense cholmod_l_copy_dense
+#define CHOLMOD_transpose cholmod_l_transpose
+#define CHOLMOD_sdmult cholmod_l_sdmult
+#define CHOLMOD_norm_dense cholmod_l_norm_dense
+#define CHOLMOD_norm_sparse cholmod_l_norm_sparse
+#define CHOLMOD_free_sparse cholmod_l_free_sparse
+#define CHOLMOD_free_dense cholmod_l_free_dense
+#define CHOLMOD_start cholmod_l_start
+#define CHOLMOD_read_sparse cholmod_l_read_sparse
+#define CHOLMOD_allocate_dense cholmod_l_allocate_dense
+#define CHOLMOD_finish cholmod_l_finish
+
+#else
+
+#define CHOLMOD_print_sparse cholmod_print_sparse
+#define CHOLMOD_print_dense cholmod_print_dense
+#define CHOLMOD_copy_sparse cholmod_copy_sparse
+#define CHOLMOD_copy_dense cholmod_copy_dense
+#define CHOLMOD_transpose cholmod_transpose
+#define CHOLMOD_sdmult cholmod_sdmult
+#define CHOLMOD_norm_dense cholmod_norm_dense
+#define CHOLMOD_norm_sparse cholmod_norm_sparse
+#define CHOLMOD_free_sparse cholmod_free_sparse
+#define CHOLMOD_free_dense cholmod_free_dense
+#define CHOLMOD_start cholmod_start
+#define CHOLMOD_read_sparse cholmod_read_sparse
+#define CHOLMOD_allocate_dense cholmod_allocate_dense
+#define CHOLMOD_finish cholmod_finish
+
+#endif
+
+/* ========================================================================== */
+/* === random numbers ======================================================= */
+/* ========================================================================== */
+
+#define MY_RAND_MAX 32767
+
+static unsigned long next = 1 ;
+
+static Int my_rand (void)
+{
+ next = next * 1103515245 + 12345 ;
+ return ((unsigned)(next/65536) % (MY_RAND_MAX+1)) ;
+}
+
+static void my_srand (unsigned seed)
+{
+ next = seed ;
+}
+
+/* ========================================================================== */
+/* === memory management ==================================================== */
+/* ========================================================================== */
+
+void *my_malloc (size_t size) ;
+void *my_calloc (size_t n, size_t size) ;
+void *my_realloc (void *p, size_t size) ;
+
+Int my_tries = -1 ;
+
+void *my_malloc (size_t size)
+{
+ if (my_tries == 0) return (NULL) ; /* pretend to fail */
+ if (my_tries > 0) my_tries-- ;
+ return (malloc (size)) ;
+}
+
+void *my_calloc (size_t n, size_t size)
+{
+ if (my_tries == 0) return (NULL) ; /* pretend to fail */
+ if (my_tries > 0) my_tries-- ;
+ return (calloc (n, size)) ;
+}
+
+void *my_realloc (void *p, size_t size)
+{
+ if (my_tries == 0) return (NULL) ; /* pretend to fail */
+ if (my_tries > 0) my_tries-- ;
+ return (realloc (p, size)) ;
+}
+
+static void normal_memory_handler (KLU_common *Common)
+{
+ Common->malloc_memory = malloc ;
+ Common->calloc_memory = calloc ;
+ Common->realloc_memory = realloc ;
+ Common->free_memory = free ;
+ my_tries = -1 ;
+}
+
+static void test_memory_handler (KLU_common *Common)
+{
+ Common->malloc_memory = my_malloc ;
+ Common->calloc_memory = my_calloc ;
+ Common->realloc_memory = my_realloc ;
+ Common->free_memory = free ;
+ my_tries = -1 ;
+}
+
+
+/* ========================================================================== */
+/* === print_sparse ========================================================= */
+/* ========================================================================== */
+
+/* print a sparse matrix */
+
+static void print_sparse (Int n, Int isreal, Int *Ap, Int *Ai, double *Ax,
+ double *Az)
+{
+ double ax, az ;
+ Int i, j, p ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf ("column "ID":\n", j) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ if (isreal)
+ {
+ ax = Ax [p] ;
+ az = 0 ;
+ }
+ else if (Az)
+ {
+ /* split complex */
+ ax = Ax [p] ;
+ az = Az [p] ;
+ }
+ else
+ {
+ /* merged complex */
+ ax = Ax [2*p ] ;
+ az = Ax [2*p+1] ;
+ }
+ printf (" row "ID" : %g", i, ax) ;
+ if (!isreal)
+ {
+ printf (" + (%g)i", az) ;
+ }
+ printf ("\n") ;
+ }
+ }
+ fflush (stdout) ;
+}
+
+
+/* ========================================================================== */
+/* === print_int ============================================================ */
+/* ========================================================================== */
+
+/* print an Int vector */
+
+static void print_int (Int n, Int *P)
+{
+ Int j ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" "ID" : "ID"\n", j, P [j]) ;
+ }
+ fflush (stdout) ;
+}
+
+
+/* ========================================================================== */
+/* === print_double ========================================================= */
+/* ========================================================================== */
+
+/* print a double vector */
+
+static void print_double (Int n, double *X)
+{
+ Int j ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (" "ID" : %g\n", j, X [j]) ;
+ }
+ fflush (stdout) ;
+}
+
+
+/* ========================================================================== */
+/* === ludump =============================================================== */
+/* ========================================================================== */
+
+/* extract and print the LU factors */
+
+static void ludump (KLU_symbolic *Symbolic, KLU_numeric *Numeric, Int isreal,
+ cholmod_common *ch, KLU_common *Common)
+{
+ Int *Lp, *Li, *Up, *Ui, *Fp, *Fi, *P, *Q, *R ;
+ double *Lx, *Ux, *Fx, *Lz, *Uz, *Fz, *Rs ;
+ Int n, lnz, unz, fnz, nb, result ;
+
+ if (Symbolic == NULL || Numeric == NULL)
+ {
+ return ;
+ }
+
+ n = Symbolic->n ;
+ lnz = Numeric->lnz ;
+ unz = Numeric->unz ;
+ fnz = Numeric->Offp [n] ;
+ nb = Symbolic->nblocks ;
+
+ printf ("n "ID" lnz "ID" unz "ID" fnz "ID" nblocks "ID" isreal "ID"\n",
+ n, lnz, unz, fnz, nb, isreal) ;
+ fflush (stdout) ;
+
+ Lp = malloc ((n+1) * sizeof (Int)) ;
+ Li = malloc (lnz * sizeof (Int)) ;
+ Lx = malloc (lnz * sizeof (double)) ;
+ Lz = malloc (lnz * sizeof (double)) ;
+
+ Up = malloc ((n+1) * sizeof (Int)) ;
+ Ui = malloc (unz * sizeof (Int)) ;
+ Ux = malloc (unz * sizeof (double)) ;
+ Uz = malloc (unz * sizeof (double)) ;
+
+ Fp = malloc ((n+1) * sizeof (Int)) ;
+ Fi = malloc (fnz * sizeof (Int)) ;
+ Fx = malloc (fnz * sizeof (double)) ;
+ Fz = malloc (fnz * sizeof (double)) ;
+
+ P = malloc (n * sizeof (Int)) ;
+ Q = malloc (n * sizeof (Int)) ;
+ Rs = malloc (n * sizeof (double)) ;
+ R = malloc ((nb+1) * sizeof (double)) ;
+
+ if (isreal)
+ {
+ result = klu_extract (Numeric, Symbolic, Lp, Li, Lx,
+ Up, Ui, Ux, Fp, Fi, Fx, P, Q, Rs, R, Common) ;
+ }
+ else
+ {
+ result = klu_z_extract (Numeric, Symbolic, Lp, Li, Lx, Lz,
+ Up, Ui, Ux, Uz, Fp, Fi, Fx, Fz, P, Q, Rs, R, Common) ;
+ }
+
+ if (my_tries != 0) OK (result) ;
+
+ if (ch->print >= 5)
+ {
+ printf ("------ L:\n") ; print_sparse (n, isreal, Lp, Li, Lx, Lz) ;
+ printf ("------ U:\n") ; print_sparse (n, isreal, Up, Ui, Ux, Uz) ;
+ printf ("------ F:\n") ; print_sparse (n, isreal, Fp, Fi, Fx, Fz) ;
+ printf ("------ P:\n") ; print_int (n, P) ;
+ printf ("------ Q:\n") ; print_int (n, Q) ;
+ printf ("------ Rs:\n") ; print_double (n, Rs) ;
+ printf ("------ R:\n") ; print_int (nb+1, R) ;
+ }
+
+ free (Lp) ;
+ free (Li) ;
+ free (Lx) ;
+ free (Lz) ;
+
+ free (Up) ;
+ free (Ui) ;
+ free (Ux) ;
+ free (Uz) ;
+
+ free (Fp) ;
+ free (Fi) ;
+ free (Fx) ;
+ free (Fz) ;
+
+ free (P) ;
+ free (Q) ;
+ free (Rs) ;
+ free (R) ;
+}
+
+
+/* ========================================================================== */
+/* === randperm ============================================================= */
+/* ========================================================================== */
+
+/* return a random permutation vector */
+
+static Int *randperm (Int n, Int seed)
+{
+ Int *p, k, j, t ;
+ p = malloc (n * sizeof (Int)) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ p [k] = k ;
+ }
+ my_srand (seed) ; /* get new random number seed */
+ for (k = 0 ; k < n ; k++)
+ {
+ j = k + (my_rand ( ) % (n-k)) ; /* j = my_rand in range k to n-1 */
+ t = p [j] ; /* swap p[k] and p[j] */
+ p [j] = p [k] ;
+ p [k] = t ;
+ }
+ return (p) ;
+}
+
+
+/* ========================================================================== */
+/* === do_1_solve =========================================================== */
+/* ========================================================================== */
+
+static double do_1_solve (cholmod_sparse *A, cholmod_dense *B,
+ cholmod_dense *Xknown, Int *Puser, Int *Quser,
+ KLU_common *Common, cholmod_common *ch, Int *nan)
+{
+ Int *Ai, *Ap ;
+ double *Ax, *Bx, *Xknownx, *Xx, *Ax2, *Axx ;
+ KLU_symbolic *Symbolic = NULL ;
+ KLU_numeric *Numeric = NULL ;
+ cholmod_dense *X = NULL, *R = NULL ;
+ cholmod_sparse *AT = NULL, *A2 = NULL, *AT2 = NULL ;
+ double one [2], minusone [2],
+ rnorm, anorm, bnorm, xnorm, relresid, relerr, err = 0. ;
+ Int i, j, nrhs2, isreal, n, nrhs, transpose, step, k, save, tries ;
+
+ printf ("\ndo_1_solve: btf "ID" maxwork %g scale "ID" ordering "ID" user: "
+ ID" P,Q: %d halt: "ID"\n",
+ Common->btf, Common->maxwork, Common->scale, Common->ordering,
+ Common->user_data ? (*((Int *) Common->user_data)) : -1,
+ (Puser != NULL || Quser != NULL), Common->halt_if_singular) ;
+ fflush (stdout) ;
+ fflush (stderr) ;
+
+ CHOLMOD_print_sparse (A, "A", ch) ;
+ CHOLMOD_print_dense (B, "B", ch) ;
+
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ n = A->nrow ;
+ isreal = (A->xtype == CHOLMOD_REAL) ;
+ Bx = B->x ;
+ Xknownx = Xknown->x ;
+ nrhs = B->ncol ;
+
+ one [0] = 1 ;
+ one [1] = 0 ;
+
+ minusone [0] = -1 ;
+ minusone [1] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic analysis */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic = NULL ;
+ my_tries = 0 ;
+ for (tries = 0 ; Symbolic == NULL && my_tries == 0 ; tries++)
+ {
+ my_tries = tries ;
+ if (Puser != NULL || Quser != NULL)
+ {
+ Symbolic = klu_analyze_given (n, Ap, Ai, Puser, Quser, Common) ;
+ }
+ else
+ {
+ Symbolic = klu_analyze (n, Ap, Ai, Common) ;
+ }
+ }
+ printf ("sym try "ID" btf "ID" ordering "ID"\n",
+ tries, Common->btf, Common->ordering) ;
+ if (Symbolic == NULL)
+ {
+ printf ("Symbolic is null\n") ;
+ return (998) ;
+ }
+ my_tries = -1 ;
+
+ /* create a modified version of A */
+
+ A2 = CHOLMOD_copy_sparse (A, ch) ;
+ Ax2 = A2->x ;
+ my_srand (42) ;
+ for (k = 0 ; k < Ap [n] * (isreal ? 1:2) ; k++)
+ {
+ Ax2 [k] = Ax [k] *
+ (1 + 1e-4 * ((double) my_rand ( )) / ((double) MY_RAND_MAX)) ;
+ }
+
+ AT = isreal ? NULL : CHOLMOD_transpose (A, 1, ch) ;
+ AT2 = isreal ? NULL : CHOLMOD_transpose (A2, 1, ch) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize then solve */
+ /* ---------------------------------------------------------------------- */
+
+ for (step = 1 ; step <= 3 ; step++)
+ {
+ printf ("step: "ID"\n", step) ;
+ fflush (stdout) ;
+
+ /* ------------------------------------------------------------------ */
+ /* factorization or refactorization */
+ /* ------------------------------------------------------------------ */
+
+ /* step 1: factor
+ step 2: refactor with same A
+ step 3: refactor with modified A, and scaling forced on
+ and solve each time
+ */
+
+ if (step == 1)
+ {
+ /* numeric factorization */
+
+ Numeric = NULL ;
+ my_tries = 0 ;
+ for (tries = 0 ; Numeric == NULL && my_tries == 0 ; tries++)
+ {
+ my_tries = tries ;
+ if (isreal)
+ {
+ Numeric = klu_factor (Ap, Ai, Ax, Symbolic, Common) ;
+ }
+ else
+ {
+ Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, Common) ;
+ }
+ }
+ printf ("num try "ID" btf "ID"\n", tries, Common->btf) ;
+ my_tries = -1 ;
+
+ if (Common->status == KLU_OK ||
+ (Common->status == KLU_SINGULAR && !Common->halt_if_singular))
+ {
+ OK (Numeric) ;
+ }
+ else
+ {
+ FAIL (Numeric) ;
+ }
+
+ if (Common->status < KLU_OK)
+ {
+ printf ("factor failed: "ID"\n", Common->status) ;
+ }
+
+ }
+ else if (step == 2)
+ {
+
+ /* numeric refactorization with same values, same scaling */
+ if (isreal)
+ {
+ klu_refactor (Ap, Ai, Ax, Symbolic, Numeric, Common) ;
+ }
+ else
+ {
+ klu_z_refactor (Ap, Ai, Ax, Symbolic, Numeric, Common) ;
+ }
+
+ }
+ else
+ {
+
+ /* numeric refactorization with different values */
+ save = Common->scale ;
+ if (Common->scale == 0)
+ {
+ Common->scale = 1 ;
+ }
+ for (tries = 0 ; tries <= 1 ; tries++)
+ {
+ my_tries = tries ;
+ if (isreal)
+ {
+ klu_refactor (Ap, Ai, Ax2, Symbolic, Numeric, Common) ;
+ }
+ else
+ {
+ klu_z_refactor (Ap, Ai, Ax2, Symbolic, Numeric, Common) ;
+ }
+ }
+ my_tries = -1 ;
+ Common->scale = save ;
+ }
+
+ if (Common->status == KLU_SINGULAR)
+ {
+ printf ("# singular column : "ID"\n", Common->singular_col) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* diagnostics */
+ /* ------------------------------------------------------------------ */
+
+ Axx = (step == 3) ? Ax2 : Ax ;
+
+ if (isreal)
+ {
+ klu_rgrowth (Ap, Ai, Axx, Symbolic, Numeric, Common) ;
+ klu_condest (Ap, Axx, Symbolic, Numeric, Common) ;
+ klu_rcond (Symbolic, Numeric, Common) ;
+ klu_flops (Symbolic, Numeric, Common) ;
+ }
+ else
+ {
+ klu_z_rgrowth (Ap, Ai, Axx, Symbolic, Numeric, Common) ;
+ klu_z_condest (Ap, Axx, Symbolic, Numeric, Common) ;
+ klu_z_rcond (Symbolic, Numeric, Common) ;
+ klu_z_flops (Symbolic, Numeric, Common) ;
+ }
+
+ printf ("growth %g condest %g rcond %g flops %g\n",
+ Common->rgrowth, Common->condest, Common->rcond, Common->flops) ;
+
+ ludump (Symbolic, Numeric, isreal, ch, Common) ;
+
+ if (Numeric == NULL || Common->status < KLU_OK)
+ {
+ continue ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* solve */
+ /* ------------------------------------------------------------------ */
+
+ /* forward/backsolve to solve A*X=B or A'*X=B */
+ for (transpose = (isreal ? 0 : -1) ; transpose <= 1 ; transpose++)
+ {
+
+ for (nrhs2 = 1 ; nrhs2 <= nrhs ; nrhs2++)
+ {
+ /* mangle B so that it has only nrhs2 columns */
+ B->ncol = nrhs2 ;
+
+ X = CHOLMOD_copy_dense (B, ch) ;
+ CHOLMOD_print_dense (X, "X before solve", ch) ;
+ Xx = X->x ;
+
+ if (isreal)
+ {
+ if (transpose)
+ {
+ /* solve A'x=b */
+ klu_tsolve (Symbolic, Numeric, n, nrhs2, Xx, Common) ;
+ }
+ else
+ {
+ /* solve A*x=b */
+ klu_solve (Symbolic, Numeric, n, nrhs2, Xx, Common) ;
+ }
+ }
+ else
+ {
+ if (transpose)
+ {
+ /* solve A'x=b (if 1) or A.'x=b (if -1) */
+ klu_z_tsolve (Symbolic, Numeric, n, nrhs2, Xx,
+ (transpose == 1), Common) ;
+ }
+ else
+ {
+ /* solve A*x=b */
+ klu_z_solve (Symbolic, Numeric, n, nrhs2, Xx, Common) ;
+ }
+ }
+
+ CHOLMOD_print_dense (X, "X", ch) ;
+
+ /* compute the residual, R = B-A*X, B-A'*X, or B-A.'*X */
+ R = CHOLMOD_copy_dense (B, ch) ;
+ if (transpose == -1)
+ {
+ /* R = B-A.'*X (use A.' explicitly) */
+ CHOLMOD_sdmult ((step == 3) ? AT2 : AT,
+ 0, minusone, one, X, R, ch) ;
+ }
+ else
+ {
+ /* R = B-A*X or B-A'*X */
+ CHOLMOD_sdmult ((step == 3) ? A2 :A,
+ transpose, minusone, one, X, R, ch) ;
+ }
+
+ CHOLMOD_print_dense (R, "R", ch) ;
+
+ /* compute the norms of R, A, X, and B */
+ rnorm = CHOLMOD_norm_dense (R, 1, ch) ;
+ anorm = CHOLMOD_norm_sparse ((step == 3) ? A2 : A, 1, ch) ;
+ xnorm = CHOLMOD_norm_dense (X, 1, ch) ;
+ bnorm = CHOLMOD_norm_dense (B, 1, ch) ;
+
+ CHOLMOD_free_dense (&R, ch) ;
+
+ /* relative residual = norm (r) / (norm (A) * norm (x)) */
+ relresid = rnorm ;
+ if (anorm > 0)
+ {
+ relresid /= anorm ;
+ }
+ if (xnorm > 0)
+ {
+ relresid /= xnorm ;
+ }
+
+ if (SCALAR_IS_NAN (relresid))
+ {
+ *nan = TRUE ;
+ }
+ else
+ {
+ err = MAX (err, relresid) ;
+ }
+
+ /* relative error = norm (x - xknown) / norm (xknown) */
+ /* overwrite X with X - Xknown */
+ if (transpose || step == 3)
+ {
+ /* not computed */
+ relerr = -1 ;
+ }
+ else
+ {
+ for (j = 0 ; j < nrhs2 ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ if (isreal)
+ {
+ Xx [i+j*n] -= Xknownx [i+j*n] ;
+ }
+ else
+ {
+ Xx [2*(i+j*n) ] -= Xknownx [2*(i+j*n) ] ;
+ Xx [2*(i+j*n)+1] -= Xknownx [2*(i+j*n)+1] ;
+ }
+ }
+ }
+ relerr = CHOLMOD_norm_dense (X, 1, ch) ;
+ xnorm = CHOLMOD_norm_dense (Xknown, 1, ch) ;
+ if (xnorm > 0)
+ {
+ relerr /= xnorm ;
+ }
+
+ if (SCALAR_IS_NAN (relerr))
+ {
+ *nan = TRUE ;
+ }
+ else
+ {
+ err = MAX (relerr, err) ;
+ }
+
+ }
+
+ CHOLMOD_free_dense (&X, ch) ;
+
+ printf (ID" "ID" relresid %10.3g relerr %10.3g %g\n",
+ transpose, nrhs2, relresid, relerr, err) ;
+
+ B->ncol = nrhs ; /* restore B */
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free factorization and temporary matrices, and return */
+ /* ---------------------------------------------------------------------- */
+
+ klu_free_symbolic (&Symbolic, Common) ;
+ if (isreal)
+ {
+ klu_free_numeric (&Numeric, Common) ;
+ }
+ else
+ {
+ klu_z_free_numeric (&Numeric, Common) ;
+ }
+ CHOLMOD_free_sparse (&A2, ch) ;
+ CHOLMOD_free_sparse (&AT, ch) ;
+ CHOLMOD_free_sparse (&AT2, ch) ;
+ fflush (stdout) ;
+ fflush (stderr) ;
+ return (err) ;
+}
+
+
+/* ========================================================================== */
+/* === do_solves ============================================================ */
+/* ========================================================================== */
+
+/* test KLU with many options */
+
+static double do_solves (cholmod_sparse *A, cholmod_dense *B, cholmod_dense *X,
+ Int *Puser, Int *Quser, KLU_common *Common, cholmod_common *ch, Int *nan)
+{
+ double err, maxerr = 0 ;
+ Int n = A->nrow, sflag ;
+ *nan = FALSE ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test KLU with the system A*X=B and default options */
+ /* ---------------------------------------------------------------------- */
+
+ maxerr = do_1_solve (A, B, X, NULL, NULL, Common, ch, nan) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test with non-default options */
+ /* ---------------------------------------------------------------------- */
+
+ Common->user_order = klu_cholmod ;
+ for (Common->btf = 0 ; Common->btf <= 2 ; Common->btf++)
+ {
+ Common->maxwork = (Common->btf == 2) ? 0.001 : 0 ;
+
+ for (Common->halt_if_singular = 0 ; Common->halt_if_singular <= 1 ;
+ Common->halt_if_singular++)
+ {
+ for (Common->scale = 0 ; Common->scale <= 2 ; Common->scale++)
+
+ {
+ fprintf (stderr, ".") ;
+ fflush (stderr) ;
+
+ /* orderings: 0: AMD, 1: COLAMD, 2: natural, 3: user function */
+ for (Common->ordering = 0 ; Common->ordering <= 3 ;
+ Common->ordering++)
+ {
+ err = do_1_solve (A, B, X, NULL, NULL, Common, ch, nan) ;
+ maxerr = MAX (maxerr, err) ;
+ }
+
+ /* user-ordering, unsymmetric case */
+ Common->ordering = 3 ;
+ Common->user_data = &sflag ;
+ sflag = 0 ;
+ err = do_1_solve (A, B, X, NULL, NULL, Common, ch, nan) ;
+ maxerr = MAX (maxerr, err) ;
+ Common->user_data = NULL ;
+
+ /* Puser and Quser, but only for small matrices */
+ Common->ordering = 2 ;
+ if (n < 200)
+ {
+ err = do_1_solve (A, B, X, Puser, Quser, Common, ch, nan) ;
+ maxerr = MAX (maxerr, err) ;
+ }
+ }
+ }
+ }
+
+ /* restore defaults */
+ Common->btf = TRUE ;
+ Common->maxwork = 0 ;
+ Common->ordering = 0 ;
+ Common->scale = -1 ;
+ Common->halt_if_singular = TRUE ;
+ Common->user_order = NULL ;
+
+ my_tries = -1 ;
+ return (maxerr) ;
+}
+
+
+/* ========================================================================== */
+/* === main ================================================================= */
+/* ========================================================================== */
+
+int main (void)
+{
+ KLU_common Common ;
+ cholmod_sparse *A, *A2 ;
+ cholmod_dense *X, *B ;
+ cholmod_common ch ;
+ Int *Ap, *Ai, *Puser, *Quser, *Gunk ;
+ double *Ax, *Bx, *Xx, *A2x ;
+ double one [2], zero [2], xsave, maxerr ;
+ Int n, i, j, nz, save, isreal, k, nan ;
+ KLU_symbolic *Symbolic, *Symbolic2 ;
+ KLU_numeric *Numeric ;
+
+ one [0] = 1 ;
+ one [1] = 0 ;
+ zero [0] = 0 ;
+ zero [1] = 0 ;
+
+ printf ("klu test: -------------------------------------------------\n") ;
+ OK (klu_defaults (&Common)) ;
+ CHOLMOD_start (&ch) ;
+ ch.print = 0 ;
+ normal_memory_handler (&Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* read in a sparse matrix from stdin */
+ /* ---------------------------------------------------------------------- */
+
+ A = CHOLMOD_read_sparse (stdin, &ch) ;
+
+ if (A->nrow != A->ncol || A->stype != 0)
+ {
+ fprintf (stderr, "error: only square unsymmetric matrices handled\n") ;
+ CHOLMOD_free_sparse (&A, &ch) ;
+ return (0) ;
+ }
+ if (!(A->xtype == CHOLMOD_REAL || A->xtype == CHOLMOD_COMPLEX))
+ {
+ fprintf (stderr, "error: only real or complex matrices hanlded\n") ;
+ CHOLMOD_free_sparse (&A, &ch) ;
+ return (0) ;
+ }
+
+ n = A->nrow ;
+ Ap = A->p ;
+ Ai = A->i ;
+ Ax = A->x ;
+ nz = Ap [n] ;
+ isreal = (A->xtype == CHOLMOD_REAL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct random permutations */
+ /* ---------------------------------------------------------------------- */
+
+ Puser = randperm (n, n) ;
+ Quser = randperm (n, n) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* select known solution to Ax=b */
+ /* ---------------------------------------------------------------------- */
+
+ X = CHOLMOD_allocate_dense (n, NRHS, n, A->xtype, &ch) ;
+ Xx = X->x ;
+ for (j = 0 ; j < NRHS ; j++)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ if (isreal)
+ {
+ Xx [i] = 1 + ((double) i) / ((double) n) + j * 100;
+ }
+ else
+ {
+ Xx [2*i ] = 1 + ((double) i) / ((double) n) + j * 100 ;
+ Xx [2*i+1] = - ((double) i+1) / ((double) n + j) ;
+ if (j == NRHS-1)
+ {
+ Xx [2*i+1] = 0 ; /* zero imaginary part */
+ }
+ else if (j == NRHS-2)
+ {
+ Xx [2*i] = 0 ; /* zero real part */
+ }
+ }
+ }
+ Xx += isreal ? n : 2*n ;
+ }
+
+ /* B = A*X */
+ B = CHOLMOD_allocate_dense (n, NRHS, n, A->xtype, &ch) ;
+ CHOLMOD_sdmult (A, 0, one, zero, X, B, &ch) ;
+ Bx = B->x ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test KLU */
+ /* ---------------------------------------------------------------------- */
+
+ test_memory_handler (&Common) ;
+ maxerr = do_solves (A, B, X, Puser, Quser, &Common, &ch, &nan) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* basic error checking */
+ /* ---------------------------------------------------------------------- */
+
+ FAIL (klu_defaults (NULL)) ;
+
+ FAIL (klu_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
+ NULL, NULL, NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
+ NULL, NULL, NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_z_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
+ NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_z_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
+ NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_analyze (0, NULL, NULL, NULL)) ;
+ FAIL (klu_analyze (0, NULL, NULL, &Common)) ;
+
+ FAIL (klu_analyze_given (0, NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_analyze_given (0, NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_cholmod (0, NULL, NULL, NULL, NULL)) ;
+
+ FAIL (klu_factor (NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_factor (NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_z_factor (NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_z_factor (NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_refactor (NULL, NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_refactor (NULL, NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_z_refactor (NULL, NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_z_refactor (NULL, NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_rgrowth (NULL, NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_rgrowth (NULL, NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_z_rgrowth (NULL, NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_z_rgrowth (NULL, NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_condest (NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_condest (NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_z_condest (NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_z_condest (NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_flops (NULL, NULL, NULL)) ;
+ FAIL (klu_flops (NULL, NULL, &Common)) ;
+
+ FAIL (klu_z_flops (NULL, NULL, NULL)) ;
+ FAIL (klu_z_flops (NULL, NULL, &Common)) ;
+
+ FAIL (klu_rcond (NULL, NULL, NULL)) ;
+ FAIL (klu_rcond (NULL, NULL, &Common)) ;
+
+ FAIL (klu_z_rcond (NULL, NULL, NULL)) ;
+ FAIL (klu_z_rcond (NULL, NULL, &Common)) ;
+
+ FAIL (klu_free_symbolic (NULL, NULL)) ;
+ OK (klu_free_symbolic (NULL, &Common)) ;
+
+ FAIL (klu_free_numeric (NULL, NULL)) ;
+ OK (klu_free_numeric (NULL, &Common)) ;
+
+ FAIL (klu_z_free_numeric (NULL, NULL)) ;
+ OK (klu_z_free_numeric (NULL, &Common)) ;
+
+ FAIL (klu_scale (0, 0, NULL, NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_scale (0, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ;
+ OK (klu_scale (-1, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_z_scale (0, 0, NULL, NULL, NULL, NULL, NULL, NULL)) ;
+ FAIL (klu_z_scale (0, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ;
+ OK (klu_z_scale (-1, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ;
+
+ FAIL (klu_solve (NULL, NULL, 0, 0, NULL, NULL)) ;
+ FAIL (klu_solve (NULL, NULL, 0, 0, NULL, &Common)) ;
+
+ FAIL (klu_z_solve (NULL, NULL, 0, 0, NULL, NULL)) ;
+ FAIL (klu_z_solve (NULL, NULL, 0, 0, NULL, &Common)) ;
+
+ FAIL (klu_tsolve (NULL, NULL, 0, 0, NULL, NULL)) ;
+ FAIL (klu_tsolve (NULL, NULL, 0, 0, NULL, &Common)) ;
+
+ FAIL (klu_z_tsolve (NULL, NULL, 0, 0, NULL, 0, NULL)) ;
+ FAIL (klu_z_tsolve (NULL, NULL, 0, 0, NULL, 0, &Common)) ;
+
+ FAIL (klu_malloc (0, 0, NULL)) ;
+ FAIL (klu_malloc (0, 0, &Common)) ;
+ FAIL (klu_malloc (Int_MAX, 1, &Common)) ;
+
+ FAIL (klu_realloc (0, 0, 0, NULL, NULL)) ;
+ FAIL (klu_realloc (0, 0, 0, NULL, &Common)) ;
+ FAIL (klu_realloc (Int_MAX, 1, 0, NULL, &Common)) ;
+ Gunk = (Int *) klu_realloc (1, 0, sizeof (Int), NULL, &Common) ;
+ OK (Gunk) ;
+ OK (klu_realloc (Int_MAX, 1, sizeof (Int), Gunk, &Common)) ;
+ OK (Common.status == KLU_TOO_LARGE) ;
+ klu_free (Gunk, 1, sizeof (Int), &Common) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* mangle the matrix, and other error checking */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nerror handling:\n") ;
+ Symbolic = klu_analyze (n, Ap, Ai, &Common) ;
+ OK (Symbolic) ;
+
+ Xx = X->x ;
+ if (nz > 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* row index out of bounds */
+ /* ------------------------------------------------------------------ */
+
+ save = Ai [0] ;
+ Ai [0] = -1 ;
+ FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
+ if (isreal)
+ {
+ FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
+ }
+ else
+ {
+ FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
+ }
+ Ai [0] = save ;
+
+ /* ------------------------------------------------------------------ */
+ /* row index out of bounds */
+ /* ------------------------------------------------------------------ */
+
+ save = Ai [0] ;
+ Ai [0] = Int_MAX ;
+ FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
+ if (isreal)
+ {
+ FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
+ }
+ else
+ {
+ FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
+ }
+ Ai [0] = save ;
+
+ /* ------------------------------------------------------------------ */
+ /* column pointers mangled */
+ /* ------------------------------------------------------------------ */
+
+ save = Ap [n] ;
+ Ap [n] = -1 ;
+ FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
+ if (isreal)
+ {
+ FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
+ }
+ else
+ {
+ FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
+ }
+ Ap [n] = save ;
+
+ /* ------------------------------------------------------------------ */
+ /* column pointers mangled */
+ /* ------------------------------------------------------------------ */
+
+ save = Ap [n] ;
+ Ap [n] = Ap [n-1] - 1 ;
+ FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
+ if (isreal)
+ {
+ FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
+ }
+ else
+ {
+ FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
+ }
+ Ap [n] = save ;
+
+ /* ------------------------------------------------------------------ */
+ /* duplicates */
+ /* ------------------------------------------------------------------ */
+
+ if (n > 1 && Ap [1] - Ap [0] > 1)
+ {
+ save = Ai [1] ;
+ Ai [1] = Ai [0] ;
+ FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
+ if (isreal)
+ {
+ FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
+ }
+ else
+ {
+ FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
+ }
+ Ai [1] = save ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* invalid ordering */
+ /* ------------------------------------------------------------------ */
+
+ save = Common.ordering ;
+ Common.ordering = 42 ;
+ FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
+ Common.ordering = save ;
+
+ /* ------------------------------------------------------------------ */
+ /* invalid ordering (klu_cholmod, with NULL user_ordering) */
+ /* ------------------------------------------------------------------ */
+
+ save = Common.ordering ;
+ Common.user_order = NULL ;
+ Common.ordering = 3 ;
+ FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
+ Common.ordering = save ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* tests with valid symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ Common.halt_if_singular = FALSE ;
+ Common.scale = 0 ;
+ Numeric = NULL ;
+
+ if (nz > 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Int overflow */
+ /* ------------------------------------------------------------------ */
+
+ if (n == 100)
+ {
+ Common.ordering = 2 ;
+ Symbolic2 = klu_analyze (n, Ap, Ai, &Common) ;
+ OK (Symbolic2) ;
+ Common.memgrow = Int_MAX ;
+ if (isreal)
+ {
+ Numeric = klu_factor (Ap, Ai, Ax, Symbolic2, &Common) ;
+ }
+ else
+ {
+ Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic2, &Common) ;
+ }
+ Common.memgrow = 1.2 ;
+ Common.ordering = 0 ;
+ klu_free_symbolic (&Symbolic2, &Common) ;
+ klu_free_numeric (&Numeric, &Common) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* Int overflow again */
+ /* ------------------------------------------------------------------ */
+
+ Common.initmem = Int_MAX ;
+ Common.initmem_amd = Int_MAX ;
+ if (isreal)
+ {
+ Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ;
+ }
+ else
+ {
+ Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, &Common) ;
+ }
+ Common.initmem = 10 ;
+ Common.initmem_amd = 1.2 ;
+ klu_free_numeric (&Numeric, &Common) ;
+
+ /* ------------------------------------------------------------------ */
+ /* mangle the matrix */
+ /* ------------------------------------------------------------------ */
+
+ save = Ai [0] ;
+ Ai [0] = -1 ;
+
+ if (isreal)
+ {
+ Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ;
+ }
+ else
+ {
+ Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, &Common) ;
+ }
+ FAIL (Numeric) ;
+ Ai [0] = save ;
+
+ /* ------------------------------------------------------------------ */
+ /* nan and inf handling */
+ /* ------------------------------------------------------------------ */
+
+ xsave = Ax [0] ;
+ Ax [0] = one [0] / zero [0] ;
+ if (isreal)
+ {
+ Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ;
+ klu_rcond (Symbolic, Numeric, &Common) ;
+ klu_condest (Ap, Ax, Symbolic, Numeric, &Common) ;
+ }
+ else
+ {
+ Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, &Common) ;
+ klu_z_rcond (Symbolic, Numeric, &Common) ;
+ klu_z_condest (Ap, Ax, Symbolic, Numeric, &Common) ;
+ }
+ printf ("Nan case: rcond %g condest %g\n",
+ Common.rcond, Common.condest) ;
+ OK (Numeric) ;
+ Ax [0] = xsave ;
+
+ /* ------------------------------------------------------------------ */
+ /* mangle the matrix again */
+ /* ------------------------------------------------------------------ */
+
+ save = Ai [0] ;
+ Ai [0] = -1 ;
+ if (isreal)
+ {
+ FAIL (klu_refactor (Ap, Ai, Ax, Symbolic, Numeric, &Common)) ;
+ }
+ else
+ {
+ FAIL (klu_z_refactor (Ap, Ai, Ax, Symbolic, Numeric, &Common)) ;
+ }
+ Ai [0] = save ;
+
+ /* ------------------------------------------------------------------ */
+ /* all zero */
+ /* ------------------------------------------------------------------ */
+
+ A2 = CHOLMOD_copy_sparse (A, &ch) ;
+ A2x = A2->x ;
+ for (k = 0 ; k < nz * (isreal ? 1:2) ; k++)
+ {
+ A2x [k] = 0 ;
+ }
+ for (Common.halt_if_singular = 0 ; Common.halt_if_singular <= 1 ;
+ Common.halt_if_singular++)
+ {
+ for (Common.scale = -1 ; Common.scale <= 2 ; Common.scale++)
+ {
+ if (isreal)
+ {
+ klu_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ;
+ klu_condest (Ap, A2x, Symbolic, Numeric, &Common) ;
+ }
+ else
+ {
+ klu_z_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ;
+ klu_z_condest (Ap, A2x, Symbolic, Numeric, &Common) ;
+ }
+ OK (Common.status = KLU_SINGULAR) ;
+ }
+ }
+ CHOLMOD_free_sparse (&A2, &ch) ;
+
+ /* ------------------------------------------------------------------ */
+ /* all one, or all 1i for complex case */
+ /* ------------------------------------------------------------------ */
+
+ A2 = CHOLMOD_copy_sparse (A, &ch) ;
+ A2x = A2->x ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ if (isreal)
+ {
+ A2x [k] = 1 ;
+ }
+ else
+ {
+ A2x [2*k ] = 0 ;
+ A2x [2*k+1] = 1 ;
+ }
+ }
+ Common.halt_if_singular = 0 ;
+ Common.scale = 0 ;
+ if (isreal)
+ {
+ klu_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ;
+ klu_condest (Ap, A2x, Symbolic, Numeric, &Common) ;
+ }
+ else
+ {
+ klu_z_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ;
+ klu_z_condest (Ap, A2x, Symbolic, Numeric, &Common) ;
+ }
+ OK (Common.status = KLU_SINGULAR) ;
+ CHOLMOD_free_sparse (&A2, &ch) ;
+ }
+
+ klu_free_symbolic (&Symbolic, &Common) ;
+ if (isreal)
+ {
+ klu_free_numeric (&Numeric, &Common) ;
+ }
+ else
+ {
+ klu_z_free_numeric (&Numeric, &Common) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free problem and quit */
+ /* ---------------------------------------------------------------------- */
+
+ CHOLMOD_free_dense (&X, &ch) ;
+ CHOLMOD_free_dense (&B, &ch) ;
+ CHOLMOD_free_sparse (&A, &ch) ;
+ free (Puser) ;
+ free (Quser) ;
+ CHOLMOD_finish (&ch) ;
+ fprintf (stderr, " maxerr %10.3e", maxerr) ;
+ printf (" maxerr %10.3e", maxerr) ;
+ if (maxerr < 1e-8)
+ {
+ fprintf (stderr, " test passed") ;
+ printf (" test passed") ;
+ }
+ else
+ {
+ fprintf (stderr, " test FAILED") ;
+ printf (" test FAILED") ;
+ }
+ if (nan)
+ {
+ fprintf (stderr, " *") ;
+ printf (" *") ;
+ }
+ fprintf (stderr, "\n") ;
+ printf ("\n-----------------------------------------------------------\n") ;
+ return (0) ;
+}
diff --git a/KLU/Tcov/klutests b/KLU/Tcov/klutests
new file mode 100755
index 0000000..9b110bd
--- /dev/null
+++ b/KLU/Tcov/klutests
@@ -0,0 +1,31 @@
+#!/bin/csh
+
+# 57 unique statements:
+./klutest < ../Matrix/impcol_a.mtx
+
+# 20:
+./klutest < ../Matrix/GD99_cc.mtx
+
+# 17:
+./klutest < ../Matrix/two.mtx
+
+# 10:
+./klutest < ../Matrix/w156.mtx
+
+# 3, xsize memgrow in klu_kernel
+./klutest < ../Matrix/arrow.mtx
+
+# 3, xsize memgrow in klu_kernel, 1 in klu_z_condest,
+./klutest < ../Matrix/arrowc.mtx
+
+# 2 in klu_z_kernel (if pivot == 0 and halt_if_singular, and in complex divide)
+./klutest < ../Matrix/onec.mtx
+
+# 1 in klu_kernel (if pivot == 0 and halt if singular)
+./klutest < ../Matrix/one.mtx
+
+# 1 in klu_z_condest:
+./klutest < ../Matrix/1c.mtx
+
+# 1 in klu_z_condest:
+./klutest < ../Matrix/ctina.mtx
diff --git a/KLU/Tcov/vklultests b/KLU/Tcov/vklultests
new file mode 100755
index 0000000..8aa8dcf
--- /dev/null
+++ b/KLU/Tcov/vklultests
@@ -0,0 +1,31 @@
+#!/bin/csh
+
+# 57 unique statements:
+valgrind ./klultest < ../Matrix/impcol_a.mtx
+
+# 20:
+valgrind ./klultest < ../Matrix/GD99_cc.mtx
+
+# 17:
+valgrind ./klultest < ../Matrix/two.mtx
+
+# 10:
+valgrind ./klultest < ../Matrix/w156.mtx
+
+# 3, xsize memgrow in klu_kernel
+valgrind ./klultest < ../Matrix/arrow.mtx
+
+# 3, xsize memgrow in klu_kernel, 1 in klu_z_condest,
+valgrind ./klultest < ../Matrix/arrowc.mtx
+
+# 2 in klu_z_kernel (if pivot == 0 and halt_if_singular, and in complex divide)
+valgrind ./klultest < ../Matrix/onec.mtx
+
+# 1 in klu_kernel (if pivot == 0 and halt if singular)
+valgrind ./klultest < ../Matrix/one.mtx
+
+# 1 in klu_z_condest:
+valgrind ./klultest < ../Matrix/1c.mtx
+
+# 1 in klu_z_condest:
+valgrind ./klultest < ../Matrix/ctina.mtx
diff --git a/KLU/Tcov/vklutests b/KLU/Tcov/vklutests
new file mode 100755
index 0000000..7dfada9
--- /dev/null
+++ b/KLU/Tcov/vklutests
@@ -0,0 +1,31 @@
+#!/bin/csh
+
+# 57 unique statements:
+valgrind ./klutest < ../Matrix/impcol_a.mtx
+
+# 20:
+valgrind ./klutest < ../Matrix/GD99_cc.mtx
+
+# 17:
+valgrind ./klutest < ../Matrix/two.mtx
+
+# 10:
+valgrind ./klutest < ../Matrix/w156.mtx
+
+# 3, xsize memgrow in klu_kernel
+valgrind ./klutest < ../Matrix/arrow.mtx
+
+# 3, xsize memgrow in klu_kernel, 1 in klu_z_condest,
+valgrind ./klutest < ../Matrix/arrowc.mtx
+
+# 2 in klu_z_kernel (if pivot == 0 and halt_if_singular, and in complex divide)
+valgrind ./klutest < ../Matrix/onec.mtx
+
+# 1 in klu_kernel (if pivot == 0 and halt if singular)
+valgrind ./klutest < ../Matrix/one.mtx
+
+# 1 in klu_z_condest:
+valgrind ./klutest < ../Matrix/1c.mtx
+
+# 1 in klu_z_condest:
+valgrind ./klutest < ../Matrix/ctina.mtx
diff --git a/KLU/User/Makefile b/KLU/User/Makefile
new file mode 100644
index 0000000..faf6173
--- /dev/null
+++ b/KLU/User/Makefile
@@ -0,0 +1,26 @@
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+all: libklu_cholmod.a
+
+I = -I../../CHOLMOD/Include -I../../UFconfig -I../Include -I../../AMD/Include \
+ -I../../BTF/Include -I../../COLAMD
+
+libklu_cholmod.a: library klu_cholmod.c klu_cholmod.h
+ $(CC) $(CFLAGS) $(I) -c klu_cholmod.c
+ $(AR) libklu_cholmod.a klu_cholmod.o
+ $(RANLIB) libklu_cholmod.a
+
+distclean: purge
+
+purge: clean
+ - $(RM) *.o *.a
+
+clean:
+ - $(RM) $(CLEAN)
+
+library:
+ ( cd ../../AMD ; $(MAKE) library )
+ ( cd ../../COLAMD ; $(MAKE) library )
+ ( cd ../../CHOLMOD/Lib ; $(MAKE) )
diff --git a/KLU/User/README.txt b/KLU/User/README.txt
new file mode 100644
index 0000000..e3249d3
--- /dev/null
+++ b/KLU/User/README.txt
@@ -0,0 +1,2 @@
+This directory contains a sample user-ordering function, klu_cholmod.
+Its use (and the use of CHOLMOD) is optional.
diff --git a/KLU/User/klu_cholmod.c b/KLU/User/klu_cholmod.c
new file mode 100644
index 0000000..8b16118
--- /dev/null
+++ b/KLU/User/klu_cholmod.c
@@ -0,0 +1,114 @@
+/* ========================================================================== */
+/* === klu_cholmod ========================================================== */
+/* ========================================================================== */
+
+/* klu_cholmod: user-defined ordering function to interface KLU to CHOLMOD.
+ *
+ * This routine is an example of a user-provided ordering function for KLU.
+ * Its return value is klu_cholmod's estimate of max (nnz(L),nnz(U)):
+ * 0 if error,
+ * -1 if OK, but estimate of max (nnz(L),nnz(U)) not computed
+ * > 0 if OK and estimate computed.
+ *
+ * This function can be assigned to KLU's Common->user_order function pointer.
+ */
+
+#include "klu_cholmod.h"
+#include "cholmod.h"
+#define TRUE 1
+#define FALSE 0
+
+int klu_cholmod
+(
+ /* inputs */
+ int n, /* A is n-by-n */
+ int Ap [ ], /* column pointers */
+ int Ai [ ], /* row indices */
+ /* outputs */
+ int Perm [ ], /* fill-reducing permutation */
+ /* user-defined */
+ klu_common *Common /* user-defined data is in Common->user_data */
+)
+{
+ double one [2] = {1,0}, zero [2] = {0,0}, lnz = 0 ;
+ cholmod_sparse Amatrix, *A, *AT, *S ;
+ cholmod_factor *L ;
+ cholmod_common cm ;
+ int *P ;
+ int k, symmetric ;
+
+ if (Ap == NULL || Ai == NULL || Perm == NULL || n < 0)
+ {
+ /* invalid inputs */
+ return (0) ;
+ }
+
+ /* start CHOLMOD */
+ cholmod_start (&cm) ;
+ cm.supernodal = CHOLMOD_SIMPLICIAL ;
+ cm.print = 0 ;
+
+ /* use KLU memory management routines for CHOLMOD */
+ cm.malloc_memory = Common->malloc_memory ;
+ cm.realloc_memory = Common->realloc_memory ;
+ cm.calloc_memory = Common->calloc_memory ;
+ cm.free_memory = Common->free_memory ;
+
+ /* construct a CHOLMOD version of the input matrix A */
+ A = &Amatrix ;
+ A->nrow = n ; /* A is n-by-n */
+ A->ncol = n ;
+ A->nzmax = Ap [n] ; /* with nzmax entries */
+ A->packed = TRUE ; /* there is no A->nz array */
+ A->stype = 0 ; /* A is unsymmetric */
+ A->itype = CHOLMOD_INT ;
+ A->xtype = CHOLMOD_PATTERN ;
+ A->dtype = CHOLMOD_DOUBLE ;
+ A->nz = NULL ;
+ A->p = Ap ; /* column pointers */
+ A->i = Ai ; /* row indices */
+ A->x = NULL ; /* no numerical values */
+ A->z = NULL ;
+ A->sorted = FALSE ; /* columns of A are not sorted */
+
+ /* get the user_data; default is symmetric if user_data is NULL */
+ symmetric = (Common->user_data == NULL) ? TRUE :
+ (((int *) (Common->user_data)) [0] != 0) ;
+
+ /* AT = pattern of A' */
+ AT = cholmod_transpose (A, 0, &cm) ;
+ if (symmetric)
+ {
+ /* S = the symmetric pattern of A+A' */
+ S = cholmod_add (A, AT, one, zero, FALSE, FALSE, &cm) ;
+ cholmod_free_sparse (&AT, &cm) ;
+ if (S != NULL)
+ {
+ S->stype = 1 ;
+ }
+ }
+ else
+ {
+ /* S = A'. CHOLMOD will order S*S', which is A'*A */
+ S = AT ;
+ }
+
+ /* order and analyze S or S*S' */
+ L = cholmod_analyze (S, &cm) ;
+
+ /* copy the permutation from L to the output */
+ if (L != NULL)
+ {
+ P = L->Perm ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Perm [k] = P [k] ;
+ }
+ lnz = cm.lnz ;
+ }
+
+ cholmod_free_sparse (&S, &cm) ;
+ cholmod_free_factor (&L, &cm) ;
+ cholmod_finish (&cm) ;
+ return (lnz) ;
+}
diff --git a/KLU/User/klu_cholmod.h b/KLU/User/klu_cholmod.h
new file mode 100644
index 0000000..e9c4d27
--- /dev/null
+++ b/KLU/User/klu_cholmod.h
@@ -0,0 +1,8 @@
+#include "klu.h"
+#include "UFconfig.h"
+
+int klu_cholmod (int n, int Ap [ ], int Ai [ ], int Perm [ ], klu_common *) ;
+
+UF_long klu_l_cholmod (UF_long n, UF_long Ap [ ], UF_long Ai [ ],
+ UF_long Perm [ ], klu_l_common *) ;
+
diff --git a/KLU/User/klu_l_cholmod.c b/KLU/User/klu_l_cholmod.c
new file mode 100644
index 0000000..c04577b
--- /dev/null
+++ b/KLU/User/klu_l_cholmod.c
@@ -0,0 +1,114 @@
+/* ========================================================================== */
+/* === klu_cholmod ========================================================== */
+/* ========================================================================== */
+
+/* klu_l_cholmod: user-defined ordering function to interface KLU to CHOLMOD.
+ *
+ * This routine is an example of a user-provided ordering function for KLU.
+ * Its return value is klu_l_cholmod's estimate of max (nnz(L),nnz(U)):
+ * 0 if error,
+ * -1 if OK, but estimate of max (nnz(L),nnz(U)) not computed
+ * > 0 if OK and estimate computed.
+ *
+ * This function can be assigned to KLU's Common->user_order function pointer.
+ */
+
+#include "klu_cholmod.h"
+#include "cholmod.h"
+#define TRUE 1
+#define FALSE 0
+
+UF_long klu_l_cholmod
+(
+ /* inputs */
+ UF_long n, /* A is n-by-n */
+ UF_long Ap [ ], /* column pointers */
+ UF_long Ai [ ], /* row indices */
+ /* outputs */
+ UF_long Perm [ ], /* fill-reducing permutation */
+ /* user-defined */
+ klu_l_common *Common /* user-defined data is in Common->user_data */
+)
+{
+ double one [2] = {1,0}, zero [2] = {0,0}, lnz = 0 ;
+ cholmod_sparse Amatrix, *A, *AT, *S ;
+ cholmod_factor *L ;
+ cholmod_common cm ;
+ UF_long *P ;
+ UF_long k, symmetric ;
+
+ if (Ap == NULL || Ai == NULL || Perm == NULL || n < 0)
+ {
+ /* invalid inputs */
+ return (0) ;
+ }
+
+ /* start CHOLMOD */
+ cholmod_l_start (&cm) ;
+ cm.supernodal = CHOLMOD_SIMPLICIAL ;
+ cm.print = 0 ;
+
+ /* use KLU memory management routines for CHOLMOD */
+ cm.malloc_memory = Common->malloc_memory ;
+ cm.realloc_memory = Common->realloc_memory ;
+ cm.calloc_memory = Common->calloc_memory ;
+ cm.free_memory = Common->free_memory ;
+
+ /* construct a CHOLMOD version of the input matrix A */
+ A = &Amatrix ;
+ A->nrow = n ; /* A is n-by-n */
+ A->ncol = n ;
+ A->nzmax = Ap [n] ; /* with nzmax entries */
+ A->packed = TRUE ; /* there is no A->nz array */
+ A->stype = 0 ; /* A is unsymmetric */
+ A->itype = CHOLMOD_INT ;
+ A->xtype = CHOLMOD_PATTERN ;
+ A->dtype = CHOLMOD_DOUBLE ;
+ A->nz = NULL ;
+ A->p = Ap ; /* column pointers */
+ A->i = Ai ; /* row indices */
+ A->x = NULL ; /* no numerical values */
+ A->z = NULL ;
+ A->sorted = FALSE ; /* columns of A are not sorted */
+
+ /* get the user_data; default is symmetric if user_data is NULL */
+ symmetric = (Common->user_data == NULL) ? TRUE :
+ (((UF_long *) (Common->user_data)) [0] != 0) ;
+
+ /* AT = pattern of A' */
+ AT = cholmod_l_transpose (A, 0, &cm) ;
+ if (symmetric)
+ {
+ /* S = the symmetric pattern of A+A' */
+ S = cholmod_l_add (A, AT, one, zero, FALSE, FALSE, &cm) ;
+ cholmod_l_free_sparse (&AT, &cm) ;
+ if (S != NULL)
+ {
+ S->stype = 1 ;
+ }
+ }
+ else
+ {
+ /* S = A'. CHOLMOD will order S*S', which is A'*A */
+ S = AT ;
+ }
+
+ /* order and analyze S or S*S' */
+ L = cholmod_l_analyze (S, &cm) ;
+
+ /* copy the permutation from L to the output */
+ if (L != NULL)
+ {
+ P = L->Perm ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Perm [k] = P [k] ;
+ }
+ lnz = cm.lnz ;
+ }
+
+ cholmod_l_free_sparse (&S, &cm) ;
+ cholmod_l_free_factor (&L, &cm) ;
+ cholmod_l_finish (&cm) ;
+ return (lnz) ;
+}
diff --git a/LDL/Demo/Makefile b/LDL/Demo/Makefile
new file mode 100644
index 0000000..6cee722
--- /dev/null
+++ b/LDL/Demo/Makefile
@@ -0,0 +1,82 @@
+#-------------------------------------------------------------------------------
+# LDL Demo Makefile
+#-------------------------------------------------------------------------------
+
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../../UFconfig -I../Include
+
+C = $(CC) $(CFLAGS) $(I)
+
+all: ldlsimple ldllsimple ldlmain ldllmain ldlamd ldllamd
+
+library:
+ ( cd ../../AMD ; $(MAKE) library )
+ ( cd ../Lib ; $(MAKE) )
+
+#-------------------------------------------------------------------------------
+# stand-alone C programs:
+#-------------------------------------------------------------------------------
+
+ldlmain: ldlmain.c library
+ $(C) ldlmain.c ../Lib/libldl.a -o ldlmain -lm
+ - ./ldlmain > my_ldlmain.out
+ - diff ldlmain.out my_ldlmain.out
+
+ldllmain: ldlmain.c library
+ $(C) -DLDL_LONG ldlmain.c ../Lib/libldl.a -o ldllmain -lm
+ - ./ldllmain > my_ldllmain.out
+ - diff ldlmain.out my_ldllmain.out
+
+ldlsimple: ldlsimple.c library
+ $(C) ldlsimple.c ../Lib/libldl.a -o ldlsimple -lm
+ - ./ldlsimple > my_ldlsimple.out
+ - diff ldlsimple.out my_ldlsimple.out
+
+ldllsimple: ldlsimple.c library
+ $(C) $(I) -DLDL_LONG ldlsimple.c ../Lib/libldl.a -o ldllsimple -lm
+ - ./ldllsimple > my_ldllsimple.out
+ - diff ldlsimple.out my_ldllsimple.out
+
+ldlamd: ldlmain.c library
+ - $(C) -I../../AMD/Include -DUSE_AMD \
+ ldlmain.c ../../AMD/Lib/libamd.a ../Lib/libldl.a -o ldlamd -lm
+ - ./ldlamd > my_ldlamd.out
+ - diff ldlamd.out my_ldlamd.out
+
+ldllamd: ldlmain.c library
+ - $(C) -DLDL_LONG $(I) -I../../AMD/Include -DUSE_AMD \
+ ldlmain.c ../../AMD/Lib/libamd.a ../Lib/libldl.a -o ldllamd -lm
+ - ./ldllamd > my_ldllamd.out
+ - diff ldllamd.out my_ldllamd.out
+
+run:
+ - ./ldlsimple > my_ldlsimple.out
+ - diff ldlsimple.out my_ldlsimple.out
+ - ./ldllsimple > my_ldllsimple.out
+ - diff ldlsimple.out my_ldllsimple.out
+ - ./ldlmain > my_ldlmain.out
+ - diff ldlmain.out my_ldlmain.out
+ - ./ldllmain > my_ldllmain.out
+ - diff ldlmain.out my_ldllmain.out
+ - ./ldlamd > my_ldlamd.out
+ - diff ldlamd.out my_ldlamd.out
+ - ./ldllamd > my_ldllamd.out
+ - diff ldllamd.out my_ldllamd.out
+
+
+#-------------------------------------------------------------------------------
+# clean-up:
+#-------------------------------------------------------------------------------
+
+distclean: purge
+
+purge: clean
+ - $(RM) ldlmain ldllmain ldlsimple ldllsimple ldlamd ldllamd
+ - $(RM) my_ldlmain.out my_ldlamd.out my_ldlsimple.out my_ldllamd.out
+ - $(RM) my_ldllsimple.out my_ldllmain.out
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/LDL/Demo/ldlamd.out b/LDL/Demo/ldlamd.out
new file mode 100644
index 0000000..005fbbb
--- /dev/null
+++ b/LDL/Demo/ldlamd.out
@@ -0,0 +1,1206 @@
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/1 n: 1 entries: 1
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 1
+ nz, number of nonzeros in A: 1
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 1
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 36
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 1
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 1
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/1 n: 1 entries: 2 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 1
+ nz, number of nonzeros in A: 1
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 1
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 52
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 1
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 1
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 8.32667e-17
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 8.32667e-17
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 4
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 2
+ nz, number of nonzeros in A: 4
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 2
+ nonzeros in pattern of A+A' (excl. diagonal): 2
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 80
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 1
+ nonzeros in L (including diagonal): 3
+ # divide operations for LDL' or LU: 1
+ # multiply-subtract operations for LDL': 1
+ # multiply-subtract operations for LU: 1
+ max nz. in any column of L (incl. diagonal): 2
+
+ chol flop count for real A, sqrt counted as 1 flop: 5
+ LDL' flop count for real A: 3
+ LDL' flop count for complex A: 17
+ LU flop count for real A (with no pivoting): 3
+ LU flop count for complex A (with no pivoting): 17
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 5.55112e-17
+Factorize A=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 5.55112e-17
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 5 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 2
+ nz, number of nonzeros in A: 4
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 2
+ nonzeros in pattern of A+A' (excl. diagonal): 2
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 112
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 1
+ nonzeros in L (including diagonal): 3
+ # divide operations for LDL' or LU: 1
+ # multiply-subtract operations for LDL': 1
+ # multiply-subtract operations for LU: 1
+ max nz. in any column of L (incl. diagonal): 2
+
+ chol flop count for real A, sqrt counted as 1 flop: 5
+ LDL' flop count for real A: 3
+ LDL' flop count for complex A: 17
+ LU flop count for real A (with no pivoting): 3
+ LU flop count for complex A (with no pivoting): 17
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 1.11022e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 1.11022e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 3
+ nz, number of nonzeros in A: 9
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 3
+ nonzeros in pattern of A+A' (excl. diagonal): 6
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 136
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 3
+ nonzeros in L (including diagonal): 6
+ # divide operations for LDL' or LU: 3
+ # multiply-subtract operations for LDL': 4
+ # multiply-subtract operations for LU: 5
+ max nz. in any column of L (incl. diagonal): 3
+
+ chol flop count for real A, sqrt counted as 1 flop: 14
+ LDL' flop count for real A: 11
+ LDL' flop count for complex A: 59
+ LU flop count for real A (with no pivoting): 13
+ LU flop count for complex A (with no pivoting): 67
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.11022e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.11022e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 11 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 3
+ nz, number of nonzeros in A: 9
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 3
+ nonzeros in pattern of A+A' (excl. diagonal): 6
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 196
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 3
+ nonzeros in L (including diagonal): 6
+ # divide operations for LDL' or LU: 3
+ # multiply-subtract operations for LDL': 4
+ # multiply-subtract operations for LU: 5
+ max nz. in any column of L (incl. diagonal): 3
+
+ chol flop count for real A, sqrt counted as 1 flop: 14
+ LDL' flop count for real A: 11
+ LDL' flop count for complex A: 59
+ LU flop count for real A (with no pivoting): 13
+ LU flop count for complex A (with no pivoting): 67
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.38778e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.38778e-16
+
+
+--------------------------------------------------------
+Input matrix: name: HB/can_24 n: 24 entries: 160
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 1516
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 96 Flop count: 632
+Ax=b not solved since D(1,1) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 146 Flop count: 1360
+Ax=b not solved since D(5,5) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: HB/can_24 n: 24 entries: 188 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2368
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 96 Flop count: 632
+Ax=b not solved since D(1,1) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 146 Flop count: 1360
+Ax=b not solved since D(5,5) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: FIDAP/ex5 n: 27 entries: 279
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 27
+ nz, number of nonzeros in A: 279
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 27
+ nonzeros in pattern of A+A' (excl. diagonal): 252
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2180
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 126
+ nonzeros in L (including diagonal): 153
+ # divide operations for LDL' or LU: 126
+ # multiply-subtract operations for LDL': 414
+ # multiply-subtract operations for LU: 702
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 981
+ LDL' flop count for real A: 954
+ LDL' flop count for complex A: 4446
+ LU flop count for real A (with no pivoting): 1530
+ LU flop count for complex A (with no pivoting): 6750
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 126 Flop count: 954
+relative maxnorm of residual: 2.59625e-10
+Factorize A=LDL' and solve Ax=b
+Nz in L: 276 Flop count: 4206
+relative maxnorm of residual: 2.72848e-10
+
+
+--------------------------------------------------------
+Input matrix: name: FIDAP/ex5 n: 27 entries: 325 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 27
+ nz, number of nonzeros in A: 279
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 27
+ nonzeros in pattern of A+A' (excl. diagonal): 252
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 3592
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 126
+ nonzeros in L (including diagonal): 153
+ # divide operations for LDL' or LU: 126
+ # multiply-subtract operations for LDL': 414
+ # multiply-subtract operations for LU: 702
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 981
+ LDL' flop count for real A: 954
+ LDL' flop count for complex A: 4446
+ LU flop count for real A (with no pivoting): 1530
+ LU flop count for complex A (with no pivoting): 6750
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 126 Flop count: 954
+relative maxnorm of residual: 3.27418e-10
+Factorize A=LDL' and solve Ax=b
+Nz in L: 276 Flop count: 4206
+relative maxnorm of residual: 2.32376e-10
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk01 n: 48 entries: 400
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 400
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 352
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 3416
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 441
+ nonzeros in L (including diagonal): 489
+ # divide operations for LDL' or LU: 441
+ # multiply-subtract operations for LDL': 2760
+ # multiply-subtract operations for LU: 5079
+ max nz. in any column of L (incl. diagonal): 20
+
+ chol flop count for real A, sqrt counted as 1 flop: 6009
+ LDL' flop count for real A: 5961
+ LDL' flop count for complex A: 26049
+ LU flop count for real A (with no pivoting): 10599
+ LU flop count for complex A (with no pivoting): 44601
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 441 Flop count: 5961
+relative maxnorm of residual: 2.38712e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 829 Flop count: 20103
+relative maxnorm of residual: 2.27374e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk01 n: 48 entries: 472 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 400
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 352
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 5500
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 441
+ nonzeros in L (including diagonal): 489
+ # divide operations for LDL' or LU: 441
+ # multiply-subtract operations for LDL': 2760
+ # multiply-subtract operations for LU: 5079
+ max nz. in any column of L (incl. diagonal): 20
+
+ chol flop count for real A, sqrt counted as 1 flop: 6009
+ LDL' flop count for real A: 5961
+ LDL' flop count for complex A: 26049
+ LU flop count for real A (with no pivoting): 10599
+ LU flop count for complex A (with no pivoting): 44601
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 441 Flop count: 5961
+relative maxnorm of residual: 2.27374e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 829 Flop count: 20103
+relative maxnorm of residual: 3.83693e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm01 n: 48 entries: 24
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 24
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 1728
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 48
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 48
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm01 n: 48 entries: 26 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 24
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2028
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 48
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 48
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: Pothen/mesh1e1 n: 48 entries: 306
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 306
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 258
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2964
+ # of memory compactions: 1
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 288
+ nonzeros in L (including diagonal): 336
+ # divide operations for LDL' or LU: 288
+ # multiply-subtract operations for LDL': 1171
+ # multiply-subtract operations for LU: 2054
+ max nz. in any column of L (incl. diagonal): 13
+
+ chol flop count for real A, sqrt counted as 1 flop: 2678
+ LDL' flop count for real A: 2630
+ LDL' flop count for complex A: 11960
+ LU flop count for real A (with no pivoting): 4396
+ LU flop count for complex A (with no pivoting): 19024
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 288 Flop count: 2630
+relative maxnorm of residual: 5.96745e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 511 Flop count: 7383
+relative maxnorm of residual: 6.93889e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 306
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 258
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 4596
+ # of memory compactions: 1
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 288
+ nonzeros in L (including diagonal): 336
+ # divide operations for LDL' or LU: 288
+ # multiply-subtract operations for LDL': 1171
+ # multiply-subtract operations for LU: 2054
+ max nz. in any column of L (incl. diagonal): 13
+
+ chol flop count for real A, sqrt counted as 1 flop: 2678
+ LDL' flop count for real A: 2630
+ LDL' flop count for complex A: 11960
+ LU flop count for real A (with no pivoting): 4396
+ LU flop count for complex A (with no pivoting): 19024
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 288 Flop count: 2630
+relative maxnorm of residual: 5.55112e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 511 Flop count: 7383
+relative maxnorm of residual: 5.55112e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Bai/bfwb62 n: 62 entries: 342
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 62
+ nz, number of nonzeros in A: 342
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 62
+ nonzeros in pattern of A+A' (excl. diagonal): 280
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 3576
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 226
+ nonzeros in L (including diagonal): 288
+ # divide operations for LDL' or LU: 226
+ # multiply-subtract operations for LDL': 623
+ # multiply-subtract operations for LU: 1020
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 1534
+ LDL' flop count for real A: 1472
+ LDL' flop count for complex A: 7018
+ LU flop count for real A (with no pivoting): 2266
+ LU flop count for complex A (with no pivoting): 10194
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 226 Flop count: 1472
+relative maxnorm of residual: 5.55112e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 662 Flop count: 11350
+relative maxnorm of residual: 1.11022e-15
+
+
+--------------------------------------------------------
+Input matrix: name: Bai/bfwb62 n: 62 entries: 407 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 62
+ nz, number of nonzeros in A: 342
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 62
+ nonzeros in pattern of A+A' (excl. diagonal): 280
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 5456
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 226
+ nonzeros in L (including diagonal): 288
+ # divide operations for LDL' or LU: 226
+ # multiply-subtract operations for LDL': 623
+ # multiply-subtract operations for LU: 1020
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 1534
+ LDL' flop count for real A: 1472
+ LDL' flop count for complex A: 7018
+ LU flop count for real A (with no pivoting): 2266
+ LU flop count for complex A (with no pivoting): 10194
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 226 Flop count: 1472
+relative maxnorm of residual: 5.68434e-14
+Factorize A=LDL' and solve Ax=b
+Nz in L: 662 Flop count: 11350
+relative maxnorm of residual: 2.15827e-12
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk02 n: 66 entries: 4356
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 4356
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 4290
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 22968
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 2145
+ nonzeros in L (including diagonal): 2211
+ # divide operations for LDL' or LU: 2145
+ # multiply-subtract operations for LDL': 47905
+ # multiply-subtract operations for LU: 93665
+ max nz. in any column of L (incl. diagonal): 66
+
+ chol flop count for real A, sqrt counted as 1 flop: 98021
+ LDL' flop count for real A: 97955
+ LDL' flop count for complex A: 402545
+ LU flop count for real A (with no pivoting): 189475
+ LU flop count for complex A (with no pivoting): 768625
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 7.50219e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 7.50219e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 4356
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 4290
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 43936
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 2145
+ nonzeros in L (including diagonal): 2211
+ # divide operations for LDL' or LU: 2145
+ # multiply-subtract operations for LDL': 47905
+ # multiply-subtract operations for LU: 93665
+ max nz. in any column of L (incl. diagonal): 66
+
+ chol flop count for real A, sqrt counted as 1 flop: 98021
+ LDL' flop count for real A: 97955
+ LDL' flop count for complex A: 402545
+ LU flop count for real A (with no pivoting): 189475
+ LU flop count for complex A (with no pivoting): 768625
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 8.59759e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 8.59759e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm02 n: 66 entries: 66
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 66
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2376
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 66
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 66
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm02 n: 66 entries: 72 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 66
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2932
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 66
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 66
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid perm)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ap)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+Largest residual during all tests: 3.27418e-10
+
+ldlamd: all tests passed
diff --git a/LDL/Demo/ldllamd.out b/LDL/Demo/ldllamd.out
new file mode 100644
index 0000000..689e42d
--- /dev/null
+++ b/LDL/Demo/ldllamd.out
@@ -0,0 +1,1206 @@
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/1 n: 1 entries: 1
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 1
+ nz, number of nonzeros in A: 1
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 1
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 72
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 1
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 1
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/1 n: 1 entries: 2 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 1
+ nz, number of nonzeros in A: 1
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 1
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 104
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 1
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 1
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 8.32667e-17
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 8.32667e-17
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 4
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 2
+ nz, number of nonzeros in A: 4
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 2
+ nonzeros in pattern of A+A' (excl. diagonal): 2
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 160
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 1
+ nonzeros in L (including diagonal): 3
+ # divide operations for LDL' or LU: 1
+ # multiply-subtract operations for LDL': 1
+ # multiply-subtract operations for LU: 1
+ max nz. in any column of L (incl. diagonal): 2
+
+ chol flop count for real A, sqrt counted as 1 flop: 5
+ LDL' flop count for real A: 3
+ LDL' flop count for complex A: 17
+ LU flop count for real A (with no pivoting): 3
+ LU flop count for complex A (with no pivoting): 17
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 5.55112e-17
+Factorize A=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 5.55112e-17
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 5 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 2
+ nz, number of nonzeros in A: 4
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 2
+ nonzeros in pattern of A+A' (excl. diagonal): 2
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 224
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 1
+ nonzeros in L (including diagonal): 3
+ # divide operations for LDL' or LU: 1
+ # multiply-subtract operations for LDL': 1
+ # multiply-subtract operations for LU: 1
+ max nz. in any column of L (incl. diagonal): 2
+
+ chol flop count for real A, sqrt counted as 1 flop: 5
+ LDL' flop count for real A: 3
+ LDL' flop count for complex A: 17
+ LU flop count for real A (with no pivoting): 3
+ LU flop count for complex A (with no pivoting): 17
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 1.11022e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 1.11022e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 3
+ nz, number of nonzeros in A: 9
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 3
+ nonzeros in pattern of A+A' (excl. diagonal): 6
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 272
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 3
+ nonzeros in L (including diagonal): 6
+ # divide operations for LDL' or LU: 3
+ # multiply-subtract operations for LDL': 4
+ # multiply-subtract operations for LU: 5
+ max nz. in any column of L (incl. diagonal): 3
+
+ chol flop count for real A, sqrt counted as 1 flop: 14
+ LDL' flop count for real A: 11
+ LDL' flop count for complex A: 59
+ LU flop count for real A (with no pivoting): 13
+ LU flop count for complex A (with no pivoting): 67
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.11022e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.11022e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 11 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 3
+ nz, number of nonzeros in A: 9
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 3
+ nonzeros in pattern of A+A' (excl. diagonal): 6
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 392
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 3
+ nonzeros in L (including diagonal): 6
+ # divide operations for LDL' or LU: 3
+ # multiply-subtract operations for LDL': 4
+ # multiply-subtract operations for LU: 5
+ max nz. in any column of L (incl. diagonal): 3
+
+ chol flop count for real A, sqrt counted as 1 flop: 14
+ LDL' flop count for real A: 11
+ LDL' flop count for complex A: 59
+ LU flop count for real A (with no pivoting): 13
+ LU flop count for complex A (with no pivoting): 67
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.38778e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.38778e-16
+
+
+--------------------------------------------------------
+Input matrix: name: HB/can_24 n: 24 entries: 160
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 3032
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 96 Flop count: 632
+Ax=b not solved since D(1,1) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 146 Flop count: 1360
+Ax=b not solved since D(5,5) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: HB/can_24 n: 24 entries: 188 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 4736
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 96 Flop count: 632
+Ax=b not solved since D(1,1) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 146 Flop count: 1360
+Ax=b not solved since D(5,5) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: FIDAP/ex5 n: 27 entries: 279
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 27
+ nz, number of nonzeros in A: 279
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 27
+ nonzeros in pattern of A+A' (excl. diagonal): 252
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 4360
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 126
+ nonzeros in L (including diagonal): 153
+ # divide operations for LDL' or LU: 126
+ # multiply-subtract operations for LDL': 414
+ # multiply-subtract operations for LU: 702
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 981
+ LDL' flop count for real A: 954
+ LDL' flop count for complex A: 4446
+ LU flop count for real A (with no pivoting): 1530
+ LU flop count for complex A (with no pivoting): 6750
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 126 Flop count: 954
+relative maxnorm of residual: 2.59625e-10
+Factorize A=LDL' and solve Ax=b
+Nz in L: 276 Flop count: 4206
+relative maxnorm of residual: 2.72848e-10
+
+
+--------------------------------------------------------
+Input matrix: name: FIDAP/ex5 n: 27 entries: 325 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 27
+ nz, number of nonzeros in A: 279
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 27
+ nonzeros in pattern of A+A' (excl. diagonal): 252
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 7184
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 126
+ nonzeros in L (including diagonal): 153
+ # divide operations for LDL' or LU: 126
+ # multiply-subtract operations for LDL': 414
+ # multiply-subtract operations for LU: 702
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 981
+ LDL' flop count for real A: 954
+ LDL' flop count for complex A: 4446
+ LU flop count for real A (with no pivoting): 1530
+ LU flop count for complex A (with no pivoting): 6750
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 126 Flop count: 954
+relative maxnorm of residual: 3.27418e-10
+Factorize A=LDL' and solve Ax=b
+Nz in L: 276 Flop count: 4206
+relative maxnorm of residual: 2.32376e-10
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk01 n: 48 entries: 400
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 400
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 352
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 6832
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 441
+ nonzeros in L (including diagonal): 489
+ # divide operations for LDL' or LU: 441
+ # multiply-subtract operations for LDL': 2760
+ # multiply-subtract operations for LU: 5079
+ max nz. in any column of L (incl. diagonal): 20
+
+ chol flop count for real A, sqrt counted as 1 flop: 6009
+ LDL' flop count for real A: 5961
+ LDL' flop count for complex A: 26049
+ LU flop count for real A (with no pivoting): 10599
+ LU flop count for complex A (with no pivoting): 44601
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 441 Flop count: 5961
+relative maxnorm of residual: 2.38712e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 829 Flop count: 20103
+relative maxnorm of residual: 2.27374e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk01 n: 48 entries: 472 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 400
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 352
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 11000
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 441
+ nonzeros in L (including diagonal): 489
+ # divide operations for LDL' or LU: 441
+ # multiply-subtract operations for LDL': 2760
+ # multiply-subtract operations for LU: 5079
+ max nz. in any column of L (incl. diagonal): 20
+
+ chol flop count for real A, sqrt counted as 1 flop: 6009
+ LDL' flop count for real A: 5961
+ LDL' flop count for complex A: 26049
+ LU flop count for real A (with no pivoting): 10599
+ LU flop count for complex A (with no pivoting): 44601
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 441 Flop count: 5961
+relative maxnorm of residual: 2.27374e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 829 Flop count: 20103
+relative maxnorm of residual: 3.83693e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm01 n: 48 entries: 24
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 24
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 3456
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 48
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 48
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm01 n: 48 entries: 26 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 24
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 4056
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 48
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 48
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: Pothen/mesh1e1 n: 48 entries: 306
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 306
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 258
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 5928
+ # of memory compactions: 1
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 288
+ nonzeros in L (including diagonal): 336
+ # divide operations for LDL' or LU: 288
+ # multiply-subtract operations for LDL': 1171
+ # multiply-subtract operations for LU: 2054
+ max nz. in any column of L (incl. diagonal): 13
+
+ chol flop count for real A, sqrt counted as 1 flop: 2678
+ LDL' flop count for real A: 2630
+ LDL' flop count for complex A: 11960
+ LU flop count for real A (with no pivoting): 4396
+ LU flop count for complex A (with no pivoting): 19024
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 288 Flop count: 2630
+relative maxnorm of residual: 5.96745e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 511 Flop count: 7383
+relative maxnorm of residual: 6.93889e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 306
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 258
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 9192
+ # of memory compactions: 1
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 288
+ nonzeros in L (including diagonal): 336
+ # divide operations for LDL' or LU: 288
+ # multiply-subtract operations for LDL': 1171
+ # multiply-subtract operations for LU: 2054
+ max nz. in any column of L (incl. diagonal): 13
+
+ chol flop count for real A, sqrt counted as 1 flop: 2678
+ LDL' flop count for real A: 2630
+ LDL' flop count for complex A: 11960
+ LU flop count for real A (with no pivoting): 4396
+ LU flop count for complex A (with no pivoting): 19024
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 288 Flop count: 2630
+relative maxnorm of residual: 5.55112e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 511 Flop count: 7383
+relative maxnorm of residual: 5.55112e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Bai/bfwb62 n: 62 entries: 342
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 62
+ nz, number of nonzeros in A: 342
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 62
+ nonzeros in pattern of A+A' (excl. diagonal): 280
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 7152
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 226
+ nonzeros in L (including diagonal): 288
+ # divide operations for LDL' or LU: 226
+ # multiply-subtract operations for LDL': 623
+ # multiply-subtract operations for LU: 1020
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 1534
+ LDL' flop count for real A: 1472
+ LDL' flop count for complex A: 7018
+ LU flop count for real A (with no pivoting): 2266
+ LU flop count for complex A (with no pivoting): 10194
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 226 Flop count: 1472
+relative maxnorm of residual: 5.55112e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 662 Flop count: 11350
+relative maxnorm of residual: 1.11022e-15
+
+
+--------------------------------------------------------
+Input matrix: name: Bai/bfwb62 n: 62 entries: 407 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 62
+ nz, number of nonzeros in A: 342
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 62
+ nonzeros in pattern of A+A' (excl. diagonal): 280
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 10912
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 226
+ nonzeros in L (including diagonal): 288
+ # divide operations for LDL' or LU: 226
+ # multiply-subtract operations for LDL': 623
+ # multiply-subtract operations for LU: 1020
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 1534
+ LDL' flop count for real A: 1472
+ LDL' flop count for complex A: 7018
+ LU flop count for real A (with no pivoting): 2266
+ LU flop count for complex A (with no pivoting): 10194
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 226 Flop count: 1472
+relative maxnorm of residual: 5.68434e-14
+Factorize A=LDL' and solve Ax=b
+Nz in L: 662 Flop count: 11350
+relative maxnorm of residual: 2.15827e-12
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk02 n: 66 entries: 4356
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 4356
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 4290
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 45936
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 2145
+ nonzeros in L (including diagonal): 2211
+ # divide operations for LDL' or LU: 2145
+ # multiply-subtract operations for LDL': 47905
+ # multiply-subtract operations for LU: 93665
+ max nz. in any column of L (incl. diagonal): 66
+
+ chol flop count for real A, sqrt counted as 1 flop: 98021
+ LDL' flop count for real A: 97955
+ LDL' flop count for complex A: 402545
+ LU flop count for real A (with no pivoting): 189475
+ LU flop count for complex A (with no pivoting): 768625
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 7.50219e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 7.50219e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 4356
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 4290
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 87872
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 2145
+ nonzeros in L (including diagonal): 2211
+ # divide operations for LDL' or LU: 2145
+ # multiply-subtract operations for LDL': 47905
+ # multiply-subtract operations for LU: 93665
+ max nz. in any column of L (incl. diagonal): 66
+
+ chol flop count for real A, sqrt counted as 1 flop: 98021
+ LDL' flop count for real A: 97955
+ LDL' flop count for complex A: 402545
+ LU flop count for real A (with no pivoting): 189475
+ LU flop count for complex A (with no pivoting): 768625
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 8.59759e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 8.59759e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm02 n: 66 entries: 66
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 66
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 4752
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 66
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 66
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm02 n: 66 entries: 72 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 8
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 66
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 5864
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 66
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 66
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid perm)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ap)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+Largest residual during all tests: 3.27418e-10
+
+ldlamd: all tests passed
diff --git a/LDL/Demo/ldllsimple.c b/LDL/Demo/ldllsimple.c
new file mode 100644
index 0000000..74ee915
--- /dev/null
+++ b/LDL/Demo/ldllsimple.c
@@ -0,0 +1,73 @@
+/* ========================================================================== */
+/* === ldllsimple.c: a simple LDL main program (long integer version) ====== */
+/* ========================================================================== */
+
+/* LDLSIMPLE: this is a very simple main program that illustrates the basic
+ * usage of the LDL routines. The output of this program is in ldlsimple.out.
+ * This program factorizes the matrix
+ *
+ * A =[ ...
+ * 1.7 0 0 0 0 0 0 0 .13 0
+ * 0 1. 0 0 .02 0 0 0 0 .01
+ * 0 0 1.5 0 0 0 0 0 0 0
+ * 0 0 0 1.1 0 0 0 0 0 0
+ * 0 .02 0 0 2.6 0 .16 .09 .52 .53
+ * 0 0 0 0 0 1.2 0 0 0 0
+ * 0 0 0 0 .16 0 1.3 0 0 .56
+ * 0 0 0 0 .09 0 0 1.6 .11 0
+ * .13 0 0 0 .52 0 0 .11 1.4 0
+ * 0 .01 0 0 .53 0 .56 0 0 3.1 ] ;
+ *
+ * and then solves a system Ax=b whose true solution is
+ * x = [.1 .2 .3 .4 .5 .6 .7 .8 .9 1]' ;
+ *
+ * Note that Li and Lx are statically allocated, with length 13. This is just
+ * enough to hold the factor L, but normally this size is not known until after
+ * ldl_symbolic has analyzed the matrix. The size of Li and Lx must be greater
+ * than or equal to lnz = Lp [N], which is 13 for this matrix L.
+ *
+ * LDL Version 1.3, Copyright (c) 2006 by Timothy A Davis,
+ * University of Florida. All Rights Reserved. See README for the License.
+ */
+
+#ifndef LDL_LONG
+#define LDL_LONG
+#endif
+
+#include <stdio.h>
+#include "ldl.h"
+#define N 10 /* A is 10-by-10 */
+#define ANZ 19 /* # of nonzeros on diagonal and upper triangular part of A */
+#define LNZ 13 /* # of nonzeros below the diagonal of L */
+
+int main (void)
+{
+ /* only the upper triangular part of A is required */
+ UF_long Ap[N+1] = {0, 1, 2, 3, 4, 6, 7, 9, 11, 15, ANZ},
+ Ai [ANZ] = {0, 1, 2, 3, 1,4, 5, 4,6, 4,7, 0,4,7,8, 1,4,6,9 } ;
+ double Ax [ANZ] = {1.7, 1., 1.5, 1.1, .02,2.6, 1.2, .16,1.3, .09,1.6,
+ .13,.52,.11,1.4, .01,.53,.56,3.1},
+ b [N] = {.287, .22, .45, .44, 2.486, .72, 1.55, 1.424, 1.621, 3.759};
+ double Lx [LNZ], D [N], Y [N] ;
+ UF_long Li [LNZ], Lp [N+1], Parent [N], Lnz [N], Flag [N], Pattern [N], d, i ;
+
+ /* factorize A into LDL' (P and Pinv not used) */
+ ldl_l_symbolic (N, Ap, Ai, Lp, Parent, Lnz, Flag, NULL, NULL) ;
+ printf ("Nonzeros in L, excluding diagonal: %d\n", Lp [N]) ;
+ d = ldl_l_numeric (N, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Pattern,
+ Flag, NULL, NULL) ;
+
+ if (d == N)
+ {
+ /* solve Ax=b, overwriting b with the solution x */
+ ldl_l_lsolve (N, b, Lp, Li, Lx) ;
+ ldl_l_dsolve (N, b, D) ;
+ ldl_l_ltsolve (N, b, Lp, Li, Lx) ;
+ for (i = 0 ; i < N ; i++) printf ("x [%d] = %g\n", i, b [i]) ;
+ }
+ else
+ {
+ printf ("ldl_l_numeric failed, D (%d,%d) is zero\n", d, d) ;
+ }
+ return (0) ;
+}
diff --git a/LDL/Demo/ldlmain.c b/LDL/Demo/ldlmain.c
new file mode 100644
index 0000000..715d7c3
--- /dev/null
+++ b/LDL/Demo/ldlmain.c
@@ -0,0 +1,397 @@
+/* ========================================================================== */
+/* === ldlmain.c: LDL main program, for demo and testing ==================== */
+/* ========================================================================== */
+
+/* LDLMAIN: this main program has two purposes. It provides an example of how
+ * to use the LDL routines, and it tests the package. The output of this
+ * program is in ldlmain.out (without AMD) and ldlamd.out (with AMD). If you
+ * did not download and install AMD, then the compilation of this program will
+ * not work with USE_AMD defined. Compare your output with ldlmain.out and
+ * ldlamd.out.
+ *
+ * The program reads in a set of matrices, in the Matrix/ subdirectory.
+ * The format of the files is as follows:
+ *
+ * one line with the matrix description
+ * one line with 2 integers: n jumbled
+ * n+1 lines, containing the Ap array of size n+1 (column pointers)
+ * nz lines, containing the Ai array of size nz (row indices)
+ * nz lines, containing the Ax array of size nz (numerical values)
+ * n lines, containing the P permutation array of size n
+ *
+ * The Ap, Ai, Ax, and P data structures are described in ldl.c.
+ * The jumbled flag is 1 if the matrix could contain unsorted columns and/or
+ * duplicate entries, and 0 otherwise.
+ *
+ * Once the matrix is read in, it is checked to see if it is valid. Some
+ * matrices are invalid by design, to test the error-checking routines. If
+ * valid, the matrix factorized twice (A and P*A*P'). A linear
+ * system Ax=b is set up and solved, and the residual computed.
+ * If any system is not solved accurately, this test will fail.
+ *
+ * This program can also be compiled as a MATLAB mexFunction, with the command
+ * "mex ldlmain.c ldl.c". You can then run the program in MATLAB, with the
+ * command "ldlmain".
+ *
+ * LDL Copyright (c) by Timothy A Davis,
+ * University of Florida. All Rights Reserved. See README for the License.
+ */
+
+#ifdef MATLAB_MEX_FILE
+#ifndef LDL_LONG
+#define LDL_LONG
+#endif
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "ldl.h"
+
+#define NMATRICES 30 /* number of test matrices in Matrix/ directory */
+#define LEN 200 /* string length */
+
+#ifdef USE_AMD /* get AMD include file, if using AMD */
+#include "amd.h"
+#define PROGRAM "ldlamd"
+#else
+#define PROGRAM "ldlmain"
+#endif
+
+#ifdef MATLAB_MEX_FILE
+#include "mex.h"
+#define EXIT_ERROR mexErrMsgTxt ("failure") ;
+#define EXIT_OK
+#else
+#define EXIT_ERROR exit (EXIT_FAILURE) ;
+#define EXIT_OK exit (EXIT_SUCCESS) ;
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* ALLOC_MEMORY: allocate a block of memory */
+/* -------------------------------------------------------------------------- */
+
+#define ALLOC_MEMORY(p,type,size) \
+p = (type *) malloc ((((size) <= 0) ? 1 : (size)) * sizeof (type)) ; \
+if (p == (type *) NULL) \
+{ \
+ printf (PROGRAM ": out of memory\n") ; \
+ EXIT_ERROR ; \
+}
+
+/* -------------------------------------------------------------------------- */
+/* FREE_MEMORY: free a block of memory */
+/* -------------------------------------------------------------------------- */
+
+#define FREE_MEMORY(p,type) \
+if (p != (type *) NULL) \
+{ \
+ free (p) ; \
+ p = (type *) NULL ; \
+}
+
+/* -------------------------------------------------------------------------- */
+/* stand-alone main program, or MATLAB mexFunction */
+/* -------------------------------------------------------------------------- */
+
+#ifdef MATLAB_MEX_FILE
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout[ ],
+ int nargin,
+ const mxArray *pargin[ ]
+)
+#else
+int main (void)
+#endif
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef USE_AMD
+ double Info [AMD_INFO] ;
+#endif
+ double r, rnorm, flops, maxrnorm = 0. ;
+ double *Ax, *Lx, *B, *D, *X, *Y ;
+ LDL_int matrix, *Ai, *Ap, *Li, *Lp, *P, *Pinv, *Perm, *PermInv, n, i, j, p,
+ nz, *Flag, *Pattern, *Lnz, *Parent, trial, lnz, d, jumbled ;
+ FILE *f ;
+ char s [LEN] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check the error-checking routines with null matrices */
+ /* ---------------------------------------------------------------------- */
+
+ i = 1 ;
+ n = -1 ;
+ if (LDL_valid_perm (n, (LDL_int *) NULL, &i)
+ || !LDL_valid_perm (0, (LDL_int *) NULL, &i)
+ || LDL_valid_matrix (n, (LDL_int *) NULL, (LDL_int *) NULL)
+ || LDL_valid_matrix (0, &i, &i))
+ {
+ printf (PROGRAM ": ldl error-checking routine failed\n") ;
+ EXIT_ERROR ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read in a factorize a set of matrices */
+ /* ---------------------------------------------------------------------- */
+
+ for (matrix = 1 ; matrix <= NMATRICES ; matrix++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* read in the matrix and the permutation */
+ /* ------------------------------------------------------------------ */
+
+ sprintf (s, "../Matrix/A%02d", (int) matrix) ;
+ if ((f = fopen (s, "r")) == (FILE *) NULL)
+ {
+ printf (PROGRAM ": could not open file: %s\n", s) ;
+ EXIT_ERROR ;
+ }
+ fgets (s, LEN, f) ;
+ printf ("\n\n--------------------------------------------------------");
+ printf ("\nInput matrix: %s", s) ;
+ printf ("--------------------------------------------------------\n\n");
+ fscanf (f, LDL_ID " " LDL_ID, &n, &jumbled) ;
+ n = (n < 0) ? (0) : (n) ;
+ ALLOC_MEMORY (P, LDL_int, n) ;
+ ALLOC_MEMORY (Ap, LDL_int, n+1) ;
+ for (j = 0 ; j <= n ; j++)
+ {
+ fscanf (f, LDL_ID, &Ap [j]) ;
+ }
+ nz = Ap [n] ;
+ ALLOC_MEMORY (Ai, LDL_int, nz) ;
+ ALLOC_MEMORY (Ax, double, nz) ;
+ for (p = 0 ; p < nz ; p++)
+ {
+ fscanf (f, LDL_ID , &Ai [p]) ;
+ }
+ for (p = 0 ; p < nz ; p++)
+ {
+ fscanf (f, "%lg", &Ax [p]) ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ fscanf (f, LDL_ID , &P [j]) ;
+ }
+ fclose (f) ;
+
+ /* ------------------------------------------------------------------ */
+ /* check the matrix A and the permutation P */
+ /* ------------------------------------------------------------------ */
+
+ ALLOC_MEMORY (Flag, LDL_int, n) ;
+
+ /* To test the error-checking routines, some of the input matrices
+ * are not valid. So this error is expected to occur. */
+ if (!LDL_valid_matrix (n, Ap, Ai) || !LDL_valid_perm (n, P, Flag))
+ {
+ printf (PROGRAM ": invalid matrix and/or permutation\n") ;
+ FREE_MEMORY (P, LDL_int) ;
+ FREE_MEMORY (Ap, LDL_int) ;
+ FREE_MEMORY (Ai, LDL_int) ;
+ FREE_MEMORY (Ax, double) ;
+ FREE_MEMORY (Flag, LDL_int) ;
+ continue ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* get the AMD permutation, if available */
+ /* ------------------------------------------------------------------ */
+
+#ifdef USE_AMD
+
+ /* recompute the permutation with AMD */
+ /* Assume that AMD produces a valid permutation P. */
+
+#ifdef LDL_LONG
+
+ if (amd_l_order (n, Ap, Ai, P, (double *) NULL, Info) < AMD_OK)
+ {
+ printf (PROGRAM ": call to AMD failed\n") ;
+ EXIT_ERROR ;
+ }
+ amd_l_control ((double *) NULL) ;
+ amd_l_info (Info) ;
+
+#else
+
+ if (amd_order (n, Ap, Ai, P, (double *) NULL, Info) < AMD_OK)
+ {
+ printf (PROGRAM ": call to AMD failed\n") ;
+ EXIT_ERROR ;
+ }
+ amd_control ((double *) NULL) ;
+ amd_info (Info) ;
+
+#endif
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* allocate workspace and the first part of LDL factorization */
+ /* ------------------------------------------------------------------ */
+
+ ALLOC_MEMORY (Pinv, LDL_int, n) ;
+ ALLOC_MEMORY (Y, double, n) ;
+ ALLOC_MEMORY (Pattern, LDL_int, n) ;
+ ALLOC_MEMORY (Lnz, LDL_int, n) ;
+ ALLOC_MEMORY (Lp, LDL_int, n+1) ;
+ ALLOC_MEMORY (Parent, LDL_int, n) ;
+ ALLOC_MEMORY (D, double, n) ;
+ ALLOC_MEMORY (B, double, n) ;
+ ALLOC_MEMORY (X, double, n) ;
+
+ /* ------------------------------------------------------------------ */
+ /* factorize twice, with and without permutation */
+ /* ------------------------------------------------------------------ */
+
+ for (trial = 1 ; trial <= 2 ; trial++)
+ {
+
+ if (trial == 1)
+ {
+ printf ("Factorize PAP'=LDL' and solve Ax=b\n") ;
+ Perm = P ;
+ PermInv = Pinv ;
+ }
+ else
+ {
+ printf ("Factorize A=LDL' and solve Ax=b\n") ;
+ Perm = (LDL_int *) NULL ;
+ PermInv = (LDL_int *) NULL ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* symbolic factorization to get Lp, Parent, Lnz, and Pinv */
+ /* -------------------------------------------------------------- */
+
+ LDL_symbolic (n, Ap, Ai, Lp, Parent, Lnz, Flag, Perm, PermInv) ;
+ lnz = Lp [n] ;
+
+ /* find # of nonzeros in L, and flop count for LDL_numeric */
+ flops = 0 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ flops += ((double) Lnz [j]) * (Lnz [j] + 2) ;
+ }
+ printf ("Nz in L: "LDL_ID" Flop count: %g\n", lnz, flops) ;
+
+ /* -------------------------------------------------------------- */
+ /* allocate remainder of L, of size lnz */
+ /* -------------------------------------------------------------- */
+
+ ALLOC_MEMORY (Li, LDL_int, lnz) ;
+ ALLOC_MEMORY (Lx, double, lnz) ;
+
+ /* -------------------------------------------------------------- */
+ /* numeric factorization to get Li, Lx, and D */
+ /* -------------------------------------------------------------- */
+
+ d = LDL_numeric (n, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D,
+ Y, Flag, Pattern, Perm, PermInv) ;
+
+ /* -------------------------------------------------------------- */
+ /* solve, or report singular case */
+ /* -------------------------------------------------------------- */
+
+ if (d != n)
+ {
+ printf ("Ax=b not solved since D("LDL_ID","LDL_ID") is zero.\n", d, d) ;
+ }
+ else
+ {
+ /* construct the right-hand-side, B */
+ for (i = 0 ; i < n ; i++)
+ {
+ B [i] = 1 + ((double) i) / 100 ;
+ }
+
+ /* solve Ax=b */
+ if (trial == 1)
+ {
+ /* the factorization is LDL' = PAP' */
+ LDL_perm (n, Y, B, P) ; /* y = Pb */
+ LDL_lsolve (n, Y, Lp, Li, Lx) ; /* y = L\y */
+ LDL_dsolve (n, Y, D) ; /* y = D\y */
+ LDL_ltsolve (n, Y, Lp, Li, Lx) ; /* y = L'\y */
+ LDL_permt (n, X, Y, P) ; /* x = P'y */
+ }
+ else
+ {
+ /* the factorization is LDL' = A */
+ for (i = 0 ; i < n ; i++) /* x = b */
+ {
+ X [i] = B [i] ;
+ }
+ LDL_lsolve (n, X, Lp, Li, Lx) ; /* x = L\x */
+ LDL_dsolve (n, X, D) ; /* x = D\x */
+ LDL_ltsolve (n, X, Lp, Li, Lx) ; /* x = L'\x */
+ }
+
+ /* compute the residual y = Ax-b */
+ /* note that this code can tolerate a jumbled matrix */
+ for (i = 0 ; i < n ; i++)
+ {
+ Y [i] = -B [i] ;
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ Y [Ai [p]] += Ax [p] * X [j] ;
+ }
+ }
+ /* rnorm = norm (y, inf) */
+ rnorm = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ r = (Y [i] > 0) ? (Y [i]) : (-Y [i]) ;
+ rnorm = (r > rnorm) ? (r) : (rnorm) ;
+ }
+ maxrnorm = (rnorm > maxrnorm) ? (rnorm) : (maxrnorm) ;
+ printf ("relative maxnorm of residual: %g\n", rnorm) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* free the size-lnz part of L */
+ /* -------------------------------------------------------------- */
+
+ FREE_MEMORY (Li, LDL_int) ;
+ FREE_MEMORY (Lx, double) ;
+
+ }
+
+ /* free everything */
+ FREE_MEMORY (P, LDL_int) ;
+ FREE_MEMORY (Ap, LDL_int) ;
+ FREE_MEMORY (Ai, LDL_int) ;
+ FREE_MEMORY (Ax, double) ;
+ FREE_MEMORY (Pinv, LDL_int) ;
+ FREE_MEMORY (Y, double) ;
+ FREE_MEMORY (Flag, LDL_int) ;
+ FREE_MEMORY (Pattern, LDL_int) ;
+ FREE_MEMORY (Lnz, LDL_int) ;
+ FREE_MEMORY (Lp, LDL_int) ;
+ FREE_MEMORY (Parent, LDL_int) ;
+ FREE_MEMORY (D, double) ;
+ FREE_MEMORY (B, double) ;
+ FREE_MEMORY (X, double) ;
+ }
+
+ printf ("\nLargest residual during all tests: %g\n", maxrnorm) ;
+ if (maxrnorm < 1e-8)
+ {
+ printf ("\n" PROGRAM ": all tests passed\n") ;
+ EXIT_OK ;
+ }
+ else
+ {
+ printf ("\n" PROGRAM ": one more tests failed (residual too high)\n") ;
+ EXIT_ERROR ;
+ }
+}
diff --git a/LDL/Demo/ldlmain.out b/LDL/Demo/ldlmain.out
new file mode 100644
index 0000000..f4f8474
--- /dev/null
+++ b/LDL/Demo/ldlmain.out
@@ -0,0 +1,334 @@
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/1 n: 1 entries: 1
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/1 n: 1 entries: 2 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 8.32667e-17
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 8.32667e-17
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 4
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 5.55112e-17
+Factorize A=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 5.55112e-17
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 5 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 1.11022e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 1.11022e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.11022e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.11022e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 11 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.38778e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.38778e-16
+
+
+--------------------------------------------------------
+Input matrix: name: HB/can_24 n: 24 entries: 160
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 96 Flop count: 632
+Ax=b not solved since D(1,1) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 146 Flop count: 1360
+Ax=b not solved since D(5,5) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: HB/can_24 n: 24 entries: 188 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 96 Flop count: 632
+Ax=b not solved since D(1,1) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 146 Flop count: 1360
+Ax=b not solved since D(5,5) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: FIDAP/ex5 n: 27 entries: 279
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 126 Flop count: 954
+relative maxnorm of residual: 2.59625e-10
+Factorize A=LDL' and solve Ax=b
+Nz in L: 276 Flop count: 4206
+relative maxnorm of residual: 2.72848e-10
+
+
+--------------------------------------------------------
+Input matrix: name: FIDAP/ex5 n: 27 entries: 325 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 126 Flop count: 954
+relative maxnorm of residual: 3.27418e-10
+Factorize A=LDL' and solve Ax=b
+Nz in L: 276 Flop count: 4206
+relative maxnorm of residual: 2.32376e-10
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk01 n: 48 entries: 400
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 441 Flop count: 5961
+relative maxnorm of residual: 2.38712e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 829 Flop count: 20103
+relative maxnorm of residual: 2.27374e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk01 n: 48 entries: 472 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 441 Flop count: 5961
+relative maxnorm of residual: 2.27374e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 829 Flop count: 20103
+relative maxnorm of residual: 3.83693e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm01 n: 48 entries: 24
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm01 n: 48 entries: 26 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: Pothen/mesh1e1 n: 48 entries: 306
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 288 Flop count: 2630
+relative maxnorm of residual: 5.96745e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 511 Flop count: 7383
+relative maxnorm of residual: 6.93889e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 288 Flop count: 2630
+relative maxnorm of residual: 5.55112e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 511 Flop count: 7383
+relative maxnorm of residual: 5.55112e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Bai/bfwb62 n: 62 entries: 342
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 226 Flop count: 1472
+relative maxnorm of residual: 5.55112e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 662 Flop count: 11350
+relative maxnorm of residual: 1.11022e-15
+
+
+--------------------------------------------------------
+Input matrix: name: Bai/bfwb62 n: 62 entries: 407 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 226 Flop count: 1472
+relative maxnorm of residual: 5.68434e-14
+Factorize A=LDL' and solve Ax=b
+Nz in L: 662 Flop count: 11350
+relative maxnorm of residual: 2.15827e-12
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk02 n: 66 entries: 4356
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 7.50219e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 7.50219e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 8.59759e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 8.59759e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm02 n: 66 entries: 66
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm02 n: 66 entries: 72 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid perm)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ap)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+Largest residual during all tests: 3.27418e-10
+
+ldlmain: all tests passed
diff --git a/LDL/Demo/ldlsimple.c b/LDL/Demo/ldlsimple.c
new file mode 100644
index 0000000..bb795f5
--- /dev/null
+++ b/LDL/Demo/ldlsimple.c
@@ -0,0 +1,69 @@
+/* ========================================================================== */
+/* === ldlsimple.c: a simple LDL main program ============================== */
+/* ========================================================================== */
+
+/* LDLSIMPLE: this is a very simple main program that illustrates the basic
+ * usage of the LDL routines. The output of this program is in ldlsimple.out.
+ * This program factorizes the matrix
+ *
+ * A =[ ...
+ * 1.7 0 0 0 0 0 0 0 .13 0
+ * 0 1. 0 0 .02 0 0 0 0 .01
+ * 0 0 1.5 0 0 0 0 0 0 0
+ * 0 0 0 1.1 0 0 0 0 0 0
+ * 0 .02 0 0 2.6 0 .16 .09 .52 .53
+ * 0 0 0 0 0 1.2 0 0 0 0
+ * 0 0 0 0 .16 0 1.3 0 0 .56
+ * 0 0 0 0 .09 0 0 1.6 .11 0
+ * .13 0 0 0 .52 0 0 .11 1.4 0
+ * 0 .01 0 0 .53 0 .56 0 0 3.1 ] ;
+ *
+ * and then solves a system Ax=b whose true solution is
+ * x = [.1 .2 .3 .4 .5 .6 .7 .8 .9 1]' ;
+ *
+ * Note that Li and Lx are statically allocated, with length 13. This is just
+ * enough to hold the factor L, but normally this size is not known until after
+ * ldl_symbolic has analyzed the matrix. The size of Li and Lx must be greater
+ * than or equal to lnz = Lp [N], which is 13 for this matrix L.
+ *
+ * LDL Version 1.3, Copyright (c) 2006 by Timothy A Davis,
+ * University of Florida. All Rights Reserved. See README for the License.
+ */
+
+#include <stdio.h>
+#include "ldl.h"
+#define N 10 /* A is 10-by-10 */
+#define ANZ 19 /* # of nonzeros on diagonal and upper triangular part of A */
+#define LNZ 13 /* # of nonzeros below the diagonal of L */
+
+int main (void)
+{
+ /* only the upper triangular part of A is required */
+ int Ap [N+1] = {0, 1, 2, 3, 4, 6, 7, 9, 11, 15, ANZ},
+ Ai [ANZ] = {0, 1, 2, 3, 1,4, 5, 4,6, 4,7, 0,4,7,8, 1,4,6,9 } ;
+ double Ax [ANZ] = {1.7, 1., 1.5, 1.1, .02,2.6, 1.2, .16,1.3, .09,1.6,
+ .13,.52,.11,1.4, .01,.53,.56,3.1},
+ b [N] = {.287, .22, .45, .44, 2.486, .72, 1.55, 1.424, 1.621, 3.759};
+ double Lx [LNZ], D [N], Y [N] ;
+ int Li [LNZ], Lp [N+1], Parent [N], Lnz [N], Flag [N], Pattern [N], d, i ;
+
+ /* factorize A into LDL' (P and Pinv not used) */
+ ldl_symbolic (N, Ap, Ai, Lp, Parent, Lnz, Flag, NULL, NULL) ;
+ printf ("Nonzeros in L, excluding diagonal: %d\n", Lp [N]) ;
+ d = ldl_numeric (N, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Pattern,
+ Flag, NULL, NULL) ;
+
+ if (d == N)
+ {
+ /* solve Ax=b, overwriting b with the solution x */
+ ldl_lsolve (N, b, Lp, Li, Lx) ;
+ ldl_dsolve (N, b, D) ;
+ ldl_ltsolve (N, b, Lp, Li, Lx) ;
+ for (i = 0 ; i < N ; i++) printf ("x [%d] = %g\n", i, b [i]) ;
+ }
+ else
+ {
+ printf ("ldl_numeric failed, D (%d,%d) is zero\n", d, d) ;
+ }
+ return (0) ;
+}
diff --git a/LDL/Demo/ldlsimple.out b/LDL/Demo/ldlsimple.out
new file mode 100644
index 0000000..acb48b5
--- /dev/null
+++ b/LDL/Demo/ldlsimple.out
@@ -0,0 +1,11 @@
+Nonzeros in L, excluding diagonal: 13
+x [0] = 0.1
+x [1] = 0.2
+x [2] = 0.3
+x [3] = 0.4
+x [4] = 0.5
+x [5] = 0.6
+x [6] = 0.7
+x [7] = 0.8
+x [8] = 0.9
+x [9] = 1
diff --git a/LDL/Doc/ChangeLog b/LDL/Doc/ChangeLog
new file mode 100644
index 0000000..48c322d
--- /dev/null
+++ b/LDL/Doc/ChangeLog
@@ -0,0 +1,39 @@
+May 31, 2007: version 2.0.0
+
+ * C-callable 64-bit version added
+
+ * ported to 64-bit MATLAB
+
+ * subdirectories added (Source/, Include/, Lib/, Demo/, Doc/, MATLAB/)
+
+Dec 12, 2006: version 1.3.4
+
+ * minor MATLAB cleanup
+
+Sept 11, 2006: version 1.3.1
+
+ * The ldl m-file renamed to ldlsparse, to avoid name conflict with the
+ new MATLAB ldl function (in MATLAB 7.3).
+
+Apr 30, 2006: version 1.3
+
+ * requires AMD v2.0. ldlmain.c demo program modified, since AMD can now
+ handle jumbled matrices. Minor change to Makefile.
+
+Aug 30, 2005:
+
+ * Makefile changed to use ../UFconfig/UFconfig.mk. License changed to
+ GNU LGPL.
+
+July 4, 2005:
+
+ * user guide added. Since no changes to the code were made,
+ the version number (1.1) and code release date (Apr 22, 2005)
+ were left unchanged.
+
+Apr. 22, 2005: LDL v1.1 released.
+
+ * No real changes were made. The code was revised so
+ that each routine fits on a single page in the documentation.
+
+Dec 31, 2003: LDL v1.0 released.
diff --git a/LDL/Doc/Makefile b/LDL/Doc/Makefile
new file mode 100644
index 0000000..4303388
--- /dev/null
+++ b/LDL/Doc/Makefile
@@ -0,0 +1,33 @@
+#-------------------------------------------------------------------------------
+# Makefile for the LDL documentation
+#-------------------------------------------------------------------------------
+
+default: ldl_userguide.pdf
+
+include ../../UFconfig/UFconfig.mk
+
+#-------------------------------------------------------------------------------
+# clean-up:
+#-------------------------------------------------------------------------------
+
+distclean: purge
+
+purge: clean
+ - $(RM) *.dvi *.aux *.log *.bak *.bbl *.blg *.ps
+
+clean:
+ - $(RM) $(CLEAN)
+
+#-------------------------------------------------------------------------------
+# user guide:
+#-------------------------------------------------------------------------------
+
+ldl_userguide.pdf: ldl_userguide.tex ldl.bib
+ latex ldl_userguide
+ - bibtex ldl_userguide
+ latex ldl_userguide
+ latex ldl_userguide
+ dvips ldl_userguide -o ldl_userguide.ps
+ pdflatex ldl_userguide
+ pdflatex ldl_userguide
+ - $(RM) *.dvi *.aux *.log *.bak *.bbl *.blg *.ps
diff --git a/LDL/Doc/ldl.bib b/LDL/Doc/ldl.bib
new file mode 100644
index 0000000..3d87f16
--- /dev/null
+++ b/LDL/Doc/ldl.bib
@@ -0,0 +1,150 @@
+ at string{TOMS = "{ACM} Trans. Math. Softw."}
+ at string{SIMAX = "{SIAM} J. Matrix Anal. Applic."}
+ at string{SIAMJSC = "{SIAM} J. Sci. Comput."}
+ at string{SIAMJSSC = "{SIAM} J. Sci. Statist. Comput."}
+
+ at article{AmestoyDavisDuff96,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={An approximate minimum degree ordering algorithm},
+ journal=SIMAX,
+ year={1996}
+ ,volume={17}
+ ,number={4}
+ ,pages={886-905}
+ }
+
+ at article{AmestoyDavisDuff03,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={381-388}}
+
+ at article{Davis05,
+ author={Davis, T. A},
+ title={Algorithm 849: a concise sparse Cholesky factorization package},
+ journal=TOMS,
+ year={2005},
+ volume={31},
+ number={4},
+ pages={587--591}
+ }
+
+ at article{GeorgeLiu79,
+ author={George, A. and Liu, J. W. H.},
+ month={Jun.},
+ year={1979},
+ title={The Design of a User Interface for a Sparse Matrix Package},
+ journal=TOMS,
+ annote={f},
+ volume={5},
+ number={2},
+ pages={139-162},
+ keywords={software user interface SPARSPAK}}
+
+ at book{GeorgeLiu,
+ author={George, A. and Liu, J. W. H.},
+ year={1981},
+ title={Computer Solution of Large Sparse Positive Definite Systems},
+ address={Englewood Cliffs, New Jersey},
+ publisher={Prentice-Hall},
+ keywords={ positive definite systems},
+ annote={sh}
+ }
+
+ at article{GilbertMolerSchreiber,
+ author={Gilbert, J. R. and Moler, C. and Schreiber, R.},
+ title={Sparse matrices in {MATLAB}: design and implementation},
+ journal=SIMAX,
+ year={1992}
+ ,volume={13}
+ ,number={1}
+ ,pages={333-356}
+ ,annote={f}
+ }
+
+ at article{GilbertNgPeyton94,
+ author={Gilbert, J. R. and Ng, E. G. and Peyton, B. W.},
+ title={An efficient algorithm to compute row and column counts for sparse {C}holesky factorization},
+ journal=SIMAX,
+ year={1994}
+ ,volume={15}
+ ,number={4}
+ ,pages={1075-1091}
+ ,annote={f}
+ }
+
+ at article{GilbertPeierls88,
+ author={Gilbert, J. R. and Peierls, T.},
+ year={1988},
+ title={Sparse Partial Pivoting in Time Proportional to Arithmetic Operations},
+ journal=SIAMJSSC,
+ annote={f},
+ volume={9},
+ pages={862-874},
+ keywords={316 partial pivoting, graph algorithms}}
+
+ at article{Liu86c,
+ author={Liu, J. W. H.},
+ month={Jun.},
+ year={1986},
+ title={A Compact Row Storage Scheme for {C}holesky Factors Using Elimination Trees},
+ journal=TOMS,
+ volume={12},
+ number={2},
+ pages={127-148},
+ annote={f. previously Report CS-84-02, Dept. Computer Science, York University (1984)}}
+
+ at article{Liu90a,
+ author={Liu, J. W. H.},
+ title={The Role of Elimination Trees in Sparse Factorization},
+ journal=SIMAX,
+ year={1990}
+ ,volume={11}
+ ,number={1}
+ ,pages={134-172}
+ ,annote={f}
+ }
+
+ at article{Liu91,
+ author={Liu, J. W. H.},
+ title={A generalized envelope method for sparse factorization by rows},
+ journal=TOMS,
+ year={1991}
+ ,volume={17}
+ ,number={1}
+ ,pages={112-129}
+ ,annote={f}
+ }
+
+ at article{NgPeyton93,
+ author={Ng, E. G. and Peyton, B. W.},
+ title={A supernodal {Cholesky} factorization algorithm for shared-memory multiprocessors},
+ journal=SIAMJSC,
+ year={1993}
+ ,volume={14}
+ ,pages={761-769}
+ ,annote={f}
+ }
+
+ at article{RothbergGupta91,
+ author={Rothberg, E. and Gupta, A.},
+ title={Efficient sparse matrix factorization on high-performance workstations - {E}xploiting the memory hierarchy},
+ journal=TOMS,
+ year={1991}
+ ,volume={17}
+ ,number={3}
+ ,pages={313-334}
+ ,annote={f}
+ }
+
+ at techreport{Stewart03,
+ author={Stewart, G. W.},
+ title={Building an old-fashioned sparse solver},
+ institution={Univ. Maryland (www.umd.cs.edu/$\sim$stewart)},
+ year={2003}
+ ,annote={f}
+ }
+
diff --git a/LDL/Doc/ldl_userguide.pdf b/LDL/Doc/ldl_userguide.pdf
new file mode 100644
index 0000000..bfe0615
Binary files /dev/null and b/LDL/Doc/ldl_userguide.pdf differ
diff --git a/LDL/Doc/ldl_userguide.tex b/LDL/Doc/ldl_userguide.tex
new file mode 100644
index 0000000..6208a59
--- /dev/null
+++ b/LDL/Doc/ldl_userguide.tex
@@ -0,0 +1,651 @@
+\documentclass[12pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+%-------------------------------------------------------------------------------
+\begin{document}
+%-------------------------------------------------------------------------------
+
+\title{User Guide for LDL, a concise sparse Cholesky package}
+\author{Timothy A. Davis\thanks{
+Dept.~of Computer and Information Science and Engineering,
+Univ.~of Florida, Gainesville, FL, USA.
+email: davis at cise.ufl.edu.
+http://www.cise.ufl.edu/$\sim$davis.
+This work was supported by the National
+Science Foundation, under grant CCR-0203270.
+Portions of the work were done while on sabbatical at Stanford University
+and Lawrence Berkeley National Laboratory (with funding from Stanford
+University and the SciDAC program).
+}}
+
+\date{Nov 1, 2007}
+
+\maketitle
+
+%-------------------------------------------------------------------------------
+\begin{abstract}
+The {\tt LDL} software package is a set of short, concise routines for
+factorizing symmetric positive-definite sparse matrices, with some
+applicability to symmetric indefinite matrices. Its primary purpose is
+to illustrate much of the basic theory of sparse matrix algorithms in as
+concise a code as possible, including an elegant method
+of sparse symmetric factorization that computes the factorization row-by-row
+but stores it column-by-column. The entire symbolic and numeric factorization
+consists of less than 50 lines of code. The package is written in C,
+and includes a MATLAB interface.
+\end{abstract}
+%-------------------------------------------------------------------------------
+
+%-------------------------------------------------------------------------------
+\section{Overview}
+%-------------------------------------------------------------------------------
+
+{\tt LDL} is a set of short, concise routines that compute the $\m{LDL}\tr$
+factorization of a sparse symmetric matrix $\m{A}$. Its primary purpose is
+to illustrate much of the basic theory of sparse matrix algorithms in as
+compact a code as possible, including an elegant method of
+sparse symmetric factorization (related to \cite{Liu86c,Liu91}).
+The lower triangular factor $\m{L}$ is computed row-by-row, in contrast to the
+conventional column-by-column method.
+Although it does not achieve the same level of performance
+as methods based on dense matrix kernels
+(such as \cite{NgPeyton93,RothbergGupta91}),
+its performance is competitive with column-by-column methods that do not
+use dense kernels \cite{GeorgeLiu79, GeorgeLiu, GilbertMolerSchreiber}.
+
+Section~\ref{Algorithm} gives a brief description of the algorithm
+used in the symbolic and numeric factorization. A more detailed tutorial-level
+discussion may be found in \cite{Stewart03}. Details
+of the concise implementation of this method are given in
+Section~\ref{Implementation}. Sections~\ref{MATLAB}~and~\ref{C} give an
+overview of how to use the package in MATLAB and in a stand-alone C program.
+
+%-------------------------------------------------------------------------------
+\section{Algorithm}
+\label{Algorithm}
+%-------------------------------------------------------------------------------
+
+The underlying numerical algorithm is described below. The $k$th
+step solves a lower triangular system of dimension $k-1$ to compute the
+$k$th row of $\m{L}$ and the $d_{kk}$ entry of the diagonal matrix $\m{D}$.
+Colon notation is used for submatrices. For example,
+$\m{L}_{k,1:k-1}$ refers to the first $k-1$ columns of
+the $k$th row of $\m{L}$. Similarly, $\m{L}_{1:k-1,1:k-1}$ refers to
+the leading $(k-1)$-by-$(k-1)$ submatrix of $\m{L}$.
+%---------------
+\vspace{-0.2in}
+\begin{tabbing}
+\hspace{2em} \= \hspace{2em} \= \hspace{2em} \= \\
+{\bf Algorithm~1
+($\m{LDL}\tr$ factorization of a $n$-by-$n$ symmetric matrix $\m{A}$)} \\
+\> {\bf for} $k = 1$ {\bf to} $n$ \\
+\>\> (step 1) Solve $\m{L}_{1:k-1,1:k-1}\m{y} = \m{A}_{1:k-1,k}$ for $\m{y}$ \\
+\>\> (step 2) $\m{L}_{k,1:k-1} = (\m{D}_{1:k-1,1:k-1}^{-1} \m{y})\tr$ \\
+\>\> (step 3) $l_{kk} = 1$ \\
+\>\> (step 4) $d_{kk} = a_{kk} - \m{L}_{k,1:k-1}\m{y}$ \\
+\> {\bf end for}
+\end{tabbing}
+%---------------
+
+The algorithm computes an $\m{LDL}\tr$ factorization without numerical pivoting.
+It can thus factorize any symmetric positive definite matrix, and any
+symmetric indefinite matrix whose leading minors are all well-conditioned.
+
+When $\m{A}$ and $\m{L}$ are sparse, step 1 of Algorithm~1 requires a
+triangular solve of the form $\m{Lx}=\m{b}$, where all three terms in
+the equation are sparse. This is the most costly step of the Algorithm.
+Steps 2 through 4 are fairly straightforward.
+
+Let ${\cal X}$ and ${\cal B}$ refer to the set of indices of nonzero entries
+in $\m{x}$ and $\m{b}$, respectively, in the lower triangular system
+$\m{Lx}=\m{b}$. To compute $\m{x}$ efficiently
+the nonzero pattern ${\cal X}$ must be found first.
+In the general case when $\m{L}$ is arbitrary \cite{GilbertPeierls88},
+the nonzero
+pattern ${\cal X}$ is the set of nodes reachable via paths in the graph $G_L$
+from all nodes in the set ${\cal B}$, and where the graph $G_L$ has
+$n$ nodes and a directed edge $(j,i)$ if and only if $l_{ij}$ is nonzero.
+To compute the numerical solution to $\m{Lx}=\m{b}$ by accessing the columns of
+$\m{L}$ one at a time, ${\cal X}$ can be traversed
+in any topological order of the subgraph of $G_L$ consisting of nodes in
+${\cal X}$. That is, $x_j$ must be computed before $x_i$ if there is a path
+from $j$ to $i$ in $G_L$. The natural order ($1, 2, \ldots, n$) is one such
+ordering, but that requires a costly sort of ${\cal X}$.
+With a graph traversal and topological sort, the solution of $\m{Lx}=\m{b}$
+can be computed using Algorithm~2 below.
+The computation of ${\cal X}$ and $\m{x}$ both take
+time proportional to the floating-point operation count.
+%---------------
+\vspace{-0.2in}
+\begin{tabbing}
+\hspace{2em} \= \hspace{2em} \= \hspace{2em} \= \\
+{\bf Algorithm~2
+(Solve $\m{Lx}=\m{b}$, where $\m{L}$ is lower triangular with unit diagonal)} \\
+\> ${\cal X} = \mbox{Reach}_{G_L} ({\cal B})$ \\
+\> $\m{x} = \m{b}$ \\
+\> {\bf for} $i \in {\cal X}$ in any topological order \\
+\>\> $\m{x}_{i+1:n} = \m{x}_{i+1:n} - \m{L}_{i+1:n,i} x_i$ \\
+\> {\bf end for}
+\end{tabbing}
+%---------------
+
+The general result also governs the pattern of $\m{y}$ in Algorithm~1.
+However, in this case $\m{L}$ arises from a sparse Cholesky factorization,
+and is governed by the elimination tree \cite{Liu90a}.
+A general graph traversal is not required.
+In the elimination tree, the parent of node $i$ is the smallest $j > i$
+such that $l_{ji}$ is nonzero. Node $i$ has no parent if column $i$ of
+$\m{L}$ is completely zero below the diagonal; $i$ is a root of the
+elimination tree in this case. The nonzero pattern of $\m{x}$ is the
+union of all the nodes on the paths from any node $i$ (where $b_i$ is nonzero) to the
+root of the elimination tree \cite[Thm 2.4]{Liu86c}. It is referred to here as a tree,
+but in general it can be a forest.
+
+Rather than a general topological sort of the subgraph of $G_L$ consisting
+nodes reachable from nodes in ${\cal B}$, a simpler
+tree traversal can be used. First, select any nonzero entry $b_i$
+and follow the path from $i$ to the root of tree.
+Nodes along this path are marked and placed in a stack,
+with $i$ at the top of the
+stack and the root at the bottom.
+Repeat for every other nonzero entry in $b_i$, in arbitrary order, but stop
+just before reaching a marked node (the result can be empty if $i$ is already
+in the stack). The stack now contains ${\cal X}$, a topological ordering of
+the nonzero pattern of $\m{x}$, which can be used in Algorithm~2 to solve
+$\m{Lx}=\m{b}$. The time to compute ${\cal X}$
+using an elimination tree traversal is much faster than the general graph
+traversal, taking time proportional to the size of ${\cal X}$ rather than the
+number of floating-point operations required to compute $\m{x}$.
+
+In the $k$th step of the factorization, the set ${\cal X}$ becomes the
+nonzero pattern of row $k$ of $\m{L}$. This step requires the elimination
+tree of $\m{L}_{1:k-1,1:k-1}$, and must construct the elimination tree of
+$\m{L}_{1:k,1:k}$ for step $k+1$. Recall that the parent of $i$ in the
+tree is the smallest $j$ such that $i < j$ and $l_{ji} \ne 0$.
+Thus, if any node $i$ already has a parent $j$, then $j$ will remain the
+parent of $i$ in the elimination trees of all other larger leading submatrices
+of $\m{L}$, and in the elimination tree of $\m{L}$ itself.
+If $l_{ki} \ne 0$ and $i$ does not have a parent in the elimination tree of
+$\m{L}_{1:k-1,1:k-1}$, then the parent of $i$ is $k$
+in the elimination tree of $\m{L}_{1:k,1:k}$.
+Node $k$ becomes the parent of any node $i \in {\cal X}$ that does not yet
+have a parent.
+
+Since Algorithm~2 traverses $\m{L}$ in column order, $\m{L}$ is stored in a
+conventional sparse column representation. Each column $j$ is stored as a list
+of nonzero values and their corresponding row indices. When row $k$ is
+computed, the new entries can be placed at the end of each list. As
+a by-product of computing $\m{L}$ one row at a time,
+the columns of $\m{L}$ are computed in a sorted manner. This is a convenient
+form of the output.
+MATLAB requires the columns of its sparse matrices to be sorted, for example.
+Sorted columns improve the speed of Algorithm~2, since the memory access
+pattern is more regular. The conventional column-by-column algorithm
+\cite{GeorgeLiu79,GeorgeLiu} does not produce columns of $\m{L}$ with
+sorted row indices.
+
+A simple symbolic pre-analysis can be obtained by repeating the subtree traversals.
+All that is required to compute the nonzero pattern of
+the $k$th row of $\m{L}$ is the partially constructed elimination tree
+and the nonzero pattern of the $k$th column of $\m{A}$. This is computed
+in time proportional to the size of this set, using the elimination tree
+traversal. Once constructed, the number of nonzeros in each column of
+$\m{L}$ is incremented, for each entry in ${\cal X}$, and then ${\cal X}$
+is discarded. The set ${\cal X}$ need not be constructed in topological
+order, so no stack is required. The run time of the symbolic analysis
+algorithm is thus proportional to the number of nonzeros in $\m{L}$.
+This is more costly than the optimal algorithm \cite{GilbertNgPeyton94},
+which takes time essentially proportional to the number of nonzeros in $\m{A}$.
+The memory requirements are just the matrix $\m{A}$ and a few size-$n$ integer
+arrays. The result of the algorithm is the elimination tree, a count
+of the number of nonzeros in each column of $\m{L}$, and
+the cumulative sum of the column counts.
+
+%-------------------------------------------------------------------------------
+\section{Implementation}
+\label{Implementation}
+%-------------------------------------------------------------------------------
+
+Because of its simplicity, the implementation of this algorithm leads to
+a very short, concise code. The symbolic analysis routine {\tt ldl\_symbolic}
+shown in Figure~\ref{ldlsymbolic}
+consists of only 18 lines of executable C code.
+This includes 5 lines of code to allow for a
+sparsity-preserving ordering $\m{P}$ so that either $\m{A}$ or $\m{PAP}\tr$
+can be analyzed, 3 lines of code to compute the cumulative sum of
+the column counts, and one line of code to speed up a {\tt for} loop.
+An additional line of code allows for a more general form of the input
+sparse matrix $\m{A}$.
+
+The {\tt n}-by-{\tt n} sparse matrix $\m{A}$ is provided in compressed column
+form as an {\tt int} array {\tt Ap} of length {\tt n+1},
+an {\tt int} array {\tt Ai} of length {\tt nz},
+and a {\tt double} array {\tt Ax} also of length {\tt nz},
+where {\tt nz} is the number of entries in the matrix.
+The numerical values of entries in column $j$ are stored in
+{\tt Ax[Ap[j]} $\ldots$ {\tt Ap[j+1]-1]}
+and the corresponding row indices are in
+{\tt Ai[Ap[j]} $\ldots$ {\tt Ap[j+1]-1]}.
+With {\tt Ap[0] = 0}, the number of entries in the matrix is {\tt nz = Ap[n]}.
+If no fill-reducing ordering {\tt P} is provided,
+only entries in the upper triangular part of $\m{A}$ are considered.
+If {\tt P} is provided and row/column {\tt i} of the
+matrix $\m{A}$ is the {\tt k}-th row/column of $\m{PAP}\tr$, then {\tt P[k]=i}.
+Only entries in the upper
+triangular part of $\m{PAP}\tr$ are considered. These entries may be
+in the lower triangular part of $\m{A}$, so to ensure that the correct matrix
+is factorized, all entries of $\m{A}$ should be provided when using the
+permutation input {\tt P}.
+
+The outputs of {\tt ldl\_symbolic} are three size-{\tt n} arrays:
+{\tt Parent} holds the elimination tree,
+{\tt Lnz} holds the counts of the number of entries in each column of
+$\m{L}$, and
+{\tt Lp} holds the cumulative sum of {\tt Lnz}.
+The size-{\tt n} array {\tt Flag} is used as workspace.
+None of the output or workspace arrays need to be initialized.
+
+\begin{figure}
+\caption{{\tt ldl\_symbolic:} finding the elimination tree and column counts}
+\label{ldlsymbolic}
+{\scriptsize
+\begin{verbatim}
+void ldl_symbolic
+(
+ int n, /* A and L are n-by-n, where n >= 0 */
+ int Ap [ ], /* input of size n+1, not modified */
+ int Ai [ ], /* input of size nz=Ap[n], not modified */
+ int Lp [ ], /* output of size n+1, not defined on input */
+ int Parent [ ], /* output of size n, not defined on input */
+ int Lnz [ ], /* output of size n, not defined on input */
+ int Flag [ ], /* workspace of size n, not defn. on input or output */
+ int P [ ], /* optional input of size n */
+ int Pinv [ ] /* optional output of size n (used if P is not NULL) */
+)
+{
+ int i, k, p, kk, p2 ;
+ if (P)
+ {
+ /* If P is present then compute Pinv, the inverse of P */
+ for (k = 0 ; k < n ; k++)
+ {
+ Pinv [P [k]] = k ;
+ }
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ /* L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) */
+ Parent [k] = -1 ; /* parent of k is not yet known */
+ Flag [k] = k ; /* mark node k as visited */
+ Lnz [k] = 0 ; /* count of nonzeros in column k of L */
+ kk = (P) ? (P [k]) : (k) ; /* kth original, or permuted, column */
+ p2 = Ap [kk+1] ;
+ for (p = Ap [kk] ; p < p2 ; p++)
+ {
+ /* A (i,k) is nonzero (original or permuted A) */
+ i = (Pinv) ? (Pinv [Ai [p]]) : (Ai [p]) ;
+ if (i < k)
+ {
+ /* follow path from i to root of etree, stop at flagged node */
+ for ( ; Flag [i] != k ; i = Parent [i])
+ {
+ /* find parent of i if not yet determined */
+ if (Parent [i] == -1) Parent [i] = k ;
+ Lnz [i]++ ; /* L (k,i) is nonzero */
+ Flag [i] = k ; /* mark i as visited */
+ }
+ }
+ }
+ }
+ /* construct Lp index array from Lnz column counts */
+ Lp [0] = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Lp [k+1] = Lp [k] + Lnz [k] ;
+ }
+}
+\end{verbatim}
+}
+\end{figure}
+
+The {\tt ldl\_numeric} numeric factorization routine shown
+in Figure~\ref{ldlnumeric} consists of only 31 lines of
+executable code. It includes this same subtree traversal algorithm
+as {\tt ldl\_symbolic},
+except that each path is placed on a stack that holds
+nonzero pattern of the $k$th row of $\m{L}$.
+This traversal is followed by a sparse forward solve
+using this pattern, and all of the nonzero entries in
+the resulting $k$th row of $\m{L}$ are appended to their respective columns
+in the data structure of $\m{L}$.
+
+\begin{figure}
+\caption{{\tt ldl\_numeric:} numeric factorization}
+\label{ldlnumeric}
+{\scriptsize
+\begin{verbatim}
+int ldl_numeric /* returns n if successful, k if D (k,k) is zero */
+(
+ int n, /* A and L are n-by-n, where n >= 0 */
+ int Ap [ ], /* input of size n+1, not modified */
+ int Ai [ ], /* input of size nz=Ap[n], not modified */
+ double Ax [ ], /* input of size nz=Ap[n], not modified */
+ int Lp [ ], /* input of size n+1, not modified */
+ int Parent [ ], /* input of size n, not modified */
+ int Lnz [ ], /* output of size n, not defn. on input */
+ int Li [ ], /* output of size lnz=Lp[n], not defined on input */
+ double Lx [ ], /* output of size lnz=Lp[n], not defined on input */
+ double D [ ], /* output of size n, not defined on input */
+ double Y [ ], /* workspace of size n, not defn. on input or output */
+ int Pattern [ ], /* workspace of size n, not defn. on input or output */
+ int Flag [ ], /* workspace of size n, not defn. on input or output */
+ int P [ ], /* optional input of size n */
+ int Pinv [ ] /* optional input of size n */
+)
+{
+ double yi, l_ki ;
+ int i, k, p, kk, p2, len, top ;
+ for (k = 0 ; k < n ; k++)
+ {
+ /* compute nonzero Pattern of kth row of L, in topological order */
+ Y [k] = 0.0 ; /* Y(0:k) is now all zero */
+ top = n ; /* stack for pattern is empty */
+ Flag [k] = k ; /* mark node k as visited */
+ Lnz [k] = 0 ; /* count of nonzeros in column k of L */
+ kk = (P) ? (P [k]) : (k) ; /* kth original, or permuted, column */
+ p2 = Ap [kk+1] ;
+ for (p = Ap [kk] ; p < p2 ; p++)
+ {
+ i = (Pinv) ? (Pinv [Ai [p]]) : (Ai [p]) ; /* get A(i,k) */
+ if (i <= k)
+ {
+ Y [i] += Ax [p] ; /* scatter A(i,k) into Y (sum duplicates) */
+ for (len = 0 ; Flag [i] != k ; i = Parent [i])
+ {
+ Pattern [len++] = i ; /* L(k,i) is nonzero */
+ Flag [i] = k ; /* mark i as visited */
+ }
+ while (len > 0) Pattern [--top] = Pattern [--len] ;
+ }
+ }
+ /* compute numerical values kth row of L (a sparse triangular solve) */
+ D [k] = Y [k] ; /* get D(k,k) and clear Y(k) */
+ Y [k] = 0.0 ;
+ for ( ; top < n ; top++)
+ {
+ i = Pattern [top] ; /* Pattern [top:n-1] is pattern of L(:,k) */
+ yi = Y [i] ; /* get and clear Y(i) */
+ Y [i] = 0.0 ;
+ p2 = Lp [i] + Lnz [i] ;
+ for (p = Lp [i] ; p < p2 ; p++)
+ {
+ Y [Li [p]] -= Lx [p] * yi ;
+ }
+ l_ki = yi / D [i] ; /* the nonzero entry L(k,i) */
+ D [k] -= l_ki * yi ;
+ Li [p] = k ; /* store L(k,i) in column form of L */
+ Lx [p] = l_ki ;
+ Lnz [i]++ ; /* increment count of nonzeros in col i */
+ }
+ if (D [k] == 0.0) return (k) ; /* failure, D(k,k) is zero */
+ }
+ return (n) ; /* success, diagonal of D is all nonzero */
+}
+\end{verbatim}
+}
+\end{figure}
+
+After the matrix is factorized, the {\tt ldl\_lsolve}, {\tt ldl\_dsolve},
+and {\tt ldl\_ltsolve} routines shown in Figure~\ref{ldlsolve}
+are provided to solve
+$\m{Lx}=\m{b}$, $\m{Dx}=\m{b}$, and $\m{L}\tr\m{x}=\m{b}$, respectively.
+Together, they solve $\m{Ax}=\m{b}$, and consist of only 10 lines of executable
+code. If a fill-reducing permutation is used,
+{\tt ldl\_perm} and {\tt ldl\_permt} must be used to permute $\m{b}$ and
+$\m{x}$ accordingly.
+
+\begin{figure}
+\caption{Solve routines}
+\label{ldlsolve}
+{\scriptsize
+\begin{verbatim}
+void ldl_lsolve
+(
+ int n, /* L is n-by-n, where n >= 0 */
+ double X [ ], /* size n. right-hand-side on input, soln. on output */
+ int Lp [ ], /* input of size n+1, not modified */
+ int Li [ ], /* input of size lnz=Lp[n], not modified */
+ double Lx [ ] /* input of size lnz=Lp[n], not modified */
+)
+{
+ int j, p, p2 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ p2 = Lp [j+1] ;
+ for (p = Lp [j] ; p < p2 ; p++)
+ {
+ X [Li [p]] -= Lx [p] * X [j] ;
+ }
+ }
+}
+
+void ldl_dsolve
+(
+ int n, /* D is n-by-n, where n >= 0 */
+ double X [ ], /* size n. right-hand-side on input, soln. on output */
+ double D [ ] /* input of size n, not modified */
+)
+{
+ int j ;
+ for (j = 0 ; j < n ; j++)
+ {
+ X [j] /= D [j] ;
+ }
+}
+
+void ldl_ltsolve
+(
+ int n, /* L is n-by-n, where n >= 0 */
+ double X [ ], /* size n. right-hand-side on input, soln. on output */
+ int Lp [ ], /* input of size n+1, not modified */
+ int Li [ ], /* input of size lnz=Lp[n], not modified */
+ double Lx [ ] /* input of size lnz=Lp[n], not modified */
+)
+{
+ int j, p, p2 ;
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ p2 = Lp [j+1] ;
+ for (p = Lp [j] ; p < p2 ; p++)
+ {
+ X [j] -= Lx [p] * X [Li [p]] ;
+ }
+ }
+}
+\end{verbatim}
+}
+\end{figure}
+
+In addition to appearing as a Collected Algorithm of the ACM \cite{Davis05},
+{\tt LDL} is available at http://www.cise.ufl.edu/research/sparse.
+
+%-------------------------------------------------------------------------------
+\section{Using LDL in MATLAB}
+\label{MATLAB}
+%-------------------------------------------------------------------------------
+
+The simplest way to use {\tt LDL} is within MATLAB. Once the {\tt ldlsparse}
+mexFunction is compiled and installed, the MATLAB statement
+{\tt [L, D, Parent, fl] = ldlsparse (A)} returns the sparse factorization
+{\tt A = (L+I)*D*(L+I)'}, where {\tt L} is lower triangular, {\tt D} is a
+diagonal matrix, and {\tt I} is the {\tt n}-by-{\tt n}
+identity matrix ({\tt ldlsparse} does not return the unit diagonal of {\tt L}).
+The elimination tree is returned in {\tt Parent}.
+If no zero on the diagonal of {\tt D} is encountered, {\tt fl} is the
+floating-point operation count. Otherwise, {\tt D(-fl,-fl)} is the first
+zero entry encountered. Let {\tt d=-fl}. The function returns the
+factorization of {\tt A (1:d,1:d)}, where rows {\tt d+1} to {\tt n} of {\tt L}
+and {\tt D} are all zero. If a sparsity preserving permutation {\tt P} is
+passed, {\tt [L, D, Parent, fl] = ldlsparse (A,P)}
+operates on {\tt A(P,P)} without
+forming it explicitly.
+
+The statement {\tt x = ldlsparse (A, [ ], b)} is roughly equivalent to
+{\tt x = A}$\backslash${\tt b}, when {\tt A} is sparse, real, and symmetric.
+The $\m{LDL}\tr$ factorization of {\tt A} is performed. If {\tt P} is
+provided, {\tt x = ldlsparse (A, P, b)} still performs
+{\tt x = A}$\backslash${\tt b}, except that {\tt A(P,P)} is factorized
+instead.
+
+%-------------------------------------------------------------------------------
+\section{Using LDL in a C program}
+\label{C}
+%-------------------------------------------------------------------------------
+
+The C-callable {\tt LDL} library consists of nine user-callable routines
+and one include file.
+
+\begin{itemize}
+\item {\tt ldl\_symbolic}: given the nonzero pattern of a sparse symmetric
+ matrix $\m{A}$ and an optional permutation $\m{P}$, analyzes either
+ $\m{A}$ or $\m{PAP}\tr$, and returns the elimination tree, the
+ number of nonzeros in each column of $\m{L}$, and the {\tt Lp} array
+ for the sparse matrix data structure for $\m{L}$.
+ Duplicate entries are allowed in the columns of $\m{A}$, and the
+ row indices in each column need not be sorted.
+ Providing a sparsity-preserving ordering is critical for obtaining
+ good performance. A minimum degree ordering
+ (such as AMD \cite{AmestoyDavisDuff96,AmestoyDavisDuff03})
+ or a graph-partitioning based ordering are appropriate.
+\item {\tt ldl\_numeric}: given {\tt Lp} and the elimination tree computed
+ by {\tt ldl\_symbolic}, and an optional permutation $\m{P}$,
+ returns the numerical factorization of $\m{A}$ or $\m{PAP}\tr$.
+ Duplicate entries are allowed in the columns of $\m{A}$
+ (any duplicate entries are summed), and the
+ row indices in each column need not be sorted.
+ The data structure for $\m{L}$ is the same as $\m{A}$, except that
+ no duplicates appear, and each column has sorted row indices.
+\item {\tt ldl\_lsolve}: given the factor $\m{L}$ computed by
+ {\tt ldl\_numeric}, solves the linear system $\m{Lx}=\m{b}$, where
+ $\m{x}$ and $\m{b}$ are full $n$-by-1 vectors.
+\item {\tt ldl\_dsolve}: given the factor $\m{D}$ computed by
+ {\tt ldl\_numeric}, solves the linear system $\m{Dx}=\m{b}$.
+\item {\tt ldl\_ltsolve}: given the factor $\m{L}$ computed by
+ {\tt ldl\_numeric}, solves the linear system $\m{L}\tr\m{x}=\m{b}$.
+\item {\tt ldl\_perm}: given a vector $\m{b}$ and a permutation $\m{P}$,
+ returns $\m{x}=\m{Pb}$.
+\item {\tt ldl\_permt}: given a vector $\m{b}$ and a permutation $\m{P}$,
+ returns $\m{x}=\m{P}\tr\m{b}$.
+\item {\tt ldl\_valid\_perm}: Except for checking if the diagonal of
+ $\m{D}$ is zero, none of the above routines check their inputs for errors.
+ This routine checks the validity of a permutation $\m{P}$.
+\item {\tt ldl\_valid\_matrix}: checks if a matrix $\m{A}$ is valid as input
+ to {\tt ldl\_symbolic} and {\tt ldl\_numeric}.
+\end{itemize}
+
+Note that the primary input to the {\tt ldl\_symbolic} and
+{\tt ldl\_numeric} is the sparse matrix $\m{A}$. It is provided in
+column-oriented form, and only the upper triangular part is accessed.
+This is slightly different than the primary output: the matrix $\m{L}$,
+which is lower triangular in column-oriented form.
+If you wish to factorize a symmetric matrix $\m{A}$ for which only the lower
+triangular part is supplied, you would need to transpose $\m{A}$ before
+passing it {\tt ldl\_symbolic} and {\tt ldl\_numeric}.
+
+An additional set of routines is available for use in a 64-bit environment.
+Each routine name changes uniformly; {\tt ldl\_symbolic} becomes
+{\tt ldl\_l\_symbolic}, and each {\tt int} parameter becomes type
+{\tt UF\_long}. The {\tt UF\_long} type is {\tt long}, except for
+Microsoft Windows 64, where it becomes {\tt \_\_int64}.
+
+\begin{figure}
+\caption{Example of use}
+\label{ldlsimple}
+{\scriptsize
+\begin{verbatim}
+#include <stdio.h>
+#include "ldl.h"
+#define N 10 /* A is 10-by-10 */
+#define ANZ 19 /* # of nonzeros on diagonal and upper triangular part of A */
+#define LNZ 13 /* # of nonzeros below the diagonal of L */
+
+int main (void)
+{
+ /* only the upper triangular part of A is required */
+ int Ap [N+1] = {0, 1, 2, 3, 4, 6, 7, 9, 11, 15, ANZ},
+ Ai [ANZ] = {0, 1, 2, 3, 1,4, 5, 4,6, 4,7, 0,4,7,8, 1,4,6,9 } ;
+ double Ax [ANZ] = {1.7, 1., 1.5, 1.1, .02,2.6, 1.2, .16,1.3, .09,1.6,
+ .13,.52,.11,1.4, .01,.53,.56,3.1},
+ b [N] = {.287, .22, .45, .44, 2.486, .72, 1.55, 1.424, 1.621, 3.759};
+ double Lx [LNZ], D [N], Y [N] ;
+ int Li [LNZ], Lp [N+1], Parent [N], Lnz [N], Flag [N], Pattern [N], d, i ;
+
+ /* factorize A into LDL' (P and Pinv not used) */
+ ldl_symbolic (N, Ap, Ai, Lp, Parent, Lnz, Flag, NULL, NULL) ;
+ printf ("Nonzeros in L, excluding diagonal: %d\n", Lp [N]) ;
+ d = ldl_numeric (N, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Pattern,
+ Flag, NULL, NULL) ;
+
+ if (d == N)
+ {
+ /* solve Ax=b, overwriting b with the solution x */
+ ldl_lsolve (N, b, Lp, Li, Lx) ;
+ ldl_dsolve (N, b, D) ;
+ ldl_ltsolve (N, b, Lp, Li, Lx) ;
+ for (i = 0 ; i < N ; i++) printf ("x [%d] = %g\n", i, b [i]) ;
+ }
+ else
+ {
+ printf ("ldl_numeric failed, D (%d,%d) is zero\n", d, d) ;
+ }
+ return (0) ;
+}
+\end{verbatim}
+}
+\end{figure}
+
+The program in Figure~\ref{ldlsimple}
+illustrates the basic usage of the {\tt LDL} routines.
+It analyzes and factorizes the sparse symmetric positive-definite matrix
+{\small
+\[
+\m{A} = \left[
+\begin{array}{cccccccccc}
+ 1.7 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & .13 & 0 \\
+ 0 & 1. & 0 & 0 & .02 & 0 & 0 & 0 & 0 & .01 \\
+ 0 & 0 & 1.5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 1.1 & 0 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & .02 & 0 & 0 & 2.6 & 0 & .16 & .09 & .52 & .53 \\
+ 0 & 0 & 0 & 0 & 0 & 1.2 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & .16 & 0 & 1.3 & 0 & 0 & .56 \\
+ 0 & 0 & 0 & 0 & .09 & 0 & 0 & 1.6 & .11 & 0 \\
+ .13 & 0 & 0 & 0 & .52 & 0 & 0 & .11 & 1.4 & 0 \\
+ 0 & .01 & 0 & 0 & .53 & 0 & .56 & 0 & 0 & 3.1 \\
+\end{array}
+\right]
+\]
+}
+and then solves a system $\m{Ax}=\m{b}$ whose true solution is
+$x_i = i/10$. Note that {\tt Li} and {\tt Lx} are statically allocated.
+Normally they would be allocated after their size, {\tt Lp[n]},
+is determined by {\tt ldl\_symbolic}.
+More example programs are included with the {\tt LDL} package.
+
+\section{Acknowledgments}
+
+I would like to thank Pete Stewart for his comments on an earlier draft
+of this software and its accompanying paper.
+
+\newpage
+\bibliographystyle{plain}
+\bibliography{ldl}
+
+\end{document}
diff --git a/LDL/Doc/lesser.txt b/LDL/Doc/lesser.txt
new file mode 100644
index 0000000..8add30a
--- /dev/null
+++ b/LDL/Doc/lesser.txt
@@ -0,0 +1,504 @@
+ GNU LESSER GENERAL PUBLIC LICENSE
+ Version 2.1, February 1999
+
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diff --git a/LDL/Include/ldl.h b/LDL/Include/ldl.h
new file mode 100644
index 0000000..5840be3
--- /dev/null
+++ b/LDL/Include/ldl.h
@@ -0,0 +1,104 @@
+/* ========================================================================== */
+/* === ldl.h: include file for the LDL package ============================= */
+/* ========================================================================== */
+
+/* LDL Copyright (c) Timothy A Davis,
+ * University of Florida. All Rights Reserved. See README for the License.
+ */
+
+#include "UFconfig.h"
+
+#ifdef LDL_LONG
+#define LDL_int UF_long
+#define LDL_ID UF_long_id
+
+#define LDL_symbolic ldl_l_symbolic
+#define LDL_numeric ldl_l_numeric
+#define LDL_lsolve ldl_l_lsolve
+#define LDL_dsolve ldl_l_dsolve
+#define LDL_ltsolve ldl_l_ltsolve
+#define LDL_perm ldl_l_perm
+#define LDL_permt ldl_l_permt
+#define LDL_valid_perm ldl_l_valid_perm
+#define LDL_valid_matrix ldl_l_valid_matrix
+
+#else
+#define LDL_int int
+#define LDL_ID "%d"
+
+#define LDL_symbolic ldl_symbolic
+#define LDL_numeric ldl_numeric
+#define LDL_lsolve ldl_lsolve
+#define LDL_dsolve ldl_dsolve
+#define LDL_ltsolve ldl_ltsolve
+#define LDL_perm ldl_perm
+#define LDL_permt ldl_permt
+#define LDL_valid_perm ldl_valid_perm
+#define LDL_valid_matrix ldl_valid_matrix
+
+#endif
+
+/* ========================================================================== */
+/* === int version ========================================================== */
+/* ========================================================================== */
+
+void ldl_symbolic (int n, int Ap [ ], int Ai [ ], int Lp [ ],
+ int Parent [ ], int Lnz [ ], int Flag [ ], int P [ ], int Pinv [ ]) ;
+
+int ldl_numeric (int n, int Ap [ ], int Ai [ ], double Ax [ ],
+ int Lp [ ], int Parent [ ], int Lnz [ ], int Li [ ], double Lx [ ],
+ double D [ ], double Y [ ], int Pattern [ ], int Flag [ ],
+ int P [ ], int Pinv [ ]) ;
+
+void ldl_lsolve (int n, double X [ ], int Lp [ ], int Li [ ],
+ double Lx [ ]) ;
+
+void ldl_dsolve (int n, double X [ ], double D [ ]) ;
+
+void ldl_ltsolve (int n, double X [ ], int Lp [ ], int Li [ ],
+ double Lx [ ]) ;
+
+void ldl_perm (int n, double X [ ], double B [ ], int P [ ]) ;
+void ldl_permt (int n, double X [ ], double B [ ], int P [ ]) ;
+
+int ldl_valid_perm (int n, int P [ ], int Flag [ ]) ;
+int ldl_valid_matrix ( int n, int Ap [ ], int Ai [ ]) ;
+
+/* ========================================================================== */
+/* === long version ========================================================= */
+/* ========================================================================== */
+
+void ldl_l_symbolic (UF_long n, UF_long Ap [ ], UF_long Ai [ ], UF_long Lp [ ],
+ UF_long Parent [ ], UF_long Lnz [ ], UF_long Flag [ ], UF_long P [ ],
+ UF_long Pinv [ ]) ;
+
+UF_long ldl_l_numeric (UF_long n, UF_long Ap [ ], UF_long Ai [ ], double Ax [ ],
+ UF_long Lp [ ], UF_long Parent [ ], UF_long Lnz [ ], UF_long Li [ ],
+ double Lx [ ], double D [ ], double Y [ ], UF_long Pattern [ ],
+ UF_long Flag [ ], UF_long P [ ], UF_long Pinv [ ]) ;
+
+void ldl_l_lsolve (UF_long n, double X [ ], UF_long Lp [ ], UF_long Li [ ],
+ double Lx [ ]) ;
+
+void ldl_l_dsolve (UF_long n, double X [ ], double D [ ]) ;
+
+void ldl_l_ltsolve (UF_long n, double X [ ], UF_long Lp [ ], UF_long Li [ ],
+ double Lx [ ]) ;
+
+void ldl_l_perm (UF_long n, double X [ ], double B [ ], UF_long P [ ]) ;
+void ldl_l_permt (UF_long n, double X [ ], double B [ ], UF_long P [ ]) ;
+
+UF_long ldl_l_valid_perm (UF_long n, UF_long P [ ], UF_long Flag [ ]) ;
+UF_long ldl_l_valid_matrix ( UF_long n, UF_long Ap [ ], UF_long Ai [ ]) ;
+
+/* ========================================================================== */
+/* === LDL version ========================================================== */
+/* ========================================================================== */
+
+#define LDL_DATE "Nov 1, 2007"
+#define LDL_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define LDL_MAIN_VERSION 2
+#define LDL_SUB_VERSION 0
+#define LDL_SUBSUB_VERSION 1
+#define LDL_VERSION LDL_VERSION_CODE(LDL_MAIN_VERSION,LDL_SUB_VERSION)
+
diff --git a/LDL/Lib/Makefile b/LDL/Lib/Makefile
new file mode 100644
index 0000000..350412c
--- /dev/null
+++ b/LDL/Lib/Makefile
@@ -0,0 +1,32 @@
+#-------------------------------------------------------------------------------
+# Makefile for the LDL library
+#-------------------------------------------------------------------------------
+
+default: all
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../../UFconfig -I../Include
+
+C = $(CC) $(CFLAGS) $(I)
+
+all: libldl.a
+
+#-------------------------------------------------------------------------------
+# the ldl library:
+#-------------------------------------------------------------------------------
+
+libldl.a: ../Source/ldl.c ../Include/ldl.h
+ $(C) -c ../Source/ldl.c -o ldl.o
+ $(C) -DLDL_LONG -c ../Source/ldl.c -o ldll.o
+ $(AR) libldl.a ldl.o ldll.o
+ - $(RANLIB) libldl.a
+
+distclean: purge
+
+purge: clean
+ - $(RM) libldl.a
+
+clean:
+ - $(RM) $(CLEAN)
+
diff --git a/LDL/MATLAB/Contents.m b/LDL/MATLAB/Contents.m
new file mode 100644
index 0000000..c772027
--- /dev/null
+++ b/LDL/MATLAB/Contents.m
@@ -0,0 +1,39 @@
+% LDL package: simple sparse LDL factorization
+%
+% Primary routines:
+%
+% ldlsparse - LDL' factorization of a real, sparse, symmetric matrix
+% ldlsymbol - symbolic Cholesky factorization
+%
+% Helper routines:
+%
+% ldldemo - demo program for LDL
+% ldlrow - an m-file description of the algorithm used by LDL
+% ldltest - test program for LDL
+% ldlmain2 - compiles and runs a longer test program for LDL
+% ldl_install - compile and install the LDL package for use in MATLAB.
+% ldl_make - compile LDL
+%
+% Example:
+%
+% [L, D, Parent, fl] = ldlsparse (A)
+
+% Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida
+
+% LDL License: GNU Lesser General Public License as published by the
+% Free Software Foundation; either version 2.1 of the License, or
+% (at your option) any later version.
+%
+% Availability:
+%
+% http://www.cise.ufl.edu/research/sparse/ldl
+%
+% Acknowledgements:
+%
+% This work was supported by the National Science Foundation, under
+% grant CCR-0203270.
+%
+% Portions of this work were done while on sabbatical at Stanford University
+% and Lawrence Berkeley National Laboratory (with funding from the SciDAC
+% program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon
+% for making this sabbatical possible.
diff --git a/LDL/MATLAB/Makefile b/LDL/MATLAB/Makefile
new file mode 100644
index 0000000..9e93381
--- /dev/null
+++ b/LDL/MATLAB/Makefile
@@ -0,0 +1,27 @@
+#-------------------------------------------------------------------------------
+# Makefile for the LDL mexFunction
+#-------------------------------------------------------------------------------
+
+default: mex
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../../UFconfig -I../Include
+
+MX = $(MEX) $(I) -DLDL_LONG
+
+mex: ldlmex.c ../Source/ldl.c ../Include/ldl.h ldlsymbolmex.c
+ - $(MX) -output ldlsparse ../Source/ldl.c ldlmex.c
+ - $(MX) -output ldlsymbol ../Source/ldl.c ldlsymbolmex.c
+
+#-------------------------------------------------------------------------------
+# clean-up:
+#-------------------------------------------------------------------------------
+
+distclean: purge
+
+purge: clean
+ - $(RM) *.mex*
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/LDL/MATLAB/ldl_install.m b/LDL/MATLAB/ldl_install.m
new file mode 100644
index 0000000..02eb14f
--- /dev/null
+++ b/LDL/MATLAB/ldl_install.m
@@ -0,0 +1,17 @@
+function ldl_install
+%LDL_INSTALL compile and install the LDL package for use in MATLAB.
+% Your current working directory must be LDL for this function to work.
+%
+% Example:
+% ldl_install
+%
+% See also ldlsparse, ldlsymbol
+
+% Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida
+
+ldl_make
+addpath (pwd) ;
+fprintf ('LDL has been compiled and installed. The path:\n') ;
+disp (pwd) ;
+fprintf ('has been added to your path. Use pathtool to add it permanently.\n');
+ldldemo
diff --git a/LDL/MATLAB/ldl_make.m b/LDL/MATLAB/ldl_make.m
new file mode 100644
index 0000000..8e0acf5
--- /dev/null
+++ b/LDL/MATLAB/ldl_make.m
@@ -0,0 +1,18 @@
+function ldl_make
+%LDL_MAKE compile LDL
+%
+% Example:
+% ldl_make % compiles ldlsparse and ldlsymbol
+%
+% See also ldlsparse, ldlsymbol
+
+% Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida
+
+d = '' ;
+if (~isempty (strfind (computer, '64')))
+ d = '-largeArrayDims' ;
+end
+eval (sprintf ('mex -O %s -DLDL_LONG -I../../UFconfig -I../Include -output ldlsparse ../Source/ldl.c ldlmex.c', d)) ;
+eval (sprintf ('mex -O %s -DLDL_LONG -I../../UFconfig -I../Include -output ldlsymbol ../Source/ldl.c ldlsymbolmex.c', d)) ;
+fprintf ('LDL successfully compiled.\n') ;
+
diff --git a/LDL/MATLAB/ldldemo.m b/LDL/MATLAB/ldldemo.m
new file mode 100644
index 0000000..3d37765
--- /dev/null
+++ b/LDL/MATLAB/ldldemo.m
@@ -0,0 +1,124 @@
+function ldldemo
+%LDLDEMO demo program for LDL
+%
+% Example:
+% ldldemo
+%
+% See also ldlsparse.
+
+% Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida
+
+% compile the LDLSPARSE and LDLSYMBOL mexFunctions
+help ldlsparse
+
+fprintf ('\nTesting ldlsparse and ldlsymbol:\n') ;
+
+% create a small random symmetric positive definite sparse matrix
+n = 100 ;
+d = 0.03 ;
+rand ('state', 0) ;
+randn ('state', 0) ;
+A = sprandn (n, n, d) ;
+A = speye (n) + A*A' ;
+b = randn (n, 1) ;
+
+figure (1)
+clf
+subplot (2,2,1) ;
+spy (A) ;
+title ('original matrix') ;
+
+% permute for sparsity
+p = symamd (A) ;
+C = A (p,p) ;
+
+subplot (2,2,2) ;
+spy (C) ;
+title ('permuted matrix') ;
+drawnow
+
+% factorize, without using ldlsparse's internal permutation
+[L, D, Parent, fl] = ldlsparse (C) ;
+L = L + speye (n) ;
+err = norm (L*D*L' - C, 1) ;
+fprintf ('norm (LDL''-PAP'') = %g\n', err) ;
+
+% solve Ax=b
+x = L' \ (D \ (L \ (b (p)))) ;
+x (p) = x ;
+resid = norm (A*x-b) ;
+fprintf ('residual %g for ldlsparse, flops %10.1f\n', resid, fl) ;
+
+% solve Ax=b with one call to ldlsparse
+x = ldlsparse (C, [ ], b (p)) ;
+x (p) = x ;
+resid = norm (A*x-b) ;
+fprintf ('residual %g for ldlsparse solve\n', resid) ;
+
+subplot (2,2,3) ;
+spy (L + D + L') ;
+title ('L+D+L''') ;
+
+subplot (2,2,4) ;
+treeplot (Parent)
+title ('elimination tree') ;
+
+% try ldlrow (this will be slow)
+[L, D] = ldlrow (C) ;
+x = L' \ (D \ (L \ (b (p)))) ;
+x (p) = x ;
+resid = norm (A*x-b) ;
+fprintf ('residual %g for ldlrow.m\n', resid) ;
+
+% factorize, using ldlsparse's internal permutation
+[L, D, Parent, fl] = ldlsparse (A, p) ;
+L = L + speye (n) ;
+err = norm (L*D*L' - C, 1) ;
+fprintf ('norm (LDL''-PAP'') = %g\n', err) ;
+
+% solve Ax=b
+x = L' \ (D \ (L \ (b (p)))) ;
+x (p) = x ;
+resid = norm (A*x-b) ;
+fprintf ('residual %g for ldlsparse, flops %10.1f\n', resid, fl) ;
+
+% solve Ax=b with one call to ldlsparse
+x = ldlsparse (A, p, b) ;
+resid = norm (A*x-b) ;
+fprintf ('residual %g for ldlsparse solve\n\n', resid) ;
+
+% compare ldlsymbol and symbfact
+[Lnz, Parent, fl] = ldlsymbol (A) ;
+fprintf ('Original matrix: nz in L: %5d flop count: %g\n', sum (Lnz), fl) ;
+
+Lnz2 = symbfact (A) - 1 ;
+Parent2 = etree (A) ;
+fl2 = sum (Lnz2 .* (Lnz2 + 2)) ;
+if (any (Lnz ~= Lnz2))
+ error ('Lnz mismatch') ;
+end
+if (any (Parent ~= Parent2))
+ error ('Parent mismatch') ;
+end
+if (fl ~= fl2)
+ error ('fl mismatch') ;
+end
+
+[Lnz, Parent, fl] = ldlsymbol (A, p) ;
+fprintf ('Permuted matrix: nz in L: %5d flop count: %g\n', sum (Lnz), fl) ;
+
+Lnz2 = symbfact (A (p,p)) - 1 ;
+Parent2 = etree (A (p,p)) ;
+fl2 = sum (Lnz2 .* (Lnz2 + 2)) ;
+if (any (Lnz ~= Lnz2))
+ error ('Lnz mismatch') ;
+end
+if (any (Parent ~= Parent2))
+ error ('Parent mismatch') ;
+end
+if (fl ~= fl2)
+ error ('fl mismatch') ;
+end
+
+
+fprintf ('\nldldemo: all tests passed\n') ;
diff --git a/LDL/MATLAB/ldldemo.out b/LDL/MATLAB/ldldemo.out
new file mode 100644
index 0000000..5fbb881
--- /dev/null
+++ b/LDL/MATLAB/ldldemo.out
@@ -0,0 +1,45 @@
+ldldemo
+ LDLSPARSE LDL' factorization of a real, sparse, symmetric matrix
+
+ Example:
+ [L, D, Parent, fl] = ldlsparse (A)
+ [L, D, Parent, fl] = ldlsparse (A, P)
+ [x, fl] = ldlsparse (A, [ ], b)
+ [x, fl] = ldlsparse (A, P, b)
+
+ Let I = speye (size (A,1)). The factorization is (L+I)*D*(L+I)' = A or A(P,P).
+ A must be sparse, square, and real. Only the diagonal and upper triangular
+ part of A or A(P,P) are accessed. L is lower triangular with unit diagonal,
+ but the diagonal is not returned. D is a diagonal sparse matrix. P is either
+ a permutation of 1:n, or an empty vector, where n = size (A,1). If not
+ present, or empty, then P=1:n is assumed. Parent is the elimination tree of
+ A or A(P,P). If positive, fl is the floating point operation count, or
+ negative if any entry on the diagonal of D is zero.
+
+ In the x = ldlsparse (A, P, b) usage, the LDL' factorization is not returned.
+ Instead, the system A*x=b is solved for x, where both b and x are dense.
+
+ If a zero entry on the diagonal of D is encountered, the LDL' factorization is
+ terminated at that point. If there is no fl output argument, an error occurs.
+ Otherwise, fl is negative, and let d=-fl. D(d,d) is the first zero entry on
+ the diagonal of D. A partial factorization is returned. Let B = A, or A(P,P)
+ if P is present. Let F = (L+I)*D*(L+I)'. Then F (1:d,1:d) = B (1:d,1:d).
+ Rows d+1 to n of L and D are all zero.
+
+ See also chol, ldl, ldlsymbol, symbfact, etree
+
+
+Testing ldlsparse and ldlsymbol:
+norm (LDL'-PAP') = 6.51562e-15
+residual 3.55986e-15 for ldlsparse, flops 14813.0
+residual 3.86691e-15 for ldlsparse solve
+residual 3.64202e-15 for ldlrow.m
+norm (LDL'-PAP') = 6.63575e-15
+residual 2.96267e-15 for ldlsparse, flops 14813.0
+residual 3.53833e-15 for ldlsparse solve
+
+Original matrix: nz in L: 2206 flop count: 81044
+Permuted matrix: nz in L: 893 flop count: 14813
+
+ldldemo: all tests passed
+diary off
diff --git a/LDL/MATLAB/ldlmain2.m b/LDL/MATLAB/ldlmain2.m
new file mode 100644
index 0000000..fcbc5c4
--- /dev/null
+++ b/LDL/MATLAB/ldlmain2.m
@@ -0,0 +1,48 @@
+function ldlmain2
+%LDLMAIN2 compiles and runs a longer test program for LDL
+%
+% Example:
+% ldlmain2
+%
+% See also ldlsparse.
+
+% Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida
+
+help ldlmain2
+
+detail = 0 ;
+
+ldl_make
+
+d = '' ;
+if (~isempty (strfind (computer, '64')))
+ d = '-largeArrayDims' ;
+end
+
+mx = sprintf ('mex -O %s -DLDL_LONG -DDLONG -I../../UFconfig -I../Include', d) ;
+
+% compile ldlmain without AMD
+cmd = sprintf ('%s ../Demo/ldlmain.c ../Source/ldl.c', mx) ;
+if (detail)
+ fprintf ('%s\n', cmd) ;
+end
+eval (cmd) ;
+ldlmain
+
+% compile ldlamd (ldlmain with AMD)
+cmd = sprintf ('%s -I../../AMD/Include', mx) ;
+
+files = {'amd_order', 'amd_dump', 'amd_postorder', 'amd_post_tree', ...
+ 'amd_aat', 'amd_2', 'amd_1', 'amd_defaults', 'amd_control', ...
+ 'amd_info', 'amd_valid', 'amd_global', 'amd_preprocess' } ;
+for i = 1 : length (files)
+ cmd = sprintf ('%s ../../AMD/Source/%s.c', cmd, files {i}) ;
+end
+
+cmd = [cmd ' -DUSE_AMD -output ldlamd ../Demo/ldlmain.c ../Source/ldl.c'] ;
+if (detail)
+ fprintf ('%s\n', cmd) ;
+end
+eval (cmd) ;
+ldlamd
+
diff --git a/LDL/MATLAB/ldlmain2.out b/LDL/MATLAB/ldlmain2.out
new file mode 100644
index 0000000..2181907
--- /dev/null
+++ b/LDL/MATLAB/ldlmain2.out
@@ -0,0 +1,1551 @@
+ldlmain2
+ LDLMAIN2 compiles and runs a longer test program for LDL
+
+ Example:
+ ldlmain2
+
+ See also ldlsparse.
+
+LDL successfully compiled.
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/1 n: 1 entries: 1
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/1 n: 1 entries: 2 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 8.32667e-17
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 8.32667e-17
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 4
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 5.55112e-17
+Factorize A=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 5.55112e-17
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 5 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 1.11022e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 1.11022e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.11022e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.11022e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 11 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.38778e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.38778e-16
+
+
+--------------------------------------------------------
+Input matrix: name: HB/can_24 n: 24 entries: 160
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 96 Flop count: 632
+Ax=b not solved since D(1,1) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 146 Flop count: 1360
+Ax=b not solved since D(5,5) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: HB/can_24 n: 24 entries: 188 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 96 Flop count: 632
+Ax=b not solved since D(1,1) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 146 Flop count: 1360
+Ax=b not solved since D(5,5) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: FIDAP/ex5 n: 27 entries: 279
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 126 Flop count: 954
+relative maxnorm of residual: 2.59625e-10
+Factorize A=LDL' and solve Ax=b
+Nz in L: 276 Flop count: 4206
+relative maxnorm of residual: 2.72848e-10
+
+
+--------------------------------------------------------
+Input matrix: name: FIDAP/ex5 n: 27 entries: 325 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 126 Flop count: 954
+relative maxnorm of residual: 3.27418e-10
+Factorize A=LDL' and solve Ax=b
+Nz in L: 276 Flop count: 4206
+relative maxnorm of residual: 2.32376e-10
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk01 n: 48 entries: 400
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 441 Flop count: 5961
+relative maxnorm of residual: 2.38712e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 829 Flop count: 20103
+relative maxnorm of residual: 2.27374e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk01 n: 48 entries: 472 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 441 Flop count: 5961
+relative maxnorm of residual: 2.27374e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 829 Flop count: 20103
+relative maxnorm of residual: 3.83693e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm01 n: 48 entries: 24
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm01 n: 48 entries: 26 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: Pothen/mesh1e1 n: 48 entries: 306
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 288 Flop count: 2630
+relative maxnorm of residual: 5.96745e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 511 Flop count: 7383
+relative maxnorm of residual: 6.93889e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 288 Flop count: 2630
+relative maxnorm of residual: 5.55112e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 511 Flop count: 7383
+relative maxnorm of residual: 5.55112e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Bai/bfwb62 n: 62 entries: 342
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 226 Flop count: 1472
+relative maxnorm of residual: 5.55112e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 662 Flop count: 11350
+relative maxnorm of residual: 1.11022e-15
+
+
+--------------------------------------------------------
+Input matrix: name: Bai/bfwb62 n: 62 entries: 407 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 226 Flop count: 1472
+relative maxnorm of residual: 5.68434e-14
+Factorize A=LDL' and solve Ax=b
+Nz in L: 662 Flop count: 11350
+relative maxnorm of residual: 2.15827e-12
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk02 n: 66 entries: 4356
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 7.50219e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 7.50219e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 8.59759e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 8.59759e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm02 n: 66 entries: 66
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm02 n: 66 entries: 72 (jumbled version)
+--------------------------------------------------------
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid perm)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ap)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai)
+--------------------------------------------------------
+
+ldlmain: invalid matrix and/or permutation
+
+Largest residual during all tests: 3.27418e-10
+
+ldlmain: all tests passed
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/1 n: 1 entries: 1
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 1
+ nz, number of nonzeros in A: 1
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 1
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 36
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 1
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 1
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 0
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/1 n: 1 entries: 2 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 1
+ nz, number of nonzeros in A: 1
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 1
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 52
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 1
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 1
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 8.32667e-17
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 8.32667e-17
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 4
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 2
+ nz, number of nonzeros in A: 4
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 2
+ nonzeros in pattern of A+A' (excl. diagonal): 2
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 80
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 1
+ nonzeros in L (including diagonal): 3
+ # divide operations for LDL' or LU: 1
+ # multiply-subtract operations for LDL': 1
+ # multiply-subtract operations for LU: 1
+ max nz. in any column of L (incl. diagonal): 2
+
+ chol flop count for real A, sqrt counted as 1 flop: 5
+ LDL' flop count for real A: 3
+ LDL' flop count for complex A: 17
+ LU flop count for real A (with no pivoting): 3
+ LU flop count for complex A (with no pivoting): 17
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 5.55112e-17
+Factorize A=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 5.55112e-17
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 5 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 2
+ nz, number of nonzeros in A: 4
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 2
+ nonzeros in pattern of A+A' (excl. diagonal): 2
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 112
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 1
+ nonzeros in L (including diagonal): 3
+ # divide operations for LDL' or LU: 1
+ # multiply-subtract operations for LDL': 1
+ # multiply-subtract operations for LU: 1
+ max nz. in any column of L (incl. diagonal): 2
+
+ chol flop count for real A, sqrt counted as 1 flop: 5
+ LDL' flop count for real A: 3
+ LDL' flop count for complex A: 17
+ LU flop count for real A (with no pivoting): 3
+ LU flop count for complex A (with no pivoting): 17
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 1.11022e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 1 Flop count: 3
+relative maxnorm of residual: 1.11022e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 3
+ nz, number of nonzeros in A: 9
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 3
+ nonzeros in pattern of A+A' (excl. diagonal): 6
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 136
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 3
+ nonzeros in L (including diagonal): 6
+ # divide operations for LDL' or LU: 3
+ # multiply-subtract operations for LDL': 4
+ # multiply-subtract operations for LU: 5
+ max nz. in any column of L (incl. diagonal): 3
+
+ chol flop count for real A, sqrt counted as 1 flop: 14
+ LDL' flop count for real A: 11
+ LDL' flop count for complex A: 59
+ LU flop count for real A (with no pivoting): 13
+ LU flop count for complex A (with no pivoting): 67
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.11022e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.11022e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 11 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 3
+ nz, number of nonzeros in A: 9
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 3
+ nonzeros in pattern of A+A' (excl. diagonal): 6
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 196
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 3
+ nonzeros in L (including diagonal): 6
+ # divide operations for LDL' or LU: 3
+ # multiply-subtract operations for LDL': 4
+ # multiply-subtract operations for LU: 5
+ max nz. in any column of L (incl. diagonal): 3
+
+ chol flop count for real A, sqrt counted as 1 flop: 14
+ LDL' flop count for real A: 11
+ LDL' flop count for complex A: 59
+ LU flop count for real A (with no pivoting): 13
+ LU flop count for complex A (with no pivoting): 67
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.38778e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 3 Flop count: 11
+relative maxnorm of residual: 1.38778e-16
+
+
+--------------------------------------------------------
+Input matrix: name: HB/can_24 n: 24 entries: 160
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 1516
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 96 Flop count: 632
+Ax=b not solved since D(1,1) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 146 Flop count: 1360
+Ax=b not solved since D(5,5) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: HB/can_24 n: 24 entries: 188 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2368
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 96 Flop count: 632
+Ax=b not solved since D(1,1) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 146 Flop count: 1360
+Ax=b not solved since D(5,5) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: FIDAP/ex5 n: 27 entries: 279
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 27
+ nz, number of nonzeros in A: 279
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 27
+ nonzeros in pattern of A+A' (excl. diagonal): 252
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2180
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 126
+ nonzeros in L (including diagonal): 153
+ # divide operations for LDL' or LU: 126
+ # multiply-subtract operations for LDL': 414
+ # multiply-subtract operations for LU: 702
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 981
+ LDL' flop count for real A: 954
+ LDL' flop count for complex A: 4446
+ LU flop count for real A (with no pivoting): 1530
+ LU flop count for complex A (with no pivoting): 6750
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 126 Flop count: 954
+relative maxnorm of residual: 2.59625e-10
+Factorize A=LDL' and solve Ax=b
+Nz in L: 276 Flop count: 4206
+relative maxnorm of residual: 2.72848e-10
+
+
+--------------------------------------------------------
+Input matrix: name: FIDAP/ex5 n: 27 entries: 325 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 27
+ nz, number of nonzeros in A: 279
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 27
+ nonzeros in pattern of A+A' (excl. diagonal): 252
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 3592
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 126
+ nonzeros in L (including diagonal): 153
+ # divide operations for LDL' or LU: 126
+ # multiply-subtract operations for LDL': 414
+ # multiply-subtract operations for LU: 702
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 981
+ LDL' flop count for real A: 954
+ LDL' flop count for complex A: 4446
+ LU flop count for real A (with no pivoting): 1530
+ LU flop count for complex A (with no pivoting): 6750
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 126 Flop count: 954
+relative maxnorm of residual: 3.27418e-10
+Factorize A=LDL' and solve Ax=b
+Nz in L: 276 Flop count: 4206
+relative maxnorm of residual: 2.32376e-10
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk01 n: 48 entries: 400
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 400
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 352
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 3416
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 441
+ nonzeros in L (including diagonal): 489
+ # divide operations for LDL' or LU: 441
+ # multiply-subtract operations for LDL': 2760
+ # multiply-subtract operations for LU: 5079
+ max nz. in any column of L (incl. diagonal): 20
+
+ chol flop count for real A, sqrt counted as 1 flop: 6009
+ LDL' flop count for real A: 5961
+ LDL' flop count for complex A: 26049
+ LU flop count for real A (with no pivoting): 10599
+ LU flop count for complex A (with no pivoting): 44601
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 441 Flop count: 5961
+relative maxnorm of residual: 2.38712e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 829 Flop count: 20103
+relative maxnorm of residual: 2.27374e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk01 n: 48 entries: 472 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 400
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 352
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 5500
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 441
+ nonzeros in L (including diagonal): 489
+ # divide operations for LDL' or LU: 441
+ # multiply-subtract operations for LDL': 2760
+ # multiply-subtract operations for LU: 5079
+ max nz. in any column of L (incl. diagonal): 20
+
+ chol flop count for real A, sqrt counted as 1 flop: 6009
+ LDL' flop count for real A: 5961
+ LDL' flop count for complex A: 26049
+ LU flop count for real A (with no pivoting): 10599
+ LU flop count for complex A (with no pivoting): 44601
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 441 Flop count: 5961
+relative maxnorm of residual: 2.27374e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 829 Flop count: 20103
+relative maxnorm of residual: 3.83693e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm01 n: 48 entries: 24
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 24
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 1728
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 48
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 48
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm01 n: 48 entries: 26 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 24
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2028
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 48
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 48
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+Ax=b not solved since D(3,3) is zero.
+
+
+--------------------------------------------------------
+Input matrix: name: Pothen/mesh1e1 n: 48 entries: 306
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 306
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 258
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2964
+ # of memory compactions: 1
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 288
+ nonzeros in L (including diagonal): 336
+ # divide operations for LDL' or LU: 288
+ # multiply-subtract operations for LDL': 1171
+ # multiply-subtract operations for LU: 2054
+ max nz. in any column of L (incl. diagonal): 13
+
+ chol flop count for real A, sqrt counted as 1 flop: 2678
+ LDL' flop count for real A: 2630
+ LDL' flop count for complex A: 11960
+ LU flop count for real A (with no pivoting): 4396
+ LU flop count for complex A (with no pivoting): 19024
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 288 Flop count: 2630
+relative maxnorm of residual: 5.96745e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 511 Flop count: 7383
+relative maxnorm of residual: 6.93889e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 48
+ nz, number of nonzeros in A: 306
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 48
+ nonzeros in pattern of A+A' (excl. diagonal): 258
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 4596
+ # of memory compactions: 1
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 288
+ nonzeros in L (including diagonal): 336
+ # divide operations for LDL' or LU: 288
+ # multiply-subtract operations for LDL': 1171
+ # multiply-subtract operations for LU: 2054
+ max nz. in any column of L (incl. diagonal): 13
+
+ chol flop count for real A, sqrt counted as 1 flop: 2678
+ LDL' flop count for real A: 2630
+ LDL' flop count for complex A: 11960
+ LU flop count for real A (with no pivoting): 4396
+ LU flop count for complex A (with no pivoting): 19024
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 288 Flop count: 2630
+relative maxnorm of residual: 5.55112e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 511 Flop count: 7383
+relative maxnorm of residual: 5.55112e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Bai/bfwb62 n: 62 entries: 342
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 62
+ nz, number of nonzeros in A: 342
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 62
+ nonzeros in pattern of A+A' (excl. diagonal): 280
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 3576
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 226
+ nonzeros in L (including diagonal): 288
+ # divide operations for LDL' or LU: 226
+ # multiply-subtract operations for LDL': 623
+ # multiply-subtract operations for LU: 1020
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 1534
+ LDL' flop count for real A: 1472
+ LDL' flop count for complex A: 7018
+ LU flop count for real A (with no pivoting): 2266
+ LU flop count for complex A (with no pivoting): 10194
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 226 Flop count: 1472
+relative maxnorm of residual: 5.55112e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 662 Flop count: 11350
+relative maxnorm of residual: 1.11022e-15
+
+
+--------------------------------------------------------
+Input matrix: name: Bai/bfwb62 n: 62 entries: 407 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 62
+ nz, number of nonzeros in A: 342
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 62
+ nonzeros in pattern of A+A' (excl. diagonal): 280
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 5456
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 226
+ nonzeros in L (including diagonal): 288
+ # divide operations for LDL' or LU: 226
+ # multiply-subtract operations for LDL': 623
+ # multiply-subtract operations for LU: 1020
+ max nz. in any column of L (incl. diagonal): 9
+
+ chol flop count for real A, sqrt counted as 1 flop: 1534
+ LDL' flop count for real A: 1472
+ LDL' flop count for complex A: 7018
+ LU flop count for real A (with no pivoting): 2266
+ LU flop count for complex A (with no pivoting): 10194
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 226 Flop count: 1472
+relative maxnorm of residual: 5.68434e-14
+Factorize A=LDL' and solve Ax=b
+Nz in L: 662 Flop count: 11350
+relative maxnorm of residual: 2.15827e-12
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk02 n: 66 entries: 4356
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 4356
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 4290
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 22968
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 2145
+ nonzeros in L (including diagonal): 2211
+ # divide operations for LDL' or LU: 2145
+ # multiply-subtract operations for LDL': 47905
+ # multiply-subtract operations for LU: 93665
+ max nz. in any column of L (incl. diagonal): 66
+
+ chol flop count for real A, sqrt counted as 1 flop: 98021
+ LDL' flop count for real A: 97955
+ LDL' flop count for complex A: 402545
+ LU flop count for real A (with no pivoting): 189475
+ LU flop count for complex A (with no pivoting): 768625
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 7.50219e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 7.50219e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 4356
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 4290
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 43936
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 2145
+ nonzeros in L (including diagonal): 2211
+ # divide operations for LDL' or LU: 2145
+ # multiply-subtract operations for LDL': 47905
+ # multiply-subtract operations for LU: 93665
+ max nz. in any column of L (incl. diagonal): 66
+
+ chol flop count for real A, sqrt counted as 1 flop: 98021
+ LDL' flop count for real A: 97955
+ LDL' flop count for complex A: 402545
+ LU flop count for real A (with no pivoting): 189475
+ LU flop count for complex A (with no pivoting): 768625
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 8.59759e-13
+Factorize A=LDL' and solve Ax=b
+Nz in L: 2145 Flop count: 97955
+relative maxnorm of residual: 8.59759e-13
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm02 n: 66 entries: 66
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 66
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2376
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 66
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 66
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+
+
+--------------------------------------------------------
+Input matrix: name: HB/bcsstm02 n: 66 entries: 72 (jumbled version)
+--------------------------------------------------------
+
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK, but jumbled
+ n, dimension of A: 66
+ nz, number of nonzeros in A: 66
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 66
+ nonzeros in pattern of A+A' (excl. diagonal): 0
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 2932
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 0
+ nonzeros in L (including diagonal): 66
+ # divide operations for LDL' or LU: 0
+ # multiply-subtract operations for LDL': 0
+ # multiply-subtract operations for LU: 0
+ max nz. in any column of L (incl. diagonal): 1
+
+ chol flop count for real A, sqrt counted as 1 flop: 66
+ LDL' flop count for real A: 0
+ LDL' flop count for complex A: 0
+ LU flop count for real A (with no pivoting): 0
+ LU flop count for complex A (with no pivoting): 0
+
+Factorize PAP'=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+Factorize A=LDL' and solve Ax=b
+Nz in L: 0 Flop count: 0
+relative maxnorm of residual: 2.22045e-16
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid perm)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ap)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+
+--------------------------------------------------------
+Input matrix: name: Dense/3 n: 3 entries: 9 (invalid Ai)
+--------------------------------------------------------
+
+ldlamd: invalid matrix and/or permutation
+
+Largest residual during all tests: 3.27418e-10
+
+ldlamd: all tests passed
+
+diary off
diff --git a/LDL/MATLAB/ldlmex.c b/LDL/MATLAB/ldlmex.c
new file mode 100644
index 0000000..7842cd4
--- /dev/null
+++ b/LDL/MATLAB/ldlmex.c
@@ -0,0 +1,368 @@
+/* ========================================================================== */
+/* === ldlmex.c: LDL mexFunction =========================================== */
+/* ========================================================================== */
+
+/* MATLAB interface for numerical LDL' factorization using the LDL sparse matrix
+ * package.
+ *
+ * MATLAB calling syntax is:
+ *
+ * [L, D, Parent, flops] = ldl (A)
+ * [L, D, Parent, flops] = ldl (A, P)
+ * [x, flops] = ldl (A, [ ], b)
+ * [x, flops] = ldl (A, P, b)
+ *
+ * The factorization is L*D*L' = A or L*D*L' = A(P,P). A must be sparse,
+ * square, and real. L is lower triangular with unit diagonal, but the diagonal
+ * is not returned. D is diagonal sparse matrix. Let n = size (A,1). If P is
+ * not present or empty, the factorization is:
+ *
+ * (L + speye (n)) * D * (L + speye (n))' = A
+ *
+ * otherwise, the factorization is
+ *
+ * (L + speye (n)) * D * (L + speye (n))' = A(P,P)
+ *
+ * P is a permutation of 1:n, an output of AMD, SYMAMD, or SYMRCM, for example.
+ * Only the diagonal and upper triangular part of A or A(P,P) is accessed; the
+ * lower triangular part is ignored.
+ *
+ * The elimination tree is returned in the Parent array.
+ *
+ * In the x = ldl (A, P, b) usage, the LDL' factorization is not returned.
+ * Instead, the system A*x=b is solved for x, where b is a dense n-by-m matrix,
+ * using P as the fill-reducing ordering for the LDL' factorization of A(P,P).
+ * If P is not present or equal to [ ], it is assumed to be the identity
+ * permutation.
+ *
+ * If no zero entry on the diagonal of D is encountered, then the flops argument
+ * is the floating point count.
+ *
+ * If any entry on the diagonal of D is zero, then the LDL' factorization is
+ * terminated at that point. If there is no flops output argument, an error
+ * message is printed and no outputs are returned. Otherwise, flops is
+ * negative, d = -flops, and D (d,d) is the first zero entry on the diagonal of
+ * D. A partial factorization is returned. Let B = A if P is not present or
+ * empty, or B = A(P,P) otherwise. Then the factorization is
+ *
+ * LDL = (L + speye (n)) * D * (L + speye (n))'
+ * LDL (1:d, 1:d) = B (1:d,1:d)
+ *
+ * That is, the LDL' factorization of B (1:d,1:d) is in the first d rows and
+ * columns of L and D. The rest of L and D are zero.
+ *
+ * LDL Copyright (c) by Timothy A Davis,
+ * University of Florida. All Rights Reserved. See README for the License.
+ */
+
+#ifndef LDL_LONG
+#define LDL_LONG
+#endif
+
+#include "ldl.h"
+#include "mex.h"
+
+/* ========================================================================== */
+/* === LDL mexFunction ====================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout[ ],
+ int nargin,
+ const mxArray *pargin[ ]
+)
+{
+ UF_long i, n, *Pattern, *Flag, *Li, *Lp, *Ap, *Ai, *Lnz, *Parent, do_chol,
+ nrhs = 0, lnz, do_solve, *P, *Pinv, nn, k, j, permute, *Dp = NULL, *Di,
+ d, do_flops, psrc, pdst ;
+ double *Y, *D, *Lx, *Ax, flops, *X = NULL, *B = NULL, *p ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs and allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ do_chol = (nargin > 0) && (nargin <= 2) && (nargout <= 4) ;
+ do_solve = (nargin == 3) && (nargout <= 2) ;
+ if (!(do_chol || do_solve))
+ {
+ mexErrMsgTxt ("Usage:\n"
+ " [L, D, etree, flopcount] = ldl (A) ;\n"
+ " [L, D, etree, flopcount] = ldl (A, P) ;\n"
+ " [x, flopcount] = ldl (A, [ ], b) ;\n"
+ " [x, flopcount] = ldl (A, P, b) ;\n"
+ "The etree and flopcount arguments are optional.") ;
+ }
+ n = mxGetM (pargin [0]) ;
+ if (!mxIsSparse (pargin [0]) || n != mxGetN (pargin [0])
+ || mxIsComplex (pargin [0]))
+ {
+ mexErrMsgTxt ("ldl: A must be sparse, square, and real") ;
+ }
+ if (do_solve)
+ {
+ if (mxIsSparse (pargin [2]) || n != mxGetM (pargin [2])
+ || !mxIsDouble (pargin [2]) || mxIsComplex (pargin [2]))
+ {
+ mexErrMsgTxt (
+ "ldl: b must be dense, real, and with proper dimension") ;
+ }
+ }
+ nn = (n == 0) ? 1 : n ;
+
+ /* get sparse matrix A */
+ Ap = (UF_long *) mxGetJc (pargin [0]) ;
+ Ai = (UF_long *) mxGetIr (pargin [0]) ;
+ Ax = mxGetPr (pargin [0]) ;
+
+ /* get fill-reducing ordering, if present */
+ permute = ((nargin > 1) && !mxIsEmpty (pargin [1])) ;
+ if (permute)
+ {
+ if (mxGetM (pargin [1]) * mxGetN (pargin [1]) != n ||
+ mxIsSparse (pargin [1]))
+ {
+ mexErrMsgTxt ("ldl: invalid input permutation\n") ;
+ }
+ P = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+ Pinv = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+ p = mxGetPr (pargin [1]) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = p [k] - 1 ; /* convert to 0-based */
+ }
+ }
+ else
+ {
+ P = (UF_long *) NULL ;
+ Pinv = (UF_long *) NULL ;
+ }
+
+ /* allocate first part of L */
+ Lp = (UF_long *) mxMalloc ((n+1) * sizeof (UF_long)) ;
+ Parent = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+
+ /* get workspace */
+ Y = (double *) mxMalloc (nn * sizeof (double)) ;
+ Flag = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+ Pattern = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+ Lnz = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+
+ /* make sure the input P is valid */
+ if (permute && !ldl_l_valid_perm (n, P, Flag))
+ {
+ mexErrMsgTxt ("ldl: invalid input permutation\n") ;
+ }
+
+ /* note that we assume that the input matrix is valid */
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization to get Lp, Parent, Lnz, and optionally Pinv */
+ /* ---------------------------------------------------------------------- */
+
+ ldl_l_symbolic (n, Ap, Ai, Lp, Parent, Lnz, Flag, P, Pinv) ;
+ lnz = Lp [n] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create outputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_chol)
+ {
+ /* create the output matrix L, using the Lp array from ldl_l_symbolic */
+ pargout [0] = mxCreateSparse (n, n, lnz+1, mxREAL) ;
+ mxFree (mxGetJc (pargout [0])) ;
+ mxSetJc (pargout [0], (void *) Lp) ; /* Lp is not mxFree'd */
+ Li = (UF_long *) mxGetIr (pargout [0]) ;
+ Lx = mxGetPr (pargout [0]) ;
+
+ /* create sparse diagonal matrix D */
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateSparse (n, n, nn, mxREAL) ;
+ Dp = (UF_long *) mxGetJc (pargout [1]) ;
+ Di = (UF_long *) mxGetIr (pargout [1]) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ Dp [j] = j ;
+ Di [j] = j ;
+ }
+ Dp [n] = n ;
+ D = mxGetPr (pargout [1]) ;
+ }
+ else
+ {
+ D = (double *) mxMalloc (nn * sizeof (double)) ;
+ }
+
+ /* return elimination tree (add 1 to change from 0-based to 1-based) */
+ if (nargout > 2)
+ {
+ pargout [2] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ p = mxGetPr (pargout [2]) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ p [i] = Parent [i] + 1 ;
+ }
+ }
+
+ do_flops = (nargout == 4) ? (3) : (-1) ;
+ }
+ else
+ {
+ /* create L and D as temporary matrices */
+ Li = (UF_long *) mxMalloc ((lnz+1) * sizeof (UF_long)) ;
+ Lx = (double *) mxMalloc ((lnz+1) * sizeof (double)) ;
+ D = (double *) mxMalloc (nn * sizeof (double)) ;
+
+ /* create solution x */
+ nrhs = mxGetN (pargin [2]) ;
+ pargout [0] = mxCreateDoubleMatrix (n, nrhs, mxREAL) ;
+ X = mxGetPr (pargout [0]) ;
+ B = mxGetPr (pargin [2]) ;
+
+ do_flops = (nargout == 2) ? (1) : (-1) ;
+ }
+
+ if (do_flops >= 0)
+ {
+ /* find flop count for ldl_l_numeric */
+ flops = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ flops += ((double) Lnz [k]) * (Lnz [k] + 2) ;
+ }
+ if (do_solve)
+ {
+ /* add flop count for solve */
+ for (k = 0 ; k < n ; k++)
+ {
+ flops += 4 * ((double) Lnz [k]) + 1 ;
+ }
+ }
+ pargout [do_flops] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ p = mxGetPr (pargout [do_flops]) ;
+ p [0] = flops ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization to get Li, Lx, and D */
+ /* ---------------------------------------------------------------------- */
+
+ d = ldl_l_numeric (n, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Flag,
+ Pattern, P, Pinv) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* singular case : truncate the factorization */
+ /* ---------------------------------------------------------------------- */
+
+ if (d != n)
+ {
+ /* D [d] is zero: report error, or clean up */
+ if (do_chol && do_flops < 0)
+ {
+ mexErrMsgTxt ("ldl: zero pivot encountered\n") ;
+ }
+ else
+ {
+ /* L and D are incomplete, compact them */
+ if (do_chol)
+ {
+ for (k = d ; k < n ; k++)
+ {
+ Dp [k] = d ;
+ }
+ Dp [n] = d ;
+ }
+ for (k = d ; k < n ; k++)
+ {
+ D [k] = 0 ;
+ }
+ pdst = 0 ;
+ for (k = 0 ; k < d ; k++)
+ {
+ for (psrc = Lp [k] ; psrc < Lp [k] + Lnz [k] ; psrc++)
+ {
+ Li [pdst] = Li [psrc] ;
+ Lx [pdst] = Lx [psrc] ;
+ pdst++ ;
+ }
+ }
+ for (k = 0 ; k < d ; k++)
+ {
+ Lp [k+1] = Lp [k] + Lnz [k] ;
+ }
+ for (k = d ; k <= n ; k++)
+ {
+ Lp [k] = pdst ;
+ }
+ if (do_flops >= 0)
+ {
+ /* return -d instead of the flop count (convert to 1-based) */
+ p = mxGetPr (pargout [do_flops]) ;
+ p [0] = -(1+d) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_solve)
+ {
+ if (permute)
+ {
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ ldl_l_perm (n, Y, B, P) ; /* y = Pb */
+ ldl_l_lsolve (n, Y, Lp, Li, Lx) ; /* y = L\y */
+ ldl_l_dsolve (n, Y, D) ; /* y = D\y */
+ ldl_l_ltsolve (n, Y, Lp, Li, Lx) ; /* y = L'\y */
+ ldl_l_permt (n, X, Y, P) ; /* x = P'y */
+ X += n ;
+ B += n ;
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < nrhs ; j++)
+ {
+ for (k = 0 ; k < n ; k++) /* x = b */
+ {
+ X [k] = B [k] ;
+ }
+ ldl_l_lsolve (n, X, Lp, Li, Lx) ; /* x = L\x */
+ ldl_l_dsolve (n, X, D) ; /* x = D\x */
+ ldl_l_ltsolve (n, X, Lp, Li, Lx) ; /* x = L'\x */
+ X += n ;
+ B += n ;
+ }
+ }
+ /* free the matrix L */
+ mxFree (Lp) ;
+ mxFree (Li) ;
+ mxFree (Lx) ;
+ mxFree (D) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_chol && nargout < 2)
+ {
+ mxFree (D) ;
+ }
+ if (permute)
+ {
+ mxFree (P) ;
+ mxFree (Pinv) ;
+ }
+ mxFree (Parent) ;
+ mxFree (Y) ;
+ mxFree (Flag) ;
+ mxFree (Pattern) ;
+ mxFree (Lnz) ;
+}
diff --git a/LDL/MATLAB/ldlrow.m b/LDL/MATLAB/ldlrow.m
new file mode 100644
index 0000000..4c2f836
--- /dev/null
+++ b/LDL/MATLAB/ldlrow.m
@@ -0,0 +1,82 @@
+function [L, D] = ldlrow (A)
+%LDLROW an m-file description of the algorithm used by LDL
+%
+% Example:
+% [L, D] = ldlrow (A)
+%
+% Compute the L*D*L' factorization of A, by rows. Returns
+% full L and D matrices. This routine serves as an outline
+% of the numerical factorization performed by ldl.c.
+%
+% Here is a diagram of how L is computed. "a" means an
+% entry that is accessed at the kth step, and "c" means an
+% entry that is computed. A "-" means neither accessed nor
+% computed. A "1" means the value of the entry is L (the
+% unit diagonal of L), and it is accessed at the kth step.
+% A "." means the value is zero.
+%
+% The L matrix
+%
+% 1 . . . . . . .
+% a 1 . . . . . .
+% a a 1 . . . . .
+% a a a 1 . . . .
+% c c c c c . . . <- kth row of L
+% - - - - - - . .
+% - - - - - - - .
+% - - - - - - - -
+%
+% The A matrix:
+%
+% the kth column of A
+% v
+% - - - - a - - -
+% - - - - a - - -
+% - - - - a - - -
+% - - - - a - - -
+% - - - - a - - - <- kth row of A
+% - - - - - - - -
+% - - - - - - - -
+% - - - - - - - -
+%
+% The D matrix:
+%
+% the kth column of D
+% v
+% a . . . . . . .
+% . a . . . . . .
+% . . a . . . . .
+% . . . a . . . .
+% . . . . c . . . <- kth row of D
+% . . . . . . . .
+% . . . . . . . .
+% . . . . . . . .
+%
+% See also ldlsparse.
+
+% Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida
+
+[m n] = size (A) ;
+L = zeros (n, n) ;
+D = zeros (n, 1) ;
+A = full (A) ;
+
+L (1, 1) = 1 ;
+D (1) = A (1,1) ;
+
+for k = 2:n
+
+ % note the sparse triangular solve. For the sparse
+ % case, the pattern of y is the same as the pattern of
+ % the kth row of L.
+ y = L (1:k-1, 1:k-1) \ A (1:k-1, k) ;
+
+ % scale row k of L
+ L (k, 1:k-1) = (y ./ D (1:k-1))' ;
+ L (k, k) = 1 ;
+
+ % compute the diagonal
+ D (k) = A (k,k) - L (k, 1:k-1) * y ;
+end
+
+D = diag (D) ;
diff --git a/LDL/MATLAB/ldlsparse.m b/LDL/MATLAB/ldlsparse.m
new file mode 100644
index 0000000..164a9f3
--- /dev/null
+++ b/LDL/MATLAB/ldlsparse.m
@@ -0,0 +1,33 @@
+function [arg1, arg2, arg3, arg4] = ldlsparse (A, P, b) %#ok
+%LDLSPARSE LDL' factorization of a real, sparse, symmetric matrix
+%
+% Example:
+% [L, D, Parent, fl] = ldlsparse (A)
+% [L, D, Parent, fl] = ldlsparse (A, P)
+% [x, fl] = ldlsparse (A, [ ], b)
+% [x, fl] = ldlsparse (A, P, b)
+%
+% Let I = speye (size (A,1)). The factorization is (L+I)*D*(L+I)' = A or A(P,P).
+% A must be sparse, square, and real. Only the diagonal and upper triangular
+% part of A or A(P,P) are accessed. L is lower triangular with unit diagonal,
+% but the diagonal is not returned. D is a diagonal sparse matrix. P is either
+% a permutation of 1:n, or an empty vector, where n = size (A,1). If not
+% present, or empty, then P=1:n is assumed. Parent is the elimination tree of
+% A or A(P,P). If positive, fl is the floating point operation count, or
+% negative if any entry on the diagonal of D is zero.
+%
+% In the x = ldlsparse (A, P, b) usage, the LDL' factorization is not returned.
+% Instead, the system A*x=b is solved for x, where both b and x are dense.
+%
+% If a zero entry on the diagonal of D is encountered, the LDL' factorization is
+% terminated at that point. If there is no fl output argument, an error occurs.
+% Otherwise, fl is negative, and let d=-fl. D(d,d) is the first zero entry on
+% the diagonal of D. A partial factorization is returned. Let B = A, or A(P,P)
+% if P is present. Let F = (L+I)*D*(L+I)'. Then F (1:d,1:d) = B (1:d,1:d).
+% Rows d+1 to n of L and D are all zero.
+%
+% See also chol, ldl, ldlsymbol, symbfact, etree
+
+% Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida
+
+error ('ldlsparse mexFunction not found') ;
diff --git a/LDL/MATLAB/ldlsymbol.m b/LDL/MATLAB/ldlsymbol.m
new file mode 100644
index 0000000..c046cb3
--- /dev/null
+++ b/LDL/MATLAB/ldlsymbol.m
@@ -0,0 +1,35 @@
+function [Lnz, Parent, fl] = ldlsymbol (A, P) %#ok
+%LDLSYMBOL symbolic Cholesky factorization
+%
+% Example:
+% [Lnz, Parent, fl] = ldlsymbol (A)
+% [Lnz, Parent, fl] = ldlsymbol (A, P)
+%
+% P is a permutation of 1:n, an output of AMD, SYMAMD, or SYMRCM, for example.
+% Only the diagonal and upper triangular part of A or A(P,P) is accessed; the
+% lower triangular part is ignored. If P is not provided, then P = 1:n is
+% assumed.
+%
+% The elimination tree is returned in the Parent array. The number of nonzeros
+% in each column of L is returned in Lnz. fl is the floating point operation
+% count for a subsequent LDL' factorization. This mexFunction replicates the
+% following MATLAB computations, using ldl_symbolic:
+%
+% Lnz = symbfact (A) - 1 ;
+% Parent = etree (A) ;
+% fl = sum (Lnz .* (Lnz + 2)) ;
+%
+% or, if P is provided,
+%
+% Lnz = symbfact (A (P,P)) - 1 ;
+% Parent = etree (A (P,P)) ;
+% fl = sum (Lnz .* (Lnz + 2)) ;
+%
+% Note that this routine is not required by LDL, since LDL does its own
+% symbolic factorization.
+%
+% See also ldlsparse, symbfact, etree
+
+% Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida
+
+error ('ldlsymbol mexFunction not found') ;
diff --git a/LDL/MATLAB/ldlsymbolmex.c b/LDL/MATLAB/ldlsymbolmex.c
new file mode 100644
index 0000000..9631b20
--- /dev/null
+++ b/LDL/MATLAB/ldlsymbolmex.c
@@ -0,0 +1,178 @@
+/* ========================================================================== */
+/* === ldlsymbolmex.c: LDLSYMBOL mexFunction =============================== */
+/* ========================================================================== */
+
+/* MATLAB interface for symbolic LDL' factorization using the LDL sparse matrix
+ * package. This mexFunction is not required by the LDL mexFunction.
+ *
+ * MATLAB calling syntax is:
+ *
+ * [Lnz, Parent, flopcount] = ldlsymbol (A)
+ * [Lnz, Parent, flopcount] = ldlsymbol (A, P)
+ *
+ * P is a permutation of 1:n, an output of AMD, SYMAMD, or SYMRCM, for example.
+ * Only the diagonal and upper triangular part of A or A(P,P) is accessed; the
+ * lower triangular part is ignored.
+ *
+ * The elimination tree is returned in the Parent array. The number of nonzeros
+ * in each column of L is returned in Lnz. This mexFunction replicates the
+ * following MATLAB computations, using ldl_l_symbolic:
+ *
+ * Lnz = symbfact (A) - 1 ;
+ * Parent = etree (A) ;
+ * flopcount = sum (Lnz .* (Lnz + 2)) ;
+ *
+ * or, if P is provided,
+ *
+ * B = A (P,P) ;
+ * Lnz = symbfact (B) - 1 ;
+ * Parent = etree (B) ;
+ * flopcount = sum (Lnz .* (Lnz + 2)) ;
+ *
+ * This code is faster than the above MATLAB statements, typically by a factor
+ * of 4 to 40 (median speedup of 9) in MATLAB 6.5 on a Pentium 4 Linux laptop
+ * (excluding the B=A(P,P) time), on a wide range of symmetric sparse matrices.
+ *
+ * LDL Version 1.3, Copyright (c) 2006 by Timothy A Davis,
+ * University of Florida. All Rights Reserved. See README for the License.
+ */
+
+#ifndef LDL_LONG
+#define LDL_LONG
+#endif
+
+#include "ldl.h"
+#include "mex.h"
+
+/* ========================================================================== */
+/* === LDLSYMBOL mexFunction ================================================ */
+/* ========================================================================== */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout[ ],
+ int nargin,
+ const mxArray *pargin[ ]
+)
+{
+ UF_long i, n, *Pattern, *Flag, *Lp, *Ap, *Ai, *Lnz, *Parent,
+ *P, *Pinv, nn, k, j, permute ;
+ double flops, *p ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs and allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin == 0 || nargin > 2)
+ {
+ mexErrMsgTxt ("Usage:\n"
+ " [Lnz, Parent, flopcount] = ldl (A) ;\n"
+ " [Lnz, Parent, flopcount] = ldl (A, P) ;\n") ;
+ }
+ n = mxGetM (pargin [0]) ;
+ if (!mxIsSparse (pargin [0]) || n != mxGetN (pargin [0])
+ || mxIsComplex (pargin [0]))
+ {
+ mexErrMsgTxt ("ldlsymbol: A must be sparse, square, and real") ;
+ }
+
+ nn = (n == 0) ? 1 : n ;
+
+ /* get sparse matrix A */
+ Ap = (UF_long *) mxGetJc (pargin [0]) ;
+ Ai = (UF_long *) mxGetIr (pargin [0]) ;
+
+ /* get fill-reducing ordering, if present */
+ permute = ((nargin > 1) && !mxIsEmpty (pargin [1])) ;
+ if (permute)
+ {
+ if (mxGetM (pargin [1]) * mxGetN (pargin [1]) != n ||
+ mxIsSparse (pargin [1]))
+ {
+ mexErrMsgTxt ("ldlsymbol: invalid input permutation\n") ;
+ }
+ P = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+ Pinv = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+ p = mxGetPr (pargin [1]) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = p [k] - 1 ; /* convert to 0-based */
+ }
+ }
+ else
+ {
+ P = (UF_long *) NULL ;
+ Pinv = (UF_long *) NULL ;
+ }
+
+ /* allocate first part of L */
+ Lp = (UF_long *) mxMalloc ((n+1) * sizeof (UF_long)) ;
+ Parent = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+
+ /* get workspace */
+ Flag = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+ Pattern = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+ Lnz = (UF_long *) mxMalloc (nn * sizeof (UF_long)) ;
+
+ /* make sure the input P is valid */
+ if (permute && !ldl_l_valid_perm (n, P, Flag))
+ {
+ mexErrMsgTxt ("ldlsymbol: invalid input permutation\n") ;
+ }
+
+ /* note that we assume that the input matrix is valid */
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization to get Lp, Parent, Lnz, and optionally Pinv */
+ /* ---------------------------------------------------------------------- */
+
+ ldl_l_symbolic (n, Ap, Ai, Lp, Parent, Lnz, Flag, P, Pinv) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create outputs */
+ /* ---------------------------------------------------------------------- */
+
+ /* create the output Lnz vector */
+ pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ p = mxGetPr (pargout [0]) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ p [j] = Lnz [j] ;
+ }
+
+ /* return elimination tree (add 1 to change from 0-based to 1-based) */
+ if (nargout > 1)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, n, mxREAL) ;
+ p = mxGetPr (pargout [1]) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ p [i] = Parent [i] + 1 ;
+ }
+ }
+
+ if (nargout > 2)
+ {
+ /* find flop count for ldl_l_numeric */
+ flops = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ flops += ((double) Lnz [k]) * (Lnz [k] + 2) ;
+ }
+ pargout [2] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ p = mxGetPr (pargout [2]) ;
+ p [0] = flops ;
+ }
+
+ if (permute)
+ {
+ mxFree (P) ;
+ mxFree (Pinv) ;
+ }
+ mxFree (Lp) ;
+ mxFree (Parent) ;
+ mxFree (Flag) ;
+ mxFree (Pattern) ;
+ mxFree (Lnz) ;
+}
diff --git a/LDL/MATLAB/ldltest.m b/LDL/MATLAB/ldltest.m
new file mode 100644
index 0000000..912c18e
--- /dev/null
+++ b/LDL/MATLAB/ldltest.m
@@ -0,0 +1,188 @@
+function ldltest
+%LDLTEST test program for LDL
+%
+% Example:
+% ldltest
+% See also ldlsparse.
+
+% Copyright 2006-2007 by Timothy A. Davis, Univ. of Florida
+
+help ldlsparse
+
+A = sparse ([ ]) ;
+
+[L, D, Parent, fl] = ldlsparse (A) ; %#ok
+[L, D, Parent, fl] = ldlsparse (A, [ ]) ; %#ok
+
+try
+ [L, D, Parent, fl] = ldlsparse (A, [1 2]) ;
+ fprintf ('L = ') ; disp (L)
+ fprintf ('D = ') ; disp (D)
+ fprintf ('Parent = ') ; disp (Parent)
+ fprintf ('fl = %g\n', fl) ;
+ ok = 0 ;
+catch
+ ok = 1 ;
+end
+if (~ok)
+ error ('?') ;
+end
+
+try
+ ldlsparse
+ ok = 0 ;
+catch
+ ok = 1 ;
+end
+if (~ok)
+ error ('?')
+end
+
+try
+ [L, D, Parent, fl] = ldlsparse (1) ; %#ok
+ ok = 0 ;
+catch
+ ok = 1 ;
+end
+if (~ok)
+ error ('?')
+end
+
+try
+ x = ldlsparse (1,2) ; %#ok
+ ok = 0 ;
+catch
+ ok = 1 ;
+end
+if (~ok)
+ error ('?')
+end
+
+A =[ ...
+1.7 0 0 0 0 0 0 0 .13 0
+ 0 1.0 0 0 .02 0 0 0 0 .01
+ 0 0 1.5 0 0 0 0 0 0 0
+ 0 0 0 1.1 0 0 0 0 0 0
+ 0 .02 0 0 2.6 0 .16 .09 .52 .53
+ 0 0 0 0 0 1.2 0 0 0 0
+ 0 0 0 0 .16 0 1.3 0 0 .56
+ 0 0 0 0 .09 0 0 1.6 .11 0
+.13 0 0 0 .52 0 0 .11 1.4 0
+ 0 .01 0 0 .53 0 .56 0 0 3.1 ] ;
+A = sparse (A) ;
+b = [ ...
+ .98 .64 .05
+ .58 .20 .44
+ .42 .37 .30
+ .51 .78 .84
+ .33 .68 .01
+ .43 .46 .76
+ .22 .56 .97
+ .57 .79 .99
+ .76 .05 .78
+ .52 .60 .43 ] ;
+P = [3 10 2 5 8 6 9 7 1 4] ;
+I = speye (10) ;
+
+[L, D, Parent, fl] = ldlsparse (A) ;
+err = norm ((L+I)*D*(L+I)'-A, 1) ;
+fprintf ('err: %g fl: %g\n', err, fl) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+Parent2 = etree (A) ;
+if (any (Parent2 ~= Parent))
+ error ('?') ;
+end
+
+[L, D, Parent] = ldlsparse (A) ; %#ok
+err = norm ((L+I)*D*(L+I)'-A, 1) ;
+fprintf ('err: %g\n', err) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+[L, D] = ldlsparse (A) ;
+err = norm ((L+I)*D*(L+I)'-A, 1) ;
+fprintf ('err: %g\n', err) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+L2 = ldlsparse (A) ;
+err = norm (L - L2, 1) ;
+fprintf ('err: %g\n', err) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+x = ldlsparse (A, [ ], b) ;
+err = norm (A*x-b, 1) ;
+fprintf ('err: %g\n', err) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+[x, fl] = ldlsparse (A, [ ], b) ;
+err = norm (A*x-b, 1) ;
+fprintf ('err: %g fl: %g\n', err, fl) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+[L, D, Parent, fl] = ldlsparse (A, P) ;
+err = norm ((L+I)*D*(L+I)'-A(P,P), 1) ;
+fprintf ('err: %g fl: %g\n', err, fl) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+Parent2 = etree (A (P,P)) ;
+if (any (Parent2 ~= Parent))
+ error ('?') ;
+end
+
+figure (1)
+clf
+subplot (2,2,1), spy (A), title ('original matrix') ;
+subplot (2,2,2), spy (A (P,P)), title ('permuted matrix') ;
+subplot (2,2,3), spy (L+D+L'), title ('L+D+L''') ;
+subplot (2,2,4), treeplot (Parent), title ('elimination tree') ;
+
+[L, D, Parent] = ldlsparse (A, P) ;
+err = norm ((L+I)*D*(L+I)'-A(P,P), 1) ;
+fprintf ('err: %g\n', err) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+[L, D] = ldlsparse (A, P) ;
+err = norm ((L+I)*D*(L+I)'-A(P,P), 1) ;
+fprintf ('err: %g\n', err) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+L2 = ldlsparse (A, P) ;
+err = norm (L - L2, 1) ;
+fprintf ('err: %g\n', err) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+x = ldlsparse (A, P, b) ;
+err = norm (A*x-b, 1) ;
+fprintf ('err: %g\n', err) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+[x, fl] = ldlsparse (A, P, b) ;
+err = norm (A*x-b, 1) ;
+fprintf ('err: %g fl: %g\n', err, fl) ;
+if (err > 1e-14)
+ error ('?') ;
+end ;
+
+fprintf ('\nldl: all tests passed\n') ;
diff --git a/LDL/MATLAB/ldltest.out b/LDL/MATLAB/ldltest.out
new file mode 100644
index 0000000..0702997
--- /dev/null
+++ b/LDL/MATLAB/ldltest.out
@@ -0,0 +1,45 @@
+ldltest
+ LDLSPARSE LDL' factorization of a real, sparse, symmetric matrix
+
+ Example:
+ [L, D, Parent, fl] = ldlsparse (A)
+ [L, D, Parent, fl] = ldlsparse (A, P)
+ [x, fl] = ldlsparse (A, [ ], b)
+ [x, fl] = ldlsparse (A, P, b)
+
+ Let I = speye (size (A,1)). The factorization is (L+I)*D*(L+I)' = A or A(P,P).
+ A must be sparse, square, and real. Only the diagonal and upper triangular
+ part of A or A(P,P) are accessed. L is lower triangular with unit diagonal,
+ but the diagonal is not returned. D is a diagonal sparse matrix. P is either
+ a permutation of 1:n, or an empty vector, where n = size (A,1). If not
+ present, or empty, then P=1:n is assumed. Parent is the elimination tree of
+ A or A(P,P). If positive, fl is the floating point operation count, or
+ negative if any entry on the diagonal of D is zero.
+
+ In the x = ldlsparse (A, P, b) usage, the LDL' factorization is not returned.
+ Instead, the system A*x=b is solved for x, where both b and x are dense.
+
+ If a zero entry on the diagonal of D is encountered, the LDL' factorization is
+ terminated at that point. If there is no fl output argument, an error occurs.
+ Otherwise, fl is negative, and let d=-fl. D(d,d) is the first zero entry on
+ the diagonal of D. A partial factorization is returned. Let B = A, or A(P,P)
+ if P is present. Let F = (L+I)*D*(L+I)'. Then F (1:d,1:d) = B (1:d,1:d).
+ Rows d+1 to n of L and D are all zero.
+
+ See also chol, ldl, ldlsymbol, symbfact, etree
+
+err: 4.44089e-16 fl: 61
+err: 4.44089e-16
+err: 4.44089e-16
+err: 0
+err: 5.68989e-16
+err: 5.68989e-16 fl: 123
+err: 4.57967e-16 fl: 57
+err: 4.57967e-16
+err: 4.57967e-16
+err: 0
+err: 6.36644e-16
+err: 6.36644e-16 fl: 119
+
+ldl: all tests passed
+diary off
diff --git a/LDL/Makefile b/LDL/Makefile
new file mode 100644
index 0000000..91eb29d
--- /dev/null
+++ b/LDL/Makefile
@@ -0,0 +1,55 @@
+#------------------------------------------------------------------------------
+# LDL Makefile
+#------------------------------------------------------------------------------
+
+default: demo
+
+include ../UFconfig/UFconfig.mk
+
+# Compile all C code, including the C-callable routine.
+demo:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+
+# Compile all C code, including the C-callable routine and the mexFunctions.
+all:
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+ ( cd MATLAB ; $(MAKE) )
+
+# compile just the C-callable libraries (not mexFunctions or Demos)
+library:
+ ( cd Lib ; $(MAKE) )
+
+# remove object files, but keep the compiled programs and library archives
+clean:
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+ ( cd MATLAB ; $(MAKE) clean )
+ ( cd Doc ; $(MAKE) clean )
+
+# clean, and then remove compiled programs and library archives
+purge:
+ ( cd Lib ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd MATLAB ; $(MAKE) purge )
+ ( cd Doc ; $(MAKE) purge )
+
+distclean: purge
+
+# create PDF documents for the original distribution
+doc:
+ ( cd Doc ; $(MAKE) )
+
+# get ready for distribution
+dist: purge
+ ( cd Demo ; $(MAKE) dist )
+ ( cd Doc ; $(MAKE) )
+
+ccode: library
+
+lib: library
+
+# compile the MATLAB mexFunction
+mex:
+ ( cd MATLAB ; $(MAKE) )
diff --git a/LDL/Matrix/A01 b/LDL/Matrix/A01
new file mode 100644
index 0000000..e96ce3d
--- /dev/null
+++ b/LDL/Matrix/A01
@@ -0,0 +1,3 @@
+name: Dense/0 n: 0 entries: 0
+0 0
+0
diff --git a/LDL/Matrix/A02 b/LDL/Matrix/A02
new file mode 100644
index 0000000..c5ac877
--- /dev/null
+++ b/LDL/Matrix/A02
@@ -0,0 +1,3 @@
+name: Dense/0 n: 0 entries: 0 (jumbled version)
+0 1
+0
diff --git a/LDL/Matrix/A03 b/LDL/Matrix/A03
new file mode 100644
index 0000000..5f371a6
--- /dev/null
+++ b/LDL/Matrix/A03
@@ -0,0 +1,7 @@
+name: Dense/1 n: 1 entries: 1
+1 0
+0
+1
+0
+1.90275
+0
diff --git a/LDL/Matrix/A04 b/LDL/Matrix/A04
new file mode 100644
index 0000000..c203274
--- /dev/null
+++ b/LDL/Matrix/A04
@@ -0,0 +1,9 @@
+name: Dense/1 n: 1 entries: 2 (jumbled version)
+1 1
+0
+2
+0
+0
+1.90275
+0.606843
+0
diff --git a/LDL/Matrix/A05 b/LDL/Matrix/A05
new file mode 100644
index 0000000..5cec713
--- /dev/null
+++ b/LDL/Matrix/A05
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diff --git a/LDL/Matrix/A13 b/LDL/Matrix/A13
new file mode 100644
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diff --git a/LDL/Matrix/A18 b/LDL/Matrix/A18
new file mode 100644
index 0000000..085c056
--- /dev/null
+++ b/LDL/Matrix/A18
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diff --git a/LDL/Matrix/A21 b/LDL/Matrix/A21
new file mode 100644
index 0000000..aa427b8
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diff --git a/LDL/Matrix/A22 b/LDL/Matrix/A22
new file mode 100644
index 0000000..c6d98e0
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diff --git a/LDL/Matrix/A23 b/LDL/Matrix/A23
new file mode 100644
index 0000000..741d99b
--- /dev/null
+++ b/LDL/Matrix/A23
@@ -0,0 +1,267 @@
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diff --git a/LDL/Matrix/A24 b/LDL/Matrix/A24
new file mode 100644
index 0000000..8912d95
--- /dev/null
+++ b/LDL/Matrix/A24
@@ -0,0 +1,279 @@
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diff --git a/LDL/Matrix/A25 b/LDL/Matrix/A25
new file mode 100644
index 0000000..4bddf37
--- /dev/null
+++ b/LDL/Matrix/A25
@@ -0,0 +1,3 @@
+name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 99)
+0 0
+99
diff --git a/LDL/Matrix/A26 b/LDL/Matrix/A26
new file mode 100644
index 0000000..dd14c8e
--- /dev/null
+++ b/LDL/Matrix/A26
@@ -0,0 +1,15 @@
+name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99)
+2 0
+0
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+4
+0
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+0.389047
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diff --git a/LDL/Matrix/A27 b/LDL/Matrix/A27
new file mode 100644
index 0000000..9803cf7
--- /dev/null
+++ b/LDL/Matrix/A27
@@ -0,0 +1,27 @@
+name: Dense/3 n: 3 entries: 9 (invalid perm)
+3 0
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diff --git a/LDL/Matrix/A28 b/LDL/Matrix/A28
new file mode 100644
index 0000000..0bf505e
--- /dev/null
+++ b/LDL/Matrix/A28
@@ -0,0 +1,27 @@
+name: Dense/3 n: 3 entries: 9 (invalid Ap)
+3 0
+0
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diff --git a/LDL/Matrix/A29 b/LDL/Matrix/A29
new file mode 100644
index 0000000..4dcf64d
--- /dev/null
+++ b/LDL/Matrix/A29
@@ -0,0 +1,27 @@
+name: Dense/3 n: 3 entries: 9 (invalid Ai)
+3 0
+0
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diff --git a/LDL/Matrix/A30 b/LDL/Matrix/A30
new file mode 100644
index 0000000..a0b9f0a
--- /dev/null
+++ b/LDL/Matrix/A30
@@ -0,0 +1,27 @@
+name: Dense/3 n: 3 entries: 9 (invalid Ai)
+3 0
+0
+3
+6
+9
+0
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diff --git a/LDL/README.txt b/LDL/README.txt
new file mode 100644
index 0000000..7be8dd1
--- /dev/null
+++ b/LDL/README.txt
@@ -0,0 +1,136 @@
+LDL Version 2.0: a sparse LDL' factorization and solve package.
+ Written in C, with both a C and MATLAB mexFunction interface.
+
+These routines are not terrifically fast (they do not use dense matrix kernels),
+but the code is very short and concise. The purpose is to illustrate the
+algorithms in a very concise and readable manner, primarily for educational
+purposes. Although the code is very concise, this package is slightly faster
+than the built-in sparse Cholesky factorization in MATLAB 6.5 (chol), when
+using the same input permutation.
+
+Requires UFconfig, in the ../UFconfig directory relative to this directory.
+
+Quick start (Unix, or Windows with Cygwin):
+
+ To compile, test, and install LDL, you may wish to first obtain a copy of
+ AMD v2.0 from http://www.cise.ufl.edu/research/sparse, and place it in the
+ ../AMD directory, relative to this directory. Next, type "make", which
+ will compile the LDL library and three demo main programs (one of which
+ requires AMD). It will also compile the LDL MATLAB mexFunction (if you
+ have MATLAB). Typing "make clean" will remove non-essential files.
+ AMD v2.0 or later is required. Its use is optional.
+
+Quick start (for MATLAB users);
+
+ To compile, test, and install the LDL mexFunctions (ldlsparse and
+ ldlsymbol), start MATLAB in this directory and type ldl_install.
+ This works on any system supported by MATLAB.
+
+--------------------------------------------------------------------------------
+
+LDL Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved.
+
+LDL License:
+
+ Your use or distribution of LDL or any modified version of
+ LDL implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU LGPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/ldl
+
+Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grant CCR-0203270.
+
+ Portions of this work were done while on sabbatical at Stanford University
+ and Lawrence Berkeley National Laboratory (with funding from the SciDAC
+ program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon
+ for making this sabbatical possible. I would like to thank Pete Stewart
+ for his comments on a draft of this software and paper.
+
+--------------------------------------------------------------------------------
+Files and directories in this distribution:
+--------------------------------------------------------------------------------
+
+ Documentation, and compiling:
+
+ README.txt this file
+ Makefile for compiling LDL
+ ChangeLog changes since V1.0 (Dec 31, 2003)
+ License license
+ lesser.txt the GNU LGPL license
+
+ ldl_userguide.pdf user guide in PDF
+ ldl_userguide.ps user guide in postscript
+ ldl_userguide.tex user guide in Latex
+ ldl.bib bibliography for user guide
+
+ The LDL library itself:
+
+ ldl.c the C-callable routines
+ ldl.h include file for any code that calls LDL
+
+ A simple C main program that demonstrates how to use LDL:
+
+ ldlsimple.c a stand-alone C program, uses the basic features of LDL
+ ldlsimple.out output of ldlsimple
+
+ ldllsimple.c long integer version of ldlsimple.c
+
+ Demo C program, for testing LDL and providing an example of its use
+
+ ldlmain.c a stand-alone C main program that uses and tests LDL
+ Matrix a directory containing matrices used by ldlmain.c
+ ldlmain.out output of ldlmain
+ ldlamd.out output of ldlamd (ldlmain.c compiled with AMD)
+ ldllamd.out output of ldllamd (ldlmain.c compiled with AMD, long)
+
+ MATLAB-related, not required for use in a regular C program
+
+ Contents.m a list of the MATLAB-callable routines
+ ldl.m MATLAB help file for the LDL mexFunction
+ ldldemo.m MATLAB demo of how to use the LDL mexFunction
+ ldldemo.out diary output of ldldemo
+ ldltest.m to test the LDL mexFunction
+ ldltest.out diary output of ldltest
+ ldlmex.c the LDL mexFunction for MATLAB
+ ldlrow.m the numerical algorithm that LDL is based on
+ ldlmain2.m compiles and runs ldlmain.c as a MATLAB mexFunction
+ ldlmain2.out output of ldlmain2.m
+ ldlsymbolmex.c symbolic factorization using LDL (see SYMBFACT, ETREE)
+ ldlsymbol.m help file for the LDLSYMBOL mexFunction
+
+ ldl_install.m compile, install, and test LDL functions
+ ldl_make.m compile LDL (ldlsparse and ldlsymbol)
+
+ ldlsparse.m help for ldlsparse
+
+See ldl.c for a description of how to use the code from a C program. Type
+"help ldl" in MATLAB for information on how to use LDL in a MATLAB program.
diff --git a/LDL/Source/ldl.c b/LDL/Source/ldl.c
new file mode 100644
index 0000000..a9b35c8
--- /dev/null
+++ b/LDL/Source/ldl.c
@@ -0,0 +1,507 @@
+/* ========================================================================== */
+/* === ldl.c: sparse LDL' factorization and solve package =================== */
+/* ========================================================================== */
+
+/* LDL: a simple set of routines for sparse LDL' factorization. These routines
+ * are not terrifically fast (they do not use dense matrix kernels), but the
+ * code is very short. The purpose is to illustrate the algorithms in a very
+ * concise manner, primarily for educational purposes. Although the code is
+ * very concise, this package is slightly faster than the built-in sparse
+ * Cholesky factorization in MATLAB 7.0 (chol), when using the same input
+ * permutation.
+ *
+ * The routines compute the LDL' factorization of a real sparse symmetric
+ * matrix A (or PAP' if a permutation P is supplied), and solve upper
+ * and lower triangular systems with the resulting L and D factors. If A is
+ * positive definite then the factorization will be accurate. A can be
+ * indefinite (with negative values on the diagonal D), but in this case no
+ * guarantee of accuracy is provided, since no numeric pivoting is performed.
+ *
+ * The n-by-n sparse matrix A is in compressed-column form. The nonzero values
+ * in column j are stored in Ax [Ap [j] ... Ap [j+1]-1], with corresponding row
+ * indices in Ai [Ap [j] ... Ap [j+1]-1]. Ap [0] = 0 is required, and thus
+ * nz = Ap [n] is the number of nonzeros in A. Ap is an int array of size n+1.
+ * The int array Ai and the double array Ax are of size nz. This data structure
+ * is identical to the one used by MATLAB, except for the following
+ * generalizations. The row indices in each column of A need not be in any
+ * particular order, although they must be in the range 0 to n-1. Duplicate
+ * entries can be present; any duplicates are summed. That is, if row index i
+ * appears twice in a column j, then the value of A (i,j) is the sum of the two
+ * entries. The data structure used here for the input matrix A is more
+ * flexible than MATLAB's, which requires sorted columns with no duplicate
+ * entries.
+ *
+ * Only the diagonal and upper triangular part of A (or PAP' if a permutation
+ * P is provided) is accessed. The lower triangular parts of the matrix A or
+ * PAP' can be present, but they are ignored.
+ *
+ * The optional input permutation is provided as an array P of length n. If
+ * P [k] = j, the row and column j of A is the kth row and column of PAP'.
+ * If P is present then the factorization is LDL' = PAP' or L*D*L' = A(P,P) in
+ * 0-based MATLAB notation. If P is not present (a null pointer) then no
+ * permutation is performed, and the factorization is LDL' = A.
+ *
+ * The lower triangular matrix L is stored in the same compressed-column
+ * form (an int Lp array of size n+1, an int Li array of size Lp [n], and a
+ * double array Lx of the same size as Li). It has a unit diagonal, which is
+ * not stored. The row indices in each column of L are always returned in
+ * ascending order, with no duplicate entries. This format is compatible with
+ * MATLAB, except that it would be more convenient for MATLAB to include the
+ * unit diagonal of L. Doing so here would add additional complexity to the
+ * code, and is thus omitted in the interest of keeping this code short and
+ * readable.
+ *
+ * The elimination tree is held in the Parent [0..n-1] array. It is normally
+ * not required by the user, but it is required by ldl_numeric. The diagonal
+ * matrix D is held as an array D [0..n-1] of size n.
+ *
+ * --------------------
+ * C-callable routines:
+ * --------------------
+ *
+ * ldl_symbolic: Given the pattern of A, computes the Lp and Parent arrays
+ * required by ldl_numeric. Takes time proportional to the number of
+ * nonzeros in L. Computes the inverse Pinv of P if P is provided.
+ * Also returns Lnz, the count of nonzeros in each column of L below
+ * the diagonal (this is not required by ldl_numeric).
+ * ldl_numeric: Given the pattern and numerical values of A, the Lp array,
+ * the Parent array, and P and Pinv if applicable, computes the
+ * pattern and numerical values of L and D.
+ * ldl_lsolve: Solves Lx=b for a dense vector b.
+ * ldl_dsolve: Solves Dx=b for a dense vector b.
+ * ldl_ltsolve: Solves L'x=b for a dense vector b.
+ * ldl_perm: Computes x=Pb for a dense vector b.
+ * ldl_permt: Computes x=P'b for a dense vector b.
+ * ldl_valid_perm: checks the validity of a permutation vector
+ * ldl_valid_matrix: checks the validity of the sparse matrix A
+ *
+ * ----------------------------
+ * Limitations of this package:
+ * ----------------------------
+ *
+ * In the interest of keeping this code simple and readable, ldl_symbolic and
+ * ldl_numeric assume their inputs are valid. You can check your own inputs
+ * prior to calling these routines with the ldl_valid_perm and ldl_valid_matrix
+ * routines. Except for the two ldl_valid_* routines, no routine checks to see
+ * if the array arguments are present (non-NULL). Like all C routines, no
+ * routine can determine if the arrays are long enough and don't overlap.
+ *
+ * The ldl_numeric does check the numerical factorization, however. It returns
+ * n if the factorization is successful. If D (k,k) is zero, then k is
+ * returned, and L is only partially computed.
+ *
+ * No pivoting to control fill-in is performed, which is often critical for
+ * obtaining good performance. I recommend that you compute the permutation P
+ * using AMD or SYMAMD (approximate minimum degree ordering routines), or an
+ * appropriate graph-partitioning based ordering. See the ldldemo.m routine for
+ * an example in MATLAB, and the ldlmain.c stand-alone C program for examples of
+ * how to find P. Routines for manipulating compressed-column matrices are
+ * available in UMFPACK. AMD, SYMAMD, UMFPACK, and this LDL package are all
+ * available at http://www.cise.ufl.edu/research/sparse.
+ *
+ * -------------------------
+ * Possible simplifications:
+ * -------------------------
+ *
+ * These routines could be made even simpler with a few additional assumptions.
+ * If no input permutation were performed, the caller would have to permute the
+ * matrix first, but the computation of Pinv, and the use of P and Pinv could be
+ * removed. If only the diagonal and upper triangular part of A or PAP' are
+ * present, then the tests in the "if (i < k)" statement in ldl_symbolic and
+ * "if (i <= k)" in ldl_numeric, are always true, and could be removed (i can
+ * equal k in ldl_symbolic, but then the body of the if statement would
+ * correctly do no work since Flag [k] == k). If we could assume that no
+ * duplicate entries are present, then the statement Y [i] += Ax [p] could be
+ * replaced with Y [i] = Ax [p] in ldl_numeric.
+ *
+ * --------------------------
+ * Description of the method:
+ * --------------------------
+ *
+ * LDL computes the symbolic factorization by finding the pattern of L one row
+ * at a time. It does this based on the following theory. Consider a sparse
+ * system Lx=b, where L, x, and b, are all sparse, and where L comes from a
+ * Cholesky (or LDL') factorization. The elimination tree (etree) of L is
+ * defined as follows. The parent of node j is the smallest k > j such that
+ * L (k,j) is nonzero. Node j has no parent if column j of L is completely zero
+ * below the diagonal (j is a root of the etree in this case). The nonzero
+ * pattern of x is the union of the paths from each node i to the root, for
+ * each nonzero b (i). To compute the numerical solution to Lx=b, we can
+ * traverse the columns of L corresponding to nonzero values of x. This
+ * traversal does not need to be done in the order 0 to n-1. It can be done in
+ * any "topological" order, such that x (i) is computed before x (j) if i is a
+ * descendant of j in the elimination tree.
+ *
+ * The row-form of the LDL' factorization is shown in the MATLAB function
+ * ldlrow.m in this LDL package. Note that row k of L is found via a sparse
+ * triangular solve of L (1:k-1, 1:k-1) \ A (1:k-1, k), to use 1-based MATLAB
+ * notation. Thus, we can start with the nonzero pattern of the kth column of
+ * A (above the diagonal), follow the paths up to the root of the etree of the
+ * (k-1)-by-(k-1) leading submatrix of L, and obtain the pattern of the kth row
+ * of L. Note that we only need the leading (k-1)-by-(k-1) submatrix of L to
+ * do this. The elimination tree can be constructed as we go.
+ *
+ * The symbolic factorization does the same thing, except that it discards the
+ * pattern of L as it is computed. It simply counts the number of nonzeros in
+ * each column of L and then constructs the Lp index array when it's done. The
+ * symbolic factorization does not need to do this in topological order.
+ * Compare ldl_symbolic with the first part of ldl_numeric, and note that the
+ * while (len > 0) loop is not present in ldl_symbolic.
+ *
+ * LDL Version 1.3, Copyright (c) 2006 by Timothy A Davis,
+ * University of Florida. All Rights Reserved. Developed while on sabbatical
+ * at Stanford University and Lawrence Berkeley National Laboratory. Refer to
+ * the README file for the License. Available at
+ * http://www.cise.ufl.edu/research/sparse.
+ */
+
+#include "ldl.h"
+
+/* ========================================================================== */
+/* === ldl_symbolic ========================================================= */
+/* ========================================================================== */
+
+/* The input to this routine is a sparse matrix A, stored in column form, and
+ * an optional permutation P. The output is the elimination tree
+ * and the number of nonzeros in each column of L. Parent [i] = k if k is the
+ * parent of i in the tree. The Parent array is required by ldl_numeric.
+ * Lnz [k] gives the number of nonzeros in the kth column of L, excluding the
+ * diagonal.
+ *
+ * One workspace vector (Flag) of size n is required.
+ *
+ * If P is NULL, then it is ignored. The factorization will be LDL' = A.
+ * Pinv is not computed. In this case, neither P nor Pinv are required by
+ * ldl_numeric.
+ *
+ * If P is not NULL, then it is assumed to be a valid permutation. If
+ * row and column j of A is the kth pivot, the P [k] = j. The factorization
+ * will be LDL' = PAP', or A (p,p) in MATLAB notation. The inverse permutation
+ * Pinv is computed, where Pinv [j] = k if P [k] = j. In this case, both P
+ * and Pinv are required as inputs to ldl_numeric.
+ *
+ * The floating-point operation count of the subsequent call to ldl_numeric
+ * is not returned, but could be computed after ldl_symbolic is done. It is
+ * the sum of (Lnz [k]) * (Lnz [k] + 2) for k = 0 to n-1.
+ */
+
+void LDL_symbolic
+(
+ LDL_int n, /* A and L are n-by-n, where n >= 0 */
+ LDL_int Ap [ ], /* input of size n+1, not modified */
+ LDL_int Ai [ ], /* input of size nz=Ap[n], not modified */
+ LDL_int Lp [ ], /* output of size n+1, not defined on input */
+ LDL_int Parent [ ], /* output of size n, not defined on input */
+ LDL_int Lnz [ ], /* output of size n, not defined on input */
+ LDL_int Flag [ ], /* workspace of size n, not defn. on input or output */
+ LDL_int P [ ], /* optional input of size n */
+ LDL_int Pinv [ ] /* optional output of size n (used if P is not NULL) */
+)
+{
+ LDL_int i, k, p, kk, p2 ;
+ if (P)
+ {
+ /* If P is present then compute Pinv, the inverse of P */
+ for (k = 0 ; k < n ; k++)
+ {
+ Pinv [P [k]] = k ;
+ }
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ /* L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) */
+ Parent [k] = -1 ; /* parent of k is not yet known */
+ Flag [k] = k ; /* mark node k as visited */
+ Lnz [k] = 0 ; /* count of nonzeros in column k of L */
+ kk = (P) ? (P [k]) : (k) ; /* kth original, or permuted, column */
+ p2 = Ap [kk+1] ;
+ for (p = Ap [kk] ; p < p2 ; p++)
+ {
+ /* A (i,k) is nonzero (original or permuted A) */
+ i = (Pinv) ? (Pinv [Ai [p]]) : (Ai [p]) ;
+ if (i < k)
+ {
+ /* follow path from i to root of etree, stop at flagged node */
+ for ( ; Flag [i] != k ; i = Parent [i])
+ {
+ /* find parent of i if not yet determined */
+ if (Parent [i] == -1) Parent [i] = k ;
+ Lnz [i]++ ; /* L (k,i) is nonzero */
+ Flag [i] = k ; /* mark i as visited */
+ }
+ }
+ }
+ }
+ /* construct Lp index array from Lnz column counts */
+ Lp [0] = 0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ Lp [k+1] = Lp [k] + Lnz [k] ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === ldl_numeric ========================================================== */
+/* ========================================================================== */
+
+/* Given a sparse matrix A (the arguments n, Ap, Ai, and Ax) and its symbolic
+ * analysis (Lp and Parent, and optionally P and Pinv), compute the numeric LDL'
+ * factorization of A or PAP'. The outputs of this routine are arguments Li,
+ * Lx, and D. It also requires three size-n workspaces (Y, Pattern, and Flag).
+ */
+
+LDL_int LDL_numeric /* returns n if successful, k if D (k,k) is zero */
+(
+ LDL_int n, /* A and L are n-by-n, where n >= 0 */
+ LDL_int Ap [ ], /* input of size n+1, not modified */
+ LDL_int Ai [ ], /* input of size nz=Ap[n], not modified */
+ double Ax [ ], /* input of size nz=Ap[n], not modified */
+ LDL_int Lp [ ], /* input of size n+1, not modified */
+ LDL_int Parent [ ], /* input of size n, not modified */
+ LDL_int Lnz [ ], /* output of size n, not defn. on input */
+ LDL_int Li [ ], /* output of size lnz=Lp[n], not defined on input */
+ double Lx [ ], /* output of size lnz=Lp[n], not defined on input */
+ double D [ ], /* output of size n, not defined on input */
+ double Y [ ], /* workspace of size n, not defn. on input or output */
+ LDL_int Pattern [ ],/* workspace of size n, not defn. on input or output */
+ LDL_int Flag [ ], /* workspace of size n, not defn. on input or output */
+ LDL_int P [ ], /* optional input of size n */
+ LDL_int Pinv [ ] /* optional input of size n */
+)
+{
+ double yi, l_ki ;
+ LDL_int i, k, p, kk, p2, len, top ;
+ for (k = 0 ; k < n ; k++)
+ {
+ /* compute nonzero Pattern of kth row of L, in topological order */
+ Y [k] = 0.0 ; /* Y(0:k) is now all zero */
+ top = n ; /* stack for pattern is empty */
+ Flag [k] = k ; /* mark node k as visited */
+ Lnz [k] = 0 ; /* count of nonzeros in column k of L */
+ kk = (P) ? (P [k]) : (k) ; /* kth original, or permuted, column */
+ p2 = Ap [kk+1] ;
+ for (p = Ap [kk] ; p < p2 ; p++)
+ {
+ i = (Pinv) ? (Pinv [Ai [p]]) : (Ai [p]) ; /* get A(i,k) */
+ if (i <= k)
+ {
+ Y [i] += Ax [p] ; /* scatter A(i,k) into Y (sum duplicates) */
+ for (len = 0 ; Flag [i] != k ; i = Parent [i])
+ {
+ Pattern [len++] = i ; /* L(k,i) is nonzero */
+ Flag [i] = k ; /* mark i as visited */
+ }
+ while (len > 0) Pattern [--top] = Pattern [--len] ;
+ }
+ }
+ /* compute numerical values kth row of L (a sparse triangular solve) */
+ D [k] = Y [k] ; /* get D(k,k) and clear Y(k) */
+ Y [k] = 0.0 ;
+ for ( ; top < n ; top++)
+ {
+ i = Pattern [top] ; /* Pattern [top:n-1] is pattern of L(:,k) */
+ yi = Y [i] ; /* get and clear Y(i) */
+ Y [i] = 0.0 ;
+ p2 = Lp [i] + Lnz [i] ;
+ for (p = Lp [i] ; p < p2 ; p++)
+ {
+ Y [Li [p]] -= Lx [p] * yi ;
+ }
+ l_ki = yi / D [i] ; /* the nonzero entry L(k,i) */
+ D [k] -= l_ki * yi ;
+ Li [p] = k ; /* store L(k,i) in column form of L */
+ Lx [p] = l_ki ;
+ Lnz [i]++ ; /* increment count of nonzeros in col i */
+ }
+ if (D [k] == 0.0) return (k) ; /* failure, D(k,k) is zero */
+ }
+ return (n) ; /* success, diagonal of D is all nonzero */
+}
+
+
+/* ========================================================================== */
+/* === ldl_lsolve: solve Lx=b ============================================== */
+/* ========================================================================== */
+
+void LDL_lsolve
+(
+ LDL_int n, /* L is n-by-n, where n >= 0 */
+ double X [ ], /* size n. right-hand-side on input, soln. on output */
+ LDL_int Lp [ ], /* input of size n+1, not modified */
+ LDL_int Li [ ], /* input of size lnz=Lp[n], not modified */
+ double Lx [ ] /* input of size lnz=Lp[n], not modified */
+)
+{
+ LDL_int j, p, p2 ;
+ for (j = 0 ; j < n ; j++)
+ {
+ p2 = Lp [j+1] ;
+ for (p = Lp [j] ; p < p2 ; p++)
+ {
+ X [Li [p]] -= Lx [p] * X [j] ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === ldl_dsolve: solve Dx=b ============================================== */
+/* ========================================================================== */
+
+void LDL_dsolve
+(
+ LDL_int n, /* D is n-by-n, where n >= 0 */
+ double X [ ], /* size n. right-hand-side on input, soln. on output */
+ double D [ ] /* input of size n, not modified */
+)
+{
+ LDL_int j ;
+ for (j = 0 ; j < n ; j++)
+ {
+ X [j] /= D [j] ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === ldl_ltsolve: solve L'x=b ============================================ */
+/* ========================================================================== */
+
+void LDL_ltsolve
+(
+ LDL_int n, /* L is n-by-n, where n >= 0 */
+ double X [ ], /* size n. right-hand-side on input, soln. on output */
+ LDL_int Lp [ ], /* input of size n+1, not modified */
+ LDL_int Li [ ], /* input of size lnz=Lp[n], not modified */
+ double Lx [ ] /* input of size lnz=Lp[n], not modified */
+)
+{
+ int j, p, p2 ;
+ for (j = n-1 ; j >= 0 ; j--)
+ {
+ p2 = Lp [j+1] ;
+ for (p = Lp [j] ; p < p2 ; p++)
+ {
+ X [j] -= Lx [p] * X [Li [p]] ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === ldl_perm: permute a vector, x=Pb ===================================== */
+/* ========================================================================== */
+
+void LDL_perm
+(
+ LDL_int n, /* size of X, B, and P */
+ double X [ ], /* output of size n. */
+ double B [ ], /* input of size n. */
+ LDL_int P [ ] /* input permutation array of size n. */
+)
+{
+ LDL_int j ;
+ for (j = 0 ; j < n ; j++)
+ {
+ X [j] = B [P [j]] ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === ldl_permt: permute a vector, x=P'b =================================== */
+/* ========================================================================== */
+
+void LDL_permt
+(
+ LDL_int n, /* size of X, B, and P */
+ double X [ ], /* output of size n. */
+ double B [ ], /* input of size n. */
+ LDL_int P [ ] /* input permutation array of size n. */
+)
+{
+ LDL_int j ;
+ for (j = 0 ; j < n ; j++)
+ {
+ X [P [j]] = B [j] ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === ldl_valid_perm: check if a permutation vector is valid =============== */
+/* ========================================================================== */
+
+LDL_int LDL_valid_perm /* returns 1 if valid, 0 otherwise */
+(
+ LDL_int n,
+ LDL_int P [ ], /* input of size n, a permutation of 0:n-1 */
+ LDL_int Flag [ ] /* workspace of size n */
+)
+{
+ LDL_int j, k ;
+ if (n < 0 || !Flag)
+ {
+ return (0) ; /* n must be >= 0, and Flag must be present */
+ }
+ if (!P)
+ {
+ return (1) ; /* If NULL, P is assumed to be the identity perm. */
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ Flag [j] = 0 ; /* clear the Flag array */
+ }
+ for (k = 0 ; k < n ; k++)
+ {
+ j = P [k] ;
+ if (j < 0 || j >= n || Flag [j] != 0)
+ {
+ return (0) ; /* P is not valid */
+ }
+ Flag [j] = 1 ;
+ }
+ return (1) ; /* P is valid */
+}
+
+
+/* ========================================================================== */
+/* === ldl_valid_matrix: check if a sparse matrix is valid ================== */
+/* ========================================================================== */
+
+/* This routine checks to see if a sparse matrix A is valid for input to
+ * ldl_symbolic and ldl_numeric. It returns 1 if the matrix is valid, 0
+ * otherwise. A is in sparse column form. The numerical values in column j
+ * are stored in Ax [Ap [j] ... Ap [j+1]-1], with row indices in
+ * Ai [Ap [j] ... Ap [j+1]-1]. The Ax array is not checked.
+ */
+
+LDL_int LDL_valid_matrix
+(
+ LDL_int n,
+ LDL_int Ap [ ],
+ LDL_int Ai [ ]
+)
+{
+ LDL_int j, p ;
+ if (n < 0 || !Ap || !Ai || Ap [0] != 0)
+ {
+ return (0) ; /* n must be >= 0, and Ap and Ai must be present */
+ }
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Ap [j] > Ap [j+1])
+ {
+ return (0) ; /* Ap must be monotonically nondecreasing */
+ }
+ }
+ for (p = 0 ; p < Ap [n] ; p++)
+ {
+ if (Ai [p] < 0 || Ai [p] >= n)
+ {
+ return (0) ; /* row indices must be in the range 0 to n-1 */
+ }
+ }
+ return (1) ; /* matrix is valid */
+}
diff --git a/LINFACTOR/Contents.m b/LINFACTOR/Contents.m
new file mode 100644
index 0000000..49e814e
--- /dev/null
+++ b/LINFACTOR/Contents.m
@@ -0,0 +1,22 @@
+% LINFACTOR
+%
+% This simple MATLAB function shows you how to use LU or CHOL to factor a matrix
+% and then solve a linear system A*x=b.
+%
+% Files
+% linfactor - factorize a matrix, or use the factors to solve Ax=b.
+% lintests - test linfactor with many different kinds of systems.
+% lintest - test A*x=b, using linfactor, x=A\b, and (ack!) the explicit inv(A).
+%
+% Example:
+% F = linfactor (A) ; % factor A, returning an object F
+% x = linfactor (F,b) ; % solve Ax=b using F (the factorization of A)
+% lintests ; % test linfactor with various kinds of systems
+
+% Copyright 2007, Timothy A. Davis, University of Florida.
+%
+% License: this software is free for any use. No warranty included or implied.
+% You must agree to only one condition to use this software: you must be aware
+% that you have been told that using inv(A) is a horrible, awful, and absoluty
+% abysmal method for solving a linear system of equations. If you do not
+% agree to this condition, you must delete this software.
diff --git a/LINFACTOR/README.txt b/LINFACTOR/README.txt
new file mode 100644
index 0000000..c5d16c8
--- /dev/null
+++ b/LINFACTOR/README.txt
@@ -0,0 +1,60 @@
+LINFACTOR factorize a matrix, or use the factors to solve Ax=b.
+
+Uses LU or CHOL to factorize A, or uses a previously computed factorization to
+solve a linear system. This function automatically selects an LU or Cholesky
+factorization, depending on the matrix. A better method would be for you to
+select it yourself. Note that mldivide uses a faster method for detecting
+whether or not A is a candidate for sparse Cholesky factorization (see spsym in
+the CHOLMOD package, for example).
+
+Example:
+
+ F = linfactor (A) ; % factorizes A into the object F
+
+ x = linfactor (F,b) ; % uses F to solve Ax=b
+
+ norm (A*x-b)
+
+A second output is the time taken by the method, ignoring the overhead of
+determining which method to use. This makes for a fairer comparison between
+methods, since normally the user will know if the matrix is supposed to be
+symmetric positive definite or not, and whether or not the matrix is sparse.
+Also, the overhead here is much higher than mldivide or spsym.
+
+This function has its limitations:
+
+(1) determining whether or not the matrix is symmetric via nnz(A-A') is slow.
+mldivide (and spsym in CHOLMOD) do it much faster.
+
+(2) MATLAB really needs a sparse linsolve. See cs_lsolve, cs_ltsolve, and
+cs_usolve in CSparse, for example.
+
+(3) this function really needs to be written as a mexFunction.
+
+(4) the full power of mldivide is not brought to bear. For example, UMFPACK is
+not very fast for sparse tridiagonal matrices. It's about a factor of four
+slower than a specialized tridiagonal solver as used in mldivide.
+
+(5) permuting a sparse vector or matrix is slower in MATLAB than it should be;
+a built-in linfactor would reduce this overhead.
+
+(6) mldivide when using UMFPACK uses relaxed partial pivoting and then
+iterative refinement. This leads to sparser LU factors, and typically accurate
+results. linfactor uses sparse LU without iterative refinement.
+
+The primary purpose of this function is to answer The Perennially Asked
+Question (or The PAQ for short (*)): "Why not use x=inv(A)*b to solve Ax=b?
+How do I use LU or CHOL to solve Ax=b?" The full answer is below. The short
+answer to The PAQ (*) is "PAQ=LU ... ;-) ... never EVER use inv(A) to solve
+Ax=b."
+
+The secondary purpose of this function is to provide a prototype for some of
+the functionality of a true MATLAB built-in linfactor function.
+
+Finally, the third purpose of this function is that you might find it actually
+useful for production use, since its syntax is simpler than factorizing the
+matrix yourself and then using the factors to solve the system.
+
+See also lu, chol, mldivide, linsolve, umfpack, cholmod.
+
+Oh, did I tell you never to use inv(A) to solve Ax=b?
diff --git a/LINFACTOR/linfactor.m b/LINFACTOR/linfactor.m
new file mode 100644
index 0000000..2d74f04
--- /dev/null
+++ b/LINFACTOR/linfactor.m
@@ -0,0 +1,187 @@
+function [result, t] = linfactor (arg1, arg2)
+%LINFACTOR factorize a matrix, or use the factors to solve Ax=b.
+% Uses LU or CHOL to factorize A, or uses a previously computed factorization to
+% solve a linear system. This function automatically selects an LU or Cholesky
+% factorization, depending on the matrix. A better method would be for you to
+% select it yourself. Note that mldivide uses a faster method for detecting
+% whether or not A is a candidate for sparse Cholesky factorization (see spsym
+% in the CHOLMOD package, for example).
+%
+% Example:
+% F = linfactor (A) ; % factorizes A into the object F
+% x = linfactor (F,b) ; % uses F to solve Ax=b
+% norm (A*x-b)
+%
+% A second output is the time taken by the method, ignoring the overhead of
+% determining which method to use. This makes for a fairer comparison between
+% methods, since normally the user will know if the matrix is supposed to be
+% symmetric positive definite or not, and whether or not the matrix is sparse.
+% Also, the overhead here is much higher than mldivide or spsym.
+%
+% This function has its limitations:
+%
+% (1) determining whether or not the matrix is symmetric via nnz(A-A') is slow.
+% mldivide (and spsym in CHOLMOD) do it much faster.
+%
+% (2) MATLAB really needs a sparse linsolve. See cs_lsolve, cs_ltsolve, and
+% cs_usolve in CSparse, for example.
+%
+% (3) this function really needs to be written as a mexFunction.
+%
+% (4) the full power of mldivide is not brought to bear. For example, UMFPACK
+% is not very fast for sparse tridiagonal matrices. It's about a factor of
+% four slower than a specialized tridiagonal solver as used in mldivide.
+%
+% (5) permuting a sparse vector or matrix is slower in MATLAB than it should be;
+% a built-in linfactor would reduce this overhead.
+%
+% (6) mldivide when using UMFPACK uses relaxed partial pivoting and then
+% iterative refinement. This leads to sparser LU factors, and typically
+% accurate results. linfactor uses sparse LU without iterative refinement.
+%
+% The primary purpose of this function is to answer The Perennially Asked
+% Question (or The PAQ for short (*)): "Why not use x=inv(A)*b to solve Ax=b?
+% How do I use LU or CHOL to solve Ax=b?" The full answer is below. The short
+% answer to The PAQ (*) is "PAQ=LU ... ;-) ... never EVER use inv(A) to solve
+% Ax=b."
+%
+% The secondary purpose of this function is to provide a prototype for some of
+% the functionality of a true MATLAB built-in linfactor function.
+%
+% Finally, the third purpose of this function is that you might find it actually
+% useful for production use, since its syntax is simpler than factorizing the
+% matrix yourself and then using the factors to solve the system.
+%
+% See also lu, chol, mldivide, linsolve, umfpack, cholmod.
+%
+% Oh, did I tell you never to use inv(A) to solve Ax=b?
+%
+% Requires MATLAB 7.3 (R2006b) or later.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+% VERSION 1.1.0, Nov 1, 2007
+
+if (nargin < 1 | nargin > 2 | nargout > 2) %#ok
+ error ('Usage: F=linfactor(A) or x=linfactor(F,b)') ;
+end
+
+if (nargin == 1)
+
+ %---------------------------------------------------------------------------
+ % F = linfactor (A) ;
+ %---------------------------------------------------------------------------
+
+ A = arg1 ;
+ [m n] = size (A) ;
+ if (m ~= n)
+ error ('linfactor: A must be square') ;
+ end
+
+ if (issparse (A))
+
+ % try sparse Cholesky (CHOLMOD): L*L' = P*A*P'
+ if (nnz (A-A') == 0 & all (diag (A) > 0)) %#ok
+ try
+ tic ;
+ [L, g, PT] = chol (A, 'lower') ;
+ t = toc ;
+ if (g == 0)
+ result.L = L ;
+ result.LT = L' ; % takes more memory, but solve is faster
+ result.P = PT' ; % ditto. Need a sparse linsolve here...
+ result.PT = PT ;
+ result.kind = 'sparse Cholesky: L*L'' = P*A*P''' ;
+ result.code = 0 ;
+ return
+ end
+ catch
+ % matrix is symmetric, but not positive definite
+ % (or we ran out of memory)
+ end
+ end
+
+ % try sparse LU (UMFPACK, with row scaling): L*U = P*(R\A)*Q
+ tic ;
+ [L, U, P, Q, R] = lu (A) ;
+ t = toc ;
+ result.L = L ;
+ result.U = U ;
+ result.P = P ;
+ result.Q = Q ;
+ result.R = R ;
+ result.kind = 'sparse LU: L*U = P*(R\A)*Q where R is diagonal' ;
+ result.code = 1 ;
+
+ else
+
+ % try dense Cholesky (LAPACK): L*L' = A
+ if (nnz (A-A') == 0 & all (diag (A) > 0)) %#ok
+ try
+ tic ;
+ L = chol (A, 'lower') ;
+ t = toc ;
+ result.L = L ;
+ result.kind = 'dense Cholesky: L*L'' = A' ;
+ result.code = 2 ;
+ return
+ catch
+ % matrix is symmetric, but not positive definite
+ % (or we ran out of memory)
+ end
+ end
+
+ % try dense LU (LAPACK): L*U = A(p,:)
+ tic ;
+ [L, U, p] = lu (A, 'vector') ;
+ t = toc ;
+ result.L = L ;
+ result.U = U ;
+ result.p = p ;
+ result.kind = 'dense LU: L*U = A(p,:)' ;
+ result.code = 3 ;
+
+ end
+
+else
+
+ %---------------------------------------------------------------------------
+ % x = linfactor (F,b)
+ %---------------------------------------------------------------------------
+
+ F = arg1 ;
+ b = arg2 ;
+
+ if (F.code == 0)
+
+ % sparse Cholesky: MATLAB could use a sparse linsolve here ...
+ tic ;
+ result = F.PT * (F.LT \ (F.L \ (F.P * b))) ;
+ t = toc ;
+
+ elseif (F.code == 1)
+
+ % sparse LU: MATLAB could use a sparse linsolve here too ...
+ tic ;
+ result = F.Q * (F.U \ (F.L \ (F.P * (F.R \ b)))) ;
+ t = toc ;
+
+ elseif (F.code == 2)
+
+ % dense Cholesky: result = F.L' \ (F.L \ b) ;
+ lower.LT = true ;
+ upper.LT = true ;
+ upper.TRANSA = true ;
+ tic ;
+ result = linsolve (F.L, linsolve (F.L, b, lower), upper) ;
+ t = toc ;
+
+ elseif (F.code == 3)
+
+ % dense LU: result = F.U \ (F.L \ b (F.p,:)) ;
+ lower.LT = true ;
+ upper.UT = true ;
+ tic ;
+ result = linsolve (F.U, linsolve (F.L, b (F.p,:), lower), upper) ;
+ t = toc ;
+ end
+end
diff --git a/LINFACTOR/lintest.m b/LINFACTOR/lintest.m
new file mode 100644
index 0000000..e5bf059
--- /dev/null
+++ b/LINFACTOR/lintest.m
@@ -0,0 +1,153 @@
+function lintest (A,b)
+%LINTEST test A*x=b, using linfactor, x=A\b, and (ack!) the explicit inv(A).
+% The results printed include the breakeven point, which is the number of
+% systems Ax=b that must be solved with the same A but different b for the
+% inv(A) method to be faster than linfactor. Using inv(A) is always
+% numerically dubious, and typically slower. However because of MATLAB's
+% interpretive overhead, linfactor can be slightly slower in its
+% forward/backsolves. A true linfactor mexFunction would probably be just as
+% fast as inv(A)*b when A is full. You should never ever use inv(A) to solve
+% a linear system.
+%
+% Example:
+% load west0479
+% b = rand (size (west0479,1), 1) ;
+% lintest (west0479, b) ;
+%
+% See also linfactor, lintests, mldivide
+
+% Copyright 2007, Timothy A. Davis
+
+%-------------------------------------------------------------------------------
+% warmup, to make sure functions are loaded, for accurate timings
+%-------------------------------------------------------------------------------
+
+F = linfactor (1) ;
+x = linfactor (F, 1) ; %#ok
+F = linfactor (sparse (1)) ;
+x = linfactor (F, 1) ; %#ok
+F = linfactor (sparse (-1)) ;
+x = linfactor (F, 1) ; %#ok
+S = inv (1) ;
+x = S*1 ; %#ok
+S = inv (sparse (1)) ;
+x = S*1 ; %#ok
+S = inv (sparse (-1)) ;
+x = S*1 ; %#ok
+x = rand (2) \ rand (2,1) ; %#ok
+x = sparse (rand (2)) \ rand (2,1) ; %#ok
+clear x F S
+
+%-------------------------------------------------------------------------------
+% linfactor
+%-------------------------------------------------------------------------------
+
+% do this several times for accurate timings
+t1 = 0 ;
+trials = 0 ;
+while (t1 < 1)
+ [F, t] = linfactor (A) ; % factorize A
+ t1 = t1 + t ;
+ trials = trials + 1 ;
+end
+t1 = t1 / trials ;
+
+% do this several times for accurate timings
+t2 = 0 ;
+trials = 0 ;
+while (t2 < 1)
+ [x, t] = linfactor (F, b) ; % use the factors to solve Ax=b
+ t2 = t2 + t ;
+ trials = trials + 1 ;
+end
+t2 = t2 / trials ;
+
+resid = norm (A*x-b,1) / (norm (A,1) * norm (x,1) + norm (b,1)) ;
+
+fprintf ('%-16s factor time: %10.6f solve time: %10.6f resid: %8.2e\n', ...
+ F.kind (1:(find(F.kind == ':', 1, 'first'))), t1, t2, resid) ;
+
+%-------------------------------------------------------------------------------
+% inv
+%-------------------------------------------------------------------------------
+
+% Try again using inv(A)*b. This is a really horrible way to solve Ax=b. I'm
+% doing it here precisely to show that it is typically slower, except when there
+% are a huge number of right-hand-sides to solve and A is small. inv(A) also
+% tends to be less accurate, but random matrices do not trigger that problem.
+% It fails hopelessly when A is large, sparse, and where max(diff(r)) is large
+% where [p,q,r,s] = dmperm(A). Never, ever use inv(A) to solve a linear system.
+% Oh, did I tell you never to use inv(A) to solve Ax=b?
+
+try
+
+ % do this several times for accurate timings
+ t3 = 0 ;
+ trials = 0 ;
+ while (t3 < 1)
+ tic ;
+ S = inv (A) ; %#ok
+ t = toc ;
+ t3 = t3 + t ;
+ trials = trials + 1 ;
+ end
+ t3 = t3 / trials ;
+
+ % do this several times for accurate timings
+ t4 = 0 ;
+ trials = 0 ;
+ while (t4 < 1)
+ tic ;
+ x = S*b ;
+ t = toc ;
+ t4 = t4 + t ;
+ trials = trials + 1 ;
+ end
+ t4 = t4 / trials ;
+
+ resid = norm (A*x-b,1) / (norm (A,1) * norm (x,1) + norm (b,1)) ;
+
+ fprintf ('%-16s factor time: %10.6f solve time: %10.6f resid: %8.2e\n', ...
+ 'inv(A)', t3, t4, resid) ;
+
+ % determine the breakeven point where using inv(A) is faster
+ nrhs = max (1, ceil ((t3 - t1) / (t2 - t4))) ;
+ if (t1 < t3 & t2 < t4) %#ok
+ fprintf ('inv(A) breakeven: never\n') ;
+ elseif (t3 < t1 & t4 < t2) %#ok
+ fprintf ('inv(A) breakeven: > 0\n') ;
+ elseif (t1 < t3 & t4 < t2) %#ok
+ fprintf ('inv(A) breakeven: > %d\n', nrhs) ;
+ else
+ fprintf ('inv(A) breakeven: < %d\n', nrhs) ;
+ end
+
+catch
+
+ % inv(A) probably ran out of memory
+ fprintf ('inv(A) failed\n') ;
+ fprintf ('inv(A) breakeven: never\n') ;
+end
+
+%-------------------------------------------------------------------------------
+% backslash
+%-------------------------------------------------------------------------------
+
+% do this several times for accurate timings
+t0 = 0 ;
+trials = 0 ;
+while (t0 < 1)
+ tic ;
+ x = A\b ; % solve Ax=b
+ t = toc ;
+ t0 = t0 + t ;
+ trials = trials + 1 ;
+end
+t0 = t0 / trials ;
+
+resid = norm (A*x-b,1) / (norm (A,1) * norm (x,1) + norm (b,1)) ;
+
+fprintf ('%-16s total time: %10.6f resid: %8.2e\n', ...
+ 'x = A\b', t0, resid) ;
+fprintf ('\n') ;
+
diff --git a/LINFACTOR/lintests.m b/LINFACTOR/lintests.m
new file mode 100644
index 0000000..e434dfc
--- /dev/null
+++ b/LINFACTOR/lintests.m
@@ -0,0 +1,69 @@
+function lintests
+%LINTESTS test linfactor with many different kinds of systems.
+% Compares x=A\b, linfactor and (ack!) inv(A)*b. You should never, ever use
+% inv(A) to solve a linear system.
+%
+% Example
+% lintests
+%
+% See also lintest, linfactor, mldivide.
+
+% Copyright 2007, Timothy A. Davis
+
+rand ('state', 0) ;
+help linfactor
+
+for n = [100 1000 2000]
+
+ fprintf ('\nn: %d (with all nonzero matrix A)\n', n) ;
+
+ % dense LU
+ A = rand (n) ;
+ b = rand (n,1) ;
+ lintest (A,b) ;
+
+ % sparse LU
+ A = sparse (A) ;
+ lintest (A,b) ;
+
+ % dense Cholesky
+ A = A*A' + 10*eye(n) ;
+ lintest (A,b) ;
+
+ % sparse Cholesky
+ A = sparse (A) ;
+ lintest (A,b) ;
+
+end
+
+for n = [1000 2000 1e5]
+
+ % note that UMFPACK is not particularly fast for tridiagonal matrices
+ % (see "doc mldivide", which uses a specialized tridiagonal solver)
+ fprintf ('\nn: %d (sparse tridiagonal matrix)\n', n) ;
+
+ % sparse LU
+ e = rand (n, 1) ;
+ b = rand (n, 1) ;
+ A = spdiags ([e 4*e e], -1:1, n, n) ;
+ lintest (A,b) ;
+
+ % sparse Cholesky
+ e = ones (n, 1) ;
+ A = spdiags ([e 4*e e], -1:1, n, n) ;
+ lintest (A,b) ;
+
+end
+
+% sparse LU again
+fprintf ('\nwest0479:\n') ;
+load west0479 ;
+n = size (west0479, 1) ;
+b = rand (n, 1) ;
+lintest (west0479, b) ;
+
+% completely break inv(A) with a simple 2-by-2 matrix ...
+fprintf ('\nbreak inv(A) with a trivial 2-by-2 matrix:\n') ;
+s = warning ('off', 'MATLAB:singularMatrix') ;
+lintest (rand(2) * realmin/2, ones(2,1)) ;
+warning (s) ;
diff --git a/MATLAB_Tools/Contents.m b/MATLAB_Tools/Contents.m
new file mode 100644
index 0000000..2ea2ee2
--- /dev/null
+++ b/MATLAB_Tools/Contents.m
@@ -0,0 +1,19 @@
+% MATLAB_TOOLS: a collection of small tools for use in MATLAB
+%
+% Files
+% gipper - zip selected files and subdirectories (gipper = grep + zip)
+% hprintf - fprintf with hypertext links not highlighted in the command window.
+% pagerankdemo - draw a 6-node web and compute its pagerank
+%
+% Directories:
+% shellgui draw a pretty seashell
+% waitmex use a waitbar in a C mexFunction
+%
+% Examples:
+% gipper % add all files in current directory X to X.zip
+% hprintf (format, arg1, ...) % fprint with links not highlighted
+% pagerankdemo % run the pagerank demo
+% shellgui % draw a pretty seashell
+% waitmex % example mexFunction that creates a waitbar
+%
+% Copyright 2007, Tim Davis, University of Florida
diff --git a/MATLAB_Tools/getversion.m b/MATLAB_Tools/getversion.m
new file mode 100644
index 0000000..53d4694
--- /dev/null
+++ b/MATLAB_Tools/getversion.m
@@ -0,0 +1,48 @@
+function v = getversion
+%GETVERSION return MATLAB version number as a double.
+% GETVERSION determines the MATLAB version, and returns it as a double. This
+% allows simple inequality comparisons to select code variants based on ranges
+% of MATLAB versions.
+%
+% As of MATLAB 7.5, the version numbers are listed below:
+%
+% MATLAB version getversion return value
+% ------------------------------- -----------------------
+% 7.5.0.342 (R2007b) 7.5
+% 7.4.0.287 (R2007a) 7.4
+% 7.3.0.267 (R2006b) 7.3
+% 7.2.0.232 (R2006a) 7.2
+% 7.1.0.246 (R14) Service Pack 3 7.1
+% 7.0.4.365 (R14) Service Pack 2 7.04
+% 7.0.1.24704 (R14) Service Pack 1 7.01
+% 6.5.2.202935 (R13) Service Pack 2 6.52
+% 6.1.0.4865 (R12.1) 6.1
+% ...
+% 5.3.1.something (R11.1) 5.31
+% 3.2 whatever 3.2
+%
+% Example:
+%
+% v = getversion ;
+% if (v >= 7.0)
+% this code is for MATLAB 7.x and later
+% elseif (v == 6.52)
+% this code is for MATLAB 6.5.2
+% else
+% this code is for MATLAB versions prior to 6.5.2
+% end
+%
+% This getversion function has been tested on versions 6.1 through 7.5, but it
+% should work in any MATLAB that has the functions version, sscanf, and length.
+%
+% See also version, ver, verLessThan.
+
+% Copyright 2007, Timothy A. Davis, Univ. of Florida
+
+% This function does not use ver, in the interest of speed and portability.
+% "version" is a built-in that is about 100 times faster than the ver m-file.
+% ver returns a struct, and structs do not exist in old versions of MATLAB.
+% All 3 functions used here (version, sscanf, and length) are built-in.
+
+v = sscanf (version, '%d.%d.%d') ;
+v = 10.^(0:-1:-(length(v)-1)) * v ;
diff --git a/MATLAB_Tools/gipper.m b/MATLAB_Tools/gipper.m
new file mode 100644
index 0000000..d282d82
--- /dev/null
+++ b/MATLAB_Tools/gipper.m
@@ -0,0 +1,223 @@
+function files_out = gipper (directory, include, exclude, exclude_hidden)
+%GIPPER zip selected files and subdirectories (gipper = grep + zip)
+%
+% files = gipper (directory, include, exclude, exclude_hidden) ;
+%
+% Creates a zip file of all files and subdirectories in a directory. A file in
+% the directory or any of its subdirectories whose name matches any expression
+% in 'include' via regexp is added to the zip file. A file that matches any
+% expression in 'exclude' is not added. A subdirectory whose name or full
+% pathname matches any expression in 'exclude' is not searched. The name of
+% the zip file is the name of the directory, with '.zip' appended.
+%
+% 'include' and 'exclude' are either cells of strings, or just single strings.
+%
+% With no outputs, a list of files is printed and the user is prompted before
+% proceeding. Otherwise, the gipper proceeds without prompting and returns a
+% list of files that were added to the zip file.
+%
+% By default, all files and subdirectories of the directory are included, except
+% that hidden files and directories (those whose names start with a dot, '.')
+% are excluded.
+%
+% If any parameter is empty or not present, the defaults are used:
+% directory: defaults to the current directory
+% include: defaults to include all files and directories
+% exclude: defaults to exclude nothing, as modified by 'exclude_hidden'
+% exclude_hidden: 1 (exclude hidden files and directories)
+%
+% Empty directories or subdirectories are never included.
+%
+% Example:
+% % suppose 'X' is the name of the current directory.
+%
+% % include all files in X (except hidden files) in the zip file ../X.zip
+% gipper
+%
+% % create mytoolbox.zip archive of the 'X/mytoolbox' directory
+% gipper mytoolbox
+%
+% % only include *.m files in ../X.zip
+% gipper '' '\.m$'
+%
+% % create ../X.zip, but exclude compiled object and MEX files
+% gipper ('', '', { '\.o$' '\.obj$', ['\.' mexext '$'] })
+%
+% % include everything, including hidden files, in ../X.zip
+% gipper ('', '', '', 0)
+%
+% % zip mytoolbox, except hidden files and the mytoolbox/old directory
+% gipper mytoolbox '' old
+%
+% % these are the same, except gipper also traverses subdirectories
+% gipper ('', { '\.m$', '\.*mat$' })
+% zip ('../X', { '*.m', '*.mat' })
+%
+% See also zip, regexp, unzip.
+
+% NOTE: if the directory name is empty or not present, and you hit control-C
+% while the gipper is running, your current directory will now be the parent.
+% You must install the gipper first, by placing it in your MATLAB path.
+
+% Copyright 2007, Timothy A. Davis, Univ. of Florida. Win one for the gipper.
+% Created May 2007, using MATLAB 7.4 (R2007a). Requires MATLAB 6.5 or later.
+
+% exclude hidden files and directories by default
+if (nargin < 4)
+ exclude_hidden = 1 ;
+end
+
+% exclude nothing by default (as modified by exclude_hidden)
+if (nargin < 3)
+ exclude = { } ;
+end
+exclude = cleanup (exclude) ;
+
+% append the hidden file and directory rule, if requested
+if (exclude_hidden)
+ exclude = union (exclude, { '^\.', [ '\' filesep '\.' ] }) ;
+end
+
+% always exclude '.' and '..' files
+exclude = union (exclude, { '^\.$', '^\.\.$' }) ;
+
+% include all files by default
+if (nargin < 2 || isempty (include))
+ include = { '.' } ;
+end
+include = cleanup (include) ;
+
+% operate on the current directory, if not specified
+if (nargin < 1 || isempty (directory))
+ here = pwd ;
+ directory = here ((find (here == filesep, 1, 'last') + 1) : end) ;
+ % use try-catch so that if a failure occurs, we go back to current
+ % directory. Unfortunately, this mechanism does not catch a control-C.
+ gipper_found = 0 ;
+ try
+ % run the gipper in the parent
+ cd ('..') ;
+ % if gipper.m is not in the path, it will no longer exist
+ gipper_found = ~isempty (which ('gipper')) ;
+ if (gipper_found)
+ if (nargout == 0)
+ fprintf ('Note that if you terminate gipper with control-C, ') ;
+ fprintf ('your\ndirectory be changed to the parent') ;
+ fprintf (' (as in "cd ..").\n') ;
+ gipper (directory, include, exclude, exclude_hidden) ;
+ else
+ files_out = gipper (directory, include, exclude,exclude_hidden);
+ end
+ end
+ catch
+ cd (here) ;
+ rethrow (lasterror) ;
+ end
+ % go back to where we started
+ cd (here) ;
+ if (~gipper_found)
+ fprintf ('To install the gipper, type "pathtool" and add\n') ;
+ fprintf ('the directory in which it resides:\n') ;
+ fprintf ('%s\n', which (mfilename)) ;
+ error ('You must install the gipper first.') ;
+ end
+ return
+else
+ if (nargout == 0)
+ fprintf ('\ngipper: creating %s%s%s.zip\n', pwd, filesep, directory) ;
+ end
+end
+
+% get the list of files to zip
+n = 0 ;
+files = { } ;
+for file = dir (directory)'
+ [files, n] = finder (files, n, directory, file.name, include, exclude) ;
+end
+files = files (1:n)' ;
+
+% cannot create an empty zip file
+if (isempty (files))
+ warning ('gipper:nothing', 'nothing to zip; no zip file created') ;
+ if (nargout > 0)
+ files_out = files ;
+ end
+ return
+end
+
+% return the list of files, or confirm
+if (nargout == 0)
+ % print the list of files and ask for confirmation first
+ fprintf ('Creating a zip archive containing these files:\n\n') ;
+ for k = 1:length(files)
+ fprintf (' %s\n', files {k}) ;
+ end
+ fprintf ('\nCreating the zip archive: %s', directory) ;
+ if (isempty (regexp (directory, '\.zip$', 'once')))
+ fprintf ('.zip') ;
+ end
+ fprintf ('\n') ;
+ reply = input ('Proceed? (yes or no, default is yes): ', 's') ;
+ if (~isempty (reply) && lower (reply (1)) == 'n')
+ fprintf ('zip file not created\n') ;
+ return
+ end
+else
+ % zip the files without asking
+ files_out = files ;
+end
+
+% zip the files
+zip (directory, files) ;
+
+
+%-------------------------------------------------------------------------------
+function [files, n] = finder (files, n, prefix, name, include, exclude)
+% finder: return a list of files to zip
+% fullname includes the entire path to the file or directory
+fullname = [prefix filesep name] ;
+if (isdir (fullname))
+ % always traverse a subdirectory to look for files to include, unless the
+ % directory name or fullname itself is explicitly excluded.
+ if (~(grep (name, exclude) || grep (fullname, exclude)))
+ % the directory is selected, recursively traverse it
+ for file = dir (fullname)'
+ [files, n] = finder (files, n, fullname, file.name, ...
+ include, exclude) ;
+ end
+ end
+else
+ % this is a file, apply the include/exclude rules to just the file name
+ % itself not the fullname.
+ if (grep (name, include) && ~grep (name, exclude))
+ % the file is selected for the archive. Use a dynamic-table approach
+ % to speed up the dynamic growth of the table.
+ n = n + 1 ;
+ files {n} = fullname ;
+ if (n == length (files))
+ files {2*n} = [ ] ;
+ end
+ end
+end
+
+
+%-------------------------------------------------------------------------------
+function match = grep (string, list)
+% grep: determine if a string matches an expression in a list
+match = 0 ;
+for expression = list
+ if (~isempty (regexp (string, expression {1}, 'once')))
+ match = 1 ;
+ return ;
+ end
+end
+
+
+%-------------------------------------------------------------------------------
+function s = cleanup (s)
+% cleanup: ensure the input list is in the proper format
+s = s (:)' ; % make sure it is a row vector
+if (ischar (s))
+ s = { s } ; % if it is a string, convert it into a cell with one string
+end
+
diff --git a/MATLAB_Tools/hprintf.m b/MATLAB_Tools/hprintf.m
new file mode 100644
index 0000000..65706a8
--- /dev/null
+++ b/MATLAB_Tools/hprintf.m
@@ -0,0 +1,88 @@
+function count = hprintf (varargin)
+%HPRINTF fprintf with hypertext links not highlighted in the command window.
+% hprintf does this by replacing the string "href=" with "HREF=". If the file
+% descriptor is not present, the output defaults to the command window, just
+% like fprintf. Note that all browsers accept either href= or HREF=, so your
+% hypertext links will not be affected except within the MATLAB Command Window.
+% General usage is identical to fprintf:
+%
+% hprintf (format, arg1, arg2, ...)
+% hprintf (fid, format, arg1, arg2, ...)
+% count = hprintf ( ... same as above ... )
+%
+% Example:
+% fprintf ('<a href="http://www.mathworks.com">MathWorks</a>\n') ;
+% fprintf ('<a href="http://hitchhikers.movies.go.com">%d</a>\n', 42) ;
+% hprintf ('<a href="http://www.mathworks.com">MathWorks</a>\n') ;
+% hprintf ('<a href="http://hitchhikers.movies.go.com">%d</a>\n', 42) ;
+%
+% For a discussion, see Kristin's blog and the comments there at
+% http://blogs.mathworks.com/desktop/2007/07/09
+% (<a href="http://blogs.mathworks.com/desktop/2007/07/09">Kristin's blog</a>).
+%
+% NOTE: the examples above are modified by "help hprintf" so that you cannot
+% see the HREF= text. To see the examples properly (without hypertext
+% highlighting) use:
+%
+% edit hprintf
+%
+% To try the examples above, use hprintf with no inputs (note that this usage
+% of hprintf also flags an error, to exactly mimic the fprintf behavior):
+%
+% hprintf
+%
+% Here is a slightly more complex example that has the advantage of being
+% printed properly by "help hprintf":
+%
+% % a string template with hypertext contents:
+% str = '<a AREF="http://www.mathworks.com">MathWorks</a>\n' ;
+% % made into an active hypertext, which will be underlined when
+% % displayed in the command window:
+% hstr = strrep (str, 'AREF', 'href') ;
+% fprintf (hstr) ;
+% % displays: '<a href="http://www.mathworks.com">MathWorks</a>'
+% hprintf (hstr) ;
+% % displays: '<a HREF="http://www.mathworks.com">MathWorks</a>'
+%
+% See also fprintf, strrep, sprintf.
+
+% Copyright 2007, T. Davis, with thanks to 'us' (us at neurol dot unizh dot ch)
+% for suggestions.
+
+% Aug 25, 2007
+
+if (nargin < 1)
+
+ % try hprintf
+ help hprintf
+ fprintf ('\nhypertext highlighting with fprintf:\n\n') ;
+ fprintf ('<a href="http://www.mathworks.com">MathWorks</a>\n') ;
+ fprintf ('<a href="http://hitchhikers.movies.go.com">%d</a>\n', 42) ;
+ fprintf ('\nhypertext highlighting turned off with hprintf:\n\n') ;
+ hprintf ('<a href="http://www.mathworks.com">MathWorks</a>\n') ;
+ hprintf ('<a href="http://hitchhikers.movies.go.com">%d</a>\n\n', 42) ;
+
+ % flag an error, to mimic fprintf behavior
+ error ('Not enough input arguments') ;
+
+elseif (nargout > 1)
+
+ % mimic fprintf
+ error ('Too many output arguments') ;
+
+else
+
+ if (ischar (varargin {1}))
+ % mimic fprintf ('hello world %d\n', 42), with no file ID
+ cnt = fprintf (strrep (sprintf (varargin {:}), 'href=', 'HREF=')) ;
+ else
+ % mimic fprintf (fid, 'hello world %d\n', 42), with file ID given
+ cnt = fprintf (varargin {1}, ...
+ strrep (sprintf (varargin {2:end}), 'href=', 'HREF=')) ;
+ end
+ if (nargout > 0)
+ % return the fprintf output
+ count = cnt ;
+ end
+end
+
diff --git a/MATLAB_Tools/pagerankdemo.m b/MATLAB_Tools/pagerankdemo.m
new file mode 100644
index 0000000..6aeba50
--- /dev/null
+++ b/MATLAB_Tools/pagerankdemo.m
@@ -0,0 +1,234 @@
+function pagerankdemo (steps)
+% PAGERANKDEMO draw a 6-node web and compute its pagerank
+%
+% PAGERANKDEMO draws the 6-node "tiny web" in Section 2.11 of "Numerical
+% Computing with MATLAB", by Cleve Moler, SIAM, 2004. It then simulates the
+% computation of Google's PageRank algorithm, by randomly selecting links to
+% traverse. If a link is traversed, the edge and the target node are displayed
+% in red. If the "random surfer" jumps to an arbitrary page, the target node
+% is displayed in blue. The number of hits at each node, and the page rank
+% (in %) are displayed % on each node. Note that after a large number of
+% steps, the PageRanks (in percentages) converge to the values given in Section
+% 2.11 of Moler (alpha: .321, sigma: .2007, beta: .1705, delta: .1368,
+% gamma: .1066, rho: .0643). See http://www.mathworks.com/moler for more
+% details (the pagerank M-file, in particular).
+%
+% Note that this method is NOT how the PageRank is actually computed. Instead
+% the eigenvalue problem A*x=x is solved for x, where A is the Markov
+% transition matrix, A = p*G*D + e*z', where G is the binary matrix used here.
+% The method here is a simplistic random-hopping demonstration of the Markov
+% process, to motivate the A*x=x formulation of the problem. In this example,
+% A does control how the transitions are made, but the matrix A is not formed
+% explicitly.
+%
+% This demo only operates on a single graph. It is meant as a simple demo
+% only, suitable for in-class use. To compute the PageRanks for an arbitrary
+% graph, use pagerank.m, or the power method (repeat x=A*x until convergence,
+% where A is the Markov transition matrix of the web).
+%
+% Example:
+% pagerankdemo
+% pagerankdemo (1000) % run 1000 steps with no user input, then quit
+%
+% See also pagerank
+%
+% I suggest single-stepping a dozen times or so to see the link traversal in
+% process, and then type "1000". Hit control-C to quit.
+%
+% Copyright 2007, Tim Davis, University of Florida
+
+% Initial graph
+Graph = graphinit ;
+rand ('state', 0) ;
+n = size (Graph.G, 1) ;
+
+help pagerankdemo
+
+% initialize the page counts
+hits = zeros (1,n) ;
+oldwhere = 1 ;
+where = 1 ;
+hits (where) = 1 ;
+set (Graph.node (where), 'FaceColor', [0 0 1]) ;
+
+p = 0.85 ; % probability a link will be followed
+c = sum (Graph.G) ; % outgoing degree
+
+links = cell (1,n) ;
+for k = 1:n
+ links {k} = find (Graph.G (:,k)) ;
+end
+
+follow_link = 0 ;
+if (nargin < 1)
+ input ('hit enter to start at node alpha: ') ;
+end
+
+% write the stats to the figure
+set (Graph.nodelabel (where), 'string', ...
+ sprintf ('%s %d (%3.1f%%)', Graph.nodes {where}, hits (where), ...
+ 100 * hits (where) / sum (hits))) ;
+
+if (nargin < 1)
+ input ('hit enter to take one step: ') ;
+ steps = 1 ;
+end
+
+% repeat
+while (1)
+
+ % clear the old color and old arrow
+ set (Graph.node (where), 'FaceColor', [0 1 0]) ;
+ if (follow_link)
+ set (Graph.arrows (where,oldwhere), 'LineWidth', 2) ;
+ set (Graph.arrows (where,oldwhere), 'Color', [0 0 0]) ;
+ end
+
+ % determine where to go to next
+ oldwhere = where ;
+ if (c (where) == 0 || rand > p)
+ % no outgoing links, or ignore the links
+ follow_link = 0 ;
+ where = floor (n * rand + 1) ;
+ set (Graph.node (where), 'FaceColor', [0 0 1]) ;
+ else
+ % move along the link
+ follow_link = 1 ;
+ where = links{where}(floor (c (where) * rand + 1)) ;
+ set (Graph.node (where), 'FaceColor', [1 0 0]) ;
+ set (Graph.arrows (where,oldwhere), 'LineWidth', 5) ;
+ set (Graph.arrows (where,oldwhere), 'Color', [1 0 0]) ;
+ end
+
+ % increment the hit count
+ hits (where) = hits (where) + 1 ;
+
+ % write the stats to the figure
+ for k = 1:n
+ set (Graph.nodelabel (k), 'string', ...
+ sprintf ('%s %d (%3.1f%%)', Graph.nodes {k}, hits (k), ...
+ 100 * hits (k) / sum (hits))) ;
+ end
+
+ drawnow
+
+ % go the next step
+ steps = steps - 1 ;
+ if (steps <= 0)
+ if (nargin > 0)
+ break ;
+ end
+ steps = input ...
+ ('number of steps to make (default 1, control-C to quit): ') ;
+ if (steps == 0)
+ break ;
+ end
+ if (isempty (steps))
+ steps = 1 ;
+ end
+ end
+
+end
+
+%-------------------------------------------------------------------------------
+
+function Graph = graphinit
+% GRAPHINIT create the tiny-web example in Moler, section 2.11, and draw it.
+% Example
+% G = graphinit ;
+
+figure (1)
+clf
+
+nodes = { 'alpha', 'beta', 'gamma', 'delta', 'rho', 'sigma' } ;
+
+xy = [
+0 4
+1 3
+1 2
+2 4
+2 0
+0 0
+] ;
+
+x = xy (:,1) ;
+y = xy (:,2) ;
+
+% scale x and y to be in the range 0.1 to 0.9
+x = 0.8 * x / 2 + .1 ;
+y = 0.8 * y / 4 + .1 ;
+xy = [x y] ;
+
+xy_delta = [
+ .08 .04 0
+-.03 -.02 -1
+ .04 0 0
+-.05 .04 -1
+-.03 0 -1
+ .03 0 0
+] ;
+
+xd = xy_delta (:,1) ;
+yd = xy_delta (:,2) ;
+tjust = xy_delta (:,3) ;
+
+G = [
+0 0 0 1 0 1
+1 0 0 0 0 0
+0 1 0 0 0 0
+0 1 1 0 0 0
+0 0 1 0 0 0
+1 0 1 0 0 0 ] ;
+
+clf
+
+n = size (G,1) ;
+
+axes ('Position', [0 0 1 1], 'Visible', 'off') ;
+
+node = zeros (n,1) ;
+nodelabel = zeros (n,1) ;
+for k = 1:n
+ node (k) = annotation ('ellipse', [x(k)-.025 y(k)-.025 .05 .05]) ;
+ set (node (k), 'LineWidth', 2) ;
+ set (node (k), 'FaceColor', [0 1 0]) ;
+ nodelabel (k) = text (x (k) + xd (k), y (k) + yd (k), nodes {k}, ...
+ 'Units', 'normalized', 'FontSize', 16) ;
+ if (tjust (k) < 0)
+ set (nodelabel (k), 'HorizontalAlignment', 'right') ;
+ end
+end
+
+
+axis off
+
+% Yes, I realize that this is overkill; arrows should be sparse.
+% This example is not meant for large graphs.
+arrows = zeros (n,n) ;
+
+[i j] = find (G) ;
+for k = 1:length (i)
+ % get the center of the two nodes
+ figx = [x(j(k)) x(i(k))] ;
+ figy = [y(j(k)) y(i(k))] ;
+% [figx figy] = dsxy2figxy (gca, axx, axy);
+ % shorten the arrows by s units at each end
+ s = 0.03 ;
+ len = sqrt (diff (figx)^2 + diff (figy)^2) ;
+ fy (1) = diff (figy) * (s/len) + figy(1) ;
+ fy (2) = diff (figy) * (1-s/len) + figy(1) ;
+ fx (1) = diff (figx) * (s/len) + figx(1) ;
+ fx (2) = diff (figx) * (1-s/len) + figx(1) ;
+ arrows (i(k),j(k)) = annotation ('arrow', fx, fy) ;
+ set (arrows (i(k),j(k)), 'LineWidth', 2) ;
+ set (arrows (i(k),j(k)), 'HeadLength', 20) ;
+ set (arrows (i(k),j(k)), 'HeadWidth', 20) ;
+end
+
+Graph.G = G ;
+Graph.nodes = nodes ;
+Graph.node = node ;
+Graph.xy = xy ;
+Graph.xy_delta = xy_delta ;
+Graph.nodelabel = nodelabel ;
+Graph.arrows = arrows ;
diff --git a/MATLAB_Tools/shellgui/Contents.m b/MATLAB_Tools/shellgui/Contents.m
new file mode 100644
index 0000000..784b9c2
--- /dev/null
+++ b/MATLAB_Tools/shellgui/Contents.m
@@ -0,0 +1,9 @@
+% SHELLGUI
+%
+% Files
+% shellgui - GUI interface for seashell function
+% seashell - draws a pretty Florida seashell, using a 3D parametric surface.
+%
+
+% Example
+% shellgui
diff --git a/MATLAB_Tools/shellgui/seashell.m b/MATLAB_Tools/shellgui/seashell.m
new file mode 100644
index 0000000..afa2b8c
--- /dev/null
+++ b/MATLAB_Tools/shellgui/seashell.m
@@ -0,0 +1,119 @@
+function seashell (a, b, c, n, azimuth, elevation, res)
+% SEASHELL draws a pretty Florida seashell, using a 3D parametric surface.
+%
+% Usage:
+%
+% seashell (a, b, c, n, azimuth, elevation, res)
+% seashell ('spin') ;
+%
+% All arguments are optional. The first four control the coefficients of
+% the parametric surface (u and v are the surface parameters):
+%
+% x = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* cos(n*v) ;
+% y = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* sin(n*v) ;
+% z = b*v/(2*pi) + a*(1-v/(2*pi)) .* sin(u) ;
+%
+% a,b: these determine how pointy or flat the shell is (informally...)
+% c: determines how much the shell overlaps with itself
+% n: the number of spirals in the shell
+%
+% azimuth, elevation: determines the viewing angle (see the 'view' function)
+% res: the mesh size (res-by-res). A larger number gives a smoother surface.
+%
+% If the azimuth is Inf, then the seashell view is spun dynamically.
+% Also try seashell ('spin') ;
+%
+% References:
+% T. Davis & K. Sigmon, MATLAB Primer, 7th edition, CRC Press, 2005, pp. 80.
+% von Seggern, CRC Standard Curves and Surfaces, 2nd edition, CRC Press,
+% 1993, pp. 306-307.
+%
+% Example:
+% seashell ; % draws the front cover of the MATLAB Primer
+% seashell (-0.5) ; % draws the back cover
+% seashell (a,b,c,n,az,el,res) ; % all options, defaults:
+% % a=-0.2, b=0.5, c=0.1, n=2, az=-150, el=10, res=128
+%
+% for a = -1:.1:1
+% seashell (a) ;
+% drawnow ;
+% end
+% for b = -1:.1:1
+% seashell (-.2, b) ;
+% drawnow
+% end
+%
+% See also SHELLGUI, SURF, VIEW, LINSPACE, MESHGRID, SHADING, LIGHTING,
+% LIGHTANGLE, COLORMAP, AXIS, MATERIAL, SIN, COS, PI.
+
+% Copyright 2006, Tim Davis, University of Florida
+
+% use default input parameters, if not present
+if (nargin == 1 && ischar (a))
+ in = -1 ;
+else
+ in = nargin ;
+end
+if (in < 1)
+ a = -0.2 ;
+end
+if (in < 2)
+ b = 0.5 ;
+end
+if (in < 3)
+ c = 0.1 ;
+end
+if (in < 4)
+ n = 2 ;
+end
+if (in < 5)
+ azimuth = -150 ;
+end
+if (in < 6)
+ elevation = 10 ;
+end
+if (in < 7)
+ res = 128 ;
+end
+if (in == -1)
+ azimuth = Inf ;
+end
+
+% sanity checks
+if (a == 0)
+ a = 0.01 ;
+end
+if (n <= 0)
+ n = 0.1 ;
+end
+
+% construct the res-by-res mesh
+t = linspace(0, 2*pi, res) ;
+[u,v] = meshgrid(t) ;
+
+% define the surface
+x = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* cos(n*v) ;
+y = (a*(1-v/(2*pi)).*(1+cos(u)) + c) .* sin(n*v) ;
+z = b*v/(2*pi) + a*(1-v/(2*pi)) .* sin(u) ;
+
+% plot the surface
+surf(x,y,z,y)
+shading interp
+
+axis off
+axis equal
+colormap(hsv(1024))
+material shiny
+lighting gouraud
+lightangle(80, -40)
+lightangle(-90, 60)
+
+% fix the view, or spin the seashell
+if (isfinite (azimuth))
+ view([azimuth elevation])
+else
+ for az = -180:10:180
+ view ([az elevation])
+ drawnow
+ end
+end
diff --git a/MATLAB_Tools/shellgui/shellgui.fig b/MATLAB_Tools/shellgui/shellgui.fig
new file mode 100644
index 0000000..1b4bc17
Binary files /dev/null and b/MATLAB_Tools/shellgui/shellgui.fig differ
diff --git a/MATLAB_Tools/shellgui/shellgui.m b/MATLAB_Tools/shellgui/shellgui.m
new file mode 100644
index 0000000..fe6aa2b
--- /dev/null
+++ b/MATLAB_Tools/shellgui/shellgui.m
@@ -0,0 +1,324 @@
+function varargout = shellgui(varargin)
+%SHELLGUI GUI interface for seashell function
+% Timothy A. Davis, Chapman Hall / CRC Press, 7th edition.
+% Controls the parameters a, b, c, n, azimuth, and elevation, using
+% sliders. To the whole range of each parameter, click on the button to
+% the right of each slider.
+%
+% Example:
+% shellgui
+%
+% See also GUIDE, SEASHELL
+
+% Copyright 2006 Timothy A. Davis
+
+% Last Modified by GUIDE v2.5 29-Jul-2006 11:33:37
+
+% Begin initialization code - DO NOT EDIT
+gui_Singleton = 1;
+gui_State = struct('gui_Name', mfilename, ...
+ 'gui_Singleton', gui_Singleton, ...
+ 'gui_OpeningFcn', @shellgui_OpeningFcn, ...
+ 'gui_OutputFcn', @shellgui_OutputFcn, ...
+ 'gui_LayoutFcn', [] , ...
+ 'gui_Callback', []);
+if nargin && ischar(varargin{1})
+ gui_State.gui_Callback = str2func(varargin{1});
+end
+
+if nargout
+ [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
+else
+ gui_mainfcn(gui_State, varargin{:});
+end
+% End initialization code - DO NOT EDIT
+
+
+
+% --- Executes just before shellgui is made visible.
+function shellgui_OpeningFcn(hObject, eventdata, handles, varargin) %#ok
+% This function has no output args, see OutputFcn.
+% hObject handle to figure
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+% varargin command line arguments to shellgui (see VARARGIN)
+
+% Choose default command line output for shellgui
+handles.output = hObject;
+
+% Update handles structure
+guidata(hObject, handles);
+
+% UIWAIT makes shellgui wait for user response (see UIRESUME)
+% uiwait(handles.figure1);
+
+
+% --- Outputs from this function are returned to the command line.
+function varargout = shellgui_OutputFcn(hObject, eventdata, handles) %#ok
+% varargout cell array for returning output args (see VARARGOUT);
+% hObject handle to figure
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+% Get default command line output from handles structure
+varargout{1} = handles.output;
+
+
+% --- Executes on slider movement.
+function slider1_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to slider1 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+% Hints: get(hObject,'Value') returns position of slider
+% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
+
+global a b c n azimuth elevation
+a = get (hObject, 'Value') ;
+seashell (a, b, c, n, azimuth, elevation) ;
+
+% --- Executes during object creation, after setting all properties.
+function slider1_CreateFcn(hObject, eventdata, handles) %#ok
+% hObject handle to slider1 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles empty - handles not created until after all CreateFcns called
+
+% Hint: slider controls usually have a light gray background.
+if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
+ set(hObject,'BackgroundColor',[.9 .9 .9]);
+end
+
+
+
+
+% --- Executes on slider movement.
+function slider2_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to slider2 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+% Hints: get(hObject,'Value') returns position of slider
+% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
+
+global a b c n azimuth elevation
+b = get (hObject, 'Value') ;
+seashell (a, b, c, n, azimuth, elevation) ;
+
+% --- Executes during object creation, after setting all properties.
+function slider2_CreateFcn(hObject, eventdata, handles) %#ok
+% hObject handle to slider2 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles empty - handles not created until after all CreateFcns called
+
+% Hint: slider controls usually have a light gray background.
+if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
+ set(hObject,'BackgroundColor',[.9 .9 .9]);
+end
+
+global a b c n azimuth elevation
+a = -0.2 ;
+b = 0.5 ;
+c = 0.1 ;
+n = 2 ;
+azimuth = -150 ;
+elevation = 10 ;
+
+seashell ;
+
+
+
+% --- Executes on slider movement.
+function slider3_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to slider3 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+% Hints: get(hObject,'Value') returns position of slider
+% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
+
+global a b c n azimuth elevation
+c = get (hObject, 'Value') ;
+seashell (a, b, c, n, azimuth, elevation) ;
+
+% --- Executes during object creation, after setting all properties.
+function slider3_CreateFcn(hObject, eventdata, handles) %#ok
+% hObject handle to slider3 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles empty - handles not created until after all CreateFcns called
+
+% Hint: slider controls usually have a light gray background.
+if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
+ set(hObject,'BackgroundColor',[.9 .9 .9]);
+end
+
+
+
+
+% --- Executes on slider movement.
+function slider4_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to slider2 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+% Hints: get(hObject,'Value') returns position of slider
+% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
+
+
+global a b c n azimuth elevation
+n = get (hObject, 'Value') ;
+seashell (a, b, c, n, azimuth, elevation) ;
+
+% --- Executes during object creation, after setting all properties.
+function slider4_CreateFcn(hObject, eventdata, handles) %#ok
+% hObject handle to slider2 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles empty - handles not created until after all CreateFcns called
+
+% Hint: slider controls usually have a light gray background.
+if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
+ set(hObject,'BackgroundColor',[.9 .9 .9]);
+end
+
+
+
+% --- Executes on slider movement.
+function slider8_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to slider8 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+% Hints: get(hObject,'Value') returns position of slider
+% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
+
+
+global a b c n azimuth elevation
+azimuth = get (hObject, 'Value') ;
+seashell (a, b, c, n, azimuth, elevation) ;
+
+% --- Executes during object creation, after setting all properties.
+function slider8_CreateFcn(hObject, eventdata, handles) %#ok
+% hObject handle to slider8 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles empty - handles not created until after all CreateFcns called
+
+% Hint: slider controls usually have a light gray background.
+if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
+ set(hObject,'BackgroundColor',[.9 .9 .9]);
+end
+
+
+% --- Executes on slider movement.
+function slider9_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to slider9 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+% Hints: get(hObject,'Value') returns position of slider
+% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
+
+
+global a b c n azimuth elevation
+elevation = get (hObject, 'Value') ;
+seashell (a, b, c, n, azimuth, elevation) ;
+
+% --- Executes during object creation, after setting all properties.
+function slider9_CreateFcn(hObject, eventdata, handles) %#ok
+% hObject handle to slider9 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles empty - handles not created until after all CreateFcns called
+
+% Hint: slider controls usually have a light gray background.
+if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
+ set(hObject,'BackgroundColor',[.9 .9 .9]);
+end
+
+
+
+
+% --- Executes on button press in pushbutton3.
+function pushbutton3_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to pushbutton3 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+global a b c n azimuth elevation
+seashell (a, b, c, n, Inf, elevation) ;
+seashell (a, b, c, n, azimuth, elevation) ;
+
+
+% --- Executes on button press in pushbutton4.
+function pushbutton4_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to pushbutton4 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+global a b c n azimuth elevation
+for a2 = -1:.1:1
+ seashell (a2, b, c, n, azimuth, elevation) ;
+ drawnow
+end
+seashell (a, b, c, n, azimuth, elevation) ;
+
+% --- Executes on button press in pushbutton5.
+function pushbutton5_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to pushbutton5 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+global a b c n azimuth elevation
+for b2 = -1:.1:1
+ seashell (a, b2, c, n, azimuth, elevation) ;
+ drawnow
+end
+seashell (a, b, c, n, azimuth, elevation) ;
+
+% --- Executes on button press in pushbutton6.
+function pushbutton6_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to pushbutton6 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+
+global a b c n azimuth elevation
+for c2 = -1:.1:1
+ seashell (a, b, c2, n, azimuth, elevation) ;
+ drawnow
+end
+seashell (a, b, c, n, azimuth, elevation) ;
+
+% --- Executes on button press in pushbutton7.
+function pushbutton7_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to pushbutton7 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+global a b c n azimuth elevation
+for n2 = 0:.5:8
+ seashell (a, b, c, n2, azimuth, elevation) ;
+ drawnow
+end
+seashell (a, b, c, n, azimuth, elevation) ;
+
+% --- Executes on button press in pushbutton8.
+function pushbutton8_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to pushbutton8 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+
+global a b c n azimuth elevation
+for el = -80:10:80
+ seashell (a, b, c, n, azimuth, el) ;
+ drawnow
+end
+seashell (a, b, c, n, azimuth, elevation) ;
+
+
+% --- Executes on button press in pushbutton9.
+function pushbutton9_Callback(hObject, eventdata, handles) %#ok
+% hObject handle to pushbutton9 (see GCBO)
+% eventdata reserved - to be defined in a future version of MATLAB
+% handles structure with handles and user data (see GUIDATA)
+
+web ('http://www.cise.ufl.edu/research/sparse/MATLAB') ;
+
diff --git a/MATLAB_Tools/waitmex/README.txt b/MATLAB_Tools/waitmex/README.txt
new file mode 100644
index 0000000..64b78b8
--- /dev/null
+++ b/MATLAB_Tools/waitmex/README.txt
@@ -0,0 +1,26 @@
+WAITMEX provides a simple way of using a waitbar from within a C mexFunction.
+
+Files:
+
+ README.txt this file
+ waitexample.c a C mexFunction that uses the waitmex.c functions
+ waitexample.m help for waitexample
+ waitex.m a MATLAB m-file equivalent of waitexample.m
+ waitmex.c four functions for accessing a waitbar in a mexFunction
+ waitmex.h include file required for using waitmex.c
+ waitmex.m compiles the waitexample mexFunction
+
+For more help, and to compile, install, and test the waitmex functions, type:
+
+ waitmex
+
+in the MATLAB Command Window. For details on how to call the waitmex functions,
+see waitmex.c, and see the examples given in waitexample.c.
+
+These functions should be easily adaptable to any of the many replacements for
+waitbar posted on the MATLAB Central File Exchange, particularly if they use
+the same input and output arguments as the MATLAB waitbar.
+
+Copyright 2007, Tim Davis, University of Florida.
+http://www.cise.ufl.edu/~davis
+Aug 27, 2007
diff --git a/MATLAB_Tools/waitmex/waitex.m b/MATLAB_Tools/waitmex/waitex.m
new file mode 100644
index 0000000..08d48e3
--- /dev/null
+++ b/MATLAB_Tools/waitmex/waitex.m
@@ -0,0 +1,39 @@
+function result = waitex
+%WAITEX same as the waitexample mexFunction, just in M instead of C.
+% The only purpose of this function is to serve as a precise description of
+% what the waitexample mexFunction does.
+%
+% Example:
+% waitex % draw a waitbar, make progress, and then close the waitbar
+% h = waitex ; % same as above, except leave the waitbar on the screen
+% % and return the handle h to the waitbar.
+%
+% See also waitbar, waitexample.
+
+% Copyright 2007, T. Davis
+
+x = 0 ;
+h = waitbar (0, 'Please wait...') ;
+for i = 0:100
+ if (i == 50)
+ waitbar (i/100, h, 'over half way there') ;
+ else
+ waitbar (i/100, h) ;
+ end
+ % do some useless work
+ for j = 0:1e5
+ x = useless (x) ;
+ end
+end
+
+if (nargout > 0)
+ % h is return to the caller, leave the waitbar on the screen
+ result = h ;
+else
+ % close the waitbar, and do not return the handle h
+ close (h) ;
+end
+
+function x = useless (x)
+%USELESS do some useless work (x = useless (x) just increments x)
+x = x + 1 ;
diff --git a/MATLAB_Tools/waitmex/waitexample.c b/MATLAB_Tools/waitmex/waitexample.c
new file mode 100644
index 0000000..c327af5
--- /dev/null
+++ b/MATLAB_Tools/waitmex/waitexample.c
@@ -0,0 +1,49 @@
+#include "waitmex.h"
+
+/* The MATLAB equivalent of this function is give in waitex.m.
+ Compile with:
+
+ mex waitexample.c waitmex.c
+ */
+
+void useless (double *x) ;
+
+void useless (double *x) { (*x)++ ; }
+
+void mexFunction (int nargout, mxArray *pargout [ ],
+ int nargin, const mxArray *pargin [ ])
+{
+ int i, j ;
+ double x = 0 ;
+ waitbar *h ;
+
+ /* just like h = waitbar (0, 'Please wait...') in MATLAB */
+ h = waitbar_create (0, "Please wait...") ;
+
+ for (i = 0 ; i <= 100 ; i++)
+ {
+ if (i == 50)
+ {
+ /* just like waitbar (i/100, h, 'over half way there') in MATLAB */
+ waitbar_update (((double) i) / 100., h, "over half way there") ;
+ }
+ else
+ {
+ /* just like waitbar (i/100, h) in MATLAB */
+ waitbar_update (((double) i) / 100., h, NULL) ;
+ }
+
+ /* do some useless work */
+ for (j = 0 ; j <= 10000000 ; j++) useless (&x) ;
+ }
+ if (nargout > 0)
+ {
+ /* return the handle to the waitbar, if requested */
+ pargout [0] = waitbar_return (h) ;
+ }
+ else
+ {
+ /* just like close (h) in MATLAB */
+ waitbar_destroy (h) ;
+ }
+}
diff --git a/MATLAB_Tools/waitmex/waitexample.m b/MATLAB_Tools/waitmex/waitexample.m
new file mode 100644
index 0000000..43f5fed
--- /dev/null
+++ b/MATLAB_Tools/waitmex/waitexample.m
@@ -0,0 +1,13 @@
+function waitexample
+%WAITEXAMPLE a C mexFunction that serves as an example for waitmex.
+%
+% Example:
+% waitexample % draw a waitbar, make progress, and then close the waitbar
+% h = waitexample; % same as above, except leave the waitbar on the screen
+% % and return the handle h to the waitbar.
+%
+% See also waitbar, waitex.
+
+% Copyright 2007, T. Davis
+
+error ('waitexample mexFunction not found ... it must be compiled first') ;
diff --git a/MATLAB_Tools/waitmex/waitmex.c b/MATLAB_Tools/waitmex/waitmex.c
new file mode 100644
index 0000000..ee36fd7
--- /dev/null
+++ b/MATLAB_Tools/waitmex/waitmex.c
@@ -0,0 +1,153 @@
+/* -------------------------------------------------------------------------- */
+/* waitmex functions */
+/* -------------------------------------------------------------------------- */
+
+/* This file includes the following functions for handling waitbars in MATLAB:
+
+ waitbar_create: create a waitbar
+ waitbar_update: update a waitbar
+ waitbar_destroy: destroy a waitbar
+ waitbar_return: return a waitbar
+
+ in C MATLAB equivalent
+ ---- -----------------
+ h = waitbar_create (x,msg) h = waitbar (x,msg)
+ waitbar_update (x,h,NULL) waitbar (x,h)
+ waitbar_update (x,h,msg) waitbar (x,h,msg)
+ waitbar_destroy (h) close (h)
+ waitbar_return (h) for returning h from a mexFunction
+
+ Tim Davis, 2007, University of Florida.
+*/
+
+#include "waitmex.h"
+
+/* -------------------------------------------------------------------------- */
+/* waitbar_create: create a waitbar */
+/* -------------------------------------------------------------------------- */
+
+/* Create a waitbar and return a point to the new waitbar. Example:
+ * h = waitbar_create (x, "Please wait...") in C is just like
+ * h = waitbar (x, 'Please wait') in MATLAB, where x is a fraction between
+ * 0 and 1.
+*/
+
+waitbar *waitbar_create /* return a pointer to the new waitbar */
+(
+ double fraction, /* fraction from 0 to 1 */
+ char *message /* message to display */
+)
+{
+ int error ;
+ waitbar *h ;
+
+ h = mxMalloc (sizeof (waitbar)) ;
+ h->fraction = mxCreateDoubleScalar (fraction) ;
+ h->message = mxCreateString (message) ;
+
+ /* h = waitbar (fraction, message) ; */
+ h->inputs [0] = h->fraction ;
+ h->inputs [1] = h->message ;
+ error = mexCallMATLAB (1, h->outputs, 2, h->inputs, "waitbar") ;
+ if (error)
+ {
+ mexErrMsgTxt ("unable to create waitbar") ;
+ }
+
+ /* save the MATLAB handle h in the waitbar struct */
+ h->handle = h->outputs [0] ;
+
+ return (h) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* waitbar_update: update a waitbar */
+/* -------------------------------------------------------------------------- */
+
+/* Update the length of the bar in an existing waitbar. Example:
+ * waitbar_update (x, h, NULL) in C is just like waitbar (x,h) in MATLAB,
+ * where h is the handle to the existing waitbar. The message is not changed.
+ * To change the message, use waitbar_update (x, h, "new message"), which is
+ * just like waitbar (x, h, 'new message') in MATLAB.
+ */
+
+void waitbar_update
+(
+ double fraction,
+ waitbar *h,
+ char *message
+)
+{
+ int error ;
+ if (h == NULL) return ; /* nothing to do */
+ (* mxGetPr (h->fraction)) = fraction ; /* update the fraction */
+ h->inputs [0] = h->fraction ; /* define the inputs x and h */
+ h->inputs [1] = h->handle ;
+
+ if (message == NULL)
+ {
+ /* use the existing message; waitbar (x,h) in MATLAB */
+ error = mexCallMATLAB (0, h->outputs, 2, h->inputs, "waitbar") ;
+ }
+ else
+ {
+ /* define a new message; waitbar (x,h,message) in MATLAB */
+ mxDestroyArray (h->message) ;
+ h->message = mxCreateString (message) ;
+ h->inputs [2] = h->message ;
+ error = mexCallMATLAB (0, h->outputs, 3, h->inputs, "waitbar") ;
+ }
+ if (error)
+ {
+ mexErrMsgTxt ("unable to update waitbar") ;
+ }
+}
+
+/* -------------------------------------------------------------------------- */
+/* waitbar_destroy: destroy a waitbar */
+/* -------------------------------------------------------------------------- */
+
+/* Destroys a waitbar; same as close(h) in MATLAB */
+
+void waitbar_destroy
+(
+ waitbar *h
+)
+{
+ int error ;
+ if (h == NULL) return ; /* nothing to do */
+ h->inputs [0] = h->handle ;
+ mxDestroyArray (h->fraction) ; /* free the internal mxArrays */
+ mxDestroyArray (h->message) ;
+ error = mexCallMATLAB (0, h->outputs, 1, h->inputs, "close") ;
+ mxDestroyArray (h->handle) ;
+ mxFree (h) ;
+ if (error)
+ {
+ mexErrMsgTxt ("error closing waitbar") ;
+ }
+}
+
+/* -------------------------------------------------------------------------- */
+/* waitbar_return: return a waitbar handle to the caller */
+/* -------------------------------------------------------------------------- */
+
+/* This function frees the space used internally in a mexFunction for managing
+ * the waitbar, and returns the mxArray handle to the caller. The waitbar still
+ * exists in MATLAB. Example: pargout [0] = waitbar_return (h) to return the
+ * MATLAB handle to the caller of your mexFunction.
+ */
+
+mxArray *waitbar_return
+(
+ waitbar *h
+)
+{
+ mxArray *handle ;
+ if (h == NULL) return (NULL) ; /* nothing to do */
+ handle = h->handle ; /* get the MATLAB handle */
+ mxDestroyArray (h->fraction) ; /* free the internal mxArrays */
+ mxDestroyArray (h->message) ;
+ mxFree (h) ;
+ return (handle) ; /* return the MATLAB handle */
+}
diff --git a/MATLAB_Tools/waitmex/waitmex.h b/MATLAB_Tools/waitmex/waitmex.h
new file mode 100644
index 0000000..b2cf6c3
--- /dev/null
+++ b/MATLAB_Tools/waitmex/waitmex.h
@@ -0,0 +1,23 @@
+/* -------------------------------------------------------------------------- */
+/* waitmex include file */
+/* -------------------------------------------------------------------------- */
+
+#ifndef _WAITMEX_H
+#define _WAITMEX_H
+#include "mex.h"
+
+typedef struct waitbar_struct
+{
+ mxArray *inputs [3] ; /* waitbar inputs */
+ mxArray *outputs [2] ; /* waitbar outputs */
+ mxArray *handle ; /* handle from waitbar */
+ mxArray *fraction ; /* fraction from 0 to 1 (a scalar) */
+ mxArray *message ; /* waitbar message */
+
+} waitbar ;
+
+waitbar *waitbar_create (double, char *) ;
+void waitbar_update (double, waitbar *, char *) ;
+void waitbar_destroy (waitbar *) ;
+mxArray *waitbar_return (waitbar *) ;
+#endif
diff --git a/MATLAB_Tools/waitmex/waitmex.m b/MATLAB_Tools/waitmex/waitmex.m
new file mode 100644
index 0000000..baab217
--- /dev/null
+++ b/MATLAB_Tools/waitmex/waitmex.m
@@ -0,0 +1,35 @@
+function waitmex
+%WAITMEX a small library for using a waitbar within a C mexFunction.
+% This waitmex function compiles an example mexFunction, adds the current
+% directory to your MATLAB path, and runs two examples (one in C, one in M).
+%
+% in C MATLAB M-file equivalent
+% ---- ------------------------
+% h = waitbar_create (x,msg) ; h = waitbar (x,msg)
+% waitbar_update (x,h,NULL) ; waitbar (x,h)
+% waitbar_update (x,h,msg) ; waitbar (x,h,msg)
+% waitbar_destroy (h) ; close (h)
+% waitbar_return (h) ; for returning h from a mexFunction
+%
+% Example:
+% waitmex
+%
+%
+% See also waitex, waitexample, waitbar, pathtool.
+
+% Copyright 2007, T. Davis
+
+help waitmex
+
+fprintf ('\ncompiling an example:\n') ;
+fprintf ('mex waitexample.c waitmex.c\n') ;
+mex waitexample.c waitmex.c
+addpath (pwd) ;
+
+fprintf ('\ntrying the example mexFunction:\n') ;
+fprintf ('waitexample\n') ;
+waitexample
+
+fprintf ('\ntrying the m-file equivalent of waitexample:\n') ;
+fprintf ('waitex\n') ;
+waitex
diff --git a/MESHND/Contents.m b/MESHND/Contents.m
new file mode 100644
index 0000000..4a0038a
--- /dev/null
+++ b/MESHND/Contents.m
@@ -0,0 +1,26 @@
+%MESHND: creation and nested dissection of regular 2D and 3D meshes.
+%
+% meshnd - creation and nested dissection of a regular 2D or 3D mesh.
+% meshnd_quality - test the ordering quality computed by meshnd.
+% meshsparse - convert a 2D or 3D mesh into a sparse matrix matrix.
+% meshnd_example - example usage of meshnd and meshsparse.
+%
+% The outputs of the meshnd example and meshnd_quality are in meshd.png,
+% meshnd_quality_out.txt, and meshnd_quality.png.
+%
+% Example:
+% % with no inputs or outputs, meshnd runs a demo:
+% meshnd
+%
+% % create the sparse matrix for a 7-by-5-by-2 mesh:
+% A = meshsparse (meshnd (7,5,2)) ;
+%
+% % create a 7-by-5-by-2 mesh and find the nested dissection ordering:
+% [G p] = meshnd (7,5,2) ;
+% A = meshsparse (G) ;
+% subplot (1,2,1) ; spy (A) ;
+% subplot (1,2,2) ; spy (A (p,p)) ;
+%
+
+% Copyright 2007, Timothy A. Davis, Univ. of Florida
+% VERSION 1.1.0, Nov 1, 2007
diff --git a/MESHND/README.txt b/MESHND/README.txt
new file mode 100644
index 0000000..4a0038a
--- /dev/null
+++ b/MESHND/README.txt
@@ -0,0 +1,26 @@
+%MESHND: creation and nested dissection of regular 2D and 3D meshes.
+%
+% meshnd - creation and nested dissection of a regular 2D or 3D mesh.
+% meshnd_quality - test the ordering quality computed by meshnd.
+% meshsparse - convert a 2D or 3D mesh into a sparse matrix matrix.
+% meshnd_example - example usage of meshnd and meshsparse.
+%
+% The outputs of the meshnd example and meshnd_quality are in meshd.png,
+% meshnd_quality_out.txt, and meshnd_quality.png.
+%
+% Example:
+% % with no inputs or outputs, meshnd runs a demo:
+% meshnd
+%
+% % create the sparse matrix for a 7-by-5-by-2 mesh:
+% A = meshsparse (meshnd (7,5,2)) ;
+%
+% % create a 7-by-5-by-2 mesh and find the nested dissection ordering:
+% [G p] = meshnd (7,5,2) ;
+% A = meshsparse (G) ;
+% subplot (1,2,1) ; spy (A) ;
+% subplot (1,2,2) ; spy (A (p,p)) ;
+%
+
+% Copyright 2007, Timothy A. Davis, Univ. of Florida
+% VERSION 1.1.0, Nov 1, 2007
diff --git a/MESHND/meshnd.m b/MESHND/meshnd.m
new file mode 100644
index 0000000..8849ec9
--- /dev/null
+++ b/MESHND/meshnd.m
@@ -0,0 +1,114 @@
+function [G, p, pinv, Gnew] = meshnd (arg1,n,k)
+%MESHND creation and nested dissection of a regular 2D or 3D mesh.
+% [p G pinv Gnew] = meshnd (m,n) constructs a m-by-n 2D mesh G, and then finds
+% a permuted mesh Gnew where Gnew = pinv(G) and G = p(Gnew). meshnd(m,n,k)
+% creates an m-by-n-by-k 3D mesh.
+%
+% [p G pinv Gnew] = meshnd (G) does not construct G, but uses the mesh G as
+% given on input instead.
+%
+% Example:
+% [G p pinv Gnew] = meshnd (4,5) ;
+%
+% returns
+% Gnew =
+% 1 2 17 9 10
+% 7 8 18 15 16
+% 3 5 19 11 13
+% 4 6 20 12 14
+% G =
+% 1 2 3 4 5
+% 6 7 8 9 10
+% 11 12 13 14 15
+% 16 17 18 19 20
+%
+% With no inputs, a few example meshes are generated and plotted.
+%
+% See also nested, numgrid.
+
+% Copyright 2007, Timothy A. Davis, Univ. of Florida
+
+% get the inputs and create the mesh if not provided on input
+if (nargin == 0)
+
+ % run a simple example
+ meshnd_example ;
+
+elseif (nargin == 1)
+
+ % the mesh is provided on input
+ G = arg1 ;
+ [m n k] = size (G) ;
+
+elseif (nargin == 2)
+
+ % create the m-by-n-by-k mesh in "natural" (row-major) order. This is how
+ % a typical 2D mesh is ordered. A column-major order would be better, since
+ % in that case G(:) would equal 1:(m*n) ... but let's stick with tradition.
+ m = arg1 ;
+ k = 1 ;
+ G = reshape (1:(m*n*k), n, m, k)' ;
+
+elseif (nargin == 3)
+
+ % create the m-by-n-by-k mesh in column-major order. The first m-by-n-by-1
+ % slice is in column-major order, followed by all the other slices 2 to k.
+ m = arg1 ;
+ G = reshape (1:(m*n*k), m, n, k) ;
+
+else
+
+ error ('Usage: [G p pinv Gnew] = meshnd(G), meshnd(m,n) or meshnd(m,n,k)') ;
+
+end
+
+if (nargout > 1)
+ p = nd2 (G)' ; % order the mesh
+end
+
+if (nargout > 2)
+ pinv (p) = 1:(m*n*k) ; % find the inverse permutation
+end
+
+if (nargout > 3)
+ Gnew = pinv (G) ; % find the permuted mesh
+end
+
+%-------------------------------------------------------------------------------
+
+function p = nd2 (G)
+%ND2 p = nd2 (G) permutes a 2D or 3D mesh G.
+% Compare with nestdiss which uses p as a scalar offset and returns a modified
+% mesh G that corresponds to Gnew in meshnd. Here, the scalar offset p in
+% nestdiss is not needed. Instead, p is a permutation, and the modified mesh
+% Gnew is not returned.
+
+[m n k] = size (G) ;
+
+if (max ([m n k]) <= 2)
+
+ % G is small; do not cut it
+ p = G (:) ;
+
+elseif k >= max (m,n)
+
+ % cut G along the middle slice, cutting k in half
+ s = ceil (k/2) ;
+ middle = G (:,:,s) ;
+ p = [(nd2 (G (:,:,1:s-1))) ; (nd2 (G (:,:,s+1:k))) ; middle(:)] ;
+
+elseif n >= max (m,k)
+
+ % cut G along the middle column, cutting n in half
+ s = ceil (n/2) ;
+ middle = G (:,s,:) ;
+ p = [(nd2 (G (:,1:s-1,:))) ; (nd2 (G (:,s+1:n,:))) ; middle(:)] ;
+
+else
+
+ % cut G along the middle row, cutting m in half
+ s = ceil (m/2) ;
+ middle = G (s,:,:) ;
+ p = [(nd2 (G (1:s-1,:,:))) ; (nd2 (G (s+1:m,:,:))) ; middle(:)] ;
+
+end
diff --git a/MESHND/meshnd.png b/MESHND/meshnd.png
new file mode 100644
index 0000000..db883de
Binary files /dev/null and b/MESHND/meshnd.png differ
diff --git a/MESHND/meshnd_example.m b/MESHND/meshnd_example.m
new file mode 100644
index 0000000..b24cbd8
--- /dev/null
+++ b/MESHND/meshnd_example.m
@@ -0,0 +1,106 @@
+function meshnd_example
+%MESHND_EXAMPLE example usage of meshnd and meshsparse.
+%
+% Example:
+% meshnd_example
+%
+% See also meshnd.
+
+% Copyright 2007, Timothy A. Davis, Univ. of Florida
+
+help meshnd
+
+% 2D mesh, compare with Cleve Moler's demos
+
+m = 7 ;
+n = 7 ;
+
+[G p pinv Gnew] = meshnd (m,n) ;
+fprintf ('Original mesh:\n') ;
+disp (G) ;
+fprintf ('Permuted node numbers using meshnd.m (nested dissection):\n') ;
+disp (Gnew) ;
+
+Moler = nested (n+2) ;
+Moler = Moler (2:n+1,2:n+1) ;
+fprintf ('Cleve Moler''s nested dissection ordering, using nested.m\n') ;
+disp (Moler) ;
+fprintf ('Difference between nested.m and meshnd.m:\n') ;
+disp (Gnew-Moler) ;
+
+% 2D and 3D meshes
+
+stencils = [5 9 7 27] ;
+mm = [7 7 7 7] ;
+nn = [7 7 7 7] ;
+kk = [1 1 7 7] ;
+
+for s = 1:4
+
+ m = mm (s) ;
+ n = nn (s) ;
+ k = kk (s) ;
+ [G p] = meshnd (mm (s), nn (s), kk (s)) ;
+ A = meshsparse (G, stencils (s)) ;
+ C = A (p,p) ;
+ parent = etree (C) ;
+ try
+ L = chol (C, 'lower') ;
+ catch
+ % old version of MATLAB
+ L = chol (C)' ;
+ end
+ subplot (4,5,(s-1)*5 + 1) ;
+ do_spy (A) ;
+ if (k > 1)
+ title (sprintf ('%d-by-%d-by-%d mesh, %d-point stencil', ...
+ m, n, k, stencils (s))) ;
+ else
+ title (sprintf ('%d-by-%d mesh, %d-point stencil', ...
+ m, n, stencils (s))) ;
+ end
+ subplot (4,5,(s-1)*5 + 2) ;
+ do_spy (C) ;
+ title ('nested dissection') ;
+ subplot (4,5,(s-1)*5 + 3) ;
+ treeplot (parent) ;
+ title ('etree') ;
+ xlabel ('') ;
+ subplot (4,5,(s-1)*5 + 4) ;
+ do_spy (L) ;
+ title (sprintf ('Cholesky with nd, nnz %d', nnz (L))) ;
+ try
+ % use the built-in AMD
+ p = amd (A) ;
+ catch
+ try
+ % use AMD from SuiteSparse
+ p = amd2 (A) ;
+ catch
+ % use the older built-in SYMAMD
+ p = symamd (A) ;
+ end
+ end
+ try
+ L = chol (A (p,p), 'lower') ;
+ catch
+ % old version of MATLAB
+ L = chol (A (p,p))' ;
+ end
+ subplot (4,5,(s-1)*5 + 5) ;
+ do_spy (L) ;
+ title (sprintf ('Cholesky with amd, nnz %d', nnz (L))) ;
+
+end
+
+%-------------------------------------------------------------------------------
+
+function do_spy (A)
+%DO_SPY use cspy(A) to plot a matrix, or spy(A) if cspy not installed.
+try
+ % This function is in CSparse. It generates better looking plots than spy.
+ cspy (A) ;
+catch
+ spy (A) ;
+end
+
diff --git a/MESHND/meshnd_quality.m b/MESHND/meshnd_quality.m
new file mode 100644
index 0000000..74779c5
--- /dev/null
+++ b/MESHND/meshnd_quality.m
@@ -0,0 +1,159 @@
+function meshnd_quality (do_metis)
+%MESHND_QUALITY test the ordering quality computed by meshnd.
+% The fill-in and flop count for sparse Cholesky factorization using the meshnd
+% nested dissection ordering is computed with AMD. If SuiteSparse is installed
+% with METIS, and if requested, then the metis nested dissection ordering is
+% also compared.
+%
+% Example:
+% meshnd_quality % compare MESHND and AMD
+% meshnd_quality (1) % also compare with METIS
+%
+% See also meshnd, meshsparse, nested, amd, metis.
+
+% Copyright 2007, Timothy A. Davis, Univ. of Florida
+
+stencils = [5 9 7 27] ;
+
+if (nargin < 1)
+ do_metis = 0 ;
+end
+if (do_metis)
+ if (exist ('metis') ~= 3) %#ok
+ % METIS not installed
+ do_metis = 0 ;
+ end
+end
+
+figure (1)
+clf
+
+for sk = 1:4
+
+ stencil = stencils (sk) ;
+
+ is3D = (stencil == 7 | stencil == 27) ; %#ok
+ if (is3D)
+ s = 2.^(3:.1:7) ; % mesh size up to 127-by-127-by-127
+ else
+ s = 2.^(3:.1:10) - 1 ; % mesh size up to 1023-by-1023
+ end
+ t = length (s) ;
+ lnz = nan * zeros (3,t) ;
+ fl = nan * zeros (3,t) ;
+
+ try
+
+ for t = 1:length (s)
+
+ n = floor (s (t)) ;
+
+ % create the mesh and the matrix, and get nested dissection ordering
+ if (is3D)
+ fprintf ('3D mesh: %d-by-%d-by-%d, %d-point stencil\n', ...
+ n, n, n, stencil) ;
+ [G p] = meshnd (n, n, n) ;
+ else
+ fprintf ('2D mesh: %d-by-%d, %d-point stencil\n', n, n,stencil);
+ [G p] = meshnd (n, n) ;
+ end
+ A = meshsparse (G, stencil) ;
+
+ % ND results
+ c = symbfact (A (p,p)) ;
+ lnz (1,t) = sum (c) ;
+ fl (1,t) = sum (c.^2) ;
+ fprintf (' MESHND: nnz(L) %8.3e flops %8.3e\n', ...
+ lnz (1,t), fl (1,t)) ;
+ clear G
+
+ % AMD results
+ try
+ p = amd (A) ;
+ catch
+ % assume SuiteSparse is installed
+ p = amd2 (A) ;
+ end
+ c = symbfact (A (p,p)) ;
+ lnz (2,t) = sum (c) ;
+ fl (2,t) = sum (c.^2) ;
+ fprintf (' AMD: nnz(L) %8.3e flops %8.3e\n', ...
+ lnz (2,t), fl (2,t)) ;
+
+ % METIS results (requires SuiteSparse and METIS)
+ if (do_metis)
+ p = metis (A) ;
+ c = symbfact (A (p,p)) ;
+ lnz (3,t) = sum (c) ;
+ fl (3,t) = sum (c.^2) ;
+ fprintf (...
+ ' METIS: nnz(L) %8.3e flops %8.3e\n', ...
+ lnz (3,t), fl (3,t)) ;
+ end
+
+ % plot the relative nnz(L) results
+ subplot (2, 4, 2*sk - 1) ;
+ loglog (s (1:t), lnz (2,1:t) ./ lnz (1,1:t), 'b-') ;
+ hold on
+ if (do_metis)
+ loglog (s (1:t), lnz (3,1:t) ./ lnz (1,1:t), 'r-') ;
+ end
+ loglog (s (1:t), ones (1,t), 'k-') ;
+ if (do_metis)
+ ylabel ('nnz(L) for AMD or METIS / nnz(L) for meshnd') ;
+ legend ('AMD', 'METIS') ;
+ else
+ ylabel ('nnz(L) for AMD / nnz(L) for meshnd') ;
+ end
+ xlabel ('mesh size') ;
+ axis ([min(s) max(s) .1 10]) ;
+ set (gca, 'YTick', [.1 .25 .5 .8 1 1.25 2 4 10]) ;
+ if (is3D)
+ set (gca, 'XTick', [1 10 100]) ;
+ title (sprintf ('3D mesh, %d-point stencil', stencil)) ;
+ else
+ set (gca, 'XTick', [1 10 100 1000]) ;
+ title (sprintf ('2D mesh, %d-point stencil', stencil)) ;
+ end
+
+ % plot the relative flop results
+ subplot (2, 4, 2*sk) ;
+ loglog (s (1:t), fl (2,1:t) ./ fl (1,1:t), 'b-') ;
+ hold on
+ if (do_metis)
+ loglog (s (1:t), fl (3,1:t) ./ fl (1,1:t), 'r-') ;
+ end
+ loglog (s (1:t), ones (1,t), 'k-') ;
+ ylabel ('flops for AMD or METIS / flops for meshnd') ;
+ if (do_metis)
+ ylabel ('flops for AMD or METIS / flops for meshnd') ;
+ legend ('AMD', 'METIS') ;
+ else
+ ylabel ('nnz(L) for AMD / nnz(L) for meshnd') ;
+ end
+ xlabel ('mesh size') ;
+ axis ([min(s) max(s) .1 10]) ;
+ set (gca, 'YTick', [.1 .25 .5 .8 1 1.25 2 4 10]) ;
+ if (is3D)
+ set (gca, 'XTick', [1 10 100]) ;
+ title (sprintf ('3D mesh, %d-point stencil', stencil)) ;
+ else
+ set (gca, 'XTick', [1 10 100 1000]) ;
+ title (sprintf ('2D mesh, %d-point stencil', stencil)) ;
+ end
+
+ drawnow
+
+ end
+
+ catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+ end
+
+end
diff --git a/MESHND/meshnd_quality.png b/MESHND/meshnd_quality.png
new file mode 100644
index 0000000..3b1c53e
Binary files /dev/null and b/MESHND/meshnd_quality.png differ
diff --git a/MESHND/meshnd_quality_out.txt b/MESHND/meshnd_quality_out.txt
new file mode 100644
index 0000000..b6cbdbc
--- /dev/null
+++ b/MESHND/meshnd_quality_out.txt
@@ -0,0 +1,890 @@
+profile on
+meshnd_quality
+2D mesh: 7-by-7, 5-point stencil
+ MESHND: nnz(L) 2.880e+02 flops 1.926e+03
+ AMD: nnz(L) 2.550e+02 flops 1.483e+03
+ METIS: nnz(L) 2.680e+02 flops 1.656e+03
+2D mesh: 7-by-7, 5-point stencil
+ MESHND: nnz(L) 2.880e+02 flops 1.926e+03
+ AMD: nnz(L) 2.550e+02 flops 1.483e+03
+ METIS: nnz(L) 2.680e+02 flops 1.656e+03
+2D mesh: 8-by-8, 5-point stencil
+ MESHND: nnz(L) 4.210e+02 flops 3.141e+03
+ AMD: nnz(L) 3.540e+02 flops 2.192e+03
+ METIS: nnz(L) 3.800e+02 flops 2.568e+03
+2D mesh: 8-by-8, 5-point stencil
+ MESHND: nnz(L) 4.210e+02 flops 3.141e+03
+ AMD: nnz(L) 3.540e+02 flops 2.192e+03
+ METIS: nnz(L) 3.800e+02 flops 2.568e+03
+2D mesh: 9-by-9, 5-point stencil
+ MESHND: nnz(L) 6.000e+02 flops 5.078e+03
+ AMD: nnz(L) 5.060e+02 flops 3.722e+03
+ METIS: nnz(L) 5.230e+02 flops 3.947e+03
+2D mesh: 10-by-10, 5-point stencil
+ MESHND: nnz(L) 7.970e+02 flops 7.331e+03
+ AMD: nnz(L) 6.480e+02 flops 4.936e+03
+ METIS: nnz(L) 6.840e+02 flops 5.656e+03
+2D mesh: 11-by-11, 5-point stencil
+ MESHND: nnz(L) 1.008e+03 flops 9.920e+03
+ AMD: nnz(L) 8.160e+02 flops 6.636e+03
+ METIS: nnz(L) 8.610e+02 flops 7.713e+03
+2D mesh: 11-by-11, 5-point stencil
+ MESHND: nnz(L) 1.008e+03 flops 9.920e+03
+ AMD: nnz(L) 8.160e+02 flops 6.636e+03
+ METIS: nnz(L) 8.610e+02 flops 7.713e+03
+2D mesh: 12-by-12, 5-point stencil
+ MESHND: nnz(L) 1.234e+03 flops 1.287e+04
+ AMD: nnz(L) 1.035e+03 flops 9.143e+03
+ METIS: nnz(L) 1.076e+03 flops 1.014e+04
+2D mesh: 13-by-13, 5-point stencil
+ MESHND: nnz(L) 1.558e+03 flops 1.792e+04
+ AMD: nnz(L) 1.253e+03 flops 1.166e+04
+ METIS: nnz(L) 1.301e+03 flops 1.292e+04
+2D mesh: 15-by-15, 5-point stencil
+ MESHND: nnz(L) 2.272e+03 flops 2.936e+04
+ AMD: nnz(L) 1.798e+03 flops 1.886e+04
+ METIS: nnz(L) 1.916e+03 flops 2.178e+04
+2D mesh: 16-by-16, 5-point stencil
+ MESHND: nnz(L) 2.663e+03 flops 3.553e+04
+ AMD: nnz(L) 2.118e+03 flops 2.307e+04
+ METIS: nnz(L) 2.351e+03 flops 3.014e+04
+2D mesh: 17-by-17, 5-point stencil
+ MESHND: nnz(L) 3.180e+03 flops 4.567e+04
+ AMD: nnz(L) 2.433e+03 flops 2.755e+04
+ METIS: nnz(L) 2.678e+03 flops 3.446e+04
+2D mesh: 18-by-18, 5-point stencil
+ MESHND: nnz(L) 3.719e+03 flops 5.614e+04
+ AMD: nnz(L) 2.900e+03 flops 3.612e+04
+ METIS: nnz(L) 3.068e+03 flops 4.065e+04
+2D mesh: 20-by-20, 5-point stencil
+ MESHND: nnz(L) 4.861e+03 flops 7.836e+04
+ AMD: nnz(L) 3.702e+03 flops 4.831e+04
+ METIS: nnz(L) 3.931e+03 flops 5.721e+04
+2D mesh: 21-by-21, 5-point stencil
+ MESHND: nnz(L) 5.556e+03 flops 9.475e+04
+ AMD: nnz(L) 4.162e+03 flops 5.684e+04
+ METIS: nnz(L) 4.525e+03 flops 7.004e+04
+2D mesh: 23-by-23, 5-point stencil
+ MESHND: nnz(L) 6.980e+03 flops 1.283e+05
+ AMD: nnz(L) 5.349e+03 flops 8.331e+04
+ METIS: nnz(L) 5.677e+03 flops 9.672e+04
+2D mesh: 24-by-24, 5-point stencil
+ MESHND: nnz(L) 7.632e+03 flops 1.432e+05
+ AMD: nnz(L) 5.787e+03 flops 8.703e+04
+ METIS: nnz(L) 6.285e+03 flops 1.069e+05
+2D mesh: 26-by-26, 5-point stencil
+ MESHND: nnz(L) 9.466e+03 flops 1.938e+05
+ AMD: nnz(L) 7.144e+03 flops 1.174e+05
+ METIS: nnz(L) 7.424e+03 flops 1.322e+05
+2D mesh: 28-by-28, 5-point stencil
+ MESHND: nnz(L) 1.138e+04 flops 2.446e+05
+ AMD: nnz(L) 8.516e+03 flops 1.479e+05
+ METIS: nnz(L) 9.940e+03 flops 2.166e+05
+2D mesh: 31-by-31, 5-point stencil
+ MESHND: nnz(L) 1.479e+04 flops 3.498e+05
+ AMD: nnz(L) 1.092e+04 flops 2.059e+05
+ METIS: nnz(L) 1.283e+04 flops 2.945e+05
+2D mesh: 33-by-33, 5-point stencil
+ MESHND: nnz(L) 1.724e+04 flops 4.275e+05
+ AMD: nnz(L) 1.281e+04 flops 2.623e+05
+ METIS: nnz(L) 1.402e+04 flops 3.099e+05
+2D mesh: 35-by-35, 5-point stencil
+ MESHND: nnz(L) 2.016e+04 flops 5.258e+05
+ AMD: nnz(L) 1.485e+04 flops 3.194e+05
+ METIS: nnz(L) 1.684e+04 flops 4.089e+05
+2D mesh: 38-by-38, 5-point stencil
+ MESHND: nnz(L) 2.491e+04 flops 6.928e+05
+ AMD: nnz(L) 1.830e+04 flops 4.217e+05
+ METIS: nnz(L) 1.888e+04 flops 4.522e+05
+2D mesh: 41-by-41, 5-point stencil
+ MESHND: nnz(L) 2.992e+04 flops 8.803e+05
+ AMD: nnz(L) 2.173e+04 flops 5.265e+05
+ METIS: nnz(L) 2.416e+04 flops 6.691e+05
+2D mesh: 44-by-44, 5-point stencil
+ MESHND: nnz(L) 3.559e+04 flops 1.103e+06
+ AMD: nnz(L) 2.701e+04 flops 7.580e+05
+ METIS: nnz(L) 2.805e+04 flops 7.813e+05
+2D mesh: 47-by-47, 5-point stencil
+ MESHND: nnz(L) 4.198e+04 flops 1.384e+06
+ AMD: nnz(L) 3.031e+04 flops 8.216e+05
+ METIS: nnz(L) 3.359e+04 flops 1.007e+06
+2D mesh: 50-by-50, 5-point stencil
+ MESHND: nnz(L) 4.848e+04 flops 1.683e+06
+ AMD: nnz(L) 3.591e+04 flops 1.042e+06
+ METIS: nnz(L) 3.832e+04 flops 1.173e+06
+2D mesh: 54-by-54, 5-point stencil
+ MESHND: nnz(L) 5.879e+04 flops 2.177e+06
+ AMD: nnz(L) 4.362e+04 flops 1.368e+06
+ METIS: nnz(L) 4.469e+04 flops 1.391e+06
+2D mesh: 58-by-58, 5-point stencil
+ MESHND: nnz(L) 6.973e+04 flops 2.730e+06
+ AMD: nnz(L) 5.255e+04 flops 1.801e+06
+ METIS: nnz(L) 5.679e+04 flops 2.062e+06
+2D mesh: 63-by-63, 5-point stencil
+ MESHND: nnz(L) 8.542e+04 flops 3.578e+06
+ AMD: nnz(L) 6.195e+04 flops 2.170e+06
+ METIS: nnz(L) 6.725e+04 flops 2.471e+06
+2D mesh: 67-by-67, 5-point stencil
+ MESHND: nnz(L) 9.898e+04 flops 4.353e+06
+ AMD: nnz(L) 7.249e+04 flops 2.712e+06
+ METIS: nnz(L) 7.963e+04 flops 3.303e+06
+2D mesh: 72-by-72, 5-point stencil
+ MESHND: nnz(L) 1.179e+05 flops 5.442e+06
+ AMD: nnz(L) 9.047e+04 flops 3.802e+06
+ METIS: nnz(L) 9.518e+04 flops 4.119e+06
+2D mesh: 77-by-77, 5-point stencil
+ MESHND: nnz(L) 1.395e+05 flops 6.816e+06
+ AMD: nnz(L) 1.030e+05 flops 4.537e+06
+ METIS: nnz(L) 1.038e+05 flops 4.305e+06
+2D mesh: 83-by-83, 5-point stencil
+ MESHND: nnz(L) 1.666e+05 flops 8.648e+06
+ AMD: nnz(L) 1.249e+05 flops 6.030e+06
+ METIS: nnz(L) 1.275e+05 flops 5.935e+06
+2D mesh: 89-by-89, 5-point stencil
+ MESHND: nnz(L) 1.965e+05 flops 1.077e+07
+ AMD: nnz(L) 1.506e+05 flops 8.109e+06
+ METIS: nnz(L) 1.479e+05 flops 6.985e+06
+2D mesh: 96-by-96, 5-point stencil
+ MESHND: nnz(L) 2.346e+05 flops 1.361e+07
+ AMD: nnz(L) 1.890e+05 flops 1.119e+07
+ METIS: nnz(L) 1.780e+05 flops 8.883e+06
+2D mesh: 102-by-102, 5-point stencil
+ MESHND: nnz(L) 2.714e+05 flops 1.664e+07
+ AMD: nnz(L) 2.122e+05 flops 1.239e+07
+ METIS: nnz(L) 2.082e+05 flops 1.146e+07
+2D mesh: 110-by-110, 5-point stencil
+ MESHND: nnz(L) 3.253e+05 flops 2.117e+07
+ AMD: nnz(L) 2.568e+05 flops 1.617e+07
+ METIS: nnz(L) 2.463e+05 flops 1.439e+07
+2D mesh: 118-by-118, 5-point stencil
+ MESHND: nnz(L) 3.827e+05 flops 2.637e+07
+ AMD: nnz(L) 3.013e+05 flops 1.973e+07
+ METIS: nnz(L) 2.714e+05 flops 1.511e+07
+2D mesh: 127-by-127, 5-point stencil
+ MESHND: nnz(L) 4.556e+05 flops 3.326e+07
+ AMD: nnz(L) 3.501e+05 flops 2.484e+07
+ METIS: nnz(L) 3.516e+05 flops 2.392e+07
+2D mesh: 136-by-136, 5-point stencil
+ MESHND: nnz(L) 5.336e+05 flops 4.098e+07
+ AMD: nnz(L) 4.319e+05 flops 3.296e+07
+ METIS: nnz(L) 3.998e+05 flops 2.760e+07
+2D mesh: 146-by-146, 5-point stencil
+ MESHND: nnz(L) 6.322e+05 flops 5.135e+07
+ AMD: nnz(L) 5.053e+05 flops 3.980e+07
+ METIS: nnz(L) 4.773e+05 flops 3.598e+07
+2D mesh: 156-by-156, 5-point stencil
+ MESHND: nnz(L) 7.403e+05 flops 6.317e+07
+ AMD: nnz(L) 6.154e+05 flops 5.580e+07
+ METIS: nnz(L) 5.572e+05 flops 4.390e+07
+2D mesh: 167-by-167, 5-point stencil
+ MESHND: nnz(L) 8.668e+05 flops 7.834e+07
+ AMD: nnz(L) 6.652e+05 flops 5.757e+07
+ METIS: nnz(L) 6.114e+05 flops 4.667e+07
+2D mesh: 180-by-180, 5-point stencil
+ MESHND: nnz(L) 1.030e+06 flops 9.857e+07
+ AMD: nnz(L) 8.558e+05 flops 8.577e+07
+ METIS: nnz(L) 7.593e+05 flops 6.550e+07
+2D mesh: 193-by-193, 5-point stencil
+ MESHND: nnz(L) 1.210e+06 flops 1.225e+08
+ AMD: nnz(L) 9.532e+05 flops 9.653e+07
+ METIS: nnz(L) 8.647e+05 flops 7.595e+07
+2D mesh: 206-by-206, 5-point stencil
+ MESHND: nnz(L) 1.408e+06 flops 1.505e+08
+ AMD: nnz(L) 1.150e+06 flops 1.205e+08
+ METIS: nnz(L) 1.040e+06 flops 1.007e+08
+2D mesh: 221-by-221, 5-point stencil
+ MESHND: nnz(L) 1.656e+06 flops 1.871e+08
+ AMD: nnz(L) 1.305e+06 flops 1.469e+08
+ METIS: nnz(L) 1.194e+06 flops 1.202e+08
+2D mesh: 237-by-237, 5-point stencil
+ MESHND: nnz(L) 1.941e+06 flops 2.321e+08
+ AMD: nnz(L) 1.541e+06 flops 1.839e+08
+ METIS: nnz(L) 1.429e+06 flops 1.594e+08
+2D mesh: 255-by-255, 5-point stencil
+ MESHND: nnz(L) 2.300e+06 flops 2.914e+08
+ AMD: nnz(L) 1.834e+06 flops 2.329e+08
+ METIS: nnz(L) 1.652e+06 flops 1.903e+08
+2D mesh: 273-by-273, 5-point stencil
+ MESHND: nnz(L) 2.685e+06 flops 3.588e+08
+ AMD: nnz(L) 2.166e+06 flops 2.976e+08
+ METIS: nnz(L) 1.954e+06 flops 2.460e+08
+2D mesh: 293-by-293, 5-point stencil
+ MESHND: nnz(L) 3.163e+06 flops 4.466e+08
+ AMD: nnz(L) 2.522e+06 flops 3.557e+08
+ METIS: nnz(L) 2.301e+06 flops 3.051e+08
+2D mesh: 314-by-314, 5-point stencil
+ MESHND: nnz(L) 3.714e+06 flops 5.527e+08
+ AMD: nnz(L) 3.181e+06 flops 5.084e+08
+ METIS: nnz(L) 2.639e+06 flops 3.652e+08
+2D mesh: 336-by-336, 5-point stencil
+ MESHND: nnz(L) 4.325e+06 flops 6.799e+08
+ AMD: nnz(L) 3.763e+06 flops 6.432e+08
+ METIS: nnz(L) 3.172e+06 flops 4.801e+08
+2D mesh: 361-by-361, 5-point stencil
+ MESHND: nnz(L) 5.088e+06 flops 8.480e+08
+ AMD: nnz(L) 4.281e+06 flops 8.179e+08
+ METIS: nnz(L) 3.709e+06 flops 6.032e+08
+2D mesh: 387-by-387, 5-point stencil
+ MESHND: nnz(L) 5.959e+06 flops 1.050e+09
+ AMD: nnz(L) 5.229e+06 flops 1.056e+09
+ METIS: nnz(L) 4.294e+06 flops 7.027e+08
+2D mesh: 414-by-414, 5-point stencil
+ MESHND: nnz(L) 6.944e+06 flops 1.293e+09
+ AMD: nnz(L) 6.008e+06 flops 1.184e+09
+ METIS: nnz(L) 4.992e+06 flops 9.106e+08
+2D mesh: 444-by-444, 5-point stencil
+ MESHND: nnz(L) 8.135e+06 flops 1.600e+09
+ AMD: nnz(L) 7.243e+06 flops 1.637e+09
+ METIS: nnz(L) 6.077e+06 flops 1.208e+09
+2D mesh: 476-by-476, 5-point stencil
+ MESHND: nnz(L) 9.501e+06 flops 1.979e+09
+ AMD: nnz(L) 8.346e+06 flops 1.859e+09
+ METIS: nnz(L) 7.009e+06 flops 1.473e+09
+2D mesh: 511-by-511, 5-point stencil
+ MESHND: nnz(L) 1.116e+07 flops 2.462e+09
+ AMD: nnz(L) 9.426e+06 flops 2.345e+09
+ METIS: nnz(L) 8.167e+06 flops 1.822e+09
+2D mesh: 547-by-547, 5-point stencil
+ MESHND: nnz(L) 1.299e+07 flops 3.027e+09
+ AMD: nnz(L) 1.190e+07 flops 3.313e+09
+ METIS: nnz(L) 9.654e+06 flops 2.351e+09
+2D mesh: 587-by-587, 5-point stencil
+ MESHND: nnz(L) 1.525e+07 flops 3.755e+09
+ AMD: nnz(L) 1.410e+07 flops 4.259e+09
+ METIS: nnz(L) 1.120e+07 flops 2.798e+09
+2D mesh: 629-by-629, 5-point stencil
+ MESHND: nnz(L) 1.784e+07 flops 4.634e+09
+ AMD: nnz(L) 1.539e+07 flops 4.645e+09
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+ AMD: nnz(L) 7.604e+04 flops 8.543e+06
+ METIS: nnz(L) 6.937e+04 flops 6.329e+06
+3D mesh: 13-by-13-by-13, 7-point stencil
+ MESHND: nnz(L) 1.549e+05 flops 1.942e+07
+ AMD: nnz(L) 1.045e+05 flops 1.382e+07
+ METIS: nnz(L) 1.072e+05 flops 1.244e+07
+3D mesh: 14-by-14-by-14, 7-point stencil
+ MESHND: nnz(L) 2.147e+05 flops 3.111e+07
+ AMD: nnz(L) 1.517e+05 flops 2.320e+07
+ METIS: nnz(L) 1.332e+05 flops 1.707e+07
+3D mesh: 16-by-16-by-16, 7-point stencil
+ MESHND: nnz(L) 3.859e+05 flops 7.201e+07
+ AMD: nnz(L) 2.810e+05 flops 6.000e+07
+ METIS: nnz(L) 2.347e+05 flops 3.751e+07
+3D mesh: 17-by-17-by-17, 7-point stencil
+ MESHND: nnz(L) 5.150e+05 flops 1.082e+08
+ AMD: nnz(L) 3.773e+05 flops 9.681e+07
+ METIS: nnz(L) 3.416e+05 flops 6.752e+07
+3D mesh: 18-by-18-by-18, 7-point stencil
+ MESHND: nnz(L) 6.624e+05 flops 1.547e+08
+ AMD: nnz(L) 4.883e+05 flops 1.344e+08
+ METIS: nnz(L) 4.306e+05 flops 9.356e+07
+3D mesh: 19-by-19-by-19, 7-point stencil
+ MESHND: nnz(L) 8.464e+05 flops 2.186e+08
+ AMD: nnz(L) 6.447e+05 flops 2.091e+08
+ METIS: nnz(L) 5.905e+05 flops 1.515e+08
+3D mesh: 21-by-21-by-21, 7-point stencil
+ MESHND: nnz(L) 1.311e+06 flops 4.129e+08
+ AMD: nnz(L) 1.040e+06 flops 4.105e+08
+ METIS: nnz(L) 9.257e+05 flops 2.940e+08
+3D mesh: 22-by-22-by-22, 7-point stencil
+ MESHND: nnz(L) 1.603e+06 flops 5.504e+08
+ AMD: nnz(L) 1.274e+06 flops 5.573e+08
+ METIS: nnz(L) 1.060e+06 flops 3.527e+08
+3D mesh: 24-by-24-by-24, 7-point stencil
+ MESHND: nnz(L) 2.319e+06 flops 9.398e+08
+ AMD: nnz(L) 1.875e+06 flops 9.692e+08
+ METIS: nnz(L) 1.563e+06 flops 6.256e+08
+3D mesh: 25-by-25-by-25, 7-point stencil
+ MESHND: nnz(L) 2.805e+06 flops 1.237e+09
+ AMD: nnz(L) 2.407e+06 flops 1.448e+09
+ METIS: nnz(L) 1.830e+06 flops 7.686e+08
+3D mesh: 27-by-27-by-27, 7-point stencil
+ MESHND: nnz(L) 3.940e+06 flops 2.003e+09
+ AMD: nnz(L) 3.388e+06 flops 2.407e+09
+ METIS: nnz(L) 2.580e+06 flops 1.289e+09
+3D mesh: 29-by-29-by-29, 7-point stencil
+ MESHND: nnz(L) 5.356e+06 flops 3.133e+09
+ AMD: nnz(L) 4.974e+06 flops 4.313e+09
+ METIS: nnz(L) 3.524e+06 flops 1.995e+09
+3D mesh: 32-by-32-by-32, 7-point stencil
+ MESHND: nnz(L) 8.114e+06 flops 5.700e+09
+ AMD: nnz(L) 7.747e+06 flops 8.358e+09
+ METIS: nnz(L) 5.462e+06 flops 3.875e+09
+3D mesh: 34-by-34-by-34, 7-point stencil
+ MESHND: nnz(L) 1.064e+07 flops 8.405e+09
+ AMD: nnz(L) 1.046e+07 flops 1.327e+10
+ METIS: nnz(L) 7.356e+06 flops 6.089e+09
+3D mesh: 36-by-36-by-36, 7-point stencil
+ MESHND: nnz(L) 1.355e+07 flops 1.188e+10
+ AMD: nnz(L) 1.300e+07 flops 1.701e+10
+ METIS: nnz(L) 9.141e+06 flops 8.339e+09
+3D mesh: 39-by-39-by-39, 7-point stencil
+ MESHND: nnz(L) 1.929e+07 flops 1.978e+10
+ AMD: nnz(L) 1.989e+07 flops 3.346e+10
+ METIS: nnz(L) 1.304e+07 flops 1.376e+10
+3D mesh: 42-by-42-by-42, 7-point stencil
+ MESHND: nnz(L) 2.635e+07 flops 3.117e+10
+ AMD: nnz(L) 2.643e+07 flops 4.924e+10
+ METIS: nnz(L) 1.793e+07 flops 2.216e+10
+3D mesh: 45-by-45-by-45, 7-point stencil
+ MESHND: nnz(L) 3.543e+07 flops 4.791e+10
+ AMD: nnz(L) 3.935e+07 flops 9.450e+10
+ METIS: nnz(L) 2.439e+07 flops 3.474e+10
+3D mesh: 48-by-48-by-48, 7-point stencil
+ MESHND: nnz(L) 4.627e+07 flops 7.053e+10
+ AMD: nnz(L) 5.230e+07 flops 1.364e+11
+ METIS: nnz(L) 3.194e+07 flops 5.087e+10
+3D mesh: 51-by-51-by-51, 7-point stencil
+ MESHND: nnz(L) 6.040e+07 flops 1.037e+11
+ AMD: nnz(L) 6.736e+07 flops 1.961e+11
+ METIS: nnz(L) 4.172e+07 flops 7.570e+10
+3D mesh: 55-by-55-by-55, 7-point stencil
+ MESHND: nnz(L) 8.329e+07 flops 1.650e+11
+ AMD: nnz(L) 1.034e+08 flops 3.906e+11
+ METIS: nnz(L) 5.757e+07 flops 1.215e+11
+3D mesh: 59-by-59-by-59, 7-point stencil
+ MESHND: nnz(L) 1.119e+08 flops 2.539e+11
+ AMD: nnz(L) 1.341e+08 flops 5.484e+11
+ METIS: nnz(L) 7.938e+07 flops 1.918e+11
+3D mesh: 64-by-64-by-64, 7-point stencil
+ MESHND: nnz(L) 1.566e+08 flops 4.141e+11
+ AMD: nnz(L) 1.842e+08 flops 8.278e+11
+ METIS: nnz(L) 1.162e+08 flops 3.359e+11
+3D mesh: 68-by-68-by-68, 7-point stencil
+ MESHND: nnz(L) 2.025e+08 flops 6.011e+11
+ AMD: nnz(L) 2.698e+08 flops 1.634e+12
+ METIS: nnz(L) 1.470e+08 flops 4.750e+11
+3D mesh: 73-by-73-by-73, 7-point stencil
+ MESHND: nnz(L) 2.736e+08 flops 9.344e+11
+ AMD: nnz(L) 3.668e+08 flops 2.354e+12
+ METIS: nnz(L) 2.022e+08 flops 7.528e+11
+3D mesh: 78-by-78-by-78, 7-point stencil
+ MESHND: nnz(L) 3.618e+08 flops 1.399e+12
+ AMD: nnz(L) 5.023e+08 flops 3.914e+12
+ METIS: nnz(L) 2.656e+08 flops 1.121e+12
+3D mesh: 84-by-84-by-84, 7-point stencil
+ MESHND: nnz(L) 4.913e+08 flops 2.189e+12
+ AMD: nnz(L) 6.984e+08 flops 6.325e+12
+ METIS: nnz(L) 3.599e+08 flops 1.738e+12
+3D mesh: 90-by-90-by-90, 7-point stencil
+ MESHND: nnz(L) 6.565e+08 flops 3.348e+12
+ AMD: nnz(L) 9.696e+08 flops 1.028e+13
+ METIS: nnz(L) 4.872e+08 flops 2.720e+12
+3D mesh: 97-by-97-by-97, 7-point stencil
+ MESHND: nnz(L) 8.967e+08 flops 5.291e+12
+ AMD: nnz(L) 1.441e+09 flops 1.913e+13
+ METIS: nnz(L) 7.002e+08 flops 4.607e+12
+3D mesh: 103-by-103-by-103, 7-point stencil
+ MESHND: nnz(L) 1.155e+09 flops 7.634e+12
+ AMD: nnz(L) 1.911e+09 flops 2.882e+13
+ METIS: nnz(L) 8.864e+08 flops 6.511e+12
+3D mesh: 111-by-111-by-111, 7-point stencil
+ MESHND: nnz(L) 1.576e+09 flops 1.203e+13
+ AMD: nnz(L) 2.729e+09 flops 4.858e+13
+ METIS: nnz(L) 1.233e+09 flops 1.044e+13
+3D mesh: 119-by-119-by-119, 7-point stencil
+ MESHND: nnz(L) 2.101e+09 flops 1.836e+13
+ AMD: nnz(L) 3.913e+09 flops 8.547e+13
+ METIS: nnz(L) 1.624e+09 flops 1.564e+13
+3D mesh: 128-by-128-by-128, 7-point stencil
+ MESHND: nnz(L) 2.830e+09 flops 2.843e+13
+ AMD: nnz(L) 5.174e+09 flops 1.317e+14
+ METIS: nnz(L) 2.214e+09 flops 2.465e+13
+3D mesh: 8-by-8-by-8, 27-point stencil
+ MESHND: nnz(L) 2.222e+04 flops 1.217e+06
+ AMD: nnz(L) 2.493e+04 flops 1.673e+06
+ METIS: nnz(L) 2.437e+04 flops 1.511e+06
+3D mesh: 8-by-8-by-8, 27-point stencil
+ MESHND: nnz(L) 2.222e+04 flops 1.217e+06
+ AMD: nnz(L) 2.493e+04 flops 1.673e+06
+ METIS: nnz(L) 2.437e+04 flops 1.511e+06
+3D mesh: 9-by-9-by-9, 27-point stencil
+ MESHND: nnz(L) 3.920e+04 flops 2.663e+06
+ AMD: nnz(L) 4.592e+04 flops 4.291e+06
+ METIS: nnz(L) 4.200e+04 flops 3.188e+06
+3D mesh: 9-by-9-by-9, 27-point stencil
+ MESHND: nnz(L) 3.920e+04 flops 2.663e+06
+ AMD: nnz(L) 4.592e+04 flops 4.291e+06
+ METIS: nnz(L) 4.200e+04 flops 3.188e+06
+3D mesh: 10-by-10-by-10, 27-point stencil
+ MESHND: nnz(L) 6.278e+04 flops 5.167e+06
+ AMD: nnz(L) 7.465e+04 flops 8.732e+06
+ METIS: nnz(L) 6.872e+04 flops 6.315e+06
+3D mesh: 11-by-11-by-11, 27-point stencil
+ MESHND: nnz(L) 9.422e+04 flops 9.146e+06
+ AMD: nnz(L) 1.214e+05 flops 1.789e+07
+ METIS: nnz(L) 1.056e+05 flops 1.112e+07
+3D mesh: 12-by-12-by-12, 27-point stencil
+ MESHND: nnz(L) 1.349e+05 flops 1.537e+07
+ AMD: nnz(L) 1.755e+05 flops 2.951e+07
+ METIS: nnz(L) 1.569e+05 flops 1.964e+07
+3D mesh: 12-by-12-by-12, 27-point stencil
+ MESHND: nnz(L) 1.349e+05 flops 1.537e+07
+ AMD: nnz(L) 1.755e+05 flops 2.951e+07
+ METIS: nnz(L) 1.569e+05 flops 1.964e+07
+3D mesh: 13-by-13-by-13, 27-point stencil
+ MESHND: nnz(L) 1.965e+05 flops 2.620e+07
+ AMD: nnz(L) 2.612e+05 flops 5.341e+07
+ METIS: nnz(L) 2.149e+05 flops 2.970e+07
+3D mesh: 14-by-14-by-14, 27-point stencil
+ MESHND: nnz(L) 2.720e+05 flops 4.148e+07
+ AMD: nnz(L) 3.461e+05 flops 7.622e+07
+ METIS: nnz(L) 2.886e+05 flops 4.459e+07
+3D mesh: 16-by-16-by-16, 27-point stencil
+ MESHND: nnz(L) 4.793e+05 flops 9.220e+07
+ AMD: nnz(L) 6.963e+05 flops 2.274e+08
+ METIS: nnz(L) 5.179e+05 flops 1.017e+08
+3D mesh: 17-by-17-by-17, 27-point stencil
+ MESHND: nnz(L) 6.368e+05 flops 1.382e+08
+ AMD: nnz(L) 9.422e+05 flops 3.422e+08
+ METIS: nnz(L) 6.736e+05 flops 1.468e+08
+3D mesh: 18-by-18-by-18, 27-point stencil
+ MESHND: nnz(L) 8.181e+05 flops 1.965e+08
+ AMD: nnz(L) 1.214e+06 flops 5.202e+08
+ METIS: nnz(L) 8.633e+05 flops 2.066e+08
+3D mesh: 19-by-19-by-19, 27-point stencil
+ MESHND: nnz(L) 1.040e+06 flops 2.744e+08
+ AMD: nnz(L) 1.721e+06 flops 8.973e+08
+ METIS: nnz(L) 1.097e+06 flops 2.900e+08
+3D mesh: 21-by-21-by-21, 27-point stencil
+ MESHND: nnz(L) 1.596e+06 flops 5.086e+08
+ AMD: nnz(L) 2.601e+06 flops 1.580e+09
+ METIS: nnz(L) 1.710e+06 flops 5.433e+08
+3D mesh: 22-by-22-by-22, 27-point stencil
+ MESHND: nnz(L) 1.948e+06 flops 6.750e+08
+ AMD: nnz(L) 2.931e+06 flops 1.800e+09
+ METIS: nnz(L) 2.057e+06 flops 7.039e+08
+3D mesh: 24-by-24-by-24, 27-point stencil
+ MESHND: nnz(L) 2.775e+06 flops 1.128e+09
+ AMD: nnz(L) 4.552e+06 flops 3.473e+09
+ METIS: nnz(L) 3.009e+06 flops 1.205e+09
+3D mesh: 25-by-25-by-25, 27-point stencil
+ MESHND: nnz(L) 3.341e+06 flops 1.479e+09
+ AMD: nnz(L) 5.806e+06 flops 5.075e+09
+ METIS: nnz(L) 3.561e+06 flops 1.534e+09
+3D mesh: 27-by-27-by-27, 27-point stencil
+ MESHND: nnz(L) 4.666e+06 flops 2.373e+09
+ AMD: nnz(L) 8.688e+06 flops 9.583e+09
+ METIS: nnz(L) 4.884e+06 flops 2.434e+09
+3D mesh: 29-by-29-by-29, 27-point stencil
+ MESHND: nnz(L) 6.307e+06 flops 3.674e+09
+ AMD: nnz(L) 1.030e+07 flops 1.066e+10
+ METIS: nnz(L) 6.503e+06 flops 3.713e+09
+3D mesh: 32-by-32-by-32, 27-point stencil
+ MESHND: nnz(L) 9.468e+06 flops 6.588e+09
+ AMD: nnz(L) 1.689e+07 flops 2.414e+10
+ METIS: nnz(L) 9.909e+06 flops 6.799e+09
+3D mesh: 34-by-34-by-34, 27-point stencil
+ MESHND: nnz(L) 1.235e+07 flops 9.670e+09
+ AMD: nnz(L) 2.352e+07 flops 4.169e+10
+ METIS: nnz(L) 1.277e+07 flops 9.824e+09
+3D mesh: 36-by-36-by-36, 27-point stencil
+ MESHND: nnz(L) 1.568e+07 flops 1.357e+10
+ AMD: nnz(L) 2.655e+07 flops 4.624e+10
+ METIS: nnz(L) 1.622e+07 flops 1.391e+10
+3D mesh: 39-by-39-by-39, 27-point stencil
+ MESHND: nnz(L) 2.218e+07 flops 2.239e+10
+ AMD: nnz(L) 4.294e+07 flops 9.642e+10
+ METIS: nnz(L) 2.277e+07 flops 2.263e+10
+3D mesh: 42-by-42-by-42, 27-point stencil
+ MESHND: nnz(L) 3.012e+07 flops 3.502e+10
+ AMD: nnz(L) 5.621e+07 flops 1.440e+11
+ METIS: nnz(L) 3.128e+07 flops 3.594e+10
+3D mesh: 45-by-45-by-45, 27-point stencil
+ MESHND: nnz(L) 4.029e+07 flops 5.341e+10
+ AMD: nnz(L) 7.698e+07 flops 2.221e+11
+ METIS: nnz(L) 4.137e+07 flops 5.373e+10
+3D mesh: 48-by-48-by-48, 27-point stencil
+ MESHND: nnz(L) 5.234e+07 flops 7.814e+10
+ AMD: nnz(L) 9.967e+07 flops 3.390e+11
+ METIS: nnz(L) 5.464e+07 flops 8.076e+10
+3D mesh: 51-by-51-by-51, 27-point stencil
+ MESHND: nnz(L) 6.795e+07 flops 1.143e+11
+ AMD: nnz(L) 1.553e+08 flops 7.073e+11
+ METIS: nnz(L) 7.030e+07 flops 1.164e+11
+3D mesh: 55-by-55-by-55, 27-point stencil
+ MESHND: nnz(L) 9.324e+07 flops 1.807e+11
+ AMD: nnz(L) 1.987e+08 flops 9.362e+11
+ METIS: nnz(L) 9.495e+07 flops 1.813e+11
+3D mesh: 59-by-59-by-59, 27-point stencil
+ MESHND: nnz(L) 1.247e+08 flops 2.765e+11
+ AMD: nnz(L) 3.106e+08 flops 2.025e+12
+ METIS: nnz(L) 1.263e+08 flops 2.766e+11
+3D mesh: 64-by-64-by-64, 27-point stencil
+ MESHND: nnz(L) 1.736e+08 flops 4.483e+11
+ AMD: nnz(L) 3.518e+08 flops 2.143e+12
+ METIS: nnz(L) 1.778e+08 flops 4.557e+11
+3D mesh: 68-by-68-by-68, 27-point stencil
+ MESHND: nnz(L) 2.237e+08 flops 6.482e+11
+ AMD: nnz(L) 4.708e+08 flops 3.377e+12
+ METIS: nnz(L) 2.286e+08 flops 6.596e+11
+3D mesh: 73-by-73-by-73, 27-point stencil
+ MESHND: nnz(L) 3.009e+08 flops 1.002e+12
+ AMD: nnz(L) 6.676e+08 flops 5.964e+12
+ METIS: nnz(L) 3.050e+08 flops 1.004e+12
+3D mesh: 78-by-78-by-78, 27-point stencil
+ MESHND: nnz(L) 3.965e+08 flops 1.495e+12
+ AMD: nnz(L) 8.348e+08 flops 8.647e+12
+ METIS: nnz(L) 4.022e+08 flops 1.502e+12
+3D mesh: 84-by-84-by-84, 27-point stencil
+ MESHND: nnz(L) 5.363e+08 flops 2.329e+12
+ AMD: nnz(L) 1.115e+09 flops 1.179e+13
+ METIS: nnz(L) 5.543e+08 flops 2.445e+12
+3D mesh: 90-by-90-by-90, 27-point stencil
+ MESHND: nnz(L) 7.137e+08 flops 3.548e+12
+ AMD: nnz(L) 1.585e+09 flops 2.062e+13
+ METIS: nnz(L) 7.255e+08 flops 3.572e+12
+3D mesh: 97-by-97-by-97, 27-point stencil
+ MESHND: nnz(L) 9.707e+08 flops 5.583e+12
+ AMD: nnz(L) 2.101e+09 flops 3.018e+13
+ METIS: nnz(L) 9.926e+08 flops 5.662e+12
+3D mesh: 103-by-103-by-103, 27-point stencil
+ MESHND: nnz(L) 1.246e+09 flops 8.032e+12
+ AMD: nnz(L) 3.387e+09 flops 7.019e+13
+ METIS: nnz(L) 1.323e+09 flops 9.197e+12
+3D mesh: 111-by-111-by-111, 27-point stencil
+ MESHND: nnz(L) 1.694e+09 flops 1.261e+13
+ AMD: nnz(L) 4.288e+09 flops 9.780e+13
+ METIS: nnz(L) 1.789e+09 flops 1.437e+13
diff --git a/MESHND/meshsparse.m b/MESHND/meshsparse.m
new file mode 100644
index 0000000..4b8bcb1
--- /dev/null
+++ b/MESHND/meshsparse.m
@@ -0,0 +1,144 @@
+function A = meshsparse (G, stencil)
+%MESHSPARSE convert a 2D or 3D mesh into a sparse matrix matrix.
+%
+% Example:
+% A = meshsparse (G)
+% A = meshsparse (G,5) % 2D 5-point stencil (default for 2D case)
+% A = meshsparse (G,9) % 2D 9-point stencil
+% A = meshsparse (G,7) % 3D 7-point stencil (default for 3D case)
+% A = meshsparse (G,27) % 3D 27-point stencil
+% A = meshsparse (G,stencil) % user-provided stencil
+%
+% To create a sparse matrix for an m-by-n 2D mesh or m-by-n-by-k 3D mesh, use
+%
+% A = meshsparse (meshnd (m,n)) ;
+% A = meshsparse (meshnd (m,n,k)) ;
+%
+% G is an m-by-n-by-k matrix, with entries numbered 1 to m*n*k (with k=1 for
+% the 2D case). The entries in G can appear in any order, but no duplicate
+% entries can appear. That is sort(G(:))' must equal 1:m*n*k. A is returned as
+% a sparse matrix with m*n*k rows and columns whose pattern depends on the
+% stencil. The number of nonzeros in most rows/columns of A is equal to the
+% number of points in the stencil. For examples on how to specify your own
+% stencil, see the contents of meshsparse.m.
+%
+% See also meshnd.
+
+% Copyright 2007, Timothy A. Davis, Univ. of Florida
+
+if (nargin < 2)
+ [m n k] = size (G) ;
+ if (k == 1)
+ stencil = 5 ; % 2D default is a 5-point stencil
+ else
+ stencil = 7 ; % 3D default is a 7-point stencil
+ end
+end
+
+if (numel (stencil) == 1)
+
+ % create the stencil
+
+ if (stencil == 5)
+
+ % 5-point stencil (2D)
+ stencil = [
+ -1 0 % north
+ 1 0 % south
+ 0 1 % east
+ 0 -1 ] ; % west
+
+ elseif (stencil == 9)
+
+ % 9-point stencil (2D)
+ stencil = [
+ -1 0 % north
+ 1 0 % south
+ 0 1 % east
+ 0 -1 % west
+ -1 -1 % north-west
+ -1 1 % north-east
+ 1 -1 % south-west
+ 1 1 ] ; % south-east
+
+ elseif (stencil == 7)
+
+ % 7-point stencil (3D)
+ stencil = [
+ -1 0 0 % north
+ 1 0 0 % south
+ 0 1 0 % east
+ 0 -1 0 % west
+ 0 0 -1 % up
+ 0 0 1] ; % down
+
+ elseif (stencil == 27)
+
+ % 27-point stencil (3D)
+ stencil = zeros (26, 3) ;
+ t = 0 ;
+ for i = -1:1
+ for j = -1:1
+ for k = -1:1
+ if (~(i == 0 & j == 0 & k == 0)) %#ok
+ t = t + 1 ;
+ stencil (t,:) = [i j k] ;
+ end
+ end
+ end
+ end
+ end
+end
+
+stencil = fix (stencil) ;
+[npoints d] = size (stencil) ;
+if (d == 2)
+ % append zeros onto a 2D stencil to make it "3D"
+ stencil = [stencil zeros(npoints,1)] ;
+end
+[npoints d] = size (stencil) ;
+if (d ~= 3)
+ error ('invalid stencil') ;
+end
+
+[m n k] = size (G) ;
+i1 = 1:m ;
+j1 = 1:n ;
+k1 = 1:k ;
+
+Ti = zeros (npoints*m*n*k, 1) ;
+Tj = zeros (npoints*m*n*k, 1) ;
+nz = 0 ;
+
+for point = 1:npoints
+
+ % find the overlapping rows of G
+ idelta = stencil (point,1) ;
+ i2 = i1 + idelta ;
+ ki = find (i2 >= 1 & i2 <= m) ;
+
+ % find the overlapping columns of G
+ jdelta = stencil (point,2) ;
+ j2 = j1 + jdelta ;
+ kj = find (j2 >= 1 & j2 <= n) ;
+
+ % find the overlapping slices of G
+ kdelta = stencil (point,3) ;
+ k2 = k1 + kdelta ;
+ kk = find (k2 >= 1 & k2 <= k) ;
+
+ % find the nodes in G the shifted G that touch
+ g2 = G (i2 (ki), j2 (kj), k2 (kk)) ; % shifted mesh
+ g1 = G (i1 (ki), j1 (kj), k1 (kk)) ; % unshifted mesh
+
+ % place the edges in the triplet list
+ e = numel (g1) ;
+ Ti ((nz+1):(nz+e)) = g1 (:) ;
+ Tj ((nz+1):(nz+e)) = g2 (:) ;
+ nz = nz + e ;
+end
+
+% convert the triplets into a sparse matrix
+Ti = Ti (1:nz) ;
+Tj = Tj (1:nz) ;
+A = npoints * speye (m*n*k) - sparse (Ti, Tj, 1, m*n*k, m*n*k) ;
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..b56e0c8
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,99 @@
+#-------------------------------------------------------------------------------
+# Makefile for all UF sparse matrix packages
+#-------------------------------------------------------------------------------
+
+include UFconfig/UFconfig.mk
+
+# Compile the default rules for each package
+default:
+ ( cd UFconfig/xerbla ; $(MAKE) )
+# ( cd metis-4.0 ; $(MAKE) )
+ ( cd AMD ; $(MAKE) )
+ ( cd CAMD ; $(MAKE) )
+ ( cd COLAMD ; $(MAKE) )
+ ( cd BTF ; $(MAKE) )
+ ( cd KLU ; $(MAKE) )
+ ( cd LDL ; $(MAKE) )
+ ( cd CCOLAMD ; $(MAKE) )
+ ( cd UMFPACK ; $(MAKE) )
+ ( cd CHOLMOD ; $(MAKE) )
+ ( cd CSparse ; $(MAKE) )
+ ( cd CXSparse ; $(MAKE) )
+# ( cd LPDASA ; $(MAKE) )
+# ( cd PARAKLETE ; $(MAKE) )
+
+library: default
+
+# Compile the MATLAB mexFunctions (except RBio and UFcollection)
+mex:
+ ( cd AMD ; $(MAKE) mex )
+ ( cd CAMD ; $(MAKE) mex )
+ ( cd COLAMD ; $(MAKE) mex )
+ ( cd BTF ; $(MAKE) mex )
+ ( cd KLU ; $(MAKE) mex )
+ ( cd LDL ; $(MAKE) mex )
+ ( cd CCOLAMD ; $(MAKE) mex )
+ ( cd CHOLMOD ; $(MAKE) mex )
+ ( cd UMFPACK ; $(MAKE) mex )
+ ( cd CXSparse ; $(MAKE) mex )
+ ( cd CSparse ; $(MAKE) mex )
+
+# Remove all files not in the original distribution
+purge:
+ ( cd UFconfig/xerbla ; $(MAKE) purge )
+# ( cd metis-4.0 ; $(MAKE) realclean )
+ ( cd AMD ; $(MAKE) purge )
+ ( cd CAMD ; $(MAKE) purge )
+ ( cd COLAMD ; $(MAKE) purge )
+ ( cd BTF ; $(MAKE) purge )
+ ( cd KLU ; $(MAKE) purge )
+ ( cd LDL ; $(MAKE) purge )
+ ( cd CCOLAMD ; $(MAKE) purge )
+ ( cd UMFPACK ; $(MAKE) purge )
+ ( cd CHOLMOD ; $(MAKE) purge )
+ ( cd CSparse ; $(MAKE) purge )
+ ( cd CXSparse ; $(MAKE) purge )
+ ( cd RBio ; $(RM) *.mex* )
+ ( cd UFcollection ; $(RM) *.mex* )
+ ( cd SSMULT ; $(RM) *.mex* )
+# ( cd LPDASA ; $(MAKE) purge )
+# ( cd PARAKLETE ; $(MAKE) purge )
+
+# Remove all files not in the original distribution, but keep the libraries
+clean:
+ ( cd UFconfig/xerbla ; $(MAKE) clean )
+# ( cd metis-4.0 ; $(MAKE) clean )
+ ( cd AMD ; $(MAKE) clean )
+ ( cd CAMD ; $(MAKE) clean )
+ ( cd COLAMD ; $(MAKE) clean )
+ ( cd BTF ; $(MAKE) clean )
+ ( cd KLU ; $(MAKE) clean )
+ ( cd LDL ; $(MAKE) clean )
+ ( cd CCOLAMD ; $(MAKE) clean )
+ ( cd UMFPACK ; $(MAKE) clean )
+ ( cd CHOLMOD ; $(MAKE) clean )
+ ( cd CSparse ; $(MAKE) clean )
+ ( cd CXSparse ; $(MAKE) clean )
+# ( cd LPDASA ; $(MAKE) clean )
+# ( cd PARAKLETE ; $(MAKE) clean )
+
+distclean: purge
+
+# Create CXSparse from CSparse. Note that the CXSparse directory should
+# initially not exist.
+cx:
+ ( cd CSparse ; $(MAKE) purge )
+ ( cd CXSparse_newfiles ; tar cfv - * | gzip -9 > ../CXSparse_newfiles.tar.gz )
+ ./CSparse_to_CXSparse CSparse CXSparse CXSparse_newfiles.tar.gz
+ ( cd CXSparse/Demo ; $(MAKE) )
+ ( cd CXSparse/Demo ; $(MAKE) > cs_demo.out )
+ ( cd CXSparse ; $(MAKE) purge )
+
+# statement coverage (Linux only); this requires a lot of time.
+# The umfpack tcov requires a lot of disk space
+cov:
+ ( cd CXSparse ; $(MAKE) cov )
+ ( cd CSparse ; $(MAKE) cov )
+ ( cd KLU ; $(MAKE) cov )
+ ( cd CHOLMOD ; $(MAKE) cov )
+ ( cd UMFPACK ; $(MAKE) cov )
diff --git a/RBio/Contents.m b/RBio/Contents.m
new file mode 100644
index 0000000..ca63642
--- /dev/null
+++ b/RBio/Contents.m
@@ -0,0 +1,24 @@
+% RBio: MATLAB toolbox for reading/writing sparse matrices in the Rutherford/
+% Boeing format, and for reading/writing problems in the UF Sparse Matrix
+% Collection from/to a set of files in a directory.
+%
+% RBread - read a sparse matrix from a Rutherford/Boeing file
+% RBreade - read a symmetric finite-element matrix from a R/B file
+% RBtype - determine the Rutherford/Boeing type of a sparse matrix
+% RBwrite - write a sparse matrix to a Rutherford/Boeing file
+% RBraw - read the raw contents of a Rutherford/Boeing file
+% RBfix - read a possibly corrupted matrix from a R/B file
+% RBinstall - install the RBio toolbox for use in MATLAB
+% RBmake - compile the RBio toolbox for use in MATLAB
+%
+% Example:
+%
+% load west0479
+% C = west0479 ;
+% RBwrite ('mywest', C, 'WEST0479 chemical eng. problem', 'west0479')
+% A = RBread ('mywest') ;
+% norm (A-C,1)
+%
+% See also UFget, mread, mwrite.
+
+% Copyright 2007, Timothy A. Davis
diff --git a/RBio/Doc/ChangeLog b/RBio/Doc/ChangeLog
new file mode 100644
index 0000000..8d118f6
--- /dev/null
+++ b/RBio/Doc/ChangeLog
@@ -0,0 +1,10 @@
+Nov 1, 2007: version 1.1.1
+
+ * minor lint cleanup
+
+May 31, 2007: version 1.1
+
+ * port to 64-bit MATLAB. Tested on Linux 32-bit and 64-bit. Not tested on
+ Windows, since I do not have a Fortran compiler on that platform.
+
+Dec 1, 2006: version 1.0 released
diff --git a/RBio/Doc/License.txt b/RBio/Doc/License.txt
new file mode 100644
index 0000000..b06998a
--- /dev/null
+++ b/RBio/Doc/License.txt
@@ -0,0 +1,20 @@
+RBio toolbox. Copyright (C) 2006-2007, Timothy A. Davis
+RBio is also available under other licenses; contact authors for details.
+http://www.cise.ufl.edu/research/sparse
+
+--------------------------------------------------------------------------------
+
+RBio is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+RBio is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+
diff --git a/RBio/Doc/dodiff b/RBio/Doc/dodiff
new file mode 100755
index 0000000..2280b11
--- /dev/null
+++ b/RBio/Doc/dodiff
@@ -0,0 +1,15 @@
+
+# complex vs real
+diff ../RBcread_64.f ../RBrread_64.f
+diff ../RBcread_32.f ../RBrread_32.f
+
+# 32 vs 64 bit
+diff ../RBcread_32.f ../RBcread_64.f
+diff ../RBcsplit_32.f ../RBcsplit_64.f
+diff ../RBraw_mex_32.f ../RBraw_mex_64.f
+diff ../RBread_32.f ../RBread_64.f
+diff ../RBread_mex_32.f ../RBread_mex_64.f
+diff ../RBrread_32.f ../RBrread_64.f
+diff ../RBtype_mex_32.f ../RBtype_mex_64.f
+diff ../RBwrite_32.f ../RBwrite_64.f
+diff ../RBwrite_mex_32.f ../RBwrite_mex_64.f
diff --git a/RBio/Doc/gpl.txt b/RBio/Doc/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/RBio/Doc/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it. (Some other Free Software Foundation software is covered by
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+
+ When we speak of free software, we are referring to freedom, not
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+have the freedom to distribute copies of free software (and charge for
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+that everyone understands that there is no warranty for this free
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+ Finally, any free program is threatened constantly by software
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+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
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diff --git a/RBio/RBcread_32.f b/RBio/RBcread_32.f
new file mode 100644
index 0000000..d197af5
--- /dev/null
+++ b/RBio/RBcread_32.f
@@ -0,0 +1,255 @@
+c=======================================================================
+c=== RBio/RBcread_32 ===================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RB*read: read a Rutherford/Boeing matrix
+c-----------------------------------------------------------------------
+
+ subroutine RBcread
+ $ (nrow, ncol, nnz, ptrfmt, indfmt, valfmt,
+ $ mkind, skind, Ap, Ai, Ax, nzeros, w, cp, info, nw, nnz1)
+ integer*4
+ $ nrow, ncol, nnz, mkind, skind, p, j, i, alen, llen, k,
+ $ ilast, nzeros, info, nw, nnz1
+ integer*4
+ $ Ap (ncol+1), Ai (nnz1), w (nw), cp (ncol+1)
+ complex*16 Ax (nnz1), x
+ character ptrfmt*16, indfmt*16, valfmt*20
+
+c ----------------------------------------------------------------
+c read the column pointers and row indices
+c ----------------------------------------------------------------
+
+ call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind,
+ $ Ap, Ai, w, cp, info, nw)
+ if (info .ne. 0) then
+c error: pattern is invalid
+ return
+ endif
+
+c ----------------------------------------------------------------
+c read the values
+c ----------------------------------------------------------------
+
+c read nnz values
+ read (7, valfmt, err = 94, end = 94) (Ax (p), p = 1, nnz)
+
+c ----------------------------------------------------------------
+c construct upper triangular part for symmetric matrices
+c ----------------------------------------------------------------
+
+c If skind is zero, then the upper part is not constructed. This
+c allows the caller to skip this part, and create the upper part
+c of a symmetric (S,H,Z) matrix. Just pass skind = 0.
+
+ if (skind .gt. 0) then
+
+c ------------------------------------------------------------
+c shift the matrix by adding gaps to the top of each column
+c ------------------------------------------------------------
+
+ do 30 j = ncol, 1, -1
+
+c number of entries in lower tri. part (incl. diagonal)
+ llen = Ap (j+1) - Ap (j)
+
+c number of entries in entire column
+ alen = cp (j+1) - cp (j)
+
+c move the column from Ai (Ap(j) ... Ap(j+1)-1)
+c down to Ai (cp(j+1)-llen ... cp(j+1)-1), leaving a gap
+c at Ai (Ap(j) ... cp(j+1)-llen)
+
+ do 20 k = 1, llen
+ Ai (cp (j+1) - k) = Ai (Ap (j+1) - k)
+ Ax (cp (j+1) - k) = Ax (Ap (j+1) - k)
+20 continue
+30 continue
+
+c ------------------------------------------------------------
+c populate the upper triangular part
+c ------------------------------------------------------------
+
+c create temporary column pointers to point to the gaps
+ do 40 j = 1, ncol
+ w (j) = cp (j)
+40 continue
+
+ do 60 j = 1, ncol
+
+c scan the entries in the lower tri. part, in
+c Ai (cp(j+1)-llen ... cp(j+1)-1)
+ llen = Ap (j+1) - Ap (j)
+ do 50 k = 1, llen
+
+c get the A(i,j) entry in the lower triangular part
+ i = Ai (cp (j+1) - k)
+ x = Ax (cp (j+1) - k)
+
+c add A(j,i) as the next entry in column i (excl diag)
+ if (i .ne. j) then
+ p = w (i)
+ w (i) = w (i) + 1
+ Ai (p) = j
+
+ if (skind .eq. 1) then
+c *SA matrix
+ Ax (p) = x
+ elseif (skind .eq. 2) then
+c *HA matrix
+ Ax (p) = dconjg (x)
+ else
+c *ZA matrix
+ Ax (p) = -x
+ endif
+
+ endif
+
+50 continue
+60 continue
+
+c finalize the column pointers
+ do 70 j = 1, ncol+1
+ Ap (j) = cp (j)
+70 continue
+
+ endif
+
+c ----------------------------------------------------------------
+c count the number of explicit zeros
+c ----------------------------------------------------------------
+
+ nzeros = 0
+ do 90 j = 1, ncol
+ cp (j) = nzeros + 1
+ do 80 p = Ap (j), Ap (j+1)-1
+ if (Ax (p) .eq. 0) then
+ nzeros = nzeros + 1
+ endif
+80 continue
+90 continue
+ cp (ncol+1) = nzeros + 1
+
+c ----------------------------------------------------------------
+c matrix is valid
+c ----------------------------------------------------------------
+
+ info = 0
+ return
+
+c ----------------------------------------------------------------
+c error return
+c ----------------------------------------------------------------
+
+94 info = -94
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RB*zeros: extract explicit zero entries
+c-----------------------------------------------------------------------
+c
+c nrow-by-ncol: size of A and Z
+c cp: column pointers of Z on input
+c Ap, Ai, Ax: matrix with zeros on input, pruned on output
+c Zp, Zi, Zx: empty matrix on input, pattern of zeros on output
+c
+c-----------------------------------------------------------------------
+
+ subroutine RBczeros
+ $ (nrow, ncol, cp, Ap, Ai, Ax, Zp, Zi, Zx)
+ integer*4
+ $ nrow, ncol, Ap (ncol+1), Ai (*), Zp (ncol+1), Zi (*),
+ $ cp (*), i, j, p, pa, pz, p1
+ complex*16 Ax (*), x
+ double precision Zx (*)
+
+c ----------------------------------------------------------------
+c copy the column pointers if Z is being constructed
+c ----------------------------------------------------------------
+
+ do 10 j = 1, ncol+1
+ Zp (j) = cp (j)
+10 continue
+
+c ----------------------------------------------------------------
+c split the matrix
+c ----------------------------------------------------------------
+
+ pa = 1
+ pz = 1
+ do 30 j = 1, ncol
+c save the new start of column j of A
+ p1 = Ap (j)
+ Ap (j) = pa
+ pz = Zp (j)
+c split column j of A
+ do 20 p = p1, Ap (j+1)-1
+ i = Ai (p)
+ x = Ax (p)
+ if (x .eq. 0) then
+c copy into Z
+ Zi (pz) = i
+ Zx (pz) = 1
+ pz = pz + 1
+ else
+c copy into A
+ Ai (pa) = i
+ Ax (pa) = x
+ pa = pa + 1
+ endif
+20 continue
+30 continue
+ Ap (ncol+1) = pa
+
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RB*prune: discard explicit zero entries
+c-----------------------------------------------------------------------
+c
+c nrow-by-ncol: size of A
+c Ap, Ai, Ax: matrix with zeros on input, pruned on output
+c
+c-----------------------------------------------------------------------
+
+ subroutine RBcprune
+ $ (nrow, ncol, Ap, Ai, Ax)
+ integer*4
+ $ nrow, ncol, Ap (ncol+1), Ai (*), i, j, p, pa, pz, p1
+ complex*16 Ax (*), x
+
+c ----------------------------------------------------------------
+c prune the matrix
+c ----------------------------------------------------------------
+
+ pa = 1
+ do 20 j = 1, ncol
+c save the new start of column j of A
+ p1 = Ap (j)
+ Ap (j) = pa
+c prune column j of A
+ do 10 p = p1, Ap (j+1)-1
+ i = Ai (p)
+ x = Ax (p)
+ if (x .ne. 0) then
+c copy into A
+ Ai (pa) = i
+ Ax (pa) = x
+ pa = pa + 1
+ endif
+10 continue
+20 continue
+ Ap (ncol+1) = pa
+
+ return
+ end
diff --git a/RBio/RBcread_64.f b/RBio/RBcread_64.f
new file mode 100644
index 0000000..7943851
--- /dev/null
+++ b/RBio/RBcread_64.f
@@ -0,0 +1,255 @@
+c=======================================================================
+c=== RBio/RBcread_64 ===================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RB*read: read a Rutherford/Boeing matrix
+c-----------------------------------------------------------------------
+
+ subroutine RBcread
+ $ (nrow, ncol, nnz, ptrfmt, indfmt, valfmt,
+ $ mkind, skind, Ap, Ai, Ax, nzeros, w, cp, info, nw, nnz1)
+ integer*8
+ $ nrow, ncol, nnz, mkind, skind, p, j, i, alen, llen, k,
+ $ ilast, nzeros, info, nw, nnz1
+ integer*8
+ $ Ap (ncol+1), Ai (nnz1), w (nw), cp (ncol+1)
+ complex*16 Ax (nnz1), x
+ character ptrfmt*16, indfmt*16, valfmt*20
+
+c ----------------------------------------------------------------
+c read the column pointers and row indices
+c ----------------------------------------------------------------
+
+ call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind,
+ $ Ap, Ai, w, cp, info, nw)
+ if (info .ne. 0) then
+c error: pattern is invalid
+ return
+ endif
+
+c ----------------------------------------------------------------
+c read the values
+c ----------------------------------------------------------------
+
+c read nnz values
+ read (7, valfmt, err = 94, end = 94) (Ax (p), p = 1, nnz)
+
+c ----------------------------------------------------------------
+c construct upper triangular part for symmetric matrices
+c ----------------------------------------------------------------
+
+c If skind is zero, then the upper part is not constructed. This
+c allows the caller to skip this part, and create the upper part
+c of a symmetric (S,H,Z) matrix. Just pass skind = 0.
+
+ if (skind .gt. 0) then
+
+c ------------------------------------------------------------
+c shift the matrix by adding gaps to the top of each column
+c ------------------------------------------------------------
+
+ do 30 j = ncol, 1, -1
+
+c number of entries in lower tri. part (incl. diagonal)
+ llen = Ap (j+1) - Ap (j)
+
+c number of entries in entire column
+ alen = cp (j+1) - cp (j)
+
+c move the column from Ai (Ap(j) ... Ap(j+1)-1)
+c down to Ai (cp(j+1)-llen ... cp(j+1)-1), leaving a gap
+c at Ai (Ap(j) ... cp(j+1)-llen)
+
+ do 20 k = 1, llen
+ Ai (cp (j+1) - k) = Ai (Ap (j+1) - k)
+ Ax (cp (j+1) - k) = Ax (Ap (j+1) - k)
+20 continue
+30 continue
+
+c ------------------------------------------------------------
+c populate the upper triangular part
+c ------------------------------------------------------------
+
+c create temporary column pointers to point to the gaps
+ do 40 j = 1, ncol
+ w (j) = cp (j)
+40 continue
+
+ do 60 j = 1, ncol
+
+c scan the entries in the lower tri. part, in
+c Ai (cp(j+1)-llen ... cp(j+1)-1)
+ llen = Ap (j+1) - Ap (j)
+ do 50 k = 1, llen
+
+c get the A(i,j) entry in the lower triangular part
+ i = Ai (cp (j+1) - k)
+ x = Ax (cp (j+1) - k)
+
+c add A(j,i) as the next entry in column i (excl diag)
+ if (i .ne. j) then
+ p = w (i)
+ w (i) = w (i) + 1
+ Ai (p) = j
+
+ if (skind .eq. 1) then
+c *SA matrix
+ Ax (p) = x
+ elseif (skind .eq. 2) then
+c *HA matrix
+ Ax (p) = dconjg (x)
+ else
+c *ZA matrix
+ Ax (p) = -x
+ endif
+
+ endif
+
+50 continue
+60 continue
+
+c finalize the column pointers
+ do 70 j = 1, ncol+1
+ Ap (j) = cp (j)
+70 continue
+
+ endif
+
+c ----------------------------------------------------------------
+c count the number of explicit zeros
+c ----------------------------------------------------------------
+
+ nzeros = 0
+ do 90 j = 1, ncol
+ cp (j) = nzeros + 1
+ do 80 p = Ap (j), Ap (j+1)-1
+ if (Ax (p) .eq. 0) then
+ nzeros = nzeros + 1
+ endif
+80 continue
+90 continue
+ cp (ncol+1) = nzeros + 1
+
+c ----------------------------------------------------------------
+c matrix is valid
+c ----------------------------------------------------------------
+
+ info = 0
+ return
+
+c ----------------------------------------------------------------
+c error return
+c ----------------------------------------------------------------
+
+94 info = -94
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RB*zeros: extract explicit zero entries
+c-----------------------------------------------------------------------
+c
+c nrow-by-ncol: size of A and Z
+c cp: column pointers of Z on input
+c Ap, Ai, Ax: matrix with zeros on input, pruned on output
+c Zp, Zi, Zx: empty matrix on input, pattern of zeros on output
+c
+c-----------------------------------------------------------------------
+
+ subroutine RBczeros
+ $ (nrow, ncol, cp, Ap, Ai, Ax, Zp, Zi, Zx)
+ integer*8
+ $ nrow, ncol, Ap (ncol+1), Ai (*), Zp (ncol+1), Zi (*),
+ $ cp (*), i, j, p, pa, pz, p1
+ complex*16 Ax (*), x
+ double precision Zx (*)
+
+c ----------------------------------------------------------------
+c copy the column pointers if Z is being constructed
+c ----------------------------------------------------------------
+
+ do 10 j = 1, ncol+1
+ Zp (j) = cp (j)
+10 continue
+
+c ----------------------------------------------------------------
+c split the matrix
+c ----------------------------------------------------------------
+
+ pa = 1
+ pz = 1
+ do 30 j = 1, ncol
+c save the new start of column j of A
+ p1 = Ap (j)
+ Ap (j) = pa
+ pz = Zp (j)
+c split column j of A
+ do 20 p = p1, Ap (j+1)-1
+ i = Ai (p)
+ x = Ax (p)
+ if (x .eq. 0) then
+c copy into Z
+ Zi (pz) = i
+ Zx (pz) = 1
+ pz = pz + 1
+ else
+c copy into A
+ Ai (pa) = i
+ Ax (pa) = x
+ pa = pa + 1
+ endif
+20 continue
+30 continue
+ Ap (ncol+1) = pa
+
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RB*prune: discard explicit zero entries
+c-----------------------------------------------------------------------
+c
+c nrow-by-ncol: size of A
+c Ap, Ai, Ax: matrix with zeros on input, pruned on output
+c
+c-----------------------------------------------------------------------
+
+ subroutine RBcprune
+ $ (nrow, ncol, Ap, Ai, Ax)
+ integer*8
+ $ nrow, ncol, Ap (ncol+1), Ai (*), i, j, p, pa, pz, p1
+ complex*16 Ax (*), x
+
+c ----------------------------------------------------------------
+c prune the matrix
+c ----------------------------------------------------------------
+
+ pa = 1
+ do 20 j = 1, ncol
+c save the new start of column j of A
+ p1 = Ap (j)
+ Ap (j) = pa
+c prune column j of A
+ do 10 p = p1, Ap (j+1)-1
+ i = Ai (p)
+ x = Ax (p)
+ if (x .ne. 0) then
+c copy into A
+ Ai (pa) = i
+ Ax (pa) = x
+ pa = pa + 1
+ endif
+10 continue
+20 continue
+ Ap (ncol+1) = pa
+
+ return
+ end
diff --git a/RBio/RBcsplit_32.f b/RBio/RBcsplit_32.f
new file mode 100644
index 0000000..cff74a1
--- /dev/null
+++ b/RBio/RBcsplit_32.f
@@ -0,0 +1,25 @@
+c=======================================================================
+c=== RBio/RBcsplit_32 ==================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBcsplit: split a complex matrix into its real and imaginary parts
+c-----------------------------------------------------------------------
+
+ subroutine RBcsplit (Cx, Ax, Az, nnz)
+ integer*4
+ $ nnz, i
+ complex*16 Cx (*)
+ double precision Ax (*), Az (*)
+ do 10 i = 1, nnz
+ Ax (i) = dreal (Cx (i))
+ Az (i) = dimag (Cx (i))
+10 continue
+ return
+ end
+
diff --git a/RBio/RBcsplit_64.f b/RBio/RBcsplit_64.f
new file mode 100644
index 0000000..3ac9e72
--- /dev/null
+++ b/RBio/RBcsplit_64.f
@@ -0,0 +1,25 @@
+c=======================================================================
+c=== RBio/RBcsplit_64 ==================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBcsplit: split a complex matrix into its real and imaginary parts
+c-----------------------------------------------------------------------
+
+ subroutine RBcsplit (Cx, Ax, Az, nnz)
+ integer*8
+ $ nnz, i
+ complex*16 Cx (*)
+ double precision Ax (*), Az (*)
+ do 10 i = 1, nnz
+ Ax (i) = dreal (Cx (i))
+ Az (i) = dimag (Cx (i))
+10 continue
+ return
+ end
+
diff --git a/RBio/RBfix.m b/RBio/RBfix.m
new file mode 100644
index 0000000..ad9a52d
--- /dev/null
+++ b/RBio/RBfix.m
@@ -0,0 +1,135 @@
+function [A, Z, title, key, mtype] = RBfix (filename)
+%RBFIX read a possibly corrupted matrix from a R/B file
+% (assembled format only). Usage:
+%
+% [A Z title key mtype] = RBfix (filename)
+%
+% The Rutherford/Boeing format stores a sparse matrix in a file in compressed-
+% column form, using 3 arrays: Ap, Ai, and Ax. The row indices of entries in
+% A(:,j) are in Ai(p1:p2) and the corresponding numerical values are Ax(p1:p2),
+% where p1 = Ap(j) and p2 = Ap(j+1)-1. The row indices ought to be sorted, and
+% no duplicates should appear, but this function ignores that requirement.
+% Duplicate entries are summed if they exist, and A is returned with sorted
+% columns. Symmetric matrices are stored with just their lower triangular
+% parts in the file. Normally, it is an error if entries are present in the
+% upper triangular part of a matrix that is declared in the file to be
+% symmetric. This function simply ignores those entries.
+%
+% If CHOLMOD is installed, this function is faster and uses less memory.
+%
+% Example:
+%
+% load west0479
+% RBwrite ('mywest', west0479, [ ], 'My west0479 file', 'west0479') ;
+% [A Z title key mtype] = RBfix ('mywest') ;
+% isequal (A, west0479)
+% title, key, mtype
+%
+% See also mread, RBread, RBwrite, RBreade, sparse2.
+
+% Optionally uses the CHOLMOD sparse2 mexFunction.
+
+% Copyright 2007, Timothy A. Davis
+
+%-------------------------------------------------------------------------------
+% read in the raw contents of the Rutherford/Boeing file
+%-------------------------------------------------------------------------------
+
+[mtype Ap Ai Ax title key nrow] = RBraw (filename) ;
+mtype = lower (mtype) ;
+
+%-------------------------------------------------------------------------------
+% determine dimension, number of entries, and convert numerical entries
+%-------------------------------------------------------------------------------
+
+% number of columns
+ncol = length (Ap) - 1 ;
+
+% number of entries
+nz = length (Ai) ;
+
+% check column pointers
+if (any (Ap ~= sort (Ap)) | (Ap (1) ~= 1) | (Ap (ncol+1) - 1 ~= nz)) %#ok
+ error ('invalid column pointers') ;
+end
+
+% check row indices
+if ((double (max (Ai)) > nrow) | double (min (Ai)) < 1) %#ok
+ error ('invalid row indices') ;
+end
+
+% Ax can be empty, for a p*a matrix
+if (~isempty (Ax))
+ if (mtype (1) == 'c')
+ % Ax is real, with real/imaginary parts interleaved
+ if (2 * nz ~= length (Ax))
+ error ('invalid matrix') ;
+ end
+ Ax = Ax (1:2:end) + (1i * Ax (2:2:end)) ;
+ elseif (mtype (1) == 'i')
+ Ax = double (Ax) ;
+ end
+ % numerical values must be of the right size
+ if (nz ~= length (Ax))
+ error ('invalid matrix') ;
+ end
+end
+
+%-------------------------------------------------------------------------------
+% create the triplet form
+%-------------------------------------------------------------------------------
+
+% construct column indices
+Aj = zeros (nz,1) ;
+for j = 1:ncol
+ p1 = Ap (j) ;
+ p2 = Ap (j+1) - 1 ;
+ Aj (p1:p2) = j ;
+end
+
+%-------------------------------------------------------------------------------
+% create the sparse matrix form
+%-------------------------------------------------------------------------------
+
+if (exist ('sparse2') == 3) %#ok
+ % Use sparse2 in CHOLMOD. It's faster, allows integer Ai and Aj, and
+ % returns the Z matrix as the 2nd output argument.
+ if (isempty (Ax))
+ Ax = 1 ;
+ end
+ % numerical matrix
+ [A Z] = sparse2 (Ai, Aj, Ax, nrow, ncol) ;
+else
+ % stick with MATLAB, without CHOLMOD. This is slower and takes more memory.
+ Ai = double (Ai) ;
+ Aj = double (Aj) ;
+ if (isempty (Ax))
+ % pattern-only matrix
+ A = spones (sparse (Ai, Aj, 1, nrow, ncol)) ;
+ Z = sparse (nrow, ncol) ;
+ else
+ % numerical matrix
+ A = sparse (Ai, Aj, Ax, nrow, ncol) ;
+ % determine the pattern of explicit zero entries
+ S = spones (sparse (Ai, Aj, 1, nrow, ncol)) ;
+ Z = S - spones (A) ;
+ end
+end
+
+% check for entries in upper part
+if (any (mtype (2) == 'shz') & nnz (triu (A,1) > 0)) %#ok
+ fprintf ('entries in upper triangular part of %s matrix ignored\n', mtype);
+end
+
+% add the upper triangular part
+if (mtype (2) == 's')
+ A = A + tril (A,-1).' ;
+ Z = Z + tril (Z,-1)' ;
+elseif (mtype (2) == 'h')
+ A = A + tril (A,-1)' ;
+ Z = Z + tril (Z,-1)' ;
+elseif (mtype (2) == 'z')
+ A = A - tril (A,-1).' ;
+ Z = Z + tril (Z,-1)' ;
+end
+
diff --git a/RBio/RBinstall.m b/RBio/RBinstall.m
new file mode 100644
index 0000000..d2a42f9
--- /dev/null
+++ b/RBio/RBinstall.m
@@ -0,0 +1,29 @@
+%RBINSTALL install the RBio toolbox for use in MATLAB
+% Compiles the Fortran mexFunctions RBread, RBwrite, RBtype, and RBraw, and
+% the C mexFunction UFfull_write, and adds the current directory to the MATLAB
+% path.
+%
+% Example:
+%
+% RBinstall
+%
+% See also RBread, RBwrite, RBtype, RBraw.
+%
+% Copyright 2007, Timothy A. Davis
+
+help RBio
+
+RBmake
+
+s = pwd ;
+addpath (s) ;
+
+cd Test
+testRB1
+cd (s)
+
+fprintf ('\nRBio is ready to use. Your path has been modified for this\n') ;
+fprintf ('session, by adding the following path:\n') ;
+fprintf ('%s\n', s) ;
+fprintf ('Use the pathtool to modify your path permanently.\n') ;
+
diff --git a/RBio/RBmake.m b/RBio/RBmake.m
new file mode 100644
index 0000000..65efa81
--- /dev/null
+++ b/RBio/RBmake.m
@@ -0,0 +1,30 @@
+%RBMAKE compile the RBio toolbox for use in MATLAB
+% Compiles the Fortran mexFunctions RBread, RBwrite, RBtype, and RBraw.
+%
+% Example:
+%
+% RBmake
+%
+% See also RBread, RBwrite, RBtype, RBraw, RBinstall.
+%
+% Copyright 2007, Timothy A. Davis
+
+if (~isempty (strfind (computer, '64')))
+ fprintf ('Compiling 64-bit version of RBio.\n') ;
+ mex -O -output RBread RBread_mex_64.f RBread_64.f RBrread_64.f ...
+ RBcread_64.f RBcsplit_64.f
+ mex -O -output RBtype RBtype_mex_64.f RBwrite_64.f
+ mex -O -output RBwrite RBwrite_mex_64.f RBwrite_64.f
+ mex -O -output RBraw RBraw_mex_64.f RBread_64.f
+else
+ fprintf ('Compiling 32-bit version of RBio.\n') ;
+ mex -O -output RBread RBread_mex_32.f RBread_32.f RBrread_32.f ...
+ RBcread_32.f RBcsplit_32.f
+ mex -O -output RBtype RBtype_mex_32.f RBwrite_32.f
+ mex -O -output RBwrite RBwrite_mex_32.f RBwrite_32.f
+ mex -O -output RBraw RBraw_mex_32.f RBread_32.f
+end
+
+fprintf ('Note: Fortran compiler is required; this will fail otherwise...\n') ;
+
+fprintf ('RBio successfully compiled.\n') ;
diff --git a/RBio/RBraw.m b/RBio/RBraw.m
new file mode 100644
index 0000000..903b5e0
--- /dev/null
+++ b/RBio/RBraw.m
@@ -0,0 +1,32 @@
+function [mtype, Ap, Ai, Ax, title, key, nrow] = RBraw (filename) %#ok
+%RBRAW read the raw contents of a Rutherford/Boeing file
+%
+% [mtype Ap Ai Ax title key nrow] = RBraw (filename)
+%
+% mtype: Rutherford/Boeing matrix type (psa, rua, rsa, rse, ...)
+% Ap: column pointers (1-based)
+% Ai: row indices (1-based)
+% Ax: numerical values (real, complex, or integer). Empty for p*a matrices.
+% A complex matrix is read in as a single double array Ax, where the kth
+% entry has real value Ax(2*k-1) and imaginary value Ax(2*k).
+% title: a string containing the title from the first line of the R/B file
+% key: a string containing the 8-character key, from the 1st line of the file
+% nrow: number of rows in the matrix
+%
+% This function works for both assembled and unassembled (finite-element)
+% matrices. It is also useful for checking the contents of a Rutherford/Boeing
+% file in detail, in case the file has invalid column pointers, unsorted
+% columns, duplicate entries, entries in the upper triangular part of the file
+% for a symmetric matrix, etc.
+%
+% Example:
+%
+% load west0479
+% RBwrite ('mywest', west0479, [ ], 'My west0479 file', 'west0479') ;
+% [mtype Ap Ai Ax title key nrow] = RBraw ('mywest') ;
+%
+% See also RBfix, RBread, RBreade.
+
+% Copyright 2007, Timothy A. Davis
+
+error ('RBraw mexFunction not found') ;
diff --git a/RBio/RBraw_mex_32.f b/RBio/RBraw_mex_32.f
new file mode 100644
index 0000000..54f59a8
--- /dev/null
+++ b/RBio/RBraw_mex_32.f
@@ -0,0 +1,214 @@
+c=======================================================================
+c=== RBio/RBraw_mex_32 =================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBraw mexFunction: read the raw contents of a Rutherford/Boeing file
+c-----------------------------------------------------------------------
+c
+c [mtype Ap Ai Ax title key nrow] = RBraw (filename)
+c
+c mtype: Rutherford/Boeing matrix type (psa, rua, rsa, rse, ...)
+c Ap: column pointers (1-based)
+c Ai: row indices (1-based)
+c Ax: numerical values (real, complex, or integer). Empty for p*a
+c matrices. A complex matrix is read in as a single double array
+c Ax, where the kth entry has real value Ax(2*k-1) and imaginary
+c value Ax(2*k).
+c title: a string containing the title from the first line of the file
+c key: a string containing the 8-char key, from 1st line of the file
+c nrow: number of rows in the matrix
+c
+c This function works for both assembled and unassembled (finite-
+c element) matrices. It is also useful for checking the contents of a
+c Rutherford/Boeing file in detail, in case the file has invalid column
+c pointers, unsorted columns, duplicate entries, entries in the upper
+c triangular part of the file for a symmetric matrix, etc.
+c
+c Example:
+c
+c load west0479
+c RBwrite ('mywest', west0479, [ ], 'My west0479 file', 'west0479') ;
+c [mtype Ap Ai Ax title key nrow] = RBraw ('mywest') ;
+c
+c See also RBfix, RBread, RBreade.
+c-----------------------------------------------------------------------
+
+ subroutine mexfunction (nargout, pargout, nargin, pargin)
+ integer*4
+ $ pargout (*), pargin (*)
+ integer*4 nargout, nargin
+
+c ----------------------------------------------------------------
+c MATLAB functions
+c ----------------------------------------------------------------
+
+ integer*4 mxIsChar, mxClassIDFromClassName
+
+ integer*4
+ $ mxGetString, mxCreateString, mxCreateDoubleScalar,
+ $ mxCreateNumericMatrix, mxGetData
+
+c ----------------------------------------------------------------
+c local variables
+c ----------------------------------------------------------------
+
+ integer*4
+ $ nrow, ncol, nnz, mkind, info, skind, k, nelnz, one, zero
+ integer*4 iclass, cmplex, wcmplex
+ character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16,
+ $ valfmt*20, filename*1024
+ double precision x
+
+c ----------------------------------------------------------------
+c check inputs
+c ----------------------------------------------------------------
+
+ if (nargin .ne. 1 .or. nargout .gt. 7 .or.
+ $ mxIsChar (pargin (1)) .ne. 1) then
+ call mexErrMsgTxt
+ $ ('Usage: [mtype Ap Ai Ax title key nrow] = RBraw (filename)')
+ endif
+
+c ----------------------------------------------------------------
+c get filename and open file
+c ----------------------------------------------------------------
+
+ if (mxGetString (pargin (1), filename, 1024) .ne. 0) then
+ call mexErrMsgTxt ('filename too long')
+ endif
+ close (unit = 7)
+ open (unit = 7, file = filename, status = 'OLD', err = 998)
+
+c ----------------------------------------------------------------
+c read the header and determine the matrix type
+c ----------------------------------------------------------------
+
+ call RBheader (title, key, mtype, nrow, ncol, nnz,
+ $ ptrfmt, indfmt, valfmt,
+ $ mkind, cmplex, skind, nelnz, info)
+ call RBerr (info)
+
+c ----------------------------------------------------------------
+c return the matrix type to MATLAB
+c ----------------------------------------------------------------
+
+ pargout (1) = mxCreateString (mtype)
+
+c ----------------------------------------------------------------
+c read in the column pointers
+c ----------------------------------------------------------------
+
+ iclass = mxClassIDFromClassName ('int32')
+ one = 1
+ zero = 0
+ wcmplex = 0
+ if (nargout .ge. 2) then
+ pargout (2) = mxCreateNumericMatrix
+ $ (ncol+1, one, iclass, wcmplex)
+ call RBiread (ptrfmt, ncol+1,
+ $ %val(mxGetData (pargout (2))), info)
+ call RBerr (info)
+ endif
+
+c ----------------------------------------------------------------
+c read in the row indices
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 3) then
+ pargout (3) = mxCreateNumericMatrix
+ $ (nnz, one, iclass, wcmplex)
+ call RBiread (indfmt, nnz,
+ $ %val(mxGetData (pargout (3))), info)
+ if (info .lt. 0) then
+ info = -93
+ endif
+ call RBerr (info)
+ endif
+
+c ----------------------------------------------------------------
+c read in the numerical values
+c ----------------------------------------------------------------
+
+ if (nelnz .eq. 0) then
+ k = nnz
+ else
+ k = nelnz
+ endif
+
+ if (nargout .ge. 4) then
+
+ if (mkind .eq. 1) then
+
+c pattern-only: create an empty numerical array
+ pargout (4) = mxCreateNumericMatrix (zero, zero,
+ $ mxClassIDFromClassName ('double'), wcmplex)
+
+ elseif (mkind .eq. 3) then
+
+c read in the numerical values (integer)
+ pargout (4) = mxCreateNumericMatrix
+ $ (k, one, iclass, wcmplex)
+ call RBiread (valfmt, k,
+ $ %val(mxGetData (pargout (4))), info)
+ call RBerr (info)
+
+ else
+
+c read in the numerical values (real or complex)
+ if (cmplex .eq. 1) then
+ k = 2*k
+ endif
+ pargout (4) = mxCreateNumericMatrix (k, one,
+ $ mxClassIDFromClassName ('double'), wcmplex)
+ call RBxread (valfmt, k,
+ $ %val(mxGetData (pargout (4))), info)
+ call RBerr (info)
+ endif
+
+ endif
+
+c ----------------------------------------------------------------
+c return the title
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 5) then
+ pargout (5) = mxCreateString (title)
+ endif
+
+c ----------------------------------------------------------------
+c return the key
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 6) then
+ pargout (6) = mxCreateString (key)
+ endif
+
+c ----------------------------------------------------------------
+c return the number of rows
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 7) then
+ x = nrow
+ pargout (7) = mxCreateDoubleScalar (x)
+ endif
+
+c ----------------------------------------------------------------
+c close file
+c ----------------------------------------------------------------
+
+ close (unit = 7)
+ return
+
+c ----------------------------------------------------------------
+c error return
+c ----------------------------------------------------------------
+
+998 call mexErrMsgTxt ('error opening file')
+ end
+
diff --git a/RBio/RBraw_mex_64.f b/RBio/RBraw_mex_64.f
new file mode 100644
index 0000000..cd99274
--- /dev/null
+++ b/RBio/RBraw_mex_64.f
@@ -0,0 +1,214 @@
+c=======================================================================
+c=== RBio/RBraw_mex_64 =================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBraw mexFunction: read the raw contents of a Rutherford/Boeing file
+c-----------------------------------------------------------------------
+c
+c [mtype Ap Ai Ax title key nrow] = RBraw (filename)
+c
+c mtype: Rutherford/Boeing matrix type (psa, rua, rsa, rse, ...)
+c Ap: column pointers (1-based)
+c Ai: row indices (1-based)
+c Ax: numerical values (real, complex, or integer). Empty for p*a
+c matrices. A complex matrix is read in as a single double array
+c Ax, where the kth entry has real value Ax(2*k-1) and imaginary
+c value Ax(2*k).
+c title: a string containing the title from the first line of the file
+c key: a string containing the 8-char key, from 1st line of the file
+c nrow: number of rows in the matrix
+c
+c This function works for both assembled and unassembled (finite-
+c element) matrices. It is also useful for checking the contents of a
+c Rutherford/Boeing file in detail, in case the file has invalid column
+c pointers, unsorted columns, duplicate entries, entries in the upper
+c triangular part of the file for a symmetric matrix, etc.
+c
+c Example:
+c
+c load west0479
+c RBwrite ('mywest', west0479, [ ], 'My west0479 file', 'west0479') ;
+c [mtype Ap Ai Ax title key nrow] = RBraw ('mywest') ;
+c
+c See also RBfix, RBread, RBreade.
+c-----------------------------------------------------------------------
+
+ subroutine mexfunction (nargout, pargout, nargin, pargin)
+ integer*8
+ $ pargout (*), pargin (*)
+ integer*4 nargout, nargin
+
+c ----------------------------------------------------------------
+c MATLAB functions
+c ----------------------------------------------------------------
+
+ integer*4 mxIsChar, mxClassIDFromClassName
+
+ integer*8
+ $ mxGetString, mxCreateString, mxCreateDoubleScalar,
+ $ mxCreateNumericMatrix, mxGetData
+
+c ----------------------------------------------------------------
+c local variables
+c ----------------------------------------------------------------
+
+ integer*8
+ $ nrow, ncol, nnz, mkind, info, skind, k, nelnz, one, zero
+ integer*4 iclass, cmplex, wcmplex
+ character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16,
+ $ valfmt*20, filename*1024
+ double precision x
+
+c ----------------------------------------------------------------
+c check inputs
+c ----------------------------------------------------------------
+
+ if (nargin .ne. 1 .or. nargout .gt. 7 .or.
+ $ mxIsChar (pargin (1)) .ne. 1) then
+ call mexErrMsgTxt
+ $ ('Usage: [mtype Ap Ai Ax title key nrow] = RBraw (filename)')
+ endif
+
+c ----------------------------------------------------------------
+c get filename and open file
+c ----------------------------------------------------------------
+
+ if (mxGetString (pargin (1), filename, 1024) .ne. 0) then
+ call mexErrMsgTxt ('filename too long')
+ endif
+ close (unit = 7)
+ open (unit = 7, file = filename, status = 'OLD', err = 998)
+
+c ----------------------------------------------------------------
+c read the header and determine the matrix type
+c ----------------------------------------------------------------
+
+ call RBheader (title, key, mtype, nrow, ncol, nnz,
+ $ ptrfmt, indfmt, valfmt,
+ $ mkind, cmplex, skind, nelnz, info)
+ call RBerr (info)
+
+c ----------------------------------------------------------------
+c return the matrix type to MATLAB
+c ----------------------------------------------------------------
+
+ pargout (1) = mxCreateString (mtype)
+
+c ----------------------------------------------------------------
+c read in the column pointers
+c ----------------------------------------------------------------
+
+ iclass = mxClassIDFromClassName ('int64')
+ one = 1
+ zero = 0
+ wcmplex = 0
+ if (nargout .ge. 2) then
+ pargout (2) = mxCreateNumericMatrix
+ $ (ncol+1, one, iclass, wcmplex)
+ call RBiread (ptrfmt, ncol+1,
+ $ %val(mxGetData (pargout (2))), info)
+ call RBerr (info)
+ endif
+
+c ----------------------------------------------------------------
+c read in the row indices
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 3) then
+ pargout (3) = mxCreateNumericMatrix
+ $ (nnz, one, iclass, wcmplex)
+ call RBiread (indfmt, nnz,
+ $ %val(mxGetData (pargout (3))), info)
+ if (info .lt. 0) then
+ info = -93
+ endif
+ call RBerr (info)
+ endif
+
+c ----------------------------------------------------------------
+c read in the numerical values
+c ----------------------------------------------------------------
+
+ if (nelnz .eq. 0) then
+ k = nnz
+ else
+ k = nelnz
+ endif
+
+ if (nargout .ge. 4) then
+
+ if (mkind .eq. 1) then
+
+c pattern-only: create an empty numerical array
+ pargout (4) = mxCreateNumericMatrix (zero, zero,
+ $ mxClassIDFromClassName ('double'), wcmplex)
+
+ elseif (mkind .eq. 3) then
+
+c read in the numerical values (integer)
+ pargout (4) = mxCreateNumericMatrix
+ $ (k, one, iclass, wcmplex)
+ call RBiread (valfmt, k,
+ $ %val(mxGetData (pargout (4))), info)
+ call RBerr (info)
+
+ else
+
+c read in the numerical values (real or complex)
+ if (cmplex .eq. 1) then
+ k = 2*k
+ endif
+ pargout (4) = mxCreateNumericMatrix (k, one,
+ $ mxClassIDFromClassName ('double'), wcmplex)
+ call RBxread (valfmt, k,
+ $ %val(mxGetData (pargout (4))), info)
+ call RBerr (info)
+ endif
+
+ endif
+
+c ----------------------------------------------------------------
+c return the title
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 5) then
+ pargout (5) = mxCreateString (title)
+ endif
+
+c ----------------------------------------------------------------
+c return the key
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 6) then
+ pargout (6) = mxCreateString (key)
+ endif
+
+c ----------------------------------------------------------------
+c return the number of rows
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 7) then
+ x = nrow
+ pargout (7) = mxCreateDoubleScalar (x)
+ endif
+
+c ----------------------------------------------------------------
+c close file
+c ----------------------------------------------------------------
+
+ close (unit = 7)
+ return
+
+c ----------------------------------------------------------------
+c error return
+c ----------------------------------------------------------------
+
+998 call mexErrMsgTxt ('error opening file')
+ end
+
diff --git a/RBio/RBread.m b/RBio/RBread.m
new file mode 100644
index 0000000..b0a1485
--- /dev/null
+++ b/RBio/RBread.m
@@ -0,0 +1,27 @@
+function [A, Z, title, key, mtype] = RBread (filename) %#ok
+%RBREAD read a sparse matrix from a Rutherford/Boeing file
+% Usage:
+% [A Z title key mtype] = RBread (filename)
+%
+% A: a sparse matrix (no explicit zero entries)
+% Z: binary pattern of explicit zero entries in Rutherford/Boeing file.
+% This always has the same size as A, and is always sparse.
+% title: the 72-character title string in the file
+% key: the 8-character matrix name in the file
+% mtype: the Rutherford/Boeing type (see RBwrite for a description).
+% This function does not support finite-element matrices (use RBreade
+% instead).
+%
+% Example:
+% load west0479
+% C = west0479 ;
+% RBwrite ('mywest', C, 'WEST0479 chemical eng. problem', 'west0479')
+% A = RBread ('mywest') ;
+% norm (A-C,1)
+%
+% See also RBwrite, RBreade, RBtype.
+
+% Copyright 2007, Timothy A. Davis
+
+error ('RBread mexFunction not found') ;
+
diff --git a/RBio/RBread_32.f b/RBio/RBread_32.f
new file mode 100644
index 0000000..140653d
--- /dev/null
+++ b/RBio/RBread_32.f
@@ -0,0 +1,464 @@
+c=======================================================================
+c=== RBio/RBread_32 ====================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBheader: read Rutherford/Boeing header lines
+c-----------------------------------------------------------------------
+c
+c Rutherford/Boeing file type is a 3-character string:
+c
+c (1) R: real, C: complex, P: pattern only, I: integer
+c mkind: R: 0, P: 1, C: 2, I: 3
+c
+c (2) S: symmetric, U: unsymmetric, H: Hermitian, Z: skew symmetric,
+c R: rectangular
+c skind: R: -1, U: 0, S: 1, H: 2, Z: 3
+c
+c (3) A: assembled, E: element form
+c nelnz = 0 for A, number of elements for E
+c
+c pattern matrices are given numerical values of 1 (except PZA).
+c PZA matrices have +1 in the lower triangular part and -1 in
+c the upper triangular part.
+c
+c The matrix is nrow-by-ncol with nnz entries.
+c For symmetric matrices, Ai and Ax are of size 2*nnz (the upper
+c triangular part is constructed). To skip this construction,
+c pass skind = 0 to RBpattern.
+c-----------------------------------------------------------------------
+
+ subroutine RBheader (title, key, mtype, nrow, ncol, nnz,
+ $ ptrfmt, indfmt, valfmt, mkind, cmplex, skind, nelnz, info)
+
+ integer*4
+ $ nrow, ncol, nnz, totcrd, ptrcrd, nelnz,
+ $ indcrd, valcrd, mkind, skind, info
+ integer*4 cmplex
+ character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16,
+ $ valfmt*20, rhstyp*3
+ logical fem
+
+c ----------------------------------------------------------------
+c read header lines 1-4
+c ----------------------------------------------------------------
+
+ read (7, 10, err = 91, end = 91)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd,
+ $ mtype, nrow, ncol, nnz, nelnz,
+ $ ptrfmt, indfmt, valfmt
+10 format (a72, a8 / 4i14 / a3, 11x, 4i14 / 2a16, a20)
+
+ if (nrow .lt. 0 .or. ncol .lt. 0 .or. nnz .lt. 0) then
+c error: invalid matrix dimensions
+ info = -6
+ return
+ endif
+
+c ----------------------------------------------------------------
+c skip the Harwell/Boeing header line 5, if present
+c ----------------------------------------------------------------
+
+ read (7, 20, err = 91, end = 91) rhstyp
+20 format (a3)
+ if ((rhstyp (1:1) .eq. 'F' .or. rhstyp (1:1) .eq. 'f' .or.
+ $ rhstyp (1:1) .eq. 'M' .or. rhstyp (1:1) .eq. 'm')) then
+c This is the 5th line Harwell/Boeing format. Ignore it.
+ call mexErrMsgTxt ('Harwell/Boeing RHS ignored')
+ else
+c Backspace one record, since we just read in one row of
+c the column pointers.
+ backspace (unit = 7)
+ endif
+
+c ----------------------------------------------------------------
+c determine if real, pattern, integer, or complex
+c ----------------------------------------------------------------
+
+ if (mtype (1:1) .eq. 'R' .or. mtype (1:1) .eq. 'r') then
+
+c real
+ mkind = 0
+ cmplex = 0
+
+ elseif (mtype (1:1) .eq. 'P' .or. mtype (1:1) .eq. 'p') then
+
+c pattern
+ mkind = 1
+ cmplex = 0
+
+ elseif (mtype (1:1) .eq. 'C' .or. mtype (1:1) .eq. 'c') then
+
+c complex
+ mkind = 2
+ cmplex = 1
+
+ elseif (mtype (1:1) .eq. 'I' .or. mtype (1:1) .eq. 'i') then
+
+c integer
+ mkind = 3
+ cmplex = 0
+
+ else
+
+c error: invalid matrix type
+ info = -5
+ return
+
+ endif
+
+c ----------------------------------------------------------------
+c determine if the upper part must be constructed
+c ----------------------------------------------------------------
+
+ if (mtype (2:2) .eq. 'R' .or. mtype (2:2) .eq. 'r') then
+
+c rectangular: RRA, PRA, IRA, and CRA matrices
+ skind = -1
+
+ elseif (mtype (2:2) .eq. 'U' .or. mtype (2:2) .eq. 'u') then
+
+c unsymmetric: RUA, PUA, IUA, and CUA matrices
+ skind = 0
+
+ elseif (mtype (2:2) .eq. 'S' .or. mtype (2:2) .eq. 's') then
+
+c symmetric: RSA, PSA, ISA, and CSA matrices
+ skind = 1
+
+ elseif (mtype (2:2) .eq. 'H' .or. mtype (2:2) .eq. 'h') then
+
+c Hermitian: CHA (PHA, IHA, and RHA are valid, but atypical)
+ skind = 2
+
+ elseif (mtype (2:2) .eq. 'Z' .or. mtype (2:2) .eq. 'z') then
+
+c skew symmetric: RZA, PZA, IZA, and CZA
+ skind = 3
+
+ else
+
+c error: invalid matrix type
+ info = -5
+ return
+
+ endif
+
+c ----------------------------------------------------------------
+c assembled matrices or elemental matrices (**A, **E)
+c ----------------------------------------------------------------
+
+ if (mtype (3:3) .eq. 'A' .or. mtype (3:3) .eq. 'a') then
+
+c assembled - ignore nelnz
+ fem = .false.
+ nelnz = 0
+
+ elseif (mtype (3:3) .eq. 'E' .or. mtype (3:3) .eq. 'e') then
+
+c finite-element
+ fem = .true.
+ continue
+
+ else
+
+c error: invalid matrix type
+ info = -5
+ return
+
+ endif
+
+c ----------------------------------------------------------------
+c assembled matrices must be square if skind is not R
+c ----------------------------------------------------------------
+
+ if (.not. fem .and. skind .ne. -1 .and. nrow .ne. ncol) then
+
+c error: invalid matrix dimensions
+ info = -6
+ return
+
+ endif
+
+c ----------------------------------------------------------------
+c matrix is valid
+c ----------------------------------------------------------------
+
+ info = 0
+ return
+
+c ----------------------------------------------------------------
+c error reading file
+c ----------------------------------------------------------------
+
+91 info = -91
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBpattern: read the column pointers and row indices
+c-----------------------------------------------------------------------
+
+c w and cp are both of size ncol+1 (undefined on input).
+c
+c The matrix is contained in Ap, Ai, and Ax on output (undefined on
+c input). It has nzeros explicit zero entries. cp (1..ncol+1) are
+c the column pointers for the matrix Z that will contain all the
+c explicit zero entries. Ax is not read in (see RBrread and
+c RBcread).
+c
+c info is returned as:
+c 0 ok
+c -1 invalid column pointers
+c -2 row index out of range
+c -3 duplicate entry
+c -4 entries in upper triangular part of symmetric matrix
+c -5 invalid matrix type
+c -6 invalid dimensions
+c -7 matrix contains unsorted columns
+c -91 error reading file (header)
+c -92 error reading file (column pointers)
+c -93 error reading file (row indices)
+c -94 error reading file (numerical values: A, or sparse b)
+c-----------------------------------------------------------------------
+
+ subroutine RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind,
+ $ Ap, Ai, w, cp, info, nw)
+ integer*4
+ $ nrow, ncol, nnz, skind, info, Ap (ncol+1), Ai (nnz),
+ $ nw, w (nw), cp (ncol+1)
+ character ptrfmt*16, indfmt*16
+ integer*4
+ $ j, i, p, ilast
+
+c ----------------------------------------------------------------
+c read the pointers and check them
+c ----------------------------------------------------------------
+
+ call RBiread (ptrfmt, ncol+1, Ap, info)
+ if (info .lt. 0) then
+ return
+ endif
+
+ if (Ap (1) .ne. 1 .or. Ap (ncol+1) - 1 .ne. nnz) then
+c error: invalid matrix (col pointers)
+ info = -1
+ return
+ endif
+ do 10 j = 2, ncol+1
+ if (Ap (j) .lt. Ap (j-1)) then
+c error: invalid matrix (col pointers)
+ info = -1
+ return
+ endif
+10 continue
+
+c ----------------------------------------------------------------
+c read the row indices and check them
+c ----------------------------------------------------------------
+
+ call RBiread (indfmt, nnz, Ai, info)
+ if (info .lt. 0) then
+ info = -93
+ return
+ endif
+
+ do 20 i = 1, nrow
+ w (i) = -1
+20 continue
+
+ do 40 j = 1, ncol
+ ilast = 0
+ do 30 p = Ap (j), Ap (j+1) - 1
+ i = Ai (p)
+ if (i .lt. 1 .or. i .gt. nrow) then
+c error: row index out of range
+c print *, 'column j, rows!', j, i, nrow
+ info = -2
+ return
+ endif
+ if (w (i) .eq. j) then
+c error: duplicate entry in matrix
+c print *, 'column j, duplicate!', j, i
+ info = -3
+ return
+ endif
+ w (i) = j
+ if (i .lt. ilast) then
+c error: matrix contains unsorted columns
+c print *, 'column j, unsorted!', j, i, ilast
+ info = -7
+ return
+ endif
+ ilast = i
+30 continue
+40 continue
+
+c ----------------------------------------------------------------
+c construct new column pointers for symmetric matrices
+c ----------------------------------------------------------------
+
+ if (skind .gt. 0) then
+
+c ------------------------------------------------------------
+c compute the column counts for the whole matrix
+c ------------------------------------------------------------
+
+ do 50 j = 1, ncol+1
+ w (j) = 0
+50 continue
+
+ do 70 j = 1, ncol
+ do 60 p = Ap (j), Ap (j+1)-1
+ i = Ai (p)
+ if (i .eq. j) then
+c diagonal entry, only appears as A(j,j)
+ w (j) = w (j) + 1
+ elseif (i .gt. j) then
+c entry in lower triangular part, A(i,j) will be
+c duplicated as A(j,i), so count it in both cols
+ w (i) = w (i) + 1
+ w (j) = w (j) + 1
+ else
+c error: entry in upper triangular part
+ info = -4
+ return
+ endif
+60 continue
+70 continue
+
+c ------------------------------------------------------------
+c compute the new column pointers
+c ------------------------------------------------------------
+
+ cp (1) = 1
+ do 80 j = 2, ncol+1
+ cp (j) = cp (j-1) + w (j-1)
+80 continue
+
+ endif
+
+c ----------------------------------------------------------------
+c matrix is valid
+c ----------------------------------------------------------------
+
+ info = 0
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBmangle: convert 1-based matrix into 0-based
+c-----------------------------------------------------------------------
+
+ subroutine RBmangle (ncol, Ap, Ai, nnz)
+ integer*4
+ $ ncol, nnz, p, j, Ap (ncol+1), Ai (*)
+ nnz = Ap (ncol + 1) - 1
+
+ do 10 j = 1, ncol+1
+ Ap (j) = Ap (j) - 1
+10 continue
+ do 20 p = 1, nnz
+ Ai (p) = Ai (p) - 1
+20 continue
+
+ return
+ end
+
+c-----------------------------------------------------------------------
+
+ subroutine RBiread (ifmt, n, I, info)
+ integer*4
+ $ n, I (n), info, p
+ character ifmt*16
+ info = 0
+ read (7, ifmt, err = 92, end = 92) (I (p), p = 1, n)
+ return
+92 info = -92
+ return
+ end
+
+c-----------------------------------------------------------------------
+
+ subroutine RBxread (xfmt, n, X, info)
+ integer*4
+ $ mkind, n, info, p
+ double precision X (n)
+ character xfmt*20
+ info = 0
+ read (7, xfmt, err = 94, end = 94) (X (p), p = 1, n)
+ return
+94 info = -94
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBerr: report an error to MATLAB
+c-----------------------------------------------------------------------
+c
+c info = 0 is OK, info < 0 is a fatal error, info > 0 is a warning
+
+ subroutine RBerr (info)
+ integer*4
+ $ info
+
+ if (info .eq. -7) then
+ call mexErrMsgTxt ('matrix contains unsorted columns')
+
+ elseif (info .eq. -1) then
+ call mexErrMsgTxt ('invalid matrix (col pointers)')
+
+ elseif (info .eq. -2) then
+ call mexErrMsgTxt ('row index out of range)')
+
+ elseif (info .eq. -3) then
+ call mexErrMsgTxt ('duplicate entry in matrix')
+
+ elseif (info .eq. -4) then
+ call mexErrMsgTxt ('invalid symmetric matrix')
+
+ elseif (info .eq. -5) then
+ call mexErrMsgTxt ('invalid matrix type')
+
+ elseif (info .eq. -6) then
+ call mexErrMsgTxt ('invalid matrix dimensions')
+
+ elseif (info .eq. -911) then
+ call mexErrMsgTxt ('finite-element form not supported')
+
+ elseif (info .eq. -91) then
+ call mexErrMsgTxt ('error reading file (header)')
+
+ elseif (info .eq. -92) then
+ call mexErrMsgTxt ('error reading file (column pointers)')
+
+ elseif (info .eq. -93) then
+ call mexErrMsgTxt ('error reading file (row indices)')
+
+ elseif (info .eq. -94) then
+ call mexErrMsgTxt ('error reading file (numerical values)')
+
+ elseif (info .eq. -95) then
+ call mexErrMsgTxt ('error reading file (right-hand-side)')
+
+ elseif (info .lt. 0) then
+ print *, info
+ call mexErrMsgTxt ('error (unspecified)')
+
+ elseif (info .gt. 0) then
+ print *, info
+ call mexErrMsgTxt ('warning (unspecified)')
+
+ endif
+ return
+ end
+
diff --git a/RBio/RBread_64.f b/RBio/RBread_64.f
new file mode 100644
index 0000000..8ca9378
--- /dev/null
+++ b/RBio/RBread_64.f
@@ -0,0 +1,464 @@
+c=======================================================================
+c=== RBio/RBread_64 ====================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBheader: read Rutherford/Boeing header lines
+c-----------------------------------------------------------------------
+c
+c Rutherford/Boeing file type is a 3-character string:
+c
+c (1) R: real, C: complex, P: pattern only, I: integer
+c mkind: R: 0, P: 1, C: 2, I: 3
+c
+c (2) S: symmetric, U: unsymmetric, H: Hermitian, Z: skew symmetric,
+c R: rectangular
+c skind: R: -1, U: 0, S: 1, H: 2, Z: 3
+c
+c (3) A: assembled, E: element form
+c nelnz = 0 for A, number of elements for E
+c
+c pattern matrices are given numerical values of 1 (except PZA).
+c PZA matrices have +1 in the lower triangular part and -1 in
+c the upper triangular part.
+c
+c The matrix is nrow-by-ncol with nnz entries.
+c For symmetric matrices, Ai and Ax are of size 2*nnz (the upper
+c triangular part is constructed). To skip this construction,
+c pass skind = 0 to RBpattern.
+c-----------------------------------------------------------------------
+
+ subroutine RBheader (title, key, mtype, nrow, ncol, nnz,
+ $ ptrfmt, indfmt, valfmt, mkind, cmplex, skind, nelnz, info)
+
+ integer*8
+ $ nrow, ncol, nnz, totcrd, ptrcrd, nelnz,
+ $ indcrd, valcrd, mkind, skind, info
+ integer*4 cmplex
+ character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16,
+ $ valfmt*20, rhstyp*3
+ logical fem
+
+c ----------------------------------------------------------------
+c read header lines 1-4
+c ----------------------------------------------------------------
+
+ read (7, 10, err = 91, end = 91)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd,
+ $ mtype, nrow, ncol, nnz, nelnz,
+ $ ptrfmt, indfmt, valfmt
+10 format (a72, a8 / 4i14 / a3, 11x, 4i14 / 2a16, a20)
+
+ if (nrow .lt. 0 .or. ncol .lt. 0 .or. nnz .lt. 0) then
+c error: invalid matrix dimensions
+ info = -6
+ return
+ endif
+
+c ----------------------------------------------------------------
+c skip the Harwell/Boeing header line 5, if present
+c ----------------------------------------------------------------
+
+ read (7, 20, err = 91, end = 91) rhstyp
+20 format (a3)
+ if ((rhstyp (1:1) .eq. 'F' .or. rhstyp (1:1) .eq. 'f' .or.
+ $ rhstyp (1:1) .eq. 'M' .or. rhstyp (1:1) .eq. 'm')) then
+c This is the 5th line Harwell/Boeing format. Ignore it.
+ call mexErrMsgTxt ('Harwell/Boeing RHS ignored')
+ else
+c Backspace one record, since we just read in one row of
+c the column pointers.
+ backspace (unit = 7)
+ endif
+
+c ----------------------------------------------------------------
+c determine if real, pattern, integer, or complex
+c ----------------------------------------------------------------
+
+ if (mtype (1:1) .eq. 'R' .or. mtype (1:1) .eq. 'r') then
+
+c real
+ mkind = 0
+ cmplex = 0
+
+ elseif (mtype (1:1) .eq. 'P' .or. mtype (1:1) .eq. 'p') then
+
+c pattern
+ mkind = 1
+ cmplex = 0
+
+ elseif (mtype (1:1) .eq. 'C' .or. mtype (1:1) .eq. 'c') then
+
+c complex
+ mkind = 2
+ cmplex = 1
+
+ elseif (mtype (1:1) .eq. 'I' .or. mtype (1:1) .eq. 'i') then
+
+c integer
+ mkind = 3
+ cmplex = 0
+
+ else
+
+c error: invalid matrix type
+ info = -5
+ return
+
+ endif
+
+c ----------------------------------------------------------------
+c determine if the upper part must be constructed
+c ----------------------------------------------------------------
+
+ if (mtype (2:2) .eq. 'R' .or. mtype (2:2) .eq. 'r') then
+
+c rectangular: RRA, PRA, IRA, and CRA matrices
+ skind = -1
+
+ elseif (mtype (2:2) .eq. 'U' .or. mtype (2:2) .eq. 'u') then
+
+c unsymmetric: RUA, PUA, IUA, and CUA matrices
+ skind = 0
+
+ elseif (mtype (2:2) .eq. 'S' .or. mtype (2:2) .eq. 's') then
+
+c symmetric: RSA, PSA, ISA, and CSA matrices
+ skind = 1
+
+ elseif (mtype (2:2) .eq. 'H' .or. mtype (2:2) .eq. 'h') then
+
+c Hermitian: CHA (PHA, IHA, and RHA are valid, but atypical)
+ skind = 2
+
+ elseif (mtype (2:2) .eq. 'Z' .or. mtype (2:2) .eq. 'z') then
+
+c skew symmetric: RZA, PZA, IZA, and CZA
+ skind = 3
+
+ else
+
+c error: invalid matrix type
+ info = -5
+ return
+
+ endif
+
+c ----------------------------------------------------------------
+c assembled matrices or elemental matrices (**A, **E)
+c ----------------------------------------------------------------
+
+ if (mtype (3:3) .eq. 'A' .or. mtype (3:3) .eq. 'a') then
+
+c assembled - ignore nelnz
+ fem = .false.
+ nelnz = 0
+
+ elseif (mtype (3:3) .eq. 'E' .or. mtype (3:3) .eq. 'e') then
+
+c finite-element
+ fem = .true.
+ continue
+
+ else
+
+c error: invalid matrix type
+ info = -5
+ return
+
+ endif
+
+c ----------------------------------------------------------------
+c assembled matrices must be square if skind is not R
+c ----------------------------------------------------------------
+
+ if (.not. fem .and. skind .ne. -1 .and. nrow .ne. ncol) then
+
+c error: invalid matrix dimensions
+ info = -6
+ return
+
+ endif
+
+c ----------------------------------------------------------------
+c matrix is valid
+c ----------------------------------------------------------------
+
+ info = 0
+ return
+
+c ----------------------------------------------------------------
+c error reading file
+c ----------------------------------------------------------------
+
+91 info = -91
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBpattern: read the column pointers and row indices
+c-----------------------------------------------------------------------
+
+c w and cp are both of size ncol+1 (undefined on input).
+c
+c The matrix is contained in Ap, Ai, and Ax on output (undefined on
+c input). It has nzeros explicit zero entries. cp (1..ncol+1) are
+c the column pointers for the matrix Z that will contain all the
+c explicit zero entries. Ax is not read in (see RBrread and
+c RBcread).
+c
+c info is returned as:
+c 0 ok
+c -1 invalid column pointers
+c -2 row index out of range
+c -3 duplicate entry
+c -4 entries in upper triangular part of symmetric matrix
+c -5 invalid matrix type
+c -6 invalid dimensions
+c -7 matrix contains unsorted columns
+c -91 error reading file (header)
+c -92 error reading file (column pointers)
+c -93 error reading file (row indices)
+c -94 error reading file (numerical values: A, or sparse b)
+c-----------------------------------------------------------------------
+
+ subroutine RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind,
+ $ Ap, Ai, w, cp, info, nw)
+ integer*8
+ $ nrow, ncol, nnz, skind, info, Ap (ncol+1), Ai (nnz),
+ $ nw, w (nw), cp (ncol+1)
+ character ptrfmt*16, indfmt*16
+ integer*8
+ $ j, i, p, ilast
+
+c ----------------------------------------------------------------
+c read the pointers and check them
+c ----------------------------------------------------------------
+
+ call RBiread (ptrfmt, ncol+1, Ap, info)
+ if (info .lt. 0) then
+ return
+ endif
+
+ if (Ap (1) .ne. 1 .or. Ap (ncol+1) - 1 .ne. nnz) then
+c error: invalid matrix (col pointers)
+ info = -1
+ return
+ endif
+ do 10 j = 2, ncol+1
+ if (Ap (j) .lt. Ap (j-1)) then
+c error: invalid matrix (col pointers)
+ info = -1
+ return
+ endif
+10 continue
+
+c ----------------------------------------------------------------
+c read the row indices and check them
+c ----------------------------------------------------------------
+
+ call RBiread (indfmt, nnz, Ai, info)
+ if (info .lt. 0) then
+ info = -93
+ return
+ endif
+
+ do 20 i = 1, nrow
+ w (i) = -1
+20 continue
+
+ do 40 j = 1, ncol
+ ilast = 0
+ do 30 p = Ap (j), Ap (j+1) - 1
+ i = Ai (p)
+ if (i .lt. 1 .or. i .gt. nrow) then
+c error: row index out of range
+c print *, 'column j, rows!', j, i, nrow
+ info = -2
+ return
+ endif
+ if (w (i) .eq. j) then
+c error: duplicate entry in matrix
+c print *, 'column j, duplicate!', j, i
+ info = -3
+ return
+ endif
+ w (i) = j
+ if (i .lt. ilast) then
+c error: matrix contains unsorted columns
+c print *, 'column j, unsorted!', j, i, ilast
+ info = -7
+ return
+ endif
+ ilast = i
+30 continue
+40 continue
+
+c ----------------------------------------------------------------
+c construct new column pointers for symmetric matrices
+c ----------------------------------------------------------------
+
+ if (skind .gt. 0) then
+
+c ------------------------------------------------------------
+c compute the column counts for the whole matrix
+c ------------------------------------------------------------
+
+ do 50 j = 1, ncol+1
+ w (j) = 0
+50 continue
+
+ do 70 j = 1, ncol
+ do 60 p = Ap (j), Ap (j+1)-1
+ i = Ai (p)
+ if (i .eq. j) then
+c diagonal entry, only appears as A(j,j)
+ w (j) = w (j) + 1
+ elseif (i .gt. j) then
+c entry in lower triangular part, A(i,j) will be
+c duplicated as A(j,i), so count it in both cols
+ w (i) = w (i) + 1
+ w (j) = w (j) + 1
+ else
+c error: entry in upper triangular part
+ info = -4
+ return
+ endif
+60 continue
+70 continue
+
+c ------------------------------------------------------------
+c compute the new column pointers
+c ------------------------------------------------------------
+
+ cp (1) = 1
+ do 80 j = 2, ncol+1
+ cp (j) = cp (j-1) + w (j-1)
+80 continue
+
+ endif
+
+c ----------------------------------------------------------------
+c matrix is valid
+c ----------------------------------------------------------------
+
+ info = 0
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBmangle: convert 1-based matrix into 0-based
+c-----------------------------------------------------------------------
+
+ subroutine RBmangle (ncol, Ap, Ai, nnz)
+ integer*8
+ $ ncol, nnz, p, j, Ap (ncol+1), Ai (*)
+ nnz = Ap (ncol + 1) - 1
+
+ do 10 j = 1, ncol+1
+ Ap (j) = Ap (j) - 1
+10 continue
+ do 20 p = 1, nnz
+ Ai (p) = Ai (p) - 1
+20 continue
+
+ return
+ end
+
+c-----------------------------------------------------------------------
+
+ subroutine RBiread (ifmt, n, I, info)
+ integer*8
+ $ n, I (n), info, p
+ character ifmt*16
+ info = 0
+ read (7, ifmt, err = 92, end = 92) (I (p), p = 1, n)
+ return
+92 info = -92
+ return
+ end
+
+c-----------------------------------------------------------------------
+
+ subroutine RBxread (xfmt, n, X, info)
+ integer*8
+ $ mkind, n, info, p
+ double precision X (n)
+ character xfmt*20
+ info = 0
+ read (7, xfmt, err = 94, end = 94) (X (p), p = 1, n)
+ return
+94 info = -94
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBerr: report an error to MATLAB
+c-----------------------------------------------------------------------
+c
+c info = 0 is OK, info < 0 is a fatal error, info > 0 is a warning
+
+ subroutine RBerr (info)
+ integer*8
+ $ info
+
+ if (info .eq. -7) then
+ call mexErrMsgTxt ('matrix contains unsorted columns')
+
+ elseif (info .eq. -1) then
+ call mexErrMsgTxt ('invalid matrix (col pointers)')
+
+ elseif (info .eq. -2) then
+ call mexErrMsgTxt ('row index out of range)')
+
+ elseif (info .eq. -3) then
+ call mexErrMsgTxt ('duplicate entry in matrix')
+
+ elseif (info .eq. -4) then
+ call mexErrMsgTxt ('invalid symmetric matrix')
+
+ elseif (info .eq. -5) then
+ call mexErrMsgTxt ('invalid matrix type')
+
+ elseif (info .eq. -6) then
+ call mexErrMsgTxt ('invalid matrix dimensions')
+
+ elseif (info .eq. -911) then
+ call mexErrMsgTxt ('finite-element form not supported')
+
+ elseif (info .eq. -91) then
+ call mexErrMsgTxt ('error reading file (header)')
+
+ elseif (info .eq. -92) then
+ call mexErrMsgTxt ('error reading file (column pointers)')
+
+ elseif (info .eq. -93) then
+ call mexErrMsgTxt ('error reading file (row indices)')
+
+ elseif (info .eq. -94) then
+ call mexErrMsgTxt ('error reading file (numerical values)')
+
+ elseif (info .eq. -95) then
+ call mexErrMsgTxt ('error reading file (right-hand-side)')
+
+ elseif (info .lt. 0) then
+ print *, info
+ call mexErrMsgTxt ('error (unspecified)')
+
+ elseif (info .gt. 0) then
+ print *, info
+ call mexErrMsgTxt ('warning (unspecified)')
+
+ endif
+ return
+ end
+
diff --git a/RBio/RBread_mex_32.f b/RBio/RBread_mex_32.f
new file mode 100644
index 0000000..38d1dba
--- /dev/null
+++ b/RBio/RBread_mex_32.f
@@ -0,0 +1,239 @@
+c=======================================================================
+c=== RBio/RBread_mex_32 ================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBread mexFunction: read a sparse matrix from a Rutherford/Boeing file
+c-----------------------------------------------------------------------
+c
+c [A Z title key mtype] = RBread (filename)
+c
+c A: a sparse matrix (no explicit zero entries)
+c Z: binary pattern of explicit zero entries in Rutherford/Boeing file.
+c This always has the same size as A, and is always sparse.
+c
+c title: the 72-character title string in the file
+c key: the 8-character matrix name in the file
+c mtype: see RBwrite.m for a description.
+c
+c-----------------------------------------------------------------------
+
+ subroutine mexfunction (nargout, pargout, nargin, pargin)
+ integer*4
+ $ pargout (*), pargin (*)
+ integer*4 nargout, nargin
+
+c ----------------------------------------------------------------
+c MATLAB functions
+c ----------------------------------------------------------------
+
+ integer*4 mxIsChar, mxClassIDFromClassName
+
+ integer*4
+ $ mxGetM, mxGetN, mxCreateSparse, mxGetJc, mxGetData,
+ $ mxGetIr, mxGetPr, mxGetPi, mxGetString, mxCreateString,
+ $ mxCreateNumericMatrix
+
+c ----------------------------------------------------------------
+c local variables
+c ----------------------------------------------------------------
+
+ integer*4
+ $ nrow, ncol, nnz, mkind, w, cp,
+ $ skind, wmat, cpmat, Zmat, nw,
+ $ Ap, Ai, Ax, Az, Cmat, Cx, nzeros, info, Zp, Zi, Zx, i,
+ $ nnz2, nnz1, nelnz, one
+ integer*4 iclass, cmplex, wcmplex
+ character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16,
+ $ valfmt*20, filename*1024
+
+c ----------------------------------------------------------------
+c check inputs
+c ----------------------------------------------------------------
+
+ if (nargin .ne. 1 .or. nargout .gt. 5 .or.
+ $ mxIsChar (pargin (1)) .ne. 1) then
+ call mexErrMsgTxt
+ $ ('Usage: [A Z title key mtype] = RBread (filename)')
+ endif
+
+c ----------------------------------------------------------------
+c get filename and open file
+c ----------------------------------------------------------------
+
+ if (mxGetString (pargin (1), filename, 1024) .ne. 0) then
+ call mexErrMsgTxt ('filename too long')
+ endif
+ close (unit = 7)
+ open (unit = 7, file = filename, status = 'OLD', err = 998)
+ rewind (unit = 7)
+
+c ----------------------------------------------------------------
+c read the header and determine the matrix type
+c ----------------------------------------------------------------
+
+ call RBheader (title, key, mtype, nrow, ncol, nnz,
+ $ ptrfmt, indfmt, valfmt, mkind, cmplex, skind, nelnz, info)
+ if (nelnz .ne. 0) then
+c finite-element matrices not supported
+ info = -5
+ endif
+ call RBerr (info)
+
+c ----------------------------------------------------------------
+c allocate result A
+c ----------------------------------------------------------------
+
+ if (skind .gt. 0) then
+c allocate enough space for upper triangular part (S,H,Z)
+ nnz1 = 2 * nnz
+ else
+ nnz1 = nnz
+ endif
+ nnz1 = max (nnz1, 1)
+
+ pargout (1) = mxCreateSparse (nrow, ncol, nnz1, cmplex)
+ Ap = mxGetJc (pargout (1))
+ Ai = mxGetIr (pargout (1))
+ Ax = mxGetPr (pargout (1))
+ Az = mxGetPi (pargout (1))
+
+c ----------------------------------------------------------------
+c allocate workspace
+c ----------------------------------------------------------------
+
+ iclass = mxClassIDFromClassName ('int32')
+ nw = max (nrow,ncol) + 1
+ wcmplex = 0
+ one = 1
+ wmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex)
+ cpmat = mxCreateNumericMatrix (ncol+1, one, iclass, wcmplex)
+ w = mxGetData (wmat)
+ cp = mxGetData (cpmat)
+
+c ----------------------------------------------------------------
+c read in the sparse matrix
+c ----------------------------------------------------------------
+
+ if (mkind .eq. 2) then
+c complex matrices
+ Cmat = mxCreateNumericMatrix (2 * nnz1, one,
+ $ mxClassIDFromClassName ('double'), wcmplex)
+ Cx = mxGetData (Cmat)
+ call RBcread (nrow, ncol, nnz, ptrfmt, indfmt, valfmt,
+ $ mkind, skind, %val (Ap), %val (Ai), %val (Cx), nzeros,
+ $ %val (w), %val (cp), info, nw, nnz1)
+ else
+c real, pattern, and integer matrices
+ call RBrread (nrow, ncol, nnz, ptrfmt, indfmt, valfmt,
+ $ mkind, skind, %val (Ap), %val (Ai), %val (Ax), nzeros,
+ $ %val (w), %val (cp), info, nw, nnz1)
+ endif
+ call RBerr (info)
+ close (unit = 7)
+
+c ----------------------------------------------------------------
+c extract or discard explicit zero entries
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 2) then
+
+c ------------------------------------------------------------
+c extract explicit zeros from A and store them in Z
+c ------------------------------------------------------------
+
+ pargout (2) = mxCreateSparse
+ $ (nrow, ncol, max (nzeros,1), wcmplex)
+ Zp = mxGetJc (pargout (2))
+ Zi = mxGetIr (pargout (2))
+ Zx = mxGetPr (pargout (2))
+
+ if (mkind .eq. 2) then
+c complex matrices
+ call RBczeros (nrow, ncol, %val (cp),
+ $ %val (Ap), %val (Ai), %val (Cx),
+ $ %val (Zp), %val (Zi), %val (Zx))
+ else
+c real, pattern-only, and integer matrices
+ call RBrzeros (nrow, ncol, %val (cp),
+ $ %val (Ap), %val (Ai), %val (Ax),
+ $ %val (Zp), %val (Zi), %val (Zx))
+ endif
+
+c convert Z to zero-based
+ call RBmangle (ncol, %val (Zp), %val (Zi), i)
+
+ else
+
+c ------------------------------------------------------------
+c discard explicit zero entries from A (do not keep them)
+c ------------------------------------------------------------
+
+ if (mkind .eq. 2) then
+c complex matrices
+ call RBcprune (nrow, ncol,
+ $ %val (Ap), %val (Ai), %val (Cx))
+ else
+c real, pattern-only, and integer matrices
+ call RBrprune (nrow, ncol,
+ $ %val (Ap), %val (Ai), %val (Ax))
+ endif
+
+ endif
+
+c ----------------------------------------------------------------
+c convert A to final MATLAB form (zero-based, split complex)
+c ----------------------------------------------------------------
+
+ call RBmangle (ncol, %val (Ap), %val (Ai), nnz2)
+
+ if (mkind .eq. 2) then
+c convert Fortran-style complex values to MATLAB-style
+ call RBcsplit (%val (Cx), %val (Ax), %val (Az), nnz2)
+ call mxDestroyArray (%val (Cmat))
+ endif
+
+c ----------------------------------------------------------------
+c return title
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 3) then
+ pargout (3) = mxCreateString (title)
+ endif
+
+c ----------------------------------------------------------------
+c return key
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 4) then
+ pargout (4) = mxCreateString (key)
+ endif
+
+c ----------------------------------------------------------------
+c return the matrix type to MATLAB
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 5) then
+ pargout (5) = mxCreateString (mtype)
+ endif
+
+c ----------------------------------------------------------------
+c free workspace and return
+c ----------------------------------------------------------------
+
+ call mxDestroyArray (%val (wmat))
+ call mxDestroyArray (%val (cpmat))
+ return
+
+c ----------------------------------------------------------------
+c error return
+c ----------------------------------------------------------------
+
+998 call mexErrMsgTxt ('error opening file')
+ end
+
diff --git a/RBio/RBread_mex_64.f b/RBio/RBread_mex_64.f
new file mode 100644
index 0000000..ddba795
--- /dev/null
+++ b/RBio/RBread_mex_64.f
@@ -0,0 +1,239 @@
+c=======================================================================
+c=== RBio/RBread_mex_64 ================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBread mexFunction: read a sparse matrix from a Rutherford/Boeing file
+c-----------------------------------------------------------------------
+c
+c [A Z title key mtype] = RBread (filename)
+c
+c A: a sparse matrix (no explicit zero entries)
+c Z: binary pattern of explicit zero entries in Rutherford/Boeing file.
+c This always has the same size as A, and is always sparse.
+c
+c title: the 72-character title string in the file
+c key: the 8-character matrix name in the file
+c mtype: see RBwrite.m for a description.
+c
+c-----------------------------------------------------------------------
+
+ subroutine mexfunction (nargout, pargout, nargin, pargin)
+ integer*8
+ $ pargout (*), pargin (*)
+ integer*4 nargout, nargin
+
+c ----------------------------------------------------------------
+c MATLAB functions
+c ----------------------------------------------------------------
+
+ integer*4 mxIsChar, mxClassIDFromClassName
+
+ integer*8
+ $ mxGetM, mxGetN, mxCreateSparse, mxGetJc, mxGetData,
+ $ mxGetIr, mxGetPr, mxGetPi, mxGetString, mxCreateString,
+ $ mxCreateNumericMatrix
+
+c ----------------------------------------------------------------
+c local variables
+c ----------------------------------------------------------------
+
+ integer*8
+ $ nrow, ncol, nnz, mkind, w, cp,
+ $ skind, wmat, cpmat, Zmat, nw,
+ $ Ap, Ai, Ax, Az, Cmat, Cx, nzeros, info, Zp, Zi, Zx, i,
+ $ nnz2, nnz1, nelnz, one
+ integer*4 iclass, cmplex, wcmplex
+ character title*72, key*8, mtype*3, ptrfmt*16, indfmt*16,
+ $ valfmt*20, filename*1024
+
+c ----------------------------------------------------------------
+c check inputs
+c ----------------------------------------------------------------
+
+ if (nargin .ne. 1 .or. nargout .gt. 5 .or.
+ $ mxIsChar (pargin (1)) .ne. 1) then
+ call mexErrMsgTxt
+ $ ('Usage: [A Z title key mtype] = RBread (filename)')
+ endif
+
+c ----------------------------------------------------------------
+c get filename and open file
+c ----------------------------------------------------------------
+
+ if (mxGetString (pargin (1), filename, 1024) .ne. 0) then
+ call mexErrMsgTxt ('filename too long')
+ endif
+ close (unit = 7)
+ open (unit = 7, file = filename, status = 'OLD', err = 998)
+ rewind (unit = 7)
+
+c ----------------------------------------------------------------
+c read the header and determine the matrix type
+c ----------------------------------------------------------------
+
+ call RBheader (title, key, mtype, nrow, ncol, nnz,
+ $ ptrfmt, indfmt, valfmt, mkind, cmplex, skind, nelnz, info)
+ if (nelnz .ne. 0) then
+c finite-element matrices not supported
+ info = -5
+ endif
+ call RBerr (info)
+
+c ----------------------------------------------------------------
+c allocate result A
+c ----------------------------------------------------------------
+
+ if (skind .gt. 0) then
+c allocate enough space for upper triangular part (S,H,Z)
+ nnz1 = 2 * nnz
+ else
+ nnz1 = nnz
+ endif
+ nnz1 = max (nnz1, 1)
+
+ pargout (1) = mxCreateSparse (nrow, ncol, nnz1, cmplex)
+ Ap = mxGetJc (pargout (1))
+ Ai = mxGetIr (pargout (1))
+ Ax = mxGetPr (pargout (1))
+ Az = mxGetPi (pargout (1))
+
+c ----------------------------------------------------------------
+c allocate workspace
+c ----------------------------------------------------------------
+
+ iclass = mxClassIDFromClassName ('int64')
+ nw = max (nrow,ncol) + 1
+ wcmplex = 0
+ one = 1
+ wmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex)
+ cpmat = mxCreateNumericMatrix (ncol+1, one, iclass, wcmplex)
+ w = mxGetData (wmat)
+ cp = mxGetData (cpmat)
+
+c ----------------------------------------------------------------
+c read in the sparse matrix
+c ----------------------------------------------------------------
+
+ if (mkind .eq. 2) then
+c complex matrices
+ Cmat = mxCreateNumericMatrix (2 * nnz1, one,
+ $ mxClassIDFromClassName ('double'), wcmplex)
+ Cx = mxGetData (Cmat)
+ call RBcread (nrow, ncol, nnz, ptrfmt, indfmt, valfmt,
+ $ mkind, skind, %val (Ap), %val (Ai), %val (Cx), nzeros,
+ $ %val (w), %val (cp), info, nw, nnz1)
+ else
+c real, pattern, and integer matrices
+ call RBrread (nrow, ncol, nnz, ptrfmt, indfmt, valfmt,
+ $ mkind, skind, %val (Ap), %val (Ai), %val (Ax), nzeros,
+ $ %val (w), %val (cp), info, nw, nnz1)
+ endif
+ call RBerr (info)
+ close (unit = 7)
+
+c ----------------------------------------------------------------
+c extract or discard explicit zero entries
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 2) then
+
+c ------------------------------------------------------------
+c extract explicit zeros from A and store them in Z
+c ------------------------------------------------------------
+
+ pargout (2) = mxCreateSparse
+ $ (nrow, ncol, max (nzeros,1), wcmplex)
+ Zp = mxGetJc (pargout (2))
+ Zi = mxGetIr (pargout (2))
+ Zx = mxGetPr (pargout (2))
+
+ if (mkind .eq. 2) then
+c complex matrices
+ call RBczeros (nrow, ncol, %val (cp),
+ $ %val (Ap), %val (Ai), %val (Cx),
+ $ %val (Zp), %val (Zi), %val (Zx))
+ else
+c real, pattern-only, and integer matrices
+ call RBrzeros (nrow, ncol, %val (cp),
+ $ %val (Ap), %val (Ai), %val (Ax),
+ $ %val (Zp), %val (Zi), %val (Zx))
+ endif
+
+c convert Z to zero-based
+ call RBmangle (ncol, %val (Zp), %val (Zi), i)
+
+ else
+
+c ------------------------------------------------------------
+c discard explicit zero entries from A (do not keep them)
+c ------------------------------------------------------------
+
+ if (mkind .eq. 2) then
+c complex matrices
+ call RBcprune (nrow, ncol,
+ $ %val (Ap), %val (Ai), %val (Cx))
+ else
+c real, pattern-only, and integer matrices
+ call RBrprune (nrow, ncol,
+ $ %val (Ap), %val (Ai), %val (Ax))
+ endif
+
+ endif
+
+c ----------------------------------------------------------------
+c convert A to final MATLAB form (zero-based, split complex)
+c ----------------------------------------------------------------
+
+ call RBmangle (ncol, %val (Ap), %val (Ai), nnz2)
+
+ if (mkind .eq. 2) then
+c convert Fortran-style complex values to MATLAB-style
+ call RBcsplit (%val (Cx), %val (Ax), %val (Az), nnz2)
+ call mxDestroyArray (%val (Cmat))
+ endif
+
+c ----------------------------------------------------------------
+c return title
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 3) then
+ pargout (3) = mxCreateString (title)
+ endif
+
+c ----------------------------------------------------------------
+c return key
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 4) then
+ pargout (4) = mxCreateString (key)
+ endif
+
+c ----------------------------------------------------------------
+c return the matrix type to MATLAB
+c ----------------------------------------------------------------
+
+ if (nargout .ge. 5) then
+ pargout (5) = mxCreateString (mtype)
+ endif
+
+c ----------------------------------------------------------------
+c free workspace and return
+c ----------------------------------------------------------------
+
+ call mxDestroyArray (%val (wmat))
+ call mxDestroyArray (%val (cpmat))
+ return
+
+c ----------------------------------------------------------------
+c error return
+c ----------------------------------------------------------------
+
+998 call mexErrMsgTxt ('error opening file')
+ end
+
diff --git a/RBio/RBreade.m b/RBio/RBreade.m
new file mode 100644
index 0000000..2c81c59
--- /dev/null
+++ b/RBio/RBreade.m
@@ -0,0 +1,136 @@
+function [A, Z, title, key, mtype] = RBreade (filename)
+%RBREADE read a symmetric finite-element matrix from a R/B file
+% Usage:
+% [A Z title key mtype] = RBreade (filename)
+%
+% The file must contain a Rutherford/Boeing matrix of type *se or *he, where *
+% can be r, p, i, or c. See RBread for a description of the outputs.
+%
+% If CHOLMOD is installed, this function is faster and uses less memory.
+%
+% Example:
+%
+% [A Z title key mtype] = RBreade ('lap_25.pse') ;
+%
+% See also RBread, RBraw, sparse2.
+
+% Optionally uses the CHOLMOD sparse2 mexFunction.
+
+% Copyright 2007, Timothy A. Davis
+
+%-------------------------------------------------------------------------------
+% read in the raw contents of the Rutherford/Boeing file
+%-------------------------------------------------------------------------------
+
+[mtype Ap Ai Ax title key n] = RBraw (filename) ;
+mtype = lower (mtype) ;
+if (~(mtype (2) == 's' | mtype (2) == 'h') | (mtype (3) ~= 'e')) %#ok
+ error ('RBreade is only for symmetric unassembled finite-element matrices');
+end
+
+%-------------------------------------------------------------------------------
+% determine dimension, number of elements, and convert numerical entries
+%-------------------------------------------------------------------------------
+
+Ap = double (Ap) ;
+Ai = double (Ai) ;
+
+% number of elements
+ne = length (Ap) - 1 ;
+
+% dimension.
+if (max (Ai) > n)
+ error ('invalid dimension') ;
+end
+
+% determine number of numerical entries
+nz = 0 ;
+for e = 1:ne
+ p1 = Ap (e) ;
+ p2 = Ap (e+1) - 1 ;
+ nu = p2 - p1 + 1 ;
+ nz = nz + (nu * (nu+1)/2) ;
+end
+
+% Ax can be empty, for a pse matrix
+if (~isempty (Ax))
+ if (mtype (1) == 'c')
+ % Ax is real, with real/imaginary parts interleaved
+ if (2 * nz ~= length (Ax))
+ error ('invalid matrix (wrong number of complex values)') ;
+ end
+ Ax = Ax (1:2:end) + (1i * Ax (2:2:end)) ;
+ elseif (mtype (1) == 'i')
+ Ax = double (Ax) ;
+ end
+ % numerical values must be of the right size
+ if (nz ~= length (Ax))
+ error ('invalid matrix (wrong number of values)') ;
+ end
+end
+
+%-------------------------------------------------------------------------------
+% create triplet form
+%-------------------------------------------------------------------------------
+
+% row and column indices for triplet form of the matrix
+ii = zeros (nz, 1) ;
+jj = zeros (nz, 1) ;
+
+nx = 0 ;
+
+% create triplet row and column indices from finite-element pattern
+for e = 1:ne
+ p1 = Ap (e) ;
+ p2 = Ap (e+1) - 1 ;
+ for p = p1:p2
+ j = Ai (p) ;
+ for pp = p:p2
+ i = Ai (pp) ;
+ nx = nx + 1 ;
+ ii (nx) = max (i,j) ;
+ jj (nx) = min (i,j) ;
+ end
+ end
+end
+
+%-------------------------------------------------------------------------------
+% create the sparse matrix form
+%-------------------------------------------------------------------------------
+
+if (exist ('sparse2') == 3) %#ok
+ % Use sparse2 in CHOLMOD. It's faster, allows integer Ai and Aj, and
+ % returns the Z matrix as the 2nd output argument.
+ if (isempty (Ax))
+ Ax = 1 ;
+ end
+ % numerical matrix
+ [A Z] = sparse2 (ii, jj, Ax, n, n) ;
+else
+ % stick with MATLAB, without CHOLMOD. This is slower and takes more memory.
+ if (isempty (Ax))
+ % pattern-only matrix
+ A = spones (sparse (ii, jj, 1, n, n)) ;
+ Z = sparse (n, n) ;
+ else
+ % numerical matrix
+ A = sparse (ii, jj, Ax, n, n) ;
+ % determine the pattern of explicit zero entries
+ S = spones (sparse (ii, jj, 1, n, n)) ;
+ Z = S - spones (A) ;
+ end
+end
+
+% add the upper triangular part
+if (mtype (2) == 's')
+ A = A + tril (A,-1).' ;
+elseif (mtype (2) == 'h')
+ A = A + tril (A,-1)' ;
+end
+Z = Z + tril (Z,-1)' ;
+
+% remove duplicates created from triplet form for a pattern-only matrix
+if (mtype (1) == 'p')
+ A = spones (A) ;
+end
+
diff --git a/RBio/RBrread_32.f b/RBio/RBrread_32.f
new file mode 100644
index 0000000..938dc80
--- /dev/null
+++ b/RBio/RBrread_32.f
@@ -0,0 +1,299 @@
+c=======================================================================
+c=== RBio/RBrread_32 ===================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RB*read: read a Rutherford/Boeing matrix
+c-----------------------------------------------------------------------
+
+ subroutine RBrread
+ $ (nrow, ncol, nnz, ptrfmt, indfmt, valfmt,
+ $ mkind, skind, Ap, Ai, Ax, nzeros, w, cp, info, nw, nnz1)
+ integer*4
+ $ nrow, ncol, nnz, mkind, skind, p, j, i, alen, llen, k,
+ $ ilast, nzeros, info, nw, nnz1
+ integer*4
+ $ Ap (ncol+1), Ai (nnz1), w (nw), cp (ncol+1)
+ double precision Ax (nnz1), x
+ character ptrfmt*16, indfmt*16, valfmt*20
+ character*4 s
+
+c ----------------------------------------------------------------
+c read the column pointers and row indices
+c ----------------------------------------------------------------
+
+ call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind,
+ $ Ap, Ai, w, cp, info, nw)
+ if (info .ne. 0) then
+c error: pattern is invalid
+ return
+ endif
+
+c ----------------------------------------------------------------
+c read the values
+c ----------------------------------------------------------------
+
+ if (mkind .eq. 1) then
+
+c pattern-only matrix, set all values to 1
+ do 10 i = 1, nnz
+ Ax (i) = 1
+10 continue
+
+ elseif (mkind .eq. 3) then
+
+c Read in nnz integer values, then convert them to real.
+c use Ai as workspace. If the matrix is symmetric, Ai is
+c twice as big as nnz, so use Ai (nnz+1...2*nnz) as workspace.
+c Otherwise, for an iua matrix, use Ai (1..nnz) and then
+c rewind the file and read Ap and Ai back in again.
+
+ if (skind .le. 0) then
+ k = 0
+ else
+ k = nnz
+ endif
+ read (7, valfmt, err = 94, end = 94) (Ai(p), p = k+1, k+nnz)
+ do 5 p = 1, nnz
+ Ax (p) = Ai (p+k)
+5 continue
+ if (skind .le. 0) then
+c now that Ai has been destroyed, rewind the file and read
+c in Ap and Ai again. Skip the 4-line header first.
+ rewind (unit = 7)
+ read (7, 15) (s (k:k), k = 1,4)
+15 format (a1 / a1 / a1 / a1)
+ call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind,
+ $ Ap, Ai, w, cp, info, nw)
+ if (info .ne. 0) then
+c error: pattern is invalid. This 'cannot' happen,
+c because the pattern was already read in above.
+ return
+ endif
+ endif
+
+ else
+
+c read nnz values
+ read (7, valfmt, err = 94, end = 94) (Ax (p), p = 1, nnz)
+
+ endif
+
+c ----------------------------------------------------------------
+c construct upper triangular part for symmetric matrices
+c ----------------------------------------------------------------
+
+c If skind is zero, then the upper part is not constructed. This
+c allows the caller to skip this part, and create the upper part
+c of a symmetric (S,H,Z) matrix. Just pass skind = 0.
+
+ if (skind .gt. 0) then
+
+c ------------------------------------------------------------
+c shift the matrix by adding gaps to the top of each column
+c ------------------------------------------------------------
+
+ do 30 j = ncol, 1, -1
+
+c number of entries in lower tri. part (incl. diagonal)
+ llen = Ap (j+1) - Ap (j)
+
+c number of entries in entire column
+ alen = cp (j+1) - cp (j)
+
+c move the column from Ai (Ap(j) ... Ap(j+1)-1)
+c down to Ai (cp(j+1)-llen ... cp(j+1)-1), leaving a gap
+c at Ai (Ap(j) ... cp(j+1)-llen)
+
+ do 20 k = 1, llen
+ Ai (cp (j+1) - k) = Ai (Ap (j+1) - k)
+ Ax (cp (j+1) - k) = Ax (Ap (j+1) - k)
+20 continue
+30 continue
+
+c ------------------------------------------------------------
+c populate the upper triangular part
+c ------------------------------------------------------------
+
+c create temporary column pointers to point to the gaps
+ do 40 j = 1, ncol
+ w (j) = cp (j)
+40 continue
+
+ do 60 j = 1, ncol
+
+c scan the entries in the lower tri. part, in
+c Ai (cp(j+1)-llen ... cp(j+1)-1)
+ llen = Ap (j+1) - Ap (j)
+ do 50 k = 1, llen
+
+c get the A(i,j) entry in the lower triangular part
+ i = Ai (cp (j+1) - k)
+ x = Ax (cp (j+1) - k)
+
+c add A(j,i) as the next entry in column i (excl diag)
+ if (i .ne. j) then
+ p = w (i)
+ w (i) = w (i) + 1
+ Ai (p) = j
+
+ if (skind .eq. 1) then
+c *SA matrix
+ Ax (p) = x
+ elseif (skind .eq. 2) then
+c *HA matrix
+ Ax (p) = x
+ else
+c *ZA matrix
+ Ax (p) = -x
+ endif
+
+ endif
+
+50 continue
+60 continue
+
+c finalize the column pointers
+ do 70 j = 1, ncol+1
+ Ap (j) = cp (j)
+70 continue
+
+ endif
+
+c ----------------------------------------------------------------
+c count the number of explicit zeros
+c ----------------------------------------------------------------
+
+ nzeros = 0
+ do 90 j = 1, ncol
+ cp (j) = nzeros + 1
+ do 80 p = Ap (j), Ap (j+1)-1
+ if (Ax (p) .eq. 0) then
+ nzeros = nzeros + 1
+ endif
+80 continue
+90 continue
+ cp (ncol+1) = nzeros + 1
+
+c ----------------------------------------------------------------
+c matrix is valid
+c ----------------------------------------------------------------
+
+ info = 0
+ return
+
+c ----------------------------------------------------------------
+c error return
+c ----------------------------------------------------------------
+
+94 info = -94
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RB*zeros: extract explicit zero entries
+c-----------------------------------------------------------------------
+c
+c nrow-by-ncol: size of A and Z
+c cp: column pointers of Z on input
+c Ap, Ai, Ax: matrix with zeros on input, pruned on output
+c Zp, Zi, Zx: empty matrix on input, pattern of zeros on output
+c
+c-----------------------------------------------------------------------
+
+ subroutine RBrzeros
+ $ (nrow, ncol, cp, Ap, Ai, Ax, Zp, Zi, Zx)
+ integer*4
+ $ nrow, ncol, Ap (ncol+1), Ai (*), Zp (ncol+1), Zi (*),
+ $ cp (*), i, j, p, pa, pz, p1
+ double precision Ax (*), x
+ double precision Zx (*)
+
+c ----------------------------------------------------------------
+c copy the column pointers if Z is being constructed
+c ----------------------------------------------------------------
+
+ do 10 j = 1, ncol+1
+ Zp (j) = cp (j)
+10 continue
+
+c ----------------------------------------------------------------
+c split the matrix
+c ----------------------------------------------------------------
+
+ pa = 1
+ pz = 1
+ do 30 j = 1, ncol
+c save the new start of column j of A
+ p1 = Ap (j)
+ Ap (j) = pa
+ pz = Zp (j)
+c split column j of A
+ do 20 p = p1, Ap (j+1)-1
+ i = Ai (p)
+ x = Ax (p)
+ if (x .eq. 0) then
+c copy into Z
+ Zi (pz) = i
+ Zx (pz) = 1
+ pz = pz + 1
+ else
+c copy into A
+ Ai (pa) = i
+ Ax (pa) = x
+ pa = pa + 1
+ endif
+20 continue
+30 continue
+ Ap (ncol+1) = pa
+
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RB*prune: discard explicit zero entries
+c-----------------------------------------------------------------------
+c
+c nrow-by-ncol: size of A
+c Ap, Ai, Ax: matrix with zeros on input, pruned on output
+c
+c-----------------------------------------------------------------------
+
+ subroutine RBrprune
+ $ (nrow, ncol, Ap, Ai, Ax)
+ integer*4
+ $ nrow, ncol, Ap (ncol+1), Ai (*), i, j, p, pa, pz, p1
+ double precision Ax (*), x
+
+c ----------------------------------------------------------------
+c prune the matrix
+c ----------------------------------------------------------------
+
+ pa = 1
+ do 20 j = 1, ncol
+c save the new start of column j of A
+ p1 = Ap (j)
+ Ap (j) = pa
+c prune column j of A
+ do 10 p = p1, Ap (j+1)-1
+ i = Ai (p)
+ x = Ax (p)
+ if (x .ne. 0) then
+c copy into A
+ Ai (pa) = i
+ Ax (pa) = x
+ pa = pa + 1
+ endif
+10 continue
+20 continue
+ Ap (ncol+1) = pa
+
+ return
+ end
diff --git a/RBio/RBrread_64.f b/RBio/RBrread_64.f
new file mode 100644
index 0000000..9b941a3
--- /dev/null
+++ b/RBio/RBrread_64.f
@@ -0,0 +1,299 @@
+c=======================================================================
+c=== RBio/RBrread_64 ===================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RB*read: read a Rutherford/Boeing matrix
+c-----------------------------------------------------------------------
+
+ subroutine RBrread
+ $ (nrow, ncol, nnz, ptrfmt, indfmt, valfmt,
+ $ mkind, skind, Ap, Ai, Ax, nzeros, w, cp, info, nw, nnz1)
+ integer*8
+ $ nrow, ncol, nnz, mkind, skind, p, j, i, alen, llen, k,
+ $ ilast, nzeros, info, nw, nnz1
+ integer*8
+ $ Ap (ncol+1), Ai (nnz1), w (nw), cp (ncol+1)
+ double precision Ax (nnz1), x
+ character ptrfmt*16, indfmt*16, valfmt*20
+ character*4 s
+
+c ----------------------------------------------------------------
+c read the column pointers and row indices
+c ----------------------------------------------------------------
+
+ call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind,
+ $ Ap, Ai, w, cp, info, nw)
+ if (info .ne. 0) then
+c error: pattern is invalid
+ return
+ endif
+
+c ----------------------------------------------------------------
+c read the values
+c ----------------------------------------------------------------
+
+ if (mkind .eq. 1) then
+
+c pattern-only matrix, set all values to 1
+ do 10 i = 1, nnz
+ Ax (i) = 1
+10 continue
+
+ elseif (mkind .eq. 3) then
+
+c Read in nnz integer values, then convert them to real.
+c use Ai as workspace. If the matrix is symmetric, Ai is
+c twice as big as nnz, so use Ai (nnz+1...2*nnz) as workspace.
+c Otherwise, for an iua matrix, use Ai (1..nnz) and then
+c rewind the file and read Ap and Ai back in again.
+
+ if (skind .le. 0) then
+ k = 0
+ else
+ k = nnz
+ endif
+ read (7, valfmt, err = 94, end = 94) (Ai(p), p = k+1, k+nnz)
+ do 5 p = 1, nnz
+ Ax (p) = Ai (p+k)
+5 continue
+ if (skind .le. 0) then
+c now that Ai has been destroyed, rewind the file and read
+c in Ap and Ai again. Skip the 4-line header first.
+ rewind (unit = 7)
+ read (7, 15) (s (k:k), k = 1,4)
+15 format (a1 / a1 / a1 / a1)
+ call RBpattern (ptrfmt, indfmt, nrow, ncol, nnz, skind,
+ $ Ap, Ai, w, cp, info, nw)
+ if (info .ne. 0) then
+c error: pattern is invalid. This 'cannot' happen,
+c because the pattern was already read in above.
+ return
+ endif
+ endif
+
+ else
+
+c read nnz values
+ read (7, valfmt, err = 94, end = 94) (Ax (p), p = 1, nnz)
+
+ endif
+
+c ----------------------------------------------------------------
+c construct upper triangular part for symmetric matrices
+c ----------------------------------------------------------------
+
+c If skind is zero, then the upper part is not constructed. This
+c allows the caller to skip this part, and create the upper part
+c of a symmetric (S,H,Z) matrix. Just pass skind = 0.
+
+ if (skind .gt. 0) then
+
+c ------------------------------------------------------------
+c shift the matrix by adding gaps to the top of each column
+c ------------------------------------------------------------
+
+ do 30 j = ncol, 1, -1
+
+c number of entries in lower tri. part (incl. diagonal)
+ llen = Ap (j+1) - Ap (j)
+
+c number of entries in entire column
+ alen = cp (j+1) - cp (j)
+
+c move the column from Ai (Ap(j) ... Ap(j+1)-1)
+c down to Ai (cp(j+1)-llen ... cp(j+1)-1), leaving a gap
+c at Ai (Ap(j) ... cp(j+1)-llen)
+
+ do 20 k = 1, llen
+ Ai (cp (j+1) - k) = Ai (Ap (j+1) - k)
+ Ax (cp (j+1) - k) = Ax (Ap (j+1) - k)
+20 continue
+30 continue
+
+c ------------------------------------------------------------
+c populate the upper triangular part
+c ------------------------------------------------------------
+
+c create temporary column pointers to point to the gaps
+ do 40 j = 1, ncol
+ w (j) = cp (j)
+40 continue
+
+ do 60 j = 1, ncol
+
+c scan the entries in the lower tri. part, in
+c Ai (cp(j+1)-llen ... cp(j+1)-1)
+ llen = Ap (j+1) - Ap (j)
+ do 50 k = 1, llen
+
+c get the A(i,j) entry in the lower triangular part
+ i = Ai (cp (j+1) - k)
+ x = Ax (cp (j+1) - k)
+
+c add A(j,i) as the next entry in column i (excl diag)
+ if (i .ne. j) then
+ p = w (i)
+ w (i) = w (i) + 1
+ Ai (p) = j
+
+ if (skind .eq. 1) then
+c *SA matrix
+ Ax (p) = x
+ elseif (skind .eq. 2) then
+c *HA matrix
+ Ax (p) = x
+ else
+c *ZA matrix
+ Ax (p) = -x
+ endif
+
+ endif
+
+50 continue
+60 continue
+
+c finalize the column pointers
+ do 70 j = 1, ncol+1
+ Ap (j) = cp (j)
+70 continue
+
+ endif
+
+c ----------------------------------------------------------------
+c count the number of explicit zeros
+c ----------------------------------------------------------------
+
+ nzeros = 0
+ do 90 j = 1, ncol
+ cp (j) = nzeros + 1
+ do 80 p = Ap (j), Ap (j+1)-1
+ if (Ax (p) .eq. 0) then
+ nzeros = nzeros + 1
+ endif
+80 continue
+90 continue
+ cp (ncol+1) = nzeros + 1
+
+c ----------------------------------------------------------------
+c matrix is valid
+c ----------------------------------------------------------------
+
+ info = 0
+ return
+
+c ----------------------------------------------------------------
+c error return
+c ----------------------------------------------------------------
+
+94 info = -94
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RB*zeros: extract explicit zero entries
+c-----------------------------------------------------------------------
+c
+c nrow-by-ncol: size of A and Z
+c cp: column pointers of Z on input
+c Ap, Ai, Ax: matrix with zeros on input, pruned on output
+c Zp, Zi, Zx: empty matrix on input, pattern of zeros on output
+c
+c-----------------------------------------------------------------------
+
+ subroutine RBrzeros
+ $ (nrow, ncol, cp, Ap, Ai, Ax, Zp, Zi, Zx)
+ integer*8
+ $ nrow, ncol, Ap (ncol+1), Ai (*), Zp (ncol+1), Zi (*),
+ $ cp (*), i, j, p, pa, pz, p1
+ double precision Ax (*), x
+ double precision Zx (*)
+
+c ----------------------------------------------------------------
+c copy the column pointers if Z is being constructed
+c ----------------------------------------------------------------
+
+ do 10 j = 1, ncol+1
+ Zp (j) = cp (j)
+10 continue
+
+c ----------------------------------------------------------------
+c split the matrix
+c ----------------------------------------------------------------
+
+ pa = 1
+ pz = 1
+ do 30 j = 1, ncol
+c save the new start of column j of A
+ p1 = Ap (j)
+ Ap (j) = pa
+ pz = Zp (j)
+c split column j of A
+ do 20 p = p1, Ap (j+1)-1
+ i = Ai (p)
+ x = Ax (p)
+ if (x .eq. 0) then
+c copy into Z
+ Zi (pz) = i
+ Zx (pz) = 1
+ pz = pz + 1
+ else
+c copy into A
+ Ai (pa) = i
+ Ax (pa) = x
+ pa = pa + 1
+ endif
+20 continue
+30 continue
+ Ap (ncol+1) = pa
+
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RB*prune: discard explicit zero entries
+c-----------------------------------------------------------------------
+c
+c nrow-by-ncol: size of A
+c Ap, Ai, Ax: matrix with zeros on input, pruned on output
+c
+c-----------------------------------------------------------------------
+
+ subroutine RBrprune
+ $ (nrow, ncol, Ap, Ai, Ax)
+ integer*8
+ $ nrow, ncol, Ap (ncol+1), Ai (*), i, j, p, pa, pz, p1
+ double precision Ax (*), x
+
+c ----------------------------------------------------------------
+c prune the matrix
+c ----------------------------------------------------------------
+
+ pa = 1
+ do 20 j = 1, ncol
+c save the new start of column j of A
+ p1 = Ap (j)
+ Ap (j) = pa
+c prune column j of A
+ do 10 p = p1, Ap (j+1)-1
+ i = Ai (p)
+ x = Ax (p)
+ if (x .ne. 0) then
+c copy into A
+ Ai (pa) = i
+ Ax (pa) = x
+ pa = pa + 1
+ endif
+10 continue
+20 continue
+ Ap (ncol+1) = pa
+
+ return
+ end
diff --git a/RBio/RBtype.m b/RBio/RBtype.m
new file mode 100644
index 0000000..d72d439
--- /dev/null
+++ b/RBio/RBtype.m
@@ -0,0 +1,39 @@
+function [mtype, mkind, skind] = RBtype (A) %#ok
+%RBTYPE determine the Rutherford/Boeing type of a sparse matrix
+% Usage:
+% [mtype mkind skind] = RBtype (A)
+%
+% A must be a sparse matrix. RBtype determines the Rutherford/Boeing type of A.
+% Very little memory is used (just size(A,2) integer workspace), so this can
+% succeed where a test such as nnz(A-A')==0 will fail.
+%
+% mkind: R: (0), A is real, and not binary
+% P: (1), A is binary (all values or 0 or 1)
+% C: (2), A is complex
+% I: (3), A is integer
+%
+% skind: R: (-1), A is rectangular
+% U: (0), A is unsymmetric (not S, H, or Z)
+% S: (1), A is symmetric (nnz(A-A.') is 0)
+% H: (2), A is Hermitian (nnz(A-A') is 0)
+% Z: (3), A is skew symmetric (nnz(A+A.') is 0)
+%
+% mtype is a 3-character string, where mtype(1) is the mkind
+% ('R', 'P', or 'C'). mtype(2) is the skind ('R', 'U', 'S', 'H', or 'Z'),
+% and mtype(3) is 'A'.
+%
+% Example:
+% load west0479
+% A = west0479 ;
+% RBtype (A)
+% RBtype (spones (A))
+% RBtype (2*spones (A))
+% C = A+A' ;
+% RBtype (C)
+%
+% See also RBread, RBwrite.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+error ('RBtype mexFunction not found') ;
+
diff --git a/RBio/RBtype_mex_32.f b/RBio/RBtype_mex_32.f
new file mode 100644
index 0000000..77dff16
--- /dev/null
+++ b/RBio/RBtype_mex_32.f
@@ -0,0 +1,128 @@
+c=======================================================================
+c=== RBio/RBtype_mex_32 ================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBtype mexFunction:
+c-----------------------------------------------------------------------
+c
+c [mtype mkind skind] = RBtype (A)
+c
+c A: a sparse matrix. Determines the Rutherford/Boeing type of the
+c matrix. Very little memory is used (just size(A,2) integer
+c workspace), so this can succeed where a test such as nnz(A-A')==0
+c will fail.
+c
+c mkind: r: (0), A is real, and not binary
+c p: (1), A is binary
+c c: (2), A is complex
+c i: (3), A is integer
+c
+c skind: r: (-1), A is rectangular
+c u: (0), A is unsymmetric (not S, H, Z, below)
+c s: (1), A is symmetric (nnz(A-A.') is 0)
+c h: (2), A is Hermitian (nnz(A-A') is 0)
+c z: (3), A is skew symmetric (nnz(A+A.') is 0)
+c
+c mtype is a 3-character string, where mtype(1) is the mkind
+c ('r', 'p', 'c', or 'i'). mtype(2) is the skind ('r', 'u', 's', 'h',
+c or 'z'), and mtype(3) is always 'a'.
+c-----------------------------------------------------------------------
+
+ subroutine mexfunction (nargout, pargout, nargin, pargin)
+ integer*4
+ $ pargout (*), pargin (*)
+ integer*4 nargout, nargin
+
+c ----------------------------------------------------------------
+c MATLAB functions
+c ----------------------------------------------------------------
+
+ integer*4 mxClassIDFromClassName,
+ $ mxIsClass, mxIsSparse, mxIsComplex
+
+ integer*4
+ $ mxGetM, mxGetN, mxGetJc, mxGetIr, mxGetPr, mxGetPi,
+ $ mxGetData, mxCreateNumericMatrix, mxCreateDoubleScalar,
+ $ mxCreateString
+
+c ----------------------------------------------------------------
+c local variables
+c ----------------------------------------------------------------
+
+ integer*4
+ $ nrow, ncol, nnz, mkind, cp, skind, cpmat,
+ $ Ap, Ai, Ax, Az, kmin, kmax, one
+ integer*4 iclass, cmplex, wcmplex
+ character mtype*3
+ double precision t
+
+c ----------------------------------------------------------------
+c check inputs
+c ----------------------------------------------------------------
+
+ if (nargin .ne. 1 .or. nargout .gt. 3) then
+ call mexErrMsgTxt ('[mtype mkind skind] = RBtype (A)')
+ endif
+
+c ----------------------------------------------------------------
+c get A
+c ----------------------------------------------------------------
+
+ if (mxIsClass (pargin (1), 'double') .ne. 1 .or.
+ $ mxIsSparse (pargin (1)) .ne. 1) then
+ call mexErrMsgTxt ('A must be sparse and double')
+ endif
+ cmplex = mxIsComplex (pargin (1))
+ Ap = mxGetJc (pargin (1))
+ Ai = mxGetIr (pargin (1))
+ Ax = mxGetPr (pargin (1))
+ Az = mxGetPi (pargin (1))
+ nrow = mxGetM (pargin (1))
+ ncol = mxGetN (pargin (1))
+
+c ----------------------------------------------------------------
+c allocate workspace
+c ----------------------------------------------------------------
+
+ iclass = mxClassIDFromClassName ('int32')
+ one = 1
+ wcmplex = 0
+ cpmat = mxCreateNumericMatrix (ncol+1, one, iclass, wcmplex)
+ cp = mxGetData (cpmat)
+
+c ----------------------------------------------------------------
+c determine the mtype of A
+c ----------------------------------------------------------------
+
+ call RBkind (nrow, ncol, %val(Ap), %val(Ai), %val(Ax),
+ $ %val(Az), cmplex, mkind, skind, mtype, nnz, %val(cp),
+ $ kmin, kmax)
+
+c ----------------------------------------------------------------
+c return the result
+c ----------------------------------------------------------------
+
+ pargout (1) = mxCreateString (mtype)
+ if (nargout .ge. 2) then
+ t = mkind
+ pargout (2) = mxCreateDoubleScalar (t)
+ endif
+ if (nargout .ge. 3) then
+ t = skind
+ pargout (3) = mxCreateDoubleScalar (t)
+ endif
+
+c ----------------------------------------------------------------
+c free workspace
+c ----------------------------------------------------------------
+
+ call mxDestroyArray (%val (cpmat))
+ return
+ end
+
diff --git a/RBio/RBtype_mex_64.f b/RBio/RBtype_mex_64.f
new file mode 100644
index 0000000..9190ffc
--- /dev/null
+++ b/RBio/RBtype_mex_64.f
@@ -0,0 +1,128 @@
+c=======================================================================
+c=== RBio/RBtype_mex_64 ================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBtype mexFunction:
+c-----------------------------------------------------------------------
+c
+c [mtype mkind skind] = RBtype (A)
+c
+c A: a sparse matrix. Determines the Rutherford/Boeing type of the
+c matrix. Very little memory is used (just size(A,2) integer
+c workspace), so this can succeed where a test such as nnz(A-A')==0
+c will fail.
+c
+c mkind: r: (0), A is real, and not binary
+c p: (1), A is binary
+c c: (2), A is complex
+c i: (3), A is integer
+c
+c skind: r: (-1), A is rectangular
+c u: (0), A is unsymmetric (not S, H, Z, below)
+c s: (1), A is symmetric (nnz(A-A.') is 0)
+c h: (2), A is Hermitian (nnz(A-A') is 0)
+c z: (3), A is skew symmetric (nnz(A+A.') is 0)
+c
+c mtype is a 3-character string, where mtype(1) is the mkind
+c ('r', 'p', 'c', or 'i'). mtype(2) is the skind ('r', 'u', 's', 'h',
+c or 'z'), and mtype(3) is always 'a'.
+c-----------------------------------------------------------------------
+
+ subroutine mexfunction (nargout, pargout, nargin, pargin)
+ integer*8
+ $ pargout (*), pargin (*)
+ integer*4 nargout, nargin
+
+c ----------------------------------------------------------------
+c MATLAB functions
+c ----------------------------------------------------------------
+
+ integer*4 mxClassIDFromClassName,
+ $ mxIsClass, mxIsSparse, mxIsComplex
+
+ integer*8
+ $ mxGetM, mxGetN, mxGetJc, mxGetIr, mxGetPr, mxGetPi,
+ $ mxGetData, mxCreateNumericMatrix, mxCreateDoubleScalar,
+ $ mxCreateString
+
+c ----------------------------------------------------------------
+c local variables
+c ----------------------------------------------------------------
+
+ integer*8
+ $ nrow, ncol, nnz, mkind, cp, skind, cpmat,
+ $ Ap, Ai, Ax, Az, kmin, kmax, one
+ integer*4 iclass, cmplex, wcmplex
+ character mtype*3
+ double precision t
+
+c ----------------------------------------------------------------
+c check inputs
+c ----------------------------------------------------------------
+
+ if (nargin .ne. 1 .or. nargout .gt. 3) then
+ call mexErrMsgTxt ('[mtype mkind skind] = RBtype (A)')
+ endif
+
+c ----------------------------------------------------------------
+c get A
+c ----------------------------------------------------------------
+
+ if (mxIsClass (pargin (1), 'double') .ne. 1 .or.
+ $ mxIsSparse (pargin (1)) .ne. 1) then
+ call mexErrMsgTxt ('A must be sparse and double')
+ endif
+ cmplex = mxIsComplex (pargin (1))
+ Ap = mxGetJc (pargin (1))
+ Ai = mxGetIr (pargin (1))
+ Ax = mxGetPr (pargin (1))
+ Az = mxGetPi (pargin (1))
+ nrow = mxGetM (pargin (1))
+ ncol = mxGetN (pargin (1))
+
+c ----------------------------------------------------------------
+c allocate workspace
+c ----------------------------------------------------------------
+
+ iclass = mxClassIDFromClassName ('int64')
+ one = 1
+ wcmplex = 0
+ cpmat = mxCreateNumericMatrix (ncol+1, one, iclass, wcmplex)
+ cp = mxGetData (cpmat)
+
+c ----------------------------------------------------------------
+c determine the mtype of A
+c ----------------------------------------------------------------
+
+ call RBkind (nrow, ncol, %val(Ap), %val(Ai), %val(Ax),
+ $ %val(Az), cmplex, mkind, skind, mtype, nnz, %val(cp),
+ $ kmin, kmax)
+
+c ----------------------------------------------------------------
+c return the result
+c ----------------------------------------------------------------
+
+ pargout (1) = mxCreateString (mtype)
+ if (nargout .ge. 2) then
+ t = mkind
+ pargout (2) = mxCreateDoubleScalar (t)
+ endif
+ if (nargout .ge. 3) then
+ t = skind
+ pargout (3) = mxCreateDoubleScalar (t)
+ endif
+
+c ----------------------------------------------------------------
+c free workspace
+c ----------------------------------------------------------------
+
+ call mxDestroyArray (%val (cpmat))
+ return
+ end
+
diff --git a/RBio/RBwrite.m b/RBio/RBwrite.m
new file mode 100644
index 0000000..059fb5a
--- /dev/null
+++ b/RBio/RBwrite.m
@@ -0,0 +1,36 @@
+function mtype = RBwrite (filename, A, Z, title, key) %#ok
+%RBWRITE write a sparse matrix to a Rutherford/Boeing file
+% Usage:
+% mtype = RBwrite (filename, A, Z, title, key)
+%
+% filename: name of the file to create
+% A: a sparse matrix
+% Z: binary pattern of explicit zero entries to include in the
+% Rutherford/Boeing file. This always has the same size as A, and is
+% always sparse. Not used if empty ([ ]), or if nnz(Z) is 0.
+% title: title for 1st line of Rutherford/Boeing file, up to 72 characters
+% key: matrix key, up to 8 characters, for 1st line of the file
+%
+% Z is optional. RBwrite (filename, A) uses a default title and key, and does
+% not include any explicit zeros. RBwrite (filname, A, 'title...', 'key') uses
+% the given title and key. A must be sparse. Z must be empty, or sparse.
+%
+% mtype is a 3-character string with the Rutherford/Boeing type used:
+% mtype(1): r: real, p: pattern, c: complex, i: integer
+% mtype(2): r: rectangular, u: unsymmetric, s: symmetric,
+% h: Hermitian, Z: skew symmetric
+% mtype(3): a: assembled matrix, e: finite-element (not used by RBwrite)
+%
+% Example:
+% load west0479
+% C = west0479 ;
+% RBwrite ('west0479', C, 'WEST0479 chemical eng. problem', 'west0479')
+% A = RBread ('west0479') ;
+% norm (A-C,1)
+%
+% See also RBread, RBtype.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+error ('RBwrite mexFunction not found') ;
+
diff --git a/RBio/RBwrite_32.f b/RBio/RBwrite_32.f
new file mode 100644
index 0000000..5ecde32
--- /dev/null
+++ b/RBio/RBwrite_32.f
@@ -0,0 +1,713 @@
+c=======================================================================
+c=== RBio/RBwrite_32 ===================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBkind: determine the type of a MATLAB matrix
+c-----------------------------------------------------------------------
+c
+c input: a zero-based MATLAB sparse matrix
+c
+c nrow number of rows of A
+c ncol number of columns of A
+c Ap size ncol+1, column pointers
+c Ai size nnz, row indices (nnz = Ap (ncol+1))
+c Ax size nnz, real values
+c Az size nnz, imaginary values (not accessed if A is real)
+c cmplex 1 if A is complex, 0 otherwise
+c
+c output:
+c mkind: r: 0 (real), p: 1 (pattern), c: 2 (complex),
+c i: 3 (integer)
+c skind: r: -1 (rectangular), u: 0 (unsymmetric), s: 1 symmetric,
+c h: 2 (Hermitian), z: 3 (skew symmetric)
+c
+c workspace:
+c munch size ncol+1, not defined on input or output
+c
+c Note that the MATLAB matrix is zero-based (Ap and Ai). 1 must be
+c added whenever they are used (see "1+" in the code below).
+c
+c See also SuiteSparse/CHOLMOD/MatrixOps/cholmod_symmetry.c, which
+c also determines if the diagonal is positive.
+c-----------------------------------------------------------------------
+
+ subroutine RBkind (nrow, ncol, Ap, Ai, Ax, Az,
+ $ cmplex, mkind, skind, mtype, nnz, munch, kmin, kmax)
+
+ integer*4
+ $ nrow, ncol, Ap (ncol+1), Ai (*), mkind, skind,
+ $ munch (ncol+1), p, i, j, pt, nnz, k, kmin, kmax
+ integer*4 cmplex
+ double precision Ax (*), Az (*), x_r, x_i, xtr, xti
+ logical is_p, is_s, is_h, is_z, is_int
+ character mtype*3
+
+c ----------------------------------------------------------------
+c determine numeric type (I*A, R*A, P*A, C*A)
+c ----------------------------------------------------------------
+
+c pattern: if real and all entries are 1.
+c integer: if real and all entries are integers.
+c complex: if cmplex is 1.
+c real: otherwise.
+
+ nnz = 1+ (Ap (ncol+1) - 1)
+ kmin = 0
+ kmax = 0
+
+ if (cmplex .eq. 1) then
+c complex matrix (C*A)
+ mtype (1:1) = 'c'
+ mkind = 2
+ else
+c select P** format if all entries are equal to 1
+c select I** format if all entries are integer and
+c between -99,999,999 and +999,999,999
+ is_p = .true.
+ is_int = .true.
+ k = dint (Ax (1))
+ kmin = k
+ kmax = k
+ do 10 p = 1, nnz
+ if (Ax (p) .ne. 1) then
+ is_p = .false.
+ endif
+ k = dint (Ax (p))
+ kmin = min (kmin, k)
+ kmax = max (kmax, k)
+ if (k .ne. Ax (p)) then
+ is_int = .false.
+ endif
+ if (k .le. -99999999 .or. k .ge. 999999999) then
+c use real format for really big integers
+ is_int = .false.
+ endif
+ if (.not. is_int .and. .not. is_p) then
+ goto 20
+ endif
+10 continue
+20 continue
+ if (is_p) then
+c pattern-only matrix (P*A)
+ mtype (1:1) = 'p'
+ mkind = 1
+ elseif (is_int) then
+c integer matrix (I*A)
+ mtype (1:1) = 'i'
+ mkind = 3
+ else
+c real matrix (R*A)
+ mtype (1:1) = 'r'
+ mkind = 0
+ endif
+ endif
+
+c only assembled matrices are handled
+ mtype (3:3) = 'a'
+
+c ----------------------------------------------------------------
+c determine symmetry (*RA, *UA, *SA, *HA, *ZA)
+c ----------------------------------------------------------------
+
+c Note that A must have sorted columns for this method to work.
+c This is not checked, since all MATLAB matrices "should" have
+c sorted columns. Use spcheck(A) to check for this, if needed.
+
+ if (nrow .ne. ncol) then
+c rectangular matrix (*RA), no need to check values or pattern
+ mtype (2:2) = 'r'
+ skind = -1
+ return
+ endif
+
+c if complex, the matrix is Hermitian until proven otherwise
+ is_h = (cmplex .eq. 1)
+
+c the matrix is symmetric until proven otherwise
+ is_s = .true.
+
+c a non-pattern matrix is skew symmetric until proven otherwise
+ is_z = (mkind .ne. 1)
+
+c if this method returns early, the matrix is unsymmetric
+ mtype (2:2) = 'u'
+ skind = 0
+
+c initialize the munch pointers
+ do 30 j = 1, ncol
+ munch (j) = 1+ (Ap (j))
+30 continue
+
+ do 50 j = 1, ncol
+
+c consider all entries not yet munched in column j
+ do 40 p = munch (j), 1+ (Ap (j+1)-1)
+
+ i = 1+ (Ai (p))
+
+ if (i .lt. j) then
+c entry A(i,j) is unmatched, matrix is unsymmetric
+ return
+ endif
+
+c get the A(j,i) entry, if it exists
+ pt = munch (i)
+
+c munch the A(j,i) entry
+ munch (i) = pt + 1
+
+ if (pt .ge. 1+ (Ap (i+1))) then
+c entry A(j,i) doesn't exist, matrix unsymmetric
+ return
+ endif
+
+ if (1+ (Ai (pt)) .ne. j) then
+c entry A(j,i) doesn't exist, matrix unsymmetric
+ return
+ endif
+
+c A(j,i) exists; check its value with A(i,j)
+
+ if (cmplex .eq. 1) then
+
+c get A(i,j)
+ x_r = Ax (p)
+ x_i = Az (p)
+c get A(j,i)
+ xtr = Ax (pt)
+ xti = Az (pt)
+ if (x_r .ne. xtr .or. x_i .ne. xti) then
+c the matrix cannot be *SA
+ is_s = .false.
+ endif
+ if (x_r .ne. -xtr .or. x_i .ne. -xti) then
+c the matrix cannot be *ZA
+ is_z = .false.
+ endif
+ if (x_r .ne. xtr .or. x_i .ne. -xti) then
+c the matrix cannot be *HA
+ is_h = .false.
+ endif
+
+ else
+
+c get A(i,j)
+ x_r = Ax (p)
+c get A(j,i)
+ xtr = Ax (pt)
+ if (x_r .ne. xtr) then
+c the matrix cannot be *SA
+ is_s = .false.
+ endif
+ if (x_r .ne. -xtr) then
+c the matrix cannot be *ZA
+ is_z = .false.
+ endif
+
+ endif
+
+ if (.not. (is_s .or. is_z .or. is_h)) then
+c matrix is unsymmetric; terminate the test
+ return
+ endif
+
+40 continue
+50 continue
+
+c ----------------------------------------------------------------
+c return the symmetry
+c ----------------------------------------------------------------
+
+ if (is_h) then
+c Hermitian matrix (*HA)
+ mtype (2:2) = 'h'
+ skind = 2
+ elseif (is_s) then
+c symmetric matrix (*SA)
+ mtype (2:2) = 's'
+ skind = 1
+ elseif (is_z) then
+c skew symmetric matrix (*ZA)
+ mtype (2:2) = 'z'
+ skind = 3
+ endif
+
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBformat: determine the format required for an array of values
+c-----------------------------------------------------------------------
+c
+c This function ensures that a sufficiently wide format is used that
+c can accurately represent the data. It also ensures that when printed,
+c the numerical values all have at least one blank space between them.
+c This makes it trivial for a program written in C (say) to read in a
+c matrix generated by RBwrite.
+
+c ww, valfmt, valn, and is_int must be defined on input. They
+c are modified on output.
+c-----------------------------------------------------------------------
+
+ subroutine RBformat (nnz, x, ww, valfmt, valn, is_int,
+ $ kmin, kmax)
+ integer*4
+ $ nnz, i, ww, k, nf (18), valn, nd (9), kmin, kmax
+ double precision x (nnz), e, a, b
+ logical is_int
+ character*20 f (18), d (9), valfmt
+ character*80 s
+
+c ----------------------------------------------------------------
+c define all possible formats
+c ----------------------------------------------------------------
+
+ f (1) = '(8E9.1) '
+ f (2) = '(8E10.2) '
+ f (3) = '(7E11.3) '
+ f (4) = '(6E12.4) '
+ f (5) = '(6E13.5) '
+ f (6) = '(5E14.6) '
+ f (7) = '(5E15.7) '
+ f (8) = '(5E16.8) '
+ f (9) = '(4E17.9) '
+ f (10) = '(4E18.10) '
+ f (11) = '(4E19.11) '
+ f (12) = '(4E20.12) '
+ f (13) = '(3E21.13) '
+ f (14) = '(3E22.14) '
+ f (15) = '(3E23.15) '
+ f (16) = '(3E24.16) '
+ f (17) = '(3E25.17) '
+ f (18) = '(3E26.18) '
+
+ nf (1) = 8
+ nf (2) = 8
+ nf (3) = 7
+ nf (4) = 6
+ nf (5) = 6
+ nf (6) = 5
+ nf (7) = 5
+ nf (8) = 5
+ nf (9) = 4
+ nf (10) = 4
+ nf (11) = 4
+ nf (12) = 4
+ nf (13) = 3
+ nf (14) = 3
+ nf (15) = 3
+ nf (16) = 3
+ nf (17) = 3
+ nf (18) = 3
+
+ if (is_int) then
+
+c ------------------------------------------------------------
+c use an integer format
+c ------------------------------------------------------------
+
+ call RBiformat (kmin, kmax, valfmt, valn, ww)
+
+ else
+
+c ------------------------------------------------------------
+c determine if the matrix has huge values or NaN's
+c ------------------------------------------------------------
+
+ do 10 i = 1, nnz
+ a = abs (x (i))
+ if (a .ne. 0) then
+ if (a .ne. a .or. a < 1d-90 .or. a > 1d90) then
+ ww = 18
+ valfmt = '(2E30.18E3) '
+ valn = 2
+ return
+ endif
+ endif
+10 continue
+
+c ------------------------------------------------------------
+c find the required precision for a real or complex matrix
+c ------------------------------------------------------------
+
+ do 20 i = 1, nnz
+ a = x (i)
+ do 30 k = ww,18
+c write the value to a string, read back in, and check
+ write (unit = s, fmt = f(k)) a
+ read (unit = s, fmt = f(k)) b
+ if (a .eq. b) then
+ ww = max (ww, k)
+ goto 40
+ endif
+30 continue
+40 continue
+ ww = max (ww, k)
+20 continue
+
+c valn is the number of entries per line
+ valfmt = f (ww)
+ valn = nf (ww)
+
+ endif
+
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBwrite: write portions of the matrix to the file
+c-----------------------------------------------------------------------
+c
+c task 0: just count the total number of entries in the matrix
+c task 1: do task 0, and also construct w and cp
+c task 2: write the row indices
+c task 3: write the numerical values
+c
+c Note that the MATLAB arrays A and Z are zero-based. "1+" is added
+c to each use of Ap, Ai, Zp, and Zi.
+c-----------------------------------------------------------------------
+
+ subroutine RBwrite (task, nrow, ncol, skind, cmplex, doZ, Ap,
+ $ Ai, Ax, Az, Zp, Zi, mkind,
+ $ indfmt, indn, valfmt, valn, nnz, w, cp)
+
+ integer*4
+ $ task, nrow, ncol, Ap (*), Ai (*), Zp (*), Zi (*),
+ $ cp (*), w (*), nnz, znz, ibuf (80), j, i, nbuf, pa, pz,
+ $ paend, pzend, ia, iz, skind, indn, valn, p, mkind
+ integer*4 cmplex
+ logical doZ
+ double precision xbuf (80), xr, xi, Ax (*), Az (*)
+ character valfmt*20, indfmt*20
+
+c ----------------------------------------------------------------
+c determine number of entries in Z
+c ----------------------------------------------------------------
+
+ if (doZ) then
+ znz = 1+ (Zp (ncol+1) - 1)
+ else
+ znz = 0
+ endif
+
+c clear the nonzero counts
+ nnz = 0
+ do 10 j = 1, ncol
+ w (j) = 0
+10 continue
+
+c start with an empty buffer
+ nbuf = 0
+
+ if (znz .eq. 0) then
+
+c ------------------------------------------------------------
+c no Z present
+c ------------------------------------------------------------
+
+ do 30 j = 1, ncol
+
+ do 20 pa = 1+ (Ap (j)), 1+ (Ap (j+1) - 1)
+
+ i = 1+ (Ai (pa))
+ xr = Ax (pa)
+ if (cmplex .eq. 1) then
+ xi = Az (pa)
+ endif
+
+ if (skind .le. 0 .or. i .ge. j) then
+
+c consider the (i,j) entry with value (xr,xi)
+ nnz = nnz + 1
+ if (task .eq. 1) then
+c only determining nonzero counts
+ w (j) = w (j) + 1
+ elseif (task .eq. 2) then
+c printing the row indices
+ call RBiprint (indfmt, ibuf, nbuf, i, indn)
+ elseif (task .eq. 3) then
+c printing the numerical values
+ call RBxprint (valfmt, xbuf, nbuf, xr,
+ $ valn, mkind)
+ if (cmplex .eq. 1) then
+ call RBxprint (valfmt, xbuf, nbuf, xi,
+ $ valn, mkind)
+ endif
+ endif
+
+ endif
+
+20 continue
+30 continue
+
+ else
+
+c ------------------------------------------------------------
+c symmetric, unsymmetric or rectangular matrix, with Z present
+c ------------------------------------------------------------
+
+ do 40 j = 1, ncol
+
+c find the set union of A (:,j) and Z (:,j)
+
+ pa = 1+ (Ap (j))
+ pz = 1+ (Zp (j))
+ paend = 1+ (Ap (j+1) - 1)
+ pzend = 1+ (Zp (j+1) - 1)
+
+c while entries appear in A or Z
+70 continue
+
+c get the next entry from A(:,j)
+ if (pa .le. paend) then
+ ia = 1+ (Ai (pa))
+ else
+ ia = 1+ nrow
+ endif
+
+c get the next entry from Z(:,j)
+ if (pz .le. pzend) then
+ iz = 1+ (Zi (pz))
+ else
+ iz = 1+ nrow
+ endif
+
+c exit loop if neither entry is present
+ if (ia .gt. nrow .and. iz .gt. nrow) goto 80
+
+ if (ia .lt. iz) then
+c get A (i,j)
+ i = ia
+ xr = Ax (pa)
+ if (cmplex .eq. 1) then
+ xi = Az (pa)
+ endif
+ pa = pa + 1
+ else if (iz .lt. ia) then
+c get Z (i,j)
+ i = iz
+ xr = 0
+ xi = 0
+ pz = pz + 1
+ else
+c get A (i,j), and delete its matched Z(i,j)
+ i = ia
+ xr = Ax (pa)
+ if (cmplex .eq. 1) then
+ xi = Az (pa)
+ endif
+ pa = pa + 1
+ pz = pz + 1
+ endif
+
+ if (skind .le. 0 .or. i .ge. j) then
+
+c consider the (i,j) entry with value (xr,xi)
+ nnz = nnz + 1
+ if (task .eq. 1) then
+c only determining nonzero counts
+ w (j) = w (j) + 1
+ elseif (task .eq. 2) then
+c printing the row indices
+ call RBiprint (indfmt, ibuf, nbuf, i, indn)
+ elseif (task .eq. 3) then
+c printing the numerical values
+ call RBxprint (valfmt, xbuf, nbuf, xr,
+ $ valn, mkind)
+ if (cmplex .eq. 1) then
+ call RBxprint (valfmt, xbuf, nbuf, xi,
+ $ valn, mkind)
+ endif
+ endif
+
+ endif
+
+ goto 70
+
+c end of while loop
+80 continue
+
+40 continue
+
+ endif
+
+c ----------------------------------------------------------------
+c determine the new column pointers, or finish printing
+c ----------------------------------------------------------------
+
+ if (task .eq. 1) then
+
+ cp (1) = 1
+ do 100 j = 2, ncol+1
+ cp (j) = cp (j-1) + w (j-1)
+100 continue
+
+ else if (task .eq. 2) then
+
+ call RBiflush (indfmt, ibuf, nbuf)
+
+ elseif (task .eq. 3) then
+
+ call RBxflush (valfmt, xbuf, nbuf, mkind)
+
+ endif
+
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBiprint: print a single integer to the file, flush buffer if needed
+c-----------------------------------------------------------------------
+
+ subroutine RBiprint (indfmt, ibuf, nbuf, i, indn)
+ character indfmt*20
+ integer*4
+ $ ibuf (80), nbuf, i, indn
+ if (nbuf .ge. indn) then
+ call RBiflush (indfmt, ibuf, nbuf)
+ nbuf = 0
+ endif
+ nbuf = nbuf + 1
+ ibuf (nbuf) = i
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBiflush: flush the integer buffer to the file
+c-----------------------------------------------------------------------
+
+ subroutine RBiflush (indfmt, ibuf, nbuf)
+ character indfmt*20
+ integer*4
+ $ ibuf (*), nbuf, k
+ write (unit = 7, fmt = indfmt, err = 999) (ibuf (k), k = 1,nbuf)
+ return
+999 call mexErrMsgTxt ('error writing ints')
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBxprint: print a single real to the file, flush the buffer if needed
+c-----------------------------------------------------------------------
+
+ subroutine RBxprint (valfmt, xbuf, nbuf, x, valn, mkind)
+ character valfmt*20
+ integer*4
+ $ nbuf, valn, mkind
+ double precision xbuf (80), x
+ if (nbuf .ge. valn) then
+ call RBxflush (valfmt, xbuf, nbuf, mkind)
+ nbuf = 0
+ endif
+ nbuf = nbuf + 1
+ xbuf (nbuf) = x
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBxflush: flush the real buffer to the file
+c-----------------------------------------------------------------------
+
+ subroutine RBxflush (valfmt, xbuf, nbuf, mkind)
+ character valfmt*20
+ integer*4
+ $ nbuf, k, ibuf (80), mkind
+ double precision xbuf (80)
+ if (mkind .eq. 3) then
+c convert to integer first; valfmt is (10I8), for example
+ do 10 k = 1,nbuf
+ ibuf (k) = dint (xbuf (k))
+10 continue
+ write (unit = 7, fmt = valfmt, err = 999)
+ $ (ibuf (k), k = 1,nbuf)
+ else
+ write (unit = 7, fmt = valfmt, err = 999)
+ $ (xbuf (k), k = 1,nbuf)
+ endif
+ return
+999 call mexErrMsgTxt ('error writing numerical values')
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBiformat: determine format for printing an integer
+c-----------------------------------------------------------------------
+
+ subroutine RBiformat (kmin, kmax, indfmt, indn, ww)
+ integer*4
+ $ n, indn, kmin, kmax, ww
+ character*20 indfmt
+
+ if (kmin .ge. 0. and. kmax .le. 9) then
+ indfmt = '(40I2) '
+ ww = 2
+ indn = 40
+ elseif (kmin .ge. -9 .and. kmax .le. 99) then
+ indfmt = '(26I3) '
+ ww = 3
+ indn = 26
+ elseif (kmin .ge. -99 .and. kmax .le. 999) then
+ indfmt = '(20I4) '
+ ww = 4
+ indn = 20
+ elseif (kmin .ge. -999 .and. kmax .le. 9999) then
+ indfmt = '(16I5) '
+ ww = 5
+ indn = 16
+ elseif (kmin .ge. -9999 .and. kmax .le. 99999) then
+ indfmt = '(13I6) '
+ ww = 6
+ indn = 13
+ elseif (kmin .ge. -99999 .and. kmax .le. 999999) then
+ indfmt = '(11I7) '
+ ww = 7
+ indn = 11
+ elseif (kmin .ge. -999999 .and. kmax .le. 9999999) then
+ indfmt = '(10I8) '
+ ww = 8
+ indn = 10
+ elseif (kmin .ge. -9999999 .and. kmax .le. 99999999) then
+ indfmt = '(8I9) '
+ ww = 9
+ indn = 8
+ elseif (kmin .ge. -99999999 .and. kmax .le. 999999999) then
+ indfmt = '(8I10) '
+ ww = 10
+ indn = 8
+ else
+ indfmt = '(5I15) '
+ ww = 15
+ indn = 5
+ endif
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBcards: determine number of cards required
+c-----------------------------------------------------------------------
+
+ subroutine RBcards (nitems, nperline, ncards)
+ integer*4
+ $ nitems, nperline, ncards
+ if (nitems .eq. 0) then
+ ncards = 0
+ else
+ ncards = ((nitems-1) / nperline) + 1
+ endif
+ return
+ end
+
diff --git a/RBio/RBwrite_64.f b/RBio/RBwrite_64.f
new file mode 100644
index 0000000..5b7f2cb
--- /dev/null
+++ b/RBio/RBwrite_64.f
@@ -0,0 +1,713 @@
+c=======================================================================
+c=== RBio/RBwrite_64 ===================================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBkind: determine the type of a MATLAB matrix
+c-----------------------------------------------------------------------
+c
+c input: a zero-based MATLAB sparse matrix
+c
+c nrow number of rows of A
+c ncol number of columns of A
+c Ap size ncol+1, column pointers
+c Ai size nnz, row indices (nnz = Ap (ncol+1))
+c Ax size nnz, real values
+c Az size nnz, imaginary values (not accessed if A is real)
+c cmplex 1 if A is complex, 0 otherwise
+c
+c output:
+c mkind: r: 0 (real), p: 1 (pattern), c: 2 (complex),
+c i: 3 (integer)
+c skind: r: -1 (rectangular), u: 0 (unsymmetric), s: 1 symmetric,
+c h: 2 (Hermitian), z: 3 (skew symmetric)
+c
+c workspace:
+c munch size ncol+1, not defined on input or output
+c
+c Note that the MATLAB matrix is zero-based (Ap and Ai). 1 must be
+c added whenever they are used (see "1+" in the code below).
+c
+c See also SuiteSparse/CHOLMOD/MatrixOps/cholmod_symmetry.c, which
+c also determines if the diagonal is positive.
+c-----------------------------------------------------------------------
+
+ subroutine RBkind (nrow, ncol, Ap, Ai, Ax, Az,
+ $ cmplex, mkind, skind, mtype, nnz, munch, kmin, kmax)
+
+ integer*8
+ $ nrow, ncol, Ap (ncol+1), Ai (*), mkind, skind,
+ $ munch (ncol+1), p, i, j, pt, nnz, k, kmin, kmax
+ integer*4 cmplex
+ double precision Ax (*), Az (*), x_r, x_i, xtr, xti
+ logical is_p, is_s, is_h, is_z, is_int
+ character mtype*3
+
+c ----------------------------------------------------------------
+c determine numeric type (I*A, R*A, P*A, C*A)
+c ----------------------------------------------------------------
+
+c pattern: if real and all entries are 1.
+c integer: if real and all entries are integers.
+c complex: if cmplex is 1.
+c real: otherwise.
+
+ nnz = 1+ (Ap (ncol+1) - 1)
+ kmin = 0
+ kmax = 0
+
+ if (cmplex .eq. 1) then
+c complex matrix (C*A)
+ mtype (1:1) = 'c'
+ mkind = 2
+ else
+c select P** format if all entries are equal to 1
+c select I** format if all entries are integer and
+c between -99,999,999 and +999,999,999
+ is_p = .true.
+ is_int = .true.
+ k = dint (Ax (1))
+ kmin = k
+ kmax = k
+ do 10 p = 1, nnz
+ if (Ax (p) .ne. 1) then
+ is_p = .false.
+ endif
+ k = dint (Ax (p))
+ kmin = min (kmin, k)
+ kmax = max (kmax, k)
+ if (k .ne. Ax (p)) then
+ is_int = .false.
+ endif
+ if (k .le. -99999999 .or. k .ge. 999999999) then
+c use real format for really big integers
+ is_int = .false.
+ endif
+ if (.not. is_int .and. .not. is_p) then
+ goto 20
+ endif
+10 continue
+20 continue
+ if (is_p) then
+c pattern-only matrix (P*A)
+ mtype (1:1) = 'p'
+ mkind = 1
+ elseif (is_int) then
+c integer matrix (I*A)
+ mtype (1:1) = 'i'
+ mkind = 3
+ else
+c real matrix (R*A)
+ mtype (1:1) = 'r'
+ mkind = 0
+ endif
+ endif
+
+c only assembled matrices are handled
+ mtype (3:3) = 'a'
+
+c ----------------------------------------------------------------
+c determine symmetry (*RA, *UA, *SA, *HA, *ZA)
+c ----------------------------------------------------------------
+
+c Note that A must have sorted columns for this method to work.
+c This is not checked, since all MATLAB matrices "should" have
+c sorted columns. Use spcheck(A) to check for this, if needed.
+
+ if (nrow .ne. ncol) then
+c rectangular matrix (*RA), no need to check values or pattern
+ mtype (2:2) = 'r'
+ skind = -1
+ return
+ endif
+
+c if complex, the matrix is Hermitian until proven otherwise
+ is_h = (cmplex .eq. 1)
+
+c the matrix is symmetric until proven otherwise
+ is_s = .true.
+
+c a non-pattern matrix is skew symmetric until proven otherwise
+ is_z = (mkind .ne. 1)
+
+c if this method returns early, the matrix is unsymmetric
+ mtype (2:2) = 'u'
+ skind = 0
+
+c initialize the munch pointers
+ do 30 j = 1, ncol
+ munch (j) = 1+ (Ap (j))
+30 continue
+
+ do 50 j = 1, ncol
+
+c consider all entries not yet munched in column j
+ do 40 p = munch (j), 1+ (Ap (j+1)-1)
+
+ i = 1+ (Ai (p))
+
+ if (i .lt. j) then
+c entry A(i,j) is unmatched, matrix is unsymmetric
+ return
+ endif
+
+c get the A(j,i) entry, if it exists
+ pt = munch (i)
+
+c munch the A(j,i) entry
+ munch (i) = pt + 1
+
+ if (pt .ge. 1+ (Ap (i+1))) then
+c entry A(j,i) doesn't exist, matrix unsymmetric
+ return
+ endif
+
+ if (1+ (Ai (pt)) .ne. j) then
+c entry A(j,i) doesn't exist, matrix unsymmetric
+ return
+ endif
+
+c A(j,i) exists; check its value with A(i,j)
+
+ if (cmplex .eq. 1) then
+
+c get A(i,j)
+ x_r = Ax (p)
+ x_i = Az (p)
+c get A(j,i)
+ xtr = Ax (pt)
+ xti = Az (pt)
+ if (x_r .ne. xtr .or. x_i .ne. xti) then
+c the matrix cannot be *SA
+ is_s = .false.
+ endif
+ if (x_r .ne. -xtr .or. x_i .ne. -xti) then
+c the matrix cannot be *ZA
+ is_z = .false.
+ endif
+ if (x_r .ne. xtr .or. x_i .ne. -xti) then
+c the matrix cannot be *HA
+ is_h = .false.
+ endif
+
+ else
+
+c get A(i,j)
+ x_r = Ax (p)
+c get A(j,i)
+ xtr = Ax (pt)
+ if (x_r .ne. xtr) then
+c the matrix cannot be *SA
+ is_s = .false.
+ endif
+ if (x_r .ne. -xtr) then
+c the matrix cannot be *ZA
+ is_z = .false.
+ endif
+
+ endif
+
+ if (.not. (is_s .or. is_z .or. is_h)) then
+c matrix is unsymmetric; terminate the test
+ return
+ endif
+
+40 continue
+50 continue
+
+c ----------------------------------------------------------------
+c return the symmetry
+c ----------------------------------------------------------------
+
+ if (is_h) then
+c Hermitian matrix (*HA)
+ mtype (2:2) = 'h'
+ skind = 2
+ elseif (is_s) then
+c symmetric matrix (*SA)
+ mtype (2:2) = 's'
+ skind = 1
+ elseif (is_z) then
+c skew symmetric matrix (*ZA)
+ mtype (2:2) = 'z'
+ skind = 3
+ endif
+
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBformat: determine the format required for an array of values
+c-----------------------------------------------------------------------
+c
+c This function ensures that a sufficiently wide format is used that
+c can accurately represent the data. It also ensures that when printed,
+c the numerical values all have at least one blank space between them.
+c This makes it trivial for a program written in C (say) to read in a
+c matrix generated by RBwrite.
+
+c ww, valfmt, valn, and is_int must be defined on input. They
+c are modified on output.
+c-----------------------------------------------------------------------
+
+ subroutine RBformat (nnz, x, ww, valfmt, valn, is_int,
+ $ kmin, kmax)
+ integer*8
+ $ nnz, i, ww, k, nf (18), valn, nd (9), kmin, kmax
+ double precision x (nnz), e, a, b
+ logical is_int
+ character*20 f (18), d (9), valfmt
+ character*80 s
+
+c ----------------------------------------------------------------
+c define all possible formats
+c ----------------------------------------------------------------
+
+ f (1) = '(8E9.1) '
+ f (2) = '(8E10.2) '
+ f (3) = '(7E11.3) '
+ f (4) = '(6E12.4) '
+ f (5) = '(6E13.5) '
+ f (6) = '(5E14.6) '
+ f (7) = '(5E15.7) '
+ f (8) = '(5E16.8) '
+ f (9) = '(4E17.9) '
+ f (10) = '(4E18.10) '
+ f (11) = '(4E19.11) '
+ f (12) = '(4E20.12) '
+ f (13) = '(3E21.13) '
+ f (14) = '(3E22.14) '
+ f (15) = '(3E23.15) '
+ f (16) = '(3E24.16) '
+ f (17) = '(3E25.17) '
+ f (18) = '(3E26.18) '
+
+ nf (1) = 8
+ nf (2) = 8
+ nf (3) = 7
+ nf (4) = 6
+ nf (5) = 6
+ nf (6) = 5
+ nf (7) = 5
+ nf (8) = 5
+ nf (9) = 4
+ nf (10) = 4
+ nf (11) = 4
+ nf (12) = 4
+ nf (13) = 3
+ nf (14) = 3
+ nf (15) = 3
+ nf (16) = 3
+ nf (17) = 3
+ nf (18) = 3
+
+ if (is_int) then
+
+c ------------------------------------------------------------
+c use an integer format
+c ------------------------------------------------------------
+
+ call RBiformat (kmin, kmax, valfmt, valn, ww)
+
+ else
+
+c ------------------------------------------------------------
+c determine if the matrix has huge values or NaN's
+c ------------------------------------------------------------
+
+ do 10 i = 1, nnz
+ a = abs (x (i))
+ if (a .ne. 0) then
+ if (a .ne. a .or. a < 1d-90 .or. a > 1d90) then
+ ww = 18
+ valfmt = '(2E30.18E3) '
+ valn = 2
+ return
+ endif
+ endif
+10 continue
+
+c ------------------------------------------------------------
+c find the required precision for a real or complex matrix
+c ------------------------------------------------------------
+
+ do 20 i = 1, nnz
+ a = x (i)
+ do 30 k = ww,18
+c write the value to a string, read back in, and check
+ write (unit = s, fmt = f(k)) a
+ read (unit = s, fmt = f(k)) b
+ if (a .eq. b) then
+ ww = max (ww, k)
+ goto 40
+ endif
+30 continue
+40 continue
+ ww = max (ww, k)
+20 continue
+
+c valn is the number of entries per line
+ valfmt = f (ww)
+ valn = nf (ww)
+
+ endif
+
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBwrite: write portions of the matrix to the file
+c-----------------------------------------------------------------------
+c
+c task 0: just count the total number of entries in the matrix
+c task 1: do task 0, and also construct w and cp
+c task 2: write the row indices
+c task 3: write the numerical values
+c
+c Note that the MATLAB arrays A and Z are zero-based. "1+" is added
+c to each use of Ap, Ai, Zp, and Zi.
+c-----------------------------------------------------------------------
+
+ subroutine RBwrite (task, nrow, ncol, skind, cmplex, doZ, Ap,
+ $ Ai, Ax, Az, Zp, Zi, mkind,
+ $ indfmt, indn, valfmt, valn, nnz, w, cp)
+
+ integer*8
+ $ task, nrow, ncol, Ap (*), Ai (*), Zp (*), Zi (*),
+ $ cp (*), w (*), nnz, znz, ibuf (80), j, i, nbuf, pa, pz,
+ $ paend, pzend, ia, iz, skind, indn, valn, p, mkind
+ integer*4 cmplex
+ logical doZ
+ double precision xbuf (80), xr, xi, Ax (*), Az (*)
+ character valfmt*20, indfmt*20
+
+c ----------------------------------------------------------------
+c determine number of entries in Z
+c ----------------------------------------------------------------
+
+ if (doZ) then
+ znz = 1+ (Zp (ncol+1) - 1)
+ else
+ znz = 0
+ endif
+
+c clear the nonzero counts
+ nnz = 0
+ do 10 j = 1, ncol
+ w (j) = 0
+10 continue
+
+c start with an empty buffer
+ nbuf = 0
+
+ if (znz .eq. 0) then
+
+c ------------------------------------------------------------
+c no Z present
+c ------------------------------------------------------------
+
+ do 30 j = 1, ncol
+
+ do 20 pa = 1+ (Ap (j)), 1+ (Ap (j+1) - 1)
+
+ i = 1+ (Ai (pa))
+ xr = Ax (pa)
+ if (cmplex .eq. 1) then
+ xi = Az (pa)
+ endif
+
+ if (skind .le. 0 .or. i .ge. j) then
+
+c consider the (i,j) entry with value (xr,xi)
+ nnz = nnz + 1
+ if (task .eq. 1) then
+c only determining nonzero counts
+ w (j) = w (j) + 1
+ elseif (task .eq. 2) then
+c printing the row indices
+ call RBiprint (indfmt, ibuf, nbuf, i, indn)
+ elseif (task .eq. 3) then
+c printing the numerical values
+ call RBxprint (valfmt, xbuf, nbuf, xr,
+ $ valn, mkind)
+ if (cmplex .eq. 1) then
+ call RBxprint (valfmt, xbuf, nbuf, xi,
+ $ valn, mkind)
+ endif
+ endif
+
+ endif
+
+20 continue
+30 continue
+
+ else
+
+c ------------------------------------------------------------
+c symmetric, unsymmetric or rectangular matrix, with Z present
+c ------------------------------------------------------------
+
+ do 40 j = 1, ncol
+
+c find the set union of A (:,j) and Z (:,j)
+
+ pa = 1+ (Ap (j))
+ pz = 1+ (Zp (j))
+ paend = 1+ (Ap (j+1) - 1)
+ pzend = 1+ (Zp (j+1) - 1)
+
+c while entries appear in A or Z
+70 continue
+
+c get the next entry from A(:,j)
+ if (pa .le. paend) then
+ ia = 1+ (Ai (pa))
+ else
+ ia = 1+ nrow
+ endif
+
+c get the next entry from Z(:,j)
+ if (pz .le. pzend) then
+ iz = 1+ (Zi (pz))
+ else
+ iz = 1+ nrow
+ endif
+
+c exit loop if neither entry is present
+ if (ia .gt. nrow .and. iz .gt. nrow) goto 80
+
+ if (ia .lt. iz) then
+c get A (i,j)
+ i = ia
+ xr = Ax (pa)
+ if (cmplex .eq. 1) then
+ xi = Az (pa)
+ endif
+ pa = pa + 1
+ else if (iz .lt. ia) then
+c get Z (i,j)
+ i = iz
+ xr = 0
+ xi = 0
+ pz = pz + 1
+ else
+c get A (i,j), and delete its matched Z(i,j)
+ i = ia
+ xr = Ax (pa)
+ if (cmplex .eq. 1) then
+ xi = Az (pa)
+ endif
+ pa = pa + 1
+ pz = pz + 1
+ endif
+
+ if (skind .le. 0 .or. i .ge. j) then
+
+c consider the (i,j) entry with value (xr,xi)
+ nnz = nnz + 1
+ if (task .eq. 1) then
+c only determining nonzero counts
+ w (j) = w (j) + 1
+ elseif (task .eq. 2) then
+c printing the row indices
+ call RBiprint (indfmt, ibuf, nbuf, i, indn)
+ elseif (task .eq. 3) then
+c printing the numerical values
+ call RBxprint (valfmt, xbuf, nbuf, xr,
+ $ valn, mkind)
+ if (cmplex .eq. 1) then
+ call RBxprint (valfmt, xbuf, nbuf, xi,
+ $ valn, mkind)
+ endif
+ endif
+
+ endif
+
+ goto 70
+
+c end of while loop
+80 continue
+
+40 continue
+
+ endif
+
+c ----------------------------------------------------------------
+c determine the new column pointers, or finish printing
+c ----------------------------------------------------------------
+
+ if (task .eq. 1) then
+
+ cp (1) = 1
+ do 100 j = 2, ncol+1
+ cp (j) = cp (j-1) + w (j-1)
+100 continue
+
+ else if (task .eq. 2) then
+
+ call RBiflush (indfmt, ibuf, nbuf)
+
+ elseif (task .eq. 3) then
+
+ call RBxflush (valfmt, xbuf, nbuf, mkind)
+
+ endif
+
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBiprint: print a single integer to the file, flush buffer if needed
+c-----------------------------------------------------------------------
+
+ subroutine RBiprint (indfmt, ibuf, nbuf, i, indn)
+ character indfmt*20
+ integer*8
+ $ ibuf (80), nbuf, i, indn
+ if (nbuf .ge. indn) then
+ call RBiflush (indfmt, ibuf, nbuf)
+ nbuf = 0
+ endif
+ nbuf = nbuf + 1
+ ibuf (nbuf) = i
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBiflush: flush the integer buffer to the file
+c-----------------------------------------------------------------------
+
+ subroutine RBiflush (indfmt, ibuf, nbuf)
+ character indfmt*20
+ integer*8
+ $ ibuf (*), nbuf, k
+ write (unit = 7, fmt = indfmt, err = 999) (ibuf (k), k = 1,nbuf)
+ return
+999 call mexErrMsgTxt ('error writing ints')
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBxprint: print a single real to the file, flush the buffer if needed
+c-----------------------------------------------------------------------
+
+ subroutine RBxprint (valfmt, xbuf, nbuf, x, valn, mkind)
+ character valfmt*20
+ integer*8
+ $ nbuf, valn, mkind
+ double precision xbuf (80), x
+ if (nbuf .ge. valn) then
+ call RBxflush (valfmt, xbuf, nbuf, mkind)
+ nbuf = 0
+ endif
+ nbuf = nbuf + 1
+ xbuf (nbuf) = x
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBxflush: flush the real buffer to the file
+c-----------------------------------------------------------------------
+
+ subroutine RBxflush (valfmt, xbuf, nbuf, mkind)
+ character valfmt*20
+ integer*8
+ $ nbuf, k, ibuf (80), mkind
+ double precision xbuf (80)
+ if (mkind .eq. 3) then
+c convert to integer first; valfmt is (10I8), for example
+ do 10 k = 1,nbuf
+ ibuf (k) = dint (xbuf (k))
+10 continue
+ write (unit = 7, fmt = valfmt, err = 999)
+ $ (ibuf (k), k = 1,nbuf)
+ else
+ write (unit = 7, fmt = valfmt, err = 999)
+ $ (xbuf (k), k = 1,nbuf)
+ endif
+ return
+999 call mexErrMsgTxt ('error writing numerical values')
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBiformat: determine format for printing an integer
+c-----------------------------------------------------------------------
+
+ subroutine RBiformat (kmin, kmax, indfmt, indn, ww)
+ integer*8
+ $ n, indn, kmin, kmax, ww
+ character*20 indfmt
+
+ if (kmin .ge. 0. and. kmax .le. 9) then
+ indfmt = '(40I2) '
+ ww = 2
+ indn = 40
+ elseif (kmin .ge. -9 .and. kmax .le. 99) then
+ indfmt = '(26I3) '
+ ww = 3
+ indn = 26
+ elseif (kmin .ge. -99 .and. kmax .le. 999) then
+ indfmt = '(20I4) '
+ ww = 4
+ indn = 20
+ elseif (kmin .ge. -999 .and. kmax .le. 9999) then
+ indfmt = '(16I5) '
+ ww = 5
+ indn = 16
+ elseif (kmin .ge. -9999 .and. kmax .le. 99999) then
+ indfmt = '(13I6) '
+ ww = 6
+ indn = 13
+ elseif (kmin .ge. -99999 .and. kmax .le. 999999) then
+ indfmt = '(11I7) '
+ ww = 7
+ indn = 11
+ elseif (kmin .ge. -999999 .and. kmax .le. 9999999) then
+ indfmt = '(10I8) '
+ ww = 8
+ indn = 10
+ elseif (kmin .ge. -9999999 .and. kmax .le. 99999999) then
+ indfmt = '(8I9) '
+ ww = 9
+ indn = 8
+ elseif (kmin .ge. -99999999 .and. kmax .le. 999999999) then
+ indfmt = '(8I10) '
+ ww = 10
+ indn = 8
+ else
+ indfmt = '(5I15) '
+ ww = 15
+ indn = 5
+ endif
+ return
+ end
+
+
+c-----------------------------------------------------------------------
+c RBcards: determine number of cards required
+c-----------------------------------------------------------------------
+
+ subroutine RBcards (nitems, nperline, ncards)
+ integer*8
+ $ nitems, nperline, ncards
+ if (nitems .eq. 0) then
+ ncards = 0
+ else
+ ncards = ((nitems-1) / nperline) + 1
+ endif
+ return
+ end
+
diff --git a/RBio/RBwrite_mex_32.f b/RBio/RBwrite_mex_32.f
new file mode 100644
index 0000000..3a4ea30
--- /dev/null
+++ b/RBio/RBwrite_mex_32.f
@@ -0,0 +1,324 @@
+c=======================================================================
+c=== RBio/RBwrite_mex_32 ===============================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBwrite mexFunction: write a sparse matrix to a Rutherford/Boeing file
+c-----------------------------------------------------------------------
+c
+c mtype = RBwrite (filename, A, Z, title, key)
+c
+c A: a sparse matrix (no explicit zero entries)
+c Z: binary pattern of explicit zero entries to include in the
+c Rutherford/Boeing file. This always has the same size as A,
+c and is always sparse. Not used if [ ], or if nnz(Z) is 0.
+c title: title of Rutherford/Boeing file, up to 72 characters
+c key: the name of the matrix, up to 8 characters
+c
+c Z is optional. RBwrite (filename, A) uses a default
+c title and key, and does not include any explicit zeros.
+c RBwrite (filname, A, 'title...', 'key') uses the given title and
+c key, with no Z matrix.
+c
+c A must be sparse. Z must be empty, or sparse.
+c
+c mtype is a 3-character string with the file-type used
+c mtype(1): r: 0 (real), p: 1 (pattern), c: 2 (complex),
+c i: 3 (ineger)
+c mtype(2): r: -1 (rectangular), u: 0 (unsymmetric), s: 1 symmetric,
+c h: 2 (Hermitian), z: 3 (skew symmetric)
+c mtype(3): a: assembled matrix
+c-----------------------------------------------------------------------
+
+ subroutine mexfunction (nargout, pargout, nargin, pargin)
+ integer*4
+ $ pargout (*), pargin (*)
+ integer*4 nargout, nargin
+
+c ----------------------------------------------------------------
+c MATLAB functions
+c ----------------------------------------------------------------
+
+ integer*4 mxIsChar, mxClassIDFromClassName,
+ $ mxIsClass, mxIsSparse, mxIsComplex
+
+ integer*4
+ $ mxGetM, mxGetN, mxGetJc, mxGetIr, mxGetPr, mxGetPi,
+ $ mxGetString, mxGetData, mxCreateNumericMatrix,
+ $ mxCreateString
+
+c ----------------------------------------------------------------
+c local variables
+c ----------------------------------------------------------------
+
+ integer*4
+ $ nrow, ncol, nnz, mkind, cp, info, zmin, zmax,
+ $ skind, wmat, cpmat, ww, kmin, kmax, task,
+ $ Ap, Ai, Ax, Az, Zp, Zi, Zx, Zz, znz, zrow, zcol, i,
+ $ mzkind, szkind, totcrd, ptrcrd, indcrd, valcrd, nw, one,
+ $ w, valn, valn2, indn, nnz2, ptrn, i1, ititle, vals
+ integer*4 iclass, cmplex, wcmplex
+ character title*72, key*8, mtype*3, ptrfmt*20, indfmt*20,
+ $ valfmt*20, filename*1024, fmt2*20, ztype*3
+ double precision t
+ logical doZ, l1, is_int
+
+c ----------------------------------------------------------------
+c check inputs
+c ----------------------------------------------------------------
+
+ if (nargin .lt. 2 .or. nargin .gt. 5. .or. nargout .gt. 2 .or.
+ $ mxIsChar (pargin (1)) .ne. 1) then
+ call mexErrMsgTxt
+ $ ('[m s] = RBwrite (filename, A, Z, title, key)')
+ endif
+
+c ----------------------------------------------------------------
+c get filename
+c ----------------------------------------------------------------
+
+ if (mxGetString (pargin (1), filename, 1024) .ne. 0) then
+ call mexErrMsgTxt ('filename too long')
+ endif
+ close (unit = 7)
+ open (unit = 7, file = filename, err = 998)
+
+c ----------------------------------------------------------------
+c get A
+c ----------------------------------------------------------------
+
+ if (mxIsClass (pargin (2), 'double') .ne. 1 .or.
+ $ mxIsSparse (pargin (2)) .ne. 1) then
+ call mexErrMsgTxt ('A must be sparse and double')
+ endif
+ cmplex = mxIsComplex (pargin (2))
+ Ap = mxGetJc (pargin (2))
+ Ai = mxGetIr (pargin (2))
+ Ax = mxGetPr (pargin (2))
+ Az = mxGetPi (pargin (2))
+ nrow = mxGetM (pargin (2))
+ ncol = mxGetN (pargin (2))
+
+c ----------------------------------------------------------------
+c get title and key
+c ----------------------------------------------------------------
+
+ do 5 i = 1, 72
+ title (i:i) = ' '
+5 continue
+ key = ' '
+
+ ititle = 99
+ do 15 i = 3, nargin
+ if (mxIsChar (pargin (i)) .eq. 1) then
+ if (ititle .eq. 99) then
+c get the title, up to 72 characters long
+ i1 = mxGetString (pargin (i), title, 72)
+ ititle = i
+ else
+c get the key, up to 8 characters long
+ i1 = mxGetString (pargin (i), key, 8)
+ endif
+ endif
+15 continue
+
+c place a marker in the title, so we know that the
+c Rutherford/Boeing file was generated by the RBwrite mexFunction.
+
+ title (72:72) = '|'
+
+c ----------------------------------------------------------------
+c get Z, if present
+c ----------------------------------------------------------------
+
+ if (nargin .ge. 3 .and. ititle .gt. 3) then
+
+ zrow = mxGetM (pargin (3))
+ zcol = mxGetN (pargin (3))
+
+ if (zrow .eq. 0 .or. zcol .eq. 0) then
+
+c --------------------------------------------------------
+c Z matrix is empty
+c --------------------------------------------------------
+
+ doZ = .false.
+
+ else
+
+c --------------------------------------------------------
+c get the Z matrix
+c --------------------------------------------------------
+
+ if (mxIsClass (pargin (3), 'double') .ne. 1 .or.
+ $ mxIsSparse (pargin (3)) .ne. 1 .or.
+ $ mxIsComplex (pargin (3)) .ne. 0 .or.
+ $ zrow .ne. nrow .or. zcol .ne. ncol) then
+ call mexErrMsgTxt
+ $ ('Z must be sparse, double, real, and same size as A')
+ endif
+ Zp = mxGetJc (pargin (3))
+ Zi = mxGetIr (pargin (3))
+ Zx = mxGetPr (pargin (3))
+ Zz = mxGetPi (pargin (3))
+ doZ = .true.
+
+ endif
+
+ else
+
+c ------------------------------------------------------------
+c no Z matrix is present
+c ------------------------------------------------------------
+
+ doZ = .false.
+
+ endif
+
+c ----------------------------------------------------------------
+c get workspace
+c ----------------------------------------------------------------
+
+ iclass = mxClassIDFromClassName ('int32')
+ nw = max (nrow, ncol) + 1
+ one = 1
+ wcomplex = 0
+ wmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex)
+ cpmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex)
+ w = mxGetData (wmat)
+ cp = mxGetData (cpmat)
+
+c ----------------------------------------------------------------
+c determine the matrix type (RSA, RUA, etc)
+c ----------------------------------------------------------------
+
+c find the symmetry of A (mkind, skind), and nnz(A)
+ call RBkind (nrow, ncol, %val(Ap), %val(Ai), %val(Ax),
+ $ %val(Az), cmplex, mkind, skind, mtype, nnz, %val(cp),
+ $ kmin, kmax)
+
+ if (doZ) then
+c find the symmetry of Z and find nnz(Z)
+ call RBkind (nrow, ncol, %val(Zp), %val(Zi), %val(Zx),
+ $ %val(Zz), 0, mzkind, szkind, ztype, znz, %val(cp),
+ $ zmin, zmax)
+ if (znz .eq. 0) then
+c ignore the Z matrix
+ doZ = .false.
+ elseif (szkind .le. 0) then
+c if Z is unsymmetric, then A+Z is unsymmetric too
+ skind = szkind
+ endif
+ endif
+
+ pargout (1) = mxCreateString (mtype)
+
+c ----------------------------------------------------------------
+c determine the required precision
+c ----------------------------------------------------------------
+
+ indfmt = ' '
+ valfmt = ' '
+ is_int = mkind .eq. 3
+ ww = 1
+ if (mkind .ne. 1) then
+ call RBformat (nnz, %val (Ax), ww, valfmt, valn, is_int,
+ $ kmin, kmax)
+ if (cmplex .eq. 1) then
+ call RBformat (nnz, %val (Az), ww, valfmt, valn, is_int,
+ $ kmin, kmax)
+ endif
+ endif
+
+c ----------------------------------------------------------------
+c determine the number of entries in the matrix A+Z
+c ----------------------------------------------------------------
+
+ task = 1
+ call RBwrite (task, nrow, ncol, skind, cmplex, doZ, %val(Ap),
+ $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind,
+ $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp))
+
+ if (nnz2 .eq. 0) then
+ call mexErrMsgTxt ('empty matrices not handled')
+ endif
+
+c determine pointer format. ncol+1 integers, largest is nnz2+1
+ call RBiformat (1, nnz2+1, ptrfmt, ptrn, i)
+ call RBcards (ncol+1, ptrn, ptrcrd)
+
+c determine row index format. nnz2 integers, largest is nrow
+ call RBiformat (1, nrow, indfmt, indn, i)
+ call RBcards (nnz2, indn, indcrd)
+
+c determine how many lines for the numerical values
+ if (mkind .eq. 0 .or. mkind .eq. 3) then
+c real or integer
+ vals = 1
+ elseif (mkind .eq. 1) then
+c pattern
+ vals = 0
+ else
+c complex
+ vals = 2
+ endif
+ call RBcards (vals*nnz2, valn, valcrd)
+
+c ----------------------------------------------------------------
+c determine total number of cards
+c ----------------------------------------------------------------
+
+ totcrd = ptrcrd + indcrd + valcrd
+
+c ----------------------------------------------------------------
+c write the header
+c ----------------------------------------------------------------
+
+ write (unit = 7, fmt = 10, err = 999)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd,
+ $ mtype, nrow, ncol, nnz2, 0,
+ $ ptrfmt, indfmt, valfmt
+10 format (a72, a8 / 4i14 / a3, 11x, 4i14 / 2a16, a20)
+
+c ----------------------------------------------------------------
+c write the pointers
+c ----------------------------------------------------------------
+
+ call RBiflush (ptrfmt, %val (cp), ncol+1)
+
+c ----------------------------------------------------------------
+c write the row indices
+c ----------------------------------------------------------------
+
+ task = 2
+ call RBwrite (task, nrow, ncol, skind, cmplex, doZ, %val(Ap),
+ $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind,
+ $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp))
+
+c ----------------------------------------------------------------
+c write the numerical values
+c ----------------------------------------------------------------
+
+ if (mkind .ne. 1) then
+ task = 3
+ call RBwrite(task, nrow, ncol, skind, cmplex, doZ, %val(Ap),
+ $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind,
+ $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp))
+ endif
+
+c ----------------------------------------------------------------
+c free workspace and return
+c ----------------------------------------------------------------
+
+ close (unit = 7)
+ call mxDestroyArray (%val (cpmat))
+ return
+998 call mexErrMsgTxt ('error openning file')
+999 call mexErrMsgTxt ('error writing file')
+ end
diff --git a/RBio/RBwrite_mex_64.f b/RBio/RBwrite_mex_64.f
new file mode 100644
index 0000000..b76a5d2
--- /dev/null
+++ b/RBio/RBwrite_mex_64.f
@@ -0,0 +1,324 @@
+c=======================================================================
+c=== RBio/RBwrite_mex_64 ===============================================
+c=======================================================================
+
+c RBio: a MATLAB toolbox for reading and writing sparse matrices in
+c Rutherford/Boeing format.
+c Copyright (c) 2007, Timothy A. Davis, Univ. of Florida
+
+
+c-----------------------------------------------------------------------
+c RBwrite mexFunction: write a sparse matrix to a Rutherford/Boeing file
+c-----------------------------------------------------------------------
+c
+c mtype = RBwrite (filename, A, Z, title, key)
+c
+c A: a sparse matrix (no explicit zero entries)
+c Z: binary pattern of explicit zero entries to include in the
+c Rutherford/Boeing file. This always has the same size as A,
+c and is always sparse. Not used if [ ], or if nnz(Z) is 0.
+c title: title of Rutherford/Boeing file, up to 72 characters
+c key: the name of the matrix, up to 8 characters
+c
+c Z is optional. RBwrite (filename, A) uses a default
+c title and key, and does not include any explicit zeros.
+c RBwrite (filname, A, 'title...', 'key') uses the given title and
+c key, with no Z matrix.
+c
+c A must be sparse. Z must be empty, or sparse.
+c
+c mtype is a 3-character string with the file-type used
+c mtype(1): r: 0 (real), p: 1 (pattern), c: 2 (complex),
+c i: 3 (ineger)
+c mtype(2): r: -1 (rectangular), u: 0 (unsymmetric), s: 1 symmetric,
+c h: 2 (Hermitian), z: 3 (skew symmetric)
+c mtype(3): a: assembled matrix
+c-----------------------------------------------------------------------
+
+ subroutine mexfunction (nargout, pargout, nargin, pargin)
+ integer*8
+ $ pargout (*), pargin (*)
+ integer*4 nargout, nargin
+
+c ----------------------------------------------------------------
+c MATLAB functions
+c ----------------------------------------------------------------
+
+ integer*4 mxIsChar, mxClassIDFromClassName,
+ $ mxIsClass, mxIsSparse, mxIsComplex
+
+ integer*8
+ $ mxGetM, mxGetN, mxGetJc, mxGetIr, mxGetPr, mxGetPi,
+ $ mxGetString, mxGetData, mxCreateNumericMatrix,
+ $ mxCreateString
+
+c ----------------------------------------------------------------
+c local variables
+c ----------------------------------------------------------------
+
+ integer*8
+ $ nrow, ncol, nnz, mkind, cp, info, zmin, zmax,
+ $ skind, wmat, cpmat, ww, kmin, kmax, task,
+ $ Ap, Ai, Ax, Az, Zp, Zi, Zx, Zz, znz, zrow, zcol, i,
+ $ mzkind, szkind, totcrd, ptrcrd, indcrd, valcrd, nw, one,
+ $ w, valn, valn2, indn, nnz2, ptrn, i1, ititle, vals
+ integer*4 iclass, cmplex, wcmplex
+ character title*72, key*8, mtype*3, ptrfmt*20, indfmt*20,
+ $ valfmt*20, filename*1024, fmt2*20, ztype*3
+ double precision t
+ logical doZ, l1, is_int
+
+c ----------------------------------------------------------------
+c check inputs
+c ----------------------------------------------------------------
+
+ if (nargin .lt. 2 .or. nargin .gt. 5. .or. nargout .gt. 2 .or.
+ $ mxIsChar (pargin (1)) .ne. 1) then
+ call mexErrMsgTxt
+ $ ('[m s] = RBwrite (filename, A, Z, title, key)')
+ endif
+
+c ----------------------------------------------------------------
+c get filename
+c ----------------------------------------------------------------
+
+ if (mxGetString (pargin (1), filename, 1024) .ne. 0) then
+ call mexErrMsgTxt ('filename too long')
+ endif
+ close (unit = 7)
+ open (unit = 7, file = filename, err = 998)
+
+c ----------------------------------------------------------------
+c get A
+c ----------------------------------------------------------------
+
+ if (mxIsClass (pargin (2), 'double') .ne. 1 .or.
+ $ mxIsSparse (pargin (2)) .ne. 1) then
+ call mexErrMsgTxt ('A must be sparse and double')
+ endif
+ cmplex = mxIsComplex (pargin (2))
+ Ap = mxGetJc (pargin (2))
+ Ai = mxGetIr (pargin (2))
+ Ax = mxGetPr (pargin (2))
+ Az = mxGetPi (pargin (2))
+ nrow = mxGetM (pargin (2))
+ ncol = mxGetN (pargin (2))
+
+c ----------------------------------------------------------------
+c get title and key
+c ----------------------------------------------------------------
+
+ do 5 i = 1, 72
+ title (i:i) = ' '
+5 continue
+ key = ' '
+
+ ititle = 99
+ do 15 i = 3, nargin
+ if (mxIsChar (pargin (i)) .eq. 1) then
+ if (ititle .eq. 99) then
+c get the title, up to 72 characters long
+ i1 = mxGetString (pargin (i), title, 72)
+ ititle = i
+ else
+c get the key, up to 8 characters long
+ i1 = mxGetString (pargin (i), key, 8)
+ endif
+ endif
+15 continue
+
+c place a marker in the title, so we know that the
+c Rutherford/Boeing file was generated by the RBwrite mexFunction.
+
+ title (72:72) = '|'
+
+c ----------------------------------------------------------------
+c get Z, if present
+c ----------------------------------------------------------------
+
+ if (nargin .ge. 3 .and. ititle .gt. 3) then
+
+ zrow = mxGetM (pargin (3))
+ zcol = mxGetN (pargin (3))
+
+ if (zrow .eq. 0 .or. zcol .eq. 0) then
+
+c --------------------------------------------------------
+c Z matrix is empty
+c --------------------------------------------------------
+
+ doZ = .false.
+
+ else
+
+c --------------------------------------------------------
+c get the Z matrix
+c --------------------------------------------------------
+
+ if (mxIsClass (pargin (3), 'double') .ne. 1 .or.
+ $ mxIsSparse (pargin (3)) .ne. 1 .or.
+ $ mxIsComplex (pargin (3)) .ne. 0 .or.
+ $ zrow .ne. nrow .or. zcol .ne. ncol) then
+ call mexErrMsgTxt
+ $ ('Z must be sparse, double, real, and same size as A')
+ endif
+ Zp = mxGetJc (pargin (3))
+ Zi = mxGetIr (pargin (3))
+ Zx = mxGetPr (pargin (3))
+ Zz = mxGetPi (pargin (3))
+ doZ = .true.
+
+ endif
+
+ else
+
+c ------------------------------------------------------------
+c no Z matrix is present
+c ------------------------------------------------------------
+
+ doZ = .false.
+
+ endif
+
+c ----------------------------------------------------------------
+c get workspace
+c ----------------------------------------------------------------
+
+ iclass = mxClassIDFromClassName ('int64')
+ nw = max (nrow, ncol) + 1
+ one = 1
+ wcomplex = 0
+ wmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex)
+ cpmat = mxCreateNumericMatrix (nw, one, iclass, wcmplex)
+ w = mxGetData (wmat)
+ cp = mxGetData (cpmat)
+
+c ----------------------------------------------------------------
+c determine the matrix type (RSA, RUA, etc)
+c ----------------------------------------------------------------
+
+c find the symmetry of A (mkind, skind), and nnz(A)
+ call RBkind (nrow, ncol, %val(Ap), %val(Ai), %val(Ax),
+ $ %val(Az), cmplex, mkind, skind, mtype, nnz, %val(cp),
+ $ kmin, kmax)
+
+ if (doZ) then
+c find the symmetry of Z and find nnz(Z)
+ call RBkind (nrow, ncol, %val(Zp), %val(Zi), %val(Zx),
+ $ %val(Zz), 0, mzkind, szkind, ztype, znz, %val(cp),
+ $ zmin, zmax)
+ if (znz .eq. 0) then
+c ignore the Z matrix
+ doZ = .false.
+ elseif (szkind .le. 0) then
+c if Z is unsymmetric, then A+Z is unsymmetric too
+ skind = szkind
+ endif
+ endif
+
+ pargout (1) = mxCreateString (mtype)
+
+c ----------------------------------------------------------------
+c determine the required precision
+c ----------------------------------------------------------------
+
+ indfmt = ' '
+ valfmt = ' '
+ is_int = mkind .eq. 3
+ ww = 1
+ if (mkind .ne. 1) then
+ call RBformat (nnz, %val (Ax), ww, valfmt, valn, is_int,
+ $ kmin, kmax)
+ if (cmplex .eq. 1) then
+ call RBformat (nnz, %val (Az), ww, valfmt, valn, is_int,
+ $ kmin, kmax)
+ endif
+ endif
+
+c ----------------------------------------------------------------
+c determine the number of entries in the matrix A+Z
+c ----------------------------------------------------------------
+
+ task = 1
+ call RBwrite (task, nrow, ncol, skind, cmplex, doZ, %val(Ap),
+ $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind,
+ $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp))
+
+ if (nnz2 .eq. 0) then
+ call mexErrMsgTxt ('empty matrices not handled')
+ endif
+
+c determine pointer format. ncol+1 integers, largest is nnz2+1
+ call RBiformat (1, nnz2+1, ptrfmt, ptrn, i)
+ call RBcards (ncol+1, ptrn, ptrcrd)
+
+c determine row index format. nnz2 integers, largest is nrow
+ call RBiformat (1, nrow, indfmt, indn, i)
+ call RBcards (nnz2, indn, indcrd)
+
+c determine how many lines for the numerical values
+ if (mkind .eq. 0 .or. mkind .eq. 3) then
+c real or integer
+ vals = 1
+ elseif (mkind .eq. 1) then
+c pattern
+ vals = 0
+ else
+c complex
+ vals = 2
+ endif
+ call RBcards (vals*nnz2, valn, valcrd)
+
+c ----------------------------------------------------------------
+c determine total number of cards
+c ----------------------------------------------------------------
+
+ totcrd = ptrcrd + indcrd + valcrd
+
+c ----------------------------------------------------------------
+c write the header
+c ----------------------------------------------------------------
+
+ write (unit = 7, fmt = 10, err = 999)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd,
+ $ mtype, nrow, ncol, nnz2, 0,
+ $ ptrfmt, indfmt, valfmt
+10 format (a72, a8 / 4i14 / a3, 11x, 4i14 / 2a16, a20)
+
+c ----------------------------------------------------------------
+c write the pointers
+c ----------------------------------------------------------------
+
+ call RBiflush (ptrfmt, %val (cp), ncol+1)
+
+c ----------------------------------------------------------------
+c write the row indices
+c ----------------------------------------------------------------
+
+ task = 2
+ call RBwrite (task, nrow, ncol, skind, cmplex, doZ, %val(Ap),
+ $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind,
+ $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp))
+
+c ----------------------------------------------------------------
+c write the numerical values
+c ----------------------------------------------------------------
+
+ if (mkind .ne. 1) then
+ task = 3
+ call RBwrite(task, nrow, ncol, skind, cmplex, doZ, %val(Ap),
+ $ %val(Ai), %val(Ax), %val(Az), %val(Zp), %val(Zi), mkind,
+ $ indfmt, indn, valfmt, valn, nnz2, %val(w), %val(cp))
+ endif
+
+c ----------------------------------------------------------------
+c free workspace and return
+c ----------------------------------------------------------------
+
+ close (unit = 7)
+ call mxDestroyArray (%val (cpmat))
+ return
+998 call mexErrMsgTxt ('error openning file')
+999 call mexErrMsgTxt ('error writing file')
+ end
diff --git a/RBio/README.txt b/RBio/README.txt
new file mode 100644
index 0000000..943a394
--- /dev/null
+++ b/RBio/README.txt
@@ -0,0 +1,102 @@
+RBio: Version 1.1.1, Nov 1, 2007. A MATLAB Toolbox for reading/writing sparse
+matrices in Rutherford/Boeing format.
+
+To install, cd to the RBio directory and type "RBinstall" in the MATLAB
+command window. RBio is written in Fortran because the Rutherford/Boeing
+format can require Fortran I/O statements, depending on how the files are
+stored. Files created by RBio do not require the Fortran I/O library to read
+them, however.
+
+--------------------------------------------------------------------------------
+MATLAB help for RBio:
+--------------------------------------------------------------------------------
+
+ RBio - MATLAB toolbox for reading/writing sparse matrices in the Rutherford/
+ Boeing format, and for reading/writing problems in the UF Sparse Matrix
+ Collection from/to a set of files in a directory.
+
+ RBread - read a sparse matrix from a Rutherford/Boeing file
+ RBreade - read a symmetric finite-element matrix from a R/B file
+ RBtype - determine the Rutherford/Boeing type of a sparse matrix
+ RBwrite - write a sparse matrix to a Rutherford/Boeing file
+ RBraw - read the raw contents of a Rutherford/Boeing file
+ RBfix - read a possibly corrupted matrix from a R/B file
+ RBinstall - install the RBio toolbox for use in MATLAB
+
+ Example:
+
+ load west0479
+ C = west0479 ;
+ RBwrite ('mywest', C, 'WEST0479 chemical eng. problem', 'west0479')
+ A = RBread ('mywest') ;
+ norm (A-C,1)
+
+ See also UFget, mread, mwrite.
+
+ Copyright 2007, Timothy A. Davis
+
+--------------------------------------------------------------------------------
+Files and directories:
+--------------------------------------------------------------------------------
+
+ README.txt this file
+ Contents.m MATLAB help for the RBio toolbox
+
+ RBfix.m read a possibly corrupted R/B file
+ RBinstall.m compile and install RBio for use in MATLAB, and run tests
+ RBmake.m compile RBio for use in MATLAB
+ RBraw.m MATLAB help for RBraw
+ RBreade.m read a finite-element sparse matrix
+ RBread.m MATLAB help for RBread
+ RBtype.m MATLAB help for RBtype
+ RBwrite.m MATLAB help for RBwrite
+
+ RBcread_32.f read a complex sparse matrix, compare with RBrread_*.f
+ RBcread_64.f
+
+ RBcsplit_32.f split a complex matrix into its real and imaginary parts
+ RBcsplit_64.f
+
+ RBraw_mex_32.f mexFunction to read the raw contents of a R/B file
+ RBraw_mex_64.f
+
+ RBread_32.f utility routines for either real or complex matrices
+ RBread_64.f
+
+ RBread_mex_32.f mexFunction to read a real or complex sparse matrix
+ RBread_mex_64.f
+
+ RBrread_32.f read a real sparse matrix, compare with RBcread_*.f
+ RBrread_64.f
+
+ RBtype_mex_32.f mexFunction to determine the Rutherford/Boeing type
+ RBtype_mex_64.f
+
+ RBwrite_32.f write a real or complex sparse matrix
+ RBwrite_64.f
+
+ RBwrite_mex_32.f mexFunction to write a real or complex sparse matrix
+ RBwrite_mex_64.f
+
+./Test: directory with test codes and matrices
+
+ testRB1.m simple test script for RBio
+ testRB2.m simple test script for RBio (requires UFget)
+ bcsstk01.rb HB/bcsstk01 Problem.A from UF Sparse Matrix Collection
+ farm.rb Meszaros/farm Problem.A from UF Sparse Matrix Collection
+ lap_25.pse original Harwell/Boeing version of lap_25 (finite-element)
+ lap_25.rb HB/lap_25 Problem.A from UF Sparse Matrix Collection
+ west0479.rb sparse matrix west0479 from UF Sparse Matrix Collection
+ west0479.rua original Harwell/Boeing version of west0479
+
+ Note that the west0479 matrix provided in the Test directory is the correct
+ version. The MATLAB statement "load west0479" gives you a matrix that is
+ slightly incorrect (as of MATLAB Version 7.3, R2006b).
+
+./Doc: directory with additional documentation and license
+
+ ChangeLog changes since first release
+ dodiff compare 32-bit and 64-bit codes, real and complex
+ gpl.txt GNU license
+ License.txt license
+
diff --git a/RBio/Test/bcsstk01.rb b/RBio/Test/bcsstk01.rb
new file mode 100644
index 0000000..c5ffcf9
--- /dev/null
+++ b/RBio/Test/bcsstk01.rb
@@ -0,0 +1,72 @@
+HB/bcsstk01; 1982; J. Lewis; ed: I. Duff et al. |23
+ 68 3 9 56
+rsa 48 48 224 0
+(20I4) (26I3) (4E20.12)
+ 1 9 17 25 31 37 43 49 55 62 66 70 75 85 95 104 112 120 127 132
+ 136 141 144 146 149 154 158 161 164 167 169 173 178 183 185 188 191 196 201 205
+ 208 211 213 216 219 221 222 224 225
+ 1 5 6 7 11 19 25 30 2 4 6 8 10 20 24 26 3 4 5 9 21 23 27 28 4 8
+ 10 22 27 28 5 7 11 21 23 29 6 12 20 24 25 30 7 11 12 13 31 36 8 10 12 14
+ 18 32 9 10 11 15 17 33 34 10 16 33 34 11 15 17 35 12 14 18 31 36 13 17 18 19
+ 23 37 42 43 47 48 14 15 16 18 20 22 38 44 45 46 15 16 17 21 39 40 44 45 46 16
+ 20 22 39 40 44 45 46 17 18 19 23 41 43 47 48 18 24 37 42 43 47 48 19 23 24 43
+ 48 20 22 24 44 21 22 23 45 46 22 45 46 23 47 24 43 48 25 29 30 31 35 26 28 32
+ 34 27 28 33 28 32 34 29 31 35 30 36 31 35 36 37 32 34 36 38 42 33 34 35 39 41
+ 34 40 35 39 41 36 38 42 37 41 42 43 47 38 40 42 44 46 39 40 41 45 40 44 46 41
+ 43 47 42 48 43 47 48 44 45 46 45 46 46 47 48 48
+ 0.283226851852E+07 0.100000000000E+07 0.208333333333E+07 -0.333333333333E+04
+ 0.100000000000E+07 -0.280000000000E+07 -0.289351851852E+05 0.208333333333E+07
+ 0.163544753086E+07 -0.200000000000E+07 0.555555555555E+07 -0.666666666667E+04
+ -0.200000000000E+07 -0.308641975309E+05 0.555555555555E+07 -0.159791666667E+07
+ 0.172436728395E+07 -0.208333333333E+07 -0.277777777778E+07 -0.168000000000E+07
+ -0.154320987654E+05 -0.277777777778E+07 -0.289351851852E+05 -0.208333333333E+07
+ 0.100333333333E+10 0.200000000000E+07 0.400000000000E+09 -0.333333333333E+07
+ 0.208333333333E+07 0.100000000000E+09 0.106750000000E+10 -0.100000000000E+07
+ 0.200000000000E+09 0.277777777778E+07 0.333333333333E+09 -0.833333333333E+06
+ 0.153533333333E+10 -0.200000000000E+07 -0.555555555555E+07 0.666666666667E+09
+ -0.208333333333E+07 0.100000000000E+09 0.283226851852E+07 -0.100000000000E+07
+ 0.208333333333E+07 -0.280000000000E+07 -0.289351851852E+05 0.208333333333E+07
+ 0.163544753086E+07 0.200000000000E+07 0.555555555555E+07 -0.308641975309E+05
+ 0.555555555555E+07 -0.159791666667E+07 0.172436728395E+07 -0.208333333333E+07
+ -0.277777777778E+07 -0.154320987654E+05 -0.277777777778E+07 -0.289351851852E+05
+ -0.208333333333E+07 0.100333333333E+10 -0.333333333333E+07 0.208333333333E+07
+ 0.100000000000E+09 0.106750000000E+10 0.277777777778E+07 0.333333333333E+09
+ -0.833333333333E+06 0.153533333333E+10 -0.555555555555E+07 0.666666666667E+09
+ -0.208333333333E+07 0.100000000000E+09 0.283609946950E+07 -0.214928529451E+07
+ 0.235916180402E+07 -0.333333333333E+04 -0.100000000000E+07 -0.289351851852E+05
+ 0.208333333333E+07 -0.383095098171E+04 -0.114928529451E+07 0.275828470683E+06
+ 0.176741074446E+07 0.517922131816E+06 0.429857058902E+07 -0.555555555555E+07
+ -0.666666666667E+04 0.200000000000E+07 -0.159791666667E+07 -0.131963213599E+06
+ -0.517922131816E+06 0.229857058902E+07 0.389003806848E+07 -0.263499027470E+07
+ 0.277777777778E+07 -0.168000000000E+07 -0.289351851852E+05 -0.208333333333E+07
+ -0.517922131816E+06 -0.216567078453E+07 -0.551656941367E+06 0.197572063531E+10
+ -0.200000000000E+07 0.400000000000E+09 0.208333333333E+07 0.100000000000E+09
+ -0.229857058902E+07 0.551656941366E+06 0.486193650990E+09 0.152734651547E+10
+ -0.109779731332E+09 0.100000000000E+07 0.200000000000E+09 -0.833333333333E+06
+ 0.114928529451E+07 0.229724661236E+09 -0.557173510779E+08 0.156411143711E+10
+ -0.200000000000E+07 -0.208333333333E+07 0.100000000000E+09 -0.275828470683E+06
+ -0.557173510779E+08 0.109411960038E+08 0.283226851852E+07 0.100000000000E+07
+ 0.208333333333E+07 -0.289351851852E+05 0.208333333333E+07 0.163544753086E+07
+ -0.200000000000E+07 -0.555555555555E+07 -0.159791666667E+07 0.172436728395E+07
+ -0.208333333333E+07 0.277777777778E+07 -0.289351851852E+05 -0.208333333333E+07
+ 0.100333333333E+10 0.208333333333E+07 0.100000000000E+09 0.106750000000E+10
+ -0.833333333333E+06 0.153533333333E+10 -0.208333333333E+07 0.100000000000E+09
+ 0.608796296296E+05 0.125000000000E+07 0.416666666667E+06 -0.416666666667E+04
+ 0.125000000000E+07 0.337291666667E+07 -0.250000000000E+07 -0.833333333333E+04
+ -0.250000000000E+07 0.241171296296E+07 -0.416666666667E+06 -0.235500000000E+07
+ 0.150000000000E+10 0.250000000000E+07 0.500000000000E+09 0.501833333333E+09
+ -0.125000000000E+07 0.250000000000E+09 0.502500000000E+09 -0.250000000000E+07
+ 0.398587962963E+07 -0.125000000000E+07 0.416666666667E+06 -0.392500000000E+07
+ 0.341149691358E+07 0.250000000000E+07 0.694444444444E+07 -0.385802469136E+05
+ 0.694444444445E+07 0.243100308642E+07 -0.416666666667E+06 -0.347222222222E+07
+ -0.192901234568E+05 -0.347222222222E+07 0.150416666667E+10 -0.416666666667E+07
+ 0.133516666667E+10 0.347222222222E+07 0.416666666667E+09 0.216916666667E+10
+ -0.694444444444E+07 0.833333333333E+09 0.398587962963E+07 -0.125000000000E+07
+ 0.416666666667E+06 -0.416666666667E+04 -0.125000000000E+07 0.341149691358E+07
+ 0.250000000000E+07 -0.694444444445E+07 -0.833333333333E+04 0.250000000000E+07
+ 0.243100308642E+07 -0.416666666667E+06 0.347222222222E+07 -0.235500000000E+07
+ 0.150416666667E+10 -0.250000000000E+07 0.500000000000E+09 0.133516666667E+10
+ 0.125000000000E+07 0.250000000000E+09 0.216916666667E+10 -0.250000000000E+07
+ 0.647105806113E+05 0.239928529451E+07 0.140838195984E+06 0.350487988027E+07
+ 0.517922131816E+06 -0.479857058902E+07 0.457738374749E+07 0.134990274700E+06
+ 0.247238730198E+10 0.961679848804E+09 -0.109779731332E+09 0.531278103775E+09
diff --git a/RBio/Test/farm.rb b/RBio/Test/farm.rb
new file mode 100644
index 0000000..7d8995c
--- /dev/null
+++ b/RBio/Test/farm.rb
@@ -0,0 +1,10 @@
+Meszaros/farm; 2004; ; ed: C. Meszaros |1710
+ 6 1 2 3
+ira 7 17 41 0
+(26I3) (40I2) (20I4)
+ 1 2 3 4 5 6 9 13 15 18 21 24 28 32 36 40 41 42
+ 1 2 3 6 7 1 2 3 1 2 3 4 1 2 1 2 4 1 2 5 1 2 4 1 2 3 6 1 2 4 6 1 2 3 7 1 2 4 7 3
+ 4
+ 1 1 1 1 1 4 1 20 4 1 15 40 2 1 2 1 35 1 1 1
+ 1 1 50 250 2 30 1 250 2 15 1 125 1 20 1 125 1 10 1 1
+ 1
diff --git a/RBio/Test/lap_25.pse b/RBio/Test/lap_25.pse
new file mode 100644
index 0000000..03be42b
--- /dev/null
+++ b/RBio/Test/lap_25.pse
@@ -0,0 +1,10 @@
+1FINITE ELEMENT PROBLEM. LAPLACIAN ON A 5 BY 5 GRID. LAP 25
+ 6 2 4 0 0
+PSE 25 16 64 0
+(16I5) (16I5) (16I5)
+ 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61
+ 65
+ 1 2 6 7 6 7 11 12 11 12 16 17 16 17 21 22
+ 2 3 7 8 7 8 12 13 12 13 17 18 17 18 22 23
+ 3 4 8 9 8 9 13 14 13 14 18 19 18 19 23 24
+ 4 5 9 10 9 10 14 15 14 15 19 20 19 20 24 25
diff --git a/RBio/Test/lap_25.rb b/RBio/Test/lap_25.rb
new file mode 100644
index 0000000..5787e58
--- /dev/null
+++ b/RBio/Test/lap_25.rb
@@ -0,0 +1,9 @@
+HB/lap_25; 1980; I. Duff; ed: I. Duff et al. |1177
+ 5 1 4 0
+psa 25 25 97 0
+(26I3) (26I3)
+ 1 5 10 15 20 23 27 32 37 42 45 49 54 59 64 67 71 76 81 86 89 91 93 95 97 98
+ 1 2 6 7 2 3 6 7 8 3 4 7 8 9 4 5 8 9 10 5 9 10 6 7 11 12
+ 7 8 11 12 13 8 9 12 13 14 9 10 13 14 15 10 14 15 11 12 16 17 12 13 16 17
+ 18 13 14 17 18 19 14 15 18 19 20 15 19 20 16 17 21 22 17 18 21 22 23 18 19 22
+ 23 24 19 20 23 24 25 20 24 25 21 22 22 23 23 24 24 25 25
diff --git a/RBio/Test/testRB1.m b/RBio/Test/testRB1.m
new file mode 100644
index 0000000..28ff195
--- /dev/null
+++ b/RBio/Test/testRB1.m
@@ -0,0 +1,65 @@
+function testRB1
+%testRB1: test the RBio toolbox.
+%
+% Example:
+% testRB1
+%
+% See also UFget, RBread, RBreade, testRB2.
+
+% Copyright 2006, Timothy A. Davis
+
+files = {
+'bcsstk01.rb'
+'farm.rb'
+'lap_25.pse'
+'lap_25.rb'
+'west0479.rb'
+'west0479.rua' } ;
+
+for k = 1:length(files)
+ file = files {k} ;
+ fprintf ('%s : ', file) ;
+ if (file (end) == 'e')
+ [A Z] = RBreade (file) ;
+ else
+ [A Z] = RBread (file) ;
+ end
+ fprintf ('%s\n', RBtype (A)) ;
+ RBwrite ('temp.rb', A, Z) ;
+ [A2 Z2] = RBread ('temp.rb') ;
+ if (~isequal (A, A2))
+ fprintf ('test failed: %s (A differs)\n', file) ;
+ error ('!') ;
+ end
+ if (~isequal (Z, Z2))
+ fprintf ('test failed: %s (Z differs)\n', file) ;
+ error ('!') ;
+ end
+end
+
+load west0479
+C = west0479 ;
+RBwrite ('mywest', C, 'WEST0479 chemical eng. problem', 'west0479') ;
+A = RBread ('mywest') ;
+if (~isequal (A, C))
+ error ('test failed: west0479 (MATLAB version)') ;
+end
+fprintf ('west0479 (MATLAB matrix) : %s\n', RBtype (A)) ;
+
+if (~strcmp (RBtype (A), 'rua'))
+ error ('test failed: RBtype(A)\n') ;
+end
+if (~strcmp (RBtype (spones (A)), 'pua'))
+ error ('test failed: RBtype(spones(A))\n') ;
+end
+if (~strcmp (RBtype (2*spones (A)), 'iua'))
+ error ('test failed: RBtype(2*spones(A))\n') ;
+end
+C = A+A' ;
+if (~strcmp (RBtype (C), 'rsa'))
+ error ('test failed: RBtype(A+A'')\n') ;
+end
+
+delete ('mywest') ;
+delete ('temp.rb') ;
+fprintf ('testRB1: all tests passed\n') ;
diff --git a/RBio/Test/testRB2.m b/RBio/Test/testRB2.m
new file mode 100644
index 0000000..4371252
--- /dev/null
+++ b/RBio/Test/testRB2.m
@@ -0,0 +1,60 @@
+function testRB2
+%testRB2: test the RBio toolbox. UFget is required.
+% Note that UFget requires the Nov 25, 2006, revision of the UF_Index.mat file,
+% or later, to access all the Problems used by this test.
+%
+% Example:
+% testRB2
+%
+% See also UFget, RBread, RBreade, testRB1.
+
+% Copyright 2006, Timothy A. Davis
+
+Problem = UFget ('Meszaros/farm') ;
+disp (Problem) ;
+A = RBread ('farm.rb') ;
+if (~isequal (A, Problem.A))
+ error ('test failure: farm.rb') ;
+end
+fprintf ('mtype: %s\n', RBtype (A)) ;
+
+Problem = UFget ('HB/bcsstk01') ;
+disp (Problem) ;
+A = RBread ('bcsstk01.rb') ;
+if (~isequal (A, Problem.A))
+ error ('test failure: bcsstk01.rb') ;
+end
+fprintf ('mtype: %s\n', RBtype (A)) ;
+
+Problem = UFget ('HB/lap_25') ;
+disp (Problem) ;
+A = RBread ('lap_25.rb') ;
+if (~isequal (A, Problem.A))
+ error ('test failure: lap_25.rb') ;
+end
+A = RBreade ('lap_25.pse') ;
+if (~isequal (A, Problem.A))
+ error ('test failure: lap_25.pse') ;
+end
+fprintf ('mtype: %s\n', RBtype (A)) ;
+
+Problem = UFget ('HB/west0479') ;
+disp (Problem) ;
+[A Z] = RBread ('west0479.rb') ;
+if (~isequal (A, Problem.A))
+ error ('test failure: west0479.rb') ;
+end
+if (~isequal (Z, Problem.Zeros))
+ error ('test failure: west0479.rb') ;
+end
+[A Z] = RBread ('west0479.rua') ;
+if (~isequal (A, Problem.A))
+ error ('test failure: west0479.rua') ;
+end
+if (~isequal (Z, Problem.Zeros))
+ error ('test failure: west0479.rua') ;
+end
+fprintf ('mtype: %s\n', RBtype (A)) ;
+
+fprintf ('testRB2: all tests passed\n') ;
+
diff --git a/RBio/Test/west0479.rb b/RBio/Test/west0479.rb
new file mode 100644
index 0000000..3a10523
--- /dev/null
+++ b/RBio/Test/west0479.rb
@@ -0,0 +1,512 @@
+HB/west0479; 1983; A. Westerberg; ed: I. Duff et al. |267
+ 508 30 96 382
+rua 479 479 1910 0
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diff --git a/RBio/Test/west0479.rua b/RBio/Test/west0479.rua
new file mode 100644
index 0000000..ca1ce0a
--- /dev/null
+++ b/RBio/Test/west0479.rua
@@ -0,0 +1,721 @@
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+ .121497400000E+00 .121497400000E+00 -.113835200000E+01 .212305200000E-01
+ .605557500000E+00 -.194901800000E-01 .363496300000E-03 .335792700000E+00
+ -.135338300000E+00 .252409000000E-02 .106730900000E+00 -.953547800000E+00
+ .177838800000E-01 -.907592200000E+00 -.571182200000E+01 -.935684100000E+00
+ -.103465500000E+01 -.432409300000E-01 .100000000000E+01 -.259561100000E-04
+ -.521749100000E-01 .100000000000E+01 -.392189000000E-03 -.117631400000E+00
+ .100000000000E+01 -.196001600000E-01 .531407800000E+01 -.100218400000E+01
+ .344837200000E+00 -.264786200000E+00 -.100000000000E+01 -.100000000000E+01
+ -.100000000000E+01 .176697100000E+01 -.174740600000E+00 .991497300000E+02
+ -.100000000000E+01 -.331139800000E-04 .172639600000E+03 -.100000000000E+01
+ -.411081200000E-04 .356639800000E+03 -.100000000000E+01 -.845871800000E-04
+ .200000800000E+03 .250000000000E+01 .331139800000E-04 .349003300000E+03
+ .250000000000E+01 .411081200000E-04 .722067800000E+03 .250000000000E+01
+ .845871800000E-04 .100000000000E+01 -.144856500000E-05 .100000000000E+01
+ -.511329200000E-03 .100000000000E+01 -.954388700000E+00 .100502500000E+01
+ -.343519000000E-02 .100287400000E+01 -.430169700000E-01 .100138700000E+01
+ -.953547800000E+00 .100000000000E+01 -.494556000000E-04 .100000000000E+01
+ -.217755700000E-02 .100000000000E+01 -.428715300000E-01 .100000000000E+01
+ -.100000000000E+01 .150000000000E+01 .500000000000E+00 .100000000000E+01
+ -.316220000000E+06 -.121325800000E+05 -.100000000000E+01 -.204518100000E+05
+ .915275100000E+04 .914635700000E+01 .377349200000E-02 .224870600000E+04
+ -.125053300000E+00 .675883800000E-01 .650871200000E+02 -.188590400000E+00
+ -.915275100000E+04 .754394300000E+00 -.915275100000E+04 -.690478300000E+04
+ .100000000000E+01 .185692900000E+00 -.500000000000E+00 .191679400000E-03
+ .266845200000E+01 .889484000000E+00 .523971000000E+00 .259027300000E+01
+ .120903600000E+00 .100000000000E+01 .366077300000E+00 .183233300000E-01
+ .530708300000E+00 .261203200000E+01 .121438100000E+00 .100000000000E+01
+ .363274800000E+00 .193984800000E-01 .531148500000E+00 .261344700000E+01
+ .121473100000E+00 .100000000000E+01 .363091700000E+00 .194704500000E-01
+ .531316200000E+00 .261398600000E+01 .121486400000E+00 .100000000000E+01
+ .363021900000E+00 .194979300000E-01 .537533400000E+00 .263388000000E+01
+ .121979600000E+00 .100000000000E+01 .360435800000E+00 .205384600000E-01
+ .710928300000E+00 .313046700000E+01 .135735800000E+00 .100000000000E+01
+ .288309100000E+00 .714898800000E-01
diff --git a/README.txt b/README.txt
new file mode 100644
index 0000000..f0d7ec4
--- /dev/null
+++ b/README.txt
@@ -0,0 +1,135 @@
+SuiteSparse: A Suite of Sparse matrix packages
+
+------------------
+SuiteSparse/README
+------------------
+
+================================================================================
+QUICK START FOR MATLAB USERS: unzip the SuiteSparse.zip file, then in the
+MATLAB Command Window, cd to the SuiteSparse directory and type
+SuiteSparse_install. All packages will be compiled, and several demos will be
+run.
+================================================================================
+
+Nov 1, 2007. SuiteSparse version 3.1
+
+ AMD approximate minimum degree ordering
+
+ CAMD constrained approximate minimum degree ordering
+
+ COLAMD column approximate minimum degree ordering
+
+ CCOLAMD constrained column approximate minimum degree ordering
+
+ BTF permutation to block triangular form
+
+ KLU sparse LU factorization, primarily for circuit simulation.
+ Requires AMD, COLAMD, and BTF. Optionally uses CHOLMOD,
+ CAMD, CCOLAMD, and METIS.
+
+ UMFPACK sparse LU factorization. Requires AMD and the BLAS.
+
+ CHOLMOD sparse Cholesky factorization. Requires AMD, COLAMD, CCOLAMD,
+ the BLAS, and LAPACK. Optionally uses METIS.
+
+ UFconfig configuration file for all the above packages. The
+ UFconfig/UFconfig.mk is included in the Makefile's of all
+ packages. CSparse and RBio do not use UFconfig.
+
+ CSparse a concise sparse matrix package, developed for my upcoming
+ book, "Direct Methods for Sparse Linear Systems", to be
+ published by SIAM.
+
+ CXSparse CSparse Extended. Includes support for complex matrices
+ and both int or long integers.
+
+ RBio read/write sparse matrices in Rutherford/Boeing format
+
+ UFcollection toolbox for managing the UF Sparse Matrix Collection
+
+ LPDASA LP dual active set algorithm (to appear)
+
+ MESHND 2D and 3D mesh generation and nested dissection ordering
+
+ SSMULT sparse matrix multiply for MATLAB
+
+ LINFACTOR simple m-file demonstrating how to use LU and CHOL in
+ MATLAB to solve Ax=b
+
+ MATLAB_Tools various simple m-files for use in MATLAB
+
+CHOLMOD optionally uses METIS 4.0.1
+(http://www-users.cs.umn.edu/~karypis/metis). To use METIS, place a copy of
+the metis-4.0 directory in the same directory (CHOLMOD_ACM_TOMS) containing
+this README file. The use of METIS will improve the ordering quality in
+CHOLMOD.
+
+Refer to each package for license, copyright, and author information. All
+codes are authored or co-authored by Timothy A. Davis, CISE Dept., Univ. of
+Florida. email: my last name @ cise dot ufl dot edu.
+
+================================================================================
+If you use SuiteSparse_install in MATLAB, stop reading here.
+================================================================================
+
+
+
+----------------------------
+To use "make" in Unix/Linux:
+----------------------------
+
+(1) Use the right BLAS and LAPACK libraries
+
+ See http://www.netlib.org/blas for the Fortran reference BLAS (slow, but
+ they work). See http://www.tacc.utexas.edu/~kgoto/ or
+ http://www.cs.utexas.edu/users/flame/goto/ for an optimized BLAS. See
+ http://www.netlib.org/lapack for LAPACK. The UFconfig/UFconfig.mk file
+ assumes the vanilla BLAS (-lblas). You should use an optimized BLAS;
+ otherwise UMFPACK and CHOLMOD will be slow. Change -lblas to -l(your BLAS
+ library here) in the UFconfig/UFconfig.mk file.
+
+(2) Configure METIS (or don't use METIS)
+
+ cd to metis-4.0 and edit the Makefile.in file. I recommend making these
+ changes to metis-4.0/Makefile.in:
+
+ CC = gcc
+ OPTFLAGS = -O3
+ COPTIONS = -fexceptions -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE
+
+ Next, cd to metis-4.0 and type "make".
+
+ If you do not wish to use METIS, then edit the UFconfig/UFconfig.mk file,
+ and change the line
+
+ CHOLMOD_CONFIG =
+
+ to
+
+ CHOLMOD_CONFIG = -DNPARTITION
+
+ Also change the line
+
+ METIS = ../../metis-4.0/libmetis.a
+
+ to
+
+ METIS =
+
+(3) Make other changes to UFconfig/UFconfig.mk as needed
+
+ Edit the UFconfig/UFconfig.mk file as needed. Directions are in that file.
+ If you have compiled SuiteSparse already (partially or completely), then
+ whenever you edit the UFconfig/UFconfig.mk file, you should then type
+ "make purge" (or "make realclean") in this directory.
+
+(4) Type "make" in this directory. All packages will be be compiled. METIS
+ will be compiled if you have it. Several demos will be run.
+
+ The libraries will appear in */Lib/*.a. Include files, as needed by user
+ programs that use CHOLMOD, AMD, CAMD, COLAMD, CCOLAMD, BTF, KLU, UMFPACK,
+ LDL, etc. are in */Include/*.h.
+
+ The METIS library is in metis-4.0/libmetis.a. METIS Include files (not
+ needed by the end user of SuiteSparse) are in located in metis-4.0/Lib/*.h.
+
diff --git a/SSMULT/Contents.m b/SSMULT/Contents.m
new file mode 100644
index 0000000..fafca51
--- /dev/null
+++ b/SSMULT/Contents.m
@@ -0,0 +1,18 @@
+% SSMULT: sparse matrix multiplication (sparse times sparse)
+%
+% SSMULT computes C=A*B where A and B are sparse. It is typically faster
+% than C=A*B in MATLAB 7.4 (or earlier), and always uses less memory.
+%
+% ssmult - multiplies two sparse matrices.
+% ssmult_install - compiles, installs, and tests ssmult.
+% ssmult_unsorted - multiplies two sparse matrices, returning non-standard result.
+% ssmultsym - computes nnz(C), memory, and flops to compute C=A*B; A and B sparse.
+% ssmult_test - tests ssmult, ssmultsym (sparse times sparse matrix multiply)
+% ssmult_demo - simple demo for ssmult.
+% sstest - exhaustive performance test for SSMULT.
+% sstest2 - exhaustive performance test for SSMULT. Requires UFget.
+%
+% Example:
+% C = ssmult(A,B) ; % computes C = A*B
+%
+% Copyright 2007, Timothy A. Davis, University of Florida
diff --git a/SSMULT/README.txt b/SSMULT/README.txt
new file mode 100644
index 0000000..98f59b8
--- /dev/null
+++ b/SSMULT/README.txt
@@ -0,0 +1,87 @@
+SSMULT version 1.1.0, Nov 1, 2007.
+Distributed under the GNU GPL license (see below). Copyright (c) 2007, Timothy
+A. Davis, University of Florida. SSMULT is also available under other
+licenses; contact the author for details.
+http://www.cise.ufl.edu/research/sparse
+
+SSMULT is a MATLAB toolbox for multiplying two sparse matrices, C = A*B. It
+always uses less memory than the built-in C=A*B (in MATLAB 7.4 or earlier, at
+least). It is typically faster, particularly when A or B are complex. It is
+also much faster when A or B are diagonal or permutations of diagonal matrices.
+Requires MATLAB 6.1 or later (it may work on earlier versions; it has been
+tested on MATLAB 6.1, 6.5, 7.0.1, 7.0.4, 7.1, 7.2, 7.3, and 7.4). Works on
+32-bit and 64-bit MATLAB. Either A or B, or both, can be complex. It should
+work in 64-bit Windows, but it has only been tested on Linux for the 64-bit
+case. Only "double" sparse matrices are supported.
+
+To compile, install, and test, type
+
+ ssmult_install
+
+in the MATLAB command window. Then edit your path (with pathtool, or startup.m)
+to add the SSMULT directory to your MATLAB path. For more extensive tests
+(which require the UFget package) type sstest2 after installing SSMULT.
+
+For best performance, do not use the "lcc" compiler that ships with MATLAB 7.4
+(or earlier) for Windows. Use another compiler instead. Type "mex -setup" or
+"doc mex" for more information. For Linux/Unix/Mac, edit your mexopts.sh file
+and use the option:
+
+ COPTIMFLAGS='-O3 -DNDEBUG'
+
+Note that there is a workaround for a minor "gcc -O" bug (handling floating-
+point underflow) in ssmult_template.c. Use -DNO_GCC_BUG if this bug does not
+affect you, and you might slightly increase your performance.
+
+The Results directory contains the result of sstest on various platforms.
+The first three are all on the same laptop, an Intel Core Duo (2GHz, 2GB
+memory, 2MB of cache):
+
+CoreDuo_Linux.png MATLAB 7.4, Intel Core Duo, Linux, gcc v4.1, -O3
+CoreDuo_MS_lcc.png MATLAB 7.4, same laptop as above, lcc compiler.
+CoreDuo_MS_vc2005.png MATLAB 7.4, same laptop, MS VC++ 2005 compiler.
+
+Opteron64_Linux.png MATLAB 7.3, AMD Opteron (64-bit)
+Pentium4M_Linux.png MATLAB 7.3, Pentium 4M, Linux, gcc version 4.1, -O3
+
+These results show that ssmult is always faster for the matrices in this test,
+when using gcc -O3 in Linux. Comparing the CoreDuo_*.png results, you can see
+that lcc generates very slow code; these results are on the same laptop. If
+you see that ssmult is slower than C=A*B in sstest, then check your compiler
+and its optimization options. In particular, "lcc" as the default compiler
+used by the "mex" function in MATLAB on Windows will lead to poor performance.
+In particular, Microsoft provides Visual C++ 2005 Express Edition for free.
+Intel's compiler also generates high-quality code.
+
+If you do not have a C compiler for Windows (other than "lcc" provided with
+MATLAB) do the following. Download and install the following from
+www.microsoft.com:
+
+ Microsoft Visual C++ 2005 Express Edition
+ Microsoft Platform SDK (Windows Server 2003)
+
+Next, install the compiler for use in the MATLAB "mex" command:
+
+ Right click My Computer and select Properties.
+ Click the Advanced tab.
+ Click the Environment Variables button.
+ Create a new environment variable called MSSdk and set its value to the
+ path to the Microsoft Platform SDK. The default location is
+ C:\Program Files\Microsoft Platform SDK for Windows Server 2003 R2\
+ In MATLAB, type the command "mex -setup". Select the Microsoft Visual C++
+ 2005 Express Edition compiler.
+
+--------------------------------------------------------------------------------
+
+SSMULT is free software; you can redistribute it and/or modify it under the
+terms of the GNU General Public License as published by the Free Software
+Foundation; either version 2 of the License, or (at your option) any later
+version.
+
+SSMULT is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with
+this Module; if not, write to the Free Software Foundation, Inc., 51 Franklin
+Street, Fifth Floor, Boston, MA 02110-1301, USA.
diff --git a/SSMULT/Results/CoreDuo_Linux.png b/SSMULT/Results/CoreDuo_Linux.png
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diff --git a/SSMULT/Results/Opteron64_sstest2.png b/SSMULT/Results/Opteron64_sstest2.png
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diff --git a/SSMULT/Results/Pentium4M_Linux.png b/SSMULT/Results/Pentium4M_Linux.png
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diff --git a/SSMULT/gpl.txt b/SSMULT/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/SSMULT/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
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+
+This section is intended to make thoroughly clear what is believed to
+be a consequence of the rest of this License.
+
+ 8. If the distribution and/or use of the Program is restricted in
+certain countries either by patents or by copyrighted interfaces, the
+original copyright holder who places the Program under this License
+may add an explicit geographical distribution limitation excluding
+those countries, so that distribution is permitted only in or among
+countries not thus excluded. In such case, this License incorporates
+the limitation as if written in the body of this License.
+
+ 9. The Free Software Foundation may publish revised and/or new versions
+of the General Public License from time to time. Such new versions will
+be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+Each version is given a distinguishing version number. If the Program
+specifies a version number of this License which applies to it and "any
+later version", you have the option of following the terms and conditions
+either of that version or of any later version published by the Free
+Software Foundation. If the Program does not specify a version number of
+this License, you may choose any version ever published by the Free Software
+Foundation.
+
+ 10. If you wish to incorporate parts of the Program into other free
+programs whose distribution conditions are different, write to the author
+to ask for permission. For software which is copyrighted by the Free
+Software Foundation, write to the Free Software Foundation; we sometimes
+make exceptions for this. Our decision will be guided by the two goals
+of preserving the free status of all derivatives of our free software and
+of promoting the sharing and reuse of software generally.
+
+ NO WARRANTY
+
+ 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
+FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
+OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
+PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
+OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
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+TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
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+REPAIR OR CORRECTION.
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+ 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
+REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
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+OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
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+YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
+PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGES.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+
+Also add information on how to contact you by electronic and paper mail.
+
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
+
+ Gnomovision version 69, Copyright (C) year name of author
+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ <signature of Ty Coon>, 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Library General
+Public License instead of this License.
diff --git a/SSMULT/ssmult.c b/SSMULT/ssmult.c
new file mode 100644
index 0000000..2c826c6
--- /dev/null
+++ b/SSMULT/ssmult.c
@@ -0,0 +1,487 @@
+/* ========================================================================== */
+/* === ssmult =============================================================== */
+/* ========================================================================== */
+
+/* C = ssmult (A,B) multiplies two sparse matrices A and B, in MATLAB. Either
+ * A or B, or both, can be complex. C is returned as a proper MATLAB sparse
+ * matrix, with sorted row indices and no explicit zero entries. If A or B are
+ * complex, but the imaginary part of C is computed to be zero, then C is
+ * returned as a real sparse matrix (as in MATLAB).
+ *
+ * These extra checks (sorting, dropping zeros, and dropping the complex part
+ * if it is all zero) take time, particulary the requirement that C have sorted
+ * columns. If you are interested in speed, try compiling with -DUNSORTED. The
+ * resulting matrix C can have columns with unsorted row indices, but many
+ * MATLAB functions work just fine when given a matrix with unsorted columns.
+ *
+ * When compiled to return C sorted, this function is called SSMULT. When
+ * compiled without returning C sorted, this function is called SSMULT_UNSORTED.
+ *
+ * Copyright 2007, Timothy A. Davis, University of Florida
+ */
+
+#include "ssmult.h"
+
+#ifndef UNSORTED
+
+/* -------------------------------------------------------------------------- */
+/* merge Left [0..nleft-1] and Right [0..nright-1] into S [0..nleft+nright-1] */
+/* -------------------------------------------------------------------------- */
+
+static void merge
+(
+ Int S [ ], /* output of length nleft + nright */
+ const Int Left [ ], /* left input of length nleft */
+ const Int nleft,
+ const Int Right [ ], /* right input of length nright */
+ const Int nright
+)
+{
+ Int p, pleft, pright ;
+
+ /* merge the two inputs, Left and Right, while both inputs exist */
+ for (p = 0, pleft = 0, pright = 0 ; pleft < nleft && pright < nright ; p++)
+ {
+ if (Left [pleft] < Right [pright])
+ {
+ S [p] = Left [pleft++] ;
+ }
+ else
+ {
+ S [p] = Right [pright++] ;
+ }
+ }
+
+ /* either input is exhausted; copy the remaining list into S */
+ for ( ; pleft < nleft ; p++)
+ {
+ S [p] = Left [pleft++] ;
+ }
+ for ( ; pright < nright ; p++)
+ {
+ S [p] = Right [pright++] ;
+ }
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* SORT(a,b) sorts [a b] in ascending order, so that a < b holds on output */
+/* -------------------------------------------------------------------------- */
+
+#define SORT(a,b) { if (a > b) { t = a ; a = b ; b = t ; } }
+
+
+/* -------------------------------------------------------------------------- */
+/* BUBBLE(a,b) sorts [a b] in ascending order, and sets done to 0 if it swaps */
+/* -------------------------------------------------------------------------- */
+
+#define BUBBLE(a,b) { if (a > b) { t = a ; a = b ; b = t ; done = 0 ; } }
+
+
+/* -------------------------------------------------------------------------- */
+/* mergesort */
+/* -------------------------------------------------------------------------- */
+
+/* mergesort (A, W, n) sorts an Int array A of length n in ascending order. W is
+ * a workspace array of size n. function is used for sorting the row indices
+ * in each column of C. Small lists (of length SMALL or less) are sorted with
+ * a bubble sort. A value of 10 for SMALL works well on an Intel Core Duo, an
+ * Intel Pentium 4M, and a 64-bit AMD Opteron. SMALL must be in the range 4 to
+ * 10. */
+
+#ifndef SMALL
+#define SMALL 10
+#endif
+
+static void mergesort
+(
+ Int A [ ], /* array to sort, of size n */
+ Int W [ ], /* workspace of size n */
+ Int n
+)
+{
+ if (n <= SMALL)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* bubble sort for small lists of length SMALL or less */
+ /* ------------------------------------------------------------------ */
+
+ Int t, done ;
+ switch (n)
+ {
+
+#if SMALL >= 10
+ case 10:
+ /* 10-element bubble sort */
+ done = 1 ;
+ BUBBLE (A [0], A [1]) ;
+ BUBBLE (A [1], A [2]) ;
+ BUBBLE (A [2], A [3]) ;
+ BUBBLE (A [3], A [4]) ;
+ BUBBLE (A [4], A [5]) ;
+ BUBBLE (A [5], A [6]) ;
+ BUBBLE (A [6], A [7]) ;
+ BUBBLE (A [7], A [8]) ;
+ BUBBLE (A [8], A [9]) ;
+ if (done) return ;
+#endif
+
+#if SMALL >= 9
+ case 9:
+ /* 9-element bubble sort */
+ done = 1 ;
+ BUBBLE (A [0], A [1]) ;
+ BUBBLE (A [1], A [2]) ;
+ BUBBLE (A [2], A [3]) ;
+ BUBBLE (A [3], A [4]) ;
+ BUBBLE (A [4], A [5]) ;
+ BUBBLE (A [5], A [6]) ;
+ BUBBLE (A [6], A [7]) ;
+ BUBBLE (A [7], A [8]) ;
+ if (done) return ;
+#endif
+
+#if SMALL >= 8
+ case 8:
+ /* 7-element bubble sort */
+ done = 1 ;
+ BUBBLE (A [0], A [1]) ;
+ BUBBLE (A [1], A [2]) ;
+ BUBBLE (A [2], A [3]) ;
+ BUBBLE (A [3], A [4]) ;
+ BUBBLE (A [4], A [5]) ;
+ BUBBLE (A [5], A [6]) ;
+ BUBBLE (A [6], A [7]) ;
+ if (done) return ;
+#endif
+
+#if SMALL >= 7
+ case 7:
+ /* 7-element bubble sort */
+ done = 1 ;
+ BUBBLE (A [0], A [1]) ;
+ BUBBLE (A [1], A [2]) ;
+ BUBBLE (A [2], A [3]) ;
+ BUBBLE (A [3], A [4]) ;
+ BUBBLE (A [4], A [5]) ;
+ BUBBLE (A [5], A [6]) ;
+ if (done) return ;
+#endif
+
+#if SMALL >= 6
+ case 6:
+ /* 6-element bubble sort */
+ done = 1 ;
+ BUBBLE (A [0], A [1]) ;
+ BUBBLE (A [1], A [2]) ;
+ BUBBLE (A [2], A [3]) ;
+ BUBBLE (A [3], A [4]) ;
+ BUBBLE (A [4], A [5]) ;
+ if (done) return ;
+#endif
+
+#if SMALL >= 5
+ case 5:
+ /* 5-element bubble sort */
+ done = 1 ;
+ BUBBLE (A [0], A [1]) ;
+ BUBBLE (A [1], A [2]) ;
+ BUBBLE (A [2], A [3]) ;
+ BUBBLE (A [3], A [4]) ;
+ if (done) return ;
+#endif
+
+ case 4:
+ /* 4-element bubble sort */
+ done = 1 ;
+ BUBBLE (A [0], A [1]) ;
+ BUBBLE (A [1], A [2]) ;
+ BUBBLE (A [2], A [3]) ;
+ if (done) return ;
+
+ case 3:
+ /* 3-element bubble sort */
+ done = 1 ;
+ BUBBLE (A [0], A [1]) ;
+ BUBBLE (A [1], A [2]) ;
+ if (done) return ;
+
+ case 2:
+ /* 2-element bubble sort */
+ SORT (A [0], A [1]) ;
+
+ case 1:
+ case 0:
+ /* nothing to do */
+ ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* recursive mergesort if A has length 5 or more */
+ /* ------------------------------------------------------------------ */
+
+ Int n1, n2, n3, n4, n12, n34, n123 ;
+
+ n12 = n / 2 ; /* split n into n12 and n34 */
+ n34 = n - n12 ;
+
+ n1 = n12 / 2 ; /* split n12 into n1 and n2 */
+ n2 = n12 - n1 ;
+
+ n3 = n34 / 2 ; /* split n34 into n3 and n4 */
+ n4 = n34 - n3 ;
+
+ n123 = n12 + n3 ; /* start of 4th subset = n1 + n2 + n3 */
+
+ mergesort (A, W, n1) ; /* sort A [0 ... n1-1] */
+ mergesort (A + n1, W, n2) ; /* sort A [n1 ... n12-1] */
+ mergesort (A + n12, W, n3) ; /* sort A [n12 ... n123-1] */
+ mergesort (A + n123, W, n4) ; /* sort A [n123 ... n-1] */
+
+ /* merge A [0 ... n1-1] and A [n1 ... n12-1] into W [0 ... n12-1] */
+ merge (W, A, n1, A + n1, n2) ;
+
+ /* merge A [n12 ... n123-1] and A [n123 ... n-1] into W [n12 ... n-1] */
+ merge (W + n12, A + n12, n3, A + n123, n4) ;
+
+ /* merge W [0 ... n12-1] and W [n12 ... n-1] into A [0 ... n-1] */
+ merge (A, W, n12, W + n12, n34) ;
+ }
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* ssmult mexFunction */
+/* -------------------------------------------------------------------------- */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double *Ax, *Az, *Bx, *Bz, *Cx, *Cz, *W, *Wz ;
+ double bkj, bzkj, cij, czij ;
+ Int *Ap, *Ai, *Bp, *Bi, *Cp, *Ci, *Flag ;
+ Int Anrow, Ancol, Bnrow, Bncol, p, i, j, k, cnz, pb, pa, pbend, paend, mark,
+ pc, pcstart, blen, drop, zallzero, pend, needs_sorting, pcmax ;
+ int A_is_complex, B_is_complex, C_is_complex, A_is_diagonal,
+ A_is_permutation ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs and workspace */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin != 2 || nargout > 1)
+ {
+ mexErrMsgTxt ("Usage: C = ssmult (A,B)") ;
+ }
+
+ Ap = mxGetJc (pargin [0]) ;
+ Ai = mxGetIr (pargin [0]) ;
+ Ax = mxGetPr (pargin [0]) ;
+ Az = mxGetPi (pargin [0]) ;
+ Anrow = mxGetM (pargin [0]) ;
+ Ancol = mxGetN (pargin [0]) ;
+ A_is_complex = mxIsComplex (pargin [0]) ;
+
+ Bp = mxGetJc (pargin [1]) ;
+ Bi = mxGetIr (pargin [1]) ;
+ Bx = mxGetPr (pargin [1]) ;
+ Bz = mxGetPi (pargin [1]) ;
+ Bnrow = mxGetM (pargin [1]) ;
+ Bncol = mxGetN (pargin [1]) ;
+ B_is_complex = mxIsComplex (pargin [1]) ;
+
+ if (Ancol != Bnrow || !mxIsSparse (pargin [0]) || !mxIsSparse (pargin [1]))
+ {
+ mexErrMsgTxt ("wrong dimensions, or A and B not sparse") ;
+ }
+
+#ifndef MATLAB_6p1_OR_EARLIER
+ if (!mxIsDouble (pargin [0]) || !mxIsDouble (pargin [1]))
+ {
+ mexErrMsgTxt ("A and B must be of class 'double'") ;
+ }
+#endif
+
+ Flag = mxCalloc (Anrow, sizeof (Int)) ; /* workspace */
+ Cp = mxMalloc ((Bncol+1) * sizeof (Int)) ; /* allocate C column pointers */
+
+ /* ---------------------------------------------------------------------- */
+ /* compute # of nonzeros in result */
+ /* ---------------------------------------------------------------------- */
+
+ pb = 0 ;
+ cnz = 0 ;
+ mark = 0 ;
+ for (j = 0 ; j < Bncol ; j++)
+ {
+ /* Compute nnz (C (:,j)) */
+ mark-- ; /* Flag [0..n-1] != mark is now true */
+ pb = Bp [j] ;
+ pbend = Bp [j+1] ;
+ pcstart = cnz ;
+ pcmax = cnz + Anrow ;
+ Cp [j] = cnz ;
+ /* cnz += nnz (C (:,j)), stopping early if nnz(C(:,j)) == Anrow */
+ for ( ; pb < pbend && cnz < pcmax ; pb++)
+ {
+ k = Bi [pb] ; /* nonzero entry B(k,j) */
+ paend = Ap [k+1] ;
+ for (pa = Ap [k] ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ; /* nonzero entry A(i,k) */
+ if (Flag [i] != mark)
+ {
+ /* C(i,j) is a new nonzero */
+ Flag [i] = mark ; /* mark i as appearing in C(:,j) */
+ cnz++ ;
+ }
+ }
+ }
+ if (cnz < pcstart)
+ {
+ /* integer overflow has occurred */
+ mexErrMsgTxt ("problem too large") ;
+ }
+ }
+ Cp [Bncol] = cnz ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate C */
+ /* ---------------------------------------------------------------------- */
+
+ Ci = mxMalloc (MAX (cnz,1) * sizeof (Int)) ;
+ Cx = mxMalloc (MAX (cnz,1) * sizeof (double)) ;
+ C_is_complex = A_is_complex || B_is_complex ;
+ Cz = (C_is_complex) ? mxMalloc (MAX (cnz,1) * sizeof (double)) : NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = A*B */
+ /* ---------------------------------------------------------------------- */
+
+ if (A_is_complex)
+ {
+ if (B_is_complex)
+ {
+ /* all of C, A, and B are complex */
+#define ACOMPLEX
+#define BCOMPLEX
+#include "ssmult_template.c"
+ }
+ else
+ {
+ /* C and A are complex, B is real */
+#define ACOMPLEX
+#include "ssmult_template.c"
+ }
+ }
+ else
+ {
+ if (B_is_complex)
+ {
+ /* C and B are complex, A is real */
+#define BCOMPLEX
+#include "ssmult_template.c"
+ }
+ else
+ {
+ /* all of C, A, and B are real */
+#include "ssmult_template.c"
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ mxFree (Flag) ;
+
+#ifndef UNSORTED
+
+ /* ---------------------------------------------------------------------- */
+ /* convert C to real if Cz is all zero */
+ /* ---------------------------------------------------------------------- */
+
+ if (C_is_complex && zallzero)
+ {
+ C_is_complex = 0 ;
+ mxFree (Cz) ;
+ Cz = NULL ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* drop zeros from C and reduce its size, if any zeros appear */
+ /* ---------------------------------------------------------------------- */
+
+ if (drop)
+ {
+ if (C_is_complex)
+ {
+ for (cnz = 0, p = 0, j = 0 ; j < Bncol ; j++)
+ {
+ Cp [j] = cnz ;
+ pend = Cp [j+1] ;
+ for ( ; p < pend ; p++)
+ {
+ if (Cx [p] != 0 || Cz [p] != 0)
+ {
+ Ci [cnz] = Ci [p] ; /* keep this entry */
+ Cx [cnz] = Cx [p] ;
+ Cz [cnz] = Cz [p] ;
+ cnz++ ;
+ }
+ }
+ }
+ Cz = mxRealloc (Cz, MAX (cnz,1) * sizeof (double)) ;
+ }
+ else
+ {
+ for (cnz = 0, p = 0, j = 0 ; j < Bncol ; j++)
+ {
+ Cp [j] = cnz ;
+ pend = Cp [j+1] ;
+ for ( ; p < pend ; p++)
+ {
+ if (Cx [p] != 0)
+ {
+ Ci [cnz] = Ci [p] ; /* keep this entry */
+ Cx [cnz] = Cx [p] ;
+ cnz++ ;
+ }
+ }
+ }
+ }
+ Cp [Bncol] = cnz ;
+ Ci = mxRealloc (Ci, MAX (cnz,1) * sizeof (Int)) ;
+ Cx = mxRealloc (Cx, MAX (cnz,1) * sizeof (double)) ;
+ }
+
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* return C */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = mxCreateSparse (0, 0, 0, C_is_complex ? mxCOMPLEX : mxREAL) ;
+ mxFree (mxGetJc (pargout [0])) ;
+ mxFree (mxGetIr (pargout [0])) ;
+ mxFree (mxGetPr (pargout [0])) ;
+ mxFree (mxGetPi (pargout [0])) ;
+ mxSetJc (pargout [0], Cp) ;
+ mxSetIr (pargout [0], Ci) ;
+ mxSetPr (pargout [0], Cx) ;
+ mxSetPi (pargout [0], Cz) ;
+ mxSetNzmax (pargout [0], MAX (cnz,1)) ;
+ mxSetM (pargout [0], Anrow) ;
+ mxSetN (pargout [0], Bncol) ;
+}
diff --git a/SSMULT/ssmult.h b/SSMULT/ssmult.h
new file mode 100644
index 0000000..960a690
--- /dev/null
+++ b/SSMULT/ssmult.h
@@ -0,0 +1,24 @@
+/* ========================================================================== */
+/* === ssmult.h ============================================================= */
+/* ========================================================================== */
+
+/* Include file for ssmult.c and ssmultsym.c
+ * Copyright 2007, Timothy A. Davis, University of Florida
+ */
+
+#include "mex.h"
+#include <stdlib.h>
+
+/* define the MATLAB integer */
+#ifdef IS64
+#define Int mwSignedIndex
+#else
+#define Int int
+#endif
+
+/* turn off debugging */
+#ifndef NDEBUG
+#define NDEBUG
+#endif
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
diff --git a/SSMULT/ssmult.m b/SSMULT/ssmult.m
new file mode 100644
index 0000000..4425cb2
--- /dev/null
+++ b/SSMULT/ssmult.m
@@ -0,0 +1,20 @@
+function C = ssmult (A,B) %#ok
+%SSMULT multiplies two sparse matrices.
+% C = ssmult (A,B) computes C=A*B where A and B are sparse. This function is
+% typically faster than C=A*B in MATLAB 7.4, and always uses less memory.
+% Either A or B, or both, can be complex. Only matrices of class "double" are
+% supported.
+%
+% Example:
+% load west0479
+% A = west0479 ;
+% B = sprand (west0479) ;
+% C = A*B ;
+% D = ssmult (A,B) ;
+% C-D
+%
+% See also ssmultsym, mtimes.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+error ('ssmult mexFunction not found') ;
diff --git a/SSMULT/ssmult_demo.m b/SSMULT/ssmult_demo.m
new file mode 100644
index 0000000..6c96388
--- /dev/null
+++ b/SSMULT/ssmult_demo.m
@@ -0,0 +1,18 @@
+function ssmult_demo
+%SSMULT_DEMO simple demo for ssmult.
+%
+% Example:
+% ssmult_demo
+%
+% See also ssmult, ssmult_unsorted, ssmultsym, sstest, sstest2.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+type ssmult_demo
+load west0479
+A = west0479 ;
+B = sprand (A) ;
+C = A*B ;
+D = ssmult (A,B) ;
+err = norm (C-D,1) / norm (C,1) ;
+fprintf ('ssmult west0479 error: %g\n', err) ;
diff --git a/SSMULT/ssmult_install.m b/SSMULT/ssmult_install.m
new file mode 100644
index 0000000..d0dd7d5
--- /dev/null
+++ b/SSMULT/ssmult_install.m
@@ -0,0 +1,74 @@
+function ssmult_install (dotests)
+%SSMULT_INSTALL compiles, installs, and tests ssmult.
+% Note that the "lcc" compiler provided with MATLAB for Windows can generate
+% slow code; use another compiler if possible. Your current directory must be
+% SSMULT for ssmult_install to work properly. If you use Linux/Unix/Mac, I
+% recommend that you use COPTIMFLAGS='-O3 -DNDEBUG' in your mexopts.sh file.
+%
+% Example:
+% ssmult_install % compile and install
+% ssmult_install (0) % just compile and install, do not test
+%
+% See also ssmult, ssmultsym, ssmult_unsorted, sstest, sstest2, mtimes.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+%-------------------------------------------------------------------------------
+% print an introduction
+%-------------------------------------------------------------------------------
+
+help ssmult
+help ssmult_install
+
+%-------------------------------------------------------------------------------
+% compile ssmult and add it to the path
+%-------------------------------------------------------------------------------
+
+d = '' ;
+if (~isempty (strfind (computer, '64')))
+ % 64-bit MATLAB
+ d = ' -largeArrayDims -DIS64' ;
+end
+
+v = getversion ;
+if (v < 6.5)
+ % mxIsDouble is false for a double sparse matrix in MATLAB 6.1 or earlier
+ d = [d ' -DMATLAB_6p1_OR_EARLIER'] ;
+end
+
+cmd = sprintf ('mex -O%s ssmult.c', d) ;
+disp (cmd) ;
+eval (cmd) ;
+
+cmd = sprintf ('mex -O%s ssmultsym.c', d) ;
+disp (cmd) ;
+eval (cmd) ;
+
+cmd = sprintf ('mex -O%s -DUNSORTED ssmult.c -output ssmult_unsorted', d) ;
+disp (cmd) ;
+eval (cmd) ;
+
+addpath (pwd) ;
+fprintf ('\nssmult has been compiled, and the following directory has been\n') ;
+fprintf ('added to your MATLAB path. Use pathtool to add it permanently:\n') ;
+fprintf ('\n%s\n\n', pwd) ;
+fprintf ('If you cannot save your path with pathtool, add the following\n') ;
+fprintf ('to your MATLAB startup.m file (type "doc startup" for help):\n') ;
+fprintf ('\naddpath (''%s'') ;\n\n', pwd) ;
+
+%-------------------------------------------------------------------------------
+% test ssmult and ssmultsym
+%-------------------------------------------------------------------------------
+
+if (nargin < 1)
+ dotests = 1 ;
+end
+if (dotests)
+ ssmult_test ;
+end
+
+%-------------------------------------------------------------------------------
+function v = getversion
+% determine the MATLAB version, and return it as a double.
+v = sscanf (version, '%d.%d.%d') ;
+v = 10.^(0:-1:-(length(v)-1)) * v ;
diff --git a/SSMULT/ssmult_template.c b/SSMULT/ssmult_template.c
new file mode 100644
index 0000000..dc83f94
--- /dev/null
+++ b/SSMULT/ssmult_template.c
@@ -0,0 +1,419 @@
+/* ========================================================================== */
+/* === ssmult_template.c ==================================================== */
+/* ========================================================================== */
+
+/* C = A*B, where A and B are sparse. The column pointers for C (the Cp array)
+ * have already been computed. entries are dropped. This code fragment is
+ * #include'd into ssmult.c four times, with all four combinations of ACOMPLEX
+ * (defined or not) and BCOMPLEX (defined or not).
+ *
+ * By default, C is returned with sorted column indices, and with explicit
+ * zero entries dropped. If C is complex with an all-zero imaginary part, then
+ * the imaginary part is freed and C becomes real. Thus, C is a pure MATLAB
+ * sparse matrix.
+ *
+ * If UNSORTED is defined (-DUNSORTED), then the nonzero pattern of C is
+ * returned with unsorted column indices, explicit zeros may be present in C,
+ * and the imaginary of a complex C may be all zero. This is much faster than
+ * returning a pure MATLAB sparse matrix.
+ *
+ * If the compiler bug discussed below does not affect you, then uncomment the
+ * following line, or compile with code with -DNO_GCC_BUG.
+
+#define NO_GCC_BUG
+
+ * The gcc bug occurs when cij underflows to zero:
+ *
+ * cij = aik * bkj ;
+ * if (cij == 0)
+ * {
+ * drop this entry
+ * }
+ *
+ * If cij underflows, cij is zero but the above test is incorrectly FALSE with
+ * gcc -O, using gcc version 4.1.0 on an Intel Pentium. The bug does not appear
+ * on an AMD Opteron with the same compiler. The solution is to store cij to
+ * memory first, and then to read it back in and test it, which is slower.
+ */
+
+/* -------------------------------------------------------------------------- */
+/* MULT: multiply (or multiply and accumulate, depending on op) */
+/* -------------------------------------------------------------------------- */
+
+/* op can be "=" or "+=" */
+
+#ifdef ACOMPLEX
+#ifdef BCOMPLEX
+#define MULT(x,z,op) \
+ x op Ax [pa] * bkj - Az [pa] * bzkj ; \
+ z op Az [pa] * bkj + Ax [pa] * bzkj ;
+#else
+#define MULT(x,z,op) \
+ x op Ax [pa] * bkj ; \
+ z op Az [pa] * bkj ;
+#endif
+#else
+#ifdef BCOMPLEX
+#define MULT(x,z,op) \
+ x op Ax [pa] * bkj ; \
+ z op Ax [pa] * bzkj ;
+#else
+#define MULT(x,z,op) \
+ x op Ax [pa] * bkj ;
+#endif
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* ASSIGN_BKJ: copy B(k,j) into a local scalar */
+/* -------------------------------------------------------------------------- */
+
+#ifdef BCOMPLEX
+#define ASSIGN_BKJ \
+ bkj = Bx [pb] ; \
+ bzkj = Bz [pb] ;
+#else
+#define ASSIGN_BKJ \
+ bkj = Bx [pb] ;
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* DROP_CHECK: check if an entry must be dropped */
+/* -------------------------------------------------------------------------- */
+
+#ifndef UNSORTED
+#if defined (ACOMPLEX) || defined (BCOMPLEX)
+#define DROP_CHECK(x,z) \
+ if (x == 0 && z == 0) drop = 1 ; \
+ if (z != 0) zallzero = 0 ;
+#else
+#define DROP_CHECK(x,z) if (x == 0) drop = 1 ;
+#endif
+#else
+#define DROP_CHECK(x,z)
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* sparse matrix multiply template */
+/* -------------------------------------------------------------------------- */
+
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize drop tests */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef UNSORTED
+ drop = 0 ; /* true if any entry in C is zero */
+ zallzero = 1 ; /* true if Cz is all zero */
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* quick check if A is diagonal, or a permutation matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (Anrow == Ancol && Ap [Ancol] == Ancol)
+ {
+ /* A is square, with n == nnz (A); check the pattern */
+ A_is_permutation = 1 ;
+ A_is_diagonal = 1 ;
+ for (j = 0 ; j < Ancol ; j++)
+ {
+ if (Ap [j] != j)
+ {
+ /* A has a column with no entries, or more than 1 entry */
+ A_is_permutation = 0 ;
+ A_is_diagonal = 0 ;
+ break ;
+ }
+ }
+ mark-- ; /* Flag [0..n-1] != mark is now true */
+ for (j = 0 ; j < Ancol && (A_is_permutation || A_is_diagonal) ; j++)
+ {
+ /* A has one entry in each column, so j == Ap [j] */
+ i = Ai [j] ;
+ if (i != j)
+ {
+ /* A is not diagonal, but might still be a permutation */
+ A_is_diagonal = 0 ;
+ }
+ if (Flag [i] == mark)
+ {
+ /* row i appears twice; A is neither permutation nor diagonal */
+ A_is_permutation = 0 ;
+ A_is_diagonal = 0 ;
+ }
+ /* mark row i, so we know if we see it again */
+ Flag [i] = mark ;
+ }
+ }
+ else
+ {
+ /* A is not square, or nnz (A) is not equal to n */
+ A_is_permutation = 0 ;
+ A_is_diagonal = 0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef UNSORTED
+ W = NULL ;
+ if (!A_is_diagonal)
+ {
+#if defined (ACOMPLEX) || defined (BCOMPLEX)
+ W = mxMalloc (Anrow * 2 * sizeof (double)) ;
+ Wz = W + Anrow ;
+#else
+ W = mxMalloc (Anrow * sizeof (double)) ;
+#endif
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* compute C one column at a time */
+ /* ---------------------------------------------------------------------- */
+
+ if (A_is_diagonal)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* C = A*B where A is diagonal */
+ /* ------------------------------------------------------------------ */
+
+ pb = 0 ;
+ for (j = 0 ; j < Bncol ; j++)
+ {
+ pcstart = pb ;
+ pbend = Bp [j+1] ; /* column B is in Bi,Bx,Bz [pb ... pbend+1] */
+ for ( ; pb < pbend ; pb++)
+ {
+ k = Bi [pb] ; /* nonzero entry B(k,j) */
+ ASSIGN_BKJ ;
+ Ci [pb] = k ;
+ pa = k ;
+ MULT (Cx [pb], Cz [pb], =) ; /* C(k,j) = A(k,k)*B(k,j) */
+#ifdef NO_GCC_BUG
+ DROP_CHECK (Cx [pb], Cz [pb]) ; /* check if C(k,j) == 0 */
+#endif
+ }
+
+#ifndef UNSORTED
+#ifndef NO_GCC_BUG
+ for (pc = pcstart ; pc < pbend ; pc++)
+ {
+ DROP_CHECK (Cx [pc], Cz [pc]) ; /* check if C(k,j) == 0 */
+ }
+#endif
+#endif
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* C = A*B, general case, or A permutation */
+ /* ------------------------------------------------------------------ */
+
+ pb = 0 ;
+ cnz = 0 ;
+ for (j = 0 ; j < Bncol ; j++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* compute jth column of C: C(:,j) = A * B(:,j) */
+ /* -------------------------------------------------------------- */
+
+ pbend = Bp [j+1] ; /* column B is in Bi,Bx,Bz [pb ... pbend+1] */
+ pcstart = cnz ; /* start of column j in C */
+ blen = pbend - pb ; /* number of entries in B */
+ needs_sorting = 0 ; /* true if column j needs sorting */
+
+ if (blen == 0)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* nothing to do, B(:,j) and C(:,j) are empty */
+ /* ---------------------------------------------------------- */
+
+ continue ;
+
+ }
+ else if (blen == 1)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* B(:,j) contains only one nonzero */
+ /* ---------------------------------------------------------- */
+
+ /* since there is only one entry in B, just scale column A(:,k):
+ * C(:,j) = A(:,k) * B(k,j)
+ * C is sorted only if A is sorted on input */
+
+ k = Bi [pb] ; /* nonzero entry B(k,j) */
+ ASSIGN_BKJ ;
+ paend = Ap [k+1] ;
+ for (pa = Ap [k] ; pa < paend ; pa++, cnz++)
+ {
+ Ci [cnz] = Ai [pa] ; /* nonzero entry A(i,k) */
+ MULT (Cx [cnz], Cz [cnz], =) ; /* C(i,j) = A(i,k)*B(k,j) */
+#ifdef NO_GCC_BUG
+ DROP_CHECK (Cx [cnz], Cz [cnz]) ; /* check C(i,j) == 0 */
+#endif
+ }
+ pb++ ;
+
+#ifndef UNSORTED
+#ifndef NO_GCC_BUG
+ for (pc = pcstart ; pc < cnz ; pc++)
+ {
+ DROP_CHECK (Cx [pc], Cz [pc]) ; /* check if C(i,j) == 0 */
+ }
+#endif
+#endif
+
+ }
+ else
+ {
+
+ /* ---------------------------------------------------------- */
+ /* B(:,j) has two or more entries */
+ /* ---------------------------------------------------------- */
+
+ if (A_is_permutation)
+ {
+
+ /* ------------------------------------------------------ */
+ /* A is a permutation matrix */
+ /* ------------------------------------------------------ */
+
+ needs_sorting = 1 ;
+ for ( ; pb < pbend ; pb++)
+ {
+ k = Bi [pb] ; /* nonzero entry B(k,j) */
+ ASSIGN_BKJ ;
+ i = Ai [k] ; /* nonzero entry A(i,k) */
+ Ci [pb] = i ;
+ pa = k ;
+ /* C(i,j) = A(i,k)*B(k,j) */
+#ifndef UNSORTED
+ MULT (W [i], Wz [i], =) ;
+#else
+ MULT (Cx [pb], Cz [pb], =) ;
+#endif
+ }
+ cnz = pbend ;
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------ */
+ /* general case */
+ /* ------------------------------------------------------ */
+
+ /* first entry in jth column of B is simpler */
+ /* C(:,j) = A (:,k) * B (k,j) */
+ k = Bi [pb] ; /* nonzero entry B(k,j) */
+ ASSIGN_BKJ ;
+ paend = Ap [k+1] ;
+ for (pa = Ap [k] ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ; /* nonzero entry A(i,k) */
+ Flag [i] = cnz ;
+ Ci [cnz] = i ; /* new entry C(i,j) */
+ /* C(i,j) = A(i,k)*B(k,j) */
+#ifndef UNSORTED
+ MULT (W [i], Wz [i], =) ;
+#else
+ MULT (Cx [cnz], Cz [cnz], =) ;
+#endif
+ cnz++ ;
+ }
+ pb++ ;
+ for ( ; pb < pbend ; pb++)
+ {
+ k = Bi [pb] ; /* nonzero entry B(k,j) */
+ ASSIGN_BKJ ;
+ /* C(:,j) += A (:,k) * B (k,j) */
+ paend = Ap [k+1] ;
+ for (pa = Ap [k] ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ; /* nonzero entry A(i,k) */
+ pc = Flag [i] ;
+ if (pc < pcstart)
+ {
+ pc = cnz++ ;
+ Flag [i] = pc ;
+ Ci [pc] = i ; /* new entry C(i,j) */
+ /* C(i,j) = A(i,k)*B(k,j) */
+#ifndef UNSORTED
+ MULT (W [i], Wz [i], =) ;
+ needs_sorting = 1 ;
+#else
+ MULT (Cx [pc], Cz [pc], =) ;
+#endif
+ }
+ else
+ {
+ /* C(i,j) += A(i,k)*B(k,j) */
+#ifndef UNSORTED
+ MULT (W [i], Wz [i], +=) ;
+#else
+ MULT (Cx [pc], Cz [pc], +=) ;
+#endif
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------- */
+ /* sort the pattern of C(:,j) and gather the values of C(:,j) */
+ /* ---------------------------------------------------------- */
+
+#ifndef UNSORTED
+ /* Sort the row indices in C(:,j). Use Cx as Int workspace.
+ * This assumes sizeof (Int) < sizeof (double). If blen <= 1,
+ * or if subsequent entries in B(:,j) appended entries onto C,
+ * there is no need to sort C(:,j), assuming A is sorted. */
+ if (needs_sorting)
+ {
+ mergesort (Ci + pcstart, (Int *) (Cx + pcstart),
+ cnz - pcstart) ;
+ }
+ for (pc = pcstart ; pc < cnz ; pc++)
+ {
+#if defined (ACOMPLEX) || defined (BCOMPLEX)
+ i = Ci [pc] ;
+ cij = W [i] ; /* get C(i,j) from W */
+ czij = Wz [i] ;
+ Cx [pc] = cij ; /* copy C(i,j) into C */
+ Cz [pc] = czij ;
+#else
+ cij = W [Ci [pc]] ; /* get C(i,j) from W */
+ Cx [pc] = cij ; /* copy C(i,j) into C */
+#endif
+ DROP_CHECK (cij, czij) ; /* check if C(i,j) == 0 */
+ }
+#endif
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef UNSORTED
+ mxFree (W) ;
+#endif
+
+
+}
+
+#undef ACOMPLEX
+#undef BCOMPLEX
+#undef MULT
+#undef ASSIGN_BKJ
+#undef DROP_CHECK
diff --git a/SSMULT/ssmult_test.m b/SSMULT/ssmult_test.m
new file mode 100644
index 0000000..d979156
--- /dev/null
+++ b/SSMULT/ssmult_test.m
@@ -0,0 +1,115 @@
+function ssmult_test
+%SSMULT_TEST tests ssmult, ssmultsym (sparse times sparse matrix multiply)
+%
+% Example:
+% ssmult_test
+%
+% See also ssmult, ssmult_unsorted, ssmultsym, sstest, sstest2.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+fprintf ('Please wait while your new ssmult function is tested ...\n') ;
+
+ssmult_demo ;
+
+fprintf ('\ntesting large matrices (may fail if you are low on memory):\n')
+rand ('state', 0) ;
+
+n = 10000 ;
+A = sprand (n, n, 0.01) ;
+B = sprand (n, n, 0.001) ;
+test_large (A,B) ;
+
+msg = { 'real', 'complex' } ;
+
+% all of these calls to ssmult should fail:
+fprintf ('\ntesting error handling (the errors below are expected):\n') ;
+A = { 3, 'gunk', sparse(1), sparse(1), sparse(rand(3,2)) } ;
+B = { 4, 0 , 5, msg, sparse(rand(3,4)) } ;
+for k = 1:length(A)
+ try
+ % the following statement is supposed to fail
+ C = ssmult (A {k}, B {k}) ; %#ok
+ error ('test failed\n') ;
+ catch
+ disp (lasterr) ;
+ end
+end
+fprintf ('error handling tests: ok.\n') ;
+
+% err should be zero:
+rand ('state', 0)
+for Acomplex = 0:1
+ for Bcomplex = 0:1
+ err = 0 ;
+ fprintf ('\ntesting C = A*B where A is %s, B is %s\n', ...
+ msg {Acomplex+1}, msg {Bcomplex+1}) ;
+ for m = [ 0:30 100 ]
+ fprintf ('.') ;
+ for n = [ 0:30 100 ]
+ for k = [ 0:30 100 ]
+ A = sprand (m,k,0.1) ;
+ if (Acomplex)
+ A = A + 1i*sprand (A) ;
+ end
+ B = sprand (k,n,0.1) ;
+ if (Bcomplex)
+ B = B + 1i*sprand (B) ;
+ end
+ C = A*B ;
+ D = ssmult (A,B) ;
+ s = ssmultsym (A,B) ;
+ err = max (err, norm (C-D,1)) ;
+ err = max (err, nnz (C-D)) ;
+ err = max (err, isreal (D) ~= (norm (imag (D), 1) == 0)) ;
+ err = max (err, s.nz > nnz (C)) ;
+ [i j x] = find (D) ; %#ok
+ if (~isempty (x))
+ err = max (err, any (x == 0)) ;
+ end
+ end
+ end
+ end
+ fprintf (' maximum error: %g\n', err) ;
+ end
+end
+
+sstest ;
+fprintf ('\nSSMULT tests complete.\n') ;
+
+
+
+%-------------------------------------------------------------------------------
+function test_large (A,B)
+% test large matrices
+n = size (A,1) ;
+fprintf ('dimension %d nnz(A): %d nnz(B): %d\n', n, nnz (A), nnz (B)) ;
+c = ssmultsym (A,B) ;
+fprintf ('nnz(C): %d flops: %g memory: %g MB\n', ...
+ c.nz, c.flops, c.memory/2^20) ;
+try
+ % warmup for accurate timings
+ C = A*B ; %#ok
+ D = ssmult (A,B) ; %#ok
+ E = ssmult_unsorted (A,B) ; %#ok
+ tic ;
+ C = A*B ;
+ t1 = toc ;
+ tic ;
+ D = ssmult (A,B) ;
+ t2 = toc ;
+ tic ;
+ E = ssmult_unsorted (A,B) ;
+ t3 = toc ;
+ E = E'' ; % sort E, to be safe ...
+ fprintf ('MATLAB time: %g\n', t1) ;
+ err = norm (C-D,1) ;
+ fprintf ('SSMULT time: %g err: %g\n', t2, err) ;
+ err = norm (C-E,1) ;
+ fprintf ('SSMULT_UNSORTED time: %g err: %g\n', t3, err) ;
+catch
+ disp (lasterr)
+ fprintf ('tests with large random matrices failed ...\n') ;
+end
+clear C D E
+
diff --git a/SSMULT/ssmult_unsorted.m b/SSMULT/ssmult_unsorted.m
new file mode 100644
index 0000000..8bde44b
--- /dev/null
+++ b/SSMULT/ssmult_unsorted.m
@@ -0,0 +1,37 @@
+function C = ssmult_unsorted (A,B) %#ok
+%SSMULT_UNSORTED multiplies two sparse matrices, returning non-standard result.
+% C = ssmult_unsorted (A,B) computes C=A*B where A and B are sparse. It returns
+% C with unsorted row indices in its columns, and possibly with explicit zero
+% entries due to numeric cancellation. This does *NOT* conform to the MATLAB
+% standard (as of MATLAB 7.4 ...) for MATLAB sparse matrices. However, such
+% matrices are often safe to use in subsequent operations (such as C*X where
+% X is a full matrix). Computing C'' (a double transpose) gives a sorted
+% result. This function is typically MUCH faster than C=A*B in MATLAB 7.4, and
+% uses less memory. Either A or B, or both, can be complex. Only matrices of
+% class "double" are supported. The primary reason for this function is to
+% demonstrate how much performance MATLAB loses by insisting on keeping its
+% sparse matrices sorted.
+%
+% *** USE AT YOUR OWN RISK. USE SSMULT TO BE SAFE. ***
+%
+% Example:
+% load west0479
+% A = west0479 ;
+% B = sprand (west0479) ;
+% tic ; C = A*B ; toc
+% tic ; D = ssmult_unsorted (A,B) ; toc
+% C-D
+%
+% To see that the result D from ssmult_unsorted has unsorted columns:
+%
+% spparms ('spumoni', 1)
+% colamd (D) ;
+% spparms ('spumoni', 0)
+%
+% See also ssmult, ssmultsym, mtimes.
+%
+% *** USE AT YOUR OWN RISK. USE SSMULT TO BE SAFE. ***
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+error ('ssmult_unsorted mexFunction not found') ;
diff --git a/SSMULT/ssmultsym.c b/SSMULT/ssmultsym.c
new file mode 100644
index 0000000..441ec3e
--- /dev/null
+++ b/SSMULT/ssmultsym.c
@@ -0,0 +1,160 @@
+/* ========================================================================== */
+/* === ssmultsym ============================================================ */
+/* ========================================================================== */
+
+/* s = ssmultsym (A,B) computes nnz(A*B), and the flops and memory required to
+ * compute it, where A and B are both sparse. Either A or B, or both, can be
+ * complex. Memory usage includes C itself, and workspace. If C is m-by-n,
+ * ssmultsym requires only 4*m bytes for 32-bit MATLAB, 8*m for 64-bit MATLAB.
+ *
+ * Copyright 2007, Timothy A. Davis, University of Florida.
+ */
+
+#include "ssmult.h"
+
+/* -------------------------------------------------------------------------- */
+/* ssmultsym mexFunction */
+/* -------------------------------------------------------------------------- */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ double cnz, flops, mem, e, multadds ;
+ Int *Ap, *Ai, *Bp, *Bi, *Flag ;
+ Int Anrow, Ancol, Bnrow, Bncol, i, j, k, pb, pa, pbend, paend, mark,
+ A_is_complex, B_is_complex, C_is_complex, pbstart, cjnz ;
+ static const char *snames [ ] =
+ {
+ "nz", /* # of nonzeros in C=A*B */
+ "flops", /* flop count required to compute C=A*B */
+ "memory" /* memory requirement in bytes */
+ } ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs and workspace */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargin != 2 || nargout > 1)
+ {
+ mexErrMsgTxt ("Usage: s = ssmultsym (A,B)") ;
+ }
+
+ Ap = mxGetJc (pargin [0]) ;
+ Ai = mxGetIr (pargin [0]) ;
+ Anrow = mxGetM (pargin [0]) ;
+ Ancol = mxGetN (pargin [0]) ;
+ A_is_complex = mxIsComplex (pargin [0]) ;
+
+ Bp = mxGetJc (pargin [1]) ;
+ Bi = mxGetIr (pargin [1]) ;
+ Bnrow = mxGetM (pargin [1]) ;
+ Bncol = mxGetN (pargin [1]) ;
+ B_is_complex = mxIsComplex (pargin [1]) ;
+
+ if (Ancol != Bnrow || !mxIsSparse (pargin [0]) || !mxIsSparse (pargin [1]))
+ {
+ mexErrMsgTxt ("wrong dimensions, or A and B not sparse") ;
+ }
+
+#ifndef MATLAB_6p1_OR_EARLIER
+ if (!mxIsDouble (pargin [0]) || !mxIsDouble (pargin [1]))
+ {
+ mexErrMsgTxt ("A and B must be of class 'double'") ;
+ }
+#endif
+
+ Flag = mxCalloc (Anrow, sizeof (Int)) ; /* workspace */
+
+ /* ---------------------------------------------------------------------- */
+ /* compute # of nonzeros in result, flop count, and memory */
+ /* ---------------------------------------------------------------------- */
+
+ pb = 0 ;
+ cnz = 0 ;
+ multadds = 0 ;
+ for (j = 0 ; j < Bncol ; j++) /* compute C(:,j) */
+ {
+ mark = j+1 ;
+ pbstart = Bp [j] ;
+ pbend = Bp [j+1] ;
+ cjnz = 0 ;
+ for ( ; pb < pbend ; pb++)
+ {
+ k = Bi [pb] ; /* nonzero entry B(k,j) */
+ pa = Ap [k] ;
+ paend = Ap [k+1] ;
+ multadds += (paend - pa) ; /* one mult-add per entry in A(:,k) */
+ if (cjnz == Anrow)
+ {
+ /* C(:,j) is already completely dense; no need to scan A.
+ * Continue scanning B(:,j) to compute flop count. */
+ continue ;
+ }
+ for ( ; pa < paend ; pa++)
+ {
+ i = Ai [pa] ; /* nonzero entry A(i,k) */
+ if (Flag [i] != mark)
+ {
+ /* C(i,j) is a new nonzero */
+ Flag [i] = mark ; /* mark i as appearing in C(:,j) */
+ cjnz++ ;
+ }
+ }
+ }
+ cnz += cjnz ;
+ }
+
+ C_is_complex = A_is_complex || B_is_complex ;
+ e = (C_is_complex ? 2 : 1) ;
+
+ mem =
+ Anrow * sizeof (Int) /* Flag */
+#ifndef UNSORTED
+ /* the workspace W is not required if C is returned unsorted */
+ + e * Anrow * sizeof (double) /* W */
+#endif
+ + (Bncol+1) * sizeof (Int) /* Cp */
+ + cnz * sizeof (Int) /* Ci */
+ + e * cnz * sizeof (double) ; /* Cx and Cx */
+
+ if (A_is_complex)
+ {
+ if (B_is_complex)
+ {
+ /* all of C, A, and B are complex */
+ flops = 8 * multadds - 2 * cnz ;
+ }
+ else
+ {
+ /* C and A are complex, B is real */
+ flops = 4 * multadds - 2 * cnz ;
+ }
+ }
+ else
+ {
+ if (B_is_complex)
+ {
+ /* C and B are complex, A is real */
+ flops = 4 * multadds - 2 * cnz ;
+ }
+ else
+ {
+ /* all of C, A, and B are real */
+ flops = 2 * multadds - cnz ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return result */
+ /* ---------------------------------------------------------------------- */
+
+ pargout [0] = mxCreateStructMatrix (1, 1, 3, snames) ;
+ mxSetFieldByNumber (pargout [0], 0, 0, mxCreateScalarDouble (cnz)) ;
+ mxSetFieldByNumber (pargout [0], 0, 1, mxCreateScalarDouble (flops)) ;
+ mxSetFieldByNumber (pargout [0], 0, 2, mxCreateScalarDouble (mem)) ;
+}
diff --git a/SSMULT/ssmultsym.m b/SSMULT/ssmultsym.m
new file mode 100644
index 0000000..e3f047b
--- /dev/null
+++ b/SSMULT/ssmultsym.m
@@ -0,0 +1,33 @@
+function s = ssmultsym (A,B) %#ok
+%SSMULTSYM computes nnz(C), memory, and flops to compute C=A*B; A and B sparse.
+% s = ssmultsym (A,B) returns a struct s with the following fields:
+%
+% s.nz nnz (A*B), assuming no numerical cancelation
+% s.flops flops required to compute C=A*B
+% s.memory memory required to compute C=A*B, including C itself.
+%
+% Either A or B, or both, can be complex. Only matrices of class "double" are
+% supported. If i is the size of an integer (4 bytes on 32-bit MATLAB, 8 bytes
+% on 64-bit MATLAB) and x is the size of an entry (8 bytes if real, 16 if
+% complex), and [m n]=size(C), then the memory usage of SSMULT is
+% (i+x)*nnz(C) + i*(n+1) for C itself, and (i+x)*m for temporary workspace.
+% SSMULTSYM itself does not compute C, and uses only i*m workspace.
+%
+% Example:
+% load west0479
+% A = west0479 ;
+% B = sprand (west0479) ;
+% C = A*B ;
+% D = ssmult (A,B) ;
+% C-D
+% ssmultsym (A,B)
+% nnz (C)
+% whos ('C')
+% [m n] = size (C)
+% mem = 12*nnz(C) + 4*(n+1) + (12*m) % assuming real, 32-bit MATLAB
+%
+% See also ssmult, mtimes.
+
+% Copyright 2007, Timothy A. Davis, University of Florida
+
+error ('ssmultsym mexFunction not found') ;
diff --git a/SSMULT/sstest.m b/SSMULT/sstest.m
new file mode 100644
index 0000000..422e4b6
--- /dev/null
+++ b/SSMULT/sstest.m
@@ -0,0 +1,163 @@
+function sstest
+%SSTEST exhaustive performance test for SSMULT.
+%
+% Example
+% sstest
+%
+% See also ssmult, ssmultsym, ssmult_unsorted, ssmult_install, sstest2, mtimes.
+
+% Copyright 2007, Timothy A. Davis, University of Florida.
+
+N = [500:50:1000 1100:100:3000 3200:200:5000 ] ;
+
+rand ('state',0) ;
+
+% warmup for more accurate timings
+A = sparse (1) ;
+B = sparse (1) ;
+C = A*B ;
+D = ssmult(A,B) ;
+err = norm (C-D,1) ;
+if (err > 0)
+ error ('test failure') ;
+end
+clear C D
+
+titles = { ...
+ 'C=A*B blue, C=B*A red, both real', ...
+ 'A real, B complex', 'A complex, B real', 'both complex' } ;
+
+xlabels = { '(A random, B diagonal)', '(A random, B permutation)', ...
+ '(A random, B tridiagonal)' } ;
+
+fprintf ('\nIn the next plots, speedup is the time for MATLAB C=A*B divided\n');
+fprintf ('by the time for C=ssmult(A,B). The X-axis is n, the dimension\n') ;
+fprintf ('of the square matrices A and B. A is a sparse random matrix with\n');
+fprintf ('1%% nonzero values. B is diagonal in the first row of plots,\n') ;
+fprintf ('a permutation in the 2nd row, and tridiagonal in the third.\n') ;
+fprintf ('C=A*B is in blue, C=B*A is in red. A and B are both real in the\n') ;
+fprintf ('first column of plots, B is complex in the 2nd, A in the 3rd, and\n');
+fprintf ('both are complex in the 4th column of plots. You will want to\n') ;
+fprintf ('maximize the figure; otherwise the text is too hard to read.\n') ;
+
+tlim = 0.1 ;
+figure (1) ;
+clf ;
+
+for fig = 1:3
+
+ fprintf ('Testing C=A*B and C=B*A %s\n', xlabels {fig}) ;
+
+ T = zeros (length(N),4,4) ;
+
+ for k = 1:length(N)
+
+ n = N (k) ;
+ try
+
+ A = sprand (n,n,0.01) ;
+ if (fig == 1)
+ % B diagonal
+ B = spdiags (rand (n,1), 0, n, n) ;
+ elseif (fig == 2)
+ % B permutation
+ B = spdiags (rand (n,1), 0, n, n) ;
+ B = B (:,randperm(n)) ;
+ else
+ % B tridiagonal
+ B = spdiags (rand (n,3), -1:1, n, n) ;
+ end
+
+ for kind = 1:4
+
+ if (kind == 2)
+ % A complex, B real
+ A = A + 1i*sprand (A) ;
+ elseif (kind == 3)
+ % A real, B complex
+ A = real (A) ;
+ B = B + 1i*sprand (B) ;
+ elseif (kind == 4)
+ % both complex
+ A = A + 1i*sprand (A) ;
+ B = B + 1i*sprand (B) ;
+ end
+
+ t1 = 0 ;
+ trials = 0 ;
+ tic
+ while (t1 < tlim)
+ C = A*B ;
+ trials = trials + 1 ;
+ t1 = toc ;
+ end
+ t1 = t1 / trials ;
+
+ t2 = 0 ;
+ trials = 0 ;
+ tic
+ while (t2 < tlim)
+ D = ssmult (A,B) ;
+ trials = trials + 1 ;
+ t2 = toc ;
+ end
+ t2 = t2 / trials ;
+
+ err = norm (C-D,1) ;
+ if (err > 0)
+ error ('test failure') ;
+ end
+ clear C
+ clear D
+
+ t3 = 0 ;
+ trials = 0 ;
+ tic
+ while (t3 < tlim)
+ C = B*A ;
+ trials = trials + 1 ;
+ t3 = toc ;
+ end
+ t3 = t3 / trials ;
+
+ t4 = 0 ;
+ trials = 0 ;
+ tic
+ while (t4 < tlim)
+ D = ssmult (B,A) ;
+ trials = trials + 1 ;
+ t4 = toc ;
+ end
+ t4 = t4 / trials ;
+
+ err = norm (C-D,1) ;
+ if (err > 0)
+ error ('test failure') ;
+ end
+ clear C
+ clear D
+
+ T (k,kind,1) = t1 ;
+ T (k,kind,2) = t2 ;
+ T (k,kind,3) = t3 ;
+ T (k,kind,4) = t4 ;
+ subplot (3,4,kind + 4*(fig-1)) ;
+ plot (N(1:k), T (1:k,kind,1) ./ T (1:k,kind,2), 'o', ...
+ N(1:k), T (1:k,kind,3) ./ T (1:k,kind,4), 'rx', ...
+ [N(1) n], [1 1], 'k') ;
+ xlabel (['n ' xlabels{fig}]) ;
+ ylabel ('speedup') ;
+ axis tight
+ title (titles {kind}) ;
+ drawnow
+
+ end
+
+ catch
+ % probably because we ran out of memory ...
+ disp (lasterr) ;
+ break ;
+ end
+ end
+end
+
diff --git a/SSMULT/sstest2.m b/SSMULT/sstest2.m
new file mode 100644
index 0000000..89f2dea
--- /dev/null
+++ b/SSMULT/sstest2.m
@@ -0,0 +1,215 @@
+function sstest2
+%SSTEST2 exhaustive performance test for SSMULT. Requires UFget.
+% UFget is available at http://www.cise.ufl.edu/research/sparse, or in MATLAB
+% Central.
+%
+% Example
+% sstest2
+%
+% See also ssmult, ssmultsym, ssmult_unsorted, ssmult_install, sstest, UFget, mtimes.
+
+% Copyright 2007, Timothy A. Davis, University of Florida.
+
+help sstest2
+
+try
+ index = UFget ;
+catch
+ fprintf ('\nsstest2 requires UFget.\n') ;
+ fprintf ('see http://www.cise.ufl.edu/research/sparse\n') ;
+ return ;
+end
+[ignore, f] = sort (index.nnz) ; %#ok
+
+nmat = length (f) ;
+TM = zeros (nmat, 4) ;
+T1 = zeros (nmat, 4) ;
+TU = zeros (nmat, 4) ;
+tlim = 0.01 ;
+
+tmin = 1 ;
+tmax = 0 ;
+
+check = 1 ;
+rand ('state', 0)
+
+for k = 1:nmat
+
+ Prob = UFget (f (k), index) ;
+ A = Prob.A ;
+ clear Prob
+
+ for kind = 1:4
+
+ try
+ if (~isreal (A))
+ A = spones (A) ;
+ end
+ B = A' ;
+
+ if (kind == 2)
+ A = sprand (A) + 1i*sprand(A) ;
+ B = sprand (B) ;
+ elseif (kind == 3)
+ A = sprand (A) ;
+ B = sprand (B) + 1i*sprand(B) ;
+ elseif (kind == 4)
+ A = sprand (A) + 1i*sprand(A) ;
+ B = sprand (B) + 1i*sprand(B) ;
+ end
+
+ C = A*B ; % warmup
+
+ if (check)
+
+ D = ssmult (A,B) ;
+ err = norm (C-D,1) ;
+ if (err > 0)
+ fprintf ('err: %g\n', err) ;
+ error ('!')
+ end
+ clear D
+
+ D = ssmult_unsorted (A,B) ;
+ err = norm (C-D,1) ;
+ if (err > 0)
+ fprintf ('err: %g\n', err) ;
+ error ('!')
+ end
+ clear D
+
+ else
+
+ % warmup, for accurate timings
+ C = ssmult_unsorted (A,B) ; %#ok
+ C = ssmult (A,B) ; %#ok
+ clear C
+
+ end
+
+ tr = 0 ;
+ tm = 0 ;
+ tic
+ while (tm < tlim)
+ C = A*B ; %#ok
+ clear C
+ tr = tr + 1 ;
+ tm = toc ;
+ end
+ tm = tm / tr ;
+
+ tr = 0 ;
+ t1 = 0 ;
+ tic
+ while (t1 < tlim)
+ C = ssmult (A,B) ; %#ok
+ clear C
+ tr = tr + 1 ;
+ t1 = toc ;
+ end
+ t1 = t1 / tr ;
+
+ tr = 0 ;
+ tu = 0 ;
+ tic
+ while (tu < tlim)
+ C = ssmult_unsorted (A,B) ; %#ok
+ clear C
+ tr = tr + 1 ;
+ tu = toc ;
+ end
+ tu = tu / tr ;
+
+ fprintf ('%4d: %4d ', k, f(k)) ;
+ fprintf (...
+ 'MATLAB %12.6f SSMULT %12.6f unsorted %12.6f speedup %12.3f', ....
+ tm, t1, tu, tm / t1) ;
+
+ if (tm < t1)
+ fprintf (' ****') ;
+ end
+ fprintf ('\n') ;
+
+ TM (k,kind) = tm ;
+ T1 (k,kind) = t1 ;
+ TU (k,kind) = tu ;
+
+ tmin = min (tmin, tm) ;
+ tmax = max (tmax, tm) ;
+
+ catch
+ disp (lasterr)
+ TM (k,kind) = 1 ;
+ T1 (k,kind) = 1 ;
+ TU (k,kind) = 1 ;
+ end
+
+ end
+
+ for kind = 1:4
+
+ subplot (2,4,kind) ;
+ r = TM (1:k,kind) ./ T1 (1:k,kind) ;
+ rmin = min (r) ;
+ rmax = max (r) ;
+ loglog (TM (1:k,kind), r, 'o', ...
+ [tmin tmax], [1 1], 'r-', ...
+ [tmin tmax], [1.1 1.1], 'r-', ...
+ [tmin tmax], [1/1.1 1/1.1], 'r-', ...
+ [tmin tmax], [2 2], 'g-', ...
+ [tmin tmax], [1.5 1.5], 'g-', ...
+ [tmin tmax], [1/1.5 1/1.5], 'g-', ...
+ [tmin tmax], [.5 .5], 'g-' );
+ if (k > 2)
+ axis ([tmin tmax rmin rmax]) ;
+ end
+ xlabel ('MATLAB time') ;
+ ylabel ('MATLAB/SM time') ;
+ if (kind == 1)
+ title ('real*real') ;
+ elseif (kind == 2)
+ title ('complex*real') ;
+ elseif (kind == 3)
+ title ('real*complex') ;
+ elseif (kind == 4)
+ title ('complex*complex') ;
+ end
+
+ subplot (2,4,kind+4) ;
+ r = T1 (1:k,kind) ./ TU (1:k,kind) ;
+ rmin = min (r) ;
+ rmax = max (r) ;
+ loglog (TM (1:k,kind), r, 'o', ...
+ [tmin tmax], [1 1], 'r-', ...
+ [tmin tmax], [1.1 1.1], 'r-', ...
+ [tmin tmax], [1/1.1 1/1.1], 'r-', ...
+ [tmin tmax], [2 2], 'g-', ...
+ [tmin tmax], [1.5 1.5], 'g-', ...
+ [tmin tmax], [1/1.5 1/1.5], 'g-', ...
+ [tmin tmax], [.5 .5], 'g-' );
+ if (k > 2)
+ axis ([tmin tmax rmin rmax]) ;
+ end
+ xlabel ('MATLAB time') ;
+ ylabel ('SSMULT/unsorted time') ;
+ if (kind == 1)
+ title ('real*real') ;
+ elseif (kind == 2)
+ title ('complex*real') ;
+ elseif (kind == 3)
+ title ('real*complex') ;
+ elseif (kind == 4)
+ title ('complex*complex') ;
+ end
+
+ end
+
+ drawnow
+
+ clear A B C
+ save sstest2_results.mat TM T1 TU f
+ diary off
+ diary on
+
+end
+
diff --git a/SuiteSparse_demo.m b/SuiteSparse_demo.m
new file mode 100644
index 0000000..2fc6c1c
--- /dev/null
+++ b/SuiteSparse_demo.m
@@ -0,0 +1,129 @@
+function SuiteSparse_demo (matrixpath)
+%SUITESPARSE_DEMO a demo of all packages in SuiteSparse
+%
+% Example:
+% SuiteSparse_demo
+%
+% See also umfpack, cholmod, amd, camd, colamd, ccolamd, btf, klu,
+% CSparse, CXSparse, ldlsparse
+
+% Copyright (c) Timothy A. Davis, Univ. of Florida
+
+if (nargin < 1)
+ try
+ % older versions of MATLAB do not have an input argument to mfilename
+ p = mfilename ('fullpath') ;
+ t = strfind (p, filesep) ;
+ matrixpath = [ p(1:t(end)) 'CXSparse/Matrix' ] ;
+ catch
+ % mfilename failed, assume we're in the SuiteSparse directory
+ matrixpath = 'CXSparse/Matrix' ;
+ end
+end
+
+input ('Hit enter to run the CXSparse demo: ') ;
+try
+ cs_demo (0, matrixpath)
+catch
+ fprintf ('\nIf you have an older version of MATLAB, you must run the\n') ;
+ fprintf ('SuiteSparse_demo while in the SuiteSparse directory.\n\n') ;
+ fprintf ('CXSparse demo failed\n' )
+end
+
+input ('Hit enter to run the UMFPACK demo: ') ;
+try
+ umfpack_demo (1)
+catch
+ disp (lasterr) ;
+ fprintf ('UMFPACK demo failed\n' )
+end
+
+input ('Hit enter to run the CHOLMOD demo: ') ;
+try
+ cholmod_demo
+catch
+ disp (lasterr) ;
+ fprintf ('CHOLMOD demo failed\n' )
+end
+
+input ('Hit enter to run the CHOLMOD graph partitioning demo: ') ;
+try
+ graph_demo
+catch
+ disp (lasterr) ;
+ fprintf ('graph_demo failed, probably because METIS not installed\n') ;
+end
+
+input ('Hit enter to run the AMD demo: ') ;
+try
+ amd_demo
+catch
+ disp (lasterr) ;
+ fprintf ('AMD demo failed\n' )
+end
+
+input ('Hit enter to run the CAMD demo: ') ;
+try
+ camd_demo
+catch
+ disp (lasterr) ;
+ fprintf ('CAMD demo failed\n' )
+end
+
+input ('Hit enter to run the COLAMD demo: ') ;
+try
+ colamd_demo
+catch
+ disp (lasterr) ;
+ fprintf ('COLAMD demo failed\n' )
+end
+
+input ('Hit enter to run the CCOLAMD demo: ') ;
+try
+ ccolamd_demo
+catch
+ disp (lasterr) ;
+ fprintf ('CCOLAMD demo failed\n' )
+end
+
+input ('Hit enter to run the BTF demo: ') ;
+try
+ btf_demo
+catch
+ disp (lasterr) ;
+ fprintf ('BTF demo failed\n' )
+end
+
+input ('Hit enter to run the KLU demo: ') ;
+try
+ klu_demo
+catch
+ disp (lasterr) ;
+ fprintf ('KLU demo failed\n' )
+end
+
+input ('Hit enter to run the LDL demo: ') ;
+try
+ ldldemo
+catch
+ disp (lasterr) ;
+ fprintf ('LDL demo failed\n' )
+end
+
+input ('Hit enter to run the SSMULT demo: ') ;
+try
+ ssmult_demo
+catch
+ disp (lasterr) ;
+ fprintf ('SSMULT demo failed\n' )
+end
+
+input ('Hit enter to run the MESHND demo: ') ;
+try
+ meshnd_example
+catch
+ disp (lasterr) ;
+ fprintf ('MESHND demo failed\n' )
+end
+
+fprintf ('\n\n---- SuiteSparse demos complete\n') ;
diff --git a/SuiteSparse_install.m b/SuiteSparse_install.m
new file mode 100644
index 0000000..ee1249e
--- /dev/null
+++ b/SuiteSparse_install.m
@@ -0,0 +1,279 @@
+function SuiteSparse_install (do_demo)
+%SuiteSparse_install: compiles and installs all of SuiteSparse
+% A Suite of Sparse matrix packages, authored or co-authored by Tim Davis, Univ.
+% Florida. You must be in the same directory as SuiteSparse_install to use this.
+%
+% Packages in SuiteSparse:
+%
+% UMFPACK sparse LU factorization (multifrontal)
+% CHOLMOD sparse Cholesky factorization, and many other operations
+% AMD sparse symmetric approximate minimum degree ordering
+% COLAMD sparse column approximate minimum degree ordering
+% CAMD constrained AMD
+% CCOLAMD constrained COLAMD
+% CSparse a Concise Sparse matrix package (32-bit/real only)
+% CXSparse extended version of CSparse (32-bit/64-bit/real/complex)
+% UFget interface to UF Sparse Matrix Collection (MATLAB 7.0 or later)
+% KLU sparse LU factorization (left-looking)
+% BTF permutation to block triangular form (like dmperm)
+% LDL sparse LDL' factorization
+% UFcollection tools for managing the UF Sparse Matrix Collection
+% RBio read/write Rutherford/Boeing files (requires Fortran compiler)
+% SSMULT sparse matrix times sparse matrix
+% MESHND 2D and 3D regular mesh generation and nested dissection
+% LINFACTOR illustrates the use of LU and CHOL (MATLAB 7.3 or later)
+% MATLAB_Tools various simple m-files and demos
+%
+% CXSparse is installed in place of CSparse; cd to CSparse/MATLAB and type
+% cs_install if you wish to use the latter. Since Microsoft Windows does not
+% support ANSI C99, CXSparse does not support complex matrices on Windows.
+%
+% Except where noted, all packages work on MATLAB 6.1 or later. They have not
+% been tested on earlier versions, but they might work there. Please let me
+% know if you try SuiteSparse on MATLAB 6.0 or earlier, whether it works or not.
+%
+% Example:
+% SuiteSparse_install
+% help SuiteSparse % for more details
+%
+% See also AMD, COLAMD, CAMD, CCOLAMD, CHOLMOD, UMFPACK, CSPARSE, CXSPARSE,
+% UFget, RBio, UFcollection, KLU, BTF, MESHND, SSMULT, LINFACTOR,
+% SuiteSparse, PATHTOOL, PATH.
+
+% Copyright 1990-2007, Timothy A. Davis.
+% http://www.cise.ufl.edu/research/sparse
+% In collaboration with Patrick Amestoy, Yanqing Chen, Iain Duff, John Gilbert,
+% Steve Hadfield, Bill Hager, Stefan Larimore, Esmond Ng, Eka Palamadai, and
+% Siva Rajamanickam.
+
+paths = { } ;
+SuiteSparse = pwd ;
+
+% add MATLAB_Tools to the path (for getversion)
+cd ([SuiteSparse '/MATLAB_Tools']) ;
+paths = add_to_path (paths, pwd) ;
+cd (SuiteSparse) ;
+
+% determine the MATLAB version (6.1, 6.5, 7.0, ...)
+v = getversion ;
+pc = ispc ;
+
+% check if METIS 4.0.1 is present where it's supposed to be
+have_metis = exist ('metis-4.0', 'dir') ;
+if (~have_metis)
+ fprintf ('CHOLMOD and KLU optionally use METIS 4.0.1. Download it\n') ;
+ fprintf ('from http://glaros.dtc.umn.edu/gkhome/views/metis\n');
+ fprintf ('and place the metis-4.0 directory in this directory.\n') ;
+ fprintf ('Now compiling without METIS...\n\n') ;
+end
+
+% print the introduction
+help SuiteSparse_install
+
+fprintf ('MATLAB version %g (%s)\n', v, version) ;
+
+% add SuiteSparse to the path
+fprintf ('\nPlease wait while SuiteSparse is compiled and installed...\n') ;
+paths = add_to_path (paths, SuiteSparse) ;
+
+% compile and install UMFPACK
+try
+ cd ([SuiteSparse '/UMFPACK/MATLAB']) ;
+ paths = add_to_path (paths, pwd) ;
+ umfpack_make
+catch
+ try
+ fprintf ('Trying to install with lcc_lib/libmwlapack.lib instead\n') ;
+ umfpack_make ('lcc_lib/libmwlapack.lib') ;
+ catch
+ fprintf ('UMFPACK not installed\n') ;
+ end
+end
+
+% compile and install CHOLMOD
+try
+ % determine whether or not to compile CHOLMOD
+ cd ([SuiteSparse '/CHOLMOD/MATLAB']) ;
+ paths = add_to_path (paths, pwd) ;
+ if (have_metis)
+ cholmod_make
+ else
+ cholmod_make ('no metis') ;
+ end
+catch
+ fprintf ('CHOLMOD not installed\n') ;
+end
+
+% compile and install AMD
+try
+ cd ([SuiteSparse '/AMD/MATLAB']) ;
+ paths = add_to_path (paths, pwd) ;
+ amd_make
+catch
+ fprintf ('AMD not installed\n') ;
+end
+
+% compile and install COLAMD
+try
+ cd ([SuiteSparse '/COLAMD/MATLAB']) ;
+ paths = add_to_path (paths, pwd) ;
+ colamd_make
+catch
+ fprintf ('COLAMD not installed\n') ;
+end
+
+% compile and install CCOLAMD
+try
+ cd ([SuiteSparse '/CCOLAMD/MATLAB']) ;
+ paths = add_to_path (paths, pwd) ;
+ ccolamd_make
+catch
+ fprintf ('CCOLAMD not installed\n') ;
+end
+
+% compile and install CAMD
+try
+ cd ([SuiteSparse '/CAMD/MATLAB']) ;
+ paths = add_to_path (paths, pwd) ;
+ camd_make
+catch
+ fprintf ('CAMD not installed\n') ;
+end
+
+% compile and install CXSparse and UFget
+try
+ cd ([SuiteSparse '/CXSparse/MATLAB/CSparse']) ;
+ paths = add_to_path (paths, [SuiteSparse '/CXSparse/MATLAB/CSparse']) ;
+ paths = add_to_path (paths, [SuiteSparse '/CXSparse/MATLAB/Demo']) ;
+ if (v >= 7.0)
+ paths = add_to_path (paths, [SuiteSparse '/CXSparse/MATLAB/UFget']) ;
+ fprintf ('UFget installed successfully\n') ;
+ else
+ fprintf ('UFget skipped; requires MATLAB 7.0 or later\n') ;
+ end
+ if (pc)
+ % Windows does not support ANSI C99 complex, which CXSparse requires
+ fprintf ('Compiling CXSparse without complex support\n') ;
+ cs_make (1, 0) ;
+ else
+ cs_make (1) ;
+ end
+catch
+ fprintf ('CXSparse not installed\n') ;
+end
+
+% compile and install LDL
+try
+ cd ([SuiteSparse '/LDL/MATLAB']) ;
+ paths = add_to_path (paths, pwd) ;
+ ldl_make
+catch
+ fprintf ('LDL not installed\n') ;
+end
+
+% compile and install BTF
+try
+ cd ([SuiteSparse '/BTF/MATLAB']) ;
+ paths = add_to_path (paths, pwd) ;
+ btf_make
+catch
+ fprintf ('BTF not installed\n') ;
+end
+
+% compile and install KLU
+try
+ cd ([SuiteSparse '/KLU/MATLAB']) ;
+ paths = add_to_path (paths, pwd) ;
+ klu_make (have_metis) ;
+catch
+ fprintf ('KLU not installed\n') ;
+end
+
+% compile and install SSMULT
+try
+ cd ([SuiteSparse '/SSMULT']) ;
+ paths = add_to_path (paths, pwd) ;
+ ssmult_install (0) ;
+catch
+ fprintf ('SSMULT not installed\n') ;
+end
+
+% compile and install UFcollection
+try
+ % do not try to compile with large-file I/O for MATLAB 6.5 or earlier
+ cd ([SuiteSparse '/UFcollection']) ;
+ paths = add_to_path (paths, pwd) ;
+ UFcollection_install (v < 7.0) ;
+catch
+ fprintf ('UFcollection not installed\n') ;
+end
+
+% install LINFACTOR, MESHND, MATLAB_Tools/*
+try
+ cd ([SuiteSparse '/MESHND']) ;
+ paths = add_to_path (paths, pwd) ;
+ if (v > 7.2)
+ % LINFACTOR requires MATLAB 7.3 or later
+ cd ([SuiteSparse '/LINFACTOR']) ;
+ paths = add_to_path (paths, pwd) ;
+ fprintf ('LINFACTOR installed\n') ;
+ end
+ cd ([SuiteSparse '/MATLAB_Tools/shellgui']) ;
+ paths = add_to_path (paths, pwd) ;
+ cd ([SuiteSparse '/MATLAB_Tools/waitmex']) ;
+ paths = add_to_path (paths, pwd) ;
+ fprintf ('MESHND, MATLAB_Tools installed\n') ;
+catch
+ fprintf ('LINFACTOR, MESHND, or MATLAB_Tools not installed\n') ;
+end
+
+% compile and install RBio (not on Windows ... no default Fortran compiler)
+if (~pc)
+ try
+ cd ([SuiteSparse '/RBio']) ;
+ RBmake
+ paths = add_to_path (paths, pwd) ;
+ catch
+ disp (lasterr)
+ fprintf ('RBio not installed (Fortran compiler required).\n') ;
+ end
+end
+
+% post-install wrapup
+
+cd (SuiteSparse)
+fprintf ('SuiteSparse is now installed.\n') ;
+
+if (nargin < 1)
+ % ask if demo should be run
+ y = input ('Hit enter to run the SuiteSparse demo (or "n" to quit): ', 's') ;
+ if (isempty (y))
+ y = 'y' ;
+ end
+ do_demo = (y (1) ~= 'n') ;
+end
+if (do_demo)
+ try
+ SuiteSparse_demo ;
+ catch
+ fprintf ('SuiteSparse demo failed\n') ;
+ end
+end
+
+fprintf ('\nSuiteSparse installation is complete. The following paths\n') ;
+fprintf ('have been added for this session. Use pathtool to add them\n') ;
+fprintf ('permanently. If you cannot save the new path because of file\n');
+fprintf ('permissions, then add these commands to your startup.m file.\n') ;
+fprintf ('Type "doc startup" and "doc pathtool" for more information.\n\n') ;
+for k = 1:length (paths)
+ fprintf ('addpath %s\n', paths {k}) ;
+end
+cd (SuiteSparse)
+
+fprintf ('\nSuiteSparse for MATLAB %g installation complete\n', getversion) ;
+
+%-------------------------------------------------------------------------------
+function paths = add_to_path (paths, newpath)
+% add a path
+addpath (newpath) ;
+paths = [paths { newpath } ] ; %#ok
diff --git a/SuiteSparse_test.m b/SuiteSparse_test.m
new file mode 100644
index 0000000..01647ae
--- /dev/null
+++ b/SuiteSparse_test.m
@@ -0,0 +1,191 @@
+function SuiteSparse_test
+% SuiteSparse_test exhaustive test of all SuiteSparse packages
+%
+% Your current directory must be SuiteSparse for this function to work.
+% SuiteSparse_install must be run prior to running this test. Warning:
+% this test takes a *** long **** time.
+%
+% Example:
+% SuiteSparse_test
+%
+% See also SuiteSparse_install, SuiteSparse_demo.
+
+% Copyright 2007, Tim Davis, University of Florida
+
+npackages = 13 ;
+h = waitbar (0, 'SuiteSparse test:') ;
+SuiteSparse = pwd ;
+
+v = getversion ;
+if (v < 7)
+ error ('SuiteSparse_test requires MATLAB 7.0 or later') ;
+end
+
+% if at UF, ensure pre-installed UF Sparse Matrix Collection is used
+uf = { '/cise/homes/davis/Install/UFget', 'd:/UFget', '/share/UFget' } ;
+for k = 1:length(uf)
+ if (exist (uf {k}, 'dir'))
+ addpath (uf {k}) ;
+ break ;
+ end
+end
+
+try
+
+ %---------------------------------------------------------------------------
+ % CSparse (32-bit MATLAB only)
+ %---------------------------------------------------------------------------
+
+ if (isempty (strfind (computer, '64')))
+ % compile and install CSparse (not installed by SuiteSparse_install)
+ waitbar (1/(npackages+1), h, 'SuiteSparse test: CSparse') ;
+ addpath ([SuiteSparse '/CSparse/MATLAB/CSparse']) ;
+ addpath ([SuiteSparse '/CSparse/MATLAB/Demo']) ;
+ cd ([SuiteSparse '/CSparse/MATLAB/CSparse']) ;
+ cs_make ;
+
+ % test CSparse
+ cd ([SuiteSparse '/CSparse/MATLAB/Test']) ;
+ testall ;
+
+ % uninstall CSparse by removing it from path
+ rmpath ([SuiteSparse '/CSparse/MATLAB/CSparse']) ;
+ rmpath ([SuiteSparse '/CSparse/MATLAB/Demo']) ;
+ end
+
+ %---------------------------------------------------------------------------
+ % CXSparse
+ %---------------------------------------------------------------------------
+
+ waitbar (2/(npackages+1), h, 'SuiteSparse test: CXSparse') ;
+ cd ([SuiteSparse '/CXSparse/MATLAB/Test']) ;
+ testall ;
+
+ %---------------------------------------------------------------------------
+ % COLAMD
+ %---------------------------------------------------------------------------
+
+ waitbar (3/(npackages+1), h, 'SuiteSparse test: COLAMD') ;
+ cd ([SuiteSparse '/COLAMD/MATLAB']) ;
+ colamd_test ;
+
+ %---------------------------------------------------------------------------
+ % CCOLAMD
+ %---------------------------------------------------------------------------
+
+ waitbar (4/(npackages+1), h, 'SuiteSparse test: CCOLAMD') ;
+ cd ([SuiteSparse '/CCOLAMD/MATLAB']) ;
+ ccolamd_test ;
+
+ %---------------------------------------------------------------------------
+ % UMFPACK
+ %---------------------------------------------------------------------------
+
+ waitbar (5/(npackages+1), h, 'SuiteSparse test: UMFPACK') ;
+ cd ([SuiteSparse '/UMFPACK/MATLAB']) ;
+ umfpack_test (800) ;
+
+ %---------------------------------------------------------------------------
+ % CHOLMOD
+ %---------------------------------------------------------------------------
+
+ waitbar (6/(npackages+1), h, 'SuiteSparse test: CHOLMOD') ;
+ cd ([SuiteSparse '/CHOLMOD/MATLAB/Test']) ;
+ cholmod_test ;
+
+ %---------------------------------------------------------------------------
+ % BTF
+ %---------------------------------------------------------------------------
+
+ waitbar (7/(npackages+1), h, 'SuiteSparse test: BTF') ;
+ cd ([SuiteSparse '/BTF/MATLAB/Test']) ;
+ btf_test ;
+
+ %---------------------------------------------------------------------------
+ % KLU
+ %---------------------------------------------------------------------------
+
+ waitbar (8/(npackages+1), h, 'SuiteSparse test: KLU') ;
+ cd ([SuiteSparse '/KLU/MATLAB/Test']) ;
+ klu_test ;
+
+ %---------------------------------------------------------------------------
+ % LDL
+ %---------------------------------------------------------------------------
+
+ waitbar (9/(npackages+1), h, 'SuiteSparse test: LDL') ;
+ cd ([SuiteSparse '/LDL/MATLAB']) ;
+ ldlmain2 ;
+ ldltest ;
+
+ %---------------------------------------------------------------------------
+ % LINFACTOR: MATLAB 7.3 (R2006b) or later required
+ %---------------------------------------------------------------------------
+
+ if (v > 7.2)
+ waitbar (10/(npackages+1), h, 'SuiteSparse test: LINFACTOR') ;
+ cd ([SuiteSparse '/LINFACTOR']) ;
+ lintests ;
+ end
+
+ %---------------------------------------------------------------------------
+ % MESHND
+ %---------------------------------------------------------------------------
+
+ waitbar (11/(npackages+1), h, 'SuiteSparse test: MESHND') ;
+ cd ([SuiteSparse '/MESHND']) ;
+ meshnd_quality ;
+
+ %---------------------------------------------------------------------------
+ % SSMULT
+ %---------------------------------------------------------------------------
+
+ waitbar (12/(npackages+1), h, 'SuiteSparse test: SSMULT') ;
+ cd ([SuiteSparse '/SSMULT']) ;
+ ssmult_test ;
+
+ %---------------------------------------------------------------------------
+ % MATLAB_Tools
+ %---------------------------------------------------------------------------
+
+ waitbar (13/(npackages+1), h, 'SuiteSparse test: MATLAB Tools') ;
+ cd ([SuiteSparse '/MATLAB_Tools']) ;
+ figure (1) ;
+ clf
+ pagerankdemo (1000) ;
+ figure (2) ;
+ clf
+ seashell ;
+ shellgui ;
+ cd ([SuiteSparse '/MATLAB_Tools/waitmex']) ;
+ waitmex ;
+ url = 'http://www.cise.ufl.edu/research/sparse' ;
+ fprintf ('<a href="%s">Click here for more details</a>\n', url) ;
+ hprintf ('or see <a href="%s">\n', url) ;
+
+ %---------------------------------------------------------------------------
+ % AMD, CAMD, UFcollection, UFget
+ %---------------------------------------------------------------------------
+
+ % no exhaustive tests; tested via other packages
+
+catch
+
+ %---------------------------------------------------------------------------
+ % test failure
+ %---------------------------------------------------------------------------
+
+ cd (SuiteSparse) ;
+ disp (lasterr) ;
+ fprintf ('SuiteSparse test: FAILED\n') ;
+ return
+
+end
+
+%-------------------------------------------------------------------------------
+% test OK
+%-------------------------------------------------------------------------------
+
+close (h) ;
+fprintf ('SuiteSparse test: OK\n') ;
+cd (SuiteSparse) ;
diff --git a/UFcollection/Contents.m b/UFcollection/Contents.m
new file mode 100644
index 0000000..61c1919
--- /dev/null
+++ b/UFcollection/Contents.m
@@ -0,0 +1,39 @@
+% UFcollection: software for managing the UF Sparse Matrix Collection
+%
+% To create the index:
+%
+% UFindex - create the index for the UF Sparse Matrix Collection
+% UFstats - compute matrix statistics for the UF Sparse Matrix Collection
+%
+% To create the web pages:
+%
+% UFallpages - create all web pages for the UF Sparse Matrix Collection
+% UFgplot - draw a plot of the graph of a sparse matrix
+% UFint - print an integer to a string, adding commas every 3 digits
+% UFlist - create a web page index for the UF Sparse Matrix Collection
+% UFlists - create the web pages for each matrix list (group, name, etc.)
+% UFlocation - URL and top-level directory of the UF Sparse Matrix Collection
+% UFpage - create web page for a matrix in UF Sparse Matrix Collection
+% UFpages - create web page for each matrix in UF Sparse Matrix Collection
+% dsxy2figxy - Transform point or position from axis to figure coords
+%
+% To create the Matrix Market and Rutherford/Boeing versions of the collection:
+%
+% UFexport - export to Matrix Market and Rutherford/Boeing formats
+% UFread - read a Problem in Matrix Market or Rutherford/Boeing format
+% UFwrite - write a Problem in Matrix Market or Rutherford/Boeing format
+% UFfull_read - read a full matrix using a subset of Matrix Market format
+% UFfull_write - write a full matrix using a subset of Matrix Market format
+%
+% Other:
+%
+% UFcollection_install - install the UFcollection toolbox
+%
+% Example:
+% UFindex % create index (UF_Index.mat) for use by UFget
+% UFallpages % create all web pages for the UF Sparse Matrix Collection
+%
+% Requires UFget, CSparse, CHOLMOD, AMD, COLAMD, METIS.
+
+% Copyright 2006-2007, Timothy A. Davis
+
diff --git a/UFcollection/Doc/ChangeLog b/UFcollection/Doc/ChangeLog
new file mode 100644
index 0000000..fcda4ab
--- /dev/null
+++ b/UFcollection/Doc/ChangeLog
@@ -0,0 +1,20 @@
+Nov 1, 2007, version 1.1.1
+
+ * added isND field to the index
+
+ * minor change to web page creation
+
+May 31, 2007, version 1.1.0
+
+ * port to 64-bit MATLAB
+
+Dec 12, 2006, version 1.0.1
+
+ * very minor MATLAB cleanup
+
+Dec 2, 2006, version 1.0.
+
+ * UFcollection Version 1.0 released. Used for substantial changes to the
+ UF Sparse Matrix Collection. See the Change Log for that collection
+ at http://www.cise.ufl.edu/research/sparse/mat/ChangeLog.
+
diff --git a/UFcollection/Doc/License.txt b/UFcollection/Doc/License.txt
new file mode 100644
index 0000000..1fbc603
--- /dev/null
+++ b/UFcollection/Doc/License.txt
@@ -0,0 +1,22 @@
+UFcollection toolbox. Version 1.0. Copyright (C) 2006,
+Timothy A. Davis
+UFcollection is also available under other licenses; contact authors for
+details.
+http://www.cise.ufl.edu/research/sparse
+
+--------------------------------------------------------------------------------
+
+UFcollection is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+UFcollection is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this Module; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+
diff --git a/UFcollection/Doc/gpl.txt b/UFcollection/Doc/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/UFcollection/Doc/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it. (Some other Free Software Foundation software is covered by
+the GNU Library General Public License instead.) You can apply it to
+your programs, too.
+
+ When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+this service if you wish), that you receive source code or can get it
+if you want it, that you can change the software or use pieces of it
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+anyone to deny you these rights or to ask you to surrender the rights.
+These restrictions translate to certain responsibilities for you if you
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+
+ For example, if you distribute copies of such a program, whether
+gratis or for a fee, you must give the recipients all the rights that
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+
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+that everyone understands that there is no warranty for this free
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+original copyright holder who places the Program under this License
+may add an explicit geographical distribution limitation excluding
+those countries, so that distribution is permitted only in or among
+countries not thus excluded. In such case, this License incorporates
+the limitation as if written in the body of this License.
+
+ 9. The Free Software Foundation may publish revised and/or new versions
+of the General Public License from time to time. Such new versions will
+be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+Each version is given a distinguishing version number. If the Program
+specifies a version number of this License which applies to it and "any
+later version", you have the option of following the terms and conditions
+either of that version or of any later version published by the Free
+Software Foundation. If the Program does not specify a version number of
+this License, you may choose any version ever published by the Free Software
+Foundation.
+
+ 10. If you wish to incorporate parts of the Program into other free
+programs whose distribution conditions are different, write to the author
+to ask for permission. For software which is copyrighted by the Free
+Software Foundation, write to the Free Software Foundation; we sometimes
+make exceptions for this. Our decision will be guided by the two goals
+of preserving the free status of all derivatives of our free software and
+of promoting the sharing and reuse of software generally.
+
+ NO WARRANTY
+
+ 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
+FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
+OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
+PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
+OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
+TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
+PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
+REPAIR OR CORRECTION.
+
+ 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
+REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
+INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
+OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
+TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
+YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
+PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGES.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+
+Also add information on how to contact you by electronic and paper mail.
+
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
+
+ Gnomovision version 69, Copyright (C) year name of author
+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ <signature of Ty Coon>, 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Library General
+Public License instead of this License.
diff --git a/UFcollection/README.txt b/UFcollection/README.txt
new file mode 100644
index 0000000..54870d9
--- /dev/null
+++ b/UFcollection/README.txt
@@ -0,0 +1,176 @@
+UFcollection, Version 1.1.1, Nov 1, 2007.
+
+UFcollection is a MATLAB toolbox for managing the UF Sparse Matrix Collection.
+If you are a MATLAB user of the collection, you would not normally need to use
+this toolbox. It contains code for creating the index for the collection (the
+UF_Index.mat file in the UFget package), for creating the web pages for the
+collection, and creating the Matrix Market and Rutherford/Boeing versions of
+the matrices. This code is posted here primarily so that users of the
+collection can see how the matrices and their statistics were generated.
+
+This software (UFread, specifically) also allows the user to keep a single copy
+of the collection for use both inside MATLAB and outside MATLAB. The MM/ and
+RB/ versions of the collection can be read into MATLAB via UFread, even without
+explicitly extracting the tar files. They can also be read by non-MATLAB
+programs. Since the whole collection is about 8GB in size (compressed, as of
+Dec 2006), this can save some space. UFread is much slower than UFget,
+however.
+
+
+--------------------------------------------------------------------------------
+MATLAB help for the UFcollection toolbox:
+--------------------------------------------------------------------------------
+
+ UFcollection: software for managing the UF Sparse Matrix Collection
+
+ To create the index:
+
+ UFindex - create the index for the UF Sparse Matrix Collection
+ UFstats - compute matrix statistics for the UF Sparse Matrix Collection
+
+ To create the web pages:
+
+ UFallpages - create all web pages for the UF Sparse Matrix Collection
+ UFgplot - draw a plot of the graph of a sparse matrix
+ UFint - print an integer to a string, adding commas every 3 digits
+ UFlist - create a web page index for the UF Sparse Matrix Collection
+ UFlists - create the web pages for each matrix list (group, name, etc.)
+ UFlocation - URL and top-level directory of the UF Sparse Matrix Collection
+ UFpage - create web page for a matrix in UF Sparse Matrix Collection
+ UFpages - create web page for each matrix in UF Sparse Matrix Collection
+ dsxy2figxy - Transform point or position from axis to figure coords
+
+ To create the Matrix Market and Rutherford/Boeing versions of the collection:
+
+ UFexport - export to Matrix Market and Rutherford/Boeing formats
+ UFread - read a Problem in Matrix Market or Rutherford/Boeing format
+ UFwrite - write a Problem in Matrix Market or Rutherford/Boeing format
+ UFfull_read - read a full matrix using a subset of Matrix Market format
+ UFfull_write - write a full matrix using a subset of Matrix Market format
+
+ Example:
+ UFindex % create index (UF_Index.mat) for use by UFget
+ UFallpages % create all web pages for the UF Sparse Matrix Collection
+
+ Requires UFget, CSparse, CHOLMOD, AMD, COLAMD, RBio, and METIS.
+
+ Copyright 2007, Timothy A. Davis
+
+--------------------------------------------------------------------------------
+Files:
+--------------------------------------------------------------------------------
+
+ Contents.m MATLAB help
+ dsxy2figxy.m convert XY points for plot annotations
+ Makefile Unix/Linux installation, or use UFcollection_install
+ README.txt this file
+ UFallpages.m create all web pages
+ UFexport.m export to MM and RB
+ UFcollection_install.m installation
+ UFfull_read.m read a full matrix
+ UFfull_write.c write a full matrix
+ UFfull_write.m MATLAB help for UFfull_write
+ UFgplot.m plot a graph
+ UFindex.m create UF_Index.mat
+ UFint.m print an integer
+ UFlist.m create a web page index
+ UFlists.m create all web page indices
+ UFlocation.m URL and directory for the collection
+ UFpage.m create a web page for a matrix
+ UFpages.m create web pages for all matrices
+ UFread.m read a Problem
+ UFstats.m compute statistics about a matrix
+ UFwrite.m write a Problem
+
+./Doc:
+ gpl.txt GNU GPL license
+ License.txt
+
+--------------------------------------------------------------------------------
+To add a matrix to the collection:
+--------------------------------------------------------------------------------
+
+These instructions are for the maintainer of the collection (that is, just
+notes to myself), but they also indicate how the above software is used.
+
+Requires most of SuiteSparse (UFget, CHOLMOD, AMD, COLAMD, CSparse, RBio, and
+UFcollection), and METIS 4.0.1.
+
+1) Get the matrix into MATLAB (method depending on how the matrix was
+ submitted). Use load and sparse2, RBread, mread, or specialized code
+ written just for that matrix.
+
+2) Add the matrix to the end of UF_Listing.txt (a line in the form Group/Name).
+
+3) Create a new directory /cise/research/sparse/public_html/mat/Group,
+ where Group is the new matrix group. Add a README.txt file to this
+ directory, the first line of which is a one-line summary that will appear
+ in the top-level web page for the collection. Skip this step if adding a
+ matrix to an existing group.
+
+4) Create the Problem struct; type "help UFwrite" for details. Required fields:
+
+ Problem.name full name of the matrix (Group/Name)
+ Problem.title short descriptive title
+ Problem.A the sparse matrix
+ Problem.id integer corresponding to the line number in UF_Listing.txt
+ Problem.date date the matrix was created, or added to the collection
+ Problem.author matrix author
+ Problem.ed matrix editor/collector
+ Problem.kind a string. For a description, see:
+
+ http://www.cise.ufl.edu/research/sparse/matrices/kind.html
+
+ optional fields:
+
+ Problem.Zeros binary pattern of explicit zero entries
+ Problem.b right-hand-side
+ Problem.x solution
+ Problem.notes a char array
+ Problem.aux auxiliary matrices (contents are problem dependent)
+
+ Save to a MATLAB mat-file. In the mat directory, do:
+
+ save (Problem.name, 'Problem', '-v7') ;
+
+5) Compute matrix statistics and extend the UF_Index:
+
+ UFindex (ids)
+
+ where ids is a list of the new matrix id's.
+
+ If updating UF_Index.mat, a copy must exist in the current directory for
+ UFindex to find it. (At UF, do so in the 2sparse/Matrix directory,
+ and copy the current UF_Index.mat there first).
+
+ Copy the new UF_Index.mat file into /cise/research/sparse/public_html/mat.
+
+6) Update the web pages:
+
+ In the /cise/research/sparse/public_html directory, do:
+
+ UFlists
+ UFpages (1, ids)
+
+7) Export the matrix in Matrix Market and Rutherford/Boeing formats.
+
+ UFexport (ids)
+
+ or
+
+ UFexport (ids, 'check')
+
+ then tar and compress the resulting MM/Group/Name and RB/Group/Name
+ directories, one per Problem (if UFexport has not already done so).
+ Copy the MM and RB matrices from the 2sparse/MM and /RB directories into
+ the sparse/public_html directory.
+
+8) Make the collection world-readable. In /cise/research/sparse/public_html do:
+
+ chmod -R og+rX mat matrices MM RB
+
+9) Optional: if a new group was added, manually edit the
+ /cise/research/sparse/public_html/matrices/index.html file, adding a
+ new thumbnail image to the Sample Gallery. If a new Problem.kind was
+ introduced, describe it in the matrices/kind.html file.
+
diff --git a/UFcollection/UFallpages.m b/UFcollection/UFallpages.m
new file mode 100644
index 0000000..e441c49
--- /dev/null
+++ b/UFcollection/UFallpages.m
@@ -0,0 +1,20 @@
+function UFallpages (figures)
+%UFALLPAGES create all web pages for the UF Sparse Matrix Collection
+% with the exception of the top-level index.html file (which is created
+% manually).
+%
+% Example:
+%
+% UFallpages
+% UFallpages(0) % does not create figures (assumes they already exist)
+%
+% See also UFget, UFlists, UFpages.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+if (nargin < 1)
+ figures = 1 ;
+end
+UFlists ;
+UFpages (figures) ;
+
diff --git a/UFcollection/UFcollection_install.m b/UFcollection/UFcollection_install.m
new file mode 100644
index 0000000..529fe77
--- /dev/null
+++ b/UFcollection/UFcollection_install.m
@@ -0,0 +1,29 @@
+function UFcollection_install (nlargefile)
+%UFCOLLECTION_INSTALL install the UFcollection toolbox
+%
+% Example:
+% UFcollection_install
+%
+% See also UFget.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+if (nargin < 1)
+ % try with large-file I/O
+ nlargefile = 0 ;
+end
+
+if (nlargefile)
+ fprintf ('Trying to compile without large file support...\n') ;
+ mex -I../UFconfig -DNLARGEFILE UFfull_write.c
+else
+ try
+ mex -I../UFconfig UFfull_write.c
+ catch
+ fprintf ('Trying to compile without large file support...\n') ;
+ mex -I../UFconfig -DNLARGEFILE UFfull_write.c
+ end
+end
+
+addpath (pwd) ;
+fprintf ('UFcollection toolbox successfully compiled.\n') ;
diff --git a/UFcollection/UFexport.m b/UFcollection/UFexport.m
new file mode 100644
index 0000000..f5f2881
--- /dev/null
+++ b/UFcollection/UFexport.m
@@ -0,0 +1,78 @@
+function UFexport (list, check, tmp)
+%UFEXPORT export to Matrix Market and Rutherford/Boeing formats
+%
+% Example:
+% UFexport ; % export the entire collection
+% UFexport (list) ; % just export matrices whose id's are given in the list
+% UFexport (list, 'check') ; % also read them back in, to check
+%
+% If the list is empty, all matrices in the collection are exported.
+% A 3rd argument tmp changes the tmp directory for UFread.
+%
+% See also UFget, UFwrite, RBio, mwrite.
+
+
+% Copyright 2006-2007, Timothy A. Davis
+
+%-------------------------------------------------------------------------------
+% get the input arguments
+%-------------------------------------------------------------------------------
+
+index = UFget ;
+nmat = length (index.nrows) ;
+
+if (nargin < 1 || isempty (list))
+ list = 1:nmat ;
+end
+
+check = ((nargin > 1) && strcmp (check, 'check')) ;
+
+if (nargin < 3)
+ tmp = '' ;
+end
+
+%-------------------------------------------------------------------------------
+% determine the top-level directory to use
+%-------------------------------------------------------------------------------
+
+[url topdir] = UFlocation ;
+
+%-------------------------------------------------------------------------------
+% export the matrices
+%-------------------------------------------------------------------------------
+
+for id = list
+
+ % get the MATLAB version
+ Problem = UFget (id, index) ;
+ disp (Problem) ;
+
+ % create the MM and RB versions
+ UFwrite (Problem, [topdir 'MM'], 'MM', 'tar') ;
+ UFwrite (Problem, [topdir 'RB'], 'RB', 'tar') ;
+
+ % check the new MM and RB versions
+ if (check)
+ for format = { 'MM' , 'RB' }
+ try
+ if (isempty (tmp))
+ P2 = UFread ([topdir format{1} filesep Problem.name]) ;
+ else
+ P2 = UFread ([topdir format{1} filesep Problem.name], tmp) ;
+ end
+ catch
+ % The Problem may be too large for two copies to be in the
+ % MATLAB workspace at the same time. This is not an error,
+ % but it means that the Problem cannot be checked.
+ P2 = [ ] ;
+ fprintf ('Unable to read %s/%s\n', format {1}, Problem.name) ;
+ fprintf ('%s\n', lasterr) ;
+ end
+ if (~isempty (P2) && ~isequal (Problem, P2))
+ error ('%s version mismatch: %s\n', format {1}, Problem.name) ;
+ end
+ clear P2
+ end
+ end
+end
+
diff --git a/UFcollection/UFfull_read.m b/UFcollection/UFfull_read.m
new file mode 100644
index 0000000..4c63b7e
--- /dev/null
+++ b/UFcollection/UFfull_read.m
@@ -0,0 +1,65 @@
+function A = UFfull_read (file)
+%UFFULL_READ read a full matrix using a subset of Matrix Market format
+% This function reads in a file generated by UFfull_write. It cannot read
+% arbitrary Matrix Market formatted files. See UFfull_write for a description
+% of the file format.
+%
+% Example:
+% x = rand (8)
+% UFfull_write ('xfile', x)
+% y = UFfull_read ('xfile')
+% norm (x-y)
+%
+% See also mread, mwrite, RBwrite, RBread.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+% open the file
+f = fopen (file, 'r') ;
+if (f < 0)
+ error (['cannot open: ' file]) ;
+end
+
+% ignore the header line - determine real/complex from # of entries in each row
+s = fgetl (f) ; %#ok
+
+% read in the # of rows and columns
+[siz count] = fscanf (f, '%d %d', 2) ;
+if (count ~= 2)
+ error (['invalid file: ' file]) ;
+end
+m = siz (1) ;
+n = siz (2) ;
+
+% read in the rest of the matrix
+A = fscanf (f, '%g') ;
+
+% This is an unfortunate workaround. fscanf in C and MATLAB, and the read
+% statement in Fortran, cannot interpret the character strings 'Inf', '-Inf',
+% or 'NaN' as the appropriate value. Thus, a special huge value (1e308) is
+% used to represent these values (Inf and NaN both become 1e308). A sparse
+% matrix typically won't included any Inf's or NaN's, but auxiliary arrays can,
+% for some problems. For example, the bounds of an LP can be +Inf or -Inf;
+% lo(i) = -Inf means that there is no lower bound on the ith variable.
+%
+% The identical workaround is used in UFfull_write, mread, mwrite, RBread, and
+% RBwrite. 1e308 was chosen because it's close to the largest IEEE double
+% precision number of 1.7977e308, and because the string '1e308' is short,
+% leading to more compact files. Note that NaN's are treated as +Inf.
+A (A == 1e308) = Inf ;
+A (A == -1e308) = -Inf ;
+
+% reshape the matrix into its final form
+if (length (A) == m*n)
+ % this is a real matrix
+ A = reshape (A, m, n) ;
+elseif (length (A) == 2*m*n)
+ % this is a complex matrix
+ A = reshape (A (1:2:end), m, n) + reshape (A (2:2:end), m, n) * 1i ;
+else
+ error (['invalid file: ' file]) ;
+end
+
+% close the file
+fclose (f) ;
+
diff --git a/UFcollection/UFfull_write.c b/UFcollection/UFfull_write.c
new file mode 100644
index 0000000..edee0d2
--- /dev/null
+++ b/UFcollection/UFfull_write.c
@@ -0,0 +1,164 @@
+/* ========================================================================== */
+/* === UFcollection/UFfull ================================================== */
+/* ========================================================================== */
+
+/* UFcollection: a MATLAB toolbox for managing the UF Sparse Matrix Collection.
+ * Copyright (c) 2007, Timothy A. Davis, Univ. Florida. */
+
+/* ========================================================================== */
+
+/* UFfull_write (filename, X): write a full matrix to a file. A small subset of
+ * the Matrix Market format is used. The first line is one of:
+ *
+ * %%MatrixMarket matrix real complex general
+ * %%MatrixMarket matrix array complex general
+ *
+ * The 2nd line contains two numbers: m and n, where X is m-by-n. The next
+ * m*n lines contain the numerical values (one per line if real, two per line
+ * if complex, containing the real and imaginary parts). The values are
+ * listed in column-major order. The resulting file can be read by any
+ * Matrix Market reader, or by UFfull_read. No comments or blank lines are
+ * used.
+ */
+
+#ifndef NLARGEFILE
+#include "io64.h"
+#endif
+
+#include "UFconfig.h"
+#include "mex.h"
+#include <math.h>
+#define MAXLINE 1030
+#define BIG 1e308
+
+/* -------------------------------------------------------------------------- */
+/* print_value */
+/* -------------------------------------------------------------------------- */
+
+static void print_value (FILE *f, double x, char *s)
+{
+ double y ;
+ int k, width ;
+
+ /* change -inf to -BIG, and change +inf and nan to +BIG */
+ if (x != x || x >= BIG)
+ {
+ x = BIG ;
+ }
+ else if (x <= -BIG)
+ {
+ x = -BIG ;
+ }
+
+ /* convert to int and back again */
+ k = (int) x ;
+ y = (double) k ;
+ if (y == x)
+ {
+ /* x is a small integer */
+ fprintf (f, "%d", k) ;
+ }
+ else
+ {
+ /* x is not an integer, use the smallest width possible */
+ for (width = 6 ; width < 20 ; width++)
+ {
+ /* write the value to a string, read it back in, and check */
+ sprintf (s, "%.*g", width, x) ;
+ sscanf (s, "%lg", &y) ;
+ if (x == y) break ;
+ }
+ fprintf (f, "%s", s) ;
+ }
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* UFfull */
+/* -------------------------------------------------------------------------- */
+
+void mexFunction
+(
+ int nargout,
+ mxArray *pargout [ ],
+ int nargin,
+ const mxArray *pargin [ ]
+)
+{
+ int iscomplex ;
+ size_t nrow, ncol, i, j ;
+ double *Ax, *Az ;
+ char filename [MAXLINE], s [MAXLINE] ;
+ FILE *f ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (nargout > 0 || nargin != 2)
+ {
+ mexErrMsgTxt ("usage: UFfull (filename,A)") ;
+ }
+ if (mxIsSparse (pargin [1]) || !mxIsClass (pargin [1], "double"))
+ {
+ mexErrMsgTxt ("A must be full and double") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get filename and open the file */
+ /* ---------------------------------------------------------------------- */
+
+ if (!mxIsChar (pargin [0]))
+ {
+ mexErrMsgTxt ("first parameter must be a filename") ;
+ }
+ mxGetString (pargin [0], filename, MAXLINE) ;
+ f = fopen (filename, "w") ;
+ if (f == NULL)
+ {
+ mexErrMsgTxt ("error openning file") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ iscomplex = mxIsComplex (pargin [1]) ;
+ nrow = mxGetM (pargin [1]) ;
+ ncol = mxGetN (pargin [1]) ;
+ Ax = mxGetPr (pargin [1]) ;
+ Az = mxGetPi (pargin [1]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* write the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (iscomplex)
+ {
+ fprintf (f, "%%%%MatrixMarket matrix array complex general\n") ;
+ }
+ else
+ {
+ fprintf (f, "%%%%MatrixMarket matrix array real general\n") ;
+ }
+ fprintf (f, "%d %d\n", nrow, ncol) ;
+ for (j = 0 ; j < ncol ; j++)
+ {
+ for (i = 0 ; i < nrow ; i++)
+ {
+ print_value (f, Ax [i + j*nrow], s) ;
+ if (iscomplex)
+ {
+ fprintf (f, " ") ;
+ print_value (f, Az [i + j*nrow], s) ;
+ }
+ fprintf (f, "\n") ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* close the file */
+ /* ---------------------------------------------------------------------- */
+
+ fclose (f) ;
+}
diff --git a/UFcollection/UFfull_write.m b/UFcollection/UFfull_write.m
new file mode 100644
index 0000000..7d42907
--- /dev/null
+++ b/UFcollection/UFfull_write.m
@@ -0,0 +1,29 @@
+function UFfull_write (filename, A) %#ok
+%UFFULL_WRITE write a full matrix using a subset of Matrix Market format
+% Usage:
+%
+% UFfull_write (filename, A)
+%
+% A small subset of the Matrix Market format is used. The first line is one of:
+%
+% %%MatrixMarket matrix real complex general
+% %%MatrixMarket matrix array complex general
+%
+% The second line contains two numbers: m and n, where A is m-by-n. The next
+% m*n lines contain the numerical values (one per line if real, two per line
+% if complex, containing the real and imaginary parts). The values are listed
+% in column-major order. The resulting file can be read by any Matrix Market
+% reader, or by UFfull_read. No comments or blank lines are used.
+%
+% Example:
+% x = rand (8)
+% UFfull_write ('xfile', x)
+% y = UFfull_read ('xfile')
+% norm (x-y)
+%
+% See also mread, mwrite, RBwrite, RBread.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+error ('UFfull_write mexFunction not found') ;
+
diff --git a/UFcollection/UFgplot.m b/UFcollection/UFgplot.m
new file mode 100644
index 0000000..96ffd9b
--- /dev/null
+++ b/UFcollection/UFgplot.m
@@ -0,0 +1,133 @@
+function UFgplot (A, xyz, directed, nodename)
+%UFGPLOT draw a plot of the graph of a sparse matrix
+% Usage:
+% UFgplot (A, xyz, directed, nodename)
+%
+% A: a square sparse matrix of size n-by-n.
+% xyz: an n-by-2 or n-by-3 array of the XY or XYZ coordinates of each node.
+% directed: 1 if A is directed, 0 otherwise. 0 if not present.
+% nodename: a char array with n rows, or empty, containing the name of each
+% node. Not used if not present.
+%
+% Example:
+%
+% Problem = UFget ('Pajek/football') ;
+% UFgplot (Problem.A, Problem.aux.coord, 1, Problem.aux.nodename) ;
+%
+% See also gplot, UFget.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+%-------------------------------------------------------------------------------
+% check inputs
+%-------------------------------------------------------------------------------
+
+[m n] = size (A) ;
+if (m ~= n)
+ error ('A must be square') ;
+end
+
+if (nargin < 4)
+ nodename = [ ] ;
+end
+if (nargin < 3)
+ directed = 0 ;
+end
+
+%-------------------------------------------------------------------------------
+% determine if 2D or 3D
+%-------------------------------------------------------------------------------
+
+if (size (xyz, 2) == 2)
+
+ %---------------------------------------------------------------------------
+ % no Z coordinates, draw a 2D graph
+ %---------------------------------------------------------------------------
+
+ xy = xyz ;
+ if (directed)
+ ti = '2D directed graph' ;
+ else
+ ti = '2D undirected graph' ;
+ end
+
+else
+
+ %---------------------------------------------------------------------------
+ % a 3D graph; rotate for better viewing
+ %---------------------------------------------------------------------------
+
+ dx = -45 ;
+ dy = 45 ;
+ dz = 45 ;
+ a = dx * (2*pi/360) ;
+ xrotation = [
+ 1 0 0
+ 0 cos(a) sin(a)
+ 0 -sin(a) cos(a) ] ;
+ b = dy * (2*pi/360) ;
+ yrotation = [
+ cos(b) 0 -sin(b)
+ 0 1 0
+ sin(b) 0 cos(b) ] ;
+ c = dz * (2*pi/360) ;
+ zrotation = [
+ cos(c) sin(c) 0
+ -sin(c) cos(c) 0
+ 0 0 1 ] ;
+ r = xrotation * yrotation * zrotation ;
+ xy = xyz * r ;
+ xy = xy (:,1:2) ;
+ if (directed)
+ ti = '3D directed graph' ;
+ else
+ ti = '3D undirected graph' ;
+ end
+end
+
+%-------------------------------------------------------------------------------
+% draw the graph
+%-------------------------------------------------------------------------------
+
+[X,Y] = gplot (A, xy) ;
+if (n < 100)
+ msize = 12 ;
+else
+ msize = 6 ;
+end
+
+if (n < 200)
+ if (directed)
+ plot (X, Y, 'mo', 'MarkerEdgeColor', 'k', ...
+ 'MarkerFaceColor', [.49 1 .63], 'MarkerSize', msize) ;
+ hold on
+ axis equal
+ axis off
+ for k = 0:(length(X) / 3)-1
+ [x1 y1] = dsxy2figxy (gca, X (3*k+1), Y (3*k+1)) ;
+ [x2 y2] = dsxy2figxy (gca, X (3*k+2), Y (3*k+2)) ;
+ annotation ('arrow', [x1 x2], [y1 y2], 'Color', [1 0 1], ...
+ 'HeadWidth', 4, 'HeadLength', 8) ;
+ end
+ else
+ plot (X, Y, '-mo', 'MarkerEdgeColor', 'k', ...
+ 'MarkerFaceColor', [.49 1 .63], 'MarkerSize', msize) ;
+ hold on
+ axis equal
+ axis off
+ end
+ if (~isempty (nodename) && n < 100)
+ for k = 1:n
+ text (xy (k,1), xy (k,2), [' ' nodename(k,:)], ...
+ 'Interpreter', 'none') ;
+ end
+ end
+else
+ plot (X, Y, '-m.', 'MarkerEdgeColor', 'k') ;
+ axis equal
+ axis off
+end
+
+title (ti) ;
+
+hold off
diff --git a/UFcollection/UFindex.m b/UFcollection/UFindex.m
new file mode 100644
index 0000000..5bfb030
--- /dev/null
+++ b/UFcollection/UFindex.m
@@ -0,0 +1,396 @@
+function UF_Index = UFindex (matrixlist)
+%UFINDEX create the index for the UF Sparse Matrix Collection
+%
+% UF_Index = UFindex (matrixlist)
+%
+% matrixlist: an integer list, in the range of 1 to the length of the
+% UF_Listing.txt file, containing a list of matrices for which to modify
+% the UF_Index entries. If matrixlist is not present, then the UF_Index
+% is created from scratch.
+%
+% UF_Index: a struct containing the index information, with the
+% following fields, assuming that there are n matrices in the collection:
+%
+% LastRevisionDate: a string with the date and time the index was updated.
+% DowloadTimeStamp: date and time the index was last downloaded.
+%
+% Group: an n-by-1 cell array. Group {i} is the group for matrix i.
+% Name: n-by-1 cell array. Name {i} is the name of matrix i.
+%
+% The following fields are n-by-1 vectors unless otherwise specified.
+% nrows(id) gives the number of rows of the matrix with id = Problem.id,
+% for example.
+%
+% nrows number of rows
+% ncols number of columns
+% nnz number of entries in A
+% RBtype Rutherford/Boeing type, an n-by-3 char array
+% isBinary 1 if binary, 0 otherwise
+% isReal 1 if real, 0 if complex
+% cholcand 1 if a candidate for sparse Cholesky, 0 otherwise
+% numerical_symmetry numeric symmetry (0 to 1, where 1=symmetric)
+% pattern_symmetry pattern symmetry (0 to 1, where 1=symmetric)
+% nnzdiag nnz (diag (A)) if A is square, 0 otherwise
+% nzero nnz (Problem.Zeros)
+% amd_lnz nnz(L) for chol(C(p,p)) where, C=A+A', p=amd(C)
+% amd_flops flop count for chol(C(p,p)) where, C=A+A', p=amd(C)
+% amd_vnz nnz in Householder vectors for qr(A(:,colamd(A)))
+% amd_rnz nnz in R for qr(A(:,colamd(A)))
+% metis_lnz nnz(L) for chol(C(p,p)) where, C=A+A', p=metis(C)
+% metis_flops flop count for chol(C(p,p)) where, C=A+A', p=metis(C)
+% metis_vnz nnz in Householder vectors for qr(A(:,metis(A,'col')))
+% metis_rnz nnz in R for qr(A(:,metis(A,'col')))
+% nblocks # of blocks from dmperm
+% sprank sprank(A)
+% nzoff # of entries not in diagonal blocks from dmperm
+% ncc # of strongly connected components
+% dmperm_lnz nnz(L), using dmperm plus amd or metis
+% dmperm_unz nnz(U), using dmperm plus amd or metis
+% dmperm_flops flop count with dperm plus
+% dmperm_vnz nnz in Householder vectors for dmperm plus
+% dmperm_rnz nnz in R for dmperm plus
+% posdef 1 if positive definite, 0 otherwise
+% isND 1 if a 2D/3D problem, 0 otherwise
+%
+% If the statistic is not computed, it is set to -2. Some statistics are not
+% computed for rectangular or structurally singular matrices, for example.
+% If an attempt to compute the statistic was made, but failed, it is set to -1.
+%
+% Example:
+% UFindex
+% UFindex (267:300)
+%
+% See also UFstats, amd, metis, RBtype, cs_scc, cs_sqr, cs_dmperm.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+% Requires the SuiteSparse set of packages: CHOLMOD, AMD, COLAMD, RBio, CSparse;
+% and METIS.
+
+% 10/13/2001: Created by Erich Mirabal
+% 12/6/2001, 1/17/2003, 11/16/2006: modified by Tim Davis
+
+%-------------------------------------------------------------------------------
+% initialize an empty index
+%-------------------------------------------------------------------------------
+
+% load the filenames
+[url topdir] = UFlocation ;
+files = textread ([topdir 'mat' filesep 'UF_Listing.txt'], '%s') ;
+
+% if no input, assume we have to do the whole file list
+create_new = 0 ;
+if (nargin < 1)
+ matrixlist = 1:length(files) ;
+ create_new = 1 ;
+else
+ % validate the input : range is limited by the files variable
+ if (min (matrixlist) < 1) || (max (matrixlist) > length (files))
+ error ('%s: %s', mfilename, 'Invalid input parameter.') ;
+ end
+end
+
+if (~create_new)
+ % load the index from file
+ fprintf ('Loading existing UF_Index.mat file\n') ;
+ UF_Index = load ('UF_Index.mat') ;
+ UF_Index = UF_Index.UF_Index ;
+end
+
+% revision tracking device
+UF_Index.LastRevisionDate = datestr (now) ;
+
+% the index structure needs a download date for version tracking
+UF_Index.DownloadTimeStamp = now ;
+
+% start the index from scratch
+if (create_new)
+
+ fprintf ('Creating new UF_Index.mat file\n') ;
+ nothing = -ones (1, length (files)) ;
+
+ UF_Index.Group = cell (size (files)) ;
+ UF_Index.Name = cell (size (files)) ;
+
+ UF_Index.nrows = nothing ;
+ UF_Index.ncols = nothing ;
+ UF_Index.nnz = nothing ;
+ UF_Index.nzero = nothing ;
+ UF_Index.pattern_symmetry = nothing ;
+ UF_Index.numerical_symmetry = nothing ;
+ UF_Index.isBinary = nothing ;
+ UF_Index.isReal = nothing ;
+
+ % removed has_b, has_guess, has_x, has_Zeros, is_lp, has_coord, zdiag
+
+ UF_Index.nnzdiag = nothing ;
+
+ UF_Index.posdef = nothing ;
+
+ UF_Index.amd_lnz = nothing ;
+ UF_Index.amd_flops = nothing ;
+ UF_Index.amd_vnz = nothing ;
+ UF_Index.amd_rnz = nothing ;
+
+ UF_Index.metis_lnz = nothing ;
+ UF_Index.metis_flops = nothing ;
+ UF_Index.metis_vnz = nothing ;
+ UF_Index.metis_rnz = nothing ;
+
+ UF_Index.nblocks = nothing ;
+ UF_Index.sprank = nothing ;
+ UF_Index.nzoff = nothing ;
+
+ UF_Index.dmperm_lnz = nothing ;
+ UF_Index.dmperm_unz = nothing ;
+ UF_Index.dmperm_flops = nothing ;
+ UF_Index.dmperm_vnz = nothing ;
+ UF_Index.dmperm_rnz = nothing ;
+
+ % added RBtype, cholcand, ncc
+ UF_Index.RBtype = char (' '*ones (length (files),3)) ;
+ UF_Index.cholcand = nothing ;
+ UF_Index.ncc = nothing ;
+
+ % added isND
+ UF_Index.isND = nothing ;
+
+else
+
+ % make sure we have the right length for the arrays
+ if length (UF_Index.nrows) < max (matrixlist)
+
+ len = max (matrixlist) - length (UF_Index.nrows) ;
+ nothing = -ones (1, len) ;
+
+ if (len > 0)
+
+ % don't worry about the cell arrays, only append to numeric arrays
+ UF_Index.nrows = [UF_Index.nrows nothing] ;
+ UF_Index.ncols = [UF_Index.ncols nothing] ;
+ UF_Index.nnz = [UF_Index.nnz nothing] ;
+ UF_Index.nzero = [UF_Index.nzero nothing] ;
+ UF_Index.pattern_symmetry = [UF_Index.pattern_symmetry nothing] ;
+ UF_Index.numerical_symmetry = [UF_Index.numerical_symmetry nothing];
+ UF_Index.isBinary = [UF_Index.isBinary nothing] ;
+ UF_Index.isReal = [UF_Index.isReal nothing] ;
+
+ UF_Index.nnzdiag = [UF_Index.nnzdiag nothing] ;
+
+ UF_Index.posdef = [UF_Index.posdef nothing] ;
+
+ UF_Index.amd_lnz = [UF_Index.amd_lnz nothing] ;
+ UF_Index.amd_flops = [UF_Index.amd_flops nothing] ;
+ UF_Index.amd_vnz = [UF_Index.amd_vnz nothing] ;
+ UF_Index.amd_rnz = [UF_Index.amd_rnz nothing] ;
+
+ UF_Index.metis_lnz = [UF_Index.metis_lnz nothing] ;
+ UF_Index.metis_flops= [UF_Index.metis_flops nothing] ;
+ UF_Index.metis_vnz = [UF_Index.metis_vnz nothing] ;
+ UF_Index.metis_rnz = [UF_Index.metis_rnz nothing] ;
+
+ UF_Index.nblocks = [UF_Index.nblocks nothing] ;
+ UF_Index.sprank = [UF_Index.sprank nothing] ;
+ UF_Index.nzoff = [UF_Index.nzoff nothing] ;
+
+ UF_Index.dmperm_lnz = [UF_Index.dmperm_lnz nothing] ;
+ UF_Index.dmperm_unz = [UF_Index.dmperm_unz nothing] ;
+ UF_Index.dmperm_flops= [UF_Index.dmperm_flops nothing] ;
+ UF_Index.dmperm_vnz = [UF_Index.dmperm_vnz nothing] ;
+ UF_Index.dmperm_rnz = [UF_Index.dmperm_rnz nothing] ;
+
+ UF_Index.RBtype = [UF_Index.RBtype ; char (' '*ones (len,3))] ;
+ UF_Index.cholcand = [UF_Index.cholcand nothing] ;
+ UF_Index.ncc = [UF_Index.ncc nothing] ;
+
+ UF_Index.isND = [UF_Index.isND nothing] ;
+ end
+
+ end
+end
+
+fprintf ('Will process %d files\n', length (matrixlist)) ;
+
+nmat = length (UF_Index.nrows) ;
+filesize = zeros (nmat,1) ;
+
+%-------------------------------------------------------------------------------
+% look through the directory listing, and sort matrixlist by size
+%-------------------------------------------------------------------------------
+
+for i = matrixlist
+
+ % note that the matrix is not loaded in this for loop
+ ffile = deblank (files {i}) ;
+
+ % group is the first part of the string up to the character before
+ % the last file separator
+ gi = find (ffile == filesep) ;
+ gi = gi (end) ;
+ groupN = char (ffile (1:gi-1)) ;
+
+ % name is the last section of the string after the last file separator
+ matrixN = char (ffile (gi+1:end)) ;
+
+ % get the directory info of the .mat file
+ fileInfo = dir ([topdir 'mat' filesep ffile '.mat']) ;
+
+ % set the file's data into the data arrays
+ UF_Index.Name {i} = matrixN ;
+ UF_Index.Group {i} = groupN ;
+
+ if (length (fileInfo) > 0) %#ok
+ filesize (i) = fileInfo.bytes ;
+ else
+ filesize (i) = 9999999999 ;
+ end
+ % fprintf ('%s / %s filesize %d\n', groupN, matrixN, fileInfo.bytes) ;
+
+end
+
+fprintf ('\n======================================================\n') ;
+fprintf ('Matrices will processed in the following order:\n') ;
+for i = matrixlist
+ ffile = deblank (files {i}) ;
+ fprintf ('Matrix %d: %s filesize %d\n', i, ffile, filesize (i)) ;
+ if (filesize (i) == 9999999999)
+ fprintf ('skip this file\n') ;
+ continue ;
+ end
+end
+
+%-------------------------------------------------------------------------------
+% load the matrices
+%-------------------------------------------------------------------------------
+
+% metis (A,'col') fails with a seg fault for these matrices:
+skip_metis = [850 858 1257 1258] ;
+
+% these matrices are known to be positive definite, and indefinite,
+% respectively, but sparse Cholesky fails (on a 4GB Penitum 4) on some of them:
+known_posdef = [ 939 1252 1267 1268 1423 1453 1455 ] ;
+known_indef = [ 1348:1368 1586 1411 ] ;
+
+% these matrices are known to be irreducible, but dmperm fails
+known_irreducible = 916 ;
+
+for k = 1:length (matrixlist)
+
+ %---------------------------------------------------------------------------
+ % get the matrix
+ %---------------------------------------------------------------------------
+
+ id = matrixlist (k) ;
+ ffile = deblank (files {id}) ;
+ fprintf ('\n============================== Matrix %d: %s\n', id, ffile) ;
+ if (filesize (id) == 9999999999)
+ fprintf ('skip this file\n') ;
+ continue ;
+ end
+ load ([topdir 'mat' filesep ffile]) ;
+
+ % display the Problem struct
+ disp (Problem) ;
+
+ %---------------------------------------------------------------------------
+ % get all stats
+ %---------------------------------------------------------------------------
+
+ nometis = any (id == skip_metis) ;
+ if (nometis)
+ fprintf ('skip metis - will fail\n') ;
+ end
+
+ fprintf ('%s/%s\n', UF_Index.Group {id}, UF_Index.Name {id}) ;
+
+ if (isfield (Problem, 'Zeros'))
+ stats = UFstats (Problem.A, Problem.kind, nometis, Problem.Zeros) ;
+ else
+ stats = UFstats (Problem.A, Problem.kind, nometis) ;
+ end
+
+ %---------------------------------------------------------------------------
+ % fix special cases
+ %---------------------------------------------------------------------------
+
+ if (stats.posdef == -1)
+ if (any (id == known_posdef))
+ fprintf ('known posdef\n') ;
+ stats.posdef = 1 ;
+ elseif (any (id == known_indef))
+ fprintf ('known indef\n') ;
+ stats.posdef = 0 ;
+ end
+ end
+ if (any (id == known_irreducible) && stats.sprank < 0)
+ % full sprank, and not reducible to block triangular form,
+ % but the matrix is to big for dmperm
+ fprintf ('known irreducible\n') ;
+ stats.sprank = stats.nrows ;
+ stats.nzoff = 0 ;
+ stats.nblocks = 1 ;
+ stats.ncc = 1 ;
+ end
+
+ % display the stats
+ disp (stats) ;
+
+ %---------------------------------------------------------------------------
+ % save the stats in the index
+ %---------------------------------------------------------------------------
+
+ UF_Index.nrows (id) = stats.nrows ;
+ UF_Index.ncols (id) = stats.ncols ;
+ UF_Index.nnz (id) = stats.nnz ;
+ UF_Index.nzero (id) = stats.nzero ;
+
+ UF_Index.pattern_symmetry (id) = stats.psym ;
+ UF_Index.numerical_symmetry (id) = stats.nsym ;
+ UF_Index.isBinary (id) = stats.isBinary ;
+ UF_Index.isReal (id) = stats.isReal ;
+
+ UF_Index.nnzdiag (id) = stats.nnzdiag ;
+
+ UF_Index.posdef (id) = stats.posdef ;
+
+ UF_Index.amd_lnz (id) = stats.amd_lnz ;
+ UF_Index.amd_flops (id) = stats.amd_flops ;
+ UF_Index.amd_vnz (id) = stats.amd_vnz ;
+ UF_Index.amd_rnz (id) = stats.amd_rnz ;
+
+ UF_Index.metis_lnz (id) = stats.metis_lnz ;
+ UF_Index.metis_flops (id) = stats.metis_flops ;
+ UF_Index.metis_vnz (id) = stats.metis_vnz ;
+ UF_Index.metis_rnz (id) = stats.metis_rnz ;
+
+ UF_Index.nblocks (id) = stats.nblocks ;
+ UF_Index.sprank (id) = stats.sprank ;
+ UF_Index.nzoff (id) = stats.nzoff ;
+
+ UF_Index.dmperm_lnz (id) = stats.dmperm_lnz ;
+ UF_Index.dmperm_unz (id) = stats.dmperm_unz ;
+ UF_Index.dmperm_flops (id) = stats.dmperm_flops ;
+ UF_Index.dmperm_vnz (id) = stats.dmperm_vnz ;
+ UF_Index.dmperm_rnz (id) = stats.dmperm_rnz ;
+
+ UF_Index.RBtype (id,:) = stats.RBtype ;
+ UF_Index.cholcand (id) = stats.cholcand ;
+ UF_Index.ncc (id) = stats.ncc ;
+
+ UF_Index.isND (id) = stats.isND ;
+
+ %---------------------------------------------------------------------------
+ % clear the problem and save the index
+ %---------------------------------------------------------------------------
+
+ clear Problem
+ save UF_Index UF_Index
+
+ % flush the diary
+ if (strcmp (get (0, 'Diary'), 'on'))
+ diary off
+ diary on
+ end
+end
+
+
diff --git a/UFcollection/UFint.m b/UFcollection/UFint.m
new file mode 100644
index 0000000..c7977df
--- /dev/null
+++ b/UFcollection/UFint.m
@@ -0,0 +1,40 @@
+function s = UFint (x)
+%UFINT print an integer to a string, adding commas every 3 digits
+% If negative, the result is the single character '-'.
+%
+% Example:
+% UFint (-2)
+% UFint (2^30)
+%
+% See also sprintf.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+if (x < 0)
+ s = '-' ;
+ return
+end
+t = sprintf ('%d', fix (x)) ;
+len = length (t) ;
+if (len <= 3 || len > 12 || ~isempty (strfind (t, 'e')))
+ s = t ;
+elseif (len == 4)
+ s = [ t(1) ',' t(2:4) ] ;
+elseif (len == 5)
+ s = [ t(1:2) ',' t(3:5) ] ;
+elseif (len == 6)
+ s = [ t(1:3) ',' t(4:6) ] ;
+elseif (len == 7)
+ s = [ t(1) ',' t(2:4) ',' t(5:7) ] ;
+elseif (len == 8)
+ s = [ t(1:2) ',' t(3:5) ',' t(6:8) ] ;
+elseif (len == 9)
+ s = [ t(1:3) ',' t(4:6) ',' t(7:9) ] ;
+elseif (len == 10)
+ s = [ t(1) ',' t(2:4) ',' t(5:7) ',' t(8:10) ] ;
+elseif (len == 11)
+ s = [ t(1:2) ',' t(3:5) ',' t(6:8) ',' t(9:11) ] ;
+elseif (len == 12)
+ s = [ t(1:3) ',' t(4:6) ',' t(7:9) ',' t(10:12) ] ;
+end
+
diff --git a/UFcollection/UFlist.m b/UFcollection/UFlist.m
new file mode 100644
index 0000000..44e46e7
--- /dev/null
+++ b/UFcollection/UFlist.m
@@ -0,0 +1,339 @@
+function UFlist (what, group)
+%UFLIST create a web page index for the UF Sparse Matrix Collection
+%
+% Usage: UFlist (what)
+%
+% what:
+% 'group' sort by group, then filename
+% 'name' sort by name
+% 'dimension' sort by max row or col dimension
+% 'id' sort by id (default, if "what" is not present)
+% 'number of nonzeros' sort by number of nonzeros
+% 'type' sort by type, then dimension
+% 'symmetry' sort by symmetry. Rectangular matrices first, sorted by
+% min(nrow,ncol)-max(nrow,ncol), then numerical symmetry
+% 0 to just less than one. Then numerical symmetry = 1
+% but not spd (sorted by dimension). Then spd sorted
+% by dimension.
+%
+% If two arguments are present, only that group is created.
+% In this case, "what" must be "group".
+%
+% Example:
+%
+% UFlist ('id')
+% UFlist ('group', 'HB')
+%
+% See also UFget, UFint.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+index = UFget ;
+
+if (nargin < 1)
+ what = 'id' ;
+end
+
+by_group = (nargin > 1) ;
+
+% create the primary directory
+[url topdir] = UFlocation ;
+matrices = [topdir 'matrices'] ;
+if (~exist (matrices, 'dir'))
+ mkdir (matrices) ;
+end
+
+if (by_group)
+ fprintf ('group: %s\n', group) ;
+ loc = '../' ;
+ if (~exist ([matrices filesep group], 'dir'))
+ mkdir ([matrices filesep group]) ;
+ end
+ f = fopen ([matrices filesep group filesep 'index.html'], 'w') ;
+else
+ fprintf ('list: %s\n', what) ;
+ f = fopen ([matrices filesep 'list_by_' what '.html'], 'w') ;
+ loc = '' ;
+end
+if (f < 0)
+ error ('unable to create html file\n') ;
+end
+
+nmat = length (index.nrows) ;
+
+% add the header
+fprintf (f, ...
+ '<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">\n') ;
+fprintf (f, '<html lang="EN"><head>\n') ;
+fprintf (f, '<meta http-equiv="content-type" content="text/html; charset=') ;
+fprintf (f, 'iso-8859-1">') ;
+if (by_group)
+ fprintf (f, '<title>UF Sparse Matrix Collection - %s group', group) ;
+else
+ fprintf (f, '<title>UF Sparse Matrix Collection - sorted by ') ;
+ if (strcmp (what, 'nnz'))
+ fprintf (f, 'number of nonzeros') ;
+ else
+ fprintf (f, '%s', what) ;
+ end
+end
+fprintf (f, '</title></head>\n') ;
+fprintf (f, '<body bgcolor="#ffffff" link="#0021a5">\n') ;
+fprintf (f, ...
+ '<li><a href="%sindex.html">UF Sparse Matrix Collection</a><hr>\n', loc) ;
+if (by_group)
+ fprintf (f, '<p>UF Sparse Matrix Collection: %s group.<p>\n', group) ;
+else
+ fprintf (f, '<p>UF Sparse Matrix Collection, sorted by %s.\n', what) ;
+ fprintf (f, ' Click on a column header to sort by that column.<p>\n') ;
+end
+
+% add link to mat/<group>/README.txt
+if (by_group)
+ fprintf (f, '<li><a href="../../mat/%s/README.txt">', group) ;
+ fprintf (f, 'Click here for a description of the %s group.</a>\n', group) ;
+end
+
+fprintf (f, '<li><a href="%sgroups.html">', loc) ;
+fprintf (f, 'Click here for a list of all matrix groups.</a>\n') ;
+
+fprintf (f, '<li><a href="%slist_by_id.html">', loc) ;
+fprintf (f, 'Click here for a list of all matrices.</a>\n') ;
+
+fprintf (f, '<p><table border=1>\n') ;
+
+% sort by filename
+[ignore, iname] = sort (lower (index.Name)) ;
+
+if (by_group)
+
+ list = [ ] ;
+ for i = 1:nmat
+ if (strcmp (group, index.Group {i}))
+ list = [list i] ; %#ok
+ end
+ end
+ [ignore i] = sort (lower (index.Name (list))) ;
+ list = list (i) ;
+
+ if (isempty (list))
+ error ('empty group!') ;
+ end
+
+elseif (strcmp (what, 'group'))
+
+ % sort by filename, then stable sort by group
+ [ignore, i] = sort (lower (index.Group (iname))) ;
+ list = iname (i) ;
+
+elseif (strcmp (what, 'name'))
+
+ % sort by filename only
+ list = iname' ;
+
+elseif (strcmp (what, 'dimension'))
+
+ % sort by filename, then stable sort by max dimension
+ [ignore, i] = sort (max (index.nrows (iname), index.ncols (iname))) ;
+ list = iname (i) ;
+
+elseif (strcmp (what, 'id'))
+
+ list = 1:nmat ;
+
+elseif (strcmp (what, 'nnz'))
+
+ % sort by filename, then stable sort by nnz
+ [ignore, i] = sort (index.nnz (iname)) ;
+ list = iname (i) ;
+
+elseif (strcmp (what, 'symmetry'))
+
+% 'symmetry' sort by symmetry. Rectangular matrices first, sorted by
+% min(nrow,ncol)-max(nrow,ncol), then numerical symmetry
+% 0 to just less than one. Then numerical symmetry = 1
+% but not spd (sorted by dimension). Then spd sorted
+% by dimension.
+
+
+ s1 = min (index.nrows, index.ncols) - max (index.nrows, index.ncols) ;
+ s2 = index.numerical_symmetry ;
+ s2 (find (s2) == -1) = 1 ;
+ s3 = index.posdef ;
+ s3 (find (s3) == -1) = 2 ;
+ s4 = max (index.nrows, index.ncols) ;
+
+ [ignore list] = sortrows ([s1' s2' s3' s4'], [1 2 3 4]) ;
+
+elseif (strcmp (what, 'type'))
+
+ [ignore i1] = sort (max (index.nrows, index.ncols)) ;
+ s = index.RBtype (i1,:) ;
+ [ignore i2] = sortrows (s) ;
+ list = i1 (i2) ;
+
+else
+ error ('unknown list') ;
+end
+
+% ensure list is a row vector
+list = list (:)' ;
+
+% print the header
+fprintf (f, '<tr>\n') ;
+
+if (by_group)
+ fprintf (f, '<th>thumbnail</th>\n') ;
+ fprintf (f, '<th>Group\n') ;
+ fprintf (f, 'and Name</th>\n') ;
+ fprintf (f, '<th>id</th>\n') ;
+ fprintf (f, '<th>download</th>\n') ;
+ fprintf (f, '<th># rows</th>\n') ;
+ fprintf (f, '<th># cols</th>\n') ;
+ fprintf (f, '<th>nonzeros</th>\n') ;
+ fprintf (f, '<th>type</th>\n') ;
+ fprintf (f, '<th>sym</th>\n') ;
+ fprintf (f, '<th>spd?</th>\n') ;
+else
+ fprintf (f, '<th>thumbnail</th>\n') ;
+ fprintf (f, '<th><a href=%slist_by_group.html>Group</a>\n', loc) ;
+ fprintf (f, 'and <a href=%slist_by_name.html>Name</a></th>\n', loc) ;
+ fprintf (f, '<th><a href=%slist_by_id.html>id</a></th>\n', loc) ;
+ fprintf (f, '<th>download</th>\n') ;
+ fprintf (f, '<th><a href=%slist_by_dimension.html># rows</a></th>\n', loc) ;
+ fprintf (f, '<th><a href=%slist_by_dimension.html># cols</a></th>\n', loc) ;
+ fprintf (f, '<th><a href=%slist_by_nnz.html>nonzeros</a></th>\n', loc) ;
+ fprintf (f, '<th><a href=%slist_by_type.html>type</a></th>\n', loc) ;
+ fprintf (f, '<th><a href=%slist_by_symmetry.html>sym</a></th>\n', loc) ;
+ fprintf (f, '<th><a href=%slist_by_symmetry.html>spd?</a></th>\n', loc) ;
+end
+
+for id = list
+
+ group = index.Group {id} ;
+ name = index.Name {id} ;
+ nrows = index.nrows (id) ;
+ ncols = index.ncols (id) ;
+ nz = index.nnz (id) ;
+ sym = index.numerical_symmetry (id) ;
+ mtype = index.RBtype (id,:) ;
+
+ s = index.posdef (id) ;
+ if (s == 0)
+ ss = '-' ;
+ elseif (s == 1)
+ ss = 'yes' ;
+ else
+ ss = '?' ;
+ end
+
+ fprintf (f, '<tr>\n') ;
+
+ % thumbnail link to the matrix page
+ fprintf (f, '<td>\n') ;
+ w = 'width="96" height="72"' ;
+ if (by_group)
+ fprintf (f, '<a href="%s.html"><img %s alt="%s/%s"', ...
+ name, w, group, name) ;
+ fprintf (f, ' src="%s_thumb.png"></a>\n', name) ;
+ else
+ fprintf (f, '<a href="%s/%s.html"><img %s alt="%s/%s"', ...
+ group, name, w, group, name) ;
+ fprintf (f, ' src="%s/%s_thumb.png"></a>\n', group, name) ;
+ end
+ fprintf (f, '</td>\n') ;
+
+ % group
+ if (by_group)
+ fprintf (f, '<td>%s/', group) ;
+ else
+ fprintf (f, '<td><a href="%s/index.html">%s</a>/', group, group);
+ end
+
+ % name
+ if (by_group)
+ fprintf (f, '<a href="%s.html">%s</a></td>\n', name, name) ;
+ else
+ fprintf (f, '<a href="%s/%s.html">%s</a></td>\n', group, name, name) ;
+ end
+
+ % id
+ fprintf (f, '<td>%d</td>\n', id) ;
+
+ % download links
+ fprintf (f, '<td>\n') ;
+ fprintf (f, '<a href="%s../mat/%s/%s.mat">MAT</a>', loc, group, name) ;
+ fprintf (f, ', <a href="%s../MM/%s/%s.tar.gz">MM</a>', loc, group, name) ;
+ fprintf (f, ', <a href="%s../RB/%s/%s.tar.gz">RB</a>', loc, group, name) ;
+ fprintf (f, '</td>\n') ;
+
+ % nrow
+ fprintf (f, '<td align=right>%s</td>\n', UFint (nrows)) ;
+
+ % ncols
+ fprintf (f, '<td align=right>%s</td>\n', UFint (ncols)) ;
+
+ % nz
+ fprintf (f, '<td align=right>%s</td>\n', UFint (nz)) ;
+
+ % print the Rutherford/Boeing type
+ mattype = '' ;
+ if (mtype (1) == 'r')
+ mattype = 'real' ;
+ elseif (mtype (1) == 'c')
+ mattype = 'complex' ;
+ elseif (mtype (1) == 'i')
+ mattype = 'integer' ;
+ elseif (mtype (1) == 'p')
+ mattype = 'binary' ;
+ end
+ if (mtype (2) == 'r')
+ mattype = [mattype ' rectangular'] ; %#ok
+ elseif (mtype (2) == 'u')
+ mattype = [mattype ' unsymmetric'] ; %#ok
+ elseif (mtype (2) == 's')
+ mattype = [mattype ' symmetric'] ; %#ok
+ elseif (mtype (2) == 'h')
+ mattype = [mattype ' Hermitian'] ; %#ok
+ elseif (mtype (2) == 'z')
+ mattype = [mattype ' skew-symmetric'] ; %#ok
+ end
+ fprintf (f, '<td>%s</td>\n', mattype) ;
+
+ % numerical symmetry (as a percentage)
+ if (sym == -1)
+ fprintf (f, '<td align=right>?</td>\n') ;
+ elseif (sym == 1)
+ fprintf (f, '<td align=right>yes</td>\n') ;
+ elseif (nrows ~= ncols)
+ fprintf (f, '<td align=right>-</td>\n') ;
+ else
+ if (sym > 0 && sym < 0.01)
+ fprintf (f, '<td align=right>%5.2f%%</td>\n', sym * 100) ;
+ else
+ fprintf (f, '<td align=right>%5.0f%%</td>\n', sym * 100) ;
+ end
+ end
+
+ % positive definite?
+ fprintf (f, '<td>%s</td>\n', ss) ;
+
+ fprintf (f, '</tr>\n\n') ;
+end
+
+fprintf (f, '</table>\n\n') ;
+
+fprintf (f, '<p><p><i>Maintained by <a href="http://www.cise.ufl.edu/~davis">');
+fprintf (f, 'Tim Davis</a>, last updated %s.', date) ;
+fprintf (f, '<br>Matrix pictures by <a href=') ;
+fprintf (f, '"%sCSparse/CSparse/MATLAB/CSparse/cspy.m">cspy</a>, a MATLAB', ...
+ url) ;
+fprintf (f, ' function in the <a href="%sCSparse">CSparse</a> package.\n', ...
+ url) ;
+fprintf (f, '<br>See <a href="%smat/UFget">UFget</a> to download directly', ...
+ url) ;
+fprintf (f, ' into MATLAB.') ;
+fprintf (f, '</body>\n') ;
+fprintf (f, '</html>\n') ;
+
+fclose (f) ;
diff --git a/UFcollection/UFlists.m b/UFcollection/UFlists.m
new file mode 100644
index 0000000..8d4cb7e
--- /dev/null
+++ b/UFcollection/UFlists.m
@@ -0,0 +1,114 @@
+function UFlists
+%UFLISTS create the web pages for each matrix list (group, name, etc.)
+% Places the web pages in the matrices/ subdirectory of the current directory.
+%
+% Example:
+% UFlists
+%
+% See also UFget, UFlist
+
+% Copyright 2006-2007, Timothy A. Davis
+
+% create all the web pages for the lists
+UFlist ('group') ;
+UFlist ('name') ;
+UFlist ('id') ;
+UFlist ('dimension') ;
+UFlist ('nnz') ;
+UFlist ('symmetry') ;
+UFlist ('type') ;
+
+% do all the group pages, and the list of groups
+index = UFget ;
+nmat = length (index.nrows) ;
+
+[ignore, i] = sort (index.Group) ;
+g = index.Group (i) ;
+
+% create the primary directory
+[url topdir] = UFlocation ;
+matrices = [topdir 'matrices'] ;
+if (~exist (matrices, 'dir'))
+ mkdir (matrices) ;
+end
+
+% create the groups.html file
+f = fopen ([matrices filesep 'groups.html'], 'w') ;
+if (f < 0)
+ error ('unable to create groups.html file\n') ;
+end
+
+% add the header
+fprintf (f, ...
+ '<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">\n') ;
+fprintf (f, '<html lang="EN"><head>\n') ;
+fprintf (f, '<meta http-equiv="content-type" content="text/html; charset=') ;
+fprintf (f, 'iso-8859-1"><title>UF Sparse Matrix Collection: group list') ;
+fprintf (f, '</title></head>\n') ;
+fprintf (f, '<body bgcolor="#ffffff" link="#0021a5">\n') ;
+fprintf (f, '<li><a href="./index.html">UF Sparse Matrix Collection</a>\n') ;
+
+fprintf (f, '<p>List of matrix groups in the UF Sparse Matrix Collection:\n') ;
+fprintf (f, '<p><table border=1>\n') ;
+fprintf (f, '<th>Group</th>\n') ;
+fprintf (f, '<th># matrices</th>\n') ;
+fprintf (f, '<th>details</th>\n') ;
+fprintf (f, '<th>description</th>\n') ;
+
+% find all the groups
+group = '' ;
+ngroup = 0 ;
+for i = 1:nmat
+ if (strcmp (group, g {i}))
+ continue
+ end
+ group = g {i} ;
+ ngroup = ngroup + 1 ;
+ groups {ngroup} = group ; %#ok
+end
+
+nmat = 0 ;
+for i = 1:ngroup
+ group = groups {i} ;
+ UFlist ('group', group) ;
+ fprintf (f, '<tr>\n') ;
+
+ % link to group
+ fprintf (f, '<td><a href="%s/index.html">%s</a></td>\n', group, group) ;
+
+ % number of matrices
+ d = dir ([topdir 'mat' filesep group filesep '*.mat']) ;
+ nmat_group = size (d,1) ;
+ fprintf (f, '<td>%d</td>\n', nmat_group) ;
+ nmat = nmat + nmat_group ;
+
+ % link to README.txt file ("details")
+ f2 = fopen ([topdir filesep 'mat' filesep group filesep 'README.txt'], 'r');
+ if (f2 < 0)
+ error (['no README file for group: ' group]) ;
+ else
+ s = fgets (f2) ;
+ fprintf (f, ...
+ '<td><a href="../mat/%s/README.txt">details</a></td>\n', group) ;
+ end
+
+ % one-line description (first line of README.txt)
+ fprintf (f, '<td>%s</td>\n', s) ;
+ fclose (f2);
+
+ fprintf (f, '</tr>\n') ;
+end
+fprintf (f, '</table>\n') ;
+
+fprintf (f, '<p>Total number of matrices in UF Sparse Matrix Collection:') ;
+fprintf (f, ' %d\n', nmat) ;
+fprintf (f, '<p><p><i>Maintained by <a href="http://www.cise.ufl.edu/~davis">');
+fprintf (f, 'Tim Davis</a>, last updated %s.', date) ;
+fprintf (f, '<br>Matrix pictures by <a href=') ;
+fprintf (f, '"%sCSparse/CSparse/MATLAB/CSparse/cspy.m">cspy</a>, a MATLAB', ...
+ url) ;
+fprintf (f, ' function in the <a href="%sCSparse">CSparse</a> package.\n', ...
+ url) ;
+fprintf (f, '</body>\n') ;
+fprintf (f, '</html>\n') ;
+fclose (f) ;
diff --git a/UFcollection/UFlocation.m b/UFcollection/UFlocation.m
new file mode 100644
index 0000000..f22399d
--- /dev/null
+++ b/UFcollection/UFlocation.m
@@ -0,0 +1,17 @@
+function [url, topdir] = UFlocation
+%UFLOCATION URL and top-level directory of the UF Sparse Matrix Collection
+%
+% Example:
+% [url, topdir] = UFlocation
+%
+% See also UFget.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+params = UFget_defaults ;
+t = find (params.dir == filesep) ;
+topdir = regexprep (params.dir (1:t(end-1)), '[\/\\]', filesep) ;
+
+t = find (params.url == '/') ;
+url = params.url (1:t(end)) ;
+
diff --git a/UFcollection/UFpage.m b/UFcollection/UFpage.m
new file mode 100644
index 0000000..09e99cf
--- /dev/null
+++ b/UFcollection/UFpage.m
@@ -0,0 +1,604 @@
+function UFpage (matrix, index, figures)
+%UFPAGE create web page for a matrix in UF Sparse Matrix Collection
+%
+% Usage:
+% UFpage (matrix, index, figures)
+%
+% matrix: id or name of matrix to create the web page for.
+% index: the UF index, from UFget.
+% figures: 1 if the figures are to be created, 0 otherwise
+%
+% Example:
+%
+% UFpage (267)
+% UFpage ('HB/west0479')
+%
+% See also UFget, cspy, UFgplot, UFint.
+
+% This function assumes that the mat/, MM/, and RB/ directories all reside in
+% the same parent directory, given by the download directory specified by
+% UFget_defaults.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+%-------------------------------------------------------------------------------
+% get inputs
+%-------------------------------------------------------------------------------
+
+if (nargin < 2)
+ index = UFget ;
+end
+if (nargin < 3)
+ figures = 1 ;
+end
+
+%-------------------------------------------------------------------------------
+% get the Problem and its contents
+%-------------------------------------------------------------------------------
+
+Problem = UFget (matrix,index) ;
+disp (Problem) ;
+fullname = Problem.name ;
+s = strfind (fullname, '/') ;
+grp = fullname (1:s-1) ;
+name = fullname (s+1:end) ;
+id = Problem.id ;
+
+% create the primary directory
+[url topdir] = UFlocation ;
+matrices = [topdir 'matrices'] ;
+if (~exist (matrices, 'dir'))
+ mkdir (matrices) ;
+end
+
+% create the group directory
+if (~exist ([matrices filesep grp], 'dir'))
+ mkdir ([matrices filesep grp]) ;
+end
+
+% determine the full path of the problem
+fullpath = regexprep ([matrices filesep fullname], '[\/\\]', filesep) ;
+
+ptitle = Problem.title ;
+
+z = 0 ;
+if (isfield (Problem, 'Zeros'))
+ z = nnz (Problem.Zeros) ;
+ Problem = rmfield (Problem, 'Zeros') ;
+end
+
+nblocks = index.nblocks (id) ;
+ncc = index.ncc (id) ;
+
+has_b = isfield (Problem, 'b') ;
+has_x = isfield (Problem, 'x') ;
+has_aux = isfield (Problem, 'aux') ;
+
+if (has_b)
+ b = Problem.b ;
+ Problem = rmfield (Problem, 'b') ;
+ if (iscell (b))
+ b = sprintf ('cell %d-by-%d\n', size (b)) ;
+ elseif (issparse (b))
+ b = sprintf ('sparse %d-by-%d\n', size (b)) ;
+ else
+ b = sprintf ('full %d-by-%d\n', size (b)) ;
+ end
+end
+
+if (has_x)
+ x = Problem.x ;
+ Problem = rmfield (Problem, 'x') ;
+ if (iscell (x))
+ x = sprintf ('cell %d-by-%d\n', size (x)) ;
+ elseif (issparse (x))
+ x = sprintf ('sparse %d-by-%d\n', size (x)) ;
+ else
+ x = sprintf ('full %d-by-%d\n', size (x)) ;
+ end
+end
+
+nodename = [ ] ;
+if (has_aux)
+ aux = Problem.aux ;
+ Problem = rmfield (Problem, 'aux') ;
+ auxfields = fields (aux) ;
+ has_coord = isfield (aux, 'coord') ;
+ has_nodename = isfield (aux, 'nodename') ;
+ auxs = cell (1, length (auxfields)) ;
+ for k = 1:length(auxfields)
+ siz = size (aux.(auxfields{k})) ;
+ if (iscell (aux.(auxfields{k})))
+ auxs {k} = sprintf ('cell %d-by-%d\n', siz) ;
+ elseif (issparse (aux.(auxfields{k})))
+ auxs {k} = sprintf ('sparse %d-by-%d\n', siz) ;
+ else
+ auxs {k} = sprintf ('full %d-by-%d\n', siz) ;
+ end
+ end
+ if (has_coord)
+ xyz = aux.coord ;
+ end
+ if (has_nodename)
+ nodename = aux.nodename ;
+ end
+ clear aux
+else
+ has_coord = 0 ;
+end
+
+kind = Problem.kind ;
+if (isfield (Problem, 'notes'))
+ notes = Problem.notes ;
+else
+ notes = '' ;
+end
+
+au = Problem.author ;
+ed = Problem.ed ;
+da = Problem.date ;
+
+m = index.nrows (id) ;
+n = index.ncols (id) ;
+nz = index.nnz (id) ;
+nnzdiag = index.nnzdiag (id) ;
+
+if (strfind (kind, 'graph'))
+ bipartite = ~isempty (strfind (kind, 'bipartite')) ;
+ directed = ~isempty (regexp (kind, '\<directed', 'once')) ;
+else
+ bipartite = (m ~= n) ;
+ directed = (index.pattern_symmetry (id) < 1) ;
+end
+
+%-------------------------------------------------------------------------------
+% create the pictures
+%-------------------------------------------------------------------------------
+
+if (figures)
+
+ try
+ A = Problem.A ;
+ catch
+ fprintf ('failed to extract A from Problem struct\n') ;
+ A = sparse (0) ;
+ end
+ clear Problem
+
+ %---------------------------------------------------------------------------
+ % create the gplot
+ %---------------------------------------------------------------------------
+
+ do_gplot = has_coord ;
+ if (do_gplot)
+ UFgplot (A, xyz, directed, nodename) ;
+ print (gcf, '-dpng', '-r128', [fullpath '_gplot.png']) ;
+ print (gcf, '-dpng', '-r512', [fullpath '_gplot_big.png']) ;
+ end
+
+ %---------------------------------------------------------------------------
+ % create the thumbnail picture
+ %---------------------------------------------------------------------------
+
+ cspy (A, 16) ;
+ print (gcf, '-dpng', '-r12', [fullpath '_thumb.png']) ;
+
+ %---------------------------------------------------------------------------
+ % create the regular picture
+ %---------------------------------------------------------------------------
+
+ cspy (A, 128) ;
+ print (gcf, '-dpng', '-r64', [fullpath '.png']) ;
+
+ %---------------------------------------------------------------------------
+ % create the dmperm figure, but not for graphs
+ %---------------------------------------------------------------------------
+
+ do_dmspy = (nblocks > 1) & (isempty (strfind (kind, 'graph'))) ;
+ if (do_dmspy)
+ try
+ cs_dmspy (A, 128) ;
+ title ('Dulmage-Mendelsohn permutation') ;
+ catch
+ fprintf ('dmspy failed\n') ;
+ delete ([fullpath '_dmperm.png']) ;
+ do_dmspy = 0 ;
+ end
+ print (gcf, '-dpng', '-r64', [fullpath '_dmperm.png']) ;
+ end
+
+ %---------------------------------------------------------------------------
+ % create the ccspy figure
+ %---------------------------------------------------------------------------
+
+ do_scc = (ncc > 1) ;
+ if (do_dmspy && m == n && nnzdiag == n)
+ % don't do scc for a square matrix with zero-free diagonal
+ do_scc = 0 ;
+ end
+ if (do_scc)
+ try
+ ccspy (A, bipartite, 128) ;
+ if (bipartite)
+ title ('connected components of the bipartite graph') ;
+ else
+ title ('strongly connected components of the graph') ;
+ end
+ print (gcf, '-dpng', '-r64', [fullpath '_scc.png']) ;
+ catch
+ fprintf ('ccspy failed\n') ;
+ delete ([fullpath '_cc.png']) ;
+ do_scc = 0 ;
+ end
+ end
+
+else
+
+ %---------------------------------------------------------------------------
+ % the plots already exist - check the files
+ %---------------------------------------------------------------------------
+
+ do_scc = exist ([fullpath '_scc.png'], 'file') ;
+ do_dmspy = exist ([fullpath '_dmperm.png'], 'file') ;
+ do_gplot = exist ([fullpath '_gplot.png'], 'file') ;
+
+end
+
+clear Problem
+
+%-------------------------------------------------------------------------------
+% create the web page for the matrix
+%-------------------------------------------------------------------------------
+
+f = fopen ([fullpath '.html'], 'w') ;
+if (f < 0)
+ error ('unable to create matrix web page') ;
+end
+
+% add the header
+fprintf (f,'<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">\n');
+fprintf (f, '<html lang="EN"><head>\n') ;
+fprintf (f, '<meta http-equiv="content-type" content="text/html; charset=') ;
+fprintf (f, 'iso-8859-1"><title>%s sparse matrix</title></head>\n', fullname) ;
+fprintf (f, '<body bgcolor="#ffffff" link="#0021a5">\n') ;
+
+% link to UF collection
+fprintf (f, '<li><a href="..">UF Sparse Matrix Collection</a>\n') ;
+
+% link to group
+fprintf (f, '<li><a href="./index.html">Matrix group: %s</a>\n', grp) ;
+
+% add link to mat/<group>/README.txt
+fprintf (f, '<li><a href="../../mat/%s/README.txt">', grp) ;
+fprintf (f, 'Click here for a description of the %s group.</a>\n', grp) ;
+
+% link to all matrices
+fprintf (f, '<li><a href="../list_by_id.html">') ;
+fprintf (f, 'Click here for a list of all matrices</a>\n') ;
+
+% link to all groups
+fprintf (f, '<li><a href="../groups.html">') ;
+fprintf (f, 'Click here for a list of all matrix groups</a>\n') ;
+
+% matrix name and description
+fprintf (f, '<p><hr><li>Matrix: %s\n', fullname) ;
+fprintf (f, '<li>Description: %s\n', ptitle) ;
+
+% download link for MATLAB format
+fprintf (f, ...
+ '<li><a href="../../mat/%s.mat">download as a MATLAB mat-file</a>',...
+ fullname) ;
+fsize (f, [topdir 'mat/' fullname '.mat']) ;
+
+fprintf (f, 'Use <a href="%smat/UFget.html">UFget</a>(%d)', url, id) ;
+fprintf (f, ' or UFget(''%s'') in MATLAB.\n', fullname) ;
+
+% download link for Matrix Market format
+fprintf (f, ...
+'<li><a href="../../MM/%s.tar.gz">download in Matrix Market format</a>',...
+fullname) ;
+fsize (f, [topdir 'MM/' fullname '.tar.gz']) ;
+
+% download link for Rutherford/Boeing format
+fprintf (f, ...
+'<li><a href="../../RB/%s.tar.gz">download in Rutherford/Boeing format</a>',...
+fullname) ;
+fsize (f, [topdir 'RB/' fullname '.tar.gz']) ;
+
+%-------------------------------------------------------------------------------
+% link to images
+%-------------------------------------------------------------------------------
+
+fprintf (f, '<p><img alt="%s" src="%s.png"></a>\n', fullname, name) ;
+
+% dmspy, if it exists
+if (do_dmspy)
+ fprintf (f, '<p><img alt="dmperm of %s" src="%s_dmperm.png">\n', ...
+ fullname, name) ;
+end
+
+% ccspy, if it exists
+if (do_scc)
+ fprintf (f, '<p><img alt="scc of %s" src="%s_scc.png">\n', ...
+ fullname, name) ;
+end
+
+% gplot, if it exists
+if (do_gplot)
+ fprintf (f, '<p>') ;
+ fprintf (f, ...
+'<a href="%s_gplot_big.png"><img alt="%s graph" src="%s_gplot.png"></a>\n', ...
+ name, fullname, name) ;
+end
+
+%-------------------------------------------------------------------------------
+% table of matrix properties
+%-------------------------------------------------------------------------------
+
+fprintf (f, '<p><table border=1>\n') ;
+stat (f, '<i><a href="../legend.html">Matrix properties</a></i>', '%s', ' ') ;
+stat (f, 'number of rows', '%s', UFint (m)) ;
+stat (f, 'number of columns', '%s', UFint (n)) ;
+stat (f, 'nonzeros', '%s', UFint (nz)) ;
+
+srank = index.sprank (id) ;
+if (srank == min (m,n))
+ stat (f, 'structural full rank?', '%s', 'yes') ;
+else
+ stat (f, 'structural full rank?', '%s', 'no') ;
+end
+stat (f, 'structural rank', '%s', UFint (srank)) ;
+
+stat (f, '# of blocks from dmperm', '%s', UFint (nblocks)) ;
+stat (f, '# strongly connected comp.', '%s', UFint (ncc)) ;
+
+if (srank == min (m,n))
+ stat (f, 'entries not in dmperm blocks', '%s', ...
+ UFint (index.nzoff (id))) ;
+end
+
+stat (f, 'explicit zero entries', '%s', UFint (z)) ;
+
+s = index.pattern_symmetry (id) ;
+if (s == 1)
+ stat (f, 'nonzero pattern symmetry', '%s', 'symmetric') ;
+else
+ stat (f, 'nonzero pattern symmetry', '%8.0f%%', s*100) ;
+end
+
+s = index.numerical_symmetry (id) ;
+if (s == -1)
+ stat (f, 'numeric value symmetry', '%s', 'unknown') ;
+elseif (s == 1)
+ stat (f, 'numeric value symmetry', '%s', 'symmetric') ;
+else
+ stat (f, 'numeric value symmetry', '%8.0f%%', s*100) ;
+end
+
+% print the Rutherford/Boeing type
+mtype = index.RBtype (id,:) ;
+ss = '-' ;
+if (mtype (1) == 'r')
+ ss = 'real' ;
+elseif (mtype (1) == 'c')
+ ss = 'complex' ;
+elseif (mtype (1) == 'i')
+ ss = 'integer' ;
+elseif (mtype (1) == 'p')
+ ss = 'binary' ;
+end
+stat (f, 'type', '%s', ss) ;
+
+ss = '-' ;
+if (mtype (2) == 'r')
+ ss = 'rectangular' ;
+elseif (mtype (2) == 'u')
+ ss = 'unsymmetric' ;
+elseif (mtype (2) == 's')
+ ss = 'symmetric' ;
+elseif (mtype (2) == 'h')
+ ss = 'Hermitian' ;
+elseif (mtype (2) == 'z')
+ ss = 'skew-symmetric' ;
+end
+stat (f, 'structure', '%s', ss) ;
+
+if (index.cholcand (id) == 1)
+ ss = 'yes' ;
+elseif (index.cholcand (id) == 0)
+ ss = 'no' ;
+else
+ ss = '?' ;
+end
+stat (f, 'Cholesky candidate?', '%s', ss) ;
+
+s = index.posdef (id) ;
+if (s == 0)
+ ss = 'no' ;
+elseif (s == 1)
+ ss = 'yes' ;
+else
+ ss = 'unknown' ;
+end
+stat (f, 'positive definite?', '%s', ss) ;
+
+fprintf (f, '</table><p>\n') ;
+
+%-------------------------------------------------------------------------------
+% problem author, ed, kind
+%-------------------------------------------------------------------------------
+
+fprintf (f, '<p><table border=1>\n') ;
+fprintf (f, '<tr><td>author</td><td align=left>%s</td>\n', au) ;
+fprintf (f, '<tr><td>editor</td><td align=left>%s</td>\n', ed) ;
+fprintf (f, '<tr><td>date</td><td align=left>%s</td>\n', da) ;
+fprintf (f, '<tr><td><a href=../kind.html>kind</a></td><td align=left>%s</td>\n', kind);
+s = index.isND (id) ;
+if (s == 0)
+ ss = 'no' ;
+else
+ ss = 'yes' ;
+end
+fprintf (f, '<tr><td>2D/3D problem?</td><td align=left>%s</td>\n', ss) ;
+fprintf (f, '</table><p>\n') ;
+
+%-------------------------------------------------------------------------------
+% fields
+%-------------------------------------------------------------------------------
+
+if (has_b || has_x || has_aux)
+ fprintf (f, '<p><table border=1>\n') ;
+ stat (f, 'Additional fields', '%s', 'size and type') ;
+ if (has_b)
+ stat (f, 'b', '%s', b) ;
+ end
+ if (has_x)
+ stat (f, 'x', '%s', x) ;
+ end
+ if (has_aux)
+ for k = 1:length(auxfields)
+ stat (f, auxfields{k}, '%s', char (auxs{k})) ;
+ end
+ end
+ fprintf (f, '</table><p>\n') ;
+end
+
+%-------------------------------------------------------------------------------
+% Notes
+%-------------------------------------------------------------------------------
+
+if (~isempty (notes))
+ fprintf (f, '<p>Notes:<p><pre>\n') ;
+ for k = 1:size(notes,1)
+ fprintf (f, '%s\n', notes (k,:)) ;
+ end
+ fprintf (f, '</pre>\n') ;
+end
+
+%-------------------------------------------------------------------------------
+% ordering statistics
+%-------------------------------------------------------------------------------
+
+fprintf (f, '<p><table border=1>\n') ;
+if (nblocks == 1 || index.nzoff (id) == -2)
+
+ stat (f, ...
+ '<i><a href="../legend.html">Ordering statistics:</a></i>', ...
+ '%s', '<i>AMD</i>', '<i>METIS</i>') ;
+
+ if (index.amd_lnz (id) > -2)
+ stat (f, 'nnz(chol(P*(A+A''+s*I)*P''))', '%s', ...
+ UFint (index.amd_lnz (id)), ...
+ UFint (index.metis_lnz (id))) ;
+ stat (f, 'Cholesky flop count', '%7.1e', ...
+ index.amd_flops (id), ...
+ index.metis_flops (id)) ;
+ stat (f, 'nnz(L+U), no partial pivoting', '%s', ...
+ UFint (2*index.amd_lnz (id) - min(m,n)), ...
+ UFint (2*index.metis_lnz (id) - min(m,n))) ;
+ end
+
+ stat (f, 'nnz(V) for QR, upper bound nnz(L) for LU', '%s', ...
+ UFint (index.amd_vnz (id)), ...
+ UFint (index.metis_vnz (id))) ;
+ stat (f, 'nnz(R) for QR, upper bound nnz(U) for LU', '%s', ...
+ UFint (index.amd_rnz (id)), ...
+ UFint (index.metis_rnz (id))) ;
+
+else
+
+ stat (f, ...
+ '<i><a href="../legend.html">Ordering statistics:</a></i>', ...
+ '%s', '<i>AMD</i>', '<i>METIS</i>', '<i>DMPERM+</i>') ;
+
+ if (index.amd_lnz (id) > -2)
+ stat (f, 'nnz(chol(P*(A+A''+s*I)*P''))', '%s', ...
+ UFint (index.amd_lnz (id)), ...
+ UFint (index.metis_lnz (id)), ...
+ UFint (index.dmperm_lnz (id))) ;
+ stat (f, 'Cholesky flop count', '%7.1e', ...
+ index.amd_flops (id), ...
+ index.metis_flops (id), ...
+ index.dmperm_flops (id)) ;
+ stat (f, 'nnz(L+U), no partial pivoting', '%s', ...
+ UFint (2*index.amd_lnz (id) - min(m,n)), ...
+ UFint (2*index.metis_lnz (id) - min(m,n)), ...
+ UFint (index.dmperm_lnz (id) + index.dmperm_unz (id)-min(m,n))) ;
+ end
+
+ stat (f, 'nnz(V) for QR, upper bound nnz(L) for LU', '%s', ...
+ UFint (index.amd_vnz (id)), ...
+ UFint (index.metis_vnz (id)), ...
+ UFint (index.dmperm_vnz (id))) ;
+ stat (f, 'nnz(R) for QR, upper bound nnz(U) for LU', '%s', ...
+ UFint (index.amd_rnz (id)), ...
+ UFint (index.metis_rnz (id)), ...
+ UFint (index.dmperm_rnz (id))) ;
+
+end
+fprintf (f, '</table><p>\n') ;
+
+%-------------------------------------------------------------------------------
+% note regarding orderings
+%-------------------------------------------------------------------------------
+
+if (z > 0)
+ fprintf (f, '<p><i>Note that all matrix statistics (except nonzero');
+ fprintf (f, ' pattern symmetry) exclude the %d explicit zero entries.\n',z);
+ fprintf (f, '<i>\n') ;
+end
+
+%-------------------------------------------------------------------------------
+% etc ...
+%-------------------------------------------------------------------------------
+
+fprintf (f, '<p><p><i>Maintained by <a href="http://www.cise.ufl.edu/~davis">');
+fprintf (f, 'Tim Davis</a>, last updated %s.', date) ;
+fprintf (f, '<br>Matrix pictures by <a href=') ;
+fprintf (f, '"%sCSparse/CSparse/MATLAB/CSparse/cspy.m">cspy</a>, a ', url) ;
+fprintf (f, 'MATLAB function in the <a href="%sCSparse">CSparse</a>', url) ;
+fprintf (f, ' package.\n</body>\n</html>\n') ;
+
+fclose (f) ;
+
+
+%-------------------------------------------------------------------------------
+
+function fsize (f, filename)
+% fsize: print the filesize
+d = dir (regexprep (filename, '[\/\\]', filesep)) ;
+if (isempty (d))
+ fprintf ('\n') ;
+elseif (d.bytes < 1024)
+ fprintf (f, ', file size: %4d bytes.\n', d.bytes) ;
+elseif (d.bytes > 2^20)
+ fprintf (f, ', file size: %8.0f MB.\n', d.bytes / 2^20) ;
+else
+ fprintf (f, ', file size: %8.0f KB.\n', d.bytes / 2^10) ;
+end
+
+
+%-------------------------------------------------------------------------------
+
+function stat (f, what, format, value1, value2, value3)
+% stat: print one row of a table
+s = val (format, value1) ;
+fprintf (f, '<tr><td>%s</td><td align=right>%s</td>\n', what, s) ;
+if (nargin > 4)
+ fprintf (f, '<td align=right>%s</td>\n', val (format, value2)) ;
+end
+if (nargin > 5)
+ fprintf (f, '<td align=right>%s</td>\n', val (format, value3)) ;
+end
+fprintf (f, '</tr>\n') ;
+
+
+%-------------------------------------------------------------------------------
+
+function s = val (format, value)
+% val: print a value in a table
+if (~ischar (value) && value < 0)
+ s = '-' ;
+else
+ s = sprintf (format, value) ;
+end
diff --git a/UFcollection/UFpages.m b/UFcollection/UFpages.m
new file mode 100644
index 0000000..dec3f78
--- /dev/null
+++ b/UFcollection/UFpages.m
@@ -0,0 +1,30 @@
+function UFpages (figures, list)
+%UFPAGES create web page for each matrix in UF Sparse Matrix Collection
+% Usage: UFpages (figures, list)
+%
+% figures: 1 if figures are to be created, 0 otherwise
+% list: list of matrix id's to process. All matrices in the collection are
+% processed if not present.
+%
+% Example:
+%
+% UFpages % create all the pages
+% UFpages (0) % create all the pages, but not the figures
+% UFpages (1,1:10) % create pages for just matrices 1 to 10
+% UFpages (0,1:10) % ditto, but do not create the figures
+%
+% See also UFpage, UFget.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+if (nargin < 1)
+ figures = 1 ;
+end
+index = UFget ;
+if (nargin < 2)
+ list = 1:length (index.nrows) ;
+end
+for i = list
+ UFpage (i, index, figures) ;
+end
+
diff --git a/UFcollection/UFread.m b/UFcollection/UFread.m
new file mode 100644
index 0000000..9b07eb3
--- /dev/null
+++ b/UFcollection/UFread.m
@@ -0,0 +1,449 @@
+function Problem = UFread (directory, tmp)
+%UFREAD read a Problem in Matrix Market or Rutherford/Boeing format
+% containing a set of files created by UFwrite, in either Matrix Market or
+% Rutherford/Boeing format. See UFwrite for a description of the Problem struct.
+%
+% Usage: Problem = UFread (directory)
+%
+% Example:
+%
+% load west0479
+% clear Problem
+% Problem.name = 'HB/west0479' ;
+% Problem.title = '8 STAGE COLUMN SECTION, ALL SECTIONS RIGOROUS (CHEM.ENG.)';
+% Problem.A = west0479 ;
+% Problem.id = 267 ; % the id number of west0479 in the UF collection
+% Problem.date = '1983' ;
+% Problem.author = 'A. Westerberg' ;
+% Problem.ed = 'I. Duff, R. Grimes, J. Lewis'
+% Problem.kind = 'chemical process simulation problem' ;
+% UFwrite (Problem, 'RB/', '') ;
+% Prob3 = UFread ('RB/HB/west0479')
+% isequal (Problem, Prob3)
+%
+% This part of the example requires CHOLMOD, for the mread function:
+%
+% UFwrite (Problem, 'MM/') ;
+% Prob2 = UFread ('MM/HB/west0479')
+% isequal (Problem, Prob2)
+%
+% You can also compare this Problem with the version in the UF Sparse Matrix
+% Collection, with UFget(267) or UFget('HB/west0479'). Note that this includes
+% the 22 explicit zero entries present in the west0479 Harwell/Boeing matrix,
+% but not included in the MATLAB west0479.mat demo matrix. Those entries are
+% present in the UF Sparse Matrix Collection. This example assumes your current
+% directory is the RBio directory, containing the west0479 problem in the
+% RBio/Test directory:
+%
+% Prob5 = UFget ('HB/west0479')
+% Prob6 = UFread ('Test/west0479')
+% isequal (Prob5, Prob6)
+%
+% The directory can be a compressed tar file of the form "name.tar.gz", in
+% which case the tarfile is uncompressed into a temporary directory, and
+% the temporary directory is deleted when done. The '.tar.gz' should not be
+% part of the directory argument. In this case, a 2nd input argument can be
+% provided: Problem = UFread (directory, tmp). The problem is extracted into
+% the tmp directory. If tmp is not present, the output of the tempdir function
+% is used instead.
+%
+% Note that UFget is much faster than UFread. UFread is useful if you are
+% short on disk space, and want to have just one copy of the collection that
+% can be read by MATLAB (via UFread) and a non-MATLAB program (the MM or RB
+% versions of the collection).
+%
+% See also UFwrite, mread, mwrite, RBread, RBread, UFget, untar, tempdir.
+
+% Optionally uses the CHOLMOD mread mexFunction, for reading Problems in
+% Matrix Market format.
+
+% Copyright 2006-2007, Timothy A. Davis, Univ. of Florida
+
+%-------------------------------------------------------------------------------
+% determine the Problem name from the directory name
+%-------------------------------------------------------------------------------
+
+directory = regexprep (directory, '[\/\\]', filesep) ;
+t = find (directory == filesep) ;
+if (isempty (t))
+ name = directory ;
+else
+ name = directory (t(end)+1:end) ;
+end
+
+%-------------------------------------------------------------------------------
+% open the directory, or untar the tar.gz file
+%-------------------------------------------------------------------------------
+
+d = dir (directory) ;
+is_tar = 0 ;
+
+if (isempty (d))
+ % look for a .tar.gz file
+ if (nargin < 2)
+ tmpdir = [tempname '_UFread_' name] ;
+ else
+ tmpdir = [tmp filesep name] ;
+ end
+ try
+ % try untaring the problem
+ untar ([directory '.tar.gz'], tmpdir) ;
+ catch
+ % untar failed, make sure tmpdir is deleted
+ try
+ rmdir (tmpdir, 's') ;
+ catch
+ end
+ error (['unable to read problem: ' directory]) ;
+ end
+ directory = [tmpdir filesep name] ;
+ d = dir (directory) ;
+ is_tar = 1 ;
+end
+
+%-------------------------------------------------------------------------------
+% read the problem
+%-------------------------------------------------------------------------------
+
+try
+
+ %---------------------------------------------------------------------------
+ % get name, title, id, kind, date, author, editor, notes from master file
+ %---------------------------------------------------------------------------
+
+ masterfile = [directory filesep name] ;
+ [Problem notes RB] = get_header (masterfile) ;
+
+ %---------------------------------------------------------------------------
+ % get the A and Zero matrices from the master file and add to the Problem
+ %---------------------------------------------------------------------------
+
+ if (RB)
+ % read in the primary Rutherford/Boeing file
+ [Problem.A Zeros] = RBread ([masterfile '.rb']) ;
+ else
+ % read in the primary Matrix Market file. Get patterns as binary.
+ [Problem.A Zeros] = mread ([masterfile '.mtx'], 1) ;
+ end
+ if (nnz (Zeros) > 0)
+ Problem.Zeros = Zeros ;
+ end
+
+ % add the notes after A and Zeros
+ if (~isempty (notes))
+ Problem.notes = notes ;
+ end
+
+ namelen = length (name) ;
+
+ %---------------------------------------------------------------------------
+ % read b, x, aux (incl. any aux.cell sequences), stored as separate files
+ %---------------------------------------------------------------------------
+
+ for k = 1:length(d)
+
+ % get the next filename in the directory
+ file = d(k).name ;
+ fullfilename = [directory filesep file] ;
+
+ if (length (file) < length (name) + 1)
+
+ % unrecognized file; skip it
+ continue
+
+ elseif (strcmp (file, [name '.mtx']))
+
+ % skip the master file; already read in
+ continue
+
+ elseif (strcmp (file, [name '_b.mtx']))
+
+ % read in b as a Matrix Market file
+ Problem.b = mtx_read (fullfilename, RB) ;
+
+ elseif (strcmp (file, [name '_x.mtx']))
+
+ % read in x as a Matrix Market file
+ Problem.x = mtx_read (fullfilename, RB) ;
+
+ elseif (strcmp (file, [name '_b.rb']))
+
+ % read in b as a Rutherford/Boeing file
+ Problem.b = RBread (fullfilename) ;
+
+ elseif (strcmp (file, [name '_x.rb']))
+
+ % read in x as a Rutherford/Boeing file
+ Problem.x = RBread (fullfilename) ;
+
+ elseif (strcmp (file (1:length(name)+1), [name '_']))
+
+ % read in an aux component, in the form name_whatever.mtx
+ thedot = find (file == '.', 1, 'last') ;
+ ext = file (thedot:end) ;
+
+ if (strcmp (ext, '.txt'))
+
+ % get a txt file
+ % first, determine the longest line in the file
+ f = fopen (fullfilename) ;
+ if (f < 0)
+ error (['cannot open ' fullfilename]) ;
+ end
+ len = 0 ;
+ nline = 0 ;
+ while (1)
+ s = fgetl (f) ;
+ if (~ischar (s))
+ break
+ end
+ len = max (len, length (s)) ;
+ nline = nline + 1 ;
+ end
+ fclose (f) ;
+ % next, read in the file as a char array
+ C = repmat (' ', nline, len) ;
+ f = fopen (fullfilename) ;
+ if (f < 0)
+ error (['cannot open ' fullfilename]) ;
+ end
+ i = 0 ;
+ while (1)
+ s = fgetl (f) ;
+ if (~ischar (s))
+ break
+ end
+ i = i + 1 ;
+ len = length (s) ;
+ if (len > 0)
+ C (i, 1:len) = s ;
+ end
+ end
+ fclose (f) ;
+
+ elseif (strcmp (ext, '.mtx'))
+
+ % read a full or sparse auxiliary matrix in the Matrix Market
+ % form, or a full auxiliary matrix in the Rutherford/Boeing form.
+ C = mtx_read (fullfilename, RB) ;
+
+ elseif (strcmp (ext, '.rb'))
+
+ % read in a sparse matrix, for a Rutherford/Boeing collection
+ C = RBread (fullfilename) ;
+
+ else
+
+ % this file is not recognized - skip it.
+ C = [ ] ;
+
+ end
+
+ % determine the name of the component and place it in the Problem
+ if (~isempty (C))
+ % Determine if this is part of an aux.whatever cell sequence.
+ % These filenames have the form name_whatever_#.mtx, where name
+ % is the name of the Problem, and # is a number (1 or more
+ % digts) greater than zero. If # = i, this becomes the
+ % aux.whatever{i} matrix.
+ suffix = file (namelen+2:thedot-1) ;
+ t = find (suffix == '_', 1, 'last') ;
+ what = suffix (1:t-1) ;
+ i = str2num (suffix (t+1:end)) ; %#ok
+ if (~isempty (i) && i > 0 && ~isempty (what))
+ % this is part of aux.whatever{i} cell array
+ Problem.aux.(what) {i,1} = C ;
+ elseif (~isempty (suffix))
+ % this is not a cell, simply an aux.whatever matrix
+ Problem.aux.(suffix) = C ;
+ end
+ end
+ end
+ end
+
+ %---------------------------------------------------------------------------
+ % delete the uncompressed version of the tar file
+ %---------------------------------------------------------------------------
+
+ if (is_tar)
+ rmdir (tmpdir, 's') ;
+ end
+
+catch
+
+ %---------------------------------------------------------------------------
+ % catch the error, delete the temp directory, and rethrow the error
+ %---------------------------------------------------------------------------
+
+ try
+ if (is_tar)
+ rmdir (tmpdir, 's') ;
+ end
+ catch
+ end
+ rethrow (lasterror) ;
+
+end
+
+
+%-------------------------------------------------------------------------------
+% get_header: get the header of the master file (Group/name/name.txt or .mtx)
+%-------------------------------------------------------------------------------
+
+function [Problem, notes, RB] = get_header (masterfile)
+% Get the name, title, id, kind, date, author, editor and notes from the master
+% file. The name, title, and id are required. They appear as structured
+% comments in the Matrix Market file (masterfile.mtx) or in the text file for
+% a problem in Rutherford/Boeing format (masterfile.txt). RB is returned as
+% 1 if the problem is in Rutherford/Boeing format, 0 otherwise.
+
+% first assume it's in Matrix Market format
+f = fopen ([masterfile '.mtx'], 'r') ;
+if (f < 0)
+ % oops, that failed. This must be a problem in Rutherford/Boeing format
+ RB = 1 ;
+ f = fopen ([masterfile '.txt'], 'r') ;
+ if (f < 0)
+ % oops again, this is not a valid problem in the UF Sparse collection
+ error (['invalid problem: ' masterfile]) ;
+ end
+else
+ % we found the Matrix Market file
+ RB = 0 ;
+end
+Problem = [ ] ;
+notes = [ ] ;
+
+while (1)
+
+ % get the next line
+ s = fgetl (f) ;
+ if (~ischar (s) || length (s) < 3 || s (1) ~= '%')
+ % end of file or end of leading comments ... no notes found
+ fclose (f) ;
+ [Problem notes] = valid_problem (Problem, [ ]) ;
+ return ;
+ end
+
+ % remove the leading '% ' and get the first token
+ s = s (3:end) ;
+ [t r] = strtok (s) ;
+
+ % parse the line
+ if (strcmp (t, 'name:'))
+
+ % get the Problem.name. It must be of the form Group/Name.
+ Problem.name = strtrim (r) ;
+ if (length (find (Problem.name == '/')) ~= 1)
+ fclose (f) ;
+ error (['invalid problem name ' Problem.name]) ;
+ end
+
+ elseif (s (1) == '[')
+
+ % get the Problem.title
+ k = find (s == ']', 1, 'last') ;
+ if (isempty (k))
+ fclose (f) ;
+ error ('invalid problem title') ;
+ end
+ Problem.title = s (2:k-1) ;
+
+ elseif (strcmp (t, 'id:'))
+
+ % get the Problem.id
+ Problem.id = str2num (r) ; %#ok
+ if (isempty (Problem.id) || Problem.id < 0)
+ fclose (f) ;
+ error ('invalid problem id') ;
+ end
+
+ elseif (strcmp (t, 'kind:'))
+
+ % get the Problem.kind
+ Problem.kind = strtrim (r) ;
+
+ elseif (strcmp (t, 'date:'))
+
+ % get the Problem.date
+ Problem.date = strtrim (r) ;
+
+ elseif (strcmp (t, 'author:'))
+
+ % get the Problem.author
+ Problem.author = strtrim (r) ;
+
+ elseif (strcmp (t, 'ed:'))
+
+ % get the Problem.ed
+ Problem.ed = strtrim (r) ;
+
+ elseif (strcmp (t, 'notes:'))
+
+ % get the notes, which always appear last
+ k = 0 ;
+ notes = [ ] ;
+ while (1)
+ % get the next line
+ s = fgetl (f) ;
+ if (~ischar (s) || length (s) < 2 || ~strcmp (s (1:2), '% '))
+ % end of file or end of notes ... convert notes to char array
+ fclose (f) ;
+ [Problem notes] = valid_problem (Problem, notes) ;
+ return ;
+ end
+ % add the line to the notes
+ k = k + 1 ;
+ notes {k} = s ; %#ok
+ end
+ end
+end
+
+
+%-------------------------------------------------------------------------------
+% valid_problem: determine if a problem is valid, and finalizes the notes
+%-------------------------------------------------------------------------------
+
+function [Problem, notes] = valid_problem (Problem, notes)
+% make sure the required fields (name, title, id, date, author, ed) are present.
+% Convert notes to char, and strip off the leading '% ', inserted when the notes
+% were printed in the Matrix Market file.
+if (~isfield (Problem, 'name') || ~isfield (Problem, 'title') || ...
+ ~isfield (Problem, 'id') || ~isfield (Problem, 'date') || ...
+ ~isfield (Problem, 'author') || ~isfield (Problem, 'ed') || ...
+ ~isfield (Problem, 'kind'))
+ error ('invalid Problem mfile') ;
+end
+if (~isempty (notes))
+ notes = char (notes) ;
+ notes = notes (:, 3:end) ;
+end
+
+
+%-------------------------------------------------------------------------------
+% mtx_read: read a *.mtx file
+%-------------------------------------------------------------------------------
+
+% In the Rutherford/Boeing form, a *.mtx file is used only for full matrices,
+% using a tiny subset of the Matrix Market format. In the Matrix Market form,
+% the *.mtx is used for all b, x, and aux matrices (both full and sparse).
+
+function C = mtx_read (file, RB)
+
+if (~RB)
+
+ % Get a Matrix Market file, using full Matrix Market features.
+ C = mread (file, 1) ;
+
+else
+
+ % mread is not installed. The RB format uses a tiny subset of the Matrix
+ % Market format for full matrices: just the one header line, and no comment
+ % or blank lines permitted. Allowable header lines are:
+ % %%MatrixMarket matrix array real general
+ % %%MatrixMarket matrix array complex general
+ % This tiny subset can be read by UFfull_read.
+ C = UFfull_read (file) ;
+
+end
+
diff --git a/UFcollection/UFstats.m b/UFcollection/UFstats.m
new file mode 100644
index 0000000..2d0093d
--- /dev/null
+++ b/UFcollection/UFstats.m
@@ -0,0 +1,610 @@
+function stats = UFstats (A, kind, nometis, Z)
+%UFSTATS compute matrix statistics for the UF Sparse Matrix Collection
+% Example:
+% stats = UFstats (A,kind,nometis,Z)
+%
+% A: a sparse matrix
+% kind: a string with the Problem.kind
+% nometis: if nonzero then metis(A,'col') is not used, nor is metis used in the
+% dmperm+ ordering.
+% Z: empty, or a sparse matrix the same size as A. Only used for psym and
+% nzero statistics, described below.
+%
+% Requires amd, cholmod, metis, RBio, and CSparse. Computes the following
+% statistics, returning them as fields in the stats struct:
+%
+% nrows number of rows
+% ncols number of columns
+% nnz number of entries in A
+% RBtype Rutherford/Boeing type
+% isBinary 1 if binary, 0 otherwise
+% isReal 1 if real, 0 if complex
+% cholcand 1 if a candidate for sparse Cholesky, 0 otherwise
+% nsym numeric symmetry (0 to 1, where 1=symmetric)
+% psym pattern symmetry (0 to 1, where 1=symmetric)
+% nnzdiag nnz (diag (A)) if A is square, 0 otherwise
+% nzero nnz (Z)
+% amd_lnz nnz(L) for chol(C(p,p)) where, C=A+A', p=amd(C)
+% amd_flops flop count for chol(C(p,p)) where, C=A+A', p=amd(C)
+% amd_vnz nnz in Householder vectors for qr(A(:,colamd(A)))
+% amd_rnz nnz in R for qr(A(:,colamd(A)))
+% metis_lnz nnz(L) for chol(C(p,p)) where, C=A+A', p=metis(C)
+% metis_flops flop count for chol(C(p,p)) where, C=A+A', p=metis(C)
+% metis_vnz nnz in Householder vectors for qr(A(:,metis(A,'col')))
+% metis_rnz nnz in R for qr(A(:,metis(A,'col')))
+% nblocks # of blocks from dmperm
+% sprank sprank(A)
+% nzoff # of entries not in diagonal blocks from dmperm
+% ncc # of strongly connected components
+% dmperm_lnz nnz(L), using dmperm plus amd or metis
+% dmperm_unz nnz(U), using dmperm plus amd or metis
+% dmperm_flops flop count with dperm plus
+% dmperm_vnz nnz in Householder vectors for dmperm plus
+% dmperm_rnz nnz in R for dmperm plus
+% posdef 1 if positive definite, 0 otherwise
+% isND 1 if a 2D/3D problem, 0 otherwise
+%
+% The *_lnz, *_unz, and *_flops statistics are not computed for rectangular
+% or structurally singular matrices. nzoff and the dmperm_* stats are not
+% computed for structurally singular matrices. If a statistic is not computed,
+% it is set to -2. If an attempt to compute the statistic was made but failed,
+% it is set to -1.
+%
+% See also UFget, UFindex, amd, metis, RBtype, cs_scc, cs_sqr, dmperm.
+
+% Copyright 2006-2007, Timothy A. Davis
+
+% Requires the SuiteSparse set of packages: CHOLMOD, AMD, COLAMD, RBio, CSparse;
+% and METIS.
+
+if (nargin < 3)
+ nometis = 0 ;
+end
+
+%-------------------------------------------------------------------------------
+% ensure the matrix is sparse
+%-------------------------------------------------------------------------------
+
+if (~issparse (A))
+ A = sparse (A) ;
+end
+
+%-------------------------------------------------------------------------------
+% basic stats
+%-------------------------------------------------------------------------------
+
+tic ;
+[m n] = size (A) ;
+stats.nrows = m ;
+stats.ncols = n ;
+stats.nnz = nnz (A) ;
+stats.RBtype = RBtype (A) ; % Rutherford/Boeing type
+stats.isBinary = (stats.RBtype (1) == 'p') ;
+stats.isReal = (stats.RBtype (1) ~= 'c') ;
+
+fprintf ('RBtype: %s time: %g\n', stats.RBtype, toc) ;
+
+%-------------------------------------------------------------------------------
+% symmetry and Cholesky candidacy
+%-------------------------------------------------------------------------------
+
+% get the symmetry
+tic ;
+[s xmatched pmatched nzoffdiag nnzdiag] = spsym (A) ;
+
+stats.cholcand = (s >= 6) ; % check if Cholesky candidate
+
+if (m ~= n)
+ stats.nsym = 0 ;
+ stats.psym = 0 ;
+elseif (nzoffdiag > 0)
+ stats.nsym = xmatched / nzoffdiag ;
+ stats.psym = pmatched / nzoffdiag ;
+else
+ stats.nsym = 1 ;
+ stats.psym = 1 ;
+end
+
+fprintf ('cholcand: %d\n', stats.cholcand) ;
+fprintf ('nsym: %g psym: %g time: %g\n', stats.nsym, stats.psym, toc) ;
+tic ;
+
+stats.nnzdiag = nnzdiag ;
+
+if (nargin > 3)
+ stats.nzero = nnz (Z) ;
+
+ % recompute the pattern symmetry with Z included
+ if (m == n)
+ try
+ AZ = A+Z ;
+ if (nnz (AZ) ~= nnz (A) + nnz (Z))
+ error ('A and Z overlap!')
+ end
+ [s xmatched pmatched nzoffdiag] = spsym (AZ) ;
+ clear AZ
+ if (nzoffdiag > 0)
+ stats.psym = pmatched / nzoffdiag ;
+ else
+ stats.psym = 1 ;
+ end
+ catch
+ fprintf ('failed to compute symmetry of pattern of A+Z\n') ;
+ end
+ end
+
+else
+ stats.nzero = 0 ;
+end
+
+fprintf ('nsym: %g psym: %g time: %g\n', stats.nsym, stats.psym, toc) ;
+tic ;
+
+%-------------------------------------------------------------------------------
+% intialize ordering statistics
+%-------------------------------------------------------------------------------
+
+% if square, Cholesky of C(p,p) where C=A+A', p = amd(C)
+stats.amd_lnz = -1 ; % nnz (chol (C))
+stats.amd_flops = -1 ; % flop counts for chol (C)
+
+% if square or rectangular
+stats.amd_vnz = -1 ; % nnz (V), upper bound on L, for A(:,colamd(A))
+stats.amd_rnz = -1 ; % nnz (R), upper bound on U, for A(:,colamd(A))
+
+% if square, Cholesky of C(p,p) where C=A+A', p = metis(C)
+stats.metis_lnz = -1 ; % nnz (chol (C))
+stats.metis_flops = -1 ; % flop counts for chol (C)
+
+% if square or rectangular
+stats.metis_vnz = -1 ; % nnz (V), upper bound on L, for A(:,metis(A))
+stats.metis_rnz = -1 ; % nnz (R), upper bound on U, for A(:,metis(A))
+
+% dmperm analysis
+stats.nblocks = -1 ; % # of blocks in block-triangular form
+stats.sprank = -1 ; % structural rank
+stats.nzoff = -1 ; % # of entries of A in off-diagonal blocks
+
+% cs_scc2
+stats.ncc = -1 ; % # of strongly connected components
+
+% dmperm: best of amd/metis on each square block, best of colamd/metis
+% on rectangular blocks
+stats.dmperm_lnz = -1 ; % nnz (L), for square struct full rank matrices
+stats.dmperm_unz = -1 ; % nnz (U) + nzoff, for square struct full rank mat
+stats.dmperm_flops = -1 ; % Cholesky flop count of each square block
+stats.dmperm_vnz = -1 ; % nnz (V), upper bound on L
+stats.dmperm_rnz = -1 ; % nnz (R), upper bound on U
+
+stats.isND = -1 ; % 1 if 2D/3D problem, 0 otherwise
+
+d = max (m,n) ;
+
+% if the matrix has a symmetric nonzero pattern, nzoff will always be zero
+if (stats.psym == 1)
+ stats.nzoff = 0 ;
+end
+
+%-------------------------------------------------------------------------------
+% determine if positive definite
+%-------------------------------------------------------------------------------
+
+if (~stats.cholcand)
+
+ % not a candidate for Cholesky, so it cannot be positive definite
+ stats.posdef = 0 ;
+
+else
+
+ % try chol
+ try
+ [x, cstats] = cholmod2 (A, ones (stats.ncols,1)) ;
+ rcond = cstats (1) ;
+ fprintf ('rcond: %g\n', rcond) ;
+ stats.posdef = (rcond > 0) ;
+ catch
+ % chol failed
+ disp (lasterr) ;
+ fprintf ('sparse Cholesky failed\n') ;
+ stats.posdef = -1 ;
+ end
+ clear x cstats
+end
+
+fprintf ('posdef: %d time: %g\n', stats.posdef, toc) ;
+tic ;
+
+%-------------------------------------------------------------------------------
+% transpose A if m < n, for ordering methods
+%-------------------------------------------------------------------------------
+
+if (m < n)
+ try
+ A = A' ; % A is now tall and thin, or square
+ catch
+ disp (lasterr) ;
+ fprintf ('transpose failed...\n') ;
+ return ;
+ end
+ [m n] = size (A) ;
+end
+
+if (~isreal (A))
+ try
+ A = spones (A) ;
+ catch
+ disp (lasterr) ;
+ fprintf ('conversion from complex failed...\n') ;
+ return ;
+ end
+end
+
+fprintf ('computed A transpose if needed, time: %g\n', toc) ;
+tic ;
+
+%-------------------------------------------------------------------------------
+% order entire matrix with AMD and METIS, if square
+%-------------------------------------------------------------------------------
+
+if (m == n)
+
+ tic ;
+ try
+ if (stats.RBtype (2) == 'u')
+ C = A|A' ;
+ else
+ C = A ;
+ end
+ catch
+ disp (lasterr) ;
+ fprintf ('A+A'' failed\n') ;
+ end
+ fprintf ('computed A+A'', time: %g\n', toc) ;
+
+ % order the whole matrix with AMD
+ tic ;
+ try
+ p = amd (C) ;
+ c = symbfact (C (p,p)) ;
+ stats.amd_lnz = sum (c) ;
+ stats.amd_flops = sum (c.^2) ;
+ catch
+ disp (lasterr) ;
+ fprintf ('amd failed\n') ;
+ end
+ clear p c
+ fprintf ('AMD lnz %d flops %g time: %g\n', ...
+ stats.amd_lnz, stats.amd_flops, toc) ;
+
+ % order the whole matrix with METIS
+ tic ;
+ try
+ p = metis (C) ;
+ c = symbfact (C (p,p)) ;
+ stats.metis_lnz = sum (c) ;
+ stats.metis_flops = sum (c.^2) ;
+ catch
+ disp (lasterr) ;
+ fprintf ('metis failed\n') ;
+ end
+ clear p c C
+ fprintf ('METIS lnz %d flops %g time: %g\n', ...
+ stats.metis_lnz, stats.metis_flops, toc) ;
+
+else
+
+ % not computed if rectangular
+ stats.amd_lnz = -2 ;
+ stats.amd_flops = -2 ;
+ stats.metis_lnz = -2 ;
+ stats.metis_flops = -2 ;
+
+end
+
+%-------------------------------------------------------------------------------
+% order entire matrix with COLAMD, for LU bounds
+%-------------------------------------------------------------------------------
+
+tic ;
+try
+ % do not ignore any rows, and do not do etree postordering
+ q = colamd2mex (A, [d 10]) ;
+ [vnz,rnz] = cs_sqr (A (:,q)) ;
+ stats.amd_rnz = rnz ;
+ stats.amd_vnz = vnz ;
+catch
+ disp (lasterr) ;
+ fprintf ('colamd2 and cs_sqr failed\n') ;
+end
+clear q
+fprintf ('COLAMD rnz %d vnz %d time: %g\n', stats.amd_rnz, stats.amd_vnz, toc) ;
+tic ;
+
+%-------------------------------------------------------------------------------
+% order entire matrix with METIS, for LU bounds
+%-------------------------------------------------------------------------------
+
+if (~nometis)
+ try
+ q = metis (A, 'col') ;
+ [vnz,rnz] = cs_sqr (A (:,q)) ;
+ stats.metis_rnz = rnz ;
+ stats.metis_vnz = vnz ;
+ catch
+ disp (lasterr) ;
+ fprintf ('metis(A''*A) and cs_sqr failed\n') ;
+ end
+end
+clear q
+fprintf ('METIS rnz %d vnz %d time: %g\n', ...
+ stats.metis_rnz, stats.metis_vnz, toc) ;
+tic ;
+
+%-------------------------------------------------------------------------------
+% strongly connected components
+%-------------------------------------------------------------------------------
+
+try
+ % find the # of strongly connected components of the graph of a square A,
+ % or # of connected components of the bipartite graph of a rectangular A.
+ % [p,q,r,s] = cs_scc2 (A) ;
+ if (m == n)
+ [p r] = cs_scc (A) ;
+ else
+ [p r] = cs_scc (spaugment (A)) ;
+ end
+ stats.ncc = length (r) - 1 ;
+ clear p r
+catch
+ disp (lasterr) ;
+ fprintf ('cs_scc failed\n') ;
+end
+
+fprintf ('scc %d, time: %g\n', stats.ncc, toc) ;
+tic ;
+
+%-------------------------------------------------------------------------------
+% isND
+%-------------------------------------------------------------------------------
+
+s = 0 ;
+if (strfind (kind, 'structural'))
+ s = 1 ;
+elseif (strfind (kind, 'fluid'))
+ s = 1 ;
+elseif (strfind (kind, '2D'))
+ s = 1 ;
+elseif (strfind (kind, 'reduction'))
+ s = 1 ;
+elseif (strfind (kind, 'electromagnetics'))
+ s = 1 ;
+elseif (strfind (kind, 'semiconductor'))
+ s = 1 ;
+elseif (strfind (kind, 'thermal'))
+ s = 1 ;
+elseif (strfind (kind, 'materials'))
+ s = 1 ;
+elseif (strfind (kind, 'acoustics'))
+ s = 1 ;
+elseif (strfind (kind, 'vision'))
+ s = 1 ;
+elseif (strfind (kind, 'robotics'))
+ s = 1 ;
+end
+stats.isND = s ;
+
+fprintf ('isND %d\n', stats.isND) ;
+
+%-------------------------------------------------------------------------------
+% Dulmage-Mendelsohn permutation, and order each block
+%-------------------------------------------------------------------------------
+
+try
+ % find the Dulmage-Mendelsohn decomposition
+ [p,q,r,s,cc,rr] = cs_dmperm (A) ;
+ nblocks = length (r) - 1 ;
+ stats.nblocks = nblocks ;
+ stats.sprank = rr(4)-1 ;
+catch
+ disp (lasterr) ;
+ fprintf ('cs_dmperm failed\n') ;
+end
+
+fprintf ('sprank %d, time: %g\n', stats.sprank, toc) ;
+fprintf ('nblocks %d\n', stats.nblocks) ;
+tic
+
+ok_square = 1 ;
+ok_vnz = 1 ;
+
+try
+
+ mm = diff (r) ;
+ nn = diff (s) ;
+ square = all (mm == nn) ;
+
+ if (~square)
+
+ % not computed if the matrix is rectangular
+ stats.dmperm_lnz = -2 ;
+ stats.dmperm_unz = -2 ;
+ stats.dmperm_flops = -2 ;
+
+ end
+
+ if (stats.sprank < min (m,n))
+
+ % do not report DMPERM results for structurally singular matrices
+ stats.nzoff = -2 ;
+ stats.dmperm_lnz = -2 ;
+ stats.dmperm_unz = -2 ;
+ stats.dmperm_flops = -2 ;
+ stats.dmperm_vnz = -2 ;
+ stats.dmperm_rnz = -2 ;
+
+ elseif (nblocks == n && m == n)
+
+ % square triangular or diagonal
+ C = A (p,q) ;
+ clear p q r s
+
+ stats.nzoff = nnz (triu (C, 1)) ;
+ stats.dmperm_lnz = n ;
+ stats.dmperm_unz = n + stats.nzoff ;
+ stats.dmperm_flops = n ;
+ stats.dmperm_vnz = n ;
+ stats.dmperm_rnz = nnz (C) ;
+
+ elseif (nblocks == 1 && m == n)
+
+ % only one block of structural full rank, so don't redo analysis
+ clear p q r s
+
+ stats.nzoff = 0 ;
+ if (stats.metis_lnz < 0 || stats.amd_lnz < stats.metis_lnz)
+ stats.dmperm_lnz = stats.amd_lnz ;
+ stats.dmperm_unz = stats.amd_lnz ;
+ stats.dmperm_flops = stats.amd_flops ;
+ else
+ stats.dmperm_lnz = stats.metis_lnz ;
+ stats.dmperm_unz = stats.metis_lnz ;
+ stats.dmperm_flops = stats.metis_flops ;
+ end
+
+ if (stats.metis_vnz < 0 || stats.amd_rnz < stats.metis_rnz)
+ stats.dmperm_vnz = stats.amd_vnz ;
+ stats.dmperm_rnz = stats.amd_rnz ;
+ else
+ stats.dmperm_vnz = stats.metis_vnz ;
+ stats.dmperm_rnz = stats.metis_rnz ;
+ end
+
+ else
+
+ % analyze each block of the permuted matrix
+ C = A (p,q) ;
+ clear p q
+
+ nzoff = nnz (C) ;
+ lnz = 0 ;
+ unz = 0 ;
+ flops = 0 ;
+ vnz = 0 ;
+ rnz = 0 ;
+
+ for k = 1:nblocks
+ i1 = r (k) ;
+ i2 = r (k+1) - 1 ;
+ j1 = s (k) ;
+ j2 = s (k+1) - 1 ;
+
+ if (i2-i1 == 1 && j2-j1 == 1)
+ % singleton case
+ nzoff = nzoff - 1 ;
+ unz = unz + 1 ;
+ lnz = lnz + 1 ;
+ flops = flops + 1 ;
+ rnz = rnz + 1 ;
+ vnz = vnz + 1 ;
+ continue ;
+ end
+
+ % get the kth block
+ S = C (i1:i2, j1:j2) ;
+ [ms ns] = size (S) ;
+ nzoff = nzoff - nnz (S) ;
+
+ if (ok_square)
+ try
+ if (square)
+
+ % all blocks are square, analyze a square block
+ % best of amd and metis
+ if (nometis)
+ [pblock c] = analyze (S|S', 'sym', 1) ;
+ else
+ [pblock c] = analyze (S|S', 'sym', 3) ;
+ end
+ lnzblock = sum (c) ;
+ unz = unz + lnzblock ;
+ lnz = lnz + lnzblock ;
+ flops = flops + sum (c.^2) ;
+ clear c pblock
+
+ end
+ catch
+ % ordering failed, but keep going to compute nzoff
+ ok_square = 0 ;
+ end
+ end
+
+ if (ok_vnz)
+ try
+
+ % analyze a rectangular block, or LU bounds for square block
+ if (ms < ns)
+ S = S' ;
+ end
+ % best of amd and metis
+ try
+ if (nometis)
+ pblock = analyze (S, 'col', 1) ;
+ else
+ pblock = analyze (S, 'col', 3) ;
+ end
+ catch
+ pblock = colamd2mex (S, [d 10]) ;
+ end
+ [vnz2,rnz2] = cs_sqr (S (:, pblock)) ;
+ rnz = rnz + rnz2 ;
+ vnz = vnz + vnz2 ;
+
+ catch
+ % ordering failed, but keep going to compute nzoff
+ ok_vnz = 0 ;
+ end
+ end
+
+ clear S pblock
+
+ end
+
+ stats.nzoff = nzoff ;
+
+ if (ok_square)
+ if (~square)
+ stats.dmperm_unz = -2 ;
+ stats.dmperm_lnz = -2 ;
+ stats.dmperm_flops = -2 ;
+ else
+ stats.dmperm_lnz = lnz ;
+ stats.dmperm_unz = unz + nzoff ;
+ stats.dmperm_flops = flops ;
+ end
+ end
+
+ if (ok_vnz)
+ stats.dmperm_vnz = vnz ;
+ stats.dmperm_rnz = rnz + nzoff ;
+ end
+
+ clear C r s
+
+ end
+
+ if (~ok_square)
+ disp (lasterr) ;
+ fprintf ('cs_dmperm (square: lnz, unz, flops) ordering failed\n') ;
+ end
+ if (~ok_vnz)
+ disp (lasterr) ;
+ fprintf ('cs_dmperm (LU bounds: vnz, rnz) ordering failed\n') ;
+ end
+
+catch
+ disp (lasterr) ;
+ fprintf ('cs_dmperm ordering and nzoff failed\n') ;
+end
+
+fprintf ('dmperm stats done, time %g\n', toc) ;
+fprintf ('UFstats done\n') ;
diff --git a/UFcollection/UFwrite.m b/UFcollection/UFwrite.m
new file mode 100644
index 0000000..ead6d46
--- /dev/null
+++ b/UFcollection/UFwrite.m
@@ -0,0 +1,444 @@
+function UFwrite (Problem, Master, arg3, arg4)
+%UFWRITE write a Problem in Matrix Market or Rutherford/Boeing format
+% containing a set of text files in either Matrix Market or Rutherford/Boeing
+% format. The Problem can be read from the files back into MATLAB via UFread.
+% See http://www.cise.ufl.edu/research/sparse/matrices for the UF Sparse
+% Matrix Collection home page. The Problem directory is optionally compressed
+% via tar and gzip. Arguments 3 and 4, below, are optional and can appear in
+% any order.
+%
+% UFwrite (Problem) % Matrix Market format, no tar, use current dir.
+%
+% The following usages write the Problem into the Master/Group/Name directory,
+% where Problem.name = 'Group/Name' is given in the Problem.
+%
+% UFwrite (Problem, Master) % Matrix Market, no tar
+% UFwrite (Problem, Master, 'MM') % ditto
+% UFwrite (Problem, Master, 'RB') % Rutherford/Boeing, no tar
+% UFwrite (Problem, Master, 'tar') % Matrix Market, with tar
+% UFwrite (Problem, Master, 'MM', 'tar') % ditto
+% UFwrite (Problem, Master, 'RB', 'tar') % Rutherford/Boeing, with tar
+%
+% Problem is a struct, in the UF Sparse Matrix format (see below). Master is
+% the top-level directory in which directory containing the problem will be
+% placed. Master defaults to the current working directory if not present (an
+% empty string also means the current directory will be used).
+%
+% The following fields are always present in a UF Sparse Matrix Problem:
+%
+% name the group directory and problem name (i.e. 'HB/arc130')
+%
+% title short descriptive title
+%
+% A an m-by-n sparse matrix, real or complex
+%
+% id an integer in the range of 1 to the # of problems in the
+% collection. Identical to the line number of
+% http://www.cise.ufl.edu/research/sparse/mat/UF_Listing.txt
+% containing the Problem.name. New matrices are always added at
+% the end of this list.
+%
+% date a string containing the date the matrix was created, or added
+% to the collection if the creating date is unknown (but is likely
+% close to the creation date); empty string otherwise.
+%
+% author a string containing the name of the author; the computational
+% scientist who created the matrix from his or her application.
+% Empty string, or "author unknown" if unknown.
+%
+% ed a string containing the name of the editor/collector; the person
+% who acquired the matrix from the author, for inclusion in this
+% (or other) sparse matrix / graph collections.
+%
+% kind a string (i.e. 'directed graph') describing the type of problem;
+% a list of words from a well-defined set (see the UF Sparse
+% Matrix Collection home page for a description, or
+% http://www.cise.ufl.edu/research/sparse/matrices/kind.html).
+%
+% A Problem struct may also have the following optional fields.
+%
+% Zeros pattern of explicit zero entries in A as a binary m-by-n matrix.
+% These entries are provided by the matrix submittor with zero
+% numerical value. MATLAB drops explicit zero entries from any
+% sparse matrix. These entries can be important to the problem,
+% if (for example) the matrix is first in a series of matrices
+% arising in a nonlinear solver (those entries will become nonzero
+% later). These entries are thus kept in the binary matrix Zeros.
+%
+% b right-hand-side, any size, real or complex, full or sparse
+%
+% x supposed solution to A*x=b, any size, real or complex, full or
+% sparse
+%
+% notes a character array with notes about the problem.
+%
+% aux a struct, containing auxiliary information. The contents of
+% this struct are problem dependent, but its fields must not
+% end with '_[0-9]*' where [0-9]* means zero or more digits, nor
+% can there be an aux.b or aux.x matrix (there can be aux.b
+% and aux.x cells). The aux struct must not include any structs,
+% just matrices and cell arrays of matrices. The matrices in aux
+% can be full or sparse, and real, complex, or char.
+%
+% -------------------------------------------------
+% for Problems written in Rutherford/Boeing format:
+% -------------------------------------------------
+%
+% The Problem.name (including the full 'Group/Name'), date, author, and editor
+% define the Rutherford/Boeing title (first line of the file), followed by a
+% '|' in the 72nd column, and then up to 8 characters of the key. If the key
+% is an empty string, the Problem.id is used as the key. The A and Zeros
+% matrices are merged and written to this file. The full name, title, id,
+% kind, date, author, editor, and notes are written to a file of the same name
+% as the primary file, but with a .txt extension.
+%
+% Additional Rutherford/Boeing files are created for b, x, and each sparse
+% matrix in aux. Full arrays are written using a tiny subset of the Matrix
+% Market format. The first line of the file is the header, either of:
+%
+% %%MatrixMarket array real general
+% %%MatrixMarket array complex general
+%
+% The 2nd row contains the # of rows and columns, and subsequent lines contain
+% one matrix entry each (two values if complex) listed in column-major order.
+% No comments or blank lines are permitted. The header is ignored when the
+% matrix is read back in by UFread; the real/complex case is determined by how
+% many entries appear on each line. You can of course read these files with
+% mread, the Matrix Market reader. The header is added only to make it easier
+% for functions *other* than UFread to read and understand the data (the file
+% can be read in by mread, for example, but mread is not required). Thus, a
+% complete Rutherord/Boeing directory can be read/written via UFread/UFwrite,
+% without requiring the installation of mread/mwrite (in CHOLMOD), or
+% mmread/mmread (M-file functions from NIST that read/write a Matrix Market
+% file).
+%
+% ---------------------------------------------
+% for Problems written in Matrix Market format:
+% ---------------------------------------------
+%
+% The name, title, A, id, Zeros, kind, date, author, editor, and notes fields of
+% the Problem are written to the primary Matrix Market file, with a .mtx
+% extension. Additional Matrix Market files are created for b (as name_b),
+% x (as name_x), and each sparse or full matrix in aux.
+%
+% -----------------
+% for both formats:
+% -----------------
+%
+% A matrix Problem.aux.whatever is written out as name_whatever.xxx, without
+% the 'aux' part. If Problem.aux.whatever is a char array, it is written as
+% the file name_whatever.txt, with one line per row of the char array (trailing
+% spaces in each line are not printed). If aux.whatever is a cell array, each
+% entry aux.whatever{i} is written as the file name_whatever_<i>.xxx
+% (name_whatever_1.mtx, name_whatever_2.mtx, etc). All files are placed in the
+% single directory, given by the Problem.name (Group/Name, or 'HB/arc130' for
+% example). Each directory can only hold one MATLAB Problem struct of the UF
+% Sparse Matrix Collection.
+%
+% Example:
+%
+% Problem = UFget ('HB/arc130') % get the HB/arc130 MATLAB Problem
+% UFwrite (Problem) ; % write a MM version in current directory
+% UFwrite (Problem, 'MM') ; % write a MM version in MM/HB/arc130
+% UFwrite (Problem, '', 'RB') ; % write a RB version in current directory
+%
+% See also mwrite, mread, RBwrite, RBread, UFread, UFget, tar
+
+% Optionally uses the CHOLMOD mwrite mexFunction, for writing Problems in
+% Matrix Market format.
+
+% Copyright 2006-2007, Timothy A. Davis, University of Florida.
+
+%-------------------------------------------------------------------------------
+% check inputs
+%-------------------------------------------------------------------------------
+
+if (nargin < 2)
+ % place the result in the current directory
+ Master = '' ;
+end
+if (nargin < 3)
+ arg3 = '' ;
+end
+if (nargin < 4)
+ arg4 = '' ;
+end
+arg3 = lower (arg3) ;
+arg4 = lower (arg4) ;
+
+do_tar = (strcmp (arg3, 'tar') | strcmp (arg4, 'tar')) ;
+RB = (strcmp (arg3, 'rb') | strcmp (arg4, 'rb')) ;
+
+Master = regexprep (Master, '[\/\\]', filesep) ;
+if (~isempty (Master) && Master (end) ~= filesep)
+ Master = [Master filesep] ;
+end
+
+%-------------------------------------------------------------------------------
+% create the problem directory. Do not report any errors
+%-------------------------------------------------------------------------------
+
+t = find (Problem.name == '/') ;
+group = Problem.name (1:t-1) ;
+name = Problem.name (t+1:end) ;
+groupdir = [Master group] ;
+probdir = [groupdir filesep name] ;
+probname = [probdir filesep name] ;
+
+s = warning ('query', 'MATLAB:MKDIR:DirectoryExists') ; % get current state
+warning ('off', 'MATLAB:MKDIR:DirectoryExists') ;
+mkdir (groupdir) ;
+mkdir (probdir) ;
+warning (s) ; % restore state
+
+%-------------------------------------------------------------------------------
+% write the name, title, id, kind, date, author, ed, list of fields, and notes
+%-------------------------------------------------------------------------------
+
+cfile = [probname '.txt'] ;
+if (RB)
+ prefix = '%' ;
+else
+ prefix = '' ;
+end
+cf = fopen (cfile, 'w') ;
+print_header (cf, prefix, Problem.name) ;
+fprintf (cf, '%s [%s]\n', prefix, Problem.title) ;
+fprintf (cf, '%s id: %d\n', prefix, Problem.id) ;
+fprintf (cf, '%s date: %s\n', prefix, Problem.date) ;
+fprintf (cf, '%s author: %s\n', prefix, Problem.author) ;
+fprintf (cf, '%s ed: %s\n', prefix, Problem.ed) ;
+fprintf (cf, '%s fields:', prefix) ;
+s = fields (Problem) ;
+for k = 1:length(s)
+ fprintf (cf, ' %s', s {k}) ;
+end
+fprintf (cf, '\n') ;
+if (isfield (Problem, 'aux'))
+ aux = Problem.aux ;
+ fprintf (cf, '%s aux:', prefix) ;
+ auxfields = fields (aux) ;
+ for k = 1:length(auxfields)
+ fprintf (cf, ' %s', auxfields {k}) ;
+ end
+ fprintf (cf, '\n') ;
+else
+ auxfields = { } ;
+end
+fprintf (cf, '%s kind: %s\n', prefix, Problem.kind) ;
+print_separator (cf, prefix) ;
+if (isfield (Problem, 'notes'))
+ fprintf (cf, '%s notes:\n', prefix) ;
+ for k = 1:size (Problem.notes,1)
+ fprintf (cf, '%s %s\n', prefix, Problem.notes (k,:)) ;
+ end
+ print_separator (cf, prefix) ;
+end
+fclose(cf) ;
+
+%-------------------------------------------------------------------------------
+% write out the A and Z matrices to the RB or MM primary file
+%-------------------------------------------------------------------------------
+
+A = Problem.A ;
+[m n] = size (A) ;
+if (~issparse (A) || m == 0 || n == 0)
+ error ('A must be sparse and non-empty') ;
+end
+if (isfield (Problem, 'Zeros'))
+ Z = Problem.Zeros ;
+ if (any (size (A) ~= size (Z)) || ~isreal (Z) || ~issparse (Z))
+ error ('Zeros must have same size as A, and be sparse and real') ;
+ end
+else
+ Z = [ ] ;
+end
+
+% use the Problem.id number as the RB key
+key = sprintf ('%d', Problem.id) ;
+
+if (RB)
+ % write the files in Rutherford/Boeing form
+ ptitle = [Problem.name '; ' Problem.date '; ' etal(Problem.author)] ;
+ ptitle = [ptitle '; ed: ' etal(Problem.ed)] ;
+ % note that b, g, and x are NOT written to the RB file
+ RBwrite ([probname '.rb'], A, Z, ptitle, key) ;
+else
+ % write the files in Matrix Market form
+ mwrite ([probname '.mtx'], A, Z, cfile) ;
+ delete (cfile) ; % the comments file has been included in the .mtx file.
+end
+
+%-------------------------------------------------------------------------------
+% write out the b and x matrices as separate files
+%-------------------------------------------------------------------------------
+
+if (isfield (Problem, 'b'))
+ write_component (probname, Problem.name, 'b', Problem.b, cfile, ...
+ prefix, RB, [key 'b']) ;
+end
+if (isfield (Problem, 'x'))
+ write_component (probname, Problem.name, 'x', Problem.x, cfile, ...
+ prefix, RB, [key 'x']) ;
+end
+
+%-------------------------------------------------------------------------------
+% write out each component of aux, each in a separate file
+%-------------------------------------------------------------------------------
+
+for k = 1:length(auxfields)
+ what = auxfields {k} ;
+ X = aux.(what) ;
+
+ if (~iscell (X) && (strcmp (what, 'b') || strcmp (what, 'x')))
+ % aux.b or aux.x would get written out with the same filename as the
+ % Problem.b and Problem.x matrices, and read back in by UFread as
+ % Problem.b and Problem.x instead of aux.b and aux.x.
+ error (['invalid aux component: ' what]) ;
+ end
+
+ if (regexp (what, '_[0-9]*\>'))
+ % aux.whatever_42 would be written as the file name_whatever_42, which
+ % would be intrepretted as aux.whatever{42} when read back in by UFread.
+ error (['invalid aux component: ' what]) ;
+ end
+
+ if (iscell (X))
+ len = length (X) ;
+ for i = 1:len
+ % this problem includes a sequence of matrices in the new
+ % format (kind = 'sequence', and Problem.id > 1377).
+ write_component (probname, Problem.name, ...
+ sprintf (fmt (i, len), what, i) , X{i}, cfile, ...
+ prefix, RB, [key what(1) sprintf('%d', i)]) ;
+ end
+ else
+ % This is a non-cell component of aux. For an LP problem, this might
+ % be c, lo, or hi. For an Oberwolfach model reduction problem, this
+ % might be M, C, or E. For a graph in the Pajek collection, it could
+ % be a vector 'year', with the publication of each article in the graph.
+ % The possibilities are endless, and problem dependent. Adding new
+ % components to aux can be done without modifying UFread or UFwrite.
+ write_component (probname, Problem.name, what, X, cfile, ...
+ prefix, RB, [key what]) ;
+ end
+end
+
+%-------------------------------------------------------------------------------
+% tar up the result, if requested
+%-------------------------------------------------------------------------------
+
+if (do_tar)
+ try
+ tar ([probdir '.tar.gz'], probdir) ;
+ rmdir (probdir, 's') ;
+ catch
+ warning ('SuiteSparse:UFwrite', ...
+ 'unable to create tar file; directly left uncompressed') ;
+ end
+end
+
+
+
+%-------------------------------------------------------------------------------
+% fmt
+%-------------------------------------------------------------------------------
+
+function s = fmt (i, len)
+% fmt: determine the format to use for the name of component in a aux.cell array
+if (len < 10)
+ s = '%s_%d' ; % x1 through x9
+elseif (len < 100)
+ if (i < 10)
+ s = '%s_0%d' ; % x01 through x09
+ else
+ s = '%s_%d' ; % x10 through x99
+ end
+else
+ if (i < 10)
+ s = '%s_00%d' ; % x001 through x009
+ elseif (i < 100)
+ s = '%s_0%d' ; % x010 through x099
+ else
+ s = '%s_%d' ; % x100 through x999
+ end
+end
+
+
+%-------------------------------------------------------------------------------
+% write_component
+%-------------------------------------------------------------------------------
+
+function write_component (probname, name, what, X, cfile, prefix, RB, key)
+% write_component: write out a single component of the Problem to a file
+if (isempty (X))
+ % empty matrices (one or more zero dimensions) are not supported
+ error (['invalid component: ' what ' (cannot be empty)']) ;
+elseif (ischar (X))
+ % Write out a char array as a text file. Remove trailing spaces from the
+ % strings. Keep the leading spaces; they might be significant.
+ ff = fopen ([probname '_' what '.txt'], 'w') ;
+ for i = 1:size (X,1)
+ fprintf (ff, '%s\n', deblank (X (i,:))) ;
+ end
+ fclose (ff) ;
+elseif (RB)
+ % write out a full or sparse matrix in Rutherford/Boeing format
+ if (issparse (X))
+ % write out the component as a Rutherford/Boeing sparse matrix
+ RBwrite ([probname '_' what '.rb'], X, [ ], [name '_' what], key) ;
+ else
+ % Write out a full matrix in column oriented form,
+ % using a tiny subset of the Matrix Market format for full matrices.
+ UFfull_write ([probname '_' what '.mtx'], X) ;
+ end
+else
+ % write out the component in Matrix Market format (full or sparse)
+ cf = fopen (cfile, 'w') ;
+ print_header (cf, prefix, name, what) ;
+ print_separator (cf, prefix) ;
+ fclose(cf) ;
+ mwrite ([probname '_' what '.mtx'], X, cfile) ;
+ delete (cfile) ;
+end
+
+
+%-------------------------------------------------------------------------------
+% print_separator
+%-------------------------------------------------------------------------------
+
+function print_separator (cf, prefix)
+% print_separator: print a separator line in the comment file
+fprintf (cf, '%s---------------------------------------', prefix) ;
+fprintf (cf, '----------------------------------------\n') ;
+
+
+%-------------------------------------------------------------------------------
+% print_header
+%-------------------------------------------------------------------------------
+
+function print_header (cf, prefix, name, what)
+% print_header: print the header to the comment file
+print_separator (cf, prefix) ;
+fprintf (cf, '%s UF Sparse Matrix Collection, Tim Davis\n', prefix) ;
+fprintf (cf, '%s http://www.cise.ufl.edu/research/sparse/matrices/%s\n', ...
+ prefix, name) ;
+fprintf (cf, '%s name: %s', prefix, name) ;
+if (nargin > 3)
+ fprintf (cf, ' : %s matrix', what) ;
+end
+fprintf (cf, '\n') ;
+
+
+%-------------------------------------------------------------------------------
+% etal
+%-------------------------------------------------------------------------------
+
+function s = etal(name)
+% etal: change a long list of authors to first author 'et al.'
+t = find (name == ',') ;
+if (length (t) > 1)
+ s = [name(1:t(1)-1) ' et al.'] ;
+else
+ s = name ;
+end
diff --git a/UFcollection/dsxy2figxy.m b/UFcollection/dsxy2figxy.m
new file mode 100644
index 0000000..e8cfbaa
--- /dev/null
+++ b/UFcollection/dsxy2figxy.m
@@ -0,0 +1,57 @@
+function varargout = dsxy2figxy(varargin)
+%DSXY2FIGXY Transform point or position from axis to figure coords
+% Transforms [axx axy] or [xypos] from axes hAx (data) coords into coords
+% wrt GCF for placing annotation objects that use figure coords into data
+% space. The annotation objects this can be used for are
+% arrow, doublearrow, textarrow
+% ellipses (coordinates must be transformed to [x, y, width, height])
+% Note that line, text, and rectangle anno objects already are placed
+% on a plot using axes coordinates and must be located within an axes.
+% Example to compute a position and apply to an annotation:
+% Example:
+% [axx axy] = ginput(2);
+% [figx figy] = getaxannopos(gca, axx, axy);
+% har = annotation('textarrow',figx,figy);
+% set(har,'String',['(' num2str(axx(2)) ',' num2str(axy(2)) ')'])
+%
+% See also annotation, plot, ginput.
+
+% Copyright 2006-2007, The MathWorks, Inc. Used by permission (see
+% http://www.mathworks.com/access/helpdesk/help/techdoc/creating_plots/
+% bquk5ia-4.html).
+
+%% Obtain arguments (only limited argument checking is performed).
+% Determine if axes handle is specified
+if length(varargin{1})== 1 && ishandle(varargin{1}) && ...
+ strcmp(get(varargin{1},'type'),'axes')
+ hAx = varargin{1};
+ varargin = varargin(2:end);
+else
+ hAx = gca;
+end;
+% Parse either a position vector or two 2-D point tuples
+if length(varargin)==1 % Must be a 4-element POS vector
+ pos = varargin{1};
+else
+ [x,y] = deal(varargin{:}); % Two tuples (start & end points)
+end
+%% Get limits
+axun = get(hAx,'Units');
+set(hAx,'Units','normalized'); % Need normaized units to do the xform
+axpos = get(hAx,'Position');
+axlim = axis(hAx); % Get the axis limits [xlim ylim (zlim)]
+axwidth = diff(axlim(1:2));
+axheight = diff(axlim(3:4));
+%% Transform data from figure space to data space
+if exist('x','var') % Transform a and return pair of points
+ varargout{1} = (x-axlim(1))*axpos(3)/axwidth + axpos(1);
+ varargout{2} = (y-axlim(3))*axpos(4)/axheight + axpos(2);
+else % Transform and return a position rectangle
+ pos(1) = (pos(1)-axlim(1))/axwidth*axpos(3) + axpos(1);
+ pos(2) = (pos(2)-axlim(3))/axheight*axpos(4) + axpos(2);
+ pos(3) = pos(3)*axpos(3)/axwidth;
+ pos(4) = pos(4)*axpos(4)/axheight;
+ varargout{1} = pos;
+end
+%% Restore axes units
+set(hAx,'Units',axun)
diff --git a/UFconfig/README.txt b/UFconfig/README.txt
new file mode 100644
index 0000000..eb26fe1
--- /dev/null
+++ b/UFconfig/README.txt
@@ -0,0 +1,34 @@
+UFconfig contains configuration settings for all many of the software packages
+that I develop or co-author. Note that older versions of some of these packages
+do not require UFconfig.
+
+ Package Description
+ ------- -----------
+ AMD approximate minimum degree ordering
+ CAMD constrained AMD
+ COLAMD column approximate minimum degree ordering
+ CCOLAMD constrained approximate minimum degree ordering
+ UMFPACK sparse LU factorization, with the BLAS
+ CXSparse int/long/real/complex version of CSparse
+ CHOLMOD sparse Cholesky factorization, update/downdate
+ KLU sparse LU factorization, BLAS-free
+ BTF permutation to block triangular form
+ LDL concise sparse LDL'
+ LPDASA LP Dual Active Set Algorithm
+
+UFconfig is not required by:
+
+ CSparse a Concise Sparse matrix package
+ RBio read/write files in Rutherford/Boeing format
+ UFcollection tools for managing the UF Sparse Matrix Collection
+ LINFACTOR simple m-file to show how to use LU and CHOL to solve Ax=b
+ MESHND 2D and 3D mesh generation and nested dissection ordering
+ MATLAB_Tools misc collection of m-files
+ SSMULT sparse matrix times sparse matrix, for use in MATLAB
+
+In addition, the xerbla/ directory contains Fortan and C versions of the
+BLAS/LAPACK xerbla routine, which is called when an invalid input is passed to
+the BLAS or LAPACK. The xerbla provided here does not print any message, so
+the entire Fortran I/O library does not need to be linked into a C application.
+Most versions of the BLAS contain xerbla, but those from K. Goto do not. Use
+this if you need too.
diff --git a/UFconfig/UFconfig.h b/UFconfig/UFconfig.h
new file mode 100644
index 0000000..36c1bd3
--- /dev/null
+++ b/UFconfig/UFconfig.h
@@ -0,0 +1,117 @@
+/* ========================================================================== */
+/* === UFconfig.h =========================================================== */
+/* ========================================================================== */
+
+/* Configuration file for SuiteSparse: a Suite of Sparse matrix packages
+ * (AMD, COLAMD, CCOLAMD, CAMD, CHOLMOD, UMFPACK, CXSparse, and others).
+ *
+ * UFconfig.h provides the definition of the long integer. On most systems,
+ * a C program can be compiled in LP64 mode, in which long's and pointers are
+ * both 64-bits, and int's are 32-bits. Windows 64, however, uses the LLP64
+ * model, in which int's and long's are 32-bits, and long long's and pointers
+ * are 64-bits.
+ *
+ * SuiteSparse packages that include long integer versions are
+ * intended for the LP64 mode. However, as a workaround for Windows 64
+ * (and perhaps other systems), the long integer can be redefined.
+ *
+ * If _WIN64 is defined, then the __int64 type is used instead of long.
+ *
+ * The long integer can also be defined at compile time. For example, this
+ * could be added to UFconfig.mk:
+ *
+ * CFLAGS = -O -D'UF_long=long long' -D'UF_long_max=9223372036854775801' \
+ * -D'UF_long_id="%lld"'
+ *
+ * This file defines UF_long as either long (on all but _WIN64) or
+ * __int64 on Windows 64. The intent is that a UF_long is always a 64-bit
+ * integer in a 64-bit code. ptrdiff_t might be a better choice than long;
+ * it is always the same size as a pointer.
+ *
+ * This file also defines the SUITESPARSE_VERSION and related definitions.
+ *
+ * Copyright (c) 2007, University of Florida. No licensing restrictions
+ * apply to this file or to the UFconfig directory. Author: Timothy A. Davis.
+ */
+
+#ifndef _UFCONFIG_H
+#define _UFCONFIG_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <limits.h>
+
+/* ========================================================================== */
+/* === UF_long ============================================================== */
+/* ========================================================================== */
+
+#ifndef UF_long
+
+#ifdef _WIN64
+
+#define UF_long __int64
+#define UF_long_max _I64_MAX
+#define UF_long_id "%I64d"
+
+#else
+
+#define UF_long long
+#define UF_long_max LONG_MAX
+#define UF_long_id "%ld"
+
+#endif
+#endif
+
+/* ========================================================================== */
+/* === SuiteSparse version ================================================== */
+/* ========================================================================== */
+
+/* SuiteSparse is not a package itself, but a collection of packages, some of
+ * which must be used together (UMFPACK requires AMD, CHOLMOD requires AMD,
+ * COLAMD, CAMD, and CCOLAMD, etc). A version number is provided here for the
+ * collection itself. The versions of packages within each version of
+ * SuiteSparse are meant to work together. Combining one packge from one
+ * version of SuiteSparse, with another package from another version of
+ * SuiteSparse, may or may not work.
+ *
+ * SuiteSparse Version 3.1.0 contains the following packages:
+ *
+ * AMD version 2.2.0
+ * CAMD version 2.2.0
+ * COLAMD version 2.7.1
+ * CCOLAMD version 2.7.1
+ * CHOLMOD version 1.6.0
+ * CSparse version 2.2.1
+ * CXSparse version 2.2.1
+ * KLU version 1.0.1
+ * BTF version 1.0.1
+ * LDL version 2.0.1
+ * UFconfig version number is the same as SuiteSparse
+ * UMFPACK version 5.2.0
+ * RBio version 1.1.1
+ * UFcollection version 1.1.1
+ * LINFACTOR version 1.1.0
+ * MESHND version 1.1.0
+ * SSMULT version 1.1.0
+ * MATLAB_Tools no specific version number
+ *
+ * Other package dependencies:
+ * BLAS required by CHOLMOD and UMFPACK
+ * LAPACK required by CHOLMOD
+ * METIS 4.0.1 required by CHOLMOD (optional) and KLU (optional)
+ */
+
+#define SUITESPARSE_DATE "Nov 1, 2007"
+#define SUITESPARSE_VER_CODE(main,sub) ((main) * 1000 + (sub))
+#define SUITESPARSE_MAIN_VERSION 3
+#define SUITESPARSE_SUB_VERSION 1
+#define SUITESPARSE_SUBSUB_VERSION 0
+#define SUITESPARSE_VERSION \
+ SUITESPARSE_VER_CODE(SUITESPARSE_MAIN_VERSION,SUITESPARSE_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+#endif
diff --git a/UFconfig/UFconfig.mk b/UFconfig/UFconfig.mk
new file mode 100644
index 0000000..5f4f8e2
--- /dev/null
+++ b/UFconfig/UFconfig.mk
@@ -0,0 +1,310 @@
+#===============================================================================
+# UFconfig.mk: common configuration file for the SuiteSparse
+#===============================================================================
+
+# This file contains all configuration settings for all packages authored or
+# co-authored by Tim Davis at the University of Florida:
+#
+# Package Version Description
+# ------- ------- -----------
+# AMD 1.2 or later approximate minimum degree ordering
+# COLAMD 2.4 or later column approximate minimum degree ordering
+# CCOLAMD 1.0 or later constrained column approximate minimum degree ordering
+# CAMD any constrained approximate minimum degree ordering
+# UMFPACK 4.5 or later sparse LU factorization, with the BLAS
+# CHOLMOD any sparse Cholesky factorization, update/downdate
+# KLU 0.8 or later sparse LU factorization, BLAS-free
+# BTF 0.8 or later permutation to block triangular form
+# LDL 1.2 or later concise sparse LDL'
+# LPDASA any linear program solve (dual active set algorithm)
+# CXSparse any extended version of CSparse (int/long, real/complex)
+#
+# The UFconfig directory and the above packages should all appear in a single
+# directory, in order for the Makefile's within each package to find this file.
+#
+# To enable an option of the form "# OPTION = ...", edit this file and
+# delete the "#" in the first column of the option you wish to use.
+
+#------------------------------------------------------------------------------
+# Generic configuration
+#------------------------------------------------------------------------------
+
+# C compiler and compiler flags: These will normally not give you optimal
+# performance. You should select the optimization parameters that are best
+# for your system. On Linux, use "CFLAGS = -O3 -fexceptions" for example.
+CC = cc
+CFLAGS = -O
+
+# ranlib, and ar, for generating libraries
+RANLIB = ranlib
+AR = ar cr
+
+# delete and rename a file
+RM = rm -f
+MV = mv -f
+
+# Fortran compiler (not normally required)
+F77 = f77
+F77FLAGS = -O
+F77LIB =
+
+# C and Fortran libraries
+LIB = -lm
+
+# For compiling MATLAB mexFunctions (MATLAB 7.5)
+MEX = mex -O -largeArrayDims -lmwlapack -lmwblas
+
+# For compiling MATLAB mexFunctions (MATLAB 7.3 and 7.4)
+# MEX = mex -O -largeArrayDims -lmwlapack
+
+# For MATLAB 7.2 or earlier, you must use one of these options:
+# MEX = mex -O -lmwlapack
+# MEX = mex -O
+
+# Which version of MAKE you are using (default is "make")
+# MAKE = make
+# MAKE = gmake
+
+#------------------------------------------------------------------------------
+# BLAS and LAPACK configuration:
+#------------------------------------------------------------------------------
+
+# UMFPACK and CHOLMOD both require the BLAS. CHOLMOD also requires LAPACK.
+# See Kazushige Goto's BLAS at http://www.cs.utexas.edu/users/flame/goto/ or
+# http://www.tacc.utexas.edu/~kgoto/ for the best BLAS to use with CHOLMOD.
+# LAPACK is at http://www.netlib.org/lapack/ . You can use the standard
+# Fortran LAPACK along with Goto's BLAS to obtain very good performance.
+# CHOLMOD gets a peak numeric factorization rate of 3.6 Gflops on a 3.2 GHz
+# Pentium 4 (512K cache, 4GB main memory) with the Goto BLAS, and 6 Gflops
+# on a 2.5Ghz dual-core AMD Opteron.
+
+# These settings will probably not work, since there is no fixed convention for
+# naming the BLAS and LAPACK library (*.a or *.so) files.
+
+# Using the Goto BLAS:
+# BLAS = -lgoto -lgfortran -lgfortranbegin
+
+# This is probably slow ... it might connect to the Standard Reference BLAS:
+BLAS = -lblas -lgfortran -lgfortranbegin
+LAPACK = -llapack
+
+# The BLAS might not contain xerbla, an error-handling routine for LAPACK and
+# the BLAS. Also, the standard xerbla requires the Fortran I/O library, and
+# stops the application program if an error occurs. A C version of xerbla
+# distributed with this software (UFconfig/xerbla/libcerbla.a) includes a
+# Fortran-callable xerbla routine that prints nothing and does not stop the
+# application program. This is optional.
+# XERBLA = ../../UFconfig/xerbla/libcerbla.a
+
+# If you wish to use the XERBLA in LAPACK and/or the BLAS instead,
+# use this option:
+XERBLA =
+
+# If you wish to use the Fortran UFconfig/xerbla/xerbla.f instead, use this:
+# XERBLA = ../../UFconfig/xerbla/libxerbla.a
+
+#------------------------------------------------------------------------------
+# METIS, optionally used by CHOLMOD
+#------------------------------------------------------------------------------
+
+# If you do not have METIS, or do not wish to use it in CHOLMOD, you must
+# compile CHOLMOD with the -DNPARTITION flag. You must also use the
+# "METIS =" option, below.
+
+# The path is relative to where it is used, in CHOLMOD/Lib, CHOLMOD/MATLAB, etc.
+# You may wish to use an absolute path. METIS is optional. Compile
+# CHOLMOD with -DNPARTITION if you do not wish to use METIS.
+METIS_PATH = ../../metis-4.0
+METIS = ../../metis-4.0/libmetis.a
+
+# If you use CHOLMOD_CONFIG = -DNPARTITION then you must use the following
+# options:
+# METIS_PATH =
+# METIS =
+
+#------------------------------------------------------------------------------
+# UMFPACK configuration:
+#------------------------------------------------------------------------------
+
+# Configuration flags for UMFPACK. See UMFPACK/Source/umf_config.h for details.
+#
+# -DNBLAS do not use the BLAS. UMFPACK will be very slow.
+# -D'LONGBLAS=long' or -DLONGBLAS='long long' defines the integers used by
+# LAPACK and the BLAS (defaults to 'int')
+# -DNSUNPERF do not use the Sun Perf. Library (default is use it on Solaris)
+# -DNPOSIX do not use POSIX routines sysconf and times.
+# -DGETRUSAGE use getrusage
+# -DNO_TIMER do not use any timing routines
+# -DNRECIPROCAL do not multiply by the reciprocal
+# -DNO_DIVIDE_BY_ZERO do not divide by zero
+
+UMFPACK_CONFIG =
+
+#------------------------------------------------------------------------------
+# CHOLMOD configuration
+#------------------------------------------------------------------------------
+
+# CHOLMOD Library Modules, which appear in libcholmod.a:
+# Core requires: none
+# Check requires: Core
+# Cholesky requires: Core, AMD, COLAMD. optional: Partition, Supernodal
+# MatrixOps requires: Core
+# Modify requires: Core
+# Partition requires: Core, CCOLAMD, METIS. optional: Cholesky
+# Supernodal requires: Core, BLAS, LAPACK
+#
+# CHOLMOD test/demo Modules (all are GNU GPL, do not appear in libcholmod.a):
+# Tcov requires: Core, Check, Cholesky, MatrixOps, Modify, Supernodal
+# optional: Partition
+# Valgrind same as Tcov
+# Demo requires: Core, Check, Cholesky, MatrixOps, Supernodal
+# optional: Partition
+#
+# Configuration flags:
+# -DNCHECK do not include the Check module. License GNU LGPL
+# -DNCHOLESKY do not include the Cholesky module. License GNU LGPL
+# -DNPARTITION do not include the Partition module. License GNU LGPL
+# also do not include METIS.
+# -DNGPL do not include any GNU GPL Modules in the CHOLMOD library:
+# -DNMATRIXOPS do not include the MatrixOps module. License GNU GPL
+# -DNMODIFY do not include the Modify module. License GNU GPL
+# -DNSUPERNODAL do not include the Supernodal module. License GNU GPL
+#
+# -DNPRINT do not print anything.
+# -D'LONGBLAS=long' or -DLONGBLAS='long long' defines the integers used by
+# LAPACK and the BLAS (defaults to 'int')
+# -DNSUNPERF for Solaris only. If defined, do not use the Sun
+# Performance Library
+
+CHOLMOD_CONFIG =
+
+#------------------------------------------------------------------------------
+# Linux
+#------------------------------------------------------------------------------
+
+# Using default compilers:
+# CC = gcc
+CFLAGS = -O3
+
+# alternatives:
+# CFLAGS = -g -fexceptions \
+ -Wall -W -Wshadow -Wmissing-prototypes -Wstrict-prototypes \
+ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi
+# CFLAGS = -O3 -fexceptions \
+ -Wall -W -Werror -Wshadow -Wmissing-prototypes -Wstrict-prototypes \
+ -Wredundant-decls -Wnested-externs -Wdisabled-optimization -ansi
+# CFLAGS = -O3 -fexceptions -D_FILE_OFFSET_BITS=64 -D_LARGEFILE64_SOURCE
+# CFLAGS = -O3
+
+# consider:
+# -fforce-addr -fmove-all-movables -freduce-all-givs -ftsp-ordering
+# -frename-registers -ffast-math -funroll-loops
+
+# Using the Goto BLAS:
+# BLAS = -lgoto -lfrtbegin -lg2c $(XERBLA) -lpthread
+
+# Using Intel's icc and ifort compilers:
+# (does not work for mexFunctions unless you add a mexopts.sh file)
+# F77 = ifort
+# CC = icc
+# CFLAGS = -O3 -xN -vec_report=0
+# CFLAGS = -g
+# old (broken): CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0
+
+# 64bit:
+# F77FLAGS = -O -m64
+# CFLAGS = -O3 -fexceptions -m64
+# BLAS = -lgoto64 -lfrtbegin -lg2c -lpthread $(XERBLA)
+# LAPACK = -llapack64
+
+
+# SUSE Linux 10.1, AMD Opteron, with GOTO Blas
+# F77 = gfortran
+# BLAS = -lgoto_opteron64 -lgfortran
+
+# SUSE Linux 10.1, Intel Pentium, with GOTO Blas
+# F77 = gfortran
+# BLAS = -lgoto -lgfortran
+
+#------------------------------------------------------------------------------
+# Solaris
+#------------------------------------------------------------------------------
+
+# 32-bit
+# CFLAGS = -KPIC -dalign -xc99=%none -Xc -xlibmieee -xO5 -xlibmil
+
+# 64-bit
+# CFLAGS = -KPIC -dalign -xc99=%none -Xc -xlibmieee -xO5 -xlibmil -xarch=v9
+
+# BLAS = -xlic_lib=sunperf
+# LAPACK =
+
+#------------------------------------------------------------------------------
+# Compaq Alpha
+#------------------------------------------------------------------------------
+
+# 64-bit mode only
+# CFLAGS = -O2 -std1
+# BLAS = -ldxml
+# LAPACK =
+
+#------------------------------------------------------------------------------
+# Macintosh
+#------------------------------------------------------------------------------
+
+# CC = gcc
+# CFLAGS = -O3 -fno-common -no-cpp-precomp -fexceptions
+# LIB = -lstdc++
+# BLAS = -framework Accelerate
+# LAPACK = -framework Accelerate
+
+#------------------------------------------------------------------------------
+# IBM RS 6000
+#------------------------------------------------------------------------------
+
+# BLAS = -lessl
+# LAPACK =
+
+# 32-bit mode:
+# CFLAGS = -O4 -qipa -qmaxmem=16384 -qproto
+# F77FLAGS = -O4 -qipa -qmaxmem=16384
+
+# 64-bit mode:
+# CFLAGS = -O4 -qipa -qmaxmem=16384 -q64 -qproto
+# F77FLAGS = -O4 -qipa -qmaxmem=16384 -q64
+# AR = ar -X64
+
+#------------------------------------------------------------------------------
+# SGI IRIX
+#------------------------------------------------------------------------------
+
+# BLAS = -lscsl
+# LAPACK =
+
+# 32-bit mode
+# CFLAGS = -O
+
+# 64-bit mode (32 bit int's and 64-bit long's):
+# CFLAGS = -64
+# F77FLAGS = -64
+
+# SGI doesn't have ranlib
+# RANLIB = echo
+
+#------------------------------------------------------------------------------
+# AMD Opteron (64 bit)
+#------------------------------------------------------------------------------
+
+# BLAS = -lgoto_opteron64 -lg2c
+# LAPACK = -llapack_opteron64
+
+# SUSE Linux 10.1, AMD Opteron
+# F77 = gfortran
+# BLAS = -lgoto_opteron64 -lgfortran
+# LAPACK = -llapack_opteron64
+
+#------------------------------------------------------------------------------
+# remove object files and profile output
+#------------------------------------------------------------------------------
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.tcov *.gcov gmon.out *.bak *.d
diff --git a/UFconfig/xerbla/Makefile b/UFconfig/xerbla/Makefile
new file mode 100644
index 0000000..7eb2d58
--- /dev/null
+++ b/UFconfig/xerbla/Makefile
@@ -0,0 +1,31 @@
+# Makefile for null-output xerbla
+
+default: ccode
+
+include ../UFconfig.mk
+
+ccode: libcerbla.a
+
+fortran: libxerbla.a
+
+all: libxerbla.a libcerbla.a
+
+# Fortran version:
+libxerbla.a: xerbla.f
+ $(F77) $(F77FLAGS) -c xerbla.f
+ $(AR) libxerbla.a xerbla.o
+ - $(RM) xerbla.o
+
+# C version:
+libcerbla.a: xerbla.c xerbla.h
+ $(CC) $(CFLAGS) -c xerbla.c
+ $(AR) libcerbla.a xerbla.o
+ - $(RM) xerbla.o
+
+distclean: purge
+
+purge: clean
+ - $(RM) *.o *.a
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/UFconfig/xerbla/xerbla.c b/UFconfig/xerbla/xerbla.c
new file mode 100644
index 0000000..5107f03
--- /dev/null
+++ b/UFconfig/xerbla/xerbla.c
@@ -0,0 +1,12 @@
+
+void xerbla_ (char *srname, int *info)
+{
+ /* do nothing */ ;
+}
+
+
+void xerbla (char *srname, int *info)
+{
+ /* do nothing */ ;
+}
+
diff --git a/UFconfig/xerbla/xerbla.f b/UFconfig/xerbla/xerbla.f
new file mode 100644
index 0000000..4272004
--- /dev/null
+++ b/UFconfig/xerbla/xerbla.f
@@ -0,0 +1,46 @@
+ SUBROUTINE XERBLA( SRNAME, INFO )
+*
+* -- LAPACK auxiliary routine (version 3.0) --
+* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
+* Courant Institute, Argonne National Lab, and Rice University
+* September 30, 1994
+*
+* .. Scalar Arguments ..
+ CHARACTER*6 SRNAME
+ INTEGER INFO
+* ..
+*
+* Purpose
+* =======
+*
+* XERBLA is an error handler for the LAPACK routines.
+* It is called by an LAPACK routine if an input parameter has an
+* invalid value. A message is printed and execution stops.
+*
+* Installers may consider modifying the STOP statement in order to
+* call system-specific exception-handling facilities.
+*
+* Arguments
+* =========
+*
+* SRNAME (input) CHARACTER*6
+* The name of the routine which called XERBLA.
+*
+* INFO (input) INTEGER
+* The position of the invalid parameter in the parameter list
+* of the calling routine.
+*
+* =====================================================================
+*
+* .. Executable Statements ..
+*
+***** WRITE( *, FMT = 9999 )SRNAME, INFO
+*
+***** STOP
+*
+***** 9999 FORMAT( ' ** On entry to ', A6, ' parameter number ', I2, ' had ',
+***** $ 'an illegal value' )
+*
+* End of XERBLA
+*
+ END
diff --git a/UFconfig/xerbla/xerbla.h b/UFconfig/xerbla/xerbla.h
new file mode 100644
index 0000000..b332eb3
--- /dev/null
+++ b/UFconfig/xerbla/xerbla.h
@@ -0,0 +1,2 @@
+void xerbla_ (char *srname, int *info) ;
+void xerbla (char *srname, int *info) ;
diff --git a/UMFPACK/Demo/HB/arc130.rua b/UMFPACK/Demo/HB/arc130.rua
new file mode 100644
index 0000000..3b4aa4a
--- /dev/null
+++ b/UMFPACK/Demo/HB/arc130.rua
@@ -0,0 +1,506 @@
+1UNSYMMETRIC MATRIX FROM LASER PROBLEM. A.R.CURTIS, OCT 1974 ARC130
+ 502 9 65 428 0
+RUA 130 130 1282 0
+(16I5) (20I4) (1P3D24.15)
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+ 25 130
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diff --git a/UMFPACK/Demo/HB/can_24.psa b/UMFPACK/Demo/HB/can_24.psa
new file mode 100644
index 0000000..bd5377c
--- /dev/null
+++ b/UMFPACK/Demo/HB/can_24.psa
@@ -0,0 +1,12 @@
+1SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981. CAN 24
+ 8 2 6 0 0
+PSA 24 24 92 0
+(16I5) (16I5)
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diff --git a/UMFPACK/Demo/HB/fs_183_6.rua b/UMFPACK/Demo/HB/fs_183_6.rua
new file mode 100644
index 0000000..95cffc4
--- /dev/null
+++ b/UMFPACK/Demo/HB/fs_183_6.rua
@@ -0,0 +1,361 @@
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diff --git a/UMFPACK/Demo/HB/qc324.cua b/UMFPACK/Demo/HB/qc324.cua
new file mode 100644
index 0000000..12fcb73
--- /dev/null
+++ b/UMFPACK/Demo/HB/qc324.cua
@@ -0,0 +1,19516 @@
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diff --git a/UMFPACK/Demo/HB/west0067.rua b/UMFPACK/Demo/HB/west0067.rua
new file mode 100644
index 0000000..865876e
--- /dev/null
+++ b/UMFPACK/Demo/HB/west0067.rua
@@ -0,0 +1,115 @@
+1U CAVETT PROBLEM WITH 5 COMPONENTS ( CHEM. ENG. FROM WESTERBERG ) WEST0067
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diff --git a/UMFPACK/Demo/Makefile b/UMFPACK/Demo/Makefile
new file mode 100644
index 0000000..9107259
--- /dev/null
+++ b/UMFPACK/Demo/Makefile
@@ -0,0 +1,176 @@
+#-------------------------------------------------------------------------------
+# compile the UMFPACK demos (for GNU make and original make)
+#-------------------------------------------------------------------------------
+
+# UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis.
+# All Rights Reserved. See ../Doc/License for License.
+
+default: libs run
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(UMFPACK_CONFIG) -I../Include -I../../AMD/Include \
+ -I../../UFconfig
+
+INC = ../Include/umfpack.h ../../AMD/Include/amd.h ../../UFconfig/UFconfig.h
+
+LIBS = $(BLAS) $(XERBLA) $(LIB)
+
+../Lib/libumfpack.a:
+ ( cd ../Lib ; $(MAKE) )
+
+../../AMD/Lib/libamd.a:
+ ( cd ../../AMD ; $(MAKE) library )
+
+UMFPACK = ../Lib/libumfpack.a ../../AMD/Lib/libamd.a
+
+libs:
+ ( cd ../Lib ; $(MAKE) )
+ ( cd ../../AMD ; $(MAKE) library )
+
+#-------------------------------------------------------------------------------
+# Create the demo programs, run them, and compare the output
+#-------------------------------------------------------------------------------
+
+dist: umfpack_di_demo.c umfpack_dl_demo.c umfpack_zi_demo.c umfpack_zl_demo.c
+
+umfpack_simple: umfpack_simple.c $(INC) $(UMFPACK)
+ $(C) -o umfpack_simple umfpack_simple.c $(UMFPACK) $(LIBS)
+
+# the GNU rules are simpler:
+# umfpack_%_demo.c: umfpack_xx_demo.c umfpack_%_demo.sed
+# - sed -f umfpack_$*_demo.sed < umfpack_xx_demo.c > umfpack_$*_demo.c
+#
+# umfpack_%_demo: umfpack_%_demo.c $(INC) $(UMFPACK)
+# $(C) -o umfpack_$*_demo umfpack_$*_demo.c $(UMFPACK) $(LIBS)
+# ./umfpack_$*_demo > my_umfpack_$*_demo.out
+
+# but do this via brute-force, so we can use just a single Makefile:
+
+# double-precision, int verion:
+umfpack_di_demo.c: umfpack_xx_demo.c umfpack_di_demo.sed
+ - sed -f umfpack_di_demo.sed < umfpack_xx_demo.c > umfpack_di_demo.c
+
+umfpack_di_demo: umfpack_di_demo.c $(INC) $(UMFPACK)
+ $(C) -o umfpack_di_demo umfpack_di_demo.c $(UMFPACK) $(LIBS)
+
+# double-precision, UF_long verion:
+umfpack_dl_demo.c: umfpack_xx_demo.c umfpack_dl_demo.sed
+ - sed -f umfpack_dl_demo.sed < umfpack_xx_demo.c > umfpack_dl_demo.c
+
+umfpack_dl_demo: umfpack_dl_demo.c $(INC) $(UMFPACK)
+ $(C) -o umfpack_dl_demo umfpack_dl_demo.c $(UMFPACK) $(LIBS)
+
+# complex, int verion:
+umfpack_zi_demo.c: umfpack_xx_demo.c umfpack_zi_demo.sed
+ - sed -f umfpack_zi_demo.sed < umfpack_xx_demo.c > umfpack_zi_demo.c
+
+umfpack_zi_demo: umfpack_zi_demo.c $(INC) $(UMFPACK)
+ $(C) -o umfpack_zi_demo umfpack_zi_demo.c $(UMFPACK) $(LIBS)
+
+# complex, UF_long verion:
+umfpack_zl_demo.c: umfpack_xx_demo.c umfpack_zl_demo.sed
+ - sed -f umfpack_zl_demo.sed < umfpack_xx_demo.c > umfpack_zl_demo.c
+
+umfpack_zl_demo: umfpack_zl_demo.c $(INC) $(UMFPACK)
+ $(C) -o umfpack_zl_demo umfpack_zl_demo.c $(UMFPACK) $(LIBS)
+
+run: umfpack_di_demo umfpack_zi_demo umfpack_dl_demo umfpack_zl_demo umfpack_simple
+ ./umfpack_simple
+ ./umfpack_di_demo > my_umfpack_di_demo.out
+ - diff umfpack_di_demo.out my_umfpack_di_demo.out
+ ./umfpack_dl_demo > my_umfpack_dl_demo.out
+ - diff umfpack_dl_demo.out my_umfpack_dl_demo.out
+ ./umfpack_zi_demo > my_umfpack_zi_demo.out
+ - diff umfpack_zi_demo.out my_umfpack_zi_demo.out
+ ./umfpack_zl_demo > my_umfpack_zl_demo.out
+ - diff umfpack_zl_demo.out my_umfpack_zl_demo.out
+
+#-------------------------------------------------------------------------------
+# create a demo program that reads in Harwell/Boeing matrices, and run it
+#-------------------------------------------------------------------------------
+
+# the output of "make hb" is in the file umf4.out
+hb: $(UMFPACK) umf4 readhb readhb_nozeros readhb_size
+ - ./readhb_nozeros < HB/can_24.psa > tmp/A
+ - ./readhb_size < HB/can_24.psa > tmp/Asize
+ - ./umf4
+ - ./readhb_nozeros < HB/west0067.rua > tmp/A
+ - ./readhb_size < HB/west0067.rua > tmp/Asize
+ - ./umf4
+ - ./readhb_nozeros < HB/fs_183_6.rua > tmp/A
+ - ./readhb_size < HB/fs_183_6.rua > tmp/Asize
+ - ./umf4
+ - ./readhb < HB/fs_183_6.rua > tmp/A
+ - ./readhb_size < HB/fs_183_6.rua > tmp/Asize
+ - ./umf4
+ - ./readhb < HB/arc130.rua > tmp/A
+ - ./readhb_size < HB/arc130.rua > tmp/Asize
+ - ./umf4
+ - ./readhb_nozeros < HB/arc130.rua > tmp/A
+ - ./readhb_size < HB/arc130.rua > tmp/Asize
+ - ./umf4
+ - ./readhb_nozeros < HB/arc130.rua > tmp/A
+ - ./readhb_size < HB/arc130.rua > tmp/Asize
+ - ./umf4 a 1e-6
+
+umf4: umf4.c $(UMFPACK)
+ $(C) -o umf4 umf4.c $(UMFPACK) $(LIBS)
+
+readhb: readhb.f
+ $(F77) $(F77FLAGS) -o readhb readhb.f $(F77LIB)
+
+readhb_size: readhb_size.f
+ $(F77) $(F77FLAGS) -o readhb_size readhb_size.f $(F77LIB)
+
+readhb_nozeros: readhb_nozeros.f
+ $(F77) $(F77FLAGS) -o readhb_nozeros readhb_nozeros.f $(F77LIB)
+
+#-------------------------------------------------------------------------------
+# compile the FORTRAN interface and demo
+#-------------------------------------------------------------------------------
+
+fortran: $(UMFPACK) umf4hb.f umf4_f77wrapper.o umf4zhb.f umf4_f77zwrapper.o $(UMFPACK)
+ $(F77) $(F77FLAGS) -o umf4hb umf4hb.f umf4_f77wrapper.o \
+ $(UMFPACK) $(LIBS)
+ - ./umf4hb < HB/west0067.rua > my_umf4hb.out
+ - diff my_umf4hb.out umf4hb.out
+ $(F77) $(F77FLAGS) -o umf4zhb umf4zhb.f umf4_f77zwrapper.o \
+ $(UMFPACK) $(LIBS)
+ - ./umf4zhb < HB/qc324.cua > my_umf4zhb.out
+ - diff my_umf4zhb.out umf4zhb.out
+
+fortran64: $(UMFPACK) umf4hb64.f umf4_f77wrapper64.o umf4_f77zwrapper64.o $(UMFPACK)
+ $(F77) $(F77FLAGS) -o umf4hb64 umf4hb64.f umf4_f77wrapper64.o \
+ $(UMFPACK) $(LIBS)
+ - ./umf4hb64 < HB/west0067.rua > my_umf4hb64.out
+ - diff my_umf4hb64.out umf4hb64.out
+
+umf4_f77wrapper.o: umf4_f77wrapper.c $(INC)
+ $(C) -c umf4_f77wrapper.c -o umf4_f77wrapper.o
+
+umf4_f77zwrapper.o: umf4_f77zwrapper.c $(INC)
+ $(C) -c umf4_f77zwrapper.c -o umf4_f77zwrapper.o
+
+umf4_f77wrapper64.o: umf4_f77wrapper.c $(INC)
+ $(C) -DDLONG -c umf4_f77wrapper.c -o umf4_f77wrapper64.o
+
+umf4_f77zwrapper64.o: umf4_f77zwrapper.c $(INC)
+ $(C) -DDLONG -c umf4_f77zwrapper.c -o umf4_f77zwrapper64.o
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+purge: clean
+ - $(RM) umfpack_simple a.out
+ - $(RM) umfpack_di_demo my_umfpack_di_demo.out
+ - $(RM) umfpack_dl_demo my_umfpack_dl_demo.out
+ - $(RM) umfpack_zi_demo my_umfpack_zi_demo.out
+ - $(RM) umfpack_zl_demo my_umfpack_zl_demo.out
+ - $(RM) umf4hb umf4zhb *.umf my_umf4hb.out
+ - $(RM) umf4hb64 my_umf4hb64.out my_umf4zhb.out
+ - $(RM) umf4 readhb readhb_nozeros readhb_size tmp/*
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/UMFPACK/Demo/dodefault b/UMFPACK/Demo/dodefault
new file mode 100755
index 0000000..c5a9d35
--- /dev/null
+++ b/UMFPACK/Demo/dodefault
@@ -0,0 +1,36 @@
+#!/bin/csh
+# usage: dodefault file.rsa.gz
+#
+# file.rsa.gz is a compressed Harwell/Boeing file containing
+# a symmetric positive definite matrix
+#
+echo '================================================================='
+echo 'Matrix:: ' $1:t:r:r
+
+echo '3' > tmp/control.umf4 ; # 1: print level
+echo '0.2' >> tmp/control.umf4 ; # 2: dense row control
+echo '0.2' >> tmp/control.umf4 ; # 3: dense col control
+echo '0.1' >> tmp/control.umf4 ; # 4: pivot tol (offdiag) DEFAULT
+echo '32' >> tmp/control.umf4 ; # 5: block size
+echo '0' >> tmp/control.umf4 ; # 6: auto strategy, DEFAULT
+echo '0.7' >> tmp/control.umf4 ; # 7: initial alloc
+echo '2' >> tmp/control.umf4 ; # 8: max iter. refinement
+echo '1' >> tmp/control.umf4 ; # 9:
+echo '0' >> tmp/control.umf4 ; # 10:
+echo '0' >> tmp/control.umf4 ; # 11:
+echo '0' >> tmp/control.umf4 ; # 12:
+echo '0.01' >> tmp/control.umf4 ; # 13: 2-by-2 tolerance
+echo '0' >> tmp/control.umf4 ; # 14: Q fixed (auto)
+echo '10' >> tmp/control.umf4 ; # 15: AMD dense row control
+echo '0.001' >> tmp/control.umf4 ; # 16: diag pivot tolerance DEFAULT
+echo '0' >> tmp/control.umf4 ; # 17: scaling, NON-DEFAULT
+echo '0.5' >> tmp/control.umf4 ; # 18: frontal matrix alloc.
+echo '0' >> tmp/control.umf4 ; # 19: drop tolerance
+echo '1' >> tmp/control.umf4 ; # 20: AMD/COLAMD aggressive absorption
+
+zcat $1 | readhb_nozeros > tmp/A
+zcat $1 | readhb_size > tmp/Asize
+umf4
+
+echo '================================================================='
+
diff --git a/UMFPACK/Demo/dospd b/UMFPACK/Demo/dospd
new file mode 100755
index 0000000..46714ac
--- /dev/null
+++ b/UMFPACK/Demo/dospd
@@ -0,0 +1,36 @@
+#!/bin/csh
+# usage: dospd file.rsa.gz
+#
+# file.rsa.gz is a compressed Harwell/Boeing file containing
+# a symmetric positive definite matrix
+#
+echo '================================================================='
+echo 'Matrix:: ' $1:t:r:r
+
+echo '3' > tmp/control.umf4 ; # 1: print level
+echo '0.2' >> tmp/control.umf4 ; # 2: dense row control
+echo '0.2' >> tmp/control.umf4 ; # 3: dense col control
+echo '0' >> tmp/control.umf4 ; # 4: pivot tol (offdiag) NON-DEFAULT
+echo '32' >> tmp/control.umf4 ; # 5: block size
+echo '3' >> tmp/control.umf4 ; # 6: symmetric strategy, NON-DEFAULT
+echo '0.7' >> tmp/control.umf4 ; # 7: initial alloc
+echo '2' >> tmp/control.umf4 ; # 8: max iter. refinement
+echo '1' >> tmp/control.umf4 ; # 9:
+echo '0' >> tmp/control.umf4 ; # 10:
+echo '0' >> tmp/control.umf4 ; # 11:
+echo '0' >> tmp/control.umf4 ; # 12:
+echo '0.01' >> tmp/control.umf4 ; # 13: 2-by-2 tolerance
+echo '0' >> tmp/control.umf4 ; # 14: Q fixed (auto)
+echo '10' >> tmp/control.umf4 ; # 15: AMD dense row control
+echo '0' >> tmp/control.umf4 ; # 16: diag pivot tolerance, NON-DEFAULT
+echo '0' >> tmp/control.umf4 ; # 17: scaling, NON-DEFAULT
+echo '0.5' >> tmp/control.umf4 ; # 18: frontal matrix alloc.
+echo '0' >> tmp/control.umf4 ; # 19: drop tolerance
+echo '1' >> tmp/control.umf4 ; # 20: AMD/COLAMD aggressive absorption
+
+zcat $1 | readhb_nozeros > tmp/A
+zcat $1 | readhb_size > tmp/Asize
+umf4 s
+
+echo '================================================================='
+
diff --git a/UMFPACK/Demo/readhb.f b/UMFPACK/Demo/readhb.f
new file mode 100644
index 0000000..aed8691
--- /dev/null
+++ b/UMFPACK/Demo/readhb.f
@@ -0,0 +1,115 @@
+c=======================================================================
+c== readhb =============================================================
+c=======================================================================
+
+c-----------------------------------------------------------------------
+c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE
+c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for
+c License. web: http://www.cise.ufl.edu/research/sparse/umfpack
+c-----------------------------------------------------------------------
+
+c readhb:
+c read a sparse matrix in the Harwell/Boeing format and
+c output a matrix in triplet format.
+c
+c usage (for example):
+c
+c in a Unix shell:
+c readhb < HB/arc130.rua > tmp/A
+c
+c Then, in MATLAB, you can do the following:
+c >> load tmp/A
+c >> A = spconvert (A) ;
+c >> spy (A)
+
+ integer nzmax, nmax
+ parameter (nzmax = 20000000, nmax = 250000)
+ integer Ptr (nmax), Index (nzmax), n, nz, totcrd, ptrcrd,
+ $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, row, col, p
+ character title*72, key*30, type*3, ptrfmt*16,
+ $ indfmt*16, valfmt*20, rhsfmt*20
+ logical sym
+ double precision Value (nzmax), skew
+ character rhstyp*3
+ integer nzrhs, nel
+
+ integer ne, nnz
+
+c-----------------------------------------------------------------------
+
+c read header information from Harwell/Boeing matrix
+
+ read (5, 10, err = 998)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd, rhscrd,
+ $ type, nrow, ncol, nz, nel,
+ $ ptrfmt, indfmt, valfmt, rhsfmt
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+ read (5, 20, err = 998) rhstyp,nrhs,nzrhs
+ endif
+10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+20 format (a3, 11x, 2i14)
+
+ skew = 0.0
+ if (type (2:2) .eq. 'Z' .or. type (2:2) .eq. 'z') skew = -1.0
+ if (type (2:2) .eq. 'S' .or. type (2:2) .eq. 's') skew = 1.0
+ sym = skew .ne. 0.0
+
+ write (0, 31) key
+31 format ('Matrix key: ', a8)
+
+ n = max (nrow, ncol)
+
+ if (n .ge. nmax .or. nz .gt. nzmax) then
+ write (0, *) 'Matrix too big!'
+ write (0, *) '(recompile readhb.f with larger nzmax, nmax)'
+ stop
+ endif
+
+ read (5, ptrfmt, err = 998) (Ptr (p), p = 1, ncol+1)
+ read (5, indfmt, err = 998) (Index (p), p = 1, nz)
+
+ do 55 col = ncol+2, n+1
+ Ptr (col) = Ptr (ncol+1)
+55 continue
+
+c read the values
+ if (valcrd .gt. 0) then
+ read (5, valfmt, err = 998) (Value (p), p = 1, nz)
+ else
+ do 50 p = 1, nz
+ Value (p) = 1
+50 continue
+ endif
+
+c create the triplet form of the input matrix
+
+ ne = 0
+ nnz = 0
+ do 100 col = 1, n
+ do 90 p = Ptr (col), Ptr (col+1) - 1
+ row = Index (p)
+
+ ne = ne + 1
+ nnz = nnz + 1
+ write (6, 200) row, col, Value (p)
+
+ if (sym .and. row .ne. col) then
+ ne = ne + 1
+ if (Value (p) .ne. 0) then
+ nnz = nnz + 1
+ write (6, 200) col, row, skew * Value (p)
+ endif
+ endif
+
+90 continue
+100 continue
+200 format (2i7, e30.18e3)
+
+c write (0,*) 'Number of entries: ',ne,' True nonzeros: ', nnz
+ stop
+
+998 write (0,*) 'Read error: Harwell/Boeing matrix'
+ stop
+ end
diff --git a/UMFPACK/Demo/readhb_nozeros.f b/UMFPACK/Demo/readhb_nozeros.f
new file mode 100644
index 0000000..11a135d
--- /dev/null
+++ b/UMFPACK/Demo/readhb_nozeros.f
@@ -0,0 +1,122 @@
+c=======================================================================
+c== readhb_nozeros =====================================================
+c=======================================================================
+
+c-----------------------------------------------------------------------
+c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE
+c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for
+c License. web: http://www.cise.ufl.edu/research/sparse/umfpack
+c-----------------------------------------------------------------------
+
+c readhb_nozeros:
+c read a sparse matrix in the Harwell/Boeing format and
+c output a matrix in triplet format.
+c Identical to readhb, except that this version removes explicit
+c zero entries from the matrix.
+c
+c usage (for example):
+c
+c in a Unix shell:
+c readhb_nozeros < HB/arc130.rua > tmp/A
+c
+c Then, in MATLAB, you can do the following:
+c >> load tmp/A
+c >> A = spconvert (A) ;
+c >> spy (A)
+
+ integer nzmax, nmax
+ parameter (nzmax = 10000000, nmax = 250000)
+ integer Ptr (nmax), Index (nzmax), n, nz, totcrd, ptrcrd,
+ $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, row, col, p
+ character title*72, key*30, type*3, ptrfmt*16,
+ $ indfmt*16, valfmt*20, rhsfmt*20
+ logical sym
+ double precision Value (nzmax), skew
+ character rhstyp*3
+ integer nzrhs, nel
+
+ integer ne, nnz
+
+c-----------------------------------------------------------------------
+
+c read header information from Harwell/Boeing matrix
+
+ read (5, 10, err = 998)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd, rhscrd,
+ $ type, nrow, ncol, nz, nel,
+ $ ptrfmt, indfmt, valfmt, rhsfmt
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+ read (5, 20, err = 998) rhstyp,nrhs,nzrhs
+ endif
+10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+20 format (a3, 11x, 2i14)
+
+ skew = 0.0
+ if (type (2:2) .eq. 'Z' .or. type (2:2) .eq. 'z') skew = -1.0
+ if (type (2:2) .eq. 'S' .or. type (2:2) .eq. 's') skew = 1.0
+ sym = skew .ne. 0.0
+
+ write (0, 31) key
+31 format ('Matrix key: ', a8)
+
+ n = max (nrow, ncol)
+
+ if (n .ge. nmax .or. nz .gt. nzmax) then
+ write (0, *) 'Matrix too big!'
+ write (0, *) '(recompile readhb_nozeros.f with larger',
+ $ ' nzmax, nmax)'
+ stop
+ endif
+
+ read (5, ptrfmt, err = 998) (Ptr (p), p = 1, ncol+1)
+ read (5, indfmt, err = 998) (Index (p), p = 1, nz)
+
+ do 55 col = ncol+2, n+1
+ Ptr (col) = Ptr (ncol+1)
+55 continue
+
+c read the values
+ if (valcrd .gt. 0) then
+ read (5, valfmt, err = 998) (Value (p), p = 1, nz)
+ else
+ do 50 p = 1, nz
+ Value (p) = 1
+50 continue
+ endif
+
+c create the triplet form of the input matrix
+
+ ne = 0
+ nnz = 0
+ do 100 col = 1, n
+ do 90 p = Ptr (col), Ptr (col+1) - 1
+ row = Index (p)
+
+c remove zeros, to compare fairly with LU in MATLAB
+c (MATLAB always removes explicit zeros)
+ ne = ne + 1
+ if (Value (p) .ne. 0) then
+ nnz = nnz + 1
+ write (6, 200) row, col, Value (p)
+ endif
+
+ if (sym .and. row .ne. col) then
+ ne = ne + 1
+ if (Value (p) .ne. 0) then
+ nnz = nnz + 1
+ write (6, 200) col, row, skew * Value (p)
+ endif
+ endif
+
+90 continue
+100 continue
+200 format (2i7, e30.18e3)
+
+c write (0,*) 'Number of entries: ',ne,' True nonzeros: ', nnz
+ stop
+
+998 write (0,*) 'Read error: Harwell/Boeing matrix'
+ stop
+ end
diff --git a/UMFPACK/Demo/readhb_size.f b/UMFPACK/Demo/readhb_size.f
new file mode 100644
index 0000000..8556cd7
--- /dev/null
+++ b/UMFPACK/Demo/readhb_size.f
@@ -0,0 +1,47 @@
+c=======================================================================
+c== readhb_size ========================================================
+c=======================================================================
+
+c-----------------------------------------------------------------------
+c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE
+c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for
+c License. web: http://www.cise.ufl.edu/research/sparse/umfpack
+c-----------------------------------------------------------------------
+
+c readhb_size:
+c read a sparse matrix in the Harwell/Boeing format and output the
+c size of the matrix (# rows, # columns, and # of entries)
+c
+c usage (for example):
+c
+c readhb_size < HB/arc130.rua > tmp/Asize
+
+ integer nz, totcrd, ptrcrd,
+ $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs
+ character title*72, key*30, type*3, ptrfmt*16,
+ $ indfmt*16, valfmt*20, rhsfmt*20
+ character rhstyp*3
+ integer nzrhs, nel
+
+c-----------------------------------------------------------------------
+
+c read header information from Harwell/Boeing matrix
+
+ read (5, 10, err = 998)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd, rhscrd,
+ $ type, nrow, ncol, nz, nel,
+ $ ptrfmt, indfmt, valfmt, rhsfmt
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+ read (5, 20, err = 998) rhstyp,nrhs,nzrhs
+ endif
+10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+20 format (a3, 11x, 2i14)
+
+ write (6, *) nrow, ncol, nz
+ stop
+998 write (0, *) 'Read error'
+ stop
+ end
+
diff --git a/UMFPACK/Demo/simple_compile b/UMFPACK/Demo/simple_compile
new file mode 100755
index 0000000..1e3ed9a
--- /dev/null
+++ b/UMFPACK/Demo/simple_compile
@@ -0,0 +1,111 @@
+#!/bin/csh
+
+# This one-line command compiles all of UMFPACK and the double/int demo.
+# It forms a useful prototype for Microsoft Visual Studio, which does not
+# have the flexibility of Unix/Linux "make". The latter can be configured
+# to compile one file multiple times (as required by UMFPACK). Here,
+# that requirement is solved with a single file, umf_multicompile.c.
+#
+# No BLAS is used here. You should modify this to add your BLAS.
+# Otherwise your performance will be low.
+
+cc -DDINT -DNBLAS -I../../UFconfig \
+ -I../Include -I../Source -I../../AMD/Include -I../../AMD/Source \
+ umfpack_di_demo.c \
+ ../Source/umf_multicompile.c \
+ ../Source/umfpack_global.c \
+ ../Source/umf_ltsolve.c \
+ ../Source/umf_utsolve.c \
+ ../Source/umf_triplet.c \
+ ../Source/umf_assemble.c \
+ ../Source/umf_store_lu.c \
+ ../Source/umfpack_solve.c \
+ ../../AMD/Source/amd_1.c \
+ ../../AMD/Source/amd_2.c \
+ ../../AMD/Source/amd_aat.c \
+ ../../AMD/Source/amd_control.c \
+ ../../AMD/Source/amd_defaults.c \
+ ../../AMD/Source/amd_global.c \
+ ../../AMD/Source/amd_dump.c \
+ ../../AMD/Source/amd_info.c \
+ ../../AMD/Source/amd_order.c \
+ ../../AMD/Source/amd_post_tree.c \
+ ../../AMD/Source/amd_postorder.c \
+ ../../AMD/Source/amd_preprocess.c \
+ ../../AMD/Source/amd_valid.c \
+ ../Source/umf_2by2.c \
+ ../Source/umf_analyze.c \
+ ../Source/umf_apply_order.c \
+ ../Source/umf_blas3_update.c \
+ ../Source/umf_build_tuples.c \
+ ../Source/umf_colamd.c \
+ ../Source/umf_create_element.c \
+ ../Source/umf_dump.c \
+ ../Source/umf_extend_front.c \
+ ../Source/umf_free.c \
+ ../Source/umf_fsize.c \
+ ../Source/umf_garbage_collection.c \
+ ../Source/umf_get_memory.c \
+ ../Source/umf_grow_front.c \
+ ../Source/umf_init_front.c \
+ ../Source/umf_is_permutation.c \
+ ../Source/umf_kernel.c \
+ ../Source/umf_kernel_init.c \
+ ../Source/umf_kernel_wrapup.c \
+ ../Source/umf_local_search.c \
+ ../Source/umf_lsolve.c \
+ ../Source/umf_malloc.c \
+ ../Source/umf_mem_alloc_element.c \
+ ../Source/umf_mem_alloc_head_block.c \
+ ../Source/umf_mem_alloc_tail_block.c \
+ ../Source/umf_mem_free_tail_block.c \
+ ../Source/umf_mem_init_memoryspace.c \
+ ../Source/umf_realloc.c \
+ ../Source/umf_report_perm.c \
+ ../Source/umf_report_vector.c \
+ ../Source/umf_row_search.c \
+ ../Source/umf_scale.c \
+ ../Source/umf_scale_column.c \
+ ../Source/umf_set_stats.c \
+ ../Source/umf_singletons.c \
+ ../Source/umf_solve.c \
+ ../Source/umf_start_front.c \
+ ../Source/umf_symbolic_usage.c \
+ ../Source/umf_transpose.c \
+ ../Source/umf_tuple_lengths.c \
+ ../Source/umf_usolve.c \
+ ../Source/umf_valid_numeric.c \
+ ../Source/umf_valid_symbolic.c \
+ ../Source/umfpack_col_to_triplet.c \
+ ../Source/umfpack_defaults.c \
+ ../Source/umfpack_free_numeric.c \
+ ../Source/umfpack_free_symbolic.c \
+ ../Source/umfpack_get_determinant.c \
+ ../Source/umfpack_get_lunz.c \
+ ../Source/umfpack_get_numeric.c \
+ ../Source/umfpack_get_symbolic.c \
+ ../Source/umfpack_load_numeric.c \
+ ../Source/umfpack_load_symbolic.c \
+ ../Source/umfpack_numeric.c \
+ ../Source/umfpack_qsymbolic.c \
+ ../Source/umfpack_report_control.c \
+ ../Source/umfpack_report_info.c \
+ ../Source/umfpack_report_matrix.c \
+ ../Source/umfpack_report_numeric.c \
+ ../Source/umfpack_report_perm.c \
+ ../Source/umfpack_report_status.c \
+ ../Source/umfpack_report_symbolic.c \
+ ../Source/umfpack_report_triplet.c \
+ ../Source/umfpack_report_vector.c \
+ ../Source/umfpack_save_numeric.c \
+ ../Source/umfpack_save_symbolic.c \
+ ../Source/umfpack_scale.c \
+ ../Source/umfpack_symbolic.c \
+ ../Source/umfpack_tictoc.c \
+ ../Source/umfpack_timer.c \
+ ../Source/umfpack_transpose.c \
+ ../Source/umfpack_triplet_to_col.c \
+ -lm
+
+# now run the demo
+./a.out
diff --git a/UMFPACK/Demo/umf4.c b/UMFPACK/Demo/umf4.c
new file mode 100644
index 0000000..628a034
--- /dev/null
+++ b/UMFPACK/Demo/umf4.c
@@ -0,0 +1,650 @@
+/* ========================================================================== */
+/* === umf4 ================================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Demo program for UMFPACK. Reads in a triplet-form matrix in the
+ * directory tmp/A, whose size and # of nonzeros are in the file tmp/Asize.
+ * Then calls UMFPACK to analyze, factor, and solve the system.
+ *
+ * Syntax:
+ *
+ * umf4 default "auto" strategy, 1-norm row scaling
+ * umf4 a default "auto" strategy, 1-norm row scaling
+ * umf4 u unsymmetric strategy, 1-norm row scaling
+ * umf4 s symmetric strategy, 1-norm row scaling
+ * umf4 2 2-by-2 strategy, maxnorm row scaling
+ * umf4 A default "auto" strategy, maxnorm row scaling
+ * umf4 U unsymmetric strategy, maxnorm row scaling
+ * umf4 S symmetric strategy, maxnorm row scaling
+ * umf4 T 2-by-2 strategy , maxnorm row scaling
+ *
+ * To test a matrix in the Harwell/Boeing format, do the following:
+ *
+ * readhb < HB/arc130.rua > tmp/A
+ * readhb_size < HB/arc130.rua > tmp/Asize
+ * umf4
+ *
+ * The above options do not drop any nonzero entry in L or U. To compute an
+ * incomplete factorization, you can add a second argument to give the drop
+ * tolerance. Entries less than or equal to the drop tolerance are then
+ * removed from L and U during factorization, unless dropping those entries
+ * does not save any memory space. For example:
+ *
+ * umf4 a 1e-6 default "auto" strategy, 1-norm row scaling,
+ * drop tolerance of 1e-6.
+ *
+ * Note that adding a drop tolerance can lead to an apparent (but not real)
+ * increase in peak memory usage. This is illustrated in the arc130.rua
+ * matrix. With a drop tolerance, garbage collection happens to be avoided
+ * for this matrix. During garbage collection, both internal and external
+ * fragmentation in the memory space is removed. Peak memory usage includes
+ * all internal memory fragmentation, even though this can be removed via
+ * garbage collection.
+ *
+ * Control parameters can also be set in the optional tmp/control.umf4 file.
+ * The right-hand-side can be provided in the optional tmp/b file. The solution
+ * is written to tmp/x, and the output statistics are written to tmp/info.umf4.
+ *
+ * After the matrix is factorized, solved, and the LU factors deallocated,
+ * this program then test the AMD ordering routine. This call to AMD is NOT
+ * part of the UMFPACK analysis, factorize, or solve steps. It is just a
+ * separate test of the AMD ordering routine. If the matrix is unsymmetric,
+ * AMD orders the pattern of A+A'.
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include "umfpack.h"
+#include "amd.h"
+
+#define SMAX 256
+#define ABS(x) ((x) >= 0 ? (x) : -(x))
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+
+#define XTRUE(i,n) (1.0 + ((double) i) / ((double) n))
+
+#ifndef FALSE
+#define FALSE 0
+#endif
+
+#ifndef TRUE
+#define TRUE 1
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* err: compute the relative error, ||x-xtrue||/||xtrue|| */
+/* -------------------------------------------------------------------------- */
+
+static double err
+(
+ int n,
+ double x [ ]
+)
+{
+ int i ;
+ double enorm, e, abse, absxtrue, xnorm ;
+ enorm = 0 ;
+ xnorm = 0 ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ if (isnan (x [i]))
+ {
+ enorm = x [i] ;
+ break ;
+ }
+ e = x [i] - XTRUE (i,n) ;
+ abse = ABS (e) ;
+ enorm = MAX (enorm, abse) ;
+ }
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* XTRUE is positive, but do this in case XTRUE is redefined */
+ absxtrue = ABS (XTRUE (i,n)) ;
+ xnorm = MAX (xnorm, absxtrue) ;
+ }
+
+ if (xnorm == 0)
+ {
+ xnorm = 1 ;
+ }
+ return (enorm / xnorm) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* resid: compute the relative residual, ||Ax-b||/||b|| or ||A'x-b||/||b|| */
+/* -------------------------------------------------------------------------- */
+
+static double resid
+(
+ int n,
+ int Ap [ ],
+ int Ai [ ],
+ double Ax [ ],
+ double x [ ],
+ double r [ ],
+ double b [ ],
+ int transpose
+)
+{
+ int i, j, p ;
+ double rnorm, absr, absb, bnorm ;
+ for (i = 0 ; i < n ; i++)
+ {
+ r [i] = 0 ;
+ }
+
+ if (transpose)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ r [j] += Ax [p] * x [i] ;
+ }
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ r [i] += Ax [p] * x [j] ;
+ }
+ }
+ }
+
+ for (i = 0 ; i < n ; i++)
+ {
+ r [i] -= b [i] ;
+ }
+ rnorm = 0. ;
+ bnorm = 0. ;
+ for (i = 0 ; i < n ; i++)
+ {
+ if (isnan (r [i]))
+ {
+ rnorm = r [i] ;
+ break ;
+ }
+ absr = ABS (r [i]) ;
+ rnorm = MAX (rnorm, absr) ;
+ }
+ for (i = 0 ; i < n ; i++)
+ {
+ if (isnan (b [i]))
+ {
+ bnorm = b [i] ;
+ break ;
+ }
+ absb = ABS (b [i]) ;
+ bnorm = MAX (bnorm, absb) ;
+ }
+ if (bnorm == 0)
+ {
+ bnorm = 1 ;
+ }
+ return (rnorm / bnorm) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* Atimesx: compute y = A*x or A'*x, where x (i) = 1 + i/n */
+/* -------------------------------------------------------------------------- */
+
+static void Atimesx
+(
+ int n,
+ int Ap [ ],
+ int Ai [ ],
+ double Ax [ ],
+ double y [ ],
+ int transpose
+)
+{
+ int i, j, p ;
+ for (i = 0 ; i < n ; i++)
+ {
+ y [i] = 0 ;
+ }
+ if (transpose)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ y [j] += Ax [p] * XTRUE (i,n) ;
+ }
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ y [i] += Ax [p] * XTRUE (j,n) ;
+ }
+ }
+ }
+}
+
+/* -------------------------------------------------------------------------- */
+/* main program */
+/* -------------------------------------------------------------------------- */
+
+int main (int argc, char **argv)
+{
+ int i, j, k, n, nz, *Ap, *Ai, *Ti, *Tj, status, *Pamd, nrow, ncol, rhs ;
+ double *Ax, *b, *x, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], aij,
+ *Tx, *r, amd_Control [AMD_CONTROL], amd_Info [AMD_INFO], tamd [2],
+ stats [2], droptol ;
+ void *Symbolic, *Numeric ;
+ FILE *f, *f2 ;
+ char s [SMAX] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* set controls */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\n===========================================================\n"
+ "=== UMFPACK v%d.%d.%d ========================================\n"
+ "===========================================================\n",
+ UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION) ;
+
+ umfpack_di_defaults (Control) ;
+ Control [UMFPACK_PRL] = 3 ;
+ Control [UMFPACK_BLOCK_SIZE] = 32 ;
+
+ f = fopen ("tmp/control.umf4", "r") ;
+ if (f != (FILE *) NULL)
+ {
+ printf ("Reading control file tmp/control.umf4\n") ;
+ for (i = 0 ; i < UMFPACK_CONTROL ; i++)
+ {
+ fscanf (f, "%lg\n", & Control [i]) ;
+ }
+ fclose (f) ;
+ }
+
+ if (argc > 1)
+ {
+ char *s = argv [1] ;
+
+ /* get the strategy */
+ if (s [0] == 'u')
+ {
+ Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ }
+ else if (s [0] == 'a')
+ {
+ Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_AUTO ;
+ }
+ else if (s [0] == 's')
+ {
+ Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_SYMMETRIC ;
+ }
+ else if (s [0] == '2')
+ {
+ Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_2BY2 ;
+ }
+ else if (s [0] == 'U')
+ {
+ Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ Control [UMFPACK_SCALE] = UMFPACK_SCALE_MAX ;
+ }
+ else if (s [0] == 'A')
+ {
+ Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_AUTO ;
+ Control [UMFPACK_SCALE] = UMFPACK_SCALE_MAX ;
+ }
+ else if (s [0] == 'S')
+ {
+ Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_SYMMETRIC ;
+ Control [UMFPACK_SCALE] = UMFPACK_SCALE_MAX ;
+ }
+ else if (s [0] == 'T')
+ {
+ Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_2BY2 ;
+ Control [UMFPACK_SCALE] = UMFPACK_SCALE_MAX ;
+ }
+ else
+ {
+ printf ("unrecognized strategy: %s\n", argv [1]) ;
+ }
+
+ if (s [1] == 'n')
+ {
+ /* no aggressive absorption */
+ Control [UMFPACK_AGGRESSIVE] = FALSE ;
+ }
+ }
+
+ if (argc > 2)
+ {
+ /* get the drop tolerance */
+ sscanf (argv [2], "%lg", &droptol) ;
+ printf ("droptol %g\n", droptol) ;
+ Control [UMFPACK_DROPTOL] = droptol ;
+ }
+
+ umfpack_di_report_control (Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* open the matrix file (tmp/A) */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("File: tmp/A\n") ;
+ f = fopen ("tmp/A", "r") ;
+ if (!f)
+ {
+ printf ("Unable to open file\n") ;
+ exit (1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get n and nz */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("File: tmp/Asize\n") ;
+ f2 = fopen ("tmp/Asize", "r") ;
+ if (f2)
+ {
+ fscanf (f2, "%d %d %d\n", &nrow, &ncol, &nz) ;
+ fclose (f2) ;
+ }
+ else
+ {
+ nrow = 1 ;
+ ncol = 1 ;
+ }
+ nz = 0 ;
+ while (fgets (s, SMAX, f) != (char *) NULL)
+ {
+ sscanf (s, "%d %d %lg", &i, &j, &aij) ;
+#ifdef ZERO_BASED
+ /* matrix is zero based */
+ i++ ;
+ j++ ;
+#endif
+ nrow = MAX (nrow, i) ;
+ ncol = MAX (ncol, j) ;
+ nz++ ;
+ }
+ fclose (f) ;
+ n = MAX (nrow, ncol) ;
+
+ printf ("n %d nrow %d ncol %d nz %d\n", n, nrow, ncol, nz) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate space for the input triplet form */
+ /* ---------------------------------------------------------------------- */
+
+ Ti = (int *) malloc (nz * sizeof (int)) ;
+ Tj = (int *) malloc (nz * sizeof (int)) ;
+ Tx = (double *) malloc (nz * sizeof (double)) ;
+ if (!Ti || !Tj || !Tx)
+ {
+ printf ("out of memory for input matrix\n") ;
+ exit (1) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read in the triplet form */
+ /* ---------------------------------------------------------------------- */
+
+ f2 = fopen ("tmp/A", "r") ;
+ if (!f2)
+ {
+ printf ("Unable to open file\n") ;
+ exit (1) ;
+ }
+
+ k = 0 ;
+ while (fgets (s, SMAX, f2) != (char *) NULL)
+ {
+ sscanf (s, "%d %d %lg", &i, &j, &aij) ;
+#ifndef ZERO_BASED
+ i-- ; /* convert to 0-based */
+ j-- ;
+#endif
+ if (k >= nz)
+ {
+ printf ("Error! Matrix size is wrong\n") ;
+ exit (1) ;
+ }
+ Ti [k] = i ;
+ Tj [k] = j ;
+ Tx [k] = aij ;
+ k++ ;
+ }
+ fclose (f2) ;
+
+ (void) umfpack_di_report_triplet (nrow, ncol, nz, Ti, Tj, Tx, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert to column form */
+ /* ---------------------------------------------------------------------- */
+
+ /* convert to column form */
+ Ap = (int *) malloc ((n+1) * sizeof (int)) ;
+ Ai = (int *) malloc (nz * sizeof (int)) ;
+ Ax = (double *) malloc (nz * sizeof (double)) ;
+ b = (double *) malloc (n * sizeof (double)) ;
+ r = (double *) malloc (n * sizeof (double)) ;
+ x = (double *) malloc (n * sizeof (double)) ;
+ if (!Ap || !Ai || !Ax || !b || !r)
+ {
+ printf ("out of memory") ;
+ exit (1) ;
+ }
+ umfpack_tic (stats) ;
+ status = umfpack_di_triplet_to_col (nrow, ncol, nz, Ti, Tj, Tx, Ap, Ai, Ax,
+ (int *) NULL) ;
+ umfpack_toc (stats) ;
+ printf ("triplet-to-col time: wall %g cpu %g\n", stats [0], stats [1]) ;
+ if (status != UMFPACK_OK)
+ {
+ umfpack_di_report_status (Control, status) ;
+ printf ("umfpack_di_triplet_to_col failed") ;
+ exit (1) ;
+ }
+
+ /* print the column-form of A */
+ (void) umfpack_di_report_matrix (nrow, ncol, Ap, Ai, Ax, 1, Control) ;
+
+ /* b = A * xtrue */
+ rhs = FALSE ;
+ if (nrow == ncol)
+ {
+ f = fopen ("tmp/b", "r") ;
+ if (f != (FILE *) NULL)
+ {
+ printf ("Reading tmp/b\n") ;
+ rhs = TRUE ;
+ for (i = 0 ; i < n ; i++)
+ {
+ fscanf (f, "%lg\n", &b [i]) ;
+ }
+ fclose (f) ;
+ }
+ else
+ {
+ Atimesx (n, Ap, Ai, Ax, b, FALSE) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the triplet form */
+ /* ---------------------------------------------------------------------- */
+
+ free (Ti) ;
+ free (Tj) ;
+ free (Tx) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_symbolic (nrow, ncol, Ap, Ai, Ax, &Symbolic,
+ Control, Info) ;
+
+ umfpack_di_report_info (Control, Info) ;
+ if (status != UMFPACK_OK)
+ {
+ umfpack_di_report_status (Control, status) ;
+ printf ("umfpack_di_symbolic failed") ;
+ exit (1) ;
+ }
+
+ /* print the symbolic factorization */
+ (void) umfpack_di_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info);
+ if (status < UMFPACK_OK)
+ {
+ umfpack_di_report_info (Control, Info) ;
+ umfpack_di_report_status (Control, status) ;
+ fprintf (stderr, "umfpack_di_numeric failed: %d\n", status) ;
+ printf ("umfpack_di_numeric failed\n") ;
+ exit (1) ;
+ }
+
+ /* print the numeric factorization */
+ (void) umfpack_di_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrow == ncol && status == UMFPACK_OK)
+ {
+ status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric,
+ Control, Info) ;
+
+ umfpack_di_report_info (Control, Info) ;
+ umfpack_di_report_status (Control, status) ;
+ if (status < UMFPACK_OK)
+ {
+ printf ("umfpack_di_solve failed\n") ;
+ exit (1) ;
+ }
+ (void) umfpack_di_report_vector (n, x, Control) ;
+ printf ("relative maxnorm of residual, ||Ax-b||/||b||: %g\n",
+ resid (n, Ap, Ai, Ax, x, r, b, FALSE)) ;
+ if (!rhs)
+ {
+ printf ("relative maxnorm of error, ||x-xtrue||/||xtrue||: %g\n\n",
+ err (n, x)) ;
+ }
+
+ f = fopen ("tmp/x", "w") ;
+ if (f != (FILE *) NULL)
+ {
+ printf ("Writing tmp/x\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ fprintf (f, "%30.20e\n", x [i]) ;
+ }
+ fclose (f) ;
+ }
+ else
+ {
+ printf ("Unable to write output x!\n") ;
+ exit (1) ;
+ }
+
+ f = fopen ("tmp/info.umf4", "w") ;
+ if (f != (FILE *) NULL)
+ {
+ printf ("Writing tmp/info.umf4\n") ;
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ fprintf (f, "%30.20e\n", Info [i]) ;
+ }
+ fclose (f) ;
+ }
+ else
+ {
+ printf ("Unable to write output info!\n") ;
+ exit (1) ;
+ }
+ }
+ else
+ {
+ /* don't solve, just report the results */
+ umfpack_di_report_info (Control, Info) ;
+ umfpack_di_report_status (Control, status) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the Symbolic and Numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_di_free_symbolic (&Symbolic) ;
+ umfpack_di_free_numeric (&Numeric) ;
+
+ printf ("umf4 done, strategy: %g\n", Control [UMFPACK_STRATEGY]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test just AMD ordering (not part of UMFPACK, but a separate test) */
+ /* ---------------------------------------------------------------------- */
+
+ /* first make the matrix square */
+ if (ncol < n)
+ {
+ for (j = ncol+1 ; j <= n ; j++)
+ {
+ Ap [j] = Ap [ncol] ;
+ }
+ }
+
+ printf (
+ "\n\n===========================================================\n"
+ "=== AMD ===================================================\n"
+ "===========================================================\n") ;
+ printf ("\n\n------- Now trying the AMD ordering. This not part of\n"
+ "the UMFPACK analysis or factorization, above, but a separate\n"
+ "test of just the AMD ordering routine.\n") ;
+ Pamd = (int *) malloc (n * sizeof (int)) ;
+ if (!Pamd)
+ {
+ printf ("out of memory\n") ;
+ exit (1) ;
+ }
+ amd_defaults (amd_Control) ;
+ amd_control (amd_Control) ;
+ umfpack_tic (tamd) ;
+ status = amd_order (n, Ap, Ai, Pamd, amd_Control, amd_Info) ;
+ umfpack_toc (tamd) ;
+ printf ("AMD ordering time: cpu %10.2f wall %10.2f\n",
+ tamd [1], tamd [0]) ;
+ if (status != AMD_OK)
+ {
+ printf ("amd failed: %d\n", status) ;
+ exit (1) ;
+ }
+ amd_info (amd_Info) ;
+ free (Pamd) ;
+ printf ("AMD test done\n") ;
+
+ return (0) ;
+}
diff --git a/UMFPACK/Demo/umf4.out b/UMFPACK/Demo/umf4.out
new file mode 100644
index 0000000..a76b120
--- /dev/null
+++ b/UMFPACK/Demo/umf4.out
@@ -0,0 +1,1912 @@
+cc -O3 -I../Include -I../../AMD/Include -I../../UFconfig -o umf4 umf4.c ../Lib/libumfpack.a ../../AMD/Lib/libamd.a -lblas -lgfortran -lgfortranbegin -lm
+f77 -O -o readhb readhb.f
+f77 -O -o readhb_nozeros readhb_nozeros.f
+f77 -O -o readhb_size readhb_size.f
+./readhb_nozeros < HB/can_24.psa > tmp/A
+./readhb_size < HB/can_24.psa > tmp/Asize
+./umf4
+
+===========================================================
+=== UMFPACK v5.2.0 ========================================
+===========================================================
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: int
+
+ 0: print level: 3
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+File: tmp/A
+File: tmp/Asize
+n 24 nrow 24 ncol 24 nz 160
+triplet-form matrix, n_row = 24, n_col = 24 nz = 160. OK
+
+triplet-to-col time: wall 0 cpu 0
+column-form matrix, n_row 24 n_col 24, nz = 160. OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 24
+ number of columns in matrix A: 24
+ entries in matrix A: 160
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 0
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 24
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 136
+ nz on diagonal of matrix S: 24
+ fraction of nz on diagonal: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 1.00300e+03
+ est. nz in L+U (incl. diagonal): 218
+ est. largest front (# entries): 64
+ est. max nz in any column of L: 8
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 725
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 131
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 763 - -
+ peak size (Units) 3244 - -
+ final size (Units) 393 - -
+ Numeric final size (Units) 598 - -
+ Numeric final size (MBytes) 0.0 - -
+ peak memory usage (Units) 3840 - -
+ peak memory usage (MBytes) 0.0 - -
+ numeric factorization flops 2.37900e+03 - -
+ nz in L (incl diagonal) 149 - -
+ nz in U (incl diagonal) 208 - -
+ nz in L+U (incl diagonal) 333 - -
+ largest front (# entries) 182 - -
+ largest # rows in front 13 - -
+ largest # columns in front 14 - -
+
+Symbolic object: OK
+
+Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 24
+ number of columns in matrix A: 24
+ entries in matrix A: 160
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 0
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 24
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 136
+ nz on diagonal of matrix S: 24
+ fraction of nz on diagonal: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 1.00300e+03
+ est. nz in L+U (incl. diagonal): 218
+ est. largest front (# entries): 64
+ est. max nz in any column of L: 8
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 725
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 131
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 4.00000e+00
+ maximum sum (abs (rows of A)): 9.00000e+00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 763 711 93%
+ peak size (Units) 3244 2709 84%
+ final size (Units) 393 133 34%
+ Numeric final size (Units) 598 326 55%
+ Numeric final size (MBytes) 0.0 0.0 55%
+ peak memory usage (Units) 3840 3305 86%
+ peak memory usage (MBytes) 0.0 0.0 86%
+ numeric factorization flops 2.37900e+03 1.57000e+02 7%
+ nz in L (incl diagonal) 149 53 36%
+ nz in U (incl diagonal) 208 73 35%
+ nz in L+U (incl diagonal) 333 102 31%
+ largest front (# entries) 182 78 43%
+ largest # rows in front 13 7 54%
+ largest # columns in front 14 13 93%
+
+ initial allocation ratio used: 1.2
+ # of forced updates due to frontal growth: 0
+ number of off-diagonal pivots: 10
+ nz in L (incl diagonal), if none dropped 53
+ nz in U (incl diagonal), if none dropped 73
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 24
+ min abs. value on diagonal of U: 1.11e-01
+ max abs. value on diagonal of U: 2.50e-01
+ estimate of reciprocal of condition number: 4.44e-01
+ indices in compressed pattern: 76
+ numerical values stored in Numeric object: 102
+ numeric factorization defragmentations: 0
+ numeric factorization reallocations: 0
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.06000e+03
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 7.86e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.21700e+03
+
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+dense vector, n = 24. OK
+
+relative maxnorm of residual, ||Ax-b||/||b||: 2.58379e-16
+relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.92754e-15
+
+Writing tmp/x
+Writing tmp/info.umf4
+umf4 done, strategy: 0
+
+
+===========================================================
+=== AMD ===================================================
+===========================================================
+
+
+------- Now trying the AMD ordering. This not part of
+the UMFPACK analysis or factorization, above, but a separate
+test of just the AMD ordering routine.
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+AMD ordering time: cpu 0.00 wall 0.00
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 24
+ nz, number of nonzeros in A: 160
+ symmetry of A: 1.0000
+ number of nonzeros on diagonal: 24
+ nonzeros in pattern of A+A' (excl. diagonal): 136
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 1516
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 97
+ nonzeros in L (including diagonal): 121
+ # divide operations for LDL' or LU: 97
+ # multiply-subtract operations for LDL': 275
+ # multiply-subtract operations for LU: 453
+ max nz. in any column of L (incl. diagonal): 8
+
+ chol flop count for real A, sqrt counted as 1 flop: 671
+ LDL' flop count for real A: 647
+ LDL' flop count for complex A: 3073
+ LU flop count for real A (with no pivoting): 1003
+ LU flop count for complex A (with no pivoting): 4497
+
+AMD test done
+./readhb_nozeros < HB/west0067.rua > tmp/A
+./readhb_size < HB/west0067.rua > tmp/Asize
+./umf4
+
+===========================================================
+=== UMFPACK v5.2.0 ========================================
+===========================================================
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: int
+
+ 0: print level: 3
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+File: tmp/A
+File: tmp/Asize
+n 67 nrow 67 ncol 67 nz 294
+triplet-form matrix, n_row = 67, n_col = 67 nz = 294. OK
+
+triplet-to-col time: wall 0 cpu 0
+column-form matrix, n_row 67 n_col 67, nz = 294. OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 67
+ number of columns in matrix A: 67
+ entries in matrix A: 294
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 1
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S not square or diagonal not preserved
+ symbolic factorization defragmentations: 1
+ symbolic memory usage (Units): 1639
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 252
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 1711 - -
+ peak size (Units) 6115 - -
+ final size (Units) 1628 - -
+ Numeric final size (Units) 2108 - -
+ Numeric final size (MBytes) 0.0 - -
+ peak memory usage (Units) 7476 - -
+ peak memory usage (MBytes) 0.1 - -
+ numeric factorization flops 1.41920e+04 - -
+ nz in L (incl diagonal) 542 - -
+ nz in U (incl diagonal) 902 - -
+ nz in L+U (incl diagonal) 1377 - -
+ largest front (# entries) 483 - -
+ largest # rows in front 21 - -
+ largest # columns in front 23 - -
+
+Symbolic object: OK
+
+Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 67
+ number of columns in matrix A: 67
+ entries in matrix A: 294
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 1
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S not square or diagonal not preserved
+ symbolic factorization defragmentations: 1
+ symbolic memory usage (Units): 1639
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 252
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.01
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 6.59006e+00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 1711 1577 92%
+ peak size (Units) 6115 3581 59%
+ final size (Units) 1628 682 42%
+ Numeric final size (Units) 2108 1129 54%
+ Numeric final size (MBytes) 0.0 0.0 54%
+ peak memory usage (Units) 7476 4942 66%
+ peak memory usage (MBytes) 0.1 0.0 66%
+ numeric factorization flops 1.41920e+04 2.50100e+03 18%
+ nz in L (incl diagonal) 542 323 60%
+ nz in U (incl diagonal) 902 339 38%
+ nz in L+U (incl diagonal) 1377 595 43%
+ largest front (# entries) 483 80 17%
+ largest # rows in front 21 10 48%
+ largest # columns in front 23 11 48%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 323
+ nz in U (incl diagonal), if none dropped 339
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 67
+ min abs. value on diagonal of U: 2.74e-02
+ max abs. value on diagonal of U: 2.28e+00
+ estimate of reciprocal of condition number: 1.20e-02
+ indices in compressed pattern: 263
+ numerical values stored in Numeric object: 599
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 6.16500e+03
+ iterative refinement steps taken: 1
+ iterative refinement steps attempted: 1
+ sparse backward error omega1: 1.32e-16
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 8.66600e+03
+
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+dense vector, n = 67. OK
+
+relative maxnorm of residual, ||Ax-b||/||b||: 9.15507e-17
+relative maxnorm of error, ||x-xtrue||/||xtrue||: 2.349e-15
+
+Writing tmp/x
+Writing tmp/info.umf4
+umf4 done, strategy: 0
+
+
+===========================================================
+=== AMD ===================================================
+===========================================================
+
+
+------- Now trying the AMD ordering. This not part of
+the UMFPACK analysis or factorization, above, but a separate
+test of just the AMD ordering routine.
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+AMD ordering time: cpu 0.00 wall 0.00
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 67
+ nz, number of nonzeros in A: 294
+ symmetry of A: 0.0342
+ number of nonzeros on diagonal: 2
+ nonzeros in pattern of A+A' (excl. diagonal): 574
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 5164
+ # of memory compactions: 1
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 930
+ nonzeros in L (including diagonal): 997
+ # divide operations for LDL' or LU: 930
+ # multiply-subtract operations for LDL': 9170
+ # multiply-subtract operations for LU: 17410
+ max nz. in any column of L (incl. diagonal): 33
+
+ chol flop count for real A, sqrt counted as 1 flop: 19337
+ LDL' flop count for real A: 19270
+ LDL' flop count for complex A: 81730
+ LU flop count for real A (with no pivoting): 35750
+ LU flop count for complex A (with no pivoting): 147650
+
+AMD test done
+./readhb_nozeros < HB/fs_183_6.rua > tmp/A
+./readhb_size < HB/fs_183_6.rua > tmp/Asize
+./umf4
+
+===========================================================
+=== UMFPACK v5.2.0 ========================================
+===========================================================
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: int
+
+ 0: print level: 3
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+File: tmp/A
+File: tmp/Asize
+n 183 nrow 183 ncol 183 nz 1000
+triplet-form matrix, n_row = 183, n_col = 183 nz = 1000. OK
+
+triplet-to-col time: wall 0 cpu 0
+column-form matrix, n_row 183 n_col 183, nz = 1000. OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 183
+ number of columns in matrix A: 183
+ entries in matrix A: 1000
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric 2-by-2
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 36
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 4
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 147
+ symmetry of nonzero pattern: 0.490515
+ nz in S+S' (excl. diagonal): 1114
+ nz on diagonal of matrix S: 147
+ fraction of nz on diagonal: 1.000000
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 7
+ # unmatched: 7
+ symmetry of P2*S: 0.490515
+ nz in P2*S+(P2*S)' (excl. diag.): 1114
+ nz on diagonal of P2*S: 147
+ fraction of nz on diag of P2*S: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 1.02930e+04
+ est. nz in L+U (incl. diagonal): 1625
+ est. largest front (# entries): 196
+ est. max nz in any column of L: 14
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 4846
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 763
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 4458 - -
+ peak size (Units) 26277 - -
+ final size (Units) 15717 - -
+ Numeric final size (Units) 16951 - -
+ Numeric final size (MBytes) 0.1 - -
+ peak memory usage (Units) 29687 - -
+ peak memory usage (MBytes) 0.2 - -
+ numeric factorization flops 2.67903e+05 - -
+ nz in L (incl diagonal) 2122 - -
+ nz in U (incl diagonal) 9931 - -
+ nz in L+U (incl diagonal) 11870 - -
+ largest front (# entries) 2337 - -
+ largest # rows in front 21 - -
+ largest # columns in front 136 - -
+
+Symbolic object: OK
+
+Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 183
+ number of columns in matrix A: 183
+ entries in matrix A: 1000
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric 2-by-2
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 36
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 4
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 147
+ symmetry of nonzero pattern: 0.490515
+ nz in S+S' (excl. diagonal): 1114
+ nz on diagonal of matrix S: 147
+ fraction of nz on diagonal: 1.000000
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 7
+ # unmatched: 7
+ symmetry of P2*S: 0.490515
+ nz in P2*S+(P2*S)' (excl. diag.): 1114
+ nz on diagonal of P2*S: 147
+ fraction of nz on diag of P2*S: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 1.02930e+04
+ est. nz in L+U (incl. diagonal): 1625
+ est. largest front (# entries): 196
+ est. max nz in any column of L: 14
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 4846
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 763
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.84689e-01
+ maximum sum (abs (rows of A)): 8.73139e+08
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 4458 4090 92%
+ peak size (Units) 26277 8488 32%
+ final size (Units) 15717 1658 11%
+ Numeric final size (Units) 16951 2801 17%
+ Numeric final size (MBytes) 0.1 0.0 17%
+ peak memory usage (Units) 29687 11898 40%
+ peak memory usage (MBytes) 0.2 0.1 40%
+ numeric factorization flops 2.67903e+05 7.82700e+03 3%
+ nz in L (incl diagonal) 2122 838 39%
+ nz in U (incl diagonal) 9931 804 8%
+ nz in L+U (incl diagonal) 11870 1459 12%
+ largest front (# entries) 2337 420 18%
+ largest # rows in front 21 14 67%
+ largest # columns in front 136 36 26%
+
+ initial allocation ratio used: 0.265
+ # of forced updates due to frontal growth: 0
+ number of off-diagonal pivots: 3
+ nz in L (incl diagonal), if none dropped 838
+ nz in U (incl diagonal), if none dropped 804
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 183
+ min abs. value on diagonal of U: 2.30e-09
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 2.30e-09
+ indices in compressed pattern: 550
+ numerical values stored in Numeric object: 1396
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 2.73290e+04
+ iterative refinement steps taken: 1
+ iterative refinement steps attempted: 2
+ sparse backward error omega1: 2.78e-16
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 3.51560e+04
+
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+dense vector, n = 183. OK
+
+relative maxnorm of residual, ||Ax-b||/||b||: 1.55669e-16
+relative maxnorm of error, ||x-xtrue||/||xtrue||: 9.12839e-07
+
+Writing tmp/x
+Writing tmp/info.umf4
+umf4 done, strategy: 0
+
+
+===========================================================
+=== AMD ===================================================
+===========================================================
+
+
+------- Now trying the AMD ordering. This not part of
+the UMFPACK analysis or factorization, above, but a separate
+test of just the AMD ordering routine.
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+AMD ordering time: cpu 0.00 wall 0.00
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 183
+ nz, number of nonzeros in A: 1000
+ symmetry of A: 0.4431
+ number of nonzeros on diagonal: 183
+ nonzeros in pattern of A+A' (excl. diagonal): 1272
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 12692
+ # of memory compactions: 1
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 882
+ nonzeros in L (including diagonal): 1065
+ # divide operations for LDL' or LU: 882
+ # multiply-subtract operations for LDL': 3378
+ # multiply-subtract operations for LU: 5874
+ max nz. in any column of L (incl. diagonal): 15
+
+ chol flop count for real A, sqrt counted as 1 flop: 7821
+ LDL' flop count for real A: 7638
+ LDL' flop count for complex A: 34962
+ LU flop count for real A (with no pivoting): 12630
+ LU flop count for complex A (with no pivoting): 54930
+
+AMD test done
+./readhb < HB/fs_183_6.rua > tmp/A
+./readhb_size < HB/fs_183_6.rua > tmp/Asize
+./umf4
+
+===========================================================
+=== UMFPACK v5.2.0 ========================================
+===========================================================
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: int
+
+ 0: print level: 3
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+File: tmp/A
+File: tmp/Asize
+n 183 nrow 183 ncol 183 nz 1069
+triplet-form matrix, n_row = 183, n_col = 183 nz = 1069. OK
+
+triplet-to-col time: wall 0 cpu 0
+column-form matrix, n_row 183 n_col 183, nz = 1069. OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 183
+ number of columns in matrix A: 183
+ entries in matrix A: 1069
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric 2-by-2
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 29
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 4
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 154
+ symmetry of nonzero pattern: 0.446860
+ nz in S+S' (excl. diagonal): 1286
+ nz on diagonal of matrix S: 154
+ fraction of nz on diagonal: 1.000000
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 7
+ # unmatched: 7
+ symmetry of P2*S: 0.446860
+ nz in P2*S+(P2*S)' (excl. diag.): 1286
+ nz on diagonal of P2*S: 154
+ fraction of nz on diag of P2*S: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 1.78450e+04
+ est. nz in L+U (incl. diagonal): 2080
+ est. largest front (# entries): 400
+ est. max nz in any column of L: 20
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 4966
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 773
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 4742 - -
+ peak size (Units) 26357 - -
+ final size (Units) 17822 - -
+ Numeric final size (Units) 19056 - -
+ Numeric final size (MBytes) 0.1 - -
+ peak memory usage (Units) 29809 - -
+ peak memory usage (MBytes) 0.2 - -
+ numeric factorization flops 3.51312e+05 - -
+ nz in L (incl diagonal) 2633 - -
+ nz in U (incl diagonal) 10968 - -
+ nz in L+U (incl diagonal) 13418 - -
+ largest front (# entries) 3220 - -
+ largest # rows in front 25 - -
+ largest # columns in front 140 - -
+
+Symbolic object: OK
+
+Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 183
+ number of columns in matrix A: 183
+ entries in matrix A: 1069
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric 2-by-2
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 29
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 4
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 154
+ symmetry of nonzero pattern: 0.446860
+ nz in S+S' (excl. diagonal): 1286
+ nz on diagonal of matrix S: 154
+ fraction of nz on diagonal: 1.000000
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 7
+ # unmatched: 7
+ symmetry of P2*S: 0.446860
+ nz in P2*S+(P2*S)' (excl. diag.): 1286
+ nz on diagonal of P2*S: 154
+ fraction of nz on diag of P2*S: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 1.78450e+04
+ est. nz in L+U (incl. diagonal): 2080
+ est. largest front (# entries): 400
+ est. max nz in any column of L: 20
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 4966
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 773
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.84689e-01
+ maximum sum (abs (rows of A)): 8.73139e+08
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 4742 4372 92%
+ peak size (Units) 26357 11189 42%
+ final size (Units) 17822 2107 12%
+ Numeric final size (Units) 19056 3250 17%
+ Numeric final size (MBytes) 0.1 0.0 17%
+ peak memory usage (Units) 29809 14641 49%
+ peak memory usage (MBytes) 0.2 0.1 49%
+ numeric factorization flops 3.51312e+05 1.19670e+04 3%
+ nz in L (incl diagonal) 2633 1136 43%
+ nz in U (incl diagonal) 10968 870 8%
+ nz in L+U (incl diagonal) 13418 1823 14%
+ largest front (# entries) 3220 728 23%
+ largest # rows in front 25 20 80%
+ largest # columns in front 140 58 41%
+
+ initial allocation ratio used: 0.282
+ # of forced updates due to frontal growth: 1
+ number of off-diagonal pivots: 3
+ nz in L (incl diagonal), if none dropped 1136
+ nz in U (incl diagonal), if none dropped 870
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 183
+ min abs. value on diagonal of U: 2.30e-09
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 2.30e-09
+ indices in compressed pattern: 741
+ numerical values stored in Numeric object: 1781
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 1
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 3.04790e+04
+ iterative refinement steps taken: 1
+ iterative refinement steps attempted: 2
+ sparse backward error omega1: 3.97e-16
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 4.24460e+04
+
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+dense vector, n = 183. OK
+
+relative maxnorm of residual, ||Ax-b||/||b||: 1.55669e-16
+relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.0186e-06
+
+Writing tmp/x
+Writing tmp/info.umf4
+umf4 done, strategy: 0
+
+
+===========================================================
+=== AMD ===================================================
+===========================================================
+
+
+------- Now trying the AMD ordering. This not part of
+the UMFPACK analysis or factorization, above, but a separate
+test of just the AMD ordering routine.
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+AMD ordering time: cpu 0.00 wall 0.00
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 183
+ nz, number of nonzeros in A: 1069
+ symmetry of A: 0.4176
+ number of nonzeros on diagonal: 183
+ nonzeros in pattern of A+A' (excl. diagonal): 1402
+ # dense rows/columns of A+A': 0
+ memory used, in bytes: 13316
+ # of memory compactions: 1
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 1072
+ nonzeros in L (including diagonal): 1255
+ # divide operations for LDL' or LU: 1072
+ # multiply-subtract operations for LDL': 5320
+ # multiply-subtract operations for LU: 9568
+ max nz. in any column of L (incl. diagonal): 21
+
+ chol flop count for real A, sqrt counted as 1 flop: 11895
+ LDL' flop count for real A: 11712
+ LDL' flop count for complex A: 52208
+ LU flop count for real A (with no pivoting): 20208
+ LU flop count for complex A (with no pivoting): 86192
+
+AMD test done
+./readhb < HB/arc130.rua > tmp/A
+./readhb_size < HB/arc130.rua > tmp/Asize
+./umf4
+
+===========================================================
+=== UMFPACK v5.2.0 ========================================
+===========================================================
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: int
+
+ 0: print level: 3
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+File: tmp/A
+File: tmp/Asize
+n 130 nrow 130 ncol 130 nz 1282
+triplet-form matrix, n_row = 130, n_col = 130 nz = 1282. OK
+
+triplet-to-col time: wall 0 cpu 0
+column-form matrix, n_row 130 n_col 130, nz = 1282. OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 130
+ number of columns in matrix A: 130
+ entries in matrix A: 1282
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 6
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 7
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 124
+ symmetry of nonzero pattern: 0.841193
+ nz in S+S' (excl. diagonal): 1204
+ nz on diagonal of matrix S: 124
+ fraction of nz on diagonal: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 8.27000e+03
+ est. nz in L+U (incl. diagonal): 1336
+ est. largest front (# entries): 324
+ est. max nz in any column of L: 18
+ number of "dense" rows/columns in S+S': 2
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 4766
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 644
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 4729 - -
+ peak size (Units) 25036 - -
+ final size (Units) 12837 - -
+ Numeric final size (Units) 13731 - -
+ Numeric final size (MBytes) 0.1 - -
+ peak memory usage (Units) 27695 - -
+ peak memory usage (MBytes) 0.2 - -
+ numeric factorization flops 9.41610e+04 - -
+ nz in L (incl diagonal) 1009 - -
+ nz in U (incl diagonal) 7849 - -
+ nz in L+U (incl diagonal) 8728 - -
+ largest front (# entries) 2337 - -
+ largest # rows in front 19 - -
+ largest # columns in front 123 - -
+
+Symbolic object: OK
+
+Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 130
+ number of columns in matrix A: 130
+ entries in matrix A: 1282
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 6
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 7
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 124
+ symmetry of nonzero pattern: 0.841193
+ nz in S+S' (excl. diagonal): 1204
+ nz on diagonal of matrix S: 124
+ fraction of nz on diagonal: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 8.27000e+03
+ est. nz in L+U (incl. diagonal): 1336
+ est. largest front (# entries): 324
+ est. max nz in any column of L: 18
+ number of "dense" rows/columns in S+S': 2
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 4766
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 644
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 7.94859e-01
+ maximum sum (abs (rows of A)): 1.08460e+06
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 4729 4451 94%
+ peak size (Units) 25036 6477 26%
+ final size (Units) 12837 1054 8%
+ Numeric final size (Units) 13731 1883 14%
+ Numeric final size (MBytes) 0.1 0.0 14%
+ peak memory usage (Units) 27695 9136 33%
+ peak memory usage (MBytes) 0.2 0.1 33%
+ numeric factorization flops 9.41610e+04 4.20900e+03 4%
+ nz in L (incl diagonal) 1009 417 41%
+ nz in U (incl diagonal) 7849 787 10%
+ nz in L+U (incl diagonal) 8728 1074 12%
+ largest front (# entries) 2337 270 12%
+ largest # rows in front 19 18 95%
+ largest # columns in front 123 15 12%
+
+ initial allocation ratio used: 0.36
+ # of forced updates due to frontal growth: 0
+ number of off-diagonal pivots: 0
+ nz in L (incl diagonal), if none dropped 417
+ nz in U (incl diagonal), if none dropped 796
+ number of small entries dropped 9
+ nonzeros on diagonal of U: 130
+ min abs. value on diagonal of U: 9.22e-07
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 9.22e-07
+ indices in compressed pattern: 79
+ numerical values stored in Numeric object: 977
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.80440e+04
+ iterative refinement steps taken: 1
+ iterative refinement steps attempted: 1
+ sparse backward error omega1: 1.06e-16
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 2.22530e+04
+
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+dense vector, n = 130. OK
+
+relative maxnorm of residual, ||Ax-b||/||b||: 4.12105e-16
+relative maxnorm of error, ||x-xtrue||/||xtrue||: 2.15116e-10
+
+Writing tmp/x
+Writing tmp/info.umf4
+umf4 done, strategy: 0
+
+
+===========================================================
+=== AMD ===================================================
+===========================================================
+
+
+------- Now trying the AMD ordering. This not part of
+the UMFPACK analysis or factorization, above, but a separate
+test of just the AMD ordering routine.
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+AMD ordering time: cpu 0.00 wall 0.00
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 130
+ nz, number of nonzeros in A: 1282
+ symmetry of A: 0.7587
+ number of nonzeros on diagonal: 130
+ nonzeros in pattern of A+A' (excl. diagonal): 1430
+ # dense rows/columns of A+A': 2
+ memory used, in bytes: 11544
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 756
+ nonzeros in L (including diagonal): 886
+ # divide operations for LDL' or LU: 756
+ # multiply-subtract operations for LDL': 2959
+ # multiply-subtract operations for LU: 5162
+ max nz. in any column of L (incl. diagonal): 18
+
+ chol flop count for real A, sqrt counted as 1 flop: 6804
+ LDL' flop count for real A: 6674
+ LDL' flop count for complex A: 30476
+ LU flop count for real A (with no pivoting): 11080
+ LU flop count for complex A (with no pivoting): 48100
+
+AMD test done
+./readhb_nozeros < HB/arc130.rua > tmp/A
+./readhb_size < HB/arc130.rua > tmp/Asize
+./umf4
+
+===========================================================
+=== UMFPACK v5.2.0 ========================================
+===========================================================
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: int
+
+ 0: print level: 3
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+File: tmp/A
+File: tmp/Asize
+n 130 nrow 130 ncol 130 nz 1037
+triplet-form matrix, n_row = 130, n_col = 130 nz = 1037. OK
+
+triplet-to-col time: wall 0 cpu 0
+column-form matrix, n_row 130 n_col 130, nz = 1037. OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 130
+ number of columns in matrix A: 130
+ entries in matrix A: 1037
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 54
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 5
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 76
+ symmetry of nonzero pattern: 0.733224
+ nz in S+S' (excl. diagonal): 774
+ nz on diagonal of matrix S: 76
+ fraction of nz on diagonal: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 5.81700e+03
+ est. nz in L+U (incl. diagonal): 858
+ est. largest front (# entries): 289
+ est. max nz in any column of L: 17
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 4118
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 534
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 3326 - -
+ peak size (Units) 9801 - -
+ final size (Units) 4259 - -
+ Numeric final size (Units) 5153 - -
+ Numeric final size (MBytes) 0.0 - -
+ peak memory usage (Units) 12149 - -
+ peak memory usage (MBytes) 0.1 - -
+ numeric factorization flops 2.47640e+04 - -
+ nz in L (incl diagonal) 606 - -
+ nz in U (incl diagonal) 2537 - -
+ nz in L+U (incl diagonal) 3013 - -
+ largest front (# entries) 459 - -
+ largest # rows in front 17 - -
+ largest # columns in front 48 - -
+
+Symbolic object: OK
+
+Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 130
+ number of columns in matrix A: 130
+ entries in matrix A: 1037
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 54
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 5
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 76
+ symmetry of nonzero pattern: 0.733224
+ nz in S+S' (excl. diagonal): 774
+ nz on diagonal of matrix S: 76
+ fraction of nz on diagonal: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 5.81700e+03
+ est. nz in L+U (incl. diagonal): 858
+ est. largest front (# entries): 289
+ est. max nz in any column of L: 17
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 4118
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 534
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.01
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 7.94859e-01
+ maximum sum (abs (rows of A)): 1.08460e+06
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 3326 3062 92%
+ peak size (Units) 9801 6376 65%
+ final size (Units) 4259 1141 27%
+ Numeric final size (Units) 5153 1970 38%
+ Numeric final size (MBytes) 0.0 0.0 38%
+ peak memory usage (Units) 12149 8724 72%
+ peak memory usage (MBytes) 0.1 0.1 72%
+ numeric factorization flops 2.47640e+04 4.10700e+03 17%
+ nz in L (incl diagonal) 606 409 67%
+ nz in U (incl diagonal) 2537 792 31%
+ nz in L+U (incl diagonal) 3013 1071 36%
+ largest front (# entries) 459 240 52%
+ largest # rows in front 17 16 94%
+ largest # columns in front 48 15 31%
+
+ initial allocation ratio used: 0.755
+ # of forced updates due to frontal growth: 0
+ number of off-diagonal pivots: 0
+ nz in L (incl diagonal), if none dropped 409
+ nz in U (incl diagonal), if none dropped 792
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 130
+ min abs. value on diagonal of U: 9.22e-07
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 9.22e-07
+ indices in compressed pattern: 70
+ numerical values stored in Numeric object: 782
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.58270e+04
+ iterative refinement steps taken: 1
+ iterative refinement steps attempted: 1
+ sparse backward error omega1: 1.06e-16
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.99340e+04
+
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+dense vector, n = 130. OK
+
+relative maxnorm of residual, ||Ax-b||/||b||: 2.74736e-16
+relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.92322e-10
+
+Writing tmp/x
+Writing tmp/info.umf4
+umf4 done, strategy: 0
+
+
+===========================================================
+=== AMD ===================================================
+===========================================================
+
+
+------- Now trying the AMD ordering. This not part of
+the UMFPACK analysis or factorization, above, but a separate
+test of just the AMD ordering routine.
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+AMD ordering time: cpu 0.00 wall 0.00
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 130
+ nz, number of nonzeros in A: 1037
+ symmetry of A: 0.4939
+ number of nonzeros on diagonal: 130
+ nonzeros in pattern of A+A' (excl. diagonal): 1366
+ # dense rows/columns of A+A': 2
+ memory used, in bytes: 11236
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 725
+ nonzeros in L (including diagonal): 855
+ # divide operations for LDL' or LU: 725
+ # multiply-subtract operations for LDL': 2742
+ # multiply-subtract operations for LU: 4759
+ max nz. in any column of L (incl. diagonal): 18
+
+ chol flop count for real A, sqrt counted as 1 flop: 6339
+ LDL' flop count for real A: 6209
+ LDL' flop count for complex A: 28461
+ LU flop count for real A (with no pivoting): 10243
+ LU flop count for complex A (with no pivoting): 44597
+
+AMD test done
+./readhb_nozeros < HB/arc130.rua > tmp/A
+./readhb_size < HB/arc130.rua > tmp/Asize
+./umf4 a 1e-6
+
+===========================================================
+=== UMFPACK v5.2.0 ========================================
+===========================================================
+droptol 1e-06
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: int
+
+ 0: print level: 3
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 1e-06
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+File: tmp/A
+File: tmp/Asize
+n 130 nrow 130 ncol 130 nz 1037
+triplet-form matrix, n_row = 130, n_col = 130 nz = 1037. OK
+
+triplet-to-col time: wall 0 cpu 0
+column-form matrix, n_row 130 n_col 130, nz = 1037. OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 130
+ number of columns in matrix A: 130
+ entries in matrix A: 1037
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 54
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 5
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 76
+ symmetry of nonzero pattern: 0.733224
+ nz in S+S' (excl. diagonal): 774
+ nz on diagonal of matrix S: 76
+ fraction of nz on diagonal: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 5.81700e+03
+ est. nz in L+U (incl. diagonal): 858
+ est. largest front (# entries): 289
+ est. max nz in any column of L: 17
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 4118
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 534
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 3326 - -
+ peak size (Units) 9801 - -
+ final size (Units) 4259 - -
+ Numeric final size (Units) 5153 - -
+ Numeric final size (MBytes) 0.0 - -
+ peak memory usage (Units) 12149 - -
+ peak memory usage (MBytes) 0.1 - -
+ numeric factorization flops 2.47640e+04 - -
+ nz in L (incl diagonal) 606 - -
+ nz in U (incl diagonal) 2537 - -
+ nz in L+U (incl diagonal) 3013 - -
+ largest front (# entries) 459 - -
+ largest # rows in front 17 - -
+ largest # columns in front 48 - -
+
+Symbolic object: OK
+
+Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 130
+ number of columns in matrix A: 130
+ entries in matrix A: 1037
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: symmetric
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 54
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 5
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 76
+ symmetry of nonzero pattern: 0.733224
+ nz in S+S' (excl. diagonal): 774
+ nz on diagonal of matrix S: 76
+ fraction of nz on diagonal: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 5.81700e+03
+ est. nz in L+U (incl. diagonal): 858
+ est. largest front (# entries): 289
+ est. max nz in any column of L: 17
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 4118
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 534
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 7.94859e-01
+ maximum sum (abs (rows of A)): 1.08460e+06
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 3326 2762 83%
+ peak size (Units) 9801 5323 54%
+ final size (Units) 4259 457 11%
+ Numeric final size (Units) 5153 1286 25%
+ Numeric final size (MBytes) 0.0 0.0 25%
+ peak memory usage (Units) 12149 7671 63%
+ peak memory usage (MBytes) 0.1 0.1 63%
+ numeric factorization flops 2.47640e+04 4.10700e+03 17%
+ nz in L (incl diagonal) 606 318 52%
+ nz in U (incl diagonal) 2537 285 11%
+ nz in L+U (incl diagonal) 3013 473 16%
+ largest front (# entries) 459 240 52%
+ largest # rows in front 17 16 94%
+ largest # columns in front 48 15 31%
+
+ initial allocation ratio used: 0.755
+ # of forced updates due to frontal growth: 0
+ number of off-diagonal pivots: 0
+ nz in L (incl diagonal), if none dropped 409
+ nz in U (incl diagonal), if none dropped 792
+ number of small entries dropped 598
+ nonzeros on diagonal of U: 130
+ min abs. value on diagonal of U: 9.22e-07
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 9.22e-07
+ indices in compressed pattern: 82
+ numerical values stored in Numeric object: 386
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 2.06060e+04
+ iterative refinement steps taken: 2
+ iterative refinement steps attempted: 2
+ sparse backward error omega1: 1.47e-16
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 2.47130e+04
+
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+dense vector, n = 130. OK
+
+relative maxnorm of residual, ||Ax-b||/||b||: 2.74736e-16
+relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.92269e-10
+
+Writing tmp/x
+Writing tmp/info.umf4
+umf4 done, strategy: 0
+
+
+===========================================================
+=== AMD ===================================================
+===========================================================
+
+
+------- Now trying the AMD ordering. This not part of
+the UMFPACK analysis or factorization, above, but a separate
+test of just the AMD ordering routine.
+
+AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
+ dense row parameter: 10
+ (rows with more than max (10 * sqrt (n), 16) entries are
+ considered "dense", and placed last in output permutation)
+ aggressive absorption: yes
+ size of AMD integer: 4
+
+AMD ordering time: cpu 0.00 wall 0.00
+
+AMD version 2.2.0, May 31, 2007, results:
+ status: OK
+ n, dimension of A: 130
+ nz, number of nonzeros in A: 1037
+ symmetry of A: 0.4939
+ number of nonzeros on diagonal: 130
+ nonzeros in pattern of A+A' (excl. diagonal): 1366
+ # dense rows/columns of A+A': 2
+ memory used, in bytes: 11236
+ # of memory compactions: 0
+
+ The following approximate statistics are for a subsequent
+ factorization of A(P,P) + A(P,P)'. They are slight upper
+ bounds if there are no dense rows/columns in A+A', and become
+ looser if dense rows/columns exist.
+
+ nonzeros in L (excluding diagonal): 725
+ nonzeros in L (including diagonal): 855
+ # divide operations for LDL' or LU: 725
+ # multiply-subtract operations for LDL': 2742
+ # multiply-subtract operations for LU: 4759
+ max nz. in any column of L (incl. diagonal): 18
+
+ chol flop count for real A, sqrt counted as 1 flop: 6339
+ LDL' flop count for real A: 6209
+ LDL' flop count for complex A: 28461
+ LU flop count for real A (with no pivoting): 10243
+ LU flop count for complex A (with no pivoting): 44597
+
+AMD test done
diff --git a/UMFPACK/Demo/umf4_f77wrapper.c b/UMFPACK/Demo/umf4_f77wrapper.c
new file mode 100644
index 0000000..f08d0b3
--- /dev/null
+++ b/UMFPACK/Demo/umf4_f77wrapper.c
@@ -0,0 +1,507 @@
+/* ========================================================================== */
+/* === umf4_f77wrapper ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* FORTRAN interface for the C-callable UMFPACK library (double / int version
+ * only and double / UF_long versions only). This is HIGHLY non-portable. You
+ * will need to modify this depending on how your FORTRAN and C compilers
+ * behave. This has been tested in Linux, Sun Solaris, SGI IRIX, and IBM AIX,
+ * with various compilers. It has not been exhaustively tested on all possible
+ * combinations of C and FORTRAN compilers. The UF_long version works on
+ * Solaris, SGI IRIX, and IBM AIX when the UMFPACK library is compiled in
+ * 64-bit mode.
+ *
+ * Only a subset of UMFPACK's capabilities are provided. Refer to the UMFPACK
+ * User Guide for details.
+ *
+ * For some C and FORTRAN compilers, the FORTRAN compiler appends a single
+ * underscore ("_") after each routine name. C doesn't do this, so the
+ * translation is made here. Other FORTRAN compilers treat underscores
+ * differently. For example, a FORTRAN call to a_b gets translated to a call
+ * to a_b__ by g77, and to a_b_ by most other FORTRAN compilers. Thus, the
+ * FORTRAN names here do not use underscores. The xlf compiler in IBM AIX
+ * doesn't add an underscore.
+ *
+ * The matrix A is passed to UMFPACK in compressed column form, with 0-based
+ * indices. In FORTRAN, for an m-by-n matrix A with nz entries, the row
+ * indices of the first column (column 1) are in Ai (Ap (1) + 1 ... Ap (2)),
+ * with values in Ax (Ap (1) + 1 ... Ap (2)). The last column (column n) is
+ * in Ai (Ap (n) + 1 ... Ap (n+1)) and Ax (Ap (n) + 1 ... Ap (n+1)). The row
+ * indices in Ai are in the range 0 to m-1. They must be sorted, with no
+ * duplicate entries allowed. Refer to umfpack_di_triplet_to_col for a more
+ * flexible format for the input matrix. The following defintions apply
+ * for each of the routines in this file:
+ *
+ * integer m, n, Ap (n+1), Ai (nz), symbolic, numeric, filenum, status
+ * double precision Ax (nz), control (20), info (90), x (n), b (n)
+ *
+ * UMFPACK's status is returned in either a status argument, or in info (1).
+ * It is zero if everything is OK, 1 if the matrix is singular (this is a
+ * warning, not an error), and negative if an error occurred. See umfpack.h
+ * for more details on the contents of the control and info arrays, and the
+ * value of the sys argument.
+ *
+ * For the Numeric and Symbolic handles, it's probably safe to assume that a
+ * FORTRAN integer is sufficient to store a C pointer. If that doesn't work,
+ * try defining numeric and symbolic as integer arrays of size 2, or as
+ * integer*8, in the FORTRAN routine that calls these wrapper routines.
+ * The latter is required on Solaris, SGI IRIX, and IBM AIX when UMFPACK is
+ * compiled in 64-bit mode.
+ *
+ * If you want to use 64-bit integers, try compiling this file with the -DDLONG
+ * compiler option (via "make fortran64"). First modify your UFconfig.mk
+ * file to compile UMFPACK in LP64 mode (see the User Guide for details).
+ * Your FORTRAN code should use integer*8. See umf4hb64.f for an example.
+ *
+ * Tested with the following compilers:
+ * * Solaris with cc and f77 from Sun WorkShop 6 update 1
+ * (32-bit and 64-bit modes)
+ * * SGI Irix with MIPSpro cc and f77 compilers version 7.4
+ * (32-bit and 64-bit modes)
+ * * Linux with GNU gcc and Intel's icc, and GNU g77 and Intel's
+ * ifc FORTRAN compiler. See the comments above about g77 and
+ * underscores. Only supports 32-bit mode.
+ * * IBM AIX xlc and xlf compilers.
+ * (32-bit and 64-bit modes)
+ *
+ * This interface files when using the ABSOFT Fortran compiler on both
+ * Linux and Windows. There is no known fix.
+ */
+
+#include "umfpack.h"
+#include <ctype.h>
+#include <stdio.h>
+#ifdef NULL
+#undef NULL
+#endif
+#define NULL 0
+#define LEN 200
+
+/* -------------------------------------------------------------------------- */
+/* integer type: int or UF_long */
+/* -------------------------------------------------------------------------- */
+
+#if defined (DLONG)
+
+#define Int UF_long
+#define UMFPACK_defaults umfpack_dl_defaults
+#define UMFPACK_free_numeric umfpack_dl_free_numeric
+#define UMFPACK_free_symbolic umfpack_dl_free_symbolic
+#define UMFPACK_numeric umfpack_dl_numeric
+#define UMFPACK_report_control umfpack_dl_report_control
+#define UMFPACK_report_info umfpack_dl_report_info
+#define UMFPACK_save_numeric umfpack_dl_save_numeric
+#define UMFPACK_save_symbolic umfpack_dl_save_symbolic
+#define UMFPACK_load_numeric umfpack_dl_load_numeric
+#define UMFPACK_load_symbolic umfpack_dl_load_symbolic
+#define UMFPACK_scale umfpack_dl_scale
+#define UMFPACK_solve umfpack_dl_solve
+#define UMFPACK_symbolic umfpack_dl_symbolic
+
+#else
+
+#define Int int
+#define UMFPACK_defaults umfpack_di_defaults
+#define UMFPACK_free_numeric umfpack_di_free_numeric
+#define UMFPACK_free_symbolic umfpack_di_free_symbolic
+#define UMFPACK_numeric umfpack_di_numeric
+#define UMFPACK_report_control umfpack_di_report_control
+#define UMFPACK_report_info umfpack_di_report_info
+#define UMFPACK_save_numeric umfpack_di_save_numeric
+#define UMFPACK_save_symbolic umfpack_di_save_symbolic
+#define UMFPACK_load_numeric umfpack_di_load_numeric
+#define UMFPACK_load_symbolic umfpack_di_load_symbolic
+#define UMFPACK_scale umfpack_di_scale
+#define UMFPACK_solve umfpack_di_solve
+#define UMFPACK_symbolic umfpack_di_symbolic
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* construct a file name from a file number (not user-callable) */
+/* -------------------------------------------------------------------------- */
+
+static void make_filename (Int filenum, char *prefix, char *filename)
+{
+ char *psrc, *pdst ;
+#ifdef DLONG
+ sprintf (filename, "%s%ld.umf", prefix, filenum) ;
+#else
+ sprintf (filename, "%s%d.umf", prefix, filenum) ;
+#endif
+ /* remove any spaces in the filename */
+ pdst = filename ;
+ for (psrc = filename ; *psrc ; psrc++)
+ {
+ if (!isspace (*psrc)) *pdst++ = *psrc ;
+ }
+ *pdst = '\0' ;
+}
+
+/* ========================================================================== */
+/* === with underscore ====================================================== */
+/* ========================================================================== */
+
+/* Solaris, Linux, and SGI IRIX. Probably Compaq Alpha as well. */
+
+/* -------------------------------------------------------------------------- */
+/* umf4def: set default control parameters */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4def (control) */
+
+void umf4def_ (double Control [UMFPACK_CONTROL])
+{
+ UMFPACK_defaults (Control) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4pcon: print control parameters */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4pcon (control) */
+
+void umf4pcon_ (double Control [UMFPACK_CONTROL])
+{
+ fflush (stdout) ;
+ UMFPACK_report_control (Control) ;
+ fflush (stdout) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4sym: pre-ordering and symbolic factorization */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4sym (m, n, Ap, Ai, Ax, symbolic, control, info) */
+
+void umf4sym_ (Int *m, Int *n, Int Ap [ ], Int Ai [ ],
+ double Ax [ ], void **Symbolic,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_symbolic (*m, *n, Ap, Ai, Ax, Symbolic, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4num: numeric factorization */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) */
+
+void umf4num_ (Int Ap [ ], Int Ai [ ], double Ax [ ],
+ void **Symbolic, void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_numeric (Ap, Ai, Ax, *Symbolic, Numeric, Control, Info);
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4solr: solve a linear system with iterative refinement */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info) */
+
+void umf4solr_ (Int *sys, Int Ap [ ], Int Ai [ ], double Ax [ ],
+ double x [ ], double b [ ], void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_solve (*sys, Ap, Ai, Ax, x, b, *Numeric, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4sol: solve a linear system without iterative refinement */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4sol (sys, x, b, numeric, control, info) */
+
+void umf4sol_ (Int *sys, double x [ ], double b [ ], void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ Control [UMFPACK_IRSTEP] = 0 ;
+ (void) UMFPACK_solve (*sys, (Int *) NULL, (Int *) NULL, (double *) NULL,
+ x, b, *Numeric, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4scal: scale a vector using UMFPACK's scale factors */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4scal (x, b, numeric, status) */
+
+void umf4scal_ (double x [ ], double b [ ], void **Numeric, Int *status)
+{
+ *status = UMFPACK_scale (x, b, *Numeric) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4pinf: print info */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4pinf (control) */
+
+void umf4pinf_ (double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ fflush (stdout) ;
+ UMFPACK_report_info (Control, Info) ;
+ fflush (stdout) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4fnum: free the Numeric object */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4fnum (numeric) */
+
+void umf4fnum_ (void **Numeric)
+{
+ UMFPACK_free_numeric (Numeric) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4fsym: free the Symbolic object */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4fsym (symbolic) */
+
+void umf4fsym_ (void **Symbolic)
+{
+ UMFPACK_free_symbolic (Symbolic) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4snum: save the Numeric object to a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4snum (numeric, filenum, status) */
+
+void umf4snum_ (void **Numeric, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "n", filename) ;
+ *status = UMFPACK_save_numeric (*Numeric, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4ssym: save the Symbolic object to a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4ssym (symbolic, filenum, status) */
+
+void umf4ssym_ (void **Symbolic, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "s", filename) ;
+ *status = UMFPACK_save_symbolic (*Symbolic, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4lnum: load the Numeric object from a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4lnum (numeric, filenum, status) */
+
+void umf4lnum_ (void **Numeric, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "n", filename) ;
+ *status = UMFPACK_load_numeric (Numeric, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4lsym: load the Symbolic object from a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4lsym (symbolic, filenum, status) */
+
+void umf4lsym_ (void **Symbolic, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "s", filename) ;
+ *status = UMFPACK_load_symbolic (Symbolic, filename) ;
+}
+
+/* ========================================================================== */
+/* === with no underscore =================================================== */
+/* ========================================================================== */
+
+/* IBM AIX. Probably Microsoft Windows and HP Unix as well. */
+
+/* -------------------------------------------------------------------------- */
+/* umf4def: set default control parameters */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4def (control) */
+
+void umf4def (double Control [UMFPACK_CONTROL])
+{
+ UMFPACK_defaults (Control) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4pcon: print control parameters */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4pcon (control) */
+
+void umf4pcon (double Control [UMFPACK_CONTROL])
+{
+ fflush (stdout) ;
+ UMFPACK_report_control (Control) ;
+ fflush (stdout) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4sym: pre-ordering and symbolic factorization */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4sym (m, n, Ap, Ai, Ax, symbolic, control, info) */
+
+void umf4sym (Int *m, Int *n, Int Ap [ ], Int Ai [ ],
+ double Ax [ ], void **Symbolic,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_symbolic (*m, *n, Ap, Ai, Ax, Symbolic, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4num: numeric factorization */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info) */
+
+void umf4num (Int Ap [ ], Int Ai [ ], double Ax [ ],
+ void **Symbolic, void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_numeric (Ap, Ai, Ax, *Symbolic, Numeric, Control, Info);
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4solr: solve a linear system with iterative refinement */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info) */
+
+void umf4solr (Int *sys, Int Ap [ ], Int Ai [ ], double Ax [ ],
+ double x [ ], double b [ ], void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_solve (*sys, Ap, Ai, Ax, x, b, *Numeric, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4sol: solve a linear system without iterative refinement */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4sol (sys, x, b, numeric, control, info) */
+
+void umf4sol (Int *sys, double x [ ], double b [ ], void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ Control [UMFPACK_IRSTEP] = 0 ;
+ (void) UMFPACK_solve (*sys, (Int *) NULL, (Int *) NULL, (double *) NULL,
+ x, b, *Numeric, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4scal: scale a vector using UMFPACK's scale factors */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4scal (x, b, numeric, status) */
+
+void umf4scal (double x [ ], double b [ ], void **Numeric, Int *status)
+{
+ *status = UMFPACK_scale (x, b, *Numeric) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4pinf: print info */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4pinf (control) */
+
+void umf4pinf (double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ fflush (stdout) ;
+ UMFPACK_report_info (Control, Info) ;
+ fflush (stdout) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4fnum: free the Numeric object */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4fnum (numeric) */
+
+void umf4fnum (void **Numeric)
+{
+ UMFPACK_free_numeric (Numeric) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4fsym: free the Symbolic object */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4fsym (symbolic) */
+
+void umf4fsym (void **Symbolic)
+{
+ UMFPACK_free_symbolic (Symbolic) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4snum: save the Numeric object to a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4snum (numeric, filenum, status) */
+
+void umf4snum (void **Numeric, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "n", filename) ;
+ *status = UMFPACK_save_numeric (*Numeric, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4ssym: save the Symbolic object to a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4ssym (symbolic, filenum, status) */
+
+void umf4ssym (void **Symbolic, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "s", filename) ;
+ *status = UMFPACK_save_symbolic (*Symbolic, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4lnum: load the Numeric object from a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4lnum (numeric, filenum, status) */
+
+void umf4lnum (void **Numeric, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "n", filename) ;
+ *status = UMFPACK_load_numeric (Numeric, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4lsym: load the Symbolic object from a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4lsym (symbolic, filenum, status) */
+
+void umf4lsym (void **Symbolic, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "s", filename) ;
+ *status = UMFPACK_load_symbolic (Symbolic, filename) ;
+}
diff --git a/UMFPACK/Demo/umf4_f77zwrapper.c b/UMFPACK/Demo/umf4_f77zwrapper.c
new file mode 100644
index 0000000..5fb1535
--- /dev/null
+++ b/UMFPACK/Demo/umf4_f77zwrapper.c
@@ -0,0 +1,462 @@
+/* ========================================================================== */
+/* === umf4_f77zwrapper ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* FORTRAN interface for the C-callable UMFPACK library (complex / int version
+ * only and complex / UF_long versions only). This is HIGHLY non-portable. You
+ * will need to modify this depending on how your FORTRAN and C compilers
+ * behave.
+ *
+ * See umf4z_f77wrapper.c for more information.
+ *
+ * The complex values are provided in two separate arrays. Ax contains the
+ * real part and Az contains the imaginary part. The solution vector is in
+ * x (the real part) and xz (the imaginary part. b is the real part of the
+ * right-hand-side and bz is the imaginary part. Does not support the
+ * packed complex type.
+ */
+
+#include "umfpack.h"
+#include <ctype.h>
+#include <stdio.h>
+#ifdef NULL
+#undef NULL
+#endif
+#define NULL 0
+#define LEN 200
+
+/* -------------------------------------------------------------------------- */
+/* integer type: int or UF_long */
+/* -------------------------------------------------------------------------- */
+
+#if defined (ZLONG)
+
+#define Int UF_long
+#define UMFPACK_defaults umfpack_zl_defaults
+#define UMFPACK_free_numeric umfpack_zl_free_numeric
+#define UMFPACK_free_symbolic umfpack_zl_free_symbolic
+#define UMFPACK_numeric umfpack_zl_numeric
+#define UMFPACK_report_control umfpack_zl_report_control
+#define UMFPACK_report_info umfpack_zl_report_info
+#define UMFPACK_save_numeric umfpack_zl_save_numeric
+#define UMFPACK_save_symbolic umfpack_zl_save_symbolic
+#define UMFPACK_load_numeric umfpack_zl_load_numeric
+#define UMFPACK_load_symbolic umfpack_zl_load_symbolic
+#define UMFPACK_scale umfpack_zl_scale
+#define UMFPACK_solve umfpack_zl_solve
+#define UMFPACK_symbolic umfpack_zl_symbolic
+
+#else
+
+#define Int int
+#define UMFPACK_defaults umfpack_zi_defaults
+#define UMFPACK_free_numeric umfpack_zi_free_numeric
+#define UMFPACK_free_symbolic umfpack_zi_free_symbolic
+#define UMFPACK_numeric umfpack_zi_numeric
+#define UMFPACK_report_control umfpack_zi_report_control
+#define UMFPACK_report_info umfpack_zi_report_info
+#define UMFPACK_save_numeric umfpack_zi_save_numeric
+#define UMFPACK_save_symbolic umfpack_zi_save_symbolic
+#define UMFPACK_load_numeric umfpack_zi_load_numeric
+#define UMFPACK_load_symbolic umfpack_zi_load_symbolic
+#define UMFPACK_scale umfpack_zi_scale
+#define UMFPACK_solve umfpack_zi_solve
+#define UMFPACK_symbolic umfpack_zi_symbolic
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* construct a file name from a file number (not user-callable) */
+/* -------------------------------------------------------------------------- */
+
+static void make_filename (Int filenum, char *prefix, char *filename)
+{
+ char *psrc, *pdst ;
+#ifdef ZLONG
+ sprintf (filename, "%s%ld.umf", prefix, filenum) ;
+#else
+ sprintf (filename, "%s%d.umf", prefix, filenum) ;
+#endif
+ /* remove any spaces in the filename */
+ pdst = filename ;
+ for (psrc = filename ; *psrc ; psrc++)
+ {
+ if (!isspace (*psrc)) *pdst++ = *psrc ;
+ }
+ *pdst = '\0' ;
+}
+
+/* ========================================================================== */
+/* === with underscore ====================================================== */
+/* ========================================================================== */
+
+/* Solaris, Linux, and SGI IRIX. Probably Compaq Alpha as well. */
+
+/* -------------------------------------------------------------------------- */
+/* umf4zdef: set default control parameters */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zdef (control) */
+
+void umf4zdef_ (double Control [UMFPACK_CONTROL])
+{
+ UMFPACK_defaults (Control) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zpcon: print control parameters */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zpcon (control) */
+
+void umf4zpcon_ (double Control [UMFPACK_CONTROL])
+{
+ fflush (stdout) ;
+ UMFPACK_report_control (Control) ;
+ fflush (stdout) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zsym: pre-ordering and symbolic factorization */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zsym (m, n, Ap, Ai, Ax, Az, symbolic, control, info) */
+
+void umf4zsym_ (Int *m, Int *n, Int Ap [ ], Int Ai [ ],
+ double Ax [ ], double Az [ ], void **Symbolic,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_symbolic (*m, *n, Ap, Ai, Ax, Az, Symbolic, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4znum: numeric factorization */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4znum (Ap, Ai, Ax, Az, symbolic, numeric, control, info) */
+
+void umf4znum_ (Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ],
+ void **Symbolic, void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_numeric (Ap, Ai, Ax, Az, *Symbolic, Numeric, Control, Info);
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zsolr: solve a linear system with iterative refinement */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zsolr (sys, Ap, Ai, Ax, Az, x, xz, b, bz, numeric, control, info) */
+
+void umf4zsolr_ (Int *sys, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ],
+ double x [ ], double xz [ ], double b [ ], double bz [ ], void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_solve (*sys, Ap, Ai, Ax, Az, x, xz, b, bz,
+ *Numeric, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zsol: solve a linear system without iterative refinement */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zsol (sys, x, xz, b, bz, numeric, control, info) */
+
+void umf4zsol_ (Int *sys, double x [ ], double xz [ ], double b [ ],
+ double bz [ ], void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ Control [UMFPACK_IRSTEP] = 0 ;
+ (void) UMFPACK_solve (*sys, (Int *) NULL, (Int *) NULL, (double *) NULL,
+ (double *) NULL, x, xz, b, bz, *Numeric, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zscal: scale a vector using UMFPACK's scale factors */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zscal (x, xz, b, bz, numeric, status) */
+
+void umf4zscal_ (double x [ ], double xz [ ], double b [ ], double bz [ ],
+ void **Numeric, Int *status)
+{
+ *status = UMFPACK_scale (x, xz, b, bz, *Numeric) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zpinf: print info */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zpinf (control) */
+
+void umf4zpinf_ (double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ fflush (stdout) ;
+ UMFPACK_report_info (Control, Info) ;
+ fflush (stdout) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zfnum: free the Numeric object */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zfnum (numeric) */
+
+void umf4zfnum_ (void **Numeric)
+{
+ UMFPACK_free_numeric (Numeric) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zfsym: free the Symbolic object */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zfsym (symbolic) */
+
+void umf4zfsym_ (void **Symbolic)
+{
+ UMFPACK_free_symbolic (Symbolic) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zsnum: save the Numeric object to a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zsnum (numeric, filenum, status) */
+
+void umf4zsnum_ (void **Numeric, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "n", filename) ;
+ *status = UMFPACK_save_numeric (*Numeric, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zssym: save the Symbolic object to a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zssym (symbolic, filenum, status) */
+
+void umf4zssym_ (void **Symbolic, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "s", filename) ;
+ *status = UMFPACK_save_symbolic (*Symbolic, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zlnum: load the Numeric object from a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zlnum (numeric, filenum, status) */
+
+void umf4zlnum_ (void **Numeric, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "n", filename) ;
+ *status = UMFPACK_load_numeric (Numeric, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zlsym: load the Symbolic object from a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zlsym (symbolic, filenum, status) */
+
+void umf4zlsym_ (void **Symbolic, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "s", filename) ;
+ *status = UMFPACK_load_symbolic (Symbolic, filename) ;
+}
+
+/* ========================================================================== */
+/* === with no underscore =================================================== */
+/* ========================================================================== */
+
+/* IBM AIX. Probably Microsoft Windows and HP Unix as well. */
+
+/* -------------------------------------------------------------------------- */
+/* umf4zdef: set default control parameters */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zdef (control) */
+
+void umf4zdef (double Control [UMFPACK_CONTROL])
+{
+ UMFPACK_defaults (Control) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zpcon: print control parameters */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zpcon (control) */
+
+void umf4zpcon (double Control [UMFPACK_CONTROL])
+{
+ fflush (stdout) ;
+ UMFPACK_report_control (Control) ;
+ fflush (stdout) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zsym: pre-ordering and symbolic factorization */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zsym (m, n, Ap, Ai, Ax, Az, symbolic, control, info) */
+
+void umf4zsym (Int *m, Int *n, Int Ap [ ], Int Ai [ ],
+ double Ax [ ], double Az [ ], void **Symbolic,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_symbolic (*m, *n, Ap, Ai, Ax, Az, Symbolic, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4znum: numeric factorization */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4znum (Ap, Ai, Ax, Az, symbolic, numeric, control, info) */
+
+void umf4znum (Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ],
+ void **Symbolic, void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_numeric (Ap, Ai, Ax, Az, *Symbolic, Numeric, Control, Info);
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zsolr: solve a linear system with iterative refinement */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zsolr (sys, Ap, Ai, Ax, Az, x, xz, b, bz, numeric, control, info) */
+
+void umf4zsolr (Int *sys, Int Ap [ ], Int Ai [ ], double Ax [ ], double Az [ ],
+ double x [ ], double xz [ ], double b [ ], double bz [ ], void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ (void) UMFPACK_solve (*sys, Ap, Ai, Ax, Az, x, xz, b, bz,
+ *Numeric, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zsol: solve a linear system without iterative refinement */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zsol (sys, x, xz, b, bz, numeric, control, info) */
+
+void umf4zsol (Int *sys, double x [ ], double xz [ ], double b [ ],
+ double bz [ ], void **Numeric,
+ double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ Control [UMFPACK_IRSTEP] = 0 ;
+ (void) UMFPACK_solve (*sys, (Int *) NULL, (Int *) NULL, (double *) NULL,
+ (double *) NULL, x, xz, b, bz, *Numeric, Control, Info) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zscal: scale a vector using UMFPACK's scale factors */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zscal (x, xz, b, bz, numeric, status) */
+
+void umf4zscal (double x [ ], double xz [ ], double b [ ], double bz [ ],
+ void **Numeric, Int *status)
+{
+ *status = UMFPACK_scale (x, xz, b, bz, *Numeric) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zpinf: print info */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zpinf (control) */
+
+void umf4zpinf (double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ fflush (stdout) ;
+ UMFPACK_report_info (Control, Info) ;
+ fflush (stdout) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zfnum: free the Numeric object */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zfnum (numeric) */
+
+void umf4zfnum (void **Numeric)
+{
+ UMFPACK_free_numeric (Numeric) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zfsym: free the Symbolic object */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zfsym (symbolic) */
+
+void umf4zfsym (void **Symbolic)
+{
+ UMFPACK_free_symbolic (Symbolic) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zsnum: save the Numeric object to a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zsnum (numeric, filenum, status) */
+
+void umf4zsnum (void **Numeric, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "n", filename) ;
+ *status = UMFPACK_save_numeric (*Numeric, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zssym: save the Symbolic object to a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zssym (symbolic, filenum, status) */
+
+void umf4zssym (void **Symbolic, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "s", filename) ;
+ *status = UMFPACK_save_symbolic (*Symbolic, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zlnum: load the Numeric object from a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zlnum (numeric, filenum, status) */
+
+void umf4zlnum (void **Numeric, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "n", filename) ;
+ *status = UMFPACK_load_numeric (Numeric, filename) ;
+}
+
+/* -------------------------------------------------------------------------- */
+/* umf4zlsym: load the Symbolic object from a file */
+/* -------------------------------------------------------------------------- */
+
+/* call umf4zlsym (symbolic, filenum, status) */
+
+void umf4zlsym (void **Symbolic, Int *filenum, Int *status)
+{
+ char filename [LEN] ;
+ make_filename (*filenum, "s", filename) ;
+ *status = UMFPACK_load_symbolic (Symbolic, filename) ;
+}
+
diff --git a/UMFPACK/Demo/umf4hb.f b/UMFPACK/Demo/umf4hb.f
new file mode 100644
index 0000000..263ed8e
--- /dev/null
+++ b/UMFPACK/Demo/umf4hb.f
@@ -0,0 +1,353 @@
+c=======================================================================
+c== umf4hb =============================================================
+c=======================================================================
+
+c-----------------------------------------------------------------------
+c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE
+c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for
+c License. web: http://www.cise.ufl.edu/research/sparse/umfpack
+c-----------------------------------------------------------------------
+
+c umf4hb:
+c read a sparse matrix in the Harwell/Boeing format, factorizes
+c it, and solves Ax=b. Also saves and loads the factors to/from a
+c file. Saving to a file is not required, it's just here to
+c demonstrate how to use this feature of UMFPACK. This program
+c only works on square RUA-type matrices.
+c
+c This is HIGHLY non-portable. It may not work with your C and
+c FORTRAN compilers. See umf4_f77wrapper.c for more details.
+c
+c usage (for example):
+c
+c in a Unix shell:
+c umf4hb < HB/arc130.rua
+
+ integer
+ $ nzmax, nmax
+ parameter (nzmax = 5000000, nmax = 160000)
+ integer
+ $ Ap (nmax), Ai (nzmax), n, nz, totcrd, ptrcrd, i, j, p,
+ $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, nzrhs, nel,
+ $ numeric, symbolic, status, sys, filenum
+
+ character title*72, key*30, type*3, ptrfmt*16,
+ $ indfmt*16, valfmt*20, rhsfmt*20
+ double precision Ax (nzmax), x (nmax), b (nmax), aij, xj,
+ $ r (nmax), control (20), info (90)
+ character rhstyp*3
+
+c ----------------------------------------------------------------
+c read the Harwell/Boeing matrix
+c ----------------------------------------------------------------
+
+ read (5, 10, err = 998)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd, rhscrd,
+ $ type, nrow, ncol, nz, nel,
+ $ ptrfmt, indfmt, valfmt, rhsfmt
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+ read (5, 20, err = 998) rhstyp, nrhs, nzrhs
+ endif
+10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+20 format (a3, 11x, 2i14)
+
+ print *, 'Matrix key: ', key
+
+ n = nrow
+ if (type .ne. 'RUA' .or. nrow .ne. ncol) then
+ print *, 'Error: can only handle square RUA matrices'
+ stop
+ endif
+ if (n .ge. nmax .or. nz .gt. nzmax) then
+ print *, ' Matrix too big!'
+ stop
+ endif
+
+c read the matrix (1-based)
+ read (5, ptrfmt, err = 998) (Ap (p), p = 1, ncol+1)
+ read (5, indfmt, err = 998) (Ai (p), p = 1, nz)
+ read (5, valfmt, err = 998) (Ax (p), p = 1, nz)
+
+c ----------------------------------------------------------------
+c create the right-hand-side, assume x (i) = 1 + i/n
+c ----------------------------------------------------------------
+
+ do 30 i = 1,n
+ b (i) = 0
+30 continue
+c b = A*x
+ do 50 j = 1,n
+ xj = j
+ xj = 1 + xj / n
+ do 40 p = Ap (j), Ap (j+1)-1
+ i = Ai (p)
+ aij = Ax (p)
+ b (i) = b (i) + aij * xj
+40 continue
+50 continue
+
+c ----------------------------------------------------------------
+c convert from 1-based to 0-based
+c ----------------------------------------------------------------
+
+ do 60 j = 1, n+1
+ Ap (j) = Ap (j) - 1
+60 continue
+ do 70 p = 1, nz
+ Ai (p) = Ai (p) - 1
+70 continue
+
+c ----------------------------------------------------------------
+c factor the matrix and save to a file
+c ----------------------------------------------------------------
+
+c set default parameters
+ call umf4def (control)
+
+c print control parameters. set control (1) to 1 to print
+c error messages only
+ control (1) = 2
+ call umf4pcon (control)
+
+c pre-order and symbolic analysis
+ call umf4sym (n, n, Ap, Ai, Ax, symbolic, control, info)
+
+c print statistics computed so far
+c call umf4pinf (control, info) could also be done.
+ print 80, info (1), info (16),
+ $ (info (21) * info (4)) / 2**20,
+ $ (info (22) * info (4)) / 2**20,
+ $ info (23), info (24), info (25)
+80 format ('symbolic analysis:',/,
+ $ ' status: ', f5.0, /,
+ $ ' time: ', e10.2, ' (sec)'/,
+ $ ' estimates (upper bound) for numeric LU:', /,
+ $ ' size of LU: ', f10.2, ' (MB)', /,
+ $ ' memory needed: ', f10.2, ' (MB)', /,
+ $ ' flop count: ', e10.2, /
+ $ ' nnz (L): ', f10.0, /
+ $ ' nnz (U): ', f10.0)
+
+c check umf4sym error condition
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4sym: ', info (1)
+ stop
+ endif
+
+c numeric factorization
+ call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info)
+
+c print statistics for the numeric factorization
+c call umf4pinf (control, info) could also be done.
+ print 90, info (1), info (66),
+ $ (info (41) * info (4)) / 2**20,
+ $ (info (42) * info (4)) / 2**20,
+ $ info (43), info (44), info (45)
+90 format ('numeric factorization:',/,
+ $ ' status: ', f5.0, /,
+ $ ' time: ', e10.2, /,
+ $ ' actual numeric LU statistics:', /,
+ $ ' size of LU: ', f10.2, ' (MB)', /,
+ $ ' memory needed: ', f10.2, ' (MB)', /,
+ $ ' flop count: ', e10.2, /
+ $ ' nnz (L): ', f10.0, /
+ $ ' nnz (U): ', f10.0)
+
+c check umf4num error condition
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4num: ', info (1)
+ stop
+ endif
+
+c save the symbolic analysis to the file s0.umf
+c note that this is not needed until another matrix is
+c factorized, below.
+ filenum = 0
+ call umf4ssym (symbolic, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4ssym: ', status
+ stop
+ endif
+
+c save the LU factors to the file n0.umf
+ call umf4snum (numeric, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4snum: ', status
+ stop
+ endif
+
+c free the symbolic analysis
+ call umf4fsym (symbolic)
+
+c free the numeric factorization
+ call umf4fnum (numeric)
+
+c No LU factors (symbolic or numeric) are in memory at this point.
+
+c ----------------------------------------------------------------
+c load the LU factors back in, and solve the system
+c ----------------------------------------------------------------
+
+c At this point the program could terminate and load the LU
+C factors (numeric) from the n0.umf file, and solve the
+c system (see below). Note that the symbolic object is not
+c required.
+
+c load the numeric factorization back in (filename: n0.umf)
+ call umf4lnum (numeric, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4lnum: ', status
+ stop
+ endif
+
+c solve Ax=b, without iterative refinement
+ sys = 0
+ call umf4sol (sys, x, b, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4sol: ', info (1)
+ stop
+ endif
+
+c free the numeric factorization
+ call umf4fnum (numeric)
+
+c No LU factors (symbolic or numeric) are in memory at this point.
+
+c print final statistics
+ call umf4pinf (control, info)
+
+c print the residual. x (i) should be 1 + i/n
+ call resid (n, nz, Ap, Ai, Ax, x, b, r)
+
+c ----------------------------------------------------------------
+c load the symbolic analysis back in, and factorize a new matrix
+c ----------------------------------------------------------------
+
+c Again, the program could terminate here, recreate the matrix,
+c and refactorize. Note that umf4sym is not called.
+
+c load the symbolic factorization back in (filename: s0.umf)
+ call umf4lsym (symbolic, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4lsym: ', status
+ stop
+ endif
+
+c arbitrarily change the values of the matrix but not the pattern
+ do 100 p = 1, nz
+ Ax (p) = Ax (p) + 3.14159 / 100.0
+100 continue
+
+c numeric factorization of the modified matrix
+ call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4num: ', info (1)
+ stop
+ endif
+
+c free the symbolic analysis
+ call umf4fsym (symbolic)
+
+c create a new right-hand-side, assume x (i) = 7 - i/n
+ do 110 i = 1,n
+ b (i) = 0
+110 continue
+c b = A*x, with the modified matrix A (note that A is now 0-based)
+ do 130 j = 1,n
+ xj = j
+ xj = 7 - xj / n
+ do 120 p = Ap (j) + 1, Ap (j+1)
+ i = Ai (p) + 1
+ aij = Ax (p)
+ b (i) = b (i) + aij * xj
+120 continue
+130 continue
+
+c ----------------------------------------------------------------
+c solve Ax=b, with iterative refinement
+c ----------------------------------------------------------------
+
+ sys = 0
+ call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4solr: ', info (1)
+ stop
+ endif
+
+c print the residual. x (i) should be 7 - i/n
+ call resid (n, nz, Ap, Ai, Ax, x, b, r)
+
+c ----------------------------------------------------------------
+c solve Ax=b, without iterative refinement, broken into steps
+c ----------------------------------------------------------------
+
+c the factorization is PAQ=LU, PRAQ=LU, or P(R\A)Q=LU.
+
+c x = R*b (or x=R\b, or x=b, as appropriate)
+ call umf4scal (x, b, numeric, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4scal: ', status
+ stop
+ endif
+
+c solve P'Lr=x for r (using r as workspace)
+ sys = 3
+ call umf4sol (sys, r, x, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4sol: ', info (1)
+ stop
+ endif
+
+c solve UQ'x=r for x
+ sys = 9
+ call umf4sol (sys, x, r, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4sol: ', info (1)
+ stop
+ endif
+
+c free the numeric factorization
+ call umf4fnum (numeric)
+
+c print the residual. x (i) should be 7 - i/n
+ call resid (n, nz, Ap, Ai, Ax, x, b, r)
+
+ stop
+998 print *, 'Read error: Harwell/Boeing matrix'
+ stop
+ end
+
+c=======================================================================
+c== resid ==============================================================
+c=======================================================================
+
+c Compute the residual, r = Ax-b, its max-norm, and print the max-norm
+C Note that A is zero-based.
+
+ subroutine resid (n, nz, Ap, Ai, Ax, x, b, r)
+ integer
+ $ n, nz, Ap (n+1), Ai (n), j, i, p
+ double precision Ax (nz), x (n), b (n), r (n), rmax, aij
+
+ do 10 i = 1, n
+ r (i) = -b (i)
+10 continue
+
+ do 30 j = 1,n
+ do 20 p = Ap (j) + 1, Ap (j+1)
+ i = Ai (p) + 1
+ aij = Ax (p)
+ r (i) = r (i) + aij * x (j)
+20 continue
+30 continue
+
+ rmax = 0
+ do 40 i = 1, n
+ rmax = max (rmax, r (i))
+40 continue
+
+ print *, 'norm (A*x-b): ', rmax
+ return
+ end
diff --git a/UMFPACK/Demo/umf4hb.out b/UMFPACK/Demo/umf4hb.out
new file mode 100644
index 0000000..e8b3113
--- /dev/null
+++ b/UMFPACK/Demo/umf4hb.out
@@ -0,0 +1,136 @@
+ Matrix key: WEST0067
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: int
+
+ 0: print level: 2
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+symbolic analysis:
+ status: 0.
+ time: 0.00E+00 (sec)
+ estimates (upper bound) for numeric LU:
+ size of LU: 0.02 (MB)
+ memory needed: 0.06 (MB)
+ flop count: 0.14E+05
+ nnz (L): 542.
+ nnz (U): 902.
+numeric factorization:
+ status: 0.
+ time: 0.00E+00
+ actual numeric LU statistics:
+ size of LU: 0.01 (MB)
+ memory needed: 0.04 (MB)
+ flop count: 0.25E+04
+ nnz (L): 323.
+ nnz (U): 339.
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 67
+ number of columns in matrix A: 67
+ entries in matrix A: 294
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 1
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S not square or diagonal not preserved
+ symbolic factorization defragmentations: 1
+ symbolic memory usage (Units): 1639
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 252
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 6.59006e+00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 1711 1577 92%
+ peak size (Units) 6115 3581 59%
+ final size (Units) 1628 682 42%
+ Numeric final size (Units) 2108 1129 54%
+ Numeric final size (MBytes) 0.0 0.0 54%
+ peak memory usage (Units) 7476 4942 66%
+ peak memory usage (MBytes) 0.1 0.0 66%
+ numeric factorization flops 1.41920e+04 2.50100e+03 18%
+ nz in L (incl diagonal) 542 323 60%
+ nz in U (incl diagonal) 902 339 38%
+ nz in L+U (incl diagonal) 1377 595 43%
+ largest front (# entries) 483 80 17%
+ largest # rows in front 21 10 48%
+ largest # columns in front 23 11 48%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 323
+ nz in U (incl diagonal), if none dropped 339
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 67
+ min abs. value on diagonal of U: 2.74e-02
+ max abs. value on diagonal of U: 2.28e+00
+ estimate of reciprocal of condition number: 1.20e-02
+ indices in compressed pattern: 263
+ numerical values stored in Numeric object: 599
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.19000e+03
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 3.69100e+03
+
+ norm (A*x-b): 0.
+ norm (A*x-b): 0.
+ norm (A*x-b): 0.
diff --git a/UMFPACK/Demo/umf4hb64.f b/UMFPACK/Demo/umf4hb64.f
new file mode 100644
index 0000000..c4ef6ff
--- /dev/null
+++ b/UMFPACK/Demo/umf4hb64.f
@@ -0,0 +1,353 @@
+c=======================================================================
+c== umf4hb =============================================================
+c=======================================================================
+
+c-----------------------------------------------------------------------
+c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE
+c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for
+c License. web: http://www.cise.ufl.edu/research/sparse/umfpack
+c-----------------------------------------------------------------------
+
+c umf4hb64:
+c read a sparse matrix in the Harwell/Boeing format, factorizes
+c it, and solves Ax=b. Also saves and loads the factors to/from a
+c file. Saving to a file is not required, it's just here to
+c demonstrate how to use this feature of UMFPACK. This program
+c only works on square RUA-type matrices.
+c
+c This is HIGHLY non-portable. It may not work with your C and
+c FORTRAN compilers. See umf4_f77wrapper.c for more details.
+c
+c usage (for example):
+c
+c in a Unix shell:
+c umf4hb64 < HB/arc130.rua
+
+ integer*8
+ $ nzmax, nmax
+ parameter (nzmax = 5000000, nmax = 160000)
+ integer*8
+ $ Ap (nmax), Ai (nzmax), n, nz, totcrd, ptrcrd, i, j, p,
+ $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, nzrhs, nel,
+ $ numeric, symbolic, status, sys, filenum
+
+ character title*72, key*30, type*3, ptrfmt*16,
+ $ indfmt*16, valfmt*20, rhsfmt*20
+ double precision Ax (nzmax), x (nmax), b (nmax), aij, xj,
+ $ r (nmax), control (20), info (90)
+ character rhstyp*3
+
+c ----------------------------------------------------------------
+c read the Harwell/Boeing matrix
+c ----------------------------------------------------------------
+
+ read (5, 10, err = 998)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd, rhscrd,
+ $ type, nrow, ncol, nz, nel,
+ $ ptrfmt, indfmt, valfmt, rhsfmt
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+ read (5, 20, err = 998) rhstyp, nrhs, nzrhs
+ endif
+10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+20 format (a3, 11x, 2i14)
+
+ print *, 'Matrix key: ', key
+
+ n = nrow
+ if (type .ne. 'RUA' .or. nrow .ne. ncol) then
+ print *, 'Error: can only handle square RUA matrices'
+ stop
+ endif
+ if (n .ge. nmax .or. nz .gt. nzmax) then
+ print *, ' Matrix too big!'
+ stop
+ endif
+
+c read the matrix (1-based)
+ read (5, ptrfmt, err = 998) (Ap (p), p = 1, ncol+1)
+ read (5, indfmt, err = 998) (Ai (p), p = 1, nz)
+ read (5, valfmt, err = 998) (Ax (p), p = 1, nz)
+
+c ----------------------------------------------------------------
+c create the right-hand-side, assume x (i) = 1 + i/n
+c ----------------------------------------------------------------
+
+ do 30 i = 1,n
+ b (i) = 0
+30 continue
+c b = A*x
+ do 50 j = 1,n
+ xj = j
+ xj = 1 + xj / n
+ do 40 p = Ap (j), Ap (j+1)-1
+ i = Ai (p)
+ aij = Ax (p)
+ b (i) = b (i) + aij * xj
+40 continue
+50 continue
+
+c ----------------------------------------------------------------
+c convert from 1-based to 0-based
+c ----------------------------------------------------------------
+
+ do 60 j = 1, n+1
+ Ap (j) = Ap (j) - 1
+60 continue
+ do 70 p = 1, nz
+ Ai (p) = Ai (p) - 1
+70 continue
+
+c ----------------------------------------------------------------
+c factor the matrix and save to a file
+c ----------------------------------------------------------------
+
+c set default parameters
+ call umf4def (control)
+
+c print control parameters. set control (1) to 1 to print
+c error messages only
+ control (1) = 2
+ call umf4pcon (control)
+
+c pre-order and symbolic analysis
+ call umf4sym (n, n, Ap, Ai, Ax, symbolic, control, info)
+
+c print statistics computed so far
+c call umf4pinf (control, info) could also be done.
+ print 80, info (1), info (16),
+ $ (info (21) * info (4)) / 2**20,
+ $ (info (22) * info (4)) / 2**20,
+ $ info (23), info (24), info (25)
+80 format ('symbolic analysis:',/,
+ $ ' status: ', f5.0, /,
+ $ ' time: ', e10.2, ' (sec)'/,
+ $ ' estimates (upper bound) for numeric LU:', /,
+ $ ' size of LU: ', f10.2, ' (MB)', /,
+ $ ' memory needed: ', f10.2, ' (MB)', /,
+ $ ' flop count: ', e10.2, /
+ $ ' nnz (L): ', f10.0, /
+ $ ' nnz (U): ', f10.0)
+
+c check umf4sym error condition
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4sym: ', info (1)
+ stop
+ endif
+
+c numeric factorization
+ call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info)
+
+c print statistics for the numeric factorization
+c call umf4pinf (control, info) could also be done.
+ print 90, info (1), info (66),
+ $ (info (41) * info (4)) / 2**20,
+ $ (info (42) * info (4)) / 2**20,
+ $ info (43), info (44), info (45)
+90 format ('numeric factorization:',/,
+ $ ' status: ', f5.0, /,
+ $ ' time: ', e10.2, /,
+ $ ' actual numeric LU statistics:', /,
+ $ ' size of LU: ', f10.2, ' (MB)', /,
+ $ ' memory needed: ', f10.2, ' (MB)', /,
+ $ ' flop count: ', e10.2, /
+ $ ' nnz (L): ', f10.0, /
+ $ ' nnz (U): ', f10.0)
+
+c check umf4num error condition
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4num: ', info (1)
+ stop
+ endif
+
+c save the symbolic analysis to the file s0.umf
+c note that this is not needed until another matrix is
+c factorized, below.
+ filenum = 0
+ call umf4ssym (symbolic, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4ssym: ', status
+ stop
+ endif
+
+c save the LU factors to the file n0.umf
+ call umf4snum (numeric, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4snum: ', status
+ stop
+ endif
+
+c free the symbolic analysis
+ call umf4fsym (symbolic)
+
+c free the numeric factorization
+ call umf4fnum (numeric)
+
+c No LU factors (symbolic or numeric) are in memory at this point.
+
+c ----------------------------------------------------------------
+c load the LU factors back in, and solve the system
+c ----------------------------------------------------------------
+
+c At this point the program could terminate and load the LU
+C factors (numeric) from the n0.umf file, and solve the
+c system (see below). Note that the symbolic object is not
+c required.
+
+c load the numeric factorization back in (filename: n0.umf)
+ call umf4lnum (numeric, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4lnum: ', status
+ stop
+ endif
+
+c solve Ax=b, without iterative refinement
+ sys = 0
+ call umf4sol (sys, x, b, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4sol: ', info (1)
+ stop
+ endif
+
+c free the numeric factorization
+ call umf4fnum (numeric)
+
+c No LU factors (symbolic or numeric) are in memory at this point.
+
+c print final statistics
+ call umf4pinf (control, info)
+
+c print the residual. x (i) should be 1 + i/n
+ call resid (n, nz, Ap, Ai, Ax, x, b, r)
+
+c ----------------------------------------------------------------
+c load the symbolic analysis back in, and factorize a new matrix
+c ----------------------------------------------------------------
+
+c Again, the program could terminate here, recreate the matrix,
+c and refactorize. Note that umf4sym is not called.
+
+c load the symbolic factorization back in (filename: s0.umf)
+ call umf4lsym (symbolic, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4lsym: ', status
+ stop
+ endif
+
+c arbitrarily change the values of the matrix but not the pattern
+ do 100 p = 1, nz
+ Ax (p) = Ax (p) + 3.14159 / 100.0
+100 continue
+
+c numeric factorization of the modified matrix
+ call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4num: ', info (1)
+ stop
+ endif
+
+c free the symbolic analysis
+ call umf4fsym (symbolic)
+
+c create a new right-hand-side, assume x (i) = 7 - i/n
+ do 110 i = 1,n
+ b (i) = 0
+110 continue
+c b = A*x, with the modified matrix A (note that A is now 0-based)
+ do 130 j = 1,n
+ xj = j
+ xj = 7 - xj / n
+ do 120 p = Ap (j) + 1, Ap (j+1)
+ i = Ai (p) + 1
+ aij = Ax (p)
+ b (i) = b (i) + aij * xj
+120 continue
+130 continue
+
+c ----------------------------------------------------------------
+c solve Ax=b, with iterative refinement
+c ----------------------------------------------------------------
+
+ sys = 0
+ call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4solr: ', info (1)
+ stop
+ endif
+
+c print the residual. x (i) should be 7 - i/n
+ call resid (n, nz, Ap, Ai, Ax, x, b, r)
+
+c ----------------------------------------------------------------
+c solve Ax=b, without iterative refinement, broken into steps
+c ----------------------------------------------------------------
+
+c the factorization is PAQ=LU, PRAQ=LU, or P(R\A)Q=LU.
+
+c x = R*b (or x=R\b, or x=b, as appropriate)
+ call umf4scal (x, b, numeric, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4scal: ', status
+ stop
+ endif
+
+c solve P'Lr=x for r (using r as workspace)
+ sys = 3
+ call umf4sol (sys, r, x, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4sol: ', info (1)
+ stop
+ endif
+
+c solve UQ'x=r for x
+ sys = 9
+ call umf4sol (sys, x, r, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4sol: ', info (1)
+ stop
+ endif
+
+c free the numeric factorization
+ call umf4fnum (numeric)
+
+c print the residual. x (i) should be 7 - i/n
+ call resid (n, nz, Ap, Ai, Ax, x, b, r)
+
+ stop
+998 print *, 'Read error: Harwell/Boeing matrix'
+ stop
+ end
+
+c=======================================================================
+c== resid ==============================================================
+c=======================================================================
+
+c Compute the residual, r = Ax-b, its max-norm, and print the max-norm
+C Note that A is zero-based.
+
+ subroutine resid (n, nz, Ap, Ai, Ax, x, b, r)
+ integer*8
+ $ n, nz, Ap (n+1), Ai (n), j, i, p
+ double precision Ax (nz), x (n), b (n), r (n), rmax, aij
+
+ do 10 i = 1, n
+ r (i) = -b (i)
+10 continue
+
+ do 30 j = 1,n
+ do 20 p = Ap (j) + 1, Ap (j+1)
+ i = Ai (p) + 1
+ aij = Ax (p)
+ r (i) = r (i) + aij * x (j)
+20 continue
+30 continue
+
+ rmax = 0
+ do 40 i = 1, n
+ rmax = max (rmax, r (i))
+40 continue
+
+ print *, 'norm (A*x-b): ', rmax
+ return
+ end
diff --git a/UMFPACK/Demo/umf4hb64.out b/UMFPACK/Demo/umf4hb64.out
new file mode 100644
index 0000000..9189d17
--- /dev/null
+++ b/UMFPACK/Demo/umf4hb64.out
@@ -0,0 +1,136 @@
+ Matrix key: WEST0067
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: UF_long
+
+ 0: print level: 2
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 8 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+symbolic analysis:
+ status: 0.
+ time: 0.00E+00 (sec)
+ estimates (upper bound) for numeric LU:
+ size of LU: 0.02 (MB)
+ memory needed: 0.08 (MB)
+ flop count: 0.14E+05
+ nnz (L): 542.
+ nnz (U): 902.
+numeric factorization:
+ status: 0.
+ time: 0.00E+00
+ actual numeric LU statistics:
+ size of LU: 0.01 (MB)
+ memory needed: 0.06 (MB)
+ flop count: 0.25E+04
+ nnz (L): 323.
+ nnz (U): 339.
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 67
+ number of columns in matrix A: 67
+ entries in matrix A: 294
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 1
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S not square or diagonal not preserved
+ symbolic factorization defragmentations: 1
+ symbolic memory usage (Units): 1595
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 241
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 6.59006e+00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 1517 1448 95%
+ peak size (Units) 3917 2423 62%
+ final size (Units) 981 435 44%
+ Numeric final size (Units) 1381 802 58%
+ Numeric final size (MBytes) 0.0 0.0 58%
+ peak memory usage (Units) 5133 3639 71%
+ peak memory usage (MBytes) 0.1 0.1 71%
+ numeric factorization flops 1.41920e+04 2.50100e+03 18%
+ nz in L (incl diagonal) 542 323 60%
+ nz in U (incl diagonal) 902 339 38%
+ nz in L+U (incl diagonal) 1377 595 43%
+ largest front (# entries) 483 80 17%
+ largest # rows in front 21 10 48%
+ largest # columns in front 23 11 48%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 323
+ nz in U (incl diagonal), if none dropped 339
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 67
+ min abs. value on diagonal of U: 2.74e-02
+ max abs. value on diagonal of U: 2.28e+00
+ estimate of reciprocal of condition number: 1.20e-02
+ indices in compressed pattern: 249
+ numerical values stored in Numeric object: 605
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.19000e+03
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 3.69100e+03
+
+ norm (A*x-b): 3.10862447E-15
+ norm (A*x-b): 2.13162821E-14
+ norm (A*x-b): 2.13162821E-14
diff --git a/UMFPACK/Demo/umf4zhb.f b/UMFPACK/Demo/umf4zhb.f
new file mode 100644
index 0000000..003c3e4
--- /dev/null
+++ b/UMFPACK/Demo/umf4zhb.f
@@ -0,0 +1,279 @@
+c=======================================================================
+c== umf4zhb ============================================================
+c=======================================================================
+
+c-----------------------------------------------------------------------
+c UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE
+c Dept, Univ. of Florida. All Rights Reserved. See ../Doc/License for
+c License. web: http://www.cise.ufl.edu/research/sparse/umfpack
+c-----------------------------------------------------------------------
+
+c umf4zhb:
+c read a sparse matrix in the Harwell/Boeing format, factorizes
+c it, and solves Ax=b. Also saves and loads the factors to/from a
+c file. Saving to a file is not required, it's just here to
+c demonstrate how to use this feature of UMFPACK. This program
+c only works on square CUA-type matrices.
+c
+c This is HIGHLY non-portable. It may not work with your C and
+c FORTRAN compilers. See umf4z_f77wrapper.c for more details.
+c
+c usage (for example):
+c
+c in a Unix shell:
+c umf4zhb < HB/arc130.cua
+
+ integer
+ $ nzmax, nmax
+ parameter (nzmax = 5000000, nmax = 160000)
+ integer
+ $ Ap (nmax), Ai (nzmax), n, nz, totcrd, ptrcrd, i, j, p,
+ $ indcrd, valcrd, rhscrd, ncol, nrow, nrhs, nzrhs, nel,
+ $ numeric, symbolic, status, sys, filenum
+
+ character title*72, key*30, type*3, ptrfmt*16,
+ $ indfmt*16, valfmt*20, rhsfmt*20
+ double precision Ax (nzmax), x (nmax), b (nmax),
+ $ control (20), info (90)
+ complex*16 AA (nzmax), XX (nmax), BB (nmax), r (nmax), aij, xj
+ double precision Az (nmax), xz (nmax), bz (nmax), xi, xr
+ character rhstyp*3
+
+c ----------------------------------------------------------------
+c read the Harwell/Boeing matrix
+c ----------------------------------------------------------------
+
+ read (5, 10, err = 998)
+ $ title, key,
+ $ totcrd, ptrcrd, indcrd, valcrd, rhscrd,
+ $ type, nrow, ncol, nz, nel,
+ $ ptrfmt, indfmt, valfmt, rhsfmt
+ if (rhscrd .gt. 0) then
+c new Harwell/Boeing format:
+ read (5, 20, err = 998) rhstyp, nrhs, nzrhs
+ endif
+10 format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+20 format (a3, 11x, 2i14)
+
+ print *, 'Matrix key: ', key
+
+ n = nrow
+ if (type .ne. 'CUA' .or. nrow .ne. ncol) then
+ print *, 'Error: can only handle square CUA matrices'
+ stop
+ endif
+ if (n .ge. nmax .or. nz .gt. nzmax) then
+ print *, ' Matrix too big!'
+ stop
+ endif
+
+c read the matrix (1-based)
+ read (5, ptrfmt, err = 998) (Ap (p), p = 1, ncol+1)
+ read (5, indfmt, err = 998) (Ai (p), p = 1, nz)
+ read (5, valfmt, err = 998) (AA (p), p = 1, nz)
+
+ do 15 p = 1, nz
+ Ax (p) = dble (AA (p))
+ Az (p) = imag (AA (p))
+15 continue
+
+c ----------------------------------------------------------------
+c create the right-hand-side, assume
+c x (i) = (1 + i/n), (n + i/100)
+c ----------------------------------------------------------------
+
+ do 30 i = 1,n
+ BB (i) = 0
+30 continue
+c b = A*x
+ do 50 j = 1,n
+ xr = j
+ xi = n
+ xi = xi + xr/100
+ xr = 1 + xr / n
+ xj = dcmplx (xr, xi)
+ do 40 p = Ap (j), Ap (j+1)-1
+ i = Ai (p)
+ aij = AA (p)
+ BB (i) = BB (i) + aij * xj
+40 continue
+50 continue
+ do 32 i = 1,n
+ b (i) = dble (BB (i))
+ bz (i) = imag (BB (i))
+32 continue
+
+c ----------------------------------------------------------------
+c convert from 1-based to 0-based
+c ----------------------------------------------------------------
+
+ do 60 j = 1, n+1
+ Ap (j) = Ap (j) - 1
+60 continue
+ do 70 p = 1, nz
+ Ai (p) = Ai (p) - 1
+70 continue
+
+c ----------------------------------------------------------------
+c factor the matrix and save to a file
+c ----------------------------------------------------------------
+
+c set default parameters
+ call umf4zdef (control)
+
+c print control parameters. set control (1) to 1 to print
+c error messages only
+ control (1) = 2
+ call umf4zpcon (control)
+
+c pre-order and symbolic analysis
+ call umf4zsym (n, n, Ap, Ai, Ax, Az, symbolic, control, info)
+
+c print statistics computed so far
+c call umf4zpinf (control, info) could also be done.
+ print 80, info (1), info (16),
+ $ (info (21) * info (4)) / 2**20,
+ $ (info (22) * info (4)) / 2**20,
+ $ info (23), info (24), info (25)
+80 format ('symbolic analysis:',/,
+ $ ' status: ', f5.0, /,
+ $ ' time: ', e10.2, ' (sec)'/,
+ $ ' estimates (upper bound) for numeric LU:', /,
+ $ ' size of LU: ', f10.2, ' (MB)', /,
+ $ ' memory needed: ', f10.2, ' (MB)', /,
+ $ ' flop count: ', e10.2, /
+ $ ' nnz (L): ', f10.0, /
+ $ ' nnz (U): ', f10.0)
+
+c check umf4zsym error condition
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4zsym: ', info (1)
+ stop
+ endif
+
+c numeric factorization
+ call umf4znum (Ap, Ai, Ax, Az, symbolic, numeric, control, info)
+
+c print statistics for the numeric factorization
+c call umf4zpinf (control, info) could also be done.
+ print 90, info (1), info (66),
+ $ (info (41) * info (4)) / 2**20,
+ $ (info (42) * info (4)) / 2**20,
+ $ info (43), info (44), info (45)
+90 format ('numeric factorization:',/,
+ $ ' status: ', f5.0, /,
+ $ ' time: ', e10.2, /,
+ $ ' actual numeric LU statistics:', /,
+ $ ' size of LU: ', f10.2, ' (MB)', /,
+ $ ' memory needed: ', f10.2, ' (MB)', /,
+ $ ' flop count: ', e10.2, /
+ $ ' nnz (L): ', f10.0, /
+ $ ' nnz (U): ', f10.0)
+
+c check umf4znum error condition
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4znum: ', info (1)
+ stop
+ endif
+
+c save the symbolic analysis to the file s42.umf
+c note that this is not needed until another matrix is
+c factorized, below.
+ filenum = 42
+ call umf4zssym (symbolic, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4zssym: ', status
+ stop
+ endif
+
+c save the LU factors to the file n0.umf
+ call umf4zsnum (numeric, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4zsnum: ', status
+ stop
+ endif
+
+c free the symbolic analysis
+ call umf4zfsym (symbolic)
+
+c free the numeric factorization
+ call umf4zfnum (numeric)
+
+c No LU factors (symbolic or numeric) are in memory at this point.
+
+c ----------------------------------------------------------------
+c load the LU factors back in, and solve the system
+c ----------------------------------------------------------------
+
+c At this point the program could terminate and load the LU
+C factors (numeric) from the n0.umf file, and solve the
+c system (see below). Note that the symbolic object is not
+c required.
+
+c load the numeric factorization back in (filename: n0.umf)
+ call umf4zlnum (numeric, filenum, status)
+ if (status .lt. 0) then
+ print *, 'Error occurred in umf4zlnum: ', status
+ stop
+ endif
+
+c solve Ax=b, without iterative refinement
+ sys = 0
+ call umf4zsol (sys, x, xz, b, bz, numeric, control, info)
+ if (info (1) .lt. 0) then
+ print *, 'Error occurred in umf4zsol: ', info (1)
+ stop
+ endif
+ do 33 i = 1,n
+ XX (i) = dcmplx (x (i), xz (i))
+33 continue
+
+c free the numeric factorization
+ call umf4zfnum (numeric)
+
+c No LU factors (symbolic or numeric) are in memory at this point.
+
+c print final statistics
+ call umf4zpinf (control, info)
+
+c print the residual. x (i) should be 1 + i/n
+ call resid (n, nz, Ap, Ai, AA, XX, BB, r)
+
+ stop
+998 print *, 'Read error: Harwell/Boeing matrix'
+ stop
+ end
+
+c=======================================================================
+c== resid ==============================================================
+c=======================================================================
+
+c Compute the residual, r = Ax-b, its max-norm, and print the max-norm
+C Note that A is zero-based.
+
+ subroutine resid (n, nz, Ap, Ai, A, x, b, r)
+ integer
+ $ n, nz, Ap (n+1), Ai (n), j, i, p
+ complex*16 A (nz), x (n), b (n), r (n), aij
+ double precision rmax
+
+ do 10 i = 1, n
+ r (i) = -b (i)
+10 continue
+
+ do 30 j = 1,n
+ do 20 p = Ap (j) + 1, Ap (j+1)
+ i = Ai (p) + 1
+ aij = A (p)
+ r (i) = r (i) + aij * x (j)
+20 continue
+30 continue
+
+ rmax = 0
+ do 40 i = 1, n
+ rmax = max (rmax, abs (r (i)))
+40 continue
+
+ print *, 'norm (A*x-b): ', rmax
+ return
+ end
diff --git a/UMFPACK/Demo/umf4zhb.out b/UMFPACK/Demo/umf4zhb.out
new file mode 100644
index 0000000..d6916e5
--- /dev/null
+++ b/UMFPACK/Demo/umf4zhb.out
@@ -0,0 +1,151 @@
+ Matrix key: QC324
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double complex
+ Int (generic integer) defined as: int
+
+ 0: print level: 2
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 16 (in bytes)
+
+symbolic analysis:
+ status: 0.
+ time: 0.00E+00 (sec)
+ estimates (upper bound) for numeric LU:
+ size of LU: 1.17 (MB)
+ memory needed: 2.40 (MB)
+ flop count: 0.26E+08
+ nnz (L): 24027.
+ nnz (U): 39609.
+numeric factorization:
+ status: 0.
+ time: 0.10E-01
+ actual numeric LU statistics:
+ size of LU: 0.72 (MB)
+ memory needed: 1.14 (MB)
+ flop count: 0.14E+08
+ nnz (L): 23247.
+ nnz (U): 23247.
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 324
+ number of columns in matrix A: 324
+ entries in matrix A: 26730
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: symmetric
+ ordering used: amd on A+A'
+ modify Q during factorization: no
+ prefer diagonal pivoting: yes
+ pivots with zero Markowitz cost: 0
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 324
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 324
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 26406
+ nz on diagonal of matrix S: 324
+ fraction of nz on diagonal: 1.000000
+ AMD statistics, for strict diagonal pivoting:
+ est. flops for LU factorization: 1.55342e+07
+ est. nz in L+U (incl. diagonal): 47730
+ est. largest front (# entries): 14641
+ est. max nz in any column of L: 121
+ number of "dense" rows/columns in S+S': 0
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 63473
+ symbolic memory usage (MBytes): 0.5
+ Symbolic size (Units): 1425
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.01
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 2.55982e-01
+ maximum sum (abs (rows of A)): 1.82217e+00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 98341 97691 99%
+ peak size (Units) 307744 142557 46%
+ final size (Units) 150384 92058 61%
+ Numeric final size (Units) 153188 94700 62%
+ Numeric final size (MBytes) 1.2 0.7 62%
+ peak memory usage (Units) 314864 149677 48%
+ peak memory usage (MBytes) 2.4 1.1 48%
+ numeric factorization flops 2.56313e+07 1.43519e+07 56%
+ nz in L (incl diagonal) 24027 23247 97%
+ nz in U (incl diagonal) 39609 23247 59%
+ nz in L+U (incl diagonal) 63312 46170 73%
+ largest front (# entries) 19723 6724 34%
+ largest # rows in front 121 82 68%
+ largest # columns in front 163 82 50%
+
+ initial allocation ratio used: 1.2
+ # of forced updates due to frontal growth: 0
+ number of off-diagonal pivots: 0
+ nz in L (incl diagonal), if none dropped 23247
+ nz in U (incl diagonal), if none dropped 23247
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 324
+ min abs. value on diagonal of U: 5.47e-03
+ max abs. value on diagonal of U: 8.25e-01
+ estimate of reciprocal of condition number: 6.63e-03
+ indices in compressed pattern: 485
+ numerical values stored in Numeric object: 46170
+ numeric factorization defragmentations: 0
+ numeric factorization reallocations: 0
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.01
+ numeric factorization wallclock time (sec): 0.01
+ numeric factorization mflops (CPU time): 1435.19
+ numeric factorization mflops (wallclock): 1435.19
+ symbolic + numeric wall clock time (sec): 0.02
+ symbolic + numeric mflops (wall clock): 717.60
+
+ solve flops: 3.70332e+05
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.47223e+07
+
+ norm (A*x-b): 0.
diff --git a/UMFPACK/Demo/umfpack_di_demo.c b/UMFPACK/Demo/umfpack_di_demo.c
new file mode 100644
index 0000000..0ebf80a
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_di_demo.c
@@ -0,0 +1,760 @@
+/* ========================================================================== */
+/* === umfpack_di_demo ====================================================== */
+/* ========================================================================== */
+
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ A demo of UMFPACK: umfpack_di_* version.
+
+ First, factor and solve a 5-by-5 system, Ax=b, using default parameters.
+ Then solve A'x=b using the factors of A. Modify one entry (A (1,4) = 0,
+ where the row and column indices range from 0 to 4. The pattern of A
+ has not changed (it has explicitly zero entry), so a reanalysis with
+ umfpack_di_symbolic does not need to be done. Refactorize (with
+ umfpack_di_numeric), and solve Ax=b. Note that the pivot ordering has
+ changed. Next, change all of the entries in A, but not the pattern.
+
+ Finally, compute C = A', and do the symbolic and numeric factorization of C.
+ Factorizing A' can sometimes be better than factorizing A itself (less work
+ and memory usage). Solve C'x=b twice; the solution is the same as the
+ solution to Ax=b.
+
+ A note about zero-sized arrays: UMFPACK uses many user-provided arrays of
+ size n (order of the matrix), and of size nz (the number of nonzeros in a
+ matrix). n cannot be zero; UMFPACK does not handle zero-dimensioned arrays.
+ However, nz can be zero. If you attempt to malloc an array of size nz = 0,
+ however, malloc will return a null pointer which UMFPACK will report as a
+ "missing argument." Thus, nz1 in this code is set to MAX (nz,1), and
+ similarly for lnz and unz. Lnz can never be zero, however, since L is always
+ unit diagonal.
+*/
+
+/* -------------------------------------------------------------------------- */
+/* definitions */
+/* -------------------------------------------------------------------------- */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "umfpack.h"
+
+#define ABS(x) ((x) >= 0 ? (x) : -(x))
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#ifndef TRUE
+#define TRUE (1)
+#endif
+#ifndef FALSE
+#define FALSE (0)
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* triplet form of the matrix. The triplets can be in any order. */
+/* -------------------------------------------------------------------------- */
+
+static int n = 5, nz = 12 ;
+static int Arow [ ] = { 0, 4, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4} ;
+static int Acol [ ] = { 0, 4, 0, 2, 1, 2, 1, 4, 3, 2, 1, 2} ;
+static double Aval [ ] = {2., 1., 3., 4., -1., -3., 3., 6., 2., 1., 4., 2.} ;
+static double b [ ] = {8., 45., -3., 3., 19.}, x [5], r [5] ;
+
+
+/* -------------------------------------------------------------------------- */
+/* error: print a message and exit */
+/* -------------------------------------------------------------------------- */
+
+static void error
+(
+ char *message
+)
+{
+ printf ("\n\n====== error: %s =====\n\n", message) ;
+ exit (1) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* resid: compute the residual, r = Ax-b or r = A'x=b and return maxnorm (r) */
+/* -------------------------------------------------------------------------- */
+
+static double resid
+(
+ int transpose,
+ int Ap [ ],
+ int Ai [ ],
+ double Ax [ ]
+)
+{
+ int i, j, p ;
+ double norm ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ r [i] = -b [i] ;
+ }
+ if (transpose)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ r [j] += Ax [p] * x [i] ;
+ }
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ r [i] += Ax [p] * x [j] ;
+ }
+ }
+ }
+ norm = 0. ;
+ for (i = 0 ; i < n ; i++)
+ {
+ norm = MAX (ABS (r [i]), norm) ;
+ }
+ return (norm) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* main program */
+/* -------------------------------------------------------------------------- */
+
+int main (int argc, char **argv)
+{
+ double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux,
+ *W, t [2], *Dx, rnorm, *Rb, *y, *Rs ;
+ int *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up,
+ *P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1,
+ status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1,
+ *Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc,
+ nzud, do_recip ;
+ void *Symbolic, *Numeric ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (t) ;
+
+ printf ("\nUMFPACK V%d.%d (%s) demo: _di_ version\n",
+ UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ;
+
+ /* get the default control parameters */
+ umfpack_di_defaults (Control) ;
+
+ /* change the default print level for this demo */
+ /* (otherwise, nothing will print) */
+ Control [UMFPACK_PRL] = 6 ;
+
+ /* print the license agreement */
+ umfpack_di_report_status (Control, UMFPACK_OK) ;
+ Control [UMFPACK_PRL] = 5 ;
+
+ /* print the control parameters */
+ umfpack_di_report_control (Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print A and b, and convert A to column-form */
+ /* ---------------------------------------------------------------------- */
+
+ /* print the right-hand-side */
+ printf ("\nb: ") ;
+ (void) umfpack_di_report_vector (n, b, Control) ;
+
+ /* print the triplet form of the matrix */
+ printf ("\nA: ") ;
+ (void) umfpack_di_report_triplet (n, n, nz, Arow, Acol, Aval,
+ Control) ;
+
+ /* convert to column form */
+ nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */
+ Ap = (int *) malloc ((n+1) * sizeof (int)) ;
+ Ai = (int *) malloc (nz1 * sizeof (int)) ;
+ Ax = (double *) malloc (nz1 * sizeof (double)) ;
+ if (!Ap || !Ai || !Ax)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_di_triplet_to_col (n, n, nz, Arow, Acol, Aval,
+ Ap, Ai, Ax, (int *) NULL) ;
+
+ if (status < 0)
+ {
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_triplet_to_col failed") ;
+ }
+
+ /* print the column-form of A */
+ printf ("\nA: ") ;
+ (void) umfpack_di_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_symbolic (n, n, Ap, Ai, Ax, &Symbolic,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_di_report_info (Control, Info) ;
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_symbolic failed") ;
+ }
+
+ /* print the symbolic factorization */
+
+ printf ("\nSymbolic factorization of A: ") ;
+ (void) umfpack_di_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_di_report_info (Control, Info) ;
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_numeric failed") ;
+ }
+
+ /* print the numeric factorization */
+ printf ("\nNumeric factorization of A: ") ;
+ (void) umfpack_di_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b,
+ Numeric, Control, Info) ;
+ umfpack_di_report_info (Control, Info) ;
+ umfpack_di_report_status (Control, status) ;
+ if (status < 0)
+ {
+ error ("umfpack_di_solve failed") ;
+ }
+ printf ("\nx (solution of Ax=b): ") ;
+ (void) umfpack_di_report_vector (n, x, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the determinant */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_get_determinant (x, r, Numeric, Info) ;
+ umfpack_di_report_status (Control, status) ;
+ if (status < 0)
+ {
+ error ("umfpack_di_get_determinant failed") ;
+ }
+ printf ("determinant: (%g", x [0]) ;
+ printf (") * 10^(%g)\n", r [0]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, broken down into steps */
+ /* ---------------------------------------------------------------------- */
+
+ /* Rb = R*b */
+ Rb = (double *) malloc (n * sizeof (double)) ;
+ y = (double *) malloc (n * sizeof (double)) ;
+ if (!Rb || !y) error ("out of memory") ;
+
+ status = umfpack_di_scale (Rb, b, Numeric) ;
+ if (status < 0) error ("umfpack_di_scale failed") ;
+ /* solve Ly = P*(Rb) */
+ status = umfpack_di_solve (UMFPACK_Pt_L, Ap, Ai, Ax, y, Rb,
+ Numeric, Control, Info) ;
+ if (status < 0) error ("umfpack_di_solve failed") ;
+ /* solve UQ'x=y */
+ status = umfpack_di_solve (UMFPACK_U_Qt, Ap, Ai, Ax, x, y,
+ Numeric, Control, Info) ;
+ if (status < 0) error ("umfpack_di_solve failed") ;
+ printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ;
+ (void) umfpack_di_report_vector (n, x, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ free (Rb) ;
+ free (y) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve A'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_solve (UMFPACK_At, Ap, Ai, Ax, x, b,
+ Numeric, Control, Info) ;
+ umfpack_di_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ error ("umfpack_di_solve failed") ;
+ }
+ printf ("\nx (solution of A'x=b): ") ;
+ (void) umfpack_di_report_vector (n, x, Control) ;
+ rnorm = resid (TRUE, Ap, Ai, Ax) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify one numerical value in the column-form of A */
+ /* ---------------------------------------------------------------------- */
+
+ /* change A (1,4), look for row index 1 in column 4. */
+ row = 1 ;
+ col = 4 ;
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ if (row == Ai [p])
+ {
+ printf ("\nchanging A (%d,%d) to zero\n", row, col) ;
+ Ax [p] = 0.0 ;
+ break ;
+ }
+ }
+ printf ("\nmodified A: ") ;
+ (void) umfpack_di_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* redo the numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */
+ /* doesn't have to be redone, no matter how much we change Ax. */
+
+ /* We don't need the Numeric object any more, so free it. */
+ umfpack_di_free_numeric (&Numeric) ;
+
+ /* Note that a memory leak would have occurred if the old Numeric */
+ /* had not been free'd with umfpack_di_free_numeric above. */
+ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_di_report_info (Control, Info) ;
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of modified A: ") ;
+ (void) umfpack_di_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, with the modified A */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b,
+ Numeric, Control, Info) ;
+ umfpack_di_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_solve failed") ;
+ }
+ printf ("\nx (with modified A): ") ;
+ (void) umfpack_di_report_vector (n, x, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify all of the numerical values of A, but not the pattern */
+ /* ---------------------------------------------------------------------- */
+
+ for (col = 0 ; col < n ; col++)
+ {
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ row = Ai [p] ;
+ printf ("changing ") ;
+ printf ("A (%d,%d) from %g", row, col, Ax [p]) ;
+ Ax [p] = Ax [p] + col*10 - row ;
+ printf (" to %g\n", Ax [p]) ;
+ }
+ }
+ printf ("\ncompletely modified A (same pattern): ") ;
+ (void) umfpack_di_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* save the Symbolic object to file, free it, and load it back in */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the default filename, "symbolic.umf" */
+ printf ("\nSaving symbolic object:\n") ;
+ status = umfpack_di_save_symbolic (Symbolic, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_save_symbolic failed") ;
+ }
+ printf ("\nFreeing symbolic object:\n") ;
+ umfpack_di_free_symbolic (&Symbolic) ;
+ printf ("\nLoading symbolic object:\n") ;
+ status = umfpack_di_load_symbolic (&Symbolic, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_load_symbolic failed") ;
+ }
+ printf ("\nDone loading symbolic object\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* redo the numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_di_free_numeric (&Numeric) ;
+ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_di_report_info (Control, Info) ;
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of completely modified A: ") ;
+ (void) umfpack_di_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, with the modified A */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b,
+ Numeric, Control, Info) ;
+ umfpack_di_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_solve failed") ;
+ }
+ printf ("\nx (with completely modified A): ") ;
+ (void) umfpack_di_report_vector (n, x, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the symbolic and numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_di_free_symbolic (&Symbolic) ;
+ umfpack_di_free_numeric (&Numeric) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = transpose of A */
+ /* ---------------------------------------------------------------------- */
+
+ Cp = (int *) malloc ((n+1) * sizeof (int)) ;
+ Ci = (int *) malloc (nz1 * sizeof (int)) ;
+ Cx = (double *) malloc (nz1 * sizeof (double)) ;
+ if (!Cp || !Ci || !Cx)
+ {
+ error ("out of memory") ;
+ }
+ status = umfpack_di_transpose (n, n, Ap, Ai, Ax,
+ (int *) NULL, (int *) NULL, Cp, Ci, Cx) ;
+ if (status < 0)
+ {
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_transpose failed: ") ;
+ }
+ printf ("\nC (transpose of A): ") ;
+ (void) umfpack_di_report_matrix (n, n, Cp, Ci, Cx, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization of C */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_symbolic (n, n, Cp, Ci, Cx, &Symbolic,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_di_report_info (Control, Info) ;
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_symbolic failed") ;
+ }
+ printf ("\nSymbolic factorization of C: ") ;
+ (void) umfpack_di_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the contents of Symbolic into user arrays print them */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nGet the contents of the Symbolic object for C:\n") ;
+ printf ("(compare with umfpack_di_report_symbolic output, above)\n") ;
+ Pinit = (int *) malloc ((n+1) * sizeof (int)) ;
+ Qinit = (int *) malloc ((n+1) * sizeof (int)) ;
+ Front_npivcol = (int *) malloc ((n+1) * sizeof (int)) ;
+ Front_1strow = (int *) malloc ((n+1) * sizeof (int)) ;
+ Front_leftmostdesc = (int *) malloc ((n+1) * sizeof (int)) ;
+ Front_parent = (int *) malloc ((n+1) * sizeof (int)) ;
+ Chain_start = (int *) malloc ((n+1) * sizeof (int)) ;
+ Chain_maxrows = (int *) malloc ((n+1) * sizeof (int)) ;
+ Chain_maxcols = (int *) malloc ((n+1) * sizeof (int)) ;
+ if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start ||
+ !Chain_maxrows || !Chain_maxcols || !Front_1strow ||
+ !Front_leftmostdesc)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_di_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains,
+ Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+ if (status < 0)
+ {
+ error ("symbolic factorization invalid") ;
+ }
+
+ printf ("From the Symbolic object, C is of dimension %d-by-%d\n", nr, nc);
+ printf (" with nz = %d, number of fronts = %d,\n", nz, nfr) ;
+ printf (" number of frontal matrix chains = %d\n", nchains) ;
+
+ printf ("\nPivot columns in each front, and parent of each front:\n") ;
+ k = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fnpiv = Front_npivcol [i] ;
+ printf (" Front %d: parent front: %d number of pivot cols: %d\n",
+ i, Front_parent [i], fnpiv) ;
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ col = Qinit [k] ;
+ printf (
+ " %d-th pivot column is column %d in original matrix\n",
+ k, col) ;
+ k++ ;
+ }
+ }
+
+ printf ("\nNote that the column ordering, above, will be refined\n") ;
+ printf ("in the numeric factorization below. The assignment of pivot\n") ;
+ printf ("columns to frontal matrices will always remain unchanged.\n") ;
+
+ printf ("\nTotal number of pivot columns in frontal matrices: %d\n", k) ;
+
+ printf ("\nFrontal matrix chains:\n") ;
+ for (j = 0 ; j < nchains ; j++)
+ {
+ printf (" Frontal matrices %d to %d are factorized in a single\n",
+ Chain_start [j], Chain_start [j+1] - 1) ;
+ printf (" working array of size %d-by-%d\n",
+ Chain_maxrows [j], Chain_maxcols [j]) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization of C */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_numeric (Cp, Ci, Cx, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ error ("umfpack_di_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of C: ") ;
+ (void) umfpack_di_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extract the LU factors of C and print them */
+ /* ---------------------------------------------------------------------- */
+
+ if (umfpack_di_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0)
+ {
+ error ("umfpack_di_get_lunz failed") ;
+ }
+ /* ensure arrays are not of zero size */
+ lnz1 = MAX (lnz,1) ;
+ unz1 = MAX (unz,1) ;
+ Lp = (int *) malloc ((n+1) * sizeof (int)) ;
+ Lj = (int *) malloc (lnz1 * sizeof (int)) ;
+ Lx = (double *) malloc (lnz1 * sizeof (double)) ;
+ Up = (int *) malloc ((n+1) * sizeof (int)) ;
+ Ui = (int *) malloc (unz1 * sizeof (int)) ;
+ Ux = (double *) malloc (unz1 * sizeof (double)) ;
+ P = (int *) malloc (n * sizeof (int)) ;
+ Q = (int *) malloc (n * sizeof (int)) ;
+ Dx = (double *) NULL ; /* D vector not requested */
+ Rs = (double *) malloc (n * sizeof (double)) ;
+ if (!Lp || !Lj || !Lx || !Up || !Ui || !Ux || !P || !Q || !Rs)
+ {
+ error ("out of memory") ;
+ }
+ status = umfpack_di_get_numeric (Lp, Lj, Lx, Up, Ui, Ux,
+ P, Q, Dx, &do_recip, Rs, Numeric) ;
+ if (status < 0)
+ {
+ error ("umfpack_di_get_numeric failed") ;
+ }
+
+ printf ("\nL (lower triangular factor of C): ") ;
+ (void) umfpack_di_report_matrix (n, n, Lp, Lj, Lx, 0, Control) ;
+ printf ("\nU (upper triangular factor of C): ") ;
+ (void) umfpack_di_report_matrix (n, n, Up, Ui, Ux, 1, Control) ;
+ printf ("\nP: ") ;
+ (void) umfpack_di_report_perm (n, P, Control) ;
+ printf ("\nQ: ") ;
+ (void) umfpack_di_report_perm (n, Q, Control) ;
+ printf ("\nScale factors: row i of A is to be ") ;
+ if (do_recip)
+ {
+ printf ("multiplied by the ith scale factor\n") ;
+ }
+ else
+ {
+ printf ("divided by the ith scale factor\n") ;
+ }
+ for (i = 0 ; i < n ; i++) printf ("%d: %g\n", i, Rs [i]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to triplet form and print it */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that L is in row-form, so it is the row indices that are created */
+ /* by umfpack_di_col_to_triplet. */
+
+ printf ("\nConverting L to triplet form, and printing it:\n") ;
+ Li = (int *) malloc (lnz1 * sizeof (int)) ;
+ if (!Li)
+ {
+ error ("out of memory") ;
+ }
+ if (umfpack_di_col_to_triplet (n, Lp, Li) < 0)
+ {
+ error ("umfpack_di_col_to_triplet failed") ;
+ }
+ printf ("\nL, in triplet form: ") ;
+ (void) umfpack_di_report_triplet (n, n, lnz, Li, Lj, Lx, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* save the Numeric object to file, free it, and load it back in */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the default filename, "numeric.umf" */
+ printf ("\nSaving numeric object:\n") ;
+ status = umfpack_di_save_numeric (Numeric, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_save_numeric failed") ;
+ }
+ printf ("\nFreeing numeric object:\n") ;
+ umfpack_di_free_numeric (&Numeric) ;
+ printf ("\nLoading numeric object:\n") ;
+ status = umfpack_di_load_numeric (&Numeric, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_load_numeric failed") ;
+ }
+ printf ("\nDone loading numeric object\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve C'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_di_solve (UMFPACK_At, Cp, Ci, Cx, x, b,
+ Numeric, Control, Info) ;
+ umfpack_di_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_solve failed") ;
+ }
+ printf ("\nx (solution of C'x=b): ") ;
+ (void) umfpack_di_report_vector (n, x, Control) ;
+ rnorm = resid (TRUE, Cp, Ci, Cx) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve C'x=b again, using umfpack_di_wsolve instead */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nSolving C'x=b again, using umfpack_di_wsolve instead:\n") ;
+ Wi = (int *) malloc (n * sizeof (int)) ;
+ W = (double *) malloc (5*n * sizeof (double)) ;
+ if (!Wi || !W)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_di_wsolve (UMFPACK_At, Cp, Ci, Cx, x, b,
+ Numeric, Control, Info, Wi, W) ;
+ umfpack_di_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_di_report_status (Control, status) ;
+ error ("umfpack_di_wsolve failed") ;
+ }
+ printf ("\nx (solution of C'x=b): ") ;
+ (void) umfpack_di_report_vector (n, x, Control) ;
+ rnorm = resid (TRUE, Cp, Ci, Cx) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free everything */
+ /* ---------------------------------------------------------------------- */
+
+ /* This is not strictly required since the process is exiting and the */
+ /* system will reclaim the memory anyway. It's useful, though, just as */
+ /* a list of what is currently malloc'ed by this program. Plus, it's */
+ /* always a good habit to explicitly free whatever you malloc. */
+
+ free (Ap) ;
+ free (Ai) ;
+ free (Ax) ;
+
+ free (Cp) ;
+ free (Ci) ;
+ free (Cx) ;
+
+ free (Pinit) ;
+ free (Qinit) ;
+ free (Front_npivcol) ;
+ free (Front_1strow) ;
+ free (Front_leftmostdesc) ;
+ free (Front_parent) ;
+ free (Chain_start) ;
+ free (Chain_maxrows) ;
+ free (Chain_maxcols) ;
+
+ free (Lp) ;
+ free (Lj) ;
+ free (Lx) ;
+
+ free (Up) ;
+ free (Ui) ;
+ free (Ux) ;
+
+ free (P) ;
+ free (Q) ;
+
+ free (Li) ;
+
+ free (Wi) ;
+ free (W) ;
+
+ umfpack_di_free_symbolic (&Symbolic) ;
+ umfpack_di_free_numeric (&Numeric) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print the total time spent in this demo */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_toc (t) ;
+ printf ("\numfpack_di_demo complete.\nTotal time: %5.2f seconds"
+ " (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ;
+ return (0) ;
+}
diff --git a/UMFPACK/Demo/umfpack_di_demo.out b/UMFPACK/Demo/umfpack_di_demo.out
new file mode 100644
index 0000000..be6d587
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_di_demo.out
@@ -0,0 +1,1523 @@
+
+UMFPACK V5.2 (Nov 1, 2007) demo: _di_ version
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+
+UMFPACK License:
+
+ UMFPACK is available under alternate licenses,
+ contact T. Davis for details.
+
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU General Public
+ License as published by the Free Software Foundation; either
+ version 2 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU GPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability: http://www.cise.ufl.edu/research/sparse/umfpack
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: int
+
+ 0: print level: 5
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+
+b: dense vector, n = 5.
+ 0 : (8)
+ 1 : (45)
+ 2 : (-3)
+ 3 : (3)
+ 4 : (19)
+ dense vector OK
+
+
+A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12.
+ 0 : 0 0 (2)
+ 1 : 4 4 (1)
+ 2 : 1 0 (3)
+ 3 : 1 2 (4)
+ 4 : 2 1 (-1)
+ 5 : 2 2 (-3)
+ 6 : 0 1 (3)
+ 7 : 1 4 (6)
+ 8 : 2 3 (2)
+ 9 : 3 2 (1)
+ 10 : 4 1 (4)
+ 11 : 4 2 (2)
+ triplet-form matrix OK
+
+
+A: column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2)
+ row 1 : (3)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (3)
+ row 2 : (-1)
+ row 4 : (4)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (4)
+ row 2 : (-3)
+ row 3 : (1)
+ row 4 : (2)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (2)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (6)
+ row 4 : (1)
+ column-form matrix OK
+
+
+Symbolic factorization of A: Symbolic object:
+ matrix to be factorized:
+ n_row: 5 n_col: 5
+ number of entries: 12
+ block size used for dense matrix kernels: 32
+ strategy used: unsymmetric
+ ordering used: colamd on A
+
+ performn column etree postorder: yes
+ prefer diagonal pivoting (attempt P=Q): no
+ variable-size part of Numeric object:
+ minimum initial size (Units): 80 (MBytes): 0.0
+ estimated peak size (Units): 1301 (MBytes): 0.0
+ estimated final size (Units): 15 (MBytes): 0.0
+ symbolic factorization memory usage (Units): 151 (MBytes): 0.0
+ frontal matrices / supercolumns:
+ number of frontal chains: 1
+ number of frontal matrices: 1
+ largest frontal matrix row dimension: 3
+ largest frontal matrix column dimension: 3
+
+ Frontal chain: 0. Frontal matrices 0 to 0
+ Largest frontal matrix in Frontal chain: 3-by-3
+ Front: 0 pivot cols: 3 (pivot columns 0 to 2)
+ pivot row candidates: 2 to 4
+ leftmost descendant: 0
+ 1st new candidate row : 2
+ parent: (none)
+
+Initial column permutation, Q1: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Initial row permutation, P1: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 1
+ 4 : 4
+ permutation vector OK
+
+ Symbolic object: OK
+
+
+Numeric factorization of A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.30000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 87
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 1292
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 4
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 4
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 6
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.42857e-01
+ max abs. value on diagonal of U: 2.19231e+00
+ reciprocal condition number estimate: 6.52e-02
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.2)
+ 1 : (0.0769231)
+ 2 : (0.166667)
+ 3 : (1)
+ 4 : (0.142857)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 4 : (0.307692)
+ row 3 : (0.285714)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.576923)
+
+ column 3: length 1.
+ row 4 : (3.23077)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.571429)
+
+ row 2: length 1.
+ col 4 : (0.6)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (-0.5)
+ col 4 : (-0.166667)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.333333)
+ 1 : (1)
+ 2 : (0.4)
+ 3 : (0.142857)
+ 4 : (-2.19231)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.30000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 80 70 88%
+ peak size (Units) 1301 1292 99%
+ final size (Units) 15 13 87%
+ Numeric final size (Units) 92 88 96%
+ Numeric final size (MBytes) 0.0 0.0 96%
+ peak memory usage (Units) 1487 1478 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 6.00000e+00 46%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.43e-01
+ max abs. value on diagonal of U: 2.19e+00
+ estimate of reciprocal of condition number: 6.52e-02
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.19000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 1.18e-16
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.25000e+02
+
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+
+x (solution of Ax=b): dense vector, n = 5.
+ 0 : (1)
+ 1 : (2)
+ 2 : (3)
+ 3 : (4)
+ 4 : (5)
+ dense vector OK
+
+maxnorm of residual: 1.06581e-14
+
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+determinant: (1.14) * 10^(2)
+
+x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5.
+ 0 : (1)
+ 1 : (2)
+ 2 : (3)
+ 3 : (4)
+ 4 : (5)
+ dense vector OK
+
+maxnorm of residual: 1.06581e-14
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.30000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 80 70 88%
+ peak size (Units) 1301 1292 99%
+ final size (Units) 15 13 87%
+ Numeric final size (Units) 92 88 96%
+ Numeric final size (MBytes) 0.0 0.0 96%
+ peak memory usage (Units) 1487 1478 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 6.00000e+00 46%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.43e-01
+ max abs. value on diagonal of U: 2.19e+00
+ estimate of reciprocal of condition number: 6.52e-02
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.11000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 7.64e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.17000e+02
+
+
+x (solution of A'x=b): dense vector, n = 5.
+ 0 : (1.81579)
+ 1 : (1.45614)
+ 2 : (1.5)
+ 3 : (-24.8509)
+ 4 : (10.2632)
+ dense vector OK
+
+maxnorm of residual: 7.10543e-15
+
+
+changing A (1,4) to zero
+
+modified A: column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2)
+ row 1 : (3)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (3)
+ row 2 : (-1)
+ row 4 : (4)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (4)
+ row 2 : (-3)
+ row 3 : (1)
+ row 4 : (2)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (2)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (0)
+ row 4 : (1)
+ column-form matrix OK
+
+
+Numeric factorization of modified A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 7.00000e+00
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 86
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 1292
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 4
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 3
+ number of entries stored in U (excl diag): 1
+ factorization floating-point operations: 4
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.50000e-01
+ max abs. value on diagonal of U: 1.00000e+00
+ reciprocal condition number estimate: 1.50e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.2)
+ 1 : (0.142857)
+ 2 : (0.166667)
+ 3 : (1)
+ 4 : (0.142857)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 1
+ 3 : 4
+ 4 : 0
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 1
+ 4 : 4
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 2 : (0.571429)
+ row 3 : (0.285714)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.933333)
+
+ column 3: length 1.
+ row 4 : (1.05)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.142857)
+
+ row 2: length 0. End of Uchain.
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (-0.5)
+ col 3 : (-0.166667)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.333333)
+ 1 : (1)
+ 2 : (0.428571)
+ 3 : (0.571429)
+ 4 : (-0.15)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 7.00000e+00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 80 70 88%
+ peak size (Units) 1301 1292 99%
+ final size (Units) 15 12 80%
+ Numeric final size (Units) 92 87 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 1487 1478 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 4.00000e+00 31%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 8 80%
+ nz in L+U (incl diagonal) 15 12 80%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 8
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.50e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 1.50e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 8
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.17000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 7.89e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.21000e+02
+
+
+x (with modified A): dense vector, n = 5.
+ 0 : (11)
+ 1 : (-4.66667)
+ 2 : (3)
+ 3 : (0.666667)
+ 4 : (31.6667)
+ dense vector OK
+
+maxnorm of residual: 7.10543e-15
+
+changing A (0,0) from 2 to 2
+changing A (1,0) from 3 to 2
+changing A (0,1) from 3 to 13
+changing A (2,1) from -1 to 7
+changing A (4,1) from 4 to 10
+changing A (1,2) from 4 to 23
+changing A (2,2) from -3 to 15
+changing A (3,2) from 1 to 18
+changing A (4,2) from 2 to 18
+changing A (2,3) from 2 to 30
+changing A (1,4) from 0 to 39
+changing A (4,4) from 1 to 37
+
+completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2)
+ row 1 : (2)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (13)
+ row 2 : (7)
+ row 4 : (10)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (23)
+ row 2 : (15)
+ row 3 : (18)
+ row 4 : (18)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (30)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (39)
+ row 4 : (37)
+ column-form matrix OK
+
+
+Saving symbolic object:
+
+Freeing symbolic object:
+
+Loading symbolic object:
+
+Done loading symbolic object
+
+Numeric factorization of completely modified A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.50000e+01
+ maximum sum (abs (rows of A)): 6.50000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 87
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 1292
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 4
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 4
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 6
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.33333e-01
+ max abs. value on diagonal of U: 1.00000e+00
+ reciprocal condition number estimate: 1.33e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.0666667)
+ 1 : (0.015625)
+ 2 : (0.0192308)
+ 3 : (0.0555556)
+ 4 : (0.0153846)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 4 : (0.359375)
+ row 3 : (0.276923)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.234375)
+
+ column 3: length 1.
+ row 4 : (1.07052)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.153846)
+
+ row 2: length 1.
+ col 4 : (0.866667)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (0.288462)
+ col 4 : (0.134615)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.576923)
+ 1 : (1)
+ 2 : (0.133333)
+ 3 : (0.569231)
+ 4 : (-0.367821)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.50000e+01
+ maximum sum (abs (rows of A)): 6.50000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 80 70 88%
+ peak size (Units) 1301 1292 99%
+ final size (Units) 15 13 87%
+ Numeric final size (Units) 92 88 96%
+ Numeric final size (MBytes) 0.0 0.0 96%
+ peak memory usage (Units) 1487 1478 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 6.00000e+00 46%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.33e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 1.33e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.19000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 1.04e-16
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.25000e+02
+
+
+x (with completely modified A): dense vector, n = 5.
+ 0 : (8.50124)
+ 1 : (-0.692499)
+ 2 : (0.166667)
+ 3 : (-0.0217502)
+ 4 : (0.619594)
+ dense vector OK
+
+maxnorm of residual: 3.55271e-15
+
+
+C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2)
+ row 1 : (13)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (2)
+ row 2 : (23)
+ row 4 : (39)
+
+ column 2: start: 5 end: 7 entries: 3
+ row 1 : (7)
+ row 2 : (15)
+ row 3 : (30)
+
+ column 3: start: 8 end: 8 entries: 1
+ row 2 : (18)
+
+ column 4: start: 9 end: 11 entries: 3
+ row 1 : (10)
+ row 2 : (18)
+ row 4 : (37)
+ column-form matrix OK
+
+
+Symbolic factorization of C: Symbolic object:
+ matrix to be factorized:
+ n_row: 5 n_col: 5
+ number of entries: 12
+ block size used for dense matrix kernels: 32
+ strategy used: unsymmetric
+ ordering used: colamd on A
+
+ performn column etree postorder: yes
+ prefer diagonal pivoting (attempt P=Q): no
+ variable-size part of Numeric object:
+ minimum initial size (Units): 81 (MBytes): 0.0
+ estimated peak size (Units): 1302 (MBytes): 0.0
+ estimated final size (Units): 16 (MBytes): 0.0
+ symbolic factorization memory usage (Units): 151 (MBytes): 0.0
+ frontal matrices / supercolumns:
+ number of frontal chains: 1
+ number of frontal matrices: 1
+ largest frontal matrix row dimension: 3
+ largest frontal matrix column dimension: 3
+
+ Frontal chain: 0. Frontal matrices 0 to 0
+ Largest frontal matrix in Frontal chain: 3-by-3
+ Front: 0 pivot cols: 3 (pivot columns 0 to 2)
+ pivot row candidates: 2 to 4
+ leftmost descendant: 0
+ 1st new candidate row : 2
+ parent: (none)
+
+Initial column permutation, Q1: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Initial row permutation, P1: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 1
+ 4 : 4
+ permutation vector OK
+
+ Symbolic object: OK
+
+
+Get the contents of the Symbolic object for C:
+(compare with umfpack_di_report_symbolic output, above)
+From the Symbolic object, C is of dimension 5-by-5
+ with nz = 12, number of fronts = 1,
+ number of frontal matrix chains = 1
+
+Pivot columns in each front, and parent of each front:
+ Front 0: parent front: -1 number of pivot cols: 3
+ 0-th pivot column is column 3 in original matrix
+ 1-th pivot column is column 2 in original matrix
+ 2-th pivot column is column 0 in original matrix
+
+Note that the column ordering, above, will be refined
+in the numeric factorization below. The assignment of pivot
+columns to frontal matrices will always remain unchanged.
+
+Total number of pivot columns in frontal matrices: 3
+
+Frontal matrix chains:
+ Frontal matrices 0 to 0 are factorized in a single
+ working array of size 3-by-3
+
+Numeric factorization of C: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 4.00000e+00
+ maximum sum (abs (rows of A)): 7.60000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 88
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 1293
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 3
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 5
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 6
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.43243e-01
+ max abs. value on diagonal of U: 1.00000e+00
+ reciprocal condition number estimate: 2.43e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.25)
+ 1 : (0.0333333)
+ 2 : (0.0135135)
+ 3 : (0.0333333)
+ 4 : (0.0131579)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 1.
+ row 4 : (0.233333)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.866667)
+
+ column 3: length 1.
+ row 4 : (0.684685)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.513158)
+
+ row 2: length 1.
+ col 4 : (0.5)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 3.
+ col 1 : (0.202703)
+ col 3 : (0.243243)
+ col 4 : (0.310811)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.243243)
+ 1 : (1)
+ 2 : (0.5)
+ 3 : (0.486842)
+ 4 : (-0.784685)
+ dense vector OK
+
+ Numeric object: OK
+
+
+L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8.
+
+ row 0: start: 0 end: 0 entries: 1
+ column 0 : (1)
+
+ row 1: start: 1 end: 1 entries: 1
+ column 1 : (1)
+
+ row 2: start: 2 end: 2 entries: 1
+ column 2 : (1)
+
+ row 3: start: 3 end: 3 entries: 1
+ column 3 : (1)
+
+ row 4: start: 4 end: 7 entries: 4
+ column 1 : (0.233333)
+ column 2 : (0.866667)
+ column 3 : (0.684685)
+ column 4 : (1)
+ row-form matrix OK
+
+
+U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10.
+
+ column 0: start: 0 end: 0 entries: 1
+ row 0 : (0.243243)
+
+ column 1: start: 1 end: 2 entries: 2
+ row 0 : (0.202703)
+ row 1 : (1)
+
+ column 2: start: 3 end: 3 entries: 1
+ row 2 : (0.5)
+
+ column 3: start: 4 end: 5 entries: 2
+ row 0 : (0.243243)
+ row 3 : (0.486842)
+
+ column 4: start: 6 end: 9 entries: 4
+ row 0 : (0.310811)
+ row 2 : (0.5)
+ row 3 : (0.513158)
+ row 4 : (-0.784685)
+ column-form matrix OK
+
+
+P: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Scale factors: row i of A is to be multiplied by the ith scale factor
+0: 0.25
+1: 0.0333333
+2: 0.0135135
+3: 0.0333333
+4: 0.0131579
+
+Converting L to triplet form, and printing it:
+
+L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8.
+ 0 : 0 0 (1)
+ 1 : 1 1 (1)
+ 2 : 2 2 (1)
+ 3 : 3 3 (1)
+ 4 : 4 1 (0.233333)
+ 5 : 4 2 (0.866667)
+ 6 : 4 3 (0.684685)
+ 7 : 4 4 (1)
+ triplet-form matrix OK
+
+
+Saving numeric object:
+
+Freeing numeric object:
+
+Loading numeric object:
+
+Done loading numeric object
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 4.00000e+00
+ maximum sum (abs (rows of A)): 7.60000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 81 71 88%
+ peak size (Units) 1302 1293 99%
+ final size (Units) 16 14 88%
+ Numeric final size (Units) 93 89 96%
+ Numeric final size (MBytes) 0.0 0.0 96%
+ peak memory usage (Units) 1488 1479 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 6.00000e+00 46%
+ nz in L (incl diagonal) 9 8 89%
+ nz in U (incl diagonal) 11 10 91%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 8
+ nz in U (incl diagonal), if none dropped 10
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.43e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 2.43e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.11000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 8.07e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.17000e+02
+
+
+x (solution of C'x=b): dense vector, n = 5.
+ 0 : (8.50124)
+ 1 : (-0.692499)
+ 2 : (0.166667)
+ 3 : (-0.0217502)
+ 4 : (0.619594)
+ dense vector OK
+
+maxnorm of residual: 3.55271e-15
+
+
+Solving C'x=b again, using umfpack_di_wsolve instead:
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 4.00000e+00
+ maximum sum (abs (rows of A)): 7.60000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 81 71 88%
+ peak size (Units) 1302 1293 99%
+ final size (Units) 16 14 88%
+ Numeric final size (Units) 93 89 96%
+ Numeric final size (MBytes) 0.0 0.0 96%
+ peak memory usage (Units) 1488 1479 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 6.00000e+00 46%
+ nz in L (incl diagonal) 9 8 89%
+ nz in U (incl diagonal) 11 10 91%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 8
+ nz in U (incl diagonal), if none dropped 10
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.43e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 2.43e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.11000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 8.07e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.17000e+02
+
+
+x (solution of C'x=b): dense vector, n = 5.
+ 0 : (8.50124)
+ 1 : (-0.692499)
+ 2 : (0.166667)
+ 3 : (-0.0217502)
+ 4 : (0.619594)
+ dense vector OK
+
+maxnorm of residual: 3.55271e-15
+
+
+umfpack_di_demo complete.
+Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time)
diff --git a/UMFPACK/Demo/umfpack_di_demo.sed b/UMFPACK/Demo/umfpack_di_demo.sed
new file mode 100644
index 0000000..9d5d64f
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_di_demo.sed
@@ -0,0 +1,78 @@
+/::/d
+1,$s/_xx_/_di_/g
+1,$s/Int/int/g
+1,$s/WSIZE/5/
+1,$s/%ld/%d/g
+/define ABS/ {
+ s/ABS/ABS(x) ((x) >= 0 ? (x) : -(x))/
+ }
+/, rz \[i\]/ {
+ s/, rz \[i\]//
+ }
+/, Avalz/ {
+ s/, Avalz//
+ }
+/, rz/ {
+ s/, rz//
+ }
+/, bz/ {
+ s/, bz//
+ }
+/, xz/ {
+ s/, xz//
+ }
+
+/, Lz/ {
+ s/, Lz//
+ }
+/, Uz/ {
+ s/, Uz//
+ }
+/, Dz/ {
+ s/, Dz//
+ }
+/, Az/ {
+ s/, Az//
+ }
+/, Cz, TRUE/ {
+ s/, Cz, TRUE//
+ }
+/, Cz/ {
+ s/, Cz//
+ }
+/, Rbz/ {
+ s/, Rbz//
+ }
+/, yz/ {
+ s/, yz//
+ }
+
+/ || !Lz/ {
+ s/ || !Lz//
+ }
+/ || !Uz/ {
+ s/ || !Uz//
+ }
+/ || !Dz/ {
+ s/ || !Dz//
+ }
+/ || !Az/ {
+ s/ || !Az//
+ }
+/ || !Cz/ {
+ s/ || !Cz//
+ }
+
+/rz/d
+/Rbz/d
+/yz/d
+/Avalz/d
+/Az/d
+/Cz/d
+/bz/d
+/xz/d
+/Lz/d
+/Uz/d
+/Dz/d
+/complex/d
+
diff --git a/UMFPACK/Demo/umfpack_dl_demo.c b/UMFPACK/Demo/umfpack_dl_demo.c
new file mode 100644
index 0000000..eaa8668
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_dl_demo.c
@@ -0,0 +1,760 @@
+/* ========================================================================== */
+/* === umfpack_dl_demo ====================================================== */
+/* ========================================================================== */
+
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ A demo of UMFPACK: umfpack_dl_* version.
+
+ First, factor and solve a 5-by-5 system, Ax=b, using default parameters.
+ Then solve A'x=b using the factors of A. Modify one entry (A (1,4) = 0,
+ where the row and column indices range from 0 to 4. The pattern of A
+ has not changed (it has explicitly zero entry), so a reanalysis with
+ umfpack_dl_symbolic does not need to be done. Refactorize (with
+ umfpack_dl_numeric), and solve Ax=b. Note that the pivot ordering has
+ changed. Next, change all of the entries in A, but not the pattern.
+
+ Finally, compute C = A', and do the symbolic and numeric factorization of C.
+ Factorizing A' can sometimes be better than factorizing A itself (less work
+ and memory usage). Solve C'x=b twice; the solution is the same as the
+ solution to Ax=b.
+
+ A note about zero-sized arrays: UMFPACK uses many user-provided arrays of
+ size n (order of the matrix), and of size nz (the number of nonzeros in a
+ matrix). n cannot be zero; UMFPACK does not handle zero-dimensioned arrays.
+ However, nz can be zero. If you attempt to malloc an array of size nz = 0,
+ however, malloc will return a null pointer which UMFPACK will report as a
+ "missing argument." Thus, nz1 in this code is set to MAX (nz,1), and
+ similarly for lnz and unz. Lnz can never be zero, however, since L is always
+ unit diagonal.
+*/
+
+/* -------------------------------------------------------------------------- */
+/* definitions */
+/* -------------------------------------------------------------------------- */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "umfpack.h"
+
+#define ABS(x) ((x) >= 0 ? (x) : -(x))
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#ifndef TRUE
+#define TRUE (1)
+#endif
+#ifndef FALSE
+#define FALSE (0)
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* triplet form of the matrix. The triplets can be in any order. */
+/* -------------------------------------------------------------------------- */
+
+static UF_long n = 5, nz = 12 ;
+static UF_long Arow [ ] = { 0, 4, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4} ;
+static UF_long Acol [ ] = { 0, 4, 0, 2, 1, 2, 1, 4, 3, 2, 1, 2} ;
+static double Aval [ ] = {2., 1., 3., 4., -1., -3., 3., 6., 2., 1., 4., 2.} ;
+static double b [ ] = {8., 45., -3., 3., 19.}, x [5], r [5] ;
+
+
+/* -------------------------------------------------------------------------- */
+/* error: print a message and exit */
+/* -------------------------------------------------------------------------- */
+
+static void error
+(
+ char *message
+)
+{
+ printf ("\n\n====== error: %s =====\n\n", message) ;
+ exit (1) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* resid: compute the residual, r = Ax-b or r = A'x=b and return maxnorm (r) */
+/* -------------------------------------------------------------------------- */
+
+static double resid
+(
+ UF_long transpose,
+ UF_long Ap [ ],
+ UF_long Ai [ ],
+ double Ax [ ]
+)
+{
+ UF_long i, j, p ;
+ double norm ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ r [i] = -b [i] ;
+ }
+ if (transpose)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ r [j] += Ax [p] * x [i] ;
+ }
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ r [i] += Ax [p] * x [j] ;
+ }
+ }
+ }
+ norm = 0. ;
+ for (i = 0 ; i < n ; i++)
+ {
+ norm = MAX (ABS (r [i]), norm) ;
+ }
+ return (norm) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* main program */
+/* -------------------------------------------------------------------------- */
+
+int main (int argc, char **argv)
+{
+ double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux,
+ *W, t [2], *Dx, rnorm, *Rb, *y, *Rs ;
+ UF_long *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up,
+ *P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1,
+ status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1,
+ *Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc,
+ nzud, do_recip ;
+ void *Symbolic, *Numeric ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (t) ;
+
+ printf ("\nUMFPACK V%d.%d (%s) demo: _dl_ version\n",
+ UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ;
+
+ /* get the default control parameters */
+ umfpack_dl_defaults (Control) ;
+
+ /* change the default print level for this demo */
+ /* (otherwise, nothing will print) */
+ Control [UMFPACK_PRL] = 6 ;
+
+ /* print the license agreement */
+ umfpack_dl_report_status (Control, UMFPACK_OK) ;
+ Control [UMFPACK_PRL] = 5 ;
+
+ /* print the control parameters */
+ umfpack_dl_report_control (Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print A and b, and convert A to column-form */
+ /* ---------------------------------------------------------------------- */
+
+ /* print the right-hand-side */
+ printf ("\nb: ") ;
+ (void) umfpack_dl_report_vector (n, b, Control) ;
+
+ /* print the triplet form of the matrix */
+ printf ("\nA: ") ;
+ (void) umfpack_dl_report_triplet (n, n, nz, Arow, Acol, Aval,
+ Control) ;
+
+ /* convert to column form */
+ nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */
+ Ap = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Ai = (UF_long *) malloc (nz1 * sizeof (UF_long)) ;
+ Ax = (double *) malloc (nz1 * sizeof (double)) ;
+ if (!Ap || !Ai || !Ax)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_dl_triplet_to_col (n, n, nz, Arow, Acol, Aval,
+ Ap, Ai, Ax, (UF_long *) NULL) ;
+
+ if (status < 0)
+ {
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_triplet_to_col failed") ;
+ }
+
+ /* print the column-form of A */
+ printf ("\nA: ") ;
+ (void) umfpack_dl_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_dl_symbolic (n, n, Ap, Ai, Ax, &Symbolic,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_info (Control, Info) ;
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_symbolic failed") ;
+ }
+
+ /* print the symbolic factorization */
+
+ printf ("\nSymbolic factorization of A: ") ;
+ (void) umfpack_dl_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_info (Control, Info) ;
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_numeric failed") ;
+ }
+
+ /* print the numeric factorization */
+ printf ("\nNumeric factorization of A: ") ;
+ (void) umfpack_dl_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_dl_solve (UMFPACK_A, Ap, Ai, Ax, x, b,
+ Numeric, Control, Info) ;
+ umfpack_dl_report_info (Control, Info) ;
+ umfpack_dl_report_status (Control, status) ;
+ if (status < 0)
+ {
+ error ("umfpack_dl_solve failed") ;
+ }
+ printf ("\nx (solution of Ax=b): ") ;
+ (void) umfpack_dl_report_vector (n, x, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the determinant */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_dl_get_determinant (x, r, Numeric, Info) ;
+ umfpack_dl_report_status (Control, status) ;
+ if (status < 0)
+ {
+ error ("umfpack_dl_get_determinant failed") ;
+ }
+ printf ("determinant: (%g", x [0]) ;
+ printf (") * 10^(%g)\n", r [0]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, broken down into steps */
+ /* ---------------------------------------------------------------------- */
+
+ /* Rb = R*b */
+ Rb = (double *) malloc (n * sizeof (double)) ;
+ y = (double *) malloc (n * sizeof (double)) ;
+ if (!Rb || !y) error ("out of memory") ;
+
+ status = umfpack_dl_scale (Rb, b, Numeric) ;
+ if (status < 0) error ("umfpack_dl_scale failed") ;
+ /* solve Ly = P*(Rb) */
+ status = umfpack_dl_solve (UMFPACK_Pt_L, Ap, Ai, Ax, y, Rb,
+ Numeric, Control, Info) ;
+ if (status < 0) error ("umfpack_dl_solve failed") ;
+ /* solve UQ'x=y */
+ status = umfpack_dl_solve (UMFPACK_U_Qt, Ap, Ai, Ax, x, y,
+ Numeric, Control, Info) ;
+ if (status < 0) error ("umfpack_dl_solve failed") ;
+ printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ;
+ (void) umfpack_dl_report_vector (n, x, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ free (Rb) ;
+ free (y) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve A'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_dl_solve (UMFPACK_At, Ap, Ai, Ax, x, b,
+ Numeric, Control, Info) ;
+ umfpack_dl_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ error ("umfpack_dl_solve failed") ;
+ }
+ printf ("\nx (solution of A'x=b): ") ;
+ (void) umfpack_dl_report_vector (n, x, Control) ;
+ rnorm = resid (TRUE, Ap, Ai, Ax) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify one numerical value in the column-form of A */
+ /* ---------------------------------------------------------------------- */
+
+ /* change A (1,4), look for row index 1 in column 4. */
+ row = 1 ;
+ col = 4 ;
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ if (row == Ai [p])
+ {
+ printf ("\nchanging A (%ld,%ld) to zero\n", row, col) ;
+ Ax [p] = 0.0 ;
+ break ;
+ }
+ }
+ printf ("\nmodified A: ") ;
+ (void) umfpack_dl_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* redo the numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */
+ /* doesn't have to be redone, no matter how much we change Ax. */
+
+ /* We don't need the Numeric object any more, so free it. */
+ umfpack_dl_free_numeric (&Numeric) ;
+
+ /* Note that a memory leak would have occurred if the old Numeric */
+ /* had not been free'd with umfpack_dl_free_numeric above. */
+ status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_info (Control, Info) ;
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of modified A: ") ;
+ (void) umfpack_dl_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, with the modified A */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_dl_solve (UMFPACK_A, Ap, Ai, Ax, x, b,
+ Numeric, Control, Info) ;
+ umfpack_dl_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_solve failed") ;
+ }
+ printf ("\nx (with modified A): ") ;
+ (void) umfpack_dl_report_vector (n, x, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify all of the numerical values of A, but not the pattern */
+ /* ---------------------------------------------------------------------- */
+
+ for (col = 0 ; col < n ; col++)
+ {
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ row = Ai [p] ;
+ printf ("changing ") ;
+ printf ("A (%ld,%ld) from %g", row, col, Ax [p]) ;
+ Ax [p] = Ax [p] + col*10 - row ;
+ printf (" to %g\n", Ax [p]) ;
+ }
+ }
+ printf ("\ncompletely modified A (same pattern): ") ;
+ (void) umfpack_dl_report_matrix (n, n, Ap, Ai, Ax, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* save the Symbolic object to file, free it, and load it back in */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the default filename, "symbolic.umf" */
+ printf ("\nSaving symbolic object:\n") ;
+ status = umfpack_dl_save_symbolic (Symbolic, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_save_symbolic failed") ;
+ }
+ printf ("\nFreeing symbolic object:\n") ;
+ umfpack_dl_free_symbolic (&Symbolic) ;
+ printf ("\nLoading symbolic object:\n") ;
+ status = umfpack_dl_load_symbolic (&Symbolic, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_load_symbolic failed") ;
+ }
+ printf ("\nDone loading symbolic object\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* redo the numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_dl_free_numeric (&Numeric) ;
+ status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_info (Control, Info) ;
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of completely modified A: ") ;
+ (void) umfpack_dl_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, with the modified A */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_dl_solve (UMFPACK_A, Ap, Ai, Ax, x, b,
+ Numeric, Control, Info) ;
+ umfpack_dl_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_solve failed") ;
+ }
+ printf ("\nx (with completely modified A): ") ;
+ (void) umfpack_dl_report_vector (n, x, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the symbolic and numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_dl_free_symbolic (&Symbolic) ;
+ umfpack_dl_free_numeric (&Numeric) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = transpose of A */
+ /* ---------------------------------------------------------------------- */
+
+ Cp = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Ci = (UF_long *) malloc (nz1 * sizeof (UF_long)) ;
+ Cx = (double *) malloc (nz1 * sizeof (double)) ;
+ if (!Cp || !Ci || !Cx)
+ {
+ error ("out of memory") ;
+ }
+ status = umfpack_dl_transpose (n, n, Ap, Ai, Ax,
+ (UF_long *) NULL, (UF_long *) NULL, Cp, Ci, Cx) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_transpose failed: ") ;
+ }
+ printf ("\nC (transpose of A): ") ;
+ (void) umfpack_dl_report_matrix (n, n, Cp, Ci, Cx, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization of C */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_dl_symbolic (n, n, Cp, Ci, Cx, &Symbolic,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_info (Control, Info) ;
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_symbolic failed") ;
+ }
+ printf ("\nSymbolic factorization of C: ") ;
+ (void) umfpack_dl_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the contents of Symbolic into user arrays print them */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nGet the contents of the Symbolic object for C:\n") ;
+ printf ("(compare with umfpack_dl_report_symbolic output, above)\n") ;
+ Pinit = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Qinit = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Front_npivcol = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Front_1strow = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Front_leftmostdesc = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Front_parent = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Chain_start = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Chain_maxrows = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Chain_maxcols = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start ||
+ !Chain_maxrows || !Chain_maxcols || !Front_1strow ||
+ !Front_leftmostdesc)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_dl_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains,
+ Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+ if (status < 0)
+ {
+ error ("symbolic factorization invalid") ;
+ }
+
+ printf ("From the Symbolic object, C is of dimension %ld-by-%ld\n", nr, nc);
+ printf (" with nz = %ld, number of fronts = %ld,\n", nz, nfr) ;
+ printf (" number of frontal matrix chains = %ld\n", nchains) ;
+
+ printf ("\nPivot columns in each front, and parent of each front:\n") ;
+ k = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fnpiv = Front_npivcol [i] ;
+ printf (" Front %ld: parent front: %ld number of pivot cols: %ld\n",
+ i, Front_parent [i], fnpiv) ;
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ col = Qinit [k] ;
+ printf (
+ " %ld-th pivot column is column %ld in original matrix\n",
+ k, col) ;
+ k++ ;
+ }
+ }
+
+ printf ("\nNote that the column ordering, above, will be refined\n") ;
+ printf ("in the numeric factorization below. The assignment of pivot\n") ;
+ printf ("columns to frontal matrices will always remain unchanged.\n") ;
+
+ printf ("\nTotal number of pivot columns in frontal matrices: %ld\n", k) ;
+
+ printf ("\nFrontal matrix chains:\n") ;
+ for (j = 0 ; j < nchains ; j++)
+ {
+ printf (" Frontal matrices %ld to %ld are factorized in a single\n",
+ Chain_start [j], Chain_start [j+1] - 1) ;
+ printf (" working array of size %ld-by-%ld\n",
+ Chain_maxrows [j], Chain_maxcols [j]) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization of C */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_dl_numeric (Cp, Ci, Cx, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ error ("umfpack_dl_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of C: ") ;
+ (void) umfpack_dl_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extract the LU factors of C and print them */
+ /* ---------------------------------------------------------------------- */
+
+ if (umfpack_dl_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0)
+ {
+ error ("umfpack_dl_get_lunz failed") ;
+ }
+ /* ensure arrays are not of zero size */
+ lnz1 = MAX (lnz,1) ;
+ unz1 = MAX (unz,1) ;
+ Lp = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Lj = (UF_long *) malloc (lnz1 * sizeof (UF_long)) ;
+ Lx = (double *) malloc (lnz1 * sizeof (double)) ;
+ Up = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Ui = (UF_long *) malloc (unz1 * sizeof (UF_long)) ;
+ Ux = (double *) malloc (unz1 * sizeof (double)) ;
+ P = (UF_long *) malloc (n * sizeof (UF_long)) ;
+ Q = (UF_long *) malloc (n * sizeof (UF_long)) ;
+ Dx = (double *) NULL ; /* D vector not requested */
+ Rs = (double *) malloc (n * sizeof (double)) ;
+ if (!Lp || !Lj || !Lx || !Up || !Ui || !Ux || !P || !Q || !Rs)
+ {
+ error ("out of memory") ;
+ }
+ status = umfpack_dl_get_numeric (Lp, Lj, Lx, Up, Ui, Ux,
+ P, Q, Dx, &do_recip, Rs, Numeric) ;
+ if (status < 0)
+ {
+ error ("umfpack_dl_get_numeric failed") ;
+ }
+
+ printf ("\nL (lower triangular factor of C): ") ;
+ (void) umfpack_dl_report_matrix (n, n, Lp, Lj, Lx, 0, Control) ;
+ printf ("\nU (upper triangular factor of C): ") ;
+ (void) umfpack_dl_report_matrix (n, n, Up, Ui, Ux, 1, Control) ;
+ printf ("\nP: ") ;
+ (void) umfpack_dl_report_perm (n, P, Control) ;
+ printf ("\nQ: ") ;
+ (void) umfpack_dl_report_perm (n, Q, Control) ;
+ printf ("\nScale factors: row i of A is to be ") ;
+ if (do_recip)
+ {
+ printf ("multiplied by the ith scale factor\n") ;
+ }
+ else
+ {
+ printf ("divided by the ith scale factor\n") ;
+ }
+ for (i = 0 ; i < n ; i++) printf ("%ld: %g\n", i, Rs [i]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to triplet form and print it */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that L is in row-form, so it is the row indices that are created */
+ /* by umfpack_dl_col_to_triplet. */
+
+ printf ("\nConverting L to triplet form, and printing it:\n") ;
+ Li = (UF_long *) malloc (lnz1 * sizeof (UF_long)) ;
+ if (!Li)
+ {
+ error ("out of memory") ;
+ }
+ if (umfpack_dl_col_to_triplet (n, Lp, Li) < 0)
+ {
+ error ("umfpack_dl_col_to_triplet failed") ;
+ }
+ printf ("\nL, in triplet form: ") ;
+ (void) umfpack_dl_report_triplet (n, n, lnz, Li, Lj, Lx, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* save the Numeric object to file, free it, and load it back in */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the default filename, "numeric.umf" */
+ printf ("\nSaving numeric object:\n") ;
+ status = umfpack_dl_save_numeric (Numeric, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_save_numeric failed") ;
+ }
+ printf ("\nFreeing numeric object:\n") ;
+ umfpack_dl_free_numeric (&Numeric) ;
+ printf ("\nLoading numeric object:\n") ;
+ status = umfpack_dl_load_numeric (&Numeric, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_load_numeric failed") ;
+ }
+ printf ("\nDone loading numeric object\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve C'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_dl_solve (UMFPACK_At, Cp, Ci, Cx, x, b,
+ Numeric, Control, Info) ;
+ umfpack_dl_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_solve failed") ;
+ }
+ printf ("\nx (solution of C'x=b): ") ;
+ (void) umfpack_dl_report_vector (n, x, Control) ;
+ rnorm = resid (TRUE, Cp, Ci, Cx) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve C'x=b again, using umfpack_dl_wsolve instead */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nSolving C'x=b again, using umfpack_dl_wsolve instead:\n") ;
+ Wi = (UF_long *) malloc (n * sizeof (UF_long)) ;
+ W = (double *) malloc (5*n * sizeof (double)) ;
+ if (!Wi || !W)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_dl_wsolve (UMFPACK_At, Cp, Ci, Cx, x, b,
+ Numeric, Control, Info, Wi, W) ;
+ umfpack_dl_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_dl_report_status (Control, status) ;
+ error ("umfpack_dl_wsolve failed") ;
+ }
+ printf ("\nx (solution of C'x=b): ") ;
+ (void) umfpack_dl_report_vector (n, x, Control) ;
+ rnorm = resid (TRUE, Cp, Ci, Cx) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free everything */
+ /* ---------------------------------------------------------------------- */
+
+ /* This is not strictly required since the process is exiting and the */
+ /* system will reclaim the memory anyway. It's useful, though, just as */
+ /* a list of what is currently malloc'ed by this program. Plus, it's */
+ /* always a good habit to explicitly free whatever you malloc. */
+
+ free (Ap) ;
+ free (Ai) ;
+ free (Ax) ;
+
+ free (Cp) ;
+ free (Ci) ;
+ free (Cx) ;
+
+ free (Pinit) ;
+ free (Qinit) ;
+ free (Front_npivcol) ;
+ free (Front_1strow) ;
+ free (Front_leftmostdesc) ;
+ free (Front_parent) ;
+ free (Chain_start) ;
+ free (Chain_maxrows) ;
+ free (Chain_maxcols) ;
+
+ free (Lp) ;
+ free (Lj) ;
+ free (Lx) ;
+
+ free (Up) ;
+ free (Ui) ;
+ free (Ux) ;
+
+ free (P) ;
+ free (Q) ;
+
+ free (Li) ;
+
+ free (Wi) ;
+ free (W) ;
+
+ umfpack_dl_free_symbolic (&Symbolic) ;
+ umfpack_dl_free_numeric (&Numeric) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print the total time spent in this demo */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_toc (t) ;
+ printf ("\numfpack_dl_demo complete.\nTotal time: %5.2f seconds"
+ " (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ;
+ return (0) ;
+}
diff --git a/UMFPACK/Demo/umfpack_dl_demo.out b/UMFPACK/Demo/umfpack_dl_demo.out
new file mode 100644
index 0000000..fbcc7ec
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_dl_demo.out
@@ -0,0 +1,1523 @@
+
+UMFPACK V5.2 (Nov 1, 2007) demo: _dl_ version
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+
+UMFPACK License:
+
+ UMFPACK is available under alternate licenses,
+ contact T. Davis for details.
+
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU General Public
+ License as published by the Free Software Foundation; either
+ version 2 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU GPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability: http://www.cise.ufl.edu/research/sparse/umfpack
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double
+ Int (generic integer) defined as: UF_long
+
+ 0: print level: 5
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 8 pointer: 8 double: 8 Entry: 8 (in bytes)
+
+
+b: dense vector, n = 5.
+ 0 : (8)
+ 1 : (45)
+ 2 : (-3)
+ 3 : (3)
+ 4 : (19)
+ dense vector OK
+
+
+A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12.
+ 0 : 0 0 (2)
+ 1 : 4 4 (1)
+ 2 : 1 0 (3)
+ 3 : 1 2 (4)
+ 4 : 2 1 (-1)
+ 5 : 2 2 (-3)
+ 6 : 0 1 (3)
+ 7 : 1 4 (6)
+ 8 : 2 3 (2)
+ 9 : 3 2 (1)
+ 10 : 4 1 (4)
+ 11 : 4 2 (2)
+ triplet-form matrix OK
+
+
+A: column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2)
+ row 1 : (3)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (3)
+ row 2 : (-1)
+ row 4 : (4)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (4)
+ row 2 : (-3)
+ row 3 : (1)
+ row 4 : (2)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (2)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (6)
+ row 4 : (1)
+ column-form matrix OK
+
+
+Symbolic factorization of A: Symbolic object:
+ matrix to be factorized:
+ n_row: 5 n_col: 5
+ number of entries: 12
+ block size used for dense matrix kernels: 32
+ strategy used: unsymmetric
+ ordering used: colamd on A
+
+ performn column etree postorder: yes
+ prefer diagonal pivoting (attempt P=Q): no
+ variable-size part of Numeric object:
+ minimum initial size (Units): 69 (MBytes): 0.0
+ estimated peak size (Units): 681 (MBytes): 0.0
+ estimated final size (Units): 10 (MBytes): 0.0
+ symbolic factorization memory usage (Units): 138 (MBytes): 0.0
+ frontal matrices / supercolumns:
+ number of frontal chains: 1
+ number of frontal matrices: 1
+ largest frontal matrix row dimension: 3
+ largest frontal matrix column dimension: 3
+
+ Frontal chain: 0. Frontal matrices 0 to 0
+ Largest frontal matrix in Frontal chain: 3-by-3
+ Front: 0 pivot cols: 3 (pivot columns 0 to 2)
+ pivot row candidates: 2 to 4
+ leftmost descendant: 0
+ 1st new candidate row : 2
+ parent: (none)
+
+Initial column permutation, Q1: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Initial row permutation, P1: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 1
+ 4 : 4
+ permutation vector OK
+
+ Symbolic object: OK
+
+
+Numeric factorization of A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.30000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 67
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 675
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 4
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 4
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 6
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.42857e-01
+ max abs. value on diagonal of U: 2.19231e+00
+ reciprocal condition number estimate: 6.52e-02
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.2)
+ 1 : (0.0769231)
+ 2 : (0.166667)
+ 3 : (1)
+ 4 : (0.142857)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 4 : (0.307692)
+ row 3 : (0.285714)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.576923)
+
+ column 3: length 1.
+ row 4 : (3.23077)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.571429)
+
+ row 2: length 1.
+ col 4 : (0.6)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (-0.5)
+ col 4 : (-0.166667)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.333333)
+ 1 : (1)
+ 2 : (0.4)
+ 3 : (0.142857)
+ 4 : (-2.19231)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.30000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 69 64 93%
+ peak size (Units) 681 675 99%
+ final size (Units) 10 11 110%
+ Numeric final size (Units) 69 68 99%
+ Numeric final size (MBytes) 0.0 0.0 99%
+ peak memory usage (Units) 832 826 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 6.00000e+00 46%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.43e-01
+ max abs. value on diagonal of U: 2.19e+00
+ estimate of reciprocal of condition number: 6.52e-02
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.19000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 1.18e-16
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.25000e+02
+
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+
+x (solution of Ax=b): dense vector, n = 5.
+ 0 : (1)
+ 1 : (2)
+ 2 : (3)
+ 3 : (4)
+ 4 : (5)
+ dense vector OK
+
+maxnorm of residual: 1.06581e-14
+
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+determinant: (1.14) * 10^(2)
+
+x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5.
+ 0 : (1)
+ 1 : (2)
+ 2 : (3)
+ 3 : (4)
+ 4 : (5)
+ dense vector OK
+
+maxnorm of residual: 1.06581e-14
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.30000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 69 64 93%
+ peak size (Units) 681 675 99%
+ final size (Units) 10 11 110%
+ Numeric final size (Units) 69 68 99%
+ Numeric final size (MBytes) 0.0 0.0 99%
+ peak memory usage (Units) 832 826 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 6.00000e+00 46%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.43e-01
+ max abs. value on diagonal of U: 2.19e+00
+ estimate of reciprocal of condition number: 6.52e-02
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.11000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 7.64e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.17000e+02
+
+
+x (solution of A'x=b): dense vector, n = 5.
+ 0 : (1.81579)
+ 1 : (1.45614)
+ 2 : (1.5)
+ 3 : (-24.8509)
+ 4 : (10.2632)
+ dense vector OK
+
+maxnorm of residual: 7.10543e-15
+
+
+changing A (1,4) to zero
+
+modified A: column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2)
+ row 1 : (3)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (3)
+ row 2 : (-1)
+ row 4 : (4)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (4)
+ row 2 : (-3)
+ row 3 : (1)
+ row 4 : (2)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (2)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (0)
+ row 4 : (1)
+ column-form matrix OK
+
+
+Numeric factorization of modified A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 7.00000e+00
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 66
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 675
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 4
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 3
+ number of entries stored in U (excl diag): 1
+ factorization floating-point operations: 4
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.50000e-01
+ max abs. value on diagonal of U: 1.00000e+00
+ reciprocal condition number estimate: 1.50e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.2)
+ 1 : (0.142857)
+ 2 : (0.166667)
+ 3 : (1)
+ 4 : (0.142857)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 1
+ 3 : 4
+ 4 : 0
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 1
+ 4 : 4
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 2 : (0.571429)
+ row 3 : (0.285714)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.933333)
+
+ column 3: length 1.
+ row 4 : (1.05)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.142857)
+
+ row 2: length 0. End of Uchain.
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (-0.5)
+ col 3 : (-0.166667)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.333333)
+ 1 : (1)
+ 2 : (0.428571)
+ 3 : (0.571429)
+ 4 : (-0.15)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 7.00000e+00
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 69 64 93%
+ peak size (Units) 681 675 99%
+ final size (Units) 10 10 100%
+ Numeric final size (Units) 69 67 97%
+ Numeric final size (MBytes) 0.0 0.0 97%
+ peak memory usage (Units) 832 826 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 4.00000e+00 31%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 8 80%
+ nz in L+U (incl diagonal) 15 12 80%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 8
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.50e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 1.50e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 8
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.17000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 7.89e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.21000e+02
+
+
+x (with modified A): dense vector, n = 5.
+ 0 : (11)
+ 1 : (-4.66667)
+ 2 : (3)
+ 3 : (0.666667)
+ 4 : (31.6667)
+ dense vector OK
+
+maxnorm of residual: 7.10543e-15
+
+changing A (0,0) from 2 to 2
+changing A (1,0) from 3 to 2
+changing A (0,1) from 3 to 13
+changing A (2,1) from -1 to 7
+changing A (4,1) from 4 to 10
+changing A (1,2) from 4 to 23
+changing A (2,2) from -3 to 15
+changing A (3,2) from 1 to 18
+changing A (4,2) from 2 to 18
+changing A (2,3) from 2 to 30
+changing A (1,4) from 0 to 39
+changing A (4,4) from 1 to 37
+
+completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2)
+ row 1 : (2)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (13)
+ row 2 : (7)
+ row 4 : (10)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (23)
+ row 2 : (15)
+ row 3 : (18)
+ row 4 : (18)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (30)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (39)
+ row 4 : (37)
+ column-form matrix OK
+
+
+Saving symbolic object:
+
+Freeing symbolic object:
+
+Loading symbolic object:
+
+Done loading symbolic object
+
+Numeric factorization of completely modified A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.50000e+01
+ maximum sum (abs (rows of A)): 6.50000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 67
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 675
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 4
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 4
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 6
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.33333e-01
+ max abs. value on diagonal of U: 1.00000e+00
+ reciprocal condition number estimate: 1.33e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.0666667)
+ 1 : (0.015625)
+ 2 : (0.0192308)
+ 3 : (0.0555556)
+ 4 : (0.0153846)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 4 : (0.359375)
+ row 3 : (0.276923)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.234375)
+
+ column 3: length 1.
+ row 4 : (1.07052)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.153846)
+
+ row 2: length 1.
+ col 4 : (0.866667)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (0.288462)
+ col 4 : (0.134615)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.576923)
+ 1 : (1)
+ 2 : (0.133333)
+ 3 : (0.569231)
+ 4 : (-0.367821)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.50000e+01
+ maximum sum (abs (rows of A)): 6.50000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 69 64 93%
+ peak size (Units) 681 675 99%
+ final size (Units) 10 11 110%
+ Numeric final size (Units) 69 68 99%
+ Numeric final size (MBytes) 0.0 0.0 99%
+ peak memory usage (Units) 832 826 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 6.00000e+00 46%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.33e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 1.33e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.19000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 1.04e-16
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.25000e+02
+
+
+x (with completely modified A): dense vector, n = 5.
+ 0 : (8.50124)
+ 1 : (-0.692499)
+ 2 : (0.166667)
+ 3 : (-0.0217502)
+ 4 : (0.619594)
+ dense vector OK
+
+maxnorm of residual: 3.55271e-15
+
+
+C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2)
+ row 1 : (13)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (2)
+ row 2 : (23)
+ row 4 : (39)
+
+ column 2: start: 5 end: 7 entries: 3
+ row 1 : (7)
+ row 2 : (15)
+ row 3 : (30)
+
+ column 3: start: 8 end: 8 entries: 1
+ row 2 : (18)
+
+ column 4: start: 9 end: 11 entries: 3
+ row 1 : (10)
+ row 2 : (18)
+ row 4 : (37)
+ column-form matrix OK
+
+
+Symbolic factorization of C: Symbolic object:
+ matrix to be factorized:
+ n_row: 5 n_col: 5
+ number of entries: 12
+ block size used for dense matrix kernels: 32
+ strategy used: unsymmetric
+ ordering used: colamd on A
+
+ performn column etree postorder: yes
+ prefer diagonal pivoting (attempt P=Q): no
+ variable-size part of Numeric object:
+ minimum initial size (Units): 71 (MBytes): 0.0
+ estimated peak size (Units): 683 (MBytes): 0.0
+ estimated final size (Units): 12 (MBytes): 0.0
+ symbolic factorization memory usage (Units): 138 (MBytes): 0.0
+ frontal matrices / supercolumns:
+ number of frontal chains: 1
+ number of frontal matrices: 1
+ largest frontal matrix row dimension: 3
+ largest frontal matrix column dimension: 3
+
+ Frontal chain: 0. Frontal matrices 0 to 0
+ Largest frontal matrix in Frontal chain: 3-by-3
+ Front: 0 pivot cols: 3 (pivot columns 0 to 2)
+ pivot row candidates: 2 to 4
+ leftmost descendant: 0
+ 1st new candidate row : 2
+ parent: (none)
+
+Initial column permutation, Q1: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Initial row permutation, P1: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 1
+ 4 : 4
+ permutation vector OK
+
+ Symbolic object: OK
+
+
+Get the contents of the Symbolic object for C:
+(compare with umfpack_dl_report_symbolic output, above)
+From the Symbolic object, C is of dimension 5-by-5
+ with nz = 12, number of fronts = 1,
+ number of frontal matrix chains = 1
+
+Pivot columns in each front, and parent of each front:
+ Front 0: parent front: -1 number of pivot cols: 3
+ 0-th pivot column is column 3 in original matrix
+ 1-th pivot column is column 2 in original matrix
+ 2-th pivot column is column 0 in original matrix
+
+Note that the column ordering, above, will be refined
+in the numeric factorization below. The assignment of pivot
+columns to frontal matrices will always remain unchanged.
+
+Total number of pivot columns in frontal matrices: 3
+
+Frontal matrix chains:
+ Frontal matrices 0 to 0 are factorized in a single
+ working array of size 3-by-3
+
+Numeric factorization of C: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 4.00000e+00
+ maximum sum (abs (rows of A)): 7.60000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 69
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 677
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 3
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 5
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 6
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.43243e-01
+ max abs. value on diagonal of U: 1.00000e+00
+ reciprocal condition number estimate: 2.43e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.25)
+ 1 : (0.0333333)
+ 2 : (0.0135135)
+ 3 : (0.0333333)
+ 4 : (0.0131579)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 1.
+ row 4 : (0.233333)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.866667)
+
+ column 3: length 1.
+ row 4 : (0.684685)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.513158)
+
+ row 2: length 1.
+ col 4 : (0.5)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 3.
+ col 1 : (0.202703)
+ col 3 : (0.243243)
+ col 4 : (0.310811)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.243243)
+ 1 : (1)
+ 2 : (0.5)
+ 3 : (0.486842)
+ 4 : (-0.784685)
+ dense vector OK
+
+ Numeric object: OK
+
+
+L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8.
+
+ row 0: start: 0 end: 0 entries: 1
+ column 0 : (1)
+
+ row 1: start: 1 end: 1 entries: 1
+ column 1 : (1)
+
+ row 2: start: 2 end: 2 entries: 1
+ column 2 : (1)
+
+ row 3: start: 3 end: 3 entries: 1
+ column 3 : (1)
+
+ row 4: start: 4 end: 7 entries: 4
+ column 1 : (0.233333)
+ column 2 : (0.866667)
+ column 3 : (0.684685)
+ column 4 : (1)
+ row-form matrix OK
+
+
+U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10.
+
+ column 0: start: 0 end: 0 entries: 1
+ row 0 : (0.243243)
+
+ column 1: start: 1 end: 2 entries: 2
+ row 0 : (0.202703)
+ row 1 : (1)
+
+ column 2: start: 3 end: 3 entries: 1
+ row 2 : (0.5)
+
+ column 3: start: 4 end: 5 entries: 2
+ row 0 : (0.243243)
+ row 3 : (0.486842)
+
+ column 4: start: 6 end: 9 entries: 4
+ row 0 : (0.310811)
+ row 2 : (0.5)
+ row 3 : (0.513158)
+ row 4 : (-0.784685)
+ column-form matrix OK
+
+
+P: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Scale factors: row i of A is to be multiplied by the ith scale factor
+0: 0.25
+1: 0.0333333
+2: 0.0135135
+3: 0.0333333
+4: 0.0131579
+
+Converting L to triplet form, and printing it:
+
+L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8.
+ 0 : 0 0 (1)
+ 1 : 1 1 (1)
+ 2 : 2 2 (1)
+ 3 : 3 3 (1)
+ 4 : 4 1 (0.233333)
+ 5 : 4 2 (0.866667)
+ 6 : 4 3 (0.684685)
+ 7 : 4 4 (1)
+ triplet-form matrix OK
+
+
+Saving numeric object:
+
+Freeing numeric object:
+
+Loading numeric object:
+
+Done loading numeric object
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 4.00000e+00
+ maximum sum (abs (rows of A)): 7.60000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 71 66 93%
+ peak size (Units) 683 677 99%
+ final size (Units) 12 13 108%
+ Numeric final size (Units) 71 70 99%
+ Numeric final size (MBytes) 0.0 0.0 99%
+ peak memory usage (Units) 834 828 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 6.00000e+00 46%
+ nz in L (incl diagonal) 9 8 89%
+ nz in U (incl diagonal) 11 10 91%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 8
+ nz in U (incl diagonal), if none dropped 10
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.43e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 2.43e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.11000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 8.07e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.17000e+02
+
+
+x (solution of C'x=b): dense vector, n = 5.
+ 0 : (8.50124)
+ 1 : (-0.692499)
+ 2 : (0.166667)
+ 3 : (-0.0217502)
+ 4 : (0.619594)
+ dense vector OK
+
+maxnorm of residual: 3.55271e-15
+
+
+Solving C'x=b again, using umfpack_dl_wsolve instead:
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 8 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 4.00000e+00
+ maximum sum (abs (rows of A)): 7.60000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 71 66 93%
+ peak size (Units) 683 677 99%
+ final size (Units) 12 13 108%
+ Numeric final size (Units) 71 70 99%
+ Numeric final size (MBytes) 0.0 0.0 99%
+ peak memory usage (Units) 834 828 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 1.30000e+01 6.00000e+00 46%
+ nz in L (incl diagonal) 9 8 89%
+ nz in U (incl diagonal) 11 10 91%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 8
+ nz in U (incl diagonal), if none dropped 10
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.43e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 2.43e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.11000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 8.07e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.17000e+02
+
+
+x (solution of C'x=b): dense vector, n = 5.
+ 0 : (8.50124)
+ 1 : (-0.692499)
+ 2 : (0.166667)
+ 3 : (-0.0217502)
+ 4 : (0.619594)
+ dense vector OK
+
+maxnorm of residual: 3.55271e-15
+
+
+umfpack_dl_demo complete.
+Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time)
diff --git a/UMFPACK/Demo/umfpack_dl_demo.sed b/UMFPACK/Demo/umfpack_dl_demo.sed
new file mode 100644
index 0000000..7c1f326
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_dl_demo.sed
@@ -0,0 +1,77 @@
+/::/d
+1,$s/_xx_/_dl_/g
+1,$s/Int/UF_long/g
+1,$s/WSIZE/5/
+/define ABS/ {
+ s/ABS/ABS(x) ((x) >= 0 ? (x) : -(x))/
+ }
+/, rz \[i\]/ {
+ s/, rz \[i\]//
+ }
+/, Avalz/ {
+ s/, Avalz//
+ }
+/, rz/ {
+ s/, rz//
+ }
+/, bz/ {
+ s/, bz//
+ }
+/, xz/ {
+ s/, xz//
+ }
+
+/, Lz/ {
+ s/, Lz//
+ }
+/, Uz/ {
+ s/, Uz//
+ }
+/, Dz/ {
+ s/, Dz//
+ }
+/, Az/ {
+ s/, Az//
+ }
+/, Cz, TRUE/ {
+ s/, Cz, TRUE//
+ }
+/, Cz/ {
+ s/, Cz//
+ }
+/, Rbz/ {
+ s/, Rbz//
+ }
+/, yz/ {
+ s/, yz//
+ }
+
+/ || !Lz/ {
+ s/ || !Lz//
+ }
+/ || !Uz/ {
+ s/ || !Uz//
+ }
+/ || !Dz/ {
+ s/ || !Dz//
+ }
+/ || !Az/ {
+ s/ || !Az//
+ }
+/ || !Cz/ {
+ s/ || !Cz//
+ }
+
+/rz/d
+/Rbz/d
+/yz/d
+/Avalz/d
+/Az/d
+/Cz/d
+/bz/d
+/xz/d
+/Lz/d
+/Uz/d
+/Dz/d
+/complex/d
+
diff --git a/UMFPACK/Demo/umfpack_simple.c b/UMFPACK/Demo/umfpack_simple.c
new file mode 100644
index 0000000..f16bb5a
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_simple.c
@@ -0,0 +1,30 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include <stdio.h>
+#include "umfpack.h"
+
+int n = 5 ;
+int Ap [ ] = {0, 2, 5, 9, 10, 12} ;
+int Ai [ ] = { 0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4} ;
+double Ax [ ] = {2., 3., 3., -1., 4., 4., -3., 1., 2., 2., 6., 1.} ;
+double b [ ] = {8., 45., -3., 3., 19.} ;
+double x [5] ;
+
+int main (void)
+{
+ double *null = (double *) NULL ;
+ int i ;
+ void *Symbolic, *Numeric ;
+ (void) umfpack_di_symbolic (n, n, Ap, Ai, Ax, &Symbolic, null, null) ;
+ (void) umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, null, null) ;
+ umfpack_di_free_symbolic (&Symbolic) ;
+ (void) umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, null, null) ;
+ umfpack_di_free_numeric (&Numeric) ;
+ for (i = 0 ; i < n ; i++) printf ("x [%d] = %g\n", i, x [i]) ;
+ return (0) ;
+}
+
diff --git a/UMFPACK/Demo/umfpack_xx_demo.c b/UMFPACK/Demo/umfpack_xx_demo.c
new file mode 100644
index 0000000..013f70c
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_xx_demo.c
@@ -0,0 +1,811 @@
+/* ========================================================================== */
+/* === umfpack_xx_demo ====================================================== */
+/* ========================================================================== */
+
+::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+:: Do not attempt to compile this file! It is processed via sed scripts into
+:: four different C demo programs:
+::
+:: umfpack_di_demo.c: double precision, int integers
+:: umfpack_dl_demo.c: double precision, UF_long integers
+:: umfpack_zi_demo.c: complex double precision, int integers
+:: umfpack_zl_demo.c: complex double precision, UF_long integers
+::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ A demo of UMFPACK: umfpack_xx_* version.
+
+ First, factor and solve a 5-by-5 system, Ax=b, using default parameters.
+ Then solve A'x=b using the factors of A. Modify one entry (A (1,4) = 0,
+ where the row and column indices range from 0 to 4. The pattern of A
+ has not changed (it has explicitly zero entry), so a reanalysis with
+ umfpack_xx_symbolic does not need to be done. Refactorize (with
+ umfpack_xx_numeric), and solve Ax=b. Note that the pivot ordering has
+ changed. Next, change all of the entries in A, but not the pattern.
+
+ Finally, compute C = A', and do the symbolic and numeric factorization of C.
+ Factorizing A' can sometimes be better than factorizing A itself (less work
+ and memory usage). Solve C'x=b twice; the solution is the same as the
+ solution to Ax=b.
+
+ A note about zero-sized arrays: UMFPACK uses many user-provided arrays of
+ size n (order of the matrix), and of size nz (the number of nonzeros in a
+ matrix). n cannot be zero; UMFPACK does not handle zero-dimensioned arrays.
+ However, nz can be zero. If you attempt to malloc an array of size nz = 0,
+ however, malloc will return a null pointer which UMFPACK will report as a
+ "missing argument." Thus, nz1 in this code is set to MAX (nz,1), and
+ similarly for lnz and unz. Lnz can never be zero, however, since L is always
+ unit diagonal.
+*/
+
+/* -------------------------------------------------------------------------- */
+/* definitions */
+/* -------------------------------------------------------------------------- */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "umfpack.h"
+
+/* use a cheap approximate absolute value for complex numbers: */
+::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+:: ABS is |xreal|+|ximag| for the complex case, and |x| for the real case.
+::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+#define ABS
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#ifndef TRUE
+#define TRUE (1)
+#endif
+#ifndef FALSE
+#define FALSE (0)
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* triplet form of the matrix. The triplets can be in any order. */
+/* -------------------------------------------------------------------------- */
+
+::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+:: Int is either int or UF_long:
+::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+static Int n = 5, nz = 12 ;
+static Int Arow [ ] = { 0, 4, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4} ;
+static Int Acol [ ] = { 0, 4, 0, 2, 1, 2, 1, 4, 3, 2, 1, 2} ;
+static double Aval [ ] = {2., 1., 3., 4., -1., -3., 3., 6., 2., 1., 4., 2.} ;
+static double Avalz[ ] = {1., .4, .1, .2, -1., -.2, 0., 6., 3., 0., .3, .3} ;
+static double b [ ] = {8., 45., -3., 3., 19.}, x [5], r [5] ;
+static double bz[ ] = {1., -5., -2., 0., 2.2}, xz[5], rz[5] ;
+
+/* Avalz, bz: imaginary part of A and b */
+
+/* -------------------------------------------------------------------------- */
+/* error: print a message and exit */
+/* -------------------------------------------------------------------------- */
+
+static void error
+(
+ char *message
+)
+{
+ printf ("\n\n====== error: %s =====\n\n", message) ;
+ exit (1) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* resid: compute the residual, r = Ax-b or r = A'x=b and return maxnorm (r) */
+/* A' is the complex conjugate transpose, not the array transpose */
+/* -------------------------------------------------------------------------- */
+
+static double resid
+(
+ Int transpose,
+ Int Ap [ ],
+ Int Ai [ ],
+ double Ax [ ]
+ , double Az [ ]
+)
+{
+ Int i, j, p ;
+ double norm ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ r [i] = -b [i] ;
+ rz[i] = -bz[i] ;
+ }
+ if (transpose)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ /* complex: r(j) += conj (Aij) * x (i) */
+ r [j] += Ax [p] * x [i] ;
+ r [j] += Az [p] * xz[i] ;
+ rz[j] -= Az [p] * x [i] ;
+ rz[j] += Ax [p] * xz[i] ;
+ }
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ r [i] += Ax [p] * x [j] ;
+ r [i] -= Az [p] * xz[j] ;
+ rz[i] += Az [p] * x [j] ;
+ rz[i] += Ax [p] * xz[j] ;
+ }
+ }
+ }
+ norm = 0. ;
+ for (i = 0 ; i < n ; i++)
+ {
+ norm = MAX (ABS (r [i], rz [i]), norm) ;
+ }
+ return (norm) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* main program */
+/* -------------------------------------------------------------------------- */
+
+int main (int argc, char **argv)
+{
+ double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux,
+ *W, t [2], *Dx, rnorm, *Rb, *y, *Rs ;
+ double *Az, *Lz, *Uz, *Dz, *Cz, *Rbz, *yz ;
+ Int *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up,
+ *P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1,
+ status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1,
+ *Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc,
+ nzud, do_recip ;
+ void *Symbolic, *Numeric ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (t) ;
+
+ printf ("\nUMFPACK V%d.%d (%s) demo: _xx_ version\n",
+ UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ;
+
+ /* get the default control parameters */
+ umfpack_xx_defaults (Control) ;
+
+ /* change the default print level for this demo */
+ /* (otherwise, nothing will print) */
+ Control [UMFPACK_PRL] = 6 ;
+
+ /* print the license agreement */
+ umfpack_xx_report_status (Control, UMFPACK_OK) ;
+ Control [UMFPACK_PRL] = 5 ;
+
+ /* print the control parameters */
+ umfpack_xx_report_control (Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print A and b, and convert A to column-form */
+ /* ---------------------------------------------------------------------- */
+
+ /* print the right-hand-side */
+ printf ("\nb: ") ;
+ (void) umfpack_xx_report_vector (n, b, bz, Control) ;
+
+ /* print the triplet form of the matrix */
+ printf ("\nA: ") ;
+ (void) umfpack_xx_report_triplet (n, n, nz, Arow, Acol, Aval, Avalz,
+ Control) ;
+
+ /* convert to column form */
+ nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */
+ Ap = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Ai = (Int *) malloc (nz1 * sizeof (Int)) ;
+ Ax = (double *) malloc (nz1 * sizeof (double)) ;
+ Az = (double *) malloc (nz1 * sizeof (double)) ;
+ if (!Ap || !Ai || !Ax || !Az)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_xx_triplet_to_col (n, n, nz, Arow, Acol, Aval, Avalz,
+ Ap, Ai, Ax, Az, (Int *) NULL) ;
+
+ if (status < 0)
+ {
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_triplet_to_col failed") ;
+ }
+
+ /* print the column-form of A */
+ printf ("\nA: ") ;
+ (void) umfpack_xx_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_xx_symbolic (n, n, Ap, Ai, Ax, Az, &Symbolic,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_info (Control, Info) ;
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_symbolic failed") ;
+ }
+
+ /* print the symbolic factorization */
+
+ printf ("\nSymbolic factorization of A: ") ;
+ (void) umfpack_xx_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_xx_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_info (Control, Info) ;
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_numeric failed") ;
+ }
+
+ /* print the numeric factorization */
+ printf ("\nNumeric factorization of A: ") ;
+ (void) umfpack_xx_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_xx_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_xx_report_info (Control, Info) ;
+ umfpack_xx_report_status (Control, status) ;
+ if (status < 0)
+ {
+ error ("umfpack_xx_solve failed") ;
+ }
+ printf ("\nx (solution of Ax=b): ") ;
+ (void) umfpack_xx_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the determinant */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_xx_get_determinant (x, xz, r, Numeric, Info) ;
+ umfpack_xx_report_status (Control, status) ;
+ if (status < 0)
+ {
+ error ("umfpack_xx_get_determinant failed") ;
+ }
+ printf ("determinant: (%g", x [0]) ;
+ printf ("+ (%g)i", xz [0]) ; /* complex */
+ printf (") * 10^(%g)\n", r [0]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, broken down into steps */
+ /* ---------------------------------------------------------------------- */
+
+ /* Rb = R*b */
+ Rb = (double *) malloc (n * sizeof (double)) ;
+ Rbz = (double *) malloc (n * sizeof (double)) ;
+ y = (double *) malloc (n * sizeof (double)) ;
+ yz = (double *) malloc (n * sizeof (double)) ;
+ if (!Rb || !y) error ("out of memory") ;
+ if (!Rbz || !yz) error ("out of memory") ;
+
+ status = umfpack_xx_scale (Rb, Rbz, b, bz, Numeric) ;
+ if (status < 0) error ("umfpack_xx_scale failed") ;
+ /* solve Ly = P*(Rb) */
+ status = umfpack_xx_solve (UMFPACK_Pt_L, Ap, Ai, Ax, Az, y, yz, Rb, Rbz,
+ Numeric, Control, Info) ;
+ if (status < 0) error ("umfpack_xx_solve failed") ;
+ /* solve UQ'x=y */
+ status = umfpack_xx_solve (UMFPACK_U_Qt, Ap, Ai, Ax, Az, x, xz, y, yz,
+ Numeric, Control, Info) ;
+ if (status < 0) error ("umfpack_xx_solve failed") ;
+ printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ;
+ (void) umfpack_xx_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ free (Rb) ;
+ free (Rbz) ;
+ free (y) ;
+ free (yz) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve A'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ /* note that this is the complex conjugate transpose, A' */
+ status = umfpack_xx_solve (UMFPACK_At, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_xx_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ error ("umfpack_xx_solve failed") ;
+ }
+ printf ("\nx (solution of A'x=b): ") ;
+ (void) umfpack_xx_report_vector (n, x, xz, Control) ;
+ rnorm = resid (TRUE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify one numerical value in the column-form of A */
+ /* ---------------------------------------------------------------------- */
+
+ /* change A (1,4), look for row index 1 in column 4. */
+ row = 1 ;
+ col = 4 ;
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ if (row == Ai [p])
+ {
+ printf ("\nchanging A (%ld,%ld) to zero\n", row, col) ;
+ Ax [p] = 0.0 ;
+ Az [p] = 0.0 ;
+ break ;
+ }
+ }
+ printf ("\nmodified A: ") ;
+ (void) umfpack_xx_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* redo the numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */
+ /* doesn't have to be redone, no matter how much we change Ax. */
+
+ /* We don't need the Numeric object any more, so free it. */
+ umfpack_xx_free_numeric (&Numeric) ;
+
+ /* Note that a memory leak would have occurred if the old Numeric */
+ /* had not been free'd with umfpack_xx_free_numeric above. */
+ status = umfpack_xx_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_info (Control, Info) ;
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of modified A: ") ;
+ (void) umfpack_xx_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, with the modified A */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_xx_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_xx_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_solve failed") ;
+ }
+ printf ("\nx (with modified A): ") ;
+ (void) umfpack_xx_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify all of the numerical values of A, but not the pattern */
+ /* ---------------------------------------------------------------------- */
+
+ for (col = 0 ; col < n ; col++)
+ {
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ row = Ai [p] ;
+ printf ("changing ") ;
+ /* complex: */ printf ("real part of ") ;
+ printf ("A (%ld,%ld) from %g", row, col, Ax [p]) ;
+ Ax [p] = Ax [p] + col*10 - row ;
+ printf (" to %g\n", Ax [p]) ;
+ }
+ }
+ printf ("\ncompletely modified A (same pattern): ") ;
+ (void) umfpack_xx_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* save the Symbolic object to file, free it, and load it back in */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the default filename, "symbolic.umf" */
+ printf ("\nSaving symbolic object:\n") ;
+ status = umfpack_xx_save_symbolic (Symbolic, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_save_symbolic failed") ;
+ }
+ printf ("\nFreeing symbolic object:\n") ;
+ umfpack_xx_free_symbolic (&Symbolic) ;
+ printf ("\nLoading symbolic object:\n") ;
+ status = umfpack_xx_load_symbolic (&Symbolic, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_load_symbolic failed") ;
+ }
+ printf ("\nDone loading symbolic object\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* redo the numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_xx_free_numeric (&Numeric) ;
+ status = umfpack_xx_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_info (Control, Info) ;
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of completely modified A: ") ;
+ (void) umfpack_xx_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, with the modified A */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_xx_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_xx_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_solve failed") ;
+ }
+ printf ("\nx (with completely modified A): ") ;
+ (void) umfpack_xx_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the symbolic and numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_xx_free_symbolic (&Symbolic) ;
+ umfpack_xx_free_numeric (&Numeric) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = transpose of A */
+ /* ---------------------------------------------------------------------- */
+
+ Cp = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Ci = (Int *) malloc (nz1 * sizeof (Int)) ;
+ Cx = (double *) malloc (nz1 * sizeof (double)) ;
+ Cz = (double *) malloc (nz1 * sizeof (double)) ;
+ if (!Cp || !Ci || !Cx || !Cz)
+ {
+ error ("out of memory") ;
+ }
+ status = umfpack_xx_transpose (n, n, Ap, Ai, Ax, Az,
+ (Int *) NULL, (Int *) NULL, Cp, Ci, Cx, Cz, TRUE) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_transpose failed: ") ;
+ }
+ printf ("\nC (transpose of A): ") ;
+ (void) umfpack_xx_report_matrix (n, n, Cp, Ci, Cx, Cz, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization of C */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_xx_symbolic (n, n, Cp, Ci, Cx, Cz, &Symbolic,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_info (Control, Info) ;
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_symbolic failed") ;
+ }
+ printf ("\nSymbolic factorization of C: ") ;
+ (void) umfpack_xx_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the contents of Symbolic into user arrays print them */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nGet the contents of the Symbolic object for C:\n") ;
+ printf ("(compare with umfpack_xx_report_symbolic output, above)\n") ;
+ Pinit = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Qinit = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Front_npivcol = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Front_1strow = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Front_leftmostdesc = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Front_parent = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Chain_start = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Chain_maxrows = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Chain_maxcols = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start ||
+ !Chain_maxrows || !Chain_maxcols || !Front_1strow ||
+ !Front_leftmostdesc)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_xx_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains,
+ Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+ if (status < 0)
+ {
+ error ("symbolic factorization invalid") ;
+ }
+
+ printf ("From the Symbolic object, C is of dimension %ld-by-%ld\n", nr, nc);
+ printf (" with nz = %ld, number of fronts = %ld,\n", nz, nfr) ;
+ printf (" number of frontal matrix chains = %ld\n", nchains) ;
+
+ printf ("\nPivot columns in each front, and parent of each front:\n") ;
+ k = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fnpiv = Front_npivcol [i] ;
+ printf (" Front %ld: parent front: %ld number of pivot cols: %ld\n",
+ i, Front_parent [i], fnpiv) ;
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ col = Qinit [k] ;
+ printf (
+ " %ld-th pivot column is column %ld in original matrix\n",
+ k, col) ;
+ k++ ;
+ }
+ }
+
+ printf ("\nNote that the column ordering, above, will be refined\n") ;
+ printf ("in the numeric factorization below. The assignment of pivot\n") ;
+ printf ("columns to frontal matrices will always remain unchanged.\n") ;
+
+ printf ("\nTotal number of pivot columns in frontal matrices: %ld\n", k) ;
+
+ printf ("\nFrontal matrix chains:\n") ;
+ for (j = 0 ; j < nchains ; j++)
+ {
+ printf (" Frontal matrices %ld to %ld are factorized in a single\n",
+ Chain_start [j], Chain_start [j+1] - 1) ;
+ printf (" working array of size %ld-by-%ld\n",
+ Chain_maxrows [j], Chain_maxcols [j]) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization of C */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_xx_numeric (Cp, Ci, Cx, Cz, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ error ("umfpack_xx_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of C: ") ;
+ (void) umfpack_xx_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extract the LU factors of C and print them */
+ /* ---------------------------------------------------------------------- */
+
+ if (umfpack_xx_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0)
+ {
+ error ("umfpack_xx_get_lunz failed") ;
+ }
+ /* ensure arrays are not of zero size */
+ lnz1 = MAX (lnz,1) ;
+ unz1 = MAX (unz,1) ;
+ Lp = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Lj = (Int *) malloc (lnz1 * sizeof (Int)) ;
+ Lx = (double *) malloc (lnz1 * sizeof (double)) ;
+ Lz = (double *) malloc (lnz1 * sizeof (double)) ;
+ Up = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Ui = (Int *) malloc (unz1 * sizeof (Int)) ;
+ Ux = (double *) malloc (unz1 * sizeof (double)) ;
+ Uz = (double *) malloc (unz1 * sizeof (double)) ;
+ P = (Int *) malloc (n * sizeof (Int)) ;
+ Q = (Int *) malloc (n * sizeof (Int)) ;
+ Dx = (double *) NULL ; /* D vector not requested */
+ Dz = (double *) NULL ;
+ Rs = (double *) malloc (n * sizeof (double)) ;
+ if (!Lp || !Lj || !Lx || !Lz || !Up || !Ui || !Ux || !Uz || !P || !Q || !Rs)
+ {
+ error ("out of memory") ;
+ }
+ status = umfpack_xx_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz,
+ P, Q, Dx, Dz, &do_recip, Rs, Numeric) ;
+ if (status < 0)
+ {
+ error ("umfpack_xx_get_numeric failed") ;
+ }
+
+ printf ("\nL (lower triangular factor of C): ") ;
+ (void) umfpack_xx_report_matrix (n, n, Lp, Lj, Lx, Lz, 0, Control) ;
+ printf ("\nU (upper triangular factor of C): ") ;
+ (void) umfpack_xx_report_matrix (n, n, Up, Ui, Ux, Uz, 1, Control) ;
+ printf ("\nP: ") ;
+ (void) umfpack_xx_report_perm (n, P, Control) ;
+ printf ("\nQ: ") ;
+ (void) umfpack_xx_report_perm (n, Q, Control) ;
+ printf ("\nScale factors: row i of A is to be ") ;
+ if (do_recip)
+ {
+ printf ("multiplied by the ith scale factor\n") ;
+ }
+ else
+ {
+ printf ("divided by the ith scale factor\n") ;
+ }
+ for (i = 0 ; i < n ; i++) printf ("%ld: %g\n", i, Rs [i]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to triplet form and print it */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that L is in row-form, so it is the row indices that are created */
+ /* by umfpack_xx_col_to_triplet. */
+
+ printf ("\nConverting L to triplet form, and printing it:\n") ;
+ Li = (Int *) malloc (lnz1 * sizeof (Int)) ;
+ if (!Li)
+ {
+ error ("out of memory") ;
+ }
+ if (umfpack_xx_col_to_triplet (n, Lp, Li) < 0)
+ {
+ error ("umfpack_xx_col_to_triplet failed") ;
+ }
+ printf ("\nL, in triplet form: ") ;
+ (void) umfpack_xx_report_triplet (n, n, lnz, Li, Lj, Lx, Lz, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* save the Numeric object to file, free it, and load it back in */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the default filename, "numeric.umf" */
+ printf ("\nSaving numeric object:\n") ;
+ status = umfpack_xx_save_numeric (Numeric, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_save_numeric failed") ;
+ }
+ printf ("\nFreeing numeric object:\n") ;
+ umfpack_xx_free_numeric (&Numeric) ;
+ printf ("\nLoading numeric object:\n") ;
+ status = umfpack_xx_load_numeric (&Numeric, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_load_numeric failed") ;
+ }
+ printf ("\nDone loading numeric object\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve C'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_xx_solve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_xx_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_solve failed") ;
+ }
+ printf ("\nx (solution of C'x=b): ") ;
+ (void) umfpack_xx_report_vector (n, x, xz, Control) ;
+ rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve C'x=b again, using umfpack_xx_wsolve instead */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nSolving C'x=b again, using umfpack_xx_wsolve instead:\n") ;
+ Wi = (Int *) malloc (n * sizeof (Int)) ;
+ ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+ :: WSIZE is 5 for the real case, 10 for complex.
+ ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+ W = (double *) malloc (WSIZE*n * sizeof (double)) ;
+ if (!Wi || !W)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_xx_wsolve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz,
+ Numeric, Control, Info, Wi, W) ;
+ umfpack_xx_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_xx_report_status (Control, status) ;
+ error ("umfpack_xx_wsolve failed") ;
+ }
+ printf ("\nx (solution of C'x=b): ") ;
+ (void) umfpack_xx_report_vector (n, x, xz, Control) ;
+ rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free everything */
+ /* ---------------------------------------------------------------------- */
+
+ /* This is not strictly required since the process is exiting and the */
+ /* system will reclaim the memory anyway. It's useful, though, just as */
+ /* a list of what is currently malloc'ed by this program. Plus, it's */
+ /* always a good habit to explicitly free whatever you malloc. */
+
+ free (Ap) ;
+ free (Ai) ;
+ free (Ax) ;
+ free (Az) ;
+
+ free (Cp) ;
+ free (Ci) ;
+ free (Cx) ;
+ free (Cz) ;
+
+ free (Pinit) ;
+ free (Qinit) ;
+ free (Front_npivcol) ;
+ free (Front_1strow) ;
+ free (Front_leftmostdesc) ;
+ free (Front_parent) ;
+ free (Chain_start) ;
+ free (Chain_maxrows) ;
+ free (Chain_maxcols) ;
+
+ free (Lp) ;
+ free (Lj) ;
+ free (Lx) ;
+ free (Lz) ;
+
+ free (Up) ;
+ free (Ui) ;
+ free (Ux) ;
+ free (Uz) ;
+
+ free (P) ;
+ free (Q) ;
+
+ free (Li) ;
+
+ free (Wi) ;
+ free (W) ;
+
+ umfpack_xx_free_symbolic (&Symbolic) ;
+ umfpack_xx_free_numeric (&Numeric) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print the total time spent in this demo */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_toc (t) ;
+ printf ("\numfpack_xx_demo complete.\nTotal time: %5.2f seconds"
+ " (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ;
+ return (0) ;
+}
diff --git a/UMFPACK/Demo/umfpack_zi_demo.c b/UMFPACK/Demo/umfpack_zi_demo.c
new file mode 100644
index 0000000..ea63767
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_zi_demo.c
@@ -0,0 +1,793 @@
+/* ========================================================================== */
+/* === umfpack_zi_demo ====================================================== */
+/* ========================================================================== */
+
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ A demo of UMFPACK: umfpack_zi_* version.
+
+ First, factor and solve a 5-by-5 system, Ax=b, using default parameters.
+ Then solve A'x=b using the factors of A. Modify one entry (A (1,4) = 0,
+ where the row and column indices range from 0 to 4. The pattern of A
+ has not changed (it has explicitly zero entry), so a reanalysis with
+ umfpack_zi_symbolic does not need to be done. Refactorize (with
+ umfpack_zi_numeric), and solve Ax=b. Note that the pivot ordering has
+ changed. Next, change all of the entries in A, but not the pattern.
+
+ Finally, compute C = A', and do the symbolic and numeric factorization of C.
+ Factorizing A' can sometimes be better than factorizing A itself (less work
+ and memory usage). Solve C'x=b twice; the solution is the same as the
+ solution to Ax=b.
+
+ A note about zero-sized arrays: UMFPACK uses many user-provided arrays of
+ size n (order of the matrix), and of size nz (the number of nonzeros in a
+ matrix). n cannot be zero; UMFPACK does not handle zero-dimensioned arrays.
+ However, nz can be zero. If you attempt to malloc an array of size nz = 0,
+ however, malloc will return a null pointer which UMFPACK will report as a
+ "missing argument." Thus, nz1 in this code is set to MAX (nz,1), and
+ similarly for lnz and unz. Lnz can never be zero, however, since L is always
+ unit diagonal.
+*/
+
+/* -------------------------------------------------------------------------- */
+/* definitions */
+/* -------------------------------------------------------------------------- */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "umfpack.h"
+
+/* use a cheap approximate absolute value for complex numbers: */
+#define ABS(x,z) ((x) >= 0 ? (x) : -(x)) + ((z) >= 0 ? (z) : -(z))
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#ifndef TRUE
+#define TRUE (1)
+#endif
+#ifndef FALSE
+#define FALSE (0)
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* triplet form of the matrix. The triplets can be in any order. */
+/* -------------------------------------------------------------------------- */
+
+static int n = 5, nz = 12 ;
+static int Arow [ ] = { 0, 4, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4} ;
+static int Acol [ ] = { 0, 4, 0, 2, 1, 2, 1, 4, 3, 2, 1, 2} ;
+static double Aval [ ] = {2., 1., 3., 4., -1., -3., 3., 6., 2., 1., 4., 2.} ;
+static double Avalz[ ] = {1., .4, .1, .2, -1., -.2, 0., 6., 3., 0., .3, .3} ;
+static double b [ ] = {8., 45., -3., 3., 19.}, x [5], r [5] ;
+static double bz[ ] = {1., -5., -2., 0., 2.2}, xz[5], rz[5] ;
+
+/* Avalz, bz: imaginary part of A and b */
+
+/* -------------------------------------------------------------------------- */
+/* error: print a message and exit */
+/* -------------------------------------------------------------------------- */
+
+static void error
+(
+ char *message
+)
+{
+ printf ("\n\n====== error: %s =====\n\n", message) ;
+ exit (1) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* resid: compute the residual, r = Ax-b or r = A'x=b and return maxnorm (r) */
+/* A' is the complex conjugate transpose, not the array transpose */
+/* -------------------------------------------------------------------------- */
+
+static double resid
+(
+ int transpose,
+ int Ap [ ],
+ int Ai [ ],
+ double Ax [ ]
+ , double Az [ ]
+)
+{
+ int i, j, p ;
+ double norm ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ r [i] = -b [i] ;
+ rz[i] = -bz[i] ;
+ }
+ if (transpose)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ /* complex: r(j) += conj (Aij) * x (i) */
+ r [j] += Ax [p] * x [i] ;
+ r [j] += Az [p] * xz[i] ;
+ rz[j] -= Az [p] * x [i] ;
+ rz[j] += Ax [p] * xz[i] ;
+ }
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ r [i] += Ax [p] * x [j] ;
+ r [i] -= Az [p] * xz[j] ;
+ rz[i] += Az [p] * x [j] ;
+ rz[i] += Ax [p] * xz[j] ;
+ }
+ }
+ }
+ norm = 0. ;
+ for (i = 0 ; i < n ; i++)
+ {
+ norm = MAX (ABS (r [i], rz [i]), norm) ;
+ }
+ return (norm) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* main program */
+/* -------------------------------------------------------------------------- */
+
+int main (int argc, char **argv)
+{
+ double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux,
+ *W, t [2], *Dx, rnorm, *Rb, *y, *Rs ;
+ double *Az, *Lz, *Uz, *Dz, *Cz, *Rbz, *yz ;
+ int *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up,
+ *P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1,
+ status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1,
+ *Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc,
+ nzud, do_recip ;
+ void *Symbolic, *Numeric ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (t) ;
+
+ printf ("\nUMFPACK V%d.%d (%s) demo: _zi_ version\n",
+ UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ;
+
+ /* get the default control parameters */
+ umfpack_zi_defaults (Control) ;
+
+ /* change the default print level for this demo */
+ /* (otherwise, nothing will print) */
+ Control [UMFPACK_PRL] = 6 ;
+
+ /* print the license agreement */
+ umfpack_zi_report_status (Control, UMFPACK_OK) ;
+ Control [UMFPACK_PRL] = 5 ;
+
+ /* print the control parameters */
+ umfpack_zi_report_control (Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print A and b, and convert A to column-form */
+ /* ---------------------------------------------------------------------- */
+
+ /* print the right-hand-side */
+ printf ("\nb: ") ;
+ (void) umfpack_zi_report_vector (n, b, bz, Control) ;
+
+ /* print the triplet form of the matrix */
+ printf ("\nA: ") ;
+ (void) umfpack_zi_report_triplet (n, n, nz, Arow, Acol, Aval, Avalz,
+ Control) ;
+
+ /* convert to column form */
+ nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */
+ Ap = (int *) malloc ((n+1) * sizeof (int)) ;
+ Ai = (int *) malloc (nz1 * sizeof (int)) ;
+ Ax = (double *) malloc (nz1 * sizeof (double)) ;
+ Az = (double *) malloc (nz1 * sizeof (double)) ;
+ if (!Ap || !Ai || !Ax || !Az)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_zi_triplet_to_col (n, n, nz, Arow, Acol, Aval, Avalz,
+ Ap, Ai, Ax, Az, (int *) NULL) ;
+
+ if (status < 0)
+ {
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_triplet_to_col failed") ;
+ }
+
+ /* print the column-form of A */
+ printf ("\nA: ") ;
+ (void) umfpack_zi_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zi_symbolic (n, n, Ap, Ai, Ax, Az, &Symbolic,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_info (Control, Info) ;
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_symbolic failed") ;
+ }
+
+ /* print the symbolic factorization */
+
+ printf ("\nSymbolic factorization of A: ") ;
+ (void) umfpack_zi_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_info (Control, Info) ;
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_numeric failed") ;
+ }
+
+ /* print the numeric factorization */
+ printf ("\nNumeric factorization of A: ") ;
+ (void) umfpack_zi_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zi_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_zi_report_info (Control, Info) ;
+ umfpack_zi_report_status (Control, status) ;
+ if (status < 0)
+ {
+ error ("umfpack_zi_solve failed") ;
+ }
+ printf ("\nx (solution of Ax=b): ") ;
+ (void) umfpack_zi_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the determinant */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zi_get_determinant (x, xz, r, Numeric, Info) ;
+ umfpack_zi_report_status (Control, status) ;
+ if (status < 0)
+ {
+ error ("umfpack_zi_get_determinant failed") ;
+ }
+ printf ("determinant: (%g", x [0]) ;
+ printf ("+ (%g)i", xz [0]) ; /* complex */
+ printf (") * 10^(%g)\n", r [0]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, broken down into steps */
+ /* ---------------------------------------------------------------------- */
+
+ /* Rb = R*b */
+ Rb = (double *) malloc (n * sizeof (double)) ;
+ Rbz = (double *) malloc (n * sizeof (double)) ;
+ y = (double *) malloc (n * sizeof (double)) ;
+ yz = (double *) malloc (n * sizeof (double)) ;
+ if (!Rb || !y) error ("out of memory") ;
+ if (!Rbz || !yz) error ("out of memory") ;
+
+ status = umfpack_zi_scale (Rb, Rbz, b, bz, Numeric) ;
+ if (status < 0) error ("umfpack_zi_scale failed") ;
+ /* solve Ly = P*(Rb) */
+ status = umfpack_zi_solve (UMFPACK_Pt_L, Ap, Ai, Ax, Az, y, yz, Rb, Rbz,
+ Numeric, Control, Info) ;
+ if (status < 0) error ("umfpack_zi_solve failed") ;
+ /* solve UQ'x=y */
+ status = umfpack_zi_solve (UMFPACK_U_Qt, Ap, Ai, Ax, Az, x, xz, y, yz,
+ Numeric, Control, Info) ;
+ if (status < 0) error ("umfpack_zi_solve failed") ;
+ printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ;
+ (void) umfpack_zi_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ free (Rb) ;
+ free (Rbz) ;
+ free (y) ;
+ free (yz) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve A'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ /* note that this is the complex conjugate transpose, A' */
+ status = umfpack_zi_solve (UMFPACK_At, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_zi_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ error ("umfpack_zi_solve failed") ;
+ }
+ printf ("\nx (solution of A'x=b): ") ;
+ (void) umfpack_zi_report_vector (n, x, xz, Control) ;
+ rnorm = resid (TRUE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify one numerical value in the column-form of A */
+ /* ---------------------------------------------------------------------- */
+
+ /* change A (1,4), look for row index 1 in column 4. */
+ row = 1 ;
+ col = 4 ;
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ if (row == Ai [p])
+ {
+ printf ("\nchanging A (%d,%d) to zero\n", row, col) ;
+ Ax [p] = 0.0 ;
+ Az [p] = 0.0 ;
+ break ;
+ }
+ }
+ printf ("\nmodified A: ") ;
+ (void) umfpack_zi_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* redo the numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */
+ /* doesn't have to be redone, no matter how much we change Ax. */
+
+ /* We don't need the Numeric object any more, so free it. */
+ umfpack_zi_free_numeric (&Numeric) ;
+
+ /* Note that a memory leak would have occurred if the old Numeric */
+ /* had not been free'd with umfpack_zi_free_numeric above. */
+ status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_info (Control, Info) ;
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of modified A: ") ;
+ (void) umfpack_zi_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, with the modified A */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zi_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_zi_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_solve failed") ;
+ }
+ printf ("\nx (with modified A): ") ;
+ (void) umfpack_zi_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify all of the numerical values of A, but not the pattern */
+ /* ---------------------------------------------------------------------- */
+
+ for (col = 0 ; col < n ; col++)
+ {
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ row = Ai [p] ;
+ printf ("changing ") ;
+ /* complex: */ printf ("real part of ") ;
+ printf ("A (%d,%d) from %g", row, col, Ax [p]) ;
+ Ax [p] = Ax [p] + col*10 - row ;
+ printf (" to %g\n", Ax [p]) ;
+ }
+ }
+ printf ("\ncompletely modified A (same pattern): ") ;
+ (void) umfpack_zi_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* save the Symbolic object to file, free it, and load it back in */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the default filename, "symbolic.umf" */
+ printf ("\nSaving symbolic object:\n") ;
+ status = umfpack_zi_save_symbolic (Symbolic, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_save_symbolic failed") ;
+ }
+ printf ("\nFreeing symbolic object:\n") ;
+ umfpack_zi_free_symbolic (&Symbolic) ;
+ printf ("\nLoading symbolic object:\n") ;
+ status = umfpack_zi_load_symbolic (&Symbolic, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_load_symbolic failed") ;
+ }
+ printf ("\nDone loading symbolic object\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* redo the numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_zi_free_numeric (&Numeric) ;
+ status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_info (Control, Info) ;
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of completely modified A: ") ;
+ (void) umfpack_zi_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, with the modified A */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zi_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_zi_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_solve failed") ;
+ }
+ printf ("\nx (with completely modified A): ") ;
+ (void) umfpack_zi_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the symbolic and numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_zi_free_symbolic (&Symbolic) ;
+ umfpack_zi_free_numeric (&Numeric) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = transpose of A */
+ /* ---------------------------------------------------------------------- */
+
+ Cp = (int *) malloc ((n+1) * sizeof (int)) ;
+ Ci = (int *) malloc (nz1 * sizeof (int)) ;
+ Cx = (double *) malloc (nz1 * sizeof (double)) ;
+ Cz = (double *) malloc (nz1 * sizeof (double)) ;
+ if (!Cp || !Ci || !Cx || !Cz)
+ {
+ error ("out of memory") ;
+ }
+ status = umfpack_zi_transpose (n, n, Ap, Ai, Ax, Az,
+ (int *) NULL, (int *) NULL, Cp, Ci, Cx, Cz, TRUE) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_transpose failed: ") ;
+ }
+ printf ("\nC (transpose of A): ") ;
+ (void) umfpack_zi_report_matrix (n, n, Cp, Ci, Cx, Cz, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization of C */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zi_symbolic (n, n, Cp, Ci, Cx, Cz, &Symbolic,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_info (Control, Info) ;
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_symbolic failed") ;
+ }
+ printf ("\nSymbolic factorization of C: ") ;
+ (void) umfpack_zi_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the contents of Symbolic into user arrays print them */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nGet the contents of the Symbolic object for C:\n") ;
+ printf ("(compare with umfpack_zi_report_symbolic output, above)\n") ;
+ Pinit = (int *) malloc ((n+1) * sizeof (int)) ;
+ Qinit = (int *) malloc ((n+1) * sizeof (int)) ;
+ Front_npivcol = (int *) malloc ((n+1) * sizeof (int)) ;
+ Front_1strow = (int *) malloc ((n+1) * sizeof (int)) ;
+ Front_leftmostdesc = (int *) malloc ((n+1) * sizeof (int)) ;
+ Front_parent = (int *) malloc ((n+1) * sizeof (int)) ;
+ Chain_start = (int *) malloc ((n+1) * sizeof (int)) ;
+ Chain_maxrows = (int *) malloc ((n+1) * sizeof (int)) ;
+ Chain_maxcols = (int *) malloc ((n+1) * sizeof (int)) ;
+ if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start ||
+ !Chain_maxrows || !Chain_maxcols || !Front_1strow ||
+ !Front_leftmostdesc)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_zi_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains,
+ Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+ if (status < 0)
+ {
+ error ("symbolic factorization invalid") ;
+ }
+
+ printf ("From the Symbolic object, C is of dimension %d-by-%d\n", nr, nc);
+ printf (" with nz = %d, number of fronts = %d,\n", nz, nfr) ;
+ printf (" number of frontal matrix chains = %d\n", nchains) ;
+
+ printf ("\nPivot columns in each front, and parent of each front:\n") ;
+ k = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fnpiv = Front_npivcol [i] ;
+ printf (" Front %d: parent front: %d number of pivot cols: %d\n",
+ i, Front_parent [i], fnpiv) ;
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ col = Qinit [k] ;
+ printf (
+ " %d-th pivot column is column %d in original matrix\n",
+ k, col) ;
+ k++ ;
+ }
+ }
+
+ printf ("\nNote that the column ordering, above, will be refined\n") ;
+ printf ("in the numeric factorization below. The assignment of pivot\n") ;
+ printf ("columns to frontal matrices will always remain unchanged.\n") ;
+
+ printf ("\nTotal number of pivot columns in frontal matrices: %d\n", k) ;
+
+ printf ("\nFrontal matrix chains:\n") ;
+ for (j = 0 ; j < nchains ; j++)
+ {
+ printf (" Frontal matrices %d to %d are factorized in a single\n",
+ Chain_start [j], Chain_start [j+1] - 1) ;
+ printf (" working array of size %d-by-%d\n",
+ Chain_maxrows [j], Chain_maxcols [j]) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization of C */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zi_numeric (Cp, Ci, Cx, Cz, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ error ("umfpack_zi_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of C: ") ;
+ (void) umfpack_zi_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extract the LU factors of C and print them */
+ /* ---------------------------------------------------------------------- */
+
+ if (umfpack_zi_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0)
+ {
+ error ("umfpack_zi_get_lunz failed") ;
+ }
+ /* ensure arrays are not of zero size */
+ lnz1 = MAX (lnz,1) ;
+ unz1 = MAX (unz,1) ;
+ Lp = (int *) malloc ((n+1) * sizeof (int)) ;
+ Lj = (int *) malloc (lnz1 * sizeof (int)) ;
+ Lx = (double *) malloc (lnz1 * sizeof (double)) ;
+ Lz = (double *) malloc (lnz1 * sizeof (double)) ;
+ Up = (int *) malloc ((n+1) * sizeof (int)) ;
+ Ui = (int *) malloc (unz1 * sizeof (int)) ;
+ Ux = (double *) malloc (unz1 * sizeof (double)) ;
+ Uz = (double *) malloc (unz1 * sizeof (double)) ;
+ P = (int *) malloc (n * sizeof (int)) ;
+ Q = (int *) malloc (n * sizeof (int)) ;
+ Dx = (double *) NULL ; /* D vector not requested */
+ Dz = (double *) NULL ;
+ Rs = (double *) malloc (n * sizeof (double)) ;
+ if (!Lp || !Lj || !Lx || !Lz || !Up || !Ui || !Ux || !Uz || !P || !Q || !Rs)
+ {
+ error ("out of memory") ;
+ }
+ status = umfpack_zi_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz,
+ P, Q, Dx, Dz, &do_recip, Rs, Numeric) ;
+ if (status < 0)
+ {
+ error ("umfpack_zi_get_numeric failed") ;
+ }
+
+ printf ("\nL (lower triangular factor of C): ") ;
+ (void) umfpack_zi_report_matrix (n, n, Lp, Lj, Lx, Lz, 0, Control) ;
+ printf ("\nU (upper triangular factor of C): ") ;
+ (void) umfpack_zi_report_matrix (n, n, Up, Ui, Ux, Uz, 1, Control) ;
+ printf ("\nP: ") ;
+ (void) umfpack_zi_report_perm (n, P, Control) ;
+ printf ("\nQ: ") ;
+ (void) umfpack_zi_report_perm (n, Q, Control) ;
+ printf ("\nScale factors: row i of A is to be ") ;
+ if (do_recip)
+ {
+ printf ("multiplied by the ith scale factor\n") ;
+ }
+ else
+ {
+ printf ("divided by the ith scale factor\n") ;
+ }
+ for (i = 0 ; i < n ; i++) printf ("%d: %g\n", i, Rs [i]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to triplet form and print it */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that L is in row-form, so it is the row indices that are created */
+ /* by umfpack_zi_col_to_triplet. */
+
+ printf ("\nConverting L to triplet form, and printing it:\n") ;
+ Li = (int *) malloc (lnz1 * sizeof (int)) ;
+ if (!Li)
+ {
+ error ("out of memory") ;
+ }
+ if (umfpack_zi_col_to_triplet (n, Lp, Li) < 0)
+ {
+ error ("umfpack_zi_col_to_triplet failed") ;
+ }
+ printf ("\nL, in triplet form: ") ;
+ (void) umfpack_zi_report_triplet (n, n, lnz, Li, Lj, Lx, Lz, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* save the Numeric object to file, free it, and load it back in */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the default filename, "numeric.umf" */
+ printf ("\nSaving numeric object:\n") ;
+ status = umfpack_zi_save_numeric (Numeric, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_save_numeric failed") ;
+ }
+ printf ("\nFreeing numeric object:\n") ;
+ umfpack_zi_free_numeric (&Numeric) ;
+ printf ("\nLoading numeric object:\n") ;
+ status = umfpack_zi_load_numeric (&Numeric, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_load_numeric failed") ;
+ }
+ printf ("\nDone loading numeric object\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve C'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zi_solve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_zi_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_solve failed") ;
+ }
+ printf ("\nx (solution of C'x=b): ") ;
+ (void) umfpack_zi_report_vector (n, x, xz, Control) ;
+ rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve C'x=b again, using umfpack_zi_wsolve instead */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nSolving C'x=b again, using umfpack_zi_wsolve instead:\n") ;
+ Wi = (int *) malloc (n * sizeof (int)) ;
+ W = (double *) malloc (10*n * sizeof (double)) ;
+ if (!Wi || !W)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_zi_wsolve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz,
+ Numeric, Control, Info, Wi, W) ;
+ umfpack_zi_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zi_report_status (Control, status) ;
+ error ("umfpack_zi_wsolve failed") ;
+ }
+ printf ("\nx (solution of C'x=b): ") ;
+ (void) umfpack_zi_report_vector (n, x, xz, Control) ;
+ rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free everything */
+ /* ---------------------------------------------------------------------- */
+
+ /* This is not strictly required since the process is exiting and the */
+ /* system will reclaim the memory anyway. It's useful, though, just as */
+ /* a list of what is currently malloc'ed by this program. Plus, it's */
+ /* always a good habit to explicitly free whatever you malloc. */
+
+ free (Ap) ;
+ free (Ai) ;
+ free (Ax) ;
+ free (Az) ;
+
+ free (Cp) ;
+ free (Ci) ;
+ free (Cx) ;
+ free (Cz) ;
+
+ free (Pinit) ;
+ free (Qinit) ;
+ free (Front_npivcol) ;
+ free (Front_1strow) ;
+ free (Front_leftmostdesc) ;
+ free (Front_parent) ;
+ free (Chain_start) ;
+ free (Chain_maxrows) ;
+ free (Chain_maxcols) ;
+
+ free (Lp) ;
+ free (Lj) ;
+ free (Lx) ;
+ free (Lz) ;
+
+ free (Up) ;
+ free (Ui) ;
+ free (Ux) ;
+ free (Uz) ;
+
+ free (P) ;
+ free (Q) ;
+
+ free (Li) ;
+
+ free (Wi) ;
+ free (W) ;
+
+ umfpack_zi_free_symbolic (&Symbolic) ;
+ umfpack_zi_free_numeric (&Numeric) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print the total time spent in this demo */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_toc (t) ;
+ printf ("\numfpack_zi_demo complete.\nTotal time: %5.2f seconds"
+ " (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ;
+ return (0) ;
+}
diff --git a/UMFPACK/Demo/umfpack_zi_demo.out b/UMFPACK/Demo/umfpack_zi_demo.out
new file mode 100644
index 0000000..9bee8db
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_zi_demo.out
@@ -0,0 +1,1523 @@
+
+UMFPACK V5.2 (Nov 1, 2007) demo: _zi_ version
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+
+UMFPACK License:
+
+ UMFPACK is available under alternate licenses,
+ contact T. Davis for details.
+
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU General Public
+ License as published by the Free Software Foundation; either
+ version 2 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU GPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability: http://www.cise.ufl.edu/research/sparse/umfpack
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double complex
+ Int (generic integer) defined as: int
+
+ 0: print level: 5
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 16 (in bytes)
+
+
+b: dense vector, n = 5.
+ 0 : (8 + 1i)
+ 1 : (45 - 5i)
+ 2 : (-3 - 2i)
+ 3 : (3 + 0i)
+ 4 : (19 + 2.2i)
+ dense vector OK
+
+
+A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12.
+ 0 : 0 0 (2 + 1i)
+ 1 : 4 4 (1 + 0.4i)
+ 2 : 1 0 (3 + 0.1i)
+ 3 : 1 2 (4 + 0.2i)
+ 4 : 2 1 (-1 - 1i)
+ 5 : 2 2 (-3 - 0.2i)
+ 6 : 0 1 (3 + 0i)
+ 7 : 1 4 (6 + 6i)
+ 8 : 2 3 (2 + 3i)
+ 9 : 3 2 (1 + 0i)
+ 10 : 4 1 (4 + 0.3i)
+ 11 : 4 2 (2 + 0.3i)
+ triplet-form matrix OK
+
+
+A: column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2 + 1i)
+ row 1 : (3 + 0.1i)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (3 + 0i)
+ row 2 : (-1 - 1i)
+ row 4 : (4 + 0.3i)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (4 + 0.2i)
+ row 2 : (-3 - 0.2i)
+ row 3 : (1 + 0i)
+ row 4 : (2 + 0.3i)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (2 + 3i)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (6 + 6i)
+ row 4 : (1 + 0.4i)
+ column-form matrix OK
+
+
+Symbolic factorization of A: Symbolic object:
+ matrix to be factorized:
+ n_row: 5 n_col: 5
+ number of entries: 12
+ block size used for dense matrix kernels: 32
+ strategy used: unsymmetric
+ ordering used: colamd on A
+
+ performn column etree postorder: yes
+ prefer diagonal pivoting (attempt P=Q): no
+ variable-size part of Numeric object:
+ minimum initial size (Units): 90 (MBytes): 0.0
+ estimated peak size (Units): 2542 (MBytes): 0.0
+ estimated final size (Units): 25 (MBytes): 0.0
+ symbolic factorization memory usage (Units): 151 (MBytes): 0.0
+ frontal matrices / supercolumns:
+ number of frontal chains: 1
+ number of frontal matrices: 1
+ largest frontal matrix row dimension: 3
+ largest frontal matrix column dimension: 3
+
+ Frontal chain: 0. Frontal matrices 0 to 0
+ Largest frontal matrix in Frontal chain: 3-by-3
+ Front: 0 pivot cols: 3 (pivot columns 0 to 2)
+ pivot row candidates: 2 to 4
+ leftmost descendant: 0
+ 1st new candidate row : 2
+ parent: (none)
+
+Initial column permutation, Q1: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Initial row permutation, P1: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 1
+ 4 : 4
+ permutation vector OK
+
+ Symbolic object: OK
+
+
+Numeric factorization of A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.93000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 106
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 2527
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 4
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 4
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 34
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.34629e-01
+ max abs. value on diagonal of U: 1.77313e+00
+ reciprocal condition number estimate: 7.59e-02
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.166667)
+ 1 : (0.0518135)
+ 2 : (0.0980392)
+ 3 : (1)
+ 4 : (0.125)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 4 : (0.207254 + 0.0103627i)
+ row 3 : (0.25 + 0.0375i)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.379275 - 0.174093i)
+
+ column 3: length 1.
+ row 4 : (3.00161 + 1.2864i)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.5 + 0.0375i)
+
+ row 2: length 1.
+ col 4 : (0.5 + 0i)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (-0.294118 - 0.0196078i)
+ col 4 : (-0.0980392 - 0.0980392i)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.196078 + 0.294118i)
+ 1 : (1 + 0i)
+ 2 : (0.333333 + 0.166667i)
+ 3 : (0.125 + 0.05i)
+ 4 : (-1.6422 - 0.668715i)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.93000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 90 80 89%
+ peak size (Units) 2542 2527 99%
+ final size (Units) 25 21 84%
+ Numeric final size (Units) 113 107 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 2751 2736 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 3.40000e+01 51%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.35e-01
+ max abs. value on diagonal of U: 1.77e+00
+ estimate of reciprocal of condition number: 7.59e-02
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.02800e+03
+ iterative refinement steps taken: 1
+ iterative refinement steps attempted: 1
+ sparse backward error omega1: 5.28e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.06200e+03
+
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+
+x (solution of Ax=b): dense vector, n = 5.
+ 0 : (0.121188 - 0.561001i)
+ 1 : (2.39887 + 0.666938i)
+ 2 : (3 + 0i)
+ 3 : (1.57395 - 1.52801i)
+ 4 : (2.3876 - 3.04245i)
+ dense vector OK
+
+maxnorm of residual: 1.77636e-15
+
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+determinant: (-1.7814+ (2.3784)i) * 10^(2)
+
+x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5.
+ 0 : (0.121188 - 0.561001i)
+ 1 : (2.39887 + 0.666938i)
+ 2 : (3 + 0i)
+ 3 : (1.57395 - 1.52801i)
+ 4 : (2.3876 - 3.04245i)
+ dense vector OK
+
+maxnorm of residual: 1.77636e-14
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.93000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 90 80 89%
+ peak size (Units) 2542 2527 99%
+ final size (Units) 25 21 84%
+ Numeric final size (Units) 113 107 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 2751 2736 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 3.40000e+01 51%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.35e-01
+ max abs. value on diagonal of U: 1.77e+00
+ estimate of reciprocal of condition number: 7.59e-02
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 4.80000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 7.82e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 5.14000e+02
+
+
+x (solution of A'x=b): dense vector, n = 5.
+ 0 : (3.39246 + 0.13257i)
+ 1 : (0.31463 + 1.38626i)
+ 2 : (0.461538 + 0.692308i)
+ 3 : (-20.9089 - 1.55801i)
+ 4 : (9.04015 - 0.613724i)
+ dense vector OK
+
+maxnorm of residual: 4.52416e-15
+
+
+changing A (1,4) to zero
+
+modified A: column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2 + 1i)
+ row 1 : (3 + 0.1i)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (3 + 0i)
+ row 2 : (-1 - 1i)
+ row 4 : (4 + 0.3i)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (4 + 0.2i)
+ row 2 : (-3 - 0.2i)
+ row 3 : (1 + 0i)
+ row 4 : (2 + 0.3i)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (2 + 3i)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (0 + 0i)
+ row 4 : (1 + 0.4i)
+ column-form matrix OK
+
+
+Numeric factorization of modified A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.02000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 104
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 2527
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 3
+ number of entries stored in L (excl diag): 1
+ number of nonzeros in U (excl diag): 4
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 17
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.34629e-01
+ max abs. value on diagonal of U: 1.00000e+00
+ reciprocal condition number estimate: 1.35e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.166667)
+ 1 : (0.136986)
+ 2 : (0.0980392)
+ 3 : (1)
+ 4 : (0.125)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 4 : (0.547945 + 0.0273973i)
+ row 3 : (0.25 + 0.0375i)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (1.00274 - 0.460274i)
+
+ column 3: length 0. Start of Lchain.
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.5 + 0.0375i)
+
+ row 2: length 1.
+ col 4 : (0.5 + 0i)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (-0.294118 - 0.0196078i)
+ col 4 : (-0.0980392 - 0.0980392i)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.196078 + 0.294118i)
+ 1 : (1 + 0i)
+ 2 : (0.333333 + 0.166667i)
+ 3 : (0.125 + 0.05i)
+ 4 : (-0.50137 + 0.230137i)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.02000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 90 80 89%
+ peak size (Units) 2542 2527 99%
+ final size (Units) 25 19 76%
+ Numeric final size (Units) 113 105 93%
+ Numeric final size (MBytes) 0.0 0.0 93%
+ peak memory usage (Units) 2751 2736 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 1.70000e+01 25%
+ nz in L (incl diagonal) 10 8 80%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 12 80%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 8
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.35e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 1.35e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 8
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 5.15000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 6.01e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 5.32000e+02
+
+
+x (with modified A): dense vector, n = 5.
+ 0 : (10.9256 - 2.23085i)
+ 1 : (-5.36071 - 1.82131i)
+ 2 : (3 + 0i)
+ 3 : (-1.60191 - 1.88814i)
+ 4 : (32.7361 - 2.90097i)
+ dense vector OK
+
+maxnorm of residual: 4.66294e-15
+
+changing real part of A (0,0) from 2 to 2
+changing real part of A (1,0) from 3 to 2
+changing real part of A (0,1) from 3 to 13
+changing real part of A (2,1) from -1 to 7
+changing real part of A (4,1) from 4 to 10
+changing real part of A (1,2) from 4 to 23
+changing real part of A (2,2) from -3 to 15
+changing real part of A (3,2) from 1 to 18
+changing real part of A (4,2) from 2 to 18
+changing real part of A (2,3) from 2 to 30
+changing real part of A (1,4) from 0 to 39
+changing real part of A (4,4) from 1 to 37
+
+completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2 + 1i)
+ row 1 : (2 + 0.1i)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (13 + 0i)
+ row 2 : (7 - 1i)
+ row 4 : (10 + 0.3i)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (23 + 0.2i)
+ row 2 : (15 - 0.2i)
+ row 3 : (18 + 0i)
+ row 4 : (18 + 0.3i)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (30 + 3i)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (39 + 0i)
+ row 4 : (37 + 0.4i)
+ column-form matrix OK
+
+
+Saving symbolic object:
+
+Freeing symbolic object:
+
+Loading symbolic object:
+
+Done loading symbolic object
+
+Numeric factorization of completely modified A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.60000e+01
+ maximum sum (abs (rows of A)): 6.60000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 106
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 2527
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 4
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 4
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 34
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.39754e-01
+ max abs. value on diagonal of U: 1.00000e+00
+ reciprocal condition number estimate: 1.40e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.0625)
+ 1 : (0.0155521)
+ 2 : (0.0177936)
+ 3 : (0.0555556)
+ 4 : (0.0151515)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 4 : (0.357698 + 0.00311042i)
+ row 3 : (0.272727 + 0.00454545i)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.204044 - 0.0895801i)
+
+ column 3: length 1.
+ row 4 : (1.0818 - 0.0116951i)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.151515 + 0.00454545i)
+
+ row 2: length 1.
+ col 4 : (0.8125 + 0i)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (0.266904 - 0.00355872i)
+ col 4 : (0.124555 - 0.0177936i)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.533808 + 0.0533808i)
+ 1 : (1 + 0i)
+ 2 : (0.125 + 0.0625i)
+ 3 : (0.560606 + 0.00606061i)
+ 4 : (-0.329747 + 0.0696386i)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.60000e+01
+ maximum sum (abs (rows of A)): 6.60000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 90 80 89%
+ peak size (Units) 2542 2527 99%
+ final size (Units) 25 21 84%
+ Numeric final size (Units) 113 107 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 2751 2736 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 3.40000e+01 51%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.40e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 1.40e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 5.23000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 8.05e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 5.57000e+02
+
+
+x (with completely modified A): dense vector, n = 5.
+ 0 : (7.56307 - 3.68974i)
+ 1 : (-0.831991 + 0.0627998i)
+ 2 : (0.166667 + 0i)
+ 3 : (-0.00206892 - 0.107735i)
+ 4 : (0.658245 + 0.0407649i)
+ dense vector OK
+
+maxnorm of residual: 9.10383e-15
+
+
+C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2 - 1i)
+ row 1 : (13 + 0i)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (2 - 0.1i)
+ row 2 : (23 - 0.2i)
+ row 4 : (39 + 0i)
+
+ column 2: start: 5 end: 7 entries: 3
+ row 1 : (7 + 1i)
+ row 2 : (15 + 0.2i)
+ row 3 : (30 - 3i)
+
+ column 3: start: 8 end: 8 entries: 1
+ row 2 : (18 + 0i)
+
+ column 4: start: 9 end: 11 entries: 3
+ row 1 : (10 - 0.3i)
+ row 2 : (18 - 0.3i)
+ row 4 : (37 - 0.4i)
+ column-form matrix OK
+
+
+Symbolic factorization of C: Symbolic object:
+ matrix to be factorized:
+ n_row: 5 n_col: 5
+ number of entries: 12
+ block size used for dense matrix kernels: 32
+ strategy used: unsymmetric
+ ordering used: colamd on A
+
+ performn column etree postorder: yes
+ prefer diagonal pivoting (attempt P=Q): no
+ variable-size part of Numeric object:
+ minimum initial size (Units): 91 (MBytes): 0.0
+ estimated peak size (Units): 2543 (MBytes): 0.0
+ estimated final size (Units): 26 (MBytes): 0.0
+ symbolic factorization memory usage (Units): 151 (MBytes): 0.0
+ frontal matrices / supercolumns:
+ number of frontal chains: 1
+ number of frontal matrices: 1
+ largest frontal matrix row dimension: 3
+ largest frontal matrix column dimension: 3
+
+ Frontal chain: 0. Frontal matrices 0 to 0
+ Largest frontal matrix in Frontal chain: 3-by-3
+ Front: 0 pivot cols: 3 (pivot columns 0 to 2)
+ pivot row candidates: 2 to 4
+ leftmost descendant: 0
+ 1st new candidate row : 2
+ parent: (none)
+
+Initial column permutation, Q1: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Initial row permutation, P1: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 1
+ 4 : 4
+ permutation vector OK
+
+ Symbolic object: OK
+
+
+Get the contents of the Symbolic object for C:
+(compare with umfpack_zi_report_symbolic output, above)
+From the Symbolic object, C is of dimension 5-by-5
+ with nz = 12, number of fronts = 1,
+ number of frontal matrix chains = 1
+
+Pivot columns in each front, and parent of each front:
+ Front 0: parent front: -1 number of pivot cols: 3
+ 0-th pivot column is column 3 in original matrix
+ 1-th pivot column is column 2 in original matrix
+ 2-th pivot column is column 0 in original matrix
+
+Note that the column ordering, above, will be refined
+in the numeric factorization below. The assignment of pivot
+columns to frontal matrices will always remain unchanged.
+
+Total number of pivot columns in frontal matrices: 3
+
+Frontal matrix chains:
+ Frontal matrices 0 to 0 are factorized in a single
+ working array of size 3-by-3
+
+Numeric factorization of C: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 5.10000e+00
+ maximum sum (abs (rows of A)): 7.64000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 107
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 2528
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 3
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 5
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 34
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.40964e-01
+ max abs. value on diagonal of U: 9.13625e-01
+ reciprocal condition number estimate: 2.64e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.196078)
+ 1 : (0.0319489)
+ 2 : (0.0133869)
+ 3 : (0.030303)
+ 4 : (0.013089)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 1.
+ row 4 : (0.240091 + 0.0591529i)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.847284 + 0.423642i)
+
+ column 3: length 1.
+ row 4 : (0.659838 - 0.0126577i)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.510471 + 0i)
+
+ row 2: length 1.
+ col 4 : (0.392157 - 0.0196078i)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 3.
+ col 1 : (0.200803 + 0.00267738i)
+ col 3 : (0.240964 - 0.00401606i)
+ col 4 : (0.307898 - 0.00267738i)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.240964 + 0i)
+ 1 : (0.909091 - 0.0909091i)
+ 2 : (0.392157 - 0.196078i)
+ 3 : (0.484293 - 0.0052356i)
+ 4 : (-0.677403 - 0.143059i)
+ dense vector OK
+
+ Numeric object: OK
+
+
+L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8.
+
+ row 0: start: 0 end: 0 entries: 1
+ column 0 : (1 + 0i)
+
+ row 1: start: 1 end: 1 entries: 1
+ column 1 : (1 + 0i)
+
+ row 2: start: 2 end: 2 entries: 1
+ column 2 : (1 + 0i)
+
+ row 3: start: 3 end: 3 entries: 1
+ column 3 : (1 + 0i)
+
+ row 4: start: 4 end: 7 entries: 4
+ column 1 : (0.240091 + 0.0591529i)
+ column 2 : (0.847284 + 0.423642i)
+ column 3 : (0.659838 - 0.0126577i)
+ column 4 : (1 + 0i)
+ row-form matrix OK
+
+
+U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10.
+
+ column 0: start: 0 end: 0 entries: 1
+ row 0 : (0.240964 + 0i)
+
+ column 1: start: 1 end: 2 entries: 2
+ row 0 : (0.200803 + 0.00267738i)
+ row 1 : (0.909091 - 0.0909091i)
+
+ column 2: start: 3 end: 3 entries: 1
+ row 2 : (0.392157 - 0.196078i)
+
+ column 3: start: 4 end: 5 entries: 2
+ row 0 : (0.240964 - 0.00401606i)
+ row 3 : (0.484293 - 0.0052356i)
+
+ column 4: start: 6 end: 9 entries: 4
+ row 0 : (0.307898 - 0.00267738i)
+ row 2 : (0.392157 - 0.0196078i)
+ row 3 : (0.510471 + 0i)
+ row 4 : (-0.677403 - 0.143059i)
+ column-form matrix OK
+
+
+P: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Scale factors: row i of A is to be multiplied by the ith scale factor
+0: 0.196078
+1: 0.0319489
+2: 0.0133869
+3: 0.030303
+4: 0.013089
+
+Converting L to triplet form, and printing it:
+
+L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8.
+ 0 : 0 0 (1 + 0i)
+ 1 : 1 1 (1 + 0i)
+ 2 : 2 2 (1 + 0i)
+ 3 : 3 3 (1 + 0i)
+ 4 : 4 1 (0.240091 + 0.0591529i)
+ 5 : 4 2 (0.847284 + 0.423642i)
+ 6 : 4 3 (0.659838 - 0.0126577i)
+ 7 : 4 4 (1 + 0i)
+ triplet-form matrix OK
+
+
+Saving numeric object:
+
+Freeing numeric object:
+
+Loading numeric object:
+
+Done loading numeric object
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 5.10000e+00
+ maximum sum (abs (rows of A)): 7.64000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 91 81 89%
+ peak size (Units) 2543 2528 99%
+ final size (Units) 26 22 85%
+ Numeric final size (Units) 114 108 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 2752 2737 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 3.40000e+01 51%
+ nz in L (incl diagonal) 9 8 89%
+ nz in U (incl diagonal) 11 10 91%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 8
+ nz in U (incl diagonal), if none dropped 10
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.41e-01
+ max abs. value on diagonal of U: 9.14e-01
+ estimate of reciprocal of condition number: 2.64e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 4.80000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 9.42e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 5.14000e+02
+
+
+x (solution of C'x=b): dense vector, n = 5.
+ 0 : (7.56307 - 3.68974i)
+ 1 : (-0.831991 + 0.0627998i)
+ 2 : (0.166667 + 0i)
+ 3 : (-0.00206892 - 0.107735i)
+ 4 : (0.658245 + 0.0407649i)
+ dense vector OK
+
+maxnorm of residual: 4.88498e-15
+
+
+Solving C'x=b again, using umfpack_zi_wsolve instead:
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: int
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 8-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 151
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 52
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 5.10000e+00
+ maximum sum (abs (rows of A)): 7.64000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 91 81 89%
+ peak size (Units) 2543 2528 99%
+ final size (Units) 26 22 85%
+ Numeric final size (Units) 114 108 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 2752 2737 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 3.40000e+01 51%
+ nz in L (incl diagonal) 9 8 89%
+ nz in U (incl diagonal) 11 10 91%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 8
+ nz in U (incl diagonal), if none dropped 10
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.41e-01
+ max abs. value on diagonal of U: 9.14e-01
+ estimate of reciprocal of condition number: 2.64e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 4.80000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 9.42e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 5.14000e+02
+
+
+x (solution of C'x=b): dense vector, n = 5.
+ 0 : (7.56307 - 3.68974i)
+ 1 : (-0.831991 + 0.0627998i)
+ 2 : (0.166667 + 0i)
+ 3 : (-0.00206892 - 0.107735i)
+ 4 : (0.658245 + 0.0407649i)
+ dense vector OK
+
+maxnorm of residual: 4.88498e-15
+
+
+umfpack_zi_demo complete.
+Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time)
diff --git a/UMFPACK/Demo/umfpack_zi_demo.sed b/UMFPACK/Demo/umfpack_zi_demo.sed
new file mode 100644
index 0000000..c337cf5
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_zi_demo.sed
@@ -0,0 +1,8 @@
+/::/d
+1,$s/_xx_/_zi_/g
+1,$s/Int/int/g
+1,$s/WSIZE/10/
+1,$s/%ld/%d/g
+/define ABS/ {
+ s/ABS/ABS(x,z) ((x) >= 0 ? (x) : -(x)) + ((z) >= 0 ? (z) : -(z))/
+ }
diff --git a/UMFPACK/Demo/umfpack_zl_demo.c b/UMFPACK/Demo/umfpack_zl_demo.c
new file mode 100644
index 0000000..8f2ebaa
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_zl_demo.c
@@ -0,0 +1,793 @@
+/* ========================================================================== */
+/* === umfpack_zl_demo ====================================================== */
+/* ========================================================================== */
+
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ A demo of UMFPACK: umfpack_zl_* version.
+
+ First, factor and solve a 5-by-5 system, Ax=b, using default parameters.
+ Then solve A'x=b using the factors of A. Modify one entry (A (1,4) = 0,
+ where the row and column indices range from 0 to 4. The pattern of A
+ has not changed (it has explicitly zero entry), so a reanalysis with
+ umfpack_zl_symbolic does not need to be done. Refactorize (with
+ umfpack_zl_numeric), and solve Ax=b. Note that the pivot ordering has
+ changed. Next, change all of the entries in A, but not the pattern.
+
+ Finally, compute C = A', and do the symbolic and numeric factorization of C.
+ Factorizing A' can sometimes be better than factorizing A itself (less work
+ and memory usage). Solve C'x=b twice; the solution is the same as the
+ solution to Ax=b.
+
+ A note about zero-sized arrays: UMFPACK uses many user-provided arrays of
+ size n (order of the matrix), and of size nz (the number of nonzeros in a
+ matrix). n cannot be zero; UMFPACK does not handle zero-dimensioned arrays.
+ However, nz can be zero. If you attempt to malloc an array of size nz = 0,
+ however, malloc will return a null pointer which UMFPACK will report as a
+ "missing argument." Thus, nz1 in this code is set to MAX (nz,1), and
+ similarly for lnz and unz. Lnz can never be zero, however, since L is always
+ unit diagonal.
+*/
+
+/* -------------------------------------------------------------------------- */
+/* definitions */
+/* -------------------------------------------------------------------------- */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "umfpack.h"
+
+/* use a cheap approximate absolute value for complex numbers: */
+#define ABS(x,z) ((x) >= 0 ? (x) : -(x)) + ((z) >= 0 ? (z) : -(z))
+
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#ifndef TRUE
+#define TRUE (1)
+#endif
+#ifndef FALSE
+#define FALSE (0)
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* triplet form of the matrix. The triplets can be in any order. */
+/* -------------------------------------------------------------------------- */
+
+static UF_long n = 5, nz = 12 ;
+static UF_long Arow [ ] = { 0, 4, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4} ;
+static UF_long Acol [ ] = { 0, 4, 0, 2, 1, 2, 1, 4, 3, 2, 1, 2} ;
+static double Aval [ ] = {2., 1., 3., 4., -1., -3., 3., 6., 2., 1., 4., 2.} ;
+static double Avalz[ ] = {1., .4, .1, .2, -1., -.2, 0., 6., 3., 0., .3, .3} ;
+static double b [ ] = {8., 45., -3., 3., 19.}, x [5], r [5] ;
+static double bz[ ] = {1., -5., -2., 0., 2.2}, xz[5], rz[5] ;
+
+/* Avalz, bz: imaginary part of A and b */
+
+/* -------------------------------------------------------------------------- */
+/* error: print a message and exit */
+/* -------------------------------------------------------------------------- */
+
+static void error
+(
+ char *message
+)
+{
+ printf ("\n\n====== error: %s =====\n\n", message) ;
+ exit (1) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* resid: compute the residual, r = Ax-b or r = A'x=b and return maxnorm (r) */
+/* A' is the complex conjugate transpose, not the array transpose */
+/* -------------------------------------------------------------------------- */
+
+static double resid
+(
+ UF_long transpose,
+ UF_long Ap [ ],
+ UF_long Ai [ ],
+ double Ax [ ]
+ , double Az [ ]
+)
+{
+ UF_long i, j, p ;
+ double norm ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ r [i] = -b [i] ;
+ rz[i] = -bz[i] ;
+ }
+ if (transpose)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ /* complex: r(j) += conj (Aij) * x (i) */
+ r [j] += Ax [p] * x [i] ;
+ r [j] += Az [p] * xz[i] ;
+ rz[j] -= Az [p] * x [i] ;
+ rz[j] += Ax [p] * xz[i] ;
+ }
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ r [i] += Ax [p] * x [j] ;
+ r [i] -= Az [p] * xz[j] ;
+ rz[i] += Az [p] * x [j] ;
+ rz[i] += Ax [p] * xz[j] ;
+ }
+ }
+ }
+ norm = 0. ;
+ for (i = 0 ; i < n ; i++)
+ {
+ norm = MAX (ABS (r [i], rz [i]), norm) ;
+ }
+ return (norm) ;
+}
+
+
+/* -------------------------------------------------------------------------- */
+/* main program */
+/* -------------------------------------------------------------------------- */
+
+int main (int argc, char **argv)
+{
+ double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], *Ax, *Cx, *Lx, *Ux,
+ *W, t [2], *Dx, rnorm, *Rb, *y, *Rs ;
+ double *Az, *Lz, *Uz, *Dz, *Cz, *Rbz, *yz ;
+ UF_long *Ap, *Ai, *Cp, *Ci, row, col, p, lnz, unz, nr, nc, *Lp, *Li, *Ui, *Up,
+ *P, *Q, *Lj, i, j, k, anz, nfr, nchains, *Qinit, fnpiv, lnz1, unz1, nz1,
+ status, *Front_npivcol, *Front_parent, *Chain_start, *Wi, *Pinit, n1,
+ *Chain_maxrows, *Chain_maxcols, *Front_1strow, *Front_leftmostdesc,
+ nzud, do_recip ;
+ void *Symbolic, *Numeric ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (t) ;
+
+ printf ("\nUMFPACK V%d.%d (%s) demo: _zl_ version\n",
+ UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_DATE) ;
+
+ /* get the default control parameters */
+ umfpack_zl_defaults (Control) ;
+
+ /* change the default print level for this demo */
+ /* (otherwise, nothing will print) */
+ Control [UMFPACK_PRL] = 6 ;
+
+ /* print the license agreement */
+ umfpack_zl_report_status (Control, UMFPACK_OK) ;
+ Control [UMFPACK_PRL] = 5 ;
+
+ /* print the control parameters */
+ umfpack_zl_report_control (Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print A and b, and convert A to column-form */
+ /* ---------------------------------------------------------------------- */
+
+ /* print the right-hand-side */
+ printf ("\nb: ") ;
+ (void) umfpack_zl_report_vector (n, b, bz, Control) ;
+
+ /* print the triplet form of the matrix */
+ printf ("\nA: ") ;
+ (void) umfpack_zl_report_triplet (n, n, nz, Arow, Acol, Aval, Avalz,
+ Control) ;
+
+ /* convert to column form */
+ nz1 = MAX (nz,1) ; /* ensure arrays are not of size zero. */
+ Ap = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Ai = (UF_long *) malloc (nz1 * sizeof (UF_long)) ;
+ Ax = (double *) malloc (nz1 * sizeof (double)) ;
+ Az = (double *) malloc (nz1 * sizeof (double)) ;
+ if (!Ap || !Ai || !Ax || !Az)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_zl_triplet_to_col (n, n, nz, Arow, Acol, Aval, Avalz,
+ Ap, Ai, Ax, Az, (UF_long *) NULL) ;
+
+ if (status < 0)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_triplet_to_col failed") ;
+ }
+
+ /* print the column-form of A */
+ printf ("\nA: ") ;
+ (void) umfpack_zl_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zl_symbolic (n, n, Ap, Ai, Ax, Az, &Symbolic,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_info (Control, Info) ;
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_symbolic failed") ;
+ }
+
+ /* print the symbolic factorization */
+
+ printf ("\nSymbolic factorization of A: ") ;
+ (void) umfpack_zl_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_info (Control, Info) ;
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_numeric failed") ;
+ }
+
+ /* print the numeric factorization */
+ printf ("\nNumeric factorization of A: ") ;
+ (void) umfpack_zl_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zl_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_zl_report_info (Control, Info) ;
+ umfpack_zl_report_status (Control, status) ;
+ if (status < 0)
+ {
+ error ("umfpack_zl_solve failed") ;
+ }
+ printf ("\nx (solution of Ax=b): ") ;
+ (void) umfpack_zl_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the determinant */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zl_get_determinant (x, xz, r, Numeric, Info) ;
+ umfpack_zl_report_status (Control, status) ;
+ if (status < 0)
+ {
+ error ("umfpack_zl_get_determinant failed") ;
+ }
+ printf ("determinant: (%g", x [0]) ;
+ printf ("+ (%g)i", xz [0]) ; /* complex */
+ printf (") * 10^(%g)\n", r [0]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, broken down into steps */
+ /* ---------------------------------------------------------------------- */
+
+ /* Rb = R*b */
+ Rb = (double *) malloc (n * sizeof (double)) ;
+ Rbz = (double *) malloc (n * sizeof (double)) ;
+ y = (double *) malloc (n * sizeof (double)) ;
+ yz = (double *) malloc (n * sizeof (double)) ;
+ if (!Rb || !y) error ("out of memory") ;
+ if (!Rbz || !yz) error ("out of memory") ;
+
+ status = umfpack_zl_scale (Rb, Rbz, b, bz, Numeric) ;
+ if (status < 0) error ("umfpack_zl_scale failed") ;
+ /* solve Ly = P*(Rb) */
+ status = umfpack_zl_solve (UMFPACK_Pt_L, Ap, Ai, Ax, Az, y, yz, Rb, Rbz,
+ Numeric, Control, Info) ;
+ if (status < 0) error ("umfpack_zl_solve failed") ;
+ /* solve UQ'x=y */
+ status = umfpack_zl_solve (UMFPACK_U_Qt, Ap, Ai, Ax, Az, x, xz, y, yz,
+ Numeric, Control, Info) ;
+ if (status < 0) error ("umfpack_zl_solve failed") ;
+ printf ("\nx (solution of Ax=b, solve is split into 3 steps): ") ;
+ (void) umfpack_zl_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ free (Rb) ;
+ free (Rbz) ;
+ free (y) ;
+ free (yz) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve A'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ /* note that this is the complex conjugate transpose, A' */
+ status = umfpack_zl_solve (UMFPACK_At, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_zl_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ error ("umfpack_zl_solve failed") ;
+ }
+ printf ("\nx (solution of A'x=b): ") ;
+ (void) umfpack_zl_report_vector (n, x, xz, Control) ;
+ rnorm = resid (TRUE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify one numerical value in the column-form of A */
+ /* ---------------------------------------------------------------------- */
+
+ /* change A (1,4), look for row index 1 in column 4. */
+ row = 1 ;
+ col = 4 ;
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ if (row == Ai [p])
+ {
+ printf ("\nchanging A (%ld,%ld) to zero\n", row, col) ;
+ Ax [p] = 0.0 ;
+ Az [p] = 0.0 ;
+ break ;
+ }
+ }
+ printf ("\nmodified A: ") ;
+ (void) umfpack_zl_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* redo the numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* The pattern (Ap and Ai) hasn't changed, so the symbolic factorization */
+ /* doesn't have to be redone, no matter how much we change Ax. */
+
+ /* We don't need the Numeric object any more, so free it. */
+ umfpack_zl_free_numeric (&Numeric) ;
+
+ /* Note that a memory leak would have occurred if the old Numeric */
+ /* had not been free'd with umfpack_zl_free_numeric above. */
+ status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_info (Control, Info) ;
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of modified A: ") ;
+ (void) umfpack_zl_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, with the modified A */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zl_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_zl_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_solve failed") ;
+ }
+ printf ("\nx (with modified A): ") ;
+ (void) umfpack_zl_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* modify all of the numerical values of A, but not the pattern */
+ /* ---------------------------------------------------------------------- */
+
+ for (col = 0 ; col < n ; col++)
+ {
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ row = Ai [p] ;
+ printf ("changing ") ;
+ /* complex: */ printf ("real part of ") ;
+ printf ("A (%ld,%ld) from %g", row, col, Ax [p]) ;
+ Ax [p] = Ax [p] + col*10 - row ;
+ printf (" to %g\n", Ax [p]) ;
+ }
+ }
+ printf ("\ncompletely modified A (same pattern): ") ;
+ (void) umfpack_zl_report_matrix (n, n, Ap, Ai, Ax, Az, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* save the Symbolic object to file, free it, and load it back in */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the default filename, "symbolic.umf" */
+ printf ("\nSaving symbolic object:\n") ;
+ status = umfpack_zl_save_symbolic (Symbolic, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_save_symbolic failed") ;
+ }
+ printf ("\nFreeing symbolic object:\n") ;
+ umfpack_zl_free_symbolic (&Symbolic) ;
+ printf ("\nLoading symbolic object:\n") ;
+ status = umfpack_zl_load_symbolic (&Symbolic, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_load_symbolic failed") ;
+ }
+ printf ("\nDone loading symbolic object\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* redo the numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_zl_free_numeric (&Numeric) ;
+ status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_info (Control, Info) ;
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of completely modified A: ") ;
+ (void) umfpack_zl_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve Ax=b, with the modified A */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zl_solve (UMFPACK_A, Ap, Ai, Ax, Az, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_zl_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_solve failed") ;
+ }
+ printf ("\nx (with completely modified A): ") ;
+ (void) umfpack_zl_report_vector (n, x, xz, Control) ;
+ rnorm = resid (FALSE, Ap, Ai, Ax, Az) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the symbolic and numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_zl_free_symbolic (&Symbolic) ;
+ umfpack_zl_free_numeric (&Numeric) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = transpose of A */
+ /* ---------------------------------------------------------------------- */
+
+ Cp = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Ci = (UF_long *) malloc (nz1 * sizeof (UF_long)) ;
+ Cx = (double *) malloc (nz1 * sizeof (double)) ;
+ Cz = (double *) malloc (nz1 * sizeof (double)) ;
+ if (!Cp || !Ci || !Cx || !Cz)
+ {
+ error ("out of memory") ;
+ }
+ status = umfpack_zl_transpose (n, n, Ap, Ai, Ax, Az,
+ (UF_long *) NULL, (UF_long *) NULL, Cp, Ci, Cx, Cz, TRUE) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_transpose failed: ") ;
+ }
+ printf ("\nC (transpose of A): ") ;
+ (void) umfpack_zl_report_matrix (n, n, Cp, Ci, Cx, Cz, 1, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization of C */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zl_symbolic (n, n, Cp, Ci, Cx, Cz, &Symbolic,
+ Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_info (Control, Info) ;
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_symbolic failed") ;
+ }
+ printf ("\nSymbolic factorization of C: ") ;
+ (void) umfpack_zl_report_symbolic (Symbolic, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the contents of Symbolic into user arrays print them */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nGet the contents of the Symbolic object for C:\n") ;
+ printf ("(compare with umfpack_zl_report_symbolic output, above)\n") ;
+ Pinit = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Qinit = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Front_npivcol = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Front_1strow = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Front_leftmostdesc = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Front_parent = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Chain_start = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Chain_maxrows = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Chain_maxcols = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ if (!Pinit || !Qinit || !Front_npivcol || !Front_parent || !Chain_start ||
+ !Chain_maxrows || !Chain_maxcols || !Front_1strow ||
+ !Front_leftmostdesc)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_zl_get_symbolic (&nr, &nc, &n1, &anz, &nfr, &nchains,
+ Pinit, Qinit, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+ if (status < 0)
+ {
+ error ("symbolic factorization invalid") ;
+ }
+
+ printf ("From the Symbolic object, C is of dimension %ld-by-%ld\n", nr, nc);
+ printf (" with nz = %ld, number of fronts = %ld,\n", nz, nfr) ;
+ printf (" number of frontal matrix chains = %ld\n", nchains) ;
+
+ printf ("\nPivot columns in each front, and parent of each front:\n") ;
+ k = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fnpiv = Front_npivcol [i] ;
+ printf (" Front %ld: parent front: %ld number of pivot cols: %ld\n",
+ i, Front_parent [i], fnpiv) ;
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ col = Qinit [k] ;
+ printf (
+ " %ld-th pivot column is column %ld in original matrix\n",
+ k, col) ;
+ k++ ;
+ }
+ }
+
+ printf ("\nNote that the column ordering, above, will be refined\n") ;
+ printf ("in the numeric factorization below. The assignment of pivot\n") ;
+ printf ("columns to frontal matrices will always remain unchanged.\n") ;
+
+ printf ("\nTotal number of pivot columns in frontal matrices: %ld\n", k) ;
+
+ printf ("\nFrontal matrix chains:\n") ;
+ for (j = 0 ; j < nchains ; j++)
+ {
+ printf (" Frontal matrices %ld to %ld are factorized in a single\n",
+ Chain_start [j], Chain_start [j+1] - 1) ;
+ printf (" working array of size %ld-by-%ld\n",
+ Chain_maxrows [j], Chain_maxcols [j]) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization of C */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zl_numeric (Cp, Ci, Cx, Cz, Symbolic, &Numeric,
+ Control, Info) ;
+ if (status < 0)
+ {
+ error ("umfpack_zl_numeric failed") ;
+ }
+ printf ("\nNumeric factorization of C: ") ;
+ (void) umfpack_zl_report_numeric (Numeric, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extract the LU factors of C and print them */
+ /* ---------------------------------------------------------------------- */
+
+ if (umfpack_zl_get_lunz (&lnz, &unz, &nr, &nc, &nzud, Numeric) < 0)
+ {
+ error ("umfpack_zl_get_lunz failed") ;
+ }
+ /* ensure arrays are not of zero size */
+ lnz1 = MAX (lnz,1) ;
+ unz1 = MAX (unz,1) ;
+ Lp = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Lj = (UF_long *) malloc (lnz1 * sizeof (UF_long)) ;
+ Lx = (double *) malloc (lnz1 * sizeof (double)) ;
+ Lz = (double *) malloc (lnz1 * sizeof (double)) ;
+ Up = (UF_long *) malloc ((n+1) * sizeof (UF_long)) ;
+ Ui = (UF_long *) malloc (unz1 * sizeof (UF_long)) ;
+ Ux = (double *) malloc (unz1 * sizeof (double)) ;
+ Uz = (double *) malloc (unz1 * sizeof (double)) ;
+ P = (UF_long *) malloc (n * sizeof (UF_long)) ;
+ Q = (UF_long *) malloc (n * sizeof (UF_long)) ;
+ Dx = (double *) NULL ; /* D vector not requested */
+ Dz = (double *) NULL ;
+ Rs = (double *) malloc (n * sizeof (double)) ;
+ if (!Lp || !Lj || !Lx || !Lz || !Up || !Ui || !Ux || !Uz || !P || !Q || !Rs)
+ {
+ error ("out of memory") ;
+ }
+ status = umfpack_zl_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz,
+ P, Q, Dx, Dz, &do_recip, Rs, Numeric) ;
+ if (status < 0)
+ {
+ error ("umfpack_zl_get_numeric failed") ;
+ }
+
+ printf ("\nL (lower triangular factor of C): ") ;
+ (void) umfpack_zl_report_matrix (n, n, Lp, Lj, Lx, Lz, 0, Control) ;
+ printf ("\nU (upper triangular factor of C): ") ;
+ (void) umfpack_zl_report_matrix (n, n, Up, Ui, Ux, Uz, 1, Control) ;
+ printf ("\nP: ") ;
+ (void) umfpack_zl_report_perm (n, P, Control) ;
+ printf ("\nQ: ") ;
+ (void) umfpack_zl_report_perm (n, Q, Control) ;
+ printf ("\nScale factors: row i of A is to be ") ;
+ if (do_recip)
+ {
+ printf ("multiplied by the ith scale factor\n") ;
+ }
+ else
+ {
+ printf ("divided by the ith scale factor\n") ;
+ }
+ for (i = 0 ; i < n ; i++) printf ("%ld: %g\n", i, Rs [i]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to triplet form and print it */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that L is in row-form, so it is the row indices that are created */
+ /* by umfpack_zl_col_to_triplet. */
+
+ printf ("\nConverting L to triplet form, and printing it:\n") ;
+ Li = (UF_long *) malloc (lnz1 * sizeof (UF_long)) ;
+ if (!Li)
+ {
+ error ("out of memory") ;
+ }
+ if (umfpack_zl_col_to_triplet (n, Lp, Li) < 0)
+ {
+ error ("umfpack_zl_col_to_triplet failed") ;
+ }
+ printf ("\nL, in triplet form: ") ;
+ (void) umfpack_zl_report_triplet (n, n, lnz, Li, Lj, Lx, Lz, Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* save the Numeric object to file, free it, and load it back in */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the default filename, "numeric.umf" */
+ printf ("\nSaving numeric object:\n") ;
+ status = umfpack_zl_save_numeric (Numeric, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_save_numeric failed") ;
+ }
+ printf ("\nFreeing numeric object:\n") ;
+ umfpack_zl_free_numeric (&Numeric) ;
+ printf ("\nLoading numeric object:\n") ;
+ status = umfpack_zl_load_numeric (&Numeric, (char *) NULL) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_load_numeric failed") ;
+ }
+ printf ("\nDone loading numeric object\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve C'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ status = umfpack_zl_solve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz,
+ Numeric, Control, Info) ;
+ umfpack_zl_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_solve failed") ;
+ }
+ printf ("\nx (solution of C'x=b): ") ;
+ (void) umfpack_zl_report_vector (n, x, xz, Control) ;
+ rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* solve C'x=b again, using umfpack_zl_wsolve instead */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nSolving C'x=b again, using umfpack_zl_wsolve instead:\n") ;
+ Wi = (UF_long *) malloc (n * sizeof (UF_long)) ;
+ W = (double *) malloc (10*n * sizeof (double)) ;
+ if (!Wi || !W)
+ {
+ error ("out of memory") ;
+ }
+
+ status = umfpack_zl_wsolve (UMFPACK_At, Cp, Ci, Cx, Cz, x, xz, b, bz,
+ Numeric, Control, Info, Wi, W) ;
+ umfpack_zl_report_info (Control, Info) ;
+ if (status < 0)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ error ("umfpack_zl_wsolve failed") ;
+ }
+ printf ("\nx (solution of C'x=b): ") ;
+ (void) umfpack_zl_report_vector (n, x, xz, Control) ;
+ rnorm = resid (TRUE, Cp, Ci, Cx, Cz) ;
+ printf ("maxnorm of residual: %g\n\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free everything */
+ /* ---------------------------------------------------------------------- */
+
+ /* This is not strictly required since the process is exiting and the */
+ /* system will reclaim the memory anyway. It's useful, though, just as */
+ /* a list of what is currently malloc'ed by this program. Plus, it's */
+ /* always a good habit to explicitly free whatever you malloc. */
+
+ free (Ap) ;
+ free (Ai) ;
+ free (Ax) ;
+ free (Az) ;
+
+ free (Cp) ;
+ free (Ci) ;
+ free (Cx) ;
+ free (Cz) ;
+
+ free (Pinit) ;
+ free (Qinit) ;
+ free (Front_npivcol) ;
+ free (Front_1strow) ;
+ free (Front_leftmostdesc) ;
+ free (Front_parent) ;
+ free (Chain_start) ;
+ free (Chain_maxrows) ;
+ free (Chain_maxcols) ;
+
+ free (Lp) ;
+ free (Lj) ;
+ free (Lx) ;
+ free (Lz) ;
+
+ free (Up) ;
+ free (Ui) ;
+ free (Ux) ;
+ free (Uz) ;
+
+ free (P) ;
+ free (Q) ;
+
+ free (Li) ;
+
+ free (Wi) ;
+ free (W) ;
+
+ umfpack_zl_free_symbolic (&Symbolic) ;
+ umfpack_zl_free_numeric (&Numeric) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print the total time spent in this demo */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_toc (t) ;
+ printf ("\numfpack_zl_demo complete.\nTotal time: %5.2f seconds"
+ " (CPU time), %5.2f seconds (wallclock time)\n", t [1], t [0]) ;
+ return (0) ;
+}
diff --git a/UMFPACK/Demo/umfpack_zl_demo.out b/UMFPACK/Demo/umfpack_zl_demo.out
new file mode 100644
index 0000000..f34ec93
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_zl_demo.out
@@ -0,0 +1,1523 @@
+
+UMFPACK V5.2 (Nov 1, 2007) demo: _zl_ version
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+
+UMFPACK License:
+
+ UMFPACK is available under alternate licenses,
+ contact T. Davis for details.
+
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU General Public
+ License as published by the Free Software Foundation; either
+ version 2 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU GPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability: http://www.cise.ufl.edu/research/sparse/umfpack
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Control:
+ Matrix entry defined as: double complex
+ Int (generic integer) defined as: UF_long
+
+ 0: print level: 5
+ 1: dense row parameter: 0.2
+ "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
+ 2: dense column parameter: 0.2
+ "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
+ 3: pivot tolerance: 0.1
+ 4: block size for dense matrix kernels: 32
+ 5: strategy: 0 (auto)
+ 6: initial allocation ratio: 0.7
+ 7: max iterative refinement steps: 2
+ 12: 2-by-2 pivot tolerance: 0.01
+ 13: Q fixed during numerical factorization: 0 (auto)
+ 14: AMD dense row/col parameter: 10
+ "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
+ Only used if the AMD ordering is used.
+ 15: diagonal pivot tolerance: 0.001
+ Only used if diagonal pivoting is attempted.
+ 16: scaling: 1 (divide each row by sum of abs. values in each row)
+ 17: frontal matrix allocation ratio: 0.5
+ 18: drop tolerance: 0
+ 19: AMD and COLAMD aggressive absorption: 1 (yes)
+
+ The following options can only be changed at compile-time:
+ 8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ 9: compiled for ANSI C
+ 10: CPU timer is POSIX times ( ) routine.
+ 11: compiled for normal operation (debugging disabled)
+ computer/operating system: Linux
+ size of int: 4 UF_long: 8 Int: 8 pointer: 8 double: 8 Entry: 16 (in bytes)
+
+
+b: dense vector, n = 5.
+ 0 : (8 + 1i)
+ 1 : (45 - 5i)
+ 2 : (-3 - 2i)
+ 3 : (3 + 0i)
+ 4 : (19 + 2.2i)
+ dense vector OK
+
+
+A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12.
+ 0 : 0 0 (2 + 1i)
+ 1 : 4 4 (1 + 0.4i)
+ 2 : 1 0 (3 + 0.1i)
+ 3 : 1 2 (4 + 0.2i)
+ 4 : 2 1 (-1 - 1i)
+ 5 : 2 2 (-3 - 0.2i)
+ 6 : 0 1 (3 + 0i)
+ 7 : 1 4 (6 + 6i)
+ 8 : 2 3 (2 + 3i)
+ 9 : 3 2 (1 + 0i)
+ 10 : 4 1 (4 + 0.3i)
+ 11 : 4 2 (2 + 0.3i)
+ triplet-form matrix OK
+
+
+A: column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2 + 1i)
+ row 1 : (3 + 0.1i)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (3 + 0i)
+ row 2 : (-1 - 1i)
+ row 4 : (4 + 0.3i)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (4 + 0.2i)
+ row 2 : (-3 - 0.2i)
+ row 3 : (1 + 0i)
+ row 4 : (2 + 0.3i)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (2 + 3i)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (6 + 6i)
+ row 4 : (1 + 0.4i)
+ column-form matrix OK
+
+
+Symbolic factorization of A: Symbolic object:
+ matrix to be factorized:
+ n_row: 5 n_col: 5
+ number of entries: 12
+ block size used for dense matrix kernels: 32
+ strategy used: unsymmetric
+ ordering used: colamd on A
+
+ performn column etree postorder: yes
+ prefer diagonal pivoting (attempt P=Q): no
+ variable-size part of Numeric object:
+ minimum initial size (Units): 74 (MBytes): 0.0
+ estimated peak size (Units): 1301 (MBytes): 0.0
+ estimated final size (Units): 15 (MBytes): 0.0
+ symbolic factorization memory usage (Units): 138 (MBytes): 0.0
+ frontal matrices / supercolumns:
+ number of frontal chains: 1
+ number of frontal matrices: 1
+ largest frontal matrix row dimension: 3
+ largest frontal matrix column dimension: 3
+
+ Frontal chain: 0. Frontal matrices 0 to 0
+ Largest frontal matrix in Frontal chain: 3-by-3
+ Front: 0 pivot cols: 3 (pivot columns 0 to 2)
+ pivot row candidates: 2 to 4
+ leftmost descendant: 0
+ 1st new candidate row : 2
+ parent: (none)
+
+Initial column permutation, Q1: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Initial row permutation, P1: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 1
+ 4 : 4
+ permutation vector OK
+
+ Symbolic object: OK
+
+
+Numeric factorization of A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.93000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 74
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 1292
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 4
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 4
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 34
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.34629e-01
+ max abs. value on diagonal of U: 1.77313e+00
+ reciprocal condition number estimate: 7.59e-02
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.166667)
+ 1 : (0.0518135)
+ 2 : (0.0980392)
+ 3 : (1)
+ 4 : (0.125)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 4 : (0.207254 + 0.0103627i)
+ row 3 : (0.25 + 0.0375i)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.379275 - 0.174093i)
+
+ column 3: length 1.
+ row 4 : (3.00161 + 1.2864i)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.5 + 0.0375i)
+
+ row 2: length 1.
+ col 4 : (0.5 + 0i)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (-0.294118 - 0.0196078i)
+ col 4 : (-0.0980392 - 0.0980392i)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.196078 + 0.294118i)
+ 1 : (1 + 0i)
+ 2 : (0.333333 + 0.166667i)
+ 3 : (0.125 + 0.05i)
+ 4 : (-1.6422 - 0.668715i)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.93000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 74 69 93%
+ peak size (Units) 1301 1292 99%
+ final size (Units) 15 13 87%
+ Numeric final size (Units) 79 75 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 1463 1454 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 3.40000e+01 51%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.35e-01
+ max abs. value on diagonal of U: 1.77e+00
+ estimate of reciprocal of condition number: 7.59e-02
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 1.02800e+03
+ iterative refinement steps taken: 1
+ iterative refinement steps attempted: 1
+ sparse backward error omega1: 5.28e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 1.06200e+03
+
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+
+x (solution of Ax=b): dense vector, n = 5.
+ 0 : (0.121188 - 0.561001i)
+ 1 : (2.39887 + 0.666938i)
+ 2 : (3 + 0i)
+ 3 : (1.57395 - 1.52801i)
+ 4 : (2.3876 - 3.04245i)
+ dense vector OK
+
+maxnorm of residual: 1.77636e-15
+
+
+UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
+
+UMFPACK V5.2.0 (Nov 1, 2007): OK
+
+determinant: (-1.7814+ (2.3784)i) * 10^(2)
+
+x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5.
+ 0 : (0.121188 - 0.561001i)
+ 1 : (2.39887 + 0.666938i)
+ 2 : (3 + 0i)
+ 3 : (1.57395 - 1.52801i)
+ 4 : (2.3876 - 3.04245i)
+ dense vector OK
+
+maxnorm of residual: 1.77636e-14
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.93000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 74 69 93%
+ peak size (Units) 1301 1292 99%
+ final size (Units) 15 13 87%
+ Numeric final size (Units) 79 75 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 1463 1454 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 3.40000e+01 51%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.35e-01
+ max abs. value on diagonal of U: 1.77e+00
+ estimate of reciprocal of condition number: 7.59e-02
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 4.80000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 7.82e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 5.14000e+02
+
+
+x (solution of A'x=b): dense vector, n = 5.
+ 0 : (3.39246 + 0.13257i)
+ 1 : (0.31463 + 1.38626i)
+ 2 : (0.461538 + 0.692308i)
+ 3 : (-20.9089 - 1.55801i)
+ 4 : (9.04015 - 0.613724i)
+ dense vector OK
+
+maxnorm of residual: 4.52416e-15
+
+
+changing A (1,4) to zero
+
+modified A: column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2 + 1i)
+ row 1 : (3 + 0.1i)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (3 + 0i)
+ row 2 : (-1 - 1i)
+ row 4 : (4 + 0.3i)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (4 + 0.2i)
+ row 2 : (-3 - 0.2i)
+ row 3 : (1 + 0i)
+ row 4 : (2 + 0.3i)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (2 + 3i)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (0 + 0i)
+ row 4 : (1 + 0.4i)
+ column-form matrix OK
+
+
+Numeric factorization of modified A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.02000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 73
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 1292
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 3
+ number of entries stored in L (excl diag): 1
+ number of nonzeros in U (excl diag): 4
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 17
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.34629e-01
+ max abs. value on diagonal of U: 1.00000e+00
+ reciprocal condition number estimate: 1.35e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.166667)
+ 1 : (0.136986)
+ 2 : (0.0980392)
+ 3 : (1)
+ 4 : (0.125)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 4 : (0.547945 + 0.0273973i)
+ row 3 : (0.25 + 0.0375i)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (1.00274 - 0.460274i)
+
+ column 3: length 0. Start of Lchain.
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.5 + 0.0375i)
+
+ row 2: length 1.
+ col 4 : (0.5 + 0i)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (-0.294118 - 0.0196078i)
+ col 4 : (-0.0980392 - 0.0980392i)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.196078 + 0.294118i)
+ 1 : (1 + 0i)
+ 2 : (0.333333 + 0.166667i)
+ 3 : (0.125 + 0.05i)
+ 4 : (-0.50137 + 0.230137i)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.00000e+00
+ maximum sum (abs (rows of A)): 1.02000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 74 69 93%
+ peak size (Units) 1301 1292 99%
+ final size (Units) 15 12 80%
+ Numeric final size (Units) 79 74 94%
+ Numeric final size (MBytes) 0.0 0.0 94%
+ peak memory usage (Units) 1463 1454 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 1.70000e+01 25%
+ nz in L (incl diagonal) 10 8 80%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 12 80%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 8
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.35e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 1.35e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 8
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 5.15000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 6.01e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 5.32000e+02
+
+
+x (with modified A): dense vector, n = 5.
+ 0 : (10.9256 - 2.23085i)
+ 1 : (-5.36071 - 1.82131i)
+ 2 : (3 + 0i)
+ 3 : (-1.60191 - 1.88814i)
+ 4 : (32.7361 - 2.90097i)
+ dense vector OK
+
+maxnorm of residual: 4.66294e-15
+
+changing real part of A (0,0) from 2 to 2
+changing real part of A (1,0) from 3 to 2
+changing real part of A (0,1) from 3 to 13
+changing real part of A (2,1) from -1 to 7
+changing real part of A (4,1) from 4 to 10
+changing real part of A (1,2) from 4 to 23
+changing real part of A (2,2) from -3 to 15
+changing real part of A (3,2) from 1 to 18
+changing real part of A (4,2) from 2 to 18
+changing real part of A (2,3) from 2 to 30
+changing real part of A (1,4) from 0 to 39
+changing real part of A (4,4) from 1 to 37
+
+completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2 + 1i)
+ row 1 : (2 + 0.1i)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (13 + 0i)
+ row 2 : (7 - 1i)
+ row 4 : (10 + 0.3i)
+
+ column 2: start: 5 end: 8 entries: 4
+ row 1 : (23 + 0.2i)
+ row 2 : (15 - 0.2i)
+ row 3 : (18 + 0i)
+ row 4 : (18 + 0.3i)
+
+ column 3: start: 9 end: 9 entries: 1
+ row 2 : (30 + 3i)
+
+ column 4: start: 10 end: 11 entries: 2
+ row 1 : (39 + 0i)
+ row 4 : (37 + 0.4i)
+ column-form matrix OK
+
+
+Saving symbolic object:
+
+Freeing symbolic object:
+
+Loading symbolic object:
+
+Done loading symbolic object
+
+Numeric factorization of completely modified A: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 1.60000e+01
+ maximum sum (abs (rows of A)): 6.60000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 74
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 1292
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 4
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 4
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 34
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.39754e-01
+ max abs. value on diagonal of U: 1.00000e+00
+ reciprocal condition number estimate: 1.40e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.0625)
+ 1 : (0.0155521)
+ 2 : (0.0177936)
+ 3 : (0.0555556)
+ 4 : (0.0151515)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 2.
+ row 4 : (0.357698 + 0.00311042i)
+ row 3 : (0.272727 + 0.00454545i)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.204044 - 0.0895801i)
+
+ column 3: length 1.
+ row 4 : (1.0818 - 0.0116951i)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.151515 + 0.00454545i)
+
+ row 2: length 1.
+ col 4 : (0.8125 + 0i)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 2.
+ col 1 : (0.266904 - 0.00355872i)
+ col 4 : (0.124555 - 0.0177936i)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.533808 + 0.0533808i)
+ 1 : (1 + 0i)
+ 2 : (0.125 + 0.0625i)
+ 3 : (0.560606 + 0.00606061i)
+ 4 : (-0.329747 + 0.0696386i)
+ dense vector OK
+
+ Numeric object: OK
+
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 1.60000e+01
+ maximum sum (abs (rows of A)): 6.60000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 74 69 93%
+ peak size (Units) 1301 1292 99%
+ final size (Units) 15 13 87%
+ Numeric final size (Units) 79 75 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 1463 1454 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 3.40000e+01 51%
+ nz in L (incl diagonal) 10 9 90%
+ nz in U (incl diagonal) 10 9 90%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 9
+ nz in U (incl diagonal), if none dropped 9
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 1.40e-01
+ max abs. value on diagonal of U: 1.00e+00
+ estimate of reciprocal of condition number: 1.40e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 5.23000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 8.05e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 5.57000e+02
+
+
+x (with completely modified A): dense vector, n = 5.
+ 0 : (7.56307 - 3.68974i)
+ 1 : (-0.831991 + 0.0627998i)
+ 2 : (0.166667 + 0i)
+ 3 : (-0.00206892 - 0.107735i)
+ 4 : (0.658245 + 0.0407649i)
+ dense vector OK
+
+maxnorm of residual: 9.10383e-15
+
+
+C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12.
+
+ column 0: start: 0 end: 1 entries: 2
+ row 0 : (2 - 1i)
+ row 1 : (13 + 0i)
+
+ column 1: start: 2 end: 4 entries: 3
+ row 0 : (2 - 0.1i)
+ row 2 : (23 - 0.2i)
+ row 4 : (39 + 0i)
+
+ column 2: start: 5 end: 7 entries: 3
+ row 1 : (7 + 1i)
+ row 2 : (15 + 0.2i)
+ row 3 : (30 - 3i)
+
+ column 3: start: 8 end: 8 entries: 1
+ row 2 : (18 + 0i)
+
+ column 4: start: 9 end: 11 entries: 3
+ row 1 : (10 - 0.3i)
+ row 2 : (18 - 0.3i)
+ row 4 : (37 - 0.4i)
+ column-form matrix OK
+
+
+Symbolic factorization of C: Symbolic object:
+ matrix to be factorized:
+ n_row: 5 n_col: 5
+ number of entries: 12
+ block size used for dense matrix kernels: 32
+ strategy used: unsymmetric
+ ordering used: colamd on A
+
+ performn column etree postorder: yes
+ prefer diagonal pivoting (attempt P=Q): no
+ variable-size part of Numeric object:
+ minimum initial size (Units): 75 (MBytes): 0.0
+ estimated peak size (Units): 1302 (MBytes): 0.0
+ estimated final size (Units): 16 (MBytes): 0.0
+ symbolic factorization memory usage (Units): 138 (MBytes): 0.0
+ frontal matrices / supercolumns:
+ number of frontal chains: 1
+ number of frontal matrices: 1
+ largest frontal matrix row dimension: 3
+ largest frontal matrix column dimension: 3
+
+ Frontal chain: 0. Frontal matrices 0 to 0
+ Largest frontal matrix in Frontal chain: 3-by-3
+ Front: 0 pivot cols: 3 (pivot columns 0 to 2)
+ pivot row candidates: 2 to 4
+ leftmost descendant: 0
+ 1st new candidate row : 2
+ parent: (none)
+
+Initial column permutation, Q1: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Initial row permutation, P1: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 1
+ 4 : 4
+ permutation vector OK
+
+ Symbolic object: OK
+
+
+Get the contents of the Symbolic object for C:
+(compare with umfpack_zl_report_symbolic output, above)
+From the Symbolic object, C is of dimension 5-by-5
+ with nz = 12, number of fronts = 1,
+ number of frontal matrix chains = 1
+
+Pivot columns in each front, and parent of each front:
+ Front 0: parent front: -1 number of pivot cols: 3
+ 0-th pivot column is column 3 in original matrix
+ 1-th pivot column is column 2 in original matrix
+ 2-th pivot column is column 0 in original matrix
+
+Note that the column ordering, above, will be refined
+in the numeric factorization below. The assignment of pivot
+columns to frontal matrices will always remain unchanged.
+
+Total number of pivot columns in frontal matrices: 3
+
+Frontal matrix chains:
+ Frontal matrices 0 to 0 are factorized in a single
+ working array of size 3-by-3
+
+Numeric factorization of C: Numeric object:
+ n_row: 5 n_col: 5
+ relative pivot tolerance used: 0.1
+ relative symmetric pivot tolerance used: 0.001
+ matrix scaled: yes (divided each row by sum abs value in each row)
+ minimum sum (abs (rows of A)): 5.10000e+00
+ maximum sum (abs (rows of A)): 7.64000e+01
+ initial allocation parameter used: 0.7
+ frontal matrix allocation parameter used: 0.5
+ final total size of Numeric object (Units): 75
+ final total size of Numeric object (MBytes): 0.0
+ peak size of variable-size part (Units): 1293
+ peak size of variable-size part (MBytes): 0.0
+ largest actual frontal matrix size: 4
+ memory defragmentations: 1
+ memory reallocations: 1
+ costly memory reallocations: 0
+ entries in compressed pattern (L and U): 2
+ number of nonzeros in L (excl diag): 3
+ number of entries stored in L (excl diag): 2
+ number of nonzeros in U (excl diag): 5
+ number of entries stored in U (excl diag): 2
+ factorization floating-point operations: 34
+ number of nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.40964e-01
+ max abs. value on diagonal of U: 9.13625e-01
+ reciprocal condition number estimate: 2.64e-01
+
+Scale factors applied via multiplication
+Scale factors, Rs: dense vector, n = 5.
+ 0 : (0.196078)
+ 1 : (0.0319489)
+ 2 : (0.0133869)
+ 3 : (0.030303)
+ 4 : (0.013089)
+ dense vector OK
+
+
+P: row permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: column permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+L in Numeric object, in column-oriented compressed-pattern form:
+ Diagonal entries are all equal to 1.0 (not stored)
+
+ column 0: length 0.
+
+ column 1: length 1.
+ row 4 : (0.240091 + 0.0591529i)
+
+ column 2: add 1 entries. length 1. Start of Lchain.
+ row 4 : (0.847284 + 0.423642i)
+
+ column 3: length 1.
+ row 4 : (0.659838 - 0.0126577i)
+
+ column 4: length 0. Start of Lchain.
+
+
+U in Numeric object, in row-oriented compressed-pattern form:
+ Diagonal is stored separately.
+
+ row 4: length 0. End of Uchain.
+
+ row 3: length 1. End of Uchain.
+ col 4 : (0.510471 + 0i)
+
+ row 2: length 1.
+ col 4 : (0.392157 - 0.0196078i)
+
+ row 1: length 0. End of Uchain.
+
+ row 1: length 0.
+
+ row 0: length 3.
+ col 1 : (0.200803 + 0.00267738i)
+ col 3 : (0.240964 - 0.00401606i)
+ col 4 : (0.307898 - 0.00267738i)
+
+
+diagonal of U: dense vector, n = 5.
+ 0 : (0.240964 + 0i)
+ 1 : (0.909091 - 0.0909091i)
+ 2 : (0.392157 - 0.196078i)
+ 3 : (0.484293 - 0.0052356i)
+ 4 : (-0.677403 - 0.143059i)
+ dense vector OK
+
+ Numeric object: OK
+
+
+L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8.
+
+ row 0: start: 0 end: 0 entries: 1
+ column 0 : (1 + 0i)
+
+ row 1: start: 1 end: 1 entries: 1
+ column 1 : (1 + 0i)
+
+ row 2: start: 2 end: 2 entries: 1
+ column 2 : (1 + 0i)
+
+ row 3: start: 3 end: 3 entries: 1
+ column 3 : (1 + 0i)
+
+ row 4: start: 4 end: 7 entries: 4
+ column 1 : (0.240091 + 0.0591529i)
+ column 2 : (0.847284 + 0.423642i)
+ column 3 : (0.659838 - 0.0126577i)
+ column 4 : (1 + 0i)
+ row-form matrix OK
+
+
+U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10.
+
+ column 0: start: 0 end: 0 entries: 1
+ row 0 : (0.240964 + 0i)
+
+ column 1: start: 1 end: 2 entries: 2
+ row 0 : (0.200803 + 0.00267738i)
+ row 1 : (0.909091 - 0.0909091i)
+
+ column 2: start: 3 end: 3 entries: 1
+ row 2 : (0.392157 - 0.196078i)
+
+ column 3: start: 4 end: 5 entries: 2
+ row 0 : (0.240964 - 0.00401606i)
+ row 3 : (0.484293 - 0.0052356i)
+
+ column 4: start: 6 end: 9 entries: 4
+ row 0 : (0.307898 - 0.00267738i)
+ row 2 : (0.392157 - 0.0196078i)
+ row 3 : (0.510471 + 0i)
+ row 4 : (-0.677403 - 0.143059i)
+ column-form matrix OK
+
+
+P: permutation vector, n = 5.
+ 0 : 2
+ 1 : 3
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Q: permutation vector, n = 5.
+ 0 : 3
+ 1 : 2
+ 2 : 0
+ 3 : 4
+ 4 : 1
+ permutation vector OK
+
+
+Scale factors: row i of A is to be multiplied by the ith scale factor
+0: 0.196078
+1: 0.0319489
+2: 0.0133869
+3: 0.030303
+4: 0.013089
+
+Converting L to triplet form, and printing it:
+
+L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8.
+ 0 : 0 0 (1 + 0i)
+ 1 : 1 1 (1 + 0i)
+ 2 : 2 2 (1 + 0i)
+ 3 : 3 3 (1 + 0i)
+ 4 : 4 1 (0.240091 + 0.0591529i)
+ 5 : 4 2 (0.847284 + 0.423642i)
+ 6 : 4 3 (0.659838 - 0.0126577i)
+ 7 : 4 4 (1 + 0i)
+ triplet-form matrix OK
+
+
+Saving numeric object:
+
+Freeing numeric object:
+
+Loading numeric object:
+
+Done loading numeric object
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 5.10000e+00
+ maximum sum (abs (rows of A)): 7.64000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 75 70 93%
+ peak size (Units) 1302 1293 99%
+ final size (Units) 16 14 88%
+ Numeric final size (Units) 80 76 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 1464 1455 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 3.40000e+01 51%
+ nz in L (incl diagonal) 9 8 89%
+ nz in U (incl diagonal) 11 10 91%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 8
+ nz in U (incl diagonal), if none dropped 10
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.41e-01
+ max abs. value on diagonal of U: 9.14e-01
+ estimate of reciprocal of condition number: 2.64e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 4.80000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 9.42e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 5.14000e+02
+
+
+x (solution of C'x=b): dense vector, n = 5.
+ 0 : (7.56307 - 3.68974i)
+ 1 : (-0.831991 + 0.0627998i)
+ 2 : (0.166667 + 0i)
+ 3 : (-0.00206892 - 0.107735i)
+ 4 : (0.658245 + 0.0407649i)
+ dense vector OK
+
+maxnorm of residual: 4.88498e-15
+
+
+Solving C'x=b again, using umfpack_zl_wsolve instead:
+UMFPACK V5.2.0 (Nov 1, 2007), Info:
+ matrix entry defined as: double complex
+ Int (generic integer) defined as: UF_long
+ BLAS library used: Fortran BLAS. size of BLAS integer: 4
+ MATLAB: no.
+ CPU timer: POSIX times ( ) routine.
+ number of rows in matrix A: 5
+ number of columns in matrix A: 5
+ entries in matrix A: 12
+ memory usage reported in: 16-byte Units
+ size of int: 4 bytes
+ size of UF_long: 8 bytes
+ size of pointer: 8 bytes
+ size of numerical entry: 16 bytes
+
+ strategy used: unsymmetric
+ ordering used: colamd on A
+ modify Q during factorization: yes
+ prefer diagonal pivoting: no
+ pivots with zero Markowitz cost: 2
+ submatrix S after removing zero-cost pivots:
+ number of "dense" rows: 0
+ number of "dense" columns: 0
+ number of empty rows: 0
+ number of empty columns 0
+ submatrix S square and diagonal preserved
+ pattern of square submatrix S:
+ number rows and columns 3
+ symmetry of nonzero pattern: 1.000000
+ nz in S+S' (excl. diagonal): 4
+ nz on diagonal of matrix S: 2
+ fraction of nz on diagonal: 0.666667
+ 2-by-2 pivoting to place large entries on diagonal:
+ # of small diagonal entries of S: 1
+ # unmatched: 0
+ symmetry of P2*S: 0.000000
+ nz in P2*S+(P2*S)' (excl. diag.): 6
+ nz on diagonal of P2*S: 3
+ fraction of nz on diag of P2*S: 1.000000
+ symbolic factorization defragmentations: 0
+ symbolic memory usage (Units): 138
+ symbolic memory usage (MBytes): 0.0
+ Symbolic size (Units): 41
+ Symbolic size (MBytes): 0
+ symbolic factorization CPU time (sec): 0.00
+ symbolic factorization wallclock time(sec): 0.00
+
+ matrix scaled: yes (divided each row by sum of abs values in each row)
+ minimum sum (abs (rows of A)): 5.10000e+00
+ maximum sum (abs (rows of A)): 7.64000e+01
+
+ symbolic/numeric factorization: upper bound actual %
+ variable-sized part of Numeric object:
+ initial size (Units) 75 70 93%
+ peak size (Units) 1302 1293 99%
+ final size (Units) 16 14 88%
+ Numeric final size (Units) 80 76 95%
+ Numeric final size (MBytes) 0.0 0.0 95%
+ peak memory usage (Units) 1464 1455 99%
+ peak memory usage (MBytes) 0.0 0.0 99%
+ numeric factorization flops 6.70000e+01 3.40000e+01 51%
+ nz in L (incl diagonal) 9 8 89%
+ nz in U (incl diagonal) 11 10 91%
+ nz in L+U (incl diagonal) 15 13 87%
+ largest front (# entries) 9 4 44%
+ largest # rows in front 3 2 67%
+ largest # columns in front 3 2 67%
+
+ initial allocation ratio used: 0.7
+ # of forced updates due to frontal growth: 0
+ nz in L (incl diagonal), if none dropped 8
+ nz in U (incl diagonal), if none dropped 10
+ number of small entries dropped 0
+ nonzeros on diagonal of U: 5
+ min abs. value on diagonal of U: 2.41e-01
+ max abs. value on diagonal of U: 9.14e-01
+ estimate of reciprocal of condition number: 2.64e-01
+ indices in compressed pattern: 2
+ numerical values stored in Numeric object: 9
+ numeric factorization defragmentations: 1
+ numeric factorization reallocations: 1
+ costly numeric factorization reallocations: 0
+ numeric factorization CPU time (sec): 0.00
+ numeric factorization wallclock time (sec): 0.00
+
+ solve flops: 4.80000e+02
+ iterative refinement steps taken: 0
+ iterative refinement steps attempted: 0
+ sparse backward error omega1: 9.42e-17
+ sparse backward error omega2: 0.00e+00
+ solve CPU time (sec): 0.00
+ solve wall clock time (sec): 0.00
+
+ total symbolic + numeric + solve flops: 5.14000e+02
+
+
+x (solution of C'x=b): dense vector, n = 5.
+ 0 : (7.56307 - 3.68974i)
+ 1 : (-0.831991 + 0.0627998i)
+ 2 : (0.166667 + 0i)
+ 3 : (-0.00206892 - 0.107735i)
+ 4 : (0.658245 + 0.0407649i)
+ dense vector OK
+
+maxnorm of residual: 4.88498e-15
+
+
+umfpack_zl_demo complete.
+Total time: 0.00 seconds (CPU time), 0.01 seconds (wallclock time)
diff --git a/UMFPACK/Demo/umfpack_zl_demo.sed b/UMFPACK/Demo/umfpack_zl_demo.sed
new file mode 100644
index 0000000..67516d3
--- /dev/null
+++ b/UMFPACK/Demo/umfpack_zl_demo.sed
@@ -0,0 +1,7 @@
+/::/d
+1,$s/_xx_/_zl_/g
+1,$s/Int/UF_long/g
+1,$s/WSIZE/10/
+/define ABS/ {
+ s/ABS/ABS(x,z) ((x) >= 0 ? (x) : -(x)) + ((z) >= 0 ? (z) : -(z))/
+ }
diff --git a/UMFPACK/Doc/ChangeLog b/UMFPACK/Doc/ChangeLog
new file mode 100644
index 0000000..82f50aa
--- /dev/null
+++ b/UMFPACK/Doc/ChangeLog
@@ -0,0 +1,472 @@
+Nov 1, 2007, version 5.2.0
+
+ * change of license to GNU GPL from GNU LGPL. This is the primary change to
+ this version.
+
+ * minor lint cleanup
+
+ * port to MATLAB 7.5 (added -lmwblas to mex command)
+
+ * added info output to the umfpack_btf command.
+
+May 31, 2007, version 5.1.0
+
+ * port to 64-bit MATLAB
+
+ * Makefiles updated to reflect directory changes to AMD (UMFPACK v5.1.0
+ requires AMD v2.2.0)
+
+ * Source/Makefile and GNUMakefile moved to Lib/
+
+Dec 12, 2006: version 5.0.3
+
+ * minor MATLAB cleanup. Renamed umfpack mexFunction to umfpack2, to avoid
+ filename clash with the built-in version of umfpack.
+
+Dec 2, 2006, version 5.0.2
+
+ * minor change to umfpack_report_info: does not print timings less
+ than 0.001 seconds.
+
+ * bug fix for complex case when using a non-gcc compiler (simplified the
+ scaling of the pivot column). Does not affect the use of UMFPACK in
+ MATLAB.
+
+Aug 31, 2006, version 5.0.1
+
+ * Minor correction to comments in umfpack_get_numeric.h.
+
+May 5, 2006, version 5.0
+
+ * Tcov subdirectory added. This has existed since the first C version of
+ UMFPACK, but is only now included in the released version. It provides
+ a near 100% test coverage for UMFPACK. The code isn't pretty, but it
+ works.
+
+ * now uses CHOLMOD's method for interfacing to the BLAS, including the
+ BLAS_INT definition. This way, the UF_long version of UMFPACK can
+ call the int BLAS.
+
+ * revised to use AMD v2.0
+
+Apr 7, 2006
+
+ * Minor correction to UMFPACK/Source/Makefile, for those who
+ do not have GNU make. No change to version number, because
+ no code was modified.
+
+Oct 10, 2005, version 4.6
+
+ * umf_solve.c modified for the complex case. A, X, and b can be
+ split complex or unsplit. Prior version required the form of
+ A, X, and B to be identical (all split or all unsplit).
+ (Thanks to David Bateman).
+
+ * added Cygwin to architecture detection.
+
+ * added UMFPACK_SUBSUB_VERSION
+
+Aug. 30, 2005: v4.5 released
+
+ * License changed to GNU LGPL.
+
+ * The Make/ directory removed; configurations are now in ../UFconfig.
+
+ * requires AMD v1.2 or later
+
+ * added UMFPACK_MAIN_VERSION and UMFPACK_SUB_VERSION, defined as 4 and 5,
+ respectively, for version 4.5. These macros will be updated for all
+ future versions. See Include/umfpack.h for details.
+
+ * function pointers used for malloc, free, calloc, realloc, printf,
+ hypot, and complex divide. Defined in AMD/Source/amd_global.c,
+ AMD/Source/amd_internal.h, UMFPACK/Source/umfpack_global.c,
+ and UMFPACK/Include/umfpack_global.h.
+ Compile-time dependence on The MathWorks "util.h", ut* routines
+ and ut* macros removed.
+
+Jan. 28, 2005: v4.4 released
+
+ * bug fix: when Qinit is provided to umfpack_*_qsymbolic,
+ only the symmetric and unsymmetric strategies are now permitted.
+ The auto and 2-by-2 strategies are not allowed. In v4.3 and
+ earlier, providing Qinit and requesting the symmetric strategy
+ did not always work (you got the unsymmetric strategy instead).
+ This does not affect umfpack_*_symbolic, which computes its own
+ ordering and can use all 4 strategies (auto, symmetric, unsymmetric,
+ and 2-by-2).
+
+ * umfpack_get_determinant added. (Thanks to David Bateman).
+
+ * packed complex case added for all routines (previously only used in
+ umfpack_report_vector). This allows arrays of ANSI C/C++ complex
+ type to be passed directly to UMFPACK.
+
+ * added umf_multicomple.c to assist in the compilation of UMFPACK
+ in Microsoft Visual Studio, which does not have the required
+ flexibility of the Unix "make" command.
+
+ * local variable declarations reordered to encourage double-word
+ alignment of double's and Entry's, for better performance.
+
+ * note that with the exception of the behavior when a user-provided
+ ordering is passed to umfpack_*_qsymbolic, versions 4.1 through 4.4
+ have comparable performance (ordering quality, memory usage,
+ and run time). v4.1 is much better than v4.0 in performance.
+
+Jan. 11, 2005: v4.3.1 released
+
+ * bug fix in umf_solve. This bug is only the 4th one found in the C
+ versions of UMFPACK to date (Version 3.0 to 4.3.1, from March 2001 to
+ Jan. 2005, excluding workarounds for quirky compilers). No bugs have
+ been reported in the last Fortran version of UMFPACK (MA38, or UMFPACK
+ V2.2.1) since its release in Jan. 1998.
+
+ In Version 4.3, a bug in umf_solve caused iterative refinement
+ to be disabled when solving A'x=b or A.'x=b after factorizing A.
+ Modified the umfpack mexFunction to factorize A and then solve A'x=b
+ when performing the operation x=b/A (as "umfpack(b,'/',A). Note that
+ this has no effect on the use of UMFPACK in MATLAB itself, since MATLAB
+ does not use the umfpack mexFunction for x=b/A. When computing x=b/A,
+ MATLAB factorizes A' and computes x=(A'\b')' instead. The following
+ source code files changed:
+
+ UMFPACK/MATLAB/umfpackmex.c (see above)
+ UMFPACK/Source/umf_solve.c (see source code: 2 lines changed)
+ UMFPACK/Include/umfpack.h (version and date changed)
+ UMFPACK/MATLAB/umfpack_test.m (new file)
+
+Jan. 16, 2004: v4.3 released.
+
+ * user interface of v4.3 is upwardly-compatible with v4.2 and v4.1.
+ No bugs found in v4.1 (except for one workaround for an old compiler).
+ These changes add features only.
+
+ * Note that v4.0 has a bug in umf_scale_column.c. The bug was patched
+ in that version on Jan. 12, 2004. The bug does not appear in v4.1
+ and later. The bug is thus present in MATLAB 6.5, but it occurs
+ very rarely, fortunately. It can occur when dividing a nonzero entry
+ in the pivot column by the pivot value results in an underflow.
+
+ * <float.h> added to umfpackmex.c, for DBL_EPSILON. Some non-standard
+ compilers (Microsoft Visual C++) require this.
+
+ * #pragma added to umf_analyze.c, as a workaround around a bug in an
+ old Intel compiler.
+
+ * mexFunction interface to MATLAB modified. Call to mexCallMATLAB removed,
+ which can be slow. In V4.1 it was used only to get MATLAB's
+ spparms ('spumoni') value.
+
+ * The AMD mexFunction was also modified in the same way (v1.1), with
+ the call to mexCallMATLAB removed. Note that UMFPACK v4.1 through
+ v4.3 can use either AMD v1.0 or AMD v1.1.
+
+ * -DNO_DIVIDE_BY_ZERO option added. If this non-default option is enabled
+ at compile time, and if the pivot value is zero, then no division
+ occurs (zeros on the diagonal of U are treated as if they were equal
+ to one). By default, the division by zero does occur.
+
+ * -DNO_TIMER option added. If this non-default option is enabled at
+ compile time, then no timers (times ( ), clock ( ), getrusage ( ))
+ are used.
+
+V4.2: A special release for COMSOL, Inc., only (FEMLAB)
+
+ * drop tolerance added. A few new parameters in the Control array are used,
+ and a few new Info entries.
+
+May 6, 2003: V4.1 released.
+
+ * No bugs were found in the prior version, Version 4.0. New features
+ added only. Major changes throughout the code. User interface
+ nearly unchanged, however.
+
+ * Version 4.1 is upward-compatible with Version 4.0. The calling
+ sequence of some user-callable routines in Version 4.0 have changed
+ in this version. The routines umfpack_*_symbolic, umfpack_*_qsymbolic,
+ umfpack_*_get_symbolic, and umfpack_*_get_numeric have new arguments
+ added to them. The new arguments are optional. If you want to use
+ a calling sequence similar to v4.0, simply pass NULL pointers in
+ place of the new arguments. There are two new timing routines,
+ umfpack_tic and umfpack_toc. A new user-callable routine,
+ umfpack_*_scale, has been added.
+
+ * "auto", "unsymmetric", "symmetric", and "2-by-2" strategies added.
+ The symmetric strategy uses AMD on A+A' as the column preordering,
+ followed by a postorder of the assembly tree of A+A'. Column ordering
+ refinement is turned off, and diagonal entries are prefered as pivots.
+ V4.0 only had the unsymmetric strategy. The 2-by-2 strategy does row
+ permutations and attempts to find a zero-free diagonal while at the
+ same time maintaining structural symmetry, and then uses the
+ symmetric strategy on the permuted matrix.
+
+ * row-scaling added. The default is to divide each row by the sum of
+ the absolute values of each row. Other options are no scaling,
+ and to divide each row by the max abs value in each row.
+
+ * Matrices with upper bound memory usage greater than the maximum integer
+ (2GB for 32-bit int's) can now be factorized (assuming the actual
+ memory usage is still less than the maximum integer). With this change,
+ the UMFPACK_ERROR_problem_too_large error code is no longer returned.
+
+ * The current frontal matrix (Work->Fx) is no longer allocated as a
+ static size, via malloc. It can grow and shrink, and is allocated
+ from Numeric->Memory.
+
+ * The AMD (Version 1.0) package is now required. It is available
+ separately. To compile UMFPACK, it must appear as ../AMD if you are
+ in the main UMFPACK directory.
+
+ * The UMFPACK mexFunction now uses the internal utMalloc, utRealloc,
+ and utFree routines, by default (except on Windows).
+
+ * Three control parameters for modifying relaxed amalgamation removed.
+ These values are now fixed at compile-time.
+
+ * Many new statistics added to Info, and new control parameters added.
+
+ * The umfpack mexFunction now returns permutation matrices for P and Q,
+ not permutation vectors. It also returns the scale factors as a
+ diagonal matrix. The factorization is now L*U = P*(R\A)*Q.
+
+ * Option added for controlling the initial allocation of the workspace for
+ the current frontal matrix.
+
+ * pivot tolerance of zero treated differently. symmetric pivot tolerance
+ added.
+
+ * Makefile and GNUmakefile changed. umf_* routines with no double or
+ complex values are now compiled just twice (int and long versions)
+ rather than 4 times.
+
+ * New routines added to save and load the Numeric and Symbolic objects
+ to/from binary files.
+
+ * Simple Fortran interface added.
+
+Apr 11, 2002:
+
+ * Version 4.0 released.
+
+ * bug fix: the Microsoft compiler doesn't handle NaN's properly.
+ utIsNaN, and other ut* routines, added for MathWorks version
+ to handle this properly.
+
+Apr 1, 2002:
+
+ * bug fix: if a column was all NaN's, then UMFPACK would fail
+ to find a pivot row. umf_row_search.c and umf_internal.h
+ modified to fix this problem.
+
+Mar 9, 2002: V4.0beta released
+
+ * Map argument added to umfpack_*_triplet_to_col. New files
+ (umf_triplet.[ch]) added.
+ * minor changes made so that UMFPACK can be compiled with g++
+ * additional error checking added to umfpack_*_numeric, for
+ detecting more changes in pattern (Ap, Ai) since last
+ call to umfpack_*_symbolic
+
+Feb 21, 2002:
+
+ * User Guide explains the Makefile vs. GNUmakefile
+
+ * umf_config.h modified, so that the complex SCSL C-BLAS uses
+ (void *) arguments instead of (scsl_zomplex *). gcc generates
+ some spurious warnings (cc doesn't complain). Affects the SGI
+ IRIX only.
+
+ * ported to Compaq Alpha
+
+Feb 20, 2002: V4.0 (alpha) released.
+
+ * V4.0 not yet ported to the Compaq Alpha (V3.2 was ported).
+
+Feb 6 to Feb 19, 2002:
+
+ * Relaxed restrictions on sizes of arrays for umfpack_*_transpose and
+ umfpack_*_triplet_to_col. Size of "max(n,nz)" now just size nz.
+
+ * workspace for umfpack_*_wsolve increased in size.
+
+ * two user arrays for umfpack_*_get_symbolic increased in size,
+ by 1 (Chain_maxrows, Chain_maxcols).
+
+ * lu_normest.m added.
+
+Jan 18 to Feb 5, 2002:
+
+ * The matrix A can be complex, singular, and/or rectangular.
+ The solve step that uses the LU factors can only handle
+ matrices that are complex or real, singuluar or non-singular,
+ and *** square ***, however.
+
+ * Estimate of the condition number computed:
+ (min (abs (diag (U))) / (max (abs (diag (U)))))
+
+ * Forward/backsolves can solve with A.' as well as A'.
+
+ * char * arguments removed from user-callable routines to make it
+ easier for Fortran to call UMFPACK. No Fortran interface is (yet)
+ provided, however.
+
+ The solve codes for umfpack_*_*solve changed to #define'd
+ integers:
+
+ UMFPACK_A Ax=b
+ UMFPACK_At A'x=b
+ UMFPACK_Aat A.'x=b
+ UMFPACK_Pt_L P'Lx=b
+ UMFPACK_L Lx=b
+ UMFPACK_Lt_P L'Px=b
+ UMFPACK_Lat_P L.'Px=b
+ UMFPACK_Lt L'x=b
+ UMFPACK_U_Qt UQ'x=b
+ UMFPACK_U Ux=b
+ UMFPACK_Q_Ut QU'x=b
+ UMFPACK_Q_Uat QU.'x=b
+ UMFPACK_Ut U'x=b
+ UMFPACK_Uat U.'x=b
+
+ All arguments are now either int, long scalars (pass by value),
+ or int, long, double arrays (pass by reference), or void * pointers
+ (pass by value or reference). A void * pointer is of size 32 or 64
+ bits on most machines. There is no need for the caller (C or Fortran)
+ to dereference the void * pointers, so these can be treated as
+ integer*4 or integer*8 in Fortran. A Fortran interface would have to
+ have all arguments passed by reference.
+
+ * All user-callable routine names changed. The four sets are now:
+ umfpack_di_* real (double precision), int's as integers
+ umfpack_dl_* real (double precision), longs's as integers
+ umfpack_zi_* real (double precision), int's as integers
+ umfpack_zl_* real (double precision), longs's as integers
+
+ * Ptree (row preordering) and info on pivotal rows for each front
+ added to Symbolic object (extracted by umfpack_*_get_symbolic).
+ Ptree added as output argument to "umfpack (A, 'symbolic')"
+ mexFunction.
+
+ * umfpack_*_transpose can do A' or A.'
+
+ * umfpack_wsolve.c file removed (now generated from umfpack_solve.c).
+
+ * Can now extract just the diagonal of U with umfpack_*_get_numeric,
+ without having to extract the entire matrix U.
+
+ * UMFPACK_ERROR_singular_matrix (-2) removed.
+
+ * UMFPACK_WARNING_singular_matrix (1) added.
+
+ * Control [UMFPACK_PIVOT_OPTION] removed. No longer any symmetric
+ pivot option (conflicts with the handling of singular and
+ rectangular matrices).
+
+ * Iterative refinement can do Ax=b, A'x=b, or A.'x=b.
+
+ * Most floating-point operations done in macros, to support the complex
+ versions.
+
+ * Info [UMFPACK_N] is now Info [UMFPACK_NROW]
+
+ * Info [UMFPACK_NCOL], Info [UMFPACK_UDIAG_NZ], Info [UMFPACK_UDIAG_NZ]
+ added.
+
+ * umfpack_* routines with "n" as input now use two arguments,
+ n_row and n_col.
+
+ * umfpack mexFunction now explicitly transposes A for b/A. It computes
+ it using the array transpose as (A.'\b.').'
+
+January 1, 2002: UMFPACK Version 3.2 released. Submitted to ACM Trans.
+ on Mathematical Software.
+
+ * The umfpack mexFunction now returns the Info array when the matrix
+ is singular. Returned an empty array prior to this change.
+
+ * Renamed variable that conflicted with system library routines
+ (system and j1).
+
+ * Added a #ifdef MATHWORKS definition, so the built-in UMFPACK routine
+ (in a future release of MATLAB) can use the internal ut* memory
+ allocation routines, ut* assertion routine, and utPrintf.
+
+ * MAX and MIN are not defined if they are already defined.
+
+ * A bug fix in umf_kernel_init (a variable was not properly initialized).
+
+ * Removed unused variables.
+
+October 8, 2001: UMFPACK Version 3.1 released.
+
+August-October, 2001:
+
+ * added umfpack_btf M-file.
+
+ * modified the BLAS update in the frontal matrix. If there are only
+ a few pivots in remaining in the current front, then the BLAS3 update
+ is delayed to include pivots in the next front.
+
+ * Removed the special-case handling of dense columns from the numerical
+ factorization (kept it in the colamd preordering). This improves the
+ performance of UMFPACK on dense matrices by a factor of 5 or so, and
+ simplifies the code.
+
+ * Added a symmetric-preference pivoting option. The option slightly
+ (but uniformly) improves the ordering when factorizing matrices with
+ symmetric nonzero pattern. That class of matrix is better handled by
+ the symmetric-pattern multifrontal method (MA41 in the Harwell
+ Subroutine Library), however.
+
+ * Fixed the detection of integer overflow. The 32-bit version cannot
+ make use of more than 2GB of main memory (use the 64-bit version
+ in that case, instead). The 32-bit version did not correctly detect
+ when it was trying to factorize too large of a matrix.
+
+May 4, 2001:
+
+ * SGI port extended. It can now call the SCSL Scientific Library, with
+ 64-bit BLAS. Make.sgi and umf_config.h modified.
+
+April 30, 2001: UMFPACK Version 3.0 released. Changes since 3.0Beta release:
+
+ * long integer version added (umfpack_l_* user-callable routines).
+
+ * Peak memory usage in the numerical factorization reduced by a total of
+ 12n integers (8n temporary workspace used during numerical factorization,
+ and 4n for the permanent LU factors which was allocated
+ at the beginning of factorization).
+
+ * Ported to the IBM RS 6000 and Compaq Alpha, with help from Anshul Gupta
+ and Friedrich Grund, respectively.
+
+ * 64-bit version added. Uses dgemm_64, dgemv_64, and dger_64 in the Sun
+ Performance Library. 64-bit versions with the BLAS might not work on
+ any other platform, because they take int's as their integer input
+ arguments instead of long's. Unfortunately, the proposed ANSI
+ definition of the C-BLAS also uses int's as input integer arguments.
+ It ought to use long's, or include a version that uses long's, just
+ like the Sun Performance Library BLAS.
+
+ * Additional statistics returned in Info:
+ Info [UMFPACK_SIZE_OF_INT] sizeof (int)
+ Info [UMFPACK_SIZE_OF_LONG] sizeof (long)
+ Info [UMFPACK_SIZE_OF_POINTER] sizeof (void *)
+ Info [UMFPACK_SIZE_OF_ENTRY] (was Info [UMFPACK_WORD])
+ Info [UMFPACK_MAX_FRONT_SIZE_ESTIMATE] est. front matrix size
+ Info [UMFPACK_MAX_FRONT_SIZE] actual max frontal matrix size.
+ Contents of Info rearranged.
+
+ * UMFPACK_ERROR_bad_configurution error code replaced with
+ UMFPACK_ERROR_problem_too_large error code. The "bad configuration"
+ error occured when sizeof (int) < sizeof (size_t). Now, the int
+ version of UMFPACK can use 32-bit int's and 64-bit pointers, and the
+ long version can use 64-bit long's and 64-bit pointers. Both versions
+ check to see if the array sizes allocated are larger than what can be
+ accessed by an integer index variable (int or long, depending on the
+ version), and returns UMFPACK_ERROR_problem_too_large if they become
+ too large.
+
+March 15, 2001: UMFPACK Version 3.0Beta released.
+
diff --git a/UMFPACK/Doc/License b/UMFPACK/Doc/License
new file mode 100644
index 0000000..19f2fa9
--- /dev/null
+++ b/UMFPACK/Doc/License
@@ -0,0 +1,38 @@
+UMFPACK Version 5.1.1, Copyright 1995-2007 by Timothy A. Davis.
+All Rights Reserved.
+UMFPACK is available under alternate licenses, contact T. Davis for details.
+
+UMFPACK License:
+
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU General Public
+ License as published by the Free Software Foundation; either
+ version 2 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU GPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/umfpack
+
diff --git a/UMFPACK/Doc/Makefile b/UMFPACK/Doc/Makefile
new file mode 100644
index 0000000..41cf07e
--- /dev/null
+++ b/UMFPACK/Doc/Makefile
@@ -0,0 +1,59 @@
+#-------------------------------------------------------------------------------
+# UMFPACK Makefile for compiling on Unix systems (for GNU or original make)
+#-------------------------------------------------------------------------------
+
+# UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis.
+# All Rights Reserved. See ../Doc/License for License.
+
+default: dist
+
+include ../../UFconfig/UFconfig.mk
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+# Note that UserGuide.tex is created from UserGuide.stex, the files in
+# the ../Include directory, and the ../Demo/umfpack_simple.c file.
+purge: clean
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+ - $(RM) UserGuide.tex
+
+clean:
+ - $(RM) $(CLEAN)
+
+#-------------------------------------------------------------------------------
+# Create the User Guide and Quick Start Guide
+#-------------------------------------------------------------------------------
+
+UMFPACK = umfpack_col_to_triplet umfpack_defaults umfpack_free_numeric \
+ umfpack_free_symbolic umfpack_get_numeric umfpack_get_lunz \
+ umfpack_get_determinant \
+ umfpack_get_symbolic umfpack_numeric umfpack_qsymbolic \
+ umfpack_report_control umfpack_report_info umfpack_report_matrix \
+ umfpack_report_numeric umfpack_report_perm umfpack_report_status \
+ umfpack_report_symbolic umfpack_report_triplet \
+ umfpack_report_vector umfpack_solve umfpack_symbolic \
+ umfpack_transpose umfpack_triplet_to_col umfpack_scale
+
+UMFPACKW = umfpack_wsolve
+
+USER = $(UMFPACKW) $(UMFPACK)
+
+SRC = $(addprefix ../Include/, $(addsuffix .h,$(USER))) ../Demo/umfpack_simple.c
+
+UserGuide.pdf: UserGuide.stex UserGuide.sed1 UserGuide.sed2 $(SRC) UserGuide.bib
+ sed -f UserGuide.sed1 < UserGuide.stex | sed -f UserGuide.sed2 \
+ | expand -8 > UserGuide.tex
+ pdflatex UserGuide
+ bibtex UserGuide
+ pdflatex UserGuide
+ pdflatex UserGuide
+
+QuickStart.pdf: QuickStart.tex
+ pdflatex QuickStart
+ pdflatex QuickStart
+
+dist: QuickStart.pdf UserGuide.pdf
+ - $(RM) *.aux *.bbl *.blg *.log *.toc
+ - $(RM) UserGuide.tex
diff --git a/UMFPACK/Doc/QuickStart.pdf b/UMFPACK/Doc/QuickStart.pdf
new file mode 100644
index 0000000..34bc326
Binary files /dev/null and b/UMFPACK/Doc/QuickStart.pdf differ
diff --git a/UMFPACK/Doc/QuickStart.tex b/UMFPACK/Doc/QuickStart.tex
new file mode 100644
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--- /dev/null
+++ b/UMFPACK/Doc/QuickStart.tex
@@ -0,0 +1,1026 @@
+%-------------------------------------------------------------------------------
+% The QuickStart.tex file.
+%-------------------------------------------------------------------------------
+
+\documentclass[11pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+\begin{document}
+
+\author{Timothy A. Davis \\
+Dept. of Computer and Information Science and Engineering \\
+Univ. of Florida, Gainesville, FL}
+\title{UMFPACK Version 5.2 Quick Start Guide}
+\date{Nov 1, 2007}
+\maketitle
+
+%-------------------------------------------------------------------------------
+\begin{abstract}
+ UMFPACK is a set of routines for solving unsymmetric sparse linear
+ systems, $\m{Ax}=\m{b}$, using the Unsymmetric-pattern MultiFrontal method
+ and direct sparse LU factorization. It is written in ANSI/ISO C, with a
+ MATLAB interface. UMFPACK relies on the Level-3
+ Basic Linear Algebra Subprograms (dense matrix multiply) for its
+ performance. This code works on Windows and many versions of Unix (Sun
+ Solaris, Red Hat Linux, IBM AIX, SGI IRIX, and Compaq Alpha).
+ This is a ``quick start'' guide for Unix users of the C interface.
+\end{abstract}
+%-------------------------------------------------------------------------------
+
+UMFPACK Version 5.2, Copyright\copyright 1995-2006 by Timothy A. Davis.
+All Rights Reserved. Refer to the UMFPACK User Guide
+for the License. See \newline
+http://www.cise.ufl.edu/research/sparse/umfpack
+for the code and full documentation.
+
+%-------------------------------------------------------------------------------
+\section{Overview}
+%-------------------------------------------------------------------------------
+
+UMFPACK is a set of routines for solving systems of linear
+equations, $\m{Ax}=\m{b}$, when $\m{A}$ is sparse and unsymmetric.
+The sparse matrix $\m{A}$ can be square or rectangular, singular
+or non-singular, and real or complex (or any combination). Only square
+matrices $\m{A}$ can be used to solve $\m{Ax}=\m{b}$ or related systems.
+Rectangular matrices can only be factorized.
+
+UMFPACK is a built-in routine in MATLAB used by the forward and
+backslash operator, and the {\tt lu} routine.
+The following is a short
+introduction to Unix users of the C interface of UMFPACK.
+
+%-------------------------------------------------------------------------------
+
+The C-callable UMFPACK library consists of 32 user-callable routines and one
+include file. Twenty-eight of the routines come in four versions, with
+different sizes of integers and for real or complex floating-point numbers.
+This Quick Start Guide assumes you are working with real matrices
+(not complex) and with {\tt int}'s as integers (not {\tt long}'s).
+Refer to the User Guide for information about the complex and
+long integer versions. The include file {\tt umfpack.h}
+must be included in any C program that uses UMFPACK.
+
+For more details, see:
+{\em A column pre-ordering strategy for the unsymmetric-pattern multifrontal method},
+Davis, T. A.,
+ACM Trans. Math. Software, vol 30. no 2, 2004, pp. 165-195, and
+{\em Algorithm 832: {UMFPACK}, an unsymmetric-pattern multifrontal method},
+same issue, pp. 196-199.
+
+%-------------------------------------------------------------------------------
+\section{Primary routines, and a simple example}
+%-------------------------------------------------------------------------------
+
+Five primary UMFPACK routines are required to factorize $\m{A}$ or
+solve $\m{Ax}=\m{b}$. An overview of the primary features of the routines
+is given in Section~\ref{Primary}.
+Additional routines are available for passing a different column ordering
+to UMFPACK, changing default parameters, manipulating sparse matrices,
+getting the LU factors, save and loading the LU factors from a file,
+computing the determinant,
+and reporting results. See the User Guide for more information.
+
+\begin{itemize}
+\item {\tt umfpack\_di\_symbolic}:
+
+ Pre-orders the columns of $\m{A}$ to reduce fill-in and performs a
+ symbolic analysis.
+ Returns an opaque {\tt Symbolic} object as a {\tt void *}
+ pointer. The object contains the symbolic analysis and is needed for the
+ numerical factorization.
+
+\item {\tt umfpack\_di\_numeric}:
+
+ Numerically scales and then factorizes a sparse matrix
+ $\m{PAQ}$, $\m{PRAQ}$, or $\m{PR}^{-1}\m{AQ}$ into the product $\m{LU}$,
+ where
+ $\m{P}$ and $\m{Q}$ are permutation matrices, $\m{R}$ is a diagonal
+ matrix of scale factors, $\m{L}$ is lower triangular with unit diagonal,
+ and $\m{U}$ is upper triangular. Requires the
+ symbolic ordering and analysis computed by {\tt umfpack\_di\_symbolic}.
+ Returns an opaque {\tt Numeric} object as a
+ {\tt void *} pointer. The object contains the numerical factorization and
+ is used by {\tt umfpack\_di\_solve}.
+
+\item {\tt umfpack\_di\_solve}:
+
+ Solves a sparse linear system ($\m{Ax}=\m{b}$, $\m{A}\tr\m{x}=\m{b}$, or
+ systems involving just $\m{L}$ or $\m{U}$), using the numeric factorization
+ computed by {\tt umfpack\_di\_numeric}.
+
+\item {\tt umfpack\_di\_free\_symbolic}:
+
+ Frees the {\tt Symbolic} object created by {\tt umfpack\_di\_symbolic}.
+
+\item {\tt umfpack\_di\_free\_numeric}:
+
+ Frees the {\tt Numeric} object created by {\tt umfpack\_di\_numeric}.
+
+\end{itemize}
+
+The matrix $\m{A}$ is represented in compressed column form, which is
+identical to the sparse matrix representation used by MATLAB. It consists
+of three arrays, where the matrix is {\tt m}-by-{\tt n},
+with {\tt nz} entries:
+
+{\footnotesize
+\begin{verbatim}
+ int Ap [n+1] ;
+ int Ai [nz] ;
+ double Ax [nz] ;
+\end{verbatim}
+}
+
+All nonzeros are entries, but an entry may be numerically zero. The row indices
+of entries in column {\tt j} are stored in
+ {\tt Ai[Ap[j]} ... {\tt Ap[j+1]-1]}.
+The corresponding numerical values are stored in
+ {\tt Ax[Ap[j]} ... {\tt Ap[j+1]-1]}.
+
+No duplicate row indices may be present, and the row indices in any given
+column must be sorted in ascending order. The first entry {\tt Ap[0]} must be
+zero. The total number of entries in the matrix is thus {\tt nz = Ap[n]}.
+Except for the fact that extra zero entries can be included, there is thus a
+unique compressed column representation of any given matrix $\m{A}$.
+
+Here is a simple main program, {\tt umfpack\_simple.c}, that illustrates the
+basic usage of UMFPACK.
+
+{\footnotesize
+\begin{verbatim}
+ #include <stdio.h>
+ #include "umfpack.h"
+
+ int n = 5 ;
+ int Ap [ ] = {0, 2, 5, 9, 10, 12} ;
+ int Ai [ ] = { 0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4} ;
+ double Ax [ ] = {2., 3., 3., -1., 4., 4., -3., 1., 2., 2., 6., 1.} ;
+ double b [ ] = {8., 45., -3., 3., 19.} ;
+ double x [5] ;
+
+ int main (void)
+ {
+ double *null = (double *) NULL ;
+ int i ;
+ void *Symbolic, *Numeric ;
+ (void) umfpack_di_symbolic (n, n, Ap, Ai, Ax, &Symbolic, null, null) ;
+ (void) umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, null, null) ;
+ umfpack_di_free_symbolic (&Symbolic) ;
+ (void) umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, x, b, Numeric, null, null) ;
+ umfpack_di_free_numeric (&Numeric) ;
+ for (i = 0 ; i < n ; i++) printf ("x [%d] = %g\n", i, x [i]) ;
+ return (0) ;
+ }
+\end{verbatim}
+}
+
+The {\tt Ap}, {\tt Ai}, and {\tt Ax} arrays represent the matrix
+\[
+\m{A} = \left[
+\begin{array}{rrrrr}
+ 2 & 3 & 0 & 0 & 0 \\
+ 3 & 0 & 4 & 0 & 6 \\
+ 0 & -1 & -3 & 2 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 4 & 2 & 0 & 1 \\
+\end{array}
+\right].
+\]
+and the solution is $\m{x} = [1 \, 2 \, 3 \, 4 \, 5]\tr$. The program uses
+default control settings and does not return any statistics about the ordering,
+factorization, or solution ({\tt Control} and {\tt Info} are both
+{\tt (double *) NULL}).
+
+For routines to manipulate a simpler ``triplet-form'' data structure for your
+sparse matrix $\m{A}$, refer to the UMFPACK User Guide.
+
+%-------------------------------------------------------------------------------
+\section{Synopsis of primary C-callable routines}
+\label{Synopsis}
+%-------------------------------------------------------------------------------
+
+The matrix $\m{A}$ is {\tt m}-by-{\tt n} with {\tt nz} entries.
+The optional {\tt umfpack\_di\_defaults} routine loads the default control
+parameters into the {\tt Control} array. The settings can then be modified
+before passing the array to the other routines. Refer to Section~\ref{Primary}
+for more details.
+
+{\footnotesize
+\begin{verbatim}
+ #include "umfpack.h"
+ int status, sys, n, m, nz, Ap [n+1], Ai [nz] ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], Ax [nz], X [n], B [n] ;
+ void *Symbolic, *Numeric ;
+
+ status = umfpack_di_symbolic (m, n, Ap, Ai, Ax, &Symbolic, Control, Info) ;
+ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ;
+ status = umfpack_di_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ;
+ umfpack_di_free_symbolic (&Symbolic) ;
+ umfpack_di_free_numeric (&Numeric) ;
+ umfpack_di_defaults (Control) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\section{Installation}
+\label{Install}
+%-------------------------------------------------------------------------------
+
+You will need to install both UMFPACK v5.2 and AMD v2.2 to use UMFPACK.
+Note that UMFPACK v5.2 cannot use AMD v1.2 or earlier.
+The {\tt UMFPACK} and {\tt AMD} subdirectories must be placed side-by-side
+within the same parent directory. AMD is a stand-alone package that
+is required by UMFPACK. UMFPACK can be compiled without the
+BLAS but your performance will be much less than what it should be.
+
+System-dependent configurations are in the {\tt UFconfig/UFconfig.mk}
+file. The default
+settings will work on most systems, except for the BLAS definition.
+Sample configurations are provided
+for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha.
+
+To compile and install both packages,
+go to the UMFPACK directory and type {\tt make}. This will compile the
+libraries ({\tt AMD/Lib/libamd.a} and {\tt UMFPACK/Lib/libumfpack.a}).
+A demo of the AMD ordering routine will be compiled and tested in
+the {\tt AMD/Demo} directory, and five demo programs will then be
+compiled and tested in the {\tt UMFPACK/Demo} directory.
+The outputs of these demo programs will then be compared with output
+files in the distribution. Expect to see a few differences, such as
+residual norms, compile-time control settings, and perhaps memory usage
+differences.
+
+To use {\tt make} to compile the MATLAB mexFunctions for MATLAB
+and AMD, you can either type {\tt make mex} in the UMFPACK directory.
+You may first need to edit the {\tt UFconfig/UFconfig.mk} file to
+modify the definition of the {\tt MEX}, if you have a version of MATLAB
+older than Version 7.2. Remove the {\tt -largeArrayDims} definition.
+If you use the MATLAB command {\tt umfpack\_make} in the MATLAB directory,
+then this case is handled for you automatically.
+
+If you compile UMFPACK and AMD and then later change the
+{\tt UFconfig/UFconfig.mk} file
+then you should type {\tt make purge} and then {\tt make} to recompile.
+
+Here are the various parameters that you can control in your
+{\tt UFconfig/UFconfig.mk} file:
+
+\begin{itemize}
+\item {\tt CC = } your C compiler, such as {\tt cc}.
+\item {\tt RANLIB = } your system's {\tt ranlib} program, if needed.
+\item {\tt CFLAGS = } optimization flags, such as {\tt -O}.
+\item {\tt UMFPACK\_CONFIG = } configuration settings, for the BLAS,
+ memory allocation routines, and timing routines.
+\item {\tt LIB = } your libraries, such as {\tt -lm} or {\tt -lblas}.
+\item {\tt RM =} the command to delete a file.
+\item {\tt MV =} the command to rename a file.
+\item {\tt MEX =} the command to compile a MATLAB mexFunction.
+\item {\tt F77 =} the command to compile a Fortran program (optional).
+\item {\tt F77FLAGS =} the Fortran compiler flags (optional).
+\item {\tt F77LIB =} the Fortran libraries (optional).
+\end{itemize}
+
+The {\tt UMFPACK\_CONFIG} string can include combinations of the following;
+most deal with how the BLAS are called:
+\begin{itemize}
+\item {\tt -DNBLAS} if you do not have any BLAS at all.
+\item {\tt -DNSUNPERF} if you are on Solaris but do not have the Sun
+ Performance Library.
+\item {\tt -DLONGBLAS} if your BLAS takes non-{\tt int} integer arguments.
+\item {\tt -DBLAS\_INT = } the integer used by the BLAS.
+
+\item {\tt -DBLAS\_NO\_UNDERSCORE}
+ for controlling how C calls the Fortran BLAS.
+ This is set automatically for Windows,
+ Sun Solaris, SGI Irix, Red Hat Linux, Compaq Alpha, and
+ AIX (the IBM RS 6000).
+
+\item {\tt -DGETRUSAGE} if you have the {\tt getrusage} function.
+\item {\tt -DNPOSIX} if you do not have the POSIX-compliant
+ {\tt sysconf} and {\tt times} routines.
+\item {\tt -DNRECIPROCAL} controls a trade-off between speed and accuracy.
+ This is off by default (speed preferred over accuracy) except when
+ compiling for MATLAB.
+\end{itemize}
+
+When you compile your program that uses the C-callable UMFPACK library,
+you need to add the both {\tt UMFPACK/Lib/libumfpack.a} and
+{\tt AMD/Lib/libamd.a}
+libraries, and you need to tell your compiler to look in the
+directories {\tt UMFPACK/Include} and {\tt AMD/Include} for include
+files. See {\tt UMFPACK/Demo/Makefile} for an example.
+You do not need to directly include any AMD include files in your
+program, unless you directly call AMD routines. You only need the
+\begin{verbatim}
+#include "umfpack.h"
+\end{verbatim}
+statement, as described in Section~\ref{Synopsis}.
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{The primary UMFPACK routines}
+\label{Primary}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_di\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+int umfpack_di_symbolic
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+Purpose:
+
+ Given nonzero pattern of a sparse matrix A in column-oriented form,
+ umfpack_di_symbolic performs a column pre-ordering to reduce fill-in
+ (using COLAMD or AMD) and a symbolic factorization. This is required
+ before the matrix can be numerically factorized with umfpack_di_numeric.
+
+ For the following discussion, let S be the submatrix of A obtained after
+ eliminating all pivots of zero Markowitz cost. S has dimension
+ (n_row-n1-nempty_row) -by- (n_col-n1-nempty_col), where
+ n1 = Info [UMFPACK_COL_SINGLETONS] + Info [UMFPACK_ROW_SINGLETONS],
+ nempty_row = Info [UMFPACK_NEMPTY_ROW] and
+ nempty_col = Info [UMFPACK_NEMPTY_COL].
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ int n_row ; Input argument, not modified.
+ int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0.
+
+ int Ap [n_col+1] ; Input argument, not modified.
+
+ Ap is an integer array of size n_col+1. On input, it holds the
+ "pointers" for the column form of the sparse matrix A. Column j of
+ the matrix A is held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The first
+ entry, Ap [0], must be zero, and Ap [j] <= Ap [j+1] must hold for all
+ j in the range 0 to n_col-1. The value nz = Ap [n_col] is thus the
+ total number of entries in the pattern of the matrix A. nz must be
+ greater than or equal to zero.
+
+ int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ The nonzero pattern (row indices) for column j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j
+ must be in ascending order, and no duplicate row indices may be present.
+ Row indices must be in the range 0 to n_row-1 (the matrix is 0-based).
+
+ double Ax [nz] ; Optional input argument, not modified.
+
+ The numerical values of the sparse matrix A. The nonzero pattern (row
+ indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and
+ the corresponding numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)]. Used only by the 2-by-2 strategy to
+ determine whether entries are "large" or "small". You do not have to
+ pass the same numerical values to umfpack_di_numeric. If Ax is not
+ present (a (double *) NULL pointer), then any entry in A is assumed to
+ be "large".
+
+ void **Symbolic ; Output argument.
+
+ **Symbolic is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Symbolic object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Only the primary parameters are listed below:
+
+ Control [UMFPACK_STRATEGY]: This is the most important control
+ parameter. It determines what kind of ordering and pivoting
+ strategy that UMFPACK should use. It is new to Version 4.1
+ There are 4 options:
+
+ UMFPACK_STRATEGY_AUTO: This is the default. The input matrix is
+ analyzed to determine how symmetric the nonzero pattern is, and
+ how many entries there are on the diagonal. It then selects one
+ of the following strategies. Refer to the User Guide for a
+ description of how the strategy is automatically selected.
+
+ UMFPACK_STRATEGY_UNSYMMETRIC: Use the unsymmetric strategy. COLAMD
+ is used to order the columns of A, followed by a postorder of
+ the column elimination tree. No attempt is made to perform
+ diagonal pivoting. The column ordering is refined during
+ factorization. This strategy was the only one provided with
+ UMFPACK V4.0.
+
+ In the numerical factorization, the
+ Control [UMFPACK_SYM_PIVOT_TOLERANCE] parameter is ignored. A
+ pivot is selected if its magnitude is >=
+ Control [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the
+ largest entry in its column.
+
+ UMFPACK_STRATEGY_SYMMETRIC: Use the symmetric strategy (new to
+ Version 4.1). In this method, the approximate minimum degree
+ ordering (AMD) is applied to A+A', followed by a postorder of
+ the elimination tree of A+A'. UMFPACK attempts to perform
+ diagonal pivoting during numerical factorization. No refinement
+ of the column preordering is performed during factorization.
+
+ In the numerical factorization, a nonzero entry on the diagonal
+ is selected as the pivot if its magnitude is >= Control
+ [UMFPACK_SYM_PIVOT_TOLERANCE] (default 0.001) times the largest
+ entry in its column. If this is not acceptable, then an
+ off-diagonal pivot is selected with magnitude >= Control
+ [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the largest entry
+ in its column.
+
+ UMFPACK_STRATEGY_2BY2: a row permutation P2 is found that places
+ large entries on the diagonal. The matrix P2*A is then
+ factorized using the symmetric strategy, described above.
+ Refer to the User Guide for more information.
+
+ Control [UMFPACK_2BY2_TOLERANCE]: a diagonal entry S (k,k) is
+ considered "small" if it is < tol * max (abs (S (:,k))), where S a
+ submatrix of the scaled input matrix, with pivots of zero Markowitz
+ cost removed.
+
+ Control [UMFPACK_SCALE]: This parameter is new to V4.1. See
+ umfpack_numeric.h for a description. Only affects the 2-by-2
+ strategy. Default: UMFPACK_SCALE_SUM.
+
+ double Info [UMFPACK_INFO] ; Output argument, not defined on input.
+
+ Contains statistics about the symbolic analysis. If a (double *) NULL
+ pointer is passed, then no statistics are returned in Info (this is not
+ an error condition). The entire Info array is cleared (all entries set
+ to -1) and then the following statistics are computed (only the
+ primary statistics are listed):
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ Each column of the input matrix contained row indices
+ in increasing order, with no duplicates. Only in this case
+ does umfpack_di_symbolic compute a valid symbolic factorization.
+ For the other cases below, no Symbolic object is created
+ (*Symbolic is (void *) NULL).
+
+ UMFPACK_ERROR_n_nonpositive
+
+ n is less than or equal to zero.
+
+ UMFPACK_ERROR_invalid_matrix
+
+ Number of entries in the matrix is negative, Ap [0] is nonzero,
+ a column has a negative number of entries, a row index is out of
+ bounds, or the columns of input matrix were jumbled (unsorted
+ columns or duplicate entries).
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to perform the symbolic analysis. If the
+ analysis requires more than 2GB of memory and you are using
+ the 32-bit ("int") version of UMFPACK, then you are guaranteed
+ to run out of memory. Try using the 64-bit version of UMFPACK.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments is missing.
+
+ UMFPACK_ERROR_internal_error
+
+ Something very serious went wrong. This is a bug.
+ Please contact the author (davis at cise.ufl.edu).
+
+ Info [UMFPACK_SIZE_OF_UNIT]: the number of bytes in a Unit,
+ for memory usage statistics below.
+
+ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]: the amount of memory (in Units)
+ required for umfpack_di_symbolic to complete. This count includes
+ the size of the Symbolic object itself, which is also reported in
+ Info [UMFPACK_SYMBOLIC_SIZE].
+
+ Info [UMFPACK_NUMERIC_SIZE_ESTIMATE]: an estimate of the final size (in
+ Units) of the entire Numeric object (both fixed-size and variable-
+ sized parts), which holds the LU factorization (including the L, U,
+ P and Q matrices).
+
+ Info [UMFPACK_PEAK_MEMORY_ESTIMATE]: an estimate of the total amount of
+ memory (in Units) required by umfpack_di_symbolic and
+ umfpack_di_numeric to perform both the symbolic and numeric
+ factorization. This is the larger of the amount of memory needed
+ in umfpack_di_numeric itself, and the amount of memory needed in
+ umfpack_di_symbolic (Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]). The
+ count includes the size of both the Symbolic and Numeric objects
+ themselves. It can be a very loose upper bound, particularly when
+ the symmetric or 2-by-2 strategies are used.
+
+ Info [UMFPACK_FLOPS_ESTIMATE]: an estimate of the total floating-point
+ operations required to factorize the matrix. This is a "true"
+ theoretical estimate of the number of flops that would be performed
+ by a flop-parsimonious sparse LU algorithm. It assumes that no
+ extra flops are performed except for what is strictly required to
+ compute the LU factorization. It ignores, for example, the flops
+ performed by umfpack_di_numeric to add contribution blocks of
+ frontal matrices together. If L and U are the upper bound on the
+ pattern of the factors, then this flop count estimate can be
+ represented in MATLAB (for real matrices, not complex) as:
+
+ Lnz = full (sum (spones (L))) - 1 ; % nz in each col of L
+ Unz = full (sum (spones (U')))' - 1 ; % nz in each row of U
+ flops = 2*Lnz*Unz + sum (Lnz) ;
+
+ The actual "true flop" count found by umfpack_di_numeric will be
+ less than this estimate.
+
+ Info [UMFPACK_LNZ_ESTIMATE]: an estimate of the number of nonzeros in
+ L, including the diagonal. Since L is unit-diagonal, the diagonal
+ of L is not stored. This estimate is a strict upper bound on the
+ actual nonzeros in L to be computed by umfpack_di_numeric.
+
+ Info [UMFPACK_UNZ_ESTIMATE]: an estimate of the number of nonzeros in
+ U, including the diagonal. This estimate is a strict upper bound on
+ the actual nonzeros in U to be computed by umfpack_di_numeric.
+
+ Info [UMFPACK_SYMBOLIC_TIME]: The CPU time taken, in seconds.
+
+ Info [UMFPACK_STRATEGY_USED]: The ordering strategy used:
+ UMFPACK_STRATEGY_SYMMETRIC, UMFPACK_STRATEGY_UNSYMMETRIC, or
+ UMFPACK_STRATEGY_2BY2.
+\end{verbatim}
+}
+
+
+%-------------------------------------------------------------------------------
+\newpage
+\subsection{umfpack\_di\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+int umfpack_di_numeric
+(
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ void *Symbolic,
+ void **Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+Purpose:
+
+ Given a sparse matrix A in column-oriented form, and a symbolic analysis
+ computed by umfpack_di_symbolic, the umfpack_di_numeric routine performs the
+ numerical factorization, PAQ=LU, PRAQ=LU, or P(R\A)Q=LU, where P and Q are
+ permutation matrices (represented as permutation vectors), R is the row
+ scaling, L is unit-lower triangular, and U is upper triangular. This is
+ required before the system Ax=b (or other related linear systems) can be
+ solved. umfpack_di_numeric can be called multiple times for each call to
+ umfpack_di_symbolic, to factorize a sequence of matrices with identical
+ nonzero pattern. Simply compute the Symbolic object once, with
+ umfpack_di_symbolic, and reuse it for subsequent matrices.
+ umfpack_di_numeric safely detects if the pattern changes, and sets an
+ appropriate error code.
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ int Ap [n_col+1] ; Input argument, not modified.
+
+ This must be identical to the Ap array passed to umfpack_di_symbolic.
+ The value of n_col is what was passed to umfpack_di_symbolic (this is
+ held in the Symbolic object).
+
+ int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ This must be identical to the Ai array passed to umfpack_di_symbolic.
+
+ double Ax [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ The numerical values of the sparse matrix A. The nonzero pattern (row
+ indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and
+ the corresponding numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)].
+
+ void *Symbolic ; Input argument, not modified.
+
+ The Symbolic object, which holds the symbolic factorization computed by
+ umfpack_di_symbolic. The Symbolic object is not modified by
+ umfpack_di_numeric.
+
+ void **Numeric ; Output argument.
+
+ **Numeric is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Numeric object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Only the primary parameters are listed below:
+
+ Control [UMFPACK_PIVOT_TOLERANCE]: relative pivot tolerance for
+ threshold partial pivoting with row interchanges. In any given
+ column, an entry is numerically acceptable if its absolute value is
+ greater than or equal to Control [UMFPACK_PIVOT_TOLERANCE] times
+ the largest absolute value in the column. A value of 1.0 gives true
+ partial pivoting. If less than or equal to zero, then any nonzero
+ entry is numerically acceptable as a pivot (this is changed from
+ Version 4.0). Default: 0.1.
+
+ Smaller values tend to lead to sparser LU factors, but the solution
+ to the linear system can become inaccurate. Larger values can lead
+ to a more accurate solution (but not always), and usually an
+ increase in the total work.
+
+ Control [UMFPACK_SYM_PIVOT_TOLERANCE]: This parameter is new to V4.1.
+ If diagonal pivoting is attempted (the symmetric or symmetric-2by2
+ strategies are used) then this parameter is used to control when the
+ diagonal entry is selected in a given pivot column. The absolute
+ value of the entry must be >= Control [UMFPACK_SYM_PIVOT_TOLERANCE]
+ times the largest absolute value in the column. A value of zero
+ will ensure that no off-diagonal pivoting is performed, except that
+ zero diagonal entries are not selected if there are any off-diagonal
+ nonzero entries.
+
+ If an off-diagonal pivot is selected, an attempt is made to restore
+ symmetry later on. Suppose A (i,j) is selected, where i != j.
+ If column i has not yet been selected as a pivot column, then
+ the entry A (j,i) is redefined as a "diagonal" entry, except that
+ the tighter tolerance (Control [UMFPACK_PIVOT_TOLERANCE]) is
+ applied. This strategy has an effect similar to 2-by-2 pivoting
+ for symmetric indefinite matrices. If a 2-by-2 block pivot with
+ nonzero structure
+
+ i j
+ i: 0 x
+ j: x 0
+
+ is selected in a symmetric indefinite factorization method, the
+ 2-by-2 block is inverted and a rank-2 update is applied. In
+ UMFPACK, this 2-by-2 block would be reordered as
+
+ j i
+ i: x 0
+ j: 0 x
+
+ In both cases, the symmetry of the Schur complement is preserved.
+
+ Control [UMFPACK_SCALE]: This parameter is new to V4.1. Version 4.0
+ did not scale the matrix. Note that the user's input matrix is
+ never modified, only an internal copy is scaled.
+
+ There are three valid settings for this parameter. If any other
+ value is provided, the default is used.
+
+ UMFPACK_SCALE_NONE: no scaling is performed.
+
+ UMFPACK_SCALE_SUM: each row of the input matrix A is divided by
+ the sum of the absolute values of the entries in that row.
+ The scaled matrix has an infinity norm of 1.
+
+ UMFPACK_SCALE_MAX: each row of the input matrix A is divided by
+ the maximum the absolute values of the entries in that row.
+ In the scaled matrix the largest entry in each row has
+ a magnitude exactly equal to 1.
+
+ Scaling is very important for the "symmetric" strategy when
+ diagonal pivoting is attempted. It also improves the performance
+ of the "unsymmetric" strategy.
+
+ Default: UMFPACK_SCALE_SUM.
+
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ Contains statistics about the numeric factorization. If a
+ (double *) NULL pointer is passed, then no statistics are returned in
+ Info (this is not an error condition). The following statistics are
+ computed in umfpack_di_numeric (only the primary statistics are listed):
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ Numeric factorization was successful. umfpack_di_numeric
+ computed a valid numeric factorization.
+
+ UMFPACK_WARNING_singular_matrix
+
+ Numeric factorization was successful, but the matrix is
+ singular. umfpack_di_numeric computed a valid numeric
+ factorization, but you will get a divide by zero in
+ umfpack_di_solve. For the other cases below, no Numeric object
+ is created (*Numeric is (void *) NULL).
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to complete the numeric factorization.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments are missing.
+
+ UMFPACK_ERROR_invalid_Symbolic_object
+
+ Symbolic object provided as input is invalid.
+
+ UMFPACK_ERROR_different_pattern
+
+ The pattern (Ap and/or Ai) has changed since the call to
+ umfpack_di_symbolic which produced the Symbolic object.
+
+ Info [UMFPACK_NUMERIC_SIZE]: the actual final size (in Units) of the
+ entire Numeric object, including the final size of the variable
+ part of the object. Info [UMFPACK_NUMERIC_SIZE_ESTIMATE],
+ an estimate, was computed by umfpack_di_symbolic. The estimate is
+ normally an upper bound on the actual final size, but this is not
+ guaranteed.
+
+ Info [UMFPACK_PEAK_MEMORY]: the actual peak memory usage (in Units) of
+ both umfpack_di_symbolic and umfpack_di_numeric. An estimate,
+ Info [UMFPACK_PEAK_MEMORY_ESTIMATE], was computed by
+ umfpack_di_symbolic. The estimate is normally an upper bound on the
+ actual peak usage, but this is not guaranteed. With testing on
+ hundreds of matrix arising in real applications, I have never
+ observed a matrix where this estimate or the Numeric size estimate
+ was less than the actual result, but this is theoretically possible.
+ Please send me one if you find such a matrix.
+
+ Info [UMFPACK_FLOPS]: the actual count of the (useful) floating-point
+ operations performed. An estimate, Info [UMFPACK_FLOPS_ESTIMATE],
+ was computed by umfpack_di_symbolic. The estimate is guaranteed to
+ be an upper bound on this flop count. The flop count excludes
+ "useless" flops on zero values, flops performed during the pivot
+ search (for tentative updates and assembly of candidate columns),
+ and flops performed to add frontal matrices together.
+
+ Info [UMFPACK_LNZ]: the actual nonzero entries in final factor L,
+ including the diagonal. This excludes any zero entries in L,
+ although some of these are stored in the Numeric object. The
+ Info [UMFPACK_LU_ENTRIES] statistic does account for all
+ explicitly stored zeros, however. Info [UMFPACK_LNZ_ESTIMATE],
+ an estimate, was computed by umfpack_di_symbolic. The estimate is
+ guaranteed to be an upper bound on Info [UMFPACK_LNZ].
+
+ Info [UMFPACK_UNZ]: the actual nonzero entries in final factor U,
+ including the diagonal. This excludes any zero entries in U,
+ although some of these are stored in the Numeric object. The
+ Info [UMFPACK_LU_ENTRIES] statistic does account for all
+ explicitly stored zeros, however. Info [UMFPACK_UNZ_ESTIMATE],
+ an estimate, was computed by umfpack_di_symbolic. The estimate is
+ guaranteed to be an upper bound on Info [UMFPACK_UNZ].
+
+ Info [UMFPACK_NUMERIC_TIME]: The CPU time taken, in seconds.
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\subsection{umfpack\_di\_solve}
+
+{\footnotesize
+\begin{verbatim}
+int umfpack_di_solve
+(
+ int sys,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ double X [ ],
+ const double B [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+Purpose:
+
+ Given LU factors computed by umfpack_di_numeric (PAQ=LU, PRAQ=LU, or
+ P(R\A)Q=LU) and the right-hand-side, B, solve a linear system for the
+ solution X. Iterative refinement is optionally performed. Only square
+ systems are handled. Singular matrices result in a divide-by-zero for all
+ systems except those involving just the matrix L. Iterative refinement is
+ not performed for singular matrices.
+
+ In the discussion below, n is equal to n_row and n_col, because only
+ square systems are handled.
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ int sys ; Input argument, not modified.
+
+ Defines which system to solve. (') is the linear algebraic transpose.
+
+ sys value system solved
+
+ UMFPACK_A Ax=b
+ UMFPACK_At A'x=b
+ UMFPACK_Pt_L P'Lx=b
+ UMFPACK_L Lx=b
+ UMFPACK_Lt_P L'Px=b
+ UMFPACK_Lt L'x=b
+ UMFPACK_U_Qt UQ'x=b
+ UMFPACK_U Ux=b
+ UMFPACK_Q_Ut QU'x=b
+ UMFPACK_Ut U'x=b
+
+ Iterative refinement can be optionally performed when sys is any of
+ the following:
+
+ UMFPACK_A Ax=b
+ UMFPACK_At A'x=b
+
+ For the other values of the sys argument, iterative refinement is not
+ performed (Control [UMFPACK_IRSTEP], Ap, Ai, and Ax are ignored).
+
+ int Ap [n+1] ; Input argument, not modified.
+ int Ai [nz] ; Input argument, not modified.
+ double Ax [nz] ; Input argument, not modified.
+
+ If iterative refinement is requested (Control [UMFPACK_IRSTEP] >= 1,
+ Ax=b or A'x=b is being solved, and A is nonsingular), then
+ these arrays must be identical to the same ones passed to
+ umfpack_di_numeric. The umfpack_di_solve routine does not check the
+ contents of these arguments, so the results are undefined if Ap, Ai, Ax,
+ are modified between the calls the umfpack_di_numeric and
+ umfpack_di_solve. These three arrays do not need to be present (NULL
+ pointers can be passed) if Control [UMFPACK_IRSTEP] is zero, or if a
+ system other than Ax=b or A'x=b is being solved, or if A is
+ singular, since in each of these cases A is not accessed.
+
+ double X [n] ; Output argument.
+
+ The solution to the linear system, where n = n_row = n_col is the
+ dimension of the matrices A, L, and U.
+
+ double B [n] ; Input argument, not modified.
+
+ The right-hand side vector, b, stored as a conventional array of size n
+ (or two arrays of size n for complex versions). This routine does not
+ solve for multiple right-hand-sides, nor does it allow b to be stored in
+ a sparse-column form.
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_di_numeric.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used.
+
+ Control [UMFPACK_IRSTEP]: The maximum number of iterative refinement
+ steps to attempt. A value less than zero is treated as zero. If
+ less than 1, or if Ax=b or A'x=b is not being solved, or
+ if A is singular, then the Ap, Ai, and Ax arguments are not
+ accessed. Default: 2.
+
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ Contains statistics about the solution factorization. If a
+ (double *) NULL pointer is passed, then no statistics are returned in
+ Info (this is not an error condition). The following statistics are
+ computed in umfpack_di_solve (only the primary statistics are listed):
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ The linear system was successfully solved.
+
+ UMFPACK_WARNING_singular_matrix
+
+ A divide-by-zero occurred. Your solution will contain Inf's
+ and/or NaN's. Some parts of the solution may be valid. For
+ example, solving Ax=b with
+
+ A = [2 0] b = [ 1 ] returns x = [ 0.5 ]
+ [0 0] [ 0 ] [ Inf ]
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to solve the linear system.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments are missing. The B and X
+ arguments are always required. Info and Control are not
+ required. Ap, Ai and Ax are required if Ax=b or
+ A'x=b is to be solved, the (default) iterative
+ refinement is requested, and the matrix A is nonsingular.
+
+ UMFPACK_ERROR_invalid_system
+
+ The sys argument is not valid, or the matrix A is not square.
+
+ UMFPACK_ERROR_invalid_Numeric_object
+
+ The Numeric object is not valid.
+
+ Info [UMFPACK_SOLVE_FLOPS]: the number of floating point operations
+ performed to solve the linear system. This includes the work
+ taken for all iterative refinement steps, including the backtrack
+ (if any).
+
+ Info [UMFPACK_SOLVE_TIME]: The time taken, in seconds.
+\end{verbatim}
+}
+
+
+%-------------------------------------------------------------------------------
+\newpage
+
+\subsection{umfpack\_di\_free\_symbolic}
+{\footnotesize
+\begin{verbatim}
+void umfpack_di_free_symbolic
+(
+ void **Symbolic
+) ;
+
+Purpose:
+
+ Deallocates the Symbolic object and sets the Symbolic handle to NULL.
+
+Arguments:
+
+ void **Symbolic ; Input argument, deallocated and Symbolic is
+ set to (void *) NULL on output.
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{umfpack\_di\_free\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+void umfpack_di_free_numeric
+(
+ void **Numeric
+) ;
+
+Purpose:
+
+ Deallocates the Numeric object and sets the Numeric handle to NULL.
+
+Arguments:
+
+ void **Numeric ; Input argument, deallocated and Numeric is
+ set to (void *) NULL on output.
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{umfpack\_di\_defaults}
+
+{\footnotesize
+\begin{verbatim}
+void umfpack_di_defaults
+(
+ double Control [UMFPACK_CONTROL]
+) ;
+
+Purpose:
+
+ Sets the default control parameter settings.
+
+Arguments:
+
+ double Control [UMFPACK_CONTROL] ; Output argument.
+
+ Control is set to the default control parameter settings.
+\end{verbatim}
+}
+\end{document}
diff --git a/UMFPACK/Doc/UserGuide.bib b/UMFPACK/Doc/UserGuide.bib
new file mode 100644
index 0000000..540f12e
--- /dev/null
+++ b/UMFPACK/Doc/UserGuide.bib
@@ -0,0 +1,322 @@
+ at string{TOMS = "ACM Trans. Math. Softw."}
+ at string{SIMAX = "SIAM J. Matrix Anal. Applic."}
+ at string{SINUM = "SIAM J. Numer. Anal."}
+ at string{SIAMJSC = "SIAM J. Sci. Comput."}
+ at string{SIAMJSSC = "SIAM J. Sci. Statist. Comput."}
+ at string{IJNME = "Internat. J. Numer. Methods Eng."}
+ at string{SIAMJADM = "SIAM J. Alg. Disc. Meth."}
+
+ at article{AmestoyDavisDuff96,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={An approximate minimum degree ordering algorithm},
+ journal=SIMAX,
+ year={1996}
+ ,volume={17}
+ ,number={4}
+ ,pages={886-905}}
+
+ at article{AmestoyDavisDuff03,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={Algorithm 837: {AMD}, an approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={381-388}}
+
+ at techreport{AmestoyDavisDuff03_user,
+ author={Amestoy, P. R. and Davis, T. A. and Duff, I. S.},
+ title={{AMD} Version 1.0 User Guide},
+ institution={CISE Dept., Univ. of Florida},
+ year={2003}
+ ,number={TR-03-011}
+ ,address={Gainesville, FL}
+ ,note={www.cise.ufl.edu/tech-reports.}
+ }
+
+ at article{Davis03,
+ author={Davis, T. A.},
+ title={A column pre-ordering strategy for the unsymmetric-pattern multifrontal method},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={2}
+ ,pages={165-195}}
+
+ at article{Davis03_algo,
+ author={Davis, T. A.},
+ title={Algorithm 832: {UMFPACK}, an unsymmetric-pattern multifrontal method},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={2}
+ ,pages={196-199}}
+
+ at techreport{Davis03_umf,
+ author={Davis, T. A.},
+ title={{UMFPACK} User Guide},
+ institution={Univ. of Florida, CISE Dept.},
+ year={2005}
+ ,number={TR-04-003 (revised)}
+ ,address={Gainesville, FL}
+ ,note={(www.cise.ufl.edu/tech-reports)}
+ }
+
+ at techreport{Davis03_umfquick,
+ author={Davis, T. A.},
+ title={{UMFPACK} Quick Start Guide},
+ institution={Univ. of Florida, CISE Dept.},
+ year={2005}
+ ,number={TR-04-005 (revised)}
+ ,address={Gainesville, FL}
+ ,note={(www.cise.ufl.edu/tech-reports)}
+ }
+
+ at article{DavisDuff97,
+ author={Davis, T. A. and Duff, I. S.},
+ title={An unsymmetric-pattern multifrontal method for sparse {LU} factorization},
+ journal=SIMAX,
+ year={1997}
+ ,volume={18}
+ ,number={1}
+ ,pages={140-158}}
+
+ at article{DavisDuff99,
+ author={Davis, T. A. and Duff, I. S.},
+ title={A combined unifrontal/multifrontal method for unsymmetric sparse matrices},
+ journal=TOMS,
+ volume={25},
+ number={1},
+ pages={1-19},
+ year={1999}}
+
+ at article{SuperLU99,
+ author={Demmel, J. W. and Eisenstat, S. C. and Gilbert, J. R. and Li, X. S. and Liu, J. W. H.},
+ title={A supernodal approach to sparse partial pivoting},
+ journal=SIMAX,
+ year={1999}
+ ,volume={20}
+ ,number={3}
+ ,pages={720-755}
+ ,note={www.netlib.org}
+ }
+
+ at article{ACM679a,
+ author={Dongarra, J. J. and Du Croz, J. and Duff, I. S. and Hammarling, S.},
+ title={A set of level-3 basic linear algebra subprograms},
+ journal=TOMS,
+ year={1990}
+ ,volume={16}
+ ,number={1}
+ ,pages={1--17}}
+
+ at article{netlib,
+ author={Dongarra, J. J. and Grosse, E.},
+ title={Distribution of mathematical software via electronic mail},
+ journal={Comm. ACM},
+ year={1987}
+ ,volume={30}
+ ,pages={403-407}
+ ,note={www.netlib.org}
+ }
+
+ at article{Duff78b,
+ author={Duff, I. S. and Reid, J. K.},
+ year={1978},
+ title={Algorithm 529: Permutations to Block Triangular Form},
+ journal=TOMS,
+ volume={4},
+ annote={f},
+ number={2},
+ pages={189-192},
+ keywords={102 ordering block triangular form}}
+
+ at article{Duff81b,
+ author={Duff, I. S.},
+ year={1981},
+ title={Algorithm 575: Permutations for a Zero-Free Diagonal},
+ journal=TOMS,
+ annote={f},
+ volume={7},
+ pages={387-390},
+ keywords={ordering, zero-free diagonal}}
+
+ at techreport{GotoVandeGeijn02,
+ author = {Goto, K. and van de Geijn, R.},
+ title = {On Reducing {TLB} Misses in Matrix Multiplication, {FLAME} Working Note 9},
+ institution={The University of Texas at Austin, Department of Computer Sciences},
+ number={TR-2002-55},
+ month={Nov.},
+ year={2002}}
+
+ at article{GeorgeNg85,
+ author={George, A. and Ng, E. G.},
+ year={1985},
+ title={An Implementation of {G}aussian Elimination with
+ Partial Pivoting for Sparse Systems},
+ journal=SIAMJSSC,
+ volume={6},
+ number={2},
+ pages={390-409}}
+
+ at article{GeorgeNg87,
+ author={George, A. and Ng, E. G.},
+ year={1987},
+ title={Symbolic Factorization for Sparse {G}aussian Elimination
+ with Partial Pivoting},
+ journal={SIAM J. Sci. Statist. Comput.},
+ volume={8},
+ number={6},
+ pages={877-898}}
+
+ at article{GilbertMolerSchreiber,
+ author={Gilbert, J. R. and Moler, C. and Schreiber, R.},
+ title={Sparse matrices in {MATLAB}: design and implementation},
+ journal=SIMAX,
+ year={1992}
+ ,volume={13}
+ ,number={1}
+ ,pages={333-356}}
+
+ at article{GilbertPeierls88,
+ author={Gilbert, J. R. and Peierls, T.},
+ year={1988},
+ title={Sparse Partial Pivoting in Time Proportional to Arithmetic Operations},
+ journal={SIAM J. Sci. Statist. Comput.},
+ volume={9},
+ pages={862-874}}
+
+ at article{Gustavson78,
+ author={Gustavson, F. G.},
+ year={1978},
+ title={Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition},
+ journal=TOMS,
+ volume={4},
+ number={3},
+ pages={250-269}}
+
+ at techreport{Larimore98,
+ author={Larimore, S. I.},
+ title={An approximate minimum degree column ordering algorithm},
+ institution={Univ. of Florida, CISE Dept.},
+ year={1998}
+ ,number={TR-98-016}
+ ,address={Gainesville, FL}
+ ,note={www.cise.ufl.edu/tech-reports}}
+
+ at article{DavisGilbertLarimoreNg00,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={A column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={353-376}}
+
+ at article{DavisGilbertLarimoreNg00_algo,
+ author={Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.},
+ title={Algorithm 836: {COLAMD}, a column approximate minimum degree ordering algorithm},
+ journal=TOMS,
+ year={2004}
+ ,volume={30}
+ ,number={3}
+ ,pages={377-380}}
+
+ at INCOLLECTION{GilbertNg93,
+ author = {J. R. Gilbert and E. G. Ng},
+ editor = {A. George and J. R. Gilbert and J. W.H. Liu},
+ year = 1993,
+ title = {Predicting Structure in Nonsymmetric Sparse Matrix Factorizations},
+ booktitle = {Graph Theory and Sparse Matrix Computation},
+ series = {Volume 56 of the {IMA} Volumes in Mathematics and its Applications},
+ pages = {107-139},
+ publisher = {Springer-Verlag}
+}
+
+
+ at techreport{ATLAS,
+ author={Whaley, R. C and Petitet, A. and Dongarra, J. J.},
+ title={Automated Emperical Optimization of Software and the {ATLAS} Project},
+ institution={Computer Science Department, The University of Tennessee},
+ year={2000}
+ ,number={LAPACK Working Note 147}
+ ,month={September}
+ ,note={www.netlib.org/atlas}
+ }
+
+ at article{DaydeDuff99,
+ author = "M. J. Dayd\'{e} and I. S. Duff",
+ title = "The {RISC} {BLAS}: A Blocked Implementation of Level 3 {BLAS} for {RISC} Processors",
+ journal = TOMS,
+ volume = "25",
+ number = "3",
+ month = {Sept.},
+ year ="1999"
+ }
+
+
+ at article{ardd:89,
+ author = {M. Arioli and J. W. Demmel and I. S. Duff},
+ year = "1989",
+ title = {Solving sparse linear systems with sparse backward error},
+ journal = SIMAX,
+ volume = {10},
+ pages = {165-190}
+}
+
+
+ at article{DavisHager99,
+ author={Davis, T. A. and Hager, W. W.},
+ title={Modifying a sparse {C}holesky factorization},
+ journal=SIMAX,
+ year={1999}
+ ,volume={20}
+ ,number={3}
+ ,pages={606-627}
+ }
+
+
+ at article{dusc:96,
+ author = {I. S. Duff and J. A. Scott},
+ title = {The design of a new frontal code for solving sparse unsymmetric systems},
+ journal = TOMS,
+ year = "1996",
+ volume = "22",
+ number = "1",
+ pages = "30-45"
+ }
+
+
+ at article{Duff78a,
+ author={Duff, I. S. and Reid, J. K.},
+ year={1978},
+ title={An Implementation of {T}arjan's Algorithm for the Block Triangularization of a Matrix},
+ journal=TOMS,
+ volume={4},
+ number={2},
+ pages={137-147}
+ }
+
+ at book{GeorgeLiu,
+ author={George, A. and Liu, J. W. H.},
+ year={1981},
+ title={Computer Solution of Large Sparse Positive Definite Systems},
+ publisher={Englewood Cliffs, New Jersey: Prentice-Hall}
+ }
+
+ at article{GilbertNgPeyton94,
+ author={Gilbert, J. R. and Ng, E. G. and Peyton, B. W.},
+ title={An efficient algorithm to compute row and column counts for sparse {C}holesky factorization},
+ journal=SIMAX,
+ year={1994}
+ ,volume={15}
+ ,number={4}
+ ,pages={1075-1091}
+ }
+
+ at techreport{DuffGrimesLewis87b,
+ author={Duff, I. S. and Grimes, R. G. and Lewis, J. G.},
+ year={1987},
+ title={Users' Guide for the Harwell-Boeing Sparse Matrix Test Collection},
+ institution={AERE Harwell Laboratory, United Kingdom Atomic Energy Authority}}
+
diff --git a/UMFPACK/Doc/UserGuide.pdf b/UMFPACK/Doc/UserGuide.pdf
new file mode 100644
index 0000000..3f5161a
Binary files /dev/null and b/UMFPACK/Doc/UserGuide.pdf differ
diff --git a/UMFPACK/Doc/UserGuide.sed1 b/UMFPACK/Doc/UserGuide.sed1
new file mode 100644
index 0000000..c49e8c1
--- /dev/null
+++ b/UMFPACK/Doc/UserGuide.sed1
@@ -0,0 +1,33 @@
+/INCLUDE umfpack_col_to_triplet.h/r ../Include/umfpack_col_to_triplet.h
+/INCLUDE umfpack_defaults.h/r ../Include/umfpack_defaults.h
+/INCLUDE umfpack_free_numeric.h/r ../Include/umfpack_free_numeric.h
+/INCLUDE umfpack_free_symbolic.h/r ../Include/umfpack_free_symbolic.h
+/INCLUDE umfpack_get_lunz.h/r ../Include/umfpack_get_lunz.h
+/INCLUDE umfpack_get_numeric.h/r ../Include/umfpack_get_numeric.h
+/INCLUDE umfpack_get_symbolic.h/r ../Include/umfpack_get_symbolic.h
+/INCLUDE umfpack_get_scale.h/r ../Include/umfpack_get_scale.h
+/INCLUDE umfpack_numeric.h/r ../Include/umfpack_numeric.h
+/INCLUDE umfpack_qsymbolic.h/r ../Include/umfpack_qsymbolic.h
+/INCLUDE umfpack_report_control.h/r ../Include/umfpack_report_control.h
+/INCLUDE umfpack_report_info.h/r ../Include/umfpack_report_info.h
+/INCLUDE umfpack_report_matrix.h/r ../Include/umfpack_report_matrix.h
+/INCLUDE umfpack_report_numeric.h/r ../Include/umfpack_report_numeric.h
+/INCLUDE umfpack_report_perm.h/r ../Include/umfpack_report_perm.h
+/INCLUDE umfpack_report_status.h/r ../Include/umfpack_report_status.h
+/INCLUDE umfpack_report_symbolic.h/r ../Include/umfpack_report_symbolic.h
+/INCLUDE umfpack_report_triplet.h/r ../Include/umfpack_report_triplet.h
+/INCLUDE umfpack_report_vector.h/r ../Include/umfpack_report_vector.h
+/INCLUDE umfpack_simple.c/r ../Demo/umfpack_simple.c
+/INCLUDE umfpack_solve.h/r ../Include/umfpack_solve.h
+/INCLUDE umfpack_scale.h/r ../Include/umfpack_scale.h
+/INCLUDE umfpack_symbolic.h/r ../Include/umfpack_symbolic.h
+/INCLUDE umfpack_timer.h/r ../Include/umfpack_timer.h
+/INCLUDE umfpack_tictoc.h/r ../Include/umfpack_tictoc.h
+/INCLUDE umfpack_transpose.h/r ../Include/umfpack_transpose.h
+/INCLUDE umfpack_triplet_to_col.h/r ../Include/umfpack_triplet_to_col.h
+/INCLUDE umfpack_wsolve.h/r ../Include/umfpack_wsolve.h
+/INCLUDE umfpack_load_numeric.h/r ../Include/umfpack_load_numeric.h
+/INCLUDE umfpack_load_symbolic.h/r ../Include/umfpack_load_symbolic.h
+/INCLUDE umfpack_save_numeric.h/r ../Include/umfpack_save_numeric.h
+/INCLUDE umfpack_save_symbolic.h/r ../Include/umfpack_save_symbolic.h
+/INCLUDE umfpack_get_determinant.h/r ../Include/umfpack_get_determinant.h
diff --git a/UMFPACK/Doc/UserGuide.sed2 b/UMFPACK/Doc/UserGuide.sed2
new file mode 100644
index 0000000..0df47d9
--- /dev/null
+++ b/UMFPACK/Doc/UserGuide.sed2
@@ -0,0 +1,3 @@
+/[/][*]/d
+/[*][/]/d
+/INCLUDE umfpack/d
diff --git a/UMFPACK/Doc/UserGuide.stex b/UMFPACK/Doc/UserGuide.stex
new file mode 100644
index 0000000..271419c
--- /dev/null
+++ b/UMFPACK/Doc/UserGuide.stex
@@ -0,0 +1,2712 @@
+%-------------------------------------------------------------------------------
+% The UserGuide.stex file. Processed into UserGuide.tex via sed.
+%-------------------------------------------------------------------------------
+
+\documentclass[11pt]{article}
+
+\newcommand{\m}[1]{{\bf{#1}}} % for matrices and vectors
+\newcommand{\tr}{^{\sf T}} % transpose
+\newcommand{\he}{^{\sf H}} % complex conjugate transpose
+\newcommand{\implies}{\rightarrow}
+
+\topmargin 0in
+\textheight 9in
+\oddsidemargin 0pt
+\evensidemargin 0pt
+\textwidth 6.5in
+
+\begin{document}
+
+\author{Timothy A. Davis \\
+Dept. of Computer and Information Science and Engineering \\
+Univ. of Florida, Gainesville, FL}
+\title{UMFPACK Version 5.2.0 User Guide}
+\date{Nov 1, 2007}
+\maketitle
+
+%-------------------------------------------------------------------------------
+\begin{abstract}
+ UMFPACK is a set of routines for solving unsymmetric sparse linear
+ systems, $\m{Ax}=\m{b}$, using the Unsymmetric MultiFrontal method
+ and direct sparse LU factorization. It is written in ANSI/ISO C, with a
+ MATLAB interface. UMFPACK relies on the Level-3 Basic
+ Linear Algebra Subprograms (dense matrix multiply) for its performance.
+ This code works on Windows and many versions of Unix (Sun Solaris,
+ Red Hat Linux, IBM AIX, SGI IRIX, and Compaq Alpha).
+\end{abstract}
+%-------------------------------------------------------------------------------
+
+Technical Report TR-04-003 (revised)
+
+UMFPACK Version 5.2.0, Copyright\copyright 1995-2006 by Timothy A. Davis.
+All Rights Reserved.
+UMFPACK is available under alternate licences; contact T. Davis for details.
+
+{\bf UMFPACK License:}
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU General Public
+ License as published by the Free Software Foundation; either
+ version 2 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU GPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+{\bf Availability:}
+ http://www.cise.ufl.edu/research/sparse/umfpack
+
+{\bf Acknowledgments:}
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+ The upgrade to Version 4.1 and the inclusion of the
+ symmetric and 2-by-2 pivoting strategies
+ were done while the author was on sabbatical at
+ Stanford University and Lawrence Berkeley National Laboratory.
+
+%-------------------------------------------------------------------------------
+\newpage
+%-------------------------------------------------------------------------------
+
+\tableofcontents
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Overview}
+%-------------------------------------------------------------------------------
+
+UMFPACK\footnote{Pronounced with two syllables: umph-pack}
+is a set of routines for solving systems of linear
+equations, $\m{Ax}=\m{b}$, when $\m{A}$ is sparse and unsymmetric. It is based
+on the Unsymmetric-pattern MultiFrontal method \cite{DavisDuff97,DavisDuff99}.
+UMFPACK factorizes
+$\m{PAQ}$, $\m{PRAQ}$, or $\m{PR}^{-1}\m{AQ}$ into the product $\m{LU}$,
+where $\m{L}$ and $\m{U}$
+are lower and upper triangular, respectively, $\m{P}$ and $\m{Q}$ are
+permutation matrices, and $\m{R}$ is a diagonal matrix of row scaling factors
+(or $\m{R}=\m{I}$ if row-scaling is not used). Both $\m{P}$ and $\m{Q}$ are
+chosen to reduce fill-in (new nonzeros in $\m{L}$ and $\m{U}$ that are not
+present in $\m{A}$). The permutation $\m{P}$ has the dual role of reducing
+fill-in and maintaining numerical accuracy (via relaxed partial pivoting
+and row interchanges).
+
+The sparse matrix $\m{A}$ can be square or rectangular, singular
+or non-singular, and real or complex (or any combination). Only square
+matrices $\m{A}$ can be used to solve $\m{Ax}=\m{b}$ or related systems.
+Rectangular matrices can only be factorized.
+
+UMFPACK first finds a column pre-ordering that reduces fill-in, without regard
+to numerical values. It scales and analyzes the matrix, and then automatically
+selects one of three strategies for pre-ordering the rows and columns:
+{\em unsymmetric},
+{\em 2-by-2}, and
+{\em symmetric}. These strategies are described below.
+
+First, all pivots with zero Markowitz cost are eliminated and placed in the
+LU factors. The remaining submatrix $\m{S}$ is then analyzed.
+The following rules are applied, and the first one that matches defines
+the strategy.
+
+\begin{itemize}
+\item Rule 1: $\m{A}$ rectangular $\implies$ unsymmetric.
+\item Rule 2:
+ If the zero-Markowitz elimination results in a rectangular $\m{S}$,
+ or an $\m{S}$ whose diagonal has not been preserved, the
+ unsymmetric strategy is used.
+\item The symmetry $\sigma_1$ of $\m{S}$ is computed. It is defined as
+ the number of {\em matched} off-diagonal entries, divided by the
+ total number of off-diagonal entries. An entry $s_{ij}$ is matched
+ if $s_{ji}$ is also an entry. They need not be numerically equal.
+ An {\em entry} is a value in $\m{A}$ which is present
+ in the input data structure. All nonzeros are entries, but some entries
+ may be numerically zero.
+ Rule 3: $\sigma_1 < 0.1 \implies$ unsymmetric.
+ The matrix is very unsymmetric.
+\item Let $d$ be the number of nonzero entries on the diagonal of $\m{S}$.
+ Let $\m{S}$ be $\nu$-by-$\nu$.
+ Rule 4: $(\sigma_1 \ge 0.7) \:\wedge\: (d = \nu) \implies$ symmetric.
+ The matrix has a nearly symmetric nonzero pattern, and a zero-free
+ diagonal.
+\end{itemize}
+
+If the strategy has not yet been determined,
+the 2-by-2 strategy is attempted. A row permutation $\m{P}_2$
+is found which attempts to reduce the number of small
+diagonal entries of $\m{P}_2 \m{S}$.
+An entry $s_{ij}$ is determined to be small if
+$|s_{ij}| < 0.01 \max |s_{*j}|$, or large otherwise.
+If $s_{ii}$ is numerically small, the method attempts to swap
+two rows $i$ and $j$, such that both $s_{ij}$ and $s_{ji}$ are large.
+Once these rows are swapped,
+they remain in place. Let $\sigma_2$ be the symmetry of $\m{P}_2 \m{S}$,
+and let $d_2$ be the number of nonzero entries (either small or large)
+on the diagonal of $\m{P}_2 \m{S}$.
+
+\begin{itemize}
+\item Rule 5:
+ ($\sigma_2 > 1.1 \sigma_1) \:\wedge\: (d_2 > 0.9 \nu) \implies$ 2-by-2.
+ The 2-by-2 permutation has made the matrix significantly more symmetric.
+\item Rule 6: $\sigma_2 < 0.7 \sigma_1 \implies$ unsymmetric.
+ The 2-by-2 strategy has significantly deteriorated the symmetry,
+\item Rule 7: $\sigma_2 < 0.25 \implies$ unsymmetric.
+ The matrix is still very unsymmetric.
+\item Rule 8: $\sigma_2 \ge 0.51 \implies$ 2-by-2.
+ The matrix is roughly symmetric.
+\item Rule 9: $\sigma_2 \ge 0.999 \sigma_1 \implies$ 2-by-2.
+ The 2-by-2 permutation has preserved symmetry, or made it only
+ slightly worse.
+\item Rule 10: if no rule has yet triggered, use the unsymmetric strategy.
+\end{itemize}
+
+Each strategy is described below:
+\begin{itemize}
+\item {\em unsymmetric}:
+The column pre-ordering of $\m{S}$ is computed by a modified version of COLAMD
+\cite{DavisGilbertLarimoreNg00_algo,DavisGilbertLarimoreNg00,Larimore98}.
+The method finds a symmetric permutation $\m{Q}$ of the matrix $\m{S}\tr\m{S}$
+(without forming $\m{S}\tr\m{S}$ explicitly). This is a good choice for
+$\m{Q}$, since the Cholesky factors of $\m{(SQ)\tr(SQ)}$ are an upper bound (in
+terms of nonzero pattern) of the factor $\m{U}$ for the unsymmetric LU
+factorization ($\m{PSQ}=\m{LU}$) regardless of the choice of $\m{P}$
+\cite{GeorgeNg85,GeorgeNg87,GilbertNg93}. This modified version of
+COLAMD also computes the column elimination tree and post-orders the
+tree. It finds the upper bound on the number of nonzeros in L and U.
+It also has a different threshold for determining dense rows and columns.
+During factorization, the column pre-ordering can be modified.
+Columns within a single super-column can be reshuffled, to reduce fill-in.
+Threshold partial pivoting is used with no preference given to the diagonal
+entry. Within a given pivot column $j$, an entry $a_{ij}$ can be chosen if
+$|a_{ij}| \ge 0.1 \max |a_{*j}|$. Among those numerically acceptable
+entries, the sparsest row $i$ is chosen as the pivot row.
+
+\item {\em 2-by-2}:
+The symmetric strategy (see below) is applied to the matrix $\m{P}_2 \m{S}$,
+rather than $\m{S}$.
+
+\item {\em symmetric}:
+The column ordering is computed from AMD
+\cite{AmestoyDavisDuff96,AmestoyDavisDuff03},
+applied to the pattern of $\m{S}+\m{S}\tr$
+followed by a post-ordering of the supernodal elimination
+tree of $\m{S}+\m{S}\tr$.
+No modification of the column pre-ordering is made during numerical
+factorization. Threshold partial pivoting is used, with a strong
+preference given to the diagonal entry. The diagonal entry is chosen if
+$a_{jj} \ge 0.001 \max |a_{*j}|$. Otherwise, a sparse row is selected,
+using the same method used by the unsymmetric strategy.
+
+\end{itemize}
+
+The symmetric and 2-by-2 strategies, and their automatic selection,
+are new to Version 4.1. Version 4.0 only used the unsymmetric strategy.
+
+Once the strategy is selected,
+the factorization of the matrix $\m{A}$ is broken down into the factorization
+of a sequence of dense rectangular frontal matrices. The frontal matrices are
+related to each other by a supernodal column elimination tree, in which each
+node in the tree represents one frontal matrix. This analysis phase also
+determines upper bounds on the memory usage, the floating-point operation count,
+and the number of nonzeros in the LU factors.
+
+UMFPACK factorizes each {\em chain} of frontal matrices in a single working
+array, similar to how the unifrontal method \cite{dusc:96} factorizes the whole
+matrix. A chain of frontal matrices is a sequence of fronts where the parent
+of front $i$ is $i$+1 in the supernodal column elimination tree. For the
+nonsingular matrices factorized with the unsymmetric strategy, there are
+exactly the same number of chains as there are leaves in the supernodal
+column elimination tree. UMFPACK is an
+outer-product based, right-looking method. At the $k$-th step of Gaussian
+elimination, it represents the updated submatrix $\m{A}_k$ as an implicit
+summation of a set of dense sub-matrices (referred to as {\em elements},
+borrowing a phrase from finite-element methods) that arise when the frontal
+matrices are factorized and their pivot rows and columns eliminated.
+
+Each frontal matrix represents the elimination of one or more columns;
+each column of $\m{A}$ will be eliminated in a specific frontal matrix,
+and which frontal matrix will be used for which column is determined by
+the pre-analysis phase. The pre-analysis phase also determines the worst-case
+size of each frontal matrix so that they can hold any candidate pivot column
+and any candidate pivot row. From the perspective of the analysis phase, any
+candidate pivot column in the frontal matrix is identical (in terms of nonzero
+pattern), and so is any row. However, the numeric factorization phase has
+more information than the analysis phase. It uses this information to reorder
+the columns within each frontal matrix to reduce fill-in. Similarly, since
+the number of nonzeros in each row and column are maintained (more precisely,
+COLMMD-style approximate degrees \cite{GilbertMolerSchreiber}), a pivot row can
+be selected based on sparsity-preserving criteria (low degree) as well as
+numerical considerations (relaxed threshold partial pivoting).
+
+When the symmetric or 2-by-2 strategies are used,
+the column preordering is not refined during numeric factorization.
+Row pivoting for sparsity and numerical accuracy is performed if the
+diagonal entry is too small.
+
+More details of the method, including experimental results, are
+described in \cite{Davis03,Davis03_algo}, available at
+http://www.cise.ufl.edu/tech-reports.
+
+%-------------------------------------------------------------------------------
+\section{Availability}
+%-------------------------------------------------------------------------------
+
+In addition to appearing as a Collected Algorithm of the ACM,
+UMFPACK is available at http://www.cise.ufl.edu/research/sparse.
+It is included as a built-in routine in MATLAB.
+Version 4.0 (in MATLAB 6.5)
+does not have the symmetric or 2-by-2 strategies and it takes
+less advantage of the level-3
+BLAS \cite{DaydeDuff99,ACM679a,ATLAS,GotoVandeGeijn02}.
+Versions 5.x through v4.1 tend to be much faster than Version 4.0,
+particularly on unsymmetric matrices with mostly symmetric
+nonzero pattern (such as finite element and circuit simulation matrices).
+Version 3.0 and following make
+use of a modified version of COLAMD V2.0 by Timothy A.~Davis, Stefan
+Larimore, John Gilbert, and Esmond Ng. The original COLAMD V2.1 is available in
+as a built-in routine in MATLAB V6.0 (or later), and at
+http://www.cise.ufl.edu/research/sparse.
+These codes are also available in Netlib \cite{netlib} at
+http://www.netlib.org.
+UMFPACK Versions 2.2.1 and earlier, co-authored with Iain Duff,
+are available at http://www.cise.ufl.edu/research/sparse and as
+MA38 (functionally equivalent to Version 2.2.1) in the Harwell
+Subroutine Library.
+
+{\bf NOTE: you must use the correct version of AMD with UMFPACK; using
+an old version of AMD with a newer version of UMFPACK can fail.}
+
+%-------------------------------------------------------------------------------
+\section{Primary changes from prior versions}
+%-------------------------------------------------------------------------------
+
+A detailed list of changes is in the {\tt ChangeLog} file.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 5.2.0}
+%-------------------------------------------------------------------------------
+
+Change of license from GNU Lesser GPL to the GNU GPL.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 5.1.0}
+%-------------------------------------------------------------------------------
+
+Port of MATLAB interface to 64-bit MATLAB.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 5.0.3}
+%-------------------------------------------------------------------------------
+
+Renamed the MATLAB function to {\tt umfpack2}, so as not to confict with
+itself (the MATLAB built-in version of UMFPACK).
+
+%-------------------------------------------------------------------------------
+\subsection{Version 5.0}
+%-------------------------------------------------------------------------------
+
+Changed {\tt long} to {\tt UF\_long}, controlled by the {\tt UFconfig.h}
+file. A {\tt UF\_long} is normally just {\tt long}, except on the Windows 64
+(WIN64) platform. In that case, it becomes {\tt \_\_int64}.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.6}
+%-------------------------------------------------------------------------------
+
+Added additional options to {\tt umf\_solve.c}.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.5}
+%-------------------------------------------------------------------------------
+
+Added function pointers for malloc, calloc, realloc, free, printf, hypot,
+and complex divisiion, so that these functions can be redefined at run-time.
+Added a version number so you can determine the
+version of UMFPACK at run time or compile time. UMFPACK requires AMD v2.0
+or later.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.4}
+%-------------------------------------------------------------------------------
+
+Bug fix in strategy selection in {\tt umfpack\_*\_qsymbolic}.
+Added packed complex case for all complex input/output arguments.
+Added {\tt umfpack\_get\_determinant}.
+Added minimal support for Microsoft Visual Studio
+(the {\tt umf\_multicompile.c} file).
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.3.1}
+%-------------------------------------------------------------------------------
+
+Minor bug fix in the forward/backsolve. This bug had the effect of turning
+off iterative refinement when solving $\m{A}\tr\m{x}=\m{b}$ after factorizing
+$\m{A}$. UMFPACK mexFunction now factorizes $\m{A}\tr$ in its forward-slash
+operation.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.3}
+%-------------------------------------------------------------------------------
+
+No changes are visible to the C or MATLAB user, except the presence of
+one new control parameter in the {\tt Control} array,
+and three new statistics in the {\tt Info} array.
+The primary change is the addition of an (optional) drop tolerance.
+
+%-------------------------------------------------------------------------------
+\subsection{Version 4.1}
+%-------------------------------------------------------------------------------
+
+The following is a summary of the main changes that are visible to the C
+or MATLAB user:
+
+\begin{enumerate}
+
+\item New ordering strategies added. No changes are required in user code
+ (either C or MATLAB) to use the new default strategy, which is an automatic
+ selection of the unsymmetric, symmetric, or 2-by-2 strategies.
+
+\item Row scaling added. This is only visible to the MATLAB caller when using
+ the form {\tt [L,U,P,Q,R] = umfpack (A)}, to retrieve the LU factors.
+ Likewise, it is only visible to the C caller when the LU factors are
+ retrieved, or when solving systems with just $\m{L}$ or $\m{U}$.
+ New C-callable and MATLAB-callable routines are included to get and to
+ apply the scale factors computed by UMFPACK. Row scaling is enabled by
+ default, but can be disabled. Row scaling usually leads to a better
+ factorization, particularly when the symmetric strategy is used.
+
+\item Error code {\tt UMFPACK\_ERROR\_problem\_to\_large} removed.
+ Version 4.0 would generate this error when the upper bound memory usage
+ exceeded 2GB (for the {\tt int} version), even when the actual memory
+ usage was less than this. The new version properly handles this case,
+ and can successfully factorize the matrix if sufficient memory is
+ available.
+
+\item New control parameters and statistics provided.
+
+\item The AMD symmetric approximate minimum degree ordering routine added
+ \cite{AmestoyDavisDuff96,AmestoyDavisDuff03}.
+ It is used by UMFPACK, and can also be called independently from C or
+ MATLAB.
+
+\item The {\tt umfpack} mexFunction now returns permutation matrices, not
+ permutation vectors, when using the form {\tt [L,U,P,Q] = umfpack (A)}
+ or the new form {\tt [L,U,P,Q,R] = umfpack (A)}.
+
+\item New arguments added to the user-callable routines
+ {\tt umfpack\_*\_symbolic},
+ {\tt umfpack\_*\_qsymbolic},
+ {\tt umfpack\_*\_get\_numeric}, and
+ {\tt umfpack\_*\_get\_symbolic}.
+ The symbolic analysis now makes use of the numerical values of the matrix
+ $\m{A}$, to guide the 2-by-2 strategy. The subsequent matrix passed to
+ the numeric factorization step does not have to have the same numerical
+ values. All of the new arguments are optional. If you do not wish to
+ include them, simply pass {\tt NULL} pointers instead. The 2-by-2 strategy
+ will assume all entries are numerically large, for example.
+
+\item New routines added to save and load the {\tt Numeric} and {\tt Symbolic}
+ objects to and from a binary file.
+
+\item A Fortran interface added. It provides access to a subset of
+ UMFPACK's features.
+
+\item You can compute an incomplete LU factorization, by dropping small
+ entries from $\m{L}$ and $\m{U}$. By default, no nonzero entry is
+ dropped, no matter how small in absolute value. This feature is new
+ to Version 4.3.
+
+\end{enumerate}
+
+%-------------------------------------------------------------------------------
+\section{Using UMFPACK in MATLAB}
+%-------------------------------------------------------------------------------
+
+The easiest way to use UMFPACK is within MATLAB. Version 4.3 is a built-in
+routine in MATLAB 7.0.4, and is used in {\tt x = A}$\backslash${\tt b} when
+{\tt A} is sparse, square, unsymmetric (or symmetric but not positive definite),
+and with nonzero entries that are not confined in a narrow band.
+It is also used for the {\tt [L,U,P,Q] = lu (A)} usage of {\tt lu}.
+Type {\tt help lu} in MATLAB 6.5 or later for more details.
+
+To use the UMFPACK mexFunction, you must download and compile it,
+since the mexFunction itself is not part of MATLAB.
+The following discussion assumes that
+you have MATLAB Version 6.0 or later (which includes the BLAS, and the
+{\tt colamd} ordering routine). To compile both the UMFPACK and AMD
+mexFunctions, just type {\tt make} in the Unix system shell,
+while in the {\tt UMFPACK} directory.
+You can also type {\tt umfpack\_make} in MATLAB, if you are in the
+{\tt UMFPACK/MATLAB} directory, or if that directory is in your MATLAB path.
+This works on any system with MATLAB, including Windows.
+See Section~\ref{Install} for more details on how to install UMFPACK.
+Once installed, the UMFPACK mexFunction can analyze, factor, and solve linear
+systems. Table~\ref{matlab} summarizes some of the more common uses
+of the UMFPACK mexFunction within MATLAB.
+
+An optional input argument can be used to modify the control parameters for
+UMFPACK, and an optional output argument provides statistics on the
+factorization.
+
+Refer to the AMD User Guide for more details about the AMD mexFunction.
+
+\begin{table}
+\caption{Using UMFPACK's MATLAB interface}
+\label{matlab}
+\vspace{0.1in}
+{\footnotesize
+\begin{tabular}{l|l|l}
+\hline
+Function & Using UMFPACK & MATLAB 6.0 equivalent \\
+\hline
+ & & \\
+\begin{minipage}[t]{1.5in}
+Solve $\m{Ax}=\m{b}$.
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+x = umfpack (A,'\',b) ;
+\end{verbatim}
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+x = A \ b ;
+\end{verbatim}
+\end{minipage}
+ \\
+ & & \\
+\hline
+ & & \\
+\begin{minipage}[t]{1.5in}
+Solve $\m{Ax}=\m{b}$ using a different row and column pre-ordering
+(symmetric ordering).
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+S = spones (A) ;
+Q = symamd (S+S') ;
+Control = umfpack ;
+Control (6) = 3 ;
+x = umfpack (A,Q,'\',b,Control) ;
+\end{verbatim}
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+spparms ('autommd',0) ;
+S = spones (A) ;
+Q = symamd (S+S') ;
+x = A (Q,Q) \ b (Q) ;
+x (Q) = x ;
+spparms ('autommd',1) ;
+\end{verbatim}
+\end{minipage}
+ \\
+ & & \\
+\hline
+ & & \\
+\begin{minipage}[t]{1.5in}
+Solve $\m{A}\tr\m{x}\tr = \m{b}\tr$.
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+x = umfpack (b,'/',A) ;
+\end{verbatim}
+Note: $\m{A}$ is factorized.
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+x = b / A ;
+\end{verbatim}
+Note: $\m{A}\tr$ is factorized.
+\end{minipage}
+ \\
+ & & \\
+\hline
+ & & \\
+\begin{minipage}[t]{1.5in}
+Scale and factorize $\m{A}$, then solve $\m{Ax}=\m{b}$.
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+[L,U,P,Q,R] = umfpack (A) ;
+c = P * (R \ b) ;
+x = Q * (U \ (L \ c)) ;
+\end{verbatim}
+\end{minipage}
+&
+\begin{minipage}[t]{2.2in}
+\begin{verbatim}
+[m n] = size (A) ;
+r = full (sum (abs (A), 2)) ;
+r (find (r == 0)) = 1 ;
+R = spdiags (r, 0, m, m) ;
+I = speye (n) ;
+Q = I (:, colamd (A)) ;
+[L,U,P] = lu ((R\A)*Q) ;
+c = P * (R \ b) ;
+x = Q * (U \ (L \ c)) ;
+\end{verbatim}
+\end{minipage}
+ \\
+ & & \\
+\hline
+\end{tabular}
+}
+\end{table}
+
+Note: in MATLAB 6.5 or later, use {\tt spparms ('autoamd',0)} in addition to
+{\tt spparms ('autommd',0)}, in Table~\ref{matlab}, to turn off MATLAB's
+default reordering.
+
+UMFPACK requires
+{\tt b} to be a dense vector (real or complex) of the appropriate dimension.
+This is more restrictive than what you can do with MATLAB's
+backslash or forward slash. See {\tt umfpack\_solve} for an M-file that
+removes this restriction.
+This restriction does not apply to the built-in backslash operator
+in MATLAB 6.5 or later, which uses UMFPACK to factorize the matrix.
+You can do this yourself in MATLAB:
+
+{\footnotesize
+\begin{verbatim}
+ [L,U,P,Q,R] = umfpack (A) ;
+ x = Q * (U \ (L \ (P * (R \ b)))) ;
+\end{verbatim}
+}
+
+or, with no row scaling:
+
+{\footnotesize
+\begin{verbatim}
+ [L,U,P,Q] = umfpack (A) ;
+ x = Q * (U \ (L \ (P * b))) ;
+\end{verbatim}
+}
+
+The above examples do not make use of the iterative refinement
+that is built into
+{\tt x = }{\tt umfpack (A,'}$\backslash${\tt ',b)}
+however.
+
+MATLAB's {\tt [L,U,P] = lu(A)} returns a lower triangular {\tt L}, an upper
+triangular {\tt U}, and a permutation matrix {\tt P} such that {\tt P*A} is
+equal to {\tt L*U}. UMFPACK behaves differently. By default, it scales
+the rows of {\tt A} and reorders the columns of {\tt A} prior to
+factorization, so that {\tt L*U} is equal to {\tt P*(R}$\backslash${\tt A)*Q},
+where {\tt R} is a diagonal sparse matrix of scale factors for the rows
+of {\tt A}. The scale factors {\tt R} are applied to {\tt A} via the MATLAB
+expression {\tt R}$\backslash${\tt A} to avoid multiplying by
+the reciprocal, which can be numerically inaccurate.
+
+There are more options; you can provide your own column pre-ordering (in which
+case UMFPACK does not call COLAMD or AMD), you can modify other control settings
+(similar to the {\tt spparms} in MATLAB), and you can get various statistics on
+the analysis, factorization, and solution of the linear system. Type
+{\tt umfpack\_details} and {\tt umfpack\_report} in MATLAB for more
+information. Two demo M-files are provided. Just type {\tt umfpack\_simple}
+and {\tt umfpack\_demo} to run them.
+The output of these two programs should be about the same
+as the files {\tt umfpack\_simple.m.out} and {\tt umfpack\_demo.m.out}
+that are provided.
+
+Factorizing {\tt A'} (or {\tt A.'}) and using the transposed factors can
+sometimes be faster than factorizing {\tt A}. It can also be preferable to
+factorize {\tt A'} if {\tt A} is rectangular. UMFPACK pre-orders the columns
+to maintain sparsity; the row ordering is not determined until the matrix
+is factorized. Thus, if {\tt A} is {\tt m} by {\tt n} with structural
+rank {\tt m}
+and {\tt m} $<$ {\tt n}, then {\tt umfpack} might not find a factor
+{\tt U} with a structurally zero-free diagonal.
+Unless the matrix ill-conditioned or
+poorly scaled, factorizing {\tt A'} in this case will guarantee that both
+factors will have zero-free diagonals. Note that there is no guarantee
+as to the size of the diagonal entries of {\tt U}; UMFPACK does not do a
+rank-revealing factorization. Here's how you can factorize {\tt A'}
+and get the factors of {\tt A} instead:
+
+\begin{verbatim}
+ [l,u,p,q] = umfpack (A') ;
+ L = u' ;
+ U = l' ;
+ P = q ;
+ Q = p ;
+ clear l u p q
+\end{verbatim}
+
+This is an alternative to {\tt [L,U,P,Q]=umfpack(A)}.
+
+A simple M-file ({\tt umfpack\_btf}) is provided that first permutes the matrix
+to upper block triangular form, using MATLAB's {\tt dmperm} routine, and then
+solves each block. The LU factors are not returned. Its usage is simple:
+{\tt x = umfpack\_btf(A,b)}. Type {\tt help umfpack\_btf} for more options.
+An estimate of the 1-norm of {\tt L*U-P*A*Q} can be computed in MATLAB
+as {\tt lu\_normest(P*A*Q,L,U)}, using the {\tt lu\_normest.m} M-file
+by Hager and Davis \cite{DavisHager99} that is included with the
+UMFPACK distribution. With row scaling enabled, use
+{\tt lu\_normest(P*(R}$\backslash${\tt A)*Q,L,U)} instead.
+
+One issue you may encounter is how UMFPACK allocates its memory when being used
+in a mexFunction. One part of its working space is of variable size. The
+symbolic analysis phase determines an upper bound on the size of this memory,
+but not all of this memory will typically be used in the numerical
+factorization. UMFPACK tries to allocate a decent amount of working space.
+This is 70\% of the upper bound, by default, for the unsymmetric strategy.
+For the symmetric strategy, the fraction of the upper bound is computed
+automatically (assuming a best-case scenario with no numerical pivoting
+required during numeric factorization).
+If this initial allocation fails, it reduces its request
+and uses less memory. If the space is not large enough during factorization,
+it is increased via {\tt mxRealloc}.
+
+However, {\tt mxMalloc} and {\tt mxRealloc} abort the {\tt umfpack} mexFunction
+if they fail, so this strategy does not work in MATLAB.
+
+To compute the determinant with UMFPACK:
+
+\begin{verbatim}
+ d = umfpack (A, 'det') ;
+ [d e] = umfpack (A, 'det') ;
+\end{verbatim}
+
+The first case is identical to MATLAB's {\tt det}.
+The second case returns the determinant in the form
+$d \times 10^e$, which avoids overflow if $e$ is large.
+
+%-------------------------------------------------------------------------------
+\section{Using UMFPACK in a C program}
+\label{C}
+%-------------------------------------------------------------------------------
+
+The C-callable UMFPACK library consists of 32 user-callable routines and one
+include file. All but three of the routines come in four versions, with
+different sizes of integers and for real or complex floating-point numbers:
+\begin{enumerate}
+\item {\tt umfpack\_di\_*}: real double precision, {\tt int} integers.
+\item {\tt umfpack\_dl\_*}: real double precision, {\tt UF\_long} integers.
+\item {\tt umfpack\_zi\_*}: complex double precision, {\tt int} integers.
+\item {\tt umfpack\_zl\_*}: complex double precision, {\tt UF\_long} integers.
+\end{enumerate}
+where {\tt *} denotes the specific name of one of the routines.
+Routine names beginning with {\tt umf\_} are internal to the package,
+and should not be called by the user. The include file {\tt umfpack.h}
+must be included in any C program that uses UMFPACK.
+The other three routines are the same for all four versions.
+
+In addition, the C-callable AMD library distributed with UMFPACK
+includes 4 user-callable routines (in two versions with {\tt int} and
+{\tt UF\_long} integers) and one include file. Refer to the AMD documentation
+for more details.
+
+Use only one version for any one problem; do not attempt to use one version
+to analyze the matrix and another version to factorize the matrix, for example.
+
+The notation {\tt umfpack\_di\_*} refers to all user-callable routines
+for the real double precision and {\tt int} integer case. The notation
+{\tt umfpack\_*\_numeric}, for example, refers all four versions
+(real/complex, int/UF\_long) of a single operation
+(in this case numeric factorization).
+
+%-------------------------------------------------------------------------------
+\subsection{The size of an integer}
+%-------------------------------------------------------------------------------
+
+The {\tt umfpack\_di\_*} and {\tt umfpack\_zi\_*} routines use {\tt int} integer
+arguments; those starting with {\tt umfpack\_dl\_} or {\tt umfpack\_zl\_}
+use {\tt UF\_long} integer arguments. If you compile UMFPACK in the standard
+ILP32 mode (32-bit {\tt int}'s, {\tt long}'s, and pointers) then the versions
+are essentially identical. You will be able to solve problems using up to 2GB
+of memory. If you compile UMFPACK in the standard LP64 mode, the size of an
+{\tt int} remains 32-bits, but the size of a {\tt long} and a pointer both get
+promoted to 64-bits. In the LP64 mode, the {\tt umfpack\_dl\_*}
+and {\tt umfpack\_zl\_*} routines can solve huge
+problems (not limited to 2GB), limited of course by the amount of available
+memory. The only drawback to the 64-bit mode is that not all BLAS libraries
+support 64-bit integers. This limits the performance you will obtain.
+Those that do support 64-bit integers are specific to particular
+architectures, and are not portable. UMFPACK and AMD should be compiled
+in the same mode.
+If you compile UMFPACK and AMD in the LP64 mode,
+be sure to add {\tt -DLP64} to the compilation command. See the examples in
+the {\tt UFconfig/UFconfig.mk} file.
+
+%-------------------------------------------------------------------------------
+\subsection{Real and complex floating-point}
+%-------------------------------------------------------------------------------
+
+The {\tt umfpack\_di\_*} and {\tt umfpack\_dl\_*} routines take (real) double
+precision arguments, and return double precision arguments. In the
+{\tt umfpack\_zi\_*} and {\tt umfpack\_zl\_*} routines, these same arguments
+hold the real part of the matrices; and second double precision arrays hold
+the imaginary part of the input and output matrices. Internally, complex
+numbers are stored in arrays with their real and imaginary parts interleaved,
+as required by the BLAS (``packed'' complex form).
+
+New to Version 4.4 is the option of providing input/output arguments
+in packed complex form.
+
+%-------------------------------------------------------------------------------
+\subsection{Primary routines, and a simple example}
+%-------------------------------------------------------------------------------
+
+Five primary UMFPACK routines are required to factorize $\m{A}$ or
+solve $\m{Ax}=\m{b}$. They are fully described in Section~\ref{Primary}:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_symbolic}:
+
+ Pre-orders the columns of $\m{A}$ to reduce fill-in.
+ Returns an opaque {\tt Symbolic} object as a {\tt void *}
+ pointer. The object contains the symbolic analysis and is needed for the
+ numeric factorization. This routine requires only $O(|\m{A}|)$ space,
+ where $|\m{A}|$ is the number of nonzero entries in the matrix. It computes
+ upper bounds on the nonzeros in $\m{L}$ and $\m{U}$, the floating-point
+ operations required, and the memory usage of {\tt umfpack\_*\_numeric}. The
+ {\tt Symbolic} object is small; it contains just the column pre-ordering,
+ the supernodal column elimination tree, and information about each frontal
+ matrix. It is no larger than about $13n$ integers if $\m{A}$ is
+ $n$-by-$n$.
+
+\item {\tt umfpack\_*\_numeric}:
+
+ Numerically scales and then factorizes a sparse matrix into
+ $\m{PAQ}$, $\m{PRAQ}$, or $\m{PR}^{-1}\m{AQ}$ into the product $\m{LU}$,
+ where
+ $\m{P}$ and $\m{Q}$ are permutation matrices, $\m{R}$ is a diagonal
+ matrix of scale factors, $\m{L}$ is lower triangular with unit diagonal,
+ and $\m{U}$ is upper triangular. Requires the
+ symbolic ordering and analysis computed by {\tt umfpack\_*\_symbolic}
+ or {\tt umfpack\_*\_qsymbolic}.
+ Returns an opaque {\tt Numeric} object as a
+ {\tt void *} pointer. The object contains the numerical factorization and
+ is used by {\tt umfpack\_*\_solve}. You can factorize a new matrix with a
+ different values (but identical pattern) as the matrix analyzed by
+ {\tt umfpack\_*\_symbolic} or {\tt umfpack\_*\_qsymbolic} by re-using the
+ {\tt Symbolic} object (this feature is available when using UMFPACK in a
+ C or Fortran program, but not in MATLAB).
+ The matrix
+ $\m{U}$ will have zeros on the diagonal if $\m{A}$ is singular; this
+ produces a warning, but the factorization is still valid.
+
+\item {\tt umfpack\_*\_solve}:
+
+ Solves a sparse linear system ($\m{Ax}=\m{b}$, $\m{A}\tr\m{x}=\m{b}$, or
+ systems involving just $\m{L}$ or $\m{U}$), using the numeric factorization
+ computed by {\tt umfpack\_*\_numeric}. Iterative refinement with sparse
+ backward error \cite{ardd:89} is used by default. The matrix $\m{A}$ must
+ be square. If it is singular, then a divide-by-zero will occur, and your
+ solution with contain IEEE Inf's or NaN's in the appropriate places.
+
+\item {\tt umfpack\_*\_free\_symbolic}:
+
+ Frees the {\tt Symbolic} object created by {\tt umfpack\_*\_symbolic}
+ or {\tt umfpack\_*\_qsymbolic}.
+
+\item {\tt umfpack\_*\_free\_numeric}:
+
+ Frees the {\tt Numeric} object created by {\tt umfpack\_*\_numeric}.
+
+\end{itemize}
+
+Be careful not to free a {\tt Symbolic} object with
+{\tt umfpack\_*\_free\_numeric}. Nor should you attempt to free a {\tt Numeric}
+object with {\tt umfpack\_*\_free\_symbolic}.
+Failure to free these objects will lead to memory leaks.
+
+The matrix $\m{A}$ is represented in compressed column form, which is
+identical to the sparse matrix representation used by MATLAB. It consists
+of three or four arrays, where the matrix is {\tt m}-by-{\tt n},
+with {\tt nz} entries. For the {\tt int} version of UMFPACK:
+
+{\footnotesize
+\begin{verbatim}
+ int Ap [n+1] ;
+ int Ai [nz] ;
+ double Ax [nz] ;
+\end{verbatim}
+}
+
+For the {\tt UF\_long} version of UMFPACK:
+
+{\footnotesize
+\begin{verbatim}
+ UF_long Ap [n+1] ;
+ UF_long Ai [nz] ;
+ double Ax [nz] ;
+\end{verbatim}
+}
+
+The complex versions add another array for the imaginary part:
+
+{\footnotesize
+\begin{verbatim}
+ double Az [nz] ;
+\end{verbatim}
+}
+
+Alternatively, if {\tt Az} is {\tt NULL},
+the real part of the $k$th entry is located in
+{\tt Ax[2*k]} and the imaginary part is located in
+{\tt Ax[2*k+1]}, and the {\tt Ax} array is of size {\tt 2*nz}.
+
+All nonzeros are entries, but an entry may be numerically zero. The row indices
+of entries in column {\tt j} are stored in
+ {\tt Ai[Ap[j]} \ldots {\tt Ap[j+1]-1]}.
+The corresponding numerical values are stored in
+ {\tt Ax[Ap[j]} \ldots {\tt Ap[j+1]-1]}.
+The imaginary part, for the complex versions, is stored in
+ {\tt Az[Ap[j]} \ldots {\tt Ap[j+1]-1]}
+ (see above for the packed complex case).
+
+No duplicate row indices may be present, and the row indices in any given
+column must be sorted in ascending order. The first entry {\tt Ap[0]} must be
+zero. The total number of entries in the matrix is thus {\tt nz = Ap[n]}.
+Except for the fact that extra zero entries can be included, there is thus a
+unique compressed column representation of any given matrix $\m{A}$.
+For a more flexible method for providing an input matrix to UMFPACK,
+see Section~\ref{triplet}.
+
+Here is a simple main program, {\tt umfpack\_simple.c}, that illustrates the
+basic usage of UMFPACK. See Section~\ref{Synopsis} for a short description
+of each calling sequence, including a list of options for the first
+argument of {\tt umfpack\_di\_solve}.
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_simple.c via sed
+\end{verbatim}
+}
+
+The {\tt Ap}, {\tt Ai}, and {\tt Ax} arrays represent the matrix
+\[
+\m{A} = \left[
+\begin{array}{rrrrr}
+ 2 & 3 & 0 & 0 & 0 \\
+ 3 & 0 & 4 & 0 & 6 \\
+ 0 & -1 & -3 & 2 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 4 & 2 & 0 & 1 \\
+\end{array}
+\right].
+\]
+and the solution to $\m{Ax}=\m{b}$ is $\m{x} = [1 \, 2 \, 3 \, 4 \, 5]\tr$.
+The program uses default control settings and does not return any statistics
+about the ordering, factorization, or solution ({\tt Control} and {\tt Info}
+are both {\tt (double *) NULL}). It also ignores the status value returned by
+most user-callable UMFPACK routines.
+
+%-------------------------------------------------------------------------------
+\subsection{A note about zero-sized arrays}
+%-------------------------------------------------------------------------------
+
+UMFPACK uses many user-provided arrays of
+size {\tt m} or {\tt n} (the order of the matrix), and of size
+{\tt nz} (the number of nonzeros in a matrix). UMFPACK does not handle
+zero-dimensioned arrays;
+it returns an error code if {\tt m} or {\tt n}
+are zero. However, {\tt nz} can be zero, since all singular matrices are
+handled correctly. If you attempt to {\tt malloc} an array of size {\tt nz}
+= 0, however, {\tt malloc} will return a null pointer which UMFPACK will report
+as a missing argument. If you {\tt malloc} an array of
+size {\tt nz} to pass to UMFPACK, make sure that you handle the {\tt nz} = 0
+case correctly (use a size equal to the maximum of {\tt nz} and 1, or use a
+size of {\tt nz+1}).
+
+%-------------------------------------------------------------------------------
+\subsection{Alternative routines}
+%-------------------------------------------------------------------------------
+
+Three alternative routines are provided that modify UMFPACK's default
+behavior. They are fully described in Section~\ref{Alternative}:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_defaults}:
+
+ Sets the default control parameters in the {\tt Control} array. These can
+ then be modified as desired before passing the array to the other UMFPACK
+ routines. Control parameters are summarized in Section~\ref{control_param}.
+ Three particular parameters deserve special notice.
+ UMFPACK uses relaxed partial pivoting, where a candidate pivot entry is
+ numerically acceptable if its magnitude is greater than or equal to a
+ tolerance parameter times the magnitude of the largest entry in the same
+ column. The parameter {\tt Control [UMFPACK\_PIVOT\_TOLERANCE]} has a
+ default value of 0.1, and is used for the unsymmetric strategy.
+ For complex matrices, a cheap approximation of the absolute value is
+ used for the threshold pivoting test
+ ($|a| \approx |a_{\mbox{real}}|+|a_{\mbox{imag}}|$).
+
+ For the symmetric strategy, a second tolerance is used for diagonal
+ entries: \newline {\tt Control [UMFPACK\_SYM\_PIVOT\_TOLERANCE]}, with
+ a default value of 0.001. The first parameter (with a default of 0.1)
+ is used for any off-diagonal candidate pivot entries.
+
+ These two parameters may be too small for some matrices, particularly for
+ ill-conditioned or poorly scaled ones. With the default pivot tolerances
+ and default iterative refinement,
+ {\tt x = umfpack (A,'}$\backslash${\tt ',b)}
+ is just as accurate as (or more accurate) than
+ {\tt x = A}$\backslash${\tt b}
+ in MATLAB 6.1 for nearly all matrices.
+
+ If {\tt Control [UMFPACK\_PIVOT\_TOLERANCE]} is zero, than any
+ nonzero entry is acceptable as a pivot (this is changed from Version 4.0,
+ which treated a value of 0.0 the same as 1.0). If the symmetric strategy is
+ used, and {\tt Control [UMFPACK\_SYM\_PIVOT\_TOLERANCE]} is zero, then any
+ nonzero entry on the diagonal is accepted as a pivot. Off-diagonal pivoting
+ will still occur if the diagonal entry is exactly zero. The
+ {\tt Control [UMFPACK\_SYM\_PIVOT\_TOLERANCE]} parameter is new to Version
+ 4.1. It is similar in function to the pivot tolerance for left-looking
+ methods (the MATLAB {\tt THRESH} option in {\tt [L,U,P] = lu (A, THRESH)},
+ and the pivot tolerance parameter in SuperLU).
+
+ The parameter {\tt Control [UMFPACK\_STRATEGY]} can be used to bypass
+ UMFPACK's automatic strategy selection. The automatic strategy nearly
+ always selects the best method. When it does not, the different methods
+ nearly always give about the same quality of results. There may be
+ cases where the automatic strategy fails to pick a good strategy. Also,
+ you can save some computing time if you know the right strategy for your
+ set of matrix problems.
+
+\item {\tt umfpack\_*\_qsymbolic}:
+
+ An alternative to {\tt umfpack\_*\_symbolic}. Allows the user to specify
+ his or her own column pre-ordering, rather than using the default COLAMD
+ or AMD pre-orderings. For example, a graph partitioning-based order
+ of $\m{A}\tr\m{A}$ would be suitable for UMFPACK's unsymmetric strategy.
+ A partitioning of $\m{A}+\m{A}\tr$ would be suitable for UMFPACK's
+ symmetric or 2-by-2 strategies.
+
+\item {\tt umfpack\_*\_wsolve}:
+
+ An alternative to {\tt umfpack\_*\_solve} which does not dynamically
+ allocate any memory. Requires the user to pass two additional work
+ arrays.
+
+\end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsection{Matrix manipulation routines}
+\label{triplet}
+%-------------------------------------------------------------------------------
+
+The compressed column data structure is compact, and simplifies the UMFPACK
+routines that operate on the sparse matrix $\m{A}$. However, it can be
+inconvenient for the user to generate. Section~\ref{Manipulate} presents the
+details of routines for manipulating sparse matrices in {\em triplet} form,
+compressed column form, and compressed row form (the transpose of the
+compressed column form). The triplet form of a matrix consists of three or
+four arrays. For the {\tt int} version of UMFPACK:
+
+{\footnotesize
+\begin{verbatim}
+ int Ti [nz] ;
+ int Tj [nz] ;
+ double Tx [nz] ;
+\end{verbatim}
+}
+
+For the {\tt UF\_long} version:
+
+{\footnotesize
+\begin{verbatim}
+ UF_long Ti [nz] ;
+ UF_long Tj [nz] ;
+ double Tx [nz] ;
+\end{verbatim}
+}
+
+The complex versions use another array to hold the imaginary part:
+
+{\footnotesize
+\begin{verbatim}
+ double Tz [nz] ;
+\end{verbatim}
+}
+
+The {\tt k}-th triplet is $(i,j,a_{ij})$, where $i =$ {\tt Ti[k]},
+$j =$ {\tt Tj[k]}, and $a_{ij} =$ {\tt Tx[k]}. For the complex versions,
+{\tt Tx[k]} is the real part of $a_{ij}$ and
+{\tt Tz[k]} is the imaginary part.
+The triplets can be in any
+order in the {\tt Ti}, {\tt Tj}, and {\tt Tx} arrays (and {\tt Tz} for
+the complex versions), and duplicate entries may
+exist.
+If {\tt Tz} is NULL, then the array {\tt Tx} becomes of size {\tt 2*nz},
+and the real and imaginary parts of the
+{\tt k}-th triplet are located in {\tt Tx[2*k]} and {\tt Tx[2*k+1]},
+respectively.
+Any duplicate entries are summed when the triplet form is converted to
+compressed column form. This is a convenient way to create a matrix arising in
+finite-element methods, for example.
+
+Four routines are provided for manipulating sparse matrices:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_triplet\_to\_col}:
+
+ Converts a triplet form of a matrix to compressed column form (ready for
+ input to \newline
+ {\tt umfpack\_*\_symbolic}, {\tt umfpack\_*\_qsymbolic}, and
+ {\tt umfpack\_*\_numeric}). Identical to {\tt A = spconvert(i,j,x)} in
+ MATLAB, except that zero entries are not removed, so that the pattern of
+ entries in the compressed column form of $\m{A}$ are fully under user
+ control. This is important if you want to factorize a new matrix with the
+ {\tt Symbolic} object from a prior matrix with the same pattern as the new
+ one.
+
+\item {\tt umfpack\_*\_col\_to\_triplet}:
+
+ The opposite of {\tt umfpack\_*\_triplet\_to\_col}. Identical to
+ {\tt [i,j,x] = find(A)} in MATLAB, except that numerically zero entries
+ may be included.
+
+\item {\tt umfpack\_*\_transpose}:
+
+ Transposes and optionally permutes a column form matrix \cite{Gustavson78}.
+ Identical to
+ {\tt R = A(P,Q)'} (linear algebraic transpose, using the complex conjugate)
+ or {\tt R = A(P,Q).'} (the array transpose)
+ in MATLAB, except for the presence of numerically zero entries.
+
+ Factorizing $\m{A}\tr$ and then solving $\m{Ax}=\m{b}$ with the transposed
+ factors can sometimes be much faster or much slower than factorizing
+ $\m{A}$. It is highly dependent on your particular matrix.
+
+\item {\tt umfpack\_*\_scale}:
+
+ Applies the row scale factors to a user-provided vector. This is not
+ required to solve the sparse linear system $\m{Ax}=\m{b}$ or
+ $\m{A}\tr\m{x}=\m{b}$, since {\tt umfpack\_*\_solve} applies the scale
+ factors for those systems.
+
+\end{itemize}
+
+It is quite easy to add matrices in triplet form, subtract them, transpose
+them, permute them, construct a submatrix, and multiply a triplet-form matrix
+times a vector. UMFPACK does not provide code for these basic operations,
+however. Refer to the discussion of
+{\tt umfpack\_*\_triplet\_to\_col} in Section~\ref{Manipulate} for more details
+on how to compute these operations in your own code.
+The only primary matrix operation not provided by UMFPACK is the
+multiplication of two sparse matrices \cite{Gustavson78}.
+The CHOLMOD provides many of these matrix operations, which
+can then be used in conjunction with UMFPACK.
+See my web page for details.
+
+%-------------------------------------------------------------------------------
+\subsection{Getting the contents of opaque objects}
+%-------------------------------------------------------------------------------
+
+There are cases where you may wish to do more with the LU factorization
+of a matrix than solve a linear system. The opaque {\tt Symbolic} and
+{\tt Numeric} objects are just that - opaque. You cannot do anything with them
+except to pass them back to subsequent calls to UMFPACK. Three routines
+are provided for copying their contents into user-provided arrays using simpler
+data structures. Four routines are provided for saving and loading the
+{\tt Numeric} and {\tt Symbolic} objects to/from binary files.
+An additional routine is provided that computes the determinant.
+They are fully described in Section~\ref{Get}:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_get\_lunz}:
+
+ Returns the number of nonzeros in $\m{L}$ and $\m{U}$.
+
+\item {\tt umfpack\_*\_get\_numeric}:
+
+ Copies $\m{L}$, $\m{U}$, $\m{P}$, $\m{Q}$, and $\m{R}$
+ from the {\tt Numeric} object
+ into arrays provided by the user. The matrix $\m{L}$ is returned in
+ compressed row form (with the column indices in each row sorted in ascending
+ order). The matrix $\m{U}$ is returned in compressed column form (with
+ sorted columns). There are no explicit zero entries in $\m{L}$ and $\m{U}$,
+ but such entries may exist in the {\tt Numeric} object. The permutations
+ $\m{P}$ and $\m{Q}$ are represented as permutation vectors, where
+ {\tt P[k] = i} means that row {\tt i} of the original matrix is the
+ the {\tt k}-th row of $\m{PAQ}$, and where
+ {\tt Q[k] = j} means that column {\tt j} of the original matrix is the
+ {\tt k}-th column of $\m{PAQ}$. This is identical to how MATLAB uses
+ permutation vectors (type {\tt help colamd} in MATLAB 6.1 or later).
+
+\item {\tt umfpack\_*\_get\_symbolic}:
+
+ Copies the contents of the {\tt Symbolic} object (the initial row and column
+ preordering, supernodal column elimination tree, and information
+ about each frontal matrix) into arrays provided by the user.
+
+\item {\tt umfpack\_*\_get\_determinant}:
+
+ Computes the determinant from the diagonal of $\m{U}$ and the permutations
+ $\m{P}$ and $\m{Q}$. This is mostly of theoretical interest.
+ It is not a good test to determine if your matrix is singular or not.
+
+\item {\tt umfpack\_*\_save\_numeric}:
+
+ Saves a copy of the {\tt Numeric} object to a file, in binary format.
+
+\item {\tt umfpack\_*\_load\_numeric}:
+
+ Creates a {\tt Numeric} object by loading it from a file created
+ by {\tt umfpack\_*\_save\_numeric}.
+
+\item {\tt umfpack\_*\_save\_symbolic}:
+
+ Saves a copy of the {\tt Symbolic} object to a file, in binary format.
+
+\item {\tt umfpack\_*\_load\_symbolic}:
+
+ Creates a {\tt Symbolic} object by loading it from a file created
+ by {\tt umfpack\_*\_save\_symbolic}.
+
+\end{itemize}
+
+UMFPACK itself does not make use of these routines;
+they are provided solely for returning the contents of the opaque
+{\tt Symbolic} and {\tt Numeric} objects to the user, and saving/loading
+them to/from a binary file. None of them do any computation, except for
+{\tt umfpack\_*\_get\_determinant}.
+
+%-------------------------------------------------------------------------------
+\subsection{Reporting routines}
+\label{Reporting}
+%-------------------------------------------------------------------------------
+
+None of the UMFPACK routines discussed so far prints anything, even when an
+error occurs. UMFPACK provides you with nine routines for printing the input
+and output arguments (including the {\tt Control} settings and {\tt Info}
+statistics) of UMFPACK routines discussed above. They are fully described in
+Section~\ref{Report}:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_report\_status}:
+
+ Prints the status (return value) of other {\tt umfpack\_*} routines.
+
+\item {\tt umfpack\_*\_report\_info}:
+
+ Prints the statistics returned in the {\tt Info} array by
+ {\tt umfpack\_*\_*symbolic},
+ {\tt umfpack\_*\_numeric}, and {\tt umfpack\_*\_*solve}.
+
+\item {\tt umfpack\_*\_report\_control}:
+
+ Prints the {\tt Control} settings.
+
+\item {\tt umfpack\_*\_report\_matrix}:
+
+ Verifies and prints a compressed column-form or compressed row-form sparse
+ matrix.
+
+\item {\tt umfpack\_*\_report\_triplet}:
+
+ Verifies and prints a matrix in triplet form.
+
+\item {\tt umfpack\_*\_report\_symbolic}:
+
+ Verifies and prints a {\tt Symbolic} object.
+
+\item {\tt umfpack\_*\_report\_numeric}:
+
+ Verifies and prints a {\tt Numeric} object.
+
+\item {\tt umfpack\_*\_report\_perm}:
+
+ Verifies and prints a permutation vector.
+
+\item {\tt umfpack\_*\_report\_vector}:
+
+ Verifies and prints a real or complex vector.
+
+\end{itemize}
+
+The {\tt umfpack\_*\_report\_*} routines behave slightly differently when
+compiled
+into the C-callable UMFPACK library than when used in the MATLAB mexFunction.
+MATLAB stores its sparse matrices using the same compressed column data
+structure discussed above, where row and column indices of an $m$-by-$n$
+matrix are in the range 0 to $m-1$ or $n-1$, respectively\footnote{Complex
+matrices in MATLAB use the split array form, with one {\tt double} array
+for the real part and another array for the imaginary part. UMFPACK
+supports that format, as well as the packed complex format (new to Version 4.4).}
+It prints them as if they are in the range 1 to $m$ or $n$.
+The UMFPACK mexFunction behaves the same way.
+
+You can control how much the {\tt umfpack\_*\_report\_*} routines print by
+modifying the {\tt Control [UMFPACK\_PRL]} parameter. Its default value is 1.
+Here is a summary of how the routines use this print level parameter:
+
+\begin{itemize}
+\item {\tt umfpack\_*\_report\_status}:
+
+ No output if the print level is 0 or less, even when an error occurs.
+ If 1, then error messages are printed, and nothing is printed if
+ the status is {\tt UMFPACK\_OK}. A warning message is printed if
+ the matrix is singular. If 2 or more, then the status is always
+ printed. If 4 or more, then the UMFPACK Copyright is printed.
+ If 6 or more, then the UMFPACK License is printed. See also the first page
+ of this User Guide for the Copyright and License.
+
+\item {\tt umfpack\_*\_report\_control}:
+
+ No output if the print level is 1 or less. If 2 or more, all of
+ {\tt Control} is printed.
+
+\item {\tt umfpack\_*\_report\_info}:
+
+ No output if the print level is 1 or less. If 2 or more, all of
+ {\tt Info} is printed.
+
+\item all other {\tt umfpack\_*\_report\_*} routines:
+
+ If the print level is 2 or less, then these routines return silently without
+ checking their inputs. If 3 or more, the inputs are fully verified and a
+ short status summary is printed. If 4, then the first few entries of the
+ input arguments are printed. If 5, then all of the input arguments are
+ printed.
+
+\end{itemize}
+
+This print level parameter has an additional effect on the MATLAB mexFunction.
+If zero, then no warnings of singular or nearly singular matrices are
+printed (similar to the MATLAB commands
+{\tt warning off MATLAB:singularMatrix} and
+{\tt warning off MATLAB:nearlySingularMatrix}).
+
+%-------------------------------------------------------------------------------
+\subsection{Utility routines}
+%-------------------------------------------------------------------------------
+
+UMFPACK v4.0 included a routine that returns the time used by the process,
+{\tt umfpack\_timer}. The routine uses either {\tt getrusage} (which is
+preferred), or the ANSI C {\tt clock} routine if that is not available.
+It is fully described in Section~\ref{Utility}. It is still available in
+UMFPACK v4.1 and following, but not used internally.
+Two new timing routines are provided in UMFPACK Version 4.1 and following,
+{\tt umfpack\_tic} and {\tt umfpack\_toc}. They use POSIX-compliant
+{\tt sysconf} and {\tt times} routines to find both the CPU time
+and wallclock time.
+These three routines are the only user-callable
+routine that is identical in all four {\tt int}/{\tt UF\_long}, real/complex
+versions (there is no {\tt umfpack\_di\_timer} routine, for example).
+
+%-------------------------------------------------------------------------------
+\subsection{Control parameters}
+\label{control_param}
+%-------------------------------------------------------------------------------
+
+UMFPACK uses an optional {\tt double} array (currently of size 20)
+to modify its control parameters. If you pass {\tt (double *) NULL} instead
+of a {\tt Control} array, then defaults are used. These defaults provide
+nearly optimal performance (both speed, memory usage, and numerical accuracy)
+for a wide range of matrices from real applications.
+
+This array will almost certainly grow in size in future releases,
+so be sure to dimension your {\tt Control} array to be of size
+{\tt UMFPACK\_CONTROL}. That constant is currently defined to be 20,
+but may increase in future versions, since all 20 entries are in use.
+
+The contents of this array may be modified by the user
+(see {\tt umfpack\_*\_defaults}). Each
+user-callable routine includes a complete description of how each control
+setting modifies its behavior. Table~\ref{control} summarizes the entire
+contents of the {\tt Control} array.
+Note that ANSI C uses 0-based indexing, while MATLAB uses 1-based
+indexing. Thus, {\tt Control(1)} in MATLAB is the same as
+{\tt Control[0]} or {\tt Control[UMFPACK\_PRL]} in ANSI C.
+
+\begin{table}
+\caption{UMFPACK Control parameters}
+\label{control}
+{\footnotesize
+\begin{tabular}{llll}
+\hline
+
+MATLAB & ANSI C & default & description \\
+\hline
+{\tt Control(1)} & {\tt Control[UMFPACK\_PRL]} & 1 & printing level \\
+{\tt Control(2)} & {\tt Control[UMFPACK\_DENSE\_ROW]} & 0.2 & dense row parameter \\
+{\tt Control(3)} & {\tt Control[UMFPACK\_DENSE\_COL]} & 0.2 & dense column parameter \\
+{\tt Control(4)} & {\tt Control[UMFPACK\_PIVOT\_TOLERANCE]} & 0.1 & partial pivoting tolerance \\
+{\tt Control(5)} & {\tt Control[UMFPACK\_BLOCK\_SIZE]} & 32 & BLAS block size \\
+{\tt Control(6)} & {\tt Control[UMFPACK\_STRATEGY]} & 0 (auto) & select strategy \\
+{\tt Control(7)} & {\tt Control[UMFPACK\_ALLOC\_INIT]} & 0.7 & initial memory allocation \\
+{\tt Control(8)} & {\tt Control[UMFPACK\_IRSTEP]} & 2 & max iter. refinement steps \\
+{\tt Control(13)} & {\tt Control[UMFPACK\_2BY2\_TOLERANCE]} & 0.01 & defines ``large'' entries \\
+{\tt Control(14)} & {\tt Control[UMFPACK\_FIXQ]} & 0 (auto) & fix or modify Q \\
+{\tt Control(15)} & {\tt Control[UMFPACK\_AMD\_DENSE]} & 10 & AMD dense row/column parameter \\
+{\tt Control(16)} & {\tt Control[UMFPACK\_SYM\_PIVOT\_TOLERANCE]} & 0.001 & for diagonal entries \\
+{\tt Control(17)} & {\tt Control[UMFPACK\_SCALE]} & 1 (sum) & row scaling (none, sum, or max) \\
+{\tt Control(18)} & {\tt Control[UMFPACK\_FRONT\_ALLOC\_INIT]} & 0.5 & frontal matrix allocation ratio \\
+{\tt Control(19)} & {\tt Control[UMFPACK\_DROPTOL]} & 0 & drop tolerance \\
+{\tt Control(20)} & {\tt Control[UMFPACK\_AGGRESSIVE]} & 1 (yes) & aggressive absorption \\
+ & & & in AMD and COLAMD \\
+%
+\hline
+\multicolumn{4}{l}{Can only be changed at compile time:} \\
+{\tt Control(9)} & {\tt Control[UMFPACK\_COMPILED\_WITH\_BLAS]} & - & true if BLAS is used \\
+{\tt Control(10)} & {\tt Control[UMFPACK\_COMPILED\_FOR\_MATLAB]} & - & true for mexFunction \\
+{\tt Control(11)} & {\tt Control[UMFPACK\_COMPILED\_WITH\_GETRUSAGE]} & - & 1 if {\tt getrusage} used \\
+{\tt Control(12)} & {\tt Control[UMFPACK\_COMPILED\_IN\_DEBUG\_MODE]} & - & true if debug mode enabled \\
+\hline
+\end{tabular}
+}
+\end{table}
+
+Let $\alpha_r = ${\tt Control [UMFPACK\_DENSE\_ROW]},
+ $\alpha_c = ${\tt Control [UMFPACK\_DENSE\_COL]}, and
+ $\alpha = ${\tt Control [UMFPACK\_AMD\_DENSE]}.
+Suppose the submatrix $\m{S}$, obtained after eliminating pivots with
+zero Markowitz cost, is $m$-by-$n$.
+Then a row is considered ``dense'' if it has more than
+$\max (16, 16 \alpha_r \sqrt{n})$ entries.
+A column is considered ``dense'' if it has more than
+$\max (16, 16 \alpha_c \sqrt{m})$ entries.
+These rows and columns are treated different in COLAMD and during numerical
+factorization. In COLAMD, dense columns are placed last in their natural
+order, and dense rows are ignored. During numerical factorization, dense
+rows are stored differently.
+In AMD, a row/column of the square matrix $\m{S}+\m{S}\tr$ is
+considered ``dense'' if it has more than $\max (16, \alpha \sqrt{n})$ entries.
+These rows/columns are placed last in AMD's output ordering.
+For more details on the control parameters, refer to the documentation of
+{\tt umfpack\_*\_qsymbolic}, {\tt umfpack\_*\_numeric}, {\tt umfpack\_*\_solve},
+and the {\tt umfpack\_*\_report\_*} routines,
+in Sections~\ref{Primary}~through~\ref{Report}, below.
+
+%-------------------------------------------------------------------------------
+\subsection{Error codes}
+\label{error_codes}
+%-------------------------------------------------------------------------------
+
+Many of the routines return a {\tt status} value.
+This is also returned as the first entry in the {\tt Info} array, for
+those routines with that argument. The following list summarizes
+all of the error codes in UMFPACK. Each error code is given a
+specific name in the {\tt umfpack.h} include file, so you can use
+those constants instead of hard-coded values in your program.
+Future versions may report additional error codes.
+
+A value of zero means everything was successful, and the matrix is
+non-singular. A value greater than zero means the routine was successful,
+but a warning occurred.
+A negative value means the routine was not successful.
+In this case, no {\tt Symbolic} or {\tt Numeric} object was created.
+
+\begin{itemize}
+\item {\tt UMFPACK\_OK}, (0): UMFPACK was successful.
+
+\item {\tt UMFPACK\_WARNING\_singular\_matrix}, (1): Matrix is singular.
+ There are exact zeros on the diagonal of $\m{U}$.
+
+\item {\tt UMFPACK\_WARNING\_determinant\_underflow}, (2):
+ The determinant is nonzero, but smaller in magnitude than
+ the smallest positive floating-point number.
+
+\item {\tt UMFPACK\_WARNING\_determinant\_overflow}, (3):
+ The determinant is larger in magnitude than
+ the largest positive floating-point number (IEEE Inf).
+
+\item {\tt UMFPACK\_ERROR\_out\_of\_memory}, (-1): Not enough memory.
+ The ANSI C {\tt malloc} or {\tt realloc} routine failed.
+
+\item {\tt UMFPACK\_ERROR\_invalid\_Numeric\_object}, (-3):
+ Routines that take a {\tt Numeric} object as input (or load it
+ from a file) check this object and return this error code if it is
+ invalid. This can be caused by a memory leak or overrun in your
+ program, which can overwrite part of the Numeric object. It can also
+ be caused by passing a Symbolic object by mistake, or some other pointer.
+ If you try to factorize a matrix using one version of UMFPACK and
+ then use the factors in another version, this error code will trigger as
+ well. You cannot factor your matrix using
+ version 4.0 and then solve with version 4.1, for example.\footnote{
+ Exception: v4.3, v4.3.1, and v4.4 use identical data structures
+ for the {\tt Numeric} and {\tt Symbolic} objects}.
+ You cannot use different precisions of the same version
+ (real and complex, for example).
+ It is possible for the {\tt Numeric} object to be corrupted by your
+ program in subtle ways that are not detectable by this quick check.
+ In this case, you may see an
+ {\tt UMFPACK\_ERROR\_different\_pattern} error code, or even an
+ {\tt UMFPACK\_ERROR\_internal\_error}.
+
+\item {\tt UMFPACK\_ERROR\_invalid\_Symbolic\_object}, (-4):
+ Routines that take a {\tt Symbolic} object as input (or load it
+ from a file) check this object and return this error code if it is
+ invalid. The causes of this error are analogous to the
+ {\tt UMFPACK\_ERROR\_invalid\_Numeric\_object} error described above.
+
+\item {\tt UMFPACK\_ERROR\_argument\_missing}, (-5):
+ Some arguments of some are optional (you can pass a {\tt NULL} pointer
+ instead of an array). This error code occurs if you pass a {\tt NULL}
+ pointer when that argument is required to be present.
+
+\item {\tt UMFPACK\_ERROR\_n\_nonpositive} (-6):
+ The number of rows or columns of the matrix must be greater than zero.
+
+\item {\tt UMFPACK\_ERROR\_invalid\_matrix} (-8):
+ The matrix is invalid. For the column-oriented input, this error
+ code will occur if the contents of {\tt Ap} and/or {\tt Ai} are invalid.
+
+ {\tt Ap} is an integer array of size {\tt n\_col+1}.
+ On input, it holds the
+ ``pointers'' for the column form of the sparse matrix $\m{A}$.
+ Column {\tt j} of
+ the matrix A is held in {\tt Ai [(Ap [j])} \ldots {\tt (Ap [j+1]-1)]}.
+ The first entry, {\tt Ap [0]}, must be zero,
+ and {\tt Ap [j]} $\le$ {\tt Ap [j+1]} must hold for all
+ {\tt j} in the range 0 to {\tt n\_col-1}.
+ The value {\tt nz = Ap [n\_col]} is thus the
+ total number of entries in the pattern of the matrix A.
+ {\tt nz} must be greater than or equal to zero.
+
+ The nonzero pattern (row indices) for column {\tt j} is stored in
+ {\tt Ai [(Ap [j])} \ldots {\tt (Ap [j+1]-1)]}. The row indices in a given
+ column {\tt j}
+ must be in ascending order, and no duplicate row indices may be present.
+ Row indices must be in the range 0 to {\tt n\_row-1}
+ (the matrix is 0-based).
+
+ Some routines take a triplet-form input, with arguments
+ {\tt nz}, {\tt Ti}, and {\tt Tj}. This error code is returned
+ if {\tt nz} is less than zero,
+ if any row index in {\tt Ti} is outside the range 0 to {\tt n\_col-1}, or
+ if any column index in {\tt Tj} is outside the range 0 to {\tt n\_row-1}.
+
+\item {\tt UMFPACK\_ERROR\_different\_pattern}, (-11):
+ The most common cause of this error is that the pattern of the
+ matrix has changed between the symbolic and numeric factorization.
+ It can also occur if the {\tt Numeric} or {\tt Symbolic} object has
+ been subtly corrupted by your program.
+
+\item {\tt UMFPACK\_ERROR\_invalid\_system}, (-13):
+ The {\tt sys} argument provided to one of the solve routines is invalid.
+
+\item {\tt UMFPACK\_ERROR\_invalid\_permutation}, (-15):
+ The permutation vector provided as input is invalid.
+
+\item {\tt UMFPACK\_ERROR\_file\_IO}, (-17):
+ This error code is returned by the routines that save and load
+ the {\tt Numeric} or {\tt Symbolic} objects to/from a file, if a
+ file I/O error has occurred. The file may not exist or may not be readable,
+ you may be trying to create a file that you don't have permission to create,
+ or you may be out of disk space. The file you are trying to read might
+ be the wrong one, and an earlier end-of-file condition would then result
+ in this error.
+
+\item {\tt UMFPACK\_ERROR\_internal\_error}, (-911):
+ An internal error has occurred, of unknown cause. This is either a bug
+ in UMFPACK, or the result of a memory overrun from your program.
+ Try modifying the file {\tt AMD/Include/amd\_internal.h} and adding
+ the statement {\tt \#undef NDEBUG}, to enable the debugging mode.
+ Recompile UMFPACK and rerun your program.
+ A failed assertion might occur which
+ can give you a better indication as to what is going wrong. Be aware that
+ UMFPACK will be extraordinarily slow when running in debug mode.
+ If all else fails, contact the developer (davis at cise.ufl.edu) with
+ as many details as possible.
+
+\end{itemize}
+
+%-------------------------------------------------------------------------------
+\subsection{Larger examples}
+%-------------------------------------------------------------------------------
+
+Full examples of all user-callable UMFPACK routines
+are available in four stand-alone C main programs, {\tt umfpack\_*\_demo.c}.
+Another example is
+the UMFPACK mexFunction, {\tt umfpackmex.c}. The mexFunction accesses only the
+user-callable C interface to UMFPACK. The only features that it does not use
+are the support for the triplet form (MATLAB's sparse arrays are already in the
+compressed column form) and the ability to reuse the {\tt Symbolic} object to
+numerically factorize a matrix whose pattern is the same as a prior matrix
+analyzed by {\tt umfpack\_*\_symbolic} or {\tt umfpack\_*\_qsymbolic}. The
+latter is an important feature, but the mexFunction does not return its opaque
+{\tt Symbolic} and {\tt Numeric} objects to MATLAB. Instead, it gets the
+contents of these objects after extracting them via the {\tt umfpack\_*\_get\_*}
+routines, and returns them as MATLAB sparse matrices.
+
+The {\tt umf4.c} program for reading matrices in Harwell/Boeing format
+\cite{DuffGrimesLewis87b} is provided. It requires three Fortran 77 programs
+({\tt readhb.f}, {\tt readhb\_nozeros.f}, and {\tt readhb\_size.f})
+for reading in the sample Harwell/Boeing files in the {\tt UMFPACK/Demo/HB}
+directory. More matrices are available at
+http://www.cise.ufl.edu/research/sparse/matrices.
+Type {\tt make hb} in the {\tt UMFPACK/Demo/HB} directory
+to compile and run this demo. This program was used for the experimental
+results in \cite{Davis03}.
+
+%-------------------------------------------------------------------------------
+\section{Synopsis of C-callable routines}
+\label{Synopsis}
+%-------------------------------------------------------------------------------
+
+Each subsection, below, summarizes the input variables, output variables, return
+values, and calling sequences of the routines in one category. Variables with
+the same name as those already listed in a prior category have the same size
+and type.
+
+The real, {\tt UF\_long} integer {\tt umfpack\_dl\_*} routines are
+identical to the real, {\tt int} routines, except that {\tt \_di\_} is replaced
+with {\tt \_dl\_} in the name, and all {\tt int} arguments become
+{\tt UF\_long}.
+Similarly, the complex, {\tt UF\_long} integer {\tt umfpack\_zl\_*} routines are
+identical to the complex, {\tt int} routines, except that {\tt \_zi\_} is
+replaced
+with {\tt \_zl\_} in the name, and all {\tt int} arguments become
+{\tt UF\_long}.
+Only the real and complex {\tt int} versions are listed in the synopsis below.
+
+The matrix $\m{A}$ is {\tt m}-by-{\tt n} with {\tt nz} entries.
+
+The {\tt sys} argument of {\tt umfpack\_*\_solve}
+is an integer in the range 0 to 14 which defines which linear system is
+to be solved.
+\footnote{Integer values for {\tt sys} are used instead of strings (as in LINPACK
+and LAPACK) to avoid C-to-Fortran portability issues.}
+Valid values are listed in Table~\ref{sys}.
+The notation $\m{A}\he$ refers to the matrix transpose, which is the
+complex conjugate transpose for complex matrices ({\tt A'} in MATLAB).
+The array transpose is $\m{A}\tr$, which is {\tt A.'} in MATLAB.
+
+\begin{table}
+\begin{center}
+\caption{UMFPACK {\tt sys} parameter}
+\label{sys}
+{\footnotesize
+\begin{tabular}{ll|l}
+\hline
+Value & & system \\
+\hline
+& & \\
+{\tt UMFPACK\_A} & (0) & $\m{Ax}=\m{b}$ \\
+{\tt UMFPACK\_At} & (1) & $\m{A}\he\m{x}=\m{b}$ \\
+{\tt UMFPACK\_Aat} & (2) & $\m{A}\tr\m{x}=\m{b}$ \\
+& & \\
+\hline
+& & \\
+{\tt UMFPACK\_Pt\_L} & (3) & $\m{P}\tr\m{Lx}=\m{b}$ \\
+{\tt UMFPACK\_L} & (4) & $\m{Lx}=\m{b}$ \\
+{\tt UMFPACK\_Lt\_P} & (5) & $\m{L}\he\m{Px}=\m{b}$ \\
+{\tt UMFPACK\_Lat\_P} & (6) & $\m{L}\tr\m{Px}=\m{b}$ \\
+{\tt UMFPACK\_Lt} & (7) & $\m{L}\he\m{x}=\m{b}$ \\
+{\tt UMFPACK\_Lat} & (8) & $\m{L}\tr\m{x}=\m{b}$ \\
+& & \\
+\hline
+& & \\
+{\tt UMFPACK\_U\_Qt} & (9) & $\m{UQ}\tr\m{x}=\m{b}$ \\
+{\tt UMFPACK\_U} & (10) & $\m{Ux}=\m{b}$ \\
+{\tt UMFPACK\_Q\_Ut} & (11) & $\m{QU}\he\m{x}=\m{b}$ \\
+{\tt UMFPACK\_Q\_Uat} & (12) & $\m{QU}\tr\m{x}=\m{b}$ \\
+{\tt UMFPACK\_Ut} & (13) & $\m{U}\he\m{x}=\m{b}$ \\
+{\tt UMFPACK\_Uat} & (14) & $\m{U}\tr\m{x}=\m{b}$ \\
+& & \\
+\hline
+\end{tabular}
+}
+\end{center}
+\end{table}
+
+%-------------------------------------------------------------------------------
+\subsection{Primary routines: real/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+#include "umfpack.h"
+int status, sys, n, m, nz, Ap [n+1], Ai [nz] ;
+double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], Ax [nz], X [n], B [n] ;
+void *Symbolic, *Numeric ;
+
+status = umfpack_di_symbolic (m, n, Ap, Ai, Ax, &Symbolic, Control, Info) ;
+status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info) ;
+status = umfpack_di_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ;
+umfpack_di_free_symbolic (&Symbolic) ;
+umfpack_di_free_numeric (&Numeric) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{Alternative routines: real/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+int Qinit [n], Wi [n] ;
+double W [5*n] ;
+
+umfpack_di_defaults (Control) ;
+status = umfpack_di_qsymbolic (m, n, Ap, Ai, Ax, Qinit, &Symbolic, Control, Info) ;
+status = umfpack_di_wsolve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info, Wi, W) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{Matrix manipulation routines: real/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+int Ti [nz], Tj [nz], P [m], Q [n], Rp [m+1], Ri [nz], Map [nz] ;
+double Tx [nz], Rx [nz], Y [m], Z [m] ;
+
+status = umfpack_di_col_to_triplet (n, Ap, Tj) ;
+status = umfpack_di_triplet_to_col (m, n, nz, Ti, Tj, Tx, Ap, Ai, Ax, Map) ;
+status = umfpack_di_transpose (m, n, Ap, Ai, Ax, P, Q, Rp, Ri, Rx) ;
+status = umfpack_di_scale (Y, Z, Numeric) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{Getting the contents of opaque objects: real/{\tt int}}
+%-------------------------------------------------------------------------------
+
+The {\tt filename} string should be large enough to hold the name of a file.
+
+{\footnotesize
+\begin{verbatim}
+int lnz, unz, Lp [m+1], Lj [lnz], Up [n+1], Ui [unz], do_recip ;
+double Lx [lnz], Ux [unz], D [min (m,n)], Rs [m], Mx [1], Ex [1] ;
+int nfr, nchains, P1 [m], Q1 [n], Front_npivcol [n+1], Front_parent [n+1], Front_1strow [n+1],
+ Front_leftmostdesc [n+1], Chain_start [n+1], Chain_maxrows [n+1], Chain_maxcols [n+1] ;
+char filename [100] ;
+
+status = umfpack_di_get_lunz (&lnz, &unz, &m, &n, &nz_udiag, Numeric) ;
+status = umfpack_di_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, D,
+ &do_recip, Rs, Numeric) ;
+status = umfpack_di_get_symbolic (&m, &n, &n1, &nz, &nfr, &nchains, P1, Q1,
+ Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc,
+ Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ;
+status = umfpack_di_load_numeric (&Numeric, filename) ;
+status = umfpack_di_save_numeric (Numeric, filename) ;
+status = umfpack_di_load_symbolic (&Symbolic, filename) ;
+status = umfpack_di_save_symbolic (Symbolic, filename) ;
+status = umfapck_di_get_determinant (Mx, Ex, Numeric, Info) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{Reporting routines: real/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+
+umfpack_di_report_status (Control, status) ;
+umfpack_di_report_control (Control) ;
+umfpack_di_report_info (Control, Info) ;
+status = umfpack_di_report_matrix (m, n, Ap, Ai, Ax, 1, Control) ;
+status = umfpack_di_report_matrix (m, n, Rp, Ri, Rx, 0, Control) ;
+status = umfpack_di_report_numeric (Numeric, Control) ;
+status = umfpack_di_report_perm (m, P, Control) ;
+status = umfpack_di_report_perm (n, Q, Control) ;
+status = umfpack_di_report_symbolic (Symbolic, Control) ;
+status = umfpack_di_report_triplet (m, n, nz, Ti, Tj, Tx, Control) ;
+status = umfpack_di_report_vector (n, X, Control) ;
+\end{verbatim}
+}
+
+
+
+
+
+
+%-------------------------------------------------------------------------------
+\subsection{Primary routines: complex/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+double Az [nz], Xx [n], Xz [n], Bx [n], Bz [n] ;
+
+status = umfpack_zi_symbolic (m, n, Ap, Ai, Ax, Az, &Symbolic, Control, Info) ;
+status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric, Control, Info) ;
+status = umfpack_zi_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info) ;
+umfpack_zi_free_symbolic (&Symbolic) ;
+umfpack_zi_free_numeric (&Numeric) ;
+\end{verbatim}
+}
+
+The arrays {\tt Ax}, {\tt Bx}, and {\tt Xx} double in size if
+any imaginary argument ({\tt Az}, {\tt Xz}, or {\tt Bz}) is {\tt NULL}.
+
+%-------------------------------------------------------------------------------
+\subsection{Alternative routines: complex/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+double Wz [10*n] ;
+
+umfpack_zi_defaults (Control) ;
+status = umfpack_zi_qsymbolic (m, n, Ap, Ai, Ax, Az, Qinit, &Symbolic, Control, Info) ;
+status = umfpack_zi_wsolve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric, Control, Info, Wi, Wz) ;
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{Matrix manipulation routines: complex/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+double Tz [nz], Rz [nz], Yx [m], Yz [m], Zx [m], Zz [m] ;
+
+status = umfpack_zi_col_to_triplet (n, Ap, Tj) ;
+status = umfpack_zi_triplet_to_col (m, n, nz, Ti, Tj, Tx, Tz, Ap, Ai, Ax, Az, Map) ;
+status = umfpack_zi_transpose (m, n, Ap, Ai, Ax, Az, P, Q, Rp, Ri, Rx, Rz, 1) ;
+status = umfpack_zi_transpose (m, n, Ap, Ai, Ax, Az, P, Q, Rp, Ri, Rx, Rz, 0) ;
+status = umfpack_zi_scale (Yx, Yz, Zx, Zz, Numeric) ;
+\end{verbatim}
+}
+
+The arrays {\tt Tx}, {\tt Rx}, {\tt Yx}, and {\tt Zx} double in size if
+any imaginary argument ({\tt Tz}, {\tt Rz}, {\tt Yz}, or {\tt Zz}) is {\tt NULL}.
+
+%-------------------------------------------------------------------------------
+\subsection{Getting the contents of opaque objects: complex/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+double Lz [lnz], Uz [unz], Dx [min (m,n)], Dz [min (m,n)], Mz [1] ;
+
+status = umfpack_zi_get_lunz (&lnz, &unz, &m, &n, &nz_udiag, Numeric) ;
+status = umfpack_zi_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q, Dx, Dz,
+ &do_recip, Rs, Numeric) ;
+status = umfpack_zi_get_symbolic (&m, &n, &n1, &nz, &nfr, &nchains, P1, Q1,
+ Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc,
+ Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ;
+status = umfpack_zi_load_numeric (&Numeric, filename) ;
+status = umfpack_zi_save_numeric (Numeric, filename) ;
+status = umfpack_zi_load_symbolic (&Symbolic, filename) ;
+status = umfpack_zi_save_symbolic (Symbolic, filename) ;
+status = umfapck_zi_get_determinant (Mx, Mz, Ex, Numeric, Info) ;
+\end{verbatim}
+}
+
+The arrays {\tt Lx}, {\tt Ux}, {\tt Dx}, and {\tt Mx} double in size if
+any imaginary argument ({\tt Lz}, {\tt Uz}, {\tt Dz}, or {\tt Mz}) is {\tt NULL}.
+
+%-------------------------------------------------------------------------------
+\subsection{Reporting routines: complex/{\tt int}}
+%-------------------------------------------------------------------------------
+
+{\footnotesize
+\begin{verbatim}
+
+umfpack_zi_report_status (Control, status) ;
+umfpack_zi_report_control (Control) ;
+umfpack_zi_report_info (Control, Info) ;
+status = umfpack_zi_report_matrix (m, n, Ap, Ai, Ax, Az, 1, Control) ;
+status = umfpack_zi_report_matrix (m, n, Rp, Ri, Rx, Rz, 0, Control) ;
+status = umfpack_zi_report_numeric (Numeric, Control) ;
+status = umfpack_zi_report_perm (m, P, Control) ;
+status = umfpack_zi_report_perm (n, Q, Control) ;
+status = umfpack_zi_report_symbolic (Symbolic, Control) ;
+status = umfpack_zi_report_triplet (m, n, nz, Ti, Tj, Tx, Tz, Control) ;
+status = umfpack_zi_report_vector (n, Xx, Xz, Control) ;
+\end{verbatim}
+}
+
+The arrays {\tt Ax}, {\tt Rx}, {\tt Tx}, and {\tt Xx} double in size if
+any imaginary argument ({\tt Az}, {\tt Rz}, {\tt Tz}, or {\tt Xz}) is {\tt NULL}.
+
+
+
+
+%-------------------------------------------------------------------------------
+\subsection{Utility routines}
+%-------------------------------------------------------------------------------
+
+These routines are the same in all four versions of UMFPACK.
+
+{\footnotesize
+\begin{verbatim}
+double t, s [2] ;
+
+t = umfpack_timer ( ) ;
+umfpack_tic (s) ;
+umfpack_toc (s) ;
+
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\subsection{AMD ordering routines}
+%-------------------------------------------------------------------------------
+
+UMFPACK makes use of the AMD ordering package for its symmetric ordering
+strategy. You may also use these four user-callable routines in your own C
+programs. You need to include the {\tt amd.h} file only if you make direct
+calls to the AMD routines themselves. The {\tt int} versions are summarized
+below; {\tt UF\_long} versions are also available. Refer to the AMD User Guide
+for more information, or to the file {\tt amd.h} which documents these routines.
+
+{\footnotesize
+\begin{verbatim}
+#include "amd.h"
+double amd_control [AMD_CONTROL], amd_info [AMD_INFO] ;
+
+amd_defaults (amd_control) ;
+status = amd_order (n, Ap, Ai, P, amd_control, amd_info) ;
+amd_control (amd_control) ;
+amd_info (amd_info) ;
+
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\section{Using UMFPACK in a Fortran program}
+%-------------------------------------------------------------------------------
+
+UMFPACK includes a basic Fortran 77 interface to some of the C-callable
+UMFPACK routines.
+Since interfacing C and Fortran programs is not portable, this interface might
+not work with all C and Fortran compilers. Refer to Section~\ref{Install} for
+more details. The following Fortran routines are provided.
+The list includes the C-callable routines that the Fortran interface
+routine calls. Refer to the corresponding C routines in Section~\ref{C} for
+more details on what the Fortran routine does.
+
+\begin{itemize}
+\item {\tt umf4def}: sets the default control parameters
+ ({\tt umfpack\_di\_defaults}).
+
+\item {\tt umf4sym}: pre-ordering and symbolic factorization
+ ({\tt umfpack\_di\_symbolic}).
+
+\item {\tt umf4num}: numeric factorization
+ ({\tt umfpack\_di\_numeric}).
+
+\item {\tt umf4solr}: solve a linear system with iterative refinement
+ ({\tt umfpack\_di\_solve}).
+
+\item {\tt umf4sol}: solve a linear system without iterative refinement
+ ({\tt umfpack\_di\_solve}). Sets {\tt Control [UMFPACK\_IRSTEP]}
+ to zero, and does not require the matrix $\m{A}$.
+
+\item {\tt umf4scal}: scales a vector using UMFPACK's scale factors
+ ({\tt umfpack\_di\_scale}).
+
+\item {\tt umf4fnum}: free the {\tt Numeric} object
+ ({\tt umfpack\_di\_free\_numeric}).
+
+\item {\tt umf4fsym}: free the {\tt Symbolic} object
+ ({\tt umfpack\_di\_free\_symbolic}).
+
+\item {\tt umf4pcon}: prints the control parameters
+ ({\tt umfpack\_di\_report\_control}).
+
+\item {\tt umf4pinf}: print statistics
+ ({\tt umfpack\_di\_report\_info}).
+
+\item {\tt umf4snum}: save the {\tt Numeric} object to a file
+ ({\tt umfpack\_di\_save\_numeric}).
+
+\item {\tt umf4ssym}: save the {\tt Symbolic} object to a file
+ ({\tt umfpack\_di\_save\_symbolic}).
+
+\item {\tt umf4lnum}: load the {\tt Numeric} object from a file
+ ({\tt umfpack\_di\_load\_numeric}).
+
+\item {\tt umf4lsym}: load the {\tt Symbolic} object from a file
+ ({\tt umfpack\_di\_load\_symbolic}).
+\end{itemize}
+
+The matrix $\m{A}$ is passed to UMFPACK in compressed column form, with 0-based
+indices. In Fortran, for an {\tt m}-by-{\tt n} matrix $\m{A}$ with {\tt nz}
+entries, the row indices of the first column (column 1) are in
+{\tt Ai (Ap(1)+1} \ldots {\tt Ap(2))}, with values in
+{\tt Ax (Ap(1)+1} \ldots {\tt Ap(2))}. The last column (column {\tt n}) is in
+{\tt Ai (Ap(n)+1} \ldots {\tt Ap(n+1))} and
+{\tt Ax (Ap(n)+1} \ldots {\tt Ap(n+1))}.
+The number of entries in the matrix is thus {\tt nz = Ap (n+1)}.
+The row indices in {\tt Ai} are in the range 0 to {\tt m}-1. They must be
+sorted, with no duplicate entries allowed. None of the UMFPACK routines
+modify the input matrix $\m{A}$.
+The following definitions apply for the Fortran routines:
+
+{\footnotesize
+\begin{verbatim}
+ integer m, n, Ap (n+1), Ai (nz), symbolic, numeric, filenum, status
+ double precision Ax (nz), control (20), info (90), x (n), b (n)
+\end{verbatim}
+}
+
+UMFPACK's status is returned in either a {\tt status} argument, or in
+{\tt info (1)}.
+It is zero if UMFPACK was successful, 1 if the matrix is singular (this is a
+warning, not an error), and negative if an error occurred.
+Section~\ref{error_codes} summarizes the possible values of {\tt status}
+and {\tt info (1)}.
+See Table~\ref{sys} for a list of the values of the {\tt sys} argument.
+See Table~\ref{control} for a list of the control parameters (the
+Fortran usage is the same as the MATLAB usage for this array).
+
+For the {\tt Numeric} and {\tt Symbolic} handles, it is probably safe to
+assume that a Fortran {\tt integer} is sufficient to store a C pointer. If
+that does not work, try defining {\tt numeric} and {\tt symbolic} in your
+Fortran program as integer arrays of size 2. You will need to define them
+as {\tt integer*8} if you compile UMFPACK in the 64-bit mode.
+
+To avoid passing strings between C and Fortran in the load/save routines,
+a file number is passed instead, and the C interface constructs a file name
+(if {\tt filenum} is 42, the {\tt Numeric} file name is {\tt n42.umf}, and
+the {\tt Symbolic} file name is {\tt s42.umf}).
+
+The following is a summary of the calling sequence of each Fortran
+interface routine. An example of their use is in the {\tt Demo/umf4hb.f}
+file. That routine also includes an example of how to convert a 1-based
+sparse matrix into 0-based form. For more details on the arguments of each
+routine, refer to the arguments of the same name in the corresponding
+C-callable routine, in Sections~\ref{Primary}~through~\ref{Utility}.
+The only exception is the {\tt control} argument of {\tt umf4sol},
+which sets {\tt control (8)} to zero to disable iterative refinement.
+Note that the solve routines do not overwrite {\tt b} with the solution,
+but return their solution in a different array, {\tt x}.
+
+{\footnotesize
+\begin{verbatim}
+ call umf4def (control)
+ call umf4sym (m, n, Ap, Ai, Ax, symbolic, control, info)
+ call umf4num (Ap, Ai, Ax, symbolic, numeric, control, info)
+ call umf4solr (sys, Ap, Ai, Ax, x, b, numeric, control, info)
+ call umf4sol (sys, x, b, numeric, control, info)
+ call umf4scal (x, b, numeric, status)
+ call umf4fnum (numeric)
+ call umf4fsym (symbolic)
+ call umf4pcon (control)
+ call umf4pinf (control)
+ call umf4snum (numeric, filenum, status)
+ call umf4ssym (symbolic, filenum, status)
+ call umf4lnum (numeric, filenum, status)
+ call umf4lsym (symbolic, filenum, status)
+\end{verbatim}
+}
+
+Access to the complex routines in UMFPACK is provided by the interface
+routines in {\tt umf4\_f77zwrapper.c}. The following is a synopsis
+of each routine. All the arguments are the same as the real versions,
+except {\tt Az}, {\tt xz}, and {\tt bz} are the imaginary parts of
+the matrix, solution, and right-hand side, respectively. The
+{\tt Ax}, {\tt x}, and {\tt b} are the real parts.
+
+{\footnotesize
+\begin{verbatim}
+ call umf4zdef (control)
+ call umf4zsym (m, n, Ap, Ai, Ax, Az, symbolic, control, info)
+ call umf4znum (Ap, Ai, Ax, Az, symbolic, numeric, control, info)
+ call umf4zsolr (sys, Ap, Ai, Ax, Az, x, xz, b, bz, numeric, control, info)
+ call umf4zsol (sys, x, xz, b, bz, numeric, control, info)
+ call umf4zscal (x, xz, b, bz, numeric, status)
+ call umf4zfnum (numeric)
+ call umf4zfsym (symbolic)
+ call umf4zpcon (control)
+ call umf4zpinf (control)
+ call umf4zsnum (numeric, filenum, status)
+ call umf4zssym (symbolic, filenum, status)
+ call umf4zlnum (numeric, filenum, status)
+ call umf4zlsym (symbolic, filenum, status)
+\end{verbatim}
+}
+
+The Fortran interface does not support the packed complex case.
+
+%-------------------------------------------------------------------------------
+\section{Installation}
+\label{Install}
+%-------------------------------------------------------------------------------
+
+%-------------------------------------------------------------------------------
+\subsection{Installing the C library}
+%-------------------------------------------------------------------------------
+
+The following discussion assumes you have the {\tt make} program, either in
+Unix, or in Windows with Cygwin\footnote{www.cygwin.com}.
+You can skip this section and go to next one if all you want to use is
+the UMFPACK and AMD mexFunctions in MATLAB.
+
+You will need to install both UMFPACK and AMD to use UMFPACK.
+The {\tt UMFPACK} and {\tt AMD} subdirectories must be placed side-by-side
+within the same directory. AMD is a stand-alone package that
+is required by UMFPACK. UMFPACK can be compiled without the
+BLAS \cite{DaydeDuff99,ACM679a,ATLAS,GotoVandeGeijn02},
+but your performance will be much less than what it should be.
+
+System-dependent configurations are in the {\tt UFconfig/UFconfig.mk}
+file. The default
+settings will work on most systems, except that UMFPACK will be compiled so
+that it does not use the BLAS. Sample configurations are provided
+for Linux, Sun Solaris, SGI IRIX, IBM AIX, and the DEC/Compaq Alpha.
+
+To compile and install both packages,
+go to the {\tt UMFPACK} directory and type {\tt make}. This will compile the
+libraries ({\tt AMD/Lib/libamd.a} and {\tt UMFPACK/Lib/libumfpack.a}).
+A demo of the AMD ordering routine will be compiled and tested in
+the {\tt AMD/Demo} directory, and five demo programs will then be
+compiled and tested in the {\tt UMFPACK/Demo} directory.
+The outputs of these demo programs will then be compared with output
+files in the distribution. Expect to see a few differences, such as
+residual norms, compile-time control settings, and perhaps memory usage
+differences.
+
+To use {\tt make} to compile the MATLAB mexFunctions for MATLAB
+and AMD, you can either type {\tt make mex} in the UMFPACK directory.
+You may first need to edit the {\tt UFconfig/UFconfig.mk} file to
+modify the definition of the {\tt MEX}, if you have a version of MATLAB
+older than Version 7.2. Remove the {\tt -largeArrayDims} definition.
+If you use the MATLAB command {\tt umfpack\_make} in the MATLAB directory,
+then this case is handled for you automatically.
+
+If you have the GNU version of {\tt make}, the {\tt Lib/GNUmakefile} and
+{\tt MATLAB/GNUmakefile} files are used. These are much more concise than
+what the ``old'' version of {\tt make} can handle. If you do not have
+GNU {\tt make}, the {\tt Lib/Makefile} and {\tt MATLAB/Makefile} files
+are used instead. Each UMFPACK source file is compiled into four
+versions ({\tt double} / complex, and {\tt int} / {\tt UF\_long}). A proper
+old-style {\tt Makefile} is cumbersome in this case, so these two
+{\tt Makefile}'s have been constructed by brute force. They ignore
+dependencies, and simply compile everything. I highly recommend using GNU
+{\tt make} if you wish to modify UMFPACK.
+
+If you compile UMFPACK and AMD and then later change the
+{\tt UFconfig/UFconfig.mk} file
+then you should type {\tt make purge} and then {\tt make} to recompile.
+
+Here are the various parameters that you can control in your
+{\tt UFconfig/UFconfig.mk} file:
+
+\begin{itemize}
+\item {\tt CC = } your C compiler, such as {\tt cc}.
+\item {\tt RANLIB = } your system's {\tt ranlib} program, if needed.
+\item {\tt CFLAGS = } optimization flags, such as {\tt -O}.
+\item {\tt UMFPACK\_CONFIG = } configuration settings for the BLAS,
+ memory allocation routines, and timing routines.
+\item {\tt LIB = } your libraries, such as {\tt -lm} or {\tt -lblas}.
+\item {\tt RM =} the command to delete a file.
+\item {\tt MV =} the command to rename a file.
+\item {\tt MEX =} the command to compile a MATLAB mexFunction.
+ If you are using MATLAB 5, you need to add {\tt -DNBLAS} and
+ {\tt -DNUTIL} to this command.
+\item {\tt F77 =} the command to compile a Fortran program (optional).
+\item {\tt F77FLAGS =} the Fortran compiler flags (optional).
+\item {\tt F77LIB =} the Fortran libraries (optional).
+\end{itemize}
+
+The {\tt UMFPACK\_CONFIG} string can include combinations of the following;
+most deal with how the BLAS are called:
+\begin{itemize}
+\item {\tt -DNBLAS} if you do not have any BLAS at all.
+\item {\tt -DNSUNPERF} if you are on Solaris but do not have the Sun
+ Performance Library (for the BLAS).
+\item {\tt -DLONGBLAS} if your BLAS takes non-{\tt int} integer arguments.
+\item {\tt -DBLAS\_INT = } the integer used by the BLAS.
+
+\item {\tt -DBLAS\_NO\_UNDERSCORE}
+ for controlling how C calls the Fortran BLAS.
+ This is set automatically for Windows,
+ Sun Solaris, SGI Irix, Red Hat Linux, Compaq Alpha, and
+ AIX (the IBM RS 6000).
+
+\item {\tt -DGETRUSAGE} if you have the {\tt getrusage} function.
+\item {\tt -DNPOSIX} if you do not have the POSIX-compliant
+ {\tt sysconf} and {\tt times} routines used by
+ {\tt umfpack\_tic} and {\tt umfpack\_toc}.
+\item {\tt -DNRECIPROCAL} controls a trade-off between speed and accuracy.
+ If defined (or if the pivot value itself is less than $10^{-12}$),
+ then the pivot column is divided by the pivot value during numeric
+ factorization. Otherwise, it is multiplied by the reciprocal of the
+ pivot, which is faster but can be less accurate. The default is
+ to multiply by the reciprocal unless the pivot value is small.
+ This option also modifies how the rows of the matrix $\m{A}$ are
+ scaled. If {\tt -DNRECIPROCAL} is defined (or if any scale factor is
+ less than $10^{-12}$), entries in the rows of $\m{A}$ are divided
+ by the scale factors. Otherwise, they are multiplied by the reciprocal.
+ When compiling the complex routines with the GNU {\tt gcc} compiler, the
+ pivot column is always divided by the pivot entry, because of a
+ numerical accuracy issue encountered with {\tt gcc} version 3.2 with a
+ few complex matrices on a Pentium 4M (running Linux). You can still
+ use {\tt -DNRECIPROCAL} to control how the scale factors
+ for the rows of $\m{A}$ are applied.
+\item {\tt -DNO\_DIVIDE\_BY\_ZERO} controls how UMFPACK treats zeros
+ on the diagonal of $\m{U}$, for a singular matrix $\m{A}$.
+ If defined, then no division by
+ zero is performed (a zero entry on the diagonal of $\m{U}$ is
+ treated as if it were equal to one). By default,
+ UMFPACK will divide by zero.
+\item {\tt -DNO\_TIMER} controls whether or not timing routines
+ are to be called. If defined, no timers are used.
+ Timers are included by default.
+\end{itemize}
+
+If a Fortran BLAS package is used you may see compiler warnings. The BLAS
+routines
+{\tt dgemm}, {\tt dgemv}, {\tt dger}, {\tt dtrsm}, {\tt dtrsv}, {\tt dscal}
+and their corresponding complex versions are used.
+Header files are not provided for the Fortran
+BLAS. You may safely ignore all of these warnings.
+
+I highly recommend the recent BLAS by Goto and van de Geijn
+\cite{GotoVandeGeijn02}. Using this BLAS increased the performance
+of UMFPACK by up to 50\% on a Dell Latitude C840 laptop (2GHz Pentium 4M,
+512K L2 cache, 1GB main memory). The peak performance of
+{\tt umfpack\_di\_numeric} with Goto and van de Geijn's BLAS is 1.6 Gflops
+on this computer. In MATLAB, the peak performance of UMFPACK on
+a dense matrix (stored in sparse format) is 900 Mflops, as compared to
+1 Gflop for {\tt x = A}$\backslash${\tt b}
+when {\tt A} is stored as a regular full matrix.
+
+When you compile your program that uses the C-callable UMFPACK library,
+you need to link your program with both libraries
+({\tt UMFPACK/Lib/libumfpack.a} and {\tt AMD/Lib/libamd.a})
+and you need to tell your compiler to look in the
+directories {\tt UMFPACK/Include} and {\tt AMD/Include} for include
+files. See {\tt UMFPACK/Demo/Makefile} for an example.
+You do not need to directly include any AMD include files in your
+program, unless you directly call AMD routines. You only need the
+\begin{verbatim}
+#include "umfpack.h"
+\end{verbatim}
+statement, as described in Section~\ref{Synopsis}.
+
+If you would like to compile both 32-bit and 64-bit versions of the libraries,
+you will need to do it in two steps. Modify your {\tt UFconfig/UFconfig.mk}
+file, and select the 32-bit option. Type {\tt make} in the {\tt UMFPACK}
+directory, which creates the {\tt UMFPACK/Lib/libumfpack.a} and
+{\tt AMD/Lib/libamd.a} libraries. Rename those two files. Edit your
+{\tt UFconfig/UFconfig.mk} file and select the 64-bit option.
+Type {\tt make purge},
+and then {\tt make}, and you will create the 64-bit libraries.
+You can use the same {\tt umfpack.h} include file for both 32-bit and
+64-bit versions. Simply link your program with the appropriate 32-bit
+or 64-bit compiled version of the UMFPACK and AMD libraries.
+
+Type {\tt make hb} in the {\tt UMFPACK/Demo/HB} directory
+to compile and run a C program that reads in and factorizes
+Harwell/Boeing matrices. Note that this uses a stand-alone Fortran
+program to read in the Fortran-formatted Harwell/Boeing matrices and
+write them to a file which can be read by a C program.
+
+The {\tt umf\_multicompile.c} file has been added to assist in the
+compilation of UMFPACK in Microsoft Visual Studio, for Windows.
+
+%-------------------------------------------------------------------------------
+\subsection{Installing the MATLAB interface}
+%-------------------------------------------------------------------------------
+
+If all you want to do is use the UMFPACK mexFunction in MATLAB, you can skip
+the use of the {\tt make} command described above. Simply type
+{\tt umfpack\_make} in MATLAB while in the {\tt UMFPACK/MATLAB} directory.
+You can also type {\tt amd\_make} in the {\tt AMD/MATLAB} directory
+to compile the stand-alone AMD mexFunction (this is not required to
+compile the UMFPACK mexFunction). This works on any computer with MATLAB,
+including Windows.
+
+If you are using Windows and the {\tt lcc} compiler bundled with
+MATLAB 6.1, then you may need to copy the
+{\tt UMFPACK}$\backslash${\tt MATLAB}$\backslash${\tt lcc\_lib}$\backslash${\tt libmwlapack.lib}
+file into the
+{\tt <matlab>}$\backslash${\tt extern}$\backslash${\tt lib}$\backslash${\tt win32}$\backslash${\tt lcc}$\backslash$
+directory.
+Next, type {\tt mex -setup}
+at the MATLAB prompt, and ask MATLAB to select the {\tt lcc} compiler.
+MATLAB 6.1 has built-in BLAS, but in that version of MATLAB the BLAS
+cannot be accessed by a mexFunction compiled by {\tt lcc} without first copying
+this file to the location listed above.
+If you have MATLAB 6.5 or later, you can probably skip this step.
+
+%-------------------------------------------------------------------------------
+\subsection{Installing the Fortran interface}
+%-------------------------------------------------------------------------------
+
+Once the 32-bit C-callable UMFPACK library is compiled, you can also compile
+the Fortran interface, by typing {\tt make fortran}. This will create
+the {\tt umf4hb} program, test it, and compare the output with the
+file {\tt umf4hb.out} in the distribution.
+If you compiled UMFPACK in 64-bit mode, you need to use {\tt make fortran64}
+instead, which compiles the {\tt umf4hb64} program and compares its output
+with the file {\tt umf4hb64.out}.
+Refer to the comments in the {\tt Demo/umf4\_f77wrapper.c} file
+for more details.
+
+This interface is {\bf highly} non-portable, since it depends
+on how C and Fortran are interfaced.
+Because of this issue, the interface is included in the {\tt Demo} directory,
+and not as a primary part of the UMFPACK library. The interface routines are
+not included in the compiled {\tt UMFPACK/Lib/libumfpack.a} library, but left
+as stand-alone compiled files ({\tt umf4\_f77wrapper.o} and
+{\tt umf4\_f77wrapper64.o} in the {\tt Demo} directory).
+You may need to modify the interface routines in the file
+{\tt umf4\_f77wrapper.c} if you are using compilers for which this interface
+has not been tested.
+
+%-------------------------------------------------------------------------------
+\subsection{Known Issues}
+%-------------------------------------------------------------------------------
+
+The Microsoft C or C++ compilers on a Pentium badly break the IEEE 754 standard,
+and do not treat NaN's properly. According to IEEE 754, the expression
+{\tt (x != x)} is supposed to be true if and only if {\tt x} is NaN. For
+non-compliant compilers in Windows that expression is always false, and another
+test must be used: {\tt (x < x)} is true if and only if {\tt x}
+is NaN. For compliant compilers, {\tt (x < x)} is always false, for any
+value of {\tt x} (including NaN).
+To cover both cases, UMFPACK when running under Microsoft Windows
+defines the following macro, which is true if and only if {\tt x} is NaN,
+regardless of whether your compiler is compliant or not:
+
+\begin{verbatim}
+#define SCALAR_IS_NAN(x) (((x) != (x)) || ((x) < (x)))
+\end{verbatim}
+
+If your compiler breaks this test, then UMFPACK will fail catastrophically
+if it encounters a NaN. You will not just see NaN's in your output; UMFPACK
+will probably crash with a segmentation fault. In that case, you might try to
+see if the common (but non-ANSI C) routine {\tt isnan} is available, and modify
+the macro {\tt SCALAR\_IS\_NAN} in {\tt umf\_version.h} accordingly. The
+simpler (and IEEE 754-compliant) test {\tt (x != x)} is always true with Linux
+on a PC, and on every Unix compiler I have tested.
+
+Some compilers will complain about the Fortran BLAS being defined implicitly.
+C prototypes for the BLAS are not used, except the C-BLAS. Some compilers
+will complain about unrecognized {\tt \#pragma}'s. You may safely ignore
+all of these warnings.
+
+%-------------------------------------------------------------------------------
+\section{Future work}
+\label{Future}
+%-------------------------------------------------------------------------------
+
+Here are a few features that are not in the current version of UMFPACK,
+in no particular
+order. They may appear in a future release of UMFPACK. If you are interested,
+let me know and I could consider including them:
+
+\begin{enumerate}
+
+\item Remove the restriction that the column-oriented form be given with
+ sorted columns. This has already been done in AMD Version 2.0.
+
+\item Future versions may have different default {\tt Control} parameters.
+ Future versions may return more statistics in the {\tt Info} array, and
+ they may use more entries in the {\tt Control} array.
+ These two arrays will probably become larger, since there are very few
+ unused entries. If they change in size, the constants
+ {\tt UMFPACK\_CONTROL} and {\tt UMFPACK\_INFO} defined in {\tt umfpack.h}
+ will be changed to reflect their new size. Your C program should use
+ these constants when declaring the size of these two arrays. Do not
+ define them as {\tt Control [20]} and {\tt Info [90]}.
+
+\item Forward/back solvers for the conventional row or column-form data
+ structure for $\m{L}$ and $\m{U}$ (the output of
+ {\tt umfpack\_*\_di\_get\_numeric}). This would enable a separate
+ solver that could be used to write a MATLAB mexFunction
+ {\tt x = lu\_refine (A, b, L, U, P, Q, R)} that gives MATLAB access
+ to the iterative refinement algorithm with sparse backward error
+ analysis. It would also be easier to handle sparse right-hand sides
+ in this data structure, and end up with good asymptotic run-time
+ in this case
+ (particularly for $\m{Lx}=\m{b}$; see \cite{GilbertPeierls88}).
+ See also CSparse and
+ CXSparse for software for handling sparse right-hand sides.
+
+\item Complex absolute value computations could be
+ based on FDLIBM (see \newline
+ http://www.netlib.org/fdlibm),
+ using the {\tt hypot(x,y)} routine.
+
+\item When using iterative refinement, the residual $\m{Ax}-\m{b}$ could be
+ returned by {\tt umfpack\_solve}.
+
+\item The solve routines could handle multiple right-hand sides, and sparse
+ right-hand sides. See {\tt umfpack\_solve} for the MATLAB version
+ of this feature.
+ See also CSparse and
+ CXSparse for software for handling sparse right-hand sides.
+
+\item An option to redirect the error and diagnostic output.
+
+\item Permutation to block-triangular-form \cite{Duff78a} for the C-callable
+ interface. There are two routines in the ACM Collected
+ Algorithms (529 and 575) \cite{Duff81b,Duff78b}
+ that could be translated from Fortran
+ to C and included in UMFPACK. This would result in better performance
+ for matrices from circuit simulation and
+ chemical process engineering. See {\tt umfpack\_btf.m} for the MATLAB
+ version of this feature. KLU includes this feature.
+ See also {\tt cs\_dmperm} in CSparse and CXSparse.
+
+\item The ability to use user-provided work arrays, so that {\tt malloc},
+ {\tt free}, and {\tt realloc} realloc are not called. The
+ {\tt umfpack\_*\_wsolve} routine is one example.
+
+\item A method that takes time proportional to the number of nonzeros in
+ $\m{A}$ to compute the symbolic factorization \cite{GilbertNgPeyton94}.
+ This would improve the performance of the symmetric and 2-by-2 strategies,
+ and the unsymmetric strategy when dense rows are present.
+ The current method takes
+ time proportional to the number of nonzeros in the upper bound of $\m{U}$.
+ The method used in UMFPACK exploits super-columns, however, so this
+ bound is rarely reached.
+ See {\tt cs\_counts} in CSparse and CXSparse,
+ and {\tt cholmod\_analyze} in CHOLMOD.
+
+\item Other basic sparse matrix operations, such as sparse matrix
+ multiplication, could be included.
+
+\item A more complete Fortran interface.
+
+\item A C++ interface.
+
+\item A parallel version using MPI. This would require a large amount
+ of effort.
+
+\end{enumerate}
+
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{The primary UMFPACK routines}
+\label{Primary}
+%-------------------------------------------------------------------------------
+
+The include files are the same for all four versions of
+UMFPACK. The generic integer type is {\tt Int}, which is an {\tt int} or
+{\tt UF\_long}, depending on which version of UMFPACK you are using.
+
+\subsection{umfpack\_*\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_numeric.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_solve}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_solve.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_free\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_free_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_free\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_free_numeric.h via sed
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Alternative routines}
+\label{Alternative}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_*\_defaults}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_defaults.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_qsymbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_qsymbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_wsolve}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_wsolve.h via sed
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Matrix manipulation routines}
+\label{Manipulate}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_*\_col\_to\_triplet}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_col_to_triplet.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_triplet\_to\_col}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_triplet_to_col.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_transpose}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_transpose.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_scale}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_scale.h via sed
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Getting the contents of opaque objects}
+\label{Get}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_*\_get\_lunz}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_get_lunz.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_get\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_get_numeric.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_get\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_get_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_save\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_save_numeric.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_load\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_load_numeric.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_save\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_save_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_load\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_load_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_get\_determinant}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_get_determinant.h via sed
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Reporting routines}
+\label{Report}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_*\_report\_status}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_status.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_control}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_control.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_info}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_info.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_matrix}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_matrix.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_numeric}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_numeric.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_perm}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_perm.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_symbolic}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_symbolic.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_triplet}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_triplet.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_*\_report\_vector}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_report_vector.h via sed
+\end{verbatim}
+}
+
+%-------------------------------------------------------------------------------
+\newpage
+\section{Utility routines}
+\label{Utility}
+%-------------------------------------------------------------------------------
+
+\subsection{umfpack\_timer}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_timer.h via sed
+\end{verbatim}
+}
+
+\newpage
+\subsection{umfpack\_tic and umfpack\_toc}
+
+{\footnotesize
+\begin{verbatim}
+INCLUDE umfpack_tictoc.h via sed
+\end{verbatim}
+}
+
+
+%-------------------------------------------------------------------------------
+\newpage
+% References
+%-------------------------------------------------------------------------------
+
+\bibliographystyle{plain}
+\bibliography{UserGuide}
+
+\end{document}
diff --git a/UMFPACK/Doc/gpl.txt b/UMFPACK/Doc/gpl.txt
new file mode 100644
index 0000000..3912109
--- /dev/null
+++ b/UMFPACK/Doc/gpl.txt
@@ -0,0 +1,340 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it. (Some other Free Software Foundation software is covered by
+the GNU Library General Public License instead.) You can apply it to
+your programs, too.
+
+ When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+this service if you wish), that you receive source code or can get it
+if you want it, that you can change the software or use pieces of it
+in new free programs; and that you know you can do these things.
+
+ To protect your rights, we need to make restrictions that forbid
+anyone to deny you these rights or to ask you to surrender the rights.
+These restrictions translate to certain responsibilities for you if you
+distribute copies of the software, or if you modify it.
+
+ For example, if you distribute copies of such a program, whether
+gratis or for a fee, you must give the recipients all the rights that
+you have. You must make sure that they, too, receive or can get the
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+rights.
+
+ We protect your rights with two steps: (1) copyright the software, and
+(2) offer you this license which gives you legal permission to copy,
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+
+ Also, for each author's protection and ours, we want to make certain
+that everyone understands that there is no warranty for this free
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+
+ GNU GENERAL PUBLIC LICENSE
+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
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+
+ How to Apply These Terms to Your New Programs
+
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+free software which everyone can redistribute and change under these terms.
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+convey the exclusion of warranty; and each file should have at least
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+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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+
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+ Gnomovision version 69, Copyright (C) year name of author
+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
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+
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+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ <signature of Ty Coon>, 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Library General
+Public License instead of this License.
diff --git a/UMFPACK/Include/umfpack.h b/UMFPACK/Include/umfpack.h
new file mode 100644
index 0000000..c720aba
--- /dev/null
+++ b/UMFPACK/Include/umfpack.h
@@ -0,0 +1,438 @@
+/* ========================================================================== */
+/* === umfpack.h ============================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This is the umfpack.h include file, and should be included in all user code
+ that uses UMFPACK. Do not include any of the umf_* header files in user
+ code. All routines in UMFPACK starting with "umfpack_" are user-callable.
+ All other routines are prefixed "umf_XY_", (where X is d or z, and Y is
+ i or l) and are not user-callable.
+*/
+
+#ifndef UMFPACK_H
+#define UMFPACK_H
+
+/* -------------------------------------------------------------------------- */
+/* Make it easy for C++ programs to include UMFPACK */
+/* -------------------------------------------------------------------------- */
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* define UF_long */
+#include "UFconfig.h"
+
+/* -------------------------------------------------------------------------- */
+/* size of Info and Control arrays */
+/* -------------------------------------------------------------------------- */
+
+/* These might be larger in future versions, since there are only 3 unused
+ * entries in Info, and no unused entries in Control. */
+
+#define UMFPACK_INFO 90
+#define UMFPACK_CONTROL 20
+
+/* -------------------------------------------------------------------------- */
+/* User-callable routines */
+/* -------------------------------------------------------------------------- */
+
+/* Primary routines: */
+#include "umfpack_symbolic.h"
+#include "umfpack_numeric.h"
+#include "umfpack_solve.h"
+#include "umfpack_free_symbolic.h"
+#include "umfpack_free_numeric.h"
+
+/* Alternative routines: */
+#include "umfpack_defaults.h"
+#include "umfpack_qsymbolic.h"
+#include "umfpack_wsolve.h"
+
+/* Matrix manipulation routines: */
+#include "umfpack_triplet_to_col.h"
+#include "umfpack_col_to_triplet.h"
+#include "umfpack_transpose.h"
+#include "umfpack_scale.h"
+
+/* Getting the contents of the Symbolic and Numeric opaque objects: */
+#include "umfpack_get_lunz.h"
+#include "umfpack_get_numeric.h"
+#include "umfpack_get_symbolic.h"
+#include "umfpack_save_numeric.h"
+#include "umfpack_load_numeric.h"
+#include "umfpack_save_symbolic.h"
+#include "umfpack_load_symbolic.h"
+#include "umfpack_get_determinant.h"
+
+/* Reporting routines (the above 14 routines print nothing): */
+#include "umfpack_report_status.h"
+#include "umfpack_report_info.h"
+#include "umfpack_report_control.h"
+#include "umfpack_report_matrix.h"
+#include "umfpack_report_triplet.h"
+#include "umfpack_report_vector.h"
+#include "umfpack_report_symbolic.h"
+#include "umfpack_report_numeric.h"
+#include "umfpack_report_perm.h"
+
+/* Utility routines: */
+#include "umfpack_timer.h"
+#include "umfpack_tictoc.h"
+
+/* AMD */
+#include "amd.h"
+
+/* global function pointers */
+#include "umfpack_global.h"
+
+/* -------------------------------------------------------------------------- */
+/* Version, copyright, and license */
+/* -------------------------------------------------------------------------- */
+
+#define UMFPACK_VERSION "UMFPACK V5.2.0 (Nov 1, 2007)"
+
+#define UMFPACK_COPYRIGHT \
+"UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.\n"
+
+#define UMFPACK_LICENSE_PART1 \
+"\nUMFPACK License:\n" \
+"\n" \
+" UMFPACK is available under alternate licenses,\n" \
+" contact T. Davis for details.\n" \
+"\n" \
+" Your use or distribution of UMFPACK or any modified version of\n" \
+" UMFPACK implies that you agree to this License.\n" \
+"\n" \
+" This library is free software; you can redistribute it and/or\n" \
+" modify it under the terms of the GNU General Public\n" \
+" License as published by the Free Software Foundation; either\n" \
+" version 2 of the License, or (at your option) any later version.\n" \
+"\n" \
+" This library is distributed in the hope that it will be useful,\n" \
+" but WITHOUT ANY WARRANTY; without even the implied warranty of\n" \
+" MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU\n" \
+" General Public License for more details.\n" \
+"\n" \
+" You should have received a copy of the GNU General Public\n" \
+" License along with this library; if not, write to the Free Software\n" \
+" Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301\n" \
+" USA\n" \
+
+#define UMFPACK_LICENSE_PART2 \
+"\n" \
+" Permission is hereby granted to use or copy this program under the\n" \
+" terms of the GNU GPL, provided that the Copyright, this License,\n" \
+" and the Availability of the original version is retained on all copies.\n" \
+" User documentation of any code that uses this code or any modified\n" \
+" version of this code must cite the Copyright, this License, the\n" \
+" Availability note, and \"Used by permission.\" Permission to modify\n" \
+" the code and to distribute modified code is granted, provided the\n" \
+" Copyright, this License, and the Availability note are retained,\n" \
+" and a notice that the code was modified is included.\n"
+
+#define UMFPACK_LICENSE_PART3 \
+"\n" \
+"Availability: http://www.cise.ufl.edu/research/sparse/umfpack\n" \
+"\n"
+
+/* UMFPACK Version 4.5 and later will include the following definitions.
+ * As an example, to test if the version you are using is 4.5 or later:
+ *
+ * #ifdef UMFPACK_VER
+ * if (UMFPACK_VER >= UMFPACK_VER_CODE (4,5)) ...
+ * #endif
+ *
+ * This also works during compile-time:
+ *
+ * #if defined(UMFPACK_VER) && (UMFPACK >= UMFPACK_VER_CODE (4,5))
+ * printf ("This is version 4.5 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ *
+ * Versions 4.4 and earlier of UMFPACK do not include a #define'd version
+ * number, although they do include the UMFPACK_VERSION string, defined
+ * above.
+ */
+
+#define UMFPACK_DATE "Nov 1, 2007"
+#define UMFPACK_VER_CODE(main,sub) ((main) * 1000 + (sub))
+#define UMFPACK_MAIN_VERSION 5
+#define UMFPACK_SUB_VERSION 2
+#define UMFPACK_SUBSUB_VERSION 0
+#define UMFPACK_VER UMFPACK_VER_CODE(UMFPACK_MAIN_VERSION,UMFPACK_SUB_VERSION)
+
+/* -------------------------------------------------------------------------- */
+/* contents of Info */
+/* -------------------------------------------------------------------------- */
+
+/* Note that umfpack_report.m must coincide with these definitions. S is
+ * the submatrix of A after removing row/col singletons and empty rows/cols. */
+
+/* returned by all routines that use Info: */
+#define UMFPACK_STATUS 0 /* UMFPACK_OK, or other result */
+#define UMFPACK_NROW 1 /* n_row input value */
+#define UMFPACK_NCOL 16 /* n_col input value */
+#define UMFPACK_NZ 2 /* # of entries in A */
+
+/* computed in UMFPACK_*symbolic and UMFPACK_numeric: */
+#define UMFPACK_SIZE_OF_UNIT 3 /* sizeof (Unit) */
+
+/* computed in UMFPACK_*symbolic: */
+#define UMFPACK_SIZE_OF_INT 4 /* sizeof (int) */
+#define UMFPACK_SIZE_OF_LONG 5 /* sizeof (UF_long) */
+#define UMFPACK_SIZE_OF_POINTER 6 /* sizeof (void *) */
+#define UMFPACK_SIZE_OF_ENTRY 7 /* sizeof (Entry), real or complex */
+#define UMFPACK_NDENSE_ROW 8 /* number of dense rows */
+#define UMFPACK_NEMPTY_ROW 9 /* number of empty rows */
+#define UMFPACK_NDENSE_COL 10 /* number of dense rows */
+#define UMFPACK_NEMPTY_COL 11 /* number of empty rows */
+#define UMFPACK_SYMBOLIC_DEFRAG 12 /* # of memory compactions */
+#define UMFPACK_SYMBOLIC_PEAK_MEMORY 13 /* memory used by symbolic analysis */
+#define UMFPACK_SYMBOLIC_SIZE 14 /* size of Symbolic object, in Units */
+#define UMFPACK_SYMBOLIC_TIME 15 /* time (sec.) for symbolic analysis */
+#define UMFPACK_SYMBOLIC_WALLTIME 17 /* wall clock time for sym. analysis */
+#define UMFPACK_STRATEGY_USED 18 /* strategy used: sym, unsym, 2by2 */
+#define UMFPACK_ORDERING_USED 19 /* ordering used: colamd, amd, given */
+#define UMFPACK_QFIXED 31 /* whether Q is fixed or refined */
+#define UMFPACK_DIAG_PREFERRED 32 /* whether diagonal pivoting attempted*/
+#define UMFPACK_PATTERN_SYMMETRY 33 /* symmetry of pattern of S */
+#define UMFPACK_NZ_A_PLUS_AT 34 /* nnz (S+S'), excl. diagonal */
+#define UMFPACK_NZDIAG 35 /* nnz (diag (S)) */
+
+/* AMD statistics, computed in UMFPACK_*symbolic: */
+#define UMFPACK_SYMMETRIC_LUNZ 36 /* nz in L+U, if AMD ordering used */
+#define UMFPACK_SYMMETRIC_FLOPS 37 /* flops for LU, if AMD ordering used */
+#define UMFPACK_SYMMETRIC_NDENSE 38 /* # of "dense" rows/cols in S+S' */
+#define UMFPACK_SYMMETRIC_DMAX 39 /* max nz in cols of L, for AMD */
+
+/* statistics for 2-by-2 strategy */
+#define UMFPACK_2BY2_NWEAK 51 /* number of weak diagonal entries*/
+#define UMFPACK_2BY2_UNMATCHED 52 /* # of weak diagonals not matched*/
+#define UMFPACK_2BY2_PATTERN_SYMMETRY 53 /* symmetry of pattern of P*S */
+#define UMFPACK_2BY2_NZ_PA_PLUS_PAT 54 /* nz in PS+(PS)' */
+#define UMFPACK_2BY2_NZDIAG 55 /* nz on diagonal of PS+(PS)' */
+
+/* statistcs for singleton pruning */
+#define UMFPACK_COL_SINGLETONS 56 /* # of column singletons */
+#define UMFPACK_ROW_SINGLETONS 57 /* # of row singletons */
+#define UMFPACK_N2 58 /* size of S */
+#define UMFPACK_S_SYMMETRIC 59 /* 1 if S square and symmetricly perm.*/
+
+/* estimates computed in UMFPACK_*symbolic: */
+#define UMFPACK_NUMERIC_SIZE_ESTIMATE 20 /* final size of Numeric->Memory */
+#define UMFPACK_PEAK_MEMORY_ESTIMATE 21 /* for symbolic & numeric */
+#define UMFPACK_FLOPS_ESTIMATE 22 /* flop count */
+#define UMFPACK_LNZ_ESTIMATE 23 /* nz in L, incl. diagonal */
+#define UMFPACK_UNZ_ESTIMATE 24 /* nz in U, incl. diagonal */
+#define UMFPACK_VARIABLE_INIT_ESTIMATE 25 /* initial size of Numeric->Memory*/
+#define UMFPACK_VARIABLE_PEAK_ESTIMATE 26 /* peak size of Numeric->Memory */
+#define UMFPACK_VARIABLE_FINAL_ESTIMATE 27 /* final size of Numeric->Memory */
+#define UMFPACK_MAX_FRONT_SIZE_ESTIMATE 28 /* max frontal matrix size */
+#define UMFPACK_MAX_FRONT_NROWS_ESTIMATE 29 /* max # rows in any front */
+#define UMFPACK_MAX_FRONT_NCOLS_ESTIMATE 30 /* max # columns in any front */
+
+/* exact values, (estimates shown above) computed in UMFPACK_numeric: */
+#define UMFPACK_NUMERIC_SIZE 40 /* final size of Numeric->Memory */
+#define UMFPACK_PEAK_MEMORY 41 /* for symbolic & numeric */
+#define UMFPACK_FLOPS 42 /* flop count */
+#define UMFPACK_LNZ 43 /* nz in L, incl. diagonal */
+#define UMFPACK_UNZ 44 /* nz in U, incl. diagonal */
+#define UMFPACK_VARIABLE_INIT 45 /* initial size of Numeric->Memory*/
+#define UMFPACK_VARIABLE_PEAK 46 /* peak size of Numeric->Memory */
+#define UMFPACK_VARIABLE_FINAL 47 /* final size of Numeric->Memory */
+#define UMFPACK_MAX_FRONT_SIZE 48 /* max frontal matrix size */
+#define UMFPACK_MAX_FRONT_NROWS 49 /* max # rows in any front */
+#define UMFPACK_MAX_FRONT_NCOLS 50 /* max # columns in any front */
+
+/* computed in UMFPACK_numeric: */
+#define UMFPACK_NUMERIC_DEFRAG 60 /* # of garbage collections */
+#define UMFPACK_NUMERIC_REALLOC 61 /* # of memory reallocations */
+#define UMFPACK_NUMERIC_COSTLY_REALLOC 62 /* # of costlly memory realloc's */
+#define UMFPACK_COMPRESSED_PATTERN 63 /* # of integers in LU pattern */
+#define UMFPACK_LU_ENTRIES 64 /* # of reals in LU factors */
+#define UMFPACK_NUMERIC_TIME 65 /* numeric factorization time */
+#define UMFPACK_UDIAG_NZ 66 /* nz on diagonal of U */
+#define UMFPACK_RCOND 67 /* est. reciprocal condition # */
+#define UMFPACK_WAS_SCALED 68 /* none, max row, or sum row */
+#define UMFPACK_RSMIN 69 /* min (max row) or min (sum row) */
+#define UMFPACK_RSMAX 70 /* max (max row) or max (sum row) */
+#define UMFPACK_UMIN 71 /* min abs diagonal entry of U */
+#define UMFPACK_UMAX 72 /* max abs diagonal entry of U */
+#define UMFPACK_ALLOC_INIT_USED 73 /* alloc_init parameter used */
+#define UMFPACK_FORCED_UPDATES 74 /* # of forced updates */
+#define UMFPACK_NUMERIC_WALLTIME 75 /* numeric wall clock time */
+#define UMFPACK_NOFF_DIAG 76 /* number of off-diagonal pivots */
+
+#define UMFPACK_ALL_LNZ 77 /* nz in L, if no dropped entries */
+#define UMFPACK_ALL_UNZ 78 /* nz in U, if no dropped entries */
+#define UMFPACK_NZDROPPED 79 /* # of dropped small entries */
+
+/* computed in UMFPACK_solve: */
+#define UMFPACK_IR_TAKEN 80 /* # of iterative refinement steps taken */
+#define UMFPACK_IR_ATTEMPTED 81 /* # of iter. refinement steps attempted */
+#define UMFPACK_OMEGA1 82 /* omega1, sparse backward error estimate */
+#define UMFPACK_OMEGA2 83 /* omega2, sparse backward error estimate */
+#define UMFPACK_SOLVE_FLOPS 84 /* flop count for solve */
+#define UMFPACK_SOLVE_TIME 85 /* solve time (seconds) */
+#define UMFPACK_SOLVE_WALLTIME 86 /* solve time (wall clock, seconds) */
+
+/* Info [87, 88, 89] unused */
+
+/* Unused parts of Info may be used in future versions of UMFPACK. */
+
+/* -------------------------------------------------------------------------- */
+
+/* Info [UMFPACK_ORDERING_USED] is one of the following: */
+#define UMFPACK_ORDERING_COLAMD 0 /* COLAMD(A) */
+#define UMFPACK_ORDERING_AMD 1 /* AMD(A+A') */
+#define UMFPACK_ORDERING_GIVEN 2 /* Q is provided on input */
+
+/* -------------------------------------------------------------------------- */
+/* contents of Control */
+/* -------------------------------------------------------------------------- */
+
+/* used in all UMFPACK_report_* routines: */
+#define UMFPACK_PRL 0 /* print level */
+
+/* used in UMFPACK_*symbolic only: */
+#define UMFPACK_DENSE_ROW 1 /* dense row parameter */
+#define UMFPACK_DENSE_COL 2 /* dense col parameter */
+#define UMFPACK_BLOCK_SIZE 4 /* BLAS-3 block size */
+#define UMFPACK_STRATEGY 5 /* auto, symmetric, unsym., or 2by2 */
+#define UMFPACK_2BY2_TOLERANCE 12 /* 2-by-2 pivot tolerance */
+#define UMFPACK_FIXQ 13 /* -1: no fixQ, 0: default, 1: fixQ */
+#define UMFPACK_AMD_DENSE 14 /* for AMD ordering */
+#define UMFPACK_AGGRESSIVE 19 /* whether or not to use aggressive
+ * absorption in AMD and COLAMD */
+
+/* used in UMFPACK_numeric only: */
+#define UMFPACK_PIVOT_TOLERANCE 3 /* threshold partial pivoting setting */
+#define UMFPACK_ALLOC_INIT 6 /* initial allocation ratio */
+#define UMFPACK_SYM_PIVOT_TOLERANCE 15 /* threshold, only for diag. entries */
+#define UMFPACK_SCALE 16 /* what row scaling to do */
+#define UMFPACK_FRONT_ALLOC_INIT 17 /* frontal matrix allocation ratio */
+#define UMFPACK_DROPTOL 18 /* drop tolerance for entries in L,U */
+
+/* used in UMFPACK_*solve only: */
+#define UMFPACK_IRSTEP 7 /* max # of iterative refinements */
+
+/* compile-time settings - Control [8..11] cannot be changed at run time: */
+#define UMFPACK_COMPILED_WITH_BLAS 8 /* uses the BLAS */
+#define UMFPACK_COMPILED_FOR_MATLAB 9 /* 1 if MATLAB mexFunction, etc. */
+#define UMFPACK_COMPILED_WITH_GETRUSAGE 10 /* uses getrusage timer, or not */
+#define UMFPACK_COMPILED_IN_DEBUG_MODE 11 /* debugging enabled (very slow!) */
+
+/* -------------------------------------------------------------------------- */
+
+/* Control [UMFPACK_STRATEGY] is one of the following: */
+#define UMFPACK_STRATEGY_AUTO 0 /* use sym. or unsym. strategy */
+#define UMFPACK_STRATEGY_UNSYMMETRIC 1 /* COLAMD(A), coletree postorder,
+ not prefer diag*/
+#define UMFPACK_STRATEGY_2BY2 2 /* AMD(PA+PA'), no coletree postorder,
+ prefer diag(PA) where P is pseudo
+ max transversal */
+#define UMFPACK_STRATEGY_SYMMETRIC 3 /* AMD(A+A'), no coletree postorder,
+ prefer diagonal */
+
+/* Control [UMFPACK_SCALE] is one of the following: */
+#define UMFPACK_SCALE_NONE 0 /* no scaling */
+#define UMFPACK_SCALE_SUM 1 /* default: divide each row by sum (abs (row))*/
+#define UMFPACK_SCALE_MAX 2 /* divide each row by max (abs (row)) */
+
+/* -------------------------------------------------------------------------- */
+/* default values of Control: */
+/* -------------------------------------------------------------------------- */
+
+#define UMFPACK_DEFAULT_PRL 1
+#define UMFPACK_DEFAULT_DENSE_ROW 0.2
+#define UMFPACK_DEFAULT_DENSE_COL 0.2
+#define UMFPACK_DEFAULT_PIVOT_TOLERANCE 0.1
+#define UMFPACK_DEFAULT_2BY2_TOLERANCE 0.01
+#define UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE 0.001
+#define UMFPACK_DEFAULT_BLOCK_SIZE 32
+#define UMFPACK_DEFAULT_ALLOC_INIT 0.7
+#define UMFPACK_DEFAULT_FRONT_ALLOC_INIT 0.5
+#define UMFPACK_DEFAULT_IRSTEP 2
+#define UMFPACK_DEFAULT_SCALE UMFPACK_SCALE_SUM
+#define UMFPACK_DEFAULT_STRATEGY UMFPACK_STRATEGY_AUTO
+#define UMFPACK_DEFAULT_AMD_DENSE AMD_DEFAULT_DENSE
+#define UMFPACK_DEFAULT_FIXQ 0
+#define UMFPACK_DEFAULT_AGGRESSIVE 1
+#define UMFPACK_DEFAULT_DROPTOL 0
+
+/* default values of Control may change in future versions of UMFPACK. */
+
+/* -------------------------------------------------------------------------- */
+/* status codes */
+/* -------------------------------------------------------------------------- */
+
+#define UMFPACK_OK (0)
+
+/* status > 0 means a warning, but the method was successful anyway. */
+/* A Symbolic or Numeric object was still created. */
+#define UMFPACK_WARNING_singular_matrix (1)
+
+/* The following warnings were added in umfpack_*_get_determinant */
+#define UMFPACK_WARNING_determinant_underflow (2)
+#define UMFPACK_WARNING_determinant_overflow (3)
+
+/* status < 0 means an error, and the method was not successful. */
+/* No Symbolic of Numeric object was created. */
+#define UMFPACK_ERROR_out_of_memory (-1)
+#define UMFPACK_ERROR_invalid_Numeric_object (-3)
+#define UMFPACK_ERROR_invalid_Symbolic_object (-4)
+#define UMFPACK_ERROR_argument_missing (-5)
+#define UMFPACK_ERROR_n_nonpositive (-6)
+#define UMFPACK_ERROR_invalid_matrix (-8)
+#define UMFPACK_ERROR_different_pattern (-11)
+#define UMFPACK_ERROR_invalid_system (-13)
+#define UMFPACK_ERROR_invalid_permutation (-15)
+#define UMFPACK_ERROR_internal_error (-911) /* yes, call me if you get this! */
+#define UMFPACK_ERROR_file_IO (-17)
+
+/* -------------------------------------------------------------------------- */
+/* solve codes */
+/* -------------------------------------------------------------------------- */
+
+/* Solve the system ( )x=b, where ( ) is defined below. "t" refers to the */
+/* linear algebraic transpose (complex conjugate if A is complex), or the (') */
+/* operator in MATLAB. "at" refers to the array transpose, or the (.') */
+/* operator in MATLAB. */
+
+#define UMFPACK_A (0) /* Ax=b */
+#define UMFPACK_At (1) /* A'x=b */
+#define UMFPACK_Aat (2) /* A.'x=b */
+
+#define UMFPACK_Pt_L (3) /* P'Lx=b */
+#define UMFPACK_L (4) /* Lx=b */
+#define UMFPACK_Lt_P (5) /* L'Px=b */
+#define UMFPACK_Lat_P (6) /* L.'Px=b */
+#define UMFPACK_Lt (7) /* L'x=b */
+#define UMFPACK_Lat (8) /* L.'x=b */
+
+#define UMFPACK_U_Qt (9) /* UQ'x=b */
+#define UMFPACK_U (10) /* Ux=b */
+#define UMFPACK_Q_Ut (11) /* QU'x=b */
+#define UMFPACK_Q_Uat (12) /* QU.'x=b */
+#define UMFPACK_Ut (13) /* U'x=b */
+#define UMFPACK_Uat (14) /* U.'x=b */
+
+/* -------------------------------------------------------------------------- */
+
+/* Integer constants are used for status and solve codes instead of enum */
+/* to make it easier for a Fortran code to call UMFPACK. */
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* UMFPACK_H */
diff --git a/UMFPACK/Include/umfpack_col_to_triplet.h b/UMFPACK/Include/umfpack_col_to_triplet.h
new file mode 100644
index 0000000..948a65e
--- /dev/null
+++ b/UMFPACK/Include/umfpack_col_to_triplet.h
@@ -0,0 +1,110 @@
+/* ========================================================================== */
+/* === umfpack_col_to_triplet =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_col_to_triplet
+(
+ int n_col,
+ const int Ap [ ],
+ int Tj [ ]
+) ;
+
+UF_long umfpack_dl_col_to_triplet
+(
+ UF_long n_col,
+ const UF_long Ap [ ],
+ UF_long Tj [ ]
+) ;
+
+int umfpack_zi_col_to_triplet
+(
+ int n_col,
+ const int Ap [ ],
+ int Tj [ ]
+) ;
+
+UF_long umfpack_zl_col_to_triplet
+(
+ UF_long n_col,
+ const UF_long Ap [ ],
+ UF_long Tj [ ]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n_col, *Tj, *Ap, status ;
+ status = umfpack_di_col_to_triplet (n_col, Ap, Tj) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_col, *Tj, *Ap, status ;
+ status = umfpack_dl_col_to_triplet (n_col, Ap, Tj) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n_col, *Tj, *Ap, status ;
+ status = umfpack_zi_col_to_triplet (n_col, Ap, Tj) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_col, *Tj, *Ap, status ;
+ status = umfpack_zl_col_to_triplet (n_col, Ap, Tj) ;
+
+Purpose:
+
+ Converts a column-oriented matrix to a triplet form. Only the column
+ pointers, Ap, are required, and only the column indices of the triplet form
+ are constructed. This routine is the opposite of umfpack_*_triplet_to_col.
+ The matrix may be singular and/or rectangular. Analogous to [i, Tj, x] =
+ find (A) in MATLAB, except that zero entries present in the column-form of
+ A are present in the output, and i and x are not created (those are just Ai
+ and Ax+Az*1i, respectively, for a column-form matrix A).
+
+Returns:
+
+ UMFPACK_OK if successful
+ UMFPACK_ERROR_argument_missing if Ap or Tj is missing
+ UMFPACK_ERROR_n_nonpositive if n_col <= 0
+ UMFPACK_ERROR_invalid_matrix if Ap [n_col] < 0, Ap [0] != 0, or
+ Ap [j] > Ap [j+1] for any j in the range 0 to n-1.
+ Unsorted columns and duplicate entries do not cause an error (these would
+ only be evident by examining Ai). Empty rows and columns are OK.
+
+Arguments:
+
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix. Restriction: n_col > 0.
+ (n_row is not required)
+
+ Int Ap [n_col+1] ; Input argument, not modified.
+
+ The column pointers of the column-oriented form of the matrix. See
+ umfpack_*_*symbolic for a description. The number of entries in
+ the matrix is nz = Ap [n_col]. Restrictions on Ap are the same as those
+ for umfpack_*_transpose. Ap [0] must be zero, nz must be >= 0, and
+ Ap [j] <= Ap [j+1] and Ap [j] <= Ap [n_col] must be true for all j in
+ the range 0 to n_col-1. Empty columns are OK (that is, Ap [j] may equal
+ Ap [j+1] for any j in the range 0 to n_col-1).
+
+ Int Tj [nz] ; Output argument.
+
+ Tj is an integer array of size nz on input, where nz = Ap [n_col].
+ Suppose the column-form of the matrix is held in Ap, Ai, Ax, and Az
+ (see umfpack_*_*symbolic for a description). Then on output, the
+ triplet form of the same matrix is held in Ai (row indices), Tj (column
+ indices), and Ax (numerical values). Note, however, that this routine
+ does not require Ai and Ax (or Az for the complex version) in order to
+ do the conversion.
+*/
diff --git a/UMFPACK/Include/umfpack_defaults.h b/UMFPACK/Include/umfpack_defaults.h
new file mode 100644
index 0000000..a588d4f
--- /dev/null
+++ b/UMFPACK/Include/umfpack_defaults.h
@@ -0,0 +1,69 @@
+/* ========================================================================== */
+/* === umfpack_defaults ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_defaults
+(
+ double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_dl_defaults
+(
+ double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_zi_defaults
+(
+ double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_zl_defaults
+(
+ double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_di_defaults (Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_dl_defaults (Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_zi_defaults (Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_zl_defaults (Control) ;
+
+Purpose:
+
+ Sets the default control parameter settings.
+
+Arguments:
+
+ double Control [UMFPACK_CONTROL] ; Output argument.
+
+ Control is set to the default control parameter settings. You can
+ then modify individual settings by changing specific entries in the
+ Control array. If Control is a (double *) NULL pointer, then
+ umfpack_*_defaults returns silently (no error is generated, since
+ passing a NULL pointer for Control to any UMFPACK routine is valid).
+*/
diff --git a/UMFPACK/Include/umfpack_free_numeric.h b/UMFPACK/Include/umfpack_free_numeric.h
new file mode 100644
index 0000000..986a6ab
--- /dev/null
+++ b/UMFPACK/Include/umfpack_free_numeric.h
@@ -0,0 +1,67 @@
+/* ========================================================================== */
+/* === umfpack_free_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_free_numeric
+(
+ void **Numeric
+) ;
+
+void umfpack_dl_free_numeric
+(
+ void **Numeric
+) ;
+
+void umfpack_zi_free_numeric
+(
+ void **Numeric
+) ;
+
+void umfpack_zl_free_numeric
+(
+ void **Numeric
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ umfpack_di_free_numeric (&Numeric) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ umfpack_dl_free_numeric (&Numeric) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ umfpack_zi_free_numeric (&Numeric) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ umfpack_zl_free_numeric (&Numeric) ;
+
+Purpose:
+
+ Deallocates the Numeric object and sets the Numeric handle to NULL. This
+ routine is the only valid way of destroying the Numeric object.
+
+Arguments:
+
+ void **Numeric ; Input argument, set to (void *) NULL on output.
+
+ Numeric points to a valid Numeric object, computed by umfpack_*_numeric.
+ No action is taken if Numeric is a (void *) NULL pointer.
+*/
diff --git a/UMFPACK/Include/umfpack_free_symbolic.h b/UMFPACK/Include/umfpack_free_symbolic.h
new file mode 100644
index 0000000..ad3aeb6
--- /dev/null
+++ b/UMFPACK/Include/umfpack_free_symbolic.h
@@ -0,0 +1,67 @@
+/* ========================================================================== */
+/* === umfpack_free_symbolic ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_free_symbolic
+(
+ void **Symbolic
+) ;
+
+void umfpack_dl_free_symbolic
+(
+ void **Symbolic
+) ;
+
+void umfpack_zi_free_symbolic
+(
+ void **Symbolic
+) ;
+
+void umfpack_zl_free_symbolic
+(
+ void **Symbolic
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ umfpack_di_free_symbolic (&Symbolic) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ umfpack_dl_free_symbolic (&Symbolic) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ umfpack_zi_free_symbolic (&Symbolic) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ umfpack_zl_free_symbolic (&Symbolic) ;
+
+Purpose:
+
+ Deallocates the Symbolic object and sets the Symbolic handle to NULL. This
+ routine is the only valid way of destroying the Symbolic object.
+
+Arguments:
+
+ void **Symbolic ; Input argument, set to (void *) NULL on output.
+
+ Points to a valid Symbolic object computed by umfpack_*_symbolic.
+ No action is taken if Symbolic is a (void *) NULL pointer.
+*/
diff --git a/UMFPACK/Include/umfpack_get_determinant.h b/UMFPACK/Include/umfpack_get_determinant.h
new file mode 100644
index 0000000..702c1f1
--- /dev/null
+++ b/UMFPACK/Include/umfpack_get_determinant.h
@@ -0,0 +1,196 @@
+/* ========================================================================== */
+/* === UMFPACK_get_determinant ============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* UMFPACK_get_determinant contributed by David Bateman, Motorola, Paris. */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_get_determinant
+(
+ double *Mx,
+ double *Ex,
+ void *NumericHandle,
+ double User_Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_dl_get_determinant
+(
+ double *Mx,
+ double *Ex,
+ void *NumericHandle,
+ double User_Info [UMFPACK_INFO]
+) ;
+
+int umfpack_zi_get_determinant
+(
+ double *Mx,
+ double *Mz,
+ double *Ex,
+ void *NumericHandle,
+ double User_Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_zl_get_determinant
+(
+ double *Mx,
+ double *Mz,
+ double *Ex,
+ void *NumericHandle,
+ double User_Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status ;
+ double Mx, Ex, Info [UMFPACK_INFO] ;
+ status = umfpack_di_get_determinant (&Mx, &Ex, Numeric, Info) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status ;
+ double Mx, Ex, Info [UMFPACK_INFO] ;
+ status = umfpack_dl_get_determinant (&Mx, &Ex, Numeric, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status ;
+ double Mx, Mz, Ex, Info [UMFPACK_INFO] ;
+ status = umfpack_zi_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status ;
+ double *Mx, *Mz, *Ex, Info [UMFPACK_INFO] ;
+ status = umfpack_zl_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ;
+
+packed complex int Syntax:
+
+ Same as above, except Mz is NULL.
+
+Author: Contributed by David Bateman, Motorola, Paris
+
+Purpose:
+
+ Using the LU factors and the permutation vectors contained in the Numeric
+ object, calculate the determinant of the matrix A.
+
+ The value of the determinant can be returned in two forms, depending on
+ whether Ex is NULL or not. If Ex is NULL then the value of the determinant
+ is returned on Mx and Mz for the real and imaginary parts. However, to
+ avoid over- or underflows, the determinant can be split into a mantissa
+ and exponent, and the parts returned separately, in which case Ex is not
+ NULL. The actual determinant is then given by
+
+ double det ;
+ det = Mx * pow (10.0, Ex) ;
+
+ for the double case, or
+
+ double det [2] ;
+ det [0] = Mx * pow (10.0, Ex) ; // real part
+ det [1] = Mz * pow (10.0, Ex) ; // imaginary part
+
+ for the complex case. Information on if the determinant will or has
+ over or under-flowed is given by Info [UMFPACK_STATUS].
+
+ In the "packed complex" syntax, Mx [0] holds the real part and Mx [1]
+ holds the imaginary part. Mz is not used (it is NULL).
+
+Returns:
+
+ Returns UMFPACK_OK if sucessful. Returns UMFPACK_ERROR_out_of_memory if
+ insufficient memory is available for the n_row integer workspace that
+ umfpack_*_get_determinant allocates to construct pivots from the
+ permutation vectors. Returns UMFPACK_ERROR_invalid_Numeric_object if the
+ Numeric object provided as input is invalid. Returns
+ UMFPACK_WARNING_singular_matrix if the determinant is zero. Returns
+ UMFPACK_WARNING_determinant_underflow or
+ UMFPACK_WARNING_determinant_overflow if the determinant has underflowed
+ overflowed (for the case when Ex is NULL), or will overflow if Ex is not
+ NULL and det is computed (see above) in the user program.
+
+Arguments:
+
+ double *Mx ; Output argument (array of size 1, or size 2 if Mz is NULL)
+ double *Mz ; Output argument (optional)
+ double *Ex ; Output argument (optional)
+
+ The determinant returned in mantissa/exponent form, as discussed above.
+ If Mz is NULL, then both the original and imaginary parts will be
+ returned in Mx. If Ex is NULL then the determinant is returned directly
+ in Mx and Mz (or Mx [0] and Mx [1] if Mz is NULL), rather than in
+ mantissa/exponent form.
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric.
+
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ Contains information about the calculation of the determinant. If a
+ (double *) NULL pointer is passed, then no statistics are returned in
+ Info (this is not an error condition). The following statistics are
+ computed in umfpack_*_determinant:
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ The determinant was successfully found.
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to solve the linear system.
+
+ UMFPACK_ERROR_argument_missing
+
+ Mx is missing (NULL).
+
+ UMFPACK_ERROR_invalid_Numeric_object
+
+ The Numeric object is not valid.
+
+ UMFPACK_ERROR_invalid_system
+
+ The matrix is rectangular. Only square systems can be
+ handled.
+
+ UMFPACK_WARNING_singluar_matrix
+
+ The determinant is zero or NaN. The matrix is singular.
+
+ UMFPACK_WARNING_determinant_underflow
+
+ When passing from mantissa/exponent form to the determinant
+ an underflow has or will occur. If the mantissa/exponent from
+ of obtaining the determinant is used, the underflow will occur
+ in the user program. If the single argument method of
+ obtaining the determinant is used, the underflow has already
+ occurred.
+
+ UMFPACK_WARNING_determinant_overflow
+
+ When passing from mantissa/exponent form to the determinant
+ an overflow has or will occur. If the mantissa/exponent from
+ of obtaining the determinant is used, the overflow will occur
+ in the user program. If the single argument method of
+ obtaining the determinant is used, the overflow has already
+ occurred.
+
+
+*/
diff --git a/UMFPACK/Include/umfpack_get_lunz.h b/UMFPACK/Include/umfpack_get_lunz.h
new file mode 100644
index 0000000..512cffa
--- /dev/null
+++ b/UMFPACK/Include/umfpack_get_lunz.h
@@ -0,0 +1,137 @@
+/* ========================================================================== */
+/* === umfpack_get_lunz ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_get_lunz
+(
+ int *lnz,
+ int *unz,
+ int *n_row,
+ int *n_col,
+ int *nz_udiag,
+ void *Numeric
+) ;
+
+UF_long umfpack_dl_get_lunz
+(
+ UF_long *lnz,
+ UF_long *unz,
+ UF_long *n_row,
+ UF_long *n_col,
+ UF_long *nz_udiag,
+ void *Numeric
+) ;
+
+int umfpack_zi_get_lunz
+(
+ int *lnz,
+ int *unz,
+ int *n_row,
+ int *n_col,
+ int *nz_udiag,
+ void *Numeric
+) ;
+
+UF_long umfpack_zl_get_lunz
+(
+ UF_long *lnz,
+ UF_long *unz,
+ UF_long *n_row,
+ UF_long *n_col,
+ UF_long *nz_udiag,
+ void *Numeric
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, lnz, unz, n_row, n_col, nz_udiag ;
+ status = umfpack_di_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag,
+ Numeric) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, lnz, unz, n_row, n_col, nz_udiag ;
+ status = umfpack_dl_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag,
+ Numeric) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, lnz, unz, n_row, n_col, nz_udiag ;
+ status = umfpack_zi_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag,
+ Numeric) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, lnz, unz, n_row, n_col, nz_udiag ;
+ status = umfpack_zl_get_lunz (&lnz, &unz, &n_row, &n_col, &nz_udiag,
+ Numeric) ;
+
+Purpose:
+
+ Determines the size and number of nonzeros in the LU factors held by the
+ Numeric object. These are also the sizes of the output arrays required
+ by umfpack_*_get_numeric.
+
+ The matrix L is n_row -by- min(n_row,n_col), with lnz nonzeros, including
+ the entries on the unit diagonal of L.
+
+ The matrix U is min(n_row,n_col) -by- n_col, with unz nonzeros, including
+ nonzeros on the diagonal of U.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_invalid_Numeric_object if Numeric is not a valid object.
+ UMFPACK_ERROR_argument_missing if any other argument is (Int *) NULL.
+
+Arguments:
+
+ Int *lnz ; Output argument.
+
+ The number of nonzeros in L, including the diagonal (which is all
+ one's). This value is the required size of the Lj and Lx arrays as
+ computed by umfpack_*_get_numeric. The value of lnz is identical to
+ Info [UMFPACK_LNZ], if that value was returned by umfpack_*_numeric.
+
+ Int *unz ; Output argument.
+
+ The number of nonzeros in U, including the diagonal. This value is the
+ required size of the Ui and Ux arrays as computed by
+ umfpack_*_get_numeric. The value of unz is identical to
+ Info [UMFPACK_UNZ], if that value was returned by umfpack_*_numeric.
+
+ Int *n_row ; Output argument.
+ Int *n_col ; Output argument.
+
+ The order of the L and U matrices. L is n_row -by- min(n_row,n_col)
+ and U is min(n_row,n_col) -by- n_col.
+
+ Int *nz_udiag ; Output argument.
+
+ The number of numerically nonzero values on the diagonal of U. The
+ matrix is singular if nz_diag < min(n_row,n_col). A divide-by-zero
+ will occur if nz_diag < n_row == n_col when solving a sparse system
+ involving the matrix U in umfpack_*_*solve. The value of nz_udiag is
+ identical to Info [UMFPACK_UDIAG_NZ] if that value was returned by
+ umfpack_*_numeric.
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric.
+*/
diff --git a/UMFPACK/Include/umfpack_get_numeric.h b/UMFPACK/Include/umfpack_get_numeric.h
new file mode 100644
index 0000000..45ba0e6
--- /dev/null
+++ b/UMFPACK/Include/umfpack_get_numeric.h
@@ -0,0 +1,254 @@
+/* ========================================================================== */
+/* === umfpack_get_numeric ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_get_numeric
+(
+ int Lp [ ],
+ int Lj [ ],
+ double Lx [ ],
+ int Up [ ],
+ int Ui [ ],
+ double Ux [ ],
+ int P [ ],
+ int Q [ ],
+ double Dx [ ],
+ int *do_recip,
+ double Rs [ ],
+ void *Numeric
+) ;
+
+UF_long umfpack_dl_get_numeric
+(
+ UF_long Lp [ ],
+ UF_long Lj [ ],
+ double Lx [ ],
+ UF_long Up [ ],
+ UF_long Ui [ ],
+ double Ux [ ],
+ UF_long P [ ],
+ UF_long Q [ ],
+ double Dx [ ],
+ UF_long *do_recip,
+ double Rs [ ],
+ void *Numeric
+) ;
+
+int umfpack_zi_get_numeric
+(
+ int Lp [ ],
+ int Lj [ ],
+ double Lx [ ], double Lz [ ],
+ int Up [ ],
+ int Ui [ ],
+ double Ux [ ], double Uz [ ],
+ int P [ ],
+ int Q [ ],
+ double Dx [ ], double Dz [ ],
+ int *do_recip,
+ double Rs [ ],
+ void *Numeric
+) ;
+
+UF_long umfpack_zl_get_numeric
+(
+ UF_long Lp [ ],
+ UF_long Lj [ ],
+ double Lx [ ], double Lz [ ],
+ UF_long Up [ ],
+ UF_long Ui [ ],
+ double Ux [ ], double Uz [ ],
+ UF_long P [ ],
+ UF_long Q [ ],
+ double Dx [ ], double Dz [ ],
+ UF_long *do_recip,
+ double Rs [ ],
+ void *Numeric
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ;
+ double *Lx, *Ux, *Dx, *Rs ;
+ status = umfpack_di_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, Dx,
+ &do_recip, Rs, Numeric) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ;
+ double *Lx, *Ux, *Dx, *Rs ;
+ status = umfpack_dl_get_numeric (Lp, Lj, Lx, Up, Ui, Ux, P, Q, Dx,
+ &do_recip, Rs, Numeric) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ;
+ double *Lx, *Lz, *Ux, *Uz, *Dx, *Dz, *Rs ;
+ status = umfpack_zi_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q,
+ Dx, Dz, &do_recip, Rs, Numeric) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long *Lp, *Lj, *Up, *Ui, *P, *Q, status, do_recip ;
+ double *Lx, *Lz, *Ux, *Uz, *Dx, *Dz, *Rs ;
+ status = umfpack_zl_get_numeric (Lp, Lj, Lx, Lz, Up, Ui, Ux, Uz, P, Q,
+ Dx, Dz, &do_recip, Rs, Numeric) ;
+
+packed complex int/UF_long Syntax:
+
+ Same as above, except Lz, Uz, and Dz are all NULL.
+
+Purpose:
+
+ This routine copies the LU factors and permutation vectors from the Numeric
+ object into user-accessible arrays. This routine is not needed to solve a
+ linear system. Note that the output arrays Lp, Lj, Lx, Up, Ui, Ux, P, Q,
+ Dx, and Rs are not allocated by umfpack_*_get_numeric; they must exist on
+ input.
+
+ All output arguments are optional. If any of them are NULL
+ on input, then that part of the LU factorization is not copied. You can
+ use this routine to extract just the parts of the LU factorization that
+ you want. For example, to retrieve just the column permutation Q, use:
+
+ #define noD (double *) NULL
+ #define noI (int *) NULL
+ status = umfpack_di_get_numeric (noI, noI, noD, noI, noI, noD, noI,
+ Q, noD, noI, noD, Numeric) ;
+
+Returns:
+
+ Returns UMFPACK_OK if successful. Returns UMFPACK_ERROR_out_of_memory
+ if insufficient memory is available for the 2*max(n_row,n_col) integer
+ workspace that umfpack_*_get_numeric allocates to construct L and/or U.
+ Returns UMFPACK_ERROR_invalid_Numeric_object if the Numeric object provided
+ as input is invalid.
+
+Arguments:
+
+ Int Lp [n_row+1] ; Output argument.
+ Int Lj [lnz] ; Output argument.
+ double Lx [lnz] ; Output argument. Size 2*lnz for packed complex case.
+ double Lz [lnz] ; Output argument for complex versions.
+
+ The n_row-by-min(n_row,n_col) matrix L is returned in compressed-row
+ form. The column indices of row i and corresponding numerical values
+ are in:
+
+ Lj [Lp [i] ... Lp [i+1]-1]
+ Lx [Lp [i] ... Lp [i+1]-1] real part
+ Lz [Lp [i] ... Lp [i+1]-1] imaginary part (complex versions)
+
+ respectively. Each row is stored in sorted order, from low column
+ indices to higher. The last entry in each row is the diagonal, which
+ is numerically equal to one. The sizes of Lp, Lj, Lx, and Lz are
+ returned by umfpack_*_get_lunz. If Lp, Lj, or Lx are not present,
+ then the matrix L is not returned. This is not an error condition.
+ The L matrix can be printed if n_row, Lp, Lj, Lx (and Lz for the split
+ complex case) are passed to umfpack_*_report_matrix (using the
+ "row" form).
+
+ If Lx is present and Lz is NULL, then both real
+ and imaginary parts are returned in Lx[0..2*lnz-1], with Lx[2*k]
+ and Lx[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int Up [n_col+1] ; Output argument.
+ Int Ui [unz] ; Output argument.
+ double Ux [unz] ; Output argument. Size 2*unz for packed complex case.
+ double Uz [unz] ; Output argument for complex versions.
+
+ The min(n_row,n_col)-by-n_col matrix U is returned in compressed-column
+ form. The row indices of column j and corresponding numerical values
+ are in
+
+ Ui [Up [j] ... Up [j+1]-1]
+ Ux [Up [j] ... Up [j+1]-1] real part
+ Uz [Up [j] ... Up [j+1]-1] imaginary part (complex versions)
+
+ respectively. Each column is stored in sorted order, from low row
+ indices to higher. The last entry in each column is the diagonal
+ (assuming that it is nonzero). The sizes of Up, Ui, Ux, and Uz are
+ returned by umfpack_*_get_lunz. If Up, Ui, or Ux are not present,
+ then the matrix U is not returned. This is not an error condition.
+ The U matrix can be printed if n_col, Up, Ui, Ux (and Uz for the
+ split complex case) are passed to umfpack_*_report_matrix (using the
+ "column" form).
+
+ If Ux is present and Uz is NULL, then both real
+ and imaginary parts are returned in Ux[0..2*unz-1], with Ux[2*k]
+ and Ux[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int P [n_row] ; Output argument.
+
+ The permutation vector P is defined as P [k] = i, where the original
+ row i of A is the kth pivot row in PAQ. If you do not want the P vector
+ to be returned, simply pass (Int *) NULL for P. This is not an error
+ condition. You can print P and Q with umfpack_*_report_perm.
+
+ Int Q [n_col] ; Output argument.
+
+ The permutation vector Q is defined as Q [k] = j, where the original
+ column j of A is the kth pivot column in PAQ. If you not want the Q
+ vector to be returned, simply pass (Int *) NULL for Q. This is not
+ an error condition. Note that Q is not necessarily identical to
+ Qtree, the column pre-ordering held in the Symbolic object. Refer to
+ the description of Qtree and Front_npivcol in umfpack_*_get_symbolic for
+ details.
+
+ double Dx [min(n_row,n_col)] ; Output argument. Size 2*n for
+ the packed complex case.
+ double Dz [min(n_row,n_col)] ; Output argument for complex versions.
+
+ The diagonal of U is also returned in Dx and Dz. You can extract the
+ diagonal of U without getting all of U by passing a non-NULL Dx (and
+ Dz for the complex version) and passing Up, Ui, and Ux as NULL. Dx is
+ the real part of the diagonal, and Dz is the imaginary part.
+
+ If Dx is present and Dz is NULL, then both real
+ and imaginary parts are returned in Dx[0..2*min(n_row,n_col)-1],
+ with Dx[2*k] and Dx[2*k+1] being the real and imaginary part of the kth
+ entry.
+
+ Int *do_recip ; Output argument.
+
+ This argument defines how the scale factors Rs are to be interpretted.
+
+ If do_recip is TRUE (one), then the scale factors Rs [i] are to be used
+ by multiplying row i by Rs [i]. Otherwise, the entries in row i are to
+ be divided by Rs [i].
+
+ If UMFPACK has been compiled with gcc, or for MATLAB as either a
+ built-in routine or as a mexFunction, then the NRECIPROCAL flag is
+ set, and do_recip will always be FALSE (zero).
+
+ double Rs [n_row] ; Output argument.
+
+ The row scale factors are returned in Rs [0..n_row-1]. Row i of A is
+ scaled by dividing or multiplying its values by Rs [i]. If default
+ scaling is in use, Rs [i] is the sum of the absolute values of row i
+ (or its reciprocal). If max row scaling is in use, then Rs [i] is the
+ maximum absolute value in row i (or its reciprocal).
+ Otherwise, Rs [i] = 1. If row i is all zero, Rs [i] = 1 as well. For
+ the complex version, an approximate absolute value is used
+ (|x_real|+|x_imag|).
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric.
+*/
diff --git a/UMFPACK/Include/umfpack_get_symbolic.h b/UMFPACK/Include/umfpack_get_symbolic.h
new file mode 100644
index 0000000..21b7cc2
--- /dev/null
+++ b/UMFPACK/Include/umfpack_get_symbolic.h
@@ -0,0 +1,339 @@
+/* ========================================================================== */
+/* === umfpack_get_symbolic ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_get_symbolic
+(
+ int *n_row,
+ int *n_col,
+ int *n1,
+ int *nz,
+ int *nfr,
+ int *nchains,
+ int P [ ],
+ int Q [ ],
+ int Front_npivcol [ ],
+ int Front_parent [ ],
+ int Front_1strow [ ],
+ int Front_leftmostdesc [ ],
+ int Chain_start [ ],
+ int Chain_maxrows [ ],
+ int Chain_maxcols [ ],
+ void *Symbolic
+) ;
+
+UF_long umfpack_dl_get_symbolic
+(
+ UF_long *n_row,
+ UF_long *n_col,
+ UF_long *n1,
+ UF_long *nz,
+ UF_long *nfr,
+ UF_long *nchains,
+ UF_long P [ ],
+ UF_long Q [ ],
+ UF_long Front_npivcol [ ],
+ UF_long Front_parent [ ],
+ UF_long Front_1strow [ ],
+ UF_long Front_leftmostdesc [ ],
+ UF_long Chain_start [ ],
+ UF_long Chain_maxrows [ ],
+ UF_long Chain_maxcols [ ],
+ void *Symbolic
+) ;
+
+int umfpack_zi_get_symbolic
+(
+ int *n_row,
+ int *n_col,
+ int *n1,
+ int *nz,
+ int *nfr,
+ int *nchains,
+ int P [ ],
+ int Q [ ],
+ int Front_npivcol [ ],
+ int Front_parent [ ],
+ int Front_1strow [ ],
+ int Front_leftmostdesc [ ],
+ int Chain_start [ ],
+ int Chain_maxrows [ ],
+ int Chain_maxcols [ ],
+ void *Symbolic
+) ;
+
+UF_long umfpack_zl_get_symbolic
+(
+ UF_long *n_row,
+ UF_long *n_col,
+ UF_long *n1,
+ UF_long *nz,
+ UF_long *nfr,
+ UF_long *nchains,
+ UF_long P [ ],
+ UF_long Q [ ],
+ UF_long Front_npivcol [ ],
+ UF_long Front_parent [ ],
+ UF_long Front_1strow [ ],
+ UF_long Front_leftmostdesc [ ],
+ UF_long Chain_start [ ],
+ UF_long Chain_maxrows [ ],
+ UF_long Chain_maxcols [ ],
+ void *Symbolic
+) ;
+
+/*
+
+double int Syntax:
+
+ #include "umfpack.h"
+ int status, n_row, n_col, nz, nfr, nchains, *P, *Q,
+ *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc,
+ *Chain_start, *Chain_maxrows, *Chain_maxcols ;
+ void *Symbolic ;
+ status = umfpack_di_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains,
+ P, Q, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status, n_row, n_col, nz, nfr, nchains, *P, *Q,
+ *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc,
+ *Chain_start, *Chain_maxrows, *Chain_maxcols ;
+ void *Symbolic ;
+ status = umfpack_dl_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains,
+ P, Q, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int status, n_row, n_col, nz, nfr, nchains, *P, *Q,
+ *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc,
+ *Chain_start, *Chain_maxrows, *Chain_maxcols ;
+ void *Symbolic ;
+ status = umfpack_zi_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains,
+ P, Q, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status, n_row, n_col, nz, nfr, nchains, *P, *Q,
+ *Front_npivcol, *Front_parent, *Front_1strow, *Front_leftmostdesc,
+ *Chain_start, *Chain_maxrows, *Chain_maxcols ;
+ void *Symbolic ;
+ status = umfpack_zl_get_symbolic (&n_row, &n_col, &nz, &nfr, &nchains,
+ P, Q, Front_npivcol, Front_parent, Front_1strow,
+ Front_leftmostdesc, Chain_start, Chain_maxrows, Chain_maxcols,
+ Symbolic) ;
+
+Purpose:
+
+ Copies the contents of the Symbolic object into simple integer arrays
+ accessible to the user. This routine is not needed to factorize and/or
+ solve a sparse linear system using UMFPACK. Note that the output arrays
+ P, Q, Front_npivcol, Front_parent, Front_1strow, Front_leftmostdesc,
+ Chain_start, Chain_maxrows, and Chain_maxcols are not allocated by
+ umfpack_*_get_symbolic; they must exist on input.
+
+ All output arguments are optional. If any of them are NULL
+ on input, then that part of the symbolic analysis is not copied. You can
+ use this routine to extract just the parts of the symbolic analysis that
+ you want. For example, to retrieve just the column permutation Q, use:
+
+ #define noI (int *) NULL
+ status = umfpack_di_get_symbolic (noI, noI, noI, noI, noI, noI, noI,
+ Q, noI, noI, noI, noI, noI, noI, noI, Symbolic) ;
+
+ The only required argument the last one, the pointer to the Symbolic object.
+
+ The Symbolic object is small. Its size for an n-by-n square matrix varies
+ from 4*n to 13*n, depending on the matrix. The object holds the initial
+ column permutation, the supernodal column elimination tree, and information
+ about each frontal matrix. You can print it with umfpack_*_report_symbolic.
+
+Returns:
+
+ Returns UMFPACK_OK if successful, UMFPACK_ERROR_invalid_Symbolic_object
+ if Symbolic is an invalid object.
+
+Arguments:
+
+ Int *n_row ; Output argument.
+ Int *n_col ; Output argument.
+
+ The dimensions of the matrix A analyzed by the call to
+ umfpack_*_symbolic that generated the Symbolic object.
+
+ Int *n1 ; Output argument.
+
+ The number of pivots with zero Markowitz cost (they have just one entry
+ in the pivot row, or the pivot column, or both). These appear first in
+ the output permutations P and Q.
+
+ Int *nz ; Output argument.
+
+ The number of nonzeros in A.
+
+ Int *nfr ; Output argument.
+
+ The number of frontal matrices that will be used by umfpack_*_numeric
+ to factorize the matrix A. It is in the range 0 to n_col.
+
+ Int *nchains ; Output argument.
+
+ The frontal matrices are related to one another by the supernodal
+ column elimination tree. Each node in this tree is one frontal matrix.
+ The tree is partitioned into a set of disjoint paths, and a frontal
+ matrix chain is one path in this tree. Each chain is factorized using
+ a unifrontal technique, with a single working array that holds each
+ frontal matrix in the chain, one at a time. nchains is in the range
+ 0 to nfr.
+
+ Int P [n_row] ; Output argument.
+
+ The initial row permutation. If P [k] = i, then this means that
+ row i is the kth row in the pre-ordered matrix. In general, this P is
+ not the same as the final row permutation computed by umfpack_*_numeric.
+
+ For the unsymmetric strategy, P defines the row-merge order. Let j be
+ the column index of the leftmost nonzero entry in row i of A*Q. Then
+ P defines a sort of the rows according to this value. A row can appear
+ earlier in this ordering if it is aggressively absorbed before it can
+ become a pivot row. If P [k] = i, row i typically will not be the kth
+ pivot row.
+
+ For the symmetric strategy, P = Q. For the 2-by-2 strategy, P is the
+ row permutation that places large entries on the diagonal of P*A*Q.
+ If no pivoting occurs during numerical factorization, P [k] = i also
+ defines the final permutation of umfpack_*_numeric, for either the
+ symmetric or 2-by-2 strategies.
+
+ Int Q [n_col] ; Output argument.
+
+ The initial column permutation. If Q [k] = j, then this means that
+ column j is the kth pivot column in the pre-ordered matrix. Q is
+ not necessarily the same as the final column permutation Q, computed by
+ umfpack_*_numeric. The numeric factorization may reorder the pivot
+ columns within each frontal matrix to reduce fill-in. If the matrix is
+ structurally singular, and if the symmetric or 2-by-2 strategies or
+ used (or if Control [UMFPACK_FIXQ] > 0), then this Q will be the same
+ as the final column permutation computed in umfpack_*_numeric.
+
+ Int Front_npivcol [n_col+1] ; Output argument.
+
+ This array should be of size at least n_col+1, in order to guarantee
+ that it will be large enough to hold the output. Only the first nfr+1
+ entries are used, however.
+
+ The kth frontal matrix holds Front_npivcol [k] pivot columns. Thus, the
+ first frontal matrix, front 0, is used to factorize the first
+ Front_npivcol [0] columns; these correspond to the original columns
+ Q [0] through Q [Front_npivcol [0]-1]. The next frontal matrix
+ is used to factorize the next Front_npivcol [1] columns, which are thus
+ the original columns Q [Front_npivcol [0]] through
+ Q [Front_npivcol [0] + Front_npivcol [1] - 1], and so on. Columns
+ with no entries at all are put in a placeholder "front",
+ Front_npivcol [nfr]. The sum of Front_npivcol [0..nfr] is equal to
+ n_col.
+
+ Any modifications that umfpack_*_numeric makes to the initial column
+ permutation are constrained to within each frontal matrix. Thus, for
+ the first frontal matrix, Q [0] through Q [Front_npivcol [0]-1] is some
+ permutation of the columns Q [0] through
+ Q [Front_npivcol [0]-1]. For second frontal matrix,
+ Q [Front_npivcol [0]] through Q [Front_npivcol [0] + Front_npivcol[1]-1]
+ is some permutation of the same portion of Q, and so on. All pivot
+ columns are numerically factorized within the frontal matrix originally
+ determined by the symbolic factorization; there is no delayed pivoting
+ across frontal matrices.
+
+ Int Front_parent [n_col+1] ; Output argument.
+
+ This array should be of size at least n_col+1, in order to guarantee
+ that it will be large enough to hold the output. Only the first nfr+1
+ entries are used, however.
+
+ Front_parent [0..nfr] holds the supernodal column elimination tree
+ (including the placeholder front nfr, which may be empty). Each node in
+ the tree corresponds to a single frontal matrix. The parent of node f
+ is Front_parent [f].
+
+ Int Front_1strow [n_col+1] ; Output argument.
+
+ This array should be of size at least n_col+1, in order to guarantee
+ that it will be large enough to hold the output. Only the first nfr+1
+ entries are used, however.
+
+ Front_1strow [k] is the row index of the first row in A (P,Q)
+ whose leftmost entry is in a pivot column for the kth front. This is
+ necessary only to properly factorize singular matrices. Rows in the
+ range Front_1strow [k] to Front_1strow [k+1]-1 first become pivot row
+ candidates at the kth front. Any rows not eliminated in the kth front
+ may be selected as pivot rows in the parent of k (Front_parent [k])
+ and so on up the tree.
+
+ Int Front_leftmostdesc [n_col+1] ; Output argument.
+
+ This array should be of size at least n_col+1, in order to guarantee
+ that it will be large enough to hold the output. Only the first nfr+1
+ entries are used, however.
+
+ Front_leftmostdesc [k] is the leftmost descendant of front k, or k
+ if the front has no children in the tree. Since the rows and columns
+ (P and Q) have been post-ordered via a depth-first-search of
+ the tree, rows in the range Front_1strow [Front_leftmostdesc [k]] to
+ Front_1strow [k+1]-1 form the entire set of candidate pivot rows for
+ the kth front (some of these will typically have already been selected
+ by fronts in the range Front_leftmostdesc [k] to front k-1, before
+ the factorization reaches front k).
+
+ Chain_start [n_col+1] ; Output argument.
+
+ This array should be of size at least n_col+1, in order to guarantee
+ that it will be large enough to hold the output. Only the first
+ nchains+1 entries are used, however.
+
+ The kth frontal matrix chain consists of frontal matrices Chain_start[k]
+ through Chain_start [k+1]-1. Thus, Chain_start [0] is always 0, and
+ Chain_start [nchains] is the total number of frontal matrices, nfr. For
+ two adjacent fronts f and f+1 within a single chain, f+1 is always the
+ parent of f (that is, Front_parent [f] = f+1).
+
+ Int Chain_maxrows [n_col+1] ; Output argument.
+ Int Chain_maxcols [n_col+1] ; Output argument.
+
+ These arrays should be of size at least n_col+1, in order to guarantee
+ that they will be large enough to hold the output. Only the first
+ nchains entries are used, however.
+
+ The kth frontal matrix chain requires a single working array of
+ dimension Chain_maxrows [k] by Chain_maxcols [k], for the unifrontal
+ technique that factorizes the frontal matrix chain. Since the symbolic
+ factorization only provides an upper bound on the size of each frontal
+ matrix, not all of the working array is necessarily used during the
+ numerical factorization.
+
+ Note that the upper bound on the number of rows and columns of each
+ frontal matrix is computed by umfpack_*_symbolic, but all that is
+ required by umfpack_*_numeric is the maximum of these two sets of
+ values for each frontal matrix chain. Thus, the size of each
+ individual frontal matrix is not preserved in the Symbolic object.
+
+ void *Symbolic ; Input argument, not modified.
+
+ The Symbolic object, which holds the symbolic factorization computed by
+ umfpack_*_symbolic. The Symbolic object is not modified by
+ umfpack_*_get_symbolic.
+*/
diff --git a/UMFPACK/Include/umfpack_global.h b/UMFPACK/Include/umfpack_global.h
new file mode 100644
index 0000000..51c64dd
--- /dev/null
+++ b/UMFPACK/Include/umfpack_global.h
@@ -0,0 +1,22 @@
+/* ========================================================================== */
+/* === umfpack_global ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* prototypes for global variables, and basic operators for complex values */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN double (*umfpack_hypot) (double, double) ;
+EXTERN int (*umfpack_divcomplex) (double, double, double, double, double *, double *) ;
+
+double umf_hypot (double x, double y) ;
+int umf_divcomplex (double, double, double, double, double *, double *) ;
+
diff --git a/UMFPACK/Include/umfpack_load_numeric.h b/UMFPACK/Include/umfpack_load_numeric.h
new file mode 100644
index 0000000..0b84c99
--- /dev/null
+++ b/UMFPACK/Include/umfpack_load_numeric.h
@@ -0,0 +1,95 @@
+/* ========================================================================== */
+/* === umfpack_load_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_load_numeric
+(
+ void **Numeric,
+ char *filename
+) ;
+
+UF_long umfpack_dl_load_numeric
+(
+ void **Numeric,
+ char *filename
+) ;
+
+int umfpack_zi_load_numeric
+(
+ void **Numeric,
+ char *filename
+) ;
+
+UF_long umfpack_zl_load_numeric
+(
+ void **Numeric,
+ char *filename
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_di_load_numeric (&Numeric, filename) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_dl_load_numeric (&Numeric, filename) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_zi_load_numeric (&Numeric, filename) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_zl_load_numeric (&Numeric, filename) ;
+
+Purpose:
+
+ Loads a Numeric object from a file created by umfpack_*_save_numeric. The
+ Numeric handle passed to this routine is overwritten with the new object.
+ If that object exists prior to calling this routine, a memory leak will
+ occur. The contents of Numeric are ignored on input.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_out_of_memory if not enough memory is available.
+ UMFPACK_ERROR_file_IO if an I/O error occurred.
+
+Arguments:
+
+ void **Numeric ; Output argument.
+
+ **Numeric is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Numeric object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ char *filename ; Input argument, not modified.
+
+ A string that contains the filename from which to read the Numeric
+ object.
+*/
diff --git a/UMFPACK/Include/umfpack_load_symbolic.h b/UMFPACK/Include/umfpack_load_symbolic.h
new file mode 100644
index 0000000..8bd5728
--- /dev/null
+++ b/UMFPACK/Include/umfpack_load_symbolic.h
@@ -0,0 +1,95 @@
+/* ========================================================================== */
+/* === umfpack_load_symbolic ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_load_symbolic
+(
+ void **Symbolic,
+ char *filename
+) ;
+
+UF_long umfpack_dl_load_symbolic
+(
+ void **Symbolic,
+ char *filename
+) ;
+
+int umfpack_zi_load_symbolic
+(
+ void **Symbolic,
+ char *filename
+) ;
+
+UF_long umfpack_zl_load_symbolic
+(
+ void **Symbolic,
+ char *filename
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_di_load_symbolic (&Symbolic, filename) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_dl_load_symbolic (&Symbolic, filename) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_zi_load_symbolic (&Symbolic, filename) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_zl_load_symbolic (&Symbolic, filename) ;
+
+Purpose:
+
+ Loads a Symbolic object from a file created by umfpack_*_save_symbolic. The
+ Symbolic handle passed to this routine is overwritten with the new object.
+ If that object exists prior to calling this routine, a memory leak will
+ occur. The contents of Symbolic are ignored on input.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_out_of_memory if not enough memory is available.
+ UMFPACK_ERROR_file_IO if an I/O error occurred.
+
+Arguments:
+
+ void **Symbolic ; Output argument.
+
+ **Symbolic is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Symbolic object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ char *filename ; Input argument, not modified.
+
+ A string that contains the filename from which to read the Symbolic
+ object.
+*/
diff --git a/UMFPACK/Include/umfpack_numeric.h b/UMFPACK/Include/umfpack_numeric.h
new file mode 100644
index 0000000..d871ef1
--- /dev/null
+++ b/UMFPACK/Include/umfpack_numeric.h
@@ -0,0 +1,543 @@
+/* ========================================================================== */
+/* === umfpack_numeric ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_numeric
+(
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ void *Symbolic,
+ void **Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_dl_numeric
+(
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ void *Symbolic,
+ void **Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+int umfpack_zi_numeric
+(
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ void *Symbolic,
+ void **Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_zl_numeric
+(
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ void *Symbolic,
+ void **Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic, *Numeric ;
+ int *Ap, *Ai, status ;
+ double *Ax, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info);
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic, *Numeric ;
+ UF_long *Ap, *Ai, status ;
+ double *Ax, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric, Control, Info);
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic, *Numeric ;
+ int *Ap, *Ai, status ;
+ double *Ax, *Az, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ status = umfpack_zi_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic, *Numeric ;
+ UF_long *Ap, *Ai, status ;
+ double *Ax, *Az, Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+
+packed complex Syntax:
+
+ Same as above, except that Az is NULL.
+
+Purpose:
+
+ Given a sparse matrix A in column-oriented form, and a symbolic analysis
+ computed by umfpack_*_*symbolic, the umfpack_*_numeric routine performs the
+ numerical factorization, PAQ=LU, PRAQ=LU, or P(R\A)Q=LU, where P and Q are
+ permutation matrices (represented as permutation vectors), R is the row
+ scaling, L is unit-lower triangular, and U is upper triangular. This is
+ required before the system Ax=b (or other related linear systems) can be
+ solved. umfpack_*_numeric can be called multiple times for each call to
+ umfpack_*_*symbolic, to factorize a sequence of matrices with identical
+ nonzero pattern. Simply compute the Symbolic object once, with
+ umfpack_*_*symbolic, and reuse it for subsequent matrices. This routine
+ safely detects if the pattern changes, and sets an appropriate error code.
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ Int Ap [n_col+1] ; Input argument, not modified.
+
+ This must be identical to the Ap array passed to umfpack_*_*symbolic.
+ The value of n_col is what was passed to umfpack_*_*symbolic (this is
+ held in the Symbolic object).
+
+ Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ This must be identical to the Ai array passed to umfpack_*_*symbolic.
+
+ double Ax [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+ Size 2*nz for packed complex case.
+
+ The numerical values of the sparse matrix A. The nonzero pattern (row
+ indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and
+ the corresponding numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)].
+
+ double Az [nz] ; Input argument, not modified, for complex versions.
+
+ For the complex versions, this holds the imaginary part of A. The
+ imaginary part of column j is held in Az [(Ap [j]) ... (Ap [j+1]-1)].
+
+ If Az is NULL, then both real
+ and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ void *Symbolic ; Input argument, not modified.
+
+ The Symbolic object, which holds the symbolic factorization computed by
+ umfpack_*_*symbolic. The Symbolic object is not modified by
+ umfpack_*_numeric.
+
+ void **Numeric ; Output argument.
+
+ **Numeric is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Numeric object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PIVOT_TOLERANCE]: relative pivot tolerance for
+ threshold partial pivoting with row interchanges. In any given
+ column, an entry is numerically acceptable if its absolute value is
+ greater than or equal to Control [UMFPACK_PIVOT_TOLERANCE] times
+ the largest absolute value in the column. A value of 1.0 gives true
+ partial pivoting. If less than or equal to zero, then any nonzero
+ entry is numerically acceptable as a pivot. Default: 0.1.
+
+ Smaller values tend to lead to sparser LU factors, but the solution
+ to the linear system can become inaccurate. Larger values can lead
+ to a more accurate solution (but not always), and usually an
+ increase in the total work.
+
+ For complex matrices, a cheap approximate of the absolute value
+ is used for the threshold partial pivoting test (|a_real| + |a_imag|
+ instead of the more expensive-to-compute exact absolute value
+ sqrt (a_real^2 + a_imag^2)).
+
+ Control [UMFPACK_SYM_PIVOT_TOLERANCE]:
+ If diagonal pivoting is attempted (the symmetric or symmetric-2by2
+ strategies are used) then this parameter is used to control when the
+ diagonal entry is selected in a given pivot column. The absolute
+ value of the entry must be >= Control [UMFPACK_SYM_PIVOT_TOLERANCE]
+ times the largest absolute value in the column. A value of zero
+ will ensure that no off-diagonal pivoting is performed, except that
+ zero diagonal entries are not selected if there are any off-diagonal
+ nonzero entries.
+
+ If an off-diagonal pivot is selected, an attempt is made to restore
+ symmetry later on. Suppose A (i,j) is selected, where i != j.
+ If column i has not yet been selected as a pivot column, then
+ the entry A (j,i) is redefined as a "diagonal" entry, except that
+ the tighter tolerance (Control [UMFPACK_PIVOT_TOLERANCE]) is
+ applied. This strategy has an effect similar to 2-by-2 pivoting
+ for symmetric indefinite matrices. If a 2-by-2 block pivot with
+ nonzero structure
+
+ i j
+ i: 0 x
+ j: x 0
+
+ is selected in a symmetric indefinite factorization method, the
+ 2-by-2 block is inverted and a rank-2 update is applied. In
+ UMFPACK, this 2-by-2 block would be reordered as
+
+ j i
+ i: x 0
+ j: 0 x
+
+ In both cases, the symmetry of the Schur complement is preserved.
+
+ Control [UMFPACK_SCALE]: Note that the user's input matrix is
+ never modified, only an internal copy is scaled.
+
+ There are three valid settings for this parameter. If any other
+ value is provided, the default is used.
+
+ UMFPACK_SCALE_NONE: no scaling is performed.
+
+ UMFPACK_SCALE_SUM: each row of the input matrix A is divided by
+ the sum of the absolute values of the entries in that row.
+ The scaled matrix has an infinity norm of 1.
+
+ UMFPACK_SCALE_MAX: each row of the input matrix A is divided by
+ the maximum the absolute values of the entries in that row.
+ In the scaled matrix the largest entry in each row has
+ a magnitude exactly equal to 1.
+
+ Note that for complex matrices, a cheap approximate absolute value
+ is used, |a_real| + |a_imag|, instead of the exact absolute value
+ sqrt ((a_real)^2 + (a_imag)^2).
+
+ Scaling is very important for the "symmetric" strategy when
+ diagonal pivoting is attempted. It also improves the performance
+ of the "unsymmetric" strategy.
+
+ Default: UMFPACK_SCALE_SUM.
+
+ Control [UMFPACK_ALLOC_INIT]:
+
+ When umfpack_*_numeric starts, it allocates memory for the Numeric
+ object. Part of this is of fixed size (approximately n double's +
+ 12*n integers). The remainder is of variable size, which grows to
+ hold the LU factors and the frontal matrices created during
+ factorization. A estimate of the upper bound is computed by
+ umfpack_*_*symbolic, and returned by umfpack_*_*symbolic in
+ Info [UMFPACK_VARIABLE_PEAK_ESTIMATE] (in Units).
+
+ If Control [UMFPACK_ALLOC_INIT] is >= 0, umfpack_*_numeric initially
+ allocates space for the variable-sized part equal to this estimate
+ times Control [UMFPACK_ALLOC_INIT]. Typically, for matrices for
+ which the "unsymmetric" strategy applies, umfpack_*_numeric needs
+ only about half the estimated memory space, so a setting of 0.5 or
+ 0.6 often provides enough memory for umfpack_*_numeric to factorize
+ the matrix with no subsequent increases in the size of this block.
+
+ If the matrix is ordered via AMD, then this non-negative parameter
+ is ignored. The initial allocation ratio computed automatically,
+ as 1.2 * (nz + Info [UMFPACK_SYMMETRIC_LUNZ]) /
+ (Info [UMFPACK_LNZ_ESTIMATE] + Info [UMFPACK_UNZ_ESTIMATE] -
+ min (n_row, n_col)).
+
+ If Control [UMFPACK_ALLOC_INIT] is negative, then umfpack_*_numeric
+ allocates a space with initial size (in Units) equal to
+ (-Control [UMFPACK_ALLOC_INIT]).
+
+ Regardless of the value of this parameter, a space equal to or
+ greater than the the bare minimum amount of memory needed to start
+ the factorization is always initially allocated. The bare initial
+ memory required is returned by umfpack_*_*symbolic in
+ Info [UMFPACK_VARIABLE_INIT_ESTIMATE] (an exact value, not an
+ estimate).
+
+ If the variable-size part of the Numeric object is found to be too
+ small sometime after numerical factorization has started, the memory
+ is increased in size by a factor of 1.2. If this fails, the
+ request is reduced by a factor of 0.95 until it succeeds, or until
+ it determines that no increase in size is possible. Garbage
+ collection then occurs.
+
+ The strategy of attempting to "malloc" a working space, and
+ re-trying with a smaller space, may not work when UMFPACK is used
+ as a mexFunction MATLAB, since mxMalloc aborts the mexFunction if it
+ fails. This issue does not affect the use of UMFPACK as a part of
+ the built-in x=A\b in MATLAB 6.5 and later.
+
+ If you are using the umfpack mexFunction, decrease the magnitude of
+ Control [UMFPACK_ALLOC_INIT] if you run out of memory in MATLAB.
+
+ Default initial allocation size: 0.7. Thus, with the default
+ control settings and the "unsymmetric" strategy, the upper-bound is
+ reached after two reallocations (0.7 * 1.2 * 1.2 = 1.008).
+
+ Changing this parameter has little effect on fill-in or operation
+ count. It has a small impact on run-time (the extra time required
+ to do the garbage collection and memory reallocation).
+
+ Control [UMFPACK_FRONT_ALLOC_INIT]:
+
+ When UMFPACK starts the factorization of each "chain" of frontal
+ matrices, it allocates a working array to hold the frontal matrices
+ as they are factorized. The symbolic factorization computes the
+ size of the largest possible frontal matrix that could occur during
+ the factorization of each chain.
+
+ If Control [UMFPACK_FRONT_ALLOC_INIT] is >= 0, the following
+ strategy is used. If the AMD ordering was used, this non-negative
+ parameter is ignored. A front of size (d+2)*(d+2) is allocated,
+ where d = Info [UMFPACK_SYMMETRIC_DMAX]. Otherwise, a front of
+ size Control [UMFPACK_FRONT_ALLOC_INIT] times the largest front
+ possible for this chain is allocated.
+
+ If Control [UMFPACK_FRONT_ALLOC_INIT] is negative, then a front of
+ size (-Control [UMFPACK_FRONT_ALLOC_INIT]) is allocated (where the
+ size is in terms of the number of numerical entries). This is done
+ regardless of the ordering method or ordering strategy used.
+
+ Default: 0.5.
+
+ Control [UMFPACK_DROPTOL]:
+
+ Entries in L and U with absolute value less than or equal to the
+ drop tolerance are removed from the data structures (unless leaving
+ them there reduces memory usage by reducing the space required
+ for the nonzero pattern of L and U).
+
+ Default: 0.0.
+
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ Contains statistics about the numeric factorization. If a
+ (double *) NULL pointer is passed, then no statistics are returned in
+ Info (this is not an error condition). The following statistics are
+ computed in umfpack_*_numeric:
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ Numeric factorization was successful. umfpack_*_numeric
+ computed a valid numeric factorization.
+
+ UMFPACK_WARNING_singular_matrix
+
+ Numeric factorization was successful, but the matrix is
+ singular. umfpack_*_numeric computed a valid numeric
+ factorization, but you will get a divide by zero in
+ umfpack_*_*solve. For the other cases below, no Numeric object
+ is created (*Numeric is (void *) NULL).
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to complete the numeric factorization.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments are missing.
+
+ UMFPACK_ERROR_invalid_Symbolic_object
+
+ Symbolic object provided as input is invalid.
+
+ UMFPACK_ERROR_different_pattern
+
+ The pattern (Ap and/or Ai) has changed since the call to
+ umfpack_*_*symbolic which produced the Symbolic object.
+
+ Info [UMFPACK_NROW]: the value of n_row stored in the Symbolic object.
+
+ Info [UMFPACK_NCOL]: the value of n_col stored in the Symbolic object.
+
+ Info [UMFPACK_NZ]: the number of entries in the input matrix.
+ This value is obtained from the Symbolic object.
+
+ Info [UMFPACK_SIZE_OF_UNIT]: the number of bytes in a Unit, for memory
+ usage statistics below.
+
+ Info [UMFPACK_VARIABLE_INIT]: the initial size (in Units) of the
+ variable-sized part of the Numeric object. If this differs from
+ Info [UMFPACK_VARIABLE_INIT_ESTIMATE], then the pattern (Ap and/or
+ Ai) has changed since the last call to umfpack_*_*symbolic, which is
+ an error condition.
+
+ Info [UMFPACK_VARIABLE_PEAK]: the peak size (in Units) of the
+ variable-sized part of the Numeric object. This size is the amount
+ of space actually used inside the block of memory, not the space
+ allocated via UMF_malloc. You can reduce UMFPACK's memory
+ requirements by setting Control [UMFPACK_ALLOC_INIT] to the ratio
+ Info [UMFPACK_VARIABLE_PEAK] / Info[UMFPACK_VARIABLE_PEAK_ESTIMATE].
+ This will ensure that no memory reallocations occur (you may want to
+ add 0.001 to make sure that integer roundoff does not lead to a
+ memory size that is 1 Unit too small; otherwise, garbage collection
+ and reallocation will occur).
+
+ Info [UMFPACK_VARIABLE_FINAL]: the final size (in Units) of the
+ variable-sized part of the Numeric object. It holds just the
+ sparse LU factors.
+
+ Info [UMFPACK_NUMERIC_SIZE]: the actual final size (in Units) of the
+ entire Numeric object, including the final size of the variable
+ part of the object. Info [UMFPACK_NUMERIC_SIZE_ESTIMATE],
+ an estimate, was computed by umfpack_*_*symbolic. The estimate is
+ normally an upper bound on the actual final size, but this is not
+ guaranteed.
+
+ Info [UMFPACK_PEAK_MEMORY]: the actual peak memory usage (in Units) of
+ both umfpack_*_*symbolic and umfpack_*_numeric. An estimate,
+ Info [UMFPACK_PEAK_MEMORY_ESTIMATE], was computed by
+ umfpack_*_*symbolic. The estimate is normally an upper bound on the
+ actual peak usage, but this is not guaranteed. With testing on
+ hundreds of matrix arising in real applications, I have never
+ observed a matrix where this estimate or the Numeric size estimate
+ was less than the actual result, but this is theoretically possible.
+ Please send me one if you find such a matrix.
+
+ Info [UMFPACK_FLOPS]: the actual count of the (useful) floating-point
+ operations performed. An estimate, Info [UMFPACK_FLOPS_ESTIMATE],
+ was computed by umfpack_*_*symbolic. The estimate is guaranteed to
+ be an upper bound on this flop count. The flop count excludes
+ "useless" flops on zero values, flops performed during the pivot
+ search (for tentative updates and assembly of candidate columns),
+ and flops performed to add frontal matrices together.
+
+ For the real version, only (+ - * /) are counted. For the complex
+ version, the following counts are used:
+
+ operation flops
+ c = 1/b 6
+ c = a*b 6
+ c -= a*b 8
+
+ Info [UMFPACK_LNZ]: the actual nonzero entries in final factor L,
+ including the diagonal. This excludes any zero entries in L,
+ although some of these are stored in the Numeric object. The
+ Info [UMFPACK_LU_ENTRIES] statistic does account for all
+ explicitly stored zeros, however. Info [UMFPACK_LNZ_ESTIMATE],
+ an estimate, was computed by umfpack_*_*symbolic. The estimate is
+ guaranteed to be an upper bound on Info [UMFPACK_LNZ].
+
+ Info [UMFPACK_UNZ]: the actual nonzero entries in final factor U,
+ including the diagonal. This excludes any zero entries in U,
+ although some of these are stored in the Numeric object. The
+ Info [UMFPACK_LU_ENTRIES] statistic does account for all
+ explicitly stored zeros, however. Info [UMFPACK_UNZ_ESTIMATE],
+ an estimate, was computed by umfpack_*_*symbolic. The estimate is
+ guaranteed to be an upper bound on Info [UMFPACK_UNZ].
+
+ Info [UMFPACK_NUMERIC_DEFRAG]: The number of garbage collections
+ performed during umfpack_*_numeric, to compact the contents of the
+ variable-sized workspace used by umfpack_*_numeric. No estimate was
+ computed by umfpack_*_*symbolic. In the current version of UMFPACK,
+ garbage collection is performed and then the memory is reallocated,
+ so this statistic is the same as Info [UMFPACK_NUMERIC_REALLOC],
+ below. It may differ in future releases.
+
+ Info [UMFPACK_NUMERIC_REALLOC]: The number of times that the Numeric
+ object was increased in size from its initial size. A rough upper
+ bound on the peak size of the Numeric object was computed by
+ umfpack_*_*symbolic, so reallocations should be rare. However, if
+ umfpack_*_numeric is unable to allocate that much storage, it
+ reduces its request until either the allocation succeeds, or until
+ it gets too small to do anything with. If the memory that it
+ finally got was small, but usable, then the reallocation count
+ could be high. No estimate of this count was computed by
+ umfpack_*_*symbolic.
+
+ Info [UMFPACK_NUMERIC_COSTLY_REALLOC]: The number of times that the
+ system realloc library routine (or mxRealloc for the mexFunction)
+ had to move the workspace. Realloc can sometimes increase the size
+ of a block of memory without moving it, which is much faster. This
+ statistic will always be <= Info [UMFPACK_NUMERIC_REALLOC]. If your
+ memory space is fragmented, then the number of "costly" realloc's
+ will be equal to Info [UMFPACK_NUMERIC_REALLOC].
+
+ Info [UMFPACK_COMPRESSED_PATTERN]: The number of integers used to
+ represent the pattern of L and U.
+
+ Info [UMFPACK_LU_ENTRIES]: The total number of numerical values that
+ are stored for the LU factors. Some of the values may be explicitly
+ zero in order to save space (allowing for a smaller compressed
+ pattern).
+
+ Info [UMFPACK_NUMERIC_TIME]: The CPU time taken, in seconds.
+
+ Info [UMFPACK_RCOND]: A rough estimate of the condition number, equal
+ to min (abs (diag (U))) / max (abs (diag (U))), or zero if the
+ diagonal of U is all zero.
+
+ Info [UMFPACK_UDIAG_NZ]: The number of numerically nonzero values on
+ the diagonal of U.
+
+ Info [UMFPACK_UMIN]: the smallest absolute value on the diagonal of U.
+
+ Info [UMFPACK_UMAX]: the smallest absolute value on the diagonal of U.
+
+ Info [UMFPACK_MAX_FRONT_SIZE]: the size of the
+ largest frontal matrix (number of entries).
+
+ Info [UMFPACK_NUMERIC_WALLTIME]: The wallclock time taken, in seconds.
+
+ Info [UMFPACK_MAX_FRONT_NROWS]: the max number of
+ rows in any frontal matrix.
+
+ Info [UMFPACK_MAX_FRONT_NCOLS]: the max number of
+ columns in any frontal matrix.
+
+ Info [UMFPACK_WAS_SCALED]: the scaling used, either UMFPACK_SCALE_NONE,
+ UMFPACK_SCALE_SUM, or UMFPACK_SCALE_MAX.
+
+ Info [UMFPACK_RSMIN]: if scaling is performed, the smallest scale factor
+ for any row (either the smallest sum of absolute entries, or the
+ smallest maximum of absolute entries).
+
+ Info [UMFPACK_RSMAX]: if scaling is performed, the largest scale factor
+ for any row (either the largest sum of absolute entries, or the
+ largest maximum of absolute entries).
+
+ Info [UMFPACK_ALLOC_INIT_USED]: the initial allocation parameter used.
+
+ Info [UMFPACK_FORCED_UPDATES]: the number of BLAS-3 updates to the
+ frontal matrices that were required because the frontal matrix
+ grew larger than its current working array.
+
+ Info [UMFPACK_NOFF_DIAG]: number of off-diagonal pivots selected, if the
+ symmetric or 2-by-2 strategies are used.
+
+ Info [UMFPACK_NZDROPPED]: the number of entries smaller in absolute
+ value than Control [UMFPACK_DROPTOL] that were dropped from L and U.
+ Note that entries on the diagonal of U are never dropped.
+
+ Info [UMFPACK_ALL_LNZ]: the number of entries in L, including the
+ diagonal, if no small entries are dropped.
+
+ Info [UMFPACK_ALL_UNZ]: the number of entries in U, including the
+ diagonal, if no small entries are dropped.
+
+ Only the above listed Info [...] entries are accessed. The remaining
+ entries of Info are not accessed or modified by umfpack_*_numeric.
+ Future versions might modify different parts of Info.
+*/
diff --git a/UMFPACK/Include/umfpack_qsymbolic.h b/UMFPACK/Include/umfpack_qsymbolic.h
new file mode 100644
index 0000000..00f9cd4
--- /dev/null
+++ b/UMFPACK/Include/umfpack_qsymbolic.h
@@ -0,0 +1,150 @@
+/* ========================================================================== */
+/* === umfpack_qsymbolic ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_qsymbolic
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ const int Qinit [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_dl_qsymbolic
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ const UF_long Qinit [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+int umfpack_zi_qsymbolic
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ const int Qinit [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_zl_qsymbolic
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ const UF_long Qinit [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ int n_row, n_col, *Ap, *Ai, *Qinit, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ;
+ status = umfpack_di_qsymbolic (n_row, n_col, Ap, Ai, Ax, Qinit,
+ &Symbolic, Control, Info) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ UF_long n_row, n_col, *Ap, *Ai, *Qinit, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ;
+ status = umfpack_dl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Qinit,
+ &Symbolic, Control, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ int n_row, n_col, *Ap, *Ai, *Qinit, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ;
+ status = umfpack_zi_qsymbolic (n_row, n_col, Ap, Ai, Ax, Az, Qinit,
+ &Symbolic, Control, Info) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ UF_long n_row, n_col, *Ap, *Ai, *Qinit, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ;
+ status = umfpack_zl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Az, Qinit,
+ &Symbolic, Control, Info) ;
+
+packed complex Syntax:
+
+ Same as above, except Az is NULL.
+
+Purpose:
+
+ Given the nonzero pattern of a sparse matrix A in column-oriented form, and
+ a sparsity preserving column pre-ordering Qinit, umfpack_*_qsymbolic
+ performs the symbolic factorization of A*Qinit (or A (:,Qinit) in MATLAB
+ notation). This is identical to umfpack_*_symbolic, except that neither
+ COLAMD nor AMD are called and the user input column order Qinit is used
+ instead. Note that in general, the Qinit passed to umfpack_*_qsymbolic
+ can differ from the final Q found in umfpack_*_numeric. The unsymmetric
+ strategy will perform a column etree postordering done in
+ umfpack_*_qsymbolic and sparsity-preserving modifications are made within
+ each frontal matrix during umfpack_*_numeric. The symmetric and 2-by-2
+ strategies will preserve Qinit, unless the matrix is structurally singular.
+
+ See umfpack_*_symbolic for more information.
+
+ *** WARNING *** A poor choice of Qinit can easily cause umfpack_*_numeric
+ to use a huge amount of memory and do a lot of work. The "default" symbolic
+ analysis method is umfpack_*_symbolic, not this routine. If you use this
+ routine, the performance of UMFPACK is your responsibility; UMFPACK will
+ not try to second-guess a poor choice of Qinit.
+
+Returns:
+
+ The value of Info [UMFPACK_STATUS]; see umfpack_*_symbolic.
+ Also returns UMFPACK_ERROR_invalid_permuation if Qinit is not a valid
+ permutation vector.
+
+Arguments:
+
+ All arguments are the same as umfpack_*_symbolic, except for the following:
+
+ Int Qinit [n_col] ; Input argument, not modified.
+
+ The user's fill-reducing initial column pre-ordering. This must be a
+ permutation of 0..n_col-1. If Qinit [k] = j, then column j is the kth
+ column of the matrix A (:,Qinit) to be factorized. If Qinit is an
+ (Int *) NULL pointer, then COLAMD or AMD are called instead.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If Qinit is not NULL, then only two strategies are recognized:
+ the unsymmetric strategy and the symmetric strategy.
+ If Control [UMFPACK_STRATEGY] is UMFPACK_STRATEGY_SYMMETRIC,
+ then the symmetric strategy is used. Otherwise the unsymmetric
+ strategy is used.
+*/
diff --git a/UMFPACK/Include/umfpack_report_control.h b/UMFPACK/Include/umfpack_report_control.h
new file mode 100644
index 0000000..361a353
--- /dev/null
+++ b/UMFPACK/Include/umfpack_report_control.h
@@ -0,0 +1,76 @@
+/* ========================================================================== */
+/* === umfpack_report_control =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_report_control
+(
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_dl_report_control
+(
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_zi_report_control
+(
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+void umfpack_zl_report_control
+(
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_di_report_control (Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_dl_report_control (Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_zi_report_control (Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ umfpack_zl_report_control (Control) ;
+
+Purpose:
+
+ Prints the current control settings. Note that with the default print
+ level, nothing is printed. Does nothing if Control is (double *) NULL.
+
+Arguments:
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 1 or less: no output
+ 2 or more: print all of Control
+ Default: 1
+*/
diff --git a/UMFPACK/Include/umfpack_report_info.h b/UMFPACK/Include/umfpack_report_info.h
new file mode 100644
index 0000000..5822721
--- /dev/null
+++ b/UMFPACK/Include/umfpack_report_info.h
@@ -0,0 +1,86 @@
+/* ========================================================================== */
+/* === umfpack_report_info ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_report_info
+(
+ const double Control [UMFPACK_CONTROL],
+ const double Info [UMFPACK_INFO]
+) ;
+
+void umfpack_dl_report_info
+(
+ const double Control [UMFPACK_CONTROL],
+ const double Info [UMFPACK_INFO]
+) ;
+
+void umfpack_zi_report_info
+(
+ const double Control [UMFPACK_CONTROL],
+ const double Info [UMFPACK_INFO]
+) ;
+
+void umfpack_zl_report_info
+(
+ const double Control [UMFPACK_CONTROL],
+ const double Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ umfpack_di_report_info (Control, Info) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ umfpack_dl_report_info (Control, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ umfpack_zi_report_info (Control, Info) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO] ;
+ umfpack_zl_report_info (Control, Info) ;
+
+Purpose:
+
+ Reports statistics from the umfpack_*_*symbolic, umfpack_*_numeric, and
+ umfpack_*_*solve routines.
+
+Arguments:
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 0 or less: no output, even when an error occurs
+ 1: error messages only
+ 2 or more: error messages, and print all of Info
+ Default: 1
+
+ double Info [UMFPACK_INFO] ; Input argument, not modified.
+
+ Info is an output argument of several UMFPACK routines.
+ The contents of Info are printed on standard output.
+*/
diff --git a/UMFPACK/Include/umfpack_report_matrix.h b/UMFPACK/Include/umfpack_report_matrix.h
new file mode 100644
index 0000000..0d17e2d
--- /dev/null
+++ b/UMFPACK/Include/umfpack_report_matrix.h
@@ -0,0 +1,203 @@
+/* ========================================================================== */
+/* === umfpack_report_matrix ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_matrix
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ int col_form,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_matrix
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ UF_long col_form,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_matrix
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ int col_form,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_matrix
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ UF_long col_form,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, *Ap, *Ai, status ;
+ double *Ax, Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_report_matrix (n_row, n_col, Ap, Ai, Ax, 1, Control) ;
+or:
+ status = umfpack_di_report_matrix (n_row, n_col, Ap, Ai, Ax, 0, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, *Ap, *Ai, status ;
+ double *Ax, Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_report_matrix (n_row, n_col, Ap, Ai, Ax, 1, Control) ;
+or:
+ status = umfpack_dl_report_matrix (n_row, n_col, Ap, Ai, Ax, 0, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, *Ap, *Ai, status ;
+ double *Ax, *Az, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 1,
+ Control) ;
+or:
+ status = umfpack_zi_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 0,
+ Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, *Ap, *Ai, status ;
+ double *Ax, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 1,
+ Control) ;
+or:
+ status = umfpack_zl_report_matrix (n_row, n_col, Ap, Ai, Ax, Az, 0,
+ Control) ;
+
+packed complex Syntax:
+
+ Same as above, except Az is NULL.
+
+Purpose:
+
+ Verifies and prints a row or column-oriented sparse matrix.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked).
+
+ Otherwise (where n is n_col for the column form and n_row for row
+ and let ni be n_row for the column form and n_col for row):
+
+ UMFPACK_OK if the matrix is valid.
+
+ UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0.
+ UMFPACK_ERROR_argument_missing if Ap and/or Ai are missing.
+ UMFPACK_ERROR_invalid_matrix if Ap [n] < 0, if Ap [0] is not zero,
+ if Ap [j+1] < Ap [j] for any j in the range 0 to n-1,
+ if any row index in Ai is not in the range 0 to ni-1, or
+ if the row indices in any column are not in
+ ascending order, or contain duplicates.
+ UMFPACK_ERROR_out_of_memory if out of memory.
+
+Arguments:
+
+ Int n_row ; Input argument, not modified.
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_row matrix. Restriction: n_row > 0 and n_col > 0.
+
+ Int Ap [n+1] ; Input argument, not modified.
+
+ n is n_row for a row-form matrix, and n_col for a column-form matrix.
+
+ Ap is an integer array of size n+1. If col_form is true (nonzero),
+ then on input, it holds the "pointers" for the column form of the
+ sparse matrix A. The row indices of column j of the matrix A are held
+ in Ai [(Ap [j]) ... (Ap [j+1]-1)]. Otherwise, Ap holds the
+ row pointers, and the column indices of row j of the matrix are held
+ in Ai [(Ap [j]) ... (Ap [j+1]-1)].
+
+ The first entry, Ap [0], must be zero, and Ap [j] <= Ap [j+1] must hold
+ for all j in the range 0 to n-1. The value nz = Ap [n] is thus the
+ total number of entries in the pattern of the matrix A.
+
+ Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n].
+
+ If col_form is true (nonzero), then the nonzero pattern (row indices)
+ for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)]. Row indices
+ must be in the range 0 to n_row-1 (the matrix is 0-based).
+
+ Otherwise, the nonzero pattern (column indices) for row j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)]. Column indices must be in the range 0
+ to n_col-1 (the matrix is 0-based).
+
+ double Ax [nz] ; Input argument, not modified, of size nz = Ap [n].
+ Size 2*nz for packed complex case.
+
+ The numerical values of the sparse matrix A.
+
+ If col_form is true (nonzero), then the nonzero pattern (row indices)
+ for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the
+ corresponding (real) numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)]. The imaginary parts are stored in
+ Az [(Ap [j]) ... (Ap [j+1]-1)], for the complex versions
+ (see below if Az is NULL).
+
+ Otherwise, the nonzero pattern (column indices) for row j
+ is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding
+ (real) numerical values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)].
+ The imaginary parts are stored in Az [(Ap [j]) ... (Ap [j+1]-1)],
+ for the complex versions (see below if Az is NULL).
+
+ No numerical values are printed if Ax is NULL.
+
+ double Az [nz] ; Input argument, not modified, for complex versions.
+
+ The imaginary values of the sparse matrix A. See the description
+ of Ax, above.
+
+ If Az is NULL, then both real
+ and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int col_form ; Input argument, not modified.
+
+ The matrix is in row-oriented form if form is col_form is false (0).
+ Otherwise, the matrix is in column-oriented form.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/UMFPACK/Include/umfpack_report_numeric.h b/UMFPACK/Include/umfpack_report_numeric.h
new file mode 100644
index 0000000..ff4eb11
--- /dev/null
+++ b/UMFPACK/Include/umfpack_report_numeric.h
@@ -0,0 +1,112 @@
+/* ========================================================================== */
+/* === umfpack_report_numeric =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_numeric
+(
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_numeric
+(
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_numeric
+(
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_numeric
+(
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ status = umfpack_di_report_numeric (Numeric, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ status = umfpack_dl_report_numeric (Numeric, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ status = umfpack_zi_report_numeric (Numeric, Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ status = umfpack_zl_report_numeric (Numeric, Control) ;
+
+Purpose:
+
+ Verifies and prints a Numeric object (the LU factorization, both its pattern
+ numerical values, and permutation vectors P and Q). This routine checks the
+ object more carefully than the computational routines. Normally, this check
+ is not required, since umfpack_*_numeric either returns (void *) NULL, or a
+ valid Numeric object. However, if you suspect that your own code has
+ corrupted the Numeric object (by overruning memory bounds, for example),
+ then this routine might be able to detect a corrupted Numeric object. Since
+ this is a complex object, not all such user-generated errors are guaranteed
+ to be caught by this routine.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked).
+
+ Otherwise:
+
+ UMFPACK_OK if the Numeric object is valid.
+ UMFPACK_ERROR_invalid_Numeric_object if the Numeric object is invalid.
+ UMFPACK_ERROR_out_of_memory if out of memory.
+
+Arguments:
+
+ void *Numeric ; Input argument, not modified.
+
+ The Numeric object, which holds the numeric factorization computed by
+ umfpack_*_numeric.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/UMFPACK/Include/umfpack_report_perm.h b/UMFPACK/Include/umfpack_report_perm.h
new file mode 100644
index 0000000..4810e32
--- /dev/null
+++ b/UMFPACK/Include/umfpack_report_perm.h
@@ -0,0 +1,112 @@
+/* ========================================================================== */
+/* === umfpack_report_perm ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_perm
+(
+ int np,
+ const int Perm [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_perm
+(
+ UF_long np,
+ const UF_long Perm [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_perm
+(
+ int np,
+ const int Perm [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_perm
+(
+ UF_long np,
+ const UF_long Perm [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int np, *Perm, status ;
+ double Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_report_perm (np, Perm, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long np, *Perm, status ;
+ double Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_report_perm (np, Perm, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int np, *Perm, status ;
+ double Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_report_perm (np, Perm, Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long np, *Perm, status ;
+ double Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_report_perm (np, Perm, Control) ;
+
+Purpose:
+
+ Verifies and prints a permutation vector.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked).
+
+ Otherwise:
+ UMFPACK_OK if the permutation vector is valid (this includes that case
+ when Perm is (Int *) NULL, which is not an error condition).
+ UMFPACK_ERROR_n_nonpositive if np <= 0.
+ UMFPACK_ERROR_out_of_memory if out of memory.
+ UMFPACK_ERROR_invalid_permutation if Perm is not a valid permutation vector.
+
+Arguments:
+
+ Int np ; Input argument, not modified.
+
+ Perm is an integer vector of size np. Restriction: np > 0.
+
+ Int Perm [np] ; Input argument, not modified.
+
+ A permutation vector of size np. If Perm is not present (an (Int *)
+ NULL pointer), then it is assumed to be the identity permutation. This
+ is consistent with its use as an input argument to umfpack_*_qsymbolic,
+ and is not an error condition. If Perm is present, the entries in Perm
+ must range between 0 and np-1, and no duplicates may exist.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/UMFPACK/Include/umfpack_report_status.h b/UMFPACK/Include/umfpack_report_status.h
new file mode 100644
index 0000000..24376ae
--- /dev/null
+++ b/UMFPACK/Include/umfpack_report_status.h
@@ -0,0 +1,90 @@
+/* ========================================================================== */
+/* === umfpack_report_status ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_di_report_status
+(
+ const double Control [UMFPACK_CONTROL],
+ int status
+) ;
+
+void umfpack_dl_report_status
+(
+ const double Control [UMFPACK_CONTROL],
+ UF_long status
+) ;
+
+void umfpack_zi_report_status
+(
+ const double Control [UMFPACK_CONTROL],
+ int status
+) ;
+
+void umfpack_zl_report_status
+(
+ const double Control [UMFPACK_CONTROL],
+ UF_long status
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ umfpack_di_report_status (Control, status) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ umfpack_dl_report_status (Control, status) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ umfpack_zi_report_status (Control, status) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ umfpack_zl_report_status (Control, status) ;
+
+Purpose:
+
+ Prints the status (return value) of other umfpack_* routines.
+
+Arguments:
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 0 or less: no output, even when an error occurs
+ 1: error messages only
+ 2 or more: print status, whether or not an error occurred
+ 4 or more: also print the UMFPACK Copyright
+ 6 or more: also print the UMFPACK License
+ Default: 1
+
+ Int status ; Input argument, not modified.
+
+ The return value from another umfpack_* routine.
+*/
diff --git a/UMFPACK/Include/umfpack_report_symbolic.h b/UMFPACK/Include/umfpack_report_symbolic.h
new file mode 100644
index 0000000..eb61182
--- /dev/null
+++ b/UMFPACK/Include/umfpack_report_symbolic.h
@@ -0,0 +1,111 @@
+/* ========================================================================== */
+/* === umfpack_report_symbolic ============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_symbolic
+(
+ void *Symbolic,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_symbolic
+(
+ void *Symbolic,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_symbolic
+(
+ void *Symbolic,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_symbolic
+(
+ void *Symbolic,
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ status = umfpack_di_report_symbolic (Symbolic, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ status = umfpack_dl_report_symbolic (Symbolic, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ double Control [UMFPACK_CONTROL] ;
+ int status ;
+ status = umfpack_zi_report_symbolic (Symbolic, Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ double Control [UMFPACK_CONTROL] ;
+ UF_long status ;
+ status = umfpack_zl_report_symbolic (Symbolic, Control) ;
+
+Purpose:
+
+ Verifies and prints a Symbolic object. This routine checks the object more
+ carefully than the computational routines. Normally, this check is not
+ required, since umfpack_*_*symbolic either returns (void *) NULL, or a valid
+ Symbolic object. However, if you suspect that your own code has corrupted
+ the Symbolic object (by overruning memory bounds, for example), then this
+ routine might be able to detect a corrupted Symbolic object. Since this is
+ a complex object, not all such user-generated errors are guaranteed to be
+ caught by this routine.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] is <= 2 (no inputs are checked).
+
+ Otherwise:
+
+ UMFPACK_OK if the Symbolic object is valid.
+ UMFPACK_ERROR_invalid_Symbolic_object if the Symbolic object is invalid.
+ UMFPACK_ERROR_out_of_memory if out of memory.
+
+Arguments:
+
+ void *Symbolic ; Input argument, not modified.
+
+ The Symbolic object, which holds the symbolic factorization computed by
+ umfpack_*_*symbolic.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/UMFPACK/Include/umfpack_report_triplet.h b/UMFPACK/Include/umfpack_report_triplet.h
new file mode 100644
index 0000000..4e7a605
--- /dev/null
+++ b/UMFPACK/Include/umfpack_report_triplet.h
@@ -0,0 +1,153 @@
+/* ========================================================================== */
+/* === umfpack_report_triplet =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_triplet
+(
+ int n_row,
+ int n_col,
+ int nz,
+ const int Ti [ ],
+ const int Tj [ ],
+ const double Tx [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_triplet
+(
+ UF_long n_row,
+ UF_long n_col,
+ UF_long nz,
+ const UF_long Ti [ ],
+ const UF_long Tj [ ],
+ const double Tx [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_triplet
+(
+ int n_row,
+ int n_col,
+ int nz,
+ const int Ti [ ],
+ const int Tj [ ],
+ const double Tx [ ], const double Tz [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_triplet
+(
+ UF_long n_row,
+ UF_long n_col,
+ UF_long nz,
+ const UF_long Ti [ ],
+ const UF_long Tj [ ],
+ const double Tx [ ], const double Tz [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, nz, *Ti, *Tj, status ;
+ double *Tx, Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, nz, *Ti, *Tj, status ;
+ double *Tx, Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, nz, *Ti, *Tj, status ;
+ double *Tx, *Tz, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Tz,
+ Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, nz, *Ti, *Tj, status ;
+ double *Tx, *Tz, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_report_triplet (n_row, n_col, nz, Ti, Tj, Tx, Tz,
+ Control) ;
+
+packed complex Syntax:
+
+ Same as above, except Tz is NULL.
+
+Purpose:
+
+ Verifies and prints a matrix in triplet form.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked).
+
+ Otherwise:
+
+ UMFPACK_OK if the Triplet matrix is OK.
+ UMFPACK_ERROR_argument_missing if Ti and/or Tj are missing.
+ UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0.
+ UMFPACK_ERROR_invalid_matrix if nz < 0, or
+ if any row or column index in Ti and/or Tj
+ is not in the range 0 to n_row-1 or 0 to n_col-1, respectively.
+
+Arguments:
+
+ Int n_row ; Input argument, not modified.
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix.
+
+ Int nz ; Input argument, not modified.
+
+ The number of entries in the triplet form of the matrix.
+
+ Int Ti [nz] ; Input argument, not modified.
+ Int Tj [nz] ; Input argument, not modified.
+ double Tx [nz] ; Input argument, not modified.
+ Size 2*nz for packed complex case.
+ double Tz [nz] ; Input argument, not modified, for complex versions.
+
+ Ti, Tj, Tx (and Tz for complex versions) hold the "triplet" form of a
+ sparse matrix. The kth nonzero entry is in row i = Ti [k], column
+ j = Tj [k], the real numerical value of a_ij is Tx [k], and the
+ imaginary part of a_ij is Tz [k] (for complex versions). The row and
+ column indices i and j must be in the range 0 to n_row-1 or 0 to
+ n_col-1, respectively. Duplicate entries may be present. The
+ "triplets" may be in any order. Tx and Tz are optional; if Tx is
+ not present ((double *) NULL), then the numerical values are
+ not printed.
+
+ If Tx is present and Tz is NULL, then both real
+ and imaginary parts are contained in Tx[0..2*nz-1], with Tx[2*k]
+ and Tx[2*k+1] being the real and imaginary part of the kth entry.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/UMFPACK/Include/umfpack_report_vector.h b/UMFPACK/Include/umfpack_report_vector.h
new file mode 100644
index 0000000..2c4c386
--- /dev/null
+++ b/UMFPACK/Include/umfpack_report_vector.h
@@ -0,0 +1,133 @@
+/* ========================================================================== */
+/* === umfpack_report_vector ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_report_vector
+(
+ int n,
+ const double X [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_dl_report_vector
+(
+ UF_long n,
+ const double X [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+int umfpack_zi_report_vector
+(
+ int n,
+ const double Xx [ ], const double Xz [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+UF_long umfpack_zl_report_vector
+(
+ UF_long n,
+ const double Xx [ ], const double Xz [ ],
+ const double Control [UMFPACK_CONTROL]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n, status ;
+ double *X, Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_report_vector (n, X, Control) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n, status ;
+ double *X, Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_report_vector (n, X, Control) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n, status ;
+ double *Xx, *Xz, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_report_vector (n, Xx, Xz, Control) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n, status ;
+ double *Xx, *Xz, Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_report_vector (n, Xx, Xz, Control) ;
+
+Purpose:
+
+ Verifies and prints a dense vector.
+
+Returns:
+
+ UMFPACK_OK if Control [UMFPACK_PRL] <= 2 (the input is not checked).
+
+ Otherwise:
+
+ UMFPACK_OK if the vector is valid.
+ UMFPACK_ERROR_argument_missing if X or Xx is missing.
+ UMFPACK_ERROR_n_nonpositive if n <= 0.
+
+Arguments:
+
+ Int n ; Input argument, not modified.
+
+ X is a real or complex vector of size n. Restriction: n > 0.
+
+ double X [n] ; Input argument, not modified. For real versions.
+
+ A real vector of size n. X must not be (double *) NULL.
+
+ double Xx [n or 2*n] ; Input argument, not modified. For complex versions.
+ double Xz [n or 0] ; Input argument, not modified. For complex versions.
+
+ A complex vector of size n, in one of two storage formats.
+ Xx must not be (double *) NULL.
+
+ If Xz is not (double *) NULL, then Xx [i] is the real part of X (i) and
+ Xz [i] is the imaginary part of X (i). Both vectors are of length n.
+ This is the "split" form of the complex vector X.
+
+ If Xz is (double *) NULL, then Xx holds both real and imaginary parts,
+ where Xx [2*i] is the real part of X (i) and Xx [2*i+1] is the imaginary
+ part of X (i). Xx is of length 2*n doubles. If you have an ANSI C99
+ compiler with the intrinsic double _Complex type, then Xx can be of
+ type double _Complex in the calling routine and typecast to (double *)
+ when passed to umfpack_*_report_vector (this is untested, however).
+ This is the "merged" form of the complex vector X.
+
+ Note that all complex routines in UMFPACK V4.4 and later use this same
+ strategy for their complex arguments. The split format is useful for
+ MATLAB, which holds its real and imaginary parts in seperate arrays.
+ The packed format is compatible with the intrinsic double _Complex
+ type in ANSI C99, and is also compatible with SuperLU's method of
+ storing complex matrices. In Version 4.3, this routine was the only
+ one that allowed for packed complex arguments.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_PRL]: printing level.
+
+ 2 or less: no output. returns silently without checking anything.
+ 3: fully check input, and print a short summary of its status
+ 4: as 3, but print first few entries of the input
+ 5: as 3, but print all of the input
+ Default: 1
+*/
diff --git a/UMFPACK/Include/umfpack_save_numeric.h b/UMFPACK/Include/umfpack_save_numeric.h
new file mode 100644
index 0000000..708e581
--- /dev/null
+++ b/UMFPACK/Include/umfpack_save_numeric.h
@@ -0,0 +1,90 @@
+/* ========================================================================== */
+/* === umfpack_save_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_save_numeric
+(
+ void *Numeric,
+ char *filename
+) ;
+
+UF_long umfpack_dl_save_numeric
+(
+ void *Numeric,
+ char *filename
+) ;
+
+int umfpack_zi_save_numeric
+(
+ void *Numeric,
+ char *filename
+) ;
+
+UF_long umfpack_zl_save_numeric
+(
+ void *Numeric,
+ char *filename
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_di_save_numeric (Numeric, filename) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_dl_save_numeric (Numeric, filename) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_zi_save_numeric (Numeric, filename) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Numeric ;
+ status = umfpack_zl_save_numeric (Numeric, filename) ;
+
+Purpose:
+
+ Saves a Numeric object to a file, which can later be read by
+ umfpack_*_load_numeric. The Numeric object is not modified.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_invalid_Numeric_object if Numeric is not valid.
+ UMFPACK_ERROR_file_IO if an I/O error occurred.
+
+Arguments:
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric or loaded by umfpack_*_load_numeric.
+
+ char *filename ; Input argument, not modified.
+
+ A string that contains the filename to which the Numeric
+ object is written.
+*/
diff --git a/UMFPACK/Include/umfpack_save_symbolic.h b/UMFPACK/Include/umfpack_save_symbolic.h
new file mode 100644
index 0000000..2dffdd6
--- /dev/null
+++ b/UMFPACK/Include/umfpack_save_symbolic.h
@@ -0,0 +1,90 @@
+/* ========================================================================== */
+/* === umfpack_save_symbolic================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_save_symbolic
+(
+ void *Symbolic,
+ char *filename
+) ;
+
+UF_long umfpack_dl_save_symbolic
+(
+ void *Symbolic,
+ char *filename
+) ;
+
+int umfpack_zi_save_symbolic
+(
+ void *Symbolic,
+ char *filename
+) ;
+
+UF_long umfpack_zl_save_symbolic
+(
+ void *Symbolic,
+ char *filename
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_di_save_symbolic (Symbolic, filename) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_dl_save_symbolic (Symbolic, filename) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_zi_save_symbolic (Symbolic, filename) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long status ;
+ char *filename ;
+ void *Symbolic ;
+ status = umfpack_zl_save_symbolic (Symbolic, filename) ;
+
+Purpose:
+
+ Saves a Symbolic object to a file, which can later be read by
+ umfpack_*_load_symbolic. The Symbolic object is not modified.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_invalid_Symbolic_object if Symbolic is not valid.
+ UMFPACK_ERROR_file_IO if an I/O error occurred.
+
+Arguments:
+
+ void *Symbolic ; Input argument, not modified.
+
+ Symbolic must point to a valid Symbolic object, computed by
+ umfpack_*_symbolic or loaded by umfpack_*_load_symbolic.
+
+ char *filename ; Input argument, not modified.
+
+ A string that contains the filename to which the Symbolic
+ object is written.
+*/
diff --git a/UMFPACK/Include/umfpack_scale.h b/UMFPACK/Include/umfpack_scale.h
new file mode 100644
index 0000000..62fc32a
--- /dev/null
+++ b/UMFPACK/Include/umfpack_scale.h
@@ -0,0 +1,112 @@
+/* ========================================================================== */
+/* === umfpack_scale ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_scale
+(
+ double X [ ],
+ const double B [ ],
+ void *Numeric
+) ;
+
+UF_long umfpack_dl_scale
+(
+ double X [ ],
+ const double B [ ],
+ void *Numeric
+) ;
+
+int umfpack_zi_scale
+(
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric
+) ;
+
+UF_long umfpack_zl_scale
+(
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double *B, *X ;
+ status = umfpack_di_scale (X, B, Numeric) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double *B, *X ;
+ status = umfpack_dl_scale (X, B, Numeric) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double *Bx, *Bz, *Xx, *Xz ;
+ status = umfpack_zi_scale (Xx, Xz, Bx, Bz, Numeric) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ double *Bx, *Bz, *Xx, *Xz ;
+ status = umfpack_zl_scale (Xx, Xz, Bx, Bz, Numeric) ;
+
+packed complex Syntax:
+
+ Same as above, except both Xz and Bz are NULL.
+
+Purpose:
+
+ Given LU factors computed by umfpack_*_numeric (PAQ=LU, PRAQ=LU, or
+ P(R\A)Q=LU), and a vector B, this routine computes X = B, X = R*B, or
+ X = R\B, as appropriate. X and B must be vectors equal in length to the
+ number of rows of A.
+
+Returns:
+
+ The status code is returned. UMFPACK_OK is returned if successful.
+ UMFPACK_ERROR_invalid_Numeric_object is returned in the Numeric
+ object is invalid. UMFPACK_ERROR_argument_missing is returned if
+ any of the input vectors are missing (X and B for the real version,
+ and Xx and Bx for the complex version).
+
+Arguments:
+
+ double X [n_row] ; Output argument.
+ or:
+ double Xx [n_row] ; Output argument, real part.
+ Size 2*n_row for packed complex case.
+ double Xz [n_row] ; Output argument, imaginary part.
+
+ The output vector X. If either Xz or Bz are NULL, the vector
+ X is in packed complex form, with the kth entry in Xx [2*k] and
+ Xx [2*k+1], and likewise for B.
+
+ double B [n_row] ; Input argument, not modified.
+ or:
+ double Bx [n_row] ; Input argument, not modified, real part.
+ Size 2*n_row for packed complex case.
+ double Bz [n_row] ; Input argument, not modified, imaginary part.
+
+ The input vector B. See above if either Xz or Bz are NULL.
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric.
+
+*/
diff --git a/UMFPACK/Include/umfpack_solve.h b/UMFPACK/Include/umfpack_solve.h
new file mode 100644
index 0000000..0932091
--- /dev/null
+++ b/UMFPACK/Include/umfpack_solve.h
@@ -0,0 +1,301 @@
+/* ========================================================================== */
+/* === umfpack_solve ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_solve
+(
+ int sys,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ double X [ ],
+ const double B [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_dl_solve
+(
+ UF_long sys,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ double X [ ],
+ const double B [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+int umfpack_zi_solve
+(
+ int sys,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_zl_solve
+(
+ UF_long sys,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, *Ap, *Ai, sys ;
+ double *B, *X, *Ax, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, *Ap, *Ai, sys ;
+ double *B, *X, *Ax, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_solve (sys, Ap, Ai, Ax, X, B, Numeric, Control, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, *Ap, *Ai, sys ;
+ double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, Info [UMFPACK_INFO],
+ Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric,
+ Control, Info) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, *Ap, *Ai, sys ;
+ double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, Info [UMFPACK_INFO],
+ Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric,
+ Control, Info) ;
+
+packed complex Syntax:
+
+ Same as above, Xz, Bz, and Az are NULL.
+
+Purpose:
+
+ Given LU factors computed by umfpack_*_numeric (PAQ=LU, PRAQ=LU, or
+ P(R\A)Q=LU) and the right-hand-side, B, solve a linear system for the
+ solution X. Iterative refinement is optionally performed. Only square
+ systems are handled. Singular matrices result in a divide-by-zero for all
+ systems except those involving just the matrix L. Iterative refinement is
+ not performed for singular matrices. In the discussion below, n is equal
+ to n_row and n_col, because only square systems are handled.
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ Int sys ; Input argument, not modified.
+
+ Defines which system to solve. (') is the linear algebraic transpose
+ (complex conjugate if A is complex), and (.') is the array transpose.
+
+ sys value system solved
+ UMFPACK_A Ax=b
+ UMFPACK_At A'x=b
+ UMFPACK_Aat A.'x=b
+ UMFPACK_Pt_L P'Lx=b
+ UMFPACK_L Lx=b
+ UMFPACK_Lt_P L'Px=b
+ UMFPACK_Lat_P L.'Px=b
+ UMFPACK_Lt L'x=b
+ UMFPACK_U_Qt UQ'x=b
+ UMFPACK_U Ux=b
+ UMFPACK_Q_Ut QU'x=b
+ UMFPACK_Q_Uat QU.'x=b
+ UMFPACK_Ut U'x=b
+ UMFPACK_Uat U.'x=b
+
+ Iterative refinement can be optionally performed when sys is any of
+ the following:
+
+ UMFPACK_A Ax=b
+ UMFPACK_At A'x=b
+ UMFPACK_Aat A.'x=b
+
+ For the other values of the sys argument, iterative refinement is not
+ performed (Control [UMFPACK_IRSTEP], Ap, Ai, Ax, and Az are ignored).
+
+ Int Ap [n+1] ; Input argument, not modified.
+ Int Ai [nz] ; Input argument, not modified.
+ double Ax [nz] ; Input argument, not modified.
+ Size 2*nz for packed complex case.
+ double Az [nz] ; Input argument, not modified, for complex versions.
+
+ If iterative refinement is requested (Control [UMFPACK_IRSTEP] >= 1,
+ Ax=b, A'x=b, or A.'x=b is being solved, and A is nonsingular), then
+ these arrays must be identical to the same ones passed to
+ umfpack_*_numeric. The umfpack_*_solve routine does not check the
+ contents of these arguments, so the results are undefined if Ap, Ai, Ax,
+ and/or Az are modified between the calls the umfpack_*_numeric and
+ umfpack_*_solve. These three arrays do not need to be present (NULL
+ pointers can be passed) if Control [UMFPACK_IRSTEP] is zero, or if a
+ system other than Ax=b, A'x=b, or A.'x=b is being solved, or if A is
+ singular, since in each of these cases A is not accessed.
+
+ If Az, Xz, or Bz are NULL, then both real
+ and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ double X [n] ; Output argument.
+ or:
+ double Xx [n] ; Output argument, real part
+ Size 2*n for packed complex case.
+ double Xz [n] ; Output argument, imaginary part.
+
+ The solution to the linear system, where n = n_row = n_col is the
+ dimension of the matrices A, L, and U.
+
+ If Az, Xz, or Bz are NULL, then both real
+ and imaginary parts are returned in Xx[0..2*n-1], with Xx[2*k] and
+ Xx[2*k+1] being the real and imaginary part of the kth entry.
+
+ double B [n] ; Input argument, not modified.
+ or:
+ double Bx [n] ; Input argument, not modified, real part.
+ Size 2*n for packed complex case.
+ double Bz [n] ; Input argument, not modified, imaginary part.
+
+ The right-hand side vector, b, stored as a conventional array of size n
+ (or two arrays of size n for complex versions). This routine does not
+ solve for multiple right-hand-sides, nor does it allow b to be stored in
+ a sparse-column form.
+
+ If Az, Xz, or Bz are NULL, then both real
+ and imaginary parts are contained in Bx[0..2*n-1], with Bx[2*k]
+ and Bx[2*k+1] being the real and imaginary part of the kth entry.
+
+ void *Numeric ; Input argument, not modified.
+
+ Numeric must point to a valid Numeric object, computed by
+ umfpack_*_numeric.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used. Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_IRSTEP]: The maximum number of iterative refinement
+ steps to attempt. A value less than zero is treated as zero. If
+ less than 1, or if Ax=b, A'x=b, or A.'x=b is not being solved, or
+ if A is singular, then the Ap, Ai, Ax, and Az arguments are not
+ accessed. Default: 2.
+
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ Contains statistics about the solution factorization. If a
+ (double *) NULL pointer is passed, then no statistics are returned in
+ Info (this is not an error condition). The following statistics are
+ computed in umfpack_*_solve:
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ The linear system was successfully solved.
+
+ UMFPACK_WARNING_singular_matrix
+
+ A divide-by-zero occurred. Your solution will contain Inf's
+ and/or NaN's. Some parts of the solution may be valid. For
+ example, solving Ax=b with
+
+ A = [2 0] b = [ 1 ] returns x = [ 0.5 ]
+ [0 0] [ 0 ] [ Inf ]
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to solve the linear system.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments are missing. The B, X, (or
+ Bx and Xx for the complex versions) arguments
+ are always required. Info and Control are not required. Ap,
+ Ai, Ax are required if Ax=b,
+ A'x=b, A.'x=b is to be solved, the (default) iterative
+ refinement is requested, and the matrix A is nonsingular.
+
+ UMFPACK_ERROR_invalid_system
+
+ The sys argument is not valid, or the matrix A is not square.
+
+ UMFPACK_ERROR_invalid_Numeric_object
+
+ The Numeric object is not valid.
+
+ Info [UMFPACK_NROW], Info [UMFPACK_NCOL]:
+ The dimensions of the matrix A (L is n_row-by-n_inner and
+ U is n_inner-by-n_col, with n_inner = min(n_row,n_col)).
+
+ Info [UMFPACK_NZ]: the number of entries in the input matrix, Ap [n],
+ if iterative refinement is requested (Ax=b, A'x=b, or A.'x=b is
+ being solved, Control [UMFPACK_IRSTEP] >= 1, and A is nonsingular).
+
+ Info [UMFPACK_IR_TAKEN]: The number of iterative refinement steps
+ effectively taken. The number of steps attempted may be one more
+ than this; the refinement algorithm backtracks if the last
+ refinement step worsens the solution.
+
+ Info [UMFPACK_IR_ATTEMPTED]: The number of iterative refinement steps
+ attempted. The number of times a linear system was solved is one
+ more than this (once for the initial Ax=b, and once for each Ay=r
+ solved for each iterative refinement step attempted).
+
+ Info [UMFPACK_OMEGA1]: sparse backward error estimate, omega1, if
+ iterative refinement was performed, or -1 if iterative refinement
+ not performed.
+
+ Info [UMFPACK_OMEGA2]: sparse backward error estimate, omega2, if
+ iterative refinement was performed, or -1 if iterative refinement
+ not performed.
+
+ Info [UMFPACK_SOLVE_FLOPS]: the number of floating point operations
+ performed to solve the linear system. This includes the work
+ taken for all iterative refinement steps, including the backtrack
+ (if any).
+
+ Info [UMFPACK_SOLVE_TIME]: The time taken, in seconds.
+
+ Info [UMFPACK_SOLVE_WALLTIME]: The wallclock time taken, in seconds.
+
+ Only the above listed Info [...] entries are accessed. The remaining
+ entries of Info are not accessed or modified by umfpack_*_solve.
+ Future versions might modify different parts of Info.
+*/
diff --git a/UMFPACK/Include/umfpack_symbolic.h b/UMFPACK/Include/umfpack_symbolic.h
new file mode 100644
index 0000000..1deacc2
--- /dev/null
+++ b/UMFPACK/Include/umfpack_symbolic.h
@@ -0,0 +1,536 @@
+/* ========================================================================== */
+/* === umfpack_symbolic ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_symbolic
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_dl_symbolic
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+int umfpack_zi_symbolic
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+UF_long umfpack_zl_symbolic
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ void **Symbolic,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ int n_row, n_col, *Ap, *Ai, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ;
+ status = umfpack_di_symbolic (n_row, n_col, Ap, Ai, Ax,
+ &Symbolic, Control, Info) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ UF_long n_row, n_col, *Ap, *Ai, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax ;
+ status = umfpack_dl_symbolic (n_row, n_col, Ap, Ai, Ax,
+ &Symbolic, Control, Info) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ int n_row, n_col, *Ap, *Ai, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ;
+ status = umfpack_zi_symbolic (n_row, n_col, Ap, Ai, Ax, Az,
+ &Symbolic, Control, Info) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Symbolic ;
+ UF_long n_row, n_col, *Ap, *Ai, status ;
+ double Control [UMFPACK_CONTROL], Info [UMFPACK_INFO], *Ax, *Az ;
+ status = umfpack_zl_symbolic (n_row, n_col, Ap, Ai, Ax, Az,
+ &Symbolic, Control, Info) ;
+
+packed complex Syntax:
+
+ Same as above, except Az is NULL.
+
+Purpose:
+
+ Given nonzero pattern of a sparse matrix A in column-oriented form,
+ umfpack_*_symbolic performs a column pre-ordering to reduce fill-in
+ (using COLAMD or AMD) and a symbolic factorization. This is required
+ before the matrix can be numerically factorized with umfpack_*_numeric.
+ If you wish to bypass the COLAMD or AMD pre-ordering and provide your own
+ ordering, use umfpack_*_qsymbolic instead.
+
+ Since umfpack_*_symbolic and umfpack_*_qsymbolic are very similar, options
+ for both routines are discussed below.
+
+ For the following discussion, let S be the submatrix of A obtained after
+ eliminating all pivots of zero Markowitz cost. S has dimension
+ (n_row-n1-nempty_row) -by- (n_col-n1-nempty_col), where
+ n1 = Info [UMFPACK_COL_SINGLETONS] + Info [UMFPACK_ROW_SINGLETONS],
+ nempty_row = Info [UMFPACK_NEMPTY_ROW] and
+ nempty_col = Info [UMFPACK_NEMPTY_COL].
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ Int n_row ; Input argument, not modified.
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0.
+
+ Int Ap [n_col+1] ; Input argument, not modified.
+
+ Ap is an integer array of size n_col+1. On input, it holds the
+ "pointers" for the column form of the sparse matrix A. Column j of
+ the matrix A is held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The first
+ entry, Ap [0], must be zero, and Ap [j] <= Ap [j+1] must hold for all
+ j in the range 0 to n_col-1. The value nz = Ap [n_col] is thus the
+ total number of entries in the pattern of the matrix A. nz must be
+ greater than or equal to zero.
+
+ Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ The nonzero pattern (row indices) for column j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j
+ must be in ascending order, and no duplicate row indices may be present.
+ Row indices must be in the range 0 to n_row-1 (the matrix is 0-based).
+ See umfpack_*_triplet_to_col for how to sort the columns of a matrix
+ and sum up the duplicate entries. See umfpack_*_report_matrix for how
+ to print the matrix A.
+
+ double Ax [nz] ; Optional input argument, not modified.
+ Size 2*nz for packed complex case.
+
+ The numerical values of the sparse matrix A. The nonzero pattern (row
+ indices) for column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and
+ the corresponding numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)]. Used only by the 2-by-2 strategy to
+ determine whether entries are "large" or "small". You do not have to
+ pass the same numerical values to umfpack_*_numeric. If Ax is not
+ present (a (double *) NULL pointer), then any entry in A is assumed to
+ be "large".
+
+ double Az [nz] ; Optional input argument, not modified, for complex
+ versions.
+
+ For the complex versions, this holds the imaginary part of A. The
+ imaginary part of column j is held in Az [(Ap [j]) ... (Ap [j+1]-1)].
+
+ If Az is NULL, then both real
+ and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ Used by the 2-by-2 strategy only. See the description of Ax, above.
+
+ void **Symbolic ; Output argument.
+
+ **Symbolic is the address of a (void *) pointer variable in the user's
+ calling routine (see Syntax, above). On input, the contents of this
+ variable are not defined. On output, this variable holds a (void *)
+ pointer to the Symbolic object (if successful), or (void *) NULL if
+ a failure occurred.
+
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+
+ If a (double *) NULL pointer is passed, then the default control
+ settings are used (the defaults are suitable for all matrices,
+ ranging from those with highly unsymmetric nonzero pattern, to
+ symmetric matrices). Otherwise, the settings are determined from the
+ Control array. See umfpack_*_defaults on how to fill the Control
+ array with the default settings. If Control contains NaN's, the
+ defaults are used. The following Control parameters are used:
+
+ Control [UMFPACK_STRATEGY]: This is the most important control
+ parameter. It determines what kind of ordering and pivoting
+ strategy that UMFPACK should use. There are 4 options:
+
+ UMFPACK_STRATEGY_AUTO: This is the default. The input matrix is
+ analyzed to determine how symmetric the nonzero pattern is, and
+ how many entries there are on the diagonal. It then selects one
+ of the following strategies. Refer to the User Guide for a
+ description of how the strategy is automatically selected.
+
+ UMFPACK_STRATEGY_UNSYMMETRIC: Use the unsymmetric strategy. COLAMD
+ is used to order the columns of A, followed by a postorder of
+ the column elimination tree. No attempt is made to perform
+ diagonal pivoting. The column ordering is refined during
+ factorization.
+
+ In the numerical factorization, the
+ Control [UMFPACK_SYM_PIVOT_TOLERANCE] parameter is ignored. A
+ pivot is selected if its magnitude is >=
+ Control [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the
+ largest entry in its column.
+
+ UMFPACK_STRATEGY_SYMMETRIC: Use the symmetric strategy
+ In this method, the approximate minimum degree
+ ordering (AMD) is applied to A+A', followed by a postorder of
+ the elimination tree of A+A'. UMFPACK attempts to perform
+ diagonal pivoting during numerical factorization. No refinement
+ of the column pre-ordering is performed during factorization.
+
+ In the numerical factorization, a nonzero entry on the diagonal
+ is selected as the pivot if its magnitude is >= Control
+ [UMFPACK_SYM_PIVOT_TOLERANCE] (default 0.001) times the largest
+ entry in its column. If this is not acceptable, then an
+ off-diagonal pivot is selected with magnitude >= Control
+ [UMFPACK_PIVOT_TOLERANCE] (default 0.1) times the largest entry
+ in its column.
+
+ UMFPACK_STRATEGY_2BY2: a row permutation P2 is found that places
+ large entries on the diagonal. The matrix P2*A is then
+ factorized using the symmetric strategy, described above.
+ Refer to the User Guide for more information.
+
+ Control [UMFPACK_DENSE_COL]:
+ If COLAMD is used, columns with more than
+ max (16, Control [UMFPACK_DENSE_COL] * 16 * sqrt (n_row)) entries
+ are placed placed last in the column pre-ordering. Default: 0.2.
+
+ Control [UMFPACK_DENSE_ROW]:
+ Rows with more than max (16, Control [UMFPACK_DENSE_ROW] * 16 *
+ sqrt (n_col)) entries are treated differently in the COLAMD
+ pre-ordering, and in the internal data structures during the
+ subsequent numeric factorization. Default: 0.2.
+
+ Control [UMFPACK_AMD_DENSE]: rows/columns in A+A' with more than
+ max (16, Control [UMFPACK_AMD_DENSE] * sqrt (n)) entries
+ (where n = n_row = n_col) are ignored in the AMD pre-ordering.
+ Default: 10.
+
+ Control [UMFPACK_BLOCK_SIZE]: the block size to use for Level-3 BLAS
+ in the subsequent numerical factorization (umfpack_*_numeric).
+ A value less than 1 is treated as 1. Default: 32. Modifying this
+ parameter affects when updates are applied to the working frontal
+ matrix, and can indirectly affect fill-in and operation count.
+ Assuming the block size is large enough (8 or so), this parameter
+ has a modest effect on performance.
+
+ Control [UMFPACK_2BY2_TOLERANCE]: a diagonal entry S (k,k) is
+ considered "small" if it is < tol * max (abs (S (:,k))), where S a
+ submatrix of the scaled input matrix, with pivots of zero Markowitz
+ cost removed.
+
+ Control [UMFPACK_SCALE]: See umfpack_numeric.h for a description.
+ Only affects the 2-by-2 strategy. Default: UMFPACK_SCALE_SUM.
+
+ Control [UMFPACK_FIXQ]: If > 0, then the pre-ordering Q is not modified
+ during numeric factorization. If < 0, then Q may be modified. If
+ zero, then this is controlled automatically (the unsymmetric
+ strategy modifies Q, the others do not). Default: 0.
+
+ Control [UMFPACK_AGGRESSIVE]: If nonzero, aggressive absorption is used
+ in COLAMD and AMD. Default: 1.
+
+ double Info [UMFPACK_INFO] ; Output argument, not defined on input.
+
+ Contains statistics about the symbolic analysis. If a (double *) NULL
+ pointer is passed, then no statistics are returned in Info (this is not
+ an error condition). The entire Info array is cleared (all entries set
+ to -1) and then the following statistics are computed:
+
+ Info [UMFPACK_STATUS]: status code. This is also the return value,
+ whether or not Info is present.
+
+ UMFPACK_OK
+
+ Each column of the input matrix contained row indices
+ in increasing order, with no duplicates. Only in this case
+ does umfpack_*_symbolic compute a valid symbolic factorization.
+ For the other cases below, no Symbolic object is created
+ (*Symbolic is (void *) NULL).
+
+ UMFPACK_ERROR_n_nonpositive
+
+ n is less than or equal to zero.
+
+ UMFPACK_ERROR_invalid_matrix
+
+ Number of entries in the matrix is negative, Ap [0] is nonzero,
+ a column has a negative number of entries, a row index is out of
+ bounds, or the columns of input matrix were jumbled (unsorted
+ columns or duplicate entries).
+
+ UMFPACK_ERROR_out_of_memory
+
+ Insufficient memory to perform the symbolic analysis. If the
+ analysis requires more than 2GB of memory and you are using
+ the 32-bit ("int") version of UMFPACK, then you are guaranteed
+ to run out of memory. Try using the 64-bit version of UMFPACK.
+
+ UMFPACK_ERROR_argument_missing
+
+ One or more required arguments is missing.
+
+ UMFPACK_ERROR_internal_error
+
+ Something very serious went wrong. This is a bug.
+ Please contact the author (davis at cise.ufl.edu).
+
+ Info [UMFPACK_NROW]: the value of the input argument n_row.
+
+ Info [UMFPACK_NCOL]: the value of the input argument n_col.
+
+ Info [UMFPACK_NZ]: the number of entries in the input matrix
+ (Ap [n_col]).
+
+ Info [UMFPACK_SIZE_OF_UNIT]: the number of bytes in a Unit,
+ for memory usage statistics below.
+
+ Info [UMFPACK_SIZE_OF_INT]: the number of bytes in an int.
+
+ Info [UMFPACK_SIZE_OF_LONG]: the number of bytes in a UF_long.
+
+ Info [UMFPACK_SIZE_OF_POINTER]: the number of bytes in a void *
+ pointer.
+
+ Info [UMFPACK_SIZE_OF_ENTRY]: the number of bytes in a numerical entry.
+
+ Info [UMFPACK_NDENSE_ROW]: number of "dense" rows in A. These rows are
+ ignored when the column pre-ordering is computed in COLAMD. They
+ are also treated differently during numeric factorization. If > 0,
+ then the matrix had to be re-analyzed by UMF_analyze, which does
+ not ignore these rows.
+
+ Info [UMFPACK_NEMPTY_ROW]: number of "empty" rows in A, as determined
+ These are rows that either have no entries, or whose entries are
+ all in pivot columns of zero-Markowitz-cost pivots.
+
+ Info [UMFPACK_NDENSE_COL]: number of "dense" columns in A. COLAMD
+ orders these columns are ordered last in the factorization, but
+ before "empty" columns.
+
+ Info [UMFPACK_NEMPTY_COL]: number of "empty" columns in A. These are
+ columns that either have no entries, or whose entries are all in
+ pivot rows of zero-Markowitz-cost pivots. These columns are
+ ordered last in the factorization, to the right of "dense" columns.
+
+ Info [UMFPACK_SYMBOLIC_DEFRAG]: number of garbage collections
+ performed during ordering and symbolic pre-analysis.
+
+ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]: the amount of memory (in Units)
+ required for umfpack_*_symbolic to complete. This count includes
+ the size of the Symbolic object itself, which is also reported in
+ Info [UMFPACK_SYMBOLIC_SIZE].
+
+ Info [UMFPACK_SYMBOLIC_SIZE]: the final size of the Symbolic object (in
+ Units). This is fairly small, roughly 2*n to 13*n integers,
+ depending on the matrix.
+
+ Info [UMFPACK_VARIABLE_INIT_ESTIMATE]: the Numeric object contains two
+ parts. The first is fixed in size (O (n_row+n_col)). The
+ second part holds the sparse LU factors and the contribution blocks
+ from factorized frontal matrices. This part changes in size during
+ factorization. Info [UMFPACK_VARIABLE_INIT_ESTIMATE] is the exact
+ size (in Units) required for this second variable-sized part in
+ order for the numerical factorization to start.
+
+ Info [UMFPACK_VARIABLE_PEAK_ESTIMATE]: the estimated peak size (in
+ Units) of the variable-sized part of the Numeric object. This is
+ usually an upper bound, but that is not guaranteed.
+
+ Info [UMFPACK_VARIABLE_FINAL_ESTIMATE]: the estimated final size (in
+ Units) of the variable-sized part of the Numeric object. This is
+ usually an upper bound, but that is not guaranteed. It holds just
+ the sparse LU factors.
+
+ Info [UMFPACK_NUMERIC_SIZE_ESTIMATE]: an estimate of the final size (in
+ Units) of the entire Numeric object (both fixed-size and variable-
+ sized parts), which holds the LU factorization (including the L, U,
+ P and Q matrices).
+
+ Info [UMFPACK_PEAK_MEMORY_ESTIMATE]: an estimate of the total amount of
+ memory (in Units) required by umfpack_*_symbolic and
+ umfpack_*_numeric to perform both the symbolic and numeric
+ factorization. This is the larger of the amount of memory needed
+ in umfpack_*_numeric itself, and the amount of memory needed in
+ umfpack_*_symbolic (Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]). The
+ count includes the size of both the Symbolic and Numeric objects
+ themselves. It can be a very loose upper bound, particularly when
+ the symmetric or 2-by-2 strategies are used.
+
+ Info [UMFPACK_FLOPS_ESTIMATE]: an estimate of the total floating-point
+ operations required to factorize the matrix. This is a "true"
+ theoretical estimate of the number of flops that would be performed
+ by a flop-parsimonious sparse LU algorithm. It assumes that no
+ extra flops are performed except for what is strictly required to
+ compute the LU factorization. It ignores, for example, the flops
+ performed by umfpack_di_numeric to add contribution blocks of
+ frontal matrices together. If L and U are the upper bound on the
+ pattern of the factors, then this flop count estimate can be
+ represented in MATLAB (for real matrices, not complex) as:
+
+ Lnz = full (sum (spones (L))) - 1 ; % nz in each col of L
+ Unz = full (sum (spones (U')))' - 1 ; % nz in each row of U
+ flops = 2*Lnz*Unz + sum (Lnz) ;
+
+ The actual "true flop" count found by umfpack_*_numeric will be
+ less than this estimate.
+
+ For the real version, only (+ - * /) are counted. For the complex
+ version, the following counts are used:
+
+ operation flops
+ c = 1/b 6
+ c = a*b 6
+ c -= a*b 8
+
+ Info [UMFPACK_LNZ_ESTIMATE]: an estimate of the number of nonzeros in
+ L, including the diagonal. Since L is unit-diagonal, the diagonal
+ of L is not stored. This estimate is a strict upper bound on the
+ actual nonzeros in L to be computed by umfpack_*_numeric.
+
+ Info [UMFPACK_UNZ_ESTIMATE]: an estimate of the number of nonzeros in
+ U, including the diagonal. This estimate is a strict upper bound on
+ the actual nonzeros in U to be computed by umfpack_*_numeric.
+
+ Info [UMFPACK_MAX_FRONT_SIZE_ESTIMATE]: estimate of the size of the
+ largest frontal matrix (# of entries), for arbitrary partial
+ pivoting during numerical factorization.
+
+ Info [UMFPACK_SYMBOLIC_TIME]: The CPU time taken, in seconds.
+
+ Info [UMFPACK_SYMBOLIC_WALLTIME]: The wallclock time taken, in seconds.
+
+ Info [UMFPACK_STRATEGY_USED]: The ordering strategy used:
+ UMFPACK_STRATEGY_SYMMETRIC, UMFPACK_STRATEGY_UNSYMMETRIC, or
+ UMFPACK_STRATEGY_2BY2.
+
+ Info [UMFPACK_ORDERING_USED]: The ordering method used:
+ UMFPACK_ORDERING_COLAMD or UMFPACK_ORDERING_AMD. It can be
+ UMFPACK_ORDERING_GIVEN for umfpack_*_qsymbolic.
+
+ Info [UMFPACK_QFIXED]: 1 if the column pre-ordering will be refined
+ during numerical factorization, 0 if not.
+
+ Info [UMFPACK_DIAG_PREFERED]: 1 if diagonal pivoting will be attempted,
+ 0 if not.
+
+ Info [UMFPACK_COL_SINGLETONS]: the matrix A is analyzed by first
+ eliminating all pivots with zero Markowitz cost. This count is the
+ number of these pivots with exactly one nonzero in their pivot
+ column.
+
+ Info [UMFPACK_ROW_SINGLETONS]: the number of zero-Markowitz-cost
+ pivots with exactly one nonzero in their pivot row.
+
+ Info [UMFPACK_PATTERN_SYMMETRY]: the symmetry of the pattern of S.
+
+ Info [UMFPACK_NZ_A_PLUS_AT]: the number of off-diagonal entries in S+S'.
+
+ Info [UMFPACK_NZDIAG]: the number of entries on the diagonal of S.
+
+ Info [UMFPACK_N2]: if S is square, and nempty_row = nempty_col, this
+ is equal to n_row - n1 - nempty_row.
+
+ Info [UMFPACK_S_SYMMETRIC]: 1 if S is square and its diagonal has been
+ preserved, 0 otherwise.
+
+
+ Info [UMFPACK_MAX_FRONT_NROWS_ESTIMATE]: estimate of the max number of
+ rows in any frontal matrix, for arbitrary partial pivoting.
+
+ Info [UMFPACK_MAX_FRONT_NCOLS_ESTIMATE]: estimate of the max number of
+ columns in any frontal matrix, for arbitrary partial pivoting.
+
+ ------------------------------------------------------------------------
+ The next four statistics are computed only if AMD is used:
+ ------------------------------------------------------------------------
+
+ Info [UMFPACK_SYMMETRIC_LUNZ]: The number of nonzeros in L and U,
+ assuming no pivoting during numerical factorization, and assuming a
+ zero-free diagonal of U. Excludes the entries on the diagonal of
+ L. If the matrix has a purely symmetric nonzero pattern, this is
+ often a lower bound on the nonzeros in the actual L and U computed
+ in the numerical factorization, for matrices that fit the criteria
+ for the "symmetric" strategy.
+
+ Info [UMFPACK_SYMMETRIC_FLOPS]: The floating-point operation count in
+ the numerical factorization phase, assuming no pivoting. If the
+ pattern of the matrix is symmetric, this is normally a lower bound
+ on the floating-point operation count in the actual numerical
+ factorization, for matrices that fit the criteria for the symmetric
+ or 2-by-2 strategies
+
+ Info [UMFPACK_SYMMETRIC_NDENSE]: The number of "dense" rows/columns of
+ S+S' that were ignored during the AMD ordering. These are placed
+ last in the output order. If > 0, then the
+ Info [UMFPACK_SYMMETRIC_*] statistics, above are rough upper bounds.
+
+ Info [UMFPACK_SYMMETRIC_DMAX]: The maximum number of nonzeros in any
+ column of L, if no pivoting is performed during numerical
+ factorization. Excludes the part of the LU factorization for
+ pivots with zero Markowitz cost.
+
+ ------------------------------------------------------------------------
+ The following statistics are computed only if the 2-by-2 strategy is
+ used or attempted:
+ ------------------------------------------------------------------------
+
+ Info [UMFPACK_2BY2_NWEAK]: the number of small diagonal entries in S.
+
+ Info [UMFPACK_2BY2_UNMATCHED]: the number of small diagonal entries
+ in P2*S.
+
+ Info [UMFPACK_2BY2_PATTERN_SYMMETRY]: the symmetry of P2*S.
+
+ Info [UMFPACK_2BY2_NZ_PA_PLUS_AT]: the number of off-diagonal entries
+ in (P2*S)+(P2*S)'.
+
+ Info [UMFPACK_2BY2_NZDIAG]: the number of nonzero entries on the
+ diagonal of P2*S.
+
+
+ At the start of umfpack_*_symbolic, all of Info is set of -1, and then
+ after that only the above listed Info [...] entries are accessed.
+ Future versions might modify different parts of Info.
+*/
diff --git a/UMFPACK/Include/umfpack_tictoc.h b/UMFPACK/Include/umfpack_tictoc.h
new file mode 100644
index 0000000..da10426
--- /dev/null
+++ b/UMFPACK/Include/umfpack_tictoc.h
@@ -0,0 +1,60 @@
+/* ========================================================================== */
+/* === umfpack_tictoc ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_tic (double stats [2]) ;
+
+void umfpack_toc (double stats [2]) ;
+
+
+/*
+Syntax (for all versions: di, dl, zi, and zl):
+
+ #include "umfpack.h"
+ double stats [2] ;
+ umfpack_tic (stats) ;
+ ...
+ umfpack_toc (stats) ;
+
+Purpose:
+
+ umfpack_tic returns the CPU time and wall clock time used by the process.
+ The CPU time includes both "user" and "system" time (the latter is time
+ spent by the system on behalf of the process, and is thus charged to the
+ process). umfpack_toc returns the CPU time and wall clock time since the
+ last call to umfpack_tic with the same stats array.
+
+ Typical usage:
+
+ umfpack_tic (stats) ;
+ ... do some work ...
+ umfpack_toc (stats) ;
+
+ then stats [1] contains the time in seconds used by the code between
+ umfpack_tic and umfpack_toc, and stats [0] contains the wall clock time
+ elapsed between the umfpack_tic and umfpack_toc. These two routines act
+ just like tic and toc in MATLAB, except that the both process time and
+ wall clock time are returned.
+
+ This routine normally uses the sysconf and times routines in the POSIX
+ standard. If -DNPOSIX is defined at compile time, then the ANSI C clock
+ routine is used instead, and only the CPU time is returned (stats [0]
+ is set to zero).
+
+ umfpack_tic and umfpack_toc are the routines used internally in UMFPACK
+ to time the symbolic analysis, numerical factorization, and the forward/
+ backward solve.
+
+Arguments:
+
+ double stats [2]:
+
+ stats [0]: wall clock time, in seconds
+ stats [1]: CPU time, in seconds
+*/
diff --git a/UMFPACK/Include/umfpack_timer.h b/UMFPACK/Include/umfpack_timer.h
new file mode 100644
index 0000000..413a177
--- /dev/null
+++ b/UMFPACK/Include/umfpack_timer.h
@@ -0,0 +1,39 @@
+/* ========================================================================== */
+/* === umfpack_timer ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+double umfpack_timer ( void ) ;
+
+/*
+Syntax (for all versions: di, dl, zi, and zl):
+
+ #include "umfpack.h"
+ double t ;
+ t = umfpack_timer ( ) ;
+
+Purpose:
+
+ Returns the CPU time used by the process. Includes both "user" and "system"
+ time (the latter is time spent by the system on behalf of the process, and
+ is thus charged to the process). It does not return the wall clock time.
+ See umfpack_tic and umfpack_toc (the file umfpack_tictoc.h) for the timer
+ used internally by UMFPACK.
+
+ This routine uses the Unix getrusage routine, if available. It is less
+ subject to overflow than the ANSI C clock routine. If getrusage is not
+ available, the portable ANSI C clock routine is used instead.
+ Unfortunately, clock ( ) overflows if the CPU time exceeds 2147 seconds
+ (about 36 minutes) when sizeof (clock_t) is 4 bytes. If you have getrusage,
+ be sure to compile UMFPACK with the -DGETRUSAGE flag set; see umf_config.h
+ and the User Guide for details. Even the getrusage routine can overlow.
+
+Arguments:
+
+ None.
+*/
diff --git a/UMFPACK/Include/umfpack_transpose.h b/UMFPACK/Include/umfpack_transpose.h
new file mode 100644
index 0000000..b12bb0b
--- /dev/null
+++ b/UMFPACK/Include/umfpack_transpose.h
@@ -0,0 +1,216 @@
+/* ========================================================================== */
+/* === umfpack_transpose ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_transpose
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ const int P [ ],
+ const int Q [ ],
+ int Rp [ ],
+ int Ri [ ],
+ double Rx [ ]
+) ;
+
+UF_long umfpack_dl_transpose
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ const UF_long P [ ],
+ const UF_long Q [ ],
+ UF_long Rp [ ],
+ UF_long Ri [ ],
+ double Rx [ ]
+) ;
+
+int umfpack_zi_transpose
+(
+ int n_row,
+ int n_col,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ const int P [ ],
+ const int Q [ ],
+ int Rp [ ],
+ int Ri [ ],
+ double Rx [ ], double Rz [ ],
+ int do_conjugate
+) ;
+
+UF_long umfpack_zl_transpose
+(
+ UF_long n_row,
+ UF_long n_col,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ const UF_long P [ ],
+ const UF_long Q [ ],
+ UF_long Rp [ ],
+ UF_long Ri [ ],
+ double Rx [ ], double Rz [ ],
+ UF_long do_conjugate
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri ;
+ double *Ax, *Rx ;
+ status = umfpack_di_transpose (n_row, n_col, Ap, Ai, Ax, P, Q, Rp, Ri, Rx) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri ;
+ double *Ax, *Rx ;
+ status = umfpack_dl_transpose (n_row, n_col, Ap, Ai, Ax, P, Q, Rp, Ri, Rx) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri, do_conjugate ;
+ double *Ax, *Az, *Rx, *Rz ;
+ status = umfpack_zi_transpose (n_row, n_col, Ap, Ai, Ax, Az, P, Q,
+ Rp, Ri, Rx, Rz, do_conjugate) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, status, *Ap, *Ai, *P, *Q, *Rp, *Ri, do_conjugate ;
+ double *Ax, *Az, *Rx, *Rz ;
+ status = umfpack_zl_transpose (n_row, n_col, Ap, Ai, Ax, Az, P, Q,
+ Rp, Ri, Rx, Rz, do_conjugate) ;
+
+packed complex Syntax:
+
+ Same as above, except Az are Rz are NULL.
+
+Purpose:
+
+ Transposes and optionally permutes a sparse matrix in row or column-form,
+ R = (PAQ)'. In MATLAB notation, R = (A (P,Q))' or R = (A (P,Q)).' doing
+ either the linear algebraic transpose or the array transpose. Alternatively,
+ this routine can be viewed as converting A (P,Q) from column-form to
+ row-form, or visa versa (for the array transpose). Empty rows and columns
+ may exist. The matrix A may be singular and/or rectangular.
+
+ umfpack_*_transpose is useful if you want to factorize A' or A.' instead of
+ A. Factorizing A' or A.' instead of A can be much better, particularly if
+ AA' is much sparser than A'A. You can still solve Ax=b if you factorize
+ A' or A.', by solving with the sys argument UMFPACK_At or UMFPACK_Aat,
+ respectively, in umfpack_*_*solve.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_out_of_memory if umfpack_*_transpose fails to allocate a
+ size-max (n_row,n_col) workspace.
+ UMFPACK_ERROR_argument_missing if Ai, Ap, Ri, and/or Rp are missing.
+ UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0
+ UMFPACK_ERROR_invalid_permutation if P and/or Q are invalid.
+ UMFPACK_ERROR_invalid_matrix if Ap [n_col] < 0, if Ap [0] != 0,
+ if Ap [j] > Ap [j+1] for any j in the range 0 to n_col-1,
+ if any row index i is < 0 or >= n_row, or if the row indices
+ in any column are not in ascending order.
+
+Arguments:
+
+ Int n_row ; Input argument, not modified.
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0.
+
+ Int Ap [n_col+1] ; Input argument, not modified.
+
+ The column pointers of the column-oriented form of the matrix A. See
+ umfpack_*_symbolic for a description. The number of entries in
+ the matrix is nz = Ap [n_col]. Ap [0] must be zero, Ap [n_col] must be
+ => 0, and Ap [j] <= Ap [j+1] and Ap [j] <= Ap [n_col] must be true for
+ all j in the range 0 to n_col-1. Empty columns are OK (that is, Ap [j]
+ may equal Ap [j+1] for any j in the range 0 to n_col-1).
+
+ Int Ai [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+
+ The nonzero pattern (row indices) for column j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j
+ must be in ascending order, and no duplicate row indices may be present.
+ Row indices must be in the range 0 to n_row-1 (the matrix is 0-based).
+
+ double Ax [nz] ; Input argument, not modified, of size nz = Ap [n_col].
+ Size 2*nz if Az or Rz are NULL.
+ double Az [nz] ; Input argument, not modified, for complex versions.
+
+ If present, these are the numerical values of the sparse matrix A.
+ The nonzero pattern (row indices) for column j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)], and the corresponding real numerical
+ values are stored in Ax [(Ap [j]) ... (Ap [j+1]-1)]. The imaginary
+ values are stored in Az [(Ap [j]) ... (Ap [j+1]-1)]. The values are
+ transposed only if Ax and Rx are present.
+ This is not an error conditions; you are able to transpose
+ and permute just the pattern of a matrix.
+
+ If Az or Rz are NULL, then both real
+ and imaginary parts are contained in Ax[0..2*nz-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int P [n_row] ; Input argument, not modified.
+
+ The permutation vector P is defined as P [k] = i, where the original
+ row i of A is the kth row of PAQ. If you want to use the identity
+ permutation for P, simply pass (Int *) NULL for P. This is not an error
+ condition. P is a complete permutation of all the rows of A; this
+ routine does not support the creation of a transposed submatrix of A
+ (R = A (1:3,:)' where A has more than 3 rows, for example, cannot be
+ done; a future version might support this operation).
+
+ Int Q [n_col] ; Input argument, not modified.
+
+ The permutation vector Q is defined as Q [k] = j, where the original
+ column j of A is the kth column of PAQ. If you want to use the identity
+ permutation for Q, simply pass (Int *) NULL for Q. This is not an error
+ condition. Q is a complete permutation of all the columns of A; this
+ routine does not support the creation of a transposed submatrix of A.
+
+ Int Rp [n_row+1] ; Output argument.
+
+ The column pointers of the matrix R = (A (P,Q))' or (A (P,Q)).', in the
+ same form as the column pointers Ap for the matrix A.
+
+ Int Ri [nz] ; Output argument.
+
+ The row indices of the matrix R = (A (P,Q))' or (A (P,Q)).' , in the
+ same form as the row indices Ai for the matrix A.
+
+ double Rx [nz] ; Output argument.
+ Size 2*nz if Az or Rz are NULL.
+ double Rz [nz] ; Output argument, imaginary part for complex versions.
+
+ If present, these are the numerical values of the sparse matrix R,
+ in the same form as the values Ax and Az of the matrix A.
+
+ If Az or Rz are NULL, then both real
+ and imaginary parts are contained in Rx[0..2*nz-1], with Rx[2*k]
+ and Rx[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int do_conjugate ; Input argument for complex versions only.
+
+ If true, and if Ax and Rx are present, then the linear
+ algebraic transpose is computed (complex conjugate). If false, the
+ array transpose is computed instead.
+*/
diff --git a/UMFPACK/Include/umfpack_triplet_to_col.h b/UMFPACK/Include/umfpack_triplet_to_col.h
new file mode 100644
index 0000000..cb45278
--- /dev/null
+++ b/UMFPACK/Include/umfpack_triplet_to_col.h
@@ -0,0 +1,263 @@
+/* ========================================================================== */
+/* === umfpack_triplet_to_col =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_triplet_to_col
+(
+ int n_row,
+ int n_col,
+ int nz,
+ const int Ti [ ],
+ const int Tj [ ],
+ const double Tx [ ],
+ int Ap [ ],
+ int Ai [ ],
+ double Ax [ ],
+ int Map [ ]
+) ;
+
+UF_long umfpack_dl_triplet_to_col
+(
+ UF_long n_row,
+ UF_long n_col,
+ UF_long nz,
+ const UF_long Ti [ ],
+ const UF_long Tj [ ],
+ const double Tx [ ],
+ UF_long Ap [ ],
+ UF_long Ai [ ],
+ double Ax [ ],
+ UF_long Map [ ]
+) ;
+
+int umfpack_zi_triplet_to_col
+(
+ int n_row,
+ int n_col,
+ int nz,
+ const int Ti [ ],
+ const int Tj [ ],
+ const double Tx [ ], const double Tz [ ],
+ int Ap [ ],
+ int Ai [ ],
+ double Ax [ ], double Az [ ],
+ int Map [ ]
+) ;
+
+UF_long umfpack_zl_triplet_to_col
+(
+ UF_long n_row,
+ UF_long n_col,
+ UF_long nz,
+ const UF_long Ti [ ],
+ const UF_long Tj [ ],
+ const double Tx [ ], const double Tz [ ],
+ UF_long Ap [ ],
+ UF_long Ai [ ],
+ double Ax [ ], double Az [ ],
+ UF_long Map [ ]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ;
+ double *Tx, *Ax ;
+ status = umfpack_di_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx,
+ Ap, Ai, Ax, Map) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ;
+ double *Tx, *Ax ;
+ status = umfpack_dl_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx,
+ Ap, Ai, Ax, Map) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ int n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ;
+ double *Tx, *Tz, *Ax, *Az ;
+ status = umfpack_zi_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx, Tz,
+ Ap, Ai, Ax, Az, Map) ;
+
+UF_long Syntax:
+
+ #include "umfpack.h"
+ UF_long n_row, n_col, nz, *Ti, *Tj, *Ap, *Ai, status, *Map ;
+ double *Tx, *Tz, *Ax, *Az ;
+ status = umfpack_zl_triplet_to_col (n_row, n_col, nz, Ti, Tj, Tx, Tz,
+ Ap, Ai, Ax, Az, Map) ;
+
+packed complex Syntax:
+
+ Same as above, except Tz and Az are NULL.
+
+Purpose:
+
+ Converts a sparse matrix from "triplet" form to compressed-column form.
+ Analogous to A = spconvert (Ti, Tj, Tx + Tz*1i) in MATLAB, except that
+ zero entries present in the triplet form are present in A.
+
+ The triplet form of a matrix is a very simple data structure for basic
+ sparse matrix operations. For example, suppose you wish to factorize a
+ matrix A coming from a finite element method, in which A is a sum of
+ dense submatrices, A = E1 + E2 + E3 + ... . The entries in each element
+ matrix Ei can be concatenated together in the three triplet arrays, and
+ any overlap between the elements will be correctly summed by
+ umfpack_*_triplet_to_col.
+
+ Transposing a matrix in triplet form is simple; just interchange the
+ use of Ti and Tj. You can construct the complex conjugate transpose by
+ negating Tz, for the complex versions.
+
+ Permuting a matrix in triplet form is also simple. If you want the matrix
+ PAQ, or A (P,Q) in MATLAB notation, where P [k] = i means that row i of
+ A is the kth row of PAQ and Q [k] = j means that column j of A is the kth
+ column of PAQ, then do the following. First, create inverse permutations
+ Pinv and Qinv such that Pinv [i] = k if P [k] = i and Qinv [j] = k if
+ Q [k] = j. Next, for the mth triplet (Ti [m], Tj [m], Tx [m], Tz [m]),
+ replace Ti [m] with Pinv [Ti [m]] and replace Tj [m] with Qinv [Tj [m]].
+
+ If you have a column-form matrix with duplicate entries or unsorted
+ columns, you can sort it and sum up the duplicates by first converting it
+ to triplet form with umfpack_*_col_to_triplet, and then converting it back
+ with umfpack_*_triplet_to_col.
+
+ Constructing a submatrix is also easy. Just scan the triplets and remove
+ those entries outside the desired subset of 0...n_row-1 and 0...n_col-1,
+ and renumber the indices according to their position in the subset.
+
+ You can do all these operations on a column-form matrix by first
+ converting it to triplet form with umfpack_*_col_to_triplet, doing the
+ operation on the triplet form, and then converting it back with
+ umfpack_*_triplet_to_col.
+
+ The only operation not supported easily in the triplet form is the
+ multiplication of two sparse matrices (UMFPACK does not provide this
+ operation).
+
+ You can print the input triplet form with umfpack_*_report_triplet, and
+ the output matrix with umfpack_*_report_matrix.
+
+ The matrix may be singular (nz can be zero, and empty rows and/or columns
+ may exist). It may also be rectangular and/or complex.
+
+Returns:
+
+ UMFPACK_OK if successful.
+ UMFPACK_ERROR_argument_missing if Ap, Ai, Ti, and/or Tj are missing.
+ UMFPACK_ERROR_n_nonpositive if n_row <= 0 or n_col <= 0.
+ UMFPACK_ERROR_invalid_matrix if nz < 0, or if for any k, Ti [k] and/or
+ Tj [k] are not in the range 0 to n_row-1 or 0 to n_col-1, respectively.
+ UMFPACK_ERROR_out_of_memory if unable to allocate sufficient workspace.
+
+Arguments:
+
+ Int n_row ; Input argument, not modified.
+ Int n_col ; Input argument, not modified.
+
+ A is an n_row-by-n_col matrix. Restriction: n_row > 0 and n_col > 0.
+ All row and column indices in the triplet form must be in the range
+ 0 to n_row-1 and 0 to n_col-1, respectively.
+
+ Int nz ; Input argument, not modified.
+
+ The number of entries in the triplet form of the matrix. Restriction:
+ nz >= 0.
+
+ Int Ti [nz] ; Input argument, not modified.
+ Int Tj [nz] ; Input argument, not modified.
+ double Tx [nz] ; Input argument, not modified.
+ Size 2*nz if Tz or Az are NULL.
+ double Tz [nz] ; Input argument, not modified, for complex versions.
+
+ Ti, Tj, Tx, and Tz hold the "triplet" form of a sparse matrix. The kth
+ nonzero entry is in row i = Ti [k], column j = Tj [k], and the real part
+ of a_ij is Tx [k]. The imaginary part of a_ij is Tz [k], for complex
+ versions. The row and column indices i and j must be in the range 0 to
+ n_row-1 and 0 to n_col-1, respectively. Duplicate entries may be
+ present; they are summed in the output matrix. This is not an error
+ condition. The "triplets" may be in any order. Tx, Tz, Ax, and Az
+ are optional. Ax is computed only if both Ax and Tx are present
+ (not (double *) NULL). This is not error condition; the routine can
+ create just the pattern of the output matrix from the pattern of the
+ triplets.
+
+ If Az or Tz are NULL, then both real
+ and imaginary parts are contained in Tx[0..2*nz-1], with Tx[2*k]
+ and Tx[2*k+1] being the real and imaginary part of the kth entry.
+
+ Int Ap [n_col+1] ; Output argument.
+
+ Ap is an integer array of size n_col+1 on input. On output, Ap holds
+ the "pointers" for the column form of the sparse matrix A. Column j of
+ the matrix A is held in Ai [(Ap [j]) ... (Ap [j+1]-1)]. The first
+ entry, Ap [0], is zero, and Ap [j] <= Ap [j+1] holds for all j in the
+ range 0 to n_col-1. The value nz2 = Ap [n_col] is thus the total
+ number of entries in the pattern of the matrix A. Equivalently, the
+ number of duplicate triplets is nz - Ap [n_col].
+
+ Int Ai [nz] ; Output argument.
+
+ Ai is an integer array of size nz on input. Note that only the first
+ Ap [n_col] entries are used.
+
+ The nonzero pattern (row indices) for column j is stored in
+ Ai [(Ap [j]) ... (Ap [j+1]-1)]. The row indices in a given column j
+ are in ascending order, and no duplicate row indices are present.
+ Row indices are in the range 0 to n_col-1 (the matrix is 0-based).
+
+ double Ax [nz] ; Output argument. Size 2*nz if Tz or Az are NULL.
+ double Az [nz] ; Output argument for complex versions.
+
+ Ax and Az (for the complex versions) are double arrays of size nz on
+ input. Note that only the first Ap [n_col] entries are used
+ in both arrays.
+
+ Ax is optional; if Tx and/or Ax are not present (a (double *) NULL
+ pointer), then Ax is not computed. If present, Ax holds the
+ numerical values of the the real part of the sparse matrix A and Az
+ holds the imaginary parts. The nonzero pattern (row indices) for
+ column j is stored in Ai [(Ap [j]) ... (Ap [j+1]-1)], and the
+ corresponding numerical values are stored in
+ Ax [(Ap [j]) ... (Ap [j+1]-1)]. The imaginary parts are stored in
+ Az [(Ap [j]) ... (Ap [j+1]-1)], for the complex versions.
+
+ If Az or Tz are NULL, then both real
+ and imaginary parts are returned in Ax[0..2*nz2-1], with Ax[2*k]
+ and Ax[2*k+1] being the real and imaginary part of the kth entry.
+
+ int Map [nz] ; Optional output argument.
+
+ If Map is present (a non-NULL pointer to an Int array of size nz), then
+ on output it holds the position of the triplets in the column-form
+ matrix. That is, suppose p = Map [k], and the k-th triplet is i=Ti[k],
+ j=Tj[k], and aij=Tx[k]. Then i=Ai[p], and aij will have been summed
+ into Ax[p] (or simply aij=Ax[p] if there were no duplicate entries also
+ in row i and column j). Also, Ap[j] <= p < Ap[j+1]. The Map array is
+ not computed if it is (Int *) NULL. The Map array is useful for
+ converting a subsequent triplet form matrix with the same pattern as the
+ first one, without calling this routine. If Ti and Tj do not change,
+ then Ap, and Ai can be reused from the prior call to
+ umfpack_*_triplet_to_col. You only need to recompute Ax (and Az for the
+ split complex version). This code excerpt properly sums up all
+ duplicate values (for the real version):
+
+ for (p = 0 ; p < Ap [n_col] ; p++) Ax [p] = 0 ;
+ for (k = 0 ; k < nz ; k++) Ax [Map [k]] += Tx [k] ;
+
+ This feature is useful (along with the reuse of the Symbolic object) if
+ you need to factorize a sequence of triplet matrices with identical
+ nonzero pattern (the order of the triplets in the Ti,Tj,Tx arrays must
+ also remain unchanged). It is faster than calling this routine for
+ each matrix, and requires no workspace.
+*/
diff --git a/UMFPACK/Include/umfpack_wsolve.h b/UMFPACK/Include/umfpack_wsolve.h
new file mode 100644
index 0000000..38d15ba
--- /dev/null
+++ b/UMFPACK/Include/umfpack_wsolve.h
@@ -0,0 +1,172 @@
+/* ========================================================================== */
+/* === umfpack_wsolve ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+int umfpack_di_wsolve
+(
+ int sys,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ],
+ double X [ ],
+ const double B [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO],
+ int Wi [ ],
+ double W [ ]
+) ;
+
+UF_long umfpack_dl_wsolve
+(
+ UF_long sys,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ],
+ double X [ ],
+ const double B [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO],
+ UF_long Wi [ ],
+ double W [ ]
+) ;
+
+int umfpack_zi_wsolve
+(
+ int sys,
+ const int Ap [ ],
+ const int Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO],
+ int Wi [ ],
+ double W [ ]
+) ;
+
+UF_long umfpack_zl_wsolve
+(
+ UF_long sys,
+ const UF_long Ap [ ],
+ const UF_long Ai [ ],
+ const double Ax [ ], const double Az [ ],
+ double Xx [ ], double Xz [ ],
+ const double Bx [ ], const double Bz [ ],
+ void *Numeric,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO],
+ UF_long Wi [ ],
+ double W [ ]
+) ;
+
+/*
+double int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, *Ap, *Ai, *Wi, sys ;
+ double *B, *X, *Ax, *W, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_di_wsolve (sys, Ap, Ai, Ax, X, B, Numeric,
+ Control, Info, Wi, W) ;
+
+double UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, *Ap, *Ai, *Wi, sys ;
+ double *B, *X, *Ax, *W, Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_dl_wsolve (sys, Ap, Ai, Ax, X, B, Numeric,
+ Control, Info, Wi, W) ;
+
+complex int Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ int status, *Ap, *Ai, *Wi, sys ;
+ double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, *W,
+ Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_zi_wsolve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric,
+ Control, Info, Wi, W) ;
+
+complex UF_long Syntax:
+
+ #include "umfpack.h"
+ void *Numeric ;
+ UF_long status, *Ap, *Ai, *Wi, sys ;
+ double *Bx, *Bz, *Xx, *Xz, *Ax, *Az, *W,
+ Info [UMFPACK_INFO], Control [UMFPACK_CONTROL] ;
+ status = umfpack_zl_wsolve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz, Numeric,
+ Control, Info, Wi, W) ;
+
+packed complex Syntax:
+
+ Same as above, except Az, Xz, and Bz are NULL.
+
+Purpose:
+
+ Given LU factors computed by umfpack_*_numeric (PAQ=LU) and the
+ right-hand-side, B, solve a linear system for the solution X. Iterative
+ refinement is optionally performed. This routine is identical to
+ umfpack_*_solve, except that it does not dynamically allocate any workspace.
+ When you have many linear systems to solve, this routine is faster than
+ umfpack_*_solve, since the workspace (Wi, W) needs to be allocated only
+ once, prior to calling umfpack_*_wsolve.
+
+Returns:
+
+ The status code is returned. See Info [UMFPACK_STATUS], below.
+
+Arguments:
+
+ Int sys ; Input argument, not modified.
+ Int Ap [n+1] ; Input argument, not modified.
+ Int Ai [nz] ; Input argument, not modified.
+ double Ax [nz] ; Input argument, not modified.
+ Size 2*nz in packed complex case.
+ double X [n] ; Output argument.
+ double B [n] ; Input argument, not modified.
+ void *Numeric ; Input argument, not modified.
+ double Control [UMFPACK_CONTROL] ; Input argument, not modified.
+ double Info [UMFPACK_INFO] ; Output argument.
+
+ for complex versions:
+ double Az [nz] ; Input argument, not modified, imaginary part
+ double Xx [n] ; Output argument, real part.
+ Size 2*n in packed complex case.
+ double Xz [n] ; Output argument, imaginary part
+ double Bx [n] ; Input argument, not modified, real part.
+ Size 2*n in packed complex case.
+ double Bz [n] ; Input argument, not modified, imaginary part
+
+ The above arguments are identical to umfpack_*_solve, except that the
+ error code UMFPACK_ERROR_out_of_memory will not be returned in
+ Info [UMFPACK_STATUS], since umfpack_*_wsolve does not allocate any
+ memory.
+
+ Int Wi [n] ; Workspace.
+ double W [c*n] ; Workspace, where c is defined below.
+
+ The Wi and W arguments are workspace used by umfpack_*_wsolve. They
+ need not be initialized on input, and their contents are undefined on
+ output. The size of W depends on whether or not iterative refinement is
+ used, and which version (real or complex) is called. Iterative
+ refinement is performed if Ax=b, A'x=b, or A.'x=b is being solved,
+ Control [UMFPACK_IRSTEP] > 0, and A is nonsingular. The size of W is
+ given below:
+
+ no iter. with iter.
+ refinement refinement
+ umfpack_di_wsolve n 5*n
+ umfpack_dl_wsolve n 5*n
+ umfpack_zi_wsolve 4*n 10*n
+ umfpack_zl_wsolve 4*n 10*n
+*/
diff --git a/UMFPACK/Lib/GNUmakefile b/UMFPACK/Lib/GNUmakefile
new file mode 100644
index 0000000..559ed99
--- /dev/null
+++ b/UMFPACK/Lib/GNUmakefile
@@ -0,0 +1,258 @@
+#-------------------------------------------------------------------------------
+# UMFPACK Makefile for compiling on Unix systems (for GNU Make)
+#-------------------------------------------------------------------------------
+
+default: ../Lib/libumfpack.a
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(UMFPACK_CONFIG) \
+ -I../Include -I../Source -I../../AMD/Include -I../../UFconfig
+
+#-------------------------------------------------------------------------------
+# source files
+#-------------------------------------------------------------------------------
+
+# non-user-callable umf_*.[ch] files:
+UMFCH = umf_assemble umf_blas3_update umf_build_tuples umf_create_element \
+ umf_dump umf_extend_front umf_garbage_collection umf_get_memory \
+ umf_init_front umf_kernel umf_kernel_init umf_kernel_wrapup \
+ umf_local_search umf_lsolve umf_ltsolve umf_mem_alloc_element \
+ umf_mem_alloc_head_block umf_mem_alloc_tail_block \
+ umf_mem_free_tail_block umf_mem_init_memoryspace \
+ umf_report_vector umf_row_search umf_scale_column \
+ umf_set_stats umf_solve umf_symbolic_usage umf_transpose \
+ umf_tuple_lengths umf_usolve umf_utsolve umf_valid_numeric \
+ umf_valid_symbolic umf_grow_front umf_start_front umf_2by2 \
+ umf_store_lu umf_scale
+
+# non-user-callable umf_*.[ch] files, int/UF_long versions only (no real/complex):
+UMFINT = umf_analyze umf_apply_order umf_colamd umf_free umf_fsize \
+ umf_is_permutation umf_malloc umf_realloc umf_report_perm \
+ umf_singletons
+
+# non-user-callable, created from umf_ltsolve.c, umf_utsolve.c,
+# umf_triplet.c, and umf_assemble.c , with int/UF_long and real/complex versions:
+UMF_CREATED = umf_lhsolve umf_uhsolve umf_triplet_map_nox \
+ umf_triplet_nomap_x umf_triplet_nomap_nox umf_triplet_map_x \
+ umf_assemble_fixq umf_store_lu_drop
+
+# non-user-callable, int/UF_long and real/complex versions:
+UMF = $(UMF_CREATED) $(UMFCH)
+
+# user-callable umfpack_*.[ch] files (int/UF_long and real/complex):
+UMFPACK = umfpack_col_to_triplet umfpack_defaults umfpack_free_numeric \
+ umfpack_free_symbolic umfpack_get_numeric umfpack_get_lunz \
+ umfpack_get_symbolic umfpack_get_determinant umfpack_numeric \
+ umfpack_qsymbolic umfpack_report_control umfpack_report_info \
+ umfpack_report_matrix umfpack_report_numeric umfpack_report_perm \
+ umfpack_report_status umfpack_report_symbolic umfpack_report_triplet \
+ umfpack_report_vector umfpack_solve umfpack_symbolic \
+ umfpack_transpose umfpack_triplet_to_col umfpack_scale \
+ umfpack_load_numeric umfpack_save_numeric \
+ umfpack_load_symbolic umfpack_save_symbolic
+
+# user-callable, created from umfpack_solve.c (umfpack_wsolve.h exists, though):
+# with int/UF_long and real/complex versions:
+UMFPACKW = umfpack_wsolve
+
+USER = $(UMFPACKW) $(UMFPACK)
+
+# user-callable, only one version for int/UF_long, real/complex, *.[ch] files:
+GENERIC = umfpack_timer umfpack_tictoc umfpack_global
+
+#-------------------------------------------------------------------------------
+# include files:
+#-------------------------------------------------------------------------------
+
+INC = ../Include/umfpack.h ../../UFconfig/UFconfig.h \
+ ../Source/umf_config.h ../Source/umf_version.h \
+ ../Source/umf_internal.h ../Source/umf_triplet.h \
+ $(addprefix ../Source/, $(addsuffix .h,$(UMFCH))) \
+ $(addprefix ../Source/, $(addsuffix .h,$(UMFINT))) \
+ $(addprefix ../Include/, $(addsuffix .h,$(USER))) \
+ $(addprefix ../Include/, $(addsuffix .h,$(GENERIC))) \
+ ../../AMD/Include/amd_internal.h ../../AMD/Include/amd.h
+
+#-------------------------------------------------------------------------------
+# object files for each version
+#-------------------------------------------------------------------------------
+
+DI = $(addsuffix .o, $(subst umf_,umf_di_,$(UMF)) $(subst umfpack_,umfpack_di_,$(USER)))
+DL = $(addsuffix .o, $(subst umf_,umf_dl_,$(UMF)) $(subst umfpack_,umfpack_dl_,$(USER)))
+ZI = $(addsuffix .o, $(subst umf_,umf_zi_,$(UMF)) $(subst umfpack_,umfpack_zi_,$(USER)))
+ZL = $(addsuffix .o, $(subst umf_,umf_zl_,$(UMF)) $(subst umfpack_,umfpack_zl_,$(USER)))
+II = $(addsuffix .o, $(subst umf_,umf_i_,$(UMFINT)))
+LL = $(addsuffix .o, $(subst umf_,umf_l_,$(UMFINT)))
+GN = $(addsuffix .o, $(subst umfpack_,umfpack_gn_,$(GENERIC)))
+
+#-------------------------------------------------------------------------------
+# compile each int and UF_long routine (with no real/complex version)
+#-------------------------------------------------------------------------------
+
+umf_i_%.o: ../Source/umf_%.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+umf_l_%.o: ../Source/umf_%.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# compile each routine in the DI version
+#-------------------------------------------------------------------------------
+
+umf_di_%.o: ../Source/umf_%.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+umf_di_%hsolve.o: ../Source/umf_%tsolve.c $(INC)
+ $(C) -DDINT -DCONJUGATE_SOLVE -c $< -o $@
+
+umf_di_triplet_map_x.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DDINT -DDO_MAP -DDO_VALUES -c $< -o $@
+
+umf_di_triplet_map_nox.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DDINT -DDO_MAP -c $< -o $@
+
+umf_di_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DDINT -DDO_VALUES -c $< -o $@
+
+umf_di_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+umf_di_assemble_fixq.o: ../Source/umf_assemble.c $(INC)
+ $(C) -DDINT -DFIXQ -c $< -o $@
+
+umf_di_store_lu_drop.o: ../Source/umf_store_lu.c $(INC)
+ $(C) -DDINT -DDROP -c $< -o $@
+
+umfpack_di_wsolve.o: ../Source/umfpack_solve.c $(INC)
+ $(C) -DDINT -DWSOLVE -c $< -o $@
+
+umfpack_di_%.o: ../Source/umfpack_%.c $(INC)
+ $(C) -DDINT -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# compile each routine in the DL version
+#-------------------------------------------------------------------------------
+
+umf_dl_%.o: ../Source/umf_%.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+umf_dl_%hsolve.o: ../Source/umf_%tsolve.c $(INC)
+ $(C) -DDLONG -DCONJUGATE_SOLVE -c $< -o $@
+
+umf_dl_triplet_map_x.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DDLONG -DDO_MAP -DDO_VALUES -c $< -o $@
+
+umf_dl_triplet_map_nox.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DDLONG -DDO_MAP -c $< -o $@
+
+umf_dl_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DDLONG -DDO_VALUES -c $< -o $@
+
+umf_dl_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+umf_dl_assemble_fixq.o: ../Source/umf_assemble.c $(INC)
+ $(C) -DDLONG -DFIXQ -c $< -o $@
+
+umf_dl_store_lu_drop.o: ../Source/umf_store_lu.c $(INC)
+ $(C) -DDLONG -DDROP -c $< -o $@
+
+umfpack_dl_wsolve.o: ../Source/umfpack_solve.c $(INC)
+ $(C) -DDLONG -DWSOLVE -c $< -o $@
+
+umfpack_dl_%.o: ../Source/umfpack_%.c $(INC)
+ $(C) -DDLONG -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# compile each routine in the ZI version
+#-------------------------------------------------------------------------------
+
+umf_zi_%.o: ../Source/umf_%.c $(INC)
+ $(C) -DZINT -c $< -o $@
+
+umf_zi_%hsolve.o: ../Source/umf_%tsolve.c $(INC)
+ $(C) -DZINT -DCONJUGATE_SOLVE -c $< -o $@
+
+umf_zi_triplet_map_x.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DZINT -DDO_MAP -DDO_VALUES -c $< -o $@
+
+umf_zi_triplet_map_nox.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DZINT -DDO_MAP -c $< -o $@
+
+umf_zi_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DZINT -DDO_VALUES -c $< -o $@
+
+umf_zi_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DZINT -c $< -o $@
+
+umf_zi_assemble_fixq.o: ../Source/umf_assemble.c $(INC)
+ $(C) -DZINT -DFIXQ -c $< -o $@
+
+umf_zi_store_lu_drop.o: ../Source/umf_store_lu.c $(INC)
+ $(C) -DZINT -DDROP -c $< -o $@
+
+umfpack_zi_wsolve.o: ../Source/umfpack_solve.c $(INC)
+ $(C) -DZINT -DWSOLVE -c $< -o $@
+
+umfpack_zi_%.o: ../Source/umfpack_%.c $(INC)
+ $(C) -DZINT -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# compile each routine in the ZL version
+#-------------------------------------------------------------------------------
+
+umf_zl_%.o: ../Source/umf_%.c $(INC)
+ $(C) -DZLONG -c $< -o $@
+
+umf_zl_%hsolve.o: ../Source/umf_%tsolve.c $(INC)
+ $(C) -DZLONG -DCONJUGATE_SOLVE -c $< -o $@
+
+umf_zl_triplet_map_x.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DZLONG -DDO_MAP -DDO_VALUES -c $< -o $@
+
+umf_zl_triplet_map_nox.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DZLONG -DDO_MAP -c $< -o $@
+
+umf_zl_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DZLONG -DDO_VALUES -c $< -o $@
+
+umf_zl_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC)
+ $(C) -DZLONG -c $< -o $@
+
+umf_zl_assemble_fixq.o: ../Source/umf_assemble.c $(INC)
+ $(C) -DZLONG -DFIXQ -c $< -o $@
+
+umf_zl_store_lu_drop.o: ../Source/umf_store_lu.c $(INC)
+ $(C) -DZLONG -DDROP -c $< -o $@
+
+umfpack_zl_wsolve.o: ../Source/umfpack_solve.c $(INC)
+ $(C) -DZLONG -DWSOLVE -c $< -o $@
+
+umfpack_zl_%.o: ../Source/umfpack_%.c $(INC)
+ $(C) -DZLONG -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# Create the generic routines (GN) using a generic rule
+#-------------------------------------------------------------------------------
+
+umfpack_gn_%.o: ../Source/umfpack_%.c $(INC)
+ $(C) -c $< -o $@
+
+#-------------------------------------------------------------------------------
+# Create the ../Lib/libumfpack.a library
+#-------------------------------------------------------------------------------
+
+../Lib/libumfpack.a: $(II) $(LL) $(GN) $(DI) $(DL) $(ZI) $(ZL)
+ $(AR) ../Lib/libumfpack.a $^
+ - $(RANLIB) ../Lib/libumfpack.a
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+purge: clean
+ - $(RM) ../Lib/libumfpack.a
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/UMFPACK/Lib/Makefile b/UMFPACK/Lib/Makefile
new file mode 100644
index 0000000..8444719
--- /dev/null
+++ b/UMFPACK/Lib/Makefile
@@ -0,0 +1,483 @@
+#-------------------------------------------------------------------------------
+# UMFPACK Makefile for compiling on Unix systems (for original make only)
+#-------------------------------------------------------------------------------
+
+# This is a very ugly Makefile, and is only provided for those who do not
+# have GNU make. Note that it is not used if you have GNU make. It ignores
+# dependency checking and just compiles everything.
+
+default: everything
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(UMFPACK_CONFIG) -I../Include -I../../AMD/Include \
+ -I../Source
+
+everything:
+ $(C) -c ../Source/umfpack_global.c -o umfpack_gn_global.o
+ $(C) -DDINT -c ../Source/umf_analyze.c -o umf_i_analyze.o
+ $(C) -DDINT -c ../Source/umf_apply_order.c -o umf_i_apply_order.o
+ $(C) -DDINT -c ../Source/umf_colamd.c -o umf_i_colamd.o
+ $(C) -DDINT -c ../Source/umf_free.c -o umf_i_free.o
+ $(C) -DDINT -c ../Source/umf_fsize.c -o umf_i_fsize.o
+ $(C) -DDINT -c ../Source/umf_is_permutation.c -o umf_i_is_permutation.o
+ $(C) -DDINT -c ../Source/umf_malloc.c -o umf_i_malloc.o
+ $(C) -DDINT -c ../Source/umf_realloc.c -o umf_i_realloc.o
+ $(C) -DDINT -c ../Source/umf_report_perm.c -o umf_i_report_perm.o
+ $(C) -DDINT -c ../Source/umf_singletons.c -o umf_i_singletons.o
+ $(C) -DDLONG -c ../Source/umf_analyze.c -o umf_l_analyze.o
+ $(C) -DDLONG -c ../Source/umf_apply_order.c -o umf_l_apply_order.o
+ $(C) -DDLONG -c ../Source/umf_colamd.c -o umf_l_colamd.o
+ $(C) -DDLONG -c ../Source/umf_free.c -o umf_l_free.o
+ $(C) -DDLONG -c ../Source/umf_fsize.c -o umf_l_fsize.o
+ $(C) -DDLONG -c ../Source/umf_is_permutation.c -o umf_l_is_permutation.o
+ $(C) -DDLONG -c ../Source/umf_malloc.c -o umf_l_malloc.o
+ $(C) -DDLONG -c ../Source/umf_realloc.c -o umf_l_realloc.o
+ $(C) -DDLONG -c ../Source/umf_report_perm.c -o umf_l_report_perm.o
+ $(C) -DDLONG -c ../Source/umf_singletons.c -o umf_l_singletons.o
+ $(C) -c ../Source/umfpack_timer.c -o umfpack_gn_timer.o
+ $(C) -c ../Source/umfpack_tictoc.c -o umfpack_gn_tictoc.o
+ $(C) -DDINT -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c -o umf_di_lhsolve.o
+ $(C) -DDINT -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c -o umf_di_uhsolve.o
+ $(C) -DDINT -DDO_MAP -c ../Source/umf_triplet.c -o umf_di_triplet_map_nox.o
+ $(C) -DDINT -DDO_VALUES -c ../Source/umf_triplet.c -o umf_di_triplet_nomap_x.o
+ $(C) -DDINT -c ../Source/umf_triplet.c -o umf_di_triplet_nomap_nox.o
+ $(C) -DDINT -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c -o umf_di_triplet_map_x.o
+ $(C) -DDINT -DFIXQ -c ../Source/umf_assemble.c -o umf_di_assemble_fixq.o
+ $(C) -DDINT -DDROP -c ../Source/umf_store_lu.c -o umf_di_store_lu_drop.o
+ $(C) -DDINT -c ../Source/umf_assemble.c -o umf_di_assemble.o
+ $(C) -DDINT -c ../Source/umf_blas3_update.c -o umf_di_blas3_update.o
+ $(C) -DDINT -c ../Source/umf_build_tuples.c -o umf_di_build_tuples.o
+ $(C) -DDINT -c ../Source/umf_create_element.c -o umf_di_create_element.o
+ $(C) -DDINT -c ../Source/umf_dump.c -o umf_di_dump.o
+ $(C) -DDINT -c ../Source/umf_extend_front.c -o umf_di_extend_front.o
+ $(C) -DDINT -c ../Source/umf_garbage_collection.c -o umf_di_garbage_collection.o
+ $(C) -DDINT -c ../Source/umf_get_memory.c -o umf_di_get_memory.o
+ $(C) -DDINT -c ../Source/umf_init_front.c -o umf_di_init_front.o
+ $(C) -DDINT -c ../Source/umf_kernel.c -o umf_di_kernel.o
+ $(C) -DDINT -c ../Source/umf_kernel_init.c -o umf_di_kernel_init.o
+ $(C) -DDINT -c ../Source/umf_kernel_wrapup.c -o umf_di_kernel_wrapup.o
+ $(C) -DDINT -c ../Source/umf_local_search.c -o umf_di_local_search.o
+ $(C) -DDINT -c ../Source/umf_lsolve.c -o umf_di_lsolve.o
+ $(C) -DDINT -c ../Source/umf_ltsolve.c -o umf_di_ltsolve.o
+ $(C) -DDINT -c ../Source/umf_mem_alloc_element.c -o umf_di_mem_alloc_element.o
+ $(C) -DDINT -c ../Source/umf_mem_alloc_head_block.c -o umf_di_mem_alloc_head_block.o
+ $(C) -DDINT -c ../Source/umf_mem_alloc_tail_block.c -o umf_di_mem_alloc_tail_block.o
+ $(C) -DDINT -c ../Source/umf_mem_free_tail_block.c -o umf_di_mem_free_tail_block.o
+ $(C) -DDINT -c ../Source/umf_mem_init_memoryspace.c -o umf_di_mem_init_memoryspace.o
+ $(C) -DDINT -c ../Source/umf_report_vector.c -o umf_di_report_vector.o
+ $(C) -DDINT -c ../Source/umf_row_search.c -o umf_di_row_search.o
+ $(C) -DDINT -c ../Source/umf_scale_column.c -o umf_di_scale_column.o
+ $(C) -DDINT -c ../Source/umf_set_stats.c -o umf_di_set_stats.o
+ $(C) -DDINT -c ../Source/umf_solve.c -o umf_di_solve.o
+ $(C) -DDINT -c ../Source/umf_symbolic_usage.c -o umf_di_symbolic_usage.o
+ $(C) -DDINT -c ../Source/umf_transpose.c -o umf_di_transpose.o
+ $(C) -DDINT -c ../Source/umf_tuple_lengths.c -o umf_di_tuple_lengths.o
+ $(C) -DDINT -c ../Source/umf_usolve.c -o umf_di_usolve.o
+ $(C) -DDINT -c ../Source/umf_utsolve.c -o umf_di_utsolve.o
+ $(C) -DDINT -c ../Source/umf_valid_numeric.c -o umf_di_valid_numeric.o
+ $(C) -DDINT -c ../Source/umf_valid_symbolic.c -o umf_di_valid_symbolic.o
+ $(C) -DDINT -c ../Source/umf_grow_front.c -o umf_di_grow_front.o
+ $(C) -DDINT -c ../Source/umf_start_front.c -o umf_di_start_front.o
+ $(C) -DDINT -c ../Source/umf_2by2.c -o umf_di_2by2.o
+ $(C) -DDINT -c ../Source/umf_store_lu.c -o umf_di_store_lu.o
+ $(C) -DDINT -c ../Source/umf_scale.c -o umf_di_scale.o
+ $(C) -DDINT -DWSOLVE -c ../Source/umfpack_solve.c -o umfpack_di_wsolve.o
+ $(C) -DDINT -c ../Source/umfpack_col_to_triplet.c -o umfpack_di_col_to_triplet.o
+ $(C) -DDINT -c ../Source/umfpack_defaults.c -o umfpack_di_defaults.o
+ $(C) -DDINT -c ../Source/umfpack_free_numeric.c -o umfpack_di_free_numeric.o
+ $(C) -DDINT -c ../Source/umfpack_free_symbolic.c -o umfpack_di_free_symbolic.o
+ $(C) -DDINT -c ../Source/umfpack_get_numeric.c -o umfpack_di_get_numeric.o
+ $(C) -DDINT -c ../Source/umfpack_get_lunz.c -o umfpack_di_get_lunz.o
+ $(C) -DDINT -c ../Source/umfpack_get_symbolic.c -o umfpack_di_get_symbolic.o
+ $(C) -DDINT -c ../Source/umfpack_get_determinant.c -o umfpack_di_get_determinant.o
+ $(C) -DDINT -c ../Source/umfpack_numeric.c -o umfpack_di_numeric.o
+ $(C) -DDINT -c ../Source/umfpack_qsymbolic.c -o umfpack_di_qsymbolic.o
+ $(C) -DDINT -c ../Source/umfpack_report_control.c -o umfpack_di_report_control.o
+ $(C) -DDINT -c ../Source/umfpack_report_info.c -o umfpack_di_report_info.o
+ $(C) -DDINT -c ../Source/umfpack_report_matrix.c -o umfpack_di_report_matrix.o
+ $(C) -DDINT -c ../Source/umfpack_report_numeric.c -o umfpack_di_report_numeric.o
+ $(C) -DDINT -c ../Source/umfpack_report_perm.c -o umfpack_di_report_perm.o
+ $(C) -DDINT -c ../Source/umfpack_report_status.c -o umfpack_di_report_status.o
+ $(C) -DDINT -c ../Source/umfpack_report_symbolic.c -o umfpack_di_report_symbolic.o
+ $(C) -DDINT -c ../Source/umfpack_report_triplet.c -o umfpack_di_report_triplet.o
+ $(C) -DDINT -c ../Source/umfpack_report_vector.c -o umfpack_di_report_vector.o
+ $(C) -DDINT -c ../Source/umfpack_solve.c -o umfpack_di_solve.o
+ $(C) -DDINT -c ../Source/umfpack_symbolic.c -o umfpack_di_symbolic.o
+ $(C) -DDINT -c ../Source/umfpack_transpose.c -o umfpack_di_transpose.o
+ $(C) -DDINT -c ../Source/umfpack_triplet_to_col.c -o umfpack_di_triplet_to_col.o
+ $(C) -DDINT -c ../Source/umfpack_scale.c -o umfpack_di_scale.o
+ $(C) -DDINT -c ../Source/umfpack_load_numeric.c -o umfpack_di_load_numeric.o
+ $(C) -DDINT -c ../Source/umfpack_save_numeric.c -o umfpack_di_save_numeric.o
+ $(C) -DDINT -c ../Source/umfpack_load_symbolic.c -o umfpack_di_load_symbolic.o
+ $(C) -DDINT -c ../Source/umfpack_save_symbolic.c -o umfpack_di_save_symbolic.o
+ $(C) -DDLONG -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c -o umf_dl_lhsolve.o
+ $(C) -DDLONG -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c -o umf_dl_uhsolve.o
+ $(C) -DDLONG -DDO_MAP -c ../Source/umf_triplet.c -o umf_dl_triplet_map_nox.o
+ $(C) -DDLONG -DDO_VALUES -c ../Source/umf_triplet.c -o umf_dl_triplet_nomap_x.o
+ $(C) -DDLONG -c ../Source/umf_triplet.c -o umf_dl_triplet_nomap_nox.o
+ $(C) -DDLONG -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c -o umf_dl_triplet_map_x.o
+ $(C) -DDLONG -DFIXQ -c ../Source/umf_assemble.c -o umf_dl_assemble_fixq.o
+ $(C) -DDLONG -DDROP -c ../Source/umf_store_lu.c -o umf_dl_store_lu_drop.o
+ $(C) -DDLONG -c ../Source/umf_assemble.c -o umf_dl_assemble.o
+ $(C) -DDLONG -c ../Source/umf_blas3_update.c -o umf_dl_blas3_update.o
+ $(C) -DDLONG -c ../Source/umf_build_tuples.c -o umf_dl_build_tuples.o
+ $(C) -DDLONG -c ../Source/umf_create_element.c -o umf_dl_create_element.o
+ $(C) -DDLONG -c ../Source/umf_dump.c -o umf_dl_dump.o
+ $(C) -DDLONG -c ../Source/umf_extend_front.c -o umf_dl_extend_front.o
+ $(C) -DDLONG -c ../Source/umf_garbage_collection.c -o umf_dl_garbage_collection.o
+ $(C) -DDLONG -c ../Source/umf_get_memory.c -o umf_dl_get_memory.o
+ $(C) -DDLONG -c ../Source/umf_init_front.c -o umf_dl_init_front.o
+ $(C) -DDLONG -c ../Source/umf_kernel.c -o umf_dl_kernel.o
+ $(C) -DDLONG -c ../Source/umf_kernel_init.c -o umf_dl_kernel_init.o
+ $(C) -DDLONG -c ../Source/umf_kernel_wrapup.c -o umf_dl_kernel_wrapup.o
+ $(C) -DDLONG -c ../Source/umf_local_search.c -o umf_dl_local_search.o
+ $(C) -DDLONG -c ../Source/umf_lsolve.c -o umf_dl_lsolve.o
+ $(C) -DDLONG -c ../Source/umf_ltsolve.c -o umf_dl_ltsolve.o
+ $(C) -DDLONG -c ../Source/umf_mem_alloc_element.c -o umf_dl_mem_alloc_element.o
+ $(C) -DDLONG -c ../Source/umf_mem_alloc_head_block.c -o umf_dl_mem_alloc_head_block.o
+ $(C) -DDLONG -c ../Source/umf_mem_alloc_tail_block.c -o umf_dl_mem_alloc_tail_block.o
+ $(C) -DDLONG -c ../Source/umf_mem_free_tail_block.c -o umf_dl_mem_free_tail_block.o
+ $(C) -DDLONG -c ../Source/umf_mem_init_memoryspace.c -o umf_dl_mem_init_memoryspace.o
+ $(C) -DDLONG -c ../Source/umf_report_vector.c -o umf_dl_report_vector.o
+ $(C) -DDLONG -c ../Source/umf_row_search.c -o umf_dl_row_search.o
+ $(C) -DDLONG -c ../Source/umf_scale_column.c -o umf_dl_scale_column.o
+ $(C) -DDLONG -c ../Source/umf_set_stats.c -o umf_dl_set_stats.o
+ $(C) -DDLONG -c ../Source/umf_solve.c -o umf_dl_solve.o
+ $(C) -DDLONG -c ../Source/umf_symbolic_usage.c -o umf_dl_symbolic_usage.o
+ $(C) -DDLONG -c ../Source/umf_transpose.c -o umf_dl_transpose.o
+ $(C) -DDLONG -c ../Source/umf_tuple_lengths.c -o umf_dl_tuple_lengths.o
+ $(C) -DDLONG -c ../Source/umf_usolve.c -o umf_dl_usolve.o
+ $(C) -DDLONG -c ../Source/umf_utsolve.c -o umf_dl_utsolve.o
+ $(C) -DDLONG -c ../Source/umf_valid_numeric.c -o umf_dl_valid_numeric.o
+ $(C) -DDLONG -c ../Source/umf_valid_symbolic.c -o umf_dl_valid_symbolic.o
+ $(C) -DDLONG -c ../Source/umf_grow_front.c -o umf_dl_grow_front.o
+ $(C) -DDLONG -c ../Source/umf_start_front.c -o umf_dl_start_front.o
+ $(C) -DDLONG -c ../Source/umf_2by2.c -o umf_dl_2by2.o
+ $(C) -DDLONG -c ../Source/umf_store_lu.c -o umf_dl_store_lu.o
+ $(C) -DDLONG -c ../Source/umf_scale.c -o umf_dl_scale.o
+ $(C) -DDLONG -DWSOLVE -c ../Source/umfpack_solve.c -o umfpack_dl_wsolve.o
+ $(C) -DDLONG -c ../Source/umfpack_col_to_triplet.c -o umfpack_dl_col_to_triplet.o
+ $(C) -DDLONG -c ../Source/umfpack_defaults.c -o umfpack_dl_defaults.o
+ $(C) -DDLONG -c ../Source/umfpack_free_numeric.c -o umfpack_dl_free_numeric.o
+ $(C) -DDLONG -c ../Source/umfpack_free_symbolic.c -o umfpack_dl_free_symbolic.o
+ $(C) -DDLONG -c ../Source/umfpack_get_numeric.c -o umfpack_dl_get_numeric.o
+ $(C) -DDLONG -c ../Source/umfpack_get_lunz.c -o umfpack_dl_get_lunz.o
+ $(C) -DDLONG -c ../Source/umfpack_get_symbolic.c -o umfpack_dl_get_symbolic.o
+ $(C) -DDLONG -c ../Source/umfpack_get_determinant.c -o umfpack_dl_get_determinant.o
+ $(C) -DDLONG -c ../Source/umfpack_numeric.c -o umfpack_dl_numeric.o
+ $(C) -DDLONG -c ../Source/umfpack_qsymbolic.c -o umfpack_dl_qsymbolic.o
+ $(C) -DDLONG -c ../Source/umfpack_report_control.c -o umfpack_dl_report_control.o
+ $(C) -DDLONG -c ../Source/umfpack_report_info.c -o umfpack_dl_report_info.o
+ $(C) -DDLONG -c ../Source/umfpack_report_matrix.c -o umfpack_dl_report_matrix.o
+ $(C) -DDLONG -c ../Source/umfpack_report_numeric.c -o umfpack_dl_report_numeric.o
+ $(C) -DDLONG -c ../Source/umfpack_report_perm.c -o umfpack_dl_report_perm.o
+ $(C) -DDLONG -c ../Source/umfpack_report_status.c -o umfpack_dl_report_status.o
+ $(C) -DDLONG -c ../Source/umfpack_report_symbolic.c -o umfpack_dl_report_symbolic.o
+ $(C) -DDLONG -c ../Source/umfpack_report_triplet.c -o umfpack_dl_report_triplet.o
+ $(C) -DDLONG -c ../Source/umfpack_report_vector.c -o umfpack_dl_report_vector.o
+ $(C) -DDLONG -c ../Source/umfpack_solve.c -o umfpack_dl_solve.o
+ $(C) -DDLONG -c ../Source/umfpack_symbolic.c -o umfpack_dl_symbolic.o
+ $(C) -DDLONG -c ../Source/umfpack_transpose.c -o umfpack_dl_transpose.o
+ $(C) -DDLONG -c ../Source/umfpack_triplet_to_col.c -o umfpack_dl_triplet_to_col.o
+ $(C) -DDLONG -c ../Source/umfpack_scale.c -o umfpack_dl_scale.o
+ $(C) -DDLONG -c ../Source/umfpack_load_numeric.c -o umfpack_dl_load_numeric.o
+ $(C) -DDLONG -c ../Source/umfpack_save_numeric.c -o umfpack_dl_save_numeric.o
+ $(C) -DDLONG -c ../Source/umfpack_load_symbolic.c -o umfpack_dl_load_symbolic.o
+ $(C) -DDLONG -c ../Source/umfpack_save_symbolic.c -o umfpack_dl_save_symbolic.o
+ $(C) -DZINT -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c -o umf_zi_lhsolve.o
+ $(C) -DZINT -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c -o umf_zi_uhsolve.o
+ $(C) -DZINT -DDO_MAP -c ../Source/umf_triplet.c -o umf_zi_triplet_map_nox.o
+ $(C) -DZINT -DDO_VALUES -c ../Source/umf_triplet.c -o umf_zi_triplet_nomap_x.o
+ $(C) -DZINT -c ../Source/umf_triplet.c -o umf_zi_triplet_nomap_nox.o
+ $(C) -DZINT -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c -o umf_zi_triplet_map_x.o
+ $(C) -DZINT -DFIXQ -c ../Source/umf_assemble.c -o umf_zi_assemble_fixq.o
+ $(C) -DZINT -DDROP -c ../Source/umf_store_lu.c -o umf_zi_store_lu_drop.o
+ $(C) -DZINT -c ../Source/umf_assemble.c -o umf_zi_assemble.o
+ $(C) -DZINT -c ../Source/umf_blas3_update.c -o umf_zi_blas3_update.o
+ $(C) -DZINT -c ../Source/umf_build_tuples.c -o umf_zi_build_tuples.o
+ $(C) -DZINT -c ../Source/umf_create_element.c -o umf_zi_create_element.o
+ $(C) -DZINT -c ../Source/umf_dump.c -o umf_zi_dump.o
+ $(C) -DZINT -c ../Source/umf_extend_front.c -o umf_zi_extend_front.o
+ $(C) -DZINT -c ../Source/umf_garbage_collection.c -o umf_zi_garbage_collection.o
+ $(C) -DZINT -c ../Source/umf_get_memory.c -o umf_zi_get_memory.o
+ $(C) -DZINT -c ../Source/umf_init_front.c -o umf_zi_init_front.o
+ $(C) -DZINT -c ../Source/umf_kernel.c -o umf_zi_kernel.o
+ $(C) -DZINT -c ../Source/umf_kernel_init.c -o umf_zi_kernel_init.o
+ $(C) -DZINT -c ../Source/umf_kernel_wrapup.c -o umf_zi_kernel_wrapup.o
+ $(C) -DZINT -c ../Source/umf_local_search.c -o umf_zi_local_search.o
+ $(C) -DZINT -c ../Source/umf_lsolve.c -o umf_zi_lsolve.o
+ $(C) -DZINT -c ../Source/umf_ltsolve.c -o umf_zi_ltsolve.o
+ $(C) -DZINT -c ../Source/umf_mem_alloc_element.c -o umf_zi_mem_alloc_element.o
+ $(C) -DZINT -c ../Source/umf_mem_alloc_head_block.c -o umf_zi_mem_alloc_head_block.o
+ $(C) -DZINT -c ../Source/umf_mem_alloc_tail_block.c -o umf_zi_mem_alloc_tail_block.o
+ $(C) -DZINT -c ../Source/umf_mem_free_tail_block.c -o umf_zi_mem_free_tail_block.o
+ $(C) -DZINT -c ../Source/umf_mem_init_memoryspace.c -o umf_zi_mem_init_memoryspace.o
+ $(C) -DZINT -c ../Source/umf_report_vector.c -o umf_zi_report_vector.o
+ $(C) -DZINT -c ../Source/umf_row_search.c -o umf_zi_row_search.o
+ $(C) -DZINT -c ../Source/umf_scale_column.c -o umf_zi_scale_column.o
+ $(C) -DZINT -c ../Source/umf_set_stats.c -o umf_zi_set_stats.o
+ $(C) -DZINT -c ../Source/umf_solve.c -o umf_zi_solve.o
+ $(C) -DZINT -c ../Source/umf_symbolic_usage.c -o umf_zi_symbolic_usage.o
+ $(C) -DZINT -c ../Source/umf_transpose.c -o umf_zi_transpose.o
+ $(C) -DZINT -c ../Source/umf_tuple_lengths.c -o umf_zi_tuple_lengths.o
+ $(C) -DZINT -c ../Source/umf_usolve.c -o umf_zi_usolve.o
+ $(C) -DZINT -c ../Source/umf_utsolve.c -o umf_zi_utsolve.o
+ $(C) -DZINT -c ../Source/umf_valid_numeric.c -o umf_zi_valid_numeric.o
+ $(C) -DZINT -c ../Source/umf_valid_symbolic.c -o umf_zi_valid_symbolic.o
+ $(C) -DZINT -c ../Source/umf_grow_front.c -o umf_zi_grow_front.o
+ $(C) -DZINT -c ../Source/umf_start_front.c -o umf_zi_start_front.o
+ $(C) -DZINT -c ../Source/umf_2by2.c -o umf_zi_2by2.o
+ $(C) -DZINT -c ../Source/umf_store_lu.c -o umf_zi_store_lu.o
+ $(C) -DZINT -c ../Source/umf_scale.c -o umf_zi_scale.o
+ $(C) -DZINT -DWSOLVE -c ../Source/umfpack_solve.c -o umfpack_zi_wsolve.o
+ $(C) -DZINT -c ../Source/umfpack_col_to_triplet.c -o umfpack_zi_col_to_triplet.o
+ $(C) -DZINT -c ../Source/umfpack_defaults.c -o umfpack_zi_defaults.o
+ $(C) -DZINT -c ../Source/umfpack_free_numeric.c -o umfpack_zi_free_numeric.o
+ $(C) -DZINT -c ../Source/umfpack_free_symbolic.c -o umfpack_zi_free_symbolic.o
+ $(C) -DZINT -c ../Source/umfpack_get_numeric.c -o umfpack_zi_get_numeric.o
+ $(C) -DZINT -c ../Source/umfpack_get_lunz.c -o umfpack_zi_get_lunz.o
+ $(C) -DZINT -c ../Source/umfpack_get_symbolic.c -o umfpack_zi_get_symbolic.o
+ $(C) -DZINT -c ../Source/umfpack_get_determinant.c -o umfpack_zi_get_determinant.o
+ $(C) -DZINT -c ../Source/umfpack_numeric.c -o umfpack_zi_numeric.o
+ $(C) -DZINT -c ../Source/umfpack_qsymbolic.c -o umfpack_zi_qsymbolic.o
+ $(C) -DZINT -c ../Source/umfpack_report_control.c -o umfpack_zi_report_control.o
+ $(C) -DZINT -c ../Source/umfpack_report_info.c -o umfpack_zi_report_info.o
+ $(C) -DZINT -c ../Source/umfpack_report_matrix.c -o umfpack_zi_report_matrix.o
+ $(C) -DZINT -c ../Source/umfpack_report_numeric.c -o umfpack_zi_report_numeric.o
+ $(C) -DZINT -c ../Source/umfpack_report_perm.c -o umfpack_zi_report_perm.o
+ $(C) -DZINT -c ../Source/umfpack_report_status.c -o umfpack_zi_report_status.o
+ $(C) -DZINT -c ../Source/umfpack_report_symbolic.c -o umfpack_zi_report_symbolic.o
+ $(C) -DZINT -c ../Source/umfpack_report_triplet.c -o umfpack_zi_report_triplet.o
+ $(C) -DZINT -c ../Source/umfpack_report_vector.c -o umfpack_zi_report_vector.o
+ $(C) -DZINT -c ../Source/umfpack_solve.c -o umfpack_zi_solve.o
+ $(C) -DZINT -c ../Source/umfpack_symbolic.c -o umfpack_zi_symbolic.o
+ $(C) -DZINT -c ../Source/umfpack_transpose.c -o umfpack_zi_transpose.o
+ $(C) -DZINT -c ../Source/umfpack_triplet_to_col.c -o umfpack_zi_triplet_to_col.o
+ $(C) -DZINT -c ../Source/umfpack_scale.c -o umfpack_zi_scale.o
+ $(C) -DZINT -c ../Source/umfpack_load_numeric.c -o umfpack_zi_load_numeric.o
+ $(C) -DZINT -c ../Source/umfpack_save_numeric.c -o umfpack_zi_save_numeric.o
+ $(C) -DZINT -c ../Source/umfpack_load_symbolic.c -o umfpack_zi_load_symbolic.o
+ $(C) -DZINT -c ../Source/umfpack_save_symbolic.c -o umfpack_zi_save_symbolic.o
+ $(C) -DZLONG -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c -o umf_zl_lhsolve.o
+ $(C) -DZLONG -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c -o umf_zl_uhsolve.o
+ $(C) -DZLONG -DDO_MAP -c ../Source/umf_triplet.c -o umf_zl_triplet_map_nox.o
+ $(C) -DZLONG -DDO_VALUES -c ../Source/umf_triplet.c -o umf_zl_triplet_nomap_x.o
+ $(C) -DZLONG -c ../Source/umf_triplet.c -o umf_zl_triplet_nomap_nox.o
+ $(C) -DZLONG -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c -o umf_zl_triplet_map_x.o
+ $(C) -DZLONG -DFIXQ -c ../Source/umf_assemble.c -o umf_zl_assemble_fixq.o
+ $(C) -DZLONG -DDROP -c ../Source/umf_store_lu.c -o umf_zl_store_lu_drop.o
+ $(C) -DZLONG -c ../Source/umf_assemble.c -o umf_zl_assemble.o
+ $(C) -DZLONG -c ../Source/umf_blas3_update.c -o umf_zl_blas3_update.o
+ $(C) -DZLONG -c ../Source/umf_build_tuples.c -o umf_zl_build_tuples.o
+ $(C) -DZLONG -c ../Source/umf_create_element.c -o umf_zl_create_element.o
+ $(C) -DZLONG -c ../Source/umf_dump.c -o umf_zl_dump.o
+ $(C) -DZLONG -c ../Source/umf_extend_front.c -o umf_zl_extend_front.o
+ $(C) -DZLONG -c ../Source/umf_garbage_collection.c -o umf_zl_garbage_collection.o
+ $(C) -DZLONG -c ../Source/umf_get_memory.c -o umf_zl_get_memory.o
+ $(C) -DZLONG -c ../Source/umf_init_front.c -o umf_zl_init_front.o
+ $(C) -DZLONG -c ../Source/umf_kernel.c -o umf_zl_kernel.o
+ $(C) -DZLONG -c ../Source/umf_kernel_init.c -o umf_zl_kernel_init.o
+ $(C) -DZLONG -c ../Source/umf_kernel_wrapup.c -o umf_zl_kernel_wrapup.o
+ $(C) -DZLONG -c ../Source/umf_local_search.c -o umf_zl_local_search.o
+ $(C) -DZLONG -c ../Source/umf_lsolve.c -o umf_zl_lsolve.o
+ $(C) -DZLONG -c ../Source/umf_ltsolve.c -o umf_zl_ltsolve.o
+ $(C) -DZLONG -c ../Source/umf_mem_alloc_element.c -o umf_zl_mem_alloc_element.o
+ $(C) -DZLONG -c ../Source/umf_mem_alloc_head_block.c -o umf_zl_mem_alloc_head_block.o
+ $(C) -DZLONG -c ../Source/umf_mem_alloc_tail_block.c -o umf_zl_mem_alloc_tail_block.o
+ $(C) -DZLONG -c ../Source/umf_mem_free_tail_block.c -o umf_zl_mem_free_tail_block.o
+ $(C) -DZLONG -c ../Source/umf_mem_init_memoryspace.c -o umf_zl_mem_init_memoryspace.o
+ $(C) -DZLONG -c ../Source/umf_report_vector.c -o umf_zl_report_vector.o
+ $(C) -DZLONG -c ../Source/umf_row_search.c -o umf_zl_row_search.o
+ $(C) -DZLONG -c ../Source/umf_scale_column.c -o umf_zl_scale_column.o
+ $(C) -DZLONG -c ../Source/umf_set_stats.c -o umf_zl_set_stats.o
+ $(C) -DZLONG -c ../Source/umf_solve.c -o umf_zl_solve.o
+ $(C) -DZLONG -c ../Source/umf_symbolic_usage.c -o umf_zl_symbolic_usage.o
+ $(C) -DZLONG -c ../Source/umf_transpose.c -o umf_zl_transpose.o
+ $(C) -DZLONG -c ../Source/umf_tuple_lengths.c -o umf_zl_tuple_lengths.o
+ $(C) -DZLONG -c ../Source/umf_usolve.c -o umf_zl_usolve.o
+ $(C) -DZLONG -c ../Source/umf_utsolve.c -o umf_zl_utsolve.o
+ $(C) -DZLONG -c ../Source/umf_valid_numeric.c -o umf_zl_valid_numeric.o
+ $(C) -DZLONG -c ../Source/umf_valid_symbolic.c -o umf_zl_valid_symbolic.o
+ $(C) -DZLONG -c ../Source/umf_grow_front.c -o umf_zl_grow_front.o
+ $(C) -DZLONG -c ../Source/umf_start_front.c -o umf_zl_start_front.o
+ $(C) -DZLONG -c ../Source/umf_2by2.c -o umf_zl_2by2.o
+ $(C) -DZLONG -c ../Source/umf_store_lu.c -o umf_zl_store_lu.o
+ $(C) -DZLONG -c ../Source/umf_scale.c -o umf_zl_scale.o
+ $(C) -DZLONG -DWSOLVE -c ../Source/umfpack_solve.c -o umfpack_zl_wsolve.o
+ $(C) -DZLONG -c ../Source/umfpack_col_to_triplet.c -o umfpack_zl_col_to_triplet.o
+ $(C) -DZLONG -c ../Source/umfpack_defaults.c -o umfpack_zl_defaults.o
+ $(C) -DZLONG -c ../Source/umfpack_free_numeric.c -o umfpack_zl_free_numeric.o
+ $(C) -DZLONG -c ../Source/umfpack_free_symbolic.c -o umfpack_zl_free_symbolic.o
+ $(C) -DZLONG -c ../Source/umfpack_get_numeric.c -o umfpack_zl_get_numeric.o
+ $(C) -DZLONG -c ../Source/umfpack_get_lunz.c -o umfpack_zl_get_lunz.o
+ $(C) -DZLONG -c ../Source/umfpack_get_symbolic.c -o umfpack_zl_get_symbolic.o
+ $(C) -DZLONG -c ../Source/umfpack_get_determinant.c -o umfpack_zl_get_determinant.o
+ $(C) -DZLONG -c ../Source/umfpack_numeric.c -o umfpack_zl_numeric.o
+ $(C) -DZLONG -c ../Source/umfpack_qsymbolic.c -o umfpack_zl_qsymbolic.o
+ $(C) -DZLONG -c ../Source/umfpack_report_control.c -o umfpack_zl_report_control.o
+ $(C) -DZLONG -c ../Source/umfpack_report_info.c -o umfpack_zl_report_info.o
+ $(C) -DZLONG -c ../Source/umfpack_report_matrix.c -o umfpack_zl_report_matrix.o
+ $(C) -DZLONG -c ../Source/umfpack_report_numeric.c -o umfpack_zl_report_numeric.o
+ $(C) -DZLONG -c ../Source/umfpack_report_perm.c -o umfpack_zl_report_perm.o
+ $(C) -DZLONG -c ../Source/umfpack_report_status.c -o umfpack_zl_report_status.o
+ $(C) -DZLONG -c ../Source/umfpack_report_symbolic.c -o umfpack_zl_report_symbolic.o
+ $(C) -DZLONG -c ../Source/umfpack_report_triplet.c -o umfpack_zl_report_triplet.o
+ $(C) -DZLONG -c ../Source/umfpack_report_vector.c -o umfpack_zl_report_vector.o
+ $(C) -DZLONG -c ../Source/umfpack_solve.c -o umfpack_zl_solve.o
+ $(C) -DZLONG -c ../Source/umfpack_symbolic.c -o umfpack_zl_symbolic.o
+ $(C) -DZLONG -c ../Source/umfpack_transpose.c -o umfpack_zl_transpose.o
+ $(C) -DZLONG -c ../Source/umfpack_triplet_to_col.c -o umfpack_zl_triplet_to_col.o
+ $(C) -DZLONG -c ../Source/umfpack_scale.c -o umfpack_zl_scale.o
+ $(C) -DZLONG -c ../Source/umfpack_load_numeric.c -o umfpack_zl_load_numeric.o
+ $(C) -DZLONG -c ../Source/umfpack_save_numeric.c -o umfpack_zl_save_numeric.o
+ $(C) -DZLONG -c ../Source/umfpack_load_symbolic.c -o umfpack_zl_load_symbolic.o
+ $(C) -DZLONG -c ../Source/umfpack_save_symbolic.c -o umfpack_zl_save_symbolic.o
+ $(AR) ../Lib/libumfpack.a \
+ umfpack_gn_global.o \
+ umf_i_analyze.o umf_i_apply_order.o umf_i_colamd.o umf_i_free.o \
+ umf_i_fsize.o umf_i_is_permutation.o umf_i_malloc.o umf_i_realloc.o \
+ umf_i_report_perm.o umf_i_singletons.o \
+ umf_l_analyze.o umf_l_apply_order.o umf_l_colamd.o umf_l_free.o \
+ umf_l_fsize.o umf_l_is_permutation.o umf_l_malloc.o umf_l_realloc.o \
+ umf_l_report_perm.o umf_l_singletons.o \
+ umfpack_gn_timer.o umfpack_gn_tictoc.o \
+ umf_di_lhsolve.o \
+ umf_di_uhsolve.o umf_di_triplet_map_nox.o umf_di_triplet_nomap_x.o \
+ umf_di_triplet_nomap_nox.o umf_di_triplet_map_x.o \
+ umf_di_assemble_fixq.o umf_di_store_lu_drop.o umf_di_assemble.o \
+ umf_di_blas3_update.o umf_di_build_tuples.o \
+ umf_di_create_element.o umf_di_dump.o umf_di_extend_front.o \
+ umf_di_garbage_collection.o umf_di_get_memory.o \
+ umf_di_init_front.o umf_di_kernel.o umf_di_kernel_init.o \
+ umf_di_kernel_wrapup.o umf_di_local_search.o umf_di_lsolve.o \
+ umf_di_ltsolve.o umf_di_mem_alloc_element.o \
+ umf_di_mem_alloc_head_block.o umf_di_mem_alloc_tail_block.o \
+ umf_di_mem_free_tail_block.o umf_di_mem_init_memoryspace.o \
+ umf_di_report_vector.o umf_di_row_search.o umf_di_scale_column.o \
+ umf_di_set_stats.o umf_di_solve.o umf_di_symbolic_usage.o \
+ umf_di_transpose.o umf_di_tuple_lengths.o umf_di_usolve.o \
+ umf_di_utsolve.o umf_di_valid_numeric.o umf_di_valid_symbolic.o \
+ umf_di_grow_front.o umf_di_start_front.o umf_di_2by2.o \
+ umf_di_store_lu.o umf_di_scale.o umfpack_di_wsolve.o \
+ umfpack_di_col_to_triplet.o umfpack_di_defaults.o \
+ umfpack_di_free_numeric.o umfpack_di_free_symbolic.o \
+ umfpack_di_get_numeric.o umfpack_di_get_lunz.o \
+ umfpack_di_get_symbolic.o umfpack_di_get_determinant.o \
+ umfpack_di_numeric.o \
+ umfpack_di_qsymbolic.o umfpack_di_report_control.o \
+ umfpack_di_report_info.o umfpack_di_report_matrix.o \
+ umfpack_di_report_numeric.o umfpack_di_report_perm.o \
+ umfpack_di_report_status.o umfpack_di_report_symbolic.o \
+ umfpack_di_report_triplet.o umfpack_di_report_vector.o \
+ umfpack_di_solve.o umfpack_di_symbolic.o umfpack_di_transpose.o \
+ umfpack_di_triplet_to_col.o umfpack_di_scale.o \
+ umfpack_di_load_numeric.o umfpack_di_save_numeric.o \
+ umfpack_di_load_symbolic.o umfpack_di_save_symbolic.o \
+ umf_dl_lhsolve.o \
+ umf_dl_uhsolve.o umf_dl_triplet_map_nox.o umf_dl_triplet_nomap_x.o \
+ umf_dl_triplet_nomap_nox.o umf_dl_triplet_map_x.o \
+ umf_dl_assemble_fixq.o umf_dl_store_lu_drop.o umf_dl_assemble.o \
+ umf_dl_blas3_update.o umf_dl_build_tuples.o \
+ umf_dl_create_element.o umf_dl_dump.o umf_dl_extend_front.o \
+ umf_dl_garbage_collection.o umf_dl_get_memory.o \
+ umf_dl_init_front.o umf_dl_kernel.o umf_dl_kernel_init.o \
+ umf_dl_kernel_wrapup.o umf_dl_local_search.o umf_dl_lsolve.o \
+ umf_dl_ltsolve.o umf_dl_mem_alloc_element.o \
+ umf_dl_mem_alloc_head_block.o umf_dl_mem_alloc_tail_block.o \
+ umf_dl_mem_free_tail_block.o umf_dl_mem_init_memoryspace.o \
+ umf_dl_report_vector.o umf_dl_row_search.o umf_dl_scale_column.o \
+ umf_dl_set_stats.o umf_dl_solve.o umf_dl_symbolic_usage.o \
+ umf_dl_transpose.o umf_dl_tuple_lengths.o umf_dl_usolve.o \
+ umf_dl_utsolve.o umf_dl_valid_numeric.o umf_dl_valid_symbolic.o \
+ umf_dl_grow_front.o umf_dl_start_front.o umf_dl_2by2.o \
+ umf_dl_store_lu.o umf_dl_scale.o umfpack_dl_wsolve.o \
+ umfpack_dl_col_to_triplet.o umfpack_dl_defaults.o \
+ umfpack_dl_free_numeric.o umfpack_dl_free_symbolic.o \
+ umfpack_dl_get_numeric.o umfpack_dl_get_lunz.o \
+ umfpack_dl_get_symbolic.o umfpack_dl_get_determinant.o \
+ umfpack_dl_numeric.o \
+ umfpack_dl_qsymbolic.o umfpack_dl_report_control.o \
+ umfpack_dl_report_info.o umfpack_dl_report_matrix.o \
+ umfpack_dl_report_numeric.o umfpack_dl_report_perm.o \
+ umfpack_dl_report_status.o umfpack_dl_report_symbolic.o \
+ umfpack_dl_report_triplet.o umfpack_dl_report_vector.o \
+ umfpack_dl_solve.o umfpack_dl_symbolic.o umfpack_dl_transpose.o \
+ umfpack_dl_triplet_to_col.o umfpack_dl_scale.o \
+ umfpack_dl_load_numeric.o umfpack_dl_save_numeric.o \
+ umfpack_dl_load_symbolic.o umfpack_dl_save_symbolic.o \
+ umf_zi_lhsolve.o \
+ umf_zi_uhsolve.o umf_zi_triplet_map_nox.o umf_zi_triplet_nomap_x.o \
+ umf_zi_triplet_nomap_nox.o umf_zi_triplet_map_x.o \
+ umf_zi_assemble_fixq.o umf_zi_store_lu_drop.o umf_zi_assemble.o \
+ umf_zi_blas3_update.o umf_zi_build_tuples.o \
+ umf_zi_create_element.o umf_zi_dump.o umf_zi_extend_front.o \
+ umf_zi_garbage_collection.o umf_zi_get_memory.o \
+ umf_zi_init_front.o umf_zi_kernel.o umf_zi_kernel_init.o \
+ umf_zi_kernel_wrapup.o umf_zi_local_search.o umf_zi_lsolve.o \
+ umf_zi_ltsolve.o umf_zi_mem_alloc_element.o \
+ umf_zi_mem_alloc_head_block.o umf_zi_mem_alloc_tail_block.o \
+ umf_zi_mem_free_tail_block.o umf_zi_mem_init_memoryspace.o \
+ umf_zi_report_vector.o umf_zi_row_search.o umf_zi_scale_column.o \
+ umf_zi_set_stats.o umf_zi_solve.o umf_zi_symbolic_usage.o \
+ umf_zi_transpose.o umf_zi_tuple_lengths.o umf_zi_usolve.o \
+ umf_zi_utsolve.o umf_zi_valid_numeric.o umf_zi_valid_symbolic.o \
+ umf_zi_grow_front.o umf_zi_start_front.o umf_zi_2by2.o \
+ umf_zi_store_lu.o umf_zi_scale.o umfpack_zi_wsolve.o \
+ umfpack_zi_col_to_triplet.o umfpack_zi_defaults.o \
+ umfpack_zi_free_numeric.o umfpack_zi_free_symbolic.o \
+ umfpack_zi_get_numeric.o umfpack_zi_get_lunz.o \
+ umfpack_zi_get_symbolic.o umfpack_zi_get_determinant.o \
+ umfpack_zi_numeric.o \
+ umfpack_zi_qsymbolic.o umfpack_zi_report_control.o \
+ umfpack_zi_report_info.o umfpack_zi_report_matrix.o \
+ umfpack_zi_report_numeric.o umfpack_zi_report_perm.o \
+ umfpack_zi_report_status.o umfpack_zi_report_symbolic.o \
+ umfpack_zi_report_triplet.o umfpack_zi_report_vector.o \
+ umfpack_zi_solve.o umfpack_zi_symbolic.o umfpack_zi_transpose.o \
+ umfpack_zi_triplet_to_col.o umfpack_zi_scale.o \
+ umfpack_zi_load_numeric.o umfpack_zi_save_numeric.o \
+ umfpack_zi_load_symbolic.o umfpack_zi_save_symbolic.o \
+ umf_zl_lhsolve.o \
+ umf_zl_uhsolve.o umf_zl_triplet_map_nox.o umf_zl_triplet_nomap_x.o \
+ umf_zl_triplet_nomap_nox.o umf_zl_triplet_map_x.o \
+ umf_zl_assemble_fixq.o umf_zl_store_lu_drop.o umf_zl_assemble.o \
+ umf_zl_blas3_update.o umf_zl_build_tuples.o \
+ umf_zl_create_element.o umf_zl_dump.o umf_zl_extend_front.o \
+ umf_zl_garbage_collection.o umf_zl_get_memory.o \
+ umf_zl_init_front.o umf_zl_kernel.o umf_zl_kernel_init.o \
+ umf_zl_kernel_wrapup.o umf_zl_local_search.o umf_zl_lsolve.o \
+ umf_zl_ltsolve.o umf_zl_mem_alloc_element.o \
+ umf_zl_mem_alloc_head_block.o umf_zl_mem_alloc_tail_block.o \
+ umf_zl_mem_free_tail_block.o umf_zl_mem_init_memoryspace.o \
+ umf_zl_report_vector.o umf_zl_row_search.o umf_zl_scale_column.o \
+ umf_zl_set_stats.o umf_zl_solve.o umf_zl_symbolic_usage.o \
+ umf_zl_transpose.o umf_zl_tuple_lengths.o umf_zl_usolve.o \
+ umf_zl_utsolve.o umf_zl_valid_numeric.o umf_zl_valid_symbolic.o \
+ umf_zl_grow_front.o umf_zl_start_front.o umf_zl_2by2.o \
+ umf_zl_store_lu.o umf_zl_scale.o umfpack_zl_wsolve.o \
+ umfpack_zl_col_to_triplet.o umfpack_zl_defaults.o \
+ umfpack_zl_free_numeric.o umfpack_zl_free_symbolic.o \
+ umfpack_zl_get_numeric.o umfpack_zl_get_lunz.o \
+ umfpack_zl_get_symbolic.o umfpack_zl_get_determinant.o \
+ umfpack_zl_numeric.o \
+ umfpack_zl_qsymbolic.o umfpack_zl_report_control.o \
+ umfpack_zl_report_info.o umfpack_zl_report_matrix.o \
+ umfpack_zl_report_numeric.o umfpack_zl_report_perm.o \
+ umfpack_zl_report_status.o umfpack_zl_report_symbolic.o \
+ umfpack_zl_report_triplet.o umfpack_zl_report_vector.o \
+ umfpack_zl_solve.o umfpack_zl_symbolic.o umfpack_zl_transpose.o \
+ umfpack_zl_triplet_to_col.o umfpack_zl_scale.o \
+ umfpack_zl_load_numeric.o umfpack_zl_save_numeric.o \
+ umfpack_zl_load_symbolic.o umfpack_zl_save_symbolic.o
+ - $(RANLIB) ../Lib/libumfpack.a
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+purge: clean
+ - $(RM) ../Lib/libumfpack.a
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/UMFPACK/Lib/libumfpack.def b/UMFPACK/Lib/libumfpack.def
new file mode 100644
index 0000000..72e6991
--- /dev/null
+++ b/UMFPACK/Lib/libumfpack.def
@@ -0,0 +1,105 @@
+LIBRARY libumfpack.dll
+EXPORTS
+umfpack_di_col_to_triplet
+umfpack_di_defaults
+umfpack_di_free_numeric
+umfpack_di_free_symbolic
+umfpack_di_get_numeric
+umfpack_di_get_lunz
+umfpack_di_get_symbolic
+umfpack_di_get_determinant
+umfpack_di_numeric
+umfpack_di_qsymbolic
+umfpack_di_report_control
+umfpack_di_report_info
+umfpack_di_report_matrix
+umfpack_di_report_numeric
+umfpack_di_report_perm
+umfpack_di_report_status
+umfpack_di_report_symbolic
+umfpack_di_report_triplet
+umfpack_di_report_vector
+umfpack_di_solve
+umfpack_di_wsolve
+umfpack_di_symbolic
+umfpack_di_transpose
+umfpack_di_triplet_to_col
+umfpack_di_scale
+umfpack_dl_col_to_triplet
+umfpack_dl_defaults
+umfpack_dl_free_numeric
+umfpack_dl_free_symbolic
+umfpack_dl_get_numeric
+umfpack_dl_get_lunz
+umfpack_dl_get_symbolic
+umfpack_dl_get_determinant
+umfpack_dl_numeric
+umfpack_dl_qsymbolic
+umfpack_dl_report_control
+umfpack_dl_report_info
+umfpack_dl_report_matrix
+umfpack_dl_report_numeric
+umfpack_dl_report_perm
+umfpack_dl_report_status
+umfpack_dl_report_symbolic
+umfpack_dl_report_triplet
+umfpack_dl_report_vector
+umfpack_dl_solve
+umfpack_dl_wsolve
+umfpack_dl_symbolic
+umfpack_dl_transpose
+umfpack_dl_triplet_to_col
+umfpack_dl_scale
+umfpack_zi_col_to_triplet
+umfpack_zi_defaults
+umfpack_zi_free_numeric
+umfpack_zi_free_symbolic
+umfpack_zi_get_numeric
+umfpack_zi_get_lunz
+umfpack_zi_get_symbolic
+umfpack_zi_get_determinant
+umfpack_zi_numeric
+umfpack_zi_qsymbolic
+umfpack_zi_report_control
+umfpack_zi_report_info
+umfpack_zi_report_matrix
+umfpack_zi_report_numeric
+umfpack_zi_report_perm
+umfpack_zi_report_status
+umfpack_zi_report_symbolic
+umfpack_zi_report_triplet
+umfpack_zi_report_vector
+umfpack_zi_solve
+umfpack_zi_wsolve
+umfpack_zi_symbolic
+umfpack_zi_transpose
+umfpack_zi_triplet_to_col
+umfpack_zi_scale
+umfpack_zl_col_to_triplet
+umfpack_zl_defaults
+umfpack_zl_free_numeric
+umfpack_zl_free_symbolic
+umfpack_zl_get_numeric
+umfpack_zl_get_lunz
+umfpack_zl_get_symbolic
+umfpack_zl_get_determinant
+umfpack_zl_numeric
+umfpack_zl_qsymbolic
+umfpack_zl_report_control
+umfpack_zl_report_info
+umfpack_zl_report_matrix
+umfpack_zl_report_numeric
+umfpack_zl_report_perm
+umfpack_zl_report_status
+umfpack_zl_report_symbolic
+umfpack_zl_report_triplet
+umfpack_zl_report_vector
+umfpack_zl_solve
+umfpack_zl_wsolve
+umfpack_zl_symbolic
+umfpack_zl_transpose
+umfpack_zl_triplet_to_col
+umfpack_zl_scale
+umfpack_timer
+umfpack_tic
+umfpack_toc
diff --git a/UMFPACK/MATLAB/Contents.m b/UMFPACK/MATLAB/Contents.m
new file mode 100644
index 0000000..b936449
--- /dev/null
+++ b/UMFPACK/MATLAB/Contents.m
@@ -0,0 +1,32 @@
+%Contents of the UMFPACK sparse matrix toolbox:
+%
+% umfpack2 - computes x=A\b, x=A/b, or lu (A) for a sparse matrix A
+% umfpack_make - to compile umfpack2 for use in MATLAB
+% umfpack_install - to compile and install umfpack2 and amd2 for use in MATLAB
+% umfpack_details - details on all the options for using umfpack2 in MATLAB
+% umfpack_report - prints optional control settings and statistics
+% umfpack_demo - a lenghty demo
+% umfpack_simple - a simple demo
+% umfpack_btf - factorize A using a block triangular form
+% umfpack_solve - x = A\b or x = b/A
+% lu_normest - estimates norm (L*U-A, 1) without forming L*U-A
+% luflop - given L and U, computes # of flops required to compute them
+% umfpack_test - for testing umfpack2 (requires UFget)
+%
+% Example:
+% x = umfpack2 (A, '\', b) ; % same as x = A\b, if A square and unsymmetric
+%
+% See also these built-in functions:
+% umfpack the built-in version of UMFPACK
+% amd symmetric minimum degree ordering
+% colamd unsymmetric column approx minimum degree ordering
+% symamd symmetric approx minimum degree ordering, based on colamd
+%
+% NOTE: UMFPACK is a built-in function in MATLAB, used in x=A\b. This is the
+% source code for the built-in umfpack, but the MATLAB function has been renamed
+% here to umfpack2, to avoid a filename clash with itself.
+%
+% Copyright 1995-2007 by Timothy A. Davis.
+% All Rights Reserved. Type umfpack_details for License.
+
+help Contents
diff --git a/UMFPACK/MATLAB/GNUmakefile b/UMFPACK/MATLAB/GNUmakefile
new file mode 100644
index 0000000..b6e7ad1
--- /dev/null
+++ b/UMFPACK/MATLAB/GNUmakefile
@@ -0,0 +1,240 @@
+#-------------------------------------------------------------------------------
+# UMFPACK GNUmakefile for the UMFPACK MATLAB mexFunction (GNU "make" only)
+#-------------------------------------------------------------------------------
+
+default: umfpack2 luflop
+
+include ../../UFconfig/UFconfig.mk
+
+I = -I../Include -I../Source -I../../AMD/Include -I../../UFconfig
+
+MX = $(MEX) $(I)
+
+
+#-------------------------------------------------------------------------------
+# source files
+#-------------------------------------------------------------------------------
+
+# non-user-callable umf_*.[ch] files:
+UMFCH = umf_assemble umf_blas3_update \
+ umf_build_tuples umf_create_element \
+ umf_dump umf_extend_front umf_garbage_collection \
+ umf_get_memory umf_init_front umf_kernel \
+ umf_kernel_init umf_kernel_wrapup \
+ umf_local_search umf_lsolve umf_ltsolve \
+ umf_mem_alloc_element umf_mem_alloc_head_block \
+ umf_mem_alloc_tail_block umf_mem_free_tail_block \
+ umf_mem_init_memoryspace \
+ umf_report_vector umf_row_search umf_scale_column \
+ umf_set_stats umf_solve umf_symbolic_usage umf_transpose \
+ umf_tuple_lengths umf_usolve umf_utsolve umf_valid_numeric \
+ umf_valid_symbolic umf_grow_front umf_start_front umf_2by2 \
+ umf_store_lu umf_scale
+
+# non-user-callable umf_*.[ch] files, int/UF_long versions only (no real/complex):
+UMFINT = umf_analyze umf_apply_order umf_colamd umf_free umf_fsize \
+ umf_is_permutation umf_malloc umf_realloc umf_report_perm \
+ umf_singletons
+
+# non-user-callable and user-callable amd_*.[ch] files (int/UF_long versions only):
+AMD = amd_aat amd_1 amd_2 amd_dump amd_postorder amd_post_tree amd_defaults \
+ amd_order amd_control amd_info amd_valid amd_preprocess amd_global
+
+# non-user-callable, created from umf_ltsolve.c, umf_utsolve.c,
+# umf_triplet.c, and umf_assemble.c , with int/UF_long and real/complex versions:
+UMF_CREATED = umf_lhsolve umf_uhsolve umf_triplet_map_nox \
+ umf_triplet_nomap_x umf_triplet_nomap_nox umf_triplet_map_x \
+ umf_assemble_fixq umf_store_lu_drop
+
+# non-user-callable, int/UF_long and real/complex versions:
+UMF = $(UMF_CREATED) $(UMFCH)
+
+# user-callable umfpack_*.[ch] files (int/UF_long and real/complex):
+UMFPACK = umfpack_col_to_triplet umfpack_defaults umfpack_free_numeric \
+ umfpack_free_symbolic umfpack_get_numeric umfpack_get_lunz \
+ umfpack_get_symbolic umfpack_get_determinant umfpack_numeric \
+ umfpack_qsymbolic umfpack_report_control umfpack_report_info \
+ umfpack_report_matrix umfpack_report_numeric umfpack_report_perm \
+ umfpack_report_status umfpack_report_symbolic umfpack_report_triplet \
+ umfpack_report_vector umfpack_solve umfpack_symbolic \
+ umfpack_transpose umfpack_triplet_to_col umfpack_scale \
+ umfpack_load_numeric umfpack_save_numeric \
+ umfpack_load_symbolic umfpack_save_symbolic
+
+# user-callable, created from umfpack_solve.c (umfpack_wsolve.h exists, though):
+# with int/UF_long and real/complex versions:
+UMFPACKW = umfpack_wsolve
+
+USER = $(UMFPACKW) $(UMFPACK)
+
+# user-callable, only one version for int/UF_long, real/complex, *.[ch] files:
+GENERIC = umfpack_timer umfpack_tictoc umfpack_global
+
+#-------------------------------------------------------------------------------
+# include files:
+#-------------------------------------------------------------------------------
+
+AMDH = ../../AMD/Include/amd_internal.h ../../AMD/Include/amd.h \
+ ../../UFconfig/UFconfig.h
+
+INC1 = umf_config.h umf_version.h umf_internal.h umf_triplet.h
+
+INC = ../Include/umfpack.h \
+ $(addprefix ../Source/, $(INC1)) \
+ $(addprefix ../Source/, $(addsuffix .h,$(UMFCH))) \
+ $(addprefix ../Source/, $(addsuffix .h,$(UMFINT))) \
+ $(addprefix ../Include/, $(addsuffix .h,$(USER))) \
+ $(addprefix ../Include/, $(addsuffix .h,$(GENERIC))) \
+ $(AMDH)
+
+#-------------------------------------------------------------------------------
+# Create the umfpack and amd mexFunctions for MATLAB (int versions only)
+#-------------------------------------------------------------------------------
+
+MEXI = $(addsuffix .o, $(subst umf_,umf_m_,$(UMFINT)))
+MEXDI = $(addsuffix .o, $(subst umf_,umf_md_,$(UMF)) $(subst umfpack_,umfpack_md_,$(USER)))
+MEXZI = $(addsuffix .o, $(subst umf_,umf_mz_,$(UMF)) $(subst umfpack_,umfpack_mz_,$(USER)) )
+MEXAMD = $(addsuffix .o, $(subst amd_,amd_m_,$(AMD)))
+MEXGN = $(addsuffix .o, $(subst umfpack_,umfpack_m_,$(GENERIC)))
+
+MEXUMFPACK = $(MEXI) $(MEXDI) $(MEXZI) $(MEXGN)
+
+# Note that mex has no "-o" option, thus the need for $(MV) commands.
+# If it did, then the rules would be much simpler:
+# $(MX) -DDLONG -c $< -o $@
+
+#----------------------------------------
+# integer-only routines (no real/complex):
+#----------------------------------------
+
+amd_m_%.o: ../../AMD/Source/amd_%.c $(AMDH)
+ $(MX) -DDLONG -c $<
+ - $(MV) amd_$*.o $@
+
+umf_m_%.o: ../Source/umf_%.c $(INC)
+ $(MX) -DDLONG -c $<
+ - $(MV) umf_$*.o $@
+
+#----------------------------------------
+# Double precision, int version, for MATLAB
+#----------------------------------------
+
+umf_md_%.o: ../Source/umf_%.c $(INC)
+ $(MX) -DDLONG -c $<
+ - $(MV) umf_$*.o $@
+
+umf_md_%hsolve.o: ../Source/umf_%tsolve.c $(INC)
+ $(MX) -DDLONG -DCONJUGATE_SOLVE -c $<
+ - $(MV) umf_$*tsolve.o $@
+
+umf_md_triplet_map_x.o: ../Source/umf_triplet.c $(INC)
+ $(MX) -DDLONG -DDO_MAP -DDO_VALUES -c $<
+ - $(MV) umf_triplet.o $@
+
+umf_md_triplet_map_nox.o: ../Source/umf_triplet.c $(INC)
+ $(MX) -DDLONG -DDO_MAP -c $<
+ - $(MV) umf_triplet.o $@
+
+umf_md_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC)
+ $(MX) -DDLONG -DDO_VALUES -c $<
+ - $(MV) umf_triplet.o $@
+
+umf_md_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC)
+ $(MX) -DDLONG -c $<
+ - $(MV) umf_triplet.o $@
+
+umf_md_assemble_fixq.o: ../Source/umf_assemble.c $(INC)
+ $(MX) -DDLONG -DFIXQ -c $<
+ - $(MV) umf_assemble.o $@
+
+umf_md_store_lu_drop.o: ../Source/umf_store_lu.c $(INC)
+ $(MX) -DDLONG -DDROP -c $<
+ - $(MV) umf_store_lu.o $@
+
+umfpack_md_wsolve.o: ../Source/umfpack_solve.c $(INC)
+ $(MX) -DDLONG -DWSOLVE -c $<
+ - $(MV) umfpack_solve.o $@
+
+umfpack_md_%.o: ../Source/umfpack_%.c $(INC)
+ $(MX) -DDLONG -c $<
+ - $(MV) umfpack_$*.o $@
+
+#----------------------------------------
+# Complex double precision, int version, for MATLAB
+#----------------------------------------
+
+umf_mz_%.o: ../Source/umf_%.c $(INC)
+ $(MX) -DZLONG -c $<
+ - $(MV) umf_$*.o $@
+
+umf_mz_%hsolve.o: ../Source/umf_%tsolve.c $(INC)
+ $(MX) -DZLONG -DCONJUGATE_SOLVE -c $<
+ - $(MV) umf_$*tsolve.o $@
+
+umf_mz_triplet_map_x.o: ../Source/umf_triplet.c $(INC)
+ $(MX) -DZLONG -DDO_MAP -DDO_VALUES -c $<
+ - $(MV) umf_triplet.o $@
+
+umf_mz_triplet_map_nox.o: ../Source/umf_triplet.c $(INC)
+ $(MX) -DZLONG -DDO_MAP -c $<
+ - $(MV) umf_triplet.o $@
+
+umf_mz_triplet_nomap_x.o: ../Source/umf_triplet.c $(INC)
+ $(MX) -DZLONG -DDO_VALUES -c $<
+ - $(MV) umf_triplet.o $@
+
+umf_mz_triplet_nomap_nox.o: ../Source/umf_triplet.c $(INC)
+ $(MX) -DZLONG -c $<
+ - $(MV) umf_triplet.o $@
+
+umf_mz_assemble_fixq.o: ../Source/umf_assemble.c $(INC)
+ $(MX) -DZLONG -DFIXQ -c $<
+ - $(MV) umf_assemble.o $@
+
+umf_mz_store_lu_drop.o: ../Source/umf_store_lu.c $(INC)
+ $(MX) -DZLONG -DDROP -c $<
+ - $(MV) umf_store_lu.o $@
+
+umfpack_mz_wsolve.o: ../Source/umfpack_solve.c $(INC)
+ $(MX) -DZLONG -DWSOLVE -c $<
+ - $(MV) umfpack_solve.o $@
+
+umfpack_mz_%.o: ../Source/umfpack_%.c $(INC)
+ $(MX) -DZLONG -c $<
+ - $(MV) umfpack_$*.o $@
+
+#----------------------------------------
+# Generic routines for MATLAB
+#----------------------------------------
+
+umfpack_m_timer.o: ../Source/umfpack_timer.c $(INC)
+ $(MX) -c $<
+ - $(MV) umfpack_timer.o $@
+
+umfpack_m_tictoc.o: ../Source/umfpack_tictoc.c $(INC)
+ $(MX) -c $<
+ - $(MV) umfpack_tictoc.o $@
+
+umfpack_m_global.o: ../Source/umfpack_global.c $(INC)
+ $(MX) -c $<
+ - $(MV) umfpack_global.o $@
+
+#----------------------------------------
+# umfpack mexFunction
+#----------------------------------------
+
+umfpack2: umfpackmex.c $(MEXUMFPACK) $(MEXAMD)
+ $(MX) -output umfpack2 umfpackmex.c $(MEXUMFPACK) $(MEXAMD)
+
+luflop: luflopmex.c
+ $(MX) -output luflop luflopmex.c
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+purge: clean
+ - $(RM) *.mex*
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/UMFPACK/MATLAB/Makefile b/UMFPACK/MATLAB/Makefile
new file mode 100644
index 0000000..4eab588
--- /dev/null
+++ b/UMFPACK/MATLAB/Makefile
@@ -0,0 +1,445 @@
+#-------------------------------------------------------------------------------
+# UMFPACK Makefile for the UMFPACK MATLAB mexFunction (old "make" only)
+#-------------------------------------------------------------------------------
+
+# This is a very ugly Makefile, and is only provided for those who do not
+# have GNU make. Note that it is not used if you have GNU make. It ignores
+# dependency checking and just compiles everything.
+
+default: umfpack luflop
+
+include ../../UFconfig/UFconfig.mk
+
+MX = $(MEX) -I../Include -I../Source -I../../AMD/Include -I../../UFconfig
+
+umfpack:
+ $(MX) -c ../Source/umfpack_global.c
+ $(MV) -f umfpack_global.o umfpack_m_global.o
+ $(MX) -DDLONG -c ../Source/umf_analyze.c
+ $(MV) -f umf_analyze.o umf_m_analyze.o
+ $(MX) -DDLONG -c ../Source/umf_apply_order.c
+ $(MV) -f umf_apply_order.o umf_m_apply_order.o
+ $(MX) -DDLONG -c ../Source/umf_colamd.c
+ $(MV) -f umf_colamd.o umf_m_colamd.o
+ $(MX) -DDLONG -c ../Source/umf_free.c
+ $(MV) -f umf_free.o umf_m_free.o
+ $(MX) -DDLONG -c ../Source/umf_fsize.c
+ $(MV) -f umf_fsize.o umf_m_fsize.o
+ $(MX) -DDLONG -c ../Source/umf_is_permutation.c
+ $(MV) -f umf_is_permutation.o umf_m_is_permutation.o
+ $(MX) -DDLONG -c ../Source/umf_malloc.c
+ $(MV) -f umf_malloc.o umf_m_malloc.o
+ $(MX) -DDLONG -c ../Source/umf_realloc.c
+ $(MV) -f umf_realloc.o umf_m_realloc.o
+ $(MX) -DDLONG -c ../Source/umf_report_perm.c
+ $(MV) -f umf_report_perm.o umf_m_report_perm.o
+ $(MX) -DDLONG -c ../Source/umf_singletons.c
+ $(MV) -f umf_singletons.o umf_m_singletons.o
+ $(MX) -DDLONG -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c
+ $(MV) -f umf_ltsolve.o umf_md_lhsolve.o
+ $(MX) -DDLONG -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c
+ $(MV) -f umf_utsolve.o umf_md_uhsolve.o
+ $(MX) -DDLONG -DDO_MAP -c ../Source/umf_triplet.c
+ $(MV) -f umf_triplet.o umf_md_triplet_map_nox.o
+ $(MX) -DDLONG -DDO_VALUES -c ../Source/umf_triplet.c
+ $(MV) -f umf_triplet.o umf_md_triplet_nomap_x.o
+ $(MX) -DDLONG -c ../Source/umf_triplet.c
+ $(MV) -f umf_triplet.o umf_md_triplet_nomap_nox.o
+ $(MX) -DDLONG -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c
+ $(MV) -f umf_triplet.o umf_md_triplet_map_x.o
+ $(MX) -DDLONG -DFIXQ -c ../Source/umf_assemble.c
+ $(MV) -f umf_assemble.o umf_md_assemble_fixq.o
+ $(MX) -DDLONG -DDROP -c ../Source/umf_store_lu.c
+ $(MV) -f umf_store_lu.o umf_md_store_lu_drop.o
+ $(MX) -DDLONG -c ../Source/umf_assemble.c
+ $(MV) -f umf_assemble.o umf_md_assemble.o
+ $(MX) -DDLONG -c ../Source/umf_blas3_update.c
+ $(MV) -f umf_blas3_update.o umf_md_blas3_update.o
+ $(MX) -DDLONG -c ../Source/umf_build_tuples.c
+ $(MV) -f umf_build_tuples.o umf_md_build_tuples.o
+ $(MX) -DDLONG -c ../Source/umf_create_element.c
+ $(MV) -f umf_create_element.o umf_md_create_element.o
+ $(MX) -DDLONG -c ../Source/umf_dump.c
+ $(MV) -f umf_dump.o umf_md_dump.o
+ $(MX) -DDLONG -c ../Source/umf_extend_front.c
+ $(MV) -f umf_extend_front.o umf_md_extend_front.o
+ $(MX) -DDLONG -c ../Source/umf_garbage_collection.c
+ $(MV) -f umf_garbage_collection.o umf_md_garbage_collection.o
+ $(MX) -DDLONG -c ../Source/umf_get_memory.c
+ $(MV) -f umf_get_memory.o umf_md_get_memory.o
+ $(MX) -DDLONG -c ../Source/umf_init_front.c
+ $(MV) -f umf_init_front.o umf_md_init_front.o
+ $(MX) -DDLONG -c ../Source/umf_kernel.c
+ $(MV) -f umf_kernel.o umf_md_kernel.o
+ $(MX) -DDLONG -c ../Source/umf_kernel_init.c
+ $(MV) -f umf_kernel_init.o umf_md_kernel_init.o
+ $(MX) -DDLONG -c ../Source/umf_kernel_wrapup.c
+ $(MV) -f umf_kernel_wrapup.o umf_md_kernel_wrapup.o
+ $(MX) -DDLONG -c ../Source/umf_local_search.c
+ $(MV) -f umf_local_search.o umf_md_local_search.o
+ $(MX) -DDLONG -c ../Source/umf_lsolve.c
+ $(MV) -f umf_lsolve.o umf_md_lsolve.o
+ $(MX) -DDLONG -c ../Source/umf_ltsolve.c
+ $(MV) -f umf_ltsolve.o umf_md_ltsolve.o
+ $(MX) -DDLONG -c ../Source/umf_mem_alloc_element.c
+ $(MV) -f umf_mem_alloc_element.o umf_md_mem_alloc_element.o
+ $(MX) -DDLONG -c ../Source/umf_mem_alloc_head_block.c
+ $(MV) -f umf_mem_alloc_head_block.o umf_md_mem_alloc_head_block.o
+ $(MX) -DDLONG -c ../Source/umf_mem_alloc_tail_block.c
+ $(MV) -f umf_mem_alloc_tail_block.o umf_md_mem_alloc_tail_block.o
+ $(MX) -DDLONG -c ../Source/umf_mem_free_tail_block.c
+ $(MV) -f umf_mem_free_tail_block.o umf_md_mem_free_tail_block.o
+ $(MX) -DDLONG -c ../Source/umf_mem_init_memoryspace.c
+ $(MV) -f umf_mem_init_memoryspace.o umf_md_mem_init_memoryspace.o
+ $(MX) -DDLONG -c ../Source/umf_report_vector.c
+ $(MV) -f umf_report_vector.o umf_md_report_vector.o
+ $(MX) -DDLONG -c ../Source/umf_row_search.c
+ $(MV) -f umf_row_search.o umf_md_row_search.o
+ $(MX) -DDLONG -c ../Source/umf_scale_column.c
+ $(MV) -f umf_scale_column.o umf_md_scale_column.o
+ $(MX) -DDLONG -c ../Source/umf_set_stats.c
+ $(MV) -f umf_set_stats.o umf_md_set_stats.o
+ $(MX) -DDLONG -c ../Source/umf_solve.c
+ $(MV) -f umf_solve.o umf_md_solve.o
+ $(MX) -DDLONG -c ../Source/umf_symbolic_usage.c
+ $(MV) -f umf_symbolic_usage.o umf_md_symbolic_usage.o
+ $(MX) -DDLONG -c ../Source/umf_transpose.c
+ $(MV) -f umf_transpose.o umf_md_transpose.o
+ $(MX) -DDLONG -c ../Source/umf_tuple_lengths.c
+ $(MV) -f umf_tuple_lengths.o umf_md_tuple_lengths.o
+ $(MX) -DDLONG -c ../Source/umf_usolve.c
+ $(MV) -f umf_usolve.o umf_md_usolve.o
+ $(MX) -DDLONG -c ../Source/umf_utsolve.c
+ $(MV) -f umf_utsolve.o umf_md_utsolve.o
+ $(MX) -DDLONG -c ../Source/umf_valid_numeric.c
+ $(MV) -f umf_valid_numeric.o umf_md_valid_numeric.o
+ $(MX) -DDLONG -c ../Source/umf_valid_symbolic.c
+ $(MV) -f umf_valid_symbolic.o umf_md_valid_symbolic.o
+ $(MX) -DDLONG -c ../Source/umf_grow_front.c
+ $(MV) -f umf_grow_front.o umf_md_grow_front.o
+ $(MX) -DDLONG -c ../Source/umf_start_front.c
+ $(MV) -f umf_start_front.o umf_md_start_front.o
+ $(MX) -DDLONG -c ../Source/umf_2by2.c
+ $(MV) -f umf_2by2.o umf_md_2by2.o
+ $(MX) -DDLONG -c ../Source/umf_store_lu.c
+ $(MV) -f umf_store_lu.o umf_md_store_lu.o
+ $(MX) -DDLONG -c ../Source/umf_scale.c
+ $(MV) -f umf_scale.o umf_md_scale.o
+ $(MX) -DDLONG -DWSOLVE -c ../Source/umfpack_solve.c
+ $(MV) -f umfpack_solve.o umfpack_md_wsolve.o
+ $(MX) -DDLONG -c ../Source/umfpack_col_to_triplet.c
+ $(MV) -f umfpack_col_to_triplet.o umfpack_md_col_to_triplet.o
+ $(MX) -DDLONG -c ../Source/umfpack_defaults.c
+ $(MV) -f umfpack_defaults.o umfpack_md_defaults.o
+ $(MX) -DDLONG -c ../Source/umfpack_free_numeric.c
+ $(MV) -f umfpack_free_numeric.o umfpack_md_free_numeric.o
+ $(MX) -DDLONG -c ../Source/umfpack_free_symbolic.c
+ $(MV) -f umfpack_free_symbolic.o umfpack_md_free_symbolic.o
+ $(MX) -DDLONG -c ../Source/umfpack_get_numeric.c
+ $(MV) -f umfpack_get_numeric.o umfpack_md_get_numeric.o
+ $(MX) -DDLONG -c ../Source/umfpack_get_lunz.c
+ $(MV) -f umfpack_get_lunz.o umfpack_md_get_lunz.o
+ $(MX) -DDLONG -c ../Source/umfpack_get_symbolic.c
+ $(MV) -f umfpack_get_symbolic.o umfpack_md_get_symbolic.o
+ $(MX) -DDLONG -c ../Source/umfpack_get_determinant.c
+ $(MV) -f umfpack_get_determinant.o umfpack_md_get_determinant.o
+ $(MX) -DDLONG -c ../Source/umfpack_numeric.c
+ $(MV) -f umfpack_numeric.o umfpack_md_numeric.o
+ $(MX) -DDLONG -c ../Source/umfpack_qsymbolic.c
+ $(MV) -f umfpack_qsymbolic.o umfpack_md_qsymbolic.o
+ $(MX) -DDLONG -c ../Source/umfpack_report_control.c
+ $(MV) -f umfpack_report_control.o umfpack_md_report_control.o
+ $(MX) -DDLONG -c ../Source/umfpack_report_info.c
+ $(MV) -f umfpack_report_info.o umfpack_md_report_info.o
+ $(MX) -DDLONG -c ../Source/umfpack_report_matrix.c
+ $(MV) -f umfpack_report_matrix.o umfpack_md_report_matrix.o
+ $(MX) -DDLONG -c ../Source/umfpack_report_numeric.c
+ $(MV) -f umfpack_report_numeric.o umfpack_md_report_numeric.o
+ $(MX) -DDLONG -c ../Source/umfpack_report_perm.c
+ $(MV) -f umfpack_report_perm.o umfpack_md_report_perm.o
+ $(MX) -DDLONG -c ../Source/umfpack_report_status.c
+ $(MV) -f umfpack_report_status.o umfpack_md_report_status.o
+ $(MX) -DDLONG -c ../Source/umfpack_report_symbolic.c
+ $(MV) -f umfpack_report_symbolic.o umfpack_md_report_symbolic.o
+ $(MX) -DDLONG -c ../Source/umfpack_report_triplet.c
+ $(MV) -f umfpack_report_triplet.o umfpack_md_report_triplet.o
+ $(MX) -DDLONG -c ../Source/umfpack_report_vector.c
+ $(MV) -f umfpack_report_vector.o umfpack_md_report_vector.o
+ $(MX) -DDLONG -c ../Source/umfpack_solve.c
+ $(MV) -f umfpack_solve.o umfpack_md_solve.o
+ $(MX) -DDLONG -c ../Source/umfpack_symbolic.c
+ $(MV) -f umfpack_symbolic.o umfpack_md_symbolic.o
+ $(MX) -DDLONG -c ../Source/umfpack_transpose.c
+ $(MV) -f umfpack_transpose.o umfpack_md_transpose.o
+ $(MX) -DDLONG -c ../Source/umfpack_triplet_to_col.c
+ $(MV) -f umfpack_triplet_to_col.o umfpack_md_triplet_to_col.o
+ $(MX) -DDLONG -c ../Source/umfpack_scale.c
+ $(MV) -f umfpack_scale.o umfpack_md_scale.o
+ $(MX) -DDLONG -c ../Source/umfpack_load_numeric.c
+ $(MV) -f umfpack_load_numeric.o umfpack_md_load_numeric.o
+ $(MX) -DDLONG -c ../Source/umfpack_save_numeric.c
+ $(MV) -f umfpack_save_numeric.o umfpack_md_save_numeric.o
+ $(MX) -DDLONG -c ../Source/umfpack_load_symbolic.c
+ $(MV) -f umfpack_load_symbolic.o umfpack_md_load_symbolic.o
+ $(MX) -DDLONG -c ../Source/umfpack_save_symbolic.c
+ $(MV) -f umfpack_save_symbolic.o umfpack_md_save_symbolic.o
+ $(MX) -DZLONG -DCONJUGATE_SOLVE -c ../Source/umf_ltsolve.c
+ $(MV) -f umf_ltsolve.o umf_mz_lhsolve.o
+ $(MX) -DZLONG -DCONJUGATE_SOLVE -c ../Source/umf_utsolve.c
+ $(MV) -f umf_utsolve.o umf_mz_uhsolve.o
+ $(MX) -DZLONG -DDO_MAP -c ../Source/umf_triplet.c
+ $(MV) -f umf_triplet.o umf_mz_triplet_map_nox.o
+ $(MX) -DZLONG -DDO_VALUES -c ../Source/umf_triplet.c
+ $(MV) -f umf_triplet.o umf_mz_triplet_nomap_x.o
+ $(MX) -DZLONG -c ../Source/umf_triplet.c
+ $(MV) -f umf_triplet.o umf_mz_triplet_nomap_nox.o
+ $(MX) -DZLONG -DDO_MAP -DDO_VALUES -c ../Source/umf_triplet.c
+ $(MV) -f umf_triplet.o umf_mz_triplet_map_x.o
+ $(MX) -DZLONG -DFIXQ -c ../Source/umf_assemble.c
+ $(MV) -f umf_assemble.o umf_mz_assemble_fixq.o
+ $(MX) -DZLONG -DDROP -c ../Source/umf_store_lu.c
+ $(MV) -f umf_store_lu.o umf_mz_store_lu_drop.o
+ $(MX) -DZLONG -c ../Source/umf_assemble.c
+ $(MV) -f umf_assemble.o umf_mz_assemble.o
+ $(MX) -DZLONG -c ../Source/umf_blas3_update.c
+ $(MV) -f umf_blas3_update.o umf_mz_blas3_update.o
+ $(MX) -DZLONG -c ../Source/umf_build_tuples.c
+ $(MV) -f umf_build_tuples.o umf_mz_build_tuples.o
+ $(MX) -DZLONG -c ../Source/umf_create_element.c
+ $(MV) -f umf_create_element.o umf_mz_create_element.o
+ $(MX) -DZLONG -c ../Source/umf_dump.c
+ $(MV) -f umf_dump.o umf_mz_dump.o
+ $(MX) -DZLONG -c ../Source/umf_extend_front.c
+ $(MV) -f umf_extend_front.o umf_mz_extend_front.o
+ $(MX) -DZLONG -c ../Source/umf_garbage_collection.c
+ $(MV) -f umf_garbage_collection.o umf_mz_garbage_collection.o
+ $(MX) -DZLONG -c ../Source/umf_get_memory.c
+ $(MV) -f umf_get_memory.o umf_mz_get_memory.o
+ $(MX) -DZLONG -c ../Source/umf_init_front.c
+ $(MV) -f umf_init_front.o umf_mz_init_front.o
+ $(MX) -DZLONG -c ../Source/umf_kernel.c
+ $(MV) -f umf_kernel.o umf_mz_kernel.o
+ $(MX) -DZLONG -c ../Source/umf_kernel_init.c
+ $(MV) -f umf_kernel_init.o umf_mz_kernel_init.o
+ $(MX) -DZLONG -c ../Source/umf_kernel_wrapup.c
+ $(MV) -f umf_kernel_wrapup.o umf_mz_kernel_wrapup.o
+ $(MX) -DZLONG -c ../Source/umf_local_search.c
+ $(MV) -f umf_local_search.o umf_mz_local_search.o
+ $(MX) -DZLONG -c ../Source/umf_lsolve.c
+ $(MV) -f umf_lsolve.o umf_mz_lsolve.o
+ $(MX) -DZLONG -c ../Source/umf_ltsolve.c
+ $(MV) -f umf_ltsolve.o umf_mz_ltsolve.o
+ $(MX) -DZLONG -c ../Source/umf_mem_alloc_element.c
+ $(MV) -f umf_mem_alloc_element.o umf_mz_mem_alloc_element.o
+ $(MX) -DZLONG -c ../Source/umf_mem_alloc_head_block.c
+ $(MV) -f umf_mem_alloc_head_block.o umf_mz_mem_alloc_head_block.o
+ $(MX) -DZLONG -c ../Source/umf_mem_alloc_tail_block.c
+ $(MV) -f umf_mem_alloc_tail_block.o umf_mz_mem_alloc_tail_block.o
+ $(MX) -DZLONG -c ../Source/umf_mem_free_tail_block.c
+ $(MV) -f umf_mem_free_tail_block.o umf_mz_mem_free_tail_block.o
+ $(MX) -DZLONG -c ../Source/umf_mem_init_memoryspace.c
+ $(MV) -f umf_mem_init_memoryspace.o umf_mz_mem_init_memoryspace.o
+ $(MX) -DZLONG -c ../Source/umf_report_vector.c
+ $(MV) -f umf_report_vector.o umf_mz_report_vector.o
+ $(MX) -DZLONG -c ../Source/umf_row_search.c
+ $(MV) -f umf_row_search.o umf_mz_row_search.o
+ $(MX) -DZLONG -c ../Source/umf_scale_column.c
+ $(MV) -f umf_scale_column.o umf_mz_scale_column.o
+ $(MX) -DZLONG -c ../Source/umf_set_stats.c
+ $(MV) -f umf_set_stats.o umf_mz_set_stats.o
+ $(MX) -DZLONG -c ../Source/umf_solve.c
+ $(MV) -f umf_solve.o umf_mz_solve.o
+ $(MX) -DZLONG -c ../Source/umf_symbolic_usage.c
+ $(MV) -f umf_symbolic_usage.o umf_mz_symbolic_usage.o
+ $(MX) -DZLONG -c ../Source/umf_transpose.c
+ $(MV) -f umf_transpose.o umf_mz_transpose.o
+ $(MX) -DZLONG -c ../Source/umf_tuple_lengths.c
+ $(MV) -f umf_tuple_lengths.o umf_mz_tuple_lengths.o
+ $(MX) -DZLONG -c ../Source/umf_usolve.c
+ $(MV) -f umf_usolve.o umf_mz_usolve.o
+ $(MX) -DZLONG -c ../Source/umf_utsolve.c
+ $(MV) -f umf_utsolve.o umf_mz_utsolve.o
+ $(MX) -DZLONG -c ../Source/umf_valid_numeric.c
+ $(MV) -f umf_valid_numeric.o umf_mz_valid_numeric.o
+ $(MX) -DZLONG -c ../Source/umf_valid_symbolic.c
+ $(MV) -f umf_valid_symbolic.o umf_mz_valid_symbolic.o
+ $(MX) -DZLONG -c ../Source/umf_grow_front.c
+ $(MV) -f umf_grow_front.o umf_mz_grow_front.o
+ $(MX) -DZLONG -c ../Source/umf_start_front.c
+ $(MV) -f umf_start_front.o umf_mz_start_front.o
+ $(MX) -DZLONG -c ../Source/umf_2by2.c
+ $(MV) -f umf_2by2.o umf_mz_2by2.o
+ $(MX) -DZLONG -c ../Source/umf_store_lu.c
+ $(MV) -f umf_store_lu.o umf_mz_store_lu.o
+ $(MX) -DZLONG -c ../Source/umf_scale.c
+ $(MV) -f umf_scale.o umf_mz_scale.o
+ $(MX) -DZLONG -DWSOLVE -c ../Source/umfpack_solve.c
+ $(MV) -f umfpack_solve.o umfpack_mz_wsolve.o
+ $(MX) -DZLONG -c ../Source/umfpack_col_to_triplet.c
+ $(MV) -f umfpack_col_to_triplet.o umfpack_mz_col_to_triplet.o
+ $(MX) -DZLONG -c ../Source/umfpack_defaults.c
+ $(MV) -f umfpack_defaults.o umfpack_mz_defaults.o
+ $(MX) -DZLONG -c ../Source/umfpack_free_numeric.c
+ $(MV) -f umfpack_free_numeric.o umfpack_mz_free_numeric.o
+ $(MX) -DZLONG -c ../Source/umfpack_free_symbolic.c
+ $(MV) -f umfpack_free_symbolic.o umfpack_mz_free_symbolic.o
+ $(MX) -DZLONG -c ../Source/umfpack_get_numeric.c
+ $(MV) -f umfpack_get_numeric.o umfpack_mz_get_numeric.o
+ $(MX) -DZLONG -c ../Source/umfpack_get_lunz.c
+ $(MV) -f umfpack_get_lunz.o umfpack_mz_get_lunz.o
+ $(MX) -DZLONG -c ../Source/umfpack_get_symbolic.c
+ $(MV) -f umfpack_get_symbolic.o umfpack_mz_get_symbolic.o
+ $(MX) -DZLONG -c ../Source/umfpack_get_determinant.c
+ $(MV) -f umfpack_get_determinant.o umfpack_mz_get_determinant.o
+ $(MX) -DZLONG -c ../Source/umfpack_numeric.c
+ $(MV) -f umfpack_numeric.o umfpack_mz_numeric.o
+ $(MX) -DZLONG -c ../Source/umfpack_qsymbolic.c
+ $(MV) -f umfpack_qsymbolic.o umfpack_mz_qsymbolic.o
+ $(MX) -DZLONG -c ../Source/umfpack_report_control.c
+ $(MV) -f umfpack_report_control.o umfpack_mz_report_control.o
+ $(MX) -DZLONG -c ../Source/umfpack_report_info.c
+ $(MV) -f umfpack_report_info.o umfpack_mz_report_info.o
+ $(MX) -DZLONG -c ../Source/umfpack_report_matrix.c
+ $(MV) -f umfpack_report_matrix.o umfpack_mz_report_matrix.o
+ $(MX) -DZLONG -c ../Source/umfpack_report_numeric.c
+ $(MV) -f umfpack_report_numeric.o umfpack_mz_report_numeric.o
+ $(MX) -DZLONG -c ../Source/umfpack_report_perm.c
+ $(MV) -f umfpack_report_perm.o umfpack_mz_report_perm.o
+ $(MX) -DZLONG -c ../Source/umfpack_report_status.c
+ $(MV) -f umfpack_report_status.o umfpack_mz_report_status.o
+ $(MX) -DZLONG -c ../Source/umfpack_report_symbolic.c
+ $(MV) -f umfpack_report_symbolic.o umfpack_mz_report_symbolic.o
+ $(MX) -DZLONG -c ../Source/umfpack_report_triplet.c
+ $(MV) -f umfpack_report_triplet.o umfpack_mz_report_triplet.o
+ $(MX) -DZLONG -c ../Source/umfpack_report_vector.c
+ $(MV) -f umfpack_report_vector.o umfpack_mz_report_vector.o
+ $(MX) -DZLONG -c ../Source/umfpack_solve.c
+ $(MV) -f umfpack_solve.o umfpack_mz_solve.o
+ $(MX) -DZLONG -c ../Source/umfpack_symbolic.c
+ $(MV) -f umfpack_symbolic.o umfpack_mz_symbolic.o
+ $(MX) -DZLONG -c ../Source/umfpack_transpose.c
+ $(MV) -f umfpack_transpose.o umfpack_mz_transpose.o
+ $(MX) -DZLONG -c ../Source/umfpack_triplet_to_col.c
+ $(MV) -f umfpack_triplet_to_col.o umfpack_mz_triplet_to_col.o
+ $(MX) -DZLONG -c ../Source/umfpack_scale.c
+ $(MV) -f umfpack_scale.o umfpack_mz_scale.o
+ $(MX) -DZLONG -c ../Source/umfpack_load_numeric.c
+ $(MV) -f umfpack_load_numeric.o umfpack_mz_load_numeric.o
+ $(MX) -DZLONG -c ../Source/umfpack_save_numeric.c
+ $(MV) -f umfpack_save_numeric.o umfpack_mz_save_numeric.o
+ $(MX) -DZLONG -c ../Source/umfpack_load_symbolic.c
+ $(MV) -f umfpack_load_symbolic.o umfpack_mz_load_symbolic.o
+ $(MX) -DZLONG -c ../Source/umfpack_save_symbolic.c
+ $(MV) -f umfpack_save_symbolic.o umfpack_mz_save_symbolic.o
+ $(MX) -c ../Source/umfpack_timer.c
+ $(MV) -f umfpack_timer.o umfpack_m_timer.o
+ $(MX) -c ../Source/umfpack_tictoc.c
+ $(MV) -f umfpack_tictoc.o umfpack_m_tictoc.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_global.c
+ $(MV) -f amd_global.o amd_m_global.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_aat.c
+ $(MV) -f amd_aat.o amd_m_aat.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_1.c
+ $(MV) -f amd_1.o amd_m_1.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_2.c
+ $(MV) -f amd_2.o amd_m_2.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_dump.c
+ $(MV) -f amd_dump.o amd_m_dump.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_postorder.c
+ $(MV) -f amd_postorder.o amd_m_postorder.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_post_tree.c
+ $(MV) -f amd_post_tree.o amd_m_post_tree.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_defaults.c
+ $(MV) -f amd_defaults.o amd_m_defaults.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_order.c
+ $(MV) -f amd_order.o amd_m_order.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_control.c
+ $(MV) -f amd_control.o amd_m_control.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_info.c
+ $(MV) -f amd_info.o amd_m_info.o
+ $(MX) -DDLONG -c ../../AMD/Source/amd_valid.c
+ $(MV) -f amd_valid.o amd_m_valid.o
+ $(MX) -output umfpack2 umfpackmex.c \
+ umf_m_analyze.o umf_m_apply_order.o umf_m_colamd.o umf_m_free.o \
+ umf_m_fsize.o umf_m_is_permutation.o umf_m_malloc.o \
+ umf_m_realloc.o umf_m_report_perm.o umf_m_singletons.o \
+ umf_md_lhsolve.o umf_md_uhsolve.o umf_md_triplet_map_nox.o \
+ umf_md_triplet_nomap_x.o umf_md_triplet_nomap_nox.o \
+ umf_md_triplet_map_x.o umf_md_assemble_fixq.o \
+ umf_md_store_lu_drop.o umf_md_assemble.o umf_md_blas3_update.o \
+ umf_md_build_tuples.o umf_md_create_element.o umf_md_dump.o \
+ umf_md_extend_front.o umf_md_garbage_collection.o \
+ umf_md_get_memory.o umf_md_init_front.o umf_md_kernel.o \
+ umf_md_kernel_init.o umf_md_kernel_wrapup.o umf_md_local_search.o \
+ umf_md_lsolve.o umf_md_ltsolve.o umf_md_mem_alloc_element.o \
+ umf_md_mem_alloc_head_block.o umf_md_mem_alloc_tail_block.o \
+ umf_md_mem_free_tail_block.o umf_md_mem_init_memoryspace.o \
+ umf_md_report_vector.o umf_md_row_search.o umf_md_scale_column.o \
+ umf_md_set_stats.o umf_md_solve.o umf_md_symbolic_usage.o \
+ umf_md_transpose.o umf_md_tuple_lengths.o umf_md_usolve.o \
+ umf_md_utsolve.o umf_md_valid_numeric.o umf_md_valid_symbolic.o \
+ umf_md_grow_front.o umf_md_start_front.o umf_md_2by2.o \
+ umf_md_store_lu.o umf_md_scale.o umfpack_md_wsolve.o \
+ umfpack_md_col_to_triplet.o umfpack_md_defaults.o \
+ umfpack_md_free_numeric.o umfpack_md_free_symbolic.o \
+ umfpack_md_get_numeric.o umfpack_md_get_lunz.o \
+ umfpack_md_get_symbolic.o umfpack_md_get_determinant.o \
+ umfpack_md_numeric.o \
+ umfpack_md_qsymbolic.o umfpack_md_report_control.o \
+ umfpack_md_report_info.o umfpack_md_report_matrix.o \
+ umfpack_md_report_numeric.o umfpack_md_report_perm.o \
+ umfpack_md_report_status.o umfpack_md_report_symbolic.o \
+ umfpack_md_report_triplet.o umfpack_md_report_vector.o \
+ umfpack_md_solve.o umfpack_md_symbolic.o umfpack_md_transpose.o \
+ umfpack_md_triplet_to_col.o umfpack_md_scale.o \
+ umfpack_md_load_numeric.o umfpack_md_save_numeric.o \
+ umfpack_md_load_symbolic.o umfpack_md_save_symbolic.o \
+ umf_mz_lhsolve.o umf_mz_uhsolve.o umf_mz_triplet_map_nox.o \
+ umf_mz_triplet_nomap_x.o umf_mz_triplet_nomap_nox.o \
+ umf_mz_triplet_map_x.o umf_mz_assemble_fixq.o \
+ umf_mz_store_lu_drop.o umf_mz_assemble.o umf_mz_blas3_update.o \
+ umf_mz_build_tuples.o umf_mz_create_element.o umf_mz_dump.o \
+ umf_mz_extend_front.o umf_mz_garbage_collection.o \
+ umf_mz_get_memory.o umf_mz_init_front.o umf_mz_kernel.o \
+ umf_mz_kernel_init.o umf_mz_kernel_wrapup.o umf_mz_local_search.o \
+ umf_mz_lsolve.o umf_mz_ltsolve.o umf_mz_mem_alloc_element.o \
+ umf_mz_mem_alloc_head_block.o umf_mz_mem_alloc_tail_block.o \
+ umf_mz_mem_free_tail_block.o umf_mz_mem_init_memoryspace.o \
+ umf_mz_report_vector.o umf_mz_row_search.o umf_mz_scale_column.o \
+ umf_mz_set_stats.o umf_mz_solve.o umf_mz_symbolic_usage.o \
+ umf_mz_transpose.o umf_mz_tuple_lengths.o umf_mz_usolve.o \
+ umf_mz_utsolve.o umf_mz_valid_numeric.o umf_mz_valid_symbolic.o \
+ umf_mz_grow_front.o umf_mz_start_front.o umf_mz_2by2.o \
+ umf_mz_store_lu.o umf_mz_scale.o umfpack_mz_wsolve.o \
+ umfpack_mz_col_to_triplet.o umfpack_mz_defaults.o \
+ umfpack_mz_free_numeric.o umfpack_mz_free_symbolic.o \
+ umfpack_mz_get_numeric.o umfpack_mz_get_lunz.o \
+ umfpack_mz_get_symbolic.o umfpack_mz_get_determinant.o \
+ umfpack_mz_numeric.o \
+ umfpack_mz_qsymbolic.o umfpack_mz_report_control.o \
+ umfpack_mz_report_info.o umfpack_mz_report_matrix.o \
+ umfpack_mz_report_numeric.o umfpack_mz_report_perm.o \
+ umfpack_mz_report_status.o umfpack_mz_report_symbolic.o \
+ umfpack_mz_report_triplet.o umfpack_mz_report_vector.o \
+ umfpack_mz_solve.o umfpack_mz_symbolic.o umfpack_mz_transpose.o \
+ umfpack_mz_triplet_to_col.o umfpack_mz_scale.o \
+ umfpack_mz_load_numeric.o umfpack_mz_save_numeric.o \
+ umfpack_mz_load_symbolic.o umfpack_mz_save_symbolic.o \
+ umfpack_m_timer.o umfpack_m_tictoc.o umfpack_m_global.o \
+ amd_m_global.o \
+ amd_m_aat.o amd_m_1.o amd_m_2.o amd_m_dump.o \
+ amd_m_postorder.o amd_m_post_tree.o amd_m_defaults.o amd_m_order.o \
+ amd_m_control.o amd_m_info.o amd_m_valid.o
+
+luflop: luflopmex.c
+ $(MX) -output luflop luflopmex.c
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+purge: clean
+ - $(RM) *.mex*
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/UMFPACK/MATLAB/lcc_lib/lapacksyms.def b/UMFPACK/MATLAB/lcc_lib/lapacksyms.def
new file mode 100644
index 0000000..7f8563c
--- /dev/null
+++ b/UMFPACK/MATLAB/lcc_lib/lapacksyms.def
@@ -0,0 +1,718 @@
+LIBRARY liblapack.dll
+EXPORTS
+dasum
+daxpy
+dbdsdc
+dbdsqr
+dcopy
+ddisna
+ddot
+dgbbrd
+dgbcon
+dgbequ
+dgbmv
+dgbrfs
+dgbsv
+dgbsvx
+dgbtf2
+dgbtrf
+dgbtrs
+dgebak
+dgebal
+dgebd2
+dgebrd
+dgecon
+dgeequ
+dgees
+dgeesx
+dgeev
+dgeevx
+dgegs
+dgegv
+dgehd2
+dgehrd
+dgelq2
+dgelqf
+dgels
+dgelsd
+dgelss
+dgelsx
+dgelsy
+dgemm
+dgemv
+dgeql2
+dgeqlf
+dgeqp3
+dgeqpf
+dgeqr2
+dgeqrf
+dger
+dgerfs
+dgerq2
+dgerqf
+dgesc2
+dgesdd
+dgesv
+dgesvd
+dgesvx
+dgetc2
+dgetf2
+dgetrf
+dgetri
+dgetrs
+dggbak
+dggbal
+dgges
+dggesx
+dggev
+dggevx
+dggglm
+dgghrd
+dgglse
+dggqrf
+dggrqf
+dggsvd
+dggsvp
+dgtcon
+dgtrfs
+dgtsv
+dgtsvx
+dgttrf
+dgttrs
+dgtts2
+dhgeqz
+dhsein
+dhseqr
+dlabad
+dlabrd
+dlacon
+dlacpy
+dladiv
+dlae2
+dlaebz
+dlaed0
+dlaed1
+dlaed2
+dlaed3
+dlaed4
+dlaed5
+dlaed6
+dlaed7
+dlaed8
+dlaed9
+dlaeda
+dlaein
+dlaev2
+dlaexc
+dlag2
+dlags2
+dlagtf
+dlagtm
+dlagts
+dlagv2
+dlahqr
+dlahrd
+dlaic1
+dlaln2
+dlals0
+dlalsa
+dlalsd
+dlamch
+dlamrg
+dlangb
+dlange
+dlangt
+dlanhs
+dlansb
+dlansp
+dlanst
+dlansy
+dlantb
+dlantp
+dlantr
+dlanv2
+dlapll
+dlapmt
+dlapy2
+dlapy3
+dlaqgb
+dlaqge
+dlaqp2
+dlaqps
+dlaqsb
+dlaqsp
+dlaqsy
+dlaqtr
+dlar1v
+dlar2v
+dlarf
+dlarfb
+dlarfg
+dlarft
+dlarfx
+dlargv
+dlarnv
+dlarrb
+dlarre
+dlarrf
+dlarrv
+dlartg
+dlartv
+dlaruv
+dlarz
+dlarzb
+dlarzt
+dlas2
+dlascl
+dlasd0
+dlasd1
+dlasd2
+dlasd3
+dlasd4
+dlasd5
+dlasd6
+dlasd7
+dlasd8
+dlasd9
+dlasda
+dlasdq
+dlasdt
+dlaset
+dlasq1
+dlasq2
+dlasq3
+dlasq4
+dlasq5
+dlasq6
+dlasr
+dlasrt
+dlassq
+dlasv2
+dlaswp
+dlasy2
+dlasyf
+dlatbs
+dlatdf
+dlatps
+dlatrd
+dlatrs
+dlatrz
+dlatzm
+dlauu2
+dlauum
+dnrm2
+dopgtr
+dopmtr
+dorg2l
+dorg2r
+dorgbr
+dorghr
+dorgl2
+dorglq
+dorgql
+dorgqr
+dorgr2
+dorgrq
+dorgtr
+dorm2l
+dorm2r
+dormbr
+dormhr
+dorml2
+dormlq
+dormql
+dormqr
+dormr2
+dormr3
+dormrq
+dormrz
+dormtr
+dpbcon
+dpbequ
+dpbrfs
+dpbstf
+dpbsv
+dpbsvx
+dpbtf2
+dpbtrf
+dpbtrs
+dpocon
+dpoequ
+dporfs
+dposv
+dposvx
+dpotf2
+dpotrf
+dpotri
+dpotrs
+dppcon
+dppequ
+dpprfs
+dppsv
+dppsvx
+dpptrf
+dpptri
+dpptrs
+dptcon
+dpteqr
+dptrfs
+dptsv
+dptsvx
+dpttrf
+dpttrs
+dptts2
+drot
+drotg
+drscl
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diff --git a/UMFPACK/MATLAB/lcc_lib/libmwlapack.lib b/UMFPACK/MATLAB/lcc_lib/libmwlapack.lib
new file mode 100644
index 0000000..ba94c1b
Binary files /dev/null and b/UMFPACK/MATLAB/lcc_lib/libmwlapack.lib differ
diff --git a/UMFPACK/MATLAB/lu_normest.m b/UMFPACK/MATLAB/lu_normest.m
new file mode 100644
index 0000000..e170817
--- /dev/null
+++ b/UMFPACK/MATLAB/lu_normest.m
@@ -0,0 +1,107 @@
+function rho = lu_normest (A, L, U)
+%LU_NORMEST estimates norm (L*U-A, 1) without forming L*U-A
+%
+% Example:
+%
+% rho = lu_normest (A, L, U)
+%
+% which estimates the computation of the 1-norm:
+%
+% rho = norm (A-L*U, 1)
+%
+% Authors: William W. Hager, Math Dept., Univ. of Florida
+% Timothy A. Davis, CISE Dept., Univ. of Florida
+% Gainesville, FL, 32611, USA.
+% based on normest1, contributed on November, 1997
+%
+% This code can be quite easily adapted to estimate the 1-norm of any
+% matrix E, where E itself is dense or not explicitly represented, but the
+% computation of E (and E') times a vector is easy. In this case, our matrix
+% of interest is:
+%
+% E = A-L*U
+%
+% That is, L*U is the LU factorization of A, where A, L and U
+% are sparse. This code works for dense matrices A and L too,
+% but it would not be needed in that case, since E is easy to compute
+% explicitly. For sparse A, L, and U, computing E explicitly would be quite
+% expensive, and thus normest (A-L*U) would be prohibitive.
+%
+% For a detailed description, see Davis, T. A. and Hager, W. W.,
+% Modifying a sparse Cholesky factorization, SIAM J. Matrix Analysis and
+% Applications, 1999, vol. 20, no. 3, 606-627.
+%
+% See also normest
+
+% The three places that the matrix-vector multiply E*x is used are highlighted.
+% Note that E is never formed explicity.
+
+% Copyright 1995-2007 by William W. Hager and Timothy A. Davis
+
+[m n] = size (A) ;
+
+if (m ~= n)
+ % pad A, L, and U with zeros so that they are all square
+ if (m < n)
+ U = [ U ; (sparse (n-m,n)) ] ;
+ L = [ L , (sparse (m,n-m)) ; (sparse (n-m,n)) ] ;
+ A = [ A ; (sparse (n-m,n)) ] ;
+ else
+ U = [ U , (sparse (n,m-n)) ; (sparse (m-n,m)) ] ;
+ L = [ L , (sparse (m,m-n)) ] ;
+ A = [ A , (sparse (m,m-n)) ] ;
+ end
+end
+
+[m n] = size (A) ; %#ok
+
+notvisited = ones (m, 1) ; % nonvisited(j) is zero if j is visited, 1 otherwise
+rho = 0 ; % the global rho
+
+for trial = 1:3 % {
+
+ x = notvisited ./ sum (notvisited) ;
+ rho1 = 0 ; % the current rho for this trial
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%% COMPUTE Ex1 = E*x EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ Ex1 = (A*x) - L*(U*x) ;
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ rho2 = norm (Ex1, 1) ;
+
+ while rho2 > rho1 % {
+
+ rho1 = rho2 ;
+ y = 2*(Ex1 >= 0) - 1 ;
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%% COMPUTE z = E'*y EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ z = (A'*y) - U'*(L'*y) ;
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ [zj, j] = max (abs (z .* notvisited)) ;
+ j = j (1) ;
+ if (abs (z (j)) > z'*x) % {
+ x = zeros (m, 1) ;
+ x (j) = 1 ;
+ notvisited (j) = 0 ;
+ else % } {
+ break ;
+ end % }
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%% COMPUTE Ex1 = E*x EFFICIENTLY: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ Ex1 = (A*x) - L*(U*x) ;
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+ rho2 = norm (Ex1, 1) ;
+
+ end % }
+
+ rho = max (rho, rho1) ;
+
+end % }
diff --git a/UMFPACK/MATLAB/luflop.m b/UMFPACK/MATLAB/luflop.m
new file mode 100644
index 0000000..4a871ed
--- /dev/null
+++ b/UMFPACK/MATLAB/luflop.m
@@ -0,0 +1,26 @@
+function f = luflop (L, U) %#ok
+%LUFLOP given L and U, computes # of flops required to compute them
+%
+% Example:
+% f = luflop (L, U)
+%
+% Given an LU factorization, compute how many flops took to compute it. This
+% is the same as (assuming U has a zero-free diagonal):
+%
+% Lnz = full (sum (spones (L))) - 1 ;
+% Unz = full (sum (spones (U')))' - 1 ;
+% f = 2*Lnz*Unz + sum (Lnz) ;
+%
+% except that no extra workspace is allocated for spones (L) and spones (U).
+% L and U must be sparse.
+%
+% Note: the above expression has a subtle undercount when exact numerical
+% cancelation occurs. Try [L,U,P] = lu (sparse (ones (10))) and then
+% luflop (L,U).
+%
+% See also LU
+
+% Copyright 1995-2007 by Timothy A. Davis.
+
+help luflop
+error ('luflop mexFunction not found! Use umfpack_make to compile luflop.') ;
diff --git a/UMFPACK/MATLAB/luflopmex.c b/UMFPACK/MATLAB/luflopmex.c
new file mode 100644
index 0000000..e85b95e
--- /dev/null
+++ b/UMFPACK/MATLAB/luflopmex.c
@@ -0,0 +1,121 @@
+/* ========================================================================== */
+/* === luflop mexFunction ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ f = luflop (L, U) ;
+
+ Given L and U, compute:
+
+ Lnz = full (sum (spones (L))) - 1 ;
+ Unz = full (sum (spones (U')))' - 1 ;
+ f = 2*Lnz*Unz + sum (Lnz) ;
+
+ without allocating O (lunz) space.
+
+ v5.1: port to 64-bit MATLAB
+*/
+
+#include "mex.h"
+#include "UFconfig.h"
+
+#ifndef TRUE
+#define TRUE (1)
+#endif
+#ifndef FALSE
+#define FALSE (0)
+#endif
+
+void mexFunction
+(
+ int nlhs, /* number of left-hand sides */
+ mxArray *plhs [ ], /* left-hand side matrices */
+ int nrhs, /* number of right--hand sides */
+ const mxArray *prhs [ ] /* right-hand side matrices */
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double flop_count ;
+ double *pflop ;
+ UF_long *Lp, *Li, *Up, *Ui, *Unz, n, k, row, col, p, Lnz_k, Unz_k ;
+ mxArray *Lmatrix, *Umatrix ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs L, U */
+ /* ---------------------------------------------------------------------- */
+
+ if (nrhs != 2)
+ {
+ mexErrMsgTxt ("Usage: f = luflop (L, U)") ;
+ }
+
+ Lmatrix = (mxArray *) prhs [0] ;
+ Umatrix = (mxArray *) prhs [1] ;
+
+ n = mxGetM (Lmatrix) ;
+ if (n != mxGetN (Lmatrix) || n != mxGetM (Umatrix) || n != mxGetN (Umatrix))
+ {
+ mexErrMsgTxt ("Usage: f = luflop (L, U) ; L and U must be square") ;
+ }
+
+ if (!mxIsSparse (Lmatrix) || !mxIsSparse (Umatrix))
+ {
+ mexErrMsgTxt ("Usage: f = luflop (L, U) ; L and U must be sparse") ;
+ }
+
+ Lp = (UF_long *) mxGetJc (Lmatrix) ;
+ Li = (UF_long *) mxGetIr (Lmatrix) ;
+
+ Up = (UF_long *) mxGetJc (Umatrix) ;
+ Ui = (UF_long *) mxGetIr (Umatrix) ;
+
+ Unz = (UF_long *) mxMalloc (n * sizeof (UF_long)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the nonzeros in each row of U */
+ /* ---------------------------------------------------------------------- */
+
+ for (row = 0 ; row < n ; row++)
+ {
+ Unz [row] = 0 ;
+ }
+ for (col = 0 ; col < n ; col++)
+ {
+ for (p = Up [col] ; p < Up [col+1] ; p++)
+ {
+ row = Ui [p] ;
+ Unz [row]++ ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* count the flops */
+ /* ---------------------------------------------------------------------- */
+
+ flop_count = 0.0 ;
+ for (k = 0 ; k < n ; k++)
+ {
+ /* off-diagonal nonzeros in column k of L: */
+ Lnz_k = Lp [k+1] - Lp [k] - 1 ;
+ Unz_k = Unz [k] - 1 ;
+ flop_count += (2 * Lnz_k * Unz_k) + Lnz_k ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* return the result */
+ /* ---------------------------------------------------------------------- */
+
+ plhs [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ pflop = mxGetPr (plhs [0]) ;
+ pflop [0] = flop_count ;
+}
diff --git a/UMFPACK/MATLAB/umfpack2.m b/UMFPACK/MATLAB/umfpack2.m
new file mode 100644
index 0000000..91e407d
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack2.m
@@ -0,0 +1,46 @@
+function [out1, out2, out3, out4, out5] = umfpack2(in1, in2, in3, in4, in5) %#ok
+%UMFPACK2 computes x=A\b, x=A/b, or lu (A) for a sparse matrix A
+% It is also a built-in function in MATLAB, used in x=A\b.
+%
+% Example:
+%
+% UMFPACK: | MATLAB approximate equivalent:
+% ---------------------------------------------------------------------
+% x = umfpack2 (A, '\', b) ; | x = A \ b
+% |
+% x = umfpack2 (b, '/', A) ; | x = b / A
+% |
+% [L,U,P,Q] = umfpack2 (A) ; | [m,n] = size (A) ;
+% | I = speye (n) ;
+% | Q = I (:, colamd (A)) ;
+% | [L,U,P] = lu (A*Q) ;
+% |
+% [L,U,P,Q,R] = umfpack2 (A) ; | [m,n] = size (A) ;
+% | I = speye (n) ;
+% | Q = I (:, colamd (A)) ;
+% | r = full (sum (abs (A), 2)) ;
+% | r (find (r == 0)) = 1 ;
+% | R = spdiags (r, 0, m, m) ;
+% | [L,U,P] = lu ((R\A)*Q) ;
+% |
+% [P,Q,F,C] = umfpack2 (A, 'symbolic')| [m,n] = size (A) ;
+% | I = speye (n) ;
+% | Q = I (:, colamd (A)) ;
+% | [count,h,parent,post] = ...
+% | symbfact (A*Q, 'col') ;
+%
+% A must be sparse. It can be complex, singular, and/or rectangular. A must be
+% square for '/' or '\'. b must be a full real or complex vector. For
+% [L,U,P,Q,R] = umfpack2 (A), the factorization is L*U = P*(R\A)*Q. If A has a
+% mostly symmetric nonzero pattern, then replace "colamd" with "amd" in the
+% MATLAB-equivalent column in the table above. Type umfpack_details for more
+% information.
+%
+% See also: lu_normest, colamd, amd, umfpack.
+% To use UMFPACK for an arbitrary b, see umfpack_solve.
+
+% Copyright 1995-2007 by Timothy A. Davis.
+
+help umfpack2
+error ('umfpack2 mexFunction not found') ;
+
diff --git a/UMFPACK/MATLAB/umfpack_btf.m b/UMFPACK/MATLAB/umfpack_btf.m
new file mode 100644
index 0000000..87cfc10
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_btf.m
@@ -0,0 +1,142 @@
+function [x, info] = umfpack_btf (A, b, Control)
+%UMFPACK_BTF factorize A using a block triangular form
+%
+% Example:
+% x = umfpack_btf (A, b, Control)
+%
+% solve Ax=b by first permuting the matrix A to block triangular form via dmperm
+% and then using UMFPACK to factorize each diagonal block. Adjacent 1-by-1
+% blocks are merged into a single upper triangular block, and solved via
+% MATLAB's \ operator. The Control parameter is optional (Type umfpack_details
+% and umfpack_report for details on its use). A must be square.
+%
+% See also umfpack, umfpack2, umfpack_details, dmperm
+
+% Copyright 1995-2007 by Timothy A. Davis.
+
+if (nargin < 2)
+ help umfpack_btf
+ error ('Usage: x = umfpack_btf (A, b, Control)') ;
+end
+
+[m n] = size (A) ;
+if (m ~= n)
+ help umfpack_btf
+ error ('umfpack_btf: A must be square') ;
+end
+m1 = size (b,1) ;
+if (m1 ~= n)
+ help umfpack_btf
+ error ('umfpack_btf: b has the wrong dimensions') ;
+end
+
+if (nargin < 3)
+ Control = umfpack2 ;
+end
+
+%-------------------------------------------------------------------------------
+% find the block triangular form
+%-------------------------------------------------------------------------------
+
+% dmperm built-in may segfault in MATLAB 7.4 or earlier; fixed in MATLAB 7.5
+% since dmperm now uses CSparse
+[p,q,r] = dmperm (A) ;
+nblocks = length (r) - 1 ;
+
+info = [0 0 0] ; % [nnz(L), nnz(U), nnz(F)], optional 2nd output
+
+%-------------------------------------------------------------------------------
+% solve the system
+%-------------------------------------------------------------------------------
+
+if (nblocks == 1 | sprank (A) < n) %#ok
+
+ %---------------------------------------------------------------------------
+ % matrix is irreducible or structurally singular
+ %---------------------------------------------------------------------------
+
+ [x info2] = umfpack2 (A, '\', b, Control) ;
+ info = [info2(78) info2(79) 0] ;
+
+else
+
+ %---------------------------------------------------------------------------
+ % A (p,q) is in block triangular form
+ %---------------------------------------------------------------------------
+
+ b = b (p,:) ;
+ A = A (p,q) ;
+ x = zeros (size (b)) ;
+
+ %---------------------------------------------------------------------------
+ % merge adjacent singletons into a single upper triangular block
+ %---------------------------------------------------------------------------
+
+ [r, nblocks, is_triangular] = merge_singletons (r) ;
+
+ %---------------------------------------------------------------------------
+ % solve the system: x (q) = A\b
+ %---------------------------------------------------------------------------
+
+ for k = nblocks:-1:1
+
+ % get the kth block
+ k1 = r (k) ;
+ k2 = r (k+1) - 1 ;
+
+ % solve the system
+ [x2 info2] = solver (A (k1:k2, k1:k2), b (k1:k2,:), ...
+ is_triangular (k), Control) ;
+ x (k1:k2,:) = x2 ;
+
+ % off-diagonal block back substitution
+ F2 = A (1:k1-1, k1:k2) ;
+ b (1:k1-1,:) = b (1:k1-1,:) - F2 * x (k1:k2,:) ;
+
+ info (1:2) = info (1:2) + info2 (1:2) ;
+ info (3) = info (3) + nnz (F2) ;
+
+ end
+
+ x (q,:) = x ;
+
+end
+
+%-------------------------------------------------------------------------------
+% merge_singletons
+%-------------------------------------------------------------------------------
+
+function [r, nblocks, is_triangular] = merge_singletons (r)
+%
+% Given r from [p,q,r] = dmperm (A), where A is square, return a modified r that
+% reflects the merger of adjacent singletons into a single upper triangular
+% block. is_triangular (k) is 1 if the kth block is upper triangular. nblocks
+% is the number of new blocks.
+
+nblocks = length (r) - 1 ;
+bsize = r (2:nblocks+1) - r (1:nblocks) ;
+t = [0 (bsize == 1)] ;
+z = (t (1:nblocks) == 0 & t (2:nblocks+1) == 1) | t (2:nblocks+1) == 0 ;
+y = [(find (z)) nblocks+1] ;
+r = r (y) ;
+nblocks = length (y) - 1 ;
+is_triangular = y (2:nblocks+1) - y (1:nblocks) > 1 ;
+
+%-------------------------------------------------------------------------------
+% solve Ax=b, but check for small and/or triangular systems
+%-------------------------------------------------------------------------------
+
+function [x, info] = solver (A, b, is_triangular, Control)
+if (is_triangular)
+ % back substitution only
+ x = A \ b ;
+ info = [nnz(A) 0 0] ;
+elseif (size (A,1) < 4)
+ % a very small matrix, solve it as a dense linear system
+ x = full (A) \ b ;
+ n = size (A,1) ;
+ info = [(n^2+n)/2 (n^2+n)/2 0] ;
+else
+ % solve it as a sparse linear system
+ [x info] = umfpack_solve (A, '\', b, Control) ;
+end
diff --git a/UMFPACK/MATLAB/umfpack_demo.m b/UMFPACK/MATLAB/umfpack_demo.m
new file mode 100644
index 0000000..81807ab
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_demo.m
@@ -0,0 +1,202 @@
+function umfpack_demo (c)
+%UMFPACK_DEMO a lenghty demo
+%
+% A demo of UMFPACK for MATLAB.
+%
+% Example:
+% umfpack_demo
+%
+% See also umfpack, umfpack2, umfpack_make, umfpack_details, umfpack_report,
+% and umfpack_simple.
+
+% Copyright 1995-2007 by Timothy A. Davis.
+
+%-------------------------------------------------------------------------------
+% get default control parameters
+%-------------------------------------------------------------------------------
+
+control = umfpack2 ;
+if (nargin < 1)
+ fprintf ('\nEnter the printing level for UMFPACK''s output statistics:\n') ;
+ fprintf ('0: none, 1: errors only, 2: statistics, 4: print some outputs\n');
+ c = input ('5: print all output [default is 1]: ', 's') ;
+ c = str2double (c) ;
+end
+if (isempty (c))
+ c = 1 ;
+end
+control (1) = c ;
+
+%-------------------------------------------------------------------------------
+% solve a simple system
+%-------------------------------------------------------------------------------
+
+fprintf ('\n--------------------------------------------------------------\n') ;
+fprintf ('Factor and solve a small system, Ax=b, using default parameters\n') ;
+if (control (1) > 1)
+ fprintf ('(except for verbose printing enabled)\n') ;
+end
+
+load west0067_triplet
+A = spconvert (west0067_triplet) ;
+
+n = size (A, 1) ;
+b = rand (n, 1) ;
+
+fprintf ('Solving Ax=b via UMFPACK:\n') ;
+xu = umfpack2 (A, '\', b, control) ;
+
+fprintf ('Solving Ax=b via MATLAB:\n') ;
+xm = A\b ;
+
+fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ...
+ norm (xu - xm, Inf)) ;
+
+%-------------------------------------------------------------------------------
+% spy the results
+%-------------------------------------------------------------------------------
+
+figure (1)
+clf
+
+subplot (2,3,1)
+spy (A)
+title ('The matrix A') ;
+
+subplot (2,3,2)
+[P1, Q1, Fr, Ch, Info] = umfpack2 (A, 'symbolic') ; %#ok
+treeplot (Fr (1:end-1,2)') ;
+title ('Supernodal column elimination tree') ;
+
+subplot (2,3,3)
+spy (P1 * A * Q1)
+title ('A, with initial row and column order') ;
+
+subplot (2,3,4)
+fprintf ('\n--------------------------------------------------------------\n') ;
+fprintf ('\nFactorizing [L, U, P, Q, R] = umfpack2 (A)\n') ;
+[L, U, P, Q, R] = umfpack2 (A) ;
+spy (P*A*Q)
+title ('A, with final row/column order') ;
+
+fprintf ('\nP * (R\\A) * Q - L*U should be zero:\n') ;
+fprintf ('norm (P*(R\\A)*Q - L*U, 1) = %g (exact) %g (estimated)\n', ...
+ norm (P * (R\A) * Q - L*U, 1), lu_normest (P * (R\A) * Q, L, U)) ;
+
+fprintf ('\nSolution to Ax=b via UMFPACK factorization:\n') ;
+fprintf ('x = Q * (U \\ (L \\ (P * (R \\ b))))\n') ;
+xu = Q * (U \ (L \ (P * (R \ b)))) ;
+
+fprintf ('\nUMFPACK flop count: %d\n', luflop (L, U)) ;
+
+subplot (2,3,5)
+spy (spones (L) + spones (U))
+title ('UMFPACK LU factors') ;
+
+subplot (2,3,6)
+fprintf ('\nFactorizing [L, U, P] = lu (A (:, q))\n') ;
+fprintf ('If you are using a version of MATLAB prior to V6.0, then the\n') ;
+fprintf ('following statement (q = colamd (A)) may fail. Either download\n');
+fprintf ('colamd from http://www.cise.ufl.edu/research/sparse, upgrade to\n') ;
+fprintf ('MATLAB V6.0 or later, or replace the statement with\n') ;
+fprintf ('q = colmmd (A) ;\n') ;
+try
+ q = colamd (A) ;
+catch
+ fprintf ('\n *** colamd not found, using colmmd instead *** \n') ;
+ q = colmmd (A) ;
+end
+[L, U, P] = lu (A (:,q)) ;
+spy (spones (L) + spones (U))
+title ('MATLAB LU factors') ;
+
+fprintf ('\nSolution to Ax=b via MATLAB factorization:\n') ;
+fprintf ('x = U \\ (L \\ (P * b)) ; x (q) = x ;\n') ;
+xm = U \ (L \ (P * b)) ;
+xm (q) = xm ;
+
+fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ...
+ norm (xu - xm, Inf)) ;
+
+fprintf ('\nMATLAB LU flop count: %d\n', luflop (L, U)) ;
+
+%-------------------------------------------------------------------------------
+% solve A'x=b
+%-------------------------------------------------------------------------------
+
+fprintf ('\n--------------------------------------------------------------\n') ;
+fprintf ('Solve A''x=b:\n') ;
+
+fprintf ('Solving A''x=b via UMFPACK:\n') ;
+xu = umfpack2 (b', '/', A, control) ;
+xu = xu' ;
+
+fprintf ('Solving A''x=b via MATLAB:\n') ;
+xm = (b'/A)' ;
+
+fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ...
+ norm (xu - xm, Inf)) ;
+
+%-------------------------------------------------------------------------------
+% factor A' and then solve Ax=b using the factors of A'
+%-------------------------------------------------------------------------------
+
+fprintf ('\n--------------------------------------------------------------\n') ;
+fprintf ('Compute C = A'', and compute the LU factorization of C.\n') ;
+fprintf ('Factorizing A'' can sometimes be better than factorizing A itself\n');
+fprintf ('(less work and memory usage). Solve C''x=b; the solution is the\n') ;
+fprintf ('same as the solution to Ax=b for the original A.\n');
+
+C = A' ;
+
+% factorize C (P,Q) = L*U
+[L, U, P, Q, R, info] = umfpack2 (C, control) ; %#ok
+
+fprintf ('\nP * (R\\C) * Q - L*U should be zero:\n') ;
+fprintf ('norm (P*(R\\C)*Q - L*U, 1) = %g (exact) %g (estimated)\n', ...
+ norm (P * (R\C) * Q - L*U, 1), lu_normest (P * (R\C) * Q, L, U)) ;
+
+fprintf ('\nSolution to Ax=b via UMFPACK, using the factors of C:\n') ;
+fprintf ('x = R \\ (P'' * (L'' \\ (U'' \\ (Q'' * b)))) ;\n') ;
+xu = R \ (P' * (L' \ (U' \ (Q' * b)))) ;
+
+fprintf ('Solution to Ax=b via MATLAB:\n') ;
+xm = A\b ;
+
+fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ...
+ norm (xu - xm, Inf)) ;
+
+%-------------------------------------------------------------------------------
+% solve Ax=B
+%-------------------------------------------------------------------------------
+
+fprintf ('\n--------------------------------------------------------------\n') ;
+fprintf ('\nSolve AX=B, where B is n-by-10, and sparse\n') ;
+B = sprandn (n, 10, 0.05) ;
+XU = umfpack_solve (A, '\', B, control) ;
+XM = A\B ;
+
+fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ...
+ norm (XU - XM, Inf)) ;
+
+fprintf ('\n--------------------------------------------------------------\n') ;
+fprintf ('\nSolve AX=B, where B is n-by-10, and sparse, using umfpack_btf\n') ;
+XU = umfpack_btf (A, B, control) ;
+
+fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ...
+ norm (XU - XM, Inf)) ;
+
+fprintf ('\n--------------------------------------------------------------\n') ;
+fprintf ('\nSolve A''X=B, where B is n-by-10, and sparse\n') ;
+XU = umfpack_solve (B', '/', A, control) ;
+XM = B'/A ;
+
+fprintf ('Difference between UMFPACK and MATLAB solution: %g\n', ...
+ norm (XU - XM, Inf)) ;
+
+%-------------------------------------------------------------------------------
+% compute the determinant
+%-------------------------------------------------------------------------------
+
+fprintf ('\n--------------------------------------------------------------\n') ;
+fprintf ('det(A): %g UMFPACK determinant: %g\n', det (A), umfpack2 (A, 'det'));
diff --git a/UMFPACK/MATLAB/umfpack_demo.m.out b/UMFPACK/MATLAB/umfpack_demo.m.out
new file mode 100644
index 0000000..c0c60ba
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_demo.m.out
@@ -0,0 +1,75 @@
+umfpack_demo
+
+Enter the printing level for UMFPACK's output statistics:
+0: none, 1: errors only, 2: statistics, 4: print some outputs
+5: print all output [default is 1]:
+
+--------------------------------------------------------------
+Factor and solve a small system, Ax=b, using default parameters
+Solving Ax=b via UMFPACK:
+Solving Ax=b via MATLAB:
+Difference between UMFPACK and MATLAB solution: 0
+
+--------------------------------------------------------------
+
+Factorizing [L, U, P, Q, R] = umfpack2 (A)
+
+P * (R\A) * Q - L*U should be zero:
+norm (P*(R\A)*Q - L*U, 1) = 2.77556e-16 (exact) 1.21864e-16 (estimated)
+
+Solution to Ax=b via UMFPACK factorization:
+x = Q * (U \ (L \ (P * (R \ b))))
+
+UMFPACK flop count: 2453
+
+Factorizing [L, U, P] = lu (A (:, q))
+If you are using a version of MATLAB prior to V6.0, then the
+following statement (q = colamd (A)) may fail. Either download
+colamd from http://www.cise.ufl.edu/research/sparse, upgrade to
+MATLAB V6.0 or later, or replace the statement with
+q = colmmd (A) ;
+
+Solution to Ax=b via MATLAB factorization:
+x = U \ (L \ (P * b)) ; x (q) = x ;
+Difference between UMFPACK and MATLAB solution: 5.55112e-15
+
+MATLAB LU flop count: 3160
+
+--------------------------------------------------------------
+Solve A'x=b:
+Solving A'x=b via UMFPACK:
+Solving A'x=b via MATLAB:
+Difference between UMFPACK and MATLAB solution: 1.77636e-15
+
+--------------------------------------------------------------
+Compute C = A', and compute the LU factorization of C.
+Factorizing A' can sometimes be better than factorizing A itself
+(less work and memory usage). Solve C'x=b; the solution is the
+same as the solution to Ax=b for the original A.
+
+P * (R\C) * Q - L*U should be zero:
+norm (P*(R\C)*Q - L*U, 1) = 1.17961e-16 (exact) 5.60533e-17 (estimated)
+
+Solution to Ax=b via UMFPACK, using the factors of C:
+x = R \ (P' * (L' \ (U' \ (Q' * b)))) ;
+Solution to Ax=b via MATLAB:
+Difference between UMFPACK and MATLAB solution: 3.55271e-15
+
+--------------------------------------------------------------
+
+Solve AX=B, where B is n-by-10, and sparse
+Difference between UMFPACK and MATLAB solution: 6.3926e-14
+
+--------------------------------------------------------------
+
+Solve AX=B, where B is n-by-10, and sparse, using umfpack_btf
+Difference between UMFPACK and MATLAB solution: 4.41347e-14
+
+--------------------------------------------------------------
+
+Solve A'X=B, where B is n-by-10, and sparse
+Difference between UMFPACK and MATLAB solution: 8.90054e-14
+
+--------------------------------------------------------------
+det(A): -4.07453e-05 UMFPACK determinant: -4.07453e-05
+diary off
diff --git a/UMFPACK/MATLAB/umfpack_details.m b/UMFPACK/MATLAB/umfpack_details.m
new file mode 100644
index 0000000..5eb67d7
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_details.m
@@ -0,0 +1,176 @@
+function umfpack_details
+%UMFPACK_DETAILS details on all the options for using umfpack2 in MATLAB
+%
+% Factor or solve a sparse linear system, returning either the solution x to
+% Ax=b or A'x'=b', the factorization LU=PAQ, or LU=P(R\A)Q. A must be sparse.
+% For the solve, A must be square and b must be a dense n-by-1 vector. For LU
+% factorization, A can be rectangular. In both cases, A and/or b can be real
+% or complex.
+%
+% UMFPACK analyzes the matrix and selects one of three strategies to factorize
+% the matrix. It first finds a set of k initial pivot entries of zero Markowitz
+% cost. This forms the first k rows and columns of L and U. The remaining
+% submatrix S is then analyzed, based on the symmetry of the nonzero pattern of
+% the submatrix and the values on the diagaonal. The strategies include:
+%
+% (1) unsymmetric: use a COLAMD pre-ordering, a column elimination tree
+% post-ordering, refine the column ordering during factorization,
+% and make no effort at selecting pivots on the diagonal.
+% (2) 2-by-2: like the symmetric strategy (see below), except that local
+% row permutations are first made to attempt to place large entries
+% on the diagonal.
+% (3) symmetric: use an AMD pre-ordering on the matrix S+S', an
+% elimination tree post-ordering, do not refine the column ordering
+% during factorization, and attempt to select pivots on the diagonal.
+%
+% Each of the following uses of umfpack2 (except for "Control = umfpack2") is
+% stand-alone. That is, no call to umfpack2 is required for any subsequent
+% call. In each usage, the Info output argument is optional.
+%
+% Example:
+%
+% [x, Info] = umfpack2 (A, '\', b) ;
+% [x, Info] = umfpack2 (A, '\', b, Control) ;
+% [x, Info] = umfpack2 (A, Qinit, '\', b, Control) ;
+% [x, Info] = umfpack2 (A, Qinit, '\', b) ;
+%
+% Solves Ax=b (similar to x = A\b in MATLAB).
+%
+% [x, Info] = umfpack2 (b, '/', A) ;
+% [x, Info] = umfpack2 (b, '/', A, Control) ;
+% [x, Info] = umfpack2 (b, '/', A, Qinit) ;
+% [x, Info] = umfpack2 (b, '/', A, Qinit, Control) ;
+%
+% Solves A'x'=b' (similar to x = b/A in MATLAB).
+%
+% [L, U, P, Q, R, Info] = umfpack2 (A) ;
+% [L, U, P, Q, R, Info] = umfpack2 (A, Control) ;
+% [L, U, P, Q, R, Info] = umfpack2 (A, Qinit) ;
+% [L, U, P, Q, R, Info] = umfpack2 (A, Qinit, Control) ;
+%
+% Returns the LU factorization of A. P and Q are returned as permutation
+% matrices. R is a diagonal sparse matrix of scale factors for the rows
+% of A, L is lower triangular, and U is upper triangular. The
+% factorization is L*U = P*(R\A)*Q. You can turn off scaling by setting
+% Control (17) to zero (in which case R = speye (m)), or by using the
+% following syntaxes (in which case Control (17) is ignored):
+%
+% [L, U, P, Q] = umfpack2 (A) ;
+% [L, U, P, Q] = umfpack2 (A, Control) ;
+% [L, U, P, Q] = umfpack2 (A, Qinit) ;
+% [L, U, P, Q] = umfpack2 (A, Qinit, Control) ;
+%
+% Same as above, except that no row scaling is performed. The Info array
+% is not returned, either.
+%
+% [P1, Q1, Fr, Ch, Info] = umfpack2 (A, 'symbolic') ;
+% [P1, Q1, Fr, Ch, Info] = umfpack2 (A, 'symbolic', Control) ;
+% [P1, Q1, Fr, Ch, Info] = umfpack2 (A, Qinit, 'symbolic') ;
+% [P1, Q1, Fr, Ch, Info] = umfpack2 (A, Qinit, 'symbolic', Control);
+%
+% Performs only the fill-reducing column pre-ordering (including the
+% elimination tree post-ordering) and symbolic factorization. Q1 is the
+% initial column permutation (either from colamd, amd, or the input
+% ordering Qinit), possibly followed by a column elimination tree post-
+% ordering or a symmetric elimination tree post-ordering, depending on
+% the strategy used.
+%
+% For the unsymmetric strategy, P1 is the row ordering induced by Q1
+% (row-merge order). For the 2-by-2 strategy, P1 is the row ordering that
+% places large entries on the diagonal of P1*A*Q1. For the symmetric
+% strategy, P1 = Q1.
+%
+% Fr is a (nfr+1)-by-4 array containing information about each frontal
+% matrix, where nfr <= n is the number of frontal matrices. Fr (:,1) is
+% the number of pivot columns in each front, and Fr (:,2) is the parent
+% of each front in the supercolumn elimination tree. Fr (k,2) is zero if
+% k is a root. The first Fr (1,1) columns of P1*A*Q1 are the pivot
+% columns for the first front, the next Fr (2,1) columns of P1*A*Q1
+% are the pivot columns for the second front, and so on.
+%
+% For the unsymmetric strategy, Fr (:,3) is the row index of the first
+% row in P1*A*Q1 whose leftmost nonzero entry is in a pivot column for
+% the kth front. Fr (:,4) is the leftmost descendent of the kth front.
+% Rows in the range Fr (Fr (k,4),3) to Fr (k+1,3)-1 form the entire set
+% of candidate pivot rows for the kth front (some of these will typically
+% have been selected as pivot rows of fronts Fr (k,3) to k-1, before the
+% factorization reaches the kth front. If front k is a leaf node, then
+% Fr (k,4) is k.
+%
+% Ch is a (nchains+1)-by-3 array containing information about each "chain"
+% (unifrontal sequence) of frontal matrices, and where nchains <= nfr
+% is the number of chains. The ith chain consists of frontal matrices.
+% Chain (i,1) to Chain (i+1,1)-1, and the largest front in chain i is
+% Chain (i,2)-by-Chain (i,3).
+%
+% This use of umfpack2 is not required to factor or solve a linear system
+% in MATLAB. It analyzes the matrix A and provides information only.
+% The MATLAB statement "treeplot (Fr (:,2)')" plots the column elimination
+% tree.
+%
+% Control = umfpack2 ;
+%
+% Returns a 20-by-1 vector of default parameter settings for umfpack2.
+%
+% umfpack_report (Control, Info) ;
+%
+% Prints the current Control settings, and Info
+%
+% det = umfpack2 (A, 'det') ;
+% [det dexp] = umfpack2 (A, 'det') ;
+%
+% Computes the determinant of A. The 2nd form returns the determinant
+% in the form det*10^dexp, where det is in the range +/- 1 to 10,
+% which helps to avoid overflow/underflow when dexp is out of range of
+% normal floating-point numbers.
+%
+% If present, Qinit is a user-supplied 1-by-n permutation vector. It is an
+% initial fill-reducing column pre-ordering for A; if not present, then colamd
+% or amd are used instead. If present, Control is a user-supplied 20-by-1
+% array. Control and Info are optional; if Control is not present, defaults
+% are used. If a Control entry is NaN, then the default is used for that entry.
+%
+%
+% Copyright 1995-2007 by Timothy A. Davis, University of Florida.
+% All Rights Reserved.
+% UMFPACK is available under alternate licenses, contact T. Davis for details.
+%
+% UMFPACK License:
+%
+% Your use or distribution of UMFPACK or any modified version of
+% UMFPACK implies that you agree to this License.
+%
+% This library is free software; you can redistribute it and/or
+% modify it under the terms of the GNU General Public
+% License as published by the Free Software Foundation; either
+% version 2 of the License, or (at your option) any later version.
+%
+% This library is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+% General Public License for more details.
+%
+% You should have received a copy of the GNU General Public
+% License along with this library; if not, write to the Free Software
+% Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+% USA
+%
+% Permission is hereby granted to use or copy this program under the
+% terms of the GNU GPL, provided that the Copyright, this License,
+% and the Availability of the original version is retained on all copies.
+% User documentation of any code that uses this code or any modified
+% version of this code must cite the Copyright, this License, the
+% Availability note, and "Used by permission." Permission to modify
+% the code and to distribute modified code is granted, provided the
+% Copyright, this License, and the Availability note are retained,
+% and a notice that the code was modified is included.
+%
+% Availability: http://www.cise.ufl.edu/research/sparse/umfpack
+%
+% See also umfpack, umfpack2, umfpack_make, umfpack_report,
+% umfpack_demo, and umfpack_simple.
+
+more on
+help umfpack_details
+more off
+
diff --git a/UMFPACK/MATLAB/umfpack_install.m b/UMFPACK/MATLAB/umfpack_install.m
new file mode 100644
index 0000000..921f2c5
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_install.m
@@ -0,0 +1,37 @@
+function umfpack_install
+%UMFPACK_INSTALL to compile and install umfpack2 and amd2 for use in MATLAB
+% Your current directory must be UMFPACK/MATLAB for this function to work.
+%
+% Example:
+% umfpack_install
+%
+% See also umfpack2, amd2.
+
+% Copyright 1995-2007 by Timothy A. Davis.
+
+% compile and install UMFPACK
+umfpack_path = pwd ;
+addpath (umfpack_path) ;
+try
+ umfpack_make
+catch
+ fprintf ('Trying to install with lcc_lib/libmwlapack.lib instead\n') ;
+ umfpack_make ('lcc_lib/libmwlapack.lib') ;
+end
+
+% compile and install AMD
+cd ../../AMD/MATLAB
+amd_path = pwd ;
+addpath (amd_path) ;
+amd_make ;
+
+cd (umfpack_path)
+
+fprintf ('Now trying the umfpack_simple demo.\n');
+umfpack_simple
+
+fprintf ('Added the following directories to the path. You may wish to add\n');
+fprintf ('these permanently with the MATLAB pathtool command:\n') ;
+fprintf ('%s\n', umfpack_path) ;
+fprintf ('%s\n', amd_path) ;
+
diff --git a/UMFPACK/MATLAB/umfpack_make.m b/UMFPACK/MATLAB/umfpack_make.m
new file mode 100644
index 0000000..8875ff3
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_make.m
@@ -0,0 +1,334 @@
+function umfpack_make (lapack)
+%UMFPACK_MAKE to compile umfpack2 for use in MATLAB
+%
+% Compiles the umfpack2 mexFunction and then runs a simple demo.
+%
+% Example:
+% umfpack_make % use default LAPACK and BLAS
+% umfpack_make ('lcc_lib/libmwlapack.lib') % for Windows
+% umfpack_make ('-lmwlapack -lmwblas') % for Linux, Unix, Mac
+%
+% the string gives the locations of the LAPACK and BLAS libraries.
+%
+% See also: umfpack, umfpack2, umfpack_details, umfpack_report, umfpack_demo,
+% and umfpack_simple.
+
+% Copyright 1995-2007 by Timothy A. Davis.
+
+details = 0 ;
+
+d = '' ;
+if (~isempty (strfind (computer, '64')))
+ d = ' -largeArrayDims' ;
+end
+
+v = getversion ;
+try
+ % ispc does not appear in MATLAB 5.3
+ pc = ispc ;
+catch
+ % if ispc fails, assume we are on a Windows PC if it's not unix
+ pc = ~isunix ;
+end
+fprintf ('Compiling UMFPACK for MATLAB Version %g\n', v) ;
+
+if (pc)
+ obj = 'obj' ;
+else
+ obj = 'o' ;
+end
+
+kk = 0 ;
+
+%-------------------------------------------------------------------------------
+% BLAS option
+%-------------------------------------------------------------------------------
+
+% This is exceedingly ugly. The MATLAB mex command needs to be told where to
+% fine the LAPACK and BLAS libraries, which is a real portability nightmare.
+
+if (nargin < 1)
+ if (pc)
+ if (v < 6.5)
+ % MATLAB 6.1 and earlier: use the version supplied here
+ lapack = 'lcc_lib/libmwlapack.lib' ;
+ fprintf ('Using %s. If this fails with dgemm and others\n',lapack);
+ fprintf ('undefined, then edit umfpack_make.m and modify the') ;
+ fprintf (' statement:\nlapack = ''%s'' ;\n', lapack) ;
+ elseif (v < 7.5)
+ lapack = 'libmwlapack.lib' ;
+ else
+ % MATLAB R2007b (7.5) made the problem worse
+ lapack = 'libmwlapack.lib libmwblas.lib' ;
+ end
+ else
+ % For other systems, mex should find lapack on its own, but this has
+ % been broken in MATLAB R2007a; the following is now required.
+ if (v < 7.5)
+ lapack = '-lmwlapack' ;
+ else
+ % MATLAB R2007b (7.5) made the problem worse
+ lapack = '-lmwlapack -lmwblas' ;
+ end
+ end
+end
+
+%-------------------------------------------------------------------------------
+% -DNPOSIX option (for sysconf and times timer routines)
+%-------------------------------------------------------------------------------
+
+posix = '' ;
+
+% if (~pc)
+% msg = [ ...
+% '--------------------------------------------------------------\n', ...
+% '\nUMFPACK can use the POSIX routines sysconf () and times ()\n', ...
+% 'to provide CPU time and wallclock time statistics. If you do not\n', ...
+% 'have a POSIX-compliant operating system, then UMFPACK won''t\n', ...
+% 'compile. If you don''t know which option to pick, try the\n', ...
+% 'default. If you get an error saying that sysconf and/or times\n', ...
+% 'are not defined, then recompile with the non-POSIX option.\n', ...
+% '\nPlease select one of the following options:\n', ...
+% ' 1: use POSIX sysconf and times routines (default)\n', ...
+% ' 2: do not use POSIX routines\n'] ;
+% fprintf (msg) ;
+% posix = str2num (input (': ', 's')) ;
+% if (isempty (posix))
+% posix = 1 ;
+% end
+% if (posix == 2)
+% fprintf ('\nNot using POSIX sysconf and times routines.\n') ;
+% posix = ' -DNPOSIX' ;
+% else
+% fprintf ('\nUsing POSIX sysconf and times routines.\n') ;
+% posix = '' ;
+% end
+% end
+
+%-------------------------------------------------------------------------------
+% mex command
+%-------------------------------------------------------------------------------
+
+umfdir = '../Source/' ;
+amddir = '../../AMD/Source/' ;
+incdir = ' -I../Include -I../Source -I../../AMD/Include -I../../UFconfig' ;
+mx = sprintf ('mex -O%s%s%s ', posix, incdir, d) ;
+% fprintf ('compile options:\n%s\n', mx) ;
+
+%-------------------------------------------------------------------------------
+% source files
+%-------------------------------------------------------------------------------
+
+% non-user-callable umf_*.[ch] files:
+umfch = { 'assemble', 'blas3_update', ...
+ 'build_tuples', 'create_element', ...
+ 'dump', 'extend_front', 'garbage_collection', ...
+ 'get_memory', 'init_front', 'kernel', ...
+ 'kernel_init', 'kernel_wrapup', ...
+ 'local_search', 'lsolve', 'ltsolve', ...
+ 'mem_alloc_element', 'mem_alloc_head_block', ...
+ 'mem_alloc_tail_block', 'mem_free_tail_block', ...
+ 'mem_init_memoryspace', ...
+ 'report_vector', 'row_search', 'scale_column', ...
+ 'set_stats', 'solve', 'symbolic_usage', 'transpose', ...
+ 'tuple_lengths', 'usolve', 'utsolve', 'valid_numeric', ...
+ 'valid_symbolic', 'grow_front', 'start_front', '2by2', ...
+ 'store_lu', 'scale' } ;
+
+% non-user-callable umf_*.[ch] files, int versions only (no real/complex):
+umfint = { 'analyze', 'apply_order', 'colamd', 'free', 'fsize', ...
+ 'is_permutation', 'malloc', 'realloc', 'report_perm', ...
+ 'singletons' } ;
+
+% non-user-callable and user-callable amd_*.[ch] files (int versions only):
+amdsrc = { 'aat', '1', '2', 'dump', 'postorder', 'post_tree', 'defaults', ...
+ 'order', 'control', 'info', 'valid', 'preprocess', 'global' } ;
+
+% user-callable umfpack_*.[ch] files (real/complex):
+user = { 'col_to_triplet', 'defaults', 'free_numeric', ...
+ 'free_symbolic', 'get_numeric', 'get_lunz', ...
+ 'get_symbolic', 'get_determinant', 'numeric', 'qsymbolic', ...
+ 'report_control', 'report_info', 'report_matrix', ...
+ 'report_numeric', 'report_perm', 'report_status', ...
+ 'report_symbolic', 'report_triplet', ...
+ 'report_vector', 'solve', 'symbolic', ...
+ 'transpose', 'triplet_to_col', 'scale' ...
+ 'load_numeric', 'save_numeric', 'load_symbolic', 'save_symbolic' } ;
+
+% user-callable umfpack_*.[ch], only one version
+generic = { 'timer', 'tictoc', 'global' } ;
+
+M = cell (0) ;
+
+%-------------------------------------------------------------------------------
+% Create the umfpack2 and amd2 mexFunctions for MATLAB (int versions only)
+%-------------------------------------------------------------------------------
+
+for k = 1:length(umfint)
+ [M, kk] = make (M, '%s -DDLONG -c %sumf_%s.c', 'umf_%s.%s', ...
+ 'umf_%s_%s.%s', mx, umfint {k}, umfint {k}, 'm', obj, umfdir, ...
+ kk, details) ;
+end
+
+rules = { [mx ' -DDLONG'] , [mx ' -DZLONG'] } ;
+kinds = { 'md', 'mz' } ;
+
+for what = 1:2
+
+ rule = rules {what} ;
+ kind = kinds {what} ;
+
+ [M, kk] = make (M, '%s -DCONJUGATE_SOLVE -c %sumf_%s.c', 'umf_%s.%s', ...
+ 'umf_%s_%s.%s', rule, 'ltsolve', 'lhsolve', kind, obj, umfdir, ...
+ kk, details) ;
+
+ [M, kk] = make (M, '%s -DCONJUGATE_SOLVE -c %sumf_%s.c', 'umf_%s.%s', ...
+ 'umf_%s_%s.%s', rule, 'utsolve', 'uhsolve', kind, obj, umfdir, ...
+ kk, details) ;
+
+ [M, kk] = make (M, '%s -DDO_MAP -c %sumf_%s.c', 'umf_%s.%s', ...
+ 'umf_%s_%s_map_nox.%s', rule, 'triplet', 'triplet', kind, obj, ...
+ umfdir, kk, details) ;
+
+ [M, kk] = make (M, '%s -DDO_VALUES -c %sumf_%s.c', 'umf_%s.%s', ...
+ 'umf_%s_%s_nomap_x.%s', rule, 'triplet', 'triplet', kind, obj, ...
+ umfdir, kk, details) ;
+
+ [M, kk] = make (M, '%s -c %sumf_%s.c', 'umf_%s.%s', ...
+ 'umf_%s_%s_nomap_nox.%s', rule, 'triplet', 'triplet', kind, obj, ...
+ umfdir, kk, details) ;
+
+ [M, kk] = make (M, '%s -DDO_MAP -DDO_VALUES -c %sumf_%s.c', 'umf_%s.%s', ...
+ 'umf_%s_%s_map_x.%s', rule, 'triplet', 'triplet', kind, obj, ...
+ umfdir, kk, details) ;
+
+ [M, kk] = make (M, '%s -DFIXQ -c %sumf_%s.c', 'umf_%s.%s', ...
+ 'umf_%s_%s_fixq.%s', rule, 'assemble', 'assemble', kind, obj, ...
+ umfdir, kk, details) ;
+
+ [M, kk] = make (M, '%s -DDROP -c %sumf_%s.c', 'umf_%s.%s', ...
+ 'umf_%s_%s_drop.%s', rule, 'store_lu', 'store_lu', kind, obj, ...
+ umfdir, kk, details) ;
+
+ for k = 1:length(umfch)
+ [M, kk] = make (M, '%s -c %sumf_%s.c', 'umf_%s.%s', 'umf_%s_%s.%s', ...
+ rule, umfch {k}, umfch {k}, kind, obj, umfdir, kk, details) ;
+ end
+
+ [M, kk] = make (M, '%s -DWSOLVE -c %sumfpack_%s.c', 'umfpack_%s.%s', ...
+ 'umfpack_%s_w%s.%s', rule, 'solve', 'solve', kind, obj, umfdir, ...
+ kk, details) ;
+
+ for k = 1:length(user)
+ [M, kk] = make (M, '%s -c %sumfpack_%s.c', 'umfpack_%s.%s', ...
+ 'umfpack_%s_%s.%s', rule, user {k}, user {k}, kind, obj, ...
+ umfdir, kk, details) ;
+ end
+end
+
+for k = 1:length(generic)
+ [M, kk] = make (M, '%s -c %sumfpack_%s.c', 'umfpack_%s.%s', ...
+ 'umfpack_%s_%s.%s', mx, generic {k}, generic {k}, 'm', obj, ...
+ umfdir, kk, details) ;
+end
+
+%----------------------------------------
+% AMD routines (int only)
+%----------------------------------------
+
+for k = 1:length(amdsrc)
+ [M, kk] = make (M, '%s -DDLONG -c %samd_%s.c', 'amd_%s.%s', ...
+ 'amd_%s_%s.%s', mx, amdsrc {k}, amdsrc {k}, 'm', obj, amddir, ...
+ kk, details) ;
+end
+
+%----------------------------------------
+% compile the umfpack2 mexFunction
+%----------------------------------------
+
+C = sprintf ('%s -output umfpack2 umfpackmex.c', mx) ;
+for i = 1:length (M)
+ C = [C ' ' (M {i})] ; %#ok
+end
+C = [C ' ' lapack] ;
+kk = cmd (C, kk, details) ;
+
+%----------------------------------------
+% delete the object files
+%----------------------------------------
+
+for i = 1:length (M)
+ rmfile (M {i}) ;
+end
+
+%----------------------------------------
+% compile the luflop mexFunction
+%----------------------------------------
+
+cmd (sprintf ('%s -output luflop luflopmex.c', mx), kk, details) ;
+
+fprintf ('\nUMFPACK successfully compiled\n') ;
+
+%===============================================================================
+% end of umfpack_make
+%===============================================================================
+
+
+%-------------------------------------------------------------------------------
+
+function rmfile (file)
+% rmfile: delete a file, but only if it exists
+if (length (dir (file)) > 0) %#ok
+ delete (file) ;
+end
+
+%-------------------------------------------------------------------------------
+
+function cpfile (src, dst)
+% cpfile: copy the src file to the filename dst, overwriting dst if it exists
+rmfile (dst)
+if (length (dir (src)) == 0) %#ok
+ fprintf ('File does not exist: %s\n', src) ;
+ error ('File does not exist') ;
+end
+copyfile (src, dst) ;
+
+%-------------------------------------------------------------------------------
+
+function mvfile (src, dst)
+% mvfile: move the src file to the filename dst, overwriting dst if it exists
+cpfile (src, dst) ;
+rmfile (src) ;
+
+%-------------------------------------------------------------------------------
+
+function kk = cmd (s, kk, details)
+%CMD: evaluate a command, and either print it or print a "."
+if (details)
+ fprintf ('%s\n', s) ;
+else
+ if (mod (kk, 60) == 0)
+ fprintf ('\n') ;
+ end
+ kk = kk + 1 ;
+ fprintf ('.') ;
+end
+eval (s) ;
+
+%-------------------------------------------------------------------------------
+
+function [M, kk] = make (M, s, src, dst, rule, file1, file2, kind, obj, ...
+ srcdir, kk, details)
+% make: execute a "make" command for a source file
+kk = cmd (sprintf (s, rule, srcdir, file1), kk, details) ;
+src = sprintf (src, file1, obj) ;
+dst = sprintf (dst, kind, file2, obj) ;
+mvfile (src, dst) ;
+M {end + 1} = dst ;
+
+
+%-------------------------------------------------------------------------------
+function v = getversion
+% determine the MATLAB version, and return it as a double.
+v = sscanf (version, '%d.%d.%d') ;
+v = 10.^(0:-1:-(length(v)-1)) * v ;
diff --git a/UMFPACK/MATLAB/umfpack_report.m b/UMFPACK/MATLAB/umfpack_report.m
new file mode 100644
index 0000000..627b394
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_report.m
@@ -0,0 +1,337 @@
+function umfpack_report (Control, Info)
+%UMFPACK_REPORT prints optional control settings and statistics
+%
+% Example:
+% umfpack_report (Control, Info) ;
+%
+% Prints the current Control settings for umfpack2, and the statistical
+% information returned by umfpack2 in the Info array. If Control is
+% an empty matrix, then the default control settings are printed.
+%
+% Control is 20-by-1, and Info is 90-by-1. Not all entries are used.
+%
+% Alternative usages:
+%
+% umfpack_report ([ ], Info) ; print the default control parameters
+% and the Info array.
+% umfpack_report (Control) ; print the control parameters only.
+% umfpack_report ; print the default control parameters
+% and an empty Info array.
+%
+% See also umfpack, umfpack2, umfpack_make, umfpack_details,
+% umfpack_demo, and umfpack_simple.
+
+% Copyright 1995-2007 by Timothy A. Davis.
+
+%-------------------------------------------------------------------------------
+% get inputs, use defaults if input arguments not present
+%-------------------------------------------------------------------------------
+
+% The contents of Control and Info are defined in umfpack.h
+if (nargin < 1)
+ Control = [] ;
+end
+if (nargin < 2)
+ Info = [] ;
+end
+if (isempty (Control))
+ Control = umfpack2 ;
+end
+if (isempty (Info))
+ Info = [ 0 (-ones (1, 89)) ] ;
+end
+
+%-------------------------------------------------------------------------------
+% control settings
+%-------------------------------------------------------------------------------
+
+fprintf ('\nUMFPACK: Control settings:\n\n') ;
+fprintf (' Control (1): print level: %d\n', Control (1)) ;
+fprintf (' Control (2): dense row parameter: %g\n', Control (2)) ;
+fprintf (' "dense" rows have > max (16, (%g)*16*sqrt(n_col)) entries\n', Control (2)) ;
+fprintf (' Control (3): dense column parameter: %g\n', Control (3)) ;
+fprintf (' "dense" columns have > max (16, (%g)*16*sqrt(n_row)) entries\n', Control (3)) ;
+fprintf (' Control (4): pivot tolerance: %g\n', Control (4)) ;
+fprintf (' Control (5): max block size for dense matrix kernels: %d\n', Control (5)) ;
+prstrat (' Control (6): strategy: %g ', Control (6)) ;
+fprintf (' Control (7): initial allocation ratio: %g\n', Control (7)) ;
+fprintf (' Control (8): max iterative refinement steps: %d\n', Control (8)) ;
+fprintf (' Control (13): 2-by-2 pivot tolerance: %g\n', Control (13)) ;
+fprintf (' Control (14): Q fixed during numeric factorization: %g ', Control (14)) ;
+if (Control (14) > 0)
+ fprintf ('(yes)\n') ;
+elseif (Control (14) < 0)
+ fprintf ('(no)\n') ;
+else
+ fprintf ('(auto)\n') ;
+end
+fprintf (' Control (15): AMD dense row/column parameter: %g\n', Control (15)) ;
+fprintf (' "dense" rows/columns in A+A'' have > max (16, (%g)*sqrt(n)) entries.\n', Control (15)) ;
+fprintf (' Only used if the AMD ordering is used.\n') ;
+fprintf (' Control (16): diagonal pivot tolerance: %g\n', Control (16)) ;
+fprintf (' Only used if diagonal pivoting is attempted.\n') ;
+
+fprintf (' Control (17): scaling option: %g ', Control (17)) ;
+if (Control (17) == 0)
+ fprintf ('(none)\n') ;
+elseif (Control (17) == 2)
+ fprintf ('(scale the matrix by\n') ;
+ fprintf (' dividing each row by max. abs. value in each row)\n') ;
+else
+ fprintf ('(scale the matrix by\n') ;
+ fprintf (' dividing each row by sum of abs. values in each row)\n') ;
+end
+
+fprintf (' Control (18): frontal matrix allocation ratio: %g\n', Control (18)) ;
+fprintf (' Control (19): drop tolerance: %g\n', Control (19)) ;
+fprintf (' Control (20): AMD and COLAMD aggressive absorption: %g ', Control (20)) ;
+yes_no (Control (20)) ;
+
+% compile-time options:
+
+fprintf ('\n The following options can only be changed at compile-time:\n') ;
+
+if (Control (9) == 1)
+ fprintf (' Control (9): compiled to use the BLAS\n') ;
+else
+ fprintf (' Control (9): compiled without the BLAS\n') ;
+ fprintf (' (you will not get the best possible performance)\n') ;
+end
+
+if (Control (10) == 1)
+ fprintf (' Control (10): compiled for MATLAB\n') ;
+elseif (Control (10) == 2)
+ fprintf (' Control (10): compiled for MATLAB\n') ;
+else
+ fprintf (' Control (10): not compiled for MATLAB\n') ;
+ fprintf (' Printing will be in terms of 0-based matrix indexing,\n') ;
+ fprintf (' not 1-based as is expected in MATLAB. Diary output may\n') ;
+ fprintf (' not be properly recorded.\n') ;
+end
+
+if (Control (11) == 2)
+ fprintf (' Control (11): uses POSIX times ( ) to get CPU time and wallclock time.\n') ;
+elseif (Control (11) == 1)
+ fprintf (' Control (11): uses getrusage to get CPU time.\n') ;
+else
+ fprintf (' Control (11): uses ANSI C clock to get CPU time.\n') ;
+ fprintf (' The CPU time may wrap around, type "help cputime".\n') ;
+end
+
+if (Control (12) == 1)
+ fprintf (' Control (12): compiled with debugging enabled\n') ;
+ fprintf (' ###########################################\n') ;
+ fprintf (' ### This will be exceedingly slow! ########\n') ;
+ fprintf (' ###########################################\n') ;
+else
+ fprintf (' Control (12): compiled for normal operation (no debugging)\n') ;
+end
+
+%-------------------------------------------------------------------------------
+% Info:
+%-------------------------------------------------------------------------------
+
+if (nargin == 1)
+ return
+end
+
+status = Info (1) ;
+fprintf ('\nUMFPACK status: Info (1): %d, ', status) ;
+
+if (status == 0)
+ fprintf ('OK\n') ;
+elseif (status == 1)
+ fprintf ('WARNING matrix is singular\n') ;
+elseif (status == -1)
+ fprintf ('ERROR out of memory\n') ;
+elseif (status == -3)
+ fprintf ('ERROR numeric LU factorization is invalid\n') ;
+elseif (status == -4)
+ fprintf ('ERROR symbolic LU factorization is invalid\n') ;
+elseif (status == -5)
+ fprintf ('ERROR required argument is missing\n') ;
+elseif (status == -6)
+ fprintf ('ERROR n <= 0\n') ;
+elseif (status <= -7 & status >= -12 | status == -14) %#ok
+ fprintf ('ERROR matrix A is corrupted\n') ;
+elseif (status == -13)
+ fprintf ('ERROR invalid system\n') ;
+elseif (status == -15)
+ fprintf ('ERROR invalid permutation\n') ;
+elseif (status == -911)
+ fprintf ('ERROR internal error!\n') ;
+ fprintf ('Please report this error to Tim Davis (davis at cise.ufl.edu)\n') ;
+else
+ fprintf ('ERROR unrecognized error. Info array corrupted\n') ;
+end
+
+fprintf (' (a -1 means the entry has not been computed):\n') ;
+
+fprintf ('\n Basic statistics:\n') ;
+fprintf (' Info (2): %d, # of rows of A\n', Info (2)) ;
+fprintf (' Info (17): %d, # of columns of A\n', Info (17)) ;
+fprintf (' Info (3): %d, nnz (A)\n', Info (3)) ;
+fprintf (' Info (4): %d, Unit size, in bytes, for memory usage reported below\n', Info (4)) ;
+fprintf (' Info (5): %d, size of int (in bytes)\n', Info (5)) ;
+fprintf (' Info (6): %d, size of UF_long (in bytes)\n', Info (6)) ;
+fprintf (' Info (7): %d, size of pointer (in bytes)\n', Info (7)) ;
+fprintf (' Info (8): %d, size of numerical entry (in bytes)\n', Info (8)) ;
+
+fprintf ('\n Pivots with zero Markowitz cost removed to obtain submatrix S:\n') ;
+fprintf (' Info (57): %d, # of pivots with one entry in pivot column\n', Info (57)) ;
+fprintf (' Info (58): %d, # of pivots with one entry in pivot row\n', Info (58)) ;
+fprintf (' Info (59): %d, # of rows/columns in submatrix S (if square)\n', Info (59)) ;
+fprintf (' Info (60): ') ;
+if (Info (60) > 0)
+ fprintf ('submatrix S square and diagonal preserved\n') ;
+elseif (Info (60) == 0)
+ fprintf ('submatrix S not square or diagonal not preserved\n') ;
+else
+ fprintf ('\n') ;
+end
+fprintf (' Info (9): %d, # of "dense" rows in S\n', Info (9)) ;
+fprintf (' Info (10): %d, # of empty rows in S\n', Info (10)) ;
+fprintf (' Info (11): %d, # of "dense" columns in S\n', Info (11)) ;
+fprintf (' Info (12): %d, # of empty columns in S\n', Info (12)) ;
+fprintf (' Info (34): %g, symmetry of pattern of S\n', Info (34)) ;
+fprintf (' Info (35): %d, # of off-diagonal nonzeros in S+S''\n', Info (35)) ;
+fprintf (' Info (36): %d, nnz (diag (S))\n', Info (36)) ;
+
+fprintf ('\n 2-by-2 pivoting to place large entries on diagonal:\n') ;
+fprintf (' Info (52): %d, # of small diagonal entries of S\n', Info (52)) ;
+fprintf (' Info (53): %d, # of unmatched small diagonal entries\n', Info (53)) ;
+fprintf (' Info (54): %g, symmetry of P2*S\n', Info (54)) ;
+fprintf (' Info (55): %d, # of off-diagonal entries in (P2*S)+(P2*S)''\n', Info (55)) ;
+fprintf (' Info (56): %d, nnz (diag (P2*S))\n', Info (56)) ;
+
+fprintf ('\n AMD results, for strict diagonal pivoting:\n') ;
+fprintf (' Info (37): %d, est. nz in L and U\n', Info (37)) ;
+fprintf (' Info (38): %g, est. flop count\n', Info (38)) ;
+fprintf (' Info (39): %g, # of "dense" rows in S+S''\n', Info (39)) ;
+fprintf (' Info (40): %g, est. max. nz in any column of L\n', Info (40)) ;
+
+fprintf ('\n Final strategy selection, based on the analysis above:\n') ;
+prstrat (' Info (19): %d, strategy used ', Info (19)) ;
+fprintf (' Info (20): %d, ordering used ', Info (20)) ;
+if (Info (20) == 0)
+ fprintf ('(COLAMD on A)\n') ;
+elseif (Info (20) == 1)
+ fprintf ('(AMD on A+A'')\n') ;
+elseif (Info (20) == 2)
+ fprintf ('(provided by user)\n') ;
+else
+ fprintf ('(undefined ordering option)\n') ;
+end
+fprintf (' Info (32): %d, Q fixed during numeric factorization: ', Info (32)) ;
+yes_no (Info (32)) ;
+fprintf (' Info (33): %d, prefer diagonal pivoting: ', Info (33)) ;
+yes_no (Info (33)) ;
+
+fprintf ('\n symbolic analysis time and memory usage:\n') ;
+fprintf (' Info (13): %d, defragmentations during symbolic analysis\n', Info (13)) ;
+fprintf (' Info (14): %d, memory used during symbolic analysis (Units)\n', Info (14)) ;
+fprintf (' Info (15): %d, final size of symbolic factors (Units)\n', Info (15)) ;
+fprintf (' Info (16): %.2f, symbolic analysis CPU time (seconds)\n', Info (16)) ;
+fprintf (' Info (18): %.2f, symbolic analysis wall clock time (seconds)\n', Info (18)) ;
+
+fprintf ('\n Estimates computed in the symbolic analysis:\n') ;
+fprintf (' Info (21): %d, est. size of LU factors (Units)\n', Info (21)) ;
+fprintf (' Info (22): %d, est. total peak memory usage (Units)\n', Info (22)) ;
+fprintf (' Info (23): %d, est. factorization flop count\n', Info (23)) ;
+fprintf (' Info (24): %d, est. nnz (L)\n', Info (24)) ;
+fprintf (' Info (25): %d, est. nnz (U)\n', Info (25)) ;
+fprintf (' Info (26): %d, est. initial size, variable-part of LU (Units)\n', Info (26)) ;
+fprintf (' Info (27): %d, est. peak size, of variable-part of LU (Units)\n', Info (27)) ;
+fprintf (' Info (28): %d, est. final size, of variable-part of LU (Units)\n', Info (28)) ;
+fprintf (' Info (29): %d, est. max frontal matrix size (# of entries)\n', Info (29)) ;
+fprintf (' Info (30): %d, est. max # of rows in frontal matrix\n', Info (30)) ;
+fprintf (' Info (31): %d, est. max # of columns in frontal matrix\n', Info (31)) ;
+
+fprintf ('\n Computed in the numeric factorization (estimates shown above):\n') ;
+fprintf (' Info (41): %d, size of LU factors (Units)\n', Info (41)) ;
+fprintf (' Info (42): %d, total peak memory usage (Units)\n', Info (42)) ;
+fprintf (' Info (43): %d, factorization flop count\n', Info (43)) ;
+fprintf (' Info (44): %d, nnz (L)\n', Info (44)) ;
+fprintf (' Info (45): %d, nnz (U)\n', Info (45)) ;
+fprintf (' Info (46): %d, initial size of variable-part of LU (Units)\n', Info (46)) ;
+fprintf (' Info (47): %d, peak size of variable-part of LU (Units)\n', Info (47)) ;
+fprintf (' Info (48): %d, final size of variable-part of LU (Units)\n', Info (48)) ;
+fprintf (' Info (49): %d, max frontal matrix size (# of numerical entries)\n', Info (49)) ;
+fprintf (' Info (50): %d, max # of rows in frontal matrix\n', Info (50)) ;
+fprintf (' Info (51): %d, max # of columns in frontal matrix\n', Info (51)) ;
+
+fprintf ('\n Computed in the numeric factorization (no estimates computed a priori):\n') ;
+fprintf (' Info (61): %d, defragmentations during numeric factorization\n', Info (61)) ;
+fprintf (' Info (62): %d, reallocations during numeric factorization\n', Info (62)) ;
+fprintf (' Info (63): %d, costly reallocations during numeric factorization\n', Info (63)) ;
+fprintf (' Info (64): %d, integer indices in compressed pattern of L and U\n', Info (64)) ;
+fprintf (' Info (65): %d, numerical values stored in L and U\n', Info (65)) ;
+fprintf (' Info (66): %.2f, numeric factorization CPU time (seconds)\n', Info (66)) ;
+fprintf (' Info (76): %.2f, numeric factorization wall clock time (seconds)\n', Info (76)) ;
+if (Info (66) > 0.05 & Info (43) > 0) %#ok
+fprintf (' mflops in numeric factorization phase: %.2f\n', 1e-6 * Info (43) / Info (66)) ;
+end
+fprintf (' Info (67): %d, nnz (diag (U))\n', Info (67)) ;
+fprintf (' Info (68): %g, reciprocal condition number estimate\n', Info (68)) ;
+fprintf (' Info (69): %g, matrix was ', Info (69)) ;
+if (Info (69) == 0)
+ fprintf ('not scaled\n') ;
+elseif (Info (69) == 2)
+ fprintf ('scaled (row max)\n') ;
+else
+ fprintf ('scaled (row sum)\n') ;
+end
+fprintf (' Info (70): %g, min. scale factor of rows of A\n', Info (70)) ;
+fprintf (' Info (71): %g, max. scale factor of rows of A\n', Info (71)) ;
+fprintf (' Info (72): %g, min. abs. on diagonal of U\n', Info (72)) ;
+fprintf (' Info (73): %g, max. abs. on diagonal of U\n', Info (73)) ;
+fprintf (' Info (74): %g, initial allocation parameter used\n', Info (74)) ;
+fprintf (' Info (75): %g, # of forced updates due to frontal growth\n', Info (75)) ;
+fprintf (' Info (77): %d, # of off-diaogonal pivots\n', Info (77)) ;
+fprintf (' Info (78): %d, nnz (L), if no small entries dropped\n', Info (78)) ;
+fprintf (' Info (79): %d, nnz (U), if no small entries dropped\n', Info (79)) ;
+fprintf (' Info (80): %d, # of small entries dropped\n', Info (80)) ;
+
+fprintf ('\n Computed in the solve step:\n') ;
+fprintf (' Info (81): %d, iterative refinement steps taken\n', Info (81)) ;
+fprintf (' Info (82): %d, iterative refinement steps attempted\n', Info (82)) ;
+fprintf (' Info (83): %g, omega(1), sparse-backward error estimate\n', Info (83)) ;
+fprintf (' Info (84): %g, omega(2), sparse-backward error estimate\n', Info (84)) ;
+fprintf (' Info (85): %d, solve flop count\n', Info (85)) ;
+fprintf (' Info (86): %.2f, solve CPU time (seconds)\n', Info (86)) ;
+fprintf (' Info (87): %.2f, solve wall clock time (seconds)\n', Info (87)) ;
+
+fprintf ('\n Info (88:90): unused\n\n') ;
+
+%-------------------------------------------------------------------------------
+
+function prstrat (fmt, strategy)
+% prstrat print the ordering strategy
+fprintf (fmt, strategy) ;
+if (strategy == 1)
+ fprintf ('(unsymmetric)\n') ;
+ fprintf (' Q = COLAMD (A), Q refined during numerical\n') ;
+ fprintf (' factorization, and no attempt at diagonal pivoting.\n') ;
+elseif (strategy == 2)
+ fprintf ('(symmetric, with 2-by-2 pivoting)\n') ;
+ fprintf (' P2 = row permutation to place large values on the diagonal\n') ;
+ fprintf (' Q = AMD (P2*A+(P2*A)''), Q not refined during numeric factorization,\n') ;
+ fprintf (' and diagonal pivoting attempted.\n') ;
+elseif (strategy == 3)
+ fprintf ('(symmetric)\n') ;
+ fprintf (' Q = AMD (A+A''), Q not refined during numeric factorization,\n') ;
+ fprintf (' and diagonal pivoting (P=Q'') attempted.\n') ;
+else
+ % strategy = 0 ;
+ fprintf ('(auto)\n') ;
+end
+
+%-------------------------------------------------------------------------------
+
+function yes_no (s)
+% yes_no print yes or no
+if (s == 0)
+ fprintf ('(no)\n') ;
+else
+ fprintf ('(yes)\n') ;
+end
diff --git a/UMFPACK/MATLAB/umfpack_simple.m b/UMFPACK/MATLAB/umfpack_simple.m
new file mode 100644
index 0000000..e96ef07
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_simple.m
@@ -0,0 +1,53 @@
+%UMFPACK_SIMPLE a simple demo
+%
+% Example:
+% umfpack_simple
+%
+% Copyright 1995-2007 by Timothy A. Davis.
+%
+% UMFPACK License:
+%
+% Your use or distribution of UMFPACK or any modified version of
+% UMFPACK implies that you agree to this License. UMFPACK is
+% is free software; you can redistribute it and/or
+% modify it under the terms of the GNU General Public
+% License as published by the Free Software Foundation; either
+% version 2 of the License, or (at your option) any later version.
+
+% Availability: http://www.cise.ufl.edu/research/sparse/umfpack
+%
+% See also: umfpack, umfpack2, umfpack_details
+
+help umfpack_simple
+
+format short
+
+A = [
+ 2 3 0 0 0
+ 3 0 4 0 6
+ 0 -1 -3 2 0
+ 0 0 1 0 0
+ 0 4 2 0 1
+] ;
+fprintf ('A = \n') ; disp (A) ;
+
+A = sparse (A) ;
+
+b = [8 45 -3 3 19]' ;
+fprintf ('b = \n') ; disp (b) ;
+
+fprintf ('Solution to Ax=b via UMFPACK:\n') ;
+fprintf ('x1 = umfpack2 (A, ''\\'', b)\n') ;
+
+x1 = umfpack2 (A, '\', b) ;
+fprintf ('x1 = \n') ; disp (x1) ;
+
+fprintf ('Solution to Ax=b via MATLAB:\n') ;
+fprintf ('x2 = A\\b\n') ;
+
+x2 = A\b ;
+fprintf ('x2 = \n') ; disp (x2) ;
+
+fprintf ('norm (x1-x2) should be small: %g\n', norm (x1-x2)) ;
+
+fprintf ('Type ''umfpack_demo'' for a full demo of UMFPACK\n') ;
diff --git a/UMFPACK/MATLAB/umfpack_simple.m.out b/UMFPACK/MATLAB/umfpack_simple.m.out
new file mode 100644
index 0000000..61ec207
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_simple.m.out
@@ -0,0 +1,52 @@
+umfpack_simple
+ UMFPACK_SIMPLE a simple demo
+
+ Example:
+ umfpack_simple
+
+ Copyright 1995-2007 by Timothy A. Davis.
+
+ UMFPACK License:
+
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License. UMFPACK is
+ is free software; you can redistribute it and/or
+ modify it under the terms of the GNU General Public
+ License as published by the Free Software Foundation; either
+ version 2 of the License, or (at your option) any later version.
+
+A =
+ 2 3 0 0 0
+ 3 0 4 0 6
+ 0 -1 -3 2 0
+ 0 0 1 0 0
+ 0 4 2 0 1
+
+b =
+ 8
+ 45
+ -3
+ 3
+ 19
+
+Solution to Ax=b via UMFPACK:
+x1 = umfpack2 (A, '\', b)
+x1 =
+ 1.0000
+ 2.0000
+ 3.0000
+ 4.0000
+ 5.0000
+
+Solution to Ax=b via MATLAB:
+x2 = A\b
+x2 =
+ 1.0000
+ 2.0000
+ 3.0000
+ 4.0000
+ 5.0000
+
+norm (x1-x2) should be small: 1.28037e-15
+Type 'umfpack_demo' for a full demo of UMFPACK
+diary off
diff --git a/UMFPACK/MATLAB/umfpack_solve.m b/UMFPACK/MATLAB/umfpack_solve.m
new file mode 100644
index 0000000..6464586
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_solve.m
@@ -0,0 +1,102 @@
+function [x, info] = umfpack_solve (arg1, op, arg2, Control)
+%UMFPACK_SOLVE x = A\b or x = b/A
+%
+% Example:
+% x = umfpack_solve (A, '\', b, Control)
+% x = umfpack_solve (b, '/', A, Control)
+%
+% Computes x = A\b, or b/A, where A is square. Uses UMFPACK if A is sparse.
+% The Control argument is optional.
+%
+% See also umfpack, umfpack2, umfpack_make, umfpack_details, umfpack_report,
+% and umfpack_simple.
+
+% Copyright 1995-2007 by Timothy A. Davis.
+
+%-------------------------------------------------------------------------------
+% check inputs and get default control parameters
+%-------------------------------------------------------------------------------
+
+if (op == '\')
+ A = arg1 ;
+ b = arg2 ;
+elseif (op == '/')
+ A = arg2 ;
+ b = arg1 ;
+else
+ help umfack_solve
+ error ('umfpack_solve: unrecognized operator') ;
+end
+
+[m n] = size (A) ;
+if (m ~= n)
+ help umfpack_solve
+ error ('umfpack_solve: A must be square') ;
+end
+
+[m1 n1] = size (b) ;
+if ((op == '\' & n ~= m1) | (op == '/' & n1 ~= m)) %#ok
+ help umfpack_solve
+ error ('umfpack_solve: b has the wrong dimensions') ;
+end
+
+if (nargin < 4)
+ Control = umfpack2 ;
+end
+
+info = [0 0 0] ; % [nnz(L), nnz(U), 0], optional 2nd output
+
+%-------------------------------------------------------------------------------
+% solve the system
+%-------------------------------------------------------------------------------
+
+if (op == '\')
+
+ if (~issparse (A))
+
+ % A is not sparse, so just use MATLAB
+ x = A\b ;
+
+ elseif (n1 == 1 & ~issparse (b)) %#ok
+
+ % the UMFPACK '\' requires b to be a dense column vector
+ [x info] = umfpack2 (A, '\', b, Control) ;
+ info = [info(78) info(79) 0] ;
+
+ else
+
+ % factorize with UMFPACK and do the forward/back solves in MATLAB
+ [L, U, P, Q, R, info] = umfpack2 (A, Control) ;
+ x = Q * (U \ (L \ (P * (R \ b)))) ;
+ info = [info(78) info(79) 0] ;
+
+ end
+
+else
+
+ if (~issparse (A))
+
+ % A is not sparse, so just use MATLAB
+ x = b/A ;
+
+ elseif (m1 == 1 & ~issparse (b)) %#ok
+
+ % the UMFPACK '\' requires b to be a dense column vector
+ [x info] = umfpack2 (b, '/', A, Control) ;
+ info = [info(78) info(79) 0] ;
+
+ else
+
+ % factorize with UMFPACK and do the forward/back solves in MATLAB
+ % this mimics the behavior of x = b/A, except for the row scaling
+ [L, U, P, Q, R, info] = umfpack2 (A.', Control) ;
+ x = (Q * (U \ (L \ (P * (R \ (b.')))))).' ;
+ info = [info(78) info(79) 0] ;
+
+ % an alternative method:
+ % [L, U, P, Q, r] = umfpack2 (A, Control) ;
+ % x = (R \ (P' * (L.' \ (U.' \ (Q' * b.'))))).' ;
+
+ end
+
+end
diff --git a/UMFPACK/MATLAB/umfpack_test.m b/UMFPACK/MATLAB/umfpack_test.m
new file mode 100644
index 0000000..a527695
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpack_test.m
@@ -0,0 +1,180 @@
+function umfpack_test (nmat)
+%UMFPACK_TEST for testing umfpack2 (requires UFget)
+%
+% Example:
+% umfpack_test
+% umfpack_test (100) % runs the first 100 matrices
+% See also umfpack2
+
+% Copyright 1995-2007 by Timothy A. Davis.
+
+index = UFget ;
+
+f = find (index.nrows == index.ncols) ;
+[ignore, i] = sort (index.nrows (f)) ;
+f = f (i) ;
+
+if (nargin < 1)
+ nmat = length (f) ;
+else
+ nmat = min (nmat, length (f)) ;
+end
+nmat = max (nmat, 1) ;
+f = f (1:nmat) ;
+
+Control = umfpack2 ;
+Control (1) = 0 ;
+
+figure (1)
+clf
+
+h = waitbar (0, 'UMFPACK test') ;
+
+for k = 1:nmat
+
+ i = f (k) ;
+ waitbar (k/nmat, h, 'UMFPACK test') ;
+
+ try
+
+ fprintf ('\nmatrix: %s %s %d\n', ...
+ index.Group{i}, index.Name{i}, index.nrows(i)) ;
+
+ Prob = UFget (i) ;
+ A = Prob.A ;
+ n = size (A,1) ;
+
+ b = rand (1,n) ;
+ c = b' ;
+
+ %-----------------------------------------------------------------------
+ % symbolic factorization
+ %-----------------------------------------------------------------------
+
+ [P1, Q1, Fr, Ch, Info] = umfpack2 (A, 'symbolic') ;
+ subplot (2,2,1)
+ spy (A)
+ title ('A')
+
+ subplot (2,2,2)
+ treeplot (Fr (1:end-1,2)') ;
+ title ('supercolumn etree')
+
+ %-----------------------------------------------------------------------
+ % P(R\A)Q = LU
+ %-----------------------------------------------------------------------
+
+ [L,U,P,Q,R,Info] = umfpack2 (A) ;
+ err = lu_normest (P*(R\A)*Q, L, U) ;
+ fprintf ('norm est PR\\AQ-LU: %g relative: %g\n', ...
+ err, err / norm (A,1)) ;
+
+ subplot (2,2,3)
+ spy (P*A*Q)
+ title ('PAQ') ;
+
+ cs = Info (57) ;
+ rs = Info (58) ;
+
+ subplot (2,2,4)
+ hold off
+ try
+ spy (L+U)
+ catch
+ end
+ hold on
+ if (cs > 0)
+ plot ([0 cs n n 0] + .5, [0 cs cs 0 0]+.5, 'c') ;
+ end
+ if (rs > 0)
+ plot ([0 rs rs 0 0] + cs +.5, [cs cs+rs n n cs]+.5, 'r') ;
+ end
+
+ title ('LU factors')
+ drawnow
+
+ %-----------------------------------------------------------------------
+ % PAQ = LU
+ %-----------------------------------------------------------------------
+
+ [L,U,P,Q] = umfpack2 (A) ;
+ err = lu_normest (P*A*Q, L, U) ;
+ fprintf ('norm est PAQ-LU: %g relative: %g\n', ...
+ err, err / norm (A,1)) ;
+
+ %-----------------------------------------------------------------------
+ % solve
+ %-----------------------------------------------------------------------
+
+ x1 = b/A ;
+ y1 = A\c ;
+ m1 = norm (b-x1*A) ;
+ m2 = norm (A*y1-c) ;
+
+ % factor the transpose
+ Control (8) = 2 ;
+ [x, info] = umfpack2 (A', '\', c, Control) ;
+ lunz0 = info (44) + info (45) - info (67) ;
+ r = norm (A'*x-c) ;
+
+ fprintf (':: %8.2e matlab: %8.2e %8.2e\n', r, m1, m2) ;
+
+ % factor the original matrix and solve xA=b
+ for ir = 0:4
+ Control (8) = ir ;
+ [x, info] = umfpack2 (b, '/', A, Control) ;
+ r = norm (b-x*A) ;
+ if (ir == 0)
+ lunz1 = info (44) + info (45) - info (67) ;
+ end
+ fprintf ('%d: %8.2e %d %d\n', ir, r, info (81), info (82)) ;
+ end
+
+ % factor the original matrix and solve Ax=b
+ for ir = 0:4
+ Control (8) = ir ;
+ [x, info] = umfpack2 (A, '\', c, Control) ;
+ r = norm (A*x-c) ;
+ fprintf ('%d: %8.2e %d %d\n', ir, r, info (81), info (82)) ;
+ end
+
+ fprintf (...
+ 'lunz trans %12d no trans: %12d trans/notrans: %10.4f\n', ...
+ lunz0, lunz1, lunz0 / lunz1) ;
+
+ %-----------------------------------------------------------------------
+ % get the determinant
+ %-----------------------------------------------------------------------
+
+ det1 = det (A) ;
+ det2 = umfpack2 (A, 'det') ;
+ [det3 dexp3] = umfpack2 (A, 'det') ;
+ err = abs (det1-det2) ;
+ err3 = abs (det1 - (det3 * 10^dexp3)) ;
+ denom = det1 ;
+ if (denom == 0)
+ denom = 1 ;
+ end
+ err = err / denom ;
+ err3 = err3 / denom ;
+ fprintf ('det: %20.12e + (%20.12e)i MATLAB\n', ...
+ real(det1), imag(det1)) ;
+ fprintf ('det: %20.12e + (%20.12e)i umfpack2\n', ...
+ real(det2), imag(det2)) ;
+ fprintf ('det: (%20.12e + (%20.12e)i) * 10^(%g) umfpack2\n', ...
+ real(det3), imag(det3), dexp3) ;
+ fprintf ('diff %g %g\n', err, err3) ;
+
+ catch
+ % out-of-memory is OK, other errors are not
+ disp (lasterr) ;
+ if (isempty (strfind (lasterr, 'Out of memory')))
+ error (lasterr) ; %#ok
+ else
+ fprintf ('test terminated early, but otherwise OK\n') ;
+ end
+ end
+
+end
+
+close (h) ; % close the waitbar
diff --git a/UMFPACK/MATLAB/umfpackmex.c b/UMFPACK/MATLAB/umfpackmex.c
new file mode 100644
index 0000000..13f2e66
--- /dev/null
+++ b/UMFPACK/MATLAB/umfpackmex.c
@@ -0,0 +1,1387 @@
+/* ========================================================================== */
+/* === UMFPACK mexFunction ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ MATLAB interface for umfpack.
+
+ Factor or solve a sparse linear system, returning either the solution
+ x to Ax=b or A'x'=b', or the factorization LU=P(R\A)Q or LU=PAQ. A must be
+ sparse, with nonzero dimensions, but it may be complex, singular, and/or
+ rectangular. b must be a dense n-by-1 vector (real or complex).
+ L is unit lower triangular, U is upper triangular, and R is diagonal.
+ P and Q are permutation matrices (permutations of an identity matrix).
+
+ The matrix A is scaled, by default. Each row i is divided by r (i), where
+ r (i) is the sum of the absolute values of the entries in that row. The
+ scaled matrix has an infinity norm of 1. The scale factors r (i) are
+ returned in a diagonal sparse matrix. If the factorization is:
+
+ [L, U, P, Q, R] = umfpack (A) ;
+
+ then the factorization is
+
+ L*U = P * (R \ A) * Q
+
+ This is safer than returning a matrix R such that L*U = P*R*A*Q, because
+ it avoids the division by small entries. If r(i) is subnormal, multiplying
+ by 1/r(i) would result in an IEEE Infinity, but dividing by r(i) is safe.
+
+ The factorization
+
+ [L, U, P, Q] = umfpack (A) ;
+
+ returns LU factors such that L*U = P*A*Q, with no scaling.
+
+ See umfpack.m, umfpack_details.m, and umfpack.h for details.
+
+ Note that this mexFunction accesses only the user-callable UMFPACK routines.
+ Thus, is also provides another example of how user C code can access
+ UMFPACK.
+
+ If NO_TRANSPOSE_FORWARD_SLASH is not defined at compile time, then the
+ forward slash (/) operator acts almost like x = b/A in MATLAB 6.1. It is
+ solved by factorizing the array transpose, and then x = (A.'\b.').' is
+ solved. This is the default behavior (for historical reasons), since
+ factorizing A can behave perform much differently than factorizing its
+ transpose.
+
+ If NO_TRANSPOSE_FORWARD_SLASH is defined at compile time, then the forward
+ slash operator does not act like x=b/A in MATLAB 6.1. It is solved by
+ factorizing A, and then solving via the transposed L and U matrices.
+ The solution is still x = (A.'\b.').', except that A is factorized instead
+ of A.'.
+
+ Modified for v4.3.1, Jan 10, 2005: default has been changed to
+ NO_TRANSPOSE_FORWARD_SLASH, to test iterative refinement for b/A.
+ v4.4: added method for computing the determinant.
+
+ v5.1: port to 64-bit MATLAB
+*/
+
+#define NO_TRANSPOSE_FORWARD_SLASH /* default has changed for v4.3.1 */
+
+#include "UFconfig.h"
+#include "umfpack.h"
+#include "mex.h"
+#include "matrix.h"
+#include <string.h>
+#include <math.h>
+#include <float.h>
+
+#define MIN(a,b) (((a) < (b)) ? (a) : (b))
+#define MAX(a,b) (((a) > (b)) ? (a) : (b))
+#define STRING_MATCH(s1,s2) (strcmp ((s1), (s2)) == 0)
+#ifndef TRUE
+#define TRUE (1)
+#endif
+#ifndef FALSE
+#define FALSE (0)
+#endif
+
+/* ========================================================================== */
+/* === error ================================================================ */
+/* ========================================================================== */
+
+/* Return an error message */
+
+static void error
+(
+ char *s,
+ UF_long A_is_complex,
+ int nargout,
+ mxArray *pargout [ ],
+ double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO],
+ UF_long status,
+ UF_long do_info
+)
+{
+ UF_long i ;
+ double *Out_Info ;
+ if (A_is_complex)
+ {
+ umfpack_zl_report_status (Control, status) ;
+ umfpack_zl_report_info (Control, Info) ;
+ }
+ else
+ {
+ umfpack_dl_report_status (Control, status) ;
+ umfpack_dl_report_info (Control, Info) ;
+ }
+ if (do_info > 0)
+ {
+ /* return Info */
+ pargout [do_info] = mxCreateDoubleMatrix (1, UMFPACK_INFO, mxREAL) ;
+ Out_Info = mxGetPr (pargout [do_info]) ;
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ Out_Info [i] = Info [i] ;
+ }
+ }
+ mexErrMsgTxt (s) ;
+}
+
+
+/* ========================================================================== */
+/* === UMFPACK ============================================================== */
+/* ========================================================================== */
+
+void mexFunction
+(
+ int nargout, /* number of outputs */
+ mxArray *pargout [ ], /* output arguments */
+ int nargin, /* number of inputs */
+ const mxArray *pargin [ ] /* input arguments */
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double Info [UMFPACK_INFO], Control [UMFPACK_CONTROL], dx, dz, dexp ;
+ double *Lx, *Lz, *Ux, *Uz, *Ax, *Az, *Bx, *Bz, *Xx, *Xz, *User_Control,
+ *p, *q, *Out_Info, *p1, *p2, *p3, *p4, *Ltx, *Ltz, *Rs, *Px, *Qx ;
+ void *Symbolic, *Numeric ;
+ UF_long *Lp, *Li, *Up, *Ui, *Ap, *Ai, *P, *Q, do_solve, lnz, unz, nn, i,
+ transpose, size, do_info, do_numeric, *Front_npivcol, op, k, *Rp, *Ri,
+ *Front_parent, *Chain_start, *Chain_maxrows, *Chain_maxcols, nz, status,
+ nfronts, nchains, *Ltp, *Ltj, *Qinit, print_level, status2, no_scale,
+ *Front_1strow, *Front_leftmostdesc, n_row, n_col, n_inner, sys,
+ ignore1, ignore2, ignore3, A_is_complex, B_is_complex, X_is_complex,
+ *Pp, *Pi, *Qp, *Qi, do_recip, do_det ;
+ mxArray *Amatrix, *Bmatrix, *User_Control_matrix, *User_Qinit ;
+ char *operator, *operation ;
+ mxComplexity Atype, Xtype ;
+ char warning [200] ;
+
+#ifndef NO_TRANSPOSE_FORWARD_SLASH
+ UF_long *Cp, *Ci ;
+ double *Cx, *Cz ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* define the memory manager and printf functions for UMFPACK and AMD */
+ /* ---------------------------------------------------------------------- */
+
+ /* with these settings, the UMFPACK mexFunction can use ../Lib/libumfpack.a
+ * and ../Lib/libamd.a, instead compiling UMFPACK and AMD specifically for
+ * the MATLAB mexFunction. */
+ amd_malloc = mxMalloc ;
+ amd_free = mxFree ;
+ amd_calloc = mxCalloc ;
+ amd_realloc = mxRealloc ;
+ amd_printf = mexPrintf ;
+
+ /* The default values for these function pointers are fine.
+ umfpack_hypot = umf_hypot ;
+ umfpack_divcomplex = umf_divcomplex ;
+ */
+
+ /* ---------------------------------------------------------------------- */
+ /* get inputs A, b, and the operation to perform */
+ /* ---------------------------------------------------------------------- */
+
+ User_Control_matrix = (mxArray *) NULL ;
+ User_Qinit = (mxArray *) NULL ;
+
+ do_info = 0 ;
+ do_solve = FALSE ;
+ do_numeric = TRUE ;
+ transpose = FALSE ;
+ no_scale = FALSE ;
+ do_det = FALSE ;
+
+ /* find the operator */
+ op = 0 ;
+ for (i = 0 ; i < nargin ; i++)
+ {
+ if (mxIsChar (pargin [i]))
+ {
+ op = i ;
+ break ;
+ }
+ }
+
+ if (op > 0)
+ {
+ operator = mxArrayToString (pargin [op]) ;
+
+ if (STRING_MATCH (operator, "\\"))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* matrix left divide, x = A\b */
+ /* -------------------------------------------------------------- */
+
+ /*
+ [x, Info] = umfpack (A, '\', b) ;
+ [x, Info] = umfpack (A, '\', b, Control) ;
+ [x, Info] = umfpack (A, Qinit, '\', b, Control) ;
+ [x, Info] = umfpack (A, Qinit, '\', b) ;
+ */
+
+ operation = "x = A\\b" ;
+ do_solve = TRUE ;
+ Amatrix = (mxArray *) pargin [0] ;
+ Bmatrix = (mxArray *) pargin [op+1] ;
+
+ if (nargout == 2)
+ {
+ do_info = 1 ;
+ }
+ if (op == 2)
+ {
+ User_Qinit = (mxArray *) pargin [1] ;
+ }
+ if ((op == 1 && nargin == 4) || (op == 2 && nargin == 5))
+ {
+ User_Control_matrix = (mxArray *) pargin [nargin-1] ;
+ }
+ if (nargin < 3 || nargin > 5 || nargout > 2)
+ {
+ mexErrMsgTxt ("wrong number of arguments") ;
+ }
+
+ }
+ else if (STRING_MATCH (operator, "/"))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* matrix right divide, x = b/A */
+ /* -------------------------------------------------------------- */
+
+ /*
+ [x, Info] = umfpack (b, '/', A) ;
+ [x, Info] = umfpack (b, '/', A, Control) ;
+ [x, Info] = umfpack (b, '/', A, Qinit) ;
+ [x, Info] = umfpack (b, '/', A, Qinit, Control) ;
+ */
+
+ operation = "x = b/A" ;
+ do_solve = TRUE ;
+ transpose = TRUE ;
+ Amatrix = (mxArray *) pargin [2] ;
+ Bmatrix = (mxArray *) pargin [0] ;
+
+ if (nargout == 2)
+ {
+ do_info = 1 ;
+ }
+ if (nargin == 5)
+ {
+ User_Qinit = (mxArray *) pargin [3] ;
+ User_Control_matrix = (mxArray *) pargin [4] ;
+ }
+ else if (nargin == 4)
+ {
+ /* Control is k-by-1 where k > 1, Qinit is 1-by-n */
+ if (mxGetM (pargin [3]) == 1)
+ {
+ User_Qinit = (mxArray *) pargin [3] ;
+ }
+ else
+ {
+ User_Control_matrix = (mxArray *) pargin [3] ;
+ }
+ }
+ else if (nargin < 3 || nargin > 5 || nargout > 2)
+ {
+ mexErrMsgTxt ("wrong number of arguments") ;
+ }
+
+ }
+ else if (STRING_MATCH (operator, "symbolic"))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* symbolic factorization only */
+ /* -------------------------------------------------------------- */
+
+ /*
+ [P Q Fr Ch Info] = umfpack (A, 'symbolic') ;
+ [P Q Fr Ch Info] = umfpack (A, 'symbolic', Control) ;
+ [P Q Fr Ch Info] = umfpack (A, Qinit, 'symbolic') ;
+ [P Q Fr Ch Info] = umfpack (A, Qinit, 'symbolic', Control) ;
+ */
+
+ operation = "symbolic factorization" ;
+ do_numeric = FALSE ;
+ Amatrix = (mxArray *) pargin [0] ;
+
+ if (nargout == 5)
+ {
+ do_info = 4 ;
+ }
+ if (op == 2)
+ {
+ User_Qinit = (mxArray *) pargin [1] ;
+ }
+ if ((op == 1 && nargin == 3) || (op == 2 && nargin == 4))
+ {
+ User_Control_matrix = (mxArray *) pargin [nargin-1] ;
+ }
+ if (nargin < 2 || nargin > 4 || nargout > 5 || nargout < 4)
+ {
+ mexErrMsgTxt ("wrong number of arguments") ;
+ }
+
+ }
+ else if (STRING_MATCH (operator, "det"))
+ {
+
+ /* -------------------------------------------------------------- */
+ /* compute the determinant */
+ /* -------------------------------------------------------------- */
+
+ /*
+ * [det] = umfpack (A, 'det') ;
+ * [dmantissa dexp] = umfpack (A, 'det') ;
+ */
+
+ operation = "determinant" ;
+ do_det = TRUE ;
+ Amatrix = (mxArray *) pargin [0] ;
+ if (nargin > 2 || nargout > 2)
+ {
+ mexErrMsgTxt ("wrong number of arguments") ;
+ }
+
+ }
+ else
+ {
+ mexErrMsgTxt ("operator must be '/', '\\', or 'symbolic'") ;
+ }
+ mxFree (operator) ;
+
+ }
+ else if (nargin > 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* LU factorization */
+ /* ------------------------------------------------------------------ */
+
+ /*
+ with scaling:
+ [L, U, P, Q, R, Info] = umfpack (A) ;
+ [L, U, P, Q, R, Info] = umfpack (A, Qinit) ;
+
+ scaling determined by Control settings:
+ [L, U, P, Q, R, Info] = umfpack (A, Control) ;
+ [L, U, P, Q, R, Info] = umfpack (A, Qinit, Control) ;
+
+ with no scaling:
+ [L, U, P, Q] = umfpack (A) ;
+ [L, U, P, Q] = umfpack (A, Control) ;
+ [L, U, P, Q] = umfpack (A, Qinit) ;
+ [L, U, P, Q] = umfpack (A, Qinit, Control) ;
+ */
+
+ operation = "numeric factorization" ;
+ Amatrix = (mxArray *) pargin [0] ;
+
+ no_scale = nargout <= 4 ;
+
+ if (nargout == 6)
+ {
+ do_info = 5 ;
+ }
+ if (nargin == 3)
+ {
+ User_Qinit = (mxArray *) pargin [1] ;
+ User_Control_matrix = (mxArray *) pargin [2] ;
+ }
+ else if (nargin == 2)
+ {
+ /* Control is k-by-1 where k > 1, Qinit is 1-by-n */
+ if (mxGetM (pargin [1]) == 1)
+ {
+ User_Qinit = (mxArray *) pargin [1] ;
+ }
+ else
+ {
+ User_Control_matrix = (mxArray *) pargin [1] ;
+ }
+ }
+ else if (nargin > 3 || nargout > 6 || nargout < 4)
+ {
+ mexErrMsgTxt ("wrong number of arguments") ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* return default control settings */
+ /* ------------------------------------------------------------------ */
+
+ /*
+ Control = umfpack ;
+ umfpack ;
+ */
+
+ if (nargout > 1)
+ {
+ mexErrMsgTxt ("wrong number of arguments") ;
+ }
+
+ pargout [0] = mxCreateDoubleMatrix (UMFPACK_CONTROL, 1, mxREAL) ;
+ User_Control = mxGetPr (pargout [0]) ;
+ umfpack_dl_defaults (User_Control) ;
+
+ return ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (mxGetNumberOfDimensions (Amatrix) != 2)
+ {
+ mexErrMsgTxt ("input matrix A must be 2-dimensional") ;
+ }
+ n_row = mxGetM (Amatrix) ;
+ n_col = mxGetN (Amatrix) ;
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+ if (do_solve && n_row != n_col)
+ {
+ mexErrMsgTxt ("input matrix A must square for '\\' or '/'") ;
+ }
+ if (!mxIsSparse (Amatrix))
+ {
+ mexErrMsgTxt ("input matrix A must be sparse") ;
+ }
+ if (n_row == 0 || n_col == 0)
+ {
+ mexErrMsgTxt ("input matrix A cannot have zero rows or zero columns") ;
+ }
+
+ /* The real/complex status of A determines which version to use, */
+ /* (umfpack_dl_* or umfpack_zl_*). */
+ A_is_complex = mxIsComplex (Amatrix) ;
+ Atype = A_is_complex ? mxCOMPLEX : mxREAL ;
+ Ap = (UF_long *) mxGetJc (Amatrix) ;
+ Ai = (UF_long *) mxGetIr (Amatrix) ;
+ Ax = mxGetPr (Amatrix) ;
+ Az = mxGetPi (Amatrix) ;
+
+ if (do_solve)
+ {
+
+ if (n_row != n_col)
+ {
+ mexErrMsgTxt ("A must be square for \\ or /") ;
+ }
+ if (transpose)
+ {
+ if (mxGetM (Bmatrix) != 1 || mxGetN (Bmatrix) != nn)
+ {
+ mexErrMsgTxt ("b has the wrong dimensions") ;
+ }
+ }
+ else
+ {
+ if (mxGetM (Bmatrix) != nn || mxGetN (Bmatrix) != 1)
+ {
+ mexErrMsgTxt ("b has the wrong dimensions") ;
+ }
+ }
+ if (mxGetNumberOfDimensions (Bmatrix) != 2)
+ {
+ mexErrMsgTxt ("input matrix b must be 2-dimensional") ;
+ }
+ if (mxIsSparse (Bmatrix))
+ {
+ mexErrMsgTxt ("input matrix b cannot be sparse") ;
+ }
+ if (mxGetClassID (Bmatrix) != mxDOUBLE_CLASS)
+ {
+ mexErrMsgTxt ("input matrix b must double precision matrix") ;
+ }
+
+ B_is_complex = mxIsComplex (Bmatrix) ;
+ Bx = mxGetPr (Bmatrix) ;
+ Bz = mxGetPi (Bmatrix) ;
+
+ X_is_complex = A_is_complex || B_is_complex ;
+ Xtype = X_is_complex ? mxCOMPLEX : mxREAL ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* set the Control parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (A_is_complex)
+ {
+ umfpack_zl_defaults (Control) ;
+ }
+ else
+ {
+ umfpack_dl_defaults (Control) ;
+ }
+ if (User_Control_matrix)
+ {
+ if (mxGetClassID (User_Control_matrix) != mxDOUBLE_CLASS ||
+ mxIsSparse (User_Control_matrix))
+ {
+ mexErrMsgTxt ("Control must be a dense real matrix") ;
+ }
+ size = UMFPACK_CONTROL ;
+ size = MIN (size, mxGetNumberOfElements (User_Control_matrix)) ;
+ User_Control = mxGetPr (User_Control_matrix) ;
+ for (i = 0 ; i < size ; i++)
+ {
+ Control [i] = User_Control [i] ;
+ }
+ }
+
+ if (no_scale)
+ {
+ /* turn off scaling for [L, U, P, Q] = umfpack (A) ;
+ * ignoring the input value of Control (24) for the usage
+ * [L, U, P, Q] = umfpack (A, Control) ; */
+ Control [UMFPACK_SCALE] = UMFPACK_SCALE_NONE ;
+ }
+
+ if (mxIsNaN (Control [UMFPACK_PRL]))
+ {
+ print_level = UMFPACK_DEFAULT_PRL ;
+ }
+ else
+ {
+ print_level = (UF_long) Control [UMFPACK_PRL] ;
+ }
+
+ Control [UMFPACK_PRL] = print_level ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get Qinit, if present */
+ /* ---------------------------------------------------------------------- */
+
+ if (User_Qinit)
+ {
+ if (mxGetM (User_Qinit) != 1 || mxGetN (User_Qinit) != n_col)
+ {
+ mexErrMsgTxt ("Qinit must be 1-by-n_col") ;
+ }
+ if (mxGetNumberOfDimensions (User_Qinit) != 2)
+ {
+ mexErrMsgTxt ("input Qinit must be 2-dimensional") ;
+ }
+ if (mxIsComplex (User_Qinit))
+ {
+ mexErrMsgTxt ("input Qinit must not be complex") ;
+ }
+ if (mxGetClassID (User_Qinit) != mxDOUBLE_CLASS)
+ {
+ mexErrMsgTxt ("input Qinit must be a double matrix") ;
+ }
+ if (mxIsSparse (User_Qinit))
+ {
+ mexErrMsgTxt ("input Qinit must be dense") ;
+ }
+ Qinit = (UF_long *) mxMalloc (n_col * sizeof (UF_long)) ;
+ p = mxGetPr (User_Qinit) ;
+ for (k = 0 ; k < n_col ; k++)
+ {
+ /* convert from 1-based to 0-based indexing */
+ Qinit [k] = ((UF_long) (p [k])) - 1 ;
+ }
+
+ }
+ else
+ {
+ /* umfpack_*_qsymbolic will call colamd to get Qinit. This is the */
+ /* same as calling umfpack_*_symbolic with Qinit set to NULL*/
+ Qinit = (UF_long *) NULL ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* report the inputs A and Qinit */
+ /* ---------------------------------------------------------------------- */
+
+ if (print_level >= 2)
+ {
+ /* print the operation */
+ mexPrintf ("\numfpack: %s\n", operation) ;
+ }
+
+ if (A_is_complex)
+ {
+ umfpack_zl_report_control (Control) ;
+ if (print_level >= 3) mexPrintf ("\nA: ") ;
+ (void) umfpack_zl_report_matrix (n_row, n_col, Ap, Ai, Ax, Az,
+ 1, Control) ;
+ if (Qinit)
+ {
+ if (print_level >= 3) mexPrintf ("\nQinit: ") ;
+ (void) umfpack_zl_report_perm (n_col, Qinit, Control) ;
+ }
+ }
+ else
+ {
+ umfpack_dl_report_control (Control) ;
+ if (print_level >= 3) mexPrintf ("\nA: ") ;
+ (void) umfpack_dl_report_matrix (n_row, n_col, Ap, Ai, Ax,
+ 1, Control) ;
+ if (Qinit)
+ {
+ if (print_level >= 3) mexPrintf ("\nQinit: ") ;
+ (void) umfpack_dl_report_perm (n_col, Qinit, Control) ;
+ }
+ }
+
+#ifndef NO_TRANSPOSE_FORWARD_SLASH
+ /* ---------------------------------------------------------------------- */
+ /* create the array transpose for x = b/A */
+ /* ---------------------------------------------------------------------- */
+
+ if (transpose)
+ {
+ /* note that in this case A will be square (nn = n_row = n_col) */
+ /* x = (A.'\b.').' will be computed */
+
+ /* make sure Ci and Cx exist, avoid malloc of zero-sized arrays. */
+ nz = MAX (Ap [nn], 1) ;
+
+ Cp = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ;
+ Ci = (UF_long *) mxMalloc (nz * sizeof (UF_long)) ;
+ Cx = (double *) mxMalloc (nz * sizeof (double)) ;
+ if (A_is_complex)
+ {
+ Cz = (double *) mxMalloc (nz * sizeof (double)) ;
+ status = umfpack_zl_transpose (nn, nn, Ap, Ai, Ax, Az,
+ (UF_long *) NULL, (UF_long *) NULL, Cp, Ci, Cx, Cz, FALSE) ;
+ }
+ else
+ {
+ status = umfpack_dl_transpose (nn, nn, Ap, Ai, Ax,
+ (UF_long *) NULL, (UF_long *) NULL, Cp, Ci, Cx) ;
+ }
+
+ if (status != UMFPACK_OK)
+ {
+ error ("transpose of A failed", A_is_complex, nargout, pargout,
+ Control, Info, status, do_info);
+ return ;
+ }
+
+ /* modify pointers so that C will be factorized and solved, not A */
+ Ap = Cp ;
+ Ai = Ci ;
+ Ax = Cx ;
+ if (A_is_complex)
+ {
+ Az = Cz ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* perform the symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ if (A_is_complex)
+ {
+ status = umfpack_zl_qsymbolic (n_row, n_col, Ap, Ai, Ax, Az,
+ Qinit, &Symbolic, Control, Info) ;
+ }
+ else
+ {
+ status = umfpack_dl_qsymbolic (n_row, n_col, Ap, Ai, Ax,
+ Qinit, &Symbolic, Control, Info) ;
+ }
+
+ if (Qinit)
+ {
+ mxFree (Qinit) ;
+ }
+
+ if (status < 0)
+ {
+ error ("symbolic factorization failed", A_is_complex, nargout, pargout,
+ Control, Info, status, do_info) ;
+ return ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* report the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ if (A_is_complex)
+ {
+ (void) umfpack_zl_report_symbolic (Symbolic, Control) ;
+ }
+ else
+ {
+ (void) umfpack_dl_report_symbolic (Symbolic, Control) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* perform numeric factorization, or just return symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_numeric)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* perform the numeric factorization */
+ /* ------------------------------------------------------------------ */
+
+ if (A_is_complex)
+ {
+ status = umfpack_zl_numeric (Ap, Ai, Ax, Az, Symbolic, &Numeric,
+ Control, Info) ;
+ }
+ else
+ {
+ status = umfpack_dl_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
+ Control, Info) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* free the symbolic factorization */
+ /* ------------------------------------------------------------------ */
+
+ if (A_is_complex)
+ {
+ umfpack_zl_free_symbolic (&Symbolic) ;
+ }
+ else
+ {
+ umfpack_dl_free_symbolic (&Symbolic) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* report the Numeric object */
+ /* ------------------------------------------------------------------ */
+
+ if (status < 0)
+ {
+ error ("numeric factorization failed", A_is_complex, nargout,
+ pargout, Control, Info, status, do_info);
+ return ;
+ }
+
+ if (A_is_complex)
+ {
+ (void) umfpack_zl_report_numeric (Numeric, Control) ;
+ }
+ else
+ {
+ (void) umfpack_dl_report_numeric (Numeric, Control) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* return the solution, determinant, or the factorization */
+ /* ------------------------------------------------------------------ */
+
+ if (do_solve)
+ {
+ /* -------------------------------------------------------------- */
+ /* solve Ax=b or A'x'=b', and return just the solution x */
+ /* -------------------------------------------------------------- */
+
+#ifndef NO_TRANSPOSE_FORWARD_SLASH
+ if (transpose)
+ {
+ /* A.'x.'=b.' gives the same x=b/A as solving A'x'=b' */
+ /* since C=A.' was factorized, solve with sys = UMFPACK_A */
+ /* since x and b are vectors, x.' and b.' are implicit */
+ pargout [0] = mxCreateDoubleMatrix (1, nn, Xtype) ;
+ }
+ else
+ {
+ pargout [0] = mxCreateDoubleMatrix (nn, 1, Xtype) ;
+ }
+ sys = UMFPACK_A ;
+#else
+ if (transpose)
+ {
+ /* If A is real, A'x=b is the same as A.'x=b. */
+ /* x and b are vectors, so x and b are the same as x' and b'. */
+ /* If A is complex, then A.'x.'=b.' gives the same solution x */
+ /* as the complex conjugate transpose. If we used the A'x=b */
+ /* option in umfpack_*_solve, we would have to form b' on */
+ /* input and x' on output (negating the imaginary part). */
+ /* We can save this work by just using the A.'x=b option in */
+ /* umfpack_*_solve. Then, forming x.' and b.' is implicit, */
+ /* since x and b are just vectors anyway. */
+ /* In both cases, the system to solve is A.'x=b */
+ pargout [0] = mxCreateDoubleMatrix (1, nn, Xtype) ;
+ sys = UMFPACK_Aat ;
+ }
+ else
+ {
+ pargout [0] = mxCreateDoubleMatrix (nn, 1, Xtype) ;
+ sys = UMFPACK_A ;
+ }
+#endif
+
+ /* -------------------------------------------------------------- */
+ /* print the right-hand-side, B */
+ /* -------------------------------------------------------------- */
+
+ if (print_level >= 3) mexPrintf ("\nright-hand side, b: ") ;
+ if (B_is_complex)
+ {
+ (void) umfpack_zl_report_vector (nn, Bx, Bz, Control) ;
+ }
+ else
+ {
+ (void) umfpack_dl_report_vector (nn, Bx, Control) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* solve the system */
+ /* -------------------------------------------------------------- */
+
+ Xx = mxGetPr (pargout [0]) ;
+ Xz = mxGetPi (pargout [0]) ;
+ status2 = UMFPACK_OK ;
+
+ if (A_is_complex)
+ {
+ if (!B_is_complex)
+ {
+ /* umfpack_zl_solve expects a complex B */
+ Bz = (double *) mxCalloc (nn, sizeof (double)) ;
+ }
+ status = umfpack_zl_solve (sys, Ap, Ai, Ax, Az, Xx, Xz, Bx, Bz,
+ Numeric, Control, Info) ;
+ if (!B_is_complex)
+ {
+ mxFree (Bz) ;
+ }
+ }
+ else
+ {
+ if (B_is_complex)
+ {
+ /* Ax=b when b is complex and A is sparse can be split */
+ /* into two systems, A*xr=br and A*xi=bi, where r denotes */
+ /* the real part and i the imaginary part of x and b. */
+ status2 = umfpack_dl_solve (sys, Ap, Ai, Ax, Xz, Bz,
+ Numeric, Control, Info) ;
+ }
+ status = umfpack_dl_solve (sys, Ap, Ai, Ax, Xx, Bx,
+ Numeric, Control, Info) ;
+ }
+
+#ifndef NO_TRANSPOSE_FORWARD_SLASH
+ /* -------------------------------------------------------------- */
+ /* free the transposed matrix C */
+ /* -------------------------------------------------------------- */
+
+ if (transpose)
+ {
+ mxFree (Cp) ;
+ mxFree (Ci) ;
+ mxFree (Cx) ;
+ if (A_is_complex)
+ {
+ mxFree (Cz) ;
+ }
+ }
+#endif
+
+ /* -------------------------------------------------------------- */
+ /* free the Numeric object */
+ /* -------------------------------------------------------------- */
+
+ if (A_is_complex)
+ {
+ umfpack_zl_free_numeric (&Numeric) ;
+ }
+ else
+ {
+ umfpack_dl_free_numeric (&Numeric) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* check error status */
+ /* -------------------------------------------------------------- */
+
+ if (status < 0 || status2 < 0)
+ {
+ mxDestroyArray (pargout [0]) ;
+ error ("solve failed", A_is_complex, nargout, pargout, Control,
+ Info, status, do_info) ;
+ return ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* print the solution, X */
+ /* -------------------------------------------------------------- */
+
+ if (print_level >= 3) mexPrintf ("\nsolution, x: ") ;
+ if (X_is_complex)
+ {
+ (void) umfpack_zl_report_vector (nn, Xx, Xz, Control) ;
+ }
+ else
+ {
+ (void) umfpack_dl_report_vector (nn, Xx, Control) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* warn about singular or near-singular matrices */
+ /* -------------------------------------------------------------- */
+
+ /* no warning is given if Control (1) is zero */
+
+ if (Control [UMFPACK_PRL] >= 1)
+ {
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ sprintf (warning, "matrix is singular\n"
+ "Try increasing Control (%d) and Control (%d).\n"
+ "(Suppress this warning with Control (%d) = 0.)\n",
+ 1+UMFPACK_PIVOT_TOLERANCE,
+ 1+UMFPACK_SYM_PIVOT_TOLERANCE,
+ 1+UMFPACK_PRL) ;
+ mexWarnMsgTxt (warning) ;
+ }
+ else if (Info [UMFPACK_RCOND] < DBL_EPSILON)
+ {
+ sprintf (warning, "matrix is nearly singular, rcond = %g\n"
+ "Try increasing Control (%d) and Control (%d).\n"
+ "(Suppress this warning with Control (%d) = 0.)\n",
+ Info [UMFPACK_RCOND],
+ 1+UMFPACK_PIVOT_TOLERANCE,
+ 1+UMFPACK_SYM_PIVOT_TOLERANCE,
+ 1+UMFPACK_PRL) ;
+ mexWarnMsgTxt (warning) ;
+ }
+ }
+
+ }
+ else if (do_det)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* get the determinant */
+ /* -------------------------------------------------------------- */
+
+ if (nargout == 2)
+ {
+ /* [det dexp] = umfpack (A, 'det') ;
+ * return determinant in the form det * 10^dexp */
+ p = &dexp ;
+ }
+ else
+ {
+ /* [det] = umfpack (A, 'det') ;
+ * return determinant as a single scalar (overflow or
+ * underflow is much more likely) */
+ p = (double *) NULL ;
+ }
+ if (A_is_complex)
+ {
+ status = umfpack_zl_get_determinant (&dx, &dz, p,
+ Numeric, Info) ;
+ umfpack_zl_free_numeric (&Numeric) ;
+ }
+ else
+ {
+ status = umfpack_dl_get_determinant (&dx, p,
+ Numeric, Info) ;
+ umfpack_dl_free_numeric (&Numeric) ;
+ dz = 0 ;
+ }
+ if (status < 0)
+ {
+ error ("extracting LU factors failed", A_is_complex, nargout,
+ pargout, Control, Info, status, do_info) ;
+ }
+ if (A_is_complex)
+ {
+ pargout [0] = mxCreateDoubleMatrix (1, 1, mxCOMPLEX) ;
+ p = mxGetPr (pargout [0]) ;
+ *p = dx ;
+ p = mxGetPi (pargout [0]) ;
+ *p = dz ;
+ }
+ else
+ {
+ pargout [0] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ p = mxGetPr (pargout [0]) ;
+ *p = dx ;
+ }
+ if (nargout == 2)
+ {
+ pargout [1] = mxCreateDoubleMatrix (1, 1, mxREAL) ;
+ p = mxGetPr (pargout [1]) ;
+ *p = dexp ;
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* get L, U, P, Q, and r */
+ /* -------------------------------------------------------------- */
+
+ if (A_is_complex)
+ {
+ status = umfpack_zl_get_lunz (&lnz, &unz, &ignore1, &ignore2,
+ &ignore3, Numeric) ;
+ }
+ else
+ {
+ status = umfpack_dl_get_lunz (&lnz, &unz, &ignore1, &ignore2,
+ &ignore3, Numeric) ;
+ }
+
+ if (status < 0)
+ {
+ if (A_is_complex)
+ {
+ umfpack_zl_free_numeric (&Numeric) ;
+ }
+ else
+ {
+ umfpack_dl_free_numeric (&Numeric) ;
+ }
+ error ("extracting LU factors failed", A_is_complex, nargout,
+ pargout, Control, Info, status, do_info) ;
+ return ;
+ }
+
+ /* avoid malloc of zero-sized arrays */
+ lnz = MAX (lnz, 1) ;
+ unz = MAX (unz, 1) ;
+
+ /* get temporary space, for the *** ROW *** form of L */
+ Ltp = (UF_long *) mxMalloc ((n_row+1) * sizeof (UF_long)) ;
+ Ltj = (UF_long *) mxMalloc (lnz * sizeof (UF_long)) ;
+ Ltx = (double *) mxMalloc (lnz * sizeof (double)) ;
+ if (A_is_complex)
+ {
+ Ltz = (double *) mxMalloc (lnz * sizeof (double)) ;
+ }
+ else
+ {
+ Ltz = (double *) NULL ;
+ }
+
+ /* create permanent copy of the output matrix U */
+ pargout [1] = mxCreateSparse (n_inner, n_col, unz, Atype) ;
+ Up = (UF_long *) mxGetJc (pargout [1]) ;
+ Ui = (UF_long *) mxGetIr (pargout [1]) ;
+ Ux = mxGetPr (pargout [1]) ;
+ Uz = mxGetPi (pargout [1]) ;
+
+ /* temporary space for the integer permutation vectors */
+ P = (UF_long *) mxMalloc (n_row * sizeof (UF_long)) ;
+ Q = (UF_long *) mxMalloc (n_col * sizeof (UF_long)) ;
+
+ /* get scale factors, if requested */
+ status2 = UMFPACK_OK ;
+ if (!no_scale)
+ {
+ /* create a diagonal sparse matrix for the scale factors */
+ pargout [4] = mxCreateSparse (n_row, n_row, n_row, mxREAL) ;
+ Rp = (UF_long *) mxGetJc (pargout [4]) ;
+ Ri = (UF_long *) mxGetIr (pargout [4]) ;
+ for (i = 0 ; i < n_row ; i++)
+ {
+ Rp [i] = i ;
+ Ri [i] = i ;
+ }
+ Rp [n_row] = n_row ;
+ Rs = mxGetPr (pargout [4]) ;
+ }
+ else
+ {
+ Rs = (double *) NULL ;
+ }
+
+ /* get Lt, U, P, Q, and Rs from the numeric object */
+ if (A_is_complex)
+ {
+ status = umfpack_zl_get_numeric (Ltp, Ltj, Ltx, Ltz, Up, Ui, Ux,
+ Uz, P, Q, (double *) NULL, (double *) NULL,
+ &do_recip, Rs, Numeric) ;
+ umfpack_zl_free_numeric (&Numeric) ;
+ }
+ else
+ {
+ status = umfpack_dl_get_numeric (Ltp, Ltj, Ltx, Up, Ui,
+ Ux, P, Q, (double *) NULL,
+ &do_recip, Rs, Numeric) ;
+ umfpack_dl_free_numeric (&Numeric) ;
+ }
+
+ /* for the mexFunction, -DNRECIPROCAL must be set,
+ * so do_recip must be FALSE */
+
+ if (status < 0 || status2 < 0 || do_recip)
+ {
+ mxFree (Ltp) ;
+ mxFree (Ltj) ;
+ mxFree (Ltx) ;
+ if (Ltz) mxFree (Ltz) ;
+ mxFree (P) ;
+ mxFree (Q) ;
+ mxDestroyArray (pargout [1]) ;
+ error ("extracting LU factors failed", A_is_complex, nargout,
+ pargout, Control, Info, status, do_info) ;
+ return ;
+ }
+
+ /* create sparse permutation matrix for P */
+ pargout [2] = mxCreateSparse (n_row, n_row, n_row, mxREAL) ;
+ Pp = (UF_long *) mxGetJc (pargout [2]) ;
+ Pi = (UF_long *) mxGetIr (pargout [2]) ;
+ Px = mxGetPr (pargout [2]) ;
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Pp [k] = k ;
+ Px [k] = 1 ;
+ Pi [P [k]] = k ;
+ }
+ Pp [n_row] = n_row ;
+
+ /* create sparse permutation matrix for Q */
+ pargout [3] = mxCreateSparse (n_col, n_col, n_col, mxREAL) ;
+ Qp = (UF_long *) mxGetJc (pargout [3]) ;
+ Qi = (UF_long *) mxGetIr (pargout [3]) ;
+ Qx = mxGetPr (pargout [3]) ;
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Qp [k] = k ;
+ Qx [k] = 1 ;
+ Qi [k] = Q [k] ;
+ }
+ Qp [n_col] = n_col ;
+
+ /* permanent copy of L */
+ pargout [0] = mxCreateSparse (n_row, n_inner, lnz, Atype) ;
+ Lp = (UF_long *) mxGetJc (pargout [0]) ;
+ Li = (UF_long *) mxGetIr (pargout [0]) ;
+ Lx = mxGetPr (pargout [0]) ;
+ Lz = mxGetPi (pargout [0]) ;
+
+ /* convert L from row form to column form */
+ if (A_is_complex)
+ {
+ /* non-conjugate array transpose */
+ status = umfpack_zl_transpose (n_inner, n_row, Ltp, Ltj, Ltx,
+ Ltz, (UF_long *) NULL, (UF_long *) NULL, Lp, Li, Lx, Lz,
+ FALSE) ;
+ }
+ else
+ {
+ status = umfpack_dl_transpose (n_inner, n_row, Ltp, Ltj, Ltx,
+ (UF_long *) NULL, (UF_long *) NULL, Lp, Li, Lx) ;
+ }
+
+ mxFree (Ltp) ;
+ mxFree (Ltj) ;
+ mxFree (Ltx) ;
+ if (Ltz) mxFree (Ltz) ;
+
+ if (status < 0)
+ {
+ mxFree (P) ;
+ mxFree (Q) ;
+ mxDestroyArray (pargout [0]) ;
+ mxDestroyArray (pargout [1]) ;
+ mxDestroyArray (pargout [2]) ;
+ mxDestroyArray (pargout [3]) ;
+ error ("constructing L failed", A_is_complex, nargout, pargout,
+ Control, Info, status, do_info) ;
+ return ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* print L, U, P, and Q */
+ /* -------------------------------------------------------------- */
+
+ if (A_is_complex)
+ {
+ if (print_level >= 3) mexPrintf ("\nL: ") ;
+ (void) umfpack_zl_report_matrix (n_row, n_inner, Lp, Li,
+ Lx, Lz, 1, Control) ;
+ if (print_level >= 3) mexPrintf ("\nU: ") ;
+ (void) umfpack_zl_report_matrix (n_inner, n_col, Up, Ui,
+ Ux, Uz, 1, Control) ;
+ if (print_level >= 3) mexPrintf ("\nP: ") ;
+ (void) umfpack_zl_report_perm (n_row, P, Control) ;
+ if (print_level >= 3) mexPrintf ("\nQ: ") ;
+ (void) umfpack_zl_report_perm (n_col, Q, Control) ;
+ }
+ else
+ {
+ if (print_level >= 3) mexPrintf ("\nL: ") ;
+ (void) umfpack_dl_report_matrix (n_row, n_inner, Lp, Li,
+ Lx, 1, Control) ;
+ if (print_level >= 3) mexPrintf ("\nU: ") ;
+ (void) umfpack_dl_report_matrix (n_inner, n_col, Up, Ui,
+ Ux, 1, Control) ;
+ if (print_level >= 3) mexPrintf ("\nP: ") ;
+ (void) umfpack_dl_report_perm (n_row, P, Control) ;
+ if (print_level >= 3) mexPrintf ("\nQ: ") ;
+ (void) umfpack_dl_report_perm (n_col, Q, Control) ;
+ }
+
+ mxFree (P) ;
+ mxFree (Q) ;
+
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* return the symbolic factorization */
+ /* ------------------------------------------------------------------ */
+
+ Q = (UF_long *) mxMalloc (n_col * sizeof (UF_long)) ;
+ P = (UF_long *) mxMalloc (n_row * sizeof (UF_long)) ;
+ Front_npivcol = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ;
+ Front_parent = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ;
+ Front_1strow = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ;
+ Front_leftmostdesc = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ;
+ Chain_start = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ;
+ Chain_maxrows = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ;
+ Chain_maxcols = (UF_long *) mxMalloc ((nn+1) * sizeof (UF_long)) ;
+
+ if (A_is_complex)
+ {
+ status = umfpack_zl_get_symbolic (&ignore1, &ignore2, &ignore3,
+ &nz, &nfronts, &nchains, P, Q, Front_npivcol,
+ Front_parent, Front_1strow, Front_leftmostdesc,
+ Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ;
+ umfpack_zl_free_symbolic (&Symbolic) ;
+ }
+ else
+ {
+ status = umfpack_dl_get_symbolic (&ignore1, &ignore2, &ignore3,
+ &nz, &nfronts, &nchains, P, Q, Front_npivcol,
+ Front_parent, Front_1strow, Front_leftmostdesc,
+ Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ;
+ umfpack_dl_free_symbolic (&Symbolic) ;
+ }
+
+ if (status < 0)
+ {
+ mxFree (P) ;
+ mxFree (Q) ;
+ mxFree (Front_npivcol) ;
+ mxFree (Front_parent) ;
+ mxFree (Front_1strow) ;
+ mxFree (Front_leftmostdesc) ;
+ mxFree (Chain_start) ;
+ mxFree (Chain_maxrows) ;
+ mxFree (Chain_maxcols) ;
+ error ("extracting symbolic factors failed", A_is_complex, nargout,
+ pargout, Control, Info, status, do_info) ;
+ return ;
+ }
+
+ /* create sparse permutation matrix for P */
+ pargout [0] = mxCreateSparse (n_row, n_row, n_row, mxREAL) ;
+ Pp = (UF_long *) mxGetJc (pargout [0]) ;
+ Pi = (UF_long *) mxGetIr (pargout [0]) ;
+ Px = mxGetPr (pargout [0]) ;
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Pp [k] = k ;
+ Px [k] = 1 ;
+ Pi [P [k]] = k ;
+ }
+ Pp [n_row] = n_row ;
+
+ /* create sparse permutation matrix for Q */
+ pargout [1] = mxCreateSparse (n_col, n_col, n_col, mxREAL) ;
+ Qp = (UF_long *) mxGetJc (pargout [1]) ;
+ Qi = (UF_long *) mxGetIr (pargout [1]) ;
+ Qx = mxGetPr (pargout [1]) ;
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Qp [k] = k ;
+ Qx [k] = 1 ;
+ Qi [k] = Q [k] ;
+ }
+ Qp [n_col] = n_col ;
+
+ /* create Fr */
+ pargout [2] = mxCreateDoubleMatrix (nfronts+1, 4, mxREAL) ;
+
+ p1 = mxGetPr (pargout [2]) ;
+ p2 = p1 + nfronts + 1 ;
+ p3 = p2 + nfronts + 1 ;
+ p4 = p3 + nfronts + 1 ;
+ for (i = 0 ; i <= nfronts ; i++)
+ {
+ /* convert parent, 1strow, and leftmostdesc to 1-based */
+ p1 [i] = (double) (Front_npivcol [i]) ;
+ p2 [i] = (double) (Front_parent [i] + 1) ;
+ p3 [i] = (double) (Front_1strow [i] + 1) ;
+ p4 [i] = (double) (Front_leftmostdesc [i] + 1) ;
+ }
+
+ /* create Ch */
+ pargout [3] = mxCreateDoubleMatrix (nchains+1, 3, mxREAL) ;
+ p1 = mxGetPr (pargout [3]) ;
+ p2 = p1 + nchains + 1 ;
+ p3 = p2 + nchains + 1 ;
+ for (i = 0 ; i < nchains ; i++)
+ {
+ p1 [i] = (double) (Chain_start [i] + 1) ; /* convert to 1-based */
+ p2 [i] = (double) (Chain_maxrows [i]) ;
+ p3 [i] = (double) (Chain_maxcols [i]) ;
+ }
+ p1 [nchains] = Chain_start [nchains] + 1 ;
+ p2 [nchains] = 0 ;
+ p3 [nchains] = 0 ;
+
+ mxFree (P) ;
+ mxFree (Q) ;
+ mxFree (Front_npivcol) ;
+ mxFree (Front_parent) ;
+ mxFree (Front_1strow) ;
+ mxFree (Front_leftmostdesc) ;
+ mxFree (Chain_start) ;
+ mxFree (Chain_maxrows) ;
+ mxFree (Chain_maxcols) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* report Info */
+ /* ---------------------------------------------------------------------- */
+
+ if (A_is_complex)
+ {
+ umfpack_zl_report_info (Control, Info) ;
+ }
+ else
+ {
+ umfpack_dl_report_info (Control, Info) ;
+ }
+
+ if (do_info > 0)
+ {
+ /* return Info */
+ pargout [do_info] = mxCreateDoubleMatrix (1, UMFPACK_INFO, mxREAL) ;
+ Out_Info = mxGetPr (pargout [do_info]) ;
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ Out_Info [i] = Info [i] ;
+ }
+ }
+}
diff --git a/UMFPACK/MATLAB/west.mat b/UMFPACK/MATLAB/west.mat
new file mode 100644
index 0000000..9110c2b
Binary files /dev/null and b/UMFPACK/MATLAB/west.mat differ
diff --git a/UMFPACK/MATLAB/west0067_triplet b/UMFPACK/MATLAB/west0067_triplet
new file mode 100644
index 0000000..572e5b3
--- /dev/null
+++ b/UMFPACK/MATLAB/west0067_triplet
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+39 59 0.745342
+43 59 0.472222
+45 59 -0.745342
+53 59 -0.944444
+65 59 1
+44 60 0.472222
+45 60 -0.372671
+54 60 -0.944444
+65 60 1
+36 61 -0.206995
+37 61 -0.235647
+38 61 -0.247567
+39 61 -0.207487
+45 61 1
+46 62 1.86335
+50 62 0.444444
+55 62 -1.86335
+67 62 1
+47 63 1.49068
+51 63 0.444444
+55 63 -1.49068
+67 63 1
+48 64 1.11801
+52 64 0.444444
+55 64 -1.11801
+67 64 1
+49 65 0.745342
+53 65 0.444444
+55 65 -0.745342
+67 65 1
+54 66 0.444444
+55 66 -0.372671
+67 66 1
+46 67 -0.144335
+47 67 -0.191856
+48 67 -0.24215
+49 67 -0.254119
+55 67 1
diff --git a/UMFPACK/Makefile b/UMFPACK/Makefile
new file mode 100644
index 0000000..a707234
--- /dev/null
+++ b/UMFPACK/Makefile
@@ -0,0 +1,79 @@
+#-------------------------------------------------------------------------------
+# UMFPACK makefile (for GNU make or original make)
+#-------------------------------------------------------------------------------
+
+# UMFPACK requires the AMD package to be in ../AMD
+
+default: library
+
+include ../UFconfig/UFconfig.mk
+
+# compile all C code (except hb, fortran, and fortran64), including AMD and the
+# MATLAB mexFunctions
+all:
+ ( cd ../AMD ; $(MAKE) library )
+ ( cd ../AMD ; $(MAKE) mex )
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+ ( cd MATLAB ; $(MAKE) )
+ - cat Doc/License
+
+# compile just the C-callable libraries and demo programs (not mexFunctions)
+library:
+ ( cd ../AMD ; $(MAKE) library )
+ ( cd Lib ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
+ - cat Doc/License
+
+# compile the FORTRAN interface and demo program
+fortran:
+ ( cd Demo ; $(MAKE) fortran )
+
+# compile the 64-bit FORTRAN interface and demo program
+fortran64:
+ ( cd Demo ; $(MAKE) fortran64 )
+
+# compile the Harwell/Boeing demo program
+hb:
+ ( cd Demo ; $(MAKE) hb )
+
+# remove object files, but keep the compiled programs and library archives
+clean:
+ ( cd ../AMD ; $(MAKE) clean )
+ ( cd Lib ; $(MAKE) clean )
+ ( cd Demo ; $(MAKE) clean )
+ ( cd MATLAB ; $(MAKE) clean )
+ ( cd Doc ; $(MAKE) clean )
+
+# clean, and then remove compiled programs and library archives
+purge:
+ ( cd ../AMD ; $(MAKE) purge )
+ ( cd Lib ; $(MAKE) purge )
+ ( cd Demo ; $(MAKE) purge )
+ ( cd MATLAB ; $(MAKE) purge )
+ ( cd Doc ; $(MAKE) purge )
+
+# create PDF documents for the original distribution
+doc:
+ ( cd ../AMD ; $(MAKE) doc )
+ ( cd Doc ; $(MAKE) )
+
+# get ready for distribution
+dist: purge
+ ( cd ../AMD ; $(MAKE) dist )
+ ( cd Demo ; $(MAKE) dist )
+ ( cd Doc ; $(MAKE) )
+
+distclean: purge
+
+ccode: library
+
+# compile the MATLAB mexFunction
+mex:
+ ( cd ../AMD/MATLAB ; $(MAKE) )
+ ( cd MATLAB ; $(MAKE) )
+
+# statement coverage (requires Linux; takes a lot of time and disk space)
+cov: purge
+ ( cd Tcov ; ./DO.linux ; ./covall )
+
diff --git a/UMFPACK/README.txt b/UMFPACK/README.txt
new file mode 100644
index 0000000..d4f9d7b
--- /dev/null
+++ b/UMFPACK/README.txt
@@ -0,0 +1,405 @@
+UMFPACK : a set of routines solving sparse linear systems via LU
+ factorization. Requires three other packages: the BLAS (dense matrix
+ operations), AMD (sparse matrix minimum degree ordering), and UFconfig.
+ Includes a C-callable and MATLAB interface, and a basic FORTRAN 77
+ interface to a subset of the C-callable routines. Requires AMD Version
+ 2.0 or later.
+
+The AMD, UFconfig, and UMFPACK directories must all reside in the same parent
+directory.
+
+Quick start (Unix, or Windows with Cygwin):
+
+ To compile, test, and install both UMFPACK and AMD, the UMFPACK and AMD
+ directories must be in the same parent directory. To configure, edit
+ the UFconfig/UFconfig.mk file (otherwise, you may get warnings that the
+ BLAS (dgemm, etc) are not found). You may use UMFPACK_CONFIG = -DNBLAS in
+ the UFconfig/UFconfig.mk file, to avoid using the BLAS, but UMFPACK will be
+ slow. Next, cd to this directory (UMFPACK) and type "make". To compile
+ and run a FORTRAN demo program for Harwell/Boeing matrices, type "make hb".
+ To compile a FORTRAN main program that calls the 32-bit C-callable UMFPACK
+ library, type "make fortran". When done, type "make clean" to remove
+ unused *.o files (keeps the compiled libraries and demo programs). See
+ the User Guide (Doc/UserGuide.pdf), or ../UFconfig/UFconfig.mk for more
+ details (including options for compiling in 64-bit mode).
+
+Quick start (for MATLAB users):
+
+ To compile, test, and install the UMFPACK mexFunction, cd to the
+ UMFPACK/MATLAB directory and type umfpack_make at the MATLAB prompt.
+
+ NOTE: DO NOT ATTEMPT TO USE THIS CODE IN 64-BIT MATLAB (v7.3).
+ It is not yet ported to that version of MATLAB.
+
+--------------------------------------------------------------------------------
+
+UMFPACK, Copyright (c) 1995-2006 by Timothy A. Davis. All Rights Reserved.
+UMFPACK is available under alternate licences; contact T. Davis for details.
+
+UMFPACK License:
+
+ Your use or distribution of UMFPACK or any modified version of
+ UMFPACK implies that you agree to this License.
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU General Public
+ License as published by the Free Software Foundation; either
+ version 2 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
+ USA
+
+ Permission is hereby granted to use or copy this program under the
+ terms of the GNU GPL, provided that the Copyright, this License,
+ and the Availability of the original version is retained on all copies.
+ User documentation of any code that uses this code or any modified
+ version of this code must cite the Copyright, this License, the
+ Availability note, and "Used by permission." Permission to modify
+ the code and to distribute modified code is granted, provided the
+ Copyright, this License, and the Availability note are retained,
+ and a notice that the code was modified is included.
+
+Availability:
+
+ http://www.cise.ufl.edu/research/sparse/umfpack
+
+ UMFPACK (including versions 2.2.1 and earlier, in FORTRAN) is available at
+ http://www.cise.ufl.edu/research/sparse. MA38 is available in the Harwell
+ Subroutine Library. This version of UMFPACK includes a modified form of
+ COLAMD Version 2.0, originally released on Jan. 31, 2000, also available at
+ http://www.cise.ufl.edu/research/sparse. COLAMD V2.0 is also incorporated
+ as a built-in function in MATLAB version 6.1, by The MathWorks, Inc.
+ (http://www.mathworks.com). COLAMD V1.0 appears as a column-preordering
+ in SuperLU (SuperLU is available at http://www.netlib.org).
+ UMFPACK v4.0 is a built-in routine in MATLAB 6.5.
+ UMFPACK v4.3 is a built-in routine in MATLAB 7.1.
+
+--------------------------------------------------------------------------------
+
+Refer to ../AMD/README for the License for AMD, which is a separate
+package for ordering sparse matrices that is required by UMFPACK.
+UMFPACK v4.5 cannot use AMD v1.1 or earlier. UMFPACK 5.x
+requires AMD v2.0 or later.
+
+--------------------------------------------------------------------------------
+
+This is the UMFPACK README.txt file. It is a terse overview of UMFPACK.
+Refer to the User Guide (Doc/UserGuide.pdf) for how to install and use UMFPACK,
+or to the Quick Start Guide, QuickStart.pdf.
+
+Description:
+
+ UMFPACK is a set of routines for solving unsymmetric sparse linear systems,
+ Ax=b, using the Unsymmetric MultiFrontal method. Written in ANSI/ISO C,
+ with a MATLAB (Version 6.0 or later) interface.
+
+ For best performance, UMFPACK requires an optimized BLAS library. It can
+ also be compiled without any BLAS at all. UMFPACK requires AMD Version 2.0.
+
+Authors:
+
+ Timothy A. Davis (davis at cise.ufl.edu), University of Florida.
+
+ Includes a modified version of COLAMD V2.0, by Stefan I. Larimore and
+ Timothy A. Davis, University of Florida. The COLAMD algorithm was developed
+ in collaboration with John Gilbert, Xerox Palo Alto Research Center, and
+ Esmond Ng, Lawrence Berkeley National Laboratory.
+
+ Includes AMD, by Timothy A. Davis, Patrick R. Amestoy, and Iain S. Duff.
+
+ UMFPACK Version 2.2.1 (MA38 in the Harwell Subroutine Library) is
+ co-authored with Iain S. Duff, Rutherford Appleton Laboratory.
+
+Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+
+ Portions of this work were done while on sabbatical at Stanford University
+ and Lawrence Berkeley National Laboratory (with funding from the SciDAC
+ program). I would like to thank Gene Golub, Esmond Ng, and Horst Simon
+ for making this sabbatical possible.
+
+ I would also like to thank the many researchers who provided sparse
+ matrices from a wide range of domains and used earlier versions of UMFPACK/
+ MA38 in their applications, and thus assisted in the practical development
+ of the algorithm (see http://www.cise.ufl.edu/research/sparse, future
+ contributions of matrices are always welcome).
+
+ The MathWorks, Inc., provided a pre-release of MATLAB V6 which allowed me
+ to release the first umfpack mexFunction (v3.0) about 6 months earlier than
+ I had originally planned. They also supported the extension of UMFPACK to
+ complex, singular, and rectangular matrices (UMFPACK v4.0).
+
+ Penny Anderson (The MathWorks, Inc.), Anshul Gupta (IBM), and Friedrich
+ Grund (WAIS) assisted in porting UMFPACK to different platforms. Penny
+ Anderson also incorporated UMFPACK v4.0 into MATLAB, for lu, backslash (\),
+ and forward slash (/).
+
+ David Bateman (Motorola) wrote the initial version of the packed complex
+ input option, and umfpack_get_determinant.
+
+--------------------------------------------------------------------------------
+Files and directories in the UMFPACK distribution:
+--------------------------------------------------------------------------------
+
+ ----------------------------------------------------------------------------
+ Subdirectories of the UMFPACK directory:
+ ----------------------------------------------------------------------------
+
+ Doc documentation
+ Source primary source code
+ Include include files for use in your code that calls UMFPACK
+ Demo demo programs. also serves as test of the UMFPACK installation.
+ MATLAB UMFPACK mexFunction for MATLAB, and supporting m-files
+ Lib where the compiled C-callable UMFPACK library is placed.
+
+ ----------------------------------------------------------------------------
+ Files in the UMFPACK directory:
+ ----------------------------------------------------------------------------
+
+ Makefile top-level Makefile for GNU make or original make.
+ Windows users would require Cygwin to use "make"
+
+ README.txt this file
+
+ ----------------------------------------------------------------------------
+ Doc directory: documentation
+ ----------------------------------------------------------------------------
+
+ ChangeLog change log
+ License the UMFPACK License
+ Makefile for creating the documentation
+ QuickStart.tex Quick Start guide (source)
+ QuickStart.pdf Quick Start guide (PDF)
+ UserGuide.bib User Guide (references)
+ UserGuide.sed1 sed script for processing UserGuide.stex
+ UserGuide.sed2 sed script for processing UserGuide.stex
+ UserGuide.stex User Guide (LaTeX)
+ UserGuide.pdf User Guide (PDF)
+
+ ----------------------------------------------------------------------------
+ Source directory:
+ ----------------------------------------------------------------------------
+
+ cholmod_blas.h an exact copy of CHOLMOD/Include/cholmod_blas.h
+
+ umfpack_col_to_triplet.c convert col form to triplet
+ umfpack_defaults.c set Control defaults
+ umfpack_free_numeric.c free Numeric object
+ umfpack_free_symbolic.c free Symbolic object
+ umfpack_get_determinant.c compute determinant from Numeric object
+ umfpack_get_lunz.c get nz's in L and U
+ umfpack_get_numeric.c get Numeric object
+ umfpack_get_symbolic.c get Symbolic object
+ umfpack_load_numeric.c load Numeric object from file
+ umfpack_load_symbolic.c load Symbolic object from file
+ umfpack_numeric.c numeric factorization
+ umfpack_qsymbolic.c symbolic factorization, user Q
+ umfpack_report_control.c print Control settings
+ umfpack_report_info.c print Info statistics
+ umfpack_report_matrix.c print col or row-form sparse matrix
+ umfpack_report_numeric.c print Numeric object
+ umfpack_report_perm.c print permutation
+ umfpack_report_status.c print return status
+ umfpack_report_symbolic.c print Symbolic object
+ umfpack_report_triplet.c print triplet matrix
+ umfpack_report_vector.c print dense vector
+ umfpack_save_numeric.c save Numeric object to file
+ umfpack_save_symbolic.c save Symbolic object to file
+ umfpack_scale.c scale a vector
+ umfpack_solve.c solve a linear system
+ umfpack_symbolic.c symbolic factorization
+ umfpack_tictoc.c timer
+ umfpack_timer.c timer
+ umfpack_transpose.c transpose a matrix
+ umfpack_triplet_to_col.c convert triplet to col form
+
+ umf_config.h configuration file (BLAS, memory, timer)
+ umf_internal.h definitions internal to UMFPACK
+ umf_version.h version definitions (int/UF_long, real/complex)
+
+ umf_2by2.[ch]
+ umf_analyze.[ch] symbolic factorization of A'*A
+ umf_apply_order.[ch] apply column etree postorder
+ umf_assemble.[ch] assemble elements into current front
+ umf_blas3_update.[ch] rank-k update. Uses level-3 BLAS
+ umf_build_tuples.[ch] construct tuples for elements
+ umf_colamd.[ch] COLAMD pre-ordering, modified for UMFPACK
+ umf_create_element.[ch] create a new element
+ umf_dump.[ch] debugging routines, not normally active
+ umf_extend_front.[ch] extend the current frontal matrix
+ umf_free.[ch] free memory
+ umf_fsize.[ch] determine largest front in each subtree
+ umf_garbage_collection.[ch] compact Numeric->Memory
+ umf_get_memory.[ch] make Numeric->Memory bigger
+ umf_grow_front.[ch] make current frontal matrix bigger
+ umf_init_front.[ch] initialize a new frontal matrix
+ umf_is_permutation.[ch] checks the validity of a permutation vector
+ umf_kernel.[ch] the main numeric factorization kernel
+ umf_kernel_init.[ch] initializations for umf_kernel
+ umf_kernel_wrapup.[ch] wrapup for umf_kernel
+ umf_local_search.[ch] local row and column pivot search
+ umf_lsolve.[ch] solve Lx=b
+ umf_ltsolve.[ch] solve L'x=b and L.'x=b
+ umf_malloc.[ch] malloc some memory
+ umf_mem_alloc_element.[ch] allocate element in Numeric->Memory
+ umf_mem_alloc_head_block.[ch] alloc. block at head of Numeric->Memory
+ umf_mem_alloc_tail_block.[ch] alloc. block at tail of Numeric->Memory
+ umf_mem_free_tail_block.[ch] free block at tail of Numeric->Memory
+ umf_mem_init_memoryspace.[ch] initialize Numeric->Memory
+ umf_realloc.[ch] realloc memory
+ umf_report_perm.[ch] print a permutation vector
+ umf_report_vector.[ch] print a double vector
+ umf_row_search.[ch] look for a pivot row
+ umf_scale.[ch] scale the pivot column
+ umf_scale_column.[ch] move pivot row & column into place, log P and Q
+ umf_set_stats.[ch] set statistics (final or estimates)
+ umf_singletons.[ch] find all zero-cost pivots
+ umf_solve.[ch] solve a linear system
+ umf_start_front.[ch] start a new frontal matrix for one frontal chain
+ umf_store_lu.[ch] store LU factors of current front
+ umf_symbolic_usage.[ch] determine memory usage for Symbolic object
+ umf_transpose.[ch] transpose a matrix in row or col form
+ umf_triplet.[ch] convert triplet to column form
+ umf_tuple_lengths.[ch] determine the tuple list lengths
+ umf_usolve.[ch] solve Ux=b
+ umf_utsolve.[ch] solve U'x=b and U.'x=b
+ umf_valid_numeric.[ch] checks the validity of a Numeric object
+ umf_valid_symbolic.[ch] check the validity of a Symbolic object
+
+ ----------------------------------------------------------------------------
+ Include directory:
+ ----------------------------------------------------------------------------
+
+ umfpack.h include file for user programs. Includes all of
+ the following files. This serves are source-
+ code level documenation. These files are also
+ used to construct the User Guide.
+
+ umfpack_col_to_triplet.h
+ umfpack_defaults.h
+ umfpack_free_numeric.h
+ umfpack_free_symbolic.h
+ umfpack_get_determinant.h
+ umfpack_get_lunz.h
+ umfpack_get_numeric.h
+ umfpack_get_symbolic.h
+ umfpack_load_numeric.h
+ umfpack_load_symbolic.h
+ umfpack_numeric.h
+ umfpack_qsymbolic.h
+ umfpack_report_control.h
+ umfpack_report_info.h
+ umfpack_report_matrix.h
+ umfpack_report_numeric.h
+ umfpack_report_perm.h
+ umfpack_report_status.h
+ umfpack_report_symbolic.h
+ umfpack_report_triplet.h
+ umfpack_report_vector.h
+ umfpack_save_numeric.h
+ umfpack_save_symbolic.h
+ umfpack_scale.h
+ umfpack_solve.h
+ umfpack_symbolic.h
+ umfpack_tictoc.h
+ umfpack_timer.h
+ umfpack_transpose.h
+ umfpack_triplet_to_col.h
+
+ umfpack_wsolve.h note that there is no umfpack_wsolve.c. The
+ umfpack_*_wsolve routines are created from the
+ umfpack_solve.c file.
+
+ ----------------------------------------------------------------------------
+ Demo directory:
+ ----------------------------------------------------------------------------
+
+ Makefile for GNU make or original make
+
+ umfpack_simple.c a simple demo
+ umpack_xx_demo.c template to create the demo codes below
+
+ umfpack_di_demo.sed for creating umfpack_di_demo.c
+ umfpack_dl_demo.sed for creating umfpack_dl_demo.c
+ umfpack_zi_demo.sed for creating umfpack_zi_demo.c
+ umfpack_zl_demo.sed for creating umfpack_zl_demo.c
+
+ umfpack_di_demo.c a full demo (real/int version)
+ umfpack_dl_demo.c a full demo (real/UF_long version)
+ umfpack_zi_demo.c a full demo (complex/int version)
+ umfpack_zl_demo.c a full demo (complex/UF_long version)
+
+ umfpack_di_demo.out umfpack_di_demo output
+ umfpack_dl_demo.out umfpack_dl_demo output
+ umfpack_zi_demo.out umfpack_zi_demo output
+ umfpack_zl_demo.out umfpack_zl_demo output
+
+ umf4.c a demo (real/int) for Harwell/Boeing matrices
+ umf4.out output of "make hb"
+ HB directory of sample Harwell/Boeing matrices
+ readhb.f reads HB matrices, keeps zero entries
+ readhb_nozeros.f reads HB matrices, removes zero entries
+ readhb_size.f reads HB matrix dimension, nnz
+ tmp empty directory for umf4.c demo
+
+ umf4_f77wrapper.c a simple FORTRAN interface for UMFPACK.
+ compile with "make fortran"
+ umf4hb.f a demo of the FORTRAN interface
+ umf4hb.out output of "make fortran"
+
+ umf4_f77zwrapper.c a simple FORTRAN interface for the complex
+ UMFPACK routines. compile with "make fortran"
+ umf4zhb.f a demo of the FORTRAN interface (complex)
+ umf4zhb.out output of umf4zhb with HB/qc324.cua
+
+ umf4hb64.f 64-bit version of umf4hb.f
+
+ simple_compile a single command that compiles the double/int
+ version of UMFPACK (useful prototype for
+ Microsoft Visual Studio project)
+
+ ----------------------------------------------------------------------------
+ MATLAB directory:
+ ----------------------------------------------------------------------------
+
+ Contents.m for "help umfpack" listing of toolbox contents
+ GNUmakefile a nice Makefile, for GNU make
+ Makefile an ugly Unix Makefile (for older make's)
+
+ lu_normest.m 1-norm estimate of A-L*U (by Hager & Davis).
+ luflop.m for "help luflop"
+ luflopmex.c luflop mexFunction, for computing LU flop count
+ umfpack.m for "help umfpack"
+ umfpack_btf.m solve Ax=b using umfpack and dmperm
+ umfpack_demo.m a full umfpack demo
+ umfpack_details.m the details of how to use umfpack
+ umfpack_make.m compile the umfpack mexFunction within MATLAB
+ umfpack_report.m report statistics
+ umfpack_simple.m a simple umfpack demo
+ umfpack_solve.m x=A\b or b/A for arbitrary b
+ umfpack_test.m extensive test, requires UF sparse matrices
+ umfpackmex.c the umfpack mexFunction
+ west0067.mat sparse matrix for umfpack_demo.m
+
+ umfpack_demo.m.out output of umfpack_demo.m
+ umfpack_simple.m.out output of umfpack_simple
+
+ lcc_lib/lapacksyms.def LAPACK definitions for lcc compiler (Windows)
+ lcc_lib/libmwlapack.lib LAPACK definitions for lcc compiler (Windows)
+
+ ----------------------------------------------------------------------------
+ Lib directory: libumfpack.a library placed here
+ ----------------------------------------------------------------------------
+
+ GNUmakefile a nice Makefile, for GNU make
+ Makefile an ugly Unix Makefile (for older make's)
+ libumfpack.def UMPFACK definitions for Windows
diff --git a/UMFPACK/Source/cholmod_blas.h b/UMFPACK/Source/cholmod_blas.h
new file mode 100644
index 0000000..7957968
--- /dev/null
+++ b/UMFPACK/Source/cholmod_blas.h
@@ -0,0 +1,451 @@
+/* ========================================================================== */
+/* === Include/cholmod_blas.h =============================================== */
+/* ========================================================================== */
+
+/* -----------------------------------------------------------------------------
+ * CHOLMOD/Include/cholmod_blas.h.
+ * Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
+ * CHOLMOD/Include/cholmod_blas.h is licensed under Version 2.1 of the GNU
+ * Lesser General Public License. See lesser.txt for a text of the license.
+ * CHOLMOD is also available under other licenses; contact authors for details.
+ * http://www.cise.ufl.edu/research/sparse
+ * -------------------------------------------------------------------------- */
+
+/* This does not need to be included in the user's program. */
+
+#ifndef CHOLMOD_BLAS_H
+#define CHOLMOD_BLAS_H
+
+/* ========================================================================== */
+/* === Architecture ========================================================= */
+/* ========================================================================== */
+
+#if defined (__sun) || defined (MSOL2) || defined (ARCH_SOL2)
+#define CHOLMOD_SOL2
+#define CHOLMOD_ARCHITECTURE "Sun Solaris"
+
+#elif defined (__sgi) || defined (MSGI) || defined (ARCH_SGI)
+#define CHOLMOD_SGI
+#define CHOLMOD_ARCHITECTURE "SGI Irix"
+
+#elif defined (__linux) || defined (MGLNX86) || defined (ARCH_GLNX86)
+#define CHOLMOD_LINUX
+#define CHOLMOD_ARCHITECTURE "Linux"
+
+#elif defined (_AIX) || defined (MIBM_RS) || defined (ARCH_IBM_RS)
+#define CHOLMOD_AIX
+#define CHOLMOD_ARCHITECTURE "IBM AIX"
+#define BLAS_NO_UNDERSCORE
+
+#elif defined (__alpha) || defined (MALPHA) || defined (ARCH_ALPHA)
+#define CHOLMOD_ALPHA
+#define CHOLMOD_ARCHITECTURE "Compaq Alpha"
+
+#elif defined (_WIN32) || defined (WIN32) || defined (_WIN64) || defined (WIN64)
+#if defined (__MINGW32__) || defined (__MINGW32__)
+#define CHOLMOD_MINGW
+#elif defined (__CYGWIN32__) || defined (__CYGWIN32__)
+#define CHOLMOD_CYGWIN
+#else
+#define CHOLMOD_WINDOWS
+#define BLAS_NO_UNDERSCORE
+#endif
+#define CHOLMOD_ARCHITECTURE "Microsoft Windows"
+
+#elif defined (__hppa) || defined (__hpux) || defined (MHPUX) || defined (ARCH_HPUX)
+#define CHOLMOD_HP
+#define CHOLMOD_ARCHITECTURE "HP Unix"
+#define BLAS_NO_UNDERSCORE
+
+#elif defined (__hp700) || defined (MHP700) || defined (ARCH_HP700)
+#define CHOLMOD_HP
+#define CHOLMOD_ARCHITECTURE "HP 700 Unix"
+#define BLAS_NO_UNDERSCORE
+
+#else
+/* If the architecture is unknown, and you call the BLAS, you may need to */
+/* define BLAS_BY_VALUE, BLAS_NO_UNDERSCORE, and/or BLAS_CHAR_ARG yourself. */
+#define CHOLMOD_ARCHITECTURE "unknown"
+#endif
+
+
+/* ========================================================================== */
+/* === BLAS and LAPACK names ================================================ */
+/* ========================================================================== */
+
+/* Prototypes for the various versions of the BLAS. */
+
+/* Determine if the 64-bit Sun Performance BLAS is to be used */
+#if defined(CHOLMOD_SOL2) && !defined(NSUNPERF) && defined(LONG) && defined(LONGBLAS)
+#define SUN64
+#endif
+
+#ifdef SUN64
+
+#define BLAS_DTRSV dtrsv_64_
+#define BLAS_DGEMV dgemv_64_
+#define BLAS_DTRSM dtrsm_64_
+#define BLAS_DGEMM dgemm_64_
+#define BLAS_DSYRK dsyrk_64_
+#define BLAS_DGER dger_64_
+#define BLAS_DSCAL dscal_64_
+#define LAPACK_DPOTRF dpotrf_64_
+
+#define BLAS_ZTRSV ztrsv_64_
+#define BLAS_ZGEMV zgemv_64_
+#define BLAS_ZTRSM ztrsm_64_
+#define BLAS_ZGEMM zgemm_64_
+#define BLAS_ZHERK zherk_64_
+#define BLAS_ZGER zgeru_64_
+#define BLAS_ZSCAL zscal_64_
+#define LAPACK_ZPOTRF zpotrf_64_
+
+#elif defined (BLAS_NO_UNDERSCORE)
+
+#define BLAS_DTRSV dtrsv
+#define BLAS_DGEMV dgemv
+#define BLAS_DTRSM dtrsm
+#define BLAS_DGEMM dgemm
+#define BLAS_DSYRK dsyrk
+#define BLAS_DGER dger
+#define BLAS_DSCAL dscal
+#define LAPACK_DPOTRF dpotrf
+
+#define BLAS_ZTRSV ztrsv
+#define BLAS_ZGEMV zgemv
+#define BLAS_ZTRSM ztrsm
+#define BLAS_ZGEMM zgemm
+#define BLAS_ZHERK zherk
+#define BLAS_ZGER zgeru
+#define BLAS_ZSCAL zscal
+#define LAPACK_ZPOTRF zpotrf
+
+#else
+
+#define BLAS_DTRSV dtrsv_
+#define BLAS_DGEMV dgemv_
+#define BLAS_DTRSM dtrsm_
+#define BLAS_DGEMM dgemm_
+#define BLAS_DSYRK dsyrk_
+#define BLAS_DGER dger_
+#define BLAS_DSCAL dscal_
+#define LAPACK_DPOTRF dpotrf_
+
+#define BLAS_ZTRSV ztrsv_
+#define BLAS_ZGEMV zgemv_
+#define BLAS_ZTRSM ztrsm_
+#define BLAS_ZGEMM zgemm_
+#define BLAS_ZHERK zherk_
+#define BLAS_ZGER zgeru_
+#define BLAS_ZSCAL zscal_
+#define LAPACK_ZPOTRF zpotrf_
+
+#endif
+
+/* ========================================================================== */
+/* === BLAS and LAPACK integer arguments ==================================== */
+/* ========================================================================== */
+
+/* CHOLMOD can be compiled with -D'LONGBLAS=long' for the Sun Performance
+ * Library, or -D'LONGBLAS=long long' for SGI's SCSL BLAS. This defines the
+ * integer used in the BLAS for the cholmod_l_* routines.
+ *
+ * The "int" version of CHOLMOD always uses the "int" version of the BLAS.
+ */
+
+#if defined (LONGBLAS) && defined (LONG)
+#define BLAS_INT LONGBLAS
+#else
+#define BLAS_INT int
+#endif
+
+/* If the BLAS integer is smaller than the basic CHOLMOD integer, then we need
+ * to check for integer overflow when converting from one to the other. If
+ * any integer overflows, the externally-defined blas_ok variable is set to
+ * FALSE. blas_ok should be set to TRUE before calling any BLAS_* macro.
+ */
+
+#define CHECK_BLAS_INT (sizeof (BLAS_INT) < sizeof (Int))
+#define EQ(K,k) (((BLAS_INT) K) == ((Int) k))
+
+/* ========================================================================== */
+/* === BLAS and LAPACK prototypes and macros ================================ */
+/* ========================================================================== */
+
+void BLAS_DGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta,
+ double *Y, BLAS_INT *incy) ;
+
+#define BLAS_dgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_ZGEMV (char *trans, BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *A, BLAS_INT *lda, double *X, BLAS_INT *incx, double *beta,
+ double *Y, BLAS_INT *incy) ;
+
+#define BLAS_zgemv(trans,m,n,alpha,A,lda,X,incx,beta,Y,incy) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGEMV (trans, &M, &N, alpha, A, &LDA, X, &INCX, beta, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_DTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A,
+ BLAS_INT *lda, double *X, BLAS_INT *incx) ;
+
+#define BLAS_dtrsv(uplo,trans,diag,n,A,lda,X,incx) \
+{ \
+ BLAS_INT N = n, LDA = lda, INCX = incx ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \
+ } \
+}
+
+void BLAS_ZTRSV (char *uplo, char *trans, char *diag, BLAS_INT *n, double *A,
+ BLAS_INT *lda, double *X, BLAS_INT *incx) ;
+
+#define BLAS_ztrsv(uplo,trans,diag,n,A,lda,X,incx) \
+{ \
+ BLAS_INT N = n, LDA = lda, INCX = incx ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZTRSV (uplo, trans, diag, &N, A, &LDA, X, &INCX) ; \
+ } \
+}
+
+void BLAS_DTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m,
+ BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb) ;
+
+#define BLAS_dtrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\
+ } \
+}
+
+void BLAS_ZTRSM (char *side, char *uplo, char *transa, char *diag, BLAS_INT *m,
+ BLAS_INT *n, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb) ;
+
+#define BLAS_ztrsm(side,uplo,transa,diag,m,n,alpha,A,lda,B,ldb) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, LDB = ldb ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (LDB,ldb) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZTRSM (side, uplo, transa, diag, &M, &N, alpha, A, &LDA, B, &LDB);\
+ } \
+}
+
+void BLAS_DGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n,
+ BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ;
+
+#define BLAS_dgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \
+{ \
+ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \
+ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \
+ C, &LDC) ; \
+ } \
+}
+
+void BLAS_ZGEMM (char *transa, char *transb, BLAS_INT *m, BLAS_INT *n,
+ BLAS_INT *k, double *alpha, double *A, BLAS_INT *lda, double *B,
+ BLAS_INT *ldb, double *beta, double *C, BLAS_INT *ldc) ;
+
+#define BLAS_zgemm(transa,transb,m,n,k,alpha,A,lda,B,ldb,beta,C,ldc) \
+{ \
+ BLAS_INT M = m, N = n, K = k, LDA = lda, LDB = ldb, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (K,k) && EQ (LDA,lda) \
+ && EQ (LDB,ldb) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGEMM (transa, transb, &M, &N, &K, alpha, A, &LDA, B, &LDB, beta, \
+ C, &LDC) ; \
+ } \
+}
+
+void BLAS_DSYRK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k,
+ double *alpha, double *A, BLAS_INT *lda, double *beta, double *C,
+ BLAS_INT *ldc) ;
+
+#define BLAS_dsyrk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \
+{ \
+ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DSYRK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \
+ } \
+} \
+
+void BLAS_ZHERK (char *uplo, char *trans, BLAS_INT *n, BLAS_INT *k,
+ double *alpha, double *A, BLAS_INT *lda, double *beta, double *C,
+ BLAS_INT *ldc) ;
+
+#define BLAS_zherk(uplo,trans,n,k,alpha,A,lda,beta,C,ldc) \
+{ \
+ BLAS_INT N = n, K = k, LDA = lda, LDC = ldc ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (K,k) && EQ (LDA,lda) && EQ (LDC,ldc) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZHERK (uplo, trans, &N, &K, alpha, A, &LDA, beta, C, &LDC) ; \
+ } \
+} \
+
+void LAPACK_DPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda,
+ BLAS_INT *info) ;
+
+#define LAPACK_dpotrf(uplo,n,A,lda,info) \
+{ \
+ BLAS_INT N = n, LDA = lda, INFO = 1 ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \
+ } \
+ if (blas_ok) \
+ { \
+ LAPACK_DPOTRF (uplo, &N, A, &LDA, &INFO) ; \
+ } \
+ info = INFO ; \
+}
+
+void LAPACK_ZPOTRF (char *uplo, BLAS_INT *n, double *A, BLAS_INT *lda,
+ BLAS_INT *info) ;
+
+#define LAPACK_zpotrf(uplo,n,A,lda,info) \
+{ \
+ BLAS_INT N = n, LDA = lda, INFO = 1 ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (LDA,lda) ; \
+ } \
+ if (blas_ok) \
+ { \
+ LAPACK_ZPOTRF (uplo, &N, A, &LDA, &INFO) ; \
+ } \
+ info = INFO ; \
+}
+
+/* ========================================================================== */
+
+void BLAS_DSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ;
+
+#define BLAS_dscal(n,alpha,Y,incy) \
+{ \
+ BLAS_INT N = n, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DSCAL (&N, alpha, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_ZSCAL (BLAS_INT *n, double *alpha, double *Y, BLAS_INT *incy) ;
+
+#define BLAS_zscal(n,alpha,Y,incy) \
+{ \
+ BLAS_INT N = n, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (N,n) && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZSCAL (&N, alpha, Y, &INCY) ; \
+ } \
+}
+
+void BLAS_DGER (BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy,
+ double *A, BLAS_INT *lda) ;
+
+#define BLAS_dger(m,n,alpha,X,incx,Y,incy,A,lda) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_DGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \
+ } \
+}
+
+void BLAS_ZGER (BLAS_INT *m, BLAS_INT *n, double *alpha,
+ double *X, BLAS_INT *incx, double *Y, BLAS_INT *incy,
+ double *A, BLAS_INT *lda) ;
+
+#define BLAS_zgeru(m,n,alpha,X,incx,Y,incy,A,lda) \
+{ \
+ BLAS_INT M = m, N = n, LDA = lda, INCX = incx, INCY = incy ; \
+ if (CHECK_BLAS_INT) \
+ { \
+ blas_ok &= EQ (M,m) && EQ (N,n) && EQ (LDA,lda) && EQ (INCX,incx) \
+ && EQ (INCY,incy) ; \
+ } \
+ if (blas_ok) \
+ { \
+ BLAS_ZGER (&M, &N, alpha, X, &INCX, Y, &INCY, A, &LDA) ; \
+ } \
+}
+
+#endif
diff --git a/UMFPACK/Source/umf_2by2.c b/UMFPACK/Source/umf_2by2.c
new file mode 100644
index 0000000..0e31011
--- /dev/null
+++ b/UMFPACK/Source/umf_2by2.c
@@ -0,0 +1,860 @@
+/* ========================================================================== */
+/* === UMF_2by2 ============================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Not user-callable. Computes a row permutation P so that A (P,:) has a
+ * mostly zero-free diagonal, with large entries on the diagonal. It does this
+ * by swapping pairs of rows. Once a row is swapped it is not swapped again.
+ * This is a "cheap" assignment, not a complete max. transversal or
+ * bi-partite matching. It is only a partial matching. For most matrices
+ * for which this algorithm is used, however, the matching is complete (in
+ * UMFPACK this algorithm is used for matrices with roughly symmetric pattern,
+ * and these matrices typically have a mostly-zero-free diagonal to begin with.
+ * This algorithm is not meant to be used on arbitrary unsymmetric matrices
+ * (for those matrices, UMFPACK uses its unsymmetric strategy and does not
+ * use this algorithm).
+ *
+ * Even if incomplete, the matching is usually good enough for UMFPACK's
+ * symmetric strategy, which can easily pivot off the diagonal during numerical
+ * factorization if it finds a weak diagonal entry.
+ *
+ * The algorithms works as follows. First, row scaling factors are computed,
+ * and weak diagonal entries are found. A weak entry is a value A(k,k) whose
+ * absolute value is < tol * max (abs (A (:,k))). For each weak diagonal k in
+ * increasing order of degree in A+A', the algorithm finds an index j such
+ * that A (k,j) and A (j,k) are "large" (greater than or equal to tol times
+ * the largest magnitude in their columns). Row j must also not have already
+ * been swapped. Rows j and k are then swapped. If we come to a diagonal k
+ * that has already been swapped, then it is not modified. This case occurs
+ * for "oxo" pivots:
+ *
+ * k j
+ * k o x
+ * j x o
+ *
+ * which are swapped once to obtain
+ *
+ * k j
+ * j x o
+ * k o x
+ *
+ * These two rows are then not modified any further (A (j,j) was weak, but
+ * after one swap the permuted the jth diagonal entry is strong.
+ *
+ * This algorithm only works on square matrices (real, complex, or pattern-
+ * only). The numerical values are optional. If not present, each entry is
+ * treated as numerically acceptable (tol is ignored), and the algorithm
+ * operates by just using the pattern, not the values. Each column of the
+ * input matrix A must be sorted, with no duplicate entries. The matrix A
+ * can be optionally scaled prior to the numerical test. The matrix A (:,P)
+ * has the same diagonal entries as A (:,P), except in different order. So
+ * the output permutation P can also be used to swap the columns of A.
+ */
+
+#include "umf_internal.h"
+#include "umf_2by2.h"
+
+#ifndef NDEBUG
+#include "umf_is_permutation.h"
+#endif
+
+/* x is "weak" if it is less than ctol. If x or ctol are NaN, then define
+ * x as not "weak". This is a rather arbitrary choice, made to simplify the
+ * computation. On all but a PC with Microsoft C/C++, this test becomes
+ * ((x) - ctol < 0). */
+#define WEAK(x,ctol) (SCALAR_IS_LTZERO ((x)-(ctol)))
+
+/* For flag value in Next [col] */
+#define IS_WEAK -2
+
+/* ========================================================================== */
+/* === two_by_two =========================================================== */
+/* ========================================================================== */
+
+PRIVATE Int two_by_two /* returns # unmatched weak diagonals */
+(
+ /* input, not modified */
+ Int n2, /* C is n2-by-n2 */
+ Int Cp [ ], /* size n2+1, column pointers for C */
+ Int Ci [ ], /* size snz = Cp [n2], row indices for C */
+ Int Degree [ ], /* Degree [i] = degree of row i of C+C' */
+
+ /* input, not defined on output */
+ Int Next [ ], /* Next [k] == IS_WEAK if k is a weak diagonal */
+ Int Ri [ ], /* Ri [i] is the length of row i in C */
+
+ /* output, not defined on input */
+ Int P [ ],
+
+ /* workspace, not defined on input or output */
+ Int Rp [ ],
+ Int Head [ ]
+)
+{
+ Int deg, newcol, row, col, p, p2, unmatched, k, j, j2, j_best, best, jdiff,
+ jdiff_best, jdeg, jdeg_best, cp, cp1, cp2, rp, rp1, rp2, maxdeg,
+ mindeg ;
+
+ /* ---------------------------------------------------------------------- */
+ /* place weak diagonals in the degree lists */
+ /* ---------------------------------------------------------------------- */
+
+ for (deg = 0 ; deg < n2 ; deg++)
+ {
+ Head [deg] = EMPTY ;
+ }
+
+ maxdeg = 0 ;
+ mindeg = Int_MAX ;
+ for (newcol = n2-1 ; newcol >= 0 ; newcol--)
+ {
+ if (Next [newcol] == IS_WEAK)
+ {
+ /* add this column to the list of weak nodes */
+ DEBUGm1 ((" newcol "ID" has a weak diagonal deg "ID"\n",
+ newcol, deg)) ;
+ deg = Degree [newcol] ;
+ ASSERT (deg >= 0 && deg < n2) ;
+ Next [newcol] = Head [deg] ;
+ Head [deg] = newcol ;
+ maxdeg = MAX (maxdeg, deg) ;
+ mindeg = MIN (mindeg, deg) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct R = C' (C = strong entries in pruned submatrix) */
+ /* ---------------------------------------------------------------------- */
+
+ /* Ri [0..n2-1] is the length of each row of R */
+ /* use P as temporary pointer into the row form of R [ */
+ Rp [0] = 0 ;
+ for (row = 0 ; row < n2 ; row++)
+ {
+ Rp [row+1] = Rp [row] + Ri [row] ;
+ P [row] = Rp [row] ;
+ }
+ /* Ri no longer needed for row counts */
+
+ /* all entries in C are strong */
+ for (col = 0 ; col < n2 ; col++)
+ {
+ p2 = Cp [col+1] ;
+ for (p = Cp [col] ; p < p2 ; p++)
+ {
+ /* place the column index in row = Ci [p] */
+ Ri [P [Ci [p]]++] = col ;
+ }
+ }
+
+ /* contents of P no longer needed ] */
+
+#ifndef NDEBUG
+ DEBUG0 (("==================R: row form of strong entries in A:\n")) ;
+ UMF_dump_col_matrix ((double *) NULL,
+#ifdef COMPLEX
+ (double *) NULL,
+#endif
+ Ri, Rp, n2, n2, Rp [n2]) ;
+#endif
+ ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* for each weak diagonal, find a pair of strong off-diagonal entries */
+ /* ---------------------------------------------------------------------- */
+
+ for (row = 0 ; row < n2 ; row++)
+ {
+ P [row] = EMPTY ;
+ }
+
+ unmatched = 0 ;
+ best = EMPTY ;
+ jdiff = EMPTY ;
+ jdeg = EMPTY ;
+
+ for (deg = mindeg ; deg <= maxdeg ; deg++)
+ {
+ /* find the next weak diagonal of lowest degree */
+ DEBUGm2 (("---------------------------------- Deg: "ID"\n", deg)) ;
+ for (k = Head [deg] ; k != EMPTY ; k = Next [k])
+ {
+ DEBUGm2 (("k: "ID"\n", k)) ;
+ if (P [k] == EMPTY)
+ {
+ /* C (k,k) is a weak diagonal entry. Find an index j != k such
+ * that C (j,k) and C (k,j) are both strong, and also such
+ * that Degree [j] is minimized. In case of a tie, pick
+ * the smallest index j. C and R contain the pattern of
+ * strong entries only.
+ *
+ * Note that row k of R and column k of C are both sorted. */
+
+ DEBUGm4 (("===== Weak diagonal k = "ID"\n", k)) ;
+ DEBUG1 (("Column k of C:\n")) ;
+ for (p = Cp [k] ; p < Cp [k+1] ; p++)
+ {
+ DEBUG1 ((" "ID": deg "ID"\n", Ci [p], Degree [Ci [p]]));
+ }
+ DEBUG1 (("Row k of R (strong entries only):\n")) ;
+ for (p = Rp [k] ; p < Rp [k+1] ; p++)
+ {
+ DEBUG1 ((" "ID": deg "ID"\n", Ri [p], Degree [Ri [p]]));
+ }
+
+ /* no (C (k,j), C (j,k)) pair exists yet */
+ j_best = EMPTY ;
+ jdiff_best = Int_MAX ;
+ jdeg_best = Int_MAX ;
+
+ /* pointers into column k (including values) */
+ cp1 = Cp [k] ;
+ cp2 = Cp [k+1] ;
+ cp = cp1 ;
+
+ /* pointers into row k (strong entries only, no values) */
+ rp1 = Rp [k] ;
+ rp2 = Rp [k+1] ;
+ rp = rp1 ;
+
+ /* while entries searched in column k and row k */
+ while (TRUE)
+ {
+
+ if (cp >= cp2)
+ {
+ /* no more entries in this column */
+ break ;
+ }
+
+ /* get C (j,k), which is strong */
+ j = Ci [cp] ;
+
+ if (rp >= rp2)
+ {
+ /* no more entries in this column */
+ break ;
+ }
+
+ /* get R (k,j2), which is strong */
+ j2 = Ri [rp] ;
+
+ if (j < j2)
+ {
+ /* C (j,k) is strong, but R (k,j) is not strong */
+ cp++ ;
+ continue ;
+ }
+
+ if (j2 < j)
+ {
+ /* C (k,j2) is strong, but R (j2,k) is not strong */
+ rp++ ;
+ continue ;
+ }
+
+ /* j == j2: C (j,k) is strong and R (k,j) is strong */
+
+ best = FALSE ;
+
+ if (P [j] == EMPTY)
+ {
+ /* j has not yet been matched */
+ jdeg = Degree [j] ;
+ jdiff = SCALAR_ABS (k-j) ;
+
+ DEBUG1 (("Try candidate j "ID" deg "ID" diff "ID
+ "\n", j, jdeg, jdiff)) ;
+
+ if (j_best == EMPTY)
+ {
+ /* this is the first candidate seen */
+ DEBUG1 ((" first\n")) ;
+ best = TRUE ;
+ }
+ else
+ {
+ if (jdeg < jdeg_best)
+ {
+ /* the degree of j is best seen so far. */
+ DEBUG1 ((" least degree\n")) ;
+ best = TRUE ;
+ }
+ else if (jdeg == jdeg_best)
+ {
+ /* degree of j and j_best are the same */
+ /* tie break by nearest node number */
+ if (jdiff < jdiff_best)
+ {
+ DEBUG1 ((" tie degree, closer\n")) ;
+ best = TRUE ;
+ }
+ else if (jdiff == jdiff_best)
+ {
+ /* |j-k| = |j_best-k|. For any given k
+ * and j_best there is only one other j
+ * than can be just as close as j_best.
+ * Tie break by picking the smaller of
+ * j and j_best */
+ DEBUG1 ((" tie degree, as close\n"));
+ best = j < j_best ;
+ }
+ }
+ else
+ {
+ /* j has higher degree than best so far */
+ best = FALSE ;
+ }
+ }
+ }
+
+ if (best)
+ {
+ /* j is best match for k */
+ /* found a strong pair, A (j,k) and A (k,j) */
+ DEBUG1 ((" --- Found pair k: "ID" j: " ID
+ " jdeg: "ID" jdiff: "ID"\n",
+ k, j, jdeg, jdiff)) ;
+ ASSERT (jdiff != EMPTY) ;
+ ASSERT (jdeg != EMPTY) ;
+ j_best = j ;
+ jdeg_best = jdeg ;
+ jdiff_best = jdiff ;
+ }
+
+ /* get the next entries in column k and row k */
+ cp++ ;
+ rp++ ;
+ }
+
+ /* save the pair (j,k), if we found one */
+ if (j_best != EMPTY)
+ {
+ j = j_best ;
+ DEBUGm4 ((" --- best pair j: "ID" for k: "ID"\n", j, k)) ;
+ P [k] = j ;
+ P [j] = k ;
+ }
+ else
+ {
+ /* no match was found for k */
+ unmatched++ ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize the row permutation, P */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n2 ; k++)
+ {
+ if (P [k] == EMPTY)
+ {
+ P [k] = k ;
+ }
+ }
+ ASSERT (UMF_is_permutation (P, Rp, n2, n2)) ;
+
+ return (unmatched) ;
+}
+
+
+/* ========================================================================== */
+/* === UMF_2by2 ============================================================= */
+/* ========================================================================== */
+
+GLOBAL void UMF_2by2
+(
+ /* input, not modified: */
+ Int n, /* A is n-by-n */
+ const Int Ap [ ], /* size n+1 */
+ const Int Ai [ ], /* size nz = Ap [n] */
+ const double Ax [ ], /* size nz if present */
+#ifdef COMPLEX
+ const double Az [ ], /* size nz if present */
+#endif
+ double tol, /* tolerance for determining whether or not an
+ * entry is numerically acceptable. If tol <= 0
+ * then all numerical values ignored. */
+ Int scale, /* scaling to perform (none, sum, or max) */
+ Int Cperm1 [ ], /* singleton permutations */
+#ifndef NDEBUG
+ Int Rperm1 [ ], /* not needed, since Rperm1 = Cperm1 for submatrix S */
+#endif
+ Int InvRperm1 [ ], /* inverse of Rperm1 */
+ Int n1, /* number of singletons */
+ Int nempty, /* number of empty rows/cols */
+
+ /* input, contents undefined on output: */
+ Int Degree [ ], /* Degree [j] is the number of off-diagonal
+ * entries in row/column j of S+S', where
+ * where S = A (Cperm1 [n1..], Rperm1 [n1..]).
+ * Note that S is not used, nor formed. */
+
+ /* output: */
+ Int P [ ], /* P [k] = i means original row i is kth row in S(P,:)
+ * where S = A (Cperm1 [n1..], Rperm1 [n1..]) */
+ Int *p_nweak,
+ Int *p_unmatched,
+
+ /* workspace (not defined on input or output): */
+ Int Ri [ ], /* of size >= max (nz, n) */
+ Int Rp [ ], /* of size n+1 */
+ double Rs [ ], /* of size n if present. Rs = sum (abs (A),2) or
+ * max (abs (A),2), the sum or max of each row. Unused
+ * if scale is equal to UMFPACK_SCALE_NONE. */
+ Int Head [ ], /* of size n. Head pointers for bucket sort */
+ Int Next [ ], /* of size n. Next pointers for bucket sort */
+ Int Ci [ ], /* size nz */
+ Int Cp [ ] /* size n+1 */
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry aij ;
+ double cmax, value, rs, ctol, dvalue ;
+ Int k, p, row, col, do_values, do_sum, do_max, do_scale, nweak, weak,
+ p1, p2, dfound, unmatched, n2, oldrow, newrow, oldcol, newcol, pp ;
+#ifdef COMPLEX
+ Int split = SPLIT (Az) ;
+#endif
+#ifndef NRECIPROCAL
+ Int do_recip = FALSE ;
+#endif
+
+#ifndef NDEBUG
+ /* UMF_debug += 99 ; */
+ DEBUGm3 (("\n ==================================UMF_2by2: tol %g\n", tol)) ;
+ ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ;
+ for (k = n1 ; k < n - nempty ; k++)
+ {
+ ASSERT (Cperm1 [k] == Rperm1 [k]) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* determine scaling options */
+ /* ---------------------------------------------------------------------- */
+
+ /* use the values, but only if they are present */
+ /* ignore the values if tol <= 0 */
+ do_values = (tol > 0) && (Ax != (double *) NULL) ;
+ if (do_values && (Rs != (double *) NULL))
+ {
+ do_sum = (scale == UMFPACK_SCALE_SUM) ;
+ do_max = (scale == UMFPACK_SCALE_MAX) ;
+ }
+ else
+ {
+ /* no scaling */
+ do_sum = FALSE ;
+ do_max = FALSE ;
+ }
+ do_scale = do_max || do_sum ;
+ DEBUGm3 (("do_values "ID" do_sum "ID" do_max "ID" do_scale "ID"\n",
+ do_values, do_sum, do_max, do_scale)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row scaling, if requested */
+ /* ---------------------------------------------------------------------- */
+
+ /* see also umf_kernel_init */
+
+ if (do_scale)
+ {
+#ifndef NRECIPROCAL
+ double rsmin ;
+#endif
+ for (row = 0 ; row < n ; row++)
+ {
+ Rs [row] = 0.0 ;
+ }
+ for (col = 0 ; col < n ; col++)
+ {
+ p2 = Ap [col+1] ;
+ for (p = Ap [col] ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ rs = Rs [row] ;
+ if (!SCALAR_IS_NAN (rs))
+ {
+ if (SCALAR_IS_NAN (value))
+ {
+ /* if any entry in a row is NaN, then the scale factor
+ * for the row is NaN. It will be set to 1 later. */
+ Rs [row] = value ;
+ }
+ else if (do_max)
+ {
+ Rs [row] = MAX (rs, value) ;
+ }
+ else
+ {
+ Rs [row] += value ;
+ }
+ }
+ }
+ }
+#ifndef NRECIPROCAL
+ rsmin = Rs [0] ;
+ if (SCALAR_IS_ZERO (rsmin) || SCALAR_IS_NAN (rsmin))
+ {
+ rsmin = 1.0 ;
+ }
+#endif
+ for (row = 0 ; row < n ; row++)
+ {
+ /* do not scale an empty row, or a row with a NaN */
+ rs = Rs [row] ;
+ if (SCALAR_IS_ZERO (rs) || SCALAR_IS_NAN (rs))
+ {
+ Rs [row] = 1.0 ;
+ }
+#ifndef NRECIPROCAL
+ rsmin = MIN (rsmin, Rs [row]) ;
+#endif
+ }
+
+#ifndef NRECIPROCAL
+ /* multiply by the reciprocal if Rs is not too small */
+ do_recip = (rsmin >= RECIPROCAL_TOLERANCE) ;
+ if (do_recip)
+ {
+ /* invert the scale factors */
+ for (row = 0 ; row < n ; row++)
+ {
+ Rs [row] = 1.0 / Rs [row] ;
+ }
+ }
+#endif
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the max in each column and find diagonal */
+ /* ---------------------------------------------------------------------- */
+
+ nweak = 0 ;
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSERT (Rperm1 [k] >= 0 && Rperm1 [k] < n) ;
+ ASSERT (InvRperm1 [Rperm1 [k]] == k) ;
+ }
+#endif
+
+ n2 = n - n1 - nempty ;
+
+ /* use Ri to count the number of strong entries in each row */
+ for (row = 0 ; row < n2 ; row++)
+ {
+ Ri [row] = 0 ;
+ }
+
+ pp = 0 ;
+ ctol = 0 ;
+ dvalue = 1 ;
+
+ /* construct C = pruned submatrix, strong values only, column form */
+
+ for (k = n1 ; k < n - nempty ; k++)
+ {
+ oldcol = Cperm1 [k] ;
+ newcol = k - n1 ;
+ Next [newcol] = EMPTY ;
+ DEBUGm1 (("Column "ID" newcol "ID" oldcol "ID"\n", k, newcol, oldcol)) ;
+
+ Cp [newcol] = pp ;
+
+ dfound = FALSE ;
+ p1 = Ap [oldcol] ;
+ p2 = Ap [oldcol+1] ;
+ if (do_values)
+ {
+ cmax = 0 ;
+ dvalue = 0 ;
+
+ if (!do_scale)
+ {
+ /* no scaling */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ ASSERT (oldrow >= 0 && oldrow < n) ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ ASSERT (newrow >= -n1 && newrow < n2) ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ /* if either cmax or value is NaN, define cmax as NaN */
+ if (!SCALAR_IS_NAN (cmax))
+ {
+ if (SCALAR_IS_NAN (value))
+ {
+ cmax = value ;
+ }
+ else
+ {
+ cmax = MAX (cmax, value) ;
+ }
+ }
+ if (oldrow == oldcol)
+ {
+ /* we found the diagonal entry in this column */
+ dvalue = value ;
+ dfound = TRUE ;
+ ASSERT (newrow == newcol) ;
+ }
+ }
+ }
+#ifndef NRECIPROCAL
+ else if (do_recip)
+ {
+ /* multiply by the reciprocal */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ ASSERT (oldrow >= 0 && oldrow < n) ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ ASSERT (newrow >= -n1 && newrow < n2) ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ value *= Rs [oldrow] ;
+ /* if either cmax or value is NaN, define cmax as NaN */
+ if (!SCALAR_IS_NAN (cmax))
+ {
+ if (SCALAR_IS_NAN (value))
+ {
+ cmax = value ;
+ }
+ else
+ {
+ cmax = MAX (cmax, value) ;
+ }
+ }
+ if (oldrow == oldcol)
+ {
+ /* we found the diagonal entry in this column */
+ dvalue = value ;
+ dfound = TRUE ;
+ ASSERT (newrow == newcol) ;
+ }
+ }
+ }
+#endif
+ else
+ {
+ /* divide instead */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ ASSERT (oldrow >= 0 && oldrow < n) ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ ASSERT (newrow >= -n1 && newrow < n2) ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ value /= Rs [oldrow] ;
+ /* if either cmax or value is NaN, define cmax as NaN */
+ if (!SCALAR_IS_NAN (cmax))
+ {
+ if (SCALAR_IS_NAN (value))
+ {
+ cmax = value ;
+ }
+ else
+ {
+ cmax = MAX (cmax, value) ;
+ }
+ }
+ if (oldrow == oldcol)
+ {
+ /* we found the diagonal entry in this column */
+ dvalue = value ;
+ dfound = TRUE ;
+ ASSERT (newrow == newcol) ;
+ }
+ }
+ }
+
+ ctol = tol * cmax ;
+ DEBUGm1 ((" cmax col "ID" %g ctol %g\n", oldcol, cmax, ctol)) ;
+ }
+ else
+ {
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ ASSERT (oldrow >= 0 && oldrow < n) ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ ASSERT (newrow >= -n1 && newrow < n2) ;
+ if (newrow < 0) continue ;
+ Ci [pp++] = newrow ;
+ if (oldrow == oldcol)
+ {
+ /* we found the diagonal entry in this column */
+ ASSERT (newrow == newcol) ;
+ dfound = TRUE ;
+ }
+ /* count the entries in each column */
+ Ri [newrow]++ ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* flag the weak diagonals */
+ /* ------------------------------------------------------------------ */
+
+ if (!dfound)
+ {
+ /* no diagonal entry present */
+ weak = TRUE ;
+ }
+ else
+ {
+ /* diagonal entry is present, check its value */
+ weak = (do_values) ? WEAK (dvalue, ctol) : FALSE ;
+ }
+ if (weak)
+ {
+ /* flag this column as weak */
+ DEBUG0 (("Weak!\n")) ;
+ Next [newcol] = IS_WEAK ;
+ nweak++ ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* count entries in each row that are not numerically weak */
+ /* ------------------------------------------------------------------ */
+
+ if (do_values)
+ {
+ if (!do_scale)
+ {
+ /* no scaling */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ weak = WEAK (value, ctol) ;
+ if (!weak)
+ {
+ DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ;
+ Ci [pp++] = newrow ;
+ Ri [newrow]++ ;
+ }
+ }
+ }
+#ifndef NRECIPROCAL
+ else if (do_recip)
+ {
+ /* multiply by the reciprocal */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ value *= Rs [oldrow] ;
+ weak = WEAK (value, ctol) ;
+ if (!weak)
+ {
+ DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ;
+ Ci [pp++] = newrow ;
+ Ri [newrow]++ ;
+ }
+ }
+ }
+#endif
+ else
+ {
+ /* divide instead */
+ for (p = p1 ; p < p2 ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = InvRperm1 [oldrow] - n1 ;
+ if (newrow < 0) continue ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ value /= Rs [oldrow] ;
+ weak = WEAK (value, ctol) ;
+ if (!weak)
+ {
+ DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ;
+ Ci [pp++] = newrow ;
+ Ri [newrow]++ ;
+ }
+ }
+ }
+ }
+ }
+ Cp [n2] = pp ;
+ ASSERT (AMD_valid (n2, n2, Cp, Ci) == AMD_OK) ;
+
+ if (nweak == 0)
+ {
+ /* nothing to do, quick return */
+ DEBUGm2 (("\n =============================UMF_2by2: quick return\n")) ;
+ for (k = 0 ; k < n ; k++)
+ {
+ P [k] = k ;
+ }
+ *p_nweak = 0 ;
+ *p_unmatched = 0 ;
+ return ;
+ }
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n2 ; k++)
+ {
+ P [k] = EMPTY ;
+ }
+ for (k = 0 ; k < n2 ; k++)
+ {
+ ASSERT (Degree [k] >= 0 && Degree [k] < n2) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* find the 2-by-2 permutation */
+ /* ---------------------------------------------------------------------- */
+
+ /* The matrix S is now mapped to the index range 0 to n2-1. We have
+ * S = A (Rperm [n1 .. n-nempty-1], Cperm [n1 .. n-nempty-1]), and then
+ * C = pattern of strong entries in S. A weak diagonal k in S is marked
+ * with Next [k] = IS_WEAK. */
+
+ unmatched = two_by_two (n2, Cp, Ci, Degree, Next, Ri, P, Rp, Head) ;
+
+ /* ---------------------------------------------------------------------- */
+
+ *p_nweak = nweak ;
+ *p_unmatched = unmatched ;
+
+#ifndef NDEBUG
+ DEBUGm4 (("UMF_2by2: weak "ID" unmatched "ID"\n", nweak, unmatched)) ;
+ for (row = 0 ; row < n ; row++)
+ {
+ DEBUGm2 (("P ["ID"] = "ID"\n", row, P [row])) ;
+ }
+ DEBUGm2 (("\n =============================UMF_2by2: done\n\n")) ;
+#endif
+}
diff --git a/UMFPACK/Source/umf_2by2.h b/UMFPACK/Source/umf_2by2.h
new file mode 100644
index 0000000..3cb8b45
--- /dev/null
+++ b/UMFPACK/Source/umf_2by2.h
@@ -0,0 +1,36 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_2by2
+(
+ Int n,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ double tol,
+ Int scale,
+ Int Cperm1 [ ],
+#ifndef NDEBUG
+ Int Rperm1 [ ],
+#endif
+ Int InvRperm [ ],
+ Int n1,
+ Int nempty,
+ Int Degree [ ],
+ Int P [ ],
+ Int *p_nweak,
+ Int *p_nmatched,
+ Int Ri [ ],
+ Int Rp [ ],
+ double Rs [ ],
+ Int Head [ ],
+ Int Next [ ],
+ Int Si [ ],
+ Int Sp [ ]
+) ;
diff --git a/UMFPACK/Source/umf_analyze.c b/UMFPACK/Source/umf_analyze.c
new file mode 100644
index 0000000..62e65d6
--- /dev/null
+++ b/UMFPACK/Source/umf_analyze.c
@@ -0,0 +1,705 @@
+/* ========================================================================== */
+/* === UMF_analyze ========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Symbolic LL' factorization of A'*A, to get upper bounds on the size of
+ L and U for LU = PAQ, and to determine the frontal matrices and
+ (supernodal) column elimination tree. No fill-reducing column pre-ordering
+ is used.
+
+ Returns TRUE if successful, FALSE if out of memory. UMF_analyze can only
+ run out of memory if anzmax (which is Ap [n_row]) is too small.
+
+ Uses workspace of size O(nonzeros in A). On input, the matrix A is
+ stored in row-form at the tail end of Ai. It is destroyed on output.
+ The rows of A must be sorted by increasing first column index.
+ The matrix is assumed to be valid.
+
+ Empty rows and columns have already been removed.
+
+*/
+
+#include "umf_internal.h"
+#include "umf_analyze.h"
+#include "umf_apply_order.h"
+#include "umf_fsize.h"
+
+/* ========================================================================== */
+
+GLOBAL Int UMF_analyze
+(
+ Int n_row, /* A is n_row-by-n_col */
+ Int n_col,
+ Int Ai [ ], /* Ai [Ap [0]..Ap[n_row]-1]: column indices */
+ /* destroyed on output. Note that this is NOT the */
+ /* user's Ai that was passed to UMFPACK_*symbolic */
+ /* size of Ai, Ap [n_row] = anzmax >= anz + n_col */
+ /* Ap [0] must be => n_col. The space to the */
+ /* front of Ai is used as workspace. */
+
+ Int Ap [ ], /* of size MAX (n_row, n_col) + 1 */
+ /* Ap [0..n_row]: row pointers */
+ /* Row i is in Ai [Ap [i] ... Ap [i+1]-1] */
+
+ /* rows must have smallest col index first, or be */
+ /* in sorted form. Used as workspace of size n_col */
+ /* and destroyed. */
+
+ /* Note that this is NOT the */
+ /* user's Ap that was passed to UMFPACK_*symbolic */
+
+ Int Up [ ], /* workspace of size n_col, and output column perm.
+ * for column etree postorder. */
+
+ Int fixQ,
+
+ /* temporary workspaces: */
+ Int W [ ], /* W [0..n_col-1] */
+ Int Link [ ], /* Link [0..n_col-1] */
+
+ /* output: information about each frontal matrix: */
+ Int Front_ncols [ ], /* size n_col */
+ Int Front_nrows [ ], /* of size n_col */
+ Int Front_npivcol [ ], /* of size n_col */
+ Int Front_parent [ ], /* of size n_col */
+ Int *nfr_out,
+
+ Int *p_ncompactions /* number of compactions in UMF_analyze */
+)
+{
+ /* ====================================================================== */
+ /* ==== local variables ================================================= */
+ /* ====================================================================== */
+
+ Int j, j3, col, k, row, parent, j2, pdest, p, p2, thickness, npivots, nfr,
+ i, *Winv, kk, npiv, jnext, krow, knext, pfirst, jlast, ncompactions,
+ *Front_stack, *Front_order, *Front_child, *Front_sibling,
+ Wflag, npivcol, fallrows, fallcols, fpiv, frows, fcols, *Front_size ;
+
+ nfr = 0 ;
+ DEBUG0 (("UMF_analyze: anzmax "ID" anrow "ID" ancol "ID"\n",
+ Ap [n_row], n_row, n_col)) ;
+
+ /* ====================================================================== */
+ /* ==== initializations ================================================= */
+ /* ====================================================================== */
+
+#pragma ivdep
+ for (j = 0 ; j < n_col ; j++)
+ {
+ Link [j] = EMPTY ;
+ W [j] = EMPTY ;
+ Up [j] = EMPTY ;
+
+ /* Frontal matrix data structure: */
+ Front_npivcol [j] = 0 ; /* number of pivot columns */
+ Front_nrows [j] = 0 ; /* number of rows, incl. pivot rows */
+ Front_ncols [j] = 0 ; /* number of cols, incl. pivot cols */
+ Front_parent [j] = EMPTY ; /* parent front */
+ /* Note that only non-pivotal columns are stored in a front (a "row" */
+ /* of U) during elimination. */
+ }
+
+ /* the rows must be sorted by increasing min col */
+ krow = 0 ;
+ pfirst = Ap [0] ;
+ jlast = EMPTY ;
+ jnext = EMPTY ;
+ Wflag = 0 ;
+
+ /* this test requires the size of Ai to be >= n_col + nz */
+ ASSERT (pfirst >= n_col) ; /* Ai must be large enough */
+
+ /* pdest points to the first free space in Ai */
+ pdest = 0 ;
+ ncompactions = 0 ;
+
+ /* ====================================================================== */
+ /* === compute symbolic LL' factorization (unsorted) ==================== */
+ /* ====================================================================== */
+
+ for (j = 0 ; j < n_col ; j = jnext)
+ {
+ DEBUG1 (("\n\n============Front "ID" starting. nfr = "ID"\n", j, nfr)) ;
+
+ /* ================================================================== */
+ /* === garbage collection =========================================== */
+ /* ================================================================== */
+
+ if (pdest + (n_col-j) > pfirst)
+ {
+ /* we might run out ... compact the rows of U */
+
+#ifndef NDEBUG
+ DEBUG0 (("UMF_analyze COMPACTION, j="ID" pfirst="ID"\n",
+ j, pfirst)) ;
+ for (row = 0 ; row < j ; row++)
+ {
+ if (Up [row] != EMPTY)
+ {
+ /* this is a live row of U */
+ DEBUG1 (("Live row: "ID" cols: ", row)) ;
+ p = Up [row] ;
+ ASSERT (Front_ncols [row] > Front_npivcol [row]) ;
+ p2 = p + (Front_ncols [row] - Front_npivcol [row]) ;
+ for ( ; p < p2 ; p++)
+ {
+ DEBUG1 ((ID, Ai [p])) ;
+ ASSERT (p < pfirst) ;
+ ASSERT (Ai [p] > row && Ai [p] < n_col) ;
+ }
+ DEBUG1 (("\n")) ;
+ }
+ }
+ DEBUG1 (("\nStarting to compact:\n")) ;
+#endif
+
+ pdest = 0 ;
+ ncompactions++ ;
+ for (row = 0 ; row < j ; row++)
+ {
+ if (Up [row] != EMPTY)
+ {
+ /* this is a live row of U */
+ DEBUG1 (("Live row: "ID" cols: ", row)) ;
+ ASSERT (row < n_col) ;
+ p = Up [row] ;
+ ASSERT (Front_ncols [row] > Front_npivcol [row]) ;
+ p2 = p + (Front_ncols [row] - Front_npivcol [row]) ;
+ Up [row] = pdest ;
+ for ( ; p < p2 ; p++)
+ {
+ DEBUG1 ((ID, Ai [p])) ;
+ ASSERT (p < pfirst) ;
+ ASSERT (Ai [p] > row && Ai [p] < n_col) ;
+ Ai [pdest++] = Ai [p] ;
+ ASSERT (pdest <= pfirst) ;
+ }
+ DEBUG1 (("\n")) ;
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("\nAFTER COMPACTION, j="ID" pfirst="ID"\n", j, pfirst)) ;
+ for (row = 0 ; row < j ; row++)
+ {
+ if (Up [row] != EMPTY)
+ {
+ /* this is a live row of U */
+ DEBUG1 (("Live row: "ID" cols: ", row)) ;
+ p = Up [row] ;
+ ASSERT (Front_ncols [row] > Front_npivcol [row]) ;
+ p2 = p + (Front_ncols [row] - Front_npivcol [row]) ;
+ for ( ; p < p2 ; p++)
+ {
+ DEBUG1 ((ID, Ai [p])) ;
+ ASSERT (p < pfirst) ;
+ ASSERT (Ai [p] > row && Ai [p] < n_col) ;
+ }
+ DEBUG1 (("\n")) ;
+ }
+ }
+#endif
+
+ }
+
+ if (pdest + (n_col-j) > pfirst)
+ {
+ /* :: out of memory in umf_analyze :: */
+ /* it can't happen, if pfirst >= n_col */
+ return (FALSE) ; /* internal error! */
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* is the last front a child of this one? */
+ /* ------------------------------------------------------------------ */
+
+ if (jlast != EMPTY && Link [j] == jlast)
+ {
+ /* yes - create row j by appending to jlast */
+ DEBUG1 (("GOT:last front is child of this one: j "ID" jlast "ID"\n",
+ j, jlast)) ;
+ ASSERT (jlast >= 0 && jlast < j) ;
+
+ Up [j] = Up [jlast] ;
+ Up [jlast] = EMPTY ;
+
+ /* find the parent, delete column j, and update W */
+ parent = n_col ;
+ for (p = Up [j] ; p < pdest ; )
+ {
+ j3 = Ai [p] ;
+ DEBUG1 (("Initial row of U: col "ID" ", j3)) ;
+ ASSERT (j3 >= 0 && j3 < n_col) ;
+ DEBUG1 (("W: "ID" \n", W [j3])) ;
+ ASSERT (W [j3] == Wflag) ;
+ if (j == j3)
+ {
+ DEBUG1 (("Found column j at p = "ID"\n", p)) ;
+ Ai [p] = Ai [--pdest] ;
+ }
+ else
+ {
+ if (j3 < parent)
+ {
+ parent = j3 ;
+ }
+ p++ ;
+ }
+ }
+
+ /* delete jlast from the link list of j */
+ Link [j] = Link [jlast] ;
+
+ ASSERT (Front_nrows [jlast] > Front_npivcol [jlast]) ;
+ thickness = (Front_nrows [jlast] - Front_npivcol [jlast]) ;
+ DEBUG1 (("initial thickness: "ID"\n", thickness)) ;
+
+ }
+ else
+ {
+ Up [j] = pdest ;
+ parent = n_col ;
+ /* thickness: number of (nonpivotal) rows in frontal matrix j */
+ thickness = 0 ;
+ Wflag = j ;
+ }
+
+ /* ================================================================== */
+ /* === compute row j of A*A' ======================================== */
+ /* ================================================================== */
+
+ /* ------------------------------------------------------------------ */
+ /* flag the diagonal entry in row U, but do not add to pattern */
+ /* ------------------------------------------------------------------ */
+
+ ASSERT (pdest <= pfirst) ;
+ W [j] = Wflag ;
+
+ DEBUG1 (("\nComputing row "ID" of A'*A\n", j)) ;
+ DEBUG2 ((" col: "ID" (diagonal)\n", j)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* find the rows the contribute to this column j */
+ /* ------------------------------------------------------------------ */
+
+ jnext = n_col ;
+ for (knext = krow ; knext < n_row ; knext++)
+ {
+ ASSERT (Ap [knext] < Ap [knext+1]) ;
+ ASSERT (Ap [knext] >= pfirst && Ap [knext] <= Ap [n_row]) ;
+ jnext = Ai [Ap [knext]] ;
+ ASSERT (jnext >= j) ;
+ if (jnext != j)
+ {
+ break ;
+ }
+ }
+
+ /* rows krow ... knext-1 all have first column index of j */
+ /* (or are empty) */
+
+ /* row knext has first column index of jnext */
+ /* if knext = n_row, then jnext is n_col */
+ if (knext == n_row)
+ {
+ jnext = n_col ;
+ }
+
+ ASSERT (jnext > j) ;
+ ASSERT (jnext <= n_col) ;
+
+ /* ------------------------------------------------------------------ */
+ /* for each nonzero A (k,j) in column j of A do: */
+ /* ------------------------------------------------------------------ */
+
+ for (k = krow ; k < knext ; k++)
+ {
+ p = Ap [k] ;
+ p2 = Ap [k+1] ;
+ ASSERT (p < p2) ;
+
+ /* merge row k of A into W */
+ DEBUG2 ((" ---- A row "ID" ", k)) ;
+ ASSERT (k >= 0 && k < n_row) ;
+ ASSERT (Ai [p] == j) ;
+ DEBUG2 ((" p "ID" p2 "ID"\n cols:", p, p2)) ;
+ ASSERT (p >= pfirst && p < Ap [n_row]) ;
+ ASSERT (p2 > pfirst && p2 <= Ap [n_row]) ;
+ for ( ; p < p2 ; p++)
+ {
+ /* add to pattern if seen for the first time */
+ col = Ai [p] ;
+ ASSERT (col >= j && col < n_col) ;
+ DEBUG3 ((" "ID, col)) ;
+ if (W [col] != Wflag)
+ {
+ Ai [pdest++] = col ;
+ ASSERT (pdest <= pfirst) ;
+ /* flag this column has having been seen for row j */
+ W [col] = Wflag ;
+ if (col < parent)
+ {
+ parent = col ;
+ }
+ }
+ }
+ DEBUG2 (("\n")) ;
+ thickness++ ;
+ }
+
+#ifndef NDEBUG
+ DEBUG3 (("\nRow "ID" of A'A:\n", j)) ;
+ for (p = Up [j] ; p < pdest ; p++)
+ {
+ DEBUG3 ((" "ID, Ai [p])) ;
+ }
+ DEBUG3 (("\n")) ;
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* delete rows up to but not including knext */
+ /* ------------------------------------------------------------------ */
+
+ krow = knext ;
+ pfirst = Ap [knext] ;
+
+ /* we can now use Ai [0..pfirst-1] as workspace for rows of U */
+
+ /* ================================================================== */
+ /* === compute jth row of U ========================================= */
+ /* ================================================================== */
+
+ /* for each nonzero U (k,j) in column j of U (1:j-1,:) do */
+ for (k = Link [j] ; k != EMPTY ; k = Link [k])
+ {
+ /* merge row k of U into W */
+ DEBUG2 ((" ---- U row "ID, k)) ;
+ ASSERT (k >= 0 && k < n_col) ;
+ ASSERT (Up [k] != EMPTY) ;
+ p = Up [k] ;
+ ASSERT (Front_ncols [k] > Front_npivcol [k]) ;
+ p2 = p + (Front_ncols [k] - Front_npivcol [k]) ;
+ DEBUG2 ((" p "ID" p2 "ID"\n cols:", p, p2)) ;
+ ASSERT (p <= pfirst) ;
+ ASSERT (p2 <= pfirst) ;
+ for ( ; p < p2 ; p++)
+ {
+ /* add to pattern if seen for the first time */
+ col = Ai [p] ;
+ ASSERT (col >= j && col < n_col) ;
+ DEBUG3 ((" "ID, col)) ;
+ if (W [col] != Wflag)
+ {
+ Ai [pdest++] = col ;
+ ASSERT (pdest <= pfirst) ;
+ /* flag this col has having been seen for row j */
+ W [col] = Wflag ;
+ if (col < parent)
+ {
+ parent = col ;
+ }
+ }
+ }
+ DEBUG2 (("\n")) ;
+
+ /* mark the row k as deleted */
+ Up [k] = EMPTY ;
+
+ ASSERT (Front_nrows [k] > Front_npivcol [k]) ;
+ thickness += (Front_nrows [k] - Front_npivcol [k]) ;
+ ASSERT (Front_parent [k] == j) ;
+ }
+
+#ifndef NDEBUG
+ DEBUG3 (("\nRow "ID" of U prior to supercolumn detection:\n", j));
+ for (p = Up [j] ; p < pdest ; p++)
+ {
+ DEBUG3 ((" "ID, Ai [p])) ;
+ }
+ DEBUG3 (("\n")) ;
+ DEBUG1 (("thickness, prior to supercol detect: "ID"\n", thickness)) ;
+#endif
+
+ /* ================================================================== */
+ /* === quicky mass elimination ====================================== */
+ /* ================================================================== */
+
+ /* this code detects some supernodes, but it might miss */
+ /* some because the elimination tree (created on the fly) */
+ /* is not yet post-ordered, and because the pattern of A'*A */
+ /* is also computed on the fly. */
+
+ /* j2 is incremented because the pivot columns are not stored */
+
+ for (j2 = j+1 ; j2 < jnext ; j2++)
+ {
+ ASSERT (j2 >= 0 && j2 < n_col) ;
+ if (W [j2] != Wflag || Link [j2] != EMPTY)
+ {
+ break ;
+ }
+ }
+
+ /* the loop above terminated with j2 at the first non-supernode */
+ DEBUG1 (("jnext = "ID"\n", jnext)) ;
+ ASSERT (j2 <= jnext) ;
+ jnext = j2 ;
+ j2-- ;
+ DEBUG1 (("j2 = "ID"\n", j2)) ;
+ ASSERT (j2 < n_col) ;
+
+ npivots = j2-j+1 ;
+ DEBUG1 (("Number of pivot columns: "ID"\n", npivots)) ;
+
+ /* rows j:j2 have the same nonzero pattern, except for columns j:j2-1 */
+
+ if (j2 > j)
+ {
+ /* supernode detected, prune the pattern of new row j */
+ ASSERT (parent == j+1) ;
+ ASSERT (j2 < n_col) ;
+ DEBUG1 (("Supernode detected, j "ID" to j2 "ID"\n", j, j2)) ;
+
+ parent = n_col ;
+ p2 = pdest ;
+ pdest = Up [j] ;
+ for (p = Up [j] ; p < p2 ; p++)
+ {
+ col = Ai [p] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (W [col] == Wflag) ;
+ if (col > j2)
+ {
+ /* keep this col in the pattern of the new row j */
+ Ai [pdest++] = col ;
+ if (col < parent)
+ {
+ parent = col ;
+ }
+ }
+ }
+ }
+
+ DEBUG1 (("Parent ["ID"] = "ID"\n", j, parent)) ;
+ ASSERT (parent > j2) ;
+
+ if (parent == n_col)
+ {
+ /* this front has no parent - it is the root of a subtree */
+ parent = EMPTY ;
+ }
+
+#ifndef NDEBUG
+ DEBUG3 (("\nFinal row "ID" of U after supercolumn detection:\n", j)) ;
+ for (p = Up [j] ; p < pdest ; p++)
+ {
+ ASSERT (Ai [p] >= 0 && Ai [p] < n_col) ;
+ DEBUG3 ((" "ID" ("ID")", Ai [p], W [Ai [p]])) ;
+ ASSERT (W [Ai [p]] == Wflag) ;
+ }
+ DEBUG3 (("\n")) ;
+#endif
+
+ /* ================================================================== */
+ /* === frontal matrix =============================================== */
+ /* ================================================================== */
+
+ /* front has Front_npivcol [j] pivot columns */
+ /* entire front is Front_nrows [j] -by- Front_ncols [j] */
+ /* j is first column in the front */
+
+ npivcol = npivots ;
+ fallrows = thickness ;
+ fallcols = npivots + pdest - Up [j] ;
+
+ /* number of pivots in the front (rows and columns) */
+ fpiv = MIN (npivcol, fallrows) ;
+
+ /* size of contribution block */
+ frows = fallrows - fpiv ;
+ fcols = fallcols - fpiv ;
+
+ if (frows == 0 || fcols == 0)
+ {
+ /* front has no contribution block and thus needs no parent */
+ DEBUG1 (("Frontal matrix evaporation\n")) ;
+ Up [j] = EMPTY ;
+ parent = EMPTY ;
+ }
+
+ Front_npivcol [j] = npivots ;
+ Front_nrows [j] = fallrows ;
+ Front_ncols [j] = fallcols ;
+ Front_parent [j] = parent ;
+ ASSERT (npivots > 0) ;
+
+ /* Front_parent [j] is the first column of the parent frontal matrix */
+
+ DEBUG1 (("\n\n==== Front "ID", nfr "ID" pivot columns "ID":"ID
+ " all front: "ID"-by-"ID" Parent: "ID"\n", j, nfr, j,j+npivots-1,
+ Front_nrows [j], Front_ncols [j], Front_parent [j])) ;
+ nfr++ ;
+
+ /* ================================================================== */
+ /* === prepare this row for its parent ============================== */
+ /* ================================================================== */
+
+ if (parent != EMPTY)
+ {
+ Link [j] = Link [parent] ;
+ Link [parent] = j ;
+ }
+
+ ASSERT (jnext > j) ;
+
+ jlast = j ;
+ }
+
+ /* ====================================================================== */
+ /* === postorder the fronts ============================================= */
+ /* ====================================================================== */
+
+ *nfr_out = nfr ;
+
+ Front_order = W ; /* use W for Front_order [ */
+
+ if (fixQ)
+ {
+ /* do not postorder the fronts if Q is fixed */
+ DEBUG1 (("\nNo postorder (Q is fixed)\n")) ;
+ k = 0 ;
+ /* Pragma added May 14, 2003. The Intel compiler icl 6.0 (an old
+ * version) incorrectly vectorizes this loop. */
+#pragma novector
+ for (j = 0 ; j < n_col ; j++)
+ {
+ if (Front_npivcol [j] > 0)
+ {
+ Front_order [j] = k++ ;
+ DEBUG1 (("Front order of j: "ID" is:"ID"\n", j,
+ Front_order [j])) ;
+ }
+ else
+ {
+ Front_order [j] = EMPTY ;
+ }
+ }
+ }
+ else
+ {
+
+ /* use Ap for Front_child and use Link for Front_sibling [ */
+ Front_child = Ap ;
+ Front_sibling = Link ;
+
+ /* use Ai for Front_stack, size of Ai is >= 2*n_col */
+ Front_stack = Ai ;
+ Front_size = Front_stack + n_col ;
+
+ UMF_fsize (n_col, Front_size, Front_nrows, Front_ncols,
+ Front_parent, Front_npivcol) ;
+
+ AMD_postorder (n_col, Front_parent, Front_npivcol, Front_size,
+ Front_order, Front_child, Front_sibling, Front_stack) ;
+
+ /* done with Front_child, Front_sibling, Front_size, and Front_stack ]*/
+
+ /* ------------------------------------------------------------------ */
+ /* construct the column permutation (return in Up) */
+ /* ------------------------------------------------------------------ */
+
+ /* Front_order [i] = k means that front i is kth front in the new order.
+ * i is in the range 0 to n_col-1, and k is in the range 0 to nfr-1 */
+
+ /* Use Ai as workspace for Winv [ */
+ Winv = Ai ;
+ for (k = 0 ; k < nfr ; k++)
+ {
+ Winv [k] = EMPTY ;
+ }
+
+ /* compute the inverse of Front_order, so that Winv [k] = i */
+ /* if Front_order [i] = k */
+
+ DEBUG1 (("\n\nComputing output column permutation:\n")) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ k = Front_order [i] ;
+ if (k != EMPTY)
+ {
+ DEBUG1 (("Front "ID" new order: "ID"\n", i, k)) ;
+ ASSERT (k >= 0 && k < nfr) ;
+ ASSERT (Winv [k] == EMPTY) ;
+ Winv [k] = i ;
+ }
+ }
+
+ /* Use Up as output permutation */
+ kk = 0 ;
+ for (k = 0 ; k < nfr ; k++)
+ {
+ i = Winv [k] ;
+ DEBUG1 (("Old Front "ID" New Front "ID" npivots "ID" nrows "ID
+ " ncols "ID"\n",
+ i, k, Front_npivcol [i], Front_nrows [i], Front_ncols [i])) ;
+ ASSERT (i >= 0 && i < n_col) ;
+ ASSERT (Front_npivcol [i] > 0) ;
+ for (npiv = 0 ; npiv < Front_npivcol [i] ; npiv++)
+ {
+ Up [kk] = i + npiv ;
+ DEBUG1 ((" Cperm ["ID"] = "ID"\n", kk, Up [kk])) ;
+ kk++ ;
+ }
+ }
+ ASSERT (kk == n_col) ;
+
+ /* Winv no longer needed ] */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* apply the postorder traversal to renumber the frontal matrices */
+ /* (or pack them in same order, if fixQ) */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Ai as workspace */
+
+ UMF_apply_order (Front_npivcol, Front_order, Ai, n_col, nfr) ;
+ UMF_apply_order (Front_nrows, Front_order, Ai, n_col, nfr) ;
+ UMF_apply_order (Front_ncols, Front_order, Ai, n_col, nfr) ;
+ UMF_apply_order (Front_parent, Front_order, Ai, n_col, nfr) ;
+
+ /* fix the parent to refer to the new numbering */
+ for (i = 0 ; i < nfr ; i++)
+ {
+ parent = Front_parent [i] ;
+ if (parent != EMPTY)
+ {
+ ASSERT (parent >= 0 && parent < n_col) ;
+ ASSERT (Front_order [parent] >= 0 && Front_order [parent] < nfr) ;
+ Front_parent [i] = Front_order [parent] ;
+ }
+ }
+
+ /* Front_order longer needed ] */
+
+#ifndef NDEBUG
+ DEBUG1 (("\nFinal frontal matrices:\n")) ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ DEBUG1 (("Final front "ID": npiv "ID" nrows "ID" ncols "ID" parent "
+ ID"\n", i, Front_npivcol [i], Front_nrows [i],
+ Front_ncols [i], Front_parent [i])) ;
+ }
+#endif
+
+ *p_ncompactions = ncompactions ;
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umf_analyze.h b/UMFPACK/Source/umf_analyze.h
new file mode 100644
index 0000000..733ba03
--- /dev/null
+++ b/UMFPACK/Source/umf_analyze.h
@@ -0,0 +1,23 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_analyze
+(
+ Int n_row,
+ Int n_col,
+ Int Ai [ ],
+ Int Ap [ ],
+ Int Up [ ],
+ Int fixQ,
+ Int Front_ncols [ ],
+ Int W [ ],
+ Int Link [ ],
+ Int Front_nrows [ ],
+ Int Front_npivcol [ ],
+ Int Front_parent [ ],
+ Int *nfr_out,
+ Int *p_ncompactions
+) ;
diff --git a/UMFPACK/Source/umf_apply_order.c b/UMFPACK/Source/umf_apply_order.c
new file mode 100644
index 0000000..6192af4
--- /dev/null
+++ b/UMFPACK/Source/umf_apply_order.c
@@ -0,0 +1,44 @@
+/* ========================================================================== */
+/* === UMF_apply_order ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Apply post-ordering of supernodal elimination tree.
+*/
+
+#include "umf_internal.h"
+#include "umf_apply_order.h"
+
+GLOBAL void UMF_apply_order
+(
+ Int Front [ ], /* of size nn on input, size nfr on output */
+ const Int Order [ ], /* Order [i] = k, i in the range 0..nn-1,
+ * and k in the range 0..nfr-1, means that node
+ * i is the kth node in the postordered tree. */
+ Int Temp [ ], /* workspace of size nfr */
+ Int nn, /* nodes are numbered in the range 0..nn-1 */
+ Int nfr /* the number of nodes actually in use */
+)
+{
+ Int i, k ;
+ for (i = 0 ; i < nn ; i++)
+ {
+ k = Order [i] ;
+ ASSERT (k >= EMPTY && k < nfr) ;
+ if (k != EMPTY)
+ {
+ Temp [k] = Front [i] ;
+ }
+ }
+
+ for (k = 0 ; k < nfr ; k++)
+ {
+ Front [k] = Temp [k] ;
+ }
+}
diff --git a/UMFPACK/Source/umf_apply_order.h b/UMFPACK/Source/umf_apply_order.h
new file mode 100644
index 0000000..dd7e682
--- /dev/null
+++ b/UMFPACK/Source/umf_apply_order.h
@@ -0,0 +1,14 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_apply_order
+(
+ Int Front [ ],
+ const Int Order [ ],
+ Int Temp [ ],
+ Int n_col,
+ Int nfr
+) ;
diff --git a/UMFPACK/Source/umf_assemble.c b/UMFPACK/Source/umf_assemble.c
new file mode 100644
index 0000000..04a3de3
--- /dev/null
+++ b/UMFPACK/Source/umf_assemble.c
@@ -0,0 +1,1216 @@
+/* ========================================================================== */
+/* === UMF_assemble ========================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Degree update and numerical assembly. This is compiled twice (with and
+ * without FIXQ) for each real/complex int/UF_long version, for a total of 8
+ * versions.*/
+
+#include "umf_internal.h"
+#include "umf_assemble.h"
+#include "umf_mem_free_tail_block.h"
+
+/* ========================================================================== */
+/* === row_assemble ========================================================= */
+/* ========================================================================== */
+
+PRIVATE void row_assemble
+(
+ Int row,
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+
+ Entry *S, *Fcblock, *Frow ;
+ Int tpi, e, *E, *Fcpos, *Frpos, *Row_degree, *Row_tuples, *Row_tlen, rdeg0,
+ f, nrows, ncols, *Rows, *Cols, col, ncolsleft, j ;
+ Tuple *tp, *tp1, *tp2, *tpend ;
+ Unit *Memory, *p ;
+ Element *ep ;
+
+#ifndef FIXQ
+ Int *Col_degree ;
+ Col_degree = Numeric->Cperm ;
+#endif
+
+ Row_tuples = Numeric->Uip ;
+ tpi = Row_tuples [row] ;
+ if (!tpi) return ;
+
+ Memory = Numeric->Memory ;
+ E = Work->E ;
+ Fcpos = Work->Fcpos ;
+ Frpos = Work->Frpos ;
+ Row_degree = Numeric->Rperm ;
+ Row_tlen = Numeric->Uilen ;
+ E = Work->E ;
+ Memory = Numeric->Memory ;
+ rdeg0 = Work->rdeg0 ;
+ Fcblock = Work->Fcblock ;
+
+#ifndef NDEBUG
+ DEBUG6 (("SCAN2-row: "ID"\n", row)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ;
+#endif
+
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Row_tlen [row] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ Rows = Cols + ep->ncols ;
+ if (Rows [f] == EMPTY) continue ; /* row already assembled */
+ ASSERT (row == Rows [f] && row >= 0 && row < Work->n_row) ;
+
+ if (ep->rdeg == rdeg0)
+ {
+ /* ------------------------------------------------------ */
+ /* this is an old Lson - assemble just one row */
+ /* ------------------------------------------------------ */
+
+ /* flag the row as assembled from the Lson */
+ Rows [f] = EMPTY ;
+
+ nrows = ep->nrows ;
+ ncols = ep->ncols ;
+
+ p += UNITS (Int, ncols + nrows) ;
+ S = ((Entry *) p) + f ;
+
+ DEBUG6 (("Old LSON: "ID"\n", e)) ;
+#ifndef NDEBUG
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+
+ ncolsleft = ep->ncolsleft ;
+
+ Frow = Fcblock + Frpos [row] ;
+ DEBUG6 (("LSON found (in scan2-row): "ID"\n", e)) ;
+
+ Row_degree [row] -= ncolsleft ;
+
+ if (ncols == ncolsleft)
+ {
+ /* -------------------------------------------------- */
+ /* no columns assembled out this Lson yet */
+ /* -------------------------------------------------- */
+
+#pragma ivdep
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+#ifndef FIXQ
+ Col_degree [col] -- ;
+#endif
+ /* Frow [Fcpos [col]] += *S ; */
+ ASSEMBLE (Frow [Fcpos [col]], *S) ;
+ S += nrows ;
+ }
+
+ }
+ else
+ {
+ /* -------------------------------------------------- */
+ /* some columns have been assembled out of this Lson */
+ /* -------------------------------------------------- */
+
+#pragma ivdep
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ if (col >= 0)
+ {
+ ASSERT (col < Work->n_col) ;
+#ifndef FIXQ
+ Col_degree [col] -- ;
+#endif
+ /* Frow [Fcpos [col]] += *S ; */
+ ASSEMBLE (Frow [Fcpos [col]], *S) ;
+ }
+ S += nrows ;
+ }
+
+ }
+ ep->nrowsleft-- ;
+ ASSERT (ep->nrowsleft > 0) ;
+ }
+ else
+ {
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ }
+ Row_tlen [row] = tp2 - tp1 ;
+
+#ifndef NDEBUG
+ DEBUG7 (("row assembled in scan2-row: "ID"\n", row)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ;
+ DEBUG7 (("Current frontal matrix: (scan 1b)\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+}
+
+/* ========================================================================== */
+/* === col_assemble ========================================================= */
+/* ========================================================================== */
+
+PRIVATE void col_assemble
+(
+ Int col,
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+
+ Entry *S, *Fcblock, *Fcol ;
+ Int tpi, e, *E, *Fcpos, *Frpos, *Row_degree, *Col_tuples, *Col_tlen, cdeg0,
+ f, nrows, ncols, *Rows, *Cols, row, nrowsleft, i ;
+ Tuple *tp, *tp1, *tp2, *tpend ;
+ Unit *Memory, *p ;
+ Element *ep ;
+
+#if !defined (FIXQ) || !defined (NDEBUG)
+ Int *Col_degree ;
+ Col_degree = Numeric->Cperm ;
+#endif
+
+ Col_tuples = Numeric->Lip ;
+ tpi = Col_tuples [col] ;
+ if (!tpi) return ;
+
+ Memory = Numeric->Memory ;
+ E = Work->E ;
+ Fcpos = Work->Fcpos ;
+ Frpos = Work->Frpos ;
+ Row_degree = Numeric->Rperm ;
+ Col_tlen = Numeric->Lilen ;
+ E = Work->E ;
+ Memory = Numeric->Memory ;
+ cdeg0 = Work->cdeg0 ;
+ Fcblock = Work->Fcblock ;
+
+ DEBUG6 (("SCAN2-col: "ID"\n", col)) ;
+#ifndef NDEBUG
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+#endif
+
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Col_tlen [col] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+
+ if (Cols [f] == EMPTY) continue ; /* col already assembled */
+ ASSERT (col == Cols [f] && col >= 0 && col < Work->n_col) ;
+
+ if (ep->cdeg == cdeg0)
+ {
+ /* ------------------------------------------------------ */
+ /* this is an old Uson - assemble just one col */
+ /* ------------------------------------------------------ */
+
+ /* flag the col as assembled from the Uson */
+ Cols [f] = EMPTY ;
+
+ nrows = ep->nrows ;
+ ncols = ep->ncols ;
+ Rows = Cols + ncols ;
+ p += UNITS (Int, ncols + nrows) ;
+ S = ((Entry *) p) + f * nrows ;
+
+ DEBUG6 (("Old USON: "ID"\n", e)) ;
+#ifndef NDEBUG
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+
+ nrowsleft = ep->nrowsleft ;
+
+ Fcol = Fcblock + Fcpos [col] ;
+ DEBUG6 (("USON found (in scan2-col): "ID"\n", e)) ;
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ if (nrows == nrowsleft)
+ {
+ /* -------------------------------------------------- */
+ /* no rows assembled out of this Uson yet */
+ /* -------------------------------------------------- */
+
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ ASSERT (row >= 0 && row < Work->n_row) ;
+ Row_degree [row]-- ;
+ /* Fcol [Frpos [row]] += S [i] ; */
+ ASSEMBLE (Fcol [Frpos [row]], S [i]) ;
+ }
+ }
+ else
+ {
+ /* -------------------------------------------------- */
+ /* some rows have been assembled out of this Uson */
+ /* -------------------------------------------------- */
+
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0)
+ {
+ ASSERT (row < Work->n_row) ;
+ Row_degree [row]-- ;
+ /* Fcol [Frpos [row]] += S [i] ; */
+ ASSEMBLE (Fcol [Frpos [row]], S [i]) ;
+ }
+ }
+ }
+ ep->ncolsleft-- ;
+ ASSERT (ep->ncolsleft > 0) ;
+ }
+ else
+ {
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ }
+ Col_tlen [col] = tp2 - tp1 ;
+
+#ifndef NDEBUG
+ DEBUG7 (("Column assembled in scan2-col: "ID"\n", col)) ;
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+ DEBUG7 (("Current frontal matrix: after scan2-col\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+}
+
+
+/* ========================================================================== */
+/* === UMF_assemble / UMF_assemble_fixq ===================================== */
+/* ========================================================================== */
+
+#ifndef FIXQ
+GLOBAL void UMF_assemble
+#else
+GLOBAL void UMF_assemble_fixq
+#endif
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int e, i, row, col, i2, nrows, ncols, f, tpi, extcdeg, extrdeg, rdeg0,
+ cdeg0, son_list, next, nrows_to_assemble,
+ ncols_to_assemble, ngetrows, j, j2,
+ nrowsleft, /* number of rows remaining in S */
+ ncolsleft, /* number of columns remaining in S */
+ prior_Lson, prior_Uson, *E, *Cols, *Rows, *Wm, *Woo,
+ *Row_tuples, *Row_degree, *Row_tlen,
+ *Col_tuples, *Col_tlen ;
+ Unit *Memory, *p ;
+ Element *ep ;
+ Tuple *tp, *tp1, *tp2, *tpend ;
+ Entry
+ *S, /* a pointer into the contribution block of a son */
+ *Fcblock, /* current contribution block */
+ *Fcol ; /* a column of FC */
+ Int *Frpos,
+ *Fcpos,
+ fnrows, /* number of rows in contribution block in F */
+ fncols ; /* number of columns in contribution block in F */
+
+#if !defined (FIXQ) || !defined (NDEBUG)
+ Int *Col_degree ;
+#endif
+
+#ifndef NDEBUG
+ Int n_row, n_col ;
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ DEBUG3 (("::Assemble SCANS 1-4\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+#if !defined (FIXQ) || !defined (NDEBUG)
+ Col_degree = Numeric->Cperm ; /* not updated if FIXQ is true */
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ fncols = Work->fncols ;
+ fnrows = Work->fnrows ;
+ Fcpos = Work->Fcpos ;
+ Frpos = Work->Frpos ;
+ Row_degree = Numeric->Rperm ;
+ Row_tuples = Numeric->Uip ;
+ Row_tlen = Numeric->Uilen ;
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+ E = Work->E ;
+ Memory = Numeric->Memory ;
+ Wm = Work->Wm ;
+ Woo = Work->Woo ;
+ rdeg0 = Work->rdeg0 ;
+ cdeg0 = Work->cdeg0 ;
+
+#ifndef NDEBUG
+ DEBUG6 (("============================================\n")) ;
+ DEBUG6 (("Degree update, assembly.\n")) ;
+ DEBUG6 (("pivot row pattern: fncols="ID"\n", fncols)) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Work->Fcols [j] ;
+ DEBUG6 ((ID" ", col)) ;
+ ASSERT (Fcpos [col] == j * Work->fnr_curr) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ }
+ ASSERT (Fcpos [Work->pivcol] >= 0) ;
+ DEBUG6 (("pivcol: "ID" pos "ID" fnr_curr "ID" fncols "ID"\n",
+ Work->pivcol, Fcpos [Work->pivcol], Work->fnr_curr, fncols)) ;
+ ASSERT (Fcpos [Work->pivcol] < fncols * Work->fnr_curr) ;
+ DEBUG6 (("\npivot col pattern: fnrows="ID"\n", fnrows)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Work->Frows [i] ;
+ DEBUG6 ((ID" ", row)) ;
+ ASSERT (Frpos [row] == i) ;
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ }
+ DEBUG6 (("\n")) ;
+ ASSERT (Frpos [Work->pivrow] >= 0) ;
+ ASSERT (Frpos [Work->pivrow] < fnrows) ;
+ ASSERT (Work->Flublock == (Entry *) (Numeric->Memory + E [0])) ;
+ ASSERT (Work->Fcblock == Work->Flublock + Work->nb *
+ (Work->nb + Work->fnr_curr + Work->fnc_curr)) ;
+#endif
+
+ Fcblock = Work->Fcblock ;
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the largest actual frontal matrix size (for Info only) */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (fnrows == Work->fnrows_new + 1) ;
+ ASSERT (fncols == Work->fncols_new + 1) ;
+
+ Numeric->maxnrows = MAX (Numeric->maxnrows, fnrows) ;
+ Numeric->maxncols = MAX (Numeric->maxncols, fncols) ;
+
+ /* this is safe from integer overflow, since the current frontal matrix
+ * is already allocated. */
+ Numeric->maxfrsize = MAX (Numeric->maxfrsize, fnrows * fncols) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* assemble from prior elements into the current frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG2 (("New assemble start [prior_element:"ID"\n", Work->prior_element)) ;
+
+ /* Currently no rows or columns are marked. No elements are scanned, */
+ /* that is, (ep->next == EMPTY) is true for all elements */
+
+ son_list = 0 ; /* start creating son_list [ */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine if most recent element is Lson or Uson of current front */
+ /* ---------------------------------------------------------------------- */
+
+ if (!Work->do_extend)
+ {
+ prior_Uson = ( Work->pivcol_in_front && !Work->pivrow_in_front) ;
+ prior_Lson = (!Work->pivcol_in_front && Work->pivrow_in_front) ;
+ if (prior_Uson || prior_Lson)
+ {
+ e = Work->prior_element ;
+ if (e != EMPTY)
+ {
+ ASSERT (E [e]) ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ ep->next = son_list ;
+ son_list = e ;
+#ifndef NDEBUG
+ DEBUG2 (("e "ID" is Prior son "ID" "ID"\n",
+ e, prior_Uson, prior_Lson)) ;
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+ ASSERT (E [e]) ;
+ }
+ }
+ }
+ Work->prior_element = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* SCAN1-row: scan the element lists of each new row in the pivot col */
+ /* and compute the external column degree for each frontal */
+ /* ---------------------------------------------------------------------- */
+
+ for (i2 = Work->fscan_row ; i2 < fnrows ; i2++)
+ {
+ /* Get a row */
+ row = Work->NewRows [i2] ;
+ if (row < 0) row = FLIP (row) ;
+ ASSERT (row >= 0 && row < n_row) ;
+
+ DEBUG6 (("SCAN1-row: "ID"\n", row)) ;
+#ifndef NDEBUG
+ UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ;
+#endif
+
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ tpi = Row_tuples [row] ;
+ if (!tpi) continue ;
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Row_tlen [row] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Rows = ((Int *) p) + ep->ncols ;
+ if (Rows [f] == EMPTY) continue ; /* row already assembled */
+ ASSERT (row == Rows [f]) ;
+
+ if (ep->cdeg < cdeg0)
+ {
+ /* first time seen in scan1-row */
+ ep->cdeg = ep->nrowsleft + cdeg0 ;
+ DEBUG6 (("e "ID" First seen: cdeg: "ID" ", e, ep->cdeg-cdeg0)) ;
+ ASSERT (ep->ncolsleft > 0 && ep->nrowsleft > 0) ;
+ }
+
+ ep->cdeg-- ; /* decrement external column degree */
+ DEBUG6 (("e "ID" New ext col deg: "ID"\n", e, ep->cdeg - cdeg0)) ;
+
+ /* this element is not yet in the new son list */
+ if (ep->cdeg == cdeg0 && ep->next == EMPTY)
+ {
+ /* A new LUson or Uson has been found */
+ ep->next = son_list ;
+ son_list = e ;
+ }
+
+ ASSERT (ep->cdeg >= cdeg0) ;
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Row_tlen [row] = tp2 - tp1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* SCAN1-col: scan the element lists of each new col in the pivot row */
+ /* and compute the external row degree for each frontal */
+ /* ---------------------------------------------------------------------- */
+
+ for (j2 = Work->fscan_col ; j2 < fncols ; j2++)
+ {
+ /* Get a column */
+ col = Work->NewCols [j2] ;
+ if (col < 0) col = FLIP (col) ;
+ ASSERT (col >= 0 && col < n_col) ;
+
+ DEBUG6 (("SCAN 1-col: "ID"\n", col)) ;
+#ifndef NDEBUG
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+#endif
+
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ tpi = Col_tuples [col] ;
+ if (!tpi) continue ;
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Col_tlen [col] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ if (Cols [f] == EMPTY) continue ; /* column already assembled */
+ ASSERT (col == Cols [f]) ;
+
+ if (ep->rdeg < rdeg0)
+ {
+ /* first time seen in scan1-col */
+ ep->rdeg = ep->ncolsleft + rdeg0 ;
+ DEBUG6 (("e "ID" First seen: rdeg: "ID" ", e, ep->rdeg-rdeg0)) ;
+ ASSERT (ep->ncolsleft > 0 && ep->nrowsleft > 0) ;
+ }
+
+ ep->rdeg-- ; /* decrement external row degree */
+ DEBUG6 (("e "ID" New ext row degree: "ID"\n", e, ep->rdeg-rdeg0)) ;
+
+ if (ep->rdeg == rdeg0 && ep->next == EMPTY)
+ {
+ /* A new LUson or Lson has been found */
+ ep->next = son_list ;
+ son_list = e ;
+ }
+
+ ASSERT (ep->rdeg >= rdeg0) ;
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Col_tlen [col] = tp2 - tp1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* assemble new sons via full scans */
+ /* ---------------------------------------------------------------------- */
+
+ next = EMPTY ;
+
+ for (e = son_list ; e > 0 ; e = next)
+ {
+ ASSERT (e > 0 && e <= Work->nel && E [e]) ;
+ p = Memory + E [e] ;
+ DEBUG2 (("New son: "ID"\n", e)) ;
+#ifndef NDEBUG
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+ GET_ELEMENT (ep, p, Cols, Rows, ncols, nrows, S) ;
+ nrowsleft = ep->nrowsleft ;
+ ncolsleft = ep->ncolsleft ;
+ next = ep->next ;
+ ep->next = EMPTY ;
+
+ extrdeg = (ep->rdeg < rdeg0) ? ncolsleft : (ep->rdeg - rdeg0) ;
+ extcdeg = (ep->cdeg < cdeg0) ? nrowsleft : (ep->cdeg - cdeg0) ;
+ ncols_to_assemble = ncolsleft - extrdeg ;
+ nrows_to_assemble = nrowsleft - extcdeg ;
+ DEBUG2 (("extrdeg "ID" extcdeg "ID"\n", extrdeg, extcdeg)) ;
+
+ if (extrdeg == 0 && extcdeg == 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* this is an LUson - assemble an entire contribution block */
+ /* -------------------------------------------------------------- */
+
+ DEBUG6 (("LUson found: "ID"\n", e)) ;
+
+ if (nrows == nrowsleft)
+ {
+ /* ---------------------------------------------------------- */
+ /* no rows assembled out of this LUson yet */
+ /* ---------------------------------------------------------- */
+
+ /* compute the compressed column offset vector*/
+ /* [ use Wm [0..nrows-1] for offsets */
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ Row_degree [row] -= ncolsleft ;
+ Wm [i] = Frpos [row] ;
+ }
+
+ if (ncols == ncolsleft)
+ {
+ /* ------------------------------------------------------ */
+ /* no rows or cols assembled out of LUson yet */
+ /* ------------------------------------------------------ */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ /* Fcol [Wm [i]] += S [i] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [i]) ;
+ }
+ S += nrows ;
+ }
+
+
+ }
+ else
+ {
+ /* ------------------------------------------------------ */
+ /* only cols have been assembled out of LUson */
+ /* ------------------------------------------------------ */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ if (col >= 0)
+ {
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ /* Fcol [Wm [i]] += S [i] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [i]) ;
+ }
+ }
+ S += nrows ;
+ }
+
+ }
+ /* ] done using Wm [0..nrows-1] for offsets */
+ }
+ else
+ {
+ /* ---------------------------------------------------------- */
+ /* some rows have been assembled out of this LUson */
+ /* ---------------------------------------------------------- */
+
+ /* compute the compressed column offset vector*/
+ /* [ use Woo,Wm [0..nrowsleft-1] for offsets */
+ ngetrows = 0 ;
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0)
+ {
+ Row_degree [row] -= ncolsleft ;
+ Woo [ngetrows] = i ;
+ Wm [ngetrows++] = Frpos [row] ;
+ }
+ }
+ ASSERT (ngetrows == nrowsleft) ;
+
+ if (ncols == ncolsleft)
+ {
+ /* ------------------------------------------------------ */
+ /* only rows have been assembled out of this LUson */
+ /* ------------------------------------------------------ */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrowsleft ; i++)
+ {
+ /* Fcol [Wm [i]] += S [Woo [i]] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ;
+ }
+ S += nrows ;
+ }
+
+ }
+ else
+ {
+ /* ------------------------------------------------------ */
+ /* both rows and columns have been assembled out of LUson */
+ /* ------------------------------------------------------ */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ if (col >= 0)
+ {
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrowsleft ; i++)
+ {
+ /* Fcol [Wm [i]] += S [Woo [i]] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ;
+ }
+ }
+ S += nrows ;
+ }
+
+ }
+ /* ] done using Woo,Wm [0..nrowsleft-1] */
+ }
+
+ /* deallocate the element: remove from ordered list */
+ UMF_mem_free_tail_block (Numeric, E [e]) ;
+ E [e] = 0 ;
+
+ }
+ else if (extcdeg == 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* this is a Uson - assemble all possible columns */
+ /* -------------------------------------------------------------- */
+
+ DEBUG6 (("New USON: "ID"\n", e)) ;
+ ASSERT (extrdeg > 0) ;
+
+ DEBUG6 (("New uson "ID" cols to do "ID"\n", e, ncols_to_assemble)) ;
+
+ if (ncols_to_assemble > 0)
+ {
+
+ Int skip = FALSE ;
+ if (ncols_to_assemble * 16 < ncols && nrows == 1)
+ {
+ /* this is a tall and thin frontal matrix consisting of
+ * only one column (most likely an original column). Do
+ * not assemble it. It cannot be the pivot column, since
+ * the pivot column element would be an LU son, not an Lson,
+ * of the current frontal matrix. */
+ ASSERT (nrowsleft == 1) ;
+ ASSERT (Rows [0] >= 0 && Rows [0] < Work->n_row) ;
+ skip = TRUE ;
+ Work->any_skip = TRUE ;
+ }
+
+ if (!skip)
+ {
+
+ if (nrows == nrowsleft)
+ {
+ /* -------------------------------------------------- */
+ /* no rows have been assembled out of this Uson yet */
+ /* -------------------------------------------------- */
+
+ /* compute the compressed column offset vector */
+ /* [ use Wm [0..nrows-1] for offsets */
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ Row_degree [row] -= ncols_to_assemble ;
+ Wm [i] = Frpos [row] ;
+ }
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ if ((col >= 0) && (Fcpos [col] >= 0))
+ {
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrows ; i++)
+ {
+ /* Fcol [Wm [i]] += S [i] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [i]) ;
+ }
+ /* flag the column as assembled from Uson */
+ Cols [j] = EMPTY ;
+ }
+ S += nrows ;
+ }
+
+
+ /* ] done using Wm [0..nrows-1] for offsets */
+ }
+ else
+ {
+ /* -------------------------------------------------- */
+ /* some rows have been assembled out of this Uson */
+ /* -------------------------------------------------- */
+
+ /* compute the compressed column offset vector*/
+ /* [ use Woo,Wm [0..nrows-1] for offsets */
+ ngetrows = 0 ;
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0)
+ {
+ Row_degree [row] -= ncols_to_assemble ;
+ ASSERT (row < n_row && Frpos [row] >= 0) ;
+ Woo [ngetrows] = i ;
+ Wm [ngetrows++] = Frpos [row] ;
+ }
+ }
+ ASSERT (ngetrows == nrowsleft) ;
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ if ((col >= 0) && (Fcpos [col] >= 0))
+ {
+#ifndef FIXQ
+ Col_degree [col] -= nrowsleft ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrowsleft ; i++)
+ {
+ /* Fcol [Wm [i]] += S [Woo [i]] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ;
+ }
+ /* flag the column as assembled from Uson */
+ Cols [j] = EMPTY ;
+ }
+ S += nrows ;
+ }
+
+ /* ] done using Woo,Wm */
+ }
+ ep->ncolsleft = extrdeg ;
+ }
+ }
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* this is an Lson - assemble all possible rows */
+ /* -------------------------------------------------------------- */
+
+ DEBUG6 (("New LSON: "ID"\n", e)) ;
+ ASSERT (extrdeg == 0 && extcdeg > 0) ;
+
+ DEBUG6 (("New lson "ID" rows to do "ID"\n", e, nrows_to_assemble)) ;
+
+ if (nrows_to_assemble > 0)
+ {
+
+ Int skip = FALSE ;
+ if (nrows_to_assemble * 16 < nrows && ncols == 1)
+ {
+ /* this is a tall and thin frontal matrix consisting of
+ * only one column (most likely an original column). Do
+ * not assemble it. It cannot be the pivot column, since
+ * the pivot column element would be an LU son, not an Lson,
+ * of the current frontal matrix. */
+ ASSERT (ncolsleft == 1) ;
+ ASSERT (Cols [0] >= 0 && Cols [0] < Work->n_col) ;
+ Work->any_skip = TRUE ;
+ skip = TRUE ;
+ }
+
+ if (!skip)
+ {
+
+ /* compute the compressed column offset vector */
+ /* [ use Woo,Wm [0..nrows-1] for offsets */
+ ngetrows = 0 ;
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if ((row >= 0) && (Frpos [row] >= 0))
+ {
+ ASSERT (row < n_row) ;
+ Row_degree [row] -= ncolsleft ;
+ Woo [ngetrows] = i ;
+ Wm [ngetrows++] = Frpos [row] ;
+ /* flag the row as assembled from the Lson */
+ Rows [i] = EMPTY ;
+ }
+ }
+ ASSERT (nrowsleft - ngetrows == extcdeg) ;
+ ASSERT (ngetrows == nrows_to_assemble) ;
+
+ if (ncols == ncolsleft)
+ {
+ /* -------------------------------------------------- */
+ /* no columns assembled out this Lson yet */
+ /* -------------------------------------------------- */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ ASSERT (col >= 0 && col < n_col) ;
+#ifndef FIXQ
+ Col_degree [col] -= nrows_to_assemble ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrows_to_assemble ; i++)
+ {
+ /* Fcol [Wm [i]] += S [Woo [i]] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ;
+ }
+ S += nrows ;
+ }
+
+
+ }
+ else
+ {
+ /* -------------------------------------------------- */
+ /* some columns have been assembled out of this Lson */
+ /* -------------------------------------------------- */
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ ASSERT (col < n_col) ;
+ if (col >= 0)
+ {
+#ifndef FIXQ
+ Col_degree [col] -= nrows_to_assemble ;
+#endif
+ Fcol = Fcblock + Fcpos [col] ;
+#pragma ivdep
+ for (i = 0 ; i < nrows_to_assemble ; i++)
+ {
+ /* Fcol [Wm [i]] += S [Woo [i]] ; */
+ ASSEMBLE (Fcol [Wm [i]], S [Woo [i]]) ;
+ }
+ }
+ S += nrows ;
+ }
+
+ }
+
+ /* ] done using Woo,Wm */
+
+ ep->nrowsleft = extcdeg ;
+ }
+ }
+ }
+ }
+
+ /* Note that garbage collection, and build tuples */
+ /* both destroy the son list. */
+
+ /* ] son_list now empty */
+
+ /* ---------------------------------------------------------------------- */
+ /* If frontal matrix extended, assemble old L/Usons from new rows/cols */
+ /* ---------------------------------------------------------------------- */
+
+ /* ---------------------------------------------------------------------- */
+ /* SCAN2-row: assemble rows of old Lsons from the new rows */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG7 (("Current frontal matrix: (prior to scan2-row)\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+ /* rescan the pivot row */
+ if (Work->any_skip)
+ {
+ row_assemble (Work->pivrow, Numeric, Work) ;
+ }
+
+ if (Work->do_scan2row)
+ {
+ for (i2 = Work->fscan_row ; i2 < fnrows ; i2++)
+ {
+ /* Get a row */
+ row = Work->NewRows [i2] ;
+ if (row < 0) row = FLIP (row) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ if (!(row == Work->pivrow && Work->any_skip))
+ {
+ /* assemble it */
+ row_assemble (row, Numeric, Work) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* SCAN2-col: assemble columns of old Usons from the new columns */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG7 (("Current frontal matrix: (prior to scan2-col)\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+ /* rescan the pivot col */
+ if (Work->any_skip)
+ {
+ col_assemble (Work->pivcol, Numeric, Work) ;
+ }
+
+ if (Work->do_scan2col)
+ {
+
+ for (j2 = Work->fscan_col ; j2 < fncols ; j2++)
+ {
+ /* Get a column */
+ col = Work->NewCols [j2] ;
+ if (col < 0) col = FLIP (col) ;
+ ASSERT (col >= 0 && col < n_col) ;
+ if (!(col == Work->pivcol && Work->any_skip))
+ {
+ /* assemble it */
+ col_assemble (col, Numeric, Work) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* done. the remainder of this routine is used only when in debug mode */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+
+ /* ---------------------------------------------------------------------- */
+ /* when debugging: make sure the assembly did everything that it could */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG3 (("::Assemble done\n")) ;
+
+ for (i2 = 0 ; i2 < fnrows ; i2++)
+ {
+ /* Get a row */
+ row = Work->Frows [i2] ;
+ ASSERT (row >= 0 && row < n_row) ;
+
+ DEBUG6 (("DEBUG SCAN 1: "ID"\n", row)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
+
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ tpi = Row_tuples [row] ;
+ if (!tpi) continue ;
+ tp = (Tuple *) (Memory + tpi) ;
+ tpend = tp + Row_tlen [row] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ Rows = ((Int *) p) + ep->ncols ;
+ if (Rows [f] == EMPTY) continue ; /* row already assembled */
+ ASSERT (row == Rows [f]) ;
+ extrdeg = (ep->rdeg < rdeg0) ? ep->ncolsleft : (ep->rdeg - rdeg0) ;
+ extcdeg = (ep->cdeg < cdeg0) ? ep->nrowsleft : (ep->cdeg - cdeg0) ;
+ DEBUG6 ((
+ "e "ID" After assembly ext row deg: "ID" ext col degree "ID"\n",
+ e, extrdeg, extcdeg)) ;
+
+ if (Work->any_skip)
+ {
+ /* no Lsons in any row, except for very tall and thin ones */
+ ASSERT (extrdeg >= 0) ;
+ if (extrdeg == 0)
+ {
+ /* this is an unassemble Lson */
+ ASSERT (ep->ncols == 1) ;
+ ASSERT (ep->ncolsleft == 1) ;
+ col = Cols [0] ;
+ ASSERT (col != Work->pivcol) ;
+ }
+ }
+ else
+ {
+ /* no Lsons in any row */
+ ASSERT (extrdeg > 0) ;
+ /* Uson external row degree is = number of cols left */
+ ASSERT (IMPLIES (extcdeg == 0, extrdeg == ep->ncolsleft)) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+
+ for (j2 = 0 ; j2 < fncols ; j2++)
+ {
+ /* Get a column */
+ col = Work->Fcols [j2] ;
+ ASSERT (col >= 0 && col < n_col) ;
+
+ DEBUG6 (("DEBUG SCAN 2: "ID"\n", col)) ;
+#ifndef FIXQ
+ UMF_dump_rowcol (1, Numeric, Work, col, TRUE) ;
+#else
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+#endif
+
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ tpi = Col_tuples [col] ;
+ if (!tpi) continue ;
+ tp = (Tuple *) (Memory + tpi) ;
+ tpend = tp + Col_tlen [col] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ Rows = ((Int *) p) + ep->ncols ;
+ if (Cols [f] == EMPTY) continue ; /* column already assembled */
+ ASSERT (col == Cols [f]) ;
+ extrdeg = (ep->rdeg < rdeg0) ? ep->ncolsleft : (ep->rdeg - rdeg0) ;
+ extcdeg = (ep->cdeg < cdeg0) ? ep->nrowsleft : (ep->cdeg - cdeg0) ;
+ DEBUG6 (("e "ID" After assembly ext col deg: "ID"\n", e, extcdeg)) ;
+
+ if (Work->any_skip)
+ {
+ /* no Usons in any column, except for very tall and thin ones */
+ ASSERT (extcdeg >= 0) ;
+ if (extcdeg == 0)
+ {
+ /* this is an unassemble Uson */
+ ASSERT (ep->nrows == 1) ;
+ ASSERT (ep->nrowsleft == 1) ;
+ row = Rows [0] ;
+ ASSERT (row != Work->pivrow) ;
+ }
+ }
+ else
+ {
+ /* no Usons in any column */
+ ASSERT (extcdeg > 0) ;
+ /* Lson external column degree is = number of rows left */
+ ASSERT (IMPLIES (extrdeg == 0, extcdeg == ep->nrowsleft)) ;
+ }
+ }
+ }
+#endif /* NDEBUG */
+}
diff --git a/UMFPACK/Source/umf_assemble.h b/UMFPACK/Source/umf_assemble.h
new file mode 100644
index 0000000..e976b48
--- /dev/null
+++ b/UMFPACK/Source/umf_assemble.h
@@ -0,0 +1,17 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_assemble
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
+
+GLOBAL void UMF_assemble_fixq
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/UMFPACK/Source/umf_blas3_update.c b/UMFPACK/Source/umf_blas3_update.c
new file mode 100644
index 0000000..c4e9ee7
--- /dev/null
+++ b/UMFPACK/Source/umf_blas3_update.c
@@ -0,0 +1,176 @@
+/* ========================================================================== */
+/* === UMF_blas3_update ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_internal.h"
+#include "umf_blas3_update.h"
+
+GLOBAL void UMF_blas3_update
+(
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry *L, *U, *C, *LU ;
+ Int i, j, s, k, m, n, d, nb, dc ;
+
+#ifndef NBLAS
+ Int blas_ok = TRUE ;
+#else
+#define blas_ok FALSE
+#endif
+
+ DEBUG5 (("In UMF_blas3_update "ID" "ID" "ID"\n",
+ Work->fnpiv, Work->fnrows, Work->fncols)) ;
+
+ k = Work->fnpiv ;
+ if (k == 0)
+ {
+ /* no work to do */
+ return ;
+ }
+
+ m = Work->fnrows ;
+ n = Work->fncols ;
+
+ d = Work->fnr_curr ;
+ dc = Work->fnc_curr ;
+ nb = Work->nb ;
+ ASSERT (d >= 0 && (d % 2) == 1) ;
+ C = Work->Fcblock ; /* ldc is fnr_curr */
+ L = Work->Flblock ; /* ldl is fnr_curr */
+ U = Work->Fublock ; /* ldu is fnc_curr, stored by rows */
+ LU = Work->Flublock ; /* nb-by-nb */
+
+#ifndef NDEBUG
+ DEBUG5 (("DO RANK-NB UPDATE of frontal:\n")) ;
+ DEBUG5 (("DGEMM : "ID" "ID" "ID"\n", k, m, n)) ;
+ DEBUG7 (("C block: ")) ; UMF_dump_dense (C, d, m, n) ;
+ DEBUG7 (("A block: ")) ; UMF_dump_dense (L, d, m, k) ;
+ DEBUG7 (("B' block: ")) ; UMF_dump_dense (U, dc, n, k) ;
+ DEBUG7 (("LU block: ")) ; UMF_dump_dense (LU, nb, k, k) ;
+#endif
+
+ if (k == 1)
+ {
+
+#ifndef NBLAS
+ BLAS_GER (m, n, L, U, C, d) ;
+#endif
+
+ if (!blas_ok)
+ {
+ /* rank-1 outer product to update the C block */
+ for (j = 0 ; j < n ; j++)
+ {
+ Entry u_j = U [j] ;
+ if (IS_NONZERO (u_j))
+ {
+ Entry *c_ij, *l_is ;
+ c_ij = & C [j*d] ;
+ l_is = & L [0] ;
+#pragma ivdep
+ for (i = 0 ; i < m ; i++)
+ {
+ /* C [i+j*d]-= L [i] * U [j] */
+ MULT_SUB (*c_ij, *l_is, u_j) ;
+ c_ij++ ;
+ l_is++ ;
+ }
+ }
+ }
+ }
+
+ }
+ else
+ {
+
+ /* triangular solve to update the U block */
+
+#ifndef NBLAS
+ BLAS_TRSM_RIGHT (n, k, LU, nb, U, dc) ;
+#endif
+
+ if (!blas_ok)
+ {
+ /* use plain C code if no BLAS at compile time, or if integer
+ * overflow has occurred */
+ for (s = 0 ; s < k ; s++)
+ {
+ for (i = s+1 ; i < k ; i++)
+ {
+ Entry l_is = LU [i+s*nb] ;
+ if (IS_NONZERO (l_is))
+ {
+ Entry *u_ij, *u_sj ;
+ u_ij = & U [i*dc] ;
+ u_sj = & U [s*dc] ;
+#pragma ivdep
+ for (j = 0 ; j < n ; j++)
+ {
+ /* U [i*dc+j] -= LU [i+s*nb] * U [s*dc+j] ; */
+ MULT_SUB (*u_ij, l_is, *u_sj) ;
+ u_ij++ ;
+ u_sj++ ;
+ }
+ }
+ }
+ }
+ }
+
+ /* rank-k outer product to update the C block */
+ /* C = C - L*U' (U is stored by rows, not columns) */
+
+#ifndef NBLAS
+ BLAS_GEMM (m, n, k, L, U, dc, C, d) ;
+#endif
+
+ if (!blas_ok)
+ {
+ /* use plain C code if no BLAS at compile time, or if integer
+ * overflow has occurred */
+
+ for (s = 0 ; s < k ; s++)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ Entry u_sj = U [j+s*dc] ;
+ if (IS_NONZERO (u_sj))
+ {
+ Entry *c_ij, *l_is ;
+ c_ij = & C [j*d] ;
+ l_is = & L [s*d] ;
+#pragma ivdep
+ for (i = 0 ; i < m ; i++)
+ {
+ /* C [i+j*d]-= L [i+s*d] * U [s*dc+j] */
+ MULT_SUB (*c_ij, *l_is, u_sj) ;
+ c_ij++ ;
+ l_is++ ;
+ }
+ }
+ }
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG5 (("RANK-NB UPDATE of frontal done:\n")) ;
+ DEBUG5 (("DGEMM : "ID" "ID" "ID"\n", k, m, n)) ;
+ DEBUG7 (("C block: ")) ; UMF_dump_dense (C, d, m, n) ;
+ DEBUG7 (("A block: ")) ; UMF_dump_dense (L, d, m, k) ;
+ DEBUG7 (("B' block: ")) ; UMF_dump_dense (U, dc, n, k) ;
+ DEBUG7 (("LU block: ")) ; UMF_dump_dense (LU, nb, k, k) ;
+#endif
+
+ DEBUG2 (("blas3 "ID" "ID" "ID"\n", k, Work->fnrows, Work->fncols)) ;
+}
diff --git a/UMFPACK/Source/umf_blas3_update.h b/UMFPACK/Source/umf_blas3_update.h
new file mode 100644
index 0000000..c77b9ac
--- /dev/null
+++ b/UMFPACK/Source/umf_blas3_update.h
@@ -0,0 +1,10 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_blas3_update
+(
+ WorkType *Work
+) ;
diff --git a/UMFPACK/Source/umf_build_tuples.c b/UMFPACK/Source/umf_build_tuples.c
new file mode 100644
index 0000000..c2ab324
--- /dev/null
+++ b/UMFPACK/Source/umf_build_tuples.c
@@ -0,0 +1,160 @@
+/* ========================================================================== */
+/* === UMF_build_tuples ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Construct the tuple lists from a set of packed elements (no holes in
+ elements, no internal or external fragmentation, and a packed (0..Work->nel)
+ element name space). Assume no tuple lists are currently allocated, but
+ that the tuple lengths have been initialized by UMF_tuple_lengths.
+
+ Returns TRUE if successful, FALSE if not enough memory.
+*/
+
+#include "umf_internal.h"
+#include "umf_build_tuples.h"
+#include "umf_mem_alloc_tail_block.h"
+
+GLOBAL Int UMF_build_tuples
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int e, nrows, ncols, nel, *Rows, *Cols, row, col, n_row, n_col, *E,
+ *Row_tuples, *Row_degree, *Row_tlen,
+ *Col_tuples, *Col_degree, *Col_tlen, n1 ;
+ Element *ep ;
+ Unit *p ;
+ Tuple tuple, *tp ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ E = Work->E ;
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+ Row_tuples = Numeric->Uip ;
+ Row_tlen = Numeric->Uilen ;
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ nel = Work->nel ;
+ n1 = Work->n1 ;
+
+ DEBUG3 (("BUILD_TUPLES: n_row "ID" n_col "ID" nel "ID"\n",
+ n_row, n_col, nel)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate space for the tuple lists */
+ /* ---------------------------------------------------------------------- */
+
+ /* Garbage collection and memory reallocation have already attempted to */
+ /* ensure that there is enough memory for all the tuple lists. If */
+ /* memory allocation fails here, then there is nothing more to be done. */
+
+ for (row = n1 ; row < n_row ; row++)
+ {
+ if (NON_PIVOTAL_ROW (row))
+ {
+ Row_tuples [row] = UMF_mem_alloc_tail_block (Numeric,
+ UNITS (Tuple, TUPLES (Row_tlen [row]))) ;
+ if (!Row_tuples [row])
+ {
+ /* :: out of memory for row tuples :: */
+ DEBUGm4 (("out of memory: build row tuples\n")) ;
+ return (FALSE) ; /* out of memory for row tuples */
+ }
+ Row_tlen [row] = 0 ;
+ }
+ }
+
+ /* push on stack in reverse order, so column tuples are in the order */
+ /* that they will be deleted. */
+ for (col = n_col-1 ; col >= n1 ; col--)
+ {
+ if (NON_PIVOTAL_COL (col))
+ {
+ Col_tuples [col] = UMF_mem_alloc_tail_block (Numeric,
+ UNITS (Tuple, TUPLES (Col_tlen [col]))) ;
+ if (!Col_tuples [col])
+ {
+ /* :: out of memory for col tuples :: */
+ DEBUGm4 (("out of memory: build col tuples\n")) ;
+ return (FALSE) ; /* out of memory for col tuples */
+ }
+ Col_tlen [col] = 0 ;
+ }
+ }
+
+#ifndef NDEBUG
+ UMF_dump_memory (Numeric) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* create the tuple lists (exclude element 0) */
+ /* ---------------------------------------------------------------------- */
+
+ /* for all elements, in order of creation */
+ for (e = 1 ; e <= nel ; e++)
+ {
+ DEBUG9 (("Adding tuples for element: "ID" at "ID"\n", e, E [e])) ;
+ ASSERT (E [e]) ; /* no external fragmentation */
+ p = Numeric->Memory + E [e] ;
+ GET_ELEMENT_PATTERN (ep, p, Cols, Rows, ncols) ;
+ nrows = ep->nrows ;
+ ASSERT (e != 0) ;
+ ASSERT (e == 0 || nrows == ep->nrowsleft) ;
+ ASSERT (e == 0 || ncols == ep->ncolsleft) ;
+ tuple.e = e ;
+ for (tuple.f = 0 ; tuple.f < ncols ; tuple.f++)
+ {
+ col = Cols [tuple.f] ;
+ ASSERT (col >= n1 && col < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ ASSERT (Col_tuples [col]) ;
+ tp = ((Tuple *) (Numeric->Memory + Col_tuples [col]))
+ + Col_tlen [col]++ ;
+ *tp = tuple ;
+#ifndef NDEBUG
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+#endif
+ }
+ for (tuple.f = 0 ; tuple.f < nrows ; tuple.f++)
+ {
+ row = Rows [tuple.f] ;
+ ASSERT (row >= n1 && row < n_row) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ ASSERT (Row_tuples [row]) ;
+ tp = ((Tuple *) (Numeric->Memory + Row_tuples [row]))
+ + Row_tlen [row]++ ;
+ *tp = tuple ;
+#ifndef NDEBUG
+ UMF_dump_rowcol (0, Numeric, Work, row, FALSE) ;
+#endif
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* the tuple lists are now valid, and can be scanned */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_dump_memory (Numeric) ;
+ UMF_dump_matrix (Numeric, Work, FALSE) ;
+#endif
+ DEBUG3 (("BUILD_TUPLES: done\n")) ;
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umf_build_tuples.h b/UMFPACK/Source/umf_build_tuples.h
new file mode 100644
index 0000000..0b0410c
--- /dev/null
+++ b/UMFPACK/Source/umf_build_tuples.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_build_tuples
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/UMFPACK/Source/umf_colamd.c b/UMFPACK/Source/umf_colamd.c
new file mode 100644
index 0000000..5a9b168
--- /dev/null
+++ b/UMFPACK/Source/umf_colamd.c
@@ -0,0 +1,3139 @@
+/* ========================================================================== */
+/* === UMF_colamd =========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+UMF_colamd: an approximate minimum degree column ordering algorithm,
+ used as a preordering for UMFPACK.
+
+NOTE: if this routine is used outside of UMFPACK, for a sparse Cholesky
+factorization of (AQ)'*(AQ) or a QR factorization of A, then one line should
+be removed (the "&& pivot_row_thickness > 0" expression). See the comment
+regarding the Cholesky factorization, below.
+
+Purpose:
+
+ Colamd computes a permutation Q such that the Cholesky factorization of
+ (AQ)'(AQ) has less fill-in and requires fewer floating point operations
+ than A'A. This also provides a good ordering for sparse partial
+ pivoting methods, P(AQ) = LU, where Q is computed prior to numerical
+ factorization, and P is computed during numerical factorization via
+ conventional partial pivoting with row interchanges. Colamd is the
+ column ordering method used in SuperLU, part of the ScaLAPACK library.
+ It is also available as built-in function in MATLAB Version 6,
+ available from MathWorks, Inc. (http://www.mathworks.com). This
+ routine can be used in place of colmmd in MATLAB. By default, the \
+ and / operators in MATLAB perform a column ordering (using colmmd
+ or colamd) prior to LU factorization using sparse partial pivoting,
+ in the built-in MATLAB lu(A) routine.
+
+ This code is derived from Colamd Version 2.0.
+
+Authors:
+
+ The authors of the COLAMD code itself are Stefan I. Larimore and Timothy A.
+ Davis, University of Florida. The algorithm was developed in collaboration
+ with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory.
+ The AMD metric on which this is based is by Patrick Amestoy, T. Davis,
+ and Iain Duff.
+
+Date:
+
+ UMFPACK Version: see above.
+ COLAMD Version 2.0 was released on January 31, 2000.
+
+Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+
+UMFPACK: Copyright (c) 2003 by Timothy A. Davis. All Rights Reserved.
+
+See the UMFPACK README file for the License for your use of this code.
+
+Availability:
+
+ Both UMFPACK and the original unmodified colamd/symamd library are
+ available at http://www.cise.ufl.edu/research/sparse.
+
+Changes for inclusion in UMFPACK:
+
+ * symamd, symamd_report, and colamd_report removed
+
+ * additional terms added to RowInfo, ColInfo, and stats
+
+ * Frontal matrix information computed for UMFPACK
+
+ * routines renamed
+
+ * column elimination tree post-ordering incorporated. In the original
+ version 2.0, this was performed in colamd.m.
+
+For more information, see:
+
+ Amestoy, P. R. and Davis, T. A. and Duff, I. S.,
+ An approximate minimum degree ordering algorithm,
+ SIAM J. Matrix Analysis and Applic, vol 17, no 4., pp 886-905, 1996.
+
+ Davis, T. A. and Gilbert, J. R. and Larimore, S. I. and Ng, E. G.,
+ A column approximate minimum degree ordering algorithm,
+ Univ. of Florida, CISE Dept., TR-00-005, Gainesville, FL
+ Oct. 2000. Submitted to ACM Trans. Math. Softw.
+
+*/
+
+/* ========================================================================== */
+/* === Description of user-callable routines ================================ */
+/* ========================================================================== */
+
+/*
+ ----------------------------------------------------------------------------
+ colamd_recommended: removed for UMFPACK
+ ----------------------------------------------------------------------------
+
+ ----------------------------------------------------------------------------
+ colamd_set_defaults:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ colamd_set_defaults (double knobs [COLAMD_KNOBS]) ;
+
+ Purpose:
+
+ Sets the default parameters. The use of this routine is optional.
+
+ Arguments:
+
+ double knobs [COLAMD_KNOBS] ; Output only.
+
+ Let c = knobs [COLAMD_DENSE_COL], r = knobs [COLAMD_DENSE_ROW].
+ Colamd: rows with more than max (16, r*16*sqrt(n_col))
+ entries are removed prior to ordering. Columns with more than
+ max (16, c*16*sqrt(n_row)) entries are removed prior to
+ ordering, and placed last in the output column ordering.
+
+ Symamd: removed for UMFPACK.
+
+ COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1,
+ respectively, in colamd.h. Default values of these two knobs
+ are both 0.5. Currently, only knobs [0] and knobs [1] are
+ used, but future versions may use more knobs. If so, they will
+ be properly set to their defaults by the future version of
+ colamd_set_defaults, so that the code that calls colamd will
+ not need to change, assuming that you either use
+ colamd_set_defaults, or pass a (double *) NULL pointer as the
+ knobs array to colamd or symamd.
+
+ knobs [COLAMD_AGGRESSIVE]: if nonzero, then perform aggressive
+ absorption. Otherwise, do not. This version does aggressive
+ absorption by default. COLAMD v2.1 (in MATLAB) always
+ does aggressive absorption (it doesn't have an option to turn
+ it off).
+
+ ----------------------------------------------------------------------------
+ colamd:
+ ----------------------------------------------------------------------------
+
+ C syntax:
+
+ #include "colamd.h"
+ Int UMF_colamd (Int n_row, Int n_col, Int Alen, Int *A, Int *p,
+ double knobs [COLAMD_KNOBS], Int stats [COLAMD_STATS]) ;
+
+ Purpose:
+
+ Computes a column ordering (Q) of A such that P(AQ)=LU or
+ (AQ)'AQ=LL' have less fill-in and require fewer floating point
+ operations than factorizing the unpermuted matrix A or A'A,
+ respectively.
+
+ Returns:
+
+ TRUE (1) if successful, FALSE (0) otherwise.
+
+ Arguments:
+
+ Int n_row ; Input argument.
+
+ Number of rows in the matrix A.
+ Restriction: n_row >= 0.
+ Colamd returns FALSE if n_row is negative.
+
+ Int n_col ; Input argument.
+
+ Number of columns in the matrix A.
+ Restriction: n_col >= 0.
+ Colamd returns FALSE if n_col is negative.
+
+ Int Alen ; Input argument.
+
+ Restriction (see note):
+ Alen >= 2*nnz + 8*(n_col+1) + 6*(n_row+1) + n_col
+ Colamd returns FALSE if these conditions are not met.
+
+ Note: this restriction makes an modest assumption regarding
+ the size of the two typedef's structures in colamd.h.
+ We do, however, guarantee that
+
+ Alen >= UMF_COLAMD_RECOMMENDED (nnz, n_row, n_col)
+
+ will be sufficient.
+
+ Int A [Alen] ; Input and output argument.
+
+ A is an integer array of size Alen. Alen must be at least as
+ large as the bare minimum value given above, but this is very
+ low, and can result in excessive run time. For best
+ performance, we recommend that Alen be greater than or equal to
+ UMF_COLAMD_RECOMMENDED (nnz, n_row, n_col), which adds
+ nnz/5 to the bare minimum value given above.
+
+ On input, the row indices of the entries in column c of the
+ matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices
+ in a given column c need not be in ascending order, and
+ duplicate row indices may be be present. However, colamd will
+ work a little faster if both of these conditions are met
+ (Colamd puts the matrix into this format, if it finds that the
+ the conditions are not met).
+
+ The matrix is 0-based. That is, rows are in the range 0 to
+ n_row-1, and columns are in the range 0 to n_col-1. Colamd
+ returns FALSE if any row index is out of range.
+
+ A holds the inverse permutation on output.
+
+ Int p [n_col+1] ; Both input and output argument.
+
+ p is an integer array of size n_col+1. On input, it holds the
+ "pointers" for the column form of the matrix A. Column c of
+ the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first
+ entry, p [0], must be zero, and p [c] <= p [c+1] must hold
+ for all c in the range 0 to n_col-1. The value p [n_col] is
+ thus the total number of entries in the pattern of the matrix A.
+ Colamd returns FALSE if these conditions are not met.
+
+ On output, if colamd returns TRUE, the array p holds the column
+ permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is
+ the first column index in the new ordering, and p [n_col-1] is
+ the last. That is, p [k] = j means that column j of A is the
+ kth pivot column, in AQ, where k is in the range 0 to n_col-1
+ (p [0] = j means that column j of A is the first column in AQ).
+
+ If colamd returns FALSE, then no permutation is returned, and
+ p is undefined on output.
+
+ double knobs [COLAMD_KNOBS] ; Input argument.
+
+ See colamd_set_defaults for a description.
+ The behavior is undefined if knobs contains NaN's.
+ (UMFPACK does not call umf_colamd with NaN-valued knobs).
+
+ Int stats [COLAMD_STATS] ; Output argument.
+
+ Statistics on the ordering, and error status.
+ See colamd.h for related definitions.
+ Colamd returns FALSE if stats is not present.
+
+ stats [0]: number of dense or empty rows ignored.
+
+ stats [1]: number of dense or empty columns ignored (and
+ ordered last in the output permutation p)
+ Note that a row can become "empty" if it
+ contains only "dense" and/or "empty" columns,
+ and similarly a column can become "empty" if it
+ only contains "dense" and/or "empty" rows.
+
+ stats [2]: number of garbage collections performed.
+ This can be excessively high if Alen is close
+ to the minimum required value.
+
+ stats [3]: status code. < 0 is an error code.
+ > 1 is a warning or notice.
+
+ 0 OK. Each column of the input matrix contained
+ row indices in increasing order, with no
+ duplicates.
+
+ -11 Columns of input matrix jumbled
+ (unsorted columns or duplicate entries).
+
+ stats [4]: the bad column index
+ stats [5]: the bad row index
+
+ -1 A is a null pointer
+
+ -2 p is a null pointer
+
+ -3 n_row is negative
+
+ stats [4]: n_row
+
+ -4 n_col is negative
+
+ stats [4]: n_col
+
+ -5 number of nonzeros in matrix is negative
+
+ stats [4]: number of nonzeros, p [n_col]
+
+ -6 p [0] is nonzero
+
+ stats [4]: p [0]
+
+ -7 A is too small
+
+ stats [4]: required size
+ stats [5]: actual size (Alen)
+
+ -8 a column has a zero or negative number of
+ entries (changed for UMFPACK)
+
+ stats [4]: column with <= 0 entries
+ stats [5]: number of entries in col
+
+ -9 a row index is out of bounds
+
+ stats [4]: column with bad row index
+ stats [5]: bad row index
+ stats [6]: n_row, # of rows of matrx
+
+ -10 unused
+
+ -999 (unused; see symamd.c)
+
+ Future versions may return more statistics in the stats array.
+
+ Example:
+
+ See http://www.cise.ufl.edu/~davis/colamd/example.c
+ for a complete example.
+
+ To order the columns of a 5-by-4 matrix with 11 nonzero entries in
+ the following nonzero pattern
+
+ x 0 x 0
+ x 0 x x
+ 0 x x 0
+ 0 0 x x
+ x x 0 0
+
+ with default knobs and no output statistics, do the following:
+
+ #include "colamd.h"
+ #define ALEN UMF_COLAMD_RECOMMENDED (11, 5, 4)
+ Int A [ALEN] = {1, 2, 5, 3, 5, 1, 2, 3, 4, 2, 4} ;
+ Int p [ ] = {0, 3, 5, 9, 11} ;
+ Int stats [COLAMD_STATS] ;
+ UMF_colamd (5, 4, ALEN, A, p, (double *) NULL, stats) ;
+
+ The permutation is returned in the array p, and A is destroyed.
+
+
+ ----------------------------------------------------------------------------
+ symamd: does not appear in this version for UMFPACK
+ ----------------------------------------------------------------------------
+
+ ----------------------------------------------------------------------------
+ colamd_report: does not appear in this version for UMFPACK
+ ----------------------------------------------------------------------------
+
+ ----------------------------------------------------------------------------
+ symamd_report: does not appear in this version for UMFPACK
+ ----------------------------------------------------------------------------
+
+*/
+
+/* ========================================================================== */
+/* === Scaffolding code definitions ======================================== */
+/* ========================================================================== */
+
+/* UMFPACK debugging control moved to amd_internal.h */
+
+/*
+ Our "scaffolding code" philosophy: In our opinion, well-written library
+ code should keep its "debugging" code, and just normally have it turned off
+ by the compiler so as not to interfere with performance. This serves
+ several purposes:
+
+ (1) assertions act as comments to the reader, telling you what the code
+ expects at that point. All assertions will always be true (unless
+ there really is a bug, of course).
+
+ (2) leaving in the scaffolding code assists anyone who would like to modify
+ the code, or understand the algorithm (by reading the debugging output,
+ one can get a glimpse into what the code is doing).
+
+ (3) (gasp!) for actually finding bugs. This code has been heavily tested
+ and "should" be fully functional and bug-free ... but you never know...
+
+ To enable debugging, comment out the "#define NDEBUG" above. For a MATLAB
+ mexFunction, you will also need to modify mexopts.sh to remove the -DNDEBUG
+ definition. The code will become outrageously slow when debugging is
+ enabled. To control the level of debugging output, set an environment
+ variable D to 0 (little), 1 (some), 2, 3, or 4 (lots). When debugging,
+ you should see the following message on the standard output:
+
+ colamd: debug version, D = 1 (THIS WILL BE SLOW!)
+
+ or a similar message for symamd. If you don't, then debugging has not
+ been enabled.
+
+*/
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+/* ------------------ */
+/* modified for UMFPACK: */
+#include "umf_internal.h"
+#include "umf_colamd.h"
+#include "umf_apply_order.h"
+#include "umf_fsize.h"
+/* ------------------ */
+
+/* ========================================================================== */
+/* === Definitions ========================================================== */
+/* ========================================================================== */
+
+/* ------------------ */
+/* UMFPACK: duplicate definitions moved to umf_internal.h */
+/* ------------------ */
+
+/* Row and column status */
+#define ALIVE (0)
+#define DEAD (-1)
+
+/* Column status */
+#define DEAD_PRINCIPAL (-1)
+#define DEAD_NON_PRINCIPAL (-2)
+
+/* Macros for row and column status update and checking. */
+#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark)
+#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE)
+#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE)
+#define COL_IS_DEAD(c) (Col [c].start < ALIVE)
+#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE)
+#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL)
+#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; }
+#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; }
+#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }
+
+/* ------------------ */
+/* UMFPACK: Colamd reporting mechanism moved to umf_internal.h */
+/* ------------------ */
+
+/* ========================================================================== */
+/* === Prototypes of PRIVATE routines ======================================= */
+/* ========================================================================== */
+
+PRIVATE Int init_rows_cols
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int p []
+ /* Int stats [COLAMD_STATS] */
+) ;
+
+PRIVATE void init_scoring
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ double knobs [COLAMD_KNOBS],
+ Int *p_n_row2,
+ Int *p_n_col2,
+ Int *p_max_deg
+ /* ------------------ */
+ /* added for UMFPACK */
+ , Int *p_ndense_row /* number of dense rows */
+ , Int *p_nempty_row /* number of original empty rows */
+ , Int *p_nnewlyempty_row /* number of newly empty rows */
+ , Int *p_ndense_col /* number of dense cols (excl "empty" cols) */
+ , Int *p_nempty_col /* number of original empty cols */
+ , Int *p_nnewlyempty_col /* number of newly empty cols */
+) ;
+
+PRIVATE Int find_ordering
+(
+ Int n_row,
+ Int n_col,
+ Int Alen,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ Int n_col2,
+ Int max_deg,
+ Int pfree
+ /* ------------------ */
+ /* added for UMFPACK: */
+ , Int Front_npivcol [ ]
+ , Int Front_nrows [ ]
+ , Int Front_ncols [ ]
+ , Int Front_parent [ ]
+ , Int Front_cols [ ]
+ , Int *p_nfr
+ , Int aggressive
+ , Int InFront [ ]
+ /* ------------------ */
+) ;
+
+/* ------------------ */
+/* order_children deleted for UMFPACK: */
+/* ------------------ */
+
+PRIVATE void detect_super_cols
+(
+
+#ifndef NDEBUG
+ Int n_col,
+ Colamd_Row Row [],
+#endif /* NDEBUG */
+
+ Colamd_Col Col [],
+ Int A [],
+ Int head [],
+ Int row_start,
+ Int row_length
+) ;
+
+PRIVATE Int garbage_collection
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int *pfree
+) ;
+
+PRIVATE Int clear_mark
+(
+ Int n_row,
+ Colamd_Row Row []
+) ;
+
+/* ------------------ */
+/* print_report deleted for UMFPACK */
+/* ------------------ */
+
+/* ========================================================================== */
+/* === Debugging prototypes and definitions ================================= */
+/* ========================================================================== */
+
+#ifndef NDEBUG
+
+/* ------------------ */
+/* debugging macros moved for UMFPACK */
+/* ------------------ */
+
+PRIVATE void debug_deg_lists
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int head [],
+ Int min_score,
+ Int should,
+ Int max_deg
+) ;
+
+PRIVATE void debug_mark
+(
+ Int n_row,
+ Colamd_Row Row [],
+ Int tag_mark,
+ Int max_mark
+) ;
+
+PRIVATE void debug_matrix
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A []
+) ;
+
+PRIVATE void debug_structures
+(
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int n_col2
+) ;
+
+/* ------------------ */
+/* dump_super added for UMFPACK: */
+PRIVATE void dump_super
+(
+ Int super_c,
+ Colamd_Col Col [],
+ Int n_col
+) ;
+/* ------------------ */
+
+#endif /* NDEBUG */
+
+/* ========================================================================== */
+
+
+
+/* ========================================================================== */
+/* === USER-CALLABLE ROUTINES: ============================================== */
+/* ========================================================================== */
+
+
+/* ========================================================================== */
+/* === colamd_set_defaults ================================================== */
+/* ========================================================================== */
+
+/*
+ The colamd_set_defaults routine sets the default values of the user-
+ controllable parameters for colamd:
+
+ knobs [0] rows with knobs[0]*n_col entries or more are removed
+ prior to ordering in colamd. Rows and columns with
+ knobs[0]*n_col entries or more are removed prior to
+ ordering in symamd and placed last in the output
+ ordering.
+
+ knobs [1] columns with knobs[1]*n_row entries or more are removed
+ prior to ordering in colamd, and placed last in the
+ column permutation. Symamd ignores this knob.
+
+ knobs [2] if nonzero, then perform aggressive absorption.
+
+ knobs [3..19] unused, but future versions might use this
+*/
+
+GLOBAL void UMF_colamd_set_defaults
+(
+ /* === Parameters ======================================================= */
+
+ double knobs [COLAMD_KNOBS] /* knob array */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ;
+
+#if 0
+ if (!knobs)
+ {
+ return ; /* UMFPACK always passes knobs array */
+ }
+#endif
+ for (i = 0 ; i < COLAMD_KNOBS ; i++)
+ {
+ knobs [i] = 0 ;
+ }
+ knobs [COLAMD_DENSE_ROW] = 0.2 ; /* default changed for UMFPACK */
+ knobs [COLAMD_DENSE_COL] = 0.2 ; /* default changed for UMFPACK */
+ knobs [COLAMD_AGGRESSIVE] = TRUE ; /* default is to do aggressive
+ * absorption */
+}
+
+
+/* ========================================================================== */
+/* === symamd removed for UMFPACK =========================================== */
+/* ========================================================================== */
+
+
+
+/* ========================================================================== */
+/* === colamd =============================================================== */
+/* ========================================================================== */
+
+/*
+ The colamd routine computes a column ordering Q of a sparse matrix
+ A such that the LU factorization P(AQ) = LU remains sparse, where P is
+ selected via partial pivoting. The routine can also be viewed as
+ providing a permutation Q such that the Cholesky factorization
+ (AQ)'(AQ) = LL' remains sparse.
+*/
+
+/* For UMFPACK: colamd always returns TRUE */
+
+GLOBAL Int UMF_colamd /* returns TRUE if successful, FALSE otherwise*/
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows in A */
+ Int n_col, /* number of columns in A */
+ Int Alen, /* length of A */
+ Int A [], /* row indices of A */
+ Int p [], /* pointers to columns in A */
+ double knobs [COLAMD_KNOBS],/* parameters (uses defaults if NULL) */
+ Int stats [COLAMD_STATS] /* output statistics and error codes */
+
+ /* ------------------ */
+ /* added for UMFPACK: each Front_ array is of size n_col+1 */
+ , Int Front_npivcol [ ] /* # pivot cols in each front */
+ , Int Front_nrows [ ] /* # of rows in each front (incl. pivot rows) */
+ , Int Front_ncols [ ] /* # of cols in each front (incl. pivot cols) */
+ , Int Front_parent [ ] /* parent of each front */
+ , Int Front_cols [ ] /* link list of pivot columns for each front */
+ , Int *p_nfr /* total number of frontal matrices */
+ , Int InFront [ ] /* InFront [row] = f if the original row was
+ * absorbed into front f. EMPTY if the row was
+ * empty, dense, or not absorbed. This array
+ * has size n_row+1 */
+ /* ------------------ */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int row ; /* row index */
+ Int i ; /* loop index */
+ Int nnz ; /* nonzeros in A */
+ Int Row_size ; /* size of Row [], in integers */
+ Int Col_size ; /* size of Col [], in integers */
+#if 0
+ Int need ; /* minimum required length of A */
+#endif
+ Colamd_Row *Row ; /* pointer into A of Row [0..n_row] array */
+ Colamd_Col *Col ; /* pointer into A of Col [0..n_col] array */
+ Int n_col2 ; /* number of non-dense, non-empty columns */
+ Int n_row2 ; /* number of non-dense, non-empty rows */
+ Int ngarbage ; /* number of garbage collections performed */
+ Int max_deg ; /* maximum row degree */
+ Int aggressive ; /* TRUE if doing aggressive absorption */
+#if 0
+ double default_knobs [COLAMD_KNOBS] ; /* default knobs array */
+#endif
+
+ /* ------------------ */
+ /* debugging initializations moved for UMFPACK */
+ /* ------------------ */
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Int ndense_row, nempty_row, parent, ndense_col,
+ nempty_col, k, col, nfr, *Front_child, *Front_sibling, *Front_stack,
+ *Front_order, *Front_size ;
+ Int nnewlyempty_col, nnewlyempty_row ;
+ /* ------------------ */
+
+ /* === Check the input arguments ======================================== */
+
+#if 0
+ if (!stats)
+ {
+ DEBUG0 (("colamd: stats not present\n")) ;
+ return (FALSE) ; /* UMFPACK: always passes stats [ ] */
+ }
+#endif
+
+ ASSERT (stats != (Int *) NULL) ;
+
+ for (i = 0 ; i < COLAMD_STATS ; i++)
+ {
+ stats [i] = 0 ;
+ }
+ stats [COLAMD_STATUS] = COLAMD_OK ;
+ stats [COLAMD_INFO1] = -1 ;
+ stats [COLAMD_INFO2] = -1 ;
+
+#if 0
+ if (!A) /* A is not present */
+ {
+ /* UMFPACK: always passes A [ ] */
+ DEBUG0 (("colamd: A not present\n")) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;
+ return (FALSE) ;
+ }
+
+ if (!p) /* p is not present */
+ {
+ /* UMFPACK: always passes p [ ] */
+ DEBUG0 (("colamd: p not present\n")) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;
+ return (FALSE) ;
+ }
+
+ if (n_row < 0) /* n_row must be >= 0 */
+ {
+ /* UMFPACK: does not call UMF_colamd if n <= 0 */
+ DEBUG0 (("colamd: nrow negative "ID"\n", n_row)) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ;
+ stats [COLAMD_INFO1] = n_row ;
+ return (FALSE) ;
+ }
+
+ if (n_col < 0) /* n_col must be >= 0 */
+ {
+ /* UMFPACK: does not call UMF_colamd if n <= 0 */
+ DEBUG0 (("colamd: ncol negative "ID"\n", n_col)) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;
+ stats [COLAMD_INFO1] = n_col ;
+ return (FALSE) ;
+ }
+#endif
+
+ ASSERT (A != (Int *) NULL) ;
+ ASSERT (p != (Int *) NULL) ;
+ ASSERT (n_row >= 0) ;
+ ASSERT (n_col >= 0) ;
+
+ nnz = p [n_col] ;
+
+#if 0
+ if (nnz < 0) /* nnz must be >= 0 */
+ {
+ /* UMFPACK: does not call UMF_colamd if nnz < 0 */
+ DEBUG0 (("colamd: number of entries negative "ID"\n", nnz)) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;
+ stats [COLAMD_INFO1] = nnz ;
+ return (FALSE) ;
+ }
+
+ if (p [0] != 0) /* p [0] must be exactly zero */
+ {
+ DEBUG0 (("colamd: p[0] not zero "ID"\n", p [0])) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;
+ stats [COLAMD_INFO1] = p [0] ;
+ return (FALSE) ;
+ }
+#endif
+
+ ASSERT (nnz >= 0) ;
+ ASSERT (p [0] == 0) ;
+
+ /* === If no knobs, set default knobs =================================== */
+
+#if 0
+ if (!knobs)
+ {
+ /* UMFPACK: always passes the knobs */
+ UMF_colamd_set_defaults (default_knobs) ;
+ knobs = default_knobs ;
+ }
+#endif
+
+ ASSERT (knobs != (double *) NULL) ;
+
+ /* --------------------- */
+ /* added for UMFPACK v4.1: */
+ aggressive = (knobs [COLAMD_AGGRESSIVE] != 0) ;
+ /* --------------------- */
+
+ /* === Allocate the Row and Col arrays from array A ===================== */
+
+ Col_size = UMF_COLAMD_C (n_col) ;
+ Row_size = UMF_COLAMD_R (n_row) ;
+
+#if 0
+ need = MAX (2*nnz, 4*n_col) + n_col + Col_size + Row_size ;
+ if (need > Alen)
+ {
+ /* UMFPACK: always passes enough space */
+ /* not enough space in array A to perform the ordering */
+ DEBUG0 (("colamd: Need Alen >= "ID", given only Alen = "ID"\n",
+ need, Alen)) ;
+ stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ;
+ stats [COLAMD_INFO1] = need ;
+ stats [COLAMD_INFO2] = Alen ;
+ return (FALSE) ;
+ }
+#endif
+
+ Alen -= Col_size + Row_size ;
+ Col = (Colamd_Col *) &A [Alen] ;
+ Row = (Colamd_Row *) &A [Alen + Col_size] ;
+
+ /* Size of A is now Alen >= MAX (2*nnz, 4*n_col) + n_col. The ordering
+ * requires Alen >= 2*nnz + n_col, and the postorder requires
+ * Alen >= 5*n_col. */
+
+ /* === Construct the row and column data structures ===================== */
+
+ i = init_rows_cols (n_row, n_col, Row, Col, A, p) ;
+
+#if 0
+ if (!i)
+ {
+ /* input matrix is invalid */
+ DEBUG0 (("colamd: Matrix invalid\n")) ;
+ return (FALSE) ;
+ }
+#endif
+
+ ASSERT (i) ;
+
+ /* === UMFPACK: Initialize front info =================================== */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Front_npivcol [col] = 0 ;
+ Front_nrows [col] = 0 ;
+ Front_ncols [col] = 0 ;
+ Front_parent [col] = EMPTY ;
+ Front_cols [col] = EMPTY ;
+ }
+
+ /* === Initialize scores, kill dense rows/columns ======================= */
+
+ init_scoring (n_row, n_col, Row, Col, A, p, knobs,
+ &n_row2, &n_col2, &max_deg
+ /* ------------------ */
+ /* added for UMFPACK: */
+ , &ndense_row, &nempty_row, &nnewlyempty_row
+ , &ndense_col, &nempty_col, &nnewlyempty_col
+ /* ------------------ */
+ ) ;
+ ASSERT (n_row2 == n_row - nempty_row - nnewlyempty_row - ndense_row) ;
+ ASSERT (n_col2 == n_col - nempty_col - nnewlyempty_col - ndense_col) ;
+
+ /* === Order the supercolumns =========================================== */
+
+ ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p,
+ n_col2, max_deg, 2*nnz
+ /* ------------------ */
+ /* added for UMFPACK: */
+ , Front_npivcol, Front_nrows, Front_ncols, Front_parent, Front_cols
+ , &nfr, aggressive, InFront
+ /* ------------------ */
+ ) ;
+
+ /* ------------------ */
+ /* changed for UMFPACK: */
+
+ /* A is no longer needed, so use A [0..5*nfr-1] as workspace [ [ */
+ /* This step requires Alen >= 5*n_col */
+ Front_child = A ;
+ Front_sibling = Front_child + nfr ;
+ Front_stack = Front_sibling + nfr ;
+ Front_order = Front_stack + nfr ;
+ Front_size = Front_order + nfr ;
+
+ UMF_fsize (nfr, Front_size, Front_nrows, Front_ncols,
+ Front_parent, Front_npivcol) ;
+
+ AMD_postorder (nfr, Front_parent, Front_npivcol, Front_size,
+ Front_order, Front_child, Front_sibling, Front_stack) ;
+
+ /* Front_size, Front_stack, Front_child, Front_sibling no longer needed ] */
+
+ /* use A [0..nfr-1] as workspace */
+ UMF_apply_order (Front_npivcol, Front_order, A, nfr, nfr) ;
+ UMF_apply_order (Front_nrows, Front_order, A, nfr, nfr) ;
+ UMF_apply_order (Front_ncols, Front_order, A, nfr, nfr) ;
+ UMF_apply_order (Front_parent, Front_order, A, nfr, nfr) ;
+ UMF_apply_order (Front_cols, Front_order, A, nfr, nfr) ;
+
+ /* fix the parent to refer to the new numbering */
+ for (i = 0 ; i < nfr ; i++)
+ {
+ parent = Front_parent [i] ;
+ if (parent != EMPTY)
+ {
+ Front_parent [i] = Front_order [parent] ;
+ }
+ }
+
+ /* fix InFront to refer to the new numbering */
+ for (row = 0 ; row < n_row ; row++)
+ {
+ i = InFront [row] ;
+ ASSERT (i >= EMPTY && i < nfr) ;
+ if (i != EMPTY)
+ {
+ InFront [row] = Front_order [i] ;
+ }
+ }
+
+ /* Front_order longer needed ] */
+
+ /* === Order the columns in the fronts ================================== */
+
+ /* use A [0..n_col-1] as inverse permutation */
+ for (i = 0 ; i < n_col ; i++)
+ {
+ A [i] = EMPTY ;
+ }
+ k = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ ASSERT (Front_npivcol [i] > 0) ;
+ for (col = Front_cols [i] ; col != EMPTY ; col = Col [col].nextcol)
+ {
+ ASSERT (col >= 0 && col < n_col) ;
+ DEBUG1 (("Colamd output ordering: k "ID" col "ID"\n", k, col)) ;
+ p [k] = col ;
+ ASSERT (A [col] == EMPTY) ;
+ A [col] = k ;
+ k++ ;
+ }
+ }
+
+ /* === Order the "dense" and null columns =============================== */
+
+ ASSERT (k == n_col2) ;
+ if (n_col2 < n_col)
+ {
+ for (col = 0 ; col < n_col ; col++)
+ {
+ if (A [col] == EMPTY)
+ {
+ k = Col [col].shared2.order ;
+ ASSERT (k >= n_col2 && k < n_col) ;
+ DEBUG1 (("Colamd output ordering: k "ID" col "ID
+ " (dense or null col)\n", k, col)) ;
+ p [k] = col ;
+ A [col] = k ;
+ }
+ }
+ }
+
+ /* ------------------ */
+
+ /* === Return statistics in stats ======================================= */
+
+ /* ------------------ */
+ /* modified for UMFPACK */
+ stats [COLAMD_DENSE_ROW] = ndense_row ;
+ stats [COLAMD_EMPTY_ROW] = nempty_row ;
+ stats [COLAMD_NEWLY_EMPTY_ROW] = nnewlyempty_row ;
+ stats [COLAMD_DENSE_COL] = ndense_col ;
+ stats [COLAMD_EMPTY_COL] = nempty_col ;
+ stats [COLAMD_NEWLY_EMPTY_COL] = nnewlyempty_col ;
+ ASSERT (ndense_col + nempty_col + nnewlyempty_col == n_col - n_col2) ;
+ /* ------------------ */
+ stats [COLAMD_DEFRAG_COUNT] = ngarbage ;
+ *p_nfr = nfr ;
+ DEBUG1 (("colamd: done.\n")) ;
+ return (TRUE) ;
+}
+
+
+
+
+/* ========================================================================== */
+/* === colamd_report removed for UMFPACK ==================================== */
+/* ========================================================================== */
+
+/* ========================================================================== */
+/* === symamd_report removed for UMFPACK ==================================== */
+/* ========================================================================== */
+
+
+
+/* ========================================================================== */
+/* === NON-USER-CALLABLE ROUTINES: ========================================== */
+/* ========================================================================== */
+
+/* There are no user-callable routines beyond this point in the file */
+
+
+/* ========================================================================== */
+/* === init_rows_cols ======================================================= */
+/* ========================================================================== */
+
+/*
+ Takes the column form of the matrix in A and creates the row form of the
+ matrix. Also, row and column attributes are stored in the Col and Row
+ structs. If the columns are un-sorted or contain duplicate row indices,
+ this routine will also sort and remove duplicate row indices from the
+ column form of the matrix. Returns FALSE if the matrix is invalid,
+ TRUE otherwise. Not user-callable.
+*/
+
+/* For UMFPACK, this always returns TRUE */
+
+PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* row indices of A, of size Alen */
+ Int p [] /* pointers to columns in A, of size n_col+1 */
+/*
+ Int stats [COLAMD_STATS] colamd statistics, removed for UMFPACK
+*/
+)
+{
+ /* === Local variables ================================================== */
+
+ Int col ; /* a column index */
+ Int row ; /* a row index */
+ Int *cp ; /* a column pointer */
+ Int *cp_end ; /* a pointer to the end of a column */
+
+ /* === Initialize columns, and check column pointers ==================== */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Col [col].start = p [col] ;
+ Col [col].length = p [col+1] - p [col] ;
+
+#if 0
+ if (Col [col].length < 0)
+ {
+ /* column pointers must be non-decreasing */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = Col [col].length ;
+ DEBUG0 (("colamd: col "ID" length "ID" <= 0\n",
+ col, Col [col].length));
+ return (FALSE) ;
+ }
+#endif
+
+ ASSERT (Col [col].length >= 0) ;
+
+ /* added for UMFPACK v4.1 */
+ ASSERT (Col [col].length > 0) ;
+
+ Col [col].shared1.thickness = 1 ;
+ Col [col].shared2.score = 0 ;
+ Col [col].shared3.prev = EMPTY ;
+ Col [col].shared4.degree_next = EMPTY ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Col [col].nextcol = EMPTY ;
+ Col [col].lastcol = col ;
+ /* ------------------ */
+ }
+
+ /* p [0..n_col] no longer needed, used as "head" in subsequent routines */
+
+ /* === Scan columns, compute row degrees, and check row indices ========= */
+
+ /* ------------------ */
+ /* stats [COLAMD_INFO3] = 0 ; */
+ /* number of duplicate or unsorted row indices - not computed in UMFPACK */
+ /* ------------------ */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].length = 0 ;
+ /* ------------------ */
+ /* removed for UMFPACK */
+ /* Row [row].shared2.mark = -1 ; */
+ /* ------------------ */
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Row [row].thickness = 1 ;
+ Row [row].front = EMPTY ;
+ /* ------------------ */
+ }
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+#ifndef NDEBUG
+ Int last_row = -1 ;
+#endif
+
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+
+#if 0
+ /* make sure row indices within range */
+ if (row < 0 || row >= n_row)
+ {
+ stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = row ;
+ /* ------------------ */
+ /* not needed in UMFPACK: */
+ /* stats [COLAMD_INFO3] = n_row ; */
+ /* ------------------ */
+ DEBUG0 (("colamd: row "ID" col "ID" out of bounds\n", row,col));
+ return (FALSE) ;
+ }
+#endif
+
+ ASSERT (row >= 0 && row < n_row) ;
+
+#if 0
+ /* ------------------ */
+ /* changed for UMFPACK */
+ if (row <= last_row)
+ {
+ /* row index are unsorted or repeated (or both), thus col */
+ /* is jumbled. This is an error condition for UMFPACK */
+ stats [COLAMD_STATUS] = COLAMD_ERROR_jumbled_matrix ;
+ stats [COLAMD_INFO1] = col ;
+ stats [COLAMD_INFO2] = row ;
+ DEBUG1 (("colamd: row "ID" col "ID" unsorted/duplicate\n",
+ row, col)) ;
+ return (FALSE) ;
+ }
+ /* ------------------ */
+#endif
+
+ ASSERT (row > last_row) ;
+
+ /* ------------------ */
+ /* changed for UMFPACK - jumbled columns not tolerated */
+ Row [row].length++ ;
+ /* ------------------ */
+
+#ifndef NDEBUG
+ last_row = row ;
+#endif
+ }
+ }
+
+ /* === Compute row pointers ============================================= */
+
+ /* row form of the matrix starts directly after the column */
+ /* form of matrix in A */
+ Row [0].start = p [n_col] ;
+ Row [0].shared1.p = Row [0].start ;
+ /* ------------------ */
+ /* removed for UMFPACK */
+ /* Row [0].shared2.mark = -1 ; */
+ /* ------------------ */
+ for (row = 1 ; row < n_row ; row++)
+ {
+ Row [row].start = Row [row-1].start + Row [row-1].length ;
+ Row [row].shared1.p = Row [row].start ;
+ /* ------------------ */
+ /* removed for UMFPACK */
+ /* Row [row].shared2.mark = -1 ; */
+ /* ------------------ */
+ }
+
+ /* === Create row form ================================================== */
+
+ /* ------------------ */
+ /* jumbled matrix case removed for UMFPACK */
+ /* ------------------ */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ A [(Row [*cp++].shared1.p)++] = col ;
+ }
+ }
+
+ /* === Clear the row marks and set row degrees ========================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].shared2.mark = 0 ;
+ Row [row].shared1.degree = Row [row].length ;
+ }
+
+ /* ------------------ */
+ /* recreate columns for jumbled matrix case removed for UMFPACK */
+ /* ------------------ */
+
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === init_scoring ========================================================= */
+/* ========================================================================== */
+
+/*
+ Kills dense or empty columns and rows, calculates an initial score for
+ each column, and places all columns in the degree lists. Not user-callable.
+*/
+
+PRIVATE void init_scoring
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* column form and row form of A */
+ Int head [], /* of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameters */
+ Int *p_n_row2, /* number of non-dense, non-empty rows */
+ Int *p_n_col2, /* number of non-dense, non-empty columns */
+ Int *p_max_deg /* maximum row degree */
+ /* ------------------ */
+ /* added for UMFPACK */
+ , Int *p_ndense_row /* number of dense rows */
+ , Int *p_nempty_row /* number of original empty rows */
+ , Int *p_nnewlyempty_row /* number of newly empty rows */
+ , Int *p_ndense_col /* number of dense cols (excl "empty" cols) */
+ , Int *p_nempty_col /* number of original empty cols */
+ , Int *p_nnewlyempty_col /* number of newly empty cols */
+ /* ------------------ */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int c ; /* a column index */
+ Int r, row ; /* a row index */
+ Int *cp ; /* a column pointer */
+ Int deg ; /* degree of a row or column */
+ Int *cp_end ; /* a pointer to the end of a column */
+ Int *new_cp ; /* new column pointer */
+ Int col_length ; /* length of pruned column */
+ Int score ; /* current column score */
+ Int n_col2 ; /* number of non-dense, non-empty columns */
+ Int n_row2 ; /* number of non-dense, non-empty rows */
+ Int dense_row_count ; /* remove rows with more entries than this */
+ Int dense_col_count ; /* remove cols with more entries than this */
+ Int min_score ; /* smallest column score */
+ Int max_deg ; /* maximum row degree */
+ Int next_col ; /* Used to add to degree list.*/
+
+ /* ------------------ */
+ /* added for UMFPACK */
+ Int ndense_row ; /* number of dense rows */
+ Int nempty_row ; /* number of empty rows */
+ Int nnewlyempty_row ; /* number of newly empty rows */
+ Int ndense_col ; /* number of dense cols (excl "empty" cols) */
+ Int nempty_col ; /* number of original empty cols */
+ Int nnewlyempty_col ; /* number of newly empty cols */
+ Int ne ;
+ /* ------------------ */
+
+#ifndef NDEBUG
+ Int debug_count ; /* debug only. */
+#endif /* NDEBUG */
+
+ /* === Extract knobs ==================================================== */
+
+ /* --------------------- */
+ /* old dense row/column knobs:
+ dense_row_count = MAX (0, MIN (knobs [COLAMD_DENSE_ROW] * n_col, n_col)) ;
+ dense_col_count = MAX (0, MIN (knobs [COLAMD_DENSE_COL] * n_row, n_row)) ;
+ */
+ /* new, for UMFPACK: */
+ /* Note: if knobs contains a NaN, this is undefined: */
+ dense_row_count =
+ UMFPACK_DENSE_DEGREE_THRESHOLD (knobs [COLAMD_DENSE_ROW], n_col) ;
+ dense_col_count =
+ UMFPACK_DENSE_DEGREE_THRESHOLD (knobs [COLAMD_DENSE_COL], n_row) ;
+ /* Make sure dense_*_count is between 0 and n: */
+ dense_row_count = MAX (0, MIN (dense_row_count, n_col)) ;
+ dense_col_count = MAX (0, MIN (dense_col_count, n_row)) ;
+ /* --------------------- */
+
+ DEBUG1 (("colamd: densecount: "ID" "ID"\n",
+ dense_row_count, dense_col_count)) ;
+ max_deg = 0 ;
+ n_col2 = n_col ;
+ n_row2 = n_row ;
+
+ /* --------------------- */
+ /* added for UMFPACK */
+ ndense_col = 0 ;
+ nempty_col = 0 ;
+ nnewlyempty_col = 0 ;
+ ndense_row = 0 ;
+ nempty_row = 0 ;
+ nnewlyempty_row = 0 ;
+ /* --------------------- */
+
+ /* === Kill empty columns =============================================== */
+
+ /* removed for UMFPACK v4.1. prune_singletons has already removed empty
+ * columns and empty rows */
+
+#if 0
+ /* Put the empty columns at the end in their natural order, so that LU */
+ /* factorization can proceed as far as possible. */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ deg = Col [c].length ;
+ if (deg == 0)
+ {
+ /* this is a empty column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ KILL_PRINCIPAL_COL (c) ;
+ /* --------------------- */
+ /* added for UMFPACK */
+ nempty_col++ ;
+ /* --------------------- */
+ }
+ }
+ DEBUG1 (("colamd: null columns killed: "ID"\n", n_col - n_col2)) ;
+#endif
+
+#ifndef NDEBUG
+ for (c = 0 ; c < n_col ; c++)
+ {
+ ASSERT (Col [c].length > 0) ;
+ }
+#endif
+
+ /* === Count null rows ================================================== */
+
+#if 0
+ for (r = 0 ; r < n_row ; r++)
+ {
+ deg = Row [r].shared1.degree ;
+ if (deg == 0)
+ {
+ /* this is an original empty row */
+ nempty_row++ ;
+ }
+ }
+#endif
+
+#ifndef NDEBUG
+ for (r = 0 ; r < n_row ; r++)
+ {
+ ASSERT (Row [r].shared1.degree > 0) ;
+ ASSERT (Row [r].length > 0) ;
+ }
+#endif
+
+ /* === Kill dense columns =============================================== */
+
+ /* Put the dense columns at the end, in their natural order */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+
+ /* ----------------------------------------------------------------- */
+#if 0
+ /* removed for UMFPACK v4.1: no empty columns */
+ /* skip any dead columns */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+#endif
+ ASSERT (COL_IS_ALIVE (c)) ;
+ ASSERT (Col [c].length > 0) ;
+ /* ----------------------------------------------------------------- */
+
+ deg = Col [c].length ;
+ if (deg > dense_col_count)
+ {
+ /* this is a dense column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ /* --------------------- */
+ /* added for UMFPACK */
+ ndense_col++ ;
+ /* --------------------- */
+ /* decrement the row degrees */
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ Row [*cp++].shared1.degree-- ;
+ }
+ KILL_PRINCIPAL_COL (c) ;
+ }
+ }
+ DEBUG1 (("colamd: Dense and null columns killed: "ID"\n", n_col - n_col2)) ;
+
+ /* === Kill dense and empty rows ======================================== */
+
+ /* Note that there can now be empty rows, since dense columns have
+ * been deleted. These are "newly" empty rows. */
+
+ ne = 0 ;
+ for (r = 0 ; r < n_row ; r++)
+ {
+ deg = Row [r].shared1.degree ;
+ ASSERT (deg >= 0 && deg <= n_col) ;
+ /* --------------------- */
+ /* added for UMFPACK */
+ if (deg > dense_row_count)
+ {
+ /* There is at least one dense row. Continue ordering, but */
+ /* symbolic factorization will be redone after UMF_colamd is done.*/
+ ndense_row++ ;
+ }
+ if (deg == 0)
+ {
+ /* this is a newly empty row, or original empty row */
+ ne++ ;
+ }
+ /* --------------------- */
+ if (deg > dense_row_count || deg == 0)
+ {
+ /* kill a dense or empty row */
+ KILL_ROW (r) ;
+ /* --------------------- */
+ /* added for UMFPACK */
+ Row [r].thickness = 0 ;
+ /* --------------------- */
+ --n_row2 ;
+ }
+ else
+ {
+ /* keep track of max degree of remaining rows */
+ max_deg = MAX (max_deg, deg) ;
+ }
+ }
+ nnewlyempty_row = ne - nempty_row ;
+ DEBUG1 (("colamd: Dense rows killed: "ID"\n", ndense_row)) ;
+ DEBUG1 (("colamd: Dense and null rows killed: "ID"\n", n_row - n_row2)) ;
+
+ /* === Compute initial column scores ==================================== */
+
+ /* At this point the row degrees are accurate. They reflect the number */
+ /* of "live" (non-dense) columns in each row. No empty rows exist. */
+ /* Some "live" columns may contain only dead rows, however. These are */
+ /* pruned in the code below. */
+
+ /* now find the initial matlab score for each column */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip dead column */
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ score = 0 ;
+ cp = &A [Col [c].start] ;
+ new_cp = cp ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ /* skip if dead */
+ if (ROW_IS_DEAD (row))
+ {
+ continue ;
+ }
+ /* compact the column */
+ *new_cp++ = row ;
+ /* add row's external degree */
+ score += Row [row].shared1.degree - 1 ;
+ /* guard against integer overflow */
+ score = MIN (score, n_col) ;
+ }
+ /* determine pruned column length */
+ col_length = (Int) (new_cp - &A [Col [c].start]) ;
+ if (col_length == 0)
+ {
+ /* a newly-made null column (all rows in this col are "dense" */
+ /* and have already been killed) */
+ DEBUG2 (("Newly null killed: "ID"\n", c)) ;
+ Col [c].shared2.order = --n_col2 ;
+ KILL_PRINCIPAL_COL (c) ;
+ /* --------------------- */
+ /* added for UMFPACK */
+ nnewlyempty_col++ ;
+ /* --------------------- */
+ }
+ else
+ {
+ /* set column length and set score */
+ ASSERT (score >= 0) ;
+ ASSERT (score <= n_col) ;
+ Col [c].length = col_length ;
+ Col [c].shared2.score = score ;
+ }
+ }
+ DEBUG1 (("colamd: Dense, null, and newly-null columns killed: "ID"\n",
+ n_col-n_col2)) ;
+
+ /* At this point, all empty rows and columns are dead. All live columns */
+ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */
+ /* yet). Rows may contain dead columns, but all live rows contain at */
+ /* least one live column. */
+
+#ifndef NDEBUG
+ debug_structures (n_row, n_col, Row, Col, A, n_col2) ;
+#endif /* NDEBUG */
+
+ /* === Initialize degree lists ========================================== */
+
+#ifndef NDEBUG
+ debug_count = 0 ;
+#endif /* NDEBUG */
+
+ /* clear the hash buckets */
+ for (c = 0 ; c <= n_col ; c++)
+ {
+ head [c] = EMPTY ;
+ }
+ min_score = n_col ;
+ /* place in reverse order, so low column indices are at the front */
+ /* of the lists. This is to encourage natural tie-breaking */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* only add principal columns to degree lists */
+ if (COL_IS_ALIVE (c))
+ {
+ DEBUG4 (("place "ID" score "ID" minscore "ID" ncol "ID"\n",
+ c, Col [c].shared2.score, min_score, n_col)) ;
+
+ /* === Add columns score to DList =============================== */
+
+ score = Col [c].shared2.score ;
+
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (score >= 0) ;
+ ASSERT (score <= n_col) ;
+ ASSERT (head [score] >= EMPTY) ;
+
+ /* now add this column to dList at proper score location */
+ next_col = head [score] ;
+ Col [c].shared3.prev = EMPTY ;
+ Col [c].shared4.degree_next = next_col ;
+
+ /* if there already was a column with the same score, set its */
+ /* previous pointer to this new column */
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = c ;
+ }
+ head [score] = c ;
+
+ /* see if this score is less than current min */
+ min_score = MIN (min_score, score) ;
+
+#ifndef NDEBUG
+ debug_count++ ;
+#endif /* NDEBUG */
+
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("colamd: Live cols "ID" out of "ID", non-princ: "ID"\n",
+ debug_count, n_col, n_col-debug_count)) ;
+ ASSERT (debug_count == n_col2) ;
+ debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2, max_deg) ;
+#endif /* NDEBUG */
+
+ /* === Return number of remaining columns, and max row degree =========== */
+
+ *p_n_col2 = n_col2 ;
+ *p_n_row2 = n_row2 ;
+ *p_max_deg = max_deg ;
+
+ /* --------------------- */
+ /* added for UMFPACK */
+ *p_ndense_row = ndense_row ;
+ *p_nempty_row = nempty_row ; /* original empty rows */
+ *p_nnewlyempty_row = nnewlyempty_row ;
+ *p_ndense_col = ndense_col ;
+ *p_nempty_col = nempty_col ; /* original empty cols */
+ *p_nnewlyempty_col = nnewlyempty_col ;
+ /* --------------------- */
+}
+
+
+/* ========================================================================== */
+/* === find_ordering ======================================================== */
+/* ========================================================================== */
+
+/*
+ Order the principal columns of the supercolumn form of the matrix
+ (no supercolumns on input). Uses a minimum approximate column minimum
+ degree ordering method. Not user-callable.
+*/
+
+PRIVATE Int find_ordering /* return the number of garbage collections */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Int Alen, /* size of A, 2*nnz + n_col or larger */
+ Colamd_Row Row [], /* of size n_row+1 */
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* column form and row form of A */
+ Int head [], /* of size n_col+1 */
+ Int n_col2, /* Remaining columns to order */
+ Int max_deg, /* Maximum row degree */
+ Int pfree /* index of first free slot (2*nnz on entry) */
+ /* ------------------ */
+ /* added for UMFPACK: */
+ , Int Front_npivcol [ ]
+ , Int Front_nrows [ ]
+ , Int Front_ncols [ ]
+ , Int Front_parent [ ]
+ , Int Front_cols [ ]
+ , Int *p_nfr /* number of fronts */
+ , Int aggressive
+ , Int InFront [ ]
+ /* ------------------ */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int k ; /* current pivot ordering step */
+ Int pivot_col ; /* current pivot column */
+ Int *cp ; /* a column pointer */
+ Int *rp ; /* a row pointer */
+ Int pivot_row ; /* current pivot row */
+ Int *new_cp ; /* modified column pointer */
+ Int *new_rp ; /* modified row pointer */
+ Int pivot_row_start ; /* pointer to start of pivot row */
+ Int pivot_row_degree ; /* number of columns in pivot row */
+ Int pivot_row_length ; /* number of supercolumns in pivot row */
+ Int pivot_col_score ; /* score of pivot column */
+ Int needed_memory ; /* free space needed for pivot row */
+ Int *cp_end ; /* pointer to the end of a column */
+ Int *rp_end ; /* pointer to the end of a row */
+ Int row ; /* a row index */
+ Int col ; /* a column index */
+ Int max_score ; /* maximum possible score */
+ Int cur_score ; /* score of current column */
+ unsigned Int hash ; /* hash value for supernode detection */
+ Int head_column ; /* head of hash bucket */
+ Int first_col ; /* first column in hash bucket */
+ Int tag_mark ; /* marker value for mark array */
+ Int row_mark ; /* Row [row].shared2.mark */
+ Int set_difference ; /* set difference size of row with pivot row */
+ Int min_score ; /* smallest column score */
+ Int col_thickness ; /* "thickness" (no. of columns in a supercol) */
+ Int max_mark ; /* maximum value of tag_mark */
+ Int pivot_col_thickness ; /* number of columns represented by pivot col */
+ Int prev_col ; /* Used by Dlist operations. */
+ Int next_col ; /* Used by Dlist operations. */
+ Int ngarbage ; /* number of garbage collections performed */
+
+#ifndef NDEBUG
+ Int debug_d ; /* debug loop counter */
+ Int debug_step = 0 ; /* debug loop counter */
+#endif /* NDEBUG */
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Int pivot_row_thickness ; /* number of rows represented by pivot row */
+ Int nfr = 0 ; /* number of fronts */
+ Int child ;
+ /* ------------------ */
+
+ /* === Initialization and clear mark ==================================== */
+
+ max_mark = MAX_MARK (n_col) ; /* defined in umfpack.h */
+ tag_mark = clear_mark (n_row, Row) ;
+ min_score = 0 ;
+ ngarbage = 0 ;
+ DEBUG1 (("colamd: Ordering, n_col2="ID"\n", n_col2)) ;
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ InFront [row] = EMPTY ;
+ }
+
+ /* === Order the columns ================================================ */
+
+ for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */)
+ {
+
+#ifndef NDEBUG
+ if (debug_step % 100 == 0)
+ {
+ DEBUG2 (("\n... Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ;
+ }
+ else
+ {
+ DEBUG3 (("\n-----Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ;
+ }
+ debug_step++ ;
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k, max_deg) ;
+ debug_matrix (n_row, n_col, Row, Col, A) ;
+#endif /* NDEBUG */
+
+ /* === Select pivot column, and order it ============================ */
+
+ /* make sure degree list isn't empty */
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (head [min_score] >= EMPTY) ;
+
+#ifndef NDEBUG
+ for (debug_d = 0 ; debug_d < min_score ; debug_d++)
+ {
+ ASSERT (head [debug_d] == EMPTY) ;
+ }
+#endif /* NDEBUG */
+
+ /* get pivot column from head of minimum degree list */
+ while (head [min_score] == EMPTY && min_score < n_col)
+ {
+ min_score++ ;
+ }
+ pivot_col = head [min_score] ;
+ ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;
+ next_col = Col [pivot_col].shared4.degree_next ;
+ head [min_score] = next_col ;
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = EMPTY ;
+ }
+
+ ASSERT (COL_IS_ALIVE (pivot_col)) ;
+ DEBUG3 (("Pivot col: "ID"\n", pivot_col)) ;
+
+ /* remember score for defrag check */
+ pivot_col_score = Col [pivot_col].shared2.score ;
+
+ /* the pivot column is the kth column in the pivot order */
+ Col [pivot_col].shared2.order = k ;
+
+ /* increment order count by column thickness */
+ pivot_col_thickness = Col [pivot_col].shared1.thickness ;
+ /* ------------------ */
+ /* changed for UMFPACK: */
+ k += pivot_col_thickness ;
+ /* ------------------ */
+ ASSERT (pivot_col_thickness > 0) ;
+
+ /* === Garbage_collection, if necessary ============================= */
+
+ needed_memory = MIN (pivot_col_score, n_col - k) ;
+ if (pfree + needed_memory >= Alen)
+ {
+ pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;
+ ngarbage++ ;
+ /* after garbage collection we will have enough */
+ ASSERT (pfree + needed_memory < Alen) ;
+ /* garbage collection has wiped out the Row[].shared2.mark array */
+ tag_mark = clear_mark (n_row, Row) ;
+
+#ifndef NDEBUG
+ debug_matrix (n_row, n_col, Row, Col, A) ;
+#endif /* NDEBUG */
+ }
+
+ /* === Compute pivot row pattern ==================================== */
+
+ /* get starting location for this new merged row */
+ pivot_row_start = pfree ;
+
+ /* initialize new row counts to zero */
+ pivot_row_degree = 0 ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ pivot_row_thickness = 0 ;
+ /* ------------------ */
+
+ /* [ tag pivot column as having been visited so it isn't included */
+ /* in merged pivot row */
+ Col [pivot_col].shared1.thickness = -pivot_col_thickness ;
+
+ /* pivot row is the union of all rows in the pivot column pattern */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ DEBUG4 (("Pivot col pattern %d "ID"\n", ROW_IS_ALIVE(row), row)) ;
+ /* skip if row is dead */
+ if (ROW_IS_DEAD (row))
+ {
+ continue ;
+ }
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ /* sum the thicknesses of all the rows */
+ /* ASSERT (Row [row].thickness > 0) ; */
+ pivot_row_thickness += Row [row].thickness ;
+ /* ------------------ */
+
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ /* add the column, if alive and untagged */
+ col_thickness = Col [col].shared1.thickness ;
+ if (col_thickness > 0 && COL_IS_ALIVE (col))
+ {
+ /* tag column in pivot row */
+ Col [col].shared1.thickness = -col_thickness ;
+ ASSERT (pfree < Alen) ;
+ /* place column in pivot row */
+ A [pfree++] = col ;
+ pivot_row_degree += col_thickness ;
+ /* ------------------ */
+ /* added for UMFPACK: */
+ DEBUG4 (("\t\t\tNew live column in pivot row: "ID"\n",col));
+ /* ------------------ */
+ }
+ /* ------------------ */
+ /* added for UMFPACK */
+#ifndef NDEBUG
+ if (col_thickness < 0 && COL_IS_ALIVE (col))
+ {
+ DEBUG4 (("\t\t\tOld live column in pivot row: "ID"\n",col));
+ }
+#endif
+ /* ------------------ */
+ }
+ }
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ /* pivot_row_thickness is the number of rows in frontal matrix */
+ /* both pivotal rows and nonpivotal rows */
+ /* ------------------ */
+
+ /* clear tag on pivot column */
+ Col [pivot_col].shared1.thickness = pivot_col_thickness ; /* ] */
+ max_deg = MAX (max_deg, pivot_row_degree) ;
+
+#ifndef NDEBUG
+ DEBUG3 (("check2\n")) ;
+ debug_mark (n_row, Row, tag_mark, max_mark) ;
+#endif /* NDEBUG */
+
+ /* === Kill all rows used to construct pivot row ==================== */
+
+ /* also kill pivot row, temporarily */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* may be killing an already dead row */
+ row = *cp++ ;
+
+ DEBUG2 (("Kill row in pivot col: "ID" alive? %d, front "ID"\n",
+ row, ROW_IS_ALIVE (row), Row [row].front)) ;
+
+ /* added for UMFPACK: */
+ if (ROW_IS_ALIVE (row))
+ {
+ if (Row [row].front != EMPTY)
+ {
+ /* This row represents a frontal matrix. */
+ /* Row [row].front is a child of current front */
+ child = Row [row].front ;
+ Front_parent [child] = nfr ;
+ DEBUG1 (("Front "ID" => front "ID", normal\n", child, nfr));
+ }
+ else
+ {
+ /* This is an original row. Keep track of which front
+ * is its parent in the row-merge tree. */
+ InFront [row] = nfr ;
+ DEBUG1 (("Row "ID" => front "ID", normal\n", row, nfr)) ;
+ }
+ }
+
+ KILL_ROW (row) ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Row [row].thickness = 0 ;
+ /* ------------------ */
+ }
+
+ /* === Select a row index to use as the new pivot row =============== */
+
+ pivot_row_length = pfree - pivot_row_start ;
+ if (pivot_row_length > 0)
+ {
+ /* pick the "pivot" row arbitrarily (first row in col) */
+ pivot_row = A [Col [pivot_col].start] ;
+ DEBUG3 (("Pivotal row is "ID"\n", pivot_row)) ;
+ }
+ else
+ {
+ /* there is no pivot row, since it is of zero length */
+ pivot_row = EMPTY ;
+ ASSERT (pivot_row_length == 0) ;
+ }
+ ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;
+
+ /* === Approximate degree computation =============================== */
+
+ /* Here begins the computation of the approximate degree. The column */
+ /* score is the sum of the pivot row "length", plus the size of the */
+ /* set differences of each row in the column minus the pattern of the */
+ /* pivot row itself. The column ("thickness") itself is also */
+ /* excluded from the column score (we thus use an approximate */
+ /* external degree). */
+
+ /* The time taken by the following code (compute set differences, and */
+ /* add them up) is proportional to the size of the data structure */
+ /* being scanned - that is, the sum of the sizes of each column in */
+ /* the pivot row. Thus, the amortized time to compute a column score */
+ /* is proportional to the size of that column (where size, in this */
+ /* context, is the column "length", or the number of row indices */
+ /* in that column). The number of row indices in a column is */
+ /* monotonically non-decreasing, from the length of the original */
+ /* column on input to colamd. */
+
+ /* === Compute set differences ====================================== */
+
+ DEBUG3 (("** Computing set differences phase. **\n")) ;
+
+ /* pivot row is currently dead - it will be revived later. */
+
+ DEBUG3 (("Pivot row: \n")) ;
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ DEBUG3 ((" Col: "ID"\n", col)) ;
+
+ /* clear tags used to construct pivot row pattern */
+ col_thickness = -Col [col].shared1.thickness ;
+ ASSERT (col_thickness > 0) ;
+ Col [col].shared1.thickness = col_thickness ;
+
+ /* === Remove column from degree list =========================== */
+
+ cur_score = Col [col].shared2.score ;
+ prev_col = Col [col].shared3.prev ;
+ next_col = Col [col].shared4.degree_next ;
+ ASSERT (cur_score >= 0) ;
+ ASSERT (cur_score <= n_col) ;
+ ASSERT (cur_score >= EMPTY) ;
+ if (prev_col == EMPTY)
+ {
+ head [cur_score] = next_col ;
+ }
+ else
+ {
+ Col [prev_col].shared4.degree_next = next_col ;
+ }
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = prev_col ;
+ }
+
+ /* === Scan the column ========================================== */
+
+ cp = &A [Col [col].start] ;
+ cp_end = cp + Col [col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ continue ;
+ }
+ ASSERT (row != pivot_row) ;
+ set_difference = row_mark - tag_mark ;
+ /* check if the row has been seen yet */
+ if (set_difference < 0)
+ {
+ ASSERT (Row [row].shared1.degree <= max_deg) ;
+ set_difference = Row [row].shared1.degree ;
+ }
+ /* subtract column thickness from this row's set difference */
+ set_difference -= col_thickness ;
+ ASSERT (set_difference >= 0) ;
+ ASSERT (ROW_IS_ALIVE (row)) ;
+
+ /* absorb this row if the set difference becomes zero */
+ if (set_difference == 0 && aggressive)
+ {
+ /* v4.1: do aggressive absorption */
+ DEBUG3 (("aggressive absorption. Row: "ID"\n", row)) ;
+
+ if (Row [row].front != EMPTY)
+ {
+ /* Row [row].front is a child of current front. */
+ child = Row [row].front ;
+ Front_parent [child] = nfr ;
+ DEBUG1 (("Front "ID" => front "ID", aggressive\n",
+ child, nfr)) ;
+ }
+ else
+ {
+ /* this is an original row. Keep track of which front
+ * assembles it, for the row-merge tree */
+ InFront [row] = nfr ;
+ DEBUG1 (("Row "ID" => front "ID", aggressive\n",
+ row, nfr)) ;
+ }
+
+ KILL_ROW (row) ;
+
+ /* sum the thicknesses of all the rows */
+ /* ASSERT (Row [row].thickness > 0) ; */
+ pivot_row_thickness += Row [row].thickness ;
+ Row [row].thickness = 0 ;
+
+ }
+ else
+ {
+ /* save the new mark */
+ Row [row].shared2.mark = set_difference + tag_mark ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k-pivot_row_degree, max_deg) ;
+#endif /* NDEBUG */
+
+ /* === Add up set differences for each column ======================= */
+
+ DEBUG3 (("** Adding set differences phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
+ hash = 0 ;
+ cur_score = 0 ;
+ cp = &A [Col [col].start] ;
+ /* compact the column */
+ new_cp = cp ;
+ cp_end = cp + Col [col].length ;
+
+ DEBUG4 (("Adding set diffs for Col: "ID".\n", col)) ;
+
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ ASSERT(row >= 0 && row < n_row) ;
+ row_mark = Row [row].shared2.mark ;
+ /* skip if dead */
+ if (ROW_IS_MARKED_DEAD (row_mark))
+ {
+ /* ------------------ */
+ /* changed for UMFPACK: */
+ DEBUG4 ((" Row "ID", dead\n", row)) ;
+ /* ------------------ */
+ continue ;
+ }
+ /* ------------------ */
+ /* changed for UMFPACK: */
+ /* ASSERT (row_mark > tag_mark) ; */
+ DEBUG4 ((" Row "ID", set diff "ID"\n", row, row_mark-tag_mark));
+ ASSERT (row_mark >= tag_mark) ;
+ /* ------------------ */
+ /* compact the column */
+ *new_cp++ = row ;
+ /* compute hash function */
+ hash += row ;
+ /* add set difference */
+ cur_score += row_mark - tag_mark ;
+ /* integer overflow... */
+ cur_score = MIN (cur_score, n_col) ;
+ }
+
+ /* recompute the column's length */
+ Col [col].length = (Int) (new_cp - &A [Col [col].start]) ;
+
+ /* === Further mass elimination ================================= */
+
+ if (Col [col].length == 0)
+ {
+ DEBUG4 (("further mass elimination. Col: "ID"\n", col)) ;
+ /* nothing left but the pivot row in this column */
+ KILL_PRINCIPAL_COL (col) ;
+ pivot_row_degree -= Col [col].shared1.thickness ;
+ ASSERT (pivot_row_degree >= 0) ;
+ /* order it */
+ Col [col].shared2.order = k ;
+ /* increment order count by column thickness */
+ k += Col [col].shared1.thickness ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ pivot_col_thickness += Col [col].shared1.thickness ;
+
+ /* add to column list of front ... */
+#ifndef NDEBUG
+ DEBUG1 (("Mass")) ;
+ dump_super (col, Col, n_col) ;
+#endif
+ Col [Col [col].lastcol].nextcol = Front_cols [nfr] ;
+ Front_cols [nfr] = col ;
+ /* ------------------ */
+
+ }
+ else
+ {
+ /* === Prepare for supercolumn detection ==================== */
+
+ DEBUG4 (("Preparing supercol detection for Col: "ID".\n", col));
+
+ /* save score so far */
+ Col [col].shared2.score = cur_score ;
+
+ /* add column to hash table, for supercolumn detection */
+ /* NOTE: hash is an unsigned Int to avoid a problem in ANSI C.
+ * The sign of the expression a % b is not defined when a and/or
+ * b are negative. Since hash is unsigned and n_col >= 0,
+ * this problem is avoided. */
+ hash %= n_col + 1 ;
+
+ DEBUG4 ((" Hash = "ID", n_col = "ID".\n", (Int) hash, n_col)) ;
+ ASSERT (((Int) hash) <= n_col) ;
+
+ head_column = head [hash] ;
+ if (head_column > EMPTY)
+ {
+ /* degree list "hash" is non-empty, use prev (shared3) of */
+ /* first column in degree list as head of hash bucket */
+ first_col = Col [head_column].shared3.headhash ;
+ Col [head_column].shared3.headhash = col ;
+ }
+ else
+ {
+ /* degree list "hash" is empty, use head as hash bucket */
+ first_col = - (head_column + 2) ;
+ head [hash] = - (col + 2) ;
+ }
+ Col [col].shared4.hash_next = first_col ;
+
+ /* save hash function in Col [col].shared3.hash */
+ Col [col].shared3.hash = (Int) hash ;
+ ASSERT (COL_IS_ALIVE (col)) ;
+ }
+ }
+
+ /* The approximate external column degree is now computed. */
+
+ /* === Supercolumn detection ======================================== */
+
+ DEBUG3 (("** Supercolumn detection phase. **\n")) ;
+
+ detect_super_cols (
+
+#ifndef NDEBUG
+ n_col, Row,
+#endif /* NDEBUG */
+
+ Col, A, head, pivot_row_start, pivot_row_length) ;
+
+ /* === Kill the pivotal column ====================================== */
+
+ KILL_PRINCIPAL_COL (pivot_col) ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ /* add columns to column list of front */
+#ifndef NDEBUG
+ DEBUG1 (("Pivot")) ;
+ dump_super (pivot_col, Col, n_col) ;
+#endif
+ Col [Col [pivot_col].lastcol].nextcol = Front_cols [nfr] ;
+ Front_cols [nfr] = pivot_col ;
+ /* ------------------ */
+
+ /* === Clear mark =================================================== */
+
+ tag_mark += (max_deg + 1) ;
+ if (tag_mark >= max_mark)
+ {
+ DEBUG2 (("clearing tag_mark\n")) ;
+ tag_mark = clear_mark (n_row, Row) ;
+ }
+
+#ifndef NDEBUG
+ DEBUG3 (("check3\n")) ;
+ debug_mark (n_row, Row, tag_mark, max_mark) ;
+#endif /* NDEBUG */
+
+ /* === Finalize the new pivot row, and column scores ================ */
+
+ DEBUG3 (("** Finalize scores phase. **\n")) ;
+ DEBUG3 (("pivot_row_degree "ID"\n", pivot_row_degree)) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ /* compact the pivot row */
+ new_rp = rp ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ DEBUG3 (("Col "ID" \n", col)) ;
+ /* skip dead columns */
+ if (COL_IS_DEAD (col))
+ {
+ DEBUG3 (("dead\n")) ;
+ continue ;
+ }
+ *new_rp++ = col ;
+ /* add new pivot row to column */
+ A [Col [col].start + (Col [col].length++)] = pivot_row ;
+
+ /* retrieve score so far and add on pivot row's degree. */
+ /* (we wait until here for this in case the pivot */
+ /* row's degree was reduced due to mass elimination). */
+ cur_score = Col [col].shared2.score + pivot_row_degree ;
+ DEBUG3 ((" cur_score "ID" ", cur_score)) ;
+
+ /* calculate the max possible score as the number of */
+ /* external columns minus the 'k' value minus the */
+ /* columns thickness */
+ max_score = n_col - k - Col [col].shared1.thickness ;
+ DEBUG3 ((" max_score "ID" ", max_score)) ;
+
+ /* make the score the external degree of the union-of-rows */
+ cur_score -= Col [col].shared1.thickness ;
+ DEBUG3 ((" cur_score "ID" ", cur_score)) ;
+
+ /* make sure score is less or equal than the max score */
+ cur_score = MIN (cur_score, max_score) ;
+ ASSERT (cur_score >= 0) ;
+
+ /* store updated score */
+ Col [col].shared2.score = cur_score ;
+ DEBUG3 ((" "ID"\n", cur_score)) ;
+
+ /* === Place column back in degree list ========================= */
+
+ ASSERT (min_score >= 0) ;
+ ASSERT (min_score <= n_col) ;
+ ASSERT (cur_score >= 0) ;
+ ASSERT (cur_score <= n_col) ;
+ ASSERT (head [cur_score] >= EMPTY) ;
+ next_col = head [cur_score] ;
+ Col [col].shared4.degree_next = next_col ;
+ Col [col].shared3.prev = EMPTY ;
+ if (next_col != EMPTY)
+ {
+ Col [next_col].shared3.prev = col ;
+ }
+ head [cur_score] = col ;
+
+ /* see if this score is less than current min */
+ min_score = MIN (min_score, cur_score) ;
+
+ }
+
+#ifndef NDEBUG
+ debug_deg_lists (n_row, n_col, Row, Col, head,
+ min_score, n_col2-k, max_deg) ;
+#endif /* NDEBUG */
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ /* frontal matrix can have more pivot cols than pivot rows for */
+ /* singular matrices. */
+
+ /* number of candidate pivot columns */
+ Front_npivcol [nfr] = pivot_col_thickness ;
+
+ /* all rows (not just size of contrib. block) */
+ Front_nrows [nfr] = pivot_row_thickness ;
+
+ /* all cols */
+ Front_ncols [nfr] = pivot_col_thickness + pivot_row_degree ;
+
+ Front_parent [nfr] = EMPTY ;
+
+ pivot_row_thickness -= pivot_col_thickness ;
+ DEBUG1 (("Front "ID" Pivot_row_thickness after pivot cols elim: "ID"\n",
+ nfr, pivot_row_thickness)) ;
+ pivot_row_thickness = MAX (0, pivot_row_thickness) ;
+ /* ------------------ */
+
+ /* === Resurrect the new pivot row ================================== */
+
+ if (pivot_row_degree > 0
+ /* ------------------ */
+ /* added for UMFPACK. Note that this part of the expression should be
+ * removed if this routine is used outside of UMFPACK, for a Cholesky
+ * factorization of (AQ)'(AQ) */
+ && pivot_row_thickness > 0
+ /* ------------------ */
+ )
+ {
+ /* update pivot row length to reflect any cols that were killed */
+ /* during super-col detection and mass elimination */
+ Row [pivot_row].start = pivot_row_start ;
+ Row [pivot_row].length = (Int) (new_rp - &A[pivot_row_start]) ;
+ ASSERT (Row [pivot_row].length > 0) ;
+ Row [pivot_row].shared1.degree = pivot_row_degree ;
+ Row [pivot_row].shared2.mark = 0 ;
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Row [pivot_row].thickness = pivot_row_thickness ;
+ Row [pivot_row].front = nfr ;
+ /* ------------------ */
+ /* pivot row is no longer dead */
+ }
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+
+#ifndef NDEBUG
+ DEBUG1 (("Front "ID" : "ID" "ID" "ID" ", nfr,
+ Front_npivcol [nfr], Front_nrows [nfr], Front_ncols [nfr])) ;
+ DEBUG1 ((" cols:[ ")) ;
+ debug_d = 0 ;
+ for (col = Front_cols [nfr] ; col != EMPTY ; col = Col [col].nextcol)
+ {
+ DEBUG1 ((" "ID, col)) ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (COL_IS_DEAD (col)) ;
+ debug_d++ ;
+ ASSERT (debug_d <= pivot_col_thickness) ;
+ }
+ ASSERT (debug_d == pivot_col_thickness) ;
+ DEBUG1 ((" ]\n ")) ;
+#endif
+ nfr++ ; /* one more front */
+ /* ------------------ */
+
+ }
+
+ /* === All principal columns have now been ordered ====================== */
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ *p_nfr = nfr ;
+ /* ------------------ */
+
+ return (ngarbage) ;
+}
+
+
+/* ========================================================================== */
+/* === order_children deleted for UMFPACK =================================== */
+/* ========================================================================== */
+
+/* ========================================================================== */
+/* === detect_super_cols ==================================================== */
+/* ========================================================================== */
+
+/*
+ Detects supercolumns by finding matches between columns in the hash buckets.
+ Check amongst columns in the set A [row_start ... row_start + row_length-1].
+ The columns under consideration are currently *not* in the degree lists,
+ and have already been placed in the hash buckets.
+
+ The hash bucket for columns whose hash function is equal to h is stored
+ as follows:
+
+ if head [h] is >= 0, then head [h] contains a degree list, so:
+
+ head [h] is the first column in degree bucket h.
+ Col [head [h]].headhash gives the first column in hash bucket h.
+
+ otherwise, the degree list is empty, and:
+
+ -(head [h] + 2) is the first column in hash bucket h.
+
+ For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous
+ column" pointer. Col [c].shared3.hash is used instead as the hash number
+ for that column. The value of Col [c].shared4.hash_next is the next column
+ in the same hash bucket.
+
+ Assuming no, or "few" hash collisions, the time taken by this routine is
+ linear in the sum of the sizes (lengths) of each column whose score has
+ just been computed in the approximate degree computation.
+ Not user-callable.
+*/
+
+PRIVATE void detect_super_cols
+(
+ /* === Parameters ======================================================= */
+
+#ifndef NDEBUG
+ /* these two parameters are only needed when debugging is enabled: */
+ Int n_col, /* number of columns of A */
+ Colamd_Row Row [], /* of size n_row+1 */
+#endif /* NDEBUG */
+
+ Colamd_Col Col [], /* of size n_col+1 */
+ Int A [], /* row indices of A */
+ Int head [], /* head of degree lists and hash buckets */
+ Int row_start, /* pointer to set of columns to check */
+ Int row_length /* number of columns to check */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int hash ; /* hash value for a column */
+ Int *rp ; /* pointer to a row */
+ Int c ; /* a column index */
+ Int super_c ; /* column index of the column to absorb into */
+ Int *cp1 ; /* column pointer for column super_c */
+ Int *cp2 ; /* column pointer for column c */
+ Int length ; /* length of column super_c */
+ Int prev_c ; /* column preceding c in hash bucket */
+ Int i ; /* loop counter */
+ Int *rp_end ; /* pointer to the end of the row */
+ Int col ; /* a column index in the row to check */
+ Int head_column ; /* first column in hash bucket or degree list */
+ Int first_col ; /* first column in hash bucket */
+
+ /* === Consider each column in the row ================================== */
+
+ rp = &A [row_start] ;
+ rp_end = rp + row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ if (COL_IS_DEAD (col))
+ {
+ continue ;
+ }
+
+ /* get hash number for this column */
+ hash = Col [col].shared3.hash ;
+ ASSERT (hash <= n_col) ;
+
+ /* === Get the first column in this hash bucket ===================== */
+
+ head_column = head [hash] ;
+ if (head_column > EMPTY)
+ {
+ first_col = Col [head_column].shared3.headhash ;
+ }
+ else
+ {
+ first_col = - (head_column + 2) ;
+ }
+
+ /* === Consider each column in the hash bucket ====================== */
+
+ for (super_c = first_col ; super_c != EMPTY ;
+ super_c = Col [super_c].shared4.hash_next)
+ {
+ ASSERT (COL_IS_ALIVE (super_c)) ;
+ ASSERT (Col [super_c].shared3.hash == hash) ;
+ length = Col [super_c].length ;
+
+ /* prev_c is the column preceding column c in the hash bucket */
+ prev_c = super_c ;
+
+ /* === Compare super_c with all columns after it ================ */
+
+ for (c = Col [super_c].shared4.hash_next ;
+ c != EMPTY ; c = Col [c].shared4.hash_next)
+ {
+ ASSERT (c != super_c) ;
+ ASSERT (COL_IS_ALIVE (c)) ;
+ ASSERT (Col [c].shared3.hash == hash) ;
+
+ /* not identical if lengths or scores are different */
+ if (Col [c].length != length ||
+ Col [c].shared2.score != Col [super_c].shared2.score)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* compare the two columns */
+ cp1 = &A [Col [super_c].start] ;
+ cp2 = &A [Col [c].start] ;
+
+ for (i = 0 ; i < length ; i++)
+ {
+ /* the columns are "clean" (no dead rows) */
+ ASSERT (ROW_IS_ALIVE (*cp1)) ;
+ ASSERT (ROW_IS_ALIVE (*cp2)) ;
+ /* row indices will same order for both supercols, */
+ /* no gather scatter nessasary */
+ if (*cp1++ != *cp2++)
+ {
+ break ;
+ }
+ }
+
+ /* the two columns are different if the for-loop "broke" */
+ if (i != length)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* === Got it! two columns are identical =================== */
+
+ ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;
+
+ Col [super_c].shared1.thickness += Col [c].shared1.thickness ;
+ Col [c].shared1.parent = super_c ;
+ KILL_NON_PRINCIPAL_COL (c) ;
+
+ Col [c].shared2.order = EMPTY ;
+ /* remove c from hash bucket */
+ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ /* add c to end of list of super_c */
+ ASSERT (Col [super_c].lastcol >= 0) ;
+ ASSERT (Col [super_c].lastcol < n_col) ;
+ Col [Col [super_c].lastcol].nextcol = c ;
+ Col [super_c].lastcol = Col [c].lastcol ;
+#ifndef NDEBUG
+ /* dump the supercolumn */
+ DEBUG1 (("Super")) ;
+ dump_super (super_c, Col, n_col) ;
+#endif
+ /* ------------------ */
+
+ }
+ }
+
+ /* === Empty this hash bucket ======================================= */
+
+ if (head_column > EMPTY)
+ {
+ /* corresponding degree list "hash" is not empty */
+ Col [head_column].shared3.headhash = EMPTY ;
+ }
+ else
+ {
+ /* corresponding degree list "hash" is empty */
+ head [hash] = EMPTY ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === garbage_collection =================================================== */
+/* ========================================================================== */
+
+/*
+ Defragments and compacts columns and rows in the workspace A. Used when
+ all avaliable memory has been used while performing row merging. Returns
+ the index of the first free position in A, after garbage collection. The
+ time taken by this routine is linear is the size of the array A, which is
+ itself linear in the number of nonzeros in the input matrix.
+ Not user-callable.
+*/
+
+PRIVATE Int garbage_collection /* returns the new value of pfree */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows */
+ Int n_col, /* number of columns */
+ Colamd_Row Row [], /* row info */
+ Colamd_Col Col [], /* column info */
+ Int A [], /* A [0 ... Alen-1] holds the matrix */
+ Int *pfree /* &A [0] ... pfree is in use */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int *psrc ; /* source pointer */
+ Int *pdest ; /* destination pointer */
+ Int j ; /* counter */
+ Int r ; /* a row index */
+ Int c ; /* a column index */
+ Int length ; /* length of a row or column */
+
+#ifndef NDEBUG
+ Int debug_rows ;
+ DEBUG2 (("Defrag..\n")) ;
+ for (psrc = &A[0] ; psrc < pfree ; psrc++) ASSERT (*psrc >= 0) ;
+ debug_rows = 0 ;
+#endif /* NDEBUG */
+
+ /* === Defragment the columns =========================================== */
+
+ pdest = &A[0] ;
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ psrc = &A [Col [c].start] ;
+
+ /* move and compact the column */
+ ASSERT (pdest <= psrc) ;
+ Col [c].start = (Int) (pdest - &A [0]) ;
+ length = Col [c].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ r = *psrc++ ;
+ if (ROW_IS_ALIVE (r))
+ {
+ *pdest++ = r ;
+ }
+ }
+ Col [c].length = (Int) (pdest - &A [Col [c].start]) ;
+ }
+ }
+
+ /* === Prepare to defragment the rows =================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ if (Row [r].length == 0)
+ {
+ /* :: defrag row kill :: */
+ /* This row is of zero length. cannot compact it, so kill it.
+ * NOTE: in the current version, there are no zero-length live
+ * rows when garbage_collection is called. So this code will
+ * never trigger. However, if the code is modified, or if
+ * garbage_collection is called at a different place, then rows
+ * can be of zero length. So this test is kept, just in case.
+ */
+ DEBUGm4 (("Defrag row kill\n")) ;
+ KILL_ROW (r) ;
+ }
+ else
+ {
+ /* save first column index in Row [r].shared2.first_column */
+ psrc = &A [Row [r].start] ;
+ Row [r].shared2.first_column = *psrc ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ /* flag the start of the row with the one's complement of row */
+ *psrc = ONES_COMPLEMENT (r) ;
+#ifndef NDEBUG
+ debug_rows++ ;
+#endif /* NDEBUG */
+ }
+ }
+ }
+
+ /* === Defragment the rows ============================================== */
+
+ psrc = pdest ;
+ while (psrc < pfree)
+ {
+ /* find a negative number ... the start of a row */
+ if (*psrc++ < 0)
+ {
+ psrc-- ;
+ /* get the row index */
+ r = ONES_COMPLEMENT (*psrc) ;
+ ASSERT (r >= 0 && r < n_row) ;
+ /* restore first column index */
+ *psrc = Row [r].shared2.first_column ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+
+ /* move and compact the row */
+ ASSERT (pdest <= psrc) ;
+ Row [r].start = (Int) (pdest - &A [0]) ;
+ length = Row [r].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ c = *psrc++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ *pdest++ = c ;
+ }
+ }
+ Row [r].length = (Int) (pdest - &A [Row [r].start]) ;
+
+#ifndef NDEBUG
+ debug_rows-- ;
+#endif /* NDEBUG */
+
+ }
+ }
+ /* ensure we found all the rows */
+ ASSERT (debug_rows == 0) ;
+
+ /* === Return the new value of pfree ==================================== */
+
+ return ((Int) (pdest - &A [0])) ;
+}
+
+
+/* ========================================================================== */
+/* === clear_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ Clears the Row [].shared2.mark array, and returns the new tag_mark.
+ Return value is the new tag_mark. Not user-callable.
+*/
+
+PRIVATE Int clear_mark /* return the new value for tag_mark */
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row, /* number of rows in A */
+ Colamd_Row Row [] /* Row [0 ... n-1].shared2.mark is set to zero */
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ Row [r].shared2.mark = 0 ;
+ }
+ }
+
+ /* ------------------ */
+ return (1) ;
+ /* ------------------ */
+
+}
+
+
+/* ========================================================================== */
+/* === print_report removed for UMFPACK ===================================== */
+/* ========================================================================== */
+
+
+
+/* ========================================================================== */
+/* === colamd debugging routines ============================================ */
+/* ========================================================================== */
+
+/* When debugging is disabled, the remainder of this file is ignored. */
+
+#ifndef NDEBUG
+
+
+/* ========================================================================== */
+/* === debug_structures ===================================================== */
+/* ========================================================================== */
+
+/*
+ At this point, all empty rows and columns are dead. All live columns
+ are "clean" (containing no dead rows) and simplicial (no supercolumns
+ yet). Rows may contain dead columns, but all live rows contain at
+ least one live column.
+*/
+
+PRIVATE void debug_structures
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A [],
+ Int n_col2
+)
+{
+ /* === Local variables ================================================== */
+
+ Int i ;
+ Int c ;
+ Int *cp ;
+ Int *cp_end ;
+ Int len ;
+ Int score ;
+ Int r ;
+ Int *rp ;
+ Int *rp_end ;
+ Int deg ;
+
+ /* === Check A, Row, and Col ============================================ */
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (COL_IS_ALIVE (c))
+ {
+ len = Col [c].length ;
+ score = Col [c].shared2.score ;
+ DEBUG4 (("initial live col "ID" "ID" "ID"\n", c, len, score)) ;
+ ASSERT (len > 0) ;
+ ASSERT (score >= 0) ;
+ ASSERT (Col [c].shared1.thickness == 1) ;
+ cp = &A [Col [c].start] ;
+ cp_end = cp + len ;
+ while (cp < cp_end)
+ {
+ r = *cp++ ;
+ ASSERT (ROW_IS_ALIVE (r)) ;
+ }
+ }
+ else
+ {
+ i = Col [c].shared2.order ;
+ ASSERT (i >= n_col2 && i < n_col) ;
+ }
+ }
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (ROW_IS_ALIVE (r))
+ {
+ i = 0 ;
+ len = Row [r].length ;
+ deg = Row [r].shared1.degree ;
+ ASSERT (len > 0) ;
+ ASSERT (deg > 0) ;
+ rp = &A [Row [r].start] ;
+ rp_end = rp + len ;
+ while (rp < rp_end)
+ {
+ c = *rp++ ;
+ if (COL_IS_ALIVE (c))
+ {
+ i++ ;
+ }
+ }
+ ASSERT (i > 0) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_deg_lists ====================================================== */
+/* ========================================================================== */
+
+/*
+ Prints the contents of the degree lists. Counts the number of columns
+ in the degree list and compares it to the total it should have. Also
+ checks the row degrees.
+*/
+
+PRIVATE void debug_deg_lists
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int head [],
+ Int min_score,
+ Int should,
+ Int max_deg
+)
+{
+ /* === Local variables ================================================== */
+
+ Int deg ;
+ Int col ;
+ Int have ;
+ Int row ;
+
+ /* === Check the degree lists =========================================== */
+
+ if (n_col > 10000 && UMF_debug <= 0)
+ {
+ return ;
+ }
+ have = 0 ;
+ DEBUG4 (("Degree lists: "ID"\n", min_score)) ;
+ for (deg = 0 ; deg <= n_col ; deg++)
+ {
+ col = head [deg] ;
+ if (col == EMPTY)
+ {
+ continue ;
+ }
+ DEBUG4 ((ID":", deg)) ;
+ while (col != EMPTY)
+ {
+ DEBUG4 ((" "ID, col)) ;
+ have += Col [col].shared1.thickness ;
+ ASSERT (COL_IS_ALIVE (col)) ;
+ col = Col [col].shared4.degree_next ;
+ }
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("should "ID" have "ID"\n", should, have)) ;
+ ASSERT (should == have) ;
+
+ /* === Check the row degrees ============================================ */
+
+ if (n_row > 10000 && UMF_debug <= 0)
+ {
+ return ;
+ }
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (ROW_IS_ALIVE (row))
+ {
+ ASSERT (Row [row].shared1.degree <= max_deg) ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ Ensures that the tag_mark is less that the maximum and also ensures that
+ each entry in the mark array is less than the tag mark.
+*/
+
+PRIVATE void debug_mark
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Colamd_Row Row [],
+ Int tag_mark,
+ Int max_mark
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+
+ /* === Check the Row marks ============================================== */
+
+ ASSERT (tag_mark > 0 && tag_mark <= max_mark) ;
+ if (n_row > 10000 && UMF_debug <= 0)
+ {
+ return ;
+ }
+ for (r = 0 ; r < n_row ; r++)
+ {
+ ASSERT (Row [r].shared2.mark < tag_mark) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === debug_matrix ========================================================= */
+/* ========================================================================== */
+
+/*
+ Prints out the contents of the columns and the rows.
+*/
+
+PRIVATE void debug_matrix
+(
+ /* === Parameters ======================================================= */
+
+ Int n_row,
+ Int n_col,
+ Colamd_Row Row [],
+ Colamd_Col Col [],
+ Int A []
+)
+{
+ /* === Local variables ================================================== */
+
+ Int r ;
+ Int c ;
+ Int *rp ;
+ Int *rp_end ;
+ Int *cp ;
+ Int *cp_end ;
+
+ /* === Dump the rows and columns of the matrix ========================== */
+
+ if (UMF_debug < 3)
+ {
+ return ;
+ }
+ DEBUG3 (("DUMP MATRIX:\n")) ;
+ for (r = 0 ; r < n_row ; r++)
+ {
+ DEBUG3 (("Row "ID" alive? %d\n", r, ROW_IS_ALIVE (r))) ;
+ if (ROW_IS_DEAD (r))
+ {
+ continue ;
+ }
+
+ /* ------------------ */
+ /* changed for UMFPACK: */
+ DEBUG3 (("start "ID" length "ID" degree "ID" thickness "ID"\n",
+ Row [r].start, Row [r].length, Row [r].shared1.degree,
+ Row [r].thickness)) ;
+ /* ------------------ */
+
+ rp = &A [Row [r].start] ;
+ rp_end = rp + Row [r].length ;
+ while (rp < rp_end)
+ {
+ c = *rp++ ;
+ DEBUG4 ((" %d col "ID"\n", COL_IS_ALIVE (c), c)) ;
+ }
+ }
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ DEBUG3 (("Col "ID" alive? %d\n", c, COL_IS_ALIVE (c))) ;
+ if (COL_IS_DEAD (c))
+ {
+ continue ;
+ }
+ /* ------------------ */
+ /* changed for UMFPACK: */
+ DEBUG3 (("start "ID" length "ID" shared1[thickness,parent] "ID
+ " shared2 [order,score] "ID"\n", Col [c].start, Col [c].length,
+ Col [c].shared1.thickness, Col [c].shared2.score));
+ /* ------------------ */
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ r = *cp++ ;
+ DEBUG4 ((" %d row "ID"\n", ROW_IS_ALIVE (r), r)) ;
+ }
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ DEBUG1 (("Col")) ;
+ dump_super (c, Col, n_col) ;
+ /* ------------------ */
+
+ }
+}
+
+/* ------------------ */
+/* dump_super added for UMFPACK: */
+PRIVATE void dump_super
+(
+ Int super_c,
+ Colamd_Col Col [],
+ Int n_col
+)
+{
+ Int col, ncols ;
+
+ DEBUG1 ((" =[ ")) ;
+ ncols = 0 ;
+ for (col = super_c ; col != EMPTY ; col = Col [col].nextcol)
+ {
+ DEBUG1 ((" "ID, col)) ;
+ ASSERT (col >= 0 && col < n_col) ;
+ if (col != super_c)
+ {
+ ASSERT (COL_IS_DEAD (col)) ;
+ }
+ if (Col [col].nextcol == EMPTY)
+ {
+ ASSERT (col == Col [super_c].lastcol) ;
+ }
+ ncols++ ;
+ ASSERT (ncols <= Col [super_c].shared1.thickness) ;
+ }
+ ASSERT (ncols == Col [super_c].shared1.thickness) ;
+ DEBUG1 (("]\n")) ;
+}
+/* ------------------ */
+
+
+#endif /* NDEBUG */
diff --git a/UMFPACK/Source/umf_colamd.h b/UMFPACK/Source/umf_colamd.h
new file mode 100644
index 0000000..51675a5
--- /dev/null
+++ b/UMFPACK/Source/umf_colamd.h
@@ -0,0 +1,255 @@
+/* ========================================================================== */
+/* === umf_colamd.h ========================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+
+Authors:
+
+ The authors of the COLAMD code itself are Stefan I. Larimore and Timothy A.
+ Davis, University of Florida. The algorithm was developed in collaboration
+ with John Gilbert, Xerox PARC, and Esmond Ng, Oak Ridge National Laboratory.
+
+Date:
+
+ UMFPACK Version: see above.
+ COLAMD Version 2.0 was released on January 31, 2000.
+
+Acknowledgements:
+
+ This work was supported by the National Science Foundation, under
+ grants DMS-9504974, DMS-9803599, and CCR-0203270.
+
+UMFPACK: Copyright (c) 2003 by Timothy A. Davis. All Rights Reserved.
+
+See the UMFPACK README file for the License for your use of this code.
+
+Availability:
+
+ Both UMFPACK and the original unmodified colamd/symamd library are
+ available at http://www.cise.ufl.edu/research/sparse.
+
+*/
+
+#ifndef COLAMD_H
+#define COLAMD_H
+
+/* ========================================================================== */
+/* === Include files ======================================================== */
+/* ========================================================================== */
+
+#include <stdlib.h>
+
+/* ========================================================================== */
+/* === Knob and statistics definitions ====================================== */
+/* ========================================================================== */
+
+/* size of the knobs [ ] array. Only knobs [0..2] are currently used. */
+#define COLAMD_KNOBS 20
+
+/* number of output statistics. Only stats [0..8] are currently used. */
+#define COLAMD_STATS 20
+
+/* knobs [0] and stats [0]: dense row knob and output statistic. */
+#define COLAMD_DENSE_ROW 0
+
+/* knobs [1] and stats [1]: dense column knob and output statistic. */
+#define COLAMD_DENSE_COL 1
+
+/* knobs [2]: aggressive absorption option */
+#define COLAMD_AGGRESSIVE 2
+
+/* stats [2]: memory defragmentation count output statistic */
+#define COLAMD_DEFRAG_COUNT 2
+
+/* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */
+#define COLAMD_STATUS 3
+
+/* stats [4..6]: error info, or info on jumbled columns */
+#define COLAMD_INFO1 4
+#define COLAMD_INFO2 5
+#define COLAMD_INFO3 6
+
+/* ------------------ */
+/* added for UMFPACK: */
+/* stats [7]: number of originally empty rows */
+#define COLAMD_EMPTY_ROW 7
+/* stats [8]: number of originally empty cols */
+#define COLAMD_EMPTY_COL 8
+/* stats [9]: number of rows with entries only in dense cols */
+#define COLAMD_NEWLY_EMPTY_ROW 9
+/* stats [10]: number of cols with entries only in dense rows */
+#define COLAMD_NEWLY_EMPTY_COL 10
+/* ------------------ */
+
+/* error codes returned in stats [3]: */
+#define COLAMD_OK (0)
+#define COLAMD_ERROR_jumbled_matrix (-11)
+#define COLAMD_ERROR_A_not_present (-1)
+#define COLAMD_ERROR_p_not_present (-2)
+#define COLAMD_ERROR_nrow_negative (-3)
+#define COLAMD_ERROR_ncol_negative (-4)
+#define COLAMD_ERROR_nnz_negative (-5)
+#define COLAMD_ERROR_p0_nonzero (-6)
+#define COLAMD_ERROR_A_too_small (-7)
+#define COLAMD_ERROR_col_length_negative (-8)
+#define COLAMD_ERROR_row_index_out_of_bounds (-9)
+#define COLAMD_ERROR_out_of_memory (-10)
+#define COLAMD_ERROR_internal_error (-999)
+
+/* ========================================================================== */
+/* === Row and Column structures ============================================ */
+/* ========================================================================== */
+
+/* User code that makes use of the colamd/symamd routines need not directly */
+/* reference these structures. They are used only for the COLAMD_RECOMMENDED */
+/* macro. */
+
+typedef struct Colamd_Col_struct
+{
+ Int start ; /* index for A of first row in this column, or DEAD */
+ /* if column is dead */
+ Int length ; /* number of rows in this column */
+ union
+ {
+ Int thickness ; /* number of original columns represented by this */
+ /* col, if the column is alive */
+ Int parent ; /* parent in parent tree super-column structure, if */
+ /* the column is dead */
+ } shared1 ;
+ union
+ {
+ Int score ; /* the score used to maintain heap, if col is alive */
+ Int order ; /* pivot ordering of this column, if col is dead */
+ } shared2 ;
+ union
+ {
+ Int headhash ; /* head of a hash bucket, if col is at the head of */
+ /* a degree list */
+ Int hash ; /* hash value, if col is not in a degree list */
+ Int prev ; /* previous column in degree list, if col is in a */
+ /* degree list (but not at the head of a degree list) */
+ } shared3 ;
+ union
+ {
+ Int degree_next ; /* next column, if col is in a degree list */
+ Int hash_next ; /* next column, if col is in a hash list */
+ } shared4 ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Int nextcol ; /* next column in this supercolumn */
+ Int lastcol ; /* last column in this supercolumn */
+ /* ------------------ */
+
+} Colamd_Col ;
+
+typedef struct Colamd_Row_struct
+{
+ Int start ; /* index for A of first col in this row */
+ Int length ; /* number of principal columns in this row */
+ union
+ {
+ Int degree ; /* number of principal & non-principal columns in row */
+ Int p ; /* used as a row pointer in init_rows_cols () */
+ } shared1 ;
+ union
+ {
+ Int mark ; /* for computing set differences and marking dead rows*/
+ Int first_column ;/* first column in row (used in garbage collection) */
+ } shared2 ;
+
+ /* ------------------ */
+ /* added for UMFPACK: */
+ Int thickness ; /* number of original rows represented by this row */
+ /* that are not yet pivotal */
+ Int front ; /* -1 if an original row */
+ /* k if this row represents the kth frontal matrix */
+ /* where k goes from 0 to at most n_col-1 */
+ /* ------------------ */
+
+} Colamd_Row ;
+
+
+
+/* ========================================================================== */
+/* === Colamd recommended memory size ======================================= */
+/* ========================================================================== */
+
+/*
+ The recommended length Alen of the array A passed to colamd is given by
+ the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro. It returns -1 if any
+ argument is negative. 2*nnz space is required for the row and column
+ indices of the matrix. COLAMD_C (n_col) + COLAMD_R (n_row) space is
+ required for the Col and Row arrays, respectively, which are internal to
+ colamd. An additional n_col space is the minimal amount of "elbow room",
+ and nnz/5 more space is recommended for run time efficiency.
+
+ This macro is not needed when using symamd.
+*/
+
+/* about 8*(n_col+1) integers: */
+#define UMF_COLAMD_C(n_col) ((n_col + 1) * sizeof (Colamd_Col) / sizeof (Int))
+
+/* about 6*(n_row+1) integers: */
+#define UMF_COLAMD_R(n_row) ((n_row + 1) * sizeof (Colamd_Row) / sizeof (Int))
+
+/* UMFPACK: make sure Alen is >= 5*n_col + size of Col and Row structures.
+ * Alen is typically about 2.2*nz + 9*n_col + 6*n_row, or 2.2nz+15n for
+ * square matrices. */
+#define UMF_COLAMD_RECOMMENDED(nnz, n_row, n_col) \
+( \
+((nnz) < 0 || (n_row) < 0 || (n_col) < 0) \
+? \
+ (-1) \
+: \
+ (MAX (2 * (nnz), 4 * (n_col)) + \
+ (Int) UMF_COLAMD_C (n_col) + \
+ (Int) UMF_COLAMD_R (n_row) + (n_col) + ((nnz) / 5)) \
+)
+
+/* ========================================================================== */
+/* === Prototypes of user-callable routines ================================= */
+/* ========================================================================== */
+
+/* colamd_recommended removed for UMFPACK */
+
+void UMF_colamd_set_defaults /* sets default parameters */
+( /* knobs argument is modified on output */
+ double knobs [COLAMD_KNOBS] /* parameter settings for colamd */
+) ;
+
+Int UMF_colamd /* returns (1) if successful, (0) otherwise*/
+( /* A and p arguments are modified on output */
+ Int n_row, /* number of rows in A */
+ Int n_col, /* number of columns in A */
+ Int Alen, /* size of the array A */
+ Int A [], /* row indices of A, of size Alen */
+ Int p [], /* column pointers of A, of size n_col+1 */
+ double knobs [COLAMD_KNOBS],/* parameter settings for colamd */
+ Int stats [COLAMD_STATS] /* colamd output statistics and error codes */
+ /* ------------------ */
+ /* added for UMFPACK: */
+ , Int Front_npivcol [ ]
+ , Int Front_nrows [ ]
+ , Int Front_ncols [ ]
+ , Int Front_parent [ ]
+ , Int Front_cols [ ]
+ , Int *p_nfr
+ , Int InFront [ ]
+ /* ------------------ */
+) ;
+
+/* symamd deleted for UMFPACK */
+
+/* colamd_report deleted for UMFPACK */
+
+/* symamd_report deleted for UMFPACK */
+
+#endif /* COLAMD_H */
diff --git a/UMFPACK/Source/umf_config.h b/UMFPACK/Source/umf_config.h
new file mode 100644
index 0000000..79e9f5d
--- /dev/null
+++ b/UMFPACK/Source/umf_config.h
@@ -0,0 +1,324 @@
+/* ========================================================================== */
+/* === umf_config.h ========================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This file controls the compile-time configuration of UMFPACK. Modify the
+ UFconfig/UFconfig.mk file and this file if necessary, to control these
+ options. The following flags may be given as options to your C compiler
+ (as in "cc -DNSUNPERF", for example). These flags are normally placed in
+ your UMFPACK_CONFIG string, defined in the UFconfig/UFconfig.mk file.
+
+ All of these options, except for the timer, are for accessing the BLAS.
+
+ -DNSUNPERF
+
+ Applies only to Sun Solaris. If -DNSUNPERF is set, then the Sun
+ Performance Library BLAS will not be used.
+
+ The Sun Performance Library BLAS is used by default when compiling
+ the C-callable libumfpack.a library on Sun Solaris.
+
+ -DLONGBLAS
+
+ -DNPOSIX
+
+ If -DNPOSIX is set, then your Unix operating system is not POSIX-
+ compliant, and the POSIX routines sysconf ( ) and times ( )
+ routines are not used. These routines provide CPU time and
+ wallclock time information. If -DNPOSIX is set, then the ANSI
+ C clock ( ) routine is used. If -DNPOSIX is not set, then
+ sysconf ( ) and times ( ) are used in umfpack_tic and umfpack_toc.
+ See umfpack_tictoc.c for more information.
+ The default is to use the POSIX routines, except for Windows,
+ which is not POSIX-compliant.
+
+ -DGETRUSAGE
+
+ If -DGETRUSAGE is set, then your system's getrusage ( ) routine
+ will be used for getting the process CPU time. Otherwise the ANSI
+ C clock ( ) routine will be used. The default is to use getrusage
+ ( ) on Unix systems, and to use clock on all other architectures.
+
+ -DNO_TIMER
+
+ If -DNO_TIMER is set, then no timing routines are used at all.
+
+ -DNRECIPROCAL
+
+ This option controls a tradeoff between speed and accuracy. Using
+ -DNRECIPROCAL can lead to more accurate results, but with perhaps
+ some cost in performance, particularly if floating-point division
+ is much more costly than floating-point multiplication.
+
+ This option determines the method used to scale the pivot column.
+ If set, or if the absolute value of the pivot is < 1e-12 (or is a
+ NaN), then the pivot column is divided by the pivot value.
+ Otherwise, the reciprocal of the pivot value is computed, and the
+ pivot column is multiplied by (1/pivot). Multiplying by the
+ reciprocal can be slightly less accurate than dividing by the
+ pivot, but it is often faster. See umf_scale.c.
+
+ This has a small effect on the performance of UMFPACK, at least on
+ a Pentium 4M. It may have a larger effect on other architectures
+ where floating-point division is much more costly than floating-
+ point multiplication. The RS 6000 is one such example.
+
+ By default, the method chosen is to multiply by the reciprocal
+ (sacrificing accuracy for speed), except when compiling UMFPACK
+ as a built-in routine in MATLAB, or when gcc is being used.
+
+ When MATHWORKS is defined, -DNRECIPROCAL is forced on, and the pivot
+ column is divided by the pivot value. The only way of using the
+ other method in this case is to edit this file.
+
+ If -DNRECIPROCAL is enabled, then the row scaling factors are always
+ applied by dividing each row by the scale factor, rather than
+ multiplying by the reciprocal. If -DNRECIPROCAL is not enabled
+ (the default case), then the scale factors are normally applied by
+ multiplying by the reciprocal. If, however, the smallest scale
+ factor is tiny, then the scale factors are applied via division.
+
+ -DNO_DIVIDE_BY_ZERO
+
+ If the pivot is zero, and this flag is set, then no divide-by-zero
+ occurs.
+
+ The following options are controlled by amd_internal.h:
+
+ -DMATLAB_MEX_FILE
+
+ This flag is turned on when compiling the umfpack mexFunction for
+ use in MATLAB. The -DNRECIPROCAL flag is forced on (more accurate,
+ slightly slower). The umfpack mexFunction always returns
+ L*U = P*(R\A)*Q.
+
+ -DMATHWORKS
+
+ This flag is turned on when compiling umfpack as a built-in routine
+ in MATLAB. The -DNRECIPROCAL flag is forced on.
+
+ -DNDEBUG
+
+ Debugging mode (if NDEBUG is not defined). The default, of course,
+ is no debugging. Turning on debugging takes some work (see below).
+ If you do not edit this file, then debugging is turned off anyway,
+ regardless of whether or not -DNDEBUG is specified in your compiler
+ options.
+*/
+
+/* ========================================================================== */
+/* === AMD configuration ==================================================== */
+/* ========================================================================== */
+
+/* NDEBUG, PRINTF defined in amd_internal.h */
+
+/* ========================================================================== */
+/* === reciprocal option ==================================================== */
+/* ========================================================================== */
+
+/* Force the definition NRECIPROCAL when MATHWORKS or MATLAB_MEX_FILE
+ * are defined. Do not multiply by the reciprocal in those cases. */
+
+#ifndef NRECIPROCAL
+#if defined (MATHWORKS) || defined (MATLAB_MEX_FILE)
+#define NRECIPROCAL
+#endif
+#endif
+
+/* ========================================================================== */
+/* === Microsoft Windows configuration ====================================== */
+/* ========================================================================== */
+
+#if defined (UMF_WINDOWS) || defined (UMF_MINGW)
+/* Windows isn't Unix. Profound. */
+#define NPOSIX
+#endif
+
+/* ========================================================================== */
+/* === 0-based or 1-based printing ========================================== */
+/* ========================================================================== */
+
+#if defined (MATLAB_MEX_FILE) && defined (NDEBUG)
+/* In MATLAB, matrices are 1-based to the user, but 0-based internally. */
+/* One is added to all row and column indices when printing matrices */
+/* for the MATLAB user. The +1 shift is turned off when debugging. */
+#define INDEX(i) ((i)+1)
+#else
+/* In ANSI C, matrices are 0-based and indices are reported as such. */
+/* This mode is also used for debug mode, and if MATHWORKS is defined rather */
+/* than MATLAB_MEX_FILE. */
+#define INDEX(i) (i)
+#endif
+
+/* ========================================================================== */
+/* === Timer ================================================================ */
+/* ========================================================================== */
+
+/*
+ If you have the getrusage routine (all Unix systems I've test do), then use
+ that. Otherwise, use the ANSI C clock function. Note that on many
+ systems, the ANSI clock function wraps around after only 2147 seconds, or
+ about 36 minutes. BE CAREFUL: if you compare the run time of UMFPACK with
+ other sparse matrix packages, be sure to use the same timer. See
+ umfpack_tictoc.c for the timer used internally by UMFPACK. See also
+ umfpack_timer.c for the timer used in an earlier version of UMFPACK.
+ That timer is still available as a user-callable routine, but it is no
+ longer used internally by UMFPACK.
+*/
+
+/* Sun Solaris, SGI Irix, Linux, Compaq Alpha, and IBM RS 6000 all have */
+/* getrusage. It's in BSD unix, so perhaps all unix systems have it. */
+#if defined (UMF_SOL2) || defined (UMF_SGI) || defined (UMF_LINUX) \
+|| defined (UMF_ALPHA) || defined (UMF_AIX) || defined (UMF_CYGWIN)
+#define GETRUSAGE
+#endif
+
+
+/* ========================================================================== */
+/* === BLAS ================================================================= */
+/* ========================================================================== */
+
+#include "cholmod_blas.h"
+
+
+/* -------------------------------------------------------------------------- */
+/* DGEMM */
+/* -------------------------------------------------------------------------- */
+
+/* C = C - A*B', where:
+ * A is m-by-k with leading dimension ldac
+ * B is k-by-n with leading dimension ldb
+ * C is m-by-n with leading dimension ldac */
+#ifdef COMPLEX
+#define BLAS_GEMM(m,n,k,A,B,ldb,C,ldac) \
+{ \
+ double alpha [2] = {-1,0}, beta [2] = {1,0} ; \
+ BLAS_zgemm ("N", "T", m, n, k, alpha, (double *) A, ldac, \
+ (double *) B, ldb, beta, (double *) C, ldac) ; \
+}
+#else
+#define BLAS_GEMM(m,n,k,A,B,ldb,C,ldac) \
+{ \
+ double alpha = -1, beta = 1 ; \
+ BLAS_dgemm ("N", "T", m, n, k, &alpha, A, ldac, B, ldb, &beta, C, ldac) ; \
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* GER */
+/* -------------------------------------------------------------------------- */
+
+/* A = A - x*y', where:
+ * A is m-by-n with leading dimension d
+ x is a column vector with stride 1
+ y is a column vector with stride 1 */
+#ifdef COMPLEX
+#define BLAS_GER(m,n,x,y,A,d) \
+{ \
+ double alpha [2] = {-1,0} ; \
+ BLAS_zgeru (m, n, alpha, (double *) x, 1, (double *) y, 1, \
+ (double *) A, d) ; \
+}
+#else
+#define BLAS_GER(m,n,x,y,A,d) \
+{ \
+ double alpha = -1 ; \
+ BLAS_dger (m, n, &alpha, x, 1, y, 1, A, d) ; \
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* GEMV */
+/* -------------------------------------------------------------------------- */
+
+/* y = y - A*x, where A is m-by-n with leading dimension d,
+ x is a column vector with stride 1
+ y is a column vector with stride 1 */
+#ifdef COMPLEX
+#define BLAS_GEMV(m,n,A,x,y,d) \
+{ \
+ double alpha [2] = {-1,0}, beta [2] = {1,0} ; \
+ BLAS_zgemv ("N", m, n, alpha, (double *) A, d, (double *) x, 1, beta, \
+ (double *) y, 1) ; \
+}
+#else
+#define BLAS_GEMV(m,n,A,x,y,d) \
+{ \
+ double alpha = -1, beta = 1 ; \
+ BLAS_dgemv ("N", m, n, &alpha, A, d, x, 1, &beta, y, 1) ; \
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* TRSV */
+/* -------------------------------------------------------------------------- */
+
+/* solve Lx=b, where:
+ * B is a column vector (m-by-1) with leading dimension d
+ * A is m-by-m with leading dimension d */
+#ifdef COMPLEX
+#define BLAS_TRSV(m,A,b,d) \
+{ \
+ BLAS_ztrsv ("L", "N", "U", m, (double *) A, d, (double *) b, 1) ; \
+}
+#else
+#define BLAS_TRSV(m,A,b,d) \
+{ \
+ BLAS_dtrsv ("L", "N", "U", m, A, d, b, 1) ; \
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* TRSM */
+/* -------------------------------------------------------------------------- */
+
+/* solve XL'=B where:
+ * B is m-by-n with leading dimension ldb
+ * A is n-by-n with leading dimension lda */
+#ifdef COMPLEX
+#define BLAS_TRSM_RIGHT(m,n,A,lda,B,ldb) \
+{ \
+ double alpha [2] = {1,0} ; \
+ BLAS_ztrsm ("R", "L", "T", "U", m, n, alpha, (double *) A, lda, \
+ (double *) B, ldb) ; \
+}
+#else
+#define BLAS_TRSM_RIGHT(m,n,A,lda,B,ldb) \
+{ \
+ double alpha = 1 ; \
+ BLAS_dtrsm ("R", "L", "T", "U", m, n, &alpha, A, lda, B, ldb) ; \
+}
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* SCAL */
+/* -------------------------------------------------------------------------- */
+
+/* x = s*x, where x is a stride-1 vector of length n */
+#ifdef COMPLEX
+#define BLAS_SCAL(n,s,x) \
+{ \
+ double alpha [2] ; \
+ alpha [0] = REAL_COMPONENT (s) ; \
+ alpha [1] = IMAG_COMPONENT (s) ; \
+ BLAS_zscal (n, alpha, (double *) x, 1) ; \
+}
+#else
+#define BLAS_SCAL(n,s,x) \
+{ \
+ double alpha = REAL_COMPONENT (s) ; \
+ BLAS_dscal (n, &alpha, (double *) x, 1) ; \
+}
+#endif
diff --git a/UMFPACK/Source/umf_create_element.c b/UMFPACK/Source/umf_create_element.c
new file mode 100644
index 0000000..bb487ec
--- /dev/null
+++ b/UMFPACK/Source/umf_create_element.c
@@ -0,0 +1,593 @@
+/* ========================================================================== */
+/* === UMF_create_element =================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Factorization of a frontal matrix is complete. Create a new element for
+ later assembly into a subsequent frontal matrix. Returns TRUE if
+ successful, FALSE if out of memory.
+*/
+
+#include "umf_internal.h"
+#include "umf_create_element.h"
+#include "umf_mem_alloc_element.h"
+#include "umf_mem_alloc_tail_block.h"
+#include "umf_mem_free_tail_block.h"
+#include "umf_get_memory.h"
+
+/* ========================================================================== */
+/* === copy_column ========================================================== */
+/* ========================================================================== */
+
+PRIVATE void copy_column (Int len, Entry *X, Entry *Y)
+{
+ Int i ;
+#pragma ivdep
+ for (i = 0 ; i < len ; i++)
+ {
+ Y [i] = X [i] ;
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_create_element =================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMF_create_element
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int j, col, row, *Fcols, *Frows, fnrows, fncols, *Cols, len, needunits, t1,
+ t2, size, e, i, *E, *Fcpos, *Frpos, *Rows, eloc, fnr_curr, f,
+ got_memory, *Row_tuples, *Row_degree, *Row_tlen, *Col_tuples, max_mark,
+ *Col_degree, *Col_tlen, nn, n_row, n_col, r2, c2, do_Fcpos ;
+ Entry *C, *Fcol ;
+ Element *ep ;
+ Unit *p, *Memory ;
+ Tuple *tp, *tp1, *tp2, tuple, *tpend ;
+#ifndef NDEBUG
+ DEBUG2 (("FRONTAL WRAPUP\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (Work->fnpiv == 0) ;
+ ASSERT (Work->fnzeros == 0) ;
+ Row_degree = Numeric->Rperm ;
+ Row_tuples = Numeric->Uip ;
+ Row_tlen = Numeric->Uilen ;
+ Col_degree = Numeric->Cperm ;
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ nn = MAX (n_row, n_col) ;
+ Fcols = Work->Fcols ;
+ Frows = Work->Frows ;
+ Fcpos = Work->Fcpos ;
+ Frpos = Work->Frpos ;
+ Memory = Numeric->Memory ;
+ fncols = Work->fncols ;
+ fnrows = Work->fnrows ;
+
+ tp = (Tuple *) NULL ;
+ tp1 = (Tuple *) NULL ;
+ tp2 = (Tuple *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* add the current frontal matrix to the degrees of each column */
+ /* ---------------------------------------------------------------------- */
+
+ if (!Symbolic->fixQ)
+ {
+ /* but only if the column ordering is not fixed */
+#pragma ivdep
+ for (j = 0 ; j < fncols ; j++)
+ {
+ /* add the current frontal matrix to the degree */
+ ASSERT (Fcols [j] >= 0 && Fcols [j] < n_col) ;
+ Col_degree [Fcols [j]] += fnrows ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* add the current frontal matrix to the degrees of each row */
+ /* ---------------------------------------------------------------------- */
+
+#pragma ivdep
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ /* add the current frontal matrix to the degree */
+ ASSERT (Frows [i] >= 0 && Frows [i] < n_row) ;
+ Row_degree [Frows [i]] += fncols ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Reset the external degree counters */
+ /* ---------------------------------------------------------------------- */
+
+ E = Work->E ;
+ max_mark = MAX_MARK (nn) ;
+
+ if (!Work->pivcol_in_front)
+ {
+ /* clear the external column degrees. no more Usons of current front */
+ Work->cdeg0 += (nn + 1) ;
+ if (Work->cdeg0 >= max_mark)
+ {
+ /* guard against integer overflow. This is very rare */
+ DEBUG1 (("Integer overflow, cdeg\n")) ;
+ Work->cdeg0 = 1 ;
+#pragma ivdep
+ for (e = 1 ; e <= Work->nel ; e++)
+ {
+ if (E [e])
+ {
+ ep = (Element *) (Memory + E [e]) ;
+ ep->cdeg = 0 ;
+ }
+ }
+ }
+ }
+
+ if (!Work->pivrow_in_front)
+ {
+ /* clear the external row degrees. no more Lsons of current front */
+ Work->rdeg0 += (nn + 1) ;
+ if (Work->rdeg0 >= max_mark)
+ {
+ /* guard against integer overflow. This is very rare */
+ DEBUG1 (("Integer overflow, rdeg\n")) ;
+ Work->rdeg0 = 1 ;
+#pragma ivdep
+ for (e = 1 ; e <= Work->nel ; e++)
+ {
+ if (E [e])
+ {
+ ep = (Element *) (Memory + E [e]) ;
+ ep->rdeg = 0 ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* clear row/col offsets */
+ /* ---------------------------------------------------------------------- */
+
+ if (!Work->pivrow_in_front)
+ {
+#pragma ivdep
+ for (j = 0 ; j < fncols ; j++)
+ {
+ Fcpos [Fcols [j]] = EMPTY ;
+ }
+ }
+
+ if (!Work->pivcol_in_front)
+ {
+#pragma ivdep
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Frpos [Frows [i]] = EMPTY ;
+ }
+ }
+
+ if (fncols <= 0 || fnrows <= 0)
+ {
+ /* no element to create */
+ DEBUG2 (("Element evaporation\n")) ;
+ Work->prior_element = EMPTY ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create element for later assembly */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0)
+ {
+ double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ;
+ DEBUG4 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random garbage collection (create)\n"));
+ }
+#endif
+
+ needunits = 0 ;
+ got_memory = FALSE ;
+ eloc = UMF_mem_alloc_element (Numeric, fnrows, fncols, &Rows, &Cols, &C,
+ &needunits, &ep) ;
+
+ /* if UMF_get_memory needs to be called */
+ if (Work->do_grow)
+ {
+ /* full compaction of current frontal matrix, since UMF_grow_front will
+ * be called next anyway. */
+ r2 = fnrows ;
+ c2 = fncols ;
+ do_Fcpos = FALSE ;
+ }
+ else
+ {
+ /* partial compaction. */
+ r2 = MAX (fnrows, Work->fnrows_new + 1) ;
+ c2 = MAX (fncols, Work->fncols_new + 1) ;
+ /* recompute Fcpos if pivot row is in the front */
+ do_Fcpos = Work->pivrow_in_front ;
+ }
+
+ if (!eloc)
+ {
+ /* Do garbage collection, realloc, and try again. */
+ /* Compact the current front if it needs to grow anyway. */
+ /* Note that there are no pivot rows or columns in the current front */
+ DEBUGm3 (("get_memory from umf_create_element, 1\n")) ;
+ if (!UMF_get_memory (Numeric, Work, needunits, r2, c2, do_Fcpos))
+ {
+ /* :: out of memory in umf_create_element (1) :: */
+ DEBUGm4 (("out of memory: create element (1)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ got_memory = TRUE ;
+ Memory = Numeric->Memory ;
+ eloc = UMF_mem_alloc_element (Numeric, fnrows, fncols, &Rows, &Cols, &C,
+ &needunits, &ep) ;
+ ASSERT (eloc >= 0) ;
+ if (!eloc)
+ {
+ /* :: out of memory in umf_create_element (2) :: */
+ DEBUGm4 (("out of memory: create element (2)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ }
+
+ e = ++(Work->nel) ; /* get the name of this new frontal matrix */
+ Work->prior_element = e ;
+ DEBUG8 (("wrapup e "ID" nel "ID"\n", e, Work->nel)) ;
+
+ ASSERT (e > 0 && e < Work->elen) ;
+ ASSERT (E [e] == 0) ;
+ E [e] = eloc ;
+
+ if (Work->pivcol_in_front)
+ {
+ /* the new element is a Uson of the next frontal matrix */
+ ep->cdeg = Work->cdeg0 ;
+ }
+
+ if (Work->pivrow_in_front)
+ {
+ /* the new element is an Lson of the next frontal matrix */
+ ep->rdeg = Work->rdeg0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* copy frontal matrix into the new element */
+ /* ---------------------------------------------------------------------- */
+
+#pragma ivdep
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Rows [i] = Frows [i] ;
+ }
+#pragma ivdep
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Cols [i] = Fcols [i] ;
+ }
+ Fcol = Work->Fcblock ;
+ DEBUG0 (("copy front "ID" by "ID"\n", fnrows, fncols)) ;
+ fnr_curr = Work->fnr_curr ;
+ ASSERT (fnr_curr >= 0 && fnr_curr % 2 == 1) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ copy_column (fnrows, Fcol, C) ;
+ Fcol += fnr_curr ;
+ C += fnrows ;
+ }
+
+ DEBUG8 (("element copied\n")) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* add tuples for the new element */
+ /* ---------------------------------------------------------------------- */
+
+ tuple.e = e ;
+
+ if (got_memory)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* UMF_get_memory ensures enough space exists for each new tuple */
+ /* ------------------------------------------------------------------ */
+
+ /* place (e,f) in the element list of each column */
+ for (tuple.f = 0 ; tuple.f < fncols ; tuple.f++)
+ {
+ col = Fcols [tuple.f] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ ASSERT (Col_tuples [col]) ;
+ tp = ((Tuple *) (Memory + Col_tuples [col])) + Col_tlen [col]++ ;
+ *tp = tuple ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+ /* place (e,f) in the element list of each row */
+ for (tuple.f = 0 ; tuple.f < fnrows ; tuple.f++)
+ {
+ row = Frows [tuple.f] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ ASSERT (Row_tuples [row]) ;
+ tp = ((Tuple *) (Memory + Row_tuples [row])) + Row_tlen [row]++ ;
+ *tp = tuple ;
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* place (e,f) in the element list of each column */
+ /* ------------------------------------------------------------------ */
+
+ /* might not have enough space for each tuple */
+
+ for (tuple.f = 0 ; tuple.f < fncols ; tuple.f++)
+ {
+ col = Fcols [tuple.f] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ t1 = Col_tuples [col] ;
+ DEBUG1 (("Placing on col:"ID" , tuples at "ID"\n",
+ col, Col_tuples [col])) ;
+
+ size = 0 ;
+ len = 0 ;
+
+ if (t1)
+ {
+ p = Memory + t1 ;
+ tp = (Tuple *) p ;
+ size = GET_BLOCK_SIZE (p) ;
+ len = Col_tlen [col] ;
+ tp2 = tp + len ;
+ }
+
+ needunits = UNITS (Tuple, len + 1) ;
+ DEBUG1 (("len: "ID" size: "ID" needunits: "ID"\n",
+ len, size, needunits));
+
+ if (needunits > size && t1)
+ {
+ /* prune the tuples */
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + len ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ ;
+ if (Cols [f] == EMPTY) continue ; /* already assembled */
+ ASSERT (col == Cols [f]) ;
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ len = tp2 - tp1 ;
+ Col_tlen [col] = len ;
+ needunits = UNITS (Tuple, len + 1) ;
+ }
+
+ if (needunits > size)
+ {
+ /* no room exists - reallocate elsewhere */
+ DEBUG1 (("REALLOCATE Col: "ID", size "ID" to "ID"\n",
+ col, size, 2*needunits)) ;
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0) /* a double relop, but ignore NaN case */
+ {
+ double rrr = ((double) (rand ( ))) /
+ (((double) RAND_MAX) + 1) ;
+ DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random gar. (col tuple)\n")) ;
+ }
+#endif
+
+ needunits = MIN (2*needunits, (Int) UNITS (Tuple, nn)) ;
+ t2 = UMF_mem_alloc_tail_block (Numeric, needunits) ;
+ if (!t2)
+ {
+ /* :: get memory in umf_create_element (1) :: */
+ /* get memory, reconstruct all tuple lists, and return */
+ /* Compact the current front if it needs to grow anyway. */
+ /* Note: no pivot rows or columns in the current front */
+ DEBUGm4 (("get_memory from umf_create_element, 1\n")) ;
+ return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos));
+ }
+ Col_tuples [col] = t2 ;
+ tp2 = (Tuple *) (Memory + t2) ;
+ if (t1)
+ {
+ for (i = 0 ; i < len ; i++)
+ {
+ *tp2++ = *tp1++ ;
+ }
+ UMF_mem_free_tail_block (Numeric, t1) ;
+ }
+ }
+
+ /* place the new (e,f) tuple in the element list of the column */
+ Col_tlen [col]++ ;
+ *tp2 = tuple ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* place (e,f) in the element list of each row */
+ /* ------------------------------------------------------------------ */
+
+ for (tuple.f = 0 ; tuple.f < fnrows ; tuple.f++)
+ {
+ row = Frows [tuple.f] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ t1 = Row_tuples [row] ;
+ DEBUG1 (("Placing on row:"ID" , tuples at "ID"\n",
+ row, Row_tuples [row])) ;
+
+ size = 0 ;
+ len = 0 ;
+ if (t1)
+ {
+ p = Memory + t1 ;
+ tp = (Tuple *) p ;
+ size = GET_BLOCK_SIZE (p) ;
+ len = Row_tlen [row] ;
+ tp2 = tp + len ;
+ }
+
+ needunits = UNITS (Tuple, len + 1) ;
+ DEBUG1 (("len: "ID" size: "ID" needunits: "ID"\n",
+ len, size, needunits)) ;
+
+ if (needunits > size && t1)
+ {
+ /* prune the tuples */
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + len ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e])
+ {
+ continue ; /* element already deallocated */
+ }
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ Rows = Cols + (ep->ncols) ;
+ if (Rows [f] == EMPTY) continue ; /* already assembled */
+ ASSERT (row == Rows [f]) ;
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ len = tp2 - tp1 ;
+ Row_tlen [row] = len ;
+ needunits = UNITS (Tuple, len + 1) ;
+ }
+
+ if (needunits > size)
+ {
+ /* no room exists - reallocate elsewhere */
+ DEBUG1 (("REALLOCATE Row: "ID", size "ID" to "ID"\n",
+ row, size, 2*needunits)) ;
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0) /* a double relop, but ignore NaN case */
+ {
+ double rrr = ((double) (rand ( ))) /
+ (((double) RAND_MAX) + 1) ;
+ DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random gar. (row tuple)\n")) ;
+ }
+#endif
+
+ needunits = MIN (2*needunits, (Int) UNITS (Tuple, nn)) ;
+ t2 = UMF_mem_alloc_tail_block (Numeric, needunits) ;
+ if (!t2)
+ {
+ /* :: get memory in umf_create_element (2) :: */
+ /* get memory, reconstruct all tuple lists, and return */
+ /* Compact the current front if it needs to grow anyway. */
+ /* Note: no pivot rows or columns in the current front */
+ DEBUGm4 (("get_memory from umf_create_element, 2\n")) ;
+ return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos));
+ }
+ Row_tuples [row] = t2 ;
+ tp2 = (Tuple *) (Memory + t2) ;
+ if (t1)
+ {
+ for (i = 0 ; i < len ; i++)
+ {
+ *tp2++ = *tp1++ ;
+ }
+ UMF_mem_free_tail_block (Numeric, t1) ;
+ }
+ }
+
+ /* place the new (e,f) tuple in the element list of the row */
+ Row_tlen [row]++ ;
+ *tp2 = tuple ;
+ }
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG1 (("Done extending\nFINAL: element row pattern: len="ID"\n", fncols));
+ for (j = 0 ; j < fncols ; j++) DEBUG1 ((""ID"\n", Fcols [j])) ;
+ DEBUG1 (("FINAL: element col pattern: len="ID"\n", fnrows)) ;
+ for (j = 0 ; j < fnrows ; j++) DEBUG1 ((""ID"\n", Frows [j])) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Fcols [j] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ;
+ }
+ for (j = 0 ; j < fnrows ; j++)
+ {
+ row = Frows [j] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
+ }
+ if (n_row < 1000 && n_col < 1000)
+ {
+ UMF_dump_memory (Numeric) ;
+ }
+ DEBUG1 (("New element, after filling with stuff: "ID"\n", e)) ;
+ UMF_dump_element (Numeric, Work, e, TRUE) ;
+ if (nn < 1000)
+ {
+ DEBUG4 (("Matrix dump, after New element: "ID"\n", e)) ;
+ UMF_dump_matrix (Numeric, Work, TRUE) ;
+ }
+ DEBUG3 (("FRONTAL WRAPUP DONE\n")) ;
+#endif
+
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umf_create_element.h b/UMFPACK/Source/umf_create_element.h
new file mode 100644
index 0000000..b6025bb
--- /dev/null
+++ b/UMFPACK/Source/umf_create_element.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_create_element
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
diff --git a/UMFPACK/Source/umf_dump.c b/UMFPACK/Source/umf_dump.c
new file mode 100644
index 0000000..888a316
--- /dev/null
+++ b/UMFPACK/Source/umf_dump.c
@@ -0,0 +1,1209 @@
+/* ========================================================================== */
+/* === UMF_dump ============================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* These routines, and external variables, are used only when debugging. */
+/* If debugging is disabled (for normal operation) then this entire file */
+/* becomes empty */
+
+#include "umf_internal.h"
+
+#ifndef NDEBUG
+
+/* These global debugging variables and arrays do not exist if debugging */
+/* is disabled at compile time (which is the default). */
+GLOBAL Int UMF_debug = -999 ;
+GLOBAL Int UMF_allocfail = FALSE ;
+GLOBAL double UMF_gprob = -1.0 ;
+
+/* static debugging arrays used only in UMF_dump_rowcol */
+PRIVATE Int UMF_DBflag = 0 ;
+PRIVATE Int UMF_DBpacked [UMF_DBMAX+1] ;
+PRIVATE Int UMF_DBscatter [UMF_DBMAX+1] ;
+
+/* ========================================================================== */
+/* === UMF_DBinit =========================================================== */
+/* ========================================================================== */
+
+/* clear the debugging arrays */
+
+PRIVATE void UMF_DBinit
+(
+ void
+)
+{
+ Int i ;
+
+ /* Int_MAX is defined in umfpack.h */
+ if (UMF_DBflag < 1 || UMF_DBflag == Int_MAX)
+ {
+ /* clear the debugging arrays */
+ UMF_DBflag = 0 ;
+ for (i = 0 ; i <= UMF_DBMAX ; i++)
+ {
+ UMF_DBscatter [i] = 0 ;
+ UMF_DBpacked [i] = 0 ;
+ }
+ }
+
+ UMF_DBflag++ ;
+
+ /* UMF_DBflag > UMF_DBscatter [0...UMF_DBmax] is now true */
+}
+
+/* ========================================================================== */
+/* === UMF_dump_dense ======================================================= */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_dense
+(
+ Entry *C,
+ Int dim,
+ Int m,
+ Int n
+)
+{
+
+ /* dump C [1..m,1..n], with column dimenstion dim */
+ Int i, j;
+
+ if (UMF_debug < 7) return ;
+ if (C == (Entry *) NULL)
+ {
+ DEBUG7 (("No dense matrix allocated\n")) ;
+ return ;
+ }
+ DEBUG8 ((" dimension= "ID" rows= "ID" cols= "ID"\n", dim, m, n)) ;
+
+ for (i = 0 ; i < m ; i++)
+ {
+ DEBUG9 ((ID": ", i)) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ EDEBUG9 (C [i+j*dim]) ;
+ if (j % 6 == 5) DEBUG9 (("\n ")) ;
+ }
+ DEBUG9 (("\n")) ;
+ }
+
+ for (i = 0 ; i < m ; i++)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ if (IS_ZERO (C [i+j*dim]))
+ {
+ DEBUG8 ((".")) ;
+ }
+ else
+ {
+ DEBUG8 (("X")) ;
+ }
+ }
+ DEBUG8 (("\n")) ;
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_dump_element ===================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_element
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int e,
+ Int clean
+)
+{
+
+ Int i, j, k, *Rows, *Cols, nrows, ncols, *E, row, col,
+ *Row_degree, *Col_degree ;
+ Entry *C ;
+ Element *ep ;
+ Unit *p ;
+
+ if (UMF_debug < 7) return ;
+
+ if (e == 0)
+ {
+ UMF_dump_current_front (Numeric, Work, FALSE) ;
+ return ;
+ }
+
+ DEBUG7 (("\n====================ELEMENT: "ID" ", e)) ;
+ if (!Numeric || !Work || !Numeric->Memory)
+ {
+ DEBUG7 ((" No Numeric, Work\n")) ;
+ return ;
+ }
+ DEBUG7 ((" nel: "ID" of "ID, e, Work->nel)) ;
+ E = Work->E ;
+ if (!E)
+ {
+ DEBUG7 ((" No elements\n")) ;
+ return ;
+ }
+ if (e < 0 || e > Work->nel)
+ {
+ DEBUG7 (("e out of range!\n")) ;
+ return ;
+ }
+ if (!E [e])
+ {
+ DEBUG7 ((" deallocated\n")) ;
+ return ;
+ }
+ DEBUG7 (("\n")) ;
+ Col_degree = Numeric->Cperm ;
+ Row_degree = Numeric->Rperm ;
+
+ p = Numeric->Memory + E [e] ;
+ DEBUG7 (("ep "ID"\n", (Int) (p-Numeric->Memory))) ;
+ GET_ELEMENT (ep, p, Cols, Rows, ncols, nrows, C) ;
+ DEBUG7 (("nrows "ID" nrowsleft "ID"\n", nrows, ep->nrowsleft)) ;
+ DEBUG7 (("ncols "ID" ncolsleft "ID"\n", ncols, ep->ncolsleft)) ;
+ DEBUG7 (("cdeg-cdeg0 "ID" rdeg-rdeg0 "ID" next "ID"\n",
+ ep->cdeg - Work->cdeg0, ep->rdeg - Work->rdeg0, ep->next)) ;
+
+ DEBUG8 (("rows: ")) ;
+ k = 0 ;
+ for (i = 0 ; i < ep->nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0)
+ {
+ DEBUG8 ((" "ID, row)) ;
+ ASSERT (row < Work->n_row) ;
+ if ((k++ % 10) == 9) DEBUG8 (("\n")) ;
+ ASSERT (IMPLIES (clean, NON_PIVOTAL_ROW (row))) ;
+ }
+ }
+
+ DEBUG8 (("\ncols: ")) ;
+ k = 0 ;
+ for (j = 0 ; j < ep->ncols ; j++)
+ {
+ col = Cols [j] ;
+ if (col >= 0)
+ {
+ DEBUG8 ((" "ID, col)) ;
+ ASSERT (col < Work->n_col) ;
+ if ((k++ % 10) == 9) DEBUG8 (("\n")) ;
+ ASSERT (IMPLIES (clean, NON_PIVOTAL_COL (col))) ;
+ }
+ }
+
+ DEBUG8 (("\nvalues:\n")) ;
+ if (UMF_debug >= 9)
+ {
+ for (i = 0 ; i < ep->nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0)
+ {
+ DEBUG9 ((ID": ", row)) ;
+ k = 0 ;
+ for (j = 0 ; j < ep->ncols ; j++)
+ {
+ col = Cols [j] ;
+ if (col >= 0)
+ {
+ EDEBUG9 (C [i+j*ep->nrows]) ;
+ if (k++ % 6 == 5) DEBUG9 (("\n ")) ;
+ }
+ }
+ DEBUG9 (("\n")) ;
+ }
+ }
+ }
+
+ DEBUG7 (("====================\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_rowcol ====================================================== */
+/* ========================================================================== */
+
+/* dump a row or a column, from one or more memory spaces */
+/* return exact degree */
+
+GLOBAL void UMF_dump_rowcol
+(
+ Int dumpwhich, /* 0 for row, 1 for column */
+ NumericType *Numeric,
+ WorkType *Work,
+ Int dumpindex, /* row or column index to dump */
+ Int check_degree /* true if degree is to be checked */
+)
+{
+ Entry value ;
+ Entry *C ;
+ Int f, nrows, j, jj, len, e, deg, index, n_row, n_col, *Cols, *Rows, nn,
+ dumpdeg, ncols, preve, *E, tpi, *Pattern, approx_deg, not_in_use ;
+ Tuple *tp, *tend ;
+ Element *ep ;
+ Int *Row_tuples, *Row_degree, *Row_tlen ;
+ Int *Col_tuples, *Col_degree, *Col_tlen ;
+ Unit *p ;
+ Int is_there ;
+
+ /* clear the debugging arrays */
+ UMF_DBinit () ;
+
+ if (dumpwhich == 0)
+ {
+ DEBUG7 (("\n====================ROW: "ID, dumpindex)) ;
+ }
+ else
+ {
+ DEBUG7 (("\n====================COL: "ID, dumpindex)) ;
+ }
+
+ if (dumpindex == EMPTY)
+ {
+ DEBUG7 ((" (EMPTY)\n")) ;
+ return ;
+ }
+
+ deg = 0 ;
+ approx_deg = 0 ;
+
+ if (!Numeric || !Work)
+ {
+ DEBUG7 ((" No Numeric, Work\n")) ;
+ return ;
+ }
+
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ nn = MAX (n_row, n_col) ;
+ E = Work->E ;
+
+ Col_degree = Numeric->Cperm ;
+ Row_degree = Numeric->Rperm ;
+
+ Row_tuples = Numeric->Uip ;
+ Row_tlen = Numeric->Uilen ;
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+
+ if (!E
+ || !Row_tuples || !Row_degree || !Row_tlen
+ || !Col_tuples || !Col_degree || !Col_tlen)
+ {
+ DEBUG7 ((" No E, Rows, Cols\n")) ;
+ return ;
+ }
+
+ if (dumpwhich == 0)
+ {
+ /* dump a row */
+ ASSERT (dumpindex >= 0 && dumpindex < n_row) ;
+ if (!NON_PIVOTAL_ROW (dumpindex))
+ {
+ DEBUG7 ((" Pivotal\n")) ;
+ return ;
+ }
+ len = Row_tlen [dumpindex] ;
+ dumpdeg = Row_degree [dumpindex] ;
+ tpi = Row_tuples [dumpindex] ;
+ }
+ else
+ {
+ /* dump a column */
+ ASSERT (dumpindex >= 0 && dumpindex < n_col) ;
+ if (!NON_PIVOTAL_COL (dumpindex))
+ {
+ DEBUG7 ((" Pivotal\n")) ;
+ return ;
+ }
+ len = Col_tlen [dumpindex] ;
+ dumpdeg = Col_degree [dumpindex] ;
+ tpi = Col_tuples [dumpindex] ;
+ }
+
+ p = Numeric->Memory + tpi ;
+ tp = (Tuple *) p ;
+ if (!tpi)
+ {
+ DEBUG7 ((" Nonpivotal, No tuple list tuples "ID" tlen "ID"\n",
+ tpi, len)) ;
+ return ;
+ }
+ ASSERT (p >= Numeric->Memory + Numeric->itail) ;
+ ASSERT (p < Numeric->Memory + Numeric->size) ;
+
+ DEBUG7 ((" degree: "ID" len: "ID"\n", dumpdeg, len)) ;
+ not_in_use = (p-1)->header.size - UNITS (Tuple, len) ;
+ DEBUG7 ((" Tuple list: p+1: "ID" size: "ID" units, "ID" not in use\n",
+ (Int) (p-Numeric->Memory), (p-1)->header.size, not_in_use)) ;
+ ASSERT (not_in_use >= 0) ;
+ tend = tp + len ;
+ preve = 0 ;
+ for ( ; tp < tend ; tp++)
+ {
+ /* row/col of element e, offset is f: */
+ /* DEBUG8 ((" (tp="ID")\n", tp)) ; */
+ e = tp->e ;
+ f = tp->f ;
+ DEBUG8 ((" (e="ID", f="ID")\n", e, f)) ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ /* dump the pattern and values */
+ if (E [e])
+ {
+ p = Numeric->Memory + E [e] ;
+ GET_ELEMENT (ep, p, Cols, Rows, ncols, nrows, C) ;
+ if (dumpwhich == 0)
+ {
+ Pattern = Cols ;
+ jj = ep->ncols ;
+ is_there = Rows [f] >= 0 ;
+ if (is_there) approx_deg += ep->ncolsleft ;
+ }
+ else
+ {
+ Pattern = Rows ;
+ jj = ep->nrows ;
+ is_there = Cols [f] >= 0 ;
+ if (is_there) approx_deg += ep->nrowsleft ;
+ }
+ if (!is_there)
+ {
+ DEBUG8 (("\t\tnot present\n")) ;
+ }
+ else
+ {
+ for (j = 0 ; j < jj ; j++)
+ {
+ index = Pattern [j] ;
+ value =
+ C [ (dumpwhich == 0) ? (f+nrows*j) : (j+nrows*f) ] ;
+ if (index >= 0)
+ {
+ DEBUG8 (("\t\t"ID":", index)) ;
+ EDEBUG8 (value) ;
+ DEBUG8 (("\n")) ;
+ if (dumpwhich == 0)
+ {
+ /* col must be in the range 0..n_col-1 */
+ ASSERT (index < n_col) ;
+ }
+ else
+ {
+ /* row must be in the range 0..n_row-1 */
+ ASSERT (index < n_row) ;
+ }
+
+ if (nn <= UMF_DBMAX)
+ {
+ if (UMF_DBscatter [index] != UMF_DBflag)
+ {
+ UMF_DBpacked [deg++] = index ;
+ UMF_DBscatter [index] = UMF_DBflag ;
+ }
+ }
+ }
+ }
+ }
+ /* the (e,f) tuples should be in order of their creation */
+ /* this means that garbage collection will not jumble them */
+ ASSERT (preve < e) ;
+ preve = e ;
+ }
+ else
+ {
+ DEBUG8 (("\t\tdeallocated\n")) ;
+ }
+ }
+
+ if (nn <= UMF_DBMAX)
+ {
+ if (deg > 0)
+ {
+ DEBUG7 ((" Assembled, actual deg: "ID" : ", deg)) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ index = UMF_DBpacked [j] ;
+ DEBUG8 ((ID" ", index)) ;
+ if (j % 20 == 19) DEBUG8 (("\n ")) ;
+ ASSERT (UMF_DBscatter [index] == UMF_DBflag) ;
+ }
+ DEBUG7 (("\n")) ;
+ }
+ }
+
+ /* Col_degree is not maintained when fixQ is true */
+ if (check_degree)
+ {
+ DEBUG8 ((" approx_deg "ID" dumpdeg "ID"\n", approx_deg, dumpdeg)) ;
+ ASSERT (approx_deg == dumpdeg) ;
+ }
+
+ DEBUG7 (("====================\n")) ;
+
+ /* deg is now the exact degree */
+ /* if nn <= UMF_DBMAX, then UMF_DBscatter [i] == UMF_DBflag for every i */
+ /* in the row or col, and != UMF_DBflag if not */
+
+ return ;
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_matrix ====================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_matrix
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int check_degree
+)
+{
+
+ Int e, row, col, intfrag, frag, n_row, n_col, *E, fullsize, actualsize ;
+ Element *ep ;
+ Unit *p ;
+
+ DEBUG6 (("=================================================== MATRIX:\n")) ;
+ if (!Numeric || !Work)
+ {
+ DEBUG6 (("No Numeric or Work allocated\n")) ;
+ return ;
+ }
+ if (!Numeric->Memory)
+ {
+ DEBUG6 (("No Numeric->Memory\n")) ;
+ return ;
+ }
+
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ DEBUG6 (("n_row "ID" n_col "ID" nz "ID"\n", n_row, n_col, Work->nz)) ;
+ DEBUG6 (("============================ ELEMENTS: "ID" \n", Work->nel)) ;
+ intfrag = 0 ;
+ E = Work->E ;
+ if (!E)
+ {
+ DEBUG6 (("No elements allocated\n")) ;
+ }
+ else
+ {
+ for (e = 0 ; e <= Work->nel ; e++)
+ {
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+ if (e > 0 && E [e])
+ {
+ p = Numeric->Memory + E [e] ;
+ ep = (Element *) p ;
+ ASSERT (ep->nrowsleft > 0 || ep->ncolsleft > 0) ;
+ fullsize = GET_BLOCK_SIZE (p) ;
+ actualsize = GET_ELEMENT_SIZE (ep->nrowsleft,ep->ncolsleft);
+ frag = fullsize - actualsize ;
+ intfrag += frag ;
+ DEBUG7 (("dump el: "ID", full "ID" actual "ID" frag: "ID
+ " intfrag: "ID"\n", e, fullsize, actualsize, frag,
+ intfrag)) ;
+ }
+ }
+ }
+
+ DEBUG6 (("CURRENT INTERNAL FRAG in elements: "ID" \n", intfrag)) ;
+
+
+
+ DEBUG6 (("======================================== ROWS: "ID"\n", n_row)) ;
+ UMF_debug -= 2 ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ UMF_dump_rowcol (0, Numeric, Work, row, check_degree) ;
+ }
+ UMF_debug += 2 ;
+ DEBUG6 (("======================================== COLS: "ID"\n", n_col)) ;
+ UMF_debug -= 2 ;
+ for (col = 0 ; col < n_col ; col++)
+ {
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+ }
+ UMF_debug += 2 ;
+ DEBUG6 (("============================================= END OF MATRIX:\n"));
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_current_front =============================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_current_front
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int check
+)
+{
+
+ Entry *Flublock, *Flblock, *Fublock, *Fcblock ;
+ Int fnrows_max, fncols_max, fnrows, fncols, fnpiv, *Frows, *Fcols,
+ i, j, *Fcpos, *Frpos, fnr_curr, fnc_curr, *E ;
+ if (!Work) return ;
+ DEBUG7 (("\n\n========CURRENT FRONTAL MATRIX:\n")) ;
+
+ Flublock = Work->Flublock ;
+ Flblock = Work->Flblock ;
+ Fublock = Work->Fublock ;
+ Fcblock = Work->Fcblock ;
+
+ Frows = Work->Frows ;
+ Fcols = Work->Fcols ;
+ Frpos = Work->Frpos ;
+ Fcpos = Work->Fcpos ;
+ fnrows_max = Work->fnrows_max ;
+ fncols_max = Work->fncols_max ;
+ fnr_curr = Work->fnr_curr ;
+ fnc_curr = Work->fnc_curr ;
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ fnpiv = Work->fnpiv ;
+ E = Work->E ;
+
+ DEBUG6 (("=== fnpiv= "ID"\n", fnpiv)) ;
+ DEBUG6 (("fnrows_max fncols_max "ID" "ID"\n",fnrows_max, fncols_max)) ;
+ DEBUG6 (("fnr_curr fnc_curr "ID" "ID"\n",fnr_curr, fnc_curr)) ;
+ DEBUG6 (("fnrows fncols "ID" "ID"\n",fnrows, fncols)) ;
+ ASSERT ((fnr_curr % 2 == 1) || fnr_curr == 0) ;
+ DEBUG6 (("Pivot row pattern:\n")) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ DEBUG7 ((ID" "ID" "ID" %d\n", j, Fcols [j], Fcpos [Fcols [j]],
+ j < fncols)) ;
+ if (check)
+ {
+ ASSERT (Fcols [j] >= 0 && Fcols [j] < Work->n_col) ;
+ ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ;
+ }
+ }
+ DEBUG6 (("Pivot col pattern:\n")) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ DEBUG7 ((ID" "ID" "ID" %d\n", i, Frows [i], Frpos [Frows [i]],
+ i < fnrows)) ;
+ if (check)
+ {
+ ASSERT (Frows [i] >= 0 && Frows [i] < Work->n_row) ;
+ ASSERT (Frpos [Frows [i]] == i) ;
+ }
+ }
+ if (UMF_debug < 7) return ;
+
+ if (!E [0])
+ {
+ DEBUG6 (("current front not allocated\n")) ;
+ ASSERT (!Work->Flublock) ;
+ return ;
+ }
+
+ ASSERT (Work->Flublock == (Entry *) (Numeric->Memory + E [0])) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv) ;
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Flublock, Work->nb, fnpiv, fnpiv) ;
+ if (fnpiv > 0)
+ {
+ DEBUG7 (("Pivot entry: ")) ;
+ EDEBUG7 (Flublock [(fnpiv-1)+(fnpiv-1)*Work->nb]) ;
+ DEBUG7 (("\n")) ;
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_dump_lu ========================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_lu
+(
+ NumericType *Numeric
+)
+{
+ Int i, n_row, n_col, *Cperm, *Rperm ;
+
+ DEBUG6 (("=============================================== LU factors:\n")) ;
+ if (!Numeric)
+ {
+ DEBUG6 (("No LU factors allocated\n")) ;
+ return ;
+ }
+ n_row = Numeric->n_row ;
+ n_col = Numeric->n_col ;
+ DEBUG6 (("n_row: "ID" n_col: "ID"\n", n_row, n_col)) ;
+ DEBUG6 (("nLentries: "ID" nUentries: "ID"\n",
+ Numeric->nLentries, Numeric->nUentries)) ;
+
+ if (Numeric->Cperm)
+ {
+ Cperm = Numeric->Cperm ;
+ DEBUG7 (("Column permutations: (new: old)\n")) ;
+ for (i = 0 ; i < n_col ; i++)
+ {
+ if (Cperm [i] != EMPTY)
+ {
+ DEBUG7 ((ID": "ID"\n", i, Cperm [i])) ;
+ }
+ }
+ }
+ else
+ {
+ DEBUG7 (("No Numeric->Cperm allocatated\n")) ;
+ }
+
+ if (Numeric->Rperm)
+ {
+ Rperm = Numeric->Rperm ;
+ DEBUG7 (("row permutations: (new: old)\n")) ;
+ for (i = 0 ; i < n_row ; i++)
+ {
+ if (Rperm [i] != EMPTY)
+ {
+ DEBUG7 ((ID": "ID"\n", i, Rperm [i])) ;
+ }
+ }
+ }
+ else
+ {
+ DEBUG7 (("No Numeric->Rperm allocatated\n")) ;
+ }
+
+ DEBUG6 (("========================================= END OF LU factors:\n"));
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_memory ====================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_memory
+(
+ NumericType *Numeric
+)
+{
+
+ Unit *p ;
+ Int prevsize, s ;
+ Int found ;
+
+ if (!Numeric)
+ {
+ DEBUG6 (("No memory space S allocated\n")) ;
+ return ;
+ }
+
+ DEBUG6 (("\n ============================================== MEMORY:\n")) ;
+ if (!Numeric || !Numeric->Memory)
+ {
+ DEBUG6 (("No memory space Numeric allocated\n")) ;
+ return ;
+ }
+
+ DEBUG6 (("S: "ID"\n", (Int) Numeric)) ;
+ DEBUG6 (("S->ihead : "ID"\n", Numeric->ihead)) ;
+ DEBUG6 (("S->itail : "ID"\n", Numeric->itail)) ;
+ DEBUG6 (("S->size : "ID"\n", Numeric->size)) ;
+ DEBUG6 (("S->ngarbage : "ID"\n", Numeric->ngarbage)) ;
+ DEBUG6 (("S->nrealloc : "ID"\n", Numeric->nrealloc)) ;
+ DEBUG6 ((" in use at head : "ID"\n", Numeric->ihead)) ;
+ DEBUG6 ((" free space : "ID"\n",
+ Numeric->itail - Numeric->ihead)) ;
+ DEBUG6 ((" blocks in use at tail : "ID"\n",
+ Numeric->size - Numeric->itail)) ;
+ DEBUG6 ((" total in use : "ID"\n",
+ Numeric->size - (Numeric->itail - Numeric->ihead))) ;
+
+ prevsize = 0 ;
+ found = FALSE ;
+
+ ASSERT (0 <= Numeric->ihead) ;
+ ASSERT (Numeric->ihead <= Numeric->itail) ;
+ ASSERT (Numeric->itail <= Numeric->size) ;
+
+ p = Numeric->Memory + Numeric->itail ;
+
+ while (p < Numeric->Memory + Numeric->size)
+ {
+ DEBUG8 (("p: "ID" p+1: "ID" prevsize: "ID" size: "ID,
+ (Int) (p-Numeric->Memory), (Int) (p+1-Numeric->Memory),
+ p->header.prevsize, p->header.size)) ;
+ if (p->header.size < 0)
+ {
+ DEBUG8 ((" free")) ;
+ }
+
+ if (p == Numeric->Memory + Numeric->itail)
+ {
+ ASSERT (p->header.prevsize == 0) ;
+ }
+ else
+ {
+ ASSERT (p->header.prevsize > 0) ;
+ }
+
+ ASSERT (p->header.size != 0) ;
+ s = prevsize >= 0 ? prevsize : -prevsize ;
+ ASSERT (p->header.prevsize == s) ;
+ /* no adjacent free blocks */
+ ASSERT (p->header.size > 0 || prevsize > 0) ;
+ if (Numeric->ibig != EMPTY)
+ {
+ if (p == Numeric->Memory + Numeric->ibig)
+ {
+ ASSERT (p->header.size < 0) ;
+ DEBUG8 ((" <===== Numeric->ibig")) ;
+ found = TRUE ;
+ }
+ }
+ s = p->header.size ;
+ prevsize = s ;
+ s = s >= 0 ? s : -s ;
+ p = p + 1 + s ;
+ DEBUG8 (("\n")) ;
+ }
+
+ ASSERT (p == Numeric->Memory + Numeric->size) ;
+ ASSERT (IMPLIES (Numeric->ibig != EMPTY, found)) ;
+ DEBUG6 (("============================================= END OF MEMORY:\n"));
+
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_packed_memory =============================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_packed_memory
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ Unit *p, *p3 ;
+ Int prevsize, col, row, *Rows, *Cols, ncols, nrows, k, esize,
+ *Row_tuples, *Row_degree, *Col_tuples, *Col_degree ;
+ Entry *C ;
+ Element *ep ;
+
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+ Row_tuples = Numeric->Uip ;
+ Col_tuples = Numeric->Lip ;
+
+ DEBUG6 (("============================================ PACKED MEMORY:\n")) ;
+ if (!Numeric || !Numeric->Memory)
+ {
+ DEBUG6 (("No memory space S allocated\n")) ;
+ return ;
+ }
+ DEBUG6 (("S: "ID"\n", (Int) Numeric)) ;
+ DEBUG6 (("S->ihead : "ID"\n", Numeric->ihead)) ;
+ DEBUG6 (("S->itail : "ID"\n", Numeric->itail)) ;
+ DEBUG6 (("S->size : "ID"\n", Numeric->size)) ;
+ DEBUG6 (("S->ngarbage : "ID"\n", Numeric->ngarbage)) ;
+ DEBUG6 (("S->nrealloc : "ID"\n", Numeric->nrealloc)) ;
+ DEBUG6 ((" in use at head : "ID"\n", Numeric->ihead)) ;
+ DEBUG6 ((" free space : "ID"\n",
+ Numeric->itail - Numeric->ihead)) ;
+ DEBUG6 ((" blocks in use at tail : "ID"\n",
+ Numeric->size - Numeric->itail)) ;
+ DEBUG6 ((" total in use : "ID"\n",
+ Numeric->size - (Numeric->itail - Numeric->ihead))) ;
+
+ ASSERT (0 <= Numeric->ihead) ;
+ ASSERT (Numeric->ihead <= Numeric->itail) ;
+ ASSERT (Numeric->itail <= Numeric->size) ;
+
+ for (row = 0 ; row < Work->n_row ; row++)
+ {
+ ASSERT (IMPLIES (NON_PIVOTAL_ROW (row), !Row_tuples [row])) ;
+ }
+ for (col = 0 ; col < Work->n_col ; col++)
+ {
+ ASSERT (IMPLIES (NON_PIVOTAL_COL (col), !Col_tuples [col])) ;
+ }
+
+ prevsize = 0 ;
+ p = Numeric->Memory + Numeric->itail ;
+ while (p < Numeric->Memory + Numeric->size)
+ {
+ DEBUG9 (("====================\n")) ;
+ DEBUG7 (("p: "ID" p+1: "ID" prevsize: "ID" size: "ID"\n",
+ (Int) (p-Numeric->Memory), (Int) (p+1-Numeric->Memory),
+ p->header.prevsize, p->header.size)) ;
+ ASSERT (p->header.size > 0) ;
+
+ if (p == Numeric->Memory + Numeric->itail)
+ {
+ ASSERT (p->header.prevsize == 0) ;
+ }
+ else
+ {
+ ASSERT (p->header.prevsize > 0) ;
+ }
+
+ ASSERT (p->header.prevsize == prevsize) ;
+ prevsize = p->header.size ;
+
+ if (p != Numeric->Memory + Numeric->size - 2)
+ {
+
+ p3 = p + 1 ;
+ if (p3 == Numeric->Memory + Work->E [0])
+ {
+ /* this is the current frontal matrix */
+ UMF_dump_current_front (Numeric, Work, FALSE) ;
+ }
+ else
+ {
+
+ /* this is a packed element */
+ GET_ELEMENT (ep, p3, Cols, Rows, ncols, nrows, C) ;
+ DEBUG9 (("ep "ID"\n nrows "ID" ncols "ID"\n",
+ (Int) ((p+1)-Numeric->Memory), ep->nrows, ep->ncols)) ;
+ DEBUG9 (("rows:")) ;
+ for (k = 0 ; k < ep->nrows; k++)
+ {
+ row = Rows [k] ;
+ DEBUG9 ((" "ID, row)) ;
+ ASSERT (row >= 0 && row <= Work->n_row) ;
+ if ((k % 10) == 9) DEBUG9 (("\n")) ;
+ }
+ DEBUG9 (("\ncols:")) ;
+ for (k = 0 ; k < ep->ncols; k++)
+ {
+ col = Cols [k] ;
+ DEBUG9 ((" "ID, col)) ;
+ ASSERT (col >= 0 && col <= Work->n_col) ;
+ if ((k % 10) == 9) DEBUG9 (("\n")) ;
+ }
+ DEBUG9 (("\nvalues: ")) ;
+ if (UMF_debug >= 9)
+ {
+ UMF_dump_dense (C, ep->nrows, ep->nrows, ep->ncols) ;
+ }
+ esize = GET_ELEMENT_SIZE (ep->nrows, ep->ncols) ;
+ DEBUG9 (("esize: "ID"\n", esize)) ;
+ ASSERT (esize <= p->header.size) ;
+ }
+
+ }
+ else
+ {
+ /* this is the final marker block */
+ ASSERT (p->header.size == 1) ;
+ }
+ p = p + 1 + p->header.size ;
+ }
+
+ ASSERT (Numeric->ibig == EMPTY) ;
+ ASSERT (p == Numeric->Memory + Numeric->size) ;
+ DEBUG6 (("======================================END OF PACKED MEMORY:\n")) ;
+
+}
+
+/* ========================================================================== */
+/* === UMF_dump_col_matrix ================================================== */
+/* ========================================================================== */
+
+/* This code is the same for real or complex matrices. */
+
+GLOBAL void UMF_dump_col_matrix
+(
+ const double Ax [ ], /* Ax [0..nz-1]: real values, in column order */
+#ifdef COMPLEX
+ const double Az [ ], /* Az [0..nz-1]: imag values, in column order */
+#endif
+ const Int Ai [ ], /* Ai [0..nz-1]: row indices, in column order */
+ const Int Ap [ ], /* Ap [0..n_col]: column pointers */
+ Int n_row, /* number of rows of A */
+ Int n_col, /* number of columns of A */
+ Int nz /* number of entries */
+)
+{
+ Int col, p, p1, p2, row ;
+#ifdef COMPLEX
+ Int split = SPLIT (Az) ;
+#endif
+
+ if (!Ai || !Ap) return ;
+ DEBUG6 (("============================================ COLUMN FORM:\n")) ;
+
+ ASSERT (n_col >= 0) ;
+ nz = Ap [n_col] ;
+ DEBUG2 (("UMF_dump_col: nz "ID"\n", nz)) ;
+ DEBUG2 (("n_row "ID" \n", n_row)) ;
+ DEBUG2 (("n_col "ID" \n", n_col)) ;
+
+ DEBUG6 ((" n_row = "ID", n_col ="ID" nz = "ID" Ap [0] "ID", Ap [n] "ID"\n",
+ n_row, n_col, nz, Ap [0], Ap [n_col])) ;
+ ASSERT (Ap [0] == 0) ;
+ ASSERT (Ap [n_col] == nz) ;
+ for (col = 0 ; col < n_col ; col++)
+ {
+ p1 = Ap [col] ;
+ p2 = Ap [col+1] ;
+ DEBUG6 (("col: "ID", length "ID"\n", col, p2 - p1)) ;
+ ASSERT (p2 >= p1) ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ DEBUG6 (("\t"ID" ", row)) ;
+ if (Ax != (double *) NULL)
+ {
+#ifdef COMPLEX
+ if (split)
+ {
+ DEBUG6 ((" (%e+%ei) ", Ax [p], Az [p])) ;
+ }
+ else
+ {
+ DEBUG6 ((" (%e+%ei) ", Ax [2*p], Ax [2*p+1])) ;
+ }
+#else
+ DEBUG6 ((" %e", Ax [p])) ;
+#endif
+ }
+ DEBUG6 (("\n")) ;
+ }
+ }
+ DEBUG6 (("========================================== COLUMN FORM done\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_chain ======================================================= */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_chain
+(
+ Int frontid,
+ Int Front_parent [ ],
+ Int Front_npivcol [ ],
+ Int Front_nrows [ ],
+ Int Front_ncols [ ],
+ Int nfr
+)
+{
+ Int i, len = 0 ;
+
+ /* print a list of contiguous parents */
+ i = frontid ;
+ ASSERT (Front_parent [i] == EMPTY ||
+ (Front_parent [i] > i && Front_parent [i] < nfr)) ;
+
+ len++ ;
+ DEBUG3 (("Chain:\n "ID" ["ID","ID"]("ID"-by-"ID")\n", i,
+ Front_npivcol [i],
+ MIN (Front_npivcol [i], Front_nrows [i]),
+ Front_nrows [i],
+ Front_ncols [i])) ;
+
+ for (i = frontid ; i < nfr ; i++)
+ {
+ ASSERT (Front_parent [i] == EMPTY ||
+ (Front_parent [i] > i && Front_parent [i] < nfr)) ;
+ if (Front_parent [i] == i+1)
+ {
+ len++ ;
+ DEBUG3 (("\t"ID" ["ID","ID"]("ID"-by-"ID")\n", i+1,
+ Front_npivcol [i+1],
+ MIN (Front_npivcol [i+1], Front_nrows [i+1]),
+ Front_nrows [i+1],
+ Front_ncols [i+1])) ;
+ }
+ else
+ {
+ DEBUG2 (("Length of chain: "ID"\n", len)) ;
+ return ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_start ======================================================= */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_start
+(
+ void
+)
+{
+ FILE *ff ;
+
+ AMD_debug_init ("from umfpack") ;
+
+ /* get the debug print level from the "debug.umf" file, if it exists */
+ UMF_debug = -999 ;
+ ff = fopen ("debug.umf", "r") ;
+ if (ff)
+ {
+ (void) fscanf (ff, ID, &UMF_debug) ;
+ (void) fclose (ff) ;
+ }
+
+ DEBUG0 (("umfpack: debug version (SLOW!) ")) ;
+
+ DEBUG0 ((" MATLAB: ")) ;
+#ifdef MATLAB_MEX_FILE
+ DEBUG0 (("mexFunction.\n")) ;
+#else
+#ifdef MATHWORKS
+ DEBUG0 (("yes.\n")) ;
+#else
+ DEBUG0 (("no.\n")) ;
+#endif
+#endif
+
+ UMF_gprob = -1.0 ;
+ ff = fopen ("gprob.umf", "r") ;
+ if (ff)
+ {
+ (void) fscanf (ff, "%lg", &UMF_gprob) ;
+ (void) fclose (ff) ;
+ srand (1) ; /* restart the random number generator */
+ }
+
+ if (UMF_gprob > 1.0) UMF_gprob = 1.0 ;
+ DEBUG1 (("factor: UMF_gprob: %e UMF_debug "ID"\n", UMF_gprob, UMF_debug)) ;
+
+ DEBUG2 (("sizeof: (bytes / int / Units) \n")) ;
+ DEBUG2 (("sizeof (Int) %u %u %u\n",
+ sizeof (Int), sizeof (Int) / sizeof (int), UNITS (Int, 1) )) ;
+ DEBUG2 (("sizeof (int) %u %u %u\n",
+ sizeof (int), sizeof (int) / sizeof (int), UNITS (int, 1) )) ;
+ DEBUG2 (("sizeof (size_t) %u %u %u\n",
+ sizeof (size_t), sizeof (size_t) / sizeof (size_t), UNITS (size_t, 1) )) ;
+ DEBUG2 (("sizeof (UF_long) %u %u %u\n",
+ sizeof (UF_long), sizeof (UF_long) / sizeof (UF_long), UNITS (UF_long, 1)));
+ DEBUG2 (("sizeof (double) %u %u %u\n",
+ sizeof (double), sizeof (double) / sizeof (int), UNITS (double, 1) )) ;
+ DEBUG2 (("sizeof (Unit) %u %u %u\n",
+ sizeof (Unit), sizeof (Unit) / sizeof (int), UNITS (Unit, 1) )) ;
+ DEBUG2 (("sizeof (Entry) %u %u %u\n",
+ sizeof (Entry), sizeof (Entry) / sizeof (int), UNITS (Entry, 1) )) ;
+ DEBUG2 (("sizeof (Tuple) %u %u %u\n",
+ sizeof (Tuple), sizeof (Tuple) / sizeof (int), UNITS (Tuple, 1) )) ;
+ DEBUG2 (("sizeof (Tuple *) %u %u %u\n",
+ sizeof (Tuple *), sizeof (Tuple *) / sizeof (int), UNITS (Tuple *, 1) )) ;
+ DEBUG2 (("sizeof (Element) %u %u %u\n",
+ sizeof (Element), sizeof (Element) / sizeof (int), UNITS (Element, 1) )) ;
+ DEBUG2 (("sizeof (Element *) %u %u %u\n",
+ sizeof (Element *), sizeof (Element *) / sizeof (int),
+ UNITS (Element *, 1) )) ;
+ DEBUG2 (("sizeof (WorkType) %u %u %u\n",
+ sizeof (WorkType), sizeof (WorkType) / sizeof (int),
+ UNITS (WorkType, 1) )) ;
+ DEBUG2 (("sizeof (NumericType) %u %u %u\n",
+ sizeof (NumericType), sizeof (NumericType) / sizeof (int),
+ UNITS (NumericType, 1) )) ;
+ DEBUG2 (("sizeof (SymbolicType) %u %u %u\n",
+ sizeof (SymbolicType), sizeof (SymbolicType) / sizeof (int),
+ UNITS (SymbolicType, 1) )) ;
+
+}
+
+
+/* ========================================================================== */
+/* === UMF_dump_rowmerge ==================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_rowmerge
+(
+ NumericType *Numeric,
+ SymbolicType *Symbolic,
+ WorkType *Work
+)
+{
+ Int *Front_leftmostdesc, *Front_1strow, *Front_new1strow, row1, row2,
+ fleftmost, nfr, n_row, *Row_degree, i, frontid, row ;
+
+ nfr = Symbolic->nfr ;
+ DEBUG3 (("\n================== Row merge sets: nfr "ID"\n", nfr)) ;
+ Front_leftmostdesc = Symbolic->Front_leftmostdesc ;
+ Front_1strow = Symbolic->Front_1strow ;
+ Front_new1strow = Work->Front_new1strow ;
+ n_row = Symbolic->n_row ;
+ Row_degree = Numeric->Rperm ;
+ frontid = Work->frontid ;
+
+ for (i = frontid ; i <= nfr ; i++)
+ {
+ DEBUG3 (("----------------------\n")) ;
+ if (i == nfr) DEBUG3 (("Dummy: ")) ;
+ DEBUG3 (("Front "ID" 1strow "ID" new1strow "ID" leftmostdesc "ID,
+ i, Front_1strow [i], Front_new1strow [i], Front_leftmostdesc [i])) ;
+ DEBUG3 ((" parent "ID" pivcol "ID"\n", Symbolic->Front_parent [i],
+ Symbolic->Front_npivcol [i])) ;
+
+ if (i == nfr)
+ {
+ fleftmost = -1 ;
+ row1 = Front_new1strow [i] ;
+ row2 = n_row-1 ;
+ }
+ else
+ {
+ fleftmost = Front_leftmostdesc [i] ;
+ row1 = Front_new1strow [fleftmost] ;
+ row2 = Front_1strow [i+1] - 1 ;
+ }
+ DEBUG3 (("Leftmost: "ID" Rows ["ID" to "ID"], search ["ID" to "ID"]\n",
+ fleftmost, Front_1strow [i], row2, row1, row2)) ;
+
+ for (row = row1 ; row <= row2 ; row++)
+ {
+ ASSERT (row >= 0 && row < n_row) ;
+ DEBUG3 ((" Row "ID" live: %d\n", row, NON_PIVOTAL_ROW (row))) ;
+ }
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_dump_diagonal_map ================================================ */
+/* ========================================================================== */
+
+GLOBAL void UMF_dump_diagonal_map
+(
+ Int Diagonal_map [ ],
+ Int Diagonal_imap [ ],
+ Int n1,
+ Int nn,
+ Int nempty
+)
+{
+ Int row, col ;
+ if (Diagonal_map != (Int *) NULL)
+ {
+ DEBUG2 (("\nDump the Diagonal_map: n1 "ID" nn "ID" nempty "ID"\n",
+ n1, nn, nempty)) ;
+ for (col = n1 ; col < nn - nempty ; col++)
+ {
+ row = Diagonal_map [col] ;
+ DEBUG2 ((" Diagonal_map [col = "ID"] gives "ID": ",
+ col, row)) ;
+ row = UNFLIP (row) ;
+ DEBUG2 ((" row "ID"\n", row)) ;
+ ASSERT (Diagonal_imap [row] == col) ;
+ }
+ }
+}
+
+#endif /* NDEBUG */
diff --git a/UMFPACK/Source/umf_dump.h b/UMFPACK/Source/umf_dump.h
new file mode 100644
index 0000000..71ec745
--- /dev/null
+++ b/UMFPACK/Source/umf_dump.h
@@ -0,0 +1,191 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* umf_dump.h: debugging definitions. */
+
+#ifndef NDEBUG
+
+GLOBAL void UMF_dump_dense
+(
+ Entry *C,
+ Int dim,
+ Int m,
+ Int n
+) ;
+
+GLOBAL void UMF_dump_element
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int e,
+ Int clean
+) ;
+
+GLOBAL void UMF_dump_rowcol
+(
+ Int dump_which,
+ NumericType *Numeric,
+ WorkType *Work,
+ Int dump_index,
+ Int check_degree
+) ;
+
+GLOBAL void UMF_dump_matrix
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int check_degree
+) ;
+
+GLOBAL void UMF_dump_current_front
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int check
+) ;
+
+GLOBAL void UMF_dump_lu
+(
+ NumericType *Numeric
+) ;
+
+GLOBAL void UMF_dump_memory
+(
+ NumericType *Numeric
+) ;
+
+GLOBAL void UMF_dump_packed_memory
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
+
+GLOBAL void UMF_dump_col_matrix
+(
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ const Int Ai [ ],
+ const Int Ap [ ],
+ Int n_row,
+ Int n_col,
+ Int nz
+) ;
+
+GLOBAL void UMF_dump_chain
+(
+ Int frontid,
+ Int Front_parent [ ],
+ Int Front_npivcol [ ],
+ Int Front_nrows [ ],
+ Int Front_ncols [ ],
+ Int nfr
+) ;
+
+GLOBAL void UMF_dump_rowmerge
+(
+ NumericType *Numeric,
+ SymbolicType *Symbolic,
+ WorkType *Work
+) ;
+
+GLOBAL void UMF_dump_start
+(
+ void
+) ;
+
+
+GLOBAL void UMF_dump_diagonal_map
+(
+ Int Diagonal_map [ ],
+ Int Diagonal_imap [ ],
+ Int n1,
+ Int nn,
+ Int nempty
+) ;
+
+#define UMF_DBMAX 50000
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+GLOBAL EXTERN Int UMF_debug ;
+GLOBAL EXTERN Int UMF_allocfail ;
+GLOBAL EXTERN double UMF_gprob ;
+
+#define DEBUGk(k,params) { if (UMF_debug >= (k)) { PRINTF (params) ; } }
+
+#define DEBUGm4(params) DEBUGk (-4, params)
+#define DEBUGm3(params) DEBUGk (-3, params)
+#define DEBUGm2(params) DEBUGk (-2, params)
+#define DEBUGm1(params) DEBUGk (-1, params)
+#define DEBUG0(params) DEBUGk (0, params)
+#define DEBUG1(params) DEBUGk (1, params)
+#define DEBUG2(params) DEBUGk (2, params)
+#define DEBUG3(params) DEBUGk (3, params)
+#define DEBUG4(params) DEBUGk (4, params)
+#define DEBUG5(params) DEBUGk (5, params)
+#define DEBUG6(params) DEBUGk (6, params)
+#define DEBUG7(params) DEBUGk (7, params)
+#define DEBUG8(params) DEBUGk (8, params)
+#define DEBUG9(params) DEBUGk (9, params)
+
+#define EDEBUGk(k,a) { if (UMF_debug >= (k)) { PRINT_ENTRY (a) ; } }
+
+#define EDEBUG0(a) EDEBUGk (0, a)
+#define EDEBUG1(a) EDEBUGk (1, a)
+#define EDEBUG2(a) EDEBUGk (2, a)
+#define EDEBUG3(a) EDEBUGk (3, a)
+#define EDEBUG4(a) EDEBUGk (4, a)
+#define EDEBUG5(a) EDEBUGk (5, a)
+#define EDEBUG6(a) EDEBUGk (6, a)
+#define EDEBUG7(a) EDEBUGk (7, a)
+#define EDEBUG8(a) EDEBUGk (8, a)
+#define EDEBUG9(a) EDEBUGk (9, a)
+
+/* ASSERT defined in amd_dump.h */
+
+#else
+
+/* ========================================================================== */
+/* === No debugging ========================================================= */
+/* ========================================================================== */
+
+/* turn off all debugging macros */
+
+#define DEBUGk(k,params)
+
+#define DEBUGm4(params)
+#define DEBUGm3(params)
+#define DEBUGm2(params)
+#define DEBUGm1(params)
+#define DEBUG0(params)
+#define DEBUG1(params)
+#define DEBUG2(params)
+#define DEBUG3(params)
+#define DEBUG4(params)
+#define DEBUG5(params)
+#define DEBUG6(params)
+#define DEBUG7(params)
+#define DEBUG8(params)
+#define DEBUG9(params)
+
+#define EDEBUGk(k,a)
+
+#define EDEBUG0(a)
+#define EDEBUG1(a)
+#define EDEBUG2(a)
+#define EDEBUG3(a)
+#define EDEBUG4(a)
+#define EDEBUG5(a)
+#define EDEBUG6(a)
+#define EDEBUG7(a)
+#define EDEBUG8(a)
+#define EDEBUG9(a)
+
+#endif /* NDEBUG */
diff --git a/UMFPACK/Source/umf_extend_front.c b/UMFPACK/Source/umf_extend_front.c
new file mode 100644
index 0000000..317c0c6
--- /dev/null
+++ b/UMFPACK/Source/umf_extend_front.c
@@ -0,0 +1,393 @@
+/* ========================================================================== */
+/* === UMF_extend_front ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Called by kernel. */
+
+#include "umf_internal.h"
+#include "umf_extend_front.h"
+#include "umf_grow_front.h"
+
+/* ========================================================================== */
+/* === zero_front =========================================================== */
+/* ========================================================================== */
+
+PRIVATE void zero_front (
+ Entry *Flblock, Entry *Fublock, Entry *Fcblock,
+ Int fnrows, Int fncols, Int fnr_curr, Int fnc_curr,
+ Int fnpiv, Int fnrows_extended, Int fncols_extended)
+{
+ Int j, i ;
+ Entry *F, *Fj, *Fi ;
+
+ Fj = Fcblock + fnrows ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ /* zero the new rows in the contribution block: */
+ F = Fj ;
+ Fj += fnr_curr ;
+#pragma ivdep
+ for (i = fnrows ; i < fnrows_extended ; i++)
+ {
+ /* CLEAR (Fcblock [i + j*fnr_curr]) ; */
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ }
+
+ Fj -= fnrows ;
+ for (j = fncols ; j < fncols_extended ; j++)
+ {
+ /* zero the new columns in the contribution block: */
+ F = Fj ;
+ Fj += fnr_curr ;
+#pragma ivdep
+ for (i = 0 ; i < fnrows_extended ; i++)
+ {
+ /* CLEAR (Fcblock [i + j*fnr_curr]) ; */
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ }
+
+ Fj = Flblock + fnrows ;
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ /* zero the new rows in L block: */
+ F = Fj ;
+ Fj += fnr_curr ;
+#pragma ivdep
+ for (i = fnrows ; i < fnrows_extended ; i++)
+ {
+ /* CLEAR (Flblock [i + j*fnr_curr]) ; */
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ }
+
+ Fi = Fublock + fncols ;
+ for (i = 0 ; i < fnpiv ; i++)
+ {
+ /* zero the new columns in U block: */
+ F = Fi ;
+ Fi += fnc_curr ;
+#pragma ivdep
+ for (j = fncols ; j < fncols_extended ; j++)
+ {
+ /* CLEAR (Fublock [i*fnc_curr + j]) ; */
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ }
+
+}
+
+/* ========================================================================== */
+/* === UMF_extend_front ===================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMF_extend_front
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int j, i, *Frows, row, col, *Wrow, fnr2, fnc2, *Frpos, *Fcpos, *Fcols,
+ fnrows_extended, rrdeg, ccdeg, fncols_extended, fnr_curr, fnc_curr,
+ fnrows, fncols, pos, fnpiv, *Wm ;
+ Entry *Wx, *Wy, *Fu, *Fl ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get current frontal matrix and check for frontal growth */
+ /* ---------------------------------------------------------------------- */
+
+ fnpiv = Work->fnpiv ;
+
+#ifndef NDEBUG
+ DEBUG2 (("EXTEND FRONT\n")) ;
+ DEBUG2 (("Work->fnpiv "ID"\n", fnpiv)) ;
+ ASSERT (Work->Flblock == Work->Flublock + Work->nb*Work->nb) ;
+ ASSERT (Work->Fublock == Work->Flblock + Work->fnr_curr*Work->nb) ;
+ ASSERT (Work->Fcblock == Work->Fublock + Work->nb*Work->fnc_curr) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Work->Fcblock, Work->fnr_curr, Work->fnrows, Work->fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Work->Flblock, Work->fnr_curr, Work->fnrows, fnpiv);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Work->Fublock, Work->fnc_curr, Work->fncols, fnpiv) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Work->Flublock, Work->nb, fnpiv, fnpiv) ;
+#endif
+
+ if (Work->do_grow)
+ {
+ fnr2 = UMF_FRONTAL_GROWTH * Work->fnrows_new + 2 ;
+ fnc2 = UMF_FRONTAL_GROWTH * Work->fncols_new + 2 ;
+ if (!UMF_grow_front (Numeric, fnr2, fnc2, Work, 1))
+ {
+ DEBUGm4 (("out of memory: extend front\n")) ;
+ return (FALSE) ;
+ }
+ }
+
+ fnr_curr = Work->fnr_curr ;
+ fnc_curr = Work->fnc_curr ;
+ ASSERT (Work->fnrows_new + 1 <= fnr_curr) ;
+ ASSERT (Work->fncols_new + 1 <= fnc_curr) ;
+ ASSERT (fnr_curr >= 0 && fnr_curr % 2 == 1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Frows = Work->Frows ;
+ Frpos = Work->Frpos ;
+ Fcols = Work->Fcols ;
+ Fcpos = Work->Fcpos ;
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ rrdeg = Work->rrdeg ;
+ ccdeg = Work->ccdeg ;
+
+ /* scan starts at the first new column in Fcols */
+ /* also scan the pivot column if it was not in the front */
+ Work->fscan_col = fncols ;
+ Work->NewCols = Fcols ;
+
+ /* scan1 starts at the first new row in Frows */
+ /* also scan the pivot row if it was not in the front */
+ Work->fscan_row = fnrows ;
+ Work->NewRows = Frows ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extend row pattern of the front with the new pivot column */
+ /* ---------------------------------------------------------------------- */
+
+ fnrows_extended = fnrows ;
+ fncols_extended = fncols ;
+
+#ifndef NDEBUG
+ DEBUG2 (("Pivot col, before extension: "ID"\n", fnrows)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ DEBUG2 ((" "ID": row "ID"\n", i, Frows [i])) ;
+ ASSERT (Frpos [Frows [i]] == i) ;
+ }
+ DEBUG2 (("Extending pivot column: pivcol_in_front: "ID"\n",
+ Work->pivcol_in_front)) ;
+#endif
+
+ Fl = Work->Flblock + fnpiv * fnr_curr ;
+
+ if (Work->pivcol_in_front)
+ {
+ /* extended pattern and position already in Frows, Frpos. Values above
+ * the diagonal are already in LU block. Values on and below the
+ * diagonal are in Wy [0 .. fnrows_extended-1]. Copy into the L
+ * block. */
+ fnrows_extended += ccdeg ;
+ Wy = Work->Wy ;
+
+ for (i = 0 ; i < fnrows_extended ; i++)
+ {
+ Fl [i] = Wy [i] ;
+#ifndef NDEBUG
+ row = Frows [i] ;
+ DEBUG2 ((" "ID": row "ID" ", i, row)) ;
+ EDEBUG2 (Fl [i]) ;
+ if (row == Work->pivrow) DEBUG2 ((" <- pivrow")) ;
+ DEBUG2 (("\n")) ;
+ if (i == fnrows - 1) DEBUG2 ((" :::::::\n")) ;
+ ASSERT (row >= 0 && row < Work->n_row) ;
+ ASSERT (Frpos [row] == i) ;
+#endif
+ }
+
+ }
+ else
+ {
+ /* extended pattern,values is in (Wm,Wx), not yet in the front */
+ Entry *F ;
+ Fu = Work->Flublock + fnpiv * Work->nb ;
+ Wm = Work->Wm ;
+ Wx = Work->Wx ;
+ F = Fu ;
+ for (i = 0 ; i < fnpiv ; i++)
+ {
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ F = Fl ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ CLEAR_AND_INCREMENT (F) ;
+ }
+ for (i = 0 ; i < ccdeg ; i++)
+ {
+ row = Wm [i] ;
+#ifndef NDEBUG
+ DEBUG2 ((" "ID": row "ID" (ext) ", fnrows_extended, row)) ;
+ EDEBUG2 (Wx [i]) ;
+ if (row == Work->pivrow) DEBUG2 ((" <- pivrow")) ;
+ DEBUG2 (("\n")) ;
+ ASSERT (row >= 0 && row < Work->n_row) ;
+#endif
+ pos = Frpos [row] ;
+ if (pos < 0)
+ {
+ pos = fnrows_extended++ ;
+ Frows [pos] = row ;
+ Frpos [row] = pos ;
+ }
+ Fl [pos] = Wx [i] ;
+ }
+ }
+
+ ASSERT (fnrows_extended <= fnr_curr) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extend the column pattern of the front with the new pivot row */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG6 (("Pivot row, before extension: "ID"\n", fncols)) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ DEBUG7 ((" "ID": col "ID"\n", j, Fcols [j])) ;
+ ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ;
+ }
+ DEBUG6 (("Extending pivot row:\n")) ;
+#endif
+
+ if (Work->pivrow_in_front)
+ {
+ if (Work->pivcol_in_front)
+ {
+ ASSERT (Fcols == Work->Wrow) ;
+ for (j = fncols ; j < rrdeg ; j++)
+ {
+#ifndef NDEBUG
+ col = Fcols [j] ;
+ DEBUG2 ((" "ID": col "ID" (ext)\n", j, col)) ;
+ ASSERT (col != Work->pivcol) ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ ASSERT (Fcpos [col] < 0) ;
+#endif
+ Fcpos [Fcols [j]] = j * fnr_curr ;
+ }
+ }
+ else
+ {
+ /* OUT-IN option: pivcol not in front, but pivrow is in front */
+ Wrow = Work->Wrow ;
+ ASSERT (IMPLIES (Work->pivcol_in_front, Wrow == Fcols)) ;
+ if (Wrow == Fcols)
+ {
+ /* Wrow and Fcols are equivalenced */
+ for (j = fncols ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ DEBUG2 ((" "ID": col "ID" (ext)\n", j, col)) ;
+ ASSERT (Fcpos [col] < 0) ;
+ /* Fcols [j] = col ; not needed */
+ Fcpos [col] = j * fnr_curr ;
+ }
+ }
+ else
+ {
+ for (j = fncols ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ DEBUG2 ((" "ID": col "ID" (ext)\n", j, col)) ;
+ ASSERT (Fcpos [col] < 0) ;
+ Fcols [j] = col ;
+ Fcpos [col] = j * fnr_curr ;
+ }
+ }
+ }
+ fncols_extended = rrdeg ;
+ }
+ else
+ {
+ ASSERT (Fcols != Work->Wrow) ;
+ Wrow = Work->Wrow ;
+ for (j = 0 ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ if (Fcpos [col] < 0)
+ {
+ DEBUG2 ((" col:: "ID" (ext)\n", col)) ;
+ Fcols [fncols_extended] = col ;
+ Fcpos [col] = fncols_extended * fnr_curr ;
+ fncols_extended++ ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* pivot row and column have been extended */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ ASSERT (fncols_extended <= fnc_curr) ;
+ ASSERT (fnrows_extended <= fnr_curr) ;
+
+ DEBUG6 (("Pivot col, after ext: "ID" "ID"\n", fnrows,fnrows_extended)) ;
+ for (i = 0 ; i < fnrows_extended ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG7 ((" "ID": row "ID" pos "ID" old: %d", i, row, Frpos [row],
+ i < fnrows)) ;
+ if (row == Work->pivrow ) DEBUG7 ((" <-- pivrow")) ;
+ DEBUG7 (("\n")) ;
+ ASSERT (Frpos [Frows [i]] == i) ;
+ }
+
+ DEBUG6 (("Pivot row position: "ID"\n", Frpos [Work->pivrow])) ;
+ ASSERT (Frpos [Work->pivrow] >= 0) ;
+ ASSERT (Frpos [Work->pivrow] < fnrows_extended) ;
+
+ DEBUG6 (("Pivot row, after ext: "ID" "ID"\n", fncols,fncols_extended)) ;
+ for (j = 0 ; j < fncols_extended ; j++)
+ {
+ col = Fcols [j] ;
+ DEBUG7 ((" "ID": col "ID" pos "ID" old: %d", j, col, Fcpos [col],
+ j < fncols)) ;
+ if (col == Work->pivcol ) DEBUG7 ((" <-- pivcol")) ;
+ DEBUG7 (("\n")) ;
+ ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ;
+ }
+
+ DEBUG6 (("Pivot col position: "ID"\n", Fcpos [Work->pivcol])) ;
+ ASSERT (Fcpos [Work->pivcol] >= 0) ;
+ ASSERT (Fcpos [Work->pivcol] < fncols_extended * fnr_curr) ;
+
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* Zero the newly extended frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ zero_front (Work->Flblock, Work->Fublock, Work->Fcblock,
+ fnrows, fncols, fnr_curr, fnc_curr,
+ fnpiv, fnrows_extended, fncols_extended) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize extended row and column pattern of the frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Work->fnrows = fnrows_extended ;
+ Work->fncols = fncols_extended ;
+
+ ASSERT (fnrows_extended == Work->fnrows_new + 1) ;
+ ASSERT (fncols_extended == Work->fncols_new + 1) ;
+
+ return (TRUE) ;
+
+}
diff --git a/UMFPACK/Source/umf_extend_front.h b/UMFPACK/Source/umf_extend_front.h
new file mode 100644
index 0000000..6c51986
--- /dev/null
+++ b/UMFPACK/Source/umf_extend_front.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_extend_front
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/UMFPACK/Source/umf_free.c b/UMFPACK/Source/umf_free.c
new file mode 100644
index 0000000..867ab22
--- /dev/null
+++ b/UMFPACK/Source/umf_free.c
@@ -0,0 +1,46 @@
+/* ========================================================================== */
+/* === UMF_free ============================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Free a block previously allocated by UMF_malloc and return NULL.
+ Usage is p = UMF_free (p), to ensure that we don't free it twice.
+ Also maintains the UMFPACK malloc count.
+*/
+
+#include "umf_internal.h"
+#include "umf_free.h"
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+#include "umf_malloc.h"
+#endif
+
+GLOBAL void *UMF_free
+(
+ void *p
+)
+{
+ DEBUG0 (("UMF_free: "ID"\n", (Int) p)) ;
+ if (p)
+ {
+
+ /* see AMD/Source/amd_global.c for the memory allocator selection */
+ amd_free (p) ;
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ /* One more object has been free'd. Keep track of the count. */
+ /* (purely for sanity checks). */
+ UMF_malloc_count-- ;
+ DEBUG0 ((" new malloc count: "ID"\n", UMF_malloc_count)) ;
+#endif
+
+ }
+
+ return ((void *) NULL) ;
+}
diff --git a/UMFPACK/Source/umf_free.h b/UMFPACK/Source/umf_free.h
new file mode 100644
index 0000000..cacf331
--- /dev/null
+++ b/UMFPACK/Source/umf_free.h
@@ -0,0 +1,10 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void *UMF_free
+(
+ void *p
+) ;
diff --git a/UMFPACK/Source/umf_fsize.c b/UMFPACK/Source/umf_fsize.c
new file mode 100644
index 0000000..634b525
--- /dev/null
+++ b/UMFPACK/Source/umf_fsize.c
@@ -0,0 +1,70 @@
+/* ========================================================================== */
+/* === UMF_fsize ============================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Determine the largest frontal matrix size for each subtree. Called by
+ * UMF_colamd and UMF_analyze. Only required to sort the children of each
+ * node prior to AMD_postorder. */
+
+#include "umf_internal.h"
+#include "umf_fsize.h"
+
+GLOBAL void UMF_fsize
+(
+ Int nn,
+ Int Fsize [ ],
+ Int Fnrows [ ],
+ Int Fncols [ ],
+ Int Parent [ ],
+ Int Npiv [ ]
+)
+{
+ Int j, parent, frsize, r, c ;
+
+ for (j = 0 ; j < nn ; j++)
+ {
+ Fsize [j] = EMPTY ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find max front size for tree rooted at node j, for each front j */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG1 (("\n\n========================================FRONTS:\n")) ;
+ for (j = 0 ; j < nn ; j++)
+ {
+ if (Npiv [j] > 0)
+ {
+ /* this is a frontal matrix */
+ parent = Parent [j] ;
+ r = Fnrows [j] ;
+ c = Fncols [j] ;
+ frsize = r * c ;
+ /* avoid integer overflow */
+ if (INT_OVERFLOW (((double) r) * ((double) c)))
+ {
+ /* :: frsize int overflow :: */
+ frsize = Int_MAX ;
+ }
+ DEBUG1 ((""ID" : npiv "ID" size "ID" parent "ID" ",
+ j, Npiv [j], frsize, parent)) ;
+ Fsize [j] = MAX (Fsize [j], frsize) ;
+ DEBUG1 (("Fsize [j = "ID"] = "ID"\n", j, Fsize [j])) ;
+ if (parent != EMPTY)
+ {
+ /* find the maximum frontsize of self and children */
+ ASSERT (Npiv [parent] > 0) ;
+ ASSERT (parent > j) ;
+ Fsize [parent] = MAX (Fsize [parent], Fsize [j]) ;
+ DEBUG1 (("Fsize [parent = "ID"] = "ID"\n",
+ parent, Fsize [parent]));
+ }
+ }
+ }
+}
diff --git a/UMFPACK/Source/umf_fsize.h b/UMFPACK/Source/umf_fsize.h
new file mode 100644
index 0000000..1bd83d4
--- /dev/null
+++ b/UMFPACK/Source/umf_fsize.h
@@ -0,0 +1,15 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_fsize
+(
+ Int nn,
+ Int MaxFsize [ ],
+ Int Fnrows [ ],
+ Int Fncols [ ],
+ Int Parent [ ],
+ Int Npiv [ ]
+) ;
diff --git a/UMFPACK/Source/umf_garbage_collection.c b/UMFPACK/Source/umf_garbage_collection.c
new file mode 100644
index 0000000..716270b
--- /dev/null
+++ b/UMFPACK/Source/umf_garbage_collection.c
@@ -0,0 +1,696 @@
+/* ========================================================================== */
+/* === UMF_garbage_collection =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Compress the elements at the tail of Numeric->Memory, and delete the tuples.
+ Elements are renumbered. The new numbering space is compressed, and
+ in the order of element creation (original elements of A first, followed
+ by the new elements in the order that they were formed).
+
+ Only called by UMF_get_memory.
+
+ There are 5 ways in which garbage collection can be performed:
+
+ Allocate a new working array for the current frontal matrix. In this
+ case, there are never any pivot rows/columns in the current frontal
+ matrix (fnpiv = 0), and the old working array for the current frontal
+ matrix can always be fully compacted, to fnrows-by-fncols.
+
+ UMF_kernel : UMF_extend : UMF_grow_front : UMF_get_memory
+ UMF_kernel : UMF_init_front : UMF_grow_front : UMF_get_memory
+ UMF_kernel : UMF_start_front : UMF_grow_front : UMF_get_memory
+
+ Allocate a new element. In this case, UMF_grow_front may or may not
+ be subsequently called, depending on Work->do_grow. There are never
+ any pivot rows/columns in the current frontal matrix (fnpiv=0), but one
+ may be added if UMF_init_front is to be called just after
+ UMF_create_element. If do_grow is true, then the current front can be
+ fully compacted, to fnrows-by-fncols. Otherwise, it can only be
+ partially compacted, to MAX (fnrows, fnrows_new + 1) -by-
+ MAX (fncols, fncols_new + 1).
+
+ UMF_kernel : UMF_create_element : UMF_get_memory
+
+ Allocate rows of L and columns of U. In this case, the current
+ frontal matrix is only partially compacted, to (fnrows_new + 1)-by-
+ (fncols_new + 1). There are pivots in the frontal matrix (fnpiv > 0).
+
+ UMF_kernel : UMF_store_lu : UMF_get_memory
+*/
+
+#include "umf_internal.h"
+#include "umf_garbage_collection.h"
+
+GLOBAL void UMF_garbage_collection
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int drnew, /* compact current front to drnew-by-dcnew */
+ Int dcnew,
+ Int do_Fcpos
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int size, e, n_row, n_col, nrows, ncols, nrowsleft, ncolsleft, prevsize,
+ csize, size2, i2, j2, i, j, cdeg, rdeg, *E, row, col,
+ *Rows, *Cols, *Rows2, *Cols2, nel, e2, *Row_tuples, *Col_tuples,
+ *Row_degree, *Col_degree ;
+ Entry *C, *C1, *C3, *C2 ;
+ Unit *psrc, *pdest, *p, *pnext ;
+ Element *epsrc, *epdest ;
+
+#ifndef NDEBUG
+ Int nmark ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+ Row_tuples = Numeric->Uip ;
+ Col_tuples = Numeric->Lip ;
+ E = Work->E ;
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+
+ /* note that the tuple lengths (Col_tlen and Row_tlen) are updated, but */
+ /* the tuple lists themselves are stale and are about to be destroyed */
+ /* and recreated. Do not attempt to scan them until they are recreated. */
+
+#ifndef NDEBUG
+ DEBUGm1 (("::::GARBAGE COLLECTION::::\n")) ;
+ UMF_dump_memory (Numeric) ;
+#endif
+
+ Numeric->ngarbage++ ;
+
+ /* ---------------------------------------------------------------------- */
+ /* delete the tuple lists by marking the blocks as free */
+ /* ---------------------------------------------------------------------- */
+
+ /* do not modify Row_tlen and Col_tlen */
+ /* those are needed for UMF_build_tuples */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (NON_PIVOTAL_ROW (row) && Row_tuples [row])
+ {
+ DEBUG2 (("row "ID" tuples "ID"\n", row, Row_tuples [row])) ;
+ p = Numeric->Memory + Row_tuples [row] - 1 ;
+ DEBUG2 (("Freeing tuple list row "ID", p-S "ID", size "ID"\n",
+ row, (Int) (p-Numeric->Memory), p->header.size)) ;
+ ASSERT (p->header.size > 0) ;
+ ASSERT (p >= Numeric->Memory + Numeric->itail) ;
+ ASSERT (p < Numeric->Memory + Numeric->size) ;
+ p->header.size = -p->header.size ;
+ Row_tuples [row] = 0 ;
+ }
+ }
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ if (NON_PIVOTAL_COL (col) && Col_tuples [col])
+ {
+ DEBUG2 (("col "ID" tuples "ID"\n", col, Col_tuples [col])) ;
+ p = Numeric->Memory + Col_tuples [col] - 1 ;
+ DEBUG2 (("Freeing tuple list col "ID", p-S "ID", size "ID"\n",
+ col, (Int) (p-Numeric->Memory), p->header.size)) ;
+ ASSERT (p->header.size > 0) ;
+ ASSERT (p >= Numeric->Memory + Numeric->itail) ;
+ ASSERT (p < Numeric->Memory + Numeric->size) ;
+ p->header.size = -p->header.size ;
+ Col_tuples [col] = 0 ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* mark the elements, and compress the name space */
+ /* ---------------------------------------------------------------------- */
+
+ nel = Work->nel ;
+ ASSERT (nel < Work->elen) ;
+
+#ifndef NDEBUG
+ nmark = 0 ;
+ UMF_dump_current_front (Numeric, Work, FALSE) ;
+ DEBUGm1 (("E [0] "ID" \n", E [0])) ;
+ ASSERT (IMPLIES (E [0],
+ Work->Flublock == (Entry *) (Numeric->Memory + E [0]))) ;
+ ASSERT (IMPLIES (Work->Flublock,
+ Work->Flublock == (Entry *) (Numeric->Memory + E [0]))) ;
+ ASSERT ((E [0] != 0) == (Work->Flublock != (Entry *) NULL)) ;
+#endif
+
+ e2 = 0 ;
+
+ for (e = 0 ; e <= nel ; e++) /* for all elements in order of creation */
+ {
+ if (E [e])
+ {
+ psrc = Numeric->Memory + E [e] ;
+ psrc-- ; /* get the header of this block */
+ if (e > 0)
+ {
+ e2++ ; /* do not renumber element zero */
+ }
+ ASSERT (psrc->header.size > 0) ;
+ psrc->header.size = e2 ; /* store the new name in the header */
+#ifndef NDEBUG
+ nmark++ ;
+#endif
+ DEBUG7 ((ID":: Mark e "ID" at psrc-S "ID", new e "ID"\n",
+ nmark, e, (Int) (psrc-Numeric->Memory), e2)) ;
+ E [e] = 0 ;
+ if (e == Work->prior_element)
+ {
+ Work->prior_element = e2 ;
+ }
+ }
+ }
+
+ /* all 1..e2 are now in use (element zero may or may not be in use) */
+ Work->nel = e2 ;
+ nel = Work->nel ;
+
+#ifndef NDEBUG
+ for (e = 0 ; e < Work->elen ; e++)
+ {
+ ASSERT (!E [e]) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* compress the elements */
+ /* ---------------------------------------------------------------------- */
+
+ /* point to tail marker block of size 1 + header */
+ psrc = Numeric->Memory + Numeric->size - 2 ;
+ pdest = psrc ;
+ prevsize = psrc->header.prevsize ;
+ DEBUG7 (("Starting the compression:\n")) ;
+
+ while (prevsize > 0)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* move up to the next element above the current header, and */
+ /* get the element name and size */
+ /* (if it is an element, the name will be positive) */
+ /* ------------------------------------------------------------------ */
+
+ size = prevsize ;
+ psrc -= (size + 1) ;
+ e = psrc->header.size ;
+ prevsize = psrc->header.prevsize ;
+ /* top block at tail has prevsize of 0 */
+
+ /* a free block will have a negative size, so skip it */
+ /* otherwise, if size >= 0, it holds the element name, not the size */
+
+ DEBUG8 (("psrc-S: "ID" prevsize: "ID" size: "ID,
+ (Int) (psrc-Numeric->Memory), prevsize, size)) ;
+
+ if (e == 0)
+ {
+ /* -------------------------------------------------------------- */
+ /* this is the current frontal matrix */
+ /* -------------------------------------------------------------- */
+
+ Entry *F1, *F2, *Fsrc, *Fdst ;
+ Int c, r, k, dr, dc, gap, gap1, gap2, nb ;
+
+ /* shift the frontal matrix down */
+ F1 = (Entry *) (psrc + 1) ;
+
+ /* get the size of the current front. r and c could be zero */
+ k = Work->fnpiv ;
+ dr = Work->fnr_curr ;
+ dc = Work->fnc_curr ;
+ r = Work->fnrows ;
+ c = Work->fncols ;
+ nb = Work->nb ;
+
+ ASSERT ((dr >= 0 && (dr % 2) == 1) || dr == 0) ;
+ ASSERT (drnew >= 0) ;
+ if (drnew % 2 == 0)
+ {
+ /* make sure leading frontal matrix dimension is always odd */
+ drnew++ ;
+ }
+ drnew = MIN (dr, drnew) ;
+ ASSERT ((drnew >= 0 && (drnew % 2) == 1) || drnew == 0) ;
+
+ pnext = pdest ;
+
+#ifndef NDEBUG
+ DEBUGm2 (("move front: dr "ID" dc "ID" r "ID" drnew "ID" c "ID
+ " dcnew " ID" k "ID"\n", dr, dc, r, drnew, c, dcnew, k)) ;
+ DEBUG7 (("\n")) ;
+ DEBUG7 ((ID":: Move current frontal matrix from: psrc-S: "ID" \n",
+ nmark, (Int) (psrc-Numeric->Memory))) ;
+ nmark-- ;
+ ASSERT (E [e] == 0) ;
+ ASSERT (Work->Flublock == F1) ;
+ ASSERT (Work->Flblock == Work->Flublock + nb*nb) ;
+ ASSERT (Work->Fublock == Work->Flblock + dr*nb) ;
+ ASSERT (Work->Fcblock == Work->Fublock + nb*dc) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Work->Fcblock, dr, r, c) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Work->Flblock, dr, r, k);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Work->Fublock, dc, c, k) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Work->Flublock, nb, k, k) ;
+ ASSERT (r <= drnew && c <= dcnew && drnew <= dr && dcnew <= dc) ;
+#endif
+
+ /* compact frontal matrix to drnew-by-dcnew before moving it */
+
+ /* do not compact the LU block (nb-by-nb) */
+
+ /* compact the columns of L (from dr-by-nb to drnew-by-nb) */
+ Fsrc = Work->Flblock ;
+ Fdst = Work->Flblock ;
+ ASSERT (Fdst == F1 + nb*nb) ;
+ gap1 = dr - r ;
+ gap2 = drnew - r ;
+ ASSERT (gap1 >= 0) ;
+ for (j = 0 ; j < k ; j++)
+ {
+ for (i = 0 ; i < r ; i++)
+ {
+ *Fdst++ = *Fsrc++ ;
+ }
+ Fsrc += gap1 ;
+ Fdst += gap2 ;
+ }
+ ASSERT (Fdst == F1 + nb*nb + drnew*k) ;
+ Fdst += drnew * (nb - k) ;
+
+ /* compact the rows of U (U' from dc-by-nb to dcnew-by-nb) */
+ Fsrc = Work->Fublock ;
+ ASSERT (Fdst == F1 + nb*nb + drnew*nb) ;
+ gap1 = dc - c ;
+ gap2 = dcnew - c ;
+ for (i = 0 ; i < k ; i++)
+ {
+ for (j = 0 ; j < c ; j++)
+ {
+ *Fdst++ = *Fsrc++ ;
+ }
+ Fsrc += gap1 ;
+ Fdst += gap2 ;
+ }
+ ASSERT (Fdst == F1 + nb*nb + drnew*nb + dcnew*k) ;
+ Fdst += dcnew * (nb - k) ;
+
+ /* compact the columns of C (from dr-by-dc to drnew-by-dcnew) */
+ Fsrc = Work->Fcblock ;
+ ASSERT (Fdst == F1 + nb*nb + drnew*nb + nb*dcnew) ;
+ gap1 = dr - r ;
+ gap2 = drnew - r ;
+ for (j = 0 ; j < c ; j++)
+ {
+ for (i = 0 ; i < r ; i++)
+ {
+ *Fdst++ = *Fsrc++ ;
+ }
+ Fsrc += gap1 ;
+ Fdst += gap2 ;
+ }
+ ASSERT (Fdst == F1 + nb*nb + drnew*nb + nb*dcnew + drnew*c) ;
+
+ /* recompute Fcpos, if necessary */
+ if (do_Fcpos)
+ {
+ Int *Fcols, *Fcpos ;
+ Fcols = Work->Fcols ;
+ Fcpos = Work->Fcpos ;
+ for (j = 0 ; j < c ; j++)
+ {
+ col = Fcols [j] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ ASSERT (Fcpos [col] == j * dr) ;
+ Fcpos [col] = j * drnew ;
+ }
+#ifndef NDEBUG
+ {
+ Int cnt = 0 ;
+ for (j = 0 ; j < Work->n_col ; j++)
+ {
+ if (Fcpos [j] != EMPTY) cnt++ ;
+ }
+ DEBUGm2 (("Recompute Fcpos cnt "ID" c "ID"\n", cnt, c)) ;
+ ASSERT (cnt == c) ;
+ }
+#endif
+ }
+
+#ifndef NDEBUG
+ DEBUGm2 (("Compacted front, drnew "ID" dcnew "ID"\n", drnew, dcnew)) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (F1 + nb*nb + drnew*nb + nb*dcnew, drnew, r, c) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (F1 + nb*nb, drnew, r, k) ;
+ DEBUG7 (("U block: ")) ;
+ UMF_dump_dense (F1 + nb*nb + drnew*nb, nb, k, c) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (F1, nb, k, k) ;
+#endif
+
+ /* Compacted dimensions of the new frontal matrix. */
+ Work->fnr_curr = drnew ;
+ Work->fnc_curr = dcnew ;
+ Work->fcurr_size = (drnew + nb) * (dcnew + nb) ;
+ size = UNITS (Entry, Work->fcurr_size) ;
+
+ /* make sure the object doesn't evaporate. The front can have
+ * zero size (Work->fcurr_size = 0), but the size of the memory
+ * block containing it cannot have zero size. */
+ size = MAX (1, size) ;
+
+ /* get the destination of frontal matrix */
+ pnext->header.prevsize = size ;
+ pdest -= (size + 1) ;
+ F2 = (Entry *) (pdest + 1) ;
+
+ ASSERT ((unsigned Int) psrc + 1 + size <= (unsigned Int) pnext) ;
+ ASSERT (psrc <= pdest) ;
+ ASSERT (F1 <= F2) ;
+
+ /* move the C block first */
+ Fsrc = F1 + nb*nb + drnew*nb + nb*dcnew + drnew*c ;
+ Fdst = F2 + nb*nb + drnew*nb + nb*dcnew + drnew*c ;
+ gap = drnew - r ;
+ for (j = c-1 ; j >= 0 ; j--)
+ {
+ Fsrc -= gap ;
+ Fdst -= gap ;
+ /* move column j of C */
+ for (i = r-1 ; i >= 0 ; i--)
+ {
+ *--Fdst = *--Fsrc ;
+ }
+ }
+ ASSERT (Fsrc == F1 + nb*nb + drnew*nb + nb*dcnew) ;
+ ASSERT (Fdst == F2 + nb*nb + drnew*nb + nb*dcnew) ;
+
+ /* move the U block */
+ Fsrc -= dcnew * (nb - k) ;
+ Fdst -= dcnew * (nb - k) ;
+ ASSERT (Fsrc == F1 + nb*nb + drnew*nb + dcnew*k) ;
+ ASSERT (Fdst == F2 + nb*nb + drnew*nb + dcnew*k) ;
+ gap = dcnew - c ;
+ for (i = k-1 ; i >= 0 ; i--)
+ {
+ Fsrc -= gap ;
+ Fdst -= gap ;
+ for (j = c-1 ; j >= 0 ; j--)
+ {
+ *--Fdst = *--Fsrc ;
+ }
+ }
+ ASSERT (Fsrc == F1 + nb*nb + drnew*nb) ;
+ ASSERT (Fdst == F2 + nb*nb + drnew*nb) ;
+
+ /* move the L block */
+ Fsrc -= drnew * (nb - k) ;
+ Fdst -= drnew * (nb - k) ;
+ ASSERT (Fsrc == F1 + nb*nb + drnew*k) ;
+ ASSERT (Fdst == F2 + nb*nb + drnew*k) ;
+ gap = drnew - r ;
+ for (j = k-1 ; j >= 0 ; j--)
+ {
+ Fsrc -= gap ;
+ Fdst -= gap ;
+ for (i = r-1 ; i >= 0 ; i--)
+ {
+ *--Fdst = *--Fsrc ;
+ }
+ }
+ ASSERT (Fsrc == F1 + nb*nb) ;
+ ASSERT (Fdst == F2 + nb*nb) ;
+
+ /* move the LU block */
+ Fsrc -= nb * (nb - k) ;
+ Fdst -= nb * (nb - k) ;
+ ASSERT (Fsrc == F1 + nb*k) ;
+ ASSERT (Fdst == F2 + nb*k) ;
+ gap = nb - k ;
+ for (j = k-1 ; j >= 0 ; j--)
+ {
+ Fsrc -= gap ;
+ Fdst -= gap ;
+ for (i = k-1 ; i >= 0 ; i--)
+ {
+ *--Fdst = *--Fsrc ;
+ }
+ }
+ ASSERT (Fsrc == F1) ;
+ ASSERT (Fdst == F2) ;
+
+ E [0] = (pdest + 1) - Numeric->Memory ;
+
+ Work->Flublock = (Entry *) (Numeric->Memory + E [0]) ;
+ ASSERT (Work->Flublock == F2) ;
+ Work->Flblock = Work->Flublock + nb * nb ;
+ Work->Fublock = Work->Flblock + drnew * nb ;
+ Work->Fcblock = Work->Fublock + nb * dcnew ;
+
+ pdest->header.prevsize = 0 ;
+ pdest->header.size = size ;
+
+#ifndef NDEBUG
+ DEBUG7 (("After moving compressed current frontal matrix:\n")) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Work->Fcblock, drnew, r, c) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Work->Flblock, drnew, r, k);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Work->Fublock, dcnew, c, k) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Work->Flublock, nb, k, k) ;
+#endif
+
+ }
+ else if (e > 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* this is an element, compress and move from psrc down to pdest */
+ /* -------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG7 (("\n")) ;
+ DEBUG7 ((ID":: Move element "ID": from: "ID" \n",
+ nmark, e, (Int) (psrc-Numeric->Memory))) ;
+ nmark-- ;
+ ASSERT (e <= nel) ;
+ ASSERT (E [e] == 0) ;
+#endif
+
+ /* -------------------------------------------------------------- */
+ /* get the element scalars, and pointers to C, Rows, and Cols: */
+ /* -------------------------------------------------------------- */
+
+ p = psrc + 1 ;
+ GET_ELEMENT (epsrc, p, Cols, Rows, ncols, nrows, C) ;
+ nrowsleft = epsrc->nrowsleft ;
+ ncolsleft = epsrc->ncolsleft ;
+ cdeg = epsrc->cdeg ;
+ rdeg = epsrc->rdeg ;
+
+#ifndef NDEBUG
+ DEBUG7 ((" nrows "ID" nrowsleft "ID"\n", nrows, nrowsleft)) ;
+ DEBUG7 ((" ncols "ID" ncolsleft "ID"\n", ncols, ncolsleft)) ;
+ DEBUG8 ((" Rows:")) ;
+ for (i = 0 ; i < nrows ; i++) DEBUG8 ((" "ID, Rows [i])) ;
+ DEBUG8 (("\n Cols:")) ;
+ for (j = 0 ; j < ncols ; j++) DEBUG8 ((" "ID, Cols [j])) ;
+ DEBUG8 (("\n")) ;
+#endif
+
+ /* -------------------------------------------------------------- */
+ /* determine the layout of the new element */
+ /* -------------------------------------------------------------- */
+
+ csize = nrowsleft * ncolsleft ;
+ size2 = UNITS (Element, 1)
+ + UNITS (Int, nrowsleft + ncolsleft)
+ + UNITS (Entry, csize) ;
+
+ DEBUG7 (("Old size "ID" New size "ID"\n", size, size2)) ;
+
+ pnext = pdest ;
+ pnext->header.prevsize = size2 ;
+ pdest -= (size2 + 1) ;
+
+ ASSERT (size2 <= size) ;
+ ASSERT ((unsigned Int) psrc + 1 + size <= (unsigned Int) pnext) ;
+ ASSERT (psrc <= pdest) ;
+
+ p = pdest + 1 ;
+ epdest = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols2 = (Int *) p ;
+ Rows2 = Cols2 + ncolsleft ;
+ p += UNITS (Int, nrowsleft + ncolsleft) ;
+ C2 = (Entry *) p ;
+
+ ASSERT (epdest >= epsrc) ;
+ ASSERT (Rows2 >= Rows) ;
+ ASSERT (Cols2 >= Cols) ;
+ ASSERT (C2 >= C) ;
+ ASSERT (p + UNITS (Entry, csize) == pnext) ;
+
+ /* -------------------------------------------------------------- */
+ /* move the contribution block */
+ /* -------------------------------------------------------------- */
+
+ /* overlap = psrc + size + 1 > pdest ; */
+
+ if (nrowsleft < nrows || ncolsleft < ncols)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* compress contribution block in place prior to moving it */
+ /* ---------------------------------------------------------- */
+
+ DEBUG7 (("Compress C in place prior to move:\n"));
+#ifndef NDEBUG
+ UMF_dump_dense (C, nrows, nrows, ncols) ;
+#endif
+ C1 = C ;
+ C3 = C ;
+ for (j = 0 ; j < ncols ; j++)
+ {
+ if (Cols [j] >= 0)
+ {
+ for (i = 0 ; i < nrows ; i++)
+ {
+ if (Rows [i] >= 0)
+ {
+ *C3++ = C1 [i] ;
+ }
+ }
+ }
+ C1 += nrows ;
+ }
+ ASSERT (C3-C == csize) ;
+ DEBUG8 (("Newly compressed contrib. block (all in use):\n")) ;
+#ifndef NDEBUG
+ UMF_dump_dense (C, nrowsleft, nrowsleft, ncolsleft) ;
+#endif
+ }
+
+ /* shift the contribution block down */
+ C += csize ;
+ C2 += csize ;
+ for (i = 0 ; i < csize ; i++)
+ {
+ *--C2 = *--C ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* move the row indices */
+ /* -------------------------------------------------------------- */
+
+ i2 = nrowsleft ;
+ for (i = nrows - 1 ; i >= 0 ; i--)
+ {
+ ASSERT (Rows2+i2 >= Rows+i) ;
+ if (Rows [i] >= 0)
+ {
+ Rows2 [--i2] = Rows [i] ;
+ }
+ }
+ ASSERT (i2 == 0) ;
+
+ j2 = ncolsleft ;
+ for (j = ncols - 1 ; j >= 0 ; j--)
+ {
+ ASSERT (Cols2+j2 >= Cols+j) ;
+ if (Cols [j] >= 0)
+ {
+ Cols2 [--j2] = Cols [j] ;
+ }
+ }
+ ASSERT (j2 == 0) ;
+
+ /* -------------------------------------------------------------- */
+ /* construct the new header */
+ /* -------------------------------------------------------------- */
+
+ /* E [0...e] is now valid */
+ E [e] = (pdest + 1) - Numeric->Memory ;
+ epdest = (Element *) (pdest + 1) ;
+
+ epdest->next = EMPTY ; /* destroys the son list */
+ epdest->ncols = ncolsleft ;
+ epdest->nrows = nrowsleft ;
+ epdest->ncolsleft = ncolsleft ;
+ epdest->nrowsleft = nrowsleft ;
+ epdest->rdeg = rdeg ;
+ epdest->cdeg = cdeg ;
+
+ ASSERT (size2 <= size) ;
+ pdest->header.prevsize = 0 ;
+ pdest->header.size = size2 ;
+
+ DEBUG7 (("After moving it:\n")) ;
+#ifndef NDEBUG
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+ }
+
+#ifndef NDEBUG
+ else
+ {
+ DEBUG8 ((" free\n")) ;
+ }
+#endif
+ DEBUG7 (("psrc "ID" tail "ID"\n",
+ (Int) (psrc-Numeric->Memory), Numeric->itail)) ;
+ }
+
+ ASSERT (psrc == Numeric->Memory + Numeric->itail) ;
+ ASSERT (nmark == 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* final tail pointer */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (pdest >= Numeric->Memory + Numeric->itail) ;
+ Numeric->itail = pdest - Numeric->Memory ;
+ pdest->header.prevsize = 0 ;
+ Numeric->ibig = EMPTY ;
+ Numeric->tail_usage = Numeric->size - Numeric->itail ;
+
+ /* ---------------------------------------------------------------------- */
+ /* clear the unused E [nel+1 .. Work->elen - 1] */
+ /* ---------------------------------------------------------------------- */
+
+ for (e = nel+1 ; e < Work->elen ; e++)
+ {
+ E [e] = 0 ;
+ }
+
+#ifndef NDEBUG
+ UMF_dump_packed_memory (Numeric, Work) ;
+#endif
+
+ DEBUG8 (("::::GARBAGE COLLECTION DONE::::\n")) ;
+}
diff --git a/UMFPACK/Source/umf_garbage_collection.h b/UMFPACK/Source/umf_garbage_collection.h
new file mode 100644
index 0000000..9d2d8b7
--- /dev/null
+++ b/UMFPACK/Source/umf_garbage_collection.h
@@ -0,0 +1,14 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_garbage_collection
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int drnew,
+ Int dcnew,
+ Int do_Fcpos
+) ;
diff --git a/UMFPACK/Source/umf_get_memory.c b/UMFPACK/Source/umf_get_memory.c
new file mode 100644
index 0000000..696955b
--- /dev/null
+++ b/UMFPACK/Source/umf_get_memory.c
@@ -0,0 +1,223 @@
+/* ========================================================================== */
+/* === UMF_get_memory ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Reallocate the workspace (Numeric->Memory) and shift elements downwards.
+ needunits: increase in size so that the free space is at least this many
+ Units (to which the tuple lengths is added).
+
+ Return TRUE if successful, FALSE if out of memory.
+*/
+
+#include "umf_internal.h"
+#include "umf_get_memory.h"
+#include "umf_garbage_collection.h"
+#include "umf_tuple_lengths.h"
+#include "umf_build_tuples.h"
+#include "umf_mem_free_tail_block.h"
+#include "umf_realloc.h"
+
+GLOBAL Int UMF_get_memory
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int needunits,
+ Int r2, /* compact current front to r2-by-c2 */
+ Int c2,
+ Int do_Fcpos
+)
+{
+ double nsize, bsize, tsize ;
+ Int i, minsize, newsize, newmem, costly, row, col, *Row_tlen, *Col_tlen,
+ n_row, n_col, *Row_degree, *Col_degree ;
+ Unit *mnew, *p ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get and check parameters */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG1 (("::::GET MEMORY::::\n")) ;
+ UMF_dump_memory (Numeric) ;
+#endif
+
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_tlen = Numeric->Uilen ;
+ Col_tlen = Numeric->Lilen ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize the tuple list lengths */
+ /* ---------------------------------------------------------------------- */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (NON_PIVOTAL_ROW (row))
+ {
+ Row_tlen [row] = 0 ;
+ }
+ }
+ for (col = 0 ; col < n_col ; col++)
+ {
+ if (NON_PIVOTAL_COL (col))
+ {
+ Col_tlen [col] = 0 ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine how much memory is needed for the tuples */
+ /* ---------------------------------------------------------------------- */
+
+ nsize = (double) needunits + 2 ;
+ needunits += UMF_tuple_lengths (Numeric, Work, &tsize) ;
+ nsize += tsize ;
+ needunits += 2 ; /* add 2, so that newmem >= 2 is true if realloc'd */
+
+ /* note: Col_tlen and Row_tlen are updated, but the tuple lists */
+ /* themselves are not. Do not attempt to scan the tuple lists. */
+ /* They are now stale, and are about to be destroyed and recreated. */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the desired new size of memory */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG0 (("UMF_get_memory: needunits: "ID"\n", needunits)) ;
+
+ minsize = Numeric->size + needunits ;
+ nsize += (double) Numeric->size ;
+
+ bsize = ((double) Int_MAX) / sizeof (Unit) - 1 ;
+
+ newsize = (Int) (UMF_REALLOC_INCREASE * ((double) minsize)) ;
+ nsize *= UMF_REALLOC_INCREASE ;
+ nsize += 1 ;
+
+ if (newsize < 0 || nsize > bsize)
+ {
+ /* :: realloc Numeric->Memory int overflow :: */
+ DEBUGm3 (("Realloc hit integer limit\n")) ;
+ newsize = (Int) bsize ; /* we cannot increase the size beyond bsize */
+ }
+ else
+ {
+ ASSERT (newsize <= nsize) ;
+ newsize = MAX (newsize, minsize) ;
+ }
+ newsize = MAX (newsize, Numeric->size) ;
+
+ DEBUG0 ((
+ "REALLOC MEMORY: needunits "ID" old size: "ID" new size: "ID" Units \n",
+ needunits, Numeric->size, newsize)) ;
+
+ /* Forget where the biggest free block is (we no longer need it) */
+ /* since garbage collection will occur shortly. */
+ Numeric->ibig = EMPTY ;
+
+ DEBUG0 (("Before realloc E [0] "ID"\n", Work->E [0])) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reallocate the memory, if possible, and make it bigger */
+ /* ---------------------------------------------------------------------- */
+
+ mnew = (Unit *) NULL ;
+ while (!mnew)
+ {
+ mnew = (Unit *) UMF_realloc (Numeric->Memory, newsize, sizeof (Unit)) ;
+ if (!mnew)
+ {
+ if (newsize == minsize) /* last realloc attempt failed */
+ {
+ /* We failed to get the minimum. Just stick with the */
+ /* current allocation and hope that garbage collection */
+ /* can recover enough space. */
+ mnew = Numeric->Memory ; /* no new memory available */
+ newsize = Numeric->size ;
+ }
+ else
+ {
+ /* otherwise, reduce the request and keep trying */
+ newsize = (Int) (UMF_REALLOC_REDUCTION * ((double) newsize)) ;
+ newsize = MAX (minsize, newsize) ;
+ }
+ }
+ }
+ ASSERT (mnew != (Unit *) NULL) ;
+
+ /* see if realloc had to copy, rather than just extend memory */
+ costly = (mnew != Numeric->Memory) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* extend the tail portion of memory downwards */
+ /* ---------------------------------------------------------------------- */
+
+ Numeric->Memory = mnew ;
+ if (Work->E [0])
+ {
+ Int nb, dr, dc ;
+ nb = Work->nb ;
+ dr = Work->fnr_curr ;
+ dc = Work->fnc_curr ;
+ Work->Flublock = (Entry *) (Numeric->Memory + Work->E [0]) ;
+ Work->Flblock = Work->Flublock + nb * nb ;
+ Work->Fublock = Work->Flblock + dr * nb ;
+ Work->Fcblock = Work->Fublock + nb * dc ;
+ DEBUG0 (("after realloc E [0] "ID"\n", Work->E [0])) ;
+ }
+ ASSERT (IMPLIES (!(Work->E [0]), Work->Flublock == (Entry *) NULL)) ;
+
+ newmem = newsize - Numeric->size ;
+ ASSERT (newmem == 0 || newmem >= 2) ;
+
+ if (newmem >= 2)
+ {
+ /* reallocation succeeded */
+
+ /* point to the old tail marker block of size 1 + header */
+ p = Numeric->Memory + Numeric->size - 2 ;
+
+ /* create a new block out of the newly extended memory */
+ p->header.size = newmem - 1 ;
+ i = Numeric->size - 1 ;
+ p += newmem ;
+
+ /* create a new tail marker block */
+ p->header.prevsize = newmem - 1 ;
+ p->header.size = 1 ;
+
+ Numeric->size = newsize ;
+
+ /* free the new block */
+ UMF_mem_free_tail_block (Numeric, i) ;
+
+ Numeric->nrealloc++ ;
+
+ if (costly)
+ {
+ Numeric->ncostly++ ;
+ }
+
+ }
+ DEBUG1 (("Done with realloc memory\n")) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* garbage collection on the tail of Numeric->memory (destroys tuples) */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_garbage_collection (Numeric, Work, r2, c2, do_Fcpos) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* rebuild the tuples */
+ /* ---------------------------------------------------------------------- */
+
+ return (UMF_build_tuples (Numeric, Work)) ;
+}
diff --git a/UMFPACK/Source/umf_get_memory.h b/UMFPACK/Source/umf_get_memory.h
new file mode 100644
index 0000000..317d97a
--- /dev/null
+++ b/UMFPACK/Source/umf_get_memory.h
@@ -0,0 +1,15 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_get_memory
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ Int needunits,
+ Int r2,
+ Int c2,
+ Int do_Fcpos
+) ;
diff --git a/UMFPACK/Source/umf_grow_front.c b/UMFPACK/Source/umf_grow_front.c
new file mode 100644
index 0000000..611c3a1
--- /dev/null
+++ b/UMFPACK/Source/umf_grow_front.c
@@ -0,0 +1,294 @@
+/* ========================================================================== */
+/* === UMF_grow_front ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Current frontal matrix is too small. Make it bigger. */
+
+#include "umf_internal.h"
+#include "umf_grow_front.h"
+#include "umf_mem_free_tail_block.h"
+#include "umf_mem_alloc_tail_block.h"
+#include "umf_get_memory.h"
+
+GLOBAL Int UMF_grow_front
+(
+ NumericType *Numeric,
+ Int fnr2, /* desired size is fnr2-by-fnc2 */
+ Int fnc2,
+ WorkType *Work,
+ Int do_what /* -1: UMF_start_front
+ * 0: UMF_init_front, do not recompute Fcpos
+ * 1: UMF_extend_front
+ * 2: UMF_init_front, recompute Fcpos */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double s ;
+ Entry *Fcold, *Fcnew ;
+ Int j, i, col, *Fcpos, *Fcols, fnrows_max, fncols_max, fnr_curr, nb,
+ fnrows_new, fncols_new, fnr_min, fnc_min, minsize,
+ newsize, fnrows, fncols, *E, eloc ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ if (do_what != -1) UMF_debug++ ;
+ DEBUG0 (("\n\n====================GROW FRONT: do_what: "ID"\n", do_what)) ;
+ if (do_what != -1) UMF_debug-- ;
+ ASSERT (Work->do_grow) ;
+ ASSERT (Work->fnpiv == 0) ;
+#endif
+
+ Fcols = Work->Fcols ;
+ Fcpos = Work->Fcpos ;
+ E = Work->E ;
+
+ /* ---------------------------------------------------------------------- */
+ /* The current front is too small, find the new size */
+ /* ---------------------------------------------------------------------- */
+
+ /* maximum size of frontal matrix for this chain */
+ nb = Work->nb ;
+ fnrows_max = Work->fnrows_max + nb ;
+ fncols_max = Work->fncols_max + nb ;
+ ASSERT (fnrows_max >= 0 && (fnrows_max % 2) == 1) ;
+ DEBUG0 (("Max size: "ID"-by-"ID" (incl. "ID" pivot block\n",
+ fnrows_max, fncols_max, nb)) ;
+
+ /* current dimensions of frontal matrix: fnr-by-fnc */
+ DEBUG0 (("Current : "ID"-by-"ID" (excl "ID" pivot blocks)\n",
+ Work->fnr_curr, Work->fnc_curr, nb)) ;
+ ASSERT (Work->fnr_curr >= 0) ;
+ ASSERT ((Work->fnr_curr % 2 == 1) || Work->fnr_curr == 0) ;
+
+ /* required dimensions of frontal matrix: fnr_min-by-fnc_min */
+ fnrows_new = Work->fnrows_new + 1 ;
+ fncols_new = Work->fncols_new + 1 ;
+ ASSERT (fnrows_new >= 0) ;
+ if (fnrows_new % 2 == 0) fnrows_new++ ;
+ fnrows_new += nb ;
+ fncols_new += nb ;
+ fnr_min = MIN (fnrows_new, fnrows_max) ;
+ fnc_min = MIN (fncols_new, fncols_max) ;
+ minsize = fnr_min * fnc_min ;
+ if (INT_OVERFLOW ((double) fnr_min * (double) fnc_min * sizeof (Entry)))
+ {
+ /* :: the minimum front size is bigger than the integer maximum :: */
+ return (FALSE) ;
+ }
+ ASSERT (fnr_min >= 0) ;
+ ASSERT (fnr_min % 2 == 1) ;
+
+ DEBUG0 (("Min : "ID"-by-"ID"\n", fnr_min, fnc_min)) ;
+
+ /* grow the front to fnr2-by-fnc2, but no bigger than the maximum,
+ * and no smaller than the minumum. */
+ DEBUG0 (("Desired : ("ID"+"ID")-by-("ID"+"ID")\n", fnr2, nb, fnc2, nb)) ;
+ fnr2 += nb ;
+ fnc2 += nb ;
+ ASSERT (fnr2 >= 0) ;
+ if (fnr2 % 2 == 0) fnr2++ ;
+ fnr2 = MAX (fnr2, fnr_min) ;
+ fnc2 = MAX (fnc2, fnc_min) ;
+ fnr2 = MIN (fnr2, fnrows_max) ;
+ fnc2 = MIN (fnc2, fncols_max) ;
+ DEBUG0 (("Try : "ID"-by-"ID"\n", fnr2, fnc2)) ;
+ ASSERT (fnr2 >= 0) ;
+ ASSERT (fnr2 % 2 == 1) ;
+
+ s = ((double) fnr2) * ((double) fnc2) ;
+ if (INT_OVERFLOW (s * sizeof (Entry)))
+ {
+ /* :: frontal matrix size int overflow :: */
+ /* the desired front size is bigger than the integer maximum */
+ /* compute a such that a*a*s < Int_MAX / sizeof (Entry) */
+ double a = 0.9 * sqrt ((Int_MAX / sizeof (Entry)) / s) ;
+ fnr2 = MAX (fnr_min, a * fnr2) ;
+ fnc2 = MAX (fnc_min, a * fnc2) ;
+ /* the new frontal size is a*r*a*c = a*a*s */
+ newsize = fnr2 * fnc2 ;
+ ASSERT (fnr2 >= 0) ;
+ if (fnr2 % 2 == 0) fnr2++ ;
+ fnc2 = newsize / fnr2 ;
+ }
+
+ fnr2 = MAX (fnr2, fnr_min) ;
+ fnc2 = MAX (fnc2, fnc_min) ;
+ newsize = fnr2 * fnc2 ;
+
+ ASSERT (fnr2 >= 0) ;
+ ASSERT (fnr2 % 2 == 1) ;
+ ASSERT (fnr2 >= fnr_min) ;
+ ASSERT (fnc2 >= fnc_min) ;
+ ASSERT (newsize >= minsize) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the current front if it is empty of any numerical values */
+ /* ---------------------------------------------------------------------- */
+
+ if (E [0] && do_what != 1)
+ {
+ /* free the current front, if it exists and has nothing in it */
+ DEBUG0 (("Freeing empty front\n")) ;
+ UMF_mem_free_tail_block (Numeric, E [0]) ;
+ E [0] = 0 ;
+ Work->Flublock = (Entry *) NULL ;
+ Work->Flblock = (Entry *) NULL ;
+ Work->Fublock = (Entry *) NULL ;
+ Work->Fcblock = (Entry *) NULL ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the new front, doing garbage collection if necessary */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0) /* a double relop, but ignore NaN case */
+ {
+ double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ;
+ DEBUG1 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random garbage collection (grow)\n")) ;
+ }
+#endif
+
+ DEBUG0 (("Attempt size: "ID"-by-"ID"\n", fnr2, fnc2)) ;
+ eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
+
+ if (!eloc)
+ {
+ /* Do garbage collection, realloc, and try again. Compact the current
+ * contribution block in the front to fnrows-by-fncols. Note that
+ * there are no pivot rows/columns in current front. Do not recompute
+ * Fcpos in UMF_garbage_collection. */
+ DEBUGm3 (("get_memory from umf_grow_front\n")) ;
+ if (!UMF_get_memory (Numeric, Work, 1 + UNITS (Entry, newsize),
+ Work->fnrows, Work->fncols, FALSE))
+ {
+ /* :: out of memory in umf_grow_front :: */
+ return (FALSE) ; /* out of memory */
+ }
+ DEBUG0 (("Attempt size: "ID"-by-"ID" again\n", fnr2, fnc2)) ;
+ eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
+ }
+
+ /* try again with something smaller */
+ while ((fnr2 != fnr_min || fnc2 != fnc_min) && !eloc)
+ {
+ fnr2 = MIN (fnr2 - 2, fnr2 * UMF_REALLOC_REDUCTION) ;
+ fnc2 = MIN (fnc2 - 2, fnc2 * UMF_REALLOC_REDUCTION) ;
+ ASSERT (fnr_min >= 0) ;
+ ASSERT (fnr_min % 2 == 1) ;
+ fnr2 = MAX (fnr_min, fnr2) ;
+ fnc2 = MAX (fnc_min, fnc2) ;
+ ASSERT (fnr2 >= 0) ;
+ if (fnr2 % 2 == 0) fnr2++ ;
+ newsize = fnr2 * fnc2 ;
+ DEBUGm3 (("Attempt smaller size: "ID"-by-"ID" minsize "ID"-by-"ID"\n",
+ fnr2, fnc2, fnr_min, fnc_min)) ;
+ eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
+ }
+
+ /* try again with the smallest possible size */
+ if (!eloc)
+ {
+ fnr2 = fnr_min ;
+ fnc2 = fnc_min ;
+ newsize = minsize ;
+ DEBUG0 (("Attempt minsize: "ID"-by-"ID"\n", fnr2, fnc2)) ;
+ eloc = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry, newsize)) ;
+ }
+
+ if (!eloc)
+ {
+ /* out of memory */
+ return (FALSE) ;
+ }
+
+ ASSERT (fnr2 >= 0) ;
+ ASSERT (fnr2 % 2 == 1) ;
+ ASSERT (fnr2 >= fnr_min && fnc2 >= fnc_min) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* copy the old frontal matrix into the new one */
+ /* ---------------------------------------------------------------------- */
+
+ /* old contribution block (if any) */
+ fnr_curr = Work->fnr_curr ; /* garbage collection can change fn*_curr */
+ ASSERT (fnr_curr >= 0) ;
+ ASSERT ((fnr_curr % 2 == 1) || fnr_curr == 0) ;
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ Fcold = Work->Fcblock ;
+
+ /* remove nb from the sizes */
+ fnr2 -= nb ;
+ fnc2 -= nb ;
+
+ /* new frontal matrix */
+ Work->Flublock = (Entry *) (Numeric->Memory + eloc) ;
+ Work->Flblock = Work->Flublock + nb * nb ;
+ Work->Fublock = Work->Flblock + nb * fnr2 ;
+ Work->Fcblock = Work->Fublock + nb * fnc2 ;
+ Fcnew = Work->Fcblock ;
+
+ if (E [0])
+ {
+ /* copy the old contribution block into the new one */
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Fcols [j] ;
+ DEBUG1 (("copy col "ID" \n",col)) ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Fcnew [i] = Fcold [i] ;
+ }
+ Fcnew += fnr2 ;
+ Fcold += fnr_curr ;
+ DEBUG1 (("new offset col "ID" "ID"\n",col, j * fnr2)) ;
+ Fcpos [col] = j * fnr2 ;
+ }
+ }
+ else if (do_what == 2)
+ {
+ /* just find the new column offsets */
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Fcols [j] ;
+ DEBUG1 (("new offset col "ID" "ID"\n",col, j * fnr2)) ;
+ Fcpos [col] = j * fnr2 ;
+ }
+ }
+
+ /* free the old frontal matrix */
+ UMF_mem_free_tail_block (Numeric, E [0]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* new frontal matrix size */
+ /* ---------------------------------------------------------------------- */
+
+ E [0] = eloc ;
+ Work->fnr_curr = fnr2 ; /* C block is fnr2-by-fnc2 */
+ Work->fnc_curr = fnc2 ;
+ Work->fcurr_size = newsize ; /* including LU, L, U, and C blocks */
+ Work->do_grow = FALSE ; /* the front has just been grown */
+
+ ASSERT (Work->fnr_curr >= 0) ;
+ ASSERT (Work->fnr_curr % 2 == 1) ;
+ DEBUG0 (("Newly grown front: "ID"+"ID" by "ID"+"ID"\n", Work->fnr_curr,
+ nb, Work->fnc_curr, nb)) ;
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umf_grow_front.h b/UMFPACK/Source/umf_grow_front.h
new file mode 100644
index 0000000..8078897
--- /dev/null
+++ b/UMFPACK/Source/umf_grow_front.h
@@ -0,0 +1,14 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_grow_front
+(
+ NumericType *Numeric,
+ Int fnr2,
+ Int fnc2,
+ WorkType *Work,
+ Int do_what
+) ;
diff --git a/UMFPACK/Source/umf_init_front.c b/UMFPACK/Source/umf_init_front.c
new file mode 100644
index 0000000..201f1f8
--- /dev/null
+++ b/UMFPACK/Source/umf_init_front.c
@@ -0,0 +1,268 @@
+/* ========================================================================== */
+/* === UMF_init_front ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_internal.h"
+#include "umf_init_front.h"
+#include "umf_grow_front.h"
+
+/* ========================================================================== */
+/* === zero_init_front ====================================================== */
+/* ========================================================================== */
+
+/* Set the initial frontal matrix to zero. */
+
+PRIVATE void zero_init_front (Int m, Int n, Entry *Fcblock, Int d)
+{
+ Int i, j ;
+ Entry *F, *Fj = Fcblock ;
+ for (j = 0 ; j < m ; j++)
+ {
+ F = Fj ;
+ Fj += d ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* CLEAR (Fcblock [i + j*d]) ; */
+ CLEAR (*F) ;
+ F++ ;
+ }
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_init_front ======================================================= */
+/* ========================================================================== */
+
+GLOBAL Int UMF_init_front
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int i, j, fnr_curr, row, col, *Frows, *Fcols,
+ *Fcpos, *Frpos, fncols, fnrows, *Wrow, fnr2, fnc2, rrdeg, ccdeg, *Wm,
+ fnrows_extended ;
+ Entry *Fcblock, *Fl, *Wy, *Wx ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get current frontal matrix and check for frontal growth */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG0 (("INIT FRONT\n")) ;
+ DEBUG1 (("CURR before init:\n")) ;
+ UMF_dump_current_front (Numeric, Work, FALSE) ;
+#endif
+ if (Work->do_grow)
+ {
+ fnr2 = UMF_FRONTAL_GROWTH * Work->fnrows_new + 2 ;
+ fnc2 = UMF_FRONTAL_GROWTH * Work->fncols_new + 2 ;
+ if (!UMF_grow_front (Numeric, fnr2, fnc2, Work,
+ Work->pivrow_in_front ? 2 : 0))
+ {
+ /* :: out of memory in umf_init_front :: */
+ DEBUGm4 (("out of memory: init front\n")) ;
+ return (FALSE) ;
+ }
+ }
+#ifndef NDEBUG
+ DEBUG1 (("CURR after grow:\n")) ;
+ UMF_dump_current_front (Numeric, Work, FALSE) ;
+ DEBUG1 (("fnrows new "ID" fncols new "ID"\n",
+ Work->fnrows_new, Work->fncols_new)) ;
+#endif
+ ASSERT (Work->fnpiv == 0) ;
+ fnr_curr = Work->fnr_curr ;
+ ASSERT (Work->fnrows_new + 1 <= fnr_curr) ;
+ ASSERT (Work->fncols_new + 1 <= Work->fnc_curr) ;
+ ASSERT (fnr_curr >= 0) ;
+ ASSERT (fnr_curr % 2 == 1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ /* current front is defined by pivot row and column */
+
+ Frows = Work->Frows ;
+ Fcols = Work->Fcols ;
+ Frpos = Work->Frpos ;
+ Fcpos = Work->Fcpos ;
+
+ Work->fnzeros = 0 ;
+
+ ccdeg = Work->ccdeg ;
+ rrdeg = Work->rrdeg ;
+
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+
+ /* if both pivrow and pivcol are in front, then we extend the old one */
+ /* in UMF_extend_front, rather than starting a new one here. */
+ ASSERT (! (Work->pivrow_in_front && Work->pivcol_in_front)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* place pivot column pattern in frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Fl = Work->Flblock ;
+
+ if (Work->pivcol_in_front)
+ {
+ /* Append the pivot column extension.
+ * Note that all we need to do is increment the size, since the
+ * candidate pivot column pattern is already in place in
+ * Frows [0 ... fnrows-1] (the old pattern), and
+ * Frows [fnrows ... fnrows + Work->ccdeg - 1] (the new
+ * pattern). Frpos is also properly defined. */
+ /* make a list of the new rows to scan */
+ Work->fscan_row = fnrows ; /* only scan the new rows */
+ Work->NewRows = Work->Wrp ;
+ Wy = Work->Wy ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Fl [i] = Wy [i] ;
+ }
+ fnrows_extended = fnrows + ccdeg ;
+ for (i = fnrows ; i < fnrows_extended ; i++)
+ {
+ Fl [i] = Wy [i] ;
+ /* flip the row index, since Wrp must be < 0 */
+ row = Frows [i] ;
+ Work->NewRows [i] = FLIP (row) ;
+ }
+ fnrows = fnrows_extended ;
+ }
+ else
+ {
+ /* this is a completely new column */
+ Work->fscan_row = 0 ; /* scan all the rows */
+ Work->NewRows = Frows ;
+ Wm = Work->Wm ;
+ Wx = Work->Wx ;
+ for (i = 0 ; i < ccdeg ; i++)
+ {
+ Fl [i] = Wx [i] ;
+ row = Wm [i] ;
+ Frows [i] = row ;
+ Frpos [row] = i ;
+ }
+ fnrows = ccdeg ;
+ }
+
+ Work->fnrows = fnrows ;
+
+#ifndef NDEBUG
+ DEBUG3 (("New Pivot col "ID" now in front, length "ID"\n",
+ Work->pivcol, fnrows)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ DEBUG4 ((" "ID": row "ID"\n", i, Frows [i])) ;
+ ASSERT (Frpos [Frows [i]] == i) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* place pivot row pattern in frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ Wrow = Work->Wrow ;
+ if (Work->pivrow_in_front)
+ {
+ /* append the pivot row extension */
+ Work->fscan_col = fncols ; /* only scan the new columns */
+ Work->NewCols = Work->Wp ;
+#ifndef NDEBUG
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Fcols [j] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ ASSERT (Fcpos [col] == j * fnr_curr) ;
+ }
+#endif
+ /* Wrow == Fcol for the IN_IN case, and for the OUT_IN case when
+ * the pivrow [IN][IN] happens to be the same as pivrow [OUT][IN].
+ * See UMF_local_search for more details. */
+ ASSERT (IMPLIES (Work->pivcol_in_front, Wrow == Fcols)) ;
+ if (Wrow == Fcols)
+ {
+ for (j = fncols ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ /* Fcols [j] = col ; not needed */
+ /* flip the col index, since Wp must be < 0 */
+ Work->NewCols [j] = FLIP (col) ;
+ Fcpos [col] = j * fnr_curr ;
+ }
+ }
+ else
+ {
+ for (j = fncols ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ Fcols [j] = col ;
+ /* flip the col index, since Wp must be < 0 */
+ Work->NewCols [j] = FLIP (col) ;
+ Fcpos [col] = j * fnr_curr ;
+ }
+ }
+ }
+ else
+ {
+ /* this is a completely new row */
+ Work->fscan_col = 0 ; /* scan all the columns */
+ Work->NewCols = Fcols ;
+ for (j = 0 ; j < rrdeg ; j++)
+ {
+ col = Wrow [j] ;
+ Fcols [j] = col ;
+ Fcpos [col] = j * fnr_curr ;
+ }
+ }
+
+ DEBUGm1 (("rrdeg "ID" fncols "ID"\n", rrdeg, fncols)) ;
+ fncols = rrdeg ;
+ Work->fncols = fncols ;
+
+ /* ---------------------------------------------------------------------- */
+ /* clear the frontal matrix */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (fnrows == Work->fnrows_new + 1) ;
+ ASSERT (fncols == Work->fncols_new + 1) ;
+
+ Fcblock = Work->Fcblock ;
+ ASSERT (Fcblock != (Entry *) NULL) ;
+
+ zero_init_front (fncols, fnrows, Fcblock, fnr_curr) ;
+
+#ifndef NDEBUG
+ DEBUG3 (("New Pivot row "ID" now in front, length "ID" fnr_curr "ID"\n",
+ Work->pivrow, fncols, fnr_curr)) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ DEBUG4 (("col "ID" position "ID"\n", j, Fcols [j])) ;
+ ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* current workspace usage: */
+ /* ---------------------------------------------------------------------- */
+
+ /* Fcblock [0..fnr_curr-1, 0..fnc_curr-1]: space for the new frontal
+ * matrix. Fcblock (i,j) is located at Fcblock [i+j*fnr_curr] */
+
+ return (TRUE) ;
+
+}
diff --git a/UMFPACK/Source/umf_init_front.h b/UMFPACK/Source/umf_init_front.h
new file mode 100644
index 0000000..9801b72
--- /dev/null
+++ b/UMFPACK/Source/umf_init_front.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_init_front
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/UMFPACK/Source/umf_internal.h b/UMFPACK/Source/umf_internal.h
new file mode 100644
index 0000000..cd46b03
--- /dev/null
+++ b/UMFPACK/Source/umf_internal.h
@@ -0,0 +1,734 @@
+/* ========================================================================== */
+/* === umf_internal.h ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This file is for internal use in UMFPACK itself, and should not be included
+ in user code. Use umfpack.h instead. User-accessible file names and
+ routine names all start with the letters "umfpack_". Non-user-accessible
+ file names and routine names all start with "umf_".
+*/
+
+#ifndef _UMF_INTERNAL
+#define _UMF_INTERNAL
+
+/* -------------------------------------------------------------------------- */
+/* ANSI standard include files */
+/* -------------------------------------------------------------------------- */
+
+/* from float.h: DBL_EPSILON */
+#include <float.h>
+
+/* from string.h: strcmp */
+#include <string.h>
+
+/* when debugging, assert.h and the assert macro are used (see umf_dump.h) */
+
+/* -------------------------------------------------------------------------- */
+/* Architecture */
+/* -------------------------------------------------------------------------- */
+
+#if defined (__sun) || defined (MSOL2) || defined (ARCH_SOL2)
+#define UMF_SOL2
+#define UMFPACK_ARCHITECTURE "Sun Solaris"
+
+#elif defined (__sgi) || defined (MSGI) || defined (ARCH_SGI)
+#define UMF_SGI
+#define UMFPACK_ARCHITECTURE "SGI Irix"
+
+#elif defined (__linux) || defined (MGLNX86) || defined (ARCH_GLNX86)
+#define UMF_LINUX
+#define UMFPACK_ARCHITECTURE "Linux"
+
+#elif defined (_AIX) || defined (MIBM_RS) || defined (ARCH_IBM_RS)
+#define UMF_AIX
+#define UMFPACK_ARCHITECTURE "IBM AIX"
+
+#elif defined (__alpha) || defined (MALPHA) || defined (ARCH_ALPHA)
+#define UMF_ALPHA
+#define UMFPACK_ARCHITECTURE "Compaq Alpha"
+
+#elif defined (_WIN32) || defined (WIN32)
+#if defined (__MINGW32__)
+#define UMF_MINGW
+#elif defined (__CYGWIN32__)
+#define UMF_CYGWIN
+#else
+#define UMF_WINDOWS
+#endif
+#define UMFPACK_ARCHITECTURE "Microsoft Windows"
+
+#elif defined (__hppa) || defined (__hpux) || defined (MHPUX) || defined (ARCH_HPUX)
+#define UMF_HP
+#define UMFPACK_ARCHITECTURE "HP Unix"
+
+#elif defined (__hp700) || defined (MHP700) || defined (ARCH_HP700)
+#define UMF_HP
+#define UMFPACK_ARCHITECTURE "HP 700 Unix"
+
+#else
+/* If the architecture is unknown, and you call the BLAS, you may need to */
+/* define BLAS_BY_VALUE, BLAS_NO_UNDERSCORE, and/or BLAS_CHAR_ARG yourself. */
+#define UMFPACK_ARCHITECTURE "unknown"
+#endif
+
+
+/* -------------------------------------------------------------------------- */
+/* basic definitions (see also amd_internal.h) */
+/* -------------------------------------------------------------------------- */
+
+#define ONES_COMPLEMENT(r) (-(r)-1)
+
+/* -------------------------------------------------------------------------- */
+/* AMD include file */
+/* -------------------------------------------------------------------------- */
+
+/* stdio.h, stdlib.h, limits.h, and math.h, NDEBUG definition, assert.h */
+#include "amd_internal.h"
+
+/* -------------------------------------------------------------------------- */
+/* MATLAB include files */
+/* -------------------------------------------------------------------------- */
+
+/* only used when compiling the UMFPACK mexFunction */
+#ifdef MATLAB_MEX_FILE
+#include "matrix.h"
+#include "mex.h"
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Real/complex and int/UF_long definitions, double relops */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_version.h"
+
+/* -------------------------------------------------------------------------- */
+/* Compile-time configurations */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_config.h"
+
+/* -------------------------------------------------------------------------- */
+/* umfpack include file */
+/* -------------------------------------------------------------------------- */
+
+#include "umfpack.h"
+
+/* -------------------------------------------------------------------------- */
+/* for contents of Info. This must correlate with umfpack.h */
+/* -------------------------------------------------------------------------- */
+
+#define ESTIMATE (UMFPACK_NUMERIC_SIZE_ESTIMATE - UMFPACK_NUMERIC_SIZE)
+#define ACTUAL 0
+
+/* -------------------------------------------------------------------------- */
+/* get a parameter from the Control array */
+/* -------------------------------------------------------------------------- */
+
+#define GET_CONTROL(i,default) \
+ ((Control != (double *) NULL) ? \
+ (SCALAR_IS_NAN (Control [i]) ? default : Control [i]) \
+ : default)
+
+/* -------------------------------------------------------------------------- */
+/* for clearing the external degree counters */
+/* -------------------------------------------------------------------------- */
+
+#define MAX_MARK(n) Int_MAX - (2*(n)+1)
+
+/* -------------------------------------------------------------------------- */
+/* convert number of Units to MBytes */
+/* -------------------------------------------------------------------------- */
+
+#define MBYTES(units) (((units) * sizeof (Unit)) / 1048576.0)
+
+/* -------------------------------------------------------------------------- */
+/* dense row/column macro */
+/* -------------------------------------------------------------------------- */
+
+/* In order for a row or column to be treated as "dense", it must have more */
+/* entries than the value returned by this macro. n is the dimension of the */
+/* matrix, and alpha is the dense row/column control parameter. */
+
+/* Note: this is not defined if alpha is NaN or Inf: */
+#define UMFPACK_DENSE_DEGREE_THRESHOLD(alpha,n) \
+ ((Int) MAX (16.0, (alpha) * 16.0 * sqrt ((double) (n))))
+
+/* -------------------------------------------------------------------------- */
+/* PRINTF */
+/* -------------------------------------------------------------------------- */
+
+#define PRINTFk(k,params) { if (prl >= (k)) { PRINTF (params) ; } }
+#define PRINTF1(params) PRINTFk (1, params)
+#define PRINTF2(params) PRINTFk (2, params)
+#define PRINTF3(params) PRINTFk (3, params)
+#define PRINTF4(params) PRINTFk (4, params)
+#define PRINTF5(params) PRINTFk (5, params)
+#define PRINTF6(params) PRINTFk (6, params)
+
+/* -------------------------------------------------------------------------- */
+/* Fixed control parameters */
+/* -------------------------------------------------------------------------- */
+
+/* maximum number of columns to consider at one time, in a single front */
+#define MAX_CANDIDATES 128
+
+/* reduce Numeric->Memory request by this ratio, if allocation fails */
+#define UMF_REALLOC_REDUCTION (0.95)
+
+/* increase Numeric->Memory request by this ratio, if we need more */
+#define UMF_REALLOC_INCREASE (1.2)
+
+/* increase the dimensions of the current frontal matrix by this factor
+ * when it needs to grow. */
+#define UMF_FRONTAL_GROWTH (1.2)
+
+/* largest BLAS block size permitted */
+#define MAXNB 64
+
+/* if abs (y) < RECIPROCAL_TOLERANCE, then compute x/y. Otherwise x*(1/y).
+ * Ignored if NRECIPROCAL is defined */
+#define RECIPROCAL_TOLERANCE 1e-12
+
+/* -------------------------------------------------------------------------- */
+/* Memory allocator */
+/* -------------------------------------------------------------------------- */
+
+/* See AMD/Source/amd_global.c and AMD/Source/amd.h for the
+ * definition of the memory allocator used by UMFPACK. Versions 4.4 and
+ * earlier had their memory allocator definitions here. Other global
+ * function pointers for UMFPACK are located in umf_global.c.
+ *
+ * The MATLAB mexFunction uses MATLAB's memory manager and mexPrintf, while the
+ * C-callable AMD library uses the ANSI C malloc, free, realloc, and printf
+ * routines.
+ */
+
+/* -------------------------------------------------------------------------- */
+/* Memory space definitions */
+/* -------------------------------------------------------------------------- */
+
+/* for memory alignment - assume double has worst case alignment */
+typedef double Align ;
+
+/* get number of bytes required to hold n items of a type: */
+/* note that this will not overflow, because sizeof (type) is always */
+/* greater than or equal to sizeof (Int) >= 2 */
+#define BYTES(type,n) (sizeof (type) * (n))
+
+/* ceiling of (b/u). Assumes b >= 0 and u > 0 */
+#define CEILING(b,u) (((b) + (u) - 1) / (u))
+
+/* get number of Units required to hold n items of a type: */
+#define UNITS(type,n) (CEILING (BYTES (type, n), sizeof (Unit)))
+
+/* same as DUNITS, but use double instead of int to avoid overflow */
+#define DUNITS(type,n) (ceil (BYTES (type, (double) n) / sizeof (Unit)))
+
+union Unit_union
+{ /* memory is allocated in multiples of Unit */
+ struct
+ {
+ Int
+ size, /* size, in Units, of the block, excl. header block */
+ /* size >= 0: block is in use */
+ /* size < 0: block is free, of |size| Units */
+ prevsize ; /* size, in Units, of preceding block in S->Memory */
+ /* during garbage_collection, prevsize is set to -e-1 */
+ /* for element e, or positive (and thus a free block) */
+ /* otherwise */
+ } header ; /* block header */
+ Align xxxxxx ; /* force alignment of blocks (xxxxxx is never used) */
+} ;
+
+typedef union Unit_union Unit ;
+
+/* get the size of an allocated block */
+#define GET_BLOCK_SIZE(p) (((p)-1)->header.size)
+
+/* -------------------------------------------------------------------------- */
+/* Numeric */
+/* -------------------------------------------------------------------------- */
+
+/*
+ NUMERIC_VALID and SYMBOLIC_VALID:
+ The different values of SYBOLIC_VALID and NUMERIC_VALID are chosen as a
+ first defense against corrupted *Symbolic or *Numeric pointers passed to an
+ UMFPACK routine. They also ensure that the objects are used only by the
+ same version that created them (umfpack_di_*, umfpack_dl_*, umfpack_zi_*,
+ or umfpack_zl_*). The values have also been changed since prior releases of
+ the code to ensure that all routines that operate on the objects are of the
+ same release. The values themselves are purely arbitrary. The are less
+ than the ANSI C required minimums of INT_MAX and LONG_MAX, respectively.
+*/
+
+#ifdef DINT
+#define NUMERIC_VALID 15977
+#define SYMBOLIC_VALID 41937
+#endif
+#ifdef DLONG
+#define NUMERIC_VALID 399789720
+#define SYMBOLIC_VALID 399192713
+#endif
+#ifdef ZINT
+#define NUMERIC_VALID 17957
+#define SYMBOLIC_VALID 40927
+#endif
+#ifdef ZLONG
+#define NUMERIC_VALID 129987754
+#define SYMBOLIC_VALID 110291734
+#endif
+
+typedef struct /* NumericType */
+{
+ double
+ flops, /* "true" flop count */
+ relpt, /* relative pivot tolerance used */
+ relpt2, /* relative pivot tolerance used for sym. */
+ droptol,
+ alloc_init, /* initial allocation of Numeric->memory */
+ front_alloc_init, /* frontal matrix allocation parameter */
+ rsmin, /* smallest row sum */
+ rsmax, /* largest row sum */
+ min_udiag, /* smallest abs value on diagonal of D */
+ max_udiag, /* smallest abs value on diagonal of D */
+ rcond ; /* min (D) / max (D) */
+
+ Int
+ scale ;
+
+ Int valid ; /* set to NUMERIC_VALID, for validity check */
+
+ /* Memory space for A and LU factors */
+ Unit
+ *Memory ; /* working memory for A and LU factors */
+ Int
+ ihead, /* pointer to tail of LU factors, in Numeric->Memory */
+ itail, /* pointer to top of elements & tuples, */
+ /* in Numeric->Memory */
+ ibig, /* pointer to largest free block seen in tail */
+ size ; /* size of Memory, in Units */
+
+ Int
+ *Rperm, /* pointer to row perm array, size: n+1 */
+ /* after UMF_kernel: Rperm [new] = old */
+ /* during UMF_kernel: Rperm [old] = new */
+ *Cperm, /* pointer to col perm array, size: n+1 */
+ /* after UMF_kernel: Cperm [new] = old */
+ /* during UMF_kernel: Cperm [old] = new */
+
+ *Upos, /* see UMFPACK_get_numeric for a description */
+ *Lpos,
+ *Lip,
+ *Lilen,
+ *Uip,
+ *Uilen,
+ *Upattern ; /* pattern of last row of U (if singular) */
+
+ Int
+ ulen, /* length of Upattern */
+ npiv, /* number of structural pivots found (sprank approx) */
+ nnzpiv ; /* number of numerical (nonzero) pivots found */
+
+ Entry
+ *D ; /* D [i] is the diagonal entry of U */
+
+ Int do_recip ;
+ double *Rs ; /* scale factors for the rows of A and b */
+ /* do_recip FALSE: Divide row i by Rs [i] */
+ /* do_recip TRUE: Multiply row i by Rs [i] */
+
+ Int
+ n_row, n_col, /* A is n_row-by-n_row */
+ n1 ; /* number of singletons */
+
+ /* for information only: */
+ Int
+ tail_usage, /* amount of memory allocated in tail */
+ /* head_usage is Numeric->ihead */
+ init_usage, /* memory usage just after UMF_kernel_init */
+ max_usage, /* peak memory usage (excludes internal and external */
+ /* fragmentation in the tail) */
+ ngarbage, /* number of garbage collections performed */
+ nrealloc, /* number of reallocations performed */
+ ncostly, /* number of costly reallocations performed */
+ isize, /* size of integer pattern of L and U */
+ nLentries, /* number of entries in L, excluding diagonal */
+ nUentries, /* number of entries in U, including diagonal */
+ /* Some entries may be numerically zero. */
+ lnz, /* number of nonzero entries in L, excl. diagonal */
+ all_lnz, /* lnz plus entries dropped from L */
+ unz, /* number of nonzero entries in U, excl. diagonal */
+ all_unz, /* unz plus entries dropped form U */
+ maxfrsize ; /* largest actual front size */
+
+ Int maxnrows, maxncols ; /* not the same as Symbolic->maxnrows/cols* */
+
+} NumericType ;
+
+
+
+/* -------------------------------------------------------------------------- */
+/* Element tuples for connecting elements together in a matrix */
+/* -------------------------------------------------------------------------- */
+
+typedef struct /* Tuple */
+{
+ /* The (e,f) tuples for the element lists */
+ Int
+ e, /* element */
+ f ; /* contribution to the row/col appears at this offset */
+
+} Tuple ;
+
+#define TUPLES(t) MAX (4, (t) + 1)
+
+/* Col_degree is aliased with Cperm, and Row_degree with Rperm */
+#define NON_PIVOTAL_COL(col) (Col_degree [col] >= 0)
+#define NON_PIVOTAL_ROW(row) (Row_degree [row] >= 0)
+
+/* -------------------------------------------------------------------------- */
+/* An element */
+/* -------------------------------------------------------------------------- */
+
+typedef struct /* Element */
+{
+ Int
+
+ cdeg, /* external column degree + cdeg0 offset */
+ rdeg, /* external row degree + rdeg0 offset */
+ nrowsleft, /* number of rows remaining */
+ ncolsleft, /* number of columns remaining */
+ nrows, /* number of rows */
+ ncols, /* number of columns */
+ next ; /* for list link of sons, used during assembly only */
+
+ /* followed in memory by:
+ Int
+ col [0..ncols-1], column indices of this element
+ row [0..nrows-1] ; row indices of this element
+ Entry (suitably aligned, see macro below)
+ C [0...nrows-1, 0...ncols-1] ;
+ size of C is nrows*ncols Entry's
+ */
+
+} Element ;
+
+/* macros for computing pointers to row/col indices, and contribution block: */
+
+#define GET_ELEMENT_SIZE(nr,nc) \
+(UNITS (Element, 1) + UNITS (Int, (nc) + (nr)) + UNITS (Entry, (nc) * (nr)))
+
+#define DGET_ELEMENT_SIZE(nr,nc) \
+(DUNITS (Element, 1) + DUNITS (Int, (nc) + (nr)) + DUNITS (Entry, (nc) * (nr)))
+
+#define GET_ELEMENT_COLS(ep,p,Cols) { \
+ ASSERT (p != (Unit *) NULL) ; \
+ ASSERT (p >= Numeric->Memory + Numeric->itail) ; \
+ ASSERT (p <= Numeric->Memory + Numeric->size) ; \
+ ep = (Element *) p ; \
+ p += UNITS (Element, 1) ; \
+ Cols = (Int *) p ; \
+}
+
+#define GET_ELEMENT_PATTERN(ep,p,Cols,Rows,ncm) { \
+ GET_ELEMENT_COLS (ep, p, Cols) ; \
+ ncm = ep->ncols ; \
+ Rows = Cols + ncm ; \
+}
+
+#define GET_ELEMENT(ep,p,Cols,Rows,ncm,nrm,C) { \
+ GET_ELEMENT_PATTERN (ep, p, Cols, Rows, ncm) ; \
+ nrm = ep->nrows ; \
+ p += UNITS (Int, ncm + nrm) ; \
+ C = (Entry *) p ; \
+}
+
+/* -------------------------------------------------------------------------- */
+/* Work data structure */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This data structure holds items needed only during factorization.
+ All of this is freed when UMFPACK_numeric completes. Note that some of
+ it is stored in the tail end of Numeric->S (namely, the Tuples and the
+ Elements).
+*/
+
+typedef struct /* WorkType */
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* information about each row and col of A */
+ /* ---------------------------------------------------------------------- */
+
+ /*
+ Row_tuples: pointer to tuple list (alias with Numeric->Uip)
+ Row_tlen: number of tuples (alias with Numeric->Uilen)
+ Col_tuples: pointer to tuple list (alias with Numeric->Lip)
+ Col_tlen: number of tuples (alias with Numeric->Lilen)
+ Row_degree: degree of the row or column (alias Numeric->Rperm)
+ Col_degree: degree of the row or column (alias Numeric->Cperm)
+
+ The Row_degree and Col_degree are MATLAB-style colmmd approximations,
+ are equal to the sum of the sizes of the elements (contribution blocks)
+ in each row and column. They are maintained when elements are created
+ and assembled. They are used only during the pivot row and column
+ search. They are not needed to represent the pattern of the remaining
+ matrix.
+ */
+
+ /* ---------------------------------------------------------------------- */
+ /* information about each element */
+ /* ---------------------------------------------------------------------- */
+
+ Int *E ; /* E [0 .. Work->elen-1] element "pointers" */
+ /* (offsets in Numeric->Memory) */
+
+ /* ---------------------------------------------------------------------- */
+ /* generic workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Entry *Wx, *Wy ; /* each of size maxnrows+1 */
+
+ Int /* Sizes: nn = MAX (n_row, n_col) */
+ *Wp, /* nn+1 */
+ *Wrp, /* n_col+1 */
+ *Wm, /* maxnrows+1 */
+ *Wio, /* maxncols+1 */
+ *Woi, /* maxncols+1 */
+ *Woo, /* MAX (maxnrows,maxncols)+1 */
+ *Wrow, /* pointer to Fcols, Wio, or Woi */
+ *NewRows, /* list of rows to scan */
+ *NewCols ; /* list of cols to scan */
+
+ /* ---------------------------------------------------------------------- */
+
+ Int
+ *Lpattern, /* pattern of column of L, for one Lchain */
+ *Upattern, /* pattern of row of U, for one Uchain */
+ ulen, llen ; /* length of Upattern and Lpattern */
+
+ Int
+ *Diagonal_map, /* used for symmetric pivoting, of size nn+1 */
+ *Diagonal_imap ;/* used for symmetric pivoting, of size nn+1 */
+
+ /* ---------------------------------------------------------------------- */
+
+ Int
+ n_row, n_col, /* matrix is n_row-by-n_col */
+ nz, /* nonzeros in the elements for this matrix */
+ n1, /* number of row and col singletons */
+ elen, /* max possible number of elements */
+ npiv, /* number of pivot rows and columns so far */
+ ndiscard, /* number of discarded pivot columns */
+ Wrpflag,
+ nel, /* elements in use are in the range 1..nel */
+ noff_diagonal,
+ prior_element,
+ rdeg0, cdeg0,
+ rrdeg, ccdeg,
+ Candidates [MAX_CANDIDATES], /* current candidate pivot columns */
+ nCandidates, /* number of candidates in Candidate set */
+ ksuper,
+ firstsuper,
+ jsuper,
+ ncand, /* number of candidates (some not in Candidates[ ]) */
+ nextcand, /* next candidate to place in Candidate search set */
+ lo,
+ hi,
+ pivrow, /* current pivot row */
+ pivcol, /* current pivot column */
+ do_extend, /* true if the next pivot extends the current front */
+ do_update, /* true if update should be applied */
+ nforced, /* number of forced updates because of frontal growth */
+ any_skip,
+ do_scan2row,
+ do_scan2col,
+ do_grow,
+ pivot_case,
+ frontid, /* id of current frontal matrix */
+ nfr ; /* number of frontal matrices */
+
+ /* ---------------------------------------------------------------------- */
+ /* For row-merge tree */
+ /* ---------------------------------------------------------------------- */
+
+ Int
+ *Front_new1strow ;
+
+ /* ---------------------------------------------------------------------- */
+ /* current frontal matrix, F */
+ /* ---------------------------------------------------------------------- */
+
+ Int Pivrow [MAXNB],
+ Pivcol [MAXNB] ;
+
+ Entry
+ *Flublock, /* LU block, nb-by-nb */
+ *Flblock, /* L block, fnr_curr-by-nb */
+ *Fublock, /* U block, nb-by-fnc_curr, or U' fnc_curr-by-nb */
+ *Fcblock ; /* C block, fnr_curr-by-fnc_curr */
+
+ Int
+ *Frows, /* Frows [0.. ]: row indices of F */
+
+ *Fcols, /* Fcols [0.. ]: column indices of F */
+
+ *Frpos, /* position of row indices in F, or -1 if not present */
+ /* if Frows[i] == row, then Frpos[row] == i */
+
+ *Fcpos, /* position of col indices in F, or -1 if not present */
+ /* if Fcols[j] == col, then */
+ /* Fcpos[col] == j*Work->fnr_curr */
+
+ fnrows, /* number of rows in contribution block in F */
+ fncols, /* number of columns in contribution block in F */
+ fnr_curr, /* maximum # of rows in F (leading dimension) */
+ fnc_curr, /* maximum # of columns in F */
+ fcurr_size, /* current size of F */
+ fnrows_max, /* max possible column-dimension (max # of rows) of F */
+ fncols_max, /* max possible row-dimension (max # of columns) of F */
+ nb,
+ fnpiv, /* number of pivots in F */
+ fnzeros, /* number of explicit zero entries in LU block */
+ fscan_row, /* where to start scanning rows of F in UMF_assemble */
+ fscan_col, /* where to start scanning cols of F in UMF_assemble */
+ fnrows_new, /* number of new row indices in F after pivot added */
+ fncols_new, /* number of new col indices in F after pivot added */
+ pivrow_in_front, /* true if current pivot row in Frows */
+ pivcol_in_front ; /* true if current pivot column in Fcols */
+
+ /* ----------------------------------------------------------------------
+ * Current frontal matrix
+ * ----------------------------------------------------------------------
+ * The current frontal matrix is held as a single block of memory allocated
+ * from the "tail" end of Numeric->Memory. It is subdivided into four
+ * parts: an LU block, an L block, a U block, and a C block.
+ *
+ * Let k = fnpiv, r = fnrows, and c = fncols for the following discussion.
+ * Let dr = fnr_curr and dc = fnc_curr. Note that r <= dr and c <= dc.
+ *
+ * The LU block is of dimension nb-by-nb. The first k-by-k part holds the
+ * "diagonal" part of the LU factors for these k pivot rows and columns.
+ * The k pivot row and column indices in this part are Pivrow [0..k-1] and
+ * Pivcol [0..k-1], respectively.
+ *
+ * The L block is of dimension dr-by-nb. It holds the k pivot columns,
+ * except for the leading k-by-k part in the LU block. Only the leading
+ * r-by-k part is in use.
+ *
+ * The U block is of dimension dc-by-nb. It holds the k pivot rows,
+ * except for the leading k-by-k part in the LU block. It is stored in
+ * row-oriented form. Only the leading c-by-k part is in use.
+ *
+ * The C block is of dimension dr-by-dc. It holds the current contribution
+ * block. Only the leading r-by-c part is in use. The column indices in
+ * the C block are Fcols [0..c-1], and the row indices are Frows [0..r-1].
+ *
+ * dr is always odd, to avoid bad cache behavior.
+ */
+
+} WorkType ;
+
+
+/* -------------------------------------------------------------------------- */
+/* Symbolic */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This is is constructed by UMFPACK_symbolic, and is needed by UMFPACK_numeric
+ to factor the matrix.
+*/
+
+typedef struct /* SymbolicType */
+{
+
+ double
+ num_mem_usage_est, /* estimated max Numeric->Memory size */
+ num_mem_size_est, /* estimated final Numeric->Memory size */
+ peak_sym_usage, /* peak Symbolic and SymbolicWork usage */
+ sym, /* symmetry of pattern */
+ dnum_mem_init_usage, /* min Numeric->Memory for UMF_kernel_init */
+ amd_lunz, /* nz in LU for AMD, with symmetric pivoting */
+ lunz_bound ; /* max nx in LU, for arbitrary row pivoting */
+
+ Int valid, /* set to SYMBOLIC_VALID, for validity check */
+ max_nchains,
+ nchains,
+ *Chain_start,
+ *Chain_maxrows,
+ *Chain_maxcols,
+ maxnrows, /* largest number of rows in any front */
+ maxncols, /* largest number of columns in any front */
+ *Front_npivcol, /* Front_npivcol [j] = size of jth supercolumn*/
+ *Front_1strow, /* first row index in front j */
+ *Front_leftmostdesc, /* leftmost desc of front j */
+ *Front_parent, /* super-column elimination tree */
+ *Cperm_init, /* initial column ordering */
+ *Rperm_init, /* initial row ordering */
+ *Cdeg, *Rdeg,
+ *Esize,
+ dense_row_threshold,
+ n1, /* number of singletons */
+ nempty, /* MIN (nempty_row, nempty_col) */
+ *Diagonal_map, /* initial "diagonal" (after 2by2) */
+ esize, /* size of Esize array */
+ nfr,
+ n_row, n_col, /* matrix A is n_row-by-n_col */
+ nz, /* nz of original matrix */
+ nb, /* block size for BLAS 3 */
+ num_mem_init_usage, /* min Numeric->Memory for UMF_kernel_init */
+ nempty_row, nempty_col,
+
+ strategy,
+ ordering,
+ fixQ,
+ prefer_diagonal,
+ nzaat,
+ nzdiag,
+ amd_dmax ;
+
+} SymbolicType ;
+
+
+/* -------------------------------------------------------------------------- */
+/* for debugging only: */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_dump.h"
+
+/* -------------------------------------------------------------------------- */
+/* for statement coverage testing only: */
+/* -------------------------------------------------------------------------- */
+
+#ifdef TESTING
+
+/* for testing integer overflow: */
+#ifdef TEST_FOR_INTEGER_OVERFLOW
+#undef MAX_MARK
+#define MAX_MARK(n) (3*(n))
+#endif
+
+/* for testing out-of-memory conditions: */
+#define UMF_TCOV_TEST
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+GLOBAL EXTERN int umf_fail, umf_fail_lo, umf_fail_hi ;
+GLOBAL EXTERN int umf_realloc_fail, umf_realloc_lo, umf_realloc_hi ;
+
+/* for testing malloc count: */
+#define UMF_MALLOC_COUNT
+
+#endif
+
+#endif
diff --git a/UMFPACK/Source/umf_is_permutation.c b/UMFPACK/Source/umf_is_permutation.c
new file mode 100644
index 0000000..689c65e
--- /dev/null
+++ b/UMFPACK/Source/umf_is_permutation.c
@@ -0,0 +1,56 @@
+/* ========================================================================== */
+/* === UMF_is_permutation =================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Return TRUE if P is a r-permutation vector, FALSE otherwise */
+/* P [0..r-1] must be an r-permutation of 0..n-1 */
+
+#include "umf_internal.h"
+#include "umf_is_permutation.h"
+
+GLOBAL Int UMF_is_permutation
+(
+ const Int P [ ], /* permutation of size r */
+ Int W [ ], /* workspace of size n */
+ Int n,
+ Int r
+)
+{
+ Int i, k ;
+
+ if (!P)
+ {
+ /* if P is (Int *) NULL, this is the identity permutation */
+ return (TRUE) ;
+ }
+
+ ASSERT (W != (Int *) NULL) ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = FALSE ;
+ }
+ for (k = 0 ; k < r ; k++)
+ {
+ i = P [k] ;
+ DEBUG5 (("k "ID" i "ID"\n", k, i)) ;
+ if (i < 0 || i >= n)
+ {
+ DEBUG0 (("i out of range "ID" "ID"\n", i, n)) ;
+ return (FALSE) ;
+ }
+ if (W [i])
+ {
+ DEBUG0 (("i duplicate "ID"\n", i)) ;
+ return (FALSE) ;
+ }
+ W [i] = TRUE ;
+ }
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umf_is_permutation.h b/UMFPACK/Source/umf_is_permutation.h
new file mode 100644
index 0000000..2468545
--- /dev/null
+++ b/UMFPACK/Source/umf_is_permutation.h
@@ -0,0 +1,13 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_is_permutation
+(
+ const Int P [ ],
+ Int W [ ],
+ Int n,
+ Int r
+) ;
diff --git a/UMFPACK/Source/umf_kernel.c b/UMFPACK/Source/umf_kernel.c
new file mode 100644
index 0000000..6168829
--- /dev/null
+++ b/UMFPACK/Source/umf_kernel.c
@@ -0,0 +1,300 @@
+/* ========================================================================== */
+/* === UMF_kernel =========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Primary factorization routine. Called by UMFPACK_numeric.
+ Returns:
+ UMFPACK_OK if successful,
+ UMFPACK_ERROR_out_of_memory if out of memory, or
+ UMFPACK_ERROR_different_pattern if pattern of matrix (Ap and/or Ai)
+ has changed since the call to UMFPACK_*symbolic.
+*/
+
+#include "umf_internal.h"
+#include "umf_kernel.h"
+#include "umf_kernel_init.h"
+#include "umf_init_front.h"
+#include "umf_start_front.h"
+#include "umf_assemble.h"
+#include "umf_scale_column.h"
+#include "umf_local_search.h"
+#include "umf_create_element.h"
+#include "umf_extend_front.h"
+#include "umf_blas3_update.h"
+#include "umf_store_lu.h"
+#include "umf_kernel_wrapup.h"
+
+/* perform an action, and return if out of memory */
+#define DO(action) { if (! (action)) { return (UMFPACK_ERROR_out_of_memory) ; }}
+
+GLOBAL Int UMF_kernel
+(
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int j, f1, f2, chain, nchains, *Chain_start, status, fixQ, evaporate,
+ *Front_npivcol, jmax, nb, drop ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize memory space and load the matrix. Optionally scale. */
+ /* ---------------------------------------------------------------------- */
+
+ if (!UMF_kernel_init (Ap, Ai, Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Numeric, Work, Symbolic))
+ {
+ /* UMF_kernel_init is guaranteed to succeed, since UMFPACK_numeric */
+ /* either allocates enough space or if not, UMF_kernel does not get */
+ /* called. So running out of memory here is a fatal error, and means */
+ /* that the user changed Ap and/or Ai since the call to */
+ /* UMFPACK_*symbolic. */
+ DEBUGm4 (("kernel init failed\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ nchains = Symbolic->nchains ;
+ Chain_start = Symbolic->Chain_start ;
+ Front_npivcol = Symbolic->Front_npivcol ;
+ nb = Symbolic->nb ;
+ fixQ = Symbolic->fixQ ;
+ drop = Numeric->droptol > 0.0 ;
+
+#ifndef NDEBUG
+ for (chain = 0 ; chain < nchains ; chain++)
+ {
+ Int i ;
+ f1 = Chain_start [chain] ;
+ f2 = Chain_start [chain+1] - 1 ;
+ DEBUG1 (("\nCHain: "ID" start "ID" end "ID"\n", chain, f1, f2)) ;
+ for (i = f1 ; i <= f2 ; i++)
+ {
+ DEBUG1 (("Front "ID", npivcol "ID"\n", i, Front_npivcol [i])) ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* factorize each chain of frontal matrices */
+ /* ---------------------------------------------------------------------- */
+
+ for (chain = 0 ; chain < nchains ; chain++)
+ {
+ f1 = Chain_start [chain] ;
+ f2 = Chain_start [chain+1] - 1 ;
+
+ /* ------------------------------------------------------------------ */
+ /* get the initial frontal matrix size for this chain */
+ /* ------------------------------------------------------------------ */
+
+ DO (UMF_start_front (chain, Numeric, Work, Symbolic)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* factorize each front in the chain */
+ /* ------------------------------------------------------------------ */
+
+ for (Work->frontid = f1 ; Work->frontid <= f2 ; Work->frontid++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Initialize the pivot column candidate set */
+ /* -------------------------------------------------------------- */
+
+ Work->ncand = Front_npivcol [Work->frontid] ;
+ Work->lo = Work->nextcand ;
+ Work->hi = Work->nextcand + Work->ncand - 1 ;
+ jmax = MIN (MAX_CANDIDATES, Work->ncand) ;
+ DEBUGm1 ((">>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Starting front "
+ ID", npivcol: "ID"\n", Work->frontid, Work->ncand)) ;
+ if (fixQ)
+ {
+ /* do not modify the column order */
+ jmax = 1 ;
+ }
+ DEBUGm1 (("Initial candidates: ")) ;
+ for (j = 0 ; j < jmax ; j++)
+ {
+ DEBUGm1 ((" "ID, Work->nextcand)) ;
+ ASSERT (Work->nextcand <= Work->hi) ;
+ Work->Candidates [j] = Work->nextcand++ ;
+ }
+ Work->nCandidates = jmax ;
+ DEBUGm1 (("\n")) ;
+
+ /* -------------------------------------------------------------- */
+ /* Assemble and factorize the current frontal matrix */
+ /* -------------------------------------------------------------- */
+
+ while (Work->ncand > 0)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* get the pivot row and column */
+ /* ---------------------------------------------------------- */
+
+ status = UMF_local_search (Numeric, Work, Symbolic) ;
+ if (status == UMFPACK_ERROR_different_pattern)
+ {
+ /* :: pattern change detected in umf_local_search :: */
+ /* input matrix has changed since umfpack_*symbolic */
+ DEBUGm4 (("local search failed\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ /* no pivot found, discard and try again */
+ continue ;
+ }
+
+ /* ---------------------------------------------------------- */
+ /* update if front not extended or too many zeros in L,U */
+ /* ---------------------------------------------------------- */
+
+ if (Work->do_update)
+ {
+ UMF_blas3_update (Work) ;
+ if (drop)
+ {
+ DO (UMF_store_lu_drop (Numeric, Work)) ;
+ }
+ else
+ {
+ DO (UMF_store_lu (Numeric, Work)) ;
+ }
+ }
+
+ /* ---------------------------------------------------------- */
+ /* extend the frontal matrix, or start a new one */
+ /* ---------------------------------------------------------- */
+
+ if (Work->do_extend)
+ {
+ /* extend the current front */
+ DO (UMF_extend_front (Numeric, Work)) ;
+ }
+ else
+ {
+ /* finish the current front (if any) and start a new one */
+ DO (UMF_create_element (Numeric, Work, Symbolic)) ;
+ DO (UMF_init_front (Numeric, Work)) ;
+ }
+
+ /* ---------------------------------------------------------- */
+ /* Numerical & symbolic assembly into current frontal matrix */
+ /* ---------------------------------------------------------- */
+
+ if (fixQ)
+ {
+ UMF_assemble_fixq (Numeric, Work) ;
+ }
+ else
+ {
+ UMF_assemble (Numeric, Work) ;
+ }
+
+ /* ---------------------------------------------------------- */
+ /* scale the pivot column */
+ /* ---------------------------------------------------------- */
+
+ UMF_scale_column (Numeric, Work) ;
+
+ /* ---------------------------------------------------------- */
+ /* Numerical update if enough pivots accumulated */
+ /* ---------------------------------------------------------- */
+
+ evaporate = Work->fnrows == 0 || Work->fncols == 0 ;
+ if (Work->fnpiv >= nb || evaporate)
+ {
+ UMF_blas3_update (Work) ;
+ if (drop)
+ {
+ DO (UMF_store_lu_drop (Numeric, Work)) ;
+ }
+ else
+ {
+ DO (UMF_store_lu (Numeric, Work)) ;
+ }
+
+ }
+
+ Work->pivrow_in_front = FALSE ;
+ Work->pivcol_in_front = FALSE ;
+
+ /* ---------------------------------------------------------- */
+ /* If front is empty, evaporate it */
+ /* ---------------------------------------------------------- */
+
+ if (evaporate)
+ {
+ /* This does not create an element, just evaporates it.
+ * It ensures that a front is not 0-by-c or r-by-0. No
+ * memory is allocated, so it is guaranteed to succeed. */
+ (void) UMF_create_element (Numeric, Work, Symbolic) ;
+ Work->fnrows = 0 ;
+ Work->fncols = 0 ;
+ }
+ }
+ }
+
+ /* ------------------------------------------------------------------
+ * Wrapup the current frontal matrix. This is the last in a chain
+ * in the column elimination tree. The next frontal matrix
+ * cannot overlap with the current one, which will be its sibling
+ * in the column etree.
+ * ------------------------------------------------------------------ */
+
+ UMF_blas3_update (Work) ;
+ if (drop)
+ {
+ DO (UMF_store_lu_drop (Numeric, Work)) ;
+ }
+ else
+ {
+ DO (UMF_store_lu (Numeric, Work)) ;
+ }
+ Work->fnrows_new = Work->fnrows ;
+ Work->fncols_new = Work->fncols ;
+ DO (UMF_create_element (Numeric, Work, Symbolic)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* current front is now empty */
+ /* ------------------------------------------------------------------ */
+
+ Work->fnrows = 0 ;
+ Work->fncols = 0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* end the last Lchain and Uchain and finalize the LU factors */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_kernel_wrapup (Numeric, Symbolic, Work) ;
+
+ /* note that the matrix may be singular (this is OK) */
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umf_kernel.h b/UMFPACK/Source/umf_kernel.h
new file mode 100644
index 0000000..0f5d70d
--- /dev/null
+++ b/UMFPACK/Source/umf_kernel.h
@@ -0,0 +1,18 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_kernel
+(
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
diff --git a/UMFPACK/Source/umf_kernel_init.c b/UMFPACK/Source/umf_kernel_init.c
new file mode 100644
index 0000000..ff1c69f
--- /dev/null
+++ b/UMFPACK/Source/umf_kernel_init.c
@@ -0,0 +1,1057 @@
+/* ========================================================================== */
+/* === UMF_kernel_init ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Initialize the kernel: scale the matrix, load the initial elements, and
+ build the tuple lists.
+
+ Returns TRUE if successful, FALSE if out of memory or if the pattern has
+ changed since UMFPACK_*symbolic. UMFPACK_numeric allocates at least enough
+ space for UMF_kernel_init to succeed; otherwise it does not call
+ UMF_kernel_init. So an out-of-memory condition means that the pattern must
+ have gotten larger.
+*/
+
+#include "umf_internal.h"
+#include "umf_kernel_init.h"
+#include "umf_tuple_lengths.h"
+#include "umf_build_tuples.h"
+#include "umf_mem_init_memoryspace.h"
+#include "umf_mem_alloc_element.h"
+#include "umf_mem_alloc_head_block.h"
+#include "umf_mem_alloc_tail_block.h"
+#include "umf_mem_free_tail_block.h"
+#include "umf_scale.h"
+
+/* ========================================================================== */
+/* === packsp =============================================================== */
+/* ========================================================================== */
+
+/* remove zero or small entries from a column of L or a row of U */
+
+PRIVATE Int packsp /* returns new value of pnew */
+(
+ Int pnew, /* index into Memory of next free space */
+ Int *p_p, /* ptr to index of old pattern in Memory on input,
+ new pattern on output */
+ Int *p_len, /* ptr to length of old pattern on input,
+ new pattern on output */
+ Int drop, /* TRUE if small nonzero entries are to be dropped */
+ double droptol, /* the drop tolerance */
+ Unit *Memory /* contains the sparse vector on input and output */
+)
+{
+ Entry x ;
+ double s ;
+ Entry *Bx, *Bx2 ;
+ Int p, i, len, len_new, *Bi, *Bi2 ;
+
+ /* get the pointers to the sparse vector, and its length */
+ p = *p_p ;
+ len = *p_len ;
+ Bi = (Int *) (Memory + p) ; p += UNITS (Int, len) ;
+ Bx = (Entry *) (Memory + p) ; p += UNITS (Entry, len) ;
+ DEBUGm4 ((" p "ID" len "ID" pnew "ID"\n", p, len, pnew)) ;
+
+ /* the vector resides in Bi [0..len-1] and Bx [0..len-1] */
+
+ /* first, compact the vector in place */
+ len_new = 0 ;
+ for (p = 0 ; p < len ; p++)
+ {
+ i = Bi [p] ;
+ x = Bx [p] ;
+ DEBUGm4 ((" old vector: i "ID" value: ", i)) ;
+ EDEBUGk (-4, x) ;
+ DEBUGm4 (("\n")) ;
+ ASSERT (i >= 0) ;
+ /* skip if zero or below drop tolerance */
+ if (IS_ZERO (x)) continue ;
+ if (drop)
+ {
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ }
+ /* store the value back into the vector */
+ if (len_new != p)
+ {
+ Bi [len_new] = i ;
+ Bx [len_new] = x ;
+ }
+ len_new++ ;
+ }
+ ASSERT (len_new <= len) ;
+
+ /* the vector is now in Bi [0..len_new-1] and Bx [0..len_new-1] */
+
+#ifndef NDEBUG
+ for (p = 0 ; p < len_new ; p++)
+ {
+ DEBUGm4 ((" new vector: i "ID" value: ", Bi [p])) ;
+ EDEBUGk (-4, Bx [p]) ;
+ DEBUGm4 (("\n")) ;
+ ASSERT (Bi [p] >= 0) ;
+ }
+#endif
+
+ /* allocate new space for the compacted vector */
+ *p_p = pnew ;
+ *p_len = len_new ;
+ Bi2 = (Int *) (Memory + pnew) ; pnew += UNITS (Int, len_new) ;
+ Bx2 = (Entry *) (Memory + pnew) ; pnew += UNITS (Entry, len_new) ;
+ DEBUGm4 ((" pnew "ID" len_new "ID"\n", pnew, len_new)) ;
+
+ /* shift the vector upwards, into its new space */
+ for (p = 0 ; p < len_new ; p++)
+ {
+ Bi2 [p] = Bi [p] ;
+ }
+ for (p = 0 ; p < len_new ; p++)
+ {
+ Bx2 [p] = Bx [p] ;
+ }
+
+#ifndef NDEBUG
+ for (p = 0 ; p < len_new ; p++)
+ {
+ DEBUGm4 ((" packed vec: i "ID" value: ", Bi2 [p])) ;
+ EDEBUGk (-4, Bx2 [p]) ;
+ DEBUGm4 (("\n")) ;
+ ASSERT (Bi2 [p] >= 0) ;
+ }
+#endif
+
+ /* return the pointer to the space just after the new vector */
+ return (pnew) ;
+}
+
+
+/* ========================================================================== */
+/* === UMF_kernel_init ====================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMF_kernel_init
+(
+ const Int Ap [ ], /* user's input matrix (not modified) */
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry x, pivot_value ;
+ double unused = 0, rsmin, rsmax, rs, droptol ;
+ Entry *D, *C, *Lval, **Rpx ;
+ double *Rs ;
+ Int row, k, oldcol, size, e, p1, p2, p, nz, *Rows, *Cols, *E, i, *Upos,
+ *Lpos, n_row, n_col, *Wp, *Cperm_init, *Frpos, *Fcpos, *Row_degree, nn,
+ *Row_tlen, *Col_degree, *Col_tlen, oldrow, newrow, ilast, *Wrp,
+ *Rperm_init, col, n_inner, prefer_diagonal, *Diagonal_map, nempty,
+ *Diagonal_imap, fixQ, rdeg, cdeg, nempty_col, *Esize, esize, pnew,
+ *Lip, *Uip, *Lilen, *Uilen, llen, pa, *Cdeg, *Rdeg, n1, clen, do_scale,
+ lnz, unz, lip, uip, k1, *Rperm, *Cperm, pivcol, *Li, lilen, drop,
+ **Rpi, nempty_row, dense_row_threshold, empty_elements, rpi, rpx ;
+ Element *ep ;
+ Unit *Memory ;
+#ifdef COMPLEX
+ Int split = SPLIT (Az) ;
+#endif
+#ifndef NRECIPROCAL
+ Int do_recip = FALSE ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG0 (("KERNEL INIT\n")) ;
+
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+ nempty_col = Symbolic->nempty_col ;
+ nempty_row = Symbolic->nempty_row ;
+ nempty = MIN (nempty_row, nempty_col) ;
+ ASSERT (n_row > 0 && n_col > 0) ;
+ Cperm_init = Symbolic->Cperm_init ;
+ Rperm_init = Symbolic->Rperm_init ;
+ Cdeg = Symbolic->Cdeg ;
+ Rdeg = Symbolic->Rdeg ;
+ n1 = Symbolic->n1 ;
+ dense_row_threshold = Symbolic->dense_row_threshold ;
+ DEBUG0 (("Singletons: "ID"\n", n1)) ;
+ Work->nforced = 0 ;
+ Work->ndiscard = 0 ;
+ Work->noff_diagonal = 0 ;
+
+ nz = Ap [n_col] ;
+ if (nz < 0 || Ap [0] != 0 || nz != Symbolic->nz)
+ {
+ DEBUGm4 (("nz or Ap [0] bad\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+
+ prefer_diagonal = Symbolic->prefer_diagonal ;
+ Diagonal_map = Work->Diagonal_map ;
+ Diagonal_imap = Work->Diagonal_imap ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize the Numeric->Memory space for LU, elements, and tuples */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_mem_init_memoryspace (Numeric) ;
+ DEBUG1 (("Kernel init head usage, before allocs: "ID"\n", Numeric->ihead)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize the Work and Numeric objects */
+ /* ---------------------------------------------------------------------- */
+
+ /* current front is empty */
+ Work->fnpiv = 0 ;
+ Work->fncols = 0 ;
+ Work->fnrows = 0 ;
+ Work->fncols_max = 0 ;
+ Work->fnrows_max = 0 ;
+ Work->fnzeros = 0 ;
+ Work->fcurr_size = 0 ;
+ Work->fnr_curr = 0 ;
+ Work->fnc_curr = 0 ;
+
+ Work->nz = nz ;
+ Work->prior_element = EMPTY ;
+ Work->ulen = 0 ;
+ Work->llen = 0 ;
+ Work->npiv = n1 ;
+ Work->frontid = 0 ;
+ Work->nextcand = n1 ;
+
+ Memory = Numeric->Memory ;
+ Rperm = Numeric->Rperm ;
+ Cperm = Numeric->Cperm ;
+ Row_degree = Numeric->Rperm ;
+ Col_degree = Numeric->Cperm ;
+ /* Row_tuples = Numeric->Uip ; not needed */
+ Row_tlen = Numeric->Uilen ;
+ /* Col_tuples = Numeric->Lip ; not needed */
+ Col_tlen = Numeric->Lilen ;
+
+ Lip = Numeric->Lip ;
+ Uip = Numeric->Uip ;
+ Lilen = Numeric->Lilen ;
+ Uilen = Numeric->Uilen ;
+
+ Frpos = Work->Frpos ;
+ Fcpos = Work->Fcpos ;
+ Wp = Work->Wp ;
+ Wrp = Work->Wrp ;
+
+ D = Numeric->D ;
+ Upos = Numeric->Upos ;
+ Lpos = Numeric->Lpos ;
+ for (k = 0 ; k < n_inner ; k++)
+ {
+ CLEAR (D [k]) ;
+ }
+
+ Rs = Numeric->Rs ;
+
+ for (row = 0 ; row <= n_row ; row++)
+ {
+ Lpos [row] = EMPTY ;
+ /* Row_tuples [row] = 0 ; set in UMF_build_tuples */
+ /* Row_degree [row] = 0 ; initialized below */
+ Row_tlen [row] = 0 ;
+ /* Frpos [row] = EMPTY ; do this later */
+ }
+
+ for (col = 0 ; col <= n_col ; col++)
+ {
+ Upos [col] = EMPTY ;
+ /* Col_tuples [col] = 0 ; set in UMF_build_tuples */
+ /* Col_degree [col] = 0 ; initialized below */
+ Col_tlen [col] = 0 ;
+ Fcpos [col] = EMPTY ;
+ Wrp [col] = 0 ;
+ }
+ Work->Wrpflag = 1 ;
+
+ /* When cleared, Wp [0..nn] is < 0 */
+ for (i = 0 ; i <= nn ; i++)
+ {
+ Wp [i] = EMPTY ;
+ }
+ /* In col search, Wp [row] is set to a position, which is >= 0. */
+
+ /* When cleared, Wrp [0..n_col] is < Wrpflag */
+ /* In row search, Wrp [col] is set to Wrpflag. */
+
+ /* no need to initialize Wm, Wio, Woi, and Woo */
+
+ /* clear the external degree counters */
+ Work->cdeg0 = 1 ;
+ Work->rdeg0 = 1 ;
+
+ fixQ = Symbolic->fixQ ;
+
+ E = Work->E ;
+
+ Numeric->n_row = n_row ;
+ Numeric->n_col = n_col ;
+ Numeric->npiv = 0 ;
+ Numeric->nnzpiv = 0 ;
+ Numeric->min_udiag = 0.0 ;
+ Numeric->max_udiag = 0.0 ;
+ Numeric->rcond = 0.0 ;
+ Numeric->isize = 0 ;
+ Numeric->nLentries = 0 ;
+ Numeric->nUentries = 0 ;
+ Numeric->lnz = 0 ;
+ Numeric->unz = 0 ;
+ Numeric->all_lnz = 0 ;
+ Numeric->all_unz = 0 ;
+ Numeric->maxfrsize = 0 ;
+ Numeric->maxnrows = 0 ;
+ Numeric->maxncols = 0 ;
+ Numeric->flops = 0. ;
+ Numeric->n1 = n1 ;
+ droptol = Numeric->droptol ;
+ drop = (droptol > 0) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the scale factors, if requested, and check the input matrix */
+ /* ---------------------------------------------------------------------- */
+
+ /* UMFPACK_SCALE_SUM: Rs [i] = sum of the absolute values in row i.
+ * UMFPACK_SCALE_MAX: Rs [i] = max of the absolute values in row i.
+ *
+ * If A is complex, an approximate abs is used (|xreal| + |ximag|).
+ *
+ * If min (Rs [0..n_row]) >= RECIPROCAL_TOLERANCE, then the scale
+ * factors are inverted, and the rows of A are multiplied by the scale
+ * factors. Otherwise, the rows are divided by the scale factors. If
+ * NRECIPROCAL is defined, then the rows are always divided by the scale
+ * factors.
+ *
+ * For MATLAB (either built-in routine or mexFunction), or for gcc,
+ * the rows are always divided by the scale factors.
+ */
+
+ do_scale = (Numeric->scale != UMFPACK_SCALE_NONE) ;
+
+ if (do_scale)
+ {
+ int do_max = Numeric->scale == UMFPACK_SCALE_MAX ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Rs [row] = 0.0 ;
+ }
+ for (col = 0 ; col < n_col ; col++)
+ {
+ ilast = EMPTY ;
+ p1 = Ap [col] ;
+ p2 = Ap [col+1] ;
+ if (p1 > p2)
+ {
+ /* invalid matrix */
+ DEBUGm4 (("invalid matrix (Ap)\n")) ;
+ return (FALSE) ;
+ }
+ for (p = p1 ; p < p2 ; p++)
+ {
+ Entry aij ;
+ double value ;
+ row = Ai [p] ;
+ if (row <= ilast || row >= n_row)
+ {
+ /* invalid matrix, columns must be sorted, no duplicates */
+ DEBUGm4 (("invalid matrix (Ai)\n")) ;
+ return (FALSE) ;
+ }
+ ASSIGN (aij, Ax, Az, p, split) ;
+ APPROX_ABS (value, aij) ;
+ rs = Rs [row] ;
+ if (!SCALAR_IS_NAN (rs))
+ {
+ if (SCALAR_IS_NAN (value))
+ {
+ /* if any entry in the row is NaN, then the scale factor
+ * is NaN too (for now) and then set to 1.0 below */
+ Rs [row] = value ;
+ }
+ else if (do_max)
+ {
+ Rs [row] = MAX (rs, value) ;
+ }
+ else
+ {
+ Rs [row] += value ;
+ }
+ }
+ DEBUG4 (("i "ID" j "ID" value %g, Rs[i]: %g\n",
+ row, col, value, Rs[row])) ;
+ ilast = row ;
+ }
+ }
+ DEBUG2 (("Rs[0] = %30.20e\n", Rs [0])) ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ rs = Rs [row] ;
+ if (SCALAR_IS_ZERO (rs) || SCALAR_IS_NAN (rs))
+ {
+ /* don't scale a completely zero row, or one with NaN's */
+ Rs [row] = 1.0 ;
+ }
+ }
+ rsmin = Rs [0] ;
+ rsmax = Rs [0] ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ DEBUG2 (("sum %30.20e ", Rs [row])) ;
+ rsmin = MIN (rsmin, Rs [row]) ;
+ rsmax = MAX (rsmax, Rs [row]) ;
+ DEBUG2 (("Rs["ID"] = %30.20e\n", row, Rs [row])) ;
+ }
+#ifndef NRECIPROCAL
+ /* multiply by the reciprocal if Rs is not too small */
+ do_recip = (rsmin >= RECIPROCAL_TOLERANCE) ;
+ if (do_recip)
+ {
+ /* invert the scale factors */
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Rs [row] = 1.0 / Rs [row] ;
+ }
+ }
+#endif
+ }
+ else
+ {
+ /* no scaling, rsmin and rsmax not computed */
+ rsmin = -1 ;
+ rsmax = -1 ;
+#ifndef NRECIPROCAL
+ do_recip = FALSE ;
+#endif
+ /* check the input matrix */
+ if (AMD_valid (n_row, n_col, Ap, Ai) != AMD_OK)
+ {
+ /* matrix is invalid */
+ return (FALSE) ;
+ }
+ }
+
+ Numeric->rsmin = rsmin ;
+ Numeric->rsmax = rsmax ;
+#ifndef NRECIPROCAL
+ Numeric->do_recip = do_recip ;
+#else
+ Numeric->do_recip = FALSE ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the inverse row Rperm_init permutation (use Frpos as temp) */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG3 (("\n\n===================LOAD_MATRIX:\n")) ;
+
+ for (newrow = 0 ; newrow < n_row ; newrow++)
+ {
+ oldrow = Rperm_init [newrow] ;
+ ASSERT (oldrow >= 0 && oldrow < n_row) ;
+ Frpos [oldrow] = newrow ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the diagonal imap if doing symmetric pivoting */
+ /* ---------------------------------------------------------------------- */
+
+ if (prefer_diagonal)
+ {
+ ASSERT (n_row == n_col) ;
+ ASSERT (nempty_col == Symbolic->nempty_row) ;
+ ASSERT (nempty_col == nempty) ;
+ for (i = 0 ; i < nn ; i++)
+ {
+ Diagonal_map [i] = EMPTY ;
+ Diagonal_imap [i] = EMPTY ;
+ }
+ for (k = n1 ; k < nn - nempty ; k++)
+ {
+ newrow = Symbolic->Diagonal_map [k] ;
+ Diagonal_map [k] = newrow ;
+ Diagonal_imap [newrow] = k ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate O (n_row) workspace at the tail end of Memory */
+ /* ---------------------------------------------------------------------- */
+
+ rpi = UMF_mem_alloc_tail_block (Numeric, UNITS (Int *, n_row+1)) ;
+ rpx = UMF_mem_alloc_tail_block (Numeric, UNITS (Entry *, n_row+1)) ;
+ if (!rpi || !rpx)
+ {
+ /* :: pattern change (out of memory for Rpx, Rpx) :: */
+ /* out of memory, which can only mean that the pattern has changed */
+ return (FALSE) ; /* pattern changed */
+ }
+ Rpi = (Int **) (Memory + rpx) ;
+ Rpx = (Entry **) (Memory + rpi) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the LU factors for the columns of the singletons */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG1 (("Allocating singletons:\n")) ;
+ for (k = 0 ; k < n1 ; k++)
+ {
+ lnz = Cdeg [k] - 1 ;
+ unz = Rdeg [k] - 1 ;
+
+ DEBUG1 (("Singleton k "ID" pivrow "ID" pivcol "ID" cdeg "ID" rdeg "
+ ID"\n", k, Rperm_init [k], Cperm_init [k], Cdeg [k], Rdeg [k])) ;
+ ASSERT (unz >= 0 && lnz >= 0 && (lnz == 0 || unz == 0)) ;
+ DEBUG1 ((" lnz "ID" unz "ID"\n", lnz, unz)) ;
+
+ size = UNITS (Int, lnz) + UNITS (Entry, lnz)
+ + UNITS (Int, unz) + UNITS (Entry, unz) ;
+ p = UMF_mem_alloc_head_block (Numeric, size) ;
+ DEBUG1 (("Kernel init head usage: "ID"\n", Numeric->ihead)) ;
+ if (!p)
+ {
+ /* :: pattern change (out of memory for singletons) :: */
+ DEBUG0 (("Pattern has gotten larger - kernel init failed\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+
+ Numeric->all_lnz += lnz ;
+ Numeric->all_unz += unz ;
+
+ /* allocate the column of L */
+ lip = p ;
+ p += UNITS (Int, lnz) ;
+ p += UNITS (Entry, lnz) ;
+
+ /* allocate the row of U */
+ uip = p ;
+ Rpi [k] = (Int *) (Memory + p) ;
+ p += UNITS (Int, unz) ;
+ Rpx [k] = (Entry *) (Memory + p) ;
+ /* p += UNITS (Entry, unz) ; (not needed) */
+
+ /* a single column of L (no Lchains) */
+ Lip [k] = lip ;
+ Lilen [k] = lnz ;
+
+ /* a single row of L (no Uchains) */
+ Uip [k] = uip ;
+ Uilen [k] = unz ;
+
+ Wp [k] = unz ;
+
+ /* save row and column inverse permutation */
+ k1 = ONES_COMPLEMENT (k) ;
+ Rperm [k] = k1 ; /* aliased with Row_degree */
+ Cperm [k] = k1 ; /* aliased with Col_degree */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* current frontal matrix is empty */
+ /* ---------------------------------------------------------------------- */
+
+ e = 0 ;
+ E [e] = 0 ;
+ Work->Flublock = (Entry *) NULL ;
+ Work->Flblock = (Entry *) NULL ;
+ Work->Fublock = (Entry *) NULL ;
+ Work->Fcblock = (Entry *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the column elements */
+ /* ---------------------------------------------------------------------- */
+
+ Esize = Symbolic->Esize ;
+ empty_elements = FALSE ;
+ for (k = n1 ; k < n_col - nempty_col ; k++)
+ {
+ e = k - n1 + 1 ;
+ ASSERT (e < Work->elen) ;
+ esize = Esize ? Esize [k-n1] : Cdeg [k] ;
+ if (esize > 0)
+ {
+ /* allocate an element for this column */
+ E [e] = UMF_mem_alloc_element (Numeric, esize, 1, &Rows, &Cols, &C,
+ &size, &ep) ;
+ if (E [e] <= 0)
+ {
+ /* :: pattern change (out of memory for column elements) :: */
+ return (FALSE) ; /* pattern has changed */
+ }
+ Cols [0] = k ;
+ DEBUG0 (("Got column element e "ID" esize "ID"\n", e, esize)) ;
+ }
+ else
+ {
+ /* all rows in this column are dense, or empty */
+ E [e] = 0 ;
+ empty_elements = TRUE ;
+ DEBUG0 (("column element e is empty "ID"\n", e)) ;
+ }
+ }
+ DEBUG0 (("e "ID" n_col "ID" nempty_col "ID" n1 "ID"\n", e, n_col,
+ nempty_col, n1)) ;
+ ASSERT (e == n_col - nempty_col - n1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the row elements for dense rows of A (if any) */
+ /* ---------------------------------------------------------------------- */
+
+ if (Esize)
+ {
+ for (k = n1 ; k < n_row - nempty_row ; k++)
+ {
+ rdeg = Rdeg [k] ;
+ if (rdeg > dense_row_threshold)
+ {
+ /* allocate an element for this dense row */
+ e++ ;
+ ASSERT (e < Work->elen) ;
+ E [e] = UMF_mem_alloc_element (Numeric, 1, rdeg, &Rows, &Cols,
+ &C, &size, &ep) ;
+ if (E [e] <= 0)
+ {
+ /* :: pattern change (out of memory for row elements) :: */
+ return (FALSE) ; /* pattern has changed */
+ }
+ Rows [0] = k ;
+ Rpi [k] = Cols ;
+ Rpx [k] = C ;
+ Wp [k] = rdeg ;
+ DEBUG0 (("Got row element e "ID" rdeg "ID"\n", e, rdeg)) ;
+ }
+ }
+ }
+
+ /* elements are currently in the range 0 to e */
+ Work->nel = e ;
+
+ /* ---------------------------------------------------------------------- */
+ /* create the first n1 columns of L and U */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ pivcol = Cperm_init [k] ;
+ p2 = Ap [pivcol+1] ;
+
+ /* get the kth column of L */
+ p = Lip [k] ;
+ Li = (Int *) (Memory + p) ;
+ lilen = Lilen [k] ;
+ p += UNITS (Int, lilen) ;
+ Lval = (Entry *) (Memory + p) ;
+
+ llen = 0 ;
+
+ for (pa = Ap [pivcol] ; pa < p2 ; pa++)
+ {
+ oldrow = Ai [pa] ;
+ newrow = Frpos [oldrow] ;
+ ASSIGN (x, Ax, Az, pa, split) ;
+
+ /* scale the value using the scale factors, Rs */
+ if (do_scale)
+ {
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ SCALE (x, Rs [oldrow]) ;
+ }
+ else
+#endif
+ {
+ SCALE_DIV (x, Rs [oldrow]) ;
+ }
+ }
+
+ if (newrow == k)
+ {
+ /* this is the pivot entry itself */
+ ASSERT (oldrow == Rperm_init [k]) ;
+ D [k] = x ;
+ }
+ else if (newrow < k)
+ {
+ /* this entry goes in a row of U */
+ DEBUG1 (("Singleton row of U: k "ID" newrow "ID"\n",
+ k, newrow)) ;
+ if (--(Wp [newrow]) < 0)
+ {
+ /* :: pattern change (singleton row too lengthy) :: */
+ DEBUGm4 (("bad U singleton row (too lengthy)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ *(Rpi [newrow]++) = k ;
+ *(Rpx [newrow]++) = x ;
+ }
+ else
+ {
+ /* this entry goes in a column of L */
+ DEBUG1 (("Singleton col of L: k "ID" newrow "ID"\n",
+ k, newrow)) ;
+ if (llen >= lilen)
+ {
+ DEBUGm4 (("bad L singleton col (too lengthy)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ Li [llen] = newrow ;
+ Lval [llen] = x ;
+ llen++ ;
+ }
+ }
+
+ if (llen != lilen)
+ {
+ /* :: pattern change (singleton column too lengthy) :: */
+ DEBUGm4 (("bad L singleton col (too short)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+
+ /* scale the column of L */
+ if (llen > 0)
+ {
+ pivot_value = D [k] ;
+ UMF_scale (llen, pivot_value, Lval) ;
+ }
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the elements and copy the columns of A */
+ /* ---------------------------------------------------------------------- */
+
+ /* also apply the row and column pre-ordering. */
+ for (k = n1 ; k < n_col ; k++)
+ {
+ /* The newcol is k, which is what the name of the column is in the
+ * UMFPACK kernel. The user's name for the column is oldcol. */
+ oldcol = Cperm_init [k] ;
+
+ ASSERT (oldcol >= 0 && oldcol < n_col) ;
+
+ p2 = Ap [oldcol+1] ;
+
+ cdeg = Cdeg [k] ;
+ ASSERT (cdeg >= 0) ;
+ ASSERT (IMPLIES (
+ (Symbolic->ordering != UMFPACK_ORDERING_GIVEN) && n1 > 0,
+ cdeg > 1 || cdeg == 0)) ;
+
+ /* if fixQ: set Col_degree to 0 for the NON_PIVOTAL_COL macro */
+ Col_degree [k] = fixQ ? 0 : cdeg ;
+
+ /* get the element for this column (if any) */
+ e = k - n1 + 1 ;
+ if (k < n_col - nempty_col)
+ {
+ esize = Esize ? Esize [k-n1] : cdeg ;
+ if (E [e])
+ {
+ Int ncols, nrows ;
+ Unit *pp ;
+ pp = Memory + E [e] ;
+ GET_ELEMENT (ep, pp, Cols, Rows, ncols, nrows, C) ;
+ ASSERT (ncols == 1) ;
+ ASSERT (nrows == esize) ;
+ ASSERT (Cols [0] == k) ;
+ }
+ }
+ else
+ {
+ ASSERT (cdeg == 0) ;
+ esize = 0 ;
+ }
+
+ clen = 0 ;
+
+ for (pa = Ap [oldcol] ; pa < p2 ; pa++)
+ {
+ oldrow = Ai [pa] ;
+ newrow = Frpos [oldrow] ;
+ ASSIGN (x, Ax, Az, pa, split) ;
+
+ /* scale the value using the scale factors, Rs */
+ if (do_scale)
+ {
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the reciprocal */
+ SCALE (x, Rs [oldrow]) ;
+ }
+ else
+#endif
+ {
+ /* divide instead */
+ SCALE_DIV (x, Rs [oldrow]) ;
+ }
+ }
+
+ rdeg = Rdeg [newrow] ;
+ if (newrow < n1 || rdeg > dense_row_threshold)
+ {
+ /* this entry goes in a row of U or into a dense row */
+ DEBUG1 (("Singleton/dense row of U: k "ID" newrow "ID"\n",
+ k, newrow)) ;
+ if (--(Wp [newrow]) < 0)
+ {
+ DEBUGm4 (("bad row of U or A (too lengthy)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ *(Rpi [newrow]++) = k ;
+ *(Rpx [newrow]++) = x ;
+ }
+ else
+ {
+ /* this entry goes in an initial element */
+ DEBUG1 (("In element k "ID" e "ID" newrow "ID"\n",
+ k, e, newrow)) ;
+ if (clen >= esize)
+ {
+ DEBUGm4 (("bad A column (too lengthy)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ ASSERT (E [e]) ;
+ ASSERT (k < n_col - nempty_col) ;
+ Rows [clen] = newrow ;
+ C [clen] = x ;
+ clen++ ;
+#ifndef NDEBUG
+ if (Diagonal_map && (newrow == Diagonal_map [k]))
+ {
+ DEBUG0 (("Diagonal: old: row "ID" col "ID" : "
+ "new: row "ID" col "ID" : ",
+ oldrow, oldcol, newrow, k)) ;
+ EDEBUGk (0, x) ;
+ }
+#endif
+ }
+ }
+
+ if (clen != esize)
+ {
+ /* :: pattern change (singleton column too short) :: */
+ DEBUGm4 (("bad A column (too short)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the Rpi and Rpx workspace at the tail end of memory */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_mem_free_tail_block (Numeric, rpi) ;
+ UMF_mem_free_tail_block (Numeric, rpx) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* prune zeros and small entries from the singleton rows and columns */
+ /* ---------------------------------------------------------------------- */
+
+ if (n1 > 0)
+ {
+ pnew = Lip [0] ;
+ ASSERT (pnew == 1) ;
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUGm4 (("\nPrune singleton L col "ID"\n", k)) ;
+ pnew = packsp (pnew, &Lip [k], &Lilen [k], drop, droptol, Memory) ;
+ Numeric->lnz += Lilen [k] ;
+ DEBUGm4 (("\nPrune singleton U row "ID"\n", k)) ;
+ pnew = packsp (pnew, &Uip [k], &Uilen [k], drop, droptol, Memory) ;
+ Numeric->unz += Uilen [k] ;
+ }
+ /* free the unused space at the head of memory */
+ Numeric->ihead = pnew ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize row degrees */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ if (Wp [k] != 0)
+ {
+ /* :: pattern change (singleton row too short) :: */
+ DEBUGm4 (("bad U singleton row (too short)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ }
+
+ for (k = n1 ; k < n_row ; k++)
+ {
+ DEBUG1 (("Initial row degree k "ID" oldrow "ID" Rdeg "ID"\n",
+ k, Rperm_init [k], Rdeg [k])) ;
+ rdeg = Rdeg [k] ;
+ Row_degree [k] = rdeg ;
+ if (rdeg > dense_row_threshold && Wp [k] != 0)
+ {
+ /* :: pattern change (dense row too short) :: */
+ DEBUGm4 (("bad dense row (too short)\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+ }
+
+#ifndef NDEBUG
+ if (prefer_diagonal)
+ {
+ Entry aij ;
+ Int *InvCperm, newcol ;
+ UMF_dump_diagonal_map (Diagonal_map, Diagonal_imap, n1, nn, nempty) ;
+ InvCperm = (Int *) malloc (n_col * sizeof (Int)) ;
+ ASSERT (InvCperm != (Int *) NULL) ;
+ for (newcol = 0 ; newcol < n_col ; newcol++)
+ {
+ oldcol = Cperm_init [newcol] ;
+ InvCperm [oldcol] = newcol ;
+ }
+ DEBUGm3 (("Diagonal of P2*A:\n")) ;
+ for (oldcol = 0 ; oldcol < n_col ; oldcol++)
+ {
+ newcol = InvCperm [oldcol] ;
+ for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = Frpos [oldrow] ;
+ ASSIGN (aij, Ax, Az, p, split) ;
+ if (newrow == Diagonal_map [newcol])
+ {
+ DEBUG0 (("old row "ID" col "ID" new row "ID" col "ID,
+ oldrow, oldcol, newrow, newcol)) ;
+ EDEBUGk (0, aij) ;
+ DEBUG0 ((" scaled ")) ;
+ if (do_scale)
+ {
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ SCALE (aij, Rs [oldrow]) ;
+ }
+ else
+#endif
+ {
+ SCALE_DIV (aij, Rs [oldrow]) ;
+ }
+ }
+ EDEBUGk (0, aij) ;
+ DEBUG0 (("\n")) ;
+ }
+ }
+ }
+ free (InvCperm) ;
+ }
+#endif
+
+ Col_degree [n_col] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* pack the element name space */
+ /* ---------------------------------------------------------------------- */
+
+ if (empty_elements)
+ {
+ Int e2 = 0 ;
+ DEBUG0 (("\n\n============= Packing element space\n")) ;
+ for (e = 1 ; e <= Work->nel ; e++)
+ {
+ if (E [e])
+ {
+ e2++ ;
+ E [e2] = E [e] ;
+ }
+ }
+ Work->nel = e2 ;
+ }
+
+#ifndef NDEBUG
+ DEBUG0 (("Number of initial elements: "ID"\n", Work->nel)) ;
+ for (e = 0 ; e <= Work->nel ; e++) UMF_dump_element (Numeric, Work,e,TRUE) ;
+#endif
+
+ for (e = Work->nel + 1 ; e < Work->elen ; e++)
+ {
+ E [e] = 0 ;
+ }
+
+ /* Frpos no longer needed */
+ for (row = 0 ; row <= n_row ; row++)
+ {
+ Frpos [row] = EMPTY ;
+ }
+
+ /* clear Wp */
+ for (i = 0 ; i <= nn ; i++)
+ {
+ Wp [i] = EMPTY ;
+ }
+
+ DEBUG1 (("Kernel init head usage: "ID"\n", Numeric->ihead)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* build the tuple lists */
+ /* ---------------------------------------------------------------------- */
+
+ /* if the memory usage changes, then the pattern has changed */
+
+ (void) UMF_tuple_lengths (Numeric, Work, &unused) ;
+ if (!UMF_build_tuples (Numeric, Work))
+ {
+ /* :: pattern change (out of memory in umf_build_tuples) :: */
+ /* We ran out of memory, which can only mean that */
+ /* the pattern (Ap and or Ai) has changed (gotten larger). */
+ DEBUG0 (("Pattern has gotten larger - build tuples failed\n")) ;
+ return (FALSE) ; /* pattern changed */
+ }
+
+ Numeric->init_usage = Numeric->max_usage ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the row merge sets */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i <= Symbolic->nfr ; i++)
+ {
+ Work->Front_new1strow [i] = Symbolic->Front_1strow [i] ;
+ }
+
+#ifndef NDEBUG
+ UMF_dump_rowmerge (Numeric, Symbolic, Work) ;
+ DEBUG6 (("Column form of original matrix:\n")) ;
+ UMF_dump_col_matrix (Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Ai, Ap, n_row, n_col, nz) ;
+ UMF_dump_memory (Numeric) ;
+ UMF_dump_matrix (Numeric, Work, FALSE) ;
+ DEBUG0 (("kernel init done...\n")) ;
+#endif
+
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umf_kernel_init.h b/UMFPACK/Source/umf_kernel_init.h
new file mode 100644
index 0000000..dc86d04
--- /dev/null
+++ b/UMFPACK/Source/umf_kernel_init.h
@@ -0,0 +1,18 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_kernel_init
+(
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
diff --git a/UMFPACK/Source/umf_kernel_wrapup.c b/UMFPACK/Source/umf_kernel_wrapup.c
new file mode 100644
index 0000000..d9c3cd5
--- /dev/null
+++ b/UMFPACK/Source/umf_kernel_wrapup.c
@@ -0,0 +1,467 @@
+/* ========================================================================== */
+/* === UMF_kernel_wrapup ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The matrix is factorized. Finish the LU data structure. */
+
+#include "umf_internal.h"
+#include "umf_kernel_wrapup.h"
+
+GLOBAL void UMF_kernel_wrapup
+(
+ NumericType *Numeric,
+ SymbolicType *Symbolic,
+ WorkType *Work
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry pivot_value ;
+ double d ;
+ Entry *D ;
+ Int i, k, col, row, llen, ulen, *ip, *Rperm, *Cperm, *Lilen, npiv, lp,
+ *Uilen, *Lip, *Uip, *Cperm_init, up, pivrow, pivcol, *Lpos, *Upos, *Wr,
+ *Wc, *Wp, *Frpos, *Fcpos, *Row_degree, *Col_degree, *Rperm_init,
+ n_row, n_col, n_inner, zero_pivot, nan_pivot, n1 ;
+
+#ifndef NDEBUG
+ UMF_dump_matrix (Numeric, Work, FALSE) ;
+#endif
+
+ DEBUG0 (("Kernel complete, Starting Kernel wrapup\n")) ;
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+ n_inner = MIN (n_row, n_col) ;
+ Rperm = Numeric->Rperm ;
+ Cperm = Numeric->Cperm ;
+ Lilen = Numeric->Lilen ;
+ Uilen = Numeric->Uilen ;
+ Upos = Numeric->Upos ;
+ Lpos = Numeric->Lpos ;
+ Lip = Numeric->Lip ;
+ Uip = Numeric->Uip ;
+ D = Numeric->D ;
+
+ npiv = Work->npiv ;
+ Numeric->npiv = npiv ;
+ Numeric->ulen = Work->ulen ;
+
+ ASSERT (n_row == Numeric->n_row) ;
+ ASSERT (n_col == Symbolic->n_col) ;
+ DEBUG0 (("Wrap-up: npiv "ID" ulen "ID"\n", npiv, Numeric->ulen)) ;
+ ASSERT (npiv <= n_inner) ;
+
+ /* this will be nonzero only if matrix is singular or rectangular */
+ ASSERT (IMPLIES (npiv == n_col, Work->ulen == 0)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the smallest and largest entries in D */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ pivot_value = D [k] ;
+ ABS (d, pivot_value) ;
+ zero_pivot = SCALAR_IS_ZERO (d) ;
+ nan_pivot = SCALAR_IS_NAN (d) ;
+
+ if (!zero_pivot)
+ {
+ /* the pivot is nonzero, but might be Inf or NaN */
+ Numeric->nnzpiv++ ;
+ }
+
+ if (k == 0)
+ {
+ Numeric->min_udiag = d ;
+ Numeric->max_udiag = d ;
+ }
+ else
+ {
+ /* min (abs (diag (U))) behaves as follows: If any entry is zero,
+ then the result is zero (regardless of the presence of NaN's).
+ Otherwise, if any entry is NaN, then the result is NaN.
+ Otherwise, the result is the smallest absolute value on the
+ diagonal of U.
+ */
+
+ if (SCALAR_IS_NONZERO (Numeric->min_udiag))
+ {
+ if (zero_pivot || nan_pivot)
+ {
+ Numeric->min_udiag = d ;
+ }
+ else if (!SCALAR_IS_NAN (Numeric->min_udiag))
+ {
+ /* d and min_udiag are both non-NaN */
+ Numeric->min_udiag = MIN (Numeric->min_udiag, d) ;
+ }
+ }
+
+ /*
+ max (abs (diag (U))) behaves as follows: If any entry is NaN
+ then the result is NaN. Otherise, the result is the largest
+ absolute value on the diagonal of U.
+ */
+
+ if (nan_pivot)
+ {
+ Numeric->max_udiag = d ;
+ }
+ else if (!SCALAR_IS_NAN (Numeric->max_udiag))
+ {
+ /* d and max_udiag are both non-NaN */
+ Numeric->max_udiag = MAX (Numeric->max_udiag, d) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* check if matrix is singular or rectangular */
+ /* ---------------------------------------------------------------------- */
+
+ Col_degree = Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Rperm ; /* for NON_PIVOTAL_ROW macro */
+
+ if (npiv < n_row)
+ {
+ /* finalize the row permutation */
+ k = npiv ;
+ DEBUGm3 (("Singular pivot rows "ID" to "ID"\n", k, n_row-1)) ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (NON_PIVOTAL_ROW (row))
+ {
+ Rperm [row] = ONES_COMPLEMENT (k) ;
+ DEBUGm3 (("Singular row "ID" is k: "ID" pivot row\n", row, k)) ;
+ ASSERT (!NON_PIVOTAL_ROW (row)) ;
+ Lpos [row] = EMPTY ;
+ Uip [row] = EMPTY ;
+ Uilen [row] = 0 ;
+ k++ ;
+ }
+ }
+ ASSERT (k == n_row) ;
+ }
+
+ if (npiv < n_col)
+ {
+ /* finalize the col permutation */
+ k = npiv ;
+ DEBUGm3 (("Singular pivot cols "ID" to "ID"\n", k, n_col-1)) ;
+ for (col = 0 ; col < n_col ; col++)
+ {
+ if (NON_PIVOTAL_COL (col))
+ {
+ Cperm [col] = ONES_COMPLEMENT (k) ;
+ DEBUGm3 (("Singular col "ID" is k: "ID" pivot row\n", col, k)) ;
+ ASSERT (!NON_PIVOTAL_COL (col)) ;
+ Upos [col] = EMPTY ;
+ Lip [col] = EMPTY ;
+ Lilen [col] = 0 ;
+ k++ ;
+ }
+ }
+ ASSERT (k == n_col) ;
+ }
+
+ if (npiv < n_inner)
+ {
+ /* finalize the diagonal of U */
+ DEBUGm3 (("Diag of U is zero, "ID" to "ID"\n", npiv, n_inner-1)) ;
+ for (k = npiv ; k < n_inner ; k++)
+ {
+ CLEAR (D [k]) ;
+ }
+ }
+
+ /* save the pattern of the last row of U */
+ if (Numeric->ulen > 0)
+ {
+ DEBUGm3 (("Last row of U is not empty\n")) ;
+ Numeric->Upattern = Work->Upattern ;
+ Work->Upattern = (Int *) NULL ;
+ }
+
+ DEBUG2 (("Nnzpiv: "ID" npiv "ID"\n", Numeric->nnzpiv, npiv)) ;
+ ASSERT (Numeric->nnzpiv <= npiv) ;
+ if (Numeric->nnzpiv < n_inner && !SCALAR_IS_NAN (Numeric->min_udiag))
+ {
+ /* the rest of the diagonal is zero, so min_udiag becomes 0,
+ * unless it is already NaN. */
+ Numeric->min_udiag = 0.0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* size n_row, n_col workspaces that can be used here: */
+ /* ---------------------------------------------------------------------- */
+
+ Frpos = Work->Frpos ; /* of size n_row+1 */
+ Fcpos = Work->Fcpos ; /* of size n_col+1 */
+ Wp = Work->Wp ; /* of size MAX(n_row,n_col)+1 */
+ /* Work->Upattern ; cannot be used (in Numeric) */
+ Wr = Work->Lpattern ; /* of size n_row+1 */
+ Wc = Work->Wrp ; /* of size n_col+1 or bigger */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct Rperm from inverse permutations */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Frpos for temporary copy of inverse row permutation [ */
+
+ for (pivrow = 0 ; pivrow < n_row ; pivrow++)
+ {
+ k = Rperm [pivrow] ;
+ ASSERT (k < 0) ;
+ k = ONES_COMPLEMENT (k) ;
+ ASSERT (k >= 0 && k < n_row) ;
+ Wp [k] = pivrow ;
+ Frpos [pivrow] = k ;
+ }
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Rperm [k] = Wp [k] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct Cperm from inverse permutation */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Fcpos for temporary copy of inverse column permutation [ */
+
+ for (pivcol = 0 ; pivcol < n_col ; pivcol++)
+ {
+ k = Cperm [pivcol] ;
+ ASSERT (k < 0) ;
+ k = ONES_COMPLEMENT (k) ;
+ ASSERT (k >= 0 && k < n_col) ;
+ Wp [k] = pivcol ;
+ /* save a copy of the inverse column permutation in Fcpos */
+ Fcpos [pivcol] = k ;
+ }
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Cperm [k] = Wp [k] ;
+ }
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n_col ; k++)
+ {
+ col = Cperm [k] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (Fcpos [col] == k) ; /* col is the kth pivot */
+ }
+ for (k = 0 ; k < n_row ; k++)
+ {
+ row = Rperm [k] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == k) ; /* row is the kth pivot */
+ }
+#endif
+
+#ifndef NDEBUG
+ UMF_dump_lu (Numeric) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* permute Lpos, Upos, Lilen, Lip, Uilen, and Uip */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ pivrow = Rperm [k] ;
+ Wr [k] = Uilen [pivrow] ;
+ Wp [k] = Uip [pivrow] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ Uilen [k] = Wr [k] ;
+ Uip [k] = Wp [k] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ pivrow = Rperm [k] ;
+ Wp [k] = Lpos [pivrow] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ Lpos [k] = Wp [k] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ pivcol = Cperm [k] ;
+ Wc [k] = Lilen [pivcol] ;
+ Wp [k] = Lip [pivcol] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ Lilen [k] = Wc [k] ;
+ Lip [k] = Wp [k] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ pivcol = Cperm [k] ;
+ Wp [k] = Upos [pivcol] ;
+ }
+
+ for (k = 0 ; k < npiv ; k++)
+ {
+ Upos [k] = Wp [k] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* terminate the last Uchain and last Lchain */
+ /* ---------------------------------------------------------------------- */
+
+ Upos [npiv] = EMPTY ;
+ Lpos [npiv] = EMPTY ;
+ Uip [npiv] = EMPTY ;
+ Lip [npiv] = EMPTY ;
+ Uilen [npiv] = 0 ;
+ Lilen [npiv] = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert U to the new pivot order */
+ /* ---------------------------------------------------------------------- */
+
+ n1 = Symbolic->n1 ;
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ /* this is a singleton row of U */
+ ulen = Uilen [k] ;
+ DEBUG4 (("K "ID" New U. ulen "ID" Singleton 1\n", k, ulen)) ;
+ if (ulen > 0)
+ {
+ up = Uip [k] ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (i = 0 ; i < ulen ; i++)
+ {
+ col = *ip ;
+ DEBUG4 ((" old col "ID" new col "ID"\n", col, Fcpos [col]));
+ ASSERT (col >= 0 && col < n_col) ;
+ *ip++ = Fcpos [col] ;
+ }
+ }
+ }
+
+ for (k = n1 ; k < npiv ; k++)
+ {
+ up = Uip [k] ;
+ if (up < 0)
+ {
+ /* this is the start of a new Uchain (with a pattern) */
+ ulen = Uilen [k] ;
+ DEBUG4 (("K "ID" New U. ulen "ID" End_Uchain 1\n", k, ulen)) ;
+ if (ulen > 0)
+ {
+ up = -up ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (i = 0 ; i < ulen ; i++)
+ {
+ col = *ip ;
+ DEBUG4 ((" old col "ID" new col "ID"\n", col, Fcpos [col]));
+ ASSERT (col >= 0 && col < n_col) ;
+ *ip++ = Fcpos [col] ;
+ }
+ }
+ }
+ }
+
+ ulen = Numeric->ulen ;
+ if (ulen > 0)
+ {
+ /* convert last pivot row of U to the new pivot order */
+ DEBUG4 (("K "ID" (last)\n", k)) ;
+ for (i = 0 ; i < ulen ; i++)
+ {
+ col = Numeric->Upattern [i] ;
+ DEBUG4 ((" old col "ID" new col "ID"\n", col, Fcpos [col])) ;
+ Numeric->Upattern [i] = Fcpos [col] ;
+ }
+ }
+
+ /* Fcpos no longer needed ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* convert L to the new pivot order */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ llen = Lilen [k] ;
+ DEBUG4 (("K "ID" New L. llen "ID" Singleton col\n", k, llen)) ;
+ if (llen > 0)
+ {
+ lp = Lip [k] ;
+ ip = (Int *) (Numeric->Memory + lp) ;
+ for (i = 0 ; i < llen ; i++)
+ {
+ row = *ip ;
+ DEBUG4 ((" old row "ID" new row "ID"\n", row, Frpos [row])) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ *ip++ = Frpos [row] ;
+ }
+ }
+ }
+
+ for (k = n1 ; k < npiv ; k++)
+ {
+ llen = Lilen [k] ;
+ DEBUG4 (("K "ID" New L. llen "ID" \n", k, llen)) ;
+ if (llen > 0)
+ {
+ lp = Lip [k] ;
+ if (lp < 0)
+ {
+ /* this starts a new Lchain */
+ lp = -lp ;
+ }
+ ip = (Int *) (Numeric->Memory + lp) ;
+ for (i = 0 ; i < llen ; i++)
+ {
+ row = *ip ;
+ DEBUG4 ((" old row "ID" new row "ID"\n", row, Frpos [row])) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ *ip++ = Frpos [row] ;
+ }
+ }
+ }
+
+ /* Frpos no longer needed ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* combine symbolic and numeric permutations */
+ /* ---------------------------------------------------------------------- */
+
+ Cperm_init = Symbolic->Cperm_init ;
+ Rperm_init = Symbolic->Rperm_init ;
+
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Rperm [k] = Rperm_init [Rperm [k]] ;
+ }
+
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Cperm [k] = Cperm_init [Cperm [k]] ;
+ }
+
+ /* Work object will be freed immediately upon return (to UMF_kernel */
+ /* and then to UMFPACK_numeric). */
+}
diff --git a/UMFPACK/Source/umf_kernel_wrapup.h b/UMFPACK/Source/umf_kernel_wrapup.h
new file mode 100644
index 0000000..e3e8fbd
--- /dev/null
+++ b/UMFPACK/Source/umf_kernel_wrapup.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_kernel_wrapup
+(
+ NumericType *Numeric,
+ SymbolicType *Symbolic,
+ WorkType *Work
+) ;
diff --git a/UMFPACK/Source/umf_local_search.c b/UMFPACK/Source/umf_local_search.c
new file mode 100644
index 0000000..4e7cabe
--- /dev/null
+++ b/UMFPACK/Source/umf_local_search.c
@@ -0,0 +1,1953 @@
+/* ========================================================================== */
+/* === UMF_local_search ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Perform pivot search to find pivot row and pivot column.
+ The pivot column is selected from the candidate set. The candidate set
+ corresponds to a supercolumn from colamd or UMF_analyze. The pivot column
+ is then removed from that set. Constructs the pivot column pattern and
+ values. Called by umf_kernel. Returns UMFPACK_OK if successful, or
+ UMFPACK_WARNING_singular_matrix or UMFPACK_ERROR_different_pattern if not.
+*/
+
+#include "umf_internal.h"
+#include "umf_local_search.h"
+#include "umf_row_search.h"
+#include "umf_mem_free_tail_block.h"
+
+/* relaxed amalgamation control parameters are fixed at compile time */
+#define RELAX1 0.25
+#define SYM_RELAX1 0.0
+#define RELAX2 0.1
+#define RELAX3 0.125
+
+/* ========================================================================== */
+/* === remove_candidate ===================================================== */
+/* ========================================================================== */
+
+/* Remove a column from the set of candidate pivot columns. */
+
+PRIVATE void remove_candidate (Int jj, WorkType *Work, SymbolicType *Symbolic)
+{
+
+#ifndef NDEBUG
+ Int j ;
+ DEBUGm2 (("pivot column Candidates before remove: nCand "ID" ncand "ID
+ " lo "ID" hi "ID" jj "ID"\n", Work->nCandidates, Work->ncand,
+ Work->lo, Work->hi, jj)) ;
+ for (j = 0 ; j < Work->nCandidates ; j++)
+ {
+ Int col = Work->Candidates [j] ;
+ DEBUGm2 ((ID" ", col));
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ /* ASSERT (NON_PIVOTAL_COL (col)) ; */
+ ASSERT (col >= Work->lo && col <= Work->hi) ;
+ }
+ DEBUGm2 (("\n")) ;
+#endif
+
+ if (Symbolic->fixQ)
+ {
+ DEBUGm2 (("FixQ\n")) ;
+ /* do not modify the column ordering */
+ ASSERT (Work->nCandidates == 1) ;
+ ASSERT (jj == 0) ;
+ if (Work->ncand > 1)
+ {
+ Work->Candidates [0] = Work->nextcand++ ;
+ }
+ else
+ {
+ Work->nCandidates = 0 ;
+ }
+ }
+ else
+ {
+ /* place the next candidate in the set */
+ if (Work->ncand > MAX_CANDIDATES)
+ {
+ Work->Candidates [jj] = Work->nextcand++ ;
+ }
+ else
+ {
+ ASSERT (Work->nCandidates == Work->ncand) ;
+ Work->Candidates [jj] = Work->Candidates [Work->ncand - 1] ;
+ Work->Candidates [Work->ncand - 1] = EMPTY ;
+ Work->nCandidates-- ;
+ }
+ }
+ Work->ncand-- ;
+
+#ifndef NDEBUG
+ DEBUGm2 (("pivot column Candidates after remove: nCand "ID" ncand "ID
+ " lo "ID" hi "ID" jj "ID"\n", Work->nCandidates, Work->ncand, Work->lo,
+ Work->hi, jj)) ;
+ for (j = 0 ; j < Work->nCandidates ; j++)
+ {
+ Int col = Work->Candidates [j] ;
+ DEBUGm2 ((ID" ", col));
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ /* ASSERT (NON_PIVOTAL_COL (col)) ; */
+ ASSERT (col >= Work->lo && col <= Work->hi) ;
+ }
+ DEBUGm2 (("\n")) ;
+ ASSERT (Work->ncand >= 0) ;
+ ASSERT (Work->nCandidates <= Work->ncand) ;
+#endif
+}
+
+/* ========================================================================== */
+/* === UMF_local_search ===================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMF_local_search
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double relax1 ;
+ Entry *Flblock, *Fublock, *Fs, *Fcblock, *C, *Wx, *Wy, *Fu, *Flublock,
+ *Flu ;
+ Int pos, nrows, *Cols, *Rows, e, f, status, max_cdeg, fnzeros, nb, j, col,
+ i, row, cdeg_in, rdeg [2][2], fnpiv, nothing [2], new_LUsize,
+ pivrow [2][2], pivcol [2], *Wp, *Fcpos, *Frpos, new_fnzeros, cdeg_out,
+ *Wm, *Wio, *Woi, *Woo, *Frows, *Fcols, fnrows, fncols, *E, deg, nr_in,
+ nc, thiscost, bestcost, nr_out, do_update, extra_cols, extra_rows,
+ extra_zeros, relaxed_front, do_extend, fnr_curr, fnc_curr, tpi,
+ *Col_tuples, *Col_degree, *Col_tlen, jj, jcand [2], freebie [2],
+ did_rowmerge, fnrows_new [2][2], fncols_new [2][2], search_pivcol_out,
+ *Diagonal_map, *Diagonal_imap, row2, col2 ;
+ Unit *Memory, *p ;
+ Tuple *tp, *tpend, *tp1, *tp2 ;
+ Element *ep ;
+
+#ifndef NBLAS
+ Int blas_ok = TRUE ;
+#else
+#define blas_ok FALSE
+#endif
+
+#ifndef NDEBUG
+ Int debug_ok, n_row, n_col, *Row_degree ;
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro only */
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Memory = Numeric->Memory ;
+ E = Work->E ;
+ Col_degree = Numeric->Cperm ;
+
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+
+ Wx = Work->Wx ;
+ Wy = Work->Wy ;
+ Wp = Work->Wp ;
+ Wm = Work->Wm ;
+ Woi = Work->Woi ;
+ Wio = Work->Wio ;
+ Woo = Work->Woo ;
+ Fcpos = Work->Fcpos ;
+ Frpos = Work->Frpos ;
+ Frows = Work->Frows ;
+ Fcols = Work->Fcols ;
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ nb = Work->nb ;
+ fnr_curr = Work->fnr_curr ;
+ fnc_curr = Work->fnc_curr ;
+ fnpiv = Work->fnpiv ;
+ nothing [0] = EMPTY ;
+ nothing [1] = EMPTY ;
+ relax1 = (Symbolic->prefer_diagonal) ? SYM_RELAX1 : RELAX1 ;
+ fnzeros = Work->fnzeros ;
+ new_fnzeros = fnzeros ;
+ jj = EMPTY ;
+
+ Fcblock = Work->Fcblock ; /* current contribution block */
+ Flblock = Work->Flblock ; /* current L block */
+ Fublock = Work->Fublock ; /* current U block */
+ Flublock = Work->Flublock ; /* current LU block */
+
+ /* The pivot column degree cannot exceed max_cdeg */
+ max_cdeg = Work->fnrows_max ;
+ ASSERT (Work->fnrows_max <= Symbolic->maxnrows) ;
+ ASSERT (Work->fncols_max <= Symbolic->maxncols) ;
+
+ if (fnrows == 0 && fncols == 0)
+ {
+ /* frontal matrix is empty */
+ Work->firstsuper = Work->ksuper ;
+ }
+
+#ifndef NDEBUG
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ DEBUG2 (("\n========LOCAL SEARCH: current frontal matrix: ========= \n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+ if (UMF_debug > 0 || MAX (n_row, n_col) < 1000)
+ {
+ for (i = 0 ; i < MAX (n_row, n_col) ; i++)
+ {
+ ASSERT (Wp [i] < 0) ;
+ }
+ }
+
+ DEBUGm2 ((ID" pivot column Candidates: lo "ID" hi "ID"\n",
+ Work->nCandidates, Work->lo, Work->hi)) ;
+ for (j = 0 ; j < Work->nCandidates ; j++)
+ {
+ col = Work->Candidates [j] ;
+ DEBUGm2 ((ID" ", col));
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ ASSERT (col >= Work->lo && col <= Work->hi) ;
+ }
+
+ DEBUGm2 (("\n")) ;
+ /* there are no 0-by-c or r-by-0 fronts, where c and r are > 0 */
+ /* a front is either 0-by-0, or r-by-c */
+ DEBUG2 (("\n\n::: "ID" : Npiv: "ID" + fnpiv "ID" = "ID". "
+ "size "ID"-by-"ID"\n", Work->frontid,
+ Work->npiv, Work->fnpiv, Work->npiv + Work->fnpiv, fnrows, fncols)) ;
+ ASSERT ((fnrows == 0 && fncols == 0) ||(fnrows != 0 && fncols != 0)) ;
+#endif
+
+ /* ====================================================================== */
+ /* === PIVOT SEARCH ===================================================== */
+ /* ====================================================================== */
+
+ /* initialize */
+
+ pivcol [IN] = EMPTY ;
+ pivcol [OUT] = EMPTY ;
+
+ cdeg_in = Int_MAX ;
+ cdeg_out = Int_MAX ;
+
+ pivrow [IN][IN] = EMPTY ;
+ pivrow [IN][OUT] = EMPTY ;
+ pivrow [OUT][IN] = EMPTY ;
+ pivrow [OUT][OUT] = EMPTY ;
+
+ rdeg [IN][IN] = Int_MAX ;
+ rdeg [IN][OUT] = Int_MAX ;
+ rdeg [OUT][IN] = Int_MAX ;
+ rdeg [OUT][OUT] = Int_MAX ;
+
+ freebie [IN] = FALSE ;
+ freebie [OUT] = FALSE ;
+
+ Work->pivot_case = EMPTY ;
+ bestcost = EMPTY ;
+
+ nr_out = EMPTY ;
+ nr_in = EMPTY ;
+
+ jcand [IN] = EMPTY ;
+ jcand [OUT] = EMPTY ;
+
+ fnrows_new [IN][IN] = EMPTY ;
+ fnrows_new [IN][OUT] = EMPTY ;
+ fnrows_new [OUT][IN] = EMPTY ;
+ fnrows_new [OUT][OUT] = EMPTY ;
+
+ fncols_new [IN][IN] = EMPTY ;
+ fncols_new [IN][OUT] = EMPTY ;
+ fncols_new [OUT][IN] = EMPTY ;
+ fncols_new [OUT][OUT] = EMPTY ;
+
+#ifndef NDEBUG
+ /* check Frpos */
+ DEBUG4 (("Check Frpos : fnrows "ID" col "ID" maxcdeg "ID"\n",
+ fnrows, pivcol [IN], max_cdeg)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG4 ((" row: "ID"\n", row)) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == i) ;
+ }
+ DEBUG4 (("All:\n")) ;
+ if (UMF_debug > 0 || n_row < 1000)
+ {
+ Int cnt = fnrows ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (Frpos [row] == EMPTY)
+ {
+ cnt++ ;
+ }
+ else
+ {
+ DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ;
+ }
+ }
+ ASSERT (cnt == n_row) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* find shortest column in the front, and shortest column not in the */
+ /* front, from the candidate pivot column set */
+ /* ---------------------------------------------------------------------- */
+
+ /* If there are too many candidates, then only look at the first */
+ /* MAX_CANDIDATES of them. Otherwise, if there are O(n) candidates, */
+ /* this code could take O(n^2) time. */
+
+ /* ------------------------------------------------------------------ */
+ /* look in the candidate set for the best column */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG2 (("Max candidates %d, Work->ncand "ID" jmax "ID"\n",
+ MAX_CANDIDATES, Work->ncand, Work->nCandidates)) ;
+ col = Work->Candidates [0] ;
+ ASSERT (Work->nCandidates > 0) ;
+ DEBUG3 (("Pivot column candidate: "ID" j = "ID"\n", col, j)) ;
+ ASSERT (col >= 0 && col < n_col) ;
+
+ /* there is no Col_degree if fixQ is true */
+ deg = Symbolic->fixQ ? EMPTY : Col_degree [col] ;
+
+#ifndef NDEBUG
+ DEBUG3 (("Pivot column candidate: "ID" cost: "ID" Fcpos[col] "ID"\n",
+ col, deg, Fcpos [col])) ;
+ UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ;
+ if (Symbolic->fixQ)
+ {
+ DEBUG1 (("FIXQ: Candidates "ID" pivcol "ID" npiv "ID" fnpiv "ID
+ " ndiscard "ID "\n", Work->nCandidates, col, Work->npiv,
+ Work->fnpiv, Work->ndiscard)) ;
+ ASSERT (Work->nCandidates == 1) ;
+ ASSERT (col == Work->npiv + Work->fnpiv + Work->ndiscard) ;
+ }
+#endif
+
+ if (Fcpos [col] >= 0)
+ {
+ /* best column in front, so far */
+ pivcol [IN] = col ;
+ cdeg_in = deg ; /* ignored, if fixQ is true */
+ jcand [IN] = 0 ;
+ }
+ else
+ {
+ /* best column not in front, so far */
+ pivcol [OUT] = col ;
+ cdeg_out = deg ; /* ignored, if fixQ is true */
+ jcand [OUT] = 0 ;
+ }
+
+ /* look at the rest of the candidates */
+ for (j = 1 ; j < Work->nCandidates ; j++)
+ {
+ col = Work->Candidates [j] ;
+
+ DEBUG3 (("Pivot col candidate: "ID" j = "ID"\n", col, j)) ;
+ ASSERT (col >= 0 && col < n_col) ;
+ ASSERT (!Symbolic->fixQ) ;
+ deg = Col_degree [col] ;
+#ifndef NDEBUG
+ DEBUG3 (("Pivot col candidate: "ID" cost: "ID" Fcpos[col] "ID"\n",
+ col, deg, Fcpos [col])) ;
+ UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ;
+#endif
+ if (Fcpos [col] >= 0)
+ {
+#ifndef NDEBUG
+ Int fs ;
+ fs = Fcpos [col] / fnr_curr ;
+ ASSERT (fs >= 0 && fs < fncols) ;
+#endif
+ if (deg < cdeg_in || (deg == cdeg_in && col < pivcol [IN]))
+ {
+ /* best column in front, so far */
+ pivcol [IN] = col ;
+ cdeg_in = deg ;
+ jcand [IN] = j ;
+ }
+ }
+ else
+ {
+ if (deg < cdeg_out || (deg == cdeg_out && col < pivcol [OUT]))
+ {
+ /* best column not in front, so far */
+ pivcol [OUT] = col ;
+ cdeg_out = deg ;
+ jcand [OUT] = j ;
+ }
+ }
+ }
+
+ DEBUG2 (("Pivcol in "ID" out "ID"\n", pivcol [IN], pivcol [OUT])) ;
+ ASSERT ((pivcol [IN] >= 0 && pivcol [IN] < n_col)
+ || (pivcol [OUT] >= 0 && pivcol [OUT] < n_col)) ;
+
+ cdeg_in = EMPTY ;
+ cdeg_out = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct candidate column in front, and search for pivot rows */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ /* check Frpos */
+ DEBUG4 (("Prior to col update: fnrows "ID" col "ID" maxcdeg "ID"\n",
+ fnrows, pivcol [IN], max_cdeg)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG4 ((" row: "ID"\n", row)) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == i) ;
+ }
+ DEBUG4 (("All:\n")) ;
+ if (UMF_debug > 0 || n_row < 1000)
+ {
+ Int cnt = fnrows ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (Frpos [row] == EMPTY)
+ {
+ cnt++ ;
+ }
+ else
+ {
+ DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ;
+ }
+ }
+ ASSERT (cnt == n_row) ;
+ }
+#endif
+
+ if (pivcol [IN] != EMPTY)
+ {
+
+#ifndef NDEBUG
+ DEBUG2 (("col[IN] column "ID" in front at position = "ID"\n",
+ pivcol [IN], Fcpos [pivcol [IN]])) ;
+ UMF_dump_rowcol (1, Numeric, Work, pivcol [IN], !Symbolic->fixQ) ;
+#endif
+
+ /* the only way we can have a pivcol[IN] is if the front is not empty */
+ ASSERT (fnrows > 0 && fncols > 0) ;
+
+ DEBUG4 (("Update pivot column:\n")) ;
+ Fs = Fcblock + Fcpos [pivcol [IN]] ;
+ Fu = Fublock + (Fcpos [pivcol [IN]] / fnr_curr) ;
+ Flu = Flublock + fnpiv * nb ;
+
+ /* ------------------------------------------------------------------ */
+ /* copy the pivot column from the U block into the LU block */
+ /* ------------------------------------------------------------------ */
+
+ /* This copy is permanent if the pivcol [IN] is chosen. */
+ for (i = 0 ; i < fnpiv ; i++)
+ {
+ Flu [i] = Fu [i*fnc_curr] ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* update the pivot column in the LU block using a triangular solve */
+ /* ------------------------------------------------------------------ */
+
+ /* This work will be discarded if the pivcol [OUT] is chosen instead.
+ * It is permanent if the pivcol [IN] is chosen. */
+
+ if (fnpiv > 1)
+ {
+ /* solve Lx=b, where b = U (:,k), stored in the LU block */
+
+#ifndef NBLAS
+ BLAS_TRSV (fnpiv, Flublock, Flu, nb) ;
+#endif
+ if (!blas_ok)
+ {
+ /* use plain C code if no BLAS, or on integer overflow */
+ Entry *Flub = Flublock ;
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ Entry Fuj = Flu [j] ;
+#pragma ivdep
+ for (i = j+1 ; i < fnpiv ; i++)
+ {
+ /* Flu [i] -= Flublock [i + j*nb] * Flu [j] ; */
+ MULT_SUB (Flu [i], Flub [i], Fuj) ;
+ }
+ Flub += nb ;
+ }
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* copy the pivot column from the C block into Wy */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Wy [i] = Fs [i] ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* update the pivot column of L using a matrix-vector multiply */
+ /* ------------------------------------------------------------------ */
+
+ /* this work will be discarded if the pivcol [OUT] is chosen instead */
+
+#ifdef NBLAS
+ /* no BLAS available - use plain C code instead */
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ Entry Fuj, *Flub = Flblock + j * fnr_curr ;
+ Fuj = Flu [j] ;
+ if (IS_NONZERO (Fuj))
+ {
+#pragma ivdep
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ /* Wy [i] -= Flblock [i+j*fnr_curr] * Fuj ; */
+ MULT_SUB (Wy [i], Flub [i], Fuj) ;
+ }
+ }
+ /* Flblock += fnr_curr ; */
+ }
+#else
+ /* Using 1-based notation:
+ * Wy (1:fnrows) -= Flblock (1:fnrows,1:fnpiv) * Flu (1:fnpiv) */
+ BLAS_GEMV (fnrows, fnpiv, Flblock, Flu, Wy, fnr_curr) ;
+#endif
+
+ /* ------------------------------------------------------------------ */
+
+#ifndef NDEBUG
+ DEBUG2 (("Wy after update: fnrows="ID"\n", fnrows)) ;
+ DEBUG4 ((" fnpiv="ID" \n", fnpiv)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ DEBUG4 ((ID" "ID" "ID, i, Frows [i], Frpos [Frows [i]])) ;
+ EDEBUG4 (Wy [i]) ;
+ DEBUG4 (("\n")) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* construct the candidate column */
+ /* ------------------------------------------------------------------ */
+
+ cdeg_in = fnrows ;
+
+#ifndef NDEBUG
+ /* check Frpos */
+ DEBUG4 (("After col update: fnrows "ID" col "ID" maxcdeg "ID"\n",
+ fnrows, pivcol [IN], max_cdeg)) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG4 ((" row: "ID"\n", row)) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == i) ;
+ }
+ DEBUG4 (("All:\n")) ;
+ if (UMF_debug > 0 || n_row < 1000)
+ {
+ Int cnt = fnrows ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (Frpos [row] == EMPTY)
+ {
+ cnt++ ;
+ }
+ else
+ {
+ DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ;
+ }
+ }
+ ASSERT (cnt == n_row) ;
+ }
+#endif
+
+#ifndef NDEBUG
+ /* check Frpos */
+ DEBUG4 (("COL ASSEMBLE: cdeg "ID"\nREDUCE COL in "ID" max_cdeg "ID"\n",
+ cdeg_in, pivcol [IN], max_cdeg)) ;
+ for (i = 0 ; i < cdeg_in ; i++)
+ {
+ row = Frows [i] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == i) ;
+ }
+ if (UMF_debug > 0 || n_row < 1000)
+ {
+ Int cnt = cdeg_in ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (Frpos [row] == EMPTY) cnt++ ;
+ }
+ ASSERT (cnt == n_row) ;
+ }
+#endif
+
+ /* assemble column into Wy */
+
+ ASSERT (pivcol [IN] >= 0 && pivcol [IN] < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (pivcol [IN])) ;
+
+ tpi = Col_tuples [pivcol [IN]] ;
+ if (tpi)
+ {
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Col_tlen [pivcol [IN]] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ if (Cols [f] == EMPTY) continue ; /* column already assembled */
+ ASSERT (pivcol [IN] == Cols [f]) ;
+
+ Rows = Cols + ep->ncols ;
+ nrows = ep->nrows ;
+ p += UNITS (Int, ep->ncols + nrows) ;
+ C = ((Entry *) p) + f * nrows ;
+
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0) /* skip this if already gone from element */
+ {
+ ASSERT (row < n_row) ;
+ pos = Frpos [row] ;
+ if (pos < 0)
+ {
+ /* new entry in the pattern - save Frpos */
+ ASSERT (cdeg_in < n_row) ;
+ if (cdeg_in >= max_cdeg)
+ {
+ /* :: pattern change (cdeg in failure) :: */
+ DEBUGm4 (("cdeg_in failure\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Frpos [row] = cdeg_in ;
+ Frows [cdeg_in] = row ;
+ Wy [cdeg_in++] = C [i] ;
+ }
+ else
+ {
+ /* entry already in pattern - sum values in Wy */
+ /* Wy [pos] += C [i] ; */
+ ASSERT (pos < max_cdeg) ;
+ ASSEMBLE (Wy [pos], C [i]) ;
+ }
+ }
+ }
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Col_tlen [pivcol [IN]] = tp2 - tp1 ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+#ifndef NDEBUG
+ /* check Frpos again */
+ DEBUG4 (("COL DONE: cdeg "ID"\nREDUCE COL in "ID" max_cdeg "ID"\n",
+ cdeg_in, pivcol [IN], max_cdeg)) ;
+ for (i = 0 ; i < cdeg_in ; i++)
+ {
+ row = Frows [i] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (Frpos [row] == i) ;
+ }
+ if (UMF_debug > 0 || n_row < 1000)
+ {
+ Int cnt = cdeg_in ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (Frpos [row] == EMPTY) cnt++ ;
+ }
+ ASSERT (cnt == n_row) ;
+ }
+#endif
+
+#ifndef NDEBUG
+ DEBUG4 (("Reduced column: cdeg in "ID" fnrows_max "ID"\n",
+ cdeg_in, Work->fnrows_max)) ;
+ for (i = 0 ; i < cdeg_in ; i++)
+ {
+ DEBUG4 ((" "ID" "ID" "ID, i, Frows [i], Frpos [Frows [i]])) ;
+ EDEBUG4 (Wy [i]) ;
+ DEBUG4 (("\n")) ;
+ ASSERT (i == Frpos [Frows [i]]) ;
+ }
+ ASSERT (cdeg_in <= Work->fnrows_max) ;
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* cdeg_in is now the exact degree of this column */
+ /* ------------------------------------------------------------------ */
+
+ nr_in = cdeg_in - fnrows ;
+
+ /* since there are no 0-by-x fronts, if there is a pivcol [IN] the */
+ /* front must have at least one row. */
+ ASSERT (cdeg_in > 0) ;
+
+ /* new degree of pivcol [IN], excluding current front is nr_in */
+ /* column expands by nr_in rows */
+
+ /* ------------------------------------------------------------------ */
+ /* search for two candidate pivot rows */
+ /* ------------------------------------------------------------------ */
+
+ /* for the IN_IN pivot row (if any), */
+ /* extend the pattern in place, using Fcols */
+ status = UMF_row_search (Numeric, Work, Symbolic,
+ fnrows, cdeg_in, Frows, Frpos, /* pattern of column to search */
+ pivrow [IN], rdeg [IN], Fcols, Wio, nothing, Wy,
+ pivcol [IN], freebie) ;
+ ASSERT (!freebie [IN] && !freebie [OUT]) ;
+
+ /* ------------------------------------------------------------------ */
+ /* fatal error if matrix pattern has changed since symbolic analysis */
+ /* ------------------------------------------------------------------ */
+
+ if (status == UMFPACK_ERROR_different_pattern)
+ {
+ /* :: pattern change (row search IN failure) :: */
+ DEBUGm4 (("row search IN failure\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* we now must have a structural pivot */
+ /* ------------------------------------------------------------------ */
+
+ /* Since the pivcol[IN] exists, there must be at least one row in the */
+ /* current frontal matrix, and so we must have found a structural */
+ /* pivot. The numerical value might be zero, of course. */
+
+ ASSERT (status != UMFPACK_WARNING_singular_matrix) ;
+
+ /* ------------------------------------------------------------------ */
+ /* evaluate IN_IN option */
+ /* ------------------------------------------------------------------ */
+
+ if (pivrow [IN][IN] != EMPTY)
+ {
+ /* The current front would become an (implicit) LUson.
+ * Both candidate pivot row and column are in the current front.
+ * Cost is how much the current front would expand */
+
+ /* pivrow[IN][IN] candidates are not found via row merge search */
+
+ ASSERT (fnrows >= 0 && fncols >= 0) ;
+
+ ASSERT (cdeg_in > 0) ;
+ nc = rdeg [IN][IN] - fncols ;
+
+ thiscost =
+ /* each column in front (except pivot column) grows by nr_in: */
+ (nr_in * (fncols - 1)) +
+ /* new columns not in old front: */
+ (nc * (cdeg_in - 1)) ;
+
+ /* no extra cost to relaxed amalgamation */
+
+ ASSERT (fnrows + nr_in == cdeg_in) ;
+ ASSERT (fncols + nc == rdeg [IN][IN]) ;
+
+ /* size of relaxed front (after pivot row column removed): */
+ fnrows_new [IN][IN] = (fnrows-1) + nr_in ;
+ fncols_new [IN][IN] = (fncols-1) + nc ;
+ /* relaxed_front = fnrows_new [IN][IN] * fncols_new [IN][IN] ; */
+
+ do_extend = TRUE ;
+
+ DEBUG2 (("Evaluating option IN-IN:\n")) ;
+ DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_in "ID" nc "ID"\n",
+ Work->fnzeros, fnpiv, nr_in, nc)) ;
+ DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
+
+ /* determine if BLAS-3 update should be applied before extending. */
+ /* update if too many zero entries accumulate in the LU block */
+ fnzeros = Work->fnzeros + fnpiv * (nr_in + nc) ;
+
+ DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
+
+ new_LUsize = (fnpiv+1) * (fnrows + nr_in + fncols + nc) ;
+
+ DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
+
+ /* There are fnpiv pivots currently in the front. This one
+ * will be the (fnpiv+1)st pivot, if it is extended. */
+
+ /* RELAX2 parameter uses a double relop, but ignore NaN case: */
+ do_update = fnpiv > 0 &&
+ (((double) fnzeros) / ((double) new_LUsize)) > RELAX2 ;
+
+ DEBUG2 (("do_update "ID"\n", do_update))
+
+ DEBUG2 (("option IN IN : nr "ID" nc "ID" cost "ID"(0) relax "ID
+ "\n", nr_in, nc, thiscost, do_extend)) ;
+
+ /* this is the best option seen so far */
+ Work->pivot_case = IN_IN ;
+ bestcost = thiscost ;
+
+ /* do the amalgamation and extend the front */
+ Work->do_extend = do_extend ;
+ Work->do_update = do_update ;
+ new_fnzeros = fnzeros ;
+
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* evaluate IN_OUT option */
+ /* ------------------------------------------------------------------ */
+
+ if (pivrow [IN][OUT] != EMPTY)
+ {
+ /* The current front would become a Uson of the new front.
+ * Candidate pivot column is in the current front, but the
+ * candidate pivot row is not. */
+
+ ASSERT (fnrows >= 0 && fncols > 0) ;
+ ASSERT (cdeg_in > 0) ;
+
+ /* must be at least one row outside the front */
+ /* (the pivrow [IN][OUT] itself) */
+ ASSERT (nr_in >= 1) ;
+
+ /* count columns not in current front */
+ nc = 0 ;
+#ifndef NDEBUG
+ debug_ok = FALSE ;
+#endif
+ for (i = 0 ; i < rdeg [IN][OUT] ; i++)
+ {
+ col = Wio [i] ;
+ DEBUG4 (("counting col "ID" Fcpos[] = "ID"\n", col,
+ Fcpos [col])) ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ if (Fcpos [col] < 0) nc++ ;
+#ifndef NDEBUG
+ /* we must see the pivot column somewhere */
+ if (col == pivcol [IN])
+ {
+ ASSERT (Fcpos [col] >= 0) ;
+ debug_ok = TRUE ;
+ }
+#endif
+ }
+ ASSERT (debug_ok) ;
+
+ thiscost =
+ /* each row in front grows by nc: */
+ (nc * fnrows) +
+ /* new rows not affected by front: */
+ ((nr_in-1) * (rdeg [IN][OUT]-1)) ;
+
+ /* check the cost of relaxed IN_OUT amalgamation */
+
+ extra_cols = ((fncols-1) + nc ) - (rdeg [IN][OUT] - 1) ;
+ ASSERT (extra_cols >= 0) ;
+ ASSERT (fncols + nc == extra_cols + rdeg [IN][OUT]) ;
+ extra_zeros = (nr_in-1) * extra_cols ; /* symbolic fill-in */
+
+ ASSERT (fnrows + nr_in == cdeg_in) ;
+ ASSERT (fncols + nc == rdeg [IN][OUT] + extra_cols) ;
+
+ /* size of relaxed front (after pivot column removed): */
+ fnrows_new [IN][OUT] = fnrows + (nr_in-1) ;
+ fncols_new [IN][OUT] = (fncols-1) + nc ;
+ relaxed_front = fnrows_new [IN][OUT] * fncols_new [IN][OUT] ;
+
+ /* do relaxed amalgamation if the extra zeros are no more */
+ /* than a fraction (default 0.25) of the relaxed front */
+ /* if relax = 0: no extra zeros allowed */
+ /* if relax = +inf: always amalgamate */
+
+ /* relax parameter uses a double relop, but ignore NaN case: */
+ if (extra_zeros == 0)
+ {
+ do_extend = TRUE ;
+ }
+ else
+ {
+ do_extend = ((double) extra_zeros) <
+ (relax1 * (double) relaxed_front) ;
+ }
+
+ if (do_extend)
+ {
+ /* count the cost of relaxed amalgamation */
+ thiscost += extra_zeros ;
+
+ DEBUG2 (("Evaluating option IN-OUT:\n")) ;
+ DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_in "ID" nc "ID"\n",
+ Work->fnzeros, fnpiv, nr_in, nc)) ;
+ DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
+
+ /* determine if BLAS-3 update to be applied before extending. */
+ /* update if too many zero entries accumulate in the LU block */
+ fnzeros = Work->fnzeros + fnpiv * (nr_in + nc) ;
+
+ DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
+
+ new_LUsize = (fnpiv+1) * (fnrows + nr_in + fncols + nc) ;
+
+ DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
+
+ /* RELAX3 parameter uses a double relop, ignore NaN case: */
+ do_update = fnpiv > 0 &&
+ (((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ;
+ DEBUG2 (("do_update "ID"\n", do_update))
+
+ }
+ else
+ {
+ /* the current front would not be extended */
+ do_update = fnpiv > 0 ;
+ fnzeros = 0 ;
+ DEBUG2 (("IN-OUT do_update forced true: "ID"\n", do_update)) ;
+
+ /* The new front would be just big enough to hold the new
+ * pivot row and column. */
+ fnrows_new [IN][OUT] = cdeg_in - 1 ;
+ fncols_new [IN][OUT] = rdeg [IN][OUT] - 1 ;
+
+ }
+
+ DEBUG2 (("option IN OUT: nr "ID" nc "ID" cost "ID"("ID") relax "ID
+ "\n", nr_in, nc, thiscost, extra_zeros, do_extend)) ;
+
+ if (bestcost == EMPTY || thiscost < bestcost)
+ {
+ /* this is the best option seen so far */
+ Work->pivot_case = IN_OUT ;
+ bestcost = thiscost ;
+ Work->do_extend = do_extend ;
+ Work->do_update = do_update ;
+ new_fnzeros = fnzeros ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct candidate column not in front, and search for pivot rows */
+ /* ---------------------------------------------------------------------- */
+
+ search_pivcol_out = (bestcost != 0 && pivcol [OUT] != EMPTY) ;
+ if (Symbolic->prefer_diagonal)
+ {
+ search_pivcol_out = search_pivcol_out && (pivrow [IN][IN] == EMPTY) ;
+ }
+
+ if (search_pivcol_out)
+ {
+
+#ifndef NDEBUG
+ DEBUG2 (("out_col column "ID" NOT in front at position = "ID"\n",
+ pivcol [OUT], Fcpos [pivcol [OUT]])) ;
+ UMF_dump_rowcol (1, Numeric, Work, pivcol [OUT], !Symbolic->fixQ) ;
+ DEBUG2 (("fncols "ID" fncols_max "ID"\n", fncols, Work->fncols_max)) ;
+ ASSERT (fncols < Work->fncols_max) ;
+#endif
+
+ /* Use Wx as temporary workspace to construct the pivcol [OUT] */
+
+
+ /* ------------------------------------------------------------------ */
+ /* construct the candidate column (currently not in the front) */
+ /* ------------------------------------------------------------------ */
+
+ /* Construct the column in Wx, Wm, using Wp for the positions: */
+ /* Wm [0..cdeg_out-1] list of row indices in the column */
+ /* Wx [0..cdeg_out-1] list of corresponding numerical values */
+ /* Wp [0..n-1] starts as all negative, and ends that way too. */
+
+ cdeg_out = 0 ;
+
+#ifndef NDEBUG
+ /* check Wp */
+ DEBUG4 (("COL ASSEMBLE: cdeg 0\nREDUCE COL out "ID"\n", pivcol [OUT])) ;
+ if (UMF_debug > 0 || MAX (n_row, n_col) < 1000)
+ {
+ for (i = 0 ; i < MAX (n_row, n_col) ; i++)
+ {
+ ASSERT (Wp [i] < 0) ;
+ }
+ }
+ DEBUG4 (("max_cdeg: "ID"\n", max_cdeg)) ;
+#endif
+
+ ASSERT (pivcol [OUT] >= 0 && pivcol [OUT] < n_col) ;
+ ASSERT (NON_PIVOTAL_COL (pivcol [OUT])) ;
+
+ tpi = Col_tuples [pivcol [OUT]] ;
+ if (tpi)
+ {
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Col_tlen [pivcol [OUT]] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e]) continue ; /* element already deallocated */
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ if (Cols [f] == EMPTY) continue ; /* column already assembled */
+ ASSERT (pivcol [OUT] == Cols [f]) ;
+
+ Rows = Cols + ep->ncols ;
+ nrows = ep->nrows ;
+ p += UNITS (Int, ep->ncols + nrows) ;
+ C = ((Entry *) p) + f * nrows ;
+
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ if (row >= 0) /* skip this if already gone from element */
+ {
+ ASSERT (row < n_row) ;
+ pos = Wp [row] ;
+ if (pos < 0)
+ {
+ /* new entry in the pattern - save Wp */
+ ASSERT (cdeg_out < n_row) ;
+ if (cdeg_out >= max_cdeg)
+ {
+ /* :: pattern change (cdeg out failure) :: */
+ DEBUGm4 (("cdeg out failure\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Wp [row] = cdeg_out ;
+ Wm [cdeg_out] = row ;
+ Wx [cdeg_out++] = C [i] ;
+ }
+ else
+ {
+ /* entry already in pattern - sum the values */
+ /* Wx [pos] += C [i] ; */
+ ASSEMBLE (Wx [pos], C [i]) ;
+ }
+ }
+ }
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Col_tlen [pivcol [OUT]] = tp2 - tp1 ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+#ifndef NDEBUG
+ DEBUG4 (("Reduced column: cdeg out "ID"\n", cdeg_out)) ;
+ for (i = 0 ; i < cdeg_out ; i++)
+ {
+ DEBUG4 ((" "ID" "ID" "ID, i, Wm [i], Wp [Wm [i]])) ;
+ EDEBUG4 (Wx [i]) ;
+ DEBUG4 (("\n")) ;
+ ASSERT (i == Wp [Wm [i]]) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* new degree of pivcol [OUT] is cdeg_out */
+ /* ------------------------------------------------------------------ */
+
+ /* search for two candidate pivot rows */
+ status = UMF_row_search (Numeric, Work, Symbolic,
+ 0, cdeg_out, Wm, Wp, /* pattern of column to search */
+ pivrow [OUT], rdeg [OUT], Woi, Woo, pivrow [IN], Wx,
+ pivcol [OUT], freebie) ;
+
+ /* ------------------------------------------------------------------ */
+ /* fatal error if matrix pattern has changed since symbolic analysis */
+ /* ------------------------------------------------------------------ */
+
+ if (status == UMFPACK_ERROR_different_pattern)
+ {
+ /* :: pattern change detected in umf_local_search :: */
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* Clear Wp */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < cdeg_out ; i++)
+ {
+ Wp [Wm [i]] = EMPTY ; /* clear Wp */
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* check for rectangular, singular matrix */
+ /* ------------------------------------------------------------------ */
+
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ /* Pivot column is empty, and row-merge set is empty too. The
+ * matrix is structurally singular. The current frontal matrix must
+ * be empty, too. It it weren't, and pivcol [OUT] exists, then
+ * there would be at least one row that could be selected. Since
+ * the current front is empty, pivcol [IN] must also be EMPTY.
+ */
+
+ DEBUGm4 (("Note: pivcol [OUT]: "ID" discard\n", pivcol [OUT])) ;
+ ASSERT ((Work->fnrows == 0 && Work->fncols == 0)) ;
+ ASSERT (pivcol [IN] == EMPTY) ;
+
+ /* remove the failed pivcol [OUT] from candidate set */
+ ASSERT (pivcol [OUT] == Work->Candidates [jcand [OUT]]) ;
+ remove_candidate (jcand [OUT], Work, Symbolic) ;
+ Work->ndiscard++ ;
+
+ /* delete all of the tuples, and all contributions to this column */
+ DEBUG1 (("Prune tuples of dead outcol: "ID"\n", pivcol [OUT])) ;
+ Col_tlen [pivcol [OUT]] = 0 ;
+ UMF_mem_free_tail_block (Numeric, Col_tuples [pivcol [OUT]]) ;
+ Col_tuples [pivcol [OUT]] = 0 ;
+
+ /* no pivot found at all */
+ return (UMFPACK_WARNING_singular_matrix) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+ if (freebie [IN])
+ {
+ /* the "in" row is the same as the "in" row for the "in" column */
+ Woi = Fcols ;
+ rdeg [OUT][IN] = rdeg [IN][IN] ;
+ DEBUG4 (("Freebie in, row "ID"\n", pivrow [IN][IN])) ;
+ }
+
+ if (freebie [OUT])
+ {
+ /* the "out" row is the same as the "out" row for the "in" column */
+ Woo = Wio ;
+ rdeg [OUT][OUT] = rdeg [IN][OUT] ;
+ DEBUG4 (("Freebie out, row "ID"\n", pivrow [IN][OUT])) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* evaluate OUT_IN option */
+ /* ------------------------------------------------------------------ */
+
+ if (pivrow [OUT][IN] != EMPTY)
+ {
+ /* The current front would become an Lson of the new front.
+ * The candidate pivot row is in the current front, but the
+ * candidate pivot column is not. */
+
+ ASSERT (fnrows > 0 && fncols >= 0) ;
+
+ did_rowmerge = (cdeg_out == 0) ;
+ if (did_rowmerge)
+ {
+ /* pivrow [OUT][IN] was found via row merge search */
+ /* it is not (yet) in the pivot column pattern (add it now) */
+ DEBUGm4 (("did row merge OUT col, IN row\n")) ;
+ Wm [0] = pivrow [OUT][IN] ;
+ CLEAR (Wx [0]) ;
+ cdeg_out = 1 ;
+ ASSERT (nr_out == EMPTY) ;
+ }
+
+ nc = rdeg [OUT][IN] - fncols ;
+ ASSERT (nc >= 1) ;
+
+ /* count rows not in current front */
+ nr_out = 0 ;
+#ifndef NDEBUG
+ debug_ok = FALSE ;
+#endif
+ for (i = 0 ; i < cdeg_out ; i++)
+ {
+ row = Wm [i] ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ if (Frpos [row] < 0 || Frpos [row] >= fnrows) nr_out++ ;
+#ifndef NDEBUG
+ /* we must see the pivot row somewhere */
+ if (row == pivrow [OUT][IN])
+ {
+ ASSERT (Frpos [row] >= 0) ;
+ debug_ok = TRUE ;
+ }
+#endif
+ }
+ ASSERT (debug_ok) ;
+
+ thiscost =
+ /* each column in front grows by nr_out: */
+ (nr_out * fncols) +
+ /* new cols not affected by front: */
+ ((nc-1) * (cdeg_out-1)) ;
+
+ /* check the cost of relaxed OUT_IN amalgamation */
+
+ extra_rows = ((fnrows-1) + nr_out) - (cdeg_out - 1) ;
+ ASSERT (extra_rows >= 0) ;
+ ASSERT (fnrows + nr_out == extra_rows + cdeg_out) ;
+ extra_zeros = (nc-1) * extra_rows ; /* symbolic fill-in */
+
+ ASSERT (fnrows + nr_out == cdeg_out + extra_rows) ;
+ ASSERT (fncols + nc == rdeg [OUT][IN]) ;
+
+ /* size of relaxed front (after pivot row removed): */
+ fnrows_new [OUT][IN] = (fnrows-1) + nr_out ;
+ fncols_new [OUT][IN] = fncols + (nc-1) ;
+ relaxed_front = fnrows_new [OUT][IN] * fncols_new [OUT][IN] ;
+
+ /* do relaxed amalgamation if the extra zeros are no more */
+ /* than a fraction (default 0.25) of the relaxed front */
+ /* if relax = 0: no extra zeros allowed */
+ /* if relax = +inf: always amalgamate */
+ if (did_rowmerge)
+ {
+ do_extend = FALSE ;
+ }
+ else
+ {
+ /* relax parameter uses a double relop, but ignore NaN case: */
+ if (extra_zeros == 0)
+ {
+ do_extend = TRUE ;
+ }
+ else
+ {
+ do_extend = ((double) extra_zeros) <
+ (relax1 * (double) relaxed_front) ;
+ }
+ }
+
+ if (do_extend)
+ {
+ /* count the cost of relaxed amalgamation */
+ thiscost += extra_zeros ;
+
+ DEBUG2 (("Evaluating option OUT-IN:\n")) ;
+ DEBUG2 ((" Work->fnzeros "ID" fnpiv "ID" nr_out "ID" nc "ID"\n",
+ Work->fnzeros, fnpiv, nr_out, nc)) ;
+ DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
+
+ /* determine if BLAS-3 update to be applied before extending. */
+ /* update if too many zero entries accumulate in the LU block */
+ fnzeros = Work->fnzeros + fnpiv * (nr_out + nc) ;
+
+ DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
+
+ new_LUsize = (fnpiv+1) * (fnrows + nr_out + fncols + nc) ;
+
+ DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
+
+ /* RELAX3 parameter uses a double relop, ignore NaN case: */
+ do_update = fnpiv > 0 &&
+ (((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ;
+ DEBUG2 (("do_update "ID"\n", do_update))
+ }
+ else
+ {
+ /* the current front would not be extended */
+ do_update = fnpiv > 0 ;
+ fnzeros = 0 ;
+ DEBUG2 (("OUT-IN do_update forced true: "ID"\n", do_update)) ;
+
+ /* The new front would be just big enough to hold the new
+ * pivot row and column. */
+ fnrows_new [OUT][IN] = cdeg_out - 1 ;
+ fncols_new [OUT][IN] = rdeg [OUT][IN] - 1 ;
+ }
+
+ DEBUG2 (("option OUT IN : nr "ID" nc "ID" cost "ID"("ID") relax "ID
+ "\n", nr_out, nc, thiscost, extra_zeros, do_extend)) ;
+
+ if (bestcost == EMPTY || thiscost < bestcost)
+ {
+ /* this is the best option seen so far */
+ Work->pivot_case = OUT_IN ;
+ bestcost = thiscost ;
+ Work->do_extend = do_extend ;
+ Work->do_update = do_update ;
+ new_fnzeros = fnzeros ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* evaluate OUT_OUT option */
+ /* ------------------------------------------------------------------ */
+
+ if (pivrow [OUT][OUT] != EMPTY)
+ {
+ /* Neither the candidate pivot row nor the candidate pivot column
+ * are in the current front. */
+
+ ASSERT (fnrows >= 0 && fncols >= 0) ;
+
+ did_rowmerge = (cdeg_out == 0) ;
+ if (did_rowmerge)
+ {
+ /* pivrow [OUT][OUT] was found via row merge search */
+ /* it is not (yet) in the pivot column pattern (add it now) */
+ DEBUGm4 (("did row merge OUT col, OUT row\n")) ;
+ Wm [0] = pivrow [OUT][OUT] ;
+ CLEAR (Wx [0]) ;
+ cdeg_out = 1 ;
+ ASSERT (nr_out == EMPTY) ;
+ nr_out = 1 ;
+ }
+
+ if (fnrows == 0 && fncols == 0)
+ {
+ /* the current front is completely empty */
+ ASSERT (fnpiv == 0) ;
+ nc = rdeg [OUT][OUT] ;
+ extra_cols = 0 ;
+ nr_out = cdeg_out ;
+ extra_rows = 0 ;
+ extra_zeros = 0 ;
+
+ thiscost = (nc-1) * (cdeg_out-1) ; /* new columns only */
+
+ /* size of new front: */
+ fnrows_new [OUT][OUT] = nr_out-1 ;
+ fncols_new [OUT][OUT] = nc-1 ;
+ relaxed_front = fnrows_new [OUT][OUT] * fncols_new [OUT][OUT] ;
+ }
+ else
+ {
+
+ /* count rows not in current front */
+ if (nr_out == EMPTY)
+ {
+ nr_out = 0 ;
+#ifndef NDEBUG
+ debug_ok = FALSE ;
+#endif
+ for (i = 0 ; i < cdeg_out ; i++)
+ {
+ row = Wm [i] ;
+ ASSERT (row >= 0 && row < n_row) ;
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ if (Frpos [row] < 0 || Frpos [row] >= fnrows) nr_out++ ;
+#ifndef NDEBUG
+ /* we must see the pivot row somewhere */
+ if (row == pivrow [OUT][OUT])
+ {
+ ASSERT (Frpos [row] < 0 || Frpos [row] >= fnrows) ;
+ debug_ok = TRUE ;
+ }
+#endif
+ }
+ ASSERT (debug_ok) ;
+ }
+
+ /* count columns not in current front */
+ nc = 0 ;
+#ifndef NDEBUG
+ debug_ok = FALSE ;
+#endif
+ for (i = 0 ; i < rdeg [OUT][OUT] ; i++)
+ {
+ col = Woo [i] ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ if (Fcpos [col] < 0) nc++ ;
+#ifndef NDEBUG
+ /* we must see the pivot column somewhere */
+ if (col == pivcol [OUT])
+ {
+ ASSERT (Fcpos [col] < 0) ;
+ debug_ok = TRUE ;
+ }
+#endif
+ }
+ ASSERT (debug_ok) ;
+
+ extra_cols = (fncols + (nc-1)) - (rdeg [OUT][OUT] - 1) ;
+ extra_rows = (fnrows + (nr_out-1)) - (cdeg_out - 1) ;
+ ASSERT (extra_rows >= 0) ;
+ ASSERT (extra_cols >= 0) ;
+ extra_zeros = ((nc-1) * extra_rows) + ((nr_out-1) * extra_cols);
+
+ ASSERT (fnrows + nr_out == cdeg_out + extra_rows) ;
+ ASSERT (fncols + nc == rdeg [OUT][OUT] + extra_cols) ;
+
+ thiscost =
+ /* new columns: */
+ ((nc-1) * (cdeg_out-1)) +
+ /* old columns in front grow by nr_out-1: */
+ ((nr_out-1) * (fncols - extra_cols)) ;
+
+ /* size of relaxed front: */
+ fnrows_new [OUT][OUT] = fnrows + (nr_out-1) ;
+ fncols_new [OUT][OUT] = fncols + (nc-1) ;
+ relaxed_front = fnrows_new [OUT][OUT] * fncols_new [OUT][OUT] ;
+
+ }
+
+ /* do relaxed amalgamation if the extra zeros are no more */
+ /* than a fraction (default 0.25) of the relaxed front */
+ /* if relax = 0: no extra zeros allowed */
+ /* if relax = +inf: always amalgamate */
+ if (did_rowmerge)
+ {
+ do_extend = FALSE ;
+ }
+ else
+ {
+ /* relax parameter uses a double relop, but ignore NaN case: */
+ if (extra_zeros == 0)
+ {
+ do_extend = TRUE ;
+ }
+ else
+ {
+ do_extend = ((double) extra_zeros) <
+ (relax1 * (double) relaxed_front) ;
+ }
+ }
+
+ if (do_extend)
+ {
+ /* count the cost of relaxed amalgamation */
+ thiscost += extra_zeros ;
+
+ DEBUG2 (("Evaluating option OUT-OUT:\n")) ;
+ DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_out "ID" nc "ID"\n",
+ Work->fnzeros, fnpiv, nr_out, nc)) ;
+ DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
+
+ /* determine if BLAS-3 update to be applied before extending. */
+ /* update if too many zero entries accumulate in the LU block */
+ fnzeros = Work->fnzeros + fnpiv * (nr_out + nc) ;
+
+ DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
+
+ new_LUsize = (fnpiv+1) * (fnrows + nr_out + fncols + nc) ;
+
+ DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
+
+ /* RELAX3 parameter uses a double relop, ignore NaN case: */
+ do_update = fnpiv > 0 &&
+ (((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ;
+ DEBUG2 (("do_update "ID"\n", do_update))
+ }
+ else
+ {
+ /* the current front would not be extended */
+ do_update = fnpiv > 0 ;
+ fnzeros = 0 ;
+ DEBUG2 (("OUT-OUT do_update forced true: "ID"\n", do_update)) ;
+
+ /* The new front would be just big enough to hold the new
+ * pivot row and column. */
+ fnrows_new [OUT][OUT] = cdeg_out - 1 ;
+ fncols_new [OUT][OUT] = rdeg [OUT][OUT] - 1 ;
+ }
+
+ DEBUG2 (("option OUT OUT: nr "ID" nc "ID" cost "ID"\n",
+ rdeg [OUT][OUT], cdeg_out, thiscost)) ;
+
+ if (bestcost == EMPTY || thiscost < bestcost)
+ {
+ /* this is the best option seen so far */
+ Work->pivot_case = OUT_OUT ;
+ bestcost = thiscost ;
+ Work->do_extend = do_extend ;
+ Work->do_update = do_update ;
+ new_fnzeros = fnzeros ;
+ }
+ }
+ }
+
+ /* At this point, a structural pivot has been found. */
+ /* It may be numerically zero, however. */
+ ASSERT (Work->pivot_case != EMPTY) ;
+ DEBUG2 (("local search, best option "ID", best cost "ID"\n",
+ Work->pivot_case, bestcost)) ;
+
+ /* ====================================================================== */
+ /* Pivot row and column, and extension, now determined */
+ /* ====================================================================== */
+
+ Work->fnzeros = new_fnzeros ;
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize the pivot row and column */
+ /* ---------------------------------------------------------------------- */
+
+ switch (Work->pivot_case)
+ {
+ case IN_IN:
+ DEBUG2 (("IN-IN option selected\n")) ;
+ ASSERT (fnrows > 0 && fncols > 0) ;
+ Work->pivcol_in_front = TRUE ;
+ Work->pivrow_in_front = TRUE ;
+ Work->pivcol = pivcol [IN] ;
+ Work->pivrow = pivrow [IN][IN] ;
+ Work->ccdeg = nr_in ;
+ Work->Wrow = Fcols ;
+ Work->rrdeg = rdeg [IN][IN] ;
+ jj = jcand [IN] ;
+ Work->fnrows_new = fnrows_new [IN][IN] ;
+ Work->fncols_new = fncols_new [IN][IN] ;
+ break ;
+
+ case IN_OUT:
+ DEBUG2 (("IN-OUT option selected\n")) ;
+ ASSERT (fnrows >= 0 && fncols > 0) ;
+ Work->pivcol_in_front = TRUE ;
+ Work->pivrow_in_front = FALSE ;
+ Work->pivcol = pivcol [IN] ;
+ Work->pivrow = pivrow [IN][OUT] ;
+ Work->ccdeg = nr_in ;
+ Work->Wrow = Wio ;
+ Work->rrdeg = rdeg [IN][OUT] ;
+ jj = jcand [IN] ;
+ Work->fnrows_new = fnrows_new [IN][OUT] ;
+ Work->fncols_new = fncols_new [IN][OUT] ;
+ break ;
+
+ case OUT_IN:
+ DEBUG2 (("OUT-IN option selected\n")) ;
+ ASSERT (fnrows > 0 && fncols >= 0) ;
+ Work->pivcol_in_front = FALSE ;
+ Work->pivrow_in_front = TRUE ;
+ Work->pivcol = pivcol [OUT] ;
+ Work->pivrow = pivrow [OUT][IN] ;
+ Work->ccdeg = cdeg_out ;
+ /* Wrow might be equivalenced to Fcols (Freebie in): */
+ Work->Wrow = Woi ;
+ Work->rrdeg = rdeg [OUT][IN] ;
+ /* Work->Wrow[0..fncols-1] is not there. See Fcols instead */
+ jj = jcand [OUT] ;
+ Work->fnrows_new = fnrows_new [OUT][IN] ;
+ Work->fncols_new = fncols_new [OUT][IN] ;
+ break ;
+
+ case OUT_OUT:
+ DEBUG2 (("OUT-OUT option selected\n")) ;
+ ASSERT (fnrows >= 0 && fncols >= 0) ;
+ Work->pivcol_in_front = FALSE ;
+ Work->pivrow_in_front = FALSE ;
+ Work->pivcol = pivcol [OUT] ;
+ Work->pivrow = pivrow [OUT][OUT] ;
+ Work->ccdeg = cdeg_out ;
+ /* Wrow might be equivalenced to Wio (Freebie out): */
+ Work->Wrow = Woo ;
+ Work->rrdeg = rdeg [OUT][OUT] ;
+ jj = jcand [OUT] ;
+ Work->fnrows_new = fnrows_new [OUT][OUT] ;
+ Work->fncols_new = fncols_new [OUT][OUT] ;
+ break ;
+
+ }
+
+ ASSERT (IMPLIES (fnrows == 0 && fncols == 0, Work->pivot_case == OUT_OUT)) ;
+
+ if (!Work->pivcol_in_front && pivcol [IN] != EMPTY)
+ {
+ /* clear Frpos if pivcol [IN] was searched, but not selected */
+ for (i = fnrows ; i < cdeg_in ; i++)
+ {
+ Frpos [Frows [i]] = EMPTY;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Pivot row and column have been found */
+ /* ---------------------------------------------------------------------- */
+
+ /* ---------------------------------------------------------------------- */
+ /* remove pivot column from candidate pivot column set */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (jj >= 0 && jj < Work->nCandidates) ;
+ ASSERT (Work->pivcol == Work->Candidates [jj]) ;
+ remove_candidate (jj, Work, Symbolic) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check for frontal matrix growth */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG1 (("Check frontal growth:\n")) ;
+ DEBUG1 (("fnrows_new "ID" + 1 = "ID", fnr_curr "ID"\n",
+ Work->fnrows_new, Work->fnrows_new + 1, fnr_curr)) ;
+ DEBUG1 (("fncols_new "ID" + 1 = "ID", fnc_curr "ID"\n",
+ Work->fncols_new, Work->fncols_new + 1, fnc_curr)) ;
+
+ Work->do_grow = (Work->fnrows_new + 1 > fnr_curr
+ || Work->fncols_new + 1 > fnc_curr) ;
+ if (Work->do_grow)
+ {
+ DEBUG0 (("\nNeed to grow frontal matrix, force do_update true\n")) ;
+ /* If the front must grow, then apply the pending updates and remove
+ * the current pivot rows/columns from the front prior to growing the
+ * front. This frees up as much space as possible for the new front. */
+ if (!Work->do_update && fnpiv > 0)
+ {
+ /* This update would not have to be done if the current front
+ * was big enough. */
+ Work->nforced++ ;
+ Work->do_update = TRUE ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* current pivot column */
+ /* ---------------------------------------------------------------------- */
+
+ /*
+ c1) If pivot column index is in the current front:
+
+ The pivot column pattern is in Frows [0 .. fnrows-1] and
+ the extension is in Frows [fnrows ... fnrows+ccdeg-1].
+
+ Frpos [Frows [0 .. fnrows+ccdeg-1]] is
+ equal to 0 .. fnrows+ccdeg-1. Wm is not needed.
+
+ The values are in Wy [0 .. fnrows+ccdeg-1].
+
+ c2) Otherwise, if the pivot column index is not in the current front:
+
+ c2a) If the front is being extended, old row indices in the the
+ pivot column pattern are in Frows [0 .. fnrows-1].
+
+ All entries are in Wm [0 ... ccdeg-1], with values in
+ Wx [0 .. ccdeg-1]. These may include entries already in
+ Frows [0 .. fnrows-1].
+
+ Frpos [Frows [0 .. fnrows-1]] is equal to 0 .. fnrows-1.
+ Frpos [Wm [0 .. ccdeg-1]] for new entries is < 0.
+
+ c2b) If the front is not being extended, then the entire pivot
+ column pattern is in Wm [0 .. ccdeg-1]. It includes
+ the pivot row index. It is does not contain the pattern
+ Frows [0..fnrows-1]. The intersection of these two
+ sets may or may not be empty. The values are in Wx [0..ccdeg-1]
+
+ In both cases c1 and c2, Frpos [Frows [0 .. fnrows-1]] is equal
+ to 0 .. fnrows-1, which is the pattern of the current front.
+ Any entry of Frpos that is not specified above is < 0.
+ */
+
+
+#ifndef NDEBUG
+ DEBUG2 (("\n\nSEARCH DONE: Pivot col "ID" in: ("ID") pivot row "ID" in: ("ID
+ ") extend: "ID"\n\n", Work->pivcol, Work->pivcol_in_front,
+ Work->pivrow, Work->pivrow_in_front, Work->do_extend)) ;
+ UMF_dump_rowcol (1, Numeric, Work, Work->pivcol, !Symbolic->fixQ) ;
+ DEBUG2 (("Pivot col "ID": fnrows "ID" ccdeg "ID"\n", Work->pivcol, fnrows,
+ Work->ccdeg)) ;
+ if (Work->pivcol_in_front) /* case c1 */
+ {
+ Int found = FALSE ;
+ DEBUG3 (("Pivcol in front\n")) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG3 ((ID": row:: "ID" in front ", i, row)) ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ ASSERT (Frpos [row] == i) ;
+ EDEBUG3 (Wy [i]) ;
+ if (row == Work->pivrow)
+ {
+ DEBUG3 ((" <- pivrow")) ;
+ found = TRUE ;
+ }
+ DEBUG3 (("\n")) ;
+ }
+ ASSERT (found == Work->pivrow_in_front) ;
+ found = FALSE ;
+ for (i = fnrows ; i < fnrows + Work->ccdeg ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG3 ((ID": row:: "ID" (new)", i, row)) ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ ASSERT (Frpos [row] == i) ;
+ EDEBUG3 (Wy [i]) ;
+ if (row == Work->pivrow)
+ {
+ DEBUG3 ((" <- pivrow")) ;
+ found = TRUE ;
+ }
+ DEBUG3 (("\n")) ;
+ }
+ ASSERT (found == !Work->pivrow_in_front) ;
+ }
+ else
+ {
+ if (Work->do_extend)
+ {
+ Int found = FALSE ;
+ DEBUG3 (("Pivcol not in front (extend)\n")) ;
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ row = Frows [i] ;
+ DEBUG3 ((ID": row:: "ID" in front ", i, row)) ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ ASSERT (Frpos [row] == i) ;
+ if (row == Work->pivrow)
+ {
+ DEBUG3 ((" <- pivrow")) ;
+ found = TRUE ;
+ }
+ DEBUG3 (("\n")) ;
+ }
+ ASSERT (found == Work->pivrow_in_front) ;
+ found = FALSE ;
+ DEBUG3 (("----\n")) ;
+ for (i = 0 ; i < Work->ccdeg ; i++)
+ {
+ row = Wm [i] ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ DEBUG3 ((ID": row:: "ID" ", i, row)) ;
+ EDEBUG3 (Wx [i]) ;
+ if (Frpos [row] < 0)
+ {
+ DEBUG3 ((" (new) ")) ;
+ }
+ if (row == Work->pivrow)
+ {
+ DEBUG3 ((" <- pivrow")) ;
+ found = TRUE ;
+ /* ... */
+ if (Work->pivrow_in_front) ASSERT (Frpos [row] >= 0) ;
+ else ASSERT (Frpos [row] < 0) ;
+ }
+ DEBUG3 (("\n")) ;
+ }
+ ASSERT (found) ;
+ }
+ else
+ {
+ Int found = FALSE ;
+ DEBUG3 (("Pivcol not in front (no extend)\n")) ;
+ for (i = 0 ; i < Work->ccdeg ; i++)
+ {
+ row = Wm [i] ;
+ ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
+ DEBUG3 ((ID": row:: "ID" ", i, row)) ;
+ EDEBUG3 (Wx [i]) ;
+ DEBUG3 ((" (new) ")) ;
+ if (row == Work->pivrow)
+ {
+ DEBUG3 ((" <- pivrow")) ;
+ found = TRUE ;
+ }
+ DEBUG3 (("\n")) ;
+ }
+ ASSERT (found) ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* current pivot row */
+ /* ---------------------------------------------------------------------- */
+
+ /*
+ r1) If the pivot row index is in the current front:
+
+ The pivot row pattern is in Fcols [0..fncols-1] and the extenson is
+ in Wrow [fncols .. rrdeg-1]. If the pivot column is in the current
+ front, then Fcols and Wrow are equivalenced.
+
+ r2) If the pivot row index is not in the current front:
+
+ r2a) If the front is being extended, the pivot row pattern is in
+ Fcols [0 .. fncols-1]. New entries are in Wrow [0 .. rrdeg-1],
+ but these may include entries already in Fcols [0 .. fncols-1].
+
+ r2b) Otherwise, the pivot row pattern is Wrow [0 .. rrdeg-1].
+
+ Fcpos [Fcols [0..fncols-1]] is (0..fncols-1) * fnr_curr.
+ All other entries in Fcpos are < 0.
+
+ These conditions are asserted below.
+
+ ------------------------------------------------------------------------
+ Other items in Work structure that are relevant:
+
+ pivcol: the pivot column index
+ pivrow: the pivot column index
+
+ rrdeg:
+ ccdeg:
+
+ fnrows: the number of rows in the currnt contribution block
+ fncols: the number of columns in the current contribution block
+
+ fnrows_new: the number of rows in the new contribution block
+ fncols_new: the number of rows in the new contribution block
+
+ ------------------------------------------------------------------------
+ */
+
+
+#ifndef NDEBUG
+ UMF_dump_rowcol (0, Numeric, Work, Work->pivrow, TRUE) ;
+ DEBUG2 (("Pivot row "ID":\n", Work->pivrow)) ;
+ if (Work->pivrow_in_front)
+ {
+ Int found = FALSE ;
+ for (i = 0 ; i < fncols ; i++)
+ {
+ col = Fcols [i] ;
+ DEBUG3 ((" col:: "ID" in front\n", col)) ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ ASSERT (Fcpos [col] == i * fnr_curr) ;
+ if (col == Work->pivcol) found = TRUE ;
+ }
+ ASSERT (found == Work->pivcol_in_front) ;
+ found = FALSE ;
+ ASSERT (IMPLIES (Work->pivcol_in_front, Fcols == Work->Wrow)) ;
+ for (i = fncols ; i < Work->rrdeg ; i++)
+ {
+ col = Work->Wrow [i] ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ ASSERT (Fcpos [col] < 0) ;
+ if (col == Work->pivcol) found = TRUE ;
+ else DEBUG3 ((" col:: "ID" (new)\n", col)) ;
+ }
+ ASSERT (found == !Work->pivcol_in_front) ;
+ }
+ else
+ {
+ if (Work->do_extend)
+ {
+ Int found = FALSE ;
+ for (i = 0 ; i < fncols ; i++)
+ {
+ col = Fcols [i] ;
+ DEBUG3 ((" col:: "ID" in front\n", col)) ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ ASSERT (Fcpos [col] == i * fnr_curr) ;
+ if (col == Work->pivcol) found = TRUE ;
+ }
+ ASSERT (found == Work->pivcol_in_front) ;
+ found = FALSE ;
+ for (i = 0 ; i < Work->rrdeg ; i++)
+ {
+ col = Work->Wrow [i] ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ if (Fcpos [col] >= 0) continue ;
+ if (col == Work->pivcol) found = TRUE ;
+ else DEBUG3 ((" col:: "ID" (new, extend)\n", col)) ;
+ }
+ ASSERT (found == !Work->pivcol_in_front) ;
+ }
+ else
+ {
+ Int found = FALSE ;
+ for (i = 0 ; i < Work->rrdeg ; i++)
+ {
+ col = Work->Wrow [i] ;
+ ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
+ if (col == Work->pivcol) found = TRUE ;
+ else DEBUG3 ((" col:: "ID" (all new)\n", col)) ;
+ }
+ ASSERT (found) ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* determine whether to do scan2-row and scan2-col */
+ /* ---------------------------------------------------------------------- */
+
+ if (Work->do_extend)
+ {
+ Work->do_scan2row = (fncols > 0) ;
+ Work->do_scan2col = (fnrows > 0) ;
+ }
+ else
+ {
+ Work->do_scan2row = (fncols > 0) && Work->pivrow_in_front ;
+ Work->do_scan2col = (fnrows > 0) && Work->pivcol_in_front ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG2 (("LOCAL SEARCH DONE: pivot column "ID" pivot row: "ID"\n",
+ Work->pivcol, Work->pivrow)) ;
+ DEBUG2 (("do_extend: "ID"\n", Work->do_extend)) ;
+ DEBUG2 (("do_update: "ID"\n", Work->do_update)) ;
+ DEBUG2 (("do_grow: "ID"\n", Work->do_grow)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* keep track of the diagonal */
+ /* ---------------------------------------------------------------------- */
+
+ if (Symbolic->prefer_diagonal
+ && Work->pivcol < Work->n_col - Symbolic->nempty_col)
+ {
+ Diagonal_map = Work->Diagonal_map ;
+ Diagonal_imap = Work->Diagonal_imap ;
+ ASSERT (Diagonal_map != (Int *) NULL) ;
+ ASSERT (Diagonal_imap != (Int *) NULL) ;
+
+ row2 = Diagonal_map [Work->pivcol] ;
+ col2 = Diagonal_imap [Work->pivrow] ;
+
+ if (row2 < 0)
+ {
+ /* this was an off-diagonal pivot row */
+ Work->noff_diagonal++ ;
+ row2 = UNFLIP (row2) ;
+ }
+
+ ASSERT (Diagonal_imap [row2] == Work->pivcol) ;
+ ASSERT (UNFLIP (Diagonal_map [col2]) == Work->pivrow) ;
+
+ if (row2 != Work->pivrow)
+ {
+ /* swap the diagonal map to attempt to maintain symmetry later on.
+ * Also mark the map for col2 (via FLIP) to denote that the entry
+ * now on the diagonal is not the original entry on the diagonal. */
+
+ DEBUG0 (("Unsymmetric pivot\n")) ;
+ Diagonal_map [Work->pivcol] = FLIP (Work->pivrow) ;
+ Diagonal_imap [Work->pivrow] = Work->pivcol ;
+
+ Diagonal_map [col2] = FLIP (row2) ;
+ Diagonal_imap [row2] = col2 ;
+
+ }
+ ASSERT (n_row == n_col) ;
+#ifndef NDEBUG
+ UMF_dump_diagonal_map (Diagonal_map, Diagonal_imap, Symbolic->n1,
+ Symbolic->n_col, Symbolic->nempty_col) ;
+#endif
+ }
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umf_local_search.h b/UMFPACK/Source/umf_local_search.h
new file mode 100644
index 0000000..434d66f
--- /dev/null
+++ b/UMFPACK/Source/umf_local_search.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_local_search
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
diff --git a/UMFPACK/Source/umf_lsolve.c b/UMFPACK/Source/umf_lsolve.c
new file mode 100644
index 0000000..7e1943c
--- /dev/null
+++ b/UMFPACK/Source/umf_lsolve.c
@@ -0,0 +1,152 @@
+/* ========================================================================== */
+/* === UMF_lsolve =========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* solves Lx = b, where L is the lower triangular factor of a matrix */
+/* B is overwritten with the solution X. */
+/* Returns the floating point operation count */
+
+#include "umf_internal.h"
+#include "umf_lsolve.h"
+
+GLOBAL double UMF_lsolve
+(
+ NumericType *Numeric,
+ Entry X [ ], /* b on input, solution x on output */
+ Int Pattern [ ] /* a work array of size n */
+)
+{
+ Entry xk ;
+ Entry *xp, *Lval ;
+ Int k, deg, *ip, j, row, *Lpos, *Lilen, *Lip, llen, lp, newLchain,
+ pos, npiv, n1, *Li ;
+
+ /* ---------------------------------------------------------------------- */
+
+ if (Numeric->n_row != Numeric->n_col) return (0.) ;
+ npiv = Numeric->npiv ;
+ Lpos = Numeric->Lpos ;
+ Lilen = Numeric->Lilen ;
+ Lip = Numeric->Lip ;
+ n1 = Numeric->n1 ;
+
+#ifndef NDEBUG
+ DEBUG4 (("Lsolve start:\n")) ;
+ for (j = 0 ; j < Numeric->n_row ; j++)
+ {
+ DEBUG4 (("Lsolve start "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* singletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ xk = X [k] ;
+ deg = Lilen [k] ;
+ if (deg > 0 && IS_NONZERO (xk))
+ {
+ lp = Lip [k] ;
+ Li = (Int *) (Numeric->Memory + lp) ;
+ lp += UNITS (Int, deg) ;
+ Lval = (Entry *) (Numeric->Memory + lp) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Li [j], k)) ;
+ EDEBUG4 (Lval [j]) ;
+ DEBUG4 (("\n")) ;
+ /* X [Li [j]] -= xk * Lval [j] ; */
+ MULT_SUB (X [Li [j]], xk, Lval [j]) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* rest of L */
+ /* ---------------------------------------------------------------------- */
+
+ deg = 0 ;
+
+ for (k = n1 ; k < npiv ; k++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* make column of L in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ lp = Lip [k] ;
+ newLchain = (lp < 0) ;
+ if (newLchain)
+ {
+ lp = -lp ;
+ deg = 0 ;
+ DEBUG4 (("start of chain for column of L\n")) ;
+ }
+
+ /* remove pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
+ k, Pattern [pos], pos)) ;
+ ASSERT (!newLchain) ;
+ ASSERT (deg > 0) ;
+ ASSERT (pos >= 0 && pos < deg) ;
+ ASSERT (Pattern [pos] == k) ;
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ /* concatenate the pattern */
+ ip = (Int *) (Numeric->Memory + lp) ;
+ llen = Lilen [k] ;
+ for (j = 0 ; j < llen ; j++)
+ {
+ row = *ip++ ;
+ DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
+ ASSERT (row > k) ;
+ Pattern [deg++] = row ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* use column k of L */
+ /* ------------------------------------------------------------------ */
+
+ xk = X [k] ;
+ if (IS_NONZERO (xk))
+ {
+ xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
+ EDEBUG4 (*xp) ;
+ DEBUG4 (("\n")) ;
+ /* X [Pattern [j]] -= xk * (*xp) ; */
+ MULT_SUB (X [Pattern [j]], xk, *xp) ;
+ xp++ ;
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ for (j = 0 ; j < Numeric->n_row ; j++)
+ {
+ DEBUG4 (("Lsolve done "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("Lsolve done.\n")) ;
+#endif
+
+ return (MULTSUB_FLOPS * ((double) Numeric->lnz)) ;
+}
diff --git a/UMFPACK/Source/umf_lsolve.h b/UMFPACK/Source/umf_lsolve.h
new file mode 100644
index 0000000..211adff
--- /dev/null
+++ b/UMFPACK/Source/umf_lsolve.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL double UMF_lsolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
diff --git a/UMFPACK/Source/umf_ltsolve.c b/UMFPACK/Source/umf_ltsolve.c
new file mode 100644
index 0000000..1792dfa
--- /dev/null
+++ b/UMFPACK/Source/umf_ltsolve.c
@@ -0,0 +1,226 @@
+/* ========================================================================== */
+/* === UMF_ltsolve ========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Solves L'x = b or L.'x=b, where L is the lower triangular factor of a */
+/* matrix. B is overwritten with the solution X. */
+/* Returns the floating point operation count */
+
+#include "umf_internal.h"
+#include "umf_ltsolve.h"
+
+GLOBAL double
+#ifdef CONJUGATE_SOLVE
+UMF_lhsolve /* solve L'x=b (complex conjugate transpose) */
+#else
+UMF_ltsolve /* solve L.'x=b (array transpose) */
+#endif
+(
+ NumericType *Numeric,
+ Entry X [ ], /* b on input, solution x on output */
+ Int Pattern [ ] /* a work array of size n */
+)
+{
+ Entry xk ;
+ Entry *xp, *Lval ;
+ Int k, deg, *ip, j, row, *Lpos, *Lilen, kstart, kend, *Lip, llen,
+ lp, pos, npiv, n1, *Li ;
+
+ /* ---------------------------------------------------------------------- */
+
+ if (Numeric->n_row != Numeric->n_col) return (0.) ;
+ npiv = Numeric->npiv ;
+ Lpos = Numeric->Lpos ;
+ Lilen = Numeric->Lilen ;
+ Lip = Numeric->Lip ;
+ kstart = npiv ;
+ n1 = Numeric->n1 ;
+
+#ifndef NDEBUG
+ DEBUG4 (("Ltsolve start:\n")) ;
+ for (j = 0 ; j < Numeric->n_row ; j++)
+ {
+ DEBUG4 (("Ltsolve start "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* non-singletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (kend = npiv-1 ; kend >= n1 ; kend = kstart-1)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* find the start of this Lchain */
+ /* ------------------------------------------------------------------ */
+
+ /* for (kstart = kend ; kstart >= 0 && Lip [kstart] > 0 ; kstart--) ; */
+ kstart = kend ;
+ while (kstart >= 0 && Lip [kstart] > 0)
+ {
+ kstart-- ;
+ }
+
+ /* the Lchain goes from kstart to kend */
+
+ /* ------------------------------------------------------------------ */
+ /* scan the whole chain to find the pattern of the last column of L */
+ /* ------------------------------------------------------------------ */
+
+ deg = 0 ;
+ DEBUG4 (("start of chain for column of L\n")) ;
+ for (k = kstart ; k <= kend ; k++)
+ {
+ ASSERT (k >= 0 && k < npiv) ;
+
+ /* -------------------------------------------------------------- */
+ /* make column k of L in Pattern [0..deg-1] */
+ /* -------------------------------------------------------------- */
+
+ /* remove pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
+ k, Pattern [pos], pos)) ;
+ ASSERT (k != kstart) ;
+ ASSERT (deg > 0) ;
+ ASSERT (pos >= 0 && pos < deg) ;
+ ASSERT (Pattern [pos] == k) ;
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ /* concatenate the pattern */
+ lp = Lip [k] ;
+ if (k == kstart)
+ {
+ lp = -lp ;
+ }
+ ASSERT (lp > 0) ;
+ ip = (Int *) (Numeric->Memory + lp) ;
+ llen = Lilen [k] ;
+ for (j = 0 ; j < llen ; j++)
+ {
+ row = *ip++ ;
+ DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
+ ASSERT (row > k) ;
+ Pattern [deg++] = row ;
+ }
+
+ }
+ /* Pattern [0..deg-1] is now the pattern of column kend */
+
+ /* ------------------------------------------------------------------ */
+ /* solve using this chain, in reverse order */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG4 (("Unwinding Lchain\n")) ;
+ for (k = kend ; k >= kstart ; k--)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* use column k of L */
+ /* -------------------------------------------------------------- */
+
+ ASSERT (k >= 0 && k < npiv) ;
+ lp = Lip [k] ;
+ if (k == kstart)
+ {
+ lp = -lp ;
+ }
+ ASSERT (lp > 0) ;
+ llen = Lilen [k] ;
+ xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
+ xk = X [k] ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
+ EDEBUG4 (*xp) ;
+ DEBUG4 (("\n")) ;
+
+#ifdef CONJUGATE_SOLVE
+ /* xk -= X [Pattern [j]] * conjugate (*xp) ; */
+ MULT_SUB_CONJ (xk, X [Pattern [j]], *xp) ;
+#else
+ /* xk -= X [Pattern [j]] * (*xp) ; */
+ MULT_SUB (xk, X [Pattern [j]], *xp) ;
+#endif
+
+ xp++ ;
+ }
+ X [k] = xk ;
+
+ /* -------------------------------------------------------------- */
+ /* construct column k-1 of L */
+ /* -------------------------------------------------------------- */
+
+ /* un-concatenate the pattern */
+ deg -= llen ;
+
+ /* add pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ DEBUG4 ((" k "ID" adding row "ID" at position "ID"\n",
+ k, k, pos)) ;
+ ASSERT (k != kstart) ;
+ ASSERT (pos >= 0 && pos <= deg) ;
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* singletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = n1 - 1 ; k >= 0 ; k--)
+ {
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ deg = Lilen [k] ;
+ if (deg > 0)
+ {
+ xk = X [k] ;
+ lp = Lip [k] ;
+ Li = (Int *) (Numeric->Memory + lp) ;
+ lp += UNITS (Int, deg) ;
+ Lval = (Entry *) (Numeric->Memory + lp) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Li [j], k)) ;
+ EDEBUG4 (Lval [j]) ;
+ DEBUG4 (("\n")) ;
+#ifdef CONJUGATE_SOLVE
+ /* xk -= X [Li [j]] * conjugate (Lval [j]) ; */
+ MULT_SUB_CONJ (xk, X [Li [j]], Lval [j]) ;
+#else
+ /* xk -= X [Li [j]] * Lval [j] ; */
+ MULT_SUB (xk, X [Li [j]], Lval [j]) ;
+#endif
+ }
+ X [k] = xk ;
+ }
+ }
+
+#ifndef NDEBUG
+ for (j = 0 ; j < Numeric->n_row ; j++)
+ {
+ DEBUG4 (("Ltsolve done "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("Ltsolve done.\n")) ;
+#endif
+
+ return (MULTSUB_FLOPS * ((double) Numeric->lnz)) ;
+}
diff --git a/UMFPACK/Source/umf_ltsolve.h b/UMFPACK/Source/umf_ltsolve.h
new file mode 100644
index 0000000..02f7734
--- /dev/null
+++ b/UMFPACK/Source/umf_ltsolve.h
@@ -0,0 +1,19 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL double UMF_ltsolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
+
+GLOBAL double UMF_lhsolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
diff --git a/UMFPACK/Source/umf_malloc.c b/UMFPACK/Source/umf_malloc.c
new file mode 100644
index 0000000..d7ff561
--- /dev/null
+++ b/UMFPACK/Source/umf_malloc.c
@@ -0,0 +1,92 @@
+/* ========================================================================== */
+/* === UMF_malloc =========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Allocate a block of n objects, each of a given size. This routine does not
+ handle the case when the size is 1 (allocating char's) because of potential
+ integer overflow. UMFPACK never does that.
+ Also maintains the UMFPACK malloc count.
+*/
+
+#include "umf_internal.h"
+#include "umf_malloc.h"
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+
+/*
+ UMF_malloc_count is a count of the objects malloc'd by UMFPACK. If you
+ suspect a memory leak in your program (caused by not properly destroying
+ the Symbolic and Numeric objects) then compile with -DUMF_MALLOC_COUNT and
+ check value of UMF_malloc_count. By default, UMF_MALLOC_COUNT is not
+ defined, and thus UMFPACK has no global variables.
+*/
+
+GLOBAL Int UMF_malloc_count = 0 ;
+
+#endif
+
+#ifdef UMF_TCOV_TEST
+/* For exhaustive statement coverage testing only! */
+GLOBAL int umf_fail, umf_fail_lo, umf_fail_hi ;
+GLOBAL int umf_realloc_fail, umf_realloc_lo, umf_realloc_hi ;
+#endif
+
+GLOBAL void *UMF_malloc
+(
+ Int n_objects,
+ size_t size_of_object
+)
+{
+ size_t size ;
+ void *p ;
+
+#ifdef UMF_TCOV_TEST
+ /* For exhaustive statement coverage testing only! */
+ /* Pretend to fail, to test out-of-memory conditions. */
+ umf_fail-- ;
+ if (umf_fail <= umf_fail_hi && umf_fail >= umf_fail_lo)
+ {
+ DEBUG0 (("umf_malloc: Pretend to fail %d %d %d\n",
+ umf_fail, umf_fail_hi, umf_fail_lo)) ;
+ return ((void *) NULL) ;
+ }
+#endif
+
+ DEBUG0 (("UMF_malloc: ")) ;
+
+ /* make sure that we allocate something */
+ n_objects = MAX (1, n_objects) ;
+
+ size = (size_t) n_objects ;
+ ASSERT (size_of_object > 1) ;
+ if (size > Int_MAX / size_of_object)
+ {
+ /* object is too big for integer pointer arithmetic */
+ return ((void *) NULL) ;
+ }
+ size *= size_of_object ;
+
+ /* see AMD/Source/amd_global.c for the memory allocator selection */
+ p = amd_malloc (size) ;
+
+ DEBUG0 ((ID"\n", (Int) p)) ;
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (p)
+ {
+ /* One more object has been malloc'ed. Keep track of the count. */
+ /* (purely for sanity checks). */
+ UMF_malloc_count++ ;
+ DEBUG0 ((" successful, new malloc count: "ID"\n", UMF_malloc_count)) ;
+ }
+#endif
+
+ return (p) ;
+}
diff --git a/UMFPACK/Source/umf_malloc.h b/UMFPACK/Source/umf_malloc.h
new file mode 100644
index 0000000..8ee9934
--- /dev/null
+++ b/UMFPACK/Source/umf_malloc.h
@@ -0,0 +1,25 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#ifndef _UMF_MALLOC
+#define _UMF_MALLOC
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+GLOBAL EXTERN Int UMF_malloc_count ;
+#endif
+
+GLOBAL void *UMF_malloc
+(
+ Int n_objects,
+ size_t size_of_object
+) ;
+
+#endif
diff --git a/UMFPACK/Source/umf_mem_alloc_element.c b/UMFPACK/Source/umf_mem_alloc_element.c
new file mode 100644
index 0000000..cac0db8
--- /dev/null
+++ b/UMFPACK/Source/umf_mem_alloc_element.c
@@ -0,0 +1,83 @@
+/* ========================================================================== */
+/* === UMF_mem_alloc_element ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The UMF_mem_* routines manage the Numeric->Memory memory space. */
+
+/* Allocate a nrows-by-ncols element, and initialize it. */
+/* Returns the index into Numeric->Memory if successful, or 0 on failure. */
+
+#include "umf_internal.h"
+#include "umf_mem_alloc_element.h"
+#include "umf_mem_alloc_tail_block.h"
+
+GLOBAL Int UMF_mem_alloc_element
+(
+ NumericType *Numeric,
+ Int nrows,
+ Int ncols,
+ Int **Rows,
+ Int **Cols,
+ Entry **C,
+ Int *size,
+ Element **epout
+)
+{
+
+ Element *ep ;
+ Unit *p ;
+ Int i ;
+
+ ASSERT (Numeric != (NumericType *) NULL) ;
+ ASSERT (Numeric->Memory != (Unit *) NULL) ;
+
+ *size = GET_ELEMENT_SIZE (nrows, ncols) ;
+ if (INT_OVERFLOW (DGET_ELEMENT_SIZE (nrows, ncols) + 1))
+ {
+ /* :: allocate element, int overflow :: */
+ return (0) ; /* problem is too large */
+ }
+
+ i = UMF_mem_alloc_tail_block (Numeric, *size) ;
+ (*size)++ ;
+ if (!i)
+ {
+ DEBUG0 (("alloc element failed - out of memory\n")) ;
+ return (0) ; /* out of memory */
+ }
+ p = Numeric->Memory + i ;
+
+ ep = (Element *) p ;
+
+ DEBUG2 (("alloc_element done ("ID" x "ID"): p: "ID" i "ID"\n",
+ nrows, ncols, (Int) (p-Numeric->Memory), i)) ;
+
+ /* Element data structure, in order: */
+ p += UNITS (Element, 1) ; /* (1) Element header */
+ *Cols = (Int *) p ; /* (2) col [0..ncols-1] indices */
+ *Rows = *Cols + ncols ; /* (3) row [0..nrows-1] indices */
+ p += UNITS (Int, ncols + nrows) ;
+ *C = (Entry *) p ; /* (4) C [0..nrows-1, 0..ncols-1] */
+
+ ep->nrows = nrows ; /* initialize the header information */
+ ep->ncols = ncols ;
+ ep->nrowsleft = nrows ;
+ ep->ncolsleft = ncols ;
+ ep->cdeg = 0 ;
+ ep->rdeg = 0 ;
+ ep->next = EMPTY ;
+
+ DEBUG2 (("new block size: "ID" ", GET_BLOCK_SIZE (Numeric->Memory + i))) ;
+ DEBUG2 (("Element size needed "ID"\n", GET_ELEMENT_SIZE (nrows, ncols))) ;
+
+ *epout = ep ;
+
+ /* return the offset into Numeric->Memory */
+ return (i) ;
+}
diff --git a/UMFPACK/Source/umf_mem_alloc_element.h b/UMFPACK/Source/umf_mem_alloc_element.h
new file mode 100644
index 0000000..e0b259f
--- /dev/null
+++ b/UMFPACK/Source/umf_mem_alloc_element.h
@@ -0,0 +1,17 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_mem_alloc_element
+(
+ NumericType *Numeric,
+ Int nrows,
+ Int ncols,
+ Int **Rows,
+ Int **Cols,
+ Entry **C,
+ Int *size,
+ Element **epout
+) ;
diff --git a/UMFPACK/Source/umf_mem_alloc_head_block.c b/UMFPACK/Source/umf_mem_alloc_head_block.c
new file mode 100644
index 0000000..6d7355c
--- /dev/null
+++ b/UMFPACK/Source/umf_mem_alloc_head_block.c
@@ -0,0 +1,55 @@
+/* ========================================================================== */
+/* === UMF_mem_alloc_head_block ============================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The UMF_mem_* routines manage the Numeric->Memory memory space. */
+
+/* allocate nunits from head of Numeric->Memory. No header allocated. */
+/* Returns the index into Numeric->Memory if successful, or 0 on failure. */
+
+#include "umf_internal.h"
+#include "umf_mem_alloc_head_block.h"
+
+GLOBAL Int UMF_mem_alloc_head_block
+(
+ NumericType *Numeric,
+ Int nunits
+)
+{
+ Int p, usage ;
+ DEBUG2 (("GET BLOCK: from head, size "ID" ", nunits)) ;
+
+ ASSERT (Numeric != (NumericType *) NULL) ;
+ ASSERT (Numeric->Memory != (Unit *) NULL) ;
+
+#ifndef NDEBUG
+ if (UMF_allocfail)
+ {
+ /* pretend to fail, to test garbage_collection */
+ DEBUGm2 (("UMF_mem_alloc_head_block: pretend to fail\n")) ;
+ UMF_allocfail = FALSE ; /* don't fail the next time */
+ return (0) ;
+ }
+#endif
+
+ if (nunits > (Numeric->itail - Numeric->ihead))
+ {
+ DEBUG2 ((" failed\n")) ;
+ return (0) ;
+ }
+
+ /* return p as an offset from Numeric->Memory */
+ p = Numeric->ihead ;
+ Numeric->ihead += nunits ;
+
+ DEBUG2 (("p: "ID"\n", p)) ;
+ usage = Numeric->ihead + Numeric->tail_usage ;
+ Numeric->max_usage = MAX (Numeric->max_usage, usage) ;
+ return (p) ;
+}
diff --git a/UMFPACK/Source/umf_mem_alloc_head_block.h b/UMFPACK/Source/umf_mem_alloc_head_block.h
new file mode 100644
index 0000000..510a6fa
--- /dev/null
+++ b/UMFPACK/Source/umf_mem_alloc_head_block.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_mem_alloc_head_block
+(
+ NumericType *Numeric,
+ Int nunits
+) ;
diff --git a/UMFPACK/Source/umf_mem_alloc_tail_block.c b/UMFPACK/Source/umf_mem_alloc_tail_block.c
new file mode 100644
index 0000000..a16698a
--- /dev/null
+++ b/UMFPACK/Source/umf_mem_alloc_tail_block.c
@@ -0,0 +1,134 @@
+/* ========================================================================== */
+/* === UMF_mem_alloc_tail_block ============================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The UMF_mem_* routines manage the Numeric->Memory memory space. */
+
+#include "umf_internal.h"
+#include "umf_mem_alloc_tail_block.h"
+
+/* allocate nunits from tail of Numeric->Memory */
+/* (requires nunits+1, for header). */
+/* Returns the index into Numeric->Memory if successful, or 0 on failure. */
+
+GLOBAL Int UMF_mem_alloc_tail_block
+(
+ NumericType *Numeric,
+ Int nunits
+)
+{
+ Int bigsize, usage ;
+ Unit *p, *pnext, *pbig ;
+
+ ASSERT (Numeric != (NumericType *) NULL) ;
+ ASSERT (Numeric->Memory != (Unit *) NULL) ;
+
+#ifndef NDEBUG
+ if (UMF_allocfail)
+ {
+ /* pretend to fail, to test garbage_collection */
+ DEBUGm2 (("UMF_mem_alloc_tail_block: pretend to fail\n")) ;
+ UMF_allocfail = FALSE ; /* don't fail the next time */
+ return (0) ;
+ }
+ DEBUG2 (("UMF_mem_alloc_tail_block, size: "ID" + 1 = "ID": ",
+ nunits, nunits+1)) ;
+#endif
+
+ bigsize = 0 ;
+ pbig = (Unit *) NULL ;
+
+ ASSERT (nunits > 0) ; /* size must be positive */
+ if (Numeric->ibig != EMPTY)
+ {
+ ASSERT (Numeric->ibig > Numeric->itail) ;
+ ASSERT (Numeric->ibig < Numeric->size) ;
+ pbig = Numeric->Memory + Numeric->ibig ;
+ bigsize = -pbig->header.size ;
+ ASSERT (bigsize > 0) ; /* Numeric->ibig is free */
+ ASSERT (pbig->header.prevsize >= 0) ; /* prev. is not free */
+ }
+
+ if (pbig && bigsize >= nunits)
+ {
+
+ /* use the biggest block, somewhere in middle of memory */
+ p = pbig ;
+ pnext = p + 1 + bigsize ;
+ /* next is in range */
+ ASSERT (pnext < Numeric->Memory + Numeric->size) ;
+ /* prevsize of next = this size */
+ ASSERT (pnext->header.prevsize == bigsize) ;
+ /* next is not free */
+ ASSERT (pnext->header.size > 0) ;
+ bigsize -= nunits + 1 ;
+
+ if (bigsize < 4)
+ {
+ /* internal fragmentation would be too small */
+ /* allocate the entire free block */
+ p->header.size = -p->header.size ;
+ DEBUG2 (("GET BLOCK: p: "ID" size: "ID", all of big: "ID" size: "
+ ID"\n", (Int) (p-Numeric->Memory), nunits, Numeric->ibig,
+ p->header.size)) ;
+ /* no more biggest block */
+ Numeric->ibig = EMPTY ;
+
+ }
+ else
+ {
+
+ /* allocate just the first nunits Units of the free block */
+ p->header.size = nunits ;
+ /* make a new free block */
+ Numeric->ibig += nunits + 1 ;
+ pbig = Numeric->Memory + Numeric->ibig ;
+ pbig->header.size = -bigsize ;
+ pbig->header.prevsize = nunits ;
+ pnext->header.prevsize = bigsize ;
+ DEBUG2 (("GET BLOCK: p: "ID" size: "ID", some of big: "ID" left: "
+ ID"\n", (Int) (p-Numeric->Memory), nunits, Numeric->ibig,
+ bigsize)) ;
+ }
+
+ }
+ else
+ {
+
+ /* allocate from the top of tail */
+ pnext = Numeric->Memory + Numeric->itail ;
+ DEBUG2 (("GET BLOCK: from tail ")) ;
+ if ((nunits + 1) > (Numeric->itail - Numeric->ihead))
+ {
+ DEBUG2 (("\n")) ;
+ return (0) ;
+ }
+ Numeric->itail -= (nunits + 1) ;
+ p = Numeric->Memory + Numeric->itail ;
+ p->header.size = nunits ;
+ p->header.prevsize = 0 ;
+ pnext->header.prevsize = nunits ;
+ DEBUG2 (("p: "ID" size: "ID", new tail "ID"\n",
+ (Int) (p-Numeric->Memory), nunits, Numeric->itail)) ;
+ }
+
+ Numeric->tail_usage += p->header.size + 1 ;
+ usage = Numeric->ihead + Numeric->tail_usage ;
+ Numeric->max_usage = MAX (Numeric->max_usage, usage) ;
+
+#ifndef NDEBUG
+ UMF_debug -= 10 ;
+ UMF_dump_memory (Numeric) ;
+ UMF_debug += 10 ;
+#endif
+
+ /* p points to the header. Add one to point to the usable block itself. */
+ /* return the offset into Numeric->Memory */
+ return ((p - Numeric->Memory) + 1) ;
+}
diff --git a/UMFPACK/Source/umf_mem_alloc_tail_block.h b/UMFPACK/Source/umf_mem_alloc_tail_block.h
new file mode 100644
index 0000000..d072a73
--- /dev/null
+++ b/UMFPACK/Source/umf_mem_alloc_tail_block.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_mem_alloc_tail_block
+(
+ NumericType *Numeric,
+ Int nunits
+) ;
diff --git a/UMFPACK/Source/umf_mem_free_tail_block.c b/UMFPACK/Source/umf_mem_free_tail_block.c
new file mode 100644
index 0000000..9bec421
--- /dev/null
+++ b/UMFPACK/Source/umf_mem_free_tail_block.c
@@ -0,0 +1,143 @@
+/* ========================================================================== */
+/* === UMF_mem_free_tail_block ============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The UMF_mem_* routines manage the Numeric->Memory memory space. */
+
+/* free a block from the tail of Numeric->memory */
+
+#include "umf_internal.h"
+#include "umf_mem_free_tail_block.h"
+
+GLOBAL void UMF_mem_free_tail_block
+(
+ NumericType *Numeric,
+ Int i
+)
+{
+ Unit *pprev, *pnext, *p, *pbig ;
+ Int sprev ;
+
+ ASSERT (Numeric != (NumericType *) NULL) ;
+ ASSERT (Numeric->Memory != (Unit *) NULL) ;
+ if (i == EMPTY || i == 0) return ; /* already deallocated */
+
+ /* ---------------------------------------------------------------------- */
+ /* get the block */
+ /* ---------------------------------------------------------------------- */
+
+ p = Numeric->Memory + i ;
+
+ p-- ; /* get the corresponding header */
+ DEBUG2 (("free block: p: "ID, (Int) (p-Numeric->Memory))) ;
+ ASSERT (p >= Numeric->Memory + Numeric->itail) ;
+ ASSERT (p < Numeric->Memory + Numeric->size) ;
+ ASSERT (p->header.size > 0) ; /* block not already free */
+ ASSERT (p->header.prevsize >= 0) ;
+
+ Numeric->tail_usage -= p->header.size + 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* merge with next free block, if any */
+ /* ---------------------------------------------------------------------- */
+
+ pnext = p + 1 + p->header.size ;
+ DEBUG2 (("size: "ID" next: "ID" ", p->header.size,
+ (Int) (pnext-Numeric->Memory))) ;
+ ASSERT (pnext < Numeric->Memory + Numeric->size) ;
+ ASSERT (pnext->header.prevsize == p->header.size) ;
+ ASSERT (pnext->header.size != 0) ;
+
+ if (pnext->header.size < 0)
+ {
+ /* next block is also free - merge with current block */
+ p->header.size += (-(pnext->header.size)) + 1 ;
+ DEBUG2 ((" NEXT FREE ")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* merge with previous free block, if any */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ if (p == Numeric->Memory + Numeric->itail)
+ {
+ DEBUG2 ((" at top of tail ")) ;
+ ASSERT (p->header.prevsize == 0) ;
+ }
+#endif
+
+ if (p > Numeric->Memory + Numeric->itail)
+ {
+ ASSERT (p->header.prevsize > 0) ;
+ pprev = p - 1 - p->header.prevsize ;
+ DEBUG2 ((" prev: "ID" ", (Int) (pprev-Numeric->Memory))) ;
+ ASSERT (pprev >= Numeric->Memory + Numeric->itail) ;
+ sprev = pprev->header.size ;
+ if (sprev < 0)
+ {
+ /* previous block is also free - merge it with current block */
+ ASSERT (p->header.prevsize == -sprev) ;
+ pprev->header.size = p->header.size + (-sprev) + 1 ;
+ p = pprev ;
+ DEBUG2 ((" PREV FREE ")) ;
+ /* note that p may now point to Numeric->itail */
+ }
+#ifndef NDEBUG
+ else
+ {
+ ASSERT (p->header.prevsize == sprev) ;
+ }
+#endif
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the block, p */
+ /* ---------------------------------------------------------------------- */
+
+ pnext = p + 1 + p->header.size ;
+ ASSERT (pnext < Numeric->Memory + Numeric->size) ;
+
+ if (p == Numeric->Memory + Numeric->itail)
+ {
+ /* top block in list is freed */
+ Numeric->itail = pnext - Numeric->Memory ;
+ pnext->header.prevsize = 0 ;
+ DEBUG2 ((" NEW TAIL : "ID" ", Numeric->itail)) ;
+ ASSERT (pnext->header.size > 0) ;
+ if (Numeric->ibig != EMPTY && Numeric->ibig <= Numeric->itail)
+ {
+ /* the big free block is now above the tail */
+ Numeric->ibig = EMPTY ;
+ }
+ }
+ else
+ {
+ /* keep track of the biggest free block seen */
+ if (Numeric->ibig == EMPTY)
+ {
+ Numeric->ibig = p - Numeric->Memory ;
+ }
+ else
+ {
+ pbig = Numeric->Memory + Numeric->ibig ;
+ if (-(pbig->header.size) < p->header.size)
+ {
+ Numeric->ibig = p - Numeric->Memory ;
+ }
+ }
+ /* flag the block as free, somewhere in the middle of the tail */
+ pnext->header.prevsize = p->header.size ;
+ p->header.size = -(p->header.size) ;
+ }
+
+ DEBUG2 (("new p: "ID" freesize: "ID"\n", (Int) (p-Numeric->Memory),
+ -(p->header.size))) ;
+
+}
diff --git a/UMFPACK/Source/umf_mem_free_tail_block.h b/UMFPACK/Source/umf_mem_free_tail_block.h
new file mode 100644
index 0000000..14c7324
--- /dev/null
+++ b/UMFPACK/Source/umf_mem_free_tail_block.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_mem_free_tail_block
+(
+ NumericType *Numeric,
+ Int i
+) ;
diff --git a/UMFPACK/Source/umf_mem_init_memoryspace.c b/UMFPACK/Source/umf_mem_init_memoryspace.c
new file mode 100644
index 0000000..0e05f5c
--- /dev/null
+++ b/UMFPACK/Source/umf_mem_init_memoryspace.c
@@ -0,0 +1,65 @@
+/* ========================================================================== */
+/* === UMF_mem_init_memoryspace ============================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* The UMF_mem_* routines manage the Numeric->Memory memory space. */
+
+#include "umf_internal.h"
+#include "umf_mem_init_memoryspace.h"
+
+/* initialize the LU and element workspace (Numeric->Memory) */
+
+GLOBAL void UMF_mem_init_memoryspace
+(
+ NumericType *Numeric
+)
+{
+ Unit *p ;
+
+ ASSERT (Numeric != (NumericType *) NULL) ;
+ ASSERT (Numeric->Memory != (Unit *) NULL) ;
+ ASSERT (Numeric->size >= 3) ;
+ DEBUG0 (("Init memory space, size "ID"\n", Numeric->size)) ;
+
+ Numeric->ngarbage = 0 ;
+ Numeric->nrealloc = 0 ;
+ Numeric->ncostly = 0 ;
+ Numeric->ibig = EMPTY ;
+ Numeric->ihead = 0 ;
+ Numeric->itail = Numeric->size ;
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+#endif
+
+ /* allocate the 2-unit tail marker block and initialize it */
+ Numeric->itail -= 2 ;
+ p = Numeric->Memory + Numeric->itail ;
+ DEBUG2 (("p "ID" tail "ID"\n", (Int) (p-Numeric->Memory), Numeric->itail)) ;
+ Numeric->tail_usage = 2 ;
+ p->header.prevsize = 0 ;
+ p->header.size = 1 ;
+
+ /* allocate a 1-unit head marker block at the head of memory */
+ /* this is done so that an offset of zero is treated as a NULL pointer */
+ Numeric->ihead++ ;
+
+ /* initial usage in Numeric->Memory */
+ Numeric->max_usage = 3 ;
+ Numeric->init_usage = Numeric->max_usage ;
+
+ /* Note that UMFPACK_*symbolic ensures that Numeric->Memory is of size */
+ /* at least 3, so this initialization will always succeed. */
+
+#ifndef NDEBUG
+ DEBUG2 (("init_memoryspace, all free (except one unit at head\n")) ;
+ UMF_dump_memory (Numeric) ;
+#endif
+
+}
diff --git a/UMFPACK/Source/umf_mem_init_memoryspace.h b/UMFPACK/Source/umf_mem_init_memoryspace.h
new file mode 100644
index 0000000..45d552f
--- /dev/null
+++ b/UMFPACK/Source/umf_mem_init_memoryspace.h
@@ -0,0 +1,10 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_mem_init_memoryspace
+(
+ NumericType *Numeric
+) ;
diff --git a/UMFPACK/Source/umf_multicompile.c b/UMFPACK/Source/umf_multicompile.c
new file mode 100644
index 0000000..0603560
--- /dev/null
+++ b/UMFPACK/Source/umf_multicompile.c
@@ -0,0 +1,58 @@
+/* ========================================================================== */
+/* === UMF_multicompile ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* This file is not needed if you have the Unix/Linux "make" command for
+ * compiling UMFPACK. Microsoft Visual Studio cannot be configured to compile
+ * one file multiple times, with different -D flags. In this case, you can
+ * use this file instead. To use this file, see the Demo/simple_compile file.
+ *
+ * This file includes the following source files:
+ *
+ * umf_ltsolve.c
+ * umf_utsolve.c
+ * umf_triplet.c
+ * umf_assemble.c
+ * umf_store_lu.c
+ * umfpack_solve.c
+ *
+ * This file simply compiles the above files with different pre-#define'd flags,
+ * by defining the flags and then #include'ing the source files themselves.
+ * This is a rather unconventional approach, since by convention #include is
+ * supposed to be used with *.h files not *.c. However, it is one way of
+ * working around the limitations of Microsoft Visual Studio.
+ *
+ * You still need to compile all files separately as well, with none of the
+ * pre-#define'd terms listed below.
+ */
+
+/* compile the complex conjugate forward/backsolves */
+#define CONJUGATE_SOLVE
+#include "umf_ltsolve.c"
+#include "umf_utsolve.c"
+
+/* compile umf_triplet with DO_MAP, DO_VALUES and DO_MAP, and just DO_VALUES */
+#define DO_MAP
+#include "umf_triplet.c"
+#define DO_VALUES
+#include "umf_triplet.c"
+#undef DO_MAP
+#include "umf_triplet.c"
+
+/* compile the FIXQ version of umf_assemble */
+#define FIXQ
+#include "umf_assemble.c"
+
+/* compile the DROP version of umf_store_lu */
+#define DROP
+#include "umf_store_lu.c"
+
+/* compile umfpack_wsolve */
+#define WSOLVE
+#include "umfpack_solve.c"
diff --git a/UMFPACK/Source/umf_realloc.c b/UMFPACK/Source/umf_realloc.c
new file mode 100644
index 0000000..feae25a
--- /dev/null
+++ b/UMFPACK/Source/umf_realloc.c
@@ -0,0 +1,76 @@
+/* ========================================================================== */
+/* === UMF_realloc ========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Realloc a block previously allocated by UMF_malloc.
+ Return NULL on failure (in which case the block is still allocated, and will
+ be kept at is present size). This routine is only used for Numeric->Memory.
+*/
+
+#include "umf_internal.h"
+#include "umf_realloc.h"
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+#include "umf_malloc.h"
+#endif
+
+GLOBAL void *UMF_realloc
+(
+ void *p,
+ Int n_objects,
+ size_t size_of_object
+)
+{
+ size_t size ;
+ void *p2 ;
+
+#ifdef UMF_TCOV_TEST
+ /* For exhaustive statement coverage testing only! */
+ /* Pretend to fail, to test out-of-memory conditions. */
+ umf_realloc_fail-- ;
+ if (umf_realloc_fail <= umf_realloc_hi &&
+ umf_realloc_fail >= umf_realloc_lo)
+ {
+ return ((void *) NULL) ;
+ }
+#endif
+
+ /* make sure that we allocate something */
+ n_objects = MAX (1, n_objects) ;
+
+ size = (size_t) n_objects ;
+ ASSERT (size_of_object > 1) ;
+ if (size > Int_MAX / size_of_object)
+ {
+ /* :: int overflow in umf_realloc :: */
+ return ((void *) NULL) ;
+ }
+ size *= size_of_object ;
+
+ DEBUG0 (("UMF_realloc: "ID" n_objects "ID" size_of_object "ID"\n",
+ (Int) p, n_objects, (Int) size_of_object)) ;
+
+ /* see AMD/Source/amd_global.c for the memory allocator selection */
+ p2 = amd_realloc (p, size) ;
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ /* If p didn't exist on input, and p2 exists, then a new object has been
+ * allocated. */
+ if (p == (void *) NULL && p2 != (void *) NULL)
+ {
+ UMF_malloc_count++ ;
+ }
+#endif
+
+ DEBUG0 (("UMF_realloc: "ID" new malloc count "ID"\n",
+ (Int) p2, UMF_malloc_count)) ;
+
+ return (p2) ;
+}
diff --git a/UMFPACK/Source/umf_realloc.h b/UMFPACK/Source/umf_realloc.h
new file mode 100644
index 0000000..5b2f1c2
--- /dev/null
+++ b/UMFPACK/Source/umf_realloc.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void *UMF_realloc
+(
+ void *p,
+ Int n_objects,
+ size_t size_of_object
+) ;
diff --git a/UMFPACK/Source/umf_report_perm.c b/UMFPACK/Source/umf_report_perm.c
new file mode 100644
index 0000000..aa5260d
--- /dev/null
+++ b/UMFPACK/Source/umf_report_perm.c
@@ -0,0 +1,86 @@
+/* ========================================================================== */
+/* === UMF_report_perm ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_internal.h"
+#include "umf_report_perm.h"
+
+#define PRINTF4U(params) { if (user || prl >= 4) PRINTF (params) ; }
+
+GLOBAL Int UMF_report_perm
+(
+ Int n,
+ const Int P [ ],
+ Int W [ ], /* workspace of size n */
+ Int prl,
+ Int user
+)
+{
+ Int i, k, valid, prl1 ;
+
+ ASSERT (prl >= 3) ;
+
+ PRINTF4U (("permutation vector, n = "ID". ", n)) ;
+
+ if (n <= 0)
+ {
+ PRINTF (("ERROR: length of permutation is <= 0\n\n")) ;
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+
+ if (!P)
+ {
+ /* if P is (Int *) NULL, this is the identity permutation */
+ PRINTF (("(not present)\n\n")) ;
+ return (UMFPACK_OK) ;
+ }
+
+ if (!W)
+ {
+ PRINTF (("ERROR: out of memory\n\n")) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ PRINTF4 (("\n")) ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = TRUE ;
+ }
+
+ prl1 = prl ;
+ for (k = 0 ; k < n ; k++)
+ {
+ i = P [k] ;
+ PRINTF4 ((" "ID" : "ID" ", INDEX (k), INDEX (i))) ;
+ valid = (i >= 0 && i < n) ;
+ if (valid)
+ {
+ valid = W [i] ;
+ W [i] = FALSE ;
+ }
+ if (!valid)
+ {
+ /* out of range or duplicate entry */
+ PRINTF (("ERROR: invalid\n\n")) ;
+ return (UMFPACK_ERROR_invalid_permutation) ;
+ }
+ PRINTF4 (("\n")) ;
+ if (prl == 4 && k == 9 && n > 10)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+ }
+ prl = prl1 ;
+
+ PRINTF4 ((" permutation vector ")) ;
+ PRINTF4U (("OK\n\n")) ;
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umf_report_perm.h b/UMFPACK/Source/umf_report_perm.h
new file mode 100644
index 0000000..6b18d85
--- /dev/null
+++ b/UMFPACK/Source/umf_report_perm.h
@@ -0,0 +1,14 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_report_perm
+(
+ Int n,
+ const Int P [ ],
+ Int W [ ],
+ Int prl,
+ Int user
+) ;
diff --git a/UMFPACK/Source/umf_report_vector.c b/UMFPACK/Source/umf_report_vector.c
new file mode 100644
index 0000000..5533683
--- /dev/null
+++ b/UMFPACK/Source/umf_report_vector.c
@@ -0,0 +1,111 @@
+/* ========================================================================== */
+/* === UMF_report_vector ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_internal.h"
+#include "umf_report_vector.h"
+
+/* ========================================================================== */
+/* === print_value ========================================================== */
+/* ========================================================================== */
+
+PRIVATE void print_value
+(
+ Int i,
+ const double Xx [ ],
+ const double Xz [ ], /* used for complex case only */
+ Int scalar /* if true, then print real part only */
+)
+{
+ Entry xi ;
+ /* if Xz is null, then X is in "merged" format (compatible with Entry, */
+ /* and ANSI C99 double _Complex type). */
+ PRINTF ((" "ID" :", INDEX (i))) ;
+ if (scalar)
+ {
+ PRINT_SCALAR (Xx [i]) ;
+ }
+ else
+ {
+ ASSIGN (xi, Xx, Xz, i, SPLIT (Xz)) ;
+ PRINT_ENTRY (xi) ;
+ }
+ PRINTF (("\n")) ;
+}
+
+/* ========================================================================== */
+/* === UMF_report_vector ==================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMF_report_vector
+(
+ Int n,
+ const double Xx [ ],
+ const double Xz [ ],
+ Int prl,
+ Int user,
+ Int scalar
+)
+{
+ Int n2, i ;
+
+ if (user || prl >= 4)
+ {
+ PRINTF (("dense vector, n = "ID". ", n)) ;
+ }
+
+ if (user)
+ {
+ if (!Xx)
+ {
+ PRINTF (("ERROR: vector not present\n\n")) ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+ if (n < 0)
+ {
+ PRINTF (("ERROR: length of vector is < 0\n\n")) ;
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+ }
+
+ if (user || prl >= 4)
+ {
+ PRINTF4 (("\n")) ;
+ }
+
+ if (prl == 4)
+ {
+ /* print level of 4 */
+ n2 = MIN (10, n) ;
+ for (i = 0 ; i < n2 ; i++)
+ {
+ print_value (i, Xx, Xz, scalar) ;
+ }
+ if (n2 < n)
+ {
+ PRINTF ((" ...\n")) ;
+ print_value (n-1, Xx, Xz, scalar) ;
+ }
+ }
+ else if (prl > 4)
+ {
+ /* print level 4 or more */
+ for (i = 0 ; i < n ; i++)
+ {
+ print_value (i, Xx, Xz, scalar) ;
+ }
+ }
+
+ PRINTF4 ((" dense vector ")) ;
+ if (user || prl >= 4)
+ {
+ PRINTF (("OK\n\n")) ;
+ }
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umf_report_vector.h b/UMFPACK/Source/umf_report_vector.h
new file mode 100644
index 0000000..6a758d7
--- /dev/null
+++ b/UMFPACK/Source/umf_report_vector.h
@@ -0,0 +1,15 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_report_vector
+(
+ Int n,
+ const double Xx [ ],
+ const double Xz [ ],
+ Int prl,
+ Int user,
+ Int scalar
+) ;
diff --git a/UMFPACK/Source/umf_row_search.c b/UMFPACK/Source/umf_row_search.c
new file mode 100644
index 0000000..f20ca0c
--- /dev/null
+++ b/UMFPACK/Source/umf_row_search.c
@@ -0,0 +1,837 @@
+/* ========================================================================== */
+/* === UMF_row_search ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Find two candidate pivot rows in a column: the best one in the front,
+ and the best one not in the front. Return the two pivot row patterns and
+ their exact degrees. Called by UMF_local_search.
+
+ Returns UMFPACK_OK if successful, or UMFPACK_WARNING_singular_matrix or
+ UMFPACK_ERROR_different_pattern if not.
+
+*/
+
+#include "umf_internal.h"
+#include "umf_row_search.h"
+
+GLOBAL Int UMF_row_search
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic,
+ Int cdeg0, /* length of column in Front */
+ Int cdeg1, /* length of column outside Front */
+ const Int Pattern [ ], /* pattern of column, Pattern [0..cdeg1 -1] */
+ const Int Pos [ ], /* Pos [Pattern [0..cdeg1 -1]] = 0..cdeg1 -1 */
+ Int pivrow [2], /* pivrow [IN] and pivrow [OUT] */
+ Int rdeg [2], /* rdeg [IN] and rdeg [OUT] */
+ Int W_i [ ], /* pattern of pivrow [IN], */
+ /* either Fcols or Woi */
+ Int W_o [ ], /* pattern of pivrow [OUT], */
+ /* either Wio or Woo */
+ Int prior_pivrow [2], /* the two other rows just scanned, if any */
+ const Entry Wxy [ ], /* numerical values Wxy [0..cdeg1-1],
+ either Wx or Wy */
+
+ Int pivcol, /* the candidate column being searched */
+ Int freebie [ ]
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double maxval, toler, toler2, value, pivot [2] ;
+ Int i, row, deg, col, *Frpos, fnrows, *E, j, ncols, *Cols, *Rows,
+ e, f, Wrpflag, *Fcpos, fncols, tpi, max_rdeg, nans_in_col, was_offdiag,
+ diag_row, prefer_diagonal, *Wrp, found, *Diagonal_map ;
+ Tuple *tp, *tpend, *tp1, *tp2 ;
+ Unit *Memory, *p ;
+ Element *ep ;
+ Int *Row_tuples, *Row_degree, *Row_tlen ;
+
+#ifndef NDEBUG
+ Int *Col_degree ;
+ DEBUG2 (("Row_search:\n")) ;
+ for (i = 0 ; i < cdeg1 ; i++)
+ {
+ row = Pattern [i] ;
+ DEBUG4 ((" row: "ID"\n", row)) ;
+ ASSERT (row >= 0 && row < Numeric->n_row) ;
+ ASSERT (i == Pos [row]) ;
+ }
+ /* If row is not in Pattern [0..cdeg1-1], then Pos [row] == EMPTY */
+ if (UMF_debug > 0 || Numeric->n_row < 1000)
+ {
+ Int cnt = cdeg1 ;
+ DEBUG4 (("Scan all rows:\n")) ;
+ for (row = 0 ; row < Numeric->n_row ; row++)
+ {
+ if (Pos [row] < 0)
+ {
+ cnt++ ;
+ }
+ else
+ {
+ DEBUG4 ((" row: "ID" pos "ID"\n", row, Pos [row])) ;
+ }
+ }
+ ASSERT (cnt == Numeric->n_row) ;
+ }
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro only */
+ ASSERT (pivcol >= 0 && pivcol < Work->n_col) ;
+ ASSERT (NON_PIVOTAL_COL (pivcol)) ;
+#endif
+
+ pivot [IN] = 0. ;
+ pivot [OUT] = 0. ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Row_degree = Numeric->Rperm ;
+ Row_tuples = Numeric->Uip ;
+ Row_tlen = Numeric->Uilen ;
+ Wrp = Work->Wrp ;
+ Frpos = Work->Frpos ;
+ E = Work->E ;
+ Memory = Numeric->Memory ;
+ fnrows = Work->fnrows ;
+
+ prefer_diagonal = Symbolic->prefer_diagonal ;
+ Diagonal_map = Work->Diagonal_map ;
+
+ if (Diagonal_map)
+ {
+ diag_row = Diagonal_map [pivcol] ;
+ was_offdiag = diag_row < 0 ;
+ if (was_offdiag)
+ {
+ /* the "diagonal" entry in this column was permuted here by an
+ * earlier pivot choice. The tighter off-diagonal tolerance will
+ * be used instead of the symmetric tolerance. */
+ diag_row = FLIP (diag_row) ;
+ }
+ ASSERT (diag_row >= 0 && diag_row < Numeric->n_row) ;
+ }
+ else
+ {
+ diag_row = EMPTY ; /* unused */
+ was_offdiag = EMPTY ; /* unused */
+ }
+
+ /* pivot row degree cannot exceed max_rdeg */
+ max_rdeg = Work->fncols_max ;
+
+ /* ---------------------------------------------------------------------- */
+ /* scan pivot column for candidate rows */
+ /* ---------------------------------------------------------------------- */
+
+ maxval = 0.0 ;
+ nans_in_col = FALSE ;
+
+ for (i = 0 ; i < cdeg1 ; i++)
+ {
+ APPROX_ABS (value, Wxy [i]) ;
+ if (SCALAR_IS_NAN (value))
+ {
+ nans_in_col = TRUE ;
+ maxval = value ;
+ break ;
+ }
+ /* This test can now ignore the NaN case: */
+ maxval = MAX (maxval, value) ;
+ }
+
+ /* if maxval is zero, the matrix is numerically singular */
+
+ toler = Numeric->relpt * maxval ;
+ toler2 = Numeric->relpt2 * maxval ;
+ toler2 = was_offdiag ? toler : toler2 ;
+
+ DEBUG5 (("Row_search begins [ maxval %g toler %g %g\n",
+ maxval, toler, toler2)) ;
+ if (SCALAR_IS_NAN (toler) || SCALAR_IS_NAN (toler2))
+ {
+ nans_in_col = TRUE ;
+ }
+
+ if (!nans_in_col)
+ {
+
+ /* look for the diagonal entry, if it exists */
+ found = FALSE ;
+ ASSERT (!SCALAR_IS_NAN (toler)) ;
+
+ if (prefer_diagonal)
+ {
+ ASSERT (diag_row != EMPTY) ;
+ i = Pos [diag_row] ;
+ if (i >= 0)
+ {
+ double a ;
+ ASSERT (i < cdeg1) ;
+ ASSERT (diag_row == Pattern [i]) ;
+
+ APPROX_ABS (a, Wxy [i]) ;
+
+ ASSERT (!SCALAR_IS_NAN (a)) ;
+ ASSERT (!SCALAR_IS_NAN (toler2)) ;
+
+ if (SCALAR_IS_NONZERO (a) && a >= toler2)
+ {
+ /* found it! */
+ DEBUG3 (("Symmetric pivot: "ID" "ID"\n", pivcol, diag_row));
+ found = TRUE ;
+ if (Frpos [diag_row] >= 0 && Frpos [diag_row] < fnrows)
+ {
+ pivrow [IN] = diag_row ;
+ pivrow [OUT] = EMPTY ;
+ }
+ else
+ {
+ pivrow [IN] = EMPTY ;
+ pivrow [OUT] = diag_row ;
+ }
+ }
+ }
+ }
+
+ /* either no diagonal found, or we didn't look for it */
+ if (!found)
+ {
+ if (cdeg0 > 0)
+ {
+
+ /* this is a column in the front */
+ for (i = 0 ; i < cdeg0 ; i++)
+ {
+ double a ;
+ APPROX_ABS (a, Wxy [i]) ;
+ ASSERT (!SCALAR_IS_NAN (a)) ;
+ ASSERT (!SCALAR_IS_NAN (toler)) ;
+ if (SCALAR_IS_NONZERO (a) && a >= toler)
+ {
+ row = Pattern [i] ;
+ deg = Row_degree [row] ;
+#ifndef NDEBUG
+ DEBUG6 ((ID" candidate row "ID" deg "ID" absval %g\n",
+ i, row, deg, a)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
+#endif
+ ASSERT (Frpos [row] >= 0 && Frpos [row] < fnrows) ;
+ ASSERT (Frpos [row] == i) ;
+ /* row is in the current front */
+ DEBUG4 ((" in front\n")) ;
+ if (deg < rdeg [IN]
+ /* break ties by picking the largest entry: */
+ || (deg == rdeg [IN] && a > pivot [IN])
+ /* break ties by picking the diagonal entry: */
+ /* || (deg == rdeg [IN] && row == diag_row) */
+ )
+ {
+ /* best row in front, so far */
+ pivrow [IN] = row ;
+ rdeg [IN] = deg ;
+ pivot [IN] = a ;
+ }
+ }
+ }
+ for ( ; i < cdeg1 ; i++)
+ {
+ double a ;
+ APPROX_ABS (a, Wxy [i]) ;
+ ASSERT (!SCALAR_IS_NAN (a)) ;
+ ASSERT (!SCALAR_IS_NAN (toler)) ;
+ if (SCALAR_IS_NONZERO (a) && a >= toler)
+ {
+ row = Pattern [i] ;
+ deg = Row_degree [row] ;
+#ifndef NDEBUG
+ DEBUG6 ((ID" candidate row "ID" deg "ID" absval %g\n",
+ i, row, deg, a)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
+#endif
+ ASSERT (Frpos [row] == i) ;
+ /* row is not in the current front */
+ DEBUG4 ((" NOT in front\n")) ;
+ if (deg < rdeg [OUT]
+ /* break ties by picking the largest entry: */
+ || (deg == rdeg [OUT] && a > pivot [OUT])
+ /* break ties by picking the diagonal entry: */
+ /* || (deg == rdeg [OUT] && row == diag_row) */
+ )
+ {
+ /* best row not in front, so far */
+ pivrow [OUT] = row ;
+ rdeg [OUT] = deg ;
+ pivot [OUT] = a ;
+ }
+ }
+ }
+
+ }
+ else
+ {
+
+ /* this column is not in the front */
+ for (i = 0 ; i < cdeg1 ; i++)
+ {
+ double a ;
+ APPROX_ABS (a, Wxy [i]) ;
+ ASSERT (!SCALAR_IS_NAN (a)) ;
+ ASSERT (!SCALAR_IS_NAN (toler)) ;
+ if (SCALAR_IS_NONZERO (a) && a >= toler)
+ {
+ row = Pattern [i] ;
+ deg = Row_degree [row] ;
+#ifndef NDEBUG
+ DEBUG6 ((ID" candidate row "ID" deg "ID" absval %g\n",
+ i, row, deg, a)) ;
+ UMF_dump_rowcol (0, Numeric, Work, row, TRUE) ;
+#endif
+ if (Frpos [row] >= 0 && Frpos [row] < fnrows)
+ {
+ /* row is in the current front */
+ DEBUG4 ((" in front\n")) ;
+ if (deg < rdeg [IN]
+ /* break ties by picking the largest entry: */
+ || (deg == rdeg [IN] && a > pivot [IN])
+ /* break ties by picking the diagonal entry: */
+ /* || (deg == rdeg [IN] && row == diag_row) */
+ )
+ {
+ /* best row in front, so far */
+ pivrow [IN] = row ;
+ rdeg [IN] = deg ;
+ pivot [IN] = a ;
+ }
+ }
+ else
+ {
+ /* row is not in the current front */
+ DEBUG4 ((" NOT in front\n")) ;
+ if (deg < rdeg [OUT]
+ /* break ties by picking the largest entry: */
+ || (deg == rdeg[OUT] && a > pivot [OUT])
+ /* break ties by picking the diagonal entry: */
+ /* || (deg == rdeg[OUT] && row == diag_row) */
+ )
+ {
+ /* best row not in front, so far */
+ pivrow [OUT] = row ;
+ rdeg [OUT] = deg ;
+ pivot [OUT] = a ;
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* NaN handling */
+ /* ---------------------------------------------------------------------- */
+
+ /* if cdeg1 > 0 then we must have found a pivot row ... unless NaN's */
+ /* exist. Try with no numerical tests if no pivot found. */
+
+ if (cdeg1 > 0 && pivrow [IN] == EMPTY && pivrow [OUT] == EMPTY)
+ {
+ /* cleanup for the NaN case */
+ DEBUG0 (("Found a NaN in pivot column!\n")) ;
+
+ /* grab the first entry in the pivot column, ignoring degree, */
+ /* numerical stability, and symmetric preference */
+ row = Pattern [0] ;
+ deg = Row_degree [row] ;
+ if (Frpos [row] >= 0 && Frpos [row] < fnrows)
+ {
+ /* row is in the current front */
+ DEBUG4 ((" in front\n")) ;
+ pivrow [IN] = row ;
+ rdeg [IN] = deg ;
+ }
+ else
+ {
+ /* row is not in the current front */
+ DEBUG4 ((" NOT in front\n")) ;
+ pivrow [OUT] = row ;
+ rdeg [OUT] = deg ;
+ }
+
+ /* We are now guaranteed to have a pivot, no matter how broken */
+ /* (non-IEEE compliant) the underlying numerical operators are. */
+ /* This is particularly a problem for Microsoft compilers (they do */
+ /* not handle NaN's properly). Now try to find a sparser pivot, if */
+ /* possible. */
+
+ for (i = 1 ; i < cdeg1 ; i++)
+ {
+ row = Pattern [i] ;
+ deg = Row_degree [row] ;
+
+ if (Frpos [row] >= 0 && Frpos [row] < fnrows)
+ {
+ /* row is in the current front */
+ DEBUG4 ((" in front\n")) ;
+ if (deg < rdeg [IN] || (deg == rdeg [IN] && row == diag_row))
+ {
+ /* best row in front, so far */
+ pivrow [IN] = row ;
+ rdeg [IN] = deg ;
+ }
+ }
+ else
+ {
+ /* row is not in the current front */
+ DEBUG4 ((" NOT in front\n")) ;
+ if (deg < rdeg [OUT] || (deg == rdeg [OUT] && row == diag_row))
+ {
+ /* best row not in front, so far */
+ pivrow [OUT] = row ;
+ rdeg [OUT] = deg ;
+ }
+ }
+ }
+ }
+
+ /* We found a pivot if there are entries (even zero ones) in pivot col */
+ ASSERT (IMPLIES (cdeg1 > 0, pivrow[IN] != EMPTY || pivrow[OUT] != EMPTY)) ;
+
+ /* If there are no entries in the pivot column, then no pivot is found */
+ ASSERT (IMPLIES (cdeg1 == 0, pivrow[IN] == EMPTY && pivrow[OUT] == EMPTY)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check for singular matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (cdeg1 == 0)
+ {
+ if (fnrows > 0)
+ {
+ /*
+ Get the pivrow [OUT][IN] from the current front.
+ The frontal matrix looks like this:
+
+ pivcol[OUT]
+ |
+ v
+ x x x x 0 <- so grab this row as the pivrow [OUT][IN].
+ x x x x 0
+ x x x x 0
+ 0 0 0 0 0
+
+ The current frontal matrix has some rows in it. The degree
+ of the pivcol[OUT] is zero. The column is empty, and the
+ current front does not contribute to it.
+
+ */
+ pivrow [IN] = Work->Frows [0] ;
+ DEBUGm4 (("Got zero pivrow[OUT][IN] "ID" from current front\n",
+ pivrow [IN])) ;
+ }
+ else
+ {
+
+ /*
+ Get a pivot row from the row-merge tree, use as
+ pivrow [OUT][OUT]. pivrow [IN] remains EMPTY.
+ This can only happen if the current front is 0-by-0.
+ */
+
+ Int *Front_leftmostdesc, *Front_1strow, *Front_new1strow, row1,
+ row2, fleftmost, nfr, n_row, frontid ;
+
+ ASSERT (Work->fncols == 0) ;
+
+ Front_leftmostdesc = Symbolic->Front_leftmostdesc ;
+ Front_1strow = Symbolic->Front_1strow ;
+ Front_new1strow = Work->Front_new1strow ;
+ nfr = Symbolic->nfr ;
+ n_row = Numeric->n_row ;
+ frontid = Work->frontid ;
+
+ DEBUGm4 (("Note: pivcol: "ID" is empty front "ID"\n",
+ pivcol, frontid)) ;
+#ifndef NDEBUG
+ DEBUG1 (("Calling dump rowmerge\n")) ;
+ UMF_dump_rowmerge (Numeric, Symbolic, Work) ;
+#endif
+
+ /* Row-merge set is the non-pivotal rows in the range */
+ /* Front_new1strow [Front_leftmostdesc [frontid]] to */
+ /* Front_1strow [frontid+1] - 1. */
+ /* If this is empty, then use the empty rows, in the range */
+ /* Front_new1strow [nfr] to n_row-1. */
+ /* If this too is empty, then pivrow [OUT] will be empty. */
+ /* In both cases, update Front_new1strow [...]. */
+
+ fleftmost = Front_leftmostdesc [frontid] ;
+ row1 = Front_new1strow [fleftmost] ;
+ row2 = Front_1strow [frontid+1] - 1 ;
+ DEBUG1 (("Leftmost: "ID" Rows ["ID" to "ID"] srch ["ID" to "ID"]\n",
+ fleftmost, Front_1strow [frontid], row2, row1, row2)) ;
+
+ /* look in the range row1 ... row2 */
+ for (row = row1 ; row <= row2 ; row++)
+ {
+ DEBUG3 ((" Row: "ID"\n", row)) ;
+ if (NON_PIVOTAL_ROW (row))
+ {
+ /* found it */
+ DEBUG3 ((" Row: "ID" found\n", row)) ;
+ ASSERT (Frpos [row] == EMPTY) ;
+ pivrow [OUT] = row ;
+ DEBUGm4 (("got row merge pivrow %d\n", pivrow [OUT])) ;
+ break ;
+ }
+ }
+ Front_new1strow [fleftmost] = row ;
+
+ if (pivrow [OUT] == EMPTY)
+ {
+ /* not found, look in empty row set in "dummy" front */
+ row1 = Front_new1strow [nfr] ;
+ row2 = n_row-1 ;
+ DEBUG3 (("Empty: "ID" Rows ["ID" to "ID"] srch["ID" to "ID"]\n",
+ nfr, Front_1strow [nfr], row2, row1, row2)) ;
+
+ /* look in the range row1 ... row2 */
+ for (row = row1 ; row <= row2 ; row++)
+ {
+ DEBUG3 ((" Empty Row: "ID"\n", row)) ;
+ if (NON_PIVOTAL_ROW (row))
+ {
+ /* found it */
+ DEBUG3 ((" Empty Row: "ID" found\n", row)) ;
+ ASSERT (Frpos [row] == EMPTY) ;
+ pivrow [OUT] = row ;
+ DEBUGm4 (("got dummy row pivrow %d\n", pivrow [OUT])) ;
+ break ;
+ }
+ }
+ Front_new1strow [nfr] = row ;
+ }
+
+ if (pivrow [OUT] == EMPTY)
+ {
+ /* Row-merge set is empty. We can just discard */
+ /* the candidate pivot column. */
+ DEBUG0 (("Note: row-merge set empty\n")) ;
+ DEBUGm4 (("got no pivrow \n")) ;
+ return (UMFPACK_WARNING_singular_matrix) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the candidate row in the front, if any */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ /* check Wrp */
+ ASSERT (Work->Wrpflag > 0) ;
+ if (UMF_debug > 0 || Work->n_col < 1000)
+ {
+ for (i = 0 ; i < Work->n_col ; i++)
+ {
+ ASSERT (Wrp [i] < Work->Wrpflag) ;
+ }
+ }
+#endif
+
+#ifndef NDEBUG
+ DEBUG4 (("pivrow [IN]: "ID"\n", pivrow [IN])) ;
+ UMF_dump_rowcol (0, Numeric, Work, pivrow [IN], TRUE) ;
+#endif
+
+ if (pivrow [IN] != EMPTY)
+ {
+
+ /* the row merge candidate row is not pivrow [IN] */
+ freebie [IN] = (pivrow [IN] == prior_pivrow [IN]) && (cdeg1 > 0) ;
+ ASSERT (cdeg1 >= 0) ;
+
+ if (!freebie [IN])
+ {
+ /* include current front in the degree of this row */
+
+ Fcpos = Work->Fcpos ;
+ fncols = Work->fncols ;
+
+ Wrpflag = Work->Wrpflag ;
+
+ /* -------------------------------------------------------------- */
+ /* construct the pattern of the IN row */
+ /* -------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ /* check Fcols */
+ DEBUG5 (("ROW ASSEMBLE: rdeg "ID"\nREDUCE ROW "ID"\n",
+ fncols, pivrow [IN])) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ col = Work->Fcols [j] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ ASSERT (Fcpos [col] >= 0) ;
+ }
+ if (UMF_debug > 0 || Work->n_col < 1000)
+ {
+ Int cnt = fncols ;
+ for (col = 0 ; col < Work->n_col ; col++)
+ {
+ if (Fcpos [col] < 0) cnt++ ;
+ }
+ ASSERT (cnt == Work->n_col) ;
+ }
+#endif
+
+ rdeg [IN] = fncols ;
+
+ ASSERT (pivrow [IN] >= 0 && pivrow [IN] < Work->n_row) ;
+ ASSERT (NON_PIVOTAL_ROW (pivrow [IN])) ;
+
+ /* add the pivot column itself */
+ ASSERT (Wrp [pivcol] != Wrpflag) ;
+ if (Fcpos [pivcol] < 0)
+ {
+ DEBUG3 (("Adding pivot col to pivrow [IN] pattern\n")) ;
+ if (rdeg [IN] >= max_rdeg)
+ {
+ /* :: pattern change (in) :: */
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Wrp [pivcol] = Wrpflag ;
+ W_i [rdeg [IN]++] = pivcol ;
+ }
+
+ tpi = Row_tuples [pivrow [IN]] ;
+ if (tpi)
+ {
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Row_tlen [pivrow [IN]] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e])
+ {
+ continue ; /* element already deallocated */
+ }
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ ncols = ep->ncols ;
+ Rows = Cols + ncols ;
+ if (Rows [f] == EMPTY)
+ {
+ continue ; /* row already assembled */
+ }
+ ASSERT (pivrow [IN] == Rows [f]) ;
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ ASSERT (col >= EMPTY && col < Work->n_col) ;
+ if ((col >= 0) && (Wrp [col] != Wrpflag)
+ && Fcpos [col] <0)
+ {
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ if (rdeg [IN] >= max_rdeg)
+ {
+ /* :: pattern change (rdeg in failure) :: */
+ DEBUGm4 (("rdeg [IN] >= max_rdeg failure\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Wrp [col] = Wrpflag ;
+ W_i [rdeg [IN]++] = col ;
+ }
+ }
+
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Row_tlen [pivrow [IN]] = tp2 - tp1 ;
+ }
+
+#ifndef NDEBUG
+ DEBUG4 (("Reduced IN row:\n")) ;
+ for (j = 0 ; j < fncols ; j++)
+ {
+ DEBUG6 ((" "ID" "ID" "ID"\n",
+ j, Work->Fcols [j], Fcpos [Work->Fcols [j]])) ;
+ ASSERT (Fcpos [Work->Fcols [j]] >= 0) ;
+ }
+ for (j = fncols ; j < rdeg [IN] ; j++)
+ {
+ DEBUG6 ((" "ID" "ID" "ID"\n", j, W_i [j], Wrp [W_i [j]]));
+ ASSERT (W_i [j] >= 0 && W_i [j] < Work->n_col) ;
+ ASSERT (Wrp [W_i [j]] == Wrpflag) ;
+ }
+ /* mark the end of the pattern in case we scan it by mistake */
+ /* Note that this means W_i must be of size >= fncols_max + 1 */
+ W_i [rdeg [IN]] = EMPTY ;
+#endif
+
+ /* rdeg [IN] is now the exact degree of the IN row */
+
+ /* clear Work->Wrp. */
+ Work->Wrpflag++ ;
+ /* All Wrp [0..n_col] is now < Wrpflag */
+ }
+ }
+
+#ifndef NDEBUG
+ /* check Wrp */
+ if (UMF_debug > 0 || Work->n_col < 1000)
+ {
+ for (i = 0 ; i < Work->n_col ; i++)
+ {
+ ASSERT (Wrp [i] < Work->Wrpflag) ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the candidate row not in the front, if any */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG4 (("pivrow [OUT]: "ID"\n", pivrow [OUT])) ;
+ UMF_dump_rowcol (0, Numeric, Work, pivrow [OUT], TRUE) ;
+#endif
+
+ /* If this is a candidate row from the row merge set, force it to be */
+ /* scanned (ignore prior_pivrow [OUT]). */
+
+ if (pivrow [OUT] != EMPTY)
+ {
+ freebie [OUT] = (pivrow [OUT] == prior_pivrow [OUT]) && cdeg1 > 0 ;
+ ASSERT (cdeg1 >= 0) ;
+
+ if (!freebie [OUT])
+ {
+
+ Wrpflag = Work->Wrpflag ;
+
+ /* -------------------------------------------------------------- */
+ /* construct the pattern of the row */
+ /* -------------------------------------------------------------- */
+
+ rdeg [OUT] = 0 ;
+
+ ASSERT (pivrow [OUT] >= 0 && pivrow [OUT] < Work->n_row) ;
+ ASSERT (NON_PIVOTAL_ROW (pivrow [OUT])) ;
+
+ /* add the pivot column itself */
+ ASSERT (Wrp [pivcol] != Wrpflag) ;
+ DEBUG3 (("Adding pivot col to pivrow [OUT] pattern\n")) ;
+ if (rdeg [OUT] >= max_rdeg)
+ {
+ /* :: pattern change (out) :: */
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Wrp [pivcol] = Wrpflag ;
+ W_o [rdeg [OUT]++] = pivcol ;
+
+ tpi = Row_tuples [pivrow [OUT]] ;
+ if (tpi)
+ {
+ tp = (Tuple *) (Memory + tpi) ;
+ tp1 = tp ;
+ tp2 = tp ;
+ tpend = tp + Row_tlen [pivrow [OUT]] ;
+ for ( ; tp < tpend ; tp++)
+ {
+ e = tp->e ;
+ ASSERT (e > 0 && e <= Work->nel) ;
+ if (!E [e])
+ {
+ continue ; /* element already deallocated */
+ }
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ ncols = ep->ncols ;
+ Rows = Cols + ncols ;
+ if (Rows [f] == EMPTY)
+ {
+ continue ; /* row already assembled */
+ }
+ ASSERT (pivrow [OUT] == Rows [f]) ;
+
+ for (j = 0 ; j < ncols ; j++)
+ {
+ col = Cols [j] ;
+ ASSERT (col >= EMPTY && col < Work->n_col) ;
+ if ((col >= 0) && (Wrp [col] != Wrpflag))
+ {
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ if (rdeg [OUT] >= max_rdeg)
+ {
+ /* :: pattern change (rdeg out failure) :: */
+ DEBUGm4 (("rdeg [OUT] failure\n")) ;
+ return (UMFPACK_ERROR_different_pattern) ;
+ }
+ Wrp [col] = Wrpflag ;
+ W_o [rdeg [OUT]++] = col ;
+ }
+ }
+ *tp2++ = *tp ; /* leave the tuple in the list */
+ }
+ Row_tlen [pivrow [OUT]] = tp2 - tp1 ;
+ }
+
+#ifndef NDEBUG
+ DEBUG4 (("Reduced row OUT:\n")) ;
+ for (j = 0 ; j < rdeg [OUT] ; j++)
+ {
+ DEBUG6 ((" "ID" "ID" "ID"\n", j, W_o [j], Wrp [W_o [j]])) ;
+ ASSERT (W_o [j] >= 0 && W_o [j] < Work->n_col) ;
+ ASSERT (Wrp [W_o [j]] == Wrpflag) ;
+ }
+ /* mark the end of the pattern in case we scan it by mistake */
+ /* Note that this means W_o must be of size >= fncols_max + 1 */
+ W_o [rdeg [OUT]] = EMPTY ;
+#endif
+
+ /* rdeg [OUT] is now the exact degree of the row */
+
+ /* clear Work->Wrp. */
+ Work->Wrpflag++ ;
+ /* All Wrp [0..n] is now < Wrpflag */
+
+ }
+
+ }
+ DEBUG5 (("Row_search end ] \n")) ;
+
+#ifndef NDEBUG
+ /* check Wrp */
+ if (UMF_debug > 0 || Work->n_col < 1000)
+ {
+ for (i = 0 ; i < Work->n_col ; i++)
+ {
+ ASSERT (Wrp [i] < Work->Wrpflag) ;
+ }
+ }
+#endif
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umf_row_search.h b/UMFPACK/Source/umf_row_search.h
new file mode 100644
index 0000000..e0171ee
--- /dev/null
+++ b/UMFPACK/Source/umf_row_search.h
@@ -0,0 +1,32 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_row_search
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic,
+ Int cdeg0,
+ Int cdeg1,
+ const Int Pattern [ ],
+ const Int Pos [ ],
+ Int pivrow [2],
+ Int rdeg [2],
+ Int W_i [ ],
+ Int W_o [ ],
+ Int prior_pivrow [2],
+ const Entry Wxy [ ],
+ Int pivcol,
+ Int freebie [2]
+) ;
+
+#define IN 0
+#define OUT 1
+
+#define IN_IN 0
+#define IN_OUT 1
+#define OUT_IN 2
+#define OUT_OUT 3
diff --git a/UMFPACK/Source/umf_scale.c b/UMFPACK/Source/umf_scale.c
new file mode 100644
index 0000000..04f09df
--- /dev/null
+++ b/UMFPACK/Source/umf_scale.c
@@ -0,0 +1,82 @@
+/* ========================================================================== */
+/* === UMF_scale ============================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Divide a vector of stride 1 by the pivot value. */
+
+#include "umf_internal.h"
+#include "umf_scale.h"
+
+GLOBAL void UMF_scale
+(
+ Int n,
+ Entry pivot,
+ Entry X [ ]
+)
+{
+ Entry x ;
+ double s ;
+ Int i ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the approximate absolute value of the pivot, and select method */
+ /* ---------------------------------------------------------------------- */
+
+ APPROX_ABS (s, pivot) ;
+
+ if (s < RECIPROCAL_TOLERANCE || IS_NAN (pivot))
+ {
+ /* ------------------------------------------------------------------ */
+ /* tiny, or zero, pivot case */
+ /* ------------------------------------------------------------------ */
+
+ /* The pivot is tiny, or NaN. Do not divide zero by the pivot value,
+ * and do not multiply by 1/pivot, either. */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] /= pivot ; */
+ x = X [i] ;
+
+#ifndef NO_DIVIDE_BY_ZERO
+ if (IS_NONZERO (x))
+ {
+ DIV (X [i], x, pivot) ;
+ }
+#else
+ /* Do not divide by zero */
+ if (IS_NONZERO (x) && IS_NONZERO (pivot))
+ {
+ DIV (X [i], x, pivot) ;
+ }
+#endif
+
+ }
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* normal case */
+ /* ------------------------------------------------------------------ */
+
+ /* The pivot is not tiny, and is not NaN. Don't bother to check for
+ * zeros in the pivot column, X. This is slightly more accurate than
+ * multiplying by 1/pivot (but slightly slower), particularly if the
+ * pivot column consists of only IEEE subnormals. */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] /= pivot ; */
+ x = X [i] ;
+ DIV (X [i], x, pivot) ;
+ }
+ }
+}
diff --git a/UMFPACK/Source/umf_scale.h b/UMFPACK/Source/umf_scale.h
new file mode 100644
index 0000000..99799f5
--- /dev/null
+++ b/UMFPACK/Source/umf_scale.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_scale
+(
+ Int n,
+ Entry alpha,
+ Entry X [ ]
+) ;
diff --git a/UMFPACK/Source/umf_scale_column.c b/UMFPACK/Source/umf_scale_column.c
new file mode 100644
index 0000000..9fd3796
--- /dev/null
+++ b/UMFPACK/Source/umf_scale_column.c
@@ -0,0 +1,434 @@
+/* ========================================================================== */
+/* === UMF_scale_column ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Scale the current pivot column, move the pivot row and column into place,
+ and log the permutation.
+*/
+
+#include "umf_internal.h"
+#include "umf_scale_column.h"
+#include "umf_mem_free_tail_block.h"
+#include "umf_scale.h"
+
+/* ========================================================================== */
+/* === shift_pivot_row ====================================================== */
+/* ========================================================================== */
+
+/* Except for the BLAS, most of the time is typically spent in the following
+ * shift_pivot_row routine. It copies the pivot row into the U block, and
+ * then fills in the whole in the C block by shifting the last row of C into
+ * the row vacated by the pivot row.
+ */
+
+PRIVATE void shift_pivot_row (Entry *Fd, Entry *Fs, Entry *Fe, Int len, Int d)
+{
+ Int j ;
+#pragma ivdep
+ for (j = 0 ; j < len ; j++)
+ {
+ Fd [j] = Fs [j*d] ;
+ Fs [j*d] = Fe [j*d] ;
+ }
+}
+
+/* ========================================================================== */
+/* === UMF_scale_column ===================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMF_scale_column
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry pivot_value ;
+ Entry *Fcol, *Flublock, *Flblock, *Fublock, *Fcblock ;
+ Int k, k1, fnr_curr, fnrows, fncols, *Frpos, *Fcpos, pivrow, pivcol,
+ *Frows, *Fcols, fnc_curr, fnpiv, *Row_tuples, nb,
+ *Col_tuples, *Rperm, *Cperm, fspos, col2, row2 ;
+#ifndef NDEBUG
+ Int *Col_degree, *Row_degree ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ fnpiv = Work->fnpiv ;
+
+ /* ---------------------------------------------------------------------- */
+
+ Rperm = Numeric->Rperm ;
+ Cperm = Numeric->Cperm ;
+
+ /* ---------------------------------------------------------------------- */
+
+ Flublock = Work->Flublock ;
+ Flblock = Work->Flblock ;
+ Fublock = Work->Fublock ;
+ Fcblock = Work->Fcblock ;
+
+ fnr_curr = Work->fnr_curr ;
+ fnc_curr = Work->fnc_curr ;
+ Frpos = Work->Frpos ;
+ Fcpos = Work->Fcpos ;
+ Frows = Work->Frows ;
+ Fcols = Work->Fcols ;
+ pivrow = Work->pivrow ;
+ pivcol = Work->pivcol ;
+
+ ASSERT (pivrow >= 0 && pivrow < Work->n_row) ;
+ ASSERT (pivcol >= 0 && pivcol < Work->n_col) ;
+
+#ifndef NDEBUG
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+#endif
+
+ Row_tuples = Numeric->Uip ;
+ Col_tuples = Numeric->Lip ;
+ nb = Work->nb ;
+
+#ifndef NDEBUG
+ ASSERT (fnrows == Work->fnrows_new + 1) ;
+ ASSERT (fncols == Work->fncols_new + 1) ;
+ DEBUG1 (("SCALE COL: fnrows "ID" fncols "ID"\n", fnrows, fncols)) ;
+ DEBUG2 (("\nFrontal matrix, including all space:\n"
+ "fnr_curr "ID" fnc_curr "ID" nb "ID"\n"
+ "fnrows "ID" fncols "ID" fnpiv "ID"\n",
+ fnr_curr, fnc_curr, nb, fnrows, fncols, fnpiv)) ;
+ DEBUG2 (("\nJust the active part:\n")) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Flublock, nb, fnpiv, fnpiv) ;
+#endif
+
+ /* ====================================================================== */
+ /* === Shift pivot row and column ======================================= */
+ /* ====================================================================== */
+
+ /* ---------------------------------------------------------------------- */
+ /* move pivot column into place */
+ /* ---------------------------------------------------------------------- */
+
+ /* Note that the pivot column is already in place. Just shift the last
+ * column into the position vacated by the pivot column. */
+
+ fspos = Fcpos [pivcol] ;
+
+ /* one less column in the contribution block */
+ fncols = --(Work->fncols) ;
+
+ if (fspos != fncols * fnr_curr)
+ {
+
+ Int fs = fspos / fnr_curr ;
+
+ DEBUG6 (("Shift pivot column in front\n")) ;
+ DEBUG6 (("fspos: "ID" flpos: "ID"\n", fspos, fncols * fnr_curr)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* move Fe => Fs */
+ /* ------------------------------------------------------------------ */
+
+ /* column of the contribution block: */
+ {
+ /* Fs: current position of pivot column in contribution block */
+ /* Fe: position of last column in contribution block */
+ Int i ;
+ Entry *Fs, *Fe ;
+ Fs = Fcblock + fspos ;
+ Fe = Fcblock + fncols * fnr_curr ;
+#pragma ivdep
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Fs [i] = Fe [i] ;
+ }
+ }
+
+ /* column of the U2 block */
+ {
+ /* Fs: current position of pivot column in U block */
+ /* Fe: last column in U block */
+ Int i ;
+ Entry *Fs, *Fe ;
+ Fs = Fublock + fs ;
+ Fe = Fublock + fncols ;
+#pragma ivdep
+ for (i = 0 ; i < fnpiv ; i++)
+ {
+ Fs [i * fnc_curr] = Fe [i * fnc_curr] ;
+ }
+ }
+
+ /* move column Fe to Fs in the Fcols pattern */
+ col2 = Fcols [fncols] ;
+ Fcols [fs] = col2 ;
+ Fcpos [col2] = fspos ;
+ }
+
+ /* pivot column is no longer in the frontal matrix */
+ Fcpos [pivcol] = EMPTY ;
+
+#ifndef NDEBUG
+ DEBUG2 (("\nFrontal matrix after col swap, including all space:\n"
+ "fnr_curr "ID" fnc_curr "ID" nb "ID"\n"
+ "fnrows "ID" fncols "ID" fnpiv "ID"\n",
+ fnr_curr, fnc_curr, nb,
+ fnrows, fncols, fnpiv)) ;
+ DEBUG2 (("\nJust the active part:\n")) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv+1);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Flublock, nb, fnpiv, fnpiv+1) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* move pivot row into place */
+ /* ---------------------------------------------------------------------- */
+
+ fspos = Frpos [pivrow] ;
+
+ /* one less row in the contribution block */
+ fnrows = --(Work->fnrows) ;
+
+ DEBUG6 (("Swap/shift pivot row in front:\n")) ;
+ DEBUG6 (("fspos: "ID" flpos: "ID"\n", fspos, fnrows)) ;
+
+ if (fspos == fnrows)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* move Fs => Fd */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG6 (("row case 1\n")) ;
+
+ /* row of the contribution block: */
+ {
+ Int j ;
+ Entry *Fd, *Fs ;
+ Fd = Fublock + fnpiv * fnc_curr ;
+ Fs = Fcblock + fspos ;
+#pragma ivdep
+ for (j = 0 ; j < fncols ; j++)
+ {
+ Fd [j] = Fs [j * fnr_curr] ;
+ }
+ }
+
+ /* row of the L2 block: */
+ if (Work->pivrow_in_front)
+ {
+ Int j ;
+ Entry *Fd, *Fs ;
+ Fd = Flublock + fnpiv ;
+ Fs = Flblock + fspos ;
+#pragma ivdep
+ for (j = 0 ; j <= fnpiv ; j++)
+ {
+ Fd [j * nb] = Fs [j * fnr_curr] ;
+ }
+ }
+ else
+ {
+ Int j ;
+ Entry *Fd, *Fs ;
+ Fd = Flublock + fnpiv ;
+ Fs = Flblock + fspos ;
+#pragma ivdep
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ ASSERT (IS_ZERO (Fs [j * fnr_curr])) ;
+ CLEAR (Fd [j * nb]) ;
+ }
+ Fd [fnpiv * nb] = Fs [fnpiv * fnr_curr] ;
+ }
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* move Fs => Fd */
+ /* move Fe => Fs */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG6 (("row case 2\n")) ;
+ /* this is the most common case, by far */
+
+ /* row of the contribution block: */
+ {
+ /* Fd: destination of pivot row on U block */
+ /* Fs: current position of pivot row in contribution block */
+ /* Fe: position of last row in contribution block */
+ Entry *Fd, *Fs, *Fe ;
+ Fd = Fublock + fnpiv * fnc_curr ;
+ Fs = Fcblock + fspos ;
+ Fe = Fcblock + fnrows ;
+ shift_pivot_row (Fd, Fs, Fe, fncols, fnr_curr) ;
+ }
+
+ /* row of the L2 block: */
+ if (Work->pivrow_in_front)
+ {
+ /* Fd: destination of pivot row in LU block */
+ /* Fs: current position of pivot row in L block */
+ /* Fe: last row in L block */
+ Int j ;
+ Entry *Fd, *Fs, *Fe ;
+ Fd = Flublock + fnpiv ;
+ Fs = Flblock + fspos ;
+ Fe = Flblock + fnrows ;
+#pragma ivdep
+ for (j = 0 ; j <= fnpiv ; j++)
+ {
+ Fd [j * nb] = Fs [j * fnr_curr] ;
+ Fs [j * fnr_curr] = Fe [j * fnr_curr] ;
+ }
+ }
+ else
+ {
+ Int j ;
+ Entry *Fd, *Fs, *Fe ;
+ Fd = Flublock + fnpiv ;
+ Fs = Flblock + fspos ;
+ Fe = Flblock + fnrows ;
+#pragma ivdep
+ for (j = 0 ; j < fnpiv ; j++)
+ {
+ ASSERT (IS_ZERO (Fs [j * fnr_curr])) ;
+ CLEAR (Fd [j * nb]) ;
+ Fs [j * fnr_curr] = Fe [j * fnr_curr] ;
+ }
+ Fd [fnpiv * nb] = Fs [fnpiv * fnr_curr] ;
+ Fs [fnpiv * fnr_curr] = Fe [fnpiv * fnr_curr] ;
+ }
+
+ /* move row Fe to Fs in the Frows pattern */
+ row2 = Frows [fnrows] ;
+ Frows [fspos] = row2 ;
+ Frpos [row2] = fspos ;
+
+ }
+ /* pivot row is no longer in the frontal matrix */
+ Frpos [pivrow] = EMPTY ;
+
+#ifndef NDEBUG
+ DEBUG2 (("\nFrontal matrix after row swap, including all space:\n"
+ "fnr_curr "ID" fnc_curr "ID" nb "ID"\n"
+ "fnrows "ID" fncols "ID" fnpiv "ID"\n",
+ Work->fnr_curr, Work->fnc_curr, Work->nb,
+ Work->fnrows, Work->fncols, Work->fnpiv)) ;
+ DEBUG2 (("\nJust the active part:\n")) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv+1);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv+1) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Flublock, nb, fnpiv+1, fnpiv+1) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* Frpos [row] >= 0 for each row in pivot column pattern. */
+ /* offset into pattern is given by: */
+ /* Frpos [row] == offset - 1 */
+ /* Frpos [pivrow] is EMPTY */
+
+ /* Fcpos [col] >= 0 for each col in pivot row pattern. */
+ /* Fcpos [col] == (offset - 1) * fnr_curr */
+ /* Fcpos [pivcol] is EMPTY */
+
+ /* Fcols [0..fncols-1] is the pivot row pattern (excl pivot cols) */
+ /* Frows [0..fnrows-1] is the pivot col pattern (excl pivot rows) */
+
+ /* ====================================================================== */
+ /* === scale pivot column =============================================== */
+ /* ====================================================================== */
+
+ /* pivot column (except for pivot entry itself) */
+ Fcol = Flblock + fnpiv * fnr_curr ;
+ /* fnpiv-th pivot in frontal matrix located in Flublock (fnpiv, fnpiv) */
+ pivot_value = Flublock [fnpiv + fnpiv * nb] ;
+
+ /* this is the kth global pivot */
+ k = Work->npiv + fnpiv ;
+
+ DEBUG4 (("Pivot value: ")) ;
+ EDEBUG4 (pivot_value) ;
+ DEBUG4 (("\n")) ;
+
+ UMF_scale (fnrows, pivot_value, Fcol) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* deallocate the pivot row and pivot column tuples */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_mem_free_tail_block (Numeric, Row_tuples [pivrow]) ;
+ UMF_mem_free_tail_block (Numeric, Col_tuples [pivcol]) ;
+
+ Row_tuples [pivrow] = 0 ;
+ Col_tuples [pivcol] = 0 ;
+
+ DEBUG5 (("number of pivots prior to this one: "ID"\n", k)) ;
+ ASSERT (NON_PIVOTAL_ROW (pivrow)) ;
+ ASSERT (NON_PIVOTAL_COL (pivcol)) ;
+
+ /* save row and column inverse permutation */
+ k1 = ONES_COMPLEMENT (k) ;
+ Rperm [pivrow] = k1 ; /* aliased with Row_degree */
+ Cperm [pivcol] = k1 ; /* aliased with Col_degree */
+
+ ASSERT (!NON_PIVOTAL_ROW (pivrow)) ;
+ ASSERT (!NON_PIVOTAL_COL (pivcol)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* Keep track of the pivot order. This is the kth pivot row and column. */
+ /* ---------------------------------------------------------------------- */
+
+ /* keep track of pivot rows and columns in the LU, L, and U blocks */
+ ASSERT (fnpiv < MAXNB) ;
+ Work->Pivrow [fnpiv] = pivrow ;
+ Work->Pivcol [fnpiv] = pivcol ;
+
+ /* ====================================================================== */
+ /* === one step in the factorization is done ============================ */
+ /* ====================================================================== */
+
+ /* One more step is done, except for pending updates to the U and C blocks
+ * of this frontal matrix. Those are saved up, and applied by
+ * UMF_blas3_update when enough pivots have accumulated. Also, the
+ * LU factors for these pending pivots have not yet been stored. */
+
+ Work->fnpiv++ ;
+
+#ifndef NDEBUG
+ DEBUG7 (("Current frontal matrix: (after pivcol scale)\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+}
diff --git a/UMFPACK/Source/umf_scale_column.h b/UMFPACK/Source/umf_scale_column.h
new file mode 100644
index 0000000..2306787
--- /dev/null
+++ b/UMFPACK/Source/umf_scale_column.h
@@ -0,0 +1,11 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_scale_column
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/UMFPACK/Source/umf_set_stats.c b/UMFPACK/Source/umf_set_stats.c
new file mode 100644
index 0000000..fb1f232
--- /dev/null
+++ b/UMFPACK/Source/umf_set_stats.c
@@ -0,0 +1,134 @@
+/* ========================================================================== */
+/* === UMF_set_stats ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Sets statistics in Info array. Calculates everything in double precision,
+ rather than Int or size_t, so that usage estimates can be computed even if
+ the problem is so large that it would cause integer overflow.
+
+ This routine has many double relop's, but the NaN case is ignored.
+*/
+
+#include "umf_internal.h"
+#include "umf_set_stats.h"
+#include "umf_symbolic_usage.h"
+
+GLOBAL void UMF_set_stats
+(
+ double Info [ ],
+ SymbolicType *Symbolic,
+ double max_usage, /* peak size of Numeric->Memory, in Units */
+ double num_mem_size, /* final size of Numeric->Memory, in Units */
+ double flops, /* "true flops" */
+ double lnz, /* nz in L */
+ double unz, /* nz in U */
+ double maxfrsize, /* largest front size */
+ double ulen, /* size of Numeric->Upattern */
+ double npiv, /* number of pivots found */
+ double maxnrows, /* largest #rows in front */
+ double maxncols, /* largest #cols in front */
+ Int scale, /* true if scaling the rows of A */
+ Int prefer_diagonal, /* true if diagonal pivoting (only square A) */
+ Int what /* ESTIMATE or ACTUAL */
+)
+{
+
+ double sym_size, work_usage, nn, n_row, n_col, n_inner, num_On_size1,
+ num_On_size2, num_usage, sym_maxncols, sym_maxnrows, elen, n1 ;
+
+ n_col = Symbolic->n_col ;
+ n_row = Symbolic->n_row ;
+ n1 = Symbolic->n1 ;
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+ sym_maxncols = MIN (Symbolic->maxncols + Symbolic->nb, n_col) ;
+ sym_maxnrows = MIN (Symbolic->maxnrows + Symbolic->nb, n_row) ;
+ elen = (n_col - n1) + (n_row - n1) + MIN (n_col - n1, n_row - n1) + 1 ;
+
+ /* final Symbolic object size */
+ sym_size = UMF_symbolic_usage (Symbolic->n_row, Symbolic->n_col,
+ Symbolic->nchains, Symbolic->nfr, Symbolic->esize, prefer_diagonal) ;
+
+ /* size of O(n) part of Numeric object during factorization, */
+ /* except Numeric->Memory and Numeric->Upattern */
+ num_On_size1 =
+ DUNITS (NumericType, 1) /* Numeric structure */
+ + DUNITS (Entry, n_inner+1) /* D */
+ + 4 * DUNITS (Int, n_row+1) /* Rperm, Lpos, Uilen, Uip */
+ + 4 * DUNITS (Int, n_col+1) /* Cperm, Upos, Lilen, Lip */
+ + (scale ? DUNITS (Entry, n_row) : 0) ; /* Rs, row scale factors */
+
+ /* size of O(n) part of Numeric object after factorization, */
+ /* except Numeric->Memory and Numeric->Upattern */
+ num_On_size2 =
+ DUNITS (NumericType, 1) /* Numeric structure */
+ + DUNITS (Entry, n_inner+1) /* D */
+ + DUNITS (Int, n_row+1) /* Rperm */
+ + DUNITS (Int, n_col+1) /* Cperm */
+ + 6 * DUNITS (Int, npiv+1) /* Lpos, Uilen, Uip, Upos, Lilen, Lip */
+ + (scale ? DUNITS (Entry, n_row) : 0) ; /* Rs, row scale factors */
+
+ DEBUG1 (("num O(n) size2: %g\n", num_On_size2)) ;
+
+ /* peak size of Numeric->Memory, including LU factors, current frontal
+ * matrix, elements, and tuple lists. */
+ Info [UMFPACK_VARIABLE_PEAK + what] = max_usage ;
+
+ /* final size of Numeric->Memory (LU factors only) */
+ Info [UMFPACK_VARIABLE_FINAL + what] = num_mem_size ;
+
+ /* final size of Numeric object, including Numeric->Memory and ->Upattern */
+ Info [UMFPACK_NUMERIC_SIZE + what] =
+ num_On_size2
+ + num_mem_size /* final Numeric->Memory size */
+ + DUNITS (Int, ulen+1) ;/* Numeric->Upattern (from Work->Upattern) */
+
+ DEBUG1 (("num mem size: %g\n", num_mem_size)) ;
+ DEBUG1 (("ulen units %g\n", DUNITS (Int, ulen))) ;
+ DEBUG1 (("numeric size %g\n", Info [UMFPACK_NUMERIC_SIZE + what])) ;
+
+ /* largest front size (working array size, or actual size used) */
+ Info [UMFPACK_MAX_FRONT_SIZE + what] = maxfrsize ;
+ Info [UMFPACK_MAX_FRONT_NROWS + what] = maxnrows ;
+ Info [UMFPACK_MAX_FRONT_NCOLS + what] = maxncols ;
+ DEBUGm4 (("maxnrows %g maxncols %g\n", maxnrows, maxncols)) ;
+ DEBUGm4 (("maxfrsize %g\n", maxfrsize)) ;
+
+ /* UMF_kernel usage, from work_alloc routine in umf_kernel.c */
+ work_usage =
+ /* Work-> arrays, except for current frontal matrix which is allocated
+ * inside Numeric->Memory. */
+ 2 * DUNITS (Entry, sym_maxnrows + 1) /* Wx, Wy */
+ + 2 * DUNITS (Int, n_row+1) /* Frpos, Lpattern */
+ + 2 * DUNITS (Int, n_col+1) /* Fcpos, Upattern */
+ + DUNITS (Int, nn + 1) /* Wp */
+ + DUNITS (Int, MAX (n_col, sym_maxnrows) + 1) /* Wrp */
+ + 2 * DUNITS (Int, sym_maxnrows + 1) /* Frows, Wm */
+ + 3 * DUNITS (Int, sym_maxncols + 1) /* Fcols, Wio, Woi */
+ + DUNITS (Int, MAX (sym_maxnrows, sym_maxncols) + 1) /* Woo */
+ + DUNITS (Int, elen) /* E */
+ + DUNITS (Int, Symbolic->nfr + 1) /* Front_new1strow */
+ + ((n_row == n_col) ? (2 * DUNITS (Int, nn)) : 0) ; /* Diag map,imap */
+
+ /* Peak memory for just UMFPACK_numeric. */
+ num_usage =
+ sym_size /* size of Symbolic object */
+ + num_On_size1 /* O(n) part of Numeric object (excl. Upattern) */
+ + work_usage /* Work-> arrays (including Upattern) */
+ + max_usage ; /* peak size of Numeric->Memory */
+
+ /* peak memory usage for both UMFPACK_*symbolic and UMFPACK_numeric. */
+ Info [UMFPACK_PEAK_MEMORY + what] =
+ MAX (Symbolic->peak_sym_usage, num_usage) ;
+
+ Info [UMFPACK_FLOPS + what] = flops ;
+ Info [UMFPACK_LNZ + what] = lnz ;
+ Info [UMFPACK_UNZ + what] = unz ;
+}
diff --git a/UMFPACK/Source/umf_set_stats.h b/UMFPACK/Source/umf_set_stats.h
new file mode 100644
index 0000000..f4342ce
--- /dev/null
+++ b/UMFPACK/Source/umf_set_stats.h
@@ -0,0 +1,24 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL void UMF_set_stats
+(
+ double Info [ ],
+ SymbolicType *Symbolic,
+ double max_usage,
+ double num_mem_size,
+ double flops,
+ double lnz,
+ double unz,
+ double maxfrsize,
+ double ulen,
+ double npiv,
+ double maxnrows,
+ double maxncols,
+ Int scale,
+ Int prefer_diagonal,
+ Int what
+) ;
diff --git a/UMFPACK/Source/umf_singletons.c b/UMFPACK/Source/umf_singletons.c
new file mode 100644
index 0000000..8288220
--- /dev/null
+++ b/UMFPACK/Source/umf_singletons.c
@@ -0,0 +1,917 @@
+/* ========================================================================== */
+/* === UMF_singletons ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Find and order the row and column singletons of a matrix A. If there are
+ * row and column singletons, the output is a row and column permutation such
+ * that the matrix is in the following form:
+ *
+ * x x x x x x x x x
+ * . x x x x x x x x
+ * . . x x x x x x x
+ * . . . x . . . . .
+ * . . . x x . . . .
+ * . . . x x s s s s
+ * . . . x x s s s s
+ * . . . x x s s s s
+ * . . . x x s s s s
+ *
+ * The above example has 3 column singletons (the first three columns and
+ * their corresponding pivot rows) and 2 row singletons. The singletons are
+ * ordered first, because they have zero Markowitz cost. The LU factorization
+ * for these first five rows and columns is free - there is no work to do
+ * (except to scale the pivot columns for the 2 row singletons), and no
+ * fill-in occurs. The remaining submatrix (4-by-4 in the above example)
+ * has no rows or columns with degree one. It may have empty rows or columns.
+ *
+ * This algorithm does not perform a full permutation to block triangular
+ * form. If there are one or more singletons, then the matrix can be
+ * permuted to block triangular form, but UMFPACK does not perform the full
+ * BTF permutation (see also "dmperm" in MATLAB, CSparse cs_dmperm,
+ * and SuiteSparse/BTF).
+ */
+
+#include "umf_internal.h"
+#include "umf_singletons.h"
+
+#ifndef NDEBUG
+
+/* ========================================================================== */
+/* === debug routines ======================================================= */
+/* ========================================================================== */
+
+/* Dump the singleton queue */
+
+PRIVATE void dump_singletons
+(
+ Int head, /* head of the queue */
+ Int tail, /* tail of the queue */
+ Int Next [ ], /* Next [i] is the next object after i */
+ char *name, /* "row" or "col" */
+ Int Deg [ ], /* Deg [i] is the degree of object i */
+ Int n /* objects are in the range 0 to n-1 */
+)
+{
+ Int i, next, cnt ;
+ DEBUG6 (("%s Singleton list: head "ID" tail "ID"\n", name, head, tail)) ;
+ i = head ;
+ ASSERT (head >= EMPTY && head < n) ;
+ ASSERT (tail >= EMPTY && tail < n) ;
+ cnt = 0 ;
+ while (i != EMPTY)
+ {
+ DEBUG7 ((" "ID": "ID" deg: "ID"\n", cnt, i, Deg [i])) ;
+ ASSERT (i >= 0 && i < n) ;
+ next = Next [i] ;
+ if (i == tail) ASSERT (next == EMPTY) ;
+ i = next ;
+ cnt++ ;
+ ASSERT (cnt <= n) ;
+ }
+}
+
+PRIVATE void dump_mat
+(
+ char *xname,
+ char *yname,
+ Int nx,
+ Int ny,
+ const Int Xp [ ],
+ const Int Xi [ ],
+ Int Xdeg [ ],
+ Int Ydeg [ ]
+)
+{
+ Int x, y, p, p1, p2, xdeg, do_xdeg, ydeg ;
+ DEBUG6 (("\n ==== Dump %s mat:\n", xname)) ;
+ for (x = 0 ; x < nx ; x++)
+ {
+ p1 = Xp [x] ;
+ p2 = Xp [x+1] ;
+ xdeg = Xdeg [x] ;
+ DEBUG6 (("Dump %s "ID" p1 "ID" p2 "ID" deg "ID"\n",
+ xname, x, p1, p2, xdeg)) ;
+ do_xdeg = (xdeg >= 0) ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ y = Xi [p] ;
+ DEBUG7 ((" %s "ID" deg: ", yname, y)) ;
+ ASSERT (y >= 0 && y < ny) ;
+ ydeg = Ydeg [y] ;
+ DEBUG7 ((ID"\n", ydeg)) ;
+ if (do_xdeg && ydeg >= 0)
+ {
+ xdeg-- ;
+ }
+ }
+ ASSERT (IMPLIES (do_xdeg, xdeg == 0)) ;
+ }
+}
+#endif
+
+/* ========================================================================== */
+/* === create_row_form ====================================================== */
+/* ========================================================================== */
+
+/* Create the row-form R of the column-form input matrix A. This could be done
+ * by UMF_transpose, except that Rdeg has already been computed.
+ */
+
+PRIVATE void create_row_form
+(
+ /* input, not modified: */
+ Int n_row, /* A is n_row-by-n_col, nz = Ap [n_col] */
+ Int n_col,
+ const Int Ap [ ], /* Ap [0..n_col]: column pointers for A */
+ const Int Ai [ ], /* Ai [0..nz-1]: row indices for A */
+ Int Rdeg [ ], /* Rdeg [0..n_row-1]: row degrees */
+
+ /* output, not defined on input: */
+ Int Rp [ ], /* Rp [0..n_row]: row pointers for R */
+ Int Ri [ ], /* Ri [0..nz-1]: column indices for R */
+
+ /* workspace, not defined on input or output */
+ Int W [ ] /* size n_row */
+)
+{
+ Int row, col, p, p2 ;
+
+ /* create the row pointers */
+ Rp [0] = 0 ;
+ W [0] = 0 ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Rp [row+1] = Rp [row] + Rdeg [row] ;
+ W [row] = Rp [row] ;
+ }
+
+ /* create the indices for the row-form */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ p2 = Ap [col+1] ;
+ for (p = Ap [col] ; p < p2 ; p++)
+ {
+ Ri [W [Ai [p]]++] = col ;
+ }
+ }
+}
+
+/* ========================================================================== */
+/* === order_singletons ===================================================== */
+/* ========================================================================== */
+
+PRIVATE int order_singletons /* return new number of singletons */
+(
+ Int k, /* the number of singletons so far */
+ Int head,
+ Int tail,
+ Int Next [ ],
+ Int Xdeg [ ], Int Xperm [ ], const Int Xp [ ], const Int Xi [ ],
+ Int Ydeg [ ], Int Yperm [ ], const Int Yp [ ], const Int Yi [ ]
+#ifndef NDEBUG
+ , char *xname, char *yname, Int nx, Int ny
+#endif
+)
+{
+ Int xpivot, x, y, ypivot, p, p2, deg ;
+
+#ifndef NDEBUG
+ Int i, k1 = k ;
+ dump_singletons (head, tail, Next, xname, Xdeg, nx) ;
+ dump_mat (xname, yname, nx, ny, Xp, Xi, Xdeg, Ydeg) ;
+ dump_mat (yname, xname, ny, nx, Yp, Yi, Ydeg, Xdeg) ;
+#endif
+
+ while (head != EMPTY)
+ {
+ /* remove the singleton at the head of the queue */
+ xpivot = head ;
+ DEBUG1 (("------ Order %s singleton: "ID"\n", xname, xpivot)) ;
+ head = Next [xpivot] ;
+ if (head == EMPTY) tail = EMPTY ;
+
+#ifndef NDEBUG
+ if (k % 100 == 0) dump_singletons (head, tail, Next, xname, Xdeg, nx) ;
+#endif
+
+ ASSERT (Xdeg [xpivot] >= 0) ;
+ if (Xdeg [xpivot] != 1)
+ {
+ /* This row/column x is empty. The matrix is singular.
+ * x will be ordered last in Xperm. */
+ DEBUG1 (("empty %s, after singletons removed\n", xname)) ;
+ continue ;
+ }
+
+ /* find the ypivot to match with this xpivot */
+#ifndef NDEBUG
+ /* there can only be one ypivot, since the degree of x is 1 */
+ deg = 0 ;
+ p2 = Xp [xpivot+1] ;
+ for (p = Xp [xpivot] ; p < p2 ; p++)
+ {
+ y = Xi [p] ;
+ DEBUG1 (("%s: "ID"\n", yname, y)) ;
+ if (Ydeg [y] >= 0)
+ {
+ /* this is a live index in this xpivot vector */
+ deg++ ;
+ }
+ }
+ ASSERT (deg == 1) ;
+#endif
+
+ ypivot = EMPTY ;
+ p2 = Xp [xpivot+1] ;
+ for (p = Xp [xpivot] ; p < p2 ; p++)
+ {
+ y = Xi [p] ;
+ DEBUG1 (("%s: "ID"\n", yname, y)) ;
+ if (Ydeg [y] >= 0)
+ {
+ /* this is a live index in this xpivot vector */
+ ypivot = y ;
+ break ;
+ }
+ }
+
+ DEBUG1 (("Pivot %s: "ID"\n", yname, ypivot)) ;
+ ASSERT (ypivot != EMPTY) ;
+ DEBUG1 (("deg "ID"\n", Ydeg [ypivot])) ;
+ ASSERT (Ydeg [ypivot] >= 0) ;
+
+ /* decrement the degrees after removing this singleton */
+ DEBUG1 (("p1 "ID"\n", Yp [ypivot])) ;
+ DEBUG1 (("p2 "ID"\n", Yp [ypivot+1])) ;
+ p2 = Yp [ypivot+1] ;
+ for (p = Yp [ypivot] ; p < p2 ; p++)
+ {
+ x = Yi [p] ;
+ DEBUG1 ((" %s: "ID" deg: "ID"\n", xname, x, Xdeg [x])) ;
+ if (Xdeg [x] < 0) continue ;
+ ASSERT (Xdeg [x] > 0) ;
+ if (x == xpivot) continue ;
+ deg = --(Xdeg [x]) ;
+ ASSERT (Xdeg [x] >= 0) ;
+ if (deg == 1)
+ {
+ /* this is a new singleton, put at the end of the queue */
+ Next [x] = EMPTY ;
+ if (head == EMPTY)
+ {
+ head = x ;
+ }
+ else
+ {
+ ASSERT (tail != EMPTY) ;
+ Next [tail] = x ;
+ }
+ tail = x ;
+ DEBUG1 ((" New %s singleton: "ID"\n", xname, x)) ;
+#ifndef NDEBUG
+ if (k % 100 == 0)
+ {
+ dump_singletons (head, tail, Next, xname, Xdeg, nx) ;
+ }
+#endif
+ }
+ }
+
+ /* flag the xpivot and ypivot by FLIP'ing the degrees */
+ Xdeg [xpivot] = FLIP (1) ;
+ Ydeg [ypivot] = FLIP (Ydeg [ypivot]) ;
+
+ /* keep track of the pivot row and column */
+ Xperm [k] = xpivot ;
+ Yperm [k] = ypivot ;
+ k++ ;
+
+#ifndef NDEBUG
+ if (k % 1000 == 0)
+ {
+ dump_mat (xname, yname, nx, ny, Xp, Xi, Xdeg, Ydeg) ;
+ dump_mat (yname, xname, ny, nx, Yp, Yi, Ydeg, Xdeg) ;
+ }
+#endif
+ }
+
+#ifndef NDEBUG
+ DEBUGm4 (("%s singletons: k = "ID"\n", xname, k)) ;
+ for (i = k1 ; i < k ; i++)
+ {
+ DEBUG1 ((" %s: "ID" %s: "ID"\n", xname, Xperm [i], yname, Yperm [i])) ;
+ }
+ ASSERT (k > 0) ;
+#endif
+
+ return (k) ;
+}
+
+/* ========================================================================== */
+/* === find_any_singletons ================================================== */
+/* ========================================================================== */
+
+PRIVATE Int find_any_singletons /* returns # of singletons found */
+(
+ /* input, not modified: */
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ], /* size n_col+1 */
+ const Int Ai [ ], /* size nz = Ap [n_col] */
+
+ /* input, modified on output: */
+ Int Cdeg [ ], /* size n_col */
+ Int Rdeg [ ], /* size n_row */
+
+ /* output, not defined on input: */
+ Int Cperm [ ], /* size n_col */
+ Int Rperm [ ], /* size n_row */
+ Int *p_n1r, /* # of row singletons */
+ Int *p_n1c, /* # of col singletons */
+
+ /* workspace, not defined on input or output */
+ Int Rp [ ], /* size n_row+1 */
+ Int Ri [ ], /* size nz */
+ Int W [ ], /* size n_row */
+ Int Next [ ] /* size MAX (n_row, n_col) */
+)
+{
+ Int n1, col, row, row_form, head, tail, n1r, n1c ;
+
+ /* ---------------------------------------------------------------------- */
+ /* eliminate column singletons */
+ /* ---------------------------------------------------------------------- */
+
+ n1 = 0 ;
+ n1r = 0 ;
+ n1c = 0 ;
+ row_form = FALSE ;
+
+ head = EMPTY ;
+ tail = EMPTY ;
+ for (col = n_col-1 ; col >= 0 ; col--)
+ {
+ if (Cdeg [col] == 1)
+ {
+ /* put the column singleton in the queue */
+ if (head == EMPTY) tail = col ;
+ Next [col] = head ;
+ head = col ;
+ DEBUG1 (("Column singleton: "ID"\n", col)) ;
+ }
+ }
+
+ if (head != EMPTY)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* create the row-form of A */
+ /* ------------------------------------------------------------------ */
+
+ create_row_form (n_row, n_col, Ap, Ai, Rdeg, Rp, Ri, W) ;
+ row_form = TRUE ;
+
+ /* ------------------------------------------------------------------ */
+ /* find and order the column singletons */
+ /* ------------------------------------------------------------------ */
+
+ n1 = order_singletons (0, head, tail, Next,
+ Cdeg, Cperm, Ap, Ai,
+ Rdeg, Rperm, Rp, Ri
+#ifndef NDEBUG
+ , "col", "row", n_col, n_row
+#endif
+ ) ;
+ n1c = n1 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* eliminate row singletons */
+ /* ---------------------------------------------------------------------- */
+
+ head = EMPTY ;
+ tail = EMPTY ;
+ for (row = n_row-1 ; row >= 0 ; row--)
+ {
+ if (Rdeg [row] == 1)
+ {
+ /* put the row singleton in the queue */
+ if (head == EMPTY) tail = row ;
+ Next [row] = head ;
+ head = row ;
+ DEBUG1 (("Row singleton: "ID"\n", row)) ;
+ }
+ }
+
+ if (head != EMPTY)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* create the row-form of A, if not already created */
+ /* ------------------------------------------------------------------ */
+
+ if (!row_form)
+ {
+ create_row_form (n_row, n_col, Ap, Ai, Rdeg, Rp, Ri, W) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* find and order the row singletons */
+ /* ------------------------------------------------------------------ */
+
+ n1 = order_singletons (n1, head, tail, Next,
+ Rdeg, Rperm, Rp, Ri,
+ Cdeg, Cperm, Ap, Ai
+#ifndef NDEBUG
+ , "row", "col", n_row, n_col
+#endif
+ ) ;
+ n1r = n1 - n1c ;
+ }
+
+ DEBUG0 (("n1 "ID"\n", n1)) ;
+ *p_n1r = n1r ;
+ *p_n1c = n1c ;
+ return (n1) ;
+}
+
+/* ========================================================================== */
+/* === find_user_singletons ================================================= */
+/* ========================================================================== */
+
+PRIVATE Int find_user_singletons /* returns # singletons found */
+(
+ /* input, not modified: */
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ], /* size n_col+1 */
+ const Int Ai [ ], /* size nz = Ap [n_col] */
+ const Int Quser [ ], /* size n_col if present */
+
+ /* input, modified on output: */
+ Int Cdeg [ ], /* size n_col */
+ Int Rdeg [ ], /* size n_row */
+
+ /* output, not defined on input */
+ Int Cperm [ ], /* size n_col */
+ Int Rperm [ ], /* size n_row */
+ Int *p_n1r, /* # of row singletons */
+ Int *p_n1c, /* # of col singletons */
+
+ /* workspace, not defined on input or output */
+ Int Rp [ ], /* size n_row+1 */
+ Int Ri [ ], /* size nz */
+ Int W [ ] /* size n_row */
+)
+{
+ Int n1, col, row, p, p2, pivcol, pivrow, found, k, n1r, n1c ;
+
+ n1 = 0 ;
+ n1r = 0 ;
+ n1c = 0 ;
+ *p_n1r = 0 ;
+ *p_n1c = 0 ;
+
+ /* find singletons in the user column permutation, Quser */
+ pivcol = Quser [0] ;
+ found = (Cdeg [pivcol] == 1) ;
+ DEBUG0 (("Is first col: "ID" a col singleton?: "ID"\n", pivcol, found)) ;
+ if (!found)
+ {
+ /* the first column is not a column singleton, check for a row
+ * singleton in the first column. */
+ for (p = Ap [pivcol] ; p < Ap [pivcol+1] ; p++)
+ {
+ if (Rdeg [Ai [p]] == 1)
+ {
+ DEBUG0 (("Row singleton in first col: "ID" row: "ID"\n",
+ pivcol, Ai [p])) ;
+ found = TRUE ;
+ break ;
+ }
+ }
+ }
+
+ if (!found)
+ {
+ /* no singletons in the leading part of A (:,Quser) */
+ return (0) ;
+ }
+
+ /* there is at least one row or column singleton. Look for more. */
+ create_row_form (n_row, n_col, Ap, Ai, Rdeg, Rp, Ri, W) ;
+
+ n1 = 0 ;
+
+ for (k = 0 ; k < n_col ; k++)
+ {
+ pivcol = Quser [k] ;
+ pivrow = EMPTY ;
+
+ /* ------------------------------------------------------------------ */
+ /* check if col is a column singleton, or contains a row singleton */
+ /* ------------------------------------------------------------------ */
+
+ found = (Cdeg [pivcol] == 1) ;
+
+ if (found)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* pivcol is a column singleton */
+ /* -------------------------------------------------------------- */
+
+ DEBUG0 (("Found a col singleton: k "ID" pivcol "ID"\n", k, pivcol));
+
+ /* find the pivrow to match with this pivcol */
+#ifndef NDEBUG
+ /* there can only be one pivrow, since the degree of pivcol is 1 */
+ {
+ Int deg = 0 ;
+ p2 = Ap [pivcol+1] ;
+ for (p = Ap [pivcol] ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ DEBUG1 (("row: "ID"\n", row)) ;
+ if (Rdeg [row] >= 0)
+ {
+ /* this is a live index in this column vector */
+ deg++ ;
+ }
+ }
+ ASSERT (deg == 1) ;
+ }
+#endif
+
+ p2 = Ap [pivcol+1] ;
+ for (p = Ap [pivcol] ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ DEBUG1 (("row: "ID"\n", row)) ;
+ if (Rdeg [row] >= 0)
+ {
+ /* this is a live index in this pivcol vector */
+ pivrow = row ;
+ break ;
+ }
+ }
+
+ DEBUG1 (("Pivot row: "ID"\n", pivrow)) ;
+ ASSERT (pivrow != EMPTY) ;
+ DEBUG1 (("deg "ID"\n", Rdeg [pivrow])) ;
+ ASSERT (Rdeg [pivrow] >= 0) ;
+
+ /* decrement the degrees after removing this col singleton */
+ DEBUG1 (("p1 "ID"\n", Rp [pivrow])) ;
+ DEBUG1 (("p2 "ID"\n", Rp [pivrow+1])) ;
+ p2 = Rp [pivrow+1] ;
+ for (p = Rp [pivrow] ; p < p2 ; p++)
+ {
+ col = Ri [p] ;
+ DEBUG1 ((" col: "ID" deg: "ID"\n", col, Cdeg [col])) ;
+ if (Cdeg [col] < 0) continue ;
+ ASSERT (Cdeg [col] > 0) ;
+ Cdeg [col]-- ;
+ ASSERT (Cdeg [col] >= 0) ;
+ }
+
+ /* flag the pivcol and pivrow by FLIP'ing the degrees */
+ Cdeg [pivcol] = FLIP (1) ;
+ Rdeg [pivrow] = FLIP (Rdeg [pivrow]) ;
+ n1c++ ;
+
+ }
+ else
+ {
+
+ /* -------------------------------------------------------------- */
+ /* pivcol may contain a row singleton */
+ /* -------------------------------------------------------------- */
+
+ p2 = Ap [pivcol+1] ;
+ for (p = Ap [pivcol] ; p < p2 ; p++)
+ {
+ pivrow = Ai [p] ;
+ if (Rdeg [pivrow] == 1)
+ {
+ DEBUG0 (("Row singleton in pivcol: "ID" row: "ID"\n",
+ pivcol, pivrow)) ;
+ found = TRUE ;
+ break ;
+ }
+ }
+
+ if (!found)
+ {
+ DEBUG0 (("End of user singletons\n")) ;
+ break ;
+ }
+
+#ifndef NDEBUG
+ /* there can only be one pivrow, since the degree of pivcol is 1 */
+ {
+ Int deg = 0 ;
+ p2 = Rp [pivrow+1] ;
+ for (p = Rp [pivrow] ; p < p2 ; p++)
+ {
+ col = Ri [p] ;
+ DEBUG1 (("col: "ID" cdeg::: "ID"\n", col, Cdeg [col])) ;
+ if (Cdeg [col] >= 0)
+ {
+ /* this is a live index in this column vector */
+ ASSERT (col == pivcol) ;
+ deg++ ;
+ }
+ }
+ ASSERT (deg == 1) ;
+ }
+#endif
+
+ DEBUG1 (("Pivot row: "ID"\n", pivrow)) ;
+ DEBUG1 (("pivcol deg "ID"\n", Cdeg [pivcol])) ;
+ ASSERT (Cdeg [pivcol] > 1) ;
+
+ /* decrement the degrees after removing this row singleton */
+ DEBUG1 (("p1 "ID"\n", Ap [pivcol])) ;
+ DEBUG1 (("p2 "ID"\n", Ap [pivcol+1])) ;
+ p2 = Ap [pivcol+1] ;
+ for (p = Ap [pivcol] ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ DEBUG1 ((" row: "ID" deg: "ID"\n", row, Rdeg [row])) ;
+ if (Rdeg [row] < 0) continue ;
+ ASSERT (Rdeg [row] > 0) ;
+ Rdeg [row]-- ;
+ ASSERT (Rdeg [row] >= 0) ;
+ }
+
+ /* flag the pivcol and pivrow by FLIP'ing the degrees */
+ Cdeg [pivcol] = FLIP (Cdeg [pivcol]) ;
+ Rdeg [pivrow] = FLIP (1) ;
+ n1r++ ;
+ }
+
+ /* keep track of the pivot row and column */
+ Cperm [k] = pivcol ;
+ Rperm [k] = pivrow ;
+ n1++ ;
+
+#ifndef NDEBUG
+ dump_mat ("col", "row", n_col, n_row, Ap, Ai, Cdeg, Rdeg) ;
+ dump_mat ("row", "col", n_row, n_col, Rp, Ri, Rdeg, Cdeg) ;
+#endif
+
+ }
+
+ DEBUGm4 (("User singletons found: "ID"\n", n1)) ;
+ ASSERT (n1 > 0) ;
+
+ *p_n1r = n1r ;
+ *p_n1c = n1c ;
+ return (n1) ;
+}
+
+/* ========================================================================== */
+/* === finish_permutation =================================================== */
+/* ========================================================================== */
+
+/* Complete the permutation for the pruned submatrix. The singletons are
+ * already ordered, but remove their flags. Place rows/columns that are empty
+ * in the pruned submatrix at the end of the output permutation. This can only
+ * occur if the matrix is singular.
+ */
+
+PRIVATE Int finish_permutation
+(
+ Int n1,
+ Int nx,
+ Int Xdeg [ ],
+ const Int Xuser [ ],
+ Int Xperm [ ],
+ Int *p_max_deg
+)
+{
+ Int nempty, x, deg, s, max_deg, k ;
+ nempty = 0 ;
+ s = n1 ;
+ max_deg = 0 ;
+ DEBUG0 (("n1 "ID" nempty "ID"\n", n1, nempty)) ;
+ for (k = 0 ; k < nx ; k++)
+ {
+ x = (Xuser != (Int *) NULL) ? Xuser [k] : k ;
+ DEBUG0 (("finish perm k "ID" x "ID" nx "ID"\n", k, x, nx)) ;
+ deg = Xdeg [x] ;
+ if (deg == 0)
+ {
+ /* this row/col is empty in the pruned submatrix */
+ ASSERT (s < nx - nempty) ;
+ DEBUG0 (("empty k "ID"\n", k)) ;
+ nempty++ ;
+ Xperm [nx - nempty] = x ;
+ }
+ else if (deg > 0)
+ {
+ /* this row/col is nonempty in the pruned submatrix */
+ ASSERT (s < nx - nempty) ;
+ Xperm [s++] = x ;
+ max_deg = MAX (max_deg, deg) ;
+ }
+ else
+ {
+ /* This is a singleton row/column - it is already ordered.
+ * Just clear the flag. */
+ Xdeg [x] = FLIP (deg) ;
+ }
+ }
+ ASSERT (s == nx - nempty) ;
+ *p_max_deg = max_deg ;
+ return (nempty) ;
+}
+
+/* ========================================================================== */
+/* === UMF_singletons ======================================================= */
+/* ========================================================================== */
+
+GLOBAL Int UMF_singletons
+(
+
+ /* input, not modified: */
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ], /* size n_col+1 */
+ const Int Ai [ ], /* size nz = Ap [n_col] */
+ const Int Quser [ ], /* size n_col if present */
+ Int strategy, /* strategy requested by user */
+
+ /* output, not defined on input: */
+ Int Cdeg [ ], /* size n_col */
+ Int Cperm [ ], /* size n_col */
+ Int Rdeg [ ], /* size n_row */
+ Int Rperm [ ], /* size n_row */
+ Int InvRperm [ ], /* size n_row, the inverse of Rperm */
+ Int *p_n1, /* # of col and row singletons */
+ Int *p_n1c, /* # of col singletons */
+ Int *p_n1r, /* # of row singletons */
+ Int *p_nempty_col, /* # of empty columns in pruned submatrix */
+ Int *p_nempty_row, /* # of empty columns in pruned submatrix */
+ Int *p_is_sym, /* TRUE if pruned submatrix is square and has been
+ * symmetrically permuted by Cperm and Rperm */
+ Int *p_max_rdeg, /* maximum Rdeg in pruned submatrix */
+
+ /* workspace, not defined on input or output */
+ Int Rp [ ], /* size n_row+1 */
+ Int Ri [ ], /* size nz */
+ Int W [ ], /* size n_row */
+ Int Next [ ] /* size MAX (n_row, n_col) */
+)
+{
+ Int n1, s, col, row, p, p1, p2, cdeg, last_row, is_sym, k,
+ nempty_row, nempty_col, max_cdeg, max_rdeg, n1c, n1r ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_dump_start ( ) ;
+ DEBUGm4 (("Starting umf_singletons\n")) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* scan the columns, check for errors and count row degrees */
+ /* ---------------------------------------------------------------------- */
+
+ if (Ap [0] != 0 || Ap [n_col] < 0)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Rdeg [row] = 0 ;
+ }
+ for (col = 0 ; col < n_col ; col++)
+ {
+ p1 = Ap [col] ;
+ p2 = Ap [col+1] ;
+ cdeg = p2 - p1 ;
+ if (cdeg < 0)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ last_row = EMPTY ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ row = Ai [p] ;
+ if (row <= last_row || row >= n_row)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ Rdeg [row]++ ;
+ last_row = row ;
+ }
+ Cdeg [col] = cdeg ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find singletons */
+ /* ---------------------------------------------------------------------- */
+
+ if (Quser != (Int *) NULL)
+ {
+ /* user has provided an input column ordering */
+ if (strategy == UMFPACK_STRATEGY_UNSYMMETRIC)
+ {
+ /* look for singletons, but respect the user's input permutation */
+ n1 = find_user_singletons (n_row, n_col, Ap, Ai, Quser,
+ Cdeg, Rdeg, Cperm, Rperm, &n1r, &n1c, Rp, Ri, W) ;
+ }
+ else
+ {
+ /* do not look for singletons if Quser given and strategy is
+ * not unsymmetric */
+ n1 = 0 ;
+ n1r = 0 ;
+ n1c = 0 ;
+ }
+ }
+ else
+ {
+ /* look for singletons anywhere */
+ n1 = find_any_singletons (n_row, n_col, Ap, Ai,
+ Cdeg, Rdeg, Cperm, Rperm, &n1r, &n1c, Rp, Ri, W, Next) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* eliminate empty columns and complete the column permutation */
+ /* ---------------------------------------------------------------------- */
+
+ nempty_col = finish_permutation (n1, n_col, Cdeg, Quser, Cperm, &max_cdeg) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* eliminate empty rows and complete the row permutation */
+ /* ---------------------------------------------------------------------- */
+
+ if (Quser != (Int *) NULL && strategy == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ /* rows should be symmetrically permuted according to Quser */
+ ASSERT (n_row == n_col) ;
+ nempty_row = finish_permutation (n1, n_row, Rdeg, Quser, Rperm,
+ &max_rdeg) ;
+ }
+ else
+ {
+ /* rows should not be symmetrically permuted according to Quser */
+ nempty_row = finish_permutation (n1, n_row, Rdeg, (Int *) NULL, Rperm,
+ &max_rdeg) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the inverse of Rperm */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n_row ; k++)
+ {
+ ASSERT (Rperm [k] >= 0 && Rperm [k] < n_row) ;
+ InvRperm [Rperm [k]] = k ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* see if pruned submatrix is square and has been symmetrically permuted */
+ /* ---------------------------------------------------------------------- */
+
+ if (n_row == n_col && nempty_row == nempty_col)
+ {
+ /* is_sym is true if the submatrix is square, and
+ * Rperm [n1..n_row-nempty_row-1] = Cperm [n1..n_col-nempty_col-1] */
+ is_sym = TRUE ;
+ for (s = n1 ; s < n_col - nempty_col ; s++)
+ {
+ if (Cperm [s] != Rperm [s])
+ {
+ is_sym = FALSE ;
+ break ;
+ }
+ }
+ }
+ else
+ {
+ is_sym = FALSE ;
+ }
+ DEBUGm4 (("Submatrix square and symmetrically permuted? "ID"\n", is_sym)) ;
+ DEBUGm4 (("singletons "ID" row "ID" col "ID"\n", n1, n1r, n1c)) ;
+ DEBUGm4 (("Empty cols "ID" rows "ID"\n", nempty_col, nempty_row)) ;
+ *p_n1 = n1 ;
+ *p_n1r = n1r ;
+ *p_n1c = n1c ;
+ *p_is_sym = is_sym ;
+ *p_nempty_col = nempty_col ;
+ *p_nempty_row = nempty_row ;
+ *p_max_rdeg = max_rdeg ;
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umf_singletons.h b/UMFPACK/Source/umf_singletons.h
new file mode 100644
index 0000000..5b2e498
--- /dev/null
+++ b/UMFPACK/Source/umf_singletons.h
@@ -0,0 +1,31 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_singletons
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const Int Quser [ ],
+ Int strategy,
+ Int Cdeg [ ],
+ Int Cperm [ ],
+ Int Rdeg [ ],
+ Int Rperm [ ],
+ Int InvRperm [ ],
+ Int *n1,
+ Int *n1c,
+ Int *n1r,
+ Int *nempty_col,
+ Int *nempty_row,
+ Int *is_sym,
+ Int *max_rdeg,
+ Int Rp [ ],
+ Int Ri [ ],
+ Int W [ ],
+ Int Next [ ]
+) ;
diff --git a/UMFPACK/Source/umf_solve.c b/UMFPACK/Source/umf_solve.c
new file mode 100644
index 0000000..42bf879
--- /dev/null
+++ b/UMFPACK/Source/umf_solve.c
@@ -0,0 +1,1396 @@
+/* ========================================================================== */
+/* === UMF_solve ============================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Not user-callable. Solves a linear system using the numerical factorization
+ computed by UMFPACK_numeric. No workspace is dynamically allocated. Counts
+ flops, but excludes floating-point comparisons (thus real abs (...) are
+ zero flops, but complex abs (...) takes 6 flops).
+
+ Returns UMFPACK_OK if successful, UMFPACK_ERROR_argument_missing if
+ required arguments are missing, UMFPACK_ERROR_invalid_system if the sys
+ string is not valid or if the matrix A is not square.
+
+ Uses the sparse backward error method of Arioli, Demmel, and Duff
+ (Solving sparse linear systems with sparse backward error, SIAM J. Matrix
+ Analysis and Applic., vol 10, pp. 165-190).
+
+ Added on option that allows the complex A and X to be split differently
+ than B, Oct 10, 2005. Contributed by David Bateman.
+*/
+
+#include "umf_internal.h"
+#include "umf_solve.h"
+#include "umf_lsolve.h"
+#include "umf_usolve.h"
+#include "umf_ltsolve.h"
+#include "umf_utsolve.h"
+#include "umf_report_vector.h"
+
+PRIVATE Int do_step
+(
+ double omega [3],
+ Int step,
+ const double B2 [ ],
+ Entry X [ ],
+ const Entry W [ ],
+ const double Y [ ],
+ const double Z2 [ ],
+ Entry S [ ],
+ Int n,
+ double Info [UMFPACK_INFO]
+) ;
+
+/* ========================================================================== */
+/* === UMF_solve ============================================================ */
+/* ========================================================================== */
+
+GLOBAL Int UMF_solve
+(
+ Int sys,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+ double Xx [ ],
+ const double Bx [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+ double Xz [ ],
+ const double Bz [ ],
+#endif
+ NumericType *Numeric,
+ Int irstep,
+ double Info [UMFPACK_INFO],
+ Int Pattern [ ], /* size n */
+ double SolveWork [ ] /* if irstep>0 real: size 5*n. complex:10*n */
+ /* otherwise real: size n. complex: 4*n */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry axx, wi, xj, zi, xi, aij, bi ;
+ double omega [3], d, z2i, yi, flops ;
+ Entry *W, *Z, *S, *X ;
+ double *Z2, *Y, *B2, *Rs ;
+ Int *Rperm, *Cperm, i, n, p, step, j, nz, status, p2, do_scale ;
+#ifdef COMPLEX
+ Int AXsplit ;
+ Int Bsplit ;
+#endif
+#ifndef NRECIPROCAL
+ Int do_recip = Numeric->do_recip ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_dump_lu (Numeric) ;
+ ASSERT (Numeric && Xx && Bx && Pattern && SolveWork && Info) ;
+#endif
+
+ nz = 0 ;
+ omega [0] = 0. ;
+ omega [1] = 0. ;
+ omega [2] = 0. ;
+ Rperm = Numeric->Rperm ;
+ Cperm = Numeric->Cperm ;
+ Rs = Numeric->Rs ; /* row scale factors */
+ do_scale = (Rs != (double *) NULL) ;
+ flops = 0 ;
+ Info [UMFPACK_SOLVE_FLOPS] = 0 ;
+ Info [UMFPACK_IR_TAKEN] = 0 ;
+ Info [UMFPACK_IR_ATTEMPTED] = 0 ;
+
+ /* UMFPACK_solve does not call this routine if A is rectangular */
+ ASSERT (Numeric->n_row == Numeric->n_col) ;
+ n = Numeric->n_row ;
+ if (Numeric->nnzpiv < n
+ || SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond))
+ {
+ /* Note that systems involving just L return UMFPACK_OK, even if */
+ /* A is singular (L is always has a unit diagonal). */
+ DEBUGm4 (("Note, matrix is singular in umf_solve\n")) ;
+ status = UMFPACK_WARNING_singular_matrix ;
+ irstep = 0 ;
+ }
+ else
+ {
+ status = UMFPACK_OK ;
+ }
+ irstep = MAX (0, irstep) ; /* make sure irstep is >= 0 */
+
+ W = (Entry *) SolveWork ; /* Entry W [0..n-1] */
+
+ Z = (Entry *) NULL ; /* unused if no iterative refinement */
+ S = (Entry *) NULL ;
+ Y = (double *) NULL ;
+ Z2 = (double *) NULL ;
+ B2 = (double *) NULL ;
+
+#ifdef COMPLEX
+ if (irstep > 0)
+ {
+ if (!Ap || !Ai || !Ax)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+ /* A, B, and X in split format if Az, Bz, and Xz present */
+ AXsplit = SPLIT (Az) || SPLIT(Xz);
+ Z = (Entry *) (SolveWork + 4*n) ; /* Entry Z [0..n-1] */
+ S = (Entry *) (SolveWork + 6*n) ; /* Entry S [0..n-1] */
+ Y = (double *) (SolveWork + 8*n) ; /* double Y [0..n-1] */
+ B2 = (double *) (SolveWork + 9*n) ; /* double B2 [0..n-1] */
+ Z2 = (double *) Z ; /* double Z2 [0..n-1], equiv. to Z */
+ }
+ else
+ {
+ /* A is ignored, only look at X for split/packed cases */
+ AXsplit = SPLIT(Xz);
+ }
+ Bsplit = SPLIT (Bz);
+
+ if (AXsplit)
+ {
+ X = (Entry *) (SolveWork + 2*n) ; /* Entry X [0..n-1] */
+ }
+ else
+ {
+ X = (Entry *) Xx ; /* Entry X [0..n-1] */
+ }
+#else
+ X = (Entry *) Xx ; /* Entry X [0..n-1] */
+ if (irstep > 0)
+ {
+ if (!Ap || !Ai || !Ax)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+ Z = (Entry *) (SolveWork + n) ; /* Entry Z [0..n-1] */
+ S = (Entry *) (SolveWork + 2*n) ; /* Entry S [0..n-1] */
+ Y = (double *) (SolveWork + 3*n) ; /* double Y [0..n-1] */
+ B2 = (double *) (SolveWork + 4*n) ; /* double B2 [0..n-1] */
+ Z2 = (double *) Z ; /* double Z2 [0..n-1], equiv. to Z */
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* determine which system to solve */
+ /* ---------------------------------------------------------------------- */
+
+ if (sys == UMFPACK_A)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve A x = b with optional iterative refinement */
+ /* ------------------------------------------------------------------ */
+
+ if (irstep > 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* using iterative refinement: compute Y and B2 */
+ /* -------------------------------------------------------------- */
+
+ nz = Ap [n] ;
+ Info [UMFPACK_NZ] = nz ;
+
+ /* A is stored by column */
+ /* Y (i) = ||R A_i||, 1-norm of row i of R A */
+ for (i = 0 ; i < n ; i++)
+ {
+ Y [i] = 0. ;
+ }
+ flops += (ABS_FLOPS + 1) * nz ;
+ p2 = Ap [n] ;
+ for (p = 0 ; p < p2 ; p++)
+ {
+ /* Y [Ai [p]] += ABS (Ax [p]) ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ Y [Ai [p]] += d ;
+ }
+
+ /* B2 = abs (B) */
+ flops += ABS_FLOPS * n ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* B2 [i] = ABS (B [i]) ; */
+ ASSIGN (bi, Bx, Bz, i, Bsplit) ;
+ ABS (B2 [i], bi) ;
+ }
+
+ /* scale Y and B2. */
+ if (do_scale)
+ {
+ /* Y = R Y */
+ /* B2 = R B2 */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ Y [i] *= Rs [i] ;
+ B2 [i] *= Rs [i] ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ Y [i] /= Rs [i] ;
+ B2 [i] /= Rs [i] ;
+ }
+ }
+
+ flops += 2 * n ;
+ }
+
+ }
+
+ for (step = 0 ; step <= irstep ; step++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Solve A x = b (step 0): */
+ /* x = Q (U \ (L \ (P R b))) */
+ /* and then perform iterative refinement (step > 0): */
+ /* x = x + Q (U \ (L \ (P R (b - A x)))) */
+ /* -------------------------------------------------------------- */
+
+ if (step == 0)
+ {
+ if (do_scale)
+ {
+ /* W = P R b, using X as workspace, since Z is not
+ * allocated if irstep = 0. */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ SCALE (X [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ SCALE_DIV (X [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = X [Rperm [i]] ;
+ }
+ }
+ else
+ {
+ /* W = P b, since the row scaling R = I */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [Rperm [i]] ; */
+ ASSIGN (W [i], Bx, Bz, Rperm [i], Bsplit) ;
+ }
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ /* Z [i] = B [i] ; */
+ ASSIGN (Z [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops += MULTSUB_FLOPS * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ xi = X [i] ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* Z [Ai [p]] -= Ax [p] * xi ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ MULT_SUB (Z [Ai [p]], aij, xi) ;
+ }
+ }
+ /* scale, Z = R Z */
+ if (do_scale)
+ {
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (Z [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (Z [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ }
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = Z [Rperm [i]] ;
+ }
+ }
+
+ flops += UMF_lsolve (Numeric, W, Pattern) ;
+ flops += UMF_usolve (Numeric, W, Pattern) ;
+
+ if (step == 0)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Cperm [i]] = W [i] ;
+ }
+ }
+ else
+ {
+ flops += ASSEMBLE_FLOPS * n ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [Cperm [i]] += W [i] ; */
+ ASSEMBLE (X [Cperm [i]], W [i]) ;
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* sparse backward error estimate */
+ /* -------------------------------------------------------------- */
+
+ if (irstep > 0)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* A is stored by column */
+ /* W (i) = R (b - A x)_i, residual */
+ /* Z2 (i) = R (|A||x|)_i */
+ /* ---------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [i] ; */
+ ASSIGN (W [i], Bx, Bz, i, Bsplit) ;
+ Z2 [i] = 0. ;
+ }
+ flops += (MULT_FLOPS + DECREMENT_FLOPS + ABS_FLOPS + 1) * nz ;
+ for (j = 0 ; j < n ; j++)
+ {
+ xj = X [j] ;
+ p2 = Ap [j+1] ;
+ for (p = Ap [j] ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+
+ /* axx = Ax [p] * xj ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ MULT (axx, aij, xj) ;
+
+ /* W [i] -= axx ; */
+ DECREMENT (W [i], axx) ;
+
+ /* Z2 [i] += ABS (axx) ; */
+ ABS (d, axx) ;
+ Z2 [i] += d ;
+ }
+ }
+
+ /* scale W and Z2 */
+ if (do_scale)
+ {
+ /* Z2 = R Z2 */
+ /* W = R W */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (W [i], Rs [i]) ;
+ Z2 [i] *= Rs [i] ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (W [i], Rs [i]) ;
+ Z2 [i] /= Rs [i] ;
+ }
+ }
+ flops += (SCALE_FLOPS + 1) * n ;
+ }
+
+ flops += (2*ABS_FLOPS + 5) * n ;
+ if (do_step (omega, step, B2, X, W, Y, Z2, S, n, Info))
+ {
+ /* iterative refinement is done */
+ break ;
+ }
+
+ }
+
+ }
+
+ }
+ else if (sys == UMFPACK_At)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve A' x = b with optional iterative refinement */
+ /* ------------------------------------------------------------------ */
+
+ /* A' is the complex conjugate transpose */
+
+ if (irstep > 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* using iterative refinement: compute Y */
+ /* -------------------------------------------------------------- */
+
+ nz = Ap [n] ;
+ Info [UMFPACK_NZ] = nz ;
+
+ /* A' is stored by row */
+ /* Y (i) = ||(A' R)_i||, 1-norm of row i of A' R */
+
+ if (do_scale)
+ {
+ flops += (ABS_FLOPS + 2) * nz ;
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) * Rs [Ai [p]] ; */
+ /* note that abs (aij) is the same as
+ * abs (conj (aij)) */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += (d * Rs [Ai [p]]) ;
+ }
+ Y [i] = yi ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) / Rs [Ai [p]] ; */
+ /* note that abs (aij) is the same as
+ * abs (conj (aij)) */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += (d / Rs [Ai [p]]) ;
+ }
+ Y [i] = yi ;
+ }
+ }
+ }
+ else
+ {
+ /* no scaling */
+ flops += (ABS_FLOPS + 1) * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) ; */
+ /* note that abs (aij) is the same as
+ * abs (conj (aij)) */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += d ;
+ }
+ Y [i] = yi ;
+ }
+ }
+
+ /* B2 = abs (B) */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* B2 [i] = ABS (B [i]) ; */
+ ASSIGN (bi, Bx, Bz, i, Bsplit) ;
+ ABS (B2 [i], bi) ;
+ }
+
+ }
+
+ for (step = 0 ; step <= irstep ; step++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Solve A' x = b (step 0): */
+ /* x = R P' (L' \ (U' \ (Q' b))) */
+ /* and then perform iterative refinement (step > 0): */
+ /* x = x + R P' (L' \ (U' \ (Q' (b - A' x)))) */
+ /* -------------------------------------------------------------- */
+
+ if (step == 0)
+ {
+ /* W = Q' b */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [Cperm [i]] ; */
+ ASSIGN (W [i], Bx, Bz, Cperm [i], Bsplit) ;
+ }
+ }
+ else
+ {
+ /* Z = b - A' x */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* Z [i] = B [i] ; */
+ ASSIGN (Z [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops += MULTSUB_FLOPS * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ zi = Z [i] ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* zi -= conjugate (Ax [p]) * X [Ai [p]] ; */
+ ASSIGN (aij, Ax, Az, p, Bsplit) ;
+ MULT_SUB_CONJ (zi, X [Ai [p]], aij) ;
+ }
+ Z [i] = zi ;
+ }
+ /* W = Q' Z */
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = Z [Cperm [i]] ;
+ }
+ }
+
+ flops += UMF_uhsolve (Numeric, W, Pattern) ;
+ flops += UMF_lhsolve (Numeric, W, Pattern) ;
+
+ if (step == 0)
+ {
+
+ /* X = R P' W */
+ /* do not use Z, since it isn't allocated if irstep = 0 */
+
+ /* X = P' W */
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Rperm [i]] = W [i] ;
+ }
+ if (do_scale)
+ {
+ /* X = R X */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (X [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (X [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ }
+
+ }
+ else
+ {
+
+ /* Z = P' W */
+ for (i = 0 ; i < n ; i++)
+ {
+ Z [Rperm [i]] = W [i] ;
+ }
+ if (do_scale)
+ {
+ /* Z = R Z */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (Z [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (Z [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ }
+
+ flops += ASSEMBLE_FLOPS * n ;
+ /* X += Z */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] += Z [i] ; was +=W[i] in v4.3, which is wrong */
+ ASSEMBLE (X [i], Z [i]) ; /* bug fix, v4.3.1 */
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* sparse backward error estimate */
+ /* -------------------------------------------------------------- */
+
+ if (irstep > 0)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* A' is stored by row */
+ /* W (i) = (b - A' x)_i, residual */
+ /* Z2 (i) = (|A'||x|)_i */
+ /* ---------------------------------------------------------- */
+
+ flops += (MULT_FLOPS + DECREMENT_FLOPS + ABS_FLOPS + 1) * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* wi = B [i] ; */
+ ASSIGN (wi, Bx, Bz, i, Bsplit) ;
+ z2i = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* axx = conjugate (Ax [p]) * X [Ai [p]] ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ MULT_CONJ (axx, X [Ai [p]], aij) ;
+
+ /* wi -= axx ; */
+ DECREMENT (wi, axx) ;
+
+ /* z2i += ABS (axx) ; */
+ ABS (d, axx) ;
+ z2i += d ;
+ }
+ W [i] = wi ;
+ Z2 [i] = z2i ;
+ }
+
+ flops += (2*ABS_FLOPS + 5) * n ;
+ if (do_step (omega, step, B2, X, W, Y, Z2, S, n, Info))
+ {
+ /* iterative refinement is done */
+ break ;
+ }
+
+ }
+
+ }
+
+ }
+ else if (sys == UMFPACK_Aat)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* solve A.' x = b with optional iterative refinement */
+ /* ------------------------------------------------------------------ */
+
+ /* A' is the array transpose */
+
+ if (irstep > 0)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* using iterative refinement: compute Y */
+ /* -------------------------------------------------------------- */
+
+ nz = Ap [n] ;
+ Info [UMFPACK_NZ] = nz ;
+
+ /* A.' is stored by row */
+ /* Y (i) = ||(A.' R)_i||, 1-norm of row i of A.' R */
+
+ if (do_scale)
+ {
+ flops += (ABS_FLOPS + 2) * nz ;
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) * Rs [Ai [p]] ; */
+ /* note that A.' is the array transpose,
+ * so no conjugate */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += (d * Rs [Ai [p]]) ;
+ }
+ Y [i] = yi ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) / Rs [Ai [p]] ; */
+ /* note that A.' is the array transpose,
+ * so no conjugate */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += (d / Rs [Ai [p]]) ;
+ }
+ Y [i] = yi ;
+ }
+ }
+ }
+ else
+ {
+ /* no scaling */
+ flops += (ABS_FLOPS + 1) * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ yi = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* yi += ABS (Ax [p]) */
+ /* note that A.' is the array transpose,
+ * so no conjugate */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ ABS (d, aij) ;
+ yi += d ;
+ }
+ Y [i] = yi ;
+ }
+ }
+
+ /* B2 = abs (B) */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* B2 [i] = ABS (B [i]) ; */
+ ASSIGN (bi, Bx, Bz, i, Bsplit) ;
+ ABS (B2 [i], bi) ;
+ }
+
+ }
+
+ for (step = 0 ; step <= irstep ; step++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* Solve A.' x = b (step 0): */
+ /* x = R P' (L.' \ (U.' \ (Q' b))) */
+ /* and then perform iterative refinement (step > 0): */
+ /* x = x + R P' (L.' \ (U.' \ (Q' (b - A.' x)))) */
+ /* -------------------------------------------------------------- */
+
+ if (step == 0)
+ {
+ /* W = Q' b */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [Cperm [i]] ; */
+ ASSIGN (W [i], Bx, Bz, Cperm [i], Bsplit) ;
+ }
+ }
+ else
+ {
+ /* Z = b - A.' x */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* Z [i] = B [i] ; */
+ ASSIGN (Z [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops += MULTSUB_FLOPS * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ zi = Z [i] ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* zi -= Ax [p] * X [Ai [p]] ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ MULT_SUB (zi, aij, X [Ai [p]]) ;
+ }
+ Z [i] = zi ;
+ }
+ /* W = Q' Z */
+ for (i = 0 ; i < n ; i++)
+ {
+ W [i] = Z [Cperm [i]] ;
+ }
+ }
+
+ flops += UMF_utsolve (Numeric, W, Pattern) ;
+ flops += UMF_ltsolve (Numeric, W, Pattern) ;
+
+ if (step == 0)
+ {
+
+ /* X = R P' W */
+ /* do not use Z, since it isn't allocated if irstep = 0 */
+
+ /* X = P' W */
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Rperm [i]] = W [i] ;
+ }
+ if (do_scale)
+ {
+ /* X = R X */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (X [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (X [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ }
+
+ }
+ else
+ {
+
+ /* Z = P' W */
+ for (i = 0 ; i < n ; i++)
+ {
+ Z [Rperm [i]] = W [i] ;
+ }
+ if (do_scale)
+ {
+ /* Z = R Z */
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* multiply by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE (Z [i], Rs [i]) ;
+ }
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+ for (i = 0 ; i < n ; i++)
+ {
+ SCALE_DIV (Z [i], Rs [i]) ;
+ }
+ }
+ flops += SCALE_FLOPS * n ;
+ }
+
+ flops += ASSEMBLE_FLOPS * n ;
+ /* X += Z */
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] += Z [i] ; was +=W[i] in v4.3, which is wrong */
+ ASSEMBLE (X [i], Z [i]) ; /* bug fix, v4.3.1 */
+ }
+ }
+
+ /* -------------------------------------------------------------- */
+ /* sparse backward error estimate */
+ /* -------------------------------------------------------------- */
+
+ if (irstep > 0)
+ {
+
+ /* ---------------------------------------------------------- */
+ /* A.' is stored by row */
+ /* W (i) = (b - A.' x)_i, residual */
+ /* Z (i) = (|A.'||x|)_i */
+ /* ---------------------------------------------------------- */
+
+ flops += (MULT_FLOPS + DECREMENT_FLOPS + ABS_FLOPS + 1) * nz ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* wi = B [i] ; */
+ ASSIGN (wi, Bx, Bz, i, Bsplit) ;
+ z2i = 0. ;
+ p2 = Ap [i+1] ;
+ for (p = Ap [i] ; p < p2 ; p++)
+ {
+ /* axx = Ax [p] * X [Ai [p]] ; */
+ ASSIGN (aij, Ax, Az, p, AXsplit) ;
+ MULT (axx, aij, X [Ai [p]]) ;
+
+ /* wi -= axx ; */
+ DECREMENT (wi, axx) ;
+
+ /* z2i += ABS (axx) ; */
+ ABS (d, axx) ;
+ z2i += d ;
+ }
+ W [i] = wi ;
+ Z2 [i] = z2i ;
+ }
+
+ flops += (2*ABS_FLOPS + 5) * n ;
+ if (do_step (omega, step, B2, X, W, Y, Z2, S, n, Info))
+ {
+ /* iterative refinement is done */
+ break ;
+ }
+
+ }
+
+ }
+
+ }
+ else if (sys == UMFPACK_Pt_L)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve P'Lx=b: x = L \ Pb */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [Rperm [i]] ; */
+ ASSIGN (X [i], Bx, Bz, Rperm [i], Bsplit) ;
+ }
+ flops = UMF_lsolve (Numeric, X, Pattern) ;
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_L)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve Lx=b: x = L \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_lsolve (Numeric, X, Pattern) ;
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_Lt_P)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve L'Px=b: x = P' (L' \ b) */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [i] ; */
+ ASSIGN (W [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_lhsolve (Numeric, W, Pattern) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Rperm [i]] = W [i] ;
+ }
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_Lat_P)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve L.'Px=b: x = P' (L.' \ b) */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [i] ; */
+ ASSIGN (W [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_ltsolve (Numeric, W, Pattern) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Rperm [i]] = W [i] ;
+ }
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_Lt)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve L'x=b: x = L' \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_lhsolve (Numeric, X, Pattern) ;
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_Lat)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve L.'x=b: x = L.' \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_ltsolve (Numeric, X, Pattern) ;
+ status = UMFPACK_OK ;
+
+ }
+ else if (sys == UMFPACK_U_Qt)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve UQ'x=b: x = Q (U \ b) */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* W [i] = B [i] ; */
+ ASSIGN (W [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_usolve (Numeric, W, Pattern) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ X [Cperm [i]] = W [i] ;
+ }
+
+ }
+ else if (sys == UMFPACK_U)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve Ux=b: x = U \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_usolve (Numeric, X, Pattern) ;
+
+ }
+ else if (sys == UMFPACK_Q_Ut)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve QU'x=b: x = U' \ Q'b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [Cperm [i]] ; */
+ ASSIGN (X [i], Bx, Bz, Cperm [i], Bsplit) ;
+ }
+ flops = UMF_uhsolve (Numeric, X, Pattern) ;
+
+ }
+ else if (sys == UMFPACK_Q_Uat)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve QU.'x=b: x = U.' \ Q'b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [Cperm [i]] ; */
+ ASSIGN (X [i], Bx, Bz, Cperm [i], Bsplit) ;
+ }
+ flops = UMF_utsolve (Numeric, X, Pattern) ;
+
+ }
+ else if (sys == UMFPACK_Ut)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve U'x=b: x = U' \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_uhsolve (Numeric, X, Pattern) ;
+
+ }
+ else if (sys == UMFPACK_Uat)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* Solve U'x=b: x = U' \ b */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ /* X [i] = B [i] ; */
+ ASSIGN (X [i], Bx, Bz, i, Bsplit) ;
+ }
+ flops = UMF_utsolve (Numeric, X, Pattern) ;
+
+ }
+ else
+ {
+ return (UMFPACK_ERROR_invalid_system) ;
+ }
+
+#ifdef COMPLEX
+ /* copy the solution back, from Entry X [ ] to double Xx [ ] and Xz [ ] */
+ if (AXsplit)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = REAL_COMPONENT (X [i]) ;
+ Xz [i] = IMAG_COMPONENT (X [i]) ;
+ }
+ }
+#endif
+
+ /* return UMFPACK_OK, or UMFPACK_WARNING_singular_matrix */
+ /* Note that systems involving just L will return UMFPACK_OK */
+ Info [UMFPACK_SOLVE_FLOPS] = flops ;
+ return (status) ;
+}
+
+
+/* ========================================================================== */
+/* === do_step ============================================================== */
+/* ========================================================================== */
+
+/* Perform one step of iterative refinement, for A x = b or A' x = b */
+
+PRIVATE Int do_step /* return TRUE if iterative refinement done */
+(
+ double omega [3],
+ Int step, /* which step of iterative refinement to do */
+ const double B2 [ ], /* abs (B) */
+ Entry X [ ],
+ const Entry W [ ],
+ const double Y [ ],
+ const double Z2 [ ],
+ Entry S [ ],
+ Int n,
+ double Info [UMFPACK_INFO]
+)
+{
+ double last_omega [3], tau, nctau, d1, wd1, d2, wd2, xi, yix, wi, xnorm ;
+ Int i ;
+
+ /* DBL_EPSILON is a standard ANSI C term defined in <float.h> */
+ /* It is the smallest positive x such that 1.0+x != 1.0 */
+
+ nctau = 1000 * n * DBL_EPSILON ;
+ DEBUG0 (("do_step start: nctau = %30.20e\n", nctau)) ;
+ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
+ FALSE, FALSE) == UMFPACK_OK) ;
+
+ /* for approximate flop count, assume d1 > tau is always true */
+ /* flops += (2*ABS_FLOPS + 5) * n ; (done in UMF_solve, above) */
+
+ /* ---------------------------------------------------------------------- */
+ /* save the last iteration in case we need to reinstate it */
+ /* ---------------------------------------------------------------------- */
+
+ last_omega [0] = omega [0] ;
+ last_omega [1] = omega [1] ;
+ last_omega [2] = omega [2] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute sparse backward errors: omega [1] and omega [2] */
+ /* ---------------------------------------------------------------------- */
+
+ /* xnorm = ||x|| maxnorm */
+ xnorm = 0.0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ /* xi = ABS (X [i]) ; */
+ ABS (xi, X [i]) ;
+ if (SCALAR_IS_NAN (xi))
+ {
+ xnorm = xi ;
+ break ;
+ }
+ /* no NaN's to consider here: */
+ xnorm = MAX (xnorm, xi) ;
+ }
+
+ omega [1] = 0. ;
+ omega [2] = 0. ;
+ for (i = 0 ; i < n ; i++)
+ {
+ yix = Y [i] * xnorm ;
+ tau = (yix + B2 [i]) * nctau ;
+ d1 = Z2 [i] + B2 [i] ;
+ /* wi = ABS (W [i]) ; */
+ ABS (wi, W [i]) ;
+ if (SCALAR_IS_NAN (d1))
+ {
+ omega [1] = d1 ;
+ omega [2] = d1 ;
+ break ;
+ }
+ if (SCALAR_IS_NAN (tau))
+ {
+ omega [1] = tau ;
+ omega [2] = tau ;
+ break ;
+ }
+ if (d1 > tau) /* a double relop, but no NaN's here */
+ {
+ wd1 = wi / d1 ;
+ omega [1] = MAX (omega [1], wd1) ;
+ }
+ else if (tau > 0.0) /* a double relop, but no NaN's here */
+ {
+ d2 = Z2 [i] + yix ;
+ wd2 = wi / d2 ;
+ omega [2] = MAX (omega [2], wd2) ;
+ }
+ }
+
+ omega [0] = omega [1] + omega [2] ;
+ Info [UMFPACK_OMEGA1] = omega [1] ;
+ Info [UMFPACK_OMEGA2] = omega [2] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* stop the iterations if the backward error is small, or NaN */
+ /* ---------------------------------------------------------------------- */
+
+ Info [UMFPACK_IR_TAKEN] = step ;
+ Info [UMFPACK_IR_ATTEMPTED] = step ;
+
+ if (SCALAR_IS_NAN (omega [0]))
+ {
+ DEBUG0 (("omega[0] is NaN - done.\n")) ;
+ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
+ FALSE, FALSE) == UMFPACK_OK) ;
+ return (TRUE) ;
+ }
+
+ if (omega [0] < DBL_EPSILON) /* double relop, but no NaN case here */
+ {
+ DEBUG0 (("omega[0] too small - done.\n")) ;
+ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
+ FALSE, FALSE) == UMFPACK_OK) ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* stop if insufficient decrease in omega */
+ /* ---------------------------------------------------------------------- */
+
+ /* double relop, but no NaN case here: */
+ if (step > 0 && omega [0] > last_omega [0] / 2)
+ {
+ DEBUG0 (("stop refinement\n")) ;
+ if (omega [0] > last_omega [0])
+ {
+ /* last iteration better than this one, reinstate it */
+ DEBUG0 (("last iteration better\n")) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ X [i] = S [i] ;
+ }
+ Info [UMFPACK_OMEGA1] = last_omega [1] ;
+ Info [UMFPACK_OMEGA2] = last_omega [2] ;
+ }
+ Info [UMFPACK_IR_TAKEN] = step - 1 ;
+ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
+ FALSE, FALSE) == UMFPACK_OK) ;
+ return (TRUE) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* save current solution in case we need to reinstate */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ S [i] = X [i] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* iterative refinement continues */
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
+ FALSE, FALSE) == UMFPACK_OK) ;
+ return (FALSE) ;
+}
diff --git a/UMFPACK/Source/umf_solve.h b/UMFPACK/Source/umf_solve.h
new file mode 100644
index 0000000..80a796c
--- /dev/null
+++ b/UMFPACK/Source/umf_solve.h
@@ -0,0 +1,25 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_solve
+(
+ Int sys,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+ double Xx [ ],
+ const double Bx [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+ double Xz [ ],
+ const double Bz [ ],
+#endif
+ NumericType *Numeric,
+ Int irstep,
+ double Info [UMFPACK_INFO],
+ Int Pattern [ ],
+ double SolveWork [ ]
+) ;
diff --git a/UMFPACK/Source/umf_start_front.c b/UMFPACK/Source/umf_start_front.c
new file mode 100644
index 0000000..47aa354
--- /dev/null
+++ b/UMFPACK/Source/umf_start_front.c
@@ -0,0 +1,284 @@
+/* ========================================================================== */
+/* === UMF_start_front ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Allocate the initial frontal matrix working array for a single chain. The
+ * front does not have to be big enough, since if it's too small it will get
+ * reallocated. The size computed here is just an estimate. */
+
+#include "umf_internal.h"
+#include "umf_start_front.h"
+#include "umf_grow_front.h"
+
+GLOBAL Int UMF_start_front /* returns TRUE if successful, FALSE otherwise */
+(
+ Int chain,
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+ double maxbytes ;
+ Int fnrows_max, fncols_max, fnr2, fnc2, fsize, fcurr_size, maxfrsize,
+ overflow, nb, f, cdeg ;
+
+ nb = Symbolic->nb ;
+ fnrows_max = Symbolic->Chain_maxrows [chain] ;
+ fncols_max = Symbolic->Chain_maxcols [chain] ;
+
+ DEBUGm2 (("Start Front for chain "ID". fnrows_max "ID" fncols_max "ID"\n",
+ chain, fnrows_max, fncols_max)) ;
+
+ Work->fnrows_max = fnrows_max ;
+ Work->fncols_max = fncols_max ;
+ Work->any_skip = FALSE ;
+
+ maxbytes = sizeof (Entry) *
+ (double) (fnrows_max + nb) * (double) (fncols_max + nb) ;
+ fcurr_size = Work->fcurr_size ;
+
+ if (Symbolic->prefer_diagonal)
+ {
+ /* Get a rough upper bound on the degree of the first pivot column in
+ * this front. Note that Col_degree is not maintained if diagonal
+ * pivoting is preferred. For most matrices, the first pivot column
+ * of the first frontal matrix of a new chain has only one tuple in
+ * it anyway, so this bound is exact in that case. */
+ Int col, tpi, e, *E, *Col_tuples, *Col_tlen, *Cols ;
+ Tuple *tp, *tpend ;
+ Unit *Memory, *p ;
+ Element *ep ;
+ E = Work->E ;
+ Memory = Numeric->Memory ;
+ Col_tuples = Numeric->Lip ;
+ Col_tlen = Numeric->Lilen ;
+ col = Work->nextcand ;
+ tpi = Col_tuples [col] ;
+ tp = (Tuple *) Memory + tpi ;
+ tpend = tp + Col_tlen [col] ;
+ cdeg = 0 ;
+ DEBUGm3 (("\n=============== start front: col "ID" tlen "ID"\n",
+ col, Col_tlen [col])) ;
+ for ( ; tp < tpend ; tp++)
+ {
+ DEBUG1 (("Tuple ("ID","ID")\n", tp->e, tp->f)) ;
+ e = tp->e ;
+ if (!E [e]) continue ;
+ f = tp->f ;
+ p = Memory + E [e] ;
+ ep = (Element *) p ;
+ p += UNITS (Element, 1) ;
+ Cols = (Int *) p ;
+ if (Cols [f] == EMPTY) continue ;
+ DEBUG1 ((" nrowsleft "ID"\n", ep->nrowsleft)) ;
+ cdeg += ep->nrowsleft ;
+ }
+#ifndef NDEBUG
+ DEBUGm3 (("start front cdeg: "ID" col "ID"\n", cdeg, col)) ;
+ UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
+#endif
+
+ /* cdeg is now the rough upper bound on the degree of the next pivot
+ * column. */
+
+ /* If AMD was called, we know the maximum number of nonzeros in any
+ * column of L. Use this as an upper bound for cdeg, but add 2 to
+ * account for a small amount of off-diagonal pivoting. */
+ if (Symbolic->amd_dmax > 0)
+ {
+ cdeg = MIN (cdeg, Symbolic->amd_dmax) ;
+ }
+
+ /* Increase it to account for larger columns later on.
+ * Also ensure that it's larger than zero. */
+ cdeg += 2 ;
+
+ /* cdeg cannot be larger than fnrows_max */
+ cdeg = MIN (cdeg, fnrows_max) ;
+
+ }
+ else
+ {
+ /* don't do the above cdeg computation */
+ cdeg = 0 ;
+ }
+
+ DEBUGm2 (("fnrows max "ID" fncols_max "ID"\n", fnrows_max, fncols_max)) ;
+
+ /* the current frontal matrix is empty */
+ ASSERT (Work->fnrows == 0 && Work->fncols == 0 && Work->fnpiv == 0) ;
+
+ /* maximum row dimension is always odd, to avoid bad cache effects */
+ ASSERT (fnrows_max >= 0) ;
+ ASSERT (fnrows_max % 2 == 1) ;
+
+ /* ----------------------------------------------------------------------
+ * allocate working array for current frontal matrix:
+ * minimum size: 1-by-1
+ * maximum size: fnrows_max-by-fncols_max
+ * desired size:
+ *
+ * if Numeric->front_alloc_init >= 0:
+ *
+ * for unsymmetric matrices:
+ * Numeric->front_alloc_init * (fnrows_max-by-fncols_max)
+ *
+ * for symmetric matrices (diagonal pivoting preference, actually):
+ * Numeric->front_alloc_init * (fnrows_max-by-fncols_max), or
+ * cdeg*cdeg, whichever is smaller.
+ *
+ * if Numeric->front_alloc_init < 0:
+ * allocate a front of size -Numeric->front_alloc_init.
+ *
+ * Allocate the whole thing if it's small (less than 2*nb^2). Make sure the
+ * leading dimension of the frontal matrix is odd.
+ *
+ * Also allocate the nb-by-nb LU block, the dr-by-nb L block, and the
+ * nb-by-dc U block.
+ * ---------------------------------------------------------------------- */
+
+ /* get the maximum front size, avoiding integer overflow */
+ overflow = INT_OVERFLOW (maxbytes) ;
+ if (overflow)
+ {
+ /* :: int overflow, max front size :: */
+ maxfrsize = Int_MAX / sizeof (Entry) ;
+ }
+ else
+ {
+ maxfrsize = (fnrows_max + nb) * (fncols_max + nb) ;
+ }
+ ASSERT (!INT_OVERFLOW ((double) maxfrsize * sizeof (Entry))) ;
+
+ if (Numeric->front_alloc_init < 0)
+ {
+ /* allocate a front of -Numeric->front_alloc_init entries */
+ fsize = -Numeric->front_alloc_init ;
+ fsize = MAX (1, fsize) ;
+ }
+ else
+ {
+ if (INT_OVERFLOW (Numeric->front_alloc_init * maxbytes))
+ {
+ /* :: int overflow, requested front size :: */
+ fsize = Int_MAX / sizeof (Entry) ;
+ }
+ else
+ {
+ fsize = Numeric->front_alloc_init * maxfrsize ;
+ }
+
+ if (cdeg > 0)
+ {
+ /* diagonal pivoting is in use. cdeg was computed above */
+ Int fsize2 ;
+
+ /* add the L and U blocks */
+ cdeg += nb ;
+
+ if (INT_OVERFLOW (((double) cdeg * (double) cdeg) * sizeof (Entry)))
+ {
+ /* :: int overflow, symmetric front size :: */
+ fsize2 = Int_MAX / sizeof (Entry) ;
+ }
+ else
+ {
+ fsize2 = MAX (cdeg * cdeg, fcurr_size) ;
+ }
+ fsize = MIN (fsize, fsize2) ;
+ }
+ }
+
+ fsize = MAX (fsize, 2*nb*nb) ;
+
+ /* fsize and maxfrsize are now safe from integer overflow. They both
+ * include the size of the pivot blocks. */
+ ASSERT (!INT_OVERFLOW ((double) fsize * sizeof (Entry))) ;
+
+ Work->fnrows_new = 0 ;
+ Work->fncols_new = 0 ;
+
+ /* desired size is fnr2-by-fnc2 (includes L and U blocks): */
+ DEBUGm2 ((" fsize "ID" fcurr_size "ID"\n", fsize, fcurr_size)) ;
+ DEBUGm2 ((" maxfrsize "ID" fnr_curr "ID" fnc_curr "ID"\n", maxfrsize,
+ Work->fnr_curr, Work->fnc_curr)) ;
+
+ if (fsize >= maxfrsize && !overflow)
+ {
+ /* max working array is small, allocate all of it */
+ fnr2 = fnrows_max + nb ;
+ fnc2 = fncols_max + nb ;
+ fsize = maxfrsize ;
+ DEBUGm1 ((" sufficient for ("ID"+"ID")-by-("ID"+"ID")\n",
+ fnrows_max, nb, fncols_max, nb)) ;
+ }
+ else
+ {
+ /* allocate a smaller working array */
+ if (fnrows_max <= fncols_max)
+ {
+ fnr2 = (Int) sqrt ((double) fsize) ;
+ /* make sure fnr2 is odd */
+ fnr2 = MAX (fnr2, 1) ;
+ if (fnr2 % 2 == 0) fnr2++ ;
+ fnr2 = MIN (fnr2, fnrows_max + nb) ;
+ fnc2 = fsize / fnr2 ;
+ }
+ else
+ {
+ fnc2 = (Int) sqrt ((double) fsize) ;
+ fnc2 = MIN (fnc2, fncols_max + nb) ;
+ fnr2 = fsize / fnc2 ;
+ /* make sure fnr2 is odd */
+ fnr2 = MAX (fnr2, 1) ;
+ if (fnr2 % 2 == 0)
+ {
+ fnr2++ ;
+ fnc2 = fsize / fnr2 ;
+ }
+ }
+ DEBUGm1 ((" smaller "ID"-by-"ID"\n", fnr2, fnc2)) ;
+ }
+ fnr2 = MIN (fnr2, fnrows_max + nb) ;
+ fnc2 = MIN (fnc2, fncols_max + nb) ;
+ ASSERT (fnr2 % 2 == 1) ;
+ ASSERT (fnr2 * fnc2 <= fsize) ;
+
+ fnr2 -= nb ;
+ fnc2 -= nb ;
+ ASSERT (fnr2 >= 0) ;
+ ASSERT (fnc2 >= 0) ;
+
+ if (fsize > fcurr_size)
+ {
+ DEBUGm1 ((" Grow front \n")) ;
+ Work->do_grow = TRUE ;
+ if (!UMF_grow_front (Numeric, fnr2, fnc2, Work, -1))
+ {
+ /* since the minimum front size is 1-by-1, it would be nearly
+ * impossible to run out of memory here. */
+ DEBUGm4 (("out of memory: start front\n")) ;
+ return (FALSE) ;
+ }
+ }
+ else
+ {
+ /* use the existing front */
+ DEBUGm1 ((" existing front ok\n")) ;
+ Work->fnr_curr = fnr2 ;
+ Work->fnc_curr = fnc2 ;
+ Work->Flblock = Work->Flublock + nb * nb ;
+ Work->Fublock = Work->Flblock + nb * fnr2 ;
+ Work->Fcblock = Work->Fublock + nb * fnc2 ;
+ }
+ ASSERT (Work->Flblock == Work->Flublock + Work->nb*Work->nb) ;
+ ASSERT (Work->Fublock == Work->Flblock + Work->fnr_curr*Work->nb) ;
+ ASSERT (Work->Fcblock == Work->Fublock + Work->nb*Work->fnc_curr) ;
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umf_start_front.h b/UMFPACK/Source/umf_start_front.h
new file mode 100644
index 0000000..1a1c4f2
--- /dev/null
+++ b/UMFPACK/Source/umf_start_front.h
@@ -0,0 +1,13 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_start_front
+(
+ Int chain,
+ NumericType *Numeric,
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
diff --git a/UMFPACK/Source/umf_store_lu.c b/UMFPACK/Source/umf_store_lu.c
new file mode 100644
index 0000000..97e1081
--- /dev/null
+++ b/UMFPACK/Source/umf_store_lu.c
@@ -0,0 +1,1057 @@
+/* ========================================================================== */
+/* === UMF_store_lu ========================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Store the LU factors. Called by the kernel.
+ Returns TRUE if successful, FALSE if out of memory.
+*/
+
+#include "umf_internal.h"
+#include "umf_store_lu.h"
+#include "umf_mem_alloc_head_block.h"
+#include "umf_get_memory.h"
+
+/* ========================================================================== */
+
+#ifdef DROP
+GLOBAL Int UMF_store_lu_drop
+#else
+GLOBAL Int UMF_store_lu
+#endif
+(
+ NumericType *Numeric,
+ WorkType *Work
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry pivot_value ;
+#ifdef DROP
+ double droptol ;
+#endif
+ Entry *D, *Lval, *Uval, *Fl1, *Fl2, *Fu1, *Fu2,
+ *Flublock, *Flblock, *Fublock ;
+ Int i, k, fnr_curr, fnrows, fncols, row, col, pivrow, pivcol, *Frows,
+ *Fcols, *Lpattern, *Upattern, *Lpos, *Upos, llen, ulen, fnc_curr, fnpiv,
+ uilen, lnz, unz, nb, *Lilen,
+ *Uilen, *Lip, *Uip, *Li, *Ui, pivcol_position, newLchain, newUchain,
+ pivrow_position, p, size, lip, uip, lnzi, lnzx, unzx, lnz2i, lnz2x,
+ unz2i, unz2x, zero_pivot, *Pivrow, *Pivcol, kk,
+ Lnz [MAXNB] ;
+
+#ifndef NDEBUG
+ Int *Col_degree, *Row_degree ;
+#endif
+
+#ifdef DROP
+ Int all_lnz, all_unz ;
+ droptol = Numeric->droptol ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ fnrows = Work->fnrows ;
+ fncols = Work->fncols ;
+ fnpiv = Work->fnpiv ;
+
+ Lpos = Numeric->Lpos ;
+ Upos = Numeric->Upos ;
+ Lilen = Numeric->Lilen ;
+ Uilen = Numeric->Uilen ;
+
+ Lip = Numeric->Lip ;
+ Uip = Numeric->Uip ;
+ D = Numeric->D ;
+
+ Flublock = Work->Flublock ;
+ Flblock = Work->Flblock ;
+ Fublock = Work->Fublock ;
+
+ fnr_curr = Work->fnr_curr ;
+ fnc_curr = Work->fnc_curr ;
+ Frows = Work->Frows ;
+ Fcols = Work->Fcols ;
+
+#ifndef NDEBUG
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
+#endif
+
+ Lpattern = Work->Lpattern ;
+ llen = Work->llen ;
+ Upattern = Work->Upattern ;
+ ulen = Work->ulen ;
+
+ nb = Work->nb ;
+
+#ifndef NDEBUG
+ DEBUG1 (("\nSTORE LU: fnrows "ID
+ " fncols "ID"\n", fnrows, fncols)) ;
+
+ DEBUG2 (("\nFrontal matrix, including all space:\n"
+ "fnr_curr "ID" fnc_curr "ID" nb "ID"\n"
+ "fnrows "ID" fncols "ID" fnpiv "ID"\n",
+ fnr_curr, fnc_curr, nb, fnrows, fncols, fnpiv)) ;
+
+ DEBUG2 (("\nJust the active part:\n")) ;
+ DEBUG7 (("C block: ")) ;
+ UMF_dump_dense (Work->Fcblock, fnr_curr, fnrows, fncols) ;
+ DEBUG7 (("L block: ")) ;
+ UMF_dump_dense (Work->Flblock, fnr_curr, fnrows, fnpiv);
+ DEBUG7 (("U' block: ")) ;
+ UMF_dump_dense (Work->Fublock, fnc_curr, fncols, fnpiv) ;
+ DEBUG7 (("LU block: ")) ;
+ UMF_dump_dense (Work->Flublock, nb, fnpiv, fnpiv) ;
+ DEBUG7 (("Current frontal matrix: (prior to store LU)\n")) ;
+ UMF_dump_current_front (Numeric, Work, TRUE) ;
+#endif
+
+ Pivrow = Work->Pivrow ;
+ Pivcol = Work->Pivcol ;
+
+ /* ---------------------------------------------------------------------- */
+ /* store the columns of L */
+ /* ---------------------------------------------------------------------- */
+
+ for (kk = 0 ; kk < fnpiv ; kk++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* one more pivot row and column is being stored into L and U */
+ /* ------------------------------------------------------------------ */
+
+ k = Work->npiv + kk ;
+
+ /* ------------------------------------------------------------------ */
+ /* find the kth pivot row and pivot column */
+ /* ------------------------------------------------------------------ */
+
+ pivrow = Pivrow [kk] ;
+ pivcol = Pivcol [kk] ;
+
+#ifndef NDEBUG
+ ASSERT (pivrow >= 0 && pivrow < Work->n_row) ;
+ ASSERT (pivcol >= 0 && pivcol < Work->n_col) ;
+
+ DEBUGm4 ((
+ "\n -------------------------------------------------------------"
+ "Store LU: step " ID"\n", k)) ;
+ ASSERT (k < MIN (Work->n_row, Work->n_col)) ;
+ DEBUG2 (("Store column of L, k = "ID", llen "ID"\n", k, llen)) ;
+ for (i = 0 ; i < llen ; i++)
+ {
+ row = Lpattern [i] ;
+ ASSERT (row >= 0 && row < Work->n_row) ;
+ DEBUG2 ((" Lpattern["ID"] "ID" Lpos "ID, i, row, Lpos [row])) ;
+ if (row == pivrow) DEBUG2 ((" <- pivot row")) ;
+ DEBUG2 (("\n")) ;
+ ASSERT (i == Lpos [row]) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* remove pivot row from L */
+ /* ------------------------------------------------------------------ */
+
+ /* remove pivot row index from current column of L */
+ /* if a new Lchain starts, then all entries are removed later */
+ DEBUG2 (("Removing pivrow from Lpattern, k = "ID"\n", k)) ;
+ ASSERT (!NON_PIVOTAL_ROW (pivrow)) ;
+ pivrow_position = Lpos [pivrow] ;
+ if (pivrow_position != EMPTY)
+ {
+ /* place the last entry in the column in the */
+ /* position of the pivot row index */
+ ASSERT (pivrow == Lpattern [pivrow_position]) ;
+ row = Lpattern [--llen] ;
+ /* ASSERT (NON_PIVOTAL_ROW (row)) ; */
+ Lpattern [pivrow_position] = row ;
+ Lpos [row] = pivrow_position ;
+ Lpos [pivrow] = EMPTY ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* store the pivot value, for the diagonal matrix D */
+ /* ------------------------------------------------------------------ */
+
+ /* kk-th column of LU block */
+ Fl1 = Flublock + kk * nb ;
+
+ /* kk-th column of L in the L block */
+ Fl2 = Flblock + kk * fnr_curr ;
+
+ /* kk-th pivot in frontal matrix located in Flublock [kk, kk] */
+ pivot_value = Fl1 [kk] ;
+
+ D [k] = pivot_value ;
+ zero_pivot = IS_ZERO (pivot_value) ;
+
+ DEBUG4 (("Pivot D["ID"]=", k)) ;
+ EDEBUG4 (pivot_value) ;
+ DEBUG4 (("\n")) ;
+
+ /* ------------------------------------------------------------------ */
+ /* count nonzeros in kth column of L */
+ /* ------------------------------------------------------------------ */
+
+ lnz = 0 ;
+ lnz2i = 0 ;
+ lnz2x = llen ;
+
+#ifdef DROP
+ all_lnz = 0 ;
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ x = Fl1 [i] ;
+ if (IS_ZERO (x)) continue ;
+ all_lnz++ ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ lnz++ ;
+ if (Lpos [Pivrow [i]] == EMPTY) lnz2i++ ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Entry x ;
+ double s ;
+ x = Fl2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ all_lnz++ ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ lnz++ ;
+ if (Lpos [Frows [i]] == EMPTY) lnz2i++ ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ if (IS_ZERO (Fl1 [i])) continue ;
+ lnz++ ;
+ if (Lpos [Pivrow [i]] == EMPTY) lnz2i++ ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ if (IS_ZERO (Fl2 [i])) continue ;
+ lnz++ ;
+ if (Lpos [Frows [i]] == EMPTY) lnz2i++ ;
+ }
+
+#endif
+
+ lnz2x += lnz2i ;
+
+ /* determine if we start a new Lchain or continue the old one */
+ if (llen == 0 || zero_pivot)
+ {
+ /* llen == 0 means there is no prior Lchain */
+ /* D [k] == 0 means the pivot column is empty */
+ newLchain = TRUE ;
+ }
+ else
+ {
+ newLchain =
+ /* storage for starting a new Lchain */
+ UNITS (Entry, lnz) + UNITS (Int, lnz)
+ <=
+ /* storage for continuing a prior Lchain */
+ UNITS (Entry, lnz2x) + UNITS (Int, lnz2i) ;
+ }
+
+ if (newLchain)
+ {
+ /* start a new chain for column k of L */
+ DEBUG2 (("Start new Lchain, k = "ID"\n", k)) ;
+
+ pivrow_position = EMPTY ;
+
+ /* clear the prior Lpattern */
+ for (i = 0 ; i < llen ; i++)
+ {
+ row = Lpattern [i] ;
+ Lpos [row] = EMPTY ;
+ }
+ llen = 0 ;
+
+ lnzi = lnz ;
+ lnzx = lnz ;
+ }
+ else
+ {
+ /* continue the prior Lchain */
+ DEBUG2 (("Continue Lchain, k = "ID"\n", k)) ;
+ lnzi = lnz2i ;
+ lnzx = lnz2x ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* allocate space for the column of L */
+ /* ------------------------------------------------------------------ */
+
+ size = UNITS (Int, lnzi) + UNITS (Entry, lnzx) ;
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0)
+ {
+ double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ;
+ DEBUG4 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random garbage coll. (store LU)\n"));
+ }
+#endif
+
+ p = UMF_mem_alloc_head_block (Numeric, size) ;
+ if (!p)
+ {
+ Int r2, c2 ;
+ /* Do garbage collection, realloc, and try again. */
+ /* Note that there are pivot rows/columns in current front. */
+ if (Work->do_grow)
+ {
+ /* full compaction of current frontal matrix, since
+ * UMF_grow_front will be called next anyway. */
+ r2 = fnrows ;
+ c2 = fncols ;
+ }
+ else
+ {
+ /* partial compaction. */
+ r2 = MAX (fnrows, Work->fnrows_new + 1) ;
+ c2 = MAX (fncols, Work->fncols_new + 1) ;
+ }
+ DEBUGm3 (("get_memory from umf_store_lu:\n")) ;
+ if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE))
+ {
+ DEBUGm4 (("out of memory: store LU (1)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ p = UMF_mem_alloc_head_block (Numeric, size) ;
+ if (!p)
+ {
+ DEBUGm4 (("out of memory: store LU (2)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ /* garbage collection may have moved the current front */
+ fnc_curr = Work->fnc_curr ;
+ fnr_curr = Work->fnr_curr ;
+ Flublock = Work->Flublock ;
+ Flblock = Work->Flblock ;
+ Fublock = Work->Fublock ;
+ Fl1 = Flublock + kk * nb ;
+ Fl2 = Flblock + kk * fnr_curr ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* store the column of L */
+ /* ------------------------------------------------------------------ */
+
+ lip = p ;
+
+ Li = (Int *) (Numeric->Memory + p) ;
+ p += UNITS (Int, lnzi) ;
+ Lval = (Entry *) (Numeric->Memory + p) ;
+ p += UNITS (Entry, lnzx) ;
+
+ for (i = 0 ; i < lnzx ; i++)
+ {
+ CLEAR (Lval [i]) ;
+ }
+
+ /* store the numerical entries */
+
+ if (newLchain)
+ {
+ /* flag the first column in the Lchain by negating Lip [k] */
+ lip = -lip ;
+
+ ASSERT (llen == 0) ;
+
+#ifdef DROP
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int row2, pos ;
+ x = Fl1 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ row2 = Pivrow [i] ;
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ Li [pos] = row2 ;
+ Lval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int row2, pos ;
+ x = Fl2 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ row2 = Frows [i] ;
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ Li [pos] = row2 ;
+ Lval [pos] = x ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ Int row2, pos ;
+ x = Fl1 [i] ;
+ if (IS_ZERO (x)) continue ;
+ row2 = Pivrow [i] ;
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ Li [pos] = row2 ;
+ Lval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Entry x ;
+ Int row2, pos ;
+ x = Fl2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ row2 = Frows [i] ;
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ Li [pos] = row2 ;
+ Lval [pos] = x ;
+ }
+
+#endif
+
+ }
+ else
+ {
+ ASSERT (llen > 0) ;
+
+#ifdef DROP
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int row2, pos ;
+ x = Fl1 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ row2 = Pivrow [i] ;
+ pos = Lpos [row2] ;
+ if (pos == EMPTY)
+ {
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ *Li++ = row2 ;
+ }
+ Lval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int row2, pos ;
+ x = Fl2 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ row2 = Frows [i] ;
+ pos = Lpos [row2] ;
+ if (pos == EMPTY)
+ {
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ *Li++ = row2 ;
+ }
+ Lval [pos] = x ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ Int row2, pos ;
+ x = Fl1 [i] ;
+ if (IS_ZERO (x)) continue ;
+ row2 = Pivrow [i] ;
+ pos = Lpos [row2] ;
+ if (pos == EMPTY)
+ {
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ *Li++ = row2 ;
+ }
+ Lval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fnrows ; i++)
+ {
+ Entry x ;
+ Int row2, pos ;
+ x = Fl2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ row2 = Frows [i] ;
+ pos = Lpos [row2] ;
+ if (pos == EMPTY)
+ {
+ pos = llen++ ;
+ Lpattern [pos] = row2 ;
+ Lpos [row2] = pos ;
+ *Li++ = row2 ;
+ }
+ Lval [pos] = x ;
+ }
+
+#endif
+
+ }
+ DEBUG4 (("llen "ID" lnzx "ID"\n", llen, lnzx)) ;
+ ASSERT (llen == lnzx) ;
+ ASSERT (lnz <= llen) ;
+ DEBUG4 (("lnz "ID" \n", lnz)) ;
+
+#ifdef DROP
+
+ DEBUG4 (("all_lnz "ID" \n", all_lnz)) ;
+ ASSERT (lnz <= all_lnz) ;
+ Numeric->lnz += lnz ;
+ Numeric->all_lnz += all_lnz ;
+ Lnz [kk] = all_lnz ;
+
+#else
+
+ Numeric->lnz += lnz ;
+ Numeric->all_lnz += lnz ;
+ Lnz [kk] = lnz ;
+#endif
+
+ Numeric->nLentries += lnzx ;
+ Work->llen = llen ;
+ Numeric->isize += lnzi ;
+
+ /* ------------------------------------------------------------------ */
+ /* the pivot column is fully assembled and scaled, and is now the */
+ /* k-th column of L */
+ /* ------------------------------------------------------------------ */
+
+ Lpos [pivrow] = pivrow_position ; /* not aliased */
+ Lip [pivcol] = lip ; /* aliased with Col_tuples */
+ Lilen [pivcol] = lnzi ; /* aliased with Col_tlen */
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* store the rows of U */
+ /* ---------------------------------------------------------------------- */
+
+ for (kk = 0 ; kk < fnpiv ; kk++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* one more pivot row and column is being stored into L and U */
+ /* ------------------------------------------------------------------ */
+
+ k = Work->npiv + kk ;
+
+ /* ------------------------------------------------------------------ */
+ /* find the kth pivot row and pivot column */
+ /* ------------------------------------------------------------------ */
+
+ pivrow = Pivrow [kk] ;
+ pivcol = Pivcol [kk] ;
+
+#ifndef NDEBUG
+ ASSERT (pivrow >= 0 && pivrow < Work->n_row) ;
+ ASSERT (pivcol >= 0 && pivcol < Work->n_col) ;
+
+ DEBUG2 (("Store row of U, k = "ID", ulen "ID"\n", k, ulen)) ;
+ for (i = 0 ; i < ulen ; i++)
+ {
+ col = Upattern [i] ;
+ DEBUG2 ((" Upattern["ID"] "ID, i, col)) ;
+ if (col == pivcol) DEBUG2 ((" <- pivot col")) ;
+ DEBUG2 (("\n")) ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ ASSERT (i == Upos [col]) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* get the pivot value, for the diagonal matrix D */
+ /* ------------------------------------------------------------------ */
+
+ zero_pivot = IS_ZERO (D [k]) ;
+
+ /* ------------------------------------------------------------------ */
+ /* count the nonzeros in the row of U */
+ /* ------------------------------------------------------------------ */
+
+ /* kk-th row of U in the LU block */
+ Fu1 = Flublock + kk ;
+
+ /* kk-th row of U in the U block */
+ Fu2 = Fublock + kk * fnc_curr ;
+
+ unz = 0 ;
+ unz2i = 0 ;
+ unz2x = ulen ;
+ DEBUG2 (("unz2x is "ID", lnzx "ID"\n", unz2x, lnzx)) ;
+
+ /* if row k does not end a Uchain, pivcol not included in ulen */
+ ASSERT (!NON_PIVOTAL_COL (pivcol)) ;
+ pivcol_position = Upos [pivcol] ;
+ if (pivcol_position != EMPTY)
+ {
+ unz2x-- ;
+ DEBUG2 (("(exclude pivcol) unz2x is now "ID"\n", unz2x)) ;
+ }
+
+ ASSERT (unz2x >= 0) ;
+
+#ifdef DROP
+ all_unz = 0 ;
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ x = Fu1 [i*nb] ;
+ if (IS_ZERO (x)) continue ;
+ all_unz++ ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ unz++ ;
+ if (Upos [Pivcol [i]] == EMPTY) unz2i++ ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Entry x ;
+ double s ;
+ x = Fu2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ all_unz++ ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ unz++ ;
+ if (Upos [Fcols [i]] == EMPTY) unz2i++ ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ if (IS_ZERO (Fu1 [i*nb])) continue ;
+ unz++ ;
+ if (Upos [Pivcol [i]] == EMPTY) unz2i++ ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ if (IS_ZERO (Fu2 [i])) continue ;
+ unz++ ;
+ if (Upos [Fcols [i]] == EMPTY) unz2i++ ;
+ }
+
+#endif
+
+ unz2x += unz2i ;
+
+ ASSERT (IMPLIES (k == 0, ulen == 0)) ;
+
+ /* determine if we start a new Uchain or continue the old one */
+ if (ulen == 0 || zero_pivot)
+ {
+ /* ulen == 0 means there is no prior Uchain */
+ /* D [k] == 0 means the matrix is singular (pivot row might */
+ /* not be empty, however, but start a new Uchain to prune zero */
+ /* entries for the deg > 0 test in UMF_u*solve) */
+ newUchain = TRUE ;
+ }
+ else
+ {
+ newUchain =
+ /* approximate storage for starting a new Uchain */
+ UNITS (Entry, unz) + UNITS (Int, unz)
+ <=
+ /* approximate storage for continuing a prior Uchain */
+ UNITS (Entry, unz2x) + UNITS (Int, unz2i) ;
+
+ /* this would be exact, except for the Int to Unit rounding, */
+ /* because the Upattern is stored only at the end of the Uchain */
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* allocate space for the row of U */
+ /* ------------------------------------------------------------------ */
+
+ size = 0 ;
+ if (newUchain)
+ {
+ /* store the pattern of the last row in the prior Uchain */
+ size += UNITS (Int, ulen) ;
+ unzx = unz ;
+ }
+ else
+ {
+ unzx = unz2x ;
+ }
+ size += UNITS (Entry, unzx) ;
+
+#ifndef NDEBUG
+ UMF_allocfail = FALSE ;
+ if (UMF_gprob > 0)
+ {
+ double rrr = ((double) (rand ( ))) / (((double) RAND_MAX) + 1) ;
+ DEBUG4 (("Check random %e %e\n", rrr, UMF_gprob)) ;
+ UMF_allocfail = rrr < UMF_gprob ;
+ if (UMF_allocfail) DEBUGm2 (("Random garbage coll. (store LU)\n"));
+ }
+#endif
+
+ p = UMF_mem_alloc_head_block (Numeric, size) ;
+ if (!p)
+ {
+ Int r2, c2 ;
+ /* Do garbage collection, realloc, and try again. */
+ /* Note that there are pivot rows/columns in current front. */
+ if (Work->do_grow)
+ {
+ /* full compaction of current frontal matrix, since
+ * UMF_grow_front will be called next anyway. */
+ r2 = fnrows ;
+ c2 = fncols ;
+ }
+ else
+ {
+ /* partial compaction. */
+ r2 = MAX (fnrows, Work->fnrows_new + 1) ;
+ c2 = MAX (fncols, Work->fncols_new + 1) ;
+ }
+ DEBUGm3 (("get_memory from umf_store_lu:\n")) ;
+ if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE))
+ {
+ /* :: get memory, column of L :: */
+ DEBUGm4 (("out of memory: store LU (1)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ p = UMF_mem_alloc_head_block (Numeric, size) ;
+ if (!p)
+ {
+ /* :: out of memory, column of U :: */
+ DEBUGm4 (("out of memory: store LU (2)\n")) ;
+ return (FALSE) ; /* out of memory */
+ }
+ /* garbage collection may have moved the current front */
+ fnc_curr = Work->fnc_curr ;
+ fnr_curr = Work->fnr_curr ;
+ Flublock = Work->Flublock ;
+ Flblock = Work->Flblock ;
+ Fublock = Work->Fublock ;
+ Fu1 = Flublock + kk ;
+ Fu2 = Fublock + kk * fnc_curr ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* store the row of U */
+ /* ------------------------------------------------------------------ */
+
+ uip = p ;
+
+ if (newUchain)
+ {
+ /* starting a new Uchain - flag this by negating Uip [k] */
+ uip = -uip ;
+ DEBUG2 (("Start new Uchain, k = "ID"\n", k)) ;
+
+ pivcol_position = EMPTY ;
+
+ /* end the prior Uchain */
+ /* save the current Upattern, and then */
+ /* clear it and start a new Upattern */
+ DEBUG2 (("Ending prior chain, k-1 = "ID"\n", k-1)) ;
+ uilen = ulen ;
+ Ui = (Int *) (Numeric->Memory + p) ;
+ Numeric->isize += ulen ;
+ p += UNITS (Int, ulen) ;
+ for (i = 0 ; i < ulen ; i++)
+ {
+ col = Upattern [i] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ Upos [col] = EMPTY ;
+ Ui [i] = col ;
+ }
+
+ ulen = 0 ;
+
+ }
+ else
+ {
+ /* continue the prior Uchain */
+ DEBUG2 (("Continue Uchain, k = "ID"\n", k)) ;
+ ASSERT (k > 0) ;
+
+ /* remove pivot col index from current row of U */
+ /* if a new Uchain starts, then all entries are removed later */
+ DEBUG2 (("Removing pivcol from Upattern, k = "ID"\n", k)) ;
+
+ if (pivcol_position != EMPTY)
+ {
+ /* place the last entry in the row in the */
+ /* position of the pivot col index */
+ ASSERT (pivcol == Upattern [pivcol_position]) ;
+ col = Upattern [--ulen] ;
+ ASSERT (col >= 0 && col < Work->n_col) ;
+ Upattern [pivcol_position] = col ;
+ Upos [col] = pivcol_position ;
+ Upos [pivcol] = EMPTY ;
+ }
+
+ /* this row continues the Uchain. Keep track of how much */
+ /* to trim from the k-th length to get the length of the */
+ /* (k-1)st row of U */
+ uilen = unz2i ;
+
+ }
+
+ Uval = (Entry *) (Numeric->Memory + p) ;
+ /* p += UNITS (Entry, unzx), no need to increment p */
+
+ for (i = 0 ; i < unzx ; i++)
+ {
+ CLEAR (Uval [i]) ;
+ }
+
+ if (newUchain)
+ {
+ ASSERT (ulen == 0) ;
+
+#ifdef DROP
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int col2, pos ;
+ x = Fu1 [i*nb] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ col2 = Pivcol [i] ;
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ Uval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int col2, pos ;
+ x = Fu2 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ col2 = Fcols [i] ;
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ Uval [pos] = x ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ Int col2, pos ;
+ x = Fu1 [i*nb] ;
+ if (IS_ZERO (x)) continue ;
+ col2 = Pivcol [i] ;
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ Uval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Entry x ;
+ Int col2, pos ;
+ x = Fu2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ col2 = Fcols [i] ;
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ Uval [pos] = x ;
+ }
+
+#endif
+
+ }
+ else
+ {
+
+ ASSERT (ulen > 0) ;
+
+ /* store the numerical entries and find new nonzeros */
+
+#ifdef DROP
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int col2, pos ;
+ x = Fu1 [i*nb] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ col2 = Pivcol [i] ;
+ pos = Upos [col2] ;
+ if (pos == EMPTY)
+ {
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ }
+ Uval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Entry x ;
+ double s ;
+ Int col2, pos ;
+ x = Fu2 [i] ;
+ APPROX_ABS (s, x) ;
+ if (s <= droptol) continue ;
+ col2 = Fcols [i] ;
+ pos = Upos [col2] ;
+ if (pos == EMPTY)
+ {
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ }
+ Uval [pos] = x ;
+ }
+
+#else
+
+ for (i = kk + 1 ; i < fnpiv ; i++)
+ {
+ Entry x ;
+ Int col2, pos ;
+ x = Fu1 [i*nb] ;
+ if (IS_ZERO (x)) continue ;
+ col2 = Pivcol [i] ;
+ pos = Upos [col2] ;
+ if (pos == EMPTY)
+ {
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ }
+ Uval [pos] = x ;
+ }
+
+ for (i = 0 ; i < fncols ; i++)
+ {
+ Entry x ;
+ Int col2, pos ;
+ x = Fu2 [i] ;
+ if (IS_ZERO (x)) continue ;
+ col2 = Fcols [i] ;
+ pos = Upos [col2] ;
+ if (pos == EMPTY)
+ {
+ pos = ulen++ ;
+ Upattern [pos] = col2 ;
+ Upos [col2] = pos ;
+ }
+ Uval [pos] = x ;
+ }
+
+#endif
+
+ }
+
+ ASSERT (ulen == unzx) ;
+ ASSERT (unz <= ulen) ;
+ DEBUG4 (("unz "ID" \n", unz)) ;
+
+#ifdef DROP
+
+ DEBUG4 (("all_unz "ID" \n", all_unz)) ;
+ ASSERT (unz <= all_unz) ;
+ Numeric->unz += unz ;
+ Numeric->all_unz += all_unz ;
+ /* count the "true" flops, based on LU pattern only */
+ Numeric->flops += DIV_FLOPS * Lnz [kk] /* scale pivot column */
+ + MULTSUB_FLOPS * (Lnz [kk] * all_unz) ; /* outer product */
+
+#else
+
+ Numeric->unz += unz ;
+ Numeric->all_unz += unz ;
+ /* count the "true" flops, based on LU pattern only */
+ Numeric->flops += DIV_FLOPS * Lnz [kk] /* scale pivot column */
+ + MULTSUB_FLOPS * (Lnz [kk] * unz) ; /* outer product */
+#endif
+
+ Numeric->nUentries += unzx ;
+ Work->ulen = ulen ;
+ DEBUG1 (("Work->ulen = "ID" at end of pivot step, k: "ID"\n", ulen, k));
+
+ /* ------------------------------------------------------------------ */
+ /* the pivot row is the k-th row of U */
+ /* ------------------------------------------------------------------ */
+
+ Upos [pivcol] = pivcol_position ; /* not aliased */
+ Uip [pivrow] = uip ; /* aliased with Row_tuples */
+ Uilen [pivrow] = uilen ; /* aliased with Row_tlen */
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* no more pivots in frontal working array */
+ /* ---------------------------------------------------------------------- */
+
+ Work->npiv += fnpiv ;
+ Work->fnpiv = 0 ;
+ Work->fnzeros = 0 ;
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umf_store_lu.h b/UMFPACK/Source/umf_store_lu.h
new file mode 100644
index 0000000..82627ad
--- /dev/null
+++ b/UMFPACK/Source/umf_store_lu.h
@@ -0,0 +1,17 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_store_lu
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
+
+GLOBAL Int UMF_store_lu_drop
+(
+ NumericType *Numeric,
+ WorkType *Work
+) ;
diff --git a/UMFPACK/Source/umf_symbolic_usage.c b/UMFPACK/Source/umf_symbolic_usage.c
new file mode 100644
index 0000000..31abdf9
--- /dev/null
+++ b/UMFPACK/Source/umf_symbolic_usage.c
@@ -0,0 +1,46 @@
+/* ========================================================================== */
+/* === UMF_symbolic_usage =================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Returns the final size of the Symbolic object, in Units */
+
+#include "umf_internal.h"
+#include "umf_symbolic_usage.h"
+
+GLOBAL double UMF_symbolic_usage
+(
+ Int n_row,
+ Int n_col,
+ Int nchains,
+ Int nfr,
+ Int esize, /* zero if no dense rows. Otherwise, equal to the
+ * number of non-singleton, non-empty columns */
+ Int prefer_diagonal
+)
+{
+ double units ;
+
+ units =
+ DUNITS (SymbolicType, 1) /* Symbolic structure */
+ + 2 * DUNITS (Int, n_col+1) /* Cperm_init, Cdeg */
+ + 2 * DUNITS (Int, n_row+1) /* Rperm_init, Rdeg */
+ + 3 * DUNITS (Int, nchains+1) /* Chain_ */
+ + 4 * DUNITS (Int, nfr+1) ; /* Front_ */
+
+ /* if dense rows are present */
+ units += DUNITS (Int, esize) ; /* Esize */
+
+ /* for diagonal pivoting */
+ if (prefer_diagonal)
+ {
+ units += DUNITS (Int, n_col+1) ; /* Diagonal_map */
+ }
+
+ return (units) ;
+}
diff --git a/UMFPACK/Source/umf_symbolic_usage.h b/UMFPACK/Source/umf_symbolic_usage.h
new file mode 100644
index 0000000..3fad24a
--- /dev/null
+++ b/UMFPACK/Source/umf_symbolic_usage.h
@@ -0,0 +1,15 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL double UMF_symbolic_usage
+(
+ Int n_row,
+ Int n_col,
+ Int nchains,
+ Int nfr,
+ Int esize,
+ Int prefer_diagonal
+) ;
diff --git a/UMFPACK/Source/umf_transpose.c b/UMFPACK/Source/umf_transpose.c
new file mode 100644
index 0000000..6ac7435
--- /dev/null
+++ b/UMFPACK/Source/umf_transpose.c
@@ -0,0 +1,401 @@
+/* ========================================================================== */
+/* === UMF_transpose ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Not user-callable. Computes a permuted transpose, R = (A (P,Q(1:nq)))' in
+ MATLAB notation, where R is in column-form. A is n_row-by-n_col, the
+ row-form matrix R is n_row-by-nq, where nq <= n_col. A may be singular.
+ The complex version can do transpose (') or array transpose (.').
+
+ Uses Gustavson's method (Two Fast Algorithms for Sparse Matrices:
+ Multiplication and Permuted Transposition, ACM Trans. on Math. Softw.,
+ vol 4, no 3, pp. 250-269).
+*/
+
+#include "umf_internal.h"
+#include "umf_transpose.h"
+#include "umf_is_permutation.h"
+
+GLOBAL Int UMF_transpose
+(
+ Int n_row, /* A is n_row-by-n_col */
+ Int n_col,
+ const Int Ap [ ], /* size n_col+1 */
+ const Int Ai [ ], /* size nz = Ap [n_col] */
+ const double Ax [ ], /* size nz if present */
+
+ const Int P [ ], /* P [k] = i means original row i is kth row in A(P,Q)*/
+ /* P is identity if not present */
+ /* size n_row, if present */
+
+ const Int Q [ ], /* Q [k] = j means original col j is kth col in A(P,Q)*/
+ /* Q is identity if not present */
+ /* size nq, if present */
+ Int nq, /* size of Q, ignored if Q is (Int *) NULL */
+
+ /* output matrix: Rp, Ri, Rx, and Rz: */
+ Int Rp [ ], /* size n_row+1 */
+ Int Ri [ ], /* size nz */
+ double Rx [ ], /* size nz, if present */
+
+ Int W [ ], /* size max (n_row,n_col) workspace */
+
+ Int check /* if true, then check inputs */
+#ifdef COMPLEX
+ , const double Az [ ] /* size nz */
+ , double Rz [ ] /* size nz */
+ , Int do_conjugate /* if true, then do conjugate transpose */
+ /* otherwise, do array transpose */
+#endif
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int i, j, k, p, bp, newj, do_values ;
+#ifdef COMPLEX
+ Int split ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ Int nz ;
+ ASSERT (n_col >= 0) ;
+ nz = (Ap != (Int *) NULL) ? Ap [n_col] : 0 ;
+ DEBUG2 (("UMF_transpose: "ID"-by-"ID" nz "ID"\n", n_row, n_col, nz)) ;
+#endif
+
+ if (check)
+ {
+ /* UMFPACK_symbolic skips this check */
+ /* UMFPACK_transpose always does this check */
+ if (!Ai || !Ap || !Ri || !Rp || !W)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+ if (n_row <= 0 || n_col <= 0) /* n_row,n_col must be > 0 */
+ {
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+ if (!UMF_is_permutation (P, W, n_row, n_row) ||
+ !UMF_is_permutation (Q, W, nq, nq))
+ {
+ return (UMFPACK_ERROR_invalid_permutation) ;
+ }
+ if (AMD_valid (n_row, n_col, Ap, Ai) != AMD_OK)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG2 (("UMF_transpose, input matrix:\n")) ;
+ UMF_dump_col_matrix (Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Ai, Ap, n_row, n_col, nz) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each row of A */
+ /* ---------------------------------------------------------------------- */
+
+ /* use W as workspace for RowCount */
+
+ for (i = 0 ; i < n_row ; i++)
+ {
+ W [i] = 0 ;
+ Rp [i] = 0 ;
+ }
+
+ if (Q != (Int *) NULL)
+ {
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ ASSERT (i >= 0 && i < n_row) ;
+ W [i]++ ;
+ }
+ }
+ }
+ else
+ {
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ ASSERT (i >= 0 && i < n_row) ;
+ W [i]++ ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row pointers for R = A (P,Q) */
+ /* ---------------------------------------------------------------------- */
+
+ if (P != (Int *) NULL)
+ {
+ Rp [0] = 0 ;
+ for (k = 0 ; k < n_row ; k++)
+ {
+ i = P [k] ;
+ ASSERT (i >= 0 && i < n_row) ;
+ Rp [k+1] = Rp [k] + W [i] ;
+ }
+ for (k = 0 ; k < n_row ; k++)
+ {
+ i = P [k] ;
+ ASSERT (i >= 0 && i < n_row) ;
+ W [i] = Rp [k] ;
+ }
+ }
+ else
+ {
+ Rp [0] = 0 ;
+ for (i = 0 ; i < n_row ; i++)
+ {
+ Rp [i+1] = Rp [i] + W [i] ;
+ }
+ for (i = 0 ; i < n_row ; i++)
+ {
+ W [i] = Rp [i] ;
+ }
+ }
+ ASSERT (Rp [n_row] <= Ap [n_col]) ;
+
+ /* at this point, W holds the permuted row pointers */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the row form of B */
+ /* ---------------------------------------------------------------------- */
+
+ do_values = Ax && Rx ;
+
+#ifdef COMPLEX
+ split = SPLIT (Az) && SPLIT (Rz) ;
+
+ if (do_conjugate && do_values)
+ {
+ if (Q != (Int *) NULL)
+ {
+ if (split)
+ {
+ /* R = A (P,Q)' */
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = newj ;
+ Rx [bp] = Ax [p] ;
+ Rz [bp] = -Az [p] ;
+ }
+ }
+ }
+ else
+ {
+ /* R = A (P,Q)' (merged complex values) */
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = newj ;
+ Rx [2*bp] = Ax [2*p] ;
+ Rx [2*bp+1] = -Ax [2*p+1] ;
+ }
+ }
+ }
+ }
+ else
+ {
+ if (split)
+ {
+ /* R = A (P,:)' */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = j ;
+ Rx [bp] = Ax [p] ;
+ Rz [bp] = -Az [p] ;
+ }
+ }
+ }
+ else
+ {
+ /* R = A (P,:)' (merged complex values) */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = j ;
+ Rx [2*bp] = Ax [2*p] ;
+ Rx [2*bp+1] = -Ax [2*p+1] ;
+ }
+ }
+ }
+ }
+ }
+ else
+#endif
+ {
+ if (Q != (Int *) NULL)
+ {
+ if (do_values)
+ {
+#ifdef COMPLEX
+ if (split)
+#endif
+ {
+ /* R = A (P,Q).' */
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = newj ;
+ Rx [bp] = Ax [p] ;
+#ifdef COMPLEX
+ Rz [bp] = Az [p] ;
+#endif
+ }
+ }
+ }
+#ifdef COMPLEX
+ else
+ {
+ /* R = A (P,Q).' (merged complex values) */
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = newj ;
+ Rx [2*bp] = Ax [2*p] ;
+ Rx [2*bp+1] = Ax [2*p+1] ;
+ }
+ }
+ }
+#endif
+ }
+ else
+ {
+ /* R = pattern of A (P,Q).' */
+ for (newj = 0 ; newj < nq ; newj++)
+ {
+ j = Q [newj] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ Ri [W [Ai [p]]++] = newj ;
+ }
+ }
+ }
+ }
+ else
+ {
+ if (do_values)
+ {
+#ifdef COMPLEX
+ if (split)
+#endif
+ {
+ /* R = A (P,:).' */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = j ;
+ Rx [bp] = Ax [p] ;
+#ifdef COMPLEX
+ Rz [bp] = Az [p] ;
+#endif
+ }
+ }
+ }
+#ifdef COMPLEX
+ else
+ {
+ /* R = A (P,:).' (merged complex values) */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ bp = W [Ai [p]]++ ;
+ Ri [bp] = j ;
+ Rx [2*bp] = Ax [2*p] ;
+ Rx [2*bp+1] = Ax [2*p+1] ;
+ }
+ }
+ }
+#endif
+ }
+ else
+ {
+ /* R = pattern of A (P,:).' */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ Ri [W [Ai [p]]++] = j ;
+ }
+ }
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n_row ; k++)
+ {
+ if (P != (Int *) NULL)
+ {
+ i = P [k] ;
+ }
+ else
+ {
+ i = k ;
+ }
+ DEBUG3 ((ID": W[i] "ID" Rp[k+1] "ID"\n", i, W [i], Rp [k+1])) ;
+ ASSERT (W [i] == Rp [k+1]) ;
+ }
+ DEBUG2 (("UMF_transpose, output matrix:\n")) ;
+ UMF_dump_col_matrix (Rx,
+#ifdef COMPLEX
+ Rz,
+#endif
+ Ri, Rp, n_col, n_row, Rp [n_row]) ;
+ ASSERT (AMD_valid (n_col, n_row, Rp, Ri) == AMD_OK) ;
+#endif
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umf_transpose.h b/UMFPACK/Source/umf_transpose.h
new file mode 100644
index 0000000..4c4dee9
--- /dev/null
+++ b/UMFPACK/Source/umf_transpose.h
@@ -0,0 +1,27 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_transpose
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+ const Int P [ ],
+ const Int Q [ ],
+ Int nq,
+ Int Rp [ ],
+ Int Ri [ ],
+ double Rx [ ],
+ Int W [ ],
+ Int check
+#ifdef COMPLEX
+ , const double Az [ ]
+ , double Rz [ ]
+ , Int do_conjugate
+#endif
+) ;
diff --git a/UMFPACK/Source/umf_triplet.c b/UMFPACK/Source/umf_triplet.c
new file mode 100644
index 0000000..aaca50c
--- /dev/null
+++ b/UMFPACK/Source/umf_triplet.c
@@ -0,0 +1,429 @@
+/* ========================================================================== */
+/* === UMF_triplet ========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Not user callable. Converts triplet input to column-oriented form.
+ Duplicate entries may exist (they are summed in the output). The columns
+ of the column-oriented form are in sorted order. The input is not modified.
+ Returns 1 if OK, 0 if an error occurred.
+
+ Compiled into four different routines for each version (di, dl, zi, zl),
+ for a total of 16 different routines.
+*/
+
+#include "umf_internal.h"
+#include "umf_triplet.h"
+
+#ifdef DO_MAP
+#ifdef DO_VALUES
+GLOBAL Int UMF_triplet_map_x
+#else
+GLOBAL Int UMF_triplet_map_nox
+#endif
+#else
+#ifdef DO_VALUES
+GLOBAL Int UMF_triplet_nomap_x
+#else
+GLOBAL Int UMF_triplet_nomap_nox
+#endif
+#endif
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ], /* size nz */
+ const Int Tj [ ], /* size nz */
+ Int Ap [ ], /* size n_col + 1 */
+ Int Ai [ ], /* size nz */
+ Int Rp [ ], /* size n_row + 1 */
+ Int Rj [ ], /* size nz */
+ Int W [ ], /* size max (n_row, n_col) */
+ Int RowCount [ ] /* size n_row */
+#ifdef DO_VALUES
+ , const double Tx [ ] /* size nz */
+ , double Ax [ ] /* size nz */
+ , double Rx [ ] /* size nz */
+#ifdef COMPLEX
+ , const double Tz [ ] /* size nz */
+ , double Az [ ] /* size nz */
+ , double Rz [ ] /* size nz */
+#endif
+#endif
+#ifdef DO_MAP
+ , Int Map [ ] /* size nz */
+ , Int Map2 [ ] /* size nz */
+#endif
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int i, j, k, p, cp, p1, p2, pdest, pj ;
+#ifdef DO_MAP
+ Int duplicates ;
+#endif
+#ifdef DO_VALUES
+#ifdef COMPLEX
+ Int split = SPLIT (Tz) && SPLIT (Az) && SPLIT (Rz) ;
+#endif
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each row (also counting duplicates) */
+ /* ---------------------------------------------------------------------- */
+
+ /* use W as workspace for row counts (including duplicates) */
+ for (i = 0 ; i < n_row ; i++)
+ {
+ W [i] = 0 ;
+ }
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i < 0 || i >= n_row || j < 0 || j >= n_col)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ W [i]++ ;
+#ifndef NDEBUG
+ DEBUG1 ((ID " triplet: "ID" "ID" ", k, i, j)) ;
+#ifdef DO_VALUES
+ {
+ Entry tt ;
+ ASSIGN (tt, Tx, Tz, k, split) ;
+ EDEBUG2 (tt) ;
+ DEBUG1 (("\n")) ;
+ }
+#endif
+#endif
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the row pointers */
+ /* ---------------------------------------------------------------------- */
+
+ Rp [0] = 0 ;
+ for (i = 0 ; i < n_row ; i++)
+ {
+ Rp [i+1] = Rp [i] + W [i] ;
+ W [i] = Rp [i] ;
+ }
+
+ /* W is now equal to the row pointers */
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the row form */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ p = W [Ti [k]]++ ;
+#ifdef DO_MAP
+ Map [k] = p ;
+#endif
+ Rj [p] = Tj [k] ;
+#ifdef DO_VALUES
+#ifdef COMPLEX
+ if (split)
+ {
+ Rx [p] = Tx [k] ;
+ Rz [p] = Tz [k] ;
+ }
+ else
+ {
+ Rx [2*p ] = Tx [2*k ] ;
+ Rx [2*p+1] = Tx [2*k+1] ;
+ }
+#else
+ Rx [p] = Tx [k] ;
+#endif
+#endif
+ }
+
+ /* Rp stays the same, but W [i] is advanced to the start of row i+1 */
+
+#ifndef NDEBUG
+ for (i = 0 ; i < n_row ; i++)
+ {
+ ASSERT (W [i] == Rp [i+1]) ;
+ }
+#ifdef DO_MAP
+ for (k = 0 ; k < nz ; k++)
+ {
+ /* make sure that kth triplet is mapped correctly */
+ p = Map [k] ;
+ DEBUG1 (("First row map: Map ["ID"] = "ID"\n", k, p)) ;
+ i = Ti [k] ;
+ j = Tj [k] ;
+ ASSERT (j == Rj [p]) ;
+ ASSERT (Rp [i] <= p && p < Rp [i+1]) ;
+ }
+#endif
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* sum up duplicates */
+ /* ---------------------------------------------------------------------- */
+
+ /* use W [j] to hold position in Ri/Rx/Rz of a_ij, for row i [ */
+
+ for (j = 0 ; j < n_col ; j++)
+ {
+ W [j] = EMPTY ;
+ }
+
+#ifdef DO_MAP
+ duplicates = FALSE ;
+#endif
+
+ for (i = 0 ; i < n_row ; i++)
+ {
+ p1 = Rp [i] ;
+ p2 = Rp [i+1] ;
+ pdest = p1 ;
+ /* At this point, W [j] < p1 holds true for all columns j, */
+ /* because Ri/Rx/Rz is stored in row oriented order. */
+#ifndef NDEBUG
+ if (UMF_debug >= -2)
+ {
+ for (j = 0 ; j < n_col ; j++)
+ {
+ ASSERT (W [j] < p1) ;
+ }
+ }
+#endif
+ for (p = p1 ; p < p2 ; p++)
+ {
+ j = Rj [p] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ pj = W [j] ;
+ if (pj >= p1)
+ {
+ /* this column index, j, is already in row i, at position pj */
+ ASSERT (pj < p) ;
+ ASSERT (Rj [pj] == j) ;
+#ifdef DO_MAP
+ Map2 [p] = pj ;
+ duplicates = TRUE ;
+#endif
+#ifdef DO_VALUES
+ /* sum the entry */
+#ifdef COMPLEX
+ if (split)
+ {
+ Rx [pj] += Rx [p] ;
+ Rz [pj] += Rz [p] ;
+ }
+ else
+ {
+ Rx[2*pj ] += Rx[2*p ] ;
+ Rx[2*pj+1] += Rx[2*p+1] ;
+ }
+#else
+ Rx [pj] += Rx [p] ;
+#endif
+#endif
+ }
+ else
+ {
+ /* keep the entry */
+ /* also keep track in W[j] of position of a_ij for case above */
+ W [j] = pdest ;
+#ifdef DO_MAP
+ Map2 [p] = pdest ;
+#endif
+ /* no need to move the entry if pdest is equal to p */
+ if (pdest != p)
+ {
+ Rj [pdest] = j ;
+#ifdef DO_VALUES
+#ifdef COMPLEX
+ if (split)
+ {
+ Rx [pdest] = Rx [p] ;
+ Rz [pdest] = Rz [p] ;
+ }
+ else
+ {
+ Rx [2*pdest ] = Rx [2*p ] ;
+ Rx [2*pdest+1] = Rx [2*p+1] ;
+ }
+#else
+ Rx [pdest] = Rx [p] ;
+#endif
+#endif
+ }
+ pdest++ ;
+ }
+ }
+ RowCount [i] = pdest - p1 ;
+ }
+
+ /* done using W for position of a_ij ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* merge Map and Map2 into a single Map */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef DO_MAP
+ if (duplicates)
+ {
+ for (k = 0 ; k < nz ; k++)
+ {
+ Map [k] = Map2 [Map [k]] ;
+ }
+ }
+#ifndef NDEBUG
+ else
+ {
+ /* no duplicates, so no need to recompute Map */
+ for (k = 0 ; k < nz ; k++)
+ {
+ ASSERT (Map2 [k] == k) ;
+ }
+ }
+ for (k = 0 ; k < nz ; k++)
+ {
+ /* make sure that kth triplet is mapped correctly */
+ p = Map [k] ;
+ DEBUG1 (("Second row map: Map ["ID"] = "ID"\n", k, p)) ;
+ i = Ti [k] ;
+ j = Tj [k] ;
+ ASSERT (j == Rj [p]) ;
+ ASSERT (Rp [i] <= p && p < Rp [i+1]) ;
+ }
+#endif
+#endif
+
+ /* now the kth triplet maps to p = Map [k], and thus to Rj/Rx [p] */
+
+ /* ---------------------------------------------------------------------- */
+ /* count the entries in each column */
+ /* ---------------------------------------------------------------------- */
+
+ /* [ use W as work space for column counts of A */
+ for (j = 0 ; j < n_col ; j++)
+ {
+ W [j] = 0 ;
+ }
+
+ for (i = 0 ; i < n_row ; i++)
+ {
+ for (p = Rp [i] ; p < Rp [i] + RowCount [i] ; p++)
+ {
+ j = Rj [p] ;
+ ASSERT (j >= 0 && j < n_col) ;
+ W [j]++ ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* create the column pointers */
+ /* ---------------------------------------------------------------------- */
+
+ Ap [0] = 0 ;
+ for (j = 0 ; j < n_col ; j++)
+ {
+ Ap [j+1] = Ap [j] + W [j] ;
+ }
+ /* done using W as workspace for column counts of A ] */
+
+ for (j = 0 ; j < n_col ; j++)
+ {
+ W [j] = Ap [j] ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the column form */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n_row ; i++)
+ {
+ for (p = Rp [i] ; p < Rp [i] + RowCount [i] ; p++)
+ {
+ cp = W [Rj [p]]++ ;
+#ifdef DO_MAP
+ Map2 [p] = cp ;
+#endif
+ Ai [cp] = i ;
+#ifdef DO_VALUES
+#ifdef COMPLEX
+ if (split)
+ {
+ Ax [cp] = Rx [p] ;
+ Az [cp] = Rz [p] ;
+ }
+ else
+ {
+ Ax [2*cp ] = Rx [2*p ] ;
+ Ax [2*cp+1] = Rx [2*p+1] ;
+ }
+#else
+ Ax [cp] = Rx [p] ;
+#endif
+#endif
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* merge Map and Map2 into a single Map */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef DO_MAP
+ for (k = 0 ; k < nz ; k++)
+ {
+ Map [k] = Map2 [Map [k]] ;
+ }
+#endif
+
+ /* now the kth triplet maps to p = Map [k], and thus to Ai/Ax [p] */
+
+#ifndef NDEBUG
+ for (j = 0 ; j < n_col ; j++)
+ {
+ ASSERT (W [j] == Ap [j+1]) ;
+ }
+
+ UMF_dump_col_matrix (
+#ifdef DO_VALUES
+ Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+#else
+ (double *) NULL,
+#ifdef COMPLEX
+ (double *) NULL,
+#endif
+#endif
+ Ai, Ap, n_row, n_col, nz) ;
+
+#ifdef DO_MAP
+ for (k = 0 ; k < nz ; k++)
+ {
+ /* make sure that kth triplet is mapped correctly */
+ p = Map [k] ;
+ DEBUG1 (("Col map: Map ["ID"] = "ID"\t", k, p)) ;
+ i = Ti [k] ;
+ j = Tj [k] ;
+ ASSERT (i == Ai [p]) ;
+ DEBUG1 ((" i "ID" j "ID" Ap[j] "ID" p "ID" Ap[j+1] "ID"\n",
+ i, j, Ap [j], p, Ap [j+1])) ;
+ ASSERT (Ap [j] <= p && p < Ap [j+1]) ;
+ }
+#endif
+#endif
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umf_triplet.h b/UMFPACK/Source/umf_triplet.h
new file mode 100644
index 0000000..62f9729
--- /dev/null
+++ b/UMFPACK/Source/umf_triplet.h
@@ -0,0 +1,85 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_triplet_map_x
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ],
+ const Int Tj [ ],
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Rp [ ],
+ Int Rj [ ],
+ Int W [ ],
+ Int RowCount [ ]
+ , const double Tx [ ]
+ , double Ax [ ]
+ , double Rx [ ]
+#ifdef COMPLEX
+ , const double Tz [ ]
+ , double Az [ ]
+ , double Rz [ ]
+#endif
+ , Int Map [ ]
+ , Int Map2 [ ]
+) ;
+
+GLOBAL Int UMF_triplet_map_nox
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ],
+ const Int Tj [ ],
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Rp [ ],
+ Int Rj [ ],
+ Int W [ ],
+ Int RowCount [ ]
+ , Int Map [ ]
+ , Int Map2 [ ]
+) ;
+
+GLOBAL Int UMF_triplet_nomap_x
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ],
+ const Int Tj [ ],
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Rp [ ],
+ Int Rj [ ],
+ Int W [ ],
+ Int RowCount [ ]
+ , const double Tx [ ]
+ , double Ax [ ]
+ , double Rx [ ]
+#ifdef COMPLEX
+ , const double Tz [ ]
+ , double Az [ ]
+ , double Rz [ ]
+#endif
+) ;
+
+GLOBAL Int UMF_triplet_nomap_nox
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ],
+ const Int Tj [ ],
+ Int Ap [ ],
+ Int Ai [ ],
+ Int Rp [ ],
+ Int Rj [ ],
+ Int W [ ],
+ Int RowCount [ ]
+) ;
diff --git a/UMFPACK/Source/umf_tuple_lengths.c b/UMFPACK/Source/umf_tuple_lengths.c
new file mode 100644
index 0000000..8dd349e
--- /dev/null
+++ b/UMFPACK/Source/umf_tuple_lengths.c
@@ -0,0 +1,136 @@
+/* ========================================================================== */
+/* === UMF_tuple_lengths ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Determine the tuple list lengths, and the amount of memory required for */
+/* them. Return the amount of memory needed to store all the tuples. */
+/* This routine assumes that the tuple lists themselves are either already */
+/* deallocated, or will be shortly (so Row[ ].tlen and Col[ ].tlen are */
+/* overwritten) */
+
+#include "umf_internal.h"
+#include "umf_tuple_lengths.h"
+
+GLOBAL Int UMF_tuple_lengths /* return memory usage */
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ double *p_dusage /* output argument */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double dusage ;
+ Int e, nrows, ncols, nel, i, *Rows, *Cols, row, col, n_row, n_col, *E,
+ *Row_degree, *Row_tlen, *Col_degree, *Col_tlen, usage, n1 ;
+ Element *ep ;
+ Unit *p ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ E = Work->E ;
+ Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro only */
+ Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro only */
+ Row_tlen = Numeric->Uilen ;
+ Col_tlen = Numeric->Lilen ;
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ n1 = Work->n1 ;
+ nel = Work->nel ;
+
+ DEBUG3 (("TUPLE_LENGTHS: n_row "ID" n_col "ID" nel "ID"\n",
+ n_row, n_col, nel)) ;
+ ASSERT (nel < Work->elen) ;
+
+ /* tuple list lengths already initialized to zero */
+
+ /* ---------------------------------------------------------------------- */
+ /* scan each element: count tuple list lengths (include element 0) */
+ /* ---------------------------------------------------------------------- */
+
+ for (e = 1 ; e <= nel ; e++) /* for all elements, in any order */
+ {
+ if (E [e])
+ {
+#ifndef NDEBUG
+ UMF_dump_element (Numeric, Work, e, FALSE) ;
+#endif
+ p = Numeric->Memory + E [e] ;
+ GET_ELEMENT_PATTERN (ep, p, Cols, Rows, ncols) ;
+ nrows = ep->nrows ;
+ for (i = 0 ; i < nrows ; i++)
+ {
+ row = Rows [i] ;
+ ASSERT (row == EMPTY || (row >= n1 && row < n_row)) ;
+ if (row >= n1)
+ {
+ ASSERT (NON_PIVOTAL_ROW (row)) ;
+ Row_tlen [row] ++ ;
+ }
+ }
+ for (i = 0 ; i < ncols ; i++)
+ {
+ col = Cols [i] ;
+ ASSERT (col == EMPTY || (col >= n1 && col < n_col)) ;
+ if (col >= n1)
+ {
+ ASSERT (NON_PIVOTAL_COL (col)) ;
+ Col_tlen [col] ++ ;
+ }
+ }
+ }
+ }
+
+ /* note: tuple lengths are now modified, but the tuple lists are not */
+ /* updated to reflect that fact. */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the required memory to hold all the tuple lists */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG0 (("UMF_build_tuples_usage\n")) ;
+
+ usage = 0 ;
+ dusage = 0 ;
+
+ ASSERT (Col_tlen && Col_degree) ;
+
+ for (col = n1 ; col < n_col ; col++)
+ {
+ if (NON_PIVOTAL_COL (col))
+ {
+ usage += 1 + UNITS (Tuple, TUPLES (Col_tlen [col])) ;
+ dusage += 1 + DUNITS (Tuple, TUPLES (Col_tlen [col])) ;
+ DEBUG0 ((" col: "ID" tlen "ID" usage so far: "ID"\n",
+ col, Col_tlen [col], usage)) ;
+ }
+ }
+
+ ASSERT (Row_tlen && Row_degree) ;
+
+ for (row = n1 ; row < n_row ; row++)
+ {
+ if (NON_PIVOTAL_ROW (row))
+ {
+ usage += 1 + UNITS (Tuple, TUPLES (Row_tlen [row])) ;
+ dusage += 1 + DUNITS (Tuple, TUPLES (Row_tlen [row])) ;
+ DEBUG0 ((" row: "ID" tlen "ID" usage so far: "ID"\n",
+ row, Row_tlen [row], usage)) ;
+ }
+ }
+
+ DEBUG0 (("UMF_build_tuples_usage "ID" %g\n", usage, dusage)) ;
+
+ *p_dusage = dusage ;
+ return (usage) ;
+}
diff --git a/UMFPACK/Source/umf_tuple_lengths.h b/UMFPACK/Source/umf_tuple_lengths.h
new file mode 100644
index 0000000..a31ccb9
--- /dev/null
+++ b/UMFPACK/Source/umf_tuple_lengths.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_tuple_lengths
+(
+ NumericType *Numeric,
+ WorkType *Work,
+ double *dusage
+) ;
diff --git a/UMFPACK/Source/umf_usolve.c b/UMFPACK/Source/umf_usolve.c
new file mode 100644
index 0000000..f5a127d
--- /dev/null
+++ b/UMFPACK/Source/umf_usolve.c
@@ -0,0 +1,227 @@
+/* ========================================================================== */
+/* === UMF_usolve =========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* solves Ux = b, where U is the upper triangular factor of a matrix. */
+/* B is overwritten with the solution X. */
+/* Returns the floating point operation count */
+
+#include "umf_internal.h"
+#include "umf_usolve.h"
+
+GLOBAL double UMF_usolve
+(
+ NumericType *Numeric,
+ Entry X [ ], /* b on input, solution x on output */
+ Int Pattern [ ] /* a work array of size n */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry xk ;
+ Entry *xp, *D, *Uval ;
+ Int k, deg, j, *ip, col, *Upos, *Uilen, pos,
+ *Uip, n, ulen, up, newUchain, npiv, n1, *Ui ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (Numeric->n_row != Numeric->n_col) return (0.) ;
+ n = Numeric->n_row ;
+ npiv = Numeric->npiv ;
+ Upos = Numeric->Upos ;
+ Uilen = Numeric->Uilen ;
+ Uip = Numeric->Uip ;
+ D = Numeric->D ;
+ n1 = Numeric->n1 ;
+
+#ifndef NDEBUG
+ DEBUG4 (("Usolve start: npiv = "ID" n = "ID"\n", npiv, n)) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ DEBUG4 (("Usolve start "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* singular case */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NO_DIVIDE_BY_ZERO
+ /* handle the singular part of D, up to just before the last pivot */
+ for (k = n-1 ; k >= npiv ; k--)
+ {
+ /* This is an *** intentional *** divide-by-zero, to get Inf or Nan,
+ * as appropriate. It is not a bug. */
+ ASSERT (IS_ZERO (D [k])) ;
+ xk = X [k] ;
+ /* X [k] = xk / D [k] ; */
+ DIV (X [k], xk, D [k]) ;
+ }
+#else
+ /* Do not divide by zero */
+#endif
+
+ deg = Numeric->ulen ;
+ if (deg > 0)
+ {
+ /* :: make last pivot row of U (singular matrices only) :: */
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG1 (("Last row of U: j="ID"\n", j)) ;
+ DEBUG1 (("Last row of U: Upattern[j]="ID"\n",
+ Numeric->Upattern [j]) );
+ Pattern [j] = Numeric->Upattern [j] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* nonsingletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = npiv-1 ; k >= n1 ; k--)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* use row k of U */
+ /* ------------------------------------------------------------------ */
+
+ up = Uip [k] ;
+ ulen = Uilen [k] ;
+ newUchain = (up < 0) ;
+ if (newUchain)
+ {
+ up = -up ;
+ xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
+ }
+ else
+ {
+ xp = (Entry *) (Numeric->Memory + up) ;
+ }
+
+ xk = X [k] ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ;
+ EDEBUG4 (*xp) ;
+ DEBUG4 (("\n")) ;
+ /* xk -= X [Pattern [j]] * (*xp) ; */
+ MULT_SUB (xk, X [Pattern [j]], *xp) ;
+ xp++ ;
+ }
+
+#ifndef NO_DIVIDE_BY_ZERO
+ /* Go ahead and divide by zero if D [k] is zero */
+ /* X [k] = xk / D [k] ; */
+ DIV (X [k], xk, D [k]) ;
+#else
+ /* Do not divide by zero */
+ if (IS_NONZERO (D [k]))
+ {
+ /* X [k] = xk / D [k] ; */
+ DIV (X [k], xk, D [k]) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* make row k-1 of U in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ if (k == n1) break ;
+
+ if (newUchain)
+ {
+ /* next row is a new Uchain */
+ deg = ulen ;
+ ASSERT (IMPLIES (k == 0, deg == 0)) ;
+ DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = *ip++ ;
+ DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
+ ASSERT (k <= col) ;
+ Pattern [j] = col ;
+ }
+ }
+ else
+ {
+ deg -= ulen ;
+ DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k, deg)) ;
+ ASSERT (deg >= 0) ;
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* add the pivot column */
+ DEBUG4 (("k "ID" add pivot entry at pos "ID"\n", k, pos)) ;
+ ASSERT (pos >= 0 && pos <= deg) ;
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* singletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = n1 - 1 ; k >= 0 ; k--)
+ {
+ deg = Uilen [k] ;
+ xk = X [k] ;
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ if (deg > 0)
+ {
+ up = Uip [k] ;
+ Ui = (Int *) (Numeric->Memory + up) ;
+ up += UNITS (Int, deg) ;
+ Uval = (Entry *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" k "ID" col "ID" value", k, Ui [j])) ;
+ EDEBUG4 (Uval [j]) ;
+ DEBUG4 (("\n")) ;
+ /* xk -= X [Ui [j]] * Uval [j] ; */
+ ASSERT (Ui [j] >= 0 && Ui [j] < n) ;
+ MULT_SUB (xk, X [Ui [j]], Uval [j]) ;
+ }
+ }
+
+#ifndef NO_DIVIDE_BY_ZERO
+ /* Go ahead and divide by zero if D [k] is zero */
+ /* X [k] = xk / D [k] ; */
+ DIV (X [k], xk, D [k]) ;
+#else
+ /* Do not divide by zero */
+ if (IS_NONZERO (D [k]))
+ {
+ /* X [k] = xk / D [k] ; */
+ DIV (X [k], xk, D [k]) ;
+ }
+#endif
+
+ }
+
+#ifndef NDEBUG
+ for (j = 0 ; j < n ; j++)
+ {
+ DEBUG4 (("Usolve done "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("Usolve done.\n")) ;
+#endif
+
+ return (DIV_FLOPS * ((double) n) + MULTSUB_FLOPS * ((double) Numeric->unz));
+}
diff --git a/UMFPACK/Source/umf_usolve.h b/UMFPACK/Source/umf_usolve.h
new file mode 100644
index 0000000..3b950d3
--- /dev/null
+++ b/UMFPACK/Source/umf_usolve.h
@@ -0,0 +1,12 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL double UMF_usolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
diff --git a/UMFPACK/Source/umf_utsolve.c b/UMFPACK/Source/umf_utsolve.c
new file mode 100644
index 0000000..3d557b6
--- /dev/null
+++ b/UMFPACK/Source/umf_utsolve.c
@@ -0,0 +1,332 @@
+/* ========================================================================== */
+/* === UMF_utsolve ========================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* solves U'x = b or U.'x=b, where U is the upper triangular factor of a */
+/* matrix. B is overwritten with the solution X. */
+/* Returns the floating point operation count */
+
+#include "umf_internal.h"
+#include "umf_utsolve.h"
+
+GLOBAL double
+#ifdef CONJUGATE_SOLVE
+UMF_uhsolve /* solve U'x=b (complex conjugate transpose) */
+#else
+UMF_utsolve /* solve U.'x=b (array transpose) */
+#endif
+(
+ NumericType *Numeric,
+ Entry X [ ], /* b on input, solution x on output */
+ Int Pattern [ ] /* a work array of size n */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry xk ;
+ Entry *xp, *D, *Uval ;
+ Int k, deg, j, *ip, col, *Upos, *Uilen, kstart, kend, up,
+ *Uip, n, uhead, ulen, pos, npiv, n1, *Ui ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (Numeric->n_row != Numeric->n_col) return (0.) ;
+ n = Numeric->n_row ;
+ npiv = Numeric->npiv ;
+ Upos = Numeric->Upos ;
+ Uilen = Numeric->Uilen ;
+ Uip = Numeric->Uip ;
+ D = Numeric->D ;
+ kend = 0 ;
+ n1 = Numeric->n1 ;
+
+#ifndef NDEBUG
+ DEBUG4 (("Utsolve start: npiv "ID" n "ID"\n", npiv, n)) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ DEBUG4 (("Utsolve start "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* singletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+
+#ifndef NO_DIVIDE_BY_ZERO
+ /* Go ahead and divide by zero if D [k] is zero. */
+#ifdef CONJUGATE_SOLVE
+ /* xk = X [k] / conjugate (D [k]) ; */
+ DIV_CONJ (xk, X [k], D [k]) ;
+#else
+ /* xk = X [k] / D [k] ; */
+ DIV (xk, X [k], D [k]) ;
+#endif
+#else
+ /* Do not divide by zero */
+ if (IS_NONZERO (D [k]))
+ {
+#ifdef CONJUGATE_SOLVE
+ /* xk = X [k] / conjugate (D [k]) ; */
+ DIV_CONJ (xk, X [k], D [k]) ;
+#else
+ /* xk = X [k] / D [k] ; */
+ DIV (xk, X [k], D [k]) ;
+#endif
+ }
+#endif
+
+ X [k] = xk ;
+ deg = Uilen [k] ;
+ if (deg > 0 && IS_NONZERO (xk))
+ {
+ up = Uip [k] ;
+ Ui = (Int *) (Numeric->Memory + up) ;
+ up += UNITS (Int, deg) ;
+ Uval = (Entry *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" k "ID" col "ID" value", k, Ui [j])) ;
+ EDEBUG4 (Uval [j]) ;
+ DEBUG4 (("\n")) ;
+#ifdef CONJUGATE_SOLVE
+ /* X [Ui [j]] -= xk * conjugate (Uval [j]) ; */
+ MULT_SUB_CONJ (X [Ui [j]], xk, Uval [j]) ;
+#else
+ /* X [Ui [j]] -= xk * Uval [j] ; */
+ MULT_SUB (X [Ui [j]], xk, Uval [j]) ;
+#endif
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* nonsingletons */
+ /* ---------------------------------------------------------------------- */
+
+ for (kstart = n1 ; kstart < npiv ; kstart = kend + 1)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* find the end of this Uchain */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG4 (("kstart "ID" kend "ID"\n", kstart, kend)) ;
+ /* for (kend = kstart ; kend < npiv && Uip [kend+1] > 0 ; kend++) ; */
+ kend = kstart ;
+ while (kend < npiv && Uip [kend+1] > 0)
+ {
+ kend++ ;
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* scan the whole Uchain to find the pattern of the first row of U */
+ /* ------------------------------------------------------------------ */
+
+ k = kend+1 ;
+ DEBUG4 (("\nKend "ID" K "ID"\n", kend, k)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* start with last row in Uchain of U in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ if (k == npiv)
+ {
+ deg = Numeric->ulen ;
+ if (deg > 0)
+ {
+ /* :: make last pivot row of U (singular matrices only) :: */
+ for (j = 0 ; j < deg ; j++)
+ {
+ Pattern [j] = Numeric->Upattern [j] ;
+ }
+ }
+ }
+ else
+ {
+ ASSERT (k >= 0 && k < npiv) ;
+ up = -Uip [k] ;
+ ASSERT (up > 0) ;
+ deg = Uilen [k] ;
+ DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = *ip++ ;
+ DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
+ ASSERT (k <= col) ;
+ Pattern [j] = col ;
+ }
+ }
+
+ /* empty the stack at the bottom of Pattern */
+ uhead = n ;
+
+ for (k = kend ; k > kstart ; k--)
+ {
+ /* Pattern [0..deg-1] is the pattern of row k of U */
+
+ /* -------------------------------------------------------------- */
+ /* make row k-1 of U in Pattern [0..deg-1] */
+ /* -------------------------------------------------------------- */
+
+ ASSERT (k >= 0 && k < npiv) ;
+ ulen = Uilen [k] ;
+ /* delete, and push on the stack */
+ for (j = 0 ; j < ulen ; j++)
+ {
+ ASSERT (uhead >= deg) ;
+ Pattern [--uhead] = Pattern [--deg] ;
+ }
+ DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k, deg)) ;
+ ASSERT (deg >= 0) ;
+
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* add the pivot column */
+ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
+ ASSERT (pos >= 0 && pos <= deg) ;
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ }
+
+ /* Pattern [0..deg-1] is now the pattern of the first row in Uchain */
+
+ /* ------------------------------------------------------------------ */
+ /* solve using this Uchain, in reverse order */
+ /* ------------------------------------------------------------------ */
+
+ DEBUG4 (("Unwinding Uchain\n")) ;
+ for (k = kstart ; k <= kend ; k++)
+ {
+
+ /* -------------------------------------------------------------- */
+ /* construct row k */
+ /* -------------------------------------------------------------- */
+
+ ASSERT (k >= 0 && k < npiv) ;
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* remove the pivot column */
+ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
+ ASSERT (k > kstart) ;
+ ASSERT (pos >= 0 && pos < deg) ;
+ ASSERT (Pattern [pos] == k) ;
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ up = Uip [k] ;
+ ulen = Uilen [k] ;
+ if (k > kstart)
+ {
+ /* concatenate the deleted pattern; pop from the stack */
+ for (j = 0 ; j < ulen ; j++)
+ {
+ ASSERT (deg <= uhead && uhead < n) ;
+ Pattern [deg++] = Pattern [uhead++] ;
+ }
+ DEBUG4 (("middle of chain, row of U "ID" deg "ID"\n", k, deg)) ;
+ ASSERT (deg >= 0) ;
+ }
+
+ /* -------------------------------------------------------------- */
+ /* use row k of U */
+ /* -------------------------------------------------------------- */
+
+#ifndef NO_DIVIDE_BY_ZERO
+ /* Go ahead and divide by zero if D [k] is zero. */
+#ifdef CONJUGATE_SOLVE
+ /* xk = X [k] / conjugate (D [k]) ; */
+ DIV_CONJ (xk, X [k], D [k]) ;
+#else
+ /* xk = X [k] / D [k] ; */
+ DIV (xk, X [k], D [k]) ;
+#endif
+#else
+ /* Do not divide by zero */
+ if (IS_NONZERO (D [k]))
+ {
+#ifdef CONJUGATE_SOLVE
+ /* xk = X [k] / conjugate (D [k]) ; */
+ DIV_CONJ (xk, X [k], D [k]) ;
+#else
+ /* xk = X [k] / D [k] ; */
+ DIV (xk, X [k], D [k]) ;
+#endif
+ }
+#endif
+
+ X [k] = xk ;
+ if (IS_NONZERO (xk))
+ {
+ if (k == kstart)
+ {
+ up = -up ;
+ xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
+ }
+ else
+ {
+ xp = (Entry *) (Numeric->Memory + up) ;
+ }
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ;
+ EDEBUG4 (*xp) ;
+ DEBUG4 (("\n")) ;
+#ifdef CONJUGATE_SOLVE
+ /* X [Pattern [j]] -= xk * conjugate (*xp) ; */
+ MULT_SUB_CONJ (X [Pattern [j]], xk, *xp) ;
+#else
+ /* X [Pattern [j]] -= xk * (*xp) ; */
+ MULT_SUB (X [Pattern [j]], xk, *xp) ;
+#endif
+ xp++ ;
+ }
+ }
+ }
+ ASSERT (uhead == n) ;
+ }
+
+#ifndef NO_DIVIDE_BY_ZERO
+ for (k = npiv ; k < n ; k++)
+ {
+ /* This is an *** intentional *** divide-by-zero, to get Inf or Nan,
+ * as appropriate. It is not a bug. */
+ ASSERT (IS_ZERO (D [k])) ;
+ /* For conjugate solve, D [k] == conjugate (D [k]), in this case */
+ /* xk = X [k] / D [k] ; */
+ DIV (xk, X [k], D [k]) ;
+ X [k] = xk ;
+ }
+#endif
+
+#ifndef NDEBUG
+ for (j = 0 ; j < n ; j++)
+ {
+ DEBUG4 (("Utsolve done "ID": ", j)) ;
+ EDEBUG4 (X [j]) ;
+ DEBUG4 (("\n")) ;
+ }
+ DEBUG4 (("Utsolve done.\n")) ;
+#endif
+
+ return (DIV_FLOPS * ((double) n) + MULTSUB_FLOPS * ((double) Numeric->unz));
+}
diff --git a/UMFPACK/Source/umf_utsolve.h b/UMFPACK/Source/umf_utsolve.h
new file mode 100644
index 0000000..dae3143
--- /dev/null
+++ b/UMFPACK/Source/umf_utsolve.h
@@ -0,0 +1,20 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL double UMF_utsolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
+
+
+GLOBAL double UMF_uhsolve
+(
+ NumericType *Numeric,
+ Entry X [ ],
+ Int Pattern [ ]
+) ;
diff --git a/UMFPACK/Source/umf_valid_numeric.c b/UMFPACK/Source/umf_valid_numeric.c
new file mode 100644
index 0000000..76855e3
--- /dev/null
+++ b/UMFPACK/Source/umf_valid_numeric.c
@@ -0,0 +1,47 @@
+/* ========================================================================== */
+/* === UMF_valid_numeric ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* Returns TRUE if the Numeric object is valid, FALSE otherwise. */
+/* Does not check everything. UMFPACK_report_numeric checks more. */
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+
+GLOBAL Int UMF_valid_numeric
+(
+ NumericType *Numeric
+)
+{
+ /* This routine does not check the contents of the individual arrays, so */
+ /* it can miss some errors. All it checks for is the presence of the */
+ /* arrays, and the Numeric "valid" entry. */
+
+ if (!Numeric)
+ {
+ return (FALSE) ;
+ }
+
+ if (Numeric->valid != NUMERIC_VALID)
+ {
+ /* Numeric does not point to a NumericType object */
+ return (FALSE) ;
+ }
+
+ if (Numeric->n_row <= 0 || Numeric->n_col <= 0 || !Numeric->D ||
+ !Numeric->Rperm || !Numeric->Cperm ||
+ !Numeric->Lpos || !Numeric->Upos ||
+ !Numeric->Lilen || !Numeric->Uilen || !Numeric->Lip || !Numeric->Uip ||
+ !Numeric->Memory || (Numeric->ulen > 0 && !Numeric->Upattern))
+ {
+ return (FALSE) ;
+ }
+
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umf_valid_numeric.h b/UMFPACK/Source/umf_valid_numeric.h
new file mode 100644
index 0000000..0b258e4
--- /dev/null
+++ b/UMFPACK/Source/umf_valid_numeric.h
@@ -0,0 +1,10 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_valid_numeric
+(
+ NumericType *Numeric
+) ;
diff --git a/UMFPACK/Source/umf_valid_symbolic.c b/UMFPACK/Source/umf_valid_symbolic.c
new file mode 100644
index 0000000..dd81851
--- /dev/null
+++ b/UMFPACK/Source/umf_valid_symbolic.c
@@ -0,0 +1,48 @@
+/* ========================================================================== */
+/* === UMF_valid_symbolic =================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+
+/* Returns TRUE if the Symbolic object is valid, FALSE otherwise. */
+/* The UMFPACK_report_symbolic routine does a more thorough check. */
+
+GLOBAL Int UMF_valid_symbolic
+(
+ SymbolicType *Symbolic
+)
+{
+ /* This routine does not check the contents of the individual arrays, so */
+ /* it can miss some errors. All it checks for is the presence of the */
+ /* arrays, and the Symbolic "valid" entry. */
+
+ if (!Symbolic)
+ {
+ return (FALSE) ;
+ }
+
+ if (Symbolic->valid != SYMBOLIC_VALID)
+ {
+ /* Symbolic does not point to a SymbolicType object */
+ return (FALSE) ;
+ }
+
+ if (!Symbolic->Cperm_init || !Symbolic->Rperm_init ||
+ !Symbolic->Front_npivcol || !Symbolic->Front_1strow ||
+ !Symbolic->Front_leftmostdesc ||
+ !Symbolic->Front_parent || !Symbolic->Chain_start ||
+ !Symbolic->Chain_maxrows || !Symbolic->Chain_maxcols ||
+ Symbolic->n_row <= 0 || Symbolic->n_col <= 0)
+ {
+ return (FALSE) ;
+ }
+
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umf_valid_symbolic.h b/UMFPACK/Source/umf_valid_symbolic.h
new file mode 100644
index 0000000..741a799
--- /dev/null
+++ b/UMFPACK/Source/umf_valid_symbolic.h
@@ -0,0 +1,10 @@
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+GLOBAL Int UMF_valid_symbolic
+(
+ SymbolicType *Symbolic
+) ;
diff --git a/UMFPACK/Source/umf_version.h b/UMFPACK/Source/umf_version.h
new file mode 100644
index 0000000..98d765f
--- /dev/null
+++ b/UMFPACK/Source/umf_version.h
@@ -0,0 +1,874 @@
+/* ========================================================================== */
+/* === umf_version.h ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Define routine names, depending on version being compiled.
+
+ DINT: double precision, int's as integers
+ DLONG: double precision, UF_long's as integers
+ ZLONG: complex double precision, UF_long's as integers
+ ZINT: complex double precision, int's as integers
+*/
+
+/* Set DINT as the default, if nothing is defined */
+#if !defined (DLONG) && !defined (DINT) && !defined (ZLONG) && !defined (ZINT)
+#define DINT
+#endif
+
+/* Determine if this is a real or complex version */
+#if defined (ZLONG) || defined (ZINT)
+#define COMPLEX
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* integer type (Int is int or UF_long) now defined in amd_internal.h */
+/* -------------------------------------------------------------------------- */
+
+#if defined (DLONG) || defined (ZLONG)
+#define LONG_INTEGER
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Numerical relop macros for correctly handling the NaN case */
+/* -------------------------------------------------------------------------- */
+
+/*
+SCALAR_IS_NAN(x):
+ True if x is NaN. False otherwise. The commonly-existing isnan(x)
+ function could be used, but it's not in Kernighan & Ritchie 2nd edition
+ (ANSI C). It may appear in <math.h>, but I'm not certain about
+ portability. The expression x != x is true if and only if x is NaN,
+ according to the IEEE 754 floating-point standard.
+
+SCALAR_IS_ZERO(x):
+ True if x is zero. False if x is nonzero, NaN, or +/- Inf.
+ This is (x == 0) if the compiler is IEEE 754 compliant.
+
+SCALAR_IS_NONZERO(x):
+ True if x is nonzero, NaN, or +/- Inf. False if x zero.
+ This is (x != 0) if the compiler is IEEE 754 compliant.
+
+SCALAR_IS_LTZERO(x):
+ True if x is < zero or -Inf. False if x is >= 0, NaN, or +Inf.
+ This is (x < 0) if the compiler is IEEE 754 compliant.
+*/
+
+#if defined (UMF_WINDOWS) && !defined (MATHWORKS)
+
+/* Yes, this is exceedingly ugly. Blame Microsoft, which hopelessly */
+/* violates the IEEE 754 floating-point standard in a bizarre way. */
+/* If you're using an IEEE 754-compliant compiler, then x != x is true */
+/* iff x is NaN. For Microsoft, (x < x) is true iff x is NaN. */
+/* So either way, this macro safely detects a NaN. */
+#define SCALAR_IS_NAN(x) (((x) != (x)) || (((x) < (x))))
+#define SCALAR_IS_ZERO(x) (((x) == 0.) && !SCALAR_IS_NAN(x))
+#define SCALAR_IS_NONZERO(x) (((x) != 0.) || SCALAR_IS_NAN(x))
+#define SCALAR_IS_LTZERO(x) (((x) < 0.) && !SCALAR_IS_NAN(x))
+
+#else
+
+/* These all work properly, according to the IEEE 754 standard ... except on */
+/* a PC with windows. Works fine in Linux on the same PC... */
+#define SCALAR_IS_NAN(x) ((x) != (x))
+#define SCALAR_IS_ZERO(x) ((x) == 0.)
+#define SCALAR_IS_NONZERO(x) ((x) != 0.)
+#define SCALAR_IS_LTZERO(x) ((x) < 0.)
+
+#endif
+
+/* scalar absolute value macro. If x is NaN, the result is NaN: */
+#define SCALAR_ABS(x) ((SCALAR_IS_LTZERO (x)) ? -(x) : (x))
+
+/* true if an integer (stored in double x) would overflow (or if x is NaN) */
+#define INT_OVERFLOW(x) ((!((x) * (1.0+1e-8) <= (double) Int_MAX)) \
+ || SCALAR_IS_NAN (x))
+
+/* print a scalar (avoid printing "-0" for negative zero). */
+#define PRINT_SCALAR(a) \
+{ \
+ if (SCALAR_IS_NONZERO (a)) \
+ { \
+ PRINTF ((" (%g)", (a))) ; \
+ } \
+ else \
+ { \
+ PRINTF ((" (0)")) ; \
+ } \
+}
+
+/* -------------------------------------------------------------------------- */
+/* Real floating-point arithmetic */
+/* -------------------------------------------------------------------------- */
+
+#ifndef COMPLEX
+
+#define Entry double
+
+#define SPLIT(s) (1)
+#define REAL_COMPONENT(c) (c)
+#define IMAG_COMPONENT(c) (0.)
+#define ASSIGN(c,s1,s2,p,split) { (c) = (s1)[p] ; }
+#define CLEAR(c) { (c) = 0. ; }
+#define CLEAR_AND_INCREMENT(p) { *p++ = 0. ; }
+#define IS_NAN(a) SCALAR_IS_NAN (a)
+#define IS_ZERO(a) SCALAR_IS_ZERO (a)
+#define IS_NONZERO(a) SCALAR_IS_NONZERO (a)
+#define SCALE_DIV(c,s) { (c) /= (s) ; }
+#define SCALE(c,s) { (c) *= (s) ; }
+#define ASSEMBLE(c,a) { (c) += (a) ; }
+#define ASSEMBLE_AND_INCREMENT(c,p) { (c) += *p++ ; }
+#define DECREMENT(c,a) { (c) -= (a) ; }
+#define MULT(c,a,b) { (c) = (a) * (b) ; }
+#define MULT_CONJ(c,a,b) { (c) = (a) * (b) ; }
+#define MULT_SUB(c,a,b) { (c) -= (a) * (b) ; }
+#define MULT_SUB_CONJ(c,a,b) { (c) -= (a) * (b) ; }
+#define DIV(c,a,b) { (c) = (a) / (b) ; }
+#define DIV_CONJ(c,a,b) { (c) = (a) / (b) ; }
+#define APPROX_ABS(s,a) { (s) = SCALAR_ABS (a) ; }
+#define ABS(s,a) { (s) = SCALAR_ABS (a) ; }
+#define PRINT_ENTRY(a) PRINT_SCALAR (a)
+
+/* for flop counts */
+#define MULTSUB_FLOPS 2. /* c -= a*b */
+#define DIV_FLOPS 1. /* c = a/b */
+#define ABS_FLOPS 0. /* c = abs (a) */
+#define ASSEMBLE_FLOPS 1. /* c += a */
+#define DECREMENT_FLOPS 1. /* c -= a */
+#define MULT_FLOPS 1. /* c = a*b */
+#define SCALE_FLOPS 1. /* c = a/s */
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* Complex floating-point arithmetic */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Note: An alternative to this DoubleComplex type would be to use a
+ struct { double r ; double i ; }. The problem with that method
+ (used by the Sun Performance Library, for example) is that ANSI C provides
+ no guarantee about the layout of a struct. It is possible that the sizeof
+ the struct above would be greater than 2 * sizeof (double). This would
+ mean that the complex BLAS could not be used. The method used here avoids
+ that possibility. ANSI C *does* guarantee that an array of structs has
+ the same size as n times the size of one struct.
+
+ The ANSI C99 version of the C language includes a "double _Complex" type.
+ It should be possible in that case to do the following:
+
+ #define Entry double _Complex
+
+ and remove the DoubleComplex struct. The macros, below, could then be
+ replaced with instrinsic operators. Note that the #define Real and
+ #define Imag should also be removed (they only appear in this file).
+
+ For the MULT, MULT_SUB, MULT_SUB_CONJ, and MULT_CONJ macros,
+ the output argument c cannot be the same as any input argument.
+
+*/
+
+typedef struct
+{
+ double component [2] ; /* real and imaginary parts */
+
+} DoubleComplex ;
+
+#define Entry DoubleComplex
+#define Real component [0]
+#define Imag component [1]
+
+/* for flop counts */
+#define MULTSUB_FLOPS 8. /* c -= a*b */
+#define DIV_FLOPS 9. /* c = a/b */
+#define ABS_FLOPS 6. /* c = abs (a), count sqrt as one flop */
+#define ASSEMBLE_FLOPS 2. /* c += a */
+#define DECREMENT_FLOPS 2. /* c -= a */
+#define MULT_FLOPS 6. /* c = a*b */
+#define SCALE_FLOPS 2. /* c = a/s or c = a*s */
+
+/* -------------------------------------------------------------------------- */
+
+/* real part of c */
+#define REAL_COMPONENT(c) ((c).Real)
+
+/* -------------------------------------------------------------------------- */
+
+/* imag part of c */
+#define IMAG_COMPONENT(c) ((c).Imag)
+
+/* -------------------------------------------------------------------------- */
+
+/* Return TRUE if a complex number is in split form, FALSE if in packed form */
+#define SPLIT(sz) ((sz) != (double *) NULL)
+
+/* -------------------------------------------------------------------------- */
+
+/* c = (s1) + (s2)*i, if s2 is null, then X is in "packed" format (compatible
+ * with Entry and ANSI C99 double _Complex type). */
+#define ASSIGN(c,s1,s2,p,split) \
+{ \
+ if (split) \
+ { \
+ (c).Real = (s1)[p] ; \
+ (c).Imag = (s2)[p] ; \
+ } \
+ else \
+ { \
+ (c) = ((Entry *)(s1))[p] ; \
+ } \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = 0 */
+#define CLEAR(c) \
+{ \
+ (c).Real = 0. ; \
+ (c).Imag = 0. ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* *p++ = 0 */
+#define CLEAR_AND_INCREMENT(p) \
+{ \
+ p->Real = 0. ; \
+ p->Imag = 0. ; \
+ p++ ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* True if a == 0 */
+#define IS_ZERO(a) \
+ (SCALAR_IS_ZERO ((a).Real) && SCALAR_IS_ZERO ((a).Imag))
+
+/* -------------------------------------------------------------------------- */
+
+/* True if a is NaN */
+#define IS_NAN(a) \
+ (SCALAR_IS_NAN ((a).Real) || SCALAR_IS_NAN ((a).Imag))
+
+/* -------------------------------------------------------------------------- */
+
+/* True if a != 0 */
+#define IS_NONZERO(a) \
+ (SCALAR_IS_NONZERO ((a).Real) || SCALAR_IS_NONZERO ((a).Imag))
+
+/* -------------------------------------------------------------------------- */
+
+/* c /= s */
+#define SCALE_DIV(c,s) \
+{ \
+ (c).Real /= (s) ; \
+ (c).Imag /= (s) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c *= s */
+#define SCALE(c,s) \
+{ \
+ (c).Real *= (s) ; \
+ (c).Imag *= (s) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c += a */
+#define ASSEMBLE(c,a) \
+{ \
+ (c).Real += (a).Real ; \
+ (c).Imag += (a).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c += *p++ */
+#define ASSEMBLE_AND_INCREMENT(c,p) \
+{ \
+ (c).Real += p->Real ; \
+ (c).Imag += p->Imag ; \
+ p++ ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c -= a */
+#define DECREMENT(c,a) \
+{ \
+ (c).Real -= (a).Real ; \
+ (c).Imag -= (a).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a*b, assert because c cannot be the same as a or b */
+#define MULT(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real = (a).Real * (b).Real - (a).Imag * (b).Imag ; \
+ (c).Imag = (a).Imag * (b).Real + (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a*conjugate(b), assert because c cannot be the same as a or b */
+#define MULT_CONJ(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real = (a).Real * (b).Real + (a).Imag * (b).Imag ; \
+ (c).Imag = (a).Imag * (b).Real - (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c -= a*b, assert because c cannot be the same as a or b */
+#define MULT_SUB(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real -= (a).Real * (b).Real - (a).Imag * (b).Imag ; \
+ (c).Imag -= (a).Imag * (b).Real + (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c -= a*conjugate(b), assert because c cannot be the same as a or b */
+#define MULT_SUB_CONJ(c,a,b) \
+{ \
+ ASSERT (&(c) != &(a) && &(c) != &(b)) ; \
+ (c).Real -= (a).Real * (b).Real + (a).Imag * (b).Imag ; \
+ (c).Imag -= (a).Imag * (b).Real - (a).Real * (b).Imag ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a/b, using function pointer */
+#define DIV(c,a,b) \
+{ \
+ (void) umfpack_divcomplex ((a).Real, (a).Imag, (b).Real, (b).Imag, \
+ &((c).Real), &((c).Imag)) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* c = a/conjugate(b), using function pointer */
+#define DIV_CONJ(c,a,b) \
+{ \
+ (void) umfpack_divcomplex ((a).Real, (a).Imag, (b).Real, (-(b).Imag), \
+ &((c).Real), &((c).Imag)) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* approximate absolute value, s = |r|+|i| */
+#define APPROX_ABS(s,a) \
+{ \
+ (s) = SCALAR_ABS ((a).Real) + SCALAR_ABS ((a).Imag) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* exact absolute value, s = sqrt (a.real^2 + a.imag^2) */
+#define ABS(s,a) \
+{ \
+ (s) = umfpack_hypot ((a).Real, (a).Imag) ; \
+}
+
+/* -------------------------------------------------------------------------- */
+
+/* print an entry (avoid printing "-0" for negative zero). */
+#define PRINT_ENTRY(a) \
+{ \
+ if (SCALAR_IS_NONZERO ((a).Real)) \
+ { \
+ PRINTF ((" (%g", (a).Real)) ; \
+ } \
+ else \
+ { \
+ PRINTF ((" (0")) ; \
+ } \
+ if (SCALAR_IS_LTZERO ((a).Imag)) \
+ { \
+ PRINTF ((" - %gi)", -(a).Imag)) ; \
+ } \
+ else if (SCALAR_IS_ZERO ((a).Imag)) \
+ { \
+ PRINTF ((" + 0i)")) ; \
+ } \
+ else \
+ { \
+ PRINTF ((" + %gi)", (a).Imag)) ; \
+ } \
+}
+
+/* -------------------------------------------------------------------------- */
+
+#endif /* #ifndef COMPLEX */
+
+/* -------------------------------------------------------------------------- */
+/* Double precision, with int's as integers */
+/* -------------------------------------------------------------------------- */
+
+#ifdef DINT
+
+#define UMF_analyze umf_i_analyze
+#define UMF_apply_order umf_i_apply_order
+#define UMF_assemble umfdi_assemble
+#define UMF_assemble_fixq umfdi_assemble_fixq
+#define UMF_blas3_update umfdi_blas3_update
+#define UMF_build_tuples umfdi_build_tuples
+#define UMF_build_tuples_usage umfdi_build_tuples_usage
+#define UMF_colamd umf_i_colamd
+#define UMF_colamd_set_defaults umf_i_colamd_set_defaults
+#define UMF_create_element umfdi_create_element
+#define UMF_extend_front umfdi_extend_front
+#define UMF_free umf_i_free
+#define UMF_fsize umf_i_fsize
+#define UMF_garbage_collection umfdi_garbage_collection
+#define UMF_get_memory umfdi_get_memory
+#define UMF_grow_front umfdi_grow_front
+#define UMF_init_front umfdi_init_front
+#define UMF_is_permutation umf_i_is_permutation
+#define UMF_kernel umfdi_kernel
+#define UMF_kernel_init umfdi_kernel_init
+#define UMF_kernel_init_usage umfdi_kernel_init_usage
+#define UMF_kernel_wrapup umfdi_kernel_wrapup
+#define UMF_local_search umfdi_local_search
+#define UMF_lsolve umfdi_lsolve
+#define UMF_ltsolve umfdi_ltsolve
+#define UMF_lhsolve umfdi_lhsolve
+#define UMF_malloc umf_i_malloc
+#define UMF_mem_alloc_element umfdi_mem_alloc_element
+#define UMF_mem_alloc_head_block umfdi_mem_alloc_head_block
+#define UMF_mem_alloc_tail_block umfdi_mem_alloc_tail_block
+#define UMF_mem_free_tail_block umfdi_mem_free_tail_block
+#define UMF_mem_init_memoryspace umfdi_mem_init_memoryspace
+#define UMF_realloc umf_i_realloc
+#define UMF_report_perm umf_i_report_perm
+#define UMF_report_vector umfdi_report_vector
+#define UMF_row_search umfdi_row_search
+#define UMF_scale umfdi_scale
+#define UMF_scale_column umfdi_scale_column
+#define UMF_set_stats umf_i_set_stats
+#define UMF_singletons umf_i_singletons
+#define UMF_solve umfdi_solve
+#define UMF_start_front umfdi_start_front
+#define UMF_store_lu umfdi_store_lu
+#define UMF_store_lu_drop umfdi_store_lu_drop
+#define UMF_symbolic_usage umfdi_symbolic_usage
+#define UMF_transpose umfdi_transpose
+#define UMF_tuple_lengths umfdi_tuple_lengths
+#define UMF_usolve umfdi_usolve
+#define UMF_utsolve umfdi_utsolve
+#define UMF_uhsolve umfdi_uhsolve
+#define UMF_valid_numeric umfdi_valid_numeric
+#define UMF_valid_symbolic umfdi_valid_symbolic
+#define UMF_triplet_map_x umfdi_triplet_map_x
+#define UMF_triplet_map_nox umfdi_triplet_map_nox
+#define UMF_triplet_nomap_x umfdi_triplet_nomap_x
+#define UMF_triplet_nomap_nox umfdi_triplet_nomap_nox
+#define UMF_2by2 umfdi_2by2
+
+#define UMFPACK_col_to_triplet umfpack_di_col_to_triplet
+#define UMFPACK_defaults umfpack_di_defaults
+#define UMFPACK_free_numeric umfpack_di_free_numeric
+#define UMFPACK_free_symbolic umfpack_di_free_symbolic
+#define UMFPACK_get_lunz umfpack_di_get_lunz
+#define UMFPACK_get_numeric umfpack_di_get_numeric
+#define UMFPACK_get_symbolic umfpack_di_get_symbolic
+#define UMFPACK_get_determinant umfpack_di_get_determinant
+#define UMFPACK_numeric umfpack_di_numeric
+#define UMFPACK_qsymbolic umfpack_di_qsymbolic
+#define UMFPACK_report_control umfpack_di_report_control
+#define UMFPACK_report_info umfpack_di_report_info
+#define UMFPACK_report_matrix umfpack_di_report_matrix
+#define UMFPACK_report_numeric umfpack_di_report_numeric
+#define UMFPACK_report_perm umfpack_di_report_perm
+#define UMFPACK_report_status umfpack_di_report_status
+#define UMFPACK_report_symbolic umfpack_di_report_symbolic
+#define UMFPACK_report_triplet umfpack_di_report_triplet
+#define UMFPACK_report_vector umfpack_di_report_vector
+#define UMFPACK_save_numeric umfpack_di_save_numeric
+#define UMFPACK_save_symbolic umfpack_di_save_symbolic
+#define UMFPACK_load_numeric umfpack_di_load_numeric
+#define UMFPACK_load_symbolic umfpack_di_load_symbolic
+#define UMFPACK_scale umfpack_di_scale
+#define UMFPACK_solve umfpack_di_solve
+#define UMFPACK_symbolic umfpack_di_symbolic
+#define UMFPACK_transpose umfpack_di_transpose
+#define UMFPACK_triplet_to_col umfpack_di_triplet_to_col
+#define UMFPACK_wsolve umfpack_di_wsolve
+
+/* for debugging only: */
+#define UMF_malloc_count umf_i_malloc_count
+#define UMF_debug umfdi_debug
+#define UMF_allocfail umfdi_allocfail
+#define UMF_gprob umfdi_gprob
+#define UMF_dump_dense umfdi_dump_dense
+#define UMF_dump_element umfdi_dump_element
+#define UMF_dump_rowcol umfdi_dump_rowcol
+#define UMF_dump_matrix umfdi_dump_matrix
+#define UMF_dump_current_front umfdi_dump_current_front
+#define UMF_dump_lu umfdi_dump_lu
+#define UMF_dump_memory umfdi_dump_memory
+#define UMF_dump_packed_memory umfdi_dump_packed_memory
+#define UMF_dump_col_matrix umfdi_dump_col_matrix
+#define UMF_dump_chain umfdi_dump_chain
+#define UMF_dump_start umfdi_dump_start
+#define UMF_dump_rowmerge umfdi_dump_rowmerge
+#define UMF_dump_diagonal_map umfdi_dump_diagonal_map
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Double precision, with UF_long's as integers */
+/* -------------------------------------------------------------------------- */
+
+#ifdef DLONG
+
+#define UMF_analyze umf_l_analyze
+#define UMF_apply_order umf_l_apply_order
+#define UMF_assemble umfdl_assemble
+#define UMF_assemble_fixq umfdl_assemble_fixq
+#define UMF_blas3_update umfdl_blas3_update
+#define UMF_build_tuples umfdl_build_tuples
+#define UMF_build_tuples_usage umfdl_build_tuples_usage
+#define UMF_colamd umf_l_colamd
+#define UMF_colamd_set_defaults umf_l_colamd_set_defaults
+#define UMF_create_element umfdl_create_element
+#define UMF_extend_front umfdl_extend_front
+#define UMF_free umf_l_free
+#define UMF_fsize umf_l_fsize
+#define UMF_garbage_collection umfdl_garbage_collection
+#define UMF_get_memory umfdl_get_memory
+#define UMF_grow_front umfdl_grow_front
+#define UMF_init_front umfdl_init_front
+#define UMF_is_permutation umf_l_is_permutation
+#define UMF_kernel umfdl_kernel
+#define UMF_kernel_init umfdl_kernel_init
+#define UMF_kernel_init_usage umfdl_kernel_init_usage
+#define UMF_kernel_wrapup umfdl_kernel_wrapup
+#define UMF_local_search umfdl_local_search
+#define UMF_lsolve umfdl_lsolve
+#define UMF_ltsolve umfdl_ltsolve
+#define UMF_lhsolve umfdl_lhsolve
+#define UMF_malloc umf_l_malloc
+#define UMF_mem_alloc_element umfdl_mem_alloc_element
+#define UMF_mem_alloc_head_block umfdl_mem_alloc_head_block
+#define UMF_mem_alloc_tail_block umfdl_mem_alloc_tail_block
+#define UMF_mem_free_tail_block umfdl_mem_free_tail_block
+#define UMF_mem_init_memoryspace umfdl_mem_init_memoryspace
+#define UMF_realloc umf_l_realloc
+#define UMF_report_perm umf_l_report_perm
+#define UMF_report_vector umfdl_report_vector
+#define UMF_row_search umfdl_row_search
+#define UMF_scale umfdl_scale
+#define UMF_scale_column umfdl_scale_column
+#define UMF_set_stats umf_l_set_stats
+#define UMF_singletons umf_l_singletons
+#define UMF_solve umfdl_solve
+#define UMF_start_front umfdl_start_front
+#define UMF_store_lu umfdl_store_lu
+#define UMF_store_lu_drop umfdl_store_lu_drop
+#define UMF_symbolic_usage umfdl_symbolic_usage
+#define UMF_transpose umfdl_transpose
+#define UMF_tuple_lengths umfdl_tuple_lengths
+#define UMF_usolve umfdl_usolve
+#define UMF_utsolve umfdl_utsolve
+#define UMF_uhsolve umfdl_uhsolve
+#define UMF_valid_numeric umfdl_valid_numeric
+#define UMF_valid_symbolic umfdl_valid_symbolic
+#define UMF_triplet_map_x umfdl_triplet_map_x
+#define UMF_triplet_map_nox umfdl_triplet_map_nox
+#define UMF_triplet_nomap_x umfdl_triplet_nomap_x
+#define UMF_triplet_nomap_nox umfdl_triplet_nomap_nox
+#define UMF_2by2 umfdl_2by2
+
+#define UMFPACK_col_to_triplet umfpack_dl_col_to_triplet
+#define UMFPACK_defaults umfpack_dl_defaults
+#define UMFPACK_free_numeric umfpack_dl_free_numeric
+#define UMFPACK_free_symbolic umfpack_dl_free_symbolic
+#define UMFPACK_get_lunz umfpack_dl_get_lunz
+#define UMFPACK_get_numeric umfpack_dl_get_numeric
+#define UMFPACK_get_symbolic umfpack_dl_get_symbolic
+#define UMFPACK_get_determinant umfpack_dl_get_determinant
+#define UMFPACK_numeric umfpack_dl_numeric
+#define UMFPACK_qsymbolic umfpack_dl_qsymbolic
+#define UMFPACK_report_control umfpack_dl_report_control
+#define UMFPACK_report_info umfpack_dl_report_info
+#define UMFPACK_report_matrix umfpack_dl_report_matrix
+#define UMFPACK_report_numeric umfpack_dl_report_numeric
+#define UMFPACK_report_perm umfpack_dl_report_perm
+#define UMFPACK_report_status umfpack_dl_report_status
+#define UMFPACK_report_symbolic umfpack_dl_report_symbolic
+#define UMFPACK_report_triplet umfpack_dl_report_triplet
+#define UMFPACK_report_vector umfpack_dl_report_vector
+#define UMFPACK_save_numeric umfpack_dl_save_numeric
+#define UMFPACK_save_symbolic umfpack_dl_save_symbolic
+#define UMFPACK_load_numeric umfpack_dl_load_numeric
+#define UMFPACK_load_symbolic umfpack_dl_load_symbolic
+#define UMFPACK_scale umfpack_dl_scale
+#define UMFPACK_solve umfpack_dl_solve
+#define UMFPACK_symbolic umfpack_dl_symbolic
+#define UMFPACK_transpose umfpack_dl_transpose
+#define UMFPACK_triplet_to_col umfpack_dl_triplet_to_col
+#define UMFPACK_wsolve umfpack_dl_wsolve
+
+/* for debugging only: */
+#define UMF_malloc_count umf_l_malloc_count
+#define UMF_debug umfdl_debug
+#define UMF_allocfail umfdl_allocfail
+#define UMF_gprob umfdl_gprob
+#define UMF_dump_dense umfdl_dump_dense
+#define UMF_dump_element umfdl_dump_element
+#define UMF_dump_rowcol umfdl_dump_rowcol
+#define UMF_dump_matrix umfdl_dump_matrix
+#define UMF_dump_current_front umfdl_dump_current_front
+#define UMF_dump_lu umfdl_dump_lu
+#define UMF_dump_memory umfdl_dump_memory
+#define UMF_dump_packed_memory umfdl_dump_packed_memory
+#define UMF_dump_col_matrix umfdl_dump_col_matrix
+#define UMF_dump_chain umfdl_dump_chain
+#define UMF_dump_start umfdl_dump_start
+#define UMF_dump_rowmerge umfdl_dump_rowmerge
+#define UMF_dump_diagonal_map umfdl_dump_diagonal_map
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Complex double precision, with int's as integers */
+/* -------------------------------------------------------------------------- */
+
+#ifdef ZINT
+
+#define UMF_analyze umf_i_analyze
+#define UMF_apply_order umf_i_apply_order
+#define UMF_assemble umfzi_assemble
+#define UMF_assemble_fixq umfzi_assemble_fixq
+#define UMF_blas3_update umfzi_blas3_update
+#define UMF_build_tuples umfzi_build_tuples
+#define UMF_build_tuples_usage umfzi_build_tuples_usage
+#define UMF_colamd umf_i_colamd
+#define UMF_colamd_set_defaults umf_i_colamd_set_defaults
+#define UMF_create_element umfzi_create_element
+#define UMF_extend_front umfzi_extend_front
+#define UMF_free umf_i_free
+#define UMF_fsize umf_i_fsize
+#define UMF_garbage_collection umfzi_garbage_collection
+#define UMF_get_memory umfzi_get_memory
+#define UMF_grow_front umfzi_grow_front
+#define UMF_init_front umfzi_init_front
+#define UMF_is_permutation umf_i_is_permutation
+#define UMF_kernel umfzi_kernel
+#define UMF_kernel_init umfzi_kernel_init
+#define UMF_kernel_init_usage umfzi_kernel_init_usage
+#define UMF_kernel_wrapup umfzi_kernel_wrapup
+#define UMF_local_search umfzi_local_search
+#define UMF_lsolve umfzi_lsolve
+#define UMF_ltsolve umfzi_ltsolve
+#define UMF_lhsolve umfzi_lhsolve
+#define UMF_malloc umf_i_malloc
+#define UMF_mem_alloc_element umfzi_mem_alloc_element
+#define UMF_mem_alloc_head_block umfzi_mem_alloc_head_block
+#define UMF_mem_alloc_tail_block umfzi_mem_alloc_tail_block
+#define UMF_mem_free_tail_block umfzi_mem_free_tail_block
+#define UMF_mem_init_memoryspace umfzi_mem_init_memoryspace
+#define UMF_realloc umf_i_realloc
+#define UMF_report_perm umf_i_report_perm
+#define UMF_report_vector umfzi_report_vector
+#define UMF_row_search umfzi_row_search
+#define UMF_scale umfzi_scale
+#define UMF_scale_column umfzi_scale_column
+#define UMF_set_stats umfzi_set_stats
+#define UMF_singletons umf_i_singletons
+#define UMF_solve umfzi_solve
+#define UMF_start_front umfzi_start_front
+#define UMF_store_lu umfzi_store_lu
+#define UMF_store_lu_drop umfzi_store_lu_drop
+#define UMF_symbolic_usage umfzi_symbolic_usage
+#define UMF_transpose umfzi_transpose
+#define UMF_tuple_lengths umfzi_tuple_lengths
+#define UMF_usolve umfzi_usolve
+#define UMF_utsolve umfzi_utsolve
+#define UMF_uhsolve umfzi_uhsolve
+#define UMF_valid_numeric umfzi_valid_numeric
+#define UMF_valid_symbolic umfzi_valid_symbolic
+#define UMF_triplet_map_x umfzi_triplet_map_x
+#define UMF_triplet_map_nox umfzi_triplet_map_nox
+#define UMF_triplet_nomap_x umfzi_triplet_nomap_x
+#define UMF_triplet_nomap_nox umfzi_triplet_nomap_nox
+#define UMF_2by2 umfzi_2by2
+
+#define UMFPACK_col_to_triplet umfpack_zi_col_to_triplet
+#define UMFPACK_defaults umfpack_zi_defaults
+#define UMFPACK_free_numeric umfpack_zi_free_numeric
+#define UMFPACK_free_symbolic umfpack_zi_free_symbolic
+#define UMFPACK_get_lunz umfpack_zi_get_lunz
+#define UMFPACK_get_numeric umfpack_zi_get_numeric
+#define UMFPACK_get_symbolic umfpack_zi_get_symbolic
+#define UMFPACK_get_determinant umfpack_zi_get_determinant
+#define UMFPACK_numeric umfpack_zi_numeric
+#define UMFPACK_qsymbolic umfpack_zi_qsymbolic
+#define UMFPACK_report_control umfpack_zi_report_control
+#define UMFPACK_report_info umfpack_zi_report_info
+#define UMFPACK_report_matrix umfpack_zi_report_matrix
+#define UMFPACK_report_numeric umfpack_zi_report_numeric
+#define UMFPACK_report_perm umfpack_zi_report_perm
+#define UMFPACK_report_status umfpack_zi_report_status
+#define UMFPACK_report_symbolic umfpack_zi_report_symbolic
+#define UMFPACK_report_triplet umfpack_zi_report_triplet
+#define UMFPACK_report_vector umfpack_zi_report_vector
+#define UMFPACK_save_numeric umfpack_zi_save_numeric
+#define UMFPACK_save_symbolic umfpack_zi_save_symbolic
+#define UMFPACK_load_numeric umfpack_zi_load_numeric
+#define UMFPACK_load_symbolic umfpack_zi_load_symbolic
+#define UMFPACK_scale umfpack_zi_scale
+#define UMFPACK_solve umfpack_zi_solve
+#define UMFPACK_symbolic umfpack_zi_symbolic
+#define UMFPACK_transpose umfpack_zi_transpose
+#define UMFPACK_triplet_to_col umfpack_zi_triplet_to_col
+#define UMFPACK_wsolve umfpack_zi_wsolve
+
+/* for debugging only: */
+#define UMF_malloc_count umf_i_malloc_count
+#define UMF_debug umfzi_debug
+#define UMF_allocfail umfzi_allocfail
+#define UMF_gprob umfzi_gprob
+#define UMF_dump_dense umfzi_dump_dense
+#define UMF_dump_element umfzi_dump_element
+#define UMF_dump_rowcol umfzi_dump_rowcol
+#define UMF_dump_matrix umfzi_dump_matrix
+#define UMF_dump_current_front umfzi_dump_current_front
+#define UMF_dump_lu umfzi_dump_lu
+#define UMF_dump_memory umfzi_dump_memory
+#define UMF_dump_packed_memory umfzi_dump_packed_memory
+#define UMF_dump_col_matrix umfzi_dump_col_matrix
+#define UMF_dump_chain umfzi_dump_chain
+#define UMF_dump_start umfzi_dump_start
+#define UMF_dump_rowmerge umfzi_dump_rowmerge
+#define UMF_dump_diagonal_map umfzi_dump_diagonal_map
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+/* Complex double precision, with UF_long's as integers */
+/* -------------------------------------------------------------------------- */
+
+#ifdef ZLONG
+
+#define UMF_analyze umf_l_analyze
+#define UMF_apply_order umf_l_apply_order
+#define UMF_assemble umfzl_assemble
+#define UMF_assemble_fixq umfzl_assemble_fixq
+#define UMF_blas3_update umfzl_blas3_update
+#define UMF_build_tuples umfzl_build_tuples
+#define UMF_build_tuples_usage umfzl_build_tuples_usage
+#define UMF_colamd umf_l_colamd
+#define UMF_colamd_set_defaults umf_l_colamd_set_defaults
+#define UMF_create_element umfzl_create_element
+#define UMF_extend_front umfzl_extend_front
+#define UMF_free umf_l_free
+#define UMF_fsize umf_l_fsize
+#define UMF_garbage_collection umfzl_garbage_collection
+#define UMF_get_memory umfzl_get_memory
+#define UMF_grow_front umfzl_grow_front
+#define UMF_init_front umfzl_init_front
+#define UMF_is_permutation umf_l_is_permutation
+#define UMF_kernel umfzl_kernel
+#define UMF_kernel_init umfzl_kernel_init
+#define UMF_kernel_init_usage umfzl_kernel_init_usage
+#define UMF_kernel_wrapup umfzl_kernel_wrapup
+#define UMF_local_search umfzl_local_search
+#define UMF_lsolve umfzl_lsolve
+#define UMF_ltsolve umfzl_ltsolve
+#define UMF_lhsolve umfzl_lhsolve
+#define UMF_malloc umf_l_malloc
+#define UMF_mem_alloc_element umfzl_mem_alloc_element
+#define UMF_mem_alloc_head_block umfzl_mem_alloc_head_block
+#define UMF_mem_alloc_tail_block umfzl_mem_alloc_tail_block
+#define UMF_mem_free_tail_block umfzl_mem_free_tail_block
+#define UMF_mem_init_memoryspace umfzl_mem_init_memoryspace
+#define UMF_realloc umf_l_realloc
+#define UMF_report_perm umf_l_report_perm
+#define UMF_report_vector umfzl_report_vector
+#define UMF_row_search umfzl_row_search
+#define UMF_scale umfzl_scale
+#define UMF_scale_column umfzl_scale_column
+#define UMF_set_stats umfzl_set_stats
+#define UMF_singletons umf_l_singletons
+#define UMF_solve umfzl_solve
+#define UMF_start_front umfzl_start_front
+#define UMF_store_lu umfzl_store_lu
+#define UMF_store_lu_drop umfzl_store_lu_drop
+#define UMF_symbolic_usage umfzl_symbolic_usage
+#define UMF_transpose umfzl_transpose
+#define UMF_tuple_lengths umfzl_tuple_lengths
+#define UMF_usolve umfzl_usolve
+#define UMF_utsolve umfzl_utsolve
+#define UMF_uhsolve umfzl_uhsolve
+#define UMF_valid_numeric umfzl_valid_numeric
+#define UMF_valid_symbolic umfzl_valid_symbolic
+#define UMF_triplet_map_x umfzl_triplet_map_x
+#define UMF_triplet_map_nox umfzl_triplet_map_nox
+#define UMF_triplet_nomap_x umfzl_triplet_nomap_x
+#define UMF_triplet_nomap_nox umfzl_triplet_nomap_nox
+#define UMF_2by2 umfzl_2by2
+
+#define UMFPACK_col_to_triplet umfpack_zl_col_to_triplet
+#define UMFPACK_defaults umfpack_zl_defaults
+#define UMFPACK_free_numeric umfpack_zl_free_numeric
+#define UMFPACK_free_symbolic umfpack_zl_free_symbolic
+#define UMFPACK_get_lunz umfpack_zl_get_lunz
+#define UMFPACK_get_numeric umfpack_zl_get_numeric
+#define UMFPACK_get_symbolic umfpack_zl_get_symbolic
+#define UMFPACK_get_determinant umfpack_zl_get_determinant
+#define UMFPACK_numeric umfpack_zl_numeric
+#define UMFPACK_qsymbolic umfpack_zl_qsymbolic
+#define UMFPACK_report_control umfpack_zl_report_control
+#define UMFPACK_report_info umfpack_zl_report_info
+#define UMFPACK_report_matrix umfpack_zl_report_matrix
+#define UMFPACK_report_numeric umfpack_zl_report_numeric
+#define UMFPACK_report_perm umfpack_zl_report_perm
+#define UMFPACK_report_status umfpack_zl_report_status
+#define UMFPACK_report_symbolic umfpack_zl_report_symbolic
+#define UMFPACK_report_triplet umfpack_zl_report_triplet
+#define UMFPACK_report_vector umfpack_zl_report_vector
+#define UMFPACK_save_numeric umfpack_zl_save_numeric
+#define UMFPACK_save_symbolic umfpack_zl_save_symbolic
+#define UMFPACK_load_numeric umfpack_zl_load_numeric
+#define UMFPACK_load_symbolic umfpack_zl_load_symbolic
+#define UMFPACK_scale umfpack_zl_scale
+#define UMFPACK_solve umfpack_zl_solve
+#define UMFPACK_symbolic umfpack_zl_symbolic
+#define UMFPACK_transpose umfpack_zl_transpose
+#define UMFPACK_triplet_to_col umfpack_zl_triplet_to_col
+#define UMFPACK_wsolve umfpack_zl_wsolve
+
+/* for debugging only: */
+#define UMF_malloc_count umf_l_malloc_count
+#define UMF_debug umfzl_debug
+#define UMF_allocfail umfzl_allocfail
+#define UMF_gprob umfzl_gprob
+#define UMF_dump_dense umfzl_dump_dense
+#define UMF_dump_element umfzl_dump_element
+#define UMF_dump_rowcol umfzl_dump_rowcol
+#define UMF_dump_matrix umfzl_dump_matrix
+#define UMF_dump_current_front umfzl_dump_current_front
+#define UMF_dump_lu umfzl_dump_lu
+#define UMF_dump_memory umfzl_dump_memory
+#define UMF_dump_packed_memory umfzl_dump_packed_memory
+#define UMF_dump_col_matrix umfzl_dump_col_matrix
+#define UMF_dump_chain umfzl_dump_chain
+#define UMF_dump_start umfzl_dump_start
+#define UMF_dump_rowmerge umfzl_dump_rowmerge
+#define UMF_dump_diagonal_map umfzl_dump_diagonal_map
+
+#endif
diff --git a/UMFPACK/Source/umfpack_col_to_triplet.c b/UMFPACK/Source/umfpack_col_to_triplet.c
new file mode 100644
index 0000000..f49a13d
--- /dev/null
+++ b/UMFPACK/Source/umfpack_col_to_triplet.c
@@ -0,0 +1,72 @@
+/* ========================================================================== */
+/* === UMFPACK_col_to_triplet =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User callable. Converts a column-oriented input matrix to triplet form by
+ constructing the column indices Tj from the column pointers Ap. The matrix
+ may be singular. See umfpack_col_to_triplet.h for details.
+
+*/
+
+#include "umf_internal.h"
+
+GLOBAL Int UMFPACK_col_to_triplet
+(
+ Int n_col,
+ const Int Ap [ ],
+ Int Tj [ ]
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int nz, j, p, p1, p2, length ;
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the column indices */
+ /* ---------------------------------------------------------------------- */
+
+ if (!Ap || !Tj)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+ if (n_col <= 0)
+ {
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+ if (Ap [0] != 0)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ nz = Ap [n_col] ;
+ if (nz < 0)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ for (j = 0 ; j < n_col ; j++)
+ {
+ p1 = Ap [j] ;
+ p2 = Ap [j+1] ;
+ length = p2 - p1 ;
+ if (length < 0 || p2 > nz)
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ for (p = p1 ; p < p2 ; p++)
+ {
+ Tj [p] = j ;
+ }
+ }
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_defaults.c b/UMFPACK/Source/umfpack_defaults.c
new file mode 100644
index 0000000..761ecd1
--- /dev/null
+++ b/UMFPACK/Source/umfpack_defaults.c
@@ -0,0 +1,114 @@
+/* ========================================================================== */
+/* === UMFPACK_defaults ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Sets default control parameters. See umfpack_defaults.h
+ for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL void UMFPACK_defaults
+(
+ double Control [UMFPACK_CONTROL]
+)
+{
+ Int i ;
+
+ if (!Control)
+ {
+ /* silently return if no Control array */
+ return ;
+ }
+
+ for (i = 0 ; i < UMFPACK_CONTROL ; i++)
+ {
+ Control [i] = 0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* default control settings: can be modified at run-time */
+ /* ---------------------------------------------------------------------- */
+
+ /* used in UMFPACK_report_* routines: */
+ Control [UMFPACK_PRL] = UMFPACK_DEFAULT_PRL ;
+
+ /* used in UMFPACK_*symbolic: */
+ Control [UMFPACK_DENSE_ROW] = UMFPACK_DEFAULT_DENSE_ROW ;
+ Control [UMFPACK_DENSE_COL] = UMFPACK_DEFAULT_DENSE_COL ;
+ Control [UMFPACK_AMD_DENSE] = UMFPACK_DEFAULT_AMD_DENSE ;
+ Control [UMFPACK_STRATEGY] = UMFPACK_DEFAULT_STRATEGY ;
+ Control [UMFPACK_2BY2_TOLERANCE] = UMFPACK_DEFAULT_2BY2_TOLERANCE ;
+ Control [UMFPACK_AGGRESSIVE] = UMFPACK_DEFAULT_AGGRESSIVE ;
+
+ /* used in UMFPACK_numeric: */
+ Control [UMFPACK_PIVOT_TOLERANCE] = UMFPACK_DEFAULT_PIVOT_TOLERANCE ;
+ Control [UMFPACK_SYM_PIVOT_TOLERANCE] = UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE;
+ Control [UMFPACK_BLOCK_SIZE] = UMFPACK_DEFAULT_BLOCK_SIZE ;
+ Control [UMFPACK_ALLOC_INIT] = UMFPACK_DEFAULT_ALLOC_INIT ;
+ Control [UMFPACK_FRONT_ALLOC_INIT] = UMFPACK_DEFAULT_FRONT_ALLOC_INIT ;
+ Control [UMFPACK_SCALE] = UMFPACK_DEFAULT_SCALE ;
+
+ /* used in UMFPACK_*solve: */
+ Control [UMFPACK_IRSTEP] = UMFPACK_DEFAULT_IRSTEP ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compile-time settings: cannot be modified at run-time */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef NBLAS
+ /* do not use the BLAS - use in-line C code instead */
+ Control [UMFPACK_COMPILED_WITH_BLAS] = 0 ;
+#else
+ /* use externally-provided BLAS (dgemm, dger, dgemv, zgemm, zgeru, zgemv) */
+ Control [UMFPACK_COMPILED_WITH_BLAS] = 1 ;
+#endif
+
+#ifdef MATLAB_MEX_FILE
+ /* compiled as a MATLAB mexFunction */
+ Control [UMFPACK_COMPILED_FOR_MATLAB] = 1 ;
+#else
+#ifdef MATHWORKS
+ /* compiled for internal use in MATLAB */
+ Control [UMFPACK_COMPILED_FOR_MATLAB] = 2 ;
+#else
+ /* use ANSI C malloc, free, realloc, and printf */
+ Control [UMFPACK_COMPILED_FOR_MATLAB] = 0 ;
+#endif
+#endif
+
+#ifdef NO_TIMER
+ /* no timer used */
+ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 3 ;
+#ifndef NPOSIX
+ /* uses the POSIX sysconf ( ) and times ( ) routines in UMFPACK_tic, toc */
+ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 2 ;
+#else
+#ifdef GETRUSAGE
+ /* uses the non-standard getrusage to get CPU time (Solaris) */
+ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 1 ;
+#else
+ /* uses the ANSI standard clock routine to get CPU time */
+ /* this may wrap around */
+ Control [UMFPACK_COMPILED_WITH_GETRUSAGE] = 0 ;
+#endif
+#endif
+#endif
+
+#ifndef NDEBUG
+ /* UMFPACK is compiled in debug mode. */
+ /* This is exceedingly slow. */
+ DEBUG0 (("UMFPACK is running in debug mode. This is very slow!\n")) ;
+ Control [UMFPACK_COMPILED_IN_DEBUG_MODE] = 1 ;
+#else
+ /* UMFPACK is compiled in normal (non-debug) mode */
+ Control [UMFPACK_COMPILED_IN_DEBUG_MODE] = 0 ;
+#endif
+}
diff --git a/UMFPACK/Source/umfpack_free_numeric.c b/UMFPACK/Source/umfpack_free_numeric.c
new file mode 100644
index 0000000..7e4e531
--- /dev/null
+++ b/UMFPACK/Source/umfpack_free_numeric.c
@@ -0,0 +1,57 @@
+/* ========================================================================== */
+/* === UMFPACK_free_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* User-callable. Free the entire Numeric object (consists of 11 to 13
+ * malloc'd objects. See UMFPACK_free_numeric.h for details.
+ */
+
+#include "umf_internal.h"
+#include "umf_free.h"
+
+GLOBAL void UMFPACK_free_numeric
+(
+ void **NumericHandle
+)
+{
+
+ NumericType *Numeric ;
+ if (!NumericHandle)
+ {
+ return ;
+ }
+ Numeric = *((NumericType **) NumericHandle) ;
+ if (!Numeric)
+ {
+ return ;
+ }
+
+ /* these 9 objects always exist */
+ (void) UMF_free ((void *) Numeric->D) ;
+ (void) UMF_free ((void *) Numeric->Rperm) ;
+ (void) UMF_free ((void *) Numeric->Cperm) ;
+ (void) UMF_free ((void *) Numeric->Lpos) ;
+ (void) UMF_free ((void *) Numeric->Lilen) ;
+ (void) UMF_free ((void *) Numeric->Lip) ;
+ (void) UMF_free ((void *) Numeric->Upos) ;
+ (void) UMF_free ((void *) Numeric->Uilen) ;
+ (void) UMF_free ((void *) Numeric->Uip) ;
+
+ /* Rs does not exist if scaling was not performed */
+ (void) UMF_free ((void *) Numeric->Rs) ;
+
+ /* Upattern can only exist for singular or rectangular matrices */
+ (void) UMF_free ((void *) Numeric->Upattern) ;
+
+ /* these 2 objects always exist */
+ (void) UMF_free ((void *) Numeric->Memory) ;
+ (void) UMF_free ((void *) Numeric) ;
+
+ *NumericHandle = (void *) NULL ;
+}
diff --git a/UMFPACK/Source/umfpack_free_symbolic.c b/UMFPACK/Source/umfpack_free_symbolic.c
new file mode 100644
index 0000000..b865c43
--- /dev/null
+++ b/UMFPACK/Source/umfpack_free_symbolic.c
@@ -0,0 +1,56 @@
+/* ========================================================================== */
+/* === UMFPACK_free_symbolic ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. See umfpack_free_symbolic.h for details.
+ All 10 objects comprising the Symbolic object are free'd via UMF_free.
+*/
+
+#include "umf_internal.h"
+#include "umf_free.h"
+
+GLOBAL void UMFPACK_free_symbolic
+(
+ void **SymbolicHandle
+)
+{
+
+ SymbolicType *Symbolic ;
+ if (!SymbolicHandle)
+ {
+ return ;
+ }
+ Symbolic = *((SymbolicType **) SymbolicHandle) ;
+ if (!Symbolic)
+ {
+ return ;
+ }
+
+ (void) UMF_free ((void *) Symbolic->Cperm_init) ;
+ (void) UMF_free ((void *) Symbolic->Rperm_init) ;
+ (void) UMF_free ((void *) Symbolic->Front_npivcol) ;
+ (void) UMF_free ((void *) Symbolic->Front_parent) ;
+ (void) UMF_free ((void *) Symbolic->Front_1strow) ;
+ (void) UMF_free ((void *) Symbolic->Front_leftmostdesc) ;
+ (void) UMF_free ((void *) Symbolic->Chain_start) ;
+ (void) UMF_free ((void *) Symbolic->Chain_maxrows) ;
+ (void) UMF_free ((void *) Symbolic->Chain_maxcols) ;
+ (void) UMF_free ((void *) Symbolic->Cdeg) ;
+ (void) UMF_free ((void *) Symbolic->Rdeg) ;
+
+ /* only when dense rows are present */
+ (void) UMF_free ((void *) Symbolic->Esize) ;
+
+ /* only when diagonal pivoting is prefered */
+ (void) UMF_free ((void *) Symbolic->Diagonal_map) ;
+
+ (void) UMF_free ((void *) Symbolic) ;
+ *SymbolicHandle = (void *) NULL ;
+}
diff --git a/UMFPACK/Source/umfpack_get_determinant.c b/UMFPACK/Source/umfpack_get_determinant.c
new file mode 100644
index 0000000..bfeacaa
--- /dev/null
+++ b/UMFPACK/Source/umfpack_get_determinant.c
@@ -0,0 +1,308 @@
+/* ========================================================================== */
+/* === UMFPACK_get_determinant ============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* UMFPACK_get_determinant contributed by David Bateman, Motorola, Paris. */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. From the LU factors, scale factor, and permutation vectors
+ held in the Numeric object, calculates the determinant of the matrix A.
+ See umfpack_get_determinant.h for a more detailed description.
+
+ Dynamic memory usage: calls UMF_malloc once, for a total space of
+ n integers, and then frees all of it via UMF_free when done.
+
+ Contributed by David Bateman, Motorola, Nov. 2004.
+ Modified for V4.4, Jan. 2005.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+/* ========================================================================== */
+/* === rescale_determinant ================================================== */
+/* ========================================================================== */
+
+/* If the mantissa is too big or too small, rescale it and change exponent */
+
+PRIVATE Int rescale_determinant
+(
+ Entry *d_mantissa,
+ double *d_exponent
+)
+{
+ double d_abs ;
+
+ ABS (d_abs, *d_mantissa) ;
+
+ if (SCALAR_IS_ZERO (d_abs))
+ {
+ /* the determinant is zero */
+ *d_exponent = 0 ;
+ return (FALSE) ;
+ }
+
+ if (SCALAR_IS_NAN (d_abs))
+ {
+ /* the determinant is NaN */
+ return (FALSE) ;
+ }
+
+ while (d_abs < 1.)
+ {
+ SCALE (*d_mantissa, 10.0) ;
+ *d_exponent = *d_exponent - 1.0 ;
+ ABS (d_abs, *d_mantissa) ;
+ }
+
+ while (d_abs >= 10.)
+ {
+ SCALE (*d_mantissa, 0.1) ;
+ *d_exponent = *d_exponent + 1.0 ;
+ ABS (d_abs, *d_mantissa) ;
+ }
+
+ return (TRUE) ;
+}
+
+/* ========================================================================== */
+/* === UMFPACK_get_determinant ============================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_get_determinant
+(
+ double *Mx,
+#ifdef COMPLEX
+ double *Mz,
+#endif
+ double *Ex,
+ void *NumericHandle,
+ double User_Info [UMFPACK_INFO]
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry d_mantissa, d_tmp ;
+ double d_exponent, Info2 [UMFPACK_INFO], one [2] = {1.0, 0.0}, d_sign ;
+ Entry *D ;
+ double *Info, *Rs ;
+ NumericType *Numeric ;
+ Int i, n, itmp, npiv, *Wi, *Rperm, *Cperm, do_scale ;
+
+#ifndef NRECIPROCAL
+ Int do_recip ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* check input parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (User_Info != (double *) NULL)
+ {
+ /* return Info in user's array */
+ Info = User_Info ;
+ }
+ else
+ {
+ /* no Info array passed - use local one instead */
+ Info = Info2 ;
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ }
+
+ Info [UMFPACK_STATUS] = UMFPACK_OK ;
+
+ Numeric = (NumericType *) NumericHandle ;
+ if (!UMF_valid_numeric (Numeric))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Numeric_object ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ if (Numeric->n_row != Numeric->n_col)
+ {
+ /* only square systems can be handled */
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ;
+ return (UMFPACK_ERROR_invalid_system) ;
+ }
+
+ if (Mx == (double *) NULL)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ n = Numeric->n_row ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Wi = (Int *) UMF_malloc (n, sizeof (Int)) ;
+
+ if (!Wi)
+ {
+ DEBUGm4 (("out of memory: get determinant\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the determinant */
+ /* ---------------------------------------------------------------------- */
+
+ Rs = Numeric->Rs ; /* row scale factors */
+ do_scale = (Rs != (double *) NULL) ;
+
+#ifndef NRECIPROCAL
+ do_recip = Numeric->do_recip ;
+#endif
+
+ d_mantissa = ((Entry *) one) [0] ;
+ d_exponent = 0.0 ;
+ D = Numeric->D ;
+
+ /* compute product of diagonal entries of U */
+ for (i = 0 ; i < n ; i++)
+ {
+ MULT (d_tmp, d_mantissa, D [i]) ;
+ d_mantissa = d_tmp ;
+
+ if (!rescale_determinant (&d_mantissa, &d_exponent))
+ {
+ /* the determinant is zero or NaN */
+ Info [UMFPACK_STATUS] = UMFPACK_WARNING_singular_matrix ;
+ /* no need to compute the determinant of R */
+ do_scale = FALSE ;
+ break ;
+ }
+ }
+
+ /* compute product of diagonal entries of R (or its inverse) */
+ if (do_scale)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+#ifndef NRECIPROCAL
+ if (do_recip)
+ {
+ /* compute determinant of R inverse */
+ SCALE_DIV (d_mantissa, Rs [i]) ;
+ }
+ else
+#endif
+ {
+ /* compute determinant of R */
+ SCALE (d_mantissa, Rs [i]) ;
+ }
+ if (!rescale_determinant (&d_mantissa, &d_exponent))
+ {
+ /* the determinant is zero or NaN. This is very unlikey to
+ * occur here, since the scale factors for a tiny or zero row
+ * are set to 1. */
+ Info [UMFPACK_STATUS] = UMFPACK_WARNING_singular_matrix ;
+ break ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine if P and Q are odd or even permutations */
+ /* ---------------------------------------------------------------------- */
+
+ npiv = 0 ;
+ Rperm = Numeric->Rperm ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ Wi [i] = Rperm [i] ;
+ }
+
+ for (i = 0 ; i < n ; i++)
+ {
+ while (Wi [i] != i)
+ {
+ itmp = Wi [Wi [i]] ;
+ Wi [Wi [i]] = Wi [i] ;
+ Wi [i] = itmp ;
+ npiv++ ;
+ }
+ }
+
+ Cperm = Numeric->Cperm ;
+
+ for (i = 0 ; i < n ; i++)
+ {
+ Wi [i] = Cperm [i] ;
+ }
+
+ for (i = 0 ; i < n ; i++)
+ {
+ while (Wi [i] != i)
+ {
+ itmp = Wi [Wi [i]] ;
+ Wi [Wi [i]] = Wi [i] ;
+ Wi [i] = itmp ;
+ npiv++ ;
+ }
+ }
+
+ /* if npiv is odd, the sign is -1. if it is even, the sign is +1 */
+ d_sign = (npiv % 2) ? -1. : 1. ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ (void) UMF_free ((void *) Wi) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute the magnitude and exponent of the determinant */
+ /* ---------------------------------------------------------------------- */
+
+ if (Ex == (double *) NULL)
+ {
+ /* Ex is not provided, so return the entire determinant in d_mantissa */
+ SCALE (d_mantissa, pow (10.0, d_exponent)) ;
+ }
+ else
+ {
+ Ex [0] = d_exponent ;
+ }
+
+ Mx [0] = d_sign * REAL_COMPONENT (d_mantissa) ;
+
+#ifdef COMPLEX
+ if (SPLIT (Mz))
+ {
+ Mz [0] = d_sign * IMAG_COMPONENT (d_mantissa) ;
+ }
+ else
+ {
+ Mx [1] = d_sign * IMAG_COMPONENT (d_mantissa) ;
+ }
+#endif
+
+ /* determine if the determinant has (or will) overflow or underflow */
+ if (d_exponent + 1.0 > log10 (DBL_MAX))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_WARNING_determinant_overflow ;
+ }
+ else if (d_exponent - 1.0 < log10 (DBL_MIN))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_WARNING_determinant_underflow ;
+ }
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_get_lunz.c b/UMFPACK/Source/umfpack_get_lunz.c
new file mode 100644
index 0000000..21752d3
--- /dev/null
+++ b/UMFPACK/Source/umfpack_get_lunz.c
@@ -0,0 +1,55 @@
+/* ========================================================================== */
+/* === UMFPACK_get_lunz ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Determines the number of nonzeros in L and U, and the size
+ of L and U.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+
+GLOBAL Int UMFPACK_get_lunz
+(
+ Int *lnz,
+ Int *unz,
+ Int *n_row,
+ Int *n_col,
+ Int *nz_udiag,
+ void *NumericHandle
+)
+{
+ NumericType *Numeric ;
+
+ Numeric = (NumericType *) NumericHandle ;
+
+ if (!UMF_valid_numeric (Numeric))
+ {
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+ if (!lnz || !unz || !n_row || !n_col || !nz_udiag)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ *n_row = Numeric->n_row ;
+ *n_col = Numeric->n_col ;
+
+ /* number of nz's in L below diagonal, plus the unit diagonal of L */
+ *lnz = Numeric->lnz + MIN (Numeric->n_row, Numeric->n_col) ;
+
+ /* number of nz's in U above diagonal, plus nz's on diagaonal of U */
+ *unz = Numeric->unz + Numeric->nnzpiv ;
+
+ /* number of nz's on the diagonal */
+ *nz_udiag = Numeric->nnzpiv ;
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_get_numeric.c b/UMFPACK/Source/umfpack_get_numeric.c
new file mode 100644
index 0000000..9dd2208
--- /dev/null
+++ b/UMFPACK/Source/umfpack_get_numeric.c
@@ -0,0 +1,1057 @@
+/* ========================================================================== */
+/* === UMFPACK_get_numeric ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Gets the LU factors and the permutation vectors held in the
+ Numeric object. L is returned in sparse row form with sorted rows, U is
+ returned in sparse column form with sorted columns, and P and Q are
+ returned as permutation vectors. See umfpack_get_numeric.h for a more
+ detailed description.
+
+ Returns TRUE if successful, FALSE if the Numeric object is invalid or
+ if out of memory.
+
+ Dynamic memory usage: calls UMF_malloc twice, for a total space of
+ 2*n integers, and then frees all of it via UMF_free when done.
+
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+
+PRIVATE void get_L
+(
+ Int Lp [ ],
+ Int Lj [ ],
+ double Lx [ ],
+#ifdef COMPLEX
+ double Lz [ ],
+#endif
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int Wi [ ]
+) ;
+
+PRIVATE void get_U
+(
+ Int Up [ ],
+ Int Ui [ ],
+ double Ux [ ],
+#ifdef COMPLEX
+ double Uz [ ],
+#endif
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int Wi [ ]
+) ;
+
+/* ========================================================================== */
+/* === UMFPACK_get_numeric ================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_get_numeric
+(
+ Int Lp [ ],
+ Int Lj [ ],
+ double Lx [ ],
+#ifdef COMPLEX
+ double Lz [ ],
+#endif
+ Int Up [ ],
+ Int Ui [ ],
+ double Ux [ ],
+#ifdef COMPLEX
+ double Uz [ ],
+#endif
+ Int P [ ],
+ Int Q [ ],
+ double Dx [ ],
+#ifdef COMPLEX
+ double Dz [ ],
+#endif
+ Int *p_do_recip,
+ double Rs [ ],
+ void *NumericHandle
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ NumericType *Numeric ;
+ Int getL, getU, *Rperm, *Cperm, k, nn, n_row, n_col, *Wi, *Pattern,
+ n_inner ;
+ double *Rs1 ;
+ Entry *D ;
+
+#ifndef NDEBUG
+ init_count = UMF_malloc_count ;
+#endif
+
+ Wi = (Int *) NULL ;
+ Pattern = (Int *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check input parameters */
+ /* ---------------------------------------------------------------------- */
+
+ Numeric = (NumericType *) NumericHandle ;
+ if (!UMF_valid_numeric (Numeric))
+ {
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ n_row = Numeric->n_row ;
+ n_col = Numeric->n_col ;
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ getL = Lp && Lj && Lx ;
+ getU = Up && Ui && Ux ;
+
+ if (getL || getU)
+ {
+ Wi = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ Pattern = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ if (!Wi || !Pattern)
+ {
+ (void) UMF_free ((void *) Wi) ;
+ (void) UMF_free ((void *) Pattern) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+ DEBUGm4 (("out of memory: get numeric\n")) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ ASSERT (UMF_malloc_count == init_count + 2) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get contents of Numeric */
+ /* ---------------------------------------------------------------------- */
+
+ if (P != (Int *) NULL)
+ {
+ Rperm = Numeric->Rperm ;
+ for (k = 0 ; k < n_row ; k++)
+ {
+ P [k] = Rperm [k] ;
+ }
+ }
+
+ if (Q != (Int *) NULL)
+ {
+ Cperm = Numeric->Cperm ;
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Q [k] = Cperm [k] ;
+ }
+ }
+
+ if (getL)
+ {
+ get_L (Lp, Lj, Lx,
+#ifdef COMPLEX
+ Lz,
+#endif
+ Numeric, Pattern, Wi) ;
+ }
+
+ if (getU)
+ {
+ get_U (Up, Ui, Ux,
+#ifdef COMPLEX
+ Uz,
+#endif
+ Numeric, Pattern, Wi) ;
+ }
+
+ if (Dx != (double *) NULL)
+ {
+ D = Numeric->D ;
+#ifdef COMPLEX
+ if (SPLIT (Dz))
+ {
+ for (k = 0 ; k < n_inner ; k++)
+ {
+ Dx [k] = REAL_COMPONENT (D [k]) ;
+ Dz [k] = IMAG_COMPONENT (D [k]) ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < n_inner ; k++)
+ {
+ Dx [2*k ] = REAL_COMPONENT (D [k]) ;
+ Dx [2*k+1] = IMAG_COMPONENT (D [k]) ;
+ }
+ }
+#else
+ {
+ D = Numeric->D ;
+ for (k = 0 ; k < n_inner ; k++)
+ {
+ Dx [k] = D [k] ;
+ }
+ }
+#endif
+ }
+
+ /* return the flag stating whether the scale factors are to be multiplied,
+ * or divided. If do_recip is TRUE, multiply. Otherwise, divided.
+ * If NRECIPROCAL is defined at compile time, the scale factors are always
+ * to be used by dividing.
+ */
+ if (p_do_recip != (Int *) NULL)
+ {
+#ifndef NRECIPROCAL
+ *p_do_recip = Numeric->do_recip ;
+#else
+ *p_do_recip = FALSE ;
+#endif
+ }
+
+ if (Rs != (double *) NULL)
+ {
+ Rs1 = Numeric->Rs ;
+ if (Rs1 == (double *) NULL)
+ {
+ /* R is the identity matrix. */
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Rs [k] = 1.0 ;
+ }
+ }
+ else
+ {
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Rs [k] = Rs1 [k] ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the workspace */
+ /* ---------------------------------------------------------------------- */
+
+ (void) UMF_free ((void *) Wi) ;
+ (void) UMF_free ((void *) Pattern) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+
+ return (UMFPACK_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === get_L ================================================================ */
+/* ========================================================================== */
+
+/*
+ The matrix L is stored in the following arrays in the Numeric object:
+
+ Int Lpos [0..npiv]
+ Int Lip [0..npiv], index into Numeric->Memory
+ Int Lilen [0..npiv]
+ Unit *(Numeric->Memory), pointer to memory space holding row indices
+ and numerical values
+
+ where npiv is the number of pivot entries found. If A is n_row-by-n_col,
+ then npiv <= MIN (n_row,n_col).
+
+ Let L_k denote the pattern of entries in column k of L (excluding the
+ diagonal).
+
+ An Lchain is a sequence of columns of L whose nonzero patterns are related.
+ The start of an Lchain is denoted by a negative value of Lip [k].
+
+ To obtain L_k:
+
+ (1) If column k starts an Lchain, then L_k is stored in its entirety.
+ |Lip [k]| is an index into Numeric->Memory for the integer row indices
+ in L_k. The number of entries in the column is |L_k| = Lilen [k].
+ This defines the pattern of the "leading" column of this chain.
+ Lpos [k] is not used for the first column in the chain. Column zero
+ is always a leading column.
+
+ (2) If column k does not start an Lchain, then L_k is represented as a
+ superset of L_k-1. Define Lnew_k such that (L_k-1 - {k} union Lnew_k)
+ = L_k, where Lnew_k and (L_k-1)-{k} are disjoint. Lnew_k are the
+ entries in L_k that are not in L_k-1. Lpos [k] holds the position of
+ pivot row index k in the prior pattern L_k-1 (if it is present), so
+ that the set subtraction (L_k-1)-{k} can be computed quickly, when
+ computing the pattern of L_k from L_k-1. The number of new entries in
+ L_k is stored in Lilen [k] = |Lnew_k|.
+
+ Note that this means we must have the pattern L_k-1 to compute L_k.
+
+ In both cases (1) and (2), we obtain the pattern L_k.
+
+ The numerical values are stored in Numeric->Memory, starting at the index
+ |Lip [k]| + Lilen [k]. It is stored in the same order as the entries
+ in L_k, after L_k is obtained from cases (1) or (2), above.
+
+ The advantage of using this "packed" data structure is that it can
+ dramatically reduce the amount of storage needed for the pattern of L.
+ The disadvantage is that it can be difficult for the user to access,
+ and it does not match the sparse matrix data structure used in MATLAB.
+ Thus, this routine is provided to create a conventional sparse matrix
+ data structure for L, in sparse-row form. A row-form of L appears to
+ MATLAB to be a column-oriented from of the transpose of L. If you would
+ like a column-form of L, then use UMFPACK_transpose (an example of this
+ is in umfpackmex.c).
+
+*/
+/* ========================================================================== */
+
+PRIVATE void get_L
+(
+ Int Lp [ ], /* of size n_row+1 */
+ Int Lj [ ], /* of size lnz, where lnz = Lp [n_row] */
+ double Lx [ ], /* of size lnz */
+#ifdef COMPLEX
+ double Lz [ ], /* of size lnz */
+#endif
+ NumericType *Numeric,
+ Int Pattern [ ], /* workspace of size n_row */
+ Int Wi [ ] /* workspace of size n_row */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry value ;
+ Entry *xp, *Lval ;
+ Int deg, *ip, j, row, n_row, n_col, n_inner, *Lpos, *Lilen, *Lip, p, llen,
+ lnz2, lp, newLchain, k, pos, npiv, *Li, n1 ;
+#ifdef COMPLEX
+ Int split = SPLIT (Lz) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG4 (("get_L start:\n")) ;
+ n_row = Numeric->n_row ;
+ n_col = Numeric->n_col ;
+ n_inner = MIN (n_row, n_col) ;
+ npiv = Numeric->npiv ;
+ n1 = Numeric->n1 ;
+ Lpos = Numeric->Lpos ;
+ Lilen = Numeric->Lilen ;
+ Lip = Numeric->Lip ;
+ deg = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the nonzeros in each row of L */
+ /* ---------------------------------------------------------------------- */
+
+#pragma ivdep
+ for (row = 0 ; row < n_inner ; row++)
+ {
+ /* include the diagonal entry in the row counts */
+ Wi [row] = 1 ;
+ }
+#pragma ivdep
+ for (row = n_inner ; row < n_row ; row++)
+ {
+ Wi [row] = 0 ;
+ }
+
+ /* singletons */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ deg = Lilen [k] ;
+ if (deg > 0)
+ {
+ lp = Lip [k] ;
+ Li = (Int *) (Numeric->Memory + lp) ;
+ lp += UNITS (Int, deg) ;
+ Lval = (Entry *) (Numeric->Memory + lp) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ row = Li [j] ;
+ value = Lval [j] ;
+ DEBUG4 ((" row "ID" k "ID" value", row, k)) ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ Wi [row]++ ;
+ }
+ }
+ }
+ }
+
+ /* non-singletons */
+ for (k = n1 ; k < npiv ; k++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* make column of L in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ lp = Lip [k] ;
+ newLchain = (lp < 0) ;
+ if (newLchain)
+ {
+ lp = -lp ;
+ deg = 0 ;
+ DEBUG4 (("start of chain for column of L\n")) ;
+ }
+
+ /* remove pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
+ k, Pattern [pos], pos)) ;
+ ASSERT (!newLchain) ;
+ ASSERT (deg > 0) ;
+ ASSERT (pos >= 0 && pos < deg) ;
+ ASSERT (Pattern [pos] == k) ;
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ /* concatenate the pattern */
+ ip = (Int *) (Numeric->Memory + lp) ;
+ llen = Lilen [k] ;
+ for (j = 0 ; j < llen ; j++)
+ {
+ row = *ip++ ;
+ DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
+ ASSERT (row > k && row < n_row) ;
+ Pattern [deg++] = row ;
+ }
+
+ xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
+
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
+ row = Pattern [j] ;
+ value = *xp++ ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ Wi [row]++ ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the final row form of L */
+ /* ---------------------------------------------------------------------- */
+
+ /* create the row pointers */
+ lnz2 = 0 ;
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Lp [row] = lnz2 ;
+ lnz2 += Wi [row] ;
+ Wi [row] = Lp [row] ;
+ }
+ Lp [n_row] = lnz2 ;
+ ASSERT (Numeric->lnz + n_inner == lnz2) ;
+
+ /* add entries from the rows of L (singletons) */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ deg = Lilen [k] ;
+ if (deg > 0)
+ {
+ lp = Lip [k] ;
+ Li = (Int *) (Numeric->Memory + lp) ;
+ lp += UNITS (Int, deg) ;
+ Lval = (Entry *) (Numeric->Memory + lp) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ row = Li [j] ;
+ value = Lval [j] ;
+ DEBUG4 ((" row "ID" k "ID" value", row, k)) ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ p = Wi [row]++ ;
+ Lj [p] = k ;
+#ifdef COMPLEX
+ if (split)
+ {
+
+ Lx [p] = REAL_COMPONENT (value) ;
+ Lz [p] = IMAG_COMPONENT (value) ;
+ }
+ else
+ {
+ Lx [2*p ] = REAL_COMPONENT (value) ;
+ Lx [2*p+1] = IMAG_COMPONENT (value) ;
+ }
+#else
+ Lx [p] = value ;
+#endif
+ }
+ }
+ }
+ }
+
+ /* add entries from the rows of L (non-singletons) */
+ for (k = n1 ; k < npiv ; k++)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* make column of L in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ lp = Lip [k] ;
+ newLchain = (lp < 0) ;
+ if (newLchain)
+ {
+ lp = -lp ;
+ deg = 0 ;
+ DEBUG4 (("start of chain for column of L\n")) ;
+ }
+
+ /* remove pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
+ k, Pattern [pos], pos)) ;
+ ASSERT (!newLchain) ;
+ ASSERT (deg > 0) ;
+ ASSERT (pos >= 0 && pos < deg) ;
+ ASSERT (Pattern [pos] == k) ;
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ /* concatenate the pattern */
+ ip = (Int *) (Numeric->Memory + lp) ;
+ llen = Lilen [k] ;
+ for (j = 0 ; j < llen ; j++)
+ {
+ row = *ip++ ;
+ DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
+ ASSERT (row > k) ;
+ Pattern [deg++] = row ;
+ }
+
+ xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
+
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
+ row = Pattern [j] ;
+ value = *xp++ ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ p = Wi [row]++ ;
+ Lj [p] = k ;
+#ifdef COMPLEX
+ if (split)
+ {
+ Lx [p] = REAL_COMPONENT (value) ;
+ Lz [p] = IMAG_COMPONENT (value) ;
+ }
+ else
+ {
+ Lx [2*p ] = REAL_COMPONENT (value) ;
+ Lx [2*p+1] = IMAG_COMPONENT (value) ;
+ }
+#else
+ Lx [p] = value ;
+#endif
+ }
+ }
+ }
+
+ /* add all of the diagonal entries (L is unit diagonal) */
+ for (row = 0 ; row < n_inner ; row++)
+ {
+ p = Wi [row]++ ;
+ Lj [p] = row ;
+
+#ifdef COMPLEX
+ if (split)
+ {
+ Lx [p] = 1. ;
+ Lz [p] = 0. ;
+ }
+ else
+ {
+ Lx [2*p ] = 1. ;
+ Lx [2*p+1] = 0. ;
+ }
+#else
+ Lx [p] = 1. ;
+#endif
+
+ ASSERT (Wi [row] == Lp [row+1]) ;
+ }
+
+#ifndef NDEBUG
+ DEBUG6 (("L matrix (stored by rows):")) ;
+ UMF_dump_col_matrix (Lx,
+#ifdef COMPLEX
+ Lz,
+#endif
+ Lj, Lp, n_inner, n_row, Numeric->lnz+n_inner) ;
+#endif
+
+ DEBUG4 (("get_L done:\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === get_U ================================================================ */
+/* ========================================================================== */
+
+/*
+ The matrix U is stored in the following arrays in the Numeric object:
+
+ Int Upos [0..npiv]
+ Int Uip [0..npiv], index into Numeric->Memory
+ Int Uilen [0..npiv]
+ Unit *(Numeric->Memory), pointer to memory space holding column indices
+ and numerical values
+
+ where npiv is the number of pivot entries found. If A is n_row-by-n_col,
+ then npiv <= MIN (n_row,n_col).
+
+ Let U_k denote the pattern of entries in row k of U (excluding the
+ diagonal).
+
+ A Uchain is a sequence of columns of U whose nonzero patterns are related.
+ The start of a Uchain is denoted by a negative value of Uip [k].
+
+ To obtain U_k-1:
+
+ (1) If row k is the start of a Uchain then Uip [k] is negative and |Uip [k]|
+ is an index into Numeric->Memory for the integer column indices in
+ U_k-1. The number of entries in the row is |U_k-1| = Uilen [k]. This
+ defines the pattern of the "trailing" row of this chain that ends at
+ row k-1.
+
+
+ (2) If row k is not the start of a Uchain, then U_k-1 is a subset of U_k.
+ The indices in U_k are arranged so that last Uilen [k] entries of
+ U_k are those indices not in U_k-1. Next, the pivot column index k is
+ added if it appears in row U_k-1 (it never appears in U_k). Upos [k]
+ holds the position of pivot column index k in the pattern U_k-1 (if it
+ is present), so that the set union (U_k-1)+{k} can be computed quickly,
+ when computing the pattern of U_k-1 from U_k.
+
+ Note that this means we must have the pattern U_k to compute L_k-1.
+
+ In both cases (1) and (2), we obtain the pattern U_k.
+
+ The numerical values are stored in Numeric->Memory. If k is the start of a
+ Uchain, then the offset is |Uip [k]| plus the size of the space needed to
+ store the pattern U_k-1. Otherwise, Uip [k] is the offset itself of the
+ numerical values, since in this case no pattern is stored.
+ The numerical values are stored in the same order as the entries in U_k,
+ after U_k is obtained from cases (1) or (2), above.
+
+ The advantage of using this "packed" data structure is that it can
+ dramatically reduce the amount of storage needed for the pattern of U.
+ The disadvantage is that it can be difficult for the user to access,
+ and it does not match the sparse matrix data structure used in MATLAB.
+ Thus, this routine is provided to create a conventional sparse matrix
+ data structure for U, in sparse-column form.
+
+*/
+/* ========================================================================== */
+
+PRIVATE void get_U
+(
+ Int Up [ ], /* of size n_col+1 */
+ Int Ui [ ], /* of size unz, where unz = Up [n_col] */
+ double Ux [ ], /* of size unz */
+#ifdef COMPLEX
+ double Uz [ ], /* of size unz */
+#endif
+ NumericType *Numeric,
+ Int Pattern [ ], /* workspace of size n_col */
+ Int Wi [ ] /* workspace of size n_col */
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Entry value ;
+ Entry *xp, *D, *Uval ;
+ Int deg, j, *ip, col, *Upos, *Uilen, *Uip, n_col, ulen, *Usi,
+ unz2, p, k, up, newUchain, pos, npiv, n1 ;
+#ifdef COMPLEX
+ Int split = SPLIT (Uz) ;
+#endif
+#ifndef NDEBUG
+ Int nnzpiv = 0 ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ DEBUG4 (("get_U start:\n")) ;
+ n_col = Numeric->n_col ;
+ n1 = Numeric->n1 ;
+ npiv = Numeric->npiv ;
+ Upos = Numeric->Upos ;
+ Uilen = Numeric->Uilen ;
+ Uip = Numeric->Uip ;
+ D = Numeric->D ;
+
+ /* ---------------------------------------------------------------------- */
+ /* count the nonzeros in each column of U */
+ /* ---------------------------------------------------------------------- */
+
+ for (col = 0 ; col < npiv ; col++)
+ {
+ /* include the diagonal entry in the column counts */
+ DEBUG4 (("D ["ID"] = ", col)) ;
+ EDEBUG4 (D [col]) ;
+ Wi [col] = IS_NONZERO (D [col]) ;
+ DEBUG4 ((" is nonzero: "ID"\n", Wi [col])) ;
+#ifndef NDEBUG
+ nnzpiv += IS_NONZERO (D [col]) ;
+#endif
+ }
+ DEBUG4 (("nnzpiv "ID" "ID"\n", nnzpiv, Numeric->nnzpiv)) ;
+ ASSERT (nnzpiv == Numeric->nnzpiv) ;
+ for (col = npiv ; col < n_col ; col++)
+ {
+ /* diagonal entries are zero for structurally singular part */
+ Wi [col] = 0 ;
+ }
+
+ deg = Numeric->ulen ;
+ if (deg > 0)
+ {
+ /* make last pivot row of U (singular matrices only) */
+ DEBUG0 (("Last pivot row of U: ulen "ID"\n", deg)) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ Pattern [j] = Numeric->Upattern [j] ;
+ DEBUG0 ((" column "ID"\n", Pattern [j])) ;
+ }
+ }
+
+ /* non-singletons */
+ for (k = npiv-1 ; k >= n1 ; k--)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* use row k of U */
+ /* ------------------------------------------------------------------ */
+
+ up = Uip [k] ;
+ ulen = Uilen [k] ;
+ newUchain = (up < 0) ;
+ if (newUchain)
+ {
+ up = -up ;
+ xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
+ }
+ else
+ {
+ xp = (Entry *) (Numeric->Memory + up) ;
+ }
+
+ for (j = 0 ; j < deg ; j++)
+ {
+ DEBUG4 ((" k "ID" col "ID" value\n", k, Pattern [j])) ;
+ col = Pattern [j] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ value = *xp++ ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ Wi [col]++ ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* make row k-1 of U in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ if (k == n1) break ;
+
+ if (newUchain)
+ {
+ /* next row is a new Uchain */
+ deg = ulen ;
+ DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = *ip++ ;
+ DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
+ ASSERT (k <= col) ;
+ Pattern [j] = col ;
+ }
+ }
+ else
+ {
+ deg -= ulen ;
+ DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k-1, deg));
+ ASSERT (deg >= 0) ;
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* add the pivot column */
+ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
+ ASSERT (pos >= 0 && pos <= deg) ;
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ }
+ }
+
+ /* singletons */
+ for (k = n1 - 1 ; k >= 0 ; k--)
+ {
+ deg = Uilen [k] ;
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ if (deg > 0)
+ {
+ up = Uip [k] ;
+ Usi = (Int *) (Numeric->Memory + up) ;
+ up += UNITS (Int, deg) ;
+ Uval = (Entry *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = Usi [j] ;
+ value = Uval [j] ;
+ DEBUG4 ((" k "ID" col "ID" value", k, col)) ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ Wi [col]++ ;
+ }
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* construct the final column form of U */
+ /* ---------------------------------------------------------------------- */
+
+ /* create the column pointers */
+ unz2 = 0 ;
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Up [col] = unz2 ;
+ unz2 += Wi [col] ;
+ }
+ Up [n_col] = unz2 ;
+ DEBUG1 (("Numeric->unz "ID" npiv "ID" nnzpiv "ID" unz2 "ID"\n",
+ Numeric->unz, npiv, Numeric->nnzpiv, unz2)) ;
+ ASSERT (Numeric->unz + Numeric->nnzpiv == unz2) ;
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Wi [col] = Up [col+1] ;
+ }
+
+ /* add all of the diagonal entries */
+ for (col = 0 ; col < npiv ; col++)
+ {
+ if (IS_NONZERO (D [col]))
+ {
+ p = --(Wi [col]) ;
+ Ui [p] = col ;
+#ifdef COMPLEX
+ if (split)
+ {
+
+ Ux [p] = REAL_COMPONENT (D [col]) ;
+ Uz [p] = IMAG_COMPONENT (D [col]) ;
+ }
+ else
+ {
+ Ux [2*p ] = REAL_COMPONENT (D [col]) ;
+ Ux [2*p+1] = IMAG_COMPONENT (D [col]) ;
+ }
+#else
+ Ux [p] = D [col] ;
+#endif
+ }
+ }
+
+ /* add all the entries from the rows of U */
+
+ deg = Numeric->ulen ;
+ if (deg > 0)
+ {
+ /* make last pivot row of U (singular matrices only) */
+ for (j = 0 ; j < deg ; j++)
+ {
+ Pattern [j] = Numeric->Upattern [j] ;
+ }
+ }
+
+ /* non-singletons */
+ for (k = npiv-1 ; k >= n1 ; k--)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* use row k of U */
+ /* ------------------------------------------------------------------ */
+
+ up = Uip [k] ;
+ ulen = Uilen [k] ;
+ newUchain = (up < 0) ;
+ if (newUchain)
+ {
+ up = -up ;
+ xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
+ }
+ else
+ {
+ xp = (Entry *) (Numeric->Memory + up) ;
+ }
+
+ xp += deg ;
+ for (j = deg-1 ; j >= 0 ; j--)
+ {
+ DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ;
+ col = Pattern [j] ;
+ ASSERT (col >= 0 && col < n_col) ;
+ value = *(--xp) ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ p = --(Wi [col]) ;
+ Ui [p] = k ;
+#ifdef COMPLEX
+ if (split)
+ {
+ Ux [p] = REAL_COMPONENT (value) ;
+ Uz [p] = IMAG_COMPONENT (value) ;
+ }
+ else
+ {
+ Ux [2*p ] = REAL_COMPONENT (value) ;
+ Ux [2*p+1] = IMAG_COMPONENT (value) ;
+ }
+#else
+ Ux [p] = value ;
+#endif
+
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* make row k-1 of U in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ if (newUchain)
+ {
+ /* next row is a new Uchain */
+ deg = ulen ;
+ DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = *ip++ ;
+ DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
+ ASSERT (k <= col) ;
+ Pattern [j] = col ;
+ }
+ }
+ else
+ {
+ deg -= ulen ;
+ DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k-1, deg));
+ ASSERT (deg >= 0) ;
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* add the pivot column */
+ DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
+ ASSERT (pos >= 0 && pos <= deg) ;
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ }
+ }
+
+ /* singletons */
+ for (k = n1 - 1 ; k >= 0 ; k--)
+ {
+ deg = Uilen [k] ;
+ DEBUG4 (("Singleton k "ID"\n", k)) ;
+ if (deg > 0)
+ {
+ up = Uip [k] ;
+ Usi = (Int *) (Numeric->Memory + up) ;
+ up += UNITS (Int, deg) ;
+ Uval = (Entry *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = Usi [j] ;
+ value = Uval [j] ;
+ DEBUG4 ((" k "ID" col "ID" value", k, col)) ;
+ EDEBUG4 (value) ;
+ DEBUG4 (("\n")) ;
+ if (IS_NONZERO (value))
+ {
+ p = --(Wi [col]) ;
+ Ui [p] = k ;
+#ifdef COMPLEX
+ if (split)
+ {
+ Ux [p] = REAL_COMPONENT (value) ;
+ Uz [p] = IMAG_COMPONENT (value) ;
+ }
+ else
+ {
+ Ux [2*p ] = REAL_COMPONENT (value) ;
+ Ux [2*p+1] = IMAG_COMPONENT (value) ;
+ }
+#else
+ Ux [p] = value ;
+#endif
+ }
+ }
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG6 (("U matrix:")) ;
+ UMF_dump_col_matrix (Ux,
+#ifdef COMPLEX
+ Uz,
+#endif
+ Ui, Up, Numeric->n_row, n_col, Numeric->unz + Numeric->nnzpiv) ;
+#endif
+
+}
diff --git a/UMFPACK/Source/umfpack_get_symbolic.c b/UMFPACK/Source/umfpack_get_symbolic.c
new file mode 100644
index 0000000..560d38c
--- /dev/null
+++ b/UMFPACK/Source/umfpack_get_symbolic.c
@@ -0,0 +1,191 @@
+/* ========================================================================== */
+/* === UMFPACK_get_symbolic ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Gets the symbolic information held in the Symbolic object.
+ See umfpack_get_symbolic.h for a more detailed description.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+
+GLOBAL Int UMFPACK_get_symbolic
+(
+ Int *p_n_row,
+ Int *p_n_col,
+ Int *p_n1, /* number of singletons */
+ Int *p_nz,
+ Int *p_nfr,
+ Int *p_nchains,
+ Int P [ ],
+ Int Q [ ],
+ Int Front_npivcol [ ],
+ Int Front_parent [ ],
+ Int Front_1strow [ ],
+ Int Front_leftmostdesc [ ],
+ Int Chain_start [ ],
+ Int Chain_maxrows [ ],
+ Int Chain_maxcols [ ],
+ void *SymbolicHandle
+)
+{
+ SymbolicType *Symbolic ;
+ Int k, n_row, n_col, n1, nfr, nchains, *p ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic = (SymbolicType *) SymbolicHandle ;
+ if (!UMF_valid_symbolic (Symbolic))
+ {
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get contents of Symbolic */
+ /* ---------------------------------------------------------------------- */
+
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+ n1 = Symbolic->n1 ;
+ nfr = Symbolic->nfr ;
+ nchains = Symbolic->nchains ;
+
+ if (p_n_row)
+ {
+ *p_n_row = n_row ;
+ }
+
+ if (p_n_col)
+ {
+ *p_n_col = n_col ;
+ }
+
+ if (p_n1)
+ {
+ *p_n1 = n1 ;
+ }
+
+ if (p_nz)
+ {
+ *p_nz = Symbolic->nz ;
+ }
+
+ if (p_nfr)
+ {
+ *p_nfr = nfr ;
+ }
+
+ if (p_nchains)
+ {
+ *p_nchains = nchains ;
+ }
+
+ if (P != (Int *) NULL)
+ {
+ Int *Rperm_init, *Diagonal_map ;
+ Rperm_init = Symbolic->Rperm_init ;
+ Diagonal_map = Symbolic->Diagonal_map ;
+ if (Diagonal_map != (Int *) NULL)
+ {
+ ASSERT (n_row == n_col) ;
+ /* next pivot rows are found in the diagonal map */
+ for (k = 0 ; k < n_row ; k++)
+ {
+ P [k] = Rperm_init [Diagonal_map [k]] ;
+ }
+ }
+ else
+ {
+ /* there is no diagonal map. */
+ for (k = 0 ; k < n_row ; k++)
+ {
+ P [k] = Rperm_init [k] ;
+ }
+ }
+ }
+
+ if (Q != (Int *) NULL)
+ {
+ p = Symbolic->Cperm_init ;
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Q [k] = p [k] ;
+ }
+ }
+
+ if (Front_npivcol != (Int *) NULL)
+ {
+ p = Symbolic->Front_npivcol ;
+ for (k = 0 ; k <= nfr ; k++)
+ {
+ Front_npivcol [k] = p [k] ;
+ }
+ }
+
+ if (Front_parent != (Int *) NULL)
+ {
+ p = Symbolic->Front_parent ;
+ for (k = 0 ; k <= nfr ; k++)
+ {
+ Front_parent [k] = p [k] ;
+ }
+ }
+
+ if (Front_1strow != (Int *) NULL)
+ {
+ p = Symbolic->Front_1strow ;
+ for (k = 0 ; k <= nfr ; k++)
+ {
+ Front_1strow [k] = p [k] ;
+ }
+ }
+
+ if (Front_leftmostdesc != (Int *) NULL)
+ {
+ p = Symbolic->Front_leftmostdesc ;
+ for (k = 0 ; k <= nfr ; k++)
+ {
+ Front_leftmostdesc [k] = p [k] ;
+ }
+ }
+
+ if (Chain_start != (Int *) NULL)
+ {
+ p = Symbolic->Chain_start ;
+ for (k = 0 ; k <= nchains ; k++)
+ {
+ Chain_start [k] = p [k] ;
+ }
+ }
+
+ if (Chain_maxrows != (Int *) NULL)
+ {
+ p = Symbolic->Chain_maxrows ;
+ for (k = 0 ; k < nchains ; k++)
+ {
+ Chain_maxrows [k] = p [k] ;
+ }
+ Chain_maxrows [nchains] = 0 ;
+ }
+
+ if (Chain_maxcols != (Int *) NULL)
+ {
+ p = Symbolic->Chain_maxcols ;
+ for (k = 0 ; k < nchains ; k++)
+ {
+ Chain_maxcols [k] = p [k] ;
+ }
+ Chain_maxcols [nchains] = 0 ;
+ }
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_global.c b/UMFPACK/Source/umfpack_global.c
new file mode 100644
index 0000000..b227573
--- /dev/null
+++ b/UMFPACK/Source/umfpack_global.c
@@ -0,0 +1,130 @@
+/* ========================================================================== */
+/* === UMFPACK_global ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ Global variables. UMFPACK uses these function pointers for several
+ user-redefinable functions. The amd_* functions are defined in
+ AMD/Source/amd_global.c.
+
+ Function pointer default for mexFunction
+ (see MATLAB/umfpackmex.c)
+ ---------------- ------- ---------------
+ amd_malloc malloc mxMalloc
+ amd_free free mxFree
+ amd_realloc realloc mxRealloc
+ amd_calloc calloc mxCalloc
+ amd_printf printf mexPrintf
+
+ umfpack_hypot umf_hypot umf_hypot
+ umfpack_divcomplex umf_divcomplex umf_divcomplex
+
+ This routine is compiled just once for all four versions of UMFPACK
+ (int/UF_long, double/complex).
+*/
+
+#include "umf_internal.h"
+
+double (*umfpack_hypot) (double, double) = umf_hypot ;
+int (*umfpack_divcomplex) (double, double, double, double, double *, double *)
+ = umf_divcomplex ;
+
+
+/* ========================================================================== */
+/* === umf_hypot ============================================================ */
+/* ========================================================================== */
+
+/* There is an equivalent routine called hypot in <math.h>, which conforms
+ * to ANSI C99. However, UMFPACK does not assume that ANSI C99 is available.
+ * You can use the ANSI C99 hypot routine with:
+ *
+ * #include <math.h>
+ * umfpack_hypot = hypot ;
+ *
+ * prior to calling any UMFPACK routine.
+ *
+ * s = hypot (x,y) computes s = sqrt (x*x + y*y) but does so more accurately.
+ *
+ * The NaN case for the double relops x >= y and x+y == x is safely ignored.
+ */
+
+double umf_hypot (double x, double y)
+{
+ double s, r ;
+ x = SCALAR_ABS (x) ;
+ y = SCALAR_ABS (y) ;
+ if (x >= y)
+ {
+ if (x + y == x)
+ {
+ s = x ;
+ }
+ else
+ {
+ r = y / x ;
+ s = x * sqrt (1.0 + r*r) ;
+ }
+ }
+ else
+ {
+ if (y + x == y)
+ {
+ s = y ;
+ }
+ else
+ {
+ r = x / y ;
+ s = y * sqrt (1.0 + r*r) ;
+ }
+ }
+ return (s) ;
+}
+
+
+/* ========================================================================== */
+/* === umf_divcomplex ======================================================= */
+/* ========================================================================== */
+
+/* c = a/b where c, a, and b are complex. The real and imaginary parts are
+ * passed as separate arguments to this routine. The NaN case is ignored
+ * for the double relop br >= bi. Returns TRUE (1) if the denominator is
+ * zero, FALSE (0) otherwise.
+ *
+ * This uses ACM Algo 116, by R. L. Smith, 1962, which tries to avoid
+ * underflow and overflow.
+ *
+ * c can be the same variable as a or b.
+ */
+
+int umf_divcomplex
+(
+ double ar, double ai, /* real and imaginary parts of a */
+ double br, double bi, /* real and imaginary parts of b */
+ double *cr, double *ci /* real and imaginary parts of c */
+)
+{
+ double tr, ti, r, den ;
+ if (SCALAR_ABS (br) >= SCALAR_ABS (bi))
+ {
+ r = bi / br ;
+ den = br + r * bi ;
+ tr = (ar + ai * r) / den ;
+ ti = (ai - ar * r) / den ;
+ }
+ else
+ {
+ r = br / bi ;
+ den = r * br + bi ;
+ tr = (ar * r + ai) / den ;
+ ti = (ai * r - ar) / den ;
+ }
+ *cr = tr ;
+ *ci = ti ;
+ return (SCALAR_IS_ZERO (den)) ;
+}
diff --git a/UMFPACK/Source/umfpack_load_numeric.c b/UMFPACK/Source/umfpack_load_numeric.c
new file mode 100644
index 0000000..a234902
--- /dev/null
+++ b/UMFPACK/Source/umfpack_load_numeric.c
@@ -0,0 +1,161 @@
+/* ========================================================================== */
+/* === UMFPACK_load_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Loads a Numeric object from a file created by
+ umfpack_*_save_numeric.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+#define READ(object,type,n) \
+{ \
+ object = (type *) UMF_malloc (n, sizeof (type)) ; \
+ if (object == (type *) NULL) \
+ { \
+ UMFPACK_free_numeric ((void **) &Numeric) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_out_of_memory) ; \
+ } \
+ if (fread (object, sizeof (type), n, f) != (size_t) n) \
+ { \
+ UMFPACK_free_numeric ((void **) &Numeric) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+ if (ferror (f)) \
+ { \
+ UMFPACK_free_numeric ((void **) &Numeric) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+}
+
+/* ========================================================================== */
+/* === UMFPACK_load_numeric ================================================= */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_load_numeric
+(
+ void **NumericHandle,
+ char *user_filename
+)
+{
+ NumericType *Numeric ;
+ char *filename ;
+ FILE *f ;
+
+ *NumericHandle = (void *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the filename, or use the default name if filename is NULL */
+ /* ---------------------------------------------------------------------- */
+
+ if (user_filename == (char *) NULL)
+ {
+ filename = "numeric.umf" ;
+ }
+ else
+ {
+ filename = user_filename ;
+ }
+ f = fopen (filename, "rb") ;
+ if (!f)
+ {
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the Numeric header from the file, in binary */
+ /* ---------------------------------------------------------------------- */
+
+ Numeric = (NumericType *) UMF_malloc (1, sizeof (NumericType)) ;
+ if (Numeric == (NumericType *) NULL)
+ {
+ fclose (f) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ if (fread (Numeric, sizeof (NumericType), 1, f) != 1)
+ {
+ (void) UMF_free ((void *) Numeric) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+ if (ferror (f))
+ {
+ (void) UMF_free ((void *) Numeric) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ if (Numeric->valid != NUMERIC_VALID || Numeric->n_row <= 0 ||
+ Numeric->n_col <= 0 || Numeric->npiv < 0 || Numeric->ulen < 0 ||
+ Numeric->size <= 0)
+ {
+ /* Numeric does not point to a NumericType object */
+ (void) UMF_free ((void *) Numeric) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ Numeric->D = (Entry *) NULL ;
+ Numeric->Rperm = (Int *) NULL ;
+ Numeric->Cperm = (Int *) NULL ;
+ Numeric->Lpos = (Int *) NULL ;
+ Numeric->Lilen = (Int *) NULL ;
+ Numeric->Lip = (Int *) NULL ;
+ Numeric->Upos = (Int *) NULL ;
+ Numeric->Uilen = (Int *) NULL ;
+ Numeric->Uip = (Int *) NULL ;
+ Numeric->Rs = (double *) NULL ;
+ Numeric->Memory = (Unit *) NULL ;
+ Numeric->Upattern = (Int *) NULL ;
+
+ /* umfpack_free_numeric can now be safely called if an error occurs */
+
+ /* ---------------------------------------------------------------------- */
+ /* read the rest of the Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ READ (Numeric->D, Entry, MIN (Numeric->n_row, Numeric->n_col)+1) ;
+ READ (Numeric->Rperm, Int, Numeric->n_row+1) ;
+ READ (Numeric->Cperm, Int, Numeric->n_col+1) ;
+ READ (Numeric->Lpos, Int, Numeric->npiv+1) ;
+ READ (Numeric->Lilen, Int, Numeric->npiv+1) ;
+ READ (Numeric->Lip, Int, Numeric->npiv+1) ;
+ READ (Numeric->Upos, Int, Numeric->npiv+1) ;
+ READ (Numeric->Uilen, Int, Numeric->npiv+1) ;
+ READ (Numeric->Uip, Int, Numeric->npiv+1) ;
+ if (Numeric->scale != UMFPACK_SCALE_NONE)
+ {
+ READ (Numeric->Rs, double, Numeric->n_row) ;
+ }
+ if (Numeric->ulen > 0)
+ {
+ READ (Numeric->Upattern, Int, Numeric->ulen+1) ;
+ }
+ READ (Numeric->Memory, Unit, Numeric->size) ;
+
+ /* close the file */
+ fclose (f) ;
+
+ /* make sure the Numeric object is valid */
+ if (!UMF_valid_numeric (Numeric))
+ {
+ UMFPACK_free_numeric ((void **) &Numeric) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ *NumericHandle = (void *) Numeric ;
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_load_symbolic.c b/UMFPACK/Source/umfpack_load_symbolic.c
new file mode 100644
index 0000000..10db361
--- /dev/null
+++ b/UMFPACK/Source/umfpack_load_symbolic.c
@@ -0,0 +1,165 @@
+/* ========================================================================== */
+/* === UMFPACK_load_symbolic ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Loads a Symbolic object from a file created by
+ umfpack_*_save_symbolic.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+#define READ(object,type,n) \
+{ \
+ object = (type *) UMF_malloc (n, sizeof (type)) ; \
+ if (object == (type *) NULL) \
+ { \
+ UMFPACK_free_symbolic ((void **) &Symbolic) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_out_of_memory) ; \
+ } \
+ if (fread (object, sizeof (type), n, f) != (size_t) n) \
+ { \
+ UMFPACK_free_symbolic ((void **) &Symbolic) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+ if (ferror (f)) \
+ { \
+ UMFPACK_free_symbolic ((void **) &Symbolic) ; \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+}
+
+/* ========================================================================== */
+/* === UMFPACK_load_symbolic ================================================ */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_load_symbolic
+(
+ void **SymbolicHandle,
+ char *user_filename
+)
+{
+ SymbolicType *Symbolic ;
+ char *filename ;
+ FILE *f ;
+
+ *SymbolicHandle = (void *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the filename, or use the default name if filename is NULL */
+ /* ---------------------------------------------------------------------- */
+
+ if (user_filename == (char *) NULL)
+ {
+ filename = "symbolic.umf" ;
+ }
+ else
+ {
+ filename = user_filename ;
+ }
+ f = fopen (filename, "rb") ;
+ if (!f)
+ {
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* read the Symbolic header from the file, in binary */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic = (SymbolicType *) UMF_malloc (1, sizeof (SymbolicType)) ;
+ if (Symbolic == (SymbolicType *) NULL)
+ {
+ fclose (f) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ if (fread (Symbolic, sizeof (SymbolicType), 1, f) != 1)
+ {
+ (void) UMF_free ((void *) Symbolic) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+ if (ferror (f))
+ {
+ (void) UMF_free ((void *) Symbolic) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ if (Symbolic->valid != SYMBOLIC_VALID || Symbolic->n_row <= 0 ||
+ Symbolic->n_col <= 0 || Symbolic->nfr < 0 || Symbolic->nchains < 0 ||
+ Symbolic->esize < 0)
+ {
+ /* Symbolic does not point to a Symbolic object */
+ (void) UMF_free ((void *) Symbolic) ;
+ fclose (f) ;
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ Symbolic->Cperm_init = (Int *) NULL ;
+ Symbolic->Rperm_init = (Int *) NULL ;
+ Symbolic->Front_npivcol = (Int *) NULL ;
+ Symbolic->Front_parent = (Int *) NULL ;
+ Symbolic->Front_1strow = (Int *) NULL ;
+ Symbolic->Front_leftmostdesc = (Int *) NULL ;
+ Symbolic->Chain_start = (Int *) NULL ;
+ Symbolic->Chain_maxrows = (Int *) NULL ;
+ Symbolic->Chain_maxcols = (Int *) NULL ;
+ Symbolic->Cdeg = (Int *) NULL ;
+ Symbolic->Rdeg = (Int *) NULL ;
+ Symbolic->Esize = (Int *) NULL ;
+ Symbolic->Diagonal_map = (Int *) NULL ;
+
+ /* umfpack_free_symbolic can now be safely called if an error occurs */
+
+ /* ---------------------------------------------------------------------- */
+ /* read the rest of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ READ (Symbolic->Cperm_init, Int, Symbolic->n_col+1) ;
+ READ (Symbolic->Rperm_init, Int, Symbolic->n_row+1) ;
+ READ (Symbolic->Front_npivcol, Int, Symbolic->nfr+1) ;
+ READ (Symbolic->Front_parent, Int, Symbolic->nfr+1) ;
+ READ (Symbolic->Front_1strow, Int, Symbolic->nfr+1) ;
+ READ (Symbolic->Front_leftmostdesc, Int, Symbolic->nfr+1) ;
+ READ (Symbolic->Chain_start, Int, Symbolic->nchains+1) ;
+ READ (Symbolic->Chain_maxrows, Int, Symbolic->nchains+1) ;
+ READ (Symbolic->Chain_maxcols, Int, Symbolic->nchains+1) ;
+ READ (Symbolic->Cdeg, Int, Symbolic->n_col+1) ;
+ READ (Symbolic->Rdeg, Int, Symbolic->n_row+1) ;
+ if (Symbolic->esize > 0)
+ {
+ /* only when dense rows are present */
+ READ (Symbolic->Esize, Int, Symbolic->esize) ;
+ }
+ if (Symbolic->prefer_diagonal)
+ {
+ /* only when diagonal pivoting is prefered */
+ READ (Symbolic->Diagonal_map, Int, Symbolic->n_col+1) ;
+ }
+
+ /* close the file */
+ fclose (f) ;
+
+ /* make sure the Symbolic object is valid */
+ if (!UMF_valid_symbolic (Symbolic))
+ {
+ UMFPACK_free_symbolic ((void **) &Symbolic) ;
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ *SymbolicHandle = (void *) Symbolic ;
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_numeric.c b/UMFPACK/Source/umfpack_numeric.c
new file mode 100644
index 0000000..a96a9fd
--- /dev/null
+++ b/UMFPACK/Source/umfpack_numeric.c
@@ -0,0 +1,792 @@
+/* ========================================================================== */
+/* === UMFPACK_numeric ====================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Factorizes A into its LU factors, given a symbolic
+ pre-analysis computed by UMFPACK_symbolic. See umfpack_numeric.h for a
+ description.
+
+ Dynamic memory allocation: substantial. See comments (1) through (7),
+ below. If an error occurs, all allocated space is free'd by UMF_free.
+ If successful, the Numeric object contains 11 to 13 objects allocated by
+ UMF_malloc that hold the LU factors of the input matrix.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+#include "umf_set_stats.h"
+#include "umf_kernel.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+#include "umf_realloc.h"
+
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+
+PRIVATE Int work_alloc
+(
+ WorkType *Work,
+ SymbolicType *Symbolic
+) ;
+
+PRIVATE void free_work
+(
+ WorkType *Work
+) ;
+
+PRIVATE Int numeric_alloc
+(
+ NumericType **NumericHandle,
+ SymbolicType *Symbolic,
+ double alloc_init,
+ Int scale
+) ;
+
+PRIVATE void error
+(
+ NumericType **Numeric,
+ WorkType *Work
+) ;
+
+
+/* ========================================================================== */
+/* === UMFPACK_numeric ====================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_numeric
+(
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ void *SymbolicHandle,
+ void **NumericHandle,
+ const double Control [UMFPACK_CONTROL],
+ double User_Info [UMFPACK_INFO]
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double Info2 [UMFPACK_INFO], alloc_init, relpt, relpt2, droptol,
+ front_alloc_init, stats [2] ;
+ double *Info ;
+ WorkType WorkSpace, *Work ;
+ NumericType *Numeric ;
+ SymbolicType *Symbolic ;
+ Int n_row, n_col, n_inner, newsize, i, status, *inew, npiv, ulen, scale ;
+ Unit *mnew ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the amount of time used by the process so far */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (stats) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initialize and check inputs */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ UMF_dump_start ( ) ;
+ init_count = UMF_malloc_count ;
+ DEBUGm4 (("\nUMFPACK numeric: U transpose version\n")) ;
+#endif
+
+ /* If front_alloc_init negative then allocate that size of front in
+ * UMF_start_front. If alloc_init negative, then allocate that initial
+ * size of Numeric->Memory. */
+
+ relpt = GET_CONTROL (UMFPACK_PIVOT_TOLERANCE,
+ UMFPACK_DEFAULT_PIVOT_TOLERANCE) ;
+ relpt2 = GET_CONTROL (UMFPACK_SYM_PIVOT_TOLERANCE,
+ UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE) ;
+ alloc_init = GET_CONTROL (UMFPACK_ALLOC_INIT, UMFPACK_DEFAULT_ALLOC_INIT) ;
+ front_alloc_init = GET_CONTROL (UMFPACK_FRONT_ALLOC_INIT,
+ UMFPACK_DEFAULT_FRONT_ALLOC_INIT) ;
+ scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ;
+ droptol = GET_CONTROL (UMFPACK_DROPTOL, UMFPACK_DEFAULT_DROPTOL) ;
+
+ relpt = MAX (0.0, MIN (relpt, 1.0)) ;
+ relpt2 = MAX (0.0, MIN (relpt2, 1.0)) ;
+ droptol = MAX (0.0, droptol) ;
+ front_alloc_init = MIN (1.0, front_alloc_init) ;
+
+ if (scale != UMFPACK_SCALE_NONE && scale != UMFPACK_SCALE_MAX)
+ {
+ scale = UMFPACK_DEFAULT_SCALE ;
+ }
+
+ if (User_Info != (double *) NULL)
+ {
+ /* return Info in user's array */
+ Info = User_Info ;
+ /* clear the parts of Info that are set by UMFPACK_numeric */
+ for (i = UMFPACK_NUMERIC_SIZE ; i <= UMFPACK_MAX_FRONT_NCOLS ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ for (i = UMFPACK_NUMERIC_DEFRAG ; i < UMFPACK_IR_TAKEN ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ }
+ else
+ {
+ /* no Info array passed - use local one instead */
+ Info = Info2 ;
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ }
+
+ Symbolic = (SymbolicType *) SymbolicHandle ;
+ Numeric = (NumericType *) NULL ;
+ if (!UMF_valid_symbolic (Symbolic))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Symbolic_object ;
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ /* compute alloc_init automatically for AMD ordering */
+ if (Symbolic->ordering == UMFPACK_ORDERING_AMD && alloc_init >= 0)
+ {
+ alloc_init = (Symbolic->nz + Symbolic->amd_lunz) / Symbolic->lunz_bound;
+ alloc_init = MIN (1.0, alloc_init) ;
+ alloc_init *= UMF_REALLOC_INCREASE ;
+ }
+
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+ n_inner = MIN (n_row, n_col) ;
+
+ /* check for integer overflow in Numeric->Memory minimum size */
+ if (INT_OVERFLOW (Symbolic->dnum_mem_init_usage * sizeof (Unit)))
+ {
+ /* :: int overflow, initial Numeric->Memory size :: */
+ /* There's no hope to allocate a Numeric object big enough simply to
+ * hold the initial matrix, so return an out-of-memory condition */
+ DEBUGm4 (("out of memory: numeric int overflow\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ Info [UMFPACK_STATUS] = UMFPACK_OK ;
+ Info [UMFPACK_NROW] = n_row ;
+ Info [UMFPACK_NCOL] = n_col ;
+ Info [UMFPACK_SIZE_OF_UNIT] = (double) (sizeof (Unit)) ;
+
+ if (!Ap || !Ai || !Ax || !NumericHandle)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ Info [UMFPACK_NZ] = Ap [n_col] ;
+ *NumericHandle = (void *) NULL ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the Work object */
+ /* ---------------------------------------------------------------------- */
+
+ /* (1) calls UMF_malloc 15 or 17 times, to obtain temporary workspace of
+ * size c+1 Entry's and 2*(n_row+1) + 3*(n_col+1) + (n_col+n_inner+1) +
+ * (nn+1) + * 3*(c+1) + 2*(r+1) + max(r,c) + (nfr+1) integers plus 2*nn
+ * more integers if diagonal pivoting is to be done. r is the maximum
+ * number of rows in any frontal matrix, c is the maximum number of columns
+ * in any frontal matrix, n_inner is min (n_row,n_col), nn is
+ * max (n_row,n_col), and nfr is the number of frontal matrices. For a
+ * square matrix, this is c+1 Entry's and about 8n + 3c + 2r + max(r,c) +
+ * nfr integers, plus 2n more for diagonal pivoting.
+ */
+
+ Work = &WorkSpace ;
+ Work->n_row = n_row ;
+ Work->n_col = n_col ;
+ Work->nfr = Symbolic->nfr ;
+ Work->nb = Symbolic->nb ;
+ Work->n1 = Symbolic->n1 ;
+
+ if (!work_alloc (Work, Symbolic))
+ {
+ DEBUGm4 (("out of memory: numeric work\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Numeric, Work) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ ASSERT (UMF_malloc_count == init_count + 16 + 2*Symbolic->prefer_diagonal) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ /* (2) calls UMF_malloc 10 or 11 times, for a total space of
+ * sizeof (NumericType) bytes, 4*(n_row+1) + 4*(n_row+1) integers, and
+ * (n_inner+1) Entry's, plus n_row Entry's if row scaling is to be done.
+ * sizeof (NumericType) is a small constant. Next, it calls UMF_malloc
+ * once, for the variable-sized part of the Numeric object
+ * (Numeric->Memory). The size of this object is the larger of
+ * (Control [UMFPACK_ALLOC_INIT]) * (the approximate upper bound computed
+ * by UMFPACK_symbolic), and the minimum required to start the numerical
+ * factorization. * This request is reduced if it fails.
+ */
+
+ if (!numeric_alloc (&Numeric, Symbolic, alloc_init, scale))
+ {
+ DEBUGm4 (("out of memory: initial numeric\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Numeric, Work) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
+ init_count, UMF_malloc_count)) ;
+ ASSERT (UMF_malloc_count == init_count
+ + (16 + 2*Symbolic->prefer_diagonal)
+ + (11 + (scale != UMFPACK_SCALE_NONE))) ;
+
+ /* set control parameters */
+ Numeric->relpt = relpt ;
+ Numeric->relpt2 = relpt2 ;
+ Numeric->droptol = droptol ;
+ Numeric->alloc_init = alloc_init ;
+ Numeric->front_alloc_init = front_alloc_init ;
+ Numeric->scale = scale ;
+
+ DEBUG0 (("umf relpt %g %g init %g %g inc %g red %g\n",
+ relpt, relpt2, alloc_init, front_alloc_init,
+ UMF_REALLOC_INCREASE, UMF_REALLOC_REDUCTION)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* scale and factorize */
+ /* ---------------------------------------------------------------------- */
+
+ /* (3) During numerical factorization (inside UMF_kernel), the variable-size
+ * block of memory is increased in size via a call to UMF_realloc if it is
+ * found to be too small. During factorization, this block holds the
+ * pattern and values of L and U at the top end, and the elements
+ * (contibution blocks) and the current frontal matrix (Work->F*) at the
+ * bottom end. The peak size of the variable-sized object is estimated in
+ * UMFPACK_*symbolic (Info [UMFPACK_VARIABLE_PEAK_ESTIMATE]), although this
+ * upper bound can be very loose. The size of the Symbolic object
+ * (which is currently allocated) is in Info [UMFPACK_SYMBOLIC_SIZE], and
+ * is between 2*n and 13*n integers.
+ */
+
+ DEBUG0 (("Calling umf_kernel\n")) ;
+ status = UMF_kernel (Ap, Ai, Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Numeric, Work, Symbolic) ;
+
+ Info [UMFPACK_STATUS] = status ;
+ if (status < UMFPACK_OK)
+ {
+ /* out of memory, or pattern has changed */
+ error (&Numeric, Work) ;
+ return (status) ;
+ }
+
+ Info [UMFPACK_FORCED_UPDATES] = Work->nforced ;
+ Info [UMFPACK_VARIABLE_INIT] = Numeric->init_usage ;
+ if (Symbolic->prefer_diagonal)
+ {
+ Info [UMFPACK_NOFF_DIAG] = Work->noff_diagonal ;
+ }
+
+ DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
+ init_count, UMF_malloc_count)) ;
+
+ npiv = Numeric->npiv ; /* = n_inner for nonsingular matrices */
+ ulen = Numeric->ulen ; /* = 0 for square nonsingular matrices */
+
+ /* ---------------------------------------------------------------------- */
+ /* free Work object */
+ /* ---------------------------------------------------------------------- */
+
+ /* (4) After numerical factorization all of the objects allocated in step
+ * (1) are freed via UMF_free, except that one object of size n_col+1 is
+ * kept if there are off-diagonal nonzeros in the last pivot row (can only
+ * occur for singular or rectangular matrices). This is Work->Upattern,
+ * which is transfered to Numeric->Upattern if ulen > 0.
+ */
+
+ DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
+ init_count, UMF_malloc_count)) ;
+
+ free_work (Work) ;
+
+ DEBUG0 (("malloc: init_count "ID" UMF_malloc_count "ID"\n",
+ init_count, UMF_malloc_count)) ;
+ DEBUG0 (("Numeric->ulen: "ID" scale: "ID"\n", ulen, scale)) ;
+ ASSERT (UMF_malloc_count == init_count + (ulen > 0) +
+ (11 + (scale != UMFPACK_SCALE_NONE))) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce Lpos, Lilen, Lip, Upos, Uilen and Uip to size npiv+1 */
+ /* ---------------------------------------------------------------------- */
+
+ /* (5) Six components of the Numeric object are reduced in size if the
+ * matrix is singular or rectangular. The original size is 3*(n_row+1) +
+ * 3*(n_col+1) integers. The new size is 6*(npiv+1) integers. For
+ * square non-singular matrices, these two sizes are the same.
+ */
+
+ if (npiv < n_row)
+ {
+ /* reduce Lpos, Uilen, and Uip from size n_row+1 to size npiv */
+ inew = (Int *) UMF_realloc (Numeric->Lpos, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Lpos = inew ;
+ }
+ inew = (Int *) UMF_realloc (Numeric->Uilen, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Uilen = inew ;
+ }
+ inew = (Int *) UMF_realloc (Numeric->Uip, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Uip = inew ;
+ }
+ }
+
+ if (npiv < n_col)
+ {
+ /* reduce Upos, Lilen, and Lip from size n_col+1 to size npiv */
+ inew = (Int *) UMF_realloc (Numeric->Upos, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Upos = inew ;
+ }
+ inew = (Int *) UMF_realloc (Numeric->Lilen, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Lilen = inew ;
+ }
+ inew = (Int *) UMF_realloc (Numeric->Lip, npiv+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Lip = inew ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce Numeric->Upattern from size n_col+1 to size ulen+1 */
+ /* ---------------------------------------------------------------------- */
+
+ /* (6) The size of Numeric->Upattern (formerly Work->Upattern) is reduced
+ * from size n_col+1 to size ulen + 1. If ulen is zero, the object does
+ * not exist. */
+
+ DEBUG4 (("ulen: "ID" Upattern "ID"\n", ulen, (Int) Numeric->Upattern)) ;
+ ASSERT (IMPLIES (ulen == 0, Numeric->Upattern == (Int *) NULL)) ;
+ if (ulen > 0 && ulen < n_col)
+ {
+ inew = (Int *) UMF_realloc (Numeric->Upattern, ulen+1, sizeof (Int)) ;
+ if (inew)
+ {
+ Numeric->Upattern = inew ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* reduce Numeric->Memory to hold just the LU factors at the head */
+ /* ---------------------------------------------------------------------- */
+
+ /* (7) The variable-sized block (Numeric->Memory) is reduced to hold just L
+ * and U, via a call to UMF_realloc, since the frontal matrices are no
+ * longer needed.
+ */
+
+ newsize = Numeric->ihead ;
+ if (newsize < Numeric->size)
+ {
+ mnew = (Unit *) UMF_realloc (Numeric->Memory, newsize, sizeof (Unit)) ;
+ if (mnew)
+ {
+ /* realloc succeeded (how can it fail since the size is reduced?) */
+ Numeric->Memory = mnew ;
+ Numeric->size = newsize ;
+ }
+ }
+ Numeric->ihead = Numeric->size ;
+ Numeric->itail = Numeric->ihead ;
+ Numeric->tail_usage = 0 ;
+ Numeric->ibig = EMPTY ;
+ /* UMF_mem_alloc_tail_block can no longer be called (no tail marker) */
+
+ /* ---------------------------------------------------------------------- */
+ /* report the results and return the Numeric object */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_set_stats (
+ Info,
+ Symbolic,
+ (double) Numeric->max_usage, /* actual peak Numeric->Memory */
+ (double) Numeric->size, /* actual final Numeric->Memory */
+ Numeric->flops, /* actual "true flops" */
+ (double) Numeric->lnz + n_inner, /* actual nz in L */
+ (double) Numeric->unz + Numeric->nnzpiv, /* actual nz in U */
+ (double) Numeric->maxfrsize, /* actual largest front size */
+ (double) ulen, /* actual Numeric->Upattern size */
+ (double) npiv, /* actual # pivots found */
+ (double) Numeric->maxnrows, /* actual largest #rows in front */
+ (double) Numeric->maxncols, /* actual largest #cols in front */
+ scale != UMFPACK_SCALE_NONE,
+ Symbolic->prefer_diagonal,
+ ACTUAL) ;
+
+ Info [UMFPACK_ALLOC_INIT_USED] = Numeric->alloc_init ;
+ Info [UMFPACK_NUMERIC_DEFRAG] = Numeric->ngarbage ;
+ Info [UMFPACK_NUMERIC_REALLOC] = Numeric->nrealloc ;
+ Info [UMFPACK_NUMERIC_COSTLY_REALLOC] = Numeric->ncostly ;
+ Info [UMFPACK_COMPRESSED_PATTERN] = Numeric->isize ;
+ Info [UMFPACK_LU_ENTRIES] = Numeric->nLentries + Numeric->nUentries +
+ Numeric->npiv ;
+ Info [UMFPACK_UDIAG_NZ] = Numeric->nnzpiv ;
+ Info [UMFPACK_RSMIN] = Numeric->rsmin ;
+ Info [UMFPACK_RSMAX] = Numeric->rsmax ;
+ Info [UMFPACK_WAS_SCALED] = Numeric->scale ;
+
+ /* nz in L and U with no dropping of small entries */
+ Info [UMFPACK_ALL_LNZ] = Numeric->all_lnz + n_inner ;
+ Info [UMFPACK_ALL_UNZ] = Numeric->all_unz + Numeric->nnzpiv ;
+ Info [UMFPACK_NZDROPPED] =
+ (Numeric->all_lnz - Numeric->lnz)
+ + (Numeric->all_unz - Numeric->unz) ;
+
+ /* estimate of the reciprocal of the condition number. */
+ if (SCALAR_IS_ZERO (Numeric->min_udiag)
+ || SCALAR_IS_ZERO (Numeric->max_udiag)
+ || SCALAR_IS_NAN (Numeric->min_udiag)
+ || SCALAR_IS_NAN (Numeric->max_udiag))
+ {
+ /* rcond is zero if there is any zero or NaN on the diagonal */
+ Numeric->rcond = 0.0 ;
+ }
+ else
+ {
+ /* estimate of the recipricol of the condition number. */
+ /* This is NaN if diagonal is zero-free, but has one or more NaN's. */
+ Numeric->rcond = Numeric->min_udiag / Numeric->max_udiag ;
+ }
+ Info [UMFPACK_UMIN] = Numeric->min_udiag ;
+ Info [UMFPACK_UMAX] = Numeric->max_udiag ;
+ Info [UMFPACK_RCOND] = Numeric->rcond ;
+
+ if (Numeric->nnzpiv < n_inner
+ || SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond))
+ {
+ /* there are zeros and/or NaN's on the diagonal of U */
+ DEBUG0 (("Warning, matrix is singular in umfpack_numeric\n")) ;
+ DEBUG0 (("nnzpiv "ID" n_inner "ID" rcond %g\n", Numeric->nnzpiv,
+ n_inner, Numeric->rcond)) ;
+ status = UMFPACK_WARNING_singular_matrix ;
+ Info [UMFPACK_STATUS] = status ;
+ }
+
+ Numeric->valid = NUMERIC_VALID ;
+ *NumericHandle = (void *) Numeric ;
+
+ /* Numeric has 11 to 13 objects */
+ ASSERT (UMF_malloc_count == init_count + 11 +
+ + (ulen > 0) /* Numeric->Upattern */
+ + (scale != UMFPACK_SCALE_NONE)) ; /* Numeric->Rs */
+
+ /* ---------------------------------------------------------------------- */
+ /* get the time used by UMFPACK_numeric */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_toc (stats) ;
+ Info [UMFPACK_NUMERIC_WALLTIME] = stats [0] ;
+ Info [UMFPACK_NUMERIC_TIME] = stats [1] ;
+
+ /* return UMFPACK_OK or UMFPACK_WARNING_singular_matrix */
+ return (status) ;
+
+}
+
+
+/* ========================================================================== */
+/* === numeric_alloc ======================================================== */
+/* ========================================================================== */
+
+/* Allocate the Numeric object */
+
+PRIVATE Int numeric_alloc
+(
+ NumericType **NumericHandle,
+ SymbolicType *Symbolic,
+ double alloc_init,
+ Int scale
+)
+{
+ double nsize, bsize ;
+ Int n_row, n_col, n_inner, min_usage, trying ;
+ NumericType *Numeric ;
+
+ DEBUG0 (("numeric alloc:\n")) ;
+
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+ n_inner = MIN (n_row, n_col) ;
+ *NumericHandle = (NumericType *) NULL ;
+
+ /* 1 allocation: accounted for in UMF_set_stats (num_On_size1),
+ * free'd in umfpack_free_numeric */
+ Numeric = (NumericType *) UMF_malloc (1, sizeof (NumericType)) ;
+
+ if (!Numeric)
+ {
+ return (FALSE) ; /* out of memory */
+ }
+ Numeric->valid = 0 ;
+ *NumericHandle = Numeric ;
+
+ /* 9 allocations: accounted for in UMF_set_stats (num_On_size1),
+ * free'd in umfpack_free_numeric */
+ Numeric->D = (Entry *) UMF_malloc (n_inner+1, sizeof (Entry)) ;
+ Numeric->Rperm = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ Numeric->Cperm = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Numeric->Lpos = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ Numeric->Lilen = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Numeric->Lip = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Numeric->Upos = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Numeric->Uilen = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ Numeric->Uip = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+
+ /* 1 allocation if scaling: in UMF_set_stats (num_On_size1),
+ * free'd in umfpack_free_numeric */
+ if (scale != UMFPACK_SCALE_NONE)
+ {
+ DEBUG0 (("Allocating scale factors\n")) ;
+ Numeric->Rs = (double *) UMF_malloc (n_row, sizeof (double)) ;
+ }
+ else
+ {
+ DEBUG0 (("No scale factors allocated (R = I)\n")) ;
+ Numeric->Rs = (double *) NULL ;
+ }
+
+ Numeric->Memory = (Unit *) NULL ;
+
+ /* Upattern has already been allocated as part of the Work object. If
+ * the matrix is singular or rectangular, and there are off-diagonal
+ * nonzeros in the last pivot row, then Work->Upattern is not free'd.
+ * Instead it is transfered to Numeric->Upattern. If it exists,
+ * Numeric->Upattern is free'd in umfpack_free_numeric. */
+ Numeric->Upattern = (Int *) NULL ; /* used for singular matrices only */
+
+ if (!Numeric->D || !Numeric->Rperm || !Numeric->Cperm || !Numeric->Upos ||
+ !Numeric->Lpos || !Numeric->Lilen || !Numeric->Uilen || !Numeric->Lip ||
+ !Numeric->Uip || (scale != UMFPACK_SCALE_NONE && !Numeric->Rs))
+ {
+ return (FALSE) ; /* out of memory */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate initial Numeric->Memory for LU factors and elements */
+ /* ---------------------------------------------------------------------- */
+
+ if (alloc_init < 0)
+ {
+ /* -alloc_init is the exact size to initially allocate */
+ nsize = -alloc_init ;
+ }
+ else
+ {
+ /* alloc_init is a ratio of the upper bound memory usage */
+ nsize = (alloc_init * Symbolic->num_mem_usage_est) + 1 ;
+ }
+ min_usage = Symbolic->num_mem_init_usage ;
+
+ /* Numeric->Memory must be large enough for UMF_kernel_init */
+ nsize = MAX (min_usage, nsize) ;
+
+ /* Numeric->Memory cannot be larger in size than Int_MAX / sizeof(Unit) */
+ /* For ILP32 mode: 2GB (nsize cannot be bigger than 256 Mwords) */
+ bsize = ((double) Int_MAX) / sizeof (Unit) - 1 ;
+ DEBUG0 (("bsize %g\n", bsize)) ;
+ nsize = MIN (nsize, bsize) ;
+
+ Numeric->size = (Int) nsize ;
+
+ DEBUG0 (("Num init %g usage_est %g numsize "ID" minusage "ID"\n",
+ alloc_init, Symbolic->num_mem_usage_est, Numeric->size, min_usage)) ;
+
+ /* allocates 1 object: */
+ /* keep trying until successful, or memory request is too small */
+ trying = TRUE ;
+ while (trying)
+ {
+ Numeric->Memory = (Unit *) UMF_malloc (Numeric->size, sizeof (Unit)) ;
+ if (Numeric->Memory)
+ {
+ DEBUG0 (("Successful Numeric->size: "ID"\n", Numeric->size)) ;
+ return (TRUE) ;
+ }
+ /* too much, reduce the request (but not below the minimum) */
+ /* and try again */
+ trying = Numeric->size > min_usage ;
+ Numeric->size = (Int)
+ (UMF_REALLOC_REDUCTION * ((double) Numeric->size)) ;
+ Numeric->size = MAX (min_usage, Numeric->size) ;
+ }
+
+ return (FALSE) ; /* we failed to allocate Numeric->Memory */
+}
+
+
+/* ========================================================================== */
+/* === work_alloc =========================================================== */
+/* ========================================================================== */
+
+/* Allocate the Work object. Return TRUE if successful. */
+
+PRIVATE Int work_alloc
+(
+ WorkType *Work,
+ SymbolicType *Symbolic
+)
+{
+ Int n_row, n_col, nn, maxnrows, maxncols, nfr, ok, maxnrc, n1 ;
+
+ n_row = Work->n_row ;
+ n_col = Work->n_col ;
+ nn = MAX (n_row, n_col) ;
+ nfr = Work->nfr ;
+ n1 = Symbolic->n1 ;
+ ASSERT (n1 <= n_row && n1 <= n_col) ;
+
+ maxnrows = Symbolic->maxnrows + Symbolic->nb ;
+ maxnrows = MIN (n_row, maxnrows) ;
+ maxncols = Symbolic->maxncols + Symbolic->nb ;
+ maxncols = MIN (n_col, maxncols) ;
+ maxnrc = MAX (maxnrows, maxncols) ;
+
+ DEBUG0 (("work alloc: maxnrows+nb "ID" maxncols+nb "ID"\n",
+ maxnrows, maxncols)) ;
+
+ /* 15 allocations, freed in free_work: */
+ /* accounted for in UMF_set_stats (work_usage) */
+ Work->Wx = (Entry *) UMF_malloc (maxnrows + 1, sizeof (Entry)) ;
+ Work->Wy = (Entry *) UMF_malloc (maxnrows + 1, sizeof (Entry)) ;
+ Work->Frpos = (Int *) UMF_malloc (n_row + 1, sizeof (Int)) ;
+ Work->Lpattern = (Int *) UMF_malloc (n_row + 1, sizeof (Int)) ;
+ Work->Fcpos = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ;
+ Work->Wp = (Int *) UMF_malloc (nn + 1, sizeof (Int)) ;
+ Work->Wrp = (Int *) UMF_malloc (MAX (n_col,maxnrows) + 1, sizeof (Int)) ;
+ Work->Frows = (Int *) UMF_malloc (maxnrows + 1, sizeof (Int)) ;
+ Work->Wm = (Int *) UMF_malloc (maxnrows + 1, sizeof (Int)) ;
+ Work->Fcols = (Int *) UMF_malloc (maxncols + 1, sizeof (Int)) ;
+ Work->Wio = (Int *) UMF_malloc (maxncols + 1, sizeof (Int)) ;
+ Work->Woi = (Int *) UMF_malloc (maxncols + 1, sizeof (Int)) ;
+ Work->Woo = (Int *) UMF_malloc (maxnrc + 1, sizeof (Int));
+ Work->elen = (n_col - n1) + (n_row - n1) + MIN (n_col-n1, n_row-n1) + 1 ;
+ Work->E = (Int *) UMF_malloc (Work->elen, sizeof (Int)) ;
+ Work->Front_new1strow = (Int *) UMF_malloc (nfr + 1, sizeof (Int)) ;
+
+ ok = (Work->Frpos && Work->Fcpos && Work->Lpattern
+ && Work->Wp && Work->Wrp && Work->Frows && Work->Fcols
+ && Work->Wio && Work->Woi && Work->Woo && Work->Wm
+ && Work->E && Work->Front_new1strow && Work->Wx && Work->Wy) ;
+
+ /* 2 allocations: accounted for in UMF_set_stats (work_usage) */
+ if (Symbolic->prefer_diagonal)
+ {
+ Work->Diagonal_map = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ Work->Diagonal_imap = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ ok = ok && Work->Diagonal_map && Work->Diagonal_imap ;
+ }
+ else
+ {
+ /* no diagonal map needed for rectangular matrices */
+ Work->Diagonal_map = (Int *) NULL ;
+ Work->Diagonal_imap = (Int *) NULL ;
+ }
+
+ /* 1 allocation, may become part of Numeric (if singular or rectangular): */
+ Work->Upattern = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ;
+ ok = ok && Work->Upattern ;
+
+ /* current frontal matrix does not yet exist */
+ Work->Flublock = (Entry *) NULL ;
+ Work->Flblock = (Entry *) NULL ;
+ Work->Fublock = (Entry *) NULL ;
+ Work->Fcblock = (Entry *) NULL ;
+
+ DEBUG0 (("work alloc done.\n")) ;
+ return (ok) ;
+}
+
+
+/* ========================================================================== */
+/* === free_work ============================================================ */
+/* ========================================================================== */
+
+PRIVATE void free_work
+(
+ WorkType *Work
+)
+{
+ DEBUG0 (("work free:\n")) ;
+ if (Work)
+ {
+ /* these 16 objects do exist */
+ Work->Wx = (Entry *) UMF_free ((void *) Work->Wx) ;
+ Work->Wy = (Entry *) UMF_free ((void *) Work->Wy) ;
+ Work->Frpos = (Int *) UMF_free ((void *) Work->Frpos) ;
+ Work->Fcpos = (Int *) UMF_free ((void *) Work->Fcpos) ;
+ Work->Lpattern = (Int *) UMF_free ((void *) Work->Lpattern) ;
+ Work->Upattern = (Int *) UMF_free ((void *) Work->Upattern) ;
+ Work->Wp = (Int *) UMF_free ((void *) Work->Wp) ;
+ Work->Wrp = (Int *) UMF_free ((void *) Work->Wrp) ;
+ Work->Frows = (Int *) UMF_free ((void *) Work->Frows) ;
+ Work->Fcols = (Int *) UMF_free ((void *) Work->Fcols) ;
+ Work->Wio = (Int *) UMF_free ((void *) Work->Wio) ;
+ Work->Woi = (Int *) UMF_free ((void *) Work->Woi) ;
+ Work->Woo = (Int *) UMF_free ((void *) Work->Woo) ;
+ Work->Wm = (Int *) UMF_free ((void *) Work->Wm) ;
+ Work->E = (Int *) UMF_free ((void *) Work->E) ;
+ Work->Front_new1strow =
+ (Int *) UMF_free ((void *) Work->Front_new1strow) ;
+
+ /* these objects might not exist */
+ Work->Diagonal_map = (Int *) UMF_free ((void *) Work->Diagonal_map) ;
+ Work->Diagonal_imap = (Int *) UMF_free ((void *) Work->Diagonal_imap) ;
+ }
+ DEBUG0 (("work free done.\n")) ;
+}
+
+
+/* ========================================================================== */
+/* === error ================================================================ */
+/* ========================================================================== */
+
+/* Error return from UMFPACK_numeric. Free all allocated memory. */
+
+PRIVATE void error
+(
+ NumericType **Numeric,
+ WorkType *Work
+)
+{
+ free_work (Work) ;
+ UMFPACK_free_numeric ((void **) Numeric) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+}
diff --git a/UMFPACK/Source/umfpack_qsymbolic.c b/UMFPACK/Source/umfpack_qsymbolic.c
new file mode 100644
index 0000000..3e2674f
--- /dev/null
+++ b/UMFPACK/Source/umfpack_qsymbolic.c
@@ -0,0 +1,2411 @@
+/* ========================================================================== */
+/* === UMFPACK_qsymbolic ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Performs a symbolic factorization.
+ See umfpack_qsymbolic.h and umfpack_symbolic.h for details.
+
+ Dynamic memory usage: about (3.4nz + 8n + n) integers and n double's as
+ workspace (via UMF_malloc, for a square matrix). All of it is free'd via
+ UMF_free if an error occurs. If successful, the Symbolic object contains
+ 12 to 14 objects allocated by UMF_malloc, with a total size of no more
+ than about 13*n integers.
+*/
+
+#include "umf_internal.h"
+#include "umf_symbolic_usage.h"
+#include "umf_colamd.h"
+#include "umf_set_stats.h"
+#include "umf_analyze.h"
+#include "umf_transpose.h"
+#include "umf_is_permutation.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+#include "umf_2by2.h"
+#include "umf_singletons.h"
+
+typedef struct /* SWType */
+{
+ Int *Front_npivcol ; /* size n_col + 1 */
+ Int *Front_nrows ; /* size n_col */
+ Int *Front_ncols ; /* size n_col */
+ Int *Front_parent ; /* size n_col */
+ Int *Front_cols ; /* size n_col */
+ Int *InFront ; /* size n_row */
+ Int *Ci ; /* size Clen */
+ Int *Cperm1 ; /* size n_col */
+ Int *Rperm1 ; /* size n_row */
+ Int *InvRperm1 ; /* size n_row */
+ Int *Si ; /* size nz */
+ Int *Sp ; /* size n_col + 1 */
+ double *Rs ; /* size n_row */
+ Int *Rperm_2by2 ; /* size n_row */
+
+} SWType ;
+
+PRIVATE void free_work
+(
+ SWType *SW
+) ;
+
+PRIVATE void error
+(
+ SymbolicType **Symbolic,
+ SWType *SW
+) ;
+
+/* worst-case usage for SW object */
+#define SYM_WORK_USAGE(n_col,n_row,Clen) \
+ (DUNITS (Int, Clen) + \
+ DUNITS (Int, nz) + \
+ 4 * DUNITS (Int, n_row) + \
+ 4 * DUNITS (Int, n_col) + \
+ 2 * DUNITS (Int, n_col + 1) + \
+ DUNITS (double, n_row))
+
+/* required size of Ci for code that calls UMF_transpose and UMF_analyze below*/
+#define UMF_ANALYZE_CLEN(nz,n_row,n_col,nn) \
+ ((n_col) + MAX ((nz),(n_col)) + 3*(nn)+1 + (n_col))
+
+/* size of an element (in Units), including tuples */
+#define ELEMENT_SIZE(r,c) \
+ (DGET_ELEMENT_SIZE (r, c) + 1 + (r + c) * UNITS (Tuple, 1))
+
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+
+/* ========================================================================== */
+/* === do_amd =============================================================== */
+/* ========================================================================== */
+
+PRIVATE void do_amd
+(
+ Int n,
+ const Int Ap [ ], /* size n+1 */
+ const Int Ai [ ], /* size nz = Ap [n] */
+ Int Q [ ], /* output permutation, j = Q [k] */
+ Int Qinv [ ], /* output inverse permutation, Qinv [j] = k */
+ Int Sdeg [ ], /* degree of A+A', from AMD_aat */
+ Int Clen, /* size of Ci */
+ Int Ci [ ], /* size Ci workspace */
+ double amd_Control [ ], /* AMD control parameters */
+ double amd_Info [ ], /* AMD info */
+ SymbolicType *Symbolic, /* Symbolic object */
+ double Info [ ] /* UMFPACK info */
+)
+{
+
+ if (n == 0)
+ {
+ Symbolic->amd_dmax = 0 ;
+ Symbolic->amd_lunz = 0 ;
+ Info [UMFPACK_SYMMETRIC_LUNZ] = 0 ;
+ Info [UMFPACK_SYMMETRIC_FLOPS] = 0 ;
+ Info [UMFPACK_SYMMETRIC_DMAX] = 0 ;
+ Info [UMFPACK_SYMMETRIC_NDENSE] = 0 ;
+ }
+ else
+ {
+ AMD_1 (n, Ap, Ai, Q, Qinv, Sdeg, Clen, Ci, amd_Control, amd_Info) ;
+
+ /* return estimates computed from AMD on PA+PA' */
+ Symbolic->amd_dmax = amd_Info [AMD_DMAX] ;
+ Symbolic->amd_lunz = 2 * amd_Info [AMD_LNZ] + n ;
+ Info [UMFPACK_SYMMETRIC_LUNZ] = Symbolic->amd_lunz ;
+ Info [UMFPACK_SYMMETRIC_FLOPS] = DIV_FLOPS * amd_Info [AMD_NDIV] +
+ MULTSUB_FLOPS * amd_Info [AMD_NMULTSUBS_LU] ;
+ Info [UMFPACK_SYMMETRIC_DMAX] = Symbolic->amd_dmax ;
+ Info [UMFPACK_SYMMETRIC_NDENSE] = amd_Info [AMD_NDENSE] ;
+ Info [UMFPACK_SYMBOLIC_DEFRAG] += amd_Info [AMD_NCMPA] ;
+ }
+}
+
+/* ========================================================================== */
+/* === prune_singletons ===================================================== */
+/* ========================================================================== */
+
+/* Create the submatrix after removing the n1 singletons. The matrix has
+ * row and column indices in the range 0 to n_row-n1 and 0 to n_col-n1,
+ * respectively. */
+
+PRIVATE Int prune_singletons
+(
+ Int n1,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ Int Cperm1 [ ],
+ Int InvRperm1 [ ],
+ Int Si [ ],
+ Int Sp [ ]
+#ifndef NDEBUG
+ , Int Rperm1 [ ]
+ , Int n_row
+#endif
+)
+{
+ Int row, k, pp, p, oldcol, newcol, newrow, nzdiag, do_nzdiag ;
+#ifdef COMPLEX
+ Int split = SPLIT (Az) ;
+#endif
+
+ nzdiag = 0 ;
+ do_nzdiag = (Ax != (double *) NULL) ;
+
+#ifndef NDEBUG
+ DEBUGm4 (("Prune : S = A (Cperm1 (n1+1:end), Rperm1 (n1+1:end))\n")) ;
+ for (k = 0 ; k < n_row ; k++)
+ {
+ ASSERT (Rperm1 [k] >= 0 && Rperm1 [k] < n_row) ;
+ ASSERT (InvRperm1 [Rperm1 [k]] == k) ;
+ }
+#endif
+
+ /* create the submatrix after removing singletons */
+
+ pp = 0 ;
+ for (k = n1 ; k < n_col ; k++)
+ {
+ oldcol = Cperm1 [k] ;
+ newcol = k - n1 ;
+ DEBUG5 (("Prune singletons k "ID" oldcol "ID" newcol "ID": "ID"\n",
+ k, oldcol, newcol, pp)) ;
+ Sp [newcol] = pp ; /* load column pointers */
+ for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++)
+ {
+ row = Ai [p] ;
+ DEBUG5 ((" "ID": row "ID, pp, row)) ;
+ ASSERT (row >= 0 && row < n_row) ;
+ newrow = InvRperm1 [row] - n1 ;
+ ASSERT (newrow < n_row - n1) ;
+ if (newrow >= 0)
+ {
+ DEBUG5 ((" newrow "ID, newrow)) ;
+ Si [pp++] = newrow ;
+ if (do_nzdiag)
+ {
+ /* count the number of truly nonzero entries on the
+ * diagonal of S, excluding entries that are present,
+ * but numerically zero */
+ if (newrow == newcol)
+ {
+ /* this is the diagonal entry */
+#ifdef COMPLEX
+ if (split)
+ {
+ if (SCALAR_IS_NONZERO (Ax [p]) ||
+ SCALAR_IS_NONZERO (Az [p]))
+ {
+ nzdiag++ ;
+ }
+ }
+ else
+ {
+ if (SCALAR_IS_NONZERO (Ax [2*p ]) ||
+ SCALAR_IS_NONZERO (Ax [2*p+1]))
+ {
+ nzdiag++ ;
+ }
+ }
+#else
+ if (SCALAR_IS_NONZERO (Ax [p]))
+ {
+ nzdiag++ ;
+ }
+#endif
+ }
+ }
+ }
+ DEBUG5 (("\n")) ;
+ }
+ }
+ Sp [n_col - n1] = pp ;
+
+ return (nzdiag) ;
+}
+
+/* ========================================================================== */
+/* === combine_ordering ===================================================== */
+/* ========================================================================== */
+
+PRIVATE void combine_ordering
+(
+ Int n1,
+ Int nempty_col,
+ Int n_col,
+ Int Cperm_init [ ], /* output permutation */
+ Int Cperm1 [ ], /* singleton and empty column ordering */
+ Int Qinv [ ] /* Qinv from AMD or COLAMD */
+)
+{
+ Int k, oldcol, newcol, knew ;
+
+ /* combine the singleton ordering with Qinv */
+#ifndef NDEBUG
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Cperm_init [k] = EMPTY ;
+ }
+#endif
+ for (k = 0 ; k < n1 ; k++)
+ {
+ DEBUG1 ((ID" Initial singleton: "ID"\n", k, Cperm1 [k])) ;
+ Cperm_init [k] = Cperm1 [k] ;
+ }
+ for (k = n1 ; k < n_col - nempty_col ; k++)
+ {
+ /* this is a non-singleton column */
+ oldcol = Cperm1 [k] ; /* user's name for this column */
+ newcol = k - n1 ; /* Qinv's name for this column */
+ knew = Qinv [newcol] ; /* Qinv's ordering for this column */
+ knew += n1 ; /* shift order, after singletons */
+ DEBUG1 ((" k "ID" oldcol "ID" newcol "ID" knew "ID"\n",
+ k, oldcol, newcol, knew)) ;
+ ASSERT (knew >= 0 && knew < n_col - nempty_col) ;
+ ASSERT (Cperm_init [knew] == EMPTY) ;
+ Cperm_init [knew] = oldcol ;
+ }
+ for (k = n_col - nempty_col ; k < n_col ; k++)
+ {
+ Cperm_init [k] = Cperm1 [k] ;
+ }
+#ifndef NDEBUG
+ {
+ Int *W = (Int *) malloc ((n_col + 1) * sizeof (Int)) ;
+ ASSERT (UMF_is_permutation (Cperm_init, W, n_col, n_col)) ;
+ free (W) ;
+ }
+#endif
+
+}
+
+/* ========================================================================== */
+/* === UMFPACK_qsymbolic ==================================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_qsymbolic
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ const Int Quser [ ],
+ void **SymbolicHandle,
+ const double Control [UMFPACK_CONTROL],
+ double User_Info [UMFPACK_INFO]
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double knobs [COLAMD_KNOBS], flops, f, r, c, force_fixQ,
+ Info2 [UMFPACK_INFO], drow, dcol, dtail_usage, dlf, duf, dmax_usage,
+ dhead_usage, dlnz, dunz, dmaxfrsize, dClen, dClen_analyze, sym,
+ amd_Info [AMD_INFO], dClen_amd, dr, dc, cr, cc, cp,
+ amd_Control [AMD_CONTROL], stats [2], tol ;
+ double *Info ;
+ Int i, nz, j, newj, status, f1, f2, maxnrows, maxncols, nfr, col,
+ nchains, maxrows, maxcols, p, nb, nn, *Chain_start, *Chain_maxrows,
+ *Chain_maxcols, *Front_npivcol, *Ci, Clen, colamd_stats [COLAMD_STATS],
+ fpiv, n_inner, child, parent, *Link, row, *Front_parent,
+ analyze_compactions, k, chain, is_sym, *Si, *Sp, n2, do_UMF_analyze,
+ fpivcol, fallrows, fallcols, *InFront, *F1, snz, *Front_1strow, f1rows,
+ kk, *Cperm_init, *Rperm_init, newrow, *InvRperm1, *Front_leftmostdesc,
+ Clen_analyze, strategy, Clen_amd, fixQ, prefer_diagonal, nzdiag, nzaat,
+ *Wq, *Sdeg, *Fr_npivcol, nempty, *Fr_nrows, *Fr_ncols, *Fr_parent,
+ *Fr_cols, nempty_row, nempty_col, user_auto_strategy, fail, max_rdeg,
+ head_usage, tail_usage, lnz, unz, esize, *Esize, rdeg, *Cdeg, *Rdeg,
+ *Cperm1, *Rperm1, n1, oldcol, newcol, n1c, n1r, *Rperm_2by2, oldrow,
+ dense_row_threshold, tlen, aggressive, scale, *Rp, *Ri ;
+
+ SymbolicType *Symbolic ;
+ SWType SWspace, *SW ;
+
+#ifndef NDEBUG
+ UMF_dump_start ( ) ;
+ init_count = UMF_malloc_count ;
+ PRINTF ((
+"**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n"
+ )) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get the amount of time used by the process so far */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (stats) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get control settings and check input parameters */
+ /* ---------------------------------------------------------------------- */
+
+ drow = GET_CONTROL (UMFPACK_DENSE_ROW, UMFPACK_DEFAULT_DENSE_ROW) ;
+ dcol = GET_CONTROL (UMFPACK_DENSE_COL, UMFPACK_DEFAULT_DENSE_COL) ;
+ nb = GET_CONTROL (UMFPACK_BLOCK_SIZE, UMFPACK_DEFAULT_BLOCK_SIZE) ;
+ strategy = GET_CONTROL (UMFPACK_STRATEGY, UMFPACK_DEFAULT_STRATEGY) ;
+ tol = GET_CONTROL (UMFPACK_2BY2_TOLERANCE, UMFPACK_DEFAULT_2BY2_TOLERANCE) ;
+ scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ;
+ force_fixQ = GET_CONTROL (UMFPACK_FIXQ, UMFPACK_DEFAULT_FIXQ) ;
+ AMD_defaults (amd_Control) ;
+ amd_Control [AMD_DENSE] =
+ GET_CONTROL (UMFPACK_AMD_DENSE, UMFPACK_DEFAULT_AMD_DENSE) ;
+ aggressive =
+ (GET_CONTROL (UMFPACK_AGGRESSIVE, UMFPACK_DEFAULT_AGGRESSIVE) != 0) ;
+ amd_Control [AMD_AGGRESSIVE] = aggressive ;
+
+ nb = MAX (2, nb) ;
+ nb = MIN (nb, MAXNB) ;
+ ASSERT (nb >= 0) ;
+ if (nb % 2 == 1) nb++ ; /* make sure nb is even */
+ DEBUG0 (("UMFPACK_qsymbolic: nb = "ID" aggressive = "ID"\n", nb,
+ aggressive)) ;
+
+ tol = MAX (0.0, MIN (tol, 1.0)) ;
+ if (scale != UMFPACK_SCALE_NONE && scale != UMFPACK_SCALE_MAX)
+ {
+ scale = UMFPACK_DEFAULT_SCALE ;
+ }
+
+ if (User_Info != (double *) NULL)
+ {
+ /* return Info in user's array */
+ Info = User_Info ;
+ }
+ else
+ {
+ /* no Info array passed - use local one instead */
+ Info = Info2 ;
+ }
+ /* clear all of Info */
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+
+ Info [UMFPACK_STATUS] = UMFPACK_OK ;
+ Info [UMFPACK_NROW] = n_row ;
+ Info [UMFPACK_NCOL] = n_col ;
+ Info [UMFPACK_SIZE_OF_UNIT] = (double) (sizeof (Unit)) ;
+ Info [UMFPACK_SIZE_OF_INT] = (double) (sizeof (int)) ;
+ Info [UMFPACK_SIZE_OF_LONG] = (double) (sizeof (UF_long)) ;
+ Info [UMFPACK_SIZE_OF_POINTER] = (double) (sizeof (void *)) ;
+ Info [UMFPACK_SIZE_OF_ENTRY] = (double) (sizeof (Entry)) ;
+ Info [UMFPACK_SYMBOLIC_DEFRAG] = 0 ;
+
+ if (!Ai || !Ap || !SymbolicHandle)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ *SymbolicHandle = (void *) NULL ;
+
+ if (n_row <= 0 || n_col <= 0) /* n_row, n_col must be > 0 */
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_n_nonpositive ;
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+
+ nz = Ap [n_col] ;
+ DEBUG0 (("n_row "ID" n_col "ID" nz "ID"\n", n_row, n_col, nz)) ;
+ Info [UMFPACK_NZ] = nz ;
+ if (nz < 0)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_matrix ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the requested strategy */
+ /* ---------------------------------------------------------------------- */
+
+ if (n_row != n_col)
+ {
+ /* if the matrix is rectangular, the only available strategy is
+ * unsymmetric */
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ DEBUGm3 (("Rectangular: forcing unsymmetric strategy\n")) ;
+ }
+
+ if (strategy < UMFPACK_STRATEGY_AUTO
+ || strategy > UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ /* unrecognized strategy */
+ strategy = UMFPACK_STRATEGY_AUTO ;
+ }
+
+ if (Quser != (Int *) NULL)
+ {
+ /* when the user provides Q, only symmetric and unsymmetric strategies
+ * are available */
+ if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ strategy = UMFPACK_STRATEGY_SYMMETRIC ;
+ }
+ if (strategy != UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ }
+ }
+
+ user_auto_strategy = (strategy == UMFPACK_STRATEGY_AUTO) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* determine amount of memory required for UMFPACK_symbolic */
+ /* ---------------------------------------------------------------------- */
+
+ /* The size of Clen required for UMF_colamd is always larger than */
+ /* UMF_analyze, but the max is included here in case that changes in */
+ /* future versions. */
+
+ /* This is about 2.2*nz + 9*n_col + 6*n_row, or nz/5 + 13*n_col + 6*n_row,
+ * whichever is bigger. For square matrices, it works out to
+ * 2.2nz + 15n, or nz/5 + 19n, whichever is bigger (typically 2.2nz+15n). */
+ dClen = UMF_COLAMD_RECOMMENDED ((double) nz, (double) n_row,
+ (double) n_col) ;
+
+ /* This is defined above, as max (nz,n_col) + 3*nn+1 + 2*n_col, where
+ * nn = max (n_row,n_col). It is always smaller than the space required
+ * for colamd or amd. */
+ dClen_analyze = UMF_ANALYZE_CLEN ((double) nz, (double) n_row,
+ (double) n_col, (double) nn) ;
+ dClen = MAX (dClen, dClen_analyze) ;
+
+ /* The space for AMD can be larger than what's required for colamd: */
+ dClen_amd = 2.4 * (double) nz + 8 * (double) n_inner ;
+ /* additional space for the 2-by-2 strategy */
+ dClen_amd += (double) MAX (nn, nz) ;
+ dClen = MAX (dClen, dClen_amd) ;
+
+ /* worst case total memory usage for UMFPACK_symbolic (revised below) */
+ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] =
+ SYM_WORK_USAGE (n_col, n_row, dClen) +
+ UMF_symbolic_usage (n_row, n_col, n_col, n_col, n_col, TRUE) ;
+
+ if (INT_OVERFLOW (dClen * sizeof (Int)))
+ {
+ /* :: int overflow, Clen too large :: */
+ /* Problem is too large for array indexing (Ci [i]) with an Int i. */
+ /* Cannot even analyze the problem to determine upper bounds on */
+ /* memory usage. Need to use the UF_long version, umfpack_*l_*. */
+ DEBUGm4 (("out of memory: symbolic int overflow\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ /* repeat the size calculations, in integers */
+ Clen = UMF_COLAMD_RECOMMENDED (nz, n_row, n_col) ;
+ Clen_analyze = UMF_ANALYZE_CLEN (nz, n_row, n_col, nn) ;
+ Clen = MAX (Clen, Clen_analyze) ;
+ Clen_amd = 2.4 * nz + 8 * n_inner ;
+ Clen_amd += MAX (nn, nz) ; /* for Ri, in UMF_2by2 */
+ Clen = MAX (Clen, Clen_amd) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the first part of the Symbolic object (header and Cperm_init) */
+ /* ---------------------------------------------------------------------- */
+
+ /* (1) Five calls to UMF_malloc are made, for a total space of
+ * 2 * (n_row + n_col) + 4 integers + sizeof (SymbolicType).
+ * sizeof (SymbolicType) is a small constant. This space is part of the
+ * Symbolic object and is not freed unless an error occurs. If A is square
+ * then this is about 4*n integers.
+ */
+
+ Symbolic = (SymbolicType *) UMF_malloc (1, sizeof (SymbolicType)) ;
+
+ if (!Symbolic)
+ {
+ /* If we fail here, Symbolic is NULL and thus it won't be */
+ /* dereferenced by UMFPACK_free_symbolic, as called by error ( ). */
+ DEBUGm4 (("out of memory: symbolic object\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, (SWType *) NULL) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ /* We now know that Symbolic has been allocated */
+ Symbolic->valid = 0 ;
+ Symbolic->Chain_start = (Int *) NULL ;
+ Symbolic->Chain_maxrows = (Int *) NULL ;
+ Symbolic->Chain_maxcols = (Int *) NULL ;
+ Symbolic->Front_npivcol = (Int *) NULL ;
+ Symbolic->Front_parent = (Int *) NULL ;
+ Symbolic->Front_1strow = (Int *) NULL ;
+ Symbolic->Front_leftmostdesc = (Int *) NULL ;
+ Symbolic->Esize = (Int *) NULL ;
+ Symbolic->esize = 0 ;
+
+ Symbolic->Cperm_init = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Symbolic->Rperm_init = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ Symbolic->Cdeg = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Symbolic->Rdeg = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ Symbolic->Diagonal_map = (Int *) NULL ;
+
+ Cperm_init = Symbolic->Cperm_init ;
+ Rperm_init = Symbolic->Rperm_init ;
+ Cdeg = Symbolic->Cdeg ;
+ Rdeg = Symbolic->Rdeg ;
+
+ if (!Cperm_init || !Rperm_init || !Cdeg || !Rdeg)
+ {
+ DEBUGm4 (("out of memory: symbolic perm\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, (SWType *) NULL) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ Symbolic->n_row = n_row ;
+ Symbolic->n_col = n_col ;
+ Symbolic->nz = nz ;
+ Symbolic->nb = nb ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check user's input permutation */
+ /* ---------------------------------------------------------------------- */
+
+ if (Quser != (Int *) NULL)
+ {
+ /* use Cperm_init as workspace to check input permutation */
+ if (!UMF_is_permutation (Quser, Cperm_init, n_col, n_col))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_permutation ;
+ error (&Symbolic, (SWType *) NULL) ;
+ return (UMFPACK_ERROR_invalid_permutation) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* (2) Eleven calls to UMF_malloc are made, for workspace of size
+ * Clen + nz + 7*n_col + 2*n_row + 2 integers. Clen is the larger of
+ * MAX (2*nz, 4*n_col) + 8*n_col + 6*n_row + n_col + nz/5 and
+ * 2.4*nz + 8 * MIN (n_row, n_col) + MAX (n_row, n_col, nz)
+ * If A is square and non-singular, then Clen is
+ * MAX (MAX (2*nz, 4*n) + 7*n + nz/5, 3.4*nz) + 8*n
+ * If A has at least 4*n nonzeros then Clen is
+ * MAX (2.2*nz + 7*n, 3.4*nz) + 8*n
+ * If A has at least (7/1.2)*n nonzeros, (about 5.8*n), then Clen is
+ * 3.4*nz + 8*n
+ * This space will be free'd when this routine finishes.
+ *
+ * Total space thus far is about 3.4nz + 12n integers.
+ * For the double precision, 32-bit integer version, the user's matrix
+ * requires an equivalent space of 3*nz + n integers. So this space is just
+ * slightly larger than the user's input matrix (including the numerical
+ * values themselves).
+ */
+
+ SW = &SWspace ; /* used for UMFPACK_symbolic only */
+
+ /* Note that SW->Front_* does not include the dummy placeholder front. */
+ /* This space is accounted for by the SYM_WORK_USAGE macro. */
+
+ /* this is free'd early */
+ SW->Si = (Int *) UMF_malloc (nz, sizeof (Int)) ;
+ SW->Sp = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ;
+ SW->InvRperm1 = (Int *) UMF_malloc (n_row, sizeof (Int)) ;
+ SW->Cperm1 = (Int *) UMF_malloc (n_col, sizeof (Int)) ;
+
+ /* this is free'd late */
+ SW->Ci = (Int *) UMF_malloc (Clen, sizeof (Int)) ;
+ SW->Front_npivcol = (Int *) UMF_malloc (n_col + 1, sizeof (Int)) ;
+ SW->Front_nrows = (Int *) UMF_malloc (n_col, sizeof (Int)) ;
+ SW->Front_ncols = (Int *) UMF_malloc (n_col, sizeof (Int)) ;
+ SW->Front_parent = (Int *) UMF_malloc (n_col, sizeof (Int)) ;
+ SW->Front_cols = (Int *) UMF_malloc (n_col, sizeof (Int)) ;
+ SW->Rperm1 = (Int *) UMF_malloc (n_row, sizeof (Int)) ;
+ SW->InFront = (Int *) UMF_malloc (n_row, sizeof (Int)) ;
+
+ /* this is allocated later, and free'd after Cperm1 but before Ci */
+ SW->Rperm_2by2 = (Int *) NULL ; /* will be nn Int's */
+
+ /* this is allocated last, and free'd first */
+ SW->Rs = (double *) NULL ; /* will be n_row double's */
+
+ Ci = SW->Ci ;
+ Fr_npivcol = SW->Front_npivcol ;
+ Fr_nrows = SW->Front_nrows ;
+ Fr_ncols = SW->Front_ncols ;
+ Fr_parent = SW->Front_parent ;
+ Fr_cols = SW->Front_cols ;
+ Cperm1 = SW->Cperm1 ;
+ Rperm1 = SW->Rperm1 ;
+ Si = SW->Si ;
+ Sp = SW->Sp ;
+ InvRperm1 = SW->InvRperm1 ;
+ Rperm_2by2 = (Int *) NULL ;
+ InFront = SW->InFront ;
+
+ if (!Ci || !Fr_npivcol || !Fr_nrows || !Fr_ncols || !Fr_parent || !Fr_cols
+ || !Cperm1 || !Rperm1 || !Si || !Sp || !InvRperm1 || !InFront)
+ {
+ DEBUGm4 (("out of memory: symbolic work\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ DEBUG0 (("Symbolic UMF_malloc_count - init_count = "ID"\n",
+ UMF_malloc_count - init_count)) ;
+ ASSERT (UMF_malloc_count == init_count + 17) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the row and column singletons */
+ /* ---------------------------------------------------------------------- */
+
+ /* [ use first nz + n_row + MAX (n_row, n_col) entries in Ci as workspace,
+ * and use Rperm_init as workspace */
+ ASSERT (Clen >= nz + n_row + MAX (n_row, n_col)) ;
+
+ status = UMF_singletons (n_row, n_col, Ap, Ai, Quser, strategy,
+ Cdeg, Cperm1, Rdeg,
+ Rperm1, InvRperm1, &n1, &n1c, &n1r, &nempty_col, &nempty_row, &is_sym,
+ &max_rdeg, /* workspace: */ Rperm_init, Ci, Ci + nz, Ci + nz + n_row) ;
+
+ /* ] done using Rperm_init and Ci as workspace */
+
+ /* InvRperm1 is now the inverse of Rperm1 */
+
+ if (status != UMFPACK_OK)
+ {
+ DEBUGm4 (("matrix invalid: UMF_singletons\n")) ;
+ Info [UMFPACK_STATUS] = status ;
+ error (&Symbolic, SW) ;
+ return (status) ;
+ }
+ Info [UMFPACK_NEMPTY_COL] = nempty_col ;
+ Info [UMFPACK_NEMPTY_ROW] = nempty_row ;
+ Info [UMFPACK_NDENSE_COL] = 0 ; /* # dense rows/cols recomputed below */
+ Info [UMFPACK_NDENSE_ROW] = 0 ;
+ Info [UMFPACK_COL_SINGLETONS] = n1c ;
+ Info [UMFPACK_ROW_SINGLETONS] = n1r ;
+ Info [UMFPACK_S_SYMMETRIC] = is_sym ;
+
+ nempty = MIN (nempty_col, nempty_row) ;
+ Symbolic->nempty_row = nempty_row ;
+ Symbolic->nempty_col = nempty_col ;
+
+ /* UMF_singletons has verified that the user's input matrix is valid */
+ ASSERT (AMD_valid (n_row, n_col, Ap, Ai) == AMD_OK) ;
+
+ Symbolic->n1 = n1 ;
+ Symbolic->nempty = nempty ;
+ ASSERT (n1 <= n_inner) ;
+ n2 = nn - n1 - nempty ;
+
+ dense_row_threshold =
+ UMFPACK_DENSE_DEGREE_THRESHOLD (drow, n_col - n1 - nempty_col) ;
+ Symbolic->dense_row_threshold = dense_row_threshold ;
+
+ if (!is_sym)
+ {
+ /* either the pruned submatrix rectangular, or it is square and
+ * Rperm [n1 .. n-nempty-1] is not the same as Cperm [n1 .. n-nempty-1].
+ * Switch to the unsymmetric strategy, ignoring user-requested
+ * strategy. */
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ DEBUGm4 (("Strategy: Unsymmetric singletons\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* determine symmetry, nzdiag, and degrees of S+S' */
+ /* ---------------------------------------------------------------------- */
+
+ /* S is the matrix obtained after removing singletons
+ * = A (Cperm1 [n1..n_col-nempty_col-1], Rperm1 [n1..n_row-nempty_row-1])
+ */
+
+ Wq = Rperm_init ; /* use Rperm_init as workspace for Wq [ */
+ Sdeg = Cperm_init ; /* use Cperm_init as workspace for Sdeg [ */
+ sym = EMPTY ;
+ nzaat = EMPTY ;
+ nzdiag = EMPTY ;
+ for (i = 0 ; i < AMD_INFO ; i++)
+ {
+ amd_Info [i] = EMPTY ;
+ }
+
+ if (strategy != UMFPACK_STRATEGY_UNSYMMETRIC)
+ {
+ /* This also determines the degree of each node in S+S' (Sdeg), which
+ * is needed by the 2-by-2 strategy, the symmetry of S, and the number
+ * of nonzeros on the diagonal of S. */
+ ASSERT (n_row == n_col) ;
+ ASSERT (nempty_row == nempty_col) ;
+
+ /* get the count of nonzeros on the diagonal of S, excluding explicitly
+ * zero entries. nzdiag = amd_Info [AMD_NZDIAG] counts the zero entries
+ * in S. */
+
+ nzdiag = prune_singletons (n1, nn, Ap, Ai, Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Cperm1, InvRperm1, Si, Sp
+#ifndef NDEBUG
+ , Rperm1, nn
+#endif
+ ) ;
+
+ /* use Ci as workspace to sort S into R, if needed [ */
+ if (Quser != (Int *) NULL)
+ {
+ /* need to sort the columns of S first */
+ Rp = Ci ;
+ Ri = Ci + (n_row) + 1 ;
+ (void) UMF_transpose (n2, n2, Sp, Si, (double *) NULL,
+ (Int *) NULL, (Int *) NULL, 0,
+ Rp, Ri, (double *) NULL, Wq, FALSE
+#ifdef COMPLEX
+ , (double *) NULL, (double *) NULL, FALSE
+#endif
+ ) ;
+ }
+ else
+ {
+ /* S already has sorted columns */
+ Rp = Sp ;
+ Ri = Si ;
+ }
+ ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ;
+
+ nzaat = AMD_aat (n2, Rp, Ri, Sdeg, Wq, amd_Info) ;
+ sym = amd_Info [AMD_SYMMETRY] ;
+ Info [UMFPACK_N2] = n2 ;
+ /* nzdiag = amd_Info [AMD_NZDIAG] counts the zero entries of S too */
+
+ /* done using Ci as workspace to sort S into R ] */
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n2 ; k++)
+ {
+ ASSERT (Sdeg [k] >= 0 && Sdeg [k] < n2) ;
+ }
+ ASSERT (Sp [n2] - n2 <= nzaat && nzaat <= 2 * Sp [n2]) ;
+ DEBUG0 (("Explicit zeros: "ID" %g\n", nzdiag, amd_Info [AMD_NZDIAG])) ;
+#endif
+
+ }
+
+ /* get statistics from amd_aat, if computed */
+ Symbolic->sym = sym ;
+ Symbolic->nzaat = nzaat ;
+ Symbolic->nzdiag = nzdiag ;
+ Symbolic->amd_dmax = EMPTY ;
+
+ Info [UMFPACK_PATTERN_SYMMETRY] = sym ;
+ Info [UMFPACK_NZ_A_PLUS_AT] = nzaat ;
+ Info [UMFPACK_NZDIAG] = nzdiag ;
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the initial strategy based on symmetry and nnz (diag (S)) */
+ /* ---------------------------------------------------------------------- */
+
+ if (strategy == UMFPACK_STRATEGY_AUTO)
+ {
+ if (sym < 0.10)
+ {
+ /* highly unsymmetric: use the unsymmetric strategy */
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ DEBUGm4 (("Strategy: select unsymmetric\n")) ;
+ }
+ else if (sym >= 0.7 && nzdiag == n2)
+ {
+ /* mostly symmetric, zero-free diagonal: use symmetric strategy */
+ strategy = UMFPACK_STRATEGY_SYMMETRIC ;
+ DEBUGm4 (("Strategy: select symmetric\n")) ;
+ }
+ else
+ {
+ /* Evaluate the symmetric 2-by-2 strategy, and select it, or
+ * the unsymmetric strategy if the 2-by-2 strategy doesn't look
+ * promising. */
+ strategy = UMFPACK_STRATEGY_2BY2 ;
+ DEBUGm4 (("Strategy: try 2-by-2\n")) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* try the 2-by-2 strategy */
+ /* ---------------------------------------------------------------------- */
+
+ /* (3) If the 2-by-2 strategy is attempted, additional workspace of size
+ * nn integers and nn double's is allocated, where nn = n_row = n_col.
+ * The real workspace is immediately free'd. The integer workspace of
+ * size nn remains until the end of umfpack_qsymbolic. */
+
+ /* If the resulting matrix S (Rperm_2by2, :) is too unsymmetric, then the
+ * unsymmetric strategy will be used instead. */
+
+ if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ double sym2 ;
+ Int *Blen, *W, nz_papat, nzd2, nweak, unmatched, Clen3 ;
+
+ /* ------------------------------------------------------------------ */
+ /* get workspace for UMF_2by2 */
+ /* ------------------------------------------------------------------ */
+
+ ASSERT (n_row == n_col && nn == n_row) ;
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n2 ; k++)
+ {
+ ASSERT (Sdeg [k] >= 0 && Sdeg [k] < n2) ;
+ }
+#endif
+
+ /* allocate Rperm_2by2 */
+ SW->Rperm_2by2 = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ Rperm_2by2 = SW->Rperm_2by2 ;
+ if (Rperm_2by2 == (Int *) NULL)
+ {
+ DEBUGm4 (("out of memory: Rperm_2by2\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ /* allocate Ri from the tail end of Ci [ */
+ Clen3 = Clen - (MAX (nn, nz) + 1) ;
+ Ri = Ci + Clen3 ;
+ ASSERT (Clen3 >= nz) ; /* space required for UMF_2by2 */
+
+ /* use Fr_* as workspace for Rp, Blen, and W [ */
+ Rp = Fr_npivcol ;
+ Blen = Fr_ncols ;
+ W = Fr_cols ;
+
+ if (scale != UMFPACK_SCALE_NONE)
+ {
+ SW->Rs = (double *) UMF_malloc (nn, sizeof (double)) ;
+ if (SW->Rs == (double *) NULL)
+ {
+ DEBUGm4 (("out of memory: scale factors for 2-by-2\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* find the 2-by-2 row permutation */
+ /* ------------------------------------------------------------------ */
+
+ /* find a row permutation Rperm_2by2 such that S (Rperm_2by2, :)
+ * has a healthy diagonal */
+
+ UMF_2by2 (nn, Ap, Ai, Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ tol, scale, Cperm1,
+#ifndef NDEBUG
+ Rperm1,
+#endif
+ InvRperm1, n1, nempty, Sdeg, Rperm_2by2, &nweak, &unmatched,
+ Ri, Rp, SW->Rs, Blen, W, Ci, Wq) ;
+ DEBUGm3 (("2by2: nweak "ID" unmatched "ID"\n", nweak, unmatched)) ;
+ Info [UMFPACK_2BY2_NWEAK] = nweak ;
+ Info [UMFPACK_2BY2_UNMATCHED] = unmatched ;
+
+ SW->Rs = (double *) UMF_free ((void *) SW->Rs) ;
+
+ /* R = S (Rperm_2by2,:)' */
+ (void) UMF_transpose (n2, n2, Sp, Si, (double *) NULL, Rperm_2by2,
+ (Int *) NULL, 0, Rp, Ri, (double *) NULL, W, FALSE
+#ifdef COMPLEX
+ , (double *) NULL, (double *) NULL, FALSE
+#endif
+ ) ;
+ ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ;
+
+ /* contents of Si and Sp no longer needed, but the space is
+ * still needed */
+
+ /* ------------------------------------------------------------------ */
+ /* find symmetry of S (Rperm_2by2, :)', and prepare to order with AMD */
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i < AMD_INFO ; i++)
+ {
+ amd_Info [i] = EMPTY ;
+ }
+ nz_papat = AMD_aat (n2, Rp, Ri, Sdeg, Wq, amd_Info) ;
+ sym2 = amd_Info [AMD_SYMMETRY] ;
+ nzd2 = amd_Info [AMD_NZDIAG] ;
+
+ Info [UMFPACK_2BY2_PATTERN_SYMMETRY] = sym2 ;
+ Info [UMFPACK_2BY2_NZ_PA_PLUS_PAT] = nz_papat ;
+ Info [UMFPACK_2BY2_NZDIAG] = nzd2 ;
+
+ DEBUG0 (("2by2: sym2 %g nzd2 "ID" n2 "ID"\n", sym2, nzd2, n2)) ;
+
+ /* ------------------------------------------------------------------ */
+ /* evaluate the 2-by-2 results */
+ /* ------------------------------------------------------------------ */
+
+ if (user_auto_strategy)
+ {
+ if ((sym2 > 1.1 * sym) && (nzd2 > 0.9 * n2))
+ {
+ /* 2-by-2 made it much more symmetric */
+ DEBUGm4 (("eval Strategy 2by2: much more symmetric: 2by2\n")) ;
+ strategy = UMFPACK_STRATEGY_2BY2 ;
+ }
+ else if (sym2 < 0.7 * sym)
+ {
+ /* 2-by-2 made it much more unsymmetric */
+ DEBUGm4 (("eval Strategy 2by2: much more UNsymmetric:unsym\n"));
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ }
+ else if (sym2 < 0.25)
+ {
+ DEBUGm4 (("eval Strategy 2by2: is UNsymmetric: unsym\n"));
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ }
+ else if (sym2 >= 0.51)
+ {
+ DEBUGm4 (("eval Strategy 2by2: sym2 >= 0.51: 2by2\n")) ;
+ strategy = UMFPACK_STRATEGY_2BY2 ;
+ }
+ else if (sym2 >= 0.999 * sym)
+ {
+ /* 2-by-2 improved symmetry, or made it only slightly worse */
+ DEBUGm4 (("eval Strategy 2by2: sym2 >= 0.999 sym: 2by2\n")) ;
+ strategy = UMFPACK_STRATEGY_2BY2 ;
+ }
+ else
+ {
+ /* can't decide what to do, so pick the unsymmetric strategy */
+ DEBUGm4 (("eval Strategy 2by2: punt: unsym\n"));
+ strategy = UMFPACK_STRATEGY_UNSYMMETRIC ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* if the 2-by-2 strategy is selected: */
+ /* ------------------------------------------------------------------ */
+
+ if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ if (Quser == (Int *) NULL)
+ {
+ /* 2-by-2 strategy is successful */
+ /* compute amd (S) */
+ Int *Qinv = Fr_npivcol ;
+ ASSERT (Clen3 >= (nz_papat + nz_papat/5 + nn) + 7*nn) ;
+ do_amd (n2, Rp, Ri, Wq, Qinv, Sdeg, Clen3, Ci,
+ amd_Control, amd_Info, Symbolic, Info) ;
+ /* combine the singleton ordering and the AMD ordering */
+ combine_ordering (n1, nempty, nn, Cperm_init, Cperm1, Qinv) ;
+ }
+ /* fix Rperm_2by2 to reflect A, not S */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ oldcol = Cperm1 [k] ;
+ i = k ;
+ oldrow = Rperm1 [k] ;
+ W [oldcol] = oldrow ;
+ }
+ for (k = n1 ; k < nn - nempty ; k++)
+ {
+ oldcol = Cperm1 [k] ;
+ i = Rperm_2by2 [k - n1] + n1 ;
+ oldrow = Rperm1 [i] ;
+ W [oldcol] = oldrow ;
+ }
+ for (k = nn - nempty ; k < nn ; k++)
+ {
+ oldcol = Cperm1 [k] ;
+ i = k ;
+ oldrow = Rperm1 [k] ;
+ W [oldcol] = oldrow ;
+ }
+ for (k = 0 ; k < nn ; k++)
+ {
+ Rperm_2by2 [k] = W [k] ;
+ }
+
+ /* Now, the "diagonal" entry in oldcol (where oldcol is the user's
+ * name for a column, is the entry in row oldrow (where oldrow is
+ * the user's name for a row, and oldrow = Rperm_2by2 [oldcol] */
+ }
+
+ /* Fr_* no longer needed for Rp, Blen, W ] */
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* finalize the strategy, including fixQ and prefer_diagonal */
+ /* ---------------------------------------------------------------------- */
+
+ if (strategy == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ /* use given Quser or AMD (A+A'), fix Q during factorization,
+ * prefer diagonal */
+ DEBUG0 (("\nStrategy: symmetric\n")) ;
+ ASSERT (n_row == n_col) ;
+ Symbolic->ordering = UMFPACK_ORDERING_AMD ;
+ fixQ = TRUE ;
+ prefer_diagonal = TRUE ;
+ }
+ else if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ /* use Q = given Quser or Q = AMD (PA+PA'), fix Q during factorization,
+ * prefer diagonal, and factorize PAQ, where P is found by UMF_2by2. */
+ DEBUG0 (("\nStrategy: symmetric 2-by-2\n")) ;
+ ASSERT (n_row == n_col) ;
+ Symbolic->ordering = UMFPACK_ORDERING_AMD ;
+ fixQ = TRUE ;
+ prefer_diagonal = TRUE ;
+ }
+ else
+ {
+ /* use given Quser or COLAMD (A), refine Q during factorization,
+ * no diagonal preference */
+ ASSERT (strategy == UMFPACK_STRATEGY_UNSYMMETRIC) ;
+ DEBUG0 (("\nStrategy: unsymmetric\n")) ;
+ Symbolic->ordering = UMFPACK_ORDERING_COLAMD ;
+ fixQ = FALSE ;
+ prefer_diagonal = FALSE ;
+ }
+
+ if (Quser != (Int *) NULL)
+ {
+ Symbolic->ordering = UMFPACK_ORDERING_GIVEN ;
+ }
+
+ if (force_fixQ > 0)
+ {
+ fixQ = TRUE ;
+ DEBUG0 (("Force fixQ true\n")) ;
+ }
+ else if (force_fixQ < 0)
+ {
+ fixQ = FALSE ;
+ DEBUG0 (("Force fixQ false\n")) ;
+ }
+
+ DEBUG0 (("Strategy: ordering: "ID"\n", Symbolic->ordering)) ;
+ DEBUG0 (("Strategy: fixQ: "ID"\n", fixQ)) ;
+ DEBUG0 (("Strategy: prefer diag "ID"\n", prefer_diagonal)) ;
+
+ /* get statistics from amd_aat, if computed */
+ Symbolic->strategy = strategy ;
+ Symbolic->fixQ = fixQ ;
+ Symbolic->prefer_diagonal = prefer_diagonal ;
+
+ Info [UMFPACK_STRATEGY_USED] = strategy ;
+ Info [UMFPACK_ORDERING_USED] = Symbolic->ordering ;
+ Info [UMFPACK_QFIXED] = fixQ ;
+ Info [UMFPACK_DIAG_PREFERRED] = prefer_diagonal ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the AMD ordering for the symmetric strategy */
+ /* ---------------------------------------------------------------------- */
+
+ if (strategy == UMFPACK_STRATEGY_SYMMETRIC && Quser == (Int *) NULL)
+ {
+ /* symmetric strategy for a matrix with mostly symmetric pattern */
+ Int *Qinv = Fr_npivcol ;
+ ASSERT (n_row == n_col && nn == n_row) ;
+ ASSERT (Clen >= (nzaat + nzaat/5 + nn) + 7*nn) ;
+ do_amd (n2, Sp, Si, Wq, Qinv, Sdeg, Clen, Ci,
+ amd_Control, amd_Info, Symbolic, Info) ;
+ /* combine the singleton ordering and the AMD ordering */
+ combine_ordering (n1, nempty, nn, Cperm_init, Cperm1, Qinv) ;
+ }
+ /* Sdeg no longer needed ] */
+ /* done using Rperm_init as workspace for Wq ] */
+
+ /* Contents of Si and Sp no longer needed, but the space is still needed */
+
+ /* ---------------------------------------------------------------------- */
+ /* use the user's input column ordering (already in Cperm1) */
+ /* ---------------------------------------------------------------------- */
+
+ if (Quser != (Int *) NULL)
+ {
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Cperm_init [k] = Cperm1 [k] ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* use COLAMD to order the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ if (strategy == UMFPACK_STRATEGY_UNSYMMETRIC && Quser == (Int *) NULL)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* copy the matrix into colamd workspace (colamd destroys its input) */
+ /* ------------------------------------------------------------------ */
+
+ /* C = A (Cperm1 (n1+1:end), Rperm1 (n1+1:end)), where Ci is used as
+ * the row indices and Cperm_init (on input) is used as the column
+ * pointers. */
+
+ (void) prune_singletons (n1, n_col, Ap, Ai,
+ (double *) NULL,
+#ifdef COMPLEX
+ (double *) NULL,
+#endif
+ Cperm1, InvRperm1, Ci, Cperm_init
+#ifndef NDEBUG
+ , Rperm1, n_row
+#endif
+ ) ;
+
+ /* ------------------------------------------------------------------ */
+ /* set UMF_colamd defaults */
+ /* ------------------------------------------------------------------ */
+
+ UMF_colamd_set_defaults (knobs) ;
+ knobs [COLAMD_DENSE_ROW] = drow ;
+ knobs [COLAMD_DENSE_COL] = dcol ;
+ knobs [COLAMD_AGGRESSIVE] = aggressive ;
+
+ /* ------------------------------------------------------------------ */
+ /* check input matrix and find the initial column pre-ordering */
+ /* ------------------------------------------------------------------ */
+
+ /* NOTE: umf_colamd is not given any original empty rows or columns.
+ * Those have already been removed via prune_singletons, above. The
+ * umf_colamd routine has been modified to assume that all rows and
+ * columns have at least one entry in them. It will break if it is
+ * given empty rows or columns (an assertion is triggered when running
+ * in debug mode. */
+
+ (void) UMF_colamd (
+ n_row - n1 - nempty_row,
+ n_col - n1 - nempty_col,
+ Clen, Ci, Cperm_init, knobs, colamd_stats,
+ Fr_npivcol, Fr_nrows, Fr_ncols, Fr_parent, Fr_cols, &nfr,
+ InFront) ;
+ ASSERT (colamd_stats [COLAMD_EMPTY_ROW] == 0) ;
+ ASSERT (colamd_stats [COLAMD_EMPTY_COL] == 0) ;
+
+ /* # of dense rows will be recomputed below */
+ Info [UMFPACK_NDENSE_ROW] = colamd_stats [COLAMD_DENSE_ROW] ;
+ Info [UMFPACK_NDENSE_COL] = colamd_stats [COLAMD_DENSE_COL] ;
+ Info [UMFPACK_SYMBOLIC_DEFRAG] = colamd_stats [COLAMD_DEFRAG_COUNT] ;
+
+ /* re-analyze if any "dense" rows or cols ignored by UMF_colamd */
+ do_UMF_analyze =
+ colamd_stats [COLAMD_DENSE_ROW] > 0 ||
+ colamd_stats [COLAMD_DENSE_COL] > 0 ;
+
+ /* Combine the singleton and colamd ordering into Cperm_init */
+ /* Note that colamd returns its inverse permutation in Ci */
+ combine_ordering (n1, nempty_col, n_col, Cperm_init, Cperm1, Ci) ;
+
+ /* contents of Ci no longer needed */
+
+#ifndef NDEBUG
+ for (col = 0 ; col < n_col ; col++)
+ {
+ DEBUG1 (("Cperm_init ["ID"] = "ID"\n", col, Cperm_init[col]));
+ }
+ /* make sure colamd returned a valid permutation */
+ ASSERT (Cperm_init != (Int *) NULL) ;
+ ASSERT (UMF_is_permutation (Cperm_init, Ci, n_col, n_col)) ;
+#endif
+
+ }
+ else
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* do not call colamd - use input Quser or AMD instead */
+ /* ------------------------------------------------------------------ */
+
+ /* The ordering (Quser or Qamd) is already in Cperm_init */
+ do_UMF_analyze = TRUE ;
+
+ }
+
+ Cperm_init [n_col] = EMPTY ; /* unused in Cperm_init */
+
+ /* ---------------------------------------------------------------------- */
+ /* AMD ordering, if it exists, has been copied into Cperm_init */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ DEBUG3 (("Cperm_init column permutation:\n")) ;
+ ASSERT (UMF_is_permutation (Cperm_init, Ci, n_col, n_col)) ;
+ for (k = 0 ; k < n_col ; k++)
+ {
+ DEBUG3 ((ID"\n", Cperm_init [k])) ;
+ }
+ /* ensure that empty columns have been placed last in A (:,Cperm_init) */
+ for (newj = 0 ; newj < n_col ; newj++)
+ {
+ /* empty columns will be last in A (:, Cperm_init (1:n_col)) */
+ j = Cperm_init [newj] ;
+ ASSERT (IMPLIES (newj >= n_col-nempty_col, Cdeg [j] == 0)) ;
+ ASSERT (IMPLIES (newj < n_col-nempty_col, Cdeg [j] > 0)) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization (unless colamd has already done it) */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_UMF_analyze)
+ {
+
+ Int *W, *Bp, *Bi, *Cperm2, ok, *P, Clen2, bsize, Clen0 ;
+
+ /* ------------------------------------------------------------------ */
+ /* construct column pre-ordered, pruned submatrix */
+ /* ------------------------------------------------------------------ */
+
+ /* S = column form submatrix after removing singletons and applying
+ * initial column ordering (includes singleton ordering) */
+ (void) prune_singletons (n1, n_col, Ap, Ai,
+ (double *) NULL,
+#ifdef COMPLEX
+ (double *) NULL,
+#endif
+ Cperm_init, InvRperm1, Si, Sp
+#ifndef NDEBUG
+ , Rperm1, n_row
+#endif
+ ) ;
+
+ /* ------------------------------------------------------------------ */
+ /* Ci [0 .. Clen-1] holds the following work arrays:
+
+ first Clen0 entries empty space, where Clen0 =
+ Clen - (nn+1 + 2*nn + n_col)
+ and Clen0 >= nz + n_col
+ next nn+1 entries Bp [0..nn]
+ next nn entries Link [0..nn-1]
+ next nn entries W [0..nn-1]
+ last n_col entries Cperm2 [0..n_col-1]
+
+ We have Clen >= n_col + MAX (nz,n_col) + 3*nn+1 + n_col,
+ So Clen0 >= 2*n_col as required for AMD_postorder
+ and Clen0 >= n_col + nz as required
+ */
+
+ Clen0 = Clen - (nn+1 + 2*nn + n_col) ;
+ Bp = Ci + Clen0 ;
+ Link = Bp + (nn+1) ;
+ W = Link + nn ;
+ Cperm2 = W + nn ;
+ ASSERT (Cperm2 + n_col == Ci + Clen) ;
+ ASSERT (Clen0 >= nz + n_col) ;
+ ASSERT (Clen0 >= 2*n_col) ;
+
+ /* ------------------------------------------------------------------ */
+ /* P = order that rows will be used in UMF_analyze */
+ /* ------------------------------------------------------------------ */
+
+ /* use W to mark rows, and use Link for row permutation P [ [ */
+ for (row = 0 ; row < n_row - n1 ; row++)
+ {
+ W [row] = FALSE ;
+ }
+ P = Link ;
+
+ k = 0 ;
+
+ for (col = 0 ; col < n_col - n1 ; col++)
+ {
+ /* empty columns are last in S */
+ for (p = Sp [col] ; p < Sp [col+1] ; p++)
+ {
+ row = Si [p] ;
+ if (!W [row])
+ {
+ /* this row has just been seen for the first time */
+ W [row] = TRUE ;
+ P [k++] = row ;
+ }
+ }
+ }
+
+ /* If the matrix has truly empty rows, then P will not be */
+ /* complete, and visa versa. The matrix is structurally singular. */
+ nempty_row = n_row - n1 - k ;
+ if (k < n_row - n1)
+ {
+ /* complete P by putting empty rows last in their natural order, */
+ /* rather than declaring an error (the matrix is singular) */
+ for (row = 0 ; row < n_row - n1 ; row++)
+ {
+ if (!W [row])
+ {
+ /* W [row] = TRUE ; (not required) */
+ P [k++] = row ;
+ }
+ }
+ }
+
+ /* contents of W no longer needed ] */
+
+#ifndef NDEBUG
+ DEBUG3 (("Induced row permutation:\n")) ;
+ ASSERT (k == n_row - n1) ;
+ ASSERT (UMF_is_permutation (P, W, n_row - n1, n_row - n1)) ;
+ for (k = 0 ; k < n_row - n1 ; k++)
+ {
+ DEBUG3 ((ID"\n", P [k])) ;
+ }
+#endif
+
+ /* ------------------------------------------------------------------ */
+ /* B = row-form of the pattern of S (excluding empty columns) */
+ /* ------------------------------------------------------------------ */
+
+ /* Ci [0 .. Clen-1] holds the following work arrays:
+
+ first Clen2 entries empty space, must be at least >= n_col
+ next max (nz,1) Bi [0..max (nz,1)-1]
+ next nn+1 entries Bp [0..nn]
+ next nn entries Link [0..nn-1]
+ next nn entries W [0..nn-1]
+ last n_col entries Cperm2 [0..n_col-1]
+
+ This memory usage is accounted for by the UMF_ANALYZE_CLEN
+ macro.
+ */
+
+ Clen2 = Clen0 ;
+ snz = Sp [n_col - n1] ;
+ bsize = MAX (snz, 1) ;
+ Clen2 -= bsize ;
+ Bi = Ci + Clen2 ;
+ ASSERT (Clen2 >= n_col) ;
+
+ (void) UMF_transpose (n_row - n1, n_col - n1 - nempty_col,
+ Sp, Si, (double *) NULL,
+ P, (Int *) NULL, 0, Bp, Bi, (double *) NULL, W, FALSE
+#ifdef COMPLEX
+ , (double *) NULL, (double *) NULL, FALSE
+#endif
+ ) ;
+
+ /* contents of Si and Sp no longer needed */
+
+ /* contents of P (same as Link) and W not needed */
+ /* still need Link and W as work arrays, though ] */
+
+ ASSERT (Bp [0] == 0) ;
+ ASSERT (Bp [n_row - n1] == snz) ;
+
+ /* increment Bp to point into Ci, not Bi */
+ for (i = 0 ; i <= n_row - n1 ; i++)
+ {
+ Bp [i] += Clen2 ;
+ }
+ ASSERT (Bp [0] == Clen0 - bsize) ;
+ ASSERT (Bp [n_row - n1] <= Clen0) ;
+
+ /* Ci [0 .. Clen-1] holds the following work arrays:
+
+ first Clen0 entries Ci [0 .. Clen0-1], where the col indices
+ of B are at the tail end of this part,
+ and Bp [0] = Clen2 >= n_col. Note
+ that Clen0 = Clen2 + max (snz,1).
+ next nn+1 entries Bp [0..nn]
+ next nn entries Link [0..nn-1]
+ next nn entries W [0..nn-1]
+ last n_col entries Cperm2 [0..n_col-1]
+ */
+
+ /* ------------------------------------------------------------------ */
+ /* analyze */
+ /* ------------------------------------------------------------------ */
+
+ /* only analyze the non-empty, non-singleton part of the matrix */
+ ok = UMF_analyze (
+ n_row - n1 - nempty_row,
+ n_col - n1 - nempty_col,
+ Ci, Bp, Cperm2, fixQ, W, Link,
+ Fr_ncols, Fr_nrows, Fr_npivcol,
+ Fr_parent, &nfr, &analyze_compactions) ;
+ if (!ok)
+ {
+ /* :: internal error in umf_analyze :: */
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_internal_error ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_internal_error) ;
+ }
+ Info [UMFPACK_SYMBOLIC_DEFRAG] += analyze_compactions ;
+
+ /* ------------------------------------------------------------------ */
+ /* combine the input permutation and UMF_analyze's permutation */
+ /* ------------------------------------------------------------------ */
+
+ if (!fixQ)
+ {
+ /* Cperm2 is the column etree post-ordering */
+ ASSERT (UMF_is_permutation (Cperm2, W,
+ n_col-n1-nempty_col, n_col-n1-nempty_col)) ;
+
+ /* Note that the empty columns remain at the end of Cperm_init */
+ for (k = 0 ; k < n_col - n1 - nempty_col ; k++)
+ {
+ W [k] = Cperm_init [n1 + Cperm2 [k]] ;
+ }
+
+ for (k = 0 ; k < n_col - n1 - nempty_col ; k++)
+ {
+ Cperm_init [n1 + k] = W [k] ;
+ }
+ }
+
+ ASSERT (UMF_is_permutation (Cperm_init, W, n_col, n_col)) ;
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free some of the workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* (4) The real workspace, Rs, of size n_row doubles has already been
+ * free'd. An additional workspace of size nz + n_col+1 + n_col integers
+ * is now free'd as well. */
+
+ SW->Si = (Int *) UMF_free ((void *) SW->Si) ;
+ SW->Sp = (Int *) UMF_free ((void *) SW->Sp) ;
+ SW->Cperm1 = (Int *) UMF_free ((void *) SW->Cperm1) ;
+ ASSERT (SW->Rs == (double *) NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the size of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the size of the Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ nchains = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ if (Fr_parent [i] != i+1)
+ {
+ nchains++ ;
+ }
+ }
+
+ Symbolic->nchains = nchains ;
+ Symbolic->nfr = nfr ;
+ Symbolic->esize
+ = (max_rdeg > dense_row_threshold) ? (n_col - n1 - nempty_col) : 0 ;
+
+ /* true size of Symbolic object */
+ Info [UMFPACK_SYMBOLIC_SIZE] = UMF_symbolic_usage (n_row, n_col, nchains,
+ nfr, Symbolic->esize, prefer_diagonal) ;
+
+ /* actual peak memory usage for UMFPACK_symbolic (actual nfr, nchains) */
+ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] =
+ SYM_WORK_USAGE (n_col, n_row, Clen) + Info [UMFPACK_SYMBOLIC_SIZE] ;
+ Symbolic->peak_sym_usage = Info [UMFPACK_SYMBOLIC_PEAK_MEMORY] ;
+
+ DEBUG0 (("Number of fronts: "ID"\n", nfr)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate the second part of the Symbolic object (Front_*, Chain_*) */
+ /* ---------------------------------------------------------------------- */
+
+ /* (5) UMF_malloc is called 7 or 8 times, for a total space of
+ * (4*(nfr+1) + 3*(nchains+1) + esize) integers, where nfr is the total
+ * number of frontal matrices and nchains is the total number of frontal
+ * matrix chains, and where nchains <= nfr <= n_col. esize is zero if there
+ * are no dense rows, or n_col-n1-nempty_col otherwise (n1 is the number of
+ * singletons and nempty_col is the number of empty columns). This space is
+ * part of the Symbolic object and is not free'd unless an error occurs.
+ * This is between 7 and about 8n integers when A is square.
+ */
+
+ /* Note that Symbolic->Front_* does include the dummy placeholder front */
+ Symbolic->Front_npivcol = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ;
+ Symbolic->Front_parent = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ;
+ Symbolic->Front_1strow = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ;
+ Symbolic->Front_leftmostdesc = (Int *) UMF_malloc (nfr+1, sizeof (Int)) ;
+ Symbolic->Chain_start = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ;
+ Symbolic->Chain_maxrows = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ;
+ Symbolic->Chain_maxcols = (Int *) UMF_malloc (nchains+1, sizeof (Int)) ;
+
+ fail = (!Symbolic->Front_npivcol || !Symbolic->Front_parent ||
+ !Symbolic->Front_1strow || !Symbolic->Front_leftmostdesc ||
+ !Symbolic->Chain_start || !Symbolic->Chain_maxrows ||
+ !Symbolic->Chain_maxcols) ;
+
+ if (Symbolic->esize > 0)
+ {
+ Symbolic->Esize = (Int *) UMF_malloc (Symbolic->esize, sizeof (Int)) ;
+ fail = fail || !Symbolic->Esize ;
+ }
+
+ if (fail)
+ {
+ DEBUGm4 (("out of memory: rest of symbolic object\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ DEBUG0 (("Symbolic UMF_malloc_count - init_count = "ID"\n",
+ UMF_malloc_count - init_count)) ;
+ ASSERT (UMF_malloc_count == init_count + 21
+ + (SW->Rperm_2by2 != (Int *) NULL)
+ + (Symbolic->Esize != (Int *) NULL)) ;
+
+ Front_npivcol = Symbolic->Front_npivcol ;
+ Front_parent = Symbolic->Front_parent ;
+ Front_1strow = Symbolic->Front_1strow ;
+ Front_leftmostdesc = Symbolic->Front_leftmostdesc ;
+
+ Chain_start = Symbolic->Chain_start ;
+ Chain_maxrows = Symbolic->Chain_maxrows ;
+ Chain_maxcols = Symbolic->Chain_maxcols ;
+
+ Esize = Symbolic->Esize ;
+
+ /* ---------------------------------------------------------------------- */
+ /* assign rows to fronts */
+ /* ---------------------------------------------------------------------- */
+
+ /* find InFront, unless colamd has already computed it */
+ if (do_UMF_analyze)
+ {
+
+ DEBUGm4 ((">>>>>>>>>Computing Front_1strow from scratch\n")) ;
+ /* empty rows go to dummy front nfr */
+ for (row = 0 ; row < n_row ; row++)
+ {
+ InFront [row] = nfr ;
+ }
+ /* assign the singleton pivot rows to the "empty" front */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ row = Rperm1 [k] ;
+ InFront [row] = EMPTY ;
+ }
+ DEBUG1 (("Front (EMPTY), singleton nrows "ID" ncols "ID"\n", k, k)) ;
+ newj = n1 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fpivcol = Fr_npivcol [i] ;
+ f1rows = 0 ;
+ /* for all pivot columns in front i */
+ for (kk = 0 ; kk < fpivcol ; kk++, newj++)
+ {
+ j = Cperm_init [newj] ;
+ ASSERT (IMPLIES (newj >= n_col-nempty_col,
+ Ap [j+1] - Ap [j] == 0));
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ row = Ai [p] ;
+ if (InFront [row] == nfr)
+ {
+ /* this row belongs to front i */
+ DEBUG1 ((" Row "ID" in Front "ID"\n", row, i)) ;
+ InFront [row] = i ;
+ f1rows++ ;
+ }
+ }
+ }
+ Front_1strow [i] = f1rows ;
+ DEBUG1 ((" Front "ID" has 1strows: "ID" pivcols "ID"\n",
+ i, f1rows, fpivcol)) ;
+ }
+
+ }
+ else
+ {
+
+ /* COLAMD has already computed InFront, but it is not yet
+ * InFront [row] = front i, where row is an original row. It is
+ * InFront [k-n1] = i for k in the range n1 to n_row-nempty_row,
+ * and where row = Rperm1 [k]. Need to permute InFront. Also compute
+ * # of original rows assembled into each front.
+ * [ use Ci as workspace */
+ DEBUGm4 ((">>>>>>>>>Computing Front_1strow from colamd's InFront\n")) ;
+ for (i = 0 ; i <= nfr ; i++)
+ {
+ Front_1strow [i] = 0 ;
+ }
+ /* assign the singleton pivot rows to "empty" front */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ row = Rperm1 [k] ;
+ Ci [row] = EMPTY ;
+ }
+ /* assign the non-empty rows to the front that assembled them */
+ for ( ; k < n_row - nempty_row ; k++)
+ {
+ row = Rperm1 [k] ;
+ i = InFront [k - n1] ;
+ ASSERT (i >= EMPTY && i < nfr) ;
+ if (i != EMPTY)
+ {
+ Front_1strow [i]++ ;
+ }
+ /* use Ci as permuted version of InFront */
+ Ci [row] = i ;
+ }
+ /* empty rows go to the "dummy" front */
+ for ( ; k < n_row ; k++)
+ {
+ row = Rperm1 [k] ;
+ Ci [row] = nfr ;
+ }
+ /* permute InFront so that InFront [row] = i if the original row is
+ * in front i */
+ for (row = 0 ; row < n_row ; row++)
+ {
+ InFront [row] = Ci [row] ;
+ }
+ /* ] no longer need Ci as workspace */
+ }
+
+#ifndef NDEBUG
+ for (row = 0 ; row < n_row ; row++)
+ {
+ if (InFront [row] == nfr)
+ {
+ DEBUG1 ((" Row "ID" in Dummy Front "ID"\n", row, nfr)) ;
+ }
+ else if (InFront [row] == EMPTY)
+ {
+ DEBUG1 ((" singleton Row "ID"\n", row)) ;
+ }
+ else
+ {
+ DEBUG1 ((" Row "ID" in Front "ID"\n", row, nfr)) ;
+ }
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* copy front information into Symbolic object */
+ /* ---------------------------------------------------------------------- */
+
+ k = n1 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fpivcol = Fr_npivcol [i] ;
+ DEBUG1 (("Front "ID" k "ID" npivcol "ID" nrows "ID" ncols "ID"\n",
+ i, k, fpivcol, Fr_nrows [i], Fr_ncols [i])) ;
+ k += fpivcol ;
+ /* copy Front info into Symbolic object from SW */
+ Front_npivcol [i] = fpivcol ;
+ Front_parent [i] = Fr_parent [i] ;
+ }
+
+ /* assign empty columns to dummy placehold front nfr */
+ DEBUG1 (("Dummy Cols in Front "ID" : "ID"\n", nfr, n_col-k)) ;
+ Front_npivcol [nfr] = n_col - k ;
+ Front_parent [nfr] = EMPTY ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find initial row permutation */
+ /* ---------------------------------------------------------------------- */
+
+ /* order the singleton pivot rows */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ Rperm_init [k] = Rperm1 [k] ;
+ }
+
+ /* determine the first row in each front (in the new row ordering) */
+ for (i = 0 ; i < nfr ; i++)
+ {
+ f1rows = Front_1strow [i] ;
+ DEBUG1 (("Front "ID" : npivcol "ID" parent "ID,
+ i, Front_npivcol [i], Front_parent [i])) ;
+ DEBUG1 ((" 1st rows in Front "ID" : "ID"\n", i, f1rows)) ;
+ Front_1strow [i] = k ;
+ k += f1rows ;
+ }
+
+ /* assign empty rows to dummy placehold front nfr */
+ DEBUG1 (("Rows in Front "ID" (dummy): "ID"\n", nfr, n_row-k)) ;
+ Front_1strow [nfr] = k ;
+ DEBUG1 (("nfr "ID" 1strow[nfr] "ID" nrow "ID"\n", nfr, k, n_row)) ;
+
+ /* Use Ci as temporary workspace for F1 */
+ F1 = Ci ; /* [ of size nfr+1 */
+ ASSERT (Clen >= 2*n_row + nfr+1) ;
+
+ for (i = 0 ; i <= nfr ; i++)
+ {
+ F1 [i] = Front_1strow [i] ;
+ }
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ i = InFront [row] ;
+ if (i != EMPTY)
+ {
+ newrow = F1 [i]++ ;
+ ASSERT (newrow >= n1) ;
+ Rperm_init [newrow] = row ;
+ }
+ }
+ Rperm_init [n_row] = EMPTY ; /* unused */
+
+#ifndef NDEBUG
+ for (k = 0 ; k < n_row ; k++)
+ {
+ DEBUG2 (("Rperm_init ["ID"] = "ID"\n", k, Rperm_init [k])) ;
+ }
+#endif
+
+ /* ] done using F1 */
+
+ /* ---------------------------------------------------------------------- */
+ /* find the diagonal map */
+ /* ---------------------------------------------------------------------- */
+
+ /* Rperm_init [newrow] = row gives the row permutation that is implied
+ * by the column permutation, where "row" is a row index of the original
+ * matrix A. It is not dependent on the Rperm_2by2 permutation, which
+ * only redefines the "diagonal". Both are used to construct the
+ * Diagonal_map. Diagonal_map only needs to be defined for
+ * k = n1 to nn - nempty, but go ahead and define it for all of
+ * k = 0 to nn */
+
+ if (prefer_diagonal)
+ {
+ Int *Diagonal_map ;
+ ASSERT (n_row == n_col && nn == n_row) ;
+ ASSERT (nempty_row == nempty_col && nempty == nempty_row) ;
+
+ /* allocate the Diagonal_map */
+ Symbolic->Diagonal_map = (Int *) UMF_malloc (n_col+1, sizeof (Int)) ;
+ Diagonal_map = Symbolic->Diagonal_map ;
+ if (Diagonal_map == (Int *) NULL)
+ {
+ /* :: out of memory (diagonal map) :: */
+ DEBUGm4 (("out of memory: Diagonal map\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ error (&Symbolic, SW) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ /* use Ci as workspace to compute the inverse of Rperm_init [ */
+ for (newrow = 0 ; newrow < nn ; newrow++)
+ {
+ oldrow = Rperm_init [newrow] ;
+ ASSERT (oldrow >= 0 && oldrow < nn) ;
+ Ci [oldrow] = newrow ;
+ }
+ if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ ASSERT (Rperm_2by2 != (Int *) NULL) ;
+ for (newcol = 0 ; newcol < nn ; newcol++)
+ {
+ oldcol = Cperm_init [newcol] ;
+ /* 2-by-2 pivoting done in S */
+ oldrow = Rperm_2by2 [oldcol] ;
+ newrow = Ci [oldrow] ;
+ Diagonal_map [newcol] = newrow ;
+ }
+ }
+ else
+ {
+ for (newcol = 0 ; newcol < nn ; newcol++)
+ {
+ oldcol = Cperm_init [newcol] ;
+ /* no 2-by-2 pivoting in S */
+ oldrow = oldcol ;
+ newrow = Ci [oldrow] ;
+ Diagonal_map [newcol] = newrow ;
+ }
+ }
+
+#ifndef NDEBUG
+ DEBUG1 (("\nDiagonal map:\n")) ;
+ for (newcol = 0 ; newcol < nn ; newcol++)
+ {
+ oldcol = Cperm_init [newcol] ;
+ DEBUG3 (("oldcol "ID" newcol "ID":\n", oldcol, newcol)) ;
+ for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++)
+ {
+ Entry aij ;
+ CLEAR (aij) ;
+ oldrow = Ai [p] ;
+ newrow = Ci [oldrow] ;
+ if (Ax != (double *) NULL)
+ {
+ ASSIGN (aij, Ax, Az, p, SPLIT (Az)) ;
+ }
+ if (oldrow == oldcol)
+ {
+ DEBUG2 ((" old diagonal : oldcol "ID" oldrow "ID" ",
+ oldcol, oldrow)) ;
+ EDEBUG2 (aij) ;
+ DEBUG2 (("\n")) ;
+ }
+ if (newrow == Diagonal_map [newcol])
+ {
+ DEBUG2 ((" MAP diagonal : newcol "ID" MAProw "ID" ",
+ newcol, Diagonal_map [newrow])) ;
+ EDEBUG2 (aij) ;
+ DEBUG2 (("\n")) ;
+ }
+ }
+ }
+#endif
+ /* done using Ci as workspace ] */
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the leftmost descendant of each front */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i <= nfr ; i++)
+ {
+ Front_leftmostdesc [i] = EMPTY ;
+ }
+
+ for (i = 0 ; i < nfr ; i++)
+ {
+ /* start at i and walk up the tree */
+ DEBUG2 (("Walk up front tree from "ID"\n", i)) ;
+ j = i ;
+ while (j != EMPTY && Front_leftmostdesc [j] == EMPTY)
+ {
+ DEBUG3 ((" Leftmost desc of "ID" is "ID"\n", j, i)) ;
+ Front_leftmostdesc [j] = i ;
+ j = Front_parent [j] ;
+ DEBUG3 ((" go to j = "ID"\n", j)) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* find the frontal matrix chains and max frontal matrix sizes */
+ /* ---------------------------------------------------------------------- */
+
+ maxnrows = 1 ; /* max # rows in any front */
+ maxncols = 1 ; /* max # cols in any front */
+ dmaxfrsize = 1 ; /* max frontal matrix size */
+
+ /* start the first chain */
+ nchains = 0 ; /* number of chains */
+ Chain_start [0] = 0 ; /* front 0 starts a new chain */
+ maxrows = 1 ; /* max # rows for any front in current chain */
+ maxcols = 1 ; /* max # cols for any front in current chain */
+ DEBUG1 (("Constructing chains:\n")) ;
+
+ for (i = 0 ; i < nfr ; i++)
+ {
+ /* get frontal matrix info */
+ fpivcol = Front_npivcol [i] ; /* # candidate pivot columns */
+ fallrows = Fr_nrows [i] ; /* all rows (not just Schur comp) */
+ fallcols = Fr_ncols [i] ; /* all cols (not just Schur comp) */
+ parent = Front_parent [i] ; /* parent in column etree */
+ fpiv = MIN (fpivcol, fallrows) ; /* # pivot rows and cols */
+ maxrows = MAX (maxrows, fallrows) ;
+ maxcols = MAX (maxcols, fallcols) ;
+
+ DEBUG1 (("Front: "ID", pivcol "ID", "ID"-by-"ID" parent "ID
+ ", npiv "ID" Chain: maxrows "ID" maxcols "ID"\n", i, fpivcol,
+ fallrows, fallcols, parent, fpiv, maxrows, maxcols)) ;
+
+ if (parent != i+1)
+ {
+ /* this is the end of a chain */
+ double s ;
+ DEBUG1 (("\nEnd of chain "ID"\n", nchains)) ;
+
+ /* make sure maxrows is an odd number */
+ ASSERT (maxrows >= 0) ;
+ if (maxrows % 2 == 0) maxrows++ ;
+
+ DEBUG1 (("Chain maxrows "ID" maxcols "ID"\n", maxrows, maxcols)) ;
+
+ Chain_maxrows [nchains] = maxrows ;
+ Chain_maxcols [nchains] = maxcols ;
+
+ /* keep track of the maximum front size for all chains */
+
+ /* for Info only: */
+ s = (double) maxrows * (double) maxcols ;
+ dmaxfrsize = MAX (dmaxfrsize, s) ;
+
+ /* for the subsequent numerical factorization */
+ maxnrows = MAX (maxnrows, maxrows) ;
+ maxncols = MAX (maxncols, maxcols) ;
+
+ DEBUG1 (("Chain dmaxfrsize %g\n\n", dmaxfrsize)) ;
+
+ /* start the next chain */
+ nchains++ ;
+ Chain_start [nchains] = i+1 ;
+ maxrows = 1 ;
+ maxcols = 1 ;
+ }
+ }
+
+ /* for Info only: */
+ dmaxfrsize = ceil (dmaxfrsize) ;
+ DEBUGm1 (("dmaxfrsize %30.20g Int_MAX "ID"\n", dmaxfrsize, Int_MAX)) ;
+ ASSERT (Symbolic->nchains == nchains) ;
+
+ /* For allocating objects in umfpack_numeric (does not include all possible
+ * pivots, particularly pivots from prior fronts in the chain. Need to add
+ * nb to these to get the # of columns in the L block, for example. This
+ * is the largest row dimension and largest column dimension of any frontal
+ * matrix. maxnrows is always odd. */
+ Symbolic->maxnrows = maxnrows ;
+ Symbolic->maxncols = maxncols ;
+ DEBUGm3 (("maxnrows "ID" maxncols "ID"\n", maxnrows, maxncols)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* find the initial element sizes */
+ /* ---------------------------------------------------------------------- */
+
+ if (max_rdeg > dense_row_threshold)
+ {
+ /* there are one or more dense rows in the input matrix */
+ /* count the number of dense rows in each column */
+ /* use Ci as workspace for inverse of Rperm_init [ */
+ ASSERT (Esize != (Int *) NULL) ;
+ for (newrow = 0 ; newrow < n_row ; newrow++)
+ {
+ oldrow = Rperm_init [newrow] ;
+ ASSERT (oldrow >= 0 && oldrow < nn) ;
+ Ci [oldrow] = newrow ;
+ }
+ for (col = n1 ; col < n_col - nempty_col ; col++)
+ {
+ oldcol = Cperm_init [col] ;
+ esize = Cdeg [oldcol] ;
+ ASSERT (esize > 0) ;
+ for (p = Ap [oldcol] ; p < Ap [oldcol+1] ; p++)
+ {
+ oldrow = Ai [p] ;
+ newrow = Ci [oldrow] ;
+ if (newrow >= n1 && Rdeg [oldrow] > dense_row_threshold)
+ {
+ esize-- ;
+ }
+ }
+ ASSERT (esize >= 0) ;
+ Esize [col - n1] = esize ;
+ }
+ /* done using Ci as workspace ] */
+ }
+
+ /* If there are no dense rows, then Esize [col-n1] is identical to
+ * Cdeg [col], once Cdeg is permuted below */
+
+ /* ---------------------------------------------------------------------- */
+ /* permute Cdeg and Rdeg according to initial column and row permutation */
+ /* ---------------------------------------------------------------------- */
+
+ /* use Ci as workspace [ */
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Ci [k] = Cdeg [Cperm_init [k]] ;
+ }
+ for (k = 0 ; k < n_col ; k++)
+ {
+ Cdeg [k] = Ci [k] ;
+ }
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Ci [k] = Rdeg [Rperm_init [k]] ;
+ }
+ for (k = 0 ; k < n_row ; k++)
+ {
+ Rdeg [k] = Ci [k] ;
+ }
+ /* done using Ci as workspace ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* simulate UMF_kernel_init */
+ /* ---------------------------------------------------------------------- */
+
+ /* count elements and tuples at tail, LU factors of singletons, and
+ * head and tail markers */
+
+ dlnz = n_inner ; /* upper limit of nz in L (incl diag) */
+ dunz = dlnz ; /* upper limit of nz in U (incl diag) */
+
+ /* head marker */
+ head_usage = 1 ;
+ dhead_usage = 1 ;
+
+ /* tail markers: */
+ tail_usage = 2 ;
+ dtail_usage = 2 ;
+
+ /* allocate the Rpi and Rpx workspace for UMF_kernel_init (incl. headers) */
+ tail_usage += UNITS (Int *, n_row+1) + UNITS (Entry *, n_row+1) + 2 ;
+ dtail_usage += DUNITS (Int *, n_row+1) + DUNITS (Entry *, n_row+1) + 2 ;
+ DEBUG1 (("Symbolic usage after Rpi/Rpx allocation: head "ID" tail "ID"\n",
+ head_usage, tail_usage)) ;
+
+ /* LU factors for singletons, at the head of memory */
+ for (k = 0 ; k < n1 ; k++)
+ {
+ lnz = Cdeg [k] - 1 ;
+ unz = Rdeg [k] - 1 ;
+ dlnz += lnz ;
+ dunz += unz ;
+ DEBUG1 (("singleton k "ID" pivrow "ID" pivcol "ID" lnz "ID" unz "ID"\n",
+ k, Rperm_init [k], Cperm_init [k], lnz, unz)) ;
+ head_usage += UNITS (Int, lnz) + UNITS (Entry, lnz)
+ + UNITS (Int, unz) + UNITS (Entry, unz) ;
+ dhead_usage += DUNITS (Int, lnz) + DUNITS (Entry, lnz)
+ + DUNITS (Int, unz) + DUNITS (Entry, unz) ;
+ }
+ DEBUG1 (("Symbolic init head usage: "ID" for LU singletons\n",head_usage)) ;
+
+ /* column elements: */
+ for (k = n1 ; k < n_col - nempty_col; k++)
+ {
+ esize = Esize ? Esize [k-n1] : Cdeg [k] ;
+ DEBUG2 ((" esize: "ID"\n", esize)) ;
+ ASSERT (esize >= 0) ;
+ if (esize > 0)
+ {
+ tail_usage += GET_ELEMENT_SIZE (esize, 1) + 1 ;
+ dtail_usage += DGET_ELEMENT_SIZE (esize, 1) + 1 ;
+ }
+ }
+
+ /* dense row elements */
+ if (Esize)
+ {
+ Int nrow_elements = 0 ;
+ for (k = n1 ; k < n_row - nempty_row ; k++)
+ {
+ rdeg = Rdeg [k] ;
+ if (rdeg > dense_row_threshold)
+ {
+ tail_usage += GET_ELEMENT_SIZE (1, rdeg) + 1 ;
+ dtail_usage += GET_ELEMENT_SIZE (1, rdeg) + 1 ;
+ nrow_elements++ ;
+ }
+ }
+ Info [UMFPACK_NDENSE_ROW] = nrow_elements ;
+ }
+
+ DEBUG1 (("Symbolic usage: "ID" = head "ID" + tail "ID" after els\n",
+ head_usage + tail_usage, head_usage, tail_usage)) ;
+
+ /* compute the tuple lengths */
+ if (Esize)
+ {
+ /* row tuples */
+ for (row = n1 ; row < n_row ; row++)
+ {
+ rdeg = Rdeg [row] ;
+ tlen = (rdeg > dense_row_threshold) ? 1 : rdeg ;
+ tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ;
+ dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ;
+ }
+ /* column tuples */
+ for (col = n1 ; col < n_col - nempty_col ; col++)
+ {
+ /* tlen is 1 plus the number of dense rows in this column */
+ esize = Esize [col - n1] ;
+ tlen = (esize > 0) + (Cdeg [col] - esize) ;
+ tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ;
+ dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ;
+ }
+ for ( ; col < n_col ; col++)
+ {
+ tail_usage += 1 + UNITS (Tuple, TUPLES (0)) ;
+ dtail_usage += 1 + DUNITS (Tuple, TUPLES (0)) ;
+ }
+ }
+ else
+ {
+ /* row tuples */
+ for (row = n1 ; row < n_row ; row++)
+ {
+ tlen = Rdeg [row] ;
+ tail_usage += 1 + UNITS (Tuple, TUPLES (tlen)) ;
+ dtail_usage += 1 + DUNITS (Tuple, TUPLES (tlen)) ;
+ }
+ /* column tuples */
+ for (col = n1 ; col < n_col ; col++)
+ {
+ tail_usage += 1 + UNITS (Tuple, TUPLES (1)) ;
+ dtail_usage += 1 + DUNITS (Tuple, TUPLES (1)) ;
+ }
+ }
+
+ Symbolic->num_mem_init_usage = head_usage + tail_usage ;
+ DEBUG1 (("Symbolic usage: "ID" = head "ID" + tail "ID" final\n",
+ Symbolic->num_mem_init_usage, head_usage, tail_usage)) ;
+
+ ASSERT (UMF_is_permutation (Rperm_init, Ci, n_row, n_row)) ;
+
+ /* initial head and tail usage in Numeric->Memory */
+ dmax_usage = dhead_usage + dtail_usage ;
+ dmax_usage = MAX (Symbolic->num_mem_init_usage, ceil (dmax_usage)) ;
+ Info [UMFPACK_VARIABLE_INIT_ESTIMATE] = dmax_usage ;
+
+ /* In case Symbolic->num_mem_init_usage overflows, keep as a double, too */
+ Symbolic->dnum_mem_init_usage = dmax_usage ;
+
+ /* free the Rpi and Rpx workspace */
+ tail_usage -= UNITS (Int *, n_row+1) + UNITS (Entry *, n_row+1) ;
+ dtail_usage -= DUNITS (Int *, n_row+1) + DUNITS (Entry *, n_row+1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* simulate UMF_kernel, assuming unsymmetric pivoting */
+ /* ---------------------------------------------------------------------- */
+
+ /* Use Ci as temporary workspace for link lists [ */
+ Link = Ci ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ Link [i] = EMPTY ;
+ }
+
+ flops = 0 ; /* flop count upper bound */
+
+ for (chain = 0 ; chain < nchains ; chain++)
+ {
+ double fsize ;
+ f1 = Chain_start [chain] ;
+ f2 = Chain_start [chain+1] - 1 ;
+
+ /* allocate frontal matrix working array (C, L, and U) */
+ dr = Chain_maxrows [chain] ;
+ dc = Chain_maxcols [chain] ;
+ fsize =
+ nb*nb /* LU is nb-by-nb */
+ + dr*nb /* L is dr-by-nb */
+ + nb*dc /* U is nb-by-dc, stored by rows */
+ + dr*dc ; /* C is dr by dc */
+ dtail_usage += DUNITS (Entry, fsize) ;
+ dmax_usage = MAX (dmax_usage, dhead_usage + dtail_usage) ;
+
+ for (i = f1 ; i <= f2 ; i++)
+ {
+
+ /* get frontal matrix info */
+ fpivcol = Front_npivcol [i] ; /* # candidate pivot columns */
+ fallrows = Fr_nrows [i] ; /* all rows (not just Schur comp*/
+ fallcols = Fr_ncols [i] ; /* all cols (not just Schur comp*/
+ parent = Front_parent [i] ; /* parent in column etree */
+ fpiv = MIN (fpivcol, fallrows) ; /* # pivot rows and cols */
+ f = (double) fpiv ;
+ r = fallrows - fpiv ; /* # rows in Schur comp. */
+ c = fallcols - fpiv ; /* # cols in Schur comp. */
+
+ /* assemble all children of front i in column etree */
+ for (child = Link [i] ; child != EMPTY ; child = Link [child])
+ {
+ ASSERT (child >= 0 && child < i) ;
+ ASSERT (Front_parent [child] == i) ;
+ /* free the child element and remove it from tuple lists */
+ cp = MIN (Front_npivcol [child], Fr_nrows [child]) ;
+ cr = Fr_nrows [child] - cp ;
+ cc = Fr_ncols [child] - cp ;
+ ASSERT (cp >= 0 && cr >= 0 && cc >= 0) ;
+ dtail_usage -= ELEMENT_SIZE (cr, cc) ;
+
+ }
+
+ /* The flop count computed here is "canonical". */
+
+ /* factorize the frontal matrix */
+ flops += DIV_FLOPS * (f*r + (f-1)*f/2) /* scale pivot columns */
+ /* f outer products: */
+ + MULTSUB_FLOPS * (f*r*c + (r+c)*(f-1)*f/2 + (f-1)*f*(2*f-1)/6);
+
+ /* count nonzeros and memory usage in double precision */
+ dlf = (f*f-f)/2 + f*r ; /* nz in L below diagonal */
+ duf = (f*f-f)/2 + f*c ; /* nz in U above diagonal */
+ dlnz += dlf ;
+ dunz += duf ;
+
+ /* store f columns of L and f rows of U */
+ dhead_usage +=
+ DUNITS (Entry, dlf + duf) /* numerical values (excl diag) */
+ + DUNITS (Int, r + c + f) ; /* indices (compressed) */
+
+ if (parent != EMPTY)
+ {
+ /* create new element and place in tuple lists */
+ dtail_usage += ELEMENT_SIZE (r, c) ;
+
+ /* place in link list of parent */
+ Link [i] = Link [parent] ;
+ Link [parent] = i ;
+ }
+
+ /* keep track of peak Numeric->Memory usage */
+ dmax_usage = MAX (dmax_usage, dhead_usage + dtail_usage) ;
+
+ }
+
+ /* free the current frontal matrix */
+ dtail_usage -= DUNITS (Entry, fsize) ;
+ }
+
+ dhead_usage = ceil (dhead_usage) ;
+ dmax_usage = ceil (dmax_usage) ;
+ Symbolic->num_mem_size_est = dhead_usage ;
+ Symbolic->num_mem_usage_est = dmax_usage ;
+ Symbolic->lunz_bound = dlnz + dunz - n_inner ;
+
+ /* ] done using Ci as workspace for Link array */
+
+ /* ---------------------------------------------------------------------- */
+ /* estimate total memory usage in UMFPACK_numeric */
+ /* ---------------------------------------------------------------------- */
+
+ UMF_set_stats (
+ Info,
+ Symbolic,
+ dmax_usage, /* estimated peak size of Numeric->Memory */
+ dhead_usage, /* estimated final size of Numeric->Memory */
+ flops, /* estimated "true flops" */
+ dlnz, /* estimated nz in L */
+ dunz, /* estimated nz in U */
+ dmaxfrsize, /* estimated largest front size */
+ (double) n_col, /* worst case Numeric->Upattern size */
+ (double) n_inner, /* max possible pivots to be found */
+ (double) maxnrows, /* estimated largest #rows in front */
+ (double) maxncols, /* estimated largest #cols in front */
+ TRUE, /* assume scaling is to be performed */
+ prefer_diagonal,
+ ESTIMATE) ;
+
+ /* ---------------------------------------------------------------------- */
+
+#ifndef NDEBUG
+ for (i = 0 ; i < nchains ; i++)
+ {
+ DEBUG2 (("Chain "ID" start "ID" end "ID" maxrows "ID" maxcols "ID"\n",
+ i, Chain_start [i], Chain_start [i+1] - 1,
+ Chain_maxrows [i], Chain_maxcols [i])) ;
+ UMF_dump_chain (Chain_start [i], Fr_parent, Fr_npivcol, Fr_nrows,
+ Fr_ncols, nfr) ;
+ }
+ fpivcol = 0 ;
+ for (i = 0 ; i < nfr ; i++)
+ {
+ fpivcol = MAX (fpivcol, Front_npivcol [i]) ;
+ }
+ DEBUG0 (("Max pivot cols in any front: "ID"\n", fpivcol)) ;
+ DEBUG1 (("Largest front: maxnrows "ID" maxncols "ID" dmaxfrsize %g\n",
+ maxnrows, maxncols, dmaxfrsize)) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* UMFPACK_symbolic was successful, return the object handle */
+ /* ---------------------------------------------------------------------- */
+
+ Symbolic->valid = SYMBOLIC_VALID ;
+ *SymbolicHandle = (void *) Symbolic ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /* (6) The last of the workspace is free'd. The final Symbolic object
+ * consists of 12 to 14 allocated objects. Its final total size is lies
+ * roughly between 4*n and 13*n for a square matrix, which is all that is
+ * left of the memory allocated by this routine. If an error occurs, the
+ * entire Symbolic object is free'd when this routine returns (the error
+ * return routine, below).
+ */
+
+ free_work (SW) ;
+
+ DEBUG0 (("(3)Symbolic UMF_malloc_count - init_count = "ID"\n",
+ UMF_malloc_count - init_count)) ;
+ ASSERT (UMF_malloc_count == init_count + 12
+ + (Symbolic->Esize != (Int *) NULL)
+ + (Symbolic->Diagonal_map != (Int *) NULL)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get the time used by UMFPACK_*symbolic */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_toc (stats) ;
+ Info [UMFPACK_SYMBOLIC_WALLTIME] = stats [0] ;
+ Info [UMFPACK_SYMBOLIC_TIME] = stats [1] ;
+
+ return (UMFPACK_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === free_work ============================================================ */
+/* ========================================================================== */
+
+PRIVATE void free_work
+(
+ SWType *SW
+)
+{
+ if (SW)
+ {
+ SW->Rperm_2by2 = (Int *) UMF_free ((void *) SW->Rperm_2by2) ;
+ SW->InvRperm1 = (Int *) UMF_free ((void *) SW->InvRperm1) ;
+ SW->Rs = (double *) UMF_free ((void *) SW->Rs) ;
+ SW->Si = (Int *) UMF_free ((void *) SW->Si) ;
+ SW->Sp = (Int *) UMF_free ((void *) SW->Sp) ;
+ SW->Ci = (Int *) UMF_free ((void *) SW->Ci) ;
+ SW->Front_npivcol = (Int *) UMF_free ((void *) SW->Front_npivcol);
+ SW->Front_nrows = (Int *) UMF_free ((void *) SW->Front_nrows) ;
+ SW->Front_ncols = (Int *) UMF_free ((void *) SW->Front_ncols) ;
+ SW->Front_parent = (Int *) UMF_free ((void *) SW->Front_parent) ;
+ SW->Front_cols = (Int *) UMF_free ((void *) SW->Front_cols) ;
+ SW->Cperm1 = (Int *) UMF_free ((void *) SW->Cperm1) ;
+ SW->Rperm1 = (Int *) UMF_free ((void *) SW->Rperm1) ;
+ SW->InFront = (Int *) UMF_free ((void *) SW->InFront) ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === error ================================================================ */
+/* ========================================================================== */
+
+/* Error return from UMFPACK_symbolic. Free all allocated memory. */
+
+PRIVATE void error
+(
+ SymbolicType **Symbolic,
+ SWType *SW
+)
+{
+
+ free_work (SW) ;
+ UMFPACK_free_symbolic ((void **) Symbolic) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+}
diff --git a/UMFPACK/Source/umfpack_report_control.c b/UMFPACK/Source/umfpack_report_control.c
new file mode 100644
index 0000000..30a51b9
--- /dev/null
+++ b/UMFPACK/Source/umfpack_report_control.c
@@ -0,0 +1,361 @@
+/* ========================================================================== */
+/* === UMFPACK_report_control =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints the control settings. See umfpack_report_control.h
+ for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL void UMFPACK_report_control
+(
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ double drow, dcol, relpt, relpt2, alloc_init, front_alloc_init, amd_alpha,
+ tol, force_fixQ, droptol, aggr ;
+ Int prl, nb, irstep, strategy, scale, s ;
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl < 2)
+ {
+ /* default is to print nothing */
+ return ;
+ }
+
+ PRINTF (("UMFPACK V%d.%d.%d (%s), Control:\n", UMFPACK_MAIN_VERSION,
+ UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION, UMFPACK_DATE)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* run-time options */
+ /* ---------------------------------------------------------------------- */
+
+ /* This is a "run-time" option because all four umfpack_* versions */
+ /* compiled into the UMFPACK library. */
+
+#ifdef DINT
+ PRINTF ((" Matrix entry defined as: double\n")) ;
+ PRINTF ((" Int (generic integer) defined as: int\n")) ;
+#endif
+#ifdef DLONG
+ PRINTF ((" Matrix entry defined as: double\n")) ;
+ PRINTF ((" Int (generic integer) defined as: UF_long\n")) ;
+#endif
+#ifdef ZINT
+ PRINTF ((" Matrix entry defined as: double complex\n")) ;
+ PRINTF ((" Int (generic integer) defined as: int\n")) ;
+#endif
+#ifdef ZLONG
+ PRINTF ((" Matrix entry defined as: double complex\n")) ;
+ PRINTF ((" Int (generic integer) defined as: UF_long\n")) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* printing level */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF (("\n "ID": print level: "ID"\n",
+ (Int) INDEX (UMFPACK_PRL), prl)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* dense row/col parameters */
+ /* ---------------------------------------------------------------------- */
+
+ drow = GET_CONTROL (UMFPACK_DENSE_ROW, UMFPACK_DEFAULT_DENSE_ROW) ;
+ dcol = GET_CONTROL (UMFPACK_DENSE_COL, UMFPACK_DEFAULT_DENSE_COL) ;
+
+ PRINTF ((" "ID": dense row parameter: %g\n",
+ (Int) INDEX (UMFPACK_DENSE_ROW), drow)) ;
+ PRINTF ((" \"dense\" rows have > max (16, (%g)*16*sqrt(n_col)"
+ " entries)\n", drow)) ;
+ PRINTF ((" "ID": dense column parameter: %g\n",
+ (Int) INDEX (UMFPACK_DENSE_COL), dcol)) ;
+ PRINTF ((" \"dense\" columns have > max (16, (%g)*16*sqrt(n_row)"
+ " entries)\n", dcol)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* pivot tolerance */
+ /* ---------------------------------------------------------------------- */
+
+ relpt = GET_CONTROL (UMFPACK_PIVOT_TOLERANCE,
+ UMFPACK_DEFAULT_PIVOT_TOLERANCE) ;
+ relpt = MAX (0.0, MIN (relpt, 1.0)) ;
+ PRINTF ((" "ID": pivot tolerance: %g\n",
+ (Int) INDEX (UMFPACK_PIVOT_TOLERANCE), relpt)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* block size */
+ /* ---------------------------------------------------------------------- */
+
+ nb = GET_CONTROL (UMFPACK_BLOCK_SIZE, UMFPACK_DEFAULT_BLOCK_SIZE) ;
+ nb = MAX (1, nb) ;
+ PRINTF ((" "ID": block size for dense matrix kernels: "ID"\n",
+ (Int) INDEX (UMFPACK_BLOCK_SIZE), nb)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* strategy */
+ /* ---------------------------------------------------------------------- */
+
+ strategy = GET_CONTROL (UMFPACK_STRATEGY, UMFPACK_DEFAULT_STRATEGY) ;
+ if (strategy < UMFPACK_STRATEGY_AUTO
+ || strategy > UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ strategy = UMFPACK_STRATEGY_AUTO ;
+ }
+
+ PRINTF ((" "ID": strategy: "ID,
+ (Int) INDEX (UMFPACK_STRATEGY), strategy)) ;
+
+ if (strategy == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ PRINTF ((" (symmetric)\n"
+ " Q = AMD (A+A'), Q not refined during numerical\n"
+ " factorization, and diagonal pivoting (P=Q') attempted.\n")) ;
+ }
+ else if (strategy == UMFPACK_STRATEGY_UNSYMMETRIC)
+ {
+ PRINTF ((" (unsymmetric)\n"
+ " Q = COLAMD (A), Q refined during numerical\n"
+ " factorization, and no attempt at diagonal pivoting.\n")) ;
+ }
+ else if (strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ PRINTF ((" (symmetric, with 2-by-2 block pivoting)\n"
+ " P2 = row permutation that tries to place large entries on\n"
+ " the diagonal. Q = AMD (P2*A+(P2*A)'), Q not refined during\n"
+ " numerical factorization, attempt to select pivots from the\n"
+ " diagonal of P2*A.\n")) ;
+ }
+ else /* auto strategy */
+ {
+ strategy = UMFPACK_STRATEGY_AUTO ;
+ PRINTF ((" (auto)\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* initial allocation parameter */
+ /* ---------------------------------------------------------------------- */
+
+ alloc_init = GET_CONTROL (UMFPACK_ALLOC_INIT, UMFPACK_DEFAULT_ALLOC_INIT) ;
+ if (alloc_init >= 0)
+ {
+ PRINTF ((" "ID": initial allocation ratio: %g\n",
+ (Int) INDEX (UMFPACK_ALLOC_INIT), alloc_init)) ;
+ }
+ else
+ {
+ s = -alloc_init ;
+ s = MAX (1, s) ;
+ PRINTF ((" "ID": initial allocation (in Units): "ID"\n",
+ (Int) INDEX (UMFPACK_ALLOC_INIT), s)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* maximum iterative refinement steps */
+ /* ---------------------------------------------------------------------- */
+
+ irstep = GET_CONTROL (UMFPACK_IRSTEP, UMFPACK_DEFAULT_IRSTEP) ;
+ irstep = MAX (0, irstep) ;
+ PRINTF ((" "ID": max iterative refinement steps: "ID"\n",
+ (Int) INDEX (UMFPACK_IRSTEP), irstep)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* 2-by-2 pivot tolerance */
+ /* ---------------------------------------------------------------------- */
+
+ tol = GET_CONTROL (UMFPACK_2BY2_TOLERANCE, UMFPACK_DEFAULT_2BY2_TOLERANCE) ;
+ tol = MAX (0.0, MIN (tol, 1.0)) ;
+ PRINTF ((" "ID": 2-by-2 pivot tolerance: %g\n",
+ (Int) INDEX (UMFPACK_2BY2_TOLERANCE), tol)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* force fixQ */
+ /* ---------------------------------------------------------------------- */
+
+ force_fixQ = GET_CONTROL (UMFPACK_FIXQ, UMFPACK_DEFAULT_FIXQ) ;
+ PRINTF ((" "ID": Q fixed during numerical factorization: %g ",
+ (Int) INDEX (UMFPACK_FIXQ), force_fixQ)) ;
+ if (force_fixQ > 0)
+ {
+ PRINTF (("(yes)\n")) ;
+ }
+ else if (force_fixQ < 0)
+ {
+ PRINTF (("(no)\n")) ;
+ }
+ else
+ {
+ PRINTF (("(auto)\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* AMD parameters */
+ /* ---------------------------------------------------------------------- */
+
+ amd_alpha = GET_CONTROL (UMFPACK_AMD_DENSE, UMFPACK_DEFAULT_AMD_DENSE) ;
+ PRINTF ((" "ID": AMD dense row/col parameter: %g\n",
+ (Int) INDEX (UMFPACK_AMD_DENSE), amd_alpha)) ;
+ if (amd_alpha < 0)
+ {
+ PRINTF ((" no \"dense\" rows/columns\n")) ;
+ }
+ else
+ {
+ PRINTF ((" \"dense\" rows/columns have > max (16, (%g)*sqrt(n))"
+ " entries\n", amd_alpha)) ;
+ }
+ PRINTF ((" Only used if the AMD ordering is used.\n")) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* pivot tolerance for symmetric pivoting */
+ /* ---------------------------------------------------------------------- */
+
+ relpt2 = GET_CONTROL (UMFPACK_SYM_PIVOT_TOLERANCE,
+ UMFPACK_DEFAULT_SYM_PIVOT_TOLERANCE) ;
+ relpt2 = MAX (0.0, MIN (relpt2, 1.0)) ;
+ PRINTF ((" "ID": diagonal pivot tolerance: %g\n"
+ " Only used if diagonal pivoting is attempted.\n",
+ (Int) INDEX (UMFPACK_SYM_PIVOT_TOLERANCE), relpt2)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* scaling */
+ /* ---------------------------------------------------------------------- */
+
+ scale = GET_CONTROL (UMFPACK_SCALE, UMFPACK_DEFAULT_SCALE) ;
+ if (scale != UMFPACK_SCALE_NONE && scale != UMFPACK_SCALE_MAX)
+ {
+ scale = UMFPACK_DEFAULT_SCALE ;
+ }
+ PRINTF ((" "ID": scaling: "ID, (Int) INDEX (UMFPACK_SCALE), scale)) ;
+ if (scale == UMFPACK_SCALE_NONE)
+ {
+ PRINTF ((" (no)")) ;
+ }
+ else if (scale == UMFPACK_SCALE_SUM)
+ {
+ PRINTF ((" (divide each row by sum of abs. values in each row)")) ;
+ }
+ else if (scale == UMFPACK_SCALE_MAX)
+ {
+ PRINTF ((" (divide each row by max. abs. value in each row)")) ;
+ }
+ PRINTF (("\n")) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* frontal matrix allocation parameter */
+ /* ---------------------------------------------------------------------- */
+
+ front_alloc_init = GET_CONTROL (UMFPACK_FRONT_ALLOC_INIT,
+ UMFPACK_DEFAULT_FRONT_ALLOC_INIT) ;
+ front_alloc_init = MIN (1.0, front_alloc_init) ;
+ if (front_alloc_init >= 0)
+ {
+ PRINTF ((" "ID": frontal matrix allocation ratio: %g\n",
+ (Int) INDEX (UMFPACK_FRONT_ALLOC_INIT), front_alloc_init)) ;
+ }
+ else
+ {
+ s = -front_alloc_init ;
+ s = MAX (1, s) ;
+ PRINTF ((" "ID": initial frontal matrix size (# of Entry's): "ID"\n",
+ (Int) INDEX (UMFPACK_FRONT_ALLOC_INIT), s)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* drop tolerance */
+ /* ---------------------------------------------------------------------- */
+
+ droptol = GET_CONTROL (UMFPACK_DROPTOL, UMFPACK_DEFAULT_DROPTOL) ;
+ PRINTF ((" "ID": drop tolerance: %g\n",
+ (Int) INDEX (UMFPACK_DROPTOL), droptol)) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* aggressive absorption */
+ /* ---------------------------------------------------------------------- */
+
+ aggr = GET_CONTROL (UMFPACK_AGGRESSIVE, UMFPACK_DEFAULT_AGGRESSIVE) ;
+ PRINTF ((" "ID": AMD and COLAMD aggressive absorption: %g",
+ (Int) INDEX (UMFPACK_AGGRESSIVE), aggr)) ;
+ if (aggr != 0.0)
+ {
+ PRINTF ((" (yes)\n")) ;
+ }
+ else
+ {
+ PRINTF ((" (no)\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* compile-time options */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF ((
+ "\n The following options can only be changed at compile-time:\n")) ;
+
+ PRINTF ((" "ID": BLAS library used: ",
+ (Int) INDEX (UMFPACK_COMPILED_WITH_BLAS))) ;
+
+#ifdef NBLAS
+ PRINTF (("none. UMFPACK will be slow.\n")) ;
+#else
+ PRINTF (("Fortran BLAS. size of BLAS integer: "ID"\n",
+ (Int) (sizeof (BLAS_INT)))) ;
+#endif
+
+#ifdef MATLAB_MEX_FILE
+ PRINTF ((" "ID": compiled for MATLAB\n",
+ (Int) INDEX (UMFPACK_COMPILED_FOR_MATLAB))) ;
+#else
+#ifdef MATHWORKS
+ PRINTF ((" "ID": compiled for MATLAB\n",
+ (Int) INDEX (UMFPACK_COMPILED_FOR_MATLAB))) ;
+#else
+ PRINTF ((" "ID": compiled for ANSI C\n",
+ (Int) INDEX (UMFPACK_COMPILED_FOR_MATLAB))) ;
+#endif
+#endif
+
+#ifdef NO_TIMER
+ PRINTF ((" "ID": no CPU timer \n",
+ (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ;
+#else
+#ifndef NPOSIX
+ PRINTF ((" "ID": CPU timer is POSIX times ( ) routine.\n",
+ (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ;
+#else
+#ifdef GETRUSAGE
+ PRINTF ((" "ID": CPU timer is getrusage.\n",
+ (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ;
+#else
+ PRINTF ((" "ID": CPU timer is ANSI C clock (may wrap around).\n",
+ (Int) INDEX (UMFPACK_COMPILED_WITH_GETRUSAGE))) ;
+#endif
+#endif
+#endif
+
+#ifndef NDEBUG
+ PRINTF ((
+"**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n"
+" "ID": compiled with debugging enabled. ",
+ (Int) INDEX (UMFPACK_COMPILED_IN_DEBUG_MODE))) ;
+#else
+ PRINTF ((" "ID": compiled for normal operation (debugging disabled)\n",
+ (Int) INDEX (UMFPACK_COMPILED_IN_DEBUG_MODE))) ;
+#endif
+
+ PRINTF ((" computer/operating system: %s\n", UMFPACK_ARCHITECTURE)) ;
+ PRINTF ((" size of int: %g UF_long: %g Int: %g pointer: %g"
+ " double: %g Entry: %g (in bytes)\n\n", (double) sizeof (int),
+ (double) sizeof (UF_long), (double) sizeof (Int),
+ (double) sizeof (void *), (double) sizeof (double),
+ (double) sizeof (Entry))) ;
+}
diff --git a/UMFPACK/Source/umfpack_report_info.c b/UMFPACK/Source/umfpack_report_info.c
new file mode 100644
index 0000000..ac55466
--- /dev/null
+++ b/UMFPACK/Source/umfpack_report_info.c
@@ -0,0 +1,611 @@
+/* ========================================================================== */
+/* === UMFPACK_report_info ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints the Info array. See umfpack_report_info.h for
+ details.
+*/
+
+#include "umf_internal.h"
+
+#define PRINT_INFO(format,x) \
+{ \
+ if (SCALAR_IS_NAN (x) || (!SCALAR_IS_LTZERO (x))) \
+ { \
+ PRINTF ((format, x)) ; \
+ } \
+}
+
+/* RATIO macro uses a double relop, but ignore NaN case: */
+#define RATIO(a,b,c) (((b) == 0) ? (c) : (((double) a)/((double) b)))
+
+/* ========================================================================== */
+/* === print_ratio ========================================================== */
+/* ========================================================================== */
+
+PRIVATE void print_ratio
+(
+ char *what,
+ char *format,
+ double estimate,
+ double actual
+)
+{
+ if (estimate < 0 && actual < 0) /* double relop, but ignore Nan case */
+ {
+ return ;
+ }
+ PRINTF ((" %-27s", what)) ;
+ if (estimate >= 0) /* double relop, but ignore Nan case */
+ {
+ PRINTF ((format, estimate)) ;
+ }
+ else
+ {
+ PRINTF ((" -")) ;
+ }
+ if (actual >= 0) /* double relop, but ignore Nan case */
+ {
+ PRINTF ((format, actual)) ;
+ }
+ else
+ {
+ PRINTF ((" -")) ;
+ }
+ if (estimate >= 0 && actual >= 0) /* double relop, but ignore Nan case */
+ {
+ PRINTF ((" %5.0f%%\n", 100 * RATIO (actual, estimate, 1))) ;
+ }
+ else
+ {
+ PRINTF ((" -\n")) ;
+ }
+}
+
+/* ========================================================================== */
+/* === UMFPACK_report_info ================================================== */
+/* ========================================================================== */
+
+GLOBAL void UMFPACK_report_info
+(
+ const double Control [UMFPACK_CONTROL],
+ const double Info [UMFPACK_INFO]
+)
+{
+
+ double lnz_est, unz_est, lunz_est, lnz, unz, lunz, tsym, tnum, fnum, tsolve,
+ fsolve, ttot, ftot, twsym, twnum, twsolve, twtot, n2 ;
+ Int n_row, n_col, n_inner, prl, is_sym ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get control settings and status to determine what to print */
+ /* ---------------------------------------------------------------------- */
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (!Info || prl < 2)
+ {
+ /* no output generated if Info is (double *) NULL */
+ /* or if prl is less than 2 */
+ return ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print umfpack version */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF (("UMFPACK V%d.%d.%d (%s), Info:\n", UMFPACK_MAIN_VERSION,
+ UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION, UMFPACK_DATE)) ;
+
+#ifndef NDEBUG
+ PRINTF ((
+"**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n"
+ )) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* print run-time options */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef DINT
+ PRINTF ((" matrix entry defined as: double\n")) ;
+ PRINTF ((" Int (generic integer) defined as: int\n")) ;
+#endif
+#ifdef DLONG
+ PRINTF ((" matrix entry defined as: double\n")) ;
+ PRINTF ((" Int (generic integer) defined as: UF_long\n")) ;
+#endif
+#ifdef ZINT
+ PRINTF ((" matrix entry defined as: double complex\n")) ;
+ PRINTF ((" Int (generic integer) defined as: int\n")) ;
+#endif
+#ifdef ZLONG
+ PRINTF ((" matrix entry defined as: double complex\n")) ;
+ PRINTF ((" Int (generic integer) defined as: UF_long\n")) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* print compile-time options */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF ((" BLAS library used: ")) ;
+
+#ifdef NBLAS
+ PRINTF (("none. UMFPACK will be slow.\n")) ;
+#else
+ PRINTF (("Fortran BLAS. size of BLAS integer: "ID"\n",
+ (Int) (sizeof (BLAS_INT)))) ;
+#endif
+
+ PRINTF ((" MATLAB: ")) ;
+#ifdef MATLAB_MEX_FILE
+ PRINTF (("yes.\n")) ;
+#else
+#ifdef MATHWORKS
+ PRINTF (("yes.\n")) ;
+#else
+ PRINTF (("no.\n")) ;
+#endif
+#endif
+
+ PRINTF ((" CPU timer: ")) ;
+#ifdef NO_TIMER
+ PRINTF (("none.\n")) ;
+#else
+#ifndef NPOSIX
+ PRINTF (("POSIX times ( ) routine.\n")) ;
+#else
+#ifdef GETRUSAGE
+ PRINTF (("getrusage ( ) routine.\n")) ;
+#else
+ PRINTF (("ANSI clock ( ) routine.\n")) ;
+#endif
+#endif
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* print n and nz */
+ /* ---------------------------------------------------------------------- */
+
+ n_row = (Int) Info [UMFPACK_NROW] ;
+ n_col = (Int) Info [UMFPACK_NCOL] ;
+ n_inner = MIN (n_row, n_col) ;
+
+ PRINT_INFO (" number of rows in matrix A: "ID"\n", n_row) ;
+ PRINT_INFO (" number of columns in matrix A: "ID"\n", n_col) ;
+ PRINT_INFO (" entries in matrix A: "ID"\n",
+ (Int) Info [UMFPACK_NZ]) ;
+ PRINT_INFO (" memory usage reported in: "ID"-byte Units\n",
+ (Int) Info [UMFPACK_SIZE_OF_UNIT]) ;
+
+ PRINT_INFO (" size of int: "ID" bytes\n",
+ (Int) Info [UMFPACK_SIZE_OF_INT]) ;
+ PRINT_INFO (" size of UF_long: "ID" bytes\n",
+ (Int) Info [UMFPACK_SIZE_OF_LONG]) ;
+ PRINT_INFO (" size of pointer: "ID" bytes\n",
+ (Int) Info [UMFPACK_SIZE_OF_POINTER]) ;
+ PRINT_INFO (" size of numerical entry: "ID" bytes\n",
+ (Int) Info [UMFPACK_SIZE_OF_ENTRY]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic parameters */
+ /* ---------------------------------------------------------------------- */
+
+ if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ PRINTF (("\n strategy used: symmetric\n")) ;
+ }
+ else if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_UNSYMMETRIC)
+ {
+ PRINTF (("\n strategy used: unsymmetric\n")) ;
+ }
+ else if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_2BY2)
+ {
+ PRINTF (("\n strategy used: symmetric 2-by-2\n"));
+ }
+
+ if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_AMD)
+ {
+ PRINTF ((" ordering used: amd on A+A'\n")) ;
+ }
+ else if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_COLAMD)
+ {
+ PRINTF ((" ordering used: colamd on A\n")) ;
+ }
+ else if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_GIVEN)
+ {
+ PRINTF ((" ordering used: provided by user\n")) ;
+ }
+
+ if (Info [UMFPACK_QFIXED] == 1)
+ {
+ PRINTF ((" modify Q during factorization: no\n")) ;
+ }
+ else if (Info [UMFPACK_QFIXED] == 0)
+ {
+ PRINTF ((" modify Q during factorization: yes\n")) ;
+ }
+
+ if (Info [UMFPACK_DIAG_PREFERRED] == 0)
+ {
+ PRINTF ((" prefer diagonal pivoting: no\n")) ;
+ }
+ else if (Info [UMFPACK_DIAG_PREFERRED] == 1)
+ {
+ PRINTF ((" prefer diagonal pivoting: yes\n")) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* singleton statistics */
+ /* ---------------------------------------------------------------------- */
+
+ PRINT_INFO (" pivots with zero Markowitz cost: %0.f\n",
+ Info [UMFPACK_COL_SINGLETONS] + Info [UMFPACK_ROW_SINGLETONS]) ;
+ PRINT_INFO (" submatrix S after removing zero-cost pivots:\n"
+ " number of \"dense\" rows: %.0f\n",
+ Info [UMFPACK_NDENSE_ROW]) ;
+ PRINT_INFO (" number of \"dense\" columns: %.0f\n",
+ Info [UMFPACK_NDENSE_COL]) ;
+ PRINT_INFO (" number of empty rows: %.0f\n",
+ Info [UMFPACK_NEMPTY_ROW]) ;
+ PRINT_INFO (" number of empty columns %.0f\n",
+ Info [UMFPACK_NEMPTY_COL]) ;
+ is_sym = Info [UMFPACK_S_SYMMETRIC] ;
+ if (is_sym > 0)
+ {
+ PRINTF ((" submatrix S square and diagonal preserved\n")) ;
+ }
+ else if (is_sym == 0)
+ {
+ PRINTF ((" submatrix S not square or diagonal not preserved\n"));
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics from amd_aat */
+ /* ---------------------------------------------------------------------- */
+
+ n2 = Info [UMFPACK_N2] ;
+ if (n2 >= 0)
+ {
+ PRINTF ((" pattern of square submatrix S:\n")) ;
+ }
+ PRINT_INFO (" number rows and columns %.0f\n",
+ n2) ;
+ PRINT_INFO (" symmetry of nonzero pattern: %.6f\n",
+ Info [UMFPACK_PATTERN_SYMMETRY]) ;
+ PRINT_INFO (" nz in S+S' (excl. diagonal): %.0f\n",
+ Info [UMFPACK_NZ_A_PLUS_AT]) ;
+ PRINT_INFO (" nz on diagonal of matrix S: %.0f\n",
+ Info [UMFPACK_NZDIAG]) ;
+ if (Info [UMFPACK_NZDIAG] >= 0 && n2 > 0)
+ {
+ PRINTF ((" fraction of nz on diagonal: %.6f\n",
+ Info [UMFPACK_NZDIAG] / n2)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics from 2-by-2 permutation */
+ /* ---------------------------------------------------------------------- */
+
+ PRINT_INFO (" 2-by-2 pivoting to place large entries on diagonal:\n"
+ " # of small diagonal entries of S: %.0f\n",
+ Info [UMFPACK_2BY2_NWEAK]) ;
+ PRINT_INFO (" # unmatched: %.0f\n",
+ Info [UMFPACK_2BY2_UNMATCHED]) ;
+ PRINT_INFO (" symmetry of P2*S: %.6f\n",
+ Info [UMFPACK_2BY2_PATTERN_SYMMETRY]) ;
+ PRINT_INFO (" nz in P2*S+(P2*S)' (excl. diag.): %.0f\n",
+ Info [UMFPACK_2BY2_NZ_PA_PLUS_PAT]) ;
+ PRINT_INFO (" nz on diagonal of P2*S: %.0f\n",
+ Info [UMFPACK_2BY2_NZDIAG]) ;
+ if (Info [UMFPACK_2BY2_NZDIAG] >= 0 && n2 > 0)
+ {
+ PRINTF ((" fraction of nz on diag of P2*S: %.6f\n",
+ Info [UMFPACK_2BY2_NZDIAG] / n2)) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* statistics from AMD */
+ /* ---------------------------------------------------------------------- */
+
+ if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_AMD)
+ {
+ double dmax = Info [UMFPACK_SYMMETRIC_DMAX] ;
+ PRINTF ((" AMD statistics, for strict diagonal pivoting:\n")) ;
+ PRINT_INFO (" est. flops for LU factorization: %.5e\n",
+ Info [UMFPACK_SYMMETRIC_FLOPS]) ;
+ PRINT_INFO (" est. nz in L+U (incl. diagonal): %.0f\n",
+ Info [UMFPACK_SYMMETRIC_LUNZ]) ;
+ PRINT_INFO (" est. largest front (# entries): %.0f\n",
+ dmax*dmax) ;
+ PRINT_INFO (" est. max nz in any column of L: %.0f\n",
+ dmax) ;
+ PRINT_INFO (
+ " number of \"dense\" rows/columns in S+S': %.0f\n",
+ Info [UMFPACK_SYMMETRIC_NDENSE]) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ tsym = Info [UMFPACK_SYMBOLIC_TIME] ;
+ twsym = Info [UMFPACK_SYMBOLIC_WALLTIME] ;
+
+ PRINT_INFO (" symbolic factorization defragmentations: %.0f\n",
+ Info [UMFPACK_SYMBOLIC_DEFRAG]) ;
+ PRINT_INFO (" symbolic memory usage (Units): %.0f\n",
+ Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]) ;
+ PRINT_INFO (" symbolic memory usage (MBytes): %.1f\n",
+ MBYTES (Info [UMFPACK_SYMBOLIC_PEAK_MEMORY])) ;
+ PRINT_INFO (" Symbolic size (Units): %.0f\n",
+ Info [UMFPACK_SYMBOLIC_SIZE]) ;
+ PRINT_INFO (" Symbolic size (MBytes): %.0f\n",
+ MBYTES (Info [UMFPACK_SYMBOLIC_SIZE])) ;
+ PRINT_INFO (" symbolic factorization CPU time (sec): %.2f\n",
+ tsym) ;
+ PRINT_INFO (" symbolic factorization wallclock time(sec): %.2f\n",
+ twsym) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* scaling, from numerical factorization */
+ /* ---------------------------------------------------------------------- */
+
+ if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_NONE)
+ {
+ PRINTF (("\n matrix scaled: no\n")) ;
+ }
+ else if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_SUM)
+ {
+ PRINTF (("\n matrix scaled: yes ")) ;
+ PRINTF (("(divided each row by sum of abs values in each row)\n")) ;
+ PRINTF ((" minimum sum (abs (rows of A)): %.5e\n",
+ Info [UMFPACK_RSMIN])) ;
+ PRINTF ((" maximum sum (abs (rows of A)): %.5e\n",
+ Info [UMFPACK_RSMAX])) ;
+ }
+ else if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_MAX)
+ {
+ PRINTF (("\n matrix scaled: yes ")) ;
+ PRINTF (("(divided each row by max abs value in each row)\n")) ;
+ PRINTF ((" minimum max (abs (rows of A)): %.5e\n",
+ Info [UMFPACK_RSMIN])) ;
+ PRINTF ((" maximum max (abs (rows of A)): %.5e\n",
+ Info [UMFPACK_RSMAX])) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* estimate/actual in symbolic/numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ /* double relop, but ignore NaN case: */
+ if (Info [UMFPACK_SYMBOLIC_DEFRAG] >= 0 /* UMFPACK_*symbolic called */
+ || Info [UMFPACK_NUMERIC_DEFRAG] >= 0) /* UMFPACK_numeric called */
+ {
+ PRINTF (("\n symbolic/numeric factorization: upper bound")) ;
+ PRINTF ((" actual %%\n")) ;
+ PRINTF ((" variable-sized part of Numeric object:\n")) ;
+ }
+ print_ratio (" initial size (Units)", " %20.0f",
+ Info [UMFPACK_VARIABLE_INIT_ESTIMATE], Info [UMFPACK_VARIABLE_INIT]) ;
+ print_ratio (" peak size (Units)", " %20.0f",
+ Info [UMFPACK_VARIABLE_PEAK_ESTIMATE], Info [UMFPACK_VARIABLE_PEAK]) ;
+ print_ratio (" final size (Units)", " %20.0f",
+ Info [UMFPACK_VARIABLE_FINAL_ESTIMATE], Info [UMFPACK_VARIABLE_FINAL]) ;
+ print_ratio ("Numeric final size (Units)", " %20.0f",
+ Info [UMFPACK_NUMERIC_SIZE_ESTIMATE], Info [UMFPACK_NUMERIC_SIZE]) ;
+ print_ratio ("Numeric final size (MBytes)", " %20.1f",
+ MBYTES (Info [UMFPACK_NUMERIC_SIZE_ESTIMATE]),
+ MBYTES (Info [UMFPACK_NUMERIC_SIZE])) ;
+ print_ratio ("peak memory usage (Units)", " %20.0f",
+ Info [UMFPACK_PEAK_MEMORY_ESTIMATE], Info [UMFPACK_PEAK_MEMORY]) ;
+ print_ratio ("peak memory usage (MBytes)", " %20.1f",
+ MBYTES (Info [UMFPACK_PEAK_MEMORY_ESTIMATE]),
+ MBYTES (Info [UMFPACK_PEAK_MEMORY])) ;
+ print_ratio ("numeric factorization flops", " %20.5e",
+ Info [UMFPACK_FLOPS_ESTIMATE], Info [UMFPACK_FLOPS]) ;
+
+ lnz_est = Info [UMFPACK_LNZ_ESTIMATE] ;
+ unz_est = Info [UMFPACK_UNZ_ESTIMATE] ;
+ if (lnz_est >= 0 && unz_est >= 0) /* double relop, but ignore NaN case */
+ {
+ lunz_est = lnz_est + unz_est - n_inner ;
+ }
+ else
+ {
+ lunz_est = EMPTY ;
+ }
+ lnz = Info [UMFPACK_LNZ] ;
+ unz = Info [UMFPACK_UNZ] ;
+ if (lnz >= 0 && unz >= 0) /* double relop, but ignore NaN case */
+ {
+ lunz = lnz + unz - n_inner ;
+ }
+ else
+ {
+ lunz = EMPTY ;
+ }
+ print_ratio ("nz in L (incl diagonal)", " %20.0f", lnz_est, lnz) ;
+ print_ratio ("nz in U (incl diagonal)", " %20.0f", unz_est, unz) ;
+ print_ratio ("nz in L+U (incl diagonal)", " %20.0f", lunz_est, lunz) ;
+
+ print_ratio ("largest front (# entries)", " %20.0f",
+ Info [UMFPACK_MAX_FRONT_SIZE_ESTIMATE], Info [UMFPACK_MAX_FRONT_SIZE]) ;
+ print_ratio ("largest # rows in front", " %20.0f",
+ Info [UMFPACK_MAX_FRONT_NROWS_ESTIMATE],
+ Info [UMFPACK_MAX_FRONT_NROWS]) ;
+ print_ratio ("largest # columns in front", " %20.0f",
+ Info [UMFPACK_MAX_FRONT_NCOLS_ESTIMATE],
+ Info [UMFPACK_MAX_FRONT_NCOLS]) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* numeric factorization */
+ /* ---------------------------------------------------------------------- */
+
+ tnum = Info [UMFPACK_NUMERIC_TIME] ;
+ twnum = Info [UMFPACK_NUMERIC_WALLTIME] ;
+ fnum = Info [UMFPACK_FLOPS] ;
+
+ PRINT_INFO ("\n initial allocation ratio used: %0.3g\n",
+ Info [UMFPACK_ALLOC_INIT_USED]) ;
+ PRINT_INFO (" # of forced updates due to frontal growth: %.0f\n",
+ Info [UMFPACK_FORCED_UPDATES]) ;
+ PRINT_INFO (" number of off-diagonal pivots: %.0f\n",
+ Info [UMFPACK_NOFF_DIAG]) ;
+ PRINT_INFO (" nz in L (incl diagonal), if none dropped %.0f\n",
+ Info [UMFPACK_ALL_LNZ]) ;
+ PRINT_INFO (" nz in U (incl diagonal), if none dropped %.0f\n",
+ Info [UMFPACK_ALL_UNZ]) ;
+ PRINT_INFO (" number of small entries dropped %.0f\n",
+ Info [UMFPACK_NZDROPPED]) ;
+ PRINT_INFO (" nonzeros on diagonal of U: %.0f\n",
+ Info [UMFPACK_UDIAG_NZ]) ;
+ PRINT_INFO (" min abs. value on diagonal of U: %.2e\n",
+ Info [UMFPACK_UMIN]) ;
+ PRINT_INFO (" max abs. value on diagonal of U: %.2e\n",
+ Info [UMFPACK_UMAX]) ;
+ PRINT_INFO (" estimate of reciprocal of condition number: %.2e\n",
+ Info [UMFPACK_RCOND]) ;
+ PRINT_INFO (" indices in compressed pattern: %.0f\n",
+ Info [UMFPACK_COMPRESSED_PATTERN]) ;
+ PRINT_INFO (" numerical values stored in Numeric object: %.0f\n",
+ Info [UMFPACK_LU_ENTRIES]) ;
+ PRINT_INFO (" numeric factorization defragmentations: %.0f\n",
+ Info [UMFPACK_NUMERIC_DEFRAG]) ;
+ PRINT_INFO (" numeric factorization reallocations: %.0f\n",
+ Info [UMFPACK_NUMERIC_REALLOC]) ;
+ PRINT_INFO (" costly numeric factorization reallocations: %.0f\n",
+ Info [UMFPACK_NUMERIC_COSTLY_REALLOC]) ;
+ PRINT_INFO (" numeric factorization CPU time (sec): %.2f\n",
+ tnum) ;
+ PRINT_INFO (" numeric factorization wallclock time (sec): %.2f\n",
+ twnum) ;
+
+#define TMIN 0.001
+
+ if (tnum > TMIN && fnum > 0)
+ {
+ PRINT_INFO (
+ " numeric factorization mflops (CPU time): %.2f\n",
+ 1e-6 * fnum / tnum) ;
+ }
+ if (twnum > TMIN && fnum > 0)
+ {
+ PRINT_INFO (
+ " numeric factorization mflops (wallclock): %.2f\n",
+ 1e-6 * fnum / twnum) ;
+ }
+
+ ttot = EMPTY ;
+ ftot = fnum ;
+ if (tsym >= TMIN && tnum >= 0)
+ {
+ ttot = tsym + tnum ;
+ PRINT_INFO (" symbolic + numeric CPU time (sec): %.2f\n",
+ ttot) ;
+ if (ftot > 0 && ttot > TMIN)
+ {
+ PRINT_INFO (
+ " symbolic + numeric mflops (CPU time): %.2f\n",
+ 1e-6 * ftot / ttot) ;
+ }
+ }
+
+ twtot = EMPTY ;
+ if (twsym >= TMIN && twnum >= TMIN)
+ {
+ twtot = twsym + twnum ;
+ PRINT_INFO (" symbolic + numeric wall clock time (sec): %.2f\n",
+ twtot) ;
+ if (ftot > 0 && twtot > TMIN)
+ {
+ PRINT_INFO (
+ " symbolic + numeric mflops (wall clock): %.2f\n",
+ 1e-6 * ftot / twtot) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* solve */
+ /* ---------------------------------------------------------------------- */
+
+ tsolve = Info [UMFPACK_SOLVE_TIME] ;
+ twsolve = Info [UMFPACK_SOLVE_WALLTIME] ;
+ fsolve = Info [UMFPACK_SOLVE_FLOPS] ;
+
+ PRINT_INFO ("\n solve flops: %.5e\n",
+ fsolve) ;
+ PRINT_INFO (" iterative refinement steps taken: %.0f\n",
+ Info [UMFPACK_IR_TAKEN]) ;
+ PRINT_INFO (" iterative refinement steps attempted: %.0f\n",
+ Info [UMFPACK_IR_ATTEMPTED]) ;
+ PRINT_INFO (" sparse backward error omega1: %.2e\n",
+ Info [UMFPACK_OMEGA1]) ;
+ PRINT_INFO (" sparse backward error omega2: %.2e\n",
+ Info [UMFPACK_OMEGA2]) ;
+ PRINT_INFO (" solve CPU time (sec): %.2f\n",
+ tsolve) ;
+ PRINT_INFO (" solve wall clock time (sec): %.2f\n",
+ twsolve) ;
+ if (fsolve > 0 && tsolve > TMIN)
+ {
+ PRINT_INFO (
+ " solve mflops (CPU time): %.2f\n",
+ 1e-6 * fsolve / tsolve) ;
+ }
+ if (fsolve > 0 && twsolve > TMIN)
+ {
+ PRINT_INFO (
+ " solve mflops (wall clock time): %.2f\n",
+ 1e-6 * fsolve / twsolve) ;
+ }
+
+ if (ftot >= 0 && fsolve >= 0)
+ {
+ ftot += fsolve ;
+ PRINT_INFO (
+ "\n total symbolic + numeric + solve flops: %.5e\n", ftot) ;
+ }
+
+ if (tsolve >= TMIN)
+ {
+ if (ttot >= TMIN && ftot >= 0)
+ {
+ ttot += tsolve ;
+ PRINT_INFO (
+ " total symbolic + numeric + solve CPU time: %.2f\n",
+ ttot) ;
+ if (ftot > 0 && ttot > TMIN)
+ {
+ PRINT_INFO (
+ " total symbolic + numeric + solve mflops (CPU): %.2f\n",
+ 1e-6 * ftot / ttot) ;
+ }
+ }
+ }
+
+ if (twsolve >= TMIN)
+ {
+ if (twtot >= TMIN && ftot >= 0)
+ {
+ twtot += tsolve ;
+ PRINT_INFO (
+ " total symbolic+numeric+solve wall clock time: %.2f\n",
+ twtot) ;
+ if (ftot > 0 && twtot > TMIN)
+ {
+ PRINT_INFO (
+ " total symbolic+numeric+solve mflops(wallclock) %.2f\n",
+ 1e-6 * ftot / twtot) ;
+ }
+ }
+ }
+ PRINTF (("\n")) ;
+}
diff --git a/UMFPACK/Source/umfpack_report_matrix.c b/UMFPACK/Source/umfpack_report_matrix.c
new file mode 100644
index 0000000..6074ea4
--- /dev/null
+++ b/UMFPACK/Source/umfpack_report_matrix.c
@@ -0,0 +1,201 @@
+/* ========================================================================== */
+/* === UMFPACK_report_matrix ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints a column or row-oriented matrix. See
+ umfpack_report_matrix.h for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL Int UMFPACK_report_matrix
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ Int col_form, /* 1: column form, 0: row form */
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Entry a ;
+ Int prl, i, k, length, ilast, p, nz, prl1, p1, p2, n, n_i, do_values ;
+ char *vector, *index ;
+#ifdef COMPLEX
+ Int split = SPLIT (Az) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* determine the form, and check if inputs exist */
+ /* ---------------------------------------------------------------------- */
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ if (col_form)
+ {
+ vector = "column" ; /* column vectors */
+ index = "row" ; /* with row indices */
+ n = n_col ;
+ n_i = n_row ;
+ }
+ else
+ {
+ vector = "row" ; /* row vectors */
+ index = "column" ; /* with column indices */
+ n = n_row ;
+ n_i = n_col ;
+ }
+
+ PRINTF (("%s-form matrix, n_row "ID" n_col "ID", ", vector, n_row, n_col)) ;
+
+ if (n_row <= 0 || n_col <= 0)
+ {
+ PRINTF (("ERROR: n_row <= 0 or n_col <= 0\n\n")) ;
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+
+ if (!Ap)
+ {
+ PRINTF (("ERROR: Ap missing\n\n")) ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ nz = Ap [n] ;
+ PRINTF (("nz = "ID". ", nz)) ;
+ if (nz < 0)
+ {
+ PRINTF (("ERROR: number of entries < 0\n\n")) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ if (Ap [0] != 0)
+ {
+ PRINTF (("ERROR: Ap ["ID"] = "ID" must be "ID"\n\n",
+ (Int) INDEX (0), INDEX (Ap [0]), (Int) INDEX (0))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ if (!Ai)
+ {
+ PRINTF (("ERROR: Ai missing\n\n")) ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ do_values = Ax != (double *) NULL ;
+
+ PRINTF4 (("\n")) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* check the row/column pointers, Ap */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n ; k++)
+ {
+ if (Ap [k] < 0)
+ {
+ PRINTF (("ERROR: Ap ["ID"] < 0\n\n", INDEX (k))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ if (Ap [k] > nz)
+ {
+ PRINTF (("ERROR: Ap ["ID"] > size of Ai\n\n", INDEX (k))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ }
+
+ for (k = 0 ; k < n ; k++)
+ {
+ length = Ap [k+1] - Ap [k] ;
+ if (length < 0)
+ {
+ PRINTF (("ERROR: # entries in %s "ID" is < 0\n\n",
+ vector, INDEX (k))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print each vector */
+ /* ---------------------------------------------------------------------- */
+
+ prl1 = prl ;
+
+ for (k = 0 ; k < n ; k++)
+ {
+ /* if prl is 4, print the first 10 entries of the first 10 vectors */
+ if (k < 10)
+ {
+ prl = prl1 ;
+ }
+ /* get the vector pointers */
+ p1 = Ap [k] ;
+ p2 = Ap [k+1] ;
+ length = p2 - p1 ;
+ PRINTF4 (("\n %s "ID": start: "ID" end: "ID" entries: "ID"\n",
+ vector, INDEX (k), p1, p2-1, length)) ;
+ ilast = EMPTY ;
+ for (p = p1 ; p < p2 ; p++)
+ {
+ i = Ai [p] ;
+ PRINTF4 (("\t%s "ID" ", index, INDEX (i))) ;
+ if (do_values && prl >= 4)
+ {
+ PRINTF ((":")) ;
+ ASSIGN (a, Ax, Az, p, split) ;
+ PRINT_ENTRY (a) ;
+ }
+ if (i < 0 || i >= n_i)
+ {
+ PRINTF ((" ERROR: %s index "ID" out of range in %s "ID"\n\n",
+ index, INDEX (i), vector, INDEX (k))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ if (i <= ilast)
+ {
+ PRINTF ((" ERROR: %s index "ID" out of order (or duplicate) in "
+ "%s "ID"\n\n", index, INDEX (i), vector, INDEX (k))) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ PRINTF4 (("\n")) ;
+ /* truncate printout, but continue to check matrix */
+ if (prl == 4 && (p - p1) == 9 && length > 10)
+ {
+ PRINTF4 (("\t...\n")) ;
+ prl-- ;
+ }
+ ilast = i ;
+ }
+ /* truncate printout, but continue to check matrix */
+ if (prl == 4 && k == 9 && n > 10)
+ {
+ PRINTF4 (("\n ...\n")) ;
+ prl-- ;
+ }
+ }
+ prl = prl1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* return the status of the matrix */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF4 ((" %s-form matrix ", vector)) ;
+ PRINTF (("OK\n\n")) ;
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_report_numeric.c b/UMFPACK/Source/umfpack_report_numeric.c
new file mode 100644
index 0000000..f70555f
--- /dev/null
+++ b/UMFPACK/Source/umfpack_report_numeric.c
@@ -0,0 +1,663 @@
+/* ========================================================================== */
+/* === UMFPACK_report_numeric =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints the Numeric object.
+ See umfpack_report_numeric.h for details.
+
+ Dynamic memory usage: Allocates a size n*sizeof(Int) workspace via a single
+ call to UMF_malloc and then frees all of it via UMF_free on return. The
+ workspace is not allocated if an early error return occurs before the
+ workspace is needed.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+#include "umf_report_perm.h"
+#include "umf_report_vector.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+
+PRIVATE Int report_L
+(
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int prl
+) ;
+
+
+PRIVATE Int report_U
+(
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int prl
+) ;
+
+/* ========================================================================== */
+/* === UMFPACK_report_numeric =============================================== */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_report_numeric
+(
+ void *NumericHandle,
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Int prl, *W, nn, n_row, n_col, n_inner, num_fixed_size, numeric_size,
+ npiv ;
+ NumericType *Numeric ;
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ PRINTF (("Numeric object: ")) ;
+
+ Numeric = (NumericType *) NumericHandle ;
+ if (!UMF_valid_numeric (Numeric))
+ {
+ PRINTF (("ERROR: LU factors invalid\n\n")) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ n_row = Numeric->n_row ;
+ n_col = Numeric->n_col ;
+ nn = MAX (n_row, n_col) ;
+ n_inner = MIN (n_row, n_col) ;
+ npiv = Numeric->npiv ;
+
+ DEBUG1 (("n_row "ID" n_col "ID" nn "ID" n_inner "ID" npiv "ID"\n",
+ n_row, n_col, nn, n_inner, npiv)) ;
+
+ /* size of Numeric object, except Numeric->Memory and Numeric->Upattern */
+ /* see also UMF_set_stats */
+ num_fixed_size =
+ UNITS (NumericType, 1) /* Numeric structure */
+ + UNITS (Entry, n_inner+1) /* D */
+ + UNITS (Int, n_row+1) /* Rperm */
+ + UNITS (Int, n_col+1) /* Cperm */
+ + 6 * UNITS (Int, npiv+1) /* Lpos, Uilen, Uip, Upos, Lilen, Lip */
+ + ((Numeric->scale != UMFPACK_SCALE_NONE) ?
+ UNITS (Entry, n_row) : 0) ; /* Rs */
+
+ DEBUG1 (("num fixed size: "ID"\n", num_fixed_size)) ;
+ DEBUG1 (("Numeric->size "ID"\n", Numeric->size)) ;
+ DEBUG1 (("ulen units "ID"\n", UNITS (Int, Numeric->ulen))) ;
+
+ /* size of Numeric->Memory is Numeric->size */
+ /* size of Numeric->Upattern is Numeric->ulen */
+ numeric_size = num_fixed_size + Numeric->size
+ + UNITS (Int, Numeric->ulen) ;
+
+ DEBUG1 (("numeric total size "ID"\n", numeric_size)) ;
+
+ if (prl >= 4)
+ {
+ PRINTF (("\n n_row: "ID" n_col: "ID"\n", n_row, n_col)) ;
+
+ PRINTF ((" relative pivot tolerance used: %g\n",
+ Numeric->relpt)) ;
+ PRINTF ((" relative symmetric pivot tolerance used: %g\n",
+ Numeric->relpt2)) ;
+
+ PRINTF ((" matrix scaled: ")) ;
+ if (Numeric->scale == UMFPACK_SCALE_NONE)
+ {
+ PRINTF (("no")) ;
+ }
+ else if (Numeric->scale == UMFPACK_SCALE_SUM)
+ {
+ PRINTF (("yes (divided each row by sum abs value in each row)\n")) ;
+ PRINTF ((" minimum sum (abs (rows of A)): %.5e\n",
+ Numeric->rsmin)) ;
+ PRINTF ((" maximum sum (abs (rows of A)): %.5e",
+ Numeric->rsmax)) ;
+ }
+ else if (Numeric->scale == UMFPACK_SCALE_MAX)
+ {
+ PRINTF (("yes (divided each row by max abs value in each row)\n")) ;
+ PRINTF ((" minimum max (abs (rows of A)): %.5e\n",
+ Numeric->rsmin)) ;
+ PRINTF ((" maximum max (abs (rows of A)): %.5e",
+ Numeric->rsmax)) ;
+ }
+ PRINTF (("\n")) ;
+
+ PRINTF ((" initial allocation parameter used: %g\n",
+ Numeric->alloc_init)) ;
+ PRINTF ((" frontal matrix allocation parameter used: %g\n",
+ Numeric->front_alloc_init)) ;
+ PRINTF ((" final total size of Numeric object (Units): "ID"\n",
+ numeric_size)) ;
+ PRINTF ((" final total size of Numeric object (MBytes): %.1f\n",
+ MBYTES (numeric_size))) ;
+ PRINTF ((" peak size of variable-size part (Units): "ID"\n",
+ Numeric->max_usage)) ;
+ PRINTF ((" peak size of variable-size part (MBytes): %.1f\n",
+ MBYTES (Numeric->max_usage))) ;
+ PRINTF ((" largest actual frontal matrix size: "ID"\n",
+ Numeric->maxfrsize)) ;
+ PRINTF ((" memory defragmentations: "ID"\n",
+ Numeric->ngarbage)) ;
+ PRINTF ((" memory reallocations: "ID"\n",
+ Numeric->nrealloc)) ;
+ PRINTF ((" costly memory reallocations: "ID"\n",
+ Numeric->ncostly)) ;
+ PRINTF ((" entries in compressed pattern (L and U): "ID"\n",
+ Numeric->isize)) ;
+ PRINTF ((" number of nonzeros in L (excl diag): "ID"\n",
+ Numeric->lnz)) ;
+ PRINTF ((" number of entries stored in L (excl diag): "ID"\n",
+ Numeric->nLentries)) ;
+ PRINTF ((" number of nonzeros in U (excl diag): "ID"\n",
+ Numeric->unz)) ;
+ PRINTF ((" number of entries stored in U (excl diag): "ID"\n",
+ Numeric->nUentries)) ;
+ PRINTF ((" factorization floating-point operations: %g\n",
+ Numeric->flops)) ;
+ PRINTF ((" number of nonzeros on diagonal of U: "ID"\n",
+ Numeric->nnzpiv)) ;
+ PRINTF ((" min abs. value on diagonal of U: %.5e\n",
+ Numeric->min_udiag)) ;
+ PRINTF ((" max abs. value on diagonal of U: %.5e\n",
+ Numeric->max_udiag)) ;
+ PRINTF ((" reciprocal condition number estimate: %.2e\n",
+ Numeric->rcond)) ;
+ }
+
+ W = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ if (!W)
+ {
+ PRINTF ((" ERROR: out of memory to check Numeric object\n\n")) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ if (Numeric->Rs)
+ {
+#ifndef NRECIPROCAL
+ if (Numeric->do_recip)
+ {
+ PRINTF4 (("\nScale factors applied via multiplication\n")) ;
+ }
+ else
+#endif
+ {
+ PRINTF4 (("\nScale factors applied via division\n")) ;
+ }
+ PRINTF4 (("Scale factors, Rs: ")) ;
+ (void) UMF_report_vector (n_row, Numeric->Rs, (double *) NULL,
+ prl, FALSE, TRUE) ;
+ }
+ else
+ {
+ PRINTF4 (("Scale factors, Rs: (not present)\n")) ;
+ }
+
+ PRINTF4 (("\nP: row ")) ;
+ if (UMF_report_perm (n_row, Numeric->Rperm, W, prl, 0) != UMFPACK_OK)
+ {
+ (void) UMF_free ((void *) W) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ PRINTF4 (("\nQ: column ")) ;
+ if (UMF_report_perm (n_col, Numeric->Cperm, W, prl, 0) != UMFPACK_OK)
+ {
+ (void) UMF_free ((void *) W) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ if (!report_L (Numeric, W, prl))
+ {
+ (void) UMF_free ((void *) W) ;
+ PRINTF ((" ERROR: L factor invalid\n\n")) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ if (!report_U (Numeric, W, prl))
+ {
+ (void) UMF_free ((void *) W) ;
+ PRINTF ((" ERROR: U factor invalid\n\n")) ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ /* The diagonal of U is in "merged" (Entry) form, not "split" form. */
+ PRINTF4 (("\ndiagonal of U: ")) ;
+ (void) UMF_report_vector (n_inner, (double *) Numeric->D, (double *) NULL,
+ prl, FALSE, FALSE) ;
+
+ (void) UMF_free ((void *) W) ;
+
+ PRINTF4 ((" Numeric object: ")) ;
+ PRINTF (("OK\n\n")) ;
+ return (UMFPACK_OK) ;
+}
+
+
+/* ========================================================================== */
+/* === report_L ============================================================= */
+/* ========================================================================== */
+
+PRIVATE Int report_L
+(
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int prl
+)
+{
+ Int k, deg, *ip, j, row, n_row, *Lpos, *Lilen, valid, k1,
+ *Lip, newLchain, llen, prl1, pos, lp, p, npiv, n1, *Li ;
+ Entry *xp, *Lval ;
+
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (prl >= 3) ;
+
+ n_row = Numeric->n_row ;
+ npiv = Numeric->npiv ;
+ n1 = Numeric->n1 ;
+ Lpos = Numeric->Lpos ;
+ Lilen = Numeric->Lilen ;
+ Lip = Numeric->Lip ;
+ prl1 = prl ;
+ deg = 0 ;
+
+ PRINTF4 ((
+ "\nL in Numeric object, in column-oriented compressed-pattern form:\n"
+ " Diagonal entries are all equal to 1.0 (not stored)\n")) ;
+
+ ASSERT (Pattern != (Int *) NULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print L */
+ /* ---------------------------------------------------------------------- */
+
+ k1 = 12 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print the singleton columns of L */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = 0 ; k < n1 ; k++)
+ {
+ if (k1 > 0)
+ {
+ prl = prl1 ;
+ }
+ lp = Lip [k] ;
+ deg = Lilen [k] ;
+ Li = (Int *) (Numeric->Memory + lp) ;
+ lp += UNITS (Int, deg) ;
+ Lval = (Entry *) (Numeric->Memory + lp) ;
+ if (k1-- > 0)
+ {
+ prl = prl1 ;
+ }
+ else if (prl == 4)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+ PRINTF4 (("\n column "ID":", INDEX (k))) ;
+ PRINTF4 ((" length "ID".\n", deg)) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ row = Li [j] ;
+ PRINTF4 (("\trow "ID" : ", INDEX (row))) ;
+ if (prl >= 4) PRINT_ENTRY (Lval [j]) ;
+ if (row <= k || row >= n_row)
+ {
+ return (FALSE) ;
+ }
+ PRINTF4 (("\n")) ;
+ /* truncate printout, but continue to check L */
+ if (prl == 4 && j == 9 && deg > 10)
+ {
+ PRINTF (("\t...\n")) ;
+ prl-- ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print the regular columns of L */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = n1 ; k < npiv ; k++)
+ {
+ /* if prl is 4, print the first 10 entries of the first 10 columns */
+ if (k1 > 0)
+ {
+ prl = prl1 ;
+ }
+
+ lp = Lip [k] ;
+ newLchain = (lp < 0) ;
+ if (newLchain)
+ {
+ lp = -lp ;
+ deg = 0 ;
+ }
+
+ if (k1-- > 0)
+ {
+ prl = prl1 ;
+ }
+ else if (prl == 4)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+
+ PRINTF4 (("\n column "ID":", INDEX (k))) ;
+
+ /* ------------------------------------------------------------------ */
+ /* make column of L in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ /* remove pivot row */
+ pos = Lpos [k] ;
+ if (pos != EMPTY)
+ {
+ PRINTF4 ((" remove row "ID" at position "ID".",
+ INDEX (Pattern [pos]), INDEX (pos))) ;
+ valid = (!newLchain) && (deg > 0) && (pos < deg) && (pos >= 0)
+ && (Pattern [pos] == k) ;
+ if (!valid)
+ {
+ return (FALSE) ;
+ }
+ Pattern [pos] = Pattern [--deg] ;
+ }
+
+ /* concatenate the pattern */
+ llen = Lilen [k] ;
+ if (llen < 0)
+ {
+ return (FALSE) ;
+ }
+ p = lp + UNITS (Int, llen) ;
+ xp = (Entry *) (Numeric->Memory + p) ;
+ if ((llen > 0 || deg > 0)
+ && (p + (Int) UNITS (Entry, deg) > Numeric->size))
+ {
+ return (FALSE) ;
+ }
+ if (llen > 0)
+ {
+ PRINTF4 ((" add "ID" entries.", llen)) ;
+ ip = (Int *) (Numeric->Memory + lp) ;
+ for (j = 0 ; j < llen ; j++)
+ {
+ Pattern [deg++] = *ip++ ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* print column k of L */
+ /* ------------------------------------------------------------------ */
+
+ PRINTF4 ((" length "ID".", deg)) ;
+ if (newLchain)
+ {
+ PRINTF4 ((" Start of Lchain.")) ;
+ }
+ PRINTF4 (("\n")) ;
+
+ for (j = 0 ; j < deg ; j++)
+ {
+ row = Pattern [j] ;
+ PRINTF4 (("\trow "ID" : ", INDEX (row))) ;
+ if (prl >= 4) PRINT_ENTRY (*xp) ;
+ if (row <= k || row >= n_row)
+ {
+ return (FALSE) ;
+ }
+ PRINTF4 (("\n")) ;
+ xp++ ;
+ /* truncate printout, but continue to check L */
+ if (prl == 4 && j == 9 && deg > 10)
+ {
+ PRINTF (("\t...\n")) ;
+ prl-- ;
+ }
+ }
+ }
+
+ PRINTF4 (("\n")) ;
+ return (TRUE) ;
+}
+
+
+/* ========================================================================== */
+/* === report_U ============================================================= */
+/* ========================================================================== */
+
+PRIVATE Int report_U
+(
+ NumericType *Numeric,
+ Int Pattern [ ],
+ Int prl
+)
+{
+ /* ---------------------------------------------------------------------- */
+
+ Int k, deg, j, *ip, col, *Upos, *Uilen, k1, prl1, pos,
+ *Uip, n_col, ulen, p, newUchain, up, npiv, n1, *Ui ;
+ Entry *xp, *Uval ;
+
+ /* ---------------------------------------------------------------------- */
+
+ ASSERT (prl >= 3) ;
+
+ n_col = Numeric->n_col ;
+ npiv = Numeric->npiv ;
+ n1 = Numeric->n1 ;
+ Upos = Numeric->Upos ;
+ Uilen = Numeric->Uilen ;
+ Uip = Numeric->Uip ;
+ prl1 = prl ;
+
+ PRINTF4 ((
+ "\nU in Numeric object, in row-oriented compressed-pattern form:\n"
+ " Diagonal is stored separately.\n")) ;
+
+ ASSERT (Pattern != (Int *) NULL) ;
+
+ k1 = 12 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* print the sparse part of U */
+ /* ---------------------------------------------------------------------- */
+
+ deg = Numeric->ulen ;
+ if (deg > 0)
+ {
+ /* make last pivot row of U (singular matrices only) */
+ for (j = 0 ; j < deg ; j++)
+ {
+ Pattern [j] = Numeric->Upattern [j] ;
+ }
+ }
+
+ PRINTF4 (("\n row "ID": length "ID". End of Uchain.\n", INDEX (npiv-1),
+ deg)) ;
+
+ for (k = npiv-1 ; k >= n1 ; k--)
+ {
+
+ /* ------------------------------------------------------------------ */
+ /* print row k of U */
+ /* ------------------------------------------------------------------ */
+
+ /* if prl is 3, print the first 10 entries of the first 10 columns */
+ if (k1 > 0)
+ {
+ prl = prl1 ;
+ }
+
+ up = Uip [k] ;
+ ulen = Uilen [k] ;
+ if (ulen < 0)
+ {
+ return (FALSE) ;
+ }
+ newUchain = (up < 0) ;
+ if (newUchain)
+ {
+ up = -up ;
+ p = up + UNITS (Int, ulen) ;
+ }
+ else
+ {
+ p = up ;
+ }
+ xp = (Entry *) (Numeric->Memory + p) ;
+ if (deg > 0 && (p + (Int) UNITS (Entry, deg) > Numeric->size))
+ {
+ return (FALSE) ;
+ }
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = Pattern [j] ;
+ PRINTF4 (("\tcol "ID" :", INDEX (col))) ;
+ if (prl >= 4) PRINT_ENTRY (*xp) ;
+ if (col <= k || col >= n_col)
+ {
+ return (FALSE) ;
+ }
+ PRINTF4 (("\n")) ;
+ xp++ ;
+ /* truncate printout, but continue to check U */
+ if (prl == 4 && j == 9 && deg > 10)
+ {
+ PRINTF (("\t...\n")) ;
+ prl-- ;
+ }
+ }
+
+ /* ------------------------------------------------------------------ */
+ /* make row k-1 of U in Pattern [0..deg-1] */
+ /* ------------------------------------------------------------------ */
+
+ if (k1-- > 0)
+ {
+ prl = prl1 ;
+ }
+ else if (prl == 4)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+
+ if (k > 0)
+ {
+ PRINTF4 (("\n row "ID": ", INDEX (k-1))) ;
+ }
+
+ if (newUchain)
+ {
+ /* next row is a new Uchain */
+ if (k > 0)
+ {
+ deg = ulen ;
+ PRINTF4 (("length "ID". End of Uchain.\n", deg)) ;
+ if (up + (Int) UNITS (Int, ulen) > Numeric->size)
+ {
+ return (FALSE) ;
+ }
+ ip = (Int *) (Numeric->Memory + up) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ Pattern [j] = *ip++ ;
+ }
+ }
+ }
+ else
+ {
+ if (ulen > 0)
+ {
+ PRINTF4 (("remove "ID" entries. ", ulen)) ;
+ }
+ deg -= ulen ;
+ if (deg < 0)
+ {
+ return (FALSE) ;
+ }
+ pos = Upos [k] ;
+ if (pos != EMPTY)
+ {
+ /* add the pivot column */
+ PRINTF4 (("add column "ID" at position "ID". ",
+ INDEX (k), INDEX (pos))) ;
+ if (pos < 0 || pos > deg)
+ {
+ return (FALSE) ;
+ }
+ Pattern [deg++] = Pattern [pos] ;
+ Pattern [pos] = k ;
+ }
+ PRINTF4 (("length "ID".\n", deg)) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print the singleton rows of U */
+ /* ---------------------------------------------------------------------- */
+
+ for (k = n1 - 1 ; k >= 0 ; k--)
+ {
+ if (k1 > 0)
+ {
+ prl = prl1 ;
+ }
+ up = Uip [k] ;
+ deg = Uilen [k] ;
+ Ui = (Int *) (Numeric->Memory + up) ;
+ up += UNITS (Int, deg) ;
+ Uval = (Entry *) (Numeric->Memory + up) ;
+ if (k1-- > 0)
+ {
+ prl = prl1 ;
+ }
+ else if (prl == 4)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+ PRINTF4 (("\n row "ID":", INDEX (k))) ;
+ PRINTF4 ((" length "ID".\n", deg)) ;
+ for (j = 0 ; j < deg ; j++)
+ {
+ col = Ui [j] ;
+ PRINTF4 (("\tcol "ID" : ", INDEX (col))) ;
+ if (prl >= 4) PRINT_ENTRY (Uval [j]) ;
+ if (col <= k || col >= n_col)
+ {
+ return (FALSE) ;
+ }
+ PRINTF4 (("\n")) ;
+ /* truncate printout, but continue to check U */
+ if (prl == 4 && j == 9 && deg > 10)
+ {
+ PRINTF (("\t...\n")) ;
+ prl-- ;
+ }
+ }
+ }
+
+ prl = prl1 ;
+ PRINTF4 (("\n")) ;
+ return (TRUE) ;
+}
diff --git a/UMFPACK/Source/umfpack_report_perm.c b/UMFPACK/Source/umfpack_report_perm.c
new file mode 100644
index 0000000..5f3baab
--- /dev/null
+++ b/UMFPACK/Source/umfpack_report_perm.c
@@ -0,0 +1,44 @@
+/* ========================================================================== */
+/* === UMFPACK_report_perm ================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints a permutation vector. See umfpack_report_perm.h
+ for details.
+
+ Dynamic memory usage: Allocates a size max(np,1)*sizeof(Int) workspace via
+ a single call to UMF_malloc and then frees all of it via UMF_free on return.
+*/
+
+#include "umf_internal.h"
+#include "umf_report_perm.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+GLOBAL Int UMFPACK_report_perm
+(
+ Int np,
+ const Int Perm [ ],
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Int prl, *W, status ;
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ W = (Int *) UMF_malloc (MAX (np,1), sizeof (Int)) ;
+ status = UMF_report_perm (np, Perm, W, prl, 1) ;
+ (void) UMF_free ((void *) W) ;
+ return (status) ;
+}
diff --git a/UMFPACK/Source/umfpack_report_status.c b/UMFPACK/Source/umfpack_report_status.c
new file mode 100644
index 0000000..5e4e142
--- /dev/null
+++ b/UMFPACK/Source/umfpack_report_status.c
@@ -0,0 +1,119 @@
+/* ========================================================================== */
+/* === UMFPACK_report_status ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints the return value from other UMFPACK_* routines.
+ See umfpack_report_status.h for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL void UMFPACK_report_status
+(
+ const double Control [UMFPACK_CONTROL],
+ Int status
+)
+{
+ Int prl ;
+
+ /* ---------------------------------------------------------------------- */
+ /* get control settings and status to determine what to print */
+ /* ---------------------------------------------------------------------- */
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl < 1)
+ {
+ /* no output generated if prl is less than 1 */
+ return ;
+ }
+
+ if (status == UMFPACK_OK && prl <= 1)
+ {
+ /* no output generated if prl is 1 or less and no error occurred. */
+ /* note that the default printing level is 1. */
+ return ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* print umfpack license, copyright, version, and status condition */
+ /* ---------------------------------------------------------------------- */
+
+ PRINTF (("\n")) ;
+ PRINTF4 (("%s\n", UMFPACK_COPYRIGHT)) ;
+ PRINTF6 (("%s", UMFPACK_LICENSE_PART1)) ;
+ PRINTF6 (("%s", UMFPACK_LICENSE_PART2)) ;
+ PRINTF6 (("%s", UMFPACK_LICENSE_PART3)) ;
+ PRINTF (("UMFPACK V%d.%d.%d (%s): ", UMFPACK_MAIN_VERSION,
+ UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION, UMFPACK_DATE)) ;
+
+ switch (status)
+ {
+ case UMFPACK_OK:
+ PRINTF (("OK\n")) ;
+ break ;
+
+ case UMFPACK_WARNING_singular_matrix:
+ PRINTF (("WARNING: matrix is singular\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_out_of_memory:
+ PRINTF (("ERROR: out of memory\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_invalid_Numeric_object:
+ PRINTF (("ERROR: Numeric object is invalid\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_invalid_Symbolic_object:
+ PRINTF (("ERROR: Symbolic object is invalid\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_argument_missing:
+ PRINTF (("ERROR: required argument(s) missing\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_n_nonpositive:
+ PRINTF (("ERROR: dimension (n_row or n_col) must be > 0\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_invalid_matrix:
+ PRINTF (("ERROR: input matrix is invalid\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_invalid_system:
+ PRINTF (("ERROR: system argument invalid\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_invalid_permutation:
+ PRINTF (("ERROR: invalid permutation\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_different_pattern:
+ PRINTF (("ERROR: pattern of matrix (Ap and/or Ai) has changed\n")) ;
+ break ;
+
+ case UMFPACK_ERROR_internal_error:
+ PRINTF (("INTERNAL ERROR!\n"
+ "Input arguments might be corrupted or aliased, or an internal\n"
+ "error has occurred. Check your input arguments with the\n"
+ "umfpack_*_report_* routines before calling the umfpack_*\n"
+ "computational routines. Recompile UMFPACK with debugging\n"
+ "enabled, and look for failed assertions. If all else fails\n"
+ "please report this error to Tim Davis (davis at cise.ufl.edu).\n"
+ )) ;
+ break ;
+
+ default:
+ PRINTF (("ERROR: Unrecognized error code: "ID"\n", status)) ;
+
+ }
+ PRINTF (("\n")) ;
+}
diff --git a/UMFPACK/Source/umfpack_report_symbolic.c b/UMFPACK/Source/umfpack_report_symbolic.c
new file mode 100644
index 0000000..57e134e
--- /dev/null
+++ b/UMFPACK/Source/umfpack_report_symbolic.c
@@ -0,0 +1,228 @@
+/* ========================================================================== */
+/* === UMFPACK_report_symbolic ============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints the Symbolic object. See umfpack_report_symbolic.h
+ for details. Does not print new Cdeg, Rdeg, Esize, and the Diagonal_map.
+
+ Dynamic memory usage: Allocates a size MAX (n_row,n_col)*sizeof(Int)
+ workspace via a single call to UMF_malloc and then frees all of it via
+ UMF_free on return. The workspace is not allocated if an early error
+ return occurs before the workspace is needed.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+#include "umf_report_perm.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+GLOBAL Int UMFPACK_report_symbolic
+(
+ void *SymbolicHandle,
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Int n_row, n_col, nz, nchains, nfr, maxnrows, maxncols, prl,
+ k, chain, frontid, frontid1, frontid2, kk, *Chain_start, *W,
+ *Chain_maxrows, *Chain_maxcols, *Front_npivcol, *Front_1strow,
+ *Front_leftmostdesc, *Front_parent, done, status1, status2 ;
+ SymbolicType *Symbolic ;
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ PRINTF (("Symbolic object: ")) ;
+
+ Symbolic = (SymbolicType *) SymbolicHandle ;
+ if (!UMF_valid_symbolic (Symbolic))
+ {
+ PRINTF (("ERROR: invalid\n")) ;
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ n_row = Symbolic->n_row ;
+ n_col = Symbolic->n_col ;
+
+ nz = Symbolic->nz ;
+
+ nchains = Symbolic->nchains ;
+ nfr = Symbolic->nfr ;
+ maxnrows = Symbolic->maxnrows ;
+ maxncols = Symbolic->maxncols ;
+
+ Chain_start = Symbolic->Chain_start ;
+ Chain_maxrows = Symbolic->Chain_maxrows ;
+ Chain_maxcols = Symbolic->Chain_maxcols ;
+ Front_npivcol = Symbolic->Front_npivcol ;
+ Front_1strow = Symbolic->Front_1strow ;
+ Front_leftmostdesc = Symbolic->Front_leftmostdesc ;
+ Front_parent = Symbolic->Front_parent ;
+
+ if (prl >= 4)
+ {
+
+ PRINTF (("\n matrix to be factorized:\n")) ;
+ PRINTF (("\tn_row: "ID" n_col: "ID"\n", n_row, n_col)) ;
+ PRINTF (("\tnumber of entries: "ID"\n", nz)) ;
+ PRINTF ((" block size used for dense matrix kernels: "ID"\n",
+ Symbolic->nb)) ;
+
+ PRINTF ((" strategy used: ")) ;
+ /* strategy cannot be auto */
+ if (Symbolic->strategy == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ PRINTF (("symmetric")) ;
+ }
+ else if (Symbolic->strategy == UMFPACK_STRATEGY_UNSYMMETRIC)
+ {
+ PRINTF (("unsymmetric")) ;
+ }
+ else if (Symbolic->strategy == UMFPACK_STRATEGY_2BY2)
+ {
+ PRINTF (("symmetric 2-by-2")) ;
+ }
+ PRINTF (("\n")) ;
+
+ PRINTF ((" ordering used: ")) ;
+ if (Symbolic->ordering == UMFPACK_ORDERING_COLAMD)
+ {
+ PRINTF (("colamd on A\n")) ;
+ }
+ else if (Symbolic->ordering == UMFPACK_ORDERING_AMD)
+ {
+ PRINTF (("amd on A+A'\n")) ;
+ }
+ else if (Symbolic->ordering == UMFPACK_ORDERING_GIVEN)
+ {
+ PRINTF (("provided by user")) ;
+ }
+ PRINTF (("\n")) ;
+
+ PRINTF ((" performn column etree postorder: ")) ;
+ if (Symbolic->fixQ)
+ {
+ PRINTF (("no\n")) ;
+ }
+ else
+ {
+ PRINTF (("yes\n")) ;
+ }
+
+ PRINTF ((" prefer diagonal pivoting (attempt P=Q): ")) ;
+ if (Symbolic->prefer_diagonal)
+ {
+ PRINTF (("yes\n")) ;
+ }
+ else
+ {
+ PRINTF (("no\n")) ;
+ }
+
+ PRINTF ((" variable-size part of Numeric object:\n")) ;
+ PRINTF (("\tminimum initial size (Units): %.20g (MBytes): %.1f\n",
+ Symbolic->dnum_mem_init_usage,
+ MBYTES (Symbolic->dnum_mem_init_usage))) ;
+ PRINTF (("\testimated peak size (Units): %.20g (MBytes): %.1f\n",
+ Symbolic->num_mem_usage_est,
+ MBYTES (Symbolic->num_mem_usage_est))) ;
+ PRINTF (("\testimated final size (Units): %.20g (MBytes): %.1f\n",
+ Symbolic->num_mem_size_est,
+ MBYTES (Symbolic->num_mem_size_est))) ;
+ PRINTF ((" symbolic factorization memory usage (Units):"
+ " %.20g (MBytes): %.1f\n",
+ Symbolic->peak_sym_usage,
+ MBYTES (Symbolic->peak_sym_usage))) ;
+ PRINTF ((" frontal matrices / supercolumns:\n")) ;
+ PRINTF (("\tnumber of frontal chains: "ID"\n", nchains)) ;
+ PRINTF (("\tnumber of frontal matrices: "ID"\n", nfr)) ;
+ PRINTF (("\tlargest frontal matrix row dimension: "ID"\n", maxnrows)) ;
+ PRINTF (("\tlargest frontal matrix column dimension: "ID"\n",maxncols));
+ }
+
+ k = 0 ;
+ done = FALSE ;
+
+ for (chain = 0 ; chain < nchains ; chain++)
+ {
+ frontid1 = Chain_start [chain] ;
+ frontid2 = Chain_start [chain+1] - 1 ;
+ PRINTF4 (("\n Frontal chain: "ID". Frontal matrices "ID" to "ID"\n",
+ INDEX (chain), INDEX (frontid1), INDEX (frontid2))) ;
+ PRINTF4 (("\tLargest frontal matrix in Frontal chain: "ID"-by-"ID"\n",
+ Chain_maxrows [chain], Chain_maxcols [chain])) ;
+ for (frontid = frontid1 ; frontid <= frontid2 ; frontid++)
+ {
+ kk = Front_npivcol [frontid] ;
+ PRINTF4 (("\tFront: "ID" pivot cols: "ID" (pivot columns "ID" to "
+ ID")\n", INDEX (frontid), kk, INDEX (k), INDEX (k+kk-1))) ;
+ PRINTF4 (("\t pivot row candidates: "ID" to "ID"\n",
+ INDEX (Front_1strow [Front_leftmostdesc [frontid]]),
+ INDEX (Front_1strow [frontid+1]-1))) ;
+ PRINTF4 (("\t leftmost descendant: "ID"\n",
+ INDEX (Front_leftmostdesc [frontid]))) ;
+ PRINTF4 (("\t 1st new candidate row : "ID"\n",
+ INDEX (Front_1strow [frontid]))) ;
+ PRINTF4 (("\t parent:")) ;
+ if (Front_parent [frontid] == EMPTY)
+ {
+ PRINTF4 ((" (none)\n")) ;
+ }
+ else
+ {
+ PRINTF4 ((" "ID"\n", INDEX (Front_parent [frontid]))) ;
+ }
+ done = (frontid == 20 && frontid < nfr-1 && prl == 4) ;
+ if (done)
+ {
+ PRINTF4 (("\t...\n")) ;
+ break ;
+ }
+ k += kk ;
+ }
+ if (Front_npivcol [nfr] != 0)
+ {
+ PRINTF4 (("\tFront: "ID" placeholder for "ID" empty columns\n",
+ INDEX (nfr), Front_npivcol [nfr])) ;
+ }
+ if (done)
+ {
+ break ;
+ }
+ }
+
+ W = (Int *) UMF_malloc (MAX (n_row, n_col), sizeof (Int)) ;
+ if (!W)
+ {
+ PRINTF (("ERROR: out of memory to check Symbolic object\n\n")) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ PRINTF4 (("\nInitial column permutation, Q1: ")) ;
+ status1 = UMF_report_perm (n_col, Symbolic->Cperm_init, W, prl, 0) ;
+
+ PRINTF4 (("\nInitial row permutation, P1: ")) ;
+ status2 = UMF_report_perm (n_row, Symbolic->Rperm_init, W, prl, 0) ;
+
+ (void) UMF_free ((void *) W) ;
+
+ if (status1 != UMFPACK_OK || status2 != UMFPACK_OK)
+ {
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ PRINTF4 ((" Symbolic object: ")) ;
+ PRINTF (("OK\n\n")) ;
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_report_triplet.c b/UMFPACK/Source/umfpack_report_triplet.c
new file mode 100644
index 0000000..ba11a69
--- /dev/null
+++ b/UMFPACK/Source/umfpack_report_triplet.c
@@ -0,0 +1,99 @@
+/* ========================================================================== */
+/* === UMFPACK_report_triplet =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints a matrix in triplet form. See
+ umfpack_report_triplet.h for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL Int UMFPACK_report_triplet
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ],
+ const Int Tj [ ],
+ const double Tx [ ],
+#ifdef COMPLEX
+ const double Tz [ ],
+#endif
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Entry t ;
+ Int prl, prl1, k, i, j, do_values ;
+#ifdef COMPLEX
+ Int split = SPLIT (Tz) ;
+#endif
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ PRINTF (("triplet-form matrix, n_row = "ID", n_col = "ID" nz = "ID". ",
+ n_row, n_col, nz)) ;
+
+ if (!Ti || !Tj)
+ {
+ PRINTF (("ERROR: indices not present\n\n")) ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ if (n_row <= 0 || n_col <= 0)
+ {
+ PRINTF (("ERROR: n_row or n_col is <= 0\n\n")) ;
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+
+ if (nz < 0)
+ {
+ PRINTF (("ERROR: nz is < 0\n\n")) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ PRINTF4 (("\n")) ;
+
+ do_values = Tx != (double *) NULL ;
+
+ prl1 = prl ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ i = Ti [k] ;
+ j = Tj [k] ;
+ PRINTF4 ((" "ID" : "ID" "ID" ", INDEX (k), INDEX (i), INDEX (j))) ;
+ if (do_values && prl >= 4)
+ {
+ ASSIGN (t, Tx, Tz, k, split) ;
+ PRINT_ENTRY (t) ;
+ }
+ PRINTF4 (("\n")) ;
+ if (i < 0 || i >= n_row || j < 0 || j >= n_col)
+ {
+ /* invalid triplet */
+ PRINTF (("ERROR: invalid triplet\n\n")) ;
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+ if (prl == 4 && k == 9 && nz > 10)
+ {
+ PRINTF ((" ...\n")) ;
+ prl-- ;
+ }
+ }
+ prl = prl1 ;
+
+ PRINTF4 ((" triplet-form matrix ")) ;
+ PRINTF (("OK\n\n")) ;
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_report_vector.c b/UMFPACK/Source/umfpack_report_vector.c
new file mode 100644
index 0000000..a88804c
--- /dev/null
+++ b/UMFPACK/Source/umfpack_report_vector.c
@@ -0,0 +1,43 @@
+/* ========================================================================== */
+/* === UMFPACK_report_vector ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Prints a real or complex vector.
+ See umfpack_report_vector.h for details.
+*/
+
+#include "umf_internal.h"
+#include "umf_report_vector.h"
+
+GLOBAL Int UMFPACK_report_vector
+(
+ Int n,
+ const double Xx [ ],
+#ifdef COMPLEX
+ const double Xz [ ],
+#endif
+ const double Control [UMFPACK_CONTROL]
+)
+{
+ Int prl ;
+
+#ifndef COMPLEX
+ double *Xz = (double *) NULL ;
+#endif
+
+ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
+
+ if (prl <= 2)
+ {
+ return (UMFPACK_OK) ;
+ }
+
+ return (UMF_report_vector (n, Xx, Xz, prl, TRUE, FALSE)) ;
+}
diff --git a/UMFPACK/Source/umfpack_save_numeric.c b/UMFPACK/Source/umfpack_save_numeric.c
new file mode 100644
index 0000000..0e4d8a2
--- /dev/null
+++ b/UMFPACK/Source/umfpack_save_numeric.c
@@ -0,0 +1,92 @@
+/* ========================================================================== */
+/* === UMFPACK_save_numeric ================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Saves a Numeric object to a file. It can later be read back
+ in via a call to umfpack_*_load_numeric.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+
+#define WRITE(object,type,n) \
+{ \
+ ASSERT (object != (type *) NULL) ; \
+ if (fwrite (object, sizeof (type), n, f) != (size_t) n) \
+ { \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+}
+
+/* ========================================================================== */
+/* === UMFPACK_save_numeric ================================================= */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_save_numeric
+(
+ void *NumericHandle,
+ char *user_filename
+)
+{
+ NumericType *Numeric ;
+ char *filename ;
+ FILE *f ;
+
+ /* get the Numeric object */
+ Numeric = (NumericType *) NumericHandle ;
+
+ /* make sure the Numeric object is valid */
+ if (!UMF_valid_numeric (Numeric))
+ {
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ /* get the filename, or use the default name if filename is NULL */
+ if (user_filename == (char *) NULL)
+ {
+ filename = "numeric.umf" ;
+ }
+ else
+ {
+ filename = user_filename ;
+ }
+ f = fopen (filename, "wb") ;
+ if (!f)
+ {
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ /* write the Numeric object to the file, in binary */
+ WRITE (Numeric, NumericType, 1) ;
+ WRITE (Numeric->D, Entry, MIN (Numeric->n_row, Numeric->n_col)+1) ;
+ WRITE (Numeric->Rperm, Int, Numeric->n_row+1) ;
+ WRITE (Numeric->Cperm, Int, Numeric->n_col+1) ;
+ WRITE (Numeric->Lpos, Int, Numeric->npiv+1) ;
+ WRITE (Numeric->Lilen, Int, Numeric->npiv+1) ;
+ WRITE (Numeric->Lip, Int, Numeric->npiv+1) ;
+ WRITE (Numeric->Upos, Int, Numeric->npiv+1) ;
+ WRITE (Numeric->Uilen, Int, Numeric->npiv+1) ;
+ WRITE (Numeric->Uip, Int, Numeric->npiv+1) ;
+ if (Numeric->scale != UMFPACK_SCALE_NONE)
+ {
+ WRITE (Numeric->Rs, double, Numeric->n_row) ;
+ }
+ if (Numeric->ulen > 0)
+ {
+ WRITE (Numeric->Upattern, Int, Numeric->ulen+1) ;
+ }
+ WRITE (Numeric->Memory, Unit, Numeric->size) ;
+
+ /* close the file */
+ fclose (f) ;
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_save_symbolic.c b/UMFPACK/Source/umfpack_save_symbolic.c
new file mode 100644
index 0000000..ae00189
--- /dev/null
+++ b/UMFPACK/Source/umfpack_save_symbolic.c
@@ -0,0 +1,95 @@
+/* ========================================================================== */
+/* === UMFPACK_save_symbolic ================================================ */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Saves a Symbolic object to a file. It can later be read
+ back in via a call to umfpack_*_load_symbolic.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_symbolic.h"
+
+#define WRITE(object,type,n) \
+{ \
+ ASSERT (object != (type *) NULL) ; \
+ if (fwrite (object, sizeof (type), n, f) != (size_t) n) \
+ { \
+ fclose (f) ; \
+ return (UMFPACK_ERROR_file_IO) ; \
+ } \
+}
+
+/* ========================================================================== */
+/* === UMFPACK_save_symbolic ================================================ */
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_save_symbolic
+(
+ void *SymbolicHandle,
+ char *user_filename
+)
+{
+ SymbolicType *Symbolic ;
+ char *filename ;
+ FILE *f ;
+
+ /* get the Symbolic object */
+ Symbolic = (SymbolicType *) SymbolicHandle ;
+
+ /* make sure the Symbolic object is valid */
+ if (!UMF_valid_symbolic (Symbolic))
+ {
+ return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+ }
+
+ /* get the filename, or use the default name if filename is NULL */
+ if (user_filename == (char *) NULL)
+ {
+ filename = "symbolic.umf" ;
+ }
+ else
+ {
+ filename = user_filename ;
+ }
+ f = fopen (filename, "wb") ;
+ if (!f)
+ {
+ return (UMFPACK_ERROR_file_IO) ;
+ }
+
+ /* write the Symbolic object to the file, in binary */
+ WRITE (Symbolic, SymbolicType, 1) ;
+ WRITE (Symbolic->Cperm_init, Int, Symbolic->n_col+1) ;
+ WRITE (Symbolic->Rperm_init, Int, Symbolic->n_row+1) ;
+ WRITE (Symbolic->Front_npivcol, Int, Symbolic->nfr+1) ;
+ WRITE (Symbolic->Front_parent, Int, Symbolic->nfr+1) ;
+ WRITE (Symbolic->Front_1strow, Int, Symbolic->nfr+1) ;
+ WRITE (Symbolic->Front_leftmostdesc, Int, Symbolic->nfr+1) ;
+ WRITE (Symbolic->Chain_start, Int, Symbolic->nchains+1) ;
+ WRITE (Symbolic->Chain_maxrows, Int, Symbolic->nchains+1) ;
+ WRITE (Symbolic->Chain_maxcols, Int, Symbolic->nchains+1) ;
+ WRITE (Symbolic->Cdeg, Int, Symbolic->n_col+1) ;
+ WRITE (Symbolic->Rdeg, Int, Symbolic->n_row+1) ;
+ if (Symbolic->esize > 0)
+ {
+ /* only when dense rows are present */
+ WRITE (Symbolic->Esize, Int, Symbolic->esize) ;
+ }
+ if (Symbolic->prefer_diagonal)
+ {
+ /* only when diagonal pivoting is prefered */
+ WRITE (Symbolic->Diagonal_map, Int, Symbolic->n_col+1) ;
+ }
+
+ /* close the file */
+ fclose (f) ;
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_scale.c b/UMFPACK/Source/umfpack_scale.c
new file mode 100644
index 0000000..49467a5
--- /dev/null
+++ b/UMFPACK/Source/umfpack_scale.c
@@ -0,0 +1,158 @@
+/* ========================================================================== */
+/* === UMFPACK_scale ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Applies the scale factors computed during numerical
+ factorization to a vector. See umfpack_scale.h for more details.
+
+ The LU factorization is L*U = P*R*A*Q, where P and Q are permutation
+ matrices, and R is diagonal. This routine computes X = R * B using the
+ matrix R stored in the Numeric object.
+
+ Returns FALSE if any argument is invalid, TRUE otherwise.
+
+ If R not present in the Numeric object, then R = I and no floating-point
+ work is done. B is simply copied into X.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+
+GLOBAL Int UMFPACK_scale
+(
+ double Xx [ ],
+#ifdef COMPLEX
+ double Xz [ ],
+#endif
+ const double Bx [ ],
+#ifdef COMPLEX
+ const double Bz [ ],
+#endif
+ void *NumericHandle
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ NumericType *Numeric ;
+ Int n, i ;
+ double *Rs ;
+#ifdef COMPLEX
+ Int split = SPLIT (Xz) && SPLIT (Bz) ;
+#endif
+
+ Numeric = (NumericType *) NumericHandle ;
+ if (!UMF_valid_numeric (Numeric))
+ {
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ n = Numeric->n_row ;
+ Rs = Numeric->Rs ;
+
+ if (!Xx || !Bx)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* X = R*B or R\B */
+ /* ---------------------------------------------------------------------- */
+
+ if (Rs != (double *) NULL)
+ {
+#ifndef NRECIPROCAL
+ if (Numeric->do_recip)
+ {
+ /* multiply by the scale factors */
+#ifdef COMPLEX
+ if (split)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] * Rs [i] ;
+ Xz [i] = Bz [i] * Rs [i] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [2*i ] = Bx [2*i ] * Rs [i] ;
+ Xx [2*i+1] = Bx [2*i+1] * Rs [i] ;
+ }
+ }
+#else
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] * Rs [i] ;
+ }
+#endif
+ }
+ else
+#endif
+ {
+ /* divide by the scale factors */
+#ifdef COMPLEX
+ if (split)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] / Rs [i] ;
+ Xz [i] = Bz [i] / Rs [i] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [2*i ] = Bx [2*i ] / Rs [i] ;
+ Xx [2*i+1] = Bx [2*i+1] / Rs [i] ;
+ }
+ }
+#else
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] / Rs [i] ;
+ }
+#endif
+ }
+ }
+ else
+ {
+ /* no scale factors, just copy B into X */
+#ifdef COMPLEX
+ if (split)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] ;
+ Xz [i] = Bz [i] ;
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [2*i ] = Bx [2*i ] ;
+ Xx [2*i+1] = Bx [2*i+1] ;
+ }
+ }
+#else
+ for (i = 0 ; i < n ; i++)
+ {
+ Xx [i] = Bx [i] ;
+ }
+#endif
+ }
+
+ return (UMFPACK_OK) ;
+}
diff --git a/UMFPACK/Source/umfpack_solve.c b/UMFPACK/Source/umfpack_solve.c
new file mode 100644
index 0000000..c4e8263
--- /dev/null
+++ b/UMFPACK/Source/umfpack_solve.c
@@ -0,0 +1,245 @@
+/* ========================================================================== */
+/* === UMFPACK_solve ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Solves a linear system using the numerical factorization
+ computed by UMFPACK_numeric. See umfpack_solve.h for more details.
+
+ For umfpack_*_solve:
+ Dynamic memory usage: UMFPACK_solve calls UMF_malloc twice, for
+ workspace of size c*n*sizeof(double) + n*sizeof(Int), where c is
+ defined below. On return, all of this workspace is free'd via UMF_free.
+
+ For umfpack_*_wsolve:
+ No dynamic memory usage. Input arrays are used for workspace instead.
+ Pattern is a workspace of size n Integers. The double array W must be
+ at least of size c*n, where c is defined below.
+
+ If iterative refinement is requested, and Ax=b, A'x=b or A.'x=b is being
+ solved, and the matrix A is not singular, then c is 5 for the real version
+ and 10 for the complex version. Otherwise, c is 1 for the real version and
+ 4 for the complex version.
+*/
+
+#include "umf_internal.h"
+#include "umf_valid_numeric.h"
+#include "umf_solve.h"
+
+#ifndef WSOLVE
+#include "umf_malloc.h"
+#include "umf_free.h"
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+#endif
+
+GLOBAL Int
+#ifdef WSOLVE
+UMFPACK_wsolve
+#else
+UMFPACK_solve
+#endif
+(
+ Int sys,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ double Xx [ ],
+#ifdef COMPLEX
+ double Xz [ ],
+#endif
+ const double Bx [ ],
+#ifdef COMPLEX
+ const double Bz [ ],
+#endif
+ void *NumericHandle,
+ const double Control [UMFPACK_CONTROL],
+ double User_Info [UMFPACK_INFO]
+#ifdef WSOLVE
+ , Int Pattern [ ],
+ double W [ ]
+#endif
+)
+{
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ double Info2 [UMFPACK_INFO], stats [2] ;
+ double *Info ;
+ NumericType *Numeric ;
+ Int n, i, irstep, status ;
+#ifndef WSOLVE
+ Int *Pattern, wsize ;
+ double *W ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get the amount of time used by the process so far */
+ /* ---------------------------------------------------------------------- */
+
+ umfpack_tic (stats) ;
+
+#ifndef WSOLVE
+#ifndef NDEBUG
+ init_count = UMF_malloc_count ;
+#endif
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ irstep = GET_CONTROL (UMFPACK_IRSTEP, UMFPACK_DEFAULT_IRSTEP) ;
+
+ if (User_Info != (double *) NULL)
+ {
+ /* return Info in user's array */
+ Info = User_Info ;
+ /* clear the parts of Info that are set by UMFPACK_solve */
+ for (i = UMFPACK_IR_TAKEN ; i <= UMFPACK_SOLVE_TIME ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ }
+ else
+ {
+ /* no Info array passed - use local one instead */
+ Info = Info2 ;
+ for (i = 0 ; i < UMFPACK_INFO ; i++)
+ {
+ Info [i] = EMPTY ;
+ }
+ }
+
+ Info [UMFPACK_STATUS] = UMFPACK_OK ;
+ Info [UMFPACK_SOLVE_FLOPS] = 0 ;
+
+ Numeric = (NumericType *) NumericHandle ;
+ if (!UMF_valid_numeric (Numeric))
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_Numeric_object ;
+ return (UMFPACK_ERROR_invalid_Numeric_object) ;
+ }
+
+ Info [UMFPACK_NROW] = Numeric->n_row ;
+ Info [UMFPACK_NCOL] = Numeric->n_col ;
+
+ if (Numeric->n_row != Numeric->n_col)
+ {
+ /* only square systems can be handled */
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ;
+ return (UMFPACK_ERROR_invalid_system) ;
+ }
+ n = Numeric->n_row ;
+ if (Numeric->nnzpiv < n
+ || SCALAR_IS_ZERO (Numeric->rcond) || SCALAR_IS_NAN (Numeric->rcond))
+ {
+ /* turn off iterative refinement if A is singular */
+ /* or if U has NaN's on the diagonal. */
+ irstep = 0 ;
+ }
+
+ if (!Xx || !Bx)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ if (sys >= UMFPACK_Pt_L)
+ {
+ /* no iterative refinement except for nonsingular Ax=b, A'x=b, A.'x=b */
+ irstep = 0 ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate or check the workspace */
+ /* ---------------------------------------------------------------------- */
+
+#ifdef WSOLVE
+
+ if (!W || !Pattern)
+ {
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+#else
+
+#ifdef COMPLEX
+ if (irstep > 0)
+ {
+ wsize = 10*n ; /* W, X, Z, S, Y, B2 */
+ }
+ else
+ {
+ wsize = 4*n ; /* W, X */
+ }
+#else
+ if (irstep > 0)
+ {
+ wsize = 5*n ; /* W, Z, S, Y, B2 */
+ }
+ else
+ {
+ wsize = n ; /* W */
+ }
+#endif
+
+ Pattern = (Int *) UMF_malloc (n, sizeof (Int)) ;
+ W = (double *) UMF_malloc (wsize, sizeof (double)) ;
+ if (!W || !Pattern)
+ {
+ DEBUGm4 (("out of memory: solve work\n")) ;
+ Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ (void) UMF_free ((void *) W) ;
+ (void) UMF_free ((void *) Pattern) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+#endif /* WSOLVE */
+
+ /* ---------------------------------------------------------------------- */
+ /* solve the system */
+ /* ---------------------------------------------------------------------- */
+
+ status = UMF_solve (sys, Ap, Ai, Ax, Xx, Bx,
+#ifdef COMPLEX
+ Az, Xz, Bz,
+#endif
+ Numeric, irstep, Info, Pattern, W) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the workspace (if allocated) */
+ /* ---------------------------------------------------------------------- */
+
+#ifndef WSOLVE
+ (void) UMF_free ((void *) W) ;
+ (void) UMF_free ((void *) Pattern) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get the time used by UMFPACK_*solve */
+ /* ---------------------------------------------------------------------- */
+
+ Info [UMFPACK_STATUS] = status ;
+ if (status >= 0)
+ {
+ umfpack_toc (stats) ;
+ Info [UMFPACK_SOLVE_WALLTIME] = stats [0] ;
+ Info [UMFPACK_SOLVE_TIME] = stats [1] ;
+ }
+
+ return (status) ;
+}
diff --git a/UMFPACK/Source/umfpack_symbolic.c b/UMFPACK/Source/umfpack_symbolic.c
new file mode 100644
index 0000000..41be72b
--- /dev/null
+++ b/UMFPACK/Source/umfpack_symbolic.c
@@ -0,0 +1,39 @@
+/* ========================================================================== */
+/* === UMFPACK_symbolic ===================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Performs a symbolic factorization.
+ See umfpack_symbolic.h for details.
+*/
+
+#include "umf_internal.h"
+
+GLOBAL Int UMFPACK_symbolic
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ],
+ const Int Ai [ ],
+ const double Ax [ ],
+#ifdef COMPLEX
+ const double Az [ ],
+#endif
+ void **SymbolicHandle,
+ const double Control [UMFPACK_CONTROL],
+ double Info [UMFPACK_INFO]
+)
+{
+ Int *Qinit = (Int *) NULL ;
+ return (UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, Ax,
+#ifdef COMPLEX
+ Az,
+#endif
+ Qinit, SymbolicHandle, Control, Info)) ;
+}
diff --git a/UMFPACK/Source/umfpack_tictoc.c b/UMFPACK/Source/umfpack_tictoc.c
new file mode 100644
index 0000000..7fc5fba
--- /dev/null
+++ b/UMFPACK/Source/umfpack_tictoc.c
@@ -0,0 +1,106 @@
+/* ========================================================================== */
+/* === umfpack_tictoc ======================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Returns the time in seconds used by the process, and
+ the current wall clock time. BE CAREFUL: if you compare the run time of
+ UMFPACK with other sparse matrix packages, be sure to use the same timer.
+ See umfpack_tictoc.h for details.
+
+ These routines conform to the POSIX standard. See umf_config.h for
+ more details.
+*/
+
+#include "umf_internal.h"
+
+#ifdef NO_TIMER
+
+/* -------------------------------------------------------------------------- */
+/* no timer used if -DNO_TIMER is defined at compile time */
+/* -------------------------------------------------------------------------- */
+
+void umfpack_tic (double stats [2])
+{
+ stats [0] = 0 ;
+ stats [1] = 0 ;
+}
+
+void umfpack_toc (double stats [2])
+{
+ stats [0] = 0 ;
+ stats [1] = 0 ;
+}
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* timer routines, using either times() or clock() */
+/* -------------------------------------------------------------------------- */
+
+#define TINY_TIME 1e-4
+
+#ifndef NPOSIX
+
+#include <unistd.h>
+#include <sys/times.h>
+
+void umfpack_tic (double stats [2])
+{
+ /* Return the current time */
+ /* stats [0]: current wallclock time, in seconds */
+ /* stats [1]: user + system time for the process, in seconds */
+
+ double ticks ;
+ struct tms t ;
+
+ ticks = (double) sysconf (_SC_CLK_TCK) ;
+ stats [0] = (double) times (&t) / ticks ;
+ stats [1] = (double) (t.tms_utime + t.tms_stime) / ticks ;
+
+ /* if time is tiny, just return zero */
+ if (stats [0] < TINY_TIME) stats [0] = 0 ;
+ if (stats [1] < TINY_TIME) stats [1] = 0 ;
+}
+
+#else
+
+/* Generic ANSI C: use the ANSI clock function. No wallclock time. */
+
+#include <time.h>
+
+void umfpack_tic (double stats [2])
+{
+ stats [0] = 0 ;
+ stats [1] = ((double) (clock ( ))) / ((double) (CLOCKS_PER_SEC)) ;
+ if (stats [1] < TINY_TIME) stats [1] = 0 ;
+}
+
+#endif
+
+/* -------------------------------------------------------------------------- */
+
+void umfpack_toc (double stats [2])
+{
+ /* Return the current time since the last call to umfpack_tic. */
+ /* On input, stats holds the values returned by umfpack_tic. */
+ /* On ouput, stats holds the time since the last umfpack_tic. */
+
+ double done [2] ;
+ umfpack_tic (done) ;
+
+ stats [0] = done [0] - stats [0] ;
+ stats [1] = done [1] - stats [1] ;
+
+ if (stats [0] < 0) stats [0] = 0 ;
+ if (stats [1] < 0) stats [1] = 0 ;
+
+}
+
+#endif
diff --git a/UMFPACK/Source/umfpack_timer.c b/UMFPACK/Source/umfpack_timer.c
new file mode 100644
index 0000000..8e46687
--- /dev/null
+++ b/UMFPACK/Source/umfpack_timer.c
@@ -0,0 +1,85 @@
+/* ========================================================================== */
+/* === umfpack_timer ======================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User-callable. Returns the time in seconds used by the process. BE
+ CAREFUL: if you compare the run time of UMFPACK with other sparse matrix
+ packages, be sure to use the same timer. See umfpack_timer.h for details.
+ See umfpack_tictoc.h, which is the timer used internally by UMFPACK.
+*/
+
+#include "umfpack_timer.h"
+
+#ifdef NO_TIMER
+
+/* -------------------------------------------------------------------------- */
+/* no timer used if -DNO_TIMER is defined at compile time */
+/* -------------------------------------------------------------------------- */
+
+double umfpack_timer ( void )
+{
+ return (0) ;
+}
+
+#else
+
+#ifdef GETRUSAGE
+
+/* -------------------------------------------------------------------------- */
+/* use getrusage for accurate process times (and no overflow) */
+/* -------------------------------------------------------------------------- */
+
+/*
+ This works under Solaris, SGI Irix, Linux, IBM RS 6000 (AIX), and Compaq
+ Alpha. It might work on other Unix systems, too. Includes both the "user
+ time" and the "system time". The system time is the time spent by the
+ operating system on behalf of the process, and thus should be charged to
+ the process.
+*/
+
+#include <sys/time.h>
+#include <sys/resource.h>
+
+double umfpack_timer ( void )
+{
+ struct rusage ru ;
+ double user_time, sys_time ;
+
+ (void) getrusage (RUSAGE_SELF, &ru) ;
+
+ user_time =
+ ru.ru_utime.tv_sec /* user time (seconds) */
+ + 1e-6 * ru.ru_utime.tv_usec ; /* user time (microseconds) */
+
+ sys_time =
+ ru.ru_stime.tv_sec /* system time (seconds) */
+ + 1e-6 * ru.ru_stime.tv_usec ; /* system time (microseconds) */
+
+ return (user_time + sys_time) ;
+}
+
+#else
+
+/* -------------------------------------------------------------------------- */
+/* Generic ANSI C: use the ANSI clock function */
+/* -------------------------------------------------------------------------- */
+
+/* This is portable, but may overflow. On Sun Solaris, when compiling in */
+/* 32-bit mode, the overflow occurs in only 2147 seconds (about 36 minutes). */
+
+#include <time.h>
+
+double umfpack_timer ( void )
+{
+ return (((double) (clock ( ))) / ((double) (CLOCKS_PER_SEC))) ;
+}
+
+#endif
+#endif
diff --git a/UMFPACK/Source/umfpack_transpose.c b/UMFPACK/Source/umfpack_transpose.c
new file mode 100644
index 0000000..25ea211
--- /dev/null
+++ b/UMFPACK/Source/umfpack_transpose.c
@@ -0,0 +1,108 @@
+/* ========================================================================== */
+/* === UMFPACK_transpose ==================================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User callable. Computes a permuted transpose, R = (A (P,Q))' in MATLAB
+ notation. See umfpack_transpose.h for details. A and R can be rectangular.
+ The matrix A may be singular.
+ The complex version can do transpose (') or array transpose (.').
+
+ Dynamic memory usage: A single call to UMF_malloc is made, for a workspace
+ of size max (n_row,n_col,1) * sizeof(Int). This is then free'd on return,
+ via UMF_free.
+*/
+
+#include "umf_internal.h"
+#include "umf_transpose.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_transpose
+(
+ Int n_row,
+ Int n_col,
+ const Int Ap [ ], /* size n_col+1 */
+ const Int Ai [ ], /* size nz = Ap [n_col] */
+ const double Ax [ ], /* size nz, if present */
+#ifdef COMPLEX
+ const double Az [ ], /* size nz, if present */
+#endif
+
+ const Int P [ ], /* P [k] = i means original row i is kth row in A(P,Q)*/
+ /* P is identity if not present */
+ /* size n_row, if present */
+
+ const Int Q [ ], /* Q [k] = j means original col j is kth col in A(P,Q)*/
+ /* Q is identity if not present */
+ /* size n_col, if present */
+
+ Int Rp [ ], /* size n_row+1 */
+ Int Ri [ ], /* size nz */
+ double Rx [ ] /* size nz, if present */
+#ifdef COMPLEX
+ , double Rz [ ] /* size nz, if present */
+ , Int do_conjugate /* if true, then to conjugate transpose */
+ /* otherwise, do array transpose */
+#endif
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int status, *W, nn ;
+
+#ifndef NDEBUG
+ init_count = UMF_malloc_count ;
+ UMF_dump_start ( ) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ nn = MAX (n_row, n_col) ;
+ nn = MAX (nn, 1) ;
+ W = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ if (!W)
+ {
+ DEBUGm4 (("out of memory: transpose work\n")) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ ASSERT (UMF_malloc_count == init_count + 1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* C = (A (P,Q))' or (A (P,Q)).' */
+ /* ---------------------------------------------------------------------- */
+
+ status = UMF_transpose (n_row, n_col, Ap, Ai, Ax, P, Q, n_col, Rp, Ri, Rx,
+ W, TRUE
+#ifdef COMPLEX
+ , Az, Rz, do_conjugate
+#endif
+ ) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free the workspace */
+ /* ---------------------------------------------------------------------- */
+
+ (void) UMF_free ((void *) W) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+
+ return (status) ;
+}
diff --git a/UMFPACK/Source/umfpack_triplet_to_col.c b/UMFPACK/Source/umfpack_triplet_to_col.c
new file mode 100644
index 0000000..97750d1
--- /dev/null
+++ b/UMFPACK/Source/umfpack_triplet_to_col.c
@@ -0,0 +1,225 @@
+/* ========================================================================== */
+/* === UMFPACK_triplet_to_col =============================================== */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/*
+ User callable. Converts triplet input to column-oriented form. Duplicate
+ entries may exist (they are summed in the output). The columns of the
+ column-oriented form are in sorted order. The input is not modified.
+ Returns 1 if OK, 0 if an error occurred. See umfpack_triplet_to_col.h for
+ details.
+
+ If Map is present (a non-NULL pointer to an Int array of size nz), then on
+ output it holds the position of the triplets in the column-form matrix.
+ That is, suppose p = Map [k], and the k-th triplet is i=Ti[k], j=Tj[k], and
+ aij=Tx[k]. Then i=Ai[p], and aij will have been summed into Ax[p]. Also,
+ Ap[j] <= p < Ap[j+1]. The Map array is not computed if it is (Int *) NULL.
+
+ Dynamic memory usage:
+
+ If numerical values are present, then one (two for complex version)
+ workspace of size (nz+1)*sizeof(double) is allocated via UMF_malloc.
+ Next, 4 calls to UMF_malloc are made to obtain workspace of size
+ ((nz+1) + (n_row+1) + n_row + MAX (n_row,n_col)) * sizeof(Int). All of
+ this workspace (4 to 6 objects) are free'd via UMF_free on return.
+
+ For the complex version, additional space is allocated.
+
+ An extra array of size nz*sizeof(Int) is allocated if Map is present.
+*/
+
+#include "umf_internal.h"
+#include "umf_malloc.h"
+#include "umf_free.h"
+#include "umf_triplet.h"
+
+#ifndef NDEBUG
+PRIVATE Int init_count ;
+#endif
+
+/* ========================================================================== */
+
+GLOBAL Int UMFPACK_triplet_to_col
+(
+ Int n_row,
+ Int n_col,
+ Int nz,
+ const Int Ti [ ], /* size nz */
+ const Int Tj [ ], /* size nz */
+ const double Tx [ ], /* size nz */
+#ifdef COMPLEX
+ const double Tz [ ], /* size nz */
+#endif
+ Int Ap [ ], /* size n_col + 1 */
+ Int Ai [ ], /* size nz */
+ double Ax [ ] /* size nz */
+#ifdef COMPLEX
+ , double Az [ ] /* size nz */
+#endif
+ , Int Map [ ] /* size nz */
+)
+{
+
+ /* ---------------------------------------------------------------------- */
+ /* local variables */
+ /* ---------------------------------------------------------------------- */
+
+ Int *RowCount, *Rp, *Rj, *W, nn, do_values, do_map, *Map2, status ;
+ double *Rx ;
+#ifdef COMPLEX
+ double *Rz ;
+ Int split ;
+#endif
+
+#ifndef NDEBUG
+ UMF_dump_start ( ) ;
+ init_count = UMF_malloc_count ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* check inputs */
+ /* ---------------------------------------------------------------------- */
+
+ if (!Ai || !Ap || !Ti || !Tj)
+ {
+ return (UMFPACK_ERROR_argument_missing) ;
+ }
+
+ if (n_row <= 0 || n_col <= 0) /* must be > 0 */
+ {
+ return (UMFPACK_ERROR_n_nonpositive) ;
+ }
+
+ if (nz < 0) /* nz must be >= 0 (singular matrices are OK) */
+ {
+ return (UMFPACK_ERROR_invalid_matrix) ;
+ }
+
+ nn = MAX (n_row, n_col) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ Rx = (double *) NULL ;
+
+ do_values = Ax && Tx ;
+
+ if (do_values)
+ {
+#ifdef COMPLEX
+ Rx = (double *) UMF_malloc (2*nz+2, sizeof (double)) ;
+ split = SPLIT (Tz) && SPLIT (Az) ;
+ if (split)
+ {
+ Rz = Rx + nz ;
+ }
+ else
+ {
+ Rz = (double *) NULL ;
+ }
+#else
+ Rx = (double *) UMF_malloc (nz+1, sizeof (double)) ;
+#endif
+ if (!Rx)
+ {
+ DEBUGm4 (("out of memory: triplet work \n")) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ }
+
+ do_map = (Map != (Int *) NULL) ;
+ Map2 = (Int *) NULL ;
+ if (do_map)
+ {
+ DEBUG0 (("Do map:\n")) ;
+ Map2 = (Int *) UMF_malloc (nz+1, sizeof (Int)) ;
+ if (!Map2)
+ {
+ DEBUGm4 (("out of memory: triplet map\n")) ;
+ (void) UMF_free ((void *) Rx) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+ }
+
+ Rj = (Int *) UMF_malloc (nz+1, sizeof (Int)) ;
+ Rp = (Int *) UMF_malloc (n_row+1, sizeof (Int)) ;
+ RowCount = (Int *) UMF_malloc (n_row, sizeof (Int)) ;
+ W = (Int *) UMF_malloc (nn, sizeof (Int)) ;
+ if (!Rj || !Rp || !RowCount || !W)
+ {
+ DEBUGm4 (("out of memory: triplet work (int)\n")) ;
+ (void) UMF_free ((void *) Rx) ;
+ (void) UMF_free ((void *) Map2) ;
+ (void) UMF_free ((void *) Rp) ;
+ (void) UMF_free ((void *) Rj) ;
+ (void) UMF_free ((void *) RowCount) ;
+ (void) UMF_free ((void *) W) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+ return (UMFPACK_ERROR_out_of_memory) ;
+ }
+
+ ASSERT (UMF_malloc_count == init_count + 4 +
+ (Rx != (double *) NULL) + do_map) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* convert from triplet to column form */
+ /* ---------------------------------------------------------------------- */
+
+ if (do_map)
+ {
+ if (do_values)
+ {
+ status = UMF_triplet_map_x (n_row, n_col, nz, Ti, Tj, Ap, Ai, Rp,
+ Rj, W, RowCount, Tx, Ax, Rx
+#ifdef COMPLEX
+ , Tz, Az, Rz
+#endif
+ , Map, Map2) ;
+ }
+ else
+ {
+ status = UMF_triplet_map_nox (n_row, n_col, nz, Ti, Tj, Ap, Ai, Rp,
+ Rj, W, RowCount, Map, Map2) ;
+ }
+ }
+ else
+ {
+ if (do_values)
+ {
+ status = UMF_triplet_nomap_x (n_row, n_col, nz, Ti, Tj, Ap, Ai, Rp,
+ Rj, W, RowCount , Tx, Ax, Rx
+#ifdef COMPLEX
+ , Tz, Az, Rz
+#endif
+ ) ;
+ }
+ else
+ {
+ status = UMF_triplet_nomap_nox (n_row, n_col, nz, Ti, Tj, Ap, Ai,
+ Rp, Rj, W, RowCount) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* free the workspace */
+ /* ---------------------------------------------------------------------- */
+
+ (void) UMF_free ((void *) Rx) ;
+ (void) UMF_free ((void *) Map2) ;
+ (void) UMF_free ((void *) Rp) ;
+ (void) UMF_free ((void *) Rj) ;
+ (void) UMF_free ((void *) RowCount) ;
+ (void) UMF_free ((void *) W) ;
+ ASSERT (UMF_malloc_count == init_count) ;
+
+ return (status) ;
+}
diff --git a/UMFPACK/Tcov/AMD_Demo_Makefile b/UMFPACK/Tcov/AMD_Demo_Makefile
new file mode 100644
index 0000000..2738535
--- /dev/null
+++ b/UMFPACK/Tcov/AMD_Demo_Makefile
@@ -0,0 +1,90 @@
+#-----------------------------------------------------------------------------
+# compile the AMD demo (for both GNU make or original make)
+#-----------------------------------------------------------------------------
+
+default: amd_simple amd_demo amd_demo2 amd_l_demo
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) -I../Include -I../../UFconfig
+
+INC = ../Include/amd.h ../../UFconfig/UFconfig.h
+
+library:
+ ( cd ../Source ; $(MAKE) )
+
+f77lib:
+ ( cd ../Lib ; $(MAKE) fortran )
+
+#------------------------------------------------------------------------------
+# Create the demo program, run it, and compare the output
+#------------------------------------------------------------------------------
+
+dist:
+
+amd_demo: amd_demo.c library $(INC)
+ $(C) -o amd_demo amd_demo.c ../Lib/libamd.a $(LIB)
+ ./amd_demo > my_amd_demo.out
+ - diff amd_demo.out my_amd_demo.out
+
+amd_l_demo: amd_l_demo.c library $(INC)
+ $(C) -o amd_l_demo amd_l_demo.c ../Lib/libamd.a $(LIB)
+ ./amd_l_demo > my_amd_l_demo.out
+ - diff amd_l_demo.out my_amd_l_demo.out
+
+amd_demo2: amd_demo2.c library $(INC)
+ $(C) -o amd_demo2 amd_demo2.c ../Lib/libamd.a $(LIB)
+ ./amd_demo2 > my_amd_demo2.out
+ - diff amd_demo2.out my_amd_demo2.out
+
+amd_simple: amd_simple.c library $(INC)
+ $(C) -o amd_simple amd_simple.c ../Lib/libamd.a $(LIB)
+ ./amd_simple > my_amd_simple.out
+ - diff amd_simple.out my_amd_simple.out
+
+#------------------------------------------------------------------------------
+# compile the Fortran demo
+#------------------------------------------------------------------------------
+
+fortran: amd_f77demo amd_f77simple
+
+cross: amd_f77cross
+
+amd_f77demo: amd_f77demo.f f77lib
+ $(F77) $(F77FLAGS) -o amd_f77demo amd_f77demo.f ../Lib/libamdf77.a \
+ $(F77LIB)
+ ./amd_f77demo > my_amd_f77demo.out
+ - diff amd_f77demo.out my_amd_f77demo.out
+
+amd_f77simple: amd_f77simple.f f77lib
+ $(F77) $(F77FLAGS) -o amd_f77simple amd_f77simple.f \
+ ../Lib/libamdf77.a $(F77LIB)
+ ./amd_f77simple > my_amd_f77simple.out
+ - diff amd_f77simple.out my_amd_f77simple.out
+
+amd_f77wrapper.o: amd_f77wrapper.c
+ $(C) -DDINT -c amd_f77wrapper.c
+
+amd_f77cross: amd_f77cross.f amd_f77wrapper.o ../Lib/libamd.a
+ $(F77) $(F77FLAGS) -o amd_f77cross amd_f77cross.f amd_f77wrapper.o \
+ ../Lib/libamd.a $(F77LIB)
+ ./amd_f77cross > my_amd_f77cross.out
+ - diff amd_f77cross.out my_amd_f77cross.out
+
+#------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#------------------------------------------------------------------------------
+
+clean:
+ - $(RM) $(CLEAN)
+
+purge: distclean
+
+distclean: clean
+ - $(RM) amd_demo my_amd_demo.out
+ - $(RM) amd_l_demo my_amd_l_demo.out
+ - $(RM) amd_demo2 my_amd_demo2.out
+ - $(RM) amd_simple my_amd_simple.out
+ - $(RM) amd_f77demo my_amd_f77demo.out
+ - $(RM) amd_f77simple my_amd_f77simple.out
+ - $(RM) amd_f77cross my_amd_f77cross.out
diff --git a/UMFPACK/Tcov/DO b/UMFPACK/Tcov/DO
new file mode 100755
index 0000000..699d2e8
--- /dev/null
+++ b/UMFPACK/Tcov/DO
@@ -0,0 +1,81 @@
+#!/bin/csh
+
+echo '################################################################################'
+echo 'Tcov test:' $1 $2 $3
+echo '################################################################################'
+
+#-------------------------------------------------------------------------------
+
+# get a clean directory
+# /bin/mv Out/$1_$2 `mktemp -d Trash/XXXXXX`
+
+# delete the directory
+/bin/rm -rf Out/$1_$2
+
+mkdir Out/$1_$2
+
+# put in UMFPACK (excluding Tcov and MATLAB directories) and AMD
+mkdir Out/$1_$2/UMFPACK
+mkdir Out/$1_$2/UMFPACK/Doc
+/bin/cp -prL ../Source Out/$1_$2/UMFPACK
+/bin/cp -prL ../Lib Out/$1_$2/UMFPACK
+/bin/cp -prL ../Include Out/$1_$2/UMFPACK
+/bin/cp -prL ../Demo Out/$1_$2/UMFPACK
+/bin/cp -prL Top_Makefile Out/$1_$2/UMFPACK/Makefile
+/bin/cp -prL Out/$1_$2/UMFPACK/Lib/GNUmakefile Out/$1_$2/UMFPACK/Source/Makefile
+/bin/cp -prL Demo_Makefile Out/$1_$2/UMFPACK/Demo/Makefile
+/bin/cp -prL ../Doc/License Out/$1_$2/UMFPACK/Doc
+
+# put in AMD
+/bin/cp -prL ../../AMD Out/$1_$2
+/bin/cp -prL Top_Makefile Out/$1_$2/AMD/Makefile
+/bin/cp -prL Out/$1_$2/AMD/Lib/GNUmakefile Out/$1_$2/AMD/Source/Makefile
+/bin/cp -prL AMD_Demo_Makefile Out/$1_$2/AMD/Demo/Makefile
+
+/bin/cp debug.* Out/$1_$2
+
+# put in the makefile
+/bin/cp GNUmakefile.$2 Out/$1_$2/GNUmakefile
+
+# put in the UFconfig.mk and UFconfig.h files
+mkdir Out/$1_$2/UFconfig
+/bin/cp -f Make.$1 Out/$1_$2/UFconfig/UFconfig.mk
+/bin/cp -f ../../UFconfig/UFconfig.h Out/$1_$2/UFconfig
+
+# put in the main program
+/bin/cp ut.c Out/$1_$2
+
+# put in the test matrices
+/bin/cp -f badnum*.umf Out/$1_$2
+/bin/cp -f badsym*.umf Out/$1_$2
+/bin/cp -pr TestMat Out/$1_$2
+
+# put in the gcov files
+/bin/cp -f ucov.* Out/$1_$2/UMFPACK/Source
+/bin/cp -f acov.* Out/$1_$2/AMD/Source
+
+# compile and run
+( cd Out/$1_$2 ; time make $3 > $1_$2.out )
+
+# delete the directory
+#### /bin/rm -rf Out/$1_$2
+
+# ( cd $1_$2 ; tail -5 ut.out > ut.tail ; 'rm' -rf ut.out )
+
+# for Solaris
+# ( cd Out/$1_$2 ; tcov -x ut.profile/UMFPACK/Source/umfp*.c )
+# ( cd Out/$1_$2 ; tcov -x ut.profile/UMFPACK/Source/umf_[0-c]*.c )
+# ( cd Out/$1_$2 ; tcov -x ut.profile/UMFPACK/Source/umf_[e-z]*.c )
+# ( cd Out/$1_$2 ; tcov -x ut.profile/AMD/Source/amd_[0-c]*.c )
+# ( cd Out/$1_$2 ; tcov -x ut.profile/AMD/Source/amd_de*.c )
+# ( cd Out/$1_$2 ; tcov -x ut.profile/AMD/Source/amd_[e-z]*.c )
+
+# grep -n "#####" Out/$1_$2/*cov > $1_$2.cov
+
+# cov Out/$1_$2/UMFPACK/Source/umfp*cov
+# cov Out/$1_$2/UMFPACK/Source/umf_[0-c]*cov
+# cov Out/$1_$2/UMFPACK/Source/umf_[e-z]*cov
+# cov Out/$1_$2/AMD/Source/amd_[0-c]*cov
+# cov Out/$1_$2/AMD/Source/amd_de*cov
+# cov Out/$1_$2/AMD/Source/amd_[e-z]*cov
+
diff --git a/UMFPACK/Tcov/DO.linux b/UMFPACK/Tcov/DO.linux
new file mode 100755
index 0000000..6df59d5
--- /dev/null
+++ b/UMFPACK/Tcov/DO.linux
@@ -0,0 +1,55 @@
+#
+#
+
+# ILP32, no BLAS, test for int overflow
+./DO 1 di
+./DO 1 dl
+./DO 1 zi
+./DO 1 zl
+
+# ILP32, BLAS, do not test for int overflow
+./DO 2 di
+./DO 2 dl
+./DO 2 zi
+./DO 2 zl
+
+# ILP32, no BLAS, test for int overflow, no reciprocal
+./DO 5 di
+./DO 5 dl
+./DO 5 zi
+./DO 5 zl
+
+# ILP32, BLAS, do not test for int overflow. No timers
+./DO 6 di
+./DO 6 dl
+./DO 6 zi
+./DO 6 zl
+
+# ILP32, no BLAS, test for int overflow, no divide-by-zero
+./DO 7 di
+./DO 7 dl
+./DO 7 zi
+./DO 7 zl
+
+# ILP32, BLAS, do not test for int overflow. No divide-by-zero
+./DO 8 di
+./DO 8 dl
+./DO 8 zi
+./DO 8 zl
+
+
+# ILP32, no BLAS, test for int overflow. Optimizations turned on
+./DO 1g di run
+./DO 1g dl run
+./DO 1g zi run
+./DO 1g zl run
+
+# ILP32, BLAS, do not test for int overflow. Optimizations turned on
+./DO 2g di run
+./DO 2g dl run
+./DO 2g zi run
+./DO 2g zl run
+
+# coverage summary, include lines not tested by the above 24 coverage tests
+./covall | awk -f cover.awk > cover.out
+cat cover.out
diff --git a/UMFPACK/Tcov/DO.linux.Jan24 b/UMFPACK/Tcov/DO.linux.Jan24
new file mode 100644
index 0000000..591dcd9
--- /dev/null
+++ b/UMFPACK/Tcov/DO.linux.Jan24
@@ -0,0 +1,465 @@
+################################################################################
+Tcov test: 1 di
+################################################################################
+/bin/mv: cannot stat `Out/1_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 52.85
+62.928u 18.396s 1:40.67 80.7% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 1 dl
+################################################################################
+/bin/mv: cannot stat `Out/1_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.44
+55.002u 17.076s 1:47.74 66.8% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 1 zi
+################################################################################
+/bin/mv: cannot stat `Out/1_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.08
+94.574u 19.999s 2:12.31 86.5% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 1 zl
+################################################################################
+/bin/mv: cannot stat `Out/1_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.85
+94.178u 20.267s 2:20.97 81.1% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 2 di
+################################################################################
+/bin/mv: cannot stat `Out/2_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 43.74
+54.336u 17.934s 1:27.28 82.7% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 2 dl
+################################################################################
+/bin/mv: cannot stat `Out/2_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 42.64
+54.068u 17.068s 1:26.00 82.6% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 2 zi
+################################################################################
+/bin/mv: cannot stat `Out/2_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 66.69
+75.192u 19.914s 1:51.89 84.9% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 2 zl
+################################################################################
+/bin/mv: cannot stat `Out/2_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.1
+93.816u 19.893s 2:09.71 87.6% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 3 di
+################################################################################
+/bin/mv: cannot stat `Out/3_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 49.18
+61.050u 19.339s 1:41.90 78.8% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 3 dl
+################################################################################
+/bin/mv: cannot stat `Out/3_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 42.82
+55.075u 18.830s 1:34.96 77.8% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 3 zi
+################################################################################
+/bin/mv: cannot stat `Out/3_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 84.1
+93.431u 21.713s 2:25.67 79.0% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 3 zl
+################################################################################
+/bin/mv: cannot stat `Out/3_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 84.87
+94.509u 21.778s 2:24.09 80.6% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 4 di
+################################################################################
+/bin/mv: cannot stat `Out/4_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 49.36
+60.263u 19.414s 1:41.11 78.7% 0+0k 0+0io 52pf+0w
+################################################################################
+Tcov test: 4 dl
+################################################################################
+/bin/mv: cannot stat `Out/4_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.08
+54.299u 18.897s 1:34.41 77.5% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4 zi
+################################################################################
+/bin/mv: cannot stat `Out/4_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 84.28
+92.899u 21.968s 2:18.25 83.0% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4 zl
+################################################################################
+/bin/mv: cannot stat `Out/4_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 84.85
+93.851u 21.883s 2:25.45 79.5% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 5 di
+################################################################################
+/bin/mv: cannot stat `Out/5_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 51.97
+62.156u 17.755s 1:42.14 78.2% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 5 dl
+################################################################################
+/bin/mv: cannot stat `Out/5_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 43.55
+54.453u 17.032s 1:32.39 77.3% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 5 zi
+################################################################################
+/bin/mv: cannot stat `Out/5_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 85.39
+93.782u 19.825s 2:15.94 83.5% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 5 zl
+################################################################################
+/bin/mv: cannot stat `Out/5_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 85.99
+94.275u 19.921s 2:17.38 83.1% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 6 di
+################################################################################
+/bin/mv: cannot stat `Out/6_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 0
+53.854u 17.179s 1:34.05 75.5% 0+0k 0+0io 14pf+0w
+################################################################################
+Tcov test: 6 dl
+################################################################################
+/bin/mv: cannot stat `Out/6_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 0
+53.387u 16.482s 1:31.79 76.1% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 6 zi
+################################################################################
+/bin/mv: cannot stat `Out/6_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 0
+74.485u 19.371s 1:58.33 79.3% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 6 zl
+################################################################################
+/bin/mv: cannot stat `Out/6_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 0
+93.386u 19.579s 2:23.34 78.7% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 7 di
+################################################################################
+/bin/mv: cannot stat `Out/7_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 52.13
+62.467u 17.903s 1:42.73 78.2% 0+0k 0+0io 2pf+0w
+################################################################################
+Tcov test: 7 dl
+################################################################################
+/bin/mv: cannot stat `Out/7_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.24
+54.250u 17.355s 1:35.45 75.0% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 7 zi
+################################################################################
+/bin/mv: cannot stat `Out/7_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.36
+93.683u 20.174s 2:19.06 81.8% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 7 zl
+################################################################################
+/bin/mv: cannot stat `Out/7_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.8
+93.905u 20.169s 2:18.58 82.3% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 8 di
+################################################################################
+/bin/mv: cannot stat `Out/8_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 44.16
+54.565u 17.959s 1:46.61 68.0% 0+0k 0+0io 69pf+0w
+################################################################################
+Tcov test: 8 dl
+################################################################################
+/bin/mv: cannot stat `Out/8_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 42.92
+54.176u 17.162s 1:40.86 70.7% 0+0k 0+0io 50pf+0w
+################################################################################
+Tcov test: 8 zi
+################################################################################
+/bin/mv: cannot stat `Out/8_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 66.15
+74.497u 20.146s 1:59.21 79.3% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 8 zl
+################################################################################
+/bin/mv: cannot stat `Out/8_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.29
+93.557u 20.215s 2:22.60 79.7% 0+0k 0+0io 51pf+0w
+################################################################################
+Tcov test: 1g di
+################################################################################
+/bin/mv: cannot stat `Out/1g_di': No such file or directory
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 36.37
+73.776u 18.042s 1:56.90 78.5% 0+0k 0+0io 61pf+0w
+################################################################################
+Tcov test: 1g dl
+################################################################################
+/bin/mv: cannot stat `Out/1g_dl': No such file or directory
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 30.98
+69.221u 16.983s 1:46.11 81.2% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 1g zi
+################################################################################
+/bin/mv: cannot stat `Out/1g_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.27
+104.147u 19.969s 2:30.77 82.3% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 1g zl
+################################################################################
+/bin/mv: cannot stat `Out/1g_zl': No such file or directory
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.11
+103.657u 19.929s 2:25.30 85.0% 0+0k 0+0io 32pf+0w
+################################################################################
+Tcov test: 2g di
+################################################################################
+/bin/mv: cannot stat `Out/2g_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.06e-10 (1.37e-07 shl0, 5.65e-05 arc130 1.98e-08 omega2) cputime 29.92
+68.398u 17.843s 1:45.71 81.5% 0+0k 0+0io 15pf+0w
+################################################################################
+Tcov test: 2g dl
+################################################################################
+/bin/mv: cannot stat `Out/2g_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 30.88
+70.119u 16.902s 1:46.55 81.6% 0+0k 0+0io 5pf+0w
+################################################################################
+Tcov test: 2g zi
+################################################################################
+/bin/mv: cannot stat `Out/2g_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.29e-09 omega2) cputime 49.79
+86.583u 19.904s 2:07.59 83.4% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 2g zl
+################################################################################
+/bin/mv: cannot stat `Out/2g_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 67.68
+104.484u 19.575s 2:25.99 84.9% 0+0k 0+0io 9pf+0w
+################################################################################
+Tcov test: 3g di
+################################################################################
+/bin/mv: cannot stat `Out/3g_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 35.6
+74.788u 20.351s 2:20.99 67.4% 0+0k 0+0io 6pf+0w
+################################################################################
+Tcov test: 3g dl
+################################################################################
+/bin/mv: cannot stat `Out/3g_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.32
+70.806u 19.300s 2:01.74 74.0% 0+0k 0+0io 9pf+0w
+################################################################################
+Tcov test: 3g zi
+################################################################################
+/bin/mv: cannot stat `Out/3g_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 68.26
+105.768u 22.114s 2:31.22 84.5% 0+0k 0+0io 6pf+0w
+################################################################################
+Tcov test: 3g zl
+################################################################################
+/bin/mv: cannot stat `Out/3g_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.65
+106.120u 21.851s 2:31.80 84.3% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4g di
+################################################################################
+/bin/mv: cannot stat `Out/4g_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 36.36
+74.674u 20.200s 1:58.26 80.2% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 4g dl
+################################################################################
+/bin/mv: cannot stat `Out/4g_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.27
+70.664u 19.197s 1:53.65 79.0% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4g zi
+################################################################################
+/bin/mv: cannot stat `Out/4g_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 68.53
+105.067u 22.053s 2:32.00 83.6% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 4g zl
+################################################################################
+/bin/mv: cannot stat `Out/4g_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 69.12
+105.423u 22.370s 2:33.38 83.3% 0+0k 0+0io 0pf+0w
diff --git a/UMFPACK/Tcov/DO.linux.out b/UMFPACK/Tcov/DO.linux.out
new file mode 100644
index 0000000..8b614e4
--- /dev/null
+++ b/UMFPACK/Tcov/DO.linux.out
@@ -0,0 +1,475 @@
+################################################################################
+Tcov test: 1 di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 53.07
+63.358u 18.812s 2:43.04 50.3% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 1 dl
+################################################################################
+/bin/mv: cannot stat `Out/1_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.34
+54.784u 17.836s 2:23.80 50.4% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 1 zi
+################################################################################
+/bin/mv: cannot stat `Out/1_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.4
+95.249u 20.442s 3:50.15 50.2% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 1 zl
+################################################################################
+/bin/mv: cannot stat `Out/1_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.94
+94.957u 21.488s 3:50.65 50.4% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 2 di
+################################################################################
+/bin/mv: cannot stat `Out/2_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 44.55
+54.828u 19.260s 2:24.94 51.1% 0+0k 0+0io 2pf+0w
+################################################################################
+Tcov test: 2 dl
+################################################################################
+/bin/mv: cannot stat `Out/2_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.36
+54.572u 18.252s 2:25.22 50.1% 0+0k 0+0io 2pf+0w
+################################################################################
+Tcov test: 2 zi
+################################################################################
+/bin/mv: cannot stat `Out/2_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 67.31
+75.985u 20.963s 3:11.22 50.6% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 2 zl
+################################################################################
+/bin/mv: cannot stat `Out/2_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.25
+94.456u 21.096s 3:49.94 50.2% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 3 di
+################################################################################
+/bin/mv: cannot stat `Out/3_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 50.18
+62.426u 21.521s 2:42.80 51.5% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 3 dl
+################################################################################
+/bin/mv: cannot stat `Out/3_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.28
+56.212u 20.576s 2:29.84 51.2% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 3 zi
+################################################################################
+/bin/mv: cannot stat `Out/3_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 85.12
+95.214u 23.764s 3:53.59 50.9% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 3 zl
+################################################################################
+/bin/mv: cannot stat `Out/3_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.2
+96.296u 23.560s 3:59.43 50.0% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4 di
+################################################################################
+/bin/mv: cannot stat `Out/4_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 49.83
+61.486u 21.044s 2:42.11 50.9% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 4 dl
+################################################################################
+/bin/mv: cannot stat `Out/4_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.4
+55.564u 20.220s 2:29.76 50.6% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4 zi
+################################################################################
+/bin/mv: cannot stat `Out/4_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 84.96
+94.538u 23.473s 3:53.76 50.4% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4 zl
+################################################################################
+/bin/mv: cannot stat `Out/4_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.08
+95.423u 23.338s 3:57.96 49.9% 0+0k 0+0io 2pf+0w
+################################################################################
+Tcov test: 5 di
+################################################################################
+/bin/mv: cannot stat `Out/5_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 53
+63.501u 17.943s 2:41.69 50.3% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 5 dl
+################################################################################
+/bin/mv: cannot stat `Out/5_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 43.84
+55.084u 17.315s 2:30.54 48.0% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 5 zi
+################################################################################
+/bin/mv: cannot stat `Out/5_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 86.48
+94.907u 21.155s 3:49.30 50.6% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 5 zl
+################################################################################
+/bin/mv: cannot stat `Out/5_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 86.93
+94.868u 21.236s 3:52.25 49.9% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 6 di
+################################################################################
+/bin/mv: cannot stat `Out/6_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 0
+54.642u 17.587s 2:27.30 49.0% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 6 dl
+################################################################################
+/bin/mv: cannot stat `Out/6_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 0
+54.264u 17.736s 2:20.31 51.3% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 6 zi
+################################################################################
+/bin/mv: cannot stat `Out/6_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 0
+75.619u 21.189s 3:13.07 50.1% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 6 zl
+################################################################################
+/bin/mv: cannot stat `Out/6_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 0
+94.182u 21.320s 3:49.63 50.2% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 7 di
+################################################################################
+/bin/mv: cannot stat `Out/7_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 52.86
+63.384u 19.469s 2:43.77 50.5% 0+0k 0+0io 55pf+0w
+################################################################################
+Tcov test: 7 dl
+################################################################################
+/bin/mv: cannot stat `Out/7_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.86
+54.944u 19.117s 2:26.11 50.6% 0+0k 0+0io 58pf+0w
+################################################################################
+Tcov test: 7 zi
+################################################################################
+/bin/mv: cannot stat `Out/7_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.22
+94.791u 21.833s 3:52.75 50.1% 0+0k 0+0io 60pf+0w
+################################################################################
+Tcov test: 7 zl
+################################################################################
+/bin/mv: cannot stat `Out/7_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.55
+94.694u 22.253s 3:53.30 50.1% 0+0k 0+0io 60pf+0w
+################################################################################
+Tcov test: 8 di
+################################################################################
+/bin/mv: cannot stat `Out/8_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 44.71
+54.990u 20.140s 2:29.47 50.2% 0+0k 0+0io 60pf+0w
+################################################################################
+Tcov test: 8 dl
+################################################################################
+/bin/mv: cannot stat `Out/8_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.58
+54.709u 19.432s 2:26.94 50.4% 0+0k 0+0io 60pf+0w
+################################################################################
+Tcov test: 8 zi
+################################################################################
+/bin/mv: cannot stat `Out/8_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 67.5
+75.658u 21.959s 3:14.44 50.1% 0+0k 0+0io 60pf+0w
+################################################################################
+Tcov test: 8 zl
+################################################################################
+/bin/mv: cannot stat `Out/8_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.02
+94.103u 22.569s 3:53.56 49.9% 0+0k 0+0io 57pf+0w
+################################################################################
+Tcov test: 1g di
+################################################################################
+/bin/mv: cannot stat `Out/1g_di': No such file or directory
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 36.56
+74.372u 19.090s 2:57.83 52.5% 0+0k 0+0io 61pf+0w
+################################################################################
+Tcov test: 1g dl
+################################################################################
+/bin/mv: cannot stat `Out/1g_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.58
+70.071u 18.354s 2:48.39 52.5% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 1g zi
+################################################################################
+/bin/mv: cannot stat `Out/1g_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.92
+104.920u 21.081s 4:06.48 51.1% 0+0k 0+0io 41pf+0w
+################################################################################
+Tcov test: 1g zl
+################################################################################
+/bin/mv: cannot stat `Out/1g_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.64
+104.824u 21.455s 4:06.01 51.3% 0+0k 0+0io 63pf+0w
+################################################################################
+Tcov test: 2g di
+################################################################################
+/bin/mv: cannot stat `Out/2g_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.06e-10 (1.37e-07 shl0, 5.65e-05 arc130 1.98e-08 omega2) cputime 30.1
+68.093u 19.363s 2:46.78 52.4% 0+0k 0+0io 56pf+0w
+################################################################################
+Tcov test: 2g dl
+################################################################################
+/bin/mv: cannot stat `Out/2g_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.43
+70.067u 18.610s 2:47.30 53.0% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 2g zi
+################################################################################
+/bin/mv: cannot stat `Out/2g_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.29e-09 omega2) cputime 50.74
+86.726u 20.994s 3:28.71 51.6% 0+0k 0+0io 51pf+0w
+################################################################################
+Tcov test: 2g zl
+################################################################################
+/bin/mv: cannot stat `Out/2g_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.44
+104.450u 21.097s 4:04.16 51.4% 0+0k 0+0io 37pf+0w
+################################################################################
+Tcov test: 3g di
+################################################################################
+/bin/mv: cannot stat `Out/3g_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 35.71
+75.583u 21.676s 3:00.23 53.9% 0+0k 0+0io 56pf+0w
+################################################################################
+Tcov test: 3g dl
+################################################################################
+/bin/mv: cannot stat `Out/3g_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.56
+72.222u 21.825s 2:53.57 54.1% 0+0k 0+0io 47pf+0w
+################################################################################
+Tcov test: 3g zi
+################################################################################
+/bin/mv: cannot stat `Out/3g_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 68.43
+106.248u 24.758s 4:07.88 52.8% 0+0k 0+0io 37pf+0w
+################################################################################
+Tcov test: 3g zl
+################################################################################
+/bin/mv: cannot stat `Out/3g_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.55
+106.854u 24.459s 4:10.50 52.4% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4g di
+################################################################################
+/bin/mv: cannot stat `Out/4g_di': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 36.01
+74.958u 21.536s 3:02.32 52.9% 0+0k 0+0io 32pf+0w
+################################################################################
+Tcov test: 4g dl
+################################################################################
+/bin/mv: cannot stat `Out/4g_dl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.32
+70.889u 21.137s 2:49.23 54.3% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4g zi
+################################################################################
+/bin/mv: cannot stat `Out/4g_zi': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 68.48
+105.539u 24.499s 4:08.27 52.3% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4g zl
+################################################################################
+/bin/mv: cannot stat `Out/4g_zl': No such file or directory
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.66
+106.270u 23.930s 4:06.74 52.7% 0+0k 0+0io 0pf+0w
diff --git a/UMFPACK/Tcov/DO.linux.out2 b/UMFPACK/Tcov/DO.linux.out2
new file mode 100644
index 0000000..1a5bf74
--- /dev/null
+++ b/UMFPACK/Tcov/DO.linux.out2
@@ -0,0 +1,428 @@
+################################################################################
+Tcov test: 1 di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 58.08
+65.957u 21.743s 4:14.39 34.4% 0+0k 0+0io 56pf+0w
+################################################################################
+Tcov test: 1 dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 47.61
+57.147u 19.907s 2:36.09 49.3% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 1 zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 87.9
+96.431u 21.184s 5:53.60 33.2% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 1 zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 87.89
+95.638u 21.373s 4:55.24 39.6% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 2 di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 44.76
+55.884u 18.499s 2:30.76 49.3% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 2 dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.58
+55.066u 17.643s 2:27.94 49.1% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 2 zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 68.18
+76.674u 21.814s 3:18.86 49.5% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 2 zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 87.68
+95.713u 21.981s 4:56.13 39.7% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 3 di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 52.99
+63.135u 22.242s 4:26.20 32.0% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 3 dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 45.62
+57.047u 21.076s 5:13.79 24.8% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 3 zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 85.67
+95.359u 23.257s 4:00.29 49.3% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 3 zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 87.52
+96.462u 23.746s 5:27.63 36.6% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 4 di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 6.76e-05 arc130 1.70e-08 omega2) cputime 50.86
+62.001u 21.885s 3:16.46 42.6% 0+0k 0+0io 55pf+0w
+################################################################################
+Tcov test: 4 dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.79
+55.750u 20.866s 2:41.32 47.4% 0+0k 0+0io 2pf+0w
+################################################################################
+Tcov test: 4 zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.97e-09 omega2) cputime 85.85
+95.295u 24.087s 4:09.94 47.7% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 4 zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.78
+95.469u 22.687s 3:56.27 50.0% 0+0k 0+0io 57pf+0w
+################################################################################
+Tcov test: 5 di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 54.79
+64.073u 19.475s 3:18.85 42.0% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 5 dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 44.3
+54.864u 18.963s 3:20.43 36.8% 0+0k 0+0io 2pf+0w
+################################################################################
+Tcov test: 5 zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 86.29
+94.274u 21.352s 5:45.72 33.4% 0+0k 0+0io 55pf+0w
+################################################################################
+Tcov test: 5 zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 86.48
+94.614u 20.459s 4:14.05 45.2% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 6 di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 0
+54.133u 18.431s 2:38.62 45.7% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 6 dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 0
+53.685u 17.717s 2:18.76 51.4% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 6 zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 0
+74.530u 20.591s 3:07.82 50.6% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 6 zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 0
+93.008u 21.095s 3:47.37 50.1% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 7 di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 52
+62.595u 18.109s 2:39.53 50.5% 0+0k 0+0io 2pf+0w
+################################################################################
+Tcov test: 7 dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.48
+54.331u 19.149s 2:32.31 48.2% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 7 zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 86.22
+94.291u 22.044s 4:07.57 46.9% 0+0k 0+0io 35pf+0w
+################################################################################
+Tcov test: 7 zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.77
+94.190u 21.226s 4:00.99 47.8% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 8 di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 2.67e-08 omega2) cputime 45.21
+55.138u 19.192s 2:53.18 42.9% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 8 dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 43.36
+54.424u 18.817s 2:51.32 42.7% 0+0k 0+0io 57pf+0w
+################################################################################
+Tcov test: 8 zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.81e-09 omega2) cputime 66.59
+74.890u 21.514s 4:01.29 39.9% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 8 zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 85.8
+93.133u 21.256s 4:41.13 40.6% 0+0k 0+0io 57pf+0w
+################################################################################
+Tcov test: 1g di
+################################################################################
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 36.45
+74.444u 18.155s 4:12.64 36.6% 0+0k 0+0io 4pf+0w
+################################################################################
+Tcov test: 1g dl
+################################################################################
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.88
+70.117u 18.138s 4:06.43 35.8% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 1g zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.88
+104.228u 21.576s 4:20.17 48.3% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 1g zl
+################################################################################
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.77
+103.874u 21.334s 4:04.77 51.1% 0+0k 0+0io 2pf+0w
+################################################################################
+Tcov test: 2g di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.06e-10 (1.37e-07 shl0, 5.65e-05 arc130 1.98e-08 omega2) cputime 30.14
+68.834u 18.537s 2:59.16 48.7% 0+0k 0+0io 11pf+0w
+################################################################################
+Tcov test: 2g dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 32.02
+70.467u 18.482s 2:49.67 52.4% 0+0k 0+0io 10pf+0w
+################################################################################
+Tcov test: 2g zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.29e-09 omega2) cputime 49.84
+86.839u 20.261s 3:27.29 51.6% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 2g zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 67.93
+104.755u 20.972s 4:03.31 51.6% 0+0k 0+0io 64pf+0w
+################################################################################
+Tcov test: 3g di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 36.48
+75.152u 23.653s 3:10.42 51.8% 0+0k 0+0io 1pf+0w
+################################################################################
+Tcov test: 3g dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.52
+71.320u 21.093s 3:01.30 50.9% 0+0k 0+0io 0pf+0w
+################################################################################
+Tcov test: 3g zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 67.75
+105.546u 22.796s 4:07.55 51.8% 0+0k 0+0io 40pf+0w
+################################################################################
+Tcov test: 3g zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.72
+106.281u 23.809s 4:12.22 51.5% 0+0k 0+0io 7pf+0w
+################################################################################
+Tcov test: 4g di
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 8.27e-09 omega2) cputime 35.69
+74.646u 22.580s 3:44.05 43.3% 0+0k 0+0io 46pf+0w
+################################################################################
+Tcov test: 4g dl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 31.21
+70.200u 19.713s 3:47.80 39.4% 0+0k 0+0io 9pf+0w
+################################################################################
+Tcov test: 4g zi
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 7.77e-05 arc130 2.57e-09 omega2) cputime 68.15
+105.008u 22.823s 5:40.93 37.4% 0+0k 0+0io 3pf+0w
+################################################################################
+Tcov test: 4g zl
+################################################################################
+make[2]: [umfpack_di_demo] Error 1 (ignored)
+make[2]: [umfpack_zi_demo] Error 1 (ignored)
+make[2]: [umfpack_dl_demo] Error 1 (ignored)
+make[2]: [umfpack_zl_demo] Error 1 (ignored)
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.77e-05 arc130 1.35e-09 omega2) cputime 68.44
+105.124u 22.060s 5:40.31 37.3% 0+0k 0+0io 0pf+0w
diff --git a/UMFPACK/Tcov/DO.linux2 b/UMFPACK/Tcov/DO.linux2
new file mode 100755
index 0000000..c5529a2
--- /dev/null
+++ b/UMFPACK/Tcov/DO.linux2
@@ -0,0 +1,108 @@
+#
+#
+
+./DO 1 di
+./DO 1 dl
+./DO 1 zi
+./DO 1 zl
+
+./DO 2 di
+./DO 2 dl
+./DO 2 zi
+./DO 2 zl
+
+./DO 3 di
+./DO 3 dl
+./DO 3 zi
+./DO 3 zl
+
+./DO 4 di
+./DO 4 dl
+./DO 4 zi
+./DO 4 zl
+
+./DO 5 di
+./DO 5 dl
+./DO 5 zi
+./DO 5 zl
+
+./DO 6 di
+./DO 6 dl
+./DO 6 zi
+./DO 6 zl
+
+./DO 7 di
+./DO 7 dl
+./DO 7 zi
+./DO 7 zl
+
+./DO 8 di
+./DO 8 dl
+./DO 8 zi
+./DO 8 zl
+
+
+./DO 1g di run
+./DO 1g dl run
+./DO 1g zi run
+./DO 1g zl run
+
+./DO 2g di run
+./DO 2g dl run
+./DO 2g zi run
+./DO 2g zl run
+
+./DO 3g di run
+./DO 3g dl run
+./DO 3g zi run
+./DO 3g zl run
+
+./DO 4g di run
+./DO 4g dl run
+./DO 4g zi run
+./DO 4g zl run
+
+
+
+./DO 1i di run
+./DO 1i dl run
+./DO 1i zi run
+./DO 1i zl run
+
+./DO 2i di run
+./DO 2i dl run
+./DO 2i zi run
+./DO 2i zl run
+
+./DO 3i di run
+./DO 3i dl run
+./DO 3i zi run
+./DO 3i zl run
+
+./DO 4i di run
+./DO 4i dl run
+./DO 4i zi run
+./DO 4i zl run
+
+
+
+./DO 1n di run
+./DO 1n dl run
+./DO 1n zi run
+./DO 1n zl run
+
+./DO 2n di run
+./DO 2n dl run
+./DO 2n zi run
+./DO 2n zl run
+
+./DO 3n di run
+./DO 3n dl run
+./DO 3n zi run
+./DO 3n zl run
+
+./DO 4n di run
+./DO 4n dl run
+./DO 4n zi run
+./DO 4n zl run
+
diff --git a/UMFPACK/Tcov/DO.solaris b/UMFPACK/Tcov/DO.solaris
new file mode 100755
index 0000000..51b7ffc
--- /dev/null
+++ b/UMFPACK/Tcov/DO.solaris
@@ -0,0 +1,47 @@
+#
+#
+#
+#
+
+
+ ./DOsol s1 di run
+ ./DOsol s1 dl run
+ ./DOsol s1 zi run
+ ./DOsol s1 zl run
+ ./DOsol s2 di run
+ ./DOsol s2 dl run
+ ./DOsol s2 zi run
+ ./DOsol s2 zl run
+
+ ./DOsol s3 di run
+ ./DOsol s3 dl run
+ ./DOsol s3 zi run
+ ./DOsol s3 zl run
+ ./DOsol s4 di run
+ ./DOsol s4 dl run
+ ./DOsol s4 zi run
+ ./DOsol s4 zl run
+
+ ./DOsol s5 di run
+ ./DOsol s5 dl run
+ ./DOsol s5 zi run
+ ./DOsol s5 zl run
+ ./DOsol n1 di run
+ ./DOsol n1 dl run
+ ./DOsol n1 zi run
+ ./DOsol n1 zl run
+
+ ./DOsol n2 di run
+ ./DOsol n2 dl run
+ ./DOsol n2 zi run
+ ./DOsol n2 zl run
+ ./DOsol n3 di run
+ ./DOsol n3 dl run
+ ./DOsol n3 zi run
+ ./DOsol n3 zl run
+
+ ./DOsol n4 di run
+ ./DOsol n4 dl run
+ ./DOsol n4 zi run
+ ./DOsol n4 zl run
+
diff --git a/UMFPACK/Tcov/DO.solaris.out.Jan24 b/UMFPACK/Tcov/DO.solaris.out.Jan24
new file mode 100644
index 0000000..e69de29
diff --git a/UMFPACK/Tcov/DO2 b/UMFPACK/Tcov/DO2
new file mode 100755
index 0000000..aa6f65f
--- /dev/null
+++ b/UMFPACK/Tcov/DO2
@@ -0,0 +1,9 @@
+#
+#
+
+
+DO 1g zi run
+DO 1g zl run
+DO 2g zl run
+DO 3g zl run
+DO 4g zl run
diff --git a/UMFPACK/Tcov/DO678 b/UMFPACK/Tcov/DO678
new file mode 100755
index 0000000..ea373ec
--- /dev/null
+++ b/UMFPACK/Tcov/DO678
@@ -0,0 +1,17 @@
+#
+#
+
+DO 6 di
+DO 6 dl
+DO 6 zi
+DO 6 zl
+
+DO 7 di
+DO 7 dl
+DO 7 zi
+DO 7 zl
+
+DO 8 di
+DO 8 dl
+DO 8 zi
+DO 8 zl
diff --git a/UMFPACK/Tcov/DOsol b/UMFPACK/Tcov/DOsol
new file mode 100755
index 0000000..5582679
--- /dev/null
+++ b/UMFPACK/Tcov/DOsol
@@ -0,0 +1,6 @@
+#!/bin/csh
+
+#-------------------------------------------------------------------------------
+
+mkdir SolOut/$1_$2
+DOsol2 $1 $2 $3 >& SolOut/$1_$2.stderr
diff --git a/UMFPACK/Tcov/DOsol2 b/UMFPACK/Tcov/DOsol2
new file mode 100755
index 0000000..4fd89ce
--- /dev/null
+++ b/UMFPACK/Tcov/DOsol2
@@ -0,0 +1,57 @@
+#!/bin/csh
+
+#-------------------------------------------------------------------------------
+
+echo '################################################################################'
+echo 'Tcov test:' $1 $2
+echo '################################################################################'
+
+# get a clean directory
+# /bin/mv Tests/$1_$2 `mktemp -d Trash2/XXXXXX`
+# mkdir SolOut/$1_$2
+
+# put in UMFPACK (excluding Tcov and MATLAB directories) and AMD
+mkdir SolOut/$1_$2/UMFPACK
+mkdir SolOut/$1_$2/UMFPACK/Doc
+/bin/cp -prL ../Source SolOut/$1_$2/UMFPACK
+/bin/cp -prL ../Lib SolOut/$1_$2/UMFPACK
+/bin/cp -prL ../Include SolOut/$1_$2/UMFPACK
+/bin/cp -prL ../Demo SolOut/$1_$2/UMFPACK
+/bin/cp -prL ../Makefile SolOut/$1_$2/UMFPACK/Makefile
+/bin/cp -prL ../Doc/License SolOut/$1_$2/UMFPACK/Doc
+/bin/cp -prL ../../AMD SolOut/$1_$2
+/bin/cp debug.* SolOut/$1_$2
+
+# put in the makefile
+/bin/cp GNUmakefile.$2 SolOut/$1_$2/GNUmakefile
+
+# put in the UFconfig.mk and UFconfig.h files
+mkdir SolOut/$1_$2/UFconfig
+/bin/cp -f Make.$1 SolOut/$1_$2/UFconfig/UFconfig.mk
+/bin/cp -f ../../UFconfig/UFconfig.h SolOut/$1_$2/UFconfig
+
+# put in the main program
+/bin/cp ut.c SolOut/$1_$2
+
+# put in the test matrices
+/bin/cp -f badnum*.umf SolOut/$1_$2
+/bin/cp -f badsym*.umf SolOut/$1_$2
+/bin/cp -pr TestMat SolOut/$1_$2
+
+# compile and run
+( cd SolOut/$1_$2 ; time make $3 > $1_$2.out )
+
+# for Solaris
+( cd SolOut/$1_$2 ; tail -5 ut.out > $1_$2.tail )
+( cd SolOut/$1_$2 ; tcov -x ut.profile */Source/*.c )
+( cd SolOut/$1_$2 ; grep -n "#####" *cov > $1_$2.cov )
+
+# /bin/rm -rf SolOut/$1_$2
+
+# cov $1_$2/UMFPACK/Source/umfp*cov
+# cov $1_$2/UMFPACK/Source/umf_[0-c]*cov
+# cov $1_$2/UMFPACK/Source/umf_[e-z]*cov
+# cov $1_$2/AMD/Source/amd_[0-c]*cov
+# cov $1_$2/AMD/Source/amd_de*cov
+# cov $1_$2/AMD/Source/amd_[e-z]*cov
+
diff --git a/UMFPACK/Tcov/Demo_Makefile b/UMFPACK/Tcov/Demo_Makefile
new file mode 100644
index 0000000..5063c2f
--- /dev/null
+++ b/UMFPACK/Tcov/Demo_Makefile
@@ -0,0 +1,176 @@
+#-------------------------------------------------------------------------------
+# compile the UMFPACK demos (for GNU make and original make)
+#-------------------------------------------------------------------------------
+
+# UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis.
+# All Rights Reserved. See ../Doc/License for License.
+
+default: libs run
+
+include ../../UFconfig/UFconfig.mk
+
+C = $(CC) $(CFLAGS) $(UMFPACK_CONFIG) -I../Include -I../../AMD/Include \
+ -I../../UFconfig
+
+INC = ../Include/umfpack.h ../../AMD/Include/amd.h ../../UFconfig/UFconfig.h
+
+LIBS = $(BLAS) $(XERBLA) $(LIB)
+
+../Lib/libumfpack.a:
+ ( cd ../Source ; $(MAKE) )
+
+../../AMD/Lib/libamd.a:
+ ( cd ../../AMD ; $(MAKE) library )
+
+UMFPACK = ../Lib/libumfpack.a ../../AMD/Lib/libamd.a
+
+libs:
+ ( cd ../Source ; $(MAKE) )
+ ( cd ../../AMD ; $(MAKE) library )
+
+#-------------------------------------------------------------------------------
+# Create the demo programs, run them, and compare the output
+#-------------------------------------------------------------------------------
+
+dist: umfpack_di_demo.c umfpack_dl_demo.c umfpack_zi_demo.c umfpack_zl_demo.c
+
+umfpack_simple: umfpack_simple.c $(INC) $(UMFPACK)
+ $(C) -o umfpack_simple umfpack_simple.c $(UMFPACK) $(LIBS)
+
+# the GNU rules are simpler:
+# umfpack_%_demo.c: umfpack_xx_demo.c umfpack_%_demo.sed
+# - sed -f umfpack_$*_demo.sed < umfpack_xx_demo.c > umfpack_$*_demo.c
+#
+# umfpack_%_demo: umfpack_%_demo.c $(INC) $(UMFPACK)
+# $(C) -o umfpack_$*_demo umfpack_$*_demo.c $(UMFPACK) $(LIBS)
+# ./umfpack_$*_demo > my_umfpack_$*_demo.out
+
+# but do this via brute-force, so we can use just a single Makefile:
+
+# double-precision, int verion:
+umfpack_di_demo.c: umfpack_xx_demo.c umfpack_di_demo.sed
+ - sed -f umfpack_di_demo.sed < umfpack_xx_demo.c > umfpack_di_demo.c
+
+umfpack_di_demo: umfpack_di_demo.c $(INC) $(UMFPACK)
+ $(C) -o umfpack_di_demo umfpack_di_demo.c $(UMFPACK) $(LIBS)
+
+# double-precision, UF_long verion:
+umfpack_dl_demo.c: umfpack_xx_demo.c umfpack_dl_demo.sed
+ - sed -f umfpack_dl_demo.sed < umfpack_xx_demo.c > umfpack_dl_demo.c
+
+umfpack_dl_demo: umfpack_dl_demo.c $(INC) $(UMFPACK)
+ $(C) -o umfpack_dl_demo umfpack_dl_demo.c $(UMFPACK) $(LIBS)
+
+# complex, int verion:
+umfpack_zi_demo.c: umfpack_xx_demo.c umfpack_zi_demo.sed
+ - sed -f umfpack_zi_demo.sed < umfpack_xx_demo.c > umfpack_zi_demo.c
+
+umfpack_zi_demo: umfpack_zi_demo.c $(INC) $(UMFPACK)
+ $(C) -o umfpack_zi_demo umfpack_zi_demo.c $(UMFPACK) $(LIBS)
+
+# complex, UF_long verion:
+umfpack_zl_demo.c: umfpack_xx_demo.c umfpack_zl_demo.sed
+ - sed -f umfpack_zl_demo.sed < umfpack_xx_demo.c > umfpack_zl_demo.c
+
+umfpack_zl_demo: umfpack_zl_demo.c $(INC) $(UMFPACK)
+ $(C) -o umfpack_zl_demo umfpack_zl_demo.c $(UMFPACK) $(LIBS)
+
+run: umfpack_di_demo umfpack_zi_demo umfpack_dl_demo umfpack_zl_demo umfpack_simple
+ ./umfpack_simple
+ ./umfpack_di_demo > my_umfpack_di_demo.out
+ - diff umfpack_di_demo.out my_umfpack_di_demo.out
+ ./umfpack_dl_demo > my_umfpack_dl_demo.out
+ - diff umfpack_dl_demo.out my_umfpack_dl_demo.out
+ ./umfpack_zi_demo > my_umfpack_zi_demo.out
+ - diff umfpack_zi_demo.out my_umfpack_zi_demo.out
+ ./umfpack_zl_demo > my_umfpack_zl_demo.out
+ - diff umfpack_zl_demo.out my_umfpack_zl_demo.out
+
+#-------------------------------------------------------------------------------
+# create a demo program that reads in Harwell/Boeing matrices, and run it
+#-------------------------------------------------------------------------------
+
+# the output of "make hb" is in the file umf4.out
+hb: $(UMFPACK) umf4 readhb readhb_nozeros readhb_size
+ - ./readhb_nozeros < HB/can_24.psa > tmp/A
+ - ./readhb_size < HB/can_24.psa > tmp/Asize
+ - ./umf4
+ - ./readhb_nozeros < HB/west0067.rua > tmp/A
+ - ./readhb_size < HB/west0067.rua > tmp/Asize
+ - ./umf4
+ - ./readhb_nozeros < HB/fs_183_6.rua > tmp/A
+ - ./readhb_size < HB/fs_183_6.rua > tmp/Asize
+ - ./umf4
+ - ./readhb < HB/fs_183_6.rua > tmp/A
+ - ./readhb_size < HB/fs_183_6.rua > tmp/Asize
+ - ./umf4
+ - ./readhb < HB/arc130.rua > tmp/A
+ - ./readhb_size < HB/arc130.rua > tmp/Asize
+ - ./umf4
+ - ./readhb_nozeros < HB/arc130.rua > tmp/A
+ - ./readhb_size < HB/arc130.rua > tmp/Asize
+ - ./umf4
+ - ./readhb_nozeros < HB/arc130.rua > tmp/A
+ - ./readhb_size < HB/arc130.rua > tmp/Asize
+ - ./umf4 a 1e-6
+
+umf4: umf4.c $(UMFPACK)
+ $(C) -o umf4 umf4.c $(UMFPACK) $(LIBS)
+
+readhb: readhb.f
+ $(F77) $(F77FLAGS) -o readhb readhb.f $(F77LIB)
+
+readhb_size: readhb_size.f
+ $(F77) $(F77FLAGS) -o readhb_size readhb_size.f $(F77LIB)
+
+readhb_nozeros: readhb_nozeros.f
+ $(F77) $(F77FLAGS) -o readhb_nozeros readhb_nozeros.f $(F77LIB)
+
+#-------------------------------------------------------------------------------
+# compile the FORTRAN interface and demo
+#-------------------------------------------------------------------------------
+
+fortran: $(UMFPACK) umf4hb.f umf4_f77wrapper.o umf4zhb.f umf4_f77zwrapper.o $(UMFPACK)
+ $(F77) $(F77FLAGS) -o umf4hb umf4hb.f umf4_f77wrapper.o \
+ $(UMFPACK) $(LIBS)
+ - ./umf4hb < HB/west0067.rua > my_umf4hb.out
+ - diff my_umf4hb.out umf4hb.out
+ $(F77) $(F77FLAGS) -o umf4zhb umf4zhb.f umf4_f77zwrapper.o \
+ $(UMFPACK) $(LIBS)
+ - ./umf4zhb < HB/qc324.cua > my_umf4zhb.out
+ - diff my_umf4zhb.out umf4zhb.out
+
+fortran64: $(UMFPACK) umf4hb64.f umf4_f77wrapper64.o umf4_f77zwrapper64.o $(UMFPACK)
+ $(F77) $(F77FLAGS) -o umf4hb64 umf4hb64.f umf4_f77wrapper64.o \
+ $(UMFPACK) $(LIBS)
+ - ./umf4hb64 < HB/west0067.rua > my_umf4hb64.out
+ - diff my_umf4hb64.out umf4hb64.out
+
+umf4_f77wrapper.o: umf4_f77wrapper.c $(INC)
+ $(C) -c umf4_f77wrapper.c -o umf4_f77wrapper.o
+
+umf4_f77zwrapper.o: umf4_f77zwrapper.c $(INC)
+ $(C) -c umf4_f77zwrapper.c -o umf4_f77zwrapper.o
+
+umf4_f77wrapper64.o: umf4_f77wrapper.c $(INC)
+ $(C) -DDLONG -c umf4_f77wrapper.c -o umf4_f77wrapper64.o
+
+umf4_f77zwrapper64.o: umf4_f77zwrapper.c $(INC)
+ $(C) -DDLONG -c umf4_f77zwrapper.c -o umf4_f77zwrapper64.o
+
+#-------------------------------------------------------------------------------
+# Remove all but the files in the original distribution
+#-------------------------------------------------------------------------------
+
+purge: clean
+ - $(RM) umfpack_simple a.out
+ - $(RM) umfpack_di_demo my_umfpack_di_demo.out
+ - $(RM) umfpack_dl_demo my_umfpack_dl_demo.out
+ - $(RM) umfpack_zi_demo my_umfpack_zi_demo.out
+ - $(RM) umfpack_zl_demo my_umfpack_zl_demo.out
+ - $(RM) umf4hb umf4zhb *.umf my_umf4hb.out
+ - $(RM) umf4hb64 my_umf4hb64.out my_umf4zhb.out
+ - $(RM) umf4 readhb readhb_nozeros readhb_size tmp/*
+
+clean:
+ - $(RM) $(CLEAN)
diff --git a/UMFPACK/Tcov/GNUmakefile.di b/UMFPACK/Tcov/GNUmakefile.di
new file mode 100644
index 0000000..84ab564
--- /dev/null
+++ b/UMFPACK/Tcov/GNUmakefile.di
@@ -0,0 +1,26 @@
+all: go
+
+include UFconfig/UFconfig.mk
+
+go: run
+ - ( cd UMFPACK/Source ; ./ucov.di )
+ - ( cd AMD/Source ; ./acov.di )
+
+run: prog
+ - ./ut > ut.out
+ - tail ut.out
+ #- $(RM) ut.out
+
+prog:
+ ( cd UMFPACK ; make library )
+ ( cd AMD ; make library )
+ $(CC) -DDINT $(CFLAGS) $(UMFPACK_CONFIG) -IUMFPACK/Source -IUMFPACK/Include -IAMD/Source -IAMD/Include -IUFconfig -o ut ut.c UMFPACK/Lib/libumfpack.a AMD/Lib/libamd.a $(LIB)
+
+utcov:
+ - ( cd UMFPACK/Source ; ./ucov.di )
+ - ( cd AMD/Source ; ./acov.di )
+
+
+purge:
+ ( cd UMFPACK ; make purge )
+ ( cd AMD ; make purge )
diff --git a/UMFPACK/Tcov/GNUmakefile.dl b/UMFPACK/Tcov/GNUmakefile.dl
new file mode 100644
index 0000000..174b905
--- /dev/null
+++ b/UMFPACK/Tcov/GNUmakefile.dl
@@ -0,0 +1,25 @@
+all: go
+
+include UFconfig/UFconfig.mk
+
+go: run
+ - ( cd UMFPACK/Source ; ./ucov.dl )
+ - ( cd AMD/Source ; ./acov.dl )
+
+run: prog
+ - ./ut > ut.out
+ - tail ut.out
+ #- $(RM) ut.out
+
+prog:
+ ( cd UMFPACK ; make library )
+ ( cd AMD ; make library )
+ $(CC) -DDLONG $(CFLAGS) $(UMFPACK_CONFIG) -IUMFPACK/Source -IUMFPACK/Include -IAMD/Source -IAMD/Include -IUFconfig -o ut ut.c UMFPACK/Lib/libumfpack.a AMD/Lib/libamd.a $(LIB)
+
+utcov:
+ - ( cd UMFPACK/Source ; ./ucov.dl )
+ - ( cd AMD/Source ; ./acov.dl )
+
+purge:
+ ( cd UMFPACK ; make purge )
+ ( cd AMD ; make purge )
diff --git a/UMFPACK/Tcov/GNUmakefile.zi b/UMFPACK/Tcov/GNUmakefile.zi
new file mode 100644
index 0000000..040d1a0
--- /dev/null
+++ b/UMFPACK/Tcov/GNUmakefile.zi
@@ -0,0 +1,25 @@
+all: go
+
+include UFconfig/UFconfig.mk
+
+go: run
+ - ( cd UMFPACK/Source ; ./ucov.zi )
+ - ( cd AMD/Source ; ./acov.zi )
+
+run: prog
+ - ./ut > ut.out
+ - tail ut.out
+ #- $(RM) ut.out
+
+prog:
+ ( cd UMFPACK ; make library )
+ ( cd AMD ; make library )
+ $(CC) -DZINT $(CFLAGS) $(UMFPACK_CONFIG) -IUMFPACK/Source -IUMFPACK/Include -IAMD/Source -IAMD/Include -IUFconfig -o ut ut.c UMFPACK/Lib/libumfpack.a AMD/Lib/libamd.a $(LIB)
+
+utcov:
+ - ( cd UMFPACK/Source ; ./ucov.zi )
+ - ( cd AMD/Source ; ./acov.zi )
+
+purge:
+ ( cd UMFPACK ; make purge )
+ ( cd AMD ; make purge )
diff --git a/UMFPACK/Tcov/GNUmakefile.zl b/UMFPACK/Tcov/GNUmakefile.zl
new file mode 100644
index 0000000..1a590cd
--- /dev/null
+++ b/UMFPACK/Tcov/GNUmakefile.zl
@@ -0,0 +1,25 @@
+all: go
+
+include UFconfig/UFconfig.mk
+
+go: run
+ - ( cd UMFPACK/Source ; ./ucov.zl )
+ - ( cd AMD/Source ; ./acov.zl )
+
+run: prog
+ - ./ut > ut.out
+ - tail ut.out
+ #- $(RM) ut.out
+
+prog:
+ ( cd UMFPACK ; make library )
+ ( cd AMD ; make library )
+ $(CC) -DZLONG $(CFLAGS) $(UMFPACK_CONFIG) -IUMFPACK/Source -IUMFPACK/Include -IAMD/Source -IAMD/Include -IUFconfig -o ut ut.c UMFPACK/Lib/libumfpack.a AMD/Lib/libamd.a $(LIB)
+
+utcov:
+ - ( cd UMFPACK/Source ; ./ucov.zl )
+ - ( cd AMD/Source ; ./acov.zl )
+
+purge:
+ ( cd UMFPACK ; make purge )
+ ( cd AMD ; make purge )
diff --git a/UMFPACK/Tcov/Make.1 b/UMFPACK/Tcov/Make.1
new file mode 100644
index 0000000..048b240
--- /dev/null
+++ b/UMFPACK/Tcov/Make.1
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, no BLAS, test for integer overflow.
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0
+UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.1g b/UMFPACK/Tcov/Make.1g
new file mode 100644
index 0000000..3c29ce1
--- /dev/null
+++ b/UMFPACK/Tcov/Make.1g
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, no BLAS, test for integer overflow.
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O3 -fPIC
+UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.1i b/UMFPACK/Tcov/Make.1i
new file mode 100644
index 0000000..905e265
--- /dev/null
+++ b/UMFPACK/Tcov/Make.1i
@@ -0,0 +1,21 @@
+#===============================================================================
+# ILP32 mode, no BLAS, test for integer overflow.
+#===============================================================================
+
+# Using Intel's icc compiler:
+CC = icc
+CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0
+
+UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING
+# LIB = -lm -lunwind -lcprts
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.1n b/UMFPACK/Tcov/Make.1n
new file mode 100644
index 0000000..f731477
--- /dev/null
+++ b/UMFPACK/Tcov/Make.1n
@@ -0,0 +1,21 @@
+#===============================================================================
+# ILP32 mode, no BLAS, test for integer overflow.
+#===============================================================================
+
+# Using Intel's icc compiler:
+CC = icc
+CFLAGS = -ansi
+
+UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING
+# LIB = -lm -lunwind -lcprts
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.2 b/UMFPACK/Tcov/Make.2
new file mode 100644
index 0000000..1971256
--- /dev/null
+++ b/UMFPACK/Tcov/Make.2
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, BLAS, do not test for integer overflow.
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0
+UMFPACK_CONFIG = -DTESTING
+LIB = -lblas -lgfortran -lgfortranbegin -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.2g b/UMFPACK/Tcov/Make.2g
new file mode 100644
index 0000000..5997a19
--- /dev/null
+++ b/UMFPACK/Tcov/Make.2g
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, BLAS, do not test for integer overflow.
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O3 -fPIC
+UMFPACK_CONFIG = -DTESTING
+LIB = -lblas -lgfortran -lgfortranbegin -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.2i b/UMFPACK/Tcov/Make.2i
new file mode 100644
index 0000000..7d459ca
--- /dev/null
+++ b/UMFPACK/Tcov/Make.2i
@@ -0,0 +1,20 @@
+#===============================================================================
+# ILP32 mode, BLAS, do not test for integer overflow.
+#===============================================================================
+
+# Using Intel's icc compiler:
+CC = icc
+CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0
+
+UMFPACK_CONFIG = -DTESTING
+LIB = -lblas -lgfortran -lgfortranbegin -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.2n b/UMFPACK/Tcov/Make.2n
new file mode 100644
index 0000000..922f96a
--- /dev/null
+++ b/UMFPACK/Tcov/Make.2n
@@ -0,0 +1,20 @@
+#===============================================================================
+# ILP32 mode, BLAS, do not test for integer overflow.
+#===============================================================================
+
+# Using Intel's icc compiler:
+CC = icc
+CFLAGS = -ansi
+
+UMFPACK_CONFIG = -DTESTING
+LIB = -lblas -lgfortran -lgfortranbegin -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.3 b/UMFPACK/Tcov/Make.3
new file mode 100644
index 0000000..16e130e
--- /dev/null
+++ b/UMFPACK/Tcov/Make.3
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, C interface /ATLAS BLAS, do not test for integer overflow.
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0
+UMFPACK_CONFIG = -DCBLAS -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include
+LIB = -lcblas -latlas -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.3g b/UMFPACK/Tcov/Make.3g
new file mode 100644
index 0000000..074eaad
--- /dev/null
+++ b/UMFPACK/Tcov/Make.3g
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, C interface /ATLAS BLAS, do not test for integer overflow.
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O3 -fPIC
+UMFPACK_CONFIG = -DCBLAS -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include
+LIB = -lcblas -latlas -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.3i b/UMFPACK/Tcov/Make.3i
new file mode 100644
index 0000000..a61df3d
--- /dev/null
+++ b/UMFPACK/Tcov/Make.3i
@@ -0,0 +1,20 @@
+#===============================================================================
+# ILP32 mode, C interface /ATLAS BLAS, do not test for integer overflow.
+#===============================================================================
+
+# Using Intel's icc compiler:
+CC = icc
+CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0
+
+UMFPACK_CONFIG = -DCBLAS -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include
+LIB = -lcblas -latlas -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.3n b/UMFPACK/Tcov/Make.3n
new file mode 100644
index 0000000..02b7e6b
--- /dev/null
+++ b/UMFPACK/Tcov/Make.3n
@@ -0,0 +1,20 @@
+#===============================================================================
+# ILP32 mode, C interface /ATLAS BLAS, do not test for integer overflow.
+#===============================================================================
+
+# Using Intel's icc compiler:
+CC = icc
+CFLAGS = -ansi
+
+UMFPACK_CONFIG = -DCBLAS -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include
+LIB = -lcblas -latlas -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.4 b/UMFPACK/Tcov/Make.4
new file mode 100644
index 0000000..cc8fd66
--- /dev/null
+++ b/UMFPACK/Tcov/Make.4
@@ -0,0 +1,19 @@
+#===============================================================================
+# ILP32 mode, Fortran interface to ATLAS BLAS, do not test for integer overflow.
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0
+UMFPACK_CONFIG = -DTESTING
+CONFIG = -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include
+LIB = -lf77blas -latlas -lfrtbegin -lg2c -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.4g b/UMFPACK/Tcov/Make.4g
new file mode 100644
index 0000000..272633f
--- /dev/null
+++ b/UMFPACK/Tcov/Make.4g
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, Fortran interface to ATLAS BLAS, do not test for integer overflow.
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O3 -fPIC
+UMFPACK_CONFIG = -DTESTING -I/cise/research/sparse/Install/ATLAS/Linux_P4SSE2/include
+LIB = -lf77blas -latlas -lfrtbegin -lg2c -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.4i b/UMFPACK/Tcov/Make.4i
new file mode 100644
index 0000000..9fd0203
--- /dev/null
+++ b/UMFPACK/Tcov/Make.4i
@@ -0,0 +1,20 @@
+#===============================================================================
+# ILP32 mode, Fortran interface to ATLAS BLAS, do not test for integer overflow.
+#===============================================================================
+
+# Using Intel's icc compiler:
+CC = icc
+CFLAGS = -ansi -O3 -ip -tpp7 -xW -vec_report0
+
+UMFPACK_CONFIG = -DTESTING
+LIB = -lf77blas -latlas -lfrtbegin -lg2c -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.4n b/UMFPACK/Tcov/Make.4n
new file mode 100644
index 0000000..f674ac5
--- /dev/null
+++ b/UMFPACK/Tcov/Make.4n
@@ -0,0 +1,20 @@
+#===============================================================================
+# ILP32 mode, Fortran interface to ATLAS BLAS, do not test for integer overflow.
+#===============================================================================
+
+# Using Intel's icc compiler:
+CC = icc
+CFLAGS = -ansi
+
+UMFPACK_CONFIG = -DTESTING
+LIB = -lf77blas -latlas -lfrtbegin -lg2c -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.5 b/UMFPACK/Tcov/Make.5
new file mode 100644
index 0000000..e103014
--- /dev/null
+++ b/UMFPACK/Tcov/Make.5
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, no BLAS, test for integer overflow, no reciprocal
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0
+UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING -DNRECIPROCAL
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.6 b/UMFPACK/Tcov/Make.6
new file mode 100644
index 0000000..30c8773
--- /dev/null
+++ b/UMFPACK/Tcov/Make.6
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, BLAS, do not test for integer overflow. No timers
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0
+UMFPACK_CONFIG = -DTESTING -DNO_TIMER
+LIB = -lblas -lgfortran -lgfortranbegin -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.7 b/UMFPACK/Tcov/Make.7
new file mode 100644
index 0000000..f715beb
--- /dev/null
+++ b/UMFPACK/Tcov/Make.7
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, no BLAS, test for integer overflow. No divide by zero
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0
+UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING -DNO_DIVIDE_BY_ZERO
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.8 b/UMFPACK/Tcov/Make.8
new file mode 100644
index 0000000..d1e49f9
--- /dev/null
+++ b/UMFPACK/Tcov/Make.8
@@ -0,0 +1,18 @@
+#===============================================================================
+# ILP32 mode, BLAS, do not test for integer overflow. No divide by zero.
+#===============================================================================
+
+CC = gcc
+CFLAGS = -O0 -ftest-coverage -fprofile-arcs -O0
+UMFPACK_CONFIG = -DTESTING -DNO_DIVIDE_BY_ZERO
+LIB = -lblas -lgfortran -lgfortranbegin -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.n1 b/UMFPACK/Tcov/Make.n1
new file mode 100644
index 0000000..ef57211
--- /dev/null
+++ b/UMFPACK/Tcov/Make.n1
@@ -0,0 +1,18 @@
+#===============================================================================
+# Solaris ILP32 mode, no BLAS, test for integer overflow.
+#===============================================================================
+
+CC = cc
+CFLAGS = -xO5 -xlibmil -Xc -xdepend -dalign
+UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.n2 b/UMFPACK/Tcov/Make.n2
new file mode 100644
index 0000000..b23f197
--- /dev/null
+++ b/UMFPACK/Tcov/Make.n2
@@ -0,0 +1,18 @@
+#===============================================================================
+# Solaris ILP32 mode, Sunperf BLAS, no test for integer overflow.
+#===============================================================================
+
+CC = cc
+CFLAGS = -xO5 -xlibmil -Xc -xdepend -dalign
+UMFPACK_CONFIG = -DTESTING
+LIB = -xlic_lib=sunperf -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.n3 b/UMFPACK/Tcov/Make.n3
new file mode 100644
index 0000000..7fc1b46
--- /dev/null
+++ b/UMFPACK/Tcov/Make.n3
@@ -0,0 +1,18 @@
+#===============================================================================
+# Solaris LP64 mode, no BLAS, do not test for integer overflow.
+#===============================================================================
+
+CC = cc
+CFLAGS = -xO5 -xlibmil -Xc -xdepend -dalign
+UMFPACK_CONFIG = -DNBLAS -DLP64 -xarch=v9 -DTESTING
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.n4 b/UMFPACK/Tcov/Make.n4
new file mode 100644
index 0000000..f1b437d
--- /dev/null
+++ b/UMFPACK/Tcov/Make.n4
@@ -0,0 +1,18 @@
+#===============================================================================
+# Solaris LP64 mode, Sun Performance BLAS, do not test for integer overflow.
+#===============================================================================
+
+CC = cc
+CFLAGS = -xO5 -xlibmil -Xc -xdepend -dalign
+UMFPACK_CONFIG = -DLP64 -xarch=v9 -DTESTING
+LIB = -xlic_lib=sunperf -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.s1 b/UMFPACK/Tcov/Make.s1
new file mode 100644
index 0000000..1e5deb4
--- /dev/null
+++ b/UMFPACK/Tcov/Make.s1
@@ -0,0 +1,18 @@
+#===============================================================================
+# Solaris ILP32 mode, no BLAS, test for integer overflow.
+#===============================================================================
+
+CC = cc
+CFLAGS = -Xc -g -xprofile=tcov -dalign
+UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.s2 b/UMFPACK/Tcov/Make.s2
new file mode 100644
index 0000000..b8bdfc3
--- /dev/null
+++ b/UMFPACK/Tcov/Make.s2
@@ -0,0 +1,18 @@
+#===============================================================================
+# Solaris ILP32 mode, Sunperf BLAS, no test for integer overflow.
+#===============================================================================
+
+CC = cc
+CFLAGS = -Xc -g -xprofile=tcov -dalign
+UMFPACK_CONFIG = -DTESTING
+LIB = -xlic_lib=sunperf -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.s3 b/UMFPACK/Tcov/Make.s3
new file mode 100644
index 0000000..ecce67f
--- /dev/null
+++ b/UMFPACK/Tcov/Make.s3
@@ -0,0 +1,18 @@
+#===============================================================================
+# Solaris LP64 mode, no BLAS, do not test for integer overflow.
+#===============================================================================
+
+CC = cc
+CFLAGS = -Xc -g -xprofile=tcov -dalign
+UMFPACK_CONFIG = -DNBLAS -DLP64 -xarch=v9 -DTESTING
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.s4 b/UMFPACK/Tcov/Make.s4
new file mode 100644
index 0000000..9185fdb
--- /dev/null
+++ b/UMFPACK/Tcov/Make.s4
@@ -0,0 +1,18 @@
+#===============================================================================
+# Solaris LP64 mode, Sun Performance BLAS, do not test for integer overflow.
+#===============================================================================
+
+CC = cc
+CFLAGS = -Xc -g -xprofile=tcov -dalign
+UMFPACK_CONFIG = -DLP64 -xarch=v9 -DTESTING
+LIB = -xlic_lib=sunperf -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make.s5 b/UMFPACK/Tcov/Make.s5
new file mode 100644
index 0000000..c0f72ba
--- /dev/null
+++ b/UMFPACK/Tcov/Make.s5
@@ -0,0 +1,18 @@
+#===============================================================================
+# Solaris ILP32 mode, no BLAS, test for integer overflow.
+#===============================================================================
+
+CC = cc
+CFLAGS = -Xc -g -xprofile=tcov -dalign
+UMFPACK_CONFIG = -DNBLAS -DTEST_FOR_INTEGER_OVERFLOW -DTESTING -DNRECIPROCAL
+LIB = -lm
+
+RANLIB = ranlib
+MV = mv -f
+RM = rm -f
+MEX = mex -inline -g
+AR = ar cr
+
+#===============================================================================
+
+CLEAN = *.o *.obj *.ln *.bb *.bbg *.da *.c.tcov *.c.gcov gmon.out
diff --git a/UMFPACK/Tcov/Make_file b/UMFPACK/Tcov/Make_file
new file mode 100644
index 0000000..7c50f48
--- /dev/null
+++ b/UMFPACK/Tcov/Make_file
@@ -0,0 +1,24 @@
+all: go
+
+include UFconfig/UFconfig.mk
+
+go: prog
+ - ut > ut.out
+ - tail ut.out
+ #- $(RM) ut.out
+ - ( cd UMFPACK/Source ; gcovs umf*.c )
+ - ( cd AMD/Source ; gcovs amd*.c )
+
+prog:
+ ( cd UMFPACK ; make library )
+ ( cd AMD ; make library )
+ $(CC) -DDINT $(CFLAGS) $(UMFPACK_CONFIG) -IUMFPACK/Source -IUMFPACK/Include -IAMD/Source -IAMD/Include -o ut ut.c UMFPACK/Lib/libumfpack.a AMD/Lib/libamd.a $(LIB)
+
+utcov:
+ - ( cd UMFPACK/Source ; gcovs umf*.c )
+ - ( cd AMD/Source ; gcovs amd*.c )
+
+
+purge:
+ ( cd UMFPACK ; make purge )
+ ( cd AMD ; make purge )
diff --git a/UMFPACK/Tcov/Makefile b/UMFPACK/Tcov/Makefile
new file mode 100644
index 0000000..9ac2a94
--- /dev/null
+++ b/UMFPACK/Tcov/Makefile
@@ -0,0 +1,16 @@
+
+include ../../UFconfig/UFconfig.mk
+
+linux: distclean
+ ./DO.linux
+
+sol: distclean
+ ./DO.solaris
+
+distclean:
+ - ( cd .. ; make purge )
+ - ( cd ../../AMD ; make purge )
+ - $(RM) -rf Out/*
+
+purge: distclean
+
diff --git a/UMFPACK/Tcov/README.txt b/UMFPACK/Tcov/README.txt
new file mode 100644
index 0000000..329dcc2
--- /dev/null
+++ b/UMFPACK/Tcov/README.txt
@@ -0,0 +1,76 @@
+This is the UMFPACK Tcov directory. It runs a large number of tests on
+UMFPACK and checks the statement coverage (using gcc and gcov on Linux,
+or tcov on Solaris).
+
+You must first do "make purge" in AMD and UMFPACK. You must also make
+sure the "Out" symbolic link is a valid link. It should point to a large
+scratch space, for temporary files. Finally, type DO.linux or DO.solaris.
+
+Alternatively, just type "make" in this directory, for Linux, or "make sol"
+for Solaris.
+
+The last line of each */ut.out file should read
+ALL TESTS PASSED largest maxrnorm 1e-07
+These lines are summarized at the end of the "DO.linux" test.
+
+If you see "TEST FAILURE" then something went wrong. "ERROR" messages
+in the output files tmp/*.out are OK. Those are supposed to be there;
+the test exercises the error-reporting features of UMFPACK.
+
+DO.all does all tests
+
+DO 1 di runs one test (Make.1 and GNUmakefile.di, in this case)
+
+Out/* subdirectories for each test,
+ contents can be destroyed when done.
+
+Make.1 gcc, no optimize Linux no BLAS, test int overflow
+Make.2 gcc, no optimize Linux BLAS
+Make.3 gcc, no optimize Linux ATLAS C-Blas
+Make.4 gcc, no optimize Linux ATLAS Fortran BLAS
+
+Make.5 gcc, no optimize Linux no BLAS, test int overflow
+ no reciprocal
+
+Make.1i icc, optimize, Linux no BLAS, test int overflow
+Make.2i icc, optimize, Linux BLAS
+Make.3i icc, optimize, Linux ATLAS C-Blas
+Make.4i icc, optimize, Linux ATLAS Fortran BLAS
+
+Make.1n icc, no optimize, Linux no BLAS, test int overflow
+Make.2n icc, no optimize, Linux BLAS
+Make.3n icc, no optimize, Linux ATLAS C-Blas
+Make.4n icc, no optimize, Linux ATLAS Fortran BLAS
+
+Make.1g gcc, optimize, Linux no BLAS, test int overflow
+Make.2g gcc, optimize, Linux BLAS
+Make.3g gcc, optimize, Linux ATLAS C-Blas
+Make.4g gcc, optimize, Linux ATLAS Fortran BLAS
+
+Make.s1 tcov, Solaris 32 bit, no BLAS
+Make.s2 tcov, Solaris 32 bit, Sunperf BLAS
+Make.s3 tcov, Solaris 64 bit, no BLAS
+Make.s4 tcov, Solaris 64 bit, Sunperf BLAS
+
+Make.s5 tcov, Solaris 32 bit, no BLAS, test int overflow, no recip.
+
+Make.n1 optimize, Solaris 32 bit, no BLAS
+Make.n2 optimize, Solaris 32 bit, Sunperf BLAS
+Make.n3 optimize, Solaris 64 bit, no BLAS
+Make.n4 optimize, Solaris 64 bit, Sunperf BLAS
+
+Makefile.di Makefile for *di (double, int)
+Makefile.dl Makefile for *dl (double, UF_long)
+Makefile.zi Makefile for *zi (complex, int)
+Makefile.zl Makefile for *zl (complex, UF_long)
+
+TestMat test matrices for ut.c
+
+../../UMFPACK UMFPACK original distribution
+../../AMD AMD original distribution
+../../UFconfig configuration directory for all of UFsparse
+
+covall for summarizing tcov output
+
+ut.c the test program
+
diff --git a/UMFPACK/Tcov/TestMat/S_d2q06c b/UMFPACK/Tcov/TestMat/S_d2q06c
new file mode 100644
index 0000000..175bb92
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/S_d2q06c
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diff --git a/UMFPACK/Tcov/TestMat/adlittle b/UMFPACK/Tcov/TestMat/adlittle
new file mode 100644
index 0000000..31630ae
--- /dev/null
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diff --git a/UMFPACK/Tcov/TestMat/arc130 b/UMFPACK/Tcov/TestMat/arc130
new file mode 100644
index 0000000..405ae3c
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diff --git a/UMFPACK/Tcov/TestMat/cage3 b/UMFPACK/Tcov/TestMat/cage3
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index 0000000..4f7fb2a
--- /dev/null
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diff --git a/UMFPACK/Tcov/TestMat/d_dyn b/UMFPACK/Tcov/TestMat/d_dyn
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diff --git a/UMFPACK/Tcov/TestMat/galenet b/UMFPACK/Tcov/TestMat/galenet
new file mode 100644
index 0000000..cb37c82
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/galenet
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diff --git a/UMFPACK/Tcov/TestMat/matrix1 b/UMFPACK/Tcov/TestMat/matrix1
new file mode 100644
index 0000000..b28df40
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix1
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diff --git a/UMFPACK/Tcov/TestMat/matrix10 b/UMFPACK/Tcov/TestMat/matrix10
new file mode 100644
index 0000000..5b23804
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix10
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diff --git a/UMFPACK/Tcov/TestMat/matrix11 b/UMFPACK/Tcov/TestMat/matrix11
new file mode 100644
index 0000000..5b23804
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix11
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+ 19 37 -0.20369
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+ 35 37 -0.11612
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+ 8 38 1.4435
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+ 15 38 0.93122
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+ 34 38 0.24309
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+ 16 39 1.138
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+ 3 40 0.52874
+ 7 40 0.5689
+ 15 40 0.011245
+ 17 40 -0.24634
+ 33 40 -0.71209
+ 36 40 0.49983
+ 38 40 0.13518
+ 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+ 10
+ 11
+ 12
+ 13
+ 14
+ 15
+ 16
+ 17
+ 18
+ 19
+ 20
+ 21
+ 22
+ 23
+ 24
+ 25
+ 26
+ 27
+ 28
+ 29
+ 30
+ 31
+ 32
+ 33
+ 34
+ 35
+ 36
+ 37
+ 38
+ 39
+ 40
+ 1.00608060993977391627e+06
+ 1.00608060993977391627e+06
diff --git a/UMFPACK/Tcov/TestMat/matrix12 b/UMFPACK/Tcov/TestMat/matrix12
new file mode 100644
index 0000000..694b951
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix12
@@ -0,0 +1,13 @@
+2 5 5 0
+1 2 -0.620428 -1.66558
+2 2 0.561564 0.125332
+1 4 -0.384265 1.18916
+1 5 -0.165418 0.327292
+2 5 0.285977 0.174639
+1
+2
+3
+4
+5
+0. 0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix13 b/UMFPACK/Tcov/TestMat/matrix13
new file mode 100644
index 0000000..84b015e
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix13
@@ -0,0 +1,14 @@
+5 5 6 0
+1 1 0 0.887146
+4 1 -0 -0.252864
+5 2 0 1.26913
+3 3 0.125332 -1.02788
+4 3 -1.14647 0.116721
+2 4 -1.66558 -1.3498
+1
+2
+3
+4
+5
+0. 0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix14 b/UMFPACK/Tcov/TestMat/matrix14
new file mode 100644
index 0000000..d23fe0f
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix14
@@ -0,0 +1,5 @@
+1 1 1 0
+1 1 0.0 0.0
+1
+0. 0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix15 b/UMFPACK/Tcov/TestMat/matrix15
new file mode 100644
index 0000000..b1d10a3
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix15
@@ -0,0 +1,5 @@
+1 1 1 0
+1 1 0.0 1.0
+1
+0. 1.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix16 b/UMFPACK/Tcov/TestMat/matrix16
new file mode 100644
index 0000000..5b3a3cd
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix16
@@ -0,0 +1,5 @@
+1 1 1 0
+1 1 2.0 0.0
+1
+2. 0.
+2.
diff --git a/UMFPACK/Tcov/TestMat/matrix17 b/UMFPACK/Tcov/TestMat/matrix17
new file mode 100644
index 0000000..7e3e82f
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix17
@@ -0,0 +1,5 @@
+1 1 1 1
+1 1 0.0
+1
+0. 0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix18 b/UMFPACK/Tcov/TestMat/matrix18
new file mode 100644
index 0000000..4cfe88b
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix18
@@ -0,0 +1,5 @@
+1 1 1 1
+1 1 1.0
+1
+1.
+1.
diff --git a/UMFPACK/Tcov/TestMat/matrix19 b/UMFPACK/Tcov/TestMat/matrix19
new file mode 100644
index 0000000..17860e4
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix19
@@ -0,0 +1,21 @@
+19 7 11 0
+13 1 0 0.692462
+12 2 0 0.153137
+15 2 0 0.635474
+19 2 0 1.33406
+13 3 -0 -1.24036
+11 4 0 0.267342
+14 4 -0 -1.22141
+13 5 -0 -0.287195
+15 5 0 0.105345
+15 6 -0 -1.40134
+12 7 -0 -1.31017
+1
+2
+3
+4
+5
+6
+7
+0. 0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix2 b/UMFPACK/Tcov/TestMat/matrix2
new file mode 100644
index 0000000..a49dee3
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix2
@@ -0,0 +1,44 @@
+10 10 31 1
+ 3 1 -0.037633
+ 4 1 999
+ 2 2 0.28768
+ 5 2 0.72579
+ 7 2 0.059281
+ 7 3 -0.095648
+ 2 4 -1.1465
+ 3 4 0.32729
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+ 8 4 0.29441
+ 9 4 1.6236
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+ 1 5 -0.43256
+ 6 5 1.0668
+ 2 6 1.1909
+ 8 6 -1.3362
+ 9 6 -0.69178
+ 10 6 -1.5937
+ 1 7 -1.6656
+ 3 7 0.17464
+ 5 7 2.1832
+ 7 7 -0.83235
+ 8 7 0.71432
+ 1 8 0.12533
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+ 2 9 1.1892
+ 4 9 -0.18671
+ 5 9 0.11393
+ 9 9 0.858
+ 10 9 -1.441
+ 10 10 1
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+ -8.26997501834853920855e+00
+ -8.26997501834853920855e+00
diff --git a/UMFPACK/Tcov/TestMat/matrix20 b/UMFPACK/Tcov/TestMat/matrix20
new file mode 100644
index 0000000..b7edaf1
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix20
@@ -0,0 +1,14 @@
+5 5 6 0
+1 1 0 0.887146
+4 1 -0 -0.252864
+5 2 0 1.26913
+3 3 0.125332 -1.02788
+4 3 -1.14647 0.116721
+2 4 -1.66558 -1.3498
+2
+4
+1
+3
+5
+0. 0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix21 b/UMFPACK/Tcov/TestMat/matrix21
new file mode 100644
index 0000000..d9297d9
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix21
@@ -0,0 +1,7 @@
+2 2 2 1
+1 2 -0.146115
+2 2 -1.3235
+2
+1
+0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix22 b/UMFPACK/Tcov/TestMat/matrix22
new file mode 100644
index 0000000..f734761
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix22
@@ -0,0 +1,14 @@
+13 4 7 1
+1 1 0.626436
+1 2 0.0918136
+1 3 -0.807607
+2 3 -1.40597
+10 3 -0.461337
+2 4 -0.470911
+3 4 -0.37453
+3
+4
+1
+2
+0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix23 b/UMFPACK/Tcov/TestMat/matrix23
new file mode 100644
index 0000000..99ee88f
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix23
@@ -0,0 +1,172 @@
+63 63 106 1
+1 1 -1.52981
+2 2 -1.04248
+3 3 1.53499
+4 3 0.545919
+3 4 -0.0279288
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+10 7 1.33803
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+17 21 1.423
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+12 22 0.503049
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+30 23 0.0431208
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+36 29 0.234421
+36 30 -0.936546
+37 30 -1.87221
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+38 31 3.1973
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+34 32 0.269037
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+42 33 -0.827448
+43 33 0.66343
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+46 35 0.419215
+47 35 2.20997
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+47 37 0.4969
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+54 42 1.36345
+54 43 -1.03266
+55 43 0.0381422
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+56 44 -1.49154
+44 45 1.63067
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+53 45 -0.237397
+39 46 0.115947
+50 46 0.36568
+57 47 -1.41703
+58 48 -0.480261
+59 49 -0.491017
+60 49 0.352526
+61 49 0.822323
+58 50 0.170138
+59 50 -0.516028
+62 50 -0.00397242
+63 51 -1.0594
+63 52 1.58876
+58 55 0.383227
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
+20
+21
+22
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+24
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+32
+33
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+49
+50
+51
+52
+53
+54
+55
+56
+57
+58
+59
+60
+61
+62
+63
+0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix24 b/UMFPACK/Tcov/TestMat/matrix24
new file mode 100644
index 0000000..7f3f130
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix24
@@ -0,0 +1,126 @@
+22 51 72 1
+2 1 -0.50444
+6 1 -0.116383
+7 1 0.11456
+1 2 -0.363678
+14 2 0.0242795
+16 3 -0.668072
+2 5 0.686186
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+14 7 -1.34386
+21 7 1.1986
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+13 12 -1.20775
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+11 15 -1.40864
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+22 51 -0.421509
+1
+2
+3
+4
+5
+6
+7
+8
+9
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+16
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+41
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+43
+44
+45
+46
+47
+48
+49
+50
+51
+0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix25 b/UMFPACK/Tcov/TestMat/matrix25
new file mode 100644
index 0000000..140646c
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix25
@@ -0,0 +1,13 @@
+3 3 7 1
+1 1 1.1
+2 1 2.1
+3 1 1e-30
+2 2 2.2
+3 2 3.2
+2 3 2.3
+3 3 3.3
+1
+2
+3
+ -1.09999999999998876454e-01
+ -1.09999999999998876454e-01
diff --git a/UMFPACK/Tcov/TestMat/matrix26 b/UMFPACK/Tcov/TestMat/matrix26
new file mode 100644
index 0000000..ef9e3bb
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix26
@@ -0,0 +1,12 @@
+3 3 6 1
+1 1 1.1
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+1 3 1.2
+2 1 2.1
+2 2 2.2
+2 3 2.2
+1
+2
+3
+0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix27 b/UMFPACK/Tcov/TestMat/matrix27
new file mode 100644
index 0000000..f39fd6f
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix27
@@ -0,0 +1,12 @@
+3 3 6 1
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+1 2 1.2
+1 3 1.2
+2 1 0
+2 2 0
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+1
+2
+3
+0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix28 b/UMFPACK/Tcov/TestMat/matrix28
new file mode 100644
index 0000000..d8b0447
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix28
@@ -0,0 +1,21 @@
+4 4 14 0
+2 1 2.31138513574287829400e-01 9.16904439913407642848e-01
+3 1 6.06842583541786551038e-01 4.10270206990945351944e-01
+4 1 4.85982468709299730847e-01 8.93649530913533607368e-01
+1 2 8.91298966148901583573e-01 5.78913047842685574151e-02
+2 2 7.62096833027394726656e-01 3.52868132217000363138e-01
+3 2 4.56467665168341363291e-01 8.13166497303757784820e-01
+4 2 1.85036432482243995423e-02 9.86130066092356059870e-03
+1 3 8.21407164295253289232e-01 1.38890881956949874265e-01
+2 3 4.44703364353194185998e-01 2.02765218560273158266e-01
+4 3 7.91937037427035361858e-01 6.03792479193819286998e-01
+1 4 9.21812970744802506751e-01 2.72187924969960359789e-01
+2 4 7.38207245810665324548e-01 1.98814267761062146711e-01
+3 4 1.76266144494617998939e-01 1.52739270290362695592e-02
+4 4 4.05706213062095477628e-01 7.46785676564429290458e-01
+1
+2
+3
+4
+ 1.67514846387938648453e-01 -2.30183751723616242257e-01
+ -7.05492222379558997503e-02
diff --git a/UMFPACK/Tcov/TestMat/matrix29 b/UMFPACK/Tcov/TestMat/matrix29
new file mode 100644
index 0000000..bb873fe
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix29
@@ -0,0 +1,7 @@
+2 2 2 1
+1 1 1e-300
+2 2 1e-300
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+2
+0.
+0.
diff --git a/UMFPACK/Tcov/TestMat/matrix3 b/UMFPACK/Tcov/TestMat/matrix3
new file mode 100644
index 0000000..d4491e2
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix3
@@ -0,0 +1,42 @@
+10 10 29 1
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+2
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+8
+9
+10
+ 1.13111926942419077191e-05
+ 1.13111926942419077191e-05
diff --git a/UMFPACK/Tcov/TestMat/matrix30 b/UMFPACK/Tcov/TestMat/matrix30
new file mode 100644
index 0000000..1751ba1
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix30
@@ -0,0 +1,7 @@
+2 2 2 1
+1 1 1e+300
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+1
+2
+1e600
+1e600
diff --git a/UMFPACK/Tcov/TestMat/matrix4 b/UMFPACK/Tcov/TestMat/matrix4
new file mode 100644
index 0000000..2a02179
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix4
@@ -0,0 +1,113 @@
+10 10 100 1
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diff --git a/UMFPACK/Tcov/TestMat/matrix5 b/UMFPACK/Tcov/TestMat/matrix5
new file mode 100644
index 0000000..0bf939a
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix5
@@ -0,0 +1,103 @@
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diff --git a/UMFPACK/Tcov/TestMat/matrix6 b/UMFPACK/Tcov/TestMat/matrix6
new file mode 100644
index 0000000..882f872
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix6
@@ -0,0 +1,43 @@
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diff --git a/UMFPACK/Tcov/TestMat/matrix7 b/UMFPACK/Tcov/TestMat/matrix7
new file mode 100644
index 0000000..81e1fc5
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix7
@@ -0,0 +1,43 @@
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diff --git a/UMFPACK/Tcov/TestMat/matrix8 b/UMFPACK/Tcov/TestMat/matrix8
new file mode 100644
index 0000000..33c128a
--- /dev/null
+++ b/UMFPACK/Tcov/TestMat/matrix8
@@ -0,0 +1,43 @@
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new file mode 100644
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+ 388
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+ 428
+ 434
+ 445
+ 463
+ 485
+ 568
+ 604
+ 612
+ 624
+ 629
+ 137
+ 280
+ 1
+-1.
+-1.
diff --git a/UMFPACK/Tcov/Top_Makefile b/UMFPACK/Tcov/Top_Makefile
new file mode 100644
index 0000000..a5d74f6
--- /dev/null
+++ b/UMFPACK/Tcov/Top_Makefile
@@ -0,0 +1,11 @@
+#-------------------------------------------------------------------------------
+# UMFPACK and AMD top-level makefile (for Tcov tests)
+#-------------------------------------------------------------------------------
+
+default: library
+
+include ../UFconfig/UFconfig.mk
+
+library:
+ ( cd Source ; $(MAKE) )
+ ( cd Demo ; $(MAKE) )
diff --git a/UMFPACK/Tcov/acov.di b/UMFPACK/Tcov/acov.di
new file mode 100755
index 0000000..6cd5217
--- /dev/null
+++ b/UMFPACK/Tcov/acov.di
@@ -0,0 +1,15 @@
+#!/bin/csh
+# acov.di: construct gcov files for AMD, di version
+
+gcov -o amd_i_1 amd_1.c
+gcov -o amd_i_2 amd_2.c
+gcov -o amd_i_aat amd_aat.c
+gcov -o amd_i_control amd_control.c
+gcov -o amd_i_defaults amd_defaults.c
+gcov -o amd_i_info amd_info.c
+gcov -o amd_i_order amd_order.c
+gcov -o amd_i_post_tree amd_post_tree.c
+gcov -o amd_i_postorder amd_postorder.c
+gcov -o amd_i_preprocess amd_preprocess.c
+gcov -o amd_i_valid amd_valid.c
+
diff --git a/UMFPACK/Tcov/acov.dl b/UMFPACK/Tcov/acov.dl
new file mode 100755
index 0000000..29113c1
--- /dev/null
+++ b/UMFPACK/Tcov/acov.dl
@@ -0,0 +1,15 @@
+#!/bin/csh
+# acov.dl: construct gcov files for AMD, dl version
+
+gcov -o amd_l_1 amd_1.c
+gcov -o amd_l_2 amd_2.c
+gcov -o amd_l_aat amd_aat.c
+gcov -o amd_l_control amd_control.c
+gcov -o amd_l_defaults amd_defaults.c
+gcov -o amd_l_info amd_info.c
+gcov -o amd_l_order amd_order.c
+gcov -o amd_l_post_tree amd_post_tree.c
+gcov -o amd_l_postorder amd_postorder.c
+gcov -o amd_l_preprocess amd_preprocess.c
+gcov -o amd_l_valid amd_valid.c
+
diff --git a/UMFPACK/Tcov/acov.zi b/UMFPACK/Tcov/acov.zi
new file mode 100755
index 0000000..3f8c888
--- /dev/null
+++ b/UMFPACK/Tcov/acov.zi
@@ -0,0 +1,15 @@
+#!/bin/csh
+# acov.zi: construct gcov files for AMD, zi version
+
+gcov -o amd_i_1 amd_1.c
+gcov -o amd_i_2 amd_2.c
+gcov -o amd_i_aat amd_aat.c
+gcov -o amd_i_control amd_control.c
+gcov -o amd_i_defaults amd_defaults.c
+gcov -o amd_i_info amd_info.c
+gcov -o amd_i_order amd_order.c
+gcov -o amd_i_post_tree amd_post_tree.c
+gcov -o amd_i_postorder amd_postorder.c
+gcov -o amd_i_preprocess amd_preprocess.c
+gcov -o amd_i_valid amd_valid.c
+
diff --git a/UMFPACK/Tcov/acov.zl b/UMFPACK/Tcov/acov.zl
new file mode 100755
index 0000000..db05807
--- /dev/null
+++ b/UMFPACK/Tcov/acov.zl
@@ -0,0 +1,15 @@
+#!/bin/csh
+# acov.zl: construct gcov files for AMD, zl version
+
+gcov -o amd_l_1 amd_1.c
+gcov -o amd_l_2 amd_2.c
+gcov -o amd_l_aat amd_aat.c
+gcov -o amd_l_control amd_control.c
+gcov -o amd_l_defaults amd_defaults.c
+gcov -o amd_l_info amd_info.c
+gcov -o amd_l_order amd_order.c
+gcov -o amd_l_post_tree amd_post_tree.c
+gcov -o amd_l_postorder amd_postorder.c
+gcov -o amd_l_preprocess amd_preprocess.c
+gcov -o amd_l_valid amd_valid.c
+
diff --git a/UMFPACK/Tcov/badnum.umf b/UMFPACK/Tcov/badnum.umf
new file mode 100644
index 0000000..17bbfb1
Binary files /dev/null and b/UMFPACK/Tcov/badnum.umf differ
diff --git a/UMFPACK/Tcov/badnum2.umf b/UMFPACK/Tcov/badnum2.umf
new file mode 100644
index 0000000..5a75e8b
--- /dev/null
+++ b/UMFPACK/Tcov/badnum2.umf
@@ -0,0 +1 @@
+badnum2
diff --git a/UMFPACK/Tcov/badsym.umf b/UMFPACK/Tcov/badsym.umf
new file mode 100644
index 0000000..ffd9704
Binary files /dev/null and b/UMFPACK/Tcov/badsym.umf differ
diff --git a/UMFPACK/Tcov/badsym2.umf b/UMFPACK/Tcov/badsym2.umf
new file mode 100644
index 0000000..169d272
--- /dev/null
+++ b/UMFPACK/Tcov/badsym2.umf
@@ -0,0 +1 @@
+badsym2
diff --git a/UMFPACK/Tcov/cov b/UMFPACK/Tcov/cov
new file mode 100755
index 0000000..58c85f6
--- /dev/null
+++ b/UMFPACK/Tcov/cov
@@ -0,0 +1,12 @@
+#!/bin/csh
+
+foreach file ($argv[1-])
+ echo "================================================================================"
+ echo $file
+ # cat -n $file | grep -B 5 -A 5 '#####'
+ cat -n $file | grep '#####'
+end
+echo "================================================================================"
+# echo "Total lines not covered:"
+# cat $argv[1-] | grep "#####" | wc
+
diff --git a/UMFPACK/Tcov/covall b/UMFPACK/Tcov/covall
new file mode 100755
index 0000000..4a773c9
--- /dev/null
+++ b/UMFPACK/Tcov/covall
@@ -0,0 +1,68 @@
+#!/bin/csh
+
+# only print those lines that are "#####" in all tests.
+
+foreach file ( \
+ umf_2by2.c umf_analyze.c umf_apply_order.c umf_assemble.c \
+ umf_assemble_fixq.c umf_blas3_update.c umf_build_tuples.c \
+ umf_colamd.c umf_create_element.c umf_extend_front.c \
+ umf_free.c umf_fsize.c umf_garbage_collection.c umf_get_memory.c \
+ umf_grow_front.c umf_init_front.c umf_is_permutation.c umf_kernel.c \
+ umf_kernel_init.c umf_kernel_wrapup.c umf_lhsolve.c umf_local_search.c \
+ umf_lsolve.c umf_ltsolve.c umf_malloc.c umf_mem_alloc_element.c \
+ umf_mem_alloc_head_block.c umf_mem_alloc_tail_block.c \
+ umf_mem_free_tail_block.c umf_mem_init_memoryspace.c \
+ umf_realloc.c umf_report_perm.c umf_report_vector.c umf_row_search.c \
+ umf_scale.c umf_scale_column.c umf_set_stats.c umf_singletons.c \
+ umf_solve.c umf_start_front.c umf_store_lu.c umf_store_lu_drop.c \
+ umf_symbolic_usage.c \
+ umf_transpose.c umf_triplet_map_nox.c umf_triplet_map_x.c \
+ umf_triplet_nomap_nox.c umf_triplet_nomap_x.c umf_tuple_lengths.c \
+ umf_uhsolve.c umf_usolve.c umf_utsolve.c umf_valid_numeric.c \
+ umf_valid_symbolic.c umfpack_col_to_triplet.c umfpack_defaults.c \
+ umfpack_free_numeric.c umfpack_free_symbolic.c umfpack_get_determinant.c \
+ umfpack_get_lunz.c umfpack_get_numeric.c umfpack_get_symbolic.c \
+ umfpack_load_numeric.c umfpack_load_symbolic.c umfpack_numeric.c \
+ umfpack_qsymbolic.c umfpack_report_control.c umfpack_report_info.c \
+ umfpack_report_matrix.c umfpack_report_numeric.c umfpack_report_perm.c \
+ umfpack_report_status.c umfpack_report_symbolic.c umfpack_report_triplet.c \
+ umfpack_report_vector.c umfpack_save_numeric.c umfpack_save_symbolic.c \
+ umfpack_scale.c umfpack_solve.c umfpack_symbolic.c \
+ umfpack_tictoc.c umfpack_timer.c umfpack_transpose.c \
+ umfpack_triplet_to_col.c umfpack_wsolve.c \
+ )
+ echo '================================================================================'
+ echo $file
+ echo '================================================================================'
+ cat /dev/null > Out/tcov_tmp
+ foreach fdirs (Out/?_??)
+ cat -n $fdirs/UMFPACK/Source/$file.gcov | grep '#####' >> Out/tcov_tmp
+ end
+ sort -n Out/tcov_tmp | uniq -c
+end
+
+foreach file ( \
+ amd_1.c amd_2.c amd_aat.c amd_control.c amd_defaults.c \
+ amd_info.c amd_order.c amd_postorder.c amd_post_tree.c \
+ amd_preprocess.c amd_valid.c \
+ )
+ echo '================================================================================'
+ echo $file
+ echo '================================================================================'
+ cat /dev/null > Out/tcov_tmp
+ foreach fdirs (Out/?_??)
+ cat -n $fdirs/AMD/Source/$file.gcov | grep '#####' >> Out/tcov_tmp
+ end
+ sort -n Out/tcov_tmp | uniq -c
+end
+
+
+echo '================================================================================'
+echo 'Last line of each output file: '
+echo '================================================================================'
+
+foreach file (Out/*_*/ut.out)
+ echo $file
+ tail -1 $file
+ echo '================================================================='
+end
diff --git a/UMFPACK/Tcov/cover.awk b/UMFPACK/Tcov/cover.awk
new file mode 100644
index 0000000..6652ab8
--- /dev/null
+++ b/UMFPACK/Tcov/cover.awk
@@ -0,0 +1,5 @@
+/^[a-Z]/
+
+/^=====/
+
+/^ 24/
diff --git a/UMFPACK/Tcov/cover.out b/UMFPACK/Tcov/cover.out
new file mode 100644
index 0000000..d29f7d3
--- /dev/null
+++ b/UMFPACK/Tcov/cover.out
@@ -0,0 +1,545 @@
+================================================================================
+umf_2by2.c
+================================================================================
+================================================================================
+umf_analyze.c
+================================================================================
+ 24 222 #####: 217: return (FALSE) ; /* internal error! */
+================================================================================
+umf_apply_order.c
+================================================================================
+================================================================================
+umf_assemble.c
+================================================================================
+================================================================================
+umf_assemble_fixq.c
+================================================================================
+================================================================================
+umf_blas3_update.c
+================================================================================
+================================================================================
+umf_build_tuples.c
+================================================================================
+ 24 83 #####: 78: return (FALSE) ; /* out of memory for row tuples */
+ 24 101 #####: 96: return (FALSE) ; /* out of memory for col tuples */
+================================================================================
+umf_colamd.c
+================================================================================
+ 24 2708 #####: 2703: KILL_ROW (r) ;
+================================================================================
+umf_create_element.c
+================================================================================
+ 24 253 #####: 248: return (FALSE) ; /* out of memory */
+ 24 264 #####: 259: return (FALSE) ; /* out of memory */
+ 24 440 #####: 435: return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos));
+ 24 543 #####: 538: return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos));
+================================================================================
+umf_extend_front.c
+================================================================================
+================================================================================
+umf_free.c
+================================================================================
+================================================================================
+umf_fsize.c
+================================================================================
+ 24 58 #####: 53: frsize = Int_MAX ;
+================================================================================
+umf_garbage_collection.c
+================================================================================
+================================================================================
+umf_get_memory.c
+================================================================================
+ 24 114 #####: 109: newsize = (Int) bsize ; /* we cannot increase the size beyond bsize */
+================================================================================
+umf_grow_front.c
+================================================================================
+ 24 93 #####: 88: return (FALSE) ;
+ 24 121 #####: 116: double a = 0.9 * sqrt ((Int_MAX / sizeof (Entry)) / s) ;
+ 24 122 #####: 117: fnr2 = MAX (fnr_min, a * fnr2) ;
+ 24 123 #####: 118: fnc2 = MAX (fnc_min, a * fnc2) ;
+ 24 125 #####: 120: newsize = fnr2 * fnc2 ;
+ 24 127 #####: 122: if (fnr2 % 2 == 0) fnr2++ ;
+ 24 128 #####: 123: fnc2 = newsize / fnr2 ;
+ 24 186 #####: 181: return (FALSE) ; /* out of memory */
+================================================================================
+umf_init_front.c
+================================================================================
+ 24 80 #####: 75: return (FALSE) ;
+================================================================================
+umf_is_permutation.c
+================================================================================
+================================================================================
+umf_kernel.c
+================================================================================
+================================================================================
+umf_kernel_init.c
+================================================================================
+ 24 517 #####: 512: return (FALSE) ; /* pattern changed */
+ 24 545 #####: 540: return (FALSE) ; /* pattern changed */
+ 24 609 #####: 604: return (FALSE) ; /* pattern has changed */
+ 24 645 #####: 640: return (FALSE) ; /* pattern has changed */
+ 24 713 #####: 708: return (FALSE) ; /* pattern changed */
+ 24 726 #####: 721: return (FALSE) ; /* pattern changed */
+ 24 738 #####: 733: return (FALSE) ; /* pattern changed */
+ 24 830 #####: 825: return (FALSE) ; /* pattern changed */
+ 24 866 #####: 861: return (FALSE) ; /* pattern changed */
+ 24 908 #####: 903: return (FALSE) ; /* pattern changed */
+ 24 922 #####: 917: return (FALSE) ; /* pattern changed */
+ 24 1034 #####: 1029: return (FALSE) ; /* pattern changed */
+================================================================================
+umf_kernel_wrapup.c
+================================================================================
+================================================================================
+umf_lhsolve.c
+================================================================================
+================================================================================
+umf_local_search.c
+================================================================================
+ 24 657 #####: 652: return (UMFPACK_ERROR_different_pattern) ;
+ 24 746 #####: 741: return (UMFPACK_ERROR_different_pattern) ;
+================================================================================
+umf_lsolve.c
+================================================================================
+================================================================================
+umf_ltsolve.c
+================================================================================
+================================================================================
+umf_malloc.c
+================================================================================
+================================================================================
+umf_mem_alloc_element.c
+================================================================================
+ 24 49 #####: 44: return (0) ; /* problem is too large */
+================================================================================
+umf_mem_alloc_head_block.c
+================================================================================
+================================================================================
+umf_mem_alloc_tail_block.c
+================================================================================
+================================================================================
+umf_mem_free_tail_block.c
+================================================================================
+================================================================================
+umf_mem_init_memoryspace.c
+================================================================================
+================================================================================
+umf_realloc.c
+================================================================================
+ 24 58 #####: 53: return ((void *) NULL) ;
+================================================================================
+umf_report_perm.c
+================================================================================
+================================================================================
+umf_report_vector.c
+================================================================================
+================================================================================
+umf_row_search.c
+================================================================================
+ 24 618 #####: 613: return (UMFPACK_ERROR_different_pattern) ;
+ 24 664 #####: 659: return (UMFPACK_ERROR_different_pattern) ;
+ 24 751 #####: 746: return (UMFPACK_ERROR_different_pattern) ;
+================================================================================
+umf_scale.c
+================================================================================
+================================================================================
+umf_scale_column.c
+================================================================================
+================================================================================
+umf_set_stats.c
+================================================================================
+================================================================================
+umf_singletons.c
+================================================================================
+================================================================================
+umf_solve.c
+================================================================================
+ 24 1316 #####: 1311: omega [1] = tau ;
+ 24 1317 #####: 1312: omega [2] = tau ;
+ 24 1318 #####: 1313: break ;
+================================================================================
+umf_start_front.c
+================================================================================
+ 24 156 #####: 151: maxfrsize = Int_MAX / sizeof (Entry) ;
+ 24 175 #####: 170: fsize = Int_MAX / sizeof (Entry) ;
+ 24 193 #####: 188: fsize2 = Int_MAX / sizeof (Entry) ;
+================================================================================
+umf_store_lu.c
+================================================================================
+ 24 349 #####: 344: return (FALSE) ; /* out of memory */
+ 24 355 #####: 350: return (FALSE) ; /* out of memory */
+ 24 774 #####: 769: return (FALSE) ; /* out of memory */
+ 24 781 #####: 776: return (FALSE) ; /* out of memory */
+================================================================================
+umf_store_lu_drop.c
+================================================================================
+ 24 332 #####: 327: if (Work->do_grow)
+ 24 336 #####: 331: r2 = fnrows ;
+ 24 337 #####: 332: c2 = fncols ;
+ 24 342 #####: 337: r2 = MAX (fnrows, Work->fnrows_new + 1) ;
+ 24 343 #####: 338: c2 = MAX (fncols, Work->fncols_new + 1) ;
+ 24 346 #####: 341: if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE))
+ 24 349 #####: 344: return (FALSE) ; /* out of memory */
+ 24 351 #####: 346: p = UMF_mem_alloc_head_block (Numeric, size) ;
+ 24 352 #####: 347: if (!p)
+ 24 355 #####: 350: return (FALSE) ; /* out of memory */
+ 24 358 #####: 353: fnc_curr = Work->fnc_curr ;
+ 24 359 #####: 354: fnr_curr = Work->fnr_curr ;
+ 24 360 #####: 355: Flublock = Work->Flublock ;
+ 24 361 #####: 356: Flblock = Work->Flblock ;
+ 24 362 #####: 357: Fublock = Work->Fublock ;
+ 24 363 #####: 358: Fl1 = Flublock + kk * nb ;
+ 24 364 #####: 359: Fl2 = Flblock + kk * fnr_curr ;
+ 24 497 #####: 492: pos = llen++ ;
+ 24 498 #####: 493: Lpattern [pos] = row2 ;
+ 24 499 #####: 494: Lpos [row2] = pos ;
+ 24 500 #####: 495: *Li++ = row2 ;
+ 24 756 #####: 751: if (Work->do_grow)
+ 24 760 #####: 755: r2 = fnrows ;
+ 24 761 #####: 756: c2 = fncols ;
+ 24 766 #####: 761: r2 = MAX (fnrows, Work->fnrows_new + 1) ;
+ 24 767 #####: 762: c2 = MAX (fncols, Work->fncols_new + 1) ;
+ 24 770 #####: 765: if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE))
+ 24 774 #####: 769: return (FALSE) ; /* out of memory */
+ 24 776 #####: 771: p = UMF_mem_alloc_head_block (Numeric, size) ;
+ 24 777 #####: 772: if (!p)
+ 24 781 #####: 776: return (FALSE) ; /* out of memory */
+ 24 784 #####: 779: fnc_curr = Work->fnc_curr ;
+ 24 785 #####: 780: fnr_curr = Work->fnr_curr ;
+ 24 786 #####: 781: Flublock = Work->Flublock ;
+ 24 787 #####: 782: Flblock = Work->Flblock ;
+ 24 788 #####: 783: Fublock = Work->Fublock ;
+ 24 789 #####: 784: Fu1 = Flublock + kk ;
+ 24 790 #####: 785: Fu2 = Fublock + kk * fnc_curr ;
+================================================================================
+umf_symbolic_usage.c
+================================================================================
+================================================================================
+umf_transpose.c
+================================================================================
+================================================================================
+umf_triplet_map_nox.c
+================================================================================
+================================================================================
+umf_triplet_map_x.c
+================================================================================
+================================================================================
+umf_triplet_nomap_nox.c
+================================================================================
+================================================================================
+umf_triplet_nomap_x.c
+================================================================================
+================================================================================
+umf_tuple_lengths.c
+================================================================================
+================================================================================
+umf_uhsolve.c
+================================================================================
+================================================================================
+umf_usolve.c
+================================================================================
+================================================================================
+umf_utsolve.c
+================================================================================
+================================================================================
+umf_valid_numeric.c
+================================================================================
+================================================================================
+umf_valid_symbolic.c
+================================================================================
+================================================================================
+umfpack_col_to_triplet.c
+================================================================================
+================================================================================
+umfpack_defaults.c
+================================================================================
+================================================================================
+umfpack_free_numeric.c
+================================================================================
+================================================================================
+umfpack_free_symbolic.c
+================================================================================
+================================================================================
+umfpack_get_determinant.c
+================================================================================
+ 24 219 #####: 214: Info [UMFPACK_STATUS] = UMFPACK_WARNING_singular_matrix ;
+ 24 220 #####: 215: break ;
+================================================================================
+umfpack_get_lunz.c
+================================================================================
+================================================================================
+umfpack_get_numeric.c
+================================================================================
+================================================================================
+umfpack_get_symbolic.c
+================================================================================
+================================================================================
+umfpack_load_numeric.c
+================================================================================
+ 24 101 #####: 96: (void) UMF_free ((void *) Numeric) ;
+ 24 102 #####: 97: fclose (f) ;
+ 24 103 #####: 98: return (UMFPACK_ERROR_file_IO) ;
+ 24 160 #####: 155: UMFPACK_free_numeric ((void **) &Numeric) ;
+ 24 161 #####: 156: return (UMFPACK_ERROR_invalid_Numeric_object) ;
+================================================================================
+umfpack_load_symbolic.c
+================================================================================
+ 24 101 #####: 96: (void) UMF_free ((void *) Symbolic) ;
+ 24 102 #####: 97: fclose (f) ;
+ 24 103 #####: 98: return (UMFPACK_ERROR_file_IO) ;
+ 24 164 #####: 159: UMFPACK_free_symbolic ((void **) &Symbolic) ;
+ 24 165 #####: 160: return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+================================================================================
+umfpack_numeric.c
+================================================================================
+ 24 188 #####: 183: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ 24 189 #####: 184: return (UMFPACK_ERROR_out_of_memory) ;
+================================================================================
+umfpack_qsymbolic.c
+================================================================================
+ 24 518 #####: 513: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ 24 519 #####: 514: return (UMFPACK_ERROR_out_of_memory) ;
+ 24 893 #####: 888: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ 24 894 #####: 889: error (&Symbolic, SW) ;
+ 24 895 #####: 890: return (UMFPACK_ERROR_out_of_memory) ;
+ 24 914 #####: 909: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ 24 915 #####: 910: error (&Symbolic, SW) ;
+ 24 916 #####: 911: return (UMFPACK_ERROR_out_of_memory) ;
+ 24 983 #####: 978: strategy = UMFPACK_STRATEGY_2BY2 ;
+ 24 1463 #####: 1458: Info [UMFPACK_STATUS] = UMFPACK_ERROR_internal_error ;
+ 24 1464 #####: 1459: error (&Symbolic, SW) ;
+ 24 1465 #####: 1460: return (UMFPACK_ERROR_internal_error) ;
+ 24 1817 #####: 1812: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ 24 1818 #####: 1813: error (&Symbolic, SW) ;
+ 24 1819 #####: 1814: return (UMFPACK_ERROR_out_of_memory) ;
+================================================================================
+umfpack_report_control.c
+================================================================================
+================================================================================
+umfpack_report_info.c
+================================================================================
+ 24 506 #####: 501: PRINT_INFO (
+ 24 529 #####: 524: twtot = twsym + twnum ;
+ 24 530 #####: 525: PRINT_INFO (" symbolic + numeric wall clock time (sec): %.2f\n",
+ 24 532 #####: 527: if (ftot > 0 && twtot > TMIN)
+ 24 534 #####: 529: PRINT_INFO (
+ 24 570 #####: 565: PRINT_INFO (
+ 24 601 #####: 596: if (twtot >= TMIN && ftot >= 0)
+ 24 603 #####: 598: twtot += tsolve ;
+ 24 604 #####: 599: PRINT_INFO (
+ 24 607 #####: 602: if (ftot > 0 && twtot > TMIN)
+ 24 609 #####: 604: PRINT_INFO (
+================================================================================
+umfpack_report_matrix.c
+================================================================================
+================================================================================
+umfpack_report_numeric.c
+================================================================================
+ 24 326 #####: 321: return (FALSE) ;
+ 24 332 #####: 327: PRINTF (("\t...\n")) ;
+ 24 333 #####: 328: prl-- ;
+ 24 534 #####: 529: return (FALSE) ;
+ 24 641 #####: 636: PRINTF ((" ...\n")) ;
+ 24 642 #####: 637: prl-- ;
+ 24 653 #####: 648: return (FALSE) ;
+ 24 659 #####: 654: PRINTF (("\t...\n")) ;
+ 24 660 #####: 655: prl-- ;
+================================================================================
+umfpack_report_perm.c
+================================================================================
+================================================================================
+umfpack_report_status.c
+================================================================================
+================================================================================
+umfpack_report_symbolic.c
+================================================================================
+================================================================================
+umfpack_report_triplet.c
+================================================================================
+================================================================================
+umfpack_report_vector.c
+================================================================================
+================================================================================
+umfpack_save_numeric.c
+================================================================================
+================================================================================
+umfpack_save_symbolic.c
+================================================================================
+================================================================================
+umfpack_scale.c
+================================================================================
+================================================================================
+umfpack_solve.c
+================================================================================
+================================================================================
+umfpack_symbolic.c
+================================================================================
+================================================================================
+umfpack_tictoc.c
+================================================================================
+================================================================================
+umfpack_timer.c
+================================================================================
+================================================================================
+umfpack_transpose.c
+================================================================================
+================================================================================
+umfpack_triplet_to_col.c
+================================================================================
+================================================================================
+umfpack_wsolve.c
+================================================================================
+ 24 146 #####: 141: Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ;
+ 24 147 #####: 142: return (UMFPACK_ERROR_invalid_system) ;
+ 24 160 #####: 155: Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ 24 161 #####: 156: return (UMFPACK_ERROR_argument_missing) ;
+ 24 167 #####: 162: irstep = 0 ;
+================================================================================
+amd_1.c
+================================================================================
+================================================================================
+amd_2.c
+================================================================================
+================================================================================
+amd_aat.c
+================================================================================
+================================================================================
+amd_control.c
+================================================================================
+================================================================================
+amd_defaults.c
+================================================================================
+================================================================================
+amd_info.c
+================================================================================
+================================================================================
+amd_order.c
+================================================================================
+ 24 84 #####: 79: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ 24 85 #####: 80: return (AMD_OUT_OF_MEMORY) ; /* problem too large */
+ 24 105 #####: 100: amd_free (Len) ;
+ 24 106 #####: 101: amd_free (Pinv) ;
+ 24 107 #####: 102: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ 24 108 #####: 103: return (AMD_OUT_OF_MEMORY) ;
+ 24 122 #####: 117: amd_free (Rp) ;
+ 24 123 #####: 118: amd_free (Ri) ;
+ 24 124 #####: 119: amd_free (Len) ;
+ 24 125 #####: 120: amd_free (Pinv) ;
+ 24 126 #####: 121: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ 24 127 #####: 122: return (AMD_OUT_OF_MEMORY) ;
+ 24 175 #####: 170: amd_free (Rp) ;
+ 24 176 #####: 171: amd_free (Ri) ;
+ 24 177 #####: 172: amd_free (Len) ;
+ 24 178 #####: 173: amd_free (Pinv) ;
+ 24 179 #####: 174: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ 24 180 #####: 175: return (AMD_OUT_OF_MEMORY) ;
+================================================================================
+amd_postorder.c
+================================================================================
+================================================================================
+amd_post_tree.c
+================================================================================
+================================================================================
+amd_preprocess.c
+================================================================================
+================================================================================
+amd_valid.c
+================================================================================
+================================================================================
+Last line of each output file:
+================================================================================
+Out/1_di/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.54e-08 omega2) cputime 68.89
+=================================================================
+Out/1_dl/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.54e-08 omega2) cputime 60.89
+=================================================================
+Out/1g_di/ut.out
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 53.72
+=================================================================
+Out/1g_dl/ut.out
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 46.99
+=================================================================
+Out/1g_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.84e-05 arc130 3.66e-10 omega2) cputime 89.22
+=================================================================
+Out/1g_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.84e-05 arc130 3.66e-10 omega2) cputime 87.79
+=================================================================
+Out/1_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 110.06
+=================================================================
+Out/1_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 109.89
+=================================================================
+Out/2_di/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 60.81
+=================================================================
+Out/2_dl/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 55.15
+=================================================================
+Out/2g_di/ut.out
+ALL TESTS PASSED: rnorm 1.06e-10 (1.37e-07 shl0, 5.65e-05 arc130 8.07e-09 omega2) cputime 46.87
+=================================================================
+Out/2g_dl/ut.out
+ALL TESTS PASSED: rnorm 1.06e-10 (1.37e-07 shl0, 5.65e-05 arc130 8.07e-09 omega2) cputime 42.94
+=================================================================
+Out/2g_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 5.69e-05 arc130 1.14e-09 omega2) cputime 67.54
+=================================================================
+Out/2g_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 5.69e-05 arc130 1.14e-09 omega2) cputime 68.33
+=================================================================
+Out/2_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 90.34
+=================================================================
+Out/2_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 90.37
+=================================================================
+Out/5_di/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 68.49
+=================================================================
+Out/5_dl/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 60.57
+=================================================================
+Out/5_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 109.19
+=================================================================
+Out/5_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 110.08
+=================================================================
+Out/6_di/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 0
+=================================================================
+Out/6_dl/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 0
+=================================================================
+Out/6_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 0
+=================================================================
+Out/6_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 0
+=================================================================
+Out/7_di/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.54e-08 omega2) cputime 69.52
+=================================================================
+Out/7_dl/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.54e-08 omega2) cputime 59.27
+=================================================================
+Out/7_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 109.28
+=================================================================
+Out/7_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 110.39
+=================================================================
+Out/8_di/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 61.45
+=================================================================
+Out/8_dl/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.37e-07 shl0, 6.76e-05 arc130 1.73e-08 omega2) cputime 55.82
+=================================================================
+Out/8_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 90.46
+=================================================================
+Out/8_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.40e-07 shl0, 6.77e-05 arc130 1.77e-09 omega2) cputime 89.24
+=================================================================
diff --git a/UMFPACK/Tcov/cover.out_May5 b/UMFPACK/Tcov/cover.out_May5
new file mode 100644
index 0000000..5ea1136
--- /dev/null
+++ b/UMFPACK/Tcov/cover.out_May5
@@ -0,0 +1,536 @@
+================================================================================
+umf_2by2.c
+================================================================================
+================================================================================
+umf_analyze.c
+================================================================================
+ 24 219 #####: 216: return (FALSE) ; /* internal error! */
+================================================================================
+umf_apply_order.c
+================================================================================
+================================================================================
+umf_assemble.c
+================================================================================
+================================================================================
+umf_assemble_fixq.c
+================================================================================
+================================================================================
+umf_blas3_update.c
+================================================================================
+================================================================================
+umf_build_tuples.c
+================================================================================
+ 24 80 #####: 77: return (FALSE) ; /* out of memory for row tuples */
+ 24 98 #####: 95: return (FALSE) ; /* out of memory for col tuples */
+================================================================================
+umf_colamd.c
+================================================================================
+ 24 2706 #####: 2703: KILL_ROW (r) ;
+================================================================================
+umf_create_element.c
+================================================================================
+ 24 250 #####: 247: return (FALSE) ; /* out of memory */
+ 24 261 #####: 258: return (FALSE) ; /* out of memory */
+ 24 437 #####: 434: return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos));
+ 24 540 #####: 537: return (UMF_get_memory (Numeric, Work, 0, r2, c2,do_Fcpos));
+================================================================================
+umf_extend_front.c
+================================================================================
+================================================================================
+umf_free.c
+================================================================================
+================================================================================
+umf_fsize.c
+================================================================================
+ 24 55 #####: 52: frsize = Int_MAX ;
+================================================================================
+umf_garbage_collection.c
+================================================================================
+================================================================================
+umf_get_memory.c
+================================================================================
+ 24 111 #####: 108: newsize = (Int) bsize ; /* we cannot increase the size beyond bsize */
+================================================================================
+umf_grow_front.c
+================================================================================
+ 24 90 #####: 87: return (FALSE) ;
+ 24 118 #####: 115: double a = 0.9 * sqrt ((Int_MAX / sizeof (Entry)) / s) ;
+ 24 119 #####: 116: fnr2 = MAX (fnr_min, a * fnr2) ;
+ 24 120 #####: 117: fnc2 = MAX (fnc_min, a * fnc2) ;
+ 24 122 #####: 119: newsize = fnr2 * fnc2 ;
+ 24 124 #####: 121: if (fnr2 % 2 == 0) fnr2++ ;
+ 24 125 #####: 122: fnc2 = newsize / fnr2 ;
+ 24 183 #####: 180: return (FALSE) ; /* out of memory */
+================================================================================
+umf_init_front.c
+================================================================================
+ 24 77 #####: 74: return (FALSE) ;
+================================================================================
+umf_is_permutation.c
+================================================================================
+================================================================================
+umf_kernel.c
+================================================================================
+================================================================================
+umf_kernel_init.c
+================================================================================
+ 24 514 #####: 511: return (FALSE) ; /* pattern changed */
+ 24 542 #####: 539: return (FALSE) ; /* pattern changed */
+ 24 606 #####: 603: return (FALSE) ; /* pattern has changed */
+ 24 642 #####: 639: return (FALSE) ; /* pattern has changed */
+ 24 710 #####: 707: return (FALSE) ; /* pattern changed */
+ 24 723 #####: 720: return (FALSE) ; /* pattern changed */
+ 24 735 #####: 732: return (FALSE) ; /* pattern changed */
+ 24 827 #####: 824: return (FALSE) ; /* pattern changed */
+ 24 863 #####: 860: return (FALSE) ; /* pattern changed */
+ 24 905 #####: 902: return (FALSE) ; /* pattern changed */
+ 24 919 #####: 916: return (FALSE) ; /* pattern changed */
+ 24 1031 #####: 1028: return (FALSE) ; /* pattern changed */
+================================================================================
+umf_kernel_wrapup.c
+================================================================================
+================================================================================
+umf_lhsolve.c
+================================================================================
+================================================================================
+umf_local_search.c
+================================================================================
+ 24 654 #####: 651: return (UMFPACK_ERROR_different_pattern) ;
+ 24 743 #####: 740: return (UMFPACK_ERROR_different_pattern) ;
+================================================================================
+umf_lsolve.c
+================================================================================
+================================================================================
+umf_ltsolve.c
+================================================================================
+================================================================================
+umf_malloc.c
+================================================================================
+================================================================================
+umf_mem_alloc_element.c
+================================================================================
+ 24 46 #####: 43: return (0) ; /* problem is too large */
+================================================================================
+umf_mem_alloc_head_block.c
+================================================================================
+================================================================================
+umf_mem_alloc_tail_block.c
+================================================================================
+================================================================================
+umf_mem_free_tail_block.c
+================================================================================
+================================================================================
+umf_mem_init_memoryspace.c
+================================================================================
+================================================================================
+umf_realloc.c
+================================================================================
+ 24 55 #####: 52: return ((void *) NULL) ;
+================================================================================
+umf_report_perm.c
+================================================================================
+================================================================================
+umf_report_vector.c
+================================================================================
+================================================================================
+umf_row_search.c
+================================================================================
+ 24 616 #####: 613: return (UMFPACK_ERROR_different_pattern) ;
+ 24 662 #####: 659: return (UMFPACK_ERROR_different_pattern) ;
+ 24 749 #####: 746: return (UMFPACK_ERROR_different_pattern) ;
+================================================================================
+umf_scale.c
+================================================================================
+================================================================================
+umf_scale_column.c
+================================================================================
+================================================================================
+umf_set_stats.c
+================================================================================
+================================================================================
+umf_singletons.c
+================================================================================
+================================================================================
+umf_solve.c
+================================================================================
+ 24 1313 #####: 1310: omega [1] = tau ;
+ 24 1314 #####: 1311: omega [2] = tau ;
+ 24 1315 #####: 1312: break ;
+================================================================================
+umf_start_front.c
+================================================================================
+ 24 153 #####: 150: maxfrsize = Int_MAX / sizeof (Entry) ;
+ 24 172 #####: 169: fsize = Int_MAX / sizeof (Entry) ;
+ 24 190 #####: 187: fsize2 = Int_MAX / sizeof (Entry) ;
+================================================================================
+umf_store_lu.c
+================================================================================
+ 24 346 #####: 343: return (FALSE) ; /* out of memory */
+ 24 352 #####: 349: return (FALSE) ; /* out of memory */
+ 24 771 #####: 768: return (FALSE) ; /* out of memory */
+ 24 778 #####: 775: return (FALSE) ; /* out of memory */
+================================================================================
+umf_store_lu_drop.c
+================================================================================
+ 24 326 #####: 323: Int r2, c2 ;
+ 24 329 #####: 326: if (Work->do_grow)
+ 24 333 #####: 330: r2 = fnrows ;
+ 24 334 #####: 331: c2 = fncols ;
+ 24 339 #####: 336: r2 = MAX (fnrows, Work->fnrows_new + 1) ;
+ 24 340 #####: 337: c2 = MAX (fncols, Work->fncols_new + 1) ;
+ 24 343 #####: 340: if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE))
+ 24 346 #####: 343: return (FALSE) ; /* out of memory */
+ 24 348 #####: 345: p = UMF_mem_alloc_head_block (Numeric, size) ;
+ 24 349 #####: 346: if (!p)
+ 24 352 #####: 349: return (FALSE) ; /* out of memory */
+ 24 355 #####: 352: fnc_curr = Work->fnc_curr ;
+ 24 356 #####: 353: fnr_curr = Work->fnr_curr ;
+ 24 357 #####: 354: Flublock = Work->Flublock ;
+ 24 358 #####: 355: Flblock = Work->Flblock ;
+ 24 359 #####: 356: Fublock = Work->Fublock ;
+ 24 360 #####: 357: Fl1 = Flublock + kk * nb ;
+ 24 361 #####: 358: Fl2 = Flblock + kk * fnr_curr ;
+ 24 494 #####: 491: pos = llen++ ;
+ 24 495 #####: 492: Lpattern [pos] = row2 ;
+ 24 496 #####: 493: Lpos [row2] = pos ;
+ 24 497 #####: 494: *Li++ = row2 ;
+ 24 750 #####: 747: Int r2, c2 ;
+ 24 753 #####: 750: if (Work->do_grow)
+ 24 757 #####: 754: r2 = fnrows ;
+ 24 758 #####: 755: c2 = fncols ;
+ 24 763 #####: 760: r2 = MAX (fnrows, Work->fnrows_new + 1) ;
+ 24 764 #####: 761: c2 = MAX (fncols, Work->fncols_new + 1) ;
+ 24 767 #####: 764: if (!UMF_get_memory (Numeric, Work, size, r2, c2, TRUE))
+ 24 771 #####: 768: return (FALSE) ; /* out of memory */
+ 24 773 #####: 770: p = UMF_mem_alloc_head_block (Numeric, size) ;
+ 24 774 #####: 771: if (!p)
+ 24 778 #####: 775: return (FALSE) ; /* out of memory */
+ 24 781 #####: 778: fnc_curr = Work->fnc_curr ;
+ 24 782 #####: 779: fnr_curr = Work->fnr_curr ;
+ 24 783 #####: 780: Flublock = Work->Flublock ;
+ 24 784 #####: 781: Flblock = Work->Flblock ;
+ 24 785 #####: 782: Fublock = Work->Fublock ;
+ 24 786 #####: 783: Fu1 = Flublock + kk ;
+ 24 787 #####: 784: Fu2 = Fublock + kk * fnc_curr ;
+================================================================================
+umf_symbolic_usage.c
+================================================================================
+================================================================================
+umf_transpose.c
+================================================================================
+================================================================================
+umf_triplet_map_nox.c
+================================================================================
+================================================================================
+umf_triplet_map_x.c
+================================================================================
+================================================================================
+umf_triplet_nomap_nox.c
+================================================================================
+================================================================================
+umf_triplet_nomap_x.c
+================================================================================
+================================================================================
+umf_tuple_lengths.c
+================================================================================
+================================================================================
+umf_uhsolve.c
+================================================================================
+================================================================================
+umf_usolve.c
+================================================================================
+================================================================================
+umf_utsolve.c
+================================================================================
+================================================================================
+umf_valid_numeric.c
+================================================================================
+================================================================================
+umf_valid_symbolic.c
+================================================================================
+================================================================================
+umfpack_col_to_triplet.c
+================================================================================
+================================================================================
+umfpack_defaults.c
+================================================================================
+================================================================================
+umfpack_free_numeric.c
+================================================================================
+================================================================================
+umfpack_free_symbolic.c
+================================================================================
+================================================================================
+umfpack_get_determinant.c
+================================================================================
+ 24 217 #####: 214: Info [UMFPACK_STATUS] = UMFPACK_WARNING_singular_matrix ;
+ 24 218 #####: 215: break ;
+================================================================================
+umfpack_get_lunz.c
+================================================================================
+================================================================================
+umfpack_get_numeric.c
+================================================================================
+================================================================================
+umfpack_get_symbolic.c
+================================================================================
+================================================================================
+umfpack_load_numeric.c
+================================================================================
+ 24 99 #####: 96: (void) UMF_free ((void *) Numeric) ;
+ 24 100 #####: 97: fclose (f) ;
+ 24 101 #####: 98: return (UMFPACK_ERROR_file_IO) ;
+ 24 158 #####: 155: UMFPACK_free_numeric ((void **) &Numeric) ;
+ 24 159 #####: 156: return (UMFPACK_ERROR_invalid_Numeric_object) ;
+================================================================================
+umfpack_load_symbolic.c
+================================================================================
+ 24 99 #####: 96: (void) UMF_free ((void *) Symbolic) ;
+ 24 100 #####: 97: fclose (f) ;
+ 24 101 #####: 98: return (UMFPACK_ERROR_file_IO) ;
+ 24 162 #####: 159: UMFPACK_free_symbolic ((void **) &Symbolic) ;
+ 24 163 #####: 160: return (UMFPACK_ERROR_invalid_Symbolic_object) ;
+================================================================================
+umfpack_numeric.c
+================================================================================
+ 24 186 #####: 183: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ 24 187 #####: 184: return (UMFPACK_ERROR_out_of_memory) ;
+================================================================================
+umfpack_qsymbolic.c
+================================================================================
+ 24 516 #####: 513: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ 24 517 #####: 514: return (UMFPACK_ERROR_out_of_memory) ;
+ 24 891 #####: 888: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ 24 892 #####: 889: error (&Symbolic, SW) ;
+ 24 893 #####: 890: return (UMFPACK_ERROR_out_of_memory) ;
+ 24 912 #####: 909: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ 24 913 #####: 910: error (&Symbolic, SW) ;
+ 24 914 #####: 911: return (UMFPACK_ERROR_out_of_memory) ;
+ 24 981 #####: 978: strategy = UMFPACK_STRATEGY_2BY2 ;
+ 24 1461 #####: 1458: Info [UMFPACK_STATUS] = UMFPACK_ERROR_internal_error ;
+ 24 1462 #####: 1459: error (&Symbolic, SW) ;
+ 24 1463 #####: 1460: return (UMFPACK_ERROR_internal_error) ;
+ 24 1815 #####: 1812: Info [UMFPACK_STATUS] = UMFPACK_ERROR_out_of_memory ;
+ 24 1816 #####: 1813: error (&Symbolic, SW) ;
+ 24 1817 #####: 1814: return (UMFPACK_ERROR_out_of_memory) ;
+================================================================================
+umfpack_report_control.c
+================================================================================
+================================================================================
+umfpack_report_info.c
+================================================================================
+================================================================================
+umfpack_report_matrix.c
+================================================================================
+================================================================================
+umfpack_report_numeric.c
+================================================================================
+ 24 324 #####: 321: return (FALSE) ;
+ 24 330 #####: 327: PRINTF (("\t...\n")) ;
+ 24 331 #####: 328: prl-- ;
+ 24 532 #####: 529: return (FALSE) ;
+ 24 639 #####: 636: PRINTF ((" ...\n")) ;
+ 24 640 #####: 637: prl-- ;
+ 24 651 #####: 648: return (FALSE) ;
+ 24 657 #####: 654: PRINTF (("\t...\n")) ;
+ 24 658 #####: 655: prl-- ;
+================================================================================
+umfpack_report_perm.c
+================================================================================
+================================================================================
+umfpack_report_status.c
+================================================================================
+================================================================================
+umfpack_report_symbolic.c
+================================================================================
+================================================================================
+umfpack_report_triplet.c
+================================================================================
+================================================================================
+umfpack_report_vector.c
+================================================================================
+================================================================================
+umfpack_save_numeric.c
+================================================================================
+================================================================================
+umfpack_save_symbolic.c
+================================================================================
+================================================================================
+umfpack_scale.c
+================================================================================
+================================================================================
+umfpack_solve.c
+================================================================================
+================================================================================
+umfpack_symbolic.c
+================================================================================
+================================================================================
+umfpack_tictoc.c
+================================================================================
+================================================================================
+umfpack_timer.c
+================================================================================
+================================================================================
+umfpack_transpose.c
+================================================================================
+================================================================================
+umfpack_triplet_to_col.c
+================================================================================
+================================================================================
+umfpack_wsolve.c
+================================================================================
+ 24 144 #####: 141: Info [UMFPACK_STATUS] = UMFPACK_ERROR_invalid_system ;
+ 24 145 #####: 142: return (UMFPACK_ERROR_invalid_system) ;
+ 24 158 #####: 155: Info [UMFPACK_STATUS] = UMFPACK_ERROR_argument_missing ;
+ 24 159 #####: 156: return (UMFPACK_ERROR_argument_missing) ;
+ 24 165 #####: 162: irstep = 0 ;
+================================================================================
+amd_1.c
+================================================================================
+================================================================================
+amd_2.c
+================================================================================
+================================================================================
+amd_aat.c
+================================================================================
+================================================================================
+amd_control.c
+================================================================================
+================================================================================
+amd_defaults.c
+================================================================================
+================================================================================
+amd_info.c
+================================================================================
+================================================================================
+amd_order.c
+================================================================================
+ 24 82 #####: 79: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ 24 83 #####: 80: return (AMD_OUT_OF_MEMORY) ; /* problem too large */
+ 24 103 #####: 100: amd_free (Len) ;
+ 24 104 #####: 101: amd_free (Pinv) ;
+ 24 105 #####: 102: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ 24 106 #####: 103: return (AMD_OUT_OF_MEMORY) ;
+ 24 120 #####: 117: amd_free (Rp) ;
+ 24 121 #####: 118: amd_free (Ri) ;
+ 24 122 #####: 119: amd_free (Len) ;
+ 24 123 #####: 120: amd_free (Pinv) ;
+ 24 124 #####: 121: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ 24 125 #####: 122: return (AMD_OUT_OF_MEMORY) ;
+ 24 173 #####: 170: amd_free (Rp) ;
+ 24 174 #####: 171: amd_free (Ri) ;
+ 24 175 #####: 172: amd_free (Len) ;
+ 24 176 #####: 173: amd_free (Pinv) ;
+ 24 177 #####: 174: if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ 24 178 #####: 175: return (AMD_OUT_OF_MEMORY) ;
+================================================================================
+amd_postorder.c
+================================================================================
+================================================================================
+amd_post_tree.c
+================================================================================
+================================================================================
+amd_preprocess.c
+================================================================================
+================================================================================
+amd_valid.c
+================================================================================
+================================================================================
+Last line of each output file:
+================================================================================
+Out/1_di/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 59.09
+=================================================================
+Out/1_dl/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 51.26
+=================================================================
+Out/1g_di/ut.out
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 39.95
+=================================================================
+Out/1g_dl/ut.out
+ALL TESTS PASSED: rnorm 1.03e-10 (1.19e-07 shl0, 5.65e-05 arc130 4.58e-09 omega2) cputime 34.86
+=================================================================
+Out/1g_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.84e-05 arc130 3.66e-10 omega2) cputime 75.33
+=================================================================
+Out/1g_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.84e-05 arc130 3.66e-10 omega2) cputime 75.14
+=================================================================
+Out/1_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 98.83
+=================================================================
+Out/1_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 97.77
+=================================================================
+Out/2_di/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 52.76
+=================================================================
+Out/2_dl/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 44.59
+=================================================================
+Out/2g_di/ut.out
+ALL TESTS PASSED: rnorm 1.06e-10 (1.19e-07 shl0, 5.65e-05 arc130 1.16e-08 omega2) cputime 33.96
+=================================================================
+Out/2g_dl/ut.out
+ALL TESTS PASSED: rnorm 1.06e-10 (1.19e-07 shl0, 5.65e-05 arc130 1.16e-08 omega2) cputime 30.15
+=================================================================
+Out/2g_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.69e-05 arc130 1.34e-09 omega2) cputime 58.91
+=================================================================
+Out/2g_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 5.69e-05 arc130 1.34e-09 omega2) cputime 58.82
+=================================================================
+Out/2_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 79.13
+=================================================================
+Out/2_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 79.21
+=================================================================
+Out/5_di/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 59.41
+=================================================================
+Out/5_dl/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 8.09e-05 arc130 1.44e-08 omega2) cputime 49.39
+=================================================================
+Out/5_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 98.82
+=================================================================
+Out/5_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 8.10e-05 arc130 1.13e-09 omega2) cputime 98.19
+=================================================================
+Out/6_di/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 0
+=================================================================
+Out/6_dl/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 0
+=================================================================
+Out/6_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 0
+=================================================================
+Out/6_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 0
+=================================================================
+Out/7_di/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 61.16
+=================================================================
+Out/7_dl/ut.out
+ALL TESTS PASSED: rnorm 1.35e-10 (1.19e-07 shl0, 7.08e-05 arc130 2.95e-08 omega2) cputime 49.42
+=================================================================
+Out/7_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 96.29
+=================================================================
+Out/7_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 7.31e-05 arc130 6.19e-10 omega2) cputime 95.47
+=================================================================
+Out/8_di/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 51.65
+=================================================================
+Out/8_dl/ut.out
+ALL TESTS PASSED: rnorm 1.49e-10 (1.19e-07 shl0, 6.76e-05 arc130 2.84e-08 omega2) cputime 44.36
+=================================================================
+Out/8_zi/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 78.02
+=================================================================
+Out/8_zl/ut.out
+ALL TESTS PASSED: rnorm 9.88e-05 (1.33e-07 shl0, 6.77e-05 arc130 1.65e-09 omega2) cputime 78.32
+=================================================================
diff --git a/UMFPACK/Tcov/debug.amd b/UMFPACK/Tcov/debug.amd
new file mode 100644
index 0000000..d83d2bc
--- /dev/null
+++ b/UMFPACK/Tcov/debug.amd
@@ -0,0 +1 @@
+-5
diff --git a/UMFPACK/Tcov/debug.umf b/UMFPACK/Tcov/debug.umf
new file mode 100644
index 0000000..d83d2bc
--- /dev/null
+++ b/UMFPACK/Tcov/debug.umf
@@ -0,0 +1 @@
+-5
diff --git a/UMFPACK/Tcov/ss.awk b/UMFPACK/Tcov/ss.awk
new file mode 100644
index 0000000..13a8b2d
--- /dev/null
+++ b/UMFPACK/Tcov/ss.awk
@@ -0,0 +1,3 @@
+/TestMat/
+
+/final det/
diff --git a/UMFPACK/Tcov/ucov.di b/UMFPACK/Tcov/ucov.di
new file mode 100755
index 0000000..b9f30e7
--- /dev/null
+++ b/UMFPACK/Tcov/ucov.di
@@ -0,0 +1,98 @@
+#!/bin/csh
+# ucov.di: construct gcov files for umfpack, di version
+
+gcov -o umf_i_analyze umf_analyze.c
+gcov -o umf_i_apply_order umf_apply_order.c
+gcov -o umf_i_colamd umf_colamd.c
+gcov -o umf_i_free umf_free.c
+gcov -o umf_i_fsize umf_fsize.c
+gcov -o umf_i_is_permutation umf_is_permutation.c
+gcov -o umf_i_malloc umf_malloc.c
+gcov -o umf_i_realloc umf_realloc.c
+gcov -o umf_i_report_perm umf_report_perm.c
+gcov -o umf_i_singletons umf_singletons.c
+
+gcov -o umf_di_2by2 umf_2by2.c
+gcov -o umf_di_blas3_update umf_blas3_update.c
+gcov -o umf_di_build_tuples umf_build_tuples.c
+gcov -o umf_di_create_element umf_create_element.c
+gcov -o umf_di_extend_front umf_extend_front.c
+gcov -o umf_di_garbage_collection umf_garbage_collection.c
+gcov -o umf_di_get_memory umf_get_memory.c
+gcov -o umf_di_grow_front umf_grow_front.c
+gcov -o umf_di_init_front umf_init_front.c
+gcov -o umf_di_kernel umf_kernel.c
+gcov -o umf_di_kernel_init umf_kernel_init.c
+gcov -o umf_di_kernel_wrapup umf_kernel_wrapup.c
+gcov -o umf_di_local_search umf_local_search.c
+gcov -o umf_di_lsolve umf_lsolve.c
+gcov -o umf_di_mem_alloc_element umf_mem_alloc_element.c
+gcov -o umf_di_mem_alloc_head_block umf_mem_alloc_head_block.c
+gcov -o umf_di_mem_alloc_tail_block umf_mem_alloc_tail_block.c
+gcov -o umf_di_mem_free_tail_block umf_mem_free_tail_block.c
+gcov -o umf_di_mem_init_memoryspace umf_mem_init_memoryspace.c
+gcov -o umf_di_report_vector umf_report_vector.c
+gcov -o umf_di_row_search umf_row_search.c
+gcov -o umf_di_scale umf_scale.c
+gcov -o umf_di_scale_column umf_scale_column.c
+gcov -o umf_di_set_stats umf_set_stats.c
+gcov -o umf_di_solve umf_solve.c
+gcov -o umf_di_start_front umf_start_front.c
+gcov -o umf_di_symbolic_usage umf_symbolic_usage.c
+gcov -o umf_di_transpose umf_transpose.c
+
+gcov -o umf_di_tuple_lengths umf_tuple_lengths.c
+gcov -o umf_di_usolve umf_usolve.c
+gcov -o umf_di_valid_numeric umf_valid_numeric.c
+gcov -o umf_di_valid_symbolic umf_valid_symbolic.c
+gcov -o umfpack_di_col_to_triplet umfpack_col_to_triplet.c
+gcov -o umfpack_di_defaults umfpack_defaults.c
+gcov -o umfpack_di_free_numeric umfpack_free_numeric.c
+gcov -o umfpack_di_free_symbolic umfpack_free_symbolic.c
+gcov -o umfpack_di_get_lunz umfpack_get_lunz.c
+gcov -o umfpack_di_get_numeric umfpack_get_numeric.c
+gcov -o umfpack_di_get_determinant umfpack_get_determinant.c
+gcov -o umfpack_di_get_symbolic umfpack_get_symbolic.c
+gcov -o umfpack_di_load_numeric umfpack_load_numeric.c
+gcov -o umfpack_di_load_symbolic umfpack_load_symbolic.c
+gcov -o umfpack_di_numeric umfpack_numeric.c
+gcov -o umfpack_di_qsymbolic umfpack_qsymbolic.c
+gcov -o umfpack_di_report_control umfpack_report_control.c
+gcov -o umfpack_di_report_info umfpack_report_info.c
+gcov -o umfpack_di_report_matrix umfpack_report_matrix.c
+gcov -o umfpack_di_report_numeric umfpack_report_numeric.c
+gcov -o umfpack_di_report_perm umfpack_report_perm.c
+gcov -o umfpack_di_report_status umfpack_report_status.c
+gcov -o umfpack_di_report_symbolic umfpack_report_symbolic.c
+gcov -o umfpack_di_report_triplet umfpack_report_triplet.c
+gcov -o umfpack_di_report_vector umfpack_report_vector.c
+gcov -o umfpack_di_save_numeric umfpack_save_numeric.c
+gcov -o umfpack_di_save_symbolic umfpack_save_symbolic.c
+gcov -o umfpack_di_scale umfpack_scale.c
+gcov -o umfpack_di_symbolic umfpack_symbolic.c
+gcov -o umfpack_di_transpose umfpack_transpose.c
+gcov -o umfpack_di_triplet_to_col umfpack_triplet_to_col.c
+
+gcov -o umfpack_gn_tictoc umfpack_tictoc.c
+gcov -o umfpack_gn_timer umfpack_timer.c
+
+# multiple versions
+gcov -o umf_di_uhsolve umf_utsolve.c ; mv -f umf_utsolve.c.gcov umf_uhsolve.c.gcov
+gcov -o umf_di_utsolve umf_utsolve.c
+
+gcov -o umf_di_lhsolve umf_ltsolve.c ; mv -f umf_ltsolve.c.gcov umf_lhsolve.c.gcov
+gcov -o umf_di_ltsolve umf_ltsolve.c
+
+gcov -o umfpack_di_wsolve umfpack_solve.c ; mv -f umfpack_solve.c.gcov umfpack_wsolve.c.gcov
+gcov -o umfpack_di_solve umfpack_solve.c
+
+gcov -o umf_di_store_lu_drop umf_store_lu.c ; mv -f umf_store_lu.c.gcov umf_store_lu_drop.c.gcov
+gcov -o umf_di_store_lu umf_store_lu.c
+
+gcov -o umf_di_assemble_fixq umf_assemble.c ; mv -f umf_assemble.c.gcov umf_assemble_fixq.c.gcov
+gcov -o umf_di_assemble umf_assemble.c
+
+gcov -o umf_di_triplet_map_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_x.c.gcov
+gcov -o umf_di_triplet_nomap_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_x.c.gcov
+gcov -o umf_di_triplet_map_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_nox.c.gcov
+gcov -o umf_di_triplet_nomap_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_nox.c.gcov
diff --git a/UMFPACK/Tcov/ucov.dl b/UMFPACK/Tcov/ucov.dl
new file mode 100755
index 0000000..6b949b4
--- /dev/null
+++ b/UMFPACK/Tcov/ucov.dl
@@ -0,0 +1,98 @@
+#!/bin/csh
+# ucov.dl: construct gcov files for umfpack, dl version
+
+gcov -o umf_l_analyze umf_analyze.c
+gcov -o umf_l_apply_order umf_apply_order.c
+gcov -o umf_l_colamd umf_colamd.c
+gcov -o umf_l_free umf_free.c
+gcov -o umf_l_fsize umf_fsize.c
+gcov -o umf_l_is_permutation umf_is_permutation.c
+gcov -o umf_l_malloc umf_malloc.c
+gcov -o umf_l_realloc umf_realloc.c
+gcov -o umf_l_report_perm umf_report_perm.c
+gcov -o umf_l_singletons umf_singletons.c
+
+gcov -o umf_dl_2by2 umf_2by2.c
+gcov -o umf_dl_blas3_update umf_blas3_update.c
+gcov -o umf_dl_build_tuples umf_build_tuples.c
+gcov -o umf_dl_create_element umf_create_element.c
+gcov -o umf_dl_extend_front umf_extend_front.c
+gcov -o umf_dl_garbage_collection umf_garbage_collection.c
+gcov -o umf_dl_get_memory umf_get_memory.c
+gcov -o umf_dl_grow_front umf_grow_front.c
+gcov -o umf_dl_init_front umf_init_front.c
+gcov -o umf_dl_kernel umf_kernel.c
+gcov -o umf_dl_kernel_init umf_kernel_init.c
+gcov -o umf_dl_kernel_wrapup umf_kernel_wrapup.c
+gcov -o umf_dl_local_search umf_local_search.c
+gcov -o umf_dl_lsolve umf_lsolve.c
+gcov -o umf_dl_mem_alloc_element umf_mem_alloc_element.c
+gcov -o umf_dl_mem_alloc_head_block umf_mem_alloc_head_block.c
+gcov -o umf_dl_mem_alloc_tail_block umf_mem_alloc_tail_block.c
+gcov -o umf_dl_mem_free_tail_block umf_mem_free_tail_block.c
+gcov -o umf_dl_mem_init_memoryspace umf_mem_init_memoryspace.c
+gcov -o umf_dl_report_vector umf_report_vector.c
+gcov -o umf_dl_row_search umf_row_search.c
+gcov -o umf_dl_scale umf_scale.c
+gcov -o umf_dl_scale_column umf_scale_column.c
+gcov -o umf_dl_set_stats umf_set_stats.c
+gcov -o umf_dl_solve umf_solve.c
+gcov -o umf_dl_start_front umf_start_front.c
+gcov -o umf_dl_symbolic_usage umf_symbolic_usage.c
+gcov -o umf_dl_transpose umf_transpose.c
+
+gcov -o umf_dl_tuple_lengths umf_tuple_lengths.c
+gcov -o umf_dl_usolve umf_usolve.c
+gcov -o umf_dl_valid_numeric umf_valid_numeric.c
+gcov -o umf_dl_valid_symbolic umf_valid_symbolic.c
+gcov -o umfpack_dl_col_to_triplet umfpack_col_to_triplet.c
+gcov -o umfpack_dl_defaults umfpack_defaults.c
+gcov -o umfpack_dl_free_numeric umfpack_free_numeric.c
+gcov -o umfpack_dl_free_symbolic umfpack_free_symbolic.c
+gcov -o umfpack_dl_get_lunz umfpack_get_lunz.c
+gcov -o umfpack_dl_get_numeric umfpack_get_numeric.c
+gcov -o umfpack_dl_get_determinant umfpack_get_determinant.c
+gcov -o umfpack_dl_get_symbolic umfpack_get_symbolic.c
+gcov -o umfpack_dl_load_numeric umfpack_load_numeric.c
+gcov -o umfpack_dl_load_symbolic umfpack_load_symbolic.c
+gcov -o umfpack_dl_numeric umfpack_numeric.c
+gcov -o umfpack_dl_qsymbolic umfpack_qsymbolic.c
+gcov -o umfpack_dl_report_control umfpack_report_control.c
+gcov -o umfpack_dl_report_info umfpack_report_info.c
+gcov -o umfpack_dl_report_matrix umfpack_report_matrix.c
+gcov -o umfpack_dl_report_numeric umfpack_report_numeric.c
+gcov -o umfpack_dl_report_perm umfpack_report_perm.c
+gcov -o umfpack_dl_report_status umfpack_report_status.c
+gcov -o umfpack_dl_report_symbolic umfpack_report_symbolic.c
+gcov -o umfpack_dl_report_triplet umfpack_report_triplet.c
+gcov -o umfpack_dl_report_vector umfpack_report_vector.c
+gcov -o umfpack_dl_save_numeric umfpack_save_numeric.c
+gcov -o umfpack_dl_save_symbolic umfpack_save_symbolic.c
+gcov -o umfpack_dl_scale umfpack_scale.c
+gcov -o umfpack_dl_symbolic umfpack_symbolic.c
+gcov -o umfpack_dl_transpose umfpack_transpose.c
+gcov -o umfpack_dl_triplet_to_col umfpack_triplet_to_col.c
+
+gcov -o umfpack_gn_tictoc umfpack_tictoc.c
+gcov -o umfpack_gn_timer umfpack_timer.c
+
+# multiple versions
+gcov -o umf_dl_uhsolve umf_utsolve.c ; mv -f umf_utsolve.c.gcov umf_uhsolve.c.gcov
+gcov -o umf_dl_utsolve umf_utsolve.c
+
+gcov -o umf_dl_lhsolve umf_ltsolve.c ; mv -f umf_ltsolve.c.gcov umf_lhsolve.c.gcov
+gcov -o umf_dl_ltsolve umf_ltsolve.c
+
+gcov -o umfpack_dl_wsolve umfpack_solve.c ; mv -f umfpack_solve.c.gcov umfpack_wsolve.c.gcov
+gcov -o umfpack_dl_solve umfpack_solve.c
+
+gcov -o umf_dl_store_lu_drop umf_store_lu.c ; mv -f umf_store_lu.c.gcov umf_store_lu_drop.c.gcov
+gcov -o umf_dl_store_lu umf_store_lu.c
+
+gcov -o umf_dl_assemble_fixq umf_assemble.c ; mv -f umf_assemble.c.gcov umf_assemble_fixq.c.gcov
+gcov -o umf_dl_assemble umf_assemble.c
+
+gcov -o umf_dl_triplet_map_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_x.c.gcov
+gcov -o umf_dl_triplet_nomap_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_x.c.gcov
+gcov -o umf_dl_triplet_map_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_nox.c.gcov
+gcov -o umf_dl_triplet_nomap_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_nox.c.gcov
diff --git a/UMFPACK/Tcov/ucov.zi b/UMFPACK/Tcov/ucov.zi
new file mode 100755
index 0000000..61648f3
--- /dev/null
+++ b/UMFPACK/Tcov/ucov.zi
@@ -0,0 +1,98 @@
+#!/bin/csh
+# ucov.zi: construct gcov files for umfpack, zi version
+
+gcov -o umf_i_analyze umf_analyze.c
+gcov -o umf_i_apply_order umf_apply_order.c
+gcov -o umf_i_colamd umf_colamd.c
+gcov -o umf_i_free umf_free.c
+gcov -o umf_i_fsize umf_fsize.c
+gcov -o umf_i_is_permutation umf_is_permutation.c
+gcov -o umf_i_malloc umf_malloc.c
+gcov -o umf_i_realloc umf_realloc.c
+gcov -o umf_i_report_perm umf_report_perm.c
+gcov -o umf_i_singletons umf_singletons.c
+
+gcov -o umf_zi_2by2 umf_2by2.c
+gcov -o umf_zi_blas3_update umf_blas3_update.c
+gcov -o umf_zi_build_tuples umf_build_tuples.c
+gcov -o umf_zi_create_element umf_create_element.c
+gcov -o umf_zi_extend_front umf_extend_front.c
+gcov -o umf_zi_garbage_collection umf_garbage_collection.c
+gcov -o umf_zi_get_memory umf_get_memory.c
+gcov -o umf_zi_grow_front umf_grow_front.c
+gcov -o umf_zi_init_front umf_init_front.c
+gcov -o umf_zi_kernel umf_kernel.c
+gcov -o umf_zi_kernel_init umf_kernel_init.c
+gcov -o umf_zi_kernel_wrapup umf_kernel_wrapup.c
+gcov -o umf_zi_local_search umf_local_search.c
+gcov -o umf_zi_lsolve umf_lsolve.c
+gcov -o umf_zi_mem_alloc_element umf_mem_alloc_element.c
+gcov -o umf_zi_mem_alloc_head_block umf_mem_alloc_head_block.c
+gcov -o umf_zi_mem_alloc_tail_block umf_mem_alloc_tail_block.c
+gcov -o umf_zi_mem_free_tail_block umf_mem_free_tail_block.c
+gcov -o umf_zi_mem_init_memoryspace umf_mem_init_memoryspace.c
+gcov -o umf_zi_report_vector umf_report_vector.c
+gcov -o umf_zi_row_search umf_row_search.c
+gcov -o umf_zi_scale umf_scale.c
+gcov -o umf_zi_scale_column umf_scale_column.c
+gcov -o umf_zi_set_stats umf_set_stats.c
+gcov -o umf_zi_solve umf_solve.c
+gcov -o umf_zi_start_front umf_start_front.c
+gcov -o umf_zi_symbolic_usage umf_symbolic_usage.c
+gcov -o umf_zi_transpose umf_transpose.c
+
+gcov -o umf_zi_tuple_lengths umf_tuple_lengths.c
+gcov -o umf_zi_usolve umf_usolve.c
+gcov -o umf_zi_valid_numeric umf_valid_numeric.c
+gcov -o umf_zi_valid_symbolic umf_valid_symbolic.c
+gcov -o umfpack_zi_col_to_triplet umfpack_col_to_triplet.c
+gcov -o umfpack_zi_defaults umfpack_defaults.c
+gcov -o umfpack_zi_free_numeric umfpack_free_numeric.c
+gcov -o umfpack_zi_free_symbolic umfpack_free_symbolic.c
+gcov -o umfpack_zi_get_lunz umfpack_get_lunz.c
+gcov -o umfpack_zi_get_numeric umfpack_get_numeric.c
+gcov -o umfpack_zi_get_determinant umfpack_get_determinant.c
+gcov -o umfpack_zi_get_symbolic umfpack_get_symbolic.c
+gcov -o umfpack_zi_load_numeric umfpack_load_numeric.c
+gcov -o umfpack_zi_load_symbolic umfpack_load_symbolic.c
+gcov -o umfpack_zi_numeric umfpack_numeric.c
+gcov -o umfpack_zi_qsymbolic umfpack_qsymbolic.c
+gcov -o umfpack_zi_report_control umfpack_report_control.c
+gcov -o umfpack_zi_report_info umfpack_report_info.c
+gcov -o umfpack_zi_report_matrix umfpack_report_matrix.c
+gcov -o umfpack_zi_report_numeric umfpack_report_numeric.c
+gcov -o umfpack_zi_report_perm umfpack_report_perm.c
+gcov -o umfpack_zi_report_status umfpack_report_status.c
+gcov -o umfpack_zi_report_symbolic umfpack_report_symbolic.c
+gcov -o umfpack_zi_report_triplet umfpack_report_triplet.c
+gcov -o umfpack_zi_report_vector umfpack_report_vector.c
+gcov -o umfpack_zi_save_numeric umfpack_save_numeric.c
+gcov -o umfpack_zi_save_symbolic umfpack_save_symbolic.c
+gcov -o umfpack_zi_scale umfpack_scale.c
+gcov -o umfpack_zi_symbolic umfpack_symbolic.c
+gcov -o umfpack_zi_transpose umfpack_transpose.c
+gcov -o umfpack_zi_triplet_to_col umfpack_triplet_to_col.c
+
+gcov -o umfpack_gn_tictoc umfpack_tictoc.c
+gcov -o umfpack_gn_timer umfpack_timer.c
+
+# multiple versions
+gcov -o umf_zi_uhsolve umf_utsolve.c ; mv -f umf_utsolve.c.gcov umf_uhsolve.c.gcov
+gcov -o umf_zi_utsolve umf_utsolve.c
+
+gcov -o umf_zi_lhsolve umf_ltsolve.c ; mv -f umf_ltsolve.c.gcov umf_lhsolve.c.gcov
+gcov -o umf_zi_ltsolve umf_ltsolve.c
+
+gcov -o umfpack_zi_wsolve umfpack_solve.c ; mv -f umfpack_solve.c.gcov umfpack_wsolve.c.gcov
+gcov -o umfpack_zi_solve umfpack_solve.c
+
+gcov -o umf_zi_store_lu_drop umf_store_lu.c ; mv -f umf_store_lu.c.gcov umf_store_lu_drop.c.gcov
+gcov -o umf_zi_store_lu umf_store_lu.c
+
+gcov -o umf_zi_assemble_fixq umf_assemble.c ; mv -f umf_assemble.c.gcov umf_assemble_fixq.c.gcov
+gcov -o umf_zi_assemble umf_assemble.c
+
+gcov -o umf_zi_triplet_map_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_x.c.gcov
+gcov -o umf_zi_triplet_nomap_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_x.c.gcov
+gcov -o umf_zi_triplet_map_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_nox.c.gcov
+gcov -o umf_zi_triplet_nomap_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_nox.c.gcov
diff --git a/UMFPACK/Tcov/ucov.zl b/UMFPACK/Tcov/ucov.zl
new file mode 100755
index 0000000..364e7bc
--- /dev/null
+++ b/UMFPACK/Tcov/ucov.zl
@@ -0,0 +1,98 @@
+#!/bin/csh
+# ucov.zl: construct gcov files for umfpack, zl version
+
+gcov -o umf_l_analyze umf_analyze.c
+gcov -o umf_l_apply_order umf_apply_order.c
+gcov -o umf_l_colamd umf_colamd.c
+gcov -o umf_l_free umf_free.c
+gcov -o umf_l_fsize umf_fsize.c
+gcov -o umf_l_is_permutation umf_is_permutation.c
+gcov -o umf_l_malloc umf_malloc.c
+gcov -o umf_l_realloc umf_realloc.c
+gcov -o umf_l_report_perm umf_report_perm.c
+gcov -o umf_l_singletons umf_singletons.c
+
+gcov -o umf_zl_2by2 umf_2by2.c
+gcov -o umf_zl_blas3_update umf_blas3_update.c
+gcov -o umf_zl_build_tuples umf_build_tuples.c
+gcov -o umf_zl_create_element umf_create_element.c
+gcov -o umf_zl_extend_front umf_extend_front.c
+gcov -o umf_zl_garbage_collection umf_garbage_collection.c
+gcov -o umf_zl_get_memory umf_get_memory.c
+gcov -o umf_zl_grow_front umf_grow_front.c
+gcov -o umf_zl_init_front umf_init_front.c
+gcov -o umf_zl_kernel umf_kernel.c
+gcov -o umf_zl_kernel_init umf_kernel_init.c
+gcov -o umf_zl_kernel_wrapup umf_kernel_wrapup.c
+gcov -o umf_zl_local_search umf_local_search.c
+gcov -o umf_zl_lsolve umf_lsolve.c
+gcov -o umf_zl_mem_alloc_element umf_mem_alloc_element.c
+gcov -o umf_zl_mem_alloc_head_block umf_mem_alloc_head_block.c
+gcov -o umf_zl_mem_alloc_tail_block umf_mem_alloc_tail_block.c
+gcov -o umf_zl_mem_free_tail_block umf_mem_free_tail_block.c
+gcov -o umf_zl_mem_init_memoryspace umf_mem_init_memoryspace.c
+gcov -o umf_zl_report_vector umf_report_vector.c
+gcov -o umf_zl_row_search umf_row_search.c
+gcov -o umf_zl_scale umf_scale.c
+gcov -o umf_zl_scale_column umf_scale_column.c
+gcov -o umf_zl_set_stats umf_set_stats.c
+gcov -o umf_zl_solve umf_solve.c
+gcov -o umf_zl_start_front umf_start_front.c
+gcov -o umf_zl_symbolic_usage umf_symbolic_usage.c
+gcov -o umf_zl_transpose umf_transpose.c
+
+gcov -o umf_zl_tuple_lengths umf_tuple_lengths.c
+gcov -o umf_zl_usolve umf_usolve.c
+gcov -o umf_zl_valid_numeric umf_valid_numeric.c
+gcov -o umf_zl_valid_symbolic umf_valid_symbolic.c
+gcov -o umfpack_zl_col_to_triplet umfpack_col_to_triplet.c
+gcov -o umfpack_zl_defaults umfpack_defaults.c
+gcov -o umfpack_zl_free_numeric umfpack_free_numeric.c
+gcov -o umfpack_zl_free_symbolic umfpack_free_symbolic.c
+gcov -o umfpack_zl_get_lunz umfpack_get_lunz.c
+gcov -o umfpack_zl_get_numeric umfpack_get_numeric.c
+gcov -o umfpack_zl_get_determinant umfpack_get_determinant.c
+gcov -o umfpack_zl_get_symbolic umfpack_get_symbolic.c
+gcov -o umfpack_zl_load_numeric umfpack_load_numeric.c
+gcov -o umfpack_zl_load_symbolic umfpack_load_symbolic.c
+gcov -o umfpack_zl_numeric umfpack_numeric.c
+gcov -o umfpack_zl_qsymbolic umfpack_qsymbolic.c
+gcov -o umfpack_zl_report_control umfpack_report_control.c
+gcov -o umfpack_zl_report_info umfpack_report_info.c
+gcov -o umfpack_zl_report_matrix umfpack_report_matrix.c
+gcov -o umfpack_zl_report_numeric umfpack_report_numeric.c
+gcov -o umfpack_zl_report_perm umfpack_report_perm.c
+gcov -o umfpack_zl_report_status umfpack_report_status.c
+gcov -o umfpack_zl_report_symbolic umfpack_report_symbolic.c
+gcov -o umfpack_zl_report_triplet umfpack_report_triplet.c
+gcov -o umfpack_zl_report_vector umfpack_report_vector.c
+gcov -o umfpack_zl_save_numeric umfpack_save_numeric.c
+gcov -o umfpack_zl_save_symbolic umfpack_save_symbolic.c
+gcov -o umfpack_zl_scale umfpack_scale.c
+gcov -o umfpack_zl_symbolic umfpack_symbolic.c
+gcov -o umfpack_zl_transpose umfpack_transpose.c
+gcov -o umfpack_zl_triplet_to_col umfpack_triplet_to_col.c
+
+gcov -o umfpack_gn_tictoc umfpack_tictoc.c
+gcov -o umfpack_gn_timer umfpack_timer.c
+
+# multiple versions
+gcov -o umf_zl_uhsolve umf_utsolve.c ; mv -f umf_utsolve.c.gcov umf_uhsolve.c.gcov
+gcov -o umf_zl_utsolve umf_utsolve.c
+
+gcov -o umf_zl_lhsolve umf_ltsolve.c ; mv -f umf_ltsolve.c.gcov umf_lhsolve.c.gcov
+gcov -o umf_zl_ltsolve umf_ltsolve.c
+
+gcov -o umfpack_zl_wsolve umfpack_solve.c ; mv -f umfpack_solve.c.gcov umfpack_wsolve.c.gcov
+gcov -o umfpack_zl_solve umfpack_solve.c
+
+gcov -o umf_zl_store_lu_drop umf_store_lu.c ; mv -f umf_store_lu.c.gcov umf_store_lu_drop.c.gcov
+gcov -o umf_zl_store_lu umf_store_lu.c
+
+gcov -o umf_zl_assemble_fixq umf_assemble.c ; mv -f umf_assemble.c.gcov umf_assemble_fixq.c.gcov
+gcov -o umf_zl_assemble umf_assemble.c
+
+gcov -o umf_zl_triplet_map_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_x.c.gcov
+gcov -o umf_zl_triplet_nomap_x umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_x.c.gcov
+gcov -o umf_zl_triplet_map_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_map_nox.c.gcov
+gcov -o umf_zl_triplet_nomap_nox umf_triplet.c ; mv -f umf_triplet.c.gcov umf_triplet_nomap_nox.c.gcov
diff --git a/UMFPACK/Tcov/ut.c b/UMFPACK/Tcov/ut.c
new file mode 100644
index 0000000..57847f2
--- /dev/null
+++ b/UMFPACK/Tcov/ut.c
@@ -0,0 +1,7671 @@
+/* ========================================================================== */
+/* === umfpack tcov ========================================================= */
+/* ========================================================================== */
+
+/* -------------------------------------------------------------------------- */
+/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
+/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
+/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
+/* -------------------------------------------------------------------------- */
+
+/* (Nearly) exhaustive statement-coverage testing for UMFPACK. */
+
+/* #define DEBUGGING */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <sys/types.h>
+#include <dirent.h>
+#include <errno.h>
+#include "umfpack.h"
+#include "amd.h"
+#include "umf_internal.h"
+#include "umf_is_permutation.h"
+/*
+#include "umf_free.h"
+#include "umf_malloc.h"
+*/
+#include "umf_report_perm.h"
+#include "umf_realloc.h"
+#include "umf_free.h"
+#include "umf_malloc.h"
+
+/*
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+#include "umf_malloc.h"
+#endif
+*/
+
+#define TOL 1e-3
+
+#define INULL ((Int *) NULL)
+#define DNULL ((double *) NULL)
+
+#ifdef COMPLEX
+#define CARG(real,imag) real,imag
+#define C1ARG(a) ,a
+#else
+#define CARG(real,imag) real
+#define C1ARG(a)
+#endif
+
+
+int check_tol ;
+
+static double divide (double x, double y)
+{
+ return (x/y) ;
+}
+
+/* ========================================================================== */
+/* inv_umfpack_dense: inverse of UMFPACK_DENSE_COUNT */
+/* ========================================================================== */
+
+/* the inverse of UMFPACK_DENSE_COUNT: given a col count, find alpha */
+
+static double inv_umfpack_dense (Int d, Int n)
+{
+ if (d <= 16)
+ {
+ return (0.0) ;
+ }
+ else
+ {
+ return (((double) d) / (16 * sqrt ((double) n))) ;
+ }
+}
+
+
+/* ========================================================================== */
+
+
+static void dump_mat (char *name, Int m, Int n, Int Ap [ ], Int Ai [ ], double Ax [ ]
+#ifdef COMPLEX
+ , double Az [ ]
+#endif
+ )
+{
+ Entry aa ;
+ Int j, p ;
+
+ printf ("\n%s = sparse ("ID", "ID") ;\n", name, m, n) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+#ifdef COMPLEX
+ ASSIGN (aa, Ax, Az, p, SPLIT (Az)) ;
+ printf ("%s ("ID","ID") = %30.20g + (1i * %30.20g);\n",
+ name, 1+Ai [p], j+1, REAL_COMPONENT(aa), IMAG_COMPONENT(aa)) ;
+#else
+ printf ("%s ("ID","ID") = %30.20g ;\n",
+ name, 1+Ai [p], j+1, Ax [p]) ;
+#endif
+ }
+ }
+
+}
+
+/* ========================================================================== */
+
+static void dump_vec (char *name, Int n, double X [ ], double Xz[ ])
+{
+ Int j ;
+ printf ("\n%s = [\n", name) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf ("%30.20g", X [j]) ;
+ if (Xz) printf (" + (1i*%30.20g)", Xz[j]) ;
+ printf ("\n") ;
+ }
+ printf ("] ; \n") ;
+}
+
+/* ========================================================================== */
+
+static void dump_perm (char *name, Int n, Int P [ ])
+{
+ Int j ;
+ printf ("\n%s = [\n", name) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ printf (""ID"\n", 1+P [j]) ;
+ }
+ printf ("] ; \n") ;
+ printf ("%s = %s' ;\n", name, name) ;
+}
+
+/* ========================================================================== */
+/* error: display message and exit */
+/* ========================================================================== */
+
+static void error (char *s, double x)
+{
+ printf ("TEST FAILURE: %s %g ", s, x) ;
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ printf (" umf_malloc_count "ID"\n", UMF_malloc_count) ;
+#endif
+
+ printf ("\n") ;
+ exit (1) ;
+}
+
+/* ========================================================================== */
+/* resid: compute the (possibly permuted) residual. return maxnorm of resid */
+/* ========================================================================== */
+
+static double resid
+(
+ Int n,
+ Int Ap [ ],
+ Int Ai [ ],
+ double Ax [ ], double Az [ ],
+ double x [ ], double xz [ ],
+ double b [ ], double bz [ ],
+ double r [ ], double rz [ ],
+ Int transpose,
+ Int P [ ],
+ Int Q [ ],
+ double Wx [ ] /* size 2*n double workspace */
+)
+{
+ Int i, j, k, p ;
+ double norm, ra, *wx, *wz ;
+ Entry bb, xx, aa ;
+
+ wx = Wx ;
+ wz = wx + n ;
+
+/*
+ transpose: UMFPACK_A
+
+ r = P'AQ'x - b
+ Pr = AQ'x - Pb
+ we compute and return Pr, not r.
+
+ transpose: UMFPACK_At
+
+ r = QA'Px - b
+ Q'r = A'Px - Q'b
+ we compute and return Q'r, not r.
+
+ transpose: UMFPACK_Aat
+
+ r = QA.'Px - b
+ Q'r = A.'Px - Q'b
+ we compute and return Q'r, not r.
+
+*/
+
+ if (transpose == UMFPACK_A)
+ {
+
+ if (!P) /* r = -b */
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSIGN (bb, b, bz, i, SPLIT(bz)) ;
+ r [i] = -REAL_COMPONENT (bb) ;
+ rz[i] = -IMAG_COMPONENT (bb) ;
+ }
+ }
+ else /* r = -Pb */
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSIGN (bb, b, bz, P [k], SPLIT(bz)) ;
+ r [k] = -REAL_COMPONENT (bb) ;
+ rz[k] = -IMAG_COMPONENT (bb) ;
+ }
+ }
+
+ if (!Q) /* w = x */
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSIGN (xx, x, xz, j, SPLIT(xz)) ;
+ wx[j] = REAL_COMPONENT (xx) ;
+ wz[j] = IMAG_COMPONENT (xx) ;
+ }
+ }
+ else /* w = Q'x */
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSIGN (xx, x, xz, Q [k], SPLIT(xz)) ;
+ wx[k] = REAL_COMPONENT (xx) ;
+ wz[k] = IMAG_COMPONENT (xx) ;
+ }
+ }
+
+ /* r = r + Aw */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ ASSIGN (aa, Ax, Az, p, SPLIT(Az)) ;
+ r [i] += REAL_COMPONENT(aa) * wx[j] ;
+ r [i] -= IMAG_COMPONENT(aa) * wz[j] ;
+ rz[i] += IMAG_COMPONENT(aa) * wx[j] ;
+ rz[i] += REAL_COMPONENT(aa) * wz[j] ;
+ }
+ }
+
+ /* note that we just computed Pr, not r */
+
+ }
+ else if (transpose == UMFPACK_At)
+ {
+
+ if (!Q) /* r = -b */
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSIGN (bb, b, bz, i, SPLIT(bz)) ;
+ r [i] = -REAL_COMPONENT (bb) ;
+ rz[i] = -IMAG_COMPONENT (bb) ;
+ }
+ }
+ else /* r = -Q'b */
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSIGN (bb, b, bz, Q [k], SPLIT(bz)) ;
+ r [k] = -REAL_COMPONENT (bb) ;
+ rz[k] = -IMAG_COMPONENT (bb) ;
+ }
+ }
+
+ if (!P) /* w = x */
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSIGN (xx, x, xz, j, SPLIT(xz)) ;
+ wx[j] = REAL_COMPONENT (xx) ;
+ wz[j] = IMAG_COMPONENT (xx) ;
+ }
+ }
+ else /* w = Px */
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSIGN (xx, x, xz, P [k], SPLIT(xz)) ;
+ wx[k] = REAL_COMPONENT (xx) ;
+ wz[k] = IMAG_COMPONENT (xx) ;
+ }
+ }
+
+ /* r = r + A'w */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ ASSIGN (aa, Ax, Az, p, SPLIT(Az)) ;
+ /* complex conjugate */
+ r [j] += REAL_COMPONENT(aa) * wx[i] ;
+ r [j] += IMAG_COMPONENT(aa) * wz[i] ;
+ rz[j] -= IMAG_COMPONENT(aa) * wx[i] ;
+ rz[j] += REAL_COMPONENT(aa) * wz[i] ;
+ }
+ }
+
+ /* note that we just computed Q'r, not r */
+
+ }
+ else if (transpose == UMFPACK_Aat)
+ {
+
+ if (!Q) /* r = -b */
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSIGN (bb, b, bz, i, SPLIT(bz)) ;
+ r [i] = -REAL_COMPONENT (bb) ;
+ rz[i] = -IMAG_COMPONENT (bb) ;
+ }
+ }
+ else /* r = -Q'b */
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSIGN (bb, b, bz, Q [k], SPLIT(bz)) ;
+ r [k] = -REAL_COMPONENT (bb) ;
+ rz[k] = -IMAG_COMPONENT (bb) ;
+ }
+ }
+
+ if (!P) /* w = x */
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ ASSIGN (xx, x, xz, j, SPLIT(xz)) ;
+ wx[j] = REAL_COMPONENT (xx) ;
+ wz[j] = IMAG_COMPONENT (xx) ;
+ }
+ }
+ else /* w = Px */
+ {
+ for (k = 0 ; k < n ; k++)
+ {
+ ASSIGN (xx, x, xz, P [k], SPLIT(xz)) ;
+ wx[k] = REAL_COMPONENT (xx) ;
+ wz[k] = IMAG_COMPONENT (xx) ;
+ }
+ }
+
+ /* r = r + A.'w */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ i = Ai [p] ;
+ ASSIGN (aa, Ax, Az, p, SPLIT(Az)) ;
+ /* not complex conjugate */
+ r [j] += REAL_COMPONENT(aa) * wx[i] ;
+ r [j] -= IMAG_COMPONENT(aa) * wz[i] ;
+ rz[j] += IMAG_COMPONENT(aa) * wx[i] ;
+ rz[j] += REAL_COMPONENT(aa) * wz[i] ;
+ }
+ }
+
+ /* note that we just computed Q'r, not r */
+
+ }
+
+ norm = 0. ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Entry rr ;
+
+ /* --- */
+ /* ASSIGN (rr, r [i], rz [i]) ; */
+ ASSIGN (rr, r, rz, i, TRUE) ;
+ /* --- */
+
+ ABS (ra, rr) ;
+ norm = MAX (norm, ra) ;
+ }
+ return (norm) ;
+}
+
+
+/* ========================================================================== */
+/* irand: return a random Integer in the range 0 to n-1 */
+/* ========================================================================== */
+
+static Int irand (Int n)
+{
+ return (rand ( ) % n) ;
+}
+
+/* ========================================================================== */
+/* xrand: return a random double, > 0 and <= 1 */
+/* ========================================================================== */
+
+/* rand ( ) returns an Integer in the range 0 to RAND_MAX */
+
+static double xrand ( )
+{
+ return ((1.0 + (double) rand ( )) / (1.0 + (double) RAND_MAX)) ;
+}
+
+
+/* ========================================================================== */
+/* randperm: generate a random permutation of 0..n-1 */
+/* ========================================================================== */
+
+static void randperm (Int n, Int P [ ])
+{
+ Int i, t, k ;
+ for (i = 0 ; i < n ; i++)
+ {
+ P [i] = i ;
+ }
+ for (i = n-1 ; i > 0 ; i--)
+ {
+ k = irand (i) ;
+ /* swap positions i and k */
+ t = P [k] ;
+ P [k] = P [i] ;
+ P [i] = t ;
+ }
+}
+
+/* ========================================================================== */
+/* do_solvers: test Ax=b, etc */
+/* ========================================================================== */
+
+static double do_solvers
+(
+ Int n_row,
+ Int n_col,
+ Int Ap [ ],
+ Int Ai [ ],
+ double Ax [ ], double Az [ ],
+ double b [ ], double bz [ ],
+ double Control [ ],
+ double Info [ ],
+ void *Numeric,
+ Int Lp [ ],
+ Int Li [ ],
+ double Lx [ ], double Lz [ ],
+ Int Up [ ],
+ Int Ui [ ],
+ double Ux [ ], double Uz [ ],
+ Int P [ ],
+ Int Q [ ],
+ double x [ ], double xz [ ],
+ double r [ ], double rz [ ],
+ Int W [ ],
+ double Wx [ ],
+ Int split /* TRUE if complex variables split, FALSE if merged */
+)
+{
+ double maxrnorm = 0.0, rnorm, xnorm, xa, xaz, *Rb, *Rbz,
+ *y, *yz, *Rs, *Cx, *Cz ;
+ double Con [UMFPACK_CONTROL] ;
+ Int *noP = INULL, *noQ = INULL, irstep, orig, i, prl, status, n,
+ s1, s2, do_recip, *Cp, *Ci, nz, scale ;
+ Entry bb, xx, xtrue ;
+ NumericType *Num ;
+
+#ifdef COMPLEX
+ if (split)
+ {
+ if (!Az || !bz || !xz || !Lz || !Uz || !xz) error ("bad split\n", 0.) ;
+ }
+ else
+ {
+ if ( Az || bz || xz || Lz || Uz || xz) error ("bad merge\n", 0.) ;
+ }
+ /* rz is never passed to umfpack, and is always split in ut.c */
+ if (!rz) error ("bad rz\n", 0.) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* get parameters */
+ /* ---------------------------------------------------------------------- */
+
+ n = MAX (n_row, n_col) ;
+ if (n == 0) error ("n zero", 0.) ;
+ /* n = MAX (n,1) ; */
+ /* n_inner = MIN (n_row, n_col) ; */
+
+ if (Control)
+ {
+ orig = Control [UMFPACK_IRSTEP] ;
+ prl = Control [UMFPACK_PRL] ;
+ }
+ else
+ {
+ prl = UMFPACK_DEFAULT_PRL ;
+ }
+
+ if (n_row == n_col)
+ {
+ nz = Ap [n_col] ;
+ nz = MAX (nz, Lp [n_col]) ;
+ nz = MAX (nz, Up [n_col]) ;
+ Cp = (Int *) malloc ((n_col+1) * sizeof (Int)) ;
+ Ci = (Int *) malloc ((nz+1) * sizeof (Int)) ;
+ Cx = (double *) calloc (2*(nz+1) , sizeof (double)) ;
+ if (split)
+ {
+ Cz = Cx + nz ;
+ }
+ else
+ {
+ Cz = DNULL ;
+ }
+ if (!Cp || !Ci || !Cx) error ("out of memory (0)", 0.) ;
+ }
+ else
+ {
+ Cp = INULL ;
+ Ci = INULL ;
+ Cx = DNULL ;
+ }
+
+ Num = (NumericType *) Numeric ;
+ scale = (Num->Rs != DNULL) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* error handling */
+ /* ---------------------------------------------------------------------- */
+
+ if (n_row != n_col)
+ {
+ status = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az) , CARG(x,xz), CARG(b,bz), Numeric, DNULL, DNULL) ;
+ if (status != UMFPACK_ERROR_invalid_system) error ("rectangular Ax=b should have failed\n", 0.) ;
+ }
+ else
+ {
+ status = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az) , CARG(DNULL,xz), CARG(b,bz), Numeric, DNULL, DNULL) ;
+ if (status != UMFPACK_ERROR_argument_missing) error ("missing x should have failed\n", 0.) ;
+ status = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(DNULL,Az) , CARG(DNULL,xz), CARG(b,bz), Numeric, DNULL, DNULL) ;
+ if (status != UMFPACK_ERROR_argument_missing) error ("missing Ax should have failed\n", 0.) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Ax=b */
+ /* ---------------------------------------------------------------------- */
+
+ for (irstep = -1 ; irstep <= 3 ; irstep++)
+ {
+ if (Control)
+ {
+ for (i = 0 ; i < UMFPACK_CONTROL ; i++) Con [i] = Control [i] ;
+ }
+ else
+ {
+ UMFPACK_defaults (Con) ;
+ }
+ Con [UMFPACK_PRL] = prl ;
+ Con [UMFPACK_IRSTEP] = MAX (0, irstep) ;
+
+ if (prl >= 2) printf ("1: do solve: Ax=b: "ID"\n", irstep) ;
+ if (irstep == -1)
+ {
+ status = UMFPACK_solve (UMFPACK_A, INULL, INULL, CARG(DNULL,DNULL) , CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ;
+ }
+ else
+ {
+ status = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az) , CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ;
+ }
+ UMFPACK_report_status (Con, status) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (n_row != n_col)
+ {
+ if (status != UMFPACK_ERROR_invalid_system)
+ {
+ dump_mat ("A", n_row, n_col, Ap, Ai, CARG(Ax,Az)) ;
+ error ("rectangular Ax=b should have failed\n", 0.) ;
+ }
+ /* return immediately if the matrix is rectangular */
+ return (0.) ;
+ }
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ if (prl >= 2) printf ("Ax=b singular\n") ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ;
+ error ("Ax=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("1: rnorm Ax=b is %g\n", rnorm) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ /* compare x with xtrue */
+ xnorm = 0. ;
+ for (i = 0 ; i < n ; i++)
+ {
+ REAL_COMPONENT(xtrue) = 1.0 + ((double) i) / ((double) n) ;
+#ifdef COMPLEX
+ IMAG_COMPONENT(xtrue) = 1.3 - ((double) i) / ((double) n) ;
+#endif
+ /* --- */
+ /* ASSIGN (xx, x [i] - xtrue, xz[i]-xtruez) ; */
+ ASSIGN (xx, x, xz, i, SPLIT(xz)) ;
+ DECREMENT (xx, xtrue) ;
+ /* --- */
+
+ ABS (xa, xx) ;
+ xnorm = MAX (xnorm, xa) ;
+ }
+
+#if 0
+ { FILE *f ;
+ char s [200] ;
+ sprintf (s, "b_XXXXXX") ;
+ mkstemp (s) ;
+ f = fopen (s, "w") ;
+ for (i = 0 ; i < n ; i++) fprintf (f, "%40.25e %40.25e\n", b [i], bz [i]) ;
+ fclose (f) ;
+ s [0] = 'x' ;
+ f = fopen (s, "w") ;
+ for (i = 0 ; i < n ; i++) fprintf (f, "%40.25e %40.25e\n", x [i], xz [i]) ;
+ fclose (f) ;
+ }
+#endif
+
+ if (check_tol && (status == UMFPACK_OK && (rnorm > TOL || xnorm > TOL)))
+ {
+ Con [UMFPACK_PRL] = 5 ;
+ UMFPACK_report_control (Con) ;
+ printf ("Ax=b inaccurate %g %g\n", rnorm, xnorm) ;
+ dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ;
+ printf ("\nb: ") ;
+ UMFPACK_report_vector (n, CARG(b,bz), Con) ;
+ printf ("\nx: ") ;
+ UMFPACK_report_vector (n, CARG(x,xz), Con) ;
+ error ("Ax=b inaccurate", MAX (rnorm, xnorm)) ;
+ }
+
+ maxrnorm = MAX (xnorm, maxrnorm) ;
+ }
+
+#ifdef DEBUGGING
+ printf ("\n") ;
+#endif
+ if (prl >= 2) printf ("Ax=b irstep "ID" attempted %g\n", irstep, Info [UMFPACK_IR_ATTEMPTED]) ;
+ if (irstep > Info [UMFPACK_IR_ATTEMPTED])
+ {
+ break ;
+ }
+ }
+
+ if (n != n_row && n != n_col && n <= 0) error ("huh?", 0.) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* A'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ for (irstep = 0 ; irstep <= 3 ; irstep++)
+ {
+ if (Control)
+ {
+ for (i = 0 ; i < UMFPACK_CONTROL ; i++) Con [i] = Control [i] ;
+ }
+ else
+ {
+ UMFPACK_defaults (Con) ;
+ }
+ Con [UMFPACK_PRL] = prl ;
+ Con [UMFPACK_IRSTEP] = irstep ;
+
+ if (prl >= 2) printf ("do solve: A'x=b: "ID"\n", irstep) ;
+ status = UMFPACK_solve (UMFPACK_At, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ;
+ UMFPACK_report_status (Con, status) ;
+ /* UMFPACK_report_info (Con, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ if (prl >= 2) printf ("A'x=b singular\n") ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ;
+ error ("A'x=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_At, noP, noQ, Wx) ;
+
+ if (prl >= 2) printf ("2: rnorm A'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ Con [UMFPACK_PRL] = 99 ;
+ printf ("A'x=b inaccurate %g\n", rnorm) ;
+ dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ;
+ /*
+ printf ("\nA: ") ;
+ UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ printf ("\nb: ") ;
+ UMFPACK_report_vector (n, CARG(b,bz), Con) ;
+ printf ("\nx: ") ;
+ UMFPACK_report_vector (n, CARG(x,xz), Con) ;
+ error ("A'x=b inaccurate", MAX (rnorm, xnorm)) ;
+ */
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ /* also check using UMFPACK_transpose */
+ status = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(1)) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("transposed A'x=b failed\n", 0.) ;
+ }
+
+ rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+
+ if (prl >= 2) printf ("2b: rnorm A'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ Con [UMFPACK_PRL] = 99 ;
+ printf ("transpose A'x=b inaccurate %g\n", rnorm) ;
+ /*
+ printf ("\nA: ") ;
+ UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ printf ("\nb: ") ;
+ UMFPACK_report_vector (n, CARG(b,bz), Con) ;
+ printf ("\nx: ") ;
+ UMFPACK_report_vector (n, CARG(x,xz), Con) ;
+ error ("A'x=b inaccurate", MAX (rnorm, xnorm)) ;
+ */
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ }
+ if (prl >= 2) printf ("A'x=b irstep "ID" attempted %g\n", irstep, Info [UMFPACK_IR_ATTEMPTED]) ;
+ if (irstep > Info [UMFPACK_IR_ATTEMPTED])
+ {
+ break ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* A.'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ for (irstep = 0 ; irstep <= 3 ; irstep++)
+ {
+ if (Control)
+ {
+ for (i = 0 ; i < UMFPACK_CONTROL ; i++) Con [i] = Control [i] ;
+ }
+ else
+ {
+ UMFPACK_defaults (Con) ;
+ }
+ Con [UMFPACK_PRL] = prl ;
+ Con [UMFPACK_IRSTEP] = irstep ;
+
+ if (prl >= 2) printf ("do solve: A.'x=b: "ID"\n", irstep) ;
+ status = UMFPACK_solve (UMFPACK_Aat, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ;
+ UMFPACK_report_status (Con, status) ;
+ /* UMFPACK_report_info (Con, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ if (prl >= 2) printf ("A.'x=b singular\n") ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ;
+ error ("A.'x=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_Aat, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("3: rnorm A.'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ Con [UMFPACK_PRL] = 99 ;
+ printf ("A.'x=b inaccurate %g\n", rnorm) ;
+ /*
+ dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ;
+ printf ("\nA: ") ;
+ UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ printf ("\nb: ") ;
+ UMFPACK_report_vector (n, CARG(b,bz), Con) ;
+ printf ("\nx: ") ;
+ UMFPACK_report_vector (n, CARG(x,xz), Con) ;
+ error ("A.'x=b inaccurate %g\n", MAX (rnorm, xnorm)) ;
+ */
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ /* also check using UMFPACK_transpose */
+ status = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(0)) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("transposed A.'x=b failed\n", 0.) ;
+ }
+
+ rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+
+ if (prl >= 2) printf ("2b: rnorm A'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ Con [UMFPACK_PRL] = 99 ;
+ printf ("transpose A'x=b inaccurate %g\n", rnorm) ;
+ /*
+ printf ("\nA: ") ;
+ UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ printf ("\nb: ") ;
+ UMFPACK_report_vector (n, CARG(b,bz), Con) ;
+ printf ("\nx: ") ;
+ UMFPACK_report_vector (n, CARG(x,xz), Con) ;
+ error ("A'x=b inaccurate", MAX (rnorm, xnorm)) ;
+ */
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+ if (prl >= 2) printf ("A.'x=b irstep "ID" attempted %g\n", irstep, Info [UMFPACK_IR_ATTEMPTED]) ;
+ if (irstep > Info [UMFPACK_IR_ATTEMPTED])
+ {
+ break ;
+ }
+ }
+
+ if (Control)
+ {
+ for (i = 0 ; i < UMFPACK_CONTROL ; i++) Con [i] = Control [i] ;
+ }
+ else
+ {
+ UMFPACK_defaults (Con) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* wsolve Ax=b */
+ /* ---------------------------------------------------------------------- */
+
+ /* printf ("do wsolve: Ax=b:\n") ; */
+ if (Control) Control [UMFPACK_IRSTEP] = 1 ;
+ if (prl >= 2) printf ("2: do solve: Ax=b: "ID" (wsolve) \n", irstep) ;
+ status = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info, W, Wx) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ if (prl >= 2) printf ("Ax=b wsolve singular\n") ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ;
+ error ("Ax=b wsolve failure\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("4: rnorm Ax=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ;
+ error ("wsolve inaccurate %g\n", rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+
+ if (Control) Control [UMFPACK_IRSTEP] = orig ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ /*
+ prl = 999 ;
+ */
+
+ Rs = (double *) malloc (n * sizeof (double)) ; /* [ */
+ Rb = (double *) calloc (2*n , sizeof (double)) ; /* [ */
+ y = (double *) calloc (2*n , sizeof (double)) ; /* [ */
+
+ /* ---------------------------------------------------------------------- */
+ /* Ax=b with individual calls */
+ /* ---------------------------------------------------------------------- */
+
+ if (split)
+ {
+ yz = y + n ;
+ Rbz = Rb + n ;
+ }
+ else
+ {
+ yz = DNULL ;
+ Rbz = DNULL ;
+ }
+
+ /* status = UMFPACK_get_scale (Rs, Numeric) ; */
+ status = UMFPACK_get_numeric (
+ INULL, INULL, CARG(DNULL,DNULL),
+ INULL, INULL, CARG(DNULL,DNULL),
+ INULL, INULL, CARG (DNULL,DNULL), &do_recip, Rs, Numeric) ;
+ if (status != UMFPACK_OK) error ("get Rs failed", (double) status) ;
+
+ /*
+ printf ("Rs:\n") ;
+ for (i = 0 ; i < n ; i++)
+ {
+ printf (" Rs [%d] = %g\n", i, Rs [i]) ;
+ }
+ */
+
+ if (prl >= 2) printf ("3: do solve: Ax=b in different steps:\n") ;
+ /* Rb = R*b */
+ /* dump_vec ("b", n, b, bz) ; */
+ status = UMFPACK_scale (CARG (Rb, Rbz), CARG (b,bz), Numeric) ;
+ if (status != UMFPACK_OK) error ("Rb failed", (double) status) ;
+ /* dump_vec ("R*b", n, Rb, Rbz) ; */
+
+ /*
+ UMFPACK_defaults (Con) ;
+ Con [UMFPACK_PRL] = 999 ;
+ printf ("Rb:\n") ;
+ UMFPACK_report_vector (n, CARG(Rb,Rbz), Con) ;
+ printf ("b:\n") ;
+ UMFPACK_report_vector (n, CARG(b,bz), Con) ;
+ error ("finish early\n", rnorm) ;
+ */
+
+ /* solve Ly = P*(Rb) */
+ s1 = UMFPACK_solve (UMFPACK_Pt_L, Ap, Ai, CARG(Ax,Az), CARG(y,yz), CARG(Rb,Rbz), Numeric, Control, Info) ;
+ if (! (s1 == UMFPACK_OK || s1 == UMFPACK_WARNING_singular_matrix))
+ {
+ error ("P'Ly=Rb failed", (double) status) ;
+ }
+ /* solve UQ'x=y */
+ s2 = UMFPACK_solve (UMFPACK_U_Qt, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(y,yz), Numeric, Control, Info) ;
+ if (! (s2 == UMFPACK_OK || s2 == UMFPACK_WARNING_singular_matrix))
+ {
+ error ("UQ'x=y failed", (double) status) ;
+ }
+ if (s1 == UMFPACK_OK && s2 == UMFPACK_OK)
+ {
+ rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("5: rnorm Ax=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ /* error ("Ax=b (different steps) inaccurate ", rnorm) ; */
+ printf ("Ax=b (different steps) inaccurate %g !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!", rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+
+ if (prl >= 2) printf ("4: do solve: Ax=b, different steps, own scale:\n") ;
+ /* Rb = R*b */
+
+ if (do_recip)
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSIGN (bb, b, bz, i, SPLIT(bz)) ;
+ SCALE (bb, Rs [i]) ;
+
+ if (split)
+ {
+ Rb [i] = REAL_COMPONENT(bb) ;
+ Rbz [i] = IMAG_COMPONENT(bb) ;
+ }
+ else
+ {
+ Rb [2*i] = REAL_COMPONENT(bb) ;
+ Rb [2*i+1] = IMAG_COMPONENT(bb) ;
+ }
+
+ /*
+ Rb [i] = REAL_COMPONENT(bb) * Rs [i] ;
+ Rbz [i] = IMAG_COMPONENT(bb) * Rs [i] ;
+ */
+ }
+ }
+ else
+ {
+ for (i = 0 ; i < n ; i++)
+ {
+ ASSIGN (bb, b, bz, i, SPLIT(bz)) ;
+ SCALE_DIV (bb, Rs [i]) ;
+
+ if (split)
+ {
+ Rb [i] = REAL_COMPONENT(bb) ;
+ Rbz [i] = IMAG_COMPONENT(bb) ;
+ }
+ else
+ {
+ Rb [2*i] = REAL_COMPONENT(bb) ;
+ Rb [2*i+1] = IMAG_COMPONENT(bb) ;
+ }
+
+ /*
+ Rb [i] = REAL_COMPONENT(bb) / Rs [i] ;
+ Rbz [i] = IMAG_COMPONENT(bb) / Rs [i] ;
+ */
+ }
+ }
+
+ /* solve Ly = P*(Rb) */
+ s1 = UMFPACK_solve (UMFPACK_Pt_L, Ap, Ai, CARG(Ax,Az), CARG(y,yz), CARG(Rb,Rbz), Numeric, Control, Info) ;
+ if (! (s1 == UMFPACK_OK || s1 == UMFPACK_WARNING_singular_matrix))
+ {
+ error ("P'Ly=Rb failed", (double) status) ;
+ }
+ /* solve UQ'x=y */
+ s2 = UMFPACK_solve (UMFPACK_U_Qt, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(y,yz), Numeric, Control, Info) ;
+ if (! (s2 == UMFPACK_OK || s2 == UMFPACK_WARNING_singular_matrix))
+ {
+ error ("UQ'x=y failed", (double) status) ;
+ }
+ if (s1 == UMFPACK_OK && s2 == UMFPACK_OK)
+ {
+ rnorm = resid (n, Ap, Ai, Ax, Az, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("6: rnorm Ax=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ error ("Ax=b (different steps, own scale) inaccurate ", rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* (PAQ)'x=b with individual calls, no scaling */
+ /* ---------------------------------------------------------------------- */
+
+ if (!scale)
+ {
+ int k ;
+
+ s1 = UMFPACK_solve (UMFPACK_Ut, Ap, Ai, CARG(Ax,Az), CARG(y,yz), CARG(b,bz), Numeric, Control, Info) ;
+ if (! (s1 == UMFPACK_OK || s1 == UMFPACK_WARNING_singular_matrix))
+ {
+ error ("U'y=b failed", (double) status) ;
+ }
+ s2 = UMFPACK_solve (UMFPACK_Lt, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(y,yz), Numeric, Control, Info) ;
+ if (! (s2 == UMFPACK_OK || s2 == UMFPACK_WARNING_singular_matrix))
+ {
+ error ("L'x=y failed", (double) status) ;
+ }
+
+ /* check using UMFPACK_transpose */
+ if (s1 == UMFPACK_OK && s2 == UMFPACK_OK)
+ {
+ status = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), P, Q, Cp, Ci, CARG(Cx,Cz) C1ARG(1)) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("transposed (PAQ)'x=b failed\n", 0.) ;
+ }
+ rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("99b: rnorm (PAQ)'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ;
+ dump_mat ("C", n, n, Cp, Ci, CARG(Cx,Cz)) ;
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ printf ("P = [ ") ; for (k = 0 ; k < n ; k++) printf ("%d ", P [k]) ; printf ("]\n") ;
+ printf ("Q = [ ") ; for (k = 0 ; k < n ; k++) printf ("%d ", Q [k]) ; printf ("]\n") ;
+ error ("transposed (PAQ)'x=b inaccurate\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* (PAQ).'x=b with individual calls, no scaling */
+ /* ---------------------------------------------------------------------- */
+
+ if (!scale)
+ {
+ int k ;
+
+ s1 = UMFPACK_solve (UMFPACK_Uat, Ap, Ai, CARG(Ax,Az), CARG(y,yz), CARG(b,bz), Numeric, Control, Info) ;
+ if (! (s1 == UMFPACK_OK || s1 == UMFPACK_WARNING_singular_matrix))
+ {
+ error ("U'y=b failed", (double) status) ;
+ }
+ s2 = UMFPACK_solve (UMFPACK_Lat, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(y,yz), Numeric, Control, Info) ;
+ if (! (s2 == UMFPACK_OK || s2 == UMFPACK_WARNING_singular_matrix))
+ {
+ error ("L'x=y failed", (double) status) ;
+ }
+
+ /* check using UMFPACK_transpose */
+ if (s1 == UMFPACK_OK && s2 == UMFPACK_OK)
+ {
+ status = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), P, Q, Cp, Ci, CARG(Cx,Cz) C1ARG(0)) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("transposed (PAQ).'x=b failed\n", 0.) ;
+ }
+ rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ /* printf ("98b: rnorm (PAQ)'x=b is %g\n", rnorm) ; */
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("A", n, n, Ap, Ai, CARG(Ax,Az)) ;
+ dump_mat ("C", n, n, Cp, Ci, CARG(Cx,Cz)) ;
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ printf ("P = [ ") ; for (k = 0 ; k < n ; k++) printf ("%d ", P [k]) ; printf ("]\n") ;
+ printf ("Q = [ ") ; for (k = 0 ; k < n ; k++) printf ("%d ", Q [k]) ; printf ("]\n") ;
+ error ("transposed (PAQ).'x=b inaccurate\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+ }
+
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ free (y) ; /* ] */
+ free (Rb) ; /* ] */
+ free (Rs) ; /* ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* Lx=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: Lx=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_L, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ error ("Lx=b solve singular!", 0.) ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("Lx=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("7: rnorm Lx=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("Lx=b inaccurate %g", rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* L'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: L'x=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_Lt, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("L'x=b solve singular!", 0.) ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("L'x=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_At, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("7: rnorm L'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("L'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ /* also check using UMFPACK_transpose */
+ status = UMFPACK_transpose (n, n, Lp, Li, CARG(Lx,Lz), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(1)) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("transposed L'x=b failed\n", 0.) ;
+ }
+ rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("7b: rnorm L'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("transposed L'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* L.'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: L.'x=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_Lat, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("L.'x=b solve singular!", 0.) ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("L.'x=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_Aat, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("8: rnorm L.'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("L.'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ /* also check using UMFPACK_transpose */
+ status = UMFPACK_transpose (n, n, Lp, Li, CARG(Lx,Lz), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(0)) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("transposed L'x=b failed\n", 0.) ;
+ }
+ rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("8b: rnorm L'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("8b transposed L'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* Ux=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: Ux=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_U, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ if (prl >= 2) printf ("Ux=b solve singular\n") ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("Ux=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("9: rnorm Ux=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("Ux=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* U'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: U'x=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_Ut, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ if (prl >= 2) printf ("U'x=b solve singular\n") ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("U'x=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_At, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("10: rnorm U'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("U'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ /* also check using UMFPACK_transpose */
+ status = UMFPACK_transpose (n, n, Up, Ui, CARG(Ux,Uz), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(1)) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("transposed U'x=b failed\n", 0.) ;
+ }
+ rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("10b: rnorm U'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("10b transposed U'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* U.'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: U.'x=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_Uat, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ if (prl >= 2) printf ("U.'x=b solve singular\n") ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("U.'x=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_Aat, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("11: rnorm U.'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("U.'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ /* also check using UMFPACK_transpose */
+ status = UMFPACK_transpose (n, n, Up, Ui, CARG(Ux,Uz), noP, noQ, Cp, Ci, CARG(Cx,Cz) C1ARG(0)) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("11b transposed U.'x=b failed\n", 0.) ;
+ }
+ rnorm = resid (n, Cp, Ci, Cx, Cz, x, xz, b, bz, r, rz, UMFPACK_A, noP, noQ, Wx) ;
+ if (prl >= 2) printf ("11b: rnorm U'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("11b transposed U'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* P'Lx=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: P'Lx=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_Pt_L, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("P'Lx=b solve singular!", 0.) ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("P'Lx=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_A, P, noQ, Wx) ;
+ if (prl >= 2) printf ("12: rnorm P'Lx=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("P'Lx=b inaccurate: %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* L'Px=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: L'Px=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_Lt_P, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ error ("L'Px=b solve singular!", 0.) ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("L'Px=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_At, P, noQ, Wx) ;
+ if (prl >= 2) printf ("13: rnorm L'Px=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("L'Px=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* L.'Px=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: L.'Px=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_Lat_P, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ error ("L.'Px=b solve singular!", 0.) ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("L.'Px=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Lp, Li, Lx, Lz, x, xz, b, bz, r, rz, UMFPACK_Aat, P, noQ, Wx) ;
+ if (prl >= 2) printf ("14: rnorm L.'Px=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("L", n, n, Lp, Li, CARG(Lx,Lz)) ;
+ error ("L.'Px=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* UQ'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: UQ'x=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_U_Qt, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ if (prl >= 2) printf ("UQ'x=b solve singular\n") ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("UQ'x=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_A, noP, Q, Wx) ;
+ if (prl >= 2) printf ("15: rnorm UQ'x=b is %g\n", rnorm) ;
+ if (check_tol && status == UMFPACK_OK && rnorm > TOL)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("UQ'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* QU'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: QU'x=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_Q_Ut, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ if (prl >= 2) printf ("QU'x=b solve singular\n") ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("QU'x=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_At, noP, Q, Wx) ;
+ if (prl >= 2) printf ("16: rnorm QU'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("QU'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* QU.'x=b */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl >= 2) printf ("do solve: QU.'x=b:\n") ;
+ status = UMFPACK_solve (UMFPACK_Q_Uat, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ /* UMFPACK_report_info (Control, Info) ; */
+ if (status == UMFPACK_WARNING_singular_matrix)
+ {
+ if (prl >= 2) printf ("QU.'x=b solve singular\n") ;
+ }
+ else if (status != UMFPACK_OK)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("QU.'x=b failed\n", 0.) ;
+ }
+ else
+ {
+ rnorm = resid (n, Up, Ui, Ux, Uz, x, xz, b, bz, r, rz, UMFPACK_Aat, noP, Q, Wx) ;
+ if (prl >= 2) printf ("17: rnorm QU.'x=b is %g\n", rnorm) ;
+ if (check_tol && rnorm > TOL)
+ {
+ dump_mat ("U", n, n, Up, Ui, CARG(Ux,Uz)) ;
+ error ("QU.'x=b inaccurate %g\n",rnorm) ;
+ }
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* done */
+ /* ---------------------------------------------------------------------- */
+
+ if (n_row == n_col)
+ {
+ free (Cp) ;
+ free (Ci) ;
+ free (Cx) ;
+ }
+ return (maxrnorm) ;
+}
+
+
+/* ========================================================================== */
+/* do_symnum: factor A once, and then test the solves - return if error */
+/* ========================================================================== */
+
+static double do_symnum
+(
+ Int n_row,
+ Int n_col,
+ Int Ap [ ],
+ Int Ai [ ],
+ double Ax [ ], double Az [ ],
+ double b [ ], double bz [ ],
+ double Control [ ],
+ Int Qinit [ ],
+ double x [ ], double xz [ ],
+ double r [ ], double rz [ ],
+ double Wx [ ],
+ Int P [ ],
+ Int Q [ ],
+ Int Qtree [ ],
+ Int Ptree [ ],
+ Int W [ ],
+ Int Lp [ ],
+ Int Up [ ],
+ Int save_and_load,
+ Int split, /* TRUE if complex variables split, FALSE if merged */
+ Int det_check, double det_x, double det_z
+)
+{
+ void *Symbolic, *Numeric ;
+ double *Lx, *Ux, *Lz, *Uz, rnorm, *Rs ;
+ Int *noP = INULL, *noQ = INULL, *Li, *Ui, n, n_inner, n1, do_recip ;
+ Int lnz, unz, nz, nn, nfr, nchains, nsparse_col, status ;
+ Int *Front_npivots, *Front_parent, *Chain_start, *Chain_maxrows ;
+ Int *Chain_maxcols, *Lrowi, *Lrowp, is_singular ;
+ double Info [UMFPACK_INFO], *Lrowx, *Lrowz, *Dx, *Dz ;
+ Int nnrow, nncol, nzud, *Front_1strow, *Front_leftmostdesc, prl, i ;
+ double mind, maxd, rcond ;
+ Entry d ;
+ double da, deterr ;
+ NumericType *Num ;
+ SymbolicType *Sym ;
+ double Mx [2], Mz, Exp ;
+
+#ifdef COMPLEX
+ if (split)
+ {
+ if (!Az || !bz || !xz) error ("bad split\n", 0.) ;
+ }
+ else
+ {
+ if ( Az || bz || xz) error ("bad merge\n", 0.) ;
+ }
+ if (!rz) error ("bad rz\n", 0.) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* do the symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ prl = Control ? Control [UMFPACK_PRL] : UMFPACK_DEFAULT_PRL ;
+
+ n = MAX (n_row, n_col) ;
+ n = MAX (n,1) ;
+ n_inner = MIN (n_row, n_col) ;
+
+ if (prl > 2)
+ {
+ printf ("\nA::\n") ;
+ status = UMFPACK_report_matrix (n_row, n_col, Ap, Ai, CARG(Ax,Az), 1, Control) ;
+ printf ("\nb::\n") ;
+ if (n_row == n_col) UMFPACK_report_vector (n, CARG(b,bz), Control) ;
+ }
+
+ if (Qinit)
+ {
+ /* dump_perm ("Qinit", n_col, Qinit) ; */
+ status = UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ; /* ( */
+ }
+ else
+ {
+ status = UMFPACK_symbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), &Symbolic, Control, Info) ;
+ }
+
+ UMFPACK_report_status (Control, status) ;
+ UMFPACK_report_info (Control, Info) ;
+
+ if (!Symbolic)
+ {
+ UMFPACK_report_info (Control, Info) ;
+ error ("symbolic invalid\n", 0.) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* test save and load */
+ /* ---------------------------------------------------------------------- */
+
+ status = UMFPACK_save_symbolic (Symbolic, "s.umf") ;
+ if (status != UMFPACK_OK)
+ {
+ error ("save symbolic failed\n", 0.) ;
+ }
+ UMFPACK_free_symbolic (&Symbolic) ;
+ status = UMFPACK_load_symbolic (&Symbolic, "s.umf") ;
+ if (status != UMFPACK_OK)
+ {
+ error ("load symbolic failed\n", 0.) ;
+ }
+
+ if (n < 15)
+ {
+
+ int umf_fail_save [3], memcnt ;
+
+ status = UMFPACK_save_symbolic (Symbolic, (char *) NULL) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("save symbolic failed\n", 0.) ;
+ }
+ UMFPACK_free_symbolic (&Symbolic) ;
+ status = UMFPACK_load_symbolic (&Symbolic, (char *) NULL) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("load symbolic failed\n", 0.) ;
+ }
+
+ /* test memory handling */
+ umf_fail_save [0] = umf_fail ;
+ umf_fail_save [1] = umf_fail_lo ;
+ umf_fail_save [2] = umf_fail_hi ;
+
+ umf_fail = -1 ;
+ umf_fail_lo = 0 ;
+ umf_fail_hi = 0 ;
+
+ UMFPACK_free_symbolic (&Symbolic) ;
+ status = UMFPACK_load_symbolic (&Symbolic, (char *) NULL) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("load symbolic failed\n", 0.) ;
+ }
+
+ Sym = (SymbolicType *) Symbolic ;
+
+ memcnt = 12 ;
+ if (Sym->esize > 0)
+ {
+ memcnt++ ;
+ }
+ if (Sym->prefer_diagonal > 0)
+ {
+ memcnt++ ;
+ }
+
+ for (i = 1 ; i <= memcnt ; i++)
+ {
+ umf_fail = i ;
+ UMFPACK_free_symbolic (&Symbolic) ;
+ status = UMFPACK_load_symbolic (&Symbolic, (char *) NULL) ;
+ if (status != UMFPACK_ERROR_out_of_memory)
+ {
+ error ("load symbolic should have failed\n", 0.) ;
+ }
+ }
+
+ umf_fail = memcnt + 1 ;
+
+ UMFPACK_free_symbolic (&Symbolic) ;
+ status = UMFPACK_load_symbolic (&Symbolic, (char *) NULL) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("load symbolic failed (edge)\n", 0.) ;
+ }
+
+ umf_fail = umf_fail_save [0] ;
+ umf_fail_lo = umf_fail_save [1] ;
+ umf_fail_hi = umf_fail_save [2] ;
+
+ UMFPACK_free_symbolic (&Symbolic) ;
+ status = UMFPACK_load_symbolic (&Symbolic, "s.umf") ;
+ if (status != UMFPACK_OK)
+ {
+ error ("load symbolic failed\n", 0.) ;
+ }
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the symbolic factorization */
+ /* ---------------------------------------------------------------------- */
+
+ if (prl > 2) printf ("\nSymbolic: ") ;
+ status = UMFPACK_report_symbolic (Symbolic, Control) ;
+ if (status != UMFPACK_OK)
+ {
+ UMFPACK_free_symbolic (&Symbolic) ;
+ error ("bad symbolic report\n", 0.) ;
+ }
+
+ Front_npivots = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Front_parent = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Front_1strow = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Front_leftmostdesc = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Chain_start = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Chain_maxrows = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Chain_maxcols = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+
+ if (!Front_npivots || !Front_parent || !Chain_start || !Chain_maxrows
+ || !Front_leftmostdesc || !Front_1strow
+ || !Chain_maxcols || !Qtree || !Ptree) error ("out of memory (1)",0.) ;
+
+ status = UMFPACK_get_symbolic (&nnrow, &nncol, &n1, &nz, &nfr, &nchains,
+ Ptree, Qtree, Front_npivots, Front_parent, Front_1strow, Front_leftmostdesc,
+ Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ;
+
+ if (status != UMFPACK_OK)
+ {
+ UMFPACK_report_info (Control, Info) ;
+ error ("get symbolic failed\n", 0.) ;
+ }
+
+ free (Chain_maxcols) ; /* ] */
+ free (Chain_maxrows) ; /* ] */
+ free (Chain_start) ; /* ] */
+ free (Front_leftmostdesc) ; /* ] */
+ free (Front_1strow) ; /* ] */
+ free (Front_parent) ; /* ] */
+ free (Front_npivots) ; /* ] */
+
+ if (!UMF_is_permutation (Qtree, W, n_col, n_col)) { error ("Qtree invalid\n", 0.) ; }
+ if (!UMF_is_permutation (Ptree, W, n_row, n_row)) { error ("Ptree invalid\n", 0.) ; }
+
+ /* ---------------------------------------------------------------------- */
+ /* do the numerical factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; /* [ */
+ if (status != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ is_singular = (status == UMFPACK_WARNING_singular_matrix) ;
+
+ UMFPACK_report_status (Control, status) ;
+ UMFPACK_report_info (Control, Info) ;
+
+ UMFPACK_free_symbolic (&Symbolic) ; /* ) */
+
+ if (!Numeric)
+ {
+ /* printf ("numeric bad: %g\n", Control [UMFPACK_ALLOC_INIT]) ; */
+ fflush (stdout) ;
+ return (9e10) ;
+ }
+
+ if (prl > 2) printf ("Numeric: ") ;
+ status = UMFPACK_report_numeric (Numeric, Control) ;
+ if (status != UMFPACK_OK)
+ {
+ UMFPACK_free_numeric (&Numeric) ;
+ error ("bad numeric report\n", 0.) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the determinant */
+ /* ---------------------------------------------------------------------- */
+
+ Mx [0] = 0. ;
+ Mx [1] = 0. ;
+ Mz = 0. ;
+ Exp = 0. ;
+
+ for (i = 0 ; i <= 3 ; i++)
+ {
+ if (i == 0)
+ {
+ status = UMFPACK_get_determinant (CARG (Mx, &Mz), &Exp, Numeric,
+ Info) ;
+ }
+ else if (i == 1)
+ {
+ status = UMFPACK_get_determinant (CARG (Mx, &Mz), &Exp, Numeric,
+ DNULL) ;
+ }
+ else if (i == 2)
+ {
+ status = UMFPACK_get_determinant (CARG (Mx, &Mz), DNULL, Numeric,
+ Info) ;
+ }
+ else if (i == 3)
+ {
+ status = UMFPACK_get_determinant (CARG (Mx, DNULL), DNULL, Numeric,
+ Info) ;
+ }
+ if (n_row == n_col)
+ {
+ if (status != UMFPACK_OK)
+ {
+ error ("bad det\n", 0.) ;
+ }
+ if (det_check && SCALAR_ABS (det_x < 1e100))
+ {
+
+ if (i == 0 || i == 1)
+ {
+ deterr = SCALAR_ABS (det_x - (Mx [0] * pow (10.0, Exp))) ;
+ }
+ else if (i == 2 || i == 3)
+ {
+ deterr = SCALAR_ABS (det_x - Mx [0]) ;
+ }
+
+ if (deterr > 1e-7)
+ {
+ printf ("det: real err %g i: %d\n", deterr, i) ;
+ error ("det: bad real part", det_x) ;
+ }
+
+#ifdef COMPLEX
+
+ if (i == 0 || i == 1)
+ {
+ deterr = SCALAR_ABS (det_z - (Mz * pow (10.0, Exp))) ;
+ }
+ else if (i == 2)
+ {
+ deterr = SCALAR_ABS (det_z - Mz) ;
+ }
+ else if (i == 3)
+ {
+ deterr = SCALAR_ABS (det_z - Mx [1]) ;
+ }
+
+ if (deterr > 1e-7)
+ {
+ printf ("det: imag err %g\n", deterr) ;
+ error ("det: bad imag part", det_z) ;
+ }
+#endif
+ }
+ }
+ else
+ {
+ if (status != UMFPACK_ERROR_invalid_system)
+ {
+ error ("bad det (rectangluar)\n", 0.) ;
+ }
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* test save and load */
+ /* ---------------------------------------------------------------------- */
+
+ status = UMFPACK_save_numeric (Numeric, "n.umf") ;
+ if (status != UMFPACK_OK)
+ {
+ error ("save numeric failed\n", 0.) ;
+ }
+ UMFPACK_free_numeric (&Numeric) ;
+ status = UMFPACK_load_numeric (&Numeric, "n.umf") ;
+ if (status != UMFPACK_OK)
+ {
+ error ("load numeric failed\n", 0.) ;
+ }
+
+ if (n < 15)
+ {
+ int umf_fail_save [3], memcnt ;
+
+ status = UMFPACK_save_numeric (Numeric, (char *) NULL) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("save numeric failed\n", 0.) ;
+ }
+ UMFPACK_free_numeric (&Numeric) ;
+ status = UMFPACK_load_numeric (&Numeric, (char *) NULL) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("load numeric failed\n", 0.) ;
+ }
+
+ /* test memory handling */
+ umf_fail_save [0] = umf_fail ;
+ umf_fail_save [1] = umf_fail_lo ;
+ umf_fail_save [2] = umf_fail_hi ;
+
+ umf_fail = -1 ;
+ umf_fail_lo = 0 ;
+ umf_fail_hi = 0 ;
+
+ UMFPACK_free_numeric (&Numeric) ;
+ status = UMFPACK_load_numeric (&Numeric, (char *) NULL) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("load numeric failed\n", 0.) ;
+ }
+
+ Num = (NumericType *) Numeric ;
+
+ memcnt = 11 ;
+ if (Num->scale != UMFPACK_SCALE_NONE)
+ {
+ memcnt++ ;
+ }
+ if (Num->ulen > 0)
+ {
+ memcnt++ ;
+ }
+
+ for (i = 1 ; i <= memcnt ; i++)
+ {
+ umf_fail = i ;
+ UMFPACK_free_numeric (&Numeric) ;
+ status = UMFPACK_load_numeric (&Numeric, (char *) NULL) ;
+ if (status != UMFPACK_ERROR_out_of_memory)
+ {
+ error ("load numeric should have failed\n", 0.) ;
+ }
+ }
+
+ umf_fail = memcnt + 1 ;
+
+ UMFPACK_free_numeric (&Numeric) ;
+ status = UMFPACK_load_numeric (&Numeric, (char *) NULL) ;
+ if (status != UMFPACK_OK)
+ {
+ printf ("memcnt %d\n", memcnt) ;
+ error ("load numeric failed (edge)\n", 0.) ;
+ }
+
+ umf_fail = umf_fail_save [0] ;
+ umf_fail_lo = umf_fail_save [1] ;
+ umf_fail_hi = umf_fail_save [2] ;
+
+ UMFPACK_free_numeric (&Numeric) ;
+ status = UMFPACK_load_numeric (&Numeric, "n.umf") ;
+ if (status != UMFPACK_OK)
+ {
+ error ("load numeric failed\n", 0.) ;
+ }
+
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* get the LU factorization */
+ /* ---------------------------------------------------------------------- */
+
+ status = UMFPACK_get_lunz (&lnz, &unz, &nnrow, &nncol, &nzud, Numeric) ;
+ if (status != UMFPACK_OK)
+ {
+ UMFPACK_report_info (Control, Info) ;
+ error ("get lunz failure\n", 0.) ;
+ UMFPACK_free_numeric (&Numeric) ;
+ }
+
+ /* guard against malloc of zero-sized arrays */
+ lnz = MAX (lnz,1) ;
+ unz = MAX (unz,1) ;
+
+ Rs = (double *) malloc ((n+1) * sizeof (double)) ; /* [ */
+ Li = (Int *) malloc (lnz * sizeof (Int)) ; /* [ */
+ Lx = (double *) calloc (2*lnz , sizeof (double)) ; /* [ */
+ Ui = (Int *) malloc (unz * sizeof (Int)) ; /* [ */
+ Ux = (double *) calloc (2*unz , sizeof (double)) ; /* [ */
+ Dx = (double *) calloc (2*n , sizeof (double)) ; /* [ */
+
+ Lrowp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Lrowi = (Int *) malloc (lnz * sizeof (Int)) ; /* [ */
+ Lrowx = (double *) calloc (2*lnz , sizeof (double)) ; /* [ */
+
+ if (!Li || !Lx || !Ui || !Ux || !Lrowp || !Lrowi || !Lrowx) error ("out of memory (2)\n",0.) ;
+
+ if (split)
+ {
+ Dz = Dx + n ;
+ Lrowz = Lrowx + lnz ;
+ Lz = Lx + lnz ;
+ Uz = Ux + unz ;
+ }
+ else
+ {
+ Dz = DNULL ;
+ Lrowz = DNULL ;
+ Lz = DNULL ;
+ Uz = DNULL ;
+ }
+
+ status = UMFPACK_get_numeric (Lrowp, Lrowi, CARG(Lrowx,Lrowz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(Dx,Dz), &do_recip, Rs, Numeric) ;
+ if (status != UMFPACK_OK)
+ {
+ UMFPACK_report_info (Control, Info) ;
+ error ("get LU failed\n", 0.) ;
+ }
+
+ if (!UMF_is_permutation (P, W, n_row, n_row)) { error ("P invalid\n", 0.) ; }
+ if (!UMF_is_permutation (Q, W, n_col, n_col)) { error ("Q invalid\n", 0.) ; }
+ if (prl > 2) printf ("\nP: ") ;
+ status = UMFPACK_report_perm (n_row, P, Control) ;
+ if (status != UMFPACK_OK) { error ("bad P 1\n", 0.) ; }
+ if (prl > 2) printf ("\nQ: ") ;
+ status = UMFPACK_report_perm (n_col, Q, Control) ;
+ if (status != UMFPACK_OK) { error ("bad Q 1\n", 0.) ; }
+
+ if (prl > 2) printf ("\nL row: ") ;
+ status = UMFPACK_report_matrix (n_row, n_inner, Lrowp, Lrowi, CARG(Lrowx,Lrowz), 0, Control) ;
+ if (status != UMFPACK_OK) { error ("bad Lrow\n", 0.) ; }
+
+ if (prl > 2) printf ("\nD, diag of U: ") ;
+ status = UMFPACK_report_vector (n_inner, CARG(Dx,Dz), Control) ;
+ if (status != UMFPACK_OK) { error ("bad D\n", 0.) ; }
+
+ /* --- */
+ /* ASSIGN (d, Dx [0], Dz [0]) ; */
+ ASSIGN (d, Dx, Dz, 0, SPLIT(Dz)) ;
+ /* --- */
+
+ ABS (da, d) ;
+ mind = da ;
+ maxd = da ;
+ for (i = 1 ; i < n_inner ; i++)
+ {
+ /* --- */
+ /* ASSIGN (d, Dx [i], Dz [i]) ; */
+ ASSIGN (d, Dx, Dz, i, SPLIT(Dz)) ;
+ /* --- */
+
+ ABS (da, d) ;
+ mind = MIN (mind, da) ;
+ maxd = MAX (maxd, da) ;
+ }
+ if (maxd == 0.)
+ {
+ rcond = 0. ;
+ }
+ else
+ {
+ rcond = mind / maxd ;
+ }
+ if (prl > 2) printf ("mind: %g maxd: %g rcond: %g %g\n", mind, maxd, rcond, Info [UMFPACK_RCOND]) ;
+ if (rcond == 0.0 && Info [UMFPACK_RCOND] != 0.0)
+ {
+ printf ("rcond error %30.20e %30.20e\n", rcond, Info [UMFPACK_RCOND]) ;
+ error ("rcond", 0.) ;
+ }
+ if (SCALAR_ABS (rcond - Info [UMFPACK_RCOND]) / rcond > 1e-10)
+ {
+ printf ("rcond error %30.20e %30.20e\n", rcond, Info [UMFPACK_RCOND]) ;
+ error ("rcond", 0.) ;
+ }
+
+ /* get L = Lrow' */
+ status = UMFPACK_transpose (n_inner, n_row, Lrowp, Lrowi, CARG(Lrowx,Lrowz), noP, noQ, Lp, Li, CARG(Lx,Lz) C1ARG(0)) ;
+ if (status != UMFPACK_OK)
+ {
+ error ("L=Lrow' failed\n", 0.) ;
+ }
+
+ if (prl > 2) printf ("\nL col: ") ;
+ status = UMFPACK_report_matrix (n_row, n_inner, Lp, Li, CARG(Lx,Lz), 1, Control) ;
+ if (status != UMFPACK_OK) { error ("bad Lrow\n", 0.) ; }
+
+ if (prl > 2) printf ("\nU col: ") ;
+ status = UMFPACK_report_matrix (n_inner, n_col, Up, Ui, CARG(Ux,Uz), 1, Control) ;
+ if (status != UMFPACK_OK) { error ("bad Ucol\n", 0.) ; }
+
+ free (Lrowx) ; /* ] */
+ free (Lrowi) ; /* ] */
+ free (Lrowp) ; /* ] */
+
+ rnorm = do_solvers (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Info, Numeric,
+ Lp, Li, Lx,Lz, Up, Ui, Ux,Uz, P, Q, x,xz, r,rz, W, Wx, split) ;
+
+ UMFPACK_report_info (Control, Info) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free everything */
+ /* ---------------------------------------------------------------------- */
+
+ free (Dx) ; /* ] */
+ free (Ux) ; /* ] */
+ free (Ui) ; /* ] */
+ free (Lx) ; /* ] */
+ free (Li) ; /* ] */
+ free (Rs) ; /* ] */
+
+ UMFPACK_free_numeric (&Numeric) ; /* ] */
+
+ return (rnorm) ;
+}
+
+
+/* ========================================================================== */
+/* do_once: factor A once, and then test the solves - return if error */
+/* ========================================================================== */
+
+/* exit if an error occurs. otherwise, return the largest residual norm seen. */
+
+static double do_once
+(
+ Int n_row,
+ Int n_col,
+ Int Ap [ ],
+ Int Ai [ ],
+ double Ax [ ], double Az [ ],
+ double b [ ], double bz [ ],
+ double Control [ ],
+ Int Qinit [ ],
+ Int MemControl [6],
+ Int save_and_load,
+ Int split, /* TRUE if complex variables split, FALSE if merged */
+ Int det_check, double det_x, double det_z
+)
+{
+
+ double *x, rnorm, *r, *Wx, *xz, *rz ;
+ Int *P, *Q, *Lp, *Up, *W, *Qtree, *Ptree, n ;
+
+#ifdef COMPLEX
+ if (split)
+ {
+ if (!Az || !bz) error ("bad split\n", 0.) ;
+ }
+ else
+ {
+ if ( Az || bz) error ("bad merge\n", 0.) ;
+ }
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* malloc and realloc failure control */
+ /* ---------------------------------------------------------------------- */
+
+ umf_fail = MemControl [0] ;
+ umf_fail_hi = MemControl [1] ;
+ umf_fail_lo = MemControl [2] ;
+
+ umf_realloc_fail = MemControl [3] ;
+ umf_realloc_hi = MemControl [4] ;
+ umf_realloc_lo = MemControl [5] ;
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ n = MAX (n_row, n_col) ;
+ n = MAX (n,1) ;
+
+ r = (double *) calloc (2*n , sizeof (double)) ; /* [ */
+ x = (double *) calloc (2*n , sizeof (double)) ; /* [ */
+ rz = r + n ;
+
+ if (split)
+ {
+ /* real/complex are in r/rz and x/xz */
+ xz = x + n ;
+ }
+ else
+ {
+ /* r and z are treated as array of size n Entry's */
+ xz = DNULL ;
+ }
+
+ Wx = (double *) malloc (10*n * sizeof (double)) ; /* [ */
+ P = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Q = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Qtree = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Ptree = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ W = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Lp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Up = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ if (!x || !Wx || !r || !P || !Q || !Qtree || !Ptree || !W || !Lp || !Up) error ("out of memory (3)",0.) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* report controls */
+ /* ---------------------------------------------------------------------- */
+
+ if (Control)
+ {
+ if (Control [UMFPACK_PRL] >= 2)
+ {
+ UMFPACK_report_control (Control) ;
+ }
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* do the symbolic & numeric factorization, and solvers */
+ /* ---------------------------------------------------------------------- */
+
+ rnorm = do_symnum (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, x,xz,
+ r,rz, Wx, P, Q, Qtree, Ptree, W, Lp, Up, save_and_load, split,
+ det_check, det_x, det_z) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* free workspace */
+ /* ---------------------------------------------------------------------- */
+
+ free (Up) ; /* ] */
+ free (Lp) ; /* ] */
+ free (W) ; /* ] */
+ free (Ptree) ; /* ] */
+ free (Qtree) ; /* ] */
+ free (Q) ; /* ] */
+ free (P) ; /* ] */
+ free (Wx) ; /* ] */
+ free (x) ; /* ] */
+ free (r) ; /* ] */
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (UMF_malloc_count != 0) error ("umfpack memory leak!!",0.) ;
+#endif
+
+ return (rnorm) ;
+}
+
+/* ========================================================================== */
+/* do_many: factor A once, and then test the solves - return if error */
+/* ========================================================================== */
+
+/* runs do_once with complex variables split, and again with them merged */
+
+static double do_many
+(
+ Int n_row,
+ Int n_col,
+ Int Ap [ ],
+ Int Ai [ ],
+ double Ax [ ], double Az [ ],
+ double b [ ], double bz [ ],
+ double Control [ ],
+ Int Qinit [ ],
+ Int MemControl [6],
+ Int save_and_load,
+ Int det_check, double det_x, double det_z
+)
+{
+ double rnorm, r ;
+ Entry *A, *B, a ;
+ Int p, i, nz ;
+
+ rnorm = 0 ;
+
+#ifdef COMPLEX
+
+ if (!Az || !bz) error ("do_many missing imag parts!\n", 0.) ;
+
+ nz = Ap [n_col] ;
+ A = (Entry *) malloc ((nz+1) * sizeof (Entry)) ;
+ B = (Entry *) malloc ((n_col+1) * sizeof (Entry)) ;
+ if (!A || !B) error ("out of memory (4)",0.) ;
+
+ for (p = 0 ; p < nz ; p++)
+ {
+ ASSIGN (A [p], Ax, Az, p, TRUE) ;
+ }
+ for (i = 0 ; i < n_col ; i++)
+ {
+ ASSIGN (B [i], b, bz, i, TRUE) ;
+ }
+
+ /* with complex variables merged */
+ r = do_once (n_row, n_col, Ap, Ai, (double *)A,DNULL, (double *)B,DNULL, Control, Qinit, MemControl, save_and_load, FALSE, det_check, det_x, det_z) ;
+
+ free (A) ;
+ free (B) ;
+
+ rnorm = MAX (r, rnorm) ;
+
+#endif
+
+ /* with complex variables split */
+ r = do_once (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, save_and_load, TRUE, det_check, det_x, det_z) ;
+ rnorm = MAX (r, rnorm) ;
+ return (rnorm) ;
+}
+
+
+/* ========================================================================== */
+/* bgen: b = A*xtrue, where xtrue (i) = 1 + i/n */
+/* ========================================================================== */
+
+static void bgen
+(
+ Int n,
+ Int Ap [ ],
+ Int Ai [ ],
+ double Ax [ ], double Az [ ],
+ double b [ ], double bz [ ]
+)
+{
+ Int i, col, p ;
+ double xtrue, xtruez ;
+ for (i = 0 ; i < n ; i++)
+ {
+ b [i] = 0.0 ;
+ bz[i] = 0.0 ;
+ }
+ for (col = 0 ; col < n ; col++)
+ {
+ xtrue = 1.0 + ((double) col) / ((double) n) ;
+#ifdef COMPLEX
+ xtruez= 1.3 - ((double) col) / ((double) n) ;
+#else
+ xtruez= 0. ;
+#endif
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ i = Ai [p] ;
+ b [i] += Ax [p] * xtrue ;
+ b [i] -= Az [p] * xtruez ;
+ bz[i] += Az [p] * xtrue ;
+ bz[i] += Ax [p] * xtruez ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* do_matrix: process one matrix with lots of options - exit if errors */
+/* ========================================================================== */
+
+/* return the largest residual norm seen, or exit if error occured */
+
+static double do_matrix
+(
+ Int n,
+ Int Ap [ ],
+ Int Ai [ ],
+ double Ax [ ], double Az [ ],
+
+ double Controls [UMFPACK_CONTROL][1000],
+ Int Ncontrols [UMFPACK_CONTROL],
+ Int MemControl [6],
+ Int do_dense
+)
+{
+ double Control [UMFPACK_CONTROL], *b, *bz, maxrnorm, rnorm, tol, init ;
+ Int *colhist, *rowhist, *rowdeg, *noQinit, *Qinit, *cknob, *rknob,
+ c, r, cs, rs, row, col, i, coldeg, p, d, nb, ck, rk, *Head, *Next,
+ col1, col2, d1, d2, k, status, n_amd,
+ i_tol, i_nb, i_init, n_tol, n_nb, n_init, n_scale, i_scale, scale,
+ i_pivot, n_pivot, pivopt ;
+
+ /* ---------------------------------------------------------------------- */
+ /* initializations */
+ /* ---------------------------------------------------------------------- */
+
+ maxrnorm = 0.0 ;
+
+ /* get the default control parameters */
+ UMFPACK_defaults (Control) ;
+
+ UMFPACK_report_control (Control) ;
+
+#ifdef DEBUGGING
+ Control [UMFPACK_PRL] = 5 ;
+#endif
+
+ status = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Control) ;
+ if (status != UMFPACK_OK) { error ("bad A do_matrix\n", 0.) ; }
+
+ /* ---------------------------------------------------------------------- */
+ /* allocate workspace */
+ /* ---------------------------------------------------------------------- */
+
+ rowdeg = (Int *) malloc ((n+1) * sizeof (Int)) ; /* ( */
+ rowhist = (Int *) malloc ((n+1) * sizeof (Int)) ; /* ( */
+ colhist = (Int *) malloc ((n+1) * sizeof (Int)) ; /* ( */
+ cknob = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ rknob = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+
+ /* ---------------------------------------------------------------------- */
+ /* count the dense rows and columns */
+ /* ---------------------------------------------------------------------- */
+
+ for (i = 0 ; i < n ; i++)
+ {
+ colhist [i] = 0 ;
+ rowhist [i] = 0 ;
+ rowdeg [i] = 0 ;
+ }
+
+ for (col = 0 ; col < n ; col++)
+ {
+ coldeg = Ap [col+1] - Ap [col] ;
+ colhist [coldeg]++ ;
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ rowdeg [Ai [p]]++ ;
+ }
+ }
+
+ for (row = 0 ; row < n ; row++)
+ {
+ rowhist [rowdeg [row]]++ ;
+ }
+
+ rs = 0 ;
+ if (do_dense)
+ {
+ if (n < 16)
+ {
+ rknob [rs++] = 0 ; /* all dense rows */
+ }
+ for (d = 16 ; d < n ; d++)
+ {
+ if (rowhist [d] > 0)
+ {
+ rknob [rs++] = d ;
+ }
+ }
+ }
+ rknob [rs++] = n ; /* no dense rows */
+
+ cs = 0 ;
+ if (do_dense)
+ {
+ if (n < 16)
+ {
+ cknob [cs++] = 0 ; /* all dense columns */
+ }
+ for (d = 16 ; d < n ; d++)
+ {
+ if (colhist [d] > 0)
+ {
+ cknob [cs++] = d ;
+ }
+ }
+ }
+ cknob [cs++] = n ; /* no dense cols */
+
+ free (colhist) ; /* ) */
+ free (rowhist) ; /* ) */
+
+ /* ---------------------------------------------------------------------- */
+ /* compute b assuming xtrue (i) = 1 + i/n */
+ /* ---------------------------------------------------------------------- */
+
+ b = (double *) malloc (n * sizeof (double)) ; /* [ */
+ bz= (double *) calloc (n , sizeof (double)) ; /* [ */
+ if (!b) error ("out of memory (5)",0.) ;
+ if (!bz) error ("out of memory (6)",0.) ;
+ bgen (n, Ap, Ai, Ax, Az, b, bz) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* compute Qinit = sort by colcounts */
+ /* ---------------------------------------------------------------------- */
+
+ noQinit = INULL ;
+ Qinit = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ if (!Qinit) error ("out of memory (7)",0.) ;
+ Head = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Next = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ for (d = 0 ; d <= n ; d++)
+ {
+ Head [d] = EMPTY ;
+ }
+ for (col = n-1 ; col >= 0 ; col--)
+ {
+ d = Ap [col+1] - Ap [col] ;
+ Next [col] = Head [d] ;
+ Head [d] = col ;
+ }
+ k = 0 ;
+ for (d = 0 ; d <= n ; d++)
+ {
+ for (col = Head [d] ; col != EMPTY ; col = Next [col])
+ {
+ Qinit [k++] = col ;
+ }
+ }
+ free (Next) ; /* ] */
+ free (Head) ; /* ] */
+
+ if (k != n) error ("Qinit error\n",0.) ;
+
+ /* use rowdeg for workspace */
+ if (!UMF_is_permutation (Qinit, rowdeg, n, n)) error ("Qinit, colsort, not a permutation vector",0.) ;
+
+ for (k = 1 ; k < n ; k++)
+ {
+ col1 = Qinit [k-1] ;
+ col2 = Qinit [k] ;
+ d1 = Ap [col1+1] - Ap [col1] ;
+ d2 = Ap [col2+1] - Ap [col2] ;
+ if (d1 > d2) error ("Qinit error = not sorted\n",0.) ;
+ }
+
+ free (rowdeg) ; /* ) */
+
+ /* ---------------------------------------------------------------------- */
+ /* exhaustive test */
+ /* ---------------------------------------------------------------------- */
+
+ n_tol = Ncontrols [UMFPACK_PIVOT_TOLERANCE] ;
+ n_nb = Ncontrols [UMFPACK_BLOCK_SIZE] ;
+ n_init = Ncontrols [UMFPACK_ALLOC_INIT] ;
+ n_scale = Ncontrols [UMFPACK_SCALE] ;
+ n_amd = Ncontrols [UMFPACK_AMD_DENSE] ;
+
+ printf (" cs "ID" rs "ID" : "ID" ", cs, rs,
+ 2 + (cs * rs * n_tol * n_nb * n_init )) ;
+ fflush (stdout) ;
+
+ /* with defaults - null Control array, Qinit */
+ printf ("with qinit:\n") ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, DNULL, Qinit, MemControl, FALSE, FALSE, 0., 0.) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ /* with defaults - null Control array */
+ printf ("with null control array:\n") ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, DNULL, noQinit, MemControl, FALSE, FALSE, 0., 0.) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ /* with defaults */
+ printf ("with defaults:\n") ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, noQinit, MemControl, FALSE, FALSE, 0., 0.) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf ("with defaults and qinit:\n") ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, FALSE, FALSE, 0., 0.) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ printf ("starting lengthy tests\n") ;
+
+ for (c = 0 ; c <= cs ; c++)
+ {
+ if (c == cs)
+ {
+ rs = n_amd ;
+ }
+
+ for (r = 0 ; r < rs ; r++)
+ {
+ if (c == cs)
+ {
+ Control [UMFPACK_DENSE_COL] = UMFPACK_DEFAULT_DENSE_COL ;
+ Control [UMFPACK_DENSE_ROW] = UMFPACK_DEFAULT_DENSE_ROW ;
+ Control [UMFPACK_AMD_DENSE] = Controls [UMFPACK_AMD_DENSE][r] ;
+ }
+ else
+ {
+ ck = cknob [c] ;
+ rk = rknob [r] ;
+ /* ignore columns with degree > ck and rows with degree > rk */
+ Control [UMFPACK_DENSE_COL] = inv_umfpack_dense (ck, n) ;
+ Control [UMFPACK_DENSE_ROW] = inv_umfpack_dense (rk, n) ;
+ Control [UMFPACK_AMD_DENSE] = UMFPACK_DEFAULT_AMD_DENSE ;
+ }
+
+ for (i_tol = 0 ; i_tol < n_tol ; i_tol++)
+ {
+ tol = Controls [UMFPACK_PIVOT_TOLERANCE][i_tol] ;
+ Control [UMFPACK_PIVOT_TOLERANCE] = tol ;
+
+ for (i_nb = 0 ; i_nb < n_nb ; i_nb++)
+ {
+ nb = (Int) Controls [UMFPACK_BLOCK_SIZE][i_nb] ;
+ Control [UMFPACK_BLOCK_SIZE] = (double) nb ;
+
+ for (i_init = 0 ; i_init < n_init ; i_init++)
+ {
+ init = Controls [UMFPACK_ALLOC_INIT][i_init] ;
+ Control [UMFPACK_ALLOC_INIT] = init ;
+
+ for (i_scale = 0 ; i_scale < n_scale ; i_scale++)
+ {
+ Int strategy, fixQ ;
+ scale = Controls [UMFPACK_SCALE][i_scale] ;
+ Control [UMFPACK_SCALE] = scale ;
+
+ for (strategy = UMFPACK_STRATEGY_AUTO ; strategy <= UMFPACK_STRATEGY_SYMMETRIC ; strategy ++)
+ {
+ Control [UMFPACK_STRATEGY] = strategy ;
+ {
+ rnorm = do_once (n, n, Ap, Ai, Ax,Az, b,bz, Control, noQinit, MemControl, FALSE, TRUE, FALSE, 0., 0.) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ rnorm = do_once (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, FALSE, TRUE, FALSE, 0., 0.) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ free (Qinit) ; /* ] */
+ free (bz) ; /* ] */
+ free (b) ; /* ] */
+ free (rknob) ; /* ] */
+ free (cknob) ; /* ] */
+
+ return (maxrnorm) ;
+}
+
+
+/* ========================================================================== */
+/* matgen_dense: generate a dense matrix */
+/* ========================================================================== */
+
+/* allocates Ap, Ai, Ax, and Az */
+
+static void matgen_dense
+(
+ Int n,
+ Int **Ap,
+ Int **Ai,
+ double **Ax, double **Az
+)
+{
+ Int nz, *Bp, *Bi, *Ti, *Tj, k, i, j, *P, status ;
+ double *Bx, *Tx, *Bz, *Tz ;
+
+ nz = n*n + n ;
+
+ /* allocate Bp, Bi, and Bx - but do not free them */
+ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Bi = (Int *) malloc ((nz+1) * sizeof (Int)) ;
+ Bx = (double *) malloc ((nz+1) * sizeof (double)) ;
+ Bz = (double *) calloc ((nz+1) , sizeof (double)) ;
+
+ Ti = (Int *) malloc ((nz+1) * sizeof (Int)) ; /* [ */
+ Tj = (Int *) malloc ((nz+1) * sizeof (Int)) ; /* [ */
+ Tx = (double *) malloc ((nz+1) * sizeof (double)) ; /* [ */
+ Tz = (double *) calloc ((nz+1) , sizeof (double)) ; /* [ */
+ P = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+
+ if (!Bp || !Bi || !Bx || !Ti || !Tj || !Tx || !P) error ("out of memory (8)",0.) ;
+ if (!Bz || !Tz) error ("outof memory",0.) ;
+
+ k = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ for (j = 0 ; j < n ; j++)
+ {
+ Ti [k] = i ;
+ Tj [k] = j ;
+ Tx [k] = 2.0 * (xrand ( ) - 1.0) ;
+#ifdef COMPLEX
+ Tz [k] = 2.0 * (xrand ( ) - 1.0) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+ }
+
+ /* beef up each column and row */
+ randperm (n, P) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Ti [k] = i ;
+ Tj [k] = P [i] ;
+ Tx [k] = xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+
+ if (k != nz) error ("matgen_dense error",0.) ;
+
+ /* convert to column form */
+ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ;
+ if (status != UMFPACK_OK) error ("matgen_dense triplet_to_col failed 2",0.) ;
+
+ /* return the allocated column-form */
+ *Ap = Bp ;
+ *Ai = Bi ;
+ *Ax = Bx ;
+ *Az = Bz ;
+
+ free (P) ; /* ] */
+ free (Tz) ; /* ] */
+ free (Tx) ; /* ] */
+ free (Tj) ; /* ] */
+ free (Ti) ; /* ] */
+
+}
+
+
+/* ========================================================================== */
+/* matgen_funky: generate a kind of arrowhead matrix */
+/* ========================================================================== */
+
+/* allocates Ap, Ai, Ax, and Az
+
+ A = speye (n) ;
+ A (n, 2:3) = rand (1,2) ;
+ A (3, 3:n) = rand (1, n-2) ;
+ A (3:n, 1) = rand (n-2, 1) ;
+
+ */
+
+static void matgen_funky
+(
+ Int n,
+ Int **Ap,
+ Int **Ai,
+ double **Ax, double **Az
+)
+{
+ Int nz, *Bp, *Bi, *Ti, *Tj, k, i, j, *P, status ;
+ double *Bx, *Tx, *Bz, *Tz ;
+
+ nz = 4*n + 5 ;
+
+ /* allocate Bp, Bi, and Bx - but do not free them */
+ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Bi = (Int *) malloc (nz * sizeof (Int)) ;
+ Bx = (double *) malloc (nz * sizeof (double)) ;
+ Bz = (double *) calloc (nz , sizeof (double)) ;
+
+ Ti = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Tj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Tx = (double *) malloc (nz * sizeof (double)) ; /* [ */
+ Tz = (double *) calloc (nz , sizeof (double)) ; /* [ */
+ P = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+
+ if (!Bp || !Bi || !Bx || !Ti || !Tj || !Tx || !P) error ("out of memory (9)",0.) ;
+ if (!Bz || !Tz) error ("outof memory",0.) ;
+
+ k = 0 ;
+
+ /* A = speye (n) ; */
+ for (i = 0 ; i < n ; i++)
+ {
+ Ti [k] = i ;
+ Tj [k] = i ;
+ Tx [k] = 1.0 ;
+#ifdef COMPLEX
+ Tz [k] = 1.0 ;
+#endif
+ k++ ;
+ }
+
+ /* A (n, 2:3) = rand (1,2) ; */
+ for (j = 1 ; j <= 2 ; j++)
+ {
+ Ti [k] = n-1 ;
+ Tj [k] = j ;
+ Tx [k] = 1.0 ;
+#ifdef COMPLEX
+ Tz [k] = 1.0 ;
+#endif
+ k++ ;
+ }
+
+ /* A (3, 3:n) = rand (1, n-2) ; */
+ for (j = 2 ; j < n ; j++)
+ {
+ Ti [k] = 2 ;
+ Tj [k] = j ;
+ Tx [k] = 1.0 ;
+#ifdef COMPLEX
+ Tz [k] = 1.0 ;
+#endif
+ k++ ;
+ }
+
+ /* A (3:n, 1) = rand (n-2, 1) ; */
+ for (i = 2 ; i < n ; i++)
+ {
+ Ti [k] = i ;
+ Tj [k] = 0 ;
+ Tx [k] = 1.0 ;
+#ifdef COMPLEX
+ Tz [k] = 1.0 ;
+#endif
+ k++ ;
+ }
+
+ /* convert to column form */
+ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ;
+ if (status != UMFPACK_OK) error ("matgen_dense triplet_to_col failed 1",0.) ;
+
+ /* return the allocated column-form */
+ *Ap = Bp ;
+ *Ai = Bi ;
+ *Ax = Bx ;
+ *Az = Bz ;
+
+ free (P) ; /* ] */
+ free (Tz) ; /* ] */
+ free (Tx) ; /* ] */
+ free (Tj) ; /* ] */
+ free (Ti) ; /* ] */
+
+}
+
+
+/* ========================================================================== */
+/* matgen_band: generate a banded matrix */
+/* ========================================================================== */
+
+/* allocates Ap, Ai, and Ax */
+
+static void matgen_band
+(
+ Int n,
+ Int lo, /* lo = 0: upper triangular only */
+ Int up, /* up = 0: lower triangular only */
+ Int ndrow, /* plus ndrow dense rows, each of degree rdeg */
+ Int rdeg,
+ Int ndcol, /* plus ndcol dense cols, each of degree cdeg */
+ Int cdeg,
+ Int **Ap,
+ Int **Ai,
+ double **Ax, double **Az
+)
+{
+ Int nz, *Bp, *Bi, *Ti, *Tj, k, i, j, jlo, jup, j1, i1, k1, status ;
+ double *Bx, *Bz, *Tx, *Tz ;
+
+ /* an upper bound */
+ nz = n * (lo + 1 + up) + n + ndrow*rdeg + ndcol*cdeg ;
+
+ /* allocate Bp, Bi, and Bx - but do not free them */
+ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Bi = (Int *) malloc (nz * sizeof (Int)) ;
+ Bx = (double *) malloc (nz * sizeof (double)) ;
+ Bz = (double *) calloc (nz , sizeof (double)) ;
+
+ Ti = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Tj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Tx = (double *) malloc (nz * sizeof (double)) ; /* [ */
+ Tz = (double *) calloc (nz , sizeof (double)) ; /* [ */
+
+ if (!Bp || !Bi || !Bx || !Ti || !Tj || !Tx) error ("out of memory (10)",0.) ;
+ if (!Bz || !Tz) error ("out ofmemory", 0.) ;
+
+ k = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ jlo = MAX (0, i - lo) ;
+ jup = MIN (n-1, i + up) ;
+ for (j = jlo ; j <= jup ; j++)
+ {
+ Ti [k] = i ;
+ Tj [k] = j ;
+ Tx [k] = 2.0 * (xrand ( ) - 1.0) ;
+#ifdef COMPLEX
+ Tz [k] = 2.0 * (xrand ( ) - 1.0) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+ }
+
+ /* beef up the diagonal */
+ for (i = 0 ; i < n ; i++)
+ {
+ Ti [k] = i ;
+ Tj [k] = i ;
+ Tx [k] = xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+
+ /* add ndrow rows of degree rdeg */
+ for (i1 = 0 ; i1 < ndrow ; i1++)
+ {
+ i = irand (n) ;
+ for (k1 = 0 ; k1 < rdeg ; k1++)
+ {
+ Ti [k] = i ;
+ Tj [k] = irand (n) ;
+ Tx [k] = 0.1 * xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = 0.1 * xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+ }
+
+ /* add ndcol rows of degree cdeg */
+ for (j1 = 0 ; j1 < ndcol ; j1++)
+ {
+ j = irand (n) ;
+ for (k1 = 0 ; k1 < cdeg ; k1++)
+ {
+ Ti [k] = irand (n) ;
+ Tj [k] = j ;
+ Tx [k] = 0.1 * xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = 0.1 * xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+ }
+
+ if (k > nz) error ("matgen_band error\n",0.) ;
+
+ /* convert to column form */
+ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ;
+ if (status != UMFPACK_OK) error ("matgen_band triplet_to_col failed\n",0.) ;
+
+ /* return the allocated column-form */
+ *Ap = Bp ;
+ *Ai = Bi ;
+ *Ax = Bx ;
+ *Az = Bz ;
+
+ free (Tz) ; /* ] */
+ free (Tx) ; /* ] */
+ free (Tj) ; /* ] */
+ free (Ti) ; /* ] */
+
+}
+
+
+/* ========================================================================== */
+/* test_col */
+/* ========================================================================== */
+
+static void test_col
+(
+ Int n,
+ Int Bp [ ],
+ Int Bi [ ],
+ double Bx [ ], double Bz [ ],
+ Int prl
+)
+{
+ Int *Ci, *Cj, *Ep, *Ei, k, s, t, i, j, nz, p, status, *Map, *noMap ;
+ double *Cx, *Cz, *Ex, *Ez, z, Control [UMFPACK_CONTROL] ;
+ noMap = (Int *) NULL ;
+
+ printf ("\n\n===== test col -> triplet and triplet -> col\n") ;
+
+ UMFPACK_defaults (Control) ;
+
+ Control [UMFPACK_PRL] = prl ;
+ UMFPACK_report_control (Control) ;
+
+ nz = Bp [n] ;
+
+ Ci = (Int *) malloc ((2*nz+1) * sizeof (Int)) ; /* [ */
+ Cj = (Int *) malloc ((2*nz+1) * sizeof (Int)) ; /* [ */
+ Cx = (double *) calloc (2*(2*nz+1) , sizeof (double)) ; /* [ */
+ Cz = Cx + (2*nz+1) ;
+ Ep = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Ei = (Int *) malloc ((2*nz+1) * sizeof (Int)) ; /* [ */
+ Ex = (double *) calloc (2*(2*nz+1) , sizeof (double)) ; /* [ */
+ Ez = Ex + (2*nz+1) ;
+ Map = (Int *) malloc ((2*nz+1) * sizeof (Int)) ; /* [ */
+
+ if (!Ci || !Cj || !Cx || !Ep || !Ei || !Ex) error ("out of memory (11)",0.) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test with split complex values */
+ /* ---------------------------------------------------------------------- */
+
+ /* convert B (col) to C (triplet) */
+ status = UMFPACK_col_to_triplet (n, Bp, Cj) ;
+ if (status != UMFPACK_OK) error ("col->triplet",0.) ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ Ci [k] = Bi [k] ;
+ Cx [k] = Bx [k] ;
+ Cz [k] = Bz [k] ;
+ }
+
+ /* convert C (triplet) to E (col) */
+ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), Map) ;
+ if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (1)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) error ("Ez (1)",0.) ;
+ }
+ }
+
+ /* convert C (triplet) to E (col), no map */
+ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), noMap) ;
+ if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (2)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) error ("Ez",0.) ;
+ }
+ }
+
+ /* jumble C a little bit */
+ for (k = 0 ; k < MIN (nz,4) ; k++)
+ {
+ s = irand (nz) ;
+ /* swap positions s and k */
+ t = Ci [k] ; Ci [k] = Ci [s] ; Ci [s] = t ;
+ t = Cj [k] ; Cj [k] = Cj [s] ; Cj [s] = t ;
+ z = Cx [k] ; Cx [k] = Cx [s] ; Cx [s] = z ;
+ z = Cz [k] ; Cz [k] = Cz [s] ; Cz [s] = z ;
+ }
+
+ /* convert C (triplet) to E (col) */
+ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), Map) ;
+ if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (3)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) error ("Ez",0.) ;
+ }
+ }
+
+ /* convert C (triplet) to E (col), no map */
+ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), noMap) ;
+ if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (4)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) error ("Ez",0.) ;
+ }
+ }
+
+ /* jumble C a lot */
+ for (k = 0 ; k < nz ; k++)
+ {
+ s = irand (nz) ;
+ /* swap positions s and k */
+ t = Ci [k] ; Ci [k] = Ci [s] ; Ci [s] = t ;
+ t = Cj [k] ; Cj [k] = Cj [s] ; Cj [s] = t ;
+ z = Cx [k] ; Cx [k] = Cx [s] ; Cx [s] = z ;
+ z = Cz [k] ; Cz [k] = Cz [s] ; Cz [s] = z ;
+ }
+
+ /* add duplicates to C, but preserve pattern and values */
+ for (k = nz ; k < 2*nz ; k++)
+ {
+ /* add a duplicate */
+ s = irand (k) ;
+ Ci [k] = Ci [s] ;
+ Cj [k] = Cj [s] ;
+ z = Cx [s] ;
+ Cx [s] = z/2 ;
+ Cx [k] = z/2 ;
+ z = Cz [s] ;
+ Cz [s] = z/2 ;
+ Cz [k] = z/2 ;
+ }
+
+ if (prl > 2) printf ("\ntest c->t,t->c: ") ;
+ status = UMFPACK_report_triplet (n, n, 2*nz, Ci, Cj, CARG(Cx,Cz), Control) ;
+ if (status != UMFPACK_OK) error ("report col->triplet",0.) ;
+
+ /* convert C (triplet) to E (col), no Map */
+ status = UMFPACK_triplet_to_col (n, n, 2*nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), noMap) ;
+ if (status != UMFPACK_OK) error ("t->col failed",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (5)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15)
+ {
+ printf ("%30.18e %30.18e %g\n", Bz[p], Ez[p], Bz[p]-Ez[p]) ;
+ error ("Ez (5)",0.) ;
+ }
+ }
+ }
+
+ /* convert C (triplet) to E (col) */
+ status = UMFPACK_triplet_to_col (n, n, 2*nz, Ci, Cj, CARG(Cx,Cz), Ep, Ei, CARG(Ex,Ez), Map) ;
+ if (status != UMFPACK_OK) error ("t->col failed",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (6)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [p]) > 1e-15) error ("Ex",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ez [p]) > 1e-15) error ("Ez",0.) ;
+ }
+ }
+
+ /* convert C (triplet) to E (col), using Map */
+ for (p = 0 ; p < Ep [n] ; p++)
+ {
+ Ex [p] = 0. ;
+ Ez [p] = 0. ;
+ }
+ for (k = 0 ; k < 2*nz ; k++)
+ {
+ p = Map [k] ;
+ i = Ci [k] ;
+ j = Cj [k] ;
+ if (i != Ei [p]) error ("Map", 0.) ;
+ if (!(Ep [j] <= p && p < Ep [j+1])) error ("Map Ep", 0.) ;
+ Ex [p] += Cx [k] ;
+ Ez [p] += Cz [k] ;
+ }
+
+ /* compare E and B, they should be identical */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ z = SCALAR_ABS (Bx [p] - Ex [p]) ;
+ if (z > 1e-15) error ("Ex",z) ;
+ z = SCALAR_ABS (Bz [p] - Ez [p]) ;
+ if (z > 1e-15) error ("Ez (7)",z) ;
+ }
+ }
+
+#ifdef COMPLEX
+ /* ---------------------------------------------------------------------- */
+ /* repeat, but with merged complex values */
+ /* ---------------------------------------------------------------------- */
+
+ /* convert B (col) to C (triplet) */
+ status = UMFPACK_col_to_triplet (n, Bp, Cj) ;
+ if (status != UMFPACK_OK) error ("col->triplet",0.) ;
+ for (k = 0 ; k < nz ; k++)
+ {
+ Ci [k] = Bi [k] ;
+ Cx [2*k ] = Bx [k] ;
+ Cx [2*k+1] = Bz [k] ;
+ }
+
+ /* convert C (triplet) to E (col) */
+ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), Map) ;
+ if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (7)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ;
+ }
+ }
+
+ /* convert C (triplet) to E (col) no Map */
+ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), noMap) ;
+ if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (8)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ;
+ }
+ }
+
+ /* jumble C a little bit */
+ for (k = 0 ; k < MIN (nz,4) ; k++)
+ {
+ s = irand (nz) ;
+ /* swap positions s and k */
+ t = Ci [k] ; Ci [k] = Ci [s] ; Ci [s] = t ;
+ t = Cj [k] ; Cj [k] = Cj [s] ; Cj [s] = t ;
+ z = Cx [2*k ] ; Cx [2*k ] = Cx [2*s ] ; Cx [2*s ] = z ;
+ z = Cx [2*k+1] ; Cx [2*k+1] = Cx [2*s+1] ; Cx [2*s+1] = z ;
+ }
+
+ /* convert C (triplet) to E (col) */
+ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), Map) ;
+ if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (9)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ;
+ }
+ }
+
+ /* convert C (triplet) to E (col) no Map */
+ status = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), noMap) ;
+ if (status != UMFPACK_OK) error ("t->col failed (1)",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (10)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ;
+ }
+ }
+
+ /* jumble C */
+ for (k = 0 ; k < nz ; k++)
+ {
+ s = irand (nz) ;
+ /* swap positions s and k */
+ t = Ci [k] ; Ci [k] = Ci [s] ; Ci [s] = t ;
+ t = Cj [k] ; Cj [k] = Cj [s] ; Cj [s] = t ;
+ z = Cx [2*k ] ; Cx [2*k ] = Cx [2*s ] ; Cx [2*s ] = z ;
+ z = Cx [2*k+1] ; Cx [2*k+1] = Cx [2*s+1] ; Cx [2*s+1] = z ;
+ }
+
+ /* add duplicates to C, but preserve pattern and values */
+ for (k = nz ; k < 2*nz ; k++)
+ {
+ /* add a duplicate */
+ s = irand (k) ;
+ Ci [k] = Ci [s] ;
+ Cj [k] = Cj [s] ;
+ z = Cx [2*s] ;
+ Cx [2*s] = z/2 ;
+ Cx [2*k] = z/2 ;
+ z = Cx [2*s+1] ;
+ Cx [2*s+1] = z/2 ;
+ Cx [2*k+1] = z/2 ;
+ }
+
+ if (prl > 2) printf ("\ntest c->t,t->c: ") ;
+ status = UMFPACK_report_triplet (n, n, 2*nz, Ci, Cj, CARG(Cx,DNULL), Control) ;
+ if (status != UMFPACK_OK) error ("report col->triplet",0.) ;
+
+ /* convert C (triplet) to E (col) */
+ status = UMFPACK_triplet_to_col (n, n, 2*nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), noMap) ;
+ if (status != UMFPACK_OK) error ("t->col failed",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (11)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ;
+ }
+ }
+
+ /* convert C (triplet) to E (col) */
+ status = UMFPACK_triplet_to_col (n, n, 2*nz, Ci, Cj, CARG(Cx,DNULL), Ep, Ei, CARG(Ex,DNULL), Map) ;
+ if (status != UMFPACK_OK) error ("t->col failed",0.) ;
+
+ /* compare E and B, they should be identical */
+ if (nz != Ep [n]) error ("E nz (12)",0.) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Ep [j]) error ("Ep j",0.) ;
+ if (Bp [j+1] != Ep [j+1]) error ("Ep j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ei [p]) error ("Ei",0.) ;
+ if (SCALAR_ABS (Bx [p] - Ex [2*p ]) > 1e-15) error ("Ex (merge)",0.) ;
+ if (SCALAR_ABS (Bz [p] - Ex [2*p+1]) > 1e-15) error ("Ez (merge)",0.) ;
+ }
+ }
+
+ /* convert C (triplet) to E (col), using Map */
+ for (p = 0 ; p < Ep [n] ; p++)
+ {
+ Ex [2*p ] = 0. ;
+ Ex [2*p+1] = 0. ;
+ }
+ for (k = 0 ; k < 2*nz ; k++)
+ {
+ p = Map [k] ;
+ i = Ci [k] ;
+ j = Cj [k] ;
+ if (i != Ei [p]) error ("Map", 0.) ;
+ if (!(Ep [j] <= p && p < Ep [j+1])) error ("Map Ep", 0.) ;
+ Ex [2*p ] += Cx [2*k ] ;
+ Ex [2*p+1] += Cx [2*k+1] ;
+ }
+
+ /* compare E and B, they should be identical */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ z = SCALAR_ABS (Bx [p] - Ex [2*p ]) ;
+ if (z > 1e-15) error ("Ex merged",z) ;
+ z = SCALAR_ABS (Bz [p] - Ex [2*p+1]) ;
+ if (z > 1e-15) error ("Ez merged 7",z) ;
+ }
+ }
+
+#endif
+
+ printf ("\n =============== test OK\n\n") ;
+
+ free (Map) ; /* ] */
+ free (Ex) ; /* ] */
+ free (Ei) ; /* ] */
+ free (Ep) ; /* ] */
+ free (Cx) ; /* ] */
+ free (Cj) ; /* ] */
+ free (Ci) ; /* ] */
+}
+
+/* ========================================================================== */
+/* matgen_compaction: generate a matrix to test umf_symbolic compaction */
+/* ========================================================================== */
+
+static void matgen_compaction
+(
+ Int n,
+ Int **Ap,
+ Int **Ai,
+ double **Ax, double **Az
+)
+{
+ Int nz, *Bp, *Bi, *Ti, *Tj, k, i, j, prl, status ;
+ double *Bx, *Tx, *Bz, *Tz, Control [UMFPACK_INFO] ;
+
+ prl = Control ? Control [UMFPACK_PRL] : UMFPACK_DEFAULT_PRL ;
+ UMFPACK_defaults (Control) ;
+
+ UMFPACK_report_control (Control) ;
+
+ nz = 5*n ;
+
+ /* allocate Bp, Bi, and Bx - but do not free them */
+ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Bi = (Int *) malloc (nz * sizeof (Int)) ;
+ Bx = (double *) malloc (nz * sizeof (double)) ;
+ Bz = (double *) calloc (nz , sizeof (double)) ;
+
+ Ti = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Tj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Tx = (double *) malloc (nz * sizeof (double)) ; /* [ */
+ Tz = (double *) calloc (nz , sizeof (double)) ; /* [ */
+ if (!Bp || !Bi || !Bx || !Ti || !Tj || !Tx) error ("out of memory (12)",0.) ;
+ if (!Bz || !Tz) error ("out of mery",0.) ;
+
+ k = 0 ;
+ for (i = 0 ; i < n ; i++)
+ {
+ if (i > 0)
+ {
+ Ti [k] = i ;
+ Tj [k] = i-1 ;
+ Tx [k] = xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+ Ti [k] = i ;
+ Tj [k] = i ;
+ Tx [k] = xrand ( ) ;
+ k++ ;
+ if (i < n-1)
+ {
+ Ti [k] = i ;
+ Tj [k] = i+1 ;
+ Tx [k] = xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+ }
+
+ for (j = 0 ; j < n ; j += 2)
+ {
+ Ti [k] = 0 ;
+ Tj [k] = j ;
+ Tx [k] = xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+
+ for (j = 1 ; j < n ; j += 2)
+ {
+ Ti [k] = 1 ;
+ Tj [k] = j ;
+ Tx [k] = xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+
+
+ if (prl > 2) printf ("\nmatgen_compact: ") ;
+ status = UMFPACK_report_triplet (n, n, k, Ti, Tj, CARG(Tx,Tz), Control) ;
+ if (status != UMFPACK_OK) error ("bad triplet report",0.) ;
+
+ /* convert to column form */
+ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ;
+ if (status != UMFPACK_OK) error ("matgen_compact triplet_to_col failed",0.) ;
+
+ if (prl > 2) printf ("\nmatgen_compact: ") ;
+ status = UMFPACK_report_matrix (n, n, Bp, Bi, CARG(Bx,Bz), 1, Control) ;
+ if (status != UMFPACK_OK) error ("bad A matget sparse",0.) ;
+
+ /* return the allocated column-form */
+ *Ap = Bp ;
+ *Ai = Bi ;
+ *Ax = Bx ;
+ *Az = Bz ;
+
+ free (Tz) ; /* ] */
+ free (Tx) ; /* ] */
+ free (Tj) ; /* ] */
+ free (Ti) ; /* ] */
+}
+
+
+/* ========================================================================== */
+/* matgen_sparse: generate a matrix with random pattern */
+/* ========================================================================== */
+
+/* allocates Ap, Ai, Ax, and Az */
+
+static void matgen_sparse
+(
+ Int n,
+ Int s, /* s random entries, and one more in each row and column */
+ Int ndrow, /* plus ndrow dense rows, each of degree rdeg */
+ Int rdeg,
+ Int ndcol, /* plus ndcol dense cols, each of degree cdeg */
+ Int cdeg,
+ Int **Ap,
+ Int **Ai,
+ double **Ax, double **Az,
+ Int prl,
+ Int has_nans
+)
+{
+ Int nz, *Bp, *Bi, *Ti, *Tj, k, i, j, j1, i1, k1, *P, status, *Map, p, *Cp, *Ci, *noMap ;
+ double *Bx, *Tx, *Bz, *Tz, Control [UMFPACK_CONTROL], xnan, xinf, x, *Txx, *Cx ;
+ noMap = (Int *) NULL ;
+
+ if (has_nans)
+ {
+ xnan = divide (0., 0.) ;
+ xinf = divide (1., 0.) ;
+ }
+
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_PRL] = prl ;
+ UMFPACK_report_control (Control) ;
+
+ nz = s + n + rdeg*ndrow + cdeg*ndcol ;
+ if (nz == 0) nz++ ;
+
+ /* allocate Bp, Bi, and Bx - but do not free them */
+ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Bi = (Int *) malloc ((nz+1) * sizeof (Int)) ;
+ Bx = (double *) malloc ((nz+1) * sizeof (double)) ;
+ Bz = (double *) calloc ((nz+1) , sizeof (double)) ;
+
+ Ti = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Tj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Tx = (double *) malloc (nz * sizeof (double)) ; /* [ */
+ Tz = (double *) calloc (nz , sizeof (double)) ; /* [ */
+ P = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Map = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+
+ Txx = (double *) calloc (2*(nz+1) , sizeof (double)) ; /* [ */
+ Cp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Ci = (Int *) malloc ((nz+1) * sizeof (Int)) ; /* [ */
+ Cx = (double *) calloc (2*(nz+1) , sizeof (double)) ; /* [ */
+
+ if (!Bp || !Bi || !Bx || !Ti || !Tj || !Tx || !P) error ("out of memory (13)",0.) ;
+ if (!Bz || !Tz) error ("out of m",0.) ;
+ if (!Txx || !Cx || !Cp || !Ci) error ("out of mem xx",0.) ;
+
+ for (k = 0 ; k < s ; k++)
+ {
+ Ti [k] = irand (n) ;
+ Tj [k] = irand (n) ;
+ if (has_nans)
+ {
+ x = xrand ( ) ;
+ Tx [k] = (x > 0.8) ? ((x > 0.9) ? xnan : xinf) : (2*x-1) ;
+#ifdef COMPLEX
+ x = xrand ( ) ;
+ Tz [k] = (x > 0.8) ? ((x > 0.9) ? xnan : xinf) : (2*x-1) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ }
+ else
+ {
+ Tx [k] = 2.0 * (xrand ( ) - 1.0) ;
+#ifdef COMPLEX
+ Tz [k] = 2.0 * (xrand ( ) - 1.0) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ }
+ }
+
+ /* beef up each column and row */
+ randperm (n, P) ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Ti [k] = i ;
+ Tj [k] = P [i] ;
+ Tx [k] = xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+
+ /* add ndrow rows of degree rdeg */
+ for (i1 = 0 ; i1 < ndrow ; i1++)
+ {
+ i = irand (n) ;
+ for (k1 = 0 ; k1 < rdeg ; k1++)
+ {
+ Ti [k] = i ;
+ Tj [k] = irand (n) ;
+ Tx [k] = 0.1 * xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = 0.1 * xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+ }
+
+ /* add ndcol rows of degree cdeg */
+ for (j1 = 0 ; j1 < ndcol ; j1++)
+ {
+ j = irand (n) ;
+ for (k1 = 0 ; k1 < cdeg ; k1++)
+ {
+ Ti [k] = irand (n) ;
+ Tj [k] = j ;
+ Tx [k] = 0.1 * xrand ( ) ;
+#ifdef COMPLEX
+ Tz [k] = 0.1 * xrand ( ) ;
+#else
+ Tz [k] = 0. ;
+#endif
+ k++ ;
+ }
+ }
+
+ if (k != nz) error ("matgen_sparse error",0.) ;
+
+ if (prl > 2) printf ("\nmatgen_sparse: ") ;
+ status = UMFPACK_report_triplet (n, n, k, Ti, Tj, CARG(Tx,Tz), Control) ;
+ if (status != UMFPACK_OK) error ("bad triplet report",0.) ;
+
+ /* convert to column form */
+ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), Map) ;
+ if (status != UMFPACK_OK) error ("matgen_sparse triplet_to_col failed",0.) ;
+
+ /* convert to column form, no values and no map */
+ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(DNULL,DNULL), Cp, Ci, CARG(DNULL,DNULL), noMap) ;
+ if (status != UMFPACK_OK) error ("matgen_sparse triplet_to_col failed",0.) ;
+
+ /* compare C and B, they should be identical */
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Cp [j]) error ("Cp j",0.) ;
+ if (Bp [j+1] != Cp [j+1]) error ("Cp j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ci [p]) error ("Ci",0.) ;
+ }
+ }
+
+ /* convert to column form, no values and with map */
+ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(DNULL,DNULL), Cp, Ci, CARG(DNULL,DNULL), Map) ;
+ if (status != UMFPACK_OK) error ("matgen_sparse triplet_to_col failed",0.) ;
+
+ /* compare C and B, they should be identical */
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Cp [j]) error ("Cp j",0.) ;
+ if (Bp [j+1] != Cp [j+1]) error ("Cp j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ci [p]) error ("Ci",0.) ;
+ }
+ }
+
+#ifdef COMPLEX
+ /* test with merged case too */
+ for (p = 0 ; p < k ; p++)
+ {
+ Txx [2*p ] = Tx [p] ;
+ Txx [2*p+1] = Tz [p] ;
+ }
+
+ /* convert to column form, no map */
+ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Txx,DNULL), Cp, Ci, CARG(Cx,DNULL), noMap) ;
+ if (status != UMFPACK_OK) error ("matgen_sparse triplet_to_col failed",0.) ;
+
+ /* compare C and B, they should be identical */
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Cp [j]) error ("Cp j",0.) ;
+ if (Bp [j+1] != Cp [j+1]) error ("Cp j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ci [p]) error ("Ci",0.) ;
+ if (SCALAR_ABS (Bx [p] - Cx [2*p ]) > 1e-15) error ("Cx",0.) ;
+ if (SCALAR_ABS (Bz [p] - Cx [2*p+1]) > 1e-15) error ("Cz (1)",0.) ;
+ }
+ }
+
+ /* convert to column form */
+ status = UMFPACK_triplet_to_col (n, n, k, Ti, Tj, CARG(Txx,DNULL), Cp, Ci, CARG(Cx,DNULL), Map) ;
+ if (status != UMFPACK_OK) error ("matgen_sparse triplet_to_col failed",0.) ;
+
+ /* compare C and B, they should be identical */
+ for (j = 0 ; j < n ; j++)
+ {
+ if (Bp [j] != Cp [j]) error ("Cp j",0.) ;
+ if (Bp [j+1] != Cp [j+1]) error ("Cp j",0.) ;
+ for (p = Bp [j] ; p < Bp [j+1] ; p++)
+ {
+ if (Bi [p] != Ci [p]) error ("Ci",0.) ;
+ if (SCALAR_ABS (Bx [p] - Cx [2*p ]) > 1e-15) error ("Cx",0.) ;
+ if (SCALAR_ABS (Bz [p] - Cx [2*p+1]) > 1e-15) error ("Cz (1)",0.) ;
+ }
+ }
+
+#endif
+
+ if (prl > 2) printf ("\nmatgen_sparse: ") ;
+ status = UMFPACK_report_matrix (n, n, Bp, Bi, CARG(Bx,Bz), 1, Control) ;
+ if (status != UMFPACK_OK) error ("bad A matgen sparse",0.) ;
+
+ /* check the Map */
+ for (k = 0 ; k < nz ; k++)
+ {
+ p = Map [k] ;
+ i = Ti [k] ;
+ j = Tj [k] ;
+ if (i != Bi [p]) error ("Map Bi", 0.) ;
+ if (!(Bp [j] <= p && p < Bp [j+1])) error ("Map Bp", 0.) ;
+ }
+
+ /* test triplet->col and col->triplet */
+ test_col (n, Bp, Bi, Bx,Bz, prl) ;
+
+ /* return the allocated column-form */
+ *Ap = Bp ;
+ *Ai = Bi ;
+ *Ax = Bx ;
+ *Az = Bz ;
+
+ free (Cx) ; /* ] */
+ free (Ci) ; /* ] */
+ free (Cp) ; /* ] */
+ free (Txx) ; /* ] */
+
+ free (Map) ; /* ] */
+ free (P) ; /* ] */
+ free (Tz) ; /* ] */
+ free (Tx) ; /* ] */
+ free (Tj) ; /* ] */
+ free (Ti) ; /* ] */
+
+}
+
+/* ========================================================================== */
+/* matgen_transpose: B = A(P,Q)', where P and Q are random */
+/* ========================================================================== */
+
+static void matgen_transpose
+(
+ Int n,
+ Int Ap [ ],
+ Int Ai [ ],
+ double Ax [ ], double Az [ ],
+ Int **Bp,
+ Int **Bi,
+ double **Bx, double **Bz
+)
+{
+ Int nz, *P, *Q, *Cp, *Ci, status ;
+ double *Cx, *Cz ;
+
+#ifdef DEBUGGING
+ double Control [UMFPACK_CONTROL] ;
+#endif
+
+ nz = Ap [n] ;
+ P = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Q = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+
+ Cp = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Ci = (Int *) malloc ((nz+1) * sizeof (Int)) ;
+ Cx = (double *) malloc ((nz+1) * sizeof (double)) ;
+ Cz = (double *) calloc ((nz+1) , sizeof (double)) ;
+
+ if (!P || !Q || !Bp || !Bi || !Bx) error ("out of memory (14)",0.) ;
+ if (!Cz) error ("out mem", 0.) ;
+
+ randperm (n, P) ;
+ randperm (n, Q) ;
+
+#ifdef DEBUGGING
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_PRL] = 5 ;
+ printf ("\nA: ") ;
+ status = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Control) ;
+ if (status != UMFPACK_OK) error ("bad A",0.) ;
+ printf ("Random P: ") ;
+ UMFPACK_report_perm (n, P, Control) ;
+ if (status != UMFPACK_OK) error ("bad random P",0.) ;
+ printf ("Random Q: ") ;
+ status = UMFPACK_report_perm (n, Q, Control) ;
+ if (status != UMFPACK_OK) error ("bad random Q",0.) ;
+#endif
+
+ /* do complex conjugate transpose */
+ status = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), P, Q, Cp, Ci, CARG(Cx,Cz) C1ARG(1)) ;
+ if (status != UMFPACK_OK) error ("transpose failed",0.) ;
+
+#ifdef DEBUGGING
+ printf ("\nC: ") ;
+ status = UMFPACK_report_matrix (n, n, Cp, Ci, CARG(Cx,Cz), 1, Control) ;
+ if (status != UMFPACK_OK) error ("bad C",0.) ;
+#endif
+
+ /* do not free Cp, Ci, and Cx */
+ *Bp = Cp ;
+ *Bi = Ci ;
+ *Bx = Cx ;
+ *Bz = Cz ;
+
+ free (P) ; /* ] */
+ free (Q) ; /* ] */
+}
+
+
+/* ========================================================================== */
+/* matgen_file: read a (1-based) matrix and a Qinit from a file */
+/* ========================================================================== */
+
+/* File syntax:
+ * 1st line: nrows ncols nnz isreal
+ * next nnz lines: i j x ... or ... i j xreal ximag
+ * next ncols lines: Qk
+ * one line determinant (real and imag. part if A is complex)
+ * last line determinant of real part of A only
+ */
+
+static void matgen_file
+(
+ char *filename,
+ Int *n_row,
+ Int *n_col,
+ Int **Ap,
+ Int **Ai,
+ double **Ax, double **Az,
+ Int **Qinit,
+ Int prl,
+ double *det_x,
+ double *det_z
+)
+{
+ FILE *f ;
+ Int i, j, k, *Ti, *Tj, nr, nc, nz, *Bp, *Bi, *Q, status, isreal, nz1, n ;
+ double x, *Tx, *Bx, *Tz, *Bz, ximag, Control [UMFPACK_CONTROL],
+ d_x, d_z, d_real ;
+
+ printf ("\nFile: %s\n", filename) ;
+ f = fopen (filename, "r") ;
+ if (!f) error ("bad file", 0.) ;
+
+ fscanf (f, ""ID" "ID" "ID" "ID"\n", &nr, &nc, &nz, &isreal) ;
+ n = MAX (nr, nc) ;
+ n = MAX (n,1) ;
+
+ nz1 = MAX (nz,1) ;
+ Ti = (Int *) malloc (nz1 * sizeof (Int)) ; /* [ */
+ Tj = (Int *) malloc (nz1 * sizeof (Int)) ; /* [ */
+ Tx = (double *) malloc (nz1 * sizeof (double)) ; /* [ */
+ Tz = (double *) calloc (nz1 , sizeof (double)) ; /* [ */
+
+ /* allocate Bp, Bi, Bx, and Q - but do not free them */
+ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Bi = (Int *) malloc (nz1 * sizeof (Int)) ;
+ Bx = (double *) malloc (nz1 * sizeof (double)) ;
+ Q = (Int *) malloc (n * sizeof (Int)) ;
+ Bz = (double *) calloc (nz1 , sizeof (double)) ;
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ if (isreal)
+ {
+ fscanf (f, ""ID" "ID" %lg\n", &i, &j, &x) ;
+ ximag = 0. ;
+ }
+ else
+ {
+ fscanf (f, ""ID" "ID" %lg %lg\n", &i, &j, &x, &ximag) ;
+ }
+ Ti [k] = i-1 ; /* convert to 0-based */
+ Tj [k] = j-1 ;
+ Tx [k] = x ;
+#ifdef COMPLEX
+ Tz [k] = ximag ;
+#else
+ /* the file may have a complex part, but set it to zero */
+ Tz [k] = 0. ;
+#endif
+ }
+
+ for (k = 0 ; k < nc ; k++)
+ {
+ fscanf (f, ""ID"\n", &i) ;
+ Q [k] = i-1 ; /* convert to 0-based */
+ }
+
+ if (isreal)
+ {
+ fscanf (f, "%lg\n", &d_x) ;
+ d_z = 0 ;
+ }
+ else
+ {
+ fscanf (f, "%lg %lg\n", &d_x, &d_z) ;
+ }
+ fscanf (f, "%lg\n", &d_real) ;
+ printf ("%s det: %g + (%g)i, real(A): %g\n", filename, d_x, d_z, d_real) ;
+
+#ifdef COMPLEX
+ *det_x = d_x ;
+ *det_z = d_z ;
+#else
+ /* imaginary part of matrix is ignored */
+ *det_x = d_real ;
+ *det_z = 0 ;
+#endif
+
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_PRL] = prl ;
+ if (prl > 2) printf ("\nmatgen_file: ") ;
+ status = UMFPACK_report_triplet (nr, nc, nz, Ti, Tj, CARG(Tx,Tz), Control) ;
+ if (status != UMFPACK_OK) error ("bad triplet report",0.) ;
+
+ /* convert to column form */
+ status = UMFPACK_triplet_to_col (nr, nc, nz, Ti, Tj, CARG(Tx,Tz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ;
+ if (status != UMFPACK_OK) error ("matgen_file triplet_to_col failed",0.) ;
+
+ if (prl > 2) printf ("\nmatgen_file: ") ;
+ status = UMFPACK_report_matrix (nr, nc, Bp, Bi, CARG(Bx,Bz), 1, Control) ;
+ if (status != UMFPACK_OK) error ("bad A matgen_file",0.) ;
+
+ /* return the allocated column-form */
+ *n_row = nr ;
+ *n_col = nc ;
+ *Ap = Bp ;
+ *Ai = Bi ;
+ *Ax = Bx ;
+ *Az = Bz ;
+ *Qinit = Q ;
+
+ free (Tz) ; /* ] */
+ free (Tx) ; /* ] */
+ free (Tj) ; /* ] */
+ free (Ti) ; /* ] */
+
+ fclose (f) ;
+}
+
+/* ========================================================================== */
+/* matgen_arrow: create an arrowhead matrix */
+/* ========================================================================== */
+
+static Int matgen_arrow
+(
+ Int n,
+ Int **Ap,
+ Int **Ai,
+ Int **Q
+)
+{
+ Int nz, *Bp, *Bi, i, j, p, *Qp ;
+
+ nz = n + 2*(n-1) ;
+ printf ("matgen_arrow: n = "ID" nz = "ID"\n", n, nz) ;
+
+ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ;
+ Bi = (Int *) malloc (nz * sizeof (Int)) ;
+ Qp = (Int *) malloc (n * sizeof (Int)) ;
+
+ if (!Bp || !Bi || !Qp)
+ {
+ free (Bp) ;
+ free (Bi) ;
+ free (Qp) ;
+ printf ("arrow failed\n") ;
+ return (FALSE) ;
+ }
+
+ /* row and column 0, and diagonal, are dense */
+
+ /* column 0 */
+ p = 0 ;
+ Bp [0] = p ;
+ for (i = 0 ; i < n ; i++)
+ {
+ Bi [p] = i ;
+ Qp [p] = i ;
+ p++ ;
+ }
+
+ /* columns 1 to n-1 */
+ for (j = 1 ; j < n ; j++)
+ {
+ Bp [j] = p ;
+ Bi [p] = 0 ; /* row 0 */
+ p++ ;
+ Bi [p] = j ; /* row j (diagonal) */
+ }
+
+ Bp [n] = p ;
+
+ *Ap = Bp ;
+ *Ai = Bi ;
+ *Q = Qp ;
+
+ printf ("matgen_arrow: n = "ID" nz = "ID" done.\n", n, nz) ;
+ return (TRUE) ;
+
+}
+
+
+/* ========================================================================== */
+/* do_and_free: do a matrix, its random transpose, and then free it */
+/* ========================================================================== */
+
+static double do_and_free
+(
+ Int n,
+ Int Ap [ ],
+ Int Ai [ ],
+ double Ax [ ], double Az [ ],
+
+ double Controls [UMFPACK_CONTROL][1000],
+ Int Ncontrols [UMFPACK_CONTROL],
+ Int MemControl [6],
+ Int do_dense
+)
+{
+ Int *Bp, *Bi ;
+ double *Bx, *Bz, rnorm1, rnorm2 ;
+
+ /* A */
+ rnorm1 = do_matrix (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemControl, do_dense) ;
+
+ /* B = A (P,Q), P and Q random */
+ matgen_transpose (n, Ap, Ai, Ax, Az, &Bp, &Bi, &Bx, &Bz) ;
+
+ free (Ap) ;
+ free (Ai) ;
+ free (Ax) ;
+ free (Az) ;
+
+ rnorm2 = do_matrix (n, Bp, Bi, Bx, Bz, Controls, Ncontrols, MemControl, do_dense) ;
+
+ free (Bp) ;
+ free (Bi) ;
+ free (Bx) ;
+ free (Bz) ;
+
+ return (MAX (rnorm1, rnorm2)) ;
+}
+
+/* ========================================================================== */
+/* AMD */
+/* ========================================================================== */
+
+static int do_amd
+(
+ Int n,
+ Int Ap [],
+ Int Ai [],
+ Int P []
+)
+{
+
+#if 0
+#ifndef NDEBUG
+
+ FILE *f ;
+ f = fopen ("apx.m", "w") ;
+ Int j, p, nz ;
+ if (Ap && Ai && P)
+ {
+ nz = Ap [n] ;
+ fprintf (f, "ApX = [ ") ;
+ for (j = 0 ; j <= n ; j++) fprintf (f, ID" ", Ap [j]) ;
+ fprintf (f, "] ; \n nzx = "ID" ;\n Ax = [\n", nz) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ fprintf (f, ID" "ID" 1\n", 1+j, 1+Ai [p]) ;
+ }
+ }
+ fprintf (f, ID" "ID" 0] ;\n", n, n) ;
+ fclose (f) ;
+ }
+
+#endif
+#endif
+
+#if (defined (DINT) || defined (ZINT))
+ return (amd_order (n, Ap, Ai, P, DNULL, DNULL)) ;
+#else
+ return (amd_l_order (n, Ap, Ai, P, DNULL, DNULL)) ;
+#endif
+}
+
+
+static int do_amd_transpose
+(
+ Int n,
+ Int Ap [],
+ Int Ai [],
+ Int Rp [],
+ Int Ri []
+)
+{
+ Int *W, *Flag ;
+
+#if (defined (DINT) || defined (ZINT))
+ if (amd_valid (n, n, Ap, Ai) < AMD_OK || !Ri || !Rp)
+ {
+ return (AMD_INVALID) ;
+ }
+#else
+ if (amd_l_valid (n, n, Ap, Ai) < AMD_OK || !Ri || !Rp)
+ {
+ return (AMD_INVALID) ;
+ }
+#endif
+
+ W = amd_malloc (MAX (n,1) * sizeof (Int)) ;
+ Flag = amd_malloc (MAX (n,1) * sizeof (Int)) ;
+ if (!W || !Flag)
+ {
+ amd_free (W) ;
+ amd_free (Flag) ;
+ return (AMD_OUT_OF_MEMORY) ;
+ }
+
+#if (defined (DINT) || defined (ZINT))
+ amd_preprocess (n, Ap, Ai, Rp, Ri, W, Flag) ;
+#else
+ amd_l_preprocess (n, Ap, Ai, Rp, Ri, W, Flag) ;
+#endif
+
+ amd_free (W) ;
+ amd_free (Flag) ;
+ return (AMD_OK) ;
+
+}
+
+
+
+/* ========================================================================== */
+/* do_file: read a matrix from a matrix and call do_many */
+/* ========================================================================== */
+
+static double do_file
+(
+ char *filename,
+ Int prl,
+ Int MemControl [6]
+)
+{
+ Int n_row, n_col, *Ap, *Ai, *Qinit, n, *P, s, *W, scale, row, col, p,
+ strategy, fixQ ;
+ double *Ax, *Az, Control [UMFPACK_CONTROL], *b, rnorm, *bz, maxrnorm, bad,
+ det_x, det_z ;
+
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_PRL] = prl ;
+ maxrnorm = 0 ;
+
+ /* get the matrix A and preordering Qinit */
+ matgen_file (filename, &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, prl,
+ &det_x, &det_z) ; /* [[[[[ */
+
+ check_tol = SCALAR_ABS (det_x < 1e100) ;
+
+ /* test amd, on A and A transpose */
+ if (n_row == n_col)
+ {
+ Int k, *Rp, *Ri ;
+ P = (Int *) malloc (n_row * sizeof (Int)) ; /* [ */
+ W = (Int *) malloc (n_row * sizeof (Int)) ; /* [ */
+ Rp = (Int *) malloc ((n_row+1) * sizeof (Int)) ; /* [ */
+ Ri = (Int *) malloc ((Ap [n_row]) * sizeof (Int)) ; /* [ */
+ s = do_amd (n_row, Ap, Ai, P) ;
+ if (s != AMD_OK) error ("amd2", (double) s) ;
+ s = UMF_report_perm (n_row, P, W, 3, 0) ;
+ if (s != UMFPACK_OK) error ("amd3", (double) s) ;
+ s = do_amd_transpose (n_row, Ap, Ai, Rp, Ri) ;
+ if (s != AMD_OK) error ("amd4", (double) s) ;
+ s = do_amd (n_row, Rp, Ri, P) ;
+ if (s != AMD_OK) error ("amd5", (double) s) ;
+ s = UMF_report_perm (n_row, P, W, 3, 0) ;
+ if (s != UMFPACK_OK) error ("amd6", (double) s) ;
+ free (Ri) ; /* ] */
+ free (Rp) ; /* ] */
+ free (W) ; /* ] */
+ free (P) ; /* ] */
+ }
+
+ /* do the matrix */
+ n = MAX (n_row, n_col) ;
+ n = MAX (n,1) ;
+ b = (double *) calloc (n, sizeof (double)) ; /* [ */
+ bz= (double *) calloc (n, sizeof (double)) ; /* [ */
+
+ if (n_row == n_col)
+ {
+ bgen (n, Ap, Ai, Ax,Az, b,bz) ;
+ }
+
+ if (prl == 5 && MAX (n_row, n_col) > 600)
+ {
+ /* do nothing */
+ ;
+ }
+ else if (prl >= 3 || MAX (n_row, n_col) > 15)
+ {
+
+ /* quick test */
+ printf ("Control strategy auto Q prl "ID"\n", prl) ;
+ printf ("quick test..\n") ;
+ rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, TRUE, TRUE, det_x, det_z) ;
+ printf ("quick test.. done\n") ;
+ printf ("Control strategy auto Q prl "ID" :: rnorm %g\n", prl, rnorm) ;
+ if (check_tol)
+ {
+ if (rnorm >= TOL) error ("bad do_file", rnorm) ;
+ maxrnorm = rnorm ;
+ }
+
+ /* quick test - no aggressive absorption */
+ printf ("Control strategy auto Q prl "ID" no aggressive\n", prl) ;
+ Control [UMFPACK_AGGRESSIVE] = 0 ;
+ rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, TRUE, TRUE, det_x, det_z) ;
+ printf ("Control strategy auto Q prl "ID" no aggressive:: rnorm %g\n", prl, rnorm) ;
+ if (check_tol)
+ {
+ if (rnorm >= TOL) error ("bad do_file", rnorm) ;
+ maxrnorm = rnorm ;
+ }
+
+ /* quick test - symmetric strategy, no aggressive absorption */
+ printf ("Control strategy auto Q prl "ID" no aggressive, symmetric\n", prl) ;
+ Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_SYMMETRIC ;
+ UMFPACK_report_control (Control) ;
+ rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, TRUE, TRUE, det_x, det_z) ;
+ printf ("Control strategy auto Q prl "ID" no aggressive, symmetric:: rnorm %g\n", prl, rnorm) ;
+ if (check_tol)
+ {
+ if (rnorm >= TOL) error ("bad do_file", rnorm) ;
+ maxrnorm = rnorm ;
+ }
+
+ }
+ else
+ {
+ /* full test */
+ for (strategy = -1 ; strategy <= UMFPACK_STRATEGY_SYMMETRIC ; strategy ++)
+ {
+ Control [UMFPACK_STRATEGY] = strategy ;
+ if (strategy == UMFPACK_STRATEGY_SYMMETRIC)
+ {
+ if (n < 5) UMFPACK_report_control (Control) ;
+
+ for (fixQ = -1 ; fixQ <= 1 ; fixQ++)
+ {
+ Control [UMFPACK_FIXQ] = fixQ ;
+
+
+ for (scale = -1 ; scale <= UMFPACK_SCALE_MAX ; scale++)
+ {
+ Control [UMFPACK_SCALE] = scale ;
+ printf ("Control strategy "ID" "ID" noQ prl "ID" scale "ID"\n",
+ strategy, fixQ, prl, scale) ;
+ rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemControl, TRUE, TRUE, det_x, det_z) ;
+ printf ("Control strategy "ID" "ID" noQ prl "ID" scale "ID" :: rnorm %g\n",
+ strategy, fixQ, prl, scale, rnorm) ;
+ if (check_tol)
+ {
+ maxrnorm = MAX (maxrnorm, rnorm) ;
+ if (rnorm >= TOL) error ("bad do_file", rnorm) ;
+ }
+ }
+
+ printf ("Control strategy "ID" "ID" Q\n", strategy, fixQ) ;
+ rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, TRUE, TRUE, det_x, det_z) ;
+ printf ("Control strategy "ID" "ID" Q :: rnorm %g\n",
+ strategy, fixQ, rnorm) ;
+ if (check_tol)
+ {
+ maxrnorm = MAX (maxrnorm, rnorm) ;
+ if (rnorm >= TOL) error ("bad do_file", rnorm) ;
+ }
+ }
+ Control [UMFPACK_FIXQ] = UMFPACK_DEFAULT_FIXQ ;
+ }
+ else
+ {
+ printf ("Control strategy "ID" Q prl "ID"\n", strategy, prl) ;
+ rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemControl, TRUE, TRUE, det_x, det_z) ;
+ printf ("Control strategy "ID" Q prl "ID" :: rnorm %g\n", strategy, prl, rnorm) ;
+ if (check_tol)
+ {
+ maxrnorm = MAX (maxrnorm, rnorm) ;
+ if (rnorm >= TOL) error ("bad do_file", rnorm) ;
+ }
+
+ printf ("Control strategy "ID" noQ\n", strategy) ;
+ rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemControl, TRUE, TRUE, det_x, det_z) ;
+ printf ("Control strategy "ID" noQ :: rnorm %g\n", strategy, rnorm) ;
+ if (check_tol)
+ {
+ maxrnorm = MAX (maxrnorm, rnorm) ;
+ if (rnorm >= TOL) error ("bad do_file", rnorm) ;
+ }
+
+#ifdef UMFPACK_DROPTOL
+ Control [UMFPACK_DROPTOL] = 1e-25 ;
+ printf ("Control strategy "ID" noQ droptol 1e-25\n", strategy) ;
+ rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemControl, TRUE, TRUE, det_x, det_z) ;
+ printf ("Control strategy "ID" noQ droptol 1e-25 :: rnorm %g\n", strategy, rnorm) ;
+ if (check_tol)
+ {
+ maxrnorm = MAX (maxrnorm, rnorm) ;
+ if (rnorm >= TOL) error ("bad do_file", rnorm) ;
+ }
+ Control [UMFPACK_DROPTOL] = 0 ;
+#endif
+
+ }
+ }
+ }
+
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_PRL] = 3 ;
+
+ /* scale row 0 */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ for (p = Ap [col] ; p < Ap [col+1] ; p++)
+ {
+ row = Ai [p] ;
+ if (row == 0)
+ {
+ Ax [p] *= 1e-20 ;
+ Az [p] *= 1e-20 ;
+ }
+ }
+ }
+ b [0] *= 1e-20 ;
+ bz [0] *= 1e-20 ;
+
+ printf ("Control defaults noQ tiny row 0\n") ;
+ rnorm = do_many (n_row, n_col, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemControl, TRUE, TRUE, 1e-20*det_x, 1e-20*det_z) ;
+ printf ("Control defaults noQ tiny row 0:: rnorm %g\n", rnorm) ;
+ if (check_tol)
+ {
+ maxrnorm = MAX (maxrnorm, rnorm) ;
+ if (rnorm >= TOL) error ("bad do_file", rnorm) ;
+ }
+
+ free (bz) ; /* ] */
+ free (b) ; /* ] */
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Az) ; /* ] */
+ free (Qinit) ; /* ] */
+
+ check_tol = TRUE ;
+
+ return (maxrnorm) ;
+}
+
+/* ========================================================================== */
+/* main */
+/* ========================================================================== */
+
+
+#if 0
+/* compile with -lefence and -DEFENCE */
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+EXTERN int EF_PROTECT_FREE ;
+EXTERN int EF_PROTECT_BELOW ;
+#endif
+
+
+int main (int argc, char **argv)
+{
+ double *Lx, *Ux, *x, *Cx, *Bx, *Ax, *b, *Ax2,
+ *Lz, *Uz, *xz, *Cz, *Bz, *Az, *bz,*Az2,
+ rnorm, maxrnorm, *Con, Info [UMFPACK_INFO], *Wx, *Rs, xnan, xinf, ttt,
+ Controls [UMFPACK_CONTROL][1000], Control [UMFPACK_CONTROL],
+ alphas [ ] = {-1.0, 0.0, 0.1, 0.5, 10.}, *info, maxrnorm_shl0,
+ rnorm_omega2, maxrnorm_arc130, det_x, det_z, Mx, Mz, Exp ;
+ Int Ncontrols [UMFPACK_CONTROL], c, i, n, prl, *Qinit, *Qinit2, n1,
+ *Ap, *Ai, *Aj, nz, *Ap2, *Ai2, p, j, d, s, s2, *Pinit, k, n2, *Map,
+ *Lp, *Li, *P, *Q, *Up, *Ui, lnz, unz, nn, *Cp, *Ci, *Cj, *Bi, *Bp, *Bj,
+ *Pa, *Front_npivots, *Front_parent, *Chain_start, *Chain_maxrows, *ip,
+ *Chain_maxcols, nfr, nchains, nsparse_col, *Qtree, *Ptree, nnz,
+ MemOK [6], MemBad [6], nnrow, nncol, nzud, n_row, n_col, n_row2,
+ n_col2, scale, *Front_1strow, *Front_leftmostdesc, strategy,
+ t, aggressive, *Pamd, mem1, mem2, do_recip ;
+ void *Symbolic, *Numeric ;
+ SymbolicType *Sym ;
+ NumericType *Num ;
+ DIR *dir ;
+ struct dirent *direntp ;
+ char filename [200] ;
+ FILE *f ;
+
+ /* turn off debugging */
+ { f = fopen ("debug.umf", "w") ; fprintf (f, "-45\n") ; fclose (f) ; }
+ { f = fopen ("debug.amd", "w") ; fprintf (f, "-45\n") ; fclose (f) ; }
+
+#if 0
+ /* compile with -lefence */
+ EF_PROTECT_FREE = 0 ; /* 1 to test modifications to free'd memory */
+ EF_PROTECT_BELOW = 0 ; /* 1 to test modifications above an obj. */
+#endif
+
+ c = UMFPACK_PIVOT_TOLERANCE ;
+ Controls [c][0] = UMFPACK_DEFAULT_PIVOT_TOLERANCE ;
+ Ncontrols [c] = 1 ;
+
+ c = UMFPACK_SCALE ;
+ Controls [c][0] = UMFPACK_SCALE_SUM ; /* also the default */
+ Ncontrols [c] = 1 ;
+
+ c = UMFPACK_BLOCK_SIZE ;
+ Controls [c][0] = 32 ;
+ Ncontrols [c] = 1 ;
+
+ c = UMFPACK_ALLOC_INIT ;
+ Controls [c][0] = 1.0 ;
+ Ncontrols [c] = 1 ;
+
+ c = UMFPACK_AMD_DENSE ;
+ Controls [c][0] = UMFPACK_DEFAULT_AMD_DENSE ;
+ Ncontrols [c] = 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test malloc, realloc, and free */
+ /* ---------------------------------------------------------------------- */
+
+ P = (Int *) UMF_malloc (Int_MAX, 2) ;
+ if (P) error ("should have failed\n", 0.) ;
+
+ printf ("reallocing...\n") ;
+ P = (Int *) UMF_realloc (P, 1, 4) ;
+ if (!P) error ("should have succeeded\n", 0.) ;
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (UMF_malloc_count != 1) error ("should be 1", 0.) ;
+#endif
+ printf ("ok here...\n") ;
+
+ P = UMF_free (P) ;
+ if (P) error ("should have free'd it\n", 0.) ;
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (UMF_malloc_count != 0) error ("should be 0", 0.) ;
+#endif
+
+ xnan = divide (0., 0.) ;
+ xinf = divide (1., 0.) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* malloc and realloc control */
+ /* ---------------------------------------------------------------------- */
+
+ MemOK [0] = -1 ;
+ MemOK [1] = 0 ;
+ MemOK [2] = 0 ;
+
+ MemOK [3] = -1 ;
+ MemOK [4] = 0 ;
+ MemOK [5] = 0 ;
+
+ /* malloc always succeeds */
+ umf_fail = -1 ;
+ umf_fail_lo = 0 ;
+ umf_fail_hi = 0 ;
+
+ /* realloc always succeeds */
+ umf_realloc_fail = -1 ;
+ umf_realloc_lo = 0 ;
+ umf_realloc_hi = 0 ;
+
+ UMFPACK_defaults (Control) ;
+
+ maxrnorm_shl0 = 0.0 ; /* for shl0 only */
+ maxrnorm = 0.0 ; /* for all other matrices */
+ check_tol = TRUE ;
+
+ /* ---------------------------------------------------------------------- */
+
+ printf ("load/save error handling tests:\n") ;
+
+ /* load a bad symbolic object */
+ s = UMFPACK_load_symbolic (&Symbolic, "badsym.umf") ;
+ if (s == UMFPACK_OK)
+ {
+ error ("load symbolic failed\n", 0.) ;
+ }
+ s = UMFPACK_load_symbolic (&Symbolic, "badsym2.umf") ;
+ if (s == UMFPACK_OK)
+ {
+ error ("load symbolic failed (2)\n", 0.) ;
+ }
+
+ /* load a bad numeric object */
+ s = UMFPACK_load_numeric (&Numeric, "badnum.umf") ;
+ if (s == UMFPACK_OK)
+ {
+ error ("load numeric failed\n", 0.) ;
+ }
+ s = UMFPACK_load_numeric (&Numeric, "badnum2.umf") ;
+ if (s == UMFPACK_OK)
+ {
+ error ("load numeric failed (2)\n", 0.) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test a tiny matrix */
+ /* ---------------------------------------------------------------------- */
+
+ n = 2 ;
+ printf ("\n tiny\n") ;
+ check_tol = TRUE ;
+ matgen_dense (n, &Ap, &Ai, &Ax, &Az) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 0) ;
+ printf ("rnorm tiny %g\n", rnorm) ;
+ if (rnorm > 1e-12)
+ {
+ error ("bad rnorm for tiny matrix", rnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* test a tiny matrix with a NaN in it */
+ /* ---------------------------------------------------------------------- */
+
+ c = UMFPACK_SCALE ;
+ Controls [c][0] = UMFPACK_SCALE_SUM ; /* also the default */
+ Controls [c][1] = UMFPACK_SCALE_NONE ;
+ Ncontrols [c] = 2 ;
+
+ n = 2 ;
+ printf ("\n tiny\n") ;
+ check_tol = TRUE ;
+ matgen_dense (n, &Ap, &Ai, &Ax, &Az) ;
+ Ax [0] = xnan ;
+ Az [0] = 0 ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 0) ;
+ printf ("rnorm tiny %g with NaN\n", rnorm) ;
+
+ n = 2 ;
+ printf ("\n tiny\n") ;
+ check_tol = TRUE ;
+ matgen_dense (n, &Ap, &Ai, &Ax, &Az) ;
+ Ax [1] = 1e-20 ;
+ Az [1] = 0 ;
+ Ax [2] = 2e-20 ;
+ Az [2] = 0 ;
+ Ax [3] = 3e-20 ;
+ Az [3] = 0 ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 0) ;
+ printf ("rnorm tiny %g with NaN and small row\n", rnorm) ;
+
+ n = 2 ;
+ printf ("\n tiny\n") ;
+ check_tol = TRUE ;
+ matgen_dense (n, &Ap, &Ai, &Ax, &Az) ;
+ Ax [0] = 0 ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 0) ;
+ printf ("rnorm tiny %g with small row\n", rnorm) ;
+
+ c = UMFPACK_SCALE ;
+ Controls [c][0] = UMFPACK_SCALE_SUM ; /* also the default */
+ Ncontrols [c] = 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test omega2 */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ n = 500 ;
+ printf ("\n omega 2 test\n") ;
+ matgen_sparse (n, 2*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 0, 0) ;
+
+ f = fopen ("A500", "w") ;
+ fprintf (f, ID" "ID" 0 0\n", n, n) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ fprintf (f, ID" "ID" %40.25e %40.25e\n", Ai [p], j, Ax [p], Az [p]) ;
+ }
+ }
+ fclose (f) ;
+
+ rnorm_omega2 = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 0) ;
+ printf ("rnorm %g omega-2 test\n", rnorm_omega2) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* this is not solved very accurately (about 1e-7) */
+ maxrnorm_shl0 = do_file ("TestMat/shl0", 4, MemOK) ;
+ printf ("rnorm shl0 %10.4e\n", maxrnorm_shl0) ;
+
+ /* this is not solved very accurately (about 1e-5, because of U'x=b) */
+ maxrnorm_arc130 = do_file ("TestMat/arc130", 4, MemOK) ;
+ printf ("rnorm arc130 %10.4e\n", maxrnorm_arc130) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test random sparse matrices */
+ /* ---------------------------------------------------------------------- */
+
+ n = 30 ;
+
+ printf ("sparse %7d 4*n nz's", n) ;
+ matgen_sparse (n, 4*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ; /* [[[[ */
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ; /* ]]]] */
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf ("rnorm %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ rnorm = do_file ("TestMat/matrix5", 5, MemOK) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf ("rnorm matrix 5 %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+ /* malloc always succeeds */
+ umf_fail = -1 ;
+ umf_fail_lo = 0 ;
+ umf_fail_hi = 0 ;
+
+ /* realloc always fails */
+ umf_realloc_fail = 0 ;
+ umf_realloc_lo = -9999999 ;
+ umf_realloc_hi = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* do all test matrices from TestMat directory */
+ /* ---------------------------------------------------------------------- */
+
+ /* quick tests */
+ prl = 1 ;
+
+ matgen_file ("TestMat/matrix1", &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit,
+ prl, &det_x, &det_z) ; /* [[[[[ */
+
+ Control [UMFPACK_ALLOC_INIT] = -211 ;
+
+ /* with no Qinit, out of memory in extend front */
+ s = UMFPACK_symbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), &Symbolic, Control, Info) ; /* [ */
+ if (s != UMFPACK_OK) error ("TestMat matrix1 sym", (double) s) ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; /* [ */
+ if (s != UMFPACK_ERROR_out_of_memory) error ("TestMat matrix1 num", (double) s) ;
+ UMFPACK_free_numeric (&Numeric) ; /* ] */
+ UMFPACK_free_symbolic (&Symbolic) ; /* ] */
+
+ free (Ax) ; /* ] */
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Az) ; /* ] */
+ free (Qinit) ; /* ] */
+
+ matgen_file ("TestMat/matrix10", &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, prl, &det_x, &det_z) ; /* [[[[[ */
+
+ Control [UMFPACK_ALLOC_INIT] = -1321 ;
+
+ /* with Qinit, out of memory in create front (2) */
+ s = UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ; /* [ */
+ if (s != UMFPACK_OK) error ("TestMat matrix10 qsym1", (double) s) ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; /* [ */
+ if (s != UMFPACK_ERROR_out_of_memory) error ("TestMat matrix10 qnum1", (double) s) ;
+ UMFPACK_free_numeric (&Numeric) ; /* ] */
+ UMFPACK_free_symbolic (&Symbolic) ; /* ] */
+
+ Control [UMFPACK_ALLOC_INIT] = -1326 ;
+
+ /* with Qinit, out of memory in init front */
+ s = UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ; /* [ */
+ if (s != UMFPACK_OK) error ("TestMat matrix10 qsym", (double) s) ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; /* [ */
+ if (s != UMFPACK_ERROR_out_of_memory) error ("TestMat matrix10 qnum", (double) s) ;
+ UMFPACK_free_numeric (&Numeric) ; /* ] */
+ UMFPACK_free_symbolic (&Symbolic) ; /* ] */
+
+ free (Ax) ; /* ] */
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Az) ; /* ] */
+ free (Qinit) ; /* ] */
+
+ printf ("\ndone with TestMat memory sizes.\n\n") ;
+ UMFPACK_defaults (Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test amd */
+ /* ---------------------------------------------------------------------- */
+
+ n = 50 ;
+ P = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ for (k = 0 ; k < 10 ; k++)
+ {
+ matgen_sparse (n, 4*n, 3, 2*n, 0, 0, &Ap, &Ai, &Ax, &Az, 0, 0) ; /* [[[[ */
+ for (aggressive = 0 ; aggressive <= 2 ; aggressive++)
+ {
+ for (i = 0 ; i < 3 ; i++)
+ {
+
+#if (defined (DINT) || defined (ZINT))
+
+ amd_defaults (Control) ;
+ Control [AMD_AGGRESSIVE] = aggressive ;
+ Control [AMD_DENSE] = alphas [i] ;
+ Con = (aggressive == 2) ? DNULL : Control ;
+ info = (aggressive == 2) ? DNULL : Info ;
+ amd_control (Con) ;
+ s = amd_order (n, Ap, Ai, P, Con, info) ;
+ if (s != AMD_OK) error ("amd", (double) s) ;
+ amd_info (info) ;
+
+#else
+
+ amd_l_defaults (Control) ;
+ Control [AMD_AGGRESSIVE] = aggressive ;
+ Control [AMD_DENSE] = alphas [i] ;
+ Con = (aggressive == 2) ? DNULL : Control ;
+ info = (aggressive == 2) ? DNULL : Info ;
+ amd_l_control (Con) ;
+ s = amd_l_order (n, Ap, Ai, P, Con, info) ;
+ if (s != AMD_OK) error ("amd", (double) s) ;
+ amd_l_info (info) ;
+
+#endif
+
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_PRL] = 3 ;
+ UMFPACK_report_perm (n, P, Control) ;
+ }
+ }
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Az) ; /* ] */
+ }
+ free (P) ; /* ] */
+
+ if (AMD_valid (-1, -1, INULL, INULL) >= AMD_OK) error ("amd error", 0.) ;
+ Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
+ AMD_info (Info) ;
+ Info [AMD_STATUS] = AMD_INVALID ;
+ AMD_info (Info) ;
+ Info [AMD_STATUS] = -911 ;
+ AMD_info (Info) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* malloc and realloc control */
+ /* ---------------------------------------------------------------------- */
+
+ MemOK [0] = -1 ;
+ MemOK [1] = 0 ;
+ MemOK [2] = 0 ;
+
+ MemOK [3] = -1 ;
+ MemOK [4] = 0 ;
+ MemOK [5] = 0 ;
+
+ umf_fail = -1 ;
+ umf_fail_lo = 0 ;
+ umf_fail_hi = 0 ;
+
+ umf_realloc_fail = -1 ;
+ umf_realloc_lo = 0 ;
+ umf_realloc_hi = 0 ;
+
+ for (i = 0 ; i < UMFPACK_CONTROL ; i++)
+ {
+ Ncontrols [i] = 0 ;
+ }
+
+ UMFPACK_defaults (Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* do three funky sizes to test int overflow cases */
+ /* ---------------------------------------------------------------------- */
+
+ {
+ /* Int funky_sizes [ ] = { 14402, 16400, 600000 } ; */
+ Int funky_sizes [ ] = { 144, 164, 600 } ;
+
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_PRL] = 1 ;
+ Control [UMFPACK_STRATEGY] = 3 ;
+ Control [UMFPACK_FRONT_ALLOC_INIT] = 1 ;
+
+ for (k = 0 ; k < 3 ; k++)
+ {
+ n = funky_sizes [k] ;
+
+ printf ("funky matrix, n = "ID"\n", n) ;
+ matgen_funky (n, &Ap, &Ai, &Ax, &Az) ; /* [[[[ */
+
+ b = (double *) malloc (n * sizeof (double)) ; /* [ */
+ bz= (double *) calloc (n , sizeof (double)) ; /* [ */
+ Qinit = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ if (!b) error ("out of memory (15)",0.) ;
+ if (!bz) error ("out of memory (16)",0.) ;
+ if (!Qinit) error ("out of memory (17)",0.) ;
+ bgen (n, Ap, Ai, Ax, Az, b, bz) ;
+
+ for (i = 0 ; i < n ; i++) Qinit [i] = i ;
+ fflush (stdout) ;
+
+ Control [UMFPACK_FIXQ] = 1 ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ;
+ printf ("funky matrix rnorm (fixQ): %g\n", rnorm) ;
+ fflush (stdout) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ Control [UMFPACK_FIXQ] = 0 ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ;
+ printf ("funky matrix rnorm (no fixQ): %g\n", rnorm) ;
+ fflush (stdout) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+
+ free (Qinit) ; /* ] */
+ free (bz) ; /* ] */
+ free (b) ; /* ] */
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Az) ; /* ] */
+ }
+ }
+ /* maxrnorm = 0 ; */
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* tight controls */
+ /* ---------------------------------------------------------------------- */
+
+ c = UMFPACK_PIVOT_TOLERANCE ;
+ Controls [c][0] = UMFPACK_DEFAULT_PIVOT_TOLERANCE ;
+ Ncontrols [c] = 1 ;
+
+ c = UMFPACK_SCALE ;
+ Controls [c][1] = UMFPACK_DEFAULT_SCALE ;
+ Ncontrols [c] = 1 ;
+
+ c = UMFPACK_BLOCK_SIZE ;
+ Controls [c][0] = UMFPACK_DEFAULT_BLOCK_SIZE ;
+ Ncontrols [c] = 1 ;
+
+ c = UMFPACK_ALLOC_INIT ;
+ Controls [c][0] = UMFPACK_DEFAULT_ALLOC_INIT ;
+ Ncontrols [c] = 1 ;
+
+ c = UMFPACK_AMD_DENSE ;
+ Controls [c][0] = UMFPACK_DEFAULT_AMD_DENSE ;
+ Ncontrols [c] = 1 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* license */
+ /* ---------------------------------------------------------------------- */
+
+ Control [UMFPACK_PRL] = 6 ;
+ UMFPACK_report_status (Control, UMFPACK_OK) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* do all test matrices from TestMat directory */
+ /* ---------------------------------------------------------------------- */
+
+ printf ("\nStarting TestMat:\n") ;
+ for (prl = 5 ; prl >= 0 ; prl--)
+ {
+ printf ("=====================TestMat PRL "ID"\n", prl) ;
+ dir = opendir ("TestMat") ;
+ if (!dir) { printf ("opendir TestMat failed\n") ; exit (1) ; }
+ while (TRUE)
+ {
+ errno = 0 ;
+ if ((direntp = readdir (dir)) != NULL)
+ {
+ /* skip this */
+ if (direntp->d_name [0] == '.') continue ;
+ sprintf (filename, "TestMat/%s", direntp->d_name) ;
+ rnorm = do_file (filename, prl, MemOK) ;
+
+ if (strcmp (filename, "TestMat/shl0") == 0)
+ {
+ printf ("shl0 rnorm: %g\n", rnorm) ;
+ maxrnorm_shl0 = MAX (maxrnorm_shl0, rnorm) ;
+ }
+ else if (strcmp (filename, "TestMat/arc130") == 0)
+ {
+ printf ("arc130 rnorm: %g\n", rnorm) ;
+ maxrnorm_arc130 = MAX (maxrnorm_arc130, rnorm) ;
+ }
+ else
+ {
+ printf ("other testmat rnorm: %g\n", rnorm) ;
+ maxrnorm = MAX (maxrnorm, rnorm) ;
+ }
+ }
+ else
+ {
+ if (errno != 0) { printf ("read error\n") ; exit (1) ; }
+ closedir (dir) ;
+ break ;
+ }
+ }
+ printf ("\n\n@@@@@@ Largest TestMat do_file rnorm: %g shl0: %g @@@@@@ arc130: %g\n\n", maxrnorm, maxrnorm_shl0, maxrnorm_arc130) ;
+ }
+
+ printf ("\ndone with TestMat.\n\n") ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test change of pattern */
+ /* ---------------------------------------------------------------------- */
+
+ Control [UMFPACK_PRL] = 5 ;
+ Control [UMFPACK_ALLOC_INIT] = 0. ;
+
+ matgen_file ("TestMat/matrix1", &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, 5, &det_x, &det_z) ; /* [[[[[ */
+ s = UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (!Symbolic || Info [UMFPACK_STATUS] != UMFPACK_OK) error ("p1",0.) ;
+ printf ("\nGood symbolic, pattern test: ") ;
+ s = UMFPACK_report_symbolic (Symbolic, Control) ;
+ UMFPACK_report_status (Control, s) ;
+ if (s != UMFPACK_OK) error ("p1c",0.) ;
+ UMFPACK_report_control (Control) ;
+
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ printf ("p1b status: "ID" Numeric handle bad "ID"\n", s, !Numeric) ;
+ s2 = UMFPACK_report_numeric (Numeric, Control) ;
+ if (!Numeric || s != UMFPACK_OK) error ("p1b",0.) ;
+ printf ("Good numeric, pattern test: ") ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ UMFPACK_report_status (Control, s) ;
+ if (s2 != UMFPACK_OK) error ("p1d",0.) ;
+ UMFPACK_free_numeric (&Numeric) ;
+
+ /* corrupted Ap (negative degree) */
+ c = Ap [1] ;
+ Ap [1] = -1 ;
+ printf ("Bad Ap [1] = -1: \n") ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("zzz1",0.) ;
+ Ap [1] = c ;
+
+ /* corrupted Ai (out of bounds) */
+ c = Ai [1] ;
+ Ai [1] = -1 ;
+ printf ("Bad Ai [1] = -1: \n") ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("zzz2",0.) ;
+ Ai [1] = c ;
+
+ /* corrupted Ai (out of bounds) */
+ c = Ai [1] ;
+ Ai [1] = n_row ;
+ printf ("Bad Ai [1] = "ID": \n", n_row) ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("zzz3",0.) ;
+ Ai [1] = c ;
+
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Az) ; /* ] */
+ free (Qinit) ; /* ] */
+
+ /* one more entry */
+ printf ("one more entry\n") ;
+ matgen_file ("TestMat/matrix2", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */
+ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p2",0.) ;
+ free (Ap2) ; /* ] */
+ free (Ai2) ; /* ] */
+ free (Ax2) ; /* ] */
+ free (Az2) ; /* ] */
+ free (Qinit2) ; /* ] */
+ printf ("one more entry done\n") ;
+
+ /* one less entry */
+ matgen_file ("TestMat/matrix3", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */
+ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p3",0.) ;
+ free (Ap2) ; /* ] */
+ free (Ai2) ; /* ] */
+ free (Ax2) ; /* ] */
+ free (Az2) ; /* ] */
+ free (Qinit2) ; /* ] */
+
+ /* many more entries */
+ matgen_file ("TestMat/matrix4", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */
+ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Ax2), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p4",0.) ;
+ free (Ap2) ; /* ] */
+ free (Ai2) ; /* ] */
+ free (Ax2) ; /* ] */
+ free (Az2) ; /* ] */
+ free (Qinit2) ; /* ] */
+
+ /* some more entries */
+ matgen_file ("TestMat/matrix5", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */
+ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p5",0.) ;
+ free (Ap2) ; /* ] */
+ free (Ai2) ; /* ] */
+ free (Ax2) ; /* ] */
+ free (Az2) ; /* ] */
+ free (Qinit2) ; /* ] */
+
+ /* same entries - but different pattern */
+ matgen_file ("TestMat/matrix6", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */
+ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p6",0.) ;
+ free (Ap2) ; /* ] */
+ free (Ai2) ; /* ] */
+ free (Ax2) ; /* ] */
+ free (Az2) ; /* ] */
+ free (Qinit2) ; /* ] */
+
+ /* same entries - but different pattern */
+ matgen_file ("TestMat/matrix7", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */
+ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p7",0.) ;
+ free (Ap2) ; /* ] */
+ free (Ai2) ; /* ] */
+ free (Ax2) ; /* ] */
+ free (Az2) ; /* ] */
+ free (Qinit2) ; /* ] */
+
+ /* same entries - but different pattern */
+ matgen_file ("TestMat/matrix8", &n_row2, &n_col2, &Ap2, &Ai2, &Ax2, &Az2, &Qinit2, 5, &det_x, &det_z) ; /* [[[[[ */
+ s = UMFPACK_numeric (Ap2, Ai2, CARG(Ax2,Az2), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_different_pattern) error ("p8",0.) ;
+ free (Ap2) ; /* ] */
+ free (Ai2) ; /* ] */
+ free (Ax2) ; /* ] */
+ free (Az2) ; /* ] */
+ free (Qinit2) ; /* ] */
+
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ /* start over, use a bigger matrix */
+ matgen_file ("TestMat/matrix10", &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, 5, &det_x, &det_z) ; /* [[[[[ */
+ s = UMFPACK_qsymbolic (n_row, n_col, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (prl > 2) printf ("\nGood matrix10 symbolic, pattern test: ") ;
+ s = UMFPACK_report_symbolic (Symbolic, Control) ;
+ if (!Symbolic || Info [UMFPACK_STATUS] != UMFPACK_OK) error ("p10",0.) ;
+ if (s != UMFPACK_OK) error ("p10",0.) ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (!Numeric || s != UMFPACK_OK) error ("p10b",0.) ;
+ printf ("Good matrix10matrix10 numeric, pattern test:") ;
+ s = UMFPACK_report_numeric (Numeric, Control) ;
+ if (s != UMFPACK_OK) error ("p10b",0.) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ UMFPACK_free_numeric (&Numeric) ;
+
+ /* kludge Symbolic to force a huge dmax */
+ printf ("\nKludge symbolic to force dmax int overflow:\n") ;
+ Control [UMFPACK_PRL] = 3 ;
+ Sym = (SymbolicType *) Symbolic ;
+ Sym->amd_dmax = 16400 ;
+ s = UMFPACK_report_symbolic (Symbolic, Control) ;
+ if (!Symbolic || Info [UMFPACK_STATUS] != UMFPACK_OK) error ("p10e",0.) ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ;
+ if (!Numeric || s != UMFPACK_OK) error ("p10c",0.) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ UMFPACK_free_numeric (&Numeric) ;
+
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Az) ; /* ] */
+ free (Qinit) ; /* ] */
+
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset controls */
+ /* ---------------------------------------------------------------------- */
+
+ UMFPACK_defaults (Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test realloc */
+ /* ---------------------------------------------------------------------- */
+
+ /* malloc always succeeds */
+ MemBad [0] = -1 ;
+ MemBad [1] = 0 ;
+ MemBad [2] = 0 ;
+
+ /* realloc always fails */
+ MemBad [3] = 0 ;
+ MemBad [4] = 0 ;
+ MemBad [5] = -99999 ;
+
+ c = UMFPACK_ALLOC_INIT ;
+ Ncontrols [c] = 1 ;
+ Controls [c][0] = 0.001 ;
+
+#ifdef DINT
+ printf ("\n all realloc fails sparse + dense rows %7d 4*n nz's\n", n) ;
+ matgen_sparse (n, 4*n, 3, 2*n, 0, 0, &Ap, &Ai, &Ax, &Az, 0, 0) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemBad, 0) ;
+ printf ("rnorm %g should be 9e10\n", rnorm) ;
+ if (rnorm != 9e10) error ("MemBad 1 failure", rnorm) ;
+
+ printf ("\n all realloc fails sparse %7d 30*n nz's\n", n) ;
+ matgen_sparse (n, 30*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 0, 0) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemBad, 0) ;
+ printf ("rnorm %g should be 9e10\n", rnorm) ;
+ if (rnorm != 9e10) error ("MemBad 2 failure", rnorm) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* umf_symbolic compaction test */
+ /* ---------------------------------------------------------------------- */
+
+ n = 100 ;
+ Control [UMFPACK_PRL] = 4 ;
+ Qinit = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ b = (double *) malloc (n * sizeof (double)) ; /* [ */
+ bz= (double *) calloc (n , sizeof (double)) ; /* [ */
+ for (i = 0 ; i < n ; i++) Qinit [i] = i ;
+ matgen_compaction (n, &Ap, &Ai, &Ax, &Az) ; /* [[[[ */
+ bgen (n, Ap, Ai, Ax, Az, b, bz) ;
+ printf ("\nA compaction: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Control) ;
+ if (s != UMFPACK_OK) error ("219", 0.) ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ;
+ printf ("rnorm %g A compaction\n", rnorm) ;
+ Control [UMFPACK_PRL] = 1 ;
+
+ printf ("do_and_free for compacted matrix:\n") ;
+ rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 0) ; /* ]]]] */
+ printf ("rnorm for compacted matrix %g\n", rnorm) ;
+ free (b) ; /* ] */
+ free (bz) ; /* ] */
+ free (Qinit) ; /* ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* umf_symbolic compaction test, again (read a file) */
+ /* ---------------------------------------------------------------------- */
+
+ matgen_file ("TestMat/shl0", &n_row, &n_col, &Ap, &Ai, &Ax, &Az, &Qinit, 5, &det_x, &det_z) ; /* [[[[[ */
+ n = n_row ;
+ b = (double *) malloc (n * sizeof (double)) ; /* [ */
+ bz= (double *) calloc (n , sizeof (double)) ; /* [ */
+ bgen (n, Ap, Ai, Ax, Az, b, bz) ;
+ Control [UMFPACK_PRL] = 5 ;
+ Control [UMFPACK_DENSE_ROW] = 0.1 ;
+ Control [UMFPACK_DENSE_COL] = 2.0 ;
+ printf ("\nshl0 b: ") ;
+ UMFPACK_report_vector (n, CARG(b,bz), Control) ;
+ printf ("\nshl0 A: ") ;
+ UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Control) ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ;
+ printf ("rnorm %g for shl0", rnorm) ;
+ maxrnorm_shl0 = MAX (maxrnorm_shl0, rnorm) ;
+ free (bz) ; /* ] */
+ free (b) ; /* ] */
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Az) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Qinit) ; /* ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* normal Controls */
+ /* ---------------------------------------------------------------------- */
+
+ c = UMFPACK_PIVOT_TOLERANCE ;
+ Controls [c][0] = UMFPACK_DEFAULT_PIVOT_TOLERANCE ;
+ Controls [c][1] = 0.5 ;
+ Controls [c][2] = 1.0 ;
+ Ncontrols [c] = 3 ;
+
+ c = UMFPACK_SCALE ;
+ Controls [c][0] = UMFPACK_SCALE_SUM ; /* also the default */
+ Controls [c][1] = UMFPACK_SCALE_NONE ;
+ Controls [c][2] = UMFPACK_SCALE_MAX ;
+ Ncontrols [c] = 3 ;
+
+ c = UMFPACK_BLOCK_SIZE ;
+ Controls [c][0] = 1 ;
+ Controls [c][1] = 8 ;
+ Controls [c][2] = 16 ; /* not the default */
+ Ncontrols [c] = 3 ;
+
+ c = UMFPACK_ALLOC_INIT ;
+ Controls [c][0] = 0.0 ;
+ Controls [c][1] = 0.5 ;
+ Controls [c][2] = 1.0 ; /* not the default */
+ Controls [c][3] = -10000 ;
+ Ncontrols [c] = 4 ;
+
+ c = UMFPACK_AMD_DENSE ;
+ Controls [c][0] = -1 ;
+ Controls [c][1] = 0.5 ;
+ Controls [c][2] = UMFPACK_DEFAULT_AMD_DENSE ;
+ Ncontrols [c] = 3 ;
+
+ UMFPACK_defaults (Control) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test realloc */
+ /* ---------------------------------------------------------------------- */
+
+ /* malloc always succeeds */
+ MemBad [0] = -1 ;
+ MemBad [1] = 0 ;
+ MemBad [2] = 0 ;
+
+ /* realloc always fails */
+ MemBad [3] = 0 ;
+ MemBad [4] = 0 ;
+ MemBad [5] = -99999 ;
+
+ n = 10 ;
+
+ printf ("\n all realloc fails sparse %7d 4*n nz's\n", n) ;
+ matgen_sparse (n, 4*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemBad, 1) ;
+ printf ("rnorm %g for all-realloc-fails\n", rnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset malloc and realloc failure */
+ /* ---------------------------------------------------------------------- */
+
+ umf_fail = -1 ;
+ umf_fail_lo = 0 ;
+ umf_fail_hi = 0 ;
+
+ umf_realloc_fail = -1 ;
+ umf_realloc_lo = 0 ;
+ umf_realloc_hi = 0 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test errors */
+ /* ---------------------------------------------------------------------- */
+
+ n = 32 ;
+
+ Pamd = (Int *) malloc (2*n * sizeof (Int)) ; /* [ */
+ Qinit = (Int *) malloc (2*n * sizeof (Int)) ; /* [ */
+ Pinit = (Int *) malloc (2*n * sizeof (Int)) ; /* [ */
+ Qinit2 = (Int *) malloc (2*n * sizeof (Int)) ; /* [ */
+ b = (double *) malloc (2*n * sizeof (double)) ; /* [ */
+ bz= (double *) calloc (2*n , sizeof (double)) ; /* [ */
+ x = (double *) malloc (2*n * sizeof (double)) ; /* [ */
+ xz= (double *) calloc (2*n , sizeof (double)) ; /* [ */
+ Ap2 = (Int *) malloc ((2*n+1) * sizeof (Int)) ; /* [ */
+
+ if (!Qinit || !b || !Ap2 || !Qinit2 || !Pinit) error ("out of memory (18)",0.) ;
+ if (!xz || !bz) error ("memr again",0.) ;
+
+ UMFPACK_defaults (DNULL) ;
+ UMFPACK_defaults (Control) ;
+
+ randperm (n, Pinit) ;
+
+ for (prl = 5 ; prl >= -1 ; prl--)
+ {
+ for (strategy = UMFPACK_STRATEGY_AUTO ; strategy <= UMFPACK_STRATEGY_SYMMETRIC ; strategy++)
+ {
+ Int *Rp, *Ri ;
+
+ printf ("\n[[[[ PRL = "ID" strategy = "ID"\n", prl, strategy) ;
+ for (k = 0 ; k < n ; k++) Pamd [k] = EMPTY ;
+ Control [UMFPACK_PRL] = prl ;
+ Control [UMFPACK_STRATEGY] = strategy ;
+ UMFPACK_report_control (Control) ;
+ i = UMFPACK_DENSE_DEGREE_THRESHOLD (0.2, n) ;
+ printf ("(default) dense row/col degree threshold: "ID"\n", i) ;
+
+ /* ------------------------------------------------------------------ */
+
+ matgen_sparse (n, 4*n, 10, 2*n, 10, 2*n, &Ap, &Ai, &Ax, &Az, prl, 0) ; /* [[[[ */
+ bgen (n, Ap, Ai, Ax,Az, b,bz) ;
+
+ nz = Ap [n] ;
+ Aj = (Int *) malloc ((nz+n+1) * sizeof (Int)) ; /* [ */
+ Ai2 = (Int *) malloc ((nz+n) * sizeof (Int)) ; /* [ */
+ Ax2 = (double *) malloc ((nz+n) * sizeof (double)) ; /* [ */
+ Az2 = (double *) calloc ((nz+n) , sizeof (double)) ; /* [ */
+ if (!Aj || !Ai2 || !Ax2 || !Az2) error ("out of memory (19)",0.) ;
+ Rp = Aj ;
+ Ri = Ai2 ;
+
+ /* ------------------------------------------------------------------ */
+
+ Con = (prl == -1) ? (DNULL) : Control ;
+ UMFPACK_report_control (Con) ;
+
+ /* ------------------------------------------------------------------ */
+
+ randperm (n, Qinit) ;
+ if (prl > 2) printf ("Qinit OK: ") ;
+ s = UMFPACK_report_perm (n, Qinit, Con) ;
+ if (s != UMFPACK_OK) error ("Qinit OK", 0.) ;
+
+ randperm (2*n, Qinit2) ;
+ if (prl > 2) printf ("Qinit2 OK: ") ;
+ s = UMFPACK_report_perm (2*n, Qinit2, Con) ;
+ if (s != UMFPACK_OK) error ("Qinit2 OK", 0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nb OK: ") ;
+ s = UMFPACK_report_vector (n, CARG(b,bz), Con) ;
+ if (s != UMFPACK_OK) error ("0",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nn=-1: ") ;
+ s = UMFPACK_report_vector (-1, CARG(b,bz), Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_n_nonpositive)) error ("2",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nb null: ") ;
+ s = UMFPACK_report_vector (n, CARG(DNULL,DNULL), Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_argument_missing)) error ("2",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+
+ if (prl > 2) printf ("\nA OK: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != UMFPACK_OK) error ("2a",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nA pattern OK: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(DNULL,DNULL), 1, Con) ;
+ if (s != UMFPACK_OK) error ("2c",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nA OK row: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 0, Con) ;
+ if (s != UMFPACK_OK) error ("2b",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nn=zero: ") ;
+ s = UMFPACK_report_matrix (0, 0, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_n_nonpositive)) error ("2",0.) ;
+ s = UMFPACK_symbolic (0, 0, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_n_nonpositive) error ("2b",0.) ;
+ s = UMFPACK_qsymbolic (0, 0, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_n_nonpositive) error ("2c",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = do_amd (-1, Ap, Ai, Pamd) ;
+ if (s != AMD_INVALID) error ("amd 1", (double) s) ;
+
+ s = do_amd (n, INULL, Ai, Pamd) ;
+ if (s != AMD_INVALID) error ("amd 2", (double) s) ;
+
+ s = do_amd (n, Ap, INULL, Pamd) ;
+ if (s != AMD_INVALID) error ("amd 3", (double) s) ;
+
+ s = do_amd (n, Ap, Ai, INULL) ;
+ if (s != AMD_INVALID) error ("amd 4", (double) s) ;
+
+ s = do_amd (0, Ap, Ai, Pamd) ;
+ if (s != AMD_OK) error ("amd 5", (double) s) ;
+
+ s = do_amd_transpose (-1, Ap, Ai, Rp, Ri) ;
+ if (s != AMD_INVALID) error ("amd 1t", (double) s) ;
+
+ s = do_amd_transpose (n, INULL, Ai, Rp, Ri) ;
+ if (s != AMD_INVALID) error ("amd 2t", (double) s) ;
+
+ s = do_amd_transpose (n, Ap, INULL, Rp, Ri) ;
+ if (s != AMD_INVALID) error ("amd 3t", (double) s) ;
+
+ s = do_amd_transpose (n, Ap, Ai, INULL, Ri) ;
+ if (s != AMD_INVALID) error ("amd 7t", (double) s) ;
+
+ s = do_amd_transpose (n, Ap, Ai, Rp, INULL) ;
+ if (s != AMD_INVALID) error ("amd 8t", (double) s) ;
+
+ s = do_amd_transpose (0, Ap, Ai, Rp, Ri) ;
+ if (s != AMD_OK) error ("amd 5t", (double) s) ;
+
+#if 0
+{ f = fopen ("debug.amd", "w") ; fprintf (f, "999\n") ; fclose (f) ; }
+#endif
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nAp null: ") ;
+ s = UMFPACK_report_matrix (n, n, INULL, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_argument_missing)) error ("3",0.) ;
+ s = UMFPACK_symbolic (n, n, INULL, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_argument_missing) error ("3b",0.) ;
+ s = UMFPACK_qsymbolic (n, n, INULL, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_argument_missing) error ("3c",0.) ;
+ s = UMFPACK_transpose (n, n, INULL, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("52",0.);
+
+ s = do_amd (n, Ap, Ai, Pamd) ;
+ if (s != AMD_OK) error ("amd 6b", (double) s) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nAi null: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, INULL, CARG(Ax,Az), 1, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_argument_missing)) error ("4",0.) ;
+ s = UMFPACK_symbolic (n, n, Ap, INULL, CARG(Ax,Az), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_argument_missing) error ("4b",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, INULL, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_argument_missing) error ("4c",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ Ap [0] = 1 ; /* Ap broken [ */
+ if (prl > 2) printf ("\nAp [0] != 0: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("5",0.) ;
+ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("5b",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("5c",0.) ;
+ if (prl > 2) printf ("\nCalling umfpack_transpose:\n") ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("53",0.);
+
+ s = do_amd (n, Ap, Ai, Pamd) ;
+ if (s != AMD_INVALID) error ("amd 6", (double) s) ;
+
+ Ap [0] = 0 ; /* Ap fixed ] */
+
+ /* ------------------------------------------------------------------ */
+
+ Ap [n] = -1 ; /* Ap broken [ */
+ if (prl > 2) printf ("\nnz < 0: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("6",0.) ;
+ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("6b",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("6c",0.) ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("51h",0.);
+ s = UMFPACK_col_to_triplet (n, Ap, Aj) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("52j",0.);
+
+ s = do_amd (n, Ap, Ai, Pamd) ;
+ if (s != AMD_INVALID) error ("amd 6b", (double) s) ;
+
+ Ap [n] = nz ; /* Ap fixed ] */
+
+ /* ------------------------------------------------------------------ */
+#if 0
+ Ap [n] = Int_MAX ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != UMFPACK_ERROR_problem_too_large) error ("177a",0.);
+ Ap [n] = nz ;
+#endif
+ /* ------------------------------------------------------------------ */
+
+ printf ("Ap [2] negative:\n") ;
+ UMFPACK_report_control (Con) ;
+ c = Ap [2] ; /* Ap broken [ */
+ Ap [2] = -1 ;
+ if (prl > 2) printf ("\nAp[2]<0: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("8",0.) ;
+ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("8b",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("8c",0.) ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("55",0.);
+
+ s = do_amd (n, Ap, Ai, Pamd) ;
+ if (s != AMD_INVALID) error ("amd 7", (double) s) ;
+
+ Ap [2] = c ; /* Ap fixed ] */
+
+ /* ------------------------------------------------------------------ */
+
+ c = Ap [2] ; /* Ap broken [ */
+ Ap [2] = nz+1 ;
+ if (prl > 2) printf ("\nAp [2] > nz: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("9",0.) ;
+ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ s = Info [UMFPACK_STATUS] ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("9b",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("9c",0.) ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("51i",0.);
+
+ s = do_amd (n, Ap, Ai, Pamd) ;
+ if (s != AMD_INVALID) error ("amd 8", (double) s) ;
+
+ Ap [2] = c ; /* Ap fixed ] */
+
+ /* ------------------------------------------------------------------ */
+
+ c = Ap [4] ; /* Ap broken [ */
+ Ap [4] = Ap [3]-1 ;
+ if (prl > 2) printf ("\nAp [4] < Ap [3]-1: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("10",0.) ;
+ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("8b",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("8c",0.) ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("51j",0.);
+
+ s = do_amd (n, Ap, Ai, Pamd) ;
+ if (s != AMD_INVALID) error ("amd 9", (double) s) ;
+
+ Ap [4] = c ; /* Ap fixed ] */
+
+ /* ------------------------------------------------------------------ */
+
+ c = Ai [4] ; /* Ai broken [ */
+ Ai [4] = -1 ;
+ if (prl > 2) printf ("\nAi [4] = -1: ") ;
+ s = UMFPACK_report_matrix (n , n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("12",0.) ;
+ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("12b",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("12c",0.) ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("51k",0.);
+
+ s = do_amd (n, Ap, Ai, Pamd) ;
+ if (s != AMD_INVALID) error ("amd 10", (double) s) ;
+
+ Ai [4] = c ; /* Ai fixed ] */
+
+ /* ------------------------------------------------------------------ */
+
+ if (Ap [4] - Ap [3] < 3) error ("col 3 too short",0.) ;
+ c = Ai [Ap [3] + 1] ; /* Ai broken [ */
+ Ai [Ap [3] + 1] = 0 ;
+ if (prl > 2) printf ("\ncol 3 jumbled: ") ;
+ s = UMFPACK_report_matrix (n , n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("13",0.) ;
+ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("13b",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_matrix) error ("13c",0.) ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG(Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("51k",0.);
+
+ s = do_amd (n, Ap, Ai, Pamd) ;
+ printf ("amd jumbled: %d\n", s) ;
+ if (s != AMD_OK_BUT_JUMBLED) error ("amd 11", (double) s) ;
+
+ Ai [Ap [3] + 1] = c ; /* Ai fixed ] */
+
+ /* ------------------------------------------------------------------ */
+
+#if 0
+ { f = fopen ("debug.amd", "w") ; fprintf (f, "999\n") ; fclose (f) ; }
+#endif
+
+ for (i = 0 ; i < n ; i++) Ap2 [i] = Ap [i] ;
+ for (i = n ; i <= 2*n ; i++) Ap2 [i] = nz ;
+
+ s = do_amd (2*n, Ap2, Ai, Pamd) ;
+ if (s != AMD_OK) error ("amd 12a", (double) s) ;
+
+ if (prl > 2) printf ("\nhalf empty: ") ;
+ s = UMFPACK_report_matrix (2*n, 2*n, Ap2, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != UMFPACK_OK) error ("14",0.) ;
+ s = UMFPACK_symbolic (2*n, 2*n, Ap2, Ai, CARG(DNULL,DNULL), &Symbolic, Con, Info) ;
+
+ if (!Symbolic || s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Symbolic || s != UMFPACK_OK) error ("14b",0.) ;
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ s = UMFPACK_symbolic (2*n, 2*n, Ap2, Ai, CARG(DNULL,DNULL), &Symbolic, Con, DNULL) ;
+ if (s != UMFPACK_OK) error ("13d2", 0.) ;
+ if (!Symbolic) error ("13d",0.) ;
+
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ s = UMFPACK_qsymbolic (2*n, 2*n, Ap2, Ai, CARG(DNULL,DNULL), Qinit2, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Symbolic || s != UMFPACK_OK) error ("14c",0.) ;
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ s = do_amd (2*n, Ap2, Ai, Pamd) ;
+ if (s != AMD_OK) error ("amd 12", (double) s) ;
+
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i <= n ; i++) Ap2 [i] = 0 ;
+ if (prl > 2) printf ("\nall empty: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap2, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != UMFPACK_OK) error ("141",0.) ;
+
+ s = UMFPACK_col_to_triplet (n, Ap, Aj) ;
+ if (s != UMFPACK_OK) error ("151",0.) ;
+
+ s = UMFPACK_symbolic (n, n, Ap2, Ai, CARG(DNULL,DNULL), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Symbolic || s != UMFPACK_OK) error ("142",0.) ;
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ s = UMFPACK_symbolic (n, n, Ap2, Ai, CARG(DNULL,DNULL), &Symbolic, Con, DNULL) ;
+ if (s != UMFPACK_OK) error ("142b", 0.) ;
+ if (!Symbolic) error ("143",0.) ;
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ s = UMFPACK_qsymbolic (n, n, Ap2, Ai, CARG(DNULL,DNULL), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Symbolic || s != UMFPACK_OK) error ("144",0.) ;
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ s = do_amd (n, Ap, Ai, Pamd) ;
+ if (s != AMD_OK) error ("amd 13", (double) s) ;
+
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i <= n ; i++) Ap2 [i] = Ap [i] ;
+ for (p = 0 ; p < nz ; p++)
+ {
+ Ai2 [p] = Ai [p] ;
+ Ax2 [p] = Ax [p] ;
+ }
+ for (i = n ; i < 2*n ; i++)
+ {
+ Ap2 [i] = p ; /* add a dense row 0 */
+ Ai2 [p] = 0 ;
+ Ax2 [p] = 1.0 ;
+ p++ ;
+ }
+ Ap2 [2*n] = p ;
+ if (prl > 2) printf ("\nhalf empty rows: ") ;
+ s = UMFPACK_report_matrix (2*n, 2*n, Ap2, Ai2, CARG(Ax2,Az2), 1, Con) ;
+ if (s != UMFPACK_OK) error ("30",0.) ;
+ s = UMFPACK_symbolic (2*n, 2*n, Ap2, Ai2, CARG(Ax2,Az2), &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Symbolic || s != UMFPACK_OK) error ("30b",0.) ;
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ s = UMFPACK_qsymbolic (2*n, 2*n, Ap2, Ai2, CARG(Ax2,Az2), Qinit2, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Symbolic || s != UMFPACK_OK) error ("30c",0.) ;
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ s = do_amd (2*n, Ap2, Ai2, Pamd) ;
+ if (s != AMD_OK) error ("amd 14", (double) s) ;
+
+ /* ------------------------------------------------------------------ */
+
+ for (i = 0 ; i <= 2*n ; i++) Ap2 [i] = 0 ;
+ if (prl > 2) printf ("\nall empty: ") ;
+ s = UMFPACK_report_matrix (2*n, 2*n, Ap2, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != UMFPACK_OK) error ("15",0.) ;
+
+ s = do_amd (2*n, Ap2, Ai2, Pamd) ;
+ if (s != AMD_OK) error ("amd 14b", (double) s) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nold null form was same as col_form: ") ;
+ s = UMFPACK_report_matrix (n, n, Ap, Ai, CARG(Ax,Az), 1, Con) ;
+ if (s != UMFPACK_OK) error ("16",0.) ;
+
+ /* ================================================================== */
+ /* test Numeric [ */
+ /* ================================================================== */
+
+ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; /* [ */
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Symbolic || s != UMFPACK_OK) error ("16a",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ for (scale = UMFPACK_SCALE_NONE ; scale <= UMFPACK_SCALE_MAX ; scale++)
+ {
+ if (Con) Con [UMFPACK_SCALE] = scale ;
+
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, Info) ; /* [ */
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ Info [UMFPACK_FLOPS_ESTIMATE] = -1 ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Numeric || s != UMFPACK_OK) error ("31",0.) ;
+
+ if (prl > 2) printf ("good Numeric: ") ;
+ s = UMFPACK_report_numeric ( Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("90",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_get_lunz (INULL, &unz, &nnrow, &nncol, &nzud, Numeric) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("57",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_get_lunz (&lnz, &unz, &nnrow, &nncol, &nzud, Numeric) ;
+ printf ("lnz "ID" unz "ID" nn "ID"\n", lnz, unz, nn) ;
+ if (s != UMFPACK_OK) error ("58",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ Lp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Li = (Int *) malloc ((lnz+1) * sizeof (Int)) ; /* [ */
+ Lx = (double *) malloc ((lnz+1) * sizeof (double)) ; /* [ */
+ Lz = (double *) calloc (lnz , sizeof (double)) ; /* [ */
+ Up = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Ui = (Int *) malloc ((unz+1) * sizeof (Int)) ; /* [ */
+ Ux = (double *) malloc ((unz+1) * sizeof (double)) ; /* [ */
+ Uz = (double *) calloc ((unz+1) , sizeof (double)) ; /* [ */
+ P = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Q = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Pa = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Wx = (double *) malloc ((10*n) * sizeof (double)) ; /* [ */
+ Rs = (double *) malloc ((n+1) * sizeof (double)) ; /* [ */
+ if (!Lp || !Li || !Lx || !Up || !Ui || !Ux || !P || !Q) error ("out of memory (20)",0.) ;
+ if (!Pa || !Wx || !Rs) error ("out of memory (20)",0.) ;
+ if (!Uz || !Lz) error ("out of memory (21)",0.) ;
+
+ if (prl > 2) printf ("good Numeric again: ") ;
+ s = UMFPACK_report_numeric ( Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("77",0.) ;
+
+ s = UMFPACK_get_numeric (Lp, Li, CARG(Lx,Lz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(DNULL,DNULL), &do_recip, Rs, Numeric) ;
+ if (s != UMFPACK_OK) error ("59", 0.) ;
+
+ s = UMFPACK_get_numeric (Lp, Li, CARG(Lx,Lz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(DNULL,DNULL), &do_recip, DNULL, Numeric) ;
+ if (s != UMFPACK_OK) error ("59b", 0.) ;
+
+ s = UMFPACK_get_numeric (Lp, Li, CARG(Lx,Lz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(DNULL,DNULL), INULL, DNULL, Numeric) ;
+ if (s != UMFPACK_OK) error ("59r", 0.) ;
+
+ if (prl > 2) printf ("good Numeric yet again: ") ;
+ s = UMFPACK_report_numeric ( Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("75",0.) ;
+ dump_perm ("goodP1", n, Pamd) ;
+ if (prl > 2) printf ("\nL test: ") ;
+ s = UMFPACK_report_matrix (n, n, Lp, Li, CARG(Lx,Lz), 0, Con) ;
+ if (s != UMFPACK_OK) error ("60",0.) ;
+ if (prl > 2) printf ("\nU test: ") ;
+ s = UMFPACK_report_matrix (n, n, Up, Ui, CARG(Ux,Uz), 1, Con) ;
+ if (s != UMFPACK_OK) error ("61",0.) ;
+ dump_perm ("goodP", n, Pamd) ;
+ if (prl > 2) printf ("P test: ") ;
+ s = UMFPACK_report_perm (n, P, Con) ;
+ if (s != UMFPACK_OK) error ("62",0.) ;
+ if (prl > 2) printf ("Q test: ") ;
+ s = UMFPACK_report_perm (n, Q, Con) ;
+ if (s != UMFPACK_OK) error ("63",0.) ;
+
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_OK) error ("64",0.) ;
+
+ s = UMFPACK_scale (CARG(DNULL,xz), CARG(b,bz), Numeric) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("64z",0.) ;
+
+ s = UMFPACK_scale (CARG(x,xz), CARG(DNULL,bz), Numeric) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("64y",0.) ;
+
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(DNULL,xz), CARG(b,bz), Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("64e",0.) ;
+
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(DNULL,bz), Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("64f",0.) ;
+
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(DNULL,Az), CARG(x,xz), CARG(DNULL,bz), Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("64g",0.) ;
+
+ s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info, Pa, Wx) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_OK) error ("64a",0.) ;
+
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, DNULL) ;
+ if (s != UMFPACK_OK) error ("64b",0.) ;
+
+ s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, DNULL, Pa, Wx) ;
+ if (s != UMFPACK_OK) error ("64c",0.) ;
+
+ s = UMFPACK_solve (UMFPACK_A, INULL, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_control (Con) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("65a",0.) ;
+
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(DNULL,xz), CARG(b,bz), Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("65a",0.) ;
+
+ s = UMFPACK_wsolve (UMFPACK_A, INULL, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info, Pa, Wx) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("65b",0.) ;
+
+ s = UMFPACK_solve (UMFPACK_At, INULL, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("65c",0.) ;
+
+ s = UMFPACK_wsolve (UMFPACK_At, INULL, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info, Pa, Wx) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("66",0.) ;
+
+ s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info, INULL, Wx) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("67",0.) ;
+
+ s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info, Pa, DNULL) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("68",0.) ;
+
+ if (prl > 2) printf ("erroroneous sys arg for umfpack_solve:\n") ;
+ s = UMFPACK_solve (-1, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (s != UMFPACK_ERROR_invalid_system) error ("65d",0.) ;
+
+ /* check internal error message */
+ UMFPACK_report_status (Con, UMFPACK_ERROR_internal_error) ;
+
+ /* check unrecognized error code */
+ UMFPACK_report_status (Con, 123123999) ;
+
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("70",0.) ;
+
+ s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info, Pa, Wx) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("71",0.) ;
+
+ s = UMFPACK_get_determinant (CARG (&Mx, &Mz), &Exp, (void *) NULL, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("71det",0.) ;
+
+ s = UMFPACK_get_determinant (CARG (DNULL, &Mz), &Exp, Numeric, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh??", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("72det",0.) ;
+
+ /* corrupt Numeric */
+ Num = (NumericType *) Numeric ;
+ Num->valid = 4909284 ;
+
+ s = UMFPACK_get_numeric (Lp, Li, CARG(Lx,Lz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(DNULL,DNULL), &do_recip, Rs, Numeric) ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("91",0.) ;
+
+ s = UMFPACK_save_numeric (Numeric, "nbad.umf") ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("70num",0.) ;
+
+ s = UMFPACK_get_lunz (&lnz, &unz, &nnrow, &nncol, &nzud, Numeric) ;
+ printf ("s "ID"\n", s) ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("70b",0.) ;
+
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("70",0.) ;
+
+ s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info, Pa, Wx) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("71",0.) ;
+
+ if (prl > 2) printf ("bad Numeric: ") ;
+ s = UMFPACK_report_numeric ( Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("82",0.) ;
+
+ /* fix numeric */
+ Num->valid = NUMERIC_VALID ;
+ if (prl > 2) printf ("fixed Numeric: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("82",0.) ;
+
+ /* valid Numeric, but no permissions */
+ s = UMFPACK_save_numeric (Numeric, "/root/nbad.umf") ;
+ if (s != UMFPACK_ERROR_file_IO) error ("72num",0.) ;
+
+ /* corrupt Numeric again */
+ Num->n_row = -1 ;
+
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("72",0.) ;
+
+ s = UMFPACK_wsolve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), (void *) NULL, Con, Info, Pa, Wx) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("73",0.) ;
+
+ s = UMFPACK_scale (CARG(x,xz), CARG(b,bz), (void *) NULL) ;
+ if (s != UMFPACK_ERROR_invalid_Numeric_object) error ("72f",0.) ;
+
+ /* fix numeric */
+ if (prl > 2) printf ("bad Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("81",0.) ;
+ Num->n_row = n ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("80",0.) ;
+
+ /* corrupt Numeric again (bad P), then fix it */
+ c = Num->Rperm [0] ;
+ Num->Rperm [0] = -1 ;
+ if (prl > 2) printf ("bad Numeric (P): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("200",0.) ;
+ Num->Rperm [0] = c ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("200b",0.) ;
+
+ /* corrupt Numeric again (bad Q), then fix it */
+ c = Num->Cperm [0] ;
+ Num->Cperm [0] = -1 ;
+ if (prl > 2) printf ("bad Numeric (Q): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("201",0.) ;
+ Num->Cperm [0] = c ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("201b",0.) ;
+
+ /* corrupt Numeric again (bad Lpos), then fix it */
+ for (k = 0 ; k < n ; k++)
+ {
+ if (Num->Lpos [k] != EMPTY) break ;
+ }
+ c = Num->Lpos [k] ;
+ Num->Lpos [k] = c + 1 ;
+ if (prl > 2) printf ("bad Numeric (Lpos [k]): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("204",0.) ;
+ Num->Lpos [k] = c ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("204b",0.) ;
+
+ /* corrupt Numeric again (bad Upos), then fix it */
+ for (k = 0 ; k < n ; k++)
+ {
+ if (Num->Upos [k] != EMPTY) break ;
+ }
+ c = Num->Upos [k] ;
+ Num->Upos [k] = 9999999 ;
+ if (prl > 2) printf ("bad Numeric (Upos [0]): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("204c",0.) ;
+ Num->Upos [k] = c ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("204d",0.) ;
+
+ /* corrupt Numeric again (bad Lilen), then fix it */
+ c = Num->Lilen [0] ;
+ Num->Lilen [0] = -1 ;
+ if (prl > 2) printf ("bad Numeric (Lilen [0]): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("205",0.) ;
+ Num->Lilen [0] = c ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("205b",0.) ;
+
+ /* corrupt Numeric again (bad Lip), then fix it */
+ c = Num->Lip [0] ;
+ Num->Lip [0] = -9999999 ;
+ printf ("Bad numeric (Lip [0])\n") ;
+ fflush (stdout) ;
+ if (prl > 2) printf ("bad Numeric (Lip [0]): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ fflush (stdout) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("206",0.) ;
+ Num->Lip [0] = c ;
+ printf ("Fixed numeric (Lip [0])\n") ;
+ fflush (stdout) ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("206b",0.) ;
+ fflush (stdout) ;
+
+ /* corrupt Numeric again (bad LPattern), then fix it */
+ c = Num->Memory [1].header.size ;
+ Num->Memory [1].header.size = -1 ;
+ if (prl > 2) printf ("bad Numeric (Pattern): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("208",0.) ;
+ Num->Memory [1].header.size = c ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("208b",0.) ;
+
+ /* corrupt Numeric again (bad UPattern), then fix it */
+ printf ("test 208d:\n") ;
+ for (k = n-1 ; k >= 0 ; k--)
+ {
+ if (Num->Uilen [k] > 0) break ;
+ }
+ ip = (Int *) (Num->Memory + SCALAR_ABS (Num->Uip [k])) ;
+ c = *ip ;
+ printf ("Corrupting Num->Uip [k="ID"] = "ID"\n", k, c) ;
+ *ip = -1 ;
+ if (prl > 2) printf ("bad Numeric (UPattern): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("208c",0.) ;
+ *ip = c ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("208d",0.) ;
+
+ /* corrupt Numeric again (bad Uilen), then fix it */
+ c = Num->Uilen [k] ;
+ printf ("Corrupting Num->Uilen [k="ID"] = "ID"\n", k, c) ;
+ Num->Uilen [k] = -1 ;
+ if (prl > 2) printf ("bad Numeric (Uilen [k]): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("205c",0.) ;
+ Num->Uilen [k] = c ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ if (s != UMFPACK_OK) error ("205d",0.) ;
+
+ /* corrupt Numeric again (bad Uilen), then fix it */
+ c = Num->Uilen [k-1] ;
+ Num->Uilen [k-1] = 99999 ;
+ if (prl > 2) printf ("bad Numeric (Uilen [k-1]): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("210",0.) ;
+ Num->Uilen [k-1] = c ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (s != UMFPACK_OK) error ("210b",0.) ;
+
+ /* corrupt Numeric again (bad Uip), then fix it */
+ c = Num->Uip [k] ;
+ Num->Uip [k] = -999999 ;
+ printf ("Bad numeric Uip [k]\n") ;
+ fflush (stdout) ;
+ if (prl > 2) printf ("bad Numeric (Uip [k]): ") ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ fflush (stdout) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Numeric_object)) error ("206c",0.) ;
+ Num->Uip [k] = c ;
+ printf ("Fixed numeric Uip [k]\n") ;
+ fflush (stdout) ;
+ s = UMFPACK_report_numeric (Numeric, Con) ;
+ if (prl > 2) printf ("fixed Numeric again: ") ;
+ fflush (stdout) ;
+ if (s != UMFPACK_OK) error ("206d",0.) ;
+
+ free (Rs) ; /* ] */
+ free (Wx) ; /* ] */
+ free (Pa) ; /* ] */
+ free (Q) ; /* ] */
+ free (P) ; /* ] */
+ free (Uz) ; /* ] */
+ free (Ux) ; /* ] */
+ free (Ui) ; /* ] */
+ free (Up) ; /* ] */
+ free (Lz) ; /* ] */
+ free (Lx) ; /* ] */
+ free (Li) ; /* ] */
+ free (Lp) ; /* ] */
+
+ UMFPACK_free_numeric (&Numeric) ; /* ] */
+
+ if (prl > 2) printf ("Numeric file not found:\n") ;
+ s = UMFPACK_load_numeric (&Numeric, "file_not_found") ;
+ if (s != UMFPACK_ERROR_file_IO) error ("71num",0.) ;
+
+ }
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ;
+ if (!Numeric || s != UMFPACK_OK) error ("31b",0.) ;
+ UMFPACK_free_numeric (&Numeric) ;
+
+ /* ------------------------------------------------------------------ */
+
+ /* change the pattern */
+ if (Con)
+ {
+ Con [UMFPACK_SCALE] = UMFPACK_SCALE_NONE ;
+ }
+
+ printf ("change of pattern between symbolic and numeric:\n") ;
+ c = Ap [2] ;
+ Ap [2] = -1 ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ;
+ if (s != UMFPACK_ERROR_different_pattern) error ("97a", (double) s) ;
+ Ap [2] = c ;
+
+ c = Ai [2] ;
+ Ai [2] = -1 ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ;
+ if (s != UMFPACK_ERROR_different_pattern) error ("97b", (double) s) ;
+ Ai [2] = c ;
+
+ c = Ai [2] ;
+ Ai [2] = 9990099 ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ;
+ if (s != UMFPACK_ERROR_different_pattern) error ("97c", (double) s) ;
+ Ai [2] = c ;
+
+ c = Ap [n] ;
+ Ai [Ap [n]++] = n-1 ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ;
+ if (s != UMFPACK_ERROR_different_pattern) error ("97d", (double) s) ;
+ Ap [n] = c ;
+ printf ("done testing change of pattern between symbolic and numeric.\n") ;
+
+ if (Con)
+ {
+ Con [UMFPACK_SCALE] = UMFPACK_DEFAULT_SCALE ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, DNULL) ;
+ if (!Numeric || s != UMFPACK_OK) error ("31c",0.) ;
+ UMFPACK_free_numeric (&Numeric) ;
+
+ /* ------------------------------------------------------------------ */
+
+ printf ("free nothing:\n") ;
+ UMFPACK_free_numeric ((void **) NULL) ;
+ UMFPACK_free_symbolic ((void **) NULL) ;
+ printf ("free nothing OK\n") ;
+
+ /* ------------------------------------------------------------------ */
+
+ /* test for singular matrix (IN_IN case) */
+ for (j = 0 ; j < n ; j++)
+ {
+ for (p = 0 ; p < nz ; p++) Ax2 [p] = Ax [p] ;
+ for (p = 0 ; p < nz ; p++) Az2 [p] = Az [p] ;
+ printf ("lastcol = "ID"\n", j) ;
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ Ax2 [p] = 0.0 ;
+ Az2 [p] = 0.0 ;
+ }
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax2,Az2), Symbolic, &Numeric, Con, Info) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ if (!Numeric || s != UMFPACK_WARNING_singular_matrix) error ("120",0.) ;
+ UMFPACK_free_numeric (&Numeric) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), (void *) NULL, &Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_invalid_Symbolic_object) error ("32",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_numeric (INULL, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_argument_missing) error ("32b",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ for (p = 0 ; p < nz ; p++) Ax2 [p] = 0.0 ;
+ for (p = 0 ; p < nz ; p++) Az2 [p] = 0.0 ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax2,Az2), Symbolic, &Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Numeric || s != UMFPACK_WARNING_singular_matrix) error ("33",0.) ;
+ UMFPACK_free_numeric (&Numeric) ;
+
+ /* ------------------------------------------------------------------ */
+
+ for (p = 0 ; p < nz ; p++) Ax2 [p] = Ax [p] ;
+ for (p = 0 ; p < nz ; p++) Az2 [p] = Ax [p] ;
+ i = UMFPACK_DENSE_DEGREE_THRESHOLD (0.2, n) ;
+ for (j = 0 ; j < n ; j++)
+ {
+ d = Ap [j+1] - Ap [j] ;
+ if (d > i)
+ {
+ for (p = Ap [j] ; p < Ap [j+1] ; p++)
+ {
+ Ax2 [p] = 0.0 ;
+ Az2 [p] = 0.0 ;
+ }
+ }
+ }
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax2,Az2), Symbolic, &Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Numeric || s != UMFPACK_WARNING_singular_matrix) error ("33",0.) ;
+ UMFPACK_free_numeric (&Numeric) ;
+
+ /* ------------------------------------------------------------------ */
+
+ /* corrupt the Symbolic object */
+
+ Sym = (SymbolicType *) Symbolic ;
+ printf ("32c:\n") ;
+ fflush (stdout) ;
+
+ Sym->valid = 4040404 ;
+ if (prl > 2) printf ("\nSymbolic busted: ") ;
+ s = UMFPACK_report_symbolic ((void *) Sym, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_Symbolic_object)) error ("79",0.) ;
+
+ Front_leftmostdesc = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Front_1strow = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Front_npivots = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Front_parent = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Chain_start = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Chain_maxrows = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Chain_maxcols = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Qtree = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ Ptree = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ if (!Front_npivots || !Front_parent || !Chain_start || !Chain_maxrows
+ || !Chain_maxcols || !Qtree) error ("out of memory (22)",0.) ;
+
+ s = UMFPACK_get_symbolic (&nnrow, &nncol, &n1, &nnz, &nfr, &nchains,
+ Ptree, Qtree, Front_npivots, Front_parent, Front_1strow, Front_leftmostdesc,
+ Chain_start, Chain_maxrows, Chain_maxcols, Symbolic) ;
+ if (s != UMFPACK_ERROR_invalid_Symbolic_object) error ("93", 0.) ;
+
+ free (Ptree) ; /* ] */
+ free (Qtree) ; /* ] */
+ free (Chain_maxcols) ; /* ] */
+ free (Chain_maxrows) ; /* ] */
+ free (Chain_start) ; /* ] */
+ free (Front_parent) ; /* ] */
+ free (Front_npivots) ; /* ] */
+ free (Front_1strow) ; /* ] */
+ free (Front_leftmostdesc) ; /* ] */
+
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ printf ("32c s: "ID"\n", s) ;
+ if (Numeric || s != UMFPACK_ERROR_invalid_Symbolic_object) error ("32c",0.) ;
+
+ Sym->valid = SYMBOLIC_VALID ;
+ if (prl > 2) printf ("\nSymbolic fixed: ") ;
+ s = UMFPACK_report_symbolic (Symbolic, Con) ;
+ if (s != UMFPACK_OK) error ("78",0.) ;
+
+ /* valid Symbolic, but no permissions */
+ s = UMFPACK_save_symbolic (Symbolic, "/root/sbad.umf") ;
+ if (s != UMFPACK_ERROR_file_IO) error ("72sym",0.) ;
+
+ /* corrupt Symbolic again (bad Qinit) and then fix it */
+ c = Sym->Cperm_init [0] ;
+ Sym->Cperm_init [0] = -1 ;
+ if (prl > 2) printf ("\nSymbolic busted (bad Qinit): ") ;
+ s = UMFPACK_report_symbolic (Symbolic, Con) ;
+ Sym->Cperm_init [0] = c ;
+
+ /* ------------------------------------------------------------------ */
+
+ /* corrupt the Symbolic object again */
+
+ printf ("32d:\n") ;
+ fflush (stdout) ;
+ Sym->Cperm_init = (Int *) UMF_free ((void *) Sym->Cperm_init) ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Numeric || s != UMFPACK_ERROR_invalid_Symbolic_object) error ("32d",0.) ;
+
+ s = UMFPACK_save_symbolic (Symbolic, "sbad.umf") ;
+ if (s != UMFPACK_ERROR_invalid_Symbolic_object) error ("70sym",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ UMFPACK_free_symbolic (&Symbolic) ; /* ] */
+
+ printf ("Symbolic file not found:\n") ;
+ s = UMFPACK_load_symbolic (&Symbolic, "file_not_found") ;
+ if (s != UMFPACK_ERROR_file_IO) error ("71sym",0.) ;
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (UMF_malloc_count != 0) error ("umfpack memory leak!!",0.) ;
+#endif
+
+ /* printf (" made it here "ID"\n", umf_fail) ; */
+ fflush (stdout) ;
+
+ /* == done ] ======================================================== */
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(DNULL,DNULL), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ /* printf (" made it here 3 "ID"\n", umf_fail) ; */
+ fflush (stdout) ;
+ s = Info [UMFPACK_STATUS] ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Symbolic || s != UMFPACK_OK) error ("16b",0.) ;
+ /* printf (" made it here too "ID"\n", umf_fail) ; */
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("Qinit missing: ") ;
+ s = UMFPACK_report_perm (n, INULL, Con) ;
+ if (s != UMFPACK_OK) error ("17",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(DNULL,DNULL), INULL, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!Symbolic || s != UMFPACK_OK) error ("17b",0.) ;
+ UMFPACK_free_symbolic (&Symbolic) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("Qinit n=0: ") ;
+ s = UMFPACK_report_perm (0, Qinit, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_n_nonpositive)) error ("18",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ c = Qinit [5] ;
+ Qinit [5]++ ;
+ if (prl > 2) printf ("Qinit bad: ") ;
+ s = UMFPACK_report_perm (n, Qinit, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_permutation)) error ("19",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(DNULL,DNULL), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_permutation) error ("19b",0.) ;
+ Qinit [5] = c ;
+
+ /* ------------------------------------------------------------------ */
+
+ c = Qinit [5] ;
+ Qinit [5] = -1 ;
+ if (prl > 2) printf ("Qinit bad (out of range): ") ;
+ s = UMFPACK_report_perm (n, Qinit, Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_permutation)) error ("19c",0.) ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(DNULL,DNULL), Qinit, &Symbolic, Con, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (Symbolic || s != UMFPACK_ERROR_invalid_permutation) error ("19d",0.) ;
+ Qinit [5] = c ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_col_to_triplet (n, Ap, INULL) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("20a",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ;
+ if (s != UMFPACK_OK) error ("50",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(DNULL,DNULL), Pinit, Qinit, Ap2, Ai2, CARG (DNULL,DNULL) C1ARG(0)) ;
+ if (s != UMFPACK_OK) error ("50e",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("UMFPACK transpose test R = A(P,:)'\n") ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, INULL, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(1)) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (s != UMFPACK_OK) error ("50",0.);
+ if (prl > 2) printf ("\nPinit: ") ;
+ s = UMFPACK_report_perm (n, Pinit, Con) ;
+ if (prl > 2) printf ("\nR: ") ;
+ s = UMFPACK_report_matrix (n , n, Ap2, Ai2, CARG (Ax2,Az2), 1, Con) ;
+ if (s != UMFPACK_OK) error ("50e",0.);
+ s = UMFPACK_col_to_triplet (n, Ap2, Aj) ;
+ if (s != UMFPACK_OK) error ("50i",0.);
+ if (prl > 2) printf ("\nR, triplet form: ") ;
+ s = UMFPACK_report_triplet (n, n, nz, Ai2, Aj, CARG(Ax2,Az2), Con) ;
+ if (s != UMFPACK_OK) error ("50y",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("UMFPACK transpose test R = pattern of A(P,:).'\n") ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(DNULL,DNULL), Pinit, INULL, Ap2, Ai2, CARG (DNULL,DNULL) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (s != UMFPACK_OK) error ("50f",0.);
+ if (prl > 2) printf ("\npattern of R: ") ;
+ s = UMFPACK_report_matrix (n , n, Ap2, Ai2, CARG (DNULL,DNULL), 1, Con) ;
+ if (s != UMFPACK_OK) error ("50g",0.);
+ s = UMFPACK_col_to_triplet (n, Ap2, Aj) ;
+ if (s != UMFPACK_OK) error ("50k",0.);
+ if (prl > 2) printf ("\npattern of R, triplet form: ") ;
+ s = UMFPACK_report_triplet (n, n, nz, Ai2, Aj, CARG (DNULL,DNULL), Con) ;
+ if (s != UMFPACK_OK) error ("50z",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), INULL, INULL, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_OK) error ("51a",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, INULL, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_OK) error ("51b",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), INULL, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_OK) error ("51c",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_transpose (0, 0, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_n_nonpositive) error ("54",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ c = Pinit [5] ;
+ Pinit [5] = n-1 ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_permutation) error ("51e",0.);
+ Pinit [5] = c ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_OK) error ("51d",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ c = Pinit [5] ;
+ Pinit [5] = -1 ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), Pinit, Qinit, Ap2, Ai2, CARG (Ax2,Az2) C1ARG(0)) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_permutation) error ("56",0.);
+ Pinit [5] = c ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_col_to_triplet (n, INULL, Aj) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("20b",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_col_to_triplet (0, Ap, Aj) ;
+ if (s != UMFPACK_ERROR_n_nonpositive) error ("20c",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ Ap [0] = 99 ;
+ s = UMFPACK_col_to_triplet (n, Ap, Aj) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("20d",0.) ;
+ s = do_amd_transpose (n, Ap, Aj, Ap2, Ai2) ;
+ if (s != AMD_INVALID) error ("20d_amd",0.) ;
+ Ap [0] = 0 ;
+
+ /* ------------------------------------------------------------------ */
+
+ Ap [n] = 0 ;
+ s = UMFPACK_col_to_triplet (n, Ap, Aj) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("20e",0.) ;
+ Ap [n] = nz ;
+
+ /* ------------------------------------------------------------------ */
+
+ c = Ap [3] ;
+ Ap [3] = nz+1 ;
+ s = UMFPACK_col_to_triplet (n, Ap, Aj) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("20f",0.) ;
+ s = do_amd_transpose (n, Ap, Aj, Ap2, Ai2) ;
+ if (s != AMD_INVALID) error ("20f_amd",0.) ;
+ Ap [3] = c ;
+
+ /* ------------------------------------------------------------------ */
+
+ c = Aj [0] ;
+ Aj [0] = -1 ;
+ s = do_amd_transpose (n, Ap, Aj, Ap2, Ai2) ;
+ if (s != AMD_INVALID) error ("20z_amd",0.) ;
+ Aj [0] = c ;
+
+ /* ------------------------------------------------------------------ */
+
+ c = Ap [4] ;
+ Ap [4] = Ap [3]-1 ;
+ s = UMFPACK_col_to_triplet (n, Ap, Aj) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("20i",0.) ;
+ Ap [4] = c ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_col_to_triplet (n, Ap, Aj) ;
+ if (s != UMFPACK_OK) error ("20",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nTriples OK: ") ;
+ s = UMFPACK_report_triplet (n, n, nz, Ai, Aj, CARG(Ax,Az), Con) ;
+ if (s != UMFPACK_OK) error ("21",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nTriples pattern OK: ") ;
+ s = UMFPACK_report_triplet (n, n, nz, Ai, Aj, CARG(DNULL,DNULL), Con) ;
+ if (s != UMFPACK_OK) error ("21b",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nTriples, Ai null: ") ;
+ s = UMFPACK_report_triplet (n, n, nz, INULL, Aj, CARG(Ax,Az), Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_argument_missing)) error ("22",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nTriples, nz=0: ") ;
+ s = UMFPACK_report_triplet (n, n, 0, Ai, Aj, CARG(Ax,Az), Con) ;
+ if (s != UMFPACK_OK) error ("23a",0.) ;
+
+ if (prl > 2) printf ("\nTriples, nz=-1: ") ;
+ s = UMFPACK_report_triplet (n, n, -1, Ai, Aj, CARG(Ax,Az), Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("23",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ if (prl > 2) printf ("\nTriples, n=0: ") ;
+ s = UMFPACK_report_triplet (0, 0, nz, Ai, Aj, CARG(Ax,Az), Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_n_nonpositive)) error ("24",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ Map = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+
+ c = Aj [1] ;
+ Aj [1] = -1 ;
+ if (prl > 2) printf ("\nTriples, Aj bad: ") ;
+ s = UMFPACK_report_triplet (n, n, nz, Ai, Aj, CARG(Ax,Az), Con) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_invalid_matrix)) error ("41",0.) ;
+
+ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("41",0.) ;
+
+ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("42",0.);
+
+ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(DNULL,DNULL), Ap2, Ai2, CARG (DNULL,DNULL), Map) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("42cc",0.);
+
+ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(DNULL,DNULL), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("42b",0.);
+ Aj [1] = c ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_OK) error ("42c",0.);
+
+ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), Map) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_OK) error ("42c.2",0.);
+
+ /* check the Map */
+ for (k = 0 ; k < nz ; k++)
+ {
+ p = Map [k] ;
+ i = Ai [k] ;
+ j = Aj [k] ;
+ if (i != Ai2 [p]) error ("Map Ai2.2", 0.) ;
+ if (!(Ap2 [j] <= p && p < Ap2 [j+1])) error ("Map Ap2.2", 0.) ;
+ }
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(DNULL,DNULL), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_OK) error ("42d",0.);
+
+ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(DNULL,DNULL), Ap2, Ai2, CARG (Ax2,Az2), Map) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_OK) error ("42d.1",0.);
+
+ /* check the Map */
+ for (k = 0 ; k < nz ; k++)
+ {
+ p = Map [k] ;
+ i = Ai [k] ;
+ j = Aj [k] ;
+ if (i != Ai2 [p]) error ("Map Ai2.1", 0.) ;
+ if (!(Ap2 [j] <= p && p < Ap2 [j+1])) error ("Map Ap2.1", 0.) ;
+ }
+
+ c = Aj [1] ;
+ Aj [1] = -1 ;
+ s = UMFPACK_triplet_to_col (n, n, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), Map) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("42c.3",0.);
+ Aj [1] = c ;
+
+ free (Map) ; /* ] */
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_triplet_to_col (0, 0, nz, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_n_nonpositive) error ("44",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_triplet_to_col (n, n, 0, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_OK) error ("45a",0.);
+
+ if (prl > 2) printf ("\nall empty A2: ") ;
+ s = UMFPACK_report_matrix (n , n, Ap2, Ai2, CARG (Ax2,Az2), 1, Con) ;
+ if (s != UMFPACK_OK) error ("45c",0.) ;
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_triplet_to_col (n, n, -1, Ai, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_invalid_matrix) error ("45",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ s = UMFPACK_triplet_to_col (n, n, nz, INULL, Aj, CARG(Ax,Az), Ap2, Ai2, CARG (Ax2,Az2), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_argument_missing) error ("46",0.);
+
+ /* ------------------------------------------------------------------ */
+
+ free (Az2) ; /* ] */
+ free (Ax2) ; /* ] */
+ free (Ai2) ; /* ] */
+ free (Aj) ; /* ] */
+
+ free (Az) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ap) ; /* ] */
+
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (UMF_malloc_count != 0) error ("umfpack memory leak!!",0.) ;
+#endif
+
+ printf ("\n]]]]\n\n\n") ;
+
+ }
+ }
+
+ free (Ap2) ; /* ] */
+ free (xz) ; /* ] */
+ free (x) ; /* ] */
+ free (bz) ; /* ] */
+ free (b) ; /* ] */
+ free (Qinit2) ; /* ] */
+ free (Pinit) ; /* ] */
+ free (Qinit) ; /* ] */
+ free (Pamd) ; /* ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test memory allocation */
+ /* ---------------------------------------------------------------------- */
+
+ n = 200 ;
+
+ printf ("memory test\n") ;
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (UMF_malloc_count != 0) error ("umfpack mem test starts memory leak!!\n",0.) ;
+#endif
+
+ matgen_sparse (n, 8*n, 0, 0, 4, 2*n, &Ap, &Ai, &Ax, &Az, 1, 0) ; /* [[[[ */
+ Qinit = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ b = (double *) malloc (n * sizeof (double)) ; /* [ */
+ bz= (double *) calloc (n , sizeof (double)) ; /* [ */
+ x = (double *) malloc (n * sizeof (double)) ; /* [ */
+ xz= (double *) calloc (n , sizeof (double)) ; /* [ */
+ bgen (n, Ap, Ai, Ax,Az, b,bz) ;
+
+ nz = Ap [n] ;
+
+ randperm (n, Qinit) ;
+
+ UMFPACK_defaults (Control) ;
+
+ for (prl = 5 ; prl >= -1 ; prl--)
+ {
+
+ printf ("prl "ID" memtest\n", prl) ;
+ fflush (stdout) ;
+
+ umf_realloc_fail = -1 ;
+ umf_realloc_hi = 0 ;
+ umf_realloc_lo = 0 ;
+
+ umf_fail_hi = 0 ;
+ umf_fail_lo = 0 ;
+ Control [UMFPACK_PRL] = (Int) prl ;
+
+ umf_fail = 1 ;
+ if (prl > 2) printf ("Memfail Qinit: ") ;
+ s = UMFPACK_report_perm (n, Qinit, Control) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_out_of_memory)) error ("101",0.) ;
+
+ Cp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Cj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Ci = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Cx = (double *) malloc (nz * sizeof (double)) ; /* [ */
+ Cz = (double *) calloc (nz , sizeof (double)) ; /* [ */
+ Bp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Bj = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Bi = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ Bx = (double *) malloc (nz * sizeof (double)) ; /* [ */
+ Bz = (double *) calloc (nz , sizeof (double)) ; /* [ */
+ Map = (Int *) malloc (nz * sizeof (Int)) ; /* [ */
+ if (!Cp || !Ci || !Cx || !Cj) error ("out of memory (23)",0.) ;
+ if (!Bp || !Bi || !Bx || !Bj) error ("out of memory (24)",0.) ;
+ if (!Bz || !Cz) error ("out of memory (25)",0.) ;
+
+ umf_fail = 1 ;
+ s = UMFPACK_transpose (n, n, Ap, Ai, CARG(Ax,Az), INULL, INULL, Cp, Ci, CARG(Cx,Cz) C1ARG(0)) ;
+ if (s != UMFPACK_ERROR_out_of_memory) error ("113", 0.) ;
+
+ for (k = 0 ; k < nz ; k++)
+ {
+ Ci [k] = irand (n) ;
+ Cj [k] = irand (n) ;
+ Cx [k] = 2.0 * (xrand ( ) - 1.0) ;
+#ifdef COMPLEX
+ Cx [k] = 2.0 * (xrand ( ) - 1.0) ;
+#else
+ Cx [k] = 0. ;
+#endif
+ }
+
+ for (i = 1 ; i <= 4 ; i++)
+ {
+ umf_fail = i ;
+ s = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(DNULL,DNULL), Bp, Bi, CARG(DNULL,DNULL), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_out_of_memory) error ("114", (double) i) ;
+ }
+
+
+ for (i = 1 ; i <= 5 ; i++)
+ {
+ umf_fail = i ;
+ s = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Bp, Bi, CARG(Bx,Bz), (Int *) NULL) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_out_of_memory) error ("115", (double) i) ;
+ }
+
+ for (i = 1 ; i <= 5 ; i++)
+ {
+ umf_fail = i ;
+ s = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(DNULL,DNULL), Bp, Bi, CARG(DNULL,DNULL), Map) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_out_of_memory) error ("114", (double) i) ;
+ }
+
+
+ for (i = 1 ; i <= 6 ; i++)
+ {
+ umf_fail = i ;
+ s = UMFPACK_triplet_to_col (n, n, nz, Ci, Cj, CARG(Cx,Cz), Bp, Bi, CARG(Bx,Bz), Map) ;
+ UMFPACK_report_status (Con, s) ;
+ if (s != UMFPACK_ERROR_out_of_memory) error ("115", (double) i) ;
+ }
+
+ free (Map) ; /* ] */
+ free (Bz) ; /* ] */
+ free (Bx) ; /* ] */
+ free (Bi) ; /* ] */
+ free (Bj) ; /* ] */
+ free (Bp) ; /* ] */
+ free (Cz) ; /* ] */
+ free (Cx) ; /* ] */
+ free (Ci) ; /* ] */
+ free (Cj) ; /* ] */
+ free (Cp) ; /* ] */
+
+ for (i = 1 ; i <= 24 ; i++)
+ {
+ umf_fail = i ;
+ printf ("umf_fail starts at "ID"\n", umf_fail) ;
+ fflush (stdout) ;
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (UMF_malloc_count != 0) error ("umfpack mem test starts memory leak!!\n",0.) ;
+#endif
+ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (Symbolic || Info [UMFPACK_STATUS] != UMFPACK_ERROR_out_of_memory) error ("104", (double) i) ;
+ }
+
+ umf_fail = 25 ;
+ s = UMFPACK_qsymbolic (n, n, Ap, Ai, CARG(Ax,Az), Qinit, &Symbolic, Control, Info) ; /* [ */
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (!Symbolic || s != UMFPACK_OK) error ("105", 0.) ;
+
+ umf_fail = 1 ;
+ if (prl > 2) printf ("\nMemfail Symbolic: ") ;
+ s = UMFPACK_report_symbolic (Symbolic, Control) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_out_of_memory)) error ("102",0.) ;
+
+ /* alloc reallocs succeed */
+ umf_realloc_fail = -1 ;
+ umf_realloc_hi = 0 ;
+ umf_realloc_lo = 0 ;
+
+ /* Initial Numeric->Memory allocation fails when umf_fail is 28, and never succeeds.
+ * All mallocs succeed if umf_fail is 16 + 11 + 1 */
+ umf_fail_lo = -9999999 ;
+ for (i = 1 ; i <= 29 ; i++)
+ {
+ umf_fail = i ;
+ printf ("\nDoing numeric, umf_fail = "ID"\n", umf_fail) ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (i < 29)
+ {
+ if (Numeric || s != UMFPACK_ERROR_out_of_memory) error ("106", (double) i) ;
+ }
+ else
+ {
+ if (!Numeric || s != UMFPACK_OK) error ("106z", (double) umf_fail) ;
+ UMFPACK_free_numeric (&Numeric) ;
+ }
+ }
+
+
+ /* everything succeeds, use a small alloc_init */
+ printf ("106y:\n") ;
+ Control [UMFPACK_ALLOC_INIT] = -30000 ;
+ UMFPACK_report_control (Control) ;
+ umf_fail = 29 ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (!Numeric || s != UMFPACK_OK) error ("106y", (double) umf_fail) ;
+ UMFPACK_free_numeric (&Numeric) ;
+
+ /* all malloc's succeed - no realloc during factorization */
+ umf_fail = -1 ;
+ umf_fail_lo = 0 ;
+ umf_fail_hi = 0 ;
+ umf_realloc_fail = 1 ;
+ umf_realloc_hi = 0 ;
+ umf_realloc_lo = -9999999 ;
+
+ /* restore Control */
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_PRL] = (Int) prl ;
+
+ /* alloc init the smallest size */
+ Control [UMFPACK_ALLOC_INIT] = 0.0 ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+
+ if (Numeric)
+ {
+ UMFPACK_free_numeric (&Numeric) ;
+ printf ("107 succeeded\n") ;
+ }
+
+ /* initial allocation fails once, retry succeeds */
+ umf_realloc_fail = 1 ;
+ umf_realloc_hi = 0 ;
+ umf_realloc_lo = -2 ;
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Control, Info) ; /* ( */
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (!Numeric || s != UMFPACK_OK) error ("110", (double) umf_fail) ;
+
+ /* all reallocs succeed */
+ umf_realloc_fail = -1 ;
+ umf_realloc_hi = 0 ;
+ umf_realloc_lo = 0 ;
+
+ UMFPACK_free_symbolic (&Symbolic) ; /* ] */
+
+ umf_fail = 1 ;
+ if (prl > 2) printf ("Memfail Numeric: ") ;
+ s = UMFPACK_report_numeric (Numeric, Control) ;
+ if (s != ((prl <= 2) ? UMFPACK_OK : UMFPACK_ERROR_out_of_memory)) error ("108",0.) ;
+
+ for (i = 1 ; i <= 2 ; i++)
+ {
+ umf_fail = i ;
+ printf ("\nTest 109, "ID"\n", umf_fail) ;
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (s != UMFPACK_ERROR_out_of_memory) error ("109", (double) i) ;
+ }
+
+ for (i = 1 ; i <= 2 ; i++)
+ {
+ umf_fail = i ;
+ s = UMFPACK_solve (UMFPACK_L, Ap, Ai, CARG(Ax,Az), CARG(x,xz), CARG(b,bz), Numeric, Control, Info) ;
+ if (s != Info [UMFPACK_STATUS]) error ("huh", (double) __LINE__) ;
+ UMFPACK_report_status (Control, s) ;
+ UMFPACK_report_info (Control, Info) ;
+ if (s != UMFPACK_ERROR_out_of_memory) error ("109b", (double) i) ;
+ }
+
+ s = UMFPACK_get_lunz (&lnz, &unz, &nnrow, &nncol, &nzud, Numeric) ;
+ if (s != UMFPACK_OK) error ("111", 0.) ;
+
+ Rs = (double *) malloc ((n+1) * sizeof (double)) ; /* [ */
+ Lp = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Li = (Int *) malloc ((lnz+1) * sizeof (Int)) ; /* [ */
+ Lx = (double *) malloc ((lnz+1) * sizeof (double)) ; /* [ */
+ Lz = (double *) calloc ((lnz+1) , sizeof (double)) ; /* [ */
+ Up = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Ui = (Int *) malloc ((unz+1) * sizeof (Int)) ; /* [ */
+ Ux = (double *) malloc ((unz+1) * sizeof (double)) ; /* [ */
+ Uz = (double *) calloc ((unz+1) , sizeof (double)) ; /* [ */
+ P = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ Q = (Int *) malloc ((n+1) * sizeof (Int)) ; /* [ */
+ if (!Lp || !Li || !Lx || !Up || !Ui || !Ux || !P || !Q) error ("out of memory (26)",0.) ;
+ if (!Lz || !Uz) error ("out of memory (27)",0.) ;
+
+ for (i = 1 ; i <= 2 ; i++)
+ {
+ umf_fail = i ;
+ s = UMFPACK_get_numeric (Lp, Li, CARG(Lx,Lz), Up, Ui, CARG(Ux,Uz), P, Q, CARG(DNULL,DNULL), &do_recip, Rs, Numeric) ;
+ if (s != UMFPACK_ERROR_out_of_memory) error ("112", (double) i) ;
+ }
+
+ umf_fail = 1 ;
+ s = UMFPACK_get_determinant (CARG (&Mx, &Mz), &Exp, Numeric, Info) ;
+ if (s != Info [UMFPACK_STATUS])
+ {
+ printf ("s %d %g\n", s, Info [UMFPACK_STATUS]) ;
+ error ("huh", (double) __LINE__) ;
+ }
+ if (s != UMFPACK_ERROR_out_of_memory) error ("73det",0.) ;
+
+ UMFPACK_free_numeric (&Numeric) ; /* ) */
+
+ free (Q) ; /* ] */
+ free (P) ; /* ] */
+ free (Uz) ; /* ] */
+ free (Ux) ; /* ] */
+ free (Ui) ; /* ] */
+ free (Up) ; /* ] */
+ free (Lz) ; /* ] */
+ free (Lx) ; /* ] */
+ free (Li) ; /* ] */
+ free (Lp) ; /* ] */
+ free (Rs) ; /* ] */
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (UMF_malloc_count != 0) error ("umfpack memory test leak!!\n",0.) ;
+#endif
+
+ }
+
+ free (xz) ; /* ] */
+ free (x) ; /* ] */
+ free (bz) ; /* ] */
+ free (b) ; /* ] */
+ free (Qinit) ; /* ] */
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Az) ; /* ] */
+
+ /* ---------------------------------------------------------------------- */
+ /* NaN/Inf */
+ /* ---------------------------------------------------------------------- */
+
+ umf_fail = -1 ;
+ umf_fail_lo = 0 ;
+ umf_fail_hi = 0 ;
+ umf_realloc_fail = -1 ;
+ umf_realloc_lo = 0 ;
+ umf_realloc_hi = 0 ;
+
+ printf ("matrices with NaN/Infs:\n") ;
+ n = 100 ;
+ for (k = 0 ; k <= 100 ; k++)
+ {
+ printf ("NaN/Inf %7d 4*n nz's, k= "ID"\n", n, k) ;
+ matgen_sparse (n, 4*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 1) ; /* [[[[ */
+ if (k == 100)
+ {
+ /* make a matrix of all NaN's */
+ for (i = 0 ; i < Ap [n] ; i++)
+ {
+ Ax [i] = xnan ;
+#ifdef COMPLEX
+ Az [i] = xnan ;
+#endif
+ }
+ }
+ b = (double *) malloc (n * sizeof (double)) ; /* [ */
+ bz = (double *) malloc (n * sizeof (double)) ; /* [ */
+ bgen (n, Ap, Ai, Ax, Az, b, bz) ;
+ x = (double *) malloc (n * sizeof (double)) ; /* [ */
+ xz = (double *) malloc (n * sizeof (double)) ; /* [ */
+ for (prl = 2 ; prl >= -1 ; prl--)
+ {
+ printf ("NaN / Inf matrix: \n") ;
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_PRL] = prl ;
+ for (scale = UMFPACK_SCALE_NONE ; scale <= UMFPACK_SCALE_MAX ; scale++)
+ {
+ Control [UMFPACK_SCALE] = scale ;
+ Con = (prl == -1) ? (DNULL) : Control ;
+ UMFPACK_report_control (Con) ;
+
+ s = UMFPACK_symbolic (n, n, Ap, Ai, CARG(Ax,Az), &Symbolic, Con, Info) ; /* [ */
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!(s == UMFPACK_OK || s == UMFPACK_WARNING_singular_matrix)) error ("887", 0.) ;
+
+ s = UMFPACK_numeric (Ap, Ai, CARG(Ax,Az), Symbolic, &Numeric, Con, Info) ; /* [ */
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!(s == UMFPACK_OK || s == UMFPACK_WARNING_singular_matrix)) error ("888", 0.) ;
+
+ s = UMFPACK_solve (UMFPACK_A, Ap, Ai, CARG(Ax,Az) , CARG(x,xz), CARG(b,bz), Numeric, Con, Info) ;
+ UMFPACK_report_status (Con, s) ;
+ UMFPACK_report_info (Con, Info) ;
+ if (!(s == UMFPACK_OK || s == UMFPACK_WARNING_singular_matrix)) error ("889", 0.) ;
+
+ UMFPACK_free_numeric (&Numeric) ; /* ] */
+ UMFPACK_free_symbolic (&Symbolic) ; /* ] */
+ }
+ }
+ free (xz) ; /* ] */
+ free (x) ; /* ] */
+ free (bz) ; /* ] */
+ free (b) ; /* ] */
+ free (Az) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ap) ; /* ] */
+ }
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (UMF_malloc_count != 0) error ("umfpack memory leak!!\n",0.) ;
+#endif
+
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test report routines */
+ /* ---------------------------------------------------------------------- */
+
+ n = 32 ;
+ printf ("\n so far: rnorm %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+ Qinit = (Int *) malloc (n * sizeof (Int)) ; /* [ */
+ b = (double *) malloc (n * sizeof (double)) ; /* [ */
+ bz= (double *) calloc (n , sizeof (double)) ; /* [ */
+ if (!Qinit || !b || !bz) error ("out of memory (28)",0.) ;
+ UMFPACK_defaults (Control) ;
+
+ for (prl = 5 ; prl >= 0 ; prl--)
+ {
+ printf ("\n[[[[ PRL = "ID"\n", prl) ;
+ Control [UMFPACK_PRL] = prl ;
+
+ i = UMFPACK_DENSE_DEGREE_THRESHOLD (0.2, n) ;
+ printf ("(default) dense row/col degree threshold: "ID"\n", i) ;
+
+ matgen_sparse (n, 12*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, prl, 0) ; /* [[[[ */
+ bgen (n, Ap, Ai, Ax,Az, b,bz) ;
+
+ /* also test NaN/Inf handling in solvers */
+ b [16] = xnan ;
+ b [15] = xinf ;
+
+ /* test col->triplet and triplet->col */
+ test_col (n, Ap, Ai, Ax,Az, prl) ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemOK, FALSE, FALSE, 0., 0.) ;
+ printf ("\nrnorm %10.4e %10.4e\n", rnorm, maxrnorm) ;
+ randperm (n, Qinit) ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ;
+ printf ("\nrnorm %10.4e %10.4e\n", rnorm, maxrnorm) ;
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Az) ; /* ] */
+ printf ("\n]]]]\n\n\n") ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* test report with more than 10 dense columns */
+ UMFPACK_defaults (Control) ;
+
+ printf ("\nrnorm %10.4e %10.4e\n", rnorm, maxrnorm) ;
+ Control [UMFPACK_PRL] = 4 ;
+ printf ("\nreport dense matrix with n = "ID"\n", n) ;
+ matgen_dense (n, &Ap, &Ai, &Ax, &Az) ; /* [[[[ */
+ bgen (n, Ap, Ai, Ax,Az, b,bz) ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, Qinit, MemOK, FALSE, FALSE, 0., 0.) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf ("\nrnorm %10.4e %10.4e\n", rnorm, maxrnorm) ;
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Az) ; /* ] */
+
+ free (bz) ; /* ] */
+ free (b) ; /* ] */
+ free (Qinit) ; /* ] */
+
+ Control [UMFPACK_PRL] = 5 ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test random sparse matrices */
+ /* ---------------------------------------------------------------------- */
+
+ n = 30 ;
+
+ printf ("sparse %7d 4*n nz's", n) ;
+ matgen_sparse (n, 4*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ; /* [[[[ */
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ; /* ]]]] */
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+ n = 200 ;
+
+ printf ("sparse %7d 4*n nz's", n) ;
+ matgen_sparse (n, 4*n, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ; /* [[[[ */
+
+ /*
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ;
+ */
+
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_DENSE_COL] = 0.883883 ;
+ Control [UMFPACK_DENSE_ROW] = 0.883883 ;
+ Control [UMFPACK_AMD_DENSE] = 10 ;
+ Control [UMFPACK_PIVOT_TOLERANCE] = 0.5 ;
+ Control [UMFPACK_BLOCK_SIZE] = 1 ;
+ Control [UMFPACK_ALLOC_INIT] = 0 ;
+ Control [UMFPACK_SCALE] = 0 ;
+ Control [UMFPACK_STRATEGY] = 3 ;
+ Control [UMFPACK_FIXQ] = 1 ;
+
+ b = (double *) malloc (n * sizeof (double)) ; /* [ */
+ bz= (double *) calloc (n , sizeof (double)) ; /* [ */
+ if (!b || !bz) error ("out of memory (29)",0.) ;
+ bgen (n, Ap, Ai, Ax, Az, b, bz) ;
+
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemOK, FALSE, FALSE, 0., 0.) ;
+
+ UMFPACK_defaults (Control) ;
+ Control [UMFPACK_FRONT_ALLOC_INIT] = -10 ;
+ Control [UMFPACK_PRL] = 2 ;
+
+ printf ("negative front alloc init\n") ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemOK, FALSE, FALSE, 0., 0.) ;
+
+ Control [UMFPACK_FRONT_ALLOC_INIT] = -10 ;
+ Control [UMFPACK_STRATEGY] = UMFPACK_STRATEGY_SYMMETRIC ;
+ Control [UMFPACK_AMD_DENSE] = -1 ;
+
+ printf ("symmetric strategy, no dense rows/cols\n") ;
+ rnorm = do_many (n, n, Ap, Ai, Ax,Az, b,bz, Control, INULL, MemOK, FALSE, FALSE, 0., 0.) ;
+
+ free (bz) ; /* ] */
+ free (b) ; /* ] */
+ free (Ap) ; /* ] */
+ free (Ai) ; /* ] */
+ free (Ax) ; /* ] */
+ free (Az) ; /* ] */
+
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+#if 0
+
+
+ n = 200 ;
+
+ printf ("sparse %7d few nz's", n) ;
+ matgen_sparse (n, 20, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+
+ /* ---------------------------------------------------------------------- */
+ /* test random sparse matrices + 4 dense rows */
+ /* ---------------------------------------------------------------------- */
+
+ n = 100 ;
+
+ printf ("sparse+dense rows %7d ", n) ;
+ matgen_sparse (n, 4*n, 4, 2*n, 0, 0, &Ap, &Ai, &Ax, &Az, 1, 0) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+
+ /* ---------------------------------------------------------------------- */
+ /* reset rand ( ) */
+ /* ---------------------------------------------------------------------- */
+
+ srand (1) ;
+
+ /* ---------------------------------------------------------------------- */
+ /* test random sparse matrices + 4 dense rows & cols */
+ /* ---------------------------------------------------------------------- */
+
+ n = 100 ;
+
+ /* reduce the number of controls - otherwise this takes too much time */
+
+ c = UMFPACK_BLOCK_SIZE ;
+ Controls [c][0] = UMFPACK_DEFAULT_BLOCK_SIZE ;
+ Ncontrols [c] = 1 ;
+
+ c = UMFPACK_ALLOC_INIT ;
+ Controls [c][0] = 1.0 ;
+ Ncontrols [c] = 1 ;
+
+ printf ("sparse+dense rows and cols %7d ", n) ;
+ matgen_sparse (n, 4*n, 4, 2*n, 4, 2*n, &Ap, &Ai, &Ax, &Az, 1, 0) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+ c = UMFPACK_BLOCK_SIZE ;
+ Controls [c][0] = 1 ;
+ Controls [c][1] = 8 ;
+ Controls [c][2] = UMFPACK_DEFAULT_BLOCK_SIZE ;
+ Ncontrols [c] = 3 ;
+
+ c = UMFPACK_ALLOC_INIT ;
+ Controls [c][0] = 0.0 ;
+ Controls [c][1] = 0.5 ;
+ Controls [c][2] = 1.0 ; /* not the default */
+ Ncontrols [c] = 3 ;
+
+ n = 100 ;
+
+ printf ("very sparse+dense cols %7d ", n) ;
+ matgen_sparse (n, 2, 0, 0, 4, 2*n, &Ap, &Ai, &Ax, &Az, 1, 0) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+
+ /* ---------------------------------------------------------------------- */
+ /* test all diagonal matrices */
+ /* ---------------------------------------------------------------------- */
+
+ for (n = 1 ; n < 16 ; n++)
+ {
+ printf ("diagonal %7d ", n) ;
+ matgen_band (n, 0, 0, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax, Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+ }
+
+ for (n = 100 ; n <= 500 ; n += 100)
+ {
+ printf ("diagonal %7d ", n) ;
+ matgen_band (n, 0, 0, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* test all tri-diagonal matrices */
+ /* ---------------------------------------------------------------------- */
+
+ for (n = 1 ; n < 16 ; n++)
+ {
+ printf ("tri-diagonal %7d ", n) ;
+ matgen_band (n, 1, 1, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+ }
+
+ for (n = 100 ; n <= 500 ; n += 100)
+ {
+ printf ("tri-diagonal %7d ", n) ;
+ matgen_band (n, 1, 1, 0, 0, 0, 0, &Ap, &Ai, &Ax, &Az) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+ }
+
+ /* ---------------------------------------------------------------------- */
+ /* test all tri-diagonal matrices + one "dense" row */
+ /* ---------------------------------------------------------------------- */
+
+ n = 100 ;
+
+ printf ("tri-diagonal+dense row %7d ", n) ;
+ matgen_band (n, 1, 1, 1, n, 0, 0, &Ap, &Ai, &Ax, &Az) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+
+ /* ---------------------------------------------------------------------- */
+ /* test all tri-diagonal matrices + one "dense" row and col */
+ /* ---------------------------------------------------------------------- */
+
+ n = 100 ;
+
+ printf ("tri-diagonal+dense row and col %7d ", n) ;
+ matgen_band (n, 1, 1, 1, n, 1, n, &Ap, &Ai, &Ax, &Az) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+
+
+ /* ---------------------------------------------------------------------- */
+ /* test all small dense matrices */
+ /* ---------------------------------------------------------------------- */
+
+ for (n = 1 ; n < 16 ; n++)
+ {
+ printf ("dense %7d ", n) ;
+ matgen_dense (n, &Ap, &Ai, &Ax, &Az) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+ }
+
+ for (n = 20 ; n <= 80 ; n += 20 )
+ {
+ printf ("dense %7d ", n) ;
+ matgen_dense (n, &Ap, &Ai, &Ax, &Az) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+ }
+
+ n = 130 ;
+
+ printf ("dense %7d ", n) ;
+ matgen_dense (n, &Ap, &Ai, &Ax, &Az) ;
+ rnorm = do_and_free (n, Ap, Ai, Ax,Az, Controls, Ncontrols, MemOK, 1) ;
+ maxrnorm = MAX (rnorm, maxrnorm) ;
+ printf (" %10.4e %10.4e\n", rnorm, maxrnorm) ;
+#endif
+
+ /* ---------------------------------------------------------------------- */
+ /* done with accurate matrices */
+ /* ---------------------------------------------------------------------- */
+
+ ttt = umfpack_timer ( ) ;
+
+ fprintf (stderr,
+ "ALL TESTS PASSED: rnorm %8.2e (%8.2e shl0, %8.2e arc130 %8.2e omega2) cputime %g\n",
+ maxrnorm, maxrnorm_shl0, maxrnorm_arc130, rnorm_omega2, ttt) ;
+
+ printf (
+ "ALL TESTS PASSED: rnorm %8.2e (%8.2e shl0, %8.2e arc130 %8.2e omega2) cputime %g\n",
+ maxrnorm, maxrnorm_shl0, maxrnorm_arc130, rnorm_omega2, ttt) ;
+
+#if defined (UMF_MALLOC_COUNT) || !defined (NDEBUG)
+ if (UMF_malloc_count != 0) error ("umfpack memory leak!!\n",0.) ;
+#endif
+
+ return (0) ;
+}
--
Alioth's /usr/local/bin/git-commit-notice on /srv/git.debian.org/git/debian-science/packages/suitesparse-metis.git
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